LMFDB - Embedded newform 98.4.c.h.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.4.c.h.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(3.53553 - 6.12372i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +14.1421 q^{6} -8.00000 q^{8} +(-11.5000 - 19.9186i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(3.53553 - 6.12372i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +14.1421 q^{6} -8.00000 q^{8} +(-11.5000 - 19.9186i) q^{9} +(-19.7990 + 34.2929i) q^{10} +(7.00000 - 12.1244i) q^{11} +(14.1421 + 24.4949i) q^{12} +50.9117 q^{13} +140.000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(23.0000 - 39.8372i) q^{18} +(0.707107 + 1.22474i) q^{19} -79.1960 q^{20} +28.0000 q^{22} +(-70.0000 - 121.244i) q^{23} +(-28.2843 + 48.9898i) q^{24} +(-133.500 + 231.229i) q^{25} +(50.9117 + 88.1816i) q^{26} +28.2843 q^{27} -286.000 q^{29} +(140.000 + 242.487i) q^{30} +(46.6690 - 80.8332i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-49.4975 - 85.7321i) q^{33} -2.82843 q^{34} +92.0000 q^{36} +(19.0000 + 32.9090i) q^{37} +(-1.41421 + 2.44949i) q^{38} +(180.000 - 311.769i) q^{39} +(-79.1960 - 137.171i) q^{40} -125.865 q^{41} -34.0000 q^{43} +(28.0000 + 48.4974i) q^{44} +(227.688 - 394.368i) q^{45} +(140.000 - 242.487i) q^{46} +(-261.630 - 453.156i) q^{47} -113.137 q^{48} -534.000 q^{50} +(5.00000 + 8.66025i) q^{51} +(-101.823 + 176.363i) q^{52} +(37.0000 - 64.0859i) q^{53} +(28.2843 + 48.9898i) q^{54} +277.186 q^{55} +10.0000 q^{57} +(-286.000 - 495.367i) q^{58} +(-217.082 + 375.997i) q^{59} +(-280.000 + 484.974i) q^{60} +(-7.07107 - 12.2474i) q^{61} +186.676 q^{62} +64.0000 q^{64} +(504.000 + 872.954i) q^{65} +(98.9949 - 171.464i) q^{66} +(-342.000 + 592.361i) q^{67} +(-2.82843 - 4.89898i) q^{68} -989.949 q^{69} +588.000 q^{71} +(92.0000 + 159.349i) q^{72} +(135.057 - 233.926i) q^{73} +(-38.0000 + 65.8179i) q^{74} +(943.988 + 1635.03i) q^{75} -5.65685 q^{76} +720.000 q^{78} +(-610.000 - 1056.55i) q^{79} +(158.392 - 274.343i) q^{80} +(410.500 - 711.007i) q^{81} +(-125.865 - 218.005i) q^{82} +422.850 q^{83} -28.0000 q^{85} +(-34.0000 - 58.8897i) q^{86} +(-1011.16 + 1751.39i) q^{87} +(-56.0000 + 96.9948i) q^{88} +(-309.006 - 535.214i) q^{89} +910.754 q^{90} +560.000 q^{92} +(-330.000 - 571.577i) q^{93} +(523.259 - 906.311i) q^{94} +(-14.0000 + 24.2487i) q^{95} +(-113.137 - 195.959i) q^{96} +1483.51 q^{97} -322.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 46 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 46 * q^9	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 46 q^{9} + 28 q^{11} + 560 q^{15} - 32 q^{16} + 92 q^{18} + 112 q^{22} - 280 q^{23} - 534 q^{25} - 1144 q^{29} + 560 q^{30} + 64 q^{32} + 368 q^{36} + 76 q^{37} + 720 q^{39} - 136 q^{43} + 112 q^{44} + 560 q^{46} - 2136 q^{50} + 20 q^{51} + 148 q^{53} + 40 q^{57} - 1144 q^{58} - 1120 q^{60} + 256 q^{64} + 2016 q^{65} - 1368 q^{67} + 2352 q^{71} + 368 q^{72} - 152 q^{74} + 2880 q^{78} - 2440 q^{79} + 1642 q^{81} - 112 q^{85} - 136 q^{86} - 224 q^{88} + 2240 q^{92} - 1320 q^{93} - 56 q^{95} - 1288 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 46 * q^9 + 28 * q^11 + 560 * q^15 - 32 * q^16 + 92 * q^18 + 112 * q^22 - 280 * q^23 - 534 * q^25 - 1144 * q^29 + 560 * q^30 + 64 * q^32 + 368 * q^36 + 76 * q^37 + 720 * q^39 - 136 * q^43 + 112 * q^44 + 560 * q^46 - 2136 * q^50 + 20 * q^51 + 148 * q^53 + 40 * q^57 - 1144 * q^58 - 1120 * q^60 + 256 * q^64 + 2016 * q^65 - 1368 * q^67 + 2352 * q^71 + 368 * q^72 - 152 * q^74 + 2880 * q^78 - 2440 * q^79 + 1642 * q^81 - 112 * q^85 - 136 * q^86 - 224 * q^88 + 2240 * q^92 - 1320 * q^93 - 56 * q^95 - 1288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	3.53553	−	6.12372i	0.680414	−	1.17851i	−0.294441	−	0.955670i	$-0.595133\pi$
$3$	3.53553	−	6.12372i	0.680414	−	1.17851i	0.974855	−	0.222842i	$-0.0715333\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	9.89949	+	17.1464i	0.885438	+	1.53362i	0.845211	+	0.534433i	$0.179475\pi$
$5$	9.89949	+	17.1464i	0.885438	+	1.53362i	0.0402266	+	0.999191i	$0.487192\pi$
$6$	14.1421			0.962250
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−11.5000	−	19.9186i	−0.425926	−	0.737725i
$10$	−19.7990	+	34.2929i	−0.626099	+	1.08444i
$11$	7.00000	−	12.1244i	0.191871	−	0.332330i	−0.753999	−	0.656875i	$-0.771878\pi$
$11$	7.00000	−	12.1244i	0.191871	−	0.332330i	0.945870	+	0.324545i	$0.105211\pi$
$12$	14.1421	+	24.4949i	0.340207	+	0.589256i
$13$	50.9117			1.08618			0.543091	−	0.839674i	$-0.317254\pi$
$13$	50.9117			1.08618			0.543091	+	0.839674i	$0.317254\pi$
$14$		0			0
$15$	140.000			2.40986
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−0.707107	+	1.22474i	−0.0100882	+	0.0174732i	−0.871025	−	0.491238i	$-0.836545\pi$
$17$	−0.707107	+	1.22474i	−0.0100882	+	0.0174732i	0.860937	+	0.508711i	$0.169878\pi$
$18$	23.0000	−	39.8372i	0.301175	−	0.521651i
$19$	0.707107	+	1.22474i	0.00853797	+	0.0147882i	0.870263	−	0.492588i	$-0.163949\pi$
$19$	0.707107	+	1.22474i	0.00853797	+	0.0147882i	−0.861725	+	0.507376i	$0.830616\pi$
$20$	−79.1960			−0.885438
$21$		0			0
$22$	28.0000			0.271346
$23$	−70.0000	−	121.244i	−0.634609	−	1.09918i	−0.986598	−	0.163171i	$-0.947828\pi$
$23$	−70.0000	−	121.244i	−0.634609	−	1.09918i	0.351989	−	0.936004i	$-0.385506\pi$
$24$	−28.2843	+	48.9898i	−0.240563	+	0.416667i
$25$	−133.500	+	231.229i	−1.06800	+	1.84983i
$26$	50.9117	+	88.1816i	0.384023	+	0.665148i
$27$	28.2843			0.201604
$28$		0			0
$29$	−286.000			−1.83134			−0.915670	−	0.401931i	$-0.868339\pi$
$29$	−286.000			−1.83134			−0.915670	+	0.401931i	$0.868339\pi$
$30$	140.000	+	242.487i	0.852013	+	1.47573i
$31$	46.6690	−	80.8332i	0.270387	−	0.468325i	−0.698574	−	0.715538i	$-0.746182\pi$
$31$	46.6690	−	80.8332i	0.270387	−	0.468325i	0.968961	+	0.247213i	$0.0795149\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−49.4975	−	85.7321i	−0.261103	−	0.452244i
$34$	−2.82843			−0.0142668
$35$		0			0
$36$	92.0000			0.425926
$37$	19.0000	+	32.9090i	0.0844211	+	0.146222i	0.905144	−	0.425104i	$-0.139763\pi$
$37$	19.0000	+	32.9090i	0.0844211	+	0.146222i	−0.820723	+	0.571326i	$0.806429\pi$
$38$	−1.41421	+	2.44949i	−0.00603726	+	0.0104568i
$39$	180.000	−	311.769i	0.739053	−	1.28008i
$40$	−79.1960	−	137.171i	−0.313050	−	0.542218i
$41$	−125.865			−0.479434			−0.239717	−	0.970843i	$-0.577055\pi$
$41$	−125.865			−0.479434			−0.239717	+	0.970843i	$0.577055\pi$
$42$		0			0
$43$	−34.0000			−0.120580			−0.0602901	−	0.998181i	$-0.519203\pi$
$43$	−34.0000			−0.120580			−0.0602901	+	0.998181i	$0.519203\pi$
$44$	28.0000	+	48.4974i	0.0959354	+	0.166165i
$45$	227.688	−	394.368i	0.754262	−	1.30642i
$46$	140.000	−	242.487i	0.448736	−	0.777234i
$47$	−261.630	−	453.156i	−0.811970	−	1.40637i	−0.911483	−	0.411337i	$-0.865062\pi$
$47$	−261.630	−	453.156i	−0.811970	−	1.40637i	0.0995134	−	0.995036i	$-0.468271\pi$
$48$	−113.137			−0.340207
$49$		0			0
$50$	−534.000			−1.51038
$51$	5.00000	+	8.66025i	0.0137282	+	0.0237780i
$52$	−101.823	+	176.363i	−0.271545	+	0.470330i
$53$	37.0000	−	64.0859i	0.0958932	−	0.166092i	−0.814088	−	0.580742i	$-0.802763\pi$
$53$	37.0000	−	64.0859i	0.0958932	−	0.166092i	0.909981	+	0.414650i	$0.136096\pi$
$54$	28.2843	+	48.9898i	0.0712778	+	0.123457i
$55$	277.186			0.679559
$56$		0			0
$57$	10.0000			0.0232374
$58$	−286.000	−	495.367i	−0.647477	−	1.12146i
$59$	−217.082	+	375.997i	−0.479011	+	0.829671i	−0.999710	−	0.0240689i	$-0.992338\pi$
$59$	−217.082	+	375.997i	−0.479011	+	0.829671i	0.520699	+	0.853740i	$0.325671\pi$
$60$	−280.000	+	484.974i	−0.602464	+	1.04350i
$61$	−7.07107	−	12.2474i	−0.0148419	−	0.0257070i	0.858509	−	0.512798i	$-0.171391\pi$
$61$	−7.07107	−	12.2474i	−0.0148419	−	0.0257070i	−0.873351	+	0.487091i	$0.838058\pi$
$62$	186.676			0.382385
$63$		0			0
$64$	64.0000			0.125000
$65$	504.000	+	872.954i	0.961746	+	1.66579i
$66$	98.9949	−	171.464i	0.184628	−	0.319785i
$67$	−342.000	+	592.361i	−0.623611	+	1.08013i	0.365196	+	0.930930i	$0.381002\pi$
$67$	−342.000	+	592.361i	−0.623611	+	1.08013i	−0.988808	+	0.149196i	$0.952332\pi$
$68$	−2.82843	−	4.89898i	−0.00504408	−	0.00873660i
$69$	−989.949			−1.72719
$70$		0			0
$71$	588.000			0.982856			0.491428	−	0.870918i	$-0.336475\pi$
$71$	588.000			0.982856			0.491428	+	0.870918i	$0.336475\pi$
$72$	92.0000	+	159.349i	0.150588	+	0.260825i
$73$	135.057	−	233.926i	0.216538	−	0.375055i	−0.737209	−	0.675664i	$-0.763857\pi$
$73$	135.057	−	233.926i	0.216538	−	0.375055i	0.953747	+	0.300610i	$0.0971902\pi$
$74$	−38.0000	+	65.8179i	−0.0596947	+	0.103394i
$75$	943.988	+	1635.03i	1.45336	+	2.51730i
$76$	−5.65685			−0.00853797
$77$		0			0
$78$	720.000			1.04518
$79$	−610.000	−	1056.55i	−0.868739	−	1.50470i	−0.863286	−	0.504715i	$-0.831598\pi$
$79$	−610.000	−	1056.55i	−0.868739	−	1.50470i	−0.00545246	−	0.999985i	$-0.501736\pi$
$80$	158.392	−	274.343i	0.221359	−	0.383406i
$81$	410.500	−	711.007i	0.563100	−	0.975318i
$82$	−125.865	−	218.005i	−0.169506	−	0.293592i
$83$	422.850			0.559202			0.279601	−	0.960116i	$-0.409798\pi$
$83$	422.850			0.559202			0.279601	+	0.960116i	$0.409798\pi$
$84$		0			0
$85$	−28.0000			−0.0357297
$86$	−34.0000	−	58.8897i	−0.0426316	−	0.0738400i
$87$	−1011.16	+	1751.39i	−1.24607	+	2.15826i
$88$	−56.0000	+	96.9948i	−0.0678366	+	0.117496i
$89$	−309.006	−	535.214i	−0.368028	−	0.637444i	0.621229	−	0.783629i	$-0.286634\pi$
$89$	−309.006	−	535.214i	−0.368028	−	0.637444i	−0.989257	+	0.146185i	$0.953300\pi$
$90$	910.754			1.06669
$91$		0			0
$92$	560.000			0.634609
$93$	−330.000	−	571.577i	−0.367951	−	0.637309i
$94$	523.259	−	906.311i	0.574149	−	0.994456i
$95$	−14.0000	+	24.2487i	−0.0151197	+	0.0261881i
$96$	−113.137	−	195.959i	−0.120281	−	0.208333i
$97$	1483.51			1.55286			0.776431	−	0.630202i	$-0.217028\pi$
$97$	1483.51			1.55286			0.776431	+	0.630202i	$0.217028\pi$
$98$		0			0
$99$	−322.000			−0.326891
$100$	−534.000	−	924.915i	−0.534000	−	0.924915i
$101$	−564.271	+	977.346i	−0.555912	+	0.962867i	0.441920	+	0.897054i	$0.354297\pi$
$101$	−564.271	+	977.346i	−0.555912	+	0.962867i	−0.997832	+	0.0658130i	$0.979036\pi$
$102$	−10.0000	+	17.3205i	−0.00970733	+	0.0168136i
$103$	434.164	+	751.993i	0.415334	+	0.719380i	0.995463	−	0.0951446i	$-0.0303314\pi$
$103$	434.164	+	751.993i	0.415334	+	0.719380i	−0.580129	+	0.814524i	$0.696998\pi$
$104$	−407.294			−0.384023
$105$		0			0
$106$	148.000			0.135613
$107$	842.000	+	1458.39i	0.760740	+	1.31764i	0.942469	+	0.334292i	$0.108497\pi$
$107$	842.000	+	1458.39i	0.760740	+	1.31764i	−0.181729	+	0.983349i	$0.558169\pi$
$108$	−56.5685	+	97.9796i	−0.0504010	+	0.0872971i
$109$	409.000	−	708.409i	0.359405	−	0.622507i	−0.628457	−	0.777844i	$-0.716313\pi$
$109$	409.000	−	708.409i	0.359405	−	0.622507i	0.987861	+	0.155337i	$0.0496465\pi$
$110$	277.186	+	480.100i	0.240260	+	0.416143i
$111$	268.701			0.229765
$112$		0			0
$113$	−540.000			−0.449548			−0.224774	−	0.974411i	$-0.572164\pi$
$113$	−540.000			−0.449548			−0.224774	+	0.974411i	$0.572164\pi$
$114$	10.0000	+	17.3205i	0.00821567	+	0.0142299i
$115$	1385.93	−	2400.50i	1.12381	−	1.94650i
$116$	572.000	−	990.733i	0.457835	−	0.792994i
$117$	−585.484	−	1014.09i	−0.462633	−	0.801304i
$118$	−868.327			−0.677424
$119$		0			0
$120$	−1120.00			−0.852013
$121$	567.500	+	982.939i	0.426371	+	0.738496i
$122$	14.1421	−	24.4949i	0.0104948	−	0.0181776i
$123$	−445.000	+	770.763i	−0.326214	+	0.565019i
$124$	186.676	+	323.333i	0.135194	+	0.234162i
$125$	−2811.46			−2.01171
$126$		0			0
$127$	1720.00			1.20177			0.600887	−	0.799334i	$-0.294814\pi$
$127$	1720.00			1.20177			0.600887	+	0.799334i	$0.294814\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−120.208	+	208.207i	−0.0820445	+	0.142105i
$130$	−1008.00	+	1745.91i	−0.680057	+	1.17789i
$131$	867.620	+	1502.76i	0.578659	+	1.00227i	0.995634	+	0.0933484i	$0.0297571\pi$
$131$	867.620	+	1502.76i	0.578659	+	1.00227i	−0.416975	+	0.908918i	$0.636910\pi$
$132$	395.980			0.261103
$133$		0			0
$134$	−1368.00			−0.881919
$135$	280.000	+	484.974i	0.178508	+	0.309185i
$136$	5.65685	−	9.79796i	0.00356670	−	0.00617771i
$137$	−414.000	+	717.069i	−0.258178	+	0.447178i	−0.965754	−	0.259460i	$-0.916455\pi$
$137$	−414.000	+	717.069i	−0.258178	+	0.447178i	0.707576	+	0.706638i	$0.249789\pi$
$138$	−989.949	−	1714.64i	−0.610653	−	1.05768i
$139$	−425.678			−0.259752			−0.129876	−	0.991530i	$-0.541458\pi$
$139$	−425.678			−0.259752			−0.129876	+	0.991530i	$0.541458\pi$
$140$		0			0
$141$	−3700.00			−2.20990
$142$	588.000	+	1018.45i	0.347492	+	0.601874i
$143$	356.382	−	617.271i	0.208407	−	0.360971i
$144$	−184.000	+	318.697i	−0.106481	+	0.184431i
$145$	−2831.26	−	4903.88i	−1.62154	−	2.80859i
$146$	540.230			0.306231
$147$		0			0
$148$	−152.000			−0.0844211
$149$	−1025.00	−	1775.35i	−0.563566	−	0.976124i	−0.997182	−	0.0750264i	$-0.976096\pi$
$149$	−1025.00	−	1775.35i	−0.563566	−	0.976124i	0.433616	−	0.901098i	$-0.357237\pi$
$150$	−1887.98	+	3270.07i	−1.02768	+	1.78000i
$151$	236.000	−	408.764i	0.127188	−	0.220296i	−0.795398	−	0.606087i	$-0.792738\pi$
$151$	236.000	−	408.764i	0.127188	−	0.220296i	0.922586	+	0.385791i	$0.126071\pi$
$152$	−5.65685	−	9.79796i	−0.00301863	−	0.00522842i
$153$	32.5269			0.0171872
$154$		0			0
$155$	1848.00			0.957645
$156$	720.000	+	1247.08i	0.369527	+	0.640039i
$157$	1105.92	−	1915.50i	0.562176	−	0.973717i	−0.435130	−	0.900367i	$-0.643298\pi$
$157$	1105.92	−	1915.50i	0.562176	−	0.973717i	0.997306	−	0.0733498i	$-0.0233690\pi$
$158$	1220.00	−	2113.10i	0.614291	−	1.06398i
$159$	−261.630	−	453.156i	−0.130494	−	0.226022i
$160$	633.568			0.313050
$161$		0			0
$162$	1642.00			0.796344
$163$	−1643.00	−	2845.76i	−0.789507	−	1.36747i	−0.926269	−	0.376863i	$-0.877003\pi$
$163$	−1643.00	−	2845.76i	−0.789507	−	1.36747i	0.136762	−	0.990604i	$-0.456331\pi$
$164$	251.730	−	436.009i	0.119859	−	0.207601i
$165$	980.000	−	1697.41i	0.462381	−	0.800868i
$166$	422.850	+	732.397i	0.197708	+	0.342440i
$167$	−1490.58			−0.690686			−0.345343	−	0.938476i	$-0.612237\pi$
$167$	−1490.58			−0.690686			−0.345343	+	0.938476i	$0.612237\pi$
$168$		0			0
$169$	395.000			0.179791
$170$	−28.0000	−	48.4974i	−0.0126324	−	0.0218799i
$171$	16.2635	−	28.1691i	0.00727309	−	0.0125974i
$172$	68.0000	−	117.779i	0.0301451	−	0.0522128i
$173$	1035.20	+	1793.03i	0.454943	+	0.787984i	0.998685	−	0.0512682i	$-0.0163263\pi$
$173$	1035.20	+	1793.03i	0.454943	+	0.787984i	−0.543742	+	0.839252i	$0.682993\pi$
$174$	−4044.65			−1.76221
$175$		0			0
$176$	−224.000			−0.0959354
$177$	1535.00	+	2658.70i	0.651851	+	1.12904i
$178$	618.011	−	1070.43i	0.260235	−	0.450741i
$179$	−270.000	+	467.654i	−0.112742	+	0.195274i	−0.916875	−	0.399175i	$-0.869297\pi$
$179$	−270.000	+	467.654i	−0.112742	+	0.195274i	0.804133	+	0.594449i	$0.202630\pi$
$180$	910.754	+	1577.47i	0.377131	+	0.653210i
$181$	3784.44			1.55412			0.777058	−	0.629429i	$-0.216711\pi$
$181$	3784.44			1.55412			0.777058	+	0.629429i	$0.216711\pi$
$182$		0			0
$183$	−100.000			−0.0403946
$184$	560.000	+	969.948i	0.224368	+	0.388617i
$185$	−376.181	+	651.564i	−0.149499	+	0.258940i
$186$	660.000	−	1143.15i	0.260180	−	0.450646i
$187$	9.89949	+	17.1464i	0.00387124	+	0.00670519i
$188$	2093.04			0.811970
$189$		0			0
$190$	−56.0000			−0.0213825
$191$	−514.000	−	890.274i	−0.194721	−	0.337267i	0.752088	−	0.659063i	$-0.229047\pi$
$191$	−514.000	−	890.274i	−0.194721	−	0.337267i	−0.946809	+	0.321796i	$0.895714\pi$
$192$	226.274	−	391.918i	0.0850517	−	0.147314i
$193$	−2296.00	+	3976.79i	−0.856320	+	1.48319i	0.0190956	+	0.999818i	$0.493921\pi$
$193$	−2296.00	+	3976.79i	−0.856320	+	1.48319i	−0.875415	+	0.483372i	$0.839412\pi$
$194$	1483.51	+	2569.51i	0.549020	+	0.950930i
$195$	7127.64			2.61754
$196$		0			0
$197$	794.000			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$197$	794.000			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$198$	−322.000	−	557.720i	−0.115573	−	0.200179i
$199$	−1243.09	+	2153.10i	−0.442817	+	0.766981i	−0.997897	−	0.0648153i	$-0.979354\pi$
$199$	−1243.09	+	2153.10i	−0.442817	+	0.766981i	0.555080	+	0.831797i	$0.312688\pi$
$200$	1068.00	−	1849.83i	0.377595	−	0.654014i
$201$	2418.31	+	4188.63i	0.848627	+	1.46987i
$202$	−2257.08			−0.786178
$203$		0			0
$204$	−40.0000			−0.0137282
$205$	−1246.00	−	2158.14i	−0.424509	−	0.735272i
$206$	−868.327	+	1503.99i	−0.293686	+	0.508678i
$207$	−1610.00	+	2788.60i	−0.540593	+	0.936334i
$208$	−407.294	−	705.453i	−0.135773	−	0.235165i
$209$	19.7990			0.00655275
$210$		0			0
$211$	−2748.00			−0.896588			−0.448294	−	0.893886i	$-0.647968\pi$
$211$	−2748.00			−0.896588			−0.448294	+	0.893886i	$0.647968\pi$
$212$	148.000	+	256.344i	0.0479466	+	0.0830460i
$213$	2078.89	−	3600.75i	0.668749	−	1.15831i
$214$	−1684.00	+	2916.77i	−0.537925	+	0.931713i
$215$	−336.583	−	582.979i	−0.106766	−	0.184925i
$216$	−226.274			−0.0712778
$217$		0			0
$218$	1636.00			0.508275
$219$	−955.000	−	1654.11i	−0.294671	−	0.510385i
$220$	−554.372	+	960.200i	−0.169890	+	0.294258i
$221$	−36.0000	+	62.3538i	−0.0109576	+	0.0189791i
$222$	268.701	+	465.403i	0.0812342	+	0.140702i
$223$	−3428.05			−1.02941			−0.514707	−	0.857366i	$-0.672099\pi$
$223$	−3428.05			−1.02941			−0.514707	+	0.857366i	$0.672099\pi$
$224$		0			0
$225$	6141.00			1.81956
$226$	−540.000	−	935.307i	−0.158939	−	0.275291i
$227$	−2645.29	+	4581.77i	−0.773453	+	1.33966i	0.162207	+	0.986757i	$0.448139\pi$
$227$	−2645.29	+	4581.77i	−0.773453	+	1.33966i	−0.935660	+	0.352903i	$0.885195\pi$
$228$	−20.0000	+	34.6410i	−0.00580935	+	0.0100621i
$229$	1374.62	+	2380.90i	0.396669	+	0.687051i	0.993313	−	0.115456i	$-0.0368328\pi$
$229$	1374.62	+	2380.90i	0.396669	+	0.687051i	−0.596644	+	0.802506i	$0.703499\pi$
$230$	5543.72			1.58931
$231$		0			0
$232$	2288.00			0.647477
$233$	−36.0000	−	62.3538i	−0.0101221	−	0.0175319i	0.860920	−	0.508740i	$-0.169889\pi$
$233$	−36.0000	−	62.3538i	−0.0101221	−	0.0175319i	−0.871042	+	0.491208i	$0.836555\pi$
$234$	1170.97	−	2028.18i	0.327131	−	0.566607i
$235$	5180.00	−	8972.02i	1.43790	−	2.49051i
$236$	−868.327	−	1503.99i	−0.239505	−	0.414836i
$237$	−8626.70			−2.36441
$238$		0			0
$239$	4308.00			1.16595			0.582974	−	0.812491i	$-0.301889\pi$
$239$	4308.00			1.16595			0.582974	+	0.812491i	$0.301889\pi$
$240$	−1120.00	−	1939.90i	−0.301232	−	0.521749i
$241$	770.039	−	1333.75i	0.205820	−	0.356490i	−0.744574	−	0.667540i	$-0.767347\pi$
$241$	770.039	−	1333.75i	0.205820	−	0.356490i	0.950394	+	0.311050i	$0.100681\pi$
$242$	−1135.00	+	1965.88i	−0.301490	+	0.522196i
$243$	−2520.84	−	4366.22i	−0.665480	−	1.15265i
$244$	56.5685			0.0148419
$245$		0			0
$246$	−1780.00			−0.461336
$247$	36.0000	+	62.3538i	0.00927379	+	0.0160627i
$248$	−373.352	+	646.665i	−0.0955964	+	0.165578i
$249$	1495.00	−	2589.42i	0.380489	−	0.659026i
$250$	−2811.46	−	4869.59i	−0.711249	−	1.23192i
$251$	931.967			0.234363			0.117182	−	0.993110i	$-0.462614\pi$
$251$	931.967			0.234363			0.117182	+	0.993110i	$0.462614\pi$
$252$		0			0
$253$	−1960.00			−0.487052
$254$	1720.00	+	2979.13i	0.424891	+	0.735933i
$255$	−98.9949	+	171.464i	−0.0243110	+	0.0421079i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−468.812	−	812.006i	−0.113789	−	0.197088i	0.803506	−	0.595296i	$-0.202965\pi$
$257$	−468.812	−	812.006i	−0.113789	−	0.197088i	−0.917295	+	0.398209i	$0.869632\pi$
$258$	−480.833			−0.116028
$259$		0			0
$260$	−4032.00			−0.961746
$261$	3289.00	+	5696.72i	0.780015	+	1.35103i
$262$	−1735.24	+	3005.52i	−0.409174	+	0.708709i
$263$	−3570.00	+	6183.42i	−0.837018	+	1.44976i	0.0553595	+	0.998466i	$0.482370\pi$
$263$	−3570.00	+	6183.42i	−0.837018	+	1.44976i	−0.892377	+	0.451291i	$0.850964\pi$
$264$	395.980	+	685.857i	0.0923139	+	0.159892i
$265$	1465.13			0.339630
$266$		0			0
$267$	−4370.00			−1.00165
$268$	−1368.00	−	2369.45i	−0.311806	−	0.540063i
$269$	−2305.17	+	3992.67i	−0.522485	+	0.904971i	0.477172	+	0.878810i	$0.341662\pi$
$269$	−2305.17	+	3992.67i	−0.522485	+	0.904971i	−0.999658	+	0.0261615i	$0.991672\pi$
$270$	−560.000	+	969.948i	−0.126224	+	0.218627i
$271$	1182.28	+	2047.77i	0.265013	+	0.459016i	0.967567	−	0.252614i	$-0.0812904\pi$
$271$	1182.28	+	2047.77i	0.265013	+	0.459016i	−0.702554	+	0.711630i	$0.747957\pi$
$272$	22.6274			0.00504408
$273$		0			0
$274$	−1656.00			−0.365119
$275$	1869.00	+	3237.20i	0.409836	+	0.709857i
$276$	1979.90	−	3429.29i	0.431797	−	0.747894i
$277$	−2003.00	+	3469.30i	−0.434472	+	0.752527i	−0.997252	−	0.0740794i	$-0.976398\pi$
$277$	−2003.00	+	3469.30i	−0.434472	+	0.752527i	0.562781	+	0.826606i	$0.309731\pi$
$278$	−425.678	−	737.296i	−0.0918363	−	0.159065i
$279$	−2146.78			−0.460660
$280$		0			0
$281$	−5984.00			−1.27038			−0.635188	−	0.772358i	$-0.719077\pi$
$281$	−5984.00			−1.27038			−0.635188	+	0.772358i	$0.719077\pi$
$282$	−3700.00	−	6408.59i	−0.781318	−	1.35328i
$283$	2464.27	−	4268.24i	0.517617	−	0.896538i	−0.482174	−	0.876075i	$-0.660153\pi$
$283$	2464.27	−	4268.24i	0.517617	−	0.896538i	0.999791	−	0.0204627i	$-0.00651393\pi$
$284$	−1176.00	+	2036.89i	−0.245714	+	0.425589i
$285$	98.9949	+	171.464i	0.0205753	+	0.0356374i
$286$	1425.53			0.294731
$287$		0			0
$288$	−736.000			−0.150588
$289$	2455.50	+	4253.05i	0.499796	+	0.865673i
$290$	5662.51	−	9807.76i	1.14660	−	1.98597i
$291$	5245.00	−	9084.61i	1.05659	−	1.83007i
$292$	540.230	+	935.705i	0.108269	+	0.187527i
$293$	1971.41			0.393076			0.196538	−	0.980496i	$-0.437030\pi$
$293$	1971.41			0.393076			0.196538	+	0.980496i	$0.437030\pi$
$294$		0			0
$295$	−8596.00			−1.69654
$296$	−152.000	−	263.272i	−0.0298474	−	0.0516972i
$297$	197.990	−	342.929i	0.0386820	−	0.0669991i
$298$	2050.00	−	3550.70i	0.398501	−	0.690224i
$299$	−3563.82	−	6172.71i	−0.689301	−	1.19390i
$300$	−7551.90			−1.45336
$301$		0			0
$302$	944.000			0.179871
$303$	3990.00	+	6910.88i	0.756500	+	1.31030i
$304$	11.3137	−	19.5959i	0.00213449	−	0.00369705i
$305$	140.000	−	242.487i	0.0262832	−	0.0455238i
$306$	32.5269	+	56.3383i	0.00607660	+	0.0105250i
$307$	−4767.31			−0.886270			−0.443135	−	0.896455i	$-0.646134\pi$
$307$	−4767.31			−0.886270			−0.443135	+	0.896455i	$0.646134\pi$
$308$		0			0
$309$	6140.00			1.13040
$310$	1848.00	+	3200.83i	0.338579	+	0.586435i
$311$	3388.46	−	5868.98i	0.617819	−	1.07009i	−0.372064	−	0.928207i	$-0.621350\pi$
$311$	3388.46	−	5868.98i	0.617819	−	1.07009i	0.989883	−	0.141887i	$-0.0453169\pi$
$312$	−1440.00	+	2494.15i	−0.261295	+	0.452576i
$313$	3095.01	+	5360.71i	0.558914	+	0.968068i	0.997587	+	0.0694210i	$0.0221152\pi$
$313$	3095.01	+	5360.71i	0.558914	+	0.968068i	−0.438673	+	0.898647i	$0.644551\pi$
$314$	4423.66			0.795037
$315$		0			0
$316$	4880.00			0.868739
$317$	−4913.00	−	8509.57i	−0.870478	−	1.50771i	−0.861503	−	0.507753i	$-0.830476\pi$
$317$	−4913.00	−	8509.57i	−0.870478	−	1.50771i	−0.00897524	−	0.999960i	$-0.502857\pi$
$318$	523.259	−	906.311i	0.0922733	−	0.159822i
$319$	−2002.00	+	3467.57i	−0.351381	+	0.608609i
$320$	633.568	+	1097.37i	0.110680	+	0.191703i
$321$	11907.7			2.07047
$322$		0			0
$323$	−2.00000			−0.000344529
$324$	1642.00	+	2844.03i	0.281550	+	0.487659i
$325$	−6796.71	+	11772.2i	−1.16004	+	2.00925i
$326$	3286.00	−	5691.52i	0.558266	−	0.966945i
$327$	−2892.07	−	5009.21i	−0.489088	−	0.847125i
$328$	1006.92			0.169506
$329$		0			0
$330$	3920.00			0.653906
$331$	2869.00	+	4969.25i	0.476418	+	0.825181i	0.999635	−	0.0270189i	$-0.00860142\pi$
$331$	2869.00	+	4969.25i	0.476418	+	0.825181i	−0.523216	+	0.852200i	$0.675268\pi$
$332$	−845.700	+	1464.79i	−0.139801	+	0.242142i
$333$	437.000	−	756.906i	0.0719143	−	0.124559i
$334$	−1490.58	−	2581.76i	−0.244195	−	0.422957i
$335$	−13542.5			−2.20868
$336$		0			0
$337$	−2254.00			−0.364342			−0.182171	−	0.983267i	$-0.558312\pi$
$337$	−2254.00			−0.364342			−0.182171	+	0.983267i	$0.558312\pi$
$338$	395.000	+	684.160i	0.0635656	+	0.110099i
$339$	−1909.19	+	3306.81i	−0.305879	+	0.529797i
$340$	56.0000	−	96.9948i	0.00893243	−	0.0154714i
$341$	−653.367	−	1131.66i	−0.103759	−	0.179716i
$342$	65.0538			0.0102857
$343$		0			0
$344$	272.000			0.0426316
$345$	−9800.00	−	16974.1i	−1.52932	−	2.64885i
$346$	−2070.41	+	3586.05i	−0.321693	+	0.557189i
$347$	993.000	−	1719.93i	0.153623	−	0.266082i	−0.778934	−	0.627106i	$-0.784239\pi$
$347$	993.000	−	1719.93i	0.153623	−	0.266082i	0.932557	+	0.361024i	$0.117573\pi$
$348$	−4044.65	−	7005.54i	−0.623035	−	1.07913i
$349$	6771.25			1.03856			0.519279	−	0.854605i	$-0.326200\pi$
$349$	6771.25			1.03856			0.519279	+	0.854605i	$0.326200\pi$
$350$		0			0
$351$	1440.00			0.218979
$352$	−224.000	−	387.979i	−0.0339183	−	0.0587482i
$353$	−3496.64	+	6056.36i	−0.527217	+	0.913166i	0.472280	+	0.881449i	$0.343431\pi$
$353$	−3496.64	+	6056.36i	−0.527217	+	0.913166i	−0.999497	+	0.0317177i	$0.989902\pi$
$354$	−3070.00	+	5317.40i	−0.460928	+	0.798351i
$355$	5820.90	+	10082.1i	0.870258	+	1.50733i
$356$	2472.05			0.368028
$357$		0			0
$358$	−1080.00			−0.159441
$359$	−2972.00	−	5147.66i	−0.436925	−	0.756777i	0.560525	−	0.828137i	$-0.310599\pi$
$359$	−2972.00	−	5147.66i	−0.436925	−	0.756777i	−0.997451	+	0.0713606i	$0.977266\pi$
$360$	−1821.51	+	3154.94i	−0.266672	+	0.461889i
$361$	3428.50	−	5938.34i	0.499854	−	0.865773i
$362$	3784.44	+	6554.83i	0.549463	+	0.951697i
$363$	8025.66			1.16044
$364$		0			0
$365$	5348.00			0.766924
$366$	−100.000	−	173.205i	−0.0142816	−	0.0247365i
$367$	421.436	−	729.948i	0.0599421	−	0.103823i	−0.834497	−	0.551012i	$-0.814242\pi$
$367$	421.436	−	729.948i	0.0599421	−	0.103823i	0.894439	+	0.447190i	$0.147575\pi$
$368$	−1120.00	+	1939.90i	−0.158652	+	0.274794i
$369$	1447.45	+	2507.05i	0.204204	+	0.353691i
$370$	−1504.72			−0.211424
$371$		0			0
$372$	2640.00			0.367951
$373$	2863.00	+	4958.86i	0.397428	+	0.688365i	0.993408	−	0.114634i	$-0.0365696\pi$
$373$	2863.00	+	4958.86i	0.397428	+	0.688365i	−0.595980	+	0.802999i	$0.703236\pi$
$374$	−19.7990	+	34.2929i	−0.00273738	+	0.00474129i
$375$	−9940.00	+	17216.6i	−1.36880	+	2.37083i
$376$	2093.04	+	3625.24i	0.287075	+	0.497228i
$377$	−14560.7			−1.98917
$378$		0			0
$379$	10330.0			1.40004			0.700022	−	0.714122i	$-0.253174\pi$
$379$	10330.0			1.40004			0.700022	+	0.714122i	$0.253174\pi$
$380$	−56.0000	−	96.9948i	−0.00755984	−	0.0130940i
$381$	6081.12	−	10532.8i	0.817704	−	1.41630i
$382$	1028.00	−	1780.55i	0.137689	−	0.238484i
$383$	−502.046	−	869.569i	−0.0669800	−	0.116013i	0.830591	−	0.556884i	$-0.188003\pi$
$383$	−502.046	−	869.569i	−0.0669800	−	0.116013i	−0.897571	+	0.440871i	$0.854670\pi$
$384$	905.097			0.120281
$385$		0			0
$386$	−9184.00			−1.21102
$387$	391.000	+	677.232i	0.0513583	+	0.0889551i
$388$	−2967.02	+	5139.03i	−0.388216	+	0.672409i
$389$	−2605.00	+	4511.99i	−0.339534	+	0.588090i	−0.984345	−	0.176252i	$-0.943603\pi$
$389$	−2605.00	+	4511.99i	−0.339534	+	0.588090i	0.644811	+	0.764342i	$0.276936\pi$
$390$	7127.64	+	12345.4i	0.925441	+	1.60291i
$391$	197.990			0.0256081
$392$		0			0
$393$	12270.0			1.57491
$394$	794.000	+	1375.25i	0.101526	+	0.175848i
$395$	12077.4	−	20918.6i	1.53843	−	2.66464i
$396$	644.000	−	1115.44i	0.0817228	−	0.141548i
$397$	36.7696	+	63.6867i	0.00464839	+	0.00805125i	0.868340	−	0.495969i	$-0.165187\pi$
$397$	36.7696	+	63.6867i	0.00464839	+	0.00805125i	−0.863692	+	0.504020i	$0.831854\pi$
$398$	−4972.37			−0.626238
$399$		0			0
$400$	4272.00			0.534000
$401$	249.000	+	431.281i	0.0310086	+	0.0537085i	0.881113	−	0.472905i	$-0.156795\pi$
$401$	249.000	+	431.281i	0.0310086	+	0.0537085i	−0.850105	+	0.526614i	$0.823461\pi$
$402$	−4836.61	+	8377.25i	−0.600070	+	1.03935i
$403$	2376.00	−	4115.35i	0.293690	−	0.508686i
$404$	−2257.08	−	3909.39i	−0.277956	−	0.481434i
$405$	16255.0			1.99436
$406$		0			0
$407$	532.000			0.0647918
$408$	−40.0000	−	69.2820i	−0.00485366	−	0.00840679i
$409$	−1677.96	+	2906.32i	−0.202861	+	0.351365i	−0.949449	−	0.313921i	$-0.898357\pi$
$409$	−1677.96	+	2906.32i	−0.202861	+	0.351365i	0.746588	+	0.665286i	$0.231691\pi$
$410$	2492.00	−	4316.27i	0.300173	−	0.519916i
$411$	2927.42	+	5070.44i	0.351336	+	0.608532i
$412$	−3473.31			−0.415334
$413$		0			0
$414$	−6440.00			−0.764514
$415$	4186.00	+	7250.36i	0.495139	+	0.857606i
$416$	814.587	−	1410.91i	0.0960058	−	0.166287i
$417$	−1505.00	+	2606.74i	−0.176739	+	0.306121i
$418$	19.7990	+	34.2929i	0.00231675	+	0.00401272i
$419$	14545.2			1.69589			0.847946	−	0.530082i	$-0.177839\pi$
$419$	14545.2			1.69589			0.847946	+	0.530082i	$0.177839\pi$
$420$		0			0
$421$	10854.0			1.25651			0.628256	−	0.778007i	$-0.283769\pi$
$421$	10854.0			1.25651			0.628256	+	0.778007i	$0.283769\pi$
$422$	−2748.00	−	4759.68i	−0.316992	−	0.549046i
$423$	−6017.48	+	10422.6i	−0.691678	+	1.19802i
$424$	−296.000	+	512.687i	−0.0339034	+	0.0587224i
$425$	−188.798	−	327.007i	−0.0215483	−	0.0373227i
$426$	8315.58			0.945753
$427$		0			0
$428$	−6736.00			−0.760740
$429$	−2520.00	−	4364.77i	−0.283605	−	0.491219i
$430$	673.166	−	1165.96i	0.0754952	−	0.130762i
$431$	2682.00	−	4645.36i	0.299739	−	0.519163i	−0.676337	−	0.736592i	$-0.736434\pi$
$431$	2682.00	−	4645.36i	0.299739	−	0.519163i	0.976076	+	0.217429i	$0.0697672\pi$
$432$	−226.274	−	391.918i	−0.0252005	−	0.0436486i
$433$	−6487.00			−0.719966			−0.359983	−	0.932959i	$-0.617217\pi$
$433$	−6487.00			−0.719966			−0.359983	+	0.932959i	$0.617217\pi$
$434$		0			0
$435$	−40040.0			−4.41327
$436$	1636.00	+	2833.64i	0.179702	+	0.311253i
$437$	98.9949	−	171.464i	0.0108365	−	0.0187694i
$438$	1910.00	−	3308.22i	0.208364	−	0.360897i
$439$	−6966.42	−	12066.2i	−0.757378	−	1.31182i	−0.944183	−	0.329420i	$-0.893147\pi$
$439$	−6966.42	−	12066.2i	−0.757378	−	1.31182i	0.186806	−	0.982397i	$-0.440187\pi$
$440$	−2217.49			−0.240260
$441$		0			0
$442$	−144.000			−0.0154963
$443$	−2998.00	−	5192.69i	−0.321533	−	0.556912i	0.659271	−	0.751905i	$-0.270865\pi$
$443$	−2998.00	−	5192.69i	−0.321533	−	0.556912i	−0.980805	+	0.194993i	$0.937532\pi$
$444$	−537.401	+	930.806i	−0.0574413	+	0.0994912i
$445$	6118.00	−	10596.7i	0.651733	−	1.12883i
$446$	−3428.05	−	5937.56i	−0.363953	−	0.630385i
$447$	−14495.7			−1.53383
$448$		0			0
$449$	2622.00			0.275590			0.137795	−	0.990461i	$-0.455999\pi$
$449$	2622.00			0.275590			0.137795	+	0.990461i	$0.455999\pi$
$450$	6141.00	+	10636.5i	0.643310	+	1.11425i
$451$	−881.055	+	1526.03i	−0.0919895	+	0.159330i
$452$	1080.00	−	1870.61i	0.112387	−	0.194660i
$453$	−1668.77	−	2890.40i	−0.173081	−	0.299785i
$454$	−10581.1			−1.09383
$455$		0			0
$456$	−80.0000			−0.00821567
$457$	−5604.00	−	9706.41i	−0.573619	−	0.993538i	−0.996190	−	0.0872080i	$-0.972206\pi$
$457$	−5604.00	−	9706.41i	−0.573619	−	0.993538i	0.422571	−	0.906330i	$-0.361128\pi$
$458$	−2749.23	+	4761.81i	−0.280487	+	0.485818i
$459$	−20.0000	+	34.6410i	−0.00203381	+	0.00352267i
$460$	5543.72	+	9602.00i	0.561907	+	0.973251i
$461$	9786.36			0.988712			0.494356	−	0.869260i	$-0.335404\pi$
$461$	9786.36			0.988712			0.494356	+	0.869260i	$0.335404\pi$
$462$		0			0
$463$	3952.00			0.396685			0.198342	−	0.980133i	$-0.436444\pi$
$463$	3952.00			0.396685			0.198342	+	0.980133i	$0.436444\pi$
$464$	2288.00	+	3962.93i	0.228918	+	0.396497i
$465$	6533.67	−	11316.6i	0.651595	−	1.12860i
$466$	72.0000	−	124.708i	0.00715737	−	0.0123969i
$467$	−8753.27	−	15161.1i	−0.867352	−	1.50230i	−0.864693	−	0.502301i	$-0.832487\pi$
$467$	−8753.27	−	15161.1i	−0.867352	−	1.50230i	−0.00265876	−	0.999996i	$-0.500846\pi$
$468$	4683.88			0.462633
$469$		0			0
$470$	20720.0			2.03349
$471$	−7820.00	−	13544.6i	−0.765025	−	1.32506i
$472$	1736.65	−	3007.97i	0.169356	−	0.293333i
$473$	−238.000	+	412.228i	−0.0231358	+	0.0400724i
$474$	−8626.70	−	14941.9i	−0.835944	−	1.44790i
$475$	−377.595			−0.0364742
$476$		0			0
$477$	−1702.00			−0.163374
$478$	4308.00	+	7461.67i	0.412225	+	0.713994i
$479$	−1144.10	+	1981.64i	−0.109134	+	0.189026i	−0.915420	−	0.402501i	$-0.868141\pi$
$479$	−1144.10	+	1981.64i	−0.109134	+	0.189026i	0.806286	+	0.591526i	$0.201474\pi$
$480$	2240.00	−	3879.79i	0.213003	−	0.368932i
$481$	967.322	+	1675.45i	0.0916967	+	0.158823i
$482$	3080.16			0.291073
$483$		0			0
$484$	−4540.00			−0.426371
$485$	14686.0	+	25436.9i	1.37496	+	2.38151i
$486$	5041.67	−	8732.43i	0.470566	−	0.815043i
$487$	−486.000	+	841.777i	−0.0452213	+	0.0783256i	−0.887750	−	0.460326i	$-0.847733\pi$
$487$	−486.000	+	841.777i	−0.0452213	+	0.0783256i	0.842529	+	0.538651i	$0.181066\pi$
$488$	56.5685	+	97.9796i	0.00524741	+	0.00908879i
$489$	−23235.5			−2.14877
$490$		0			0
$491$	−7404.00			−0.680525			−0.340263	−	0.940330i	$-0.610516\pi$
$491$	−7404.00			−0.680525			−0.340263	+	0.940330i	$0.610516\pi$
$492$	−1780.00	−	3083.05i	−0.163107	−	0.282509i
$493$	202.233	−	350.277i	0.0184748	−	0.0319994i
$494$	−72.0000	+	124.708i	−0.00655756	+	0.0113580i
$495$	−3187.64	−	5521.15i	−0.289442	−	0.501328i
$496$	−1493.41			−0.135194
$497$		0			0
$498$	5980.00			0.538093
$499$	6122.00	+	10603.6i	0.549215	+	0.951269i	0.998329	+	0.0577938i	$0.0184066\pi$
$499$	6122.00	+	10603.6i	0.549215	+	0.951269i	−0.449113	+	0.893475i	$0.648260\pi$
$500$	5622.91	−	9739.17i	0.502929	−	0.871098i
$501$	−5270.00	+	9127.91i	−0.469953	+	0.813982i
$502$	931.967	+	1614.21i	0.0828600	+	0.143518i
$503$	−2415.48			−0.214117			−0.107058	−	0.994253i	$-0.534143\pi$
$503$	−2415.48			−0.214117			−0.107058	+	0.994253i	$0.534143\pi$
$504$		0			0
$505$	−22344.0			−1.96890
$506$	−1960.00	−	3394.82i	−0.172199	−	0.298257i
$507$	1396.54	−	2418.87i	0.122332	−	0.211885i
$508$	−3440.00	+	5958.25i	−0.300444	+	0.520383i
$509$	2853.88	+	4943.07i	0.248519	+	0.430447i	0.963115	−	0.269090i	$-0.0867228\pi$
$509$	2853.88	+	4943.07i	0.248519	+	0.430447i	−0.714596	+	0.699537i	$0.753390\pi$
$510$	−395.980			−0.0343809
$511$		0			0
$512$	−512.000			−0.0441942
$513$	20.0000	+	34.6410i	0.00172129	+	0.00298136i
$514$	937.624	−	1624.01i	0.0804607	−	0.139362i
$515$	−8596.00	+	14888.7i	−0.735505	+	1.27393i
$516$	−480.833	−	832.827i	−0.0410222	−	0.0710526i
$517$	−7325.63			−0.623173
$518$		0			0
$519$	14640.0			1.23820
$520$	−4032.00	−	6983.63i	−0.340029	−	0.588947i
$521$	−0.707107	+	1.22474i	−5.94605e−5	+	0.000102989i	−0.866055	−	0.499949i	$-0.833352\pi$
$521$	−0.707107	+	1.22474i	−5.94605e−5	+	0.000102989i	0.865996	+	0.500051i	$0.166686\pi$
$522$	−6578.00	+	11393.4i	−0.551554	+	0.955320i
$523$	6128.49	+	10614.9i	0.512391	+	0.887487i	0.999897	+	0.0143672i	$0.00457337\pi$
$523$	6128.49	+	10614.9i	0.512391	+	0.887487i	−0.487506	+	0.873120i	$0.662093\pi$
$524$	−6940.96			−0.578659
$525$		0			0
$526$	−14280.0			−1.18372
$527$	66.0000	+	114.315i	0.00545542	+	0.00944906i
$528$	−791.960	+	1371.71i	−0.0652758	+	0.113061i
$529$	−3716.50	+	6437.17i	−0.305457	+	0.529068i
$530$	1465.13	+	2537.67i	0.120077	+	0.207980i
$531$	9985.76			0.816093
$532$		0			0
$533$	−6408.00			−0.520753
$534$	−4370.00	−	7569.06i	−0.354136	−	0.613381i
$535$	−16670.7	+	28874.6i	−1.34718	+	2.33338i
$536$	2736.00	−	4738.89i	0.220480	−	0.381882i
$537$	1909.19	+	3306.81i	0.153422	+	0.265735i
$538$	−9220.67			−0.738906
$539$		0			0
$540$	−2240.00			−0.178508
$541$	−1025.00	−	1775.35i	−0.0814569	−	0.141088i	0.822419	−	0.568882i	$-0.192624\pi$
$541$	−1025.00	−	1775.35i	−0.0814569	−	0.141088i	−0.903876	+	0.427795i	$0.859291\pi$
$542$	−2364.57	+	4095.55i	−0.187393	+	0.324573i
$543$	13380.0	−	23174.8i	1.05744	−	1.83154i
$544$	22.6274	+	39.1918i	0.00178335	+	0.00308885i
$545$	16195.6			1.27292
$546$		0			0
$547$	14554.0			1.13763			0.568815	−	0.822465i	$-0.307402\pi$
$547$	14554.0			1.13763			0.568815	+	0.822465i	$0.307402\pi$
$548$	−1656.00	−	2868.28i	−0.129089	−	0.223589i
$549$	−162.635	+	281.691i	−0.0126431	+	0.0218985i
$550$	−3738.00	+	6474.41i	−0.289798	+	0.501945i
$551$	−202.233	−	350.277i	−0.0156359	−	0.0270822i
$552$	7919.60			0.610653
$553$		0			0
$554$	−8012.00			−0.614435
$555$	2660.00	+	4607.26i	0.203443	+	0.352373i
$556$	851.357	−	1474.59i	0.0649381	−	0.112476i
$557$	−3477.00	+	6022.34i	−0.264498	+	0.458123i	−0.967432	−	0.253131i	$-0.918539\pi$
$557$	−3477.00	+	6022.34i	−0.264498	+	0.458123i	0.702934	+	0.711255i	$0.251873\pi$
$558$	−2146.78	−	3718.33i	−0.162868	−	0.282095i
$559$	−1731.00			−0.130972
$560$		0			0
$561$	140.000			0.0105362
$562$	−5984.00	−	10364.6i	−0.449146	−	0.777943i
$563$	818.123	−	1417.03i	0.0612429	−	0.106076i	−0.833778	−	0.552099i	$-0.813827\pi$
$563$	818.123	−	1417.03i	0.0612429	−	0.106076i	0.895021	+	0.446024i	$0.147160\pi$
$564$	7400.00	−	12817.2i	0.552476	−	0.956916i
$565$	−5345.73	−	9259.07i	−0.398047	−	0.689437i
$566$	9857.07			0.732020
$567$		0			0
$568$	−4704.00			−0.347492
$569$	3571.00	+	6185.15i	0.263100	+	0.455703i	0.967064	−	0.254533i	$-0.0819216\pi$
$569$	3571.00	+	6185.15i	0.263100	+	0.455703i	−0.703964	+	0.710236i	$0.748588\pi$
$570$	−197.990	+	342.929i	−0.0145489	+	0.0251995i
$571$	10303.0	−	17845.3i	0.755109	−	1.30789i	−0.190211	−	0.981743i	$-0.560917\pi$
$571$	10303.0	−	17845.3i	0.755109	−	1.30789i	0.945320	−	0.326144i	$-0.105749\pi$
$572$	1425.53	+	2469.09i	0.104203	+	0.180485i
$573$	−7269.06			−0.529964
$574$		0			0
$575$	37380.0			2.71105
$576$	−736.000	−	1274.79i	−0.0532407	−	0.0922157i
$577$	4401.74	−	7624.04i	0.317585	−	0.550074i	−0.662398	−	0.749152i	$-0.730461\pi$
$577$	4401.74	−	7624.04i	0.317585	−	0.550074i	0.979984	+	0.199078i	$0.0637946\pi$
$578$	−4911.00	+	8506.10i	−0.353409	+	0.612123i
$579$	16235.2	+	28120.1i	1.16530	+	2.01836i
$580$	22650.0			1.62154
$581$		0			0
$582$	20980.0			1.49424
$583$	−518.000	−	897.202i	−0.0367982	−	0.0637364i
$584$	−1080.46	+	1871.41i	−0.0765577	+	0.132602i
$585$	11592.0	−	20077.9i	0.819265	−	1.41901i
$586$	1971.41	+	3414.59i	0.138973	+	0.240709i
$587$	6503.97			0.457321			0.228661	−	0.973506i	$-0.426565\pi$
$587$	6503.97			0.457321			0.228661	+	0.973506i	$0.426565\pi$
$588$		0			0
$589$	132.000			0.00923424
$590$	−8596.00	−	14888.7i	−0.599816	−	1.03891i
$591$	2807.21	−	4862.24i	0.195386	−	0.338419i
$592$	304.000	−	526.543i	0.0211053	−	0.0365554i
$593$	11570.4	+	20040.5i	0.801246	+	1.38780i	0.918796	+	0.394732i	$0.129163\pi$
$593$	11570.4	+	20040.5i	0.801246	+	1.38780i	−0.117550	+	0.993067i	$0.537504\pi$
$594$	791.960			0.0547045
$595$		0			0
$596$	8200.00			0.563566
$597$	8790.00	+	15224.7i	0.602598	+	1.04373i
$598$	7127.64	−	12345.4i	0.487409	−	0.844218i
$599$	5648.00	−	9782.62i	0.385260	−	0.667291i	−0.606545	−	0.795049i	$-0.707445\pi$
$599$	5648.00	−	9782.62i	0.385260	−	0.667291i	0.991805	+	0.127759i	$0.0407783\pi$
$600$	−7551.90	−	13080.3i	−0.513842	−	0.890000i
$601$	8727.11			0.592323			0.296162	−	0.955138i	$-0.404293\pi$
$601$	8727.11			0.592323			0.296162	+	0.955138i	$0.404293\pi$
$602$		0			0
$603$	15732.0			1.06245
$604$	944.000	+	1635.06i	0.0635941	+	0.110148i
$605$	−11235.9	+	19461.2i	−0.755050	+	1.30779i
$606$	−7980.00	+	13821.8i	−0.534926	+	0.926520i
$607$	−9868.38	−	17092.5i	−0.659877	−	1.14294i	−0.980647	−	0.195783i	$-0.937275\pi$
$607$	−9868.38	−	17092.5i	−0.659877	−	1.14294i	0.320770	−	0.947157i	$-0.396058\pi$
$608$	45.2548			0.00301863
$609$		0			0
$610$	560.000			0.0371701
$611$	−13320.0	−	23070.9i	−0.881947	−	1.52758i
$612$	−65.0538	+	112.677i	−0.00429681	+	0.00744229i
$613$	−8481.00	+	14689.5i	−0.558800	+	0.967870i	0.438797	+	0.898586i	$0.355405\pi$
$613$	−8481.00	+	14689.5i	−0.558800	+	0.967870i	−0.997597	+	0.0692837i	$0.977929\pi$
$614$	−4767.31	−	8257.23i	−0.313344	−	0.542727i
$615$	−17621.1			−1.15537
$616$		0			0
$617$	−19034.0			−1.24194			−0.620972	−	0.783832i	$-0.713262\pi$
$617$	−19034.0			−1.24194			−0.620972	+	0.783832i	$0.713262\pi$
$618$	6140.00	+	10634.8i	0.399655	+	0.692223i
$619$	9338.76	−	16175.2i	0.606392	−	1.05030i	−0.385438	−	0.922734i	$-0.625950\pi$
$619$	9338.76	−	16175.2i	0.606392	−	1.05030i	0.991830	−	0.127568i	$-0.0407169\pi$
$620$	−3696.00	+	6401.66i	−0.239411	+	0.414672i
$621$	−1979.90	−	3429.29i	−0.127940	−	0.221598i
$622$	13553.8			0.873728
$623$		0			0
$624$	−5760.00			−0.369527
$625$	−11144.5	−	19302.8i	−0.713248	−	1.23538i
$626$	−6190.01	+	10721.4i	−0.395212	+	0.684527i
$627$	70.0000	−	121.244i	0.00445858	−	0.00772249i
$628$	4423.66	+	7662.00i	0.281088	+	0.486859i
$629$	−53.7401			−0.00340661
$630$		0			0
$631$	−14716.0			−0.928423			−0.464211	−	0.885724i	$-0.653662\pi$
$631$	−14716.0			−0.928423			−0.464211	+	0.885724i	$0.653662\pi$
$632$	4880.00	+	8452.41i	0.307146	+	0.531992i
$633$	−9715.65	+	16828.0i	−0.610051	+	1.05664i
$634$	9826.00	−	17019.1i	0.615521	−	1.06611i
$635$	17027.1	+	29491.9i	1.06410	+	1.84307i
$636$	2093.04			0.130494
$637$		0			0
$638$	−8008.00			−0.496928
$639$	−6762.00	−	11712.1i	−0.418624	−	0.725078i
$640$	−1267.14	+	2194.74i	−0.0782624	+	0.135554i
$641$	−2365.00	+	4096.30i	−0.145728	+	0.252409i	−0.929644	−	0.368458i	$-0.879886\pi$
$641$	−2365.00	+	4096.30i	−0.145728	+	0.252409i	0.783916	+	0.620867i	$0.213219\pi$
$642$	11907.7	+	20624.7i	0.732023	+	1.26790i
$643$	19056.5			1.16877			0.584383	−	0.811478i	$-0.301337\pi$
$643$	19056.5			1.16877			0.584383	+	0.811478i	$0.301337\pi$
$644$		0			0
$645$	−4760.00			−0.290581
$646$	−2.00000	−	3.46410i	−0.000121810	−	0.000210980i
$647$	−4671.15	+	8090.66i	−0.283836	+	0.491618i	−0.972326	−	0.233627i	$-0.924940\pi$
$647$	−4671.15	+	8090.66i	−0.283836	+	0.491618i	0.688490	+	0.725245i	$0.258274\pi$
$648$	−3284.00	+	5688.05i	−0.199086	+	0.344827i
$649$	3039.14	+	5263.95i	0.183816	+	0.318379i
$650$	−27186.8			−1.64055
$651$		0			0
$652$	13144.0			0.789507
$653$	−1887.00	−	3268.38i	−0.113084	−	0.195868i	0.803928	−	0.594727i	$-0.202740\pi$
$653$	−1887.00	−	3268.38i	−0.113084	−	0.195868i	−0.917012	+	0.398859i	$0.869406\pi$
$654$	5784.13	−	10018.4i	0.345837	−	0.599008i
$655$	−17178.0	+	29753.2i	−1.02473	+	1.77489i
$656$	1006.92	+	1744.04i	0.0599293	+	0.103801i
$657$	−6212.64			−0.368917
$658$		0			0
$659$	−21150.0			−1.25021			−0.625104	−	0.780541i	$-0.714943\pi$
$659$	−21150.0			−1.25021			−0.625104	+	0.780541i	$0.714943\pi$
$660$	3920.00	+	6789.64i	0.231191	+	0.400434i
$661$	5188.75	−	8987.18i	0.305324	−	0.528836i	−0.672010	−	0.740542i	$-0.734569\pi$
$661$	5188.75	−	8987.18i	0.305324	−	0.528836i	0.977333	+	0.211706i	$0.0679020\pi$
$662$	−5738.00	+	9938.51i	−0.336879	+	0.583491i
$663$	254.558	+	440.908i	0.0149114	+	0.0258272i
$664$	−3382.80			−0.197708
$665$		0			0
$666$	1748.00			0.101702
$667$	20020.0	+	34675.7i	1.16219	+	2.01296i
$668$	2981.16	−	5163.52i	0.172672	−	0.299076i
$669$	−12120.0	+	20992.5i	−0.700428	+	1.21318i
$670$	−13542.5	−	23456.3i	−0.780885	−	1.35253i
$671$	−197.990			−0.0113909
$672$		0			0
$673$	−1164.00			−0.0666700			−0.0333350	−	0.999444i	$-0.510613\pi$
$673$	−1164.00			−0.0666700			−0.0333350	+	0.999444i	$0.510613\pi$
$674$	−2254.00	−	3904.04i	−0.128814	−	0.223113i
$675$	−3775.95	+	6540.14i	−0.215313	+	0.372933i
$676$	−790.000	+	1368.32i	−0.0449477	+	0.0778516i
$677$	−13576.5	−	23515.1i	−0.770732	−	1.33495i	−0.937162	−	0.348893i	$-0.886558\pi$
$677$	−13576.5	−	23515.1i	−0.770732	−	1.33495i	0.166431	−	0.986053i	$-0.446776\pi$
$678$	−7636.75			−0.432578
$679$		0			0
$680$	224.000			0.0126324
$681$	18705.0	+	32398.0i	1.05254	+	1.82305i
$682$	1306.73	−	2263.33i	0.0733686	−	0.127078i
$683$	8298.00	−	14372.6i	0.464882	−	0.805199i	−0.534315	−	0.845286i	$-0.679430\pi$
$683$	8298.00	−	14372.6i	0.464882	−	0.805199i	0.999196	+	0.0400871i	$0.0127636\pi$
$684$	65.0538	+	112.677i	0.00363654	+	0.00629868i
$685$	−16393.6			−0.914403
$686$		0			0
$687$	19440.0			1.07960
$688$	272.000	+	471.118i	0.0150725	+	0.0261064i
$689$	1883.73	−	3262.72i	0.104157	−	0.180406i
$690$	19600.0	−	33948.2i	1.08139	−	1.87302i
$691$	−5649.08	−	9784.49i	−0.311000	−	0.538668i	0.667579	−	0.744539i	$-0.267331\pi$
$691$	−5649.08	−	9784.49i	−0.311000	−	0.538668i	−0.978579	+	0.205871i	$0.933997\pi$
$692$	−8281.63			−0.454943
$693$		0			0
$694$	3972.00			0.217255
$695$	−4214.00	−	7298.86i	−0.229994	−	0.398362i
$696$	8089.30	−	14011.1i	0.440552	−	0.763058i
$697$	89.0000	−	154.153i	0.00483661	−	0.00837725i
$698$	6771.25	+	11728.2i	0.367186	+	0.635985i
$699$	−509.117			−0.0275487
$700$		0			0
$701$	−2754.00			−0.148384			−0.0741920	−	0.997244i	$-0.523638\pi$
$701$	−2754.00			−0.148384			−0.0741920	+	0.997244i	$0.523638\pi$
$702$	1440.00	+	2494.15i	0.0774207	+	0.134097i
$703$	−26.8701	+	46.5403i	−0.00144157	+	0.00249687i
$704$	448.000	−	775.959i	0.0239839	−	0.0415413i
$705$	−36628.1	−	63441.8i	−1.95673	−	3.38916i
$706$	−13986.6			−0.745597
$707$		0			0
$708$	−12280.0			−0.651851
$709$	−14717.0	−	25490.6i	−0.779561	−	1.35024i	−0.932195	−	0.361956i	$-0.882109\pi$
$709$	−14717.0	−	25490.6i	−0.779561	−	1.35024i	0.152634	−	0.988283i	$-0.451224\pi$
$710$	−11641.8	+	20164.2i	−0.615365	+	1.06584i
$711$	−14030.0	+	24300.7i	−0.740037	+	1.28178i
$712$	2472.05	+	4281.71i	0.130118	+	0.225370i
$713$	−13067.3			−0.686361
$714$		0			0
$715$	14112.0			0.738124
$716$	−1080.00	−	1870.61i	−0.0563708	−	0.0976371i
$717$	15231.1	−	26381.0i	0.793327	−	1.37408i
$718$	5944.00	−	10295.3i	0.308953	−	0.535122i
$719$	8834.59	+	15302.0i	0.458240	+	0.793695i	0.998868	−	0.0475666i	$-0.0151466\pi$
$719$	8834.59	+	15302.0i	0.458240	+	0.793695i	−0.540628	+	0.841262i	$0.681813\pi$
$720$	−7286.03			−0.377131
$721$		0			0
$722$	13714.0			0.706901
$723$	−5445.00	−	9431.02i	−0.280085	−	0.485122i
$724$	−7568.87	+	13109.7i	−0.388529	+	0.672952i
$725$	38181.0	−	66131.4i	1.95587	−	3.38767i
$726$	8025.66	+	13900.9i	0.410276	+	0.710619i
$727$	28445.5			1.45115			0.725574	−	0.688144i	$-0.241574\pi$
$727$	28445.5			1.45115			0.725574	+	0.688144i	$0.241574\pi$
$728$		0			0
$729$	−13483.0			−0.685007
$730$	5348.00	+	9263.01i	0.271148	+	0.469643i
$731$	24.0416	−	41.6413i	0.00121643	−	0.00210692i
$732$	200.000	−	346.410i	0.0100987	−	0.0174914i
$733$	−11170.9	−	19348.5i	−0.562900	−	0.974971i	−0.997242	−	0.0742230i	$-0.976352\pi$
$733$	−11170.9	−	19348.5i	−0.562900	−	0.974971i	0.434342	−	0.900748i	$-0.356981\pi$
$734$	1685.74			0.0847710
$735$		0			0
$736$	−4480.00			−0.224368
$737$	4788.00	+	8293.06i	0.239306	+	0.414490i
$738$	−2894.90	+	5014.11i	−0.144394	+	0.250097i
$739$	−10335.0	+	17900.7i	−0.514451	+	0.891055i	0.485409	+	0.874287i	$0.338671\pi$
$739$	−10335.0	+	17900.7i	−0.514451	+	0.891055i	−0.999859	+	0.0167675i	$0.994662\pi$
$740$	−1504.72	−	2606.26i	−0.0747496	−	0.129470i
$741$	509.117			0.0252400
$742$		0			0
$743$	−25400.0			−1.25415			−0.627076	−	0.778958i	$-0.715749\pi$
$743$	−25400.0			−1.25415			−0.627076	+	0.778958i	$0.715749\pi$
$744$	2640.00	+	4572.61i	0.130090	+	0.225323i
$745$	20294.0	−	35150.2i	0.998004	−	1.72859i
$746$	−5726.00	+	9917.72i	−0.281024	+	0.486748i
$747$	−4862.77	−	8422.57i	−0.238179	−	0.412538i
$748$	−79.1960			−0.00387124
$749$		0			0
$750$	−39760.0			−1.93577
$751$	−14590.0	−	25270.6i	−0.708917	−	1.22788i	−0.965259	−	0.261294i	$-0.915851\pi$
$751$	−14590.0	−	25270.6i	−0.708917	−	1.22788i	0.256342	−	0.966586i	$-0.417483\pi$
$752$	−4186.07	+	7250.49i	−0.202992	+	0.351593i
$753$	3295.00	−	5707.11i	0.159464	−	0.276200i
$754$	−14560.7	−	25219.9i	−0.703277	−	1.21811i
$755$	9345.12			0.450469
$756$		0			0
$757$	−26206.0			−1.25822			−0.629110	−	0.777316i	$-0.716581\pi$
$757$	−26206.0			−1.25822			−0.629110	+	0.777316i	$0.716581\pi$
$758$	10330.0	+	17892.1i	0.494990	+	0.857348i
$759$	−6929.65	+	12002.5i	−0.331397	+	0.573996i
$760$	112.000	−	193.990i	0.00534561	−	0.00925888i
$761$	−3431.59	−	5943.69i	−0.163463	−	0.283125i	0.772646	−	0.634838i	$-0.218933\pi$
$761$	−3431.59	−	5943.69i	−0.163463	−	0.283125i	−0.936108	+	0.351712i	$0.885600\pi$
$762$	24324.5			1.15641
$763$		0			0
$764$	4112.00			0.194721
$765$	322.000	+	557.720i	0.0152182	+	0.0263587i
$766$	1004.09	−	1739.14i	0.0473620	−	0.0820334i
$767$	−11052.0	+	19142.6i	−0.520293	+	0.901174i
$768$	905.097	+	1567.67i	0.0425259	+	0.0736570i
$769$	−9058.04			−0.424761			−0.212380	−	0.977187i	$-0.568122\pi$
$769$	−9058.04			−0.424761			−0.212380	+	0.977187i	$0.568122\pi$
$770$		0			0
$771$	−6630.00			−0.309693
$772$	−9184.00	−	15907.2i	−0.428160	−	0.741595i
$773$	66.4680	−	115.126i	0.00309274	−	0.00535679i	−0.864475	−	0.502676i	$-0.832349\pi$
$773$	66.4680	−	115.126i	0.00309274	−	0.00535679i	0.867568	+	0.497319i	$0.165682\pi$
$774$	−782.000	+	1354.46i	−0.0363158	+	0.0629008i
$775$	12460.6	+	21582.5i	0.577547	+	1.00034i
$776$	−11868.1			−0.549020
$777$		0			0
$778$	−10420.0			−0.480174
$779$	−89.0000	−	154.153i	−0.00409340	−	0.00708997i
$780$	−14255.3	+	24690.9i	−0.654385	+	1.13343i
$781$	4116.00	−	7129.12i	0.188581	−	0.326633i
$782$	197.990	+	342.929i	0.00905384	+	0.0156817i
$783$	−8089.30			−0.369206
$784$		0			0
$785$	43792.0			1.99109
$786$	12270.0	+	21252.3i	0.556815	+	0.964431i
$787$	4364.97	−	7560.35i	0.197706	−	0.342436i	−0.750078	−	0.661349i	$-0.769984\pi$
$787$	4364.97	−	7560.35i	0.197706	−	0.342436i	0.947784	+	0.318913i	$0.103318\pi$
$788$	−1588.00	+	2750.50i	−0.0717895	+	0.124343i
$789$	25243.7	+	43723.4i	1.13904	+	1.97287i
$790$	48309.5			2.17567
$791$		0			0
$792$	2576.00			0.115573
$793$	−360.000	−	623.538i	−0.0161210	−	0.0279224i
$794$	−73.5391	+	127.373i	−0.00328691	+	0.00569309i
$795$	5180.00	−	8972.02i	0.231089	−	0.400258i
$796$	−4972.37	−	8612.41i	−0.221408	−	0.383491i
$797$	7517.96			0.334128			0.167064	−	0.985946i	$-0.446571\pi$
$797$	7517.96			0.334128			0.167064	+	0.985946i	$0.446571\pi$
$798$		0			0
$799$	740.000			0.0327651
$800$	4272.00	+	7399.32i	0.188798	+	0.327007i
$801$	−7107.13	+	12309.9i	−0.313506	+	0.543008i
$802$	−498.000	+	862.561i	−0.0219264	+	0.0379777i
$803$	−1890.80	−	3274.97i	−0.0830947	−	0.143924i
$804$	−19346.4			−0.848627
$805$		0			0
$806$	9504.00			0.415340
$807$	16300.0	+	28232.4i	0.711013	+	1.23151i
$808$	4514.17	−	7818.77i	0.196544	−	0.340425i
$809$	−1888.00	+	3270.11i	−0.0820501	+	0.142115i	−0.904130	−	0.427257i	$-0.859480\pi$
$809$	−1888.00	+	3270.11i	−0.0820501	+	0.142115i	0.822080	+	0.569372i	$0.192813\pi$
$810$	16255.0	+	28154.4i	0.705113	+	1.22129i
$811$	−36227.9			−1.56860			−0.784300	−	0.620382i	$-0.786977\pi$
$811$	−36227.9			−1.56860			−0.784300	+	0.620382i	$0.786977\pi$
$812$		0			0
$813$	16720.0			0.721274
$814$	532.000	+	921.451i	0.0229074	+	0.0396767i
$815$	32529.7	−	56343.2i	1.39812	−	2.42161i
$816$	80.0000	−	138.564i	0.00343206	−	0.00594450i
$817$	−24.0416	−	41.6413i	−0.00102951	−	0.00178316i
$818$	−6711.86			−0.286888
$819$		0			0
$820$	9968.00			0.424509
$821$	8205.00	+	14211.5i	0.348790	+	0.604122i	0.986035	−	0.166540i	$-0.0532594\pi$
$821$	8205.00	+	14211.5i	0.348790	+	0.604122i	−0.637245	+	0.770661i	$0.719926\pi$
$822$	−5854.84	+	10140.9i	−0.248432	+	0.430297i
$823$	−11036.0	+	19114.9i	−0.467425	+	0.809604i	−0.999307	−	0.0372144i	$-0.988152\pi$
$823$	−11036.0	+	19114.9i	−0.467425	+	0.809604i	0.531882	+	0.846818i	$0.321485\pi$
$824$	−3473.31	−	6015.95i	−0.146843	−	0.254339i
$825$	26431.7			1.11543
$826$		0			0
$827$	−11628.0			−0.488930			−0.244465	−	0.969658i	$-0.578612\pi$
$827$	−11628.0			−0.488930			−0.244465	+	0.969658i	$0.578612\pi$
$828$	−6440.00	−	11154.4i	−0.270296	−	0.468167i
$829$	15453.1	−	26765.6i	0.647417	−	1.12136i	−0.336321	−	0.941748i	$-0.609183\pi$
$829$	15453.1	−	26765.6i	0.647417	−	1.12136i	0.983738	−	0.179612i	$-0.0574841\pi$
$830$	−8372.00	+	14500.7i	−0.350116	+	0.606419i
$831$	14163.3	+	24531.6i	0.591241	+	1.02406i
$832$	3258.35			0.135773
$833$		0			0
$834$	−6020.00			−0.249947
$835$	−14756.0	−	25558.1i	−0.611560	−	1.05925i
$836$	−39.5980	+	68.5857i	−0.00163819	+	0.00283742i
$837$	1320.00	−	2286.31i	0.0545112	−	0.0944162i
$838$	14545.2	+	25193.0i	0.599588	+	1.03852i
$839$	17884.1			0.735911			0.367955	−	0.929843i	$-0.380058\pi$
$839$	17884.1			0.735911			0.367955	+	0.929843i	$0.380058\pi$
$840$		0			0
$841$	57407.0			2.35381
$842$	10854.0	+	18799.7i	0.444244	+	0.769453i
$843$	−21156.6	+	36644.4i	−0.864381	+	1.49715i
$844$	5496.00	−	9519.35i	0.224147	−	0.388234i
$845$	3910.30	+	6772.84i	0.159193	+	0.275731i
$846$	−24069.9			−0.978181
$847$		0			0
$848$	−1184.00			−0.0479466
$849$	−17425.0	−	30181.0i	−0.704387	−	1.22003i
$850$	377.595	−	654.014i	0.0152369	−	0.0263912i
$851$	2660.00	−	4607.26i	0.107149	−	0.185587i
$852$	8315.58	+	14403.0i	0.334374	+	0.579153i
$853$	−20755.0			−0.833104			−0.416552	−	0.909112i	$-0.636762\pi$
$853$	−20755.0			−0.833104			−0.416552	+	0.909112i	$0.636762\pi$
$854$		0			0
$855$	644.000			0.0257595
$856$	−6736.00	−	11667.1i	−0.268962	−	0.465856i
$857$	−22459.8	+	38901.6i	−0.895231	+	1.55059i	−0.0617133	+	0.998094i	$0.519656\pi$
$857$	−22459.8	+	38901.6i	−0.895231	+	1.55059i	−0.833518	+	0.552492i	$0.813677\pi$
$858$	5040.00	−	8729.54i	0.200539	−	0.347344i
$859$	−34.6482	−	60.0125i	−0.00137623	−	0.00238370i	0.865336	−	0.501191i	$-0.167105\pi$
$859$	−34.6482	−	60.0125i	−0.00137623	−	0.00238370i	−0.866713	+	0.498808i	$0.833771\pi$
$860$	2692.66			0.106766
$861$		0			0
$862$	10728.0			0.423895
$863$	2726.00	+	4721.57i	0.107525	+	0.186239i	0.914767	−	0.403982i	$-0.132374\pi$
$863$	2726.00	+	4721.57i	0.107525	+	0.186239i	−0.807242	+	0.590221i	$0.799041\pi$
$864$	452.548	−	783.837i	0.0178195	−	0.0308642i
$865$	−20496.0	+	35500.1i	−0.805647	+	1.39542i
$866$	−6487.00	−	11235.8i	−0.254546	−	0.440887i
$867$	34726.0			1.36027
$868$		0			0
$869$	−17080.0			−0.666743
$870$	−40040.0	−	69351.3i	−1.56033	−	2.70256i
$871$	−17411.8	+	30158.1i	−0.677355	+	1.17321i
$872$	−3272.00	+	5667.27i	−0.127069	+	0.220089i
$873$	−17060.4	−	29549.4i	−0.661404	−	1.14559i
$874$	395.980			0.0153252
$875$		0			0
$876$	7640.00			0.294671
$877$	−15553.0	−	26938.6i	−0.598845	−	1.03723i	−0.992992	−	0.118183i	$-0.962293\pi$
$877$	−15553.0	−	26938.6i	−0.598845	−	1.03723i	0.394146	−	0.919048i	$-0.371040\pi$
$878$	13932.8	−	24132.4i	0.535547	−	0.927595i
$879$	6970.00	−	12072.4i	0.267454	−	0.463244i
$880$	−2217.49	−	3840.80i	−0.0849448	−	0.147129i
$881$	5943.94			0.227306			0.113653	−	0.993521i	$-0.463745\pi$
$881$	5943.94			0.227306			0.113653	+	0.993521i	$0.463745\pi$
$882$		0			0
$883$	34796.0			1.32614			0.663068	−	0.748559i	$-0.269254\pi$
$883$	34796.0			1.32614			0.663068	+	0.748559i	$0.269254\pi$
$884$	−144.000	−	249.415i	−0.00547878	−	0.00948953i
$885$	−30391.4	+	52639.5i	−1.15435	+	1.99939i
$886$	5996.00	−	10385.4i	0.227358	−	0.393796i
$887$	−4982.27	−	8629.55i	−0.188600	−	0.326665i	0.756184	−	0.654360i	$-0.227062\pi$
$887$	−4982.27	−	8629.55i	−0.188600	−	0.326665i	−0.944784	+	0.327694i	$0.893728\pi$
$888$	−2149.60			−0.0812342
$889$		0			0
$890$	24472.0			0.921689
$891$	−5747.00	−	9954.10i	−0.216085	−	0.374270i
$892$	6856.11	−	11875.1i	0.257354	−	0.445750i
$893$	370.000	−	640.859i	0.0138651	−	0.0240151i
$894$	−14495.7	−	25107.3i	−0.542291	−	0.939276i
$895$	−10691.5			−0.399303
$896$		0			0
$897$	−50400.0			−1.87604
$898$	2622.00	+	4541.44i	0.0974357	+	0.168764i
$899$	−13347.3	+	23118.3i	−0.495171	+	0.857662i
$900$	−12282.0	+	21273.0i	−0.454889	+	0.787891i
$901$	52.3259	+	90.6311i	0.00193477	+	0.00335112i
$902$	−3524.22			−0.130093
$903$		0			0
$904$	4320.00			0.158939
$905$	37464.0	+	64889.6i	1.37607	+	2.38343i
$906$	3337.54	−	5780.80i	0.122387	−	0.211980i
$907$	14878.0	−	25769.5i	0.544670	−	0.943396i	−0.453957	−	0.891023i	$-0.649988\pi$
$907$	14878.0	−	25769.5i	0.544670	−	0.943396i	0.998628	−	0.0523731i	$-0.0166785\pi$
$908$	−10581.1	−	18327.1i	−0.386726	−	0.669830i
$909$	25956.5			0.947109
$910$		0			0
$911$	21440.0			0.779735			0.389868	−	0.920871i	$-0.372521\pi$
$911$	21440.0			0.779735			0.389868	+	0.920871i	$0.372521\pi$
$912$	−80.0000	−	138.564i	−0.00290468	−	0.00503105i
$913$	2959.95	−	5126.78i	0.107295	−	0.185840i
$914$	11208.0	−	19412.8i	0.405610	−	0.702537i
$915$	−989.949	−	1714.64i	−0.0357669	−	0.0619501i
$916$	−10996.9			−0.396669
$917$		0			0
$918$	−80.0000			−0.00287625
$919$	4144.00	+	7177.62i	0.148746	+	0.257636i	0.930764	−	0.365620i	$-0.119143\pi$
$919$	4144.00	+	7177.62i	0.148746	+	0.257636i	−0.782018	+	0.623256i	$0.785810\pi$
$920$	−11087.4	+	19204.0i	−0.397328	+	0.688193i
$921$	−16855.0	+	29193.7i	−0.603031	+	1.04448i
$922$	9786.36	+	16950.5i	0.349562	+	0.605460i
$923$	29936.1			1.06756
$924$		0			0
$925$	−10146.0			−0.360647
$926$	3952.00	+	6845.06i	0.140249	+	0.242919i
$927$	9985.76	−	17295.8i	0.353803	−	0.612805i
$928$	−4576.00	+	7925.86i	−0.161869	+	0.280366i
$929$	22790.8	+	39474.8i	0.804888	+	1.39411i	0.916367	+	0.400339i	$0.131108\pi$
$929$	22790.8	+	39474.8i	0.804888	+	1.39411i	−0.111479	+	0.993767i	$0.535559\pi$
$930$	26134.7			0.921494
$931$		0			0
$932$	288.000			0.0101221
$933$	−23960.0	−	41499.9i	−0.840745	−	1.45621i
$934$	17506.5	−	30322.2i	0.613310	−	1.06228i
$935$	−196.000	+	339.482i	−0.00685549	+	0.0118741i
$936$	4683.88	+	8112.71i	0.163565	+	0.283304i
$937$	11665.8			0.406731			0.203365	−	0.979103i	$-0.434812\pi$
$937$	11665.8			0.406731			0.203365	+	0.979103i	$0.434812\pi$
$938$		0			0
$939$	43770.0			1.52117
$940$	20720.0	+	35888.1i	0.718949	+	1.24526i
$941$	−7.07107	+	12.2474i	−0.000244963	+	0.000424288i	−0.866148	−	0.499788i	$-0.833411\pi$
$941$	−7.07107	+	12.2474i	−0.000244963	+	0.000424288i	0.865903	+	0.500212i	$0.166745\pi$
$942$	15640.0	−	27089.3i	0.540954	−	0.936960i
$943$	8810.55	+	15260.3i	0.304253	+	0.526982i
$944$	6946.62			0.239505
$945$		0			0
$946$	−952.000			−0.0327190
$947$	−7017.00	−	12153.8i	−0.240783	−	0.417049i	0.720154	−	0.693814i	$-0.244071\pi$
$947$	−7017.00	−	12153.8i	−0.240783	−	0.417049i	−0.960938	+	0.276765i	$0.910738\pi$
$948$	17253.4	−	29883.8i	0.591102	−	1.02382i
$949$	6876.00	−	11909.6i	0.235200	−	0.407378i
$950$	−377.595	−	654.014i	−0.0128956	−	0.0223358i
$951$	−69480.3			−2.36914
$952$		0			0
$953$	−42698.0			−1.45134			−0.725668	−	0.688045i	$-0.758469\pi$
$953$	−42698.0			−1.45134			−0.725668	+	0.688045i	$0.758469\pi$
$954$	−1702.00	−	2947.95i	−0.0577613	−	0.100046i
$955$	10176.7	−	17626.5i	0.344827	−	0.597258i
$956$	−8616.00	+	14923.3i	−0.291487	+	0.504870i
$957$	14156.3	+	24519.4i	0.478169	+	0.828213i
$958$	−4576.40			−0.154339
$959$		0			0
$960$	8960.00			0.301232
$961$	10539.5	+	18254.9i	0.353781	+	0.612767i
$962$	−1934.64	+	3350.90i	−0.0648393	+	0.112305i
$963$	19366.0	−	33542.9i	0.648038	−	1.12243i
$964$	3080.16	+	5334.99i	0.102910	+	0.178245i
$965$	−90917.0			−3.03287
$966$		0			0
$967$	−48492.0			−1.61261			−0.806307	−	0.591497i	$-0.798537\pi$
$967$	−48492.0			−1.61261			−0.806307	+	0.591497i	$0.798537\pi$
$968$	−4540.00	−	7863.51i	−0.150745	−	0.261098i
$969$	−7.07107	+	12.2474i	−0.000234423	+	0.000406032i
$970$	−29372.0	+	50873.8i	−0.972245	+	1.68398i
$971$	−26334.8	−	45613.2i	−0.870364	−	1.50751i	−0.861621	−	0.507553i	$-0.830550\pi$
$971$	−26334.8	−	45613.2i	−0.870364	−	1.50751i	−0.00874297	−	0.999962i	$-0.502783\pi$
$972$	20166.7			0.665480
$973$		0			0
$974$	−1944.00			−0.0639525
$975$	48060.0	+	83242.4i	1.57862	+	2.73425i
$976$	−113.137	+	195.959i	−0.00371048	+	0.00642674i
$977$	27690.0	−	47960.5i	0.906737	−	1.57051i	0.0881674	−	0.996106i	$-0.471899\pi$
$977$	27690.0	−	47960.5i	0.906737	−	1.57051i	0.818569	−	0.574408i	$-0.194768\pi$
$978$	−23235.5	−	40245.1i	−0.759704	−	1.31585i
$979$	−8652.16			−0.282456
$980$		0			0
$981$	−18814.0			−0.612319
$982$	−7404.00	−	12824.1i	−0.240602	−	0.416735i
$983$	25267.8	−	43765.0i	0.819854	−	1.42003i	−0.0859360	−	0.996301i	$-0.527388\pi$
$983$	25267.8	−	43765.0i	0.819854	−	1.42003i	0.905790	−	0.423728i	$-0.139279\pi$
$984$	3560.00	−	6166.10i	0.115334	−	0.199764i
$985$	7860.20	+	13614.3i	0.254261	+	0.440392i
$986$	808.930			0.0261274
$987$		0			0
$988$	−288.000			−0.00927379
$989$	2380.00	+	4122.28i	0.0765213	+	0.132539i
$990$	6375.27	−	11042.3i	0.204666	−	0.354492i
$991$	19856.0	−	34391.6i	0.636475	−	1.10241i	−0.349726	−	0.936852i	$-0.613725\pi$
$991$	19856.0	−	34391.6i	0.636475	−	1.10241i	0.986201	−	0.165555i	$-0.0529415\pi$
$992$	−1493.41	−	2586.66i	−0.0477982	−	0.0827889i
$993$	40573.8			1.29665
$994$		0			0
$995$	−49224.0			−1.56835
$996$	5980.00	+	10357.7i	0.190245	+	0.329513i
$997$	−1093.19	+	1893.46i	−0.0347258	+	0.0601468i	−0.882866	−	0.469625i	$-0.844389\pi$
$997$	−1093.19	+	1893.46i	−0.0347258	+	0.0601468i	0.848140	+	0.529772i	$0.177722\pi$
$998$	−12244.0	+	21207.2i	−0.388354	+	0.672648i
$999$	537.401	+	930.806i	0.0170196	+	0.0294789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.4.c.h.67.2		4
3.2	odd	2		882.4.g.ba.361.1		4
7.2	even	3	inner	98.4.c.h.79.2		4
7.3	odd	6		98.4.a.g.1.2	yes	2
7.4	even	3		98.4.a.g.1.1	✓	2
7.5	odd	6	inner	98.4.c.h.79.1		4
7.6	odd	2	inner	98.4.c.h.67.1		4
21.2	odd	6		882.4.g.ba.667.1		4
21.5	even	6		882.4.g.ba.667.2		4
21.11	odd	6		882.4.a.bg.1.2		2
21.17	even	6		882.4.a.bg.1.1		2
21.20	even	2		882.4.g.ba.361.2		4
28.3	even	6		784.4.a.y.1.1		2
28.11	odd	6		784.4.a.y.1.2		2
35.4	even	6		2450.4.a.bx.1.2		2
35.24	odd	6		2450.4.a.bx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.4.a.g.1.1	✓	2	7.4	even	3
98.4.a.g.1.2	yes	2	7.3	odd	6
98.4.c.h.67.1		4	7.6	odd	2	inner
98.4.c.h.67.2		4	1.1	even	1	trivial
98.4.c.h.79.1		4	7.5	odd	6	inner
98.4.c.h.79.2		4	7.2	even	3	inner
784.4.a.y.1.1		2	28.3	even	6
784.4.a.y.1.2		2	28.11	odd	6
882.4.a.bg.1.1		2	21.17	even	6
882.4.a.bg.1.2		2	21.11	odd	6
882.4.g.ba.361.1		4	3.2	odd	2
882.4.g.ba.361.2		4	21.20	even	2
882.4.g.ba.667.1		4	21.2	odd	6
882.4.g.ba.667.2		4	21.5	even	6
2450.4.a.bx.1.1		2	35.24	odd	6
2450.4.a.bx.1.2		2	35.4	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(3.53553 - 6.12372i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +14.1421 q^{6} -8.00000 q^{8} +(-11.5000 - 19.9186i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(3.53553 - 6.12372i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.89949 + 17.1464i) q^{5} +14.1421 q^{6} -8.00000 q^{8} +(-11.5000 - 19.9186i) q^{9} +(-19.7990 + 34.2929i) q^{10} +(7.00000 - 12.1244i) q^{11} +(14.1421 + 24.4949i) q^{12} +50.9117 q^{13} +140.000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(23.0000 - 39.8372i) q^{18} +(0.707107 + 1.22474i) q^{19} -79.1960 q^{20} +28.0000 q^{22} +(-70.0000 - 121.244i) q^{23} +(-28.2843 + 48.9898i) q^{24} +(-133.500 + 231.229i) q^{25} +(50.9117 + 88.1816i) q^{26} +28.2843 q^{27} -286.000 q^{29} +(140.000 + 242.487i) q^{30} +(46.6690 - 80.8332i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-49.4975 - 85.7321i) q^{33} -2.82843 q^{34} +92.0000 q^{36} +(19.0000 + 32.9090i) q^{37} +(-1.41421 + 2.44949i) q^{38} +(180.000 - 311.769i) q^{39} +(-79.1960 - 137.171i) q^{40} -125.865 q^{41} -34.0000 q^{43} +(28.0000 + 48.4974i) q^{44} +(227.688 - 394.368i) q^{45} +(140.000 - 242.487i) q^{46} +(-261.630 - 453.156i) q^{47} -113.137 q^{48} -534.000 q^{50} +(5.00000 + 8.66025i) q^{51} +(-101.823 + 176.363i) q^{52} +(37.0000 - 64.0859i) q^{53} +(28.2843 + 48.9898i) q^{54} +277.186 q^{55} +10.0000 q^{57} +(-286.000 - 495.367i) q^{58} +(-217.082 + 375.997i) q^{59} +(-280.000 + 484.974i) q^{60} +(-7.07107 - 12.2474i) q^{61} +186.676 q^{62} +64.0000 q^{64} +(504.000 + 872.954i) q^{65} +(98.9949 - 171.464i) q^{66} +(-342.000 + 592.361i) q^{67} +(-2.82843 - 4.89898i) q^{68} -989.949 q^{69} +588.000 q^{71} +(92.0000 + 159.349i) q^{72} +(135.057 - 233.926i) q^{73} +(-38.0000 + 65.8179i) q^{74} +(943.988 + 1635.03i) q^{75} -5.65685 q^{76} +720.000 q^{78} +(-610.000 - 1056.55i) q^{79} +(158.392 - 274.343i) q^{80} +(410.500 - 711.007i) q^{81} +(-125.865 - 218.005i) q^{82} +422.850 q^{83} -28.0000 q^{85} +(-34.0000 - 58.8897i) q^{86} +(-1011.16 + 1751.39i) q^{87} +(-56.0000 + 96.9948i) q^{88} +(-309.006 - 535.214i) q^{89} +910.754 q^{90} +560.000 q^{92} +(-330.000 - 571.577i) q^{93} +(523.259 - 906.311i) q^{94} +(-14.0000 + 24.2487i) q^{95} +(-113.137 - 195.959i) q^{96} +1483.51 q^{97} -322.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 46 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 46 * q^9	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} - 46 q^{9} + 28 q^{11} + 560 q^{15} - 32 q^{16} + 92 q^{18} + 112 q^{22} - 280 q^{23} - 534 q^{25} - 1144 q^{29} + 560 q^{30} + 64 q^{32} + 368 q^{36} + 76 q^{37} + 720 q^{39} - 136 q^{43} + 112 q^{44} + 560 q^{46} - 2136 q^{50} + 20 q^{51} + 148 q^{53} + 40 q^{57} - 1144 q^{58} - 1120 q^{60} + 256 q^{64} + 2016 q^{65} - 1368 q^{67} + 2352 q^{71} + 368 q^{72} - 152 q^{74} + 2880 q^{78} - 2440 q^{79} + 1642 q^{81} - 112 q^{85} - 136 q^{86} - 224 q^{88} + 2240 q^{92} - 1320 q^{93} - 56 q^{95} - 1288 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 - 46 * q^9 + 28 * q^11 + 560 * q^15 - 32 * q^16 + 92 * q^18 + 112 * q^22 - 280 * q^23 - 534 * q^25 - 1144 * q^29 + 560 * q^30 + 64 * q^32 + 368 * q^36 + 76 * q^37 + 720 * q^39 - 136 * q^43 + 112 * q^44 + 560 * q^46 - 2136 * q^50 + 20 * q^51 + 148 * q^53 + 40 * q^57 - 1144 * q^58 - 1120 * q^60 + 256 * q^64 + 2016 * q^65 - 1368 * q^67 + 2352 * q^71 + 368 * q^72 - 152 * q^74 + 2880 * q^78 - 2440 * q^79 + 1642 * q^81 - 112 * q^85 - 136 * q^86 - 224 * q^88 + 2240 * q^92 - 1320 * q^93 - 56 * q^95 - 1288 * q^99

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