LMFDB - Embedded newform 169.4.e.f.147.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.3
Root			$1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.f.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35234 + 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} -3.56155i q^{5} +(-11.7446 + 6.78078i) q^{6} +(23.5360 - 13.5885i) q^{7} -21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +O(q^{10})$	\(q+(1.35234 + 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} -3.56155i q^{5} +(-11.7446 + 6.78078i) q^{6} +(23.5360 - 13.5885i) q^{7} -21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +(2.78078 - 4.81645i) q^{10} +(13.2167 + 7.63068i) q^{11} +48.3002 q^{12} +42.4384 q^{14} +(26.7869 + 15.4654i) q^{15} +(-5.71165 + 9.89286i) q^{16} +(22.2732 + 38.5783i) q^{17} -75.6155i q^{18} +(20.7584 - 11.9848i) q^{19} +(-17.1540 + 9.90388i) q^{20} +236.024i q^{21} +(11.9157 + 20.6386i) q^{22} +(61.3693 - 106.295i) q^{23} +(159.276 + 91.9579i) q^{24} +112.315 q^{25} +186.054 q^{27} +(-130.897 - 75.5734i) q^{28} +(109.955 - 190.447i) q^{29} +(24.1501 + 41.8292i) q^{30} +27.0928i q^{31} +(-162.167 + 93.6274i) q^{32} +(-114.783 + 66.2699i) q^{33} +69.5616i q^{34} +(-48.3963 - 83.8249i) q^{35} +(-134.654 + 233.228i) q^{36} +(81.5729 + 47.0961i) q^{37} +37.4299 q^{38} -75.4233 q^{40} +(138.871 + 80.1771i) q^{41} +(-184.282 + 319.185i) q^{42} +(-75.6510 - 131.031i) q^{43} -84.8769i q^{44} +(-149.357 + 86.2311i) q^{45} +(165.985 - 95.8314i) q^{46} -466.948i q^{47} +(-49.6037 - 85.9161i) q^{48} +(197.797 - 342.594i) q^{49} +(151.889 + 87.6932i) q^{50} -386.870 q^{51} -120.847 q^{53} +(251.609 + 145.267i) q^{54} +(27.1771 - 47.0721i) q^{55} +(-287.766 - 498.425i) q^{56} +208.169i q^{57} +(297.393 - 171.700i) q^{58} +(380.733 - 219.816i) q^{59} -172.024i q^{60} +(68.6525 + 118.910i) q^{61} +(-21.1534 + 36.6388i) q^{62} +(-1139.69 - 658.002i) q^{63} -201.022 q^{64} -206.968 q^{66} +(-443.648 - 256.140i) q^{67} +(123.874 - 214.555i) q^{68} +(532.972 + 923.134i) q^{69} -151.147i q^{70} +(355.693 - 205.359i) q^{71} +(-888.078 + 512.732i) q^{72} +308.004i q^{73} +(73.5431 + 127.380i) q^{74} +(-487.710 + 844.739i) q^{75} +(-115.449 - 66.6543i) q^{76} +414.759 q^{77} -586.462 q^{79} +(35.2339 + 20.3423i) q^{80} +(-154.193 + 267.070i) q^{81} +(125.201 + 216.854i) q^{82} +1354.20i q^{83} +(1136.80 - 656.329i) q^{84} +(137.399 - 79.3272i) q^{85} -236.266i q^{86} +(954.918 + 1653.97i) q^{87} +(161.596 - 279.892i) q^{88} +(380.949 + 219.941i) q^{89} -269.309 q^{90} -682.617 q^{92} +(-203.769 - 117.646i) q^{93} +(364.582 - 631.474i) q^{94} +(-42.6847 - 73.9320i) q^{95} -1626.24i q^{96} +(-1308.80 + 755.634i) q^{97} +(534.979 - 308.870i) q^{98} -739.006i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.35234	+	0.780776i	0.478126	+	0.276046i	0.719635	−	0.694352i	$-0.244309\pi$
$2$	1.35234	+	0.780776i	0.478126	+	0.276046i	−0.241509	+	0.970399i	$0.577642\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	0.0577926	+	0.998329i	$0.481594\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	−0.893474	+	0.449114i	$0.851740\pi$
$4$	−2.78078	−	4.81645i	−0.347597	−	0.602056i
$5$		−	3.56155i		−	0.318555i	−0.987234	−	0.159277i	$-0.949084\pi$
$5$		−	3.56155i		−	0.318555i	0.987234	−	0.159277i	$-0.0509165\pi$
$6$	−11.7446	+	6.78078i	−0.799122	+	0.461373i
$7$	23.5360	−	13.5885i	1.27083	−	0.733712i	0.295683	−	0.955286i	$-0.404453\pi$
$7$	23.5360	−	13.5885i	1.27083	−	0.733712i	0.975144	+	0.221574i	$0.0711194\pi$
$8$		−	21.1771i		−	0.935904i
$9$	−24.2116	−	41.9358i	−0.896728	−	1.55318i
$10$	2.78078	−	4.81645i	0.0879359	−	0.152309i
$11$	13.2167	+	7.63068i	0.362272	+	0.209158i	0.670077	−	0.742292i	$-0.266261\pi$
$11$	13.2167	+	7.63068i	0.362272	+	0.209158i	−0.307805	+	0.951450i	$0.599594\pi$
$12$	48.3002			1.16192
$13$		0			0
$13$		0			0
$14$	42.4384			0.810154
$15$	26.7869	+	15.4654i	0.461090	+	0.266211i
$16$	−5.71165	+	9.89286i	−0.0892445	+	0.154576i
$17$	22.2732	+	38.5783i	0.317767	+	0.550389i	0.980022	−	0.198890i	$-0.0637336\pi$
$17$	22.2732	+	38.5783i	0.317767	+	0.550389i	−0.662255	+	0.749279i	$0.730400\pi$
$18$		−	75.6155i		−	0.990153i
$19$	20.7584	−	11.9848i	0.250647	−	0.144711i	−0.369413	−	0.929265i	$-0.620441\pi$
$19$	20.7584	−	11.9848i	0.250647	−	0.144711i	0.620061	+	0.784554i	$0.287108\pi$
$20$	−17.1540	+	9.90388i	−0.191788	+	0.110729i
$21$			236.024i			2.45260i
$22$	11.9157	+	20.6386i	0.115474	+	0.200008i
$23$	61.3693	−	106.295i	0.556365	−	0.963652i	−0.441431	−	0.897295i	$-0.645529\pi$
$23$	61.3693	−	106.295i	0.556365	−	0.963652i	0.997796	−	0.0663568i	$-0.0211376\pi$
$24$	159.276	+	91.9579i	1.35467	+	0.782117i
$25$	112.315			0.898523
$26$		0			0
$27$	186.054			1.32615
$28$	−130.897	−	75.5734i	−0.883471	−	0.510072i
$29$	109.955	−	190.447i	0.704071	−	1.21949i	−0.262955	−	0.964808i	$-0.584697\pi$
$29$	109.955	−	190.447i	0.704071	−	1.21949i	0.967026	−	0.254678i	$-0.0819694\pi$
$30$	24.1501	+	41.8292i	0.146973	+	0.254564i
$31$			27.0928i			0.156968i	0.996915	+	0.0784840i	$0.0250080\pi$
$31$			27.0928i			0.156968i	−0.996915	+	0.0784840i	$0.974992\pi$
$32$	−162.167	+	93.6274i	−0.895856	+	0.517223i
$33$	−114.783	+	66.2699i	−0.605488	+	0.349579i
$34$			69.5616i			0.350874i
$35$	−48.3963	−	83.8249i	−0.233728	−	0.404828i
$36$	−134.654	+	233.228i	−0.623400	+	1.07976i
$37$	81.5729	+	47.0961i	0.362446	+	0.209258i	0.670153	−	0.742223i	$-0.266228\pi$
$37$	81.5729	+	47.0961i	0.362446	+	0.209258i	−0.307707	+	0.951481i	$0.599562\pi$
$38$	37.4299			0.159788
$39$		0			0
$40$	−75.4233			−0.298137
$41$	138.871	+	80.1771i	0.528975	+	0.305404i	0.740599	−	0.671947i	$-0.234542\pi$
$41$	138.871	+	80.1771i	0.528975	+	0.305404i	−0.211624	+	0.977351i	$0.567875\pi$
$42$	−184.282	+	319.185i	−0.677031	+	1.17265i
$43$	−75.6510	−	131.031i	−0.268295	−	0.464700i	0.700127	−	0.714018i	$-0.253127\pi$
$43$	−75.6510	−	131.031i	−0.268295	−	0.464700i	−0.968422	+	0.249318i	$0.919793\pi$
$44$		−	84.8769i		−	0.290811i
$45$	−149.357	+	86.2311i	−0.494773	+	0.285657i
$46$	165.985	−	95.8314i	0.532025	−	0.307165i
$47$		−	466.948i		−	1.44918i	−0.689181	−	0.724589i	$-0.742030\pi$
$47$		−	466.948i		−	1.44918i	0.689181	−	0.724589i	$-0.257970\pi$
$48$	−49.6037	−	85.9161i	−0.149160	−	0.258353i
$49$	197.797	−	342.594i	0.576667	−	0.998817i
$50$	151.889	+	87.6932i	0.429607	+	0.248034i
$51$	−386.870			−1.06221
$52$		0			0
$53$	−120.847			−0.313199			−0.156600	−	0.987662i	$-0.550053\pi$
$53$	−120.847			−0.313199			−0.156600	+	0.987662i	$0.550053\pi$
$54$	251.609	+	145.267i	0.634068	+	0.366079i
$55$	27.1771	−	47.0721i	0.0666283	−	0.115404i
$56$	−287.766	−	498.425i	−0.686684	−	1.18937i
$57$			208.169i			0.483730i
$58$	297.393	−	171.700i	0.673269	−	0.388712i
$59$	380.733	−	219.816i	0.840122	−	0.485045i	−0.0171836	−	0.999852i	$-0.505470\pi$
$59$	380.733	−	219.816i	0.840122	−	0.485045i	0.857306	+	0.514808i	$0.172137\pi$
$60$		−	172.024i		−	0.370136i
$61$	68.6525	+	118.910i	0.144099	+	0.249587i	0.929037	−	0.369988i	$-0.120638\pi$
$61$	68.6525	+	118.910i	0.144099	+	0.249587i	−0.784937	+	0.619575i	$0.787305\pi$
$62$	−21.1534	+	36.6388i	−0.0433304	+	0.0750505i
$63$	−1139.69	−	658.002i	−2.27917	−	1.31588i
$64$	−201.022			−0.392621
$65$		0			0
$66$	−206.968			−0.386000
$67$	−443.648	−	256.140i	−0.808958	−	0.467052i	0.0376358	−	0.999292i	$-0.488017\pi$
$67$	−443.648	−	256.140i	−0.808958	−	0.467052i	−0.846594	+	0.532239i	$0.821351\pi$
$68$	123.874	−	214.555i	0.220910	−	0.382627i
$69$	532.972	+	923.134i	0.929887	+	1.61061i
$70$		−	151.147i		−	0.258078i
$71$	355.693	−	205.359i	0.594549	−	0.343263i	−0.172345	−	0.985037i	$-0.555134\pi$
$71$	355.693	−	205.359i	0.594549	−	0.343263i	0.766894	+	0.641774i	$0.221801\pi$
$72$	−888.078	+	512.732i	−1.45362	+	0.839251i
$73$			308.004i			0.493823i	0.969038	+	0.246912i	$0.0794158\pi$
$73$			308.004i			0.493823i	−0.969038	+	0.246912i	$0.920584\pi$
$74$	73.5431	+	127.380i	0.115530	+	0.200104i
$75$	−487.710	+	844.739i	−0.750879	+	1.30056i
$76$	−115.449	−	66.6543i	−0.174248	−	0.100602i
$77$	414.759			0.613847
$78$		0			0
$79$	−586.462			−0.835217			−0.417608	−	0.908627i	$-0.637132\pi$
$79$	−586.462			−0.835217			−0.417608	+	0.908627i	$0.637132\pi$
$80$	35.2339	+	20.3423i	0.0492409	+	0.0284293i
$81$	−154.193	+	267.070i	−0.211513	+	0.366352i
$82$	125.201	+	216.854i	0.168611	+	0.292043i
$83$			1354.20i			1.79088i	0.445182	+	0.895440i	$0.353139\pi$
$83$			1354.20i			1.79088i	−0.445182	+	0.895440i	$0.646861\pi$
$84$	1136.80	−	656.329i	1.47660	−	0.852516i
$85$	137.399	−	79.3272i	0.175329	−	0.101226i
$86$		−	236.266i		−	0.296247i
$87$	954.918	+	1653.97i	1.17676	+	2.03820i
$88$	161.596	−	279.892i	0.195752	−	0.339052i
$89$	380.949	+	219.941i	0.453714	+	0.261952i	0.709398	−	0.704809i	$-0.248967\pi$
$89$	380.949	+	219.941i	0.453714	+	0.261952i	−0.255683	+	0.966761i	$0.582300\pi$
$90$	−269.309			−0.315418
$91$		0			0
$92$	−682.617			−0.773563
$93$	−203.769	−	117.646i	−0.227202	−	0.131175i
$94$	364.582	−	631.474i	0.400040	−	0.692889i
$95$	−42.6847	−	73.9320i	−0.0460985	−	0.0798449i
$96$		−	1626.24i		−	1.72894i
$97$	−1308.80	+	755.634i	−1.36998	+	0.790959i	−0.990925	−	0.134414i	$-0.957085\pi$
$97$	−1308.80	+	755.634i	−1.36998	+	0.790959i	−0.379056	+	0.925374i	$0.623751\pi$
$98$	534.979	−	308.870i	0.551439	−	0.318374i
$99$		−	739.006i		−	0.750231i
$100$	−312.324	−	540.961i	−0.312324	−	0.540961i
$101$	168.130	−	291.209i	0.165639	−	0.286895i	−0.771243	−	0.636541i	$-0.780365\pi$
$101$	168.130	−	291.209i	0.165639	−	0.286895i	0.936882	+	0.349646i	$0.113698\pi$
$102$	−523.182	−	302.059i	−0.507870	−	0.293219i
$103$	−322.712			−0.308716			−0.154358	−	0.988015i	$-0.549331\pi$
$103$	−322.712			−0.308716			−0.154358	+	0.988015i	$0.549331\pi$
$104$		0			0
$105$	840.611			0.781288
$106$	−163.426	−	94.3542i	−0.149749	−	0.0864574i
$107$	−717.309	+	1242.42i	−0.648083	+	1.12251i	0.335498	+	0.942041i	$0.391096\pi$
$107$	−717.309	+	1242.42i	−0.648083	+	1.12251i	−0.983580	+	0.180471i	$0.942238\pi$
$108$	−517.375	−	896.119i	−0.460967	−	0.798417i
$109$			849.147i			0.746179i	0.927795	+	0.373089i	$0.121702\pi$
$109$			849.147i			0.746179i	−0.927795	+	0.373089i	$0.878298\pi$
$110$	73.5055	−	42.4384i	0.0637134	−	0.0367850i
$111$	−708.433	+	409.014i	−0.605779	+	0.349747i
$112$			310.452i			0.261919i
$113$	−807.263	−	1398.22i	−0.672044	−	1.16401i	−0.977324	−	0.211751i	$-0.932083\pi$
$113$	−807.263	−	1398.22i	−0.672044	−	1.16401i	0.305280	−	0.952263i	$-0.401250\pi$
$114$	−162.533	+	281.516i	−0.133532	+	0.231284i
$115$	−378.574	−	218.570i	−0.306976	−	0.177233i
$116$	−1223.04			−0.978931
$117$		0			0
$118$	686.509			0.535579
$119$	1048.45	+	605.321i	0.807654	+	0.466300i
$120$	327.513	−	567.269i	0.249147	−	0.431536i
$121$	−549.045	−	950.974i	−0.412506	−	0.714481i
$122$			214.409i			0.159112i
$123$	−1206.05	+	696.311i	−0.884109	+	0.510441i
$124$	130.491	−	75.3390i	0.0945035	−	0.0545616i
$125$		−	845.211i		−	0.604784i
$126$	−1027.50	−	1779.69i	−0.726487	−	1.25831i
$127$	432.587	−	749.263i	0.302251	−	0.523514i	−0.674394	−	0.738371i	$-0.735595\pi$
$127$	432.587	−	749.263i	0.302251	−	0.523514i	0.976646	+	0.214857i	$0.0689285\pi$
$128$	1025.49	+	592.066i	0.708134	+	0.408842i
$129$	1314.01			0.896836
$130$		0			0
$131$	−281.400			−0.187680			−0.0938400	−	0.995587i	$-0.529914\pi$
$131$	−281.400			−0.187680			−0.0938400	+	0.995587i	$0.529914\pi$
$132$	638.371	+	368.563i	0.420932	+	0.243025i
$133$	325.713	−	564.152i	0.212353	−	0.367806i
$134$	−399.976	−	692.779i	−0.257856	−	0.446620i
$135$		−	662.641i		−	0.422452i
$136$	816.976	−	471.681i	0.515111	−	0.297400i
$137$	2287.55	−	1320.72i	1.42656	−	0.823624i	0.429711	−	0.902967i	$-0.358616\pi$
$137$	2287.55	−	1320.72i	1.42656	−	0.823624i	0.996847	+	0.0793428i	$0.0252822\pi$
$138$			1664.53i			1.02677i
$139$	999.318	+	1730.87i	0.609791	+	1.05619i	0.991274	+	0.131814i	$0.0420801\pi$
$139$	999.318	+	1730.87i	0.609791	+	1.05619i	−0.381483	+	0.924376i	$0.624587\pi$
$140$	−269.159	+	466.196i	−0.162486	+	0.281434i
$141$	3511.98	+	2027.64i	2.09760	+	1.21105i
$142$	641.359			0.379026
$143$		0			0
$144$	553.153			0.320112
$145$	−678.286	−	391.609i	−0.388473	−	0.224285i
$146$	−240.482	+	416.527i	−0.136318	+	0.236110i
$147$	1717.80	+	2975.31i	0.963820	+	1.66939i
$148$		−	523.855i		−	0.290950i
$149$	−1518.13	+	876.491i	−0.834696	+	0.481912i	−0.855458	−	0.517872i	$-0.826724\pi$
$149$	−1518.13	+	876.491i	−0.834696	+	0.481912i	0.0207617	+	0.999784i	$0.493391\pi$
$150$	−1319.10	+	761.585i	−0.718029	+	0.414554i
$151$			2794.64i			1.50613i	0.657949	+	0.753063i	$0.271424\pi$
$151$			2794.64i			1.50613i	−0.657949	+	0.753063i	$0.728576\pi$
$152$	−253.804	−	439.601i	−0.135436	−	0.234582i
$153$	1078.54	−	1868.09i	0.569901	−	0.987098i
$154$	560.898	+	323.834i	0.293496	+	0.169450i
$155$	96.4924			0.0500030
$156$		0			0
$157$	3244.87			1.64949			0.824743	−	0.565508i	$-0.191320\pi$
$157$	3244.87			1.64949			0.824743	+	0.565508i	$0.191320\pi$
$158$	−793.099	−	457.896i	−0.399339	−	0.230558i
$159$	524.756	−	908.903i	0.261735	−	0.453338i
$160$	333.459	+	577.568i	0.164764	+	0.285380i
$161$		−	3335.68i		−	1.63285i
$162$	−417.045	+	240.781i	−0.202260	+	0.116775i
$163$	−2841.83	+	1640.73i	−1.36558	+	0.788418i	−0.990360	−	0.138517i	$-0.955766\pi$
$163$	−2841.83	+	1640.73i	−1.36558	+	0.788418i	−0.375221	+	0.926936i	$0.622433\pi$
$164$		−	891.818i		−	0.424630i
$165$	236.024	+	408.805i	0.111360	+	0.192881i
$166$	−1057.33	+	1831.35i	−0.494366	+	0.856266i
$167$	−2707.65	−	1563.26i	−1.25463	−	0.724364i	−0.282608	−	0.959235i	$-0.591200\pi$
$167$	−2707.65	−	1563.26i	−1.25463	−	0.724364i	−0.972026	+	0.234872i	$0.924533\pi$
$168$	4998.29			2.29540
$169$		0			0
$170$	247.747			0.111773
$171$	−1005.19	−	580.346i	−0.449524	−	0.259533i
$172$	−420.737	+	728.738i	−0.186517	+	0.323057i
$173$	48.7849	+	84.4980i	0.0214396	+	0.0371345i	0.876546	−	0.481318i	$-0.159842\pi$
$173$	48.7849	+	84.4980i	0.0214396	+	0.0371345i	−0.855107	+	0.518452i	$0.826508\pi$
$174$			2982.31i			1.29936i
$175$	2643.46	−	1526.20i	1.14187	−	0.659257i
$176$	−150.979	+	87.1675i	−0.0646616	+	0.0373324i
$177$			3818.06i			1.62137i
$178$	343.450	+	594.873i	0.144622	+	0.250492i
$179$	−17.3575	+	30.0640i	−0.00724782	+	0.0125536i	−0.869627	−	0.493710i	$-0.835640\pi$
$179$	−17.3575	+	30.0640i	−0.00724782	+	0.0125536i	0.862379	+	0.506264i	$0.168974\pi$
$180$	830.654	+	479.579i	0.343963	+	0.198587i
$181$	1229.35			0.504843			0.252422	−	0.967617i	$-0.418773\pi$
$181$	1229.35			0.504843			0.252422	+	0.967617i	$0.418773\pi$
$182$		0			0
$183$	−1192.45			−0.481684
$184$	−2251.01	−	1299.62i	−0.901885	−	0.520704i
$185$	167.735	−	290.526i	0.0666602	−	0.115459i
$186$	−183.710	−	318.195i	−0.0724209	−	0.125437i
$187$			679.839i			0.265854i
$188$	−2249.03	+	1298.48i	−0.872486	+	0.503730i
$189$	4378.97	−	2528.20i	1.68531	−	0.973014i
$190$		−	133.309i		−	0.0509012i
$191$	−2140.40	−	3707.28i	−0.810858	−	1.40445i	−0.912265	−	0.409602i	$-0.865668\pi$
$191$	−2140.40	−	3707.28i	−0.810858	−	1.40445i	0.101407	−	0.994845i	$-0.467666\pi$
$192$	872.903	−	1511.91i	0.328106	−	0.568296i
$193$	409.041	+	236.160i	0.152557	+	0.0880786i	0.574335	−	0.818620i	$-0.305261\pi$
$193$	409.041	+	236.160i	0.152557	+	0.0880786i	−0.421778	+	0.906699i	$0.638594\pi$
$194$	−2359.93			−0.873365
$195$		0			0
$196$	−2200.12			−0.801791
$197$	3883.58	+	2242.18i	1.40453	+	0.810908i	0.994854	−	0.101321i	$-0.0323068\pi$
$197$	3883.58	+	2242.18i	1.40453	+	0.810908i	0.409681	+	0.912229i	$0.365640\pi$
$198$	576.998	−	999.390i	0.207098	−	0.358705i
$199$	−183.120	−	317.173i	−0.0652314	−	0.112984i	0.831565	−	0.555427i	$-0.187445\pi$
$199$	−183.120	−	317.173i	−0.0652314	−	0.112984i	−0.896797	+	0.442443i	$0.854112\pi$
$200$		−	2378.51i		−	0.840931i
$201$	3852.93	−	2224.49i	1.35206	−	0.780614i
$202$	454.739	−	262.543i	0.158393	−	0.0914480i
$203$		−	5976.49i		−	2.06634i
$204$	1075.80	+	1863.34i	0.369221	+	0.639509i
$205$	285.555	−	494.596i	0.0972879	−	0.168508i
$206$	−436.418	−	251.966i	−0.147605	−	0.0852199i
$207$	−5943.41			−1.99563
$208$		0			0
$209$	365.810			0.121070
$210$	1136.80	+	656.329i	0.373554	+	0.215671i
$211$	−1061.28	+	1838.19i	−0.346262	+	0.599744i	−0.985582	−	0.169197i	$-0.945883\pi$
$211$	−1061.28	+	1838.19i	−0.346262	+	0.599744i	0.639320	+	0.768941i	$0.279216\pi$
$212$	336.047	+	582.051i	0.108867	+	0.188563i
$213$			3566.95i			1.14743i
$214$	−1940.10	+	1120.12i	−0.619730	+	0.357801i
$215$	−466.675	+	269.435i	−0.148033	+	0.0854666i
$216$		−	3940.08i		−	1.24115i
$217$	368.152	+	637.657i	0.115169	+	0.199479i
$218$	−662.994	+	1148.34i	−0.205980	+	0.356768i
$219$	−2316.54	−	1337.45i	−0.714781	−	0.412679i
$220$	−302.294			−0.0926392
$221$		0			0
$222$	−1277.39			−0.386185
$223$	5132.43	+	2963.21i	1.54122	+	0.889826i	0.998762	+	0.0497449i	$0.0158408\pi$
$223$	5132.43	+	2963.21i	1.54122	+	0.889826i	0.542461	+	0.840081i	$0.317493\pi$
$224$	−2544.52	+	4407.24i	−0.758986	+	1.31460i
$225$	−2719.34	−	4710.03i	−0.805730	−	1.39557i
$226$		−	2521.17i		−	0.742060i
$227$	−775.665	+	447.830i	−0.226796	+	0.130941i	−0.609093	−	0.793099i	$-0.708466\pi$
$227$	−775.665	+	447.830i	−0.226796	+	0.130941i	0.382297	+	0.924039i	$0.375133\pi$
$228$	1002.63	−	578.870i	0.291232	−	0.168143i
$229$		−	627.717i		−	0.181138i	−0.995890	−	0.0905692i	$-0.971131\pi$
$229$		−	627.717i		−	0.181138i	0.995890	−	0.0905692i	$-0.0288686\pi$
$230$	−341.309	−	591.164i	−0.0978488	−	0.169479i
$231$	−1801.02	+	3119.46i	−0.512981	+	0.888509i
$232$	−4033.11	−	2328.52i	−1.14132	−	0.658942i
$233$	−2303.72			−0.647734			−0.323867	−	0.946103i	$-0.604983\pi$
$233$	−2303.72			−0.647734			−0.323867	+	0.946103i	$0.604983\pi$
$234$		0			0
$235$	−1663.06			−0.461643
$236$	−2117.47	−	1222.52i	−0.584048	−	0.337200i
$237$	2546.61	−	4410.86i	0.697976	−	1.20893i
$238$	945.240	+	1637.20i	0.257440	+	0.445900i
$239$			544.622i			0.147400i	0.997280	+	0.0737001i	$0.0234808\pi$
$239$			544.622i			0.147400i	−0.997280	+	0.0737001i	$0.976519\pi$
$240$	−305.995	+	176.666i	−0.0822995	+	0.0475156i
$241$	−4699.14	+	2713.05i	−1.25601	+	0.725157i	−0.972296	−	0.233752i	$-0.924900\pi$
$241$	−4699.14	+	2713.05i	−1.25601	+	0.725157i	−0.283713	+	0.958909i	$0.591566\pi$
$242$		−	1714.73i		−	0.455483i
$243$	1172.61	+	2031.03i	0.309561	+	0.536175i
$244$	381.814	−	661.322i	0.100177	−	0.173511i
$245$	−1220.17	−	704.464i	−0.318178	−	0.183700i
$246$	−2174.65			−0.563621
$247$		0			0
$248$	573.746			0.146907
$249$	−10185.1	−	5880.39i	−2.59220	−	1.49661i
$250$	659.921	−	1143.02i	0.166948	−	0.289163i
$251$	−2610.61	−	4521.71i	−0.656494	−	1.13708i	−0.981517	−	0.191375i	$-0.938705\pi$
$251$	−2610.61	−	4521.71i	−0.656494	−	1.13708i	0.325022	−	0.945706i	$-0.394628\pi$
$252$			7319.02i			1.82958i
$253$	1622.20	−	936.580i	0.403111	−	0.232736i
$254$	1170.01	−	675.508i	0.289028	−	0.166871i
$255$			1377.86i			0.338372i
$256$	1728.63	+	2994.07i	0.422029	+	0.730975i
$257$	329.103	−	570.023i	0.0798789	−	0.138354i	−0.823319	−	0.567579i	$-0.807880\pi$
$257$	329.103	−	570.023i	0.0798789	−	0.138354i	0.903198	+	0.429225i	$0.141213\pi$
$258$	1776.99	+	1025.95i	0.428801	+	0.247568i
$259$	2559.87			0.614141
$260$		0			0
$261$	−10648.7			−2.52544
$262$	−380.550	−	219.711i	−0.0897346	−	0.0518083i
$263$	−1623.23	+	2811.51i	−0.380580	+	0.659184i	−0.991145	−	0.132782i	$-0.957609\pi$
$263$	−1623.23	+	2811.51i	−0.380580	+	0.659184i	0.610565	+	0.791966i	$0.290942\pi$
$264$	1403.40	+	2430.76i	0.327172	+	0.566679i
$265$			430.401i			0.0997711i
$266$	880.953	−	508.618i	0.203063	−	0.117238i
$267$	−3308.42	+	1910.11i	−0.758321	+	0.437817i
$268$			2849.07i			0.649384i
$269$	1292.90	+	2239.37i	0.293047	+	0.507572i	0.974529	−	0.224263i	$-0.0719976\pi$
$269$	1292.90	+	2239.37i	0.293047	+	0.507572i	−0.681482	+	0.731835i	$0.738664\pi$
$270$	517.375	−	896.119i	0.116616	−	0.201985i
$271$	856.441	+	494.466i	0.191974	+	0.110836i	0.592907	−	0.805271i	$-0.297980\pi$
$271$	856.441	+	494.466i	0.191974	+	0.110836i	−0.400932	+	0.916108i	$0.631314\pi$
$272$	−508.867			−0.113436
$273$		0			0
$274$	4124.74			0.909433
$275$	1484.44	+	857.043i	0.325510	+	0.187933i
$276$	2964.15	−	5134.06i	0.646452	−	1.11969i
$277$	4071.20	+	7051.53i	0.883086	+	1.52955i	0.847892	+	0.530169i	$0.177872\pi$
$277$	4071.20	+	7051.53i	0.883086	+	1.52955i	0.0351939	+	0.999381i	$0.488795\pi$
$278$			3120.97i			0.673322i
$279$	1136.16	−	655.961i	0.243799	−	0.140758i
$280$	−1775.17	+	1024.89i	−0.378880	+	0.218747i
$281$		−	1534.21i		−	0.325705i	−0.986650	−	0.162853i	$-0.947930\pi$
$281$		−	1534.21i		−	0.325705i	0.986650	−	0.162853i	$-0.0520695\pi$
$282$	3166.27	+	5484.14i	0.668612	+	1.15807i
$283$	−3482.50	+	6031.87i	−0.731495	+	1.26699i	0.224749	+	0.974417i	$0.427844\pi$
$283$	−3482.50	+	6031.87i	−0.731495	+	1.26699i	−0.956244	+	0.292570i	$0.905490\pi$
$284$	−1978.20	−	1142.12i	−0.413327	−	0.238634i
$285$	741.403			0.154095
$286$		0			0
$287$	4357.96			0.896314
$288$	7852.68	+	4533.75i	1.60668	+	0.927616i
$289$	1464.31	−	2536.26i	0.298048	−	0.516234i
$290$	−611.518	−	1059.18i	−0.123826	−	0.214473i
$291$		−	13124.9i		−	2.64396i
$292$	1483.48	−	856.490i	0.297309	−	0.171652i
$293$	−554.281	+	320.015i	−0.110517	+	0.0638070i	−0.554240	−	0.832357i	$-0.686991\pi$
$293$	−554.281	+	320.015i	−0.110517	+	0.0638070i	0.443723	+	0.896164i	$0.353658\pi$
$294$			5364.87i			1.06424i
$295$	−782.887	−	1356.00i	−0.154513	−	0.267625i
$296$	997.358	−	1727.48i	0.195846	−	0.339214i
$297$	2459.03	+	1419.72i	0.480428	+	0.277375i
$298$	−2737.37			−0.532120
$299$		0			0
$300$	5424.85			1.04401
$301$	−3561.05	−	2055.97i	−0.681912	−	0.393702i
$302$	−2181.99	+	3779.32i	−0.415760	+	0.720118i
$303$	1460.15	+	2529.05i	0.276843	+	0.479506i
$304$			273.813i			0.0516587i
$305$	423.503	−	244.509i	0.0795072	−	0.0459035i
$306$	2917.12	−	1684.20i	0.544969	−	0.314638i
$307$			100.406i			0.0186660i	0.999956	+	0.00933299i	$0.00297083\pi$
$307$			100.406i			0.0186660i	−0.999956	+	0.00933299i	$0.997029\pi$
$308$	−1153.35	−	1997.67i	−0.213371	−	0.369570i
$309$	1401.32	−	2427.16i	0.257988	−	0.446849i
$310$	130.491	+	75.3390i	0.0239077	+	0.0138031i
$311$	3878.92			0.707245			0.353623	−	0.935388i	$-0.384950\pi$
$311$	3878.92			0.707245			0.353623	+	0.935388i	$0.384950\pi$
$312$		0			0
$313$	−3789.39			−0.684311			−0.342155	−	0.939643i	$-0.611157\pi$
$313$	−3789.39			−0.684311			−0.342155	+	0.939643i	$0.611157\pi$
$314$	4388.19	+	2533.52i	0.788662	+	0.455334i
$315$	−2343.51	+	4059.08i	−0.419180	+	0.726041i
$316$	1630.82	+	2824.66i	0.290319	+	0.502847i
$317$			4406.81i			0.780791i	0.920647	+	0.390396i	$0.127662\pi$
$317$			4406.81i			0.780791i	−0.920647	+	0.390396i	$0.872338\pi$
$318$	1419.30	−	819.434i	0.250284	−	0.144502i
$319$	2906.48	−	1678.06i	0.510130	−	0.294524i
$320$			715.950i			0.125071i
$321$	−6229.58	−	10790.0i	−1.08318	−	1.87613i
$322$	2604.42	−	4510.99i	0.450741	−	0.780706i
$323$	924.710	+	533.882i	0.159295	+	0.0919690i
$324$	1715.11			0.294086
$325$		0			0
$326$	−5124.19			−0.870559
$327$	−6386.55	−	3687.27i	−1.08005	−	0.623568i
$328$	1697.92	−	2940.88i	0.285829	−	0.495070i
$329$	−6345.14	−	10990.1i	−1.06328	−	1.84165i
$330$			737.127i			0.122962i
$331$	−3577.98	+	2065.75i	−0.594149	+	0.343032i	−0.766736	−	0.641962i	$-0.778121\pi$
$331$	−3577.98	+	2065.75i	−0.594149	+	0.343032i	0.172587	+	0.984994i	$0.444787\pi$
$332$	6522.44	−	3765.73i	1.07821	−	0.622505i
$333$		−	4561.10i		−	0.750591i
$334$	−2441.11	−	4228.13i	−0.399916	−	0.692674i
$335$	−912.257	+	1580.07i	−0.148782	+	0.257698i
$336$	−2334.95	−	1348.08i	−0.379113	−	0.218881i
$337$	4560.82			0.737221			0.368611	−	0.929584i	$-0.379834\pi$
$337$	4560.82			0.737221			0.368611	+	0.929584i	$0.379834\pi$
$338$		0			0
$339$	14021.6			2.24646
$340$	−764.150	−	441.182i	−0.121888	−	0.0703720i
$341$	−206.737	+	358.078i	−0.0328311	+	0.0568652i
$342$	−906.240	−	1569.65i	−0.143286	−	0.248179i
$343$		−	1429.34i		−	0.225007i
$344$	−2774.86	+	1602.07i	−0.434914	+	0.251098i
$345$	3287.79	−	1898.21i	0.513069	−	0.296220i
$346$			152.360i			0.0236733i
$347$	−5034.70	−	8720.36i	−0.778896	−	1.34909i	−0.932579	−	0.360967i	$-0.882447\pi$
$347$	−5034.70	−	8720.36i	−0.778896	−	1.34909i	0.153683	−	0.988120i	$-0.450887\pi$
$348$	5310.82	−	9198.62i	0.818075	−	1.41695i
$349$	5091.64	+	2939.66i	0.780944	+	0.450878i	0.836765	−	0.547563i	$-0.184444\pi$
$349$	5091.64	+	2939.66i	0.780944	+	0.450878i	−0.0558207	+	0.998441i	$0.517778\pi$
$350$	4766.49			0.727942
$351$		0			0
$352$	−2857.76			−0.432725
$353$	7917.69	+	4571.28i	1.19381	+	0.689249i	0.959169	−	0.282833i	$-0.0912741\pi$
$353$	7917.69	+	4571.28i	1.19381	+	0.689249i	0.234644	+	0.972081i	$0.424607\pi$
$354$	−2981.05	+	5163.33i	−0.447574	+	0.775220i
$355$	−731.398	−	1266.82i	−0.109348	−	0.189397i
$356$		−	2446.43i		−	0.364215i
$357$	−9105.39	+	5257.00i	−1.34988	+	0.779356i
$358$	−46.9466	+	27.1046i	−0.00693074	+	0.00400146i
$359$			2754.32i			0.404924i	0.979290	+	0.202462i	$0.0648942\pi$
$359$			2754.32i			0.404924i	−0.979290	+	0.202462i	$0.935106\pi$
$360$	1826.12	+	3162.94i	0.267347	+	0.463059i
$361$	−3142.23	+	5442.50i	−0.458117	+	0.793483i
$362$	1662.50	+	959.845i	0.241379	+	0.139360i
$363$	9536.54			1.37889
$364$		0			0
$365$	1096.97			0.157310
$366$	−1612.60	−	931.034i	−0.230306	−	0.132967i
$367$	−1520.09	+	2632.88i	−0.216208	+	0.374483i	−0.953646	−	0.300932i	$-0.902702\pi$
$367$	−1520.09	+	2632.88i	−0.216208	+	0.374483i	0.737438	+	0.675415i	$0.236036\pi$
$368$	701.040	+	1214.24i	0.0993049	+	0.172001i
$369$		−	7764.88i		−	1.09546i
$370$	453.672	−	261.928i	0.0637440	−	0.0368026i
$371$	−2844.25	+	1642.13i	−0.398022	+	0.229798i
$372$			1308.59i			0.182385i
$373$	2692.36	+	4663.31i	0.373740	+	0.647337i	0.990138	−	0.140098i	$-0.0447418\pi$
$373$	2692.36	+	4663.31i	0.373740	+	0.647337i	−0.616397	+	0.787435i	$0.711408\pi$
$374$	−530.802	+	919.376i	−0.0733880	+	0.127112i
$375$	6356.95	+	3670.18i	0.875390	+	0.505407i
$376$	−9888.59			−1.35629
$377$		0			0
$378$	7895.84			1.07439
$379$	2965.50	+	1712.13i	0.401920	+	0.232049i	0.687312	−	0.726362i	$-0.258791\pi$
$379$	2965.50	+	1712.13i	0.401920	+	0.232049i	−0.285392	+	0.958411i	$0.592124\pi$
$380$	−237.393	+	411.177i	−0.0320474	+	0.0555077i
$381$	3756.87	+	6507.09i	0.505171	+	0.874983i
$382$		−	6684.69i		−	0.895336i
$383$	−331.675	+	191.493i	−0.0442501	+	0.0255478i	−0.521962	−	0.852969i	$-0.674800\pi$
$383$	−331.675	+	191.493i	−0.0442501	+	0.0255478i	0.477712	+	0.878517i	$0.341466\pi$
$384$	−8906.01	+	5141.89i	−1.18355	+	0.683323i
$385$		−	1477.19i		−	0.195544i
$386$	368.776	+	638.739i	0.0486275	+	0.0842253i
$387$	−3663.27	+	6344.97i	−0.481175	+	0.833419i
$388$	7278.94	+	4202.50i	0.952403	+	0.549870i
$389$	−8588.34			−1.11940			−0.559699	−	0.828696i	$-0.689083\pi$
$389$	−8588.34			−1.11940			−0.559699	+	0.828696i	$0.689083\pi$
$390$		0			0
$391$	5467.56			0.707178
$392$	−7255.15	−	4188.76i	−0.934796	−	0.539705i
$393$	1221.93	−	2116.45i	0.156841	−	0.271656i
$394$	3501.29	+	6064.41i	0.447696	+	0.775433i
$395$			2088.72i			0.266063i
$396$	−3559.38	+	2055.01i	−0.451681	+	0.260778i
$397$	6269.30	−	3619.58i	0.792562	−	0.457586i	−0.0483020	−	0.998833i	$-0.515381\pi$
$397$	6269.30	−	3619.58i	0.792562	−	0.457586i	0.840864	+	0.541247i	$0.182048\pi$
$398$		−	571.904i		−	0.0720275i
$399$	2828.71	+	4899.46i	0.354918	+	0.614737i
$400$	−641.505	+	1111.12i	−0.0801882	+	0.138890i
$401$	3697.60	+	2134.81i	0.460472	+	0.265854i	0.712243	−	0.701933i	$-0.247679\pi$
$401$	3697.60	+	2134.81i	0.460472	+	0.265854i	−0.251770	+	0.967787i	$0.581013\pi$
$402$	6947.32			0.861942
$403$		0			0
$404$	−1870.12			−0.230302
$405$	951.185	+	549.167i	0.116703	+	0.0673786i
$406$	4666.30	−	8082.27i	0.570405	−	0.987971i
$407$	718.751	+	1244.91i	0.0875360	+	0.151617i
$408$			8192.78i			0.994125i
$409$	11745.5	−	6781.26i	1.41999	−	0.819834i	0.423696	−	0.905805i	$-0.360733\pi$
$409$	11745.5	−	6781.26i	1.41999	−	0.819834i	0.996298	+	0.0859711i	$0.0273993\pi$
$410$	772.337	−	445.909i	0.0930317	−	0.0537119i
$411$			22939.9i			2.75315i
$412$	897.390	+	1554.33i	0.107309	+	0.185864i
$413$	5973.96	−	10347.2i	0.711767	−	1.23282i
$414$	−8037.54	−	4640.47i	−0.954163	−	0.550886i
$415$	4823.06			0.570494
$416$		0			0
$417$	−17357.5			−2.03837
$418$	494.701	+	285.616i	0.0578867	+	0.0334209i
$419$	7288.44	−	12624.0i	0.849794	−	1.47189i	−0.0315973	−	0.999501i	$-0.510059\pi$
$419$	7288.44	−	12624.0i	0.849794	−	1.47189i	0.881392	−	0.472386i	$-0.156607\pi$
$420$	−2337.55	−	4048.76i	−0.271573	−	0.470379i
$421$			15848.4i			1.83469i	0.398099	+	0.917343i	$0.369670\pi$
$421$			15848.4i			1.83469i	−0.398099	+	0.917343i	$0.630330\pi$
$422$	−2870.42	+	1657.24i	−0.331114	+	0.191169i
$423$	−19581.8	+	11305.6i	−2.25083	+	1.29952i
$424$			2559.18i			0.293124i
$425$	2501.62	+	4332.94i	0.285521	+	0.494537i
$426$	−2784.99	+	4823.75i	−0.316745	+	0.548618i
$427$	3231.62	+	1865.77i	0.366250	+	0.211455i
$428$	7978.70			0.901087
$429$		0			0
$430$	−841.474			−0.0943709
$431$	−9261.90	−	5347.36i	−1.03510	−	0.597618i	−0.116662	−	0.993172i	$-0.537219\pi$
$431$	−9261.90	−	5347.36i	−1.03510	−	0.597618i	−0.918443	+	0.395554i	$0.870553\pi$
$432$	−1062.67	+	1840.61i	−0.118352	+	0.204991i
$433$	−8039.50	−	13924.8i	−0.892272	−	1.54546i	−0.837145	−	0.546981i	$-0.815777\pi$
$433$	−8039.50	−	13924.8i	−0.892272	−	1.54546i	−0.0551273	−	0.998479i	$-0.517556\pi$
$434$			1149.78i			0.127168i
$435$	5890.69	−	3400.99i	0.649280	−	0.374862i
$436$	4089.87	−	2361.29i	0.449241	−	0.259370i
$437$		−	2942.01i		−	0.322049i
$438$	−2088.50	−	3617.40i	−0.227837	−	0.394625i
$439$	3017.90	−	5227.16i	0.328101	−	0.568288i	−0.654034	−	0.756465i	$-0.726925\pi$
$439$	3017.90	−	5227.16i	0.328101	−	0.568288i	0.982135	+	0.188177i	$0.0602579\pi$
$440$	−996.849	−	575.531i	−0.108007	−	0.0623577i
$441$	−19156.0			−2.06845
$442$		0			0
$443$	10201.3			1.09409			0.547043	−	0.837105i	$-0.315753\pi$
$443$	10201.3			1.09409			0.547043	+	0.837105i	$0.315753\pi$
$444$	3939.98	+	2274.75i	0.421134	+	0.243142i
$445$	783.332	−	1356.77i	0.0834461	−	0.144533i
$446$	4627.21	+	8014.56i	0.491266	+	0.850897i
$447$		−	15224.0i		−	1.61090i
$448$	−4731.26	+	2731.59i	−0.498953	+	0.288071i
$449$	5042.47	−	2911.27i	0.529997	−	0.305994i	−0.211018	−	0.977482i	$-0.567678\pi$
$449$	5042.47	−	2911.27i	0.529997	−	0.305994i	0.741015	+	0.671488i	$0.234345\pi$
$450$		−	8492.78i		−	0.889675i
$451$	1223.61	+	2119.36i	0.127755	+	0.221279i
$452$	−4489.64	+	7776.28i	−0.467201	+	0.809216i
$453$	−21018.9	−	12135.3i	−2.18003	−	1.25864i
$454$	−1398.62			−0.144583
$455$		0			0
$456$	4408.40			0.452724
$457$	−4002.42	−	2310.80i	−0.409684	−	0.236531i	0.280970	−	0.959717i	$-0.409344\pi$
$457$	−4002.42	−	2310.80i	−0.409684	−	0.236531i	−0.690654	+	0.723186i	$0.742677\pi$
$458$	490.106	−	848.889i	0.0500026	−	0.0866070i
$459$	4144.02	+	7177.65i	0.421408	+	0.729900i
$460$			2431.18i			0.246422i
$461$	4440.78	−	2563.88i	0.448650	−	0.259028i	−0.258610	−	0.965982i	$-0.583264\pi$
$461$	4440.78	−	2563.88i	0.448650	−	0.259028i	0.707260	+	0.706954i	$0.249931\pi$
$462$	−4871.20	+	2812.39i	−0.490539	+	0.283213i
$463$		−	6486.27i		−	0.651064i	−0.945531	−	0.325532i	$-0.894457\pi$
$463$		−	6486.27i		−	0.651064i	0.945531	−	0.325532i	$-0.105543\pi$
$464$	1256.04	+	2175.53i	0.125669	+	0.217665i
$465$	−419.002	+	725.733i	−0.0417866	+	0.0723764i
$466$	−3115.43	−	1798.69i	−0.309698	−	0.178804i
$467$	−12978.0			−1.28598			−0.642990	−	0.765875i	$-0.722306\pi$
$467$	−12978.0			−1.28598			−0.642990	+	0.765875i	$0.722306\pi$
$468$		0			0
$469$	−13922.3			−1.37073
$470$	−2249.03	−	1298.48i	−0.220723	−	0.127435i
$471$	−14090.3	+	24405.1i	−1.37844	+	2.38754i
$472$	−4655.07	−	8062.81i	−0.453955	−	0.786273i
$473$		−	2309.08i		−	0.224464i
$474$	6887.79	−	3976.67i	0.667440	−	0.385347i
$475$	2331.48	−	1346.08i	0.225212	−	0.130026i
$476$		−	6733.04i		−	0.648337i
$477$	2925.89	+	5067.80i	0.280854	+	0.486454i
$478$	−425.228	+	736.516i	−0.0406893	+	0.0704759i
$479$	−5030.71	−	2904.48i	−0.479873	−	0.277055i	0.240491	−	0.970651i	$-0.422692\pi$
$479$	−5030.71	−	2904.48i	−0.479873	−	0.277055i	−0.720363	+	0.693597i	$0.756025\pi$
$480$	−5791.95			−0.550761
$481$		0			0
$482$	−8473.14			−0.800707
$483$	25088.1	+	14484.6i	2.36345	+	1.36454i
$484$	−3053.54	+	5288.89i	−0.286772	+	0.496703i
$485$	2691.23	+	4661.35i	0.251964	+	0.436414i
$486$			3662.20i			0.341812i
$487$	−4665.40	+	2693.57i	−0.434106	+	0.250631i	−0.701094	−	0.713069i	$-0.747305\pi$
$487$	−4665.40	+	2693.57i	−0.434106	+	0.250631i	0.266989	+	0.963700i	$0.413971\pi$
$488$	2518.16	−	1453.86i	0.233589	−	0.134863i
$489$		−	28498.4i		−	2.63547i
$490$	−1100.06	−	1905.36i	−0.101419	−	0.175664i
$491$	7629.53	−	13214.7i	0.701255	−	1.21461i	−0.266772	−	0.963760i	$-0.585957\pi$
$491$	7629.53	−	13214.7i	0.701255	−	1.21461i	0.968026	−	0.250849i	$-0.0807097\pi$
$492$	6707.48	+	3872.57i	0.614628	+	0.354855i
$493$	9796.16			0.894922
$494$		0			0
$495$	−2632.01			−0.238990
$496$	−268.025	−	154.744i	−0.0242635	−	0.0140085i
$497$	5581.07	−	9666.69i	0.503712	−	0.872456i
$498$	−9182.55	−	15904.6i	−0.826264	−	1.43113i
$499$			1856.04i			0.166509i	0.996528	+	0.0832544i	$0.0265314\pi$
$499$			1856.04i			0.166509i	−0.996528	+	0.0832544i	$0.973469\pi$
$500$	−4070.91	+	2350.34i	−0.364114	+	0.210221i
$501$	23515.0	−	13576.4i	2.09695	−	1.21067i
$502$		−	8153.20i		−	0.724891i
$503$	−524.732	−	908.862i	−0.0465142	−	0.0805649i	0.841831	−	0.539741i	$-0.181478\pi$
$503$	−524.732	−	908.862i	−0.0465142	−	0.0805649i	−0.888345	+	0.459176i	$0.848145\pi$
$504$	−13934.6	+	24135.4i	−1.23154	+	2.13308i
$505$	−1037.16	−	598.803i	−0.0913919	−	0.0527651i
$506$	2925.04			0.256984
$507$		0			0
$508$	−4811.71			−0.420246
$509$	477.272	+	275.553i	0.0415613	+	0.0239954i	0.520637	−	0.853778i	$-0.325695\pi$
$509$	477.272	+	275.553i	0.0415613	+	0.0239954i	−0.479075	+	0.877774i	$0.659028\pi$
$510$	−1075.80	+	1863.34i	−0.0934063	+	0.161784i
$511$	4185.32	+	7249.19i	0.362324	+	0.627564i
$512$		−	4074.36i		−	0.351686i
$513$	3862.18	−	2229.83i	0.332396	−	0.191909i
$514$	890.121	−	513.911i	0.0763843	−	0.0441005i
$515$			1149.36i			0.0983431i
$516$	−3653.96	−	6328.84i	−0.311738	−	0.539945i
$517$	3563.13	−	6171.52i	0.303107	−	0.524997i
$518$	3461.83	+	1998.69i	0.293637	+	0.169531i
$519$	−847.361			−0.0716667
$520$		0			0
$521$	−8995.30			−0.756413			−0.378206	−	0.925721i	$-0.623459\pi$
$521$	−8995.30			−0.756413			−0.378206	+	0.925721i	$0.623459\pi$
$522$	−14400.7	−	8314.27i	−1.20748	−	0.697137i
$523$	−1331.96	+	2307.02i	−0.111362	+	0.192885i	−0.916320	−	0.400448i	$-0.868855\pi$
$523$	−1331.96	+	2307.02i	−0.111362	+	0.192885i	0.804958	+	0.593332i	$0.202188\pi$
$524$	782.512	+	1355.35i	0.0652370	+	0.112994i
$525$			26509.1i			2.20372i
$526$	−4390.32	+	2534.76i	−0.363930	+	0.210115i
$527$	−1045.19	+	603.443i	−0.0863935	+	0.0498793i
$528$		−	1514.04i		−	0.124792i
$529$	−1448.89	−	2509.54i	−0.119083	−	0.206258i
$530$	−336.047	+	582.051i	−0.0275414	+	0.0477032i
$531$	−18436.3	−	10644.2i	−1.50672	−	0.869906i
$532$	−3622.94			−0.295253
$533$		0			0
$534$	−5965.49			−0.483431
$535$	4424.93	+	2554.73i	0.357582	+	0.206450i
$536$	−5424.30	+	9395.16i	−0.437116	+	0.757107i
$537$	−150.744	−	261.096i	−0.0121137	−	0.0209816i
$538$			4037.86i			0.323577i
$539$	5228.46	−	3018.65i	0.417821	−	0.241229i
$540$	−3191.57	+	1842.66i	−0.254340	+	0.146843i
$541$			6169.23i			0.490270i	0.969489	+	0.245135i	$0.0788322\pi$
$541$			6169.23i			0.490270i	−0.969489	+	0.245135i	$0.921168\pi$
$542$	772.135	+	1337.38i	0.0611920	+	0.105988i
$543$	−5338.23	+	9246.08i	−0.421888	+	0.730732i
$544$	−7223.97	−	4170.76i	−0.569348	−	0.328713i
$545$	3024.28			0.237699
$546$		0			0
$547$	5140.42			0.401807			0.200904	−	0.979611i	$-0.435612\pi$
$547$	5140.42			0.401807			0.200904	+	0.979611i	$0.435612\pi$
$548$	−12722.3	−	7345.24i	−0.991735	−	0.572578i
$549$	3324.38	−	5757.99i	0.258435	−	0.447623i
$550$	1338.32	+	2318.03i	0.103756	+	0.179711i
$551$		−	5271.15i		−	0.407547i
$552$	19549.3	−	11286.8i	1.50738	−	0.870285i
$553$	−13803.0	+	7969.16i	−1.06142	+	0.612809i
$554$			12714.8i			0.975090i
$555$	1456.72	+	2523.12i	0.111413	+	0.192974i
$556$	5557.76	−	9626.32i	0.423923	−	0.734257i
$557$	2406.30	+	1389.28i	0.183049	+	0.105683i	0.588724	−	0.808334i	$-0.299630\pi$
$557$	2406.30	+	1389.28i	0.183049	+	0.105683i	−0.405675	+	0.914017i	$0.632964\pi$
$558$	2048.64			0.155422
$559$		0			0
$560$	1105.69			0.0834356
$561$	−5113.16	−	2952.08i	−0.384809	−	0.222170i
$562$	1197.87	−	2074.78i	0.0899097	−	0.155728i
$563$	2453.07	+	4248.85i	0.183632	+	0.318059i	0.943115	−	0.332468i	$-0.107881\pi$
$563$	2453.07	+	4248.85i	0.183632	+	0.318059i	−0.759483	+	0.650527i	$0.774548\pi$
$564$		−	22553.7i		−	1.68383i
$565$	−4979.84	+	2875.11i	−0.370802	+	0.214083i
$566$	−9419.08	+	5438.11i	−0.699494	+	0.403853i
$567$			8381.04i			0.620759i
$568$	−4348.91	−	7532.54i	−0.321261	−	0.556440i
$569$	−4681.58	+	8108.73i	−0.344924	+	0.597426i	−0.985340	−	0.170602i	$-0.945429\pi$
$569$	−4681.58	+	8108.73i	−0.344924	+	0.597426i	0.640416	+	0.768028i	$0.278762\pi$
$570$	1002.63	+	578.870i	0.0736766	+	0.0425372i
$571$	−7199.32			−0.527640			−0.263820	−	0.964572i	$-0.584982\pi$
$571$	−7199.32			−0.527640			−0.263820	+	0.964572i	$0.584982\pi$
$572$		0			0
$573$	37177.3			2.71048
$574$	5893.46	+	3402.59i	0.428551	+	0.247424i
$575$	6892.72	−	11938.5i	0.499906	−	0.865863i
$576$	4867.07	+	8430.01i	0.352074	+	0.609810i
$577$		−	11449.6i		−	0.826086i	−0.910711	−	0.413043i	$-0.864466\pi$
$577$		−	11449.6i		−	0.826086i	0.910711	−	0.413043i	$-0.135534\pi$
$578$	3960.50	−	2286.60i	0.285009	−	0.164550i
$579$	−3552.38	+	2050.97i	−0.254978	+	0.147211i
$580$			4355.91i			0.311843i
$581$	18401.6	+	31872.6i	1.31399	+	2.27590i
$582$	10247.6	−	17749.3i	0.729855	−	1.26415i
$583$	−1597.20	−	922.142i	−0.113463	−	0.0655081i
$584$	6522.62			0.462171
$585$		0			0
$586$	−999.439			−0.0704547
$587$	4710.65	+	2719.70i	0.331226	+	0.191233i	0.656385	−	0.754426i	$-0.272085\pi$
$587$	4710.65	+	2719.70i	0.331226	+	0.191233i	−0.325160	+	0.945659i	$0.605418\pi$
$588$	9553.63	−	16547.4i	0.670042	−	1.16055i
$589$	324.703	+	562.402i	0.0227150	+	0.0393436i
$590$		−	2445.04i		−	0.170611i
$591$	−33727.5	+	19472.6i	−2.34749	+	1.35532i
$592$	−931.831	+	537.993i	−0.0646926	+	0.0373503i
$593$			28405.8i			1.96709i	0.180651	+	0.983547i	$0.442180\pi$
$593$			28405.8i			1.96709i	−0.180651	+	0.983547i	$0.557820\pi$
$594$	2216.97	+	3839.90i	0.153137	+	0.265241i
$595$	2155.88	−	3734.10i	0.148542	−	0.257282i
$596$	8443.14	+	4874.65i	0.580276	+	0.335022i
$597$	3180.67			0.218051
$598$		0			0
$599$	−10482.3			−0.715020			−0.357510	−	0.933909i	$-0.616374\pi$
$599$	−10482.3			−0.715020			−0.357510	+	0.933909i	$0.616374\pi$
$600$	17889.1	+	10328.3i	1.21720	+	0.702750i
$601$	−1599.77	+	2770.88i	−0.108579	+	0.188064i	−0.915195	−	0.403012i	$-0.867963\pi$
$601$	−1599.77	+	2770.88i	−0.108579	+	0.188064i	0.806616	+	0.591076i	$0.201297\pi$
$602$	−3210.51	−	5560.77i	−0.217360	−	0.376479i
$603$			24806.3i			1.67527i
$604$	13460.3	−	7771.28i	0.906772	−	0.523525i
$605$	−3386.95	+	1955.45i	−0.227602	+	0.131406i
$606$			4560.20i			0.305686i
$607$	−5671.40	−	9823.15i	−0.379234	−	0.656853i	0.611717	−	0.791077i	$-0.290479\pi$
$607$	−5671.40	−	9823.15i	−0.379234	−	0.656853i	−0.990951	+	0.134224i	$0.957146\pi$
$608$	−2244.22	+	3887.10i	−0.149696	+	0.259281i
$609$	44950.0	+	25951.9i	2.99091	+	1.72680i
$610$	763.629			0.0506859
$611$		0			0
$612$	−11996.7			−0.792384
$613$	−12458.1	−	7192.70i	−0.820846	−	0.473916i	0.0298622	−	0.999554i	$-0.490493\pi$
$613$	−12458.1	−	7192.70i	−0.820846	−	0.473916i	−0.850708	+	0.525638i	$0.823826\pi$
$614$	−78.3944	+	135.783i	−0.00515267	+	0.00892469i
$615$	2479.95	+	4295.39i	0.162603	+	0.281637i
$616$		−	8783.39i		−	0.574502i
$617$	19101.7	−	11028.4i	1.24636	−	0.719588i	0.275981	−	0.961163i	$-0.410997\pi$
$617$	19101.7	−	11028.4i	1.24636	−	0.719588i	0.970382	+	0.241575i	$0.0776640\pi$
$618$	3790.14	−	2188.24i	0.246702	−	0.142433i
$619$		−	13621.4i		−	0.884477i	−0.896898	−	0.442238i	$-0.854185\pi$
$619$		−	13621.4i		−	0.884477i	0.896898	−	0.442238i	$-0.145815\pi$
$620$	−268.324	−	464.751i	−0.0173809	−	0.0301046i
$621$	11418.0	−	19776.6i	0.737824	−	1.27795i
$622$	5245.63	+	3028.57i	0.338152	+	0.195232i
$623$	11954.7			0.768789
$624$		0			0
$625$	11029.2			0.705866
$626$	−5124.57	−	2958.67i	−0.327187	−	0.188901i
$627$	−1588.47	+	2751.31i	−0.101176	+	0.175242i
$628$	−9023.27	−	15628.8i	−0.573356	−	0.993082i
$629$			4195.92i			0.265982i
$630$	−6338.46	+	3659.51i	−0.400842	+	0.231426i
$631$	16227.1	−	9368.74i	1.02376	−	0.591068i	0.108569	−	0.994089i	$-0.465373\pi$
$631$	16227.1	−	9368.74i	1.02376	−	0.591068i	0.915191	+	0.403021i	$0.132040\pi$
$632$			12419.6i			0.781683i
$633$	−9216.83	−	15964.0i	−0.578730	−	1.00239i
$634$	−3440.73	+	5959.52i	−0.215534	+	0.373317i
$635$	−2668.54	−	1540.68i	−0.166768	−	0.0962836i
$636$	−5836.91			−0.363913
$637$		0			0
$638$	5240.75			0.325209
$639$	−17223.8	−	9944.18i	−1.06630	−	0.615627i
$640$	2108.67	−	3652.33i	0.130239	−	0.225580i
$641$	14899.4	+	25806.5i	0.918081	+	1.59016i	0.802327	+	0.596884i	$0.203595\pi$
$641$	14899.4	+	25806.5i	0.918081	+	1.59016i	0.115753	+	0.993278i	$0.463072\pi$
$642$		−	19455.6i		−	1.19603i
$643$	−19904.3	+	11491.8i	−1.22076	+	0.704807i	−0.965080	−	0.261955i	$-0.915633\pi$
$643$	−19904.3	+	11491.8i	−1.22076	+	0.704807i	−0.255681	+	0.966761i	$0.582300\pi$
$644$	−16066.1	+	9275.77i	−0.983064	+	0.567573i
$645$		−	4679.90i		−	0.285692i
$646$	833.684	+	1443.98i	0.0507753	+	0.0879455i
$647$	−12452.7	+	21568.7i	−0.756672	+	1.31059i	0.187866	+	0.982195i	$0.439843\pi$
$647$	−12452.7	+	21568.7i	−0.756672	+	1.31059i	−0.944539	+	0.328400i	$0.893491\pi$
$648$	5655.77	+	3265.36i	0.342870	+	0.197956i
$649$	6709.39			0.405804
$650$		0			0
$651$	−6394.54			−0.384980
$652$	15805.0	+	9125.03i	0.949344	+	0.548104i
$653$	−5038.92	+	8727.67i	−0.301973	+	0.523033i	−0.976583	−	0.215142i	$-0.930979\pi$
$653$	−5038.92	+	8727.67i	−0.301973	+	0.523033i	0.674610	+	0.738175i	$0.264312\pi$
$654$	−5757.87	−	9972.93i	−0.344267	−	0.596288i
$655$			1002.22i			0.0597864i
$656$	−1586.36	+	915.886i	−0.0944162	+	0.0545112i
$657$	12916.4	−	7457.28i	0.766996	−	0.442825i
$658$		−	19816.5i		−	1.17406i
$659$	−6167.30	−	10682.1i	−0.364558	−	0.631433i	0.624147	−	0.781307i	$-0.285447\pi$
$659$	−6167.30	−	10682.1i	−0.364558	−	0.631433i	−0.988705	+	0.149874i	$0.952113\pi$
$660$	1312.66	−	2273.59i	0.0774169	−	0.134090i
$661$	−11041.1	−	6374.56i	−0.649694	−	0.375101i	0.138645	−	0.990342i	$-0.455725\pi$
$661$	−11041.1	−	6374.56i	−0.649694	−	0.375101i	−0.788339	+	0.615241i	$0.789059\pi$
$662$	−6451.54			−0.378771
$663$		0			0
$664$	28678.1			1.67609
$665$	−2009.26	−	1160.04i	−0.117166	−	0.0676460i
$666$	3561.20	−	6168.18i	0.207198	−	0.358877i
$667$	−13495.7	−	23375.2i	−0.783440	−	1.35696i
$668$			17388.3i			1.00715i
$669$	−44573.4	+	25734.5i	−2.57594	+	1.48722i
$670$	−2467.37	+	1424.54i	−0.142273	+	0.0821413i
$671$			2095.46i			0.120558i
$672$	−22098.3	−	38275.3i	−1.26854	−	2.19718i
$673$	−6809.12	+	11793.7i	−0.390004	+	0.675506i	−0.992450	−	0.122654i	$-0.960860\pi$
$673$	−6809.12	+	11793.7i	−0.390004	+	0.675506i	0.602446	+	0.798160i	$0.294193\pi$
$674$	6167.80	+	3560.98i	0.352485	+	0.203507i
$675$	20896.7			1.19158
$676$		0			0
$677$	9655.67			0.548150			0.274075	−	0.961708i	$-0.411628\pi$
$677$	9655.67			0.548150			0.274075	+	0.961708i	$0.411628\pi$
$678$	18962.0	+	10947.7i	1.07409	+	0.620126i
$679$	−20535.9	+	35569.3i	−1.16067	+	2.01034i
$680$	−1679.92	−	2909.70i	−0.0947381	−	0.164091i
$681$		−	7778.51i		−	0.437699i
$682$	−559.158	+	322.830i	−0.0313948	+	0.0181258i
$683$	−14130.7	+	8158.38i	−0.791650	+	0.457060i	−0.840543	−	0.541744i	$-0.817764\pi$
$683$	−14130.7	+	8158.38i	−0.791650	+	0.457060i	0.0488929	+	0.998804i	$0.484431\pi$
$684$			6455.25i			0.360852i
$685$	−4703.80	−	8147.23i	−0.262369	−	0.454437i
$686$	1116.00	−	1932.97i	0.0621123	−	0.107582i
$687$	4721.14	+	2725.75i	0.262188	+	0.151374i
$688$	1728.37			0.0957753
$689$		0			0
$690$	5928.30			0.327082
$691$	−2035.89	−	1175.42i	−0.112082	−	0.0647106i	0.442911	−	0.896566i	$-0.353946\pi$
$691$	−2035.89	−	1175.42i	−0.112082	−	0.0647106i	−0.554993	+	0.831855i	$0.687279\pi$
$692$	271.320	−	469.940i	0.0149047	−	0.0258157i
$693$	−10042.0	−	17393.3i	−0.550454	−	0.953414i
$694$		−	15723.9i		−	0.860045i
$695$	6164.58	−	3559.12i	0.336455	−	0.194252i
$696$	35026.2	−	20222.4i	1.90756	−	1.10133i
$697$			7143.20i			0.388189i
$698$	4590.44	+	7950.87i	0.248926	+	0.431153i
$699$	10003.5	−	17326.6i	0.541299	−	0.937558i
$700$	−14701.7	−	8488.05i	−0.793819	−	0.458312i
$701$	8076.90			0.435179			0.217589	−	0.976040i	$-0.430181\pi$
$701$	8076.90			0.435179			0.217589	+	0.976040i	$0.430181\pi$
$702$		0			0
$703$	2257.76			0.121128
$704$	−2656.85	−	1533.93i	−0.142236	−	0.0821197i
$705$	7221.55	−	12508.1i	0.385786	−	0.668202i
$706$	7138.30	+	12363.9i	0.380529	+	0.659095i
$707$		−	9138.55i		−	0.486125i
$708$	18389.5	−	10617.2i	0.976156	−	0.563584i
$709$	11799.5	−	6812.44i	0.625021	−	0.360856i	−0.153801	−	0.988102i	$-0.549151\pi$
$709$	11799.5	−	6812.44i	0.625021	−	0.360856i	0.778821	+	0.627246i	$0.215818\pi$
$710$		−	2284.23i		−	0.120741i
$711$	14199.2	+	24593.8i	0.748962	+	1.29724i
$712$	4657.71	−	8067.40i	0.245162	−	0.424633i
$713$	2879.82	+	1662.67i	0.151263	+	0.0873315i
$714$	−16418.2			−0.860553
$715$		0			0
$716$	193.069			0.0100773
$717$	−4096.18	−	2364.93i	−0.213354	−	0.123180i
$718$	−2150.51	+	3724.79i	−0.111778	+	0.193605i
$719$	8117.89	+	14060.6i	0.421066	+	0.729307i	0.996044	−	0.0888616i	$-0.0283229\pi$
$719$	8117.89	+	14060.6i	0.421066	+	0.729307i	−0.574978	+	0.818169i	$0.694990\pi$
$720$		−	1970.09i		−	0.101973i
$721$	−7595.36	+	4385.19i	−0.392325	+	0.226509i
$722$	−8498.75	+	4906.75i	−0.438076	+	0.252923i
$723$		−	47123.8i		−	2.42400i
$724$	−3418.54	−	5921.08i	−0.175482	−	0.303944i
$725$	12349.6	−	21390.1i	0.632623	−	1.09574i
$726$	12896.7	+	7445.91i	0.659285	+	0.380638i
$727$	−24181.2			−1.23361			−0.616803	−	0.787118i	$-0.711572\pi$
$727$	−24181.2			−1.23361			−0.616803	+	0.787118i	$0.711572\pi$
$728$		0			0
$729$	−28693.9			−1.45780
$730$	1483.48	+	856.490i	0.0752139	+	0.0434248i
$731$	3369.98	−	5836.98i	0.170511	−	0.295333i
$732$	3315.93	+	5743.36i	0.167432	+	0.290001i
$733$			3053.70i			0.153876i	0.997036	+	0.0769379i	$0.0245143\pi$
$733$			3053.70i			0.153876i	−0.997036	+	0.0769379i	$0.975486\pi$
$734$	−4111.38	+	2373.71i	−0.206749	+	0.119367i
$735$	10596.7	−	6118.03i	0.531791	−	0.307030i
$736$			22983.4i			1.15106i
$737$	−3909.05	−	6770.67i	−0.195375	−	0.338400i
$738$	6062.63	−	10500.8i	0.302396	−	0.523766i
$739$	−6957.32	−	4016.81i	−0.346318	−	0.199947i	0.316744	−	0.948511i	$-0.397410\pi$
$739$	−6957.32	−	4016.81i	−0.346318	−	0.199947i	−0.663062	+	0.748564i	$0.730744\pi$
$740$	−1865.74			−0.0926836
$741$		0			0
$742$	−5128.54			−0.253739
$743$	13977.3	+	8069.81i	0.690146	+	0.398456i	0.803667	−	0.595080i	$-0.202880\pi$
$743$	13977.3	+	8069.81i	0.690146	+	0.398456i	−0.113521	+	0.993536i	$0.536213\pi$
$744$	−2491.40	+	4315.22i	−0.122767	+	0.212639i
$745$	3121.67	+	5406.89i	0.153515	+	0.265897i
$746$			8408.53i			0.412678i
$747$	56789.6	−	32787.5i	2.78156	−	1.60593i
$748$	3274.41	−	1890.48i	0.160059	−	0.0924102i
$749$			38988.7i			1.90202i
$750$	5731.19	+	9926.71i	0.279031	+	0.483296i
$751$	−9245.56	+	16013.8i	−0.449235	+	0.778097i	−0.998336	−	0.0576584i	$-0.981637\pi$
$751$	−9245.56	+	16013.8i	−0.449235	+	0.778097i	0.549102	+	0.835755i	$0.314970\pi$
$752$	4619.45	+	2667.04i	0.224008	+	0.129331i
$753$	45344.5			2.19448
$754$		0			0
$755$	9953.28			0.479784
$756$	−24353.9	−	14060.7i	−1.17162	−	0.676434i
$757$	−80.3149	+	139.109i	−0.00385613	+	0.00667902i	−0.867947	−	0.496657i	$-0.834561\pi$
$757$	−80.3149	+	139.109i	−0.00385613	+	0.00667902i	0.864091	+	0.503336i	$0.167894\pi$
$758$	2673.59	+	4630.79i	0.128112	+	0.221897i
$759$			16267.7i			0.777973i
$760$	−1565.66	+	903.936i	−0.0747271	+	0.0431437i
$761$	−23208.7	+	13399.5i	−1.10554	+	0.638282i	−0.937670	−	0.347528i	$-0.887021\pi$
$761$	−23208.7	+	13399.5i	−1.10554	+	0.638282i	−0.167867	+	0.985810i	$0.553688\pi$
$762$			11733.1i			0.557803i
$763$	11538.7	+	19985.6i	0.547481	+	0.948264i
$764$	−11903.9	+	20618.2i	−0.563703	+	0.976363i
$765$	−6653.30	−	3841.28i	−0.314445	−	0.181545i
$766$	−598.052			−0.0282095
$767$		0			0
$768$	−30025.1			−1.41073
$769$	4456.41	+	2572.91i	0.208976	+	0.120652i	0.600835	−	0.799373i	$-0.294835\pi$
$769$	4456.41	+	2572.91i	0.208976	+	0.120652i	−0.391860	+	0.920025i	$0.628168\pi$
$770$	1153.35	−	1997.67i	0.0539792	−	0.0934947i
$771$	2858.15	+	4950.45i	0.133507	+	0.231240i
$772$		−	2626.83i		−	0.122463i
$773$	11094.3	−	6405.28i	0.516214	−	0.298036i	−0.219170	−	0.975687i	$-0.570335\pi$
$773$	11094.3	−	6405.28i	0.516214	−	0.298036i	0.735384	+	0.677650i	$0.237002\pi$
$774$	−9908.01	+	5720.39i	−0.460124	+	0.265653i
$775$			3042.94i			0.141039i
$776$	16002.1	+	27716.5i	0.740262	+	1.28217i
$777$	−11115.8	+	19253.1i	−0.513227	+	0.888934i
$778$	−11614.4	−	6705.57i	−0.535214	−	0.309006i
$779$	3843.64			0.176781
$780$		0			0
$781$	6268.13			0.287185
$782$	7394.03	+	4268.94i	0.338120	+	0.195214i
$783$	20457.5	−	35433.4i	0.933705	−	1.61722i
$784$	2259.49	+	3913.55i	0.102929	+	0.178278i
$785$		−	11556.8i		−	0.525452i
$786$	3304.95	−	1908.11i	0.149979	−	0.0865905i
$787$	−24311.9	+	14036.5i	−1.10118	+	0.635764i	−0.936530	−	0.350588i	$-0.885982\pi$
$787$	−24311.9	+	14036.5i	−1.10118	+	0.635764i	−0.164646	+	0.986353i	$0.552648\pi$
$788$		−	24940.0i		−	1.12748i
$789$	−14097.2	−	24417.0i	−0.636087	−	1.10174i
$790$	−1630.82	+	2824.66i	−0.0734455	+	0.127211i
$791$	−37999.6	−	21939.1i	−1.70810	−	0.986173i
$792$	−15650.0			−0.702144
$793$		0			0
$794$	11304.3			0.505259
$795$	−3237.11	−	1868.94i	−0.144413	−	0.0833769i
$796$	−1018.43	+	1763.98i	−0.0453485	+	0.0785459i
$797$	15046.6	+	26061.4i	0.668729	+	1.15827i	0.978260	+	0.207383i	$0.0664945\pi$
$797$	15046.6	+	26061.4i	0.668729	+	1.15827i	−0.309531	+	0.950889i	$0.600172\pi$
$798$			8834.35i			0.391896i
$799$	18014.1	−	10400.4i	0.797612	−	0.460501i
$800$	−18213.9	+	10515.8i	−0.804947	+	0.464737i
$801$		−	21300.6i		−	0.939598i
$802$	3333.62	+	5774.00i	0.146776	+	0.254223i
$803$	−2350.28	+	4070.80i	−0.103287	+	0.178899i
$804$	−21428.3	−	12371.6i	−0.939946	−	0.542678i
$805$	−11880.2			−0.520151
$806$		0			0
$807$	−22456.8			−0.979575
$808$	−6166.96	−	3560.50i	−0.268506	−	0.155022i
$809$	12168.6	−	21076.6i	0.528831	−	0.915961i	−0.470604	−	0.882344i	$-0.655964\pi$
$809$	12168.6	−	21076.6i	0.528831	−	0.915961i	0.999435	−	0.0336170i	$-0.0107026\pi$
$810$	857.553	+	1485.33i	0.0371992	+	0.0644309i
$811$			19078.7i			0.826071i	0.910715	+	0.413035i	$0.135531\pi$
$811$			19078.7i			0.826071i	−0.910715	+	0.413035i	$0.864469\pi$
$812$	−28785.4	+	16619.3i	−1.24405	+	0.718254i
$813$	−7437.89	+	4294.27i	−0.320859	+	0.185248i
$814$			2244.74i			0.0966559i
$815$	5843.56	+	10121.3i	0.251155	+	0.435013i
$816$	2209.67	−	3827.25i	0.0947963	−	0.164192i
$817$	−3140.78	−	1813.33i	−0.134495	−	0.0776505i
$818$	21178.6			0.905248
$819$		0			0
$820$	−3176.26			−0.135268
$821$	−1744.10	−	1006.96i	−0.0741408	−	0.0428052i	0.462471	−	0.886634i	$-0.346963\pi$
$821$	−1744.10	−	1006.96i	−0.0741408	−	0.0428052i	−0.536612	+	0.843829i	$0.680296\pi$
$822$	−17911.0	+	31022.7i	−0.759996	+	1.31635i
$823$	−3846.05	−	6661.55i	−0.162898	−	0.282147i	0.773009	−	0.634395i	$-0.218751\pi$
$823$	−3846.05	−	6661.55i	−0.162898	−	0.282147i	−0.935907	+	0.352248i	$0.885417\pi$
$824$			6834.10i			0.288929i
$825$	−12891.9	+	7443.12i	−0.544045	+	0.314105i
$826$	16157.7	−	9328.66i	0.680628	−	0.392961i
$827$			4762.76i			0.200263i	0.994974	+	0.100131i	$0.0319263\pi$
$827$			4762.76i			0.200263i	−0.994974	+	0.100131i	$0.968074\pi$
$828$	16527.3	+	28626.1i	0.693675	+	1.20148i
$829$	9988.83	−	17301.2i	0.418488	−	0.724842i	−0.577300	−	0.816532i	$-0.695894\pi$
$829$	9988.83	−	17301.2i	0.418488	−	0.724842i	0.995788	+	0.0916901i	$0.0292269\pi$
$830$	6522.44	+	3765.73i	0.272768	+	0.157483i
$831$	−70714.0			−2.95191
$832$		0			0
$833$	17622.3			0.732984
$834$	−23473.3	−	13552.3i	−0.974596	−	0.562683i
$835$	−5567.63	+	9643.43i	−0.230750	+	0.399670i
$836$	−1017.24	−	1761.91i	−0.0420836	−	0.0728909i
$837$			5040.72i			0.208164i
$838$	19713.0	−	11381.3i	0.812617	−	0.469165i
$839$	26514.0	−	15307.9i	1.09102	−	0.629901i	0.157172	−	0.987571i	$-0.449762\pi$
$839$	26514.0	−	15307.9i	1.09102	−	0.629901i	0.933848	+	0.357670i	$0.116429\pi$
$840$		−	17801.7i		−	0.731210i
$841$	−11985.5	−	20759.5i	−0.491431	−	0.851183i
$842$	−12374.0	+	21432.5i	−0.506458	+	0.877211i
$843$	11539.0	+	6662.04i	0.471440	+	0.272186i
$844$	11804.7			0.481439
$845$		0			0
$846$	−35308.5			−1.43491
$847$	−25844.7	−	14921.4i	−1.04845	−	0.605321i
$848$	690.233	−	1195.52i	0.0279513	−	0.0484131i
$849$	−30244.3	−	52384.7i	−1.22259	−	2.11760i
$850$			7812.83i			0.315268i
$851$	10012.1	−	5780.51i	0.403304	−	0.232848i
$852$	17180.0	−	9918.89i	0.690819	−	0.398845i
$853$		−	5660.88i		−	0.227227i	−0.993525	−	0.113614i	$-0.963757\pi$
$853$		−	5660.88i		−	0.227227i	0.993525	−	0.113614i	$-0.0362426\pi$
$854$	2913.50	+	5046.34i	0.116742	+	0.202204i
$855$	−2066.93	+	3580.03i	−0.0826755	+	0.143198i
$856$	26310.7	+	15190.5i	1.05056	+	0.606543i
$857$	−41346.1			−1.64802			−0.824012	−	0.566572i	$-0.808269\pi$
$857$	−41346.1			−1.64802			−0.824012	+	0.566572i	$0.808269\pi$
$858$		0			0
$859$	−34810.5			−1.38268			−0.691339	−	0.722530i	$-0.742979\pi$
$859$	−34810.5			−1.38268			−0.691339	+	0.722530i	$0.742979\pi$
$860$	2595.44	+	1498.48i	0.102911	+	0.0594159i
$861$	−18923.7	+	32776.8i	−0.749033	+	1.29736i
$862$	−8350.19	−	14462.9i	−0.329940	−	0.571473i
$863$		−	8360.51i		−	0.329774i	−0.986312	−	0.164887i	$-0.947274\pi$
$863$		−	8360.51i		−	0.329774i	0.986312	−	0.164887i	$-0.0527260\pi$
$864$	−30171.9	+	17419.7i	−1.18804	+	0.685916i
$865$	300.944	−	173.750i	0.0118294	−	0.00682969i
$866$		−	25108.2i		−	0.985233i
$867$	12717.0	+	22026.5i	0.498146	+	0.862815i
$868$	2047.49	−	3546.36i	0.0800651	−	0.138677i
$869$	−7751.11	−	4475.11i	−0.302576	−	0.174692i
$870$	10621.6			0.413917
$871$		0			0
$872$	17982.4			0.698352
$873$	63376.3	+	36590.3i	2.45700	+	1.41855i
$874$	2297.05	−	3978.61i	0.0889003	−	0.153980i
$875$	−11485.2	−	19892.9i	−0.443737	−	0.768576i
$876$			14876.6i			0.573784i
$877$	−35142.7	+	20289.7i	−1.35312	+	0.781223i	−0.988685	−	0.150006i	$-0.952071\pi$
$877$	−35142.7	+	20289.7i	−1.35312	+	0.781223i	−0.364434	+	0.931229i	$0.618737\pi$
$878$	8162.48	−	4712.61i	0.313748	−	0.181142i
$879$		−	5558.43i		−	0.213289i
$880$	310.452	+	537.718i	0.0118924	+	0.0205983i
$881$	5222.62	−	9045.84i	0.199721	−	0.345927i	−0.748717	−	0.662890i	$-0.769330\pi$
$881$	5222.62	−	9045.84i	0.199721	−	0.345927i	0.948438	+	0.316963i	$0.102663\pi$
$882$	−25905.4	−	14956.5i	−0.988981	−	0.570989i
$883$	−18227.6			−0.694685			−0.347343	−	0.937738i	$-0.612916\pi$
$883$	−18227.6			−0.694685			−0.347343	+	0.937738i	$0.612916\pi$
$884$		0			0
$885$	13598.2			0.516496
$886$	13795.7	+	7964.96i	0.523111	+	0.302018i
$887$	11758.8	−	20366.9i	0.445122	−	0.770974i	−0.552938	−	0.833222i	$-0.686494\pi$
$887$	11758.8	−	20366.9i	0.445122	−	0.770974i	0.998061	+	0.0622477i	$0.0198269\pi$
$888$	8661.72	+	15002.5i	0.327329	+	0.566950i
$889$		−	23512.9i		−	0.887061i
$890$	2118.67	−	1223.21i	0.0797955	−	0.0460699i
$891$	−4075.86	+	2353.20i	−0.153251	+	0.0884794i
$892$		−	32960.1i		−	1.23720i
$893$	−5596.30	−	9693.07i	−0.209712	−	0.363232i
$894$	11886.6	−	20588.1i	0.444683	−	0.770213i
$895$	107.075	+	61.8196i	0.00399901	+	0.00230883i
$896$	32181.2			1.19989
$897$		0			0
$898$	9092.21			0.337874
$899$	5159.74	+	2978.98i	0.191420	+	0.110517i
$900$	−15123.7	+	26195.1i	−0.560139	+	0.970189i
$901$	−2691.64	−	4662.06i	−0.0995245	−	0.172381i
$902$			3821.47i			0.141065i
$903$	30926.5	−	17855.4i	1.13972	−	0.658019i
$904$	−29610.2	+	17095.5i	−1.08940	+	0.628968i
$905$		−	4378.38i		−	0.160820i
$906$	−18949.9	−	32822.1i	−0.694886	−	1.20358i
$907$	−15282.3	+	26469.7i	−0.559471	+	0.969032i	0.438070	+	0.898941i	$0.355662\pi$
$907$	−15282.3	+	26469.7i	−0.559471	+	0.969032i	−0.997541	+	0.0700908i	$0.977671\pi$
$908$	4313.90	+	2490.63i	0.157667	+	0.0910292i
$909$	−16282.8			−0.594132
$910$		0			0
$911$	−32766.5			−1.19166			−0.595831	−	0.803110i	$-0.703177\pi$
$911$	−32766.5			−1.19166			−0.595831	+	0.803110i	$0.703177\pi$
$912$	−2059.38	−	1188.99i	−0.0747730	−	0.0431702i
$913$	−10333.5	+	17898.1i	−0.374577	+	0.648786i
$914$	−3608.44	−	6249.99i	−0.130587	−	0.226183i
$915$			4246.96i			0.153443i
$916$	−3023.36	+	1745.54i	−0.109055	+	0.0629632i
$917$	−6623.05	+	3823.82i	−0.238509	+	0.137703i
$918$			12942.2i			0.465312i
$919$	−10343.4	−	17915.2i	−0.371269	−	0.643057i	0.618492	−	0.785791i	$-0.287744\pi$
$919$	−10343.4	−	17915.2i	−0.371269	−	0.643057i	−0.989761	+	0.142734i	$0.954411\pi$
$920$	−4628.68	+	8017.10i	−0.165873	+	0.287300i
$921$	−755.165	−	435.995i	−0.0270179	−	0.0155988i
$922$	8007.28			0.286015
$923$		0			0
$924$	20033.0			0.713242
$925$	9161.88	+	5289.62i	0.325666	+	0.188023i
$926$	5064.32	−	8771.67i	0.179724	−	0.311290i
$927$	7813.39	+	13533.2i	0.276834	+	0.479491i
$928$			41179.0i			1.45665i
$929$	39518.6	−	22816.1i	1.39566	−	0.805782i	0.401722	−	0.915762i	$-0.368412\pi$
$929$	39518.6	−	22816.1i	1.39566	−	0.805782i	0.993934	+	0.109979i	$0.0350784\pi$
$930$	−1133.27	+	654.294i	−0.0399585	+	0.0230700i
$931$		−	9482.26i		−	0.333801i
$932$	6406.14	+	11095.8i	0.225150	+	0.389972i
$933$	−16843.5	+	29173.9i	−0.591032	+	1.02370i
$934$	−17550.8	−	10133.0i	−0.614860	−	0.354990i
$935$	2421.28			0.0846892
$936$		0			0
$937$	−17761.4			−0.619253			−0.309626	−	0.950858i	$-0.600204\pi$
$937$	−17761.4			−0.619253			−0.309626	+	0.950858i	$0.600204\pi$
$938$	−18827.7	−	10870.2i	−0.655380	−	0.378384i
$939$	16454.8	−	28500.5i	0.571866	−	0.990501i
$940$	4624.60	+	8010.04i	0.160466	+	0.277935i
$941$		−	44888.3i		−	1.55507i	−0.628841	−	0.777534i	$-0.716470\pi$
$941$		−	44888.3i		−	1.55507i	0.628841	−	0.777534i	$-0.283530\pi$
$942$	−38109.9	+	22002.8i	−1.31814	+	0.761029i
$943$	17044.8	−	9840.83i	0.588606	−	0.339832i
$944$			5022.05i			0.173150i
$945$	−9004.32	−	15595.9i	−0.309958	−	0.536864i
$946$	1802.87	−	3122.67i	0.0619624	−	0.107322i
$947$	13916.6	+	8034.78i	0.477540	+	0.275708i	0.719391	−	0.694606i	$-0.244421\pi$
$947$	13916.6	+	8034.78i	0.477540	+	0.275708i	−0.241851	+	0.970313i	$0.577754\pi$
$948$	−28326.2			−0.970457
$949$		0			0
$950$	4203.96			0.143573
$951$	−33144.2	−	19135.8i	−1.13015	−	0.652493i
$952$	12818.9	−	22203.0i	0.436411	−	0.755887i
$953$	1756.02	+	3041.51i	0.0596883	+	0.103383i	0.894325	−	0.447417i	$-0.147656\pi$
$953$	1756.02	+	3041.51i	0.0596883	+	0.103383i	−0.834637	+	0.550800i	$0.814323\pi$
$954$			9137.88i			0.310115i
$955$	−13203.7	+	7623.14i	−0.447393	+	0.258303i
$956$	2623.14	−	1514.47i	0.0887432	−	0.0512359i
$957$			29146.7i			0.984513i
$958$	−4535.50	−	7855.72i	−0.152960	−	0.264934i
$959$	35893.2	−	62168.9i	1.20861	−	2.09337i
$960$	−5384.75	−	3108.89i	−0.181034	−	0.104520i
$961$	29057.0			0.975361
$962$		0			0
$963$	69468.9			2.32461
$964$	26134.5	+	15088.8i	0.873170	+	0.504125i
$965$	841.097	−	1456.82i	0.0280579	−	0.0485977i
$966$	22618.5	+	39176.4i	0.753352	+	1.30484i
$967$		−	37011.9i		−	1.23084i	−0.788199	−	0.615421i	$-0.788986\pi$
$967$		−	37011.9i		−	1.23084i	0.788199	−	0.615421i	$-0.211014\pi$
$968$	−20138.9	+	11627.2i	−0.668685	+	0.386066i
$969$	−8030.79	+	4636.58i	−0.266240	+	0.153714i
$970$			8405.00i			0.278215i
$971$	−9766.15	−	16915.5i	−0.322771	−	0.559056i	0.658288	−	0.752766i	$-0.271281\pi$
$971$	−9766.15	−	16915.5i	−0.322771	−	0.559056i	−0.981059	+	0.193711i	$0.937948\pi$
$972$	6521.55	−	11295.7i	0.215205	−	0.372745i
$973$	47040.0	+	27158.5i	1.54988	+	0.894823i
$974$	−8412.30			−0.276743
$975$		0			0
$976$	−1568.47			−0.0514402
$977$	−26155.0	−	15100.6i	−0.856473	−	0.494485i	0.00635674	−	0.999980i	$-0.497977\pi$
$977$	−26155.0	−	15100.6i	−0.856473	−	0.494485i	−0.862830	+	0.505495i	$0.831310\pi$
$978$	22250.9	−	38539.7i	0.727511	−	1.26009i
$979$	3356.60	+	5813.81i	0.109579	+	0.189796i
$980$			7835.83i			0.255415i
$981$	35609.7	−	20559.2i	1.15895	−	0.669119i
$982$	20635.5	−	11913.9i	0.670576	−	0.387157i
$983$			38774.9i			1.25812i	0.777359	+	0.629058i	$0.216559\pi$
$983$			38774.9i			1.25812i	−0.777359	+	0.629058i	$0.783441\pi$
$984$	14745.8	+	25540.5i	0.477723	+	0.827441i
$985$	7985.65	−	13831.6i	0.258319	−	0.447421i
$986$	13247.8	+	7648.61i	0.427886	+	0.247040i
$987$	110211.			3.55425
$988$		0			0
$989$	−18570.6			−0.597079
$990$	−3559.38	−	2055.01i	−0.114267	−	0.0659722i
$991$	13864.5	−	24014.0i	0.444419	−	0.769757i	−0.553592	−	0.832788i	$-0.686743\pi$
$991$	13864.5	−	24014.0i	0.444419	−	0.769757i	0.998012	+	0.0630311i	$0.0200767\pi$
$992$	−2536.63	−	4393.57i	−0.0811875	−	0.140621i
$993$		−	35880.6i		−	1.14666i
$994$	15095.1	−	8715.13i	0.481676	−	0.278096i
$995$	−1129.63	+	652.192i	−0.0359916	+	0.0207798i
$996$			65408.2i			2.08086i
$997$	24459.1	+	42364.4i	0.776958	+	1.34573i	0.933687	+	0.358090i	$0.116572\pi$
$997$	24459.1	+	42364.4i	0.776958	+	1.34573i	−0.156729	+	0.987642i	$0.550095\pi$
$998$	−1449.16	+	2510.01i	−0.0459641	+	0.0796122i
$999$	15177.0	+	8762.42i	0.480658	+	0.277508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.f.147.3		8
13.2	odd	12		169.4.c.g.146.2		4
13.3	even	3	inner	169.4.e.f.23.2		8
13.4	even	6		169.4.b.f.168.3		4
13.5	odd	4		169.4.c.g.22.2		4
13.6	odd	12		13.4.a.b.1.1	✓	2
13.7	odd	12		169.4.a.g.1.2		2
13.8	odd	4		169.4.c.j.22.1		4
13.9	even	3		169.4.b.f.168.2		4
13.10	even	6	inner	169.4.e.f.23.3		8
13.11	odd	12		169.4.c.j.146.1		4
13.12	even	2	inner	169.4.e.f.147.2		8
39.20	even	12		1521.4.a.r.1.1		2
39.32	even	12		117.4.a.d.1.2		2
52.19	even	12		208.4.a.h.1.1		2
65.19	odd	12		325.4.a.f.1.2		2
65.32	even	12		325.4.b.e.274.2		4
65.58	even	12		325.4.b.e.274.3		4
91.6	even	12		637.4.a.b.1.1		2
104.19	even	12		832.4.a.z.1.2		2
104.45	odd	12		832.4.a.s.1.1		2
143.32	even	12		1573.4.a.b.1.2		2
156.71	odd	12		1872.4.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.1	✓	2	13.6	odd	12
117.4.a.d.1.2		2	39.32	even	12
169.4.a.g.1.2		2	13.7	odd	12
169.4.b.f.168.2		4	13.9	even	3
169.4.b.f.168.3		4	13.4	even	6
169.4.c.g.22.2		4	13.5	odd	4
169.4.c.g.146.2		4	13.2	odd	12
169.4.c.j.22.1		4	13.8	odd	4
169.4.c.j.146.1		4	13.11	odd	12
169.4.e.f.23.2		8	13.3	even	3	inner
169.4.e.f.23.3		8	13.10	even	6	inner
169.4.e.f.147.2		8	13.12	even	2	inner
169.4.e.f.147.3		8	1.1	even	1	trivial
208.4.a.h.1.1		2	52.19	even	12
325.4.a.f.1.2		2	65.19	odd	12
325.4.b.e.274.2		4	65.32	even	12
325.4.b.e.274.3		4	65.58	even	12
637.4.a.b.1.1		2	91.6	even	12
832.4.a.s.1.1		2	104.45	odd	12
832.4.a.z.1.2		2	104.19	even	12
1521.4.a.r.1.1		2	39.20	even	12
1573.4.a.b.1.2		2	143.32	even	12
1872.4.a.bb.1.2		2	156.71	odd	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35234 + 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} -3.56155i q^{5} +(-11.7446 + 6.78078i) q^{6} +(23.5360 - 13.5885i) q^{7} -21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +O(q^{10})\)	\(q+(1.35234 + 0.780776i) q^{2} +(-4.34233 + 7.52113i) q^{3} +(-2.78078 - 4.81645i) q^{4} -3.56155i q^{5} +(-11.7446 + 6.78078i) q^{6} +(23.5360 - 13.5885i) q^{7} -21.1771i q^{8} +(-24.2116 - 41.9358i) q^{9} +(2.78078 - 4.81645i) q^{10} +(13.2167 + 7.63068i) q^{11} +48.3002 q^{12} +42.4384 q^{14} +(26.7869 + 15.4654i) q^{15} +(-5.71165 + 9.89286i) q^{16} +(22.2732 + 38.5783i) q^{17} -75.6155i q^{18} +(20.7584 - 11.9848i) q^{19} +(-17.1540 + 9.90388i) q^{20} +236.024i q^{21} +(11.9157 + 20.6386i) q^{22} +(61.3693 - 106.295i) q^{23} +(159.276 + 91.9579i) q^{24} +112.315 q^{25} +186.054 q^{27} +(-130.897 - 75.5734i) q^{28} +(109.955 - 190.447i) q^{29} +(24.1501 + 41.8292i) q^{30} +27.0928i q^{31} +(-162.167 + 93.6274i) q^{32} +(-114.783 + 66.2699i) q^{33} +69.5616i q^{34} +(-48.3963 - 83.8249i) q^{35} +(-134.654 + 233.228i) q^{36} +(81.5729 + 47.0961i) q^{37} +37.4299 q^{38} -75.4233 q^{40} +(138.871 + 80.1771i) q^{41} +(-184.282 + 319.185i) q^{42} +(-75.6510 - 131.031i) q^{43} -84.8769i q^{44} +(-149.357 + 86.2311i) q^{45} +(165.985 - 95.8314i) q^{46} -466.948i q^{47} +(-49.6037 - 85.9161i) q^{48} +(197.797 - 342.594i) q^{49} +(151.889 + 87.6932i) q^{50} -386.870 q^{51} -120.847 q^{53} +(251.609 + 145.267i) q^{54} +(27.1771 - 47.0721i) q^{55} +(-287.766 - 498.425i) q^{56} +208.169i q^{57} +(297.393 - 171.700i) q^{58} +(380.733 - 219.816i) q^{59} -172.024i q^{60} +(68.6525 + 118.910i) q^{61} +(-21.1534 + 36.6388i) q^{62} +(-1139.69 - 658.002i) q^{63} -201.022 q^{64} -206.968 q^{66} +(-443.648 - 256.140i) q^{67} +(123.874 - 214.555i) q^{68} +(532.972 + 923.134i) q^{69} -151.147i q^{70} +(355.693 - 205.359i) q^{71} +(-888.078 + 512.732i) q^{72} +308.004i q^{73} +(73.5431 + 127.380i) q^{74} +(-487.710 + 844.739i) q^{75} +(-115.449 - 66.6543i) q^{76} +414.759 q^{77} -586.462 q^{79} +(35.2339 + 20.3423i) q^{80} +(-154.193 + 267.070i) q^{81} +(125.201 + 216.854i) q^{82} +1354.20i q^{83} +(1136.80 - 656.329i) q^{84} +(137.399 - 79.3272i) q^{85} -236.266i q^{86} +(954.918 + 1653.97i) q^{87} +(161.596 - 279.892i) q^{88} +(380.949 + 219.941i) q^{89} -269.309 q^{90} -682.617 q^{92} +(-203.769 - 117.646i) q^{93} +(364.582 - 631.474i) q^{94} +(-42.6847 - 73.9320i) q^{95} -1626.24i q^{96} +(-1308.80 + 755.634i) q^{97} +(534.979 - 308.870i) q^{98} -739.006i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more