LMFDB - Embedded newform 152.4.p.a.45.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(45,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("152.45");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.p (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:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.15
Character	$\chi$	$=$	152.45
Dual form			152.4.p.a.125.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95037 - 2.04843i) q^{2} +(-0.706252 + 0.407755i) q^{3} +(-0.392134 + 7.99038i) q^{4} +(-12.8180 + 7.40046i) q^{5} +(2.21271 + 0.651437i) q^{6} +26.8247 q^{7} +(17.1326 - 14.7809i) q^{8} +(-13.1675 + 22.8067i) q^{9} +(40.1591 + 11.8231i) q^{10} -49.8833i q^{11} +(-2.98117 - 5.80312i) q^{12} +(-38.4561 - 22.2026i) q^{13} +(-52.3180 - 54.9485i) q^{14} +(6.03515 - 10.4532i) q^{15} +(-63.6925 - 6.26661i) q^{16} +(-17.0158 - 29.4722i) q^{17} +(72.3994 - 17.5089i) q^{18} +(-47.2126 + 68.0439i) q^{19} +(-54.1062 - 105.323i) q^{20} +(-18.9450 + 10.9379i) q^{21} +(-102.182 + 97.2908i) q^{22} +(92.5634 - 160.324i) q^{23} +(-6.07291 + 17.4249i) q^{24} +(47.0337 - 81.4647i) q^{25} +(29.5229 + 122.078i) q^{26} -43.4952i q^{27} +(-10.5189 + 214.339i) q^{28} +(-18.4731 - 10.6654i) q^{29} +(-33.1834 + 8.02497i) q^{30} -336.831 q^{31} +(111.387 + 142.692i) q^{32} +(20.3402 + 35.2302i) q^{33} +(-27.1847 + 92.3372i) q^{34} +(-343.838 + 198.515i) q^{35} +(-177.071 - 114.156i) q^{36} -330.438i q^{37} +(231.465 - 35.9987i) q^{38} +36.2129 q^{39} +(-110.219 + 316.250i) q^{40} +(-86.7691 - 150.289i) q^{41} +(59.3552 + 17.4746i) q^{42} +(-84.5716 + 48.8274i) q^{43} +(398.587 + 19.5610i) q^{44} -389.782i q^{45} +(-508.946 + 123.082i) q^{46} +(156.165 - 270.486i) q^{47} +(47.5382 - 21.5451i) q^{48} +376.563 q^{49} +(-258.608 + 62.5409i) q^{50} +(24.0348 + 13.8765i) q^{51} +(192.487 - 298.572i) q^{52} +(-503.418 - 290.649i) q^{53} +(-89.0968 + 84.8315i) q^{54} +(369.159 + 639.403i) q^{55} +(459.575 - 396.493i) q^{56} +(5.59880 - 67.3073i) q^{57} +(14.1819 + 58.6424i) q^{58} +(172.474 - 99.5777i) q^{59} +(81.1584 + 52.3222i) q^{60} +(661.860 + 382.125i) q^{61} +(656.945 + 689.975i) q^{62} +(-353.213 + 611.783i) q^{63} +(75.0486 - 506.470i) q^{64} +657.239 q^{65} +(32.4958 - 110.377i) q^{66} +(135.307 + 78.1194i) q^{67} +(242.166 - 124.405i) q^{68} +150.973i q^{69} +(1077.25 + 317.151i) q^{70} +(-234.750 - 406.599i) q^{71} +(111.512 + 585.365i) q^{72} +(138.974 + 240.709i) q^{73} +(-676.880 + 644.476i) q^{74} +76.7128i q^{75} +(-525.183 - 403.929i) q^{76} -1338.10i q^{77} +(-70.6285 - 74.1796i) q^{78} +(-115.717 - 200.427i) q^{79} +(862.784 - 391.028i) q^{80} +(-337.786 - 585.063i) q^{81} +(-138.624 + 470.858i) q^{82} +273.136i q^{83} +(-79.9690 - 155.667i) q^{84} +(436.215 + 251.849i) q^{85} +(264.965 + 78.0076i) q^{86} +17.3955 q^{87} +(-737.321 - 854.628i) q^{88} +(-667.690 + 1156.47i) q^{89} +(-798.440 + 760.217i) q^{90} +(-1031.57 - 595.578i) q^{91} +(1244.76 + 802.486i) q^{92} +(237.888 - 137.345i) q^{93} +(-858.651 + 207.654i) q^{94} +(101.614 - 1221.58i) q^{95} +(-136.851 - 55.3578i) q^{96} +(222.145 + 384.767i) q^{97} +(-734.437 - 771.363i) q^{98} +(1137.67 + 656.837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) $ 116 * q - q^2 - 7 * q^4 - 11 * q^6 - 8 * q^7 - 46 * q^8 + 484 * q^9 - 44 * q^10 - 58 * q^12 + 24 * q^14 - 230 * q^15 - 67 * q^16 - 2 * q^17 + 196 * q^18 - 840 * q^20 + 137 * q^22 - 2 * q^23 + 77 * q^24 + 1248 * q^25 + 492 * q^26 - 96 * q^28 - 904 * q^30 + 208 * q^31 - 431 * q^32 - 180 * q^33 + 224 * q^34 - 84 * q^36 + 1552 * q^38 - 116 * q^39 - 58 * q^40 - 22 * q^41 - 568 * q^42 - 89 * q^44 - 1852 * q^46 + 202 * q^47 - 89 * q^48 + 5220 * q^49 - 942 * q^50 + 232 * q^52 - 231 * q^54 + 248 * q^55 - 2296 * q^56 - 398 * q^57 - 3620 * q^58 - 1378 * q^60 + 614 * q^62 - 796 * q^63 + 1550 * q^64 - 508 * q^65 - 797 * q^66 + 1860 * q^68 - 2968 * q^70 + 1986 * q^71 - 1596 * q^72 - 218 * q^73 + 2490 * q^74 - 4697 * q^76 + 1254 * q^78 + 1250 * q^79 + 3136 * q^80 - 3810 * q^81 - 169 * q^82 + 4136 * q^84 - 2360 * q^86 - 1404 * q^87 + 4434 * q^88 - 2 * q^89 + 1378 * q^90 - 1958 * q^92 - 4608 * q^94 + 438 * q^95 + 3410 * q^96 - 1586 * q^97 + 55 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.95037	−	2.04843i	−0.689559	−	0.724230i
$2$	−1.95037	−	2.04843i	−0.689559	−	0.724230i
$3$	−0.706252	+	0.407755i	−0.135918	+	0.0784725i	−0.566417	−	0.824119i	$-0.691671\pi$
$3$	−0.706252	+	0.407755i	−0.135918	+	0.0784725i	0.430499	+	0.902591i	$0.358338\pi$
$4$	−0.392134	+	7.99038i	−0.0490168	+	0.998798i
$5$	−12.8180	+	7.40046i	−1.14647	+	0.661917i	−0.948026	−	0.318194i	$-0.896924\pi$
$5$	−12.8180	+	7.40046i	−1.14647	+	0.661917i	−0.198449	+	0.980111i	$0.563590\pi$
$6$	2.21271	+	0.651437i	0.150556	+	0.0443246i
$7$	26.8247			1.44840			0.724198	−	0.689592i	$-0.242210\pi$
$7$	26.8247			1.44840			0.724198	+	0.689592i	$0.242210\pi$
$8$	17.1326	−	14.7809i	0.757159	−	0.653231i
$9$	−13.1675	+	22.8067i	−0.487684	+	0.844694i
$10$	40.1591	+	11.8231i	1.26994	+	0.373880i
$11$		−	49.8833i		−	1.36731i	−0.729807	−	0.683654i	$-0.760390\pi$
$11$		−	49.8833i		−	1.36731i	0.729807	−	0.683654i	$-0.239610\pi$
$12$	−2.98117	−	5.80312i	−0.0717158	−	0.139601i
$13$	−38.4561	−	22.2026i	−0.820446	−	0.473685i	0.0301244	−	0.999546i	$-0.490410\pi$
$13$	−38.4561	−	22.2026i	−0.820446	−	0.473685i	−0.850570	+	0.525862i	$0.823743\pi$
$14$	−52.3180	−	54.9485i	−0.998755	−	1.04897i
$15$	6.03515	−	10.4532i	0.103885	−	0.179933i
$16$	−63.6925	−	6.26661i	−0.995195	−	0.0979157i
$17$	−17.0158	−	29.4722i	−0.242761	−	0.420474i	0.718739	−	0.695280i	$-0.244720\pi$
$17$	−17.0158	−	29.4722i	−0.242761	−	0.420474i	−0.961500	+	0.274806i	$0.911386\pi$
$18$	72.3994	−	17.5089i	0.948039	−	0.229271i
$19$	−47.2126	+	68.0439i	−0.570069	+	0.821596i
$19$	−47.2126	+	68.0439i	−0.570069	+	0.821596i
$20$	−54.1062	−	105.323i	−0.604925	−	1.17754i
$21$	−18.9450	+	10.9379i	−0.196864	+	0.113659i
$22$	−102.182	+	97.2908i	−0.990244	+	0.942839i
$23$	92.5634	−	160.324i	0.839165	−	1.45348i	−0.0514285	−	0.998677i	$-0.516377\pi$
$23$	92.5634	−	160.324i	0.839165	−	1.45348i	0.890594	−	0.454800i	$-0.150289\pi$
$24$	−6.07291	+	17.4249i	−0.0516511	+	0.148202i
$25$	47.0337	−	81.4647i	0.376269	−	0.651718i
$26$	29.5229	+	122.078i	0.222689	+	0.920824i
$27$		−	43.4952i		−	0.310024i
$28$	−10.5189	+	214.339i	−0.0709957	+	1.44666i
$29$	−18.4731	−	10.6654i	−0.118289	−	0.0682939i	0.439688	−	0.898150i	$-0.355089\pi$
$29$	−18.4731	−	10.6654i	−0.118289	−	0.0682939i	−0.557977	+	0.829856i	$0.688422\pi$
$30$	−33.1834	+	8.02497i	−0.201948	+	0.0488384i
$31$	−336.831			−1.95151			−0.975753	−	0.218876i	$-0.929761\pi$
$31$	−336.831			−1.95151			−0.975753	+	0.218876i	$0.929761\pi$
$32$	111.387	+	142.692i	0.615332	+	0.788268i
$33$	20.3402	+	35.2302i	0.107296	+	0.185842i
$34$	−27.1847	+	92.3372i	−0.137122	+	0.465756i
$35$	−343.838	+	198.515i	−1.66055	+	0.958719i
$36$	−177.071	−	114.156i	−0.819774	−	0.528502i
$37$		−	330.438i		−	1.46821i	−0.679036	−	0.734105i	$-0.737602\pi$
$37$		−	330.438i		−	1.46821i	0.679036	−	0.734105i	$-0.262398\pi$
$38$	231.465	−	35.9987i	0.988121	−	0.153678i
$39$	36.2129			0.148685
$40$	−110.219	+	316.250i	−0.435679	+	1.25009i
$41$	−86.7691	−	150.289i	−0.330514	−	0.572467i	0.652099	−	0.758134i	$-0.273889\pi$
$41$	−86.7691	−	150.289i	−0.330514	−	0.572467i	−0.982613	+	0.185667i	$0.940555\pi$
$42$	59.3552	+	17.4746i	0.218064	+	0.0641996i
$43$	−84.5716	+	48.8274i	−0.299931	+	0.173165i	−0.642412	−	0.766359i	$-0.722066\pi$
$43$	−84.5716	+	48.8274i	−0.299931	+	0.173165i	0.342481	+	0.939525i	$0.388733\pi$
$44$	398.587	+	19.5610i	1.36566	+	0.0670210i
$45$		−	389.782i		−	1.29123i
$46$	−508.946	+	123.082i	−1.63130	+	0.394510i
$47$	156.165	−	270.486i	0.484660	−	0.839456i	−0.515184	−	0.857079i	$-0.672277\pi$
$47$	156.165	−	270.486i	0.484660	−	0.839456i	0.999845	+	0.0176230i	$0.00560988\pi$
$48$	47.5382	−	21.5451i	0.142949	−	0.0647868i
$49$	376.563			1.09785
$50$	−258.608	+	62.5409i	−0.731453	+	0.176892i
$51$	24.0348	+	13.8765i	0.0659912	+	0.0381000i
$52$	192.487	−	298.572i	0.513331	−	0.796241i
$53$	−503.418	−	290.649i	−1.30471	−	0.753277i	−0.323505	−	0.946226i	$-0.604861\pi$
$53$	−503.418	−	290.649i	−1.30471	−	0.753277i	−0.981209	+	0.192950i	$0.938195\pi$
$54$	−89.0968	+	84.8315i	−0.224529	+	0.213780i
$55$	369.159	+	639.403i	0.905045	+	1.56758i
$56$	459.575	−	396.493i	1.09667	−	0.946137i
$57$	5.59880	−	67.3073i	0.0130102	−	0.156405i
$58$	14.1819	+	58.6424i	0.0321064	+	0.132761i
$59$	172.474	−	99.5777i	0.380579	−	0.219727i	−0.297491	−	0.954725i	$-0.596150\pi$
$59$	172.474	−	99.5777i	0.380579	−	0.219727i	0.678070	+	0.734997i	$0.262817\pi$
$60$	81.1584	+	52.3222i	0.174625	+	0.112579i
$61$	661.860	+	382.125i	1.38922	+	0.802067i	0.993227	−	0.116187i	$-0.0370671\pi$
$61$	661.860	+	382.125i	1.38922	+	0.802067i	0.395993	+	0.918254i	$0.370400\pi$
$62$	656.945	+	689.975i	1.34568	+	1.41334i
$63$	−353.213	+	611.783i	−0.706360	+	1.22345i
$64$	75.0486	−	506.470i	0.146579	−	0.989199i
$65$	657.239			1.25416
$66$	32.4958	−	110.377i	0.0606054	−	0.205856i
$67$	135.307	+	78.1194i	0.246722	+	0.142445i	0.618262	−	0.785972i	$-0.287837\pi$
$67$	135.307	+	78.1194i	0.246722	+	0.142445i	−0.371540	+	0.928417i	$0.621170\pi$
$68$	242.166	−	124.405i	0.431868	−	0.221859i
$69$			150.973i			0.263405i
$70$	1077.25	+	317.151i	1.83938	+	0.541526i
$71$	−234.750	−	406.599i	−0.392391	−	0.679640i	0.600374	−	0.799720i	$-0.295019\pi$
$71$	−234.750	−	406.599i	−0.392391	−	0.679640i	−0.992764	+	0.120079i	$0.961685\pi$
$72$	111.512	+	585.365i	0.182525	+	0.958138i
$73$	138.974	+	240.709i	0.222817	+	0.385930i	0.955662	−	0.294465i	$-0.0951415\pi$
$73$	138.974	+	240.709i	0.222817	+	0.385930i	−0.732845	+	0.680395i	$0.761808\pi$
$74$	−676.880	+	644.476i	−1.06332	+	1.01242i
$75$			76.7128i			0.118107i
$76$	−525.183	−	403.929i	−0.792666	−	0.609656i
$77$		−	1338.10i		−	1.98040i
$78$	−70.6285	−	74.1796i	−0.102527	−	0.107682i
$79$	−115.717	−	200.427i	−0.164799	−	0.285441i	0.771785	−	0.635884i	$-0.219364\pi$
$79$	−115.717	−	200.427i	−0.164799	−	0.285441i	−0.936584	+	0.350443i	$0.886031\pi$
$80$	862.784	−	391.028i	1.20578	−	0.546479i
$81$	−337.786	−	585.063i	−0.463356	−	0.802556i
$82$	−138.624	+	470.858i	−0.186688	+	0.634117i
$83$			273.136i			0.361212i	0.983556	+	0.180606i	$0.0578059\pi$
$83$			273.136i			0.361212i	−0.983556	+	0.180606i	$0.942194\pi$
$84$	−79.9690	−	155.667i	−0.103873	−	0.202198i
$85$	436.215	+	251.849i	0.556638	+	0.321375i
$86$	264.965	+	78.0076i	0.332232	+	0.0978114i
$87$	17.3955			0.0214368
$88$	−737.321	−	854.628i	−0.893167	−	1.03527i
$89$	−667.690	+	1156.47i	−0.795225	+	1.37737i	0.127472	+	0.991842i	$0.459314\pi$
$89$	−667.690	+	1156.47i	−0.795225	+	1.37737i	−0.922696	+	0.385527i	$0.874020\pi$
$90$	−798.440	+	760.217i	−0.935144	+	0.890377i
$91$	−1031.57	−	595.578i	−1.18833	−	0.686083i
$92$	1244.76	+	802.486i	1.41060	+	0.909401i
$93$	237.888	−	137.345i	0.265245	−	0.153139i
$94$	−858.651	+	207.654i	−0.942161	+	0.227849i
$95$	101.614	−	1221.58i	0.109741	−	1.31928i
$96$	−136.851	−	55.3578i	−0.145492	−	0.0588534i
$97$	222.145	+	384.767i	0.232530	+	0.402754i	0.958552	−	0.284917i	$-0.0919662\pi$
$97$	222.145	+	384.767i	0.232530	+	0.402754i	−0.726022	+	0.687672i	$0.758633\pi$
$98$	−734.437	−	771.363i	−0.757034	−	0.795097i
$99$	1137.67	+	656.837i	1.15496	+	0.666814i
$100$	632.491	+	407.762i	0.632491	+	0.407762i
$101$	−892.297	−	515.168i	−0.879078	−	0.507536i	−0.00872382	−	0.999962i	$-0.502777\pi$
$101$	−892.297	−	515.168i	−0.879078	−	0.507536i	−0.870354	+	0.492426i	$0.836110\pi$
$102$	−18.4517	−	76.2980i	−0.0179117	−	0.0740650i
$103$	385.091			0.368390			0.184195	−	0.982890i	$-0.441032\pi$
$103$	385.091			0.368390			0.184195	+	0.982890i	$0.441032\pi$
$104$	−987.026	+	188.029i	−0.930633	+	0.177286i
$105$	161.891	−	280.403i	0.150466	−	0.260615i
$106$	386.477	+	1598.09i	0.354132	+	1.46434i
$107$			1502.54i			1.35753i	0.734354	+	0.678767i	$0.237485\pi$
$107$			1502.54i			1.35753i	−0.734354	+	0.678767i	$0.762515\pi$
$108$	347.543	+	17.0559i	0.309651	+	0.0151964i
$109$	647.980	−	374.111i	0.569406	−	0.328746i	−0.187506	−	0.982263i	$-0.560041\pi$
$109$	647.980	−	374.111i	0.569406	−	0.328746i	0.756912	+	0.653517i	$0.226707\pi$
$110$	589.776	−	2003.27i	0.511208	−	1.73640i
$111$	134.738	+	233.373i	0.115214	+	0.199556i
$112$	−1708.53	−	168.100i	−1.44144	−	0.141821i
$113$	−305.728			−0.254517			−0.127259	−	0.991870i	$-0.540618\pi$
$113$	−305.728			−0.254517			−0.127259	+	0.991870i	$0.540618\pi$
$114$	−148.794	+	119.805i	−0.122244	+	0.0984279i
$115$			2740.05i			2.22183i
$116$	92.4649	−	143.425i	0.0740099	−	0.114799i
$117$	1012.74	−	584.705i	0.800237	−	0.462017i
$118$	−540.365	−	159.087i	−0.421565	−	0.124111i
$119$	−456.443	−	790.582i	−0.351614	−	0.609013i
$120$	−51.1102	−	268.295i	−0.0388809	−	0.204099i
$121$	−1157.34			−0.869529
$122$	−508.113	−	2101.06i	−0.377069	−	1.55919i
$123$	122.562	+	70.7611i	0.0898457	+	0.0518724i
$124$	132.083	−	2691.41i	0.0956565	−	1.94916i
$125$		−	457.832i		−	0.327598i
$126$	1942.09	−	469.669i	1.37314	−	0.332075i
$127$	−288.254	+	499.271i	−0.201405	+	0.348843i	−0.948981	−	0.315332i	$-0.897884\pi$
$127$	−288.254	+	499.271i	−0.201405	+	0.348843i	0.747576	+	0.664176i	$0.231217\pi$
$128$	−1183.84	+	834.070i	−0.817482	+	0.575954i
$129$	39.8193	−	68.9690i	0.0271774	−	0.0470727i
$130$	−1281.86	−	1346.31i	−0.864817	−	0.908300i
$131$	−2249.35	+	1298.67i	−1.50021	+	0.866144i	−0.500206	+	0.865907i	$0.666742\pi$
$131$	−2249.35	+	1298.67i	−1.50021	+	0.866144i	−1.00000		0.000237637i	$0.999924\pi$
$132$	−289.479	+	148.711i	−0.190878	+	0.0980576i
$133$	−1266.46	+	1825.25i	−0.825687	+	1.19000i
$134$	−103.876	−	429.528i	−0.0669664	−	0.276907i
$135$	321.884	+	557.520i	0.205210	+	0.355435i
$136$	−727.150	−	253.425i	−0.458475	−	0.159787i
$137$	−824.045	+	1427.29i	−0.513890	+	0.890084i	0.485980	+	0.873970i	$0.338463\pi$
$137$	−824.045	+	1427.29i	−0.513890	+	0.890084i	−0.999870	+	0.0161138i	$0.994871\pi$
$138$	309.257	−	294.452i	0.190766	−	0.181634i
$139$	519.840	+	300.130i	0.317210	+	0.183142i	0.650149	−	0.759807i	$-0.274707\pi$
$139$	519.840	+	300.130i	0.317210	+	0.183142i	−0.332938	+	0.942949i	$0.608040\pi$
$140$	−1451.38	−	2825.24i	−0.876172	−	1.70555i
$141$			254.708i			0.152130i
$142$	−375.041	+	1273.89i	−0.221639	+	0.752833i
$143$	−1107.54	+	1918.32i	−0.647672	+	1.12180i
$144$	981.590	−	1370.10i	0.568049	−	0.792883i
$145$	315.717			0.180820
$146$	222.027	−	754.149i	0.125857	−	0.427492i
$147$	−265.949	+	153.545i	−0.149218	+	0.0861511i
$148$	2640.33	+	129.576i	1.46644	+	0.0719669i
$149$	1743.53	−	1006.62i	0.958625	−	0.553462i	0.0628755	−	0.998021i	$-0.479973\pi$
$149$	1743.53	−	1006.62i	0.958625	−	0.553462i	0.895750	+	0.444559i	$0.146640\pi$
$150$	157.141	−	149.618i	0.0855367	−	0.0814418i
$151$	−2131.55			−1.14876			−0.574380	−	0.818589i	$-0.694757\pi$
$151$	−2131.55			−1.14876			−0.574380	+	0.818589i	$0.694757\pi$
$152$	196.878	+	1863.61i	0.105059	+	0.994466i
$153$	896.219			0.473562
$154$	−2741.01	+	2609.79i	−1.43427	+	1.36560i
$155$	4317.49	−	2492.71i	2.23735	−	1.29174i
$156$	−14.2003	+	289.355i	−0.00728805	+	0.148506i
$157$	−346.742	+	200.192i	−0.176261	+	0.101765i	−0.585535	−	0.810647i	$-0.699116\pi$
$157$	−346.742	+	200.192i	−0.176261	+	0.101765i	0.409274	+	0.912412i	$0.365782\pi$
$158$	−184.871	+	627.944i	−0.0930858	+	0.316181i
$159$	474.054			0.236446
$160$	−2483.74	−	1004.70i	−1.22723	−	0.496430i
$161$	2482.98	−	4300.65i	1.21544	−	2.10521i
$162$	−539.654	+	1833.02i	−0.261723	+	0.888986i
$163$			242.009i			0.116292i	0.998308	+	0.0581461i	$0.0185189\pi$
$163$			242.009i			0.116292i	−0.998308	+	0.0581461i	$0.981481\pi$
$164$	1234.89	−	634.385i	0.587979	−	0.302056i
$165$	−521.439	−	301.053i	−0.246024	−	0.142042i
$166$	559.500	−	532.716i	0.261600	−	0.249077i
$167$	487.319	−	844.061i	0.225808	−	0.391110i	−0.730754	−	0.682641i	$-0.760831\pi$
$167$	487.319	−	844.061i	0.225808	−	0.391110i	0.956561	+	0.291531i	$0.0941646\pi$
$168$	−162.904	+	467.418i	−0.0748113	+	0.214655i
$169$	−112.587	−	195.007i	−0.0512459	−	0.0887605i
$170$	−334.885	−	1384.76i	−0.151085	−	0.624741i
$171$	−930.187	−	1972.73i	−0.415984	−	0.882214i
$172$	−356.987	−	694.907i	−0.158256	−	0.308059i
$173$	−1282.26	+	740.312i	−0.563516	+	0.325346i	−0.754556	−	0.656236i	$-0.772147\pi$
$173$	−1282.26	+	740.312i	−0.563516	+	0.325346i	0.191039	+	0.981582i	$0.438814\pi$
$174$	−33.9277	−	35.6336i	−0.0147819	−	0.0155251i
$175$	1261.66	−	2185.26i	0.544987	−	0.943946i
$176$	−312.599	+	3177.19i	−0.133881	+	1.36074i
$177$	−81.2066	+	140.654i	−0.0344851	+	0.0597299i
$178$	3671.20	−	887.831i	1.54589	−	0.373852i
$179$		−	1304.74i		−	0.544810i	−0.962183	−	0.272405i	$-0.912181\pi$
$179$		−	1304.74i		−	0.544810i	0.962183	−	0.272405i	$-0.0878190\pi$
$180$	3114.50	+	152.847i	1.28967	+	0.0632918i
$181$	2278.68	+	1315.59i	0.935761	+	0.540262i	0.888629	−	0.458627i	$-0.151659\pi$
$181$	2278.68	+	1315.59i	0.935761	+	0.540262i	0.0471318	+	0.998889i	$0.484992\pi$
$182$	791.943	+	3274.70i	0.322542	+	1.33372i
$183$	−623.253			−0.251761
$184$	−783.897	−	4114.94i	−0.314074	−	1.64868i
$185$	2445.40	+	4235.55i	0.971833	+	1.68326i
$186$	−745.309	−	219.424i	−0.293810	−	0.0864998i
$187$	−1470.17	+	848.803i	−0.574917	+	0.331928i
$188$	2100.05	+	1353.89i	0.814691	+	0.525225i
$189$		−	1166.74i		−	0.449038i
$190$	−2700.51	+	2174.38i	−1.03113	+	0.830243i
$191$	−621.184			−0.235326			−0.117663	−	0.993054i	$-0.537540\pi$
$191$	−621.184			−0.235326			−0.117663	+	0.993054i	$0.537540\pi$
$192$	153.512	+	388.297i	0.0577021	+	0.145953i
$193$	−2475.00	−	4286.83i	−0.923080	−	1.59882i	−0.794620	−	0.607107i	$-0.792330\pi$
$193$	−2475.00	−	4286.83i	−0.923080	−	1.59882i	−0.128460	−	0.991715i	$-0.541004\pi$
$194$	354.903	−	1205.49i	0.131343	−	0.446128i
$195$	−464.176	+	267.992i	−0.170463	+	0.0984170i
$196$	−147.663	+	3008.88i	−0.0538132	+	1.09653i
$197$			4451.74i			1.61002i	0.593263	+	0.805009i	$0.297840\pi$
$197$			4451.74i			1.61002i	−0.593263	+	0.805009i	$0.702160\pi$
$198$	−873.399	−	3611.52i	−0.313484	−	1.29626i
$199$	−1942.08	+	3363.78i	−0.691812	+	1.19825i	0.279432	+	0.960165i	$0.409854\pi$
$199$	−1942.08	+	3363.78i	−0.691812	+	1.19825i	−0.971244	+	0.238087i	$0.923480\pi$
$200$	−398.317	−	2090.90i	−0.140826	−	0.739245i
$201$	−127.414			−0.0447120
$202$	685.022	+	2832.58i	0.238604	+	0.986630i
$203$	−495.535	−	286.097i	−0.171329	−	0.0989166i
$204$	−120.304	+	186.606i	−0.0412889	+	0.0640443i
$205$	2224.41	+	1284.26i	0.757851	+	0.437546i
$206$	−751.070	−	788.833i	−0.254027	−	0.266799i
$207$	2437.65	+	4222.14i	0.818495	+	1.41768i
$208$	2310.23	+	1655.13i	0.770122	+	0.551743i
$209$	3394.25	+	2355.12i	1.12337	+	0.779460i
$210$	−890.133	+	215.267i	−0.292500	+	0.0707373i
$211$	2481.68	−	1432.80i	0.809696	−	0.467478i	−0.0371540	−	0.999310i	$-0.511829\pi$
$211$	2481.68	−	1432.80i	0.809696	−	0.467478i	0.846850	+	0.531831i	$0.178496\pi$
$212$	2519.80	−	3908.53i	0.816324	−	1.26622i
$213$	331.586	+	191.441i	0.106666	+	0.0615837i
$214$	3077.85	−	2930.51i	0.983166	−	0.936100i
$215$	722.691	−	1251.74i	0.229242	−	0.397060i
$216$	−642.899	−	745.183i	−0.202517	−	0.234737i
$217$	−9035.39			−2.82655
$218$	−2030.14	−	597.687i	−0.630727	−	0.185690i
$219$	−196.301	−	113.334i	−0.0605698	−	0.0349700i
$220$	−5253.83	+	2698.99i	−1.61006	+	0.827119i
$221$			1511.18i			0.459968i
$222$	215.260	−	731.164i	0.0650778	−	0.221047i
$223$	−813.524	−	1409.06i	−0.244294	−	0.423130i	0.717639	−	0.696416i	$-0.245223\pi$
$223$	−813.524	−	1409.06i	−0.244294	−	0.423130i	−0.961933	+	0.273286i	$0.911890\pi$
$224$	2987.92	+	3827.66i	0.891245	+	1.14172i
$225$	1238.63	+	2145.37i	0.367001	+	0.635665i
$226$	596.282	+	626.262i	0.175505	+	0.184329i
$227$		−	4840.48i		−	1.41530i	−0.706561	−	0.707652i	$-0.749754\pi$
$227$		−	4840.48i		−	1.41530i	0.706561	−	0.707652i	$-0.250246\pi$
$228$	535.616	+	71.1301i	0.155579	+	0.0206610i
$229$		−	5337.23i		−	1.54015i	−0.637954	−	0.770075i	$-0.720219\pi$
$229$		−	5337.23i		−	1.54015i	0.637954	−	0.770075i	$-0.279781\pi$
$230$	5612.80	−	5344.10i	1.60912	−	1.53208i
$231$	545.618	+	945.038i	0.155407	+	0.269173i
$232$	−474.136	+	90.3231i	−0.134175	+	0.0255603i
$233$	−793.666	−	1374.67i	−0.223153	−	0.386513i	0.732610	−	0.680648i	$-0.238302\pi$
$233$	−793.666	−	1374.67i	−0.223153	−	0.386513i	−0.955764	+	0.294135i	$0.904968\pi$
$234$	−3172.94	−	934.135i	−0.886417	−	0.260967i
$235$			4622.78i			1.28322i
$236$	728.031	+	1417.18i	0.200808	+	0.390892i
$237$	163.450	+	94.3681i	0.0447985	+	0.0258644i
$238$	−729.221	+	2476.92i	−0.198607	+	0.674599i
$239$	3527.03			0.954579			0.477290	−	0.878746i	$-0.341619\pi$
$239$	3527.03			0.954579			0.477290	+	0.878746i	$0.341619\pi$
$240$	−449.899	+	627.969i	−0.121004	+	0.168897i
$241$	−1378.06	+	2386.87i	−0.368335	+	0.637975i	−0.989305	−	0.145859i	$-0.953405\pi$
$241$	−1378.06	+	2386.87i	−0.368335	+	0.637975i	0.620971	+	0.783834i	$0.286739\pi$
$242$	2257.24	+	2370.74i	0.599592	+	0.629739i
$243$	1494.16	+	862.653i	0.394446	+	0.227733i
$244$	−3312.86	+	5138.67i	−0.869198	+	1.34824i
$245$	−4826.78	+	2786.74i	−1.25866	+	0.726687i
$246$	−94.0914	−	389.069i	−0.0243864	−	0.100838i
$247$	3326.36	−	1568.46i	0.856889	−	0.404042i
$248$	−5770.78	+	4978.68i	−1.47760	+	1.27478i
$249$	−111.373	−	192.903i	−0.0283452	−	0.0490953i
$250$	−937.837	+	892.940i	−0.237256	+	0.225898i
$251$	−642.083	−	370.707i	−0.161466	−	0.0932224i	0.417090	−	0.908865i	$-0.363050\pi$
$251$	−642.083	−	370.707i	−0.161466	−	0.0932224i	−0.578556	+	0.815643i	$0.696383\pi$
$252$	−4749.87	−	3062.21i	−1.18736	−	0.765480i
$253$	−7997.51	−	4617.37i	−1.98735	−	1.14740i
$254$	1584.92	−	383.293i	0.391523	−	0.0946848i
$255$	−410.771			−0.100876
$256$	4017.46	+	798.271i	0.980825	+	0.194890i
$257$	−402.191	+	696.615i	−0.0976186	+	0.169080i	−0.910698	−	0.413072i	$-0.864456\pi$
$257$	−402.191	+	696.615i	−0.0976186	+	0.169080i	0.813080	+	0.582152i	$0.197789\pi$
$258$	−218.940	+	52.9479i	−0.0528319	+	0.0127767i
$259$		−	8863.90i		−	2.12655i
$260$	−257.726	+	5251.59i	−0.0614749	+	1.25265i
$261$	486.488	−	280.874i	0.115375	−	0.0666117i
$262$	7047.29	+	2074.77i	1.66177	+	0.489236i
$263$	−1572.55	−	2723.74i	−0.368699	−	0.638606i	0.620663	−	0.784077i	$-0.286863\pi$
$263$	−1572.55	−	2723.74i	−0.368699	−	0.638606i	−0.989362	+	0.145472i	$0.953530\pi$
$264$	869.213	+	302.937i	0.202638	+	0.0706230i
$265$	8603.74			1.99443
$266$	6208.98	−	965.655i	1.43119	−	0.222587i
$267$		−	1089.02i		−	0.249613i
$268$	−677.263	+	1050.52i	−0.154367	+	0.239443i
$269$	1182.47	−	682.699i	0.268017	−	0.154739i	−0.359969	−	0.932964i	$-0.617213\pi$
$269$	1182.47	−	682.699i	0.268017	−	0.154739i	0.627986	+	0.778225i	$0.283880\pi$
$270$	514.248	−	1746.73i	0.115912	−	0.393713i
$271$	475.560	+	823.693i	0.106598	+	0.184634i	0.914390	−	0.404834i	$-0.132671\pi$
$271$	475.560	+	823.693i	0.106598	+	0.184634i	−0.807792	+	0.589468i	$0.799337\pi$
$272$	899.086	+	1983.79i	0.200423	+	0.442223i
$273$	971.399			0.215354
$274$	4530.89	−	1095.74i	0.998982	−	0.241591i
$275$	−4063.73	−	2346.19i	−0.891098	−	0.514476i
$276$	−1206.33	−	59.2016i	−0.263089	−	0.0129113i
$277$			6409.36i			1.39026i	0.718886	+	0.695128i	$0.244652\pi$
$277$			6409.36i			1.39026i	−0.718886	+	0.695128i	$0.755348\pi$
$278$	−399.084	−	1650.22i	−0.0860988	−	0.356020i
$279$	4435.22	−	7682.02i	0.951718	−	1.64842i
$280$	−2956.59	+	8483.31i	−0.631035	+	1.81062i
$281$	1207.33	−	2091.16i	0.256311	−	0.443944i	−0.708940	−	0.705269i	$-0.750826\pi$
$281$	1207.33	−	2091.16i	0.256311	−	0.443944i	0.965251	+	0.261325i	$0.0841595\pi$
$282$	521.753	−	496.775i	0.110177	−	0.104903i
$283$	2595.56	−	1498.55i	0.545195	−	0.314768i	−0.201987	−	0.979388i	$-0.564740\pi$
$283$	2595.56	−	1498.55i	0.545195	−	0.314768i	0.747182	+	0.664620i	$0.231407\pi$
$284$	3340.94	−	1716.30i	0.698057	−	0.358605i
$285$	426.340	+	904.177i	0.0886112	+	0.187926i
$286$	6089.65	−	1472.70i	1.25905	−	0.304485i
$287$	−2327.55	−	4031.44i	−0.478715	−	0.829159i
$288$	−4721.02	+	661.483i	−0.965933	+	0.135341i
$289$	1877.43	−	3251.80i	0.382135	−	0.661876i
$290$	−615.764	−	646.724i	−0.124686	−	0.130955i
$291$	−313.781	−	181.162i	−0.0632102	−	0.0364944i
$292$	−1977.86	+	1016.06i	−0.396388	+	0.203632i
$293$		−	2533.64i		−	0.505176i	−0.967574	−	0.252588i	$-0.918718\pi$
$293$		−	2533.64i		−	0.505176i	0.967574	−	0.252588i	$-0.0812818\pi$
$294$	833.225	+	245.307i	0.165288	+	0.0486619i
$295$	−1473.84	+	2552.77i	−0.290883	+	0.503824i
$296$	−4884.18	−	5661.25i	−0.959079	−	1.11167i
$297$	−2169.68			−0.423898
$298$	−5462.51	−	1608.20i	−1.06186	−	0.312620i
$299$	−7119.25	+	4110.30i	−1.37698	+	0.794999i
$300$	−612.965	−	30.0817i	−0.117965	−	0.00578923i
$301$	−2268.61	+	1309.78i	−0.434420	+	0.250812i
$302$	4157.30	+	4366.33i	0.792138	+	0.831966i
$303$	840.249			0.159310
$304$	3433.49	−	4038.02i	0.647777	−	0.761830i
$305$	−11311.6			−2.12361
$306$	−1747.96	−	1835.84i	−0.326549	−	0.342968i
$307$	4428.87	−	2557.01i	0.823352	−	0.475363i	−0.0282189	−	0.999602i	$-0.508984\pi$
$307$	4428.87	−	2557.01i	0.823352	−	0.475363i	0.851571	+	0.524239i	$0.175650\pi$
$308$	10692.0	+	524.716i	1.97802	+	0.0970730i
$309$	−271.972	+	157.023i	−0.0500709	+	0.0289085i
$310$	−13526.8	−	3982.39i	−2.47830	−	0.729628i
$311$	2751.40			0.501664			0.250832	−	0.968031i	$-0.419296\pi$
$311$	2751.40			0.501664			0.250832	+	0.968031i	$0.419296\pi$
$312$	620.419	−	535.260i	0.112578	−	0.0971254i
$313$	−666.367	+	1154.18i	−0.120336	+	0.208429i	−0.919900	−	0.392152i	$-0.871731\pi$
$313$	−666.367	+	1154.18i	−0.120336	+	0.208429i	0.799564	+	0.600581i	$0.205064\pi$
$314$	1086.35	+	319.830i	0.195244	+	0.0574810i
$315$		−	10455.8i		−	1.87021i
$316$	1646.87	−	846.026i	0.293175	−	0.150610i
$317$	−1576.42	−	910.144i	−0.279307	−	0.161258i	0.353803	−	0.935320i	$-0.384888\pi$
$317$	−1576.42	−	910.144i	−0.279307	−	0.161258i	−0.633110	+	0.774062i	$0.718222\pi$
$318$	−924.579	−	971.066i	−0.163043	−	0.171241i
$319$	−532.028	+	921.499i	−0.0933788	+	0.161737i
$320$	2786.14	+	7047.31i	0.486719	+	1.23111i
$321$	−612.668	−	1061.17i	−0.106529	−	0.184514i
$322$	−13652.3	+	3301.63i	−2.36278	+	0.571406i
$323$	2808.76	+	233.640i	0.483850	+	0.0402480i
$324$	4807.34	−	2469.62i	0.824303	−	0.423460i
$325$	−3617.46	+	2088.54i	−0.617417	+	0.356466i
$326$	495.739	−	472.007i	0.0842222	−	0.0801903i
$327$	−305.091	+	528.434i	−0.0515951	+	0.0893653i
$328$	−3707.98	−	1292.30i	−0.624204	−	0.217546i
$329$	4189.08	−	7255.70i	0.701980	−	1.21587i
$330$	400.312	+	1655.30i	0.0667771	+	0.276124i
$331$		−	2671.13i		−	0.443560i	−0.975097	−	0.221780i	$-0.928813\pi$
$331$		−	2671.13i		−	0.443560i	0.975097	−	0.221780i	$-0.0711867\pi$
$332$	−2182.46	−	107.106i	−0.360778	−	0.0177054i
$333$	7536.22	+	4351.04i	1.24019	+	0.716022i
$334$	−2679.45	+	647.990i	−0.438961	+	0.106157i
$335$	−2312.48			−0.377147
$336$	1275.20	−	577.940i	0.207047	−	0.0938370i
$337$	1005.42	+	1741.43i	0.162518	+	0.281489i	0.935771	−	0.352608i	$-0.114705\pi$
$337$	1005.42	+	1741.43i	0.162518	+	0.281489i	−0.773253	+	0.634097i	$0.781372\pi$
$338$	−179.871	+	610.962i	−0.0289459	+	0.0983194i
$339$	215.921	−	124.662i	0.0345936	−	0.0199726i
$340$	−2183.43	+	3386.77i	−0.348273	+	0.540216i
$341$			16802.3i			2.66831i
$342$	−2226.80	+	5752.97i	−0.352080	+	0.909606i
$343$	900.322			0.141728
$344$	−727.213	+	2086.59i	−0.113979	+	0.327038i
$345$	−1117.27	−	1935.16i	−0.174353	−	0.301988i
$346$	4017.35	+	1182.74i	0.624203	+	0.183770i
$347$	−7659.26	+	4422.08i	−1.18493	+	0.684119i	−0.957150	−	0.289593i	$-0.906480\pi$
$347$	−7659.26	+	4422.08i	−1.18493	+	0.684119i	−0.227780	+	0.973713i	$0.573147\pi$
$348$	−6.82139	+	138.997i	−0.00105076	+	0.0214110i
$349$		−	3778.14i		−	0.579482i	−0.957105	−	0.289741i	$-0.906431\pi$
$349$		−	3778.14i		−	0.579482i	0.957105	−	0.289741i	$-0.0935692\pi$
$350$	−6937.07	+	1677.64i	−1.05943	+	0.256210i
$351$	−965.707	+	1672.65i	−0.146854	+	0.254358i
$352$	7117.94	−	5556.35i	1.07780	−	0.841348i
$353$	−5160.86			−0.778144			−0.389072	−	0.921207i	$-0.627204\pi$
$353$	−5160.86			−0.778144			−0.389072	+	0.921207i	$0.627204\pi$
$354$	446.502	−	107.981i	0.0670377	−	0.0162122i
$355$	6018.05	+	3474.52i	0.899732	+	0.519460i
$356$	−8978.84	−	5788.59i	−1.33673	−	0.861783i
$357$	644.727	+	372.233i	0.0955814	+	0.0551840i
$358$	−2672.67	+	2544.72i	−0.394567	+	0.375678i
$359$	5609.92	+	9716.66i	0.824735	+	1.42848i	0.902121	+	0.431482i	$0.142009\pi$
$359$	5609.92	+	9716.66i	0.824735	+	1.42848i	−0.0773860	+	0.997001i	$0.524657\pi$
$360$	−5761.33	−	6677.95i	−0.843469	−	0.977664i
$361$	−2400.94	−	6425.06i	−0.350042	−	0.936734i
$362$	−1749.35	−	7233.60i	−0.253989	−	1.05025i
$363$	817.376	−	471.912i	0.118185	−	0.0682341i
$364$	5163.41	−	8009.11i	0.743506	−	1.15327i
$365$	−3562.72	−	2056.94i	−0.510908	−	0.294973i
$366$	1215.57	+	1276.69i	0.173604	+	0.182332i
$367$	−3139.01	+	5436.93i	−0.446472	+	0.773312i	−0.998153	−	0.0607431i	$-0.980653\pi$
$367$	−3139.01	+	5436.93i	−0.446472	+	0.773312i	0.551682	+	0.834055i	$0.313986\pi$
$368$	−6900.28	+	9631.40i	−0.977451	+	1.36432i
$369$	4570.12			0.644745
$370$	3906.81	−	13270.1i	0.548933	−	1.86454i
$371$	−13504.0	−	7796.56i	−1.88974	−	1.09104i
$372$	1004.15	+	1954.67i	0.139954	+	0.272433i
$373$		−	2569.66i		−	0.356707i	−0.983966	−	0.178354i	$-0.942923\pi$
$373$		−	2569.66i		−	0.356707i	0.983966	−	0.178354i	$-0.0570771\pi$
$374$	4606.08	+	1356.06i	0.636831	+	0.187488i
$375$	186.683	+	323.345i	0.0257074	+	0.0445265i
$376$	−1322.53	−	6942.38i	−0.181394	−	0.952197i
$377$	473.602	+	820.302i	0.0646995	+	0.112063i
$378$	−2389.99	+	2275.58i	−0.325206	+	0.309638i
$379$			9208.57i			1.24805i	0.781403	+	0.624027i	$0.214505\pi$
$379$			9208.57i			1.24805i	−0.781403	+	0.624027i	$0.785495\pi$
$380$	9721.05	+	1290.96i	1.31231	+	0.174276i
$381$		−	470.148i		−	0.0632189i
$382$	1211.54	+	1272.45i	0.162271	+	0.170430i
$383$	−2079.13	−	3601.16i	−0.277385	−	0.480445i	0.693349	−	0.720602i	$-0.256135\pi$
$383$	−2079.13	−	3601.16i	−0.277385	−	0.480445i	−0.970734	+	0.240157i	$0.922801\pi$
$384$	495.994	−	1071.78i	0.0659142	−	0.142432i
$385$	9902.58	+	17151.8i	1.31086	+	2.27048i
$386$	−3954.11	+	13430.8i	−0.521396	+	1.77100i
$387$		−	2571.74i		−	0.337800i
$388$	−3161.55	+	1624.15i	−0.413668	+	0.212509i
$389$	−7534.06	−	4349.79i	−0.981985	−	0.566949i	−0.0791161	−	0.996865i	$-0.525210\pi$
$389$	−7534.06	−	4349.79i	−0.981985	−	0.566949i	−0.902869	+	0.429916i	$0.858543\pi$
$390$	1454.28	+	428.149i	0.188821	+	0.0555902i
$391$	−6300.15			−0.814865
$392$	6451.49	−	5565.95i	0.831248	−	0.717151i
$393$	1059.07	−	1834.37i	0.135937	−	0.235450i
$394$	9119.09	−	8682.53i	1.16602	−	1.11020i
$395$	2966.51	+	1712.71i	0.377876	+	0.218167i
$396$	−5694.50	+	8832.89i	−0.722625	+	1.12088i
$397$	1605.43	−	926.893i	0.202957	−	0.117177i	−0.395077	−	0.918648i	$-0.629282\pi$
$397$	1605.43	−	926.893i	0.202957	−	0.117177i	0.598034	+	0.801471i	$0.295949\pi$
$398$	10678.3	−	2582.40i	1.34486	−	0.325236i
$399$	150.186	−	1805.50i	0.0188439	−	0.226536i
$400$	−3506.20	+	4893.95i	−0.438275	+	0.611743i
$401$	182.356	+	315.849i	0.0227092	+	0.0393335i	0.877157	−	0.480204i	$-0.159437\pi$
$401$	182.356	+	315.849i	0.0227092	+	0.0393335i	−0.854447	+	0.519538i	$0.826104\pi$
$402$	248.505	+	260.999i	0.0308316	+	0.0323817i
$403$	12953.2	+	7478.54i	1.60110	+	0.924398i
$404$	4466.29	−	6927.78i	0.550016	−	0.853144i
$405$	8659.48	+	4999.55i	1.06245	+	0.613407i
$406$	380.425	+	1573.06i	0.0465029	+	0.192290i
$407$	−16483.4			−2.00749
$408$	616.886	−	117.517i	0.0748540	−	0.0142597i
$409$	2222.94	−	3850.25i	0.268746	−	0.465483i	−0.699792	−	0.714347i	$-0.746724\pi$
$409$	2222.94	−	3850.25i	0.268746	−	0.465483i	0.968538	+	0.248864i	$0.0800573\pi$
$410$	−1707.69	−	7061.33i	−0.205700	−	0.850572i
$411$		−	1344.03i		−	0.161305i
$412$	−151.008	+	3077.03i	−0.0180573	+	0.367947i
$413$	4626.55	−	2671.14i	0.551229	−	0.318252i
$414$	3894.44	−	13228.1i	0.462321	−	1.57035i
$415$	−2021.33	−	3501.05i	−0.239092	−	0.414120i
$416$	−1115.37	−	7960.45i	−0.131456	−	0.938204i
$417$	−489.517			−0.0574863
$418$	−1795.74	−	11546.2i	−0.210125	−	1.35106i
$419$		−	932.437i		−	0.108717i	−0.998521	−	0.0543586i	$-0.982689\pi$
$419$		−	932.437i		−	0.108717i	0.998521	−	0.0543586i	$-0.0173114\pi$
$420$	2177.05	+	1403.53i	0.252926	+	0.163060i
$421$	85.0950	−	49.1296i	0.00985102	−	0.00568749i	−0.495066	−	0.868855i	$-0.664856\pi$
$421$	85.0950	−	49.1296i	0.00985102	−	0.00568749i	0.504917	+	0.863168i	$0.331523\pi$
$422$	−7775.18	−	2289.07i	−0.896895	−	0.264052i
$423$	4112.60	+	7123.24i	0.472722	+	0.818779i
$424$	−12920.9	+	2461.43i	−1.47994	+	0.281929i
$425$	−3201.26			−0.365374
$426$	−254.560	−	1052.61i	−0.0289518	−	0.119716i
$427$	17754.2	+	10250.4i	2.01214	+	1.16171i
$428$	−12005.9	−	589.198i	−1.35590	−	0.0665419i
$429$		−	1806.42i		−	0.203298i
$430$	−3973.61	+	960.966i	−0.445639	+	0.107772i
$431$	3178.74	−	5505.75i	0.355255	−	0.615319i	−0.631907	−	0.775044i	$-0.717728\pi$
$431$	3178.74	−	5505.75i	0.355255	−	0.615319i	0.987161	+	0.159725i	$0.0510608\pi$
$432$	−272.567	+	2770.31i	−0.0303562	+	0.308534i
$433$	−638.237	+	1105.46i	−0.0708354	+	0.122690i	−0.899268	−	0.437399i	$-0.855900\pi$
$433$	−638.237	+	1105.46i	−0.0708354	+	0.122690i	0.828432	+	0.560089i	$0.189233\pi$
$434$	17622.3	+	18508.4i	1.94908	+	2.04707i
$435$	−222.976	+	128.735i	−0.0245767	+	0.0141894i
$436$	2735.20	+	5324.31i	0.300441	+	0.584835i
$437$	6538.94	+	13867.7i	0.715789	+	1.51804i
$438$	150.701	+	623.152i	0.0164401	+	0.0679803i
$439$	−642.504	−	1112.85i	−0.0698520	−	0.120987i	0.828984	−	0.559272i	$-0.188919\pi$
$439$	−642.504	−	1112.85i	−0.0698520	−	0.120987i	−0.898836	+	0.438285i	$0.855586\pi$
$440$	15775.6	+	5498.09i	1.70926	+	0.595707i
$441$	−4958.39	+	8588.18i	−0.535405	+	0.927349i
$442$	3095.54	−	2947.35i	0.333122	−	0.317175i
$443$	6147.35	+	3549.17i	0.659299	+	0.380646i	0.792010	−	0.610508i	$-0.209035\pi$
$443$	6147.35	+	3549.17i	0.659299	+	0.380646i	−0.132711	+	0.991155i	$0.542368\pi$
$444$	−1917.57	+	985.094i	−0.204964	+	0.105294i
$445$		−	19764.9i		−	2.10549i
$446$	−1299.70	+	4414.64i	−0.137988	+	0.468698i
$447$	−820.912	+	1421.86i	−0.0868631	+	0.150451i
$448$	2013.15	−	13585.9i	0.212305	−	1.43275i
$449$	−12286.0			−1.29134			−0.645670	−	0.763616i	$-0.723422\pi$
$449$	−12286.0			−1.29134			−0.645670	+	0.763616i	$0.723422\pi$
$450$	1978.86	−	6721.50i	0.207298	−	0.704122i
$451$	−7496.89	+	4328.33i	−0.782738	+	0.451914i
$452$	119.886	−	2442.88i	0.0124756	−	0.254211i
$453$	1505.41	−	869.148i	0.156138	−	0.0901460i
$454$	−9915.39	+	9440.72i	−1.02501	+	0.975936i
$455$	17630.2			1.81652
$456$	−898.942	−	1235.90i	−0.0923176	−	0.126922i
$457$	11604.9			1.18786			0.593931	−	0.804516i	$-0.297575\pi$
$457$	11604.9			1.18786			0.593931	+	0.804516i	$0.297575\pi$
$458$	−10932.9	+	10409.6i	−1.11542	+	1.06202i
$459$	−1281.90	+	740.104i	−0.130357	+	0.0752616i
$460$	−21894.0	−	1074.47i	−2.21916	−	0.108907i
$461$	14635.9	−	8450.01i	1.47865	−	0.853701i	0.478946	−	0.877844i	$-0.341019\pi$
$461$	14635.9	−	8450.01i	1.47865	−	0.853701i	0.999709	+	0.0241430i	$0.00768571\pi$
$462$	871.689	−	2960.83i	0.0877806	−	0.298161i
$463$	7257.41			0.728467			0.364234	−	0.931308i	$-0.381331\pi$
$463$	7257.41			0.728467			0.364234	+	0.931308i	$0.381331\pi$
$464$	1109.76	+	795.072i	0.111033	+	0.0795480i
$465$	−2032.83	+	3520.96i	−0.202731	+	0.351141i
$466$	−1267.97	+	4306.88i	−0.126047	+	0.428138i
$467$			5436.13i			0.538660i	0.963048	+	0.269330i	$0.0868023\pi$
$467$			5436.13i			0.538660i	−0.963048	+	0.269330i	$0.913198\pi$
$468$	4274.89	+	8321.45i	0.422236	+	0.821921i
$469$	3629.56	+	2095.53i	0.357351	+	0.206317i
$470$	9469.44	−	9016.12i	0.929346	−	0.884856i
$471$	163.258	−	282.772i	0.0159714	−	0.0276633i
$472$	1483.06	−	4255.34i	0.144626	−	0.414974i
$473$	2435.67	+	4218.71i	0.236770	+	0.410098i
$474$	−125.482	−	518.869i	−0.0121594	−	0.0502794i
$475$	3322.59	+	7046.52i	0.320949	+	0.680666i
$476$	6496.04	−	3337.14i	0.625516	−	0.321339i
$477$	13257.5	−	7654.22i	1.27258	−	0.734722i
$478$	−6879.00	−	7224.87i	−0.658239	−	0.691334i
$479$	−2223.51	+	3851.23i	−0.212097	+	0.367363i	−0.952371	−	0.304943i	$-0.901363\pi$
$479$	−2223.51	+	3851.23i	−0.212097	+	0.367363i	0.740273	+	0.672306i	$0.234696\pi$
$480$	2163.82	−	303.183i	0.205759	−	0.0288299i
$481$	−7336.60	+	12707.4i	−0.695468	+	1.20459i
$482$	7577.06	−	1832.41i	0.716029	−	0.173162i
$483$			4049.79i			0.381515i
$484$	453.834	−	9247.62i	0.0426215	−	0.868484i
$485$	−5694.91	−	3287.96i	−0.533180	−	0.307832i
$486$	−1147.07	−	4743.17i	−0.107062	−	0.442705i
$487$	8171.59			0.760349			0.380174	−	0.924915i	$-0.375864\pi$
$487$	8171.59			0.760349			0.380174	+	0.924915i	$0.375864\pi$
$488$	16987.5	−	3236.12i	1.57580	−	0.300189i
$489$	−98.6804	−	170.920i	−0.00912573	−	0.0158062i
$490$	15122.4	+	4452.15i	1.39421	+	0.410464i
$491$	1395.97	−	805.962i	0.128308	−	0.0740785i	−0.434472	−	0.900685i	$-0.643065\pi$
$491$	1395.97	−	805.962i	0.128308	−	0.0740785i	0.562780	+	0.826607i	$0.309732\pi$
$492$	−613.469	+	951.568i	−0.0562140	+	0.0871951i
$493$			725.923i			0.0663163i
$494$	−9700.50	−	3754.76i	−0.883495	−	0.341973i
$495$	−19443.6			−1.76550
$496$	21453.6	+	2110.79i	1.94213	+	0.191083i
$497$	−6297.10	−	10906.9i	−0.568337	−	0.984389i
$498$	−177.931	+	604.370i	−0.0160106	+	0.0543825i
$499$	−4969.02	+	2868.86i	−0.445779	+	0.257371i	−0.706046	−	0.708166i	$-0.749523\pi$
$499$	−4969.02	+	2868.86i	−0.445779	+	0.257371i	0.260267	+	0.965537i	$0.416189\pi$
$500$	3658.25	+	179.532i	0.327204	+	0.0160578i
$501$			794.826i			0.0708787i
$502$	492.931	+	2038.28i	0.0438259	+	0.181221i
$503$	1079.96	−	1870.55i	0.0957317	−	0.165812i	−0.814182	−	0.580610i	$-0.802814\pi$
$503$	1079.96	−	1870.55i	0.0957317	−	0.165812i	0.909914	+	0.414797i	$0.136148\pi$
$504$	2991.28	+	15702.2i	0.264369	+	1.38776i
$505$	15249.9			1.34379
$506$	6139.74	+	25387.9i	0.539416	+	2.23049i
$507$	159.030	+	91.8160i	0.0139305	+	0.00804278i
$508$	−3876.33	−	2499.04i	−0.338552	−	0.218262i
$509$	−3820.39	−	2205.70i	−0.332683	−	0.192075i	0.324349	−	0.945938i	$-0.394855\pi$
$509$	−3820.39	−	2205.70i	−0.332683	−	0.192075i	−0.657032	+	0.753863i	$0.728188\pi$
$510$	801.154	+	841.435i	0.0695602	+	0.0730576i
$511$	3727.92	+	6456.95i	0.322727	+	0.558980i
$512$	−6200.32	−	9786.41i	−0.535191	−	0.844731i
$513$	2959.58	+	2053.52i	0.254715	+	0.176735i
$514$	2211.39	−	534.795i	0.189767	−	0.0458926i
$515$	−4936.09	+	2849.85i	−0.422350	+	0.243844i
$516$	535.474	+	345.216i	0.0456840	+	0.0294521i
$517$	−13492.7	−	7790.04i	−1.14779	−	0.662680i
$518$	−18157.1	+	17287.9i	−1.54011	+	1.46638i
$519$	603.732	−	1045.69i	0.0510614	−	0.0884410i
$520$	11260.2	−	9714.59i	0.949599	−	0.819256i
$521$	688.537			0.0578989			0.0289495	−	0.999581i	$-0.490784\pi$
$521$	688.537			0.0578989			0.0289495	+	0.999581i	$0.490784\pi$
$522$	−1524.18	−	448.729i	−0.127800	−	0.0376252i
$523$	−12741.0	−	7356.03i	−1.06525	−	0.615023i	−0.138370	−	0.990381i	$-0.544186\pi$
$523$	−12741.0	−	7356.03i	−1.06525	−	0.615023i	−0.926880	+	0.375358i	$0.877520\pi$
$524$	−9494.78	−	18482.5i	−0.791568	−	1.54086i
$525$			2057.80i			0.171066i
$526$	−2512.34	+	8533.57i	−0.208257	+	0.707379i
$527$	5731.44	+	9927.15i	0.473749	+	0.820557i
$528$	−1074.74	−	2371.36i	−0.0885835	−	0.195455i
$529$	−11052.5	−	19143.4i	−0.908396	−	1.57339i
$530$	−16780.4	−	17624.2i	−1.37528	−	1.44442i
$531$			5244.75i			0.428630i
$532$	−14087.9	−	10835.3i	−1.14809	−	0.883024i
$533$			7706.01i			0.626237i
$534$	−2230.77	+	2123.98i	−0.180777	+	0.172123i
$535$	−11119.5	−	19259.5i	−0.898575	−	1.55638i
$536$	3472.83	−	661.575i	0.279857	−	0.0533128i
$537$	532.014	+	921.476i	0.0427525	+	0.0740496i
$538$	−3704.71	−	1090.69i	−0.296880	−	0.0874035i
$539$		−	18784.2i		−	1.50110i
$540$	−4581.02	+	2353.36i	−0.365066	+	0.187541i
$541$	2206.31	+	1273.81i	0.175336	+	0.101230i	0.585099	−	0.810962i	$-0.301056\pi$
$541$	2206.31	+	1273.81i	0.175336	+	0.101230i	−0.409764	+	0.912192i	$0.634389\pi$
$542$	759.763	−	2580.66i	0.0602114	−	0.204518i
$543$	−2145.76			−0.169583
$544$	2310.10	−	5710.83i	0.182068	−	0.450091i
$545$	−5537.19	+	9590.70i	−0.435206	+	0.753799i
$546$	−1894.59	−	1989.84i	−0.148500	−	0.155966i
$547$	−1222.88	−	706.032i	−0.0955881	−	0.0551878i	0.451444	−	0.892299i	$-0.350909\pi$
$547$	−1222.88	−	706.032i	−0.0955881	−	0.0551878i	−0.547032	+	0.837112i	$0.684242\pi$
$548$	−11081.4	−	7144.13i	−0.863825	−	0.556901i
$549$	−17430.0	+	10063.2i	−1.35500	+	0.782310i
$550$	3119.75	+	12900.2i	0.241866	+	1.00012i
$551$	1597.88	−	753.437i	0.123543	−	0.0582532i
$552$	2231.52	+	2586.55i	0.172064	+	0.199440i
$553$	−3104.06	−	5376.39i	−0.238695	−	0.413431i
$554$	13129.1	−	12500.6i	1.00686	−	0.958663i
$555$	−3454.13	−	1994.24i	−0.264180	−	0.152524i
$556$	−2602.00	+	4036.03i	−0.198470	+	0.307852i
$557$	−14123.1	−	8153.98i	−1.07435	−	0.620278i	−0.144986	−	0.989434i	$-0.546314\pi$
$557$	−14123.1	−	8153.98i	−1.07435	−	0.620278i	−0.929368	+	0.369155i	$0.879647\pi$
$558$	−24386.4	+	5897.53i	−1.85010	+	0.447423i
$559$	4336.39			0.328103
$560$	23143.9	−	10489.2i	1.74644	−	0.791518i
$561$	692.207	−	1198.94i	0.0520945	−	0.0902303i
$562$	−6638.34	+	1605.40i	−0.498259	+	0.120497i
$563$			23681.5i			1.77275i	0.462972	+	0.886373i	$0.346783\pi$
$563$			23681.5i			1.77275i	−0.462972	+	0.886373i	$0.653217\pi$
$564$	−2035.22	−	99.8799i	−0.151947	−	0.00745692i
$565$	3918.81	−	2262.53i	0.291798	−	0.168469i
$566$	−8131.97	−	2394.11i	−0.603908	−	0.177795i
$567$	−9061.01	−	15694.1i	−0.671123	−	1.16242i
$568$	−10031.8	−	3496.26i	−0.741064	−	0.258274i
$569$	15211.3			1.12072			0.560360	−	0.828249i	$-0.310663\pi$
$569$	15211.3			1.12072			0.560360	+	0.828249i	$0.310663\pi$
$570$	1020.62	−	2636.80i	0.0749987	−	0.193761i
$571$		−	1154.32i		−	0.0846001i	−0.999105	−	0.0423001i	$-0.986531\pi$
$571$		−	1154.32i		−	0.0846001i	0.999105	−	0.0423001i	$-0.0134685\pi$
$572$	−14893.8	−	9601.91i	−1.08871	−	0.701881i
$573$	438.712	−	253.291i	0.0319851	−	0.0184666i
$574$	−3718.54	+	12630.6i	−0.270399	+	0.918453i
$575$	−8707.19	−	15081.3i	−0.631504	−	1.09380i
$576$	10562.7	+	8380.54i	0.764086	+	0.606231i
$577$	22347.7			1.61239			0.806195	−	0.591650i	$-0.201523\pi$
$577$	22347.7			1.61239			0.806195	+	0.591650i	$0.201523\pi$
$578$	−10322.8	+	2496.42i	−0.742855	+	0.179650i
$579$	3495.95	+	2018.39i	0.250927	+	0.144873i
$580$	−123.803	+	2522.70i	−0.00886320	+	0.180602i
$581$			7326.79i			0.523178i
$582$	240.892	+	996.091i	0.0171568	+	0.0709438i
$583$	−14498.5	+	25112.2i	−1.02996	+	1.78394i
$584$	5938.88	+	2069.81i	0.420809	+	0.146660i
$585$	−8654.17	+	14989.5i	−0.611634	+	1.05938i
$586$	−5189.98	+	4941.52i	−0.365864	+	0.348349i
$587$	−20108.9	+	11609.9i	−1.41394	+	0.816340i	−0.995757	−	0.0920214i	$-0.970667\pi$
$587$	−20108.9	+	11609.9i	−1.41394	+	0.816340i	−0.418186	+	0.908362i	$0.637334\pi$
$588$	−1122.60	−	2185.24i	−0.0787334	−	0.153262i
$589$	15902.7	−	22919.3i	1.11249	−	1.60335i
$590$	8103.70	−	1959.77i	0.565465	−	0.136750i
$591$	−1815.22	−	3144.05i	−0.126342	−	0.218831i
$592$	−2070.73	+	21046.4i	−0.143761	+	1.46115i
$593$	10187.9	−	17646.0i	0.705512	−	1.22198i	−0.260995	−	0.965340i	$-0.584050\pi$
$593$	10187.9	−	17646.0i	0.705512	−	1.22198i	0.966506	−	0.256642i	$-0.0826162\pi$
$594$	4231.68	+	4444.44i	0.292303	+	0.306999i
$595$	11701.3	+	6755.77i	0.806232	+	0.465478i
$596$	7359.62	+	14326.2i	0.505808	+	0.984602i
$597$		−	3167.57i		−	0.217153i
$598$	22304.8	+	6566.69i	1.52527	+	0.449050i
$599$	3106.29	−	5380.25i	0.211885	−	0.366996i	−0.740419	−	0.672145i	$-0.765373\pi$
$599$	3106.29	−	5380.25i	0.211885	−	0.366996i	0.952305	+	0.305149i	$0.0987063\pi$
$600$	1133.89	+	1314.29i	0.0771512	+	0.0894259i
$601$	−14863.1			−1.00878			−0.504392	−	0.863475i	$-0.668283\pi$
$601$	−14863.1			−1.00878			−0.504392	+	0.863475i	$0.668283\pi$
$602$	7107.61	+	2092.53i	0.481204	+	0.141670i
$603$	−3563.30	+	2057.27i	−0.240645	+	0.138936i
$604$	835.853	−	17031.9i	0.0563085	−	1.14738i
$605$	14834.8	−	8564.88i	0.996893	−	0.575557i
$606$	−1638.79	−	1721.19i	−0.109854	−	0.115377i
$607$	9455.06			0.632239			0.316119	−	0.948719i	$-0.397620\pi$
$607$	9455.06			0.632239			0.316119	+	0.948719i	$0.397620\pi$
$608$	−14968.2	+	842.348i	−0.998420	+	0.0561870i
$609$	466.630			0.0310489
$610$	22061.8	+	23171.0i	1.46435	+	1.53798i
$611$	−12011.0	+	6934.55i	−0.795275	+	0.459152i
$612$	−351.438	+	7161.13i	−0.0232125	+	0.472993i
$613$	−4070.23	+	2349.95i	−0.268181	+	0.154834i	−0.628061	−	0.778164i	$-0.716151\pi$
$613$	−4070.23	+	2349.95i	−0.268181	+	0.154834i	0.359880	+	0.932999i	$0.382818\pi$
$614$	−13875.8	−	4085.13i	−0.912022	−	0.268505i
$615$	−2094.66			−0.137341
$616$	−19778.4	−	22925.1i	−1.29366	−	1.49948i
$617$	13248.8	−	22947.5i	0.864465	−	1.49730i	−0.00311281	−	0.999995i	$-0.500991\pi$
$617$	13248.8	−	22947.5i	0.864465	−	1.49730i	0.867578	−	0.497302i	$-0.165676\pi$
$618$	852.095	+	250.863i	0.0554632	+	0.0163288i
$619$		−	7288.31i		−	0.473250i	−0.971601	−	0.236625i	$-0.923959\pi$
$619$		−	7288.31i		−	0.473250i	0.971601	−	0.236625i	$-0.0760413\pi$
$620$	18224.6	+	35475.9i	1.18051	+	2.29798i
$621$	−6973.34	−	4026.06i	−0.450613	−	0.260161i
$622$	−5366.24	−	5636.05i	−0.345927	−	0.363320i
$623$	−17910.6	+	31022.0i	−1.15180	+	1.99498i
$624$	−2306.49	−	226.932i	−0.147970	−	0.0145586i
$625$	9267.38	+	16051.6i	0.593112	+	1.02730i
$626$	3663.92	−	886.072i	0.233929	−	0.0565728i
$627$	−3357.51	−	279.287i	−0.213853	−	0.0177889i
$628$	−1463.64	−	2849.11i	−0.0930025	−	0.181038i
$629$	−9738.74	+	5622.66i	−0.617343	+	0.356423i
$630$	−21417.9	+	20392.6i	−1.35446	+	1.28962i
$631$	−3353.51	+	5808.46i	−0.211571	+	0.366452i	−0.952206	−	0.305455i	$-0.901191\pi$
$631$	−3353.51	+	5808.46i	−0.211571	+	0.366452i	0.740635	+	0.671907i	$0.234525\pi$
$632$	−4945.02	−	1723.43i	−0.311238	−	0.108472i
$633$	−1168.46	+	2023.83i	−0.0733684	+	0.127078i
$634$	1210.22	+	5004.30i	0.0758109	+	0.313479i
$635$		−	8532.85i		−	0.533254i
$636$	−185.893	+	3787.87i	−0.0115898	+	0.236162i
$637$	−14481.1	−	8360.69i	−0.900728	−	0.520035i
$638$	2925.28	−	707.440i	0.181525	−	0.0438994i
$639$	12364.3			0.765451
$640$	9001.93	−	19452.1i	0.555989	−	1.20142i
$641$	−9533.60	−	16512.7i	−0.587448	−	1.01749i	−0.994565	−	0.104114i	$-0.966799\pi$
$641$	−9533.60	−	16512.7i	−0.587448	−	1.01749i	0.407117	−	0.913376i	$-0.366534\pi$
$642$	−978.810	+	3324.68i	−0.0601722	+	0.204384i
$643$	11585.7	−	6688.98i	0.710566	−	0.410245i	−0.100705	−	0.994916i	$-0.532110\pi$
$643$	11585.7	−	6688.98i	0.710566	−	0.410245i	0.811270	+	0.584671i	$0.198776\pi$
$644$	33390.2	+	21526.4i	2.04310	+	1.31717i
$645$			1178.72i			0.0719569i
$646$	−4999.52	−	6209.23i	−0.304494	−	0.378172i
$647$	−4306.34			−0.261669			−0.130835	−	0.991404i	$-0.541766\pi$
$647$	−4306.34			−0.261669			−0.130835	+	0.991404i	$0.541766\pi$
$648$	−14434.9	−	5030.83i	−0.875088	−	0.304984i
$649$	−4967.26	−	8603.55i	−0.300435	−	0.520368i
$650$	11333.6	+	3336.69i	0.683909	+	0.201347i
$651$	6381.26	−	3684.22i	0.384180	−	0.221807i
$652$	−1933.75	−	94.9001i	−0.116152	−	0.00570027i
$653$		−	22299.6i		−	1.33637i	−0.743994	−	0.668186i	$-0.767071\pi$
$653$		−	22299.6i		−	1.33637i	0.743994	−	0.668186i	$-0.232929\pi$
$654$	1677.50	−	405.682i	0.100299	−	0.0242560i
$655$	19221.4	−	33292.5i	1.14663	−	1.98602i
$656$	4584.74	+	10116.0i	0.272872	+	0.602078i
$657$	−7319.72			−0.434657
$658$	−23033.0	+	5570.24i	−1.36462	+	0.330016i
$659$	−15364.9	−	8870.92i	−0.908241	−	0.524373i	−0.0283764	−	0.999597i	$-0.509034\pi$
$659$	−15364.9	−	8870.92i	−0.908241	−	0.524373i	−0.879865	+	0.475224i	$0.842367\pi$
$660$	2610.00	−	4048.45i	0.153931	−	0.238766i
$661$	−18223.6	−	10521.4i	−1.07234	−	0.619115i	−0.143519	−	0.989648i	$-0.545842\pi$
$661$	−18223.6	−	10521.4i	−1.07234	−	0.619115i	−0.928820	+	0.370532i	$0.879175\pi$
$662$	−5471.62	+	5209.68i	−0.321239	+	0.305861i
$663$	−616.190	−	1067.27i	−0.0360948	−	0.0625180i
$664$	4037.20	+	4679.52i	0.235955	+	0.273495i
$665$	2725.77	−	32768.5i	0.158949	−	1.91084i
$666$	−5785.60	−	23923.5i	−0.336618	−	1.39192i
$667$	−3419.86	+	1974.46i	−0.198527	+	0.114620i
$668$	6553.27	+	4224.85i	0.379572	+	0.244707i
$669$	1149.11	+	663.437i	0.0664081	+	0.0383407i
$670$	4510.18	+	4736.95i	0.260065	+	0.273141i
$671$	19061.6	−	33015.7i	1.09667	−	1.89949i
$672$	−3670.97	−	1484.95i	−0.210730	−	0.0852431i
$673$	9188.15			0.526266			0.263133	−	0.964760i	$-0.415244\pi$
$673$	9188.15			0.526266			0.263133	+	0.964760i	$0.415244\pi$
$674$	1606.27	−	5455.95i	0.0917970	−	0.311803i
$675$	−3543.32	−	2045.74i	−0.202048	−	0.116653i
$676$	1602.33	−	823.147i	0.0911657	−	0.0468336i
$677$		−	8845.30i		−	0.502145i	−0.967968	−	0.251073i	$-0.919217\pi$
$677$		−	8845.30i		−	0.502145i	0.967968	−	0.251073i	$-0.0807833\pi$
$678$	−676.487	−	199.162i	−0.0383190	−	0.0112814i
$679$	5958.98	+	10321.2i	0.336796	+	0.583348i
$680$	11196.0	−	2132.85i	0.631395	−	0.120281i
$681$	1973.73	+	3418.60i	0.111062	+	0.192366i
$682$	34418.2	−	32770.6i	1.93247	−	1.83996i
$683$			8533.28i			0.478063i	0.971012	+	0.239031i	$0.0768299\pi$
$683$			8533.28i			0.478063i	−0.971012	+	0.239031i	$0.923170\pi$
$684$	16127.6	−	6658.98i	0.901543	−	0.372240i
$685$		−	24393.3i		−	1.36061i
$686$	−1755.96	−	1844.25i	−0.0977300	−	0.102644i
$687$	2176.28	+	3769.43i	0.120859	+	0.209334i
$688$	5692.56	−	2579.96i	0.315446	−	0.142965i
$689$	12906.3	+	22354.4i	0.713631	+	1.23605i
$690$	−1784.97	+	6062.92i	−0.0984819	+	0.334510i
$691$			26014.5i			1.43218i	0.698007	+	0.716091i	$0.254070\pi$
$691$			26014.5i			1.43218i	−0.698007	+	0.716091i	$0.745930\pi$
$692$	−5412.56	−	10536.0i	−0.297333	−	0.578786i
$693$	30517.8	+	17619.4i	1.67283	+	0.965811i
$694$	23996.7	+	7064.79i	1.31254	+	0.386420i
$695$	−8884.40			−0.484898
$696$	298.030	−	257.122i	0.0162310	−	0.0140032i
$697$	−2952.89	+	5114.55i	−0.160471	+	0.277945i
$698$	−7739.26	+	7368.77i	−0.419678	+	0.399587i
$699$	1121.06	+	647.242i	0.0606613	+	0.0350228i
$700$	16966.4	+	10938.1i	0.916097	+	0.590601i
$701$	−2867.85	+	1655.75i	−0.154518	+	0.0892110i	−0.575265	−	0.817967i	$-0.695101\pi$
$701$	−2867.85	+	1655.75i	−0.154518	+	0.0892110i	0.420747	+	0.907178i	$0.361768\pi$
$702$	5309.80	−	1284.10i	0.285478	−	0.0690391i
$703$	22484.3	+	15600.9i	1.20628	+	0.836981i
$704$	−25264.4	−	3743.67i	−1.35254	−	0.200419i
$705$	−1884.96	−	3264.85i	−0.100697	−	0.174413i
$706$	10065.6	+	10571.7i	0.536576	+	0.563555i
$707$	−23935.6	−	13819.2i	−1.27325	−	0.735113i
$708$	−1092.03	−	704.027i	−0.0579678	−	0.0373714i
$709$	17880.2	+	10323.1i	0.947115	+	0.546817i	0.892184	−	0.451673i	$-0.149173\pi$
$709$	17880.2	+	10323.1i	0.947115	+	0.546817i	0.0549318	+	0.998490i	$0.482506\pi$
$710$	−4620.09	−	19104.1i	−0.244210	−	1.00981i
$711$	6094.78			0.321480
$712$	5654.51	+	29682.4i	0.297629	+	1.56235i
$713$	−31178.2	+	54002.3i	−1.63764	+	2.83647i
$714$	−494.960	−	2046.67i	−0.0259432	−	0.107275i
$715$		−	32785.2i		−	1.71482i
$716$	10425.4	+	511.634i	0.544155	+	0.0267048i
$717$	−2490.97	+	1438.16i	−0.129745	+	0.0749082i
$718$	8962.50	−	30442.6i	0.465846	−	1.58232i
$719$	6037.01	+	10456.4i	0.313133	+	0.542362i	0.979039	−	0.203674i	$-0.0652881\pi$
$719$	6037.01	+	10456.4i	0.313133	+	0.542362i	−0.665906	+	0.746036i	$0.731955\pi$
$720$	−2442.61	+	24826.1i	−0.126431	+	1.28502i
$721$	10330.0			0.533575
$722$	−8478.58	+	17449.4i	−0.437036	+	0.899444i
$723$		−	2247.64i		−	0.115617i
$724$	−11405.7	+	17691.6i	−0.585480	+	0.908154i
$725$	−1737.71	+	1003.27i	−0.0890167	+	0.0513938i
$726$	−2560.86	−	753.936i	−0.130913	−	0.0385416i
$727$	−2355.14	−	4079.21i	−0.120147	−	0.208101i	0.799678	−	0.600429i	$-0.205003\pi$
$727$	−2355.14	−	4079.21i	−0.120147	−	0.208101i	−0.919826	+	0.392327i	$0.871670\pi$
$728$	−26476.6	+	5043.81i	−1.34793	+	0.256780i
$729$	16833.5			0.855228
$730$	2735.12	+	11309.8i	0.138673	+	0.573416i
$731$	2878.10	+	1661.67i	0.145623	+	0.0840755i
$732$	244.399	−	4980.03i	0.0123405	−	0.251458i
$733$		−	4270.30i		−	0.215180i	−0.994195	−	0.107590i	$-0.965687\pi$
$733$		−	4270.30i		−	0.215180i	0.994195	−	0.107590i	$-0.0343134\pi$
$734$	17259.4	−	4173.96i	0.867924	−	0.209896i
$735$	2272.61	−	3936.28i	0.114050	−	0.197540i
$736$	33187.3	−	4650.03i	1.66209	−	0.232884i
$737$	3896.85	−	6749.55i	0.194766	−	0.337344i
$738$	−8913.42	−	9361.58i	−0.444590	−	0.466944i
$739$	14637.3	−	8450.87i	0.728610	−	0.420663i	−0.0893032	−	0.996004i	$-0.528464\pi$
$739$	14637.3	−	8450.87i	0.728610	−	0.420663i	0.817914	+	0.575341i	$0.195131\pi$
$740$	−34802.6	+	17878.8i	−1.72888	+	0.888157i
$741$	−1709.71	+	2464.07i	−0.0847606	+	0.122159i
$742$	10367.1	+	42868.2i	0.512923	+	2.12095i
$743$	−8881.34	−	15382.9i	−0.438526	−	0.759549i	0.559050	−	0.829134i	$-0.311166\pi$
$743$	−8881.34	−	15382.9i	−0.438526	−	0.759549i	−0.997576	+	0.0695848i	$0.977833\pi$
$744$	2045.54	−	5869.26i	0.100797	−	0.289217i
$745$	−14899.0	+	25805.8i	−0.732693	+	1.26906i
$746$	−5263.77	+	5011.78i	−0.258338	+	0.245971i
$747$	−6229.34	−	3596.51i	−0.305113	−	0.176157i
$748$	−6205.76	−	12080.1i	−0.303349	−	0.590496i
$749$			40305.2i			1.96625i
$750$	298.248	−	1013.05i	0.0145207	−	0.0493217i
$751$	−6299.31	+	10910.7i	−0.306079	+	0.530144i	−0.977501	−	0.210931i	$-0.932350\pi$
$751$	−6299.31	+	10910.7i	−0.306079	+	0.530144i	0.671422	+	0.741075i	$0.265684\pi$
$752$	−11641.6	+	16249.3i	−0.564527	+	0.787967i
$753$	604.630			0.0292616
$754$	756.635	−	2570.03i	0.0365451	−	0.124131i
$755$	27322.1	−	15774.4i	1.31702	−	0.760385i
$756$	9322.73	+	457.520i	0.448498	+	0.0220104i
$757$	−9955.59	+	5747.86i	−0.477995	+	0.275970i	−0.719580	−	0.694409i	$-0.755666\pi$
$757$	−9955.59	+	5747.86i	−0.477995	+	0.275970i	0.241586	+	0.970379i	$0.422333\pi$
$758$	18863.1	−	17960.1i	0.903878	−	0.860607i
$759$	7531.01			0.360156
$760$	−16315.2	−	22430.7i	−0.778702	−	1.07059i
$761$	−739.256			−0.0352142			−0.0176071	−	0.999845i	$-0.505605\pi$
$761$	−739.256			−0.0352142			−0.0176071	+	0.999845i	$0.505605\pi$
$762$	−963.066	+	916.961i	−0.0457850	+	0.0435932i
$763$	17381.8	−	10035.4i	0.824725	−	0.476155i
$764$	243.587	−	4963.50i	0.0115349	−	0.235043i
$765$	−11487.7	+	6632.43i	−0.542927	+	0.313459i
$766$	−3321.66	+	11282.5i	−0.156679	+	0.532186i
$767$	−8843.54			−0.416326
$768$	−3162.84	+	1074.36i	−0.148606	+	0.0504786i
$769$	−17882.2	+	30972.9i	−0.838554	+	1.45242i	0.0525495	+	0.998618i	$0.483265\pi$
$769$	−17882.2	+	30972.9i	−0.838554	+	1.45242i	−0.891104	+	0.453800i	$0.850068\pi$
$770$	15820.5	−	53737.0i	0.740432	−	2.51500i
$771$		−	655.981i		−	0.0306415i
$772$	35223.9	−	18095.2i	1.64215	−	0.843602i
$773$	15295.4	+	8830.81i	0.711692	+	0.410896i	0.811687	−	0.584092i	$-0.198549\pi$
$773$	15295.4	+	8830.81i	0.711692	+	0.410896i	−0.0999952	+	0.994988i	$0.531883\pi$
$774$	−5268.02	+	5015.83i	−0.244645	+	0.232933i
$775$	−15842.4	+	27439.9i	−0.734292	+	1.27183i
$776$	9493.13	+	3308.53i	0.439154	+	0.153053i
$777$	3614.30	+	6260.15i	0.166875	+	0.289037i
$778$	5783.94	+	23916.7i	0.266535	+	1.10213i
$779$	14322.8	+	1191.41i	0.658752	+	0.0547968i
$780$	−1959.34	−	3814.03i	−0.0899432	−	0.175082i
$781$	−20282.5	+	11710.1i	−0.929277	+	0.536518i
$782$	12287.6	+	12905.4i	0.561898	+	0.590149i
$783$	−463.895	+	803.490i	−0.0211727	+	0.0366723i
$784$	−23984.2	−	2359.77i	−1.09258	−	0.107497i
$785$	2963.02	−	5132.11i	0.134720	−	0.233341i
$786$	−5823.16	+	1408.26i	−0.264256	+	0.0639069i
$787$		−	247.455i		−	0.0112082i	−0.999984	−	0.00560408i	$-0.998216\pi$
$787$		−	247.455i		−	0.0112082i	0.999984	−	0.00560408i	$-0.00178384\pi$
$788$	−35571.1	−	1745.68i	−1.60808	−	0.0789179i
$789$	2221.24	+	1282.43i	0.100226	+	0.0578655i
$790$	−2277.40	−	9417.10i	−0.102565	−	0.424108i
$791$	−8201.05			−0.368642
$792$	29199.9	−	5562.59i	1.31007	−	0.249568i
$793$	−16968.3	−	29390.0i	−0.759853	−	1.31610i
$794$	−5029.84	−	1480.82i	−0.224814	−	0.0661868i
$795$	−6076.41	+	3508.22i	−0.271079	+	0.156508i
$796$	−26116.4	−	16837.0i	−1.16290	−	0.749715i
$797$			3653.15i			0.162360i	0.996699	+	0.0811801i	$0.0258689\pi$
$797$			3653.15i			0.162360i	−0.996699	+	0.0811801i	$0.974131\pi$
$798$	−3991.35	+	3213.74i	−0.177058	+	0.142563i
$799$	−10629.1			−0.470626
$800$	16863.3	−	2362.79i	0.745259	−	0.104422i
$801$	−17583.6	−	30455.7i	−0.775637	−	1.34344i
$802$	291.335	−	989.565i	0.0128272	−	0.0435695i
$803$	12007.4	−	6932.46i	0.527685	−	0.304659i
$804$	49.9635	−	1018.09i	0.00219164	−	0.0446583i
$805$			73500.9i			3.21809i
$806$	−9944.25	−	41119.6i	−0.434580	−	1.79699i
$807$	−556.748	+	964.315i	−0.0242856	+	0.0420638i
$808$	−22902.0	+	4362.83i	−0.997140	+	0.189955i
$809$	16249.8			0.706197			0.353099	−	0.935586i	$-0.385128\pi$
$809$	16249.8			0.706197			0.353099	+	0.935586i	$0.385128\pi$
$810$	−6647.93	−	27489.3i	−0.288376	−	1.19244i
$811$	13462.2	+	7772.39i	0.582886	+	0.336530i	0.762280	−	0.647248i	$-0.224080\pi$
$811$	13462.2	+	7772.39i	0.582886	+	0.336530i	−0.179393	+	0.983777i	$0.557413\pi$
$812$	2480.34	−	3847.32i	0.107196	−	0.166274i
$813$	−671.730	−	387.823i	−0.0289774	−	0.0167301i
$814$	32148.6	+	33765.0i	1.38428	+	1.45389i
$815$	−1790.98	−	3102.07i	−0.0769758	−	0.133326i
$816$	−1443.88	−	1034.45i	−0.0619435	−	0.0443785i
$817$	670.440	−	8059.85i	0.0287096	−	0.345139i
$818$	−12222.5	+	2955.85i	−0.522433	+	0.126344i
$819$	27166.4	−	15684.5i	1.15906	−	0.669184i
$820$	−11134.0	+	17270.3i	−0.474167	+	0.735493i
$821$	4550.18	+	2627.05i	0.193426	+	0.111674i	0.593585	−	0.804771i	$-0.297712\pi$
$821$	4550.18	+	2627.05i	0.193426	+	0.111674i	−0.400160	+	0.916445i	$0.631045\pi$
$822$	−2753.16	+	2621.36i	−0.116822	+	0.111229i
$823$	18499.3	−	32041.8i	0.783532	−	1.35712i	−0.146341	−	0.989234i	$-0.546750\pi$
$823$	18499.3	−	32041.8i	0.783532	−	1.35712i	0.929872	−	0.367882i	$-0.119917\pi$
$824$	6597.60	−	5692.01i	0.278930	−	0.240644i
$825$	3826.69			0.161489
$826$	−14495.1	−	4267.46i	−0.610593	−	0.179763i
$827$	23632.0	+	13644.0i	0.993672	+	0.573697i	0.906370	−	0.422485i	$-0.138842\pi$
$827$	23632.0	+	13644.0i	0.993672	+	0.573697i	0.0873018	+	0.996182i	$0.472176\pi$
$828$	−34692.4	+	17822.1i	−1.45609	+	0.748021i
$829$		−	43531.5i		−	1.82378i	−0.410436	−	0.911889i	$-0.634623\pi$
$829$		−	43531.5i		−	1.82378i	0.410436	−	0.911889i	$-0.365377\pi$
$830$	−3229.32	+	10968.9i	−0.135050	+	0.458718i
$831$	−2613.45	−	4526.62i	−0.109097	−	0.188961i
$832$	−14131.0	+	17810.6i	−0.588829	+	0.742152i
$833$	−6407.51	−	11098.1i	−0.266515	−	0.461618i
$834$	954.739	+	1002.74i	0.0396402	+	0.0416333i
$835$			14425.5i			0.597864i
$836$	−20149.3	+	26197.9i	−0.833587	+	1.08382i
$837$			14650.5i			0.605013i
$838$	−1910.03	+	1818.60i	−0.0787363	+	0.0749670i
$839$	18701.8	+	32392.4i	0.769555	+	1.33291i	0.937804	+	0.347165i	$0.112855\pi$
$839$	18701.8	+	32392.4i	0.769555	+	1.33291i	−0.168249	+	0.985745i	$0.553811\pi$
$840$	−1371.02	−	7196.92i	−0.0563149	−	0.295616i
$841$	−11967.0	−	20727.4i	−0.490672	−	0.849869i
$842$	−266.605	−	78.4904i	−0.0109119	−	0.00321254i
$843$			1969.18i			0.0804534i
$844$	10475.5	+	20391.4i	0.427228	+	0.831637i
$845$	2886.28	+	1666.40i	0.117504	+	0.0678411i
$846$	6570.37	−	22317.3i	0.267014	−	0.906956i
$847$	−31045.4			−1.25942
$848$	30242.6	+	21666.9i	1.22469	+	0.877409i
$849$	−1222.08	+	2116.71i	−0.0494013	+	0.0855655i
$850$	6243.63	+	6557.55i	0.251947	+	0.264614i
$851$	−52977.4	−	30586.5i	−2.13401	−	1.23207i
$852$	−1659.71	+	2574.43i	−0.0667381	+	0.103519i
$853$	15787.9	−	9115.13i	0.633724	−	0.365881i	−0.148469	−	0.988917i	$-0.547435\pi$
$853$	15787.9	−	9115.13i	0.633724	−	0.365881i	0.782193	+	0.623037i	$0.214101\pi$
$854$	−13630.0	−	56360.2i	−0.546145	−	2.25832i
$855$	26522.2	+	18402.6i	1.06087	+	0.736089i
$856$	22208.9	+	25742.4i	0.886783	+	1.02787i
$857$	6496.65	+	11252.5i	0.258951	+	0.448517i	0.965961	−	0.258687i	$-0.0832897\pi$
$857$	6496.65	+	11252.5i	0.258951	+	0.448517i	−0.707010	+	0.707204i	$0.749956\pi$
$858$	−3700.32	+	3523.18i	−0.147234	+	0.140186i
$859$	−7511.08	−	4336.52i	−0.298341	−	0.172247i	0.343357	−	0.939205i	$-0.388436\pi$
$859$	−7511.08	−	4336.52i	−0.298341	−	0.172247i	−0.641697	+	0.766958i	$0.721769\pi$
$860$	9718.48	+	6265.43i	0.385346	+	0.248430i
$861$	3287.68	+	1898.14i	0.130132	+	0.0751319i
$862$	−17477.9	+	4226.79i	−0.690601	+	0.167013i
$863$	127.159			0.00501569			0.00250784	−	0.999997i	$-0.499202\pi$
$863$	127.159			0.00501569			0.00250784	+	0.999997i	$0.499202\pi$
$864$	6206.40	−	4844.80i	0.244382	−	0.190768i
$865$	10957.3	−	18978.6i	0.430705	−	0.746002i
$866$	3509.25	−	848.667i	0.137701	−	0.0333012i
$867$			3062.12i			0.119948i
$868$	3543.09	−	72196.2i	0.138549	−	2.82316i
$869$	−9997.97	+	5772.33i	−0.390285	+	0.225331i
$870$	698.589	+	205.669i	0.0272234	+	0.00801477i
$871$	−3468.91	−	6008.33i	−0.134948	−	0.233737i
$872$	5571.84	−	15987.2i	0.216383	−	0.620867i
$873$	−11700.4			−0.453605
$874$	15653.7	−	40441.7i	0.605829	−	1.56517i
$875$		−	12281.2i		−	0.474491i
$876$	982.561	−	1524.08i	0.0378969	−	0.0587828i
$877$	27231.1	−	15721.9i	1.04850	−	0.605349i	0.126268	−	0.991996i	$-0.459700\pi$
$877$	27231.1	−	15721.9i	1.04850	−	0.605349i	0.922228	+	0.386647i	$0.126367\pi$
$878$	−1026.48	+	3486.59i	−0.0394555	+	0.134017i
$879$	1033.10	+	1789.39i	0.0396424	+	0.0686627i
$880$	−19505.8	−	43038.5i	−0.747204	−	1.64867i
$881$	14750.8			0.564095			0.282048	−	0.959400i	$-0.408986\pi$
$881$	14750.8			0.564095			0.282048	+	0.959400i	$0.408986\pi$
$882$	27263.0	−	6593.19i	1.04081	−	0.251705i
$883$	−11147.8	−	6436.16i	−0.424860	−	0.245293i	0.272294	−	0.962214i	$-0.412218\pi$
$883$	−11147.8	−	6436.16i	−0.424860	−	0.245293i	−0.697155	+	0.716921i	$0.745551\pi$
$884$	−12074.9	−	592.585i	−0.459415	−	0.0225461i
$885$		−	2403.86i		−	0.0913051i
$886$	−4719.35	−	19514.6i	−0.178950	−	0.739962i
$887$	10225.0	−	17710.3i	0.387061	−	0.670409i	−0.604992	−	0.796232i	$-0.706824\pi$
$887$	10225.0	−	17710.3i	0.387061	−	0.670409i	0.992053	+	0.125823i	$0.0401570\pi$
$888$	5757.87	+	2006.72i	0.217592	+	0.0758346i
$889$	−7732.32	+	13392.8i	−0.291714	+	0.505264i
$890$	−40486.9	+	38548.7i	−1.52486	+	1.45186i
$891$	−29184.9	+	16849.9i	−1.09734	+	0.633550i
$892$	11578.0	−	5947.83i	0.434596	−	0.223260i
$893$	11031.9	+	23396.4i	0.413404	+	0.876744i
$894$	4513.66	−	1091.57i	0.168859	−	0.0408362i
$895$	9655.69	+	16724.1i	0.360619	+	0.624610i
$896$	−31756.1	+	22373.7i	−1.18404	+	0.834210i
$897$	3351.99	−	5805.81i	0.124771	−	0.216110i
$898$	23962.2	+	25167.0i	0.890456	+	0.935227i
$899$	6222.31	+	3592.45i	0.230841	+	0.133276i
$900$	−17628.0	+	9055.85i	−0.652890	+	0.335402i
$901$			19782.4i			0.731464i
$902$	23488.0	+	6915.02i	0.867033	+	0.255261i
$903$	1068.14	−	1850.07i	0.0393637	−	0.0681799i
$904$	−5237.90	+	4518.94i	−0.192710	+	0.166259i
$905$	−38944.0			−1.43043
$906$	−4716.49	−	1388.57i	−0.172952	−	0.0509184i
$907$	19585.5	−	11307.7i	0.717006	−	0.413964i	−0.0966437	−	0.995319i	$-0.530811\pi$
$907$	19585.5	−	11307.7i	0.717006	−	0.413964i	0.813650	+	0.581355i	$0.197477\pi$
$908$	38677.3	+	1898.12i	1.41360	+	0.0693737i
$909$	23498.6	−	13566.9i	0.857425	−	0.495035i
$910$	−34385.4	−	36114.3i	−1.25260	−	1.31558i
$911$	678.360			0.0246708			0.0123354	−	0.999924i	$-0.496073\pi$
$911$	678.360			0.0246708			0.0123354	+	0.999924i	$0.496073\pi$
$912$	−778.390	+	4251.88i	−0.0282621	+	0.154379i
$913$	13624.9			0.493888
$914$	−22633.8	−	23771.8i	−0.819101	−	0.860284i
$915$	7988.84	−	4612.36i	0.288637	−	0.166645i
$916$	42646.5	+	2092.91i	1.53830	+	0.0754932i
$917$	−60338.2	+	34836.3i	−2.17289	+	1.25452i
$918$	4016.22	+	1182.40i	0.144395	+	0.0425110i
$919$	−39630.8			−1.42253			−0.711263	−	0.702926i	$-0.751876\pi$
$919$	−39630.8			−1.42253			−0.711263	+	0.702926i	$0.751876\pi$
$920$	40500.4	+	46944.0i	1.45137	+	1.68228i
$921$	−2085.27	+	3611.79i	−0.0746057	+	0.129221i
$922$	−45854.6	−	13499.9i	−1.63790	−	0.482208i
$923$			20848.3i			0.743477i
$924$	−7765.17	+	3989.12i	−0.276467	+	0.142026i
$925$	−26919.1	−	15541.7i	−0.956858	−	0.552442i
$926$	−14154.6	−	14866.3i	−0.502321	−	0.527577i
$927$	−5070.68	+	8782.68i	−0.179658	+	0.311177i
$928$	−535.791	−	3823.95i	−0.0189528	−	0.135266i
$929$	1695.72	+	2937.07i	0.0598867	+	0.103727i	0.894414	−	0.447239i	$-0.147593\pi$
$929$	1695.72	+	2937.07i	0.0598867	+	0.103727i	−0.834528	+	0.550966i	$0.814259\pi$
$930$	11177.2	−	2703.06i	0.394102	−	0.0953084i
$931$	−17778.5	+	25622.8i	−0.625852	+	0.901991i
$932$	11295.4	−	5802.64i	0.396987	−	0.203940i
$933$	−1943.18	+	1121.90i	−0.0681853	+	0.0393668i
$934$	11135.5	−	10602.5i	0.390114	−	0.371438i
$935$	12563.1	−	21759.9i	0.439418	−	0.761095i
$936$	8708.32	−	24986.7i	0.304103	−	0.872559i
$937$	1964.37	−	3402.39i	0.0684880	−	0.118625i	−0.829748	−	0.558138i	$-0.811516\pi$
$937$	1964.37	−	3402.39i	0.0684880	−	0.118625i	0.898236	+	0.439514i	$0.144849\pi$
$938$	−2786.43	−	11522.0i	−0.0969939	−	0.401072i
$939$		−	1086.86i		−	0.0377724i
$940$	−36937.8	−	1812.75i	−1.28168	−	0.0628994i
$941$	−3196.15	−	1845.30i	−0.110724	−	0.0639266i	0.443615	−	0.896217i	$-0.353696\pi$
$941$	−3196.15	−	1845.30i	−0.110724	−	0.0639266i	−0.554339	+	0.832291i	$0.687029\pi$
$942$	−897.652	+	217.085i	−0.0310478	+	0.00750852i
$943$	−32126.6			−1.10942
$944$	−11609.3	+	5261.52i	−0.400265	+	0.181407i
$945$	8634.44	+	14955.3i	0.297226	+	0.514810i
$946$	3891.28	−	13217.3i	0.133738	−	0.454263i
$947$	23407.4	−	13514.3i	0.803209	−	0.463733i	−0.0413833	−	0.999143i	$-0.513176\pi$
$947$	23407.4	−	13514.3i	0.803209	−	0.463733i	0.844592	+	0.535411i	$0.179843\pi$
$948$	−818.131	+	1269.03i	−0.0280292	+	0.0434768i
$949$		−	12342.3i		−	0.422180i
$950$	7954.03	−	20549.4i	0.271645	−	0.701800i
$951$	1484.46			0.0506173
$952$	−19505.6	−	6798.04i	−0.664053	−	0.231435i
$953$	25290.2	+	43803.9i	0.859632	+	1.48893i	0.872280	+	0.489006i	$0.162640\pi$
$953$	25290.2	+	43803.9i	0.859632	+	1.48893i	−0.0126483	+	0.999920i	$0.504026\pi$
$954$	−41536.1	−	12228.5i	−1.40962	−	0.415003i
$955$	7962.32	−	4597.05i	0.269795	−	0.155766i
$956$	−1383.07	+	28182.3i	−0.0467904	+	0.953432i
$957$		−	867.747i		−	0.0293106i
$958$	12225.6	−	2956.61i	0.412309	−	0.0997116i
$959$	−22104.7	+	38286.5i	−0.744316	+	1.28919i
$960$	−4841.29	−	3841.12i	−0.162763	−	0.129137i
$961$	83664.2			2.80837
$962$	40339.2	−	9755.51i	1.35196	−	0.326955i
$963$	−34268.0	−	19784.7i	−1.14670	−	0.662048i
$964$	−18531.6	−	11947.2i	−0.619153	−	0.399164i
$965$	63449.0	+	36632.3i	2.11658	+	1.22201i
$966$	8295.72	−	7898.58i	0.276305	−	0.263077i
$967$	27246.7	+	47192.7i	0.906097	+	1.56941i	0.819437	+	0.573169i	$0.194286\pi$
$967$	27246.7	+	47192.7i	0.906097	+	1.56941i	0.0866603	+	0.996238i	$0.472381\pi$
$968$	−19828.2	+	17106.6i	−0.658372	+	0.568003i
$969$	−2078.96	+	980.277i	−0.0689224	+	0.0324985i
$970$	4372.01	+	18078.3i	0.144718	+	0.598413i
$971$	−2026.20	+	1169.83i	−0.0669658	+	0.0386627i	−0.533109	−	0.846047i	$-0.678976\pi$
$971$	−2026.20	+	1169.83i	−0.0669658	+	0.0386627i	0.466143	+	0.884709i	$0.345643\pi$
$972$	−7478.84	+	11600.6i	−0.246794	+	0.382809i
$973$	13944.5	+	8050.88i	0.459447	+	0.265262i
$974$	−15937.6	−	16738.9i	−0.524305	−	0.550667i
$975$	1703.23	−	2950.07i	0.0559455	−	0.0969005i
$976$	−39760.8	−	28486.1i	−1.30401	−	0.934239i
$977$	−36878.5			−1.20762			−0.603812	−	0.797127i	$-0.706352\pi$
$977$	−36878.5			−1.20762			−0.603812	+	0.797127i	$0.706352\pi$
$978$	−157.654	+	535.496i	−0.00515461	+	0.0175085i
$979$	57688.7	+	33306.6i	1.88329	+	1.08732i
$980$	−20374.4	−	39660.6i	−0.664118	−	1.29277i
$981$			19704.4i			0.641298i
$982$	−4373.61	−	1287.62i	−0.142126	−	0.0418428i
$983$	7851.00	+	13598.3i	0.254739	+	0.441220i	0.964824	−	0.262895i	$-0.0846772\pi$
$983$	7851.00	+	13598.3i	0.254739	+	0.441220i	−0.710086	+	0.704115i	$0.751344\pi$
$984$	3145.71	−	599.259i	0.101912	−	0.0194143i
$985$	−32945.0	−	57062.3i	−1.06570	−	1.84584i
$986$	1487.00	−	1415.82i	0.0480282	−	0.0457290i
$987$			6832.47i			0.220344i
$988$	11228.2	+	27194.0i	0.361555	+	0.875663i
$989$			18078.5i			0.581258i
$990$	37922.1	+	39828.8i	1.21742	+	1.27863i
$991$	−27763.6	−	48087.9i	−0.889949	−	1.54144i	−0.839934	−	0.542688i	$-0.817407\pi$
$991$	−27763.6	−	48087.9i	−0.889949	−	1.54144i	−0.0500146	−	0.998748i	$-0.515927\pi$
$992$	−37518.6	−	48063.0i	−1.20082	−	1.53831i
$993$	1089.16	+	1886.49i	0.0348072	+	0.0602879i
$994$	−10060.4	+	34171.6i	−0.321021	+	1.09040i
$995$		−	57489.2i		−	1.83169i
$996$	1585.04	−	814.266i	0.0504257	−	0.0259046i
$997$	−38115.6	−	22006.1i	−1.21077	−	0.699036i	−0.247840	−	0.968801i	$-0.579721\pi$
$997$	−38115.6	−	22006.1i	−1.21077	−	0.699036i	−0.962926	+	0.269765i	$0.913054\pi$
$998$	15568.1	+	4583.35i	0.493787	+	0.145374i
$999$	−14372.5			−0.455180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.p.a.45.15	✓	116
8.5	even	2	inner	152.4.p.a.45.24	yes	116
19.11	even	3	inner	152.4.p.a.125.24	yes	116
152.125	even	6	inner	152.4.p.a.125.15	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.p.a.45.15	✓	116	1.1	even	1	trivial
152.4.p.a.45.24	yes	116	8.5	even	2	inner
152.4.p.a.125.15	yes	116	152.125	even	6	inner
152.4.p.a.125.24	yes	116	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95037 - 2.04843i) q^{2} +(-0.706252 + 0.407755i) q^{3} +(-0.392134 + 7.99038i) q^{4} +(-12.8180 + 7.40046i) q^{5} +(2.21271 + 0.651437i) q^{6} +26.8247 q^{7} +(17.1326 - 14.7809i) q^{8} +(-13.1675 + 22.8067i) q^{9} +(40.1591 + 11.8231i) q^{10} -49.8833i q^{11} +(-2.98117 - 5.80312i) q^{12} +(-38.4561 - 22.2026i) q^{13} +(-52.3180 - 54.9485i) q^{14} +(6.03515 - 10.4532i) q^{15} +(-63.6925 - 6.26661i) q^{16} +(-17.0158 - 29.4722i) q^{17} +(72.3994 - 17.5089i) q^{18} +(-47.2126 + 68.0439i) q^{19} +(-54.1062 - 105.323i) q^{20} +(-18.9450 + 10.9379i) q^{21} +(-102.182 + 97.2908i) q^{22} +(92.5634 - 160.324i) q^{23} +(-6.07291 + 17.4249i) q^{24} +(47.0337 - 81.4647i) q^{25} +(29.5229 + 122.078i) q^{26} -43.4952i q^{27} +(-10.5189 + 214.339i) q^{28} +(-18.4731 - 10.6654i) q^{29} +(-33.1834 + 8.02497i) q^{30} -336.831 q^{31} +(111.387 + 142.692i) q^{32} +(20.3402 + 35.2302i) q^{33} +(-27.1847 + 92.3372i) q^{34} +(-343.838 + 198.515i) q^{35} +(-177.071 - 114.156i) q^{36} -330.438i q^{37} +(231.465 - 35.9987i) q^{38} +36.2129 q^{39} +(-110.219 + 316.250i) q^{40} +(-86.7691 - 150.289i) q^{41} +(59.3552 + 17.4746i) q^{42} +(-84.5716 + 48.8274i) q^{43} +(398.587 + 19.5610i) q^{44} -389.782i q^{45} +(-508.946 + 123.082i) q^{46} +(156.165 - 270.486i) q^{47} +(47.5382 - 21.5451i) q^{48} +376.563 q^{49} +(-258.608 + 62.5409i) q^{50} +(24.0348 + 13.8765i) q^{51} +(192.487 - 298.572i) q^{52} +(-503.418 - 290.649i) q^{53} +(-89.0968 + 84.8315i) q^{54} +(369.159 + 639.403i) q^{55} +(459.575 - 396.493i) q^{56} +(5.59880 - 67.3073i) q^{57} +(14.1819 + 58.6424i) q^{58} +(172.474 - 99.5777i) q^{59} +(81.1584 + 52.3222i) q^{60} +(661.860 + 382.125i) q^{61} +(656.945 + 689.975i) q^{62} +(-353.213 + 611.783i) q^{63} +(75.0486 - 506.470i) q^{64} +657.239 q^{65} +(32.4958 - 110.377i) q^{66} +(135.307 + 78.1194i) q^{67} +(242.166 - 124.405i) q^{68} +150.973i q^{69} +(1077.25 + 317.151i) q^{70} +(-234.750 - 406.599i) q^{71} +(111.512 + 585.365i) q^{72} +(138.974 + 240.709i) q^{73} +(-676.880 + 644.476i) q^{74} +76.7128i q^{75} +(-525.183 - 403.929i) q^{76} -1338.10i q^{77} +(-70.6285 - 74.1796i) q^{78} +(-115.717 - 200.427i) q^{79} +(862.784 - 391.028i) q^{80} +(-337.786 - 585.063i) q^{81} +(-138.624 + 470.858i) q^{82} +273.136i q^{83} +(-79.9690 - 155.667i) q^{84} +(436.215 + 251.849i) q^{85} +(264.965 + 78.0076i) q^{86} +17.3955 q^{87} +(-737.321 - 854.628i) q^{88} +(-667.690 + 1156.47i) q^{89} +(-798.440 + 760.217i) q^{90} +(-1031.57 - 595.578i) q^{91} +(1244.76 + 802.486i) q^{92} +(237.888 - 137.345i) q^{93} +(-858.651 + 207.654i) q^{94} +(101.614 - 1221.58i) q^{95} +(-136.851 - 55.3578i) q^{96} +(222.145 + 384.767i) q^{97} +(-734.437 - 771.363i) q^{98} +(1137.67 + 656.837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) \) 116 * q - q^2 - 7 * q^4 - 11 * q^6 - 8 * q^7 - 46 * q^8 + 484 * q^9 - 44 * q^10 - 58 * q^12 + 24 * q^14 - 230 * q^15 - 67 * q^16 - 2 * q^17 + 196 * q^18 - 840 * q^20 + 137 * q^22 - 2 * q^23 + 77 * q^24 + 1248 * q^25 + 492 * q^26 - 96 * q^28 - 904 * q^30 + 208 * q^31 - 431 * q^32 - 180 * q^33 + 224 * q^34 - 84 * q^36 + 1552 * q^38 - 116 * q^39 - 58 * q^40 - 22 * q^41 - 568 * q^42 - 89 * q^44 - 1852 * q^46 + 202 * q^47 - 89 * q^48 + 5220 * q^49 - 942 * q^50 + 232 * q^52 - 231 * q^54 + 248 * q^55 - 2296 * q^56 - 398 * q^57 - 3620 * q^58 - 1378 * q^60 + 614 * q^62 - 796 * q^63 + 1550 * q^64 - 508 * q^65 - 797 * q^66 + 1860 * q^68 - 2968 * q^70 + 1986 * q^71 - 1596 * q^72 - 218 * q^73 + 2490 * q^74 - 4697 * q^76 + 1254 * q^78 + 1250 * q^79 + 3136 * q^80 - 3810 * q^81 - 169 * q^82 + 4136 * q^84 - 2360 * q^86 - 1404 * q^87 + 4434 * q^88 - 2 * q^89 + 1378 * q^90 - 1958 * q^92 - 4608 * q^94 + 438 * q^95 + 3410 * q^96 - 1586 * q^97 + 55 * q^98

Introduction

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