LMFDB - Embedded newform 99.3.k.c.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 77x^12 + 88x^11 - 577x^10 + 578x^9 + 1520x^8 + 1868x^7 - 1619x^6 - 16804x^5 + 32427x^4 + 43316x^3 - 71672x^2 + 83521
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.4
Root			$-1.95510 - 0.109518i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.c.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.47243 + 1.12826i) q^{2} +(7.54873 + 5.48447i) q^{4} +(-1.69033 - 5.20232i) q^{5} +(-4.20886 + 5.79300i) q^{7} +(11.4402 + 15.7461i) q^{8} +O(q^{10})$	\(q+(3.47243 + 1.12826i) q^{2} +(7.54873 + 5.48447i) q^{4} +(-1.69033 - 5.20232i) q^{5} +(-4.20886 + 5.79300i) q^{7} +(11.4402 + 15.7461i) q^{8} -19.9718i q^{10} +(-0.170982 - 10.9987i) q^{11} +(-6.27605 - 2.03921i) q^{13} +(-21.1510 + 15.3671i) q^{14} +(10.4262 + 32.0885i) q^{16} +(-17.5557 + 5.70418i) q^{17} +(4.95437 + 6.81910i) q^{19} +(15.7721 - 48.5415i) q^{20} +(11.8156 - 38.3850i) q^{22} +17.7114 q^{23} +(-3.98143 + 2.89268i) q^{25} +(-19.4924 - 14.1620i) q^{26} +(-63.5431 + 20.6464i) q^{28} +(-11.8017 + 16.2437i) q^{29} +(10.9215 - 33.6128i) q^{31} +45.3355i q^{32} -67.3966 q^{34} +(37.2514 + 12.1037i) q^{35} +(39.4991 + 28.6978i) q^{37} +(9.50997 + 29.2687i) q^{38} +(62.5784 - 86.1317i) q^{40} +(-18.5926 - 25.5905i) q^{41} +45.0047i q^{43} +(59.0312 - 83.9638i) q^{44} +(61.5015 + 19.9831i) q^{46} +(-0.589182 + 0.428066i) q^{47} +(-0.702488 - 2.16204i) q^{49} +(-17.0889 + 5.55254i) q^{50} +(-36.1922 - 49.8143i) q^{52} +(-21.6865 + 66.7442i) q^{53} +(-56.9295 + 19.4809i) q^{55} -139.367 q^{56} +(-59.3077 + 43.0896i) q^{58} +(19.5024 + 14.1693i) q^{59} +(-39.0806 + 12.6981i) q^{61} +(75.8481 - 104.396i) q^{62} +(-9.44556 + 29.0704i) q^{64} +36.0970i q^{65} +96.0426 q^{67} +(-163.807 - 53.2242i) q^{68} +(115.697 + 84.0586i) q^{70} +(-12.2355 - 37.6569i) q^{71} +(41.2974 - 56.8410i) q^{73} +(104.779 + 144.216i) q^{74} +78.6477i q^{76} +(64.4349 + 45.3013i) q^{77} +(-84.9861 - 27.6137i) q^{79} +(149.311 - 108.481i) q^{80} +(-35.6888 - 109.839i) q^{82} +(-24.9375 + 8.10269i) q^{83} +(59.3499 + 81.6881i) q^{85} +(-50.7771 + 156.276i) q^{86} +(171.230 - 128.519i) q^{88} +118.861 q^{89} +(38.2282 - 27.7744i) q^{91} +(133.698 + 97.1376i) q^{92} +(-2.52886 + 0.821677i) q^{94} +(27.1006 - 37.3008i) q^{95} +(-10.2296 + 31.4835i) q^{97} -8.30011i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	$ 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) $ 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	3.47243	+	1.12826i	1.73622	+	0.564130i	0.994324	−	0.106390i	$-0.0339293\pi$
$2$	3.47243	+	1.12826i	1.73622	+	0.564130i	0.741891	+	0.670521i	$0.233929\pi$
$3$		0			0
$3$		0			0
$4$	7.54873	+	5.48447i	1.88718	+	1.37112i
$5$	−1.69033	−	5.20232i	−0.338067	−	1.04046i	−0.965192	−	0.261544i	$-0.915768\pi$
$5$	−1.69033	−	5.20232i	−0.338067	−	1.04046i	0.627125	−	0.778919i	$-0.284232\pi$
$6$		0			0
$7$	−4.20886	+	5.79300i	−0.601265	+	0.827571i	−0.995823	−	0.0913001i	$-0.970898\pi$
$7$	−4.20886	+	5.79300i	−0.601265	+	0.827571i	0.394558	+	0.918871i	$0.370898\pi$
$8$	11.4402	+	15.7461i	1.43003	+	1.96826i
$9$		0			0
$10$		−	19.9718i		−	1.99718i
$11$	−0.170982	−	10.9987i	−0.0155439	−	0.999879i
$11$	−0.170982	−	10.9987i	−0.0155439	−	0.999879i
$12$		0			0
$13$	−6.27605	−	2.03921i	−0.482773	−	0.156863i	0.0575115	−	0.998345i	$-0.481683\pi$
$13$	−6.27605	−	2.03921i	−0.482773	−	0.156863i	−0.540285	+	0.841482i	$0.681683\pi$
$14$	−21.1510	+	15.3671i	−1.51078	+	1.09765i
$15$		0			0
$16$	10.4262	+	32.0885i	0.651636	+	2.00553i
$17$	−17.5557	+	5.70418i	−1.03269	+	0.335540i	−0.775851	−	0.630916i	$-0.782679\pi$
$17$	−17.5557	+	5.70418i	−1.03269	+	0.335540i	−0.256834	+	0.966456i	$0.582679\pi$
$18$		0			0
$19$	4.95437	+	6.81910i	0.260756	+	0.358900i	0.919242	−	0.393693i	$-0.128803\pi$
$19$	4.95437	+	6.81910i	0.260756	+	0.358900i	−0.658486	+	0.752593i	$0.728803\pi$
$20$	15.7721	−	48.5415i	0.788604	−	2.42707i
$21$		0			0
$22$	11.8156	−	38.3850i	0.537075	−	1.74477i
$23$	17.7114			0.770060			0.385030	−	0.922904i	$-0.374191\pi$
$23$	17.7114			0.770060			0.385030	+	0.922904i	$0.374191\pi$
$24$		0			0
$25$	−3.98143	+	2.89268i	−0.159257	+	0.115707i
$26$	−19.4924	−	14.1620i	−0.749707	−	0.544694i
$27$		0			0
$28$	−63.5431	+	20.6464i	−2.26940	+	0.737371i
$29$	−11.8017	+	16.2437i	−0.406956	+	0.560126i	−0.962473	−	0.271379i	$-0.912520\pi$
$29$	−11.8017	+	16.2437i	−0.406956	+	0.560126i	0.555517	+	0.831505i	$0.312520\pi$
$30$		0			0
$31$	10.9215	−	33.6128i	0.352305	−	1.08428i	−0.605250	−	0.796035i	$-0.706927\pi$
$31$	10.9215	−	33.6128i	0.352305	−	1.08428i	0.957555	−	0.288249i	$-0.0930732\pi$
$32$			45.3355i			1.41673i
$33$		0			0
$34$	−67.3966			−1.98225
$35$	37.2514	+	12.1037i	1.06433	+	0.345820i
$36$		0			0
$37$	39.4991	+	28.6978i	1.06754	+	0.775616i	0.975469	−	0.220136i	$-0.0706502\pi$
$37$	39.4991	+	28.6978i	1.06754	+	0.775616i	0.0920744	+	0.995752i	$0.470650\pi$
$38$	9.50997	+	29.2687i	0.250262	+	0.770228i
$39$		0			0
$40$	62.5784	−	86.1317i	1.56446	−	2.15329i
$41$	−18.5926	−	25.5905i	−0.453478	−	0.624159i	0.519662	−	0.854372i	$-0.326058\pi$
$41$	−18.5926	−	25.5905i	−0.453478	−	0.624159i	−0.973140	+	0.230212i	$0.926058\pi$
$42$		0			0
$43$			45.0047i			1.04662i	0.852142	+	0.523311i	$0.175303\pi$
$43$			45.0047i			1.04662i	−0.852142	+	0.523311i	$0.824697\pi$
$44$	59.0312	−	83.9638i	1.34162	−	1.90827i
$45$		0			0
$46$	61.5015	+	19.9831i	1.33699	+	0.434414i
$47$	−0.589182	+	0.428066i	−0.0125358	+	0.00910778i	−0.594036	−	0.804439i	$-0.702466\pi$
$47$	−0.589182	+	0.428066i	−0.0125358	+	0.00910778i	0.581500	+	0.813547i	$0.302466\pi$
$48$		0			0
$49$	−0.702488	−	2.16204i	−0.0143365	−	0.0441232i
$50$	−17.0889	+	5.55254i	−0.341779	+	0.111051i
$51$		0			0
$52$	−36.1922	−	49.8143i	−0.696004	−	0.957967i
$53$	−21.6865	+	66.7442i	−0.409179	+	1.25932i	0.508176	+	0.861253i	$0.330320\pi$
$53$	−21.6865	+	66.7442i	−0.409179	+	1.25932i	−0.917355	+	0.398070i	$0.869680\pi$
$54$		0			0
$55$	−56.9295	+	19.4809i	−1.03508	+	0.354199i
$56$	−139.367			−2.48870
$57$		0			0
$58$	−59.3077	+	43.0896i	−1.02255	+	0.742924i
$59$	19.5024	+	14.1693i	0.330549	+	0.240158i	0.740664	−	0.671876i	$-0.234511\pi$
$59$	19.5024	+	14.1693i	0.330549	+	0.240158i	−0.410114	+	0.912034i	$0.634511\pi$
$60$		0			0
$61$	−39.0806	+	12.6981i	−0.640666	+	0.208165i	−0.611294	−	0.791404i	$-0.709351\pi$
$61$	−39.0806	+	12.6981i	−0.640666	+	0.208165i	−0.0293719	+	0.999569i	$0.509351\pi$
$62$	75.8481	−	104.396i	1.22336	−	1.68381i
$63$		0			0
$64$	−9.44556	+	29.0704i	−0.147587	+	0.454226i
$65$			36.0970i			0.555338i
$66$		0			0
$67$	96.0426			1.43347			0.716736	−	0.697345i	$-0.245635\pi$
$67$	96.0426			1.43347			0.716736	+	0.697345i	$0.245635\pi$
$68$	−163.807	−	53.2242i	−2.40893	−	0.782709i
$69$		0			0
$70$	115.697	+	84.0586i	1.65281	+	1.20084i
$71$	−12.2355	−	37.6569i	−0.172331	−	0.530379i	0.827171	−	0.561951i	$-0.189949\pi$
$71$	−12.2355	−	37.6569i	−0.172331	−	0.530379i	−0.999502	+	0.0315713i	$0.989949\pi$
$72$		0			0
$73$	41.2974	−	56.8410i	0.565717	−	0.778643i	−0.426322	−	0.904572i	$-0.640191\pi$
$73$	41.2974	−	56.8410i	0.565717	−	0.778643i	0.992039	+	0.125928i	$0.0401909\pi$
$74$	104.779	+	144.216i	1.41594	+	1.94887i
$75$		0			0
$76$			78.6477i			1.03484i
$77$	64.4349	+	45.3013i	0.836817	+	0.588329i
$78$		0			0
$79$	−84.9861	−	27.6137i	−1.07577	−	0.349540i	−0.283040	−	0.959108i	$-0.591343\pi$
$79$	−84.9861	−	27.6137i	−1.07577	−	0.349540i	−0.792734	+	0.609568i	$0.791343\pi$
$80$	149.311	−	108.481i	1.86638	−	1.35601i
$81$		0			0
$82$	−35.6888	−	109.839i	−0.435229	−	1.33950i
$83$	−24.9375	+	8.10269i	−0.300452	+	0.0976228i	−0.455364	−	0.890306i	$-0.650491\pi$
$83$	−24.9375	+	8.10269i	−0.300452	+	0.0976228i	0.154912	+	0.987928i	$0.450491\pi$
$84$		0			0
$85$	59.3499	+	81.6881i	0.698234	+	0.961036i
$86$	−50.7771	+	156.276i	−0.590431	+	1.81716i
$87$		0			0
$88$	171.230	−	128.519i	1.94580	−	1.46045i
$89$	118.861			1.33552			0.667760	−	0.744377i	$-0.267253\pi$
$89$	118.861			1.33552			0.667760	+	0.744377i	$0.267253\pi$
$90$		0			0
$91$	38.2282	−	27.7744i	0.420090	−	0.305213i
$92$	133.698	+	97.1376i	1.45324	+	1.05584i
$93$		0			0
$94$	−2.52886	+	0.821677i	−0.0269028	+	0.00874125i
$95$	27.1006	−	37.3008i	0.285269	−	0.392640i
$96$		0			0
$97$	−10.2296	+	31.4835i	−0.105460	+	0.324572i	−0.989838	−	0.142199i	$-0.954583\pi$
$97$	−10.2296	+	31.4835i	−0.105460	+	0.324572i	0.884378	+	0.466771i	$0.154583\pi$
$98$		−	8.30011i		−	0.0846950i
$99$		0			0
$100$	−45.9196			−0.459196
$101$	−48.8002	−	15.8561i	−0.483170	−	0.156991i	0.0572962	−	0.998357i	$-0.481752\pi$
$101$	−48.8002	−	15.8561i	−0.483170	−	0.156991i	−0.540466	+	0.841366i	$0.681752\pi$
$102$		0			0
$103$	−97.8950	−	71.1249i	−0.950437	−	0.690533i	0.000473401	−	1.00000i	$-0.499849\pi$
$103$	−97.8950	−	71.1249i	−0.950437	−	0.690533i	−0.950910	+	0.309467i	$0.899849\pi$
$104$	−39.6897	−	122.152i	−0.381632	−	1.17454i
$105$		0			0
$106$	−150.610	+	207.296i	−1.42085	+	1.95563i
$107$	−104.318	−	143.582i	−0.974936	−	1.34188i	−0.939514	−	0.342511i	$-0.888723\pi$
$107$	−104.318	−	143.582i	−0.974936	−	1.34188i	−0.0354219	−	0.999372i	$-0.511277\pi$
$108$		0			0
$109$			81.6242i			0.748846i	0.927258	+	0.374423i	$0.122159\pi$
$109$			81.6242i			0.748846i	−0.927258	+	0.374423i	$0.877841\pi$
$110$	−219.663	+	3.41483i	−1.99694	+	0.0310439i
$111$		0			0
$112$	−229.771	−	74.6570i	−2.05152	−	0.666581i
$113$	−17.3066	+	12.5740i	−0.153156	+	0.111274i	−0.661724	−	0.749747i	$-0.730175\pi$
$113$	−17.3066	+	12.5740i	−0.153156	+	0.111274i	0.508568	+	0.861022i	$0.330175\pi$
$114$		0			0
$115$	−29.9382	−	92.1402i	−0.260332	−	0.801219i
$116$	−178.176	+	57.8929i	−1.53600	+	0.499076i
$117$		0			0
$118$	51.7341	+	71.2059i	0.438424	+	0.603439i
$119$	40.8450	−	125.708i	0.343235	−	1.05637i
$120$		0			0
$121$	−120.942	+	3.76116i	−0.999517	+	0.0310840i
$122$	−150.031			−1.22977
$123$		0			0
$124$	266.792	−	193.836i	2.15155	−	1.56319i
$125$	−88.8553	−	64.5571i	−0.710842	−	0.516457i
$126$		0			0
$127$	74.1498	−	24.0927i	0.583857	−	0.189706i	−0.00217099	−	0.999998i	$-0.500691\pi$
$127$	74.1498	−	24.0927i	0.583857	−	0.189706i	0.586027	+	0.810291i	$0.300691\pi$
$128$	40.9921	−	56.4207i	0.320251	−	0.440787i
$129$		0			0
$130$	−40.7268	+	125.344i	−0.313283	+	0.964186i
$131$			74.9602i			0.572215i	0.958197	+	0.286108i	$0.0923615\pi$
$131$			74.9602i			0.572215i	−0.958197	+	0.286108i	$0.907638\pi$
$132$		0			0
$133$	−60.3553			−0.453799
$134$	333.501	+	108.361i	2.48882	+	0.808665i
$135$		0			0
$136$	−290.659	−	211.176i	−2.13720	−	1.55276i
$137$	−48.9563	−	150.672i	−0.357345	−	1.09980i	−0.954637	−	0.297772i	$-0.903756\pi$
$137$	−48.9563	−	150.672i	−0.357345	−	1.09980i	0.597292	−	0.802024i	$-0.296244\pi$
$138$		0			0
$139$	151.750	−	208.866i	1.09173	−	1.50263i	0.245811	−	0.969318i	$-0.420946\pi$
$139$	151.750	−	208.866i	1.09173	−	1.50263i	0.845916	−	0.533316i	$-0.179054\pi$
$140$	214.818	+	295.672i	1.53442	+	2.11194i
$141$		0			0
$142$		−	144.566i		−	1.01807i
$143$	−21.3555	+	69.3769i	−0.149339	+	0.485153i
$144$		0			0
$145$	104.453	+	33.9390i	0.720369	+	0.234062i
$146$	207.534	−	150.782i	1.42146	−	1.03275i
$147$		0			0
$148$	140.776	+	433.264i	0.951189	+	2.92746i
$149$	−53.4719	+	17.3741i	−0.358872	+	0.116604i	−0.482903	−	0.875674i	$-0.660418\pi$
$149$	−53.4719	+	17.3741i	−0.358872	+	0.116604i	0.124031	+	0.992278i	$0.460418\pi$
$150$		0			0
$151$	−66.7739	−	91.9063i	−0.442211	−	0.608651i	0.528491	−	0.848939i	$-0.322758\pi$
$151$	−66.7739	−	91.9063i	−0.442211	−	0.608651i	−0.970702	+	0.240288i	$0.922758\pi$
$152$	−50.6952	+	156.024i	−0.333521	+	1.02647i
$153$		0			0
$154$	172.634	+	230.005i	1.12100	+	1.49354i
$155$	−193.325			−1.24726
$156$		0			0
$157$	−216.079	+	156.990i	−1.37630	+	0.999939i	−0.379082	+	0.925363i	$0.623760\pi$
$157$	−216.079	+	156.990i	−1.37630	+	0.999939i	−0.997215	+	0.0745755i	$0.976240\pi$
$158$	−263.953	−	191.773i	−1.67059	−	1.21375i
$159$		0			0
$160$	235.850	−	76.6322i	1.47406	−	0.478951i
$161$	−74.5447	+	102.602i	−0.463011	+	0.637279i
$162$		0			0
$163$	74.2421	−	228.494i	0.455473	−	1.40180i	−0.415106	−	0.909773i	$-0.636256\pi$
$163$	74.2421	−	228.494i	0.455473	−	1.40180i	0.870579	−	0.492028i	$-0.163744\pi$
$164$		−	295.147i		−	1.79968i
$165$		0			0
$166$	−95.7357			−0.576721
$167$	167.692	+	54.4864i	1.00414	+	0.326266i	0.764520	−	0.644600i	$-0.222976\pi$
$167$	167.692	+	54.4864i	1.00414	+	0.326266i	0.239624	+	0.970866i	$0.422976\pi$
$168$		0			0
$169$	−101.493	−	73.7393i	−0.600553	−	0.436327i
$170$	113.923	+	350.618i	0.670134	+	2.06246i
$171$		0			0
$172$	−246.827	+	339.728i	−1.43504	+	1.97517i
$173$	156.820	+	215.844i	0.906474	+	1.24765i	0.968357	+	0.249571i	$0.0802896\pi$
$173$	156.820	+	215.844i	0.906474	+	1.24765i	−0.0618825	+	0.998083i	$0.519710\pi$
$174$		0			0
$175$		−	35.2393i		−	0.201367i
$176$	351.148	−	120.161i	1.99516	−	0.682731i
$177$		0			0
$178$	412.737	+	134.107i	2.31875	+	0.753407i
$179$	−46.8686	+	34.0521i	−0.261836	+	0.190235i	−0.710956	−	0.703236i	$-0.751738\pi$
$179$	−46.8686	+	34.0521i	−0.261836	+	0.190235i	0.449120	+	0.893471i	$0.351738\pi$
$180$		0			0
$181$	−71.8552	−	221.147i	−0.396990	−	1.22181i	−0.927401	−	0.374069i	$-0.877962\pi$
$181$	−71.8552	−	221.147i	−0.396990	−	1.22181i	0.530411	−	0.847741i	$-0.322038\pi$
$182$	164.081	−	53.3133i	0.901546	−	0.292930i
$183$		0			0
$184$	202.622	+	278.885i	1.10121	+	1.51568i
$185$	82.5282	−	253.996i	0.446098	−	1.37295i
$186$		0			0
$187$	65.7401	+	192.114i	0.351551	+	1.02735i
$188$	−6.79529			−0.0361452
$189$		0			0
$190$	136.190	−	98.9477i	0.716789	−	0.520778i
$191$	11.0844	+	8.05330i	0.0580336	+	0.0421639i	0.616424	−	0.787415i	$-0.288581\pi$
$191$	11.0844	+	8.05330i	0.0580336	+	0.0421639i	−0.558390	+	0.829578i	$0.688581\pi$
$192$		0			0
$193$	−32.8507	+	10.6739i	−0.170211	+	0.0553049i	−0.392883	−	0.919589i	$-0.628522\pi$
$193$	−32.8507	+	10.6739i	−0.170211	+	0.0553049i	0.222672	+	0.974893i	$0.428522\pi$
$194$	−71.0431	+	97.7825i	−0.366202	+	0.504033i
$195$		0			0
$196$	6.55474	−	20.1734i	0.0334425	−	0.102926i
$197$			103.908i			0.527451i	0.964598	+	0.263726i	$0.0849514\pi$
$197$			103.908i			0.527451i	−0.964598	+	0.263726i	$0.915049\pi$
$198$		0			0
$199$	264.816			1.33073			0.665367	−	0.746516i	$-0.268275\pi$
$199$	264.816			1.33073			0.665367	+	0.746516i	$0.268275\pi$
$200$	−91.0968	−	29.5991i	−0.455484	−	0.147996i
$201$		0			0
$202$	−151.565	−	110.119i	−0.750323	−	0.545142i
$203$	−44.4277	−	136.735i	−0.218856	−	0.673569i
$204$		0			0
$205$	−101.702	+	139.981i	−0.496109	+	0.682835i
$206$	−259.686	−	357.427i	−1.26061	−	1.73508i
$207$		0			0
$208$		−	222.650i		−	1.07043i
$209$	74.1540	−	55.6574i	0.354804	−	0.266303i
$210$		0			0
$211$	280.549	+	91.1560i	1.32962	+	0.432019i	0.885787	−	0.464091i	$-0.153619\pi$
$211$	280.549	+	91.1560i	1.32962	+	0.432019i	0.443831	+	0.896111i	$0.353619\pi$
$212$	−529.762	+	384.895i	−2.49888	+	1.81554i
$213$		0			0
$214$	−200.240	−	616.275i	−0.935700	−	2.87979i
$215$	234.129	−	76.0730i	1.08897	−	0.353828i
$216$		0			0
$217$	148.752	+	204.740i	0.685493	+	0.943501i
$218$	−92.0934	+	283.434i	−0.422447	+	1.30016i
$219$		0			0
$220$	−536.589	−	165.172i	−2.43904	−	0.750783i
$221$	121.812			0.551186
$222$		0			0
$223$	−167.321	+	121.566i	−0.750317	+	0.545137i	−0.895925	−	0.444205i	$-0.853486\pi$
$223$	−167.321	+	121.566i	−0.750317	+	0.545137i	0.145608	+	0.989342i	$0.453486\pi$
$224$	−262.628	−	190.811i	−1.17245	−	0.851833i
$225$		0			0
$226$	−74.2828	+	24.1359i	−0.328685	+	0.106796i
$227$	−169.807	+	233.719i	−0.748049	+	1.02960i	0.250066	+	0.968229i	$0.419548\pi$
$227$	−169.807	+	233.719i	−0.748049	+	1.02960i	−0.998115	+	0.0613723i	$0.980452\pi$
$228$		0			0
$229$	−119.098	+	366.545i	−0.520077	+	1.60063i	0.253773	+	0.967264i	$0.418328\pi$
$229$	−119.098	+	366.545i	−0.520077	+	1.60063i	−0.773850	+	0.633369i	$0.781672\pi$
$230$		−	353.728i		−	1.53795i
$231$		0			0
$232$	−390.788			−1.68443
$233$	−134.930	−	43.8414i	−0.579099	−	0.188161i	0.00479806	−	0.999988i	$-0.498473\pi$
$233$	−134.930	−	43.8414i	−0.579099	−	0.188161i	−0.583897	+	0.811828i	$0.698473\pi$
$234$		0			0
$235$	3.22285	+	2.34154i	0.0137142	+	0.00996398i
$236$	69.5072	+	213.921i	0.294522	+	0.906445i
$237$		0			0
$238$	283.663	−	390.428i	1.19186	−	1.64045i
$239$	117.945	+	162.337i	0.493494	+	0.679236i	0.981028	−	0.193868i	$-0.0621035\pi$
$239$	117.945	+	162.337i	0.493494	+	0.679236i	−0.487534	+	0.873104i	$0.662103\pi$
$240$		0			0
$241$			153.553i			0.637150i	0.947898	+	0.318575i	$0.103204\pi$
$241$			153.553i			0.637150i	−0.947898	+	0.318575i	$0.896796\pi$
$242$	−424.205	−	123.393i	−1.75291	−	0.509889i
$243$		0			0
$244$	−364.651	−	118.482i	−1.49447	−	0.485584i
$245$	−10.0602	+	7.30913i	−0.0410619	+	0.0298332i
$246$		0			0
$247$	−17.1883	−	52.9001i	−0.0695881	−	0.214170i
$248$	654.214	−	212.567i	2.63796	−	0.857126i
$249$		0			0
$250$	−235.706	−	324.422i	−0.942826	−	1.29769i
$251$	56.6876	−	174.467i	0.225847	−	0.695086i	−0.772357	−	0.635188i	$-0.780923\pi$
$251$	56.6876	−	174.467i	0.225847	−	0.695086i	0.998205	−	0.0598977i	$-0.0190774\pi$
$252$		0			0
$253$	−3.02834	−	194.802i	−0.0119697	−	0.769967i
$254$	284.663			1.12072
$255$		0			0
$256$	304.915	−	221.533i	1.19107	−	0.865365i
$257$	161.097	+	117.044i	0.626836	+	0.455423i	0.855303	−	0.518129i	$-0.173371\pi$
$257$	161.097	+	117.044i	0.626836	+	0.455423i	−0.228467	+	0.973552i	$0.573371\pi$
$258$		0			0
$259$	−332.492	+	108.033i	−1.28375	+	0.417117i
$260$	−197.973	+	272.486i	−0.761434	+	1.04802i
$261$		0			0
$262$	−84.5747	+	260.294i	−0.322804	+	0.993489i
$263$			241.980i			0.920077i	0.887899	+	0.460039i	$0.152164\pi$
$263$			241.980i			0.920077i	−0.887899	+	0.460039i	$0.847836\pi$
$264$		0			0
$265$	383.882			1.44861
$266$	−209.580	−	68.0965i	−0.787893	−	0.256002i
$267$		0			0
$268$	725.000	+	526.743i	2.70522	+	1.96546i
$269$	3.50047	+	10.7733i	0.0130129	+	0.0400495i	0.957352	−	0.288924i	$-0.0932974\pi$
$269$	3.50047	+	10.7733i	0.0130129	+	0.0400495i	−0.944339	+	0.328973i	$0.893297\pi$
$270$		0			0
$271$	−134.961	+	185.757i	−0.498010	+	0.685451i	−0.981840	−	0.189710i	$-0.939245\pi$
$271$	−134.961	+	185.757i	−0.498010	+	0.685451i	0.483831	+	0.875162i	$0.339245\pi$
$272$	−366.077	−	503.861i	−1.34587	−	1.85243i
$273$		0			0
$274$		−	578.434i		−	2.11107i
$275$	32.4964	+	43.2959i	0.118169	+	0.157440i
$276$		0			0
$277$	315.242	+	102.428i	1.13806	+	0.369778i	0.816633	−	0.577157i	$-0.195838\pi$
$277$	315.242	+	102.428i	1.13806	+	0.369778i	0.321426	+	0.946935i	$0.395838\pi$
$278$	762.597	−	554.059i	2.74316	−	1.99302i
$279$		0			0
$280$	235.577	+	725.032i	0.841348	+	2.58940i
$281$	−380.048	+	123.485i	−1.35248	+	0.439449i	−0.893527	−	0.449010i	$-0.851777\pi$
$281$	−380.048	+	123.485i	−1.35248	+	0.439449i	−0.458957	+	0.888459i	$0.651777\pi$
$282$		0			0
$283$	−54.7144	−	75.3080i	−0.193337	−	0.266106i	0.701332	−	0.712835i	$-0.252589\pi$
$283$	−54.7144	−	75.3080i	−0.193337	−	0.266106i	−0.894670	+	0.446729i	$0.852589\pi$
$284$	114.166	−	351.367i	0.401993	−	1.23721i
$285$		0			0
$286$	−152.431	+	216.812i	−0.532975	+	0.758083i
$287$	226.500			0.789197
$288$		0			0
$289$	41.8574	−	30.4112i	0.144835	−	0.105229i
$290$	324.415	+	235.702i	1.11867	+	0.812764i
$291$		0			0
$292$	623.486	−	202.583i	2.13522	−	0.693777i
$293$	144.558	−	198.967i	0.493373	−	0.679070i	−0.487633	−	0.873049i	$-0.662139\pi$
$293$	144.558	−	198.967i	0.493373	−	0.679070i	0.981006	+	0.193979i	$0.0621394\pi$
$294$		0			0
$295$	40.7477	−	125.409i	0.138128	−	0.425114i
$296$			950.265i			3.21036i
$297$		0			0
$298$	−205.280			−0.688858
$299$	−111.158	−	36.1173i	−0.371764	−	0.120794i
$300$		0			0
$301$	−260.712	−	189.418i	−0.866153	−	0.629297i
$302$	−128.173	−	394.477i	−0.424415	−	1.30621i
$303$		0			0
$304$	−167.160	+	230.075i	−0.549867	+	0.756827i
$305$	132.119	+	181.846i	0.433176	+	0.596216i
$306$		0			0
$307$		−	2.17423i		−	0.00708218i	−0.999994	−	0.00354109i	$-0.998873\pi$
$307$		−	2.17423i		−	0.00708218i	0.999994	−	0.00354109i	$-0.00112717\pi$
$308$	237.948	+	695.359i	0.772557	+	2.25766i
$309$		0			0
$310$	−671.309	−	218.122i	−2.16551	−	0.703618i
$311$	−257.051	+	186.759i	−0.826531	+	0.600510i	−0.918576	−	0.395245i	$-0.870660\pi$
$311$	−257.051	+	186.759i	−0.826531	+	0.600510i	0.0920450	+	0.995755i	$0.470660\pi$
$312$		0			0
$313$	−31.0997	−	95.7151i	−0.0993602	−	0.305799i	0.889005	−	0.457897i	$-0.151397\pi$
$313$	−31.0997	−	95.7151i	−0.0993602	−	0.305799i	−0.988365	+	0.152098i	$0.951397\pi$
$314$	−927.444	+	301.345i	−2.95364	+	0.959697i
$315$		0			0
$316$	−490.091	−	674.552i	−1.55092	−	2.13466i
$317$	−86.2295	+	265.387i	−0.272017	+	0.837183i	0.717976	+	0.696068i	$0.245069\pi$
$317$	−86.2295	+	265.387i	−0.272017	+	0.837183i	−0.989993	+	0.141115i	$0.954931\pi$
$318$		0			0
$319$	180.677	+	127.026i	0.566384	+	0.398200i
$320$	167.200			0.522499
$321$		0			0
$322$	−374.613	+	272.172i	−1.16339	+	0.845256i
$323$	−125.875	−	91.4532i	−0.389705	−	0.283137i
$324$		0			0
$325$	30.8865	−	10.0356i	0.0950353	−	0.0308788i
$326$	515.601	−	709.664i	1.58160	−	2.17688i
$327$		0			0
$328$	190.248	−	585.522i	0.580023	−	1.78513i
$329$		−	5.21480i		−	0.0158504i
$330$		0			0
$331$	−64.8831			−0.196021			−0.0980107	−	0.995185i	$-0.531248\pi$
$331$	−64.8831			−0.196021			−0.0980107	+	0.995185i	$0.531248\pi$
$332$	−232.686	−	75.6041i	−0.700860	−	0.227723i
$333$		0			0
$334$	520.824	+	378.401i	1.55935	+	1.13294i
$335$	−162.344	−	499.644i	−0.484609	−	1.49147i
$336$		0			0
$337$	327.635	−	450.951i	0.972211	−	1.33813i	0.0312894	−	0.999510i	$-0.490039\pi$
$337$	327.635	−	450.951i	0.972211	−	1.33813i	0.940922	−	0.338624i	$-0.109961\pi$
$338$	−269.232	−	370.566i	−0.796544	−	1.09635i
$339$		0			0
$340$			942.144i			2.77101i
$341$	−371.564	−	114.374i	−1.08963	−	0.335409i
$342$		0			0
$343$	−318.212	−	103.393i	−0.927733	−	0.301439i
$344$	−708.648	+	514.863i	−2.06002	+	1.49669i
$345$		0			0
$346$	301.018	+	926.438i	0.869994	+	2.67757i
$347$	623.372	−	202.546i	1.79646	−	0.583705i	0.796675	−	0.604409i	$-0.206591\pi$
$347$	623.372	−	202.546i	1.79646	−	0.583705i	0.999786	+	0.0207032i	$0.00659051\pi$
$348$		0			0
$349$	−9.54591	−	13.1388i	−0.0273522	−	0.0376471i	0.795122	−	0.606450i	$-0.207407\pi$
$349$	−9.54591	−	13.1388i	−0.0273522	−	0.0376471i	−0.822474	+	0.568803i	$0.807407\pi$
$350$	39.7591	−	122.366i	0.113598	−	0.349617i
$351$		0			0
$352$	498.630	−	7.75157i	1.41656	−	0.0220215i
$353$	372.243			1.05451			0.527256	−	0.849706i	$-0.323221\pi$
$353$	372.243			1.05451			0.527256	+	0.849706i	$0.323221\pi$
$354$		0			0
$355$	−175.221	+	127.306i	−0.493581	+	0.358607i
$356$	897.252	+	651.891i	2.52037	+	1.83116i
$357$		0			0
$358$	−201.168	+	65.3633i	−0.561921	+	0.182579i
$359$	−34.0764	+	46.9022i	−0.0949205	+	0.130647i	−0.853836	−	0.520543i	$-0.825730\pi$
$359$	−34.0764	+	46.9022i	−0.0949205	+	0.130647i	0.758915	+	0.651189i	$0.225730\pi$
$360$		0			0
$361$	89.6007	−	275.763i	0.248201	−	0.763886i
$362$		−	848.991i		−	2.34528i
$363$		0			0
$364$	440.902			1.21127
$365$	−365.511	−	118.762i	−1.00140	−	0.325375i
$366$		0			0
$367$	152.162	+	110.552i	0.414611	+	0.301233i	0.775466	−	0.631389i	$-0.217515\pi$
$367$	152.162	+	110.552i	0.414611	+	0.301233i	−0.360855	+	0.932622i	$0.617515\pi$
$368$	184.662	+	568.331i	0.501799	+	1.54438i
$369$		0			0
$370$	573.147	−	788.869i	1.54905	−	2.13208i
$371$	−295.373	−	406.546i	−0.796154	−	1.09581i
$372$		0			0
$373$			470.904i			1.26248i	0.775589	+	0.631238i	$0.217453\pi$
$373$			470.904i			1.26248i	−0.775589	+	0.631238i	$0.782547\pi$
$374$	11.5236	+	741.273i	0.0308119	+	1.98201i
$375$		0			0
$376$	−13.4807	−	4.38015i	−0.0358530	−	0.0116493i
$377$	107.192	−	77.8798i	0.284330	−	0.206578i
$378$		0			0
$379$	87.4404	+	269.114i	0.230713	+	0.710063i	0.997661	+	0.0683534i	$0.0217745\pi$
$379$	87.4404	+	269.114i	0.230713	+	0.710063i	−0.766948	+	0.641710i	$0.778225\pi$
$380$	409.150	−	132.941i	1.07671	−	0.349845i
$381$		0			0
$382$	29.4036	+	40.4706i	0.0769729	+	0.105944i
$383$	−21.3848	+	65.8156i	−0.0558349	+	0.171842i	−0.975085	−	0.221832i	$-0.928796\pi$
$383$	−21.3848	+	65.8156i	−0.0558349	+	0.171842i	0.919250	+	0.393674i	$0.128796\pi$
$384$		0			0
$385$	126.755	−	411.785i	0.329235	−	1.06957i
$386$	−126.115			−0.326722
$387$		0			0
$388$	−249.891	+	181.556i	−0.644048	+	0.467928i
$389$	−477.895	−	347.211i	−1.22852	−	0.892573i	−0.231743	−	0.972777i	$-0.574443\pi$
$389$	−477.895	−	347.211i	−1.22852	−	0.892573i	−0.996778	+	0.0802044i	$0.974443\pi$
$390$		0			0
$391$	−310.935	+	101.029i	−0.795230	+	0.258386i
$392$	26.0070	−	35.7956i	0.0663444	−	0.0913153i
$393$		0			0
$394$	−117.235	+	360.813i	−0.297551	+	0.915769i
$395$			488.801i			1.23747i
$396$		0			0
$397$	−492.120			−1.23960			−0.619798	−	0.784761i	$-0.712786\pi$
$397$	−492.120			−1.23960			−0.619798	+	0.784761i	$0.712786\pi$
$398$	919.556	+	298.782i	2.31044	+	0.750708i
$399$		0			0
$400$	−134.333	−	97.5985i	−0.335832	−	0.243996i
$401$	168.128	+	517.445i	0.419272	+	1.29039i	0.908374	+	0.418159i	$0.137325\pi$
$401$	168.128	+	517.445i	0.419272	+	1.29039i	−0.489102	+	0.872227i	$0.662675\pi$
$402$		0			0
$403$	−137.087	+	188.685i	−0.340167	+	0.468200i
$404$	−281.417	−	387.337i	−0.696576	−	0.958755i
$405$		0			0
$406$		−	524.927i		−	1.29292i
$407$	308.884	−	439.345i	0.758928	−	1.07947i
$408$		0			0
$409$	−254.269	−	82.6170i	−0.621685	−	0.201998i	−0.0187966	−	0.999823i	$-0.505983\pi$
$409$	−254.269	−	82.6170i	−0.621685	−	0.201998i	−0.602888	+	0.797826i	$0.705983\pi$
$410$	−511.090	+	371.328i	−1.24656	+	0.905679i
$411$		0			0
$412$	−348.900	−	1073.81i	−0.846846	−	2.60632i
$413$	−164.166	+	53.3407i	−0.397496	+	0.129154i
$414$		0			0
$415$	84.3055	+	116.037i	0.203146	+	0.279606i
$416$	92.4487	−	284.528i	0.222232	−	0.683961i
$417$		0			0
$418$	320.291	−	109.601i	0.766245	−	0.262204i
$419$	−4.31451			−0.0102972			−0.00514858	−	0.999987i	$-0.501639\pi$
$419$	−4.31451			−0.0102972			−0.00514858	+	0.999987i	$0.501639\pi$
$420$		0			0
$421$	262.553	−	190.756i	0.623642	−	0.453103i	−0.230549	−	0.973061i	$-0.574052\pi$
$421$	262.553	−	190.756i	0.623642	−	0.453103i	0.854192	+	0.519958i	$0.174052\pi$
$422$	871.341	+	633.066i	2.06479	+	1.50016i
$423$		0			0
$424$	−1299.06	+	422.089i	−3.06381	+	0.995494i
$425$	53.3963	−	73.4937i	0.125638	−	0.172926i
$426$		0			0
$427$	90.9250	−	279.838i	0.212939	−	0.655359i
$428$		−	1655.99i		−	3.86913i
$429$		0			0
$430$	898.826			2.09029
$431$	74.8406	+	24.3172i	0.173644	+	0.0564204i	0.394549	−	0.918875i	$-0.370901\pi$
$431$	74.8406	+	24.3172i	0.173644	+	0.0564204i	−0.220905	+	0.975295i	$0.570901\pi$
$432$		0			0
$433$	279.805	+	203.290i	0.646201	+	0.469493i	0.861975	−	0.506951i	$-0.169227\pi$
$433$	279.805	+	203.290i	0.646201	+	0.469493i	−0.215774	+	0.976443i	$0.569227\pi$
$434$	285.531	+	878.775i	0.657907	+	2.02483i
$435$		0			0
$436$	−447.666	+	616.159i	−1.02676	+	1.41321i
$437$	87.7487	+	120.776i	0.200798	+	0.276375i
$438$		0			0
$439$		−	380.781i		−	0.867382i	−0.901062	−	0.433691i	$-0.857211\pi$
$439$		−	380.781i		−	0.867382i	0.901062	−	0.433691i	$-0.142789\pi$
$440$	−958.034	−	673.552i	−2.17735	−	1.53080i
$441$		0			0
$442$	422.984	+	137.436i	0.956978	+	0.310941i
$443$	−133.660	+	97.1097i	−0.301716	+	0.219209i	−0.728334	−	0.685223i	$-0.759705\pi$
$443$	−133.660	+	97.1097i	−0.301716	+	0.219209i	0.426618	+	0.904432i	$0.359705\pi$
$444$		0			0
$445$	−200.915	−	618.354i	−0.451495	−	1.38956i
$446$	−718.167	+	233.347i	−1.61024	+	0.523198i
$447$		0			0
$448$	−128.650	−	177.071i	−0.287165	−	0.395249i
$449$	143.728	−	442.349i	0.320107	−	0.985187i	−0.653495	−	0.756931i	$-0.726698\pi$
$449$	143.728	−	442.349i	0.320107	−	0.985187i	0.973601	−	0.228256i	$-0.0733022\pi$
$450$		0			0
$451$	−278.283	+	208.870i	−0.617035	+	0.463125i
$452$	−199.605			−0.441603
$453$		0			0
$454$	−853.340	+	619.988i	−1.87960	+	1.36561i
$455$	−209.110	−	151.927i	−0.459581	−	0.333905i
$456$		0			0
$457$	673.374	−	218.792i	1.47347	−	0.478758i	0.541312	−	0.840822i	$-0.317928\pi$
$457$	673.374	−	218.792i	1.47347	−	0.478758i	0.932153	+	0.362064i	$0.117928\pi$
$458$	−827.116	+	1138.43i	−1.80593	+	2.48565i
$459$		0			0
$460$	279.345	−	859.737i	0.607273	−	1.86899i
$461$		−	149.958i		−	0.325288i	−0.986685	−	0.162644i	$-0.947998\pi$
$461$		−	149.958i		−	0.325288i	0.986685	−	0.162644i	$-0.0520021\pi$
$462$		0			0
$463$	170.995			0.369319			0.184659	−	0.982803i	$-0.440882\pi$
$463$	170.995			0.369319			0.184659	+	0.982803i	$0.440882\pi$
$464$	−644.281	−	209.340i	−1.38854	−	0.451163i
$465$		0			0
$466$	−419.070	−	304.473i	−0.899293	−	0.653374i
$467$	203.908	+	627.565i	0.436634	+	1.34382i	0.891402	+	0.453213i	$0.149722\pi$
$467$	203.908	+	627.565i	0.436634	+	1.34382i	−0.454768	+	0.890610i	$0.650278\pi$
$468$		0			0
$469$	−404.230	+	556.374i	−0.861897	+	1.18630i
$470$	8.54925	+	11.7670i	0.0181899	+	0.0250362i
$471$		0			0
$472$			469.187i			0.994040i
$473$	494.992	−	7.69502i	1.04649	−	0.0162685i
$474$		0			0
$475$	−39.4510	−	12.8184i	−0.0830547	−	0.0269861i
$476$	997.770	−	724.922i	2.09615	−	1.52295i
$477$		0			0
$478$	226.397	+	696.778i	0.473633	+	1.45769i
$479$	−246.209	+	79.9982i	−0.514006	+	0.167011i	−0.554524	−	0.832168i	$-0.687099\pi$
$479$	−246.209	+	79.9982i	−0.514006	+	0.167011i	0.0405171	+	0.999179i	$0.487099\pi$
$480$		0			0
$481$	−189.378	−	260.656i	−0.393716	−	0.541904i
$482$	−173.248	+	533.203i	−0.359436	+	1.10623i
$483$		0			0
$484$	−933.583	−	634.909i	−1.92889	−	1.31179i
$485$	181.078			0.373357
$486$		0			0
$487$	42.8901	−	31.1615i	0.0880700	−	0.0639866i	−0.542879	−	0.839811i	$-0.682666\pi$
$487$	42.8901	−	31.1615i	0.0880700	−	0.0639866i	0.630949	+	0.775824i	$0.282666\pi$
$488$	−647.035	−	470.099i	−1.32589	−	0.963317i
$489$		0			0
$490$	−43.1798	+	14.0300i	−0.0881220	+	0.0286326i
$491$	200.653	−	276.175i	0.408661	−	0.562474i	−0.554230	−	0.832364i	$-0.686987\pi$
$491$	200.653	−	276.175i	0.408661	−	0.562474i	0.962891	+	0.269889i	$0.0869872\pi$
$492$		0			0
$493$	114.530	−	352.487i	0.232312	−	0.714984i
$494$		−	203.085i		−	0.411102i
$495$		0			0
$496$	1192.45			2.40414
$497$	269.644	+	87.6126i	0.542543	+	0.176283i
$498$		0			0
$499$	141.876	+	103.079i	0.284320	+	0.206571i	0.720800	−	0.693143i	$-0.243775\pi$
$499$	141.876	+	103.079i	0.284320	+	0.206571i	−0.436479	+	0.899714i	$0.643775\pi$
$500$	−316.683	−	974.649i	−0.633365	−	1.94930i
$501$		0			0
$502$	393.688	−	541.864i	0.784238	−	1.07941i
$503$	−150.976	−	207.801i	−0.300151	−	0.413123i	0.632127	−	0.774865i	$-0.282182\pi$
$503$	−150.976	−	207.801i	−0.300151	−	0.413123i	−0.932278	+	0.361742i	$0.882182\pi$
$504$		0			0
$505$			280.676i			0.555794i
$506$	209.271	−	679.852i	0.413580	−	1.34358i
$507$		0			0
$508$	691.873	+	224.803i	1.36195	+	0.442526i
$509$	−20.5517	+	14.9317i	−0.0403766	+	0.0293353i	−0.607791	−	0.794097i	$-0.707944\pi$
$509$	−20.5517	+	14.9317i	−0.0403766	+	0.0293353i	0.567414	+	0.823433i	$0.307944\pi$
$510$		0			0
$511$	155.465	+	478.471i	0.304236	+	0.936343i
$512$	1043.44	−	339.033i	2.03796	−	0.662174i
$513$		0			0
$514$	427.342	+	588.185i	0.831404	+	1.14433i
$515$	−204.539	+	629.505i	−0.397163	+	1.22234i
$516$		0			0
$517$	4.80889	+	6.40703i	0.00930154	+	0.0123927i
$518$	−1276.45			−2.46418
$519$		0			0
$520$	−568.386	+	412.957i	−1.09305	+	0.794147i
$521$	−678.602	−	493.033i	−1.30250	−	0.946320i	−0.302521	−	0.953143i	$-0.597828\pi$
$521$	−678.602	−	493.033i	−1.30250	−	0.946320i	−0.999977	+	0.00682234i	$0.997828\pi$
$522$		0			0
$523$	74.5137	−	24.2110i	0.142474	−	0.0462925i	−0.236912	−	0.971531i	$-0.576135\pi$
$523$	74.5137	−	24.2110i	0.142474	−	0.0462925i	0.379386	+	0.925239i	$0.376135\pi$
$524$	−411.117	+	565.855i	−0.784575	+	1.07988i
$525$		0			0
$526$	−273.017	+	840.260i	−0.519044	+	1.59745i
$527$			652.393i			1.23794i
$528$		0			0
$529$	−215.307			−0.407008
$530$	1333.00	+	433.119i	2.51510	+	0.817205i
$531$		0			0
$532$	−455.606	−	331.017i	−0.856402	−	0.622212i
$533$	64.5037	+	198.522i	0.121020	+	0.372461i
$534$		0			0
$535$	−570.624	+	785.397i	−1.06659	+	1.46803i
$536$	1098.75	+	1512.30i	2.04990	+	2.82145i
$537$		0			0
$538$			41.3591i			0.0768756i
$539$	−23.6594	+	8.09611i	−0.0438950	+	0.0150206i
$540$		0			0
$541$	−291.334	−	94.6601i	−0.538510	−	0.174972i	0.0271193	−	0.999632i	$-0.491367\pi$
$541$	−291.334	−	94.6601i	−0.538510	−	0.174972i	−0.565629	+	0.824660i	$0.691367\pi$
$542$	−678.224	+	492.759i	−1.25134	+	0.909149i
$543$		0			0
$544$	−258.602	−	795.894i	−0.475371	−	1.46304i
$545$	424.635	−	137.972i	0.779146	−	0.253160i
$546$		0			0
$547$	−41.3877	−	56.9653i	−0.0756631	−	0.104141i	0.769508	−	0.638637i	$-0.220502\pi$
$547$	−41.3877	−	56.9653i	−0.0756631	−	0.104141i	−0.845171	+	0.534496i	$0.820502\pi$
$548$	456.799	−	1405.88i	0.833575	−	2.56548i
$549$		0			0
$550$	63.9924	+	187.006i	0.116350	+	0.340011i
$551$	−169.237			−0.307146
$552$		0			0
$553$	517.660	−	376.102i	0.936095	−	0.680113i
$554$	979.091	+	711.352i	1.76731	+	1.28403i
$555$		0			0
$556$	2291.04	−	744.405i	4.12058	−	1.33886i
$557$	338.064	−	465.305i	0.606937	−	0.835377i	−0.389384	−	0.921076i	$-0.627312\pi$
$557$	338.064	−	465.305i	0.606937	−	0.835377i	0.996321	+	0.0856981i	$0.0273121\pi$
$558$		0			0
$559$	91.7742	−	282.452i	0.164176	−	0.505281i
$560$			1321.54i			2.35988i
$561$		0			0
$562$	−1459.01			−2.59611
$563$	350.578	+	113.910i	0.622697	+	0.202327i	0.603337	−	0.797486i	$-0.293837\pi$
$563$	350.578	+	113.910i	0.622697	+	0.202327i	0.0193596	+	0.999813i	$0.493837\pi$
$564$		0			0
$565$	94.6679	+	68.7802i	0.167554	+	0.121735i
$566$	−105.025	−	323.234i	−0.185557	−	0.571084i
$567$		0			0
$568$	452.973	−	623.464i	0.797488	−	1.09765i
$569$	162.157	+	223.190i	0.284987	+	0.392250i	0.927378	−	0.374127i	$-0.122057\pi$
$569$	162.157	+	223.190i	0.284987	+	0.392250i	−0.642391	+	0.766377i	$0.722057\pi$
$570$		0			0
$571$			57.9706i			0.101525i	0.998711	+	0.0507624i	$0.0161651\pi$
$571$			57.9706i			0.101525i	−0.998711	+	0.0507624i	$0.983835\pi$
$572$	−541.703	+	406.584i	−0.947033	+	0.710811i
$573$		0			0
$574$	786.504	+	255.551i	1.37022	+	0.445210i
$575$	−70.5167	+	51.2334i	−0.122638	+	0.0891015i
$576$		0			0
$577$	−60.6545	−	186.675i	−0.105120	−	0.323528i	0.884638	−	0.466278i	$-0.154405\pi$
$577$	−60.6545	−	186.675i	−0.105120	−	0.323528i	−0.989759	+	0.142750i	$0.954405\pi$
$578$	179.659	−	58.3747i	0.310828	−	0.100994i
$579$		0			0
$580$	602.354	+	829.069i	1.03854	+	1.42943i
$581$	58.0196	−	178.566i	0.0998616	−	0.307343i
$582$		0			0
$583$	737.805	+	227.111i	1.26553	+	0.389555i
$584$	1367.47			2.34156
$585$		0			0
$586$	726.456	−	527.801i	1.23969	−	0.900685i
$587$	577.412	+	419.514i	0.983666	+	0.714675i	0.958525	−	0.285009i	$-0.0919966\pi$
$587$	577.412	+	419.514i	0.983666	+	0.714675i	0.0251407	+	0.999684i	$0.491997\pi$
$588$		0			0
$589$	283.318	−	92.0557i	0.481016	−	0.156292i
$590$	282.987	−	389.499i	0.479640	−	0.660167i
$591$		0			0
$592$	−509.043	+	1566.67i	−0.859871	+	2.64641i
$593$		−	279.318i		−	0.471025i	−0.971871	−	0.235513i	$-0.924323\pi$
$593$		−	279.318i		−	0.471025i	0.971871	−	0.235513i	$-0.0756769\pi$
$594$		0			0
$595$	−723.014			−1.21515
$596$	−498.932	−	162.113i	−0.837135	−	0.272002i
$597$		0			0
$598$	−345.237	−	250.829i	−0.577319	−	0.419447i
$599$	−204.231	−	628.559i	−0.340953	−	1.04935i	−0.963715	−	0.266935i	$-0.913989\pi$
$599$	−204.231	−	628.559i	−0.340953	−	1.04935i	0.622761	−	0.782412i	$-0.286011\pi$
$600$		0			0
$601$	438.851	−	604.027i	0.730202	−	1.00504i	−0.268921	−	0.963162i	$-0.586667\pi$
$601$	438.851	−	604.027i	0.730202	−	1.00504i	0.999123	−	0.0418742i	$-0.0133329\pi$
$602$	−691.591	−	951.894i	−1.14882	−	1.58122i
$603$		0			0
$604$		−	1060.00i		−	1.75496i
$605$	223.998	+	622.818i	0.370245	+	1.02945i
$606$		0			0
$607$	−73.1153	−	23.7566i	−0.120454	−	0.0391378i	0.248170	−	0.968717i	$-0.420171\pi$
$607$	−73.1153	−	23.7566i	−0.120454	−	0.0391378i	−0.368624	+	0.929579i	$0.620171\pi$
$608$	−309.147	+	224.609i	−0.508466	+	0.369422i
$609$		0			0
$610$	253.603	+	780.511i	0.415743	+	1.27953i
$611$	4.57065	−	1.48510i	0.00748061	−	0.00243060i
$612$		0			0
$613$	−272.020	−	374.404i	−0.443753	−	0.610773i	0.527288	−	0.849687i	$-0.323209\pi$
$613$	−272.020	−	374.404i	−0.443753	−	0.610773i	−0.971041	+	0.238913i	$0.923209\pi$
$614$	2.45310	−	7.54986i	0.00399527	−	0.0122962i
$615$		0			0
$616$	23.8294	+	1532.85i	0.0386840	+	2.48840i
$617$	−517.342			−0.838479			−0.419240	−	0.907876i	$-0.637703\pi$
$617$	−517.342			−0.838479			−0.419240	+	0.907876i	$0.637703\pi$
$618$		0			0
$619$	765.686	−	556.304i	1.23697	−	0.898714i	0.239580	−	0.970877i	$-0.422990\pi$
$619$	765.686	−	556.304i	1.23697	−	0.898714i	0.997393	+	0.0721630i	$0.0229902\pi$
$620$	−1459.36	−	1060.29i	−2.35381	−	1.71014i
$621$		0			0
$622$	−1103.30	+	358.485i	−1.77380	+	0.576343i
$623$	−500.270	+	688.563i	−0.803002	+	1.10524i
$624$		0			0
$625$	−223.671	+	688.388i	−0.357873	+	1.10142i
$626$		−	367.453i		−	0.586985i
$627$		0			0
$628$	−2492.13			−3.96836
$629$	−857.130	−	278.498i	−1.36269	−	0.442764i
$630$		0			0
$631$	−380.181	−	276.218i	−0.602506	−	0.437746i	0.244261	−	0.969709i	$-0.421455\pi$
$631$	−380.181	−	276.218i	−0.602506	−	0.437746i	−0.846768	+	0.531963i	$0.821455\pi$
$632$	−537.451	−	1654.10i	−0.850398	−	2.61725i
$633$		0			0
$634$	−598.852	+	824.249i	−0.944561	+	1.30008i
$635$	−250.676	−	345.026i	−0.394765	−	0.543348i
$636$		0			0
$637$			15.0016i			0.0235503i
$638$	484.069	+	644.938i	0.758728	+	1.01088i
$639$		0			0
$640$	−362.809	−	117.884i	−0.566889	−	0.184193i
$641$	−105.020	+	76.3012i	−0.163837	+	0.119035i	−0.666683	−	0.745342i	$-0.732286\pi$
$641$	−105.020	+	76.3012i	−0.163837	+	0.119035i	0.502846	+	0.864376i	$0.332286\pi$
$642$		0			0
$643$	23.1565	+	71.2684i	0.0360133	+	0.110837i	0.967447	−	0.253073i	$-0.0814414\pi$
$643$	23.1565	+	71.2684i	0.0360133	+	0.110837i	−0.931434	+	0.363911i	$0.881441\pi$
$644$	−1125.44	+	365.676i	−1.74757	+	0.567820i
$645$		0			0
$646$	−333.908	−	459.584i	−0.516885	−	0.711431i
$647$	−280.018	+	861.806i	−0.432794	+	1.33200i	0.462537	+	0.886600i	$0.346939\pi$
$647$	−280.018	+	861.806i	−0.432794	+	1.33200i	−0.895331	+	0.445402i	$0.853061\pi$
$648$		0			0
$649$	152.509	−	216.923i	0.234991	−	0.334243i
$650$	118.574			0.182421
$651$		0			0
$652$	1813.60	−	1317.66i	2.78160	−	2.02095i
$653$	−852.108	−	619.092i	−1.30491	−	0.948074i	−0.304921	−	0.952378i	$-0.598630\pi$
$653$	−852.108	−	619.092i	−1.30491	−	0.948074i	−0.999991	+	0.00430333i	$0.998630\pi$
$654$		0			0
$655$	389.967	−	126.708i	0.595369	−	0.193447i
$656$	627.312	−	863.420i	0.956268	−	1.31619i
$657$		0			0
$658$	5.88365	−	18.1080i	0.00894172	−	0.0275198i
$659$		−	569.208i		−	0.863746i	−0.901935	−	0.431873i	$-0.857853\pi$
$659$		−	569.208i		−	0.863746i	0.901935	−	0.431873i	$-0.142147\pi$
$660$		0			0
$661$	−436.561			−0.660455			−0.330228	−	0.943901i	$-0.607126\pi$
$661$	−436.561			−0.660455			−0.330228	+	0.943901i	$0.607126\pi$
$662$	−225.302	−	73.2050i	−0.340335	−	0.110582i
$663$		0			0
$664$	−412.876	−	299.972i	−0.621801	−	0.451765i
$665$	102.021	+	313.987i	0.153414	+	0.472161i
$666$		0			0
$667$	−209.025	+	287.698i	−0.313380	+	0.431331i
$668$	967.032	+	1331.01i	1.44765	+	1.99252i
$669$		0			0
$670$		−	1918.15i		−	2.86290i
$671$	146.344	+	427.664i	0.218098	+	0.637353i
$672$		0			0
$673$	−1165.51	−	378.696i	−1.73181	−	0.562699i	−0.738099	−	0.674692i	$-0.764276\pi$
$673$	−1165.51	−	378.696i	−1.73181	−	0.562699i	−0.993709	+	0.111994i	$0.964276\pi$
$674$	1646.48	−	1196.24i	2.44285	−	1.77483i
$675$		0			0
$676$	−361.725	−	1113.28i	−0.535097	−	1.64686i
$677$	571.209	−	185.597i	0.843736	−	0.274146i	0.144916	−	0.989444i	$-0.453709\pi$
$677$	571.209	−	185.597i	0.843736	−	0.274146i	0.698820	+	0.715298i	$0.253709\pi$
$678$		0			0
$679$	−139.329	−	191.769i	−0.205197	−	0.282429i
$680$	−607.293	+	1869.06i	−0.893079	+	2.74861i
$681$		0			0
$682$	−1161.19	−	816.378i	−1.70262	−	1.19704i
$683$	653.422			0.956693			0.478347	−	0.878171i	$-0.341236\pi$
$683$	653.422			0.956693			0.478347	+	0.878171i	$0.341236\pi$
$684$		0			0
$685$	−701.091	+	509.373i	−1.02349	+	0.743610i
$686$	−988.315	−	718.053i	−1.44069	−	1.04672i
$687$		0			0
$688$	−1444.13	+	469.227i	−2.09903	+	0.682016i
$689$	272.211	−	374.666i	0.395081	−	0.543783i
$690$		0			0
$691$	−297.610	+	915.948i	−0.430694	+	1.32554i	0.466741	+	0.884394i	$0.345428\pi$
$691$	−297.610	+	915.948i	−0.430694	+	1.32554i	−0.897435	+	0.441146i	$0.854572\pi$
$692$			2489.43i			3.59744i
$693$		0			0
$694$	2393.14			3.44833
$695$	−1343.10	−	436.398i	−1.93251	−	0.627911i
$696$		0			0
$697$	472.379	+	343.203i	0.677731	+	0.492400i
$698$	−18.3235	−	56.3939i	−0.0262514	−	0.0807936i
$699$		0			0
$700$	193.269	−	266.012i	0.276099	−	0.380017i
$701$	190.943	+	262.811i	0.272387	+	0.374908i	0.923194	−	0.384335i	$-0.125569\pi$
$701$	190.943	+	262.811i	0.272387	+	0.374908i	−0.650807	+	0.759243i	$0.725569\pi$
$702$		0			0
$703$			411.528i			0.585388i
$704$	321.351	+	98.9180i	0.456465	+	0.140509i
$705$		0			0
$706$	1292.59	+	419.987i	1.83086	+	0.594883i
$707$	297.247	−	215.963i	0.420435	−	0.305464i
$708$		0			0
$709$	349.513	+	1075.69i	0.492966	+	1.51719i	0.820103	+	0.572216i	$0.193916\pi$
$709$	349.513	+	1075.69i	0.492966	+	1.51719i	−0.327137	+	0.944977i	$0.606084\pi$
$710$	−752.077	+	244.365i	−1.05926	+	0.344176i
$711$		0			0
$712$	1359.80	+	1871.60i	1.90983	+	2.62865i
$713$	193.434	−	595.330i	0.271296	−	0.834964i
$714$		0			0
$715$	397.018	−	6.17195i	0.555271	−	0.00863209i
$716$	−540.556			−0.754967
$717$		0			0
$718$	−171.246	+	124.418i	−0.238504	+	0.173283i
$719$	599.572	+	435.614i	0.833897	+	0.605862i	0.920659	−	0.390367i	$-0.127652\pi$
$719$	599.572	+	435.614i	0.833897	+	0.605862i	−0.0867622	+	0.996229i	$0.527652\pi$
$720$		0			0
$721$	824.052	−	267.751i	1.14293	−	0.371360i
$722$	622.265	−	856.474i	0.861862	−	1.18625i
$723$		0			0
$724$	670.462	−	2063.47i	0.926053	−	2.85010i
$725$		−	98.8116i		−	0.136292i
$726$		0			0
$727$	1305.90			1.79629			0.898144	−	0.439702i	$-0.144916\pi$
$727$	1305.90			1.79629			0.898144	+	0.439702i	$0.144916\pi$
$728$	874.676	+	284.199i	1.20148	+	0.390384i
$729$		0			0
$730$	−1135.22	−	824.784i	−1.55509	−	1.12984i
$731$	−256.715	−	790.087i	−0.351183	−	1.08083i
$732$		0			0
$733$	−148.886	+	204.924i	−0.203119	+	0.279569i	−0.898409	−	0.439160i	$-0.855276\pi$
$733$	−148.886	+	204.924i	−0.203119	+	0.279569i	0.695290	+	0.718730i	$0.255276\pi$
$734$	403.641	+	555.564i	0.549920	+	0.756899i
$735$		0			0
$736$			802.954i			1.09097i
$737$	−16.4216	−	1056.34i	−0.0222817	−	1.43330i
$738$		0			0
$739$	−185.230	−	60.1849i	−0.250650	−	0.0814411i	0.180997	−	0.983484i	$-0.442067\pi$
$739$	−185.230	−	60.1849i	−0.250650	−	0.0814411i	−0.431647	+	0.902043i	$0.642067\pi$
$740$	2016.02	−	1464.72i	2.72435	−	1.97935i
$741$		0			0
$742$	−566.973	−	1744.96i	−0.764114	−	2.35170i
$743$	150.944	−	49.0448i	0.203155	−	0.0660092i	−0.205672	−	0.978621i	$-0.565938\pi$
$743$	150.944	−	49.0448i	0.203155	−	0.0660092i	0.408827	+	0.912612i	$0.365938\pi$
$744$		0			0
$745$	180.771	+	248.810i	0.242645	+	0.333972i
$746$	−531.302	+	1635.18i	−0.712201	+	2.19193i
$747$		0			0
$748$	−557.388	+	1810.76i	−0.745171	+	2.42081i
$749$	1270.83			1.69670
$750$		0			0
$751$	103.420	−	75.1387i	0.137709	−	0.100052i	−0.516798	−	0.856107i	$-0.672876\pi$
$751$	103.420	−	75.1387i	0.137709	−	0.100052i	0.654507	+	0.756056i	$0.272876\pi$
$752$	−19.8789	−	14.4429i	−0.0264347	−	0.0192059i
$753$		0			0
$754$	460.087	−	149.491i	0.610195	−	0.198264i
$755$	−365.256	+	502.731i	−0.483782	+	0.665869i
$756$		0			0
$757$	−373.740	+	1150.25i	−0.493712	+	1.51949i	0.325242	+	0.945631i	$0.394554\pi$
$757$	−373.740	+	1150.25i	−0.493712	+	1.51949i	−0.818954	+	0.573859i	$0.805446\pi$
$758$			1033.13i			1.36297i
$759$		0			0
$760$	897.377			1.18076
$761$	−209.476	−	68.0630i	−0.275265	−	0.0894389i	0.168132	−	0.985765i	$-0.446227\pi$
$761$	−209.476	−	68.0630i	−0.275265	−	0.0894389i	−0.443396	+	0.896326i	$0.646227\pi$
$762$		0			0
$763$	−472.849	−	343.545i	−0.619723	−	0.450255i
$764$	39.5052	+	121.584i	0.0517083	+	0.159142i
$765$		0			0
$766$	−148.514	+	204.412i	−0.193883	+	0.266857i
$767$	−93.5039	−	128.697i	−0.121909	−	0.167793i
$768$		0			0
$769$		−	843.244i		−	1.09655i	−0.836299	−	0.548273i	$-0.815285\pi$
$769$		−	843.244i		−	1.09655i	0.836299	−	0.548273i	$-0.184715\pi$
$770$	904.750	−	1286.88i	1.17500	−	1.67128i
$771$		0			0
$772$	−306.522	−	99.5950i	−0.397049	−	0.129009i
$773$	−91.0506	+	66.1522i	−0.117789	+	0.0855785i	−0.645120	−	0.764081i	$-0.723193\pi$
$773$	−91.0506	+	66.1522i	−0.117789	+	0.0855785i	0.527331	+	0.849660i	$0.323193\pi$
$774$		0			0
$775$	53.7481	+	165.420i	0.0693523	+	0.213445i
$776$	−612.770	+	199.101i	−0.789652	+	0.256574i
$777$		0			0
$778$	−1267.71	−	1744.86i	−1.62945	−	2.24274i
$779$	82.3899	−	253.570i	0.105764	−	0.325507i
$780$		0			0
$781$	−412.084	+	141.013i	−0.527636	+	0.180554i
$782$	−1193.69			−1.52645
$783$		0			0
$784$	62.0522	−	45.0836i	0.0791482	−	0.0575045i
$785$	1181.96	+	858.743i	1.50568	+	1.09394i
$786$		0			0
$787$	−927.286	+	301.293i	−1.17825	+	0.382838i	−0.831718	−	0.555199i	$-0.812642\pi$
$787$	−927.286	+	301.293i	−1.17825	+	0.382838i	−0.346536	+	0.938037i	$0.612642\pi$
$788$	−569.880	+	784.373i	−0.723198	+	0.995397i
$789$		0			0
$790$	−551.495	+	1697.33i	−0.698095	+	2.14852i
$791$		−	153.179i		−	0.193653i
$792$		0			0
$793$	271.166			0.341950
$794$	−1708.85	−	555.240i	−2.15221	−	0.699294i
$795$		0			0
$796$	1999.03	+	1452.38i	2.51134	+	1.82459i
$797$	457.237	+	1407.23i	0.573698	+	1.76566i	0.640571	+	0.767899i	$0.278698\pi$
$797$	457.237	+	1407.23i	0.573698	+	1.76566i	−0.0668735	+	0.997761i	$0.521302\pi$
$798$		0			0
$799$	7.90171	−	10.8758i	0.00988950	−	0.0136117i
$800$	−131.141	−	180.500i	−0.163926	−	0.225625i
$801$		0			0
$802$			1986.48i			2.47691i
$803$	−632.236	−	444.497i	−0.787343	−	0.553546i
$804$		0			0
$805$	659.773	+	214.373i	0.819594	+	0.266302i
$806$	−688.912	+	500.524i	−0.854729	+	0.620997i
$807$		0			0
$808$	−308.612	−	949.809i	−0.381945	−	1.17551i
$809$	−156.921	+	50.9866i	−0.193969	+	0.0630242i	−0.404390	−	0.914586i	$-0.632516\pi$
$809$	−156.921	+	50.9866i	−0.193969	+	0.0630242i	0.210422	+	0.977611i	$0.432516\pi$
$810$		0			0
$811$	492.102	+	677.320i	0.606784	+	0.835166i	0.996308	−	0.0858500i	$-0.0273606\pi$
$811$	492.102	+	677.320i	0.606784	+	0.835166i	−0.389524	+	0.921016i	$0.627361\pi$
$812$	414.544	−	1275.84i	0.510522	−	1.57123i
$813$		0			0
$814$	1568.27	−	1177.09i	1.92663	−	1.44606i
$815$	−1314.19			−1.61250
$816$		0			0
$817$	−306.892	+	222.970i	−0.375632	+	0.272913i
$818$	−789.718	−	573.764i	−0.965425	−	0.701423i
$819$		0			0
$820$	−1535.45	+	498.897i	−1.87250	+	0.608411i
$821$	−755.447	+	1039.78i	−0.920154	+	1.26648i	0.0434239	+	0.999057i	$0.486173\pi$
$821$	−755.447	+	1039.78i	−0.920154	+	1.26648i	−0.963578	+	0.267427i	$0.913827\pi$
$822$		0			0
$823$	225.540	−	694.141i	0.274046	−	0.843428i	−0.715424	−	0.698691i	$-0.753766\pi$
$823$	225.540	−	694.141i	0.274046	−	0.843428i	0.989470	−	0.144737i	$-0.0462336\pi$
$824$		−	2355.15i		−	2.85819i
$825$		0			0
$826$	−630.237			−0.762998
$827$	509.083	+	165.411i	0.615578	+	0.200013i	0.600176	−	0.799868i	$-0.295097\pi$
$827$	509.083	+	165.411i	0.615578	+	0.200013i	0.0154018	+	0.999881i	$0.495097\pi$
$828$		0			0
$829$	−502.344	−	364.975i	−0.605964	−	0.440259i	0.242027	−	0.970270i	$-0.422188\pi$
$829$	−502.344	−	364.975i	−0.605964	−	0.440259i	−0.847991	+	0.530011i	$0.822188\pi$
$830$	161.825	+	498.048i	0.194970	+	0.600057i
$831$		0			0
$832$	118.562	−	163.186i	0.142502	−	0.196137i
$833$	24.6653	+	33.9488i	0.0296102	+	0.0407549i
$834$		0			0
$835$		−	964.487i		−	1.15507i
$836$	865.020	−	13.4474i	1.03471	−	0.0160854i
$837$		0			0
$838$	−14.9818	−	4.86790i	−0.0178781	−	0.00580895i
$839$	683.778	−	496.794i	0.814992	−	0.592126i	−0.100281	−	0.994959i	$-0.531974\pi$
$839$	683.778	−	496.794i	0.814992	−	0.592126i	0.915274	+	0.402833i	$0.131974\pi$
$840$		0			0
$841$	135.307	+	416.433i	0.160888	+	0.495164i
$842$	1126.92	−	366.159i	1.33839	−	0.434868i
$843$		0			0
$844$	1617.85	+	2226.78i	1.91688	+	2.63836i
$845$	−212.057	+	652.645i	−0.250955	+	0.772361i
$846$		0			0
$847$	487.237	−	716.444i	0.575251	−	0.845861i
$848$	−2367.83			−2.79225
$849$		0			0
$850$	268.335	−	194.957i	0.315688	−	0.229361i
$851$	699.584	+	508.277i	0.822073	+	0.597271i
$852$		0			0
$853$	351.600	−	114.242i	0.412192	−	0.133929i	−0.0955780	−	0.995422i	$-0.530470\pi$
$853$	351.600	−	114.242i	0.412192	−	0.133929i	0.507770	+	0.861493i	$0.330470\pi$
$854$	631.461	−	869.132i	0.739416	−	1.01772i
$855$		0			0
$856$	1067.43	−	3285.20i	1.24700	−	3.83786i
$857$		−	58.2378i		−	0.0679554i	−0.999423	−	0.0339777i	$-0.989182\pi$
$857$		−	58.2378i		−	0.0679554i	0.999423	−	0.0339777i	$-0.0108175\pi$
$858$		0			0
$859$	−708.720			−0.825052			−0.412526	−	0.910946i	$-0.635353\pi$
$859$	−708.720			−0.825052			−0.412526	+	0.910946i	$0.635353\pi$
$860$	2184.60	+	709.818i	2.54023	+	0.825370i
$861$		0			0
$862$	232.443	+	168.879i	0.269655	+	0.195916i
$863$	37.5941	+	115.703i	0.0435622	+	0.134071i	0.970472	−	0.241213i	$-0.0775453\pi$
$863$	37.5941	+	115.703i	0.0435622	+	0.134071i	−0.926910	+	0.375284i	$0.877545\pi$
$864$		0			0
$865$	857.811	−	1180.68i	0.991690	−	1.36494i
$866$	742.240	+	1021.61i	0.857089	+	1.17968i
$867$		0			0
$868$			2361.35i			2.72045i
$869$	−289.182	+	939.456i	−0.332776	+	1.08108i
$870$		0			0
$871$	−602.768	−	195.851i	−0.692042	−	0.224858i
$872$	−1285.26	+	933.797i	−1.47392	+	1.07087i
$873$		0			0
$874$	168.435	+	518.389i	0.192717	+	0.593122i
$875$	747.958	−	243.026i	0.854810	−	0.277744i
$876$		0			0
$877$	−28.4555	−	39.1656i	−0.0324464	−	0.0446586i	0.792486	−	0.609891i	$-0.208787\pi$
$877$	−28.4555	−	39.1656i	−0.0324464	−	0.0446586i	−0.824932	+	0.565232i	$0.808787\pi$
$878$	429.620	−	1322.23i	0.489317	−	1.50596i
$879$		0			0
$880$	−1218.67	−	1623.67i	−1.38485	−	1.84508i
$881$	−820.445			−0.931265			−0.465633	−	0.884978i	$-0.654173\pi$
$881$	−820.445			−0.931265			−0.465633	+	0.884978i	$0.654173\pi$
$882$		0			0
$883$	8.71172	−	6.32943i	0.00986604	−	0.00716810i	−0.582841	−	0.812586i	$-0.698059\pi$
$883$	8.71172	−	6.32943i	0.00986604	−	0.00716810i	0.592707	+	0.805418i	$0.298059\pi$
$884$	919.528	+	668.076i	1.04019	+	0.755742i
$885$		0			0
$886$	−573.690	+	186.403i	−0.647506	+	0.210387i
$887$	−380.994	+	524.394i	−0.429532	+	0.591199i	−0.967846	−	0.251545i	$-0.919061\pi$
$887$	−380.994	+	524.394i	−0.429532	+	0.591199i	0.538314	+	0.842744i	$0.319061\pi$
$888$		0			0
$889$	−172.517	+	530.952i	−0.194057	+	0.597247i
$890$		−	2373.88i		−	2.66728i
$891$		0			0
$892$	−1929.78			−2.16343
$893$	−5.83805	−	1.89690i	−0.00653757	−	0.00212418i
$894$		0			0
$895$	256.373	+	186.266i	0.286450	+	0.208118i
$896$	154.315	+	474.934i	0.172227	+	0.530060i
$897$		0			0
$898$	998.170	−	1373.86i	1.11155	−	1.52991i
$899$	417.103	+	574.093i	0.463964	+	0.638591i
$900$		0			0
$901$		−	1295.44i		−	1.43778i
$902$	−1201.98	+	411.309i	−1.33257	+	0.455997i
$903$		0			0
$904$	−395.982	−	128.663i	−0.438034	−	0.142326i
$905$	−1029.02	+	747.627i	−1.13704	+	0.826107i
$906$		0			0
$907$	182.336	+	561.174i	0.201032	+	0.618714i	0.999853	+	0.0171448i	$0.00545763\pi$
$907$	182.336	+	561.174i	0.201032	+	0.618714i	−0.798821	+	0.601569i	$0.794542\pi$
$908$	−2563.66	+	832.983i	−2.82341	+	0.917382i
$909$		0			0
$910$	−554.705	−	763.486i	−0.609566	−	0.838995i
$911$	386.627	−	1189.92i	0.424399	−	1.30617i	−0.479170	−	0.877722i	$-0.659062\pi$
$911$	386.627	−	1189.92i	0.424399	−	1.30617i	0.903569	−	0.428443i	$-0.140938\pi$
$912$		0			0
$913$	93.3827	+	272.894i	0.102281	+	0.298898i
$914$	2585.10			2.82834
$915$		0			0
$916$	−2909.34	+	2113.76i	−3.17614	+	2.30760i
$917$	−434.244	−	315.497i	−0.473549	−	0.344053i
$918$		0			0
$919$	−265.222	+	86.1758i	−0.288598	+	0.0937713i	−0.449739	−	0.893160i	$-0.648483\pi$
$919$	−265.222	+	86.1758i	−0.288598	+	0.0937713i	0.161140	+	0.986932i	$0.448483\pi$
$920$	1108.35	−	1525.51i	1.20473	−	1.65816i
$921$		0			0
$922$	169.191	−	520.717i	0.183505	−	0.564769i
$923$			261.288i			0.283085i
$924$		0			0
$925$	−240.277			−0.259758
$926$	593.767	+	192.927i	0.641217	+	0.208344i
$927$		0			0
$928$	−736.414	−	535.036i	−0.793550	−	0.576548i
$929$	133.870	+	412.010i	0.144101	+	0.443498i	0.996894	−	0.0787509i	$-0.0250932\pi$
$929$	133.870	+	412.010i	0.144101	+	0.443498i	−0.852793	+	0.522249i	$0.825093\pi$
$930$		0			0
$931$	11.2628	−	15.5019i	0.0120975	−	0.0166508i
$932$	−778.103	−	1070.97i	−0.834875	−	1.14911i
$933$		0			0
$934$			2409.24i			2.57948i
$935$	888.313	−	666.737i	0.950067	−	0.713088i
$936$		0			0
$937$	1051.31	+	341.592i	1.12200	+	0.364559i	0.810529	−	0.585698i	$-0.199180\pi$
$937$	1051.31	+	341.592i	1.12200	+	0.364559i	0.311467	+	0.950257i	$0.399180\pi$
$938$	−2031.40	+	1475.90i	−2.16567	+	1.57345i
$939$		0			0
$940$	11.4863	+	35.3513i	0.0122195	+	0.0376077i
$941$	47.3703	−	15.3916i	0.0503404	−	0.0163566i	−0.283739	−	0.958902i	$-0.591575\pi$
$941$	47.3703	−	15.3916i	0.0503404	−	0.0163566i	0.334079	+	0.942545i	$0.391575\pi$
$942$		0			0
$943$	−329.301	−	453.244i	−0.349206	−	0.480640i
$944$	−251.337	+	773.535i	−0.266247	+	0.819423i
$945$		0			0
$946$	1727.51	+	531.760i	1.82612	+	0.562114i
$947$	−643.764			−0.679793			−0.339896	−	0.940463i	$-0.610392\pi$
$947$	−643.764			−0.679793			−0.339896	+	0.940463i	$0.610392\pi$
$948$		0			0
$949$	−375.095	+	272.523i	−0.395253	+	0.287168i
$950$	−122.528	−	89.0220i	−0.128977	−	0.0937074i
$951$		0			0
$952$	2446.68	−	794.976i	2.57005	−	0.835058i
$953$	797.420	−	1097.55i	0.836747	−	1.15168i	−0.149883	−	0.988704i	$-0.547890\pi$
$953$	797.420	−	1097.55i	0.836747	−	1.15168i	0.986629	−	0.162980i	$-0.0521105\pi$
$954$		0			0
$955$	23.1594	−	71.2774i	0.0242507	−	0.0746360i
$956$			1872.31i			1.95848i
$957$		0			0
$958$	−945.203			−0.986642
$959$	1078.89	+	350.554i	1.12502	+	0.365541i
$960$		0			0
$961$	−233.078	−	169.341i	−0.242537	−	0.176214i
$962$	−363.513	−	1118.78i	−0.377872	−	1.16297i
$963$		0			0
$964$	−842.159	+	1159.13i	−0.873609	+	1.20242i
$965$	111.058	+	152.858i	0.115086	+	0.158402i
$966$		0			0
$967$			863.704i			0.893179i	0.894739	+	0.446589i	$0.147362\pi$
$967$			863.704i			0.893179i	−0.894739	+	0.446589i	$0.852638\pi$
$968$	−1442.82	−	1861.33i	−1.49052	−	1.92286i
$969$		0			0
$970$	628.782	+	204.304i	0.648229	+	0.210622i
$971$	841.772	−	611.583i	0.866913	−	0.629849i	−0.0628441	−	0.998023i	$-0.520017\pi$
$971$	841.772	−	611.583i	0.866913	−	0.629849i	0.929757	+	0.368174i	$0.120017\pi$
$972$		0			0
$973$	571.266	+	1758.18i	0.587118	+	1.80696i
$974$	184.091	−	59.8148i	0.189005	−	0.0614115i
$975$		0			0
$976$	−814.923	−	1121.65i	−0.834962	−	1.14923i
$977$	276.007	−	849.461i	0.282504	−	0.869459i	−0.704631	−	0.709574i	$-0.748888\pi$
$977$	276.007	−	849.461i	0.282504	−	0.869459i	0.987136	−	0.159885i	$-0.0511124\pi$
$978$		0			0
$979$	−20.3232	−	1307.32i	−0.0207591	−	1.33536i
$980$	−116.028			−0.118396
$981$		0			0
$982$	1008.35	−	732.609i	1.02683	−	0.746038i
$983$	153.977	+	111.871i	0.156640	+	0.113805i	0.663344	−	0.748314i	$-0.269136\pi$
$983$	153.977	+	111.871i	0.156640	+	0.113805i	−0.506705	+	0.862120i	$0.669136\pi$
$984$		0			0
$985$	540.562	−	175.639i	0.548794	−	0.178314i
$986$	795.395	−	1094.77i	0.806689	−	1.11031i
$987$		0			0
$988$	160.379	−	493.597i	0.162327	−	0.499592i
$989$			797.095i			0.805961i
$990$		0			0
$991$	−139.682			−0.140950			−0.0704751	−	0.997514i	$-0.522452\pi$
$991$	−139.682			−0.140950			−0.0704751	+	0.997514i	$0.522452\pi$
$992$	1523.85	+	495.130i	1.53614	+	0.499123i
$993$		0			0
$994$	837.470	+	608.457i	0.842525	+	0.612130i
$995$	−447.628	−	1377.66i	−0.449877	−	1.38458i
$996$		0			0
$997$	−123.310	+	169.721i	−0.123681	+	0.170232i	−0.866367	−	0.499407i	$-0.833551\pi$
$997$	−123.310	+	169.721i	−0.123681	+	0.170232i	0.742687	+	0.669639i	$0.233551\pi$
$998$	376.354	+	518.007i	0.377109	+	0.519045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.c.46.4		16
3.2	odd	2		33.3.g.a.13.1	✓	16
11.4	even	5		1089.3.c.m.604.16		16
11.6	odd	10	inner	99.3.k.c.28.4		16
11.7	odd	10		1089.3.c.m.604.1		16
12.11	even	2		528.3.bf.b.145.4		16
33.2	even	10		363.3.g.a.118.1		16
33.5	odd	10		363.3.g.f.94.4		16
33.8	even	10		363.3.g.g.40.4		16
33.14	odd	10		363.3.g.a.40.1		16
33.17	even	10		33.3.g.a.28.1	yes	16
33.20	odd	10		363.3.g.g.118.4		16
33.26	odd	10		363.3.c.e.241.1		16
33.29	even	10		363.3.c.e.241.16		16
33.32	even	2		363.3.g.f.112.4		16
132.83	odd	10		528.3.bf.b.193.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.g.a.13.1	✓	16	3.2	odd	2
33.3.g.a.28.1	yes	16	33.17	even	10
99.3.k.c.28.4		16	11.6	odd	10	inner
99.3.k.c.46.4		16	1.1	even	1	trivial
363.3.c.e.241.1		16	33.26	odd	10
363.3.c.e.241.16		16	33.29	even	10
363.3.g.a.40.1		16	33.14	odd	10
363.3.g.a.118.1		16	33.2	even	10
363.3.g.f.94.4		16	33.5	odd	10
363.3.g.f.112.4		16	33.32	even	2
363.3.g.g.40.4		16	33.8	even	10
363.3.g.g.118.4		16	33.20	odd	10
528.3.bf.b.145.4		16	12.11	even	2
528.3.bf.b.193.4		16	132.83	odd	10
1089.3.c.m.604.1		16	11.7	odd	10
1089.3.c.m.604.16		16	11.4	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.47243 + 1.12826i) q^{2} +(7.54873 + 5.48447i) q^{4} +(-1.69033 - 5.20232i) q^{5} +(-4.20886 + 5.79300i) q^{7} +(11.4402 + 15.7461i) q^{8} +O(q^{10})\)	\(q+(3.47243 + 1.12826i) q^{2} +(7.54873 + 5.48447i) q^{4} +(-1.69033 - 5.20232i) q^{5} +(-4.20886 + 5.79300i) q^{7} +(11.4402 + 15.7461i) q^{8} -19.9718i q^{10} +(-0.170982 - 10.9987i) q^{11} +(-6.27605 - 2.03921i) q^{13} +(-21.1510 + 15.3671i) q^{14} +(10.4262 + 32.0885i) q^{16} +(-17.5557 + 5.70418i) q^{17} +(4.95437 + 6.81910i) q^{19} +(15.7721 - 48.5415i) q^{20} +(11.8156 - 38.3850i) q^{22} +17.7114 q^{23} +(-3.98143 + 2.89268i) q^{25} +(-19.4924 - 14.1620i) q^{26} +(-63.5431 + 20.6464i) q^{28} +(-11.8017 + 16.2437i) q^{29} +(10.9215 - 33.6128i) q^{31} +45.3355i q^{32} -67.3966 q^{34} +(37.2514 + 12.1037i) q^{35} +(39.4991 + 28.6978i) q^{37} +(9.50997 + 29.2687i) q^{38} +(62.5784 - 86.1317i) q^{40} +(-18.5926 - 25.5905i) q^{41} +45.0047i q^{43} +(59.0312 - 83.9638i) q^{44} +(61.5015 + 19.9831i) q^{46} +(-0.589182 + 0.428066i) q^{47} +(-0.702488 - 2.16204i) q^{49} +(-17.0889 + 5.55254i) q^{50} +(-36.1922 - 49.8143i) q^{52} +(-21.6865 + 66.7442i) q^{53} +(-56.9295 + 19.4809i) q^{55} -139.367 q^{56} +(-59.3077 + 43.0896i) q^{58} +(19.5024 + 14.1693i) q^{59} +(-39.0806 + 12.6981i) q^{61} +(75.8481 - 104.396i) q^{62} +(-9.44556 + 29.0704i) q^{64} +36.0970i q^{65} +96.0426 q^{67} +(-163.807 - 53.2242i) q^{68} +(115.697 + 84.0586i) q^{70} +(-12.2355 - 37.6569i) q^{71} +(41.2974 - 56.8410i) q^{73} +(104.779 + 144.216i) q^{74} +78.6477i q^{76} +(64.4349 + 45.3013i) q^{77} +(-84.9861 - 27.6137i) q^{79} +(149.311 - 108.481i) q^{80} +(-35.6888 - 109.839i) q^{82} +(-24.9375 + 8.10269i) q^{83} +(59.3499 + 81.6881i) q^{85} +(-50.7771 + 156.276i) q^{86} +(171.230 - 128.519i) q^{88} +118.861 q^{89} +(38.2282 - 27.7744i) q^{91} +(133.698 + 97.1376i) q^{92} +(-2.52886 + 0.821677i) q^{94} +(27.1006 - 37.3008i) q^{95} +(-10.2296 + 31.4835i) q^{97} -8.30011i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8	\( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) 16 * q + 20 * q^4 + 4 * q^5 - 30 * q^7 + 40 * q^8 + 10 * q^11 + 30 * q^13 + 2 * q^14 + 16 * q^16 + 10 * q^17 - 42 * q^20 + 42 * q^22 - 132 * q^23 - 2 * q^25 - 46 * q^26 - 50 * q^28 - 160 * q^29 + 10 * q^31 - 368 * q^34 + 320 * q^35 - 126 * q^37 + 130 * q^38 + 30 * q^40 + 120 * q^41 + 206 * q^44 + 50 * q^46 + 150 * q^47 + 210 * q^49 - 330 * q^50 + 110 * q^52 - 342 * q^53 + 244 * q^55 - 524 * q^56 + 150 * q^58 - 110 * q^59 - 90 * q^61 - 40 * q^62 - 168 * q^64 + 36 * q^67 - 80 * q^68 + 340 * q^70 + 236 * q^71 - 350 * q^73 + 730 * q^74 + 390 * q^77 + 210 * q^79 + 806 * q^80 + 114 * q^82 + 190 * q^83 + 110 * q^85 - 736 * q^86 + 144 * q^88 - 76 * q^89 + 306 * q^91 + 150 * q^92 - 350 * q^94 - 430 * q^95 - 354 * q^97

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