LMFDB - Embedded newform 175.4.x.a.103.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.35
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13924 + 0.0597051i) q^{2} +(-4.65026 - 5.74259i) q^{3} +(-6.66187 - 0.700191i) q^{4} +(-0.689007 - 11.1591i) q^{5} +(-4.95490 - 6.81984i) q^{6} +(-17.8723 + 4.85610i) q^{7} +(-16.5617 - 2.62312i) q^{8} +(-5.73883 + 26.9991i) q^{9} +(-0.118690 - 12.7540i) q^{10} +(9.78282 - 2.07940i) q^{11} +(26.9585 + 41.5125i) q^{12} +(62.8114 + 32.0040i) q^{13} +(-20.6508 + 4.46520i) q^{14} +(-60.8780 + 55.8493i) q^{15} +(33.7063 + 7.16449i) q^{16} +(9.43880 + 24.5889i) q^{17} +(-8.14989 + 30.4158i) q^{18} +(-9.26872 - 88.1859i) q^{19} +(-3.22342 + 74.8228i) q^{20} +(110.997 + 80.0511i) q^{21} +(11.2691 - 1.78486i) q^{22} +(6.88543 - 131.382i) q^{23} +(61.9529 + 107.306i) q^{24} +(-124.051 + 15.3774i) q^{25} +(69.6465 + 40.2104i) q^{26} +(3.96513 - 2.02034i) q^{27} +(122.463 - 19.8367i) q^{28} +(-182.006 + 250.509i) q^{29} +(-72.6893 + 59.9911i) q^{30} +(-97.0745 + 218.033i) q^{31} +(167.546 + 44.8939i) q^{32} +(-57.4338 - 46.5090i) q^{33} +(9.28499 + 28.5763i) q^{34} +(66.5037 + 196.092i) q^{35} +(57.1358 - 175.846i) q^{36} +(20.9522 - 13.6065i) q^{37} +(-5.29415 - 101.018i) q^{38} +(-108.303 - 509.527i) q^{39} +(-17.8605 + 186.621i) q^{40} +(-201.982 + 65.6279i) q^{41} +(121.673 + 97.8246i) q^{42} +(-370.819 - 370.819i) q^{43} +(-66.6279 + 7.00287i) q^{44} +(305.239 + 45.4376i) q^{45} +(15.6883 - 149.265i) q^{46} +(496.395 + 190.548i) q^{47} +(-115.600 - 226.878i) q^{48} +(295.837 - 173.579i) q^{49} +(-142.242 + 10.1121i) q^{50} +(97.3112 - 168.548i) q^{51} +(-396.032 - 257.186i) q^{52} +(-63.1739 + 51.1572i) q^{53} +(4.63787 - 2.06491i) q^{54} +(-29.9447 - 107.735i) q^{55} +(308.734 - 33.5443i) q^{56} +(-463.314 + 463.314i) q^{57} +(-222.305 + 274.524i) q^{58} +(-169.486 + 188.233i) q^{59} +(444.667 - 329.435i) q^{60} +(-388.235 + 349.569i) q^{61} +(-123.609 + 242.596i) q^{62} +(-28.5441 - 510.403i) q^{63} +(-73.9863 - 24.0396i) q^{64} +(313.858 - 722.969i) q^{65} +(-62.6542 - 56.4141i) q^{66} +(-37.4734 + 14.3847i) q^{67} +(-45.6631 - 170.417i) q^{68} +(-786.491 + 571.419i) q^{69} +(64.0561 + 227.367i) q^{70} +(161.686 + 117.471i) q^{71} +(165.867 - 432.098i) q^{72} +(406.467 - 625.904i) q^{73} +(24.6820 - 14.2502i) q^{74} +(665.173 + 640.863i) q^{75} +593.973i q^{76} +(-164.744 + 84.6700i) q^{77} +(-92.9622 - 586.940i) q^{78} +(23.1492 + 51.9940i) q^{79} +(56.7253 - 381.068i) q^{80} +(650.789 + 289.750i) q^{81} +(-234.024 + 62.7066i) q^{82} +(-92.2650 + 582.538i) q^{83} +(-683.398 - 611.009i) q^{84} +(267.886 - 122.270i) q^{85} +(-400.312 - 444.592i) q^{86} +(2284.95 - 119.749i) q^{87} +(-167.475 + 8.77700i) q^{88} +(-247.706 - 275.106i) q^{89} +(345.028 + 69.9887i) q^{90} +(-1278.00 - 266.966i) q^{91} +(-137.862 + 870.427i) q^{92} +(1703.50 - 456.450i) q^{93} +(554.137 + 246.718i) q^{94} +(-977.689 + 164.191i) q^{95} +(-521.327 - 1170.92i) q^{96} +(-18.5125 - 116.883i) q^{97} +(347.393 - 180.085i) q^{98} +276.060i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	1.13924	+	0.0597051i	0.402783	+	0.0211089i	0.252652	−	0.967557i	$-0.418697\pi$
$2$	1.13924	+	0.0597051i	0.402783	+	0.0211089i	0.150131	+	0.988666i	$0.452031\pi$
$3$	−4.65026	−	5.74259i	−0.894943	−	1.10516i	−0.993924	−	0.110073i	$-0.964892\pi$
$3$	−4.65026	−	5.74259i	−0.894943	−	1.10516i	0.0989810	−	0.995089i	$-0.468442\pi$
$4$	−6.66187	−	0.700191i	−0.832734	−	0.0875238i
$5$	−0.689007	−	11.1591i	−0.0616266	−	0.998099i
$5$	−0.689007	−	11.1591i	−0.0616266	−	0.998099i
$6$	−4.95490	−	6.81984i	−0.337139	−	0.464031i
$7$	−17.8723	+	4.85610i	−0.965012	+	0.262205i
$7$	−17.8723	+	4.85610i	−0.965012	+	0.262205i
$8$	−16.5617	−	2.62312i	−0.731933	−	0.115927i
$9$	−5.73883	+	26.9991i	−0.212549	+	0.999965i
$10$	−0.118690	−	12.7540i	−0.00375332	−	0.403318i
$11$	9.78282	−	2.07940i	0.268148	−	0.0569967i	−0.0718751	−	0.997414i	$-0.522898\pi$
$11$	9.78282	−	2.07940i	0.268148	−	0.0569967i	0.340024	+	0.940417i	$0.389565\pi$
$12$	26.9585	+	41.5125i	0.648521	+	0.998634i
$13$	62.8114	+	32.0040i	1.34006	+	0.682793i	0.969287	−	0.245932i	$-0.0790939\pi$
$13$	62.8114	+	32.0040i	1.34006	+	0.682793i	0.370770	+	0.928725i	$0.379094\pi$
$14$	−20.6508	+	4.46520i	−0.394225	+	0.0852411i
$15$	−60.8780	+	55.8493i	−1.04791	+	0.961349i
$16$	33.7063	+	7.16449i	0.526660	+	0.111945i
$17$	9.43880	+	24.5889i	0.134661	+	0.350805i	0.984286	−	0.176583i	$-0.0565045\pi$
$17$	9.43880	+	24.5889i	0.134661	+	0.350805i	−0.849624	+	0.527389i	$0.823171\pi$
$18$	−8.14989	+	30.4158i	−0.106719	+	0.398282i
$19$	−9.26872	−	88.1859i	−0.111915	−	1.06480i	−0.895971	−	0.444112i	$-0.853519\pi$
$19$	−9.26872	−	88.1859i	−0.111915	−	1.06480i	0.784056	−	0.620690i	$-0.213147\pi$
$20$	−3.22342	+	74.8228i	−0.0360389	+	0.836545i
$21$	110.997	+	80.0511i	1.15341	+	0.831837i
$22$	11.2691	−	1.78486i	0.109209	−	0.0172970i
$23$	6.88543	−	131.382i	0.0624222	−	1.19109i	−0.770405	−	0.637554i	$-0.779946\pi$
$23$	6.88543	−	131.382i	0.0624222	−	1.19109i	0.832828	−	0.553533i	$-0.186721\pi$
$24$	61.9529	+	107.306i	0.526920	+	0.912652i
$25$	−124.051	+	15.3774i	−0.992404	+	0.123019i
$26$	69.6465	+	40.2104i	0.525339	+	0.303304i
$27$	3.96513	−	2.02034i	0.0282626	−	0.0144005i
$28$	122.463	−	19.8367i	0.826547	−	0.133885i
$29$	−182.006	+	250.509i	−1.16543	+	1.60408i	−0.476707	+	0.879062i	$0.658170\pi$
$29$	−182.006	+	250.509i	−1.16543	+	1.60408i	−0.688727	+	0.725021i	$0.741830\pi$
$30$	−72.6893	+	59.9911i	−0.442373	+	0.365094i
$31$	−97.0745	+	218.033i	−0.562423	+	1.26322i	0.378813	+	0.925473i	$0.376332\pi$
$31$	−97.0745	+	218.033i	−0.562423	+	1.26322i	−0.941236	+	0.337749i	$0.890334\pi$
$32$	167.546	+	44.8939i	0.925572	+	0.248006i
$33$	−57.4338	−	46.5090i	−0.302968	−	0.245339i
$34$	9.28499	+	28.5763i	0.0468342	+	0.144141i
$35$	66.5037	+	196.092i	0.321177	+	0.947019i
$36$	57.1358	−	175.846i	0.264518	−	0.814102i
$37$	20.9522	−	13.6065i	0.0930953	−	0.0604568i	−0.497252	−	0.867606i	$-0.665658\pi$
$37$	20.9522	−	13.6065i	0.0930953	−	0.0604568i	0.590347	+	0.807149i	$0.298991\pi$
$38$	−5.29415	−	101.018i	−0.0226007	−	0.431246i
$39$	−108.303	−	509.527i	−0.444677	−	2.09204i
$40$	−17.8605	+	186.621i	−0.0705999	+	0.737686i
$41$	−201.982	+	65.6279i	−0.769372	+	0.249984i	−0.667296	−	0.744792i	$-0.732549\pi$
$41$	−201.982	+	65.6279i	−0.769372	+	0.249984i	−0.102076	+	0.994777i	$0.532549\pi$
$42$	121.673	+	97.8246i	0.447014	+	0.359397i
$43$	−370.819	−	370.819i	−1.31510	−	1.31510i	−0.917603	−	0.397497i	$-0.869879\pi$
$43$	−370.819	−	370.819i	−1.31510	−	1.31510i	−0.397497	−	0.917603i	$-0.630121\pi$
$44$	−66.6279	+	7.00287i	−0.228285	+	0.0239937i
$45$	305.239	+	45.4376i	1.01116	+	0.150521i
$46$	15.6883	−	149.265i	0.0502852	−	0.478432i
$47$	496.395	+	190.548i	1.54057	+	0.591368i	0.972764	−	0.231797i	$-0.0744606\pi$
$47$	496.395	+	190.548i	1.54057	+	0.591368i	0.567802	+	0.823165i	$0.307794\pi$
$48$	−115.600	−	226.878i	−0.347613	−	0.682229i
$49$	295.837	−	173.579i	0.862498	−	0.506061i
$50$	−142.242	+	10.1121i	−0.402320	+	0.0286013i
$51$	97.3112	−	168.548i	0.267182	−	0.462773i
$52$	−396.032	−	257.186i	−1.05615	−	0.685872i
$53$	−63.1739	+	51.1572i	−0.163728	+	0.132585i	−0.707683	−	0.706530i	$-0.750260\pi$
$53$	−63.1739	+	51.1572i	−0.163728	+	0.132585i	0.543955	+	0.839114i	$0.316926\pi$
$54$	4.63787	−	2.06491i	0.0116877	−	0.00520369i
$55$	−29.9447	−	107.735i	−0.0734135	−	0.264126i
$56$	308.734	−	33.5443i	0.736721	−	0.0800453i
$57$	−463.314	+	463.314i	−1.07662	+	1.07662i
$58$	−222.305	+	274.524i	−0.503277	+	0.621496i
$59$	−169.486	+	188.233i	−0.373986	+	0.415354i	−0.900530	−	0.434795i	$-0.856821\pi$
$59$	−169.486	+	188.233i	−0.373986	+	0.415354i	0.526544	+	0.850148i	$0.323488\pi$
$60$	444.667	−	329.435i	0.956770	−	0.708831i
$61$	−388.235	+	349.569i	−0.814892	+	0.733732i	−0.967040	−	0.254626i	$-0.918048\pi$
$61$	−388.235	+	349.569i	−0.814892	+	0.733732i	0.152148	+	0.988358i	$0.451381\pi$
$62$	−123.609	+	242.596i	−0.253199	+	0.496932i
$63$	−28.5441	−	510.403i	−0.0570829	−	1.02071i
$64$	−73.9863	−	24.0396i	−0.144504	−	0.0469523i
$65$	313.858	−	722.969i	0.598912	−	1.37959i
$66$	−62.6542	−	56.4141i	−0.116851	−	0.105213i
$67$	−37.4734	+	14.3847i	−0.0683300	+	0.0262294i	−0.392293	−	0.919840i	$-0.628318\pi$
$67$	−37.4734	+	14.3847i	−0.0683300	+	0.0262294i	0.323963	+	0.946070i	$0.394985\pi$
$68$	−45.6631	−	170.417i	−0.0814333	−	0.303913i
$69$	−786.491	+	571.419i	−1.37221	+	0.996968i
$70$	64.0561	+	227.367i	0.109374	+	0.388223i
$71$	161.686	+	117.471i	0.270261	+	0.196356i	0.714658	−	0.699474i	$-0.246582\pi$
$71$	161.686	+	117.471i	0.270261	+	0.196356i	−0.444397	+	0.895830i	$0.646582\pi$
$72$	165.867	−	432.098i	0.271495	−	0.707267i
$73$	406.467	−	625.904i	0.651690	−	1.00351i	−0.346173	−	0.938171i	$-0.612519\pi$
$73$	406.467	−	625.904i	0.651690	−	1.00351i	0.997863	−	0.0653438i	$-0.0208144\pi$
$74$	24.6820	−	14.2502i	0.0387734	−	0.0223858i
$75$	665.173	+	640.863i	1.02410	+	0.986673i
$76$			593.973i			0.896492i
$77$	−164.744	+	84.6700i	−0.243822	+	0.125312i
$78$	−92.9622	−	586.940i	−0.134947	−	0.852024i
$79$	23.1492	+	51.9940i	0.0329683	+	0.0740479i	0.929279	−	0.369379i	$-0.120429\pi$
$79$	23.1492	+	51.9940i	0.0329683	+	0.0740479i	−0.896311	+	0.443426i	$0.853763\pi$
$80$	56.7253	−	381.068i	0.0792760	−	0.532558i
$81$	650.789	+	289.750i	0.892714	+	0.397462i
$82$	−234.024	+	62.7066i	−0.315167	+	0.0844487i
$83$	−92.2650	+	582.538i	−0.122017	+	0.770384i	0.848472	+	0.529240i	$0.177523\pi$
$83$	−92.2650	+	582.538i	−0.122017	+	0.770384i	−0.970489	+	0.241144i	$0.922477\pi$
$84$	−683.398	−	611.009i	−0.887677	−	0.793649i
$85$	267.886	−	122.270i	0.341840	−	0.156024i
$86$	−400.312	−	444.592i	−0.501939	−	0.557460i
$87$	2284.95	−	119.749i	2.81577	−	0.147568i
$88$	−167.475	+	8.77700i	−0.202874	+	0.0106322i
$89$	−247.706	−	275.106i	−0.295020	−	0.327653i	0.577352	−	0.816495i	$-0.304086\pi$
$89$	−247.706	−	275.106i	−0.295020	−	0.327653i	−0.872372	+	0.488842i	$0.837419\pi$
$90$	345.028	+	69.9887i	0.404102	+	0.0819717i
$91$	−1278.00	−	266.966i	−1.47220	−	0.307535i
$92$	−137.862	+	870.427i	−0.156230	+	0.986395i
$93$	1703.50	−	456.450i	1.89940	−	0.508943i
$94$	554.137	+	246.718i	0.608030	+	0.270712i
$95$	−977.689	+	164.191i	−1.05588	+	0.177323i
$96$	−521.327	−	1170.92i	−0.554247	−	1.24486i
$97$	−18.5125	−	116.883i	−0.0193779	−	0.122347i	0.976103	−	0.217308i	$-0.0697275\pi$
$97$	−18.5125	−	116.883i	−0.0193779	−	0.122347i	−0.995481	+	0.0949605i	$0.969728\pi$
$98$	347.393	−	180.085i	0.358081	−	0.185626i
$99$			276.060i			0.280254i
$100$	837.176	−	15.5830i	0.837176	−	0.0155830i
$101$	−1094.65	+	631.994i	−1.07843	+	0.622632i	−0.930472	−	0.366362i	$-0.880603\pi$
$101$	−1094.65	+	631.994i	−1.07843	+	0.622632i	−0.147957	+	0.988994i	$0.547270\pi$
$102$	120.924	−	186.207i	0.117385	−	0.180757i
$103$	165.060	−	429.995i	0.157901	−	0.411346i	−0.831693	−	0.555236i	$-0.812628\pi$
$103$	165.060	−	429.995i	0.157901	−	0.411346i	0.989594	+	0.143890i	$0.0459612\pi$
$104$	−956.316	−	694.804i	−0.901678	−	0.655107i
$105$	816.819	−	1293.78i	0.759175	−	1.20248i
$106$	−75.0247	+	54.5086i	−0.0687457	+	0.0499466i
$107$	−261.317	−	975.249i	−0.236098	−	0.881130i	−0.977651	−	0.210235i	$-0.932577\pi$
$107$	−261.317	−	975.249i	−0.236098	−	0.881130i	0.741553	−	0.670894i	$-0.234090\pi$
$108$	−27.8298	+	10.6829i	−0.0247956	+	0.00951814i
$109$	924.260	+	832.207i	0.812184	+	0.731294i	0.966483	−	0.256730i	$-0.0826453\pi$
$109$	924.260	+	832.207i	0.812184	+	0.731294i	−0.154299	+	0.988024i	$0.549312\pi$
$110$	−27.6819	−	124.524i	−0.0239942	−	0.107935i
$111$	−175.570	−	57.0462i	−0.150130	−	0.0487800i
$112$	−637.199	+	35.6351i	−0.537586	+	0.0300643i
$113$	−333.293	+	654.125i	−0.277465	+	0.544556i	−0.987118	−	0.159996i	$-0.948852\pi$
$113$	−333.293	+	654.125i	−0.277465	+	0.544556i	0.709652	+	0.704552i	$0.248852\pi$
$114$	−555.488	+	500.164i	−0.456371	+	0.410918i
$115$	−1470.85	+	13.6878i	−1.19267	+	0.0110991i
$116$	1387.90	−	1541.42i	1.11089	−	1.23377i
$117$	−1224.54	+	1512.18i	−0.967598	+	1.19488i
$118$	−204.324	+	204.324i	−0.159403	+	0.159403i
$119$	−288.099	−	393.624i	−0.221933	−	0.303222i
$120$	1154.75	−	765.272i	0.878445	−	0.582162i
$121$	−1124.55	+	500.682i	−0.844891	+	0.376169i
$122$	−463.165	+	375.063i	−0.343713	+	0.278333i
$123$	1316.14	+	854.712i	0.964817	+	0.626560i
$124$	799.363	−	1384.54i	0.578910	−	1.00270i
$125$	257.069	+	1373.70i	0.183944	+	0.982937i
$126$	−2.04496	−	583.177i	−0.00144587	−	0.412329i
$127$	331.358	+	650.326i	0.231522	+	0.454387i	0.977315	−	0.211791i	$-0.0679295\pi$
$127$	331.358	+	650.326i	0.231522	+	0.454387i	−0.745794	+	0.666177i	$0.767929\pi$
$128$	−1378.34	−	529.095i	−0.951791	−	0.365358i
$129$	−405.057	+	3853.86i	−0.276460	+	2.63034i
$130$	400.725	−	804.897i	0.270353	−	0.543032i
$131$	−1699.07	+	178.580i	−1.13320	+	0.119104i	−0.652503	−	0.757786i	$-0.726281\pi$
$131$	−1699.07	+	178.580i	−1.13320	+	0.119104i	−0.480692	+	0.876889i	$0.659615\pi$
$132$	350.051	+	350.051i	0.230819	+	0.230819i
$133$	593.892	+	1531.07i	0.387196	+	0.998203i
$134$	−43.5501	+	14.1503i	−0.0280758	+	0.00912238i
$135$	−25.2771	−	42.8553i	−0.0161149	−	0.0273214i
$136$	−91.8233	−	431.995i	−0.0578954	−	0.272377i
$137$	−45.5432	−	869.017i	−0.0284016	−	0.541935i	−0.975365	−	0.220595i	$-0.929200\pi$
$137$	−45.5432	−	869.017i	−0.0284016	−	0.541935i	0.946964	−	0.321340i	$-0.104133\pi$
$138$	−930.120	+	604.027i	−0.573747	+	0.372595i
$139$	42.8019	−	131.731i	0.0261181	−	0.0803831i	−0.937148	−	0.348932i	$-0.886544\pi$
$139$	42.8019	−	131.731i	0.0261181	−	0.0803831i	0.963266	+	0.268549i	$0.0865442\pi$
$140$	−305.737	−	1352.91i	−0.184568	−	0.816725i
$141$	−1214.12	−	3736.69i	−0.725161	−	2.23182i
$142$	177.185	+	143.482i	0.104712	+	0.0847938i
$143$	681.022	+	182.479i	0.398251	+	0.106711i
$144$	−386.869	+	868.922i	−0.223882	+	0.502848i
$145$	2920.86	+	1858.41i	1.67286	+	1.06436i
$146$	500.434	−	688.788i	0.283673	−	0.390442i
$147$	−2372.51	−	891.682i	−1.33117	−	0.500304i
$148$	−149.108	+	75.9744i	−0.0828150	+	0.0421964i
$149$	−648.059	−	374.157i	−0.356316	−	0.205719i	0.311148	−	0.950362i	$-0.399287\pi$
$149$	−648.059	−	374.157i	−0.356316	−	0.205719i	−0.667464	+	0.744642i	$0.732620\pi$
$150$	719.530	+	769.812i	0.391662	+	0.419032i
$151$	−1687.83	−	2923.40i	−0.909625	−	1.57552i	−0.814586	−	0.580043i	$-0.803036\pi$
$151$	−1687.83	−	2923.40i	−0.909625	−	1.57552i	−0.0950388	−	0.995474i	$-0.530298\pi$
$152$	−77.8165	+	1484.83i	−0.0415247	+	0.792338i
$153$	−718.045	+	113.727i	−0.379415	+	0.0600935i
$154$	−192.738	+	86.6235i	−0.100852	+	0.0453268i
$155$	2499.93	+	933.037i	1.29548	+	0.483506i
$156$	364.736	+	3470.23i	0.187194	+	1.78103i
$157$	−896.146	+	3344.46i	−0.455543	+	1.70011i	0.230944	+	0.972967i	$0.425818\pi$
$157$	−896.146	+	3344.46i	−0.455543	+	1.70011i	−0.686487	+	0.727142i	$0.740848\pi$
$158$	23.2683	+	60.6159i	0.0117160	+	0.0305211i
$159$	587.550	+	124.888i	0.293055	+	0.0622907i
$160$	385.535	−	1900.60i	0.190495	−	0.939097i
$161$	514.944	+	2381.53i	0.252070	+	1.16578i
$162$	724.106	+	368.950i	0.351180	+	0.178935i
$163$	360.756	+	555.515i	0.173353	+	0.266941i	0.914659	−	0.404227i	$-0.132460\pi$
$163$	360.756	+	555.515i	0.173353	+	0.266941i	−0.741305	+	0.671168i	$0.765793\pi$
$164$	1391.53	−	295.779i	0.662562	−	0.140832i
$165$	−479.426	+	672.954i	−0.226201	+	0.317512i
$166$	−139.893	+	658.143i	−0.0654083	+	0.307722i
$167$	1174.15	+	185.967i	0.544062	+	0.0861709i	0.422415	−	0.906403i	$-0.361183\pi$
$167$	1174.15	+	185.967i	0.544062	+	0.0861709i	0.121647	+	0.992573i	$0.461183\pi$
$168$	−1628.33	−	1616.95i	−0.747786	−	0.742560i
$169$	1629.65	+	2243.02i	0.741761	+	1.02095i
$170$	312.488	−	123.301i	0.140981	−	0.0556281i
$171$	2434.13	+	255.837i	1.08855	+	0.114412i
$172$	2210.70	+	2729.99i	0.980026	+	1.21023i
$173$	−5.15363	−	0.270090i	−0.00226488	−	0.000118697i	0.0512035	−	0.998688i	$-0.483694\pi$
$173$	−5.15363	−	0.270090i	−0.00226488	−	0.000118697i	−0.0534684	+	0.998570i	$0.517028\pi$
$174$	2610.25			1.13726
$175$	2142.39	−	877.230i	0.925426	−	0.378928i
$176$	344.640			0.147604
$177$	1869.10	+	97.9553i	0.793729	+	0.0415976i
$178$	−265.772	−	328.201i	−0.111913	−	0.138201i
$179$	−2420.14	−	254.367i	−1.01056	−	0.106214i	−0.415247	−	0.909709i	$-0.636305\pi$
$179$	−2420.14	−	254.367i	−1.01056	−	0.106214i	−0.595312	+	0.803495i	$0.702972\pi$
$180$	−2001.65	−	516.425i	−0.828856	−	0.213845i
$181$	−1240.52	−	1707.43i	−0.509430	−	0.701171i	0.474393	−	0.880313i	$-0.342668\pi$
$181$	−1240.52	−	1707.43i	−0.509430	−	0.701171i	−0.983823	+	0.179143i	$0.942668\pi$
$182$	−1440.01	−	380.442i	−0.586486	−	0.154946i
$183$	3812.82	+	603.892i	1.54017	+	0.243940i
$184$	−458.665	+	2157.85i	−0.183768	+	0.864559i
$185$	−166.273	−	224.433i	−0.0660790	−	0.0891926i
$186$	1967.95	−	418.300i	0.775789	−	0.164899i
$187$	143.468	+	220.922i	0.0561040	+	0.0863926i
$188$	−3173.50	−	1616.98i	−1.23112	−	0.627288i
$189$	−61.0550	+	55.3631i	−0.0234979	+	0.0213073i
$190$	−1123.63	+	128.680i	−0.429034	+	0.0491340i
$191$	−3160.59	−	671.804i	−1.19734	−	0.254503i	−0.434249	−	0.900793i	$-0.642986\pi$
$191$	−3160.59	−	671.804i	−1.19734	−	0.254503i	−0.763092	+	0.646290i	$0.776320\pi$
$192$	206.006	+	536.663i	0.0774332	+	0.201721i
$193$	372.468	−	1390.07i	0.138916	−	0.518442i	−0.861035	−	0.508546i	$-0.830183\pi$
$193$	372.468	−	1390.07i	0.138916	−	0.518442i	0.999951	−	0.00989608i	$-0.00315007\pi$
$194$	−14.1117	−	134.263i	−0.00522246	−	0.0496884i
$195$	−5611.23	+	1559.63i	−2.06066	+	0.572757i
$196$	−2092.36	+	949.218i	−0.762523	+	0.345925i
$197$	−2943.37	+	466.183i	−1.06450	+	0.168600i	−0.664026	−	0.747709i	$-0.731154\pi$
$197$	−2943.37	+	466.183i	−1.06450	+	0.168600i	−0.400472	+	0.916309i	$0.631154\pi$
$198$	−16.4822	+	314.500i	−0.00591586	+	0.112881i
$199$	457.690	+	792.742i	0.163039	+	0.282392i	0.935957	−	0.352114i	$-0.114537\pi$
$199$	457.690	+	792.742i	0.163039	+	0.282392i	−0.772918	+	0.634506i	$0.781204\pi$
$200$	2094.83	+	70.7236i	0.740634	+	0.0250046i
$201$	256.867	+	148.302i	0.0901391	+	0.0520419i
$202$	−1284.80	+	654.638i	−0.447516	+	0.228021i
$203$	2036.36	−	5361.01i	0.704061	−	1.85354i
$204$	−766.290	+	1054.71i	−0.262995	+	0.361982i
$205$	871.514	+	2208.72i	0.296923	+	0.752504i
$206$	213.716	−	480.013i	0.0722829	−	0.162350i
$207$	3507.67	+	939.878i	1.17778	+	0.315585i
$208$	1887.84	+	1528.75i	0.629319	+	0.509613i
$209$	−274.048	−	843.434i	−0.0907001	−	0.279146i
$210$	1007.80	−	1425.16i	0.331166	−	0.468313i
$211$	63.2131	−	194.550i	0.0206245	−	0.0634757i	−0.940215	−	0.340583i	$-0.889376\pi$
$211$	63.2131	−	194.550i	0.0206245	−	0.0634757i	0.960839	+	0.277107i	$0.0893757\pi$
$212$	456.676	−	296.569i	0.147946	−	0.0960775i
$213$	−77.2892	−	1474.77i	−0.0248628	−	0.474410i
$214$	−239.476	−	1126.65i	−0.0764964	−	0.359887i
$215$	−3882.50	+	4393.50i	−1.23156	+	1.39365i
$216$	−70.9691	+	23.0593i	−0.0223557	+	0.00726382i
$217$	676.154	−	4368.15i	0.211522	−	1.36649i
$218$	1003.27	+	1003.27i	0.311697	+	0.311697i
$219$	−5484.49	+	576.443i	−1.69227	+	0.177865i
$220$	124.053	+	738.681i	0.0380165	+	0.226372i
$221$	−194.079	+	1846.54i	−0.0590733	+	0.562045i
$222$	−196.611	−	75.4718i	−0.0594399	−	0.0228168i
$223$	−1840.97	−	3613.11i	−0.552828	−	1.08499i	−0.983234	−	0.182351i	$-0.941629\pi$
$223$	−1840.97	−	3613.11i	−0.552828	−	1.08499i	0.430406	−	0.902636i	$-0.358371\pi$
$224$	−3212.45	+	11.2647i	−0.958217	+	0.00336007i
$225$	296.730	−	3437.50i	0.0879200	−	1.01852i
$226$	−418.756	+	725.307i	−0.123253	+	0.213481i
$227$	−399.239	−	259.269i	−0.116733	−	0.0758074i	0.484952	−	0.874541i	$-0.338837\pi$
$227$	−399.239	−	259.269i	−0.116733	−	0.0758074i	−0.601685	+	0.798733i	$0.705504\pi$
$228$	3410.94	−	2762.13i	0.990769	−	0.802309i
$229$	225.721	−	100.498i	0.0651358	−	0.0290003i	−0.373910	−	0.927465i	$-0.621983\pi$
$229$	225.721	−	100.498i	0.0651358	−	0.0290003i	0.439046	+	0.898465i	$0.355317\pi$
$230$	−1676.47	−	72.2232i	−0.480621	−	0.0207055i
$231$	1252.33	+	552.317i	0.356697	+	0.157315i
$232$	3671.45	−	3671.45i	1.03898	−	1.03898i
$233$	−1851.18	+	2286.02i	−0.520494	+	0.642756i	−0.967829	−	0.251610i	$-0.919040\pi$
$233$	−1851.18	+	2286.02i	−0.520494	+	0.642756i	0.447335	+	0.894366i	$0.352373\pi$
$234$	−1485.33	+	1649.63i	−0.414954	+	0.460853i
$235$	1784.32	−	5670.60i	0.495304	−	1.57408i
$236$	1260.89	−	1135.31i	0.347784	−	0.313146i
$237$	190.930	−	374.722i	0.0523302	−	0.102704i
$238$	−304.713	−	465.634i	−0.0829899	−	0.126818i
$239$	−2023.02	−	657.318i	−0.547523	−	0.177901i	0.0221765	−	0.999754i	$-0.492940\pi$
$239$	−2023.02	−	657.318i	−0.547523	−	0.177901i	−0.569700	+	0.821853i	$0.692940\pi$
$240$	−2452.10	+	1446.31i	−0.659510	+	0.388996i
$241$	4112.40	+	3702.82i	1.09918	+	0.989709i	0.999986	−	0.00535872i	$-0.00170574\pi$
$241$	4112.40	+	3702.82i	1.09918	+	0.989709i	0.0991976	+	0.995068i	$0.468372\pi$
$242$	−1311.03	+	503.256i	−0.348248	+	0.133680i
$243$	−1393.52	−	5200.68i	−0.367878	−	1.37294i
$244$	2831.14	−	2056.94i	0.742807	−	0.539681i
$245$	−2140.82	−	3181.67i	−0.558252	−	0.829671i
$246$	1448.37	+	1052.30i	0.375386	+	0.272734i
$247$	2240.12	−	5835.72i	0.577067	−	1.50331i
$248$	2179.65	−	3356.37i	0.558097	−	0.859394i
$249$	3774.33	−	2179.11i	0.960597	−	0.554601i
$250$	210.847	+	1580.32i	0.0533406	+	0.399793i
$251$		−	3217.70i		−	0.809162i	−0.914502	−	0.404581i	$-0.867417\pi$
$251$		−	3217.70i		−	0.809162i	0.914502	−	0.404581i	$-0.132583\pi$
$252$	−167.222	+	3420.23i	−0.0418017	+	0.854976i
$253$	−205.837	−	1299.60i	−0.0511496	−	0.322946i
$254$	338.669	+	760.662i	0.0836612	+	0.187906i
$255$	−1947.89	−	969.774i	−0.478359	−	0.238155i
$256$	−970.127	−	431.929i	−0.236848	−	0.105451i
$257$	6001.39	−	1608.07i	1.45664	−	0.390306i	0.558312	−	0.829631i	$-0.311449\pi$
$257$	6001.39	−	1608.07i	1.45664	−	0.390306i	0.898328	+	0.439325i	$0.144782\pi$
$258$	−691.553	+	4366.30i	−0.166877	+	1.05362i
$259$	−308.390	+	344.926i	−0.0739861	+	0.0827516i
$260$	−2597.10	+	4596.56i	−0.619481	+	1.09641i
$261$	−5719.02	−	6351.61i	−1.35632	−	1.50634i
$262$	−1946.32	+	102.002i	−0.458946	+	0.0240523i
$263$	−6815.90	+	357.206i	−1.59805	+	0.0837501i	−0.830417	−	0.557143i	$-0.811898\pi$
$263$	−6815.90	+	357.206i	−1.59805	+	0.0837501i	−0.767630	+	0.640893i	$0.778564\pi$
$264$	829.206	+	920.926i	0.193311	+	0.214694i
$265$	614.395	+	669.715i	0.142423	+	0.155246i
$266$	585.174	+	1779.72i	0.134885	+	0.410232i
$267$	−427.921	+	2701.79i	−0.0980837	+	0.619276i
$268$	259.715	−	69.5904i	0.0591964	−	0.0158616i
$269$	1591.63	+	708.641i	0.360757	+	0.160619i	0.579108	−	0.815251i	$-0.303401\pi$
$269$	1591.63	+	708.641i	0.360757	+	0.160619i	−0.218351	+	0.975870i	$0.570068\pi$
$270$	−26.2381	−	50.3317i	−0.00591407	−	0.0113448i
$271$	−1005.56	−	2258.53i	−0.225401	−	0.506258i	0.765076	−	0.643940i	$-0.222701\pi$
$271$	−1005.56	−	2258.53i	−0.225401	−	0.506258i	−0.990476	+	0.137682i	$0.956035\pi$
$272$	141.980	+	896.424i	0.0316499	+	0.199830i
$273$	4409.94	+	8580.47i	0.977661	+	1.90225i
$274$		−	992.739i		−	0.218882i
$275$	−1181.59	+	408.385i	−0.259100	+	0.0895511i
$276$	5639.60	−	3256.03i	1.22994	−	0.710108i
$277$	3357.03	−	5169.37i	0.728174	−	1.12129i	−0.259649	−	0.965703i	$-0.583607\pi$
$277$	3357.03	−	5169.37i	0.728174	−	1.12129i	0.987822	−	0.155586i	$-0.0497265\pi$
$278$	56.6267	−	147.518i	0.0122167	−	0.0318256i
$279$	−5329.59	−	3872.18i	−1.14364	−	0.830900i
$280$	−587.043	−	3422.08i	−0.125295	−	0.730387i
$281$	−557.649	+	405.156i	−0.118386	+	0.0860127i	−0.645403	−	0.763842i	$-0.723311\pi$
$281$	−557.649	+	405.156i	−0.118386	+	0.0860127i	0.527017	+	0.849855i	$0.323311\pi$
$282$	−1160.08	−	4329.48i	−0.244971	−	0.914244i
$283$	−1289.34	+	494.930i	−0.270824	+	0.103960i	−0.489990	−	0.871728i	$-0.663000\pi$
$283$	−1289.34	+	494.930i	−0.270824	+	0.103960i	0.219166	+	0.975688i	$0.429666\pi$
$284$	−994.876	−	895.790i	−0.207870	−	0.187167i
$285$	5489.39	+	4850.93i	1.14092	+	1.00823i
$286$	764.953	+	248.548i	0.158156	+	0.0513880i
$287$	3291.18	−	2153.76i	0.676907	−	0.442971i
$288$	−2173.61	+	4265.96i	−0.444727	+	0.872827i
$289$	3135.55	−	2823.26i	0.638214	−	0.574651i
$290$	3216.61	+	2291.57i	0.651330	+	0.464020i
$291$	−585.124	+	649.847i	−0.117871	+	0.130910i
$292$	−3146.08	+	3885.09i	−0.630516	+	0.778622i
$293$	662.843	−	662.843i	0.132163	−	0.132163i	−0.637931	−	0.770094i	$-0.720209\pi$
$293$	662.843	−	662.843i	0.132163	−	0.132163i	0.770094	+	0.637931i	$0.220209\pi$
$294$	−2649.62	−	1157.49i	−0.525609	−	0.229613i
$295$	2217.29	+	1761.61i	0.437612	+	0.347678i
$296$	−382.697	+	170.388i	−0.0751481	+	0.0334581i
$297$	34.5891	−	28.0097i	0.00675779	−	0.00547235i
$298$	−715.957	−	464.948i	−0.139175	−	0.0903816i
$299$	4637.23	−	8031.91i	0.896915	−	1.55350i
$300$	−3982.57	−	4735.09i	−0.766446	−	0.911269i
$301$	8428.11	+	4826.64i	1.61391	+	0.924263i
$302$	−1748.30	−	3431.23i	−0.333124	−	0.653792i
$303$	8719.67	+	3347.17i	1.65324	+	0.634620i
$304$	319.393	−	3038.82i	0.0602581	−	0.573317i
$305$	4168.36	+	4091.50i	0.782557	+	0.768126i
$306$	−824.817	+	86.6918i	−0.154090	+	0.0161956i
$307$	5357.75	+	5357.75i	0.996036	+	0.996036i	0.999992	−	0.00395617i	$-0.00125929\pi$
$307$	5357.75	+	5357.75i	0.996036	+	0.996036i	−0.00395617	+	0.999992i	$0.501259\pi$
$308$	1156.79	−	448.709i	0.214006	−	0.0830115i
$309$	−3236.85	+	1051.72i	−0.595916	+	0.193625i
$310$	2792.32	+	1212.21i	0.511591	+	0.222094i
$311$	830.273	+	3906.13i	0.151384	+	0.712206i	0.986715	+	0.162459i	$0.0519426\pi$
$311$	830.273	+	3906.13i	0.151384	+	0.712206i	−0.835331	+	0.549747i	$0.814724\pi$
$312$	457.140	+	8722.75i	0.0829502	+	1.58278i
$313$	−6304.06	+	4093.90i	−1.13842	+	0.739301i	−0.969200	−	0.246277i	$-0.920793\pi$
$313$	−6304.06	+	4093.90i	−1.13842	+	0.739301i	−0.169224	+	0.985578i	$0.554126\pi$
$314$	−1220.61	+	3756.64i	−0.219372	+	0.675158i
$315$	−5675.97	+	670.198i	−1.01525	+	0.119877i
$316$	−117.811	−	362.586i	−0.0209728	−	0.0645477i
$317$	−8143.35	−	6594.36i	−1.44283	−	1.16838i	−0.955437	−	0.295194i	$-0.904616\pi$
$317$	−8143.35	−	6594.36i	−1.44283	−	1.16838i	−0.487390	−	0.873184i	$-0.662051\pi$
$318$	661.905	+	177.357i	0.116723	+	0.0312757i
$319$	−1259.62	+	2829.15i	−0.221082	+	0.496558i
$320$	−217.283	+	842.183i	−0.0379578	+	0.147123i
$321$	−4385.26	+	6035.80i	−0.762497	+	1.04949i
$322$	444.457	+	2743.88i	0.0769211	+	0.474877i
$323$	2080.91	−	1060.28i	0.358467	−	0.182648i
$324$	−4132.59	−	2385.95i	−0.708606	−	0.409114i
$325$	−8283.92	−	3004.24i	−1.41387	−	0.512754i
$326$	377.821	+	654.405i	0.0641888	+	0.111178i
$327$	480.979	−	9177.63i	0.0813401	−	1.55206i
$328$	3517.32	−	557.089i	0.592109	−	0.0937808i
$329$	−9797.02	−	994.988i	−1.64172	−	0.166734i
$330$	−586.360	+	738.033i	−0.0978124	+	0.123113i
$331$	892.806	+	8494.48i	0.148257	+	1.41057i	0.775303	+	0.631589i	$0.217597\pi$
$331$	892.806	+	8494.48i	0.148257	+	1.41057i	−0.627046	+	0.778982i	$0.715736\pi$
$332$	1022.55	−	3816.19i	0.169035	−	0.630845i
$333$	247.123	+	643.777i	0.0406674	+	0.105942i
$334$	1326.53	+	281.964i	0.217320	+	0.0461927i
$335$	186.340	+	408.258i	0.0303905	+	0.0665837i
$336$	3167.78	+	3493.46i	0.514335	+	0.567214i
$337$	−7324.34	−	3731.94i	−1.18392	−	0.603240i	−0.252650	−	0.967558i	$-0.581302\pi$
$337$	−7324.34	−	3731.94i	−1.18392	−	0.603240i	−0.931275	+	0.364318i	$0.881302\pi$
$338$	1722.64	+	2652.64i	0.277217	+	0.426877i
$339$	5306.27	−	1127.88i	0.850139	−	0.180703i
$340$	−1870.24	+	626.977i	−0.298317	+	0.100008i
$341$	−496.285	+	2334.84i	−0.0788133	+	0.370787i
$342$	2757.79	+	436.790i	0.436035	+	0.0690612i
$343$	−4444.36	+	4538.86i	−0.699629	+	0.714506i
$344$	5168.70	+	7114.11i	0.810110	+	1.11502i
$345$	6918.41	+	8382.81i	1.07964	+	1.30816i
$346$	−5.85511	−	0.615396i	−0.000909747	−	9.56183e-5i
$347$	−5193.13	−	6412.98i	−0.803406	−	0.992124i	−0.999932	−	0.0116253i	$-0.996299\pi$
$347$	−5193.13	−	6412.98i	−0.803406	−	0.992124i	0.196526	−	0.980499i	$-0.437034\pi$
$348$	−15305.9	−	802.146i	−2.35770	−	0.123562i
$349$	6865.59			1.05303			0.526513	−	0.850167i	$-0.323499\pi$
$349$	6865.59			1.05303			0.526513	+	0.850167i	$0.323499\pi$
$350$	2493.08	−	871.465i	0.380744	−	0.133091i
$351$	313.714			0.0477061
$352$	1732.43	+	90.7928i	0.262326	+	0.0137479i
$353$	−1468.83	−	1813.85i	−0.221467	−	0.273489i	0.654287	−	0.756246i	$-0.272969\pi$
$353$	−1468.83	−	1813.85i	−0.221467	−	0.273489i	−0.875754	+	0.482757i	$0.839635\pi$
$354$	2123.51	+	223.189i	0.318822	+	0.0335096i
$355$	1199.47	−	1885.20i	0.179328	−	0.281848i
$356$	1457.56	+	2006.16i	0.216996	+	0.298669i
$357$	−920.688	+	3484.89i	−0.136493	+	0.516638i
$358$	−2741.94	−	434.281i	−0.404794	−	0.0641130i
$359$	970.859	−	4567.53i	0.142730	−	0.671491i	−0.847356	−	0.531026i	$-0.821807\pi$
$359$	970.859	−	4567.53i	0.142730	−	0.671491i	0.990086	−	0.140465i	$-0.0448598\pi$
$360$	−4936.11	−	1553.21i	−0.722654	−	0.227392i
$361$	−981.736	+	208.674i	−0.143131	+	0.0304234i
$362$	−1311.31	−	2019.23i	−0.190389	−	0.293173i
$363$	8104.65	+	4129.53i	1.17186	+	0.597091i
$364$	8326.92	+	2673.34i	1.19904	+	0.384947i
$365$	−7264.58	−	4104.55i	−1.04177	−	0.588608i
$366$	4307.67	+	915.624i	0.615206	+	0.130766i
$367$	2354.09	+	6132.61i	0.334830	+	0.872261i	0.992862	+	0.119271i	$0.0380558\pi$
$367$	2354.09	+	6132.61i	0.334830	+	0.872261i	−0.658032	+	0.752990i	$0.728611\pi$
$368$	1173.37	−	4379.06i	0.166212	−	0.620310i
$369$	−612.752	−	5829.95i	−0.0864461	−	0.822480i
$370$	−176.025	−	265.611i	−0.0247327	−	0.0373201i
$371$	880.637	−	1221.07i	0.123236	−	0.170876i
$372$	−11668.1	+	1848.04i	−1.62624	+	0.257571i
$373$	269.060	−	5133.97i	0.0373496	−	0.712673i	−0.914216	−	0.405227i	$-0.867192\pi$
$373$	269.060	−	5133.97i	0.0373496	−	0.712673i	0.951566	−	0.307446i	$-0.0994743\pi$
$374$	150.255	+	260.249i	0.0207741	+	0.0359817i
$375$	6693.13	−	7864.28i	0.921685	−	1.08296i
$376$	−7721.33	−	4457.91i	−1.05904	−	0.611434i
$377$	−19449.3	+	9909.92i	−2.65701	+	1.35381i
$378$	−72.8619	+	59.4266i	−0.00991431	+	0.00808618i
$379$	216.524	−	298.019i	0.0293458	−	0.0403911i	−0.794092	−	0.607798i	$-0.792053\pi$
$379$	216.524	−	298.019i	0.0293458	−	0.0403911i	0.823438	+	0.567407i	$0.192053\pi$
$380$	6628.20	−	409.251i	0.894788	−	0.0552478i
$381$	2193.66	−	4927.03i	0.294972	−	0.662519i
$382$	−3560.56	−	954.050i	−0.476896	−	0.127784i
$383$	4103.46	+	3322.92i	0.547460	+	0.443324i	0.862721	−	0.505681i	$-0.168759\pi$
$383$	4103.46	+	3322.92i	0.547460	+	0.443324i	−0.315261	+	0.949005i	$0.602092\pi$
$384$	3371.26	+	10375.7i	0.448018	+	1.37886i
$385$	1058.35	+	1780.05i	0.140100	+	0.235636i
$386$	507.325	−	1561.38i	0.0668967	−	0.205887i
$387$	12139.8	−	7883.69i	1.59458	−	1.03553i
$388$	41.4872	+	791.623i	0.00542833	+	0.103579i
$389$	1921.84	+	9041.56i	0.250492	+	1.17847i	0.905998	+	0.423281i	$0.139122\pi$
$389$	1921.84	+	9041.56i	0.250492	+	1.17847i	−0.655506	+	0.755190i	$0.727545\pi$
$390$	−6485.67	+	1441.78i	−0.842089	+	0.187198i
$391$	3295.53	−	1070.78i	0.426245	−	0.138495i
$392$	−5354.89	+	2098.76i	−0.689956	+	0.270416i
$393$	8926.63	+	8926.63i	1.14577	+	1.14577i
$394$	−3381.04	+	355.361i	−0.432320	+	0.0454387i
$395$	564.256	−	294.149i	0.0718754	−	0.0374689i
$396$	193.295	−	1839.08i	0.0245289	−	0.233377i
$397$	4388.28	+	1684.50i	0.554764	+	0.212954i	0.619567	−	0.784944i	$-0.287308\pi$
$397$	4388.28	+	1684.50i	0.554764	+	0.212954i	−0.0648025	+	0.997898i	$0.520642\pi$
$398$	474.089	+	930.451i	0.0597083	+	0.117184i
$399$	6030.58	−	10530.4i	0.756658	−	1.32125i
$400$	−4291.45	−	370.445i	−0.536431	−	0.0463056i
$401$	−4067.26	+	7044.70i	−0.506507	+	0.877296i	0.493465	+	0.869766i	$0.335730\pi$
$401$	−4067.26	+	7044.70i	−0.506507	+	0.877296i	−0.999972	+	0.00753011i	$0.997603\pi$
$402$	283.779	+	184.288i	0.0352079	+	0.0228643i
$403$	−13075.3	+	10588.2i	−1.61620	+	1.30877i
$404$	7734.91	−	3443.80i	0.952540	−	0.424098i
$405$	2784.95	−	7461.85i	0.341691	−	0.915511i
$406$	2639.98	−	5985.90i	0.322710	−	0.731713i
$407$	176.679	−	176.679i	0.0215175	−	0.0215175i
$408$	−2053.77	+	2536.19i	−0.249207	+	0.307745i
$409$	4431.14	−	4921.28i	0.535711	−	0.594967i	−0.413150	−	0.910663i	$-0.635571\pi$
$409$	4431.14	−	4921.28i	0.535711	−	0.594967i	0.948860	+	0.315696i	$0.102238\pi$
$410$	860.993	+	2568.29i	0.103711	+	0.309363i
$411$	−4778.62	+	4302.69i	−0.573508	+	0.516389i
$412$	−1400.68	+	2749.00i	−0.167492	+	0.328722i
$413$	2115.02	−	4187.19i	0.251994	−	0.498882i
$414$	3939.97	+	1280.17i	0.467727	+	0.151974i
$415$	6564.17	+	628.220i	0.776439	+	0.0743087i
$416$	9087.04	+	8182.01i	1.07098	+	0.964317i
$417$	−955.515	+	366.788i	−0.112211	+	0.0430736i
$418$	−261.850	−	977.237i	−0.0306399	−	0.114350i
$419$	5657.30	−	4110.27i	0.659612	−	0.479236i	−0.206920	−	0.978358i	$-0.566344\pi$
$419$	5657.30	−	4110.27i	0.659612	−	0.479236i	0.866532	+	0.499122i	$0.166344\pi$
$420$	−6347.44	+	8047.09i	−0.737436	+	0.934900i
$421$	3463.98	+	2516.73i	0.401007	+	0.291349i	0.769951	−	0.638103i	$-0.220281\pi$
$421$	3463.98	+	2516.73i	0.401007	+	0.291349i	−0.368944	+	0.929452i	$0.620281\pi$
$422$	83.6306	−	217.865i	0.00964709	−	0.0251315i
$423$	−7993.34	+	12308.7i	−0.918794	+	1.41482i
$424$	1180.46	−	681.540i	0.135208	−	0.0780625i
$425$	−1549.00	−	2905.12i	−0.176794	−	0.331575i
$426$		−	1684.73i		−	0.191609i
$427$	5241.11	−	8132.89i	0.593993	−	0.921729i
$428$	1058.00	+	6679.95i	0.119487	+	0.754410i
$429$	−2119.02	−	4759.41i	−0.238479	−	0.535632i
$430$	−4685.42	+	4773.45i	−0.525468	+	0.535340i
$431$	−652.878	−	290.680i	−0.0729652	−	0.0324862i	0.369930	−	0.929060i	$-0.379382\pi$
$431$	−652.878	−	290.680i	−0.0729652	−	0.0324862i	−0.442895	+	0.896574i	$0.646048\pi$
$432$	148.125	−	39.6898i	0.0164969	−	0.00442032i
$433$	1077.89	−	6805.56i	0.119631	−	0.755322i	−0.852818	−	0.522208i	$-0.825109\pi$
$433$	1077.89	−	6805.56i	0.119631	−	0.755322i	0.972449	−	0.233114i	$-0.0748915\pi$
$434$	1031.10	−	4936.01i	0.114043	−	0.545935i
$435$	−2910.63	−	25415.4i	−0.320814	−	2.80132i
$436$	−5574.60	−	6191.21i	−0.612327	−	0.680058i
$437$	−11649.8	+	610.543i	−1.27526	+	0.0668334i
$438$	−6282.57	+	329.256i	−0.685372	+	0.0359188i
$439$	5214.79	+	5791.61i	0.566944	+	0.629655i	0.956635	−	0.291291i	$-0.0940848\pi$
$439$	5214.79	+	5791.61i	0.566944	+	0.629655i	−0.389691	+	0.920946i	$0.627418\pi$
$440$	213.335	+	1862.82i	0.0231144	+	0.201833i
$441$	2988.72	+	8983.45i	0.322721	+	0.970031i
$442$	−331.351	+	2092.07i	−0.0356579	+	0.225135i
$443$	−3687.02	+	987.935i	−0.395431	+	0.105955i	−0.451054	−	0.892496i	$-0.648952\pi$
$443$	−3687.02	+	987.935i	−0.395431	+	0.105955i	0.0556237	+	0.998452i	$0.482285\pi$
$444$	1129.68	+	502.967i	0.120748	+	0.0537607i
$445$	−2899.26	+	2953.72i	−0.308849	+	0.314652i
$446$	−1881.59	−	4226.12i	−0.199767	−	0.448683i
$447$	865.011	+	5461.47i	0.0915294	+	0.577894i
$448$	1439.04	+	70.3580i	0.151760	+	0.00741987i
$449$		−	5623.01i		−	0.591016i	−0.955340	−	0.295508i	$-0.904511\pi$
$449$		−	5623.01i		−	0.591016i	0.955340	−	0.295508i	$-0.0954889\pi$
$450$	543.283	−	3898.42i	0.0569125	−	0.408385i
$451$	−1839.49	+	1062.03i	−0.192058	+	0.110885i
$452$	2678.37	−	4124.32i	0.278716	−	0.429186i
$453$	−8939.07	+	23287.1i	−0.927139	+	2.41528i
$454$	−439.350	−	319.206i	−0.0454179	−	0.0329980i
$455$	−2098.55	+	14445.2i	−0.216223	+	1.48836i
$456$	8888.62	−	6457.96i	0.912824	−	0.663205i
$457$	3309.22	+	12350.2i	0.338728	+	1.26415i	0.899770	+	0.436364i	$0.143734\pi$
$457$	3309.22	+	12350.2i	0.338728	+	1.26415i	−0.561042	+	0.827787i	$0.689599\pi$
$458$	263.151	−	101.014i	0.0268477	−	0.0103059i
$459$	87.1040	+	78.4288i	0.00885766	+	0.00797547i
$460$	9808.16	+	938.686i	0.994148	+	0.0951444i
$461$	−5550.36	−	1803.42i	−0.560751	−	0.182199i	0.0149083	−	0.999889i	$-0.495254\pi$
$461$	−5550.36	−	1803.42i	−0.560751	−	0.182199i	−0.575659	+	0.817690i	$0.695254\pi$
$462$	1393.72	+	703.993i	0.140351	+	0.0708933i
$463$	1156.41	−	2269.59i	0.116076	−	0.227811i	−0.825658	−	0.564171i	$-0.809196\pi$
$463$	1156.41	−	2269.59i	0.116076	−	0.227811i	0.941734	+	0.336360i	$0.109196\pi$
$464$	−7929.50	+	7139.75i	−0.793357	+	0.714342i
$465$	−6267.29	−	18695.0i	−0.625029	−	1.86443i
$466$	−2245.43	+	2493.80i	−0.223214	+	0.247904i
$467$	3208.98	−	3962.77i	0.317975	−	0.392666i	−0.592950	−	0.805239i	$-0.702037\pi$
$467$	3208.98	−	3962.77i	0.317975	−	0.392666i	0.910924	+	0.412574i	$0.135370\pi$
$468$	9216.55	−	9216.55i	0.910332	−	0.910332i
$469$	599.882	−	439.062i	0.0590618	−	0.0432281i
$470$	2371.34	−	6353.65i	0.232727	−	0.623558i
$471$	23373.2	−	10406.4i	2.28658	−	1.01805i
$472$	3300.74	−	2672.89i	0.321883	−	0.260656i
$473$	−4398.74	−	2856.57i	−0.427599	−	0.277686i
$474$	239.889	−	415.499i	0.0232457	−	0.0402627i
$475$	2505.86	+	10797.0i	0.242056	+	1.04295i
$476$	1643.67	+	2824.00i	0.158272	+	0.271928i
$477$	−1018.65	−	1999.22i	−0.0977797	−	0.191903i
$478$	−2265.46	−	869.628i	−0.216778	−	0.0832131i
$479$	−1631.96	+	15527.1i	−0.155671	+	1.48111i	0.585983	+	0.810324i	$0.300709\pi$
$479$	−1631.96	+	15527.1i	−0.155671	+	1.48111i	−0.741653	+	0.670783i	$0.765958\pi$
$480$	−12707.2	+	6624.30i	−1.20834	+	0.629910i
$481$	1751.50	−	184.090i	0.166033	−	0.0174507i
$482$	4463.94	+	4463.94i	0.421840	+	0.421840i
$483$	11281.5	−	14031.8i	1.06279	−	1.32189i
$484$	7842.17	−	2548.08i	0.736493	−	0.239301i
$485$	−1291.55	+	287.116i	−0.120921	+	0.0268809i
$486$	−1277.05	−	6008.03i	−0.119193	−	0.560761i
$487$	24.6211	+	469.799i	0.00229094	+	0.0437138i	0.999536	−	0.0304665i	$-0.00969930\pi$
$487$	24.6211	+	469.799i	0.00229094	+	0.0437138i	−0.997245	+	0.0741803i	$0.976366\pi$
$488$	7346.82	−	4771.08i	0.681506	−	0.442575i
$489$	1512.49	−	4654.96i	0.139871	−	0.430480i
$490$	−2248.95	−	3752.51i	−0.207341	−	0.345961i
$491$	−2519.57	−	7754.44i	−0.231582	−	0.712735i	−0.997557	−	0.0698643i	$-0.977743\pi$
$491$	−2519.57	−	7754.44i	−0.231582	−	0.712735i	0.765975	−	0.642870i	$-0.222257\pi$
$492$	−8169.50	−	6615.53i	−0.748597	−	0.606202i
$493$	−7877.67	−	2110.81i	−0.719660	−	0.192832i
$494$	2900.46	−	6514.54i	0.264166	−	0.593326i
$495$	3080.58	−	190.208i	0.279721	−	0.0172711i
$496$	−4834.11	+	6653.59i	−0.437617	+	0.602328i
$497$	−3460.14	−	1314.32i	−0.312291	−	0.118623i
$498$	4429.98	−	2257.19i	0.398619	−	0.203107i
$499$	−14179.2	−	8186.38i	−1.27204	−	0.734414i	−0.296671	−	0.954980i	$-0.595876\pi$
$499$	−14179.2	−	8186.38i	−1.27204	−	0.734414i	−0.975372	+	0.220565i	$0.929210\pi$
$500$	−750.712	−	9331.38i	−0.0671457	−	0.834624i
$501$	−4392.16	−	7607.44i	−0.391671	−	0.678394i
$502$	192.113	−	3665.74i	0.0170806	−	0.325916i
$503$	4544.11	−	719.716i	0.402807	−	0.0637984i	0.0482559	−	0.998835i	$-0.484634\pi$
$503$	4544.11	−	719.716i	0.402807	−	0.0637984i	0.354551	+	0.935037i	$0.384634\pi$
$504$	−866.110	+	8528.04i	−0.0765468	+	0.753709i
$505$	7806.70	+	11779.8i	0.687908	+	1.03801i
$506$	−156.905	−	1492.85i	−0.0137851	−	0.131157i
$507$	5302.45	−	19789.0i	0.464478	−	1.73345i
$508$	−1752.11	−	4564.40i	−0.153026	−	0.398647i
$509$	−6597.74	−	1402.39i	−0.574538	−	0.122122i	−0.0885259	−	0.996074i	$-0.528216\pi$
$509$	−6597.74	−	1402.39i	−0.574538	−	0.122122i	−0.486012	+	0.873952i	$0.661549\pi$
$510$	−2161.22	−	1221.11i	−0.187648	−	0.106022i
$511$	−4225.04	+	13160.2i	−0.365763	+	1.13928i
$512$	9444.45	+	4812.19i	0.815214	+	0.415372i
$513$	−214.917	−	330.943i	−0.0184967	−	0.0284824i
$514$	6933.05	−	1473.66i	0.594949	−	0.126460i
$515$	−4912.08	−	1545.65i	−0.420295	−	0.132251i
$516$	5396.88	−	25390.3i	0.460435	−	2.16617i
$517$	5252.37	+	831.893i	0.446806	+	0.0707672i
$518$	−371.924	+	374.542i	−0.0315471	+	0.0317691i
$519$	22.4147	+	30.8512i	0.00189575	+	0.00260928i
$520$	−7094.47	+	11150.3i	−0.598295	+	0.940336i
$521$	−12448.7	−	1308.41i	−1.04681	−	0.110024i	−0.434521	−	0.900661i	$-0.643082\pi$
$521$	−12448.7	−	1308.41i	−1.04681	−	0.110024i	−0.612284	+	0.790638i	$0.709749\pi$
$522$	−6136.12	−	7577.47i	−0.514503	−	0.635358i
$523$	4583.84	+	240.229i	0.383246	+	0.0200851i	0.242986	−	0.970030i	$-0.421873\pi$
$523$	4583.84	+	240.229i	0.383246	+	0.0200851i	0.140259	+	0.990115i	$0.455206\pi$
$524$	11444.0			0.954075
$525$	−15000.2	−	8223.53i	−1.24698	−	0.683627i
$526$	−7786.28			−0.645433
$527$	−6277.46	−	328.988i	−0.518881	−	0.0271934i
$528$	−1602.67	−	1979.13i	−0.132097	−	0.163126i
$529$	−5113.42	−	537.442i	−0.420270	−	0.0441721i
$530$	659.959	+	799.650i	0.0540883	+	0.0655369i
$531$	−4109.47	−	5656.20i	−0.335849	−	0.462256i
$532$	−2884.39	−	10615.7i	−0.235064	−	0.865126i
$533$	−14787.1	−	2342.05i	−1.20169	−	0.190329i
$534$	−648.816	+	3052.44i	−0.0525787	+	0.247363i
$535$	−10702.8	+	3588.01i	−0.864905	+	0.289950i
$536$	658.358	−	139.938i	0.0530536	−	0.0112769i
$537$	9793.57	+	15080.8i	0.787009	+	1.21189i
$538$	1770.95	+	902.342i	0.141916	+	0.0723099i
$539$	2533.18	−	2313.26i	0.202434	−	0.184859i
$540$	138.386	+	303.195i	0.0110281	+	0.0241619i
$541$	−13056.9	−	2775.33i	−1.03763	−	0.220556i	−0.342561	−	0.939496i	$-0.611294\pi$
$541$	−13056.9	−	2775.33i	−1.03763	−	0.220556i	−0.695072	+	0.718940i	$0.744628\pi$
$542$	−1010.73	−	2633.05i	−0.0801009	−	0.208670i
$543$	−4036.32	+	15063.7i	−0.318996	+	1.19051i
$544$	477.544	+	4543.53i	0.0376370	+	0.358092i
$545$	8649.86	−	10887.3i	0.679852	−	0.855707i
$546$	4511.69	+	10038.5i	0.353631	+	0.786830i
$547$	−18190.5	+	2881.08i	−1.42188	+	0.225203i	−0.819533	−	0.573032i	$-0.805767\pi$
$547$	−18190.5	+	2881.08i	−1.42188	+	0.225203i	−0.602346	+	0.798235i	$0.705767\pi$
$548$	−305.074	+	5821.17i	−0.0237813	+	0.453773i
$549$	−7210.01	−	12488.1i	−0.560502	−	0.970818i
$550$	−1370.50	+	394.703i	−0.106251	+	0.0306003i
$551$	23778.4	+	13728.4i	1.83846	+	1.06144i
$552$	14524.6	−	7400.64i	1.11994	−	0.570638i
$553$	−666.217	−	816.837i	−0.0512305	−	0.0628127i
$554$	4133.10	−	5688.72i	0.316965	−	0.436265i
$555$	−515.615	+	1998.51i	−0.0394353	+	0.152850i
$556$	−377.377	+	847.603i	−0.0287848	+	0.0646518i
$557$	18072.7	+	4842.56i	1.37480	+	0.368376i	0.869229	−	0.494409i	$-0.164615\pi$
$557$	18072.7	+	4842.56i	1.37480	+	0.368376i	0.505570	+	0.862785i	$0.331282\pi$
$558$	−5840.51	−	4729.55i	−0.443097	−	0.358813i
$559$	−11424.0	−	35159.3i	−0.864368	−	2.66025i
$560$	836.690	+	7086.01i	0.0631368	+	0.534712i
$561$	601.499	−	1851.22i	0.0452679	−	0.139320i
$562$	−659.487	+	428.276i	−0.0494996	+	0.0321454i
$563$	−949.148	−	18110.8i	−0.0710512	−	1.35574i	−0.768843	−	0.639437i	$-0.779167\pi$
$563$	−949.148	−	18110.8i	−0.0710512	−	1.35574i	0.697792	−	0.716300i	$-0.254166\pi$
$564$	5471.94	+	25743.4i	0.408529	+	1.92198i
$565$	7529.08	+	3268.55i	0.560621	+	0.243379i
$566$	−1498.42	+	486.865i	−0.111278	+	0.0361563i
$567$	−13038.1	−	2018.20i	−0.965696	−	0.149482i
$568$	−2369.65	−	2369.65i	−0.175050	−	0.175050i
$569$	8828.52	−	927.915i	0.650459	−	0.0683659i	0.226448	−	0.974023i	$-0.427289\pi$
$569$	8828.52	−	927.915i	0.650459	−	0.0683659i	0.424010	+	0.905657i	$0.360622\pi$
$570$	5964.11	+	5854.13i	0.438262	+	0.430180i
$571$	−942.348	+	8965.84i	−0.0690648	+	0.657108i	0.904151	+	0.427214i	$0.140505\pi$
$571$	−942.348	+	8965.84i	−0.0690648	+	0.657108i	−0.973216	+	0.229894i	$0.926162\pi$
$572$	−4409.11	−	1692.50i	−0.322297	−	0.123718i
$573$	10839.7	+	21274.0i	0.790285	+	1.55102i
$574$	3878.04	−	2257.16i	0.281997	−	0.164132i
$575$	1166.17	+	16403.9i	0.0845783	+	1.18972i
$576$	1073.64	−	1859.60i	0.0776650	−	0.134520i
$577$	−22101.5	−	14352.9i	−1.59462	−	1.03556i	−0.966237	−	0.257653i	$-0.917051\pi$
$577$	−22101.5	−	14352.9i	−1.59462	−	1.03556i	−0.628382	−	0.777905i	$-0.716283\pi$
$578$	3740.71	−	3029.17i	0.269192	−	0.217987i
$579$	−9714.66	+	4325.25i	−0.697284	+	0.310451i
$580$	−18157.1	−	14425.7i	−1.29989	−	1.03275i
$581$	−1179.88	−	10859.3i	−0.0842504	−	0.775424i
$582$	−705.397	+	705.397i	−0.0502400	+	0.0502400i
$583$	−511.643	+	631.826i	−0.0363466	+	0.0448843i
$584$	−8373.63	+	9299.86i	−0.593327	+	0.658957i
$585$	17718.3	+	12622.9i	1.25224	+	0.892122i
$586$	794.713	−	715.563i	0.0560227	−	0.0504431i
$587$	630.618	−	1237.66i	0.0443414	−	0.0870249i	−0.867773	−	0.496961i	$-0.834449\pi$
$587$	630.618	−	1237.66i	0.0443414	−	0.0870249i	0.912114	+	0.409936i	$0.134449\pi$
$588$	15181.0	+	7601.48i	1.06472	+	0.533129i
$589$	20127.2	+	6539.72i	1.40803	+	0.457495i
$590$	2420.85	+	2139.29i	0.168923	+	0.149276i
$591$	16364.5	+	14734.7i	1.13899	+	1.02556i
$592$	803.705	−	308.514i	0.0557975	−	0.0214186i
$593$	1249.77	+	4664.19i	0.0865459	+	0.322994i	0.995602	−	0.0936791i	$-0.0298628\pi$
$593$	1249.77	+	4664.19i	0.0865459	+	0.322994i	−0.909057	+	0.416673i	$0.863196\pi$
$594$	41.0777	−	29.8447i	0.00283744	−	0.00206152i
$595$	−4193.99	+	3486.13i	−0.288969	+	0.240197i
$596$	4055.30	+	2946.35i	0.278711	+	0.202495i
$597$	2424.02	−	6314.78i	0.166178	−	0.432909i
$598$	5762.47	−	8873.42i	0.394055	−	0.606791i
$599$	−13836.1	+	7988.30i	−0.943789	+	0.544897i	−0.891146	−	0.453717i	$-0.850098\pi$
$599$	−13836.1	+	7988.30i	−0.943789	+	0.544897i	−0.0526426	+	0.998613i	$0.516764\pi$
$600$	−9335.37	−	12358.6i	−0.635191	−	0.840899i
$601$		−	6170.03i		−	0.418770i	−0.977833	−	0.209385i	$-0.932854\pi$
$601$		−	6170.03i		−	0.418770i	0.977833	−	0.209385i	$-0.0671462\pi$
$602$	9313.47	+	6001.91i	0.630546	+	0.406345i
$603$	−173.320	−	1094.30i	−0.0117050	−	0.0739026i
$604$	9197.14	+	20657.1i	0.619580	+	1.39160i
$605$	6361.97	+	12204.0i	0.427522	+	0.820103i
$606$	9733.97	+	4333.84i	0.652501	+	0.290512i
$607$	−3860.73	+	1034.48i	−0.258159	+	0.0691734i	−0.385577	−	0.922676i	$-0.625998\pi$
$607$	−3860.73	+	1034.48i	−0.258159	+	0.0691734i	0.127418	+	0.991849i	$0.459331\pi$
$608$	2406.07	−	15191.4i	0.160492	−	1.01331i
$609$	−40255.7	+	13236.1i	−2.67856	+	0.880712i
$610$	4504.49	+	4910.07i	0.298986	+	0.325907i
$611$	25080.9	+	27855.2i	1.66066	+	1.84435i
$612$	4863.16	−	254.867i	0.321211	−	0.0168340i
$613$	23553.4	−	1234.38i	1.55190	−	0.0813316i	0.743005	−	0.669286i	$-0.233400\pi$
$613$	23553.4	−	1234.38i	1.55190	−	0.0813316i	0.808894	+	0.587954i	$0.200066\pi$
$614$	5783.89	+	6423.66i	0.380161	+	0.422211i
$615$	8630.98	−	15275.8i	0.565910	−	1.00160i
$616$	2950.54	−	970.141i	0.192988	−	0.0634547i
$617$	−1740.57	+	10989.5i	−0.113570	+	0.717054i	0.863534	+	0.504291i	$0.168246\pi$
$617$	−1740.57	+	10989.5i	−0.113570	+	0.717054i	−0.977104	+	0.212763i	$0.931754\pi$
$618$	−3750.35	+	1004.90i	−0.244112	+	0.0654096i
$619$	−13057.6	−	5813.61i	−0.847865	−	0.377494i	−0.0636416	−	0.997973i	$-0.520271\pi$
$619$	−13057.6	−	5813.61i	−0.847865	−	0.377494i	−0.784223	+	0.620479i	$0.786938\pi$
$620$	−16000.9	−	7966.20i	−1.03647	−	0.516017i
$621$	−238.134	−	534.857i	−0.0153881	−	0.0345621i
$622$	712.666	+	4499.59i	0.0459410	+	0.290060i
$623$	5763.01	+	3713.88i	0.370610	+	0.238834i
$624$		−	17950.2i		−	1.15157i
$625$	15152.1	−	3815.14i	0.969733	−	0.244169i
$626$	−7426.27	+	4287.56i	−0.474143	+	0.273747i
$627$	−3569.10	+	5495.93i	−0.227330	+	0.350058i
$628$	8311.77	−	21652.9i	0.528146	−	1.37587i
$629$	532.334	+	386.763i	0.0337449	+	0.0245171i
$630$	−6506.31	+	424.633i	−0.411457	+	0.0268536i
$631$	−561.919	+	408.258i	−0.0354511	+	0.0257567i	−0.605370	−	0.795944i	$-0.706975\pi$
$631$	−561.919	+	408.258i	−0.0354511	+	0.0257567i	0.569919	+	0.821701i	$0.306975\pi$
$632$	−247.005	−	921.835i	−0.0155464	−	0.0580200i
$633$	−1411.18	+	541.700i	−0.0886086	+	0.0340137i
$634$	−8883.53	−	7998.77i	−0.556483	−	0.501059i
$635$	7028.74	−	4145.73i	0.439255	−	0.259084i
$636$	−3826.73	−	1243.38i	−0.238585	−	0.0775209i
$637$	24137.1	−	1434.78i	1.50133	−	0.0892434i
$638$	−1603.93	+	3147.88i	−0.0995298	+	0.195338i
$639$	−4099.51	+	3691.21i	−0.253793	+	0.228517i
$640$	−4954.54	+	15745.6i	−0.306008	+	0.972498i
$641$	−8209.27	+	9117.32i	−0.505845	+	0.561798i	−0.940934	−	0.338590i	$-0.890050\pi$
$641$	−8209.27	+	9117.32i	−0.505845	+	0.561798i	0.435089	+	0.900387i	$0.356717\pi$
$642$	−5356.24	+	6614.41i	−0.329274	+	0.406620i
$643$	−14355.7	+	14355.7i	−0.880455	+	0.880455i	−0.993581	−	0.113125i	$-0.963914\pi$
$643$	−14355.7	+	14355.7i	−0.880455	+	0.880455i	0.113125	+	0.993581i	$0.463914\pi$
$644$	−1762.97	−	16226.0i	−0.107874	−	0.992847i
$645$	43284.7	+	1864.73i	2.64238	+	0.113835i
$646$	2433.96	−	1083.67i	0.148240	−	0.0660007i
$647$	12055.9	−	9762.70i	0.732562	−	0.593217i	−0.188757	−	0.982024i	$-0.560446\pi$
$647$	12055.9	−	9762.70i	0.732562	−	0.593217i	0.921319	+	0.388807i	$0.127113\pi$
$648$	−10018.1	−	6505.86i	−0.607330	−	0.394405i
$649$	−1266.64	+	2193.88i	−0.0766100	+	0.132692i
$650$	−9258.02	−	3917.15i	−0.558661	−	0.236374i
$651$	−28228.8	+	16430.1i	−1.69950	+	0.989168i
$652$	−2014.34	−	3953.37i	−0.120993	−	0.237463i
$653$	−9438.10	−	3622.95i	−0.565607	−	0.217116i	0.0587264	−	0.998274i	$-0.481296\pi$
$653$	−9438.10	−	3622.95i	−0.565607	−	0.217116i	−0.624334	+	0.781158i	$0.714629\pi$
$654$	1095.90	−	10426.8i	0.0655247	−	0.623426i
$655$	3163.46	+	18837.1i	0.188712	+	1.12370i
$656$	−7278.24	+	764.974i	−0.433182	+	0.0455293i
$657$	14566.2	+	14566.2i	0.864964	+	0.864964i
$658$	−11101.8	−	1718.46i	−0.657739	−	0.101813i
$659$	−15392.8	+	5001.43i	−0.909893	+	0.295642i	−0.726314	−	0.687363i	$-0.758768\pi$
$659$	−15392.8	+	5001.43i	−0.909893	+	0.295642i	−0.183579	+	0.983005i	$0.558768\pi$
$660$	3665.07	−	4147.44i	0.216155	−	0.244605i
$661$	−2403.30	−	11306.6i	−0.141418	−	0.665321i	−0.990551	−	0.137142i	$-0.956208\pi$
$661$	−2403.30	−	11306.6i	−0.141418	−	0.665321i	0.849133	−	0.528179i	$-0.177125\pi$
$662$	509.958	+	9730.57i	0.0299397	+	0.571283i
$663$	11506.5	−	7472.38i	0.674018	−	0.437712i
$664$	3056.14	−	9405.83i	0.178616	−	0.549724i
$665$	16676.2	−	7682.22i	0.972444	−	0.447975i
$666$	243.096	+	748.171i	0.0141438	+	0.0435301i
$667$	31659.2	+	25637.1i	1.83785	+	1.48826i
$668$	−7691.81	−	2061.01i	−0.445516	−	0.119376i
$669$	−12187.6	+	27373.9i	−0.704336	+	1.58196i
$670$	187.911	+	476.230i	0.0108353	+	0.0274603i
$671$	−3071.14	+	4227.07i	−0.176692	+	0.243195i
$672$	15003.4	+	18395.4i	0.861263	+	1.05598i
$673$	−7107.25	+	3621.33i	−0.407079	+	0.207417i	−0.645526	−	0.763738i	$-0.723362\pi$
$673$	−7107.25	+	3621.33i	−0.407079	+	0.207417i	0.238447	+	0.971156i	$0.423362\pi$
$674$	−8121.38	−	4688.88i	−0.464130	−	0.267966i
$675$	−460.810	+	311.597i	−0.0262764	+	0.0177680i
$676$	−9285.97	−	16083.8i	−0.528332	−	0.915098i
$677$	1446.95	−	27609.5i	0.0821433	−	1.56739i	−0.577868	−	0.816131i	$-0.696115\pi$
$677$	1446.95	−	27609.5i	0.0821433	−	1.56739i	0.660011	−	0.751256i	$-0.270552\pi$
$678$	6112.46	−	968.119i	0.346236	−	0.0548383i
$679$	898.456	+	1999.07i	0.0507799	+	0.112986i
$680$	−4757.40	+	1322.31i	−0.268291	+	0.0745711i
$681$	367.690	+	3498.33i	0.0206900	+	0.196852i
$682$	−704.790	+	2630.31i	−0.0395715	+	0.147683i
$683$	−4804.52	−	12516.2i	−0.269165	−	0.701199i	−0.999830	−	0.0184623i	$-0.994123\pi$
$683$	−4804.52	−	12516.2i	−0.269165	−	0.701199i	0.730665	−	0.682737i	$-0.239210\pi$
$684$	−16036.7	−	3408.71i	−0.896461	−	0.190549i
$685$	−9666.06	+	1106.98i	−0.539155	+	0.0617453i
$686$	−5334.19	+	4905.51i	−0.296881	+	0.273022i
$687$	−1626.78	−	828.886i	−0.0903428	−	0.0460320i
$688$	−9842.19	−	15155.6i	−0.545392	−	0.839830i
$689$	−5605.27	+	1191.44i	−0.309933	+	0.0658783i
$690$	7381.25	+	9963.11i	0.407245	+	0.549694i
$691$	−268.342	+	1262.45i	−0.0147731	+	0.0695019i	−0.984917	−	0.173029i	$-0.944644\pi$
$691$	−268.342	+	1262.45i	−0.0147731	+	0.0695019i	0.970144	+	0.242531i	$0.0779777\pi$
$692$	34.1437	+	5.40783i	0.00187565	+	0.000297074i
$693$	−1340.58	−	4933.83i	−0.0734838	−	0.270448i
$694$	−5533.34	−	7615.99i	−0.302655	−	0.416569i
$695$	−1499.49	−	386.867i	−0.0818399	−	0.0211147i
$696$	−38156.8	−	4010.44i	−2.07806	−	0.218413i
$697$	−3520.18	−	4347.07i	−0.191301	−	0.236237i
$698$	7821.56	+	409.911i	0.424141	+	0.0222283i
$699$	21736.2			1.17616
$700$	−14886.6	+	4343.91i	−0.803799	+	0.234549i
$701$	−21427.5			−1.15450			−0.577250	−	0.816567i	$-0.695874\pi$
$701$	−21427.5			−1.15450			−0.577250	+	0.816567i	$0.695874\pi$
$702$	357.396	+	18.7304i	0.0192152	+	0.00100703i
$703$	−1394.11	−	1721.58i	−0.0747933	−	0.0923621i
$704$	−773.783	−	81.3279i	−0.0414248	−	0.00435392i
$705$	−40861.5	+	16123.1i	−2.18288	+	0.861322i
$706$	−1565.06	−	2154.12i	−0.0834301	−	0.114832i
$707$	16494.8	−	16610.9i	0.877441	−	0.883616i
$708$	−12383.1	−	1961.29i	−0.657324	−	0.104110i
$709$	−1074.84	+	5056.72i	−0.0569343	+	0.267855i	−0.997403	−	0.0720261i	$-0.977054\pi$
$709$	−1074.84	+	5056.72i	−0.0569343	+	0.267855i	0.940468	+	0.339881i	$0.110387\pi$
$710$	1479.04	−	2076.09i	0.0781796	−	0.109738i
$711$	−1536.64	+	326.623i	−0.0810527	+	0.0172283i
$712$	3380.81	+	5205.99i	0.177951	+	0.274021i
$713$	27977.2	+	14255.1i	1.46950	+	0.748747i
$714$	−1256.95	+	3915.16i	−0.0658827	+	0.205212i
$715$	1567.07	−	7725.31i	0.0819654	−	0.404070i
$716$	15944.6	+	3389.12i	0.832230	+	0.176896i
$717$	5632.84	+	14674.0i	0.293392	+	0.764313i
$718$	1378.75	−	5145.56i	0.0716635	−	0.267452i
$719$	−1024.52	−	9747.69i	−0.0531409	−	0.505601i	−0.988426	−	0.151706i	$-0.951523\pi$
$719$	−1024.52	−	9747.69i	−0.0531409	−	0.505601i	0.935285	−	0.353896i	$-0.115143\pi$
$720$	9962.93	+	3718.41i	0.515690	+	0.192468i
$721$	−861.894	+	8486.53i	−0.0445196	+	0.438356i
$722$	−1130.89	+	179.116i	−0.0582929	+	0.00923269i
$723$	2140.07	−	40834.9i	0.110083	−	2.10051i
$724$	7068.64	+	12243.2i	0.362851	+	0.628476i
$725$	18725.7	−	33874.6i	0.959249	−	1.73527i
$726$	8986.60	+	5188.42i	0.459400	+	0.265234i
$727$	4614.33	−	2351.12i	0.235400	−	0.119943i	−0.332312	−	0.943170i	$-0.607829\pi$
$727$	4614.33	−	2351.12i	0.235400	−	0.119943i	0.567712	+	0.823227i	$0.307829\pi$
$728$	20465.6	+	7773.77i	1.04190	+	0.395763i
$729$	−12079.6	+	16626.2i	−0.613708	+	0.844696i
$730$	−8031.05	−	5109.81i	−0.407181	−	0.259072i
$731$	5617.95	−	12618.1i	0.284251	−	0.638437i
$732$	−24977.7	−	6692.75i	−1.26120	−	0.337939i
$733$	12728.6	+	10307.4i	0.641392	+	0.519389i	0.893935	−	0.448197i	$-0.147934\pi$
$733$	12728.6	+	10307.4i	0.641392	+	0.519389i	−0.252543	+	0.967586i	$0.581267\pi$
$734$	2315.73	+	7127.08i	0.116451	+	0.358399i
$735$	−8315.68	+	27089.4i	−0.417318	+	1.35947i
$736$	7051.88	−	21703.4i	0.353173	−	1.08696i
$737$	−336.684	+	218.645i	−0.0168276	+	0.0109280i
$738$	−349.995	−	6678.30i	−0.0174573	−	0.333105i
$739$	−1253.35	−	5896.53i	−0.0623885	−	0.293515i	0.935881	−	0.352316i	$-0.114606\pi$
$739$	−1253.35	−	5896.53i	−0.0623885	−	0.293515i	−0.998270	+	0.0588009i	$0.981272\pi$
$740$	950.542	+	1611.57i	0.0472198	+	0.0800572i
$741$	−43929.3	+	14273.5i	−2.17784	+	0.707624i
$742$	1076.16	−	1338.52i	0.0532442	−	0.0662246i
$743$	22575.7	+	22575.7i	1.11470	+	1.11470i	0.992506	+	0.122193i	$0.0389926\pi$
$743$	22575.7	+	22575.7i	1.11470	+	1.11470i	0.122193	+	0.992506i	$0.461007\pi$
$744$	−29410.2	+	3091.14i	−1.44923	+	0.152321i
$745$	−3728.74	+	7489.55i	−0.183370	+	0.368316i
$746$	613.049	−	5832.77i	0.0300876	−	0.286264i
$747$	−15198.5	−	5834.16i	−0.744423	−	0.285757i
$748$	−801.080	−	1572.21i	−0.0391583	−	0.0768524i
$749$	9406.23	+	16160.9i	0.458874	+	0.788395i
$750$	8094.63	−	8559.70i	0.394099	−	0.416742i
$751$	16464.8	−	28517.9i	0.800013	−	1.38566i	−0.119593	−	0.992823i	$-0.538159\pi$
$751$	16464.8	−	28517.9i	0.800013	−	1.38566i	0.919606	−	0.392841i	$-0.128508\pi$
$752$	15366.4	+	9979.07i	0.745154	+	0.483909i
$753$	−18478.0	+	14963.2i	−0.894255	+	0.724154i
$754$	−22749.1	+	10128.6i	−1.09877	+	0.489205i
$755$	−31459.6	+	20848.8i	−1.51646	+	1.00499i
$756$	445.505	−	326.071i	0.0214324	−	0.0156866i
$757$	−13283.5	+	13283.5i	−0.637778	+	0.637778i	−0.950007	−	0.312229i	$-0.898924\pi$
$757$	−13283.5	+	13283.5i	−0.637778	+	0.637778i	0.312229	+	0.950007i	$0.398924\pi$
$758$	264.466	−	326.588i	0.0126726	−	0.0156494i
$759$	−6505.89	+	7225.52i	−0.311132	+	0.345547i
$760$	16622.9	−	154.695i	0.793391	−	0.00738338i
$761$	28381.8	−	25555.1i	1.35196	−	1.21731i	0.397993	−	0.917389i	$-0.369707\pi$
$761$	28381.8	−	25555.1i	1.35196	−	1.21731i	0.953965	−	0.299919i	$-0.0969597\pi$
$762$	2793.27	−	5482.11i	0.132795	−	0.260624i
$763$	−20559.9	−	10385.1i	−0.975516	−	0.492749i
$764$	20585.0	+	6688.48i	0.974791	+	0.316729i
$765$	1763.83	+	7934.37i	0.0833613	+	0.374991i
$766$	4476.44	+	4030.60i	0.211149	+	0.190120i
$767$	−16669.8	+	6398.96i	−0.784763	+	0.301242i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13924 + 0.0597051i) q^{2} +(-4.65026 - 5.74259i) q^{3} +(-6.66187 - 0.700191i) q^{4} +(-0.689007 - 11.1591i) q^{5} +(-4.95490 - 6.81984i) q^{6} +(-17.8723 + 4.85610i) q^{7} +(-16.5617 - 2.62312i) q^{8} +(-5.73883 + 26.9991i) q^{9} +(-0.118690 - 12.7540i) q^{10} +(9.78282 - 2.07940i) q^{11} +(26.9585 + 41.5125i) q^{12} +(62.8114 + 32.0040i) q^{13} +(-20.6508 + 4.46520i) q^{14} +(-60.8780 + 55.8493i) q^{15} +(33.7063 + 7.16449i) q^{16} +(9.43880 + 24.5889i) q^{17} +(-8.14989 + 30.4158i) q^{18} +(-9.26872 - 88.1859i) q^{19} +(-3.22342 + 74.8228i) q^{20} +(110.997 + 80.0511i) q^{21} +(11.2691 - 1.78486i) q^{22} +(6.88543 - 131.382i) q^{23} +(61.9529 + 107.306i) q^{24} +(-124.051 + 15.3774i) q^{25} +(69.6465 + 40.2104i) q^{26} +(3.96513 - 2.02034i) q^{27} +(122.463 - 19.8367i) q^{28} +(-182.006 + 250.509i) q^{29} +(-72.6893 + 59.9911i) q^{30} +(-97.0745 + 218.033i) q^{31} +(167.546 + 44.8939i) q^{32} +(-57.4338 - 46.5090i) q^{33} +(9.28499 + 28.5763i) q^{34} +(66.5037 + 196.092i) q^{35} +(57.1358 - 175.846i) q^{36} +(20.9522 - 13.6065i) q^{37} +(-5.29415 - 101.018i) q^{38} +(-108.303 - 509.527i) q^{39} +(-17.8605 + 186.621i) q^{40} +(-201.982 + 65.6279i) q^{41} +(121.673 + 97.8246i) q^{42} +(-370.819 - 370.819i) q^{43} +(-66.6279 + 7.00287i) q^{44} +(305.239 + 45.4376i) q^{45} +(15.6883 - 149.265i) q^{46} +(496.395 + 190.548i) q^{47} +(-115.600 - 226.878i) q^{48} +(295.837 - 173.579i) q^{49} +(-142.242 + 10.1121i) q^{50} +(97.3112 - 168.548i) q^{51} +(-396.032 - 257.186i) q^{52} +(-63.1739 + 51.1572i) q^{53} +(4.63787 - 2.06491i) q^{54} +(-29.9447 - 107.735i) q^{55} +(308.734 - 33.5443i) q^{56} +(-463.314 + 463.314i) q^{57} +(-222.305 + 274.524i) q^{58} +(-169.486 + 188.233i) q^{59} +(444.667 - 329.435i) q^{60} +(-388.235 + 349.569i) q^{61} +(-123.609 + 242.596i) q^{62} +(-28.5441 - 510.403i) q^{63} +(-73.9863 - 24.0396i) q^{64} +(313.858 - 722.969i) q^{65} +(-62.6542 - 56.4141i) q^{66} +(-37.4734 + 14.3847i) q^{67} +(-45.6631 - 170.417i) q^{68} +(-786.491 + 571.419i) q^{69} +(64.0561 + 227.367i) q^{70} +(161.686 + 117.471i) q^{71} +(165.867 - 432.098i) q^{72} +(406.467 - 625.904i) q^{73} +(24.6820 - 14.2502i) q^{74} +(665.173 + 640.863i) q^{75} +593.973i q^{76} +(-164.744 + 84.6700i) q^{77} +(-92.9622 - 586.940i) q^{78} +(23.1492 + 51.9940i) q^{79} +(56.7253 - 381.068i) q^{80} +(650.789 + 289.750i) q^{81} +(-234.024 + 62.7066i) q^{82} +(-92.2650 + 582.538i) q^{83} +(-683.398 - 611.009i) q^{84} +(267.886 - 122.270i) q^{85} +(-400.312 - 444.592i) q^{86} +(2284.95 - 119.749i) q^{87} +(-167.475 + 8.77700i) q^{88} +(-247.706 - 275.106i) q^{89} +(345.028 + 69.9887i) q^{90} +(-1278.00 - 266.966i) q^{91} +(-137.862 + 870.427i) q^{92} +(1703.50 - 456.450i) q^{93} +(554.137 + 246.718i) q^{94} +(-977.689 + 164.191i) q^{95} +(-521.327 - 1170.92i) q^{96} +(-18.5125 - 116.883i) q^{97} +(347.393 - 180.085i) q^{98} +276.060i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more