LMFDB - Embedded newform 169.4.c.l.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, 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:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} + 62 x^{16} - 106 x^{15} + 2016 x^{14} - 2731 x^{13} + 39895 x^{12} - 21896 x^{11} + \cdots + 16777216 $ x^18 - 4x^17 + 62x^16 - 106x^15 + 2016x^14 - 2731x^13 + 39895x^12 - 21896x^11 + 490851x^10 - 318018x^9 + 3391249x^8 - 990441x^7 + 13815033x^6 - 7349264x^5 + 28218112x^4 - 9093120x^3 + 32440320x^2 - 14680064*x + 16777216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$2.41719 + 4.18670i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.l.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91719 + 3.32067i) q^{2} +(0.139581 - 0.241762i) q^{3} +(-3.35124 - 5.80452i) q^{4} -11.3710 q^{5} +(0.535209 + 0.927008i) q^{6} +(15.5311 + 26.9007i) q^{7} -4.97517 q^{8} +(13.4610 + 23.3152i) q^{9} +O(q^{10})$	\(q+(-1.91719 + 3.32067i) q^{2} +(0.139581 - 0.241762i) q^{3} +(-3.35124 - 5.80452i) q^{4} -11.3710 q^{5} +(0.535209 + 0.927008i) q^{6} +(15.5311 + 26.9007i) q^{7} -4.97517 q^{8} +(13.4610 + 23.3152i) q^{9} +(21.8004 - 37.7594i) q^{10} +(-10.4739 + 18.1413i) q^{11} -1.87108 q^{12} -119.105 q^{14} +(-1.58718 + 2.74908i) q^{15} +(36.3483 - 62.9571i) q^{16} +(-57.1943 - 99.0635i) q^{17} -103.229 q^{18} +(-22.5884 - 39.1243i) q^{19} +(38.1070 + 66.0033i) q^{20} +8.67143 q^{21} +(-40.1609 - 69.5608i) q^{22} +(-36.9795 + 64.0504i) q^{23} +(-0.694441 + 1.20281i) q^{24} +4.29980 q^{25} +15.0530 q^{27} +(104.097 - 180.302i) q^{28} +(13.6056 - 23.5657i) q^{29} +(-6.08586 - 10.5410i) q^{30} -179.587 q^{31} +(119.473 + 206.933i) q^{32} +(2.92392 + 5.06438i) q^{33} +438.610 q^{34} +(-176.605 - 305.888i) q^{35} +(90.2224 - 156.270i) q^{36} +(177.368 - 307.211i) q^{37} +173.225 q^{38} +56.5727 q^{40} +(40.7094 - 70.5107i) q^{41} +(-16.6248 + 28.7950i) q^{42} +(128.009 + 221.718i) q^{43} +140.402 q^{44} +(-153.066 - 265.117i) q^{45} +(-141.794 - 245.594i) q^{46} -463.501 q^{47} +(-10.1471 - 17.5753i) q^{48} +(-310.933 + 538.551i) q^{49} +(-8.24355 + 14.2782i) q^{50} -31.9331 q^{51} +76.6055 q^{53} +(-28.8596 + 49.9862i) q^{54} +(119.099 - 206.285i) q^{55} +(-77.2700 - 133.836i) q^{56} -12.6117 q^{57} +(52.1692 + 90.3598i) q^{58} +(27.2338 + 47.1703i) q^{59} +21.2761 q^{60} +(247.248 + 428.246i) q^{61} +(344.303 - 596.350i) q^{62} +(-418.130 + 724.223i) q^{63} -334.634 q^{64} -22.4229 q^{66} +(-305.996 + 530.000i) q^{67} +(-383.344 + 663.972i) q^{68} +(10.3233 + 17.8805i) q^{69} +1354.34 q^{70} +(8.15278 + 14.1210i) q^{71} +(-66.9709 - 115.997i) q^{72} -321.825 q^{73} +(680.097 + 1177.96i) q^{74} +(0.600173 - 1.03953i) q^{75} +(-151.399 + 262.230i) q^{76} -650.686 q^{77} +385.324 q^{79} +(-413.317 + 715.885i) q^{80} +(-361.347 + 625.871i) q^{81} +(156.095 + 270.365i) q^{82} -663.760 q^{83} +(-29.0601 - 50.3335i) q^{84} +(650.357 + 1126.45i) q^{85} -981.671 q^{86} +(-3.79819 - 6.57866i) q^{87} +(52.1094 - 90.2561i) q^{88} +(272.861 - 472.610i) q^{89} +1173.82 q^{90} +495.709 q^{92} +(-25.0670 + 43.4174i) q^{93} +(888.620 - 1539.13i) q^{94} +(256.853 + 444.883i) q^{95} +66.7046 q^{96} +(-344.595 - 596.855i) q^{97} +(-1192.23 - 2065.01i) q^{98} -563.958 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.91719	+	3.32067i	−0.677829	+	1.17403i	0.297804	+	0.954627i	$0.403746\pi$
$2$	−1.91719	+	3.32067i	−0.677829	+	1.17403i	−0.975633	+	0.219408i	$0.929587\pi$
$3$	0.139581	−	0.241762i	0.0268625	−	0.0465271i	−0.852282	−	0.523083i	$-0.824782\pi$
$3$	0.139581	−	0.241762i	0.0268625	−	0.0465271i	0.879144	+	0.476556i	$0.158115\pi$
$4$	−3.35124	−	5.80452i	−0.418905	−	0.725565i
$5$	−11.3710			−1.01705			−0.508527	−	0.861046i	$-0.669810\pi$
$5$	−11.3710			−1.01705			−0.508527	+	0.861046i	$0.669810\pi$
$6$	0.535209	+	0.927008i	0.0364163	+	0.0630749i
$7$	15.5311	+	26.9007i	0.838603	+	1.45250i	0.891063	+	0.453879i	$0.149960\pi$
$7$	15.5311	+	26.9007i	0.838603	+	1.45250i	−0.0524604	+	0.998623i	$0.516706\pi$
$8$	−4.97517			−0.219873
$9$	13.4610	+	23.3152i	0.498557	+	0.863526i
$10$	21.8004	−	37.7594i	0.689389	−	1.19406i
$11$	−10.4739	+	18.1413i	−0.287091	+	0.497256i	−0.973114	−	0.230324i	$-0.926022\pi$
$11$	−10.4739	+	18.1413i	−0.287091	+	0.497256i	0.686023	+	0.727580i	$0.259355\pi$
$12$	−1.87108			−0.0450113
$13$		0			0
$13$		0			0
$14$	−119.105			−2.27372
$15$	−1.58718	+	2.74908i	−0.0273206	+	0.0473206i
$16$	36.3483	−	62.9571i	0.567942	−	0.983704i
$17$	−57.1943	−	99.0635i	−0.815980	−	1.41332i	−0.908622	−	0.417620i	$-0.862864\pi$
$17$	−57.1943	−	99.0635i	−0.815980	−	1.41332i	0.0926417	−	0.995700i	$-0.470469\pi$
$18$	−103.229			−1.35175
$19$	−22.5884	−	39.1243i	−0.272744	−	0.472407i	0.696819	−	0.717247i	$-0.254598\pi$
$19$	−22.5884	−	39.1243i	−0.272744	−	0.472407i	−0.969564	+	0.244840i	$0.921265\pi$
$20$	38.1070	+	66.0033i	0.426049	+	0.737939i
$21$	8.67143			0.0901077
$22$	−40.1609	−	69.5608i	−0.389197	−	0.674109i
$23$	−36.9795	+	64.0504i	−0.335250	+	0.580671i	−0.983533	−	0.180729i	$-0.942154\pi$
$23$	−36.9795	+	64.0504i	−0.335250	+	0.580671i	0.648283	+	0.761400i	$0.275488\pi$
$24$	−0.694441	+	1.20281i	−0.00590634	+	0.0102301i
$25$	4.29980			0.0343984
$26$		0			0
$27$	15.0530			0.107295
$28$	104.097	−	180.302i	0.702590	−	1.21692i
$29$	13.6056	−	23.5657i	0.0871208	−	0.150898i	−0.819172	−	0.573548i	$-0.805567\pi$
$29$	13.6056	−	23.5657i	0.0871208	−	0.150898i	0.906293	+	0.422650i	$0.138900\pi$
$30$	−6.08586	−	10.5410i	−0.0370374	−	0.0641506i
$31$	−179.587			−1.04048			−0.520239	−	0.854021i	$-0.674157\pi$
$31$	−179.587			−1.04048			−0.520239	+	0.854021i	$0.674157\pi$
$32$	119.473	+	206.933i	0.659999	+	1.14315i
$33$	2.92392	+	5.06438i	0.0154239	+	0.0267150i
$34$	438.610			2.21238
$35$	−176.605	−	305.888i	−0.852904	−	1.47727i
$36$	90.2224	−	156.270i	0.417696	−	0.723471i
$37$	177.368	−	307.211i	0.788085	−	1.36500i	−0.139054	−	0.990285i	$-0.544406\pi$
$37$	177.368	−	307.211i	0.788085	−	1.36500i	0.927139	−	0.374718i	$-0.122261\pi$
$38$	173.225			0.739496
$39$		0			0
$40$	56.5727			0.223623
$41$	40.7094	−	70.5107i	0.155067	−	0.268583i	−0.778017	−	0.628244i	$-0.783774\pi$
$41$	40.7094	−	70.5107i	0.155067	−	0.268583i	0.933083	+	0.359660i	$0.117107\pi$
$42$	−16.6248	+	28.7950i	−0.0610777	+	0.105790i
$43$	128.009	+	221.718i	0.453981	+	0.786318i	0.998629	−	0.0523465i	$-0.0166700\pi$
$43$	128.009	+	221.718i	0.453981	+	0.786318i	−0.544648	+	0.838665i	$0.683337\pi$
$44$	140.402			0.481056
$45$	−153.066	−	265.117i	−0.507059	−	0.878252i
$46$	−141.794	−	245.594i	−0.454485	−	0.787191i
$47$	−463.501			−1.43848			−0.719240	−	0.694762i	$-0.755510\pi$
$47$	−463.501			−1.43848			−0.719240	+	0.694762i	$0.755510\pi$
$48$	−10.1471	−	17.5753i	−0.0305126	−	0.0528494i
$49$	−310.933	+	538.551i	−0.906509	+	1.57012i
$50$	−8.24355	+	14.2782i	−0.0233163	+	0.0403850i
$51$	−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	$0.468349\pi$
$54$	−28.8596	+	49.9862i	−0.0727275	+	0.125968i
$55$	119.099	−	206.285i	0.291987	−	0.505736i
$56$	−77.2700	−	133.836i	−0.184386	−	0.319367i
$57$	−12.6117			−0.0293063
$58$	52.1692	+	90.3598i	0.118106	+	0.204566i
$59$	27.2338	+	47.1703i	0.0600939	+	0.104086i	0.894507	−	0.447054i	$-0.147527\pi$
$59$	27.2338	+	47.1703i	0.0600939	+	0.104086i	−0.834413	+	0.551139i	$0.814193\pi$
$60$	21.2761			0.0457789
$61$	247.248	+	428.246i	0.518965	+	0.898874i	0.999757	+	0.0220394i	$0.00701592\pi$
$61$	247.248	+	428.246i	0.518965	+	0.898874i	−0.480792	+	0.876835i	$0.659651\pi$
$62$	344.303	−	596.350i	0.705266	−	1.22156i
$63$	−418.130	+	724.223i	−0.836182	+	1.44831i
$64$	−334.634			−0.653582
$65$		0			0
$66$	−22.4229			−0.0418192
$67$	−305.996	+	530.000i	−0.557960	+	0.966415i	0.439707	+	0.898141i	$0.355082\pi$
$67$	−305.996	+	530.000i	−0.557960	+	0.966415i	−0.997667	+	0.0682737i	$0.978251\pi$
$68$	−383.344	+	663.972i	−0.683637	+	1.18409i
$69$	10.3233	+	17.8805i	0.0180113	+	0.0311965i
$70$	1354.34			2.31249
$71$	8.15278	+	14.1210i	0.0136276	+	0.0236036i	0.872759	−	0.488152i	$-0.162329\pi$
$71$	8.15278	+	14.1210i	0.0136276	+	0.0236036i	−0.859131	+	0.511755i	$0.828995\pi$
$72$	−66.9709	−	115.997i	−0.109619	−	0.189866i
$73$	−321.825			−0.515983			−0.257992	−	0.966147i	$-0.583061\pi$
$73$	−321.825			−0.515983			−0.257992	+	0.966147i	$0.583061\pi$
$74$	680.097	+	1177.96i	1.06837	+	1.85048i
$75$	0.600173	−	1.03953i	0.000924027	−	0.00160046i
$76$	−151.399	+	262.230i	−0.228508	+	0.395787i
$77$	−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	$0.411527\pi$
$80$	−413.317	+	715.885i	−0.577628	+	1.00048i
$81$	−361.347	+	625.871i	−0.495675	+	0.858534i
$82$	156.095	+	270.365i	0.210217	+	0.364107i
$83$	−663.760			−0.877797			−0.438899	−	0.898537i	$-0.644631\pi$
$83$	−663.760			−0.877797			−0.438899	+	0.898537i	$0.644631\pi$
$84$	−29.0601	−	50.3335i	−0.0377466	−	0.0653790i
$85$	650.357	+	1126.45i	0.829896	+	1.43742i
$86$	−981.671			−1.23089
$87$	−3.79819	−	6.57866i	−0.00468056	−	0.00810697i
$88$	52.1094	−	90.2561i	0.0631237	−	0.109333i
$89$	272.861	−	472.610i	0.324980	−	0.562882i	−0.656528	−	0.754302i	$-0.727976\pi$
$89$	272.861	−	472.610i	0.324980	−	0.562882i	0.981508	+	0.191419i	$0.0613090\pi$
$90$	1173.82			1.37480
$91$		0			0
$92$	495.709			0.561753
$93$	−25.0670	+	43.4174i	−0.0279498	+	0.0484104i
$94$	888.620	−	1539.13i	0.975044	−	1.68883i
$95$	256.853	+	444.883i	0.277395	+	0.480463i
$96$	66.7046			0.0709168
$97$	−344.595	−	596.855i	−0.360704	−	0.624758i	0.627373	−	0.778719i	$-0.284130\pi$
$97$	−344.595	−	596.855i	−0.360704	−	0.624758i	−0.988077	+	0.153961i	$0.950797\pi$
$98$	−1192.23	−	2065.01i	−1.22892	−	2.12855i
$99$	−563.958			−0.572524
$100$	−14.4097	−	24.9583i	−0.0144097	−	0.0249583i
$101$	−235.699	+	408.242i	−0.232207	+	0.402194i	−0.958457	−	0.285236i	$-0.907928\pi$
$101$	−235.699	+	408.242i	−0.232207	+	0.402194i	0.726250	+	0.687430i	$0.241261\pi$
$102$	61.2218	−	106.039i	0.0594300	−	0.102936i
$103$	−335.521			−0.320970			−0.160485	−	0.987038i	$-0.551306\pi$
$103$	−335.521			−0.320970			−0.160485	+	0.987038i	$0.551306\pi$
$104$		0			0
$105$	−98.6029			−0.0916444
$106$	−146.867	+	254.382i	−0.134576	+	0.233092i
$107$	−814.632	+	1410.98i	−0.736014	+	1.27481i	0.218264	+	0.975890i	$0.429961\pi$
$107$	−814.632	+	1410.98i	−0.736014	+	1.27481i	−0.954277	+	0.298923i	$0.903373\pi$
$108$	−50.4464	−	87.3757i	−0.0449463	−	0.0778494i
$109$	1518.95			1.33476			0.667381	−	0.744717i	$-0.267415\pi$
$109$	1518.95			1.33476			0.667381	+	0.744717i	$0.267415\pi$
$110$	456.670	+	790.976i	0.395835	+	0.685606i
$111$	−49.5146	−	85.7618i	−0.0423398	−	0.0733347i
$112$	2258.12			1.90511
$113$	−597.704	−	1035.25i	−0.497586	−	0.861845i	0.502410	−	0.864630i	$-0.332447\pi$
$113$	−597.704	−	1035.25i	−0.497586	−	0.861845i	−0.999996	+	0.00278476i	$0.999114\pi$
$114$	24.1790	−	41.8793i	0.0198647	−	0.0344066i
$115$	420.494	−	728.317i	0.340968	−	0.590573i
$116$	−182.383			−0.145982
$117$		0			0
$118$	−208.850			−0.162934
$119$	1776.59	−	3077.14i	1.36857	−	2.37043i
$120$	7.89649	−	13.6771i	0.00600707	−	0.0104045i
$121$	446.095	+	772.659i	0.335158	+	0.580510i
$122$	−1896.09			−1.40708
$123$	−11.3645	−	19.6840i	−0.00833094	−	0.0144296i
$124$	601.840	+	1042.42i	0.435862	+	0.754934i
$125$	1372.48			0.982069
$126$	−1603.27	−	2776.95i	−1.13358	−	1.96341i
$127$	−263.212	+	455.897i	−0.183908	+	0.318538i	−0.943208	−	0.332203i	$-0.892208\pi$
$127$	−263.212	+	455.897i	−0.183908	+	0.318538i	0.759300	+	0.650741i	$0.225542\pi$
$128$	−314.223	+	544.250i	−0.216981	+	0.375823i
$129$	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	$0.589713\pi$
$132$	19.5976	−	33.9440i	0.0129223	−	0.0223821i
$133$	701.648	−	1215.29i	0.457448	−	0.792323i
$134$	−1173.30	−	2032.22i	−0.756403	−	1.31013i
$135$	−171.168			−0.109125
$136$	284.551	+	492.858i	0.179412	+	0.310751i
$137$	−233.381	−	404.228i	−0.145541	−	0.252084i	0.784034	−	0.620718i	$-0.213159\pi$
$137$	−233.381	−	404.228i	−0.145541	−	0.252084i	−0.929575	+	0.368634i	$0.879826\pi$
$138$	−79.1670			−0.0488344
$139$	356.540	+	617.545i	0.217563	+	0.376831i	0.954062	−	0.299608i	$-0.0968558\pi$
$139$	356.540	+	617.545i	0.217563	+	0.376831i	−0.736499	+	0.676439i	$0.763522\pi$
$140$	−1183.69	+	2050.21i	−0.714572	+	1.23768i
$141$	−64.6961	+	112.057i	−0.0386411	+	0.0669284i
$142$	−62.5218			−0.0369487
$143$		0			0
$144$	1957.14			1.13261
$145$	−154.710	+	267.965i	−0.0886066	+	0.153471i
$146$	617.000	−	1068.68i	0.349748	−	0.605782i
$147$	86.8008	+	150.343i	0.0487021	+	0.0843545i
$148$	−2377.61			−1.32053
$149$	331.407	+	574.013i	0.182214	+	0.315604i	0.942634	−	0.333827i	$-0.108340\pi$
$149$	331.407	+	574.013i	0.182214	+	0.315604i	−0.760420	+	0.649431i	$0.775007\pi$
$150$	2.30129	+	3.98595i	0.00125266	+	0.00216968i
$151$	−190.862			−0.102862			−0.0514310	−	0.998677i	$-0.516378\pi$
$151$	−190.862			−0.102862			−0.0514310	+	0.998677i	$0.516378\pi$
$152$	112.381	+	194.650i	0.0599692	+	0.103870i
$153$	1539.79	−	2666.99i	0.813625	−	1.40924i
$154$	1247.49	−	2160.72i	0.652764	−	1.13062i
$155$	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	$0.755997\pi$
$158$	−738.740	+	1279.54i	−0.371969	+	0.644268i
$159$	10.6927	−	18.5203i	0.00533325	−	0.00923745i
$160$	−1358.52	−	2353.03i	−0.671254	−	1.16265i
$161$	−2297.34			−1.12457
$162$	−1385.54	−	2399.83i	−0.671966	−	1.16388i
$163$	1782.77	+	3087.85i	0.856672	+	1.48380i	0.875085	+	0.483969i	$0.160805\pi$
$163$	1782.77	+	3087.85i	0.856672	+	1.48380i	−0.0184128	+	0.999830i	$0.505861\pi$
$164$	−545.708			−0.259833
$165$	−33.2480	−	57.5872i	−0.0156870	−	0.0271706i
$166$	1272.56	−	2204.13i	0.594997	−	1.03056i
$167$	−60.3149	+	104.468i	−0.0279480	+	0.0484073i	−0.879661	−	0.475601i	$-0.842231\pi$
$167$	−60.3149	+	104.468i	−0.0279480	+	0.0484073i	0.851713	+	0.524008i	$0.175564\pi$
$168$	−43.1418			−0.0198123
$169$		0			0
$170$	−4987.44			−2.25011
$171$	608.127	−	1053.31i	0.271957	−	0.471043i
$172$	857.978	−	1486.06i	0.380350	−	0.658786i
$173$	1040.14	+	1801.57i	0.457112	+	0.791740i	0.998807	−	0.0488345i	$-0.0155507\pi$
$173$	1040.14	+	1801.57i	0.457112	+	0.791740i	−0.541695	+	0.840575i	$0.682217\pi$
$174$	29.1274			0.0126905
$175$	66.7809	+	115.668i	0.0288466	+	0.0499638i
$176$	761.417	+	1318.81i	0.326102	+	0.564825i
$177$	15.2053			0.00645708
$178$	1046.25	+	1812.17i	0.440562	+	0.763076i
$179$	276.570	−	479.033i	0.115485	−	0.200026i	−0.802489	−	0.596668i	$-0.796491\pi$
$179$	276.570	−	479.033i	0.115485	−	0.200026i	0.917974	+	0.396642i	$0.129824\pi$
$180$	−1025.92	+	1776.94i	−0.424820	+	0.735809i
$181$	−3305.19			−1.35731			−0.678655	−	0.734457i	$-0.737437\pi$
$181$	−3305.19			−1.35731			−0.678655	+	0.734457i	$0.737437\pi$
$182$		0			0
$183$	138.045			0.0557627
$184$	183.979	−	318.661i	0.0737127	−	0.127674i
$185$	−2016.85	+	3493.29i	−0.801525	+	1.38828i
$186$	−96.1166	−	166.479i	−0.0378904	−	0.0656280i
$187$	2396.19			0.937042
$188$	1553.30	+	2690.40i	0.602587	+	1.04371i
$189$	233.791	+	404.938i	0.0899777	+	0.155846i
$190$	−1969.75			−0.752107
$191$	1659.07	+	2873.59i	0.628514	+	1.08862i	0.987850	+	0.155410i	$0.0496698\pi$
$191$	1659.07	+	2873.59i	0.628514	+	1.08862i	−0.359336	+	0.933208i	$0.616997\pi$
$192$	−46.7087	+	80.9019i	−0.0175568	+	0.0304093i
$193$	−1951.09	+	3379.39i	−0.727681	+	1.26038i	0.230180	+	0.973148i	$0.426069\pi$
$193$	−1951.09	+	3379.39i	−0.727681	+	1.26038i	−0.957861	+	0.287233i	$0.907265\pi$
$194$	2642.61			0.977983
$195$		0			0
$196$	4168.04			1.51897
$197$	−1816.49	+	3146.26i	−0.656953	+	1.13788i	0.324447	+	0.945904i	$0.394822\pi$
$197$	−1816.49	+	3146.26i	−0.656953	+	1.13788i	−0.981400	+	0.191972i	$0.938512\pi$
$198$	1081.22	−	1872.72i	0.388074	−	0.672164i
$199$	−1478.62	−	2561.04i	−0.526715	−	0.912297i	−0.999515	−	0.0311274i	$-0.990090\pi$
$199$	−1478.62	−	2561.04i	−0.526715	−	0.912297i	0.472801	−	0.881169i	$-0.343243\pi$
$200$	−21.3922			−0.00756330
$201$	85.4226	+	147.956i	0.0299764	+	0.0519206i
$202$	−903.759	−	1565.36i	−0.314793	−	0.545238i
$203$	845.245			0.292239
$204$	107.015	+	185.356i	0.0367283	+	0.0636153i
$205$	−462.906	+	801.777i	−0.157711	+	0.273164i
$206$	643.258	−	1114.16i	0.217563	−	0.376830i
$207$	−1991.13			−0.668565
$208$		0			0
$209$	946.355			0.313209
$210$	189.041	−	327.428i	0.0621193	−	0.107594i
$211$	1597.03	−	2766.13i	0.521061	−	0.902504i	−0.478639	−	0.878012i	$-0.658870\pi$
$211$	1597.03	−	2766.13i	0.521061	−	0.902504i	0.999700	−	0.0244920i	$-0.00779684\pi$
$212$	−256.723	−	444.658i	−0.0831691	−	0.144053i
$213$	4.55191			0.00146428
$214$	−3123.61	−	5410.25i	−0.997783	−	1.72821i
$215$	−1455.59	−	2521.16i	−0.461723	−	0.799728i
$216$	−74.8914			−0.0235913
$217$	−2789.19	−	4831.02i	−0.872547	−	1.51130i
$218$	−2912.12	+	5043.93i	−0.904740	+	1.56706i
$219$	−44.9208	+	77.8051i	−0.0138606	+	0.0240072i
$220$	−1596.52			−0.489259
$221$		0			0
$222$	379.716			0.114797
$223$	37.5546	−	65.0465i	0.0112773	−	0.0195329i	−0.860332	−	0.509735i	$-0.829744\pi$
$223$	37.5546	−	65.0465i	0.0112773	−	0.0195329i	0.871609	+	0.490202i	$0.163077\pi$
$224$	−3711.09	+	6427.80i	−1.10695	+	1.91730i
$225$	57.8798	+	100.251i	0.0171496	+	0.0297039i
$226$	4583.65			1.34911
$227$	2161.39	+	3743.64i	0.631968	+	1.09460i	0.987149	+	0.159803i	$0.0510858\pi$
$227$	2161.39	+	3743.64i	0.631968	+	1.09460i	−0.355181	+	0.934797i	$0.615581\pi$
$228$	42.2649	+	73.2049i	0.0122766	+	0.0212636i
$229$	677.923			0.195626			0.0978132	−	0.995205i	$-0.468815\pi$
$229$	677.923			0.195626			0.0978132	+	0.995205i	$0.468815\pi$
$230$	1612.34	+	2792.65i	0.462236	+	0.800616i
$231$	−90.8237	+	157.311i	−0.0258691	+	0.0448066i
$232$	−67.6904	+	117.243i	−0.0191556	+	0.0331784i
$233$	92.9061			0.0261222			0.0130611	−	0.999915i	$-0.495842\pi$
$233$	92.9061			0.0261222			0.0130611	+	0.999915i	$0.495842\pi$
$234$		0			0
$235$	5270.47			1.46301
$236$	182.534	−	316.159i	0.0503473	−	0.0872041i
$237$	53.7841	−	93.1568i	0.0147412	−	0.0255324i
$238$	6812.11	+	11798.9i	1.85531	+	3.21349i
$239$	2082.56			0.563638			0.281819	−	0.959468i	$-0.409062\pi$
$239$	2082.56			0.563638			0.281819	+	0.959468i	$0.409062\pi$
$240$	115.383	+	199.849i	0.0310330	+	0.0537507i
$241$	−3270.63	−	5664.89i	−0.874189	−	1.51414i	−0.857624	−	0.514277i	$-0.828060\pi$
$241$	−3270.63	−	5664.89i	−0.874189	−	1.51414i	−0.0165650	−	0.999863i	$-0.505273\pi$
$242$	−3421.00			−0.908719
$243$	304.091	+	526.700i	0.0802775	+	0.139045i
$244$	1657.18	−	2870.31i	0.434795	−	0.753086i
$245$	3535.62	−	6123.87i	0.921968	−	1.59690i
$246$	87.1520			0.0225878
$247$		0			0
$248$	893.476			0.228773
$249$	−92.6486	+	160.472i	−0.0235798	+	0.0408414i
$250$	−2631.31	+	4557.57i	−0.665675	+	1.15298i
$251$	1204.64	+	2086.50i	0.302934	+	0.524697i	0.976799	−	0.214157i	$-0.0687005\pi$
$251$	1204.64	+	2086.50i	0.302934	+	0.524697i	−0.673865	+	0.738854i	$0.735367\pi$
$252$	5605.03			1.40112
$253$	−774.639	−	1341.71i	−0.192495	−	0.333411i
$254$	−1009.26	−	1748.08i	−0.249317	−	0.431829i
$255$	363.111			0.0891722
$256$	−2543.39	−	4405.28i	−0.620944	−	1.07551i
$257$	131.793	−	228.273i	0.0319885	−	0.0554057i	−0.849588	−	0.527447i	$-0.823149\pi$
$257$	131.793	−	228.273i	0.0319885	−	0.0554057i	0.881576	+	0.472041i	$0.156483\pi$
$258$	−137.023	+	237.331i	−0.0330646	+	0.0572696i
$259$	11018.9			2.64356
$260$		0			0
$261$	732.584			0.173739
$262$	1598.98	−	2769.52i	0.377044	−	0.653060i
$263$	3662.31	−	6343.31i	0.858660	−	1.48724i	−0.0145468	−	0.999894i	$-0.504631\pi$
$263$	3662.31	−	6343.31i	0.858660	−	1.48724i	0.873207	−	0.487349i	$-0.162036\pi$
$264$	−14.5470	−	25.1962i	−0.00339131	−	0.00587393i
$265$	−871.081			−0.201925
$266$	2690.39	+	4659.88i	0.620143	+	1.07412i
$267$	−76.1728	−	131.935i	−0.0174595	−	0.0302408i
$268$	4101.86			0.934930
$269$	2341.68	+	4055.91i	0.530762	+	0.919307i	0.999356	+	0.0358928i	$0.0114275\pi$
$269$	2341.68	+	4055.91i	0.530762	+	0.919307i	−0.468594	+	0.883414i	$0.655239\pi$
$270$	328.162	−	568.394i	0.0739678	−	0.128116i
$271$	−814.687	+	1411.08i	−0.182615	+	0.316299i	−0.942770	−	0.333443i	$-0.891790\pi$
$271$	−814.687	+	1411.08i	−0.182615	+	0.316299i	0.760155	+	0.649742i	$0.225123\pi$
$272$	−8315.66			−1.85372
$273$		0			0
$274$	1789.75			0.394608
$275$	−45.0357	+	78.0042i	−0.00987548	+	0.0171048i
$276$	69.1918	−	119.844i	0.0150901	−	0.0261367i
$277$	−3100.33	−	5369.93i	−0.672494	−	1.16479i	−0.977195	−	0.212345i	$-0.931890\pi$
$277$	−3100.33	−	5369.93i	−0.672494	−	1.16479i	0.304701	−	0.952448i	$-0.401443\pi$
$278$	−2734.22			−0.589883
$279$	−2417.43	−	4187.11i	−0.518737	−	0.898479i
$280$	878.638	+	1521.85i	0.187531	+	0.324813i
$281$	−2951.26			−0.626538			−0.313269	−	0.949664i	$-0.601424\pi$
$281$	−2951.26			−0.626538			−0.313269	+	0.949664i	$0.601424\pi$
$282$	−248.070	−	429.669i	−0.0523842	−	0.0907320i
$283$	−2624.58	+	4545.91i	−0.551291	+	0.954864i	0.446891	+	0.894589i	$0.352531\pi$
$283$	−2624.58	+	4545.91i	−0.551291	+	0.954864i	−0.998182	+	0.0602756i	$0.980802\pi$
$284$	54.6439	−	94.6460i	0.0114173	−	0.0197754i
$285$	143.408			0.0298061
$286$		0			0
$287$	2529.05			0.520157
$288$	−3216.45	+	5571.05i	−0.658094	+	1.13985i
$289$	−4085.88	+	7076.96i	−0.831648	+	1.44046i
$290$	−593.217	−	1027.48i	−0.120120	−	0.208054i
$291$	−192.396			−0.0387576
$292$	1078.51	+	1868.04i	0.216148	+	0.374379i
$293$	−1456.17	−	2522.15i	−0.290342	−	0.502887i	0.683549	−	0.729905i	$-0.260436\pi$
$293$	−1456.17	−	2522.15i	−0.290342	−	0.502887i	−0.973891	+	0.227018i	$0.927102\pi$
$294$	−665.655			−0.132047
$295$	−309.676	−	536.374i	−0.0611187	−	0.105861i
$296$	−882.436	+	1528.42i	−0.173279	+	0.300128i
$297$	−157.664	+	273.082i	−0.0308033	+	0.0533530i
$298$	−2541.48			−0.494040
$299$		0			0
$300$	−8.04530			−0.00154832
$301$	−3976.25	+	6887.07i	−0.761419	+	1.31882i
$302$	365.920	−	633.792i	0.0697229	−	0.120764i
$303$	65.7983	+	113.966i	0.0124753	+	0.0216079i
$304$	−3284.20			−0.619611
$305$	−2811.46	−	4869.59i	−0.527816	−	0.914203i
$306$	5904.14	+	10226.3i	1.10300	+	1.91045i
$307$	−5000.10			−0.929546			−0.464773	−	0.885430i	$-0.653864\pi$
$307$	−5000.10			−0.929546			−0.464773	+	0.885430i	$0.653864\pi$
$308$	2180.61	+	3776.92i	0.403415	+	0.698734i
$309$	−46.8325	+	81.1163i	−0.00862203	+	0.0149338i
$310$	−3915.07	+	6781.10i	−0.717294	+	1.24239i
$311$	−7840.94			−1.42964			−0.714822	−	0.699307i	$-0.753492\pi$
$311$	−7840.94			−1.42964			−0.714822	+	0.699307i	$0.753492\pi$
$312$		0			0
$313$	−7518.43			−1.35772			−0.678860	−	0.734267i	$-0.737526\pi$
$313$	−7518.43			−1.35772			−0.678860	+	0.734267i	$0.737526\pi$
$314$	5433.24	−	9410.65i	0.976483	−	1.69132i
$315$	4754.56	−	8235.15i	0.850442	−	1.47301i
$316$	−1291.32	−	2236.62i	−0.229880	−	0.398164i
$317$	−485.238			−0.0859738			−0.0429869	−	0.999076i	$-0.513687\pi$
$317$	−485.238			−0.0859738			−0.0429869	+	0.999076i	$0.513687\pi$
$318$	40.9999	+	71.0139i	0.00723006	+	0.0125228i
$319$	285.008	+	493.649i	0.0500232	+	0.0866427i
$320$	3805.13			0.664728
$321$	227.415	+	393.894i	0.0395423	+	0.0684892i
$322$	4404.43	−	7628.70i	0.762265	−	1.32028i
$323$	−2583.86	+	4475.38i	−0.445108	+	0.770949i
$324$	4843.84			0.830563
$325$		0			0
$326$	−13671.7			−2.32271
$327$	212.017	−	367.224i	0.0358550	−	0.0621026i
$328$	−202.536	+	350.802i	−0.0340950	+	0.0590543i
$329$	−7198.70	−	12468.5i	−1.20631	−	2.08940i
$330$	254.971			0.0425324
$331$	4111.44	+	7121.23i	0.682735	+	1.18253i	0.974143	+	0.225933i	$0.0725430\pi$
$331$	4111.44	+	7121.23i	0.682735	+	1.18253i	−0.291408	+	0.956599i	$0.594124\pi$
$332$	2224.42	+	3852.81i	0.367714	+	0.636899i
$333$	9550.23			1.57162
$334$	−231.270	−	400.572i	−0.0378879	−	0.0656237i
$335$	3479.48	−	6026.64i	0.567475	−	0.982896i
$336$	315.192	−	545.928i	0.0511760	−	0.0886394i
$337$	7744.78			1.25188			0.625942	−	0.779870i	$-0.284715\pi$
$337$	7744.78			1.25188			0.625942	+	0.779870i	$0.284715\pi$
$338$		0			0
$339$	−333.714			−0.0534656
$340$	4359.01	−	7550.03i	0.695296	−	1.20429i
$341$	1880.98	−	3257.95i	0.298712	−	0.517384i
$342$	2331.79	+	4038.78i	0.368681	+	0.638574i
$343$	−8662.19			−1.36360
$344$	−636.866	−	1103.08i	−0.0998184	−	0.172890i
$345$	−117.386	−	203.319i	−0.0183185	−	0.0317285i
$346$	−7976.58			−1.23937
$347$	1766.30	+	3059.33i	0.273257	+	0.473295i	0.969694	−	0.244323i	$-0.0785657\pi$
$347$	1766.30	+	3059.33i	0.273257	+	0.473295i	−0.696437	+	0.717618i	$0.745232\pi$
$348$	−25.4573	+	44.0934i	−0.00392142	+	0.00679210i
$349$	1683.09	−	2915.20i	0.258149	−	0.447127i	−0.707597	−	0.706616i	$-0.750221\pi$
$349$	1683.09	−	2915.20i	0.258149	−	0.447127i	0.965746	+	0.259489i	$0.0835542\pi$
$350$	−512.127			−0.0782123
$351$		0			0
$352$	−5005.37			−0.757919
$353$	−4983.99	+	8632.52i	−0.751476	+	1.30159i	0.195631	+	0.980677i	$0.437324\pi$
$353$	−4983.99	+	8632.52i	−0.751476	+	1.30159i	−0.947107	+	0.320917i	$0.896009\pi$
$354$	−29.1515	+	50.4919i	−0.00437680	+	0.00758084i
$355$	−92.7054	−	160.570i	−0.0138600	−	0.0240062i
$356$	−3657.70			−0.544544
$357$	−495.957	−	859.023i	−0.0735261	−	0.127351i
$358$	1060.48	+	1836.80i	0.156558	+	0.271167i
$359$	−2742.72			−0.403219			−0.201609	−	0.979466i	$-0.564617\pi$
$359$	−2742.72			−0.403219			−0.201609	+	0.979466i	$0.564617\pi$
$360$	761.527	+	1319.00i	0.111489	+	0.193104i
$361$	2409.03	−	4172.56i	0.351221	−	0.608333i
$362$	6336.69	−	10975.5i	0.920024	−	1.59353i
$363$	249.066			0.0360126
$364$		0			0
$365$	3659.47			0.524783
$366$	−264.659	+	458.402i	−0.0377976	+	0.0654674i
$367$	820.929	−	1421.89i	0.116763	−	0.202240i	−0.801720	−	0.597700i	$-0.796081\pi$
$367$	820.929	−	1421.89i	0.116763	−	0.202240i	0.918483	+	0.395460i	$0.129415\pi$
$368$	2688.28	+	4656.24i	0.380806	+	0.659575i
$369$	2191.96			0.309238
$370$	−7733.39	−	13394.6i	−1.08659	−	1.88204i
$371$	1189.77	+	2060.74i	0.166495	+	0.288378i
$372$	336.023			0.0468333
$373$	−5603.77	−	9706.01i	−0.777887	−	1.34734i	−0.933157	−	0.359468i	$-0.882958\pi$
$373$	−5603.77	−	9706.01i	−0.777887	−	1.34734i	0.155270	−	0.987872i	$-0.450375\pi$
$374$	−4593.96	+	7956.97i	−0.635155	+	1.10012i
$375$	191.573	−	331.814i	0.0263808	−	0.0456929i
$376$	2306.00			0.316284
$377$		0			0
$378$	−1792.89			−0.243958
$379$	1922.24	−	3329.41i	0.260524	−	0.451241i	−0.705857	−	0.708354i	$-0.749438\pi$
$379$	1922.24	−	3329.41i	0.260524	−	0.451241i	0.966381	+	0.257113i	$0.0827713\pi$
$380$	1721.55	−	2981.82i	0.232405	−	0.402537i
$381$	73.4791	+	127.270i	0.00988045	+	0.0171134i
$382$	−12723.0			−1.70410
$383$	6077.15	+	10525.9i	0.810778	+	1.40431i	0.912320	+	0.409477i	$0.134289\pi$
$383$	6077.15	+	10525.9i	0.810778	+	1.40431i	−0.101543	+	0.994831i	$0.532378\pi$
$384$	87.7193	+	151.934i	0.0116573	+	0.0201911i
$385$	7398.96			0.979444
$386$	−7481.22	−	12957.9i	−0.986487	−	1.70865i
$387$	−3446.27	+	5969.11i	−0.452671	+	0.784049i
$388$	−2309.64	+	4000.41i	−0.302202	+	0.523429i
$389$	−5269.41			−0.686812			−0.343406	−	0.939187i	$-0.611581\pi$
$389$	−5269.41			−0.686812			−0.343406	+	0.939187i	$0.611581\pi$
$390$		0			0
$391$	8460.07			1.09423
$392$	1546.94	−	2679.38i	0.199317	−	0.345228i
$393$	−116.414	+	201.635i	−0.0149423	+	0.0258808i
$394$	−6965.13	−	12064.0i	−0.890604	−	1.54257i
$395$	−4381.53			−0.558123
$396$	1889.96	+	3273.51i	0.239834	+	0.415404i
$397$	327.742	+	567.665i	0.0414329	+	0.0717639i	0.885998	−	0.463689i	$-0.153474\pi$
$397$	327.742	+	567.665i	0.0414329	+	0.0717639i	−0.844565	+	0.535453i	$0.820141\pi$
$398$	11339.2			1.42809
$399$	−195.874	−	339.264i	−0.0245764	−	0.0425675i
$400$	156.291	−	270.703i	0.0195363	−	0.0338379i
$401$	3849.98	−	6668.37i	0.479449	−	0.830430i	−0.520273	−	0.854000i	$-0.674170\pi$
$401$	3849.98	−	6668.37i	0.479449	−	0.830430i	0.999722	+	0.0235699i	$0.00750322\pi$
$402$	−655.086			−0.0812754
$403$		0			0
$404$	3159.53			0.389091
$405$	4108.88	−	7116.78i	0.504128	−	0.873175i
$406$	−1620.50	+	2806.78i	−0.198088	+	0.343099i
$407$	3715.47	+	6435.39i	0.452504	+	0.783760i
$408$	158.872			0.0192778
$409$	−277.600	−	480.818i	−0.0335610	−	0.0581294i	0.848757	−	0.528783i	$-0.177351\pi$
$409$	−277.600	−	480.818i	−0.0335610	−	0.0581294i	−0.882318	+	0.470654i	$0.844018\pi$
$410$	−1774.96	−	3074.32i	−0.213802	−	0.370317i
$411$	−130.303			−0.0156383
$412$	1124.41	+	1947.54i	0.134456	+	0.232884i
$413$	−845.944	+	1465.22i	−0.100790	+	0.174573i
$414$	3817.38	−	6611.89i	0.453173	−	0.784919i
$415$	7547.62			0.892767
$416$		0			0
$417$	199.065			0.0233772
$418$	−1814.34	+	3142.54i	−0.212303	+	0.367719i
$419$	−1658.50	+	2872.60i	−0.193372	+	0.334930i	−0.946366	−	0.323098i	$-0.895276\pi$
$419$	−1658.50	+	2872.60i	−0.193372	+	0.334930i	0.752994	+	0.658028i	$0.228609\pi$
$420$	330.442	+	572.343i	0.0383903	+	0.0664940i
$421$	13270.3			1.53623			0.768117	−	0.640310i	$-0.221194\pi$
$421$	13270.3			1.53623			0.768117	+	0.640310i	$0.221194\pi$
$422$	6123.61	+	10606.4i	0.706381	+	1.22349i
$423$	−6239.20	−	10806.6i	−0.717164	−	1.24216i
$424$	−381.125			−0.0436535
$425$	−245.924	−	425.954i	−0.0280684	−	0.0486160i
$426$	−8.72688	+	15.1154i	−0.000992532	+	0.00171912i
$427$	−7680.09	+	13302.3i	−0.870411	+	1.50760i
$428$	10920.1			1.23328
$429$		0			0
$430$	11162.6			1.25188
$431$	6846.11	−	11857.8i	0.765117	−	1.32522i	−0.175068	−	0.984556i	$-0.556015\pi$
$431$	6846.11	−	11857.8i	0.765117	−	1.32522i	0.940185	−	0.340665i	$-0.110652\pi$
$432$	547.152	−	947.695i	0.0609372	−	0.105546i
$433$	7594.54	+	13154.1i	0.842888	+	1.45992i	0.887443	+	0.460918i	$0.152480\pi$
$433$	7594.54	+	13154.1i	0.842888	+	1.45992i	−0.0445548	+	0.999007i	$0.514187\pi$
$434$	21389.7			2.36575
$435$	43.1893	+	74.8060i	0.00476038	+	0.00824522i
$436$	−5090.37	−	8816.78i	−0.559139	−	0.968456i
$437$	3341.23			0.365750
$438$	−172.243	−	298.334i	−0.0187902	−	0.0325456i
$439$	1401.02	−	2426.64i	0.152317	−	0.263821i	−0.779762	−	0.626076i	$-0.784660\pi$
$439$	1401.02	−	2426.64i	0.152317	−	0.263821i	0.932079	+	0.362256i	$0.117993\pi$
$440$	−592.536	+	1026.30i	−0.0642002	+	0.111198i
$441$	−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	$0.632491\pi$
$444$	−331.871	+	574.817i	−0.0354727	+	0.0614406i
$445$	−3102.71	+	5374.05i	−0.330522	+	0.572482i
$446$	143.999	+	249.413i	0.0152882	+	0.0264799i
$447$	185.033			0.0195789
$448$	−5197.25	−	9001.90i	−0.548096	−	0.949330i
$449$	2779.41	+	4814.08i	0.292135	+	0.505992i	0.974314	−	0.225192i	$-0.0723011\pi$
$449$	2779.41	+	4814.08i	0.292135	+	0.505992i	−0.682180	+	0.731185i	$0.738968\pi$
$450$	−443.867			−0.0464979
$451$	852.771	+	1477.04i	0.0890364	+	0.154216i
$452$	−4006.10	+	6938.77i	−0.416883	+	0.722063i
$453$	−26.6409	+	46.1433i	−0.00276313	+	0.00478588i
$454$	−16575.2			−1.71347
$455$		0			0
$456$	62.7453			0.00644368
$457$	−2163.85	+	3747.91i	−0.221490	+	0.383632i	−0.955261	−	0.295766i	$-0.904425\pi$
$457$	−2163.85	+	3747.91i	−0.221490	+	0.383632i	0.733771	+	0.679397i	$0.237759\pi$
$458$	−1299.71	+	2251.16i	−0.132601	+	0.229672i
$459$	−860.949	−	1491.21i	−0.0875504	−	0.151642i
$460$	−5636.71			−0.571333
$461$	−5646.36	−	9779.78i	−0.570450	−	0.988048i	−0.996520	−	0.0833575i	$-0.973436\pi$
$461$	−5646.36	−	9779.78i	−0.570450	−	0.988048i	0.426070	−	0.904690i	$-0.359898\pi$
$462$	−348.253	−	603.192i	−0.0350697	−	0.0607425i
$463$	−8582.54			−0.861478			−0.430739	−	0.902477i	$-0.641747\pi$
$463$	−8582.54			−0.861478			−0.430739	+	0.902477i	$0.641747\pi$
$464$	−989.084	−	1713.14i	−0.0989592	−	0.171402i
$465$	285.037	−	493.699i	0.0284264	−	0.0492360i
$466$	−178.119	+	308.511i	−0.0177064	+	0.0306684i
$467$	17543.0			1.73831			0.869157	−	0.494536i	$-0.164662\pi$
$467$	17543.0			1.73831			0.869157	+	0.494536i	$0.164662\pi$
$468$		0			0
$469$	−19009.8			−1.87163
$470$	−10104.5	+	17501.5i	−0.991672	+	1.71763i
$471$	−395.568	+	685.144i	−0.0386981	+	0.0670271i
$472$	−135.493	−	234.680i	−0.0132131	−	0.0228857i
$473$	−5363.01			−0.521335
$474$	206.229	+	357.199i	0.0199840	+	0.0346133i
$475$	−97.1258	−	168.227i	−0.00938197	−	0.0162501i
$476$	−23815.1			−2.29320
$477$	1031.19	+	1786.07i	0.0989830	+	0.171444i
$478$	−3992.66	+	6915.49i	−0.382050	+	0.661731i
$479$	3149.57	−	5455.22i	0.300434	−	0.520366i	−0.675801	−	0.737085i	$-0.736202\pi$
$479$	3149.57	−	5455.22i	0.300434	−	0.520366i	0.976234	+	0.216718i	$0.0695353\pi$
$480$	−758.498			−0.0721262
$481$		0			0
$482$	25081.7			2.37020
$483$	−320.665	+	555.409i	−0.0302086	+	0.0523229i
$484$	2989.94	−	5178.73i	0.280799	−	0.486358i
$485$	3918.39	+	6786.85i	0.366855	+	0.635412i
$486$	−2332.00			−0.217658
$487$	1785.86	+	3093.21i	0.166171	+	0.287817i	0.937070	−	0.349140i	$-0.113526\pi$
$487$	1785.86	+	3093.21i	0.166171	+	0.287817i	−0.770900	+	0.636957i	$0.780193\pi$
$488$	−1230.10	−	2130.60i	−0.114107	−	0.197639i
$489$	995.368			0.0920493
$490$	13556.9	+	23481.2i	1.24987	+	2.16485i
$491$	6692.61	−	11591.9i	0.615139	−	1.06545i	−0.375221	−	0.926935i	$-0.622433\pi$
$491$	6692.61	−	11591.9i	0.615139	−	1.06545i	0.990360	−	0.138517i	$-0.0442334\pi$
$492$	−76.1707	+	131.931i	−0.00697975	+	0.0120893i
$493$	−3112.66			−0.284356
$494$		0			0
$495$	6412.77			0.582288
$496$	−6527.68	+	11306.3i	−0.590931	+	1.02352i
$497$	−253.244	+	438.632i	−0.0228562	+	0.0395882i
$498$	−355.250	−	615.311i	−0.0319662	−	0.0553670i
$499$	19227.7			1.72495			0.862476	−	0.506098i	$-0.168913\pi$
$499$	19227.7			1.72495			0.862476	+	0.506098i	$0.168913\pi$
$500$	−4599.52	−	7966.61i	−0.411394	−	0.712555i
$501$	16.8377	+	29.1637i	0.00150150	+	0.00260068i
$502$	−9238.13			−0.821350
$503$	9325.62	+	16152.5i	0.826658	+	1.43181i	0.900646	+	0.434554i	$0.143094\pi$
$503$	9325.62	+	16152.5i	0.826658	+	1.43181i	−0.0739878	+	0.997259i	$0.523573\pi$
$504$	2080.27	−	3603.13i	0.183854	−	0.318445i
$505$	2680.13	−	4642.13i	0.236167	−	0.409053i
$506$	5940.53			0.521914
$507$		0			0
$508$	3528.35			0.308160
$509$	−7943.04	+	13757.8i	−0.691688	+	1.19804i	0.279596	+	0.960118i	$0.409799\pi$
$509$	−7943.04	+	13757.8i	−0.691688	+	1.19804i	−0.971284	+	0.237921i	$0.923534\pi$
$510$	−696.153	+	1205.77i	−0.0604435	+	0.104691i
$511$	−4998.31	−	8657.32i	−0.432705	−	0.749467i
$512$	14477.1			1.24961
$513$	−340.024	−	588.939i	−0.0292640	−	0.0506868i
$514$	505.346	+	875.285i	0.0433655	+	0.0751112i
$515$	3815.21			0.326443
$516$	−239.516	−	414.853i	−0.0204343	−	0.0353932i
$517$	4854.66	−	8408.52i	0.412975	−	0.715293i
$518$	−21125.4	+	36590.2i	−1.79188	+	3.10363i
$519$	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	$0.475556\pi$
$522$	−1404.50	+	2432.67i	−0.117765	+	0.203975i
$523$	−8103.15	+	14035.1i	−0.677488	+	1.17344i	0.298247	+	0.954489i	$0.403598\pi$
$523$	−8103.15	+	14035.1i	−0.677488	+	1.17344i	−0.975735	+	0.218954i	$0.929735\pi$
$524$	2795.02	+	4841.11i	0.233017	+	0.403597i
$525$	37.2855			0.00309956
$526$	14042.7	+	24322.7i	1.16405	+	2.01619i
$527$	10271.4	+	17790.5i	0.849009	+	1.47053i
$528$	425.119			0.0350396
$529$	3348.53	+	5799.83i	0.275214	+	0.476685i
$530$	1670.03	−	2892.58i	0.136871	−	0.237067i
$531$	−733.190	+	1269.92i	−0.0599204	+	0.103785i
$532$	−9405.57			−0.766510
$533$		0			0
$534$	584.151			0.0473384
$535$	9263.19	−	16044.3i	0.748565	−	1.29655i
$536$	1522.38	−	2636.84i	0.122681	−	0.212489i
$537$	−77.2081	−	133.728i	−0.00620442	−	0.0107464i
$538$	−17957.8			−1.43906
$539$	−6513.35	−	11281.5i	−0.520501	−	0.901534i
$540$	573.626	+	993.550i	0.0457129	+	0.0791770i
$541$	−2429.83			−0.193099			−0.0965496	−	0.995328i	$-0.530781\pi$
$541$	−2429.83			−0.193099			−0.0965496	+	0.995328i	$0.530781\pi$
$542$	−3123.82	−	5410.62i	−0.247564	−	0.428793i
$543$	−461.343	+	799.070i	−0.0364607	+	0.0631517i
$544$	13666.3	−	23670.7i	1.07709	−	1.86558i
$545$	−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	$0.530016\pi$
$548$	−1564.23	+	2709.33i	−0.121936	+	0.211199i
$549$	−6656.43	+	11529.3i	−0.517467	+	0.896280i
$550$	−172.684	−	299.098i	−0.0133878	−	0.0231883i
$551$	−1229.32			−0.0950468
$552$	−51.3602	−	88.9584i	−0.00396021	−	0.00685928i
$553$	5984.53	+	10365.5i	0.460195	+	0.797081i
$554$	23775.7			1.82334
$555$	563.031	+	975.198i	0.0430619	+	0.0745853i
$556$	2389.70	−	4139.09i	0.182277	−	0.315713i
$557$	−4334.35	+	7507.32i	−0.329717	+	0.571087i	−0.982456	−	0.186497i	$-0.940287\pi$
$557$	−4334.35	+	7507.32i	−0.329717	+	0.571087i	0.652739	+	0.757583i	$0.273620\pi$
$558$	18538.7			1.40646
$559$		0			0
$560$	−25677.1			−1.93760
$561$	334.464	−	579.308i	0.0251713	−	0.0435979i
$562$	5658.12	−	9800.15i	0.424686	−	0.735577i
$563$	3909.17	+	6770.89i	0.292632	+	0.506854i	0.974431	−	0.224685i	$-0.0721355\pi$
$563$	3909.17	+	6770.89i	0.292632	+	0.506854i	−0.681799	+	0.731540i	$0.738802\pi$
$564$	867.250			0.0647479
$565$	6796.50	+	11771.9i	0.506072	+	0.876543i
$566$	−10063.7	−	17430.8i	−0.747363	−	1.29447i
$567$	−22448.5			−1.66270
$568$	−40.5615	−	70.2545i	−0.00299634	−	0.00518981i
$569$	−4558.62	+	7895.76i	−0.335865	+	0.581735i	−0.983651	−	0.180087i	$-0.942362\pi$
$569$	−4558.62	+	7895.76i	−0.335865	+	0.581735i	0.647786	+	0.761823i	$0.275695\pi$
$570$	−274.940	+	476.210i	−0.0202034	+	0.0349934i
$571$	−11842.4			−0.867932			−0.433966	−	0.900929i	$-0.642886\pi$
$571$	−11842.4			−0.867932			−0.433966	+	0.900929i	$0.642886\pi$
$572$		0			0
$573$	926.302			0.0675337
$574$	−4848.67	+	8398.15i	−0.352578	+	0.610683i
$575$	−159.005	+	275.404i	−0.0115321	+	0.0199742i
$576$	−4504.52	−	7802.06i	−0.325848	−	0.564385i
$577$	10958.1			0.790623			0.395312	−	0.918547i	$-0.370637\pi$
$577$	10958.1			0.790623			0.395312	+	0.918547i	$0.370637\pi$
$578$	−15666.8	−	27135.8i	−1.12743	−	1.95277i
$579$	544.672	+	943.399i	0.0390946	+	0.0677139i
$580$	2073.88			0.148471
$581$	−10309.0	−	17855.6i	−0.736123	−	1.27500i
$582$	368.860	−	638.884i	0.0262710	−	0.0455028i
$583$	−802.358	+	1389.72i	−0.0569987	+	0.0987247i
$584$	1601.13			0.113451
$585$		0			0
$586$	11167.0			0.787209
$587$	11528.9	−	19968.6i	0.810644	−	1.40408i	−0.101770	−	0.994808i	$-0.532451\pi$
$587$	11528.9	−	19968.6i	0.810644	−	1.40408i	0.912414	−	0.409269i	$-0.134216\pi$
$588$	581.781	−	1007.67i	0.0408032	−	0.0706731i
$589$	4056.59	+	7026.22i	0.283784	+	0.491529i
$590$	2374.83			0.165712
$591$	507.097	+	878.318i	0.0352947	+	0.0611323i
$592$	−12894.1	−	22333.2i	−0.895173	−	1.55049i
$593$	9904.56			0.685888			0.342944	−	0.939356i	$-0.388576\pi$
$593$	9904.56			0.685888			0.342944	+	0.939356i	$0.388576\pi$
$594$	−604.544	−	1047.10i	−0.0417588	−	0.0723284i
$595$	−20201.6	+	34990.2i	−1.39191	+	2.41085i
$596$	2221.25	−	3847.32i	0.152661	−	0.264416i
$597$	−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	$0.240620\pi$
$600$	−2.98596	+	5.17184i	−0.000203169	+	0.000351899i
$601$	9742.19	−	16874.0i	0.661219	−	1.14526i	−0.319077	−	0.947729i	$-0.603373\pi$
$601$	9742.19	−	16874.0i	0.661219	−	1.14526i	0.980296	−	0.197536i	$-0.0632938\pi$
$602$	−15246.5	−	26407.6i	−1.03222	−	1.78787i
$603$	−16476.1			−1.11270
$604$	639.626	+	1107.87i	0.0430895	+	0.0746331i
$605$	−5072.55	−	8785.91i	−0.340873	−	0.590410i
$606$	−504.592			−0.0338245
$607$	−9927.83	−	17195.5i	−0.663852	−	1.14982i	−0.979595	−	0.200980i	$-0.935587\pi$
$607$	−9927.83	−	17195.5i	−0.663852	−	1.14982i	0.315744	−	0.948845i	$-0.397746\pi$
$608$	5397.39	−	9348.56i	0.360022	−	0.623576i
$609$	117.980	−	204.348i	0.00785026	−	0.0135971i
$610$	21560.4			1.43108
$611$		0			0
$612$	−20640.8			−1.36333
$613$	2576.79	−	4463.13i	0.169781	−	0.294069i	−0.768562	−	0.639775i	$-0.779027\pi$
$613$	2576.79	−	4463.13i	0.169781	−	0.294069i	0.938343	+	0.345707i	$0.112361\pi$
$614$	9586.14	−	16603.7i	0.630073	−	1.09132i
$615$	129.226	+	223.826i	0.00847302	+	0.0146757i
$616$	3237.27			0.211743
$617$	−462.109	−	800.396i	−0.0301520	−	0.0522248i	0.850556	−	0.525885i	$-0.176266\pi$
$617$	−462.109	−	800.396i	−0.0301520	−	0.0522248i	−0.880708	+	0.473660i	$0.842932\pi$
$618$	−179.574	−	311.031i	−0.0116885	−	0.0202451i
$619$	15690.6			1.01883			0.509417	−	0.860520i	$-0.329861\pi$
$619$	15690.6			1.01883			0.509417	+	0.860520i	$0.329861\pi$
$620$	−6843.53	−	11853.3i	−0.443295	−	0.767809i
$621$	−556.654	+	964.153i	−0.0359706	+	0.0623029i
$622$	15032.6	−	26037.2i	0.969054	−	1.67845i
$623$	16951.4			1.09012
$624$		0			0
$625$	−16144.0			−1.03322
$626$	14414.3	−	24966.2i	0.920303	−	1.59401i
$627$	132.094	−	228.793i	0.00841358	−	0.0145727i
$628$	9497.29	+	16449.8i	0.603476	+	1.04525i
$629$	−40577.8			−2.57225
$630$	18230.8	+	31576.7i	1.15291	+	1.99690i
$631$	10551.8	+	18276.2i	0.665705	+	1.15303i	0.979094	+	0.203409i	$0.0652022\pi$
$631$	10551.8	+	18276.2i	0.665705	+	1.15303i	−0.313389	+	0.949625i	$0.601464\pi$
$632$	−1917.05			−0.120659
$633$	−445.830	−	772.201i	−0.0279939	−	0.0484869i
$634$	930.294	−	1611.32i	0.0582756	−	0.100936i
$635$	2992.99	−	5184.01i	0.187044	−	0.323970i
$636$	−143.335			−0.00893650
$637$		0			0
$638$	−2185.66			−0.135629
$639$	−219.490	+	380.167i	−0.0135882	+	0.0235355i
$640$	3573.03	−	6188.67i	0.220682	−	0.382232i
$641$	3347.69	+	5798.37i	0.206280	+	0.357288i	0.950540	−	0.310602i	$-0.100531\pi$
$641$	3347.69	+	5798.37i	0.206280	+	0.357288i	−0.744260	+	0.667891i	$0.767197\pi$
$642$	−1743.99			−0.107212
$643$	−4823.85	−	8355.15i	−0.295854	−	0.512434i	0.679329	−	0.733833i	$-0.262271\pi$
$643$	−4823.85	−	8355.15i	−0.295854	−	0.512434i	−0.975183	+	0.221400i	$0.928937\pi$
$644$	7698.93	+	13334.9i	0.471087	+	0.815947i
$645$	−812.694			−0.0496121
$646$	−9907.50	−	17160.3i	−0.603414	−	1.04514i
$647$	11873.8	−	20566.0i	0.721493	−	1.24966i	−0.238909	−	0.971042i	$-0.576790\pi$
$647$	11873.8	−	20566.0i	0.721493	−	1.24966i	0.960401	−	0.278620i	$-0.0898770\pi$
$648$	1797.76	−	3113.81i	0.108986	−	0.188769i
$649$	−1140.98			−0.0690096
$650$		0			0
$651$	−1557.28			−0.0937551
$652$	11949.0	−	20696.3i	0.717729	−	1.24314i
$653$	−9916.76	+	17176.3i	−0.594292	+	1.02934i	0.399354	+	0.916797i	$0.369234\pi$
$653$	−9916.76	+	17176.3i	−0.594292	+	1.02934i	−0.993646	+	0.112547i	$0.964099\pi$
$654$	812.955	+	1408.08i	0.0486071	+	0.0841900i
$655$	9483.70			0.565738
$656$	−2959.43	−	5125.88i	−0.176138	−	0.305080i
$657$	−4332.10	−	7503.41i	−0.257247	−	0.445565i
$658$	55205.1			3.27070
$659$	−5403.70	−	9359.48i	−0.319421	−	0.553253i	0.660947	−	0.750433i	$-0.270155\pi$
$659$	−5403.70	−	9359.48i	−0.319421	−	0.553253i	−0.980367	+	0.197180i	$0.936822\pi$
$660$	−222.844	+	385.977i	−0.0131427	+	0.0227638i
$661$	6715.75	−	11632.0i	0.395178	−	0.684468i	−0.597946	−	0.801536i	$-0.704016\pi$
$661$	6715.75	−	11632.0i	0.395178	−	0.684468i	0.993124	+	0.117068i	$0.0373496\pi$
$662$	−31529.7			−1.85111
$663$		0			0
$664$	3302.32			0.193004
$665$	−7978.44	+	13819.1i	−0.465249	+	0.805835i
$666$	−18309.6	+	31713.2i	−1.06529	+	1.84514i
$667$	1006.26	+	1742.89i	0.0584146	+	0.101177i
$668$	808.520			0.0468302
$669$	−10.4838	−	18.1586i	−0.000605873	−	0.00104940i
$670$	13341.7	+	23108.4i	0.769303	+	1.33247i
$671$	−10358.6			−0.595961
$672$	1036.00	+	1794.40i	0.0594710	+	0.103007i
$673$	−10790.7	+	18690.0i	−0.618054	+	1.07050i	0.371787	+	0.928318i	$0.378745\pi$
$673$	−10790.7	+	18690.0i	−0.618054	+	1.07050i	−0.989840	+	0.142182i	$0.954588\pi$
$674$	−14848.2	+	25717.9i	−0.848564	+	1.46976i
$675$	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	$0.334715\pi$
$678$	639.793	−	1108.15i	0.0362405	−	0.0627705i
$679$	10703.9	−	18539.7i	0.604975	−	1.04785i
$680$	−3235.64	−	5604.29i	−0.182472	−	0.316051i
$681$	1206.76			0.0679048
$682$	7212.39	+	12492.2i	0.404951	+	0.701396i
$683$	−1421.11	−	2461.44i	−0.0796155	−	0.137898i	0.823469	−	0.567362i	$-0.192036\pi$
$683$	−1421.11	−	2461.44i	−0.0796155	−	0.137898i	−0.903084	+	0.429464i	$0.858703\pi$
$684$	−8151.92			−0.455697
$685$	2653.78	+	4596.48i	0.148023	+	0.256383i
$686$	16607.1	−	28764.3i	0.924287	−	1.60091i
$687$	94.6255	−	163.896i	0.00525500	−	0.00910193i
$688$	18611.6			1.03134
$689$		0			0
$690$	900.208			0.0496672
$691$	−11437.8	+	19810.8i	−0.629686	+	1.09065i	0.357929	+	0.933749i	$0.383483\pi$
$691$	−11437.8	+	19810.8i	−0.629686	+	1.09065i	−0.987615	+	0.156899i	$0.949850\pi$
$692$	6971.52	−	12075.0i	0.382973	−	0.663329i
$693$	−8758.91	−	15170.9i	−0.480121	−	0.831593i
$694$	−13545.4			−0.740886
$695$	−4054.22	−	7022.11i	−0.221274	−	0.383257i
$696$	18.8966	+	32.7299i	0.00102913	+	0.00178251i
$697$	−9313.38			−0.506125
$698$	6453.62	+	11178.0i	0.349962	+	0.606151i
$699$	12.9680	−	22.4612i	0.000701708	−	0.00121539i
$700$	447.598	−	775.262i	0.0241680	−	0.0418602i
$701$	11980.3			0.645492			0.322746	−	0.946486i	$-0.395394\pi$
$701$	11980.3			0.645492			0.322746	+	0.946486i	$0.395394\pi$
$702$		0			0
$703$	−16025.9			−0.859782
$704$	3504.92	−	6070.71i	0.187638	−	0.324998i
$705$	735.660	−	1274.20i	0.0393001	−	0.0680698i
$706$	−19110.5	−	33100.4i	−1.01874	−	1.76452i
$707$	−14642.7			−0.778918
$708$	−50.9568	−	88.2597i	−0.00270491	−	0.00468503i
$709$	−2102.38	−	3641.44i	−0.111363	−	0.192887i	0.804957	−	0.593333i	$-0.202188\pi$
$709$	−2102.38	−	3641.44i	−0.111363	−	0.192887i	−0.916320	+	0.400446i	$0.868855\pi$
$710$	710.936			0.0375788
$711$	5186.86	+	8983.91i	0.273590	+	0.473872i
$712$	−1357.53	+	2351.31i	−0.0714545	+	0.123763i
$713$	6641.04	−	11502.6i	0.348820	−	0.604175i
$714$	3803.38			0.199353
$715$		0			0
$716$	−3707.41			−0.193509
$717$	290.686	−	503.484i	0.0151407	−	0.0262245i
$718$	5258.33	−	9107.69i	0.273313	−	0.473393i
$719$	5768.50	+	9991.33i	0.299205	+	0.518239i	0.975954	−	0.217975i	$-0.0699451\pi$
$719$	5768.50	+	9991.33i	0.299205	+	0.518239i	−0.676749	+	0.736214i	$0.736612\pi$
$720$	−22254.7			−1.15192
$721$	−5211.02	−	9025.76i	−0.269166	−	0.466209i
$722$	9237.13	+	15999.2i	0.476136	+	0.824692i
$723$	−1826.07			−0.0939315
$724$	11076.5	+	19185.1i	0.568584	+	0.984817i
$725$	58.5016	−	101.328i	0.00299682	−	0.00519065i
$726$	−477.508	+	827.067i	−0.0244104	+	0.0422801i
$727$	−33899.7			−1.72940			−0.864698	−	0.502293i	$-0.832490\pi$
$727$	−33899.7			−1.72940			−0.864698	+	0.502293i	$0.832490\pi$
$728$		0			0
$729$	−19342.9			−0.982723
$730$	−7015.91	+	12151.9i	−0.355713	+	0.616113i
$731$	14642.8	−	25362.0i	0.740879	−	1.28324i
$732$	−462.622	−	801.285i	−0.0233593	−	0.0404595i
$733$	−378.221			−0.0190585			−0.00952927	−	0.999955i	$-0.503033\pi$
$733$	−378.221			−0.0190585			−0.00952927	+	0.999955i	$0.503033\pi$
$734$	3147.75	+	5452.07i	0.158291	+	0.274168i
$735$	−987.013	−	1709.56i	−0.0495327	−	0.0857931i
$736$	−17672.1			−0.885059
$737$	−6409.94	−	11102.3i	−0.320371	−	0.554898i
$738$	−4202.41	+	7278.78i	−0.209611	+	0.363056i
$739$	−11331.8	+	19627.2i	−0.564069	+	0.976996i	0.433067	+	0.901362i	$0.357431\pi$
$739$	−11331.8	+	19627.2i	−0.564069	+	0.976996i	−0.997136	+	0.0756339i	$0.975902\pi$
$740$	27035.9			1.34305
$741$		0			0
$742$	−9124.06			−0.451422
$743$	−8203.66	+	14209.2i	−0.405065	+	0.701593i	−0.994329	−	0.106348i	$-0.966084\pi$
$743$	−8203.66	+	14209.2i	−0.405065	+	0.701593i	0.589264	+	0.807940i	$0.299418\pi$
$744$	124.713	−	216.009i	0.00614541	−	0.0106442i
$745$	−3768.43	−	6527.11i	−0.185322	−	0.320986i
$746$	42974.0			2.10910
$747$	−8934.90	−	15475.7i	−0.437632	−	0.758001i
$748$	−8030.22	−	13908.7i	−0.392532	−	0.679885i
$749$	−50608.7			−2.46889
$750$	734.565	+	1272.30i	0.0357633	+	0.0619439i
$751$	−10978.9	+	19016.1i	−0.533458	+	0.923976i	0.465779	+	0.884901i	$0.345774\pi$
$751$	−10978.9	+	19016.1i	−0.533458	+	0.923976i	−0.999236	+	0.0390744i	$0.987559\pi$
$752$	−16847.5	+	29180.7i	−0.816973	+	1.41504i
$753$	672.584			0.0325502
$754$		0			0
$755$	2170.30			0.104616
$756$	1566.98	−	2714.09i	0.0753843	−	0.130569i
$757$	−10411.7	+	18033.7i	−0.499896	+	0.865846i	−1.00000		0.000119832i	$-0.999962\pi$
$757$	−10411.7	+	18033.7i	−0.499896	+	0.865846i	0.500104	+	0.865965i	$0.333295\pi$
$758$	7370.59	+	12766.2i	0.353182	+	0.611729i
$759$	−432.501			−0.0206835
$760$	−1277.89	−	2213.37i	−0.0609919	−	0.105641i
$761$	14228.1	+	24643.7i	0.677749	+	1.17390i	0.975657	+	0.219301i	$0.0703776\pi$
$761$	14228.1	+	24643.7i	0.677749	+	1.17390i	−0.297909	+	0.954594i	$0.596289\pi$
$762$	−563.494			−0.0267890
$763$	23591.0	+	40860.8i	1.11933	+	1.93874i
$764$	11119.9	−	19260.2i	0.526576	−	0.912056i
$765$	−17509.0	+	30326.4i	−0.827500	+	1.43327i
$766$	−46604.2			−2.19828
$767$		0			0
$768$	−1420.04			−0.0667203
$769$	6724.98	−	11648.0i	0.315356	−	0.546213i	−0.664157	−	0.747593i	$-0.731209\pi$
$769$	6724.98	−	11648.0i	0.315356	−	0.546213i	0.979513	+	0.201380i	$0.0645427\pi$
$770$	−14185.2	+	24569.5i	−0.663896	+	1.14990i
$771$	−36.7918	−	63.7253i	−0.00171858	−	0.00297667i
$772$	26154.3			1.21932
$773$	−13288.9	−	23017.0i	−0.618329	−	1.07098i	−0.989791	−	0.142529i	$-0.954477\pi$
$773$	−13288.9	−	23017.0i	−0.618329	−	1.07098i	0.371462	−	0.928448i	$-0.378857\pi$
$774$	−13214.3	−	22887.8i	−0.613667	−	1.06290i
$775$	−772.190			−0.0357908
$776$	1714.42	+	2969.46i	0.0793092	+	0.137368i
$777$	1538.04	−	2663.96i	0.0710125	−	0.122997i
$778$	10102.5	−	17498.0i	0.465541	−	0.806341i
$779$	−3678.24			−0.169174
$780$		0			0
$781$	−341.566			−0.0156494
$782$	−16219.6	+	28093.1i	−0.741702	+	1.28467i
$783$	204.806	−	354.735i	0.00934761	−	0.0161905i
$784$	22603.7	+	39150.8i	1.02969	+	1.78347i
$785$	32225.0			1.46517
$786$	−446.377	−	773.147i	−0.0202567	−	0.0350856i
$787$	−4140.70	−	7171.90i	−0.187548	−	0.324842i	0.756884	−	0.653549i	$-0.226721\pi$
$787$	−4140.70	−	7171.90i	−0.187548	−	0.324842i	−0.944432	+	0.328707i	$0.893387\pi$
$788$	24350.0			1.10080
$789$	−1022.38	−	1770.82i	−0.0461315	−	0.0799020i
$790$	8400.22	−	14549.6i	0.378312	−	0.655256i
$791$	18566.0	−	32157.3i	0.834555	−	1.44549i
$792$	2805.79			0.125883
$793$		0			0
$794$	−2513.37			−0.112338
$795$	−121.587	+	210.594i	−0.00542420	+	0.00939499i
$796$	−9910.40	+	17165.3i	−0.441287	+	0.764332i
$797$	−10334.4	−	17899.7i	−0.459302	−	0.795535i	0.539622	−	0.841908i	$-0.318567\pi$
$797$	−10334.4	−	17899.7i	−0.459302	−	0.795535i	−0.998924	+	0.0463725i	$0.985234\pi$
$798$	1502.11			0.0666343
$799$	26509.6	+	45916.0i	1.17377	+	2.03303i
$800$	513.709	+	889.769i	0.0227029	+	0.0393226i
$801$	14692.0			0.648085
$802$	14762.3	+	25569.1i	0.649969	+	1.12578i
$803$	3370.76	−	5838.33i	0.148134	−	0.256576i
$804$	572.544	−	991.675i	0.0251145	−	0.0434996i
$805$	26123.0			1.14375
$806$		0			0
$807$	1307.42			0.0570303
$808$	1172.64	−	2031.07i	0.0510561	−	0.0884318i
$809$	−3619.43	+	6269.03i	−0.157296	+	0.272444i	−0.933893	−	0.357554i	$-0.883611\pi$
$809$	−3619.43	+	6269.03i	−0.157296	+	0.272444i	0.776597	+	0.629998i	$0.216944\pi$
$810$	15755.0	+	27288.5i	0.683425	+	1.18373i
$811$	−13101.3			−0.567260			−0.283630	−	0.958934i	$-0.591539\pi$
$811$	−13101.3			−0.567260			−0.283630	+	0.958934i	$0.591539\pi$
$812$	−2832.62	−	4906.24i	−0.122421	−	0.212039i
$813$	227.430	+	393.921i	0.00981099	+	0.0169931i
$814$	−28493.1			−1.22688
$815$	−20271.9	−	35112.0i	−0.871282	−	1.50910i
$816$	−1160.71	+	2010.41i	−0.0497954	+	0.0862482i
$817$	5783.04	−	10016.5i	0.247641	−	0.428927i
$818$	2128.85			0.0909946
$819$		0			0
$820$	6205.25			0.264264
$821$	6046.44	−	10472.7i	0.257031	−	0.445190i	−0.708414	−	0.705797i	$-0.750589\pi$
$821$	6046.44	−	10472.7i	0.257031	−	0.445190i	0.965445	+	0.260606i	$0.0839225\pi$
$822$	249.815	−	432.693i	0.0106001	−	0.0183600i
$823$	−13520.6	−	23418.4i	−0.572659	−	0.991874i	−0.996292	−	0.0860402i	$-0.972579\pi$
$823$	−13520.6	−	23418.4i	−0.572659	−	0.991874i	0.423633	−	0.905834i	$-0.360755\pi$
$824$	1669.27			0.0705727
$825$	12.5723	+	21.7759i	0.000530559	+	0.000918955i
$826$	−3243.67	−	5618.21i	−0.136637	−	0.236662i
$827$	25572.3			1.07526			0.537628	−	0.843182i	$-0.319320\pi$
$827$	25572.3			1.07526			0.537628	+	0.843182i	$0.319320\pi$
$828$	6672.76	+	11557.6i	0.280066	+	0.485088i
$829$	8752.89	−	15160.4i	0.366707	−	0.635156i	−0.622341	−	0.782746i	$-0.713818\pi$
$829$	8752.89	−	15160.4i	0.366707	−	0.635156i	0.989049	+	0.147590i	$0.0471517\pi$
$830$	−14470.2	+	25063.2i	−0.605144	+	1.04814i
$831$	−1730.99			−0.0722593
$832$		0			0
$833$	71134.3			2.95877
$834$	−381.646	+	661.031i	−0.0158457	+	0.0274456i
$835$	685.841	−	1187.91i	0.0284246	−	0.0492328i
$836$	−3171.47	−	5493.14i	−0.131205	−	0.227254i
$837$	−2703.33			−0.111638
$838$	−6359.31	−	11014.6i	−0.262146	−	0.454051i
$839$	−14146.7	−	24502.8i	−0.582119	−	1.00826i	−0.995228	−	0.0975785i	$-0.968890\pi$
$839$	−14146.7	−	24502.8i	−0.582119	−	1.00826i	0.413108	−	0.910682i	$-0.364443\pi$
$840$	490.566			0.0201502
$841$	11824.3	+	20480.2i	0.484820	+	0.839733i
$842$	−25441.7	+	44066.3i	−1.04130	+	1.80359i
$843$	−411.940	+	713.502i	−0.0168303	+	0.0291510i
$844$	−21408.1			−0.873100
$845$		0			0
$846$	47847.0			1.94446
$847$	−13856.7	+	24000.5i	−0.562128	+	0.973635i
$848$	2784.48	−	4822.86i	0.112759	−	0.195304i
$849$	732.687	+	1269.05i	0.0296181	+	0.0513000i
$850$	1885.94			0.0761025
$851$	13118.0	+	22721.0i	0.528412	+	0.915236i
$852$	−15.2546	−	26.4217i	−0.000613395	−	0.00106243i
$853$	15866.0			0.636861			0.318430	−	0.947946i	$-0.396844\pi$
$853$	15866.0			0.636861			0.318430	+	0.947946i	$0.396844\pi$
$854$	−29448.4	−	51006.1i	−1.17998	−	2.04379i
$855$	−6915.02	+	11977.2i	−0.276595	+	0.479076i
$856$	4052.93	−	7019.88i	0.161830	−	0.280297i
$857$	23623.3			0.941607			0.470804	−	0.882238i	$-0.343964\pi$
$857$	23623.3			0.941607			0.470804	+	0.882238i	$0.343964\pi$
$858$		0			0
$859$	33403.1			1.32677			0.663387	−	0.748277i	$-0.269118\pi$
$859$	33403.1			1.32677			0.663387	+	0.748277i	$0.269118\pi$
$860$	−9756.08	+	16898.0i	−0.386837	+	0.670021i
$861$	353.009	−	611.429i	0.0139727	−	0.0242014i
$862$	26250.6	+	45467.3i	1.03724	+	1.79655i
$863$	45490.5			1.79434			0.897169	−	0.441687i	$-0.145620\pi$
$863$	45490.5			1.79434			0.897169	+	0.441687i	$0.145620\pi$
$864$	1798.42	+	3114.96i	0.0708144	+	0.122654i
$865$	−11827.4	−	20485.7i	−0.464907	−	0.805243i
$866$	−58240.8			−2.28534
$867$	1140.63	+	1975.62i	0.0446802	+	0.0773884i
$868$	−18694.5	+	32379.9i	−0.731029	+	1.26618i
$869$	−4035.85	+	6990.29i	−0.157545	+	0.272876i
$870$	−331.208			−0.0129069
$871$		0			0
$872$	−7557.03			−0.293479
$873$	9277.20	−	16068.6i	0.359663	−	0.622954i
$874$	−6405.78	+	11095.1i	−0.247916	+	0.429404i
$875$	21316.2	+	36920.8i	0.823565	+	1.42646i
$876$	602.162			0.0232251
$877$	−9785.05	−	16948.2i	−0.376759	−	0.652565i	0.613830	−	0.789438i	$-0.289628\pi$
$877$	−9785.05	−	16948.2i	−0.376759	−	0.652565i	−0.990589	+	0.136873i	$0.956295\pi$
$878$	5372.05	+	9304.67i	0.206490	+	0.357651i
$879$	−813.015			−0.0311972
$880$	−8658.07	−	14996.2i	−0.331663	−	0.574458i
$881$	1508.47	−	2612.75i	0.0576864	−	0.0999158i	−0.835740	−	0.549125i	$-0.814961\pi$
$881$	1508.47	−	2612.75i	0.0576864	−	0.0999158i	0.893426	+	0.449209i	$0.148294\pi$
$882$	32097.4	−	55594.3i	1.22537	−	2.12240i
$883$	17163.8			0.654141			0.327071	−	0.945000i	$-0.393939\pi$
$883$	17163.8			0.654141			0.327071	+	0.945000i	$0.393939\pi$
$884$		0			0
$885$	−172.900			−0.00656720
$886$	14455.2	−	25037.1i	0.548117	−	0.949367i
$887$	−14232.3	+	24651.1i	−0.538754	+	0.933149i	0.460218	+	0.887806i	$0.347771\pi$
$887$	−14232.3	+	24651.1i	−0.538754	+	0.933149i	−0.998971	+	0.0453430i	$0.985562\pi$
$888$	246.343	+	426.679i	0.00930940	+	0.0161243i
$889$	−16352.0			−0.616903
$890$	−11897.0	−	20606.2i	−0.448076	−	0.776090i
$891$	−7569.42	−	13110.6i	−0.284607	−	0.492954i
$892$	−503.418			−0.0188965
$893$	10469.8	+	18134.1i	0.392337	+	0.679548i
$894$	−354.743	+	614.434i	−0.0132711	+	0.0229863i
$895$	−3144.88	+	5447.09i	−0.117454	+	0.203437i
$896$	−19520.9			−0.727845
$897$		0			0
$898$	−21314.6			−0.792070
$899$	−2443.40	+	4232.09i	−0.0906473	+	0.157006i
$900$	387.939	−	671.929i	0.0143681	−	0.0248863i
$901$	−4381.40	−	7588.80i	−0.162004	−	0.280599i
$902$	−6539.70			−0.241406
$903$	1110.02	+	1922.61i	0.0409072	+	0.0708533i
$904$	2973.68	+	5150.56i	0.109406	+	0.189497i
$905$	37583.4			1.38046
$906$	−102.151	−	176.931i	−0.00374586	−	0.00648802i
$907$	13305.0	−	23045.0i	0.487085	−	0.843657i	−0.512804	−	0.858505i	$-0.671393\pi$
$907$	13305.0	−	23045.0i	0.487085	−	0.843657i	0.999890	+	0.0148489i	$0.00472673\pi$
$908$	14486.7	−	25091.7i	0.529469	−	0.917068i
$909$	−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	$0.906714\pi$
$912$	−458.414	+	793.996i	−0.0166443	+	0.0288288i
$913$	6952.16	−	12041.5i	0.252008	−	0.436490i
$914$	−8297.04	−	14370.9i	−0.300265	−	0.520073i
$915$	−1569.71			−0.0567137
$916$	−2271.88	−	3935.02i	−0.0819489	−	0.141940i
$917$	−12953.3	−	22435.9i	−0.466475	−	0.807958i
$918$	6602.41			0.237377
$919$	−23461.8	−	40637.0i	−0.842146	−	1.45864i	−0.888077	−	0.459695i	$-0.847959\pi$
$919$	−23461.8	−	40637.0i	−0.842146	−	1.45864i	0.0459311	−	0.998945i	$-0.485375\pi$
$920$	−2092.03	+	3623.50i	−0.0749697	+	0.129851i
$921$	−697.921	+	1208.83i	−0.0249699	+	0.0432491i
$922$	43300.6			1.54667
$923$		0			0
$924$	1217.49			0.0433468
$925$	762.648	−	1320.95i	0.0271089	−	0.0469540i
$926$	16454.4	−	28499.8i	0.583935	−	1.01141i
$927$	−4516.46	−	7822.74i	−0.160022	−	0.277166i
$928$	6502.00			0.229999
$929$	20581.9	+	35648.9i	0.726878	+	1.25899i	0.958196	+	0.286111i	$0.0923626\pi$
$929$	20581.9	+	35648.9i	0.726878	+	1.25899i	−0.231319	+	0.972878i	$0.574304\pi$
$930$	1092.94	+	1893.03i	0.0385365	+	0.0667473i
$931$	28093.9			0.988980
$932$	−311.351	−	539.276i	−0.0109427	−	0.0189534i
$933$	−1094.45	+	1895.64i	−0.0384037	+	0.0665172i
$934$	−33633.3	+	58254.5i	−1.17828	+	2.04084i
$935$	−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	$0.633627\pi$
$938$	36445.5	−	63125.5i	1.26864	−	2.19736i
$939$	−1049.43	+	1817.67i	−0.0364717	+	0.0631709i
$940$	−17662.6	−	30592.6i	−0.612863	−	1.06151i
$941$	34506.2			1.19540			0.597700	−	0.801720i	$-0.296082\pi$
$941$	34506.2			1.19540			0.597700	+	0.801720i	$0.296082\pi$
$942$	−1516.76	−	2627.11i	−0.0524615	−	0.0908659i
$943$	3010.82	+	5214.90i	0.103972	+	0.180085i
$944$	3959.61			0.136519
$945$	−2658.44	−	4604.55i	−0.0915121	−	0.158504i
$946$	10281.9	−	17808.8i	0.353376	−	0.612066i
$947$	−241.719	+	418.670i	−0.00829443	+	0.0143664i	−0.870143	−	0.492800i	$-0.835974\pi$
$947$	−241.719	+	418.670i	−0.00829443	+	0.0143664i	0.861848	+	0.507166i	$0.169307\pi$
$948$	−720.975			−0.0247006
$949$		0			0
$950$	744.835			0.0254375
$951$	−67.7302	+	117.312i	−0.00230947	+	0.00400011i
$952$	−8838.81	+	15309.3i	−0.300911	+	0.521194i
$953$	5981.33	+	10360.0i	0.203310	+	0.352143i	0.949593	−	0.313486i	$-0.101497\pi$
$953$	5981.33	+	10360.0i	0.203310	+	0.352143i	−0.746283	+	0.665629i	$0.768164\pi$
$954$	−7907.94			−0.268374
$955$	−18865.3	−	32675.7i	−0.639232	−	1.10718i
$956$	−6979.16	−	12088.3i	−0.236111	−	0.408956i
$957$	159.127			0.00537499
$958$	12076.7	+	20917.4i	0.407286	+	0.705439i
$959$	7249.35	−	12556.2i	0.244102	−	0.422797i
$960$	531.125	−	919.936i	0.0178562	−	0.0309279i
$961$	2460.54			0.0825934
$962$		0			0
$963$	−43863.2			−1.46778
$964$	−21921.3	+	37968.8i	−0.732405	+	1.26856i
$965$	22185.8	−	38427.0i	0.740091	−	1.28188i
$966$	−1229.55	−	2129.65i	−0.0409526	−	0.0709320i
$967$	−7695.43			−0.255913			−0.127957	−	0.991780i	$-0.540842\pi$
$967$	−7695.43			−0.255913			−0.127957	+	0.991780i	$0.540842\pi$
$968$	−2219.40	−	3844.11i	−0.0736923	−	0.127639i
$969$	721.318	+	1249.36i	0.0239134	+	0.0414192i
$970$	−30049.2			−0.994661
$971$	22088.9	+	38259.2i	0.730039	+	1.26446i	0.956866	+	0.290529i	$0.0938314\pi$
$971$	22088.9	+	38259.2i	0.730039	+	1.26446i	−0.226827	+	0.973935i	$0.572835\pi$
$972$	2038.16	−	3530.20i	0.0672573	−	0.116493i
$973$	−11074.9	+	19182.4i	−0.364898	+	0.632023i
$974$	−13695.4			−0.450542
$975$		0			0
$976$	35948.2			1.17897
$977$	1706.30	−	2955.40i	0.0558746	−	0.0967776i	−0.836735	−	0.547608i	$-0.815539\pi$
$977$	1706.30	−	2955.40i	0.0558746	−	0.0967776i	0.892610	+	0.450830i	$0.148872\pi$
$978$	−1908.31	+	3305.29i	−0.0623937	+	0.108069i
$979$	5715.84	+	9900.13i	0.186598	+	0.323197i
$980$	−47394.8			−1.54487
$981$	20446.6	+	35414.6i	0.665454	+	1.15260i
$982$	25662.0	+	44447.9i	0.833919	+	1.44439i
$983$	−6313.78			−0.204861			−0.102431	−	0.994740i	$-0.532662\pi$
$983$	−6313.78			−0.204861			−0.102431	+	0.994740i	$0.532662\pi$
$984$	56.5405	+	97.9310i	0.00183175	+	0.00317269i
$985$	20655.4	−	35776.1i	0.668157	−	1.15728i
$986$	5967.57	−	10336.1i	0.192745	−	0.333843i
$987$	−4019.22			−0.129618
$988$		0			0
$989$	−18934.8			−0.608789
$990$	−12294.5	+	21294.7i	−0.394692	+	0.683627i
$991$	−6088.75	+	10546.0i	−0.195172	+	0.338048i	−0.946957	−	0.321361i	$-0.895860\pi$
$991$	−6088.75	+	10546.0i	−0.195172	+	0.338048i	0.751785	+	0.659408i	$0.229193\pi$
$992$	−21455.7	−	37162.4i	−0.686714	−	1.18942i
$993$	2295.52			0.0733598
$994$	−971.034	−	1681.88i	−0.0309853	−	0.0536680i
$995$	16813.3	+	29121.6i	0.535697	+	0.927855i
$996$	1241.95			0.0395108
$997$	−8753.11	−	15160.8i	−0.278048	−	0.481593i	0.692852	−	0.721080i	$-0.256354\pi$
$997$	−8753.11	−	15160.8i	−0.278048	−	0.481593i	−0.970900	+	0.239487i	$0.923021\pi$
$998$	−36863.2	+	63849.0i	−1.16922	+	2.02515i
$999$	2669.93	−	4624.45i	0.0845574	−	0.146458i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.8	✓	9	13.9	even	3
169.4.a.l.1.2	yes	9	13.4	even	6
169.4.b.g.168.4		18	13.6	odd	12
169.4.b.g.168.15		18	13.7	odd	12
169.4.c.k.22.8		18	13.12	even	2
169.4.c.k.146.8		18	13.10	even	6
169.4.c.l.22.2		18	1.1	even	1	trivial
169.4.c.l.146.2		18	13.3	even	3	inner
169.4.e.h.23.4		36	13.2	odd	12
169.4.e.h.23.15		36	13.11	odd	12
169.4.e.h.147.4		36	13.8	odd	4
169.4.e.h.147.15		36	13.5	odd	4
1521.4.a.bg.1.8		9	39.17	odd	6
1521.4.a.bh.1.2		9	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91719 + 3.32067i) q^{2} +(0.139581 - 0.241762i) q^{3} +(-3.35124 - 5.80452i) q^{4} -11.3710 q^{5} +(0.535209 + 0.927008i) q^{6} +(15.5311 + 26.9007i) q^{7} -4.97517 q^{8} +(13.4610 + 23.3152i) q^{9} +O(q^{10})\)	\(q+(-1.91719 + 3.32067i) q^{2} +(0.139581 - 0.241762i) q^{3} +(-3.35124 - 5.80452i) q^{4} -11.3710 q^{5} +(0.535209 + 0.927008i) q^{6} +(15.5311 + 26.9007i) q^{7} -4.97517 q^{8} +(13.4610 + 23.3152i) q^{9} +(21.8004 - 37.7594i) q^{10} +(-10.4739 + 18.1413i) q^{11} -1.87108 q^{12} -119.105 q^{14} +(-1.58718 + 2.74908i) q^{15} +(36.3483 - 62.9571i) q^{16} +(-57.1943 - 99.0635i) q^{17} -103.229 q^{18} +(-22.5884 - 39.1243i) q^{19} +(38.1070 + 66.0033i) q^{20} +8.67143 q^{21} +(-40.1609 - 69.5608i) q^{22} +(-36.9795 + 64.0504i) q^{23} +(-0.694441 + 1.20281i) q^{24} +4.29980 q^{25} +15.0530 q^{27} +(104.097 - 180.302i) q^{28} +(13.6056 - 23.5657i) q^{29} +(-6.08586 - 10.5410i) q^{30} -179.587 q^{31} +(119.473 + 206.933i) q^{32} +(2.92392 + 5.06438i) q^{33} +438.610 q^{34} +(-176.605 - 305.888i) q^{35} +(90.2224 - 156.270i) q^{36} +(177.368 - 307.211i) q^{37} +173.225 q^{38} +56.5727 q^{40} +(40.7094 - 70.5107i) q^{41} +(-16.6248 + 28.7950i) q^{42} +(128.009 + 221.718i) q^{43} +140.402 q^{44} +(-153.066 - 265.117i) q^{45} +(-141.794 - 245.594i) q^{46} -463.501 q^{47} +(-10.1471 - 17.5753i) q^{48} +(-310.933 + 538.551i) q^{49} +(-8.24355 + 14.2782i) q^{50} -31.9331 q^{51} +76.6055 q^{53} +(-28.8596 + 49.9862i) q^{54} +(119.099 - 206.285i) q^{55} +(-77.2700 - 133.836i) q^{56} -12.6117 q^{57} +(52.1692 + 90.3598i) q^{58} +(27.2338 + 47.1703i) q^{59} +21.2761 q^{60} +(247.248 + 428.246i) q^{61} +(344.303 - 596.350i) q^{62} +(-418.130 + 724.223i) q^{63} -334.634 q^{64} -22.4229 q^{66} +(-305.996 + 530.000i) q^{67} +(-383.344 + 663.972i) q^{68} +(10.3233 + 17.8805i) q^{69} +1354.34 q^{70} +(8.15278 + 14.1210i) q^{71} +(-66.9709 - 115.997i) q^{72} -321.825 q^{73} +(680.097 + 1177.96i) q^{74} +(0.600173 - 1.03953i) q^{75} +(-151.399 + 262.230i) q^{76} -650.686 q^{77} +385.324 q^{79} +(-413.317 + 715.885i) q^{80} +(-361.347 + 625.871i) q^{81} +(156.095 + 270.365i) q^{82} -663.760 q^{83} +(-29.0601 - 50.3335i) q^{84} +(650.357 + 1126.45i) q^{85} -981.671 q^{86} +(-3.79819 - 6.57866i) q^{87} +(52.1094 - 90.2561i) q^{88} +(272.861 - 472.610i) q^{89} +1173.82 q^{90} +495.709 q^{92} +(-25.0670 + 43.4174i) q^{93} +(888.620 - 1539.13i) q^{94} +(256.853 + 444.883i) q^{95} +66.7046 q^{96} +(-344.595 - 596.855i) q^{97} +(-1192.23 - 2065.01i) q^{98} -563.958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

Introduction

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