LMFDB - Embedded newform 198.6.l.b.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(17,198)]

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([5, 9]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	198.17
Dual form			198.6.l.b.35.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(105.333 + 34.2249i) q^{5} +(-53.1179 - 73.1105i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(105.333 + 34.2249i) q^{5} +(-53.1179 - 73.1105i) q^{7} +(51.7771 + 37.6183i) q^{8} -443.016i q^{10} +(272.508 - 294.602i) q^{11} +(-429.276 + 139.480i) q^{13} +(-212.472 + 292.442i) q^{14} +(79.1084 - 243.470i) q^{16} +(-26.5702 + 81.7747i) q^{17} +(1123.38 - 1546.21i) q^{19} +(-1685.33 + 547.598i) q^{20} +(-1457.57 - 672.533i) q^{22} -473.422i q^{23} +(7395.59 + 5373.21i) q^{25} +(1061.23 + 1460.65i) q^{26} +(1375.14 + 446.812i) q^{28} +(-158.140 + 114.895i) q^{29} +(2400.33 + 7387.44i) q^{31} -1024.00 q^{32} +343.932 q^{34} +(-3092.89 - 9518.93i) q^{35} +(7488.06 - 5440.39i) q^{37} +(-7270.70 - 2362.39i) q^{38} +(4166.37 + 5734.52i) q^{40} +(4498.09 + 3268.05i) q^{41} -8158.45i q^{43} +(-756.811 + 6376.23i) q^{44} +(-1801.01 + 585.182i) q^{46} +(4097.72 - 5640.02i) q^{47} +(2670.01 - 8217.45i) q^{49} +(11299.5 - 34776.2i) q^{50} +(4244.91 - 5842.62i) q^{52} +(19316.0 - 6276.16i) q^{53} +(38786.9 - 21704.9i) q^{55} -5783.65i q^{56} +(632.560 + 459.582i) q^{58} +(-18883.5 - 25990.9i) q^{59} +(-38559.8 - 12528.8i) q^{61} +(25136.5 - 18262.8i) q^{62} +(1265.73 + 3895.53i) q^{64} -49990.7 q^{65} -494.609 q^{67} +(-425.123 - 1308.39i) q^{68} +(-32389.1 + 23532.1i) q^{70} +(1936.17 + 629.099i) q^{71} +(20402.8 + 28082.0i) q^{73} +(-29952.2 - 21761.6i) q^{74} +30579.5i q^{76} +(-36013.6 - 4274.55i) q^{77} +(60311.2 - 19596.3i) q^{79} +(16665.5 - 22938.1i) q^{80} +(6872.47 - 21151.3i) q^{82} +(28042.2 - 86304.9i) q^{83} +(-5597.46 + 7704.24i) q^{85} +(-31036.6 + 10084.4i) q^{86} +(25192.1 - 5002.37i) q^{88} +125403. i q^{89} +(32999.7 + 23975.7i) q^{91} +(4452.33 + 6128.11i) q^{92} +(-26521.0 - 8617.19i) q^{94} +(171249. - 124419. i) q^{95} +(45406.0 + 139745. i) q^{97} -34561.4 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8	$ 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8} - 476 q^{11} - 2560 q^{16} - 1424 q^{17} - 1656 q^{22} + 11574 q^{25} + 10480 q^{26} + 3040 q^{28} - 10658 q^{29} - 5302 q^{31} - 40960 q^{32} - 13984 q^{34} - 50 q^{35} - 4344 q^{37} + 35120 q^{38} + 19840 q^{40} - 16856 q^{41} + 6624 q^{44} - 52400 q^{46} - 10900 q^{47} - 40698 q^{49} - 6256 q^{50} + 41920 q^{52} + 10290 q^{53} + 158396 q^{55} + 42632 q^{58} + 62620 q^{59} - 134780 q^{61} - 30272 q^{62} - 40960 q^{64} - 137296 q^{65} - 36856 q^{67} - 22784 q^{68} + 79400 q^{70} + 62180 q^{71} + 100030 q^{73} + 17376 q^{74} - 162888 q^{77} + 35900 q^{79} + 79360 q^{80} - 90096 q^{82} - 12276 q^{83} + 270600 q^{85} - 137680 q^{86} - 26496 q^{88} + 406656 q^{91} + 134720 q^{92} - 91600 q^{94} - 75128 q^{95} - 364164 q^{97} + 358192 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8 - 476 * q^11 - 2560 * q^16 - 1424 * q^17 - 1656 * q^22 + 11574 * q^25 + 10480 * q^26 + 3040 * q^28 - 10658 * q^29 - 5302 * q^31 - 40960 * q^32 - 13984 * q^34 - 50 * q^35 - 4344 * q^37 + 35120 * q^38 + 19840 * q^40 - 16856 * q^41 + 6624 * q^44 - 52400 * q^46 - 10900 * q^47 - 40698 * q^49 - 6256 * q^50 + 41920 * q^52 + 10290 * q^53 + 158396 * q^55 + 42632 * q^58 + 62620 * q^59 - 134780 * q^61 - 30272 * q^62 - 40960 * q^64 - 137296 * q^65 - 36856 * q^67 - 22784 * q^68 + 79400 * q^70 + 62180 * q^71 + 100030 * q^73 + 17376 * q^74 - 162888 * q^77 + 35900 * q^79 + 79360 * q^80 - 90096 * q^82 - 12276 * q^83 + 270600 * q^85 - 137680 * q^86 - 26496 * q^88 + 406656 * q^91 + 134720 * q^92 - 91600 * q^94 - 75128 * q^95 - 364164 * q^97 + 358192 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	105.333	+	34.2249i	1.88426	+	0.612233i	0.984369	+	0.176119i	$0.0563542\pi$
$5$	105.333	+	34.2249i	1.88426	+	0.612233i	0.899891	+	0.436115i	$0.143646\pi$
$6$		0			0
$7$	−53.1179	−	73.1105i	−0.409728	−	0.563942i	0.553424	−	0.832900i	$-0.313321\pi$
$7$	−53.1179	−	73.1105i	−0.409728	−	0.563942i	−0.963152	+	0.268957i	$0.913321\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$		0			0
$10$		−	443.016i		−	1.40094i
$11$	272.508	−	294.602i	0.679043	−	0.734098i
$11$	272.508	−	294.602i	0.679043	−	0.734098i
$12$		0			0
$13$	−429.276	+	139.480i	−0.704495	+	0.228904i	−0.639288	−	0.768967i	$-0.720771\pi$
$13$	−429.276	+	139.480i	−0.704495	+	0.228904i	−0.0652070	+	0.997872i	$0.520771\pi$
$14$	−212.472	+	292.442i	−0.289722	+	0.398767i
$15$		0			0
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−26.5702	+	81.7747i	−0.0222983	+	0.0686272i	−0.961586	−	0.274502i	$-0.911487\pi$
$17$	−26.5702	+	81.7747i	−0.0222983	+	0.0686272i	0.939288	+	0.343129i	$0.111487\pi$
$18$		0			0
$19$	1123.38	−	1546.21i	0.713912	−	0.982615i	−0.285792	−	0.958292i	$-0.592257\pi$
$19$	1123.38	−	1546.21i	0.713912	−	0.982615i	0.999704	−	0.0243236i	$-0.00774320\pi$
$20$	−1685.33	+	547.598i	−0.942130	+	0.306117i
$21$		0			0
$22$	−1457.57	−	672.533i	−0.642056	−	0.296249i
$23$		−	473.422i		−	0.186608i	−0.995638	−	0.0933038i	$-0.970257\pi$
$23$		−	473.422i		−	0.186608i	0.995638	−	0.0933038i	$-0.0297428\pi$
$24$		0			0
$25$	7395.59	+	5373.21i	2.36659	+	1.71943i
$26$	1061.23	+	1460.65i	0.307876	+	0.423754i
$27$		0			0
$28$	1375.14	+	446.812i	0.331477	+	0.107703i
$29$	−158.140	+	114.895i	−0.0349178	+	0.0253693i	−0.605107	−	0.796144i	$-0.706870\pi$
$29$	−158.140	+	114.895i	−0.0349178	+	0.0253693i	0.570189	+	0.821513i	$0.306870\pi$
$30$		0			0
$31$	2400.33	+	7387.44i	0.448607	+	1.38067i	0.878479	+	0.477781i	$0.158559\pi$
$31$	2400.33	+	7387.44i	0.448607	+	1.38067i	−0.429872	+	0.902890i	$0.641441\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	343.932			0.0510241
$35$	−3092.89	−	9518.93i	−0.426770	−	1.31346i
$36$		0			0
$37$	7488.06	−	5440.39i	0.899218	−	0.653320i	−0.0390472	−	0.999237i	$-0.512432\pi$
$37$	7488.06	−	5440.39i	0.899218	−	0.653320i	0.938265	+	0.345917i	$0.112432\pi$
$38$	−7270.70	−	2362.39i	−0.816803	−	0.265395i
$39$		0			0
$40$	4166.37	+	5734.52i	0.411726	+	0.566692i
$41$	4498.09	+	3268.05i	0.417896	+	0.303619i	0.776791	−	0.629759i	$-0.216846\pi$
$41$	4498.09	+	3268.05i	0.417896	+	0.303619i	−0.358895	+	0.933378i	$0.616846\pi$
$42$		0			0
$43$		−	8158.45i		−	0.672878i	−0.941705	−	0.336439i	$-0.890777\pi$
$43$		−	8158.45i		−	0.672878i	0.941705	−	0.336439i	$-0.109223\pi$
$44$	−756.811	+	6376.23i	−0.0589327	+	0.496515i
$45$		0			0
$46$	−1801.01	+	585.182i	−0.125493	+	0.0407752i
$47$	4097.72	−	5640.02i	0.270581	−	0.372423i	−0.652005	−	0.758215i	$-0.726072\pi$
$47$	4097.72	−	5640.02i	0.270581	−	0.372423i	0.922586	+	0.385792i	$0.126072\pi$
$48$		0			0
$49$	2670.01	−	8217.45i	0.158863	−	0.488930i
$50$	11299.5	−	34776.2i	0.639194	−	1.96724i
$51$		0			0
$52$	4244.91	−	5842.62i	0.217701	−	0.299640i
$53$	19316.0	−	6276.16i	0.944558	−	0.306905i	0.204055	−	0.978959i	$-0.434588\pi$
$53$	19316.0	−	6276.16i	0.944558	−	0.306905i	0.740502	+	0.672054i	$0.234588\pi$
$54$		0			0
$55$	38786.9	−	21704.9i	1.72893	−	0.967499i
$56$		−	5783.65i		−	0.246452i
$57$		0			0
$58$	632.560	+	459.582i	0.0246906	+	0.0179388i
$59$	−18883.5	−	25990.9i	−0.706241	−	0.972057i	−0.999870	−	0.0161379i	$-0.994863\pi$
$59$	−18883.5	−	25990.9i	−0.706241	−	0.972057i	0.293629	−	0.955920i	$-0.405137\pi$
$60$		0			0
$61$	−38559.8	−	12528.8i	−1.32681	−	0.431108i	−0.441984	−	0.897023i	$-0.645725\pi$
$61$	−38559.8	−	12528.8i	−1.32681	−	0.431108i	−0.884829	+	0.465915i	$0.845725\pi$
$62$	25136.5	−	18262.8i	0.830474	−	0.603375i
$63$		0			0
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−49990.7			−1.46759
$66$		0			0
$67$	−494.609			−0.0134609			−0.00673046	−	0.999977i	$-0.502142\pi$
$67$	−494.609			−0.0134609			−0.00673046	+	0.999977i	$0.502142\pi$
$68$	−425.123	−	1308.39i	−0.0111492	−	0.0343136i
$69$		0			0
$70$	−32389.1	+	23532.1i	−0.790049	+	0.574004i
$71$	1936.17	+	629.099i	0.0455824	+	0.0148106i	0.331719	−	0.943378i	$-0.392371\pi$
$71$	1936.17	+	629.099i	0.0455824	+	0.0148106i	−0.286137	+	0.958189i	$0.592371\pi$
$72$		0			0
$73$	20402.8	+	28082.0i	0.448107	+	0.616767i	0.971990	−	0.235024i	$-0.0755168\pi$
$73$	20402.8	+	28082.0i	0.448107	+	0.616767i	−0.523882	+	0.851791i	$0.675517\pi$
$74$	−29952.2	−	21761.6i	−0.635843	−	0.461967i
$75$		0			0
$76$			30579.5i			0.607290i
$77$	−36013.6	−	4274.55i	−0.692212	−	0.0821605i
$78$		0			0
$79$	60311.2	−	19596.3i	1.08725	−	0.353269i	0.290068	−	0.957006i	$-0.406322\pi$
$79$	60311.2	−	19596.3i	1.08725	−	0.353269i	0.797184	+	0.603737i	$0.206322\pi$
$80$	16665.5	−	22938.1i	0.291134	−	0.400712i
$81$		0			0
$82$	6872.47	−	21151.3i	0.112870	−	0.347378i
$83$	28042.2	−	86304.9i	0.446803	−	1.37512i	−0.433691	−	0.901062i	$-0.642789\pi$
$83$	28042.2	−	86304.9i	0.446803	−	1.37512i	0.880494	−	0.474057i	$-0.157211\pi$
$84$		0			0
$85$	−5597.46	+	7704.24i	−0.0840317	+	0.115660i
$86$	−31036.6	+	10084.4i	−0.452510	+	0.147029i
$87$		0			0
$88$	25192.1	−	5002.37i	0.346783	−	0.0688603i
$89$			125403.i			1.67815i	0.544012	+	0.839077i	$0.316904\pi$
$89$			125403.i			1.67815i	−0.544012	+	0.839077i	$0.683096\pi$
$90$		0			0
$91$	32999.7	+	23975.7i	0.417740	+	0.303506i
$92$	4452.33	+	6128.11i	0.0548426	+	0.0754843i
$93$		0			0
$94$	−26521.0	−	8617.19i	−0.309578	−	0.100588i
$95$	171249.	−	124419.i	1.94678	−	1.41442i
$96$		0			0
$97$	45406.0	+	139745.i	0.489987	+	1.50802i	0.824626	+	0.565678i	$0.191385\pi$
$97$	45406.0	+	139745.i	0.489987	+	1.50802i	−0.334640	+	0.942346i	$0.608615\pi$
$98$	−34561.4			−0.363518
$99$		0			0
$100$	−146263.			−1.46263
$101$	−23681.3	−	72883.4i	−0.230994	−	0.710928i	−0.997628	−	0.0688423i	$-0.978069\pi$
$101$	−23681.3	−	72883.4i	−0.230994	−	0.710928i	0.766633	−	0.642085i	$-0.221931\pi$
$102$		0			0
$103$	93493.1	−	67926.7i	0.868333	−	0.630881i	−0.0618059	−	0.998088i	$-0.519686\pi$
$103$	93493.1	−	67926.7i	0.868333	−	0.630881i	0.930139	+	0.367207i	$0.119686\pi$
$104$	−27473.6	−	8926.73i	−0.249077	−	0.0809299i
$105$		0			0
$106$	−47751.9	−	65724.8i	−0.412787	−	0.568152i
$107$	95169.6	+	69144.8i	0.803598	+	0.583848i	0.911967	−	0.410263i	$-0.134563\pi$
$107$	95169.6	+	69144.8i	0.803598	+	0.583848i	−0.108370	+	0.994111i	$0.534563\pi$
$108$		0			0
$109$		−	217865.i		−	1.75639i	−0.478299	−	0.878197i	$-0.658747\pi$
$109$		−	217865.i		−	1.75639i	0.478299	−	0.878197i	$-0.341253\pi$
$110$	−130514.	−	120725.i	−1.02843	−	0.951299i
$111$		0			0
$112$	−22002.3	+	7148.99i	−0.165739	+	0.0538517i
$113$	−49162.5	+	67666.4i	−0.362191	+	0.498514i	−0.950758	−	0.309935i	$-0.899693\pi$
$113$	−49162.5	+	67666.4i	−0.362191	+	0.498514i	0.588566	+	0.808449i	$0.299693\pi$
$114$		0			0
$115$	16202.8	−	49867.2i	0.114247	−	0.351617i
$116$	966.466	−	2974.48i	0.00666871	−	0.0205242i
$117$		0			0
$118$	−75534.1	+	103964.i	−0.499388	+	0.687348i
$119$	7389.94	−	2401.14i	0.0478381	−	0.0155435i
$120$		0			0
$121$	−12529.9	−	160563.i	−0.0778007	−	0.996969i
$122$			162177.i			0.986480i
$123$		0			0
$124$	−100546.	−	73051.1i	−0.587234	−	0.426651i
$125$	391669.	+	539086.i	2.24204	+	3.08591i
$126$		0			0
$127$	133352.	+	43328.6i	0.733651	+	0.238378i	0.651932	−	0.758278i	$-0.273959\pi$
$127$	133352.	+	43328.6i	0.733651	+	0.238378i	0.0817192	+	0.996655i	$0.473959\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$		0			0
$130$	61791.9	+	190176.i	0.320681	+	0.986955i
$131$	−223510.			−1.13794			−0.568968	−	0.822359i	$-0.692657\pi$
$131$	−223510.			−1.13794			−0.568968	+	0.822359i	$0.692657\pi$
$132$		0			0
$133$	−172716.			−0.846648
$134$	611.370	+	1881.60i	0.00294132	+	0.00905245i
$135$		0			0
$136$	−4451.95	+	3234.53i	−0.0206397	+	0.0149956i
$137$	−277629.	−	90207.0i	−1.26376	−	0.410619i	−0.400924	−	0.916111i	$-0.631311\pi$
$137$	−277629.	−	90207.0i	−1.26376	−	0.410619i	−0.862831	+	0.505492i	$0.831311\pi$
$138$		0			0
$139$	262241.	+	360944.i	1.15124	+	1.58454i	0.739375	+	0.673293i	$0.235121\pi$
$139$	262241.	+	360944.i	1.15124	+	1.58454i	0.411861	+	0.911247i	$0.364879\pi$
$140$	129557.	+	94128.3i	0.558649	+	0.405882i
$141$		0			0
$142$		−	8143.23i		−	0.0338903i
$143$	−75889.9	+	164475.i	−0.310344	+	0.672604i
$144$		0			0
$145$	−20589.7	+	6690.00i	−0.0813261	+	0.0264245i
$146$	81611.1	−	112328.i	0.316860	−	0.436120i
$147$		0			0
$148$	−45762.9	+	140844.i	−0.171735	+	0.528547i
$149$	−128426.	+	395254.i	−0.473900	+	1.45851i	0.373535	+	0.927616i	$0.378146\pi$
$149$	−128426.	+	395254.i	−0.473900	+	1.45851i	−0.847435	+	0.530899i	$0.821854\pi$
$150$		0			0
$151$	−250899.	+	345333.i	−0.895483	+	1.23253i	0.0764040	+	0.997077i	$0.475656\pi$
$151$	−250899.	+	345333.i	−0.895483	+	1.23253i	−0.971887	+	0.235449i	$0.924344\pi$
$152$	116331.	−	37798.3i	0.408401	−	0.132698i
$153$		0			0
$154$	28253.9	+	142287.i	0.0960011	+	0.483464i
$155$			860295.i			2.87619i
$156$		0			0
$157$	75495.4	+	54850.6i	0.244439	+	0.177596i	0.703259	−	0.710934i	$-0.251728\pi$
$157$	75495.4	+	54850.6i	0.244439	+	0.177596i	−0.458819	+	0.888530i	$0.651728\pi$
$158$	−149097.	−	205215.i	−0.475146	−	0.653983i
$159$		0			0
$160$	−107861.	−	35046.3i	−0.333093	−	0.108229i
$161$	−34612.1	+	25147.2i	−0.105236	+	0.0764583i
$162$		0			0
$163$	−184379.	−	567461.i	−0.543555	−	1.67289i	−0.724402	−	0.689378i	$-0.757884\pi$
$163$	−184379.	−	567461.i	−0.543555	−	1.67289i	0.180847	−	0.983511i	$-0.442116\pi$
$164$	−88959.1			−0.258274
$165$		0			0
$166$	−362985.			−1.02240
$167$	−48215.5	−	148392.i	−0.133781	−	0.411736i	0.861617	−	0.507559i	$-0.169452\pi$
$167$	−48215.5	−	148392.i	−0.133781	−	0.411736i	−0.995398	+	0.0958223i	$0.969452\pi$
$168$		0			0
$169$	−135559.	+	98489.7i	−0.365101	+	0.265261i
$170$	36227.5	+	11771.0i	0.0961426	+	0.0312386i
$171$		0			0
$172$	76726.7	+	105605.i	0.197754	+	0.272185i
$173$	−371750.	−	270092.i	−0.944356	−	0.686114i	0.00510962	−	0.999987i	$-0.498374\pi$
$173$	−371750.	−	270092.i	−0.944356	−	0.686114i	−0.949465	+	0.313872i	$0.898374\pi$
$174$		0			0
$175$		−	826109.i		−	2.03912i
$176$	−50169.3	−	89653.1i	−0.122083	−	0.218164i
$177$		0			0
$178$	477060.	−	155006.i	1.12856	−	0.366690i
$179$	171044.	−	235422.i	0.399003	−	0.549180i	−0.561491	−	0.827483i	$-0.689772\pi$
$179$	171044.	−	235422.i	0.399003	−	0.549180i	0.960493	+	0.278303i	$0.0897719\pi$
$180$		0			0
$181$	−39831.4	+	122588.i	−0.0903709	+	0.278133i	−0.986020	−	0.166629i	$-0.946712\pi$
$181$	−39831.4	+	122588.i	−0.0903709	+	0.278133i	0.895649	+	0.444762i	$0.146712\pi$
$182$	50419.0	−	155174.i	0.112828	−	0.347248i
$183$		0			0
$184$	17809.3	−	24512.4i	0.0387796	−	0.0533755i
$185$	974939.	−	316777.i	2.09434	−	0.680494i
$186$		0			0
$187$	16850.4	+	30111.9i	0.0352376	+	0.0629700i
$188$			111543.i			0.230170i
$189$		0			0
$190$	−684994.	−	497678.i	−1.37658	−	1.00015i
$191$	268004.	+	368876.i	0.531567	+	0.731640i	0.987368	−	0.158442i	$-0.0506471\pi$
$191$	268004.	+	368876.i	0.531567	+	0.731640i	−0.455801	+	0.890082i	$0.650647\pi$
$192$		0			0
$193$	−354521.	−	115191.i	−0.685092	−	0.222600i	−0.0542686	−	0.998526i	$-0.517283\pi$
$193$	−354521.	−	115191.i	−0.685092	−	0.222600i	−0.630823	+	0.775927i	$0.717283\pi$
$194$	475498.	−	345470.i	0.907078	−	0.659031i
$195$		0			0
$196$	42720.2	+	131479.i	0.0794316	+	0.244465i
$197$	256010.			0.469993			0.234997	−	0.971996i	$-0.424492\pi$
$197$	256010.			0.469993			0.234997	+	0.971996i	$0.424492\pi$
$198$		0			0
$199$	−537094.			−0.961430			−0.480715	−	0.876877i	$-0.659623\pi$
$199$	−537094.			−0.961430			−0.480715	+	0.876877i	$0.659623\pi$
$200$	180791.	+	556419.i	0.319597	+	0.983618i
$201$		0			0
$202$	−247993.	+	180178.i	−0.427624	+	0.310687i
$203$	16800.1	+	5458.69i	0.0286136	+	0.00929713i
$204$		0			0
$205$	361950.	+	498182.i	0.601539	+	0.827948i
$206$	−373972.	−	271707.i	−0.614004	−	0.446100i
$207$		0			0
$208$			115550.i			0.185187i
$209$	−149385.	−	752305.i	−0.236559	−	1.19132i
$210$		0			0
$211$	−242427.	+	78769.4i	−0.374866	+	0.121801i	−0.490389	−	0.871504i	$-0.663145\pi$
$211$	−242427.	+	78769.4i	−0.374866	+	0.121801i	0.115524	+	0.993305i	$0.463145\pi$
$212$	−191008.	+	262899.i	−0.291884	+	0.401744i
$213$		0			0
$214$	145406.	−	447514.i	0.217044	−	0.667994i
$215$	279222.	−	859357.i	0.411959	−	1.26788i
$216$		0			0
$217$	412600.	−	567895.i	0.594812	−	0.818688i
$218$	−828809.	+	269296.i	−1.18117	+	0.383786i
$219$		0			0
$220$	−297943.	+	645728.i	−0.415027	+	0.899482i
$221$		−	38809.9i		−	0.0534517i
$222$		0			0
$223$	558738.	+	405947.i	0.752395	+	0.546647i	0.896568	−	0.442905i	$-0.146052\pi$
$223$	558738.	+	405947.i	0.752395	+	0.546647i	−0.144173	+	0.989552i	$0.546052\pi$
$224$	54392.7	+	74865.2i	0.0724304	+	0.0996919i
$225$		0			0
$226$	318187.	+	103385.i	0.414391	+	0.134644i
$227$	−1.02336e6	+	743517.i	−1.31815	+	0.957693i	−0.318198	+	0.948024i	$0.603078\pi$
$227$	−1.02336e6	+	743517.i	−1.31815	+	0.957693i	−0.999953	+	0.00966869i	$0.996922\pi$
$228$		0			0
$229$	334625.	+	1.02987e6i	0.421667	+	1.29776i	0.906150	+	0.422957i	$0.139008\pi$
$229$	334625.	+	1.02987e6i	0.421667	+	1.29776i	−0.484483	+	0.874801i	$0.660992\pi$
$230$	−209734.			−0.261426
$231$		0			0
$232$	−12510.2			−0.0152596
$233$	−454215.	−	1.39793e6i	−0.548115	−	1.68692i	−0.713466	−	0.700690i	$-0.752876\pi$
$233$	−454215.	−	1.39793e6i	−0.548115	−	1.68692i	0.165351	−	0.986235i	$-0.447124\pi$
$234$		0			0
$235$	624655.	−	453839.i	0.737855	−	0.536083i
$236$	488867.	+	158842.i	0.571361	+	0.185646i
$237$		0			0
$238$	−18268.9	−	25145.0i	−0.0209060	−	0.0287746i
$239$	375327.	+	272691.i	0.425026	+	0.308799i	0.779657	−	0.626207i	$-0.215394\pi$
$239$	375327.	+	272691.i	0.425026	+	0.308799i	−0.354631	+	0.935006i	$0.615394\pi$
$240$		0			0
$241$			138818.i			0.153958i	0.997033	+	0.0769790i	$0.0245275\pi$
$241$			138818.i			0.153958i	−0.997033	+	0.0769790i	$0.975473\pi$
$242$	−595330.	+	246133.i	−0.653460	+	0.270167i
$243$		0			0
$244$	616956.	−	200461.i	0.663406	−	0.215554i
$245$	562483.	−	774191.i	0.598679	−	0.824011i
$246$		0			0
$247$	−266577.	+	820439.i	−0.278022	+	0.855665i
$248$	−153621.	+	472796.i	−0.158607	+	0.488141i
$249$		0			0
$250$	1.56667e6	−	2.15634e6i	1.58536	−	2.18207i
$251$	−1.75088e6	+	568897.i	−1.75418	+	0.569966i	−0.996571	−	0.0827477i	$-0.973630\pi$
$251$	−1.75088e6	+	568897.i	−1.75418	+	0.569966i	−0.757605	+	0.652714i	$0.773630\pi$
$252$		0			0
$253$	−139471.	−	129011.i	−0.136988	−	0.126715i
$254$		−	560857.i		−	0.545467i
$255$		0			0
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−934526.	−	1.28626e6i	−0.882589	−	1.21478i	−0.975697	−	0.219124i	$-0.929680\pi$
$257$	−934526.	−	1.28626e6i	−0.882589	−	1.21478i	0.0931080	−	0.995656i	$-0.470320\pi$
$258$		0			0
$259$	−795500.	−	258474.i	−0.736870	−	0.239423i
$260$	647094.	−	470141.i	0.593654	−	0.431315i
$261$		0			0
$262$	276273.	+	850282.i	0.248648	+	0.765261i
$263$	227393.			0.202716			0.101358	−	0.994850i	$-0.467681\pi$
$263$	227393.			0.202716			0.101358	+	0.994850i	$0.467681\pi$
$264$		0			0
$265$	2.24942e6			1.96769
$266$	213488.	+	657050.i	0.184999	+	0.569370i
$267$		0			0
$268$	6402.35	−	4651.58i	0.00544506	−	0.00395606i
$269$	−332991.	−	108195.i	−0.280576	−	0.0911648i	0.165348	−	0.986235i	$-0.447125\pi$
$269$	−332991.	−	108195.i	−0.280576	−	0.0911648i	−0.445925	+	0.895070i	$0.647125\pi$
$270$		0			0
$271$	228509.	+	314516.i	0.189008	+	0.260147i	0.892996	−	0.450065i	$-0.148599\pi$
$271$	228509.	+	314516.i	0.189008	+	0.260147i	−0.703988	+	0.710212i	$0.748599\pi$
$272$	17807.8	+	12938.1i	0.0145945	+	0.0106035i
$273$		0			0
$274$			1.16766e6i			0.939597i
$275$	3.59832e6	−	714515.i	2.86925	−	0.569744i
$276$		0			0
$277$	−1.86584e6	+	606249.i	−1.46109	+	0.474735i	−0.928401	−	0.371579i	$-0.878817\pi$
$277$	−1.86584e6	+	606249.i	−1.46109	+	0.474735i	−0.532684	+	0.846314i	$0.678817\pi$
$278$	1.04897e6	−	1.44378e6i	0.814047	−	1.12044i
$279$		0			0
$280$	197945.	−	609211.i	0.150886	−	0.464379i
$281$	−185705.	+	571542.i	−0.140300	+	0.431800i	−0.996377	−	0.0850494i	$-0.972895\pi$
$281$	−185705.	+	571542.i	−0.140300	+	0.431800i	0.856076	+	0.516849i	$0.172895\pi$
$282$		0			0
$283$	659513.	−	907741.i	0.489505	−	0.673746i	−0.490792	−	0.871277i	$-0.663292\pi$
$283$	659513.	−	907741.i	0.489505	−	0.673746i	0.980297	+	0.197531i	$0.0632924\pi$
$284$	−30978.7	+	10065.6i	−0.0227912	+	0.00740531i
$285$		0			0
$286$	719505.	+	85400.0i	0.520138	+	0.0617366i
$287$		−	502450.i		−	0.360071i
$288$		0			0
$289$	1.14271e6	+	830225.i	0.804805	+	0.584725i
$290$	50900.6	+	70058.6i	0.0355408	+	0.0489177i
$291$		0			0
$292$	−528198.	−	171622.i	−0.362527	−	0.117792i
$293$	−583292.	+	423786.i	−0.396933	+	0.288388i	−0.768290	−	0.640101i	$-0.778892\pi$
$293$	−583292.	+	423786.i	−0.396933	+	0.288388i	0.371358	+	0.928490i	$0.378892\pi$
$294$		0			0
$295$	−1.09953e6	−	3.38400e6i	−0.735616	−	2.26399i
$296$	592368.			0.392973
$297$		0			0
$298$	1.66238e6			1.08440
$299$	66033.0	+	203229.i	0.0427153	+	0.131464i
$300$		0			0
$301$	−596469.	+	433360.i	−0.379465	+	0.275697i
$302$	1.62385e6	+	527622.i	1.02454	+	0.332894i
$303$		0			0
$304$	−287586.	−	395829.i	−0.178478	−	0.245654i
$305$	−3.63283e6	−	2.63941e6i	−2.23612	−	1.62464i
$306$		0			0
$307$		−	639330.i		−	0.387150i	−0.981086	−	0.193575i	$-0.937992\pi$
$307$		−	639330.i		−	0.387150i	0.981086	−	0.193575i	$-0.0620082\pi$
$308$	506370.	−	283361.i	0.304152	−	0.170201i
$309$		0			0
$310$	3.27276e6	−	1.06338e6i	1.93424	−	0.628471i
$311$	−101748.	+	140044.i	−0.0596519	+	0.0821038i	−0.837801	−	0.545976i	$-0.816159\pi$
$311$	−101748.	+	140044.i	−0.0596519	+	0.0821038i	0.778149	+	0.628080i	$0.216159\pi$
$312$		0			0
$313$	−721929.	+	2.22187e6i	−0.416518	+	1.28191i	0.494368	+	0.869253i	$0.335400\pi$
$313$	−721929.	+	2.22187e6i	−0.416518	+	1.28191i	−0.910886	+	0.412658i	$0.864600\pi$
$314$	115347.	−	355001.i	0.0660208	−	0.203191i
$315$		0			0
$316$	−596390.	+	820860.i	−0.335979	+	0.462436i
$317$	−956570.	+	310808.i	−0.534649	+	0.173718i	−0.563883	−	0.825855i	$-0.690693\pi$
$317$	−956570.	+	310808.i	−0.534649	+	0.173718i	0.0292342	+	0.999573i	$0.490693\pi$
$318$		0			0
$319$	−9245.96	+	77898.3i	−0.00508716	+	0.0428599i
$320$			453648.i			0.247654i
$321$		0			0
$322$	138449.	+	100589.i	0.0744130	+	0.0540642i
$323$	96592.0	+	132947.i	0.0515151	+	0.0709045i
$324$		0			0
$325$	−3.92420e6	−	1.27505e6i	−2.06083	−	0.669606i
$326$	−1.93085e6	+	1.40284e6i	−1.00624	+	0.731080i
$327$		0			0
$328$	109960.	+	338421.i	0.0564350	+	0.173689i
$329$	−630007.			−0.320890
$330$		0			0
$331$	2.91098e6			1.46039			0.730195	−	0.683239i	$-0.239429\pi$
$331$	2.91098e6			1.46039			0.730195	+	0.683239i	$0.239429\pi$
$332$	448675.	+	1.38088e6i	0.223402	+	0.687559i
$333$		0			0
$334$	−504919.	+	366845.i	−0.247660	+	0.179935i
$335$	−52098.8	−	16927.9i	−0.0253639	−	0.00824122i
$336$		0			0
$337$	1.02903e6	+	1.41633e6i	0.493573	+	0.679345i	0.981042	−	0.193795i	$-0.0620798\pi$
$337$	1.02903e6	+	1.41633e6i	0.493573	+	0.679345i	−0.487469	+	0.873140i	$0.662080\pi$
$338$	542238.	+	393959.i	0.258165	+	0.187568i
$339$		0			0
$340$		−	152367.i		−	0.0714817i
$341$	2.83046e6	+	1.30600e6i	1.31817	+	0.608213i
$342$		0			0
$343$	−2.18711e6	+	710636.i	−1.00377	+	0.326146i
$344$	306907.	−	422421.i	0.139833	−	0.192464i
$345$		0			0
$346$	−567983.	+	1.74807e6i	−0.255062	+	0.784999i
$347$	−169184.	+	520694.i	−0.0754284	+	0.232145i	−0.981661	−	0.190635i	$-0.938945\pi$
$347$	−169184.	+	520694.i	−0.0754284	+	0.232145i	0.906233	+	0.422779i	$0.138945\pi$
$348$		0			0
$349$	−1.33297e6	+	1.83467e6i	−0.585808	+	0.806296i	−0.994317	−	0.106458i	$-0.966049\pi$
$349$	−1.33297e6	+	1.83467e6i	−0.585808	+	0.806296i	0.408509	+	0.912754i	$0.366049\pi$
$350$	−3.14271e6	+	1.02113e6i	−1.37130	+	0.445564i
$351$		0			0
$352$	−279048.	+	301673.i	−0.120039	+	0.129771i
$353$		−	958040.i		−	0.409211i	−0.978845	−	0.204605i	$-0.934409\pi$
$353$		−	958040.i		−	0.409211i	0.978845	−	0.204605i	$-0.0655911\pi$
$354$		0			0
$355$	182412.	+	132530.i	0.0768216	+	0.0558141i
$356$	−1.17936e6	−	1.62325e6i	−0.493197	−	0.678828i
$357$		0			0
$358$	−1.10702e6	−	359693.i	−0.456508	−	0.148328i
$359$	629976.	−	457704.i	0.257981	−	0.187434i	−0.451276	−	0.892385i	$-0.649031\pi$
$359$	629976.	−	457704.i	0.257981	−	0.187434i	0.709256	+	0.704951i	$0.249031\pi$
$360$		0			0
$361$	−363604.	−	1.11906e6i	−0.146846	−	0.451944i
$362$	515588.			0.206791
$363$		0			0
$364$	−652638.			−0.258178
$365$	1.18799e6	+	3.65626e6i	0.466746	+	1.43650i
$366$		0			0
$367$	−580745.	+	421936.i	−0.225072	+	0.163524i	−0.694607	−	0.719390i	$-0.744422\pi$
$367$	−580745.	+	421936.i	−0.225072	+	0.163524i	0.469535	+	0.882914i	$0.344422\pi$
$368$	−115264.	−	37451.7i	−0.0443686	−	0.0144162i
$369$		0			0
$370$	−2.41018e6	−	3.31733e6i	−0.915262	−	1.25975i
$371$	−1.48488e6	−	1.07883e6i	−0.560089	−	0.406928i
$372$		0			0
$373$			985375.i			0.366716i	0.983046	+	0.183358i	$0.0586967\pi$
$373$			985375.i			0.366716i	−0.983046	+	0.183358i	$0.941303\pi$
$374$	93724.2	−	101323.i	0.0346476	−	0.0374567i
$375$		0			0
$376$	424336.	−	137875.i	0.154789	−	0.0502940i
$377$	51860.0	−	71379.2i	0.0187923	−	0.0258654i
$378$		0			0
$379$	−1.45123e6	+	4.46644e6i	−0.518967	+	1.59721i	0.256980	+	0.966417i	$0.417272\pi$
$379$	−1.45123e6	+	4.46644e6i	−0.518967	+	1.59721i	−0.775947	+	0.630798i	$0.782728\pi$
$380$	−1.04658e6	+	3.22104e6i	−0.371803	+	1.14429i
$381$		0			0
$382$	1.07202e6	−	1.47551e6i	0.375875	−	0.517348i
$383$	−1.54133e6	+	500810.i	−0.536908	+	0.174452i	−0.564905	−	0.825156i	$-0.691087\pi$
$383$	−1.54133e6	+	500810.i	−0.536908	+	0.174452i	0.0279969	+	0.999608i	$0.491087\pi$
$384$		0			0
$385$	−3.64713e6	−	1.68281e6i	−1.25401	−	0.578607i
$386$			1.49106e6i			0.509363i
$387$		0			0
$388$	−1.90199e6	−	1.38188e6i	−0.641401	−	0.466005i
$389$	973412.	+	1.33979e6i	0.326154	+	0.448912i	0.940334	−	0.340254i	$-0.110513\pi$
$389$	973412.	+	1.33979e6i	0.326154	+	0.448912i	−0.614180	+	0.789166i	$0.710513\pi$
$390$		0			0
$391$	38714.0	+	12578.9i	0.0128064	+	0.00416104i
$392$	447372.	−	325035.i	0.147046	−	0.106835i
$393$		0			0
$394$	−316446.	−	973921.i	−0.102697	−	0.316070i
$395$	7.02346e6			2.26495
$396$		0			0
$397$	−3.87209e6			−1.23302			−0.616509	−	0.787348i	$-0.711453\pi$
$397$	−3.87209e6			−1.23302			−0.616509	+	0.787348i	$0.711453\pi$
$398$	663885.	+	2.04323e6i	0.210080	+	0.646560i
$399$		0			0
$400$	1.89327e6	−	1.37554e6i	0.591647	−	0.429857i
$401$	156923.	+	50987.4i	0.0487334	+	0.0158344i	0.333282	−	0.942827i	$-0.391844\pi$
$401$	156923.	+	50987.4i	0.0487334	+	0.0158344i	−0.284549	+	0.958662i	$0.591844\pi$
$402$		0			0
$403$	−2.06080e6	−	2.83645e6i	−0.632083	−	0.869987i
$404$	991974.	+	720711.i	0.302376	+	0.219689i
$405$		0			0
$406$		−	70658.8i		−	0.0212741i
$407$	437804.	−	3.68855e6i	0.131007	−	1.10375i
$408$		0			0
$409$	686804.	−	223156.i	0.203013	−	0.0659631i	−0.205745	−	0.978606i	$-0.565962\pi$
$409$	686804.	−	223156.i	0.203013	−	0.0659631i	0.408759	+	0.912643i	$0.365962\pi$
$410$	1.44780e6	−	1.99273e6i	0.425353	−	0.585448i
$411$		0			0
$412$	−571379.	+	1.75852e6i	−0.165837	+	0.510393i
$413$	−897158.	+	2.76117e6i	−0.258818	+	0.796559i
$414$		0			0
$415$	5.90755e6	−	8.13104e6i	1.68379	−	2.31753i
$416$	439578.	−	142828.i	0.124538	−	0.0404649i
$417$		0			0
$418$	−2.67729e6	+	1.49819e6i	−0.749470	+	0.419399i
$419$		−	834780.i		−	0.232294i	−0.993232	−	0.116147i	$-0.962946\pi$
$419$		−	834780.i		−	0.232294i	0.993232	−	0.116147i	$-0.0370543\pi$
$420$		0			0
$421$	−2.32157e6	−	1.68672e6i	−0.638375	−	0.463807i	0.220916	−	0.975293i	$-0.429095\pi$
$421$	−2.32157e6	−	1.68672e6i	−0.638375	−	0.463807i	−0.859292	+	0.511486i	$0.829095\pi$
$422$	599313.	+	824884.i	0.163822	+	0.225482i
$423$		0			0
$424$	1.23623e6	+	401674.i	0.333952	+	0.108507i
$425$	−635895.	+	462005.i	−0.170771	+	0.124072i
$426$		0			0
$427$	1.13222e6	+	3.48463e6i	0.300513	+	0.924883i
$428$	−1.88218e6			−0.496651
$429$		0			0
$430$	−3.61433e6			−0.942662
$431$	1.74359e6	+	5.36623e6i	0.452118	+	1.39148i	0.874485	+	0.485052i	$0.161199\pi$
$431$	1.74359e6	+	5.36623e6i	0.452118	+	1.39148i	−0.422367	+	0.906425i	$0.638801\pi$
$432$		0			0
$433$	462392.	−	335947.i	0.118520	−	0.0861096i	−0.526946	−	0.849899i	$-0.676663\pi$
$433$	462392.	−	335947.i	0.118520	−	0.0861096i	0.645466	+	0.763789i	$0.276663\pi$
$434$	−2.67040e6	−	867666.i	−0.680538	−	0.221120i
$435$		0			0
$436$	2.04893e6	+	2.82011e6i	0.516191	+	0.710476i
$437$	−732009.	−	531835.i	−0.183363	−	0.133221i
$438$		0			0
$439$		−	4.82467e6i		−	1.19483i	−0.801932	−	0.597415i	$-0.796195\pi$
$439$		−	4.82467e6i		−	1.19483i	0.801932	−	0.597415i	$-0.203805\pi$
$440$	2.82477e6	+	335280.i	0.695587	+	0.0825611i
$441$		0			0
$442$	−147642.	+	47971.7i	−0.0359462	+	0.0116796i
$443$	−797787.	+	1.09806e6i	−0.193142	+	0.265838i	−0.894594	−	0.446879i	$-0.852535\pi$
$443$	−797787.	+	1.09806e6i	−0.193142	+	0.265838i	0.701452	+	0.712717i	$0.252535\pi$
$444$		0			0
$445$	−4.29189e6	+	1.32091e7i	−1.02742	+	3.16208i
$446$	853676.	−	2.62734e6i	0.203215	−	0.625431i
$447$		0			0
$448$	217571.	−	299461.i	0.0512160	−	0.0704928i
$449$	−2.33782e6	+	759604.i	−0.547262	+	0.177816i	−0.569582	−	0.821935i	$-0.692895\pi$
$449$	−2.33782e6	+	759604.i	−0.547262	+	0.177816i	0.0223199	+	0.999751i	$0.492895\pi$
$450$		0			0
$451$	2.18854e6	−	434577.i	0.506656	−	0.100606i
$452$		−	1.33824e6i		−	0.308098i
$453$		0			0
$454$	4.09345e6	+	2.97407e6i	0.932074	+	0.677191i
$455$	2.65540e6	+	3.65485e6i	0.601315	+	0.827639i
$456$		0			0
$457$	3.63774e6	+	1.18197e6i	0.814781	+	0.264738i	0.686621	−	0.727015i	$-0.259093\pi$
$457$	3.63774e6	+	1.18197e6i	0.814781	+	0.264738i	0.128160	+	0.991754i	$0.459093\pi$
$458$	3.50424e6	−	2.54598e6i	0.780603	−	0.567141i
$459$		0			0
$460$	259245.	+	797874.i	0.0571237	+	0.175809i
$461$	−6.96898e6			−1.52727			−0.763637	−	0.645646i	$-0.776588\pi$
$461$	−6.96898e6			−1.52727			−0.763637	+	0.645646i	$0.776588\pi$
$462$		0			0
$463$	1.67482e6			0.363092			0.181546	−	0.983382i	$-0.441890\pi$
$463$	1.67482e6			0.363092			0.181546	+	0.983382i	$0.441890\pi$
$464$	15463.5	+	47591.6i	0.00333435	+	0.0102621i
$465$		0			0
$466$	−4.75660e6	+	3.45587e6i	−1.01469	+	0.737213i
$467$	−4.06306e6	−	1.32017e6i	−0.862106	−	0.280115i	−0.155598	−	0.987820i	$-0.549731\pi$
$467$	−4.06306e6	−	1.32017e6i	−0.862106	−	0.280115i	−0.706508	+	0.707705i	$0.749731\pi$
$468$		0			0
$469$	26272.6	+	36161.1i	0.00551532	+	0.00759118i
$470$	−2.49862e6	−	1.81536e6i	−0.521742	−	0.379068i
$471$		0			0
$472$		−	2.05610e6i		−	0.424805i
$473$	−2.40350e6	−	2.22324e6i	−0.493959	−	0.456914i
$474$		0			0
$475$	1.66162e7	−	5.39893e6i	3.37907	−	1.09793i
$476$	−73075.8	+	100580.i	−0.0147828	+	0.0203467i
$477$		0			0
$478$	573449.	−	1.76489e6i	0.114796	−	0.353304i
$479$	−309775.	+	953388.i	−0.0616889	+	0.189859i	−0.977151	−	0.212544i	$-0.931825\pi$
$479$	−309775.	+	953388.i	−0.0616889	+	0.189859i	0.915463	+	0.402403i	$0.131825\pi$
$480$		0			0
$481$	−2.45561e6	+	3.37986e6i	−0.483947	+	0.666095i
$482$	528094.	−	171588.i	0.103537	−	0.0336411i
$483$		0			0
$484$	1.67221e6	+	1.96053e6i	0.324473	+	0.380417i
$485$			1.62739e7i			3.14149i
$486$		0			0
$487$	1.36086e6	+	988720.i	0.260010	+	0.188908i	0.710151	−	0.704049i	$-0.248626\pi$
$487$	1.36086e6	+	988720.i	0.260010	+	0.188908i	−0.450142	+	0.892957i	$0.648626\pi$
$488$	−1.52520e6	−	2.09926e6i	−0.289919	−	0.399040i
$489$		0			0
$490$	−3.64046e6	−	1.18286e6i	−0.684962	−	0.222558i
$491$	−3.53356e6	+	2.56728e6i	−0.661468	+	0.480585i	−0.867158	−	0.498032i	$-0.834056\pi$
$491$	−3.53356e6	+	2.56728e6i	−0.661468	+	0.480585i	0.205690	+	0.978617i	$0.434056\pi$
$492$		0			0
$493$	−5193.73	−	15984.6i	−0.000962414	−	0.00296200i
$494$	3.45064e6			0.636183
$495$		0			0
$496$	1.98851e6			0.362931
$497$	−56851.4	−	174971.i	−0.0103241	−	0.0317742i
$498$		0			0
$499$	−93848.9	+	68185.2i	−0.0168724	+	0.0122585i	−0.596190	−	0.802844i	$-0.703319\pi$
$499$	−93848.9	+	68185.2i	−0.0168724	+	0.0122585i	0.579317	+	0.815102i	$0.303319\pi$
$500$	−1.01397e7	−	3.29460e6i	−1.81385	−	0.589356i
$501$		0			0
$502$	4.32842e6	+	5.95756e6i	0.766603	+	1.05514i
$503$	5.95403e6	+	4.32585e6i	1.04928	+	0.762345i	0.972075	−	0.234670i	$-0.0754010\pi$
$503$	5.95403e6	+	4.32585e6i	1.04928	+	0.762345i	0.0772033	+	0.997015i	$0.475401\pi$
$504$		0			0
$505$		−	8.48754e6i		−	1.48100i
$506$	−318392.	+	690047.i	−0.0552823	+	0.119813i
$507$		0			0
$508$	−2.13363e6	+	693258.i	−0.366825	+	0.119189i
$509$	2.98700e6	−	4.11126e6i	0.511024	−	0.703364i	−0.473068	−	0.881026i	$-0.656853\pi$
$509$	2.98700e6	−	4.11126e6i	0.511024	−	0.703364i	0.984092	+	0.177662i	$0.0568534\pi$
$510$		0			0
$511$	969338.	−	2.98332e6i	0.164219	−	0.505414i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	−3.73810e6	+	5.14506e6i	−0.624085	+	0.858979i
$515$	1.21727e7	−	3.95516e6i	2.02241	−	0.657122i
$516$		0			0
$517$	−544903.	−	2.74415e6i	−0.0896588	−	0.451524i
$518$			3.34575e6i			0.547860i
$519$		0			0
$520$	−2.58837e6	−	1.88056e6i	−0.419777	−	0.304986i
$521$	−4.85149e6	−	6.67750e6i	−0.783034	−	1.07775i	−0.994941	−	0.100464i	$-0.967967\pi$
$521$	−4.85149e6	−	6.67750e6i	−0.783034	−	1.07775i	0.211907	−	0.977290i	$-0.432033\pi$
$522$		0			0
$523$	−1.08694e7	−	3.53167e6i	−1.73760	−	0.564580i	−0.743087	−	0.669195i	$-0.766639\pi$
$523$	−1.08694e7	−	3.53167e6i	−1.73760	−	0.564580i	−0.994513	+	0.104614i	$0.966639\pi$
$524$	2.89317e6	−	2.10201e6i	0.460305	−	0.334431i
$525$		0			0
$526$	−281073.	−	865055.i	−0.0442951	−	0.136326i
$527$	−667883.			−0.104755
$528$		0			0
$529$	6.21221e6			0.965178
$530$	−2.78044e6	−	8.55732e6i	−0.429956	−	1.32327i
$531$		0			0
$532$	2.23568e6	−	1.62432e6i	0.342476	−	0.248824i
$533$	−2.38675e6	−	775502.i	−0.363906	−	0.118240i
$534$		0			0
$535$	7.65806e6	+	1.05404e7i	1.15674	+	1.59211i
$536$	−25609.4	−	18606.3i	−0.00385024	−	0.00279736i
$537$		0			0
$538$			1.40051e6i			0.208607i
$539$	−1.69328e6	−	3.02591e6i	−0.251048	−	0.448626i
$540$		0			0
$541$	9.39626e6	−	3.05303e6i	1.38026	−	0.448475i	0.477507	−	0.878628i	$-0.341540\pi$
$541$	9.39626e6	−	3.05303e6i	1.38026	−	0.448475i	0.902756	+	0.430153i	$0.141540\pi$
$542$	914037.	−	1.25806e6i	0.133649	−	0.183952i
$543$		0			0
$544$	27207.9	−	83737.3i	0.00394183	−	0.0121317i
$545$	7.45641e6	−	2.29485e7i	1.07532	−	3.30950i
$546$		0			0
$547$	4.74558e6	−	6.53173e6i	0.678143	−	0.933383i	−0.321767	−	0.946819i	$-0.604277\pi$
$547$	4.74558e6	−	6.53173e6i	0.678143	−	0.933383i	0.999910	+	0.0134355i	$0.00427677\pi$
$548$	4.44206e6	−	1.44331e6i	0.631878	−	0.205310i
$549$		0			0
$550$	−7.16594e6	−	1.28056e7i	−1.01010	−	1.80507i
$551$			373589.i			0.0524222i
$552$		0			0
$553$	−4.63630e6	−	3.36847e6i	−0.644701	−	0.468403i
$554$	4.61262e6	+	6.34872e6i	0.638518	+	0.878844i
$555$		0			0
$556$	−6.78905e6	−	2.20590e6i	−0.931369	−	0.302620i
$557$	7.76602e6	−	5.64234e6i	1.06062	−	0.770587i	0.0864186	−	0.996259i	$-0.472458\pi$
$557$	7.76602e6	−	5.64234e6i	1.06062	−	0.770587i	0.974203	+	0.225672i	$0.0724578\pi$
$558$		0			0
$559$	1.13794e6	+	3.50222e6i	0.154025	+	0.474039i
$560$	−2.56225e6			−0.345264
$561$		0			0
$562$	2.40382e6			0.321041
$563$	−946199.	−	2.91210e6i	−0.125809	−	0.387200i	0.868239	−	0.496147i	$-0.165252\pi$
$563$	−946199.	−	2.91210e6i	−0.125809	−	0.387200i	−0.994048	+	0.108947i	$0.965252\pi$
$564$		0			0
$565$	−7.49433e6	+	5.44495e6i	−0.987669	+	0.717584i
$566$	−4.26846e6	−	1.38691e6i	−0.560054	−	0.181972i
$567$		0			0
$568$	76583.6	+	105408.i	0.00996012	+	0.0137089i
$569$	1.25422e6	+	911241.i	0.162402	+	0.117992i	0.666018	−	0.745936i	$-0.267997\pi$
$569$	1.25422e6	+	911241.i	0.162402	+	0.117992i	−0.503616	+	0.863928i	$0.667997\pi$
$570$		0			0
$571$		−	1.38195e6i		−	0.177379i	−0.996059	−	0.0886897i	$-0.971732\pi$
$571$		−	1.38195e6i		−	0.177379i	0.996059	−	0.0886897i	$-0.0282680\pi$
$572$	−564476.	−	2.84272e6i	−0.0721366	−	0.363282i
$573$		0			0
$574$	−1.91143e6	+	621062.i	−0.242147	+	0.0786784i
$575$	2.54380e6	−	3.50124e6i	0.320858	−	0.441623i
$576$		0			0
$577$	1.22092e6	−	3.75760e6i	0.152668	−	0.469863i	−0.845249	−	0.534372i	$-0.820548\pi$
$577$	1.22092e6	−	3.75760e6i	0.152668	−	0.469863i	0.997917	+	0.0645091i	$0.0205482\pi$
$578$	1.74590e6	−	5.37333e6i	0.217370	−	0.668997i
$579$		0			0
$580$	203602.	−	280234.i	0.0251312	−	0.0345901i
$581$	−7.79934e6	+	2.53416e6i	−0.958556	+	0.311454i
$582$		0			0
$583$	3.41480e6	−	7.40085e6i	0.416097	−	0.901800i
$584$			2.22152e6i			0.269537i
$585$		0			0
$586$	2.33317e6	+	1.69514e6i	0.280674	+	0.203921i
$587$	4.04134e6	+	5.56243e6i	0.484095	+	0.666300i	0.979285	−	0.202485i	$-0.0649017\pi$
$587$	4.04134e6	+	5.56243e6i	0.484095	+	0.666300i	−0.495190	+	0.868784i	$0.664902\pi$
$588$		0			0
$589$	1.41190e7	+	4.58754e6i	1.67693	+	0.544869i
$590$	−1.15144e7	+	8.36570e6i	−1.36179	+	0.989401i
$591$		0			0
$592$	−732207.	−	2.25350e6i	−0.0858677	−	0.264273i
$593$	−1.22366e7			−1.42898			−0.714488	−	0.699648i	$-0.753340\pi$
$593$	−1.22366e7			−1.42898			−0.714488	+	0.699648i	$0.753340\pi$
$594$		0			0
$595$	860586.			0.0996556
$596$	−2.05481e6	−	6.32407e6i	−0.236950	−	0.729257i
$597$		0			0
$598$	691507.	−	502409.i	0.0790758	−	0.0574519i
$599$	−5.25735e6	−	1.70822e6i	−0.598687	−	0.194525i	−0.00603249	−	0.999982i	$-0.501920\pi$
$599$	−5.25735e6	−	1.70822e6i	−0.598687	−	0.194525i	−0.592655	+	0.805456i	$0.701920\pi$
$600$		0			0
$601$	4.05452e6	+	5.58057e6i	0.457882	+	0.630221i	0.974068	−	0.226256i	$-0.0726486\pi$
$601$	4.05452e6	+	5.58057e6i	0.457882	+	0.630221i	−0.516186	+	0.856477i	$0.672649\pi$
$602$	2.38587e6	+	1.73344e6i	0.268322	+	0.194947i
$603$		0			0
$604$		−	6.82969e6i		−	0.761743i
$605$	4.17543e6	−	1.73415e7i	0.463781	−	1.92618i
$606$		0			0
$607$	839893.	−	272898.i	0.0925235	−	0.0300627i	−0.262389	−	0.964962i	$-0.584511\pi$
$607$	839893.	−	272898.i	0.0925235	−	0.0300627i	0.354913	+	0.934899i	$0.384511\pi$
$608$	−1.15035e6	+	1.58332e6i	−0.126203	+	0.173703i
$609$		0			0
$610$	−5.55047e6	+	1.70826e7i	−0.603956	+	1.85879i
$611$	−972379.	+	2.99268e6i	−0.105374	+	0.324307i
$612$		0			0
$613$	2.32247e6	−	3.19660e6i	0.249631	−	0.343587i	−0.665751	−	0.746174i	$-0.731889\pi$
$613$	2.32247e6	−	3.19660e6i	0.249631	−	0.343587i	0.915382	+	0.402587i	$0.131889\pi$
$614$	−2.43216e6	+	790255.i	−0.260358	+	0.0845953i
$615$		0			0
$616$	−1.70388e6	−	1.57609e6i	−0.180920	−	0.167351i
$617$			8.83605e6i			0.934426i	0.884145	+	0.467213i	$0.154742\pi$
$617$			8.83605e6i			0.934426i	−0.884145	+	0.467213i	$0.845258\pi$
$618$		0			0
$619$	−1.41759e7	−	1.02994e7i	−1.48704	−	1.08040i	−0.975202	−	0.221317i	$-0.928964\pi$
$619$	−1.41759e7	−	1.02994e7i	−1.48704	−	1.08040i	−0.511839	−	0.859081i	$-0.671036\pi$
$620$	−8.09070e6	−	1.11359e7i	−0.845292	−	1.16344i
$621$		0			0
$622$	658526.	+	213968.i	0.0682491	+	0.0221755i
$623$	9.16826e6	−	6.66113e6i	0.946382	−	0.687587i
$624$		0			0
$625$	1.39779e7	+	4.30196e7i	1.43134	+	4.40521i
$626$	9.34485e6			0.953096
$627$		0			0
$628$	−1.49308e6			−0.151072
$629$	245927.	+	756886.i	0.0247845	+	0.0762788i
$630$		0			0
$631$	−2.41947e6	+	1.75785e6i	−0.241906	+	0.175755i	−0.702132	−	0.712047i	$-0.747768\pi$
$631$	−2.41947e6	+	1.75785e6i	−0.241906	+	0.175755i	0.460226	+	0.887802i	$0.347768\pi$
$632$	3.85991e6	+	1.25416e6i	0.384401	+	0.124900i
$633$		0			0
$634$	2.36477e6	+	3.25483e6i	0.233650	+	0.321592i
$635$	1.25635e7	+	9.12789e6i	1.23645	+	0.898331i
$636$		0			0
$637$			3.89997e6i			0.380813i
$638$	307772.	−	61113.9i	0.0299348	−	0.00594413i
$639$		0			0
$640$	1.72578e6	−	560740.i	0.166547	−	0.0541143i
$641$	252749.	−	347879.i	0.0242965	−	0.0334413i	−0.796696	−	0.604380i	$-0.793421\pi$
$641$	252749.	−	347879.i	0.0242965	−	0.0334413i	0.820992	+	0.570939i	$0.193421\pi$
$642$		0			0
$643$	1.26502e6	−	3.89335e6i	0.120662	−	0.371360i	−0.872424	−	0.488751i	$-0.837453\pi$
$643$	1.26502e6	−	3.89335e6i	0.120662	−	0.371360i	0.993086	+	0.117390i	$0.0374528\pi$
$644$	211531.	−	651024.i	0.0200983	−	0.0618561i
$645$		0			0
$646$	386368.	−	531790.i	0.0364267	−	0.0501370i
$647$	−1.28291e7	+	4.16842e6i	−1.20486	+	0.391481i	−0.841545	−	0.540187i	$-0.818354\pi$
$647$	−1.28291e7	+	4.16842e6i	−1.20486	+	0.391481i	−0.363310	+	0.931668i	$0.618354\pi$
$648$		0			0
$649$	−1.28029e7	−	1.51961e6i	−1.19315	−	0.141619i
$650$			1.65046e7i			1.53222i
$651$		0			0
$652$	7.72338e6	+	5.61137e6i	0.711522	+	0.516951i
$653$	6.95309e6	+	9.57010e6i	0.638109	+	0.878281i	0.998513	−	0.0545149i	$-0.0173612\pi$
$653$	6.95309e6	+	9.57010e6i	0.638109	+	0.878281i	−0.360404	+	0.932796i	$0.617361\pi$
$654$		0			0
$655$	−2.35430e7	−	7.64959e6i	−2.14417	−	0.696683i
$656$	1.15151e6	−	836622.i	0.104474	−	0.0759049i
$657$		0			0
$658$	778732.	+	2.39669e6i	0.0701170	+	0.215798i
$659$	4.32897e6			0.388303			0.194152	−	0.980972i	$-0.437805\pi$
$659$	4.32897e6			0.388303			0.194152	+	0.980972i	$0.437805\pi$
$660$		0			0
$661$	−107456.			−0.00956592			−0.00478296	−	0.999989i	$-0.501522\pi$
$661$	−107456.			−0.00956592			−0.00478296	+	0.999989i	$0.501522\pi$
$662$	−3.59817e6	−	1.10740e7i	−0.319107	−	0.982110i
$663$		0			0
$664$	4.69858e6	−	3.41372e6i	0.413568	−	0.300474i
$665$	−1.81927e7	−	5.91118e6i	−1.59530	−	0.518346i
$666$		0			0
$667$	54394.1	+	74867.0i	0.00473410	+	0.00651592i
$668$	2.01968e6	+	1.46738e6i	0.175122	+	0.127234i
$669$		0			0
$670$			219120.i			0.0188579i
$671$	−1.41989e7	+	7.94558e6i	−1.21744	+	0.681270i
$672$		0			0
$673$	9.76795e6	−	3.17380e6i	0.831315	−	0.270111i	0.137716	−	0.990472i	$-0.456024\pi$
$673$	9.76795e6	−	3.17380e6i	0.831315	−	0.270111i	0.693599	+	0.720361i	$0.256024\pi$
$674$	4.11610e6	−	5.66533e6i	0.349009	−	0.480370i
$675$		0			0
$676$	828466.	−	2.54976e6i	0.0697281	−	0.214601i
$677$	3.75228e6	−	1.15483e7i	0.314647	−	0.968383i	−0.661253	−	0.750163i	$-0.729975\pi$
$677$	3.75228e6	−	1.15483e7i	0.314647	−	0.968383i	0.975900	−	0.218220i	$-0.0700250\pi$
$678$		0			0
$679$	7.80498e6	−	1.07426e7i	0.649677	−	0.894204i
$680$	−579640.	+	188336.i	−0.0480713	+	0.0156193i
$681$		0			0
$682$	1.46966e6	−	1.23820e7i	0.120991	−	1.01937i
$683$			2.91973e6i			0.239492i	0.992805	+	0.119746i	$0.0382081\pi$
$683$			2.91973e6i			0.239492i	−0.992805	+	0.119746i	$0.961792\pi$
$684$		0			0
$685$	−2.61562e7	−	1.90036e7i	−2.12985	−	1.54743i
$686$	5.40684e6	+	7.44187e6i	0.438665	+	0.603771i
$687$		0			0
$688$	−1.98634e6	−	645402.i	−0.159986	−	0.0519827i
$689$	−7.41651e6	+	5.38841e6i	−0.595184	+	0.432427i
$690$		0			0
$691$	−3.08666e6	−	9.49976e6i	−0.245920	−	0.756863i	−0.995484	−	0.0949314i	$-0.969737\pi$
$691$	−3.08666e6	−	9.49976e6i	−0.245920	−	0.756863i	0.749564	−	0.661932i	$-0.230263\pi$
$692$	7.35213e6			0.583644
$693$		0			0
$694$	2.18996e6			0.172599
$695$	1.52695e7	+	4.69947e7i	1.19912	+	3.69051i
$696$		0			0
$697$	−386759.	+	280997.i	−0.0301550	+	0.0219089i
$698$	8.62714e6	+	2.80313e6i	0.670237	+	0.217773i
$699$		0			0
$700$	7.76920e6	+	1.06934e7i	0.599282	+	0.824841i
$701$	4.89336e6	+	3.55524e6i	0.376108	+	0.273258i	0.759739	−	0.650228i	$-0.225327\pi$
$701$	4.89336e6	+	3.55524e6i	0.376108	+	0.273258i	−0.383631	+	0.923486i	$0.625327\pi$
$702$		0			0
$703$		−	1.76897e7i		−	1.35000i
$704$	1.49255e6	+	688674.i	0.113501	+	0.0523699i
$705$		0			0
$706$	−3.64460e6	+	1.18420e6i	−0.275194	+	0.0894158i
$707$	−4.07065e6	+	5.60276e6i	−0.306277	+	0.421555i
$708$		0			0
$709$	1.85337e6	−	5.70410e6i	0.138467	−	0.426159i	−0.857646	−	0.514241i	$-0.828074\pi$
$709$	1.85337e6	−	5.70410e6i	0.138467	−	0.426159i	0.996113	+	0.0880822i	$0.0280738\pi$
$710$	278701.	−	857754.i	0.0207488	−	0.0638582i
$711$		0			0
$712$	−4.71743e6	+	6.49299e6i	−0.348743	+	0.480004i
$713$	3.49738e6	−	1.13637e6i	0.257643	−	0.0837134i
$714$		0			0
$715$	−1.36229e7	+	1.47274e7i	−0.996560	+	1.07736i
$716$			4.65597e6i			0.339412i
$717$		0			0
$718$	−2.51990e6	−	1.83082e6i	−0.182420	−	0.132536i
$719$	−1.11312e7	−	1.53208e7i	−0.803010	−	1.10525i	−0.992365	−	0.123339i	$-0.960640\pi$
$719$	−1.11312e7	−	1.53208e7i	−0.803010	−	1.10525i	0.189355	−	0.981909i	$-0.439360\pi$
$720$		0			0
$721$	−9.93231e6	−	3.22720e6i	−0.711561	−	0.231200i
$722$	−3.80771e6	+	2.76647e6i	−0.271845	+	0.197507i
$723$		0			0
$724$	−637302.	−	1.96141e6i	−0.0451855	−	0.139067i
$725$	−1.78690e6			−0.126257
$726$		0			0
$727$	2.24536e7			1.57562			0.787809	−	0.615920i	$-0.211215\pi$
$727$	2.24536e7			1.57562			0.787809	+	0.615920i	$0.211215\pi$
$728$	806704.	+	2.48278e6i	0.0564139	+	0.173624i
$729$		0			0
$730$	1.24408e7	−	9.03876e6i	0.864054	−	0.627772i
$731$	667155.	+	216772.i	0.0461778	+	0.0150041i
$732$		0			0
$733$	−5.51408e6	−	7.58948e6i	−0.379064	−	0.521737i	0.576272	−	0.817258i	$-0.304507\pi$
$733$	−5.51408e6	−	7.58948e6i	−0.379064	−	0.521737i	−0.955336	+	0.295521i	$0.904507\pi$
$734$	2.32298e6	+	1.68775e6i	0.159150	+	0.115629i
$735$		0			0
$736$			484784.i			0.0329879i
$737$	−134785.	+	145713.i	−0.00914055	+	0.00988164i
$738$		0			0
$739$	1.48894e7	−	4.83786e6i	1.00292	−	0.325868i	0.238888	−	0.971047i	$-0.423217\pi$
$739$	1.48894e7	−	4.83786e6i	1.00292	−	0.325868i	0.764032	+	0.645179i	$0.223217\pi$
$740$	−9.64073e6	+	1.32693e7i	−0.647188	+	0.890778i
$741$		0			0
$742$	−2.26870e6	+	6.98233e6i	−0.151275	+	0.465576i
$743$	6.40364e6	−	1.97084e7i	0.425554	−	1.30972i	−0.476908	−	0.878953i	$-0.658242\pi$
$743$	6.40364e6	−	1.97084e7i	0.425554	−	1.30972i	0.902462	−	0.430769i	$-0.141758\pi$
$744$		0			0
$745$	−2.70551e7	+	3.72381e7i	−1.78590	+	2.45808i
$746$	3.74859e6	−	1.21799e6i	0.246616	−	0.0801303i
$747$		0			0
$748$	−501305.	−	231306.i	−0.0327603	−	0.0151158i
$749$		−	1.06307e7i		−	0.692402i
$750$		0			0
$751$	3.76806e6	+	2.73765e6i	0.243791	+	0.177124i	0.702971	−	0.711219i	$-0.251857\pi$
$751$	3.76806e6	+	2.73765e6i	0.243791	+	0.177124i	−0.459180	+	0.888343i	$0.651857\pi$
$752$	−1.04902e6	−	1.44385e6i	−0.0676453	−	0.0931057i
$753$		0			0
$754$	−335645.	−	109058.i	−0.0215007	−	0.00698599i
$755$	−3.82471e7	+	2.77881e7i	−2.44192	+	1.77416i
$756$		0			0
$757$	1.39888e6	+	4.30532e6i	0.0887240	+	0.273065i	0.985567	−	0.169284i	$-0.0541455\pi$
$757$	1.39888e6	+	4.30532e6i	0.0887240	+	0.273065i	−0.896843	+	0.442348i	$0.854145\pi$
$758$	1.87852e7			1.18752
$759$		0			0
$760$	1.35472e7			0.850776
$761$	8.59093e6	+	2.64402e7i	0.537748	+	1.65502i	0.737636	+	0.675198i	$0.235942\pi$
$761$	8.59093e6	+	2.64402e7i	0.537748	+	1.65502i	−0.199888	+	0.979819i	$0.564058\pi$
$762$		0			0
$763$	−1.59282e7	+	1.15725e7i	−0.990505	+	0.719644i
$764$	−6.93824e6	−	2.25437e6i	−0.430047	−	0.139731i
$765$		0			0
$766$	3.81039e6	+	5.24455e6i	0.234637	+	0.322951i
$767$	1.17315e7	+	8.52340e6i	0.720051	+	0.523148i
$768$		0			0
$769$			4.79707e6i			0.292523i	0.989246	+	0.146262i	$0.0467241\pi$
$769$			4.79707e6i			0.292523i	−0.989246	+	0.146262i	$0.953276\pi$
$770$	−1.89369e6	+	1.59546e7i	−0.115102	+	0.969748i
$771$		0			0
$772$	5.67234e6	−	1.84305e6i	0.342546	−	0.111300i
$773$	1.63771e7	−	2.25411e7i	0.985796	−	1.35683i	0.0521481	−	0.998639i	$-0.483393\pi$
$773$	1.63771e7	−	2.25411e7i	0.985796	−	1.35683i	0.933648	−	0.358192i	$-0.116607\pi$
$774$		0			0
$775$	−2.19425e7	+	6.75320e7i	−1.31229	+	4.03883i
$776$	−2.90599e6	+	8.94371e6i	−0.173236	+	0.533167i
$777$		0			0
$778$	3.89365e6	−	5.35915e6i	0.230626	−	0.317429i
$779$	1.01062e7	−	3.28369e6i	0.596682	−	0.193874i
$780$		0			0
$781$	712955.	−	398965.i	0.0418249	−	0.0234049i
$782$		−	162825.i		−	0.00952148i
$783$		0			0
$784$	−1.78949e6	−	1.30014e6i	−0.103977	−	0.0755439i
$785$	6.07493e6	+	8.36142e6i	0.351858	+	0.484290i
$786$		0			0
$787$	3.80897e6	+	1.23761e6i	0.219215	+	0.0712273i	0.416565	−	0.909106i	$-0.363234\pi$
$787$	3.80897e6	+	1.23761e6i	0.219215	+	0.0712273i	−0.197350	+	0.980333i	$0.563234\pi$
$788$	−3.31387e6	+	2.40766e6i	−0.190116	+	0.138128i
$789$		0			0
$790$	−8.68147e6	−	2.67188e7i	−0.494909	−	1.52317i
$791$	7.55854e6			0.429533
$792$		0			0
$793$	1.83003e7			1.03342
$794$	4.78617e6	+	1.47303e7i	0.269424	+	0.829202i
$795$		0			0
$796$	6.95229e6	−	5.05113e6i	0.388906	−	0.282557i
$797$	−1.77771e7	−	5.77612e6i	−0.991321	−	0.322100i	−0.231929	−	0.972733i	$-0.574504\pi$
$797$	−1.77771e7	−	5.77612e6i	−0.991321	−	0.322100i	−0.759392	+	0.650633i	$0.774504\pi$
$798$		0			0
$799$	352334.	+	484946.i	0.0195248	+	0.0268736i
$800$	−7.57309e6	−	5.50217e6i	−0.418358	−	0.303955i
$801$		0			0
$802$		−	659995.i		−	0.0362331i
$803$	1.38329e7	+	1.64187e6i	0.757052	+	0.0898565i
$804$		0			0
$805$	−4.50647e6	+	1.46424e6i	−0.245102	+	0.0796385i
$806$	−8.24321e6	+	1.13458e7i	−0.446950	+	0.615174i
$807$		0			0
$808$	1.51560e6	−	4.66454e6i	0.0816689	−	0.251351i
$809$	−8.69325e6	+	2.67551e7i	−0.466994	+	1.43726i	0.389464	+	0.921042i	$0.372660\pi$
$809$	−8.69325e6	+	2.67551e7i	−0.466994	+	1.43726i	−0.856458	+	0.516217i	$0.827340\pi$
$810$		0			0
$811$	1.21012e7	−	1.66558e7i	0.646064	−	0.889231i	−0.352857	−	0.935677i	$-0.614790\pi$
$811$	1.21012e7	−	1.66558e7i	0.646064	−	0.889231i	0.998921	+	0.0464467i	$0.0147898\pi$
$812$	−268802.	+	87339.1i	−0.0143068	+	0.00464856i
$813$		0			0
$814$	−1.45732e7	+	2.89379e6i	−0.770894	+	0.153076i
$815$		−	6.60830e7i		−	3.48494i
$816$		0			0
$817$	−1.26147e7	−	9.16508e6i	−0.661181	−	0.480376i
$818$	−1.69787e6	−	2.33692e6i	−0.0887201	−	0.122113i
$819$		0			0
$820$	−9.37036e6	−	3.04462e6i	−0.486656	−	0.158124i
$821$	−1.45024e7	+	1.05366e7i	−0.750899	+	0.545560i	−0.896105	−	0.443841i	$-0.853615\pi$
$821$	−1.45024e7	+	1.05366e7i	−0.750899	+	0.545560i	0.145206	+	0.989401i	$0.453615\pi$
$822$		0			0
$823$	−1.18258e6	−	3.63960e6i	−0.0608597	−	0.187307i	0.916004	−	0.401169i	$-0.131396\pi$
$823$	−1.18258e6	−	3.63960e6i	−0.0608597	−	0.187307i	−0.976864	+	0.213862i	$0.931396\pi$
$824$	7.39608e6			0.379476
$825$		0			0
$826$	1.16131e7			0.592238
$827$	−6.90301e6	−	2.12453e7i	−0.350974	−	1.08019i	−0.958307	−	0.285739i	$-0.907761\pi$
$827$	−6.90301e6	−	2.12453e7i	−0.350974	−	1.08019i	0.607334	−	0.794447i	$-0.292239\pi$
$828$		0			0
$829$	1.59459e7	−	1.15854e7i	0.805864	−	0.585495i	−0.106764	−	0.994284i	$-0.534049\pi$
$829$	1.59459e7	−	1.15854e7i	0.805864	−	0.585495i	0.912629	+	0.408790i	$0.134049\pi$
$830$	−3.82345e7	−	1.24231e7i	−1.92646	−	0.625944i
$831$		0			0
$832$	−1.08670e6	−	1.49571e6i	−0.0544252	−	0.0749099i
$833$	601037.	+	436679.i	0.0300116	+	0.0218047i
$834$		0			0
$835$		−	1.72808e7i		−	0.857724i
$836$	9.00877e6	+	8.33314e6i	0.445810	+	0.412376i
$837$		0			0
$838$	−3.17569e6	+	1.03185e6i	−0.156217	+	0.0507580i
$839$	4.33617e6	−	5.96823e6i	0.212668	−	0.292712i	−0.689335	−	0.724443i	$-0.742097\pi$
$839$	4.33617e6	−	5.96823e6i	0.212668	−	0.292712i	0.902002	+	0.431731i	$0.142097\pi$
$840$		0			0
$841$	−6.32649e6	+	1.94709e7i	−0.308441	+	0.949285i
$842$	−3.54704e6	+	1.09167e7i	−0.172419	+	0.530652i
$843$		0			0
$844$	2.39725e6	−	3.29954e6i	0.115840	−	0.159440i
$845$	−1.76497e7	+	5.73474e6i	−0.850347	+	0.276295i
$846$		0			0
$847$	−1.10733e7	+	9.44483e6i	−0.530356	+	0.452361i
$848$		−	5.19938e6i		−	0.248292i
$849$		0			0
$850$	2.54358e6	+	1.84802e6i	0.120753	+	0.0877322i
$851$	−2.57560e6	−	3.54501e6i	−0.121914	−	0.167801i
$852$		0			0
$853$	−2.34961e7	−	7.63434e6i	−1.10566	−	0.359252i	−0.301384	−	0.953503i	$-0.597449\pi$
$853$	−2.34961e7	−	7.63434e6i	−1.10566	−	0.359252i	−0.804280	+	0.594251i	$0.797449\pi$
$854$	1.18568e7	−	8.61447e6i	0.556318	−	0.404189i
$855$		0			0
$856$	2.32650e6	+	7.16023e6i	0.108522	+	0.333997i
$857$	1.90785e7			0.887343			0.443671	−	0.896190i	$-0.353676\pi$
$857$	1.90785e7			0.887343			0.443671	+	0.896190i	$0.353676\pi$
$858$		0			0
$859$	−2.09126e7			−0.966997			−0.483499	−	0.875345i	$-0.660634\pi$
$859$	−2.09126e7			−0.966997			−0.483499	+	0.875345i	$0.660634\pi$
$860$	4.46755e6	+	1.37497e7i	0.205979	+	0.633939i
$861$		0			0
$862$	1.82592e7	−	1.32660e7i	0.836975	−	0.608098i
$863$	1.53999e7	+	5.00374e6i	0.703869	+	0.228701i	0.639015	−	0.769194i	$-0.279342\pi$
$863$	1.53999e7	+	5.00374e6i	0.703869	+	0.228701i	0.0648533	+	0.997895i	$0.479342\pi$
$864$		0			0
$865$	−2.99138e7	−	4.11728e7i	−1.35935	−	1.87098i
$866$	−1.84957e6	−	1.34379e6i	−0.0838061	−	0.0608887i
$867$		0			0
$868$			1.12313e7i			0.505977i
$869$	1.06622e7	−	2.31079e7i	0.478956	−	1.03803i
$870$		0			0
$871$	212323.	−	68988.1i	0.00948315	−	0.00308126i
$872$	8.19571e6	−	1.12804e7i	0.365002	−	0.502383i
$873$		0			0
$874$	−1.11841e6	+	3.44211e6i	−0.0495248	+	0.152422i
$875$	1.86082e7	−	5.72702e7i	0.821646	−	2.52877i
$876$		0			0
$877$	−950562.	+	1.30834e6i	−0.0417332	+	0.0574408i	−0.829374	−	0.558694i	$-0.811302\pi$
$877$	−950562.	+	1.30834e6i	−0.0417332	+	0.0574408i	0.787640	+	0.616135i	$0.211302\pi$
$878$	−1.83541e7	+	5.96362e6i	−0.803521	+	0.261080i
$879$		0			0
$880$	−2.21613e6	−	1.11605e7i	−0.0964692	−	0.485822i
$881$		−	917933.i		−	0.0398448i	−0.999802	−	0.0199224i	$-0.993658\pi$
$881$		−	917933.i		−	0.0398448i	0.999802	−	0.0199224i	$-0.00634191\pi$
$882$		0			0
$883$	9.27294e6	+	6.73718e6i	0.400235	+	0.290788i	0.769637	−	0.638482i	$-0.220437\pi$
$883$	9.27294e6	+	6.73718e6i	0.400235	+	0.290788i	−0.369401	+	0.929270i	$0.620437\pi$
$884$	364990.	+	502366.i	0.0157091	+	0.0216217i
$885$		0			0
$886$	5.16339e6	+	1.67769e6i	0.220979	+	0.0718003i
$887$	−4.24119e6	+	3.08141e6i	−0.181000	+	0.131504i	−0.674596	−	0.738187i	$-0.735682\pi$
$887$	−4.24119e6	+	3.08141e6i	−0.181000	+	0.131504i	0.493596	+	0.869691i	$0.335682\pi$
$888$		0			0
$889$	−3.91559e6	−	1.20509e7i	−0.166166	−	0.511407i
$890$	5.55554e7			2.35099
$891$		0			0
$892$	−1.10502e7			−0.465006
$893$	−4.11733e6	−	1.26718e7i	−0.172777	−	0.531754i
$894$		0			0
$895$	2.60740e7	−	1.89438e7i	1.08805	−	0.790516i
$896$	−1.40815e6	−	457535.i	−0.0585974	−	0.0190395i
$897$		0			0
$898$	5.77941e6	+	7.95467e6i	0.239162	+	0.329178i
$899$	−1.22837e6	−	892464.i	−0.0506910	−	0.0368291i
$900$		0			0
$901$			1.74632e6i			0.0716659i
$902$	−4.35841e6	−	7.78854e6i	−0.178366	−	0.318742i
$903$		0			0
$904$	−5.09098e6	+	1.65416e6i	−0.207196	+	0.0673220i
$905$	−8.39114e6	+	1.15494e7i	−0.340565	+	0.468747i
$906$		0			0
$907$	−9.04136e6	+	2.78264e7i	−0.364935	+	1.12315i	0.585087	+	0.810971i	$0.301060\pi$
$907$	−9.04136e6	+	2.78264e7i	−0.364935	+	1.12315i	−0.950022	+	0.312184i	$0.898940\pi$
$908$	6.25424e6	−	1.92486e7i	0.251744	−	0.774790i
$909$		0			0
$910$	1.06216e7	−	1.46194e7i	0.425194	−	0.585229i
$911$	−3.19010e7	+	1.03653e7i	−1.27353	+	0.413795i	−0.866297	−	0.499530i	$-0.833506\pi$
$911$	−3.19010e7	+	1.03653e7i	−1.27353	+	0.413795i	−0.407233	+	0.913324i	$0.633506\pi$
$912$		0			0
$913$	−1.77839e7	−	3.17800e7i	−0.706074	−	1.26176i
$914$		−	1.52998e7i		−	0.605787i
$915$		0			0
$916$	−1.40170e7	−	1.01839e7i	−0.551969	−	0.401029i
$917$	1.18724e7	+	1.63409e7i	0.466245	+	0.641731i
$918$		0			0
$919$	1.57143e7	+	5.10588e6i	0.613770	+	0.199426i	0.599372	−	0.800471i	$-0.295417\pi$
$919$	1.57143e7	+	5.10588e6i	0.613770	+	0.199426i	0.0143975	+	0.999896i	$0.495417\pi$
$920$	2.71485e6	−	1.97245e6i	0.105749	−	0.0768312i
$921$		0			0
$922$	8.61414e6	+	2.65116e7i	0.333722	+	1.02709i
$923$	−918897.			−0.0355028
$924$		0			0
$925$	8.46110e7			3.25142
$926$	−2.07020e6	−	6.37141e6i	−0.0793385	−	0.244179i
$927$		0			0
$928$	161935.	−	117653.i	0.00617265	−	0.00448470i
$929$	7.80671e6	+	2.53655e6i	0.296776	+	0.0964284i	0.453621	−	0.891195i	$-0.350132\pi$
$929$	7.80671e6	+	2.53655e6i	0.296776	+	0.0964284i	−0.156845	+	0.987623i	$0.550132\pi$
$930$		0			0
$931$	−9.70643e6	−	1.33598e7i	−0.367016	−	0.505154i
$932$	1.90264e7	+	1.38235e7i	0.717492	+	0.521288i
$933$		0			0
$934$			1.70886e7i			0.640973i
$935$	744334.	+	3.74849e6i	0.0278445	+	0.140226i
$936$		0			0
$937$	−3.59213e6	+	1.16716e6i	−0.133661	+	0.0434290i	−0.375083	−	0.926991i	$-0.622386\pi$
$937$	−3.59213e6	+	1.16716e6i	−0.133661	+	0.0434290i	0.241423	+	0.970420i	$0.422386\pi$
$938$	105090.	−	144644.i	0.00389992	−	0.00536778i
$939$		0			0
$940$	−3.81755e6	+	1.17492e7i	−0.140918	+	0.433700i
$941$	−7.78411e6	+	2.39570e7i	−0.286573	+	0.881981i	0.699350	+	0.714779i	$0.253473\pi$
$941$	−7.78411e6	+	2.39570e7i	−0.286573	+	0.881981i	−0.985923	+	0.167201i	$0.946527\pi$
$942$		0			0
$943$	1.54717e6	−	2.12950e6i	0.0566577	−	0.0779826i
$944$	−7.82187e6	+	2.54148e6i	−0.285681	+	0.0928232i
$945$		0			0
$946$	−5.48683e6	+	1.18915e7i	−0.199340	+	0.432026i
$947$		−	4.95981e7i		−	1.79717i	−0.438797	−	0.898586i	$-0.644595\pi$
$947$		−	4.95981e7i		−	1.79717i	0.438797	−	0.898586i	$-0.355405\pi$
$948$		0			0
$949$	−1.26753e7	−	9.20914e6i	−0.456870	−	0.331936i
$950$	−4.10775e7	−	5.65383e7i	−1.47671	−	2.03251i
$951$		0			0
$952$	472956.	+	153673.i	0.0169133	+	0.00549547i
$953$	−1.08549e7	+	7.88654e6i	−0.387163	+	0.281290i	−0.764292	−	0.644871i	$-0.776911\pi$
$953$	−1.08549e7	+	7.88654e6i	−0.387163	+	0.281290i	0.377129	+	0.926161i	$0.376911\pi$
$954$		0			0
$955$	1.56050e7	+	4.80274e7i	0.553677	+	1.70404i
$956$	−7.42288e6			−0.262680
$957$		0			0
$958$	4.00981e6			0.141159
$959$	8.15197e6	+	2.50892e7i	0.286231	+	0.880927i
$960$		0			0
$961$	−2.56513e7	+	1.86368e7i	−0.895985	+	0.650971i
$962$	1.58931e7	+	5.16397e6i	0.553694	+	0.179906i
$963$		0			0
$964$	−1.30552e6	−	1.79689e6i	−0.0452471	−	0.0622773i
$965$	−3.34005e7	−	2.42669e7i	−1.15461	−	0.838872i
$966$		0			0
$967$		−	2.19357e7i		−	0.754371i	−0.926138	−	0.377186i	$-0.876892\pi$
$967$		−	2.19357e7i		−	0.754371i	0.926138	−	0.377186i	$-0.123108\pi$
$968$	5.39133e6	−	8.78483e6i	0.184930	−	0.301332i
$969$		0			0
$970$	6.19095e7	−	2.01156e7i	2.11265	−	0.686442i
$971$	−3.05447e7	+	4.20412e7i	−1.03965	+	1.43096i	−0.142203	+	0.989838i	$0.545419\pi$
$971$	−3.05447e7	+	4.20412e7i	−1.03965	+	1.43096i	−0.897448	+	0.441119i	$0.854581\pi$
$972$		0			0
$973$	1.24591e7	−	3.83452e7i	0.421896	−	1.29846i
$974$	2.07920e6	−	6.39913e6i	0.0702262	−	0.216134i
$975$		0			0
$976$	−6.10080e6	+	8.39703e6i	−0.205004	+	0.282164i
$977$	3.76796e7	−	1.22428e7i	1.26290	−	0.410342i	0.400375	−	0.916352i	$-0.368880\pi$
$977$	3.76796e7	−	1.22428e7i	1.26290	−	0.410342i	0.862528	+	0.506010i	$0.168880\pi$
$978$		0			0
$979$	3.69439e7	+	3.41732e7i	1.23193	+	1.13954i
$980$			1.53112e7i			0.509267i
$981$		0			0
$982$	1.41343e7	+	1.02691e7i	0.467729	+	0.339825i
$983$	−2.32366e7	−	3.19824e7i	−0.766987	−	1.05567i	−0.996601	−	0.0823852i	$-0.973746\pi$
$983$	−2.32366e7	−	3.19824e7i	−0.766987	−	1.05567i	0.229613	−	0.973282i	$-0.426254\pi$
$984$		0			0
$985$	2.69664e7	+	8.76192e6i	0.885590	+	0.287746i
$986$	−54389.4	+	39516.2i	−0.00178165	+	0.00129444i
$987$		0			0
$988$	−4.26523e6	−	1.31270e7i	−0.139011	−	0.427832i
$989$	−3.86239e6			−0.125564
$990$		0			0
$991$	4.40362e7			1.42438			0.712190	−	0.701987i	$-0.247703\pi$
$991$	4.40362e7			1.42438			0.712190	+	0.701987i	$0.247703\pi$
$992$	−2.45793e6	−	7.56474e6i	−0.0793033	−	0.244070i
$993$		0			0
$994$	−595356.	+	432551.i	−0.0191122	+	0.0138858i
$995$	−5.65739e7	−	1.83820e7i	−1.81158	−	0.588619i
$996$		0			0
$997$	2.81966e7	+	3.88093e7i	0.898377	+	1.23651i	0.970983	+	0.239149i	$0.0768683\pi$
$997$	2.81966e7	+	3.88093e7i	0.898377	+	1.23651i	−0.0726065	+	0.997361i	$0.523132\pi$
$998$	375396.	+	272741.i	0.0119306	+	0.00866810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.17.10	yes	40
3.2	odd	2		198.6.l.a.17.1	✓	40
11.2	odd	10		198.6.l.a.35.1	yes	40
33.2	even	10	inner	198.6.l.b.35.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.1	✓	40	3.2	odd	2
198.6.l.a.35.1	yes	40	11.2	odd	10
198.6.l.b.17.10	yes	40	1.1	even	1	trivial
198.6.l.b.35.10	yes	40	33.2	even	10	inner

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(105.333 + 34.2249i) q^{5} +(-53.1179 - 73.1105i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(105.333 + 34.2249i) q^{5} +(-53.1179 - 73.1105i) q^{7} +(51.7771 + 37.6183i) q^{8} -443.016i q^{10} +(272.508 - 294.602i) q^{11} +(-429.276 + 139.480i) q^{13} +(-212.472 + 292.442i) q^{14} +(79.1084 - 243.470i) q^{16} +(-26.5702 + 81.7747i) q^{17} +(1123.38 - 1546.21i) q^{19} +(-1685.33 + 547.598i) q^{20} +(-1457.57 - 672.533i) q^{22} -473.422i q^{23} +(7395.59 + 5373.21i) q^{25} +(1061.23 + 1460.65i) q^{26} +(1375.14 + 446.812i) q^{28} +(-158.140 + 114.895i) q^{29} +(2400.33 + 7387.44i) q^{31} -1024.00 q^{32} +343.932 q^{34} +(-3092.89 - 9518.93i) q^{35} +(7488.06 - 5440.39i) q^{37} +(-7270.70 - 2362.39i) q^{38} +(4166.37 + 5734.52i) q^{40} +(4498.09 + 3268.05i) q^{41} -8158.45i q^{43} +(-756.811 + 6376.23i) q^{44} +(-1801.01 + 585.182i) q^{46} +(4097.72 - 5640.02i) q^{47} +(2670.01 - 8217.45i) q^{49} +(11299.5 - 34776.2i) q^{50} +(4244.91 - 5842.62i) q^{52} +(19316.0 - 6276.16i) q^{53} +(38786.9 - 21704.9i) q^{55} -5783.65i q^{56} +(632.560 + 459.582i) q^{58} +(-18883.5 - 25990.9i) q^{59} +(-38559.8 - 12528.8i) q^{61} +(25136.5 - 18262.8i) q^{62} +(1265.73 + 3895.53i) q^{64} -49990.7 q^{65} -494.609 q^{67} +(-425.123 - 1308.39i) q^{68} +(-32389.1 + 23532.1i) q^{70} +(1936.17 + 629.099i) q^{71} +(20402.8 + 28082.0i) q^{73} +(-29952.2 - 21761.6i) q^{74} +30579.5i q^{76} +(-36013.6 - 4274.55i) q^{77} +(60311.2 - 19596.3i) q^{79} +(16665.5 - 22938.1i) q^{80} +(6872.47 - 21151.3i) q^{82} +(28042.2 - 86304.9i) q^{83} +(-5597.46 + 7704.24i) q^{85} +(-31036.6 + 10084.4i) q^{86} +(25192.1 - 5002.37i) q^{88} +125403. i q^{89} +(32999.7 + 23975.7i) q^{91} +(4452.33 + 6128.11i) q^{92} +(-26521.0 - 8617.19i) q^{94} +(171249. - 124419. i) q^{95} +(45406.0 + 139745. i) q^{97} -34561.4 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8} - 476 q^{11} - 2560 q^{16} - 1424 q^{17} - 1656 q^{22} + 11574 q^{25} + 10480 q^{26} + 3040 q^{28} - 10658 q^{29} - 5302 q^{31} - 40960 q^{32} - 13984 q^{34} - 50 q^{35} - 4344 q^{37} + 35120 q^{38} + 19840 q^{40} - 16856 q^{41} + 6624 q^{44} - 52400 q^{46} - 10900 q^{47} - 40698 q^{49} - 6256 q^{50} + 41920 q^{52} + 10290 q^{53} + 158396 q^{55} + 42632 q^{58} + 62620 q^{59} - 134780 q^{61} - 30272 q^{62} - 40960 q^{64} - 137296 q^{65} - 36856 q^{67} - 22784 q^{68} + 79400 q^{70} + 62180 q^{71} + 100030 q^{73} + 17376 q^{74} - 162888 q^{77} + 35900 q^{79} + 79360 q^{80} - 90096 q^{82} - 12276 q^{83} + 270600 q^{85} - 137680 q^{86} - 26496 q^{88} + 406656 q^{91} + 134720 q^{92} - 91600 q^{94} - 75128 q^{95} - 364164 q^{97} + 358192 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 160 * q^4 + 640 * q^8 - 476 * q^11 - 2560 * q^16 - 1424 * q^17 - 1656 * q^22 + 11574 * q^25 + 10480 * q^26 + 3040 * q^28 - 10658 * q^29 - 5302 * q^31 - 40960 * q^32 - 13984 * q^34 - 50 * q^35 - 4344 * q^37 + 35120 * q^38 + 19840 * q^40 - 16856 * q^41 + 6624 * q^44 - 52400 * q^46 - 10900 * q^47 - 40698 * q^49 - 6256 * q^50 + 41920 * q^52 + 10290 * q^53 + 158396 * q^55 + 42632 * q^58 + 62620 * q^59 - 134780 * q^61 - 30272 * q^62 - 40960 * q^64 - 137296 * q^65 - 36856 * q^67 - 22784 * q^68 + 79400 * q^70 + 62180 * q^71 + 100030 * q^73 + 17376 * q^74 - 162888 * q^77 + 35900 * q^79 + 79360 * q^80 - 90096 * q^82 - 12276 * q^83 + 270600 * q^85 - 137680 * q^86 - 26496 * q^88 + 406656 * q^91 + 134720 * q^92 - 91600 * q^94 - 75128 * q^95 - 364164 * q^97 + 358192 * q^98

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