LMFDB - Embedded newform 175.4.x.a.3.22

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			3.22
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08793 + 1.67526i) q^{2} +(2.88975 - 7.52806i) q^{3} +(1.63097 + 3.66323i) q^{4} +(-3.51457 + 10.6136i) q^{5} +(9.46764 + 13.0311i) q^{6} +(-9.35779 - 15.9822i) q^{7} +(-23.6947 - 3.75287i) q^{8} +(-28.2561 - 25.4419i) q^{9} +(-13.9569 - 17.4346i) q^{10} +(-16.6693 - 18.5131i) q^{11} +(32.2901 - 1.69225i) q^{12} +(-29.1647 - 14.8602i) q^{13} +(36.9551 + 1.71077i) q^{14} +(69.7433 + 57.1284i) q^{15} +(10.6000 - 11.7725i) q^{16} +(29.4593 - 36.3792i) q^{17} +(73.3624 - 19.6574i) q^{18} +(32.6659 + 14.5438i) q^{19} +(-44.6121 + 4.43579i) q^{20} +(-147.357 + 24.2613i) q^{21} +(49.1493 - 7.78448i) q^{22} +(-183.373 - 119.084i) q^{23} +(-96.7236 + 167.530i) q^{24} +(-100.296 - 74.6042i) q^{25} +(56.6238 - 32.6918i) q^{26} +(-79.1924 + 40.3506i) q^{27} +(43.2842 - 60.3463i) q^{28} +(-130.137 + 179.119i) q^{29} +(-171.581 + 54.6868i) q^{30} +(93.4543 - 9.82244i) q^{31} +(-41.4827 - 154.815i) q^{32} +(-187.538 + 71.9889i) q^{33} +(28.8951 + 88.9300i) q^{34} +(202.517 - 43.1489i) q^{35} +(47.1145 - 145.003i) q^{36} +(-13.6074 - 259.645i) q^{37} +(-59.9028 + 38.9013i) q^{38} +(-196.147 + 176.611i) q^{39} +(123.108 - 238.296i) q^{40} +(-36.1494 + 11.7457i) q^{41} +(119.670 - 273.256i) q^{42} +(119.914 + 119.914i) q^{43} +(40.6305 - 91.2576i) q^{44} +(369.337 - 210.480i) q^{45} +(398.993 - 177.643i) q^{46} +(-283.161 + 229.299i) 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} +(6.86927 - 131.074i) q^{52} +(269.244 + 103.353i) q^{53} +(18.5579 - 176.567i) q^{54} +(255.075 - 111.855i) q^{55} +(161.751 + 413.813i) q^{56} +(203.883 - 203.883i) q^{57} +(-158.491 - 412.883i) q^{58} +(-573.520 - 121.906i) q^{59} +(-95.5249 + 348.661i) q^{60} +(-182.077 - 856.607i) q^{61} +(-85.2165 + 167.247i) q^{62} +(-142.204 + 689.675i) q^{63} +(425.016 + 138.096i) q^{64} +(260.221 - 257.315i) q^{65} +(83.4271 - 392.494i) q^{66} +(488.534 + 395.607i) q^{67} +(181.312 + 48.5825i) q^{68} +(-1426.37 + 1036.32i) q^{69} +(-148.038 + 386.212i) q^{70} +(783.313 + 569.110i) q^{71} +(574.039 + 708.879i) q^{72} +(-177.501 - 9.30242i) q^{73} +(449.778 + 259.680i) q^{74} +(-851.454 + 539.444i) q^{75} +143.383i q^{76} +(-139.893 + 439.653i) q^{77} +(-82.4769 - 520.739i) q^{78} +(314.868 + 33.0940i) q^{79} +(87.6938 + 153.879i) q^{80} +(-32.3942 - 308.210i) q^{81} +(19.6509 - 73.3382i) q^{82} +(-129.851 + 819.846i) q^{83} +(-329.210 - 500.232i) q^{84} +(282.576 + 440.525i) q^{85} +(-331.345 + 70.4295i) q^{86} +(972.352 + 1497.29i) q^{87} +(325.496 + 501.220i) q^{88} +(1084.03 - 230.417i) q^{89} +(-49.2020 + 847.725i) q^{90} +(35.4186 + 605.176i) q^{91} +(137.154 - 865.959i) q^{92} +(196.116 - 731.914i) q^{93} +(-76.0777 - 723.831i) q^{94} +(-269.168 + 295.586i) q^{95} +(-1285.33 - 135.094i) q^{96} +(-35.9240 - 226.815i) q^{97} +(-318.476 - 606.634i) 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−1.08793	+	1.67526i	−0.384641	+	0.592295i	−0.976964	−	0.213406i	$-0.931544\pi$
$2$	−1.08793	+	1.67526i	−0.384641	+	0.592295i	0.592323	+	0.805701i	$0.298211\pi$
$3$	2.88975	−	7.52806i	0.556133	−	1.44878i	−0.310861	−	0.950455i	$-0.600617\pi$
$3$	2.88975	−	7.52806i	0.556133	−	1.44878i	0.866993	−	0.498320i	$-0.166049\pi$
$4$	1.63097	+	3.66323i	0.203872	+	0.457903i
$5$	−3.51457	+	10.6136i	−0.314352	+	0.949306i
$5$	−3.51457	+	10.6136i	−0.314352	+	0.949306i
$6$	9.46764	+	13.0311i	0.644191	+	0.886653i
$7$	−9.35779	−	15.9822i	−0.505273	−	0.862959i
$7$	−9.35779	−	15.9822i	−0.505273	−	0.862959i
$8$	−23.6947	−	3.75287i	−1.04717	−	0.165855i
$9$	−28.2561	−	25.4419i	−1.04652	−	0.942292i
$10$	−13.9569	−	17.4346i	−0.441357	−	0.551332i
$11$	−16.6693	−	18.5131i	−0.456906	−	0.507446i	0.470037	−	0.882647i	$-0.344240\pi$
$11$	−16.6693	−	18.5131i	−0.456906	−	0.507446i	−0.926944	+	0.375201i	$0.877574\pi$
$12$	32.2901	−	1.69225i	0.776779	−	0.0407093i
$13$	−29.1647	−	14.8602i	−0.622218	−	0.317036i	0.114308	−	0.993445i	$-0.463535\pi$
$13$	−29.1647	−	14.8602i	−0.622218	−	0.317036i	−0.736526	+	0.676409i	$0.763535\pi$
$14$	36.9551	+	1.71077i	0.705475	+	0.0326588i
$15$	69.7433	+	57.1284i	1.20051	+	0.983366i
$16$	10.6000	−	11.7725i	0.165625	−	0.183945i
$17$	29.4593	−	36.3792i	0.420289	−	0.519014i	−0.522393	−	0.852705i	$-0.674961\pi$
$17$	29.4593	−	36.3792i	0.420289	−	0.519014i	0.942683	+	0.333690i	$0.108294\pi$
$18$	73.3624	−	19.6574i	0.960650	−	0.257405i
$19$	32.6659	+	14.5438i	0.394424	+	0.175609i	0.594358	−	0.804200i	$-0.297406\pi$
$19$	32.6659	+	14.5438i	0.394424	+	0.175609i	−0.199934	+	0.979809i	$0.564073\pi$
$20$	−44.6121	+	4.43579i	−0.498778	+	0.0495937i
$21$	−147.357	+	24.2613i	−1.53123	+	0.252107i
$22$	49.1493	−	7.78448i	0.476303	−	0.0754389i
$23$	−183.373	−	119.084i	−1.66243	−	1.07959i	−0.903675	−	0.428219i	$-0.859141\pi$
$23$	−183.373	−	119.084i	−1.66243	−	1.07959i	−0.758755	−	0.651376i	$-0.774192\pi$
$24$	−96.7236	+	167.530i	−0.822651	+	1.42487i
$25$	−100.296	−	74.6042i	−0.802365	−	0.596834i
$26$	56.6238	−	32.6918i	0.427110	−	0.246592i
$27$	−79.1924	+	40.3506i	−0.564466	+	0.287610i
$28$	43.2842	−	60.3463i	0.292141	−	0.407299i
$29$	−130.137	+	179.119i	−0.833307	+	1.14695i	0.153991	+	0.988072i	$0.450787\pi$
$29$	−130.137	+	179.119i	−0.833307	+	1.14695i	−0.987298	+	0.158877i	$0.949213\pi$
$30$	−171.581	+	54.6868i	−1.04421	+	0.332813i
$31$	93.4543	−	9.82244i	0.541448	−	0.0569085i	0.170143	−	0.985419i	$-0.445577\pi$
$31$	93.4543	−	9.82244i	0.541448	−	0.0569085i	0.371305	+	0.928511i	$0.378910\pi$
$32$	−41.4827	−	154.815i	−0.229162	−	0.855243i
$33$	−187.538	+	71.9889i	−0.989276	+	0.379747i
$34$	28.8951	+	88.9300i	0.145749	+	0.448570i
$35$	202.517	−	43.1489i	0.978047	−	0.208386i
$36$	47.1145	−	145.003i	0.218123	−	0.671312i
$37$	−13.6074	−	259.645i	−0.0604608	−	1.15366i	−0.845416	−	0.534108i	$-0.820647\pi$
$37$	−13.6074	−	259.645i	−0.0604608	−	1.15366i	0.784955	−	0.619552i	$-0.212686\pi$
$38$	−59.9028	+	38.9013i	−0.255724	+	0.166069i
$39$	−196.147	+	176.611i	−0.805350	+	0.725140i
$40$	123.108	−	238.296i	0.486627	−	0.941946i
$41$	−36.1494	+	11.7457i	−0.137697	+	0.0447406i	−0.377055	−	0.926191i	$-0.623063\pi$
$41$	−36.1494	+	11.7457i	−0.137697	+	0.0447406i	0.239358	+	0.970931i	$0.423063\pi$
$42$	119.670	−	273.256i	0.439653	−	1.00391i
$43$	119.914	+	119.914i	0.425272	+	0.425272i	0.887014	−	0.461742i	$-0.152776\pi$
$43$	119.914	+	119.914i	0.425272	+	0.425272i	−0.461742	+	0.887014i	$0.652776\pi$
$44$	40.6305	−	91.2576i	0.139211	−	0.312673i
$45$	369.337	−	210.480i	1.22350	−	0.697257i
$46$	398.993	−	177.643i	1.27888	−	0.569393i
$47$	−283.161	+	229.299i	−0.878794	+	0.711633i	−0.958472	−	0.285187i	$-0.907944\pi$
$47$	−283.161	+	229.299i	−0.878794	+	0.711633i	0.0796780	+	0.996821i	$0.474611\pi$
$48$	−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
$52$	6.86927	−	131.074i	0.0183192	−	0.349551i
$53$	269.244	+	103.353i	0.697802	+	0.267861i	0.681302	−	0.732003i	$-0.261414\pi$
$53$	269.244	+	103.353i	0.697802	+	0.267861i	0.0165002	+	0.999864i	$0.494748\pi$
$54$	18.5579	−	176.567i	0.0467669	−	0.444957i
$55$	255.075	−	111.855i	0.625351	−	0.274227i
$56$	161.751	+	413.813i	0.385979	+	0.987465i
$57$	203.883	−	203.883i	0.473770	−	0.473770i
$58$	−158.491	−	412.883i	−0.358808	−	0.934728i
$59$	−573.520	−	121.906i	−1.26553	−	0.268996i	−0.474214	−	0.880409i	$-0.657268\pi$
$59$	−573.520	−	121.906i	−1.26553	−	0.268996i	−0.791311	+	0.611414i	$0.790601\pi$
$60$	−95.5249	+	348.661i	−0.205537	+	0.750198i
$61$	−182.077	−	856.607i	−0.382174	−	1.79799i	−0.576550	−	0.817062i	$-0.695602\pi$
$61$	−182.077	−	856.607i	−0.382174	−	1.79799i	0.194376	−	0.980927i	$-0.437732\pi$
$62$	−85.2165	+	167.247i	−0.174556	+	0.342586i
$63$	−142.204	+	689.675i	−0.284381	+	1.37922i
$64$	425.016	+	138.096i	0.830109	+	0.269719i
$65$	260.221	−	257.315i	0.496560	−	0.491015i
$66$	83.4271	−	392.494i	0.155593	−	0.732010i
$67$	488.534	+	395.607i	0.890805	+	0.721360i	0.961110	−	0.276166i	$-0.0890638\pi$
$67$	488.534	+	395.607i	0.890805	+	0.721360i	−0.0703047	+	0.997526i	$0.522397\pi$
$68$	181.312	+	48.5825i	0.323344	+	0.0866396i
$69$	−1426.37	+	1036.32i	−2.48862	+	1.80809i
$70$	−148.038	+	386.212i	−0.252771	+	0.659446i
$71$	783.313	+	569.110i	1.30933	+	0.951281i	1.00000		0.000325502i	$0.000103611\pi$
$71$	783.313	+	569.110i	1.30933	+	0.951281i	0.309327	+	0.950956i	$0.399896\pi$
$72$	574.039	+	708.879i	0.939599	+	1.16031i
$73$	−177.501	−	9.30242i	−0.284588	−	0.0149146i	−0.0904918	−	0.995897i	$-0.528844\pi$
$73$	−177.501	−	9.30242i	−0.284588	−	0.0149146i	−0.194096	+	0.980983i	$0.562177\pi$
$74$	449.778	+	259.680i	0.706563	+	0.407935i
$75$	−851.454	+	539.444i	−1.31090	+	0.830528i
$76$			143.383i			0.216410i
$77$	−139.893	+	439.653i	−0.207043	+	0.650690i
$78$	−82.4769	−	520.739i	−0.119727	−	0.755923i
$79$	314.868	+	33.0940i	0.448423	+	0.0471312i	0.326049	−	0.945353i	$-0.394283\pi$
$79$	314.868	+	33.0940i	0.448423	+	0.0471312i	0.122374	+	0.992484i	$0.460949\pi$
$80$	87.6938	+	153.879i	0.122556	+	0.215053i
$81$	−32.3942	−	308.210i	−0.0444364	−	0.422784i
$82$	19.6509	−	73.3382i	0.0264644	−	0.0987665i
$83$	−129.851	+	819.846i	−0.171723	+	1.08421i	0.739758	+	0.672873i	$0.234940\pi$
$83$	−129.851	+	819.846i	−0.171723	+	1.08421i	−0.911481	+	0.411342i	$0.865060\pi$
$84$	−329.210	−	500.232i	−0.427616	−	0.649759i
$85$	282.576	+	440.525i	0.360584	+	0.562137i
$86$	−331.345	+	70.4295i	−0.415463	+	0.0883094i
$87$	972.352	+	1497.29i	1.19824	+	1.84513i
$88$	325.496	+	501.220i	0.394295	+	0.607161i
$89$	1084.03	−	230.417i	1.29109	−	0.274429i	0.489339	−	0.872094i	$-0.337238\pi$
$89$	1084.03	−	230.417i	1.29109	−	0.274429i	0.801746	+	0.597665i	$0.203905\pi$
$90$	−49.2020	+	847.725i	−0.0576261	+	0.992867i
$91$	35.4186	+	605.176i	0.0408009	+	0.697139i
$92$	137.154	−	865.959i	0.155428	−	0.981331i
$93$	196.116	−	731.914i	0.218669	−	0.816085i
$94$	−76.0777	−	723.831i	−0.0834768	−	0.794229i
$95$	−269.168	+	295.586i	−0.290695	+	0.319226i
$96$	−1285.33	−	135.094i	−1.36650	−	0.143625i
$97$	−35.9240	−	226.815i	−0.0376034	−	0.237419i	0.961727	−	0.274010i	$-0.0883501\pi$
$97$	−35.9240	−	226.815i	−0.0376034	−	0.237419i	−0.999330	+	0.0365912i	$0.988350\pi$
$98$	−318.476	−	606.634i	−0.328275	−	0.625298i
$99$			947.204i			0.961592i
$100$	109.713	−	489.083i	0.109713	−	0.489083i
$101$	−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	$0.791716\pi$
$102$	752.969	+	39.4615i	0.730932	+	0.0383065i
$103$	163.006	+	201.295i	0.155936	+	0.192565i	0.849127	−	0.528189i	$-0.177129\pi$
$103$	163.006	+	201.295i	0.155936	+	0.192565i	−0.693191	+	0.720754i	$0.743796\pi$
$104$	635.281	+	461.559i	0.598985	+	0.435188i
$105$	260.397	−	1649.25i	0.242020	−	1.53286i
$106$	−466.062	+	338.614i	−0.427056	+	0.310274i
$107$	475.353	+	127.370i	0.429477	+	0.115078i	0.467081	−	0.884215i	$-0.345306\pi$
$107$	475.353	+	127.370i	0.429477	+	0.115078i	−0.0376034	+	0.999293i	$0.511972\pi$
$108$	−276.974	−	224.289i	−0.246776	−	0.199836i
$109$	−54.7983	+	257.806i	−0.0481534	+	0.226544i	−0.995644	−	0.0932409i	$-0.970277\pi$
$109$	−54.7983	+	257.806i	−0.0481534	+	0.226544i	0.947490	+	0.319785i	$0.103611\pi$
$110$	−90.1173	+	549.008i	−0.0781123	+	0.475872i
$111$	−1993.95	−	647.873i	−1.70502	−	0.553994i
$112$	−287.344	−	59.2472i	−0.242423	−	0.0499852i
$113$	816.013	−	1601.52i	0.679328	−	1.33326i	−0.251521	−	0.967852i	$-0.580931\pi$
$113$	816.013	−	1601.52i	0.679328	−	1.33326i	0.930849	−	0.365404i	$-0.119069\pi$
$114$	119.747	+	563.367i	0.0983804	+	0.462843i
$115$	1908.38	−	1527.71i	1.54746	−	1.23878i
$116$	−868.404	−	184.585i	−0.695080	−	0.147744i
$117$	446.010	+	1161.89i	0.352424	+	0.918096i
$118$	828.173	−	828.173i	0.646098	−	0.646098i
$119$	−857.094	−	130.396i	−0.660249	−	0.100449i
$120$	−1438.15	−	1615.38i	−1.09404	−	1.22886i
$121$	74.2572	−	706.510i	0.0557905	−	0.530811i
$122$	1633.13	+	626.900i	1.21194	+	0.465220i
$123$	−16.0408	+	306.077i	−0.0117590	+	0.224374i
$124$	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	0.824449	−	0.565936i	$-0.191485\pi$
$127$	−168.886	−	331.457i	−0.118001	−	0.231591i	−0.942451	+	0.334345i	$0.891485\pi$
$128$	302.733	−	245.148i	0.209047	−	0.169283i
$129$	1249.24	−	556.197i	0.852630	−	0.379616i
$130$	147.968	+	715.878i	0.0998282	+	0.482975i
$131$	−1029.83	+	2313.03i	−0.686844	+	1.54268i	0.146071	+	0.989274i	$0.453337\pi$
$131$	−1029.83	+	2313.03i	−0.686844	+	1.54268i	−0.832914	+	0.553402i	$0.813329\pi$
$132$	−569.581	−	569.581i	−0.375573	−	0.375573i
$133$	−73.2382	−	658.171i	−0.0477485	−	0.429103i
$134$	−1194.24	+	388.031i	−0.769898	+	0.250155i
$135$	−149.936	−	982.329i	−0.0955886	−	0.626262i
$136$	−834.555	+	751.436i	−0.526195	+	0.473788i
$137$	1230.47	−	799.075i	0.767342	−	0.498318i	−0.100634	−	0.994924i	$-0.532087\pi$
$137$	1230.47	−	799.075i	0.767342	−	0.498318i	0.867976	+	0.496606i	$0.165420\pi$
$138$	−184.318	−	3516.99i	−0.113697	−	2.16946i
$139$	326.881	−	1006.04i	0.199466	−	0.613892i	−0.800430	−	0.599426i	$-0.795395\pi$
$139$	326.881	−	1006.04i	0.199466	−	0.613892i	0.999895	−	0.0144654i	$-0.00460463\pi$
$140$	488.364	+	671.491i	0.294817	+	0.405367i
$141$	907.914	+	2794.27i	0.542270	+	1.66894i
$142$	−1805.60	+	693.105i	−1.06706	+	0.409606i
$143$	211.047	+	787.637i	0.123417	+	0.460598i
$144$	−599.029	+	62.9605i	−0.346661	+	0.0364355i
$145$	−1443.71	−	2010.75i	−0.826854	−	1.15161i
$146$	208.692	−	287.240i	0.118298	−	0.162823i
$147$	1766.68	+	2128.06i	0.991249	+	1.19401i
$148$	928.947	−	473.322i	0.515939	−	0.262884i
$149$	−1573.80	+	908.637i	−0.865309	+	0.499587i	−0.865787	−	0.500413i	$-0.833181\pi$
$149$	−1573.80	+	908.637i	−0.865309	+	0.499587i	0.000477291		1.00000i	$0.499848\pi$
$150$	22.6110	−	2013.29i	0.0123079	−	1.09589i
$151$	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	$-0.00434895\pi$
$152$	−719.427	−	467.201i	−0.383903	−	0.249309i
$153$	−1757.96	+	278.433i	−0.928904	+	0.147124i
$154$	−584.342	−	712.670i	−0.305764	−	0.372913i
$155$	−224.200	+	1026.41i	−0.116182	+	0.531889i
$156$	−966.878	−	430.482i	−0.496232	−	0.220937i
$157$	−1604.62	+	429.956i	−0.815685	+	0.218562i	−0.642459	−	0.766320i	$-0.722086\pi$
$157$	−1604.62	+	429.956i	−0.815685	+	0.218562i	−0.173226	+	0.984882i	$0.555419\pi$
$158$	−397.996	+	491.484i	−0.200398	+	0.247470i
$159$	1556.10	−	1728.22i	0.776141	−	0.861992i
$160$	1788.94	+	103.830i	0.883925	+	0.0513031i
$161$	−187.259	+	4045.07i	−0.0916653	+	1.98010i
$162$	551.575	+	281.042i	0.267505	+	0.136301i
$163$	1031.97	−	54.0835i	0.495892	−	0.0259886i	0.197249	−	0.980353i	$-0.436799\pi$
$163$	1031.97	−	54.0835i	0.495892	−	0.0259886i	0.298643	+	0.954365i	$0.403466\pi$
$164$	−101.986	−	113.267i	−0.0485595	−	0.0539307i
$165$	−104.946	−	2243.45i	−0.0495153	−	1.05850i
$166$	−1232.19	−	1109.47i	−0.576123	−	0.518744i
$167$	−691.076	−	109.456i	−0.320222	−	0.0507182i	−0.00574568	−	0.999983i	$-0.501829\pi$
$167$	−691.076	−	109.456i	−0.320222	−	0.0507182i	−0.314476	+	0.949265i	$0.601829\pi$
$168$	3582.62	−	21.8530i	1.64527	−	0.0100357i
$169$	−661.608	−	910.625i	−0.301142	−	0.414486i
$170$	−1045.42	−	5.87030i	−0.471646	−	0.00264842i
$171$	−552.988	−	1242.03i	−0.247298	−	0.555441i
$172$	−243.695	+	634.848i	−0.108032	+	0.281434i
$173$	−1196.28	+	1842.12i	−0.525733	+	0.809558i	−0.997388	−	0.0722251i	$-0.976990\pi$
$173$	−1196.28	+	1842.12i	−0.525733	+	0.809558i	0.471655	+	0.881783i	$0.343657\pi$
$174$	−3566.21			−1.55376
$175$	−253.796	+	2301.08i	−0.109630	+	0.993972i
$176$	−394.640			−0.169018
$177$	−2575.04	+	3965.22i	−1.09351	+	1.68386i
$178$	−793.335	+	2066.71i	−0.334062	+	0.870260i
$179$	99.2093	+	222.828i	0.0414260	+	0.0930443i	0.933073	−	0.359687i	$-0.117116\pi$
$179$	99.2093	+	222.828i	0.0414260	+	0.0930443i	−0.891647	+	0.452731i	$0.850450\pi$
$180$	1373.42	+	1009.68i	0.568714	+	0.418094i
$181$	−2161.38	−	2974.88i	−0.887591	−	1.22166i	−0.974260	−	0.225427i	$-0.927622\pi$
$181$	−2161.38	−	2974.88i	−0.887591	−	1.22166i	0.0866694	−	0.996237i	$-0.472378\pi$
$182$	−1052.36	−	599.053i	−0.428606	−	0.243982i
$183$	−6974.75	−	1104.69i	−2.81742	−	0.446236i
$184$	3898.06	+	3509.83i	1.56179	+	1.40624i
$185$	2803.59	+	768.118i	1.11418	+	0.305260i
$186$	1012.79	+	1124.82i	0.399254	+	0.443417i
$187$	−1164.55	+	61.0317i	−0.455405	+	0.0238667i
$188$	−1301.80	−	663.303i	−0.505021	−	0.257321i
$189$	1385.96	+	888.080i	0.533405	+	0.341790i
$190$	−202.349	−	772.504i	−0.0772630	−	0.294965i
$191$	−467.405	+	519.106i	−0.177069	+	0.196655i	−0.825146	−	0.564920i	$-0.808907\pi$
$191$	−467.405	+	519.106i	−0.177069	+	0.196655i	0.648076	+	0.761575i	$0.275574\pi$
$192$	2267.78	−	2800.48i	0.852413	−	1.05264i
$193$	307.912	−	82.5049i	0.114839	−	0.0307711i	−0.200942	−	0.979603i	$-0.564400\pi$
$193$	307.912	−	82.5049i	0.114839	−	0.0307711i	0.315781	+	0.948832i	$0.397733\pi$
$194$	419.058	+	186.577i	0.155086	+	0.0690486i
$195$	−1185.11	−	2702.53i	−0.435216	−	0.992473i
$196$	−1369.51	−	127.071i	−0.499094	−	0.0463086i
$197$	−4214.64	+	667.534i	−1.52427	+	0.241420i	−0.861637	−	0.507525i	$-0.830560\pi$
$197$	−4214.64	+	667.534i	−1.52427	+	0.241420i	−0.662631	+	0.748946i	$0.730560\pi$
$198$	−1586.82	−	1030.49i	−0.569546	−	0.369868i
$199$	−408.289	+	707.177i	−0.145441	+	0.251912i	−0.929537	−	0.368728i	$-0.879794\pi$
$199$	−408.289	+	707.177i	−0.145441	+	0.251912i	0.784096	+	0.620639i	$0.213127\pi$
$200$	2096.49	+	2144.12i	0.741223	+	0.758061i
$201$	4389.90	−	2534.51i	1.54049	−	0.889405i
$202$	1383.20	−	704.777i	0.481791	−	0.245485i
$203$	4080.52	+	403.731i	1.41082	+	0.139588i
$204$	889.679	−	1224.54i	0.305343	−	0.420269i
$205$	2.38623	−	424.955i	0.000812985	−	0.144781i
$206$	−514.561	+	54.0825i	−0.174035	+	0.0182918i
$207$	2151.68	+	8030.19i	0.722475	+	2.69631i
$208$	−484.088	+	185.824i	−0.161372	+	0.0619450i
$209$	−275.265	−	847.180i	−0.0911029	−	0.280386i
$210$	2479.64	+	2230.50i	0.814815	+	0.732948i
$211$	746.060	−	2296.14i	0.243416	−	0.749159i	−0.752476	−	0.658619i	$-0.771141\pi$
$211$	746.060	−	2296.14i	0.243416	−	0.749159i	0.995893	−	0.0905395i	$-0.0288591\pi$
$212$	60.5241	+	1154.87i	0.0196076	+	0.374135i
$213$	6547.87	−	4252.24i	2.10635	−	1.36788i
$214$	−730.529	+	657.771i	−0.233355	+	0.210114i
$215$	−1694.16	+	851.268i	−0.537398	+	0.270028i
$216$	2027.87	−	658.895i	0.638792	−	0.207556i
$217$	−1031.51	−	1401.69i	−0.322689	−	0.438493i
$218$	−372.276	−	372.276i	−0.115659	−	0.115659i
$219$	−582.962	+	1309.35i	−0.179876	+	0.404009i
$220$	825.770	+	751.966i	0.253061	+	0.230443i
$221$	−1399.77	+	623.218i	−0.426058	+	0.189693i
$222$	3254.63	−	2635.55i	0.983948	−	0.796786i
$223$	−378.990	−	743.809i	−0.113807	−	0.223359i	0.827076	−	0.562090i	$-0.190002\pi$
$223$	−378.990	−	743.809i	−0.113807	−	0.223359i	−0.940883	+	0.338731i	$0.890002\pi$
$224$	−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
$227$	299.803	−	5720.58i	0.0876591	−	1.67263i	−0.501913	−	0.864918i	$-0.667370\pi$
$227$	299.803	−	5720.58i	0.0876591	−	1.67263i	0.589572	−	0.807716i	$-0.299297\pi$
$228$	1079.40	+	414.341i	0.313529	+	0.120353i
$229$	477.996	−	4547.83i	0.137934	−	1.31235i	−0.678365	−	0.734725i	$-0.737311\pi$
$229$	477.996	−	4547.83i	0.137934	−	1.31235i	0.816299	−	0.577629i	$-0.196022\pi$
$230$	483.140	+	4859.08i	0.138510	+	1.39304i
$231$	2905.48	+	2323.61i	0.827561	+	0.661829i
$232$	3755.78	−	3755.78i	1.06284	−	1.06284i
$233$	−2394.76	−	6238.55i	−0.673329	−	1.75408i	−0.656619	−	0.754222i	$-0.728014\pi$
$233$	−2394.76	−	6238.55i	−0.673329	−	1.75408i	−0.0167097	−	0.999860i	$-0.505319\pi$
$234$	−2431.71	−	516.875i	−0.679340	−	0.144398i
$235$	−1438.50	−	3811.24i	−0.399307	−	1.05795i
$236$	−488.829	−	2299.76i	−0.134831	−	0.634329i
$237$	1159.02	−	2274.71i	0.317665	−	0.623453i
$238$	1150.91	−	1294.00i	0.313454	−	0.352426i
$239$	−3434.30	−	1115.87i	−0.929483	−	0.302007i	−0.195132	−	0.980777i	$-0.562513\pi$
$239$	−3434.30	−	1115.87i	−0.929483	−	0.302007i	−0.734351	+	0.678770i	$0.762513\pi$
$240$	1411.82	−	215.492i	0.379720	−	0.0579580i
$241$	−653.621	+	3075.04i	−0.174703	+	0.821913i	0.800279	+	0.599628i	$0.204685\pi$
$241$	−653.621	+	3075.04i	−0.174703	+	0.821913i	−0.974982	+	0.222285i	$0.928649\pi$
$242$	1102.80	+	893.033i	0.292938	+	0.237216i
$243$	−4731.82	−	1267.89i	−1.24916	−	0.334712i
$244$	2840.98	−	2064.10i	0.745391	−	0.541558i
$245$	−2584.73	−	2832.90i	−0.674009	−	0.738723i
$246$	−495.308	−	359.862i	−0.128373	−	0.0932683i
$247$	−736.567	−	909.585i	−0.189744	−	0.234314i
$248$	−2251.23	−	117.982i	−0.576425	−	0.0302092i
$249$	5796.61	+	3346.68i	1.47528	+	0.851755i
$250$	99.1216	+	2789.86i	0.0250760	+	0.705786i
$251$			3739.96i			0.940495i	0.882535	+	0.470247i	$0.155835\pi$
$251$			3739.96i			0.940495i	−0.882535	+	0.470247i	$0.844165\pi$
$252$	−2758.37	+	603.917i	−0.689527	+	0.150965i
$253$	852.082	+	5379.84i	0.211739	+	1.33687i
$254$	739.013	+	77.6734i	0.182558	+	0.0191877i
$255$	4132.87	−	854.242i	1.01494	−	0.209783i
$256$	455.036	+	4329.38i	0.111093	+	1.05698i
$257$	−1789.44	+	6678.26i	−0.434326	+	1.62093i	0.308346	+	0.951274i	$0.400224\pi$
$257$	−1789.44	+	6678.26i	−0.434326	+	1.62093i	−0.742673	+	0.669654i	$0.766442\pi$
$258$	−427.306	+	2697.91i	−0.103112	+	0.651025i
$259$	−4022.38	+	2647.18i	−0.965013	+	0.635089i
$260$	1367.02	+	533.574i	0.326072	+	0.127273i
$261$	8234.29	−	1750.25i	1.95283	−	0.415088i
$262$	−2754.56	−	4241.65i	−0.649531	−	1.00019i
$263$	−1700.71	−	2618.86i	−0.398745	−	0.614014i	0.581086	−	0.813842i	$-0.302628\pi$
$263$	−1700.71	−	2618.86i	−0.398745	−	0.614014i	−0.979831	+	0.199828i	$0.935962\pi$
$264$	4713.81	−	1001.95i	1.09892	−	0.233583i
$265$	−2043.22	+	2494.40i	−0.473638	+	0.578225i
$266$	1182.29	+	593.350i	0.272521	+	0.136769i
$267$	1397.97	−	8826.46i	0.320429	−	2.02311i
$268$	−652.413	+	2434.84i	−0.148703	+	0.554968i
$269$	147.852	+	1406.71i	0.0335118	+	0.318844i	0.998417	+	0.0562450i	$0.0179128\pi$
$269$	147.852	+	1406.71i	0.0335118	+	0.318844i	−0.964905	+	0.262599i	$0.915421\pi$
$270$	1808.78	+	817.521i	0.407699	+	0.184270i
$271$	−1003.52	−	105.474i	−0.224943	−	0.0236424i	−0.00861344	−	0.999963i	$-0.502742\pi$
$271$	−1003.52	−	105.474i	−0.224943	−	0.0236424i	−0.216329	+	0.976320i	$0.569408\pi$
$272$	−116.005	−	732.429i	−0.0258598	−	0.163272i
$273$	4658.15	+	1482.17i	1.03269	+	0.328590i
$274$			2930.69i			0.646167i
$275$	290.700	+	3100.38i	0.0637449	+	0.679854i
$276$	−6122.65	−	3534.91i	−1.33529	−	0.770930i
$277$	−4615.11	−	241.867i	−1.00106	−	0.0524636i	−0.455245	−	0.890366i	$-0.650448\pi$
$277$	−4615.11	−	241.867i	−1.00106	−	0.0524636i	−0.545820	+	0.837903i	$0.683782\pi$
$278$	1329.75	+	1642.11i	0.286883	+	0.354270i
$279$	−2890.55	−	2100.11i	−0.620261	−	0.450646i
$280$	−4960.51	+	262.379i	−1.05874	+	0.0560006i
$281$	5140.89	−	3735.08i	1.09139	−	0.792940i	0.111755	−	0.993736i	$-0.464353\pi$
$281$	5140.89	−	3735.08i	1.09139	−	0.792940i	0.979633	+	0.200796i	$0.0643529\pi$
$282$	−5668.89	−	1518.97i	−1.19708	−	0.320757i
$283$	226.578	+	183.479i	0.0475925	+	0.0385396i	0.652822	−	0.757512i	$-0.273585\pi$
$283$	226.578	+	183.479i	0.0475925	+	0.0385396i	−0.605229	+	0.796051i	$0.706918\pi$
$284$	−807.217	+	3797.66i	−0.168660	+	0.793485i
$285$	1447.36	+	2880.48i	0.300822	+	0.598684i
$286$	−1549.10	−	503.334i	−0.320281	−	0.104066i
$287$	526.000	+	467.835i	0.108184	+	0.0962210i
$288$	−2766.66	+	5429.87i	−0.566066	+	1.11097i
$289$	565.875	+	2662.23i	0.115179	+	0.541875i
$290$	4939.19	−	231.049i	1.00014	−	0.0467851i
$291$	−1811.29	−	385.001i	−0.364879	−	0.0775573i
$292$	−255.422	−	665.398i	−0.0511899	−	0.133354i
$293$	−1448.41	+	1448.41i	−0.288795	+	0.288795i	−0.836604	−	0.547809i	$-0.815462\pi$
$293$	−1448.41	+	1448.41i	−0.288795	+	0.288795i	0.547809	+	0.836604i	$0.315462\pi$
$294$	−5487.09	+	644.484i	−1.08848	+	0.127847i
$295$	3309.53	−	5658.65i	0.653180	−	1.11681i
$296$	−651.992	+	6203.29i	−0.128028	+	1.21810i
$297$	2067.09	+	793.482i	0.403855	+	0.155025i
$298$	189.982	−	3625.07i	0.0369307	−	0.704680i
$299$	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
$303$	−4870.20	+	3943.81i	−0.923386	+	0.747743i
$304$	517.475	−	230.395i	0.0976291	−	0.0434673i
$305$	9731.58	+	1078.11i	1.82698	+	0.202402i
$306$	1446.08	−	3247.96i	0.270154	−	0.606776i
$307$	5476.70	+	5476.70i	1.01815	+	1.01815i	0.999832	+	0.0183175i	$0.00583097\pi$
$307$	5476.70	+	5476.70i	1.01815	+	1.01815i	0.0183175	+	0.999832i	$0.494169\pi$
$308$	−1838.71	+	204.603i	−0.340164	+	0.0378518i
$309$	1986.41	−	645.422i	0.365704	−	0.118825i
$310$	−1475.59	−	1492.25i	−0.270347	−	0.273400i
$311$	−166.922	+	150.297i	−0.0304350	+	0.0274038i	−0.684208	−	0.729287i	$-0.739852\pi$
$311$	−166.922	+	150.297i	−0.0304350	+	0.0274038i	0.653773	+	0.756691i	$0.273185\pi$
$312$	5310.44	−	3448.64i	0.963604	−	0.625772i
$313$	−373.065	−	7118.51i	−0.0673703	−	1.28550i	−0.797970	−	0.602697i	$-0.794093\pi$
$313$	−373.065	−	7118.51i	−0.0673703	−	1.28550i	0.730600	−	0.682806i	$-0.239240\pi$
$314$	1025.42	−	3155.92i	0.184293	−	0.567194i
$315$	−6820.12	−	3933.20i	−1.21991	−	0.703525i
$316$	392.311	+	1207.41i	0.0698393	+	0.214943i
$317$	−4861.17	+	1866.03i	−0.861294	+	0.330620i	−0.748610	−	0.663011i	$-0.769278\pi$
$317$	−4861.17	+	1866.03i	−0.861294	+	0.330620i	−0.112685	+	0.993631i	$0.535945\pi$
$318$	1202.30	+	4487.05i	0.212018	+	0.791262i
$319$	5485.34	−	576.532i	0.962758	−	0.101190i
$320$	−2959.44	+	4025.59i	−0.516993	+	0.703241i
$321$	2332.50	−	3210.41i	0.405569	−	0.558217i
$322$	−6572.83	−	4714.46i	−1.13755	−	0.815921i
$323$	1491.40	−	759.907i	0.256916	−	0.130905i
$324$	1076.21	−	621.349i	0.184535	−	0.106541i
$325$	1816.46	+	3666.22i	0.310028	+	0.625739i
$326$	−1032.11	+	1787.67i	−0.175348	+	0.303711i
$327$	1782.42	+	1157.52i	0.301432	+	0.195752i
$328$	900.629	−	142.646i	0.151613	−	0.0240131i
$329$	6314.48	+	2379.81i	1.05814	+	0.398794i
$330$	3872.55	+	2264.90i	0.645990	+	0.377815i
$331$	1947.62	+	867.138i	0.323417	+	0.143995i	0.562022	−	0.827122i	$-0.310024\pi$
$331$	1947.62	+	867.138i	0.323417	+	0.143995i	−0.238605	+	0.971117i	$0.576690\pi$
$332$	−3215.07	+	861.474i	−0.531475	+	0.142408i
$333$	−6221.37	+	7682.76i	−1.02381	+	1.26430i
$334$	935.209	−	1038.65i	0.153211	−	0.170158i
$335$	−5915.79	+	3794.70i	−0.964818	+	0.618886i
$336$	−1276.37	+	1991.93i	−0.207237	+	0.323419i
$337$	−1501.68	−	765.145i	−0.242735	−	0.123680i	0.328391	−	0.944542i	$-0.393493\pi$
$337$	−1501.68	−	765.145i	−0.242735	−	0.123680i	−0.571127	+	0.820862i	$0.693493\pi$
$338$	2245.32	−	117.672i	0.361329	−	0.0189365i
$339$	−9698.22	−	10771.0i	−1.55379	−	1.72566i
$340$	−1152.87	+	1753.63i	−0.183891	+	0.279717i
$341$	−1739.66	−	1566.39i	−0.276269	−	0.248754i
$342$	2682.34	+	424.841i	0.424106	+	0.0671718i
$343$	6351.39	−	116.237i	0.999833	−	0.0182979i
$344$	−2391.30	−	3291.34i	−0.374797	−	0.515864i
$345$	−5985.97	−	18781.1i	−0.934127	−	2.93084i
$346$	−1784.56	−	4008.18i	−0.277279	−	0.622778i
$347$	4357.44	−	11351.5i	0.674120	−	1.75614i	0.0199445	−	0.999801i	$-0.493651\pi$
$347$	4357.44	−	11351.5i	0.674120	−	1.75614i	0.654176	−	0.756342i	$-0.273016\pi$
$348$	−3899.04	+	6003.99i	−0.600604	+	0.924849i
$349$	1500.54			0.230149			0.115074	−	0.993357i	$-0.463289\pi$
$349$	1500.54			0.230149			0.115074	+	0.993357i	$0.463289\pi$
$350$	−3578.80	−	2928.59i	−0.546557	−	0.447256i
$351$	2909.24			0.442404
$352$	−2174.63	+	3348.63i	−0.329284	+	0.507053i
$353$	331.497	−	863.579i	0.0499824	−	0.130209i	−0.906316	−	0.422600i	$-0.861118\pi$
$353$	331.497	−	863.579i	0.0499824	−	0.130209i	0.956299	+	0.292391i	$0.0944509\pi$
$354$	−3841.32	−	8627.75i	−0.576734	−	1.29537i
$355$	−8793.30	+	6313.57i	−1.31465	+	0.943914i
$356$	2612.09	+	3595.23i	0.388878	+	0.535244i
$357$	−3458.42	+	6075.44i	−0.512714	+	0.900690i
$358$	−481.228	−	76.2190i	−0.0710438	−	0.0112522i
$359$	1762.37	+	1586.84i	0.259092	+	0.233288i	0.788431	−	0.615123i	$-0.210893\pi$
$359$	1762.37	+	1586.84i	0.259092	+	0.233288i	−0.529339	+	0.848410i	$0.677560\pi$
$360$	−9541.23	+	3601.20i	−1.39685	+	0.527222i
$361$	−3734.03	−	4147.06i	−0.544399	−	0.604616i
$362$	7335.14	−	384.418i	1.06499	−	0.0558137i
$363$	−5104.06	−	2600.65i	−0.737999	−	0.376029i
$364$	−2159.13	+	1116.77i	−0.310904	+	0.160810i
$365$	722.570	−	1851.22i	0.103619	−	0.265472i
$366$	9438.68	−	10482.7i	1.34800	−	1.49710i
$367$	−3433.98	+	4240.61i	−0.488425	+	0.603155i	−0.960458	−	0.278426i	$-0.910187\pi$
$367$	−3433.98	+	4240.61i	−0.488425	+	0.603155i	0.472032	+	0.881581i	$0.343521\pi$
$368$	−3345.67	+	896.470i	−0.473927	+	0.126988i
$369$	1320.27	+	587.823i	0.186262	+	0.0829291i
$370$	−4336.90	+	3861.09i	−0.609365	+	0.542510i
$371$	−867.715	−	5270.27i	−0.121427	−	0.737518i
$372$	3001.03	−	475.316i	0.418269	−	0.0662472i
$373$	6478.62	+	4207.26i	0.899330	+	0.584032i	0.909402	−	0.415917i	$-0.136539\pi$
$373$	6478.62	+	4207.26i	0.899330	+	0.584032i	−0.0100722	+	0.999949i	$0.503206\pi$
$374$	1164.71	−	2017.33i	0.161031	−	0.278914i
$375$	−2732.93	−	10932.9i	−0.376341	−	1.50552i
$376$	7569.95	−	4370.51i	1.03827	−	0.599447i
$377$	6457.16	−	3290.09i	0.882123	−	0.449464i
$378$	−2995.59	+	1355.68i	−0.407610	+	0.184467i
$379$	3720.71	−	5121.12i	0.504275	−	0.694074i	−0.478666	−	0.877997i	$-0.658880\pi$
$379$	3720.71	−	5121.12i	0.504275	−	0.694074i	0.982941	+	0.183923i	$0.0588796\pi$
$380$	−1521.80	−	503.929i	−0.205439	−	0.0680290i
$381$	−2983.26	+	313.554i	−0.401147	+	0.0421623i
$382$	−361.136	−	1347.78i	−0.0483699	−	0.180519i
$383$	2174.30	−	834.636i	0.290082	−	0.111352i	−0.208975	−	0.977921i	$-0.567013\pi$
$383$	2174.30	−	834.636i	0.290082	−	0.111352i	0.499058	+	0.866569i	$0.333680\pi$
$384$	−970.667	−	2987.41i	−0.128995	−	0.397006i
$385$	−4174.63	−	3029.96i	−0.552620	−	0.401093i
$386$	−196.769	+	605.594i	−0.0259464	+	0.0798547i
$387$	−337.460	−	6439.12i	−0.0443257	−	0.845786i
$388$	772.285	−	501.528i	0.101048	−	0.0656217i
$389$	6.18949	−	5.57304i	0.000806734	−	0.000726387i	−0.668727	−	0.743508i	$-0.733161\pi$
$389$	6.18949	−	5.57304i	0.000806734	−	0.000726387i	0.669534	+	0.742782i	$0.266494\pi$
$390$	5816.76	+	954.797i	0.755239	+	0.123969i
$391$	−9734.20	+	3162.83i	−1.25903	+	0.409083i
$392$	5100.02	−	6457.51i	0.657118	−	0.832024i
$393$	14436.7	+	14436.7i	1.85301	+	1.85301i
$394$	3466.94	−	7786.87i	0.443304	−	0.995677i
$395$	−1457.87	+	3225.56i	−0.185705	+	0.410875i
$396$	−3469.82	+	1544.87i	−0.440316	+	0.196041i
$397$	2960.75	−	2397.57i	0.374297	−	0.303100i	−0.423652	−	0.905825i	$-0.639252\pi$
$397$	2960.75	−	2397.57i	0.374297	−	0.303100i	0.797949	+	0.602726i	$0.205919\pi$
$398$	−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	$0.737227\pi$
$402$	−529.926	+	10111.6i	−0.0657471	+	1.25453i
$403$	−2871.53	−	1102.28i	−0.354941	−	0.136249i
$404$	325.748	−	3099.28i	0.0401153	−	0.381671i
$405$	3385.06	+	739.407i	0.415321	+	0.0907195i
$406$	−5115.67	+	6396.71i	−0.625336	+	0.781930i
$407$	−4580.01	+	4580.01i	−0.557795	+	0.557795i
$408$	3245.20	+	8454.04i	0.393778	+	1.02583i
$409$	3502.35	+	744.447i	0.423423	+	0.0900014i	0.414695	−	0.909961i	$-0.363888\pi$
$409$	3502.35	+	744.447i	0.423423	+	0.0900014i	0.00872826	+	0.999962i	$0.497222\pi$
$410$	709.316	+	466.319i	0.0854405	+	0.0561703i
$411$	−2459.74	−	11572.2i	−0.295207	−	1.38884i
$412$	−471.532	+	925.433i	−0.0563852	+	0.110662i
$413$	3418.56	+	10306.9i	0.407304	+	1.22801i
$414$	−15793.6	−	5131.64i	−1.87491	−	0.609194i
$415$	−8245.12	−	4259.59i	−0.975270	−	0.503843i
$416$	−1090.75	+	5131.59i	−0.128554	+	0.604800i
$417$	−6628.90	−	5367.98i	−0.778462	−	0.630386i
$418$	1718.72	+	460.529i	0.201113	+	0.0538881i
$419$	4352.25	−	3162.09i	0.507449	−	0.368683i	−0.304406	−	0.952542i	$-0.598458\pi$
$419$	4352.25	−	3162.09i	0.507449	−	0.368683i	0.811855	+	0.583859i	$0.198458\pi$
$420$	6466.28	−	1735.99i	0.751243	−	0.201685i
$421$	11071.9	+	8044.18i	1.28173	+	0.931233i	0.999604	−	0.0281434i	$-0.00895950\pi$
$421$	11071.9	+	8044.18i	1.28173	+	0.931233i	0.282129	+	0.959377i	$0.408959\pi$
$422$	3034.97	+	3747.88i	0.350095	+	0.432331i
$423$	13834.8	+	725.053i	1.59024	+	0.0833411i
$424$	−5991.78	−	3459.36i	−0.686289	−	0.396229i
$425$	−5668.67	+	1450.89i	−0.646991	+	0.165596i
$426$			15595.6i			1.77373i
$427$	−11986.7	+	10926.0i	−1.35849	+	1.23828i
$428$	308.701	+	1949.06i	0.0348636	+	0.220120i
$429$	6539.25	+	687.302i	0.735939	+	0.0773503i
$430$	417.025	−	3764.28i	0.0467692	−	0.422162i
$431$	−729.340	−	6939.21i	−0.0815106	−	0.775522i	−0.956569	−	0.291505i	$-0.905844\pi$
$431$	−729.340	−	6939.21i	−0.0815106	−	0.775522i	0.875059	−	0.484017i	$-0.160823\pi$
$432$	−364.414	+	1360.01i	−0.0405853	+	0.151466i
$433$	1509.54	−	9530.87i	0.167538	−	1.05779i	−0.750375	−	0.661012i	$-0.770127\pi$
$433$	1509.54	−	9530.87i	0.167538	−	1.05779i	0.917913	−	0.396781i	$-0.129873\pi$
$434$	3470.41	−	203.110i	0.383837	−	0.0224645i
$435$	−19309.0	+	5057.79i	−2.12826	+	0.557477i
$436$	−1033.78	+	219.736i	−0.113552	+	0.0241363i
$437$	−4258.11	−	6556.91i	−0.466116	−	0.717756i
$438$	−1559.29	−	2401.10i	−0.170105	−	0.261938i
$439$	−6190.29	+	1315.79i	−0.672998	+	0.143050i	−0.531721	−	0.846920i	$-0.678454\pi$
$439$	−6190.29	+	1315.79i	−0.672998	+	0.143050i	−0.141278	+	0.989970i	$0.545121\pi$
$440$	−6463.70	+	1693.10i	−0.700330	+	0.183444i
$441$	12353.3	−	4181.10i	1.33390	−	0.451474i
$442$	478.797	−	3023.00i	0.0515250	−	0.325316i
$443$	2841.85	−	10605.9i	0.304787	−	1.13748i	−0.628342	−	0.777937i	$-0.716266\pi$
$443$	2841.85	−	10605.9i	0.304787	−	1.13748i	0.933129	−	0.359542i	$-0.117067\pi$
$444$	−878.771	−	8360.95i	−0.0939293	−	0.893678i
$445$	−1364.34	+	12315.2i	−0.145339	+	1.31190i
$446$	1658.39	+	174.304i	0.176070	+	0.0185057i
$447$	2292.36	+	14473.4i	0.242562	+	1.53148i
$448$	−1770.13	−	8084.98i	−0.186675	−	0.852632i
$449$			6844.47i			0.719400i	0.933068	+	0.359700i	$0.117121\pi$
$449$			6844.47i			0.719400i	−0.933068	+	0.359700i	$0.882879\pi$
$450$	−8824.46	−	3501.59i	−0.924420	−	0.366815i
$451$	820.032	+	473.446i	0.0856182	+	0.0494317i
$452$	7197.61	+	377.211i	0.748998	+	0.0392533i
$453$	−9637.98	−	11901.9i	−0.999629	−	1.23444i
$454$	9257.31	+	6725.83i	0.956976	+	0.695284i
$455$	−6547.55	−	1751.01i	−0.674624	−	0.180415i
$456$	−5596.08	+	4065.79i	−0.574694	+	0.417540i
$457$	−14870.7	−	3984.59i	−1.52215	−	0.407858i	−0.601699	−	0.798723i	$-0.705509\pi$
$457$	−14870.7	−	3984.59i	−1.52215	−	0.407858i	−0.920448	+	0.390865i	$0.872176\pi$
$458$	7098.79	+	5748.48i	0.724246	+	0.586483i
$459$	−865.031	+	4069.65i	−0.0879656	+	0.413845i
$460$	8708.88	+	4499.17i	0.882725	+	0.456032i
$461$	5553.80	+	1804.54i	0.561099	+	0.182312i	0.575815	−	0.817580i	$-0.304685\pi$
$461$	5553.80	+	1804.54i	0.561099	+	0.182312i	−0.0147168	+	0.999892i	$0.504685\pi$
$462$	−7053.62	+	2339.52i	−0.710312	+	0.235594i
$463$	−202.904	+	398.222i	−0.0203667	+	0.0399718i	−0.900966	−	0.433890i	$-0.857141\pi$
$463$	−202.904	+	398.222i	−0.0203667	+	0.0399718i	0.880599	+	0.473862i	$0.157141\pi$
$464$	729.219	+	3430.71i	0.0729594	+	0.343247i
$465$	7078.95	+	4653.85i	0.705975	+	0.464123i
$466$	13056.5	+	2775.25i	1.29792	+	0.275882i
$467$	−665.391	−	1733.40i	−0.0659328	−	0.171761i	0.896656	−	0.442729i	$-0.145990\pi$
$467$	−665.391	−	1733.40i	−0.0659328	−	0.171761i	−0.962588	+	0.270968i	$0.912656\pi$
$468$	−3528.86	+	3528.86i	−0.348550	+	0.348550i
$469$	1751.09	−	11509.9i	0.172404	−	1.13321i
$470$	7949.81	+	1736.50i	0.780207	+	0.170423i
$471$	−1400.21	+	13322.1i	−0.136982	+	1.30329i
$472$	13131.9	+	5040.86i	1.28060	+	0.491577i
$473$	221.100	−	4218.85i	0.0214930	−	0.410112i
$474$	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
$478$	5605.65	−	4539.37i	0.536394	−	0.434364i
$479$	−6826.41	+	3039.31i	−0.651162	+	0.289916i	−0.705610	−	0.708600i	$-0.749327\pi$
$479$	−6826.41	+	3039.31i	−0.651162	+	0.289916i	0.0544476	+	0.998517i	$0.482660\pi$
$480$	5951.22	−	13167.2i	0.565906	−	1.25208i
$481$	−3461.52	+	7774.69i	−0.328132	+	0.736997i
$482$	−4440.42	−	4440.42i	−0.419617	−	0.419617i
$483$	29910.4	+	13098.9i	2.81774	+	1.23400i
$484$	2709.22	−	880.278i	0.254434	−	0.0826708i
$485$	2533.58	+	415.876i	0.237204	+	0.0389360i
$486$	7271.92	−	6547.67i	0.678727	−	0.611128i
$487$	3066.52	−	1991.42i	0.285334	−	0.185298i	−0.394034	−	0.919096i	$-0.628921\pi$
$487$	3066.52	−	1991.42i	0.285334	−	0.185298i	0.679368	+	0.733798i	$0.262254\pi$
$488$	1099.53	+	20980.4i	0.101995	+	1.94618i
$489$	2575.00	−	7925.05i	0.238130	−	0.732889i
$490$	7557.85	−	1248.11i	0.696794	−	0.115069i
$491$	−3989.19	−	12277.5i	−0.366659	−	1.12846i	−0.948936	−	0.315470i	$-0.897838\pi$
$491$	−3989.19	−	12277.5i	−0.366659	−	1.12846i	0.582276	−	0.812991i	$-0.302162\pi$
$492$	−1147.39	+	440.442i	−0.105139	+	0.0403591i
$493$	2682.44	+	10011.0i	0.245053	+	0.914549i
$494$	2325.13	−	244.381i	0.211766	−	0.0222575i
$495$	−10053.2	−	3329.01i	−0.912845	−	0.302279i
$496$	874.982	−	1204.31i	0.0792094	−	0.109022i
$497$	1765.57	−	17844.7i	0.159350	−	1.61055i
$498$	−11912.9	+	6069.91i	−1.07194	+	0.546183i
$499$	7924.94	−	4575.47i	0.710960	−	0.410473i	−0.100456	−	0.994941i	$-0.532030\pi$
$499$	7924.94	−	4575.47i	0.710960	−	0.410473i	0.811416	+	0.584469i	$0.198697\pi$
$500$	4805.33	+	2883.36i	0.429801	+	0.257895i
$501$	−2821.03	+	4886.16i	−0.251565	+	0.435724i
$502$	−6265.42	−	4068.81i	−0.557051	−	0.361753i
$503$	15593.7	−	2469.79i	1.38228	−	0.218932i	0.579386	−	0.815054i	$-0.303293\pi$
$503$	15593.7	−	2469.79i	1.38228	−	0.218932i	0.802894	+	0.596122i	$0.203293\pi$
$504$	5957.73	−	15808.0i	0.526545	−	1.39711i
$505$	6489.71	−	5777.71i	0.571858	−	0.509118i
$506$	−9939.65	−	4425.42i	−0.873263	−	0.388802i
$507$	−8767.12	+	2349.14i	−0.767971	+	0.205777i
$508$	938.753	−	1159.26i	0.0819891	−	0.101248i
$509$	3163.42	−	3513.33i	0.275474	−	0.305944i	−0.589493	−	0.807773i	$-0.700673\pi$
$509$	3163.42	−	3513.33i	0.275474	−	0.305944i	0.864967	+	0.501829i	$0.167339\pi$
$510$	−3065.19	+	7853.00i	−0.266135	+	0.681837i
$511$	1512.34	+	2923.91i	0.130924	+	0.253123i
$512$	−4971.21	−	2532.96i	−0.429099	−	0.218637i
$513$	−3173.74	+	166.329i	−0.273146	+	0.0143150i
$514$	−9241.07	−	10263.3i	−0.793008	−	0.880725i
$515$	−2709.35	+	1022.61i	−0.231822	+	0.0874978i
$516$	4074.95	+	3669.10i	0.347654	+	0.313030i
$517$	8965.13	+	1419.94i	0.762642	+	0.120791i
$518$	−58.6702	−	9618.49i	−0.00497649	−	0.815854i
$519$	10410.6	+	14329.0i	0.880490	+	1.21189i
$520$	−7131.52	+	5120.42i	−0.601419	+	0.431818i
$521$	−5770.89	−	12961.6i	−0.485273	−	1.08994i	−0.975830	−	0.218531i	$-0.929873\pi$
$521$	−5770.89	−	12961.6i	−0.485273	−	1.08994i	0.490557	−	0.871409i	$-0.336793\pi$
$522$	−6026.19	+	15698.8i	−0.505286	+	1.31631i
$523$	−2914.24	+	4487.53i	−0.243653	+	0.375193i	−0.939247	−	0.343242i	$-0.888475\pi$
$523$	−2914.24	+	4487.53i	−0.243653	+	0.375193i	0.695594	+	0.718435i	$0.255141\pi$
$524$	−10152.8			−0.846425
$525$	16589.2	+	8560.13i	1.37907	+	0.711609i
$526$	6237.52			0.517051
$527$	2395.76	−	3689.15i	0.198029	−	0.304937i
$528$	−1140.41	+	2970.87i	−0.0939962	+	0.244868i
$529$	14495.9	+	32558.4i	1.19141	+	2.67596i
$530$	−1955.89	−	6136.66i	−0.160299	−	0.502942i
$531$	13103.9	+	18036.0i	1.07093	+	1.47400i
$532$	2291.58	−	1341.75i	0.186753	−	0.109346i
$533$	1228.83	+	194.628i	0.0998622	+	0.0158166i
$534$	13265.8	+	11944.5i	1.07503	+	0.967960i
$535$	−3022.51	+	4597.54i	−0.244252	+	0.371531i
$536$	−10091.0	−	11207.2i	−0.813181	−	0.903129i
$537$	1964.15	−	102.937i	0.157839	−	0.00827197i
$538$	−2517.47	−	1282.72i	−0.201740	−	0.102791i
$539$	8335.73	−	1878.38i	0.666133	−	0.150107i
$540$	3353.95	−	2151.40i	0.267280	−	0.171448i
$541$	2569.63	−	2853.86i	0.204209	−	0.226797i	−0.632338	−	0.774693i	$-0.717904\pi$
$541$	2569.63	−	2853.86i	0.204209	−	0.226797i	0.836546	+	0.547896i	$0.184571\pi$
$542$	1268.45	−	1566.41i	0.100525	−	0.124139i
$543$	−28640.9	+	7674.31i	−2.26353	+	0.606512i
$544$	−6854.10	−	3051.64i	−0.540197	−	0.240511i
$545$	−2543.65	−	1487.68i	−0.199923	−	0.116927i
$546$	−7550.76	+	6191.13i	−0.591837	+	0.485267i
$547$	−12828.6	+	2031.85i	−1.00276	+	0.158822i	−0.636162	−	0.771556i	$-0.719479\pi$
$547$	−12828.6	+	2031.85i	−1.00276	+	0.158822i	−0.366602	+	0.930378i	$0.619479\pi$
$548$	4934.05	+	3204.21i	0.384621	+	0.249776i
$549$	−16648.9	+	28836.7i	−1.29428	+	2.24175i
$550$	−5510.21	−	2885.99i	−0.427193	−	0.223744i
$551$	−6856.11	+	3958.38i	−0.530091	+	0.306048i
$552$	37686.6	−	19202.3i	2.90588	−	1.48062i
$553$	−2417.56	−	5341.99i	−0.185904	−	0.410785i
$554$	5426.10	−	7468.39i	0.416124	−	0.572746i
$555$	13884.1	−	18885.9i	1.06189	−	1.44444i
$556$	4218.48	−	443.380i	0.321769	−	0.0338192i
$557$	−2148.46	−	8018.17i	−0.163435	−	0.609947i	−0.998235	−	0.0593936i	$-0.981083\pi$
$557$	−2148.46	−	8018.17i	−0.163435	−	0.609947i	0.834800	−	0.550554i	$-0.185583\pi$
$558$	6662.95	−	2557.67i	0.505493	−	0.194041i
$559$	−1715.31	−	5279.19i	−0.129785	−	0.399438i
$560$	1638.71	−	2841.51i	0.123658	−	0.214421i
$561$	−2905.82	+	8943.20i	−0.218688	+	0.673052i
$562$	664.313	+	12675.9i	0.0498618	+	0.951421i
$563$	−5302.64	+	3443.57i	−0.396944	+	0.257778i	−0.727640	−	0.685959i	$-0.759383\pi$
$563$	−5302.64	+	3443.57i	−0.396944	+	0.257778i	0.330696	+	0.943737i	$0.392716\pi$
$564$	−8755.27	+	7883.28i	−0.653658	+	0.588557i
$565$	14129.9	+	14289.4i	1.05212	+	1.06400i
$566$	−553.877	+	179.966i	−0.0411329	+	0.0133649i
$567$	−4622.74	+	3401.89i	−0.342393	+	0.251968i
$568$	−16424.6	−	16424.6i	−1.21331	−	1.21331i
$569$	−7412.07	+	16647.8i	−0.546098	+	1.22656i	0.404044	+	0.914740i	$0.367604\pi$
$569$	−7412.07	+	16647.8i	−0.546098	+	1.22656i	−0.950142	+	0.311817i	$0.899062\pi$
$570$	−6400.19	−	709.044i	−0.470306	−	0.0521028i
$571$	−7250.48	+	3228.12i	−0.531389	+	0.236590i	−0.654849	−	0.755760i	$-0.727268\pi$
$571$	−7250.48	+	3228.12i	−0.531389	+	0.236590i	0.123460	+	0.992350i	$0.460601\pi$
$572$	−2541.08	+	2057.73i	−0.185748	+	0.150416i
$573$	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
$577$	−1210.75	+	23102.5i	−0.0873555	+	1.66684i	0.506476	+	0.862254i	$0.330948\pi$
$577$	−1210.75	+	23102.5i	−0.0873555	+	1.66684i	−0.593832	+	0.804589i	$0.702386\pi$
$578$	−5075.57	−	1948.33i	−0.365253	−	0.140207i
$579$	268.688	−	2556.40i	0.0192855	−	0.183489i
$580$	5011.17	−	8568.13i	0.358754	−	0.613400i
$581$	14318.1	−	5596.64i	1.02240	−	0.399635i
$582$	2615.53	−	2615.53i	0.186284	−	0.186284i
$583$	−2574.71	−	6707.35i	−0.182905	−	0.476484i
$584$	4170.92	+	886.556i	0.295537	+	0.0628184i
$585$	−13899.4	+	650.196i	−0.982340	+	0.0459526i
$586$	−850.700	−	4002.23i	−0.0599694	−	0.282134i
$587$	3475.17	−	6820.41i	0.244354	−	0.479571i	−0.735958	−	0.677027i	$-0.763268\pi$
$587$	3475.17	−	6820.41i	0.244354	−	0.479571i	0.980312	+	0.197456i	$0.0632679\pi$
$588$	−4914.15	+	9942.57i	−0.344653	+	0.697321i
$589$	3195.62	+	1038.32i	0.223554	+	0.0726371i
$590$	5879.20	+	11700.5i	0.410242	+	0.816447i
$591$	−7154.03	+	33657.1i	−0.497932	+	2.34258i
$592$	−3200.92	−	2592.05i	−0.222224	−	0.179954i
$593$	−27625.7	−	7402.28i	−1.91307	−	0.512606i	−0.992538	−	0.121939i	$-0.961089\pi$
$593$	−27625.7	−	7402.28i	−1.91307	−	0.512606i	−0.920532	−	0.390667i	$-0.872245\pi$
$594$	−3578.14	+	2599.67i	−0.247160	+	0.179572i
$595$	4396.28	−	8638.54i	0.302908	−	0.595202i
$596$	−5895.38	−	4283.24i	−0.405175	−	0.294377i
$597$	4143.81	+	5117.18i	0.284079	+	0.350808i
$598$	−14276.3	−	748.191i	−0.976259	−	0.0511636i
$599$	−651.276	−	376.014i	−0.0444247	−	0.0256486i	0.477623	−	0.878565i	$-0.341498\pi$
$599$	−651.276	−	376.014i	−0.0444247	−	0.0256486i	−0.522048	+	0.852916i	$0.674832\pi$
$600$	22199.4	−	9586.56i	1.51048	−	0.652283i
$601$		−	14534.7i		−	0.986496i	−0.869889	−	0.493248i	$-0.835809\pi$
$601$		−	14534.7i		−	0.986496i	0.869889	−	0.493248i	$-0.164191\pi$
$602$	4226.28	+	4636.57i	0.286130	+	0.313908i
$603$	−3739.07	−	23607.5i	−0.252515	−	1.59432i
$604$	7574.10	+	796.070i	0.510242	+	0.0536285i
$605$	7237.61	+	3271.21i	0.486365	+	0.219824i
$606$	−1308.49	−	12449.5i	−0.0877126	−	0.834529i
$607$	−4112.41	+	15347.7i	−0.274988	+	1.02627i	0.680862	+	0.732412i	$0.261605\pi$
$607$	−4112.41	+	15347.7i	−0.274988	+	1.02627i	−0.955850	+	0.293857i	$0.905061\pi$
$608$	896.534	−	5660.49i	0.0598014	−	0.377571i
$609$	14831.0	−	29551.7i	0.986834	−	1.96633i
$610$	−12393.4	+	15130.1i	−0.822613	+	1.00426i
$611$	11665.7	−	2479.63i	0.772415	−	0.164182i
$612$	−3887.15	−	5985.68i	−0.256746	−	0.395354i
$613$	−4072.67	−	6271.35i	−0.268342	−	0.413210i	0.678653	−	0.734459i	$-0.262564\pi$
$613$	−4072.67	−	6271.35i	−0.268342	−	0.413210i	−0.946995	+	0.321249i	$0.895897\pi$
$614$	−15133.2	+	3216.66i	−0.994667	+	0.211423i
$615$	−3192.19	−	1245.98i	−0.209303	−	0.0816954i
$616$	4964.69	−	9892.46i	0.324729	−	0.647043i
$617$	4206.18	−	26556.8i	0.274448	−	1.73280i	−0.336993	−	0.941507i	$-0.609410\pi$
$617$	4206.18	−	26556.8i	0.274448	−	1.73280i	0.611441	−	0.791290i	$-0.290590\pi$
$618$	−1079.82	+	4029.93i	−0.0702857	+	0.262310i
$619$	1794.80	+	17076.4i	0.116542	+	1.10882i	0.883924	+	0.467630i	$0.154892\pi$
$619$	1794.80	+	17076.4i	0.116542	+	1.10882i	−0.767383	+	0.641189i	$0.778441\pi$
$620$	−4125.62	+	852.743i	−0.267240	+	0.0552371i
$621$	19326.8	+	2031.33i	1.24889	+	0.131263i
$622$	−70.1883	−	443.151i	−0.00452459	−	0.0285671i
$623$	−13826.7	−	15169.0i	−0.889171	−	0.975493i
$624$			4181.22i			0.268242i
$625$	4493.43	+	14965.0i	0.287579	+	0.957757i
$626$	12331.3	+	7119.45i	0.787310	+	0.454554i
$627$	−7173.06	−	375.924i	−0.456881	−	0.0239441i
$628$	−4192.12	−	5176.84i	−0.266375	−	0.328946i
$629$	−9846.55	−	7153.93i	−0.624177	−	0.453491i
$630$	14009.0	−	7146.47i	0.885921	−	0.451940i
$631$	10236.3	−	7437.11i	0.645801	−	0.469202i	−0.216037	−	0.976385i	$-0.569313\pi$
$631$	10236.3	−	7437.11i	0.645801	−	0.469202i	0.861838	+	0.507183i	$0.169313\pi$
$632$	−7336.51	−	1965.81i	−0.461758	−	0.123728i
$633$	−15129.5	−	12251.6i	−0.949991	−	0.769287i
$634$	2162.52	−	10173.8i	0.135465	−	0.637310i
$635$	4111.50	−	627.552i	0.256945	−	0.0392183i
$636$	8868.81	+	2881.65i	0.552942	+	0.179662i
$637$	9340.62	−	6229.17i	0.580987	−	0.387455i
$638$	−5001.81	+	9816.61i	−0.310382	+	0.609159i
$639$	−7654.11	−	36009.8i	−0.473853	−	2.22930i
$640$	1537.92	+	4074.66i	0.0949870	+	0.251664i
$641$	4816.79	+	1023.84i	0.296804	+	0.0630877i	0.353907	−	0.935281i	$-0.384853\pi$
$641$	4816.79	+	1023.84i	0.296804	+	0.0630877i	−0.0571027	+	0.998368i	$0.518186\pi$
$642$	2840.69	+	7400.26i	0.174631	+	0.454930i
$643$	21817.7	−	21817.7i	1.33811	−	1.33811i	0.440221	−	0.897890i	$-0.354900\pi$
$643$	21817.7	−	21817.7i	1.33811	−	1.33811i	0.897890	−	0.440221i	$-0.145100\pi$
$644$	−15123.4	+	5911.43i	−0.925383	+	0.361713i
$645$	1512.70	+	15213.7i	0.0923449	+	0.928740i
$646$	−349.494	+	3325.22i	−0.0212859	+	0.202522i
$647$	230.028	+	88.2994i	0.0139773	+	0.00536539i	0.365347	−	0.930872i	$-0.380950\pi$
$647$	230.028	+	88.2994i	0.0139773	+	0.00536539i	−0.351369	+	0.936237i	$0.614284\pi$
$648$	−389.102	+	7424.51i	−0.0235885	+	0.450096i
$649$	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
$653$	−22426.8	+	18160.9i	−1.34399	+	1.08835i	−0.355896	+	0.934526i	$0.615824\pi$
$653$	−22426.8	+	18160.9i	−1.34399	+	1.08835i	−0.988099	+	0.153820i	$0.950842\pi$
$654$	−3878.30	+	1726.73i	−0.231886	+	0.103242i
$655$	−20930.1	−	19059.5i	−1.24856	−	1.13697i
$656$	−244.908	+	550.073i	−0.0145763	+	0.0327390i
$657$	4778.80	+	4778.80i	0.283773	+	0.283773i
$658$	−10856.5	+	7989.35i	−0.643209	+	0.473339i
$659$	2294.33	−	745.473i	0.135621	−	0.0440660i	−0.240420	−	0.970669i	$-0.577285\pi$
$659$	2294.33	−	745.473i	0.135621	−	0.0440660i	0.376041	+	0.926603i	$0.377285\pi$
$660$	8047.11	−	4043.45i	0.474596	−	0.238471i
$661$	−11631.7	+	10473.2i	−0.684447	+	0.616279i	−0.936181	−	0.351517i	$-0.885666\pi$
$661$	−11631.7	+	10473.2i	−0.684447	+	0.616279i	0.251734	+	0.967796i	$0.418999\pi$
$662$	−3571.56	+	2319.40i	−0.209687	+	0.136172i
$663$	646.633	+	12338.5i	0.0378781	+	0.722757i
$664$	6153.55	−	18938.7i	0.359645	−	1.10687i
$665$	7242.94	+	1535.87i	0.422360	+	0.0895615i
$666$	−6102.23	−	18780.7i	−0.355040	−	1.09270i
$667$	45193.8	−	17348.3i	2.62356	−	1.00709i
$668$	−726.166	−	2710.09i	−0.0420602	−	0.156971i
$669$	−6694.62	+	703.633i	−0.386889	+	0.0406637i
$670$	78.8320	−	14038.9i	0.00454559	−	0.809506i
$671$	−12823.3	+	17649.8i	−0.737764	+	1.01545i
$672$	9868.78	+	21806.7i	0.566513	+	1.25180i
$673$	10500.4	−	5350.23i	0.601429	−	0.306443i	−0.126638	−	0.991949i	$-0.540419\pi$
$673$	10500.4	−	5350.23i	0.601429	−	0.306443i	0.728067	+	0.685506i	$0.240419\pi$
$674$	2915.54	−	1683.29i	0.166621	−	0.0961986i
$675$	10953.0	+	1861.10i	0.624563	+	0.106124i
$676$	2256.76	−	3908.83i	0.128400	−	0.222396i
$677$	−26773.2	−	17386.7i	−1.51991	−	0.987039i	−0.990323	−	0.138781i	$-0.955682\pi$
$677$	−26773.2	−	17386.7i	−1.51991	−	0.987039i	−0.529583	−	0.848258i	$-0.677652\pi$
$678$	28595.2	−	4529.03i	1.61975	−	0.256543i
$679$	−3288.84	+	2696.63i	−0.185883	+	0.152411i
$680$	−5042.32	−	11498.6i	−0.284359	−	0.648456i
$681$	−42198.5	−	18788.0i	−2.37452	−	1.05720i
$682$	4516.75	−	1210.26i	0.253600	−	0.0679519i
$683$	19544.4	−	24135.3i	1.09494	−	1.35214i	0.164213	−	0.986425i	$-0.447492\pi$
$683$	19544.4	−	24135.3i	1.09494	−	1.35214i	0.930727	−	0.365714i	$-0.119175\pi$
$684$	3647.93	−	4051.44i	0.203921	−	0.226478i
$685$	4156.47	+	15868.0i	0.231840	+	0.885090i
$686$	−6715.13	+	10766.7i	−0.373739	+	0.599234i
$687$	−32855.0	−	16740.5i	−1.82460	−	0.929678i
$688$	2682.77	−	140.598i	0.148662	−	0.00779107i
$689$	−6316.58	−	7015.27i	−0.349263	−	0.387896i
$690$	37975.6	+	10404.4i	2.09523	+	0.574043i
$691$	4078.87	+	3672.63i	0.224555	+	0.202190i	0.773727	−	0.633519i	$-0.218390\pi$
$691$	4078.87	+	3672.63i	0.224555	+	0.202190i	−0.549172	+	0.835709i	$0.685057\pi$
$692$	−8699.20	−	1377.82i	−0.477881	−	0.0756890i
$693$	15138.4	−	8863.74i	0.829815	−	0.485866i
$694$	14276.2	+	19649.5i	0.780861	+	1.07476i
$695$	9528.80	+	7005.16i	0.520069	+	0.382332i
$696$	−17420.4	−	39127.0i	−0.948736	−	2.13090i
$697$	−637.638	+	1661.10i	−0.0346517	+	0.0902709i
$698$	−1632.48	+	2513.79i	−0.0885246	+	0.136316i
$699$	−53884.4			−2.91573
$700$	−8843.31	+	2823.29i	−0.477494	+	0.152443i
$701$	33292.8			1.79380			0.896900	−	0.442234i	$-0.145814\pi$
$701$	33292.8			1.79380			0.896900	+	0.442234i	$0.145814\pi$
$702$	−3165.05	+	4873.75i	−0.170167	+	0.262034i
$703$	3331.73	−	8679.44i	0.178746	−	0.465649i
$704$	−4528.12	−	10170.3i	−0.242414	−	0.544472i
$705$	−32848.1	−	184.451i	−1.75480	−	0.00985364i
$706$	1086.08	+	1494.86i	0.0578967	+	0.0796880i
$707$	87.7936	+	14393.0i	0.00467018	+	0.765638i
$708$	−18725.3	−	2965.80i	−0.993984	−	0.157432i
$709$	21898.9	+	19717.9i	1.15999	+	1.04446i	0.998339	+	0.0576105i	$0.0183481\pi$
$709$	21898.9	+	19717.9i	1.15999	+	1.04446i	0.161650	+	0.986848i	$0.448319\pi$
$710$	−1010.41	−	21599.8i	−0.0534086	−	1.14173i
$711$	−8054.97	−	8945.95i	−0.424873	−	0.471869i
$712$	−26550.4	+	1391.45i	−1.39750	+	0.0732398i
$713$	−18306.7	−	9327.72i	−0.961558	−	0.489938i
$714$	−6415.45	−	12403.4i	−0.336263	−	0.650120i
$715$	−9101.37	−	528.245i	−0.476045	−	0.0276297i
$716$	−654.461	+	726.853i	−0.0341597	+	0.0379382i
$717$	−18324.6	+	22629.0i	−0.954456	+	1.17866i
$718$	−4575.71	+	1226.06i	−0.237833	+	0.0637270i
$719$	13069.3	+	5818.83i	0.677890	+	0.301816i	0.716650	−	0.697433i	$-0.245674\pi$
$719$	13069.3	+	5818.83i	0.677890	+	0.301816i	−0.0387606	+	0.999249i	$0.512341\pi$
$720$	1437.09	−	6579.12i	0.0743851	−	0.340541i
$721$	1691.77	−	4488.87i	0.0873855	−	0.231864i
$722$	11009.8	−	1743.78i	0.567509	−	0.0898846i
$723$	21260.3	+	13806.6i	1.09361	+	0.710198i
$724$	7372.52	−	12769.6i	0.378449	−	0.655494i
$725$	26415.2	−	8256.03i	1.35315	−	0.422926i
$726$	9909.63	−	5721.33i	0.506585	−	0.292477i
$727$	−23948.9	+	12202.6i	−1.22175	+	0.622514i	−0.941370	−	0.337375i	$-0.890461\pi$
$727$	−23948.9	+	12202.6i	−1.22175	+	0.622514i	−0.280382	+	0.959889i	$0.590461\pi$
$728$	1431.91	−	14472.4i	0.0728986	−	0.736788i
$729$	−18300.2	+	25188.0i	−0.929746	+	1.27969i
$730$	2315.18	+	3224.49i	0.117382	+	0.163485i
$731$	7894.93	−	829.791i	0.399459	−	0.0419849i
$732$	−7328.89	−	27351.8i	−0.370060	−	1.38108i
$733$	25771.6	−	9892.80i	1.29863	−	0.498498i	0.391822	−	0.920041i	$-0.371845\pi$
$733$	25771.6	−	9892.80i	1.29863	−	0.498498i	0.906808	+	0.421543i	$0.138511\pi$
$734$	−3368.21	−	10366.3i	−0.169377	−	0.521290i
$735$	−28795.4	+	11271.6i	−1.44508	+	0.565659i
$736$	−10829.2	+	33328.9i	−0.542350	+	1.66918i
$737$	−819.592	−	15638.8i	−0.0409635	−	0.781629i
$738$	−2421.12	+	1572.29i	−0.120762	+	0.0784240i
$739$	−19808.6	+	17835.8i	−0.986025	+	0.887821i	−0.993691	−	0.112150i	$-0.964226\pi$
$739$	−19808.6	+	17835.8i	−0.986025	+	0.887821i	0.00766629	+	0.999971i	$0.497560\pi$
$740$	1758.79	+	11523.0i	0.0873708	+	0.572422i
$741$	−8975.90	+	2916.45i	−0.444991	+	0.144586i
$742$	9773.11	+	4280.03i	0.483534	+	0.211759i
$743$	−20939.7	−	20939.7i	−1.03392	−	1.03392i	−0.999404	−	0.0345168i	$-0.989011\pi$
$743$	−20939.7	−	20939.7i	−1.03392	−	1.03392i	−0.0345168	−	0.999404i	$-0.510989\pi$
$744$	−7393.68	+	16606.5i	−0.364335	+	0.818310i
$745$	−4112.63	−	19897.1i	−0.202249	−	0.978490i
$746$	−14096.6	+	6276.19i	−0.691838	+	0.308026i
$747$	24527.5	−	19862.0i	1.20136	−	0.972840i
$748$	−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	$-0.375303\pi$
$752$	−302.083	+	5764.09i	−0.0146487	+	0.279515i
$753$	28154.6	+	10807.6i	1.36257	+	0.523040i
$754$	−1513.17	+	14396.8i	−0.0730852	+	0.695360i
$755$	14119.7	+	15859.7i	0.680620	+	0.764495i
$756$	−992.777	+	6525.51i	−0.0477605	+	0.313929i
$757$	−386.117	+	386.117i	−0.0185385	+	0.0185385i	−0.716315	−	0.697777i	$-0.754173\pi$
$757$	−386.117	+	386.117i	−0.0185385	+	0.0185385i	0.697777	+	0.716315i	$0.254173\pi$
$758$	4531.36	+	11804.6i	0.217132	+	0.565649i
$759$	42962.0	+	9131.86i	2.05457	+	0.436713i
$760$	7487.14	−	5993.67i	0.357352	−	0.286070i
$761$	4019.38	+	18909.7i	0.191462	+	0.900756i	0.964024	+	0.265817i	$0.0856417\pi$
$761$	4019.38	+	18909.7i	0.191462	+	0.900756i	−0.772562	+	0.634940i	$0.781025\pi$
$762$	2720.29	−	5338.88i	0.129325	−	0.253815i
$763$	4633.10	−	1536.69i	0.219829	−	0.0729122i
$764$	−2663.93	−	865.563i	−0.126149	−	0.0409882i
$765$	3223.29	−	19636.8i	0.152338	−	0.928064i
$766$	−967.250	+	4550.55i	−0.0456242	+	0.214645i
$767$	14915.0	+	12077.9i	0.702152	+	0.568591i

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+(-1.08793 + 1.67526i) q^{2} +(2.88975 - 7.52806i) q^{3} +(1.63097 + 3.66323i) q^{4} +(-3.51457 + 10.6136i) q^{5} +(9.46764 + 13.0311i) q^{6} +(-9.35779 - 15.9822i) q^{7} +(-23.6947 - 3.75287i) q^{8} +(-28.2561 - 25.4419i) q^{9} +(-13.9569 - 17.4346i) q^{10} +(-16.6693 - 18.5131i) q^{11} +(32.2901 - 1.69225i) q^{12} +(-29.1647 - 14.8602i) q^{13} +(36.9551 + 1.71077i) q^{14} +(69.7433 + 57.1284i) q^{15} +(10.6000 - 11.7725i) q^{16} +(29.4593 - 36.3792i) q^{17} +(73.3624 - 19.6574i) q^{18} +(32.6659 + 14.5438i) q^{19} +(-44.6121 + 4.43579i) q^{20} +(-147.357 + 24.2613i) q^{21} +(49.1493 - 7.78448i) q^{22} +(-183.373 - 119.084i) q^{23} +(-96.7236 + 167.530i) q^{24} +(-100.296 - 74.6042i) q^{25} +(56.6238 - 32.6918i) q^{26} +(-79.1924 + 40.3506i) q^{27} +(43.2842 - 60.3463i) q^{28} +(-130.137 + 179.119i) q^{29} +(-171.581 + 54.6868i) q^{30} +(93.4543 - 9.82244i) q^{31} +(-41.4827 - 154.815i) q^{32} +(-187.538 + 71.9889i) q^{33} +(28.8951 + 88.9300i) q^{34} +(202.517 - 43.1489i) q^{35} +(47.1145 - 145.003i) q^{36} +(-13.6074 - 259.645i) q^{37} +(-59.9028 + 38.9013i) q^{38} +(-196.147 + 176.611i) q^{39} +(123.108 - 238.296i) q^{40} +(-36.1494 + 11.7457i) q^{41} +(119.670 - 273.256i) q^{42} +(119.914 + 119.914i) q^{43} +(40.6305 - 91.2576i) q^{44} +(369.337 - 210.480i) q^{45} +(398.993 - 177.643i) q^{46} +(-283.161 + 229.299i) 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} +(6.86927 - 131.074i) q^{52} +(269.244 + 103.353i) q^{53} +(18.5579 - 176.567i) q^{54} +(255.075 - 111.855i) q^{55} +(161.751 + 413.813i) q^{56} +(203.883 - 203.883i) q^{57} +(-158.491 - 412.883i) q^{58} +(-573.520 - 121.906i) q^{59} +(-95.5249 + 348.661i) q^{60} +(-182.077 - 856.607i) q^{61} +(-85.2165 + 167.247i) q^{62} +(-142.204 + 689.675i) q^{63} +(425.016 + 138.096i) q^{64} +(260.221 - 257.315i) q^{65} +(83.4271 - 392.494i) q^{66} +(488.534 + 395.607i) q^{67} +(181.312 + 48.5825i) q^{68} +(-1426.37 + 1036.32i) q^{69} +(-148.038 + 386.212i) q^{70} +(783.313 + 569.110i) q^{71} +(574.039 + 708.879i) q^{72} +(-177.501 - 9.30242i) q^{73} +(449.778 + 259.680i) q^{74} +(-851.454 + 539.444i) q^{75} +143.383i q^{76} +(-139.893 + 439.653i) q^{77} +(-82.4769 - 520.739i) q^{78} +(314.868 + 33.0940i) q^{79} +(87.6938 + 153.879i) q^{80} +(-32.3942 - 308.210i) q^{81} +(19.6509 - 73.3382i) q^{82} +(-129.851 + 819.846i) q^{83} +(-329.210 - 500.232i) q^{84} +(282.576 + 440.525i) q^{85} +(-331.345 + 70.4295i) q^{86} +(972.352 + 1497.29i) q^{87} +(325.496 + 501.220i) q^{88} +(1084.03 - 230.417i) q^{89} +(-49.2020 + 847.725i) q^{90} +(35.4186 + 605.176i) q^{91} +(137.154 - 865.959i) q^{92} +(196.116 - 731.914i) q^{93} +(-76.0777 - 723.831i) q^{94} +(-269.168 + 295.586i) q^{95} +(-1285.33 - 135.094i) q^{96} +(-35.9240 - 226.815i) q^{97} +(-318.476 - 606.634i) 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

Introduction

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