LMFDB - Embedded newform 49.4.e.a.43.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,4,Mod(8,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.8"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			43.11
Character	$\chi$	$=$	49.43
Dual form			49.4.e.a.8.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59695 - 3.25648i) q^{2} +(2.96773 + 1.42918i) q^{3} +(-2.08030 - 9.11440i) q^{4} +(9.52410 + 4.58657i) q^{5} +(12.3612 - 5.95282i) q^{6} +(-16.3066 - 8.78031i) q^{7} +(-5.06162 - 2.43755i) q^{8} +(-10.0694 - 12.6266i) q^{9} +(39.6697 - 19.1039i) q^{10} +(-34.1739 + 42.8527i) q^{11} +(6.85238 - 30.0222i) q^{12} +(-18.7277 + 23.4838i) q^{13} +(-70.9404 + 30.3001i) q^{14} +(21.7099 + 27.2234i) q^{15} +(46.3012 - 22.2975i) q^{16} +(9.96373 - 43.6539i) q^{17} -67.2678 q^{18} +71.5587 q^{19} +(21.9908 - 96.3479i) q^{20} +(-35.8450 - 49.3628i) q^{21} +(50.8008 + 222.573i) q^{22} +(37.1988 + 162.978i) q^{23} +(-11.5378 - 14.4680i) q^{24} +(-8.26430 - 10.3631i) q^{25} +(27.8395 + 121.973i) q^{26} +(-31.6276 - 138.570i) q^{27} +(-46.1046 + 166.891i) q^{28} +(-4.18669 + 18.3431i) q^{29} +145.032 q^{30} -114.344 q^{31} +(57.6317 - 252.501i) q^{32} +(-162.663 + 78.3344i) q^{33} +(-116.283 - 145.814i) q^{34} +(-115.034 - 158.416i) q^{35} +(-94.1364 + 118.043i) q^{36} +(18.8099 - 82.4114i) q^{37} +(185.834 - 233.029i) q^{38} +(-89.1416 + 42.9283i) q^{39} +(-37.0274 - 46.4309i) q^{40} +(-55.7401 - 26.8430i) q^{41} +(-253.836 - 11.4644i) q^{42} +(-148.440 + 71.4850i) q^{43} +(461.668 + 222.328i) q^{44} +(-37.9890 - 166.441i) q^{45} +(627.339 + 302.110i) q^{46} +(337.800 - 423.588i) q^{47} +169.277 q^{48} +(188.812 + 286.355i) q^{49} -55.2092 q^{50} +(91.9592 - 115.313i) q^{51} +(253.000 + 121.839i) q^{52} +(-108.336 - 474.652i) q^{53} +(-533.384 - 256.864i) q^{54} +(-522.022 + 251.392i) q^{55} +(61.1355 + 84.1907i) q^{56} +(212.367 + 102.270i) q^{57} +(48.8612 + 61.2700i) q^{58} +(203.178 - 97.8454i) q^{59} +(202.962 - 254.506i) q^{60} +(103.297 - 452.575i) q^{61} +(-296.946 + 372.358i) q^{62} +(53.3320 + 294.309i) q^{63} +(-416.265 - 521.980i) q^{64} +(-286.075 + 137.766i) q^{65} +(-167.334 + 733.139i) q^{66} -133.966 q^{67} -418.607 q^{68} +(-122.530 + 536.840i) q^{69} +(-814.617 - 36.7919i) q^{70} +(156.479 + 685.578i) q^{71} +(20.1894 + 88.4555i) q^{72} +(704.577 + 883.512i) q^{73} +(-219.522 - 275.272i) q^{74} +(-9.71544 - 42.5661i) q^{75} +(-148.864 - 652.214i) q^{76} +(933.520 - 398.725i) q^{77} +(-91.7014 + 401.770i) q^{78} -1187.92 q^{79} +543.246 q^{80} +(7.14899 - 31.3218i) q^{81} +(-232.168 + 111.806i) q^{82} +(673.830 + 844.956i) q^{83} +(-375.344 + 429.395i) q^{84} +(295.117 - 370.065i) q^{85} +(-152.703 + 669.035i) q^{86} +(-38.6406 + 48.4538i) q^{87} +(277.430 - 133.603i) q^{88} +(-881.560 - 1105.44i) q^{89} +(-640.665 - 308.528i) q^{90} +(511.582 - 218.507i) q^{91} +(1408.07 - 678.089i) q^{92} +(-339.342 - 163.418i) q^{93} +(-502.153 - 2200.08i) q^{94} +(681.532 + 328.208i) q^{95} +(531.906 - 666.989i) q^{96} -352.624 q^{97} +(1422.84 + 128.787i) q^{98} +885.192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

Coefficient data

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

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

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

$2$	2.59695	−	3.25648i	0.918161	−	1.15134i	−0.0699428	−	0.997551i	$-0.522282\pi$
$2$	2.59695	−	3.25648i	0.918161	−	1.15134i	0.988104	−	0.153787i	$-0.0491469\pi$
$3$	2.96773	+	1.42918i	0.571140	+	0.275047i	0.697082	−	0.716991i	$-0.254481\pi$
$3$	2.96773	+	1.42918i	0.571140	+	0.275047i	−0.125942	+	0.992038i	$0.540195\pi$
$4$	−2.08030	−	9.11440i	−0.260038	−	1.13930i
$5$	9.52410	+	4.58657i	0.851862	+	0.410235i	0.808268	−	0.588814i	$-0.200405\pi$
$5$	9.52410	+	4.58657i	0.851862	+	0.410235i	0.0435933	+	0.999049i	$0.486119\pi$
$6$	12.3612	−	5.95282i	0.841070	−	0.405038i
$7$	−16.3066	−	8.78031i	−0.880475	−	0.474092i
$7$	−16.3066	−	8.78031i	−0.880475	−	0.474092i
$8$	−5.06162	−	2.43755i	−0.223694	−	0.107725i
$9$	−10.0694	−	12.6266i	−0.372939	−	0.467651i
$10$	39.6697	−	19.1039i	1.25447	−	0.604119i
$11$	−34.1739	+	42.8527i	−0.936710	+	1.17460i	0.0477277	+	0.998860i	$0.484802\pi$
$11$	−34.1739	+	42.8527i	−0.936710	+	1.17460i	−0.984437	+	0.175736i	$0.943769\pi$
$12$	6.85238	−	30.0222i	0.164843	−	0.722222i
$13$	−18.7277	+	23.4838i	−0.399549	+	0.501019i	−0.940386	−	0.340109i	$-0.889536\pi$
$13$	−18.7277	+	23.4838i	−0.399549	+	0.501019i	0.540837	+	0.841127i	$0.318108\pi$
$14$	−70.9404	+	30.3001i	−1.35426	+	0.578431i
$15$	21.7099	+	27.2234i	0.373699	+	0.468603i
$16$	46.3012	−	22.2975i	0.723456	−	0.348398i
$17$	9.96373	−	43.6539i	0.142150	−	0.622802i	−0.852783	−	0.522266i	$-0.825087\pi$
$17$	9.96373	−	43.6539i	0.142150	−	0.622802i	0.994933	−	0.100536i	$-0.0320559\pi$
$18$	−67.2678			−0.880843
$19$	71.5587			0.864036			0.432018	−	0.901865i	$-0.357802\pi$
$19$	71.5587			0.864036			0.432018	+	0.901865i	$0.357802\pi$
$20$	21.9908	−	96.3479i	0.245864	−	1.07720i
$21$	−35.8450	−	49.3628i	−0.372477	−	0.512945i
$22$	50.8008	+	222.573i	0.492307	+	2.15694i
$23$	37.1988	+	162.978i	0.337238	+	1.47754i	0.804784	+	0.593568i	$0.202281\pi$
$23$	37.1988	+	162.978i	0.337238	+	1.47754i	−0.467546	+	0.883969i	$0.654862\pi$
$24$	−11.5378	−	14.4680i	−0.0981311	−	0.123053i
$25$	−8.26430	−	10.3631i	−0.0661144	−	0.0829048i
$26$	27.8395	+	121.973i	0.209991	+	0.920032i
$27$	−31.6276	−	138.570i	−0.225435	−	0.987694i
$28$	−46.1046	+	166.891i	−0.311177	+	1.12641i
$29$	−4.18669	+	18.3431i	−0.0268086	+	0.117456i	−0.986562	−	0.163389i	$-0.947757\pi$
$29$	−4.18669	+	18.3431i	−0.0268086	+	0.117456i	0.959753	+	0.280845i	$0.0906146\pi$
$30$	145.032			0.882636
$31$	−114.344			−0.662477			−0.331238	−	0.943547i	$-0.607466\pi$
$31$	−114.344			−0.662477			−0.331238	+	0.943547i	$0.607466\pi$
$32$	57.6317	−	252.501i	0.318373	−	1.39488i
$33$	−162.663	+	78.3344i	−0.858061	+	0.413221i
$34$	−116.283	−	145.814i	−0.586538	−	0.735496i
$35$	−115.034	−	158.416i	−0.555554	−	0.765063i
$36$	−94.1364	+	118.043i	−0.435817	+	0.546497i
$37$	18.8099	−	82.4114i	0.0835763	−	0.366172i	−0.915794	−	0.401648i	$-0.868438\pi$
$37$	18.8099	−	82.4114i	0.0835763	−	0.366172i	0.999371	+	0.0354760i	$0.0112947\pi$
$38$	185.834	−	233.029i	0.793324	−	0.994797i
$39$	−89.1416	+	42.9283i	−0.366002	+	0.176257i
$40$	−37.0274	−	46.4309i	−0.146364	−	0.183534i
$41$	−55.7401	−	26.8430i	−0.212320	−	0.102248i	0.324701	−	0.945817i	$-0.394736\pi$
$41$	−55.7401	−	26.8430i	−0.212320	−	0.102248i	−0.537021	+	0.843569i	$0.680451\pi$
$42$	−253.836	−	11.4644i	−0.932567	−	0.0421190i
$43$	−148.440	+	71.4850i	−0.526440	+	0.253520i	−0.678174	−	0.734901i	$-0.737228\pi$
$43$	−148.440	+	71.4850i	−0.526440	+	0.253520i	0.151734	+	0.988421i	$0.451514\pi$
$44$	461.668	+	222.328i	1.58180	+	0.761754i
$45$	−37.9890	−	166.441i	−0.125846	−	0.551367i
$46$	627.339	+	302.110i	2.01078	+	0.968342i
$47$	337.800	−	423.588i	1.04837	−	1.31461i	0.100851	−	0.994902i	$-0.467843\pi$
$47$	337.800	−	423.588i	1.04837	−	1.31461i	0.947516	−	0.319709i	$-0.103585\pi$
$48$	169.277			0.509020
$49$	188.812	+	286.355i	0.550473	+	0.834853i
$50$	−55.2092			−0.156155
$51$	91.9592	−	115.313i	0.252487	−	0.316609i
$52$	253.000	+	121.839i	0.674708	+	0.324922i
$53$	−108.336	−	474.652i	−0.280776	−	1.23016i	−0.896801	−	0.442434i	$-0.854115\pi$
$53$	−108.336	−	474.652i	−0.280776	−	1.23016i	0.616025	−	0.787727i	$-0.288742\pi$
$54$	−533.384	−	256.864i	−1.34416	−	0.647311i
$55$	−522.022	+	251.392i	−1.27981	+	0.616323i
$56$	61.1355	+	84.1907i	0.145885	+	0.200901i
$57$	212.367	+	102.270i	0.493486	+	0.237650i
$58$	48.8612	+	61.2700i	0.110617	+	0.138709i
$59$	203.178	−	97.8454i	0.448331	−	0.215905i	−0.196074	−	0.980589i	$-0.562819\pi$
$59$	203.178	−	97.8454i	0.448331	−	0.215905i	0.644405	+	0.764684i	$0.277105\pi$
$60$	202.962	−	254.506i	0.436704	−	0.547609i
$61$	103.297	−	452.575i	0.216818	−	0.949940i	−0.742995	−	0.669297i	$-0.766595\pi$
$61$	103.297	−	452.575i	0.216818	−	0.949940i	0.959812	−	0.280643i	$-0.0905476\pi$
$62$	−296.946	+	372.358i	−0.608260	+	0.762734i
$63$	53.3320	+	294.309i	0.106654	+	0.588563i
$64$	−416.265	−	521.980i	−0.813018	−	1.01949i
$65$	−286.075	+	137.766i	−0.545896	+	0.262890i
$66$	−167.334	+	733.139i	−0.312082	+	1.36732i
$67$	−133.966			−0.244276			−0.122138	−	0.992513i	$-0.538975\pi$
$67$	−133.966			−0.244276			−0.122138	+	0.992513i	$0.538975\pi$
$68$	−418.607			−0.746523
$69$	−122.530	+	536.840i	−0.213781	+	0.936637i
$70$	−814.617	−	36.7919i	−1.39093	−	0.0628210i
$71$	156.479	+	685.578i	0.261558	+	1.14596i	0.919562	+	0.392945i	$0.128544\pi$
$71$	156.479	+	685.578i	0.261558	+	1.14596i	−0.658004	+	0.753015i	$0.728599\pi$
$72$	20.1894	+	88.4555i	0.0330464	+	0.144786i
$73$	704.577	+	883.512i	1.12965	+	1.41654i	0.895909	+	0.444239i	$0.146526\pi$
$73$	704.577	+	883.512i	1.12965	+	1.41654i	0.233742	+	0.972299i	$0.424903\pi$
$74$	−219.522	−	275.272i	−0.344851	−	0.432429i
$75$	−9.71544	−	42.5661i	−0.0149579	−	0.0655348i
$76$	−148.864	−	652.214i	−0.224682	−	0.984396i
$77$	933.520	−	398.725i	1.38162	−	0.590116i
$78$	−91.7014	+	401.770i	−0.133117	+	0.583225i
$79$	−1187.92			−1.69178			−0.845892	−	0.533354i	$-0.820932\pi$
$79$	−1187.92			−1.69178			−0.845892	+	0.533354i	$0.820932\pi$
$80$	543.246			0.759209
$81$	7.14899	−	31.3218i	0.00980656	−	0.0429654i
$82$	−232.168	+	111.806i	−0.312667	+	0.150572i
$83$	673.830	+	844.956i	0.891114	+	1.11742i	0.992460	+	0.122570i	$0.0391137\pi$
$83$	673.830	+	844.956i	0.891114	+	1.11742i	−0.101346	+	0.994851i	$0.532315\pi$
$84$	−375.344	+	429.395i	−0.487540	+	0.557748i
$85$	295.117	−	370.065i	0.376588	−	0.472226i
$86$	−152.703	+	669.035i	−0.191469	+	0.838882i
$87$	−38.6406	+	48.4538i	−0.0476173	+	0.0597102i
$88$	277.430	−	133.603i	0.336070	−	0.161843i
$89$	−881.560	−	1105.44i	−1.04995	−	1.31659i	−0.946764	−	0.321927i	$-0.895669\pi$
$89$	−881.560	−	1105.44i	−1.04995	−	1.31659i	−0.103181	−	0.994663i	$-0.532902\pi$
$90$	−640.665	−	308.528i	−0.750356	−	0.361353i
$91$	511.582	−	218.507i	0.589322	−	0.251711i
$92$	1408.07	−	678.089i	1.59566	−	0.768431i
$93$	−339.342	−	163.418i	−0.378367	−	0.182212i
$94$	−502.153	−	2200.08i	−0.550991	−	2.41405i
$95$	681.532	+	328.208i	0.736039	+	0.354458i
$96$	531.906	−	666.989i	0.565494	−	0.709107i
$97$	−352.624			−0.369109			−0.184554	−	0.982822i	$-0.559084\pi$
$97$	−352.624			−0.369109			−0.184554	+	0.982822i	$0.559084\pi$
$98$	1422.84	+	128.787i	1.46662	+	0.132750i
$99$	885.192			0.898637
$100$	−77.2612	+	96.8825i	−0.0772612	+	0.0968825i
$101$	1177.72	+	567.158i	1.16027	+	0.558756i	0.912103	−	0.409962i	$-0.134458\pi$
$101$	1177.72	+	567.158i	1.16027	+	0.558756i	0.248166	+	0.968718i	$0.420172\pi$
$102$	−136.701	−	598.925i	−0.132700	−	0.581397i
$103$	1322.90	+	637.075i	1.26553	+	0.609445i	0.941631	−	0.336648i	$-0.109293\pi$
$103$	1322.90	+	637.075i	1.26553	+	0.609445i	0.323895	+	0.946093i	$0.395007\pi$
$104$	152.036	−	73.2165i	0.143349	−	0.0690333i
$105$	−114.986	−	634.542i	−0.106871	−	0.589761i
$106$	−1827.04	−	879.855i	−1.67413	−	0.806218i
$107$	214.449	+	268.911i	0.193753	+	0.242959i	0.869213	−	0.494438i	$-0.164626\pi$
$107$	214.449	+	268.911i	0.193753	+	0.242959i	−0.675460	+	0.737397i	$0.736055\pi$
$108$	−1197.18	+	576.533i	−1.06666	+	0.513676i
$109$	48.9398	−	61.3686i	0.0430054	−	0.0539270i	−0.759864	−	0.650082i	$-0.774734\pi$
$109$	48.9398	−	61.3686i	0.0430054	−	0.0539270i	0.802869	+	0.596155i	$0.203306\pi$
$110$	−537.012	+	2352.81i	−0.465474	+	2.03937i
$111$	173.604	−	217.692i	0.148448	−	0.186148i
$112$	−950.795	−	42.9423i	−0.802158	−	0.0362292i
$113$	−724.515	−	908.514i	−0.603156	−	0.756334i	0.382710	−	0.923869i	$-0.374991\pi$
$113$	−724.515	−	908.514i	−0.603156	−	0.756334i	−0.985866	+	0.167534i	$0.946419\pi$
$114$	884.548	−	425.976i	0.726715	−	0.349968i
$115$	−393.226	+	1722.84i	−0.318857	+	1.39700i
$116$	175.896			0.140789
$117$	485.097			0.383310
$118$	209.013	−	915.744i	0.163061	−	0.714416i
$119$	−545.770	+	624.364i	−0.420426	+	0.480969i
$120$	−43.5291	−	190.713i	−0.0331137	−	0.145081i
$121$	−372.323	−	1631.25i	−0.279732	−	1.22558i
$122$	−1205.54	−	1511.70i	−0.894629	−	1.12183i
$123$	−127.058	−	159.326i	−0.0931417	−	0.116796i
$124$	237.870	+	1042.18i	0.172269	+	0.754759i
$125$	−325.211	−	1424.84i	−0.232702	−	1.01954i
$126$	1096.91	+	590.632i	0.775560	+	0.417601i
$127$	−339.869	+	1489.06i	−0.237468	+	1.04042i	0.705807	+	0.708404i	$0.250585\pi$
$127$	−339.869	+	1489.06i	−0.237468	+	1.04042i	−0.943275	+	0.332012i	$0.892272\pi$
$128$	−708.880			−0.489506
$129$	−542.696			−0.370401
$130$	−294.290	+	1289.37i	−0.198546	+	0.869886i
$131$	−1139.61	+	548.807i	−0.760062	+	0.366027i	−0.773428	−	0.633884i	$-0.781460\pi$
$131$	−1139.61	+	548.807i	−0.760062	+	0.366027i	0.0133658	+	0.999911i	$0.495745\pi$
$132$	1052.36	+	1319.62i	0.693910	+	0.870136i
$133$	−1166.88	−	628.308i	−0.760762	−	0.409633i
$134$	−347.902	+	436.255i	−0.224285	+	0.281244i
$135$	334.334	−	1464.81i	0.213147	−	0.933860i
$136$	−156.841	+	196.672i	−0.0988898	+	0.124004i
$137$	−1385.98	+	667.454i	−0.864324	+	0.416237i	−0.812874	−	0.582439i	$-0.802098\pi$
$137$	−1385.98	+	667.454i	−0.864324	+	0.416237i	−0.0514497	+	0.998676i	$0.516384\pi$
$138$	1430.00	+	1793.16i	0.882100	+	1.10612i
$139$	67.9336	+	32.7151i	0.0414536	+	0.0199630i	0.454496	−	0.890749i	$-0.349819\pi$
$139$	67.9336	+	32.7151i	0.0414536	+	0.0199630i	−0.413042	+	0.910712i	$0.635534\pi$
$140$	−1204.56	+	1378.02i	−0.727171	+	0.831887i
$141$	1607.89	−	774.317i	0.960344	−	0.462477i
$142$	2638.94	+	1270.84i	1.55954	+	0.751035i
$143$	−366.346	−	1605.07i	−0.214233	−	0.938618i
$144$	−747.764	−	360.104i	−0.432734	−	0.208394i
$145$	−124.006	+	155.499i	−0.0710217	+	0.0890585i
$146$	4706.89			2.66811
$147$	151.090	+	1119.67i	0.0847736	+	0.628224i
$148$	−790.261			−0.438912
$149$	650.201	−	815.326i	0.357493	−	0.448283i	−0.570267	−	0.821460i	$-0.693160\pi$
$149$	650.201	−	815.326i	0.357493	−	0.448283i	0.927760	+	0.373177i	$0.121732\pi$
$150$	−163.846	−	78.9041i	−0.0891865	−	0.0429499i
$151$	468.594	+	2053.04i	0.252540	+	1.10645i	0.929031	+	0.370001i	$0.120643\pi$
$151$	468.594	+	2053.04i	0.252540	+	1.10645i	−0.676491	+	0.736451i	$0.736500\pi$
$152$	−362.203	−	174.428i	−0.193280	−	0.0930786i
$153$	−651.528	+	313.759i	−0.344268	+	0.165791i
$154$	1125.87	−	4075.46i	0.589124	−	2.13253i
$155$	−1089.02	−	524.446i	−0.564338	−	0.271771i
$156$	576.707	+	723.168i	0.295984	+	0.371153i
$157$	−526.808	+	253.697i	−0.267795	+	0.128963i	−0.562963	−	0.826482i	$-0.690339\pi$
$157$	−526.808	+	253.697i	−0.267795	+	0.128963i	0.295168	+	0.955445i	$0.404624\pi$
$158$	−3084.96	+	3868.42i	−1.55333	+	1.94782i
$159$	356.853	−	1563.47i	0.177989	−	0.779821i
$160$	1707.00	−	2140.51i	0.843440	−	1.05764i
$161$	824.415	−	2984.25i	0.403559	−	1.46082i
$162$	−83.4329	−	104.622i	−0.0404636	−	0.0507398i
$163$	−2994.06	+	1441.87i	−1.43873	+	0.692856i	−0.980598	−	0.196027i	$-0.937196\pi$
$163$	−2994.06	+	1441.87i	−1.43873	+	0.692856i	−0.458133	+	0.888884i	$0.651482\pi$
$164$	−128.702	+	563.879i	−0.0612799	+	0.268485i
$165$	−1908.51			−0.900467
$166$	4501.48			2.10472
$167$	−619.027	+	2712.13i	−0.286837	+	1.25671i	0.602002	+	0.798494i	$0.294370\pi$
$167$	−619.027	+	2712.13i	−0.286837	+	1.25671i	−0.888839	+	0.458219i	$0.848487\pi$
$168$	61.1096	+	337.229i	0.0280637	+	0.154868i
$169$	288.116	+	1262.32i	0.131141	+	0.574565i
$170$	−438.703	−	1922.08i	−0.197923	−	0.867159i
$171$	−720.550	−	903.541i	−0.322233	−	0.404067i
$172$	960.343	+	1204.23i	0.425729	+	0.533848i
$173$	−426.810	−	1869.98i	−0.187571	−	0.821802i	−0.977892	−	0.209110i	$-0.932943\pi$
$173$	−426.810	−	1869.98i	−0.187571	−	0.821802i	0.790321	−	0.612693i	$-0.209914\pi$
$174$	57.4407	+	251.664i	0.0250263	+	0.109647i
$175$	43.7716	+	241.550i	0.0189075	+	0.104340i
$176$	−626.784	+	2746.12i	−0.268441	+	1.17612i
$177$	742.817			0.315444
$178$	−5889.21			−2.47986
$179$	702.580	−	3078.21i	0.293370	−	1.28534i	−0.586431	−	0.809999i	$-0.699468\pi$
$179$	702.580	−	3078.21i	0.293370	−	1.28534i	0.879802	−	0.475341i	$-0.157675\pi$
$180$	−1437.98	+	692.494i	−0.595447	+	0.286752i
$181$	1088.49	+	1364.92i	0.446998	+	0.560518i	0.953373	−	0.301796i	$-0.0975861\pi$
$181$	1088.49	+	1364.92i	0.446998	+	0.560518i	−0.506375	+	0.862314i	$0.669015\pi$
$182$	616.991	−	2233.40i	0.251288	−	0.909621i
$183$	953.373	−	1195.49i	0.385111	−	0.482914i
$184$	208.982	−	915.608i	0.0837300	−	0.366845i
$185$	557.133	−	698.622i	0.221412	−	0.277642i
$186$	−1413.42	+	680.669i	−0.557189	+	0.268328i
$187$	1530.19	+	1918.80i	0.598387	+	0.750354i
$188$	−4563.48	−	2197.66i	−1.77035	−	0.852556i
$189$	−700.945	+	2537.30i	−0.269769	+	0.976517i
$190$	2838.71	−	1367.05i	1.08390	−	0.521980i
$191$	−2275.86	−	1095.99i	−0.862174	−	0.415201i	−0.0500918	−	0.998745i	$-0.515951\pi$
$191$	−2275.86	−	1095.99i	−0.862174	−	0.415201i	−0.812082	+	0.583544i	$0.801666\pi$
$192$	−489.358	−	2144.02i	−0.183939	−	0.805891i
$193$	1690.44	+	814.075i	0.630471	+	0.303619i	0.721695	−	0.692212i	$-0.243364\pi$
$193$	1690.44	+	814.075i	0.630471	+	0.303619i	−0.0912237	+	0.995830i	$0.529078\pi$
$194$	−915.747	+	1148.31i	−0.338901	+	0.424969i
$195$	−1045.89			−0.384090
$196$	2217.16	−	2316.61i	0.808004	−	0.844247i
$197$	1920.29			0.694494			0.347247	−	0.937774i	$-0.387117\pi$
$197$	1920.29			0.694494			0.347247	+	0.937774i	$0.387117\pi$
$198$	2298.80	−	2882.60i	0.825094	−	1.03464i
$199$	3896.19	+	1876.30i	1.38791	+	0.668380i	0.970670	−	0.240418i	$-0.0772844\pi$
$199$	3896.19	+	1876.30i	1.38791	+	0.668380i	0.417236	+	0.908798i	$0.362999\pi$
$200$	16.5702	+	72.5987i	0.00585844	+	0.0256675i
$201$	−397.574	−	191.461i	−0.139516	−	0.0671873i
$202$	4905.41	−	2362.32i	1.70863	−	0.822833i
$203$	229.329	−	262.353i	0.0792893	−	0.0907074i
$204$	−1242.31	−	598.266i	−0.426369	−	0.205329i
$205$	−407.757	−	511.311i	−0.138922	−	0.174202i
$206$	5510.13	−	2653.54i	1.86363	−	0.897479i
$207$	1683.29	−	2110.78i	0.565203	−	0.708742i
$208$	−343.486	+	1504.91i	−0.114502	+	0.501667i
$209$	−2445.44	+	3066.48i	−0.809351	+	1.01489i
$210$	−2364.98	−	1273.43i	−0.777139	−	0.418451i
$211$	−1999.47	−	2507.26i	−0.652366	−	0.818041i	0.340122	−	0.940381i	$-0.389531\pi$
$211$	−1999.47	−	2507.26i	−0.652366	−	0.818041i	−0.992488	+	0.122340i	$0.960960\pi$
$212$	−4100.80	+	1974.84i	−1.32851	+	0.639776i
$213$	−515.431	+	2258.25i	−0.165806	+	0.726444i
$214$	1432.62			0.457624
$215$	−1741.63			−0.552456
$216$	−177.683	+	778.480i	−0.0559713	+	0.245226i
$217$	1864.56	+	1003.98i	0.583294	+	0.314075i
$218$	−72.7509	−	318.743i	−0.0226024	−	0.0990274i
$219$	828.294	+	3629.00i	0.255575	+	1.11975i
$220$	3377.25	+	4234.94i	1.03497	+	1.29782i
$221$	838.564	+	1051.53i	0.255239	+	0.320060i
$222$	−258.069	−	1130.67i	−0.0780200	−	0.341828i
$223$	−377.849	−	1655.46i	−0.113465	−	0.497121i	−0.999442	−	0.0333932i	$-0.989369\pi$
$223$	−377.849	−	1655.46i	−0.113465	−	0.497121i	0.885978	−	0.463728i	$-0.153489\pi$
$224$	−3156.82	+	3611.42i	−0.941624	+	1.07722i
$225$	−47.6344	+	208.700i	−0.0141139	+	0.0618370i
$226$	−4840.08			−1.42459
$227$	−6424.22			−1.87837			−0.939186	−	0.343409i	$-0.888418\pi$
$227$	−6424.22			−1.87837			−0.939186	+	0.343409i	$0.888418\pi$
$228$	490.347	−	2148.35i	0.142430	−	0.624026i
$229$	2038.01	−	981.453i	0.588102	−	0.283215i	−0.116074	−	0.993241i	$-0.537031\pi$
$229$	2038.01	−	981.453i	0.588102	−	0.283215i	0.704176	+	0.710026i	$0.251317\pi$
$230$	4589.19	+	5754.66i	1.31566	+	1.64979i
$231$	3340.29	+	150.863i	0.951406	+	0.0429699i
$232$	65.9035	−	82.6404i	0.0186499	−	0.0233862i
$233$	258.748	−	1133.65i	0.0727517	−	0.318746i	−0.925437	−	0.378901i	$-0.876302\pi$
$233$	258.748	−	1133.65i	0.0727517	−	0.318746i	0.998189	+	0.0601546i	$0.0191594\pi$
$234$	1259.77	−	1579.71i	0.351940	−	0.441319i
$235$	5160.06	−	2484.95i	1.43236	−	0.689790i
$236$	−1314.47	−	1648.30i	−0.362563	−	0.454640i
$237$	−3525.42	−	1697.75i	−0.966246	−	0.465320i
$238$	615.887	+	3398.73i	0.167739	+	0.925659i
$239$	3634.15	−	1750.11i	0.983571	−	0.473663i	0.128239	−	0.991743i	$-0.459068\pi$
$239$	3634.15	−	1750.11i	0.983571	−	0.473663i	0.855332	+	0.518080i	$0.173353\pi$
$240$	1612.21	+	776.398i	0.433615	+	0.208818i
$241$	717.758	+	3144.70i	0.191846	+	0.840532i	0.975617	+	0.219482i	$0.0704366\pi$
$241$	717.758	+	3144.70i	0.191846	+	0.840532i	−0.783771	+	0.621050i	$0.786706\pi$
$242$	−6279.04	−	3023.82i	−1.66790	−	0.803218i
$243$	−2326.72	+	2917.62i	−0.614236	+	0.770227i
$244$	−4339.84			−1.13865
$245$	484.882	+	3593.27i	0.126441	+	0.937002i
$246$	−848.804			−0.219991
$247$	−1340.13	+	1680.47i	−0.345225	+	0.432898i
$248$	578.765	+	278.719i	0.148192	+	0.0713655i
$249$	792.149	+	3470.63i	0.201608	+	0.883302i
$250$	−5484.53	−	2641.21i	−1.38749	−	0.668179i
$251$	−2230.57	+	1074.19i	−0.560925	+	0.270127i	−0.692789	−	0.721141i	$-0.743618\pi$
$251$	−2230.57	+	1074.19i	−0.560925	+	0.270127i	0.131864	+	0.991268i	$0.457904\pi$
$252$	2571.50	−	1098.34i	0.642816	−	0.274559i
$253$	−8255.28	−	3975.54i	−2.05140	−	0.987904i
$254$	3966.47	+	4973.80i	0.979837	+	1.22868i
$255$	1404.72	−	676.477i	0.344968	−	0.166128i
$256$	1489.19	−	1867.39i	0.363573	−	0.455906i
$257$	−221.824	+	971.873i	−0.0538404	+	0.235890i	−0.994687	−	0.102941i	$-0.967175\pi$
$257$	−221.824	+	971.873i	−0.0538404	+	0.235890i	0.940847	+	0.338832i	$0.110032\pi$
$258$	−1409.35	+	1767.27i	−0.340087	+	0.426456i
$259$	−1030.32	+	1178.70i	−0.247186	+	0.282782i
$260$	1850.78	+	2320.81i	0.441464	+	0.553578i
$261$	273.768	−	131.840i	0.0649264	−	0.0312669i
$262$	−1172.34	+	5136.34i	−0.276439	+	1.21116i
$263$	3607.71			0.845859			0.422930	−	0.906163i	$-0.361002\pi$
$263$	3607.71			0.845859			0.422930	+	0.906163i	$0.361002\pi$
$264$	1014.28			0.236457
$265$	1145.22	−	5017.53i	0.265472	−	1.16311i
$266$	−5076.40	+	2168.23i	−1.17013	+	0.499785i
$267$	−1036.35	−	4540.56i	−0.237542	−	1.04074i
$268$	278.689	+	1221.02i	0.0635210	+	0.278304i
$269$	−1297.94	−	1627.56i	−0.294188	−	0.368900i	0.612668	−	0.790340i	$-0.290096\pi$
$269$	−1297.94	−	1627.56i	−0.294188	−	0.368900i	−0.906856	+	0.421440i	$0.861525\pi$
$270$	−3901.88	−	4892.80i	−0.879484	−	1.10284i
$271$	−1669.32	−	7313.78i	−0.374185	−	1.63941i	−0.714886	−	0.699241i	$-0.753522\pi$
$271$	−1669.32	−	7313.78i	−0.374185	−	1.63941i	0.340701	−	0.940172i	$-0.389336\pi$
$272$	−512.040	−	2243.39i	−0.114143	−	0.500095i
$273$	1830.52	+	82.6749i	0.405818	+	0.0183286i
$274$	−1425.78	+	6246.76i	−0.314360	+	1.37730i
$275$	726.510			0.159310
$276$	5147.87			1.12270
$277$	−357.910	+	1568.10i	−0.0776343	+	0.340138i	−0.998797	−	0.0490400i	$-0.984384\pi$
$277$	−357.910	+	1568.10i	−0.0776343	+	0.340138i	0.921162	+	0.389178i	$0.127241\pi$
$278$	282.956	−	136.264i	0.0610452	−	0.0293978i
$279$	1151.37	+	1443.77i	0.247064	+	0.309808i
$280$	196.114	+	1082.24i	0.0418574	+	0.230987i
$281$	3211.48	−	4027.07i	0.681782	−	0.854928i	−0.313735	−	0.949511i	$-0.601580\pi$
$281$	3211.48	−	4027.07i	0.681782	−	0.854928i	0.995517	+	0.0945827i	$0.0301517\pi$
$282$	1654.06	−	7246.91i	0.349283	−	1.53031i
$283$	−2363.29	+	2963.47i	−0.496407	+	0.622474i	−0.965415	−	0.260720i	$-0.916040\pi$
$283$	−2363.29	+	2963.47i	−0.496407	+	0.622474i	0.469008	+	0.883194i	$0.344612\pi$
$284$	5923.11	−	2852.42i	1.23758	−	0.595986i
$285$	1553.53	+	1948.07i	0.322889	+	0.404890i
$286$	−6178.24	−	2975.28i	−1.27737	−	0.615148i
$287$	673.243	+	927.134i	0.138468	+	0.190686i
$288$	−3768.54	+	1814.83i	−0.771053	+	0.371320i
$289$	2620.07	+	1261.76i	0.533293	+	0.256821i
$290$	184.340	+	807.646i	0.0373269	+	0.163540i
$291$	−1046.49	−	503.964i	−0.210813	−	0.101522i
$292$	6586.94	−	8259.77i	1.32011	−	1.65536i
$293$	4158.02			0.829058			0.414529	−	0.910036i	$-0.363946\pi$
$293$	4158.02			0.829058			0.414529	+	0.910036i	$0.363946\pi$
$294$	4038.55	+	2415.71i	0.801134	+	0.479208i
$295$	2383.86			0.470487
$296$	−296.090	+	371.285i	−0.0581415	+	0.0729071i
$297$	7018.92	+	3380.13i	1.37131	+	0.660388i
$298$	−966.548	−	4234.72i	−0.187888	−	0.823191i
$299$	−4524.01	−	2178.65i	−0.875017	−	0.421386i
$300$	−367.753	+	177.101i	−0.0707742	+	0.0340831i
$301$	3048.22	+	137.672i	0.583709	+	0.0263630i
$302$	7902.60	+	3805.69i	1.50577	+	0.725142i
$303$	2684.57	+	3366.35i	0.508992	+	0.638256i
$304$	3313.25	−	1595.58i	0.625092	−	0.301028i
$305$	3059.58	−	3836.59i	0.574397	−	0.720271i
$306$	−670.238	+	2936.50i	−0.125212	+	0.548591i
$307$	625.127	−	783.884i	0.116215	−	0.145728i	−0.720321	−	0.693640i	$-0.756006\pi$
$307$	625.127	−	783.884i	0.116215	−	0.145728i	0.836536	+	0.547912i	$0.184577\pi$
$308$	−5576.14	−	7679.01i	−1.03159	−	1.42062i
$309$	3015.51	+	3781.33i	0.555167	+	0.696157i
$310$	−4535.99	+	2184.42i	−0.831054	+	0.400214i
$311$	1766.17	−	7738.10i	0.322027	−	1.41089i	−0.511913	−	0.859037i	$-0.671063\pi$
$311$	1766.17	−	7738.10i	0.322027	−	1.41089i	0.833940	−	0.551855i	$-0.186080\pi$
$312$	555.841			0.100860
$313$	−6062.00			−1.09471			−0.547355	−	0.836900i	$-0.684365\pi$
$313$	−6062.00			−1.09471			−0.547355	+	0.836900i	$0.684365\pi$
$314$	−541.936	+	2374.38i	−0.0973988	+	0.426732i
$315$	−841.929	+	3047.64i	−0.150595	+	0.545127i
$316$	2471.22	+	10827.1i	0.439928	+	1.92745i
$317$	−390.254	−	1709.82i	−0.0691447	−	0.302943i	0.928517	−	0.371290i	$-0.121084\pi$
$317$	−390.254	−	1709.82i	−0.0691447	−	0.302943i	−0.997662	+	0.0683475i	$0.978227\pi$
$318$	−4164.68	−	5222.35i	−0.734414	−	0.920927i
$319$	−642.975	−	806.265i	−0.112852	−	0.141511i
$320$	−1570.46	−	6880.62i	−0.274347	−	1.20199i
$321$	252.105	+	1104.54i	0.0438352	+	0.192055i
$322$	−7577.15	−	10434.6i	−1.31136	−	1.80590i
$323$	712.991	−	3123.82i	0.122823	−	0.538123i
$324$	−300.351			−0.0515005
$325$	398.137			0.0679528
$326$	−3080.04	+	13494.5i	−0.523275	+	2.29262i
$327$	232.947	−	112.181i	0.0393945	−	0.0189714i
$328$	216.704	+	271.738i	0.0364801	+	0.0457446i
$329$	−9227.62	+	3941.30i	−1.54631	+	0.660459i
$330$	−4956.30	+	6215.00i	−0.826774	+	1.03674i
$331$	1003.02	−	4394.54i	0.166559	−	0.729745i	−0.820796	−	0.571222i	$-0.806470\pi$
$331$	1003.02	−	4394.54i	0.166559	−	0.729745i	0.987355	−	0.158523i	$-0.0506732\pi$
$332$	6299.50	−	7899.32i	1.04135	−	1.30582i
$333$	−1229.98	+	592.326i	−0.202410	+	0.0974753i
$334$	7224.41	+	9059.13i	1.18354	+	1.48411i
$335$	−1275.90	−	614.442i	−0.208089	−	0.100211i
$336$	−2760.33	−	1486.30i	−0.448180	−	0.241323i
$337$	−9127.32	+	4395.49i	−1.47536	+	0.710497i	−0.986787	−	0.162025i	$-0.948198\pi$
$337$	−9127.32	+	4395.49i	−1.47536	+	0.710497i	−0.488575	+	0.872522i	$0.662483\pi$
$338$	4858.93	+	2339.94i	0.781926	+	0.376556i
$339$	−851.734	−	3731.69i	−0.136460	−	0.597869i
$340$	−3986.85	−	1919.97i	−0.635934	−	0.306250i
$341$	3907.57	−	4899.94i	0.620548	−	0.778143i
$342$	−4813.59			−0.761080
$343$	−564.607	−	6327.31i	−0.0888802	−	0.996042i
$344$	925.595			0.145072
$345$	−3629.24	+	4550.93i	−0.566353	+	0.710184i
$346$	−7197.94	−	3466.35i	−1.11839	−	0.538590i
$347$	1470.92	+	6444.54i	0.227560	+	0.997006i	0.951622	+	0.307271i	$0.0994158\pi$
$347$	1470.92	+	6444.54i	0.227560	+	0.997006i	−0.724062	+	0.689735i	$0.757727\pi$
$348$	522.011	+	251.387i	0.0804102	+	0.0387235i
$349$	874.420	−	421.099i	0.134116	−	0.0645871i	−0.365622	−	0.930763i	$-0.619144\pi$
$349$	874.420	−	421.099i	0.134116	−	0.0645871i	0.499739	+	0.866176i	$0.333429\pi$
$350$	900.276	+	484.754i	0.137491	+	0.0740320i
$351$	3846.46	+	1852.36i	0.584926	+	0.281685i
$352$	8850.84	+	11098.6i	1.34020	+	1.68056i
$353$	−4277.14	+	2059.76i	−0.644898	+	0.310566i	−0.727594	−	0.686008i	$-0.759361\pi$
$353$	−4277.14	+	2059.76i	−0.644898	+	0.310566i	0.0826957	+	0.996575i	$0.473647\pi$
$354$	1929.06	−	2418.96i	0.289628	−	0.363182i
$355$	−1654.13	+	7247.22i	−0.247302	+	1.08350i
$356$	−8241.52	+	10334.5i	−1.22697	+	1.53857i
$357$	−2512.03	+	1072.94i	−0.372411	+	0.159064i
$358$	−8199.53	−	10281.9i	−1.21050	−	1.51792i
$359$	5853.29	−	2818.79i	0.860514	−	0.414402i	0.0490447	−	0.998797i	$-0.484382\pi$
$359$	5853.29	−	2818.79i	0.860514	−	0.414402i	0.811469	+	0.584395i	$0.198668\pi$
$360$	−213.421	+	935.059i	−0.0312452	+	0.136894i
$361$	−1738.36			−0.253442
$362$	7271.58			1.05576
$363$	1226.41	−	5373.24i	0.177327	−	0.776919i
$364$	−3055.80	−	4208.20i	−0.440021	−	0.605960i
$365$	2658.18	+	11646.2i	0.381193	+	1.67012i
$366$	−1417.22	−	6209.27i	−0.202403	−	0.886786i
$367$	421.388	+	528.404i	0.0599354	+	0.0751566i	0.810896	−	0.585191i	$-0.198980\pi$
$367$	421.388	+	528.404i	0.0599354	+	0.0751566i	−0.750960	+	0.660348i	$0.770409\pi$
$368$	5356.35	+	6716.65i	0.758748	+	0.951440i
$369$	222.332	+	974.099i	0.0313662	+	0.137424i
$370$	−828.199	−	3628.58i	−0.116368	−	0.509840i
$371$	−2401.00	+	8691.21i	−0.335993	+	1.21624i
$372$	−783.527	+	3432.86i	−0.109204	+	0.478455i
$373$	860.311			0.119424			0.0597121	−	0.998216i	$-0.480982\pi$
$373$	860.311			0.119424			0.0597121	+	0.998216i	$0.480982\pi$
$374$	10222.3			1.41333
$375$	1071.22	−	4693.34i	0.147514	−	0.646302i
$376$	−2742.33	+	1320.64i	−0.376130	+	0.181135i
$377$	−352.359	−	441.844i	−0.0481363	−	0.0603611i
$378$	6442.35	+	8871.87i	0.876610	+	1.20719i
$379$	−2115.34	+	2652.55i	−0.286695	+	0.359504i	−0.904235	−	0.427035i	$-0.859558\pi$
$379$	−2115.34	+	2652.55i	−0.286695	+	0.359504i	0.617540	+	0.786540i	$0.288129\pi$
$380$	1573.63	−	6894.53i	0.212436	−	0.930741i
$381$	−3136.78	+	3933.40i	−0.421791	+	0.528909i
$382$	−9479.37	+	4565.02i	−1.26965	+	0.611432i
$383$	3178.97	+	3986.30i	0.424119	+	0.531829i	0.947281	−	0.320405i	$-0.103819\pi$
$383$	3178.97	+	3986.30i	0.424119	+	0.531829i	−0.523162	+	0.852234i	$0.675248\pi$
$384$	−2103.77	−	1013.12i	−0.279576	−	0.134637i
$385$	10719.7	+	484.152i	1.41903	+	0.0640901i
$386$	7041.02	−	3390.78i	0.928442	−	0.447114i
$387$	2397.31	+	1154.48i	0.314889	+	0.151643i
$388$	733.564	+	3213.95i	0.0959821	+	0.420525i
$389$	−1559.29	−	750.917i	−0.203237	−	0.0978740i	0.329496	−	0.944157i	$-0.393121\pi$
$389$	−1559.29	−	750.917i	−0.203237	−	0.0978740i	−0.532734	+	0.846283i	$0.678835\pi$
$390$	−2716.12	+	3405.91i	−0.352657	+	0.442217i
$391$	7485.29			0.968152
$392$	−257.692	−	1909.66i	−0.0332026	−	0.246051i
$393$	−4166.40			−0.534777
$394$	4986.91	−	6253.39i	0.637658	−	0.799597i
$395$	−11313.8	−	5448.46i	−1.44117	−	0.694029i
$396$	−1841.47	−	8067.99i	−0.233680	−	1.02382i
$397$	117.884	+	56.7698i	0.0149028	+	0.00717681i	0.441320	−	0.897350i	$-0.354510\pi$
$397$	117.884	+	56.7698i	0.0149028	+	0.00717681i	−0.426418	+	0.904526i	$0.640225\pi$
$398$	16228.3	−	7815.16i	2.04385	−	0.984268i
$399$	−2565.02	−	3532.33i	−0.321834	−	0.443203i
$400$	−613.718	−	295.551i	−0.0767147	−	0.0369439i
$401$	−2865.60	−	3593.35i	−0.356861	−	0.447490i	0.570701	−	0.821158i	$-0.306671\pi$
$401$	−2865.60	−	3593.35i	−0.356861	−	0.447490i	−0.927563	+	0.373668i	$0.878100\pi$
$402$	−1655.97	+	797.473i	−0.205453	+	0.0989411i
$403$	2141.40	−	2685.23i	0.264692	−	0.331913i
$404$	2719.30	−	11914.0i	0.334877	−	1.46719i
$405$	211.747	−	265.522i	0.0259797	−	0.0325775i
$406$	−258.791	−	1428.12i	−0.0316345	−	0.174573i
$407$	2888.74	+	3622.37i	0.351817	+	0.441165i
$408$	−746.543	+	359.516i	−0.0905868	+	0.0436243i
$409$	956.332	−	4189.97i	0.115618	−	0.506554i	−0.883645	−	0.468158i	$-0.844918\pi$
$409$	956.332	−	4189.97i	0.115618	−	0.506554i	0.999263	−	0.0383961i	$-0.0122249\pi$
$410$	−2724.00			−0.328119
$411$	−5067.13			−0.608135
$412$	3054.52	−	13382.7i	0.365256	−	1.60029i
$413$	−4172.26	−	188.439i	−0.497103	−	0.0224515i
$414$	−2502.28	−	10963.2i	−0.297054	−	1.30148i
$415$	2542.18	+	11138.0i	0.300700	+	1.31745i
$416$	4850.38	+	6082.19i	0.571657	+	0.716836i
$417$	154.853	+	194.179i	0.0181851	+	0.0228033i
$418$	3635.23	+	15927.0i	0.425371	+	1.86367i
$419$	−3181.26	−	13938.0i	−0.370918	−	1.62510i	−0.724206	−	0.689584i	$-0.757793\pi$
$419$	−3181.26	−	13938.0i	−0.370918	−	1.62510i	0.353287	−	0.935515i	$-0.385064\pi$
$420$	−5544.26	+	2368.06i	−0.644124	+	0.275118i
$421$	2735.05	−	11983.0i	0.316622	−	1.38721i	−0.526813	−	0.849981i	$-0.676613\pi$
$421$	2735.05	−	11983.0i	0.316622	−	1.38721i	0.843435	−	0.537231i	$-0.180530\pi$
$422$	−13357.3			−1.54082
$423$	−8749.91			−1.00576
$424$	−608.630	+	2666.58i	−0.0697116	+	0.305426i
$425$	−534.734	+	257.514i	−0.0610315	+	0.0293912i
$426$	6015.38	+	7543.05i	0.684146	+	0.857892i
$427$	−5658.19	+	6473.00i	−0.641262	+	0.733607i
$428$	2004.84	−	2513.99i	0.226420	−	0.283922i
$429$	1206.72	−	5286.98i	0.135806	−	0.595007i
$430$	−4522.93	+	5671.57i	−0.507244	+	0.636064i
$431$	−7417.41	+	3572.04i	−0.828966	+	0.399209i	−0.799727	−	0.600364i	$-0.795023\pi$
$431$	−7417.41	+	3572.04i	−0.828966	+	0.399209i	−0.0292386	+	0.999572i	$0.509308\pi$
$432$	−4554.15	−	5710.72i	−0.507203	−	0.636012i
$433$	6108.30	+	2941.60i	0.677936	+	0.326477i	0.740973	−	0.671534i	$-0.234364\pi$
$433$	6108.30	+	2941.60i	0.677936	+	0.326477i	−0.0630373	+	0.998011i	$0.520079\pi$
$434$	8111.60	−	3464.63i	0.897165	−	0.383197i
$435$	−590.254	+	284.251i	−0.0650586	+	0.0313306i
$436$	−661.147	−	318.392i	−0.0726221	−	0.0349729i
$437$	2661.89	+	11662.5i	0.291386	+	1.27665i
$438$	13968.8	+	6727.01i	1.52387	+	0.733856i
$439$	1595.81	−	2001.08i	0.173493	−	0.217554i	−0.687481	−	0.726203i	$-0.741283\pi$
$439$	1595.81	−	2001.08i	0.173493	−	0.217554i	0.860974	+	0.508649i	$0.169855\pi$
$440$	3255.06			0.352679
$441$	1714.46	−	5267.46i	0.185127	−	0.568779i
$442$	5601.98			0.602848
$443$	−2045.04	+	2564.40i	−0.219329	+	0.275030i	−0.879307	−	0.476255i	$-0.841994\pi$
$443$	−2045.04	+	2564.40i	−0.219329	+	0.275030i	0.659978	+	0.751285i	$0.270565\pi$
$444$	−2345.28	−	1129.43i	−0.250681	−	0.120721i
$445$	−3325.89	−	14571.7i	−0.354297	−	1.55228i
$446$	−6372.23	−	3068.70i	−0.676533	−	0.325801i
$447$	3094.87	−	1490.41i	0.327477	−	0.157705i
$448$	2204.73	+	12166.7i	0.232509	+	1.28308i
$449$	1786.02	+	860.102i	0.187723	+	0.0904025i	0.525384	−	0.850865i	$-0.323922\pi$
$449$	1786.02	+	860.102i	0.187723	+	0.0904025i	−0.337661	+	0.941268i	$0.609636\pi$
$450$	555.921	+	697.103i	0.0582364	+	0.0730261i
$451$	3055.15	−	1471.28i	0.318983	−	0.153614i
$452$	−6773.34	+	8493.51i	−0.704848	+	0.883851i
$453$	−1543.52	+	6762.58i	−0.160090	+	0.701399i
$454$	−16683.4	+	20920.3i	−1.72465	+	2.16264i
$455$	5874.55	+	265.322i	0.605282	+	0.0273373i
$456$	−825.631	−	1035.31i	−0.0847888	−	0.106322i
$457$	−8966.44	+	4318.01i	−0.917795	+	0.441987i	−0.832283	−	0.554350i	$-0.812967\pi$
$457$	−8966.44	+	4318.01i	−0.917795	+	0.441987i	−0.0855117	+	0.996337i	$0.527252\pi$
$458$	2096.53	−	9185.51i	0.213896	−	0.937141i
$459$	−6364.24			−0.647184
$460$	16520.7			1.67452
$461$	−2157.91	+	9454.41i	−0.218012	+	0.955175i	0.740932	+	0.671580i	$0.234384\pi$
$461$	−2157.91	+	9454.41i	−0.218012	+	0.955175i	−0.958944	+	0.283595i	$0.908473\pi$
$462$	9165.85	−	10485.8i	0.923017	−	1.05594i
$463$	−3785.92	−	16587.2i	−0.380015	−	1.66495i	−0.697420	−	0.716662i	$-0.745669\pi$
$463$	−3785.92	−	16587.2i	−0.380015	−	1.66495i	0.317406	−	0.948290i	$-0.397188\pi$
$464$	215.156	+	942.659i	0.0215266	+	0.0943143i
$465$	−2482.40	−	3112.83i	−0.247567	−	0.310439i
$466$	−3019.74	−	3786.64i	−0.300187	−	0.376422i
$467$	−1315.50	−	5763.59i	−0.130352	−	0.571108i	−0.997347	−	0.0727918i	$-0.976809\pi$
$467$	−1315.50	−	5763.59i	−0.130352	−	0.571108i	0.866996	−	0.498316i	$-0.166048\pi$
$468$	−1009.15	−	4421.37i	−0.0996750	−	0.436705i
$469$	2184.53	+	1176.26i	0.215079	+	0.115809i
$470$	5308.24	−	23256.9i	0.520959	−	2.28247i
$471$	−1926.00			−0.188420
$472$	−1266.91			−0.123547
$473$	2009.45	−	8803.97i	0.195337	−	0.855829i
$474$	−14684.0	+	7071.45i	−1.42291	+	0.685237i
$475$	−591.382	−	741.570i	−0.0571252	−	0.0716328i
$476$	6826.07	+	3675.50i	0.657295	+	0.353921i
$477$	−4902.36	+	6147.36i	−0.470574	+	0.590081i
$478$	3738.51	−	16379.5i	0.357731	−	1.56732i
$479$	3252.23	−	4078.17i	0.310226	−	0.389011i	−0.602137	−	0.798393i	$-0.705684\pi$
$479$	3252.23	−	4078.17i	0.310226	−	0.389011i	0.912363	+	0.409381i	$0.134255\pi$
$480$	8125.11	−	3912.85i	0.772623	−	0.372076i
$481$	1583.07	+	1985.11i	0.150066	+	0.188177i
$482$	12104.6	+	5829.28i	1.14388	+	0.550864i
$483$	6711.68	−	7678.20i	0.632282	−	0.723333i
$484$	−14093.3	+	6786.99i	−1.32357	+	0.637396i
$485$	−3358.43	−	1617.33i	−0.314429	−	0.151421i
$486$	3458.76	+	15153.8i	0.322824	+	1.41439i
$487$	11935.3	+	5747.73i	1.11055	+	0.534814i	0.896961	−	0.442109i	$-0.145770\pi$
$487$	11935.3	+	5747.73i	1.11055	+	0.534814i	0.213591	+	0.976923i	$0.431484\pi$
$488$	−1626.03	+	2038.97i	−0.150833	+	0.189139i
$489$	−10946.3			−1.01228
$490$	12960.6	+	7752.54i	1.19490	+	0.714743i
$491$	−7358.25			−0.676320			−0.338160	−	0.941089i	$-0.609805\pi$
$491$	−7358.25			−0.676320			−0.338160	+	0.941089i	$0.609805\pi$
$492$	−1187.84	+	1489.50i	−0.108845	+	0.136488i
$493$	759.033	+	365.531i	0.0693410	+	0.0333929i
$494$	1992.16	+	8728.21i	0.181440	+	0.794941i
$495$	8430.65	+	4059.99i	0.765515	+	0.368652i
$496$	−5294.26	+	2549.58i	−0.479273	+	0.230805i
$497$	3467.95	−	12553.4i	0.312996	−	1.13299i
$498$	13359.2	+	6433.45i	1.20209	+	0.578895i
$499$	−6586.95	−	8259.77i	−0.590926	−	0.740998i	0.393007	−	0.919536i	$-0.371435\pi$
$499$	−6586.95	−	8259.77i	−0.590926	−	0.740998i	−0.983933	+	0.178537i	$0.942863\pi$
$500$	−12310.1	+	5928.21i	−1.10104	+	0.530235i
$501$	−5713.24	+	7164.18i	−0.509479	+	0.638866i
$502$	−2294.62	+	10053.4i	−0.204012	+	0.893835i
$503$	382.124	−	479.168i	0.0338729	−	0.0424753i	−0.764607	−	0.644497i	$-0.777067\pi$
$503$	382.124	−	479.168i	0.0338729	−	0.0424753i	0.798479	+	0.602022i	$0.205638\pi$
$504$	447.446	−	1619.68i	0.0395453	−	0.143147i
$505$	8615.38	+	10803.3i	0.759167	+	0.951965i
$506$	−34384.8	+	16558.9i	−3.02093	+	1.45480i
$507$	−949.035	+	4157.99i	−0.0831324	+	0.364227i
$508$	14278.9			1.24710
$509$	11413.6			0.993904			0.496952	−	0.867778i	$-0.334453\pi$
$509$	11413.6			0.993904			0.496952	+	0.867778i	$0.334453\pi$
$510$	1445.06	−	6331.21i	0.125467	−	0.549708i
$511$	−3731.77	−	20593.5i	−0.323060	−	1.78278i
$512$	−3475.67	−	15227.9i	−0.300009	−	1.31442i
$513$	−2263.23	−	9915.86i	−0.194784	−	0.853403i
$514$	2588.82	+	3246.27i	0.222155	+	0.278574i
$515$	9677.45	+	12135.1i	0.828037	+	1.03833i
$516$	1128.97	+	4946.34i	0.0963181	+	0.421997i
$517$	6607.94	+	28951.3i	0.562122	+	2.46282i
$518$	1162.69	+	6416.24i	0.0986212	+	0.544234i
$519$	1405.88	−	6159.58i	0.118905	−	0.520955i
$520$	1783.81			0.150434
$521$	20971.6			1.76350			0.881749	−	0.471718i	$-0.156366\pi$
$521$	20971.6			1.76350			0.881749	+	0.471718i	$0.156366\pi$
$522$	281.629	−	1233.90i	0.0236141	−	0.103460i
$523$	−6718.70	+	3235.56i	−0.561737	+	0.270518i	−0.693131	−	0.720812i	$-0.743769\pi$
$523$	−6718.70	+	3235.56i	−0.561737	+	0.270518i	0.131394	+	0.991330i	$0.458055\pi$
$524$	7372.78	+	9245.17i	0.614659	+	0.770758i
$525$	−215.318	+	779.414i	−0.0178995	+	0.0647932i
$526$	9369.05	−	11748.4i	0.776635	−	0.973870i
$527$	−1139.29	+	4991.56i	−0.0941714	+	0.412592i
$528$	−5784.84	+	7253.95i	−0.476804	+	0.597894i
$529$	−14216.1	+	6846.13i	−1.16842	+	0.562680i
$530$	−13365.4	−	16759.7i	−1.09539	−	1.37357i
$531$	−3281.33	−	1580.20i	−0.268168	−	0.129143i
$532$	−3299.18	+	11942.5i	−0.268868	+	0.973256i
$533$	1674.26	−	806.282i	0.136061	−	0.0655234i
$534$	−17477.6	−	8416.76i	−1.41635	−	0.682077i
$535$	809.059	+	3544.72i	0.0653807	+	0.286452i
$536$	678.082	+	326.547i	0.0546431	+	0.0263147i
$537$	6484.39	−	8131.17i	0.521084	−	0.653419i
$538$	−8670.79			−0.694841
$539$	−18723.5	−	1694.74i	−1.49625	−	0.135431i
$540$	−14046.4			−1.11937
$541$	3927.22	−	4924.58i	0.312097	−	0.391357i	−0.600900	−	0.799324i	$-0.705191\pi$
$541$	3927.22	−	4924.58i	0.312097	−	0.391357i	0.912996	+	0.407968i	$0.133762\pi$
$542$	−28152.3	−	13557.4i	−2.23108	−	1.07443i
$543$	1279.62	+	5606.37i	0.101130	+	0.443079i
$544$	−10448.4	−	5031.70i	−0.823480	−	0.396567i
$545$	747.579	−	360.015i	0.0587574	−	0.0282961i
$546$	5023.01	−	5746.35i	0.393709	−	0.450405i
$547$	13321.9	+	6415.49i	1.04132	+	0.501474i	0.874760	−	0.484557i	$-0.161019\pi$
$547$	13321.9	+	6415.49i	1.04132	+	0.501474i	0.166562	+	0.986031i	$0.446733\pi$
$548$	8966.70	+	11243.9i	0.698975	+	0.876487i
$549$	−6754.62	+	3252.85i	−0.525100	+	0.252875i
$550$	1886.71	−	2365.86i	0.146272	−	0.183419i
$551$	−299.594	+	1312.61i	−0.0231636	+	0.101486i
$552$	1928.77	−	2418.61i	0.148721	−	0.186490i
$553$	19370.9	+	10430.3i	1.48957	+	0.802062i
$554$	4177.02	+	5237.82i	0.320333	+	0.401685i
$555$	2651.88	−	1277.08i	0.202822	−	0.0976738i
$556$	156.856	−	687.231i	0.0119643	−	0.0524192i
$557$	−22369.4			−1.70165			−0.850827	−	0.525446i	$-0.823899\pi$
$557$	−22369.4			−1.70165			−0.850827	+	0.525446i	$0.823899\pi$
$558$	7691.66			0.583538
$559$	1101.21	−	4824.69i	0.0833202	−	0.365050i
$560$	−8858.51	−	4769.87i	−0.668465	−	0.359935i
$561$	1798.88	+	7881.39i	0.135381	+	0.593142i
$562$	−4773.99	−	20916.2i	−0.358325	−	1.56992i
$563$	1695.63	+	2126.26i	0.126931	+	0.159167i	0.841236	−	0.540668i	$-0.181828\pi$
$563$	1695.63	+	2126.26i	0.126931	+	0.159167i	−0.714305	+	0.699835i	$0.753257\pi$
$564$	−10402.3	−	13044.1i	−0.776626	−	0.973858i
$565$	−2733.40	−	11975.8i	−0.203531	−	0.891728i
$566$	3513.12	+	15392.0i	0.260897	+	1.14306i
$567$	−391.591	+	447.982i	−0.0290040	+	0.0331807i
$568$	879.093	−	3851.56i	0.0649400	−	0.284521i
$569$	−5896.78			−0.434457			−0.217228	−	0.976121i	$-0.569702\pi$
$569$	−5896.78			−0.434457			−0.217228	+	0.976121i	$0.569702\pi$
$570$	10378.3			0.762629
$571$	1130.50	−	4953.06i	0.0828548	−	0.363011i	−0.916456	−	0.400136i	$-0.868963\pi$
$571$	1130.50	−	4953.06i	0.0828548	−	0.363011i	0.999311	+	0.0371253i	$0.0118201\pi$
$572$	−13867.1	+	6678.05i	−1.01366	+	0.488152i
$573$	−5187.75	−	6505.23i	−0.378222	−	0.474276i
$574$	4767.57	+	215.325i	0.346680	+	0.0156577i
$575$	1381.54	−	1732.40i	0.100199	−	0.125645i
$576$	−2399.30	+	10512.0i	−0.173560	+	0.760418i
$577$	10107.8	−	12674.8i	0.729278	−	0.914486i	−0.269545	−	0.962988i	$-0.586873\pi$
$577$	10107.8	−	12674.8i	0.729278	−	0.914486i	0.998823	+	0.0485020i	$0.0154447\pi$
$578$	10913.1	−	5255.46i	0.785336	−	0.378198i
$579$	3853.32	+	4831.91i	0.276578	+	0.346818i
$580$	1675.25	+	806.757i	0.119933	+	0.0577565i
$581$	−3568.92	−	19694.8i	−0.254843	−	1.40633i
$582$	−4358.84	+	2099.11i	−0.310446	+	0.149503i
$583$	24042.4	+	11578.2i	1.70795	+	0.822505i
$584$	−1412.70	−	6189.44i	−0.100099	−	0.438563i
$585$	4620.11	+	2224.93i	0.326527	+	0.157247i
$586$	10798.2	−	13540.5i	0.761209	−	0.954526i
$587$	8420.62			0.592089			0.296044	−	0.955174i	$-0.404332\pi$
$587$	8420.62			0.592089			0.296044	+	0.955174i	$0.404332\pi$
$588$	9890.81	−	3706.35i	0.693691	−	0.259944i
$589$	−8182.30			−0.572404
$590$	6190.78	−	7762.99i	0.431983	−	0.541690i
$591$	5698.92	+	2744.45i	0.396653	+	0.191018i
$592$	−966.647	−	4235.16i	−0.0671097	−	0.294027i
$593$	18736.3	+	9022.92i	1.29748	+	0.624835i	0.949823	−	0.312786i	$-0.101262\pi$
$593$	18736.3	+	9022.92i	1.29748	+	0.624835i	0.347659	+	0.937621i	$0.386977\pi$
$594$	29235.1	−	14078.9i	2.01941	−	0.972498i
$595$	−8061.65	+	3443.29i	−0.555455	+	0.237246i
$596$	−8783.82	−	4230.06i	−0.603690	−	0.290722i
$597$	8881.25	+	11136.7i	0.608853	+	0.763478i
$598$	−18843.3	+	9074.48i	−1.28856	+	0.620540i
$599$	−3265.09	+	4094.29i	−0.222718	+	0.279279i	−0.880619	−	0.473825i	$-0.842873\pi$
$599$	−3265.09	+	4094.29i	−0.222718	+	0.279279i	0.657901	+	0.753104i	$0.271444\pi$
$600$	−54.5811	+	239.135i	−0.00371377	+	0.0162711i
$601$	−6816.74	+	8547.92i	−0.462663	+	0.580162i	−0.957358	−	0.288906i	$-0.906709\pi$
$601$	−6816.74	+	8547.92i	−0.462663	+	0.580162i	0.494694	+	0.869067i	$0.335280\pi$
$602$	8364.40	−	9568.92i	0.566292	−	0.647841i
$603$	1348.95	+	1691.53i	0.0911002	+	0.114236i
$604$	17737.4	−	8541.90i	1.19491	−	0.575438i
$605$	3935.81	−	17243.9i	0.264485	−	1.15878i
$606$	17934.1			1.20218
$607$	−19595.2			−1.31029			−0.655144	−	0.755504i	$-0.727392\pi$
$607$	−19595.2			−1.31029			−0.655144	+	0.755504i	$0.727392\pi$
$608$	4124.05	−	18068.6i	0.275086	−	1.20523i
$609$	1055.54	−	450.841i	0.0702340	−	0.0299984i
$610$	−4548.19	−	19926.9i	−0.301886	−	1.32265i
$611$	3621.24	+	15865.7i	0.239771	+	1.05050i
$612$	4215.10	+	5285.57i	0.278408	+	0.349112i
$613$	3122.09	+	3914.97i	0.205710	+	0.257952i	0.873975	−	0.485972i	$-0.161534\pi$
$613$	3122.09	+	3914.97i	0.205710	+	0.257952i	−0.668265	+	0.743923i	$0.732963\pi$
$614$	−929.275	−	4071.42i	−0.0610790	−	0.267604i
$615$	−479.355	−	2100.19i	−0.0314300	−	0.137704i
$616$	−5697.03	−	257.304i	−0.372630	−	0.0168297i
$617$	−3395.31	+	14875.8i	−0.221539	+	0.970628i	0.734780	+	0.678305i	$0.237285\pi$
$617$	−3395.31	+	14875.8i	−0.221539	+	0.970628i	−0.956320	+	0.292323i	$0.905572\pi$
$618$	20145.0			1.31125
$619$	698.883			0.0453804			0.0226902	−	0.999743i	$-0.492777\pi$
$619$	698.883			0.0453804			0.0226902	+	0.999743i	$0.492777\pi$
$620$	−2514.51	+	11016.8i	−0.162879	+	0.713621i
$621$	21407.4	−	10309.2i	1.38333	−	0.666176i
$622$	−20612.3	−	25847.0i	−1.32874	−	1.66619i
$623$	4669.15	+	25766.4i	0.300266	+	1.65700i
$624$	−3170.17	+	3975.26i	−0.203379	+	0.255029i
$625$	3069.11	−	13446.6i	0.196423	−	0.860585i
$626$	−15742.7	+	19740.7i	−1.00512	+	1.26038i
$627$	−11640.0	+	5605.51i	−0.741396	+	0.357037i
$628$	3408.22	+	4273.77i	0.216565	+	0.271564i
$629$	−3410.17	−	1642.25i	−0.216172	−	0.104103i
$630$	7738.12	+	10656.3i	0.489356	+	0.673900i
$631$	−15171.7	+	7306.33i	−0.957176	+	0.460951i	−0.846196	−	0.532871i	$-0.821113\pi$
$631$	−15171.7	+	7306.33i	−0.957176	+	0.460951i	−0.110979	+	0.993823i	$0.535399\pi$
$632$	6012.78	+	2895.60i	0.378442	+	0.182248i
$633$	−2350.56	−	10298.5i	−0.147593	−	0.646647i
$634$	−6581.44	−	3169.46i	−0.412275	−	0.198541i
$635$	−10066.6	+	12623.1i	−0.629105	+	0.788873i
$636$	−14992.5			−0.934733
$637$	−10260.7	−	928.739i	−0.638218	−	0.0577676i
$638$	−4295.35			−0.266543
$639$	7080.87	−	8879.13i	0.438364	−	0.549691i
$640$	−6751.44	−	3251.32i	−0.416991	−	0.200812i
$641$	−1860.33	−	8150.64i	−0.114631	−	0.502233i	−0.999348	−	0.0361035i	$-0.988505\pi$
$641$	−1860.33	−	8150.64i	−0.114631	−	0.502233i	0.884717	−	0.466129i	$-0.154352\pi$
$642$	4251.62	+	2047.47i	0.261368	+	0.125868i
$643$	15628.5	−	7526.29i	0.958520	−	0.461599i	0.111855	−	0.993725i	$-0.464321\pi$
$643$	15628.5	−	7526.29i	0.958520	−	0.461599i	0.846665	+	0.532126i	$0.178607\pi$
$644$	−28914.6	−	1305.92i	−1.76925	−	0.0799075i
$645$	−5168.69	−	2489.11i	−0.315530	−	0.151951i
$646$	−8321.03	−	10434.2i	−0.506790	−	0.635495i
$647$	7242.74	−	3487.92i	0.440095	−	0.211939i	−0.200697	−	0.979653i	$-0.564321\pi$
$647$	7242.74	−	3487.92i	0.440095	−	0.211939i	0.640792	+	0.767715i	$0.278606\pi$
$648$	−112.534	+	141.113i	−0.00682213	+	0.00855468i
$649$	−2750.44	+	12050.5i	−0.166355	+	0.728848i
$650$	1033.94	−	1296.52i	0.0623917	−	0.0782367i
$651$	4098.66	+	5644.33i	0.246757	+	0.339814i
$652$	19370.3	+	24289.6i	1.16350	+	1.45898i
$653$	15241.6	−	7339.97i	0.913399	−	0.439870i	0.0826893	−	0.996575i	$-0.473649\pi$
$653$	15241.6	−	7339.97i	0.913399	−	0.439870i	0.830710	+	0.556705i	$0.187935\pi$
$654$	239.637	−	1049.92i	0.0143280	−	0.0627752i
$655$	−13370.9			−0.797625
$656$	−3179.36			−0.189227
$657$	4061.09	−	17792.8i	0.241154	−	1.05656i
$658$	−11128.9	+	40284.9i	−0.659349	+	2.38673i
$659$	2744.99	+	12026.6i	0.162261	+	0.710910i	0.988950	+	0.148251i	$0.0473644\pi$
$659$	2744.99	+	12026.6i	0.162261	+	0.710910i	−0.826689	+	0.562659i	$0.809778\pi$
$660$	3970.27	+	17394.9i	0.234155	+	1.02590i
$661$	−13358.8	−	16751.4i	−0.786077	−	0.985710i	−0.999961	−	0.00885078i	$-0.997183\pi$
$661$	−13358.8	−	16751.4i	−0.786077	−	0.985710i	0.213883	−	0.976859i	$-0.431389\pi$
$662$	−11705.9	−	14678.7i	−0.687254	−	0.861790i
$663$	985.808	+	4319.11i	0.0577460	+	0.253002i
$664$	−1351.05	−	5919.34i	−0.0789622	−	0.345956i
$665$	−8231.71	−	11336.0i	−0.480018	−	0.661042i
$666$	−1265.30	+	5543.64i	−0.0736176	+	0.322540i
$667$	−3145.27			−0.182587
$668$	26007.2			1.50636
$669$	1244.61	−	5452.99i	0.0719273	−	0.315134i
$670$	−5314.37	+	2559.27i	−0.306436	+	0.147572i
$671$	15864.0	+	19892.8i	0.912701	+	1.14449i
$672$	−14530.0	+	6206.04i	−0.834086	+	0.356255i
$673$	−9617.56	+	12060.0i	−0.550861	+	0.690758i	−0.976839	−	0.213976i	$-0.931359\pi$
$673$	−9617.56	+	12060.0i	−0.550861	+	0.690758i	0.425978	+	0.904734i	$0.359930\pi$
$674$	−9389.43	+	41137.8i	−0.536598	+	2.35099i
$675$	−1174.63	+	1472.94i	−0.0669801	+	0.0839904i
$676$	10905.9	−	5252.01i	0.620500	−	0.298817i
$677$	9009.76	+	11297.9i	0.511482	+	0.641378i	0.968776	−	0.247938i	$-0.0797529\pi$
$677$	9009.76	+	11297.9i	0.511482	+	0.641378i	−0.457294	+	0.889315i	$0.651181\pi$
$678$	−14364.1	−	6917.37i	−0.813641	−	0.391829i
$679$	5750.11	+	3096.15i	0.324991	+	0.174992i
$680$	−2395.82	+	1153.77i	−0.135111	+	0.0650661i
$681$	−19065.4	−	9181.39i	−1.07281	−	0.516640i
$682$	−5808.76	−	25449.8i	−0.326142	−	1.42892i
$683$	−15175.3	−	7308.04i	−0.850171	−	0.409421i	−0.0425297	−	0.999095i	$-0.513542\pi$
$683$	−15175.3	−	7308.04i	−0.850171	−	0.409421i	−0.807641	+	0.589675i	$0.799256\pi$
$684$	−6736.27	+	8447.02i	−0.376561	+	0.472193i
$685$	−16261.5			−0.907039
$686$	−22071.0	−	14593.1i	−1.22839	−	0.812196i
$687$	7450.94			0.413786
$688$	−5279.02	+	6619.68i	−0.292530	+	0.366821i
$689$	13175.6	+	6345.01i	0.728518	+	0.350836i
$690$	5395.01	+	23637.1i	0.297659	+	1.30413i
$691$	−2523.54	−	1215.28i	−0.138929	−	0.0669048i	0.363128	−	0.931739i	$-0.381709\pi$
$691$	−2523.54	−	1215.28i	−0.138929	−	0.0669048i	−0.502057	+	0.864835i	$0.667423\pi$
$692$	−16155.8	+	7780.24i	−0.887504	+	0.427399i
$693$	−14434.5	−	7772.26i	−0.791228	−	0.426037i
$694$	24806.4	+	11946.1i	1.35683	+	0.653414i
$695$	496.956	+	623.163i	0.0271232	+	0.0340114i
$696$	313.692	−	151.066i	0.0170840	−	0.00822723i
$697$	−1727.18	+	2165.82i	−0.0938618	+	0.117699i
$698$	899.530	−	3941.10i	0.0487790	−	0.213715i
$699$	2388.09	−	2994.57i	0.129221	−	0.162039i
$700$	2110.53	−	901.449i	0.113958	−	0.0486737i
$701$	10064.6	+	12620.6i	0.542275	+	0.679991i	0.975171	−	0.221452i	$-0.0710798\pi$
$701$	10064.6	+	12620.6i	0.542275	+	0.679991i	−0.432896	+	0.901444i	$0.642508\pi$
$702$	16021.2	−	7715.42i	0.861371	−	0.414814i
$703$	1346.01	−	5897.25i	0.0722129	−	0.316386i
$704$	36593.6			1.95905
$705$	18865.1			1.00780
$706$	−4399.96	+	19277.5i	−0.234553	+	1.02765i
$707$	−14224.7	−	19589.2i	−0.756686	−	1.04205i
$708$	−1545.28	−	6770.33i	−0.0820272	−	0.359385i
$709$	−5764.31	−	25255.1i	−0.305336	−	1.33776i	−0.861950	−	0.506993i	$-0.830757\pi$
$709$	−5764.31	−	25255.1i	−0.305336	−	1.33776i	0.556615	−	0.830771i	$-0.312100\pi$
$710$	19304.7	+	24207.3i	1.02041	+	1.27956i
$711$	11961.6	+	14999.3i	0.630933	+	0.791165i
$712$	1767.55	+	7744.16i	0.0930364	+	0.407619i
$713$	−4253.45	−	18635.6i	−0.223412	−	0.978834i
$714$	−3029.62	+	10966.7i	−0.158797	+	0.574817i
$715$	3872.63	−	16967.1i	0.202557	−	0.887459i
$716$	−29517.6			−1.54067
$717$	13286.4			0.692036
$718$	6021.37	−	26381.4i	0.312974	−	1.37123i
$719$	12833.2	−	6180.12i	0.665641	−	0.320556i	−0.0703743	−	0.997521i	$-0.522419\pi$
$719$	12833.2	−	6180.12i	0.665641	−	0.320556i	0.736015	+	0.676965i	$0.236705\pi$
$720$	−5470.14	−	6859.34i	−0.283139	−	0.355045i
$721$	−15978.3	−	22004.0i	−0.825331	−	1.13658i
$722$	−4514.43	+	5660.92i	−0.232701	+	0.291797i
$723$	−2364.25	+	10358.4i	−0.121615	+	0.532828i
$724$	10176.0	−	12760.4i	0.522361	−	0.655021i
$725$	224.691	−	108.206i	0.0115101	−	0.00554297i
$726$	−14312.9	−	17947.8i	−0.731682	−	0.917500i
$727$	−6152.76	−	2963.01i	−0.313883	−	0.151158i	0.270309	−	0.962774i	$-0.412874\pi$
$727$	−6152.76	−	2963.01i	−0.313883	−	0.151158i	−0.584192	+	0.811615i	$0.698589\pi$
$728$	−3122.05	−	141.006i	−0.158944	−	0.00717863i
$729$	−11856.4	+	5709.76i	−0.602369	+	0.290086i
$730$	44828.9	+	21588.4i	2.27286	+	1.09455i
$731$	1641.58	+	7192.25i	0.0830591	+	0.363906i
$732$	−12879.5	−	6202.43i	−0.650327	−	0.313181i
$733$	−7596.76	+	9526.03i	−0.382800	+	0.480016i	−0.935481	−	0.353377i	$-0.885033\pi$
$733$	−7596.76	+	9526.03i	−0.382800	+	0.480016i	0.552681	+	0.833393i	$0.313605\pi$
$734$	2815.06			0.141561
$735$	−3696.44	+	11356.8i	−0.185504	+	0.569937i
$736$	43296.1			2.16836
$737$	4578.12	−	5740.78i	0.228816	−	0.286926i
$738$	3749.51	+	1805.67i	0.187021	+	0.0900645i
$739$	−585.871	−	2566.87i	−0.0291632	−	0.127772i	0.958251	−	0.285929i	$-0.0923021\pi$
$739$	−585.871	−	2566.87i	−0.0291632	−	0.127772i	−0.987414	+	0.158157i	$0.949445\pi$
$740$	−7526.52	−	3624.58i	−0.373893	−	0.180057i
$741$	−6378.85	+	3071.89i	−0.316239	+	0.152293i
$742$	22067.4	+	30389.4i	1.09181	+	1.50355i
$743$	−14411.9	−	6940.40i	−0.711602	−	0.342690i	0.0428164	−	0.999083i	$-0.486367\pi$
$743$	−14411.9	−	6940.40i	−0.711602	−	0.342690i	−0.754419	+	0.656393i	$0.772081\pi$
$744$	1319.28	+	1654.32i	0.0650096	+	0.0815194i
$745$	9932.12	−	4783.06i	0.488436	−	0.235218i
$746$	2234.19	−	2801.58i	0.109651	−	0.137498i
$747$	3883.87	−	17016.3i	0.190232	−	0.833461i
$748$	14305.4	−	17938.4i	0.699275	−	0.876863i
$749$	−1135.82	−	6267.96i	−0.0554100	−	0.305776i
$750$	−12501.8	−	15676.8i	−0.608670	−	0.763248i
$751$	−1913.87	+	921.673i	−0.0929937	+	0.0447834i	−0.479802	−	0.877377i	$-0.659292\pi$
$751$	−1913.87	+	921.673i	−0.0929937	+	0.0447834i	0.386809	+	0.922160i	$0.373577\pi$
$752$	6195.61	−	27144.7i	0.300440	−	1.31631i
$753$	−8154.94			−0.394664
$754$	−2353.91			−0.113693
$755$	−4953.48	+	21702.6i	−0.238776	+	1.04614i
$756$	24584.2	+	1110.34i	1.18270	+	0.0534160i
$757$	8137.25	+	35651.6i	0.390691	+	1.71173i	0.662228	+	0.749302i	$0.269611\pi$
$757$	8137.25	+	35651.6i	0.390691	+	1.71173i	−0.271537	+	0.962428i	$0.587532\pi$
$758$	3144.53	+	13777.1i	0.150679	+	0.660166i
$759$	−18817.7	−	23596.6i	−0.899920	−	1.12846i
$760$	−2649.63	−	3322.53i	−0.126463	−	0.158580i
$761$	−7550.97	−	33083.0i	−0.359688	−	1.57590i	−0.753971	−	0.656907i	$-0.771864\pi$
$761$	−7550.97	−	33083.0i	−0.359688	−	1.57590i	0.394283	−	0.918989i	$-0.370993\pi$
$762$	4662.95	+	20429.7i	0.221681	+	0.971247i
$763$	−1336.88	+	571.008i	−0.0634315	+	0.0270929i
$764$	−5254.86	+	23023.1i	−0.248841	+	1.09024i
$765$	−7644.30			−0.361281
$766$	21236.9			1.00172
$767$	−1507.28	+	6603.82i	−0.0709579	+	0.310887i
$768$	7088.38	−	3413.58i	0.333047	−	0.160387i
$769$	−7120.94	−	8929.37i	−0.333924	−	0.418728i	0.586316	−	0.810083i	$-0.300578\pi$
$769$	−7120.94	−	8929.37i	−0.333924	−	0.418728i	−0.920240	+	0.391355i	$0.872006\pi$
$770$	29415.2	−	33651.2i	1.37669	−	1.57494i
$771$	−2047.30	+	2567.23i	−0.0956312	+	0.119918i
$772$	3903.17	−	17100.9i	0.181967	−	0.797248i
$773$	−13662.3	+	17132.0i	−0.635704	+	0.797147i	−0.990458	−	0.137812i	$-0.955993\pi$
$773$	−13662.3	+	17132.0i	−0.635704	+	0.797147i	0.354755	+	0.934959i	$0.384564\pi$
$774$	9985.24	−	4808.64i	0.463711	−	0.223311i
$775$	944.972	+	1184.96i	0.0437992	+	0.0549225i
$776$	1784.85	+	859.537i	0.0825674	+	0.0397623i
$777$	−4742.30	+	2025.53i	−0.218956	+	0.0935206i
$778$	−6494.75	+	3127.71i	−0.299291	+	0.144131i
$779$	−3988.69	−	1920.85i	−0.183452	−	0.0883461i
$780$	2175.76	+	9532.63i	0.0998779	+	0.437594i
$781$	−34726.3	−	16723.3i	−1.59104	−	0.766207i
$782$	19438.9	−	24375.7i	0.888919	−	1.11467i
$783$	2674.21			0.122054
$784$	15127.2	+	9048.52i	0.689104	+	0.412196i
$785$	−6180.97			−0.281030
$786$	−10819.9	+	13567.8i	−0.491011	+	0.615709i
$787$	27621.3	+	13301.7i	1.25107	+	0.602484i	0.937799	−	0.347179i	$-0.112860\pi$
$787$	27621.3	+	13301.7i	1.25107	+	0.602484i	0.313272	+	0.949663i	$0.398575\pi$
$788$	−3994.79	−	17502.3i	−0.180595	−	0.791237i
$789$	10706.7	+	5156.08i	0.483104	+	0.232651i
$790$	−47124.2	+	22693.8i	−2.12229	+	1.02204i
$791$	3837.37	+	21176.3i	0.172492	+	0.951885i
$792$	−4480.50	−	2157.70i	−0.201020	−	0.0968060i
$793$	8693.68	+	10901.5i	0.389309	+	0.488178i
$794$	491.008	−	236.457i	0.0219461	−	0.0105687i
$795$	10569.7	−	13253.9i	0.471532	−	0.591282i
$796$	8996.14	−	39414.7i	0.400578	−	1.75504i
$797$	17443.4	−	21873.4i	0.775255	−	0.972138i	−0.224743	−	0.974418i	$-0.572154\pi$
$797$	17443.4	−	21873.4i	0.775255	−	0.972138i	0.999997	+	0.00227967i	$0.000725643\pi$
$798$	−18164.2	−	820.379i	−0.805771	−	0.0363924i
$799$	−15125.5	−	18966.8i	−0.669716	−	0.839798i
$800$	−3092.98	+	1489.50i	−0.136692	+	0.0658273i
$801$	−5081.20	+	22262.2i	−0.224139	+	0.982016i
$802$	−19143.5			−0.842868
$803$	−61938.9			−2.72201
$804$	−917.982	+	4021.94i	−0.0402671	+	0.176422i
$805$	21539.3	−	24641.0i	0.943055	−	1.07886i
$806$	−3183.28	−	13946.8i	−0.139114	−	0.609500i
$807$	−1525.84	−	6685.15i	−0.0665579	−	0.291609i
$808$	−4578.67	−	5741.47i	−0.199353	−	0.249981i
$809$	11845.5	+	14853.8i	0.514792	+	0.645529i	0.969494	−	0.245115i	$-0.0788256\pi$
$809$	11845.5	+	14853.8i	0.514792	+	0.645529i	−0.454702	+	0.890644i	$0.650254\pi$
$810$	−314.770	−	1379.10i	−0.0136542	−	0.0598229i
$811$	1723.23	+	7549.98i	0.0746127	+	0.326900i	0.998435	−	0.0559215i	$-0.0178097\pi$
$811$	1723.23	+	7549.98i	0.0746127	+	0.326900i	−0.923822	+	0.382821i	$0.874953\pi$
$812$	−2868.27	−	1544.42i	−0.123961	−	0.0667469i
$813$	5498.64	−	24091.1i	0.237203	−	1.03925i
$814$	19298.1			0.830955
$815$	−35129.0			−1.50983
$816$	1686.63	−	7389.59i	0.0723575	−	0.317019i
$817$	−10622.2	+	5115.37i	−0.454863	+	0.219050i
$818$	−11161.0	−	13995.4i	−0.477059	−	0.598213i
$819$	−7910.29	−	4259.30i	−0.337495	−	0.181724i
$820$	−3812.03	+	4780.14i	−0.162344	+	0.203573i
$821$	−1394.07	+	6107.80i	−0.0592610	+	0.259639i	−0.995876	−	0.0907197i	$-0.971083\pi$
$821$	−1394.07	+	6107.80i	−0.0592610	+	0.259639i	0.936615	+	0.350359i	$0.113940\pi$
$822$	−13159.1	+	16501.0i	−0.558366	+	0.700168i
$823$	35488.3	−	17090.3i	1.50309	−	0.723851i	0.512246	−	0.858839i	$-0.328814\pi$
$823$	35488.3	−	17090.3i	1.50309	−	0.723851i	0.990847	+	0.134988i	$0.0430994\pi$
$824$	−5143.11	−	6449.26i	−0.217438	−	0.272658i
$825$	2156.09	+	1038.32i	0.0909882	+	0.0438176i
$826$	−11448.8	+	13097.5i	−0.482270	+	0.551719i
$827$	8416.64	−	4053.24i	0.353900	−	0.170429i	−0.248483	−	0.968636i	$-0.579932\pi$
$827$	8416.64	−	4053.24i	0.353900	−	0.170429i	0.602383	+	0.798207i	$0.294218\pi$
$828$	−22740.3	−	10951.1i	−0.954443	−	0.459636i
$829$	10279.8	+	45038.9i	0.430680	+	1.88693i	0.461016	+	0.887392i	$0.347485\pi$
$829$	10279.8	+	45038.9i	0.430680	+	1.88693i	−0.0303367	+	0.999540i	$0.509658\pi$
$830$	42872.6	+	20646.4i	1.79293	+	0.863428i
$831$	−3303.29	+	4142.19i	−0.137894	+	0.172914i
$832$	20053.8			0.835626
$833$	14381.8	−	5389.24i	0.598198	−	0.224161i
$834$	1034.48			0.0429512
$835$	−18335.1	+	22991.4i	−0.759893	+	0.952876i
$836$	33036.4	+	15909.5i	1.36673	+	0.658182i
$837$	3616.43	+	15844.6i	0.149345	+	0.654324i
$838$	−53650.4	−	25836.7i	−2.21160	−	1.06505i
$839$	13175.3	−	6344.88i	0.542147	−	0.261084i	−0.142707	−	0.989765i	$-0.545581\pi$
$839$	13175.3	−	6344.88i	0.542147	−	0.261084i	0.684853	+	0.728681i	$0.259866\pi$
$840$	−964.710	+	3492.09i	−0.0396258	+	0.143439i
$841$	21654.8	+	10428.4i	0.887892	+	0.427586i
$842$	−31919.6	−	40025.9i	−1.30644	−	1.63822i
$843$	15286.2	−	7361.46i	0.624538	−	0.300762i
$844$	−18692.6	+	23439.8i	−0.762354	+	0.955962i
$845$	−3045.66	+	13343.9i	−0.123993	+	0.543248i
$846$	−22723.1	+	28493.9i	−0.923447	+	1.15797i
$847$	−8251.58	+	29869.3i	−0.334743	+	1.21171i
$848$	−15599.6	−	19561.3i	−0.631715	−	0.792145i
$849$	−11249.0	+	5417.22i	−0.454727	+	0.218985i
$850$	−550.089	+	2410.10i	−0.0221975	+	0.0972537i
$851$	14131.0			0.569218
$852$	21654.8			0.870754
$853$	−10074.3	+	44138.2i	−0.404380	+	1.77171i	0.204933	+	0.978776i	$0.434302\pi$
$853$	−10074.3	+	44138.2i	−0.404380	+	1.77171i	−0.609314	+	0.792929i	$0.708555\pi$
$854$	6385.11	+	35235.8i	0.255848	+	1.41188i
$855$	−2718.44	−	11910.3i	−0.108735	−	0.476401i
$856$	−429.977	−	1883.85i	−0.0171686	−	0.0752206i
$857$	−7513.62	−	9421.78i	−0.299487	−	0.375545i	0.609204	−	0.793013i	$-0.291489\pi$
$857$	−7513.62	−	9421.78i	−0.299487	−	0.375545i	−0.908691	+	0.417468i	$0.862917\pi$
$858$	−14083.1	−	17659.7i	−0.560362	−	0.702671i
$859$	5053.00	+	22138.7i	0.200706	+	0.879350i	0.970508	+	0.241068i	$0.0774975\pi$
$859$	5053.00	+	22138.7i	0.200706	+	0.879350i	−0.769803	+	0.638282i	$0.779645\pi$
$860$	3623.11	+	15873.9i	0.143660	+	0.629413i
$861$	672.958	+	3713.67i	0.0266369	+	0.146994i
$862$	−7630.42	+	33431.0i	−0.301500	+	1.32096i
$863$	24503.8			0.966535			0.483268	−	0.875473i	$-0.339450\pi$
$863$	24503.8			0.966535			0.483268	+	0.875473i	$0.339450\pi$
$864$	−36811.7			−1.44949
$865$	4511.79	−	19767.5i	0.177347	−	0.777010i
$866$	25442.2	−	12252.3i	0.998340	−	0.480775i
$867$	5972.38	+	7489.12i	0.233948	+	0.293361i
$868$	5271.78	−	19082.9i	0.206147	−	0.746218i
$869$	40595.7	−	50905.4i	1.58471	−	1.98716i
$870$	−607.204	+	2660.33i	−0.0236622	+	0.103671i
$871$	2508.87	−	3146.02i	0.0976003	−	0.122387i
$872$	−397.303	+	191.331i	−0.0154293	+	0.00743038i
$873$	3550.70	+	4452.43i	0.137655	+	0.172614i
$874$	44891.5	+	21618.6i	1.73739	+	0.836683i
$875$	−7207.48	+	26089.9i	−0.278465	+	1.00800i
$876$	31353.0	−	15098.8i	1.20927	−	0.582353i
$877$	24138.0	+	11624.2i	0.929397	+	0.447574i	0.836417	−	0.548094i	$-0.184646\pi$
$877$	24138.0	+	11624.2i	0.929397	+	0.447574i	0.0929802	+	0.995668i	$0.470361\pi$
$878$	−2372.23	−	10393.4i	−0.0911831	−	0.399499i
$879$	12339.9	+	5942.57i	0.473508	+	0.228030i
$880$	−18564.8	+	23279.5i	−0.711159	+	0.891765i
$881$	−13509.0			−0.516605			−0.258302	−	0.966064i	$-0.583163\pi$
$881$	−13509.0			−0.516605			−0.258302	+	0.966064i	$0.583163\pi$
$882$	−12701.0	−	19262.4i	−0.484880	−	0.735374i
$883$	−20400.9			−0.777515			−0.388758	−	0.921340i	$-0.627096\pi$
$883$	−20400.9			−0.777515			−0.388758	+	0.921340i	$0.627096\pi$
$884$	7839.56	−	9830.50i	0.298272	−	0.374022i
$885$	7074.66	+	3406.98i	0.268714	+	0.129406i
$886$	3040.03	+	13319.2i	0.115273	+	0.505044i
$887$	3307.91	+	1593.01i	0.125219	+	0.0603021i	0.495444	−	0.868640i	$-0.335005\pi$
$887$	3307.91	+	1593.01i	0.125219	+	0.0603021i	−0.370226	+	0.928942i	$0.620720\pi$
$888$	−1409.35	+	678.707i	−0.0532598	+	0.0256486i
$889$	18616.5	−	21297.4i	0.702338	−	0.803479i
$890$	−56089.4	−	27011.2i	−2.11250	−	1.01732i
$891$	1097.91	+	1376.74i	0.0412811	+	0.0517648i
$892$	−14302.5	+	6887.73i	−0.536865	+	0.258541i
$893$	24172.5	−	30311.4i	0.905827	−	1.13587i
$894$	3183.75	−	13948.9i	0.119106	−	0.521836i
$895$	20809.8	−	26094.7i	0.777202	−	0.974581i
$896$	11559.4	+	6224.19i	0.430998	+	0.232071i
$897$	−10312.4	−	12931.3i	−0.383857	−	0.481341i
$898$	7439.11	−	3582.49i	0.276444	−	0.133128i
$899$	478.722	−	2097.42i	0.0177600	−	0.0778119i
$900$	2001.27			0.0741210
$901$	−21799.9			−0.806059
$902$	3142.88	−	13769.9i	0.116016	−	0.508300i
$903$	8849.53	+	4765.04i	0.326129	+	0.175604i
$904$	1452.68	+	6364.59i	0.0534461	+	0.234163i
$905$	4106.57	+	17992.1i	0.150836	+	0.660858i
$906$	18013.8	+	22588.5i	0.660559	+	0.828315i
$907$	1493.56	+	1872.87i	0.0546779	+	0.0685640i	0.808418	−	0.588608i	$-0.200324\pi$
$907$	1493.56	+	1872.87i	0.0546779	+	0.0685640i	−0.753741	+	0.657172i	$0.771752\pi$
$908$	13364.3	+	58552.9i	0.488448	+	2.14003i
$909$	−4697.58	−	20581.4i	−0.171407	−	0.750983i
$910$	16119.9	−	18441.3i	0.587221	−	0.671784i
$911$	−3965.92	+	17375.8i	−0.144233	+	0.631928i	0.850191	+	0.526475i	$0.176487\pi$
$911$	−3965.92	+	17375.8i	−0.144233	+	0.631928i	−0.994424	+	0.105453i	$0.966371\pi$
$912$	12113.2			0.439812
$913$	−59236.0			−2.14723
$914$	−9223.92	+	40412.7i	−0.333808	+	1.46251i
$915$	14563.2	−	7013.28i	0.526170	−	0.253390i
$916$	−13185.0	−	16533.5i	−0.475596	−	0.596378i
$917$	23401.9	+	1056.94i	0.842747	+	0.0380623i
$918$	−16527.6	+	20725.0i	−0.594219	+	0.745127i
$919$	−6417.90	+	28118.7i	−0.230367	+	1.00930i	0.718970	+	0.695041i	$0.244614\pi$
$919$	−6417.90	+	28118.7i	−0.230367	+	1.00930i	−0.949337	+	0.314261i	$0.898243\pi$
$920$	6189.86	−	7761.84i	0.221819	−	0.278152i
$921$	2975.52	−	1432.94i	0.106457	−	0.0512670i
$922$	25184.1	+	31579.8i	0.899558	+	1.12801i
$923$	−19030.5	−	9164.60i	−0.678653	−	0.326822i
$924$	−5573.78	−	30758.6i	−0.198446	−	1.09511i
$925$	−1009.49	+	486.144i	−0.0358830	+	0.0172803i
$926$	−63847.7	−	30747.4i	−2.26584	−	1.09117i
$927$	−5276.68	−	23118.6i	−0.186957	−	0.819111i
$928$	4390.36	+	2114.29i	0.155302	+	0.0747897i
$929$	−11977.7	+	15019.6i	−0.423011	+	0.530439i	−0.946977	−	0.321300i	$-0.895880\pi$
$929$	−11977.7	+	15019.6i	−0.423011	+	0.530439i	0.523967	+	0.851739i	$0.324452\pi$
$930$	−16583.5			−0.584726
$931$	13511.1	+	20491.2i	0.475628	+	0.721343i
$932$	−10870.8			−0.382066
$933$	16300.7	−	20440.4i	0.571983	−	0.717245i
$934$	−22185.3	−	10683.9i	−0.777222	−	0.374290i
$935$	5772.99	+	25293.1i	0.201922	+	0.884677i
$936$	−2455.37	−	1182.45i	−0.0857441	−	0.0412922i
$937$	−43421.7	+	20910.8i	−1.51390	+	0.729056i	−0.992268	−	0.124115i	$-0.960391\pi$
$937$	−43421.7	+	20910.8i	−1.51390	+	0.729056i	−0.521632	+	0.853170i	$0.674677\pi$
$938$	9503.57	−	4059.17i	0.330813	−	0.141297i
$939$	−17990.4	−	8663.71i	−0.625233	−	0.301096i
$940$	−33383.3	−	41861.4i	−1.15835	−	1.45252i
$941$	30498.9	−	14687.5i	1.05657	−	0.508819i	0.176817	−	0.984244i	$-0.443420\pi$
$941$	30498.9	−	14687.5i	1.05657	−	0.508819i	0.879756	+	0.475425i	$0.157706\pi$
$942$	−5001.74	+	6271.99i	−0.173000	+	0.216935i
$943$	2301.37	−	10083.0i	0.0794728	−	0.348193i
$944$	7225.68	−	9060.71i	0.249127	−	0.312395i
$945$	−18313.4	+	20950.6i	−0.630407	+	0.721189i
$946$	−23451.5	−	29407.2i	−0.805997	−	1.01069i
$947$	24973.1	−	12026.4i	0.856933	−	0.412677i	0.0467866	−	0.998905i	$-0.485102\pi$
$947$	24973.1	−	12026.4i	0.856933	−	0.412677i	0.810146	+	0.586228i	$0.199388\pi$
$948$	−8140.05	+	35663.9i	−0.278878	+	1.22184i
$949$	−33943.4			−1.16106
$950$	−3950.70			−0.134924
$951$	1285.47	−	5632.02i	0.0438320	−	0.192041i
$952$	4284.39	−	1829.95i	0.145859	−	0.0622994i
$953$	11329.2	+	49636.3i	0.385087	+	1.68718i	0.681260	+	0.732041i	$0.261432\pi$
$953$	11329.2	+	49636.3i	0.385087	+	1.68718i	−0.296174	+	0.955134i	$0.595711\pi$
$954$	7287.55	+	31928.8i	0.247320	+	1.08358i
$955$	−16648.6	−	20876.7i	−0.564123	−	0.707387i
$956$	−23511.4	−	29482.3i	−0.795409	−	0.997412i
$957$	−755.875	−	3311.71i	−0.0255318	−	0.111862i
$958$	−4834.57	−	21181.6i	−0.163046	−	0.714350i
$959$	28461.1	+	1285.44i	0.958350	+	0.0432835i
$960$	5172.98	−	22664.3i	0.173914	−	0.761966i
$961$	−16716.5			−0.561125
$962$	10575.6			0.354440
$963$	1236.06	−	5415.52i	0.0413618	−	0.181218i
$964$	27168.9	−	13083.9i	0.907731	−	0.437140i
$965$	12366.2	+	15506.7i	0.412519	+	0.517282i
$966$	−7573.95	−	41796.3i	−0.252265	−	1.39211i
$967$	17700.4	−	22195.6i	0.588632	−	0.738122i	−0.394926	−	0.918713i	$-0.629230\pi$
$967$	17700.4	−	22195.6i	0.588632	−	0.738122i	0.983558	+	0.180591i	$0.0578012\pi$
$968$	−2091.70	+	9164.33i	−0.0694522	+	0.304290i
$969$	6580.47	−	8251.65i	0.218158	−	0.273562i
$970$	−13988.5	+	6736.49i	−0.463034	+	0.222985i
$971$	1819.91	+	2282.10i	0.0601481	+	0.0754234i	0.810996	−	0.585052i	$-0.198926\pi$
$971$	1819.91	+	2282.10i	0.0601481	+	0.0754234i	−0.750847	+	0.660476i	$0.770355\pi$
$972$	31432.6	+	15137.1i	1.03724	+	0.499510i
$973$	−820.519	−	1129.95i	−0.0270346	−	0.0372298i
$974$	49712.7	−	23940.4i	1.63542	−	0.787576i
$975$	1181.56	+	569.011i	0.0388106	+	0.0186902i
$976$	−5308.50	−	23258.0i	−0.174099	−	0.762779i
$977$	11994.4	+	5776.17i	0.392767	+	0.189147i	0.619835	−	0.784732i	$-0.287200\pi$
$977$	11994.4	+	5776.17i	0.392767	+	0.189147i	−0.227068	+	0.973879i	$0.572914\pi$
$978$	−28426.9	+	35646.2i	−0.929441	+	1.16548i
$979$	77497.4			2.52996
$980$	31741.8	−	11894.5i	1.03465	−	0.387710i
$981$	−1267.67			−0.0412574
$982$	−19109.0	+	23962.0i	−0.620971	+	0.778673i
$983$	−39711.4	−	19124.0i	−1.28850	−	0.620509i	−0.340940	−	0.940085i	$-0.610745\pi$
$983$	−39711.4	−	19124.0i	−1.28850	−	0.620509i	−0.947561	+	0.319576i	$0.896460\pi$
$984$	254.755	+	1116.16i	0.00825335	+	0.0361603i
$985$	18289.1	+	8807.56i	0.591613	+	0.284906i
$986$	3161.51	−	1522.50i	0.102113	−	0.0491749i
$987$	−33018.0	−	1491.24i	−1.06482	−	0.0480920i
$988$	18104.4	+	8718.60i	0.582972	+	0.280745i
$989$	−17172.3	−	21533.4i	−0.552121	−	0.692337i
$990$	35115.3	−	16910.6i	1.12731	−	0.542884i
$991$	19192.2	−	24066.3i	0.615198	−	0.771434i	−0.372462	−	0.928047i	$-0.621486\pi$
$991$	19192.2	−	24066.3i	0.615198	−	0.771434i	0.987660	+	0.156614i	$0.0500578\pi$
$992$	−6589.84	+	28872.0i	−0.210915	+	0.924078i
$993$	9257.30	−	11608.3i	0.295843	−	0.370975i
$994$	−31873.7	−	43893.9i	−1.01708	−	1.40063i
$995$	28501.9	+	35740.2i	0.908111	+	1.13873i
$996$	29984.8	−	14439.9i	0.953920	−	0.459384i
$997$	−3484.14	+	15265.0i	−0.110676	+	0.484903i	0.888962	+	0.457982i	$0.151428\pi$
$997$	−3484.14	+	15265.0i	−0.110676	+	0.484903i	−0.999638	+	0.0269214i	$0.991430\pi$
$998$	−44003.7			−1.39570
$999$	−12014.6			−0.380507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.43.11	yes	78
49.8	even	7	inner	49.4.e.a.8.11	✓	78
49.20	odd	14		2401.4.a.c.1.33		39
49.29	even	7		2401.4.a.d.1.33		39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.11	✓	78	49.8	even	7	inner
49.4.e.a.43.11	yes	78	1.1	even	1	trivial
2401.4.a.c.1.33		39	49.20	odd	14
2401.4.a.d.1.33		39	49.29	even	7

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.59695 - 3.25648i) q^{2} +(2.96773 + 1.42918i) q^{3} +(-2.08030 - 9.11440i) q^{4} +(9.52410 + 4.58657i) q^{5} +(12.3612 - 5.95282i) q^{6} +(-16.3066 - 8.78031i) q^{7} +(-5.06162 - 2.43755i) q^{8} +(-10.0694 - 12.6266i) q^{9} +(39.6697 - 19.1039i) q^{10} +(-34.1739 + 42.8527i) q^{11} +(6.85238 - 30.0222i) q^{12} +(-18.7277 + 23.4838i) q^{13} +(-70.9404 + 30.3001i) q^{14} +(21.7099 + 27.2234i) q^{15} +(46.3012 - 22.2975i) q^{16} +(9.96373 - 43.6539i) q^{17} -67.2678 q^{18} +71.5587 q^{19} +(21.9908 - 96.3479i) q^{20} +(-35.8450 - 49.3628i) q^{21} +(50.8008 + 222.573i) q^{22} +(37.1988 + 162.978i) q^{23} +(-11.5378 - 14.4680i) q^{24} +(-8.26430 - 10.3631i) q^{25} +(27.8395 + 121.973i) q^{26} +(-31.6276 - 138.570i) q^{27} +(-46.1046 + 166.891i) q^{28} +(-4.18669 + 18.3431i) q^{29} +145.032 q^{30} -114.344 q^{31} +(57.6317 - 252.501i) q^{32} +(-162.663 + 78.3344i) q^{33} +(-116.283 - 145.814i) q^{34} +(-115.034 - 158.416i) q^{35} +(-94.1364 + 118.043i) q^{36} +(18.8099 - 82.4114i) q^{37} +(185.834 - 233.029i) q^{38} +(-89.1416 + 42.9283i) q^{39} +(-37.0274 - 46.4309i) q^{40} +(-55.7401 - 26.8430i) q^{41} +(-253.836 - 11.4644i) q^{42} +(-148.440 + 71.4850i) q^{43} +(461.668 + 222.328i) q^{44} +(-37.9890 - 166.441i) q^{45} +(627.339 + 302.110i) q^{46} +(337.800 - 423.588i) q^{47} +169.277 q^{48} +(188.812 + 286.355i) q^{49} -55.2092 q^{50} +(91.9592 - 115.313i) q^{51} +(253.000 + 121.839i) q^{52} +(-108.336 - 474.652i) q^{53} +(-533.384 - 256.864i) q^{54} +(-522.022 + 251.392i) q^{55} +(61.1355 + 84.1907i) q^{56} +(212.367 + 102.270i) q^{57} +(48.8612 + 61.2700i) q^{58} +(203.178 - 97.8454i) q^{59} +(202.962 - 254.506i) q^{60} +(103.297 - 452.575i) q^{61} +(-296.946 + 372.358i) q^{62} +(53.3320 + 294.309i) q^{63} +(-416.265 - 521.980i) q^{64} +(-286.075 + 137.766i) q^{65} +(-167.334 + 733.139i) q^{66} -133.966 q^{67} -418.607 q^{68} +(-122.530 + 536.840i) q^{69} +(-814.617 - 36.7919i) q^{70} +(156.479 + 685.578i) q^{71} +(20.1894 + 88.4555i) q^{72} +(704.577 + 883.512i) q^{73} +(-219.522 - 275.272i) q^{74} +(-9.71544 - 42.5661i) q^{75} +(-148.864 - 652.214i) q^{76} +(933.520 - 398.725i) q^{77} +(-91.7014 + 401.770i) q^{78} -1187.92 q^{79} +543.246 q^{80} +(7.14899 - 31.3218i) q^{81} +(-232.168 + 111.806i) q^{82} +(673.830 + 844.956i) q^{83} +(-375.344 + 429.395i) q^{84} +(295.117 - 370.065i) q^{85} +(-152.703 + 669.035i) q^{86} +(-38.6406 + 48.4538i) q^{87} +(277.430 - 133.603i) q^{88} +(-881.560 - 1105.44i) q^{89} +(-640.665 - 308.528i) q^{90} +(511.582 - 218.507i) q^{91} +(1408.07 - 678.089i) q^{92} +(-339.342 - 163.418i) q^{93} +(-502.153 - 2200.08i) q^{94} +(681.532 + 328.208i) q^{95} +(531.906 - 666.989i) q^{96} -352.624 q^{97} +(1422.84 + 128.787i) q^{98} +885.192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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