LMFDB - Embedded newform 198.4.f.g.181.3

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			181.3
Root			$-15.2352i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.4.f.g.163.3

$q$-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	$-0.727102\pi$
$5$	3.57139	−	10.9916i	0.319435	−	0.983119i	0.973890	−	0.227019i	$-0.0728978\pi$
$6$		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	$0.275117\pi$
$17$	−22.6481	+	69.7036i	−0.323115	+	0.994447i	−0.972284	+	0.233803i	$0.924883\pi$
$18$		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	$-0.827099\pi$
$23$	−188.856			−1.71213			−0.856067	+	0.516864i	$0.827099\pi$
$24$		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	−0.0797094	−	0.996818i	$-0.525399\pi$
$29$	131.759	−	95.7284i	0.843689	−	0.612976i	0.923399	+	0.383842i	$0.125399\pi$
$30$		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	0.429447	−	0.903092i	$-0.358708\pi$
$41$	−77.9020	−	56.5991i	−0.296738	−	0.215593i	−0.726185	+	0.687499i	$0.758708\pi$
$42$		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	0.894256	−	0.447557i	$-0.147706\pi$
$47$	240.033	+	174.394i	0.744944	+	0.541233i	−0.149312	+	0.988790i	$0.547706\pi$
$48$		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	0.999708	−	0.0241458i	$-0.00768658\pi$
$53$	68.1924	+	209.875i	0.176735	+	0.543934i	−0.822974	+	0.568080i	$0.807687\pi$
$54$		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	−0.667221	−	0.744860i	$-0.732516\pi$
$59$	−74.7754	+	54.3275i	−0.164999	+	0.119879i	0.502222	+	0.864739i	$0.332516\pi$
$60$		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	$0.386682\pi$
$71$	−289.776	+	891.838i	−0.484367	+	1.49073i	−0.832895	+	0.553430i	$0.813318\pi$
$72$		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	−0.856688	−	0.515835i	$-0.827482\pi$
$83$	105.551	−	324.853i	0.139587	−	0.429606i	0.996275	+	0.0862294i	$0.0274818\pi$
$84$		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	$-0.513001\pi$
$89$	−68.5702			−0.0816677			−0.0408338	+	0.999166i	$0.513001\pi$
$90$		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	$0.0890560\pi$
$101$	351.070	+	1080.48i	0.345869	+	1.06448i	−0.615248	+	0.788334i	$0.710944\pi$
$102$		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	0.519093	−	0.854718i	$-0.326270\pi$
$107$	−147.631	−	107.260i	−0.133384	−	0.0969088i	−0.652476	+	0.757809i	$0.726270\pi$
$108$		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	0.462816	−	0.886454i	$-0.346839\pi$
$113$	−284.967	−	207.041i	−0.237234	−	0.172361i	−0.700050	+	0.714094i	$0.746839\pi$
$114$		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	$-0.376875\pi$
$131$	1131.22			0.754469			0.377235	+	0.926118i	$0.376875\pi$
$132$		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	−0.880018	−	0.474940i	$-0.842470\pi$
$137$	178.144	−	548.271i	0.111094	−	0.341912i	0.991112	+	0.133028i	$0.0424699\pi$
$138$		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	$-0.617670\pi$
$149$	871.328	−	2681.67i	0.479074	−	1.47444i	0.840384	−	0.541992i	$-0.182330\pi$
$150$		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	$0.258744\pi$
$167$	1204.60	+	3707.37i	0.558171	+	1.71787i	−0.129248	+	0.991612i	$0.541256\pi$
$168$		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	−0.131255	−	0.991349i	$-0.541901\pi$
$173$	−2536.33	−	1842.75i	−1.11464	−	0.809836i	−0.983389	+	0.181513i	$0.941901\pi$
$174$		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	0.547893	−	0.836548i	$-0.315430\pi$
$179$	−187.764	−	136.419i	−0.0784030	−	0.0569631i	−0.626296	+	0.779585i	$0.715430\pi$
$180$		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	−0.239754	−	0.970834i	$-0.577067\pi$
$191$	1608.82	−	1168.87i	0.609476	−	0.442810i	0.849230	+	0.528023i	$0.177067\pi$
$192$		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	$-0.835625\pi$
$197$	−4808.95			−1.73920			−0.869602	+	0.493753i	$0.835625\pi$
$198$		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	−0.485594	−	0.874185i	$-0.661397\pi$
$227$	669.479	−	486.405i	0.195748	−	0.142220i	0.681342	+	0.731965i	$0.261397\pi$
$228$		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	$-0.839120\pi$
$233$	−1606.49	−	4944.28i	−0.451695	−	1.39017i	0.423277	−	0.906000i	$-0.360880\pi$
$234$		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	0.282015	−	0.959410i	$-0.408997\pi$
$239$	−2007.38	−	1458.45i	−0.543291	−	0.394724i	−0.825306	+	0.564686i	$0.808997\pi$
$240$		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	0.898557	−	0.438857i	$-0.144616\pi$
$251$	−343.356	−	1056.74i	−0.0863443	−	0.265740i	−0.984901	+	0.173116i	$0.944616\pi$
$252$		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	$-0.341822\pi$
$257$	6015.54	−	4370.55i	1.46007	−	1.06081i	0.983344	−	0.181756i	$-0.0581782\pi$
$258$		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	$-0.774826\pi$
$263$	−6483.45			−1.52010			−0.760051	+	0.649864i	$0.774826\pi$
$264$		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	$0.237063\pi$
$269$	−1138.17	+	3502.91i	−0.257975	+	0.793964i	−0.993229	+	0.116173i	$0.962937\pi$
$270$		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	−0.999887	−	0.0150487i	$-0.995210\pi$
$281$	−857.842	+	2640.17i	−0.182116	+	0.560495i	0.817771	+	0.575544i	$0.195210\pi$
$282$		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	−0.869277	−	0.494325i	$-0.835415\pi$
$293$	−3349.09	+	2433.25i	−0.667767	+	0.485161i	0.201510	+	0.979486i	$0.435415\pi$
$294$		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	0.706452	−	0.707761i	$-0.250295\pi$
$311$	1380.12	+	1002.71i	0.251638	+	0.182825i	−0.454815	+	0.890586i	$0.650295\pi$
$312$		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	$-0.734209\pi$
$317$	−3182.71	−	9795.38i	−0.563908	−	1.73553i	0.107265	−	0.994230i	$-0.465791\pi$
$318$		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	$0.421022\pi$
$347$	−3379.87	+	10402.2i	−0.522884	+	1.60927i	−0.768463	+	0.639895i	$0.778978\pi$
$348$		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	$-0.674654\pi$
$353$	−6918.39			−1.04314			−0.521571	+	0.853208i	$0.674654\pi$
$354$		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	−0.667163	−	0.744912i	$-0.732491\pi$
$359$	−1121.48	+	814.805i	−0.164873	+	0.119788i	0.502289	+	0.864700i	$0.332491\pi$
$360$		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	0.907191	−	0.420720i	$-0.138222\pi$
$383$	−554.925	−	1707.88i	−0.0740348	−	0.227856i	−0.981225	+	0.192864i	$0.938222\pi$
$384$		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	−0.288647	−	0.957436i	$-0.593205\pi$
$389$	4087.27	−	2969.57i	0.532732	−	0.387052i	0.821379	+	0.570383i	$0.193205\pi$
$390$		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	$0.472756\pi$
$401$	−4571.55	+	14069.8i	−0.569307	+	1.75215i	−0.654793	+	0.755808i	$0.727244\pi$
$402$		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	$-0.535129\pi$
$419$	−1889.23			−0.220274			−0.110137	+	0.993916i	$0.535129\pi$
$420$		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	0.926937	−	0.375216i	$-0.122432\pi$
$431$	−389.384	−	1198.40i	−0.0435174	−	0.133933i	−0.970455	+	0.241284i	$0.922432\pi$
$432$		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	−0.0332827	−	0.999446i	$-0.510596\pi$
$443$	−9269.03	−	6734.35i	−0.994097	−	0.722254i	−0.960815	+	0.277192i	$0.910596\pi$
$444$		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	$-0.931378\pi$
$449$	−2971.25	−	9144.58i	−0.312299	−	0.961157i	0.664553	−	0.747241i	$-0.268622\pi$
$450$		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	$-0.571110\pi$
$461$	−4385.77			−0.443092			−0.221546	+	0.975150i	$0.571110\pi$
$462$		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	$0.317123\pi$
$467$	−3932.12	+	12101.8i	−0.389630	+	1.19916i	−0.933066	+	0.359706i	$0.882877\pi$
$468$		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	$-0.761976\pi$
$479$	2722.22	−	8378.13i	0.259669	−	0.799179i	0.992874	−	0.119171i	$-0.0380237\pi$
$480$		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	−0.0263837	−	0.999652i	$-0.508399\pi$
$491$	9967.98	−	7242.16i	0.916189	−	0.665650i	0.942572	+	0.334002i	$0.108399\pi$
$492$		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	0.359736	−	0.933054i	$-0.382867\pi$
$503$	−4698.43	−	3413.61i	−0.416486	−	0.302595i	−0.776222	+	0.630459i	$0.782867\pi$
$504$		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	0.965591	−	0.260066i	$-0.0837444\pi$
$509$	11674.6	+	8482.10i	1.01664	+	0.738630i	0.0510462	+	0.998696i	$0.483744\pi$
$510$		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	−0.659343	−	0.751843i	$-0.729165\pi$
$521$	−1760.57	+	1279.13i	−0.148046	+	0.107562i	0.511297	+	0.859404i	$0.329165\pi$
$522$		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	−0.793553	−	0.608501i	$-0.791771\pi$
$557$	−6047.75	+	4393.95i	−0.460056	+	0.334251i	0.333497	+	0.942751i	$0.391771\pi$
$558$		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	$0.0117609\pi$
$563$	2839.59	+	8739.34i	0.212565	+	0.654209i	−0.786752	+	0.617269i	$0.788239\pi$
$564$		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	0.151219	−	0.988500i	$-0.451680\pi$
$569$	−10073.3	−	7318.69i	−0.742171	−	0.539219i	−0.893390	+	0.449282i	$0.851680\pi$
$570$		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	0.0422062	−	0.999109i	$-0.486561\pi$
$587$	14299.5	−	10389.2i	1.00546	−	0.730508i	0.963251	+	0.268601i	$0.0865613\pi$
$588$		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	$-0.629560\pi$
$593$	−11433.4			−0.791760			−0.395880	+	0.918302i	$0.629560\pi$
$594$		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	$-0.559380\pi$
$599$	7948.27	−	24462.2i	0.542166	−	1.66862i	0.727635	−	0.685965i	$-0.240620\pi$
$600$		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	$-0.539845\pi$
$617$	−3826.92			−0.249702			−0.124851	+	0.992176i	$0.539845\pi$
$618$		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	0.900747	−	0.434344i	$-0.143020\pi$
$641$	12431.4	+	9031.94i	0.766007	+	0.556537i	−0.134740	+	0.990881i	$0.543020\pi$
$642$		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	0.817487	−	0.575947i	$-0.195367\pi$
$647$	−3001.92	−	9238.95i	−0.182407	−	0.561392i	−0.999894	+	0.0145553i	$0.995367\pi$
$648$		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	−0.914984	−	0.403489i	$-0.867797\pi$
$653$	−13582.8	+	9868.46i	−0.813989	+	0.591398i	0.100995	+	0.994887i	$0.467797\pi$
$654$		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	$-0.354355\pi$
$659$	14946.6			0.883517			0.441759	+	0.897134i	$0.354355\pi$
$660$		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	$0.403389\pi$
$677$	−8875.14	+	27314.9i	−0.503839	+	1.55066i	−0.802713	+	0.596365i	$0.796611\pi$
$678$		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	$-0.403793\pi$
$683$	10626.4			0.595326			0.297663	+	0.954671i	$0.403793\pi$
$684$		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	0.942972	−	0.332873i	$-0.108018\pi$
$701$	17034.1	+	12376.0i	0.917785	+	0.666810i	−0.0251863	+	0.999683i	$0.508018\pi$
$702$		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	−0.991378	−	0.131036i	$-0.958170\pi$
$719$	−22616.8	+	16432.1i	−1.17311	+	0.852313i	−0.181730	+	0.983348i	$0.558170\pi$
$720$		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	−0.853035	−	0.521854i	$-0.825241\pi$
$743$	2912.81	−	8964.69i	0.143823	−	0.442642i	0.996858	+	0.0792125i	$0.0252406\pi$
$744$		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	$-0.857929\pi$
$761$	−8942.97	−	27523.6i	−0.425995	−	1.31108i	0.476043	−	0.879422i	$-0.342071\pi$
$762$		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	0.982175	−	0.187967i	$-0.0601899\pi$
$773$	23789.4	+	17284.0i	1.10692	+	0.804222i	0.124741	+	0.992189i	$0.460190\pi$
$774$		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	$0.347138\pi$
$797$	−9744.15	+	29989.4i	−0.433068	+	1.33285i	−0.895053	+	0.445960i	$0.852862\pi$
$798$		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	$-0.585940\pi$
$809$	11863.1	−	36510.7i	0.515553	−	1.58671i	0.782273	−	0.622936i	$-0.214060\pi$
$810$		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	−0.942400	−	0.334489i	$-0.891436\pi$
$821$	−21536.4	+	15647.1i	−0.915499	+	0.665149i	0.0269005	+	0.999638i	$0.491436\pi$
$822$		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	$-0.918769\pi$
$827$	−7923.76	−	24386.8i	−0.333175	−	1.02541i	0.634438	−	0.772973i	$-0.281231\pi$
$828$		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	0.820288	−	0.571951i	$-0.193813\pi$
$839$	12875.5	+	9354.62i	0.529813	+	0.384931i	−0.290475	+	0.956883i	$0.593813\pi$
$840$		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	$-0.624081\pi$
$857$	−19067.8			−0.760029			−0.380015	+	0.924981i	$0.624081\pi$
$858$		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	−0.999817	−	0.0191063i	$-0.993918\pi$
$863$	−4556.25	+	14022.7i	−0.179718	+	0.553114i	0.820100	+	0.572221i	$0.193918\pi$
$864$		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	$-0.539775\pi$
$881$	−6518.05			−0.249261			−0.124630	+	0.992203i	$0.539775\pi$
$882$		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	−0.472555	−	0.881301i	$-0.656668\pi$
$887$	5800.79	−	4214.52i	0.219585	−	0.159538i	0.692140	+	0.721764i	$0.256668\pi$
$888$		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	0.956474	−	0.291816i	$-0.0942595\pi$
$911$	306.454	+	943.169i	0.0111452	+	0.0343014i	−0.945329	+	0.326117i	$0.894260\pi$
$912$		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	−0.864653	−	0.502369i	$-0.832462\pi$
$929$	3685.29	−	11342.2i	0.130151	−	0.400564i	0.994804	+	0.101805i	$0.0324618\pi$
$930$		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	−0.950837	−	0.309690i	$-0.899775\pi$
$941$	12.6325	−	38.8788i	0.000437627	−	0.00134688i	0.951275	+	0.308343i	$0.0997746\pi$
$942$		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	$-0.543920\pi$
$947$	−8016.53			−0.275081			−0.137541	+	0.990496i	$0.543920\pi$
$948$		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	−0.884034	−	0.467422i	$-0.845183\pi$
$953$	−20966.6	+	15233.1i	−0.712671	+	0.517785i	0.171364	+	0.985208i	$0.445183\pi$
$954$		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	0.548108	−	0.836408i	$-0.315348\pi$
$971$	−2359.71	−	1714.43i	−0.0779884	−	0.0566619i	−0.626096	+	0.779746i	$0.715348\pi$
$972$		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	$-0.963013\pi$
$977$	−7873.96	−	24233.5i	−0.257840	−	0.793551i	0.735416	−	0.677616i	$-0.236987\pi$
$978$		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	−0.198890	−	0.980022i	$-0.563734\pi$
$983$	20701.9	−	15040.8i	0.671706	−	0.488023i	0.870596	+	0.491999i	$0.163734\pi$
$984$		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.g.181.3	yes	12
3.2	odd	2		198.4.f.h.181.1	yes	12
11.3	even	5		2178.4.a.cf.1.6		6
11.8	odd	10		2178.4.a.cd.1.6		6
11.9	even	5	inner	198.4.f.g.163.3	✓	12
33.8	even	10		2178.4.a.cg.1.1		6
33.14	odd	10		2178.4.a.ce.1.1		6
33.20	odd	10		198.4.f.h.163.1	yes	12

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

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