LMFDB - Embedded newform 175.4.x.a.17.37

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			17.37
Character	$\chi$	$=$	175.17
Dual form			175.4.x.a.103.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99479 - 0.104542i) q^{2} +(-5.07461 + 6.26663i) q^{3} +(-3.98794 + 0.419149i) q^{4} +(-10.9489 - 2.26308i) q^{5} +(-9.46764 + 13.0311i) q^{6} +(15.9822 - 9.35779i) q^{7} +(-23.6947 + 3.75287i) q^{8} +(-7.90528 - 37.1914i) q^{9} +(-22.0773 - 3.36973i) q^{10} +(24.3674 + 5.17946i) q^{11} +(17.6106 - 27.1179i) q^{12} +(29.1647 - 14.8602i) q^{13} +(30.9028 - 20.3376i) q^{14} +(69.7433 - 57.1284i) q^{15} +(-15.4953 + 3.29363i) q^{16} +(-16.7756 + 43.7020i) q^{17} +(-19.6574 - 73.3624i) q^{18} +(3.73765 - 35.5613i) q^{19} +(44.6121 + 4.43579i) q^{20} +(-22.4619 + 147.642i) q^{21} +(49.1493 + 7.78448i) q^{22} +(-11.4431 - 218.347i) q^{23} +(96.7236 - 167.530i) q^{24} +(114.757 + 49.5565i) q^{25} +(56.6238 - 32.6918i) q^{26} +(79.1924 + 40.3506i) q^{27} +(-59.8138 + 44.0172i) q^{28} +(-130.137 - 179.119i) q^{29} +(133.151 - 121.250i) q^{30} +(38.2207 + 85.8450i) q^{31} +(154.815 - 41.4827i) q^{32} +(-156.113 + 126.418i) q^{33} +(-28.8951 + 88.9300i) q^{34} +(-196.165 + 66.2885i) q^{35} +(47.1145 + 145.003i) q^{36} +(-218.056 - 141.607i) q^{37} +(3.73814 - 71.3280i) q^{38} +(-54.8766 + 258.174i) q^{39} +(267.924 + 12.5331i) q^{40} +(36.1494 + 11.7457i) q^{41} +(-29.3718 + 296.862i) q^{42} +(119.914 - 119.914i) q^{43} +(-99.3467 - 10.4418i) q^{44} +(2.38702 + 425.095i) q^{45} +(-45.6531 - 434.360i) q^{46} +(-340.160 + 130.575i) q^{47} +(57.9927 - 113.817i) q^{48} +(167.864 - 299.117i) q^{49} +(234.096 + 86.8576i) q^{50} +(-188.734 - 326.898i) q^{51} +(-110.078 + 71.4857i) q^{52} +(-224.128 - 181.496i) q^{53} +(162.190 + 72.2117i) q^{54} +(-255.075 - 111.855i) q^{55} +(-343.576 + 281.709i) q^{56} +(203.883 + 203.883i) q^{57} +(-278.322 - 343.699i) q^{58} +(-392.333 - 435.730i) q^{59} +(-254.186 + 257.057i) q^{60} +(650.805 + 585.987i) q^{61} +(85.2165 + 167.247i) q^{62} +(-474.373 - 520.426i) q^{63} +(425.016 - 138.096i) q^{64} +(-352.951 + 96.7004i) q^{65} +(-298.196 + 268.497i) q^{66} +(-586.873 - 225.279i) q^{67} +(48.5825 - 181.312i) q^{68} +(1426.37 + 1036.32i) q^{69} +(-384.378 + 152.739i) q^{70} +(783.313 - 569.110i) q^{71} +(326.888 + 851.572i) q^{72} +(-96.8065 - 149.069i) q^{73} +(-449.778 - 259.680i) q^{74} +(-892.899 + 467.659i) q^{75} +143.383i q^{76} +(437.914 - 145.246i) q^{77} +(-82.4769 + 520.739i) q^{78} +(-128.774 + 289.231i) q^{79} +(177.110 - 0.994520i) q^{80} +(283.115 - 126.051i) q^{81} +(73.3382 + 19.6509i) q^{82} +(129.851 + 819.846i) q^{83} +(27.6927 - 598.201i) q^{84} +(282.576 - 440.525i) q^{85} +(226.666 - 251.738i) q^{86} +(1782.87 + 93.4361i) q^{87} +(-596.817 - 31.2778i) q^{88} +(741.560 - 823.586i) q^{89} +(49.2020 + 847.725i) q^{90} +(327.059 - 510.416i) q^{91} +(137.154 + 865.959i) q^{92} +(-731.914 - 196.116i) q^{93} +(-664.895 + 296.030i) q^{94} +(-121.401 + 380.899i) q^{95} +(-525.672 + 1180.68i) q^{96} +(35.9240 - 226.815i) q^{97} +(303.581 - 614.223i) q^{98} -947.204i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	1.99479	−	0.104542i	0.705263	−	0.0369613i	0.303667	−	0.952778i	$-0.401789\pi$
$2$	1.99479	−	0.104542i	0.705263	−	0.0369613i	0.401596	+	0.915817i	$0.368456\pi$
$3$	−5.07461	+	6.26663i	−0.976610	+	1.20601i	0.00193925	+	0.999998i	$0.499383\pi$
$3$	−5.07461	+	6.26663i	−0.976610	+	1.20601i	−0.978549	+	0.206014i	$0.933951\pi$
$4$	−3.98794	+	0.419149i	−0.498492	+	0.0523936i
$5$	−10.9489	−	2.26308i	−0.979300	−	0.202416i
$5$	−10.9489	−	2.26308i	−0.979300	−	0.202416i
$6$	−9.46764	+	13.0311i	−0.644191	+	0.886653i
$7$	15.9822	−	9.35779i	0.862959	−	0.505273i
$7$	15.9822	−	9.35779i	0.862959	−	0.505273i
$8$	−23.6947	+	3.75287i	−1.04717	+	0.165855i
$9$	−7.90528	−	37.1914i	−0.292788	−	1.37746i
$10$	−22.0773	−	3.36973i	−0.698146	−	0.106560i
$11$	24.3674	+	5.17946i	0.667914	+	0.141970i	0.529376	−	0.848387i	$-0.322426\pi$
$11$	24.3674	+	5.17946i	0.667914	+	0.141970i	0.138539	+	0.990357i	$0.455760\pi$
$12$	17.6106	−	27.1179i	0.423645	−	0.652356i
$13$	29.1647	−	14.8602i	0.622218	−	0.317036i	−0.114308	−	0.993445i	$-0.536465\pi$
$13$	29.1647	−	14.8602i	0.622218	−	0.317036i	0.736526	+	0.676409i	$0.236465\pi$
$14$	30.9028	−	20.3376i	0.589938	−	0.388247i
$15$	69.7433	−	57.1284i	1.20051	−	0.983366i
$16$	−15.4953	+	3.29363i	−0.242114	+	0.0514629i
$17$	−16.7756	+	43.7020i	−0.239335	+	0.623488i	−0.999661	−	0.0260535i	$-0.991706\pi$
$17$	−16.7756	+	43.7020i	−0.239335	+	0.623488i	0.760326	+	0.649542i	$0.225039\pi$
$18$	−19.6574	−	73.3624i	−0.257405	−	0.960650i
$19$	3.73765	−	35.5613i	0.0451303	−	0.429386i	−0.948507	−	0.316757i	$-0.897406\pi$
$19$	3.73765	−	35.5613i	0.0451303	−	0.429386i	0.993637	−	0.112629i	$-0.0359272\pi$
$20$	44.6121	+	4.43579i	0.498778	+	0.0495937i
$21$	−22.4619	+	147.642i	−0.233409	+	1.53419i
$22$	49.1493	+	7.78448i	0.476303	+	0.0754389i
$23$	−11.4431	−	218.347i	−0.103741	−	1.97950i	−0.184730	−	0.982789i	$-0.559141\pi$
$23$	−11.4431	−	218.347i	−0.103741	−	1.97950i	0.0809888	−	0.996715i	$-0.474192\pi$
$24$	96.7236	−	167.530i	0.822651	−	1.42487i
$25$	114.757	+	49.5565i	0.918056	+	0.396452i
$26$	56.6238	−	32.6918i	0.427110	−	0.246592i
$27$	79.1924	+	40.3506i	0.564466	+	0.287610i
$28$	−59.8138	+	44.0172i	−0.403705	+	0.297088i
$29$	−130.137	−	179.119i	−0.833307	−	1.14695i	−0.987298	−	0.158877i	$-0.949213\pi$
$29$	−130.137	−	179.119i	−0.833307	−	1.14695i	0.153991	−	0.988072i	$-0.450787\pi$
$30$	133.151	−	121.250i	0.810329	−	0.737904i
$31$	38.2207	+	85.8450i	0.221440	+	0.497362i	0.989767	−	0.142696i	$-0.0455771\pi$
$31$	38.2207	+	85.8450i	0.221440	+	0.497362i	−0.768327	+	0.640058i	$0.778910\pi$
$32$	154.815	−	41.4827i	0.855243	−	0.229162i
$33$	−156.113	+	126.418i	−0.823509	+	0.666864i
$34$	−28.8951	+	88.9300i	−0.145749	+	0.448570i
$35$	−196.165	+	66.2885i	−0.947371	+	0.320137i
$36$	47.1145	+	145.003i	0.218123	+	0.671312i
$37$	−218.056	−	141.607i	−0.968869	−	0.629191i	−0.0398432	−	0.999206i	$-0.512686\pi$
$37$	−218.056	−	141.607i	−0.968869	−	0.629191i	−0.929026	+	0.370015i	$0.879353\pi$
$38$	3.73814	−	71.3280i	0.0159581	−	0.304498i
$39$	−54.8766	+	258.174i	−0.225315	+	1.06002i
$40$	267.924	+	12.5331i	1.05906	+	0.0495416i
$41$	36.1494	+	11.7457i	0.137697	+	0.0447406i	0.377055	−	0.926191i	$-0.376937\pi$
$41$	36.1494	+	11.7457i	0.137697	+	0.0447406i	−0.239358	+	0.970931i	$0.576937\pi$
$42$	−29.3718	+	296.862i	−0.107909	+	1.09064i
$43$	119.914	−	119.914i	0.425272	−	0.425272i	−0.461742	−	0.887014i	$-0.652776\pi$
$43$	119.914	−	119.914i	0.425272	−	0.425272i	0.887014	+	0.461742i	$0.152776\pi$
$44$	−99.3467	−	10.4418i	−0.340388	−	0.0357762i
$45$	2.38702	+	425.095i	0.00790747	+	1.40821i
$46$	−45.6531	−	434.360i	−0.146330	−	1.39224i
$47$	−340.160	+	130.575i	−1.05569	+	0.405241i	−0.823433	−	0.567413i	$-0.807944\pi$
$47$	−340.160	+	130.575i	−1.05569	+	0.405241i	−0.232256	+	0.972655i	$0.574611\pi$
$48$	57.9927	−	113.817i	0.174386	−	0.342252i
$49$	167.864	−	299.117i	0.489398	−	0.872060i
$50$	234.096	+	86.8576i	0.662124	+	0.245670i
$51$	−188.734	−	326.898i	−0.518198	−	0.897546i
$52$	−110.078	+	71.4857i	−0.293560	+	0.190640i
$53$	−224.128	−	181.496i	−0.580875	−	0.470384i	0.293282	−	0.956026i	$-0.405252\pi$
$53$	−224.128	−	181.496i	−0.580875	−	0.470384i	−0.874158	+	0.485642i	$0.838586\pi$
$54$	162.190	+	72.2117i	0.408728	+	0.181977i
$55$	−255.075	−	111.855i	−0.625351	−	0.274227i
$56$	−343.576	+	281.709i	−0.819861	+	0.672232i
$57$	203.883	+	203.883i	0.473770	+	0.473770i
$58$	−278.322	−	343.699i	−0.630094	−	0.778101i
$59$	−392.333	−	435.730i	−0.865720	−	0.961479i	0.133844	−	0.991002i	$-0.457268\pi$
$59$	−392.333	−	435.730i	−0.865720	−	0.961479i	−0.999564	+	0.0295231i	$0.990601\pi$
$60$	−254.186	+	257.057i	−0.546922	+	0.553099i
$61$	650.805	+	585.987i	1.36602	+	1.22997i	0.946696	+	0.322129i	$0.104398\pi$
$61$	650.805	+	585.987i	1.36602	+	1.22997i	0.419321	+	0.907838i	$0.362268\pi$
$62$	85.2165	+	167.247i	0.174556	+	0.342586i
$63$	−474.373	−	520.426i	−0.948658	−	1.04075i
$64$	425.016	−	138.096i	0.830109	−	0.269719i
$65$	−352.951	+	96.7004i	−0.673511	+	0.184526i
$66$	−298.196	+	268.497i	−0.556142	+	0.500753i
$67$	−586.873	−	225.279i	−1.07012	−	0.410780i	−0.241389	−	0.970429i	$-0.577603\pi$
$67$	−586.873	−	225.279i	−1.07012	−	0.410780i	−0.828730	+	0.559648i	$0.810936\pi$
$68$	48.5825	−	181.312i	0.0866396	−	0.323344i
$69$	1426.37	+	1036.32i	2.48862	+	1.80809i
$70$	−384.378	+	152.739i	−0.656313	+	0.260797i
$71$	783.313	−	569.110i	1.30933	−	0.951281i	0.309327	−	0.950956i	$-0.399896\pi$
$71$	783.313	−	569.110i	1.30933	−	0.951281i	1.00000		0.000325502i	$-0.000103611\pi$
$72$	326.888	+	851.572i	0.535057	+	1.39387i
$73$	−96.8065	−	149.069i	−0.155210	−	0.239003i	0.752508	−	0.658583i	$-0.228844\pi$
$73$	−96.8065	−	149.069i	−0.155210	−	0.239003i	−0.907718	+	0.419580i	$0.862177\pi$
$74$	−449.778	−	259.680i	−0.706563	−	0.407935i
$75$	−892.899	+	467.659i	−1.37471	+	0.720008i
$76$			143.383i			0.216410i
$77$	437.914	−	145.246i	0.648116	−	0.214965i
$78$	−82.4769	+	520.739i	−0.119727	+	0.755923i
$79$	−128.774	+	289.231i	−0.183395	+	0.411912i	−0.981724	−	0.190310i	$-0.939051\pi$
$79$	−128.774	+	289.231i	−0.183395	+	0.411912i	0.798329	+	0.602221i	$0.205717\pi$
$80$	177.110	−	0.994520i	0.247519	−	0.00138988i
$81$	283.115	−	126.051i	0.388360	−	0.172909i
$82$	73.3382	+	19.6509i	0.0987665	+	0.0264644i
$83$	129.851	+	819.846i	0.171723	+	1.08421i	0.911481	+	0.411342i	$0.134940\pi$
$83$	129.851	+	819.846i	0.171723	+	1.08421i	−0.739758	+	0.672873i	$0.765060\pi$
$84$	27.6927	−	598.201i	0.0359704	−	0.777013i
$85$	282.576	−	440.525i	0.360584	−	0.562137i
$86$	226.666	−	251.738i	0.284210	−	0.315647i
$87$	1782.87	+	93.4361i	2.19705	+	0.115143i
$88$	−596.817	−	31.2778i	−0.722965	−	0.0378890i
$89$	741.560	−	823.586i	0.883205	−	0.980898i	−0.116720	−	0.993165i	$-0.537238\pi$
$89$	741.560	−	823.586i	0.883205	−	0.980898i	0.999925	+	0.0122666i	$0.00390468\pi$
$90$	49.2020	+	847.725i	0.0576261	+	0.992867i
$91$	327.059	−	510.416i	0.376759	−	0.587979i
$92$	137.154	+	865.959i	0.155428	+	0.981331i
$93$	−731.914	−	196.116i	−0.816085	−	0.218669i
$94$	−664.895	+	296.030i	−0.729561	+	0.324821i
$95$	−121.401	+	380.899i	−0.131111	+	0.411362i
$96$	−525.672	+	1180.68i	−0.558866	+	1.25523i
$97$	35.9240	−	226.815i	0.0376034	−	0.237419i	−0.961727	−	0.274010i	$-0.911650\pi$
$97$	35.9240	−	226.815i	0.0376034	−	0.237419i	0.999330	+	0.0365912i	$0.0116499\pi$
$98$	303.581	−	614.223i	0.312922	−	0.633121i
$99$		−	947.204i		−	0.961592i
$100$	−478.415	−	149.528i	−0.478415	−	0.149528i
$101$	−673.045	−	388.583i	−0.663074	−	0.382826i	0.130373	−	0.991465i	$-0.458382\pi$
$101$	−673.045	−	388.583i	−0.663074	−	0.382826i	−0.793447	+	0.608639i	$0.791716\pi$
$102$	−410.659	−	632.360i	−0.398641	−	0.613853i
$103$	−92.8239	−	241.814i	−0.0887981	−	0.231327i	0.881989	−	0.471270i	$-0.156204\pi$
$103$	−92.8239	−	241.814i	−0.0887981	−	0.231327i	−0.970787	+	0.239943i	$0.922871\pi$
$104$	−635.281	+	461.559i	−0.598985	+	0.435188i
$105$	580.058	−	1565.68i	0.539123	−	1.45519i
$106$	−466.062	−	338.614i	−0.427056	−	0.310274i
$107$	−127.370	+	475.353i	−0.115078	+	0.429477i	−0.999293	−	0.0376034i	$-0.988028\pi$
$107$	−127.370	+	475.353i	−0.115078	+	0.429477i	0.884215	+	0.467081i	$0.154694\pi$
$108$	−332.727	−	127.722i	−0.296451	−	0.113797i
$109$	−195.867	+	176.360i	−0.172116	+	0.154974i	−0.750687	−	0.660658i	$-0.770277\pi$
$109$	−195.867	+	176.360i	−0.172116	+	0.154974i	0.578571	+	0.815632i	$0.303611\pi$
$110$	−520.514	−	196.460i	−0.451173	−	0.170289i
$111$	1993.95	−	647.873i	1.70502	−	0.553994i
$112$	−216.828	+	197.641i	−0.182932	+	0.166744i
$113$	816.013	+	1601.52i	0.679328	+	1.33326i	0.930849	+	0.365404i	$0.119069\pi$
$113$	816.013	+	1601.52i	0.679328	+	1.33326i	−0.251521	+	0.967852i	$0.580931\pi$
$114$	428.016	+	385.388i	0.351644	+	0.316621i
$115$	−368.848	+	2416.56i	−0.299089	+	1.95953i
$116$	594.057	+	659.767i	0.475490	+	0.528085i
$117$	−783.226	−	967.203i	−0.618882	−	0.764256i
$118$	−828.173	−	828.173i	−0.646098	−	0.646098i
$119$	140.842	+	855.439i	0.108496	+	0.658975i
$120$	−1438.15	+	1615.38i	−1.09404	+	1.22886i
$121$	−648.984	−	288.946i	−0.487591	−	0.217090i
$122$	1359.48	+	1100.88i	1.00886	+	0.816961i
$123$	−257.050	+	166.930i	−0.188434	+	0.122371i
$124$	−188.403	−	326.324i	−0.136445	−	0.236329i
$125$	−1144.31	−	802.293i	−0.818803	−	0.574074i
$126$	−1000.68	−	988.546i	−0.707521	−	0.698942i
$127$	−168.886	+	331.457i	−0.118001	+	0.231591i	−0.942451	−	0.334345i	$-0.891485\pi$
$127$	−168.886	+	331.457i	−0.118001	+	0.231591i	0.824449	+	0.565936i	$0.191485\pi$
$128$	−363.671	+	139.600i	−0.251127	+	0.0963987i
$129$	142.939	+	1359.97i	0.0975585	+	0.928207i
$130$	−693.953	+	229.795i	−0.468182	+	0.155033i
$131$	−2518.06	−	264.659i	−1.67942	−	0.176514i	−0.783701	−	0.621138i	$-0.786671\pi$
$131$	−2518.06	−	264.659i	−1.67942	−	0.176514i	−0.895717	+	0.444624i	$0.853337\pi$
$132$	569.581	−	569.581i	0.375573	−	0.375573i
$133$	−273.040	−	603.326i	−0.178012	−	0.393346i
$134$	−1194.24	−	388.031i	−0.769898	−	0.250155i
$135$	−775.754	−	621.013i	−0.494565	−	0.395913i
$136$	233.486	−	1098.46i	0.147215	−	0.692592i
$137$	76.7854	−	1465.15i	0.0478848	−	0.913697i	−0.864061	−	0.503387i	$-0.832087\pi$
$137$	76.7854	−	1465.15i	0.0478848	−	0.913697i	0.911946	−	0.410310i	$-0.134580\pi$
$138$	2953.64	+	1918.12i	1.82196	+	1.18320i
$139$	−326.881	−	1006.04i	−0.199466	−	0.613892i	−0.999895	−	0.0144654i	$-0.995395\pi$
$139$	−326.881	−	1006.04i	−0.199466	−	0.613892i	0.800430	−	0.599426i	$-0.204605\pi$
$140$	754.510	−	346.577i	0.455484	−	0.209222i
$141$	907.914	−	2794.27i	0.542270	−	1.66894i
$142$	1503.05	−	1217.14i	0.888259	−	0.719298i
$143$	787.637	−	211.047i	0.460598	−	0.123417i
$144$	244.989	+	550.255i	0.141776	+	0.318435i
$145$	1019.50	+	2255.67i	0.583897	+	1.29188i
$146$	−208.692	−	287.240i	−0.118298	−	0.162823i
$147$	1022.61	+	2569.84i	0.573765	+	1.44188i
$148$	928.947	+	473.322i	0.515939	+	0.262884i
$149$	1573.80	−	908.637i	0.865309	−	0.499587i	−0.000477291	−	1.00000i	$-0.500152\pi$
$149$	1573.80	−	908.637i	0.865309	−	0.499587i	0.865787	+	0.500413i	$0.166819\pi$
$150$	−1732.25	+	1026.22i	−0.942918	+	0.558606i
$151$	949.627	−	1644.80i	0.511785	−	0.886438i	−0.488122	−	0.872776i	$-0.662318\pi$
$151$	949.627	−	1644.80i	0.511785	−	0.886438i	0.999907	−	0.0136622i	$-0.00434895\pi$
$152$	44.8947	+	856.642i	0.0239569	+	0.457124i
$153$	1757.96	+	278.433i	0.928904	+	0.147124i
$154$	858.361	−	335.515i	0.449147	−	0.175562i
$155$	−224.200	−	1026.41i	−0.116182	−	0.531889i
$156$	110.631	−	1052.58i	0.0567792	−	0.540218i
$157$	−429.956	−	1604.62i	−0.218562	−	0.815685i	−0.984882	−	0.173226i	$-0.944581\pi$
$157$	−429.956	−	1604.62i	−0.218562	−	0.815685i	0.766320	−	0.642459i	$-0.222086\pi$
$158$	−226.639	+	590.416i	−0.114117	+	0.297285i
$159$	2274.73	−	483.509i	1.13458	−	0.241162i
$160$	−1788.94	+	103.830i	−0.883925	+	0.0513031i
$161$	−2226.14	−	3382.60i	−1.08971	−	1.65581i
$162$	551.575	−	281.042i	0.267505	−	0.136301i
$163$	−562.825	+	866.674i	−0.270453	+	0.416461i	−0.947635	−	0.319354i	$-0.896534\pi$
$163$	−562.825	+	866.674i	−0.270453	+	0.416461i	0.677183	+	0.735815i	$0.263201\pi$
$164$	−149.085	−	31.6889i	−0.0709851	−	0.0150884i
$165$	1995.36	−	1030.84i	0.941446	−	0.486369i
$166$	344.733	+	1621.84i	0.161184	+	0.758310i
$167$	691.076	−	109.456i	0.320222	−	0.0507182i	0.00574568	−	0.999983i	$-0.498171\pi$
$167$	691.076	−	109.456i	0.320222	−	0.0507182i	0.314476	+	0.949265i	$0.398171\pi$
$168$	−21.8530	−	3582.62i	−0.0100357	−	1.64527i
$169$	−661.608	+	910.625i	−0.301142	+	0.414486i
$170$	517.625	−	908.294i	0.233530	−	0.409782i
$171$	−1352.12	+	142.114i	−0.604675	+	0.0635539i
$172$	−427.947	+	528.470i	−0.189713	+	0.234276i
$173$	−2193.46	+	114.954i	−0.963964	+	0.0505192i	−0.527819	−	0.849357i	$-0.676990\pi$
$173$	−2193.46	+	114.954i	−0.963964	+	0.0505192i	−0.436145	+	0.899876i	$0.643657\pi$
$174$	3566.21			1.55376
$175$	2297.81	−	281.848i	0.992561	−	0.121747i
$176$	−394.640			−0.169018
$177$	4721.50	−	247.443i	2.00503	−	0.105079i
$178$	1393.15	−	1720.40i	0.586637	−	0.724436i
$179$	−242.579	+	25.4961i	−0.101292	+	0.0106462i	−0.155039	−	0.987908i	$-0.549550\pi$
$179$	−242.579	+	25.4961i	−0.101292	+	0.0106462i	0.0537470	+	0.998555i	$0.482884\pi$
$180$	−187.698	−	1694.25i	−0.0777230	−	0.701567i
$181$	2161.38	−	2974.88i	0.887591	−	1.22166i	−0.0866694	−	0.996237i	$-0.527622\pi$
$181$	2161.38	−	2974.88i	0.887591	−	1.22166i	0.974260	−	0.225427i	$-0.0723776\pi$
$182$	599.053	−	1052.36i	0.243982	−	0.428606i
$183$	−6974.75	+	1104.69i	−2.81742	+	0.446236i
$184$	1090.57	+	5130.73i	0.436945	+	2.05567i
$185$	2067.00	+	2043.92i	0.821455	+	0.812281i
$186$	−1480.51	−	314.693i	−0.583637	−	0.124056i
$187$	−635.132	+	978.018i	−0.248371	+	0.382459i
$188$	1301.80	−	663.303i	0.505021	−	0.257321i
$189$	1643.26	−	96.1740i	0.632433	−	0.0370139i
$190$	−202.349	+	772.504i	−0.0772630	+	0.294965i
$191$	683.261	−	145.232i	0.258843	−	0.0550188i	−0.0766621	−	0.997057i	$-0.524426\pi$
$191$	683.261	−	145.232i	0.258843	−	0.0550188i	0.335505	+	0.942038i	$0.391093\pi$
$192$	−1291.40	+	3364.20i	−0.485408	+	1.26453i
$193$	−82.5049	−	307.912i	−0.0307711	−	0.114839i	0.948832	−	0.315781i	$-0.102267\pi$
$193$	−82.5049	−	307.912i	−0.0307711	−	0.114839i	−0.979603	+	0.200942i	$0.935600\pi$
$194$	47.9489	−	456.203i	0.0177450	−	0.168832i
$195$	1185.11	−	2702.53i	0.435216	−	0.992473i
$196$	−544.055	+	1263.22i	−0.198271	+	0.460356i
$197$	−4214.64	−	667.534i	−1.52427	−	0.241420i	−0.662631	−	0.748946i	$-0.730560\pi$
$197$	−4214.64	−	667.534i	−1.52427	−	0.241420i	−0.861637	+	0.507525i	$0.830560\pi$
$198$	−99.0229	−	1889.47i	−0.0355417	−	0.678175i
$199$	408.289	−	707.177i	0.145441	−	0.251912i	−0.784096	−	0.620639i	$-0.786873\pi$
$199$	408.289	−	707.177i	0.145441	−	0.251912i	0.929537	+	0.368728i	$0.120206\pi$
$200$	−2905.11	−	743.557i	−1.02711	−	0.262887i
$201$	4389.90	−	2534.51i	1.54049	−	0.889405i
$202$	−1383.20	−	704.777i	−0.481791	−	0.245485i
$203$	−3756.04	−	1644.92i	−1.29863	−	0.568723i
$204$	889.679	+	1224.54i	0.305343	+	0.420269i
$205$	−369.215	−	210.411i	−0.125791	−	0.0716866i
$206$	−210.444	−	472.664i	−0.0711762	−	0.159864i
$207$	−8030.19	+	2151.68i	−2.69631	+	0.722475i
$208$	−402.972	+	326.320i	−0.134332	+	0.108780i
$209$	275.265	−	847.180i	0.0911029	−	0.280386i
$210$	993.412	−	3183.84i	0.326438	−	1.04622i
$211$	746.060	+	2296.14i	0.243416	+	0.749159i	0.995893	+	0.0905395i	$0.0288591\pi$
$211$	746.060	+	2296.14i	0.243416	+	0.749159i	−0.752476	+	0.658619i	$0.771141\pi$
$212$	969.883	+	629.849i	0.314207	+	0.204048i
$213$	−408.610	+	7796.75i	−0.131444	+	2.50809i
$214$	−204.382	+	961.542i	−0.0652863	+	0.307148i
$215$	−1584.30	+	1041.55i	−0.502550	+	0.330387i
$216$	−2027.87	−	658.895i	−0.638792	−	0.207556i
$217$	1414.17	+	1014.33i	0.442397	+	0.317316i
$218$	−372.276	+	372.276i	−0.115659	+	0.115659i
$219$	1425.41	+	149.817i	0.439820	+	0.0462270i
$220$	1064.11	+	339.155i	0.326100	+	0.103936i
$221$	160.163	+	1523.85i	0.0487498	+	0.463824i
$222$	3909.77	−	1500.82i	1.18201	−	0.453731i
$223$	378.990	−	743.809i	0.113807	−	0.223359i	−0.827076	−	0.562090i	$-0.809998\pi$
$223$	378.990	−	743.809i	0.113807	−	0.223359i	0.940883	+	0.338731i	$0.109998\pi$
$224$	2086.11	−	2111.72i	0.622250	−	0.629888i
$225$	935.889	−	4659.73i	0.277300	−	1.38066i
$226$	1795.20	+	3109.37i	0.528384	+	0.915187i
$227$	−4804.26	+	3119.93i	−1.40471	+	0.912232i	−0.999998	−	0.00220984i	$-0.999297\pi$
$227$	−4804.26	+	3119.93i	−1.40471	+	0.912232i	−0.404717	+	0.914442i	$0.632630\pi$
$228$	−898.527	−	727.613i	−0.260993	−	0.211348i
$229$	4177.53	+	1859.96i	1.20550	+	0.536723i	0.908391	−	0.418122i	$-0.137311\pi$
$229$	4177.53	+	1859.96i	1.20550	+	0.536723i	0.297107	+	0.954844i	$0.403978\pi$
$230$	−483.140	+	4859.08i	−0.138510	+	1.39304i
$231$	−1312.04	+	3481.31i	−0.373706	+	0.991573i
$232$	3755.78	+	3755.78i	1.06284	+	1.06284i
$233$	−4205.37	−	5193.20i	−1.18242	−	1.46016i	−0.857550	−	0.514401i	$-0.828014\pi$
$233$	−4205.37	−	5193.20i	−1.18242	−	1.46016i	−0.324866	−	0.945760i	$-0.605319\pi$
$234$	−1663.48	−	1847.48i	−0.464723	−	0.516127i
$235$	4019.88	−	659.846i	1.11586	−	0.183164i
$236$	1747.24	+	1573.22i	0.481930	+	0.433931i
$237$	−1159.02	−	2274.71i	−0.317665	−	0.623453i
$238$	370.380	+	1691.69i	0.100875	+	0.460740i
$239$	−3434.30	+	1115.87i	−0.929483	+	0.302007i	−0.734351	−	0.678770i	$-0.762513\pi$
$239$	−3434.30	+	1115.87i	−0.929483	+	0.302007i	−0.195132	+	0.980777i	$0.562513\pi$
$240$	−892.534	+	1114.93i	−0.240053	+	0.299869i
$241$	2336.26	−	2103.57i	0.624446	−	0.562253i	−0.294987	−	0.955501i	$-0.595315\pi$
$241$	2336.26	−	2103.57i	0.624446	−	0.562253i	0.919432	+	0.393248i	$0.128649\pi$
$242$	−1324.79	−	508.540i	−0.351904	−	0.135083i
$243$	−1267.89	+	4731.82i	−0.334712	+	1.24916i
$244$	−2840.98	−	2064.10i	−0.745391	−	0.541558i
$245$	−2514.85	+	2895.11i	−0.655786	+	0.754947i
$246$	−495.308	+	359.862i	−0.128373	+	0.0932683i
$247$	−419.440	−	1092.68i	−0.108050	−	0.281480i
$248$	−1227.79	−	1890.63i	−0.314375	−	0.484094i
$249$	−5796.61	−	3346.68i	−1.47528	−	0.851755i
$250$	−2366.53	−	1480.77i	−0.598690	−	0.374609i
$251$			3739.96i			0.940495i	0.882535	+	0.470247i	$0.155835\pi$
$251$			3739.96i			0.940495i	−0.882535	+	0.470247i	$0.844165\pi$
$252$	2109.91	+	1876.59i	0.527427	+	0.469104i
$253$	852.082	−	5379.84i	0.211739	−	1.33687i
$254$	−302.239	+	678.841i	−0.0746622	+	0.167694i
$255$	1326.64	+	4006.29i	0.325794	+	0.983858i
$256$	−3976.87	+	1770.62i	−0.970916	+	0.432280i
$257$	−6678.26	−	1789.44i	−1.62093	−	0.434326i	−0.669654	−	0.742673i	$-0.733558\pi$
$257$	−6678.26	−	1789.44i	−1.62093	−	0.434326i	−0.951274	+	0.308346i	$0.900224\pi$
$258$	427.306	+	2697.91i	0.103112	+	0.651025i
$259$	−4810.15	−	222.677i	−1.15401	−	0.0534228i
$260$	1367.02	−	533.574i	0.326072	−	0.127273i
$261$	−5632.91	+	6255.98i	−1.33589	+	1.48366i
$262$	−5050.66	−	264.694i	−1.19096	−	0.0624154i
$263$	3118.35	+	163.426i	0.731124	+	0.0383166i	0.414266	−	0.910156i	$-0.364038\pi$
$263$	3118.35	+	163.426i	0.731124	+	0.0383166i	0.316859	+	0.948473i	$0.397372\pi$
$264$	3224.62	−	3581.30i	0.751749	−	0.834902i
$265$	2043.22	+	2494.40i	0.473638	+	0.578225i
$266$	−607.729	−	1174.96i	−0.140084	−	0.270833i
$267$	1397.97	+	8826.46i	0.320429	+	2.02311i
$268$	2434.84	+	652.413i	0.554968	+	0.148703i
$269$	1292.18	−	575.314i	0.292883	−	0.130400i	−0.255036	−	0.966932i	$-0.582087\pi$
$269$	1292.18	−	575.314i	0.292883	−	0.130400i	0.547918	+	0.836532i	$0.315421\pi$
$270$	−1612.38	−	1157.69i	−0.363432	−	0.260943i
$271$	−410.416	+	921.810i	−0.0919964	+	0.206627i	−0.953683	−	0.300814i	$-0.902742\pi$
$271$	−410.416	+	921.810i	−0.0919964	+	0.206627i	0.861687	+	0.507441i	$0.169408\pi$
$272$	116.005	−	732.429i	0.0258598	−	0.163272i
$273$	1538.89	+	4639.72i	0.341164	+	1.02860i
$274$		−	2930.69i		−	0.646167i
$275$	2539.66	+	1801.94i	0.556898	+	0.395132i
$276$	−6122.65	−	3534.91i	−1.33529	−	0.770930i
$277$	2517.02	+	3875.87i	0.545967	+	0.840716i	0.998702	−	0.0509295i	$-0.0162184\pi$
$277$	2517.02	+	3875.87i	0.545967	+	0.840716i	−0.452735	+	0.891645i	$0.649552\pi$
$278$	−757.232	−	1972.66i	−0.163366	−	0.425583i
$279$	2890.55	−	2100.11i	0.620261	−	0.450646i
$280$	4399.31	−	2306.87i	0.938960	−	0.492363i
$281$	5140.89	+	3735.08i	1.09139	+	0.792940i	0.979633	−	0.200796i	$-0.0643529\pi$
$281$	5140.89	+	3735.08i	1.09139	+	0.792940i	0.111755	+	0.993736i	$0.464353\pi$
$282$	1518.97	−	5668.89i	0.320757	−	1.19708i
$283$	272.187	+	104.483i	0.0571725	+	0.0219465i	0.386786	−	0.922169i	$-0.373585\pi$
$283$	272.187	+	104.483i	0.0571725	+	0.0219465i	−0.329614	+	0.944116i	$0.606918\pi$
$284$	−2885.26	+	2597.90i	−0.602848	+	0.542806i
$285$	−1770.89	−	2693.69i	−0.368064	−	0.559862i
$286$	1549.10	−	503.334i	0.320281	−	0.104066i
$287$	687.662	−	150.557i	0.141433	−	0.0309655i
$288$	−2766.66	−	5429.87i	−0.566066	−	1.11097i
$289$	2022.62	+	1821.18i	0.411688	+	0.370686i
$290$	2269.50	+	4392.99i	0.459550	+	0.889535i
$291$	1239.07	+	1376.12i	0.249606	+	0.277215i
$292$	448.540	+	553.901i	0.0898933	+	0.111009i
$293$	1448.41	+	1448.41i	0.288795	+	0.288795i	0.836604	−	0.547809i	$-0.184538\pi$
$293$	1448.41	+	1448.41i	0.288795	+	0.288795i	−0.547809	+	0.836604i	$0.684538\pi$
$294$	2308.54	+	5019.37i	0.457949	+	0.995700i
$295$	3309.53	+	5658.65i	0.653180	+	1.11681i
$296$	5698.20	+	2537.00i	1.11892	+	0.498176i
$297$	1720.72	+	1393.41i	0.336183	+	0.272236i
$298$	3044.41	−	1977.06i	0.591805	−	0.384323i
$299$	−3578.41	−	6198.00i	−0.692124	−	1.19879i
$300$	3364.80	−	2239.25i	0.647557	−	0.430944i
$301$	794.362	−	3038.62i	0.152114	−	0.581871i
$302$	1722.35	−	3380.30i	0.328179	−	0.644088i
$303$	5850.54	−	2245.81i	1.10926	−	0.425804i
$304$	59.2099	+	563.344i	0.0111708	+	0.106283i
$305$	−5799.46	−	7888.74i	−1.08877	−	1.48101i
$306$	3535.85	+	371.633i	0.660560	+	0.0694277i
$307$	−5476.70	+	5476.70i	−1.01815	+	1.01815i	−0.0183175	+	0.999832i	$0.505831\pi$
$307$	−5476.70	+	5476.70i	−1.01815	+	1.01815i	−0.999832	+	0.0183175i	$0.994169\pi$
$308$	−1685.49	+	762.783i	−0.311818	+	0.141116i
$309$	1986.41	+	645.422i	0.365704	+	0.118825i
$310$	−554.534	−	2024.02i	−0.101598	−	0.370828i
$311$	46.7002	−	219.707i	0.00851488	−	0.0400594i	−0.973685	−	0.227898i	$-0.926815\pi$
$311$	46.7002	−	219.707i	0.00851488	−	0.0400594i	0.982200	+	0.187838i	$0.0601481\pi$
$312$	331.390	−	6323.30i	0.0601323	−	1.14739i
$313$	5978.28	+	3882.34i	1.07959	+	0.701095i	0.956627	−	0.291316i	$-0.0940930\pi$
$313$	5978.28	+	3882.34i	1.07959	+	0.701095i	0.122965	+	0.992411i	$0.460760\pi$
$314$	−1025.42	−	3155.92i	−0.184293	−	0.567194i
$315$	4016.10	+	6771.64i	0.718355	+	1.21123i
$316$	392.311	−	1207.41i	0.0698393	−	0.214943i
$317$	4046.61	−	3276.88i	0.716972	−	0.580593i	−0.199879	−	0.979821i	$-0.564055\pi$
$317$	4046.61	−	3276.88i	0.716972	−	0.580593i	0.916852	+	0.399228i	$0.130722\pi$
$318$	4487.05	−	1202.30i	0.791262	−	0.212018i
$319$	−2243.38	−	5038.71i	−0.393746	−	0.884368i
$320$	−4965.98	+	550.156i	−0.867521	+	0.0961082i
$321$	−2332.50	−	3210.41i	−0.405569	−	0.558217i
$322$	−4794.29	−	6514.83i	−0.829737	−	1.12751i
$323$	1491.40	+	759.907i	0.256916	+	0.130905i
$324$	−1076.21	+	621.349i	−0.184535	+	0.106541i
$325$	4083.27	−	260.007i	0.696920	−	0.0443772i
$326$	−1032.11	+	1787.67i	−0.175348	+	0.303711i
$327$	−111.229	−	2122.38i	−0.0188104	−	0.358924i
$328$	−900.629	−	142.646i	−0.151613	−	0.0240131i
$329$	−4214.62	+	5270.02i	−0.706260	+	0.883118i
$330$	3872.55	−	2264.90i	0.645990	−	0.377815i
$331$	−222.848	+	2120.26i	−0.0370056	+	0.352085i	0.960314	+	0.278920i	$0.0899765\pi$
$331$	−222.848	+	2120.26i	−0.0370056	+	0.352085i	−0.997320	+	0.0731645i	$0.976690\pi$
$332$	−861.474	−	3215.07i	−0.142408	−	0.531475i
$333$	−3542.78	+	9229.25i	−0.583012	+	1.51880i
$334$	1367.11	−	290.587i	0.223966	−	0.0476055i
$335$	5915.79	+	3794.70i	0.964818	+	0.618886i
$336$	−138.223	−	2361.74i	−0.0224426	−	0.383462i
$337$	−1501.68	+	765.145i	−0.242735	+	0.123680i	−0.571127	−	0.820862i	$-0.693493\pi$
$337$	−1501.68	+	765.145i	−0.242735	+	0.123680i	0.328391	+	0.944542i	$0.393493\pi$
$338$	−1224.57	+	1885.67i	−0.197064	+	0.303452i
$339$	−14177.0	−	3013.42i	−2.27136	−	0.482793i
$340$	−942.250	+	1875.23i	−0.150296	+	0.299113i
$341$	486.709	+	2289.78i	0.0772925	+	0.363633i
$342$	−2682.34	+	424.841i	−0.424106	+	0.0671718i
$343$	−116.237	−	6351.39i	−0.0182979	−	0.999833i
$344$	−2391.30	+	3291.34i	−0.374797	+	0.515864i
$345$	−13271.9	−	14574.6i	−2.07112	−	2.27440i
$346$	−4363.47	+	458.619i	−0.677981	+	0.0712587i
$347$	7651.99	−	9449.42i	1.18380	−	1.46188i	0.327924	−	0.944704i	$-0.393651\pi$
$347$	7651.99	−	9449.42i	1.18380	−	1.46188i	0.855881	−	0.517173i	$-0.173016\pi$
$348$	−7149.12	+	374.670i	−1.10124	+	0.0577138i
$349$	−1500.54			−0.230149			−0.115074	−	0.993357i	$-0.536711\pi$
$349$	−1500.54			−0.230149			−0.115074	+	0.993357i	$0.536711\pi$
$350$	4554.18	−	802.445i	0.695517	−	0.122550i
$351$	2909.24			0.442404
$352$	3987.31	−	208.966i	0.603763	−	0.0316419i
$353$	−582.133	+	718.874i	−0.0877728	+	0.108390i	−0.819140	−	0.573593i	$-0.805549\pi$
$353$	−582.133	+	718.874i	−0.0877728	+	0.108390i	0.731368	+	0.681983i	$0.238882\pi$
$354$	9392.51	−	987.193i	1.41019	−	0.148217i
$355$	−9864.36	+	4458.43i	−1.47478	+	0.666561i
$356$	−2612.09	+	3595.23i	−0.388878	+	0.535244i
$357$	−6075.44	−	3458.42i	−0.900690	−	0.512714i
$358$	−481.228	+	76.2190i	−0.0710438	+	0.0112522i
$359$	493.062	+	2319.67i	0.0724869	+	0.341024i	0.999414	−	0.0342162i	$-0.0108935\pi$
$359$	493.062	+	2319.67i	0.0724869	+	0.341024i	−0.926928	+	0.375240i	$0.877560\pi$
$360$	−1651.89	−	10063.5i	−0.241839	−	1.47332i
$361$	5458.47	+	1160.23i	0.795812	+	0.169155i
$362$	4000.48	−	6160.20i	0.580831	−	0.894401i
$363$	5104.06	−	2600.65i	0.737999	−	0.376029i
$364$	−1090.35	+	2172.59i	−0.157005	+	0.312843i
$365$	722.570	+	1851.22i	0.103619	+	0.265472i
$366$	−13797.6	+	2932.78i	−1.97053	+	0.418849i
$367$	1955.49	−	5094.21i	0.278135	−	0.724566i	−0.721353	−	0.692568i	$-0.756479\pi$
$367$	1955.49	−	5094.21i	0.278135	−	0.724566i	0.999488	−	0.0319986i	$-0.0101872\pi$
$368$	896.470	+	3345.67i	0.126988	+	0.473927i
$369$	151.066	−	1437.30i	0.0213122	−	0.202772i
$370$	4336.90	+	3861.09i	0.609365	+	0.542510i
$371$	−5280.47	−	803.358i	−0.738944	−	0.112421i
$372$	3001.03	+	475.316i	0.418269	+	0.0662472i
$373$	404.288	+	7714.28i	0.0561213	+	1.07086i	0.871018	+	0.491252i	$0.163461\pi$
$373$	404.288	+	7714.28i	0.0561213	+	1.07086i	−0.814896	+	0.579607i	$0.803206\pi$
$374$	−1164.71	+	2017.33i	−0.161031	+	0.278914i
$375$	10834.6	−	3099.65i	1.49199	−	0.426841i
$376$	7569.95	−	4370.51i	1.03827	−	0.599447i
$377$	−6457.16	−	3290.09i	−0.882123	−	0.449464i
$378$	3267.90	−	363.637i	0.444664	−	0.0494801i
$379$	3720.71	+	5121.12i	0.504275	+	0.694074i	0.982941	−	0.183923i	$-0.0588796\pi$
$379$	3720.71	+	5121.12i	0.504275	+	0.694074i	−0.478666	+	0.877997i	$0.658880\pi$
$380$	324.487	−	1569.89i	0.0438048	−	0.211930i
$381$	−1220.09	−	2740.36i	−0.164060	−	0.368485i
$382$	1347.78	−	361.136i	0.180519	−	0.0483699i
$383$	1809.97	−	1465.68i	0.241475	−	0.195543i	−0.500942	−	0.865481i	$-0.667013\pi$
$383$	1809.97	−	1465.68i	0.241475	−	0.195543i	0.742417	+	0.669938i	$0.233680\pi$
$384$	970.667	−	2987.41i	0.128995	−	0.397006i
$385$	−5123.38	+	599.250i	−0.678212	+	0.0793262i
$386$	−196.769	−	605.594i	−0.0259464	−	0.0798547i
$387$	−5407.71	−	3511.81i	−0.710309	−	0.461280i
$388$	−48.1932	+	919.582i	−0.00630578	+	0.120321i
$389$	1.73165	−	8.14677i	0.000225702	−	0.00106185i	−0.978035	−	0.208443i	$-0.933161\pi$
$389$	1.73165	−	8.14677i	0.000225702	−	0.00106185i	0.978260	+	0.207381i	$0.0664939\pi$
$390$	2081.50	−	5514.86i	0.270259	−	0.716041i
$391$	9734.20	+	3162.83i	1.25903	+	0.409083i
$392$	−2854.93	+	7717.45i	−0.367846	+	0.994363i
$393$	14436.7	−	14436.7i	1.85301	−	1.85301i
$394$	−8477.09	−	890.978i	−1.08393	−	0.113926i
$395$	2064.49	−	2875.34i	0.262976	−	0.366263i
$396$	397.020	+	3777.39i	0.0503813	+	0.479346i
$397$	3556.73	−	1365.30i	0.449640	−	0.172601i	−0.123001	−	0.992406i	$-0.539252\pi$
$397$	3556.73	−	1365.30i	0.449640	−	0.172601i	0.572642	+	0.819806i	$0.305919\pi$
$398$	740.518	−	1453.35i	0.0932634	−	0.183040i
$399$	5166.39	+	1350.61i	0.648228	+	0.169461i
$400$	−1941.41	−	389.926i	−0.242677	−	0.0487407i
$401$	2387.81	+	4135.81i	0.297360	+	0.515043i	0.975531	−	0.219861i	$-0.0705604\pi$
$401$	2387.81	+	4135.81i	0.297360	+	0.515043i	−0.678171	+	0.734904i	$0.737227\pi$
$402$	8491.94	−	5514.73i	1.05358	−	0.684203i
$403$	2390.37	+	1935.68i	0.295466	+	0.239263i
$404$	2846.93	+	1267.54i	0.350595	+	0.156095i
$405$	−3385.06	+	739.407i	−0.415321	+	0.0907195i
$406$	−7664.46	−	2888.60i	−0.936899	−	0.353100i
$407$	−4580.01	−	4580.01i	−0.557795	−	0.557795i
$408$	5698.81	+	7037.44i	0.691503	+	0.853935i
$409$	2395.89	+	2660.90i	0.289655	+	0.321694i	0.870357	−	0.492422i	$-0.163888\pi$
$409$	2395.89	+	2660.90i	0.289655	+	0.321694i	−0.580702	+	0.814117i	$0.697222\pi$
$410$	−758.502	−	381.126i	−0.0913652	−	0.0459085i
$411$	8791.91	+	7916.27i	1.05517	+	0.950075i
$412$	471.532	+	925.433i	0.0563852	+	0.110662i
$413$	−10347.8	−	3292.57i	−1.23289	−	0.392293i
$414$	−15793.6	+	5131.64i	−1.87491	+	0.609194i
$415$	433.652	−	9270.28i	0.0512943	−	1.09653i
$416$	3898.71	−	3510.41i	0.459495	−	0.413731i
$417$	7963.25	+	3056.81i	0.935161	+	0.358975i
$418$	460.529	−	1718.72i	0.0538881	−	0.201113i
$419$	−4352.25	−	3162.09i	−0.507449	−	0.368683i	0.304406	−	0.952542i	$-0.401542\pi$
$419$	−4352.25	−	3162.09i	−0.507449	−	0.368683i	−0.811855	+	0.583859i	$0.801542\pi$
$420$	−1656.98	+	6486.97i	−0.192506	+	0.753647i
$421$	11071.9	−	8044.18i	1.28173	−	0.931233i	0.282129	−	0.959377i	$-0.408959\pi$
$421$	11071.9	−	8044.18i	1.28173	−	0.931233i	0.999604	+	0.0281434i	$0.00895950\pi$
$422$	1728.27	+	4502.30i	0.199362	+	0.519357i
$423$	7545.33	+	11618.8i	0.867296	+	1.33552i
$424$	5991.78	+	3459.36i	0.686289	+	0.396229i
$425$	−4090.84	+	4183.77i	−0.466906	+	0.477512i
$426$			15595.6i			1.77373i
$427$	15884.9	+	3275.29i	1.80029	+	0.371200i
$428$	308.701	−	1949.06i	0.0348636	−	0.220120i
$429$	−2674.40	+	6006.80i	−0.300982	+	0.676017i
$430$	−3051.45	+	2243.29i	−0.342219	+	0.251584i
$431$	6374.20	−	2837.98i	0.712377	−	0.317171i	−0.0183584	−	0.999831i	$-0.505844\pi$
$431$	6374.20	−	2837.98i	0.712377	−	0.317171i	0.730735	+	0.682661i	$0.239177\pi$
$432$	−1360.01	−	364.414i	−0.151466	−	0.0405853i
$433$	−1509.54	−	9530.87i	−0.167538	−	1.05779i	−0.917913	−	0.396781i	$-0.870127\pi$
$433$	−1509.54	−	9530.87i	−0.167538	−	1.05779i	0.750375	−	0.661012i	$-0.229873\pi$
$434$	2927.01	+	1875.54i	0.323735	+	0.207439i
$435$	−19309.0	−	5057.79i	−2.12826	−	0.557477i
$436$	707.184	−	785.408i	0.0776789	−	0.0862711i
$437$	−7807.50	−	409.174i	−0.854653	−	0.0447905i
$438$	2859.06	+	149.837i	0.311898	+	0.0163459i
$439$	−4234.65	+	4703.05i	−0.460384	+	0.511309i	−0.927978	−	0.372635i	$-0.878454\pi$
$439$	−4234.65	+	4703.05i	−0.460384	+	0.511309i	0.467594	+	0.883943i	$0.345121\pi$
$440$	6463.70	+	1693.10i	0.700330	+	0.183444i
$441$	−12451.6	−	3878.48i	−1.34452	−	0.418797i
$442$	478.797	+	3023.00i	0.0515250	+	0.325316i
$443$	−10605.9	−	2841.85i	−1.13748	−	0.304787i	−0.359542	−	0.933129i	$-0.617067\pi$
$443$	−10605.9	−	2841.85i	−1.13748	−	0.304787i	−0.777937	+	0.628342i	$0.783734\pi$
$444$	−7680.18	+	3419.44i	−0.820912	+	0.365494i
$445$	−9983.11	+	7339.15i	−1.06347	+	0.781819i
$446$	678.243	−	1523.36i	0.0720084	−	0.161734i
$447$	−2292.36	+	14473.4i	−0.242562	+	1.53148i
$448$	5500.43	−	6184.29i	0.580069	−	0.652188i
$449$		−	6844.47i		−	0.719400i	−0.933068	−	0.359700i	$-0.882879\pi$
$449$		−	6844.47i		−	0.719400i	0.933068	−	0.359700i	$-0.117121\pi$
$450$	1379.76	−	9393.00i	0.144539	−	0.983979i
$451$	820.032	+	473.446i	0.0856182	+	0.0494317i
$452$	−3925.48	−	6044.71i	−0.408493	−	0.629025i
$453$	5488.37	+	14297.7i	0.569241	+	1.48292i
$454$	−9257.31	+	6725.83i	−0.956976	+	0.695284i
$455$	−4736.05	+	4848.33i	−0.487977	+	0.499546i
$456$	−5596.08	−	4065.79i	−0.574694	−	0.417540i
$457$	3984.59	−	14870.7i	0.407858	−	1.52215i	−0.390865	−	0.920448i	$-0.627824\pi$
$457$	3984.59	−	14870.7i	0.407858	−	1.52215i	0.798723	−	0.601699i	$-0.205509\pi$
$458$	8527.73	+	3273.49i	0.870032	+	0.333974i
$459$	−3091.91	+	2783.96i	−0.314418	+	0.283103i
$460$	458.043	−	9791.70i	0.0464269	−	0.992479i
$461$	−5553.80	+	1804.54i	−0.561099	+	0.182312i	−0.575815	−	0.817580i	$-0.695315\pi$
$461$	−5553.80	+	1804.54i	−0.561099	+	0.182312i	0.0147168	+	0.999892i	$0.495315\pi$
$462$	−2253.30	+	7081.63i	−0.226911	+	0.713133i
$463$	−202.904	−	398.222i	−0.0203667	−	0.0399718i	0.880599	−	0.473862i	$-0.157141\pi$
$463$	−202.904	−	398.222i	−0.0203667	−	0.0399718i	−0.900966	+	0.433890i	$0.857141\pi$
$464$	2606.47	+	2346.88i	0.260781	+	0.234808i
$465$	7569.83	+	3803.63i	0.754930	+	0.379331i
$466$	−8931.71	−	9919.67i	−0.887883	−	0.986094i
$467$	1168.48	+	1442.95i	0.115783	+	0.142980i	0.831742	−	0.555162i	$-0.187344\pi$
$467$	1168.48	+	1442.95i	0.115783	+	0.142980i	−0.715959	+	0.698142i	$0.754010\pi$
$468$	3528.86	+	3528.86i	0.348550	+	0.348550i
$469$	−11487.7	+	1891.37i	−1.13103	+	0.186216i
$470$	7949.81	−	1736.50i	0.780207	−	0.170423i
$471$	12237.4	+	5448.45i	1.19718	+	0.533017i
$472$	10931.5	+	8852.13i	1.06602	+	0.863246i
$473$	3543.08	−	2300.90i	0.344421	−	0.223669i
$474$	−2549.81	−	4416.40i	−0.247081	−	0.427957i
$475$	2191.22	−	3895.69i	0.211663	−	0.376308i
$476$	−920.226	−	3352.40i	−0.0886103	−	0.322809i
$477$	−4978.28	+	9770.42i	−0.477861	+	0.937855i
$478$	−6734.03	+	2584.95i	−0.644367	+	0.247349i
$479$	−781.083	−	7431.50i	−0.0745064	−	0.708881i	−0.966471	−	0.256776i	$-0.917340\pi$
$479$	−781.083	−	7431.50i	−0.0745064	−	0.708881i	0.891965	−	0.452105i	$-0.149327\pi$
$480$	8427.50	−	11737.5i	0.801377	−	1.11613i
$481$	−8463.84	−	889.585i	−0.802324	−	0.0843277i
$482$	4440.42	−	4440.42i	0.419617	−	0.419617i
$483$	32494.3	+	3215.02i	3.06116	+	0.302874i
$484$	2709.22	+	880.278i	0.254434	+	0.0826708i
$485$	−906.629	+	2402.08i	−0.0848823	+	0.224892i
$486$	−2034.49	+	9571.50i	−0.189889	+	0.893359i
$487$	191.362	−	3651.40i	0.0178058	−	0.339755i	−0.975172	−	0.221451i	$-0.928921\pi$
$487$	191.362	−	3651.40i	0.0178058	−	0.339755i	0.992977	−	0.118304i	$-0.0377459\pi$
$488$	−17619.8	−	11442.4i	−1.63444	−	1.06142i
$489$	−2575.00	−	7925.05i	−0.238130	−	0.732889i
$490$	−4713.92	+	6038.03i	−0.434598	+	0.556675i
$491$	−3989.19	+	12277.5i	−0.366659	+	1.12846i	0.582276	+	0.812991i	$0.302162\pi$
$491$	−3989.19	+	12277.5i	−0.366659	+	1.12846i	−0.948936	+	0.315470i	$0.897838\pi$
$492$	955.130	−	773.449i	0.0875215	−	0.0708735i
$493$	10011.0	−	2682.44i	0.914549	−	0.245053i
$494$	−950.924	−	2135.81i	−0.0866075	−	0.194524i
$495$	−2143.60	+	10370.8i	−0.194642	+	0.941687i
$496$	−874.982	−	1204.31i	−0.0792094	−	0.109022i
$497$	7193.48	−	16425.7i	0.649239	−	1.48248i
$498$	−11912.9	−	6069.91i	−1.07194	−	0.546183i
$499$	−7924.94	+	4575.47i	−0.710960	+	0.410473i	−0.811416	−	0.584469i	$-0.801303\pi$
$499$	−7924.94	+	4575.47i	−0.710960	+	0.410473i	0.100456	+	0.994941i	$0.467970\pi$
$500$	4899.72	+	2719.86i	0.438245	+	0.243271i
$501$	−2821.03	+	4886.16i	−0.251565	+	0.435724i
$502$	390.984	+	7460.42i	0.0347619	+	0.663296i
$503$	−15593.7	−	2469.79i	−1.38228	−	0.218932i	−0.579386	−	0.815054i	$-0.696707\pi$
$503$	−15593.7	−	2469.79i	−1.38228	−	0.218932i	−0.802894	+	0.596122i	$0.796707\pi$
$504$	13193.2	+	10551.1i	1.16602	+	0.932504i
$505$	6489.71	+	5777.71i	0.571858	+	0.509118i
$506$	1137.30	−	10820.7i	0.0999194	−	0.950669i
$507$	−2349.14	−	8767.12i	−0.205777	−	0.767971i
$508$	534.575	−	1392.62i	0.0466889	−	0.121629i
$509$	4624.34	−	982.934i	0.402692	−	0.0855949i	−0.00211305	−	0.999998i	$-0.500673\pi$
$509$	4624.34	−	982.934i	0.402692	−	0.0855949i	0.404805	+	0.914403i	$0.367339\pi$
$510$	3065.19	+	7853.00i	0.266135	+	0.681837i
$511$	−2942.14	−	1476.56i	−0.254702	−	0.127826i
$512$	−4971.21	+	2532.96i	−0.429099	+	0.218637i
$513$	1730.91	−	2665.37i	0.148970	−	0.229394i
$514$	−13508.8	−	2871.38i	−1.15923	−	0.246403i
$515$	469.074	+	2857.67i	0.0401357	+	0.244513i
$516$	−1140.06	−	5363.56i	−0.0972643	−	0.457592i
$517$	−8965.13	+	1419.94i	−0.762642	+	0.120791i
$518$	−9618.49	+	58.6702i	−0.815854	+	0.00497649i
$519$	10410.6	−	14329.0i	0.880490	−	1.21189i
$520$	8000.17	−	3615.87i	0.674674	−	0.304935i
$521$	−14110.5	+	1483.08i	−1.18655	+	0.124712i	−0.677169	−	0.735828i	$-0.736793\pi$
$521$	−14110.5	+	1483.08i	−1.18655	+	0.124712i	−0.509384	+	0.860539i	$0.670127\pi$
$522$	−10582.4	+	13068.2i	−0.887319	+	1.09575i
$523$	−5343.43	+	280.037i	−0.446753	+	0.0234134i	−0.274387	−	0.961619i	$-0.588475\pi$
$523$	−5343.43	+	280.037i	−0.446753	+	0.0234134i	−0.172367	+	0.985033i	$0.555141\pi$
$524$	10152.8			0.846425
$525$	−9894.26	+	15829.8i	−0.822516	+	1.31594i
$526$	6237.52			0.517051
$527$	−4392.78	+	230.216i	−0.363098	+	0.0190291i
$528$	2002.64	−	2473.06i	0.165064	−	0.203837i
$529$	−35444.3	+	3725.35i	−2.91315	+	0.306185i
$530$	4336.56	+	4762.18i	0.355411	+	0.390294i
$531$	−13103.9	+	18036.0i	−1.07093	+	1.47400i
$532$	1341.75	+	2291.58i	0.109346	+	0.186753i
$533$	1228.83	−	194.628i	0.0998622	−	0.0158166i
$534$	3711.40	+	17460.7i	0.300764	+	1.41498i
$535$	2470.33	−	4916.34i	0.199629	−	0.397293i
$536$	14751.2	+	3135.47i	1.18872	+	0.252671i
$537$	1071.22	−	1649.54i	0.0860831	−	0.132556i
$538$	2517.47	−	1282.72i	0.201740	−	0.102791i
$539$	5639.67	−	6419.26i	0.450682	−	0.512982i
$540$	3353.95	+	2151.40i	0.267280	+	0.171448i
$541$	−3756.33	+	798.433i	−0.298516	+	0.0634516i	−0.354735	−	0.934967i	$-0.615429\pi$
$541$	−3756.33	+	798.433i	−0.298516	+	0.0634516i	0.0562187	+	0.998418i	$0.482096\pi$
$542$	−722.324	+	1881.72i	−0.0572445	+	0.149127i
$543$	7674.31	+	28640.9i	0.606512	+	2.26353i
$544$	−784.251	+	7461.65i	−0.0618097	+	0.588080i
$545$	2543.65	−	1487.68i	0.199923	−	0.116927i
$546$	3554.80	+	9094.37i	0.278629	+	0.712826i
$547$	−12828.6	−	2031.85i	−1.00276	−	0.158822i	−0.366602	−	0.930378i	$-0.619479\pi$
$547$	−12828.6	−	2031.85i	−1.00276	−	0.158822i	−0.636162	+	0.771556i	$0.719479\pi$
$548$	307.902	+	5875.12i	0.0240017	+	0.457979i
$549$	16648.9	−	28836.7i	1.29428	−	2.24175i
$550$	5254.45	+	3328.99i	0.407364	+	0.258088i
$551$	−6856.11	+	3958.38i	−0.530091	+	0.306048i
$552$	−37686.6	−	19202.3i	−2.90588	−	1.48062i
$553$	648.467	+	5827.60i	0.0498655	+	0.448128i
$554$	5426.10	+	7468.39i	0.416124	+	0.572746i
$555$	−23297.7	+	2581.04i	−1.78186	+	0.197403i
$556$	1725.26	+	3875.00i	0.131596	+	0.295569i
$557$	8018.17	−	2148.46i	0.609947	−	0.163435i	0.0593936	−	0.998235i	$-0.481083\pi$
$557$	8018.17	−	2148.46i	0.609947	−	0.163435i	0.550554	+	0.834800i	$0.314417\pi$
$558$	5546.48	−	4491.45i	0.420791	−	0.340750i
$559$	1715.31	−	5279.19i	0.129785	−	0.399438i
$560$	2821.31	−	1673.26i	0.212897	−	0.126264i
$561$	−2905.82	−	8943.20i	−0.218688	−	0.673052i
$562$	10645.5	+	6913.24i	0.799024	+	0.518892i
$563$	330.903	−	6314.00i	0.0247707	−	0.472653i	−0.957878	−	0.287176i	$-0.907284\pi$
$563$	330.903	−	6314.00i	0.0247707	−	0.472653i	0.982649	−	0.185477i	$-0.0593831\pi$
$564$	−2449.49	+	11523.9i	−0.182876	+	0.860363i
$565$	−5310.09	−	19381.5i	−0.395393	−	1.44316i
$566$	553.877	+	179.966i	0.0411329	+	0.0133649i
$567$	3345.25	−	4663.90i	0.247773	−	0.345442i
$568$	−16424.6	+	16424.6i	−1.21331	+	1.21331i
$569$	18123.4	+	1904.85i	1.33528	+	0.140343i	0.745113	−	0.666939i	$-0.232396\pi$
$569$	18123.4	+	1904.85i	1.33528	+	0.140343i	0.590166	+	0.807282i	$0.299062\pi$
$570$	−3814.15	−	5188.21i	−0.280275	−	0.381246i
$571$	829.605	+	7893.16i	0.0608019	+	0.578491i	0.981932	+	0.189236i	$0.0606011\pi$
$571$	829.605	+	7893.16i	0.0608019	+	0.578491i	−0.921130	+	0.389256i	$0.872732\pi$
$572$	−3052.58	+	1171.78i	−0.223138	+	0.0856547i
$573$	−2557.17	+	5018.74i	−0.186435	+	0.365900i
$574$	1356.00	−	372.218i	0.0986033	−	0.0270664i
$575$	9507.35	−	25624.0i	0.689537	−	1.85842i
$576$	−8495.86	−	14715.3i	−0.614573	−	1.06447i
$577$	19401.9	−	12599.8i	1.39985	−	0.909074i	0.399879	−	0.916568i	$-0.369052\pi$
$577$	19401.9	−	12599.8i	1.39985	−	0.909074i	0.999972	+	0.00749457i	$0.00238562\pi$
$578$	4225.09	+	3421.41i	0.304050	+	0.246214i
$579$	2348.25	+	1045.51i	0.168549	+	0.0750430i
$580$	−5011.17	−	8568.13i	−0.358754	−	0.613400i
$581$	9747.25	+	11887.9i	0.696014	+	0.848866i
$582$	2615.53	+	2615.53i	0.186284	+	0.186284i
$583$	−4521.38	−	5583.44i	−0.321195	−	0.396642i
$584$	2853.24	+	3168.84i	0.202171	+	0.224534i
$585$	6386.60	+	12362.3i	0.451374	+	0.873707i
$586$	3040.68	+	2737.84i	0.214351	+	0.193002i
$587$	−3475.17	−	6820.41i	−0.244354	−	0.479571i	0.735958	−	0.677027i	$-0.236732\pi$
$587$	−3475.17	−	6820.41i	−0.244354	−	0.479571i	−0.980312	+	0.197456i	$0.936732\pi$
$588$	−5155.25	−	9819.73i	−0.361563	−	0.688705i
$589$	3195.62	−	1038.32i	0.223554	−	0.0726371i
$590$	7193.37	+	10941.8i	0.501943	+	0.763504i
$591$	25570.9	−	23024.1i	1.77977	−	1.60251i
$592$	3845.24	+	1476.05i	0.266957	+	0.102475i
$593$	−7402.28	+	27625.7i	−0.512606	+	1.91307i	−0.121939	+	0.992538i	$0.538911\pi$
$593$	−7402.28	+	27625.7i	−0.512606	+	1.91307i	−0.390667	+	0.920532i	$0.627755\pi$
$594$	3578.14	+	2599.67i	0.247160	+	0.179572i
$595$	393.858	−	9684.86i	0.0271372	−	0.667295i
$596$	−5895.38	+	4283.24i	−0.405175	+	0.294377i
$597$	2359.70	+	6147.24i	0.161769	+	0.421423i
$598$	−7786.12	−	11989.6i	−0.532438	−	0.819883i
$599$	651.276	+	376.014i	0.0444247	+	0.0256486i	0.522048	−	0.852916i	$-0.325168\pi$
$599$	651.276	+	376.014i	0.0444247	+	0.0256486i	−0.477623	+	0.878565i	$0.658502\pi$
$600$	19401.9	−	14432.0i	1.32013	−	0.981971i
$601$		−	14534.7i		−	0.986496i	−0.869889	−	0.493248i	$-0.835809\pi$
$601$		−	14534.7i		−	0.986496i	0.869889	−	0.493248i	$-0.164191\pi$
$602$	1266.92	−	6144.44i	0.0857736	−	0.415994i
$603$	−3739.07	+	23607.5i	−0.252515	+	1.59432i
$604$	−3097.63	+	6957.40i	−0.208677	+	0.468696i
$605$	6451.76	+	4632.35i	0.433556	+	0.311292i
$606$	11435.8	−	5091.54i	0.766580	−	0.341303i
$607$	−15347.7	−	4112.41i	−1.02627	−	0.274988i	−0.293857	−	0.955850i	$-0.594939\pi$
$607$	−15347.7	−	4112.41i	−1.02627	−	0.274988i	−0.732412	+	0.680862i	$0.761605\pi$
$608$	−896.534	−	5660.49i	−0.0598014	−	0.377571i
$609$	29368.6	−	15190.4i	1.95414	−	1.01075i
$610$	−12393.4	−	15130.1i	−0.822613	−	1.00426i
$611$	−7980.29	+	8863.02i	−0.528393	+	0.586840i
$612$	−7127.32	−	373.527i	−0.470760	−	0.0246715i
$613$	7467.49	+	391.354i	0.492021	+	0.0257857i	0.296734	−	0.954960i	$-0.404103\pi$
$613$	7467.49	+	391.354i	0.492021	+	0.0257857i	0.195287	+	0.980746i	$0.437436\pi$
$614$	−10352.3	+	11497.4i	−0.680431	+	0.755696i
$615$	3192.19	−	1245.98i	0.209303	−	0.0816954i
$616$	−9831.16	+	5085.00i	−0.643033	+	0.332598i
$617$	4206.18	+	26556.8i	0.274448	+	1.73280i	0.611441	+	0.791290i	$0.290590\pi$
$617$	4206.18	+	26556.8i	0.274448	+	1.73280i	−0.336993	+	0.941507i	$0.609410\pi$
$618$	4029.93	+	1079.82i	0.262310	+	0.0702857i
$619$	15686.0	−	6983.86i	1.01854	−	0.453482i	0.171595	−	0.985168i	$-0.445108\pi$
$619$	15686.0	−	6983.86i	1.01854	−	0.453482i	0.846942	+	0.531686i	$0.178441\pi$
$620$	1324.31	+	3999.26i	0.0857834	+	0.259055i
$621$	7904.24	−	17753.2i	0.510767	−	1.14720i
$622$	70.1883	−	443.151i	0.00452459	−	0.0285671i
$623$	4144.84	−	20102.1i	0.266548	−	1.29274i
$624$		−	4181.22i		−	0.268242i
$625$	10713.3	+	11373.9i	0.685652	+	0.727929i
$626$	12331.3	+	7119.45i	0.787310	+	0.454554i
$627$	3912.09	+	6024.09i	0.249177	+	0.383699i
$628$	2387.21	+	6218.90i	0.151688	+	0.395161i
$629$	9846.55	−	7153.93i	0.624177	−	0.453491i
$630$	8719.19	+	13088.1i	0.551398	+	0.827687i
$631$	10236.3	+	7437.11i	0.645801	+	0.469202i	0.861838	−	0.507183i	$-0.169313\pi$
$631$	10236.3	+	7437.11i	0.645801	+	0.469202i	−0.216037	+	0.976385i	$0.569313\pi$
$632$	1965.81	−	7336.51i	0.123728	−	0.461758i
$633$	−18175.0	−	6976.72i	−1.14122	−	0.438072i
$634$	7729.55	−	6959.72i	0.484195	−	0.435971i
$635$	2599.23	−	3246.89i	0.162436	−	0.202911i
$636$	−8868.81	+	2881.65i	−0.552942	+	0.179662i
$637$	450.769	−	11218.1i	0.0280379	−	0.697769i
$638$	−5001.81	−	9816.61i	−0.310382	−	0.609159i
$639$	−27358.3	−	24633.5i	−1.69371	−	1.52502i
$640$	4297.72	−	705.453i	0.265441	−	0.0435711i
$641$	−3295.06	−	3659.54i	−0.203038	−	0.225496i	0.633023	−	0.774133i	$-0.281814\pi$
$641$	−3295.06	−	3659.54i	−0.203038	−	0.225496i	−0.836061	+	0.548637i	$0.815147\pi$
$642$	−4988.47	−	6160.24i	−0.306665	−	0.378700i
$643$	−21817.7	−	21817.7i	−1.33811	−	1.33811i	−0.897890	−	0.440221i	$-0.854900\pi$
$643$	−21817.7	−	21817.7i	−1.33811	−	1.33811i	−0.440221	−	0.897890i	$-0.645100\pi$
$644$	10295.5	+	12556.5i	0.629968	+	0.768316i
$645$	1512.70	−	15213.7i	0.0923449	−	0.928740i
$646$	3054.47	+	1359.94i	0.186032	+	0.0828267i
$647$	191.484	+	155.060i	0.0116352	+	0.00942202i	0.635120	−	0.772413i	$-0.280950\pi$
$647$	191.484	+	155.060i	0.0116352	+	0.00942202i	−0.623485	+	0.781835i	$0.714284\pi$
$648$	−6235.26	+	4049.23i	−0.378000	+	0.245476i
$649$	−7303.31	−	12649.7i	−0.441726	−	0.765092i
$650$	8118.07	−	945.532i	0.489872	−	0.0570567i
$651$	−13532.8	+	3714.73i	−0.814736	+	0.223643i
$652$	1881.24	−	3692.15i	0.112999	−	0.221772i
$653$	26941.2	−	10341.7i	1.61453	−	0.619761i	0.627262	−	0.778809i	$-0.284176\pi$
$653$	26941.2	−	10341.7i	1.61453	−	0.619761i	0.987271	+	0.159048i	$0.0508424\pi$
$654$	−443.757	−	4222.07i	−0.0265325	−	0.252440i
$655$	26971.0	+	8596.29i	1.60892	+	0.512801i
$656$	−598.832	−	62.9398i	−0.0356409	−	0.00374601i
$657$	−4778.80	+	4778.80i	−0.283773	+	0.283773i
$658$	−7856.32	+	10953.2i	−0.465458	+	0.648935i
$659$	2294.33	+	745.473i	0.135621	+	0.0440660i	0.376041	−	0.926603i	$-0.377285\pi$
$659$	2294.33	+	745.473i	0.135621	+	0.0440660i	−0.240420	+	0.970669i	$0.577285\pi$
$660$	−7525.29	+	4947.28i	−0.443820	+	0.291776i
$661$	3254.22	−	15309.9i	0.191490	−	0.900888i	−0.772514	−	0.634998i	$-0.781001\pi$
$661$	3254.22	−	15309.9i	0.191490	−	0.900888i	0.964003	−	0.265890i	$-0.0856658\pi$
$662$	−222.878	+	4252.76i	−0.0130852	+	0.249680i
$663$	−10362.1	−	6729.25i	−0.606987	−	0.394182i
$664$	−6153.55	−	18938.7i	−0.359645	−	1.10687i
$665$	1624.11	+	7223.67i	0.0947072	+	0.421236i
$666$	−6102.23	+	18780.7i	−0.355040	+	1.09270i
$667$	−37621.0	+	30464.9i	−2.18394	+	1.76852i
$668$	−2710.09	+	726.166i	−0.156971	+	0.0420602i
$669$	2737.95	+	6149.53i	0.158229	+	0.355388i
$670$	12197.4	+	6951.17i	0.703326	+	0.400816i
$671$	12823.3	+	17649.8i	0.737764	+	1.01545i
$672$	2647.13	+	23789.0i	0.151957	+	1.36560i
$673$	10500.4	+	5350.23i	0.601429	+	0.306443i	0.728067	−	0.685506i	$-0.240419\pi$
$673$	10500.4	+	5350.23i	0.601429	+	0.306443i	−0.126638	+	0.991949i	$0.540419\pi$
$674$	−2915.54	+	1683.29i	−0.166621	+	0.0961986i
$675$	7088.25	+	8555.00i	0.404188	+	0.487826i
$676$	2256.76	−	3908.83i	0.128400	−	0.222396i
$677$	1670.74	+	31879.6i	0.0948474	+	1.80980i	0.469821	+	0.882762i	$0.344318\pi$
$677$	1670.74	+	31879.6i	0.0948474	+	1.80980i	−0.374974	+	0.927035i	$0.622348\pi$
$678$	−28595.2	−	4529.03i	−1.61975	−	0.256543i
$679$	−1548.34	−	3961.18i	−0.0875110	−	0.223883i
$680$	−5042.32	+	11498.6i	−0.284359	+	0.648456i
$681$	4828.38	−	45938.9i	0.271694	−	2.58500i
$682$	1210.26	+	4516.75i	0.0679519	+	0.253600i
$683$	11129.6	−	28993.6i	0.623516	−	1.62432i	−0.148646	−	0.988890i	$-0.547492\pi$
$683$	11129.6	−	28993.6i	0.623516	−	1.62432i	0.772163	−	0.635425i	$-0.219175\pi$
$684$	5332.61	−	1133.48i	0.298096	−	0.0633622i
$685$	−4156.47	+	15868.0i	−0.231840	+	0.885090i
$686$	−895.856	−	12657.5i	−0.0498600	−	0.704469i
$687$	−32855.0	+	16740.5i	−1.82460	+	0.929678i
$688$	−1463.15	+	2253.05i	−0.0810785	+	0.124850i
$689$	−9233.69	−	1962.68i	−0.510560	−	0.108523i
$690$	−27998.3	−	27685.6i	−1.54475	−	1.52750i
$691$	−1141.16	−	5368.72i	−0.0628244	−	0.295566i	0.935507	−	0.353308i	$-0.114943\pi$
$691$	−1141.16	−	5368.72i	−0.0628244	−	0.295566i	−0.998332	+	0.0577422i	$0.981610\pi$
$692$	8699.20	−	1377.82i	0.477881	−	0.0756890i
$693$	−8863.74	−	15138.4i	−0.485866	−	0.829815i
$694$	14276.2	−	19649.5i	0.780861	−	1.07476i
$695$	1302.25	+	11754.8i	0.0710750	+	0.641559i
$696$	−42595.2	+	4476.93i	−2.31978	+	0.243818i
$697$	−1119.74	+	1382.76i	−0.0608510	+	0.0751447i
$698$	−2993.25	+	156.870i	−0.162315	+	0.00850659i
$699$	53884.4			2.91573
$700$	−9045.39	+	2087.12i	−0.488405	+	0.112694i
$701$	33292.8			1.79380			0.896900	−	0.442234i	$-0.145814\pi$
$701$	33292.8			1.79380			0.896900	+	0.442234i	$0.145814\pi$
$702$	5803.31	−	304.139i	0.312011	−	0.0163518i
$703$	−5850.76	+	7225.08i	−0.313891	+	0.387623i
$704$	11071.8	−	1163.69i	0.592734	−	0.0622988i
$705$	−16264.3	+	28539.5i	−0.868865	+	1.52463i
$706$	−1086.08	+	1494.86i	−0.0578967	+	0.0796880i
$707$	−14393.0	+	87.7936i	−0.765638	+	0.00467018i
$708$	−18725.3	+	2965.80i	−0.993984	+	0.157432i
$709$	6126.73	+	28824.0i	0.324533	+	1.52681i	0.773811	+	0.633417i	$0.218348\pi$
$709$	6126.73	+	28824.0i	0.324533	+	1.52681i	−0.449277	+	0.893392i	$0.648319\pi$
$710$	−19211.2	+	9924.86i	−1.01547	+	0.524611i
$711$	11774.9	+	2502.83i	0.621087	+	0.132016i
$712$	−14480.2	+	22297.6i	−0.762176	+	1.17365i
$713$	18306.7	−	9327.72i	0.961558	−	0.489938i
$714$	−12480.7	−	6263.66i	−0.654174	−	0.328308i
$715$	−9101.37	+	528.245i	−0.476045	+	0.0276297i
$716$	956.704	−	203.354i	0.0499353	−	0.0106141i
$717$	10435.0	−	27184.1i	0.543517	−	1.41591i
$718$	1226.06	+	4575.71i	0.0637270	+	0.237833i
$719$	1495.40	−	14227.8i	0.0775646	−	0.737978i	−0.884755	−	0.466057i	$-0.845674\pi$
$719$	1495.40	−	14227.8i	0.0775646	−	0.737978i	0.962320	−	0.271921i	$-0.0876590\pi$
$720$	−1437.09	−	6579.12i	−0.0743851	−	0.340541i
$721$	−3746.38	−	2996.11i	−0.193513	−	0.154759i
$722$	11009.8	+	1743.78i	0.567509	+	0.0898846i
$723$	1326.72	+	25315.3i	0.0682450	+	1.30219i
$724$	−7372.52	+	12769.6i	−0.378449	+	0.655494i
$725$	−6057.68	−	27004.3i	−0.310312	−	1.38333i
$726$	9909.63	−	5721.33i	0.506585	−	0.292477i
$727$	23948.9	+	12202.6i	1.22175	+	0.622514i	0.941370	−	0.337375i	$-0.109539\pi$
$727$	23948.9	+	12202.6i	1.22175	+	0.622514i	0.280382	+	0.959889i	$0.409539\pi$
$728$	−5834.04	+	13321.6i	−0.297011	+	0.678200i
$729$	−18300.2	−	25188.0i	−0.929746	−	1.27969i
$730$	1634.90	+	3617.25i	0.0828911	+	0.183398i
$731$	3228.85	+	7252.11i	0.163370	+	0.366934i
$732$	27351.8	−	7328.89i	1.38108	−	0.370060i
$733$	21453.2	−	17372.5i	1.08103	−	0.875398i	0.0883369	−	0.996091i	$-0.471845\pi$
$733$	21453.2	−	17372.5i	1.08103	−	0.875398i	0.992690	+	0.120692i	$0.0385115\pi$
$734$	3368.21	−	10366.3i	0.169377	−	0.521290i
$735$	−5380.71	−	30451.2i	−0.270028	−	1.52817i
$736$	−10829.2	−	33328.9i	−0.542350	−	1.66918i
$737$	−13133.8	−	8529.16i	−0.656429	−	0.426290i
$738$	151.086	−	2882.90i	0.00753599	−	0.143795i
$739$	−5541.92	+	26072.7i	−0.275863	+	1.29783i	0.593970	+	0.804487i	$0.297560\pi$
$739$	−5541.92	+	26072.7i	−0.275863	+	1.29783i	−0.869833	+	0.493346i	$0.835774\pi$
$740$	−9099.78	−	7284.64i	−0.452047	−	0.361876i
$741$	8975.90	+	2916.45i	0.444991	+	0.144586i
$742$	−10617.4	−	1050.50i	−0.525305	−	0.0519743i
$743$	−20939.7	+	20939.7i	−1.03392	+	1.03392i	−0.0345168	+	0.999404i	$0.510989\pi$
$743$	−20939.7	+	20939.7i	−1.03392	+	1.03392i	−0.999404	+	0.0345168i	$0.989011\pi$
$744$	18078.5	+	1900.12i	0.890845	+	0.0936316i
$745$	−19287.7	+	6386.93i	−0.948521	+	0.314093i
$746$	1612.94	+	15346.1i	0.0791606	+	0.753163i
$747$	29464.7	−	11310.4i	1.44318	−	0.553986i
$748$	2122.93	−	4166.49i	0.103773	−	0.203666i
$749$	2412.59	+	8789.10i	0.117696	+	0.428768i
$750$	21288.7	−	7315.81i	1.03647	−	0.356181i
$751$	−12544.3	−	21727.3i	−0.609517	−	1.05572i	−0.991320	−	0.131471i	$-0.958030\pi$
$751$	−12544.3	−	21727.3i	−0.609517	−	1.05572i	0.381802	−	0.924244i	$-0.375303\pi$
$752$	4840.81	−	3143.66i	0.234742	−	0.152443i
$753$	−23436.9	−	18978.9i	−1.13425	−	0.918496i
$754$	−13224.6	−	5887.97i	−0.638742	−	0.284386i
$755$	−14119.7	+	15859.7i	−0.680620	+	0.764495i
$756$	−6512.92	+	1072.31i	−0.313323	+	0.0515866i
$757$	−386.117	−	386.117i	−0.0185385	−	0.0185385i	0.697777	−	0.716315i	$-0.254173\pi$
$757$	−386.117	−	386.117i	−0.0185385	−	0.0185385i	−0.716315	+	0.697777i	$0.754173\pi$
$758$	7957.39	+	9826.56i	0.381300	+	0.470867i
$759$	29389.4	+	32640.3i	1.40549	+	1.56096i
$760$	1447.10	−	9480.89i	0.0690683	−	0.452511i
$761$	−14366.6	−	12935.7i	−0.684347	−	0.616189i	0.251808	−	0.967777i	$-0.418975\pi$
$761$	−14366.6	−	12935.7i	−0.684347	−	0.616189i	−0.936155	+	0.351588i	$0.885642\pi$
$762$	−2720.29	−	5338.88i	−0.129325	−	0.253815i
$763$	−1480.06	+	4651.50i	−0.0702251	+	0.220702i
$764$	−2663.93	+	865.563i	−0.126149	+	0.0409882i
$765$	−18617.6	−	7026.93i	−0.879896	−	0.332104i
$766$	3457.27	−	3112.94i	0.163076	−	0.146834i
$767$	−17917.3	−	6877.82i	−0.843490	−	0.323786i
$768$	9085.29

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+(1.99479 - 0.104542i) q^{2} +(-5.07461 + 6.26663i) q^{3} +(-3.98794 + 0.419149i) q^{4} +(-10.9489 - 2.26308i) q^{5} +(-9.46764 + 13.0311i) q^{6} +(15.9822 - 9.35779i) q^{7} +(-23.6947 + 3.75287i) q^{8} +(-7.90528 - 37.1914i) q^{9} +(-22.0773 - 3.36973i) q^{10} +(24.3674 + 5.17946i) q^{11} +(17.6106 - 27.1179i) q^{12} +(29.1647 - 14.8602i) q^{13} +(30.9028 - 20.3376i) q^{14} +(69.7433 - 57.1284i) q^{15} +(-15.4953 + 3.29363i) q^{16} +(-16.7756 + 43.7020i) q^{17} +(-19.6574 - 73.3624i) q^{18} +(3.73765 - 35.5613i) q^{19} +(44.6121 + 4.43579i) q^{20} +(-22.4619 + 147.642i) q^{21} +(49.1493 + 7.78448i) q^{22} +(-11.4431 - 218.347i) q^{23} +(96.7236 - 167.530i) q^{24} +(114.757 + 49.5565i) q^{25} +(56.6238 - 32.6918i) q^{26} +(79.1924 + 40.3506i) q^{27} +(-59.8138 + 44.0172i) q^{28} +(-130.137 - 179.119i) q^{29} +(133.151 - 121.250i) q^{30} +(38.2207 + 85.8450i) q^{31} +(154.815 - 41.4827i) q^{32} +(-156.113 + 126.418i) q^{33} +(-28.8951 + 88.9300i) q^{34} +(-196.165 + 66.2885i) q^{35} +(47.1145 + 145.003i) q^{36} +(-218.056 - 141.607i) q^{37} +(3.73814 - 71.3280i) q^{38} +(-54.8766 + 258.174i) q^{39} +(267.924 + 12.5331i) q^{40} +(36.1494 + 11.7457i) q^{41} +(-29.3718 + 296.862i) q^{42} +(119.914 - 119.914i) q^{43} +(-99.3467 - 10.4418i) q^{44} +(2.38702 + 425.095i) q^{45} +(-45.6531 - 434.360i) q^{46} +(-340.160 + 130.575i) q^{47} +(57.9927 - 113.817i) q^{48} +(167.864 - 299.117i) q^{49} +(234.096 + 86.8576i) q^{50} +(-188.734 - 326.898i) q^{51} +(-110.078 + 71.4857i) q^{52} +(-224.128 - 181.496i) q^{53} +(162.190 + 72.2117i) q^{54} +(-255.075 - 111.855i) q^{55} +(-343.576 + 281.709i) q^{56} +(203.883 + 203.883i) q^{57} +(-278.322 - 343.699i) q^{58} +(-392.333 - 435.730i) q^{59} +(-254.186 + 257.057i) q^{60} +(650.805 + 585.987i) q^{61} +(85.2165 + 167.247i) q^{62} +(-474.373 - 520.426i) q^{63} +(425.016 - 138.096i) q^{64} +(-352.951 + 96.7004i) q^{65} +(-298.196 + 268.497i) q^{66} +(-586.873 - 225.279i) q^{67} +(48.5825 - 181.312i) q^{68} +(1426.37 + 1036.32i) q^{69} +(-384.378 + 152.739i) q^{70} +(783.313 - 569.110i) q^{71} +(326.888 + 851.572i) q^{72} +(-96.8065 - 149.069i) q^{73} +(-449.778 - 259.680i) q^{74} +(-892.899 + 467.659i) q^{75} +143.383i q^{76} +(437.914 - 145.246i) q^{77} +(-82.4769 + 520.739i) q^{78} +(-128.774 + 289.231i) q^{79} +(177.110 - 0.994520i) q^{80} +(283.115 - 126.051i) q^{81} +(73.3382 + 19.6509i) q^{82} +(129.851 + 819.846i) q^{83} +(27.6927 - 598.201i) q^{84} +(282.576 - 440.525i) q^{85} +(226.666 - 251.738i) q^{86} +(1782.87 + 93.4361i) q^{87} +(-596.817 - 31.2778i) q^{88} +(741.560 - 823.586i) q^{89} +(49.2020 + 847.725i) q^{90} +(327.059 - 510.416i) q^{91} +(137.154 + 865.959i) q^{92} +(-731.914 - 196.116i) q^{93} +(-664.895 + 296.030i) q^{94} +(-121.401 + 380.899i) q^{95} +(-525.672 + 1180.68i) q^{96} +(35.9240 - 226.815i) q^{97} +(303.581 - 614.223i) q^{98} -947.204i 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

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