LMFDB - Embedded newform 198.4.f.g.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,4,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, 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:	$11.6823781811$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 651x^{10} + 154866x^{8} + 16636791x^{6} + 828488506x^{4} + 17109953235x^{2} + 84670385805 $ x^12 + 651x^10 + 154866x^8 + 16636791x^6 + 828488506x^4 + 17109953235*x^2 + 84670385805
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-2.64944i$ of defining polynomial
Character	$\chi$	$=$	198.91
Dual form			198.4.f.g.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(-3.70247 - 2.69000i) q^{5} +(-2.17534 + 6.69500i) q^{7} +(2.47214 + 7.60845i) q^{8} +O(q^{10})$	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(-3.70247 - 2.69000i) q^{5} +(-2.17534 + 6.69500i) q^{7} +(2.47214 + 7.60845i) q^{8} +9.15301 q^{10} +(-19.7086 + 30.7013i) q^{11} +(72.3928 - 52.5964i) q^{13} +(-4.35067 - 13.3900i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(-83.4632 - 60.6396i) q^{17} +(-6.51500 - 20.0511i) q^{19} +(-14.8099 + 10.7600i) q^{20} +(-4.20231 - 72.8446i) q^{22} +89.9033 q^{23} +(-32.1549 - 98.9628i) q^{25} +(-55.3031 + 170.206i) q^{26} +(22.7804 + 16.5509i) q^{28} +(48.5558 - 149.439i) q^{29} +(182.900 - 132.885i) q^{31} +32.0000 q^{32} +206.332 q^{34} +(26.0637 - 18.9364i) q^{35} +(54.0050 - 166.210i) q^{37} +(34.1130 + 24.7845i) q^{38} +(11.3137 - 34.8201i) q^{40} +(28.3857 + 87.3621i) q^{41} -11.8603 q^{43} +(92.4335 + 112.925i) q^{44} +(-145.467 + 105.688i) q^{46} +(-90.9895 - 280.037i) q^{47} +(237.402 + 172.483i) q^{49} +(168.365 + 122.325i) q^{50} +(-110.606 - 340.411i) q^{52} +(406.416 - 295.278i) q^{53} +(155.557 - 60.6544i) q^{55} -56.3163 q^{56} +(97.1116 + 298.879i) q^{58} +(144.288 - 444.073i) q^{59} +(-99.4965 - 72.2884i) q^{61} +(-139.723 + 430.023i) q^{62} +(-51.7771 + 37.6183i) q^{64} -409.517 q^{65} -874.971 q^{67} +(-333.853 + 242.558i) q^{68} +(-19.9109 + 61.2794i) q^{70} +(-90.0102 - 65.3962i) q^{71} +(-251.479 + 773.974i) q^{73} +(108.010 + 332.420i) q^{74} -84.3320 q^{76} +(-162.672 - 198.735i) q^{77} +(-352.670 + 256.230i) q^{79} +(22.6275 + 69.6403i) q^{80} +(-148.629 - 107.985i) q^{82} +(536.956 + 390.121i) q^{83} +(145.900 + 449.033i) q^{85} +(19.1903 - 13.9426i) q^{86} +(-282.312 - 74.0544i) q^{88} -1288.31 q^{89} +(194.654 + 599.084i) q^{91} +(111.127 - 342.013i) q^{92} +(476.427 + 346.145i) q^{94} +(-29.8159 + 91.7640i) q^{95} +(165.625 - 120.334i) q^{97} -586.890 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 12 q^{4} + 16 q^{5} + 6 q^{7} - 24 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 12 * q^4 + 16 * q^5 + 6 * q^7 - 24 * q^8	$ 12 q - 6 q^{2} - 12 q^{4} + 16 q^{5} + 6 q^{7} - 24 q^{8} - 68 q^{10} - 116 q^{11} - 46 q^{13} + 12 q^{14} - 48 q^{16} + 24 q^{17} - 6 q^{19} + 64 q^{20} - 22 q^{22} - 420 q^{23} - 431 q^{25} + 228 q^{26} + 4 q^{28} - 89 q^{29} - 345 q^{31} + 384 q^{32} + 168 q^{34} - 87 q^{35} + 474 q^{37} + 208 q^{38} + 8 q^{40} + 580 q^{41} - 1736 q^{43} - 44 q^{44} - 100 q^{46} - 1074 q^{47} - 553 q^{49} + 768 q^{50} + 456 q^{52} + 585 q^{53} + 1520 q^{55} - 112 q^{56} - 178 q^{58} + 1326 q^{59} + 1816 q^{61} + 940 q^{62} - 192 q^{64} - 3712 q^{65} + 1372 q^{67} + 96 q^{68} - 894 q^{70} - 484 q^{71} - 695 q^{73} + 948 q^{74} - 784 q^{76} - 158 q^{77} - 1844 q^{79} + 16 q^{80} - 820 q^{82} + 232 q^{83} + 2210 q^{85} + 1348 q^{86} + 472 q^{88} - 5052 q^{89} + 3522 q^{91} + 1040 q^{92} + 3712 q^{94} - 178 q^{95} + 1868 q^{97} - 1756 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 12 * q^4 + 16 * q^5 + 6 * q^7 - 24 * q^8 - 68 * q^10 - 116 * q^11 - 46 * q^13 + 12 * q^14 - 48 * q^16 + 24 * q^17 - 6 * q^19 + 64 * q^20 - 22 * q^22 - 420 * q^23 - 431 * q^25 + 228 * q^26 + 4 * q^28 - 89 * q^29 - 345 * q^31 + 384 * q^32 + 168 * q^34 - 87 * q^35 + 474 * q^37 + 208 * q^38 + 8 * q^40 + 580 * q^41 - 1736 * q^43 - 44 * q^44 - 100 * q^46 - 1074 * q^47 - 553 * q^49 + 768 * q^50 + 456 * q^52 + 585 * q^53 + 1520 * q^55 - 112 * q^56 - 178 * q^58 + 1326 * q^59 + 1816 * q^61 + 940 * q^62 - 192 * q^64 - 3712 * q^65 + 1372 * q^67 + 96 * q^68 - 894 * q^70 - 484 * q^71 - 695 * q^73 + 948 * q^74 - 784 * q^76 - 158 * q^77 - 1844 * q^79 + 16 * q^80 - 820 * q^82 + 232 * q^83 + 2210 * q^85 + 1348 * q^86 + 472 * q^88 - 5052 * q^89 + 3522 * q^91 + 1040 * q^92 + 3712 * q^94 - 178 * q^95 + 1868 * q^97 - 1756 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	−3.70247	−	2.69000i	−0.331159	−	0.240601i	0.409763	−	0.912192i	$-0.365611\pi$
$5$	−3.70247	−	2.69000i	−0.331159	−	0.240601i	−0.740922	+	0.671591i	$0.765611\pi$
$6$		0			0
$7$	−2.17534	+	6.69500i	−0.117457	+	0.361496i	−0.992452	−	0.122637i	$-0.960865\pi$
$7$	−2.17534	+	6.69500i	−0.117457	+	0.361496i	0.874994	+	0.484133i	$0.160865\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$		0			0
$10$	9.15301			0.289444
$11$	−19.7086	+	30.7013i	−0.540216	+	0.841526i
$11$	−19.7086	+	30.7013i	−0.540216	+	0.841526i
$12$		0			0
$13$	72.3928	−	52.5964i	1.54447	−	1.12212i	0.597020	−	0.802226i	$-0.296351\pi$
$13$	72.3928	−	52.5964i	1.54447	−	1.12212i	0.947452	−	0.319899i	$-0.103649\pi$
$14$	−4.35067	−	13.3900i	−0.0830547	−	0.255616i
$15$		0			0
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	−83.4632	−	60.6396i	−1.19075	−	0.865133i	−0.197410	−	0.980321i	$-0.563253\pi$
$17$	−83.4632	−	60.6396i	−1.19075	−	0.865133i	−0.993344	+	0.115188i	$0.963253\pi$
$18$		0			0
$19$	−6.51500	−	20.0511i	−0.0786655	−	0.242107i	0.903988	−	0.427557i	$-0.140626\pi$
$19$	−6.51500	−	20.0511i	−0.0786655	−	0.242107i	−0.982654	+	0.185450i	$0.940626\pi$
$20$	−14.8099	+	10.7600i	−0.165580	+	0.120301i
$21$		0			0
$22$	−4.20231	−	72.8446i	−0.0407244	−	0.705933i
$23$	89.9033			0.815050			0.407525	−	0.913194i	$-0.366392\pi$
$23$	89.9033			0.815050			0.407525	+	0.913194i	$0.366392\pi$
$24$		0			0
$25$	−32.1549	−	98.9628i	−0.257240	−	0.791702i
$26$	−55.3031	+	170.206i	−0.417148	+	1.28385i
$27$		0			0
$28$	22.7804	+	16.5509i	0.153753	+	0.111708i
$29$	48.5558	−	149.439i	0.310917	−	0.956903i	−0.666486	−	0.745518i	$-0.732202\pi$
$29$	48.5558	−	149.439i	0.310917	−	0.956903i	0.977403	−	0.211386i	$-0.0677976\pi$
$30$		0			0
$31$	182.900	−	132.885i	1.05967	−	0.769896i	0.0856433	−	0.996326i	$-0.472705\pi$
$31$	182.900	−	132.885i	1.05967	−	0.769896i	0.974027	+	0.226430i	$0.0727055\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	206.332			1.04076
$35$	26.0637	−	18.9364i	0.125873	−	0.0914523i
$36$		0			0
$37$	54.0050	−	166.210i	0.239956	−	0.738508i	−0.756470	−	0.654029i	$-0.773077\pi$
$37$	54.0050	−	166.210i	0.239956	−	0.738508i	0.996425	−	0.0844788i	$-0.0269225\pi$
$38$	34.1130	+	24.7845i	0.145628	+	0.105805i
$39$		0			0
$40$	11.3137	−	34.8201i	0.0447215	−	0.137639i
$41$	28.3857	+	87.3621i	0.108124	+	0.332772i	0.990451	−	0.137865i	$-0.0440240\pi$
$41$	28.3857	+	87.3621i	0.108124	+	0.332772i	−0.882327	+	0.470637i	$0.844024\pi$
$42$		0			0
$43$	−11.8603			−0.0420622			−0.0210311	−	0.999779i	$-0.506695\pi$
$43$	−11.8603			−0.0420622			−0.0210311	+	0.999779i	$0.506695\pi$
$44$	92.4335	+	112.925i	0.316702	+	0.386911i
$45$		0			0
$46$	−145.467	+	105.688i	−0.466258	+	0.338757i
$47$	−90.9895	−	280.037i	−0.282387	−	0.869097i	−0.987170	−	0.159674i	$-0.948956\pi$
$47$	−90.9895	−	280.037i	−0.282387	−	0.869097i	0.704783	−	0.709423i	$-0.251044\pi$
$48$		0			0
$49$	237.402	+	172.483i	0.692134	+	0.502865i
$50$	168.365	+	122.325i	0.476210	+	0.345986i
$51$		0			0
$52$	−110.606	−	340.411i	−0.294968	−	0.907818i
$53$	406.416	−	295.278i	1.05331	−	0.765276i	0.0804721	−	0.996757i	$-0.474357\pi$
$53$	406.416	−	295.278i	1.05331	−	0.765276i	0.972839	+	0.231481i	$0.0743572\pi$
$54$		0			0
$55$	155.557	−	60.6544i	0.381370	−	0.148703i
$56$	−56.3163			−0.134385
$57$		0			0
$58$	97.1116	+	298.879i	0.219851	+	0.676633i
$59$	144.288	−	444.073i	0.318385	−	0.979888i	−0.655954	−	0.754801i	$-0.727733\pi$
$59$	144.288	−	444.073i	0.318385	−	0.979888i	0.974339	−	0.225087i	$-0.0722666\pi$
$60$		0			0
$61$	−99.4965	−	72.2884i	−0.208840	−	0.151731i	0.478449	−	0.878115i	$-0.341199\pi$
$61$	−99.4965	−	72.2884i	−0.208840	−	0.151731i	−0.687289	+	0.726385i	$0.741199\pi$
$62$	−139.723	+	430.023i	−0.286207	+	0.880855i
$63$		0			0
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	−409.517			−0.781450
$66$		0			0
$67$	−874.971			−1.59544			−0.797722	−	0.603026i	$-0.793962\pi$
$67$	−874.971			−1.59544			−0.797722	+	0.603026i	$0.793962\pi$
$68$	−333.853	+	242.558i	−0.595377	+	0.432566i
$69$		0			0
$70$	−19.9109	+	61.2794i	−0.0339972	+	0.104633i
$71$	−90.0102	−	65.3962i	−0.150454	−	0.109311i	0.510012	−	0.860168i	$-0.329641\pi$
$71$	−90.0102	−	65.3962i	−0.150454	−	0.109311i	−0.660466	+	0.750856i	$0.729641\pi$
$72$		0			0
$73$	−251.479	+	773.974i	−0.403198	+	1.24092i	0.519193	+	0.854657i	$0.326233\pi$
$73$	−251.479	+	773.974i	−0.403198	+	1.24092i	−0.922391	+	0.386258i	$0.873767\pi$
$74$	108.010	+	332.420i	0.169674	+	0.522204i
$75$		0			0
$76$	−84.3320			−0.127283
$77$	−162.672	−	198.735i	−0.240756	−	0.294129i
$78$		0			0
$79$	−352.670	+	256.230i	−0.502259	+	0.364912i	−0.809879	−	0.586597i	$-0.800467\pi$
$79$	−352.670	+	256.230i	−0.502259	+	0.364912i	0.307620	+	0.951509i	$0.400467\pi$
$80$	22.6275	+	69.6403i	0.0316229	+	0.0973252i
$81$		0			0
$82$	−148.629	−	107.985i	−0.200163	−	0.145427i
$83$	536.956	+	390.121i	0.710103	+	0.515920i	0.883207	−	0.468984i	$-0.155380\pi$
$83$	536.956	+	390.121i	0.710103	+	0.515920i	−0.173104	+	0.984904i	$0.555380\pi$
$84$		0			0
$85$	145.900	+	449.033i	0.186177	+	0.572993i
$86$	19.1903	−	13.9426i	0.0240622	−	0.0174822i
$87$		0			0
$88$	−282.312	−	74.0544i	−0.341983	−	0.0897071i
$89$	−1288.31			−1.53439			−0.767195	−	0.641414i	$-0.778348\pi$
$89$	−1288.31			−1.53439			−0.767195	+	0.641414i	$0.778348\pi$
$90$		0			0
$91$	194.654	+	599.084i	0.224234	+	0.690122i
$92$	111.127	−	342.013i	0.125932	−	0.387579i
$93$		0			0
$94$	476.427	+	346.145i	0.522763	+	0.379809i
$95$	−29.8159	+	91.7640i	−0.0322005	+	0.0991031i
$96$		0			0
$97$	165.625	−	120.334i	0.173368	−	0.125959i	−0.497718	−	0.867339i	$-0.665828\pi$
$97$	165.625	−	120.334i	0.173368	−	0.125959i	0.671085	+	0.741380i	$0.265828\pi$
$98$	−586.890			−0.604947
$99$		0			0
$100$	−416.222			−0.416222
$101$	85.6474	−	62.2265i	0.0843786	−	0.0613046i	−0.544796	−	0.838569i	$-0.683393\pi$
$101$	85.6474	−	62.2265i	0.0843786	−	0.0613046i	0.629175	+	0.777264i	$0.283393\pi$
$102$		0			0
$103$	−148.999	+	458.571i	−0.142537	+	0.438683i	−0.996686	−	0.0813452i	$-0.974078\pi$
$103$	−148.999	+	458.571i	−0.142537	+	0.438683i	0.854149	+	0.520028i	$0.174078\pi$
$104$	579.142	+	420.771i	0.546053	+	0.396731i
$105$		0			0
$106$	−310.474	+	955.541i	−0.284490	+	0.875569i
$107$	138.975	+	427.722i	0.125563	+	0.386443i	0.994003	−	0.109351i	$-0.0348772\pi$
$107$	138.975	+	427.722i	0.125563	+	0.386443i	−0.868440	+	0.495794i	$0.834877\pi$
$108$		0			0
$109$	−1214.86			−1.06754			−0.533772	−	0.845629i	$-0.679226\pi$
$109$	−1214.86			−1.06754			−0.533772	+	0.845629i	$0.679226\pi$
$110$	−180.393	+	281.009i	−0.156362	+	0.243574i
$111$		0			0
$112$	91.1217	−	66.2038i	0.0768767	−	0.0558542i
$113$	−483.559	−	1488.24i	−0.402561	−	1.23895i	−0.922915	−	0.385004i	$-0.874200\pi$
$113$	−483.559	−	1488.24i	−0.402561	−	1.23895i	0.520354	−	0.853951i	$-0.325800\pi$
$114$		0			0
$115$	−332.865	−	241.840i	−0.269911	−	0.196102i
$116$	−508.483	−	369.434i	−0.406995	−	0.295699i
$117$		0			0
$118$	288.576	+	888.146i	0.225132	+	0.692885i
$119$	587.542	−	426.875i	0.452604	−	0.328836i
$120$		0			0
$121$	−554.140	−	1210.16i	−0.416333	−	0.909212i
$122$	245.969			0.182533
$123$		0			0
$124$	−279.446	−	860.047i	−0.202379	−	0.622859i
$125$	−323.935	+	996.968i	−0.231789	+	0.713372i
$126$		0			0
$127$	1983.67	+	1441.22i	1.38600	+	1.00699i	0.996290	+	0.0860558i	$0.0274263\pi$
$127$	1983.67	+	1441.22i	1.38600	+	1.00699i	0.389715	+	0.920936i	$0.372574\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$		0			0
$130$	662.612	−	481.416i	0.447038	−	0.324792i
$131$	2460.67			1.64114			0.820572	−	0.571543i	$-0.193655\pi$
$131$	2460.67			1.64114			0.820572	+	0.571543i	$0.193655\pi$
$132$		0			0
$133$	148.414			0.0967606
$134$	1415.73	−	1028.59i	0.912692	−	0.663109i
$135$		0			0
$136$	255.041	−	784.935i	0.160806	−	0.494909i
$137$	505.998	+	367.629i	0.315550	+	0.229260i	0.734274	−	0.678853i	$-0.237523\pi$
$137$	505.998	+	367.629i	0.315550	+	0.229260i	−0.418724	+	0.908113i	$0.637523\pi$
$138$		0			0
$139$	361.676	−	1113.12i	0.220698	−	0.679238i	−0.778002	−	0.628262i	$-0.783767\pi$
$139$	361.676	−	1113.12i	0.220698	−	0.679238i	0.998700	−	0.0509760i	$-0.0162332\pi$
$140$	−39.8218	−	122.559i	−0.0240397	−	0.0739865i
$141$		0			0
$142$	222.517			0.131502
$143$	188.016	+	3259.16i	0.109949	+	1.90590i
$144$		0			0
$145$	−581.769	+	422.680i	−0.333195	+	0.242080i
$146$	−502.959	−	1547.95i	−0.285104	−	0.877460i
$147$		0			0
$148$	−565.547	−	410.894i	−0.314106	−	0.228211i
$149$	−1602.19	−	1164.06i	−0.880919	−	0.640025i	0.0525757	−	0.998617i	$-0.483257\pi$
$149$	−1602.19	−	1164.06i	−0.880919	−	0.640025i	−0.933494	+	0.358592i	$0.883257\pi$
$150$		0			0
$151$	−788.343	−	2426.27i	−0.424864	−	1.30760i	−0.903125	−	0.429378i	$-0.858733\pi$
$151$	−788.343	−	2426.27i	−0.424864	−	1.30760i	0.478261	−	0.878218i	$-0.341267\pi$
$152$	136.452	−	99.1382i	0.0728139	−	0.0529024i
$153$		0			0
$154$	496.836	+	130.327i	0.259975	+	0.0681952i
$155$	−1034.64			−0.536157
$156$		0			0
$157$	699.558	+	2153.02i	0.355610	+	1.09446i	0.955655	+	0.294489i	$0.0951495\pi$
$157$	699.558	+	2153.02i	0.355610	+	1.09446i	−0.600045	+	0.799967i	$0.704850\pi$
$158$	269.416	−	829.177i	0.135656	−	0.417505i
$159$		0			0
$160$	−118.479	−	86.0801i	−0.0585412	−	0.0425327i
$161$	−195.570	+	601.903i	−0.0957334	+	0.294637i
$162$		0			0
$163$	399.068	−	289.940i	0.191763	−	0.139324i	−0.487761	−	0.872977i	$-0.662186\pi$
$163$	399.068	−	289.940i	0.191763	−	0.139324i	0.679524	+	0.733653i	$0.262186\pi$
$164$	367.432			0.174949
$165$		0			0
$166$	−1327.43			−0.620653
$167$	1898.37	−	1379.25i	0.879644	−	0.639099i	−0.0535135	−	0.998567i	$-0.517042\pi$
$167$	1898.37	−	1379.25i	0.879644	−	0.639099i	0.933157	+	0.359469i	$0.117042\pi$
$168$		0			0
$169$	1795.42	−	5525.73i	0.817213	−	2.51512i
$170$	−763.940	−	555.035i	−0.344656	−	0.250407i
$171$		0			0
$172$	−14.6601	+	45.1192i	−0.00649897	+	0.0200018i
$173$	915.293	+	2816.98i	0.402245	+	1.23798i	0.923174	+	0.384383i	$0.125586\pi$
$173$	915.293	+	2816.98i	0.402245	+	1.23798i	−0.520928	+	0.853601i	$0.674414\pi$
$174$		0			0
$175$	732.503			0.316412
$176$	543.846	−	212.055i	0.232920	−	0.0908196i
$177$		0			0
$178$	2084.53	−	1514.50i	0.877765	−	0.637734i
$179$	461.215	+	1419.47i	0.192586	+	0.592718i	0.999996	+	0.00272778i	$0.000868279\pi$
$179$	461.215	+	1419.47i	0.192586	+	0.592718i	−0.807411	+	0.589990i	$0.799132\pi$
$180$		0			0
$181$	1250.62	+	908.630i	0.513580	+	0.373138i	0.814180	−	0.580613i	$-0.197187\pi$
$181$	1250.62	+	908.630i	0.513580	+	0.373138i	−0.300600	+	0.953750i	$0.597187\pi$
$182$	−1019.22	−	740.509i	−0.415109	−	0.301594i
$183$		0			0
$184$	222.253	+	684.025i	0.0890474	+	0.274060i
$185$	−647.058	+	470.115i	−0.257149	+	0.186830i
$186$		0			0
$187$	3506.66	−	1367.31i	1.37130	−	0.534692i
$188$	−1177.79			−0.456911
$189$		0			0
$190$	−59.6319	−	183.528i	−0.0227692	−	0.0700765i
$191$	358.846	−	1104.41i	0.135943	−	0.418391i	−0.859792	−	0.510644i	$-0.829407\pi$
$191$	358.846	−	1104.41i	0.135943	−	0.418391i	0.995736	+	0.0922534i	$0.0294070\pi$
$192$		0			0
$193$	580.247	+	421.574i	0.216410	+	0.157231i	0.690709	−	0.723133i	$-0.257298\pi$
$193$	580.247	+	421.574i	0.216410	+	0.157231i	−0.474299	+	0.880364i	$0.657298\pi$
$194$	−126.526	+	389.407i	−0.0468250	+	0.144113i
$195$		0			0
$196$	949.608	−	689.930i	0.346067	−	0.251432i
$197$	−3628.45			−1.31227			−0.656133	−	0.754645i	$-0.727809\pi$
$197$	−3628.45			−1.31227			−0.656133	+	0.754645i	$0.727809\pi$
$198$		0			0
$199$	−1276.68			−0.454782			−0.227391	−	0.973804i	$-0.573020\pi$
$199$	−1276.68			−0.454782			−0.227391	+	0.973804i	$0.573020\pi$
$200$	673.462	−	489.299i	0.238105	−	0.172993i
$201$		0			0
$202$	−65.4288	+	201.369i	−0.0227899	+	0.0701400i
$203$	894.871	+	650.162i	0.309397	+	0.224790i
$204$		0			0
$205$	129.907	−	399.813i	0.0442591	−	0.136215i
$206$	−297.997	−	917.141i	−0.100789	−	0.310195i
$207$		0			0
$208$	−1431.72			−0.477268
$209$	743.997	+	195.161i	0.246236	+	0.0645912i
$210$		0			0
$211$	−2612.70	+	1898.24i	−0.852443	+	0.619336i	−0.925819	−	0.377968i	$-0.876623\pi$
$211$	−2612.70	+	1898.24i	−0.852443	+	0.619336i	0.0733755	+	0.997304i	$0.476623\pi$
$212$	−620.948	−	1911.08i	−0.201165	−	0.619121i
$213$		0			0
$214$	−727.684	−	528.693i	−0.232446	−	0.168882i
$215$	43.9124	+	31.9042i	0.0139293	+	0.0101202i
$216$		0			0
$217$	491.793	+	1513.58i	0.153848	+	0.473496i
$218$	1965.68	−	1428.15i	0.610700	−	0.443700i
$219$		0			0
$220$	−38.4638	−	666.748i	−0.0117874	−	0.204328i
$221$	−9231.56			−2.80987
$222$		0			0
$223$	−1015.74	−	3126.13i	−0.305018	−	0.938750i	−0.979670	−	0.200614i	$-0.935706\pi$
$223$	−1015.74	−	3126.13i	−0.305018	−	0.938750i	0.674652	−	0.738136i	$-0.264294\pi$
$224$	−69.6108	+	214.240i	−0.0207637	+	0.0639040i
$225$		0			0
$226$	2531.95	+	1839.57i	0.745232	+	0.541443i
$227$	−1943.90	+	5982.70i	−0.568374	+	1.74928i	0.0893318	+	0.996002i	$0.471527\pi$
$227$	−1943.90	+	5982.70i	−0.568374	+	1.74928i	−0.657706	+	0.753275i	$0.728473\pi$
$228$		0			0
$229$	862.762	−	626.833i	0.248965	−	0.180883i	−0.456303	−	0.889824i	$-0.650827\pi$
$229$	862.762	−	626.833i	0.248965	−	0.180883i	0.705268	+	0.708941i	$0.250827\pi$
$230$	822.886			0.235911
$231$		0			0
$232$	1257.04			0.355727
$233$	2984.89	−	2168.65i	0.839257	−	0.609756i	−0.0829060	−	0.996557i	$-0.526420\pi$
$233$	2984.89	−	2168.65i	0.839257	−	0.609756i	0.922163	+	0.386801i	$0.126420\pi$
$234$		0			0
$235$	−416.414	+	1281.59i	−0.115591	+	0.355752i
$236$	−1511.00	−	1097.81i	−0.416771	−	0.302802i
$237$		0			0
$238$	−448.842	+	1381.40i	−0.122244	+	0.376229i
$239$	2203.64	+	6782.10i	0.596408	+	1.83556i	0.547588	+	0.836748i	$0.315546\pi$
$239$	2203.64	+	6782.10i	0.596408	+	1.83556i	0.0488199	+	0.998808i	$0.484454\pi$
$240$		0			0
$241$	−3210.60			−0.858146			−0.429073	−	0.903270i	$-0.641160\pi$
$241$	−3210.60			−0.858146			−0.429073	+	0.903270i	$0.641160\pi$
$242$	2319.25	+	1306.65i	0.616061	+	0.347086i
$243$		0			0
$244$	−397.986	+	289.154i	−0.104420	+	0.0758654i
$245$	−414.995	−	1277.22i	−0.108217	−	0.333056i
$246$		0			0
$247$	−1526.26	−	1108.89i	−0.393171	−	0.285656i
$248$	1463.20	+	1063.08i	0.374650	+	0.272199i
$249$		0			0
$250$	−647.869	−	1993.94i	−0.163899	−	0.504430i
$251$	5529.55	−	4017.45i	1.39053	−	1.01028i	0.394719	−	0.918802i	$-0.370842\pi$
$251$	5529.55	−	4017.45i	1.39053	−	1.01028i	0.995807	−	0.0914745i	$-0.0291580\pi$
$252$		0			0
$253$	−1771.87	+	2760.15i	−0.440303	+	0.685886i
$254$	−4903.91			−1.21141
$255$		0			0
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	1707.99	−	5256.64i	0.414558	−	1.27588i	−0.498088	−	0.867126i	$-0.665965\pi$
$257$	1707.99	−	5256.64i	0.414558	−	1.27588i	0.912646	−	0.408751i	$-0.134035\pi$
$258$		0			0
$259$	995.298	+	723.126i	0.238783	+	0.173486i
$260$	−506.190	+	1557.89i	−0.120741	+	0.371602i
$261$		0			0
$262$	−3981.45	+	2892.69i	−0.938836	+	0.682104i
$263$	3472.45			0.814147			0.407073	−	0.913395i	$-0.366549\pi$
$263$	3472.45			0.814147			0.407073	+	0.913395i	$0.366549\pi$
$264$		0			0
$265$	−2299.04			−0.532940
$266$	−240.140	+	174.472i	−0.0553530	+	0.0402163i
$267$		0			0
$268$	−1081.52	+	3328.59i	−0.246510	+	0.758679i
$269$	−3555.78	−	2583.42i	−0.805946	−	0.585554i	0.106706	−	0.994291i	$-0.465970\pi$
$269$	−3555.78	−	2583.42i	−0.805946	−	0.585554i	−0.912652	+	0.408736i	$0.865970\pi$
$270$		0			0
$271$	−1824.70	+	5615.85i	−0.409014	+	1.25882i	0.508483	+	0.861072i	$0.330206\pi$
$271$	−1824.70	+	5615.85i	−0.409014	+	1.25882i	−0.917497	+	0.397743i	$0.869794\pi$
$272$	510.082	+	1569.87i	0.113707	+	0.349954i
$273$		0			0
$274$	−1250.90			−0.275801
$275$	3672.02	+	963.222i	0.805203	+	0.211216i
$276$		0			0
$277$	185.944	−	135.097i	0.0403333	−	0.0293038i	−0.567436	−	0.823418i	$-0.692065\pi$
$277$	185.944	−	135.097i	0.0403333	−	0.0293038i	0.607769	+	0.794114i	$0.292065\pi$
$278$	723.352	+	2226.25i	0.156057	+	0.480293i
$279$		0			0
$280$	208.509	+	151.491i	0.0445029	+	0.0323333i
$281$	−3228.10	−	2345.35i	−0.685311	−	0.497907i	0.189805	−	0.981822i	$-0.439215\pi$
$281$	−3228.10	−	2345.35i	−0.685311	−	0.497907i	−0.875115	+	0.483915i	$0.839215\pi$
$282$		0			0
$283$	626.599	+	1928.47i	0.131616	+	0.405073i	0.995048	−	0.0993917i	$-0.0316897\pi$
$283$	626.599	+	1928.47i	0.131616	+	0.405073i	−0.863432	+	0.504465i	$0.831690\pi$
$284$	−360.041	+	261.585i	−0.0752271	+	0.0546557i
$285$		0			0
$286$	−4135.58	−	5052.40i	−0.855043	−	1.04460i
$287$	−646.637			−0.132996
$288$		0			0
$289$	1770.75	+	5449.81i	0.360422	+	1.10926i
$290$	444.432	−	1367.82i	0.0899929	−	0.276970i
$291$		0			0
$292$	2633.53	+	1913.37i	0.527793	+	0.383464i
$293$	−888.434	+	2734.32i	−0.177143	+	0.545190i	−0.999725	−	0.0234567i	$-0.992533\pi$
$293$	−888.434	+	2734.32i	−0.177143	+	0.545190i	0.822582	+	0.568647i	$0.192533\pi$
$294$		0			0
$295$	−1728.78	+	1256.03i	−0.341198	+	0.247895i
$296$	1398.11			0.274539
$297$		0			0
$298$	3960.84			0.769951
$299$	6508.35	−	4728.59i	1.25882	−	0.914587i
$300$		0			0
$301$	25.8001	−	79.4046i	0.00494051	−	0.0152053i
$302$	4127.82	+	2999.03i	0.786520	+	0.571440i
$303$		0			0
$304$	−104.240	+	320.818i	−0.0196664	+	0.0605269i
$305$	173.927	+	535.292i	0.0326525	+	0.100494i
$306$		0			0
$307$	841.144			0.156373			0.0781867	−	0.996939i	$-0.475087\pi$
$307$	841.144			0.156373			0.0781867	+	0.996939i	$0.475087\pi$
$308$	−957.106	+	373.192i	−0.177066	+	0.0690409i
$309$		0			0
$310$	1674.08	−	1216.29i	0.306715	−	0.222841i
$311$	−2835.09	−	8725.51i	−0.516924	−	1.59093i	−0.779755	−	0.626085i	$-0.784656\pi$
$311$	−2835.09	−	8725.51i	−0.516924	−	1.59093i	0.262831	−	0.964842i	$-0.415344\pi$
$312$		0			0
$313$	2356.13	+	1711.83i	0.425483	+	0.309132i	0.779840	−	0.625978i	$-0.215300\pi$
$313$	2356.13	+	1711.83i	0.425483	+	0.309132i	−0.354357	+	0.935110i	$0.615300\pi$
$314$	−3662.93	−	2661.28i	−0.658316	−	0.478295i
$315$		0			0
$316$	538.832	+	1658.35i	0.0959229	+	0.295220i
$317$	1479.67	−	1075.04i	0.262165	−	0.190474i	−0.448936	−	0.893564i	$-0.648197\pi$
$317$	1479.67	−	1075.04i	0.262165	−	0.190474i	0.711101	+	0.703090i	$0.248197\pi$
$318$		0			0
$319$	3631.01	+	4435.97i	0.637297	+	0.778579i
$320$	292.896			0.0511669
$321$		0			0
$322$	−391.140	−	1203.81i	−0.0676937	−	0.208340i
$323$	−672.128	+	2068.60i	−0.115784	+	0.356346i
$324$		0			0
$325$	−7532.87	−	5472.95i	−1.28569	−	0.934107i
$326$	−304.861	+	938.266i	−0.0517935	+	0.159404i
$327$		0			0
$328$	−594.517	+	431.942i	−0.100081	+	0.0727134i
$329$	2072.78			0.347343
$330$		0			0
$331$	−6235.51			−1.03545			−0.517726	−	0.855547i	$-0.673221\pi$
$331$	−6235.51			−1.03545			−0.517726	+	0.855547i	$0.673221\pi$
$332$	2147.82	−	1560.48i	0.355051	−	0.257960i
$333$		0			0
$334$	−1450.23	+	4463.34i	−0.237584	+	0.731207i
$335$	3239.55	+	2353.67i	0.528346	+	0.383866i
$336$		0			0
$337$	304.894	−	938.367i	0.0492838	−	0.151680i	−0.923386	−	0.383873i	$-0.874590\pi$
$337$	304.894	−	938.367i	0.0492838	−	0.151680i	0.972670	+	0.232193i	$0.0745901\pi$
$338$	3590.84	+	11051.5i	0.577857	+	1.77846i
$339$		0			0
$340$	1888.56			0.301240
$341$	475.022	+	8234.24i	0.0754367	+	1.30765i
$342$		0			0
$343$	−3624.62	+	2633.44i	−0.570586	+	0.414555i
$344$	−29.3202	−	90.2384i	−0.00459547	−	0.0141434i
$345$		0			0
$346$	−4792.54	−	3481.98i	−0.744649	−	0.541019i
$347$	−9289.28	−	6749.06i	−1.43710	−	1.04412i	−0.988638	−	0.150316i	$-0.951971\pi$
$347$	−9289.28	−	6749.06i	−1.43710	−	1.04412i	−0.448465	−	0.893801i	$-0.648029\pi$
$348$		0			0
$349$	−989.860	−	3046.48i	−0.151822	−	0.467261i	0.846003	−	0.533179i	$-0.179003\pi$
$349$	−989.860	−	3046.48i	−0.151822	−	0.467261i	−0.997825	+	0.0659175i	$0.979003\pi$
$350$	−1185.21	+	861.109i	−0.181007	+	0.131509i
$351$		0			0
$352$	−630.676	+	982.442i	−0.0954976	+	0.148762i
$353$	−8669.58			−1.30718			−0.653591	−	0.756848i	$-0.726738\pi$
$353$	−8669.58			−1.30718			−0.653591	+	0.756848i	$0.726738\pi$
$354$		0			0
$355$	157.344	+	484.255i	0.0235238	+	0.0723989i
$356$	−1592.44	+	4901.03i	−0.237076	+	0.729646i
$357$		0			0
$358$	−2414.95	−	1754.57i	−0.356520	−	0.259027i
$359$	1327.01	−	4084.11i	0.195089	−	0.600421i	−0.804887	−	0.593428i	$-0.797774\pi$
$359$	1327.01	−	4084.11i	0.195089	−	0.600421i	0.999976	−	0.00699304i	$-0.00222597\pi$
$360$		0			0
$361$	5189.45	−	3770.35i	0.756589	−	0.549694i
$362$	−3091.71			−0.448885
$363$		0			0
$364$	2519.66			0.362818
$365$	3013.09	−	2189.14i	0.432088	−	0.313930i
$366$		0			0
$367$	2814.23	−	8661.31i	0.400277	−	1.23193i	−0.524498	−	0.851412i	$-0.675747\pi$
$367$	2814.23	−	8661.31i	0.400277	−	1.23193i	0.924775	−	0.380514i	$-0.124253\pi$
$368$	−1163.73	−	845.502i	−0.164847	−	0.119769i
$369$		0			0
$370$	494.308	−	1521.32i	0.0694536	−	0.213756i
$371$	1092.80	+	3363.28i	0.152925	+	0.470655i
$372$		0			0
$373$	7648.04			1.06166			0.530831	−	0.847477i	$-0.321880\pi$
$373$	7648.04			1.06166			0.530831	+	0.847477i	$0.321880\pi$
$374$	−4066.53	+	6334.67i	−0.562233	+	0.875824i
$375$		0			0
$376$	1905.71	−	1384.58i	0.261381	−	0.189905i
$377$	−4344.89	−	13372.2i	−0.593563	−	1.82680i
$378$		0			0
$379$	7525.63	+	5467.69i	1.01996	+	0.741046i	0.966275	−	0.257512i	$-0.0829027\pi$
$379$	7525.63	+	5467.69i	1.01996	+	0.741046i	0.0536869	+	0.998558i	$0.482903\pi$
$380$	312.237	+	226.853i	0.0421511	+	0.0306245i
$381$		0			0
$382$	717.692	+	2208.83i	0.0961265	+	0.295847i
$383$	−319.946	+	232.454i	−0.0426853	+	0.0310127i	−0.608923	−	0.793229i	$-0.708398\pi$
$383$	−319.946	+	232.454i	−0.0426853	+	0.0310127i	0.566238	+	0.824242i	$0.308398\pi$
$384$		0			0
$385$	67.6918	+	1173.40i	0.00896077	+	0.155330i
$386$	−1434.45			−0.189149
$387$		0			0
$388$	−253.052	−	778.815i	−0.0331103	−	0.101903i
$389$	745.903	−	2295.65i	0.0972206	−	0.299214i	−0.890605	−	0.454777i	$-0.849719\pi$
$389$	745.903	−	2295.65i	0.0972206	−	0.299214i	0.987826	+	0.155563i	$0.0497191\pi$
$390$		0			0
$391$	−7503.62	−	5451.70i	−0.970523	−	0.705126i
$392$	−725.436	+	2232.66i	−0.0934695	+	0.287670i
$393$		0			0
$394$	5870.96	−	4265.50i	0.750697	−	0.545413i
$395$	1995.01			0.254126
$396$		0			0
$397$	4882.03			0.617185			0.308592	−	0.951194i	$-0.400142\pi$
$397$	4882.03			0.617185			0.308592	+	0.951194i	$0.400142\pi$
$398$	2065.72	−	1500.83i	0.260163	−	0.189020i
$399$		0			0
$400$	−514.479	+	1583.40i	−0.0643099	+	0.197926i
$401$	−1414.86	−	1027.95i	−0.176196	−	0.128014i	0.496192	−	0.868213i	$-0.334731\pi$
$401$	−1414.86	−	1027.95i	−0.176196	−	0.128014i	−0.672388	+	0.740199i	$0.734731\pi$
$402$		0			0
$403$	6251.38	−	19239.8i	0.772713	−	2.37817i
$404$	−130.858	−	402.738i	−0.0161149	−	0.0495965i
$405$		0			0
$406$	−2212.24			−0.270423
$407$	4038.50	+	4933.80i	0.491846	+	0.600883i
$408$		0			0
$409$	−4019.59	+	2920.40i	−0.485956	+	0.353068i	−0.803627	−	0.595133i	$-0.797099\pi$
$409$	−4019.59	+	2920.40i	−0.485956	+	0.353068i	0.317671	+	0.948201i	$0.397099\pi$
$410$	259.814	+	799.626i	0.0312959	+	0.0963188i
$411$		0			0
$412$	1560.33	+	1133.65i	0.186583	+	0.135560i
$413$	2659.19	+	1932.02i	0.316829	+	0.230190i
$414$		0			0
$415$	−938.636	−	2888.82i	−0.111026	−	0.341703i
$416$	2316.57	−	1683.09i	0.273027	−	0.198365i
$417$		0			0
$418$	−1433.24	+	558.844i	−0.167708	+	0.0653922i
$419$	−11763.3			−1.37154			−0.685770	−	0.727819i	$-0.740534\pi$
$419$	−11763.3			−1.37154			−0.685770	+	0.727819i	$0.740534\pi$
$420$		0			0
$421$	−1350.16	−	4155.37i	−0.156301	−	0.481046i	0.841989	−	0.539495i	$-0.181385\pi$
$421$	−1350.16	−	4155.37i	−0.156301	−	0.481046i	−0.998290	+	0.0584485i	$0.981385\pi$
$422$	1995.92	−	6142.82i	0.230237	−	0.708597i
$423$		0			0
$424$	3251.33	+	2362.23i	0.372402	+	0.270566i
$425$	−3317.30	+	10209.6i	−0.378619	+	1.16527i
$426$		0			0
$427$	700.409	−	508.877i	0.0793798	−	0.0576728i
$428$	1798.93			0.203165
$429$		0			0
$430$	−108.557			−0.0121746
$431$	2576.48	−	1871.92i	0.287946	−	0.209205i	−0.434430	−	0.900706i	$-0.643050\pi$
$431$	2576.48	−	1871.92i	0.287946	−	0.209205i	0.722376	+	0.691501i	$0.243050\pi$
$432$		0			0
$433$	−1711.52	+	5267.53i	−0.189955	+	0.584622i	−0.999998	−	0.00174800i	$-0.999444\pi$
$433$	−1711.52	+	5267.53i	−0.189955	+	0.584622i	0.810043	+	0.586370i	$0.199444\pi$
$434$	−2575.06	−	1870.89i	−0.284808	−	0.206925i
$435$		0			0
$436$	−1501.65	+	4621.59i	−0.164944	+	0.507647i
$437$	−585.720	−	1802.66i	−0.0641163	−	0.197330i
$438$		0			0
$439$	8450.31			0.918704			0.459352	−	0.888254i	$-0.348082\pi$
$439$	8450.31			0.918704			0.459352	+	0.888254i	$0.348082\pi$
$440$	846.045	+	1033.60i	0.0916673	+	0.111989i
$441$		0			0
$442$	14937.0	−	10852.3i	1.60742	−	1.16786i
$443$	−490.145	−	1508.51i	−0.0525677	−	0.161787i	0.921326	−	0.388791i	$-0.127107\pi$
$443$	−490.145	−	1508.51i	−0.0525677	−	0.161787i	−0.973894	+	0.227004i	$0.927107\pi$
$444$		0			0
$445$	4769.94	+	3465.56i	0.508127	+	0.369176i
$446$	5318.49	+	3864.11i	0.564659	+	0.410249i
$447$		0			0
$448$	−139.222	−	428.480i	−0.0146821	−	0.0451870i
$449$	11534.2	−	8380.07i	1.21232	−	0.880802i	0.216880	−	0.976198i	$-0.430412\pi$
$449$	11534.2	−	8380.07i	1.21232	−	0.880802i	0.995439	+	0.0953968i	$0.0304120\pi$
$450$		0			0
$451$	−3241.57	−	850.310i	−0.338447	−	0.0887795i
$452$	−6259.31			−0.651357
$453$		0			0
$454$	−3887.79	−	11965.4i	−0.401901	−	1.23693i
$455$	890.836	−	2741.71i	0.0917869	−	0.282491i
$456$		0			0
$457$	−710.920	−	516.514i	−0.0727690	−	0.0528698i	0.550806	−	0.834633i	$-0.314320\pi$
$457$	−710.920	−	516.514i	−0.0727690	−	0.0528698i	−0.623575	+	0.781764i	$0.714320\pi$
$458$	−659.091	+	2028.47i	−0.0672430	+	0.206953i
$459$		0			0
$460$	−1331.46	+	967.361i	−0.134956	+	0.0980509i
$461$	−4936.37			−0.498719			−0.249360	−	0.968411i	$-0.580220\pi$
$461$	−4936.37			−0.498719			−0.249360	+	0.968411i	$0.580220\pi$
$462$		0			0
$463$	16955.6			1.70193			0.850964	−	0.525224i	$-0.176019\pi$
$463$	16955.6			1.70193			0.850964	+	0.525224i	$0.176019\pi$
$464$	−2033.93	+	1477.74i	−0.203498	+	0.147850i
$465$		0			0
$466$	−2280.26	+	7017.91i	−0.226676	+	0.697636i
$467$	7796.52	+	5664.50i	0.772548	+	0.561289i	0.902733	−	0.430201i	$-0.141557\pi$
$467$	7796.52	+	5664.50i	0.772548	+	0.561289i	−0.130185	+	0.991490i	$0.541557\pi$
$468$		0			0
$469$	1903.36	−	5857.93i	0.187396	−	0.576746i
$470$	−832.828	−	2563.18i	−0.0817351	−	0.251555i
$471$		0			0
$472$	3735.41			0.364271
$473$	233.750	−	364.126i	0.0227227	−	0.0353965i
$474$		0			0
$475$	−1774.82	+	1289.49i	−0.171441	+	0.124559i
$476$	−897.685	−	2762.79i	−0.0864397	−	0.266034i
$477$		0			0
$478$	−11538.4	−	8383.14i	−1.10409	−	0.802167i
$479$	10129.9	+	7359.82i	0.966279	+	0.702043i	0.954601	−	0.297889i	$-0.0962825\pi$
$479$	10129.9	+	7359.82i	0.966279	+	0.702043i	0.0116787	+	0.999932i	$0.496282\pi$
$480$		0			0
$481$	−4832.49	−	14872.9i	−0.458093	−	1.40986i
$482$	5194.87	−	3774.29i	0.490912	−	0.356669i
$483$		0			0
$484$	−5288.68	+	612.232i	−0.496683	+	0.0574973i
$485$	−936.919			−0.0877181
$486$		0			0
$487$	3886.11	+	11960.2i	0.361594	+	1.11287i	0.952086	+	0.305829i	$0.0989337\pi$
$487$	3886.11	+	11960.2i	0.361594	+	1.11287i	−0.590492	+	0.807043i	$0.701066\pi$
$488$	304.034	−	935.721i	0.0282028	−	0.0867994i
$489$		0			0
$490$	2172.94	+	1578.74i	0.200334	+	0.145551i
$491$	609.139	−	1874.74i	0.0559879	−	0.172313i	−0.919152	−	0.393903i	$-0.871125\pi$
$491$	609.139	−	1874.74i	0.0559879	−	0.172313i	0.975140	+	0.221590i	$0.0711246\pi$
$492$		0			0
$493$	−13114.6	+	9528.29i	−1.19807	+	0.870451i
$494$	3773.11			0.343644
$495$		0			0
$496$	−3617.23			−0.327456
$497$	633.630	−	460.359i	0.0571875	−	0.0415491i
$498$		0			0
$499$	−2278.94	+	7013.86i	−0.204448	+	0.629225i	0.795288	+	0.606232i	$0.207320\pi$
$499$	−2278.94	+	7013.86i	−0.204448	+	0.629225i	−0.999736	+	0.0229933i	$0.992680\pi$
$500$	3392.29	+	2464.64i	0.303415	+	0.220444i
$501$		0			0
$502$	−4224.20	+	13000.8i	−0.375568	+	1.15588i
$503$	3766.54	+	11592.2i	0.333880	+	1.02758i	0.967271	+	0.253745i	$0.0816624\pi$
$503$	3766.54	+	11592.2i	0.333880	+	1.02758i	−0.633391	+	0.773832i	$0.718338\pi$
$504$		0			0
$505$	−484.497			−0.0426927
$506$	−377.802	−	6548.98i	−0.0331924	−	0.575371i
$507$		0			0
$508$	7934.70	−	5764.89i	0.693002	−	0.503496i
$509$	2283.20	+	7026.95i	0.198823	+	0.611914i	0.999911	+	0.0133671i	$0.00425501\pi$
$509$	2283.20	+	7026.95i	0.198823	+	0.611914i	−0.801088	+	0.598547i	$0.795745\pi$
$510$		0			0
$511$	−4634.70	−	3367.31i	−0.401227	−	0.291509i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	3415.97	+	10513.3i	0.293136	+	0.902181i
$515$	1785.22	−	1297.04i	0.152750	−	0.110979i
$516$		0			0
$517$	10390.8	+	2725.65i	0.883918	+	0.231864i
$518$	−2460.51			−0.208704
$519$		0			0
$520$	−1012.38	−	3115.79i	−0.0853766	−	0.262762i
$521$	4180.77	−	12867.1i	0.351560	−	1.08199i	−0.606417	−	0.795147i	$-0.707394\pi$
$521$	4180.77	−	12867.1i	0.351560	−	1.08199i	0.957977	−	0.286844i	$-0.0926061\pi$
$522$		0			0
$523$	−15309.4	−	11123.0i	−1.27999	−	0.929967i	−0.280437	−	0.959872i	$-0.590479\pi$
$523$	−15309.4	−	11123.0i	−1.27999	−	0.929967i	−0.999553	+	0.0299056i	$0.990479\pi$
$524$	3041.56	−	9360.96i	0.253571	−	0.780411i
$525$		0			0
$526$	−5618.55	+	4082.11i	−0.465742	+	0.338381i
$527$	−23323.5			−1.92787
$528$		0			0
$529$	−4084.39			−0.335694
$530$	3719.93	−	2702.69i	0.304874	−	0.221504i
$531$		0			0
$532$	183.450	−	564.602i	0.0149503	−	0.0460124i
$533$	6649.85	+	4831.40i	0.540407	+	0.392629i
$534$		0			0
$535$	636.021	−	1957.47i	0.0513973	−	0.158185i
$536$	−2163.05	−	6657.18i	−0.174309	−	0.536467i
$537$		0			0
$538$	8790.36			0.704423
$539$	−9974.31	+	3889.15i	−0.797076	+	0.310793i
$540$		0			0
$541$	−10238.2	+	7438.52i	−0.813635	+	0.591140i	−0.914882	−	0.403721i	$-0.867717\pi$
$541$	−10238.2	+	7438.52i	−0.813635	+	0.591140i	0.101247	+	0.994861i	$0.467717\pi$
$542$	−3649.40	−	11231.7i	−0.289216	−	0.890117i
$543$		0			0
$544$	−2670.82	−	1940.47i	−0.210497	−	0.152935i
$545$	4497.97	+	3267.97i	0.353527	+	0.256852i
$546$		0			0
$547$	7240.20	+	22283.0i	0.565939	+	1.74178i	0.665146	+	0.746714i	$0.268369\pi$
$547$	7240.20	+	22283.0i	0.565939	+	1.74178i	−0.0992069	+	0.995067i	$0.531631\pi$
$548$	2023.99	−	1470.52i	0.157775	−	0.114630i
$549$		0			0
$550$	−7073.78	+	2758.19i	−0.548413	+	0.213835i
$551$	−3312.77			−0.256132
$552$		0			0
$553$	−948.281	−	2918.51i	−0.0729205	−	0.224426i
$554$	−142.049	+	437.182i	−0.0108936	+	0.0335272i
$555$		0			0
$556$	−3787.52	−	2751.80i	−0.288897	−	0.209896i
$557$	−7027.95	+	21629.8i	−0.534621	+	1.64539i	0.209846	+	0.977734i	$0.432704\pi$
$557$	−7027.95	+	21629.8i	−0.534621	+	1.64539i	−0.744467	+	0.667659i	$0.767296\pi$
$558$		0			0
$559$	−858.599	+	623.808i	−0.0649640	+	0.0471991i
$560$	−515.464			−0.0388970
$561$		0			0
$562$	7980.30			0.598983
$563$	1939.45	−	1409.09i	0.145183	−	0.105482i	−0.512823	−	0.858494i	$-0.671400\pi$
$563$	1939.45	−	1409.09i	0.145183	−	0.105482i	0.658006	+	0.753013i	$0.271400\pi$
$564$		0			0
$565$	−2213.01	+	6810.94i	−0.164782	+	0.507148i
$566$	−3280.91	−	2383.72i	−0.243652	−	0.177024i
$567$		0			0
$568$	275.047	−	846.506i	0.0203181	−	0.0625328i
$569$	3845.29	+	11834.6i	0.283309	+	0.871936i	0.986900	+	0.161331i	$0.0515787\pi$
$569$	3845.29	+	11834.6i	0.283309	+	0.871936i	−0.703591	+	0.710605i	$0.748421\pi$
$570$		0			0
$571$	−25337.2			−1.85697			−0.928485	−	0.371370i	$-0.878888\pi$
$571$	−25337.2			−1.85697			−0.928485	+	0.371370i	$0.878888\pi$
$572$	12631.0	+	3313.28i	0.923299	+	0.242194i
$573$		0			0
$574$	1046.28	−	760.168i	0.0760817	−	0.0552766i
$575$	−2890.84	−	8897.08i	−0.209663	−	0.645277i
$576$		0			0
$577$	13308.7	+	9669.33i	0.960222	+	0.697642i	0.953202	−	0.302333i	$-0.0977654\pi$
$577$	13308.7	+	9669.33i	0.960222	+	0.697642i	0.00702003	+	0.999975i	$0.497765\pi$
$578$	−9271.77	−	6736.34i	−0.667223	−	0.484766i
$579$		0			0
$580$	888.863	+	2735.64i	0.0636346	+	0.195847i
$581$	−3779.92	+	2746.27i	−0.269910	+	0.196101i
$582$		0			0
$583$	1055.53	+	18297.0i	0.0749840	+	1.29980i
$584$	−6510.44			−0.461308
$585$		0			0
$586$	−1776.87	−	5468.64i	−0.125259	−	0.385508i
$587$	−4916.48	+	15131.4i	−0.345698	+	1.06395i	0.615511	+	0.788129i	$0.288950\pi$
$587$	−4916.48	+	15131.4i	−0.345698	+	1.06395i	−0.961209	+	0.275821i	$0.911050\pi$
$588$		0			0
$589$	−3856.08	−	2801.60i	−0.269757	−	0.195990i
$590$	1320.67	−	4064.61i	0.0921545	−	0.283622i
$591$		0			0
$592$	−2262.19	+	1643.58i	−0.157053	+	0.114106i
$593$	26361.5			1.82552			0.912762	−	0.408492i	$-0.133945\pi$
$593$	26361.5			1.82552			0.912762	+	0.408492i	$0.133945\pi$
$594$		0			0
$595$	−3323.65			−0.229002
$596$	−6408.78	+	4656.25i	−0.440459	+	0.320012i
$597$		0			0
$598$	−4971.94	+	15302.1i	−0.339996	+	1.04640i
$599$	−12603.2	−	9156.74i	−0.859685	−	0.624598i	0.0681140	−	0.997678i	$-0.478302\pi$
$599$	−12603.2	−	9156.74i	−0.859685	−	0.624598i	−0.927799	+	0.373080i	$0.878302\pi$
$600$		0			0
$601$	818.084	−	2517.80i	0.0555247	−	0.170887i	−0.919448	−	0.393211i	$-0.871364\pi$
$601$	818.084	−	2517.80i	0.0555247	−	0.170887i	0.974973	+	0.222324i	$0.0713642\pi$
$602$	51.6002	+	158.809i	0.00349347	+	0.0107518i
$603$		0			0
$604$	−10204.5			−0.687444
$605$	−1203.65	+	5971.22i	−0.0808849	+	0.401264i
$606$		0			0
$607$	−14232.0	+	10340.2i	−0.951663	+	0.691424i	−0.951200	−	0.308576i	$-0.900148\pi$
$607$	−14232.0	+	10340.2i	−0.951663	+	0.691424i	−0.000463413		1.00000i	$0.500148\pi$
$608$	−208.480	−	641.636i	−0.0139062	−	0.0427990i
$609$		0			0
$610$	−910.692	−	661.657i	−0.0604473	−	0.0439175i
$611$	−21315.9	−	15486.9i	−1.41137	−	1.02542i
$612$		0			0
$613$	−4092.77	−	12596.3i	−0.269666	−	0.829948i	−0.990582	−	0.136924i	$-0.956278\pi$
$613$	−4092.77	−	12596.3i	−0.269666	−	0.829948i	0.720915	−	0.693023i	$-0.243722\pi$
$614$	−1361.00	+	988.825i	−0.0894552	+	0.0649930i
$615$		0			0
$616$	1109.92	−	1728.98i	0.0725971	−	0.113089i
$617$	20902.5			1.36386			0.681930	−	0.731417i	$-0.261141\pi$
$617$	20902.5			1.36386			0.681930	+	0.731417i	$0.261141\pi$
$618$		0			0
$619$	2153.70	+	6628.40i	0.139846	+	0.430401i	0.996312	−	0.0858018i	$-0.0273452\pi$
$619$	2153.70	+	6628.40i	0.139846	+	0.430401i	−0.856467	+	0.516202i	$0.827345\pi$
$620$	−1278.89	+	3936.01i	−0.0828409	+	0.254958i
$621$		0			0
$622$	14844.7	+	10785.3i	0.956944	+	0.695261i
$623$	2802.51	−	8625.24i	0.180225	−	0.554676i
$624$		0			0
$625$	−6641.64	+	4825.43i	−0.425065	+	0.308828i
$626$	−5824.67			−0.371886
$627$		0			0
$628$	9055.27			0.575390
$629$	−14586.3	+	10597.6i	−0.924635	+	0.671787i
$630$		0			0
$631$	9423.94	−	29003.9i	0.594550	−	1.82984i	0.0375960	−	0.999293i	$-0.488030\pi$
$631$	9423.94	−	29003.9i	0.594550	−	1.82984i	0.556954	−	0.830543i	$-0.311970\pi$
$632$	−2821.36	−	2049.84i	−0.177575	−	0.129016i
$633$		0			0
$634$	−1130.37	+	3478.91i	−0.0708085	+	0.217926i
$635$	−3467.60	−	10672.2i	−0.216705	−	0.666949i
$636$		0			0
$637$	26258.1			1.63326
$638$	−11089.9	−	2909.04i	−0.688172	−	0.180517i
$639$		0			0
$640$	−473.916	+	344.320i	−0.0292706	+	0.0212663i
$641$	4499.66	+	13848.5i	0.277264	+	0.853330i	0.988612	+	0.150490i	$0.0480851\pi$
$641$	4499.66	+	13848.5i	0.277264	+	0.853330i	−0.711348	+	0.702840i	$0.751915\pi$
$642$		0			0
$643$	15693.4	+	11401.9i	0.962497	+	0.699295i	0.953729	−	0.300667i	$-0.0972091\pi$
$643$	15693.4	+	11401.9i	0.962497	+	0.699295i	0.00876768	+	0.999962i	$0.497209\pi$
$644$	2048.04	+	1487.98i	0.125317	+	0.0910479i
$645$		0			0
$646$	−1344.26	−	4137.20i	−0.0818716	−	0.251975i
$647$	−24183.7	+	17570.5i	−1.46949	+	1.06765i	−0.488729	+	0.872436i	$0.662539\pi$
$647$	−24183.7	+	17570.5i	−1.46949	+	1.06765i	−0.980761	+	0.195211i	$0.937461\pi$
$648$		0			0
$649$	10789.9	+	13181.9i	0.652605	+	0.797280i
$650$	18622.3			1.12373
$651$		0			0
$652$	−609.722	−	1876.53i	−0.0366236	−	0.112716i
$653$	−6980.91	+	21485.0i	−0.418352	+	1.28756i	0.490865	+	0.871236i	$0.336681\pi$
$653$	−6980.91	+	21485.0i	−0.418352	+	1.28756i	−0.909218	+	0.416321i	$0.863319\pi$
$654$		0			0
$655$	−9110.57	−	6619.22i	−0.543480	−	0.394861i
$656$	454.171	−	1397.79i	0.0270311	−	0.0831931i
$657$		0			0
$658$	−3353.83	+	2436.70i	−0.198702	+	0.144365i
$659$	12824.3			0.758061			0.379030	−	0.925384i	$-0.376258\pi$
$659$	12824.3			0.758061			0.379030	+	0.925384i	$0.376258\pi$
$660$		0			0
$661$	−28829.4			−1.69642			−0.848209	−	0.529662i	$-0.822319\pi$
$661$	−28829.4			−1.69642			−0.848209	+	0.529662i	$0.822319\pi$
$662$	10089.3	−	7330.28i	0.592342	−	0.430361i
$663$		0			0
$664$	−1640.79	+	5049.83i	−0.0958961	+	0.295138i
$665$	−549.500	−	399.235i	−0.0320432	−	0.0232807i
$666$		0			0
$667$	4365.33	−	13435.1i	0.253413	−	0.779924i
$668$	−2900.46	−	8926.68i	−0.167997	−	0.517042i
$669$		0			0
$670$	−8008.62			−0.461791
$671$	4180.29	−	1629.97i	0.240504	−	0.0937766i
$672$		0			0
$673$	−8198.04	+	5956.22i	−0.469556	+	0.341152i	−0.797268	−	0.603625i	$-0.793722\pi$
$673$	−8198.04	+	5956.22i	−0.469556	+	0.341152i	0.327712	+	0.944778i	$0.393722\pi$
$674$	609.788	+	1876.73i	0.0348489	+	0.107254i
$675$		0			0
$676$	−18801.9	−	13660.3i	−1.06975	−	0.777216i
$677$	4086.40	+	2968.94i	0.231984	+	0.168546i	0.697704	−	0.716386i	$-0.254205\pi$
$677$	4086.40	+	2968.94i	0.231984	+	0.168546i	−0.465721	+	0.884932i	$0.654205\pi$
$678$		0			0
$679$	445.343	+	1370.62i	0.0251704	+	0.0774664i
$680$	−3055.76	+	2220.14i	−0.172328	+	0.125204i
$681$		0			0
$682$	−10448.5	−	12764.9i	−0.586649	−	0.716703i
$683$	5966.92			0.334287			0.167144	−	0.985933i	$-0.446546\pi$
$683$	5966.92			0.334287			0.167144	+	0.985933i	$0.446546\pi$
$684$		0			0
$685$	−884.520	−	2722.27i	−0.0493369	−	0.151843i
$686$	2768.96	−	8521.99i	0.154110	−	0.474302i
$687$		0			0
$688$	153.523	+	111.541i	0.00850727	+	0.00618089i
$689$	13891.0	−	42752.0i	0.768076	−	2.36389i
$690$		0			0
$691$	−4875.68	+	3542.39i	−0.268422	+	0.195020i	−0.713852	−	0.700297i	$-0.753051\pi$
$691$	−4875.68	+	3542.39i	−0.268422	+	0.195020i	0.445430	+	0.895317i	$0.353051\pi$
$692$	11847.8			0.650847
$693$		0			0
$694$	22964.4			1.25607
$695$	−4333.40	+	3148.40i	−0.236511	+	0.171836i
$696$		0			0
$697$	2928.44	−	9012.82i	0.159143	−	0.489792i
$698$	5182.97	+	3765.65i	0.281058	+	0.204201i
$699$		0			0
$700$	905.424	−	2786.61i	0.0488883	−	0.150463i
$701$	2956.72	+	9099.85i	0.159306	+	0.490295i	0.998572	−	0.0534275i	$-0.0170146\pi$
$701$	2956.72	+	9099.85i	0.159306	+	0.490295i	−0.839265	+	0.543722i	$0.817015\pi$
$702$		0			0
$703$	−3684.54			−0.197674
$704$	−134.474	−	2331.03i	−0.00719912	−	0.124793i
$705$		0			0
$706$	14027.7	−	10191.7i	0.747789	−	0.543300i
$707$	230.294	+	708.773i	0.0122505	+	0.0377032i
$708$		0			0
$709$	4172.92	+	3031.80i	0.221040	+	0.160595i	0.692795	−	0.721135i	$-0.256379\pi$
$709$	4172.92	+	3031.80i	0.221040	+	0.160595i	−0.471755	+	0.881730i	$0.656379\pi$
$710$	−823.864	−	598.572i	−0.0435480	−	0.0316395i
$711$		0			0
$712$	−3184.88	−	9802.06i	−0.167638	−	0.515938i
$713$	16443.3	−	11946.8i	0.863684	−	0.627503i
$714$		0			0
$715$	8071.01	−	12572.7i	0.422152	−	0.657611i
$716$	5970.09			0.311610
$717$		0			0
$718$	2654.02	+	8168.23i	0.137949	+	0.424562i
$719$	2171.59	−	6683.47i	0.112638	−	0.346664i	−0.878809	−	0.477173i	$-0.841661\pi$
$719$	2171.59	−	6683.47i	0.112638	−	0.346664i	0.991447	+	0.130510i	$0.0416613\pi$
$720$		0			0
$721$	−2746.01	−	1995.09i	−0.141840	−	0.103053i
$722$	−3964.38	+	12201.1i	−0.204348	+	0.628918i
$723$		0			0
$724$	5002.49	−	3634.52i	0.256790	−	0.186569i
$725$	−16350.2			−0.837562
$726$		0			0
$727$	9911.22			0.505621			0.252811	−	0.967516i	$-0.418645\pi$
$727$	9911.22			0.505621			0.252811	+	0.967516i	$0.418645\pi$
$728$	−4076.89	+	2962.03i	−0.207554	+	0.150797i
$729$		0			0
$730$	−2301.79	+	7084.19i	−0.116703	+	0.359175i
$731$	989.898	+	719.203i	0.0500858	+	0.0363894i
$732$		0			0
$733$	4564.03	−	14046.6i	0.229981	−	0.707810i	−0.767766	−	0.640730i	$-0.778632\pi$
$733$	4564.03	−	14046.6i	0.229981	−	0.707810i	0.997748	−	0.0670797i	$-0.0213682\pi$
$734$	5628.46	+	17322.6i	0.283039	+	0.871103i
$735$		0			0
$736$	2876.91			0.144082
$737$	17244.5	−	26862.7i	0.861884	−	1.34261i
$738$		0			0
$739$	24816.4	−	18030.2i	1.23530	−	0.897497i	0.238023	−	0.971259i	$-0.423501\pi$
$739$	24816.4	−	18030.2i	1.23530	−	0.897497i	0.997276	+	0.0737622i	$0.0235006\pi$
$740$	988.616	+	3042.65i	0.0491111	+	0.151149i
$741$		0			0
$742$	−5721.96	−	4157.25i	−0.283099	−	0.205684i
$743$	4848.48	+	3522.63i	0.239399	+	0.173934i	0.701015	−	0.713146i	$-0.252730\pi$
$743$	4848.48	+	3522.63i	0.239399	+	0.173934i	−0.461617	+	0.887080i	$0.652730\pi$
$744$		0			0
$745$	2800.75	+	8619.81i	0.137733	+	0.423900i
$746$	−12374.8	+	8990.80i	−0.607336	+	0.441256i
$747$		0			0
$748$	−867.073	−	15030.2i	−0.0423841	−	0.734705i
$749$	−3165.91			−0.154446
$750$		0			0
$751$	−819.025	−	2520.70i	−0.0397958	−	0.122479i	0.929185	−	0.369615i	$-0.120510\pi$
$751$	−819.025	−	2520.70i	−0.0397958	−	0.122479i	−0.968981	+	0.247136i	$0.920510\pi$
$752$	−1455.83	+	4480.59i	−0.0705967	+	0.217274i
$753$		0			0
$754$	22750.1	+	16528.9i	1.09882	+	0.798340i
$755$	−3607.85	+	11103.8i	−0.173912	+	0.535245i
$756$		0			0
$757$	24133.2	−	17533.8i	1.15870	−	0.841847i	0.169089	−	0.985601i	$-0.445917\pi$
$757$	24133.2	−	17533.8i	1.15870	−	0.841847i	0.989613	+	0.143754i	$0.0459174\pi$
$758$	−18604.4			−0.891479
$759$		0			0
$760$	−771.891			−0.0368414
$761$	16777.4	−	12189.5i	0.799186	−	0.580643i	−0.111489	−	0.993766i	$-0.535562\pi$
$761$	16777.4	−	12189.5i	0.799186	−	0.580643i	0.910675	+	0.413123i	$0.135562\pi$
$762$		0			0
$763$	2642.72	−	8133.46i	0.125391	−	0.385912i
$764$	−3757.88	−	2730.26i	−0.177952	−	0.129290i
$765$		0			0
$766$	244.417	−	752.238i	0.0115289	−	0.0354823i
$767$	−12911.2	−	39736.7i	−0.607820	−	1.87068i
$768$		0			0
$769$	20601.9			0.966092			0.483046	−	0.875595i	$-0.339530\pi$
$769$	20601.9			0.966092			0.483046	+	0.875595i	$0.339530\pi$
$770$	−1488.94	−	1819.02i	−0.0696853	−	0.0851338i
$771$		0			0
$772$	2320.99	−	1686.30i	0.108205	−	0.0786155i
$773$	8697.88	+	26769.3i	0.404710	+	1.24557i	0.921137	+	0.389239i	$0.127262\pi$
$773$	8697.88	+	26769.3i	0.404710	+	1.24557i	−0.516426	+	0.856332i	$0.672738\pi$
$774$		0			0
$775$	−19031.8	−	13827.4i	−0.882117	−	0.640896i
$776$	1325.00	+	962.668i	0.0612947	+	0.0445332i
$777$		0			0
$778$	1491.81	+	4591.31i	0.0687453	+	0.211576i
$779$	1566.77	−	1138.33i	0.0720610	−	0.0523554i
$780$		0			0
$781$	3781.73	−	1474.56i	0.173266	−	0.0675594i
$782$	18550.0			0.848268
$783$		0			0
$784$	−1450.87	−	4465.32i	−0.0660929	−	0.203413i
$785$	3201.53	−	9853.30i	0.145564	−	0.447999i
$786$		0			0
$787$	4186.83	+	3041.91i	0.189637	+	0.137779i	0.678553	−	0.734552i	$-0.262607\pi$
$787$	4186.83	+	3041.91i	0.189637	+	0.137779i	−0.488916	+	0.872331i	$0.662607\pi$
$788$	−4485.01	+	13803.5i	−0.202756	+	0.624020i
$789$		0			0
$790$	−3227.99	+	2345.27i	−0.145376	+	0.105622i
$791$	11015.7			0.495160
$792$		0			0
$793$	−11004.9			−0.492808
$794$	−7899.30	+	5739.18i	−0.353067	+	0.256519i
$795$		0			0
$796$	−1578.07	+	4856.79i	−0.0702677	+	0.216262i
$797$	−1776.57	−	1290.76i	−0.0789578	−	0.0573662i	0.547606	−	0.836736i	$-0.315539\pi$
$797$	−1776.57	−	1290.76i	−0.0789578	−	0.0573662i	−0.626564	+	0.779370i	$0.715539\pi$
$798$		0			0
$799$	−9387.04	+	28890.3i	−0.415632	+	1.27918i
$800$	−1028.96	−	3166.81i	−0.0454740	−	0.139954i
$801$		0			0
$802$	3497.72			0.154001
$803$	−18805.7	−	22974.7i	−0.826449	−	1.00966i
$804$		0			0
$805$	2343.21	−	1702.44i	0.102593	−	0.0745382i
$806$	12502.8	+	38479.5i	0.546390	+	1.68162i
$807$		0			0
$808$	685.179	+	497.812i	0.0298323	+	0.0216745i
$809$	25063.3	+	18209.5i	1.08922	+	0.791364i	0.979267	−	0.202573i	$-0.0649304\pi$
$809$	25063.3	+	18209.5i	1.08922	+	0.791364i	0.109952	+	0.993937i	$0.464930\pi$
$810$		0			0
$811$	−3139.90	−	9663.62i	−0.135952	−	0.418416i	0.859785	−	0.510656i	$-0.170597\pi$
$811$	−3139.90	−	9663.62i	−0.135952	−	0.418416i	−0.995737	+	0.0922396i	$0.970597\pi$
$812$	3579.48	−	2600.65i	0.154699	−	0.112395i
$813$		0			0
$814$	−12334.5	−	3235.50i	−0.531109	−	0.139317i
$815$	−2257.48			−0.0970258
$816$		0			0
$817$	77.2698	+	237.812i	0.00330885	+	0.0101836i
$818$	3070.69	−	9450.62i	0.131252	−	0.403953i
$819$		0			0
$820$	−1360.41	−	988.392i	−0.0579359	−	0.0420929i
$821$	−664.158	+	2044.07i	−0.0282330	+	0.0868921i	−0.964180	−	0.265248i	$-0.914546\pi$
$821$	−664.158	+	2044.07i	−0.0282330	+	0.0868921i	0.935947	+	0.352140i	$0.114546\pi$
$822$		0			0
$823$	35937.5	−	26110.1i	1.52212	−	1.10588i	0.561693	−	0.827345i	$-0.310150\pi$
$823$	35937.5	−	26110.1i	1.52212	−	1.10588i	0.960425	−	0.278538i	$-0.0898499\pi$
$824$	−3857.36			−0.163079
$825$		0			0
$826$	−6573.89			−0.276919
$827$	−32751.9	+	23795.7i	−1.37714	+	1.00055i	−0.380002	+	0.924986i	$0.624077\pi$
$827$	−32751.9	+	23795.7i	−1.37714	+	1.00055i	−0.997141	+	0.0755668i	$0.975923\pi$
$828$		0			0
$829$	6726.09	−	20700.8i	0.281794	−	0.867271i	−0.705548	−	0.708662i	$-0.749299\pi$
$829$	6726.09	−	20700.8i	0.281794	−	0.867271i	0.987341	−	0.158609i	$-0.0507010\pi$
$830$	4914.76	+	3570.78i	0.205535	+	0.149330i
$831$		0			0
$832$	−1769.70	+	5446.58i	−0.0737420	+	0.226954i
$833$	−9355.06	−	28791.9i	−0.389116	−	1.19758i
$834$		0			0
$835$	−10738.9			−0.445070
$836$	1662.07	−	2589.10i	0.0687605	−	0.107112i
$837$		0			0
$838$	19033.4	−	13828.6i	0.784605	−	0.570049i
$839$	7886.61	+	24272.5i	0.324525	+	0.998784i	0.971655	+	0.236404i	$0.0759690\pi$
$839$	7886.61	+	24272.5i	0.324525	+	0.998784i	−0.647130	+	0.762379i	$0.724031\pi$
$840$		0			0
$841$	−243.344	−	176.800i	−0.00997761	−	0.00724916i
$842$	7069.54	+	5136.32i	0.289350	+	0.210225i
$843$		0			0
$844$	3991.85	+	12285.6i	0.162802	+	0.501053i
$845$	−21511.7	+	15629.2i	−0.875769	+	0.636284i
$846$		0			0
$847$	9307.46	−	1077.46i	0.377578	−	0.0437094i
$848$	−8037.72			−0.325491
$849$		0			0
$850$	−6634.61	−	20419.2i	−0.267724	−	0.823969i
$851$	4855.23	−	14942.9i	0.195576	−	0.601920i
$852$		0			0
$853$	16902.3	+	12280.2i	0.678456	+	0.492927i	0.872845	−	0.487997i	$-0.162272\pi$
$853$	16902.3	+	12280.2i	0.678456	+	0.492927i	−0.194389	+	0.980925i	$0.562272\pi$
$854$	−535.065	+	1646.76i	−0.0214397	+	0.0659847i
$855$		0			0
$856$	−2910.73	+	2114.77i	−0.116223	+	0.0844409i
$857$	−4786.08			−0.190769			−0.0953847	−	0.995440i	$-0.530408\pi$
$857$	−4786.08			−0.190769			−0.0953847	+	0.995440i	$0.530408\pi$
$858$		0			0
$859$	−13013.8			−0.516911			−0.258455	−	0.966023i	$-0.583214\pi$
$859$	−13013.8			−0.516911			−0.258455	+	0.966023i	$0.583214\pi$
$860$	175.649	−	127.617i	0.00696465	−	0.00506011i
$861$		0			0
$862$	−1968.26	+	6057.67i	−0.0777716	+	0.239356i
$863$	−40121.7	−	29150.1i	−1.58257	−	1.14980i	−0.913674	−	0.406449i	$-0.866767\pi$
$863$	−40121.7	−	29150.1i	−1.58257	−	1.14980i	−0.668896	−	0.743356i	$-0.733233\pi$
$864$		0			0
$865$	4188.84	−	12891.9i	0.164653	−	0.506750i
$866$	−3423.05	−	10535.1i	−0.134319	−	0.413390i
$867$		0			0
$868$	6365.90			0.248932
$869$	−915.944	−	15877.4i	−0.0357552	−	0.619796i
$870$		0			0
$871$	−63341.6	+	46020.3i	−2.46412	+	1.79029i
$872$	−3003.29	−	9243.18i	−0.116633	−	0.358961i
$873$		0			0
$874$	3066.87	+	2228.21i	0.118694	+	0.0862362i
$875$	−5970.03	−	4337.48i	−0.230656	−	0.167581i
$876$		0			0
$877$	−7469.00	−	22987.2i	−0.287583	−	0.885089i	−0.985613	−	0.169020i	$-0.945940\pi$
$877$	−7469.00	−	22987.2i	−0.287583	−	0.885089i	0.698030	−	0.716069i	$-0.254060\pi$
$878$	−13672.9	+	9933.93i	−0.525555	+	0.381838i
$879$		0			0
$880$	−2584.00	−	677.821i	−0.0989849	−	0.0259651i
$881$	31630.8			1.20961			0.604806	−	0.796373i	$-0.293251\pi$
$881$	31630.8			1.20961			0.604806	+	0.796373i	$0.293251\pi$
$882$		0			0
$883$	6918.75	+	21293.7i	0.263686	+	0.811541i	0.991993	+	0.126291i	$0.0403073\pi$
$883$	6918.75	+	21293.7i	0.263686	+	0.811541i	−0.728307	+	0.685251i	$0.759693\pi$
$884$	−11410.8	+	35118.9i	−0.434149	+	1.33617i
$885$		0			0
$886$	2566.43	+	1864.62i	0.0973150	+	0.0707035i
$887$	4958.10	−	15259.5i	0.187685	−	0.577636i	−0.812299	−	0.583241i	$-0.801784\pi$
$887$	4958.10	−	15259.5i	0.187685	−	0.577636i	0.999984	+	0.00560528i	$0.00178423\pi$
$888$		0			0
$889$	−13964.1	+	10145.5i	−0.526819	+	0.382757i
$890$	−11791.9			−0.444120
$891$		0			0
$892$	−13148.0			−0.493530
$893$	−5022.25	+	3648.88i	−0.188201	+	0.136736i
$894$		0			0
$895$	2110.75	−	6496.23i	0.0788321	−	0.242620i
$896$	728.973	+	529.630i	0.0271800	+	0.0197474i
$897$		0			0
$898$	−8811.33	+	27118.5i	−0.327436	+	1.00775i
$899$	−10977.3	−	33784.8i	−0.407247	−	1.25338i
$900$		0			0
$901$	−51826.3			−1.91630
$902$	6244.57	−	2434.87i	0.230512	−	0.0898804i
$903$		0			0
$904$	10127.8	−	7358.26i	0.372616	−	0.270721i
$905$	−2186.17	−	6728.35i	−0.0802993	−	0.247136i
$906$		0			0
$907$	41220.1	+	29948.1i	1.50903	+	1.09637i	0.966605	+	0.256271i	$0.0824939\pi$
$907$	41220.1	+	29948.1i	1.50903	+	1.09637i	0.542425	+	0.840104i	$0.317506\pi$
$908$	20356.8	+	14790.0i	0.744012	+	0.540556i
$909$		0			0
$910$	1781.67	+	5483.42i	0.0649031	+	0.199751i
$911$	−6331.44	+	4600.06i	−0.230264	+	0.167296i	−0.696935	−	0.717135i	$-0.745453\pi$
$911$	−6331.44	+	4600.06i	−0.230264	+	0.167296i	0.466671	+	0.884431i	$0.345453\pi$
$912$		0			0
$913$	−22559.9	+	8796.49i	−0.817769	+	0.318862i
$914$	1757.49			0.0636024
$915$		0			0
$916$	−1318.18	−	4056.95i	−0.0475480	−	0.146338i
$917$	−5352.79	+	16474.2i	−0.192764	+	0.593267i
$918$		0			0
$919$	−9538.92	−	6930.43i	−0.342394	−	0.248764i	0.403277	−	0.915078i	$-0.367871\pi$
$919$	−9538.92	−	6930.43i	−0.342394	−	0.248764i	−0.745671	+	0.666314i	$0.767871\pi$
$920$	1017.14	−	3130.45i	0.0364502	−	0.112182i
$921$		0			0
$922$	7987.21	−	5803.05i	0.285298	−	0.207281i
$923$	−9955.69			−0.355033
$924$		0			0
$925$	−18185.1			−0.646404
$926$	−27434.7	+	19932.5i	−0.973607	+	0.707367i
$927$		0			0
$928$	1553.79	−	4782.06i	0.0549628	−	0.169158i
$929$	23048.6	+	16745.8i	0.813994	+	0.591401i	0.914986	−	0.403486i	$-0.132202\pi$
$929$	23048.6	+	16745.8i	0.813994	+	0.591401i	−0.100992	+	0.994887i	$0.532202\pi$
$930$		0			0
$931$	1911.79	−	5883.90i	0.0673002	−	0.207129i
$932$	−4560.51	−	14035.8i	−0.160284	−	0.493303i
$933$		0			0
$934$	−19274.1			−0.675232
$935$	−16661.4	−	4370.51i	−0.582765	−	0.152867i
$936$		0			0
$937$	−16174.4	+	11751.4i	−0.563923	+	0.409714i	−0.832892	−	0.553435i	$-0.813317\pi$
$937$	−16174.4	+	11751.4i	−0.563923	+	0.409714i	0.268970	+	0.963149i	$0.413317\pi$
$938$	3806.71	+	11715.9i	0.132509	+	0.407821i
$939$		0			0
$940$	4360.74	+	3168.27i	0.151310	+	0.109933i
$941$	10986.0	+	7981.79i	0.380588	+	0.276513i	0.761588	−	0.648062i	$-0.224420\pi$
$941$	10986.0	+	7981.79i	0.380588	+	0.276513i	−0.381000	+	0.924575i	$0.624420\pi$
$942$		0			0
$943$	2551.97	+	7854.14i	0.0881267	+	0.271226i
$944$	−6044.02	+	4391.24i	−0.208386	+	0.151401i
$945$		0			0
$946$	49.8406	+	863.958i	0.00171296	+	0.0296931i
$947$	54932.1			1.88496			0.942478	−	0.334269i	$-0.108489\pi$
$947$	54932.1			1.88496			0.942478	+	0.334269i	$0.108489\pi$
$948$		0			0
$949$	22503.0	+	69257.0i	0.769734	+	2.36900i
$950$	1355.84	−	4172.86i	0.0463046	−	0.142511i
$951$		0			0
$952$	4700.34	+	3415.00i	0.160020	+	0.116261i
$953$	10537.2	−	32430.2i	0.358167	−	1.10233i	−0.595983	−	0.802997i	$-0.703237\pi$
$953$	10537.2	−	32430.2i	0.358167	−	1.10233i	0.954150	−	0.299329i	$-0.0967627\pi$
$954$		0			0
$955$	−4299.49	+	3123.77i	−0.145684	+	0.105846i
$956$	28524.5			0.965009
$957$		0			0
$958$	−25042.5			−0.844559
$959$	−3561.99	+	2587.94i	−0.119940	+	0.0871417i
$960$		0			0
$961$	6588.14	−	20276.2i	0.221145	−	0.680616i
$962$	25303.3	+	18383.9i	0.848035	+	0.616133i
$963$		0			0
$964$	−3968.52	+	12213.9i	−0.132591	+	0.408073i
$965$	−1014.31	−	3121.73i	−0.0338362	−	0.104137i
$966$		0			0
$967$	33962.8			1.12944			0.564721	−	0.825282i	$-0.308984\pi$
$967$	33962.8			1.12944			0.564721	+	0.825282i	$0.308984\pi$
$968$	7837.54	−	7207.83i	0.260236	−	0.239327i
$969$		0			0
$970$	1515.97	−	1101.41i	0.0501802	−	0.0364580i
$971$	8903.01	+	27400.7i	0.294244	+	0.905591i	0.983474	+	0.181048i	$0.0579490\pi$
$971$	8903.01	+	27400.7i	0.294244	+	0.905591i	−0.689230	+	0.724543i	$0.742051\pi$
$972$		0			0
$973$	6665.60	+	4842.84i	0.219619	+	0.159563i
$974$	−20347.9	−	14783.6i	−0.669394	−	0.486343i
$975$		0			0
$976$	608.068	+	1871.44i	0.0199424	+	0.0613764i
$977$	−34031.5	+	24725.3i	−1.11439	+	0.809655i	−0.983350	−	0.181722i	$-0.941833\pi$
$977$	−34031.5	+	24725.3i	−1.11439	+	0.809655i	−0.131044	+	0.991377i	$0.541833\pi$
$978$		0			0
$979$	25390.9	−	39552.8i	0.828902	−	1.29123i
$980$	−5371.81			−0.175098
$981$		0			0
$982$	1218.28	+	3749.48i	0.0395894	+	0.121844i
$983$	−6739.22	+	20741.2i	−0.218665	+	0.672982i	0.780208	+	0.625520i	$0.215113\pi$
$983$	−6739.22	+	20741.2i	−0.218665	+	0.672982i	−0.998873	+	0.0474618i	$0.984887\pi$
$984$		0			0
$985$	13434.2	+	9760.55i	0.434569	+	0.315733i
$986$	10018.6	−	30834.2i	0.323589	−	0.995903i
$987$		0			0
$988$	−6105.02	+	4435.56i	−0.196586	+	0.142828i
$989$	−1066.28			−0.0342828
$990$		0			0
$991$	11621.1			0.372508			0.186254	−	0.982502i	$-0.440365\pi$
$991$	11621.1			0.372508			0.186254	+	0.982502i	$0.440365\pi$
$992$	5852.80	−	4252.31i	0.187325	−	0.136100i
$993$		0			0
$994$	−484.050	+	1489.75i	−0.0154458	+	0.0475373i
$995$	4726.88	+	3434.28i	0.150605	+	0.109421i
$996$		0			0
$997$	−16964.3	+	52210.7i	−0.538881	+	1.65850i	0.196230	+	0.980558i	$0.437130\pi$
$997$	−16964.3	+	52210.7i	−0.538881	+	1.65850i	−0.735111	+	0.677947i	$0.762870\pi$
$998$	−4557.88	−	14027.7i	−0.144566	−	0.444929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.4.f.g.91.1	yes	12
3.2	odd	2		198.4.f.h.91.3	yes	12
11.2	odd	10		2178.4.a.cd.1.5		6
11.4	even	5	inner	198.4.f.g.37.1	✓	12
11.9	even	5		2178.4.a.cf.1.5		6
33.2	even	10		2178.4.a.cg.1.2		6
33.20	odd	10		2178.4.a.ce.1.2		6
33.26	odd	10		198.4.f.h.37.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.4.f.g.37.1	✓	12	11.4	even	5	inner
198.4.f.g.91.1	yes	12	1.1	even	1	trivial
198.4.f.h.37.3	yes	12	33.26	odd	10
198.4.f.h.91.3	yes	12	3.2	odd	2
2178.4.a.cd.1.5		6	11.2	odd	10
2178.4.a.ce.1.2		6	33.20	odd	10
2178.4.a.cf.1.5		6	11.9	even	5
2178.4.a.cg.1.2		6	33.2	even	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(-3.70247 - 2.69000i) q^{5} +(-2.17534 + 6.69500i) q^{7} +(2.47214 + 7.60845i) q^{8} +O(q^{10})\)	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(-3.70247 - 2.69000i) q^{5} +(-2.17534 + 6.69500i) q^{7} +(2.47214 + 7.60845i) q^{8} +9.15301 q^{10} +(-19.7086 + 30.7013i) q^{11} +(72.3928 - 52.5964i) q^{13} +(-4.35067 - 13.3900i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(-83.4632 - 60.6396i) q^{17} +(-6.51500 - 20.0511i) q^{19} +(-14.8099 + 10.7600i) q^{20} +(-4.20231 - 72.8446i) q^{22} +89.9033 q^{23} +(-32.1549 - 98.9628i) q^{25} +(-55.3031 + 170.206i) q^{26} +(22.7804 + 16.5509i) q^{28} +(48.5558 - 149.439i) q^{29} +(182.900 - 132.885i) q^{31} +32.0000 q^{32} +206.332 q^{34} +(26.0637 - 18.9364i) q^{35} +(54.0050 - 166.210i) q^{37} +(34.1130 + 24.7845i) q^{38} +(11.3137 - 34.8201i) q^{40} +(28.3857 + 87.3621i) q^{41} -11.8603 q^{43} +(92.4335 + 112.925i) q^{44} +(-145.467 + 105.688i) q^{46} +(-90.9895 - 280.037i) q^{47} +(237.402 + 172.483i) q^{49} +(168.365 + 122.325i) q^{50} +(-110.606 - 340.411i) q^{52} +(406.416 - 295.278i) q^{53} +(155.557 - 60.6544i) q^{55} -56.3163 q^{56} +(97.1116 + 298.879i) q^{58} +(144.288 - 444.073i) q^{59} +(-99.4965 - 72.2884i) q^{61} +(-139.723 + 430.023i) q^{62} +(-51.7771 + 37.6183i) q^{64} -409.517 q^{65} -874.971 q^{67} +(-333.853 + 242.558i) q^{68} +(-19.9109 + 61.2794i) q^{70} +(-90.0102 - 65.3962i) q^{71} +(-251.479 + 773.974i) q^{73} +(108.010 + 332.420i) q^{74} -84.3320 q^{76} +(-162.672 - 198.735i) q^{77} +(-352.670 + 256.230i) q^{79} +(22.6275 + 69.6403i) q^{80} +(-148.629 - 107.985i) q^{82} +(536.956 + 390.121i) q^{83} +(145.900 + 449.033i) q^{85} +(19.1903 - 13.9426i) q^{86} +(-282.312 - 74.0544i) q^{88} -1288.31 q^{89} +(194.654 + 599.084i) q^{91} +(111.127 - 342.013i) q^{92} +(476.427 + 346.145i) q^{94} +(-29.8159 + 91.7640i) q^{95} +(165.625 - 120.334i) q^{97} -586.890 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 12 q^{4} + 16 q^{5} + 6 q^{7} - 24 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 12 * q^4 + 16 * q^5 + 6 * q^7 - 24 * q^8	\( 12 q - 6 q^{2} - 12 q^{4} + 16 q^{5} + 6 q^{7} - 24 q^{8} - 68 q^{10} - 116 q^{11} - 46 q^{13} + 12 q^{14} - 48 q^{16} + 24 q^{17} - 6 q^{19} + 64 q^{20} - 22 q^{22} - 420 q^{23} - 431 q^{25} + 228 q^{26} + 4 q^{28} - 89 q^{29} - 345 q^{31} + 384 q^{32} + 168 q^{34} - 87 q^{35} + 474 q^{37} + 208 q^{38} + 8 q^{40} + 580 q^{41} - 1736 q^{43} - 44 q^{44} - 100 q^{46} - 1074 q^{47} - 553 q^{49} + 768 q^{50} + 456 q^{52} + 585 q^{53} + 1520 q^{55} - 112 q^{56} - 178 q^{58} + 1326 q^{59} + 1816 q^{61} + 940 q^{62} - 192 q^{64} - 3712 q^{65} + 1372 q^{67} + 96 q^{68} - 894 q^{70} - 484 q^{71} - 695 q^{73} + 948 q^{74} - 784 q^{76} - 158 q^{77} - 1844 q^{79} + 16 q^{80} - 820 q^{82} + 232 q^{83} + 2210 q^{85} + 1348 q^{86} + 472 q^{88} - 5052 q^{89} + 3522 q^{91} + 1040 q^{92} + 3712 q^{94} - 178 q^{95} + 1868 q^{97} - 1756 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 12 * q^4 + 16 * q^5 + 6 * q^7 - 24 * q^8 - 68 * q^10 - 116 * q^11 - 46 * q^13 + 12 * q^14 - 48 * q^16 + 24 * q^17 - 6 * q^19 + 64 * q^20 - 22 * q^22 - 420 * q^23 - 431 * q^25 + 228 * q^26 + 4 * q^28 - 89 * q^29 - 345 * q^31 + 384 * q^32 + 168 * q^34 - 87 * q^35 + 474 * q^37 + 208 * q^38 + 8 * q^40 + 580 * q^41 - 1736 * q^43 - 44 * q^44 - 100 * q^46 - 1074 * q^47 - 553 * q^49 + 768 * q^50 + 456 * q^52 + 585 * q^53 + 1520 * q^55 - 112 * q^56 - 178 * q^58 + 1326 * q^59 + 1816 * q^61 + 940 * q^62 - 192 * q^64 - 3712 * q^65 + 1372 * q^67 + 96 * q^68 - 894 * q^70 - 484 * q^71 - 695 * q^73 + 948 * q^74 - 784 * q^76 - 158 * q^77 - 1844 * q^79 + 16 * q^80 - 820 * q^82 + 232 * q^83 + 2210 * q^85 + 1348 * q^86 + 472 * q^88 - 5052 * q^89 + 3522 * q^91 + 1040 * q^92 + 3712 * q^94 - 178 * q^95 + 1868 * q^97 - 1756 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more