LMFDB - Embedded newform 121.4.c.f.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.2
Root			$-1.40126 - 1.01807i$ of defining polynomial
Character	$\chi$	$=$	121.27
Dual form			121.4.c.f.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.226216 + 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(1.34106 - 4.12734i) q^{6} +(13.6952 - 9.95015i) q^{7} +(9.15848 + 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} +O(q^{10})$	\(q+(0.226216 + 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(1.34106 - 4.12734i) q^{6} +(13.6952 - 9.95015i) q^{7} +(9.15848 + 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} -9.41154 q^{10} -44.2487 q^{12} +(-23.0653 - 70.9878i) q^{13} +(10.0256 + 7.28401i) q^{14} +(61.6595 - 44.7983i) q^{15} +(15.8914 - 48.9087i) q^{16} +(25.5819 - 78.7328i) q^{17} +(-4.82297 + 3.50410i) q^{18} +(-54.9509 - 39.9242i) q^{19} +(29.6537 + 91.2648i) q^{20} -100.354 q^{21} +13.3538 q^{23} +(-20.7382 - 63.8257i) q^{24} +(-32.5930 - 23.6802i) q^{25} +(44.2055 - 32.1172i) q^{26} +(-34.5433 + 106.313i) q^{27} +(39.0455 - 120.170i) q^{28} +(136.720 - 99.3327i) q^{29} +(45.1379 + 32.7946i) q^{30} +(-20.2398 - 62.2918i) q^{31} +128.210 q^{32} +60.6025 q^{34} +(67.2532 + 206.984i) q^{35} +(49.1758 + 35.7283i) q^{36} +(-33.0535 + 24.0148i) q^{37} +(15.3653 - 47.2895i) q^{38} +(-136.736 + 420.830i) q^{39} +(-117.745 + 85.5469i) q^{40} +(222.422 + 161.599i) q^{41} +(-22.7017 - 69.8685i) q^{42} +2.28719 q^{43} -104.697 q^{45} +(3.02085 + 9.29723i) q^{46} +(-58.1247 - 42.2301i) q^{47} +(-246.638 + 179.193i) q^{48} +(-17.4397 + 53.6738i) q^{49} +(9.11361 - 28.0488i) q^{50} +(-397.036 + 288.464i) q^{51} +(-450.726 - 327.472i) q^{52} +(-46.0451 - 141.712i) q^{53} -81.8320 q^{54} +191.636 q^{56} +(124.429 + 382.954i) q^{57} +(100.086 + 72.7166i) q^{58} +(-441.425 + 320.714i) q^{59} +(175.793 - 541.036i) q^{60} +(-31.3042 + 96.3445i) q^{61} +(38.7903 - 28.1828i) q^{62} +(111.528 + 81.0300i) q^{63} +(-98.1279 - 302.007i) q^{64} +959.615 q^{65} +411.641 q^{67} +(-190.946 - 587.670i) q^{68} +(-64.0452 - 46.5316i) q^{69} +(-128.893 + 93.6462i) q^{70} +(-145.434 + 447.601i) q^{71} +(-28.4882 + 87.6775i) q^{72} +(493.986 - 358.902i) q^{73} +(-24.1969 - 17.5800i) q^{74} +(73.8027 + 227.141i) q^{75} -506.985 q^{76} -323.923 q^{78} +(302.288 + 930.348i) q^{79} +(534.881 + 388.613i) q^{80} +(714.005 - 518.755i) q^{81} +(-62.1932 + 191.411i) q^{82} +(-8.08200 + 24.8738i) q^{83} +(-605.995 + 440.281i) q^{84} +(861.047 + 625.587i) q^{85} +(0.517399 + 1.59239i) q^{86} -1001.84 q^{87} -352.887 q^{89} +(-23.6842 - 72.8926i) q^{90} +(-1022.22 - 742.689i) q^{91} +(80.6382 - 58.5871i) q^{92} +(-119.986 + 369.278i) q^{93} +(16.2527 - 50.0208i) q^{94} +(706.471 - 513.281i) q^{95} +(-614.898 - 446.750i) q^{96} +(261.918 + 806.101i) q^{97} -41.3140 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.226216	+	0.696222i	0.0799795	+	0.246152i	0.983049	−	0.183343i	$-0.0586918\pi$
$2$	0.226216	+	0.696222i	0.0799795	+	0.246152i	−0.903070	+	0.429494i	$0.858692\pi$
$3$	−4.79602	−	3.48451i	−0.922994	−	0.670594i	0.0212735	−	0.999774i	$-0.493228\pi$
$3$	−4.79602	−	3.48451i	−0.922994	−	0.670594i	−0.944267	+	0.329179i	$0.893228\pi$
$4$	6.03859	−	4.38729i	0.754823	−	0.548411i
$5$	−3.97285	+	12.2272i	−0.355342	+	1.09363i	0.600468	+	0.799648i	$0.294981\pi$
$5$	−3.97285	+	12.2272i	−0.355342	+	1.09363i	−0.955811	+	0.293983i	$0.905019\pi$
$6$	1.34106	−	4.12734i	0.0912473	−	0.280830i
$7$	13.6952	−	9.95015i	0.739472	−	0.537258i	−0.153074	−	0.988215i	$-0.548917\pi$
$7$	13.6952	−	9.95015i	0.739472	−	0.537258i	0.892546	+	0.450957i	$0.148917\pi$
$8$	9.15848	+	6.65403i	0.404752	+	0.294069i
$9$	2.51651	+	7.74502i	0.0932040	+	0.286853i
$10$	−9.41154			−0.297619
$11$		0			0
$11$		0			0
$12$	−44.2487			−1.06446
$13$	−23.0653	−	70.9878i	−0.492090	−	1.51450i	−0.821443	−	0.570291i	$-0.806830\pi$
$13$	−23.0653	−	70.9878i	−0.492090	−	1.51450i	0.329352	−	0.944207i	$-0.393170\pi$
$14$	10.0256	+	7.28401i	0.191389	+	0.139052i
$15$	61.6595	−	44.7983i	1.06136	−	0.771124i
$16$	15.8914	−	48.9087i	0.248303	−	0.764198i
$17$	25.5819	−	78.7328i	0.364971	−	1.12327i	−0.585028	−	0.811013i	$-0.698916\pi$
$17$	25.5819	−	78.7328i	0.364971	−	1.12327i	0.949999	−	0.312253i	$-0.101084\pi$
$18$	−4.82297	+	3.50410i	−0.0631548	+	0.0458846i
$19$	−54.9509	−	39.9242i	−0.663505	−	0.482065i	0.204340	−	0.978900i	$-0.434495\pi$
$19$	−54.9509	−	39.9242i	−0.663505	−	0.482065i	−0.867845	+	0.496835i	$0.834495\pi$
$20$	29.6537	+	91.2648i	0.331539	+	1.02037i
$21$	−100.354			−1.04281
$22$		0			0
$23$	13.3538			0.121064			0.0605319	−	0.998166i	$-0.480720\pi$
$23$	13.3538			0.121064			0.0605319	+	0.998166i	$0.480720\pi$
$24$	−20.7382	−	63.8257i	−0.176382	−	0.542848i
$25$	−32.5930	−	23.6802i	−0.260744	−	0.189442i
$26$	44.2055	−	32.1172i	0.333439	−	0.242258i
$27$	−34.5433	+	106.313i	−0.246217	+	0.757779i
$28$	39.0455	−	120.170i	0.263532	−	0.811069i
$29$	136.720	−	99.3327i	0.875456	−	0.636056i	−0.0565897	−	0.998398i	$-0.518023\pi$
$29$	136.720	−	99.3327i	0.875456	−	0.636056i	0.932045	+	0.362342i	$0.118023\pi$
$30$	45.1379	+	32.7946i	0.274701	+	0.199582i
$31$	−20.2398	−	62.2918i	−0.117264	−	0.360901i	0.875149	−	0.483854i	$-0.160763\pi$
$31$	−20.2398	−	62.2918i	−0.117264	−	0.360901i	−0.992412	+	0.122953i	$0.960763\pi$
$32$	128.210			0.708268
$33$		0			0
$34$	60.6025			0.305684
$35$	67.2532	+	206.984i	0.324796	+	0.999619i
$36$	49.1758	+	35.7283i	0.227666	+	0.165409i
$37$	−33.0535	+	24.0148i	−0.146864	+	0.106703i	−0.658791	−	0.752326i	$-0.728932\pi$
$37$	−33.0535	+	24.0148i	−0.146864	+	0.106703i	0.511927	+	0.859029i	$0.328932\pi$
$38$	15.3653	−	47.2895i	0.0655942	−	0.201878i
$39$	−136.736	+	420.830i	−0.561418	+	1.72787i
$40$	−117.745	+	85.5469i	−0.465429	+	0.338154i
$41$	222.422	+	161.599i	0.847230	+	0.615548i	0.924381	−	0.381471i	$-0.124582\pi$
$41$	222.422	+	161.599i	0.847230	+	0.615548i	−0.0771511	+	0.997019i	$0.524582\pi$
$42$	−22.7017	−	69.8685i	−0.0834034	−	0.256689i
$43$	2.28719			0.00811146			0.00405573	−	0.999992i	$-0.498709\pi$
$43$	2.28719			0.00811146			0.00405573	+	0.999992i	$0.498709\pi$
$44$		0			0
$45$	−104.697			−0.346830
$46$	3.02085	+	9.29723i	0.00968261	+	0.0298000i
$47$	−58.1247	−	42.2301i	−0.180391	−	0.131061i	0.493926	−	0.869504i	$-0.335562\pi$
$47$	−58.1247	−	42.2301i	−0.180391	−	0.131061i	−0.674316	+	0.738443i	$0.735562\pi$
$48$	−246.638	+	179.193i	−0.741649	+	0.538840i
$49$	−17.4397	+	53.6738i	−0.0508445	+	0.156483i
$50$	9.11361	−	28.0488i	0.0257772	−	0.0793340i
$51$	−397.036	+	288.464i	−1.09012	+	0.792020i
$52$	−450.726	−	327.472i	−1.20201	−	0.873311i
$53$	−46.0451	−	141.712i	−0.119336	−	0.367277i	0.873491	−	0.486840i	$-0.161851\pi$
$53$	−46.0451	−	141.712i	−0.119336	−	0.367277i	−0.992827	+	0.119563i	$0.961851\pi$
$54$	−81.8320			−0.206221
$55$		0			0
$56$	191.636			0.457293
$57$	124.429	+	382.954i	0.289141	+	0.889886i
$58$	100.086	+	72.7166i	0.226585	+	0.164623i
$59$	−441.425	+	320.714i	−0.974044	+	0.707684i	−0.956370	−	0.292160i	$-0.905626\pi$
$59$	−441.425	+	320.714i	−0.974044	+	0.707684i	−0.0176741	+	0.999844i	$0.505626\pi$
$60$	175.793	−	541.036i	0.378247	−	1.16413i
$61$	−31.3042	+	96.3445i	−0.0657065	+	0.202224i	−0.978520	−	0.206154i	$-0.933905\pi$
$61$	−31.3042	+	96.3445i	−0.0657065	+	0.202224i	0.912813	+	0.408378i	$0.133905\pi$
$62$	38.7903	−	28.1828i	0.0794576	−	0.0577293i
$63$	111.528	+	81.0300i	0.223035	+	0.162045i
$64$	−98.1279	−	302.007i	−0.191656	−	0.589857i
$65$	959.615			1.83116
$66$		0			0
$67$	411.641			0.750596			0.375298	−	0.926904i	$-0.377540\pi$
$67$	411.641			0.750596			0.375298	+	0.926904i	$0.377540\pi$
$68$	−190.946	−	587.670i	−0.340523	−	1.04802i
$69$	−64.0452	−	46.5316i	−0.111741	−	0.0811847i
$70$	−128.893	+	93.6462i	−0.220081	+	0.159898i
$71$	−145.434	+	447.601i	−0.243097	+	0.748176i	0.752846	+	0.658196i	$0.228680\pi$
$71$	−145.434	+	447.601i	−0.243097	+	0.748176i	−0.995944	+	0.0899799i	$0.971320\pi$
$72$	−28.4882	+	87.6775i	−0.0466300	+	0.143512i
$73$	493.986	−	358.902i	0.792009	−	0.575428i	−0.116550	−	0.993185i	$-0.537184\pi$
$73$	493.986	−	358.902i	0.792009	−	0.575428i	0.908559	+	0.417757i	$0.137184\pi$
$74$	−24.1969	−	17.5800i	−0.0380112	−	0.0276167i
$75$	73.8027	+	227.141i	0.113627	+	0.349707i
$76$	−506.985			−0.765199
$77$		0			0
$78$	−323.923			−0.470219
$79$	302.288	+	930.348i	0.430507	+	1.32497i	0.897621	+	0.440768i	$0.145294\pi$
$79$	302.288	+	930.348i	0.430507	+	1.32497i	−0.467114	+	0.884197i	$0.654706\pi$
$80$	534.881	+	388.613i	0.747518	+	0.543104i
$81$	714.005	−	518.755i	0.979431	−	0.711598i
$82$	−62.1932	+	191.411i	−0.0837572	+	0.257778i
$83$	−8.08200	+	24.8738i	−0.0106881	+	0.0328947i	−0.956258	−	0.292523i	$-0.905505\pi$
$83$	−8.08200	+	24.8738i	−0.0106881	+	0.0328947i	0.945570	+	0.325418i	$0.105505\pi$
$84$	−605.995	+	440.281i	−0.787137	+	0.571888i
$85$	861.047	+	625.587i	1.09875	+	0.798288i
$86$	0.517399	+	1.59239i	0.000648750	+	0.00199665i
$87$	−1001.84			−1.23458
$88$		0			0
$89$	−352.887			−0.420292			−0.210146	−	0.977670i	$-0.567394\pi$
$89$	−352.887			−0.420292			−0.210146	+	0.977670i	$0.567394\pi$
$90$	−23.6842	−	72.8926i	−0.0277393	−	0.0853728i
$91$	−1022.22	−	742.689i	−1.17756	−	0.855549i
$92$	80.6382	−	58.5871i	0.0913817	−	0.0663927i
$93$	−119.986	+	369.278i	−0.133784	+	0.411746i
$94$	16.2527	−	50.0208i	0.0178334	−	0.0548857i
$95$	706.471	−	513.281i	0.762973	−	0.554332i
$96$	−614.898	−	446.750i	−0.653727	−	0.474961i
$97$	261.918	+	806.101i	0.274162	+	0.843785i	0.989440	+	0.144944i	$0.0463003\pi$
$97$	261.918	+	806.101i	0.274162	+	0.843785i	−0.715277	+	0.698841i	$0.753700\pi$
$98$	−41.3140			−0.0425851
$99$		0			0
$100$	−300.708			−0.300708
$101$	−399.702	−	1230.15i	−0.393780	−	1.21193i	−0.929908	−	0.367793i	$-0.880113\pi$
$101$	−399.702	−	1230.15i	−0.393780	−	1.21193i	0.536127	−	0.844137i	$-0.319887\pi$
$102$	−290.651	−	211.170i	−0.282144	−	0.204990i
$103$	1395.75	−	1014.07i	1.33522	−	0.970091i	0.335611	−	0.942001i	$-0.391057\pi$
$103$	1395.75	−	1014.07i	1.33522	−	0.970091i	0.999605	−	0.0280904i	$-0.00894263\pi$
$104$	261.111	−	803.618i	0.246193	−	0.757704i
$105$	398.691	−	1227.04i	0.370554	−	1.14045i
$106$	88.2470	−	64.1152i	0.0808614	−	0.0587493i
$107$	−391.709	−	284.593i	−0.353906	−	0.257128i	0.396600	−	0.917992i	$-0.370190\pi$
$107$	−391.709	−	284.593i	−0.353906	−	0.257128i	−0.750506	+	0.660864i	$0.770190\pi$
$108$	257.835	+	793.535i	0.229724	+	0.707018i
$109$	64.2563			0.0564645			0.0282323	−	0.999601i	$-0.491012\pi$
$109$	64.2563			0.0564645			0.0282323	+	0.999601i	$0.491012\pi$
$110$		0			0
$111$	242.205			0.207109
$112$	−269.013	−	827.936i	−0.226958	−	0.698505i
$113$	1622.15	+	1178.56i	1.35043	+	0.981145i	0.998990	+	0.0449344i	$0.0143079\pi$
$113$	1622.15	+	1178.56i	1.35043	+	0.981145i	0.351440	+	0.936210i	$0.385692\pi$
$114$	−238.473	+	173.261i	−0.195921	+	0.142345i
$115$	−53.0527	+	163.280i	−0.0430191	+	0.132399i
$116$	389.792	−	1199.66i	0.311994	−	0.960219i
$117$	491.758	−	357.283i	0.388573	−	0.282315i
$118$	−323.145	−	234.779i	−0.252101	−	0.183162i
$119$	−433.055	−	1332.81i	−0.333597	−	1.02671i
$120$	862.797			0.656352
$121$		0			0
$122$	−74.1587			−0.0550329
$123$	−503.645	−	1550.06i	−0.369205	−	1.13629i
$124$	−395.512	−	287.356i	−0.286436	−	0.208108i
$125$	−881.102	+	640.158i	−0.630465	+	0.458060i
$126$	−31.1853	+	95.9786i	−0.0220493	+	0.0678608i
$127$	−33.8698	+	104.240i	−0.0236650	+	0.0728334i	−0.962192	−	0.272374i	$-0.912191\pi$
$127$	−33.8698	+	104.240i	−0.0236650	+	0.0728334i	0.938527	+	0.345207i	$0.112191\pi$
$128$	1017.86	−	739.518i	0.702867	−	0.510662i
$129$	−10.9694	−	7.96973i	−0.00748683	−	0.00543950i
$130$	217.080	+	668.105i	0.146456	+	0.450744i
$131$	−1156.71			−0.771469			−0.385734	−	0.922610i	$-0.626052\pi$
$131$	−1156.71			−0.771469			−0.385734	+	0.922610i	$0.626052\pi$
$132$		0			0
$133$	−1149.82			−0.749636
$134$	93.1198	+	286.593i	0.0600323	+	0.184760i
$135$	−1162.68	−	844.735i	−0.741240	−	0.538542i
$136$	758.181	−	550.851i	0.478041	−	0.347317i
$137$	61.2853	−	188.617i	0.0382186	−	0.117625i	−0.930127	−	0.367238i	$-0.880303\pi$
$137$	61.2853	−	188.617i	0.0382186	−	0.117625i	0.968346	+	0.249613i	$0.0803035\pi$
$138$	17.9082	−	55.1158i	0.0110467	−	0.0339983i
$139$	−2346.26	+	1704.66i	−1.43171	+	1.04020i	−0.442011	+	0.897010i	$0.645735\pi$
$139$	−2346.26	+	1704.66i	−1.43171	+	1.04020i	−0.989696	+	0.143186i	$0.954265\pi$
$140$	1314.21	+	954.831i	0.793366	+	0.576414i
$141$	131.616	+	405.072i	0.0786104	+	0.241938i
$142$	−344.529			−0.203607
$143$		0			0
$144$	418.789			0.242355
$145$	671.391	+	2066.33i	0.384524	+	1.18344i
$146$	361.623	+	262.734i	0.204987	+	0.148932i
$147$	270.668	−	196.652i	0.151866	−	0.110337i
$148$	−94.2367	+	290.031i	−0.0523393	+	0.161084i
$149$	−1077.96	+	3317.61i	−0.592683	+	1.82409i	−0.0267432	+	0.999642i	$0.508514\pi$
$149$	−1077.96	+	3317.61i	−0.592683	+	1.82409i	−0.565939	+	0.824447i	$0.691486\pi$
$150$	−141.445	+	102.766i	−0.0769931	+	0.0559388i
$151$	−941.148	−	683.784i	−0.507216	−	0.368514i	0.304551	−	0.952496i	$-0.401494\pi$
$151$	−941.148	−	683.784i	−0.507216	−	0.368514i	−0.811766	+	0.583982i	$0.801494\pi$
$152$	−237.610	−	731.290i	−0.126794	−	0.390233i
$153$	674.164			0.356228
$154$		0			0
$155$	842.061			0.436361
$156$	1020.61	+	3141.12i	0.523810	+	1.61212i
$157$	−276.730	−	201.056i	−0.140672	−	0.102204i	0.515224	−	0.857056i	$-0.327709\pi$
$157$	−276.730	−	201.056i	−0.140672	−	0.102204i	−0.655895	+	0.754852i	$0.727709\pi$
$158$	−579.346	+	420.919i	−0.291711	+	0.211940i
$159$	−272.965	+	840.099i	−0.136148	+	0.419020i
$160$	−509.360	+	1567.65i	−0.251678	+	0.774584i
$161$	182.883	−	132.873i	0.0895232	−	0.0650424i
$162$	522.688	+	379.755i	0.253495	+	0.184175i
$163$	−431.045	−	1326.62i	−0.207129	−	0.637479i	−0.999619	−	0.0275936i	$-0.991216\pi$
$163$	−431.045	−	1326.62i	−0.207129	−	0.637479i	0.792490	−	0.609885i	$-0.208784\pi$
$164$	2052.09			0.977082
$165$		0			0
$166$	−19.1460			−0.00895191
$167$	−147.927	−	455.273i	−0.0685447	−	0.210959i	0.910917	−	0.412590i	$-0.135376\pi$
$167$	−147.927	−	455.273i	−0.0685447	−	0.210959i	−0.979462	+	0.201631i	$0.935376\pi$
$168$	−919.089	−	667.757i	−0.422079	−	0.306658i
$169$	−2729.85	+	1983.35i	−1.24254	+	0.902755i
$170$	−240.765	+	740.998i	−0.108622	+	0.334305i
$171$	170.929	−	526.065i	0.0764401	−	0.235259i
$172$	13.8114	−	10.0346i	0.00612272	−	0.00444841i
$173$	1463.18	+	1063.06i	0.643024	+	0.467184i	0.860888	−	0.508795i	$-0.169909\pi$
$173$	1463.18	+	1063.06i	0.643024	+	0.467184i	−0.217864	+	0.975979i	$0.569909\pi$
$174$	−226.631	−	697.500i	−0.0987407	−	0.303893i
$175$	−681.990			−0.294592
$176$		0			0
$177$	3234.61			1.37361
$178$	−79.8288	−	245.688i	−0.0336147	−	0.103456i
$179$	3583.82	+	2603.80i	1.49647	+	1.08725i	0.971763	+	0.235960i	$0.0758235\pi$
$179$	3583.82	+	2603.80i	1.49647	+	1.08725i	0.524703	+	0.851285i	$0.324176\pi$
$180$	−632.224	+	459.338i	−0.261795	+	0.190206i
$181$	1053.49	−	3242.32i	0.432627	−	1.33149i	−0.462872	−	0.886425i	$-0.653181\pi$
$181$	1053.49	−	3242.32i	0.432627	−	1.33149i	0.895499	−	0.445064i	$-0.146819\pi$
$182$	285.833	−	879.703i	0.116414	−	0.358285i
$183$	485.849	−	352.990i	0.196257	−	0.142589i
$184$	122.301	+	88.8567i	0.0490007	+	0.0356011i
$185$	−162.316	−	499.558i	−0.0645067	−	0.198531i
$186$	−284.242			−0.112052
$187$		0			0
$188$	−536.267			−0.208039
$189$	584.757	+	1799.70i	0.225052	+	0.692638i
$190$	517.173	+	375.748i	0.197472	+	0.143472i
$191$	−2365.37	+	1718.54i	−0.896083	+	0.651043i	−0.937457	−	0.348101i	$-0.886827\pi$
$191$	−2365.37	+	1718.54i	−0.896083	+	0.651043i	0.0413737	+	0.999144i	$0.486827\pi$
$192$	−581.722	+	1790.36i	−0.218657	+	0.672958i
$193$	767.655	−	2362.60i	0.286306	−	0.881159i	−0.699698	−	0.714438i	$-0.746682\pi$
$193$	767.655	−	2362.60i	0.286306	−	0.881159i	0.986004	−	0.166720i	$-0.0533177\pi$
$194$	−501.975	+	364.706i	−0.185772	+	0.134971i
$195$	−4602.33	−	3343.79i	−1.69015	−	1.22797i
$196$	130.171	+	400.626i	0.0474386	+	0.146001i
$197$	5125.67			1.85375			0.926876	−	0.375369i	$-0.122484\pi$
$197$	5125.67			1.85375			0.926876	+	0.375369i	$0.122484\pi$
$198$		0			0
$199$	−7.69219			−0.00274013			−0.00137006	−	0.999999i	$-0.500436\pi$
$199$	−7.69219			−0.00274013			−0.00137006	+	0.999999i	$0.500436\pi$
$200$	−140.934	−	433.750i	−0.0498276	−	0.153354i
$201$	−1974.24	−	1434.37i	−0.692796	−	0.503346i
$202$	766.042	−	556.562i	0.266824	−	0.193859i
$203$	884.029	−	2720.76i	0.305649	−	0.940690i
$204$	−1131.96	+	3483.83i	−0.388497	+	1.19567i
$205$	−2859.54	+	2077.58i	−0.974240	+	0.707826i
$206$	1021.76	+	742.352i	0.345579	+	0.251078i
$207$	33.6050	+	103.426i	0.0112836	+	0.0347274i
$208$	−3838.46			−1.27956
$209$		0			0
$210$	944.484			0.310360
$211$	−960.222	−	2955.26i	−0.313291	−	0.964211i	−0.976452	−	0.215734i	$-0.930786\pi$
$211$	−960.222	−	2955.26i	−0.313291	−	0.964211i	0.663161	−	0.748477i	$-0.269214\pi$
$212$	−899.780	−	653.729i	−0.291496	−	0.211784i
$213$	2257.18	−	1639.94i	0.726100	−	0.527542i
$214$	109.529	−	337.096i	0.0349872	−	0.107680i
$215$	−9.08665	+	27.9658i	−0.00288234	+	0.00887095i
$216$	−1023.78	+	743.818i	−0.322496	+	0.234307i
$217$	−897.001	−	651.709i	−0.280610	−	0.203875i
$218$	14.5358	+	44.7366i	0.00451600	+	0.0138988i
$219$	−3619.76			−1.11690
$220$		0			0
$221$	−6179.13			−1.88078
$222$	54.7907	+	168.628i	0.0165645	+	0.0509802i
$223$	9.96586	+	7.24062i	0.00299266	+	0.00217430i	0.589281	−	0.807928i	$-0.299411\pi$
$223$	9.96586	+	7.24062i	0.00299266	+	0.00217430i	−0.586288	+	0.810103i	$0.699411\pi$
$224$	1755.87	−	1275.71i	0.523744	−	0.380522i
$225$	101.383	−	312.025i	0.0300394	−	0.0924518i
$226$	−453.582	+	1395.98i	−0.133504	+	0.410882i
$227$	3734.34	−	2713.16i	1.09188	−	0.793298i	0.112165	−	0.993690i	$-0.464221\pi$
$227$	3734.34	−	2713.16i	1.09188	−	0.793298i	0.979716	+	0.200391i	$0.0642214\pi$
$228$	2431.51	+	1766.59i	0.706274	+	0.513138i
$229$	1568.15	+	4826.26i	0.452516	+	1.39270i	0.874027	+	0.485877i	$0.161500\pi$
$229$	1568.15	+	4826.26i	0.452516	+	1.39270i	−0.421512	+	0.906823i	$0.638500\pi$
$230$	−125.680			−0.0360309
$231$		0			0
$232$	1913.11			0.541386
$233$	−65.4135	−	201.322i	−0.0183922	−	0.0566054i	0.941439	−	0.337183i	$-0.109474\pi$
$233$	−65.4135	−	201.322i	−0.0183922	−	0.0566054i	−0.959831	+	0.280577i	$0.909474\pi$
$234$	359.992	+	261.549i	0.100570	+	0.0730684i
$235$	747.275	−	542.927i	0.207433	−	0.150709i
$236$	−1258.52	+	3873.31i	−0.347129	+	1.06835i
$237$	1792.03	−	5515.29i	0.491159	−	1.51163i
$238$	829.964	−	603.004i	0.226044	−	0.164231i
$239$	3488.88	+	2534.82i	0.944254	+	0.686041i	0.949441	−	0.313946i	$-0.101651\pi$
$239$	3488.88	+	2534.82i	0.944254	+	0.686041i	−0.00518659	+	0.999987i	$0.501651\pi$
$240$	−1211.17	−	3727.59i	−0.325753	−	1.00256i
$241$	996.584			0.266372			0.133186	−	0.991091i	$-0.457479\pi$
$241$	996.584			0.266372			0.133186	+	0.991091i	$0.457479\pi$
$242$		0			0
$243$	−2213.80			−0.584426
$244$	233.658	+	719.125i	0.0613050	+	0.188677i
$245$	−586.993	−	426.475i	−0.153068	−	0.111210i
$246$	965.253	−	701.297i	0.250172	−	0.181761i
$247$	−1566.67	+	4821.71i	−0.403582	+	1.24210i
$248$	229.125	−	705.174i	0.0586671	−	0.180559i
$249$	125.435	−	91.1335i	0.0319241	−	0.0231942i
$250$	−645.012	−	468.628i	−0.163176	−	0.118555i
$251$	−85.5644	−	263.340i	−0.0215170	−	0.0662226i	0.939721	−	0.341941i	$-0.111084\pi$
$251$	−85.5644	−	263.340i	−0.0215170	−	0.0662226i	−0.961238	+	0.275718i	$0.911084\pi$
$252$	1028.97			0.257219
$253$		0			0
$254$	−80.2364			−0.0198208
$255$	−1949.73	−	6000.65i	−0.478811	−	1.47363i
$256$	−1310.09	−	951.838i	−0.319847	−	0.232382i
$257$	2617.31	−	1901.59i	0.635267	−	0.461548i	−0.222954	−	0.974829i	$-0.571570\pi$
$257$	2617.31	−	1901.59i	0.635267	−	0.461548i	0.858221	+	0.513281i	$0.171570\pi$
$258$	3.06724	−	9.44001i	0.000740148	−	0.00227794i
$259$	−213.724	+	657.775i	−0.0512748	+	0.157808i
$260$	5794.72	−	4210.11i	1.38220	−	1.00423i
$261$	1113.39	+	808.925i	0.264050	+	0.191844i
$262$	−261.667	−	805.328i	−0.0617017	−	0.189898i
$263$	−207.944			−0.0487544			−0.0243772	−	0.999703i	$-0.507760\pi$
$263$	−207.944			−0.0487544			−0.0243772	+	0.999703i	$0.507760\pi$
$264$		0			0
$265$	1915.67			0.444071
$266$	−260.107	−	800.526i	−0.0599555	−	0.184524i
$267$	1692.45	+	1229.64i	0.387927	+	0.281845i
$268$	2485.73	−	1805.99i	0.566567	−	0.411635i
$269$	1555.29	−	4786.70i	0.352520	−	1.08495i	−0.604913	−	0.796291i	$-0.706792\pi$
$269$	1555.29	−	4786.70i	0.352520	−	1.08495i	0.957433	−	0.288654i	$-0.0932078\pi$
$270$	325.106	−	1000.57i	0.0732790	−	0.225530i
$271$	1203.02	−	874.043i	0.269661	−	0.195920i	−0.444734	−	0.895663i	$-0.646702\pi$
$271$	1203.02	−	874.043i	0.269661	−	0.195920i	0.714395	+	0.699742i	$0.246702\pi$
$272$	−3444.19	−	2502.35i	−0.767774	−	0.557821i
$273$	2314.70	+	7123.90i	0.513157	+	1.57933i
$274$	145.183			0.0320102
$275$		0			0
$276$	−590.890			−0.128867
$277$	72.8773	+	224.293i	0.0158078	+	0.0486515i	0.958649	−	0.284590i	$-0.0918575\pi$
$277$	72.8773	+	224.293i	0.0158078	+	0.0486515i	−0.942841	+	0.333242i	$0.891858\pi$
$278$	−1717.58	−	1247.90i	−0.370553	−	0.269223i
$279$	431.517	−	313.515i	0.0925959	−	0.0672748i
$280$	−761.340	+	2343.16i	−0.162496	+	0.500110i
$281$	1518.82	−	4674.46i	0.322439	−	0.992365i	−0.650144	−	0.759811i	$-0.725292\pi$
$281$	1518.82	−	4674.46i	0.322439	−	0.992365i	0.972583	−	0.232555i	$-0.0747084\pi$
$282$	−252.246	+	183.268i	−0.0532662	+	0.0387001i
$283$	−4206.53	−	3056.22i	−0.883577	−	0.641956i	0.0506182	−	0.998718i	$-0.483881\pi$
$283$	−4206.53	−	3056.22i	−0.883577	−	0.641956i	−0.934195	+	0.356762i	$0.883881\pi$
$284$	1085.54	+	3340.94i	0.226813	+	0.698058i
$285$	−5176.78			−1.07595
$286$		0			0
$287$	4654.04			0.957210
$288$	322.642	+	992.991i	0.0660134	+	0.203169i
$289$	−1569.73	−	1140.47i	−0.319505	−	0.232134i
$290$	−1286.74	+	934.874i	−0.260552	+	0.189302i
$291$	1552.70	−	4778.73i	0.312787	−	0.962660i
$292$	1408.37	−	4334.52i	0.282255	−	0.868693i
$293$	−7184.81	+	5220.07i	−1.43256	+	1.04082i	−0.443032	+	0.896506i	$0.646097\pi$
$293$	−7184.81	+	5220.07i	−1.43256	+	1.04082i	−0.989532	+	0.144313i	$0.953903\pi$
$294$	198.143	+	143.959i	0.0393058	+	0.0285573i
$295$	−2167.71	−	6671.52i	−0.427827	−	1.31671i
$296$	−462.515			−0.0908215
$297$		0			0
$298$	−2553.64			−0.496405
$299$	−308.011	−	947.959i	−0.0595743	−	0.183351i
$300$	1442.20	+	1047.82i	0.277551	+	0.201653i
$301$	31.3235	−	22.7579i	0.00599819	−	0.00435794i
$302$	263.163	−	809.931i	0.0501434	−	0.154325i
$303$	−2369.51	+	7292.61i	−0.449257	+	1.38267i
$304$	−2825.88	+	2053.13i	−0.533143	+	0.387351i
$305$	−1053.65	−	765.524i	−0.197810	−	0.143717i
$306$	152.507	+	469.368i	0.0284910	+	0.0876862i
$307$	1497.93			0.278474			0.139237	−	0.990259i	$-0.455535\pi$
$307$	1497.93			0.278474			0.139237	+	0.990259i	$0.455535\pi$
$308$		0			0
$309$	−10227.6			−1.88293
$310$	190.488	+	586.261i	0.0349000	+	0.107411i
$311$	6055.25	+	4399.40i	1.10406	+	0.802145i	0.981718	−	0.190343i	$-0.0609601\pi$
$311$	6055.25	+	4399.40i	1.10406	+	0.802145i	0.122340	+	0.992488i	$0.460960\pi$
$312$	−4052.51	+	2944.32i	−0.735347	+	0.534261i
$313$	−203.445	+	626.140i	−0.0367393	+	0.113072i	−0.967744	−	0.251934i	$-0.918933\pi$
$313$	−203.445	+	626.140i	−0.0367393	+	0.113072i	0.931005	+	0.365007i	$0.118933\pi$
$314$	77.3787	−	238.147i	0.0139068	−	0.0428007i
$315$	−1433.85	+	1041.75i	−0.256471	+	0.186337i
$316$	5907.10	+	4291.76i	1.05158	+	0.764020i
$317$	72.2196	+	222.269i	0.0127958	+	0.0393813i	0.957251	−	0.289260i	$-0.0934092\pi$
$317$	72.2196	+	222.269i	0.0127958	+	0.0393813i	−0.944455	+	0.328641i	$0.893409\pi$
$318$	−646.645			−0.114032
$319$		0			0
$320$	4082.53			0.713189
$321$	886.976	+	2729.83i	0.154225	+	0.474655i
$322$	133.880	+	97.2695i	0.0231703	+	0.0168342i
$323$	−4549.09	+	3305.11i	−0.783647	+	0.569353i
$324$	2035.65	−	6265.09i	0.349049	−	1.07426i
$325$	−929.238	+	2859.90i	−0.158599	+	0.488119i
$326$	826.113	−	600.206i	0.140350	−	0.101970i
$327$	−308.174	−	223.902i	−0.0521164	−	0.0378648i
$328$	961.762	+	2960.00i	0.161904	+	0.498288i
$329$	−1216.23			−0.203808
$330$		0			0
$331$	8532.95			1.41696			0.708480	−	0.705731i	$-0.249381\pi$
$331$	8532.95			1.41696			0.708480	+	0.705731i	$0.249381\pi$
$332$	60.3249	+	185.661i	0.00997216	+	0.0306912i
$333$	−269.174	−	195.567i	−0.0442963	−	0.0321832i
$334$	283.508	−	205.980i	0.0464457	−	0.0337448i
$335$	−1635.39	+	5033.20i	−0.266719	+	0.820876i
$336$	−1594.76	+	4908.17i	−0.258933	+	0.796913i
$337$	9458.37	−	6871.90i	1.52887	−	1.11079i	0.572011	−	0.820246i	$-0.306163\pi$
$337$	9458.37	−	6871.90i	1.52887	−	1.11079i	0.956861	−	0.290545i	$-0.0938366\pi$
$338$	−1998.39	−	1451.92i	−0.321592	−	0.233650i
$339$	−3673.14	−	11304.8i	−0.588489	−	1.81118i
$340$	7944.14			1.26715
$341$		0			0
$342$	404.925			0.0640229
$343$	2089.49	+	6430.79i	0.328927	+	1.01233i
$344$	20.9472	+	15.2190i	0.00328313	+	0.00238533i
$345$	823.391	−	598.229i	0.128492	−	0.0933552i
$346$	−409.131	+	1259.18i	−0.0635694	+	0.195647i
$347$	−1421.11	+	4373.71i	−0.219853	+	0.676637i	0.778921	+	0.627123i	$0.215768\pi$
$347$	−1421.11	+	4373.71i	−0.219853	+	0.676637i	−0.998773	+	0.0495148i	$0.984232\pi$
$348$	−6049.67	+	4395.34i	−0.931886	+	0.677055i
$349$	5436.81	+	3950.08i	0.833885	+	0.605853i	0.920656	−	0.390375i	$-0.127655\pi$
$349$	5436.81	+	3950.08i	0.833885	+	0.605853i	−0.0867706	+	0.996228i	$0.527655\pi$
$350$	−154.277	−	474.816i	−0.0235613	−	0.0725142i
$351$	8343.72			1.26882
$352$		0			0
$353$	5738.70			0.865270			0.432635	−	0.901569i	$-0.357584\pi$
$353$	5738.70			0.865270			0.432635	+	0.901569i	$0.357584\pi$
$354$	731.721	+	2252.01i	0.109860	+	0.338115i
$355$	−4895.11	−	3556.50i	−0.731846	−	0.531717i
$356$	−2130.94	+	1548.22i	−0.317246	+	0.230493i
$357$	−2567.24	+	7901.14i	−0.380595	+	1.17135i
$358$	−1002.10	+	3084.15i	−0.147941	+	0.455315i
$359$	−3329.32	+	2418.89i	−0.489456	+	0.355611i	−0.804975	−	0.593308i	$-0.797821\pi$
$359$	−3329.32	+	2418.89i	−0.489456	+	0.355611i	0.315519	+	0.948919i	$0.397821\pi$
$360$	−958.869	−	696.659i	−0.140380	−	0.101992i
$361$	−693.885	−	2135.56i	−0.101164	−	0.311351i
$362$	2495.69			0.362349
$363$		0			0
$364$	−9431.18			−1.35804
$365$	2425.82	+	7465.91i	0.347872	+	1.07064i
$366$	355.666	+	258.407i	0.0507950	+	0.0369047i
$367$	−7817.53	+	5679.77i	−1.11191	+	0.807851i	−0.982964	−	0.183800i	$-0.941160\pi$
$367$	−7817.53	+	5679.77i	−1.11191	+	0.807851i	−0.128948	+	0.991651i	$0.541160\pi$
$368$	212.211	−	653.118i	0.0300605	−	0.0925167i
$369$	−691.859	+	2129.32i	−0.0976064	+	0.300402i
$370$	311.085	−	226.016i	0.0437095	−	0.0317568i
$371$	−2040.66	−	1482.62i	−0.285568	−	0.207477i
$372$	895.586	+	2756.33i	0.124822	+	0.384164i
$373$	141.780			0.0196812			0.00984062	−	0.999952i	$-0.496868\pi$
$373$	141.780			0.0196812			0.00984062	+	0.999952i	$0.496868\pi$
$374$		0			0
$375$	6456.42			0.889088
$376$	−251.334	−	773.527i	−0.0344723	−	0.106095i
$377$	−10204.9	−	7414.29i	−1.39411	−	1.01288i
$378$	−1120.71	+	814.241i	−0.152494	+	0.110794i
$379$	−871.345	+	2681.73i	−0.118095	+	0.363459i	−0.992580	−	0.121594i	$-0.961200\pi$
$379$	−871.345	+	2681.73i	−0.118095	+	0.363459i	0.874485	+	0.485053i	$0.161200\pi$
$380$	2014.17	−	6198.99i	0.271908	−	0.836845i
$381$	525.667	−	381.920i	0.0706844	−	0.0513552i
$382$	−1731.57	−	1258.06i	−0.231923	−	0.168502i
$383$	−1958.50	−	6027.64i	−0.261291	−	0.804172i	−0.992525	−	0.122045i	$-0.961055\pi$
$383$	−1958.50	−	6027.64i	−0.261291	−	0.804172i	0.731233	−	0.682128i	$-0.238945\pi$
$384$	−7458.53			−0.991189
$385$		0			0
$386$	1818.55			0.239797
$387$	5.75573	+	17.7143i	0.000756021	+	0.00232679i
$388$	5118.21	+	3718.60i	0.669685	+	0.486555i
$389$	7123.60	−	5175.60i	0.928486	−	0.674584i	−0.0171360	−	0.999853i	$-0.505455\pi$
$389$	7123.60	−	5175.60i	0.928486	−	0.674584i	0.945622	+	0.325269i	$0.105455\pi$
$390$	1286.90	−	3960.66i	0.167089	−	0.514246i
$391$	341.616	−	1051.38i	0.0441848	−	0.135987i
$392$	−516.868	+	375.526i	−0.0665963	+	0.0483851i
$393$	5547.61	+	4030.58i	0.712061	+	0.517343i
$394$	1159.51	+	3568.60i	0.148262	+	0.456304i
$395$	−12576.5			−1.60200
$396$		0			0
$397$	4315.26			0.545534			0.272767	−	0.962080i	$-0.412061\pi$
$397$	4315.26			0.545534			0.272767	+	0.962080i	$0.412061\pi$
$398$	−1.74010	−	5.35547i	−0.000219154	−	0.000674486i
$399$	5514.53	+	4006.54i	0.691910	+	0.502702i
$400$	−1676.12	+	1217.77i	−0.209515	+	0.152221i
$401$	111.766	−	343.979i	0.0139185	−	0.0428367i	−0.943856	−	0.330357i	$-0.892831\pi$
$401$	111.766	−	343.979i	0.0139185	−	0.0428367i	0.957775	+	0.287520i	$0.0928309\pi$
$402$	552.033	−	1698.98i	0.0684899	−	0.210790i
$403$	−3955.12	+	2873.56i	−0.488880	+	0.355192i
$404$	−7810.68	−	5674.79i	−0.961870	−	0.698840i
$405$	3506.27	+	10791.2i	0.430193	+	1.32400i
$406$	2094.24			0.255998
$407$		0			0
$408$	−5555.70			−0.674137
$409$	−2849.29	−	8769.22i	−0.344470	−	1.06017i	−0.961867	−	0.273519i	$-0.911812\pi$
$409$	−2849.29	−	8769.22i	−0.344470	−	1.06017i	0.617396	−	0.786652i	$-0.288188\pi$
$410$	−2093.33	−	1520.89i	−0.252152	−	0.183199i
$411$	−951.162	+	691.060i	−0.114154	+	0.0829378i
$412$	3979.33	−	12247.1i	0.475843	−	1.46449i
$413$	−2854.25	+	8784.48i	−0.340069	+	1.04662i
$414$	−64.4052	+	46.7931i	−0.00764575	+	0.00555496i
$415$	−272.028	−	197.640i	−0.0321767	−	0.0233777i
$416$	−2957.21	−	9101.37i	−0.348532	−	1.07267i
$417$	17192.6			2.01901
$418$		0			0
$419$	−14912.9			−1.73876			−0.869380	−	0.494144i	$-0.835481\pi$
$419$	−14912.9			−1.73876			−0.869380	+	0.494144i	$0.835481\pi$
$420$	−2975.87	−	9158.78i	−0.345732	−	1.06405i
$421$	10910.4	+	7926.88i	1.26304	+	0.917654i	0.998903	−	0.0468306i	$-0.0149121\pi$
$421$	10910.4	+	7926.88i	1.26304	+	0.917654i	0.264139	+	0.964485i	$0.414912\pi$
$422$	1840.30	−	1337.05i	0.212285	−	0.154234i
$423$	180.801	−	556.449i	0.0207822	−	0.0639610i
$424$	521.254	−	1604.26i	0.0597036	−	0.183749i
$425$	−2698.20	+	1960.36i	−0.307958	+	0.223744i
$426$	1652.37	+	1200.52i	0.187928	+	0.136538i
$427$	529.925	+	1630.94i	0.0600582	+	0.184840i
$428$	−3613.96			−0.408148
$429$		0			0
$430$	−21.5260			−0.00241413
$431$	−125.564	−	386.447i	−0.0140330	−	0.0431890i	0.943795	−	0.330532i	$-0.107228\pi$
$431$	−125.564	−	386.447i	−0.0140330	−	0.0431890i	−0.957828	+	0.287343i	$0.907228\pi$
$432$	4650.71	+	3378.94i	0.517957	+	0.376318i
$433$	1429.29	−	1038.44i	0.158631	−	0.115252i	−0.505638	−	0.862746i	$-0.668743\pi$
$433$	1429.29	−	1038.44i	0.158631	−	0.115252i	0.664269	+	0.747494i	$0.268743\pi$
$434$	250.818	−	771.938i	0.0277411	−	0.0853784i
$435$	3980.14	−	12249.6i	0.438697	−	1.35017i
$436$	388.017	−	281.911i	0.0426207	−	0.0309658i
$437$	−733.805	−	533.140i	−0.0803264	−	0.0583606i
$438$	−818.848	−	2520.16i	−0.0893289	−	0.274926i
$439$	−7824.19			−0.850634			−0.425317	−	0.905044i	$-0.639837\pi$
$439$	−7824.19			−0.850634			−0.425317	+	0.905044i	$0.639837\pi$
$440$		0			0
$441$	−459.591			−0.0496265
$442$	−1397.82	−	4302.04i	−0.150424	−	0.462958i
$443$	−9439.52	−	6858.21i	−1.01238	−	0.735538i	−0.0476744	−	0.998863i	$-0.515181\pi$
$443$	−9439.52	−	6858.21i	−1.01238	−	0.735538i	−0.964707	+	0.263325i	$0.915181\pi$
$444$	1462.58	−	1062.62i	0.156331	−	0.113581i
$445$	1401.97	−	4314.81i	0.149348	−	0.459644i
$446$	−2.78664	+	8.57640i	−0.000295855	+	0.000910547i
$447$	16730.2	−	12155.2i	1.77027	−	1.28617i
$448$	−4348.89	−	3159.66i	−0.458629	−	0.333214i
$449$	5245.64	+	16144.4i	0.551352	+	1.69689i	0.705387	+	0.708822i	$0.250773\pi$
$449$	5245.64	+	16144.4i	0.551352	+	1.69689i	−0.154035	+	0.988065i	$0.549227\pi$
$450$	240.173			0.0251597
$451$		0			0
$452$	14966.1			1.55741
$453$	2131.11	+	6558.88i	0.221034	+	0.680272i
$454$	2733.73	+	1986.17i	0.282600	+	0.205321i
$455$	13142.1	−	9548.31i	1.35409	−	0.983806i
$456$	−1408.60	+	4335.23i	−0.144658	+	0.445210i
$457$	5003.87	−	15400.3i	0.512190	−	1.57636i	−0.276146	−	0.961116i	$-0.589057\pi$
$457$	5003.87	−	15400.3i	0.512190	−	1.57636i	0.788337	−	0.615244i	$-0.210943\pi$
$458$	−3005.41	+	2183.56i	−0.306623	+	0.222775i
$459$	7486.68	+	5439.39i	0.761325	+	0.553135i
$460$	395.991	+	1218.73i	0.0401373	+	0.123530i
$461$	−8586.04			−0.867444			−0.433722	−	0.901047i	$-0.642800\pi$
$461$	−8586.04			−0.867444			−0.433722	+	0.901047i	$0.642800\pi$
$462$		0			0
$463$	−7917.20			−0.794694			−0.397347	−	0.917668i	$-0.630069\pi$
$463$	−7917.20			−0.794694			−0.397347	+	0.917668i	$0.630069\pi$
$464$	−2685.56	−	8265.31i	−0.268694	−	0.826956i
$465$	−4038.54	−	2934.17i	−0.402759	−	0.292621i
$466$	125.367	−	91.0846i	0.0124625	−	0.00905454i
$467$	−4683.14	+	14413.2i	−0.464047	+	1.42819i	0.396130	+	0.918194i	$0.370353\pi$
$467$	−4683.14	+	14413.2i	−0.464047	+	1.42819i	−0.860177	+	0.509995i	$0.829647\pi$
$468$	1402.02	−	4314.97i	0.138479	−	0.426195i
$469$	5637.51	−	4095.89i	0.555045	−	0.403264i
$470$	547.043	+	397.450i	0.0536877	+	0.0390064i
$471$	626.619	+	1928.53i	0.0613017	+	0.188667i
$472$	−6176.82			−0.602354
$473$		0			0
$474$	4245.25			0.411373
$475$	845.603	+	2602.50i	0.0816819	+	0.251391i
$476$	−8462.44	−	6148.32i	−0.814864	−	0.592033i
$477$	981.691	−	713.241i	0.0942318	−	0.0684634i
$478$	−975.555	+	3002.45i	−0.0933491	+	0.287299i
$479$	−3090.51	+	9511.62i	−0.294800	+	0.907301i	0.688489	+	0.725247i	$0.258275\pi$
$479$	−3090.51	+	9511.62i	−0.294800	+	0.907301i	−0.983289	+	0.182054i	$0.941725\pi$
$480$	7905.38	−	5743.60i	0.751729	−	0.546163i
$481$	2467.15	+	1792.49i	0.233872	+	0.169918i
$482$	225.443	+	693.843i	0.0213043	+	0.0655678i
$483$	−1340.11			−0.126246
$484$		0			0
$485$	−10896.9			−1.02021
$486$	−500.798	−	1541.30i	−0.0467421	−	0.143857i
$487$	−5699.15	−	4140.68i	−0.530294	−	0.385281i	0.290174	−	0.956974i	$-0.406287\pi$
$487$	−5699.15	−	4140.68i	−0.530294	−	0.385281i	−0.820468	+	0.571693i	$0.806287\pi$
$488$	−927.779	+	674.071i	−0.0860626	+	0.0625282i
$489$	−2555.33	+	7864.48i	−0.236310	+	0.727289i
$490$	164.134	−	505.153i	0.0151323	−	0.0465724i
$491$	−10781.3	+	7833.07i	−0.990944	+	0.719963i	−0.960128	−	0.279562i	$-0.909811\pi$
$491$	−10781.3	+	7833.07i	−0.990944	+	0.719963i	−0.0308160	+	0.999525i	$0.509811\pi$
$492$	−9841.87	−	7150.54i	−0.901841	−	0.655226i
$493$	−4323.20	−	13305.4i	−0.394944	−	1.21551i
$494$	−3711.38			−0.338022
$495$		0			0
$496$	−3368.25			−0.304917
$497$	2461.94	+	7577.09i	0.222200	+	0.683861i
$498$	91.8245	+	66.7144i	0.00826256	+	0.00600310i
$499$	16236.3	−	11796.3i	1.45658	−	1.05827i	0.472346	−	0.881413i	$-0.343407\pi$
$499$	16236.3	−	11796.3i	1.45658	−	1.05827i	0.984237	−	0.176856i	$-0.0565928\pi$
$500$	−2512.05	+	7731.30i	−0.224685	+	0.691509i
$501$	−876.943	+	2698.95i	−0.0782015	+	0.240679i
$502$	163.987	−	119.144i	0.0145799	−	0.0105929i
$503$	6296.05	+	4574.35i	0.558106	+	0.405487i	0.830765	−	0.556623i	$-0.187903\pi$
$503$	6296.05	+	4574.35i	0.558106	+	0.405487i	−0.272660	+	0.962111i	$0.587903\pi$
$504$	482.253	+	1484.22i	0.0426216	+	0.131176i
$505$	16629.3			1.46533
$506$		0			0
$507$	20003.4			1.75224
$508$	252.808	+	778.062i	0.0220798	+	0.0679545i
$509$	1194.05	+	867.531i	0.103979	+	0.0755455i	0.638560	−	0.769572i	$-0.279530\pi$
$509$	1194.05	+	867.531i	0.103979	+	0.0755455i	−0.534581	+	0.845117i	$0.679530\pi$
$510$	3736.73	−	2714.89i	0.324441	−	0.235720i
$511$	3194.11	−	9830.46i	0.276515	−	0.851025i
$512$	3476.63	−	10700.0i	0.300091	−	0.923586i
$513$	6142.66	−	4462.91i	0.528665	−	0.384098i
$514$	1916.01	+	1392.06i	0.164419	+	0.119458i
$515$	6854.12	+	21094.8i	0.586463	+	1.80495i
$516$	−101.205			−0.00863431
$517$		0			0
$518$	−506.305			−0.0429455
$519$	−3313.17	−	10196.9i	−0.280216	−	0.862417i
$520$	8788.62	+	6385.31i	0.741166	+	0.538489i
$521$	−6156.16	+	4472.71i	−0.517670	+	0.376109i	−0.815725	−	0.578439i	$-0.803662\pi$
$521$	−6156.16	+	4472.71i	−0.517670	+	0.376109i	0.298055	+	0.954549i	$0.403662\pi$
$522$	−311.324	+	958.158i	−0.0261040	+	0.0803399i
$523$	−3848.16	+	11843.4i	−0.321737	+	0.990204i	0.651155	+	0.758944i	$0.274285\pi$
$523$	−3848.16	+	11843.4i	−0.321737	+	0.990204i	−0.972892	+	0.231259i	$0.925715\pi$
$524$	−6984.91	+	5074.83i	−0.582323	+	0.423082i
$525$	3270.83	+	2376.40i	0.271906	+	0.197552i
$526$	−47.0404	−	144.775i	−0.00389935	−	0.0120010i
$527$	−5422.18			−0.448186
$528$		0			0
$529$	−11988.7			−0.985344
$530$	433.356	+	1333.73i	0.0355165	+	0.109309i
$531$	−3594.78	−	2611.76i	−0.293786	−	0.213448i
$532$	−6943.26	+	5044.57i	−0.565843	+	0.411109i
$533$	6341.31	−	19516.6i	0.515334	−	1.58603i
$534$	−473.241	+	1456.49i	−0.0383505	+	0.118031i
$535$	5035.97	−	3658.85i	0.406961	−	0.295674i
$536$	3770.01	+	2739.07i	0.303805	+	0.220727i
$537$	−8115.10	−	24975.7i	−0.652128	−	2.00704i
$538$	3684.44			0.295255
$539$		0			0
$540$	−10727.0			−0.854847
$541$	−2877.62	−	8856.40i	−0.228685	−	0.703819i	−0.997897	−	0.0648254i	$-0.979351\pi$
$541$	−2877.62	−	8856.40i	−0.228685	−	0.703819i	0.769212	−	0.638994i	$-0.220649\pi$
$542$	880.670	+	639.844i	0.0697933	+	0.0507078i
$543$	−16350.5	+	11879.3i	−1.29220	+	0.938839i
$544$	3279.86	−	10094.4i	0.258497	−	0.795573i
$545$	−255.280	+	785.672i	−0.0200642	+	0.0617514i
$546$	−4436.19	+	3223.08i	−0.347713	+	0.252629i
$547$	−8914.20	−	6476.54i	−0.696789	−	0.506247i	0.182096	−	0.983281i	$-0.441712\pi$
$547$	−8914.20	−	6476.54i	−0.696789	−	0.506247i	−0.878885	+	0.477034i	$0.841712\pi$
$548$	−457.439	−	1407.85i	−0.0356585	−	0.109745i
$549$	−824.968			−0.0641325
$550$		0			0
$551$	−11478.6			−0.887490
$552$	−276.935	−	852.317i	−0.0213535	−	0.0657192i
$553$	13397.0	+	9733.49i	1.03020	+	0.748481i
$554$	−139.672	+	101.477i	−0.0107113	+	0.00778225i
$555$	−962.244	+	2961.48i	−0.0735946	+	0.226501i
$556$	−6689.27	+	20587.4i	−0.510230	+	1.57033i
$557$	−9723.11	+	7064.25i	−0.739643	+	0.537382i	−0.892599	−	0.450851i	$-0.851121\pi$
$557$	−9723.11	+	7064.25i	−0.739643	+	0.537382i	0.152956	+	0.988233i	$0.451121\pi$
$558$	315.892	+	229.509i	0.0239656	+	0.0174120i
$559$	−52.7548	−	162.362i	−0.00399157	−	0.0122848i
$560$	11192.1			0.844555
$561$		0			0
$562$	3598.04			0.270061
$563$	2708.19	+	8334.95i	0.202729	+	0.623937i	0.999799	+	0.0200493i	$0.00638233\pi$
$563$	2708.19	+	8334.95i	0.202729	+	0.623937i	−0.797070	+	0.603887i	$0.793618\pi$
$564$	2571.94	+	1868.63i	0.192018	+	0.139510i
$565$	−20855.0	+	15152.0i	−1.55288	+	1.12823i
$566$	1176.22	−	3620.05i	0.0873505	−	0.268837i
$567$	4616.76	−	14208.9i	0.341950	−	1.05241i
$568$	−4310.31	+	3131.62i	−0.318410	+	0.231338i
$569$	−8311.16	−	6038.41i	−0.612341	−	0.444892i	0.237897	−	0.971290i	$-0.423542\pi$
$569$	−8311.16	−	6038.41i	−0.612341	−	0.444892i	−0.850238	+	0.526399i	$0.823542\pi$
$570$	−1171.07	−	3604.19i	−0.0860540	−	0.264847i
$571$	−2602.62			−0.190747			−0.0953734	−	0.995442i	$-0.530404\pi$
$571$	−2602.62			−0.190747			−0.0953734	+	0.995442i	$0.530404\pi$
$572$		0			0
$573$	17332.6			1.26366
$574$	1052.82	+	3240.24i	0.0765572	+	0.235619i
$575$	−435.242	−	316.222i	−0.0315667	−	0.0229345i
$576$	2092.11	−	1520.00i	0.151339	−	0.109954i
$577$	−6095.99	+	18761.5i	−0.439825	+	1.35364i	0.448235	+	0.893916i	$0.352053\pi$
$577$	−6095.99	+	18761.5i	−0.439825	+	1.35364i	−0.888060	+	0.459728i	$0.847947\pi$
$578$	438.925	−	1350.87i	0.0315863	−	0.0972127i
$579$	−11914.2	+	8656.17i	−0.855159	+	0.621309i
$580$	13119.8	+	9532.12i	0.939261	+	0.682413i
$581$	136.814	+	421.069i	0.00976935	+	0.0300670i
$582$	3678.30			0.261977
$583$		0			0
$584$	6912.30			0.489783
$585$	2414.88	+	7432.24i	0.170672	+	0.525274i
$586$	−5259.65	−	3821.36i	−0.370775	−	0.269384i
$587$	8184.14	−	5946.12i	0.575461	−	0.418097i	−0.261624	−	0.965170i	$-0.584258\pi$
$587$	8184.14	−	5946.12i	0.575461	−	0.418097i	0.837085	+	0.547073i	$0.184258\pi$
$588$	771.683	−	2374.99i	0.0541219	−	0.166570i
$589$	−1374.75	+	4231.05i	−0.0961725	+	0.295988i
$590$	4154.49	−	3018.41i	0.289894	−	0.210620i
$591$	−24582.8	−	17860.5i	−1.71100	−	1.24312i
$592$	649.265	+	1998.23i	0.0450754	+	0.138728i
$593$	−3130.32			−0.216774			−0.108387	−	0.994109i	$-0.534569\pi$
$593$	−3130.32			−0.216774			−0.108387	+	0.994109i	$0.534569\pi$
$594$		0			0
$595$	18016.9			1.24138
$596$	8045.98	+	24763.0i	0.552980	+	1.70190i
$597$	36.8919	+	26.8035i	0.00252912	+	0.00183751i
$598$	590.313	−	428.887i	0.0403674	−	0.0293286i
$599$	3114.92	−	9586.73i	0.212474	−	0.653928i	−0.786849	−	0.617145i	$-0.788289\pi$
$599$	3114.92	−	9586.73i	0.212474	−	0.653928i	0.999323	−	0.0367829i	$-0.0117110\pi$
$600$	−835.484	+	2571.36i	−0.0568475	+	0.174959i
$601$	3864.69	−	2807.86i	0.262303	−	0.190574i	−0.448859	−	0.893603i	$-0.648169\pi$
$601$	3864.69	−	2807.86i	0.262303	−	0.190574i	0.711162	+	0.703029i	$0.248169\pi$
$602$	22.9304	+	16.6599i	0.00155245	+	0.00112792i
$603$	1035.90	+	3188.17i	0.0699586	+	0.215310i
$604$	−8683.16			−0.584955
$605$		0			0
$606$	−5613.29			−0.376278
$607$	794.591	+	2445.50i	0.0531325	+	0.163525i	0.974102	−	0.226110i	$-0.0726010\pi$
$607$	794.591	+	2445.50i	0.0531325	+	0.163525i	−0.920969	+	0.389635i	$0.872601\pi$
$608$	−7045.27	−	5118.69i	−0.469940	−	0.341431i
$609$	−13720.3	+	9968.41i	−0.912933	+	0.663285i
$610$	294.621	−	906.751i	0.0195555	−	0.0601857i
$611$	−1657.15	+	5100.20i	−0.109724	+	0.337695i
$612$	4071.00	−	2957.75i	0.268889	−	0.195360i
$613$	10284.1	+	7471.84i	0.677604	+	0.492308i	0.872562	−	0.488504i	$-0.162457\pi$
$613$	10284.1	+	7471.84i	0.677604	+	0.492308i	−0.194958	+	0.980812i	$0.562457\pi$
$614$	338.857	+	1042.89i	0.0222722	+	0.0685468i
$615$	20953.8			1.37388
$616$		0			0
$617$	16236.1			1.05939			0.529693	−	0.848189i	$-0.322307\pi$
$617$	16236.1			1.05939			0.529693	+	0.848189i	$0.322307\pi$
$618$	−2313.64	−	7120.66i	−0.150596	−	0.463487i
$619$	−10240.0	−	7439.78i	−0.664910	−	0.483086i	0.203407	−	0.979094i	$-0.434798\pi$
$619$	−10240.0	−	7439.78i	−0.664910	−	0.483086i	−0.868318	+	0.496009i	$0.834798\pi$
$620$	5084.86	−	3694.37i	0.329376	−	0.239305i
$621$	−461.286	+	1419.69i	−0.0298080	+	0.0917396i
$622$	−1693.16	+	5211.01i	−0.109147	+	0.335921i
$623$	−4832.86	+	3511.28i	−0.310794	+	0.225805i
$624$	18409.3	+	13375.2i	1.18103	+	0.858069i
$625$	−5883.02	−	18106.1i	−0.376513	−	1.15879i
$626$	−481.955			−0.0307713
$627$		0			0
$628$	−2553.15			−0.162232
$629$	1045.18	+	3216.74i	0.0662546	+	0.203911i
$630$	−1049.65	−	762.617i	−0.0663796	−	0.0482276i
$631$	3195.59	−	2321.73i	0.201608	−	0.146477i	−0.482401	−	0.875951i	$-0.660235\pi$
$631$	3195.59	−	2321.73i	0.201608	−	0.146477i	0.684008	+	0.729474i	$0.260235\pi$
$632$	−3422.06	+	10532.0i	−0.215383	+	0.662881i
$633$	−5692.39	+	17519.4i	−0.357428	+	1.10005i
$634$	−138.411	+	100.562i	−0.00867038	+	0.00629940i
$635$	−1140.01	−	828.263i	−0.0712437	−	0.0517616i
$636$	2037.44	+	6270.59i	0.127028	+	0.390951i
$637$	4212.44			0.262014
$638$		0			0
$639$	−3832.67			−0.237274
$640$	4998.41	+	15383.5i	0.308718	+	0.950137i
$641$	5985.32	+	4348.59i	0.368808	+	0.267955i	0.756717	−	0.653743i	$-0.226802\pi$
$641$	5985.32	+	4348.59i	0.368808	+	0.267955i	−0.387908	+	0.921698i	$0.626802\pi$
$642$	−1699.92	+	1235.06i	−0.104502	+	0.0759253i
$643$	−3860.14	+	11880.3i	−0.236748	+	0.728637i	0.760136	+	0.649764i	$0.225132\pi$
$643$	−3860.14	+	11880.3i	−0.236748	+	0.728637i	−0.996885	+	0.0788729i	$0.974868\pi$
$644$	521.407	−	1604.72i	0.0319042	−	0.0981910i
$645$	141.027	−	102.462i	0.00860919	−	0.00625494i
$646$	−3330.16	−	2419.51i	−0.202823	−	0.147359i
$647$	−3236.02	−	9959.44i	−0.196632	−	0.605172i	−0.999954	−	0.00962607i	$-0.996936\pi$
$647$	−3236.02	−	9959.44i	−0.196632	−	0.605172i	0.803321	−	0.595546i	$-0.203064\pi$
$648$	9991.02			0.605685
$649$		0			0
$650$	−2201.33			−0.132836
$651$	2031.14	+	6251.22i	0.122284	+	0.376351i
$652$	−8423.18	−	6119.80i	−0.505946	−	0.367592i
$653$	−5127.50	+	3725.34i	−0.307281	+	0.223253i	−0.730729	−	0.682668i	$-0.760820\pi$
$653$	−5127.50	+	3725.34i	−0.307281	+	0.223253i	0.423448	+	0.905920i	$0.360820\pi$
$654$	86.1712	−	265.208i	0.00515223	−	0.0158569i
$655$	4595.44	−	14143.3i	0.274136	−	0.843703i
$656$	11438.2	−	8310.32i	0.680771	−	0.494609i
$657$	4022.82	+	2922.75i	0.238881	+	0.173557i
$658$	−275.130	−	846.762i	−0.0163004	−	0.0501675i
$659$	−15196.7			−0.898302			−0.449151	−	0.893456i	$-0.648274\pi$
$659$	−15196.7			−0.898302			−0.449151	+	0.893456i	$0.648274\pi$
$660$		0			0
$661$	2298.17			0.135232			0.0676161	−	0.997711i	$-0.478461\pi$
$661$	2298.17			0.135232			0.0676161	+	0.997711i	$0.478461\pi$
$662$	1930.29	+	5940.83i	0.113328	+	0.348787i
$663$	29635.2	+	21531.2i	1.73595	+	1.26124i
$664$	−239.530	+	174.029i	−0.0139994	+	0.0101711i
$665$	4568.04	−	14059.0i	0.266377	−	0.819826i
$666$	75.2662	−	231.645i	0.00437914	−	0.0134776i
$667$	1825.73	−	1326.47i	0.105986	−	0.0770033i
$668$	−2890.69	−	2100.21i	−0.167431	−	0.121646i
$669$	−22.5664	−	69.4523i	−0.00130414	−	0.00401372i
$670$	−3874.18			−0.223392
$671$		0			0
$672$	−12866.4			−0.738589
$673$	−7169.08	−	22064.2i	−0.410621	−	1.26376i	−0.916110	−	0.400928i	$-0.868688\pi$
$673$	−7169.08	−	22064.2i	−0.410621	−	1.26376i	0.505489	−	0.862833i	$-0.331312\pi$
$674$	6924.00	+	5030.58i	0.395701	+	0.287494i
$675$	3643.40	−	2647.08i	0.207755	−	0.150943i
$676$	−7782.90	+	23953.3i	−0.442814	+	1.36284i
$677$	662.958	−	2040.38i	0.0376360	−	0.115832i	−0.930473	−	0.366359i	$-0.880604\pi$
$677$	662.958	−	2040.38i	0.0376360	−	0.115832i	0.968109	+	0.250528i	$0.0806041\pi$
$678$	7039.70	−	5114.64i	0.398758	−	0.289715i
$679$	11607.8	+	8433.59i	0.656065	+	0.476659i
$680$	3723.21	+	11458.9i	0.209968	+	0.646217i
$681$	−27364.0			−1.53978
$682$		0			0
$683$	−29544.6			−1.65519			−0.827593	−	0.561329i	$-0.810290\pi$
$683$	−29544.6			−1.65519			−0.827593	+	0.561329i	$0.810290\pi$
$684$	−1275.83	−	3926.60i	−0.0713196	−	0.219499i
$685$	2062.77	+	1498.69i	0.115058	+	0.0835942i
$686$	−4004.58	+	2909.50i	−0.222880	+	0.161932i
$687$	9296.29	−	28611.1i	0.516267	−	1.58891i
$688$	36.3466	−	111.863i	0.00201410	−	0.00619876i
$689$	−8997.80	+	6537.29i	−0.497517	+	0.361467i
$690$	602.764	+	437.934i	0.0332563	+	0.0241621i
$691$	8591.62	+	26442.3i	0.472997	+	1.45573i	0.848641	+	0.528970i	$0.177422\pi$
$691$	8591.62	+	26442.3i	0.472997	+	1.45573i	−0.375644	+	0.926764i	$0.622578\pi$
$692$	13499.5			0.741579
$693$		0			0
$694$	−3366.55			−0.184139
$695$	−11521.8	−	35460.5i	−0.628845	−	1.93539i
$696$	−9175.30	−	6666.24i	−0.499696	−	0.363051i
$697$	18413.1	−	13377.9i	1.00064	−	0.727007i
$698$	−1520.23	+	4678.80i	−0.0824380	+	0.253718i
$699$	−387.785	+	1193.48i	−0.0209834	+	0.0645801i
$700$	−4118.25	+	2992.09i	−0.222365	+	0.161557i
$701$	−15935.8	−	11578.0i	−0.858613	−	0.623819i	0.0688945	−	0.997624i	$-0.478053\pi$
$701$	−15935.8	−	11578.0i	−0.858613	−	0.623819i	−0.927507	+	0.373805i	$0.878053\pi$
$702$	1887.48	+	5809.08i	0.101479	+	0.312321i
$703$	2775.09			0.148883
$704$		0			0
$705$	−5475.78			−0.292524
$706$	1298.19	+	3995.41i	0.0692038	+	0.212987i
$707$	−17714.2	−	12870.1i	−0.942308	−	0.684627i
$708$	19532.5	−	14191.2i	1.03683	−	0.753300i
$709$	5909.18	−	18186.6i	0.313010	−	0.963345i	−0.663556	−	0.748126i	$-0.730954\pi$
$709$	5909.18	−	18186.6i	0.313010	−	0.963345i	0.976566	−	0.215218i	$-0.0690464\pi$
$710$	1368.76	−	4212.62i	0.0723504	−	0.222672i
$711$	−6444.85	+	4682.46i	−0.339945	+	0.246984i
$712$	−3231.91	−	2348.12i	−0.170114	−	0.123595i
$713$	−270.279	−	831.833i	−0.0141964	−	0.0436920i
$714$	−6081.70			−0.318770
$715$		0			0
$716$	33064.8			1.72582
$717$	−7900.12	−	24314.1i	−0.411486	−	1.26642i
$718$	−2437.23	−	1770.75i	−0.126681	−	0.0920389i
$719$	−1486.52	+	1080.02i	−0.0771042	+	0.0560195i	−0.625670	−	0.780088i	$-0.715174\pi$
$719$	−1486.52	+	1080.02i	−0.0771042	+	0.0560195i	0.548565	+	0.836108i	$0.315174\pi$
$720$	−1663.79	+	5120.61i	−0.0861190	+	0.265047i
$721$	9024.91	−	27775.8i	0.466165	−	1.43471i
$722$	1329.85	−	966.196i	0.0685486	−	0.0498034i
$723$	−4779.63	−	3472.61i	−0.245860	−	0.178627i
$724$	−7863.38	−	24201.0i	−0.403647	−	1.24230i
$725$	−6808.33			−0.348765
$726$		0			0
$727$	−7555.46			−0.385442			−0.192721	−	0.981254i	$-0.561731\pi$
$727$	−7555.46			−0.385442			−0.192721	+	0.981254i	$0.561731\pi$
$728$	−4420.15	−	13603.8i	−0.225030	−	0.692570i
$729$	−8660.70	−	6292.36i	−0.440009	−	0.319685i
$730$	−4649.17	+	3377.82i	−0.235717	+	0.171258i
$731$	58.5105	−	180.077i	0.00296045	−	0.00911133i
$732$	1385.17	−	4263.12i	0.0699419	−	0.215259i
$733$	9695.77	−	7044.39i	0.488569	−	0.354966i	−0.316065	−	0.948738i	$-0.602362\pi$
$733$	9695.77	−	7044.39i	0.488569	−	0.354966i	0.804634	+	0.593771i	$0.202362\pi$
$734$	−5722.83	−	4157.88i	−0.287784	−	0.209087i
$735$	1329.17	+	4090.77i	0.0667037	+	0.205293i
$736$	1712.10			0.0857456
$737$		0			0
$738$	−1638.99			−0.0817508
$739$	8387.49	+	25814.0i	0.417508	+	1.28496i	0.909988	+	0.414635i	$0.136091\pi$
$739$	8387.49	+	25814.0i	0.417508	+	1.28496i	−0.492479	+	0.870324i	$0.663909\pi$
$740$	−3171.87	−	2304.50i	−0.157568	−	0.114480i
$741$	24315.1	−	17665.9i	1.20545	−	0.875809i
$742$	570.605	−	1756.14i	0.0282312	−	0.0868868i
$743$	9030.29	−	27792.4i	0.445881	−	1.37228i	−0.435634	−	0.900124i	$-0.643476\pi$
$743$	9030.29	−	27792.4i	0.445881	−	1.37228i	0.881515	−	0.472156i	$-0.156524\pi$
$744$	−3556.07	+	2583.64i	−0.175231	+	0.127313i
$745$	−36282.4	−	26360.7i	−1.78428	−	1.29635i
$746$	32.0730	+	98.7104i	0.00157409	+	0.00484457i
$747$	−212.987			−0.0104321
$748$		0			0
$749$	−8196.29			−0.399847
$750$	1460.55	+	4495.10i	0.0711088	+	0.218850i
$751$	7167.40	+	5207.42i	0.348258	+	0.253025i	0.748138	−	0.663543i	$-0.230948\pi$
$751$	7167.40	+	5207.42i	0.348258	+	0.253025i	−0.399880	+	0.916568i	$0.630948\pi$
$752$	−2989.10	+	2171.71i	−0.144948	+	0.105311i
$753$	−507.243	+	1561.13i	−0.0245484	+	0.0755523i
$754$	2853.48	−	8782.10i	0.137822	−	0.424172i
$755$	12099.8	−	8791.01i	0.583253	−	0.423758i
$756$	11426.9	+	8302.12i	0.549725	+	0.399398i
$757$	11042.5	+	33985.4i	0.530182	+	1.63173i	0.753835	+	0.657064i	$0.228202\pi$
$757$	11042.5	+	33985.4i	0.530182	+	1.63173i	−0.223653	+	0.974669i	$0.571798\pi$
$758$	−2064.19			−0.0989112
$759$		0			0
$760$	9885.59			0.471826
$761$	−10628.5	−	32711.3i	−0.506287	−	1.55819i	−0.798597	−	0.601867i	$-0.794424\pi$
$761$	−10628.5	−	32711.3i	−0.506287	−	1.55819i	0.292310	−	0.956324i	$-0.405576\pi$
$762$	384.815	+	279.585i	0.0182945	+	0.0132917i
$763$	880.003	−	639.359i	0.0417539	−	0.0303360i
$764$	−6743.74	+	20755.1i	−0.319345	+	0.982844i
$765$	−2678.35	+	8243.12i	−0.126583	+	0.389583i
$766$	3753.53	−	2727.10i	0.177050	−	0.128635i
$767$	32948.4	+	23938.4i	1.55110	+	1.12694i
$768$	2966.54	+	9130.06i

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.226216 + 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(1.34106 - 4.12734i) q^{6} +(13.6952 - 9.95015i) q^{7} +(9.15848 + 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} +O(q^{10})\)	\(q+(0.226216 + 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(1.34106 - 4.12734i) q^{6} +(13.6952 - 9.95015i) q^{7} +(9.15848 + 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} -9.41154 q^{10} -44.2487 q^{12} +(-23.0653 - 70.9878i) q^{13} +(10.0256 + 7.28401i) q^{14} +(61.6595 - 44.7983i) q^{15} +(15.8914 - 48.9087i) q^{16} +(25.5819 - 78.7328i) q^{17} +(-4.82297 + 3.50410i) q^{18} +(-54.9509 - 39.9242i) q^{19} +(29.6537 + 91.2648i) q^{20} -100.354 q^{21} +13.3538 q^{23} +(-20.7382 - 63.8257i) q^{24} +(-32.5930 - 23.6802i) q^{25} +(44.2055 - 32.1172i) q^{26} +(-34.5433 + 106.313i) q^{27} +(39.0455 - 120.170i) q^{28} +(136.720 - 99.3327i) q^{29} +(45.1379 + 32.7946i) q^{30} +(-20.2398 - 62.2918i) q^{31} +128.210 q^{32} +60.6025 q^{34} +(67.2532 + 206.984i) q^{35} +(49.1758 + 35.7283i) q^{36} +(-33.0535 + 24.0148i) q^{37} +(15.3653 - 47.2895i) q^{38} +(-136.736 + 420.830i) q^{39} +(-117.745 + 85.5469i) q^{40} +(222.422 + 161.599i) q^{41} +(-22.7017 - 69.8685i) q^{42} +2.28719 q^{43} -104.697 q^{45} +(3.02085 + 9.29723i) q^{46} +(-58.1247 - 42.2301i) q^{47} +(-246.638 + 179.193i) q^{48} +(-17.4397 + 53.6738i) q^{49} +(9.11361 - 28.0488i) q^{50} +(-397.036 + 288.464i) q^{51} +(-450.726 - 327.472i) q^{52} +(-46.0451 - 141.712i) q^{53} -81.8320 q^{54} +191.636 q^{56} +(124.429 + 382.954i) q^{57} +(100.086 + 72.7166i) q^{58} +(-441.425 + 320.714i) q^{59} +(175.793 - 541.036i) q^{60} +(-31.3042 + 96.3445i) q^{61} +(38.7903 - 28.1828i) q^{62} +(111.528 + 81.0300i) q^{63} +(-98.1279 - 302.007i) q^{64} +959.615 q^{65} +411.641 q^{67} +(-190.946 - 587.670i) q^{68} +(-64.0452 - 46.5316i) q^{69} +(-128.893 + 93.6462i) q^{70} +(-145.434 + 447.601i) q^{71} +(-28.4882 + 87.6775i) q^{72} +(493.986 - 358.902i) q^{73} +(-24.1969 - 17.5800i) q^{74} +(73.8027 + 227.141i) q^{75} -506.985 q^{76} -323.923 q^{78} +(302.288 + 930.348i) q^{79} +(534.881 + 388.613i) q^{80} +(714.005 - 518.755i) q^{81} +(-62.1932 + 191.411i) q^{82} +(-8.08200 + 24.8738i) q^{83} +(-605.995 + 440.281i) q^{84} +(861.047 + 625.587i) q^{85} +(0.517399 + 1.59239i) q^{86} -1001.84 q^{87} -352.887 q^{89} +(-23.6842 - 72.8926i) q^{90} +(-1022.22 - 742.689i) q^{91} +(80.6382 - 58.5871i) q^{92} +(-119.986 + 369.278i) q^{93} +(16.2527 - 50.0208i) q^{94} +(706.471 - 513.281i) q^{95} +(-614.898 - 446.750i) q^{96} +(261.918 + 806.101i) q^{97} -41.3140 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} - 26 q^{6} + 20 q^{7} - 12 q^{8} - 44 q^{9} - 200 q^{10} - 160 q^{12} + 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} - 124 q^{17} + 92 q^{18} + 72 q^{19} - 88 q^{20} - 304 q^{21} - 392 q^{23} + 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} - 128 q^{28} + 144 q^{29} - 266 q^{30} + 34 q^{31} + 416 q^{32} - 208 q^{34} - 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} - 492 q^{40} + 536 q^{41} + 140 q^{42} + 240 q^{43} + 1712 q^{45} - 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} + 232 q^{50} - 164 q^{51} - 560 q^{52} + 492 q^{53} + 440 q^{54} + 480 q^{56} - 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} + 840 q^{61} + 134 q^{62} + 248 q^{63} - 224 q^{64} + 3520 q^{65} + 3016 q^{67} + 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} - 744 q^{72} - 400 q^{73} + 6 q^{74} + 520 q^{75} - 1728 q^{76} - 1760 q^{78} + 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} + 468 q^{83} - 736 q^{84} + 452 q^{85} + 156 q^{86} - 4800 q^{87} - 7368 q^{89} + 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} + 2952 q^{95} - 952 q^{96} - 2194 q^{97} + 3480 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 8 * q^4 - 2 * q^5 - 26 * q^6 + 20 * q^7 - 12 * q^8 - 44 * q^9 - 200 * q^10 - 160 * q^12 + 80 * q^13 + 4 * q^14 + 194 * q^15 + 8 * q^16 - 124 * q^17 + 92 * q^18 + 72 * q^19 - 88 * q^20 - 304 * q^21 - 392 * q^23 + 252 * q^24 - 136 * q^25 + 40 * q^26 + 182 * q^27 - 128 * q^28 + 144 * q^29 - 266 * q^30 + 34 * q^31 + 416 * q^32 - 208 * q^34 - 172 * q^35 + 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 - 492 * q^40 + 536 * q^41 + 140 * q^42 + 240 * q^43 + 1712 * q^45 - 314 * q^46 + 272 * q^47 - 776 * q^48 + 390 * q^49 + 232 * q^50 - 164 * q^51 - 560 * q^52 + 492 * q^53 + 440 * q^54 + 480 * q^56 - 1512 * q^57 + 192 * q^58 - 634 * q^59 - 632 * q^60 + 840 * q^61 + 134 * q^62 + 248 * q^63 - 224 * q^64 + 3520 * q^65 + 3016 * q^67 + 640 * q^68 - 962 * q^69 - 284 * q^70 + 678 * q^71 - 744 * q^72 - 400 * q^73 + 6 * q^74 + 520 * q^75 - 1728 * q^76 - 1760 * q^78 + 316 * q^79 + 1544 * q^80 + 1294 * q^81 - 512 * q^82 + 468 * q^83 - 736 * q^84 + 452 * q^85 + 156 * q^86 - 4800 * q^87 - 7368 * q^89 + 1532 * q^90 - 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 + 2952 * q^95 - 952 * q^96 - 2194 * q^97 + 3480 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more