LMFDB - Embedded newform 169.4.e.h.23.4

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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.32067 + 1.91719i) q^{2} +(0.139581 + 0.241762i) q^{3} +(3.35124 - 5.80452i) q^{4} +11.3710i q^{5} +(-0.927008 - 0.535209i) q^{6} +(26.9007 + 15.5311i) q^{7} -4.97517i q^{8} +(13.4610 - 23.3152i) q^{9} +O(q^{10})$	\(q+(-3.32067 + 1.91719i) q^{2} +(0.139581 + 0.241762i) q^{3} +(3.35124 - 5.80452i) q^{4} +11.3710i q^{5} +(-0.927008 - 0.535209i) q^{6} +(26.9007 + 15.5311i) q^{7} -4.97517i q^{8} +(13.4610 - 23.3152i) q^{9} +(-21.8004 - 37.7594i) q^{10} +(18.1413 - 10.4739i) q^{11} +1.87108 q^{12} -119.105 q^{14} +(-2.74908 + 1.58718i) q^{15} +(36.3483 + 62.9571i) q^{16} +(57.1943 - 99.0635i) q^{17} +103.229i q^{18} +(39.1243 + 22.5884i) q^{19} +(66.0033 + 38.1070i) q^{20} +8.67143i q^{21} +(-40.1609 + 69.5608i) q^{22} +(36.9795 + 64.0504i) q^{23} +(1.20281 - 0.694441i) q^{24} -4.29980 q^{25} +15.0530 q^{27} +(180.302 - 104.097i) q^{28} +(13.6056 + 23.5657i) q^{29} +(6.08586 - 10.5410i) q^{30} +179.587i q^{31} +(-206.933 - 119.473i) q^{32} +(5.06438 + 2.92392i) q^{33} +438.610i q^{34} +(-176.605 + 305.888i) q^{35} +(-90.2224 - 156.270i) q^{36} +(-307.211 + 177.368i) q^{37} -173.225 q^{38} +56.5727 q^{40} +(70.5107 - 40.7094i) q^{41} +(-16.6248 - 28.7950i) q^{42} +(-128.009 + 221.718i) q^{43} -140.402i q^{44} +(265.117 + 153.066i) q^{45} +(-245.594 - 141.794i) q^{46} -463.501i q^{47} +(-10.1471 + 17.5753i) q^{48} +(310.933 + 538.551i) q^{49} +(14.2782 - 8.24355i) q^{50} +31.9331 q^{51} +76.6055 q^{53} +(-49.9862 + 28.8596i) q^{54} +(119.099 + 206.285i) q^{55} +(77.2700 - 133.836i) q^{56} +12.6117i q^{57} +(-90.3598 - 52.1692i) q^{58} +(47.1703 + 27.2338i) q^{59} +21.2761i q^{60} +(247.248 - 428.246i) q^{61} +(-344.303 - 596.350i) q^{62} +(724.223 - 418.130i) q^{63} +334.634 q^{64} -22.4229 q^{66} +(-530.000 + 305.996i) q^{67} +(-383.344 - 663.972i) q^{68} +(-10.3233 + 17.8805i) q^{69} -1354.34i q^{70} +(-14.1210 - 8.15278i) q^{71} +(-115.997 - 66.9709i) q^{72} -321.825i q^{73} +(680.097 - 1177.96i) q^{74} +(-0.600173 - 1.03953i) q^{75} +(262.230 - 151.399i) q^{76} +650.686 q^{77} +385.324 q^{79} +(-715.885 + 413.317i) q^{80} +(-361.347 - 625.871i) q^{81} +(-156.095 + 270.365i) q^{82} +663.760i q^{83} +(50.3335 + 29.0601i) q^{84} +(1126.45 + 650.357i) q^{85} -981.671i q^{86} +(-3.79819 + 6.57866i) q^{87} +(-52.1094 - 90.2561i) q^{88} +(-472.610 + 272.861i) q^{89} -1173.82 q^{90} +495.709 q^{92} +(-43.4174 + 25.0670i) q^{93} +(888.620 + 1539.13i) q^{94} +(-256.853 + 444.883i) q^{95} -66.7046i q^{96} +(596.855 + 344.595i) q^{97} +(-2065.01 - 1192.23i) q^{98} -563.958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−3.32067	+	1.91719i	−1.17403	+	0.677829i	−0.954627	−	0.297804i	$-0.903746\pi$
$2$	−3.32067	+	1.91719i	−1.17403	+	0.677829i	−0.219408	+	0.975633i	$0.570413\pi$
$3$	0.139581	+	0.241762i	0.0268625	+	0.0465271i	0.879144	−	0.476556i	$-0.158115\pi$
$3$	0.139581	+	0.241762i	0.0268625	+	0.0465271i	−0.852282	+	0.523083i	$0.824782\pi$
$4$	3.35124	−	5.80452i	0.418905	−	0.725565i
$5$			11.3710i			1.01705i	0.861046	+	0.508527i	$0.169810\pi$
$5$			11.3710i			1.01705i	−0.861046	+	0.508527i	$0.830190\pi$
$6$	−0.927008	−	0.535209i	−0.0630749	−	0.0364163i
$7$	26.9007	+	15.5311i	1.45250	+	0.838603i	0.998623	−	0.0524604i	$-0.0167063\pi$
$7$	26.9007	+	15.5311i	1.45250	+	0.838603i	0.453879	+	0.891063i	$0.350040\pi$
$8$		−	4.97517i		−	0.219873i
$9$	13.4610	−	23.3152i	0.498557	−	0.863526i
$10$	−21.8004	−	37.7594i	−0.689389	−	1.19406i
$11$	18.1413	−	10.4739i	0.497256	−	0.287091i	−0.230324	−	0.973114i	$-0.573978\pi$
$11$	18.1413	−	10.4739i	0.497256	−	0.287091i	0.727580	+	0.686023i	$0.240645\pi$
$12$	1.87108			0.0450113
$13$		0			0
$13$		0			0
$14$	−119.105			−2.27372
$15$	−2.74908	+	1.58718i	−0.0473206	+	0.0273206i
$16$	36.3483	+	62.9571i	0.567942	+	0.983704i
$17$	57.1943	−	99.0635i	0.815980	−	1.41332i	−0.0926417	−	0.995700i	$-0.529531\pi$
$17$	57.1943	−	99.0635i	0.815980	−	1.41332i	0.908622	−	0.417620i	$-0.137136\pi$
$18$			103.229i			1.35175i
$19$	39.1243	+	22.5884i	0.472407	+	0.272744i	0.717247	−	0.696819i	$-0.245402\pi$
$19$	39.1243	+	22.5884i	0.472407	+	0.272744i	−0.244840	+	0.969564i	$0.578735\pi$
$20$	66.0033	+	38.1070i	0.737939	+	0.426049i
$21$			8.67143i			0.0901077i
$22$	−40.1609	+	69.5608i	−0.389197	+	0.674109i
$23$	36.9795	+	64.0504i	0.335250	+	0.580671i	0.983533	−	0.180729i	$-0.0578457\pi$
$23$	36.9795	+	64.0504i	0.335250	+	0.580671i	−0.648283	+	0.761400i	$0.724512\pi$
$24$	1.20281	−	0.694441i	0.0102301	−	0.00590634i
$25$	−4.29980			−0.0343984
$26$		0			0
$27$	15.0530			0.107295
$28$	180.302	−	104.097i	1.21692	−	0.702590i
$29$	13.6056	+	23.5657i	0.0871208	+	0.150898i	0.906293	−	0.422650i	$-0.138900\pi$
$29$	13.6056	+	23.5657i	0.0871208	+	0.150898i	−0.819172	+	0.573548i	$0.805567\pi$
$30$	6.08586	−	10.5410i	0.0370374	−	0.0641506i
$31$			179.587i			1.04048i	0.854021	+	0.520239i	$0.174157\pi$
$31$			179.587i			1.04048i	−0.854021	+	0.520239i	$0.825843\pi$
$32$	−206.933	−	119.473i	−1.14315	−	0.659999i
$33$	5.06438	+	2.92392i	0.0267150	+	0.0154239i
$34$			438.610i			2.21238i
$35$	−176.605	+	305.888i	−0.852904	+	1.47727i
$36$	−90.2224	−	156.270i	−0.417696	−	0.723471i
$37$	−307.211	+	177.368i	−1.36500	+	0.788085i	−0.990285	−	0.139054i	$-0.955594\pi$
$37$	−307.211	+	177.368i	−1.36500	+	0.788085i	−0.374718	+	0.927139i	$0.622261\pi$
$38$	−173.225			−0.739496
$39$		0			0
$40$	56.5727			0.223623
$41$	70.5107	−	40.7094i	0.268583	−	0.155067i	−0.359660	−	0.933083i	$-0.617107\pi$
$41$	70.5107	−	40.7094i	0.268583	−	0.155067i	0.628244	+	0.778017i	$0.283774\pi$
$42$	−16.6248	−	28.7950i	−0.0610777	−	0.105790i
$43$	−128.009	+	221.718i	−0.453981	+	0.786318i	−0.998629	−	0.0523465i	$-0.983330\pi$
$43$	−128.009	+	221.718i	−0.453981	+	0.786318i	0.544648	+	0.838665i	$0.316663\pi$
$44$		−	140.402i		−	0.481056i
$45$	265.117	+	153.066i	0.878252	+	0.507059i
$46$	−245.594	−	141.794i	−0.787191	−	0.454485i
$47$		−	463.501i		−	1.43848i	−0.694762	−	0.719240i	$-0.744490\pi$
$47$		−	463.501i		−	1.43848i	0.694762	−	0.719240i	$-0.255510\pi$
$48$	−10.1471	+	17.5753i	−0.0305126	+	0.0528494i
$49$	310.933	+	538.551i	0.906509	+	1.57012i
$50$	14.2782	−	8.24355i	0.0403850	−	0.0233163i
$51$	31.9331			0.0876769
$52$		0			0
$53$	76.6055			0.198539			0.0992695	−	0.995061i	$-0.468349\pi$
$53$	76.6055			0.198539			0.0992695	+	0.995061i	$0.468349\pi$
$54$	−49.9862	+	28.8596i	−0.125968	+	0.0727275i
$55$	119.099	+	206.285i	0.291987	+	0.505736i
$56$	77.2700	−	133.836i	0.184386	−	0.319367i
$57$			12.6117i			0.0293063i
$58$	−90.3598	−	52.1692i	−0.204566	−	0.118106i
$59$	47.1703	+	27.2338i	0.104086	+	0.0600939i	0.551139	−	0.834413i	$-0.314193\pi$
$59$	47.1703	+	27.2338i	0.104086	+	0.0600939i	−0.447054	+	0.894507i	$0.647527\pi$
$60$			21.2761i			0.0457789i
$61$	247.248	−	428.246i	0.518965	−	0.898874i	−0.480792	−	0.876835i	$-0.659651\pi$
$61$	247.248	−	428.246i	0.518965	−	0.898874i	0.999757	−	0.0220394i	$-0.00701592\pi$
$62$	−344.303	−	596.350i	−0.705266	−	1.22156i
$63$	724.223	−	418.130i	1.44831	−	0.836182i
$64$	334.634			0.653582
$65$		0			0
$66$	−22.4229			−0.0418192
$67$	−530.000	+	305.996i	−0.966415	+	0.557960i	−0.898141	−	0.439707i	$-0.855082\pi$
$67$	−530.000	+	305.996i	−0.966415	+	0.557960i	−0.0682737	+	0.997667i	$0.521749\pi$
$68$	−383.344	−	663.972i	−0.683637	−	1.18409i
$69$	−10.3233	+	17.8805i	−0.0180113	+	0.0311965i
$70$		−	1354.34i		−	2.31249i
$71$	−14.1210	−	8.15278i	−0.0236036	−	0.0136276i	0.488152	−	0.872759i	$-0.337671\pi$
$71$	−14.1210	−	8.15278i	−0.0236036	−	0.0136276i	−0.511755	+	0.859131i	$0.671005\pi$
$72$	−115.997	−	66.9709i	−0.189866	−	0.109619i
$73$		−	321.825i		−	0.515983i	−0.966147	−	0.257992i	$-0.916939\pi$
$73$		−	321.825i		−	0.515983i	0.966147	−	0.257992i	$-0.0830607\pi$
$74$	680.097	−	1177.96i	1.06837	−	1.85048i
$75$	−0.600173	−	1.03953i	−0.000924027	−	0.00160046i
$76$	262.230	−	151.399i	0.395787	−	0.228508i
$77$	650.686			0.963021
$78$		0			0
$79$	385.324			0.548764			0.274382	−	0.961621i	$-0.411527\pi$
$79$	385.324			0.548764			0.274382	+	0.961621i	$0.411527\pi$
$80$	−715.885	+	413.317i	−1.00048	+	0.577628i
$81$	−361.347	−	625.871i	−0.495675	−	0.858534i
$82$	−156.095	+	270.365i	−0.210217	+	0.364107i
$83$			663.760i			0.877797i	0.898537	+	0.438899i	$0.144631\pi$
$83$			663.760i			0.877797i	−0.898537	+	0.438899i	$0.855369\pi$
$84$	50.3335	+	29.0601i	0.0653790	+	0.0377466i
$85$	1126.45	+	650.357i	1.43742	+	0.829896i
$86$		−	981.671i		−	1.23089i
$87$	−3.79819	+	6.57866i	−0.00468056	+	0.00810697i
$88$	−52.1094	−	90.2561i	−0.0631237	−	0.109333i
$89$	−472.610	+	272.861i	−0.562882	+	0.324980i	−0.754302	−	0.656528i	$-0.772024\pi$
$89$	−472.610	+	272.861i	−0.562882	+	0.324980i	0.191419	+	0.981508i	$0.438691\pi$
$90$	−1173.82			−1.37480
$91$		0			0
$92$	495.709			0.561753
$93$	−43.4174	+	25.0670i	−0.0484104	+	0.0279498i
$94$	888.620	+	1539.13i	0.975044	+	1.68883i
$95$	−256.853	+	444.883i	−0.277395	+	0.480463i
$96$		−	66.7046i		−	0.0709168i
$97$	596.855	+	344.595i	0.624758	+	0.360704i	0.778719	−	0.627373i	$-0.215870\pi$
$97$	596.855	+	344.595i	0.624758	+	0.360704i	−0.153961	+	0.988077i	$0.549203\pi$
$98$	−2065.01	−	1192.23i	−2.12855	−	1.22892i
$99$		−	563.958i		−	0.572524i
$100$	−14.4097	+	24.9583i	−0.0144097	+	0.0249583i
$101$	235.699	+	408.242i	0.232207	+	0.402194i	0.958457	−	0.285236i	$-0.0920720\pi$
$101$	235.699	+	408.242i	0.232207	+	0.402194i	−0.726250	+	0.687430i	$0.758739\pi$
$102$	−106.039	+	61.2218i	−0.102936	+	0.0594300i
$103$	335.521			0.320970			0.160485	−	0.987038i	$-0.448694\pi$
$103$	335.521			0.320970			0.160485	+	0.987038i	$0.448694\pi$
$104$		0			0
$105$	−98.6029			−0.0916444
$106$	−254.382	+	146.867i	−0.233092	+	0.134576i
$107$	−814.632	−	1410.98i	−0.736014	−	1.27481i	−0.954277	−	0.298923i	$-0.903373\pi$
$107$	−814.632	−	1410.98i	−0.736014	−	1.27481i	0.218264	−	0.975890i	$-0.429961\pi$
$108$	50.4464	−	87.3757i	0.0449463	−	0.0778494i
$109$		−	1518.95i		−	1.33476i	−0.744717	−	0.667381i	$-0.767415\pi$
$109$		−	1518.95i		−	1.33476i	0.744717	−	0.667381i	$-0.232585\pi$
$110$	−790.976	−	456.670i	−0.685606	−	0.395835i
$111$	−85.7618	−	49.5146i	−0.0733347	−	0.0423398i
$112$			2258.12i			1.90511i
$113$	−597.704	+	1035.25i	−0.497586	+	0.861845i	−0.999996	−	0.00278476i	$-0.999114\pi$
$113$	−597.704	+	1035.25i	−0.497586	+	0.861845i	0.502410	+	0.864630i	$0.332447\pi$
$114$	−24.1790	−	41.8793i	−0.0198647	−	0.0344066i
$115$	−728.317	+	420.494i	−0.590573	+	0.340968i
$116$	182.383			0.145982
$117$		0			0
$118$	−208.850			−0.162934
$119$	3077.14	−	1776.59i	2.37043	−	1.36857i
$120$	7.89649	+	13.6771i	0.00600707	+	0.0104045i
$121$	−446.095	+	772.659i	−0.335158	+	0.580510i
$122$			1896.09i			1.40708i
$123$	19.6840	+	11.3645i	0.0144296	+	0.00833094i
$124$	1042.42	+	601.840i	0.754934	+	0.435862i
$125$			1372.48i			0.982069i
$126$	−1603.27	+	2776.95i	−1.13358	+	1.96341i
$127$	263.212	+	455.897i	0.183908	+	0.318538i	0.943208	−	0.332203i	$-0.107792\pi$
$127$	263.212	+	455.897i	0.183908	+	0.318538i	−0.759300	+	0.650741i	$0.774458\pi$
$128$	544.250	−	314.223i	0.375823	−	0.216981i
$129$	−71.4707			−0.0487802
$130$		0			0
$131$	−834.024			−0.556252			−0.278126	−	0.960545i	$-0.589713\pi$
$131$	−834.024			−0.556252			−0.278126	+	0.960545i	$0.589713\pi$
$132$	33.9440	−	19.5976i	0.0223821	−	0.0129223i
$133$	701.648	+	1215.29i	0.457448	+	0.792323i
$134$	1173.30	−	2032.22i	0.756403	−	1.31013i
$135$			171.168i			0.109125i
$136$	−492.858	−	284.551i	−0.310751	−	0.179412i
$137$	−404.228	−	233.381i	−0.252084	−	0.145541i	0.368634	−	0.929575i	$-0.379826\pi$
$137$	−404.228	−	233.381i	−0.252084	−	0.145541i	−0.620718	+	0.784034i	$0.713159\pi$
$138$		−	79.1670i		−	0.0488344i
$139$	356.540	−	617.545i	0.217563	−	0.376831i	−0.736499	−	0.676439i	$-0.763522\pi$
$139$	356.540	−	617.545i	0.217563	−	0.376831i	0.954062	+	0.299608i	$0.0968558\pi$
$140$	1183.69	+	2050.21i	0.714572	+	1.23768i
$141$	112.057	−	64.6961i	0.0669284	−	0.0386411i
$142$	62.5218			0.0369487
$143$		0			0
$144$	1957.14			1.13261
$145$	−267.965	+	154.710i	−0.153471	+	0.0886066i
$146$	617.000	+	1068.68i	0.349748	+	0.605782i
$147$	−86.8008	+	150.343i	−0.0487021	+	0.0843545i
$148$			2377.61i			1.32053i
$149$	−574.013	−	331.407i	−0.315604	−	0.182214i	0.333827	−	0.942634i	$-0.391660\pi$
$149$	−574.013	−	331.407i	−0.315604	−	0.182214i	−0.649431	+	0.760420i	$0.724993\pi$
$150$	3.98595	+	2.30129i	0.00216968	+	0.00125266i
$151$		−	190.862i		−	0.102862i	−0.998677	−	0.0514310i	$-0.983622\pi$
$151$		−	190.862i		−	0.102862i	0.998677	−	0.0514310i	$-0.0163782\pi$
$152$	112.381	−	194.650i	0.0599692	−	0.103870i
$153$	−1539.79	−	2666.99i	−0.813625	−	1.40924i
$154$	−2160.72	+	1247.49i	−1.13062	+	0.652764i
$155$	−2042.09			−1.05822
$156$		0			0
$157$	−2833.96			−1.44060			−0.720302	−	0.693661i	$-0.755997\pi$
$157$	−2833.96			−1.44060			−0.720302	+	0.693661i	$0.755997\pi$
$158$	−1279.54	+	738.740i	−0.644268	+	0.371969i
$159$	10.6927	+	18.5203i	0.00533325	+	0.00923745i
$160$	1358.52	−	2353.03i	0.671254	−	1.16265i
$161$			2297.34i			1.12457i
$162$	2399.83	+	1385.54i	1.16388	+	0.671966i
$163$	3087.85	+	1782.77i	1.48380	+	0.856672i	0.999830	−	0.0184128i	$-0.00586131\pi$
$163$	3087.85	+	1782.77i	1.48380	+	0.856672i	0.483969	+	0.875085i	$0.339195\pi$
$164$		−	545.708i		−	0.259833i
$165$	−33.2480	+	57.5872i	−0.0156870	+	0.0271706i
$166$	−1272.56	−	2204.13i	−0.594997	−	1.03056i
$167$	104.468	−	60.3149i	0.0484073	−	0.0279480i	−0.475601	−	0.879661i	$-0.657769\pi$
$167$	104.468	−	60.3149i	0.0484073	−	0.0279480i	0.524008	+	0.851713i	$0.324436\pi$
$168$	43.1418			0.0198123
$169$		0			0
$170$	−4987.44			−2.25011
$171$	1053.31	−	608.127i	0.471043	−	0.271957i
$172$	857.978	+	1486.06i	0.380350	+	0.658786i
$173$	−1040.14	+	1801.57i	−0.457112	+	0.791740i	−0.998807	−	0.0488345i	$-0.984449\pi$
$173$	−1040.14	+	1801.57i	−0.457112	+	0.791740i	0.541695	+	0.840575i	$0.317783\pi$
$174$		−	29.1274i		−	0.0126905i
$175$	−115.668	−	66.7809i	−0.0499638	−	0.0288466i
$176$	1318.81	+	761.417i	0.564825	+	0.326102i
$177$			15.2053i			0.00645708i
$178$	1046.25	−	1812.17i	0.440562	−	0.763076i
$179$	−276.570	−	479.033i	−0.115485	−	0.200026i	0.802489	−	0.596668i	$-0.203509\pi$
$179$	−276.570	−	479.033i	−0.115485	−	0.200026i	−0.917974	+	0.396642i	$0.870176\pi$
$180$	1776.94	−	1025.92i	0.735809	−	0.424820i
$181$	3305.19			1.35731			0.678655	−	0.734457i	$-0.262563\pi$
$181$	3305.19			1.35731			0.678655	+	0.734457i	$0.262563\pi$
$182$		0			0
$183$	138.045			0.0557627
$184$	318.661	−	183.979i	0.127674	−	0.0737127i
$185$	−2016.85	−	3493.29i	−0.801525	−	1.38828i
$186$	96.1166	−	166.479i	0.0378904	−	0.0656280i
$187$		−	2396.19i		−	0.937042i
$188$	−2690.40	−	1553.30i	−1.04371	−	0.602587i
$189$	404.938	+	233.791i	0.155846	+	0.0899777i
$190$		−	1969.75i		−	0.752107i
$191$	1659.07	−	2873.59i	0.628514	−	1.08862i	−0.359336	−	0.933208i	$-0.616997\pi$
$191$	1659.07	−	2873.59i	0.628514	−	1.08862i	0.987850	−	0.155410i	$-0.0496698\pi$
$192$	46.7087	+	80.9019i	0.0175568	+	0.0304093i
$193$	3379.39	−	1951.09i	1.26038	−	0.727681i	0.287233	−	0.957861i	$-0.407265\pi$
$193$	3379.39	−	1951.09i	1.26038	−	0.727681i	0.973148	+	0.230180i	$0.0739314\pi$
$194$	−2642.61			−0.977983
$195$		0			0
$196$	4168.04			1.51897
$197$	−3146.26	+	1816.49i	−1.13788	+	0.656953i	−0.945904	−	0.324447i	$-0.894822\pi$
$197$	−3146.26	+	1816.49i	−1.13788	+	0.656953i	−0.191972	+	0.981400i	$0.561488\pi$
$198$	1081.22	+	1872.72i	0.388074	+	0.672164i
$199$	1478.62	−	2561.04i	0.526715	−	0.912297i	−0.472801	−	0.881169i	$-0.656757\pi$
$199$	1478.62	−	2561.04i	0.526715	−	0.912297i	0.999515	−	0.0311274i	$-0.00990975\pi$
$200$			21.3922i			0.00756330i
$201$	−147.956	−	85.4226i	−0.0519206	−	0.0299764i
$202$	−1565.36	−	903.759i	−0.545238	−	0.314793i
$203$			845.245i			0.292239i
$204$	107.015	−	185.356i	0.0367283	−	0.0636153i
$205$	462.906	+	801.777i	0.157711	+	0.273164i
$206$	−1114.16	+	643.258i	−0.376830	+	0.217563i
$207$	1991.13			0.668565
$208$		0			0
$209$	946.355			0.313209
$210$	327.428	−	189.041i	0.107594	−	0.0621193i
$211$	1597.03	+	2766.13i	0.521061	+	0.902504i	0.999700	+	0.0244920i	$0.00779684\pi$
$211$	1597.03	+	2766.13i	0.521061	+	0.902504i	−0.478639	+	0.878012i	$0.658870\pi$
$212$	256.723	−	444.658i	0.0831691	−	0.144053i
$213$		−	4.55191i		−	0.00146428i
$214$	5410.25	+	3123.61i	1.72821	+	0.997783i
$215$	−2521.16	−	1455.59i	−0.799728	−	0.461723i
$216$		−	74.8914i		−	0.0235913i
$217$	−2789.19	+	4831.02i	−0.872547	+	1.51130i
$218$	2912.12	+	5043.93i	0.904740	+	1.56706i
$219$	77.8051	−	44.9208i	0.0240072	−	0.0138606i
$220$	1596.52			0.489259
$221$		0			0
$222$	379.716			0.114797
$223$	65.0465	−	37.5546i	0.0195329	−	0.0112773i	−0.490202	−	0.871609i	$-0.663077\pi$
$223$	65.0465	−	37.5546i	0.0195329	−	0.0112773i	0.509735	+	0.860332i	$0.329744\pi$
$224$	−3711.09	−	6427.80i	−1.10695	−	1.91730i
$225$	−57.8798	+	100.251i	−0.0171496	+	0.0297039i
$226$		−	4583.65i		−	1.34911i
$227$	−3743.64	−	2161.39i	−1.09460	−	0.631968i	−0.159803	−	0.987149i	$-0.551086\pi$
$227$	−3743.64	−	2161.39i	−1.09460	−	0.631968i	−0.934797	+	0.355181i	$0.884419\pi$
$228$	73.2049	+	42.2649i	0.0212636	+	0.0122766i
$229$			677.923i			0.195626i	0.995205	+	0.0978132i	$0.0311848\pi$
$229$			677.923i			0.195626i	−0.995205	+	0.0978132i	$0.968815\pi$
$230$	1612.34	−	2792.65i	0.462236	−	0.800616i
$231$	90.8237	+	157.311i	0.0258691	+	0.0448066i
$232$	117.243	−	67.6904i	0.0331784	−	0.0191556i
$233$	−92.9061			−0.0261222			−0.0130611	−	0.999915i	$-0.504158\pi$
$233$	−92.9061			−0.0261222			−0.0130611	+	0.999915i	$0.504158\pi$
$234$		0			0
$235$	5270.47			1.46301
$236$	316.159	−	182.534i	0.0872041	−	0.0503473i
$237$	53.7841	+	93.1568i	0.0147412	+	0.0255324i
$238$	−6812.11	+	11798.9i	−1.85531	+	3.21349i
$239$		−	2082.56i		−	0.563638i	−0.959468	−	0.281819i	$-0.909062\pi$
$239$		−	2082.56i		−	0.563638i	0.959468	−	0.281819i	$-0.0909378\pi$
$240$	−199.849	−	115.383i	−0.0537507	−	0.0310330i
$241$	−5664.89	−	3270.63i	−1.51414	−	0.874189i	−0.999863	−	0.0165650i	$-0.994727\pi$
$241$	−5664.89	−	3270.63i	−1.51414	−	0.874189i	−0.514277	−	0.857624i	$-0.671940\pi$
$242$		−	3421.00i		−	0.908719i
$243$	304.091	−	526.700i	0.0802775	−	0.139045i
$244$	−1657.18	−	2870.31i	−0.434795	−	0.753086i
$245$	−6123.87	+	3535.62i	−1.59690	+	0.921968i
$246$	−87.1520			−0.0225878
$247$		0			0
$248$	893.476			0.228773
$249$	−160.472	+	92.6486i	−0.0408414	+	0.0235798i
$250$	−2631.31	−	4557.57i	−0.665675	−	1.15298i
$251$	−1204.64	+	2086.50i	−0.302934	+	0.524697i	−0.976799	−	0.214157i	$-0.931299\pi$
$251$	−1204.64	+	2086.50i	−0.302934	+	0.524697i	0.673865	+	0.738854i	$0.264633\pi$
$252$		−	5605.03i		−	1.40112i
$253$	1341.71	+	774.639i	0.333411	+	0.192495i
$254$	−1748.08	−	1009.26i	−0.431829	−	0.249317i
$255$			363.111i			0.0891722i
$256$	−2543.39	+	4405.28i	−0.620944	+	1.07551i
$257$	−131.793	−	228.273i	−0.0319885	−	0.0554057i	0.849588	−	0.527447i	$-0.176851\pi$
$257$	−131.793	−	228.273i	−0.0319885	−	0.0554057i	−0.881576	+	0.472041i	$0.843517\pi$
$258$	237.331	−	137.023i	0.0572696	−	0.0330646i
$259$	−11018.9			−2.64356
$260$		0			0
$261$	732.584			0.173739
$262$	2769.52	−	1598.98i	0.653060	−	0.377044i
$263$	3662.31	+	6343.31i	0.858660	+	1.48724i	0.873207	+	0.487349i	$0.162036\pi$
$263$	3662.31	+	6343.31i	0.858660	+	1.48724i	−0.0145468	+	0.999894i	$0.504631\pi$
$264$	14.5470	−	25.1962i	0.00339131	−	0.00587393i
$265$			871.081i			0.201925i
$266$	−4659.88	−	2690.39i	−1.07412	−	0.620143i
$267$	−131.935	−	76.1728i	−0.0302408	−	0.0174595i
$268$			4101.86i			0.934930i
$269$	2341.68	−	4055.91i	0.530762	−	0.919307i	−0.468594	−	0.883414i	$-0.655239\pi$
$269$	2341.68	−	4055.91i	0.530762	−	0.919307i	0.999356	−	0.0358928i	$-0.0114275\pi$
$270$	−328.162	−	568.394i	−0.0739678	−	0.128116i
$271$	1411.08	−	814.687i	0.316299	−	0.182615i	−0.333443	−	0.942770i	$-0.608210\pi$
$271$	1411.08	−	814.687i	0.316299	−	0.182615i	0.649742	+	0.760155i	$0.274877\pi$
$272$	8315.66			1.85372
$273$		0			0
$274$	1789.75			0.394608
$275$	−78.0042	+	45.0357i	−0.0171048	+	0.00987548i
$276$	69.1918	+	119.844i	0.0150901	+	0.0261367i
$277$	3100.33	−	5369.93i	0.672494	−	1.16479i	−0.304701	−	0.952448i	$-0.598557\pi$
$277$	3100.33	−	5369.93i	0.672494	−	1.16479i	0.977195	−	0.212345i	$-0.0681102\pi$
$278$			2734.22i			0.589883i
$279$	4187.11	+	2417.43i	0.898479	+	0.518737i
$280$	1521.85	+	878.638i	0.324813	+	0.187531i
$281$		−	2951.26i		−	0.626538i	−0.949664	−	0.313269i	$-0.898576\pi$
$281$		−	2951.26i		−	0.626538i	0.949664	−	0.313269i	$-0.101424\pi$
$282$	−248.070	+	429.669i	−0.0523842	+	0.0907320i
$283$	2624.58	+	4545.91i	0.551291	+	0.954864i	0.998182	+	0.0602756i	$0.0191979\pi$
$283$	2624.58	+	4545.91i	0.551291	+	0.954864i	−0.446891	+	0.894589i	$0.647469\pi$
$284$	−94.6460	+	54.6439i	−0.0197754	+	0.0114173i
$285$	−143.408			−0.0298061
$286$		0			0
$287$	2529.05			0.520157
$288$	−5571.05	+	3216.45i	−1.13985	+	0.658094i
$289$	−4085.88	−	7076.96i	−0.831648	−	1.44046i
$290$	593.217	−	1027.48i	0.120120	−	0.208054i
$291$			192.396i			0.0387576i
$292$	−1868.04	−	1078.51i	−0.374379	−	0.216148i
$293$	−2522.15	−	1456.17i	−0.502887	−	0.290342i	0.227018	−	0.973891i	$-0.427102\pi$
$293$	−2522.15	−	1456.17i	−0.502887	−	0.290342i	−0.729905	+	0.683549i	$0.760436\pi$
$294$		−	665.655i		−	0.132047i
$295$	−309.676	+	536.374i	−0.0611187	+	0.105861i
$296$	882.436	+	1528.42i	0.173279	+	0.300128i
$297$	273.082	−	157.664i	0.0533530	−	0.0308033i
$298$	2541.48			0.494040
$299$		0			0
$300$	−8.04530			−0.00154832
$301$	−6887.07	+	3976.25i	−1.31882	+	0.761419i
$302$	365.920	+	633.792i	0.0697229	+	0.120764i
$303$	−65.7983	+	113.966i	−0.0124753	+	0.0216079i
$304$			3284.20i			0.619611i
$305$	4869.59	+	2811.46i	0.914203	+	0.527816i
$306$	10226.3	+	5904.14i	1.91045	+	1.10300i
$307$		−	5000.10i		−	0.929546i	−0.885430	−	0.464773i	$-0.846136\pi$
$307$		−	5000.10i		−	0.929546i	0.885430	−	0.464773i	$-0.153864\pi$
$308$	2180.61	−	3776.92i	0.403415	−	0.698734i
$309$	46.8325	+	81.1163i	0.00862203	+	0.0149338i
$310$	6781.10	−	3915.07i	1.24239	−	0.717294i
$311$	7840.94			1.42964			0.714822	−	0.699307i	$-0.246508\pi$
$311$	7840.94			1.42964			0.714822	+	0.699307i	$0.246508\pi$
$312$		0			0
$313$	−7518.43			−1.35772			−0.678860	−	0.734267i	$-0.737526\pi$
$313$	−7518.43			−1.35772			−0.678860	+	0.734267i	$0.737526\pi$
$314$	9410.65	−	5433.24i	1.69132	−	0.976483i
$315$	4754.56	+	8235.15i	0.850442	+	1.47301i
$316$	1291.32	−	2236.62i	0.229880	−	0.398164i
$317$			485.238i			0.0859738i	0.999076	+	0.0429869i	$0.0136874\pi$
$317$			485.238i			0.0859738i	−0.999076	+	0.0429869i	$0.986313\pi$
$318$	−71.0139	−	40.9999i	−0.0125228	−	0.00723006i
$319$	493.649	+	285.008i	0.0866427	+	0.0500232i
$320$			3805.13i			0.664728i
$321$	227.415	−	393.894i	0.0395423	−	0.0684892i
$322$	−4404.43	−	7628.70i	−0.762265	−	1.32028i
$323$	4475.38	−	2583.86i	0.770949	−	0.445108i
$324$	−4843.84			−0.830563
$325$		0			0
$326$	−13671.7			−2.32271
$327$	367.224	−	212.017i	0.0621026	−	0.0358550i
$328$	−202.536	−	350.802i	−0.0340950	−	0.0590543i
$329$	7198.70	−	12468.5i	1.20631	−	2.08940i
$330$		−	254.971i		−	0.0425324i
$331$	−7121.23	−	4111.44i	−1.18253	−	0.682735i	−0.225933	−	0.974143i	$-0.572543\pi$
$331$	−7121.23	−	4111.44i	−1.18253	−	0.682735i	−0.956599	+	0.291408i	$0.905876\pi$
$332$	3852.81	+	2224.42i	0.636899	+	0.367714i
$333$			9550.23i			1.57162i
$334$	−231.270	+	400.572i	−0.0378879	+	0.0656237i
$335$	−3479.48	−	6026.64i	−0.567475	−	0.982896i
$336$	−545.928	+	315.192i	−0.0886394	+	0.0511760i
$337$	−7744.78			−1.25188			−0.625942	−	0.779870i	$-0.715285\pi$
$337$	−7744.78			−1.25188			−0.625942	+	0.779870i	$0.715285\pi$
$338$		0			0
$339$	−333.714			−0.0534656
$340$	7550.03	−	4359.01i	1.20429	−	0.695296i
$341$	1880.98	+	3257.95i	0.298712	+	0.517384i
$342$	−2331.79	+	4038.78i	−0.368681	+	0.638574i
$343$			8662.19i			1.36360i
$344$	1103.08	+	636.866i	0.172890	+	0.0998184i
$345$	−203.319	−	117.386i	−0.0317285	−	0.0183185i
$346$		−	7976.58i		−	1.23937i
$347$	1766.30	−	3059.33i	0.273257	−	0.473295i	−0.696437	−	0.717618i	$-0.745232\pi$
$347$	1766.30	−	3059.33i	0.273257	−	0.473295i	0.969694	+	0.244323i	$0.0785657\pi$
$348$	25.4573	+	44.0934i	0.00392142	+	0.00679210i
$349$	−2915.20	+	1683.09i	−0.447127	+	0.258149i	−0.706616	−	0.707597i	$-0.749779\pi$
$349$	−2915.20	+	1683.09i	−0.447127	+	0.258149i	0.259489	+	0.965746i	$0.416446\pi$
$350$	512.127			0.0782123
$351$		0			0
$352$	−5005.37			−0.757919
$353$	−8632.52	+	4983.99i	−1.30159	+	0.751476i	−0.980677	−	0.195631i	$-0.937324\pi$
$353$	−8632.52	+	4983.99i	−1.30159	+	0.751476i	−0.320917	+	0.947107i	$0.603991\pi$
$354$	−29.1515	−	50.4919i	−0.00437680	−	0.00758084i
$355$	92.7054	−	160.570i	0.0138600	−	0.0240062i
$356$			3657.70i			0.544544i
$357$	859.023	+	495.957i	0.127351	+	0.0735261i
$358$	1836.80	+	1060.48i	0.271167	+	0.156558i
$359$		−	2742.72i		−	0.403219i	−0.979466	−	0.201609i	$-0.935383\pi$
$359$		−	2742.72i		−	0.403219i	0.979466	−	0.201609i	$-0.0646171\pi$
$360$	761.527	−	1319.00i	0.111489	−	0.193104i
$361$	−2409.03	−	4172.56i	−0.351221	−	0.608333i
$362$	−10975.5	+	6336.69i	−1.59353	+	0.920024i
$363$	−249.066			−0.0360126
$364$		0			0
$365$	3659.47			0.524783
$366$	−458.402	+	264.659i	−0.0654674	+	0.0377976i
$367$	820.929	+	1421.89i	0.116763	+	0.202240i	0.918483	−	0.395460i	$-0.129415\pi$
$367$	820.929	+	1421.89i	0.116763	+	0.202240i	−0.801720	+	0.597700i	$0.796081\pi$
$368$	−2688.28	+	4656.24i	−0.380806	+	0.659575i
$369$		−	2191.96i		−	0.309238i
$370$	13394.6	+	7733.39i	1.88204	+	1.08659i
$371$	2060.74	+	1189.77i	0.288378	+	0.166495i
$372$			336.023i			0.0468333i
$373$	−5603.77	+	9706.01i	−0.777887	+	1.34734i	0.155270	+	0.987872i	$0.450375\pi$
$373$	−5603.77	+	9706.01i	−0.777887	+	1.34734i	−0.933157	+	0.359468i	$0.882958\pi$
$374$	4593.96	+	7956.97i	0.635155	+	1.10012i
$375$	−331.814	+	191.573i	−0.0456929	+	0.0263808i
$376$	−2306.00			−0.316284
$377$		0			0
$378$	−1792.89			−0.243958
$379$	3329.41	−	1922.24i	0.451241	−	0.260524i	−0.257113	−	0.966381i	$-0.582771\pi$
$379$	3329.41	−	1922.24i	0.451241	−	0.260524i	0.708354	+	0.705857i	$0.249438\pi$
$380$	1721.55	+	2981.82i	0.232405	+	0.402537i
$381$	−73.4791	+	127.270i	−0.00988045	+	0.0171134i
$382$			12723.0i			1.70410i
$383$	−10525.9	−	6077.15i	−1.40431	−	0.810778i	−0.409477	−	0.912320i	$-0.634289\pi$
$383$	−10525.9	−	6077.15i	−1.40431	−	0.810778i	−0.994831	+	0.101543i	$0.967622\pi$
$384$	151.934	+	87.7193i	0.0201911	+	0.0116573i
$385$			7398.96i			0.979444i
$386$	−7481.22	+	12957.9i	−0.986487	+	1.70865i
$387$	3446.27	+	5969.11i	0.452671	+	0.784049i
$388$	4000.41	−	2309.64i	0.523429	−	0.302202i
$389$	5269.41			0.686812			0.343406	−	0.939187i	$-0.388419\pi$
$389$	5269.41			0.686812			0.343406	+	0.939187i	$0.388419\pi$
$390$		0			0
$391$	8460.07			1.09423
$392$	2679.38	−	1546.94i	0.345228	−	0.199317i
$393$	−116.414	−	201.635i	−0.0149423	−	0.0258808i
$394$	6965.13	−	12064.0i	0.890604	−	1.54257i
$395$			4381.53i			0.558123i
$396$	−3273.51	−	1889.96i	−0.415404	−	0.239834i
$397$	567.665	+	327.742i	0.0717639	+	0.0414329i	0.535453	−	0.844565i	$-0.320141\pi$
$397$	567.665	+	327.742i	0.0717639	+	0.0414329i	−0.463689	+	0.885998i	$0.653474\pi$
$398$			11339.2i			1.42809i
$399$	−195.874	+	339.264i	−0.0245764	+	0.0425675i
$400$	−156.291	−	270.703i	−0.0195363	−	0.0338379i
$401$	−6668.37	+	3849.98i	−0.830430	+	0.479449i	−0.854000	−	0.520273i	$-0.825830\pi$
$401$	−6668.37	+	3849.98i	−0.830430	+	0.479449i	0.0235699	+	0.999722i	$0.492497\pi$
$402$	655.086			0.0812754
$403$		0			0
$404$	3159.53			0.389091
$405$	7116.78	−	4108.88i	0.873175	−	0.504128i
$406$	−1620.50	−	2806.78i	−0.198088	−	0.343099i
$407$	−3715.47	+	6435.39i	−0.452504	+	0.783760i
$408$		−	158.872i		−	0.0192778i
$409$	480.818	+	277.600i	0.0581294	+	0.0335610i	0.528783	−	0.848757i	$-0.322649\pi$
$409$	480.818	+	277.600i	0.0581294	+	0.0335610i	−0.470654	+	0.882318i	$0.655982\pi$
$410$	−3074.32	−	1774.96i	−0.370317	−	0.213802i
$411$		−	130.303i		−	0.0156383i
$412$	1124.41	−	1947.54i	0.134456	−	0.232884i
$413$	845.944	+	1465.22i	0.100790	+	0.174573i
$414$	−6611.89	+	3817.38i	−0.784919	+	0.453173i
$415$	−7547.62			−0.892767
$416$		0			0
$417$	199.065			0.0233772
$418$	−3142.54	+	1814.34i	−0.367719	+	0.212303i
$419$	−1658.50	−	2872.60i	−0.193372	−	0.334930i	0.752994	−	0.658028i	$-0.228609\pi$
$419$	−1658.50	−	2872.60i	−0.193372	−	0.334930i	−0.946366	+	0.323098i	$0.895276\pi$
$420$	−330.442	+	572.343i	−0.0383903	+	0.0664940i
$421$		−	13270.3i		−	1.53623i	−0.640310	−	0.768117i	$-0.721194\pi$
$421$		−	13270.3i		−	1.53623i	0.640310	−	0.768117i	$-0.278806\pi$
$422$	−10606.4	−	6123.61i	−1.22349	−	0.706381i
$423$	−10806.6	−	6239.20i	−1.24216	−	0.717164i
$424$		−	381.125i		−	0.0436535i
$425$	−245.924	+	425.954i	−0.0280684	+	0.0486160i
$426$	8.72688	+	15.1154i	0.000992532	+	0.00171912i
$427$	13302.3	−	7680.09i	1.50760	−	0.870411i
$428$	−10920.1			−1.23328
$429$		0			0
$430$	11162.6			1.25188
$431$	11857.8	−	6846.11i	1.32522	−	0.765117i	0.340665	−	0.940185i	$-0.389348\pi$
$431$	11857.8	−	6846.11i	1.32522	−	0.765117i	0.984556	+	0.175068i	$0.0560146\pi$
$432$	547.152	+	947.695i	0.0609372	+	0.105546i
$433$	−7594.54	+	13154.1i	−0.842888	+	1.45992i	0.0445548	+	0.999007i	$0.485813\pi$
$433$	−7594.54	+	13154.1i	−0.842888	+	1.45992i	−0.887443	+	0.460918i	$0.847520\pi$
$434$		−	21389.7i		−	2.36575i
$435$	−74.8060	−	43.1893i	−0.00824522	−	0.00476038i
$436$	−8816.78	−	5090.37i	−0.968456	−	0.559139i
$437$			3341.23i			0.365750i
$438$	−172.243	+	298.334i	−0.0187902	+	0.0325456i
$439$	−1401.02	−	2426.64i	−0.152317	−	0.263821i	0.779762	−	0.626076i	$-0.215340\pi$
$439$	−1401.02	−	2426.64i	−0.152317	−	0.263821i	−0.932079	+	0.362256i	$0.882007\pi$
$440$	1026.30	−	592.536i	0.111198	−	0.0642002i
$441$	16741.9			1.80778
$442$		0			0
$443$	−7539.78			−0.808636			−0.404318	−	0.914618i	$-0.632491\pi$
$443$	−7539.78			−0.808636			−0.404318	+	0.914618i	$0.632491\pi$
$444$	−574.817	+	331.871i	−0.0614406	+	0.0354727i
$445$	−3102.71	−	5374.05i	−0.330522	−	0.572482i
$446$	−143.999	+	249.413i	−0.0152882	+	0.0264799i
$447$		−	185.033i		−	0.0195789i
$448$	9001.90	+	5197.25i	0.949330	+	0.548096i
$449$	4814.08	+	2779.41i	0.505992	+	0.292135i	0.731185	−	0.682180i	$-0.238968\pi$
$449$	4814.08	+	2779.41i	0.505992	+	0.292135i	−0.225192	+	0.974314i	$0.572301\pi$
$450$		−	443.867i		−	0.0464979i
$451$	852.771	−	1477.04i	0.0890364	−	0.154216i
$452$	4006.10	+	6938.77i	0.416883	+	0.722063i
$453$	46.1433	−	26.6409i	0.00478588	−	0.00276313i
$454$	16575.2			1.71347
$455$		0			0
$456$	62.7453			0.00644368
$457$	−3747.91	+	2163.85i	−0.383632	+	0.221490i	−0.679397	−	0.733771i	$-0.737759\pi$
$457$	−3747.91	+	2163.85i	−0.383632	+	0.221490i	0.295766	+	0.955261i	$0.404425\pi$
$458$	−1299.71	−	2251.16i	−0.132601	−	0.229672i
$459$	860.949	−	1491.21i	0.0875504	−	0.151642i
$460$			5636.71i			0.571333i
$461$	9779.78	+	5646.36i	0.988048	+	0.570450i	0.904690	−	0.426070i	$-0.140102\pi$
$461$	9779.78	+	5646.36i	0.988048	+	0.570450i	0.0833575	+	0.996520i	$0.473436\pi$
$462$	−603.192	−	348.253i	−0.0607425	−	0.0350697i
$463$		−	8582.54i		−	0.861478i	−0.902477	−	0.430739i	$-0.858253\pi$
$463$		−	8582.54i		−	0.861478i	0.902477	−	0.430739i	$-0.141747\pi$
$464$	−989.084	+	1713.14i	−0.0989592	+	0.171402i
$465$	−285.037	−	493.699i	−0.0284264	−	0.0492360i
$466$	308.511	−	178.119i	0.0306684	−	0.0177064i
$467$	−17543.0			−1.73831			−0.869157	−	0.494536i	$-0.835338\pi$
$467$	−17543.0			−1.73831			−0.869157	+	0.494536i	$0.835338\pi$
$468$		0			0
$469$	−19009.8			−1.87163
$470$	−17501.5	+	10104.5i	−1.71763	+	0.991672i
$471$	−395.568	−	685.144i	−0.0386981	−	0.0670271i
$472$	135.493	−	234.680i	0.0132131	−	0.0228857i
$473$			5363.01i			0.521335i
$474$	−357.199	−	206.229i	−0.0346133	−	0.0199840i
$475$	−168.227	−	97.1258i	−0.0162501	−	0.00938197i
$476$		−	23815.1i		−	2.29320i
$477$	1031.19	−	1786.07i	0.0989830	−	0.171444i
$478$	3992.66	+	6915.49i	0.382050	+	0.661731i
$479$	−5455.22	+	3149.57i	−0.520366	+	0.300434i	−0.737085	−	0.675801i	$-0.763798\pi$
$479$	−5455.22	+	3149.57i	−0.520366	+	0.300434i	0.216718	+	0.976234i	$0.430465\pi$
$480$	758.498			0.0721262
$481$		0			0
$482$	25081.7			2.37020
$483$	−555.409	+	320.665i	−0.0523229	+	0.0302086i
$484$	2989.94	+	5178.73i	0.280799	+	0.486358i
$485$	−3918.39	+	6786.85i	−0.366855	+	0.635412i
$486$			2332.00i			0.217658i
$487$	−3093.21	−	1785.86i	−0.287817	−	0.166171i	0.349140	−	0.937070i	$-0.386474\pi$
$487$	−3093.21	−	1785.86i	−0.287817	−	0.166171i	−0.636957	+	0.770900i	$0.719807\pi$
$488$	−2130.60	−	1230.10i	−0.197639	−	0.114107i
$489$			995.368i			0.0920493i
$490$	13556.9	−	23481.2i	1.24987	−	2.16485i
$491$	−6692.61	−	11591.9i	−0.615139	−	1.06545i	−0.990360	−	0.138517i	$-0.955767\pi$
$491$	−6692.61	−	11591.9i	−0.615139	−	1.06545i	0.375221	−	0.926935i	$-0.377567\pi$
$492$	131.931	−	76.1707i	0.0120893	−	0.00697975i
$493$	3112.66			0.284356
$494$		0			0
$495$	6412.77			0.582288
$496$	−11306.3	+	6527.68i	−1.02352	+	0.590931i
$497$	−253.244	−	438.632i	−0.0228562	−	0.0395882i
$498$	355.250	−	615.311i	0.0319662	−	0.0553670i
$499$		−	19227.7i		−	1.72495i	−0.506098	−	0.862476i	$-0.668913\pi$
$499$		−	19227.7i		−	1.72495i	0.506098	−	0.862476i	$-0.331087\pi$
$500$	7966.61	+	4599.52i	0.712555	+	0.411394i
$501$	29.1637	+	16.8377i	0.00260068	+	0.00150150i
$502$		−	9238.13i		−	0.821350i
$503$	9325.62	−	16152.5i	0.826658	−	1.43181i	−0.0739878	−	0.997259i	$-0.523573\pi$
$503$	9325.62	−	16152.5i	0.826658	−	1.43181i	0.900646	−	0.434554i	$-0.143094\pi$
$504$	−2080.27	−	3603.13i	−0.183854	−	0.318445i
$505$	−4642.13	+	2680.13i	−0.409053	+	0.236167i
$506$	−5940.53			−0.521914
$507$		0			0
$508$	3528.35			0.308160
$509$	−13757.8	+	7943.04i	−1.19804	+	0.691688i	−0.960118	−	0.279596i	$-0.909799\pi$
$509$	−13757.8	+	7943.04i	−1.19804	+	0.691688i	−0.237921	+	0.971284i	$0.576466\pi$
$510$	−696.153	−	1205.77i	−0.0604435	−	0.104691i
$511$	4998.31	−	8657.32i	0.432705	−	0.749467i
$512$		−	14477.1i		−	1.24961i
$513$	588.939	+	340.024i	0.0506868	+	0.0292640i
$514$	875.285	+	505.346i	0.0751112	+	0.0433655i
$515$			3815.21i			0.326443i
$516$	−239.516	+	414.853i	−0.0204343	+	0.0353932i
$517$	−4854.66	−	8408.52i	−0.412975	−	0.715293i
$518$	36590.2	−	21125.4i	3.10363	−	1.79188i
$519$	−580.736			−0.0491166
$520$		0			0
$521$	1824.67			0.153436			0.0767179	−	0.997053i	$-0.475556\pi$
$521$	1824.67			0.153436			0.0767179	+	0.997053i	$0.475556\pi$
$522$	−2432.67	+	1404.50i	−0.203975	+	0.117765i
$523$	−8103.15	−	14035.1i	−0.677488	−	1.17344i	−0.975735	−	0.218954i	$-0.929735\pi$
$523$	−8103.15	−	14035.1i	−0.677488	−	1.17344i	0.298247	−	0.954489i	$-0.403598\pi$
$524$	−2795.02	+	4841.11i	−0.233017	+	0.403597i
$525$		−	37.2855i		−	0.00309956i
$526$	−24322.7	−	14042.7i	−2.01619	−	1.16405i
$527$	17790.5	+	10271.4i	1.47053	+	0.849009i
$528$			425.119i			0.0350396i
$529$	3348.53	−	5799.83i	0.275214	−	0.476685i
$530$	−1670.03	−	2892.58i	−0.136871	−	0.237067i
$531$	1269.92	−	733.190i	0.103785	−	0.0599204i
$532$	9405.57			0.766510
$533$		0			0
$534$	584.151			0.0473384
$535$	16044.3	−	9263.19i	1.29655	−	0.748565i
$536$	1522.38	+	2636.84i	0.122681	+	0.212489i
$537$	77.2081	−	133.728i	0.00620442	−	0.0107464i
$538$			17957.8i			1.43906i
$539$	11281.5	+	6513.35i	0.901534	+	0.520501i
$540$	993.550	+	573.626i	0.0791770	+	0.0457129i
$541$		−	2429.83i		−	0.193099i	−0.995328	−	0.0965496i	$-0.969219\pi$
$541$		−	2429.83i		−	0.193099i	0.995328	−	0.0965496i	$-0.0307806\pi$
$542$	−3123.82	+	5410.62i	−0.247564	+	0.428793i
$543$	461.343	+	799.070i	0.0364607	+	0.0631517i
$544$	−23670.7	+	13666.3i	−1.86558	+	1.07709i
$545$	17272.0			1.35752
$546$		0			0
$547$	−2409.16			−0.188315			−0.0941573	−	0.995557i	$-0.530016\pi$
$547$	−2409.16			−0.188315			−0.0941573	+	0.995557i	$0.530016\pi$
$548$	−2709.33	+	1564.23i	−0.211199	+	0.121936i
$549$	−6656.43	−	11529.3i	−0.517467	−	0.896280i
$550$	172.684	−	299.098i	0.0133878	−	0.0231883i
$551$			1229.32i			0.0950468i
$552$	88.9584	+	51.3602i	0.00685928	+	0.00396021i
$553$	10365.5	+	5984.53i	0.797081	+	0.460195i
$554$			23775.7i			1.82334i
$555$	563.031	−	975.198i	0.0430619	−	0.0745853i
$556$	−2389.70	−	4139.09i	−0.182277	−	0.315713i
$557$	7507.32	−	4334.35i	0.571087	−	0.329717i	−0.186497	−	0.982456i	$-0.559713\pi$
$557$	7507.32	−	4334.35i	0.571087	−	0.329717i	0.757583	+	0.652739i	$0.226380\pi$
$558$	−18538.7			−1.40646
$559$		0			0
$560$	−25677.1			−1.93760
$561$	579.308	−	334.464i	0.0435979	−	0.0251713i
$562$	5658.12	+	9800.15i	0.424686	+	0.735577i
$563$	−3909.17	+	6770.89i	−0.292632	+	0.506854i	−0.974431	−	0.224685i	$-0.927865\pi$
$563$	−3909.17	+	6770.89i	−0.292632	+	0.506854i	0.681799	+	0.731540i	$0.261198\pi$
$564$		−	867.250i		−	0.0647479i
$565$	−11771.9	−	6796.50i	−0.876543	−	0.506072i
$566$	−17430.8	−	10063.7i	−1.29447	−	0.747363i
$567$		−	22448.5i		−	1.66270i
$568$	−40.5615	+	70.2545i	−0.00299634	+	0.00518981i
$569$	4558.62	+	7895.76i	0.335865	+	0.581735i	0.983651	−	0.180087i	$-0.0576380\pi$
$569$	4558.62	+	7895.76i	0.335865	+	0.581735i	−0.647786	+	0.761823i	$0.724305\pi$
$570$	476.210	−	274.940i	0.0349934	−	0.0202034i
$571$	11842.4			0.867932			0.433966	−	0.900929i	$-0.357114\pi$
$571$	11842.4			0.867932			0.433966	+	0.900929i	$0.357114\pi$
$572$		0			0
$573$	926.302			0.0675337
$574$	−8398.15	+	4848.67i	−0.610683	+	0.352578i
$575$	−159.005	−	275.404i	−0.0115321	−	0.0199742i
$576$	4504.52	−	7802.06i	0.325848	−	0.564385i
$577$		−	10958.1i		−	0.790623i	−0.918547	−	0.395312i	$-0.870637\pi$
$577$		−	10958.1i		−	0.790623i	0.918547	−	0.395312i	$-0.129363\pi$
$578$	27135.8	+	15666.8i	1.95277	+	1.12743i
$579$	943.399	+	544.672i	0.0677139	+	0.0390946i
$580$			2073.88i			0.148471i
$581$	−10309.0	+	17855.6i	−0.736123	+	1.27500i
$582$	−368.860	−	638.884i	−0.0262710	−	0.0455028i
$583$	1389.72	−	802.358i	0.0987247	−	0.0569987i
$584$	−1601.13			−0.113451
$585$		0			0
$586$	11167.0			0.787209
$587$	19968.6	−	11528.9i	1.40408	−	0.810644i	0.409269	−	0.912414i	$-0.365784\pi$
$587$	19968.6	−	11528.9i	1.40408	−	0.810644i	0.994808	+	0.101770i	$0.0324506\pi$
$588$	581.781	+	1007.67i	0.0408032	+	0.0706731i
$589$	−4056.59	+	7026.22i	−0.283784	+	0.491529i
$590$		−	2374.83i		−	0.165712i
$591$	−878.318	−	507.097i	−0.0611323	−	0.0352947i
$592$	−22333.2	−	12894.1i	−1.55049	−	0.895173i
$593$			9904.56i			0.685888i	0.939356	+	0.342944i	$0.111424\pi$
$593$			9904.56i			0.685888i	−0.939356	+	0.342944i	$0.888576\pi$
$594$	−604.544	+	1047.10i	−0.0417588	+	0.0723284i
$595$	20201.6	+	34990.2i	1.39191	+	2.41085i
$596$	−3847.32	+	2221.25i	−0.264416	+	0.152661i
$597$	825.549			0.0565954
$598$		0			0
$599$	21334.5			1.45527			0.727633	−	0.685967i	$-0.240620\pi$
$599$	21334.5			1.45527			0.727633	+	0.685967i	$0.240620\pi$
$600$	−5.17184	+	2.98596i	−0.000351899	+	0.000203169i
$601$	9742.19	+	16874.0i	0.661219	+	1.14526i	0.980296	+	0.197536i	$0.0632938\pi$
$601$	9742.19	+	16874.0i	0.661219	+	1.14526i	−0.319077	+	0.947729i	$0.603373\pi$
$602$	15246.5	−	26407.6i	1.03222	−	1.78787i
$603$			16476.1i			1.11270i
$604$	−1107.87	−	639.626i	−0.0746331	−	0.0430895i
$605$	−8785.91	−	5072.55i	−0.590410	−	0.340873i
$606$		−	504.592i		−	0.0338245i
$607$	−9927.83	+	17195.5i	−0.663852	+	1.14982i	0.315744	+	0.948845i	$0.397746\pi$
$607$	−9927.83	+	17195.5i	−0.663852	+	1.14982i	−0.979595	+	0.200980i	$0.935587\pi$
$608$	−5397.39	−	9348.56i	−0.360022	−	0.623576i
$609$	−204.348	+	117.980i	−0.0135971	+	0.00785026i
$610$	−21560.4			−1.43108
$611$		0			0
$612$	−20640.8			−1.36333
$613$	4463.13	−	2576.79i	0.294069	−	0.169781i	−0.345707	−	0.938343i	$-0.612361\pi$
$613$	4463.13	−	2576.79i	0.294069	−	0.169781i	0.639775	+	0.768562i	$0.279027\pi$
$614$	9586.14	+	16603.7i	0.630073	+	1.09132i
$615$	−129.226	+	223.826i	−0.00847302	+	0.0146757i
$616$		−	3237.27i		−	0.211743i
$617$	800.396	+	462.109i	0.0522248	+	0.0301520i	0.525885	−	0.850556i	$-0.323734\pi$
$617$	800.396	+	462.109i	0.0522248	+	0.0301520i	−0.473660	+	0.880708i	$0.657068\pi$
$618$	−311.031	−	179.574i	−0.0202451	−	0.0116885i
$619$			15690.6i			1.01883i	0.860520	+	0.509417i	$0.170139\pi$
$619$			15690.6i			1.01883i	−0.860520	+	0.509417i	$0.829861\pi$
$620$	−6843.53	+	11853.3i	−0.443295	+	0.767809i
$621$	556.654	+	964.153i	0.0359706	+	0.0623029i
$622$	−26037.2	+	15032.6i	−1.67845	+	0.969054i
$623$	−16951.4			−1.09012
$624$		0			0
$625$	−16144.0			−1.03322
$626$	24966.2	−	14414.3i	1.59401	−	0.920303i
$627$	132.094	+	228.793i	0.00841358	+	0.0145727i
$628$	−9497.29	+	16449.8i	−0.603476	+	1.04525i
$629$			40577.8i			2.57225i
$630$	−31576.7	−	18230.8i	−1.99690	−	1.15291i
$631$	18276.2	+	10551.8i	1.15303	+	0.665705i	0.949625	−	0.313389i	$-0.101464\pi$
$631$	18276.2	+	10551.8i	1.15303	+	0.665705i	0.203409	+	0.979094i	$0.434798\pi$
$632$		−	1917.05i		−	0.120659i
$633$	−445.830	+	772.201i	−0.0279939	+	0.0484869i
$634$	−930.294	−	1611.32i	−0.0582756	−	0.100936i
$635$	−5184.01	+	2992.99i	−0.323970	+	0.187044i
$636$	143.335			0.00893650
$637$		0			0
$638$	−2185.66			−0.135629
$639$	−380.167	+	219.490i	−0.0235355	+	0.0135882i
$640$	3573.03	+	6188.67i	0.220682	+	0.382232i
$641$	−3347.69	+	5798.37i	−0.206280	+	0.357288i	−0.950540	−	0.310602i	$-0.899469\pi$
$641$	−3347.69	+	5798.37i	−0.206280	+	0.357288i	0.744260	+	0.667891i	$0.232803\pi$
$642$			1743.99i			0.107212i
$643$	8355.15	+	4823.85i	0.512434	+	0.295854i	0.733833	−	0.679329i	$-0.237729\pi$
$643$	8355.15	+	4823.85i	0.512434	+	0.295854i	−0.221400	+	0.975183i	$0.571063\pi$
$644$	13334.9	+	7698.93i	0.815947	+	0.471087i
$645$		−	812.694i		−	0.0496121i
$646$	−9907.50	+	17160.3i	−0.603414	+	1.04514i
$647$	−11873.8	−	20566.0i	−0.721493	−	1.24966i	−0.960401	−	0.278620i	$-0.910123\pi$
$647$	−11873.8	−	20566.0i	−0.721493	−	1.24966i	0.238909	−	0.971042i	$-0.423210\pi$
$648$	−3113.81	+	1797.76i	−0.188769	+	0.108986i
$649$	1140.98			0.0690096
$650$		0			0
$651$	−1557.28			−0.0937551
$652$	20696.3	−	11949.0i	1.24314	−	0.717729i
$653$	−9916.76	−	17176.3i	−0.594292	−	1.02934i	−0.993646	−	0.112547i	$-0.964099\pi$
$653$	−9916.76	−	17176.3i	−0.594292	−	1.02934i	0.399354	−	0.916797i	$-0.369234\pi$
$654$	−812.955	+	1408.08i	−0.0486071	+	0.0841900i
$655$		−	9483.70i		−	0.565738i
$656$	5125.88	+	2959.43i	0.305080	+	0.176138i
$657$	−7503.41	−	4332.10i	−0.445565	−	0.257247i
$658$			55205.1i			3.27070i
$659$	−5403.70	+	9359.48i	−0.319421	+	0.553253i	−0.980367	−	0.197180i	$-0.936822\pi$
$659$	−5403.70	+	9359.48i	−0.319421	+	0.553253i	0.660947	+	0.750433i	$0.270155\pi$
$660$	222.844	+	385.977i	0.0131427	+	0.0227638i
$661$	−11632.0	+	6715.75i	−0.684468	+	0.395178i	−0.801536	−	0.597946i	$-0.795984\pi$
$661$	−11632.0	+	6715.75i	−0.684468	+	0.395178i	0.117068	+	0.993124i	$0.462650\pi$
$662$	31529.7			1.85111
$663$		0			0
$664$	3302.32			0.193004
$665$	−13819.1	+	7978.44i	−0.805835	+	0.465249i
$666$	−18309.6	−	31713.2i	−1.06529	−	1.84514i
$667$	−1006.26	+	1742.89i	−0.0584146	+	0.101177i
$668$		−	808.520i		−	0.0468302i
$669$	18.1586	+	10.4838i	0.00104940	+	0.000605873i
$670$	23108.4	+	13341.7i	1.33247	+	0.769303i
$671$		−	10358.6i		−	0.595961i
$672$	1036.00	−	1794.40i	0.0594710	−	0.103007i
$673$	10790.7	+	18690.0i	0.618054	+	1.07050i	0.989840	+	0.142182i	$0.0454120\pi$
$673$	10790.7	+	18690.0i	0.618054	+	1.07050i	−0.371787	+	0.928318i	$0.621255\pi$
$674$	25717.9	−	14848.2i	1.46976	−	0.848564i
$675$	−64.7251			−0.00369077
$676$		0			0
$677$	17482.4			0.992474			0.496237	−	0.868187i	$-0.334715\pi$
$677$	17482.4			0.992474			0.496237	+	0.868187i	$0.334715\pi$
$678$	1108.15	−	639.793i	0.0627705	−	0.0362405i
$679$	10703.9	+	18539.7i	0.604975	+	1.04785i
$680$	3235.64	−	5604.29i	0.182472	−	0.316051i
$681$		−	1206.76i		−	0.0679048i
$682$	−12492.2	−	7212.39i	−0.701396	−	0.404951i
$683$	−2461.44	−	1421.11i	−0.137898	−	0.0796155i	0.429464	−	0.903084i	$-0.358703\pi$
$683$	−2461.44	−	1421.11i	−0.137898	−	0.0796155i	−0.567362	+	0.823469i	$0.692036\pi$
$684$		−	8151.92i		−	0.455697i
$685$	2653.78	−	4596.48i	0.148023	−	0.256383i
$686$	−16607.1	−	28764.3i	−0.924287	−	1.60091i
$687$	−163.896	+	94.6255i	−0.00910193	+	0.00525500i
$688$	−18611.6			−1.03134
$689$		0			0
$690$	900.208			0.0496672
$691$	−19810.8	+	11437.8i	−1.09065	+	0.629686i	−0.933749	−	0.357929i	$-0.883483\pi$
$691$	−19810.8	+	11437.8i	−1.09065	+	0.629686i	−0.156899	+	0.987615i	$0.550150\pi$
$692$	6971.52	+	12075.0i	0.382973	+	0.663329i
$693$	8758.91	−	15170.9i	0.480121	−	0.831593i
$694$			13545.4i			0.740886i
$695$	7022.11	+	4054.22i	0.383257	+	0.221274i
$696$	32.7299	+	18.8966i	0.00178251	+	0.00102913i
$697$		−	9313.38i		−	0.506125i
$698$	6453.62	−	11178.0i	0.349962	−	0.606151i
$699$	−12.9680	−	22.4612i	−0.000701708	−	0.00121539i
$700$	−775.262	+	447.598i	−0.0418602	+	0.0241680i
$701$	−11980.3			−0.645492			−0.322746	−	0.946486i	$-0.604606\pi$
$701$	−11980.3			−0.645492			−0.322746	+	0.946486i	$0.604606\pi$
$702$		0			0
$703$	−16025.9			−0.859782
$704$	6070.71	−	3504.92i	0.324998	−	0.187638i
$705$	735.660	+	1274.20i	0.0393001	+	0.0680698i
$706$	19110.5	−	33100.4i	1.01874	−	1.76452i
$707$			14642.7i			0.778918i
$708$	88.2597	+	50.9568i	0.00468503	+	0.00270491i
$709$	−3641.44	−	2102.38i	−0.192887	−	0.111363i	0.400446	−	0.916320i	$-0.368855\pi$
$709$	−3641.44	−	2102.38i	−0.192887	−	0.111363i	−0.593333	+	0.804957i	$0.702188\pi$
$710$			710.936i			0.0375788i
$711$	5186.86	−	8983.91i	0.273590	−	0.473872i
$712$	1357.53	+	2351.31i	0.0714545	+	0.123763i
$713$	−11502.6	+	6641.04i	−0.604175	+	0.348820i
$714$	−3803.38			−0.199353
$715$		0			0
$716$	−3707.41			−0.193509
$717$	503.484	−	290.686i	0.0262245	−	0.0151407i
$718$	5258.33	+	9107.69i	0.273313	+	0.473393i
$719$	−5768.50	+	9991.33i	−0.299205	+	0.518239i	−0.975954	−	0.217975i	$-0.930055\pi$
$719$	−5768.50	+	9991.33i	−0.299205	+	0.518239i	0.676749	+	0.736214i	$0.263388\pi$
$720$			22254.7i			1.15192i
$721$	9025.76	+	5211.02i	0.466209	+	0.269166i
$722$	15999.2	+	9237.13i	0.824692	+	0.476136i
$723$		−	1826.07i		−	0.0939315i
$724$	11076.5	−	19185.1i	0.568584	−	0.984817i
$725$	−58.5016	−	101.328i	−0.00299682	−	0.00519065i
$726$	827.067	−	477.508i	0.0422801	−	0.0244104i
$727$	33899.7			1.72940			0.864698	−	0.502293i	$-0.167510\pi$
$727$	33899.7			1.72940			0.864698	+	0.502293i	$0.167510\pi$
$728$		0			0
$729$	−19342.9			−0.982723
$730$	−12151.9	+	7015.91i	−0.616113	+	0.355713i
$731$	14642.8	+	25362.0i	0.740879	+	1.28324i
$732$	462.622	−	801.285i	0.0233593	−	0.0404595i
$733$			378.221i			0.0190585i	0.999955	+	0.00952927i	$0.00303331\pi$
$733$			378.221i			0.0190585i	−0.999955	+	0.00952927i	$0.996967\pi$
$734$	−5452.07	−	3147.75i	−0.274168	−	0.158291i
$735$	−1709.56	−	987.013i	−0.0857931	−	0.0495327i
$736$		−	17672.1i		−	0.885059i
$737$	−6409.94	+	11102.3i	−0.320371	+	0.554898i
$738$	4202.41	+	7278.78i	0.209611	+	0.363056i
$739$	19627.2	−	11331.8i	0.976996	−	0.564069i	0.0756339	−	0.997136i	$-0.475902\pi$
$739$	19627.2	−	11331.8i	0.976996	−	0.564069i	0.901362	+	0.433067i	$0.142569\pi$
$740$	−27035.9			−1.34305
$741$		0			0
$742$	−9124.06			−0.451422
$743$	−14209.2	+	8203.66i	−0.701593	+	0.405065i	−0.807940	−	0.589264i	$-0.799418\pi$
$743$	−14209.2	+	8203.66i	−0.701593	+	0.405065i	0.106348	+	0.994329i	$0.466084\pi$
$744$	124.713	+	216.009i	0.00614541	+	0.0106442i
$745$	3768.43	−	6527.11i	0.185322	−	0.320986i
$746$		−	42974.0i		−	2.10910i
$747$	15475.7	+	8934.90i	0.758001	+	0.437632i
$748$	−13908.7	−	8030.22i	−0.679885	−	0.392532i
$749$		−	50608.7i		−	2.46889i
$750$	734.565	−	1272.30i	0.0357633	−	0.0619439i
$751$	10978.9	+	19016.1i	0.533458	+	0.923976i	0.999236	+	0.0390744i	$0.0124409\pi$
$751$	10978.9	+	19016.1i	0.533458	+	0.923976i	−0.465779	+	0.884901i	$0.654226\pi$
$752$	29180.7	−	16847.5i	1.41504	−	0.816973i
$753$	−672.584			−0.0325502
$754$		0			0
$755$	2170.30			0.104616
$756$	2714.09	−	1566.98i	0.130569	−	0.0753843i
$757$	−10411.7	−	18033.7i	−0.499896	−	0.865846i	0.500104	−	0.865965i	$-0.333295\pi$
$757$	−10411.7	−	18033.7i	−0.499896	−	0.865846i	−1.00000		0.000119832i	$0.999962\pi$
$758$	−7370.59	+	12766.2i	−0.353182	+	0.611729i
$759$			432.501i			0.0206835i
$760$	2213.37	+	1277.89i	0.105641	+	0.0609919i
$761$	24643.7	+	14228.1i	1.17390	+	0.677749i	0.954594	−	0.297909i	$-0.0962891\pi$
$761$	24643.7	+	14228.1i	1.17390	+	0.677749i	0.219301	+	0.975657i	$0.429622\pi$
$762$		−	563.494i		−	0.0267890i
$763$	23591.0	−	40860.8i	1.11933	−	1.93874i
$764$	−11119.9	−	19260.2i	−0.526576	−	0.912056i
$765$	30326.4	−	17509.0i	1.43327	−	0.827500i
$766$	46604.2			2.19828
$767$		0			0
$768$	−1420.04			−0.0667203
$769$	11648.0	−	6724.98i	0.546213	−	0.315356i	−0.201380	−	0.979513i	$-0.564543\pi$
$769$	11648.0	−	6724.98i	0.546213	−	0.315356i	0.747593	+	0.664157i	$0.231209\pi$
$770$	−14185.2	−	24569.5i	−0.663896	−	1.14990i
$771$	36.7918	−	63.7253i	0.00171858	−	0.00297667i
$772$		−	26154.3i		−	1.21932i
$773$	23017.0	+	13288.9i	1.07098	+	0.618329i	0.928448	−	0.371462i	$-0.121143\pi$
$773$	23017.0	+	13288.9i	1.07098	+	0.618329i	0.142529	+	0.989791i	$0.454477\pi$
$774$	−22887.8	−	13214.3i	−1.06290	−	0.613667i
$775$		−	772.190i		−	0.0357908i
$776$	1714.42	−	2969.46i	0.0793092	−	0.137368i
$777$	−1538.04	−	2663.96i	−0.0710125	−	0.122997i
$778$	−17498.0	+	10102.5i	−0.806341	+	0.465541i
$779$	3678.24			0.169174
$780$		0			0
$781$	−341.566			−0.0156494
$782$	−28093.1	+	16219.6i	−1.28467	+	0.741702i
$783$	204.806	+	354.735i	0.00934761	+	0.0161905i
$784$	−22603.7	+	39150.8i	−1.02969	+	1.78347i
$785$		−	32225.0i		−	1.46517i
$786$	773.147	+	446.377i	0.0350856	+	0.0202567i
$787$	−7171.90	−	4140.70i	−0.324842	−	0.187548i	0.328707	−	0.944432i	$-0.393387\pi$
$787$	−7171.90	−	4140.70i	−0.324842	−	0.187548i	−0.653549	+	0.756884i	$0.726721\pi$
$788$			24350.0i			1.10080i
$789$	−1022.38	+	1770.82i	−0.0461315	+	0.0799020i
$790$	−8400.22	−	14549.6i	−0.378312	−	0.655256i
$791$	−32157.3	+	18566.0i	−1.44549	+	0.834555i
$792$	−2805.79			−0.125883
$793$		0			0
$794$	−2513.37			−0.112338
$795$	−210.594	+	121.587i	−0.00939499	+	0.00542420i
$796$	−9910.40	−	17165.3i	−0.441287	−	0.764332i
$797$	10334.4	−	17899.7i	0.459302	−	0.795535i	−0.539622	−	0.841908i	$-0.681433\pi$
$797$	10334.4	−	17899.7i	0.459302	−	0.795535i	0.998924	+	0.0463725i	$0.0147661\pi$
$798$		−	1502.11i		−	0.0666343i
$799$	−45916.0	−	26509.6i	−2.03303	−	1.17377i
$800$	889.769	+	513.709i	0.0393226	+	0.0227029i
$801$			14692.0i			0.648085i
$802$	14762.3	−	25569.1i	0.649969	−	1.12578i
$803$	−3370.76	−	5838.33i	−0.148134	−	0.256576i
$804$	−991.675	+	572.544i	−0.0434996	+	0.0251145i
$805$	−26123.0			−1.14375
$806$		0			0
$807$	1307.42			0.0570303
$808$	2031.07	−	1172.64i	0.0884318	−	0.0510561i
$809$	−3619.43	−	6269.03i	−0.157296	−	0.272444i	0.776597	−	0.629998i	$-0.216944\pi$
$809$	−3619.43	−	6269.03i	−0.157296	−	0.272444i	−0.933893	+	0.357554i	$0.883611\pi$
$810$	−15755.0	+	27288.5i	−0.683425	+	1.18373i
$811$			13101.3i			0.567260i	0.958934	+	0.283630i	$0.0915387\pi$
$811$			13101.3i			0.567260i	−0.958934	+	0.283630i	$0.908461\pi$
$812$	4906.24	+	2832.62i	0.212039	+	0.122421i
$813$	393.921	+	227.430i	0.0169931	+	0.00981099i
$814$		−	28493.1i		−	1.22688i
$815$	−20271.9	+	35112.0i	−0.871282	+	1.50910i
$816$	1160.71	+	2010.41i	0.0497954	+	0.0862482i
$817$	−10016.5	+	5783.04i	−0.428927	+	0.247641i
$818$	−2128.85			−0.0909946
$819$		0			0
$820$	6205.25			0.264264
$821$	10472.7	−	6046.44i	0.445190	−	0.257031i	−0.260606	−	0.965445i	$-0.583922\pi$
$821$	10472.7	−	6046.44i	0.445190	−	0.257031i	0.705797	+	0.708414i	$0.250589\pi$
$822$	249.815	+	432.693i	0.0106001	+	0.0183600i
$823$	13520.6	−	23418.4i	0.572659	−	0.991874i	−0.423633	−	0.905834i	$-0.639245\pi$
$823$	13520.6	−	23418.4i	0.572659	−	0.991874i	0.996292	−	0.0860402i	$-0.0274214\pi$
$824$		−	1669.27i		−	0.0705727i
$825$	−21.7759	−	12.5723i	−0.000918955	−	0.000530559i
$826$	−5618.21	−	3243.67i	−0.236662	−	0.136637i
$827$			25572.3i			1.07526i	0.843182	+	0.537628i	$0.180680\pi$
$827$			25572.3i			1.07526i	−0.843182	+	0.537628i	$0.819320\pi$
$828$	6672.76	−	11557.6i	0.280066	−	0.485088i
$829$	−8752.89	−	15160.4i	−0.366707	−	0.635156i	0.622341	−	0.782746i	$-0.286182\pi$
$829$	−8752.89	−	15160.4i	−0.366707	−	0.635156i	−0.989049	+	0.147590i	$0.952848\pi$
$830$	25063.2	−	14470.2i	1.04814	−	0.605144i
$831$	1730.99			0.0722593
$832$		0			0
$833$	71134.3			2.95877
$834$	−661.031	+	381.646i	−0.0274456	+	0.0158457i
$835$	685.841	+	1187.91i	0.0284246	+	0.0492328i
$836$	3171.47	−	5493.14i	0.131205	−	0.227254i
$837$			2703.33i			0.111638i
$838$	11014.6	+	6359.31i	0.454051	+	0.262146i
$839$	−24502.8	−	14146.7i	−1.00826	−	0.582119i	−0.0975785	−	0.995228i	$-0.531110\pi$
$839$	−24502.8	−	14146.7i	−1.00826	−	0.582119i	−0.910682	+	0.413108i	$0.864443\pi$
$840$			490.566i			0.0201502i
$841$	11824.3	−	20480.2i	0.484820	−	0.839733i
$842$	25441.7	+	44066.3i	1.04130	+	1.80359i
$843$	713.502	−	411.940i	0.0291510	−	0.0168303i
$844$	21408.1			0.873100
$845$		0			0
$846$	47847.0			1.94446
$847$	−24000.5	+	13856.7i	−0.973635	+	0.562128i
$848$	2784.48	+	4822.86i	0.112759	+	0.195304i
$849$	−732.687	+	1269.05i	−0.0296181	+	0.0513000i
$850$		−	1885.94i		−	0.0761025i
$851$	−22721.0	−	13118.0i	−0.915236	−	0.528412i
$852$	−26.4217	−	15.2546i	−0.00106243	−	0.000613395i
$853$			15866.0i			0.636861i	0.947946	+	0.318430i	$0.103156\pi$
$853$			15866.0i			0.636861i	−0.947946	+	0.318430i	$0.896844\pi$
$854$	−29448.4	+	51006.1i	−1.17998	+	2.04379i
$855$	6915.02	+	11977.2i	0.276595	+	0.479076i
$856$	−7019.88	+	4052.93i	−0.280297	+	0.161830i
$857$	−23623.3			−0.941607			−0.470804	−	0.882238i	$-0.656036\pi$
$857$	−23623.3			−0.941607			−0.470804	+	0.882238i	$0.656036\pi$
$858$		0			0
$859$	33403.1			1.32677			0.663387	−	0.748277i	$-0.269118\pi$
$859$	33403.1			1.32677			0.663387	+	0.748277i	$0.269118\pi$
$860$	−16898.0	+	9756.08i	−0.670021	+	0.386837i
$861$	353.009	+	611.429i	0.0139727	+	0.0242014i
$862$	−26250.6	+	45467.3i	−1.03724	+	1.79655i
$863$		−	45490.5i		−	1.79434i	−0.441687	−	0.897169i	$-0.645620\pi$
$863$		−	45490.5i		−	1.79434i	0.441687	−	0.897169i	$-0.354380\pi$
$864$	−3114.96	−	1798.42i	−0.122654	−	0.0708144i
$865$	−20485.7	−	11827.4i	−0.805243	−	0.464907i
$866$		−	58240.8i		−	2.28534i
$867$	1140.63	−	1975.62i	0.0446802	−	0.0773884i
$868$	18694.5	+	32379.9i	0.731029	+	1.26618i
$869$	6990.29	−	4035.85i	0.272876	−	0.157545i
$870$	331.208			0.0129069
$871$		0			0
$872$	−7557.03			−0.293479
$873$	16068.6	−	9277.20i	0.622954	−	0.359663i
$874$	−6405.78	−	11095.1i	−0.247916	−	0.429404i
$875$	−21316.2	+	36920.8i	−0.823565	+	1.42646i
$876$		−	602.162i		−	0.0232251i
$877$	16948.2	+	9785.05i	0.652565	+	0.376759i	0.789438	−	0.613830i	$-0.210372\pi$
$877$	16948.2	+	9785.05i	0.652565	+	0.376759i	−0.136873	+	0.990589i	$0.543705\pi$
$878$	9304.67	+	5372.05i	0.357651	+	0.206490i
$879$		−	813.015i		−	0.0311972i
$880$	−8658.07	+	14996.2i	−0.331663	+	0.574458i
$881$	−1508.47	−	2612.75i	−0.0576864	−	0.0999158i	0.835740	−	0.549125i	$-0.185039\pi$
$881$	−1508.47	−	2612.75i	−0.0576864	−	0.0999158i	−0.893426	+	0.449209i	$0.851706\pi$
$882$	−55594.3	+	32097.4i	−2.12240	+	1.22537i
$883$	−17163.8			−0.654141			−0.327071	−	0.945000i	$-0.606061\pi$
$883$	−17163.8			−0.654141			−0.327071	+	0.945000i	$0.606061\pi$
$884$		0			0
$885$	−172.900			−0.00656720
$886$	25037.1	−	14455.2i	0.949367	−	0.548117i
$887$	−14232.3	−	24651.1i	−0.538754	−	0.933149i	−0.998971	−	0.0453430i	$-0.985562\pi$
$887$	−14232.3	−	24651.1i	−0.538754	−	0.933149i	0.460218	−	0.887806i	$-0.347771\pi$
$888$	−246.343	+	426.679i	−0.00930940	+	0.0161243i
$889$			16352.0i			0.616903i
$890$	20606.2	+	11897.0i	0.776090	+	0.448076i
$891$	−13110.6	−	7569.42i	−0.492954	−	0.284607i
$892$		−	503.418i		−	0.0188965i
$893$	10469.8	−	18134.1i	0.392337	−	0.679548i
$894$	354.743	+	614.434i	0.0132711	+	0.0229863i
$895$	5447.09	−	3144.88i	0.203437	−	0.117454i
$896$	19520.9			0.727845
$897$		0			0
$898$	−21314.6			−0.792070
$899$	−4232.09	+	2443.40i	−0.157006	+	0.0906473i
$900$	387.939	+	671.929i	0.0143681	+	0.0248863i
$901$	4381.40	−	7588.80i	0.162004	−	0.280599i
$902$			6539.70i			0.241406i
$903$	−1922.61	−	1110.02i	−0.0708533	−	0.0409072i
$904$	5150.56	+	2973.68i	0.189497	+	0.109406i
$905$			37583.4i			1.38046i
$906$	−102.151	+	176.931i	−0.00374586	+	0.00648802i
$907$	−13305.0	−	23045.0i	−0.487085	−	0.843657i	0.512804	−	0.858505i	$-0.328607\pi$
$907$	−13305.0	−	23045.0i	−0.487085	−	0.843657i	−0.999890	+	0.0148489i	$0.995273\pi$
$908$	−25091.7	+	14486.7i	−0.917068	+	0.529469i
$909$	12691.0			0.463073
$910$		0			0
$911$	−52648.2			−1.91472			−0.957362	−	0.288890i	$-0.906714\pi$
$911$	−52648.2			−1.91472			−0.957362	+	0.288890i	$0.906714\pi$
$912$	−793.996	+	458.414i	−0.0288288	+	0.0166443i
$913$	6952.16	+	12041.5i	0.252008	+	0.436490i
$914$	8297.04	−	14370.9i	0.300265	−	0.520073i
$915$			1569.71i			0.0567137i
$916$	3935.02	+	2271.88i	0.141940	+	0.0819489i
$917$	−22435.9	−	12953.3i	−0.807958	−	0.466475i
$918$			6602.41i			0.237377i
$919$	−23461.8	+	40637.0i	−0.842146	+	1.45864i	0.0459311	+	0.998945i	$0.485375\pi$
$919$	−23461.8	+	40637.0i	−0.842146	+	1.45864i	−0.888077	+	0.459695i	$0.847959\pi$
$920$	2092.03	+	3623.50i	0.0749697	+	0.129851i
$921$	1208.83	−	697.921i	0.0432491	−	0.0249699i
$922$	−43300.6			−1.54667
$923$		0			0
$924$	1217.49			0.0433468
$925$	1320.95	−	762.648i	0.0469540	−	0.0271089i
$926$	16454.4	+	28499.8i	0.583935	+	1.01141i
$927$	4516.46	−	7822.74i	0.160022	−	0.277166i
$928$		−	6502.00i		−	0.229999i
$929$	−35648.9	−	20581.9i	−1.25899	−	0.726878i	−0.286111	−	0.958196i	$-0.592363\pi$
$929$	−35648.9	−	20581.9i	−1.25899	−	0.726878i	−0.972878	+	0.231319i	$0.925696\pi$
$930$	1893.03	+	1092.94i	0.0667473	+	0.0385365i
$931$			28093.9i			0.988980i
$932$	−311.351	+	539.276i	−0.0109427	+	0.0189534i
$933$	1094.45	+	1895.64i	0.0384037	+	0.0665172i
$934$	58254.5	−	33633.3i	2.04084	−	1.17828i
$935$	27247.1			0.953022
$936$		0			0
$937$	−23380.3			−0.815156			−0.407578	−	0.913170i	$-0.633627\pi$
$937$	−23380.3			−0.815156			−0.407578	+	0.913170i	$0.633627\pi$
$938$	63125.5	−	36445.5i	2.19736	−	1.26864i
$939$	−1049.43	−	1817.67i	−0.0364717	−	0.0631709i
$940$	17662.6	−	30592.6i	0.612863	−	1.06151i
$941$		−	34506.2i		−	1.19540i	−0.801720	−	0.597700i	$-0.796082\pi$
$941$		−	34506.2i		−	1.19540i	0.801720	−	0.597700i	$-0.203918\pi$
$942$	2627.11	+	1516.76i	0.0908659	+	0.0524615i
$943$	5214.90	+	3010.82i	0.180085	+	0.103972i
$944$			3959.61i			0.136519i
$945$	−2658.44	+	4604.55i	−0.0915121	+	0.158504i
$946$	−10281.9	−	17808.8i	−0.353376	−	0.612066i
$947$	418.670	−	241.719i	0.0143664	−	0.00829443i	−0.492800	−	0.870143i	$-0.664026\pi$
$947$	418.670	−	241.719i	0.0143664	−	0.00829443i	0.507166	+	0.861848i	$0.330693\pi$
$948$	720.975			0.0247006
$949$		0			0
$950$	744.835			0.0254375
$951$	−117.312	+	67.7302i	−0.00400011	+	0.00230947i
$952$	−8838.81	−	15309.3i	−0.300911	−	0.521194i
$953$	−5981.33	+	10360.0i	−0.203310	+	0.352143i	−0.949593	−	0.313486i	$-0.898503\pi$
$953$	−5981.33	+	10360.0i	−0.203310	+	0.352143i	0.746283	+	0.665629i	$0.231836\pi$
$954$			7907.94i			0.268374i
$955$	32675.7	+	18865.3i	1.10718	+	0.639232i
$956$	−12088.3	−	6979.16i	−0.408956	−	0.236111i
$957$			159.127i			0.00537499i
$958$	12076.7	−	20917.4i	0.407286	−	0.705439i
$959$	−7249.35	−	12556.2i	−0.244102	−	0.422797i
$960$	−919.936	+	531.125i	−0.0309279	+	0.0178562i
$961$	−2460.54			−0.0825934
$962$		0			0
$963$	−43863.2			−1.46778
$964$	−37968.8	+	21921.3i	−1.26856	+	0.732405i
$965$	22185.8	+	38427.0i	0.740091	+	1.28188i
$966$	1229.55	−	2129.65i	0.0409526	−	0.0709320i
$967$			7695.43i			0.255913i	0.991780	+	0.127957i	$0.0408419\pi$
$967$			7695.43i			0.255913i	−0.991780	+	0.127957i	$0.959158\pi$
$968$	3844.11	+	2219.40i	0.127639	+	0.0736923i
$969$	1249.36	+	721.318i	0.0414192	+	0.0239134i
$970$		−	30049.2i		−	0.994661i
$971$	22088.9	−	38259.2i	0.730039	−	1.26446i	−0.226827	−	0.973935i	$-0.572835\pi$
$971$	22088.9	−	38259.2i	0.730039	−	1.26446i	0.956866	−	0.290529i	$-0.0938314\pi$
$972$	−2038.16	−	3530.20i	−0.0672573	−	0.116493i
$973$	19182.4	−	11074.9i	0.632023	−	0.364898i
$974$	13695.4			0.450542
$975$		0			0
$976$	35948.2			1.17897
$977$	2955.40	−	1706.30i	0.0967776	−	0.0558746i	−0.450830	−	0.892610i	$-0.648872\pi$
$977$	2955.40	−	1706.30i	0.0967776	−	0.0558746i	0.547608	+	0.836735i	$0.315539\pi$
$978$	−1908.31	−	3305.29i	−0.0623937	−	0.108069i
$979$	−5715.84	+	9900.13i	−0.186598	+	0.323197i
$980$			47394.8i			1.54487i
$981$	−35414.6	−	20446.6i	−1.15260	−	0.665454i
$982$	44447.9	+	25662.0i	1.44439	+	0.833919i
$983$		−	6313.78i		−	0.204861i	−0.994740	−	0.102431i	$-0.967338\pi$
$983$		−	6313.78i		−	0.204861i	0.994740	−	0.102431i	$-0.0326619\pi$
$984$	56.5405	−	97.9310i	0.00183175	−	0.00317269i
$985$	−20655.4	−	35776.1i	−0.668157	−	1.15728i
$986$	−10336.1	+	5967.57i	−0.333843	+	0.192745i
$987$	4019.22			0.129618
$988$		0			0
$989$	−18934.8			−0.608789
$990$	−21294.7	+	12294.5i	−0.683627	+	0.394692i
$991$	−6088.75	−	10546.0i	−0.195172	−	0.338048i	0.751785	−	0.659408i	$-0.229193\pi$
$991$	−6088.75	−	10546.0i	−0.195172	−	0.338048i	−0.946957	+	0.321361i	$0.895860\pi$
$992$	21455.7	−	37162.4i	0.686714	−	1.18942i
$993$		−	2295.52i		−	0.0733598i
$994$	1681.88	+	971.034i	0.0536680	+	0.0309853i
$995$	29121.6	+	16813.3i	0.927855	+	0.535697i
$996$			1241.95i			0.0395108i
$997$	−8753.11	+	15160.8i	−0.278048	+	0.481593i	−0.970900	−	0.239487i	$-0.923021\pi$
$997$	−8753.11	+	15160.8i	−0.278048	+	0.481593i	0.692852	+	0.721080i	$0.256354\pi$
$998$	36863.2	+	63849.0i	1.16922	+	2.02515i
$999$	−4624.45	+	2669.93i	−0.146458	+	0.0845574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.4		36
13.2	odd	12		169.4.a.l.1.2	yes	9
13.3	even	3		169.4.b.g.168.4		18
13.4	even	6	inner	169.4.e.h.147.4		36
13.5	odd	4		169.4.c.k.146.8		18
13.6	odd	12		169.4.c.k.22.8		18
13.7	odd	12		169.4.c.l.22.2		18
13.8	odd	4		169.4.c.l.146.2		18
13.9	even	3	inner	169.4.e.h.147.15		36
13.10	even	6		169.4.b.g.168.15		18
13.11	odd	12		169.4.a.k.1.8	✓	9
13.12	even	2	inner	169.4.e.h.23.15		36
39.2	even	12		1521.4.a.bg.1.8		9
39.11	even	12		1521.4.a.bh.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.8	✓	9	13.11	odd	12
169.4.a.l.1.2	yes	9	13.2	odd	12
169.4.b.g.168.4		18	13.3	even	3
169.4.b.g.168.15		18	13.10	even	6
169.4.c.k.22.8		18	13.6	odd	12
169.4.c.k.146.8		18	13.5	odd	4
169.4.c.l.22.2		18	13.7	odd	12
169.4.c.l.146.2		18	13.8	odd	4
169.4.e.h.23.4		36	1.1	even	1	trivial
169.4.e.h.23.15		36	13.12	even	2	inner
169.4.e.h.147.4		36	13.4	even	6	inner
169.4.e.h.147.15		36	13.9	even	3	inner
1521.4.a.bg.1.8		9	39.2	even	12
1521.4.a.bh.1.2		9	39.11	even	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)

\(f(q)\)	\(=\)	\(q+(-3.32067 + 1.91719i) q^{2} +(0.139581 + 0.241762i) q^{3} +(3.35124 - 5.80452i) q^{4} +11.3710i q^{5} +(-0.927008 - 0.535209i) q^{6} +(26.9007 + 15.5311i) q^{7} -4.97517i q^{8} +(13.4610 - 23.3152i) q^{9} +O(q^{10})\)	\(q+(-3.32067 + 1.91719i) q^{2} +(0.139581 + 0.241762i) q^{3} +(3.35124 - 5.80452i) q^{4} +11.3710i q^{5} +(-0.927008 - 0.535209i) q^{6} +(26.9007 + 15.5311i) q^{7} -4.97517i q^{8} +(13.4610 - 23.3152i) q^{9} +(-21.8004 - 37.7594i) q^{10} +(18.1413 - 10.4739i) q^{11} +1.87108 q^{12} -119.105 q^{14} +(-2.74908 + 1.58718i) q^{15} +(36.3483 + 62.9571i) q^{16} +(57.1943 - 99.0635i) q^{17} +103.229i q^{18} +(39.1243 + 22.5884i) q^{19} +(66.0033 + 38.1070i) q^{20} +8.67143i q^{21} +(-40.1609 + 69.5608i) q^{22} +(36.9795 + 64.0504i) q^{23} +(1.20281 - 0.694441i) q^{24} -4.29980 q^{25} +15.0530 q^{27} +(180.302 - 104.097i) q^{28} +(13.6056 + 23.5657i) q^{29} +(6.08586 - 10.5410i) q^{30} +179.587i q^{31} +(-206.933 - 119.473i) q^{32} +(5.06438 + 2.92392i) q^{33} +438.610i q^{34} +(-176.605 + 305.888i) q^{35} +(-90.2224 - 156.270i) q^{36} +(-307.211 + 177.368i) q^{37} -173.225 q^{38} +56.5727 q^{40} +(70.5107 - 40.7094i) q^{41} +(-16.6248 - 28.7950i) q^{42} +(-128.009 + 221.718i) q^{43} -140.402i q^{44} +(265.117 + 153.066i) q^{45} +(-245.594 - 141.794i) q^{46} -463.501i q^{47} +(-10.1471 + 17.5753i) q^{48} +(310.933 + 538.551i) q^{49} +(14.2782 - 8.24355i) q^{50} +31.9331 q^{51} +76.6055 q^{53} +(-49.9862 + 28.8596i) q^{54} +(119.099 + 206.285i) q^{55} +(77.2700 - 133.836i) q^{56} +12.6117i q^{57} +(-90.3598 - 52.1692i) q^{58} +(47.1703 + 27.2338i) q^{59} +21.2761i q^{60} +(247.248 - 428.246i) q^{61} +(-344.303 - 596.350i) q^{62} +(724.223 - 418.130i) q^{63} +334.634 q^{64} -22.4229 q^{66} +(-530.000 + 305.996i) q^{67} +(-383.344 - 663.972i) q^{68} +(-10.3233 + 17.8805i) q^{69} -1354.34i q^{70} +(-14.1210 - 8.15278i) q^{71} +(-115.997 - 66.9709i) q^{72} -321.825i q^{73} +(680.097 - 1177.96i) q^{74} +(-0.600173 - 1.03953i) q^{75} +(262.230 - 151.399i) q^{76} +650.686 q^{77} +385.324 q^{79} +(-715.885 + 413.317i) q^{80} +(-361.347 - 625.871i) q^{81} +(-156.095 + 270.365i) q^{82} +663.760i q^{83} +(50.3335 + 29.0601i) q^{84} +(1126.45 + 650.357i) q^{85} -981.671i q^{86} +(-3.79819 + 6.57866i) q^{87} +(-52.1094 - 90.2561i) q^{88} +(-472.610 + 272.861i) q^{89} -1173.82 q^{90} +495.709 q^{92} +(-43.4174 + 25.0670i) q^{93} +(888.620 + 1539.13i) q^{94} +(-256.853 + 444.883i) q^{95} -66.7046i q^{96} +(596.855 + 344.595i) q^{97} +(-2065.01 - 1192.23i) q^{98} -563.958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more