LMFDB - Embedded newform 32.4.g.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,4,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$1.88806112018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	32.5
Dual form			32.4.g.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.719102 + 2.73549i) q^{2} +(-3.21198 - 7.75440i) q^{3} +(-6.96578 - 3.93419i) q^{4} +(-13.6472 - 5.65283i) q^{5} +(23.5218 - 3.21012i) q^{6} +(9.07689 + 9.07689i) q^{7} +(15.7710 - 16.2257i) q^{8} +(-30.7220 + 30.7220i) q^{9} +O(q^{10})$	\(q+(-0.719102 + 2.73549i) q^{2} +(-3.21198 - 7.75440i) q^{3} +(-6.96578 - 3.93419i) q^{4} +(-13.6472 - 5.65283i) q^{5} +(23.5218 - 3.21012i) q^{6} +(9.07689 + 9.07689i) q^{7} +(15.7710 - 16.2257i) q^{8} +(-30.7220 + 30.7220i) q^{9} +(25.2770 - 33.2666i) q^{10} +(16.7195 - 40.3646i) q^{11} +(-8.13333 + 66.6520i) q^{12} +(-38.4266 + 15.9168i) q^{13} +(-31.3569 + 18.3025i) q^{14} +123.982i q^{15} +(33.0443 + 54.8094i) q^{16} -92.5038i q^{17} +(-61.9474 - 106.132i) q^{18} +(-16.6799 + 6.90905i) q^{19} +(72.8238 + 93.0669i) q^{20} +(41.2311 - 99.5406i) q^{21} +(98.3937 + 74.7623i) q^{22} +(95.6008 - 95.6008i) q^{23} +(-176.477 - 70.1782i) q^{24} +(65.9018 + 65.9018i) q^{25} +(-15.9076 - 116.561i) q^{26} +(127.540 + 52.8290i) q^{27} +(-27.5175 - 98.9379i) q^{28} +(19.3621 + 46.7443i) q^{29} +(-339.152 - 89.1559i) q^{30} -38.1477 q^{31} +(-173.693 + 50.9787i) q^{32} -366.706 q^{33} +(253.043 + 66.5197i) q^{34} +(-72.5636 - 175.184i) q^{35} +(334.869 - 93.1367i) q^{36} +(227.529 + 94.2456i) q^{37} +(-6.90506 - 50.5961i) q^{38} +(246.851 + 246.851i) q^{39} +(-306.951 + 132.284i) q^{40} +(-279.334 + 279.334i) q^{41} +(242.643 + 184.367i) q^{42} +(112.235 - 270.960i) q^{43} +(-275.267 + 215.393i) q^{44} +(592.935 - 245.602i) q^{45} +(192.768 + 330.261i) q^{46} -321.955i q^{47} +(318.877 - 432.285i) q^{48} -178.220i q^{49} +(-227.664 + 132.883i) q^{50} +(-717.312 + 297.120i) q^{51} +(330.291 + 40.3044i) q^{52} +(-52.5056 + 126.760i) q^{53} +(-236.228 + 310.896i) q^{54} +(-456.348 + 456.348i) q^{55} +(290.431 - 4.12723i) q^{56} +(107.151 + 107.151i) q^{57} +(-141.792 + 19.3509i) q^{58} +(-332.587 - 137.762i) q^{59} +(487.770 - 863.633i) q^{60} +(33.6815 + 81.3143i) q^{61} +(27.4321 - 104.352i) q^{62} -557.721 q^{63} +(-14.5488 - 511.793i) q^{64} +614.389 q^{65} +(263.699 - 1003.12i) q^{66} +(108.572 + 262.117i) q^{67} +(-363.928 + 644.362i) q^{68} +(-1048.39 - 434.259i) q^{69} +(531.394 - 72.5216i) q^{70} +(272.246 + 272.246i) q^{71} +(13.9692 + 983.005i) q^{72} +(372.955 - 372.955i) q^{73} +(-421.424 + 554.631i) q^{74} +(299.354 - 722.704i) q^{75} +(143.370 + 17.4950i) q^{76} +(518.146 - 214.623i) q^{77} +(-852.768 + 497.746i) q^{78} -244.410i q^{79} +(-141.132 - 934.787i) q^{80} +14.3973i q^{81} +(-563.244 - 964.983i) q^{82} +(1230.52 - 509.697i) q^{83} +(-678.819 + 531.168i) q^{84} +(-522.909 + 1262.41i) q^{85} +(660.498 + 501.865i) q^{86} +(300.283 - 300.283i) q^{87} +(-391.260 - 907.878i) q^{88} +(216.134 + 216.134i) q^{89} +(245.459 + 1798.58i) q^{90} +(-493.270 - 204.319i) q^{91} +(-1042.05 + 289.823i) q^{92} +(122.529 + 295.812i) q^{93} +(880.704 + 231.519i) q^{94} +266.689 q^{95} +(953.206 + 1183.14i) q^{96} +779.862 q^{97} +(487.519 + 128.158i) q^{98} +(726.422 + 1753.74i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 116 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 212 * q^14 - 304 * q^16 - 184 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 192 * q^22 + 324 * q^23 - 48 * q^24 - 4 * q^25 + 16 * q^26 - 268 * q^27 + 376 * q^28 - 4 * q^29 + 1188 * q^30 - 752 * q^31 + 616 * q^32 - 8 * q^33 + 528 * q^34 - 460 * q^35 + 1456 * q^36 - 4 * q^37 + 980 * q^38 + 596 * q^39 - 536 * q^40 - 4 * q^41 - 2264 * q^42 + 804 * q^43 - 2044 * q^44 + 104 * q^45 - 1444 * q^46 - 2448 * q^48 - 3564 * q^50 - 1384 * q^51 - 2524 * q^52 + 748 * q^53 - 1088 * q^54 - 292 * q^55 + 1192 * q^56 - 4 * q^57 + 3200 * q^58 + 1372 * q^59 + 5752 * q^60 - 1828 * q^61 + 3384 * q^62 + 2512 * q^63 + 4952 * q^64 - 8 * q^65 + 5996 * q^66 + 2036 * q^67 + 2768 * q^68 - 1060 * q^69 + 1400 * q^70 + 220 * q^71 - 1708 * q^72 - 4 * q^73 - 3476 * q^74 - 1712 * q^75 - 5124 * q^76 + 1900 * q^77 - 11916 * q^78 - 10312 * q^80 - 6404 * q^82 + 2436 * q^83 - 6560 * q^84 + 496 * q^85 - 928 * q^86 - 1292 * q^87 + 1248 * q^88 - 4 * q^89 + 7400 * q^90 - 3604 * q^91 + 10152 * q^92 - 112 * q^93 + 12840 * q^94 - 6088 * q^95 + 17792 * q^96 - 8 * q^97 + 11224 * q^98 - 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.719102	+	2.73549i	−0.254241	+	0.967141i
$2$	−0.719102	+	2.73549i	−0.254241	+	0.967141i
$3$	−3.21198	−	7.75440i	−0.618145	−	1.49233i	−0.853855	−	0.520511i	$-0.825741\pi$
$3$	−3.21198	−	7.75440i	−0.618145	−	1.49233i	0.235710	−	0.971824i	$-0.424259\pi$
$4$	−6.96578	−	3.93419i	−0.870723	−	0.491774i
$5$	−13.6472	−	5.65283i	−1.22064	−	0.505605i	−0.323026	−	0.946390i	$-0.604700\pi$
$5$	−13.6472	−	5.65283i	−1.22064	−	0.505605i	−0.897613	+	0.440785i	$0.854700\pi$
$6$	23.5218	−	3.21012i	1.60046	−	0.218421i
$7$	9.07689	+	9.07689i	0.490106	+	0.490106i	0.908340	−	0.418233i	$-0.137351\pi$
$7$	9.07689	+	9.07689i	0.490106	+	0.490106i	−0.418233	+	0.908340i	$0.637351\pi$
$8$	15.7710	−	16.2257i	0.696988	−	0.717083i
$9$	−30.7220	+	30.7220i	−1.13785	+	1.13785i
$10$	25.2770	−	33.2666i	0.799327	−	1.05198i
$11$	16.7195	−	40.3646i	0.458285	−	1.10640i	−0.510807	−	0.859696i	$-0.670653\pi$
$11$	16.7195	−	40.3646i	0.458285	−	1.10640i	0.969091	−	0.246702i	$-0.0793468\pi$
$12$	−8.13333	+	66.6520i	−0.195658	+	1.60340i
$13$	−38.4266	+	15.9168i	−0.819817	+	0.339580i	−0.752864	−	0.658177i	$-0.771328\pi$
$13$	−38.4266	+	15.9168i	−0.819817	+	0.339580i	−0.0669538	+	0.997756i	$0.521328\pi$
$14$	−31.3569	+	18.3025i	−0.598607	+	0.349397i
$15$			123.982i			2.13414i
$16$	33.0443	+	54.8094i	0.516317	+	0.856397i
$17$		−	92.5038i		−	1.31973i	−0.751383	−	0.659867i	$-0.770613\pi$
$17$		−	92.5038i		−	1.31973i	0.751383	−	0.659867i	$-0.229387\pi$
$18$	−61.9474	−	106.132i	−0.811175	−	1.38975i
$19$	−16.6799	+	6.90905i	−0.201402	+	0.0834235i	−0.481104	−	0.876663i	$-0.659764\pi$
$19$	−16.6799	+	6.90905i	−0.201402	+	0.0834235i	0.279702	+	0.960087i	$0.409764\pi$
$20$	72.8238	+	93.0669i	0.814195	+	1.04052i
$21$	41.2311	−	99.5406i	0.428446	−	1.03436i
$22$	98.3937	+	74.7623i	0.953527	+	0.724517i
$23$	95.6008	−	95.6008i	0.866702	−	0.866702i	−0.125404	−	0.992106i	$-0.540023\pi$
$23$	95.6008	−	95.6008i	0.866702	−	0.866702i	0.992106	+	0.125404i	$0.0400228\pi$
$24$	−176.477	−	70.1782i	−1.50097	−	0.596878i
$25$	65.9018	+	65.9018i	0.527215	+	0.527215i
$26$	−15.9076	−	116.561i	−0.119990	−	0.879214i
$27$	127.540	+	52.8290i	0.909081	+	0.376553i
$28$	−27.5175	−	98.9379i	−0.185725	−	0.667768i
$29$	19.3621	+	46.7443i	0.123981	+	0.299317i	0.973668	−	0.227971i	$-0.0732090\pi$
$29$	19.3621	+	46.7443i	0.123981	+	0.299317i	−0.849687	+	0.527288i	$0.823209\pi$
$30$	−339.152	−	89.1559i	−2.06401	−	0.542585i
$31$	−38.1477			−0.221017			−0.110508	−	0.993875i	$-0.535248\pi$
$31$	−38.1477			−0.221017			−0.110508	+	0.993875i	$0.535248\pi$
$32$	−173.693	+	50.9787i	−0.959526	+	0.281620i
$33$	−366.706			−1.93440
$34$	253.043	+	66.5197i	1.27637	+	0.335530i
$35$	−72.5636	−	175.184i	−0.350442	−	0.846042i
$36$	334.869	−	93.1367i	1.55032	−	0.431189i
$37$	227.529	+	94.2456i	1.01096	+	0.418754i	0.825805	−	0.563955i	$-0.190721\pi$
$37$	227.529	+	94.2456i	1.01096	+	0.418754i	0.185156	+	0.982709i	$0.440721\pi$
$38$	−6.90506	−	50.5961i	−0.0294776	−	0.215994i
$39$	246.851	+	246.851i	1.01353	+	1.01353i
$40$	−306.951	+	132.284i	−1.21333	+	0.522898i
$41$	−279.334	+	279.334i	−1.06401	+	1.06401i	−0.0662081	+	0.997806i	$0.521090\pi$
$41$	−279.334	+	279.334i	−1.06401	+	1.06401i	−0.997806	+	0.0662081i	$0.978910\pi$
$42$	242.643	+	184.367i	0.891443	+	0.677344i
$43$	112.235	−	270.960i	0.398039	−	0.960952i	−0.590091	−	0.807337i	$-0.700908\pi$
$43$	112.235	−	270.960i	0.398039	−	0.960952i	0.988131	−	0.153616i	$-0.0490918\pi$
$44$	−275.267	+	215.393i	−0.943136	+	0.737993i
$45$	592.935	−	245.602i	1.96421	−	0.813603i
$46$	192.768	+	330.261i	0.617871	+	1.05857i
$47$		−	321.955i		−	0.999191i	−0.866259	−	0.499596i	$-0.833482\pi$
$47$		−	321.955i		−	0.999191i	0.866259	−	0.499596i	$-0.166518\pi$
$48$	318.877	−	432.285i	0.958872	−	1.29990i
$49$		−	178.220i		−	0.519592i
$50$	−227.664	+	132.883i	−0.643930	+	0.375851i
$51$	−717.312	+	297.120i	−1.96948	+	0.815787i
$52$	330.291	+	40.3044i	0.880830	+	0.107485i
$53$	−52.5056	+	126.760i	−0.136079	+	0.328524i	−0.977199	−	0.212324i	$-0.931897\pi$
$53$	−52.5056	+	126.760i	−0.136079	+	0.328524i	0.841120	+	0.540848i	$0.181897\pi$
$54$	−236.228	+	310.896i	−0.595306	+	0.783474i
$55$	−456.348	+	456.348i	−1.11880	+	1.11880i
$56$	290.431	−	4.12723i	0.693045	−	0.00984865i
$57$	107.151	+	107.151i	0.248991	+	0.248991i
$58$	−141.792	+	19.3509i	−0.321003	+	0.0438086i
$59$	−332.587	−	137.762i	−0.733884	−	0.303985i	−0.0157369	−	0.999876i	$-0.505009\pi$
$59$	−332.587	−	137.762i	−0.733884	−	0.303985i	−0.718147	+	0.695892i	$0.755009\pi$
$60$	487.770	−	863.633i	1.04951	−	1.85824i
$61$	33.6815	+	81.3143i	0.0706963	+	0.170676i	0.955278	−	0.295709i	$-0.0955560\pi$
$61$	33.6815	+	81.3143i	0.0706963	+	0.170676i	−0.884582	+	0.466385i	$0.845556\pi$
$62$	27.4321	−	104.352i	0.0561915	−	0.213754i
$63$	−557.721			−1.11534
$64$	−14.5488	−	511.793i	−0.0284156	−	0.999596i
$65$	614.389			1.17239
$66$	263.699	−	1003.12i	0.491804	−	1.87084i
$67$	108.572	+	262.117i	0.197974	+	0.477951i	0.991424	−	0.130684i	$-0.0417174\pi$
$67$	108.572	+	262.117i	0.197974	+	0.477951i	−0.793450	+	0.608635i	$0.791717\pi$
$68$	−363.928	+	644.362i	−0.649010	+	1.14912i
$69$	−1048.39	−	434.259i	−1.82916	−	0.757661i
$70$	531.394	−	72.5216i	0.907339	−	0.123828i
$71$	272.246	+	272.246i	0.455066	+	0.455066i	0.897032	−	0.441966i	$-0.145719\pi$
$71$	272.246	+	272.246i	0.455066	+	0.455066i	−0.441966	+	0.897032i	$0.645719\pi$
$72$	13.9692	+	983.005i	0.0228651	+	1.60900i
$73$	372.955	−	372.955i	0.597960	−	0.597960i	−0.341809	−	0.939769i	$-0.611040\pi$
$73$	372.955	−	372.955i	0.597960	−	0.597960i	0.939769	+	0.341809i	$0.111040\pi$
$74$	−421.424	+	554.631i	−0.662022	+	0.871277i
$75$	299.354	−	722.704i	0.460885	−	1.11268i
$76$	143.370	+	17.4950i	0.216391	+	0.0264055i
$77$	518.146	−	214.623i	0.766860	−	0.317644i
$78$	−852.768	+	497.746i	−1.23791	+	0.722547i
$79$		−	244.410i		−	0.348080i	−0.984739	−	0.174040i	$-0.944318\pi$
$79$		−	244.410i		−	0.348080i	0.984739	−	0.174040i	$-0.0556822\pi$
$80$	−141.132	−	934.787i	−0.197238	−	1.30640i
$81$			14.3973i			0.0197494i
$82$	−563.244	−	964.983i	−0.758535	−	1.29957i
$83$	1230.52	−	509.697i	1.62731	−	0.674054i	0.632384	−	0.774655i	$-0.282076\pi$
$83$	1230.52	−	509.697i	1.62731	−	0.674054i	0.994927	+	0.100600i	$0.0320764\pi$
$84$	−678.819	+	531.168i	−0.881728	+	0.689942i
$85$	−522.909	+	1262.41i	−0.667264	+	1.61092i
$86$	660.498	+	501.865i	0.828178	+	0.629274i
$87$	300.283	−	300.283i	0.370043	−	0.370043i
$88$	−391.260	−	907.878i	−0.473960	−	1.09977i
$89$	216.134	+	216.134i	0.257417	+	0.257417i	0.824003	−	0.566586i	$-0.191736\pi$
$89$	216.134	+	216.134i	0.257417	+	0.257417i	−0.566586	+	0.824003i	$0.691736\pi$
$90$	245.459	+	1798.58i	0.287486	+	2.10652i
$91$	−493.270	−	204.319i	−0.568228	−	0.235368i
$92$	−1042.05	+	289.823i	−1.18088	+	0.328436i
$93$	122.529	+	295.812i	0.136621	+	0.329831i
$94$	880.704	+	231.519i	0.966359	+	0.254035i
$95$	266.689			0.288018
$96$	953.206	+	1183.14i	1.01340	+	1.25785i
$97$	779.862			0.816319			0.408160	−	0.912911i	$-0.366171\pi$
$97$	779.862			0.816319			0.408160	+	0.912911i	$0.366171\pi$
$98$	487.519	+	128.158i	0.502519	+	0.132102i
$99$	726.422	+	1753.74i	0.737457	+	1.78038i
$100$	−199.788	−	718.328i	−0.199788	−	0.718328i
$101$	−1046.60	−	433.515i	−1.03109	−	0.427092i	−0.197985	−	0.980205i	$-0.563440\pi$
$101$	−1046.60	−	433.515i	−1.03109	−	0.427092i	−0.833106	+	0.553113i	$0.813440\pi$
$102$	−296.948	−	2175.86i	−0.288258	−	2.11218i
$103$	683.721	+	683.721i	0.654069	+	0.654069i	0.953970	−	0.299901i	$-0.0969538\pi$
$103$	683.721	+	683.721i	0.654069	+	0.654069i	−0.299901	+	0.953970i	$0.596954\pi$
$104$	−347.765	+	874.525i	−0.327896	+	0.824560i
$105$	−1125.37	+	1125.37i	−1.04595	+	1.04595i
$106$	−308.993	−	234.782i	−0.283133	−	0.215132i
$107$	−289.555	+	699.048i	−0.261611	+	0.631584i	−0.999038	−	0.0438418i	$-0.986040\pi$
$107$	−289.555	+	699.048i	−0.261611	+	0.631584i	0.737428	+	0.675426i	$0.236040\pi$
$108$	−680.580	−	869.764i	−0.606378	−	0.774936i
$109$	56.3510	−	23.3413i	0.0495179	−	0.0205110i	−0.357787	−	0.933803i	$-0.616469\pi$
$109$	56.3510	−	23.3413i	0.0495179	−	0.0205110i	0.407305	+	0.913292i	$0.366469\pi$
$110$	−920.174	−	1576.50i	−0.797592	−	1.36648i
$111$		−	2067.07i		−	1.76754i
$112$	−197.560	+	797.439i	−0.166675	+	0.672776i
$113$		−	1567.46i		−	1.30491i	−0.757828	−	0.652454i	$-0.773740\pi$
$113$		−	1567.46i		−	1.30491i	0.757828	−	0.652454i	$-0.226260\pi$
$114$	−370.163	+	216.058i	−0.304114	+	0.177506i
$115$	−1845.09	+	764.263i	−1.49614	+	0.619720i
$116$	49.0286	−	401.785i	0.0392430	−	0.321593i
$117$	691.546	−	1669.54i	0.546440	−	1.31922i
$118$	616.010	−	810.723i	0.480579	−	0.632484i
$119$	839.647	−	839.647i	0.646810	−	0.646810i
$120$	2011.70	+	1955.33i	1.53035	+	1.48747i
$121$	−408.595	−	408.595i	−0.306983	−	0.306983i
$122$	−246.655	+	33.6620i	−0.183042	+	0.0249805i
$123$	3063.28	+	1268.85i	2.24558	+	0.930150i
$124$	265.728	+	150.080i	0.192444	+	0.108690i
$125$	179.764	+	433.989i	0.128629	+	0.310538i
$126$	401.058	−	1525.64i	0.283564	−	1.07869i
$127$	−1291.26			−0.902209			−0.451105	−	0.892471i	$-0.648970\pi$
$127$	−1291.26			−0.902209			−0.451105	+	0.892471i	$0.648970\pi$
$128$	1410.47	+	328.234i	0.973975	+	0.226656i
$129$	−2461.63			−1.68011
$130$	−441.808	+	1680.65i	−0.298070	+	1.13387i
$131$	−326.012	−	787.064i	−0.217434	−	0.524932i	0.777096	−	0.629382i	$-0.216692\pi$
$131$	−326.012	−	787.064i	−0.217434	−	0.524932i	−0.994530	+	0.104450i	$0.966692\pi$
$132$	2554.39	+	1442.69i	1.68433	+	0.951288i
$133$	−214.115	−	88.6892i	−0.139595	−	0.0578220i
$134$	−795.093	+	108.510i	−0.512579	+	0.0699538i
$135$	−1441.93	−	1441.93i	−0.919271	−	0.919271i
$136$	−1500.94	−	1458.88i	−0.946358	−	0.919839i
$137$	1526.86	−	1526.86i	0.952177	−	0.952177i	−0.0467305	−	0.998908i	$-0.514880\pi$
$137$	1526.86	−	1526.86i	0.952177	−	0.952177i	0.998908	+	0.0467305i	$0.0148802\pi$
$138$	1941.81	−	2555.59i	1.19781	−	1.57642i
$139$	−181.169	+	437.382i	−0.110551	+	0.266894i	−0.969467	−	0.245224i	$-0.921139\pi$
$139$	−181.169	+	437.382i	−0.110551	+	0.266894i	0.858916	+	0.512117i	$0.171139\pi$
$140$	−183.745	+	1505.77i	−0.110923	+	0.909007i
$141$	−2496.57	+	1034.11i	−1.49113	+	0.617645i
$142$	−940.499	+	548.953i	−0.555809	+	0.324417i
$143$			1817.20i			1.06267i
$144$	−2699.04	−	668.669i	−1.56195	−	0.386961i
$145$		−	747.377i		−	0.428043i
$146$	752.021	+	1288.41i	0.426286	+	0.730338i
$147$	−1381.99	+	572.439i	−0.775405	+	0.321183i
$148$	−1214.14	−	1551.64i	−0.674335	−	0.861782i
$149$	−1162.21	+	2805.81i	−0.639004	+	1.54269i	0.189004	+	0.981976i	$0.439474\pi$
$149$	−1162.21	+	2805.81i	−0.639004	+	1.54269i	−0.828008	+	0.560716i	$0.810526\pi$
$150$	1761.68	+	1338.58i	0.958938	+	0.728629i
$151$	−262.518	+	262.518i	−0.141479	+	0.141479i	−0.774299	−	0.632820i	$-0.781897\pi$
$151$	−262.518	+	262.518i	−0.141479	+	0.141479i	0.632820	+	0.774299i	$0.281897\pi$
$152$	−150.955	+	379.607i	−0.0805533	+	0.202567i
$153$	2841.90	+	2841.90i	1.50166	+	1.50166i
$154$	214.499	+	1571.72i	0.112239	+	0.822420i
$155$	520.607	+	215.642i	0.269782	+	0.111747i
$156$	−748.352	−	2690.67i	−0.384078	−	1.38093i
$157$	−1086.34	−	2622.67i	−0.552227	−	1.33319i	−0.915802	−	0.401630i	$-0.868444\pi$
$157$	−1086.34	−	2622.67i	−0.552227	−	1.33319i	0.363575	−	0.931565i	$-0.381556\pi$
$158$	668.581	+	175.756i	0.336642	+	0.0884961i
$159$	1151.59			0.574385
$160$	2658.59	+	286.142i	1.31362	+	0.141385i
$161$	1735.52			0.849552
$162$	−39.3837	−	10.3531i	−0.0191005	−	0.00502111i
$163$	−380.057	−	917.540i	−0.182628	−	0.440903i	0.805878	−	0.592081i	$-0.201693\pi$
$163$	−380.057	−	917.540i	−0.182628	−	0.440903i	−0.988507	+	0.151178i	$0.951693\pi$
$164$	3044.73	−	846.826i	1.44972	−	0.403207i
$165$	5004.49	+	2072.93i	2.36120	+	0.978043i
$166$	509.402	+	3732.59i	0.238176	+	1.74521i
$167$	−1515.61	−	1515.61i	−0.702283	−	0.702283i	0.262617	−	0.964900i	$-0.415414\pi$
$167$	−1515.61	−	1515.61i	−0.702283	−	0.702283i	−0.964900	+	0.262617i	$0.915414\pi$
$168$	−964.863	−	2238.86i	−0.443100	−	1.02817i
$169$	−330.254	+	330.254i	−0.150320	+	0.150320i
$170$	−3077.29	−	2338.22i	−1.38834	−	1.05490i
$171$	300.181	−	724.701i	0.134242	−	0.324089i
$172$	−1847.81	+	1445.89i	−0.819153	+	0.640978i
$173$	−1837.08	+	760.945i	−0.807346	+	0.334414i	−0.747895	−	0.663817i	$-0.768935\pi$
$173$	−1837.08	+	760.945i	−0.807346	+	0.334414i	−0.0594515	+	0.998231i	$0.518935\pi$
$174$	605.487	+	1037.36i	0.263804	+	0.451964i
$175$			1196.37i			0.516782i
$176$	2764.84	−	417.430i	1.18414	−	0.178778i
$177$			3021.50i			1.28311i
$178$	−746.653	+	435.809i	−0.314404	+	0.183513i
$179$	2975.35	−	1232.43i	1.24239	−	0.514615i	0.337930	−	0.941171i	$-0.390273\pi$
$179$	2975.35	−	1232.43i	1.24239	−	0.514615i	0.904461	+	0.426556i	$0.140273\pi$
$180$	−5096.50	−	621.910i	−2.11039	−	0.257524i
$181$	1619.10	−	3908.85i	0.664899	−	1.60521i	−0.125132	−	0.992140i	$-0.539935\pi$
$181$	1619.10	−	3908.85i	0.664899	−	1.60521i	0.790030	−	0.613068i	$-0.210065\pi$
$182$	913.623	−	1202.41i	0.372100	−	0.489716i
$183$	522.359	−	522.359i	0.211005	−	0.211005i
$184$	−43.4693	−	3058.92i	−0.0174163	−	1.22558i
$185$	−2572.37	−	2572.37i	−1.02229	−	1.02229i
$186$	−897.302	+	122.459i	−0.353728	+	0.0482747i
$187$	−3733.88	−	1546.62i	−1.46015	−	0.604814i
$188$	−1266.63	+	2242.67i	−0.491376	+	0.870019i
$189$	678.148	+	1637.19i	0.260995	+	0.630097i
$190$	−191.777	+	729.525i	−0.0732261	+	0.278554i
$191$	697.265			0.264148			0.132074	−	0.991240i	$-0.457836\pi$
$191$	697.265			0.264148			0.132074	+	0.991240i	$0.457836\pi$
$192$	−3921.92	+	1756.69i	−1.47417	+	0.660301i
$193$	2386.61			0.890114			0.445057	−	0.895502i	$-0.353183\pi$
$193$	2386.61			0.890114			0.445057	+	0.895502i	$0.353183\pi$
$194$	−560.800	+	2133.30i	−0.207542	+	0.789496i
$195$	−1973.40	−	4764.22i	−0.724710	−	1.74960i
$196$	−701.151	+	1241.44i	−0.255522	+	0.452421i
$197$	−2583.07	−	1069.94i	−0.934194	−	0.386956i	−0.136926	−	0.990581i	$-0.543722\pi$
$197$	−2583.07	−	1069.94i	−0.934194	−	0.386956i	−0.797268	+	0.603625i	$0.793722\pi$
$198$	−5319.70	+	726.002i	−1.90937	+	0.260579i
$199$	2940.81	+	2940.81i	1.04758	+	1.04758i	0.998810	+	0.0487695i	$0.0155300\pi$
$199$	2940.81	+	2940.81i	1.04758	+	1.04758i	0.0487695	+	0.998810i	$0.484470\pi$
$200$	2108.65	−	29.9653i	0.745519	−	0.0105943i
$201$	1683.83	−	1683.83i	0.590886	−	0.590886i
$202$	1938.48	−	2551.21i	0.675204	−	0.888627i
$203$	−248.545	+	600.041i	−0.0859332	+	0.207461i
$204$	6165.57	+	752.365i	2.11606	+	0.258216i
$205$	5391.13	−	2233.08i	1.83675	−	0.760805i
$206$	−2361.98	+	1378.65i	−0.798868	+	0.466286i
$207$			5874.10i			1.97236i
$208$	−2142.17	−	1580.18i	−0.714101	−	0.526759i
$209$			788.794i			0.261062i
$210$	−2269.19	−	3887.70i	−0.745661	−	1.27751i
$211$	1399.25	−	579.589i	0.456533	−	0.189102i	−0.142552	−	0.989787i	$-0.545531\pi$
$211$	1399.25	−	579.589i	0.456533	−	0.189102i	0.599085	+	0.800685i	$0.295531\pi$
$212$	864.440	−	676.414i	0.280047	−	0.219134i
$213$	1236.66	−	2985.55i	0.397814	−	0.960408i
$214$	−1704.02	−	1294.76i	−0.544319	−	0.413589i
$215$	−3063.38	+	3063.38i	−0.971724	+	0.971724i
$216$	2868.63	−	1236.27i	0.903638	−	0.389433i
$217$	−346.262	−	346.262i	−0.108322	−	0.108322i
$218$	23.3278	+	170.932i	0.00724753	+	0.0531055i
$219$	−4089.97	−	1694.12i	−1.26198	−	0.522731i
$220$	4974.18	−	1383.46i	1.52436	−	0.423968i
$221$	1472.37	+	3554.61i	0.448155	+	1.08194i
$222$	5654.43	+	1486.43i	1.70946	+	0.449382i
$223$	−1100.18			−0.330374			−0.165187	−	0.986262i	$-0.552823\pi$
$223$	−1100.18			−0.330374			−0.165187	+	0.986262i	$0.552823\pi$
$224$	−2039.32	−	1113.86i	−0.608293	−	0.332246i
$225$	−4049.27			−1.19979
$226$	4287.78	+	1127.17i	1.26203	+	0.331761i
$227$	1476.27	+	3564.04i	0.431647	+	1.04209i	0.978756	+	0.205026i	$0.0657280\pi$
$227$	1476.27	+	3564.04i	0.431647	+	1.04209i	−0.547110	+	0.837061i	$0.684272\pi$
$228$	−324.839	−	1167.94i	−0.0943551	−	0.339250i
$229$	3573.95	+	1480.38i	1.03132	+	0.427188i	0.833190	−	0.552986i	$-0.186512\pi$
$229$	3573.95	+	1480.38i	1.03132	+	0.427188i	0.198134	+	0.980175i	$0.436512\pi$
$230$	−763.821	−	5596.81i	−0.218978	−	1.60453i
$231$	−3328.55	−	3328.55i	−0.948062	−	0.948062i
$232$	1063.82	+	423.041i	0.301049	+	0.119716i
$233$	−3668.67	+	3668.67i	−1.03151	+	1.03151i	−0.0320257	+	0.999487i	$0.510196\pi$
$233$	−3668.67	+	3668.67i	−1.03151	+	1.03151i	−0.999487	+	0.0320257i	$0.989804\pi$
$234$	4069.71	+	3092.29i	1.13695	+	0.863885i
$235$	−1819.96	+	4393.77i	−0.505196	+	1.21965i
$236$	1774.75	+	2268.08i	0.489518	+	0.625591i
$237$	−1895.25	+	785.040i	−0.519451	+	0.215164i
$238$	1693.05	+	2900.64i	0.461111	+	0.790002i
$239$		−	5649.23i		−	1.52895i	−0.644656	−	0.764473i	$-0.722999\pi$
$239$		−	5649.23i		−	1.52895i	0.644656	−	0.764473i	$-0.277001\pi$
$240$	−6795.40	+	4096.91i	−1.82767	+	1.10189i
$241$			5059.57i			1.35235i	0.736743	+	0.676173i	$0.236363\pi$
$241$			5059.57i			1.35235i	−0.736743	+	0.676173i	$0.763637\pi$
$242$	1411.53	−	823.884i	0.374944	−	0.218848i
$243$	3555.24	−	1472.63i	0.938553	−	0.388761i
$244$	85.2879	−	698.927i	0.0223770	−	0.183378i
$245$	−1007.45	+	2432.20i	−0.262708	+	0.634234i
$246$	−5673.73	+	7467.12i	−1.47050	+	1.93531i
$247$	530.983	−	530.983i	0.136784	−	0.136784i
$248$	−601.628	+	618.974i	−0.154046	+	0.158487i
$249$	−7904.79	−	7904.79i	−2.01183	−	2.01183i
$250$	−1316.44	+	179.660i	−0.333036	+	0.0454509i
$251$	980.968	+	406.330i	0.246686	+	0.102181i	0.502601	−	0.864519i	$-0.332377\pi$
$251$	980.968	+	406.330i	0.246686	+	0.102181i	−0.255915	+	0.966699i	$0.582377\pi$
$252$	3884.96	+	2194.18i	0.971150	+	0.548494i
$253$	−2260.48	−	5457.28i	−0.561720	−	1.35611i
$254$	928.546	−	3532.22i	0.229379	−	0.872564i
$255$	11468.8			2.81649
$256$	−1912.15	+	3622.28i	−0.466833	+	0.884346i
$257$	−1021.29			−0.247886			−0.123943	−	0.992289i	$-0.539554\pi$
$257$	−1021.29			−0.247886			−0.123943	+	0.992289i	$0.539554\pi$
$258$	1770.16	−	6733.75i	0.427152	−	1.62490i
$259$	1209.80	+	2920.72i	0.290244	+	0.700712i
$260$	−4279.70	−	2417.12i	−1.02083	−	0.576552i
$261$	−2030.92	−	841.236i	−0.481651	−	0.199506i
$262$	2387.44	−	325.824i	0.562964	−	0.0768300i
$263$	−1134.88	−	1134.88i	−0.266083	−	0.266083i	0.561437	−	0.827520i	$-0.310249\pi$
$263$	−1134.88	−	1134.88i	−0.266083	−	0.266083i	−0.827520	+	0.561437i	$0.810249\pi$
$264$	−5783.33	+	5950.07i	−1.34825	+	1.38713i
$265$	1433.10	−	1433.10i	0.332207	−	0.332207i
$266$	396.579	−	521.932i	0.0914128	−	0.120307i
$267$	981.770	−	2370.20i	0.225031	−	0.543273i
$268$	274.926	−	2253.00i	0.0626634	−	0.513521i
$269$	−2221.12	+	920.017i	−0.503435	+	0.208530i	−0.619923	−	0.784663i	$-0.712836\pi$
$269$	−2221.12	+	920.017i	−0.503435	+	0.208530i	0.116488	+	0.993192i	$0.462836\pi$
$270$	4981.28	−	2907.49i	1.12278	−	0.655348i
$271$		−	1860.26i		−	0.416984i	−0.978024	−	0.208492i	$-0.933144\pi$
$271$		−	1860.26i		−	0.416984i	0.978024	−	0.208492i	$-0.0668555\pi$
$272$	5070.08	−	3056.72i	1.13022	−	0.681401i
$273$			4481.28i			0.993477i
$274$	3078.73	+	5274.67i	0.678807	+	1.16297i
$275$	3761.95	−	1558.25i	0.824923	−	0.341694i
$276$	5594.43	+	7149.53i	1.22009	+	1.55924i
$277$	−2311.55	+	5580.58i	−0.501400	+	1.21049i	0.447322	+	0.894373i	$0.352378\pi$
$277$	−2311.55	+	5580.58i	−0.501400	+	1.21049i	−0.948721	+	0.316113i	$0.897622\pi$
$278$	−1066.17	−	810.108i	−0.230017	−	0.174774i
$279$	1171.97	−	1171.97i	0.251485	−	0.251485i
$280$	−3986.89	−	1585.44i	−0.850937	−	0.338385i
$281$	−1740.45	−	1740.45i	−0.369490	−	0.369490i	0.497801	−	0.867291i	$-0.334141\pi$
$281$	−1740.45	−	1740.45i	−0.369490	−	0.369490i	−0.867291	+	0.497801i	$0.834141\pi$
$282$	−1033.51	−	7572.96i	−0.218244	−	1.59916i
$283$	−2580.95	−	1069.06i	−0.542125	−	0.224555i	0.0947795	−	0.995498i	$-0.469785\pi$
$283$	−2580.95	−	1069.06i	−0.542125	−	0.224555i	−0.636904	+	0.770943i	$0.719785\pi$
$284$	−825.340	−	2967.48i	−0.172447	−	0.620026i
$285$	−856.600	−	2068.01i	−0.178037	−	0.429820i
$286$	−4970.92	−	1306.75i	−1.02775	−	0.270174i
$287$	−5070.96			−1.04296
$288$	3770.02	−	6902.36i	0.771357	−	1.41224i
$289$	−3643.96			−0.741697
$290$	2044.44	+	537.441i	0.413978	+	0.108826i
$291$	−2504.90	−	6047.36i	−0.504604	−	1.21822i
$292$	−4065.20	+	1130.65i	−0.814719	+	0.226597i
$293$	6531.00	+	2705.23i	1.30220	+	0.539390i	0.922599	−	0.385760i	$-0.126061\pi$
$293$	6531.00	+	2705.23i	1.30220	+	0.539390i	0.379603	+	0.925149i	$0.376061\pi$
$294$	−572.107	−	4192.06i	−0.113490	−	0.831584i
$295$	3760.12	+	3760.12i	0.742110	+	0.742110i
$296$	5117.57	−	2205.47i	1.00491	−	0.433076i
$297$	4264.84	−	4264.84i	0.833235	−	0.833235i
$298$	−6839.52	−	5196.87i	−1.32954	−	1.01022i
$299$	−2151.95	+	5195.27i	−0.416223	+	1.00485i
$300$	−4928.49	+	3856.49i	−0.948488	+	0.742181i
$301$	3478.22	−	1440.72i	0.666050	−	0.275887i
$302$	−529.337	−	906.891i	−0.100861	−	0.172800i
$303$			9508.17i			1.80274i
$304$	−929.858	−	685.913i	−0.175431	−	0.129407i
$305$		−	1300.10i		−	0.244078i
$306$	−9817.61	+	5730.38i	−1.83410	+	1.07054i
$307$	−22.1910	+	9.19181i	−0.00412543	+	0.00170881i	−0.384745	−	0.923023i	$-0.625711\pi$
$307$	−22.1910	+	9.19181i	−0.00412543	+	0.00170881i	0.380620	+	0.924732i	$0.375711\pi$
$308$	−4453.66	−	543.467i	−0.823932	−	0.100542i
$309$	3105.75	−	7497.95i	0.571780	−	1.38040i
$310$	−964.257	+	1269.04i	−0.176665	+	0.232506i
$311$	−4220.58	+	4220.58i	−0.769540	+	0.769540i	−0.978026	−	0.208485i	$-0.933147\pi$
$311$	−4220.58	+	4220.58i	−0.769540	+	0.769540i	0.208485	+	0.978026i	$0.433147\pi$
$312$	7898.43	−	112.242i	1.43321	−	0.0203669i
$313$	6090.90	+	6090.90i	1.09993	+	1.09993i	0.994418	+	0.105512i	$0.0336481\pi$
$313$	6090.90	+	6090.90i	1.09993	+	1.09993i	0.105512	+	0.994418i	$0.466352\pi$
$314$	7955.46	−	1085.72i	1.42979	−	0.195129i
$315$	7611.30	+	3152.71i	1.36142	+	0.563920i
$316$	−961.556	+	1702.51i	−0.171176	+	0.303081i
$317$	−1660.86	−	4009.67i	−0.294269	−	0.710428i	−0.999998	−	0.00194638i	$-0.999380\pi$
$317$	−1660.86	−	4009.67i	−0.294269	−	0.710428i	0.705729	−	0.708482i	$-0.250620\pi$
$318$	−828.113	+	3150.17i	−0.146032	+	0.555511i
$319$	2210.54			0.387982
$320$	−2694.53	+	7066.76i	−0.470716	+	1.23451i
$321$	6350.74			1.10425
$322$	−1248.01	+	4747.48i	−0.215991	+	0.821636i
$323$	639.114	+	1542.96i	0.110097	+	0.265797i
$324$	56.6418	−	100.289i	0.00971224	−	0.0171963i
$325$	−3581.33	−	1483.44i	−0.611251	−	0.253188i
$326$	2783.22	−	379.838i	0.472847	−	0.0645315i
$327$	−361.996	−	361.996i	−0.0612185	−	0.0612185i
$328$	127.012	+	8937.77i	0.0213813	+	1.50459i
$329$	2922.35	−	2922.35i	0.489710	−	0.489710i
$330$	−9269.20	+	12199.1i	−1.54622	+	2.03496i
$331$	3722.12	−	8985.99i	0.618085	−	1.49219i	−0.235840	−	0.971792i	$-0.575784\pi$
$331$	3722.12	−	8985.99i	0.618085	−	1.49219i	0.853924	−	0.520397i	$-0.174216\pi$
$332$	−10576.8	−	1290.65i	−1.74842	−	0.213354i
$333$	−9885.57	+	4094.74i	−1.62680	+	0.673845i
$334$	5235.80	−	3056.05i	0.857755	−	0.500657i
$335$		−	4190.90i		−	0.683502i
$336$	6818.22	−	1029.40i	1.10704	−	0.167138i
$337$		−	5211.97i		−	0.842475i	−0.906950	−	0.421238i	$-0.861596\pi$
$337$		−	5211.97i		−	0.842475i	0.906950	−	0.421238i	$-0.138404\pi$
$338$	−665.919	−	1140.89i	−0.107163	−	0.183599i
$339$	−12154.7	+	5034.66i	−1.94736	+	0.806623i
$340$	8609.05	−	6736.48i	1.37321	−	1.07452i
$341$	−637.812	+	1539.81i	−0.101289	+	0.244532i
$342$	1766.55	+	1342.28i	0.279310	+	0.212228i
$343$	4731.06	−	4731.06i	0.744761	−	0.744761i
$344$	−2626.45	−	6094.41i	−0.411654	−	0.955199i
$345$	11852.8	+	11852.8i	1.84966	+	1.84966i
$346$	−760.505	−	5572.52i	−0.118165	−	0.865839i
$347$	4987.20	+	2065.77i	0.771547	+	0.319585i	0.733499	−	0.679691i	$-0.237886\pi$
$347$	4987.20	+	2065.77i	0.771547	+	0.319585i	0.0380483	+	0.999276i	$0.487886\pi$
$348$	−3273.08	+	910.337i	−0.504182	+	0.140228i
$349$	3137.63	+	7574.92i	0.481243	+	1.16182i	0.959019	+	0.283341i	$0.0914429\pi$
$349$	3137.63	+	7574.92i	0.481243	+	1.16182i	−0.477776	+	0.878481i	$0.658557\pi$
$350$	−3272.65	−	860.311i	−0.499801	−	0.131387i
$351$	−5741.82			−0.873150
$352$	−846.331	+	7863.37i	−0.128152	+	1.19068i
$353$	8999.28			1.35689			0.678446	−	0.734650i	$-0.262654\pi$
$353$	8999.28			1.35689			0.678446	+	0.734650i	$0.262654\pi$
$354$	−8265.28	−	2172.77i	−1.24095	−	0.326218i
$355$	−2176.42	−	5254.35i	−0.325387	−	0.785555i
$356$	−655.229	−	2355.85i	−0.0975480	−	0.350730i
$357$	−9207.89	−	3814.03i	−1.36508	−	0.565434i
$358$	1231.72	+	9025.27i	0.181839	+	1.33240i
$359$	−4697.94	−	4697.94i	−0.690662	−	0.690662i	0.271715	−	0.962378i	$-0.412409\pi$
$359$	−4697.94	−	4697.94i	−0.690662	−	0.690662i	−0.962378	+	0.271715i	$0.912409\pi$
$360$	5366.13	−	13494.2i	0.785610	−	1.97557i
$361$	−4619.56	+	4619.56i	−0.673503	+	0.673503i
$362$	9528.32	+	7239.89i	1.38342	+	1.05116i
$363$	−1856.01	+	4480.80i	−0.268361	+	0.647882i
$364$	2632.18	+	3363.86i	0.379021	+	0.484379i
$365$	−7198.03	+	2981.52i	−1.03222	+	0.427561i
$366$	1053.28	+	1804.54i	0.150425	+	0.257718i
$367$		−	5942.35i		−	0.845199i	−0.906316	−	0.422600i	$-0.861118\pi$
$367$		−	5942.35i		−	0.845199i	0.906316	−	0.422600i	$-0.138882\pi$
$368$	8398.88	+	2080.76i	1.18973	+	0.294748i
$369$		−	17163.4i		−	2.42138i
$370$	8886.48	−	5186.89i	1.24861	−	0.728793i
$371$	−1627.17	+	673.997i	−0.227705	+	0.0943186i
$372$	310.268	−	2542.62i	0.0432436	−	0.354378i
$373$	−611.014	+	1475.12i	−0.0848180	+	0.204769i	−0.960598	−	0.277942i	$-0.910348\pi$
$373$	−611.014	+	1475.12i	−0.0848180	+	0.204769i	0.875780	+	0.482711i	$0.160348\pi$
$374$	6915.80	−	9101.79i	0.956170	−	1.25840i
$375$	2787.93	−	2787.93i	0.383915	−	0.383915i
$376$	−5223.96	−	5077.57i	−0.716503	−	0.696424i
$377$	−1488.04	−	1488.04i	−0.203284	−	0.203284i
$378$	−4966.18	+	677.756i	−0.675748	+	0.0922222i
$379$	3436.04	+	1423.25i	0.465692	+	0.192896i	0.603176	−	0.797608i	$-0.293902\pi$
$379$	3436.04	+	1423.25i	0.465692	+	0.192896i	−0.137484	+	0.990504i	$0.543902\pi$
$380$	−1857.70	−	1049.21i	−0.250784	−	0.141640i
$381$	4147.49	+	10012.9i	0.557697	+	1.34640i
$382$	−501.405	+	1907.36i	−0.0671574	+	0.255469i
$383$	−9327.55			−1.24443			−0.622213	−	0.782848i	$-0.713766\pi$
$383$	−9327.55			−1.24443			−0.622213	+	0.782848i	$0.713766\pi$
$384$	−1985.13	−	11991.6i	−0.263811	−	1.59360i
$385$	−8284.45			−1.09666
$386$	−1716.22	+	6528.54i	−0.226303	+	0.860866i
$387$	4876.34	+	11772.5i	0.640512	+	1.54633i
$388$	−5432.35	−	3068.12i	−0.710788	−	0.401444i
$389$	7840.37	+	3247.59i	1.02191	+	0.423288i	0.829785	−	0.558083i	$-0.188463\pi$
$389$	7840.37	+	3247.59i	1.02191	+	0.423288i	0.192123	+	0.981371i	$0.438463\pi$
$390$	14451.5	−	1972.26i	1.87636	−	0.256075i
$391$	−8843.44	−	8843.44i	−1.14382	−	1.14382i
$392$	−2891.75	−	2810.71i	−0.372590	−	0.362149i
$393$	−5056.06	+	5056.06i	−0.648968	+	0.648968i
$394$	4784.31	−	6296.56i	0.611751	−	0.805117i
$395$	−1381.61	+	3335.50i	−0.175991	+	0.424879i
$396$	1839.44	−	15074.0i	0.233422	−	1.91288i
$397$	6845.23	−	2835.39i	0.865370	−	0.358448i	0.0945649	−	0.995519i	$-0.469854\pi$
$397$	6845.23	−	2835.39i	0.865370	−	0.358448i	0.770805	+	0.637071i	$0.219854\pi$
$398$	−10159.3	+	5929.80i	−1.27949	+	0.746819i
$399$			1945.20i			0.244064i
$400$	−1434.36	+	5789.72i	−0.179295	+	0.723715i
$401$			5333.86i			0.664240i	0.943237	+	0.332120i	$0.107764\pi$
$401$			5333.86i			0.664240i	−0.943237	+	0.332120i	$0.892236\pi$
$402$	3395.25	+	5816.94i	0.421243	+	0.721698i
$403$	1465.89	−	607.190i	0.181193	−	0.0750528i
$404$	5584.84	+	7137.28i	0.687763	+	0.878943i
$405$	81.3857	−	196.482i	0.00998540	−	0.0241069i
$406$	−1462.68	−	1111.38i	−0.178796	−	0.135855i
$407$	7608.37	−	7608.37i	0.926616	−	0.926616i
$408$	−6491.75	+	16324.8i	−0.787720	+	1.98088i
$409$	−3906.82	−	3906.82i	−0.472322	−	0.472322i	0.430343	−	0.902665i	$-0.358393\pi$
$409$	−3906.82	−	3906.82i	−0.472322	−	0.472322i	−0.902665	+	0.430343i	$0.858393\pi$
$410$	2231.79	+	16353.2i	0.268830	+	1.96982i
$411$	−16744.1	−	6935.63i	−2.00955	−	0.832383i
$412$	−2072.77	−	7452.55i	−0.247859	−	0.891166i
$413$	−1768.41	−	4269.31i	−0.210696	−	0.508666i
$414$	−16068.5	−	4224.08i	−1.90755	−	0.501454i
$415$	−19674.3			−2.32716
$416$	5863.01	−	4723.58i	0.691004	−	0.556713i
$417$	3973.54			0.466631
$418$	−2157.74	−	567.223i	−0.252484	−	0.0663727i
$419$	510.706	+	1232.95i	0.0595456	+	0.143756i	0.950852	−	0.309646i	$-0.100210\pi$
$419$	510.706	+	1232.95i	0.0595456	+	0.143756i	−0.891306	+	0.453401i	$0.850210\pi$
$420$	12266.5	−	3411.68i	1.42511	−	0.396364i
$421$	−9078.42	−	3760.41i	−1.05096	−	0.435323i	−0.210727	−	0.977545i	$-0.567583\pi$
$421$	−9078.42	−	3760.41i	−1.05096	−	0.435323i	−0.840235	+	0.542222i	$0.817583\pi$
$422$	579.254	+	4244.42i	0.0668190	+	0.489609i
$423$	9891.11	+	9891.11i	1.13693	+	1.13693i
$424$	1228.70	+	2851.08i	0.140734	+	0.326558i
$425$	6096.17	−	6096.17i	0.695783	−	0.695783i
$426$	7277.67	+	5529.78i	0.827709	+	0.628917i
$427$	−432.358	+	1043.80i	−0.0490006	+	0.118298i
$428$	4767.17	−	3730.25i	0.538387	−	0.421282i
$429$	14091.3	−	5836.79i	1.58586	−	0.656883i
$430$	−6176.95	−	10582.7i	−0.692742	−	1.18685i
$431$		−	7684.54i		−	0.858820i	−0.903110	−	0.429410i	$-0.858722\pi$
$431$		−	7684.54i		−	0.858820i	0.903110	−	0.429410i	$-0.141278\pi$
$432$	1318.96	+	8736.12i	0.146895	+	0.972955i
$433$		−	989.963i		−	0.109872i	−0.998490	−	0.0549360i	$-0.982505\pi$
$433$		−	989.963i		−	0.109872i	0.998490	−	0.0549360i	$-0.0174955\pi$
$434$	1196.19	−	698.198i	0.132302	−	0.0772226i
$435$	−5795.46	+	2400.56i	−0.638784	+	0.264593i
$436$	−484.358	−	59.1047i	−0.0532031	−	0.00649221i
$437$	−934.103	+	2255.12i	−0.102252	+	0.246859i
$438$	7575.35	−	9969.81i	0.826402	−	1.08762i
$439$	1705.59	−	1705.59i	0.185429	−	0.185429i	−0.608287	−	0.793717i	$-0.708143\pi$
$439$	1705.59	−	1705.59i	0.185429	−	0.185429i	0.793717	+	0.608287i	$0.208143\pi$
$440$	207.500	+	14601.7i	0.0224822	+	1.58206i
$441$	5475.28	+	5475.28i	0.591219	+	0.591219i
$442$	−10782.4	+	1471.52i	−1.16033	+	0.158355i
$443$	14875.4	+	6161.58i	1.59537	+	0.660826i	0.990752	−	0.135687i	$-0.0433241\pi$
$443$	14875.4	+	6161.58i	1.59537	+	0.660826i	0.604622	+	0.796512i	$0.293324\pi$
$444$	−8132.23	+	14398.7i	−0.869231	+	1.53904i
$445$	−1727.84	−	4171.37i	−0.184062	−	0.444364i
$446$	791.141	−	3009.53i	0.0839947	−	0.319518i
$447$	25490.4			2.69721
$448$	4513.44	−	4777.55i	0.475982	−	0.503835i
$449$	1887.26			0.198364			0.0991819	−	0.995069i	$-0.468377\pi$
$449$	1887.26			0.198364			0.0991819	+	0.995069i	$0.468377\pi$
$450$	2911.84	−	11076.7i	0.305035	−	1.16036i
$451$	6604.84	+	15945.5i	0.689601	+	1.66484i
$452$	−6166.70	+	10918.6i	−0.641719	+	1.13621i
$453$	2878.87	+	1192.47i	0.298589	+	0.123680i
$454$	−10811.0	+	1475.42i	−1.11759	+	0.152522i
$455$	5576.74	+	5576.74i	0.574597	+	0.574597i
$456$	3428.49	−	48.7212i	0.352092	−	0.00500346i
$457$	−9275.37	+	9275.37i	−0.949417	+	0.949417i	−0.998781	−	0.0493636i	$-0.984281\pi$
$457$	−9275.37	+	9275.37i	−0.949417	+	0.949417i	0.0493636	+	0.998781i	$0.484281\pi$
$458$	−6619.59	+	8711.95i	−0.675356	+	0.888827i
$459$	4886.88	−	11798.0i	0.496950	−	1.19974i
$460$	15859.3	+	1935.26i	1.60748	+	0.196156i
$461$	6867.75	−	2844.71i	0.693846	−	0.287400i	−0.00775571	−	0.999970i	$-0.502469\pi$
$461$	6867.75	−	2844.71i	0.693846	−	0.287400i	0.701601	+	0.712570i	$0.252469\pi$
$462$	11498.8	−	6711.64i	1.15795	−	0.675874i
$463$			7678.71i			0.770756i	0.922759	+	0.385378i	$0.125929\pi$
$463$			7678.71i			0.770756i	−0.922759	+	0.385378i	$0.874071\pi$
$464$	−1922.22	+	2605.86i	−0.192321	+	0.260720i
$465$		−	4729.63i		−	0.471681i
$466$	−7397.45	−	12673.7i	−0.735365	−	1.25987i
$467$	−3867.05	+	1601.79i	−0.383182	+	0.158719i	−0.565955	−	0.824436i	$-0.691493\pi$
$467$	−3867.05	+	1601.79i	−0.383182	+	0.158719i	0.182773	+	0.983155i	$0.441493\pi$
$468$	−11385.5	+	8908.99i	−1.12456	+	0.879953i
$469$	−1393.71	+	3364.71i	−0.137219	+	0.331275i
$470$	−10710.4	−	8138.04i	−1.05113	−	0.798681i
$471$	−16847.9	+	16847.9i	−1.64822	+	1.64822i
$472$	−7480.53	+	3223.82i	−0.729490	+	0.314382i
$473$	−9060.64	−	9060.64i	−0.880780	−	0.880780i
$474$	−784.586	−	5748.97i	−0.0760279	−	0.557086i
$475$	−1554.56	−	643.919i	−0.150164	−	0.0622000i
$476$	−9152.14	+	2545.47i	−0.881276	+	0.245108i
$477$	−2281.24	−	5507.40i	−0.218974	−	0.528651i
$478$	15453.4	+	4062.37i	1.47871	+	0.388721i
$479$	5602.73			0.534436			0.267218	−	0.963636i	$-0.413896\pi$
$479$	5602.73			0.534436			0.267218	+	0.963636i	$0.413896\pi$
$480$	−6320.45	−	21534.8i	−0.601017	−	2.04776i
$481$	−10243.3			−0.971004
$482$	−13840.4	−	3638.35i	−1.30791	−	0.343822i
$483$	−5574.44	−	13457.9i	−0.525146	−	1.26782i
$484$	1238.69	+	4453.67i	0.116331	+	0.418264i
$485$	−10642.9	−	4408.43i	−0.996431	−	0.412735i
$486$	1471.77	+	10784.3i	0.137368	+	1.00655i
$487$	13338.0	+	13338.0i	1.24107	+	1.24107i	0.959556	+	0.281516i	$0.0908373\pi$
$487$	13338.0	+	13338.0i	1.24107	+	1.24107i	0.281516	+	0.959556i	$0.409163\pi$
$488$	1850.58	+	735.904i	0.171663	+	0.0682640i
$489$	−5894.23	+	5894.23i	−0.545085	+	0.545085i
$490$	−5928.78	−	4504.86i	−0.546602	−	0.415324i
$491$	6069.18	−	14652.3i	0.557837	−	1.34674i	−0.353637	−	0.935383i	$-0.615055\pi$
$491$	6069.18	−	14652.3i	0.557837	−	1.34674i	0.911475	−	0.411356i	$-0.134945\pi$
$492$	−16346.2	−	20890.1i	−1.49786	−	1.91422i
$493$	4324.03	−	1791.07i	0.395019	−	0.163622i
$494$	1070.67	+	1834.33i	0.0975133	+	0.167065i
$495$		−	28039.9i		−	2.54606i
$496$	−1260.56	−	2090.85i	−0.114115	−	0.189278i
$497$			4942.30i			0.446061i
$498$	27307.8	−	15939.1i	2.45721	−	1.43423i
$499$	3108.34	−	1287.52i	0.278855	−	0.115505i	−0.238873	−	0.971051i	$-0.576778\pi$
$499$	3108.34	−	1287.52i	0.278855	−	0.115505i	0.517728	+	0.855545i	$0.326778\pi$
$500$	455.197	−	3730.30i	0.0407141	−	0.333649i
$501$	−6884.53	+	16620.7i	−0.613928	+	1.48215i
$502$	−1816.93	+	2391.23i	−0.161541	+	0.212601i
$503$	−9569.65	+	9569.65i	−0.848289	+	0.848289i	−0.989920	−	0.141630i	$-0.954766\pi$
$503$	−9569.65	+	9569.65i	−0.848289	+	0.848289i	0.141630	+	0.989920i	$0.454766\pi$
$504$	−8795.84	+	9049.43i	−0.777377	+	0.799789i
$505$	11832.5	+	11832.5i	1.04265	+	1.04265i
$506$	16553.8	−	2259.17i	1.45436	−	0.198483i
$507$	3621.69	+	1500.15i	0.317248	+	0.131408i
$508$	8994.62	+	5080.05i	0.785575	+	0.443683i
$509$	4975.54	+	12012.0i	0.433275	+	1.04602i	0.978225	+	0.207549i	$0.0665487\pi$
$509$	4975.54	+	12012.0i	0.433275	+	1.04602i	−0.544950	+	0.838469i	$0.683451\pi$
$510$	−8247.26	+	31372.8i	−0.716068	+	2.72395i
$511$	6770.55			0.586128
$512$	−8533.67	−	7835.45i	−0.736599	−	0.676330i
$513$	−2492.36			−0.214504
$514$	734.415	−	2793.74i	0.0630227	−	0.239740i
$515$	−5465.89	−	13195.8i	−0.467681	−	1.12908i
$516$	17147.2	+	9684.50i	1.46291	+	0.826233i
$517$	−12995.6	−	5382.94i	−1.10550	−	0.457914i
$518$	−8859.55	+	1209.10i	−0.751479	+	0.102558i
$519$	11801.3	+	11801.3i	0.998114	+	0.998114i
$520$	9689.55	−	9968.91i	0.817144	−	0.840703i
$521$	11056.5	−	11056.5i	0.929743	−	0.929743i	−0.0679465	−	0.997689i	$-0.521645\pi$
$521$	11056.5	−	11056.5i	0.929743	−	0.929743i	0.997689	+	0.0679465i	$0.0216447\pi$
$522$	3761.63	−	4950.63i	0.315406	−	0.415102i
$523$	7704.74	−	18600.9i	0.644178	−	1.55518i	−0.176815	−	0.984244i	$-0.556580\pi$
$523$	7704.74	−	18600.9i	0.644178	−	1.55518i	0.820993	−	0.570938i	$-0.193420\pi$
$524$	−825.525	+	6765.11i	−0.0688230	+	0.563999i
$525$	9277.11	−	3842.71i	0.771212	−	0.319447i
$526$	3920.55	−	2288.36i	0.324989	−	0.189690i
$527$			3528.80i			0.291683i
$528$	−12117.5	−	20098.9i	−0.998765	−	1.65662i
$529$		−	6112.01i		−	0.502343i
$530$	2889.69	+	4950.79i	0.236830	+	0.405752i
$531$	14450.1	−	5985.42i	1.18094	−	0.489162i
$532$	1142.56	+	1460.16i	0.0931130	+	0.118996i
$533$	6287.74	−	15179.9i	0.510980	−	1.23361i
$534$	5777.67	+	4390.04i	0.468210	+	0.355759i
$535$	7903.20	−	7903.20i	0.638664	−	0.638664i
$536$	5965.34	+	2372.19i	0.480716	+	0.191162i
$537$	−19113.5	−	19113.5i	−1.53596	−	1.53596i
$538$	−919.485	−	6737.43i	−0.0736837	−	0.539909i
$539$	−7193.77	−	2979.76i	−0.574875	−	0.238121i
$540$	4371.35	+	15717.0i	0.348357	+	1.25250i
$541$	−3094.21	−	7470.07i	−0.245897	−	0.593648i	0.751951	−	0.659219i	$-0.229113\pi$
$541$	−3094.21	−	7470.07i	−0.245897	−	0.593648i	−0.997848	+	0.0655712i	$0.979113\pi$
$542$	5088.71	+	1337.72i	0.403282	+	0.106014i
$543$	−35511.3			−2.80651
$544$	4715.73	+	16067.2i	0.371664	+	1.26632i
$545$	−900.975			−0.0708138
$546$	−12258.5	−	3222.50i	−0.960832	−	0.252583i
$547$	6470.84	+	15622.0i	0.505801	+	1.22111i	0.946280	+	0.323349i	$0.104809\pi$
$547$	6470.84	+	15622.0i	0.505801	+	1.22111i	−0.440479	+	0.897763i	$0.645191\pi$
$548$	−16642.7	+	4628.81i	−1.29734	+	0.360827i
$549$	−3532.90	−	1463.38i	−0.274646	−	0.113762i
$550$	1557.35	+	11411.3i	0.120737	+	0.884690i
$551$	−645.918	−	645.918i	−0.0499401	−	0.0499401i
$552$	−23580.4	+	10162.2i	−1.81821	+	0.783576i
$553$	2218.49	−	2218.49i	0.170596	−	0.170596i
$554$	−13603.4	−	10336.2i	−1.04323	−	0.792680i
$555$	−11684.8	+	28209.6i	−0.893678	+	2.15753i
$556$	2982.73	−	2333.95i	0.227511	−	0.178024i
$557$	−10401.9	+	4308.63i	−0.791283	+	0.327760i	−0.741459	−	0.670998i	$-0.765866\pi$
$557$	−10401.9	+	4308.63i	−0.791283	+	0.327760i	−0.0498238	+	0.998758i	$0.515866\pi$
$558$	2363.15	+	4048.69i	0.179283	+	0.307159i
$559$			12198.5i			0.922971i
$560$	7203.92	−	9766.00i	0.543609	−	0.736944i
$561$			33921.7i			2.55290i
$562$	6012.55	−	3509.43i	0.451289	−	0.263410i
$563$	−1760.24	+	729.116i	−0.131768	+	0.0545801i	−0.447593	−	0.894237i	$-0.647719\pi$
$563$	−1760.24	+	729.116i	−0.131768	+	0.0545801i	0.315825	+	0.948817i	$0.397719\pi$
$564$	21459.0	+	2618.57i	1.60210	+	0.195499i
$565$	−8860.61	+	21391.4i	−0.659768	+	1.59282i
$566$	4780.37	−	6291.38i	0.355007	−	0.467220i
$567$	−130.683	+	130.683i	−0.00967931	+	0.00967931i
$568$	8711.00	−	123.789i	0.643496	−	0.00914451i
$569$	8079.71	+	8079.71i	0.595288	+	0.595288i	0.939055	−	0.343767i	$-0.111703\pi$
$569$	8079.71	+	8079.71i	0.595288	+	0.595288i	−0.343767	+	0.939055i	$0.611703\pi$
$570$	6273.01	−	856.104i	0.460961	−	0.0629092i
$571$	−16823.9	−	6968.69i	−1.23303	−	0.510737i	−0.331498	−	0.943456i	$-0.607554\pi$
$571$	−16823.9	−	6968.69i	−1.23303	−	0.510737i	−0.901529	+	0.432719i	$0.857554\pi$
$572$	7149.19	−	12658.2i	0.522592	−	0.925289i
$573$	−2239.60	−	5406.87i	−0.163282	−	0.394198i
$574$	3646.54	−	13871.6i	0.265163	−	1.00869i
$575$	12600.5			0.913875
$576$	16170.3	+	15276.4i	1.16973	+	1.10506i
$577$	−4098.72			−0.295723			−0.147861	−	0.989008i	$-0.547239\pi$
$577$	−4098.72			−0.295723			−0.147861	+	0.989008i	$0.547239\pi$
$578$	2620.38	−	9968.00i	0.188570	−	0.717326i
$579$	−7665.74	−	18506.7i	−0.550220	−	1.32835i
$580$	−2940.32	+	5206.07i	−0.210501	+	0.372707i
$581$	15795.7	+	6542.81i	1.12791	+	0.467197i
$582$	18343.8	−	2503.45i	1.30648	−	0.178301i
$583$	4238.73	+	4238.73i	0.301115	+	0.301115i
$584$	−169.581	−	11933.4i	−0.0120160	−	0.845558i
$585$	−18875.3	+	18875.3i	−1.33401	+	1.33401i
$586$	−12096.6	+	15920.1i	−0.852739	+	1.12228i
$587$	−437.187	+	1055.46i	−0.0307404	+	0.0742139i	−0.938504	−	0.345268i	$-0.887788\pi$
$587$	−437.187	+	1055.46i	−0.0307404	+	0.0742139i	0.907764	+	0.419482i	$0.137788\pi$
$588$	11878.7	+	1449.52i	0.833112	+	0.101662i
$589$	636.300	−	263.564i	0.0445132	−	0.0184380i
$590$	−12989.7	+	7581.85i	−0.906400	+	0.529051i
$591$			23466.8i			1.63332i
$592$	2352.99	+	15585.0i	0.163357	+	1.08199i
$593$		−	26161.0i		−	1.81164i	−0.423661	−	0.905821i	$-0.639255\pi$
$593$		−	26161.0i		−	1.81164i	0.423661	−	0.905821i	$-0.360745\pi$
$594$	8599.56	+	14733.3i	0.594014	+	1.01770i
$595$	−16205.2	+	6712.41i	−1.11655	+	0.462491i
$596$	19134.3	−	14972.4i	1.31505	−	1.02901i
$597$	13358.4	−	32250.0i	0.915783	−	2.21090i
$598$	−12664.1	−	9622.57i	−0.866012	−	0.658021i
$599$	−12392.1	+	12392.1i	−0.845288	+	0.845288i	−0.989541	−	0.144253i	$-0.953922\pi$
$599$	−12392.1	+	12392.1i	−0.845288	+	0.845288i	0.144253	+	0.989541i	$0.453922\pi$
$600$	−7005.28	−	16255.0i	−0.476649	−	1.10601i
$601$	5696.78	+	5696.78i	0.386650	+	0.386650i	0.873491	−	0.486841i	$-0.161851\pi$
$601$	5696.78	+	5696.78i	0.386650	+	0.386650i	−0.486841	+	0.873491i	$0.661851\pi$
$602$	1439.89	+	10550.6i	0.0974844	+	0.714306i
$603$	−11388.3	−	4717.20i	−0.769103	−	0.318573i
$604$	2861.44	−	795.847i	0.192765	−	0.0536135i
$605$	3266.43	+	7885.87i	0.219503	+	0.529928i
$606$	−26009.5	−	6837.34i	−1.74350	−	0.458330i
$607$	19674.4			1.31559			0.657793	−	0.753199i	$-0.271490\pi$
$607$	19674.4			1.31559			0.657793	+	0.753199i	$0.271490\pi$
$608$	2544.97	−	2050.37i	0.169757	−	0.136766i
$609$	5451.28			0.362721
$610$	3556.42	+	934.908i	0.236058	+	0.0620546i
$611$	5124.50	+	12371.6i	0.339305	+	0.819154i
$612$	−8615.50	−	30976.7i	−0.569054	−	2.04601i
$613$	25148.3	+	10416.7i	1.65698	+	0.686343i	0.997841	−	0.0656781i	$-0.0209210\pi$
$613$	25148.3	+	10416.7i	1.65698	+	0.686343i	0.659139	+	0.752021i	$0.270921\pi$
$614$	−9.18649	−	67.3130i	−0.000603806	−	0.00442432i
$615$	−34632.4	−	34632.4i	−2.27075	−	2.27075i
$616$	4689.28	−	11792.1i	0.306715	−	0.771296i
$617$	5951.82	−	5951.82i	0.388349	−	0.388349i	−0.485749	−	0.874098i	$-0.661453\pi$
$617$	5951.82	−	5951.82i	0.388349	−	0.388349i	0.874098	+	0.485749i	$0.161453\pi$
$618$	18277.2	+	13887.5i	1.18967	+	0.903946i
$619$	2222.03	−	5364.46i	0.144283	−	0.348329i	−0.835173	−	0.549987i	$-0.814633\pi$
$619$	2222.03	−	5364.46i	0.144283	−	0.348329i	0.979456	+	0.201658i	$0.0646328\pi$
$620$	−2778.06	−	3550.29i	−0.179951	−	0.229972i
$621$	17243.5	−	7142.47i	1.11426	−	0.461542i
$622$	−8510.31	−	14580.4i	−0.548605	−	0.939903i
$623$			3923.64i			0.252323i
$624$	−5372.74	+	21686.8i	−0.344682	+	1.39129i
$625$		−	18588.8i		−	1.18968i
$626$	−21041.6	+	12281.6i	−1.34343	+	0.784140i
$627$	6116.62	−	2533.59i	0.389592	−	0.161374i
$628$	−2750.83	+	22542.8i	−0.174793	+	1.43241i
$629$	8718.08	−	21047.3i	0.552643	−	1.33420i
$630$	−14097.5	+	18553.5i	−0.891520	+	1.17332i
$631$	22236.1	−	22236.1i	1.40286	−	1.40286i	0.612027	−	0.790837i	$-0.290354\pi$
$631$	22236.1	−	22236.1i	1.40286	−	1.40286i	0.790837	−	0.612027i	$-0.209646\pi$
$632$	−3965.73	−	3854.60i	−0.249602	−	0.242607i
$633$	−8988.73	−	8988.73i	−0.564407	−	0.564407i
$634$	12162.7	−	1659.90i	0.761899	−	0.103980i
$635$	17622.0	+	7299.27i	1.10127	+	0.456162i
$636$	−8021.75	−	4530.58i	−0.500130	−	0.282468i
$637$	2836.70	+	6848.39i	0.176443	+	0.425970i
$638$	−1589.60	+	6046.90i	−0.0986410	+	0.375234i
$639$	−16727.9			−1.03560
$640$	−17393.4	−	12452.6i	−1.07427	−	0.769112i
$641$	−3642.24			−0.224430			−0.112215	−	0.993684i	$-0.535795\pi$
$641$	−3642.24			−0.224430			−0.112215	+	0.993684i	$0.535795\pi$
$642$	−4566.83	+	17372.4i	−0.280745	+	1.06796i
$643$	−7521.88	−	18159.4i	−0.461328	−	1.11375i	−0.967852	−	0.251519i	$-0.919070\pi$
$643$	−7521.88	−	18159.4i	−0.461328	−	1.11375i	0.506524	−	0.862226i	$-0.330930\pi$
$644$	−12089.2	−	6827.85i	−0.739724	−	0.417787i
$645$	33594.2	+	13915.2i	2.05080	+	0.849471i
$646$	−4680.33	+	638.744i	−0.285054	+	0.0389026i
$647$	−16784.8	−	16784.8i	−1.01991	−	1.01991i	−0.999798	−	0.0201092i	$-0.993599\pi$
$647$	−16784.8	−	16784.8i	−1.01991	−	1.01991i	−0.0201092	−	0.999798i	$-0.506401\pi$
$648$	233.607	+	227.061i	0.0141620	+	0.0137651i
$649$	−11121.4	+	11121.4i	−0.672655	+	0.672655i
$650$	6633.27	−	8729.95i	0.400274	−	0.526795i
$651$	−1572.87	+	3797.24i	−0.0946937	+	0.228611i
$652$	−962.377	+	7886.60i	−0.0578061	+	0.473717i
$653$	−12553.7	+	5199.89i	−0.752316	+	0.311620i	−0.725686	−	0.688026i	$-0.758478\pi$
$653$	−12553.7	+	5199.89i	−0.752316	+	0.311620i	−0.0266300	+	0.999645i	$0.508478\pi$
$654$	1250.55	−	729.924i	0.0747711	−	0.0436426i
$655$			12584.1i			0.750688i
$656$	−24540.5	−	6079.73i	−1.46059	−	0.361850i
$657$			22915.9i			1.36078i
$658$	5892.59	+	10095.5i	0.349114	+	0.598123i
$659$	−7775.94	+	3220.90i	−0.459647	+	0.190392i	−0.600478	−	0.799642i	$-0.705023\pi$
$659$	−7775.94	+	3220.90i	−0.459647	+	0.190392i	0.140830	+	0.990034i	$0.455023\pi$
$660$	−26704.9	−	34128.2i	−1.57498	−	2.01278i
$661$	1900.75	−	4588.81i	0.111847	−	0.270021i	−0.858038	−	0.513586i	$-0.828317\pi$
$661$	1900.75	−	4588.81i	0.111847	−	0.270021i	0.969885	+	0.243564i	$0.0783168\pi$
$662$	21904.5	+	16643.6i	1.28601	+	0.977151i
$663$	22834.6	−	22834.6i	1.33759	−	1.33759i
$664$	11136.3	−	28004.5i	0.650863	−	1.63672i
$665$	2420.71	+	2420.71i	0.141160	+	0.141160i
$666$	−4092.37	−	29986.4i	−0.238102	−	1.74467i
$667$	6319.82	+	2617.76i	0.366873	+	0.151964i
$668$	4594.71	+	16520.1i	0.266130	+	0.956858i
$669$	3533.75	+	8531.23i	0.204219	+	0.493029i
$670$	11464.1	+	3013.68i	0.661042	+	0.173774i
$671$	3845.36			0.221234
$672$	−2087.09	+	19391.4i	−0.119808	+	1.11315i
$673$	−9638.42			−0.552056			−0.276028	−	0.961150i	$-0.589018\pi$
$673$	−9638.42			−0.552056			−0.276028	+	0.961150i	$0.589018\pi$
$674$	14257.3	+	3747.94i	0.814792	+	0.214192i
$675$	4923.62	+	11886.7i	0.280756	+	0.677805i
$676$	3599.76	−	1001.20i	0.204811	−	0.0569638i
$677$	−27908.0	−	11559.9i	−1.58433	−	0.656251i	−0.595239	−	0.803549i	$-0.702943\pi$
$677$	−27908.0	−	11559.9i	−1.58433	−	0.656251i	−0.989092	+	0.147297i	$0.952943\pi$
$678$	−5031.75	−	36869.6i	−0.285019	−	2.08845i
$679$	7078.72	+	7078.72i	0.400083	+	0.400083i
$680$	12236.8	+	28394.2i	0.690086	+	1.60127i
$681$	22895.2	−	22895.2i	1.28832	−	1.28832i
$682$	−3753.49	−	2852.01i	−0.210746	−	0.160131i
$683$	−11978.8	+	28919.3i	−0.671090	+	1.62015i	0.108671	+	0.994078i	$0.465340\pi$
$683$	−11978.8	+	28919.3i	−0.671090	+	1.62015i	−0.779761	+	0.626077i	$0.784660\pi$
$684$	−4942.11	+	3867.14i	−0.276266	+	0.216175i
$685$	−29468.3	+	12206.2i	−1.64369	+	0.680838i
$686$	9539.64	+	16343.9i	0.530940	+	0.909638i
$687$		−	32468.8i		−	1.80315i
$688$	18559.9	−	2802.13i	1.02847	−	0.155276i
$689$		−	5706.67i		−	0.315540i
$690$	−40946.5	+	23899.8i	−2.25914	+	1.31862i
$691$	−7238.99	+	2998.49i	−0.398530	+	0.165076i	−0.572941	−	0.819596i	$-0.694198\pi$
$691$	−7238.99	+	2998.49i	−0.398530	+	0.165076i	0.174412	+	0.984673i	$0.444198\pi$
$692$	15790.4	+	1926.86i	0.867431	+	0.105850i
$693$	−9324.84	+	22512.2i	−0.511142	+	1.23401i
$694$	−9237.18	+	12156.9i	−0.505243	+	0.664943i
$695$	4944.89	−	4944.89i	0.269885	−	0.269885i
$696$	−136.538	−	9608.09i	−0.00743598	−	0.523267i
$697$	25839.4	+	25839.4i	1.40422	+	1.40422i
$698$	−22977.4	+	3135.82i	−1.24600	+	0.170047i
$699$	40232.0	+	16664.6i	2.17699	+	0.901738i
$700$	4706.74	−	8333.64i	0.254140	−	0.449974i
$701$	3609.66	+	8714.49i	0.194486	+	0.469532i	0.990797	−	0.135356i	$-0.0432179\pi$
$701$	3609.66	+	8714.49i	0.194486	+	0.469532i	−0.796311	+	0.604888i	$0.793218\pi$
$702$	4128.95	−	15706.7i	0.221990	−	0.844459i
$703$	−4446.32			−0.238543
$704$	−20901.6	−	7969.69i	−1.11897	−	0.426661i
$705$	39916.7			2.13241
$706$	−6471.40	+	24617.4i	−0.344978	+	1.31231i
$707$	−5564.88	−	13434.8i	−0.296024	−	0.714665i
$708$	11887.2	−	21047.1i	0.630998	−	1.11723i
$709$	−8921.05	−	3695.22i	−0.472549	−	0.195736i	0.133683	−	0.991024i	$-0.457320\pi$
$709$	−8921.05	−	3695.22i	−0.472549	−	0.195736i	−0.606232	+	0.795288i	$0.707320\pi$
$710$	15938.3	−	2175.16i	0.842469	−	0.114975i
$711$	7508.77	+	7508.77i	0.396063	+	0.396063i
$712$	6915.58	−	98.2751i	0.364006	−	0.00517277i
$713$	−3646.95	+	3646.95i	−0.191556	+	0.191556i
$714$	17054.7	−	22445.4i	0.893914	−	1.17647i
$715$	10272.3	−	24799.5i	0.537290	−	1.29713i
$716$	−25574.2	−	3120.74i	−1.33485	−	0.162888i
$717$	−43806.4	+	18145.2i	−2.28170	+	0.945111i
$718$	16229.5	−	9472.86i	0.843563	−	0.492373i
$719$			36176.8i			1.87645i	0.346025	+	0.938225i	$0.387531\pi$
$719$			36176.8i			1.87645i	−0.346025	+	0.938225i	$0.612469\pi$
$720$	33054.4	+	24382.7i	1.71092	+	1.26207i
$721$			12412.1i			0.641126i
$722$	−9314.81	−	15958.7i	−0.480141	−	0.822605i
$723$	39233.9	−	16251.2i	2.01815	−	0.835947i
$724$	−26656.5	+	20858.4i	−1.36834	+	1.07071i
$725$	−1804.54	+	4356.53i	−0.0924397	+	0.223169i
$726$	−10922.5	−	8299.24i	−0.558365	−	0.424262i
$727$	−25292.8	+	25292.8i	−1.29031	+	1.29031i	−0.355723	+	0.934591i	$0.615765\pi$
$727$	−25292.8	+	25292.8i	−1.29031	+	1.29031i	−0.934591	+	0.355723i	$0.884235\pi$
$728$	−11094.6	+	4781.34i	−0.564826	+	0.243418i
$729$	−22563.8	−	22563.8i	−1.14636	−	1.14636i
$730$	−2979.80	−	21834.1i	−0.151078	−	1.10701i
$731$	−25064.8	−	10382.2i	−1.26820	−	0.525306i
$732$	−5693.70	+	1583.58i	−0.287494	+	0.0799602i
$733$	−11236.5	−	27127.4i	−0.566208	−	1.36695i	−0.904729	−	0.425989i	$-0.859926\pi$
$733$	−11236.5	−	27127.4i	−0.566208	−	1.36695i	0.338520	−	0.940959i	$-0.390074\pi$
$734$	16255.2	+	4273.16i	0.817427	+	0.214884i
$735$	22096.1			1.10888
$736$	−11731.6	+	21478.8i	−0.587542	+	1.07570i
$737$	12395.5			0.619532
$738$	46950.2	+	12342.2i	2.34182	+	0.615615i
$739$	2750.78	+	6640.98i	0.136927	+	0.330572i	0.977438	−	0.211224i	$-0.0677448\pi$
$739$	2750.78	+	6640.98i	0.136927	+	0.330572i	−0.840510	+	0.541795i	$0.817745\pi$
$740$	7798.38	+	28038.8i	0.387398	+	1.39287i
$741$	−5822.96	−	2411.95i	−0.288680	−	0.119575i
$742$	−673.607	−	4935.78i	−0.0333274	−	0.244203i
$743$	−21298.6	−	21298.6i	−1.05164	−	1.05164i	−0.998592	−	0.0530520i	$-0.983105\pi$
$743$	−21298.6	−	21298.6i	−1.05164	−	1.05164i	−0.0530520	−	0.998592i	$-0.516895\pi$
$744$	6732.19	+	2677.14i	0.331739	+	0.131920i
$745$	31721.6	−	31721.6i	1.55999	−	1.55999i
$746$	−3595.79	−	2732.18i	−0.176476	−	0.134092i
$747$	−22145.1	+	53462.9i	−1.08467	+	2.61861i
$748$	19924.7	+	25463.2i	0.973955	+	1.24469i
$749$	−8973.44	+	3716.92i	−0.437760	+	0.181326i
$750$	5621.54	+	9631.15i	0.273693	+	0.468906i
$751$		−	33892.3i		−	1.64680i	−0.567462	−	0.823400i	$-0.692075\pi$
$751$		−	33892.3i		−	1.64680i	0.567462	−	0.823400i	$-0.307925\pi$
$752$	17646.2	−	10638.8i	0.855705	−	0.515900i
$753$		−	8911.94i		−	0.431300i
$754$	5140.57	−	3000.47i	0.248287	−	0.144921i
$755$	5066.59	−	2098.65i	0.244228	−	0.101163i
$756$	1717.20	−	14072.3i	0.0826110	−	0.676991i
$757$	1447.14	−	3493.72i	0.0694813	−	0.167743i	−0.885324	−	0.464975i	$-0.846063\pi$
$757$	1447.14	−	3493.72i	0.0694813	−	0.167743i	0.954805	+	0.297232i	$0.0960634\pi$
$758$	−6364.16	+	8375.78i	−0.304956	+	0.401348i
$759$	−35057.3	+	35057.3i	−1.67655	+	1.67655i
$760$	4205.97	−	4327.23i	0.200745	−	0.206533i
$761$	−8184.04	−	8184.04i	−0.389844	−	0.389844i	0.484788	−	0.874632i	$-0.338897\pi$
$761$	−8184.04	−	8184.04i	−0.389844	−	0.389844i	−0.874632	+	0.484788i	$0.838897\pi$
$762$	−30372.7	+	4145.09i	−1.44395	+	0.197061i
$763$	723.359	+	299.625i	0.0343216	+	0.0142165i
$764$	−4857.00	−	2743.17i	−0.230000	−	0.129901i
$765$	−22719.1	−	54848.7i	−1.07374	−	2.59223i
$766$	6707.46	−	25515.4i	0.316384	−	1.20354i
$767$	14972.9			0.704878
$768$	34230.4	+	3192.88i	1.60831	+	0.150017i
$769$	−29464.8			−1.38170			−0.690850	−	0.722998i	$-0.742763\pi$
$769$	−29464.8			−1.38170			−0.690850	+	0.722998i	$0.742763\pi$
$770$	5957.37	−	22662.0i	0.278816	−	1.06063i
$771$	3280.38	+	7919.53i	0.153229	+	0.369928i
$772$	−16624.6	−	9389.38i	−0.775043	−	0.437735i
$773$	24119.4	+	9990.57i	1.12227	+	0.464859i	0.865146	−	0.501520i	$-0.167226\pi$
$773$	24119.4	+	9990.57i	1.12227	+	0.464859i	0.257122	+	0.966379i	$0.417226\pi$
$774$	−35710.2	+	4873.52i	−1.65837	+	0.226324i
$775$	−2514.00	−	2514.00i	−0.116523	−	0.116523i
$776$	12299.2	−	12653.8i	0.568965	−	0.585369i
$777$	18762.5	−	18762.5i	0.866284	−	0.866284i
$778$	−14521.8	+	19111.9i	−0.669190	+	0.880712i
$779$	2729.33	−	6589.19i	0.125531	−	0.303058i
$780$	−4997.03	+	40950.3i	−0.229388	+	1.87981i
$781$	15540.9	−	6437.26i	0.712034	−	0.294934i
$782$	30550.4	−	17831.8i	1.39704	−	0.815426i
$783$			6984.67i			0.318789i
$784$	9768.14	−	5889.16i	0.444977	−	0.268274i
$785$			41932.8i			1.90656i
$786$	−10195.0	−	17466.6i	−0.462649	−	0.792638i
$787$	−4642.61	+	1923.03i	−0.210281	+	0.0871013i	−0.485338	−	0.874327i	$-0.661303\pi$
$787$	−4642.61	+	1923.03i	−0.210281	+	0.0871013i	0.275057	+	0.961428i	$0.411303\pi$
$788$	13783.8	+	17615.3i	0.623130	+	0.796343i
$789$	−5155.11	+	12445.5i	−0.232607	+	0.561562i
$790$	−8130.71	−	6177.94i	−0.366174	−	0.278230i
$791$	14227.7	−	14227.7i	0.639543	−	0.639543i
$792$	39912.1	+	15871.5i	1.79068	+	0.712084i
$793$	−2588.53	−	2588.53i	−0.115916	−	0.115916i
$794$	2833.75	+	20764.0i	0.126657	+	0.928067i
$795$	−15716.0	−	6509.76i	−0.701117	−	0.290412i
$796$	−8915.34	−	32054.7i	−0.396980	−	1.42732i
$797$	3908.47	+	9435.87i	0.173708	+	0.419367i	0.986624	−	0.163013i	$-0.0521213\pi$
$797$	3908.47	+	9435.87i	0.173708	+	0.419367i	−0.812916	+	0.582381i	$0.802121\pi$
$798$	−5321.07	−	1398.80i	−0.236045	−	0.0620512i
$799$	−29782.1			−1.31867
$800$	−14806.3	−	8087.08i	−0.654350	−	0.357402i
$801$	−13280.1			−0.585805
$802$	−14590.7	−	3835.59i	−0.642414	−	0.168877i
$803$	−8818.53	−	21289.8i	−0.387545	−	0.935618i
$804$	−18353.7	+	5104.69i	−0.805081	+	0.223916i
$805$	−23684.8	−	9810.58i	−1.03700	−	0.429537i
$806$	606.839	+	4446.54i	0.0265198	+	0.194321i
$807$	14268.4	+	14268.4i	0.622392	+	0.622392i
$808$	−23540.0	+	10144.8i	−1.02492	+	0.441700i
$809$	−16382.1	+	16382.1i	−0.711945	+	0.711945i	−0.966942	−	0.254997i	$-0.917925\pi$
$809$	−16382.1	+	16382.1i	−0.711945	+	0.711945i	0.254997	+	0.966942i	$0.417925\pi$
$810$	478.951	+	363.920i	0.0207761	+	0.0157862i
$811$	7236.38	−	17470.2i	0.313322	−	0.756425i	−0.686256	−	0.727360i	$-0.740747\pi$
$811$	7236.38	−	17470.2i	0.313322	−	0.756425i	0.999578	−	0.0290650i	$-0.00925299\pi$
$812$	4091.99	−	3201.93i	0.176848	−	0.138382i
$813$	−14425.2	+	5975.11i	−0.622280	+	0.257757i
$814$	15341.4	+	26283.8i	0.660584	+	1.13175i
$815$			14670.2i			0.630521i
$816$	−39988.1	−	29497.3i	−1.71552	−	1.26546i
$817$			5295.03i			0.226744i
$818$	13496.5	−	7877.65i	0.576886	−	0.336718i
$819$	21431.3	−	8877.15i	0.914373	−	0.378746i
$820$	−46338.8	−	5654.58i	−1.97344	−	0.240813i
$821$	−4916.31	+	11869.0i	−0.208990	+	0.504546i	−0.993265	−	0.115868i	$-0.963035\pi$
$821$	−4916.31	+	11869.0i	−0.208990	+	0.504546i	0.784275	+	0.620413i	$0.213035\pi$
$822$	31013.0	−	40815.8i	1.31594	−	1.73189i
$823$	25989.7	−	25989.7i	1.10078	−	1.10078i	0.106465	−	0.994316i	$-0.466047\pi$
$823$	25989.7	−	25989.7i	1.10078	−	1.10078i	0.994316	−	0.106465i	$-0.0339532\pi$
$824$	21876.9	−	310.886i	0.924899	−	0.0131435i
$825$	−24166.6	−	24166.6i	−1.01984	−	1.01984i
$826$	12950.3	−	1767.38i	0.545519	−	0.0744493i
$827$	−16783.7	−	6952.03i	−0.705715	−	0.292317i	0.000815266	−	1.00000i	$-0.499740\pi$
$827$	−16783.7	−	6952.03i	−0.705715	−	0.292317i	−0.706530	+	0.707683i	$0.749740\pi$
$828$	23109.8	−	40917.7i	0.969953	−	1.71738i
$829$	5184.19	+	12515.7i	0.217194	+	0.524354i	0.994496	−	0.104774i	$-0.0334120\pi$
$829$	5184.19	+	12515.7i	0.217194	+	0.524354i	−0.777302	+	0.629128i	$0.783412\pi$
$830$	14147.8	−	53818.8i	0.591660	−	2.25070i
$831$	50698.7			2.11639
$832$	8705.19	+	19434.9i	0.362738	+	0.809837i
$833$	−16486.0			−0.685723
$834$	−2857.38	+	10869.6i	−0.118637	+	0.451298i
$835$	12116.2	+	29251.2i	0.502155	+	1.21231i
$836$	3103.27	−	5494.57i	0.128384	−	0.227313i
$837$	−4865.37	−	2015.30i	−0.200922	−	0.0832247i
$838$	−3739.98	+	510.410i	−0.154171	+	0.0210404i
$839$	−248.606	−	248.606i	−0.0102298	−	0.0102298i	0.701973	−	0.712203i	$-0.252303\pi$
$839$	−248.606	−	248.606i	−0.0102298	−	0.0102298i	−0.712203	+	0.701973i	$0.752303\pi$
$840$	511.703	+	36008.3i	0.0210184	+	1.47905i
$841$	15435.5	−	15435.5i	0.632887	−	0.632887i
$842$	16814.9	−	22129.8i	0.688216	−	0.905752i
$843$	−7905.88	+	19086.5i	−0.323005	+	0.779802i
$844$	−12027.1	−	1467.63i	−0.490509	−	0.0598553i
$845$	6373.89	−	2640.15i	0.259490	−	0.107484i
$846$	−34169.7	+	19944.3i	−1.38863	+	0.810519i
$847$		−	7417.54i		−	0.300909i
$848$	−8682.64	+	1310.89i	−0.351608	+	0.0530849i
$849$			23447.5i			0.947840i
$850$	12292.2	+	21059.8i	0.496024	+	0.849817i
$851$	30761.9	−	12742.0i	1.23914	−	0.513267i
$852$	−20360.0	+	15931.5i	−0.818689	+	0.640615i
$853$	−5935.21	+	14328.9i	−0.238239	+	0.575159i	−0.997101	−	0.0760921i	$-0.975756\pi$
$853$	−5935.21	+	14328.9i	−0.238239	+	0.575159i	0.758862	+	0.651251i	$0.225756\pi$
$854$	−2544.41	−	1933.31i	−0.101953	−	0.0774667i
$855$	−8193.23	+	8193.23i	−0.327722	+	0.327722i
$856$	6775.98	+	15723.0i	0.270559	+	0.627803i
$857$	6193.30	+	6193.30i	0.246860	+	0.246860i	0.819681	−	0.572821i	$-0.194151\pi$
$857$	6193.30	+	6193.30i	0.246860	+	0.246860i	−0.572821	+	0.819681i	$0.694151\pi$
$858$	5833.41	+	42743.7i	0.232109	+	1.70075i
$859$	9296.87	+	3850.89i	0.369272	+	0.152958i	0.559600	−	0.828763i	$-0.310955\pi$
$859$	9296.87	+	3850.89i	0.369272	+	0.152958i	−0.190327	+	0.981721i	$0.560955\pi$
$860$	33390.8	−	9286.93i	1.32397	−	0.368234i
$861$	16287.8	+	39322.3i	0.644701	+	1.55644i
$862$	21021.0	+	5525.97i	0.830600	+	0.218347i
$863$	28317.6			1.11697			0.558483	−	0.829516i	$-0.311384\pi$
$863$	28317.6			1.11697			0.558483	+	0.829516i	$0.311384\pi$
$864$	−24846.0	−	2674.16i	−0.978331	−	0.105297i
$865$	29372.5			1.15456
$866$	2708.03	+	711.885i	0.106262	+	0.0279340i
$867$	11704.3	+	28256.7i	0.458477	+	1.10686i
$868$	1049.73	+	3774.25i	0.0410485	+	0.147588i
$869$	−9865.51	−	4086.43i	−0.385114	−	0.159520i
$870$	−2399.17	−	17579.7i	−0.0934937	−	0.685065i
$871$	−8344.15	−	8344.15i	−0.324605	−	0.324605i
$872$	509.983	−	1282.45i	0.0198053	−	0.0498043i
$873$	−23958.9	+	23958.9i	−0.928851	+	0.928851i
$874$	−5497.15	−	4176.89i	−0.212750	−	0.161654i
$875$	−2307.57	+	5570.98i	−0.0891546	+	0.215238i
$876$	21824.8	+	27891.6i	0.841773	+	1.07576i
$877$	43155.1	−	17875.4i	1.66162	−	0.688267i	0.663423	−	0.748244i	$-0.269103\pi$
$877$	43155.1	−	17875.4i	1.66162	−	0.688267i	0.998200	+	0.0599774i	$0.0191029\pi$
$878$	3439.13	+	5892.12i	0.132193	+	0.226480i
$879$		−	59333.1i		−	2.27674i
$880$	−40091.9	−	9932.48i	−1.53579	−	0.380482i
$881$			9845.05i			0.376491i	0.982122	+	0.188245i	$0.0602800\pi$
$881$			9845.05i			0.376491i	−0.982122	+	0.188245i	$0.939720\pi$
$882$	−18914.8	+	11040.3i	−0.722104	+	0.421480i
$883$	−27587.3	+	11427.0i	−1.05140	+	0.435504i	−0.840391	−	0.541981i	$-0.817675\pi$
$883$	−27587.3	+	11427.0i	−1.05140	+	0.435504i	−0.211008	+	0.977484i	$0.567675\pi$
$884$	3728.31	−	30553.2i	0.141852	−	1.16246i
$885$	17080.0	−	41234.9i	0.648745	−	1.56621i
$886$	−27551.9	+	36260.6i	−1.04472	+	1.37494i
$887$	1279.94	−	1279.94i	0.0484512	−	0.0484512i	−0.682466	−	0.730917i	$-0.739093\pi$
$887$	1279.94	−	1279.94i	0.0484512	−	0.0484512i	0.730917	+	0.682466i	$0.239093\pi$
$888$	−33539.7	−	32599.8i	−1.26747	−	1.23196i
$889$	−11720.6	−	11720.6i	−0.442178	−	0.442178i
$890$	12653.2	−	1726.84i	0.476559	−	0.0650380i
$891$	581.141	+	240.717i	0.0218507	+	0.00905085i
$892$	7663.61	+	4328.31i	0.287664	+	0.162469i
$893$	2224.41	+	5370.19i	0.0833560	+	0.201239i
$894$	−18330.2	+	69728.6i	−0.685742	+	2.60858i
$895$	−47571.7			−1.77670
$896$	9823.31	+	15782.0i	0.366265	+	0.588437i
$897$	47198.3			1.75686
$898$	−1357.13	+	5162.58i	−0.0504322	+	0.191846i
$899$	−738.620	−	1783.19i	−0.0274019	−	0.0661541i
$900$	28206.4	+	15930.6i	1.04468	+	0.590023i
$901$	11725.8	+	4856.97i	0.433565	+	0.179588i
$902$	−48368.3	+	6601.02i	−1.78546	+	0.243670i
$903$	−22343.9	−	22343.9i	−0.823432	−	0.823432i
$904$	−25433.2	−	24720.5i	−0.935727	−	0.909505i
$905$	−44192.2	+	44192.2i	−1.62320	+	1.62320i
$906$	−5332.18	+	7017.60i	−0.195529	+	0.257334i
$907$	−497.655	+	1201.44i	−0.0182187	+	0.0439838i	−0.932727	−	0.360583i	$-0.882578\pi$
$907$	−497.655	+	1201.44i	−0.0182187	+	0.0439838i	0.914508	+	0.404567i	$0.132578\pi$
$908$	3738.21	−	30634.3i	0.136626	−	1.11964i
$909$	45472.0	−	18835.1i	1.65920	−	0.687262i
$910$	−19265.4	+	11244.9i	−0.701803	+	0.409630i
$911$			1357.76i			0.0493794i	0.999695	+	0.0246897i	$0.00785977\pi$
$911$			1357.76i			0.0493794i	−0.999695	+	0.0246897i	$0.992140\pi$
$912$	−2332.16	+	9413.63i	−0.0846770	+	0.341794i
$913$		−	58191.2i		−	2.10936i
$914$	−18702.7	−	32042.6i	−0.676840	−	1.15960i
$915$	−10081.5	+	4175.91i	−0.364246	+	0.150876i
$916$	−19071.3	−	24372.6i	−0.687918	−	0.879141i
$917$	4184.91	−	10103.3i	0.150707	−	0.363838i
$918$	28759.1	+	21852.0i	1.03398	+	0.785645i
$919$	−5601.39	+	5601.39i	−0.201059	+	0.201059i	−0.800453	−	0.599395i	$-0.795408\pi$
$919$	−5601.39	+	5601.39i	−0.201059	+	0.201059i	0.599395	+	0.800453i	$0.295408\pi$
$920$	−16698.3	+	41991.2i	−0.598399	+	1.50479i
$921$	142.554	+	142.554i	0.00510023	+	0.00510023i
$922$	2843.07	+	20832.3i	0.101553	+	0.744115i
$923$	−14794.8	−	6128.21i	−0.527602	−	0.218540i
$924$	10090.8	+	36281.1i	0.359268	+	1.29173i
$925$	8783.62	+	21205.5i	0.312220	+	0.753766i
$926$	−21005.0	−	5521.78i	−0.745429	−	0.195958i
$927$	−42010.6			−1.48847
$928$	−5746.02	−	7132.09i	−0.203257	−	0.252287i
$929$	22810.9			0.805598			0.402799	−	0.915288i	$-0.368037\pi$
$929$	22810.9			0.805598			0.402799	+	0.915288i	$0.368037\pi$
$930$	12937.9	+	3401.09i	0.456182	+	0.119921i
$931$	1231.33	+	2972.70i	0.0433461	+	0.104647i
$932$	39988.4	−	11121.9i	1.40543	−	0.390891i
$933$	46284.5	+	19171.7i	1.62410	+	0.672724i
$934$	−1600.86	−	11730.1i	−0.0560832	−	0.410944i
$935$	42214.0	+	42214.0i	1.47652	+	1.47652i
$936$	−16183.1	−	37551.2i	−0.565130	−	1.31133i
$937$	16556.7	−	16556.7i	0.577251	−	0.577251i	−0.356894	−	0.934145i	$-0.616164\pi$
$937$	16556.7	−	16556.7i	0.577251	−	0.577251i	0.934145	+	0.356894i	$0.116164\pi$
$938$	−8201.91	−	6232.04i	−0.285503	−	0.216933i
$939$	27667.4	−	66795.1i	0.961547	−	2.32138i
$940$	29963.4	−	23446.0i	1.03968	−	0.813536i
$941$	6945.83	−	2877.06i	0.240624	−	0.0996698i	−0.259113	−	0.965847i	$-0.583430\pi$
$941$	6945.83	−	2877.06i	0.240624	−	0.0996698i	0.499737	+	0.866177i	$0.333430\pi$
$942$	−33971.8	−	58202.5i	−1.17501	−	2.01310i
$943$			53409.0i			1.84436i
$944$	−3439.45	−	22781.2i	−0.118585	−	0.785449i
$945$		−	26176.5i		−	0.901081i
$946$	31300.8	−	18269.7i	1.07577	−	0.627908i
$947$	−25322.0	+	10488.7i	−0.868905	+	0.359912i	−0.772184	−	0.635399i	$-0.780836\pi$
$947$	−25322.0	+	10488.7i	−0.868905	+	0.359912i	−0.0967214	+	0.995311i	$0.530836\pi$
$948$	16290.4	+	1987.87i	0.558110	+	0.0681044i
$949$	−8395.14	+	20267.7i	−0.287163	+	0.693273i
$950$	2879.32	−	3789.43i	0.0983341	−	0.129416i
$951$	−25758.0	+	25758.0i	−0.878296	+	0.878296i
$952$	−381.784	−	26866.0i	−0.0129976	−	0.914635i
$953$	−1354.94	−	1354.94i	−0.0460556	−	0.0460556i	0.683704	−	0.729760i	$-0.260368\pi$
$953$	−1354.94	−	1354.94i	−0.0460556	−	0.0460556i	−0.729760	+	0.683704i	$0.760368\pi$
$954$	16705.9	−	2279.92i	0.566952	−	0.0773743i
$955$	−9515.69	−	3941.53i	−0.322430	−	0.133555i
$956$	−22225.1	+	39351.3i	−0.751895	+	1.33129i
$957$	−7100.20	−	17141.4i	−0.239829	−	0.579000i
$958$	−4028.93	+	15326.2i	−0.135876	+	0.516875i
$959$	27718.3			0.933336
$960$	63453.3	−	1803.79i	2.13328	−	0.0606429i
$961$	−28335.8			−0.951152
$962$	7365.95	−	28020.3i	0.246869	−	0.939097i
$963$	−12580.4	−	30371.9i	−0.420975	−	1.01632i
$964$	19905.3	−	35243.9i	0.665048	−	1.17752i
$965$	−32570.4	−	13491.1i	−1.08651	−	0.450046i
$966$	40822.5	−	5571.21i	1.35967	−	0.185560i
$967$	−9687.88	−	9687.88i	−0.322173	−	0.322173i	0.527427	−	0.849600i	$-0.323157\pi$
$967$	−9687.88	−	9687.88i	−0.322173	−	0.322173i	−0.849600	+	0.527427i	$0.823157\pi$
$968$	−13073.7	+	185.786i	−0.434096	+	0.00616880i
$969$	9911.89	−	9911.89i	0.328602	−	0.328602i
$970$	19712.5	−	25943.4i	0.652506	−	0.858755i
$971$	−9092.27	+	21950.7i	−0.300499	+	0.725469i	0.699443	+	0.714689i	$0.253432\pi$
$971$	−9092.27	+	21950.7i	−0.300499	+	0.725469i	−0.999942	+	0.0107805i	$0.996568\pi$
$972$	−30558.6	−	3728.97i	−1.00840	−	0.123052i
$973$	−5614.52	+	2325.61i	−0.184988	+	0.0766245i
$974$	−46077.3	+	26894.5i	−1.51582	+	0.884761i
$975$			32535.8i			1.06870i
$976$	−3343.81	+	4533.04i	−0.109665	+	0.148667i
$977$			2789.43i			0.0913426i	0.998957	+	0.0456713i	$0.0145427\pi$
$977$			2789.43i			0.0913426i	−0.998957	+	0.0456713i	$0.985457\pi$
$978$	−11885.0	−	20362.2i	−0.388591	−	0.665757i
$979$	12337.8	−	5110.48i	0.402776	−	0.166835i
$980$	16586.4	−	12978.7i	0.540645	−	0.423049i
$981$	−1014.12	+	2448.31i	−0.0330056	+	0.0796825i
$982$	35716.8	+	27138.7i	1.16066	+	0.881904i
$983$	10480.4	−	10480.4i	0.340054	−	0.340054i	−0.516334	−	0.856388i	$-0.672703\pi$
$983$	10480.4	−	10480.4i	0.340054	−	0.340054i	0.856388	+	0.516334i	$0.172703\pi$
$984$	68899.1	−	29692.8i	2.23214	−	0.961964i
$985$	29203.4	+	29203.4i	0.944666	+	0.944666i
$986$	1790.03	+	13116.3i	0.0578157	+	0.423638i
$987$	−32047.6	−	13274.6i	−1.03352	−	0.428099i
$988$	−5787.70	+	1609.73i	−0.186368	+	0.0518342i
$989$	−15174.2	−	36633.7i	−0.487877	−	1.17784i
$990$	76702.8	+	20163.5i	2.46240	+	0.647312i
$991$	−43206.7			−1.38497			−0.692485	−	0.721432i	$-0.743484\pi$
$991$	−43206.7			−1.38497			−0.692485	+	0.721432i	$0.743484\pi$
$992$	6625.97	−	1944.72i	0.212071	−	0.0622428i
$993$	−81636.3			−2.60891
$994$	−13519.6	−	3554.02i	−0.431404	−	0.113407i
$995$	−23509.7	−	56757.5i	−0.749054	−	1.80838i
$996$	23964.1	+	86162.0i	0.762382	+	2.74111i
$997$	29415.4	+	12184.3i	0.934399	+	0.387041i	0.797346	−	0.603523i	$-0.206237\pi$
$997$	29415.4	+	12184.3i	0.934399	+	0.387041i	0.137054	+	0.990564i	$0.456237\pi$
$998$	1286.77	+	9428.69i	0.0408137	+	0.299058i
$999$	24040.3	+	24040.3i	0.761362	+	0.761362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.4.g.a.5.5	✓	44
4.3	odd	2		128.4.g.a.113.10		44
8.3	odd	2		256.4.g.a.225.2		44
8.5	even	2		256.4.g.b.225.10		44
32.3	odd	8		256.4.g.a.33.2		44
32.13	even	8	inner	32.4.g.a.13.5	yes	44
32.19	odd	8		128.4.g.a.17.10		44
32.29	even	8		256.4.g.b.33.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.5	✓	44	1.1	even	1	trivial
32.4.g.a.13.5	yes	44	32.13	even	8	inner
128.4.g.a.17.10		44	32.19	odd	8
128.4.g.a.113.10		44	4.3	odd	2
256.4.g.a.33.2		44	32.3	odd	8
256.4.g.a.225.2		44	8.3	odd	2
256.4.g.b.33.10		44	32.29	even	8
256.4.g.b.225.10		44	8.5	even	2

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719102 + 2.73549i) q^{2} +(-3.21198 - 7.75440i) q^{3} +(-6.96578 - 3.93419i) q^{4} +(-13.6472 - 5.65283i) q^{5} +(23.5218 - 3.21012i) q^{6} +(9.07689 + 9.07689i) q^{7} +(15.7710 - 16.2257i) q^{8} +(-30.7220 + 30.7220i) q^{9} +O(q^{10})\)	\(q+(-0.719102 + 2.73549i) q^{2} +(-3.21198 - 7.75440i) q^{3} +(-6.96578 - 3.93419i) q^{4} +(-13.6472 - 5.65283i) q^{5} +(23.5218 - 3.21012i) q^{6} +(9.07689 + 9.07689i) q^{7} +(15.7710 - 16.2257i) q^{8} +(-30.7220 + 30.7220i) q^{9} +(25.2770 - 33.2666i) q^{10} +(16.7195 - 40.3646i) q^{11} +(-8.13333 + 66.6520i) q^{12} +(-38.4266 + 15.9168i) q^{13} +(-31.3569 + 18.3025i) q^{14} +123.982i q^{15} +(33.0443 + 54.8094i) q^{16} -92.5038i q^{17} +(-61.9474 - 106.132i) q^{18} +(-16.6799 + 6.90905i) q^{19} +(72.8238 + 93.0669i) q^{20} +(41.2311 - 99.5406i) q^{21} +(98.3937 + 74.7623i) q^{22} +(95.6008 - 95.6008i) q^{23} +(-176.477 - 70.1782i) q^{24} +(65.9018 + 65.9018i) q^{25} +(-15.9076 - 116.561i) q^{26} +(127.540 + 52.8290i) q^{27} +(-27.5175 - 98.9379i) q^{28} +(19.3621 + 46.7443i) q^{29} +(-339.152 - 89.1559i) q^{30} -38.1477 q^{31} +(-173.693 + 50.9787i) q^{32} -366.706 q^{33} +(253.043 + 66.5197i) q^{34} +(-72.5636 - 175.184i) q^{35} +(334.869 - 93.1367i) q^{36} +(227.529 + 94.2456i) q^{37} +(-6.90506 - 50.5961i) q^{38} +(246.851 + 246.851i) q^{39} +(-306.951 + 132.284i) q^{40} +(-279.334 + 279.334i) q^{41} +(242.643 + 184.367i) q^{42} +(112.235 - 270.960i) q^{43} +(-275.267 + 215.393i) q^{44} +(592.935 - 245.602i) q^{45} +(192.768 + 330.261i) q^{46} -321.955i q^{47} +(318.877 - 432.285i) q^{48} -178.220i q^{49} +(-227.664 + 132.883i) q^{50} +(-717.312 + 297.120i) q^{51} +(330.291 + 40.3044i) q^{52} +(-52.5056 + 126.760i) q^{53} +(-236.228 + 310.896i) q^{54} +(-456.348 + 456.348i) q^{55} +(290.431 - 4.12723i) q^{56} +(107.151 + 107.151i) q^{57} +(-141.792 + 19.3509i) q^{58} +(-332.587 - 137.762i) q^{59} +(487.770 - 863.633i) q^{60} +(33.6815 + 81.3143i) q^{61} +(27.4321 - 104.352i) q^{62} -557.721 q^{63} +(-14.5488 - 511.793i) q^{64} +614.389 q^{65} +(263.699 - 1003.12i) q^{66} +(108.572 + 262.117i) q^{67} +(-363.928 + 644.362i) q^{68} +(-1048.39 - 434.259i) q^{69} +(531.394 - 72.5216i) q^{70} +(272.246 + 272.246i) q^{71} +(13.9692 + 983.005i) q^{72} +(372.955 - 372.955i) q^{73} +(-421.424 + 554.631i) q^{74} +(299.354 - 722.704i) q^{75} +(143.370 + 17.4950i) q^{76} +(518.146 - 214.623i) q^{77} +(-852.768 + 497.746i) q^{78} -244.410i q^{79} +(-141.132 - 934.787i) q^{80} +14.3973i q^{81} +(-563.244 - 964.983i) q^{82} +(1230.52 - 509.697i) q^{83} +(-678.819 + 531.168i) q^{84} +(-522.909 + 1262.41i) q^{85} +(660.498 + 501.865i) q^{86} +(300.283 - 300.283i) q^{87} +(-391.260 - 907.878i) q^{88} +(216.134 + 216.134i) q^{89} +(245.459 + 1798.58i) q^{90} +(-493.270 - 204.319i) q^{91} +(-1042.05 + 289.823i) q^{92} +(122.529 + 295.812i) q^{93} +(880.704 + 231.519i) q^{94} +266.689 q^{95} +(953.206 + 1183.14i) q^{96} +779.862 q^{97} +(487.519 + 128.158i) q^{98} +(726.422 + 1753.74i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 212 q^{14} - 304 q^{16} - 184 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 192 q^{22} + 324 q^{23} - 48 q^{24} - 4 q^{25} + 16 q^{26} - 268 q^{27} + 376 q^{28} - 4 q^{29} + 1188 q^{30} - 752 q^{31} + 616 q^{32} - 8 q^{33} + 528 q^{34} - 460 q^{35} + 1456 q^{36} - 4 q^{37} + 980 q^{38} + 596 q^{39} - 536 q^{40} - 4 q^{41} - 2264 q^{42} + 804 q^{43} - 2044 q^{44} + 104 q^{45} - 1444 q^{46} - 2448 q^{48} - 3564 q^{50} - 1384 q^{51} - 2524 q^{52} + 748 q^{53} - 1088 q^{54} - 292 q^{55} + 1192 q^{56} - 4 q^{57} + 3200 q^{58} + 1372 q^{59} + 5752 q^{60} - 1828 q^{61} + 3384 q^{62} + 2512 q^{63} + 4952 q^{64} - 8 q^{65} + 5996 q^{66} + 2036 q^{67} + 2768 q^{68} - 1060 q^{69} + 1400 q^{70} + 220 q^{71} - 1708 q^{72} - 4 q^{73} - 3476 q^{74} - 1712 q^{75} - 5124 q^{76} + 1900 q^{77} - 11916 q^{78} - 10312 q^{80} - 6404 q^{82} + 2436 q^{83} - 6560 q^{84} + 496 q^{85} - 928 q^{86} - 1292 q^{87} + 1248 q^{88} - 4 q^{89} + 7400 q^{90} - 3604 q^{91} + 10152 q^{92} - 112 q^{93} + 12840 q^{94} - 6088 q^{95} + 17792 q^{96} - 8 q^{97} + 11224 q^{98} - 5424 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 116 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 212 * q^14 - 304 * q^16 - 184 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 192 * q^22 + 324 * q^23 - 48 * q^24 - 4 * q^25 + 16 * q^26 - 268 * q^27 + 376 * q^28 - 4 * q^29 + 1188 * q^30 - 752 * q^31 + 616 * q^32 - 8 * q^33 + 528 * q^34 - 460 * q^35 + 1456 * q^36 - 4 * q^37 + 980 * q^38 + 596 * q^39 - 536 * q^40 - 4 * q^41 - 2264 * q^42 + 804 * q^43 - 2044 * q^44 + 104 * q^45 - 1444 * q^46 - 2448 * q^48 - 3564 * q^50 - 1384 * q^51 - 2524 * q^52 + 748 * q^53 - 1088 * q^54 - 292 * q^55 + 1192 * q^56 - 4 * q^57 + 3200 * q^58 + 1372 * q^59 + 5752 * q^60 - 1828 * q^61 + 3384 * q^62 + 2512 * q^63 + 4952 * q^64 - 8 * q^65 + 5996 * q^66 + 2036 * q^67 + 2768 * q^68 - 1060 * q^69 + 1400 * q^70 + 220 * q^71 - 1708 * q^72 - 4 * q^73 - 3476 * q^74 - 1712 * q^75 - 5124 * q^76 + 1900 * q^77 - 11916 * q^78 - 10312 * q^80 - 6404 * q^82 + 2436 * q^83 - 6560 * q^84 + 496 * q^85 - 928 * q^86 - 1292 * q^87 + 1248 * q^88 - 4 * q^89 + 7400 * q^90 - 3604 * q^91 + 10152 * q^92 - 112 * q^93 + 12840 * q^94 - 6088 * q^95 + 17792 * q^96 - 8 * q^97 + 11224 * q^98 - 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more