LMFDB - Embedded newform 32.4.g.a.5.11

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			5.11
Character	$\chi$	$=$	32.5
Dual form			32.4.g.a.13.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81450 + 0.280314i) q^{2} +(1.64064 + 3.96085i) q^{3} +(7.84285 + 1.57789i) q^{4} +(-11.8087 - 4.89132i) q^{5} +(3.50730 + 11.6077i) q^{6} +(-5.11236 - 5.11236i) q^{7} +(21.6314 + 6.63943i) q^{8} +(6.09524 - 6.09524i) q^{9} +O(q^{10})$	\(q+(2.81450 + 0.280314i) q^{2} +(1.64064 + 3.96085i) q^{3} +(7.84285 + 1.57789i) q^{4} +(-11.8087 - 4.89132i) q^{5} +(3.50730 + 11.6077i) q^{6} +(-5.11236 - 5.11236i) q^{7} +(21.6314 + 6.63943i) q^{8} +(6.09524 - 6.09524i) q^{9} +(-31.8645 - 17.0768i) q^{10} +(15.2446 - 36.8038i) q^{11} +(6.61750 + 33.6531i) q^{12} +(-73.4903 + 30.4407i) q^{13} +(-12.9557 - 15.8218i) q^{14} -54.7973i q^{15} +(59.0205 + 24.7503i) q^{16} +66.8708i q^{17} +(18.8637 - 15.4465i) q^{18} +(-37.0353 + 15.3405i) q^{19} +(-84.8958 - 56.9946i) q^{20} +(11.8618 - 28.6368i) q^{21} +(53.2227 - 99.3112i) q^{22} +(30.1143 - 30.1143i) q^{23} +(9.19154 + 96.5717i) q^{24} +(27.1316 + 27.1316i) q^{25} +(-215.371 + 65.0750i) q^{26} +(141.085 + 58.4395i) q^{27} +(-32.0288 - 48.1622i) q^{28} +(64.4434 + 155.580i) q^{29} +(15.3604 - 154.227i) q^{30} +219.132 q^{31} +(159.176 + 86.2040i) q^{32} +170.785 q^{33} +(-18.7448 + 188.208i) q^{34} +(35.3641 + 85.3765i) q^{35} +(57.4217 - 38.1865i) q^{36} +(-286.081 - 118.499i) q^{37} +(-108.536 + 32.7945i) q^{38} +(-241.142 - 241.142i) q^{39} +(-222.963 - 184.209i) q^{40} +(64.2737 - 64.2737i) q^{41} +(41.4123 - 77.2735i) q^{42} +(-200.870 + 484.942i) q^{43} +(177.634 - 264.592i) q^{44} +(-101.791 + 42.1630i) q^{45} +(93.1984 - 76.3154i) q^{46} -392.444i q^{47} +(-1.20076 + 274.378i) q^{48} -290.727i q^{49} +(68.7567 + 83.9674i) q^{50} +(-264.865 + 109.711i) q^{51} +(-624.405 + 122.782i) q^{52} +(107.214 - 258.838i) q^{53} +(380.704 + 204.026i) q^{54} +(-360.038 + 360.038i) q^{55} +(-76.6445 - 144.531i) q^{56} +(-121.523 - 121.523i) q^{57} +(137.765 + 455.945i) q^{58} +(237.764 + 98.4852i) q^{59} +(86.4640 - 429.767i) q^{60} +(-43.9101 - 106.008i) q^{61} +(616.749 + 61.4259i) q^{62} -62.3222 q^{63} +(423.836 + 287.240i) q^{64} +1016.72 q^{65} +(480.676 + 47.8735i) q^{66} +(-333.028 - 804.000i) q^{67} +(-105.515 + 524.458i) q^{68} +(168.685 + 69.8717i) q^{69} +(75.6001 + 250.205i) q^{70} +(387.445 + 387.445i) q^{71} +(172.318 - 91.3798i) q^{72} +(-518.132 + 518.132i) q^{73} +(-771.960 - 413.708i) q^{74} +(-62.9512 + 151.978i) q^{75} +(-314.668 + 61.8759i) q^{76} +(-266.091 + 110.218i) q^{77} +(-611.099 - 746.290i) q^{78} +214.985i q^{79} +(-575.893 - 580.956i) q^{80} +421.957i q^{81} +(198.915 - 162.882i) q^{82} +(436.657 - 180.869i) q^{83} +(138.216 - 205.878i) q^{84} +(327.086 - 789.656i) q^{85} +(-701.284 + 1308.56i) q^{86} +(-510.501 + 510.501i) q^{87} +(574.119 - 694.903i) q^{88} +(-877.926 - 877.926i) q^{89} +(-298.309 + 90.1346i) q^{90} +(531.333 + 220.085i) q^{91} +(283.699 - 188.665i) q^{92} +(359.517 + 867.951i) q^{93} +(110.007 - 1104.53i) q^{94} +512.374 q^{95} +(-80.2914 + 771.900i) q^{96} +43.7563 q^{97} +(81.4949 - 818.253i) q^{98} +(-131.408 - 317.248i) 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 $

$2$	2.81450	+	0.280314i	0.995077	+	0.0991059i
$2$	2.81450	+	0.280314i	0.995077	+	0.0991059i
$3$	1.64064	+	3.96085i	0.315741	+	0.762266i	0.999471	+	0.0325307i	$0.0103567\pi$
$3$	1.64064	+	3.96085i	0.315741	+	0.762266i	−0.683730	+	0.729735i	$0.739643\pi$
$4$	7.84285	+	1.57789i	0.980356	+	0.197236i
$5$	−11.8087	−	4.89132i	−1.05620	−	0.437493i	−0.214099	−	0.976812i	$-0.568682\pi$
$5$	−11.8087	−	4.89132i	−1.05620	−	0.437493i	−0.842101	+	0.539319i	$0.818682\pi$
$6$	3.50730	+	11.6077i	0.238641	+	0.789805i
$7$	−5.11236	−	5.11236i	−0.276042	−	0.276042i	0.555485	−	0.831527i	$-0.312533\pi$
$7$	−5.11236	−	5.11236i	−0.276042	−	0.276042i	−0.831527	+	0.555485i	$0.812533\pi$
$8$	21.6314	+	6.63943i	0.955982	+	0.293424i
$9$	6.09524	−	6.09524i	0.225750	−	0.225750i
$10$	−31.8645	−	17.0768i	−1.00764	−	0.540014i
$11$	15.2446	−	36.8038i	0.417858	−	1.00880i	−0.565110	−	0.825016i	$-0.691166\pi$
$11$	15.2446	−	36.8038i	0.417858	−	1.00880i	0.982967	−	0.183781i	$-0.0588339\pi$
$12$	6.61750	+	33.6531i	0.159192	+	0.809568i
$13$	−73.4903	+	30.4407i	−1.56789	+	0.649440i	−0.986437	−	0.164142i	$-0.947515\pi$
$13$	−73.4903	+	30.4407i	−1.56789	+	0.649440i	−0.581450	+	0.813582i	$0.697515\pi$
$14$	−12.9557	−	15.8218i	−0.247325	−	0.302040i
$15$		−	54.7973i		−	0.943240i
$16$	59.0205	+	24.7503i	0.922196	+	0.386723i
$17$			66.8708i			0.954033i	0.878894	+	0.477016i	$0.158282\pi$
$17$			66.8708i			0.954033i	−0.878894	+	0.477016i	$0.841718\pi$
$18$	18.8637	−	15.4465i	0.247011	−	0.202265i
$19$	−37.0353	+	15.3405i	−0.447184	+	0.185230i	−0.594899	−	0.803800i	$-0.702808\pi$
$19$	−37.0353	+	15.3405i	−0.447184	+	0.185230i	0.147715	+	0.989030i	$0.452808\pi$
$20$	−84.8958	−	56.9946i	−0.949163	−	0.637219i
$21$	11.8618	−	28.6368i	0.123260	−	0.297575i
$22$	53.2227	−	99.3112i	0.515778	−	0.962419i
$23$	30.1143	−	30.1143i	0.273012	−	0.273012i	−0.557300	−	0.830311i	$-0.688163\pi$
$23$	30.1143	−	30.1143i	0.273012	−	0.273012i	0.830311	+	0.557300i	$0.188163\pi$
$24$	9.19154	+	96.5717i	0.0781756	+	0.821359i
$25$	27.1316	+	27.1316i	0.217053	+	0.217053i
$26$	−215.371	+	65.0750i	−1.62453	+	0.490856i
$27$	141.085	+	58.4395i	1.00563	+	0.416544i
$28$	−32.0288	−	48.1622i	−0.216174	−	0.325065i
$29$	64.4434	+	155.580i	0.412649	+	0.996224i	0.984424	+	0.175813i	$0.0562553\pi$
$29$	64.4434	+	155.580i	0.412649	+	0.996224i	−0.571774	+	0.820411i	$0.693745\pi$
$30$	15.3604	−	154.227i	0.0934806	−	0.938596i
$31$	219.132			1.26959			0.634796	−	0.772680i	$-0.281084\pi$
$31$	219.132			1.26959			0.634796	+	0.772680i	$0.281084\pi$
$32$	159.176	+	86.2040i	0.879329	+	0.476214i
$33$	170.785			0.900907
$34$	−18.7448	+	188.208i	−0.0945502	+	0.949336i
$35$	35.3641	+	85.3765i	0.170789	+	0.412322i
$36$	57.4217	−	38.1865i	0.265841	−	0.176789i
$37$	−286.081	−	118.499i	−1.27112	−	0.526515i	−0.357816	−	0.933792i	$-0.616478\pi$
$37$	−286.081	−	118.499i	−1.27112	−	0.526515i	−0.913305	+	0.407277i	$0.866478\pi$
$38$	−108.536	+	32.7945i	−0.463340	+	0.139999i
$39$	−241.142	−	241.142i	−0.990092	−	0.990092i
$40$	−222.963	−	184.209i	−0.881338	−	0.728150i
$41$	64.2737	−	64.2737i	0.244826	−	0.244826i	−0.574017	−	0.818843i	$-0.694616\pi$
$41$	64.2737	−	64.2737i	0.244826	−	0.244826i	0.818843	+	0.574017i	$0.194616\pi$
$42$	41.4123	−	77.2735i	0.152144	−	0.283894i
$43$	−200.870	+	484.942i	−0.712380	+	1.71984i	−0.0184123	+	0.999830i	$0.505861\pi$
$43$	−200.870	+	484.942i	−0.712380	+	1.71984i	−0.693967	+	0.720006i	$0.744139\pi$
$44$	177.634	−	264.592i	0.608620	−	0.906564i
$45$	−101.791	+	42.1630i	−0.337201	+	0.139673i
$46$	93.1984	−	76.3154i	0.298725	−	0.244611i
$47$		−	392.444i		−	1.21795i	−0.793188	−	0.608977i	$-0.791580\pi$
$47$		−	392.444i		−	1.21795i	0.793188	−	0.608977i	$-0.208420\pi$
$48$	−1.20076	+	274.378i	−0.00361071	+	0.825063i
$49$		−	290.727i		−	0.847602i
$50$	68.7567	+	83.9674i	0.194473	+	0.237496i
$51$	−264.865	+	109.711i	−0.727227	+	0.301227i
$52$	−624.405	+	122.782i	−1.66518	+	0.327439i
$53$	107.214	−	258.838i	0.277868	−	0.670833i	−0.721908	−	0.691989i	$-0.756735\pi$
$53$	107.214	−	258.838i	0.277868	−	0.670833i	0.999776	+	0.0211562i	$0.00673472\pi$
$54$	380.704	+	204.026i	0.959393	+	0.514157i
$55$	−360.038	+	360.038i	−0.882683	+	0.882683i
$56$	−76.6445	−	144.531i	−0.182894	−	0.344888i
$57$	−121.523	−	121.523i	−0.282388	−	0.282388i
$58$	137.765	+	455.945i	0.311886	+	1.03222i
$59$	237.764	+	98.4852i	0.524649	+	0.217317i	0.629258	−	0.777197i	$-0.283359\pi$
$59$	237.764	+	98.4852i	0.524649	+	0.217317i	−0.104609	+	0.994513i	$0.533359\pi$
$60$	86.4640	−	429.767i	0.186041	−	0.924711i
$61$	−43.9101	−	106.008i	−0.0921658	−	0.222508i	0.871074	−	0.491153i	$-0.163424\pi$
$61$	−43.9101	−	106.008i	−0.0921658	−	0.222508i	−0.963239	+	0.268645i	$0.913424\pi$
$62$	616.749	+	61.4259i	1.26334	+	0.125824i
$63$	−62.3222			−0.124633
$64$	423.836	+	287.240i	0.827805	+	0.561016i
$65$	1016.72			1.94013
$66$	480.676	+	47.8735i	0.896471	+	0.0892851i
$67$	−333.028	−	804.000i	−0.607251	−	1.46603i	−0.865978	−	0.500083i	$-0.833303\pi$
$67$	−333.028	−	804.000i	−0.607251	−	1.46603i	0.258727	−	0.965951i	$-0.416697\pi$
$68$	−105.515	+	524.458i	−0.188170	+	0.935292i
$69$	168.685	+	69.8717i	0.294309	+	0.121907i
$70$	75.6001	+	250.205i	0.129085	+	0.427218i
$71$	387.445	+	387.445i	0.647624	+	0.647624i	0.952418	−	0.304794i	$-0.0985877\pi$
$71$	387.445	+	387.445i	0.647624	+	0.647624i	−0.304794	+	0.952418i	$0.598588\pi$
$72$	172.318	−	91.3798i	0.282053	−	0.149572i
$73$	−518.132	+	518.132i	−0.830723	+	0.830723i	−0.987616	−	0.156892i	$-0.949852\pi$
$73$	−518.132	+	518.132i	−0.830723	+	0.830723i	0.156892	+	0.987616i	$0.449852\pi$
$74$	−771.960	−	413.708i	−1.21268	−	0.649899i
$75$	−62.9512	+	151.978i	−0.0969197	+	0.233985i
$76$	−314.668	+	61.8759i	−0.474933	+	0.0933902i
$77$	−266.091	+	110.218i	−0.393816	+	0.163124i
$78$	−611.099	−	746.290i	−0.887094	−	1.08334i
$79$			214.985i			0.306173i	0.988213	+	0.153086i	$0.0489213\pi$
$79$			214.985i			0.306173i	−0.988213	+	0.153086i	$0.951079\pi$
$80$	−575.893	−	580.956i	−0.804836	−	0.811911i
$81$			421.957i			0.578816i
$82$	198.915	−	162.882i	0.267884	−	0.219357i
$83$	436.657	−	180.869i	0.577462	−	0.239193i	−0.0747842	−	0.997200i	$-0.523827\pi$
$83$	436.657	−	180.869i	0.577462	−	0.239193i	0.652246	+	0.758007i	$0.273827\pi$
$84$	138.216	−	205.878i	0.179531	−	0.267418i
$85$	327.086	−	789.656i	0.417382	−	1.00765i
$86$	−701.284	+	1308.56i	−0.879319	+	1.64077i
$87$	−510.501	+	510.501i	−0.629097	+	0.629097i
$88$	574.119	−	694.903i	0.695470	−	0.841783i
$89$	−877.926	−	877.926i	−1.04562	−	1.04562i	−0.998909	−	0.0467087i	$-0.985127\pi$
$89$	−877.926	−	877.926i	−1.04562	−	1.04562i	−0.0467087	−	0.998909i	$-0.514873\pi$
$90$	−298.309	+	90.1346i	−0.349383	+	0.105567i
$91$	531.333	+	220.085i	0.612075	+	0.253530i
$92$	283.699	−	188.665i	0.321497	−	0.213801i
$93$	359.517	+	867.951i	0.400862	+	0.967767i
$94$	110.007	−	1104.53i	0.120706	−	1.21196i
$95$	512.374			0.553352
$96$	−80.2914	+	771.900i	−0.0853615	+	0.820643i
$97$	43.7563			0.0458019			0.0229009	−	0.999738i	$-0.492710\pi$
$97$	43.7563			0.0458019			0.0229009	+	0.999738i	$0.492710\pi$
$98$	81.4949	−	818.253i	0.0840023	−	0.843429i
$99$	−131.408	−	317.248i	−0.133404	−	0.322067i
$100$	169.979	+	255.600i	0.169979	+	0.255600i
$101$	427.453	+	177.057i	0.421120	+	0.174434i	0.583172	−	0.812349i	$-0.301811\pi$
$101$	427.453	+	177.057i	0.421120	+	0.174434i	−0.162052	+	0.986782i	$0.551811\pi$
$102$	−776.217	+	234.536i	−0.753500	+	0.227672i
$103$	570.431	+	570.431i	0.545691	+	0.545691i	0.925192	−	0.379500i	$-0.123904\pi$
$103$	570.431	+	570.431i	0.545691	+	0.545691i	−0.379500	+	0.925192i	$0.623904\pi$
$104$	−1791.81	+	170.541i	−1.68943	+	0.160798i
$105$	−280.144	+	280.144i	−0.260374	+	0.260374i
$106$	374.310	−	698.447i	0.342983	−	0.639992i
$107$	398.490	−	962.041i	0.360033	−	0.869196i	−0.635261	−	0.772297i	$-0.719108\pi$
$107$	398.490	−	962.041i	0.360033	−	0.869196i	0.995294	−	0.0968989i	$-0.0308924\pi$
$108$	1014.30	+	680.949i	0.903714	+	0.606707i
$109$	−129.224	+	53.5263i	−0.113554	+	0.0470357i	−0.438737	−	0.898615i	$-0.644574\pi$
$109$	−129.224	+	53.5263i	−0.113554	+	0.0470357i	0.325183	+	0.945651i	$0.394574\pi$
$110$	−1114.25	+	912.405i	−0.965816	+	0.790858i
$111$		−	1327.54i		−	1.13517i
$112$	−175.202	−	428.267i	−0.147813	−	0.361316i
$113$			772.521i			0.643121i	0.946889	+	0.321561i	$0.104207\pi$
$113$			772.521i			0.643121i	−0.946889	+	0.321561i	$0.895793\pi$
$114$	−307.963	−	376.092i	−0.253012	−	0.308985i
$115$	−502.909	+	208.312i	−0.407796	+	0.168915i
$116$	259.932	+	1321.88i	0.208052	+	1.05804i
$117$	−262.398	+	633.484i	−0.207339	+	0.500561i
$118$	641.582	+	343.836i	0.500529	+	0.268243i
$119$	341.868	−	341.868i	0.263353	−	0.263353i
$120$	363.823	−	1185.34i	0.276769	−	0.901721i
$121$	−180.963	−	180.963i	−0.135960	−	0.135960i
$122$	−93.8695	−	310.669i	−0.0696602	−	0.230547i
$123$	360.028	+	149.129i	0.263924	+	0.109321i
$124$	1718.62	+	345.766i	1.24465	+	0.250409i
$125$	423.735	+	1022.99i	0.303200	+	0.731990i
$126$	−175.406	−	17.4698i	−0.124019	−	0.0123518i
$127$	485.865			0.339477			0.169738	−	0.985489i	$-0.445708\pi$
$127$	485.865			0.339477			0.169738	+	0.985489i	$0.445708\pi$
$128$	1112.37	+	927.246i	0.768129	+	0.640295i
$129$	−2250.34			−1.53590
$130$	2861.56	+	285.000i	1.93058	+	0.192278i
$131$	−764.762	−	1846.30i	−0.510058	−	1.23139i	−0.943850	−	0.330375i	$-0.892825\pi$
$131$	−764.762	−	1846.30i	−0.510058	−	1.23139i	0.433792	−	0.901013i	$-0.357175\pi$
$132$	1339.44	+	269.480i	0.883209	+	0.177691i
$133$	267.765	+	110.912i	0.174572	+	0.0723103i
$134$	−711.935	−	2356.21i	−0.458969	−	1.51900i
$135$	−1380.19	−	1380.19i	−0.879908	−	0.879908i
$136$	−443.984	+	1446.51i	−0.279936	+	0.912038i
$137$	−1360.64	+	1360.64i	−0.848519	+	0.848519i	−0.989948	−	0.141430i	$-0.954830\pi$
$137$	−1360.64	+	1360.64i	−0.848519	+	0.848519i	0.141430	+	0.989948i	$0.454830\pi$
$138$	455.179	+	243.939i	0.280778	+	0.150474i
$139$	76.8204	−	185.461i	0.0468764	−	0.113170i	−0.898707	−	0.438550i	$-0.855492\pi$
$139$	76.8204	−	185.461i	0.0468764	−	0.113170i	0.945583	+	0.325380i	$0.105492\pi$
$140$	142.641	+	725.395i	0.0861096	+	0.437908i
$141$	1554.41	−	643.859i	0.928405	−	0.384558i
$142$	981.860	+	1199.07i	0.580252	+	0.708619i
$143$			3168.78i			1.85305i
$144$	510.603	−	208.886i	0.295488	−	0.120883i
$145$		−	2152.41i		−	1.23274i
$146$	−1603.52	+	1313.05i	−0.908963	+	0.744304i
$147$	1151.53	−	476.978i	0.646098	−	0.267623i
$148$	−2056.71	−	1380.77i	−1.14230	−	0.766883i
$149$	687.916	−	1660.78i	0.378230	−	0.913128i	−0.614068	−	0.789253i	$-0.710468\pi$
$149$	687.916	−	1660.78i	0.378230	−	0.913128i	0.992298	−	0.123875i	$-0.0395321\pi$
$150$	−219.778	+	410.095i	−0.119632	+	0.223228i
$151$	−1133.92	+	1133.92i	−0.611107	+	0.611107i	−0.943235	−	0.332128i	$-0.892234\pi$
$151$	−1133.92	+	1133.92i	−0.611107	+	0.611107i	0.332128	+	0.943235i	$0.392234\pi$
$152$	−902.979	+	85.9441i	−0.481851	+	0.0458618i
$153$	407.594	+	407.594i	0.215373	+	0.215373i
$154$	−779.809	+	235.621i	−0.408044	+	0.123291i
$155$	−2587.67	−	1071.85i	−1.34094	−	0.555437i
$156$	−1510.74	−	2271.73i	−0.775361	−	1.16592i
$157$	−368.347	−	889.267i	−0.187244	−	0.452046i	0.802183	−	0.597078i	$-0.203672\pi$
$157$	−368.347	−	889.267i	−0.187244	−	0.452046i	−0.989427	+	0.145032i	$0.953672\pi$
$158$	−60.2632	+	605.075i	−0.0303435	+	0.304666i
$159$	1201.12			0.599087
$160$	−1458.00	−	1796.53i	−0.720408	−	0.887678i
$161$	−307.911			−0.150725
$162$	−118.280	+	1187.60i	−0.0573641	+	0.575966i
$163$	988.667	+	2386.85i	0.475082	+	1.14695i	0.961889	+	0.273440i	$0.0881614\pi$
$163$	988.667	+	2386.85i	0.475082	+	1.14695i	−0.486807	+	0.873509i	$0.661839\pi$
$164$	605.506	−	402.672i	0.288305	−	0.191728i
$165$	−2016.75	−	835.365i	−0.951538	−	0.394140i
$166$	1279.67	−	386.656i	0.598325	−	0.180785i
$167$	373.791	+	373.791i	0.173202	+	0.173202i	0.788385	−	0.615182i	$-0.210918\pi$
$167$	373.791	+	373.791i	0.173202	+	0.173202i	−0.615182	+	0.788385i	$0.710918\pi$
$168$	446.719	−	540.700i	0.205150	−	0.248309i
$169$	2920.67	−	2920.67i	1.32939	−	1.32939i
$170$	1141.94	−	2130.80i	0.515191	−	0.961324i
$171$	−132.235	+	319.244i	−0.0591361	+	0.142767i
$172$	−2340.57	+	3486.38i	−1.03760	+	1.54555i
$173$	−71.8748	+	29.7715i	−0.0315870	+	0.0130837i	−0.398421	−	0.917203i	$-0.630442\pi$
$173$	−71.8748	+	29.7715i	−0.0315870	+	0.0130837i	0.366834	+	0.930286i	$0.380442\pi$
$174$	−1579.91	+	1293.71i	−0.688347	+	0.563653i
$175$		−	277.414i		−	0.119831i
$176$	1810.65	−	1794.87i	0.775472	−	0.768714i
$177$			1103.33i			0.468538i
$178$	−2224.83	−	2717.02i	−0.936843	−	1.14410i
$179$	−1660.73	+	687.899i	−0.693459	+	0.287240i	−0.701440	−	0.712728i	$-0.747459\pi$
$179$	−1660.73	+	687.899i	−0.693459	+	0.287240i	0.00798155	+	0.999968i	$0.497459\pi$
$180$	−864.856	+	170.064i	−0.358125	+	0.0704213i
$181$	−757.224	+	1828.10i	−0.310962	+	0.750728i	0.688708	+	0.725038i	$0.258178\pi$
$181$	−757.224	+	1828.10i	−0.310962	+	0.750728i	−0.999670	+	0.0256892i	$0.991822\pi$
$182$	1433.74	+	768.370i	0.583935	+	0.312942i
$183$	347.843	−	347.843i	0.140510	−	0.140510i
$184$	851.358	−	451.474i	0.341103	−	0.180886i
$185$	2798.63	+	2798.63i	1.11221	+	1.11221i
$186$	768.563	+	2543.63i	0.302977	+	1.00273i
$187$	2461.10	+	1019.42i	0.962426	+	0.398650i
$188$	619.233	−	3077.88i	0.240224	−	1.19403i
$189$	−422.516	−	1020.04i	−0.162611	−	0.392578i
$190$	1442.08	+	143.625i	0.550628	+	0.0548405i
$191$	−3023.78			−1.14551			−0.572757	−	0.819725i	$-0.694126\pi$
$191$	−3023.78			−1.14551			−0.572757	+	0.819725i	$0.694126\pi$
$192$	−442.355	+	2150.01i	−0.166272	+	0.808143i
$193$	2155.34			0.803860			0.401930	−	0.915670i	$-0.368339\pi$
$193$	2155.34			0.803860			0.401930	+	0.915670i	$0.368339\pi$
$194$	123.152	+	12.2655i	0.0455764	+	0.00453924i
$195$	1668.07	+	4027.07i	0.612578	+	1.47889i
$196$	458.735	−	2280.13i	0.167178	−	0.830952i
$197$	2832.03	+	1173.07i	1.02423	+	0.424251i	0.830628	−	0.556828i	$-0.187982\pi$
$197$	2832.03	+	1173.07i	1.02423	+	0.424251i	0.193606	+	0.981079i	$0.437982\pi$
$198$	−280.920	−	929.731i	−0.100829	−	0.333702i
$199$	751.482	+	751.482i	0.267694	+	0.267694i	0.828171	−	0.560476i	$-0.189382\pi$
$199$	751.482	+	751.482i	0.267694	+	0.267694i	−0.560476	+	0.828171i	$0.689382\pi$
$200$	406.757	+	767.034i	0.143810	+	0.271188i
$201$	2638.15	−	2638.15i	0.925774	−	0.925774i
$202$	1153.44	+	618.147i	0.401760	+	0.215310i
$203$	465.924	−	1124.84i	0.161091	−	0.388908i
$204$	−2250.41	+	442.517i	−0.772354	+	0.151875i
$205$	−1073.37	+	444.605i	−0.365695	+	0.151476i
$206$	1445.58	+	1765.38i	0.488924	+	0.597086i
$207$		−	367.108i		−	0.123265i
$208$	−5090.85	−	22.2790i	−1.69705	−	0.00742679i
$209$			1596.90i			0.528517i
$210$	−866.993	+	709.937i	−0.284896	+	0.233287i
$211$	−469.343	+	194.408i	−0.153132	+	0.0634295i	−0.457933	−	0.888987i	$-0.651410\pi$
$211$	−469.343	+	194.408i	−0.153132	+	0.0634295i	0.304801	+	0.952416i	$0.401410\pi$
$212$	1249.28	−	1860.86i	0.404722	−	0.602849i
$213$	−898.956	+	2170.27i	−0.289180	+	0.698143i
$214$	1391.23	−	2595.96i	0.444403	−	0.829236i
$215$	4744.01	−	4744.01i	1.50483	−	1.50483i
$216$	2663.87	+	2200.85i	0.839137	+	0.693283i
$217$	−1120.29	−	1120.29i	−0.350460	−	0.350460i
$218$	−378.705	+	114.427i	−0.117657	+	0.0355502i
$219$	−2902.31	−	1202.18i	−0.895525	−	0.370939i
$220$	−3391.83	+	2255.63i	−1.03944	+	0.691247i
$221$	−2035.59	−	4914.35i	−0.619587	−	1.49582i
$222$	372.127	−	3736.36i	0.112502	−	1.12959i
$223$	−6411.24			−1.92524			−0.962619	−	0.270857i	$-0.912693\pi$
$223$	−6411.24			−1.92524			−0.962619	+	0.270857i	$0.912693\pi$
$224$	−373.058	−	1254.47i	−0.111277	−	0.374187i
$225$	330.748			0.0979993
$226$	−216.548	+	2174.26i	−0.0637371	+	0.639955i
$227$	139.729	+	337.336i	0.0408553	+	0.0986334i	0.942990	−	0.332821i	$-0.108001\pi$
$227$	139.729	+	337.336i	0.0408553	+	0.0986334i	−0.902135	+	0.431455i	$0.858001\pi$
$228$	−761.338	−	1144.84i	−0.221144	−	0.332538i
$229$	−2169.11	−	898.477i	−0.625935	−	0.259271i	0.0470898	−	0.998891i	$-0.485005\pi$
$229$	−2169.11	−	898.477i	−0.625935	−	0.259271i	−0.673025	+	0.739620i	$0.735005\pi$
$230$	−1473.83	+	445.322i	−0.422529	+	0.127668i
$231$	−873.117	−	873.117i	−0.248688	−	0.248688i
$232$	361.039	+	3793.28i	0.102170	+	1.07345i
$233$	−1442.89	+	1442.89i	−0.405696	+	0.405696i	−0.880235	−	0.474539i	$-0.842615\pi$
$233$	−1442.89	+	1442.89i	−0.405696	+	0.405696i	0.474539	+	0.880235i	$0.342615\pi$
$234$	−916.093	+	1709.39i	−0.255927	+	0.477548i
$235$	−1919.57	+	4634.25i	−0.532846	+	1.28640i
$236$	1709.35	+	1147.57i	0.471480	+	0.316527i
$237$	−851.522	+	352.712i	−0.233385	+	0.0966713i
$238$	1058.02	−	866.358i	0.288156	−	0.235956i
$239$		−	2049.94i		−	0.554811i	−0.960753	−	0.277406i	$-0.910525\pi$
$239$		−	2049.94i		−	0.554811i	0.960753	−	0.277406i	$-0.0894746\pi$
$240$	1356.25	−	3234.17i	0.364773	−	0.869852i
$241$		−	3964.18i		−	1.05956i	−0.848134	−	0.529782i	$-0.822274\pi$
$241$		−	3964.18i		−	1.05956i	0.848134	−	0.529782i	$-0.177726\pi$
$242$	−458.595	−	560.048i	−0.121816	−	0.148765i
$243$	2138.00	−	885.588i	0.564414	−	0.233788i
$244$	−177.111	−	900.693i	−0.0464687	−	0.236315i
$245$	−1422.04	+	3433.11i	−0.370820	+	0.895238i
$246$	971.498	+	520.644i	0.251791	+	0.134939i
$247$	2254.76	−	2254.76i	0.580838	−	0.580838i
$248$	4740.15	+	1454.91i	1.21371	+	0.372529i
$249$	1432.79	+	1432.79i	0.364657	+	0.364657i
$250$	905.846	+	2997.98i	0.229163	+	0.758435i
$251$	−3653.50	−	1513.33i	−0.918754	−	0.380560i	−0.127353	−	0.991858i	$-0.540648\pi$
$251$	−3653.50	−	1513.33i	−0.918754	−	0.380560i	−0.791401	+	0.611297i	$0.790648\pi$
$252$	−488.784	−	98.3374i	−0.122184	−	0.0245820i
$253$	−649.240	−	1567.41i	−0.161334	−	0.389494i
$254$	1367.47	+	136.195i	0.337805	+	0.0336441i
$255$	3664.34			0.899882
$256$	2870.85	+	2921.55i	0.700891	+	0.713269i
$257$	−6137.79			−1.48975			−0.744873	−	0.667206i	$-0.767490\pi$
$257$	−6137.79			−1.48975			−0.744873	+	0.667206i	$0.767490\pi$
$258$	−6333.58	−	630.801i	−1.52834	−	0.152217i
$259$	856.743	+	2068.36i	0.205542	+	0.496223i
$260$	7973.97	+	1604.27i	1.90202	+	0.382663i
$261$	1341.10	+	555.500i	0.318053	+	0.131742i
$262$	−1634.88	−	5410.78i	−0.385509	−	1.27588i
$263$	1379.24	+	1379.24i	0.323374	+	0.323374i	0.850060	−	0.526686i	$-0.176566\pi$
$263$	1379.24	+	1379.24i	0.323374	+	0.323374i	−0.526686	+	0.850060i	$0.676566\pi$
$264$	3694.33	+	1133.92i	0.861251	+	0.264348i
$265$	−2532.12	+	2532.12i	−0.586969	+	0.586969i
$266$	722.534	+	387.219i	0.166547	+	0.0892554i
$267$	2036.97	−	4917.69i	0.466894	−	1.12718i
$268$	−1343.26	−	6831.13i	−0.306168	−	1.55701i
$269$	136.201	−	56.4164i	0.0308711	−	0.0127872i	−0.367194	−	0.930144i	$-0.619682\pi$
$269$	136.201	−	56.4164i	0.0308711	−	0.0127872i	0.398066	+	0.917357i	$0.369682\pi$
$270$	−3497.65	−	4271.42i	−0.788372	−	0.962780i
$271$		−	1576.16i		−	0.353302i	−0.984274	−	0.176651i	$-0.943474\pi$
$271$		−	1576.16i		−	0.353302i	0.984274	−	0.176651i	$-0.0565264\pi$
$272$	−1655.07	+	3946.75i	−0.368946	+	0.879805i
$273$			2465.61i			0.546614i
$274$	−4210.92	+	3448.11i	−0.928435	+	0.760248i
$275$	1412.16	−	584.936i	0.309660	−	0.128265i
$276$	1212.72	+	814.159i	0.264483	+	0.177560i
$277$	−1137.39	+	2745.89i	−0.246711	+	0.595613i	−0.997921	−	0.0644505i	$-0.979471\pi$
$277$	−1137.39	+	2745.89i	−0.246711	+	0.595613i	0.751210	+	0.660063i	$0.229471\pi$
$278$	268.199	−	500.446i	0.0578614	−	0.107967i
$279$	1335.67	−	1335.67i	0.286610	−	0.286610i
$280$	198.124	+	2081.61i	0.0422864	+	0.444286i
$281$	346.910	+	346.910i	0.0736474	+	0.0736474i	0.742971	−	0.669324i	$-0.233416\pi$
$281$	346.910	+	346.910i	0.0736474	+	0.0736474i	−0.669324	+	0.742971i	$0.733416\pi$
$282$	4555.38	−	1376.42i	0.961947	−	0.290654i
$283$	2926.90	+	1212.36i	0.614791	+	0.254655i	0.668275	−	0.743914i	$-0.267033\pi$
$283$	2926.90	+	1212.36i	0.614791	+	0.254655i	−0.0534844	+	0.998569i	$0.517033\pi$
$284$	2427.33	+	3650.02i	0.507167	+	0.762637i
$285$	840.620	+	2029.44i	0.174716	+	0.421802i
$286$	−888.253	+	8918.54i	−0.183649	+	1.84393i
$287$	−657.181			−0.135164
$288$	1495.65	−	444.780i	0.306014	−	0.0910032i
$289$	441.294			0.0898217
$290$	603.350	−	6057.96i	0.122172	−	1.22667i
$291$	71.7883	+	173.312i	0.0144615	+	0.0349132i
$292$	−4881.19	+	3246.08i	−0.978253	+	0.650556i
$293$	551.934	+	228.618i	0.110049	+	0.0455837i	0.437029	−	0.899448i	$-0.356031\pi$
$293$	551.934	+	228.618i	0.110049	+	0.0455837i	−0.326980	+	0.945031i	$0.606031\pi$
$294$	3374.68	−	1019.67i	0.669440	−	0.202273i
$295$	−2325.96	−	2325.96i	−0.459060	−	0.459060i
$296$	−5401.58	−	4462.71i	−1.06068	−	0.876317i
$297$	4301.59	−	4301.59i	0.840416	−	0.840416i
$298$	2401.68	−	4481.43i	0.466864	−	0.871148i
$299$	−1296.41	+	3129.81i	−0.250747	+	0.605357i
$300$	−733.520	+	1092.61i	−0.141166	+	0.210272i
$301$	3506.12	−	1452.28i	0.671393	−	0.278100i
$302$	−3509.28	+	2873.57i	−0.668663	+	0.547534i
$303$			1983.56i			0.376081i
$304$	−2565.53	−	11.2275i	−0.484024	−	0.00211823i
$305$			1466.60i			0.275335i
$306$	1032.92	+	1261.43i	0.192968	+	0.235657i
$307$	3795.75	−	1572.25i	0.705651	−	0.292290i	−0.000852873	−	1.00000i	$-0.500271\pi$
$307$	3795.75	−	1572.25i	0.705651	−	0.292290i	0.706503	+	0.707710i	$0.250271\pi$
$308$	−2260.82	+	444.565i	−0.418254	+	0.0822449i
$309$	−1323.52	+	3195.26i	−0.243665	+	0.588259i
$310$	−6982.54	−	3742.07i	−1.27930	−	0.685598i
$311$	−2922.48	+	2922.48i	−0.532857	+	0.532857i	−0.921421	−	0.388565i	$-0.872971\pi$
$311$	−2922.48	+	2922.48i	−0.532857	+	0.532857i	0.388565	+	0.921421i	$0.372971\pi$
$312$	−3615.20	−	6817.28i	−0.655994	−	1.23703i
$313$	4410.61	+	4410.61i	0.796493	+	0.796493i	0.982541	−	0.186048i	$-0.0595678\pi$
$313$	4410.61	+	4410.61i	0.796493	+	0.796493i	−0.186048	+	0.982541i	$0.559568\pi$
$314$	−787.439	−	2606.10i	−0.141521	−	0.468378i
$315$	735.943	+	304.838i	0.131637	+	0.0545259i
$316$	−339.222	+	1686.09i	−0.0603883	+	0.300159i
$317$	−823.383	−	1987.82i	−0.145886	−	0.352199i	0.833998	−	0.551767i	$-0.186046\pi$
$317$	−823.383	−	1987.82i	−0.145886	−	0.352199i	−0.979884	+	0.199568i	$0.936046\pi$
$318$	3380.55	+	336.690i	0.596138	+	0.0593731i
$319$	6708.36			1.17742
$320$	−3599.96	−	5465.05i	−0.628887	−	0.954704i
$321$	4464.28			0.776236
$322$	−866.616	−	86.3117i	−0.149983	−	0.0149378i
$323$	−1025.83	−	2476.58i	−0.176715	−	0.426628i
$324$	−665.800	+	3309.34i	−0.114163	+	0.567446i
$325$	−2819.82	−	1168.01i	−0.481278	−	0.199352i
$326$	2113.54	+	6994.94i	0.359074	+	1.18839i
$327$	−424.019	−	424.019i	−0.0717074	−	0.0717074i
$328$	1817.07	−	963.591i	0.305887	−	0.162212i
$329$	−2006.32	+	2006.32i	−0.336206	+	0.336206i
$330$	−5441.98	−	2916.46i	−0.907792	−	0.486503i
$331$	2294.33	−	5539.00i	0.380990	−	0.919791i	−0.610785	−	0.791797i	$-0.709146\pi$
$331$	2294.33	−	5539.00i	0.380990	−	0.919791i	0.991775	−	0.127995i	$-0.0408540\pi$
$332$	3710.03	−	729.535i	0.613296	−	0.120598i
$333$	−2466.01	+	1021.46i	−0.405816	+	0.168094i
$334$	947.256	+	1156.81i	0.155184	+	0.189515i
$335$			11123.1i			1.81409i
$336$	1408.86	−	1396.58i	0.228748	−	0.226755i
$337$		−	4177.18i		−	0.675209i	−0.941288	−	0.337604i	$-0.890383\pi$
$337$		−	4177.18i		−	0.675209i	0.941288	−	0.337604i	$-0.109617\pi$
$338$	9038.94	−	7401.54i	1.45460	−	1.19110i
$339$	−3059.84	+	1267.43i	−0.490229	+	0.203060i
$340$	3811.28	−	5677.05i	0.607928	−	0.905533i
$341$	3340.60	−	8064.91i	0.530509	−	1.28076i
$342$	−461.664	+	861.445i	−0.0729940	+	0.136204i
$343$	−3239.85	+	3239.85i	−0.510015	+	0.510015i
$344$	−7564.83	+	9156.32i	−1.18566	+	1.43510i
$345$	−1650.18	−	1650.18i	−0.257516	−	0.257516i
$346$	−210.637	+	63.6445i	−0.0327281	+	0.00988888i
$347$	−6068.09	−	2513.48i	−0.938767	−	0.388850i	−0.139769	−	0.990184i	$-0.544636\pi$
$347$	−6068.09	−	2513.48i	−0.938767	−	0.388850i	−0.798998	+	0.601334i	$0.794636\pi$
$348$	−4809.30	+	3198.27i	−0.740820	+	0.492659i
$349$	3219.82	+	7773.32i	0.493848	+	1.19225i	0.952747	+	0.303765i	$0.0982438\pi$
$349$	3219.82	+	7773.32i	0.493848	+	1.19225i	−0.458899	+	0.888488i	$0.651756\pi$
$350$	77.7629	−	780.781i	0.0118760	−	0.119241i
$351$	−12147.3			−1.84723
$352$	5599.21	−	4544.12i	0.847838	−	0.688075i
$353$	−10007.7			−1.50895			−0.754473	−	0.656331i	$-0.772107\pi$
$353$	−10007.7			−1.50895			−0.754473	+	0.656331i	$0.772107\pi$
$354$	−309.278	+	3105.32i	−0.0464348	+	0.466231i
$355$	−2680.10	−	6470.34i	−0.400690	−	0.967352i
$356$	−5500.17	−	8270.71i	−0.818844	−	1.23131i
$357$	1914.97	+	793.206i	0.283896	+	0.117594i
$358$	−4866.97	+	1470.57i	−0.718512	+	0.217100i
$359$	3853.86	+	3853.86i	0.566572	+	0.566572i	0.931166	−	0.364595i	$-0.118792\pi$
$359$	3853.86	+	3853.86i	0.566572	+	0.566572i	−0.364595	+	0.931166i	$0.618792\pi$
$360$	−2481.81	+	236.215i	−0.363341	+	0.0345823i
$361$	−3713.76	+	3713.76i	−0.541443	+	0.541443i
$362$	−2643.65	+	4932.94i	−0.383832	+	0.716214i
$363$	419.873	−	1013.66i	0.0607097	−	0.146566i
$364$	3819.89	+	2564.48i	0.550046	+	0.369273i
$365$	8652.81	−	3584.11i	1.24085	−	0.513975i
$366$	1076.51	−	881.499i	0.153743	−	0.125893i
$367$		−	2274.12i		−	0.323456i	−0.986835	−	0.161728i	$-0.948293\pi$
$367$		−	2274.12i		−	0.323456i	0.986835	−	0.161728i	$-0.0517067\pi$
$368$	2522.70	−	1032.03i	0.357350	−	0.146191i
$369$		−	783.528i		−	0.110539i
$370$	7092.25	+	8661.24i	0.996510	+	1.21696i
$371$	−1871.39	+	775.156i	−0.261881	+	0.108475i
$372$	1450.11	+	7374.49i	0.202109	+	1.02782i
$373$	4974.80	−	12010.2i	0.690577	−	1.66720i	−0.0530384	−	0.998592i	$-0.516891\pi$
$373$	4974.80	−	12010.2i	0.690577	−	1.66720i	0.743615	−	0.668608i	$-0.233109\pi$
$374$	6641.02	+	3559.05i	0.918179	+	0.492069i
$375$	−3356.70	+	3356.70i	−0.462238	+	0.462238i
$376$	2605.60	−	8489.12i	0.357377	−	1.16434i
$377$	−9471.92	−	9471.92i	−1.29398	−	1.29398i
$378$	−903.240	−	2989.35i	−0.122904	−	0.406761i
$379$	10078.6	+	4174.70i	1.36597	+	0.565805i	0.940694	−	0.339257i	$-0.110176\pi$
$379$	10078.6	+	4174.70i	1.36597	+	0.565805i	0.425280	+	0.905062i	$0.360176\pi$
$380$	4018.47	+	808.469i	0.542482	+	0.109141i
$381$	797.128	+	1924.44i	0.107187	+	0.258771i
$382$	−8510.44	−	847.607i	−1.13987	−	0.113527i
$383$	14593.3			1.94695			0.973477	−	0.228784i	$-0.0734751\pi$
$383$	14593.3			1.94695			0.973477	+	0.228784i	$0.0734751\pi$
$384$	−1847.68	+	5927.21i	−0.245545	+	0.787686i
$385$	3681.29			0.487314
$386$	6066.22	+	604.173i	0.799903	+	0.0796673i
$387$	1731.49	+	4180.19i	0.227433	+	0.549072i
$388$	343.174	+	69.0426i	0.0449021	+	0.00903378i
$389$	5607.97	+	2322.90i	0.730939	+	0.302765i	0.716938	−	0.697137i	$-0.245543\pi$
$389$	5607.97	+	2322.90i	0.730939	+	0.302765i	0.0140014	+	0.999902i	$0.495543\pi$
$390$	3565.93	+	11801.8i	0.462995	+	1.53232i
$391$	2013.77	+	2013.77i	0.260462	+	0.260462i
$392$	1930.26	−	6288.85i	0.248707	−	0.810293i
$393$	6058.21	−	6058.21i	0.777599	−	0.777599i
$394$	7641.94	+	4095.46i	0.977145	+	0.523670i
$395$	1051.56	−	2538.69i	0.133948	−	0.323380i
$396$	−530.035	−	2695.48i	−0.0672607	−	0.342052i
$397$	−1428.80	+	591.828i	−0.180628	+	0.0748187i	−0.471165	−	0.882045i	$-0.656166\pi$
$397$	−1428.80	+	591.828i	−0.180628	+	0.0748187i	0.290536	+	0.956864i	$0.406166\pi$
$398$	1904.40	+	2325.70i	0.239846	+	0.292907i
$399$			1242.54i			0.155902i
$400$	929.809	+	2272.84i	0.116226	+	0.284105i
$401$			7265.44i			0.904786i	0.891819	+	0.452393i	$0.149429\pi$
$401$			7265.44i			0.904786i	−0.891819	+	0.452393i	$0.850571\pi$
$402$	8164.58	−	6685.56i	1.01297	−	0.829466i
$403$	−16104.1	+	6670.54i	−1.99058	+	0.824524i
$404$	3073.07	+	2063.10i	0.378443	+	0.254067i
$405$	2063.92	−	4982.75i	0.253228	−	0.611346i
$406$	1626.65	−	3035.26i	0.198841	−	0.371028i
$407$	−8722.41	+	8722.41i	−1.06229	+	1.06229i
$408$	−6457.83	+	614.646i	−0.783603	+	0.0745821i
$409$	−7223.12	−	7223.12i	−0.873252	−	0.873252i	0.119573	−	0.992825i	$-0.461847\pi$
$409$	−7223.12	−	7223.12i	−0.873252	−	0.873252i	−0.992825	+	0.119573i	$0.961847\pi$
$410$	−3145.63	+	950.461i	−0.378907	+	0.114488i
$411$	−7621.59	−	3156.97i	−0.914709	−	0.378885i
$412$	3573.73	+	5373.88i	0.427342	+	0.642602i
$413$	−712.046	−	1719.03i	−0.0848365	−	0.204813i
$414$	102.906	−	1033.23i	0.0122163	−	0.122658i
$415$	−6041.03			−0.714561
$416$	−14322.0	−	1489.74i	−1.68796	−	0.175578i
$417$	860.618			0.101066
$418$	−447.634	+	4494.49i	−0.0523792	+	0.525915i
$419$	−3225.87	−	7787.95i	−0.376120	−	0.908034i	−0.992685	−	0.120730i	$-0.961476\pi$
$419$	−3225.87	−	7787.95i	−0.376120	−	0.908034i	0.616566	−	0.787304i	$-0.288524\pi$
$420$	−2639.16	+	1755.09i	−0.306614	+	0.203904i
$421$	1956.30	+	810.327i	0.226471	+	0.0938074i	0.493034	−	0.870010i	$-0.335888\pi$
$421$	1956.30	+	810.327i	0.226471	+	0.0938074i	−0.266563	+	0.963818i	$0.585888\pi$
$422$	−1375.46	+	415.599i	−0.158665	+	0.0479409i
$423$	−2392.04	−	2392.04i	−0.274953	−	0.274953i
$424$	4037.73	−	4887.19i	0.462475	−	0.559771i
$425$	−1814.31	+	1814.31i	−0.207076	+	0.207076i
$426$	−3138.47	+	5856.24i	−0.356947	+	0.666047i
$427$	−317.469	+	766.438i	−0.0359799	+	0.0868631i
$428$	4643.29	−	6916.37i	0.524397	−	0.781110i
$429$	−12551.1	+	5198.82i	−1.41252	+	0.585085i
$430$	14681.8	−	12022.2i	1.64656	−	1.34829i
$431$		−	10185.7i		−	1.13835i	−0.822216	−	0.569175i	$-0.807263\pi$
$431$		−	10185.7i		−	1.13835i	0.822216	−	0.569175i	$-0.192737\pi$
$432$	6880.54	+	6941.03i	0.766297	+	0.773033i
$433$			4456.20i			0.494576i	0.968942	+	0.247288i	$0.0795394\pi$
$433$			4456.20i			0.494576i	−0.968942	+	0.247288i	$0.920461\pi$
$434$	−2839.01	−	3467.08i	−0.314002	−	0.383468i
$435$	8525.37	−	3531.32i	0.939678	−	0.389227i
$436$	−1097.94	+	215.898i	−0.120601	+	0.0237148i
$437$	−653.325	+	1577.27i	−0.0715166	+	0.172656i
$438$	−7831.58	−	4197.09i	−0.854354	−	0.457864i
$439$	2494.47	−	2494.47i	0.271195	−	0.271195i	−0.558386	−	0.829581i	$-0.688579\pi$
$439$	2494.47	−	2494.47i	0.271195	−	0.271195i	0.829581	+	0.558386i	$0.188579\pi$
$440$	−10178.6	+	5397.69i	−1.10283	+	0.584829i
$441$	−1772.05	−	1772.05i	−0.191346	−	0.191346i
$442$	−4351.62	−	14402.1i	−0.468293	−	1.54986i
$443$	13843.2	+	5734.06i	1.48468	+	0.614974i	0.970151	−	0.242501i	$-0.0779678\pi$
$443$	13843.2	+	5734.06i	1.48468	+	0.614974i	0.514526	+	0.857475i	$0.327968\pi$
$444$	2094.71	−	10411.7i	0.223897	−	1.11288i
$445$	6072.93	+	14661.4i	0.646932	+	1.56183i
$446$	−18044.4	−	1797.16i	−1.91576	−	0.190802i
$447$	7706.71			0.815469
$448$	−698.327	−	3635.28i	−0.0736447	−	0.383373i
$449$	6724.60			0.706801			0.353400	−	0.935472i	$-0.385025\pi$
$449$	6724.60			0.706801			0.353400	+	0.935472i	$0.385025\pi$
$450$	930.891	+	92.7132i	0.0975169	+	0.00971231i
$451$	−1385.69	−	3345.35i	−0.144677	−	0.349282i
$452$	−1218.95	+	6058.77i	−0.126847	+	0.630488i
$453$	−6351.64	−	2630.94i	−0.658778	−	0.272875i
$454$	298.708	+	988.601i	0.0308790	+	0.102197i
$455$	−5197.83	−	5197.83i	−0.535556	−	0.535556i
$456$	−1821.87	−	3435.56i	−0.187099	−	0.352818i
$457$	−12569.7	+	12569.7i	−1.28662	+	1.28662i	−0.349795	+	0.936826i	$0.613749\pi$
$457$	−12569.7	+	12569.7i	−1.28662	+	1.28662i	−0.936826	+	0.349795i	$0.886251\pi$
$458$	−5853.12	−	3136.80i	−0.597158	−	0.320028i
$459$	−3907.90	+	9434.49i	−0.397396	+	0.959400i
$460$	−4272.94	+	840.224i	−0.433101	+	0.0851645i
$461$	5822.39	−	2411.71i	0.588234	−	0.243654i	−0.0686568	−	0.997640i	$-0.521871\pi$
$461$	5822.39	−	2411.71i	0.588234	−	0.243654i	0.656891	+	0.753986i	$0.271871\pi$
$462$	−2212.64	−	2702.14i	−0.222817	−	0.272110i
$463$		−	15045.1i		−	1.51016i	−0.655634	−	0.755079i	$-0.727598\pi$
$463$		−	15045.1i		−	1.51016i	0.655634	−	0.755079i	$-0.272402\pi$
$464$	−47.1651	+	10777.4i	−0.00471893	+	1.07829i
$465$		−	12007.9i		−	1.19753i
$466$	−4465.49	+	3656.56i	−0.443905	+	0.363491i
$467$	12797.5	−	5300.90i	1.26809	−	0.525260i	0.355708	−	0.934597i	$-0.384240\pi$
$467$	12797.5	−	5300.90i	1.26809	−	0.525260i	0.912383	+	0.409337i	$0.134240\pi$
$468$	−3057.51	+	4554.29i	−0.301995	+	0.449833i
$469$	−2407.78	+	5812.90i	−0.237060	+	0.572313i
$470$	−6701.67	+	12505.0i	−0.657713	+	1.22726i
$471$	2917.93	−	2917.93i	0.285459	−	0.285459i
$472$	4489.29	+	3708.99i	0.437789	+	0.361696i
$473$	14785.5	+	14785.5i	1.43729	+	1.43729i
$474$	−2495.48	+	754.015i	−0.241817	+	0.0730656i
$475$	−1421.04	−	588.616i	−0.137267	−	0.0568580i
$476$	3220.65	−	2141.79i	0.310122	−	0.206237i
$477$	−924.184	−	2231.18i	−0.0887117	−	0.214169i
$478$	574.628	−	5769.57i	0.0549850	−	0.552080i
$479$	5991.54			0.571525			0.285762	−	0.958301i	$-0.407753\pi$
$479$	5991.54			0.571525			0.285762	+	0.958301i	$0.407753\pi$
$480$	4723.74	−	8722.39i	0.449184	−	0.829419i
$481$	24631.4			2.33491
$482$	1111.21	−	11157.2i	0.105009	−	1.05435i
$483$	−505.170	−	1219.59i	−0.0475902	−	0.114893i
$484$	−1133.73	−	1704.81i	−0.106473	−	0.160106i
$485$	−516.705	−	214.026i	−0.0483760	−	0.0200380i
$486$	6265.64	−	1893.18i	0.584805	−	0.176700i
$487$	6120.86	+	6120.86i	0.569534	+	0.569534i	0.931998	−	0.362464i	$-0.118064\pi$
$487$	6120.86	+	6120.86i	0.569534	+	0.569534i	−0.362464	+	0.931998i	$0.618064\pi$
$488$	−246.003	−	2584.65i	−0.0228197	−	0.239757i
$489$	−7831.92	+	7831.92i	−0.724278	+	0.724278i
$490$	−4964.68	+	9263.87i	−0.457717	+	0.854080i
$491$	−7107.17	+	17158.2i	−0.653242	+	1.57707i	0.154803	+	0.987945i	$0.450526\pi$
$491$	−7107.17	+	17158.2i	−0.653242	+	1.57707i	−0.808045	+	0.589121i	$0.799474\pi$
$492$	2588.34	+	1737.68i	0.237178	+	0.159229i
$493$	−10403.8	+	4309.38i	−0.950430	+	0.393681i
$494$	6978.07	−	5713.99i	0.635543	−	0.520414i
$495$			4389.04i			0.398531i
$496$	12933.3	+	5423.59i	1.17081	+	0.490980i
$497$		−	3961.52i		−	0.357543i
$498$	3630.97	+	4434.23i	0.326722	+	0.399001i
$499$	276.250	−	114.426i	0.0247828	−	0.0102654i	−0.370258	−	0.928929i	$-0.620731\pi$
$499$	276.250	−	114.426i	0.0247828	−	0.0102654i	0.395040	+	0.918664i	$0.370731\pi$
$500$	1709.13	+	8691.74i	0.152869	+	0.777413i
$501$	−867.274	+	2093.78i	−0.0773392	+	0.186713i
$502$	−9858.59	−	5283.40i	−0.876515	−	0.469741i
$503$	3966.95	−	3966.95i	0.351645	−	0.351645i	−0.509076	−	0.860721i	$-0.670013\pi$
$503$	3966.95	−	3966.95i	0.351645	−	0.351645i	0.860721	+	0.509076i	$0.170013\pi$
$504$	−1348.12	−	413.784i	−0.119147	−	0.0365702i
$505$	−4181.61	−	4181.61i	−0.368474	−	0.368474i
$506$	−1387.92	−	4593.46i	−0.121938	−	0.403565i
$507$	16360.1	+	6776.58i	1.43309	+	0.593606i
$508$	3810.56	+	766.640i	0.332808	+	0.0669570i
$509$	−4067.11	−	9818.87i	−0.354168	−	0.855037i	−0.996096	−	0.0882726i	$-0.971865\pi$
$509$	−4067.11	−	9818.87i	−0.354168	−	0.855037i	0.641928	−	0.766765i	$-0.278135\pi$
$510$	10313.3	+	1027.16i	0.895452	+	0.0891836i
$511$	5297.76			0.458629
$512$	7261.06	+	9027.44i	0.626751	+	0.779219i
$513$	−6121.64			−0.526856
$514$	−17274.8	−	1720.51i	−1.48241	−	0.147643i
$515$	−3945.88	−	9526.19i	−0.337624	−	0.815095i
$516$	−17649.1	−	3550.78i	−1.50573	−	0.302935i
$517$	−14443.4	−	5982.67i	−1.22867	−	0.508931i
$518$	1831.52	+	6061.56i	0.155352	+	0.514150i
$519$	−235.841	−	235.841i	−0.0199466	−	0.0199466i
$520$	21993.1	+	6750.43i	1.85473	+	0.569280i
$521$	9171.85	−	9171.85i	0.771259	−	0.771259i	−0.207067	−	0.978327i	$-0.566392\pi$
$521$	9171.85	−	9171.85i	0.771259	−	0.771259i	0.978327	+	0.207067i	$0.0663919\pi$
$522$	3618.80	+	1939.38i	0.303430	+	0.162614i
$523$	6048.17	−	14601.6i	0.505675	−	1.22081i	−0.440676	−	0.897666i	$-0.645261\pi$
$523$	6048.17	−	14601.6i	0.505675	−	1.22081i	0.946351	−	0.323140i	$-0.104739\pi$
$524$	−3084.66	−	15686.9i	−0.257164	−	1.30780i
$525$	1098.79	−	455.135i	0.0913434	−	0.0378357i
$526$	3495.25	+	4268.48i	0.289734	+	0.353830i
$527$			14653.6i			1.21123i
$528$	10079.8	+	4226.98i	0.830812	+	0.348401i
$529$			10353.3i			0.850929i
$530$	−7836.44	+	6416.86i	−0.642251	+	0.525907i
$531$	2049.52	−	848.940i	0.167499	−	0.0693802i
$532$	1925.03	+	1292.37i	0.156881	+	0.105322i
$533$	−2766.96	+	6680.03i	−0.224860	+	0.542860i
$534$	7111.56	−	13269.9i	0.576306	−	1.07536i
$535$	−9411.29	+	9411.29i	−0.760534	+	0.760534i
$536$	−1865.76	−	19602.8i	−0.150352	−	1.57968i
$537$	−5449.33	−	5449.33i	−0.437907	−	0.437907i
$538$	399.153	−	120.605i	0.0319864	−	0.00966477i
$539$	−10699.9	−	4432.04i	−0.855059	−	0.354177i
$540$	−8646.81	−	13002.4i	−0.689073	−	1.03617i
$541$	1872.33	+	4520.21i	0.148795	+	0.359222i	0.980650	−	0.195771i	$-0.0627210\pi$
$541$	1872.33	+	4520.21i	0.148795	+	0.359222i	−0.831855	+	0.554993i	$0.812721\pi$
$542$	441.819	−	4436.10i	0.0350143	−	0.351563i
$543$	−8483.17			−0.670437
$544$	−5764.53	+	10644.2i	−0.454324	+	0.838909i
$545$	1787.78			0.140514
$546$	−691.144	+	6939.46i	−0.0541726	+	0.543923i
$547$	−1131.56	−	2731.83i	−0.0884499	−	0.213537i	0.873464	−	0.486888i	$-0.161868\pi$
$547$	−1131.56	−	2731.83i	−0.0884499	−	0.213537i	−0.961914	+	0.273351i	$0.911868\pi$
$548$	−12818.2	+	8524.34i	−0.999209	+	0.664492i
$549$	−913.789	−	378.504i	−0.0710375	−	0.0294247i
$550$	4138.49	−	1250.46i	0.320847	−	0.0969447i
$551$	−4773.36	−	4773.36i	−0.369060	−	0.369060i
$552$	3184.99	+	2631.40i	0.245584	+	0.202898i
$553$	1099.08	−	1099.08i	0.0845165	−	0.0845165i
$554$	−3970.89	+	7409.50i	−0.304525	+	0.568230i
$555$	−6493.41	+	15676.5i	−0.496630	+	1.19897i
$556$	895.128	−	1333.33i	0.0682767	−	0.101701i
$557$	−4125.91	+	1709.01i	−0.313861	+	0.130005i	−0.534053	−	0.845451i	$-0.679332\pi$
$557$	−4125.91	+	1709.01i	−0.313861	+	0.130005i	0.220192	+	0.975457i	$0.429332\pi$
$558$	4133.64	−	3384.83i	0.313604	−	0.256794i
$559$		−	41753.1i		−	3.15916i
$560$	−25.8824	+	5914.24i	−0.00195309	+	0.446289i
$561$			11420.6i			0.859494i
$562$	879.135	+	1073.62i	0.0659859	+	0.0805837i
$563$	−13629.3	+	5645.44i	−1.02026	+	0.422605i	−0.829187	−	0.558971i	$-0.811196\pi$
$563$	−13629.3	+	5645.44i	−1.02026	+	0.422605i	−0.191072	+	0.981576i	$0.561196\pi$
$564$	13207.0	−	2597.00i	0.986016	−	0.193889i
$565$	3778.65	−	9122.46i	0.281361	−	0.679265i
$566$	7897.91	+	4232.64i	0.586527	+	0.314330i
$567$	2157.20	−	2157.20i	0.159777	−	0.159777i
$568$	5808.58	+	10953.4i	0.429089	+	0.809146i
$569$	−1198.17	−	1198.17i	−0.0882777	−	0.0882777i	0.661589	−	0.749867i	$-0.269882\pi$
$569$	−1198.17	−	1198.17i	−0.0882777	−	0.0882777i	−0.749867	+	0.661589i	$0.769882\pi$
$570$	1797.05	+	5947.49i	0.132053	+	0.437040i
$571$	1981.86	+	820.913i	0.145251	+	0.0601649i	0.454125	−	0.890938i	$-0.349952\pi$
$571$	1981.86	+	820.913i	0.145251	+	0.0601649i	−0.308874	+	0.951103i	$0.599952\pi$
$572$	−4999.98	+	24852.3i	−0.365489	+	1.81665i
$573$	−4960.93	−	11976.7i	−0.361685	−	0.873186i
$574$	−1849.64	−	184.217i	−0.134499	−	0.0133956i
$575$	1634.10			0.118516
$576$	4334.18	−	832.584i	0.313526	−	0.0602274i
$577$	1653.54			0.119303			0.0596515	−	0.998219i	$-0.481001\pi$
$577$	1653.54			0.119303			0.0596515	+	0.998219i	$0.481001\pi$
$578$	1242.02	+	123.701i	0.0893795	+	0.00890185i
$579$	3536.14	+	8536.99i	0.253812	+	0.612755i
$580$	3396.26	−	16881.0i	0.243141	−	1.20853i
$581$	−3157.02	−	1307.68i	−0.225431	−	0.0933765i
$582$	153.467	+	507.911i	0.0109302	+	0.0361746i
$583$	−7891.78	−	7891.78i	−0.560625	−	0.560625i
$584$	−14648.0	+	7767.83i	−1.03791	+	0.550403i
$585$	6197.14	−	6197.14i	0.437983	−	0.437983i
$586$	1489.33	+	798.162i	0.104989	+	0.0562658i
$587$	5748.28	−	13877.6i	0.404186	−	0.975790i	−0.582453	−	0.812865i	$-0.697907\pi$
$587$	5748.28	−	13877.6i	0.404186	−	0.975790i	0.986638	−	0.162926i	$-0.0520931\pi$
$588$	9783.88	−	1923.89i	0.686191	−	0.134932i
$589$	−8115.65	+	3361.61i	−0.567741	+	0.235166i
$590$	−5894.43	−	7198.42i	−0.411304	−	0.502296i
$591$			13141.8i			0.914692i
$592$	−13951.8	−	14074.4i	−0.968607	−	0.977122i
$593$		−	10098.5i		−	0.699322i	−0.936876	−	0.349661i	$-0.886297\pi$
$593$		−	10098.5i		−	0.699322i	0.936876	−	0.349661i	$-0.113703\pi$
$594$	13312.6	−	10901.0i	0.919569	−	0.752989i
$595$	−5709.19	+	2364.83i	−0.393368	+	0.162938i
$596$	8015.74	−	11939.8i	0.550902	−	0.820590i
$597$	−1743.60	+	4209.42i	−0.119532	+	0.288576i
$598$	−4526.08	+	8445.46i	−0.309507	+	0.577526i
$599$	15005.1	−	15005.1i	1.02353	−	1.02353i	0.0238107	−	0.999716i	$-0.492420\pi$
$599$	15005.1	−	15005.1i	1.02353	−	1.02353i	0.999716	−	0.0238107i	$-0.00757989\pi$
$600$	−2370.77	+	2869.53i	−0.161310	+	0.195247i
$601$	11177.5	+	11177.5i	0.758632	+	0.758632i	0.976073	−	0.217442i	$-0.0697712\pi$
$601$	11177.5	+	11177.5i	0.758632	+	0.758632i	−0.217442	+	0.976073i	$0.569771\pi$
$602$	10275.1	−	3104.64i	0.695649	−	0.210192i
$603$	−6930.46	−	2870.69i	−0.468043	−	0.193870i
$604$	−10682.4	+	7103.97i	−0.719635	+	0.478570i
$605$	1251.79	+	3022.08i	0.0841197	+	0.203083i
$606$	−556.020	+	5582.74i	−0.0372719	+	0.374230i
$607$	−16418.5			−1.09787			−0.548935	−	0.835865i	$-0.684967\pi$
$607$	−16418.5			−1.09787			−0.548935	+	0.835865i	$0.684967\pi$
$608$	−7217.54	−	750.753i	−0.481431	−	0.0500774i
$609$	5219.73			0.347314
$610$	−411.107	+	4127.74i	−0.0272873	+	0.273979i
$611$	11946.3	+	28840.8i	0.790989	+	1.90962i
$612$	2553.56	+	3839.83i	0.168663	+	0.253621i
$613$	−954.545	−	395.385i	−0.0628935	−	0.0260513i	0.351015	−	0.936370i	$-0.385837\pi$
$613$	−954.545	−	395.385i	−0.0628935	−	0.0260513i	−0.413908	+	0.910319i	$0.635837\pi$
$614$	11123.9	−	3361.10i	0.731144	−	0.220917i
$615$	−3522.03	−	3522.03i	−0.230930	−	0.230930i
$616$	−6487.70	+	617.490i	−0.424346	+	0.0403886i
$617$	7933.23	−	7933.23i	0.517633	−	0.517633i	−0.399221	−	0.916855i	$-0.630719\pi$
$617$	7933.23	−	7933.23i	0.517633	−	0.517633i	0.916855	+	0.399221i	$0.130719\pi$
$618$	−4620.73	+	8622.07i	−0.300765	+	0.561214i
$619$	−5475.77	+	13219.7i	−0.355557	+	0.858391i	0.640356	+	0.768078i	$0.278787\pi$
$619$	−5475.77	+	13219.7i	−0.355557	+	0.858391i	−0.995913	+	0.0903128i	$0.971213\pi$
$620$	−18603.4	−	12489.4i	−1.20505	−	0.809009i
$621$	6008.56	−	2488.83i	0.388269	−	0.160826i
$622$	−9044.53	+	7406.11i	−0.583043	+	0.477424i
$623$			8976.55i			0.577268i
$624$	−8264.00	−	20200.6i	−0.530168	−	1.29595i
$625$		−	18949.0i		−	1.21274i
$626$	11177.3	+	13650.0i	0.713635	+	0.871509i
$627$	−6325.10	+	2619.94i	−0.402871	+	0.166875i
$628$	−1485.72	−	7555.60i	−0.0944057	−	0.480097i
$629$	7924.11	−	19130.5i	0.502313	−	1.21269i
$630$	1985.86	+	1064.26i	0.125585	+	0.0673034i
$631$	−14339.1	+	14339.1i	−0.904647	+	0.904647i	−0.995834	−	0.0911870i	$-0.970934\pi$
$631$	−14339.1	+	14339.1i	−0.904647	+	0.904647i	0.0911870	+	0.995834i	$0.470934\pi$
$632$	−1427.37	+	4650.42i	−0.0898385	+	0.292696i
$633$	−1540.04	−	1540.04i	−0.0967002	−	0.0967002i
$634$	−1760.20	−	5825.53i	−0.110262	−	0.364923i
$635$	−5737.42	−	2376.52i	−0.358555	−	0.148519i
$636$	9420.19	+	1895.23i	0.587319	+	0.118162i
$637$	8849.94	+	21365.6i	0.550467	+	1.32894i
$638$	18880.7	+	1880.44i	1.17162	+	0.116689i
$639$	4723.15			0.292402
$640$	−8600.17	−	16390.5i	−0.531174	−	1.01233i
$641$	−8662.28			−0.533759			−0.266879	−	0.963730i	$-0.585993\pi$
$641$	−8662.28			−0.533759			−0.266879	+	0.963730i	$0.585993\pi$
$642$	12564.7	+	1251.40i	0.772414	+	0.0769295i
$643$	3070.12	+	7411.92i	0.188295	+	0.454584i	0.989632	−	0.143630i	$-0.0458774\pi$
$643$	3070.12	+	7411.92i	0.188295	+	0.454584i	−0.801337	+	0.598214i	$0.795877\pi$
$644$	−2414.90	−	485.849i	−0.147765	−	0.0297285i
$645$	26573.5	+	11007.1i	1.62222	+	0.671945i
$646$	−2192.99	−	7257.91i	−0.133564	−	0.442041i
$647$	16839.6	+	16839.6i	1.02323	+	1.02323i	0.999724	+	0.0235089i	$0.00748380\pi$
$647$	16839.6	+	16839.6i	1.02323	+	1.02323i	0.0235089	+	0.999724i	$0.492516\pi$
$648$	−2801.55	+	9127.52i	−0.169838	+	0.553338i
$649$	7249.27	−	7249.27i	0.438457	−	0.438457i
$650$	−7608.97	−	4077.79i	−0.459151	−	0.246068i
$651$	2599.30	−	6275.26i	0.156489	−	0.377799i
$652$	3987.78	+	20279.7i	0.239530	+	1.21812i
$653$	5431.53	−	2249.81i	0.325501	−	0.134827i	−0.213948	−	0.976845i	$-0.568632\pi$
$653$	5431.53	−	2249.81i	0.325501	−	0.134827i	0.539449	+	0.842018i	$0.318632\pi$
$654$	−1074.55	−	1312.26i	−0.0642478	−	0.0784610i
$655$			25543.0i			1.52374i
$656$	5384.26	−	2202.68i	0.320457	−	0.131098i
$657$			6316.28i			0.375071i
$658$	−6209.18	+	5084.39i	−0.367871	+	0.301231i
$659$	6283.92	−	2602.88i	0.371452	−	0.153860i	−0.189145	−	0.981949i	$-0.560572\pi$
$659$	6283.92	−	2602.88i	0.371452	−	0.153860i	0.560597	+	0.828089i	$0.310572\pi$
$660$	−14499.0	−	9733.85i	−0.855107	−	0.574075i
$661$	−6288.29	+	15181.3i	−0.370024	+	0.893318i	0.623721	+	0.781647i	$0.285620\pi$
$661$	−6288.29	+	15181.3i	−0.370024	+	0.893318i	−0.993745	+	0.111671i	$0.964380\pi$
$662$	8010.05	−	14946.4i	0.470271	−	0.877505i
$663$	16125.4	−	16125.4i	0.944580	−	0.944580i
$664$	10646.4	−	1013.31i	0.622228	−	0.0592227i
$665$	−2619.44	−	2619.44i	−0.152748	−	0.152748i
$666$	−7226.93	+	2183.63i	−0.420477	+	0.127048i
$667$	6625.86	+	2744.52i	0.384639	+	0.159323i
$668$	2341.78	+	3521.38i	0.135638	+	0.203962i
$669$	−10518.5	−	25394.0i	−0.607877	−	1.46754i
$670$	−3117.97	+	31306.1i	−0.179787	+	1.80516i
$671$	−4570.91			−0.262978
$672$	4356.71	−	3535.76i	0.250095	−	0.202968i
$673$	−22750.9			−1.30309			−0.651546	−	0.758609i	$-0.725879\pi$
$673$	−22750.9			−1.30309			−0.651546	+	0.758609i	$0.725879\pi$
$674$	1170.92	−	11756.7i	0.0669172	−	0.671885i
$675$	2242.32	+	5413.44i	0.127862	+	0.308686i
$676$	27514.9	−	18297.9i	1.56548	−	1.04107i
$677$	18090.7	+	7493.42i	1.02701	+	0.425400i	0.831631	−	0.555329i	$-0.187408\pi$
$677$	18090.7	+	7493.42i	1.02701	+	0.425400i	0.195375	+	0.980729i	$0.437408\pi$
$678$	−8967.21	+	2709.46i	−0.507940	+	0.153475i
$679$	−223.698	−	223.698i	−0.0126432	−	0.0126432i
$680$	12318.2	−	14909.7i	0.694679	−	0.840826i
$681$	−1106.89	+	1106.89i	−0.0622852	+	0.0622852i
$682$	11662.8	−	21762.3i	0.654828	−	1.22188i
$683$	4949.33	−	11948.7i	0.277278	−	0.669408i	−0.722481	−	0.691391i	$-0.756998\pi$
$683$	4949.33	−	11948.7i	0.277278	−	0.669408i	0.999758	+	0.0219835i	$0.00699813\pi$
$684$	−1540.83	+	2295.13i	−0.0861332	+	0.128299i
$685$	22722.6	−	9412.02i	1.26743	−	0.524985i
$686$	−10026.7	+	8210.38i	−0.558050	+	0.456959i
$687$		−	10065.6i		−	0.558991i
$688$	−23857.9	+	23650.0i	−1.32205	+	1.31053i
$689$			22285.7i			1.23225i
$690$	−4181.88	−	5107.02i	−0.230727	−	0.281769i
$691$	−8985.78	+	3722.03i	−0.494696	+	0.204910i	−0.616062	−	0.787698i	$-0.711273\pi$
$691$	−8985.78	+	3722.03i	−0.494696	+	0.204910i	0.121365	+	0.992608i	$0.461273\pi$
$692$	−610.680	+	120.083i	−0.0335470	+	0.00659665i
$693$	−950.080	+	2293.69i	−0.0520787	+	0.125729i
$694$	−16374.1	−	8775.18i	−0.895608	−	0.479973i
$695$	−1814.30	+	1814.30i	−0.0990218	+	0.0990218i
$696$	−14432.3	+	7653.42i	−0.785998	+	0.416814i
$697$	4298.04	+	4298.04i	0.233572	+	0.233572i
$698$	6883.21	+	22780.6i	0.373257	+	1.23533i
$699$	−8082.35	−	3347.82i	−0.437343	−	0.181153i
$700$	437.728	−	2175.71i	0.0236351	−	0.117477i
$701$	−5041.79	−	12172.0i	−0.271649	−	0.655818i	0.727905	−	0.685678i	$-0.240494\pi$
$701$	−5041.79	−	12172.0i	−0.271649	−	0.655818i	−0.999554	+	0.0298593i	$0.990494\pi$
$702$	−34188.7	−	3405.07i	−1.83813	−	0.183071i
$703$	12413.0			0.665951
$704$	17032.8	−	11219.9i	0.911856	−	0.600662i
$705$	−21504.9			−1.14882
$706$	−28166.8	−	2805.30i	−1.50152	−	0.149545i
$707$	−1280.12	−	3090.47i	−0.0680958	−	0.164398i
$708$	−1740.93	+	8653.23i	−0.0924125	+	0.459334i
$709$	−29815.3	−	12349.9i	−1.57932	−	0.654176i	−0.591014	−	0.806661i	$-0.701272\pi$
$709$	−29815.3	−	12349.9i	−1.57932	−	0.654176i	−0.988306	+	0.152486i	$0.951272\pi$
$710$	−5729.43	−	18962.0i	−0.302847	−	1.00230i
$711$	1310.38	+	1310.38i	0.0691185	+	0.0691185i
$712$	−13161.8	−	24819.7i	−0.692783	−	1.30640i
$713$	6599.03	−	6599.03i	0.346614	−	0.346614i
$714$	5167.34	+	2769.27i	0.270844	+	0.145150i
$715$	15499.5	−	37419.1i	0.810697	−	1.95720i
$716$	−14110.3	+	2774.63i	−0.736491	+	0.144823i
$717$	8119.52	−	3363.22i	0.422914	−	0.175177i
$718$	9766.42	+	11927.0i	0.507632	+	0.619933i
$719$			35519.5i			1.84236i	0.389141	+	0.921178i	$0.372772\pi$
$719$			35519.5i			1.84236i	−0.389141	+	0.921178i	$0.627228\pi$
$720$	−7051.28	−	30.8584i	−0.364980	−	0.00159726i
$721$		−	5832.50i		−	0.301267i
$722$	−11493.4	+	9411.37i	−0.592438	+	0.485118i
$723$	15701.5	−	6503.78i	0.807670	−	0.334548i
$724$	−8823.33	+	13142.7i	−0.452924	+	0.674648i
$725$	−2472.69	+	5969.60i	−0.126667	+	0.305800i
$726$	1465.88	−	2735.26i	0.0749363	−	0.139828i
$727$	−6873.52	+	6873.52i	−0.350653	+	0.350653i	−0.860353	−	0.509699i	$-0.829757\pi$
$727$	−6873.52	+	6873.52i	−0.350653	+	0.350653i	0.509699	+	0.860353i	$0.329757\pi$
$728$	10032.2	+	8288.50i	0.510741	+	0.421967i
$729$	15071.3	+	15071.3i	0.765702	+	0.765702i
$730$	25358.0	−	7661.99i	1.28567	−	0.388470i
$731$	−32428.5	−	13432.3i	−1.64078	−	0.679634i
$732$	3276.93	−	2179.22i	0.165463	−	0.110036i
$733$	6189.58	+	14943.0i	0.311893	+	0.752975i	0.999635	+	0.0270204i	$0.00860190\pi$
$733$	6189.58	+	14943.0i	0.311893	+	0.752975i	−0.687742	+	0.725955i	$0.741398\pi$
$734$	637.468	−	6400.52i	0.0320564	−	0.321863i
$735$	−15931.1			−0.799492
$736$	7389.44	−	2197.49i	0.370080	−	0.110055i
$737$	−34667.2			−1.73268
$738$	219.634	−	2205.24i	0.0109550	−	0.109995i
$739$	−8349.16	−	20156.7i	−0.415601	−	1.00335i	−0.983607	−	0.180325i	$-0.942285\pi$
$739$	−8349.16	−	20156.7i	−0.415601	−	1.00335i	0.568007	−	0.823024i	$-0.307715\pi$
$740$	17533.3	+	26365.1i	0.870996	+	1.30973i
$741$	12630.0	+	5231.53i	0.626148	+	0.259359i
$742$	−5484.32	+	1657.10i	−0.271342	+	0.0819867i
$743$	−6318.96	−	6318.96i	−0.312006	−	0.312006i	0.533680	−	0.845686i	$-0.320809\pi$
$743$	−6318.96	−	6318.96i	−0.312006	−	0.312006i	−0.845686	+	0.533680i	$0.820809\pi$
$744$	2014.17	+	21162.0i	0.0992512	+	1.04279i
$745$	−16246.8	+	16246.8i	−0.798974	+	0.798974i
$746$	17368.2	−	32408.3i	0.852406	−	1.59055i
$747$	1559.09	−	3763.97i	0.0763642	−	0.184360i
$748$	17693.5	+	11878.5i	0.864892	+	0.580644i
$749$	−6955.53	+	2881.07i	−0.339318	+	0.140550i
$750$	−10388.4	+	8506.52i	−0.505773	+	0.414152i
$751$		−	4475.99i		−	0.217485i	−0.994070	−	0.108742i	$-0.965318\pi$
$751$		−	4475.99i		−	0.217485i	0.994070	−	0.108742i	$-0.0346824\pi$
$752$	9713.10	−	23162.3i	0.471011	−	1.12319i
$753$		−	16953.8i		−	0.820493i
$754$	−24003.6	−	29313.9i	−1.15936	−	1.41585i
$755$	18936.5	−	7843.74i	0.912806	−	0.378097i
$756$	−1704.21	−	8666.73i	−0.0819863	−	0.416939i
$757$	−8674.08	+	20941.1i	−0.416466	+	1.00544i	0.566897	+	0.823788i	$0.308144\pi$
$757$	−8674.08	+	20941.1i	−0.416466	+	1.00544i	−0.983363	+	0.181650i	$0.941856\pi$
$758$	27196.1	+	14574.9i	1.30317	+	0.698395i
$759$	5143.09	−	5143.09i	0.245958	−	0.245958i
$760$	11083.4	+	3401.87i	0.528995	+	0.162367i
$761$	−6136.35	−	6136.35i	−0.292303	−	0.292303i	0.545686	−	0.837989i	$-0.316269\pi$
$761$	−6136.35	−	6136.35i	−0.292303	−	0.292303i	−0.837989	+	0.545686i	$0.816269\pi$
$762$	1704.07	+	5639.78i	0.0810132	+	0.268120i
$763$	934.286	+	386.994i	0.0443295	+	0.0183619i
$764$	−23715.1	−	4771.19i	−1.12301	−	0.225936i
$765$	−2819.48	−	6806.82i	−0.133253	−	0.321701i
$766$	41072.9	+	4090.71i	1.93737	+	0.192955i
$767$	−20471.3			−0.963725
$768$	−6861.79	+	16164.2i	−0.322400	+	0.759473i
$769$	13154.1			0.616838			0.308419	−	0.951251i	$-0.400200\pi$
$769$	13154.1			0.616838			0.308419	+	0.951251i	$0.400200\pi$
$770$	10361.0	+	1031.92i	0.484915	+	0.0482957i
$771$	−10069.9	−	24310.9i	−0.470374	−	1.13558i
$772$	16904.0	+	3400.89i	0.788069	+	0.158550i
$773$	−14475.7	−	5996.05i	−0.673552	−	0.278995i	0.0195763	−	0.999808i	$-0.493768\pi$
$773$	−14475.7	−	5996.05i	−0.673552	−	0.278995i	−0.693129	+	0.720814i	$0.743768\pi$
$774$	3701.52	+	12250.5i	0.171897	+	0.568909i
$775$	5945.42	+	5945.42i	0.275569	+	0.275569i
$776$	946.511	+	290.517i	0.0437858	+	0.0134394i
$777$	−6786.86	+	6786.86i	−0.313356	+	0.313356i
$778$	15132.5	+	8109.79i	0.697335	+	0.373715i
$779$	−1394.41	+	3366.39i	−0.0641332	+	0.154831i
$780$	6728.13	+	34215.7i	0.308853	+	1.57067i
$781$	20165.9	−	8353.00i	0.923936	−	0.382707i
$782$	5103.27	+	6232.25i	0.233367	+	0.284993i
$783$			25716.1i			1.17371i
$784$	7195.58	−	17158.9i	0.327787	−	0.781655i
$785$			12302.8i			0.559369i
$786$	18749.1	−	15352.7i	0.850836	−	0.696706i
$787$	29783.0	−	12336.5i	1.34898	−	0.558768i	0.412975	−	0.910742i	$-0.364490\pi$
$787$	29783.0	−	12336.5i	1.34898	−	0.558768i	0.936010	+	0.351975i	$0.114490\pi$
$788$	20360.2	+	13668.8i	0.920436	+	0.617933i
$789$	−3200.12	+	7725.78i	−0.144395	+	0.348599i
$790$	3671.24	−	6850.37i	0.165338	−	0.308513i
$791$	3949.41	−	3949.41i	0.177528	−	0.177528i
$792$	−736.205	−	7735.00i	−0.0330302	−	0.347034i
$793$	6453.93	+	6453.93i	0.289011	+	0.289011i
$794$	−4187.26	+	1265.19i	−0.187154	+	0.0565490i
$795$	−14183.6	−	5875.05i	−0.632756	−	0.262096i
$796$	4708.01	+	7079.52i	0.209637	+	0.315235i
$797$	−179.018	−	432.187i	−0.00795626	−	0.0192081i	0.919851	−	0.392267i	$-0.128309\pi$
$797$	−179.018	−	432.187i	−0.00795626	−	0.0192081i	−0.927808	+	0.373059i	$0.878309\pi$
$798$	−348.301	+	3497.14i	−0.0154508	+	0.155134i
$799$	26243.1			1.16197
$800$	1979.84	+	6657.55i	0.0874974	+	0.294225i
$801$	−10702.3			−0.472096
$802$	−2036.60	+	20448.6i	−0.0896696	+	0.900331i
$803$	11170.5	+	26968.0i	0.490907	+	1.18516i
$804$	24853.3	−	16527.9i	1.09018	−	0.724992i
$805$	3636.02	+	1506.09i	0.159196	+	0.0659412i
$806$	−47194.9	+	14260.0i	−2.06249	+	0.623187i
$807$	446.914	+	446.914i	0.0194946	+	0.0194946i
$808$	8070.85	+	6668.03i	0.351400	+	0.290322i
$809$	−1696.33	+	1696.33i	−0.0737205	+	0.0737205i	−0.743006	−	0.669285i	$-0.766600\pi$
$809$	−1696.33	+	1696.33i	−0.0737205	+	0.0737205i	0.669285	+	0.743006i	$0.266600\pi$
$810$	7205.65	−	13445.4i	0.312569	−	0.583240i
$811$	−9036.86	+	21816.9i	−0.391279	+	0.944631i	0.598383	+	0.801210i	$0.295810\pi$
$811$	−9036.86	+	21816.9i	−0.391279	+	0.944631i	−0.989662	+	0.143421i	$0.954190\pi$
$812$	5429.04	−	8086.77i	0.234633	−	0.349495i
$813$	6242.93	−	2585.91i	0.269310	−	0.111552i
$814$	−26994.3	+	22104.2i	−1.16234	+	0.951785i
$815$		−	33021.5i		−	1.41925i
$816$	−18347.9	−	80.2956i	−0.787137	−	0.00344474i
$817$		−	21041.5i		−	0.901037i
$818$	−18304.7	−	22354.2i	−0.782409	−	0.955497i
$819$	4580.07	−	1897.13i	0.195410	−	0.0809415i
$820$	−9119.82	+	1793.31i	−0.388388	+	0.0763721i
$821$	−14759.0	+	35631.4i	−0.627397	+	1.51467i	0.215450	+	0.976515i	$0.430878\pi$
$821$	−14759.0	+	35631.4i	−0.627397	+	1.51467i	−0.842846	+	0.538155i	$0.819122\pi$
$822$	−20566.0	−	11021.7i	−0.872656	−	0.467673i
$823$	26350.3	−	26350.3i	1.11606	−	1.11606i	0.123742	−	0.992314i	$-0.460511\pi$
$823$	26350.3	−	26350.3i	1.11606	−	1.11606i	0.992314	−	0.123742i	$-0.0394894\pi$
$824$	8551.89	+	16126.6i	0.361552	+	0.681790i
$825$	4633.69	+	4633.69i	0.195545	+	0.195545i
$826$	−1522.19	−	5037.81i	−0.0641206	−	0.212213i
$827$	15258.6	+	6320.31i	0.641587	+	0.265754i	0.679667	−	0.733521i	$-0.262124\pi$
$827$	15258.6	+	6320.31i	0.641587	+	0.265754i	−0.0380800	+	0.999275i	$0.512124\pi$
$828$	579.256	−	2879.18i	0.0243122	−	0.120843i
$829$	−12319.9	−	29742.8i	−0.516148	−	1.24609i	−0.940252	−	0.340479i	$-0.889411\pi$
$829$	−12319.9	−	29742.8i	−0.516148	−	1.24609i	0.424104	−	0.905614i	$-0.360589\pi$
$830$	−17002.5	−	1693.39i	−0.711043	−	0.0708172i
$831$	−12742.1			−0.531912
$832$	−39891.6	−	8207.52i	−1.66225	−	0.342001i
$833$	19441.2			0.808640
$834$	2422.21	+	241.243i	0.100569	+	0.0100163i
$835$	−2585.65	−	6242.31i	−0.107162	−	0.258711i
$836$	−2519.73	+	12524.3i	−0.104243	+	0.518135i
$837$	30916.4	+	12806.0i	1.27673	+	0.528841i
$838$	−6896.16	−	22823.5i	−0.284277	−	0.940839i
$839$	−17943.3	−	17943.3i	−0.738347	−	0.738347i	0.233911	−	0.972258i	$-0.424848\pi$
$839$	−17943.3	−	17943.3i	−0.738347	−	0.738347i	−0.972258	+	0.233911i	$0.924848\pi$
$840$	−7919.90	+	4199.91i	−0.325312	+	0.172513i
$841$	−2806.57	+	2806.57i	−0.115075	+	0.115075i
$842$	5278.87	+	2829.04i	0.216059	+	0.115790i
$843$	−804.905	+	1943.21i	−0.0328854	+	0.0793924i
$844$	−3987.74	+	784.144i	−0.162635	+	0.0319803i
$845$	−48775.2	+	20203.4i	−1.98570	+	0.822505i
$846$	−6061.89	−	7402.93i	−0.246350	−	0.300849i
$847$			1850.30i			0.0750614i
$848$	12734.1	−	12623.2i	0.515675	−	0.511181i
$849$			13582.0i			0.549039i
$850$	−5614.97	+	4597.82i	−0.226579	+	0.185534i
$851$	−12183.7	+	5046.64i	−0.490776	+	0.203286i
$852$	−10474.8	+	15602.7i	−0.421199	+	0.627392i
$853$	12194.4	−	29439.9i	0.489482	−	1.18171i	−0.465500	−	0.885048i	$-0.654125\pi$
$853$	12194.4	−	29439.9i	0.489482	−	1.18171i	0.954981	−	0.296666i	$-0.0958747\pi$
$854$	−1108.36	+	2068.15i	−0.0444114	+	0.0828696i
$855$	3123.04	−	3123.04i	0.124919	−	0.124919i
$856$	15007.3	−	18164.6i	0.599228	−	0.725294i
$857$	−26988.2	−	26988.2i	−1.07573	−	1.07573i	−0.996887	−	0.0788412i	$-0.974878\pi$
$857$	−26988.2	−	26988.2i	−1.07573	−	1.07573i	−0.0788412	−	0.996887i	$-0.525122\pi$
$858$	−36782.3	+	11113.9i	−1.46355	+	0.442215i
$859$	9332.38	+	3865.60i	0.370683	+	0.153542i	0.560245	−	0.828327i	$-0.310707\pi$
$859$	9332.38	+	3865.60i	0.370683	+	0.153542i	−0.189562	+	0.981869i	$0.560707\pi$
$860$	44692.1	−	29721.0i	1.77208	−	1.17846i
$861$	−1078.20	−	2603.00i	−0.0426769	−	0.103031i
$862$	2855.20	−	28667.7i	0.112817	−	1.13275i
$863$	−42549.4			−1.67833			−0.839164	−	0.543878i	$-0.816956\pi$
$863$	−42549.4			−1.67833			−0.839164	+	0.543878i	$0.816956\pi$
$864$	17419.6	+	21464.3i	0.685912	+	0.845172i
$865$	994.369			0.0390862
$866$	−1249.14	+	12542.0i	−0.0490154	+	0.492141i
$867$	724.003	+	1747.90i	0.0283604	+	0.0684680i
$868$	−7018.54	−	10553.9i	−0.274453	−	0.412699i
$869$	7912.26	+	3277.36i	0.308866	+	0.127937i
$870$	24984.5	−	7549.14i	0.973627	−	0.294184i
$871$	48948.6	+	48948.6i	1.90420	+	1.90420i
$872$	−3150.68	+	299.877i	−0.122357	+	0.0116458i
$873$	266.705	−	266.705i	0.0103398	−	0.0103398i
$874$	−2280.91	+	4256.08i	−0.0882758	+	0.164719i
$875$	3063.59	−	7396.17i	0.118364	−	0.285756i
$876$	−20865.5	−	14008.0i	−0.804771	−	0.540282i
$877$	29966.3	−	12412.4i	1.15381	−	0.477923i	0.277999	−	0.960581i	$-0.410329\pi$
$877$	29966.3	−	12412.4i	1.15381	−	0.477923i	0.875809	+	0.482659i	$0.160329\pi$
$878$	7719.93	−	6321.46i	0.296737	−	0.242983i
$879$			2561.21i			0.0982792i
$880$	−30160.7	+	12338.6i	−1.15536	+	0.472653i
$881$			14567.6i			0.557088i	0.960423	+	0.278544i	$0.0898519\pi$
$881$			14567.6i			0.557088i	−0.960423	+	0.278544i	$0.910148\pi$
$882$	−4490.72	−	5484.18i	−0.171440	−	0.209367i
$883$	−43111.8	+	17857.5i	−1.64306	+	0.680580i	−0.996602	−	0.0823661i	$-0.973752\pi$
$883$	−43111.8	+	17857.5i	−1.64306	+	0.680580i	−0.646462	+	0.762946i	$0.723752\pi$
$884$	−8210.54	−	41754.5i	−0.312387	−	1.58864i
$885$	5396.72	−	13028.8i	0.204982	−	0.494870i
$886$	37354.5	+	20019.0i	1.41642	+	0.759086i
$887$	−3731.29	+	3731.29i	−0.141245	+	0.141245i	−0.774194	−	0.632949i	$-0.781844\pi$
$887$	−3731.29	+	3731.29i	−0.141245	+	0.141245i	0.632949	+	0.774194i	$0.281844\pi$
$888$	8814.09	−	28716.5i	0.333087	−	1.08521i
$889$	−2483.92	−	2483.92i	−0.0937097	−	0.0937097i
$890$	12982.5	+	42966.8i	0.488960	+	1.61826i
$891$	15529.6	+	6432.58i	0.583908	+	0.241863i
$892$	−50282.4	−	10116.2i	−1.88742	−	0.379726i
$893$	6020.31	+	14534.3i	0.225601	+	0.544649i
$894$	21690.5	+	2160.30i	0.811455	+	0.0808178i
$895$	22975.8			0.858097
$896$	−946.423	−	10427.3i	−0.0352877	−	0.388784i
$897$	−14523.7			−0.540614
$898$	18926.4	+	1885.00i	0.703321	+	0.0700481i
$899$	14121.6	+	34092.6i	0.523896	+	1.26480i
$900$	2594.00	+	521.883i	0.0960743	+	0.0193290i
$901$	17308.7	+	7169.50i	0.639996	+	0.265095i
$902$	−2962.28	−	9803.92i	−0.109349	−	0.361901i
$903$	11504.5	+	11504.5i	0.423973	+	0.423973i
$904$	−5129.10	+	16710.7i	−0.188707	+	0.614813i
$905$	17883.6	−	17883.6i	0.656876	−	0.656876i
$906$	−17139.2	−	9185.23i	−0.628491	−	0.336820i
$907$	2716.64	−	6558.56i	0.0994538	−	0.240103i	−0.866320	−	0.499490i	$-0.833521\pi$
$907$	2716.64	−	6558.56i	0.0994538	−	0.240103i	0.965773	+	0.259387i	$0.0835207\pi$
$908$	563.596	+	2866.15i	0.0205987	+	0.104754i
$909$	3684.63	−	1526.22i	0.134446	−	0.0556894i
$910$	−13172.3	−	16086.3i	−0.479843	−	0.585997i
$911$		−	26795.2i		−	0.974496i	−0.873264	−	0.487248i	$-0.838001\pi$
$911$		−	26795.2i		−	0.974496i	0.873264	−	0.487248i	$-0.161999\pi$
$912$	−4164.63	−	10180.1i	−0.151211	−	0.369624i
$913$		−	18827.9i		−	0.682491i
$914$	−38900.9	+	31854.0i	−1.40780	+	1.15278i
$915$	−5808.97	+	2406.15i	−0.209878	+	0.0869345i
$916$	−15594.3	−	10469.2i	−0.562502	−	0.377635i
$917$	−5529.21	+	13348.7i	−0.199117	+	0.480712i
$918$	−13643.4	+	25458.0i	−0.490522	+	0.915292i
$919$	−39104.1	+	39104.1i	−1.40362	+	1.40362i	−0.615423	+	0.788197i	$0.711015\pi$
$919$	−39104.1	+	39104.1i	−1.40362	+	1.40362i	−0.788197	+	0.615423i	$0.788985\pi$
$920$	−12261.7	+	1167.05i	−0.439409	+	0.0418223i
$921$	12454.9	+	12454.9i	0.445605	+	0.445605i
$922$	17063.2	−	5155.68i	0.609485	−	0.184157i
$923$	−40267.6	−	16679.4i	−1.43599	−	0.594808i
$924$	−5470.04	−	8225.40i	−0.194752	−	0.292853i
$925$	−4546.79	−	10976.9i	−0.161619	−	0.390183i
$926$	4217.34	−	42344.4i	0.149666	−	1.50272i
$927$	6953.83			0.246379
$928$	−3153.80	+	30319.8i	−0.111561	+	1.07252i
$929$	48932.6			1.72812			0.864061	−	0.503386i	$-0.167913\pi$
$929$	48932.6			1.72812			0.864061	+	0.503386i	$0.167913\pi$
$930$	3365.97	−	33796.2i	0.118682	−	1.19163i
$931$	4459.92	+	10767.2i	0.157001	+	0.379034i
$932$	−13593.1	+	9039.67i	−0.477744	+	0.317708i
$933$	−16370.2	−	6780.77i	−0.574423	−	0.237934i
$934$	37504.6	−	11332.1i	1.31390	−	0.396999i
$935$	−24076.1	−	24076.1i	−0.842108	−	0.842108i
$936$	−9882.01	+	11961.0i	−0.345089	+	0.417689i
$937$	3286.41	−	3286.41i	0.114581	−	0.114581i	−0.647492	−	0.762072i	$-0.724182\pi$
$937$	3286.41	−	3286.41i	0.114581	−	0.114581i	0.762072	+	0.647492i	$0.224182\pi$
$938$	−8406.15	+	15685.5i	−0.292612	+	0.546001i
$939$	−10233.5	+	24706.0i	−0.355654	+	0.858625i
$940$	−22367.2	+	33316.8i	−0.776104	+	1.15604i
$941$	−12857.9	+	5325.93i	−0.445438	+	0.184506i	−0.594116	−	0.804379i	$-0.702498\pi$
$941$	−12857.9	+	5325.93i	−0.445438	+	0.184506i	0.148678	+	0.988886i	$0.452498\pi$
$942$	9030.46	−	7394.59i	0.312344	−	0.255763i
$943$		−	3871.12i		−	0.133681i
$944$	11595.4	+	11697.4i	0.399788	+	0.403302i
$945$			14112.0i			0.485782i
$946$	37469.3	+	45758.5i	1.28777	+	1.57266i
$947$	24989.2	−	10350.8i	0.857485	−	0.355182i	0.0897616	−	0.995963i	$-0.471389\pi$
$947$	24989.2	−	10350.8i	0.857485	−	0.355182i	0.767723	+	0.640781i	$0.221389\pi$
$948$	−7234.90	+	1422.66i	−0.247868	+	0.0487404i
$949$	22305.4	−	53850.0i	0.762975	−	1.84199i
$950$	−3834.53	−	2055.00i	−0.130957	−	0.0701820i
$951$	6522.59	−	6522.59i	0.222407	−	0.222407i
$952$	9664.89	−	5125.28i	0.329035	−	0.174487i
$953$	16871.9	+	16871.9i	0.573488	+	0.573488i	0.933101	−	0.359614i	$-0.117092\pi$
$953$	16871.9	+	16871.9i	0.573488	+	0.573488i	−0.359614	+	0.933101i	$0.617092\pi$
$954$	−1975.69	−	6538.71i	−0.0670495	−	0.221906i
$955$	35706.9	+	14790.3i	1.20989	+	0.501154i
$956$	3234.58	−	16077.4i	0.109429	−	0.543912i
$957$	11006.0	+	26570.8i	0.371759	+	0.897504i
$958$	16863.2	+	1679.51i	0.568711	+	0.0566415i
$959$	13912.1			0.468453
$960$	15740.0	−	23225.1i	0.529173	−	0.780819i
$961$	18228.0			0.611864
$962$	69325.1	+	6904.51i	2.32342	+	0.231404i
$963$	−3434.98	−	8292.77i	−0.114943	−	0.277498i
$964$	6255.03	−	31090.4i	0.208984	−	1.03875i
$965$	−25451.8	−	10542.5i	−0.849038	−	0.351683i
$966$	−1079.94	−	3574.14i	−0.0359693	−	0.119044i
$967$	−20339.3	−	20339.3i	−0.676388	−	0.676388i	0.282793	−	0.959181i	$-0.408739\pi$
$967$	−20339.3	−	20339.3i	−0.676388	−	0.676388i	−0.959181	+	0.282793i	$0.908739\pi$
$968$	−2713.00	−	5115.98i	−0.0900816	−	0.169870i
$969$	8126.35	−	8126.35i	0.269408	−	0.269408i
$970$	−1394.27	−	747.216i	−0.0461519	−	0.0247337i
$971$	−9157.64	+	22108.5i	−0.302660	+	0.730685i	0.697244	+	0.716834i	$0.254409\pi$
$971$	−9157.64	+	22108.5i	−0.302660	+	0.730685i	−0.999904	+	0.0138517i	$0.995591\pi$
$972$	18165.3	−	3572.01i	0.599438	−	0.117873i
$973$	−1340.88	+	555.410i	−0.0441794	+	0.0182997i
$974$	15511.4	+	18943.0i	0.510286	+	0.623174i
$975$		−	13085.1i		−	0.429805i
$976$	32.1371	−	7343.46i	0.00105398	−	0.240838i
$977$		−	13599.6i		−	0.445334i	−0.974895	−	0.222667i	$-0.928524\pi$
$977$		−	13599.6i		−	0.445334i	0.974895	−	0.222667i	$-0.0714762\pi$
$978$	−24238.4	+	19847.6i	−0.792492	+	0.648932i
$979$	−45694.7	+	18927.4i	−1.49173	+	0.617897i
$980$	−16569.9	+	24681.5i	−0.540108	+	0.804513i
$981$	−461.395	+	1113.91i	−0.0150165	+	0.0362531i
$982$	−24812.8	+	46299.6i	−0.806323	+	1.50456i
$983$	19227.9	−	19227.9i	0.623882	−	0.623882i	−0.322640	−	0.946522i	$-0.604570\pi$
$983$	19227.9	−	19227.9i	0.623882	−	0.623882i	0.946522	+	0.322640i	$0.104570\pi$
$984$	6797.80	+	5616.25i	0.220229	+	0.181951i
$985$	−27704.7	−	27704.7i	−0.896189	−	0.896189i
$986$	−30489.4	+	9212.44i	−0.984767	+	0.297550i
$987$	−11238.4	−	4655.08i	−0.362433	−	0.150125i
$988$	21241.5	−	14126.0i	0.683990	−	0.454866i
$989$	8554.66	+	20652.8i	0.275048	+	0.664024i
$990$	−1230.31	+	12353.0i	−0.0394967	+	0.396569i
$991$	−10267.1			−0.329106			−0.164553	−	0.986368i	$-0.552618\pi$
$991$	−10267.1			−0.329106			−0.164553	+	0.986368i	$0.552618\pi$
$992$	34880.6	+	18890.1i	1.11639	+	0.604598i
$993$	25703.3			0.821420
$994$	1110.47	−	11149.7i	0.0354346	−	0.355782i
$995$	−5198.28	−	12549.8i	−0.165625	−	0.399853i
$996$	8976.39	+	13498.0i	0.285570	+	0.429417i
$997$	−47357.4	−	19616.1i	−1.50434	−	0.623117i	−0.529957	−	0.848025i	$-0.677792\pi$
$997$	−47357.4	−	19616.1i	−1.50434	−	0.623117i	−0.974380	+	0.224908i	$0.927792\pi$
$998$	809.581	−	244.617i	0.0256782	−	0.00775872i
$999$	−33436.9	−	33436.9i	−1.05895	−	1.05895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.4.g.a.5.11	✓	44
4.3	odd	2		128.4.g.a.113.4		44
8.3	odd	2		256.4.g.a.225.8		44
8.5	even	2		256.4.g.b.225.4		44
32.3	odd	8		256.4.g.a.33.8		44
32.13	even	8	inner	32.4.g.a.13.11	yes	44
32.19	odd	8		128.4.g.a.17.4		44
32.29	even	8		256.4.g.b.33.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.11	✓	44	1.1	even	1	trivial
32.4.g.a.13.11	yes	44	32.13	even	8	inner
128.4.g.a.17.4		44	32.19	odd	8
128.4.g.a.113.4		44	4.3	odd	2
256.4.g.a.33.8		44	32.3	odd	8
256.4.g.a.225.8		44	8.3	odd	2
256.4.g.b.33.4		44	32.29	even	8
256.4.g.b.225.4		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)

\(f(q)\)	\(=\)	\(q+(2.81450 + 0.280314i) q^{2} +(1.64064 + 3.96085i) q^{3} +(7.84285 + 1.57789i) q^{4} +(-11.8087 - 4.89132i) q^{5} +(3.50730 + 11.6077i) q^{6} +(-5.11236 - 5.11236i) q^{7} +(21.6314 + 6.63943i) q^{8} +(6.09524 - 6.09524i) q^{9} +O(q^{10})\)	\(q+(2.81450 + 0.280314i) q^{2} +(1.64064 + 3.96085i) q^{3} +(7.84285 + 1.57789i) q^{4} +(-11.8087 - 4.89132i) q^{5} +(3.50730 + 11.6077i) q^{6} +(-5.11236 - 5.11236i) q^{7} +(21.6314 + 6.63943i) q^{8} +(6.09524 - 6.09524i) q^{9} +(-31.8645 - 17.0768i) q^{10} +(15.2446 - 36.8038i) q^{11} +(6.61750 + 33.6531i) q^{12} +(-73.4903 + 30.4407i) q^{13} +(-12.9557 - 15.8218i) q^{14} -54.7973i q^{15} +(59.0205 + 24.7503i) q^{16} +66.8708i q^{17} +(18.8637 - 15.4465i) q^{18} +(-37.0353 + 15.3405i) q^{19} +(-84.8958 - 56.9946i) q^{20} +(11.8618 - 28.6368i) q^{21} +(53.2227 - 99.3112i) q^{22} +(30.1143 - 30.1143i) q^{23} +(9.19154 + 96.5717i) q^{24} +(27.1316 + 27.1316i) q^{25} +(-215.371 + 65.0750i) q^{26} +(141.085 + 58.4395i) q^{27} +(-32.0288 - 48.1622i) q^{28} +(64.4434 + 155.580i) q^{29} +(15.3604 - 154.227i) q^{30} +219.132 q^{31} +(159.176 + 86.2040i) q^{32} +170.785 q^{33} +(-18.7448 + 188.208i) q^{34} +(35.3641 + 85.3765i) q^{35} +(57.4217 - 38.1865i) q^{36} +(-286.081 - 118.499i) q^{37} +(-108.536 + 32.7945i) q^{38} +(-241.142 - 241.142i) q^{39} +(-222.963 - 184.209i) q^{40} +(64.2737 - 64.2737i) q^{41} +(41.4123 - 77.2735i) q^{42} +(-200.870 + 484.942i) q^{43} +(177.634 - 264.592i) q^{44} +(-101.791 + 42.1630i) q^{45} +(93.1984 - 76.3154i) q^{46} -392.444i q^{47} +(-1.20076 + 274.378i) q^{48} -290.727i q^{49} +(68.7567 + 83.9674i) q^{50} +(-264.865 + 109.711i) q^{51} +(-624.405 + 122.782i) q^{52} +(107.214 - 258.838i) q^{53} +(380.704 + 204.026i) q^{54} +(-360.038 + 360.038i) q^{55} +(-76.6445 - 144.531i) q^{56} +(-121.523 - 121.523i) q^{57} +(137.765 + 455.945i) q^{58} +(237.764 + 98.4852i) q^{59} +(86.4640 - 429.767i) q^{60} +(-43.9101 - 106.008i) q^{61} +(616.749 + 61.4259i) q^{62} -62.3222 q^{63} +(423.836 + 287.240i) q^{64} +1016.72 q^{65} +(480.676 + 47.8735i) q^{66} +(-333.028 - 804.000i) q^{67} +(-105.515 + 524.458i) q^{68} +(168.685 + 69.8717i) q^{69} +(75.6001 + 250.205i) q^{70} +(387.445 + 387.445i) q^{71} +(172.318 - 91.3798i) q^{72} +(-518.132 + 518.132i) q^{73} +(-771.960 - 413.708i) q^{74} +(-62.9512 + 151.978i) q^{75} +(-314.668 + 61.8759i) q^{76} +(-266.091 + 110.218i) q^{77} +(-611.099 - 746.290i) q^{78} +214.985i q^{79} +(-575.893 - 580.956i) q^{80} +421.957i q^{81} +(198.915 - 162.882i) q^{82} +(436.657 - 180.869i) q^{83} +(138.216 - 205.878i) q^{84} +(327.086 - 789.656i) q^{85} +(-701.284 + 1308.56i) q^{86} +(-510.501 + 510.501i) q^{87} +(574.119 - 694.903i) q^{88} +(-877.926 - 877.926i) q^{89} +(-298.309 + 90.1346i) q^{90} +(531.333 + 220.085i) q^{91} +(283.699 - 188.665i) q^{92} +(359.517 + 867.951i) q^{93} +(110.007 - 1104.53i) q^{94} +512.374 q^{95} +(-80.2914 + 771.900i) q^{96} +43.7563 q^{97} +(81.4949 - 818.253i) q^{98} +(-131.408 - 317.248i) 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

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