LMFDB - Embedded newform 114.4.i.c.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
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} - 6 x^{17} - 1488 x^{16} + 4798 x^{15} + 939930 x^{14} - 421443 x^{13} - 319752461 x^{12} + \cdots + 20\!\cdots\!49 $ x^18 - 6x^17 - 1488x^16 + 4798x^15 + 939930x^14 - 421443x^13 - 319752461x^12 - 722235969x^11 + 60651236964x^10 + 300466233870x^9 - 5754248160525x^8 - 46793226683178x^7 + 141508710385350x^6 + 2567891527205481x^5 + 9930325439050983x^4 + 15397443154057401x^3 + 9475016573038698x^2 + 12035110299066666*x + 20915625186935649
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.3
Root			$15.9590 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.4.i.c.85.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(16.0427 - 5.83908i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(4.07744 + 7.06234i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(16.0427 - 5.83908i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(4.07744 + 7.06234i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(5.92916 + 33.6259i) q^{10} +(18.6640 - 32.3270i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(40.8615 - 34.2869i) q^{13} +(-15.3262 + 5.57827i) q^{14} +(48.1282 + 17.5172i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-23.5973 + 133.827i) q^{17} -18.0000 q^{18} +(-17.6392 + 80.9188i) q^{19} -68.2893 q^{20} +(-4.24824 + 24.0930i) q^{21} +(57.1898 + 47.9879i) q^{22} +(-101.305 - 36.8721i) q^{23} +(22.5526 - 8.20848i) q^{24} +(127.519 - 107.001i) q^{25} +(53.3409 + 92.3891i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-5.66432 - 32.1240i) q^{28} +(30.6091 + 173.593i) q^{29} +(-51.2170 + 88.7104i) q^{30} +(-154.478 - 267.563i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(105.230 - 38.3008i) q^{33} +(-255.392 - 92.9551i) q^{34} +(106.651 + 89.4908i) q^{35} +(6.25133 - 35.4531i) q^{36} +212.032 q^{37} +(-153.253 - 62.8453i) q^{38} +160.023 q^{39} +(23.7166 - 134.504i) q^{40} +(-64.2484 - 53.9108i) q^{41} +(-45.9785 - 16.7348i) q^{42} +(137.695 - 50.1170i) q^{43} +(-114.380 + 95.9758i) q^{44} +(76.8255 + 133.066i) q^{45} +(107.807 - 186.727i) q^{46} +(-61.9839 - 351.528i) q^{47} +(8.33511 + 47.2708i) q^{48} +(138.249 - 239.454i) q^{49} +(166.465 + 288.325i) q^{50} +(-312.296 + 262.048i) q^{51} +(-200.496 + 72.9746i) q^{52} +(-369.519 - 134.494i) q^{53} +(-41.3664 - 34.7105i) q^{54} +(110.662 - 627.594i) q^{55} +65.2391 q^{56} +(-196.578 + 151.947i) q^{57} -352.542 q^{58} +(-14.6700 + 83.1977i) q^{59} +(-156.938 - 131.687i) q^{60} +(-421.231 - 153.315i) q^{61} +(580.646 - 211.338i) q^{62} +(-56.2230 + 47.1767i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(455.327 - 788.649i) q^{65} +(38.8916 + 220.565i) q^{66} +(24.9156 + 141.303i) q^{67} +(271.783 - 470.741i) q^{68} +(-161.710 - 280.091i) q^{69} +(-213.302 + 178.982i) q^{70} +(-814.367 + 296.405i) q^{71} +(67.6579 + 24.6255i) q^{72} +(274.705 + 230.505i) q^{73} +(-73.6380 + 417.622i) q^{74} +499.394 q^{75} +(177.005 - 280.023i) q^{76} +304.405 q^{77} +(-55.5753 + 315.183i) q^{78} +(-538.808 - 452.114i) q^{79} +(256.684 + 93.4253i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(128.497 - 107.822i) q^{82} +(390.454 + 676.286i) q^{83} +(48.9293 - 84.7481i) q^{84} +(402.861 + 2284.74i) q^{85} +(50.8902 + 288.612i) q^{86} +(-264.406 + 457.965i) q^{87} +(-149.312 - 258.616i) q^{88} +(-1020.83 + 856.577i) q^{89} +(-288.769 + 105.103i) q^{90} +(408.756 + 148.775i) q^{91} +(330.340 + 277.188i) q^{92} +(160.949 - 912.785i) q^{93} +713.903 q^{94} +(189.510 + 1401.16i) q^{95} -96.0000 q^{96} +(159.090 - 902.246i) q^{97} +(423.619 + 355.459i) q^{98} +(315.691 + 114.902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) $ 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$3$	2.29813	+	1.92836i	0.442276	+	0.371114i
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	16.0427	−	5.83908i	1.43491	−	0.522263i	0.496573	−	0.867995i	$-0.334591\pi$
$5$	16.0427	−	5.83908i	1.43491	−	0.522263i	0.938334	+	0.345731i	$0.112369\pi$
$6$	−4.59627	+	3.85673i	−0.312736	+	0.262417i
$7$	4.07744	+	7.06234i	0.220161	+	0.381330i	0.954857	−	0.297067i	$-0.0960083\pi$
$7$	4.07744	+	7.06234i	0.220161	+	0.381330i	−0.734696	+	0.678397i	$0.762675\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$	1.56283	+	8.86327i	0.0578827	+	0.328269i
$10$	5.92916	+	33.6259i	0.187496	+	1.06335i
$11$	18.6640	−	32.3270i	0.511582	−	0.886086i	−0.488328	−	0.872660i	$-0.662393\pi$
$11$	18.6640	−	32.3270i	0.511582	−	0.886086i	0.999910	−	0.0134260i	$-0.00427376\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	40.8615	−	34.2869i	0.871764	−	0.731497i	−0.0927046	−	0.995694i	$-0.529551\pi$
$13$	40.8615	−	34.2869i	0.871764	−	0.731497i	0.964469	+	0.264197i	$0.0851068\pi$
$14$	−15.3262	+	5.57827i	−0.292578	+	0.106490i
$15$	48.1282	+	17.5172i	0.828444	+	0.301529i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	−23.5973	+	133.827i	−0.336658	+	1.90928i	0.0735556	+	0.997291i	$0.476565\pi$
$17$	−23.5973	+	133.827i	−0.336658	+	1.90928i	−0.410213	+	0.911990i	$0.634546\pi$
$18$	−18.0000			−0.235702
$19$	−17.6392	+	80.9188i	−0.212985	+	0.977055i
$19$	−17.6392	+	80.9188i	−0.212985	+	0.977055i
$20$	−68.2893			−0.763498
$21$	−4.24824	+	24.0930i	−0.0441449	+	0.250358i
$22$	57.1898	+	47.9879i	0.554223	+	0.465048i
$23$	−101.305	−	36.8721i	−0.918419	−	0.334277i	−0.160809	−	0.986985i	$-0.551410\pi$
$23$	−101.305	−	36.8721i	−0.918419	−	0.334277i	−0.757609	+	0.652708i	$0.773633\pi$
$24$	22.5526	−	8.20848i	0.191814	−	0.0698146i
$25$	127.519	−	107.001i	1.02015	−	0.856011i
$26$	53.3409	+	92.3891i	0.402346	+	0.696884i
$27$	−13.5000	+	23.3827i	−0.0962250	+	0.166667i
$28$	−5.66432	−	32.1240i	−0.0382306	−	0.216816i
$29$	30.6091	+	173.593i	0.195999	+	1.11157i	0.910989	+	0.412431i	$0.135320\pi$
$29$	30.6091	+	173.593i	0.195999	+	1.11157i	−0.714990	+	0.699135i	$0.753569\pi$
$30$	−51.2170	+	88.7104i	−0.311697	+	0.539875i
$31$	−154.478	−	267.563i	−0.895000	−	1.55019i	−0.833804	−	0.552060i	$-0.813842\pi$
$31$	−154.478	−	267.563i	−0.895000	−	1.55019i	−0.0611962	−	0.998126i	$-0.519492\pi$
$32$	−24.5134	+	20.5692i	−0.135419	+	0.113630i
$33$	105.230	−	38.3008i	0.555099	−	0.202040i
$34$	−255.392	−	92.9551i	−1.28822	−	0.468873i
$35$	106.651	+	89.4908i	0.515066	+	0.432191i
$36$	6.25133	−	35.4531i	0.0289414	−	0.164135i
$37$	212.032			0.942105			0.471053	−	0.882105i	$-0.343874\pi$
$37$	212.032			0.942105			0.471053	+	0.882105i	$0.343874\pi$
$38$	−153.253	−	62.8453i	−0.654234	−	0.268286i
$39$	160.023			0.657029
$40$	23.7166	−	134.504i	0.0937482	−	0.531673i
$41$	−64.2484	−	53.9108i	−0.244730	−	0.205353i	0.512169	−	0.858885i	$-0.328842\pi$
$41$	−64.2484	−	53.9108i	−0.244730	−	0.205353i	−0.756899	+	0.653532i	$0.773287\pi$
$42$	−45.9785	−	16.7348i	−0.168920	−	0.0614818i
$43$	137.695	−	50.1170i	0.488334	−	0.177739i	−0.0861058	−	0.996286i	$-0.527442\pi$
$43$	137.695	−	50.1170i	0.488334	−	0.177739i	0.574439	+	0.818547i	$0.305220\pi$
$44$	−114.380	+	95.9758i	−0.391895	+	0.328839i
$45$	76.8255	+	133.066i	0.254499	+	0.440806i
$46$	107.807	−	186.727i	0.345549	−	0.598509i
$47$	−61.9839	−	351.528i	−0.192368	−	1.09097i	−0.916118	−	0.400910i	$-0.868694\pi$
$47$	−61.9839	−	351.528i	−0.192368	−	1.09097i	0.723750	−	0.690062i	$-0.242417\pi$
$48$	8.33511	+	47.2708i	0.0250640	+	0.142145i
$49$	138.249	−	239.454i	0.403058	−	0.698117i
$50$	166.465	+	288.325i	0.470833	+	0.815507i
$51$	−312.296	+	262.048i	−0.857456	+	0.719491i
$52$	−200.496	+	72.9746i	−0.534689	+	0.194611i
$53$	−369.519	−	134.494i	−0.957686	−	0.348569i	−0.184560	−	0.982821i	$-0.559086\pi$
$53$	−369.519	−	134.494i	−0.957686	−	0.348569i	−0.773126	+	0.634252i	$0.781308\pi$
$54$	−41.3664	−	34.7105i	−0.104245	−	0.0874723i
$55$	110.662	−	627.594i	0.271302	−	1.53863i
$56$	65.2391			0.155677
$57$	−196.578	+	151.947i	−0.456797	+	0.353086i
$58$	−352.542			−0.798121
$59$	−14.6700	+	83.1977i	−0.0323707	+	0.183583i	−0.996706	−	0.0811005i	$-0.974157\pi$
$59$	−14.6700	+	83.1977i	−0.0323707	+	0.183583i	0.964335	+	0.264684i	$0.0852676\pi$
$60$	−156.938	−	131.687i	−0.337677	−	0.283344i
$61$	−421.231	−	153.315i	−0.884148	−	0.321804i	−0.140266	−	0.990114i	$-0.544796\pi$
$61$	−421.231	−	153.315i	−0.884148	−	0.321804i	−0.743883	+	0.668310i	$0.767018\pi$
$62$	580.646	−	211.338i	1.18939	−	0.432902i
$63$	−56.2230	+	47.1767i	−0.112436	+	0.0943446i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	455.327	−	788.649i	0.868866	−	1.50492i
$66$	38.8916	+	220.565i	0.0725337	+	0.411359i
$67$	24.9156	+	141.303i	0.0454317	+	0.257656i	0.999061	−	0.0433281i	$-0.0137961\pi$
$67$	24.9156	+	141.303i	0.0454317	+	0.257656i	−0.953629	+	0.300984i	$0.902685\pi$
$68$	271.783	−	470.741i	0.484684	−	0.839497i
$69$	−161.710	−	280.091i	−0.282140	−	0.488680i
$70$	−213.302	+	178.982i	−0.364206	+	0.305606i
$71$	−814.367	+	296.405i	−1.36123	+	0.495448i	−0.916435	−	0.400183i	$-0.868947\pi$
$71$	−814.367	+	296.405i	−1.36123	+	0.495448i	−0.444798	+	0.895631i	$0.646724\pi$
$72$	67.6579	+	24.6255i	0.110744	+	0.0403075i
$73$	274.705	+	230.505i	0.440435	+	0.369569i	0.835872	−	0.548924i	$-0.184962\pi$
$73$	274.705	+	230.505i	0.440435	+	0.369569i	−0.395437	+	0.918493i	$0.629407\pi$
$74$	−73.6380	+	417.622i	−0.115679	+	0.656048i
$75$	499.394			0.768867
$76$	177.005	−	280.023i	0.267157	−	0.422643i
$77$	304.405			0.450522
$78$	−55.5753	+	315.183i	−0.0806751	+	0.457531i
$79$	−538.808	−	452.114i	−0.767350	−	0.643883i	0.172679	−	0.984978i	$-0.444758\pi$
$79$	−538.808	−	452.114i	−0.767350	−	0.643883i	−0.940029	+	0.341095i	$0.889202\pi$
$80$	256.684	+	93.4253i	0.358727	+	0.130566i
$81$	−76.1151	+	27.7036i	−0.104410	+	0.0380022i
$82$	128.497	−	107.822i	0.173050	−	0.145206i
$83$	390.454	+	676.286i	0.516360	+	0.894362i	0.999820	+	0.0189950i	$0.00604665\pi$
$83$	390.454	+	676.286i	0.516360	+	0.894362i	−0.483460	+	0.875367i	$0.660620\pi$
$84$	48.9293	−	84.7481i	0.0635551	−	0.110081i
$85$	402.861	+	2284.74i	0.514075	+	2.91546i
$86$	50.8902	+	288.612i	0.0638096	+	0.361882i
$87$	−264.406	+	457.965i	−0.325831	+	0.564357i
$88$	−149.312	−	258.616i	−0.180872	−	0.313279i
$89$	−1020.83	+	856.577i	−1.21582	+	1.02019i	−0.216783	+	0.976220i	$0.569556\pi$
$89$	−1020.83	+	856.577i	−1.21582	+	1.02019i	−0.999033	+	0.0439703i	$0.985999\pi$
$90$	−288.769	+	105.103i	−0.338211	+	0.123099i
$91$	408.756	+	148.775i	0.470871	+	0.171383i
$92$	330.340	+	277.188i	0.374351	+	0.314118i
$93$	160.949	−	912.785i	0.179458	−	1.01776i
$94$	713.903			0.783334
$95$	189.510	+	1401.16i	0.204666	+	1.51322i
$96$	−96.0000			−0.102062
$97$	159.090	−	902.246i	0.166528	−	0.944425i	−0.780948	−	0.624596i	$-0.785264\pi$
$97$	159.090	−	902.246i	0.166528	−	0.944425i	0.947475	−	0.319829i	$-0.103625\pi$
$98$	423.619	+	355.459i	0.436653	+	0.366395i
$99$	315.691	+	114.902i	0.320487	+	0.116648i
$100$	−625.702	+	227.737i	−0.625702	+	0.227737i
$101$	584.060	−	490.084i	0.575407	−	0.482824i	−0.308028	−	0.951377i	$-0.599669\pi$
$101$	584.060	−	490.084i	0.575407	−	0.482824i	0.883435	+	0.468553i	$0.155225\pi$
$102$	−407.674	−	706.112i	−0.395743	−	0.685446i
$103$	−133.195	+	230.701i	−0.127419	+	0.220696i	−0.922676	−	0.385577i	$-0.874003\pi$
$103$	−133.195	+	230.701i	−0.127419	+	0.220696i	0.795257	+	0.606272i	$0.207336\pi$
$104$	−74.1004	−	420.244i	−0.0698667	−	0.396234i
$105$	72.5274	+	411.323i	0.0674091	+	0.382296i
$106$	393.234	−	681.102i	0.360323	−	0.624098i
$107$	−698.901	−	1210.53i	−0.631452	−	1.09371i	−0.987255	−	0.159146i	$-0.949126\pi$
$107$	−698.901	−	1210.53i	−0.631452	−	1.09371i	0.355803	−	0.934561i	$-0.384207\pi$
$108$	82.7328	−	69.4211i	0.0737127	−	0.0618523i
$109$	1046.57	−	380.920i	0.919661	−	0.334729i	0.161557	−	0.986863i	$-0.448348\pi$
$109$	1046.57	−	380.920i	0.919661	−	0.334729i	0.758104	+	0.652134i	$0.226126\pi$
$110$	1197.69	+	435.922i	1.03814	+	0.377850i
$111$	487.278	+	408.875i	0.416670	+	0.349628i
$112$	−22.6573	+	128.496i	−0.0191153	+	0.108408i
$113$	−1341.00			−1.11637			−0.558187	−	0.829715i	$-0.688503\pi$
$113$	−1341.00			−1.11637			−0.558187	+	0.829715i	$0.688503\pi$
$114$	−231.007	−	439.954i	−0.189788	−	0.361452i
$115$	−1840.52			−1.49243
$116$	122.436	−	694.372i	0.0979995	−	0.555783i
$117$	367.753	+	308.582i	0.290588	+	0.243832i
$118$	−158.773	−	57.7885i	−0.123866	−	0.0450836i
$119$	−1041.35	+	379.019i	−0.802186	+	0.291972i
$120$	313.876	−	263.373i	0.238774	−	0.200355i
$121$	−31.1889	−	54.0208i	−0.0234327	−	0.0405866i
$122$	448.264	−	776.416i	0.332655	−	0.576176i
$123$	−43.6918	−	247.789i	−0.0320289	−	0.181645i
$124$	214.598	+	1217.05i	0.155415	+	0.881403i
$125$	353.949	−	613.057i	0.253265	−	0.438668i
$126$	−73.3940	−	127.122i	−0.0518925	−	0.0898804i
$127$	−160.476	+	134.655i	−0.112125	+	0.0940843i	−0.697127	−	0.716948i	$-0.745538\pi$
$127$	−160.476	+	134.655i	−0.112125	+	0.0940843i	0.585001	+	0.811032i	$0.301094\pi$
$128$	120.281	−	43.7786i	0.0830579	−	0.0302306i
$129$	413.086	+	150.351i	0.281940	+	0.102618i
$130$	1395.20	+	1170.71i	0.941287	+	0.789833i
$131$	−13.5273	+	76.7173i	−0.00902205	+	0.0511666i	−0.988986	−	0.148006i	$-0.952714\pi$
$131$	−13.5273	+	76.7173i	−0.00902205	+	0.0511666i	0.979964	+	0.199173i	$0.0638255\pi$
$132$	−447.936			−0.295362
$133$	−643.399	+	205.368i	−0.419472	+	0.133892i
$134$	−286.966			−0.185001
$135$	−80.0437	+	453.950i	−0.0510301	+	0.289406i
$136$	832.790	+	698.794i	0.525082	+	0.440596i
$137$	2463.42	+	896.611i	1.53623	+	0.559143i	0.965138	−	0.261741i	$-0.0842965\pi$
$137$	2463.42	+	896.611i	1.53623	+	0.559143i	0.571095	+	0.820884i	$0.306519\pi$
$138$	607.832	−	221.233i	0.374943	−	0.136468i
$139$	−821.446	+	689.275i	−0.501253	+	0.420601i	−0.858039	−	0.513585i	$-0.828317\pi$
$139$	−821.446	+	689.275i	−0.501253	+	0.420601i	0.356786	+	0.934186i	$0.383873\pi$
$140$	−278.446	−	482.282i	−0.168093	−	0.291145i
$141$	535.427	−	927.387i	0.319795	−	0.553901i
$142$	−300.978	−	1706.93i	−0.177870	−	1.00875i
$143$	−345.752	−	1960.86i	−0.202190	−	1.14668i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	1504.68	+	2606.18i	0.861770	+	1.49263i
$146$	−549.410	+	461.010i	−0.311435	+	0.261325i
$147$	779.469	−	283.703i	0.437344	−	0.159180i
$148$	−796.981	−	290.077i	−0.442645	−	0.161109i
$149$	545.287	+	457.550i	0.299810	+	0.251570i	0.780265	−	0.625449i	$-0.215084\pi$
$149$	545.287	+	457.550i	0.299810	+	0.251570i	−0.480455	+	0.877019i	$0.659529\pi$
$150$	−173.438	+	983.614i	−0.0944075	+	0.535411i
$151$	−1612.07			−0.868795			−0.434398	−	0.900721i	$-0.643039\pi$
$151$	−1612.07			−0.868795			−0.434398	+	0.900721i	$0.643039\pi$
$152$	490.065	+	445.884i	0.261510	+	0.237934i
$153$	−1223.02			−0.646245
$154$	−105.719	+	599.562i	−0.0553186	+	0.313728i
$155$	−4040.57	−	3390.44i	−2.09385	−	1.75695i
$156$	−601.488	−	218.924i	−0.308703	−	0.112359i
$157$	2223.73	−	809.371i	1.13040	−	0.411432i	0.291963	−	0.956430i	$-0.405692\pi$
$157$	2223.73	−	809.371i	1.13040	−	0.411432i	0.838438	+	0.544998i	$0.183469\pi$
$158$	1077.62	−	904.228i	0.542599	−	0.455294i
$159$	−589.851	−	1021.65i	−0.294203	−	0.509574i
$160$	−273.157	+	473.122i	−0.134969	+	0.233773i
$161$	−152.663	−	865.797i	−0.0747302	−	0.423816i
$162$	−28.1310	−	159.539i	−0.0136431	−	0.0773738i
$163$	−498.291	+	863.066i	−0.239443	+	0.414727i	−0.960555	−	0.278092i	$-0.910298\pi$
$163$	−498.291	+	863.066i	−0.239443	+	0.414727i	0.721112	+	0.692819i	$0.243631\pi$
$164$	167.741	+	290.535i	0.0798680	+	0.138335i
$165$	1464.54	−	1228.90i	0.690998	−	0.579816i
$166$	−1467.63	+	534.172i	−0.686204	+	0.249758i
$167$	−2158.56	−	785.651i	−1.00020	−	0.364045i	−0.210541	−	0.977585i	$-0.567523\pi$
$167$	−2158.56	−	785.651i	−1.00020	−	0.364045i	−0.789663	+	0.613540i	$0.789745\pi$
$168$	149.928	+	125.805i	0.0688524	+	0.0577740i
$169$	112.567	−	638.400i	0.0512368	−	0.290578i
$170$	−4639.96			−2.09335
$171$	−744.773	−	29.8786i	−0.333065	−	0.0133619i
$172$	−586.129			−0.259837
$173$	476.579	−	2702.82i	0.209443	−	1.18781i	−0.680850	−	0.732423i	$-0.738389\pi$
$173$	476.579	−	2702.82i	0.209443	−	1.18781i	0.890293	−	0.455388i	$-0.150499\pi$
$174$	−810.188	−	679.828i	−0.352990	−	0.296193i
$175$	1275.63	+	464.292i	0.551021	+	0.200555i
$176$	561.229	−	204.271i	0.240365	−	0.0874857i
$177$	−194.149	+	162.910i	−0.0824471	+	0.0691813i
$178$	−1332.60	−	2308.12i	−0.561137	−	0.971917i
$179$	−1233.00	+	2135.62i	−0.514854	+	0.891754i	0.484997	+	0.874516i	$0.338821\pi$
$179$	−1233.00	+	2135.62i	−0.514854	+	0.891754i	−0.999851	+	0.0172382i	$0.994513\pi$
$180$	−106.725	−	605.267i	−0.0441933	−	0.250633i
$181$	−108.705	−	616.499i	−0.0446410	−	0.253172i	0.954318	−	0.298793i	$-0.0965842\pi$
$181$	−108.705	−	616.499i	−0.0446410	−	0.253172i	−0.998959	+	0.0456219i	$0.985473\pi$
$182$	−434.989	+	753.423i	−0.177162	+	0.306854i
$183$	−672.396	−	1164.62i	−0.271612	−	0.470446i
$184$	−660.679	+	554.376i	−0.264706	+	0.222115i
$185$	3401.58	−	1238.07i	1.35183	−	0.492027i
$186$	1741.94	+	634.014i	0.686694	+	0.249936i
$187$	3885.80	+	3260.57i	1.51956	+	1.27506i
$188$	−247.936	+	1406.11i	−0.0961839	+	0.545486i
$189$	−220.182			−0.0847401
$190$	−2825.56	−	113.355i	−1.07888	−	0.0432823i
$191$	−304.280			−0.115272			−0.0576359	−	0.998338i	$-0.518356\pi$
$191$	−304.280			−0.115272			−0.0576359	+	0.998338i	$0.518356\pi$
$192$	33.3405	−	189.083i	0.0125320	−	0.0710724i
$193$	−2482.75	−	2083.28i	−0.925971	−	0.776982i	0.0491183	−	0.998793i	$-0.484359\pi$
$193$	−2482.75	−	2083.28i	−0.925971	−	0.776982i	−0.975090	+	0.221811i	$0.928803\pi$
$194$	1721.83	+	626.693i	0.637216	+	0.231928i
$195$	2567.20	−	934.385i	0.942775	−	0.343142i
$196$	−847.239	+	710.918i	−0.308760	+	0.259081i
$197$	601.093	+	1041.12i	0.217391	+	0.376533i	0.954010	−	0.299776i	$-0.0969119\pi$
$197$	601.093	+	1041.12i	0.217391	+	0.376533i	−0.736618	+	0.676309i	$0.763579\pi$
$198$	−335.952	+	581.886i	−0.120581	+	0.208853i
$199$	219.977	+	1247.55i	0.0783605	+	0.444405i	0.998593	+	0.0530320i	$0.0168885\pi$
$199$	219.977	+	1247.55i	0.0783605	+	0.444405i	−0.920232	+	0.391373i	$0.872000\pi$
$200$	−231.250	−	1311.48i	−0.0817593	−	0.463680i
$201$	−215.225	+	372.780i	−0.0755262	+	0.130815i
$202$	762.436	+	1320.58i	0.265568	+	0.459978i
$203$	−1101.17	+	923.987i	−0.380722	+	0.319464i
$204$	1532.35	−	557.731i	0.525913	−	0.191417i
$205$	−1345.51	−	489.726i	−0.458413	−	0.166849i
$206$	−408.135	−	342.466i	−0.138039	−	0.115829i
$207$	168.484	−	955.522i	0.0565723	−	0.320837i
$208$	853.454			0.284502
$209$	2286.64	+	2080.49i	0.756796	+	0.688567i
$210$	−835.338			−0.274494
$211$	−511.815	+	2902.65i	−0.166989	+	0.947044i	0.780000	+	0.625780i	$0.215219\pi$
$211$	−511.815	+	2902.65i	−0.166989	+	0.947044i	−0.946989	+	0.321265i	$0.895892\pi$
$212$	1204.94	+	1011.06i	0.390357	+	0.327548i
$213$	−2443.10	−	889.216i	−0.785908	−	0.286047i
$214$	2627.01	−	956.153i	0.839153	−	0.305427i
$215$	1916.37	−	1608.03i	0.607887	−	0.510078i
$216$	108.000	+	187.061i	0.0340207	+	0.0589256i
$217$	1259.75	−	2181.95i	0.394089	−	0.682582i
$218$	386.796	+	2193.63i	0.120170	+	0.681520i
$219$	186.812	+	1059.46i	0.0576418	+	0.326903i
$220$	−1274.55	+	2207.59i	−0.390592	+	0.676525i
$221$	3624.28	+	6277.44i	1.10315	+	1.91071i
$222$	−974.557	+	817.750i	−0.294631	+	0.247224i
$223$	3757.41	−	1367.58i	1.12832	−	0.410674i	0.290636	−	0.956834i	$-0.406133\pi$
$223$	3757.41	−	1367.58i	1.12832	−	0.410674i	0.837681	+	0.546160i	$0.183911\pi$
$224$	−245.219	−	89.2523i	−0.0731445	−	0.0266224i
$225$	1147.67	+	963.012i	0.340051	+	0.285337i
$226$	465.723	−	2641.25i	0.137077	−	0.777403i
$227$	−1659.79			−0.485304			−0.242652	−	0.970113i	$-0.578017\pi$
$227$	−1659.79			−0.485304			−0.242652	+	0.970113i	$0.578017\pi$
$228$	946.769	−	302.201i	0.275006	−	0.0877795i
$229$	2043.12			0.589578			0.294789	−	0.955562i	$-0.404751\pi$
$229$	2043.12			0.589578			0.294789	+	0.955562i	$0.404751\pi$
$230$	639.204	−	3625.11i	0.183252	−	1.03927i
$231$	699.564	+	587.004i	0.199255	+	0.167195i
$232$	1325.12	+	482.306i	0.374994	+	0.136487i
$233$	−4674.21	+	1701.27i	−1.31424	+	0.478344i	−0.901608	−	0.432554i	$-0.857612\pi$
$233$	−4674.21	+	1701.27i	−1.31424	+	0.478344i	−0.412631	+	0.910898i	$0.635390\pi$
$234$	−735.507	+	617.163i	−0.205477	+	0.172416i
$235$	−3047.00	−	5277.55i	−0.845805	−	1.46498i
$236$	168.962	−	292.651i	0.0466039	−	0.0807203i
$237$	−366.414	−	2078.04i	−0.100427	−	0.569548i
$238$	−384.866	−	2182.68i	−0.104820	−	0.594464i
$239$	2672.05	−	4628.12i	0.723182	−	1.25259i	−0.236536	−	0.971623i	$-0.576012\pi$
$239$	2672.05	−	4628.12i	0.723182	−	1.25259i	0.959718	−	0.280965i	$-0.0906545\pi$
$240$	409.736	+	709.684i	0.110201	+	0.190874i
$241$	995.668	−	835.464i	0.266127	−	0.223307i	−0.499953	−	0.866053i	$-0.666649\pi$
$241$	995.668	−	835.464i	0.266127	−	0.223307i	0.766080	+	0.642746i	$0.222205\pi$
$242$	117.232	−	42.6690i	0.0311403	−	0.0113341i
$243$	−228.345	−	83.1109i	−0.0602813	−	0.0219406i
$244$	1373.56	+	1152.55i	0.360382	+	0.302397i
$245$	819.700	−	4648.75i	0.213750	−	1.21224i
$246$	503.222			0.130424
$247$	2053.69	+	3911.26i	0.529040	+	1.00756i
$248$	−2471.64			−0.632861
$249$	−406.810	+	2307.13i	−0.103536	+	0.587183i
$250$	1084.56	+	910.055i	0.274375	+	0.230228i
$251$	5398.71	+	1964.97i	1.35762	+	0.494134i	0.915319	−	0.402731i	$-0.131939\pi$
$251$	5398.71	+	1964.97i	1.35762	+	0.494134i	0.442304	+	0.896865i	$0.354161\pi$
$252$	275.871	−	100.409i	0.0689613	−	0.0250999i
$253$	−3082.73	+	2586.71i	−0.766045	+	0.642788i
$254$	−209.486	−	362.841i	−0.0517493	−	0.0896325i
$255$	−3479.97	+	6027.49i	−0.854605	+	1.48022i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	735.885	+	4173.41i	0.178612	+	1.01296i	0.933892	+	0.357556i	$0.116390\pi$
$257$	735.885	+	4173.41i	0.178612	+	1.01296i	−0.755280	+	0.655403i	$0.772499\pi$
$258$	−439.597	+	761.404i	−0.106078	+	0.183732i
$259$	864.549	+	1497.44i	0.207415	+	0.359253i
$260$	−2790.40	+	2341.43i	−0.665590	+	0.558497i
$261$	−1490.76	+	542.594i	−0.353548	+	0.128681i
$262$	−146.406	−	53.2873i	−0.0345228	−	0.0125653i
$263$	5011.45	+	4205.11i	1.17498	+	0.985924i	0.999999	+	0.00135207i	$0.000430379\pi$
$263$	5011.45	+	4205.11i	1.17498	+	0.985924i	0.174980	+	0.984572i	$0.444014\pi$
$264$	155.566	−	882.261i	0.0362669	−	0.205680i
$265$	−6713.43			−1.55624
$266$	−181.045	−	1338.57i	−0.0417315	−	0.308546i
$267$	−3997.79			−0.916332
$268$	99.6623	−	565.213i	0.0227158	−	0.128828i
$269$	2535.52	+	2127.56i	0.574697	+	0.482228i	0.883201	−	0.468995i	$-0.155384\pi$
$269$	2535.52	+	2127.56i	0.574697	+	0.482228i	−0.308504	+	0.951223i	$0.599828\pi$
$270$	−866.308	−	315.310i	−0.195266	−	0.0710710i
$271$	623.025	−	226.763i	0.139653	−	0.0508297i	−0.271248	−	0.962510i	$-0.587436\pi$
$271$	623.025	−	226.763i	0.139653	−	0.0508297i	0.410901	+	0.911680i	$0.365214\pi$
$272$	−1665.58	+	1397.59i	−0.371289	+	0.311549i
$273$	652.483	+	1130.13i	0.144652	+	0.250545i
$274$	−2621.51	+	4540.60i	−0.577998	+	1.00112i
$275$	−1079.01	−	6119.38i	−0.236607	−	1.34186i
$276$	224.646	+	1274.03i	0.0489930	+	0.277853i
$277$	64.1576	−	111.124i	0.0139165	−	0.0241040i	−0.858983	−	0.512004i	$-0.828903\pi$
$277$	64.1576	−	111.124i	0.0139165	−	0.0241040i	0.872900	+	0.487900i	$0.162237\pi$
$278$	−1072.32	−	1857.31i	−0.231344	−	0.400699i
$279$	2130.06	−	1787.33i	0.457073	−	0.383530i
$280$	1046.61	−	380.936i	0.223383	−	0.0813047i
$281$	8405.27	+	3059.27i	1.78440	+	0.649468i	0.999557	+	0.0297743i	$0.00947885\pi$
$281$	8405.27	+	3059.27i	1.78440	+	0.649468i	0.784843	+	0.619694i	$0.212743\pi$
$282$	1640.64	+	1376.66i	0.346450	+	0.290706i
$283$	1295.50	−	7347.14i	0.272118	−	1.54326i	−0.475851	−	0.879526i	$-0.657860\pi$
$283$	1295.50	−	7347.14i	0.272118	−	1.54326i	0.747969	−	0.663733i	$-0.231029\pi$
$284$	3466.52			0.724297
$285$	−2266.42	+	3585.49i	−0.471057	+	0.745214i
$286$	3982.21			0.823333
$287$	118.767	−	673.562i	0.0244272	−	0.138534i
$288$	−220.621	−	185.123i	−0.0451396	−	0.0378766i
$289$	−12736.1	−	4635.55i	−2.59232	−	0.943528i
$290$	−5655.74	+	2058.52i	−1.14523	+	0.416829i
$291$	2105.47	−	1766.70i	0.424140	−	0.355896i
$292$	−717.204	−	1242.23i	−0.143737	−	0.248960i
$293$	−238.403	+	412.927i	−0.0475347	+	0.0823325i	−0.888814	−	0.458269i	$-0.848470\pi$
$293$	−238.403	+	412.927i	−0.0475347	+	0.0823325i	0.841279	+	0.540601i	$0.181803\pi$
$294$	288.080	+	1633.78i	0.0571468	+	0.324096i
$295$	250.451	+	1420.38i	0.0494299	+	0.280331i
$296$	848.129	−	1469.00i	0.166542	−	0.288460i
$297$	503.928	+	872.828i	0.0984540	+	0.170527i
$298$	−1090.57	+	915.100i	−0.211997	+	0.177887i
$299$	−5403.72	+	1966.79i	−1.04517	+	0.380410i
$300$	−1877.11	−	683.211i	−0.361249	−	0.131484i
$301$	915.388	+	768.102i	0.175289	+	0.147085i
$302$	559.865	−	3175.15i	0.106677	−	0.604998i
$303$	2287.31			0.433671
$304$	−1048.42	+	810.386i	−0.197799	+	0.152891i
$305$	−7652.92			−1.43674
$306$	424.751	−	2408.88i	0.0793510	−	0.450022i
$307$	−4310.51	−	3616.95i	−0.801348	−	0.672411i	0.147178	−	0.989110i	$-0.452981\pi$
$307$	−4310.51	−	3616.95i	−0.801348	−	0.672411i	−0.948526	+	0.316699i	$0.897425\pi$
$308$	−1144.19	−	416.451i	−0.211676	−	0.0770438i
$309$	−750.977	+	273.333i	−0.138258	+	0.0503216i
$310$	8081.14	−	6780.88i	1.48057	−	1.24235i
$311$	2573.88	+	4458.09i	0.469297	+	0.812847i	0.999384	−	0.0350967i	$-0.0111739\pi$
$311$	2573.88	+	4458.09i	0.469297	+	0.812847i	−0.530087	+	0.847943i	$0.677841\pi$
$312$	640.090	−	1108.67i	0.116147	−	0.201173i
$313$	−1647.56	−	9343.77i	−0.297526	−	1.68735i	−0.656756	−	0.754103i	$-0.728072\pi$
$313$	−1647.56	−	9343.77i	−0.297526	−	1.68735i	0.359230	−	0.933249i	$-0.383039\pi$
$314$	821.857	+	4660.98i	0.147707	+	0.837689i
$315$	−626.503	+	1085.14i	−0.112062	+	0.194097i
$316$	1406.73	+	2436.53i	0.250426	+	0.433751i
$317$	−2826.37	+	2371.61i	−0.500773	+	0.420198i	−0.857868	−	0.513870i	$-0.828211\pi$
$317$	−2826.37	+	2371.61i	−0.500773	+	0.420198i	0.357096	+	0.934068i	$0.383767\pi$
$318$	2217.12	−	806.964i	0.390974	−	0.142303i
$319$	6183.02	+	2250.44i	1.08521	+	0.394985i
$320$	−837.003	−	702.329i	−0.146218	−	0.122692i
$321$	728.178	−	4129.70i	0.126613	−	0.718061i
$322$	1758.31			0.304306
$323$	−10412.9	−	4270.07i	−1.79377	−	0.735582i
$324$	324.000			0.0555556
$325$	1541.89	−	8744.47i	0.263164	−	1.49248i
$326$	−1526.85	−	1281.18i	−0.259401	−	0.217663i
$327$	3139.70	+	1142.76i	0.530966	+	0.193256i
$328$	−630.499	+	229.483i	−0.106139	+	0.0386313i
$329$	2229.88	−	1871.09i	0.373669	−	0.313545i
$330$	1911.83	+	3311.38i	0.318917	+	0.552380i
$331$	2438.34	−	4223.33i	0.404904	−	0.701314i	−0.589406	−	0.807837i	$-0.700638\pi$
$331$	2438.34	−	4223.33i	0.404904	−	0.701314i	0.994310	+	0.106523i	$0.0339716\pi$
$332$	−542.413	−	3076.18i	−0.0896650	−	0.508515i
$333$	331.371	+	1879.30i	0.0545316	+	0.309264i
$334$	2297.09	−	3978.67i	0.376321	−	0.651807i
$335$	1224.80	+	2121.41i	0.199754	+	0.345985i
$336$	−299.856	+	251.609i	−0.0486860	+	0.0408524i
$337$	289.230	−	105.271i	0.0467518	−	0.0170163i	−0.318538	−	0.947910i	$-0.603192\pi$
$337$	289.230	−	105.271i	0.0467518	−	0.0170163i	0.365290	+	0.930894i	$0.380970\pi$
$338$	1218.31	+	443.428i	0.196057	+	0.0713589i
$339$	−3081.79	−	2585.93i	−0.493745	−	0.414302i
$340$	1611.44	−	9138.94i	0.257037	−	1.45773i
$341$	−11532.7			−1.83147
$342$	317.506	−	1456.54i	0.0502011	−	0.230294i
$343$	5051.93			0.795273
$344$	203.561	−	1154.45i	0.0319048	−	0.180941i
$345$	−4229.75	−	3549.18i	−0.660064	−	0.553859i
$346$	5157.99	+	1877.36i	0.801432	+	0.291697i
$347$	4148.09	−	1509.78i	0.641733	−	0.233572i	−0.000597265	−	1.00000i	$-0.500190\pi$
$347$	4148.09	−	1509.78i	0.641733	−	0.233572i	0.642330	+	0.766428i	$0.277968\pi$
$348$	1620.38	−	1359.66i	0.249601	−	0.209440i
$349$	4909.54	+	8503.57i	0.753013	+	1.30426i	0.946356	+	0.323126i	$0.104734\pi$
$349$	4909.54	+	8503.57i	0.753013	+	1.30426i	−0.193343	+	0.981131i	$0.561933\pi$
$350$	−1357.50	+	2351.26i	−0.207318	+	0.359086i
$351$	250.089	+	1418.32i	0.0380306	+	0.215682i
$352$	207.422	+	1176.35i	0.0314080	+	0.178124i
$353$	−222.898	+	386.071i	−0.0336081	+	0.0582110i	−0.882340	−	0.470612i	$-0.844033\pi$
$353$	−222.898	+	386.071i	−0.0336081	+	0.0582110i	0.848732	+	0.528823i	$0.177366\pi$
$354$	−253.444	−	438.977i	−0.0380519	−	0.0659078i
$355$	−11333.9	+	9510.31i	−1.69449	+	1.42184i
$356$	5008.92	−	1823.10i	0.745709	−	0.271416i
$357$	−3124.04	−	1137.06i	−0.463142	−	0.168570i
$358$	−3778.14	−	3170.24i	−0.557768	−	0.468023i
$359$	−689.855	+	3912.36i	−0.101418	+	0.575171i	0.891172	+	0.453665i	$0.149884\pi$
$359$	−689.855	+	3912.36i	−0.101418	+	0.575171i	−0.992591	+	0.121507i	$0.961227\pi$
$360$	1229.21			0.179958
$361$	−6236.71	−	2854.69i	−0.909275	−	0.416197i
$362$	1252.02			0.181781
$363$	32.4954	−	184.291i	0.00469853	−	0.0266467i
$364$	−1332.88	−	1118.42i	−0.191929	−	0.161047i
$365$	5752.96	+	2093.91i	0.824996	+	0.300274i
$366$	2527.38	−	919.892i	0.360952	−	0.131376i
$367$	−7473.68	+	6271.16i	−1.06301	+	0.891967i	−0.994401	−	0.105677i	$-0.966299\pi$
$367$	−7473.68	+	6271.16i	−1.06301	+	0.891967i	−0.0686046	+	0.997644i	$0.521855\pi$
$368$	−862.455	−	1493.82i	−0.122170	−	0.211605i
$369$	377.417	−	653.705i	0.0532453	−	0.0922236i
$370$	1257.17	+	7129.78i	0.176641	+	1.00178i
$371$	−556.852	−	3158.06i	−0.0779253	−	0.441936i
$372$	−1853.73	+	3210.76i	−0.258364	+	0.447500i
$373$	−1326.67	−	2297.86i	−0.184162	−	0.318978i	0.759132	−	0.650937i	$-0.225624\pi$
$373$	−1326.67	−	2297.86i	−0.184162	−	0.318978i	−0.943294	+	0.331959i	$0.892290\pi$
$374$	−7771.59	+	6521.14i	−1.07449	+	0.901605i
$375$	1995.62	−	726.345i	0.274809	−	0.100022i
$376$	−2683.40	−	976.676i	−0.368047	−	0.133958i
$377$	7202.69	+	6043.77i	0.983972	+	0.825650i
$378$	76.4684	−	433.674i	0.0104051	−	0.0590100i
$379$	12170.0			1.64942			0.824711	−	0.565555i	$-0.191338\pi$
$379$	12170.0			1.64942			0.824711	+	0.565555i	$0.191338\pi$
$380$	1204.57	−	5525.89i	0.162614	−	0.745980i
$381$	−628.459			−0.0845063
$382$	105.675	−	599.314i	0.0141540	−	0.0802712i
$383$	2155.73	+	1808.87i	0.287605	+	0.241329i	0.775163	−	0.631762i	$-0.217668\pi$
$383$	2155.73	+	1808.87i	0.287605	+	0.241329i	−0.487558	+	0.873091i	$0.662112\pi$
$384$	360.842	+	131.336i	0.0479535	+	0.0174536i
$385$	4883.50	−	1777.45i	0.646457	−	0.235291i
$386$	4965.51	−	4166.55i	0.654761	−	0.549409i
$387$	659.396	+	1142.11i	0.0866123	+	0.150017i
$388$	−1832.33	+	3173.69i	−0.239748	+	0.415257i
$389$	−2301.23	−	13051.0i	−0.299941	−	1.70105i	−0.646409	−	0.762991i	$-0.723730\pi$
$389$	−2301.23	−	13051.0i	−0.299941	−	1.70105i	0.346468	−	0.938062i	$-0.387381\pi$
$390$	948.800	+	5380.91i	0.123191	+	0.698649i
$391$	7325.01	−	12687.3i	0.947421	−	1.64098i
$392$	−1105.99	−	1915.63i	−0.142503	−	0.246822i
$393$	−179.026	+	150.221i	−0.0229788	+	0.0192815i
$394$	−2259.37	+	822.344i	−0.288897	+	0.105150i
$395$	−11283.9	−	4107.00i	−1.43735	−	0.523154i
$396$	−1029.42	−	863.783i	−0.130632	−	0.109613i
$397$	−515.950	+	2926.10i	−0.0652262	+	0.369916i	0.934670	+	0.355516i	$0.115695\pi$
$397$	−515.950	+	2926.10i	−0.0652262	+	0.369916i	−0.999896	+	0.0143999i	$0.995416\pi$
$398$	−2533.59			−0.319089
$399$	−1874.64	−	768.745i	−0.235212	−	0.0964546i
$400$	2663.43			0.332929
$401$	−1543.17	+	8751.78i	−0.192176	+	1.08988i	0.724208	+	0.689582i	$0.242206\pi$
$401$	−1543.17	+	8751.78i	−0.192176	+	1.08988i	−0.916384	+	0.400301i	$0.868906\pi$
$402$	−659.486	−	553.375i	−0.0818214	−	0.0686563i
$403$	−15486.1	−	5636.47i	−1.91419	−	0.696707i
$404$	−2865.82	+	1043.07i	−0.352921	+	0.128453i
$405$	−1059.33	+	888.885i	−0.129972	+	0.109059i
$406$	−1437.47	−	2489.77i	−0.175715	−	0.304348i
$407$	3957.37	−	6854.36i	0.481964	−	0.834787i
$408$	566.335	+	3211.84i	0.0687200	+	0.389730i
$409$	1630.97	+	9249.70i	0.197179	+	1.11826i	0.909281	+	0.416183i	$0.136633\pi$
$409$	1630.97	+	9249.70i	0.197179	+	1.11826i	−0.712101	+	0.702077i	$0.752256\pi$
$410$	1431.86	−	2480.06i	0.172475	−	0.298735i
$411$	3932.27	+	6810.89i	0.471933	+	0.817413i
$412$	816.269	−	684.931i	0.0976085	−	0.0819032i
$413$	−647.387	+	235.629i	−0.0771327	+	0.0280740i
$414$	1823.50	+	663.698i	0.216473	+	0.0787898i
$415$	10212.8	+	8569.59i	1.20802	+	1.01365i
$416$	−296.401	+	1680.98i	−0.0349334	+	0.198117i
$417$	−3216.96			−0.377783
$418$	−4891.91	+	3781.26i	−0.572419	+	0.442458i
$419$	−344.307			−0.0401444			−0.0200722	−	0.999799i	$-0.506390\pi$
$419$	−344.307			−0.0401444			−0.0200722	+	0.999799i	$0.506390\pi$
$420$	290.110	−	1645.29i	0.0337045	−	0.191148i
$421$	8507.37	+	7138.53i	0.984854	+	0.826391i	0.984815	−	0.173609i	$-0.0555430\pi$
$421$	8507.37	+	7138.53i	0.984854	+	0.826391i	3.95629e−5		1.00000i	$0.499987\pi$
$422$	−5539.34	−	2016.16i	−0.638984	−	0.232571i
$423$	3018.82	−	1098.76i	0.346998	−	0.126297i
$424$	−2409.88	+	2022.13i	−0.276024	+	0.231611i
$425$	11310.5	+	19590.4i	1.29092	+	2.23594i
$426$	2599.89	−	4503.15i	0.295693	−	0.512155i
$427$	−634.779	−	3600.01i	−0.0719417	−	0.408001i
$428$	970.904	+	5506.27i	0.109650	+	0.621859i
$429$	2986.66	−	5173.05i	0.336124	−	0.582184i
$430$	2501.65	+	4332.98i	0.280559	+	0.485942i
$431$	5255.69	−	4410.04i	0.587372	−	0.492864i	−0.299986	−	0.953943i	$-0.596982\pi$
$431$	5255.69	−	4410.04i	0.587372	−	0.492864i	0.887359	+	0.461080i	$0.152538\pi$
$432$	−405.947	+	147.753i	−0.0452110	+	0.0164555i
$433$	−2256.73	−	821.382i	−0.250465	−	0.0911619i	0.213737	−	0.976891i	$-0.431437\pi$
$433$	−2256.73	−	821.382i	−0.250465	−	0.0911619i	−0.464202	+	0.885729i	$0.653659\pi$
$434$	3860.09	+	3239.00i	0.426936	+	0.358242i
$435$	−1567.71	+	8890.91i	−0.172795	+	0.979969i
$436$	−4454.94			−0.489341
$437$	4770.60	−	7547.11i	0.522217	−	0.826150i
$438$	−2151.61			−0.234721
$439$	479.215	−	2717.76i	0.0520995	−	0.295471i	−0.947614	−	0.319419i	$-0.896512\pi$
$439$	479.215	−	2717.76i	0.0520995	−	0.295471i	0.999713	+	0.0239476i	$0.00762350\pi$
$440$	−3905.45	−	3277.06i	−0.423148	−	0.355063i
$441$	2338.41	+	851.110i	0.252500	+	0.0919027i
$442$	−13622.8	+	4958.31i	−1.46600	+	0.533581i
$443$	−8058.54	+	6761.92i	−0.864272	+	0.725211i	−0.962884	−	0.269915i	$-0.913004\pi$
$443$	−8058.54	+	6761.92i	−0.864272	+	0.725211i	0.0986117	+	0.995126i	$0.468560\pi$
$444$	−1272.19	−	2203.50i	−0.135981	−	0.235526i
$445$	−11375.3	+	19702.5i	−1.21177	+	2.09885i
$446$	1388.68	+	7875.61i	0.147435	+	0.836145i
$447$	370.819	+	2103.02i	0.0392375	+	0.222527i
$448$	260.956	−	451.990i	0.0275202	−	0.0476663i
$449$	−1016.44	−	1760.53i	−0.106835	−	0.185043i	0.807652	−	0.589660i	$-0.200738\pi$
$449$	−1016.44	−	1760.53i	−0.106835	−	0.185043i	−0.914486	+	0.404617i	$0.867405\pi$
$450$	−2295.35	+	1926.02i	−0.240453	+	0.201764i
$451$	−2941.91	+	1070.77i	−0.307160	+	0.111797i
$452$	5040.50	+	1834.59i	0.524524	+	0.190911i
$453$	−3704.74	−	3108.65i	−0.384247	−	0.322422i
$454$	576.438	−	3269.14i	0.0595894	−	0.337948i
$455$	7426.27			0.765163
$456$	266.410	+	1969.72i	0.0273592	+	0.202282i
$457$	5674.93			0.580880			0.290440	−	0.956893i	$-0.406198\pi$
$457$	5674.93			0.580880			0.290440	+	0.956893i	$0.406198\pi$
$458$	−709.569	+	4024.17i	−0.0723930	+	0.410561i
$459$	−2810.67	−	2358.43i	−0.285819	−	0.239830i
$460$	6918.07	+	2517.97i	0.701211	+	0.255220i
$461$	10138.4	−	3690.06i	1.02427	−	0.372805i	0.225376	−	0.974272i	$-0.427639\pi$
$461$	10138.4	−	3690.06i	1.02427	−	0.372805i	0.798898	+	0.601467i	$0.205417\pi$
$462$	−1399.13	+	1174.01i	−0.140895	+	0.118225i
$463$	6296.73	+	10906.3i	0.632039	+	1.09472i	0.987134	+	0.159893i	$0.0511149\pi$
$463$	6296.73	+	10906.3i	0.632039	+	1.09472i	−0.355096	+	0.934830i	$0.615552\pi$
$464$	−1410.17	+	2442.48i	−0.141089	+	0.244374i
$465$	−2747.77	−	15583.4i	−0.274032	−	1.55411i
$466$	−1727.52	−	9797.25i	−0.171729	−	0.973924i
$467$	5835.04	−	10106.6i	0.578187	−	1.00145i	−0.417500	−	0.908677i	$-0.637094\pi$
$467$	5835.04	−	10106.6i	0.578187	−	1.00145i	0.995687	−	0.0927726i	$-0.0295730\pi$
$468$	−960.136	−	1663.00i	−0.0948340	−	0.164257i
$469$	−896.339	+	752.118i	−0.0882497	+	0.0740503i
$470$	11453.0	−	4168.54i	1.12401	−	0.409107i
$471$	6671.19	+	2428.11i	0.652637	+	0.237540i
$472$	517.731	+	434.428i	0.0504883	+	0.0423647i
$473$	949.813	−	5386.66i	0.0923308	−	0.523634i
$474$	4220.19			0.408944
$475$	6409.08	+	12206.1i	0.619092	+	1.17906i
$476$	4432.71			0.426834
$477$	614.560	−	3485.34i	0.0589911	−	0.334555i
$478$	8187.63	+	6870.24i	0.783459	+	0.657400i
$479$	−12047.1	−	4384.77i	−1.14915	−	0.418258i	−0.303942	−	0.952690i	$-0.598303\pi$
$479$	−12047.1	−	4384.77i	−1.14915	−	0.418258i	−0.845211	+	0.534433i	$0.820525\pi$
$480$	−1540.10	+	560.552i	−0.146450	+	0.0533033i
$481$	8663.95	−	7269.92i	0.821294	−	0.689147i
$482$	1299.75	+	2251.24i	0.122826	+	0.212741i
$483$	1318.73	−	2284.11i	0.124232	−	0.215177i
$484$	43.3272	+	245.721i	0.00406905	+	0.0230767i
$485$	−2716.04	−	15403.4i	−0.254287	−	1.44213i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	5493.86	+	9515.64i	0.511192	+	0.885411i	0.999916	+	0.0129720i	$0.00412923\pi$
$487$	5493.86	+	9515.64i	0.511192	+	0.885411i	−0.488724	+	0.872439i	$0.662537\pi$
$488$	−2747.12	+	2305.11i	−0.254829	+	0.213827i
$489$	−2809.44	+	1022.55i	−0.259811	+	0.0945634i
$490$	8871.57	+	3228.99i	0.817912	+	0.297695i
$491$	5798.87	+	4865.83i	0.532992	+	0.447234i	0.869133	−	0.494578i	$-0.164677\pi$
$491$	5798.87	+	4865.83i	0.532992	+	0.447234i	−0.336141	+	0.941812i	$0.609122\pi$
$492$	−174.767	+	991.154i	−0.0160145	+	0.0908225i
$493$	−23953.7			−2.18828
$494$	−8416.91	+	2686.61i	−0.766588	+	0.244689i
$495$	5735.48			0.520789
$496$	858.393	−	4868.19i	0.0777076	−	0.440702i
$497$	−5413.85	−	4542.76i	−0.488620	−	0.410001i
$498$	−4402.88	−	1602.52i	−0.396180	−	0.144198i
$499$	15350.2	−	5587.01i	1.37709	−	0.501221i	0.455797	−	0.890084i	$-0.349354\pi$
$499$	15350.2	−	5587.01i	1.37709	−	0.501221i	0.921296	+	0.388863i	$0.127132\pi$
$500$	−2169.12	+	1820.11i	−0.194012	+	0.162796i
$501$	−3445.63	−	5968.01i	−0.307265	−	0.532198i
$502$	−5745.18	+	9950.95i	−0.510797	+	0.884726i
$503$	2069.91	+	11739.0i	0.183484	+	1.04059i	0.927887	+	0.372861i	$0.121623\pi$
$503$	2069.91	+	11739.0i	0.183484	+	1.04059i	−0.744403	+	0.667731i	$0.767266\pi$
$504$	101.958	+	578.232i	0.00901104	+	0.0511041i
$505$	6508.28	−	11272.7i	0.573494	−	0.993321i
$506$	−4024.21	−	6970.14i	−0.353554	−	0.612373i
$507$	1489.76	−	1250.06i	0.130498	−	0.109501i
$508$	787.410	−	286.594i	0.0687710	−	0.0250306i
$509$	−5329.04	−	1939.61i	−0.464058	−	0.168903i	0.0994007	−	0.995047i	$-0.468307\pi$
$509$	−5329.04	−	1939.61i	−0.464058	−	0.168903i	−0.563459	+	0.826144i	$0.690530\pi$
$510$	−10663.3	−	8947.53i	−0.925837	−	0.776870i
$511$	−507.809	+	2879.93i	−0.0439612	+	0.249316i
$512$	−512.000			−0.0441942
$513$	−1653.97	−	1504.86i	−0.142348	−	0.129515i
$514$	−8475.59			−0.727320
$515$	−789.737	+	4478.82i	−0.0675728	+	0.383224i
$516$	−1347.00	−	1130.27i	−0.114920	−	0.0964290i
$517$	−12520.7	−	4557.17i	−1.06511	−	0.387667i
$518$	−3249.64	+	1182.77i	−0.275639	+	0.100324i
$519$	6307.25	−	5292.41i	0.533444	−	0.447613i
$520$	−3642.61	−	6309.19i	−0.307191	−	0.532070i
$521$	−9047.04	+	15669.9i	−0.760764	+	1.31768i	0.181694	+	0.983355i	$0.441842\pi$
$521$	−9047.04	+	15669.9i	−0.760764	+	1.31768i	−0.942457	+	0.334326i	$0.891491\pi$
$522$	−550.964	−	3124.67i	−0.0461974	−	0.261999i
$523$	−2850.36	−	16165.2i	−0.238312	−	1.35154i	−0.835524	−	0.549453i	$-0.814836\pi$
$523$	−2850.36	−	16165.2i	−0.238312	−	1.35154i	0.597212	−	0.802083i	$-0.296275\pi$
$524$	155.802	−	269.856i	0.0129890	−	0.0224976i
$525$	2036.25	+	3526.89i	0.169275	+	0.293192i
$526$	−10022.9	+	8410.22i	−0.830835	+	0.697154i
$527$	39452.4	−	14359.5i	3.26105	−	1.18692i
$528$	1683.69	+	612.812i	0.138775	+	0.0505099i
$529$	−417.243	−	350.108i	−0.0342930	−	0.0287753i
$530$	2331.55	−	13222.9i	0.191087	−	1.08371i
$531$	−760.331			−0.0621385
$532$	2699.35	+	108.292i	0.219984	+	0.00882528i
$533$	−4473.72			−0.363561
$534$	1388.42	−	7874.11i	0.112514	−	0.638101i
$535$	−18280.7	−	15339.3i	−1.47728	−	1.23958i
$536$	1078.64	+	392.593i	0.0869219	+	0.0316370i
$537$	−6951.86	+	2530.27i	−0.558650	+	0.203332i
$538$	−5071.04	+	4255.11i	−0.406372	+	0.340987i
$539$	−5160.55	−	8938.34i	−0.412395	−	0.714289i
$540$	921.906	−	1596.79i	0.0734676	−	0.127250i
$541$	4094.11	+	23218.9i	0.325360	+	1.84521i	0.507134	+	0.861868i	$0.330705\pi$
$541$	4094.11	+	23218.9i	0.325360	+	1.84521i	−0.181774	+	0.983340i	$0.558184\pi$
$542$	230.261	+	1305.87i	0.0182482	+	0.103491i
$543$	939.015	−	1626.42i	0.0742118	−	0.128539i
$544$	−2174.26	−	3765.93i	−0.171362	−	0.296807i
$545$	14565.6	−	12222.0i	1.14481	−	0.960610i
$546$	−2452.53	+	892.649i	−0.192232	+	0.0699668i
$547$	14278.9	+	5197.10i	1.11613	+	0.406238i	0.833238	−	0.552915i	$-0.186484\pi$
$547$	14278.9	+	5197.10i	1.11613	+	0.406238i	0.282891	+	0.959152i	$0.408707\pi$
$548$	−8032.79	−	6740.31i	−0.626174	−	0.525423i
$549$	700.562	−	3973.09i	0.0544613	−	0.308866i
$550$	12427.6			0.963479
$551$	−14586.9	−	585.193i	−1.12781	−	0.0452451i
$552$	−2587.37			−0.199503
$553$	996.021	−	5648.71i	0.0765915	−	0.434372i
$554$	196.590	+	164.959i	0.0150764	+	0.0126506i
$555$	10204.7	+	3714.22i	0.780481	+	0.284072i
$556$	4030.61	−	1467.02i	0.307439	−	0.111899i
$557$	−11025.1	+	9251.16i	−0.838687	+	0.703742i	−0.957268	−	0.289202i	$-0.906610\pi$
$557$	−11025.1	+	9251.16i	−0.838687	+	0.703742i	0.118581	+	0.992944i	$0.462165\pi$
$558$	2780.60	+	4816.14i	0.210954	+	0.365382i
$559$	3908.08	−	6769.00i	0.295696	−	0.512161i
$560$	386.813	+	2193.73i	0.0291890	+	0.165539i
$561$	2642.52	+	14986.5i	0.198872	+	1.12786i
$562$	−8944.70	+	15492.7i	−0.671369	+	1.16285i
$563$	−5971.09	−	10342.2i	−0.446983	−	0.774198i	0.551205	−	0.834370i	$-0.314168\pi$
$563$	−5971.09	−	10342.2i	−0.446983	−	0.774198i	−0.998188	+	0.0601723i	$0.980835\pi$
$564$	−3281.29	+	2753.33i	−0.244977	+	0.205560i
$565$	−21513.3	+	7830.18i	−1.60189	+	0.583041i
$566$	14021.1	+	5103.27i	1.04126	+	0.378987i
$567$	−506.007	−	424.591i	−0.0374785	−	0.0314482i
$568$	−1203.91	+	6827.72i	−0.0889348	+	0.504374i
$569$	−1407.71			−0.103716			−0.0518579	−	0.998654i	$-0.516514\pi$
$569$	−1407.71			−0.103716			−0.0518579	+	0.998654i	$0.516514\pi$
$570$	−6274.92	−	5709.20i	−0.461101	−	0.419530i
$571$	−4411.29			−0.323304			−0.161652	−	0.986848i	$-0.551682\pi$
$571$	−4411.29			−0.323304			−0.161652	+	0.986848i	$0.551682\pi$
$572$	−1383.01	+	7843.43i	−0.101095	+	0.573340i
$573$	−699.276	−	586.762i	−0.0509820	−	0.0427789i
$574$	1285.41	+	467.852i	0.0934705	+	0.0340205i
$575$	−16863.8	+	6137.90i	−1.22307	+	0.445162i
$576$	441.242	−	370.246i	0.0319185	−	0.0267828i
$577$	−8528.78	−	14772.3i	−0.615351	−	1.06582i	−0.990323	−	0.138783i	$-0.955681\pi$
$577$	−8528.78	−	14772.3i	−0.615351	−	1.06582i	0.374971	−	0.927036i	$-0.377653\pi$
$578$	13553.5	−	23475.3i	0.975345	−	1.68935i
$579$	−1688.38	−	9575.30i	−0.121186	−	0.687281i
$580$	−2090.28	−	11854.5i	−0.149645	−	0.848678i
$581$	−3184.11	+	5515.03i	−0.227365	+	0.393807i
$582$	2748.49	+	4760.53i	0.195754	+	0.339056i
$583$	−11244.5	+	9435.25i	−0.798798	+	0.670271i
$584$	2695.80	−	981.192i	0.191016	−	0.0695240i
$585$	7701.61	+	2803.16i	0.544312	+	0.198113i
$586$	−730.510	−	612.971i	−0.0514968	−	0.0432109i
$587$	−3046.27	+	17276.3i	−0.214196	+	1.21477i	0.668100	+	0.744072i	$0.267108\pi$
$587$	−3046.27	+	17276.3i	−0.214196	+	1.21477i	−0.882296	+	0.470695i	$0.844003\pi$
$588$	−3317.97			−0.232706
$589$	24375.8	−	7780.54i	1.70524	−	0.544298i
$590$	−2884.58			−0.201282
$591$	−626.272	+	3551.77i	−0.0435895	+	0.247208i
$592$	2598.82	+	2180.67i	0.180424	+	0.151393i
$593$	−3672.89	−	1336.82i	−0.254346	−	0.0925745i	0.211700	−	0.977335i	$-0.432100\pi$
$593$	−3672.89	−	1336.82i	−0.254346	−	0.0925745i	−0.466047	+	0.884760i	$0.654322\pi$
$594$	−1894.15	+	689.414i	−0.130838	+	0.0476212i
$595$	−14492.9	+	12161.0i	−0.998576	+	0.837905i
$596$	−1423.64	−	2465.82i	−0.0978434	−	0.169470i
$597$	−1900.19	+	3291.23i	−0.130268	+	0.225630i
$598$	−1997.13	−	11326.3i	−0.136570	−	0.774527i
$599$	−2099.87	−	11908.9i	−0.143236	−	0.812330i	−0.968767	−	0.247973i	$-0.920235\pi$
$599$	−2099.87	−	11908.9i	−0.143236	−	0.812330i	0.825531	−	0.564357i	$-0.190876\pi$
$600$	1997.57	−	3459.90i	0.135918	−	0.235416i
$601$	4443.62	+	7696.58i	0.301596	+	0.522379i	0.976498	−	0.215528i	$-0.0691474\pi$
$601$	4443.62	+	7696.58i	0.301596	+	0.522379i	−0.674902	+	0.737908i	$0.735814\pi$
$602$	−1830.78	+	1536.20i	−0.123948	+	0.104005i
$603$	−1213.47	+	441.667i	−0.0819508	+	0.0298276i
$604$	6059.39	+	2205.44i	0.408200	+	0.148573i
$605$	−815.788	−	684.527i	−0.0548206	−	0.0460000i
$606$	−794.373	+	4505.12i	−0.0532495	+	0.301993i
$607$	16809.5			1.12402			0.562008	−	0.827132i	$-0.310029\pi$
$607$	16809.5			1.12402			0.562008	+	0.827132i	$0.310029\pi$
$608$	−1232.04	−	2346.42i	−0.0821805	−	0.156513i
$609$	−4312.41			−0.286942
$610$	2657.83	−	15073.3i	0.176414	−	1.00049i
$611$	−14585.6	−	12238.7i	−0.965742	−	0.810354i
$612$	4597.06	+	1673.19i	0.303636	+	0.110514i
$613$	17962.6	−	6537.86i	1.18353	−	0.430770i	0.326082	−	0.945341i	$-0.394271\pi$
$613$	17962.6	−	6537.86i	1.18353	−	0.430770i	0.857447	+	0.514572i	$0.172049\pi$
$614$	8621.02	−	7233.89i	0.566638	−	0.475466i
$615$	−2147.79	−	3720.09i	−0.140825	−	0.243916i
$616$	1217.62	−	2108.98i	0.0796418	−	0.137944i
$617$	−3424.68	−	19422.4i	−0.223456	−	1.26728i	−0.865614	−	0.500712i	$-0.833072\pi$
$617$	−3424.68	−	19422.4i	−0.223456	−	1.26728i	0.642158	−	0.766573i	$-0.278039\pi$
$618$	−277.550	−	1574.06i	−0.0180658	−	0.102456i
$619$	−8994.99	+	15579.8i	−0.584070	+	1.01164i	0.410921	+	0.911671i	$0.365207\pi$
$619$	−8994.99	+	15579.8i	−0.584070	+	1.01164i	−0.994991	+	0.0999679i	$0.968126\pi$
$620$	10549.2	+	18271.7i	0.683331	+	1.18356i
$621$	2229.79	−	1871.02i	0.144088	−	0.120904i
$622$	−9674.63	+	3521.28i	−0.623661	+	0.226994i
$623$	−10211.8	−	3716.79i	−0.656705	−	0.239021i
$624$	1961.35	+	1645.77i	0.125828	+	0.105583i
$625$	−1514.67	+	8590.10i	−0.0969387	+	0.549766i
$626$	18975.8			1.21154
$627$	1243.07	+	9190.72i	0.0791760	+	0.585394i
$628$	−9465.77			−0.601474
$629$	−5003.38	+	28375.6i	−0.317167	+	1.79874i
$630$	−1919.72	−	1610.83i	−0.121402	−	0.101869i
$631$	14508.9	+	5280.80i	0.915355	+	0.333162i	0.756389	−	0.654122i	$-0.226962\pi$
$631$	14508.9	+	5280.80i	0.915355	+	0.333162i	0.158966	+	0.987284i	$0.449184\pi$
$632$	−5287.57	+	1924.52i	−0.332798	+	0.121128i
$633$	−6773.57	+	5683.70i	−0.425316	+	0.356883i
$634$	−3689.57	−	6390.52i	−0.231122	−	0.400315i
$635$	−1788.21	+	3097.27i	−0.111753	+	0.193561i
$636$	819.413	+	4647.12i	0.0510878	+	0.289733i
$637$	−2561.07	−	14524.6i	−0.159299	−	0.903429i
$638$	−6579.84	+	11396.6i	−0.408304	+	0.707204i
$639$	−3899.84	−	6754.72i	−0.241432	−	0.418173i
$640$	1674.01	−	1404.66i	0.103392	−	0.0867562i
$641$	29178.5	−	10620.1i	1.79794	−	0.654397i	0.799377	−	0.600830i	$-0.205163\pi$
$641$	29178.5	−	10620.1i	1.79794	−	0.654397i	0.998564	−	0.0535673i	$-0.0170592\pi$
$642$	7881.03	+	2868.46i	0.484485	+	0.176338i
$643$	−8380.05	−	7031.70i	−0.513961	−	0.431265i	0.348559	−	0.937287i	$-0.386671\pi$
$643$	−8380.05	−	7031.70i	−0.513961	−	0.431265i	−0.862521	+	0.506022i	$0.831115\pi$
$644$	−610.653	+	3463.19i	−0.0373651	+	0.211908i
$645$	7504.95			0.458150
$646$	12026.7	−	19026.4i	0.732486	−	1.15880i
$647$	−19405.3			−1.17913			−0.589567	−	0.807719i	$-0.700702\pi$
$647$	−19405.3			−1.17913			−0.589567	+	0.807719i	$0.700702\pi$
$648$	−112.524	+	638.155i	−0.00682154	+	0.0386869i
$649$	2415.73	+	2027.04i	0.146111	+	0.122601i
$650$	16687.7	+	6073.84i	1.00700	+	0.366517i
$651$	7102.65	−	2585.15i	0.427611	−	0.155638i
$652$	3053.71	−	2562.36i	0.183424	−	0.153911i
$653$	−3410.78	−	5907.65i	−0.204402	−	0.354034i	0.745540	−	0.666461i	$-0.232192\pi$
$653$	−3410.78	−	5907.65i	−0.204402	−	0.354034i	−0.949942	+	0.312427i	$0.898858\pi$
$654$	−3341.20	+	5787.13i	−0.199773	+	0.346017i
$655$	230.943	+	1309.74i	0.0137766	+	0.0781312i
$656$	−233.023	−	1321.54i	−0.0138689	−	0.0786546i
$657$	−1613.71	+	2795.02i	−0.0958246	+	0.165973i
$658$	2910.90	+	5041.82i	0.172460	+	0.298709i
$659$	9218.85	−	7735.53i	0.544940	−	0.457259i	−0.328283	−	0.944579i	$-0.606470\pi$
$659$	9218.85	−	7735.53i	0.544940	−	0.457259i	0.873223	+	0.487320i	$0.162026\pi$
$660$	−7186.12	+	2615.53i	−0.423817	+	0.154257i
$661$	−17725.8	−	6451.67i	−1.04305	−	0.379638i	−0.237013	−	0.971507i	$-0.576168\pi$
$661$	−17725.8	−	6451.67i	−1.04305	−	0.379638i	−0.806035	+	0.591868i	$0.798390\pi$
$662$	7471.50	+	6269.33i	0.438653	+	0.368073i
$663$	−3776.10	+	21415.3i	−0.221194	+	1.25445i
$664$	6247.26			0.365122
$665$	−9122.73	+	7051.52i	−0.531976	+	0.411197i
$666$	−3816.58			−0.222056
$667$	3299.87	−	18714.5i	0.191562	−	1.08640i
$668$	7038.69	+	5906.16i	0.407687	+	0.342090i
$669$	11272.2	+	4102.75i	0.651434	+	0.237103i
$670$	−4603.72	+	1675.62i	−0.265459	+	0.0966191i
$671$	−12818.1	+	10755.6i	−0.737460	+	0.618803i
$672$	−391.435	−	677.984i	−0.0224701	−	0.0389194i
$673$	−5532.93	+	9583.32i	−0.316908	+	0.548900i	−0.979841	−	0.199778i	$-0.935978\pi$
$673$	−5532.93	+	9583.32i	−0.316908	+	0.548900i	0.662933	+	0.748678i	$0.269311\pi$
$674$	106.895	+	606.232i	0.00610896	+	0.0346457i
$675$	780.469	+	4426.26i	0.0445041	+	0.252395i
$676$	−1296.50	+	2245.60i	−0.0737652	+	0.127765i
$677$	65.2157	+	112.957i	0.00370228	+	0.00641254i	0.867871	−	0.496790i	$-0.165488\pi$
$677$	65.2157	+	112.957i	0.00370228	+	0.00641254i	−0.864168	+	0.503203i	$0.832155\pi$
$678$	6163.57	−	5171.85i	0.349131	−	0.292955i
$679$	7020.65	−	2555.31i	0.396801	−	0.144424i
$680$	17440.6	+	6347.84i	0.983551	+	0.357983i
$681$	−3814.41	−	3200.67i	−0.214638	−	0.180103i
$682$	4005.26	−	22714.9i	0.224882	−	1.27537i
$683$	−4051.20			−0.226962			−0.113481	−	0.993540i	$-0.536200\pi$
$683$	−4051.20			−0.226962			−0.113481	+	0.993540i	$0.536200\pi$
$684$	2758.55	+	1131.22i	0.154205	+	0.0632356i
$685$	44755.4			2.49637
$686$	−1754.52	+	9950.37i	−0.0976499	+	0.553800i
$687$	4695.37	+	3939.88i	0.260756	+	0.218800i
$688$	2203.13	+	801.872i	0.122083	+	0.0444347i
$689$	−19710.5	+	7174.03i	−1.08985	+	0.396674i
$690$	8459.50	−	7098.36i	0.466736	−	0.391638i
$691$	10239.3	+	17734.9i	0.563705	+	0.976366i	0.997169	+	0.0751953i	$0.0239580\pi$
$691$	10239.3	+	17734.9i	0.563705	+	0.976366i	−0.433463	+	0.901171i	$0.642709\pi$
$692$	−5489.02	+	9507.26i	−0.301534	+	0.522272i
$693$	475.735	+	2698.03i	0.0260775	+	0.147893i
$694$	1533.07	+	8694.49i	0.0838540	+	0.475559i
$695$	−9153.51	+	15854.3i	−0.499586	+	0.865309i
$696$	2115.25	+	3663.72i	0.115199	+	0.199530i
$697$	8730.80	−	7326.01i	0.474466	−	0.398124i
$698$	−18453.8	+	6716.65i	−1.00070	+	0.364225i
$699$	−14022.6	−	5103.82i	−0.758777	−	0.276172i
$700$	−4159.62	−	3490.34i	−0.224598	−	0.188460i
$701$	−1383.53	+	7846.39i	−0.0745438	+	0.422759i	0.924583	+	0.380980i	$0.124413\pi$
$701$	−1383.53	+	7846.39i	−0.0745438	+	0.422759i	−0.999127	+	0.0417785i	$0.986698\pi$
$702$	−2880.41			−0.154863
$703$	−3740.09	+	17157.4i	−0.200654	+	0.920489i
$704$	−2388.99			−0.127896
$705$	3174.63	−	18004.2i	0.169594	−	0.961814i
$706$	−683.000	−	573.105i	−0.0364094	−	0.0305511i
$707$	5842.61	+	2126.54i	0.310798	+	0.113121i
$708$	952.636	−	346.731i	0.0505682	−	0.0184053i
$709$	−4754.53	+	3989.52i	−0.251848	+	0.211325i	−0.759967	−	0.649961i	$-0.774785\pi$
$709$	−4754.53	+	3989.52i	−0.251848	+	0.211325i	0.508120	+	0.861286i	$0.330341\pi$
$710$	−14795.4	−	25626.4i	−0.782059	−	1.35457i
$711$	3165.14	−	5482.18i	0.166951	−	0.289167i
$712$	1851.22	+	10498.8i	0.0974404	+	0.552612i
$713$	5783.79	+	32801.5i	0.303793	+	1.72290i
$714$	3324.53	−	5758.26i	0.174254	−	0.301817i
$715$	−16996.4	−	29438.7i	−0.888993	−	1.53978i
$716$	7556.28	−	6340.47i	0.394401	−	0.330942i
$717$	15065.4	−	5483.37i	0.784698	−	0.285607i
$718$	−7466.26	−	2717.50i	−0.388076	−	0.141248i
$719$	−2549.50	−	2139.28i	−0.132240	−	0.110962i	0.574269	−	0.818667i	$-0.305286\pi$
$719$	−2549.50	−	2139.28i	−0.132240	−	0.110962i	−0.706509	+	0.707705i	$0.749731\pi$
$720$	−426.899	+	2421.07i	−0.0220967	+	0.125316i
$721$	−2172.39			−0.112211
$722$	7788.64	−	11292.5i	0.401472	−	0.582082i
$723$	3899.26			0.200574
$724$	−434.822	+	2466.00i	−0.0223205	+	0.126586i
$725$	22477.9	+	18861.2i	1.15146	+	0.966191i
$726$	351.696	+	128.007i	0.0179789	+	0.00654377i
$727$	24082.5	−	8765.30i	1.22857	−	0.447162i	0.355462	−	0.934691i	$-0.384324\pi$
$727$	24082.5	−	8765.30i	1.22857	−	0.447162i	0.873107	+	0.487529i	$0.162101\pi$
$728$	2665.77	−	2236.84i	0.135714	−	0.113878i
$729$	−364.500	−	631.333i	−0.0185185	−	0.0320750i
$730$	−6122.17	+	10603.9i	−0.310400	+	0.537628i
$731$	3457.77	+	19610.0i	0.174952	+	0.992203i
$732$	934.083	+	5297.45i	0.0471649	+	0.267485i
$733$	10736.0	−	18595.3i	0.540986	−	0.937016i	−0.457861	−	0.889024i	$-0.651384\pi$
$733$	10736.0	−	18595.3i	0.540986	−	0.937016i	0.998848	−	0.0479921i	$-0.0152822\pi$
$734$	−9756.20	−	16898.2i	−0.490610	−	0.849761i
$735$	10848.3	−	9102.77i	0.544413	−	0.456817i
$736$	3241.77	−	1179.91i	0.162355	−	0.0590924i
$737$	5032.93	+	1831.84i	0.251547	+	0.0915557i
$738$	1156.47	+	970.395i	0.0576834	+	0.0484021i
$739$	979.258	−	5553.65i	0.0487451	−	0.276447i	−0.950687	−	0.310153i	$-0.899620\pi$
$739$	979.258	−	5553.65i	0.0487451	−	0.276447i	0.999432	+	0.0337057i	$0.0107309\pi$
$740$	−14479.5			−0.719295
$741$	−2822.68	+	12948.8i	−0.139937	+	0.641954i
$742$	6413.56			0.317317
$743$	1466.74	−	8318.27i	0.0724217	−	0.410724i	−0.926947	−	0.375193i	$-0.877577\pi$
$743$	1466.74	−	8318.27i	0.0724217	−	0.410724i	0.999369	−	0.0355312i	$-0.0113123\pi$
$744$	−5680.17	−	4766.22i	−0.279899	−	0.234863i
$745$	11419.6	+	4156.38i	0.561585	+	0.204400i
$746$	4986.65	−	1814.99i	0.244737	−	0.0890771i
$747$	−5383.89	+	4517.62i	−0.263703	+	0.221273i
$748$	−10145.1	−	17571.8i	−0.495911	−	0.858943i
$749$	5699.46	−	9871.76i	0.278042	−	0.481584i
$750$	737.550	+	4182.86i	0.0359087	+	0.203648i
$751$	−5561.00	−	31538.0i	−0.270205	−	1.53241i	−0.753793	−	0.657112i	$-0.771778\pi$
$751$	−5561.00	−	31538.0i	−0.270205	−	1.53241i	0.483588	−	0.875295i	$-0.339333\pi$
$752$	2855.61	−	4946.06i	0.138475	−	0.239846i
$753$	8617.78	+	14926.4i	0.417064	+	0.722376i
$754$	−14405.4	+	12087.5i	−0.695773	+	0.583823i
$755$	−25862.0	+	9412.99i	−1.24664	+	0.453740i
$756$	827.613	+	301.227i	0.0398148	+	0.0144914i
$757$	−11736.0	−	9847.65i	−0.563476	−	0.472812i	0.315998	−	0.948760i	$-0.397661\pi$
$757$	−11736.0	−	9847.65i	−0.563476	−	0.472812i	−0.879474	+	0.475948i	$0.842105\pi$
$758$	−4226.60	+	23970.2i	−0.202529	+	1.14860i
$759$	−12072.6			−0.577351
$760$	10465.5	+	4291.67i	0.499507	+	0.204836i
$761$	−16480.1			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$761$	−16480.1			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$762$	218.261	−	1237.82i	0.0103763	−	0.0588472i
$763$	6957.50	+	5838.04i	0.330116	+	0.277000i
$764$	1143.72	+	416.279i	0.0541600	+	0.0197126i
$765$	−19620.6	+	7141.32i	−0.927301	+	0.337510i
$766$	−4311.46	+	3617.74i	−0.203367	+	0.170645i
$767$	2253.15	+	3902.57i	0.106071	+	0.183721i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−36.0609	−	204.511i	−0.00169101	−	0.00959020i	0.983951	−	0.178441i	$-0.0571054\pi$
$769$	−36.0609	−	204.511i	−0.00169101	−	0.00959020i	−0.985642	+	0.168851i	$0.945994\pi$
$770$	1804.87	+	10235.9i	0.0844713	+	0.479061i
$771$	−6356.69	+	11010.1i	−0.296927	+	0.514293i
$772$	6482.01	+	11227.2i	0.302192	+	0.523413i
$773$	19404.1	−	16282.0i	0.902869	−	0.757597i	−0.0678797	−	0.997694i	$-0.521623\pi$
$773$	19404.1	−	16282.0i	0.902869	−	0.757597i	0.970749	+	0.240096i	$0.0771790\pi$
$774$	−2478.52	+	902.106i	−0.115101	+	0.0418935i
$775$	−48328.5	−	17590.1i	−2.24001	−	0.815299i
$776$	−5614.58	−	4711.19i	−0.259732	−	0.217941i
$777$	−900.765	+	5108.49i	−0.0415891	+	0.235864i
$778$	26504.6			1.22138
$779$	5495.69	−	4247.96i	0.252765	−	0.195377i
$780$	−10927.8			−0.501640
$781$	−5617.45	+	31858.1i	−0.257373	+	1.45963i
$782$	22445.1	+	18833.7i	1.02639	+	0.861243i
$783$	−4472.29	−	1627.78i	−0.204121	−	0.0742939i
$784$	4157.17	−	1513.09i	0.189375	−	0.0689270i
$785$	30948.7	−	25969.1i	1.40714	−	1.18073i
$786$	−233.702	−	404.784i	−0.0106055	−	0.0183692i
$787$	−15775.8	+	27324.5i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$787$	−15775.8	+	27324.5i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$788$	−835.030	−	4735.69i	−0.0377496	−	0.214089i
$789$	3408.01	+	19327.8i	0.153775	+	0.872101i
$790$	12008.1	−	20798.6i	0.540795	−	0.936684i
$791$	−5467.83	−	9470.57i	−0.245782	−	0.425707i
$792$	2058.83	−	1727.57i	0.0923705	−	0.0775080i
$793$	−22468.8	+	8177.98i	−1.00617	+	0.366215i
$794$	−5584.10	−	2032.45i	−0.249587	−	0.0908423i
$795$	−15428.3	−	12945.9i	−0.688286	−	0.577540i
$796$	879.907	−	4990.20i	0.0391803	−	0.222202i
$797$	16310.9			0.724923			0.362461	−	0.931999i	$-0.381936\pi$
$797$	16310.9			0.724923			0.362461	+	0.931999i	$0.381936\pi$
$798$	2165.19	−	3425.34i	0.0960486	−	0.151949i
$799$	48506.6			2.14773
$800$	−925.001	+	5245.94i	−0.0408796	+	0.231840i
$801$	−9187.45	−	7709.19i	−0.405272	−	0.340063i
$802$	−16701.7	−	6078.92i	−0.735359	−	0.267649i
$803$	12578.6	−	4578.24i	0.552789	−	0.201199i
$804$	1318.97	−	1106.75i	0.0578565	−	0.0485473i
$805$	−7504.60	−	12998.3i	−0.328574	−	0.569107i
$806$	16479.9	−	28544.1i	0.720200	−	1.24742i
$807$	1724.27	+	9778.81i	0.0752133	+	0.426556i
$808$	−1059.16	−	6006.82i	−0.0461154	−	0.261534i
$809$	4482.65	−	7764.17i	0.194810	−	0.337421i	−0.752028	−	0.659131i	$-0.770924\pi$
$809$	4482.65	−	7764.17i	0.194810	−	0.337421i	0.946838	+	0.321710i	$0.104258\pi$
$810$	−1382.86	−	2395.18i	−0.0599861	−	0.103899i
$811$	−4243.30	+	3560.55i	−0.183727	+	0.154165i	−0.730012	−	0.683434i	$-0.760486\pi$
$811$	−4243.30	+	3560.55i	−0.183727	+	0.154165i	0.546286	+	0.837599i	$0.316041\pi$
$812$	5403.12	−	1966.57i	0.233513	−	0.0849916i
$813$	1869.08	+	680.288i	0.0806290	+	0.0293465i
$814$	12126.1	+	10175.0i	0.522136	+	0.438124i
$815$	−2954.45	+	16755.5i	−0.126981	+	0.720147i
$816$	−6522.78			−0.279832
$817$	1626.57	+	12026.2i	0.0696530	+	0.514985i
$818$	−18784.8			−0.802928
$819$	−679.815	+	3855.42i	−0.0290045	+	0.164493i
$820$	4387.48	+	3681.53i	0.186851	+	0.156786i
$821$	−37122.2	−	13511.4i	−1.57804	−	0.574360i	−0.603264	−	0.797541i	$-0.706134\pi$
$821$	−37122.2	−	13511.4i	−1.57804	−	0.574360i	−0.974777	+	0.223181i	$0.928356\pi$
$822$	−14780.5	+	5379.66i	−0.627165	+	0.228269i
$823$	−7787.68	+	6534.64i	−0.329844	+	0.276772i	−0.792636	−	0.609695i	$-0.791292\pi$
$823$	−7787.68	+	6534.64i	−0.329844	+	0.276772i	0.462792	+	0.886467i	$0.346848\pi$
$824$	1065.56	+	1845.61i	0.0450494	+	0.0780278i
$825$	9320.68	−	16143.9i	0.393339	−	0.681283i
$826$	−239.264	−	1356.94i	−0.0100788	−	0.0571596i
$827$	−2179.87	−	12362.6i	−0.0916582	−	0.519820i	−0.995720	−	0.0924184i	$-0.970540\pi$
$827$	−2179.87	−	12362.6i	−0.0916582	−	0.519820i	0.904062	−	0.427401i	$-0.140571\pi$
$828$	−1940.52	+	3361.09i	−0.0814467	+	0.141070i
$829$	−15601.1	−	27022.0i	−0.653619	−	1.13210i	−0.982238	−	0.187638i	$-0.939917\pi$
$829$	−15601.1	−	27022.0i	−0.653619	−	1.13210i	0.328620	−	0.944462i	$-0.393417\pi$
$830$	−20425.7	+	17139.2i	−0.854200	+	0.716759i
$831$	361.731	−	131.659i	0.0151002	−	0.00549604i
$832$	−3207.94	−	1167.59i	−0.133672	−	0.0486527i
$833$	28783.1	+	24151.9i	1.19721	+	1.00458i
$834$	1117.24	−	6336.18i	0.0463871	−	0.263074i
$835$	−39216.7			−1.62533
$836$	−5748.69	−	10948.4i	−0.237826	−	0.452941i
$837$	8341.80			0.344486
$838$	119.577	−	678.153i	0.00492925	−	0.0279551i
$839$	−1939.86	−	1627.73i	−0.0798228	−	0.0669792i	0.602003	−	0.798494i	$-0.294369\pi$
$839$	−1939.86	−	1627.73i	−0.0798228	−	0.0669792i	−0.681826	+	0.731514i	$0.738814\pi$
$840$	3139.84	+	1142.81i	0.128970	+	0.0469413i
$841$	−6279.43	+	2285.52i	−0.257470	+	0.0937113i
$842$	−17014.7	+	14277.1i	−0.696397	+	0.584347i
$843$	13417.1	+	23239.0i	0.548171	+	0.949459i
$844$	5894.85	−	10210.2i	0.240414	−	0.416408i
$845$	−1921.78	−	10899.0i	−0.0782384	−	0.443712i
$846$	1115.71	+	6327.51i	0.0453415	+	0.257145i
$847$	254.342	−	440.533i	0.0103179	−	0.0178712i
$848$	−3145.87	−	5448.81i	−0.127394	−	0.220652i
$849$	17145.2	−	14386.5i	0.693076	−	0.581560i
$850$	−42513.7	+	15473.7i	−1.71554	+	0.624406i
$851$	−21480.0	−	7818.08i	−0.865247	−	0.314924i
$852$	7966.53	+	6684.72i	0.320339	+	0.268796i
$853$	4921.68	−	27912.2i	0.197556	−	1.12040i	−0.711176	−	0.703014i	$-0.751837\pi$
$853$	4921.68	−	27912.2i	0.197556	−	1.12040i	0.908732	−	0.417381i	$-0.137052\pi$
$854$	7311.09			0.292951
$855$	−12122.7	+	3869.45i	−0.484896	+	0.154775i
$856$	−11182.4			−0.446504
$857$	5572.54	−	31603.5i	0.222117	−	1.25969i	−0.646003	−	0.763335i	$-0.723561\pi$
$857$	5572.54	−	31603.5i	0.222117	−	1.25969i	0.868120	−	0.496354i	$-0.165328\pi$
$858$	9151.66	+	7679.15i	0.364140	+	0.305550i
$859$	−12814.1	−	4663.96i	−0.508978	−	0.185253i	0.0747495	−	0.997202i	$-0.476184\pi$
$859$	−12814.1	−	4663.96i	−0.508978	−	0.185253i	−0.583728	+	0.811949i	$0.698406\pi$
$860$	−9403.13	+	3422.46i	−0.372842	+	0.135703i
$861$	1571.82	−	1318.91i	0.0622153	−	0.0522048i
$862$	6860.81	+	11883.3i	0.271091	+	0.469543i
$863$	17137.4	−	29682.9i	0.675972	−	1.17082i	−0.300211	−	0.953873i	$-0.597057\pi$
$863$	17137.4	−	29682.9i	0.675972	−	1.17082i	0.976184	−	0.216946i	$-0.0696095\pi$
$864$	−150.032	−	850.874i	−0.00590763	−	0.0335038i
$865$	−8136.32	−	46143.4i	−0.319819	−	1.81378i
$866$	2401.56	−	4159.62i	0.0942359	−	0.163221i
$867$	−20330.2	−	35212.9i	−0.796366	−	1.37935i
$868$	−7720.18	+	6478.00i	−0.301890	+	0.253315i
$869$	−24671.8	+	8979.79i	−0.963099	+	0.350539i
$870$	−16967.2	−	6175.56i	−0.661198	−	0.240656i
$871$	5862.93	+	4919.58i	0.228080	+	0.191382i
$872$	1547.18	−	8774.51i	0.0600851	−	0.340760i
$873$	8245.48			0.319665
$874$	13208.1	+	12017.3i	0.511179	+	0.465094i
$875$	5772.82			0.223037
$876$	747.247	−	4237.85i	0.0288209	−	0.163452i
$877$	14248.3	+	11955.8i	0.548611	+	0.460339i	0.874470	−	0.485079i	$-0.161209\pi$
$877$	14248.3	+	11955.8i	0.548611	+	0.460339i	−0.325859	+	0.945418i	$0.605654\pi$
$878$	5186.52	+	1887.74i	0.199358	+	0.0725605i
$879$	−1344.16	+	489.232i	−0.0515782	+	0.0187729i
$880$	7810.90	−	6554.13i	0.299211	−	0.251068i
$881$	24113.0	+	41764.9i	0.922118	+	1.59716i	0.796131	+	0.605124i	$0.206877\pi$
$881$	24113.0	+	41764.9i	0.922118	+	1.59716i	0.125987	+	0.992032i	$0.459790\pi$
$882$	−2488.48	+	4310.17i	−0.0950017	+	0.164548i
$883$	−1113.00	−	6312.16i	−0.0424185	−	0.240568i	0.956225	−	0.292632i	$-0.0945310\pi$
$883$	−1113.00	−	6312.16i	−0.0424185	−	0.240568i	−0.998644	+	0.0520643i	$0.983420\pi$
$884$	−5034.80	−	28553.8i	−0.191559	−	1.08639i
$885$	−2163.44	+	3747.18i	−0.0821730	+	0.142328i
$886$	−10519.7	−	18220.6i	−0.398889	−	0.690895i
$887$	18640.1	−	15640.9i	0.705607	−	0.592075i	−0.217756	−	0.976003i	$-0.569874\pi$
$887$	18640.1	−	15640.9i	0.705607	−	0.592075i	0.923363	+	0.383929i	$0.125429\pi$
$888$	4781.88	−	1740.46i	0.180709	−	0.0657727i
$889$	−1605.31	−	584.285i	−0.0605629	−	0.0220431i
$890$	−34855.8	−	29247.5i	−1.31278	−	1.10155i
$891$	−525.037	+	2977.63i	−0.0197412	+	0.111958i
$892$	−15994.2			−0.600365
$893$	29538.6	+	1185.02i	1.10691	+	0.0444069i
$894$	−4270.93			−0.159778
$895$	−7310.67	+	41460.9i	−0.273038	+	1.54847i
$896$	799.617	+	670.958i	0.0298140	+	0.0250169i
$897$	−16211.1	−	5900.38i	−0.603427	−	0.219630i
$898$	3820.56	−	1390.57i	0.141975	−	0.0516748i
$899$	41718.7	−	35006.1i	1.54771	−	1.29869i
$900$	−2996.36	−	5189.85i	−0.110976	−	0.192217i
$901$	26718.6	−	46277.9i	0.987929	−	1.71114i
$902$	−1087.28	−	6166.30i	−0.0401359	−	0.227622i
$903$	622.505	+	3530.40i	0.0229409	+	0.130105i
$904$	−5363.98	+	9290.69i	−0.197349	+	0.341818i
$905$	−5343.73	−	9255.60i	−0.196278	−	0.339963i
$906$	7409.49	−	6217.30i	0.271704	−	0.227987i
$907$	4692.50	−	1707.93i	0.171788	−	0.0625257i	−0.254694	−	0.967022i	$-0.581975\pi$
$907$	4692.50	−	1707.93i	0.171788	−	0.0625257i	0.426482	+	0.904496i	$0.359753\pi$
$908$	6238.76	+	2270.72i	0.228018	+	0.0829918i
$909$	5256.54	+	4410.76i	0.191802	+	0.160941i
$910$	−2579.12	+	14626.9i	−0.0939526	+	0.532832i
$911$	25671.0			0.933610			0.466805	−	0.884360i	$-0.345405\pi$
$911$	25671.0			0.933610			0.466805	+	0.884360i	$0.345405\pi$
$912$	−3972.12	−	159.353i	−0.144222	−	0.00578585i
$913$	29149.7			1.05664
$914$	−1970.88	+	11177.4i	−0.0713249	+	0.404504i
$915$	−17587.4	−	14757.6i	−0.635434	−	0.533193i
$916$	−7679.63	−	2795.16i	−0.277011	−	0.100824i
$917$	−596.960	+	217.276i	−0.0214977	+	0.00782452i
$918$	5621.33	−	4716.86i	0.202104	−	0.169586i
$919$	3930.07	+	6807.08i	0.141068	+	0.244336i	0.927899	−	0.372832i	$-0.121613\pi$
$919$	3930.07	+	6807.08i	0.141068	+	0.244336i	−0.786831	+	0.617168i	$0.788280\pi$
$920$	−7362.06	+	12751.5i	−0.263826	+	0.456960i
$921$	−2931.34	−	16624.5i	−0.104876	−	0.594782i
$922$	3746.98	+	21250.2i	0.133840	+	0.759044i
$923$	−23113.4	+	40033.6i	−0.824255	+	1.42765i
$924$	−1826.43	−	3163.47i	−0.0650273	−	0.112631i
$925$	27038.2	−	22687.7i	0.961092	−	0.806452i
$926$	−23668.0	+	8614.43i	−0.839933	+	0.305710i
$927$	−2252.93	−	819.999i	−0.0798230	−	0.0290532i
$928$	−4321.00	−	3625.75i	−0.152849	−	0.128256i
$929$	−3675.57	+	20845.2i	−0.129808	+	0.736177i	0.848528	+	0.529151i	$0.177490\pi$
$929$	−3675.57	+	20845.2i	−0.129808	+	0.736177i	−0.978335	+	0.207026i	$0.933622\pi$
$930$	31647.5			1.11587
$931$	16937.7	+	15410.7i	0.596254	+	0.542499i
$932$	19896.8			0.699292
$933$	−2681.70	+	15208.7i	−0.0940996	+	0.533665i
$934$	17879.6	+	15002.8i	0.626379	+	0.525595i
$935$	81377.6	+	29619.0i	2.84634	+	1.03598i
$936$	3608.93	−	1313.54i	0.126027	−	0.0458702i
$937$	−8604.98	+	7220.44i	−0.300013	+	0.251741i	−0.780350	−	0.625343i	$-0.784959\pi$
$937$	−8604.98	+	7220.44i	−0.300013	+	0.251741i	0.480337	+	0.877084i	$0.340515\pi$
$938$	−1170.09	−	2026.65i	−0.0407300	−	0.0705464i
$939$	14231.9	−	24650.3i	0.494611	−	0.856691i
$940$	4232.84	+	24005.6i	0.146872	+	0.832955i
$941$	3176.41	+	18014.3i	0.110041	+	0.624071i	0.989087	+	0.147334i	$0.0470693\pi$
$941$	3176.41	+	18014.3i	0.110041	+	0.624071i	−0.879046	+	0.476737i	$0.841820\pi$
$942$	−7099.33	+	12296.4i	−0.245551	+	0.425306i
$943$	4520.90	+	7830.43i	0.156120	+	0.270407i
$944$	−1035.46	+	868.855i	−0.0357006	+	0.0299564i
$945$	−3532.32	+	1285.66i	−0.121594	+	0.0442566i
$946$	10279.8	+	3741.53i	0.353303	+	0.128592i
$947$	−32022.2	−	26869.8i	−1.09882	−	0.922019i	−0.101474	−	0.994838i	$-0.532356\pi$
$947$	−32022.2	−	26869.8i	−1.09882	−	0.922019i	−0.997345	+	0.0728195i	$0.976800\pi$
$948$	−1465.65	+	8312.14i	−0.0502134	+	0.284774i
$949$	19128.1			0.654294
$950$	−26267.2	+	8384.28i	−0.897076	+	0.286339i
$951$	−11068.7			−0.377421
$952$	−1539.46	+	8730.74i	−0.0524100	+	0.297232i
$953$	−2043.31	−	1714.54i	−0.0694535	−	0.0582784i	0.607400	−	0.794396i	$-0.292213\pi$
$953$	−2043.31	−	1714.54i	−0.0694535	−	0.0582784i	−0.676854	+	0.736118i	$0.736657\pi$
$954$	6651.35	+	2420.89i	0.225729	+	0.0821586i
$955$	−4881.48	+	1776.71i	−0.165404	+	0.0602022i
$956$	−16375.3	+	13740.5i	−0.553989	+	0.464852i
$957$	9869.75	+	17094.9i	0.333379	+	0.577430i
$958$	12820.2	−	22205.3i	0.432362	−	0.748872i
$959$	3712.28	+	21053.4i	0.125001	+	0.708914i
$960$	−569.199	−	3228.09i	−0.0191363	−	0.108527i
$961$	−32831.2	+	56865.3i	−1.10205	+	1.90881i
$962$	11310.0	+	19589.5i	0.379053	+	0.656538i
$963$	9637.01	−	8086.41i	0.322480	−	0.270593i
$964$	−4885.47	+	1778.17i	−0.163227	+	0.0594096i
$965$	−51994.6	−	18924.5i	−1.73447	−	0.631296i
$966$	4040.82	+	3390.65i	0.134587	+	0.112932i
$967$	4915.93	−	27879.6i	0.163481	−	0.927144i	−0.787137	−	0.616779i	$-0.788437\pi$
$967$	4915.93	−	27879.6i	0.163481	−	0.927144i	0.950617	−	0.310366i	$-0.100452\pi$
$968$	−499.023			−0.0165694
$969$	−15695.9	−	29893.0i	−0.520357	−	0.991023i
$970$	31282.1			1.03547
$971$	−4018.90	+	22792.3i	−0.132825	+	0.753285i	0.843525	+	0.537089i	$0.180476\pi$
$971$	−4018.90	+	22792.3i	−0.132825	+	0.753285i	−0.976350	+	0.216196i	$0.930635\pi$
$972$	744.595	+	624.790i	0.0245709	+	0.0206174i
$973$	−8217.29	−	2990.85i	−0.270744	−	0.0985429i
$974$	−20650.2	+	7516.04i	−0.679336	+	0.247258i
$975$	20406.0	−	17122.6i	0.670271	−	0.562424i
$976$	−3586.11	−	6211.33i	−0.117611	−	0.203709i
$977$	6118.31	−	10597.2i	0.200350	−	0.347017i	−0.748291	−	0.663371i	$-0.769125\pi$
$977$	6118.31	−	10597.2i	0.200350	−	0.347017i	0.948641	+	0.316354i	$0.102459\pi$
$978$	−1038.33	−	5888.65i	−0.0339490	−	0.192534i
$979$	8637.80	+	48987.4i	0.281987	+	1.59923i
$980$	−9440.93	+	16352.2i	−0.307734	+	0.533011i
$981$	5011.80	+	8680.70i	0.163114	+	0.282521i
$982$	−11597.7	+	9731.66i	−0.376883	+	0.316242i
$983$	−39126.7	+	14241.0i	−1.26953	+	0.462071i	−0.886956	−	0.461854i	$-0.847185\pi$
$983$	−39126.7	+	14241.0i	−1.26953	+	0.462071i	−0.382574	+	0.923925i	$0.624962\pi$
$984$	−1891.50	−	688.449i	−0.0612792	−	0.0223038i
$985$	15722.4	+	13192.6i	0.508586	+	0.426754i
$986$	8319.03	−	47179.5i	0.268694	−	1.52384i
$987$	8732.69			0.281626
$988$	−2368.42	−	17511.1i	−0.0762647	−	0.563870i
$989$	−15797.2			−0.507909
$990$	−1991.91	+	11296.7i	−0.0639466	+	0.362659i
$991$	5197.07	+	4360.86i	0.166590	+	0.139785i	0.722271	−	0.691610i	$-0.243098\pi$
$991$	5197.07	+	4360.86i	0.166590	+	0.139785i	−0.555682	+	0.831395i	$0.687543\pi$
$992$	9290.34	+	3381.41i	0.297347	+	0.108226i
$993$	13747.7	−	5003.76i	0.439346	−	0.159909i
$994$	10827.7	−	9085.51i	0.345507	−	0.289915i
$995$	10813.6	+	18729.7i	0.344536	+	0.596754i
$996$	4685.45	−	8115.43i	0.149060	−	0.258180i
$997$	10204.5	+	57872.4i	0.324151	+	1.83835i	0.515573	+	0.856845i	$0.327579\pi$
$997$	10204.5	+	57872.4i	0.324151	+	1.83835i	−0.191422	+	0.981508i	$0.561310\pi$
$998$	5673.20	+	32174.3i	0.179942	+	1.02050i
$999$	−2862.44	+	4957.88i	−0.0906541	+	0.157018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.i.c.55.3	✓	18
19.3	odd	18		2166.4.a.bl.1.2		9
19.9	even	9	inner	114.4.i.c.85.3	yes	18
19.16	even	9		2166.4.a.bk.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.c.55.3	✓	18	1.1	even	1	trivial
114.4.i.c.85.3	yes	18	19.9	even	9	inner
2166.4.a.bk.1.2		9	19.16	even	9
2166.4.a.bl.1.2		9	19.3	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(16.0427 - 5.83908i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(4.07744 + 7.06234i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(16.0427 - 5.83908i) q^{5} +(-4.59627 + 3.85673i) q^{6} +(4.07744 + 7.06234i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.56283 + 8.86327i) q^{9} +(5.92916 + 33.6259i) q^{10} +(18.6640 - 32.3270i) q^{11} +(-6.00000 - 10.3923i) q^{12} +(40.8615 - 34.2869i) q^{13} +(-15.3262 + 5.57827i) q^{14} +(48.1282 + 17.5172i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-23.5973 + 133.827i) q^{17} -18.0000 q^{18} +(-17.6392 + 80.9188i) q^{19} -68.2893 q^{20} +(-4.24824 + 24.0930i) q^{21} +(57.1898 + 47.9879i) q^{22} +(-101.305 - 36.8721i) q^{23} +(22.5526 - 8.20848i) q^{24} +(127.519 - 107.001i) q^{25} +(53.3409 + 92.3891i) q^{26} +(-13.5000 + 23.3827i) q^{27} +(-5.66432 - 32.1240i) q^{28} +(30.6091 + 173.593i) q^{29} +(-51.2170 + 88.7104i) q^{30} +(-154.478 - 267.563i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(105.230 - 38.3008i) q^{33} +(-255.392 - 92.9551i) q^{34} +(106.651 + 89.4908i) q^{35} +(6.25133 - 35.4531i) q^{36} +212.032 q^{37} +(-153.253 - 62.8453i) q^{38} +160.023 q^{39} +(23.7166 - 134.504i) q^{40} +(-64.2484 - 53.9108i) q^{41} +(-45.9785 - 16.7348i) q^{42} +(137.695 - 50.1170i) q^{43} +(-114.380 + 95.9758i) q^{44} +(76.8255 + 133.066i) q^{45} +(107.807 - 186.727i) q^{46} +(-61.9839 - 351.528i) q^{47} +(8.33511 + 47.2708i) q^{48} +(138.249 - 239.454i) q^{49} +(166.465 + 288.325i) q^{50} +(-312.296 + 262.048i) q^{51} +(-200.496 + 72.9746i) q^{52} +(-369.519 - 134.494i) q^{53} +(-41.3664 - 34.7105i) q^{54} +(110.662 - 627.594i) q^{55} +65.2391 q^{56} +(-196.578 + 151.947i) q^{57} -352.542 q^{58} +(-14.6700 + 83.1977i) q^{59} +(-156.938 - 131.687i) q^{60} +(-421.231 - 153.315i) q^{61} +(580.646 - 211.338i) q^{62} +(-56.2230 + 47.1767i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(455.327 - 788.649i) q^{65} +(38.8916 + 220.565i) q^{66} +(24.9156 + 141.303i) q^{67} +(271.783 - 470.741i) q^{68} +(-161.710 - 280.091i) q^{69} +(-213.302 + 178.982i) q^{70} +(-814.367 + 296.405i) q^{71} +(67.6579 + 24.6255i) q^{72} +(274.705 + 230.505i) q^{73} +(-73.6380 + 417.622i) q^{74} +499.394 q^{75} +(177.005 - 280.023i) q^{76} +304.405 q^{77} +(-55.5753 + 315.183i) q^{78} +(-538.808 - 452.114i) q^{79} +(256.684 + 93.4253i) q^{80} +(-76.1151 + 27.7036i) q^{81} +(128.497 - 107.822i) q^{82} +(390.454 + 676.286i) q^{83} +(48.9293 - 84.7481i) q^{84} +(402.861 + 2284.74i) q^{85} +(50.8902 + 288.612i) q^{86} +(-264.406 + 457.965i) q^{87} +(-149.312 - 258.616i) q^{88} +(-1020.83 + 856.577i) q^{89} +(-288.769 + 105.103i) q^{90} +(408.756 + 148.775i) q^{91} +(330.340 + 277.188i) q^{92} +(160.949 - 912.785i) q^{93} +713.903 q^{94} +(189.510 + 1401.16i) q^{95} -96.0000 q^{96} +(159.090 - 902.246i) q^{97} +(423.619 + 355.459i) q^{98} +(315.691 + 114.902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8}+O(q^{10}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8	\( 18 q + 9 q^{5} - 30 q^{7} + 72 q^{8} + 18 q^{10} + 57 q^{11} - 108 q^{12} - 228 q^{13} + 6 q^{14} + 27 q^{15} + 27 q^{17} - 324 q^{18} + 105 q^{19} - 24 q^{20} + 45 q^{21} + 222 q^{22} - 576 q^{23} - 243 q^{25} - 186 q^{26} - 243 q^{27} + 60 q^{28} - 339 q^{29} - 18 q^{30} + 429 q^{31} + 288 q^{33} - 450 q^{34} + 1680 q^{35} - 318 q^{37} + 114 q^{38} - 558 q^{39} + 72 q^{40} + 531 q^{41} + 18 q^{42} + 2172 q^{43} - 444 q^{44} + 27 q^{45} - 48 q^{46} - 816 q^{47} - 249 q^{49} + 780 q^{50} - 756 q^{51} + 276 q^{52} - 744 q^{53} + 2862 q^{55} - 480 q^{56} - 171 q^{57} + 900 q^{58} - 2307 q^{59} + 168 q^{61} + 1770 q^{62} - 108 q^{63} - 576 q^{64} + 1209 q^{65} - 90 q^{66} + 1944 q^{67} + 588 q^{68} + 72 q^{69} - 3360 q^{70} - 1011 q^{71} + 4152 q^{73} + 1854 q^{74} + 2340 q^{75} - 276 q^{76} - 7686 q^{77} - 954 q^{78} - 4929 q^{79} + 144 q^{80} - 1062 q^{82} + 156 q^{83} - 360 q^{84} - 2049 q^{85} + 2064 q^{86} + 675 q^{87} - 456 q^{88} - 4785 q^{89} - 162 q^{90} + 5166 q^{91} + 3852 q^{92} + 315 q^{93} + 1368 q^{94} - 1350 q^{95} - 1728 q^{96} + 2247 q^{97} - 2538 q^{98} + 864 q^{99}+O(q^{100}) \) 18 * q + 9 * q^5 - 30 * q^7 + 72 * q^8 + 18 * q^10 + 57 * q^11 - 108 * q^12 - 228 * q^13 + 6 * q^14 + 27 * q^15 + 27 * q^17 - 324 * q^18 + 105 * q^19 - 24 * q^20 + 45 * q^21 + 222 * q^22 - 576 * q^23 - 243 * q^25 - 186 * q^26 - 243 * q^27 + 60 * q^28 - 339 * q^29 - 18 * q^30 + 429 * q^31 + 288 * q^33 - 450 * q^34 + 1680 * q^35 - 318 * q^37 + 114 * q^38 - 558 * q^39 + 72 * q^40 + 531 * q^41 + 18 * q^42 + 2172 * q^43 - 444 * q^44 + 27 * q^45 - 48 * q^46 - 816 * q^47 - 249 * q^49 + 780 * q^50 - 756 * q^51 + 276 * q^52 - 744 * q^53 + 2862 * q^55 - 480 * q^56 - 171 * q^57 + 900 * q^58 - 2307 * q^59 + 168 * q^61 + 1770 * q^62 - 108 * q^63 - 576 * q^64 + 1209 * q^65 - 90 * q^66 + 1944 * q^67 + 588 * q^68 + 72 * q^69 - 3360 * q^70 - 1011 * q^71 + 4152 * q^73 + 1854 * q^74 + 2340 * q^75 - 276 * q^76 - 7686 * q^77 - 954 * q^78 - 4929 * q^79 + 144 * q^80 - 1062 * q^82 + 156 * q^83 - 360 * q^84 - 2049 * q^85 + 2064 * q^86 + 675 * q^87 - 456 * q^88 - 4785 * q^89 - 162 * q^90 + 5166 * q^91 + 3852 * q^92 + 315 * q^93 + 1368 * q^94 - 1350 * q^95 - 1728 * q^96 + 2247 * q^97 - 2538 * q^98 + 864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more