LMFDB - Embedded newform 198.4.f.h.181.1

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			181.1
Root			$-15.2352i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.4.f.h.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 - 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-3.57139 + 10.9916i) q^{5} +(-12.8715 + 9.35167i) q^{7} +(6.47214 + 4.70228i) q^{8} +O(q^{10})$	\(q+(-0.618034 - 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-3.57139 + 10.9916i) q^{5} +(-12.8715 + 9.35167i) q^{7} +(6.47214 + 4.70228i) q^{8} +23.1145 q^{10} +(27.0144 - 24.5198i) q^{11} +(-26.0329 - 80.1210i) q^{13} +(25.7429 + 18.7033i) q^{14} +(4.94427 - 15.2169i) q^{16} +(22.6481 - 69.7036i) q^{17} +(-75.6108 - 54.9344i) q^{19} +(-14.2856 - 43.9664i) q^{20} +(-63.3353 - 36.2303i) q^{22} +188.856 q^{23} +(-6.93339 - 5.03740i) q^{25} +(-136.310 + 99.0350i) q^{26} +(19.6659 - 60.5253i) q^{28} +(-131.759 + 95.7284i) q^{29} +(-47.5853 - 146.452i) q^{31} -32.0000 q^{32} -146.581 q^{34} +(-56.8208 - 174.877i) q^{35} +(274.834 - 199.679i) q^{37} +(-57.7615 + 177.772i) q^{38} +(-74.8001 + 54.3455i) q^{40} +(77.9020 + 56.5991i) q^{41} -479.178 q^{43} +(-29.7708 + 142.863i) q^{44} +(-116.719 - 359.225i) q^{46} +(-240.033 - 174.394i) q^{47} +(-27.7718 + 85.4729i) q^{49} +(-5.29664 + 16.3014i) q^{50} +(272.620 + 198.070i) q^{52} +(-68.1924 - 209.875i) q^{53} +(173.034 + 384.501i) q^{55} -127.280 q^{56} +(263.518 + 191.457i) q^{58} +(74.7754 - 54.3275i) q^{59} +(75.0128 - 230.866i) q^{61} +(-249.160 + 181.025i) q^{62} +(19.7771 + 60.8676i) q^{64} +973.631 q^{65} +307.078 q^{67} +(90.5923 + 278.814i) q^{68} +(-297.518 + 216.159i) q^{70} +(289.776 - 891.838i) q^{71} +(-521.320 + 378.761i) q^{73} +(-549.668 - 399.357i) q^{74} +373.840 q^{76} +(-118.413 + 568.236i) q^{77} +(-169.969 - 523.111i) q^{79} +(149.600 + 108.691i) q^{80} +(59.5119 - 183.159i) q^{82} +(-105.551 + 324.853i) q^{83} +(685.269 + 497.877i) q^{85} +(296.148 + 911.451i) q^{86} +(290.140 - 31.6665i) q^{88} +68.5702 q^{89} +(1084.35 + 787.824i) q^{91} +(-611.149 + 444.026i) q^{92} +(-183.369 + 564.351i) q^{94} +(873.853 - 634.891i) q^{95} +(477.969 + 1471.04i) q^{97} +179.743 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.618034	−	1.90211i	−0.218508	−	0.672499i
$2$	−0.618034	−	1.90211i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−3.23607	+	2.35114i	−0.404508	+	0.293893i
$5$	−3.57139	+	10.9916i	−0.319435	+	0.983119i	0.654456	+	0.756100i	$0.272898\pi$
$5$	−3.57139	+	10.9916i	−0.319435	+	0.983119i	−0.973890	+	0.227019i	$0.927102\pi$
$6$		0			0
$7$	−12.8715	+	9.35167i	−0.694994	+	0.504943i	−0.878298	−	0.478114i	$-0.841321\pi$
$7$	−12.8715	+	9.35167i	−0.694994	+	0.504943i	0.183304	+	0.983056i	$0.441321\pi$
$8$	6.47214	+	4.70228i	0.286031	+	0.207813i
$9$		0			0
$10$	23.1145			0.730945
$11$	27.0144	−	24.5198i	0.740468	−	0.672092i
$11$	27.0144	−	24.5198i	0.740468	−	0.672092i
$12$		0			0
$13$	−26.0329	−	80.1210i	−0.555402	−	1.70935i	−0.694880	−	0.719126i	$-0.744543\pi$
$13$	−26.0329	−	80.1210i	−0.555402	−	1.70935i	0.139478	−	0.990225i	$-0.455457\pi$
$14$	25.7429	+	18.7033i	0.491435	+	0.357048i
$15$		0			0
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	22.6481	−	69.7036i	0.323115	−	0.994447i	−0.649169	−	0.760645i	$-0.724883\pi$
$17$	22.6481	−	69.7036i	0.323115	−	0.994447i	0.972284	−	0.233803i	$-0.0751169\pi$
$18$		0			0
$19$	−75.6108	−	54.9344i	−0.912963	−	0.663306i	0.0287995	−	0.999585i	$-0.490832\pi$
$19$	−75.6108	−	54.9344i	−0.912963	−	0.663306i	−0.941762	+	0.336279i	$0.890832\pi$
$20$	−14.2856	−	43.9664i	−0.159717	−	0.491559i
$21$		0			0
$22$	−63.3353	−	36.2303i	−0.613779	−	0.351106i
$23$	188.856			1.71213			0.856067	−	0.516864i	$-0.172901\pi$
$23$	188.856			1.71213			0.856067	+	0.516864i	$0.172901\pi$
$24$		0			0
$25$	−6.93339	−	5.03740i	−0.0554671	−	0.0402992i
$26$	−136.310	+	99.0350i	−1.02818	+	0.747014i
$27$		0			0
$28$	19.6659	−	60.5253i	0.132732	−	0.408507i
$29$	−131.759	+	95.7284i	−0.843689	+	0.612976i	−0.923399	−	0.383842i	$-0.874601\pi$
$29$	−131.759	+	95.7284i	−0.843689	+	0.612976i	0.0797094	+	0.996818i	$0.474601\pi$
$30$		0			0
$31$	−47.5853	−	146.452i	−0.275696	−	0.848505i	−0.989034	−	0.147685i	$-0.952818\pi$
$31$	−47.5853	−	146.452i	−0.275696	−	0.848505i	0.713339	−	0.700820i	$-0.247182\pi$
$32$	−32.0000			−0.176777
$33$		0			0
$34$	−146.581			−0.739368
$35$	−56.8208	−	174.877i	−0.274414	−	0.844558i
$36$		0			0
$37$	274.834	−	199.679i	1.22115	−	0.887215i	0.224952	−	0.974370i	$-0.427777\pi$
$37$	274.834	−	199.679i	1.22115	−	0.887215i	0.996195	+	0.0871547i	$0.0277775\pi$
$38$	−57.7615	+	177.772i	−0.246583	+	0.758904i
$39$		0			0
$40$	−74.8001	+	54.3455i	−0.295673	+	0.214819i
$41$	77.9020	+	56.5991i	0.296738	+	0.215593i	0.726185	−	0.687499i	$-0.241292\pi$
$41$	77.9020	+	56.5991i	0.296738	+	0.215593i	−0.429447	+	0.903092i	$0.641292\pi$
$42$		0			0
$43$	−479.178			−1.69939			−0.849697	−	0.527271i	$-0.823215\pi$
$43$	−479.178			−1.69939			−0.849697	+	0.527271i	$0.823215\pi$
$44$	−29.7708	+	142.863i	−0.102003	+	0.489485i
$45$		0			0
$46$	−116.719	−	359.225i	−0.374115	−	1.15141i
$47$	−240.033	−	174.394i	−0.744944	−	0.541233i	0.149312	−	0.988790i	$-0.452294\pi$
$47$	−240.033	−	174.394i	−0.744944	−	0.541233i	−0.894256	+	0.447557i	$0.852294\pi$
$48$		0			0
$49$	−27.7718	+	85.4729i	−0.0809674	+	0.249192i
$50$	−5.29664	+	16.3014i	−0.0149812	+	0.0461073i
$51$		0			0
$52$	272.620	+	198.070i	0.727030	+	0.528218i
$53$	−68.1924	−	209.875i	−0.176735	−	0.543934i	0.822974	−	0.568080i	$-0.192313\pi$
$53$	−68.1924	−	209.875i	−0.176735	−	0.543934i	−0.999708	+	0.0241458i	$0.992313\pi$
$54$		0			0
$55$	173.034	+	384.501i	0.424215	+	0.942657i
$56$	−127.280			−0.303724
$57$		0			0
$58$	263.518	+	191.457i	0.596578	+	0.433440i
$59$	74.7754	−	54.3275i	0.164999	−	0.119879i	−0.502222	−	0.864739i	$-0.667484\pi$
$59$	74.7754	−	54.3275i	0.164999	−	0.119879i	0.667221	+	0.744860i	$0.267484\pi$
$60$		0			0
$61$	75.0128	−	230.866i	0.157449	−	0.484579i	−0.840952	−	0.541110i	$-0.818004\pi$
$61$	75.0128	−	230.866i	0.157449	−	0.484579i	0.998401	+	0.0565314i	$0.0180041\pi$
$62$	−249.160	+	181.025i	−0.510376	+	0.370810i
$63$		0			0
$64$	19.7771	+	60.8676i	0.0386271	+	0.118882i
$65$	973.631			1.85791
$66$		0			0
$67$	307.078			0.559934			0.279967	−	0.960010i	$-0.409676\pi$
$67$	307.078			0.559934			0.279967	+	0.960010i	$0.409676\pi$
$68$	90.5923	+	278.814i	0.161558	+	0.497224i
$69$		0			0
$70$	−297.518	+	216.159i	−0.508002	+	0.369085i
$71$	289.776	−	891.838i	0.484367	−	1.49073i	−0.348528	−	0.937298i	$-0.613318\pi$
$71$	289.776	−	891.838i	0.484367	−	1.49073i	0.832895	−	0.553430i	$-0.186682\pi$
$72$		0			0
$73$	−521.320	+	378.761i	−0.835834	+	0.607269i	−0.921204	−	0.389080i	$-0.872793\pi$
$73$	−521.320	+	378.761i	−0.835834	+	0.607269i	0.0853695	+	0.996349i	$0.472793\pi$
$74$	−549.668	−	399.357i	−0.863481	−	0.627356i
$75$		0			0
$76$	373.840			0.564242
$77$	−118.413	+	568.236i	−0.175253	+	0.840994i
$78$		0			0
$79$	−169.969	−	523.111i	−0.242064	−	0.744995i	−0.996106	−	0.0881687i	$-0.971899\pi$
$79$	−169.969	−	523.111i	−0.242064	−	0.744995i	0.754042	−	0.656826i	$-0.228101\pi$
$80$	149.600	+	108.691i	0.209073	+	0.151900i
$81$		0			0
$82$	59.5119	−	183.159i	0.0801462	−	0.246665i
$83$	−105.551	+	324.853i	−0.139587	+	0.429606i	−0.996275	−	0.0862294i	$-0.972518\pi$
$83$	−105.551	+	324.853i	−0.139587	+	0.429606i	0.856688	+	0.515835i	$0.172518\pi$
$84$		0			0
$85$	685.269	+	497.877i	0.874445	+	0.635322i
$86$	296.148	+	911.451i	0.371331	+	1.14284i
$87$		0			0
$88$	290.140	−	31.6665i	0.351466	−	0.0383598i
$89$	68.5702			0.0816677			0.0408338	−	0.999166i	$-0.486999\pi$
$89$	68.5702			0.0816677			0.0408338	+	0.999166i	$0.486999\pi$
$90$		0			0
$91$	1084.35	+	787.824i	1.24913	+	0.907543i
$92$	−611.149	+	444.026i	−0.692573	+	0.503184i
$93$		0			0
$94$	−183.369	+	564.351i	−0.201202	+	0.619238i
$95$	873.853	−	634.891i	0.943741	−	0.685668i
$96$		0			0
$97$	477.969	+	1471.04i	0.500313	+	1.53981i	0.808509	+	0.588483i	$0.200275\pi$
$97$	477.969	+	1471.04i	0.500313	+	1.53981i	−0.308196	+	0.951323i	$0.599725\pi$
$98$	179.743			0.185273
$99$		0			0
$100$	34.2806			0.0342806
$101$	−351.070	−	1080.48i	−0.345869	−	1.06448i	−0.961117	−	0.276142i	$-0.910944\pi$
$101$	−351.070	−	1080.48i	−0.345869	−	1.06448i	0.615248	−	0.788334i	$-0.289056\pi$
$102$		0			0
$103$	193.993	−	140.944i	0.185580	−	0.134831i	−0.491117	−	0.871094i	$-0.663411\pi$
$103$	193.993	−	140.944i	0.185580	−	0.134831i	0.676696	+	0.736262i	$0.263411\pi$
$104$	208.263	−	640.968i	0.196364	−	0.604347i
$105$		0			0
$106$	−357.060	+	259.419i	−0.327177	+	0.237708i
$107$	147.631	+	107.260i	0.133384	+	0.0969088i	0.652476	−	0.757809i	$-0.273730\pi$
$107$	147.631	+	107.260i	0.133384	+	0.0969088i	−0.519093	+	0.854718i	$0.673730\pi$
$108$		0			0
$109$	−711.769			−0.625460			−0.312730	−	0.949842i	$-0.601243\pi$
$109$	−711.769			−0.625460			−0.312730	+	0.949842i	$0.601243\pi$
$110$	624.424	−	566.764i	0.541241	−	0.491262i
$111$		0			0
$112$	78.6634	+	242.101i	0.0663660	+	0.204254i
$113$	284.967	+	207.041i	0.237234	+	0.172361i	0.700050	−	0.714094i	$-0.253161\pi$
$113$	284.967	+	207.041i	0.237234	+	0.172361i	−0.462816	+	0.886454i	$0.653161\pi$
$114$		0			0
$115$	−674.476	+	2075.82i	−0.546915	+	1.68323i
$116$	201.310	−	619.567i	0.161130	−	0.495908i
$117$		0			0
$118$	−149.551	−	108.655i	−0.116672	−	0.0847670i
$119$	360.331	+	1108.98i	0.277576	+	0.854290i
$120$		0			0
$121$	128.554	−	1324.78i	0.0965845	−	0.995325i
$122$	−485.493			−0.360283
$123$		0			0
$124$	498.320	+	362.050i	0.360891	+	0.262202i
$125$	−1088.62	+	790.929i	−0.778954	+	0.565943i
$126$		0			0
$127$	327.642	−	1008.38i	0.228926	−	0.704561i	−0.768944	−	0.639317i	$-0.779217\pi$
$127$	327.642	−	1008.38i	0.228926	−	0.704561i	0.997869	−	0.0652443i	$-0.0207827\pi$
$128$	103.554	−	75.2365i	0.0715077	−	0.0519534i
$129$		0			0
$130$	−601.737	−	1851.96i	−0.405968	−	1.24944i
$131$	−1131.22			−0.754469			−0.377235	−	0.926118i	$-0.623125\pi$
$131$	−1131.22			−0.754469			−0.377235	+	0.926118i	$0.623125\pi$
$132$		0			0
$133$	1486.95			0.969436
$134$	−189.785	−	584.098i	−0.122350	−	0.376555i
$135$		0			0
$136$	474.347	−	344.633i	0.299080	−	0.217295i
$137$	−178.144	+	548.271i	−0.111094	+	0.341912i	−0.991112	−	0.133028i	$-0.957530\pi$
$137$	−178.144	+	548.271i	−0.111094	+	0.341912i	0.880018	+	0.474940i	$0.157530\pi$
$138$		0			0
$139$	790.581	−	574.391i	0.482419	−	0.350498i	−0.319843	−	0.947471i	$-0.603630\pi$
$139$	790.581	−	574.391i	0.482419	−	0.350498i	0.802261	+	0.596973i	$0.203630\pi$
$140$	595.035	+	432.319i	0.359212	+	0.260983i
$141$		0			0
$142$	−1875.47			−1.10835
$143$	−2667.82	−	1526.10i	−1.56010	−	0.892438i
$144$		0			0
$145$	−581.646	−	1790.12i	−0.333125	−	1.02525i
$146$	1042.64	+	757.523i	0.591024	+	0.429404i
$147$		0			0
$148$	−419.909	+	1292.35i	−0.233218	+	0.717772i
$149$	−871.328	+	2681.67i	−0.479074	+	1.47444i	0.361310	+	0.932446i	$0.382330\pi$
$149$	−871.328	+	2681.67i	−0.479074	+	1.47444i	−0.840384	+	0.541992i	$0.817670\pi$
$150$		0			0
$151$	−1192.49	−	866.396i	−0.642673	−	0.466929i	0.218095	−	0.975928i	$-0.430016\pi$
$151$	−1192.49	−	866.396i	−0.642673	−	0.466929i	−0.860767	+	0.508999i	$0.830016\pi$
$152$	−231.046	−	711.086i	−0.123291	−	0.379452i
$153$		0			0
$154$	1154.03	−	125.954i	0.603861	−	0.0659068i
$155$	1779.69			0.922248
$156$		0			0
$157$	−2379.86	−	1729.07i	−1.20977	−	0.878949i	−0.214560	−	0.976711i	$-0.568832\pi$
$157$	−2379.86	−	1729.07i	−1.20977	−	0.878949i	−0.995210	+	0.0977620i	$0.968832\pi$
$158$	−889.970	+	646.601i	−0.448115	+	0.325575i
$159$		0			0
$160$	114.284	−	351.731i	0.0564686	−	0.173792i
$161$	−2430.85	+	1766.11i	−1.18992	+	0.864530i
$162$		0			0
$163$	−371.953	−	1144.75i	−0.178734	−	0.550087i	0.821050	−	0.570856i	$-0.193388\pi$
$163$	−371.953	−	1144.75i	−0.178734	−	0.550087i	−0.999784	+	0.0207693i	$0.993388\pi$
$164$	−385.169			−0.183394
$165$		0			0
$166$	683.142			0.319410
$167$	−1204.60	−	3707.37i	−0.558171	−	1.71787i	−0.687419	−	0.726261i	$-0.741256\pi$
$167$	−1204.60	−	3707.37i	−0.558171	−	1.71787i	0.129248	−	0.991612i	$-0.458744\pi$
$168$		0			0
$169$	−3964.25	+	2880.20i	−1.80439	+	1.31097i
$170$	523.499	−	1611.16i	0.236180	−	0.726886i
$171$		0			0
$172$	1550.65	−	1126.61i	0.687419	−	0.499439i
$173$	2536.33	+	1842.75i	1.11464	+	0.809836i	0.983389	−	0.181513i	$-0.0580994\pi$
$173$	2536.33	+	1842.75i	1.11464	+	0.809836i	0.131255	+	0.991349i	$0.458099\pi$
$174$		0			0
$175$	136.351			0.0588981
$176$	−239.550	−	532.308i	−0.102595	−	0.227979i
$177$		0			0
$178$	−42.3787	−	130.428i	−0.0178450	−	0.0549214i
$179$	187.764	+	136.419i	0.0784030	+	0.0569631i	0.626296	−	0.779585i	$-0.284570\pi$
$179$	187.764	+	136.419i	0.0784030	+	0.0569631i	−0.547893	+	0.836548i	$0.684570\pi$
$180$		0			0
$181$	834.090	−	2567.06i	0.342527	−	1.05419i	−0.620367	−	0.784311i	$-0.713016\pi$
$181$	834.090	−	2567.06i	0.342527	−	1.05419i	0.962894	−	0.269878i	$-0.0869835\pi$
$182$	828.367	−	2549.45i	0.337377	−	1.03834i
$183$		0			0
$184$	1222.30	+	888.052i	0.489723	+	0.355805i
$185$	1213.25	+	3734.00i	0.482161	+	1.48394i
$186$		0			0
$187$	−1097.30	−	2438.33i	−0.429103	−	0.953519i
$188$	1186.79			0.460401
$189$		0			0
$190$	−1747.71	−	1269.78i	−0.667326	−	0.484841i
$191$	−1608.82	+	1168.87i	−0.609476	+	0.442810i	−0.849230	−	0.528023i	$-0.822933\pi$
$191$	−1608.82	+	1168.87i	−0.609476	+	0.442810i	0.239754	+	0.970834i	$0.422933\pi$
$192$		0			0
$193$	−368.954	+	1135.52i	−0.137605	+	0.423506i	−0.995986	−	0.0895071i	$-0.971471\pi$
$193$	−368.954	+	1135.52i	−0.137605	+	0.423506i	0.858381	+	0.513013i	$0.171471\pi$
$194$	2502.68	−	1818.30i	0.926195	−	0.672920i
$195$		0			0
$196$	−111.087	−	341.892i	−0.0404837	−	0.124596i
$197$	4808.95			1.73920			0.869602	−	0.493753i	$-0.164375\pi$
$197$	4808.95			1.73920			0.869602	+	0.493753i	$0.164375\pi$
$198$		0			0
$199$	2681.69			0.955277			0.477639	−	0.878556i	$-0.341493\pi$
$199$	2681.69			0.955277			0.477639	+	0.878556i	$0.341493\pi$
$200$	−21.1866	−	65.2055i	−0.00749058	−	0.0230536i
$201$		0			0
$202$	−1838.23	+	1335.55i	−0.640283	+	0.465193i
$203$	800.709	−	2464.33i	0.276841	−	0.852030i
$204$		0			0
$205$	−900.334	+	654.131i	−0.306742	+	0.222861i
$206$	−387.986	−	281.888i	−0.131225	−	0.0953402i
$207$		0			0
$208$	−1347.91			−0.449329
$209$	−3389.56	+	369.944i	−1.12182	+	0.122438i
$210$		0			0
$211$	−791.639	−	2436.41i	−0.258288	−	0.794927i	−0.993164	−	0.116726i	$-0.962760\pi$
$211$	−791.639	−	2436.41i	−0.258288	−	0.794927i	0.734877	−	0.678201i	$-0.237240\pi$
$212$	714.120	+	518.839i	0.231349	+	0.168085i
$213$		0			0
$214$	112.780	−	347.102i	0.0360257	−	0.110876i
$215$	1711.33	−	5266.93i	0.542845	−	1.67071i
$216$		0			0
$217$	1982.07	+	1440.06i	0.620053	+	0.450495i
$218$	439.897	+	1353.86i	0.136668	+	0.420621i
$219$		0			0
$220$	−1463.97	−	837.446i	−0.448639	−	0.256639i
$221$	−6174.31			−1.87932
$222$		0			0
$223$	768.686	+	558.483i	0.230830	+	0.167708i	0.697188	−	0.716888i	$-0.254434\pi$
$223$	768.686	+	558.483i	0.230830	+	0.167708i	−0.466358	+	0.884596i	$0.654434\pi$
$224$	411.887	−	299.253i	0.122859	−	0.0892621i
$225$		0			0
$226$	217.696	−	669.999i	0.0640748	−	0.197202i
$227$	−669.479	+	486.405i	−0.195748	+	0.142220i	−0.681342	−	0.731965i	$-0.738603\pi$
$227$	−669.479	+	486.405i	−0.195748	+	0.142220i	0.485594	+	0.874185i	$0.338603\pi$
$228$		0			0
$229$	167.603	+	515.830i	0.0483648	+	0.148851i	0.972322	−	0.233644i	$-0.0750649\pi$
$229$	167.603	+	515.830i	0.0483648	+	0.148851i	−0.923958	+	0.382495i	$0.875065\pi$
$230$	4365.30			1.25148
$231$		0			0
$232$	−1302.90			−0.368706
$233$	1606.49	+	4944.28i	0.451695	+	1.39017i	0.874972	+	0.484174i	$0.160880\pi$
$233$	1606.49	+	4944.28i	0.451695	+	1.39017i	−0.423277	+	0.906000i	$0.639120\pi$
$234$		0			0
$235$	2774.12	−	2015.52i	0.770058	−	0.559480i
$236$	−114.247	+	351.615i	−0.0315120	+	0.0969839i
$237$		0			0
$238$	1886.72	−	1370.78i	0.513856	−	0.373338i
$239$	2007.38	+	1458.45i	0.543291	+	0.394724i	0.825306	−	0.564686i	$-0.191003\pi$
$239$	2007.38	+	1458.45i	0.543291	+	0.394724i	−0.282015	+	0.959410i	$0.591003\pi$
$240$		0			0
$241$	−50.4887			−0.0134949			−0.00674744	−	0.999977i	$-0.502148\pi$
$241$	−50.4887			−0.0134949			−0.00674744	+	0.999977i	$0.502148\pi$
$242$	−2599.33	+	574.233i	−0.690459	+	0.152533i
$243$		0			0
$244$	300.051	+	923.463i	0.0787246	+	0.242289i
$245$	−840.300	−	610.514i	−0.219122	−	0.159201i
$246$		0			0
$247$	−2433.03	+	7488.11i	−0.626762	+	1.92898i
$248$	380.682	−	1171.62i	0.0974732	−	0.299992i
$249$		0			0
$250$	2177.24	+	1581.86i	0.550804	+	0.400182i
$251$	343.356	+	1056.74i	0.0863443	+	0.265740i	0.984901	−	0.173116i	$-0.0553836\pi$
$251$	343.356	+	1056.74i	0.0863443	+	0.265740i	−0.898557	+	0.438857i	$0.855384\pi$
$252$		0			0
$253$	5101.82	−	4630.71i	1.26778	−	1.15071i
$254$	−2120.55			−0.523838
$255$		0			0
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$	−6015.54	+	4370.55i	−1.46007	+	1.06081i	−0.476731	+	0.879049i	$0.658178\pi$
$257$	−6015.54	+	4370.55i	−1.46007	+	1.06081i	−0.983344	+	0.181756i	$0.941822\pi$
$258$		0			0
$259$	−1670.19	+	5140.31i	−0.400697	+	1.23322i
$260$	−3150.74	+	2289.14i	−0.751540	+	0.546026i
$261$		0			0
$262$	699.134	+	2151.71i	0.164858	+	0.507379i
$263$	6483.45			1.52010			0.760051	−	0.649864i	$-0.225174\pi$
$263$	6483.45			1.52010			0.760051	+	0.649864i	$0.225174\pi$
$264$		0			0
$265$	2550.40			0.591207
$266$	−918.986	−	2828.35i	−0.211829	−	0.651944i
$267$		0			0
$268$	−993.727	+	721.985i	−0.226498	+	0.164561i
$269$	1138.17	−	3502.91i	0.257975	−	0.793964i	−0.735254	−	0.677791i	$-0.762937\pi$
$269$	1138.17	−	3502.91i	0.257975	−	0.793964i	0.993229	−	0.116173i	$-0.0370627\pi$
$270$		0			0
$271$	−2734.55	+	1986.76i	−0.612959	+	0.445341i	−0.850455	−	0.526048i	$-0.823673\pi$
$271$	−2734.55	+	1986.76i	−0.612959	+	0.445341i	0.237496	+	0.971388i	$0.423673\pi$
$272$	−948.694	−	689.267i	−0.211482	−	0.153651i
$273$		0			0
$274$	1152.97			0.254210
$275$	−310.818	+	33.9233i	−0.0681564	+	0.00743874i
$276$		0			0
$277$	2633.55	+	8105.22i	0.571244	+	1.75811i	0.648628	+	0.761106i	$0.275343\pi$
$277$	2633.55	+	8105.22i	0.571244	+	1.75811i	−0.0773843	+	0.997001i	$0.524657\pi$
$278$	−1581.16	−	1148.78i	−0.341122	−	0.247839i
$279$		0			0
$280$	454.567	−	1399.01i	0.0970198	−	0.298596i
$281$	857.842	−	2640.17i	0.182116	−	0.560495i	−0.817771	−	0.575544i	$-0.804790\pi$
$281$	857.842	−	2640.17i	0.182116	−	0.560495i	0.999887	+	0.0150487i	$0.00479035\pi$
$282$		0			0
$283$	−2868.69	−	2084.22i	−0.602564	−	0.437789i	0.244224	−	0.969719i	$-0.421467\pi$
$283$	−2868.69	−	2084.22i	−0.602564	−	0.437789i	−0.846788	+	0.531930i	$0.821467\pi$
$284$	1159.10	+	3567.35i	0.242184	+	0.745364i
$285$		0			0
$286$	−1254.01	+	6017.67i	−0.259269	+	1.24417i
$287$	−1532.01			−0.315093
$288$		0			0
$289$	−370.953	−	269.513i	−0.0755045	−	0.0548572i
$290$	−3045.54	+	2212.71i	−0.616691	+	0.448052i
$291$		0			0
$292$	796.506	−	2451.39i	0.159630	−	0.491291i
$293$	3349.09	−	2433.25i	0.667767	−	0.485161i	−0.201510	−	0.979486i	$-0.564585\pi$
$293$	3349.09	−	2433.25i	0.667767	−	0.485161i	0.869277	+	0.494325i	$0.164585\pi$
$294$		0			0
$295$	330.094	+	1015.93i	0.0651486	+	0.200507i
$296$	2717.71			0.533661
$297$		0			0
$298$	5639.35			1.09624
$299$	−4916.45	−	15131.3i	−0.950923	−	2.92664i
$300$		0			0
$301$	6167.72	−	4481.11i	1.18107	−	0.858097i
$302$	−910.982	+	2803.71i	−0.173580	+	0.534224i
$303$		0			0
$304$	−1209.77	+	878.951i	−0.228241	+	0.165827i
$305$	2269.68	+	1649.02i	0.426104	+	0.309583i
$306$		0			0
$307$	3752.14			0.697545			0.348772	−	0.937208i	$-0.386599\pi$
$307$	3752.14			0.697545			0.348772	+	0.937208i	$0.386599\pi$
$308$	−952.810	−	2117.26i	−0.176271	−	0.391695i
$309$		0			0
$310$	−1099.91	−	3385.18i	−0.201519	−	0.620210i
$311$	−1380.12	−	1002.71i	−0.251638	−	0.182825i	0.454815	−	0.890586i	$-0.349705\pi$
$311$	−1380.12	−	1002.71i	−0.251638	−	0.182825i	−0.706452	+	0.707761i	$0.749705\pi$
$312$		0			0
$313$	−1098.85	+	3381.92i	−0.198437	+	0.610727i	0.801482	+	0.598019i	$0.204045\pi$
$313$	−1098.85	+	3381.92i	−0.198437	+	0.610727i	−0.999919	+	0.0127083i	$0.995955\pi$
$314$	−1818.05	+	5595.39i	−0.326748	+	1.00563i
$315$		0			0
$316$	1779.94	+	1293.20i	0.316865	+	0.230216i
$317$	3182.71	+	9795.38i	0.563908	+	1.73553i	0.671173	+	0.741301i	$0.265791\pi$
$317$	3182.71	+	9795.38i	0.563908	+	1.73553i	−0.107265	+	0.994230i	$0.534209\pi$
$318$		0			0
$319$	−1212.14	+	5816.75i	−0.212748	+	1.02093i
$320$	−739.664			−0.129214
$321$		0			0
$322$	4861.70	+	3532.23i	0.841403	+	0.611315i
$323$	−5541.56	+	4026.18i	−0.954616	+	0.693569i
$324$		0			0
$325$	−223.105	+	686.648i	−0.0380790	+	0.117195i
$326$	−1947.57	+	1414.99i	−0.330878	+	0.240397i
$327$		0			0
$328$	238.047	+	732.635i	0.0400731	+	0.123332i
$329$	4720.45			0.791023
$330$		0			0
$331$	−6577.14			−1.09218			−0.546091	−	0.837726i	$-0.683885\pi$
$331$	−6577.14			−1.09218			−0.546091	+	0.837726i	$0.683885\pi$
$332$	−422.205	−	1299.41i	−0.0697937	−	0.214803i
$333$		0			0
$334$	−6307.35	+	4582.56i	−1.03330	+	0.750738i
$335$	−1096.70	+	3375.28i	−0.178862	+	0.550482i
$336$		0			0
$337$	−531.574	+	386.211i	−0.0859249	+	0.0624281i	−0.629918	−	0.776661i	$-0.716912\pi$
$337$	−531.574	+	386.211i	−0.0859249	+	0.0624281i	0.543993	+	0.839089i	$0.316912\pi$
$338$	7928.50	+	5760.39i	1.27590	+	0.926994i
$339$		0			0
$340$	−3388.16			−0.540437
$341$	−4876.48	−	2789.54i	−0.774417	−	0.442997i
$342$		0			0
$343$	−2128.20	−	6549.92i	−0.335020	−	1.03109i
$344$	−3101.30	−	2253.23i	−0.486079	−	0.353157i
$345$		0			0
$346$	1937.58	−	5963.26i	0.301055	−	0.926552i
$347$	3379.87	−	10402.2i	0.522884	−	1.60927i	−0.245579	−	0.969377i	$-0.578978\pi$
$347$	3379.87	−	10402.2i	0.522884	−	1.60927i	0.768463	−	0.639895i	$-0.221022\pi$
$348$		0			0
$349$	−4345.06	−	3156.87i	−0.666434	−	0.484193i	0.202396	−	0.979304i	$-0.435127\pi$
$349$	−4345.06	−	3156.87i	−0.666434	−	0.484193i	−0.868830	+	0.495111i	$0.835127\pi$
$350$	−84.2696	−	259.355i	−0.0128697	−	0.0396089i
$351$		0			0
$352$	−864.460	+	784.635i	−0.130897	+	0.118810i
$353$	6918.39			1.04314			0.521571	−	0.853208i	$-0.325346\pi$
$353$	6918.39			1.04314			0.521571	+	0.853208i	$0.325346\pi$
$354$		0			0
$355$	8767.83	+	6370.20i	1.31084	+	0.952381i
$356$	−221.898	+	161.218i	−0.0330353	+	0.0240015i
$357$		0			0
$358$	143.439	−	441.460i	0.0211759	−	0.0651728i
$359$	1121.48	−	814.805i	0.164873	−	0.119788i	−0.502289	−	0.864700i	$-0.667509\pi$
$359$	1121.48	−	814.805i	0.164873	−	0.119788i	0.667163	+	0.744912i	$0.267509\pi$
$360$		0			0
$361$	579.647	+	1783.97i	0.0845090	+	0.260092i
$362$	−5398.34			−0.783786
$363$		0			0
$364$	−5361.30			−0.772002
$365$	−2301.36	−	7082.85i	−0.330023	−	1.01571i
$366$		0			0
$367$	3052.78	−	2217.97i	0.434206	−	0.315469i	−0.349122	−	0.937077i	$-0.613520\pi$
$367$	3052.78	−	2217.97i	0.434206	−	0.315469i	0.783329	+	0.621608i	$0.213520\pi$
$368$	933.753	−	2873.80i	0.132270	−	0.407084i
$369$		0			0
$370$	6352.65	−	4615.47i	0.892591	−	0.648505i
$371$	2840.41	+	2063.68i	0.397485	+	0.288790i
$372$		0			0
$373$	1267.21			0.175908			0.0879541	−	0.996125i	$-0.471967\pi$
$373$	1267.21			0.175908			0.0879541	+	0.996125i	$0.471967\pi$
$374$	−3959.81	+	3594.15i	−0.547478	+	0.496923i
$375$		0			0
$376$	−733.475	−	2257.40i	−0.100601	−	0.309619i
$377$	11099.9	+	8064.56i	1.51638	+	1.10171i
$378$		0			0
$379$	3963.80	−	12199.3i	0.537221	−	1.65340i	−0.201578	−	0.979472i	$-0.564607\pi$
$379$	3963.80	−	12199.3i	0.537221	−	1.65340i	0.738800	−	0.673925i	$-0.235393\pi$
$380$	−1335.13	+	4109.10i	−0.180239	+	0.554717i
$381$		0			0
$382$	3217.64	+	2337.75i	0.430965	+	0.313114i
$383$	554.925	+	1707.88i	0.0740348	+	0.227856i	0.981225	−	0.192864i	$-0.0617776\pi$
$383$	554.925	+	1707.88i	0.0740348	+	0.227856i	−0.907191	+	0.420720i	$0.861778\pi$
$384$		0			0
$385$	−5822.93	−	3330.94i	−0.770815	−	0.440937i
$386$	2387.92			0.314875
$387$		0			0
$388$	−5005.36	−	3636.60i	−0.654919	−	0.475826i
$389$	−4087.27	+	2969.57i	−0.532732	+	0.387052i	−0.821379	−	0.570383i	$-0.806795\pi$
$389$	−4087.27	+	2969.57i	−0.532732	+	0.387052i	0.288647	+	0.957436i	$0.406795\pi$
$390$		0			0
$391$	4277.21	−	13163.9i	0.553217	−	1.70263i
$392$	−581.661	+	422.601i	−0.0749447	+	0.0544505i
$393$		0			0
$394$	−2972.09	−	9147.16i	−0.380030	−	1.16961i
$395$	6356.85			0.809742
$396$		0			0
$397$	−9769.86			−1.23510			−0.617550	−	0.786531i	$-0.711875\pi$
$397$	−9769.86			−1.23510			−0.617550	+	0.786531i	$0.711875\pi$
$398$	−1657.38	−	5100.88i	−0.208736	−	0.642422i
$399$		0			0
$400$	−110.934	+	80.5984i	−0.0138668	+	0.0100748i
$401$	4571.55	−	14069.8i	0.569307	−	1.75215i	−0.0854861	−	0.996339i	$-0.527244\pi$
$401$	4571.55	−	14069.8i	0.569307	−	1.75215i	0.654793	−	0.755808i	$-0.272756\pi$
$402$		0			0
$403$	−10495.1	+	7625.16i	−1.29727	+	0.942522i
$404$	3676.45	+	2671.10i	0.452749	+	0.328941i
$405$		0			0
$406$	−5182.30			−0.633481
$407$	2528.38	−	12133.1i	0.307929	−	1.47768i
$408$		0			0
$409$	−585.175	−	1800.98i	−0.0707458	−	0.217733i	0.909432	−	0.415852i	$-0.136517\pi$
$409$	−585.175	−	1800.98i	−0.0707458	−	0.217733i	−0.980178	+	0.198119i	$0.936517\pi$
$410$	1800.67	+	1308.26i	0.216899	+	0.157586i
$411$		0			0
$412$	−296.395	+	912.209i	−0.0354425	+	0.109081i
$413$	−454.416	+	1398.55i	−0.0541413	+	0.166630i
$414$		0			0
$415$	−3193.69	−	2320.35i	−0.377764	−	0.274462i
$416$	833.052	+	2563.87i	0.0981821	+	0.302173i
$417$		0			0
$418$	2798.54	+	6218.69i	0.327467	+	0.727670i
$419$	1889.23			0.220274			0.110137	−	0.993916i	$-0.464871\pi$
$419$	1889.23			0.220274			0.110137	+	0.993916i	$0.464871\pi$
$420$		0			0
$421$	−5023.57	−	3649.84i	−0.581554	−	0.422523i	0.257730	−	0.966217i	$-0.417025\pi$
$421$	−5023.57	−	3649.84i	−0.581554	−	0.422523i	−0.839284	+	0.543693i	$0.817025\pi$
$422$	−4145.08	+	3011.57i	−0.478150	+	0.347396i
$423$		0			0
$424$	545.539	−	1679.00i	0.0624852	−	0.192310i
$425$	−508.153	+	369.195i	−0.0579977	+	0.0421378i
$426$		0			0
$427$	1193.45	+	3673.07i	0.135258	+	0.416282i
$428$	−729.929			−0.0824356
$429$		0			0
$430$	−11076.0			−1.24216
$431$	389.384	+	1198.40i	0.0435174	+	0.133933i	0.970455	−	0.241284i	$-0.0775684\pi$
$431$	389.384	+	1198.40i	0.0435174	+	0.133933i	−0.926937	+	0.375216i	$0.877568\pi$
$432$		0			0
$433$	7649.88	−	5557.96i	0.849029	−	0.616856i	−0.0758489	−	0.997119i	$-0.524167\pi$
$433$	7649.88	−	5557.96i	0.849029	−	0.616856i	0.924878	+	0.380263i	$0.124167\pi$
$434$	1514.17	−	4660.12i	0.167471	−	0.515422i
$435$		0			0
$436$	2303.33	−	1673.47i	0.253004	−	0.183818i
$437$	−14279.5	−	10374.7i	−1.56312	−	1.13567i
$438$		0			0
$439$	5992.08			0.651449			0.325725	−	0.945465i	$-0.394392\pi$
$439$	5992.08			0.651449			0.325725	+	0.945465i	$0.394392\pi$
$440$	−688.137	+	3302.20i	−0.0745582	+	0.357787i
$441$		0			0
$442$	3815.94	+	11744.2i	0.410646	+	1.26384i
$443$	9269.03	+	6734.35i	0.994097	+	0.722254i	0.960815	−	0.277192i	$-0.0894038\pi$
$443$	9269.03	+	6734.35i	0.994097	+	0.722254i	0.0332827	+	0.999446i	$0.489404\pi$
$444$		0			0
$445$	−244.891	+	753.696i	−0.0260875	+	0.0802890i
$446$	587.224	−	1807.29i	0.0623450	−	0.191878i
$447$		0			0
$448$	−823.774	−	598.507i	−0.0868743	−	0.0631178i
$449$	2971.25	+	9144.58i	0.312299	+	0.961157i	0.976852	+	0.213916i	$0.0686218\pi$
$449$	2971.25	+	9144.58i	0.312299	+	0.961157i	−0.664553	+	0.747241i	$0.731378\pi$
$450$		0			0
$451$	3492.28	−	381.155i	0.364623	−	0.0397958i
$452$	−1408.96			−0.146619
$453$		0			0
$454$	1338.96	+	972.810i	0.138415	+	0.100564i
$455$	−12532.1	+	9105.08i	−1.29124	+	0.938138i
$456$		0			0
$457$	−2140.15	+	6586.70i	−0.219063	+	0.674207i	0.779777	+	0.626057i	$0.215332\pi$
$457$	−2140.15	+	6586.70i	−0.219063	+	0.674207i	−0.998840	+	0.0481496i	$0.984668\pi$
$458$	877.582	−	637.601i	0.0895343	−	0.0650505i
$459$		0			0
$460$	−2697.91	−	8303.30i	−0.273458	−	0.841616i
$461$	4385.77			0.443092			0.221546	−	0.975150i	$-0.428890\pi$
$461$	4385.77			0.443092			0.221546	+	0.975150i	$0.428890\pi$
$462$		0			0
$463$	644.748			0.0647171			0.0323585	−	0.999476i	$-0.489698\pi$
$463$	644.748			0.0647171			0.0323585	+	0.999476i	$0.489698\pi$
$464$	805.238	+	2478.27i	0.0805652	+	0.247954i
$465$		0			0
$466$	8411.71	−	6111.47i	0.836191	−	0.607528i
$467$	3932.12	−	12101.8i	0.389630	−	1.19916i	−0.543436	−	0.839451i	$-0.682877\pi$
$467$	3932.12	−	12101.8i	0.389630	−	1.19916i	0.933066	−	0.359706i	$-0.117123\pi$
$468$		0			0
$469$	−3952.55	+	2871.70i	−0.389151	+	0.282735i
$470$	−5548.24	−	4031.03i	−0.544513	−	0.395612i
$471$		0			0
$472$	739.420			0.0721071
$473$	−12944.7	+	11749.4i	−1.25835	+	1.14215i
$474$		0			0
$475$	247.512	+	761.764i	0.0239087	+	0.0735834i
$476$	−3773.43	−	2741.56i	−0.363351	−	0.263990i
$477$		0			0
$478$	1533.50	−	4719.63i	0.146738	−	0.451613i
$479$	−2722.22	+	8378.13i	−0.259669	+	0.799179i	0.733205	+	0.680008i	$0.238024\pi$
$479$	−2722.22	+	8378.13i	−0.259669	+	0.799179i	−0.992874	+	0.119171i	$0.961976\pi$
$480$		0			0
$481$	−23153.2	−	16821.8i	−2.19479	−	1.59461i
$482$	31.2037	+	96.0353i	0.00294874	+	0.00907528i
$483$		0			0
$484$	2698.73	+	4589.32i	0.253449	+	0.431003i
$485$	−17876.1			−1.67363
$486$		0			0
$487$	−11476.2	−	8337.92i	−1.06783	−	0.775826i	−0.0923115	−	0.995730i	$-0.529426\pi$
$487$	−11476.2	−	8337.92i	−1.06783	−	0.775826i	−0.975521	+	0.219904i	$0.929426\pi$
$488$	1571.09	−	1141.46i	0.145737	−	0.105884i
$489$		0			0
$490$	−641.932	+	1975.66i	−0.0591827	+	0.182146i
$491$	−9967.98	+	7242.16i	−0.916189	+	0.665650i	−0.942572	−	0.334002i	$-0.891601\pi$
$491$	−9967.98	+	7242.16i	−0.916189	+	0.665650i	0.0263837	+	0.999652i	$0.491601\pi$
$492$		0			0
$493$	3688.53	+	11352.1i	0.336963	+	1.03707i
$494$	15746.9			1.43419
$495$		0			0
$496$	−2463.83			−0.223043
$497$	4610.34	+	14189.2i	0.416100	+	1.28063i
$498$		0			0
$499$	1941.02	−	1410.23i	0.174132	−	0.126515i	−0.497305	−	0.867576i	$-0.665677\pi$
$499$	1941.02	−	1410.23i	0.174132	−	0.126515i	0.671438	+	0.741061i	$0.265677\pi$
$500$	1663.26	−	5119.00i	0.148767	−	0.457858i
$501$		0			0
$502$	1797.83	−	1306.20i	0.159843	−	0.116133i
$503$	4698.43	+	3413.61i	0.416486	+	0.302595i	0.776222	−	0.630459i	$-0.217133\pi$
$503$	4698.43	+	3413.61i	0.416486	+	0.302595i	−0.359736	+	0.933054i	$0.617133\pi$
$504$		0			0
$505$	13130.0			1.15699
$506$	−11961.2	−	6842.29i	−1.05087	−	0.601141i
$507$		0			0
$508$	1310.57	+	4033.52i	0.114463	+	0.352280i
$509$	−11674.6	−	8482.10i	−1.01664	−	0.738630i	−0.0510462	−	0.998696i	$-0.516256\pi$
$509$	−11674.6	−	8482.10i	−1.01664	−	0.738630i	−0.965591	+	0.260066i	$0.916256\pi$
$510$		0			0
$511$	3168.11	−	9750.43i	0.274264	−	0.844097i
$512$	−158.217	+	486.941i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	12031.1	+	8741.09i	1.03243	+	0.750103i
$515$	856.378	+	2635.66i	0.0732748	+	0.225517i
$516$		0			0
$517$	−10760.4	+	1174.42i	−0.915366	+	0.0999051i
$518$	10809.7			0.916893
$519$		0			0
$520$	6301.47	+	4578.29i	0.531419	+	0.386099i
$521$	1760.57	−	1279.13i	0.148046	−	0.107562i	−0.511297	−	0.859404i	$-0.670835\pi$
$521$	1760.57	−	1279.13i	0.148046	−	0.107562i	0.659343	+	0.751843i	$0.270835\pi$
$522$		0			0
$523$	−1338.10	+	4118.25i	−0.111876	+	0.344318i	−0.991283	−	0.131753i	$-0.957939\pi$
$523$	−1338.10	+	4118.25i	−0.111876	+	0.344318i	0.879407	+	0.476071i	$0.157939\pi$
$524$	3660.72	−	2659.67i	0.305189	−	0.221733i
$525$		0			0
$526$	−4006.99	−	12332.3i	−0.332154	−	1.02227i
$527$	−11286.0			−0.932875
$528$		0			0
$529$	23499.4			1.93141
$530$	−1576.23	−	4851.15i	−0.129183	−	0.397586i
$531$		0			0
$532$	−4811.87	+	3496.03i	−0.392145	+	0.284910i
$533$	2506.76	−	7715.03i	0.203715	−	0.626970i
$534$		0			0
$535$	−1706.21	+	1239.63i	−0.137880	+	0.100176i
$536$	1987.45	+	1443.97i	0.160158	+	0.116362i
$537$		0			0
$538$	−7366.36			−0.590309
$539$	1345.54	+	2989.96i	0.107526	+	0.238936i
$540$		0			0
$541$	2986.67	+	9192.01i	0.237351	+	0.730491i	0.996801	+	0.0799252i	$0.0254681\pi$
$541$	2986.67	+	9192.01i	0.237351	+	0.730491i	−0.759450	+	0.650566i	$0.774532\pi$
$542$	5469.09	+	3973.53i	0.433427	+	0.314903i
$543$		0			0
$544$	−724.738	+	2230.51i	−0.0571193	+	0.175795i
$545$	2542.00	−	7823.48i	0.199793	−	0.614901i
$546$		0			0
$547$	4382.88	+	3184.35i	0.342593	+	0.248908i	0.745755	−	0.666220i	$-0.232089\pi$
$547$	4382.88	+	3184.35i	0.342593	+	0.248908i	−0.403162	+	0.915129i	$0.632089\pi$
$548$	−712.576	−	2193.08i	−0.0555470	−	0.170956i
$549$		0			0
$550$	256.622	+	570.244i	0.0198953	+	0.0442096i
$551$	15221.2			1.17685
$552$		0			0
$553$	7079.71	+	5143.71i	0.544412	+	0.395539i
$554$	13789.4	−	10018.6i	1.05750	−	0.768321i
$555$		0			0
$556$	−1207.90	+	3717.53i	−0.0921338	+	0.283559i
$557$	6047.75	−	4393.95i	0.460056	−	0.334251i	−0.333497	−	0.942751i	$-0.608229\pi$
$557$	6047.75	−	4393.95i	0.460056	−	0.334251i	0.793553	+	0.608501i	$0.208229\pi$
$558$		0			0
$559$	12474.4	+	38392.2i	0.943846	+	2.90486i
$560$	−2942.02			−0.222005
$561$		0			0
$562$	−5552.07			−0.416726
$563$	−2839.59	−	8739.34i	−0.212565	−	0.654209i	−0.999317	−	0.0369397i	$-0.988239\pi$
$563$	−2839.59	−	8739.34i	−0.212565	−	0.654209i	0.786752	−	0.617269i	$-0.211761\pi$
$564$		0			0
$565$	−3293.44	+	2392.82i	−0.245232	+	0.178171i
$566$	−2191.48	+	6744.69i	−0.162747	+	0.500884i
$567$		0			0
$568$	6069.14	−	4409.49i	0.448337	−	0.325736i
$569$	10073.3	+	7318.69i	0.742171	+	0.539219i	0.893390	−	0.449282i	$-0.148320\pi$
$569$	10073.3	+	7318.69i	0.742171	+	0.539219i	−0.151219	+	0.988500i	$0.548320\pi$
$570$		0			0
$571$	20045.5			1.46914			0.734570	−	0.678532i	$-0.237384\pi$
$571$	20045.5			1.46914			0.734570	+	0.678532i	$0.237384\pi$
$572$	12221.3	−	1333.86i	0.893354	−	0.0975027i
$573$		0			0
$574$	946.834	+	2914.06i	0.0688503	+	0.211900i
$575$	−1309.41	−	951.341i	−0.0949672	−	0.0689977i
$576$		0			0
$577$	−2871.67	+	8838.08i	−0.207191	+	0.637667i	0.792426	+	0.609969i	$0.208818\pi$
$577$	−2871.67	+	8838.08i	−0.207191	+	0.637667i	−0.999616	+	0.0276988i	$0.991182\pi$
$578$	−283.383	+	872.164i	−0.0203931	+	0.0627634i
$579$		0			0
$580$	6091.08	+	4425.43i	0.436066	+	0.316821i
$581$	−1679.32	−	5168.42i	−0.119914	−	0.369057i
$582$		0			0
$583$	−6988.27	−	3997.57i	−0.496440	−	0.283983i
$584$	−5155.10			−0.365273
$585$		0			0
$586$	−6698.17	−	4866.51i	−0.472183	−	0.343061i
$587$	−14299.5	+	10389.2i	−1.00546	+	0.730508i	−0.963251	−	0.268601i	$-0.913439\pi$
$587$	−14299.5	+	10389.2i	−1.00546	+	0.730508i	−0.0422062	+	0.999109i	$0.513439\pi$
$588$		0			0
$589$	−4447.32	+	13687.5i	−0.311118	+	0.957524i
$590$	1728.40	−	1255.75i	0.120605	−	0.0876247i
$591$		0			0
$592$	−1679.64	−	5169.39i	−0.116609	−	0.358886i
$593$	11433.4			0.791760			0.395880	−	0.918302i	$-0.370440\pi$
$593$	11433.4			0.791760			0.395880	+	0.918302i	$0.370440\pi$
$594$		0			0
$595$	−13476.4			−0.928535
$596$	−3485.31	−	10726.7i	−0.239537	−	0.737219i
$597$		0			0
$598$	−25742.9	+	18703.3i	−1.76038	+	1.27899i
$599$	−7948.27	+	24462.2i	−0.542166	+	1.66862i	0.185469	+	0.982650i	$0.440620\pi$
$599$	−7948.27	+	24462.2i	−0.542166	+	1.66862i	−0.727635	+	0.685965i	$0.759380\pi$
$600$		0			0
$601$	21698.8	−	15765.1i	1.47273	−	1.07000i	0.492919	−	0.870075i	$-0.335930\pi$
$601$	21698.8	−	15765.1i	1.47273	−	1.07000i	0.979811	−	0.199925i	$-0.0640700\pi$
$602$	−12335.4	−	8962.23i	−0.835142	−	0.606766i
$603$		0			0
$604$	5896.00			0.397193
$605$	14102.3	+	6144.31i	0.947670	+	0.412895i
$606$		0			0
$607$	7962.24	+	24505.3i	0.532417	+	1.63861i	0.749164	+	0.662384i	$0.230455\pi$
$607$	7962.24	+	24505.3i	0.532417	+	1.63861i	−0.216747	+	0.976228i	$0.569545\pi$
$608$	2419.54	+	1757.90i	0.161391	+	0.117257i
$609$		0			0
$610$	1733.88	−	5336.35i	0.115087	−	0.354201i
$611$	−7723.87	+	23771.6i	−0.511415	+	1.57397i
$612$		0			0
$613$	3611.04	+	2623.57i	0.237926	+	0.172863i	0.700359	−	0.713791i	$-0.253023\pi$
$613$	3611.04	+	2623.57i	0.237926	+	0.172863i	−0.462433	+	0.886654i	$0.653023\pi$
$614$	−2318.95	−	7137.00i	−0.152419	−	0.469098i
$615$		0			0
$616$	−3438.39	+	3120.89i	−0.224897	+	0.204130i
$617$	3826.92			0.249702			0.124851	−	0.992176i	$-0.460155\pi$
$617$	3826.92			0.249702			0.124851	+	0.992176i	$0.460155\pi$
$618$		0			0
$619$	−13548.8	−	9843.81i	−0.879764	−	0.639186i	0.0534247	−	0.998572i	$-0.482986\pi$
$619$	−13548.8	−	9843.81i	−0.879764	−	0.639186i	−0.933189	+	0.359386i	$0.882986\pi$
$620$	−5759.21	+	4184.31i	−0.373057	+	0.271042i
$621$		0			0
$622$	−1054.32	+	3244.85i	−0.0679650	+	0.209175i
$623$	−882.599	+	641.246i	−0.0567586	+	0.0412375i
$624$		0			0
$625$	−5136.73	−	15809.2i	−0.328751	−	1.01179i
$626$	7111.93			0.454073
$627$		0			0
$628$	11766.7			0.747679
$629$	−7693.85	−	23679.2i	−0.487717	−	1.50104i
$630$		0			0
$631$	16219.8	−	11784.3i	1.02329	−	0.743467i	0.0563384	−	0.998412i	$-0.482057\pi$
$631$	16219.8	−	11784.3i	1.02329	−	0.743467i	0.966956	+	0.254945i	$0.0820574\pi$
$632$	1359.75	−	4184.89i	0.0855824	−	0.263395i
$633$		0			0
$634$	16664.9	−	12107.8i	1.04392	−	0.758455i
$635$	9913.57	+	7202.63i	0.619540	+	0.450122i
$636$		0			0
$637$	7571.15			0.470926
$638$	11813.3	−	1289.33i	0.733058	−	0.0800077i
$639$		0			0
$640$	457.138	+	1406.93i	0.0282343	+	0.0868962i
$641$	−12431.4	−	9031.94i	−0.766007	−	0.556537i	0.134740	−	0.990881i	$-0.456980\pi$
$641$	−12431.4	−	9031.94i	−0.766007	−	0.556537i	−0.900747	+	0.434344i	$0.856980\pi$
$642$		0			0
$643$	−7327.24	+	22550.9i	−0.449390	+	1.38308i	0.428206	+	0.903681i	$0.359146\pi$
$643$	−7327.24	+	22550.9i	−0.449390	+	1.38308i	−0.877596	+	0.479400i	$0.840854\pi$
$644$	3714.01	−	11430.5i	0.227255	−	0.699419i
$645$		0			0
$646$	11083.1	+	8052.36i	0.675015	+	0.490427i
$647$	3001.92	+	9238.95i	0.182407	+	0.561392i	0.999894	−	0.0145553i	$-0.00463327\pi$
$647$	3001.92	+	9238.95i	0.182407	+	0.561392i	−0.817487	+	0.575947i	$0.804633\pi$
$648$		0			0
$649$	687.909	−	3301.11i	0.0416068	−	0.199661i
$650$	1443.97			0.0871340
$651$		0			0
$652$	3895.15	+	2829.99i	0.233966	+	0.169986i
$653$	13582.8	−	9868.46i	0.813989	−	0.591398i	−0.100995	−	0.994887i	$-0.532203\pi$
$653$	13582.8	−	9868.46i	0.813989	−	0.591398i	0.914984	+	0.403489i	$0.132203\pi$
$654$		0			0
$655$	4040.04	−	12434.0i	0.241004	−	0.741733i
$656$	1246.43	−	905.586i	0.0741845	−	0.0538982i
$657$		0			0
$658$	−2917.40	−	8978.83i	−0.172845	−	0.531962i
$659$	−14946.6			−0.883517			−0.441759	−	0.897134i	$-0.645645\pi$
$659$	−14946.6			−0.883517			−0.441759	+	0.897134i	$0.645645\pi$
$660$		0			0
$661$	1035.71			0.0609448			0.0304724	−	0.999536i	$-0.490299\pi$
$661$	1035.71			0.0609448			0.0304724	+	0.999536i	$0.490299\pi$
$662$	4064.89	+	12510.5i	0.238650	+	0.734491i
$663$		0			0
$664$	−2210.69	+	1606.16i	−0.129204	+	0.0938723i
$665$	−5310.48	+	16344.0i	−0.309671	+	0.953070i
$666$		0			0
$667$	−24883.4	+	18078.8i	−1.44451	+	1.04950i
$668$	12614.7	+	9165.12i	0.730655	+	0.530852i
$669$		0			0
$670$	7097.97			0.409281
$671$	−3634.37	−	8076.00i	−0.209096	−	0.464635i
$672$		0			0
$673$	2340.39	+	7202.98i	0.134050	+	0.412563i	0.995441	−	0.0953794i	$-0.0304064\pi$
$673$	2340.39	+	7202.98i	0.134050	+	0.412563i	−0.861391	+	0.507942i	$0.830406\pi$
$674$	1063.15	+	772.422i	0.0607581	+	0.0441433i
$675$		0			0
$676$	6056.83	−	18641.0i	0.344608	−	1.06059i
$677$	8875.14	−	27314.9i	0.503839	−	1.55066i	−0.298874	−	0.954293i	$-0.596611\pi$
$677$	8875.14	−	27314.9i	0.503839	−	1.55066i	0.802713	−	0.596365i	$-0.203389\pi$
$678$		0			0
$679$	−19908.8	−	14464.6i	−1.12523	−	0.817527i
$680$	2094.00	+	6444.66i	0.118090	+	0.363443i
$681$		0			0
$682$	−2292.19	+	10999.6i	−0.128699	+	0.617593i
$683$	−10626.4			−0.595326			−0.297663	−	0.954671i	$-0.596207\pi$
$683$	−10626.4			−0.595326			−0.297663	+	0.954671i	$0.596207\pi$
$684$		0			0
$685$	−5390.15	−	3916.18i	−0.300653	−	0.218437i
$686$	−11143.4	+	8096.14i	−0.620199	+	0.450601i
$687$		0			0
$688$	−2369.19	+	7291.60i	−0.131285	+	0.404055i
$689$	−15040.1	+	10927.3i	−0.831615	+	0.604204i
$690$		0			0
$691$	−9042.22	−	27829.1i	−0.497804	−	1.53208i	−0.812541	−	0.582903i	$-0.801917\pi$
$691$	−9042.22	−	27829.1i	−0.497804	−	1.53208i	0.314738	−	0.949179i	$-0.398083\pi$
$692$	−12540.3			−0.688887
$693$		0			0
$694$	−21875.0			−1.19649
$695$	3490.00	+	10741.1i	0.190480	+	0.586236i
$696$		0			0
$697$	5709.49	−	4148.19i	0.310276	−	0.225429i
$698$	−3319.33	+	10215.8i	−0.179998	+	0.553976i
$699$		0			0
$700$	−441.241	+	320.580i	−0.0238248	+	0.0173097i
$701$	−17034.1	−	12376.0i	−0.917785	−	0.666810i	0.0251863	−	0.999683i	$-0.491982\pi$
$701$	−17034.1	−	12376.0i	−0.917785	−	0.666810i	−0.942972	+	0.332873i	$0.891982\pi$
$702$		0			0
$703$	−31749.6			−1.70336
$704$	2026.73	+	1159.37i	0.108502	+	0.0620673i
$705$		0			0
$706$	−4275.80	−	13159.6i	−0.227935	−	0.701511i
$707$	14623.1	+	10624.3i	0.777876	+	0.565160i
$708$		0			0
$709$	136.765	−	420.920i	0.00724446	−	0.0222962i	−0.947369	−	0.320144i	$-0.896269\pi$
$709$	136.765	−	420.920i	0.00724446	−	0.0222962i	0.954613	+	0.297848i	$0.0962688\pi$
$710$	6698.03	−	20614.4i	0.354046	−	1.08964i
$711$		0			0
$712$	443.796	+	322.436i	0.0233595	+	0.0169716i
$713$	−8986.75	−	27658.4i	−0.472028	−	1.45275i
$714$		0			0
$715$	26302.1	−	23873.3i	1.37572	−	1.24869i
$716$	−928.356			−0.0484557
$717$		0			0
$718$	−2242.96	−	1629.61i	−0.116583	−	0.0847026i
$719$	22616.8	−	16432.1i	1.17311	−	0.852313i	0.181730	−	0.983348i	$-0.441830\pi$
$719$	22616.8	−	16432.1i	1.17311	−	0.852313i	0.991378	+	0.131036i	$0.0418303\pi$
$720$		0			0
$721$	−1178.91	+	3628.32i	−0.0608945	+	0.187414i
$722$	3035.07	−	2205.11i	0.156446	−	0.113664i
$723$		0			0
$724$	3336.36	+	10268.3i	0.171264	+	0.527095i
$725$	1395.76			0.0714995
$726$		0			0
$727$	32275.7			1.64655			0.823274	−	0.567644i	$-0.192145\pi$
$727$	32275.7			1.64655			0.823274	+	0.567644i	$0.192145\pi$
$728$	3313.47	+	10197.8i	0.168689	+	0.519170i
$729$		0			0
$730$	−12050.1	+	8754.88i	−0.610949	+	0.443880i
$731$	−10852.5	+	33400.4i	−0.549100	+	1.68996i
$732$		0			0
$733$	1650.68	−	1199.29i	0.0831778	−	0.0604322i	−0.545419	−	0.838163i	$-0.683630\pi$
$733$	1650.68	−	1199.29i	0.0831778	−	0.0604322i	0.628597	+	0.777731i	$0.283630\pi$
$734$	−6105.56	−	4435.95i	−0.307030	−	0.223071i
$735$		0			0
$736$	−6043.38			−0.302666
$737$	8295.54	−	7529.52i	0.414613	−	0.376327i
$738$		0			0
$739$	−3435.87	−	10574.5i	−0.171029	−	0.526373i	0.828401	−	0.560136i	$-0.189251\pi$
$739$	−3435.87	−	10574.5i	−0.171029	−	0.526373i	−0.999430	+	0.0337625i	$0.989251\pi$
$740$	−12705.3	−	9230.95i	−0.631157	−	0.458563i
$741$		0			0
$742$	2169.88	−	6678.21i	0.107357	−	0.330411i
$743$	−2912.81	+	8964.69i	−0.143823	+	0.442642i	−0.996858	−	0.0792125i	$-0.974759\pi$
$743$	−2912.81	+	8964.69i	−0.143823	+	0.442642i	0.853035	+	0.521854i	$0.174759\pi$
$744$		0			0
$745$	−26364.0	−	19154.6i	−1.29651	−	0.941973i
$746$	−783.180	−	2410.38i	−0.0384373	−	0.118298i
$747$		0			0
$748$	9283.78	+	5310.69i	0.453808	+	0.259596i
$749$	−2903.29			−0.141634
$750$		0			0
$751$	−21573.1	−	15673.8i	−1.04822	−	0.761577i	−0.0763479	−	0.997081i	$-0.524326\pi$
$751$	−21573.1	−	15673.8i	−1.04822	−	0.761577i	−0.971873	+	0.235504i	$0.924326\pi$
$752$	−3840.52	+	2790.30i	−0.186236	+	0.135308i
$753$		0			0
$754$	8479.58	−	26097.5i	0.409560	−	1.26049i
$755$	13781.9	−	10013.2i	0.664338	−	0.482670i
$756$		0			0
$757$	9156.10	+	28179.6i	0.439609	+	1.35298i	0.888289	+	0.459285i	$0.151894\pi$
$757$	9156.10	+	28179.6i	0.439609	+	1.35298i	−0.448680	+	0.893692i	$0.648106\pi$
$758$	−25654.3			−1.22929
$759$		0			0
$760$	8641.13			0.412430
$761$	8942.97	+	27523.6i	0.425995	+	1.31108i	0.902038	+	0.431657i	$0.142071\pi$
$761$	8942.97	+	27523.6i	0.425995	+	1.31108i	−0.476043	+	0.879422i	$0.657929\pi$
$762$		0			0
$763$	9161.51	−	6656.23i	0.434691	−	0.315821i
$764$	2458.05	−	7565.11i	0.116400	−	0.358241i
$765$		0			0
$766$	2905.62	−	2111.06i	0.137055	−	0.0995766i
$767$	−6299.39	−	4576.78i	−0.296555	−	0.215460i
$768$		0			0
$769$	−9579.01			−0.449191			−0.224596	−	0.974452i	$-0.572106\pi$
$769$	−9579.01			−0.449191			−0.224596	+	0.974452i	$0.572106\pi$
$770$	−2737.07	+	13134.5i	−0.128100	+	0.614720i
$771$		0			0
$772$	−1475.81	−	4542.09i	−0.0688027	−	0.211753i
$773$	−23789.4	−	17284.0i	−1.10692	−	0.804222i	−0.124741	−	0.992189i	$-0.539810\pi$
$773$	−23789.4	−	17284.0i	−1.10692	−	0.804222i	−0.982175	+	0.187967i	$0.939810\pi$
$774$		0			0
$775$	−407.813	+	1255.12i	−0.0189020	+	0.0581744i
$776$	−3823.75	+	11768.3i	−0.176888	+	0.544404i
$777$		0			0
$778$	8174.54	+	5939.15i	0.376698	+	0.273687i
$779$	−2780.99	−	8559.01i	−0.127907	−	0.393656i
$780$		0			0
$781$	−14039.6	−	31197.7i	−0.643249	−	1.42938i
$782$	−27682.7			−1.26590
$783$		0			0
$784$	1163.32	+	845.203i	0.0529939	+	0.0385023i
$785$	27504.7	−	19983.3i	1.25055	−	0.908580i
$786$		0			0
$787$	−5660.90	+	17422.5i	−0.256403	+	0.789128i	0.737147	+	0.675733i	$0.236173\pi$
$787$	−5660.90	+	17422.5i	−0.256403	+	0.789128i	−0.993550	+	0.113395i	$0.963827\pi$
$788$	−15562.1	+	11306.5i	−0.703523	+	0.511139i
$789$		0			0
$790$	−3928.75	−	12091.5i	−0.176935	−	0.544550i
$791$	−5604.13			−0.251909
$792$		0			0
$793$	−20450.0			−0.915763
$794$	6038.10	+	18583.4i	0.269879	+	0.830603i
$795$		0			0
$796$	−8678.14	+	6305.04i	−0.386418	+	0.280749i
$797$	9744.15	−	29989.4i	0.433068	−	1.33285i	−0.461985	−	0.886888i	$-0.652862\pi$
$797$	9744.15	−	29989.4i	0.433068	−	1.33285i	0.895053	−	0.445960i	$-0.147138\pi$
$798$		0			0
$799$	−17592.2	+	12781.5i	−0.778931	+	0.565926i
$800$	221.868	+	161.197i	0.00980529	+	0.00712396i
$801$		0			0
$802$	−29587.7			−1.30271
$803$	−4795.97	+	23014.7i	−0.210767	+	1.01142i
$804$		0			0
$805$	−10730.9	−	33026.4i	−0.469833	−	1.44600i
$806$	20990.3	+	15250.3i	0.917308	+	0.666464i
$807$		0			0
$808$	2808.56	−	8643.86i	0.122283	−	0.376349i
$809$	−11863.1	+	36510.7i	−0.515553	+	1.58671i	0.266719	+	0.963774i	$0.414060\pi$
$809$	−11863.1	+	36510.7i	−0.515553	+	1.58671i	−0.782273	+	0.622936i	$0.785940\pi$
$810$		0			0
$811$	−1306.04	−	948.897i	−0.0565492	−	0.0410854i	0.559152	−	0.829065i	$-0.311127\pi$
$811$	−1306.04	−	948.897i	−0.0565492	−	0.0410854i	−0.615701	+	0.787980i	$0.711127\pi$
$812$	3202.84	+	9857.32i	0.138421	+	0.426015i
$813$		0			0
$814$	−24641.1	+	2689.39i	−1.06102	+	0.115802i
$815$	13911.1			0.597894
$816$		0			0
$817$	36231.0	+	26323.4i	1.55148	+	1.12722i
$818$	−3064.02	+	2226.14i	−0.130967	+	0.0951529i
$819$		0			0
$820$	1375.59	−	4233.62i	0.0585824	−	0.180298i
$821$	21536.4	−	15647.1i	0.915499	−	0.665149i	−0.0269005	−	0.999638i	$-0.508564\pi$
$821$	21536.4	−	15647.1i	0.915499	−	0.665149i	0.942400	+	0.334489i	$0.108564\pi$
$822$		0			0
$823$	2098.36	+	6458.09i	0.0888752	+	0.273530i	0.985609	−	0.169040i	$-0.0540668\pi$
$823$	2098.36	+	6458.09i	0.0888752	+	0.273530i	−0.896734	+	0.442570i	$0.854067\pi$
$824$	1918.31			0.0811012
$825$		0			0
$826$	2941.05			0.123889
$827$	7923.76	+	24386.8i	0.333175	+	1.02541i	0.967614	+	0.252435i	$0.0812314\pi$
$827$	7923.76	+	24386.8i	0.333175	+	1.02541i	−0.634438	+	0.772973i	$0.718769\pi$
$828$		0			0
$829$	3935.13	−	2859.04i	0.164864	−	0.119781i	−0.502294	−	0.864697i	$-0.667510\pi$
$829$	3935.13	−	2859.04i	0.164864	−	0.119781i	0.667158	+	0.744916i	$0.267510\pi$
$830$	−2439.76	+	7508.82i	−0.102031	+	0.314018i
$831$		0			0
$832$	4361.92	−	3169.12i	0.181758	−	0.132055i
$833$	5328.79	+	3871.59i	0.221647	+	0.161036i
$834$		0			0
$835$	45052.0			1.86717
$836$	10099.1	−	9166.50i	0.417803	−	0.379223i
$837$		0			0
$838$	−1167.61	−	3593.52i	−0.0481316	−	0.148134i
$839$	−12875.5	−	9354.62i	−0.529813	−	0.384931i	0.290475	−	0.956883i	$-0.406187\pi$
$839$	−12875.5	−	9354.62i	−0.529813	−	0.384931i	−0.820288	+	0.571951i	$0.806187\pi$
$840$		0			0
$841$	659.843	−	2030.79i	0.0270549	−	0.0832665i
$842$	−3837.67	+	11811.1i	−0.157072	+	0.483419i
$843$		0			0
$844$	8290.15	+	6023.15i	0.338103	+	0.245646i
$845$	−17500.1	−	53859.7i	−0.712451	−	2.19270i
$846$		0			0
$847$	10734.2	+	18254.0i	0.435456	+	0.740514i
$848$	−3530.80			−0.142981
$849$		0			0
$850$	1016.31	+	738.389i	0.0410106	+	0.0297959i
$851$	51903.9	−	37710.4i	2.09077	−	1.51903i
$852$		0			0
$853$	11951.3	−	36782.3i	0.479723	−	1.47644i	−0.359757	−	0.933046i	$-0.617140\pi$
$853$	11951.3	−	36782.3i	0.479723	−	1.47644i	0.839480	−	0.543391i	$-0.182860\pi$
$854$	6249.01	−	4540.17i	0.250394	−	0.181922i
$855$		0			0
$856$	451.121	+	1388.41i	0.0180128	+	0.0554378i
$857$	19067.8			0.760029			0.380015	−	0.924981i	$-0.375919\pi$
$857$	19067.8			0.760029			0.380015	+	0.924981i	$0.375919\pi$
$858$		0			0
$859$	−6779.06			−0.269265			−0.134632	−	0.990896i	$-0.542985\pi$
$859$	−6779.06			−0.269265			−0.134632	+	0.990896i	$0.542985\pi$
$860$	6845.32	+	21067.7i	0.271423	+	0.835353i
$861$		0			0
$862$	2038.84	−	1481.31i	0.0805606	−	0.0585307i
$863$	4556.25	−	14022.7i	0.179718	−	0.553114i	−0.820100	−	0.572221i	$-0.806082\pi$
$863$	4556.25	−	14022.7i	0.179718	−	0.553114i	0.999817	+	0.0191063i	$0.00608208\pi$
$864$		0			0
$865$	−29313.0	+	21297.1i	−1.15222	+	0.837137i
$866$	−15299.8	−	11115.9i	−0.600354	−	0.436183i
$867$		0			0
$868$	−9799.88			−0.383214
$869$	−17418.2	−	9963.91i	−0.679945	−	0.388956i
$870$		0			0
$871$	−7994.14	−	24603.4i	−0.310989	−	0.957124i
$872$	−4606.66	−	3346.94i	−0.178901	−	0.129979i
$873$		0			0
$874$	−10908.6	+	33573.1i	−0.422183	+	1.29935i
$875$	6615.64	−	20360.8i	0.255599	−	0.786654i
$876$		0			0
$877$	15318.4	+	11129.5i	0.589812	+	0.428524i	0.842248	−	0.539090i	$-0.181232\pi$
$877$	15318.4	+	11129.5i	0.589812	+	0.428524i	−0.252436	+	0.967614i	$0.581232\pi$
$878$	−3703.31	−	11397.6i	−0.142347	−	0.438099i
$879$		0			0
$880$	6706.44	−	731.957i	0.256902	−	0.0280389i
$881$	6518.05			0.249261			0.124630	−	0.992203i	$-0.460225\pi$
$881$	6518.05			0.249261			0.124630	+	0.992203i	$0.460225\pi$
$882$		0			0
$883$	12121.9	+	8807.08i	0.461987	+	0.335653i	0.794310	−	0.607512i	$-0.207832\pi$
$883$	12121.9	+	8807.08i	0.461987	+	0.335653i	−0.332323	+	0.943166i	$0.607832\pi$
$884$	19980.5	−	14516.7i	0.760200	−	0.552318i
$885$		0			0
$886$	7080.91	−	21792.8i	0.268496	−	0.826347i
$887$	−5800.79	+	4214.52i	−0.219585	+	0.159538i	−0.692140	−	0.721764i	$-0.743332\pi$
$887$	−5800.79	+	4214.52i	−0.219585	+	0.159538i	0.472555	+	0.881301i	$0.343332\pi$
$888$		0			0
$889$	5212.79	+	16043.3i	0.196661	+	0.605260i
$890$	1584.97			0.0596946
$891$		0			0
$892$	−3800.59			−0.142661
$893$	8568.82	+	26372.1i	0.321103	+	0.988252i
$894$		0			0
$895$	−2170.04	+	1576.62i	−0.0810462	+	0.0588835i
$896$	−629.307	+	1936.81i	−0.0234639	+	0.0722146i
$897$		0			0
$898$	15557.7	−	11303.3i	0.578137	−	0.420041i
$899$	20289.4	+	14741.1i	0.752715	+	0.546879i
$900$		0			0
$901$	−16173.4			−0.598019
$902$	−2883.35	−	6407.14i	−0.106436	−	0.236513i
$903$		0			0
$904$	870.783	+	2679.99i	0.0320374	+	0.0986010i
$905$	25237.3	+	18336.0i	0.926979	+	0.673490i
$906$		0			0
$907$	−5150.29	+	15851.0i	−0.188547	+	0.580289i	−0.999991	−	0.00414084i	$-0.998682\pi$
$907$	−5150.29	+	15851.0i	−0.188547	+	0.580289i	0.811444	+	0.584430i	$0.198682\pi$
$908$	1022.87	−	3148.08i	0.0373846	−	0.115058i
$909$		0			0
$910$	25064.1	+	18210.2i	0.913042	+	0.663364i
$911$	−306.454	−	943.169i	−0.0111452	−	0.0343014i	0.945329	−	0.326117i	$-0.105740\pi$
$911$	−306.454	−	943.169i	−0.0111452	−	0.0343014i	−0.956474	+	0.291816i	$0.905740\pi$
$912$		0			0
$913$	5113.95	+	11363.8i	0.185375	+	0.411925i
$914$	13851.3			0.501270
$915$		0			0
$916$	−1755.16	−	1275.20i	−0.0633103	−	0.0459976i
$917$	14560.5	−	10578.8i	0.524351	−	0.380964i
$918$		0			0
$919$	−3965.51	+	12204.6i	−0.142340	+	0.438076i	−0.996659	−	0.0816716i	$-0.973974\pi$
$919$	−3965.51	+	12204.6i	−0.142340	+	0.438076i	0.854320	+	0.519748i	$0.173974\pi$
$920$	−14126.4	+	10263.4i	−0.506233	+	0.367800i
$921$		0			0
$922$	−2710.55	−	8342.23i	−0.0968193	−	0.297979i
$923$	−78998.7			−2.81720
$924$		0			0
$925$	−2911.39			−0.103488
$926$	−398.476	−	1226.38i	−0.0141412	−	0.0435221i
$927$		0			0
$928$	4216.28	−	3063.31i	0.149145	−	0.108360i
$929$	−3685.29	+	11342.2i	−0.130151	+	0.400564i	−0.994804	−	0.101805i	$-0.967538\pi$
$929$	−3685.29	+	11342.2i	−0.130151	+	0.400564i	0.864653	+	0.502369i	$0.167538\pi$
$930$		0			0
$931$	6795.26	−	4937.04i	0.239211	−	0.173797i
$932$	−16823.4	−	12222.9i	−0.591276	−	0.429587i
$933$		0			0
$934$	−25449.2			−0.891568
$935$	30720.0	−	3352.85i	1.07449	−	0.117273i
$936$		0			0
$937$	−9674.72	−	29775.7i	−0.337310	−	1.03813i	−0.965573	−	0.260132i	$-0.916234\pi$
$937$	−9674.72	−	29775.7i	−0.337310	−	1.03813i	0.628263	−	0.778001i	$-0.283766\pi$
$938$	7905.10	+	5743.39i	0.275171	+	0.199924i
$939$		0			0
$940$	−4238.48	+	13044.7i	−0.147068	+	0.452629i
$941$	−12.6325	+	38.8788i	−0.000437627	+	0.00134688i	−0.951275	−	0.308343i	$-0.900225\pi$
$941$	−12.6325	+	38.8788i	−0.000437627	+	0.00134688i	0.950837	+	0.309690i	$0.100225\pi$
$942$		0			0
$943$	14712.2	+	10689.1i	0.508055	+	0.369124i
$944$	−456.987	−	1406.46i	−0.0157560	−	0.0484919i
$945$		0			0
$946$	30348.9	+	17360.8i	1.04305	+	0.596667i
$947$	8016.53			0.275081			0.137541	−	0.990496i	$-0.456080\pi$
$947$	8016.53			0.275081			0.137541	+	0.990496i	$0.456080\pi$
$948$		0			0
$949$	43918.2	+	31908.4i	1.50226	+	1.09146i
$950$	1295.99	−	941.592i	0.0442605	−	0.0321571i
$951$		0			0
$952$	−2882.65	+	8871.88i	−0.0981378	+	0.302037i
$953$	20966.6	−	15233.1i	0.712671	−	0.517785i	−0.171364	−	0.985208i	$-0.554817\pi$
$953$	20966.6	−	15233.1i	0.712671	−	0.517785i	0.884034	+	0.467422i	$0.154817\pi$
$954$		0			0
$955$	−7102.09	−	21858.0i	−0.240647	−	0.740637i
$956$	−9925.02			−0.335772
$957$		0			0
$958$	17618.6			0.594186
$959$	−2834.27	−	8722.99i	−0.0954363	−	0.293723i
$960$		0			0
$961$	4917.45	−	3572.74i	0.165065	−	0.119927i
$962$	−17687.4	+	54436.4i	−0.592792	+	1.82443i
$963$		0			0
$964$	163.385	−	118.706i	0.00545879	−	0.00396604i
$965$	−11163.5	−	8110.78i	−0.372401	−	0.270565i
$966$		0			0
$967$	−4975.56			−0.165463			−0.0827317	−	0.996572i	$-0.526364\pi$
$967$	−4975.56			−0.165463			−0.0827317	+	0.996572i	$0.526364\pi$
$968$	7061.50	−	7969.64i	0.234468	−	0.264622i
$969$		0			0
$970$	11048.0	+	34002.3i	0.365702	+	1.12551i
$971$	2359.71	+	1714.43i	0.0779884	+	0.0566619i	0.626096	−	0.779746i	$-0.284652\pi$
$971$	2359.71	+	1714.43i	0.0779884	+	0.0566619i	−0.548108	+	0.836408i	$0.684652\pi$
$972$		0			0
$973$	−4804.43	+	14786.5i	−0.158297	+	0.487188i
$974$	−8767.01	+	26982.1i	−0.288412	+	0.887640i
$975$		0			0
$976$	−3142.18	−	2282.92i	−0.103052	−	0.0748716i
$977$	7873.96	+	24233.5i	0.257840	+	0.793551i	0.993257	+	0.115936i	$0.0369867\pi$
$977$	7873.96	+	24233.5i	0.257840	+	0.793551i	−0.735416	+	0.677616i	$0.763013\pi$
$978$		0			0
$979$	1852.38	−	1681.33i	0.0604723	−	0.0548882i
$980$	4154.67			0.135425
$981$		0			0
$982$	19936.0	+	14484.3i	0.647843	+	0.470686i
$983$	−20701.9	+	15040.8i	−0.671706	+	0.488023i	−0.870596	−	0.491999i	$-0.836266\pi$
$983$	−20701.9	+	15040.8i	−0.671706	+	0.488023i	0.198890	+	0.980022i	$0.436266\pi$
$984$		0			0
$985$	−17174.6	+	52858.0i	−0.555562	+	1.70984i
$986$	19313.4	−	14032.0i	0.623797	−	0.453215i
$987$		0			0
$988$	−9732.14	−	29952.4i	−0.313381	−	0.964488i
$989$	−90495.4			−2.90959
$990$		0			0
$991$	48863.5			1.56630			0.783148	−	0.621836i	$-0.213613\pi$
$991$	48863.5			1.56630			0.783148	+	0.621836i	$0.213613\pi$
$992$	1522.73	+	4686.48i	0.0487366	+	0.149996i
$993$		0			0
$994$	24140.0	−	17538.8i	0.770297	−	0.559654i
$995$	−9577.37	+	29476.1i	−0.305149	+	0.939151i
$996$		0			0
$997$	−46007.9	+	33426.7i	−1.46147	+	1.06182i	−0.478492	+	0.878092i	$0.658816\pi$
$997$	−46007.9	+	33426.7i	−1.46147	+	1.06182i	−0.982977	+	0.183728i	$0.941184\pi$
$998$	−3882.04	−	2820.47i	−0.123130	−	0.0894593i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.4.f.h.181.1	yes	12
3.2	odd	2		198.4.f.g.181.3	yes	12
11.3	even	5		2178.4.a.ce.1.1		6
11.8	odd	10		2178.4.a.cg.1.1		6
11.9	even	5	inner	198.4.f.h.163.1	yes	12
33.8	even	10		2178.4.a.cd.1.6		6
33.14	odd	10		2178.4.a.cf.1.6		6
33.20	odd	10		198.4.f.g.163.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.4.f.g.163.3	✓	12	33.20	odd	10
198.4.f.g.181.3	yes	12	3.2	odd	2
198.4.f.h.163.1	yes	12	11.9	even	5	inner
198.4.f.h.181.1	yes	12	1.1	even	1	trivial
2178.4.a.cd.1.6		6	33.8	even	10
2178.4.a.ce.1.1		6	11.3	even	5
2178.4.a.cf.1.6		6	33.14	odd	10
2178.4.a.cg.1.1		6	11.8	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.618034 - 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-3.57139 + 10.9916i) q^{5} +(-12.8715 + 9.35167i) q^{7} +(6.47214 + 4.70228i) q^{8} +O(q^{10})\)	\(q+(-0.618034 - 1.90211i) q^{2} +(-3.23607 + 2.35114i) q^{4} +(-3.57139 + 10.9916i) q^{5} +(-12.8715 + 9.35167i) q^{7} +(6.47214 + 4.70228i) q^{8} +23.1145 q^{10} +(27.0144 - 24.5198i) q^{11} +(-26.0329 - 80.1210i) q^{13} +(25.7429 + 18.7033i) q^{14} +(4.94427 - 15.2169i) q^{16} +(22.6481 - 69.7036i) q^{17} +(-75.6108 - 54.9344i) q^{19} +(-14.2856 - 43.9664i) q^{20} +(-63.3353 - 36.2303i) q^{22} +188.856 q^{23} +(-6.93339 - 5.03740i) q^{25} +(-136.310 + 99.0350i) q^{26} +(19.6659 - 60.5253i) q^{28} +(-131.759 + 95.7284i) q^{29} +(-47.5853 - 146.452i) q^{31} -32.0000 q^{32} -146.581 q^{34} +(-56.8208 - 174.877i) q^{35} +(274.834 - 199.679i) q^{37} +(-57.7615 + 177.772i) q^{38} +(-74.8001 + 54.3455i) q^{40} +(77.9020 + 56.5991i) q^{41} -479.178 q^{43} +(-29.7708 + 142.863i) q^{44} +(-116.719 - 359.225i) q^{46} +(-240.033 - 174.394i) q^{47} +(-27.7718 + 85.4729i) q^{49} +(-5.29664 + 16.3014i) q^{50} +(272.620 + 198.070i) q^{52} +(-68.1924 - 209.875i) q^{53} +(173.034 + 384.501i) q^{55} -127.280 q^{56} +(263.518 + 191.457i) q^{58} +(74.7754 - 54.3275i) q^{59} +(75.0128 - 230.866i) q^{61} +(-249.160 + 181.025i) q^{62} +(19.7771 + 60.8676i) q^{64} +973.631 q^{65} +307.078 q^{67} +(90.5923 + 278.814i) q^{68} +(-297.518 + 216.159i) q^{70} +(289.776 - 891.838i) q^{71} +(-521.320 + 378.761i) q^{73} +(-549.668 - 399.357i) q^{74} +373.840 q^{76} +(-118.413 + 568.236i) q^{77} +(-169.969 - 523.111i) q^{79} +(149.600 + 108.691i) q^{80} +(59.5119 - 183.159i) q^{82} +(-105.551 + 324.853i) q^{83} +(685.269 + 497.877i) q^{85} +(296.148 + 911.451i) q^{86} +(290.140 - 31.6665i) q^{88} +68.5702 q^{89} +(1084.35 + 787.824i) q^{91} +(-611.149 + 444.026i) q^{92} +(-183.369 + 564.351i) q^{94} +(873.853 - 634.891i) q^{95} +(477.969 + 1471.04i) q^{97} +179.743 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 12 q^{4} - 16 q^{5} + 6 q^{7} + 24 q^{8}+O(q^{10}) \) 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

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