LMFDB - Embedded newform 198.6.l.b.17.2

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			17.2
Character	$\chi$	$=$	198.17
Dual form			198.6.l.b.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-67.8638 - 22.0503i) q^{5} +(-151.878 - 209.042i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-67.8638 - 22.0503i) q^{5} +(-151.878 - 209.042i) q^{7} +(51.7771 + 37.6183i) q^{8} +285.425i q^{10} +(-350.890 - 194.749i) q^{11} +(-450.520 + 146.383i) q^{13} +(-607.513 + 836.169i) q^{14} +(79.1084 - 243.470i) q^{16} +(669.264 - 2059.78i) q^{17} +(-539.652 + 742.767i) q^{19} +(1085.82 - 352.805i) q^{20} +(-307.144 + 1575.59i) q^{22} -2680.19i q^{23} +(1591.11 + 1156.01i) q^{25} +(1113.75 + 1532.94i) q^{26} +(3931.90 + 1277.55i) q^{28} +(-1664.21 + 1209.12i) q^{29} +(2192.03 + 6746.37i) q^{31} -1024.00 q^{32} -8663.14 q^{34} +(5697.59 + 17535.4i) q^{35} +(-2143.43 + 1557.29i) q^{37} +(3492.70 + 1134.85i) q^{38} +(-2684.30 - 3694.62i) q^{40} +(-6598.33 - 4793.97i) q^{41} -7286.93i q^{43} +(6373.55 - 779.088i) q^{44} +(-10196.0 + 3312.89i) q^{46} +(7522.17 - 10353.4i) q^{47} +(-15438.1 + 47513.5i) q^{49} +(2431.00 - 7481.84i) q^{50} +(4454.99 - 6131.76i) q^{52} +(29094.8 - 9453.48i) q^{53} +(19518.5 + 20953.6i) q^{55} -16537.0i q^{56} +(6656.84 + 4836.48i) q^{58} +(11221.7 + 15445.3i) q^{59} +(-12397.2 - 4028.10i) q^{61} +(22955.2 - 16678.0i) q^{62} +(1265.73 + 3895.53i) q^{64} +33801.8 q^{65} +1154.76 q^{67} +(10708.2 + 32956.5i) q^{68} +(59665.9 - 43349.8i) q^{70} +(7194.05 + 2337.49i) q^{71} +(-31107.2 - 42815.3i) q^{73} +(8573.70 + 6229.16i) q^{74} -14689.8i q^{76} +(12581.8 + 102929. i) q^{77} +(62210.6 - 20213.5i) q^{79} +(-10737.2 + 14778.5i) q^{80} +(-10081.4 + 31027.2i) q^{82} +(-12695.5 + 39072.6i) q^{83} +(-90837.7 + 125027. i) q^{85} +(-27721.1 + 9007.14i) q^{86} +(-10842.0 - 23283.4i) q^{88} -121643. i q^{89} +(99024.4 + 71945.4i) q^{91} +(25206.0 + 34693.1i) q^{92} +(-48684.5 - 15818.6i) q^{94} +(53001.1 - 38507.6i) q^{95} +(-19151.6 - 58942.7i) q^{97} +199835. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−67.8638	−	22.0503i	−1.21399	−	0.394448i	−0.369097	−	0.929391i	$-0.620333\pi$
$5$	−67.8638	−	22.0503i	−1.21399	−	0.394448i	−0.844888	+	0.534943i	$0.820333\pi$
$6$		0			0
$7$	−151.878	−	209.042i	−1.17152	−	1.61246i	−0.652849	−	0.757488i	$-0.726427\pi$
$7$	−151.878	−	209.042i	−1.17152	−	1.61246i	−0.518672	−	0.854973i	$-0.673573\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$		0			0
$10$			285.425i			0.902593i
$11$	−350.890	−	194.749i	−0.874358	−	0.485281i
$11$	−350.890	−	194.749i	−0.874358	−	0.485281i
$12$		0			0
$13$	−450.520	+	146.383i	−0.739360	+	0.240233i	−0.654397	−	0.756152i	$-0.727077\pi$
$13$	−450.520	+	146.383i	−0.739360	+	0.240233i	−0.0849632	+	0.996384i	$0.527077\pi$
$14$	−607.513	+	836.169i	−0.828391	+	1.14018i
$15$		0			0
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	669.264	−	2059.78i	0.561662	−	1.72862i	−0.116004	−	0.993249i	$-0.537008\pi$
$17$	669.264	−	2059.78i	0.561662	−	1.72862i	0.677666	−	0.735370i	$-0.262992\pi$
$18$		0			0
$19$	−539.652	+	742.767i	−0.342949	+	0.472029i	−0.945300	−	0.326203i	$-0.894231\pi$
$19$	−539.652	+	742.767i	−0.342949	+	0.472029i	0.602351	+	0.798232i	$0.294231\pi$
$20$	1085.82	−	352.805i	0.606993	−	0.197224i
$21$		0			0
$22$	−307.144	+	1575.59i	−0.135296	+	0.694042i
$23$		−	2680.19i		−	1.05644i	−0.849107	−	0.528221i	$-0.822859\pi$
$23$		−	2680.19i		−	1.05644i	0.849107	−	0.528221i	$-0.177141\pi$
$24$		0			0
$25$	1591.11	+	1156.01i	0.509155	+	0.369922i
$26$	1113.75	+	1532.94i	0.323112	+	0.444726i
$27$		0			0
$28$	3931.90	+	1277.55i	0.947781	+	0.307953i
$29$	−1664.21	+	1209.12i	−0.367463	+	0.266977i	−0.756158	−	0.654389i	$-0.772926\pi$
$29$	−1664.21	+	1209.12i	−0.367463	+	0.266977i	0.388695	+	0.921366i	$0.372926\pi$
$30$		0			0
$31$	2192.03	+	6746.37i	0.409678	+	1.26086i	0.916926	+	0.399058i	$0.130663\pi$
$31$	2192.03	+	6746.37i	0.409678	+	1.26086i	−0.507248	+	0.861800i	$0.669337\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	−8663.14			−1.28522
$35$	5697.59	+	17535.4i	0.786178	+	2.41961i
$36$		0			0
$37$	−2143.43	+	1557.29i	−0.257397	+	0.187010i	−0.708999	−	0.705210i	$-0.750853\pi$
$37$	−2143.43	+	1557.29i	−0.257397	+	0.187010i	0.451602	+	0.892220i	$0.350853\pi$
$38$	3492.70	+	1134.85i	0.392376	+	0.127491i
$39$		0			0
$40$	−2684.30	−	3694.62i	−0.265266	−	0.365107i
$41$	−6598.33	−	4793.97i	−0.613020	−	0.445385i	0.237457	−	0.971398i	$-0.423686\pi$
$41$	−6598.33	−	4793.97i	−0.613020	−	0.445385i	−0.850476	+	0.526013i	$0.823686\pi$
$42$		0			0
$43$		−	7286.93i		−	0.600999i	−0.953782	−	0.300499i	$-0.902847\pi$
$43$		−	7286.93i		−	0.600999i	0.953782	−	0.300499i	$-0.0971533\pi$
$44$	6373.55	−	779.088i	0.496306	−	0.0606673i
$45$		0			0
$46$	−10196.0	+	3312.89i	−0.710456	+	0.230841i
$47$	7522.17	−	10353.4i	0.496705	−	0.683656i	−0.484902	−	0.874568i	$-0.661145\pi$
$47$	7522.17	−	10353.4i	0.496705	−	0.683656i	0.981607	+	0.190913i	$0.0611447\pi$
$48$		0			0
$49$	−15438.1	+	47513.5i	−0.918551	+	2.82701i
$50$	2431.00	−	7481.84i	0.137518	−	0.423237i
$51$		0			0
$52$	4454.99	−	6131.76i	0.228475	−	0.314468i
$53$	29094.8	−	9453.48i	1.42274	−	0.462277i	0.506269	−	0.862375i	$-0.331024\pi$
$53$	29094.8	−	9453.48i	1.42274	−	0.462277i	0.916472	+	0.400099i	$0.131024\pi$
$54$		0			0
$55$	19518.5	+	20953.6i	0.870040	+	0.934012i
$56$		−	16537.0i		−	0.704671i
$57$		0			0
$58$	6656.84	+	4836.48i	0.259835	+	0.188782i
$59$	11221.7	+	15445.3i	0.419688	+	0.577652i	0.965548	−	0.260225i	$-0.0837968\pi$
$59$	11221.7	+	15445.3i	0.419688	+	0.577652i	−0.545860	+	0.837877i	$0.683797\pi$
$60$		0			0
$61$	−12397.2	−	4028.10i	−0.426579	−	0.138604i	0.0878563	−	0.996133i	$-0.471998\pi$
$61$	−12397.2	−	4028.10i	−0.426579	−	0.138604i	−0.514435	+	0.857529i	$0.671998\pi$
$62$	22955.2	−	16678.0i	0.758407	−	0.551015i
$63$		0			0
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	33801.8			0.992331
$66$		0			0
$67$	1154.76			0.0314272			0.0157136	−	0.999877i	$-0.494998\pi$
$67$	1154.76			0.0314272			0.0157136	+	0.999877i	$0.494998\pi$
$68$	10708.2	+	32956.5i	0.280831	+	0.864309i
$69$		0			0
$70$	59665.9	−	43349.8i	1.45540	−	1.05741i
$71$	7194.05	+	2337.49i	0.169367	+	0.0550306i	0.392473	−	0.919764i	$-0.371620\pi$
$71$	7194.05	+	2337.49i	0.169367	+	0.0550306i	−0.223106	+	0.974794i	$0.571620\pi$
$72$		0			0
$73$	−31107.2	−	42815.3i	−0.683209	−	0.940356i	0.316758	−	0.948506i	$-0.397406\pi$
$73$	−31107.2	−	42815.3i	−0.683209	−	0.940356i	−0.999967	+	0.00815044i	$0.997406\pi$
$74$	8573.70	+	6229.16i	0.182007	+	0.132236i
$75$		0			0
$76$		−	14689.8i		−	0.291730i
$77$	12581.8	+	102929.i	0.241833	+	1.97839i
$78$		0			0
$79$	62210.6	−	20213.5i	1.12149	−	0.364395i	0.311156	−	0.950359i	$-0.399284\pi$
$79$	62210.6	−	20213.5i	1.12149	−	0.364395i	0.810337	+	0.585963i	$0.199284\pi$
$80$	−10737.2	+	14778.5i	−0.187571	+	0.258169i
$81$		0			0
$82$	−10081.4	+	31027.2i	−0.165571	+	0.509575i
$83$	−12695.5	+	39072.6i	−0.202280	+	0.622554i	0.797534	+	0.603274i	$0.206137\pi$
$83$	−12695.5	+	39072.6i	−0.202280	+	0.622554i	−0.999814	+	0.0192801i	$0.993863\pi$
$84$		0			0
$85$	−90837.7	+	125027.i	−1.36370	+	1.87697i
$86$	−27721.1	+	9007.14i	−0.404171	+	0.131323i
$87$		0			0
$88$	−10842.0	−	23283.4i	−0.149245	−	0.320509i
$89$		−	121643.i		−	1.62784i	−0.580977	−	0.813920i	$-0.697329\pi$
$89$		−	121643.i		−	1.62784i	0.580977	−	0.813920i	$-0.302671\pi$
$90$		0			0
$91$	99024.4	+	71945.4i	1.25354	+	0.910751i
$92$	25206.0	+	34693.1i	0.310480	+	0.427340i
$93$		0			0
$94$	−48684.5	−	15818.6i	−0.568292	−	0.184649i
$95$	53001.1	−	38507.6i	0.602526	−	0.437761i
$96$		0			0
$97$	−19151.6	−	58942.7i	−0.206670	−	0.636064i	−0.999641	−	0.0268045i	$-0.991467\pi$
$97$	−19151.6	−	58942.7i	−0.206670	−	0.636064i	0.792971	−	0.609259i	$-0.208533\pi$
$98$	199835.			2.10187
$99$		0			0
$100$	−31467.5			−0.314675
$101$	9075.46	+	27931.4i	0.0885248	+	0.272451i	0.985512	−	0.169605i	$-0.0542492\pi$
$101$	9075.46	+	27931.4i	0.0885248	+	0.272451i	−0.896987	+	0.442056i	$0.854249\pi$
$102$		0			0
$103$	128132.	−	93093.5i	1.19005	−	0.864622i	0.196780	−	0.980448i	$-0.436951\pi$
$103$	128132.	−	93093.5i	1.19005	−	0.864622i	0.993270	+	0.115826i	$0.0369515\pi$
$104$	−28833.3	−	9368.50i	−0.261403	−	0.0849350i
$105$		0			0
$106$	−71926.3	−	98998.1i	−0.621761	−	0.855780i
$107$	−142435.	−	103485.i	−1.20270	−	0.873815i	−0.208155	−	0.978096i	$-0.566746\pi$
$107$	−142435.	−	103485.i	−1.20270	−	0.873815i	−0.994548	+	0.104281i	$0.966746\pi$
$108$		0			0
$109$			163629.i			1.31915i	0.751637	+	0.659576i	$0.229264\pi$
$109$			163629.i			1.31915i	−0.751637	+	0.659576i	$0.770736\pi$
$110$	55586.2	−	100153.i	0.438011	−	0.789190i
$111$		0			0
$112$	−62910.5	+	20440.9i	−0.473890	+	0.153976i
$113$	62380.4	−	85859.3i	0.459571	−	0.632545i	−0.514849	−	0.857281i	$-0.672152\pi$
$113$	62380.4	−	85859.3i	0.459571	−	0.632545i	0.974420	+	0.224736i	$0.0721520\pi$
$114$		0			0
$115$	−59098.9	+	181888.i	−0.416711	+	1.28251i
$116$	10170.8	−	31302.4i	0.0701792	−	0.215989i
$117$		0			0
$118$	44886.6	−	61781.1i	0.296765	−	0.408461i
$119$	−532229.	+	172932.i	−3.44533	+	1.11946i
$120$		0			0
$121$	85196.8	+	136671.i	0.529005	+	0.848619i
$122$			52140.8i			0.317160i
$123$		0			0
$124$	−91820.9	−	66711.8i	−0.536275	−	0.389627i
$125$	48580.9	+	66865.8i	0.278093	+	0.382762i
$126$		0			0
$127$	−308759.	−	100322.i	−1.69867	−	0.551932i	−0.710289	−	0.703910i	$-0.751436\pi$
$127$	−308759.	−	100322.i	−1.69867	−	0.551932i	−0.988384	+	0.151978i	$0.951436\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$		0			0
$130$	−41781.3	−	128590.i	−0.216832	−	0.667341i
$131$	−258393.			−1.31554			−0.657769	−	0.753220i	$-0.728500\pi$
$131$	−258393.			−1.31554			−0.657769	+	0.753220i	$0.728500\pi$
$132$		0			0
$133$	237231.			1.16290
$134$	−1427.36	−	4392.98i	−0.00686709	−	0.0211347i
$135$		0			0
$136$	112138.	−	81473.0i	0.519883	−	0.377717i
$137$	−181494.	−	58971.0i	−0.826154	−	0.268434i	−0.134729	−	0.990882i	$-0.543017\pi$
$137$	−181494.	−	58971.0i	−0.826154	−	0.268434i	−0.691425	+	0.722449i	$0.743017\pi$
$138$		0			0
$139$	−138004.	−	189946.i	−0.605834	−	0.833858i	0.390393	−	0.920648i	$-0.372339\pi$
$139$	−138004.	−	189946.i	−0.605834	−	0.833858i	−0.996227	+	0.0867899i	$0.972339\pi$
$140$	−238664.	−	173399.i	−1.02912	−	0.747700i
$141$		0			0
$142$		−	30257.1i		−	0.125923i
$143$	186591.	+	36373.9i	0.763046	+	0.148748i
$144$		0			0
$145$	139601.	−	45359.2i	0.551403	−	0.179162i
$146$	−124429.	+	171261.i	−0.483101	+	0.664932i
$147$		0			0
$148$	13099.4	−	40316.0i	0.0491585	−	0.151294i
$149$	−36522.3	+	112404.i	−0.134770	+	0.414779i	−0.995554	−	0.0941912i	$-0.969974\pi$
$149$	−36522.3	+	112404.i	−0.134770	+	0.414779i	0.860784	+	0.508970i	$0.169974\pi$
$150$		0			0
$151$	72919.4	−	100365.i	0.260256	−	0.358212i	−0.658814	−	0.752306i	$-0.728942\pi$
$151$	72919.4	−	100365.i	0.260256	−	0.358212i	0.919070	+	0.394094i	$0.128942\pi$
$152$	−55883.2	+	18157.6i	−0.196188	+	0.0637453i
$153$		0			0
$154$	376013.	−	175091.i	1.27762	−	0.594926i
$155$		−	506170.i		−	1.69226i
$156$		0			0
$157$	−184622.	−	134136.i	−0.597770	−	0.434305i	0.247317	−	0.968935i	$-0.420451\pi$
$157$	−184622.	−	134136.i	−0.597770	−	0.434305i	−0.845087	+	0.534629i	$0.820451\pi$
$158$	−153793.	−	211678.i	−0.490111	−	0.674579i
$159$		0			0
$160$	69492.6	+	22579.5i	0.214604	+	0.0697292i
$161$	−560273.	+	407062.i	−1.70347	+	1.23764i
$162$		0			0
$163$	196928.	+	606081.i	0.580547	+	1.78674i	0.616460	+	0.787386i	$0.288566\pi$
$163$	196928.	+	606081.i	0.580547	+	1.78674i	−0.0359127	+	0.999355i	$0.511434\pi$
$164$	130496.			0.378867
$165$		0			0
$166$	164333.			0.462866
$167$	41285.5	+	127064.i	0.114553	+	0.352558i	0.991854	−	0.127384i	$-0.0406580\pi$
$167$	41285.5	+	127064.i	0.114553	+	0.352558i	−0.877301	+	0.479941i	$0.840658\pi$
$168$		0			0
$169$	−118842.	+	86343.7i	−0.320076	+	0.232549i
$170$	587914.	+	191025.i	1.56024	+	0.506953i
$171$		0			0
$172$	68530.4	+	94324.0i	0.176629	+	0.243109i
$173$	−60343.7	−	43842.3i	−0.153291	−	0.111372i	0.508496	−	0.861064i	$-0.330202\pi$
$173$	−60343.7	−	43842.3i	−0.153291	−	0.111372i	−0.661787	+	0.749692i	$0.730202\pi$
$174$		0			0
$175$		−	508181.i		−	1.25436i
$176$	−75173.9	+	70025.1i	−0.182930	+	0.170401i
$177$		0			0
$178$	−462757.	+	150359.i	−1.09472	+	0.355696i
$179$	204857.	−	281961.i	0.477878	−	0.657743i	−0.500217	−	0.865900i	$-0.666746\pi$
$179$	204857.	−	281961.i	0.477878	−	0.657743i	0.978095	+	0.208157i	$0.0667465\pi$
$180$		0			0
$181$	209278.	−	644092.i	0.474818	−	1.46134i	−0.371384	−	0.928479i	$-0.621117\pi$
$181$	209278.	−	644092.i	0.474818	−	1.46134i	0.846202	−	0.532862i	$-0.178883\pi$
$182$	151296.	−	465641.i	0.338570	−	1.04201i
$183$		0			0
$184$	100824.	−	138772.i	0.219543	−	0.302175i
$185$	179800.	−	58420.5i	0.386242	−	0.125498i
$186$		0			0
$187$	−635978.	+	592419.i	−1.32996	+	1.23887i
$188$			204760.i			0.422523i
$189$		0			0
$190$	−212004.	−	154030.i	−0.426050	−	0.309544i
$191$	−10709.5	−	14740.3i	−0.0212415	−	0.0292364i	0.798264	−	0.602307i	$-0.205752\pi$
$191$	−10709.5	−	14740.3i	−0.0212415	−	0.0292364i	−0.819506	+	0.573071i	$0.805752\pi$
$192$		0			0
$193$	−405781.	−	131846.i	−0.784149	−	0.254785i	−0.110538	−	0.993872i	$-0.535258\pi$
$193$	−405781.	−	131846.i	−0.784149	−	0.254785i	−0.673611	+	0.739086i	$0.735258\pi$
$194$	−200559.	+	145714.i	−0.382593	+	0.277970i
$195$		0			0
$196$	−247009.	−	760217.i	−0.459275	−	1.41350i
$197$	−499495.			−0.916993			−0.458496	−	0.888696i	$-0.651612\pi$
$197$	−499495.			−0.916993			−0.458496	+	0.888696i	$0.651612\pi$
$198$		0			0
$199$	339800.			0.608262			0.304131	−	0.952630i	$-0.401634\pi$
$199$	339800.			0.608262			0.304131	+	0.952630i	$0.401634\pi$
$200$	38895.9	+	119709.i	0.0687590	+	0.211618i
$201$		0			0
$202$	95039.4	−	69050.2i	0.163880	−	0.119066i
$203$	505515.	+	164252.i	0.860981	+	0.279750i
$204$		0			0
$205$	342080.	+	470832.i	0.568516	+	0.782495i
$206$	−512529.	−	372374.i	−0.841492	−	0.611380i
$207$		0			0
$208$			121268.i			0.194352i
$209$	334012.	−	155533.i	0.528927	−	0.246296i
$210$		0			0
$211$	7381.14	−	2398.28i	0.0114135	−	0.00370846i	−0.303305	−	0.952894i	$-0.598090\pi$
$211$	7381.14	−	2398.28i	0.0114135	−	0.00370846i	0.314718	+	0.949185i	$0.398090\pi$
$212$	−287705.	+	395992.i	−0.439651	+	0.605128i
$213$		0			0
$214$	−217622.	+	669771.i	−0.324839	+	0.999752i
$215$	−160679.	+	494519.i	−0.237063	+	0.729603i
$216$		0			0
$217$	1.07736e6	−	1.48285e6i	1.55314	−	2.13771i
$218$	622483.	−	202257.i	0.887128	−	0.288245i
$219$		0			0
$220$	−449712.	−	87666.7i	−0.626438	−	0.122117i
$221$			1.02594e6i			1.41300i
$222$		0			0
$223$	830217.	+	603188.i	1.11797	+	0.812251i	0.983900	−	0.178721i	$-0.0571960\pi$
$223$	830217.	+	603188.i	1.11797	+	0.812251i	0.134068	+	0.990972i	$0.457196\pi$
$224$	155523.	+	214059.i	0.207098	+	0.285046i
$225$		0			0
$226$	−403735.	−	131181.i	−0.525805	−	0.170845i
$227$	−140880.	+	102355.i	−0.181462	+	0.131840i	−0.674808	−	0.737993i	$-0.735774\pi$
$227$	−140880.	+	102355.i	−0.181462	+	0.131840i	0.493346	+	0.869833i	$0.335774\pi$
$228$		0			0
$229$	7054.63	+	21711.9i	0.00888967	+	0.0273596i	0.955403	−	0.295305i	$-0.0954213\pi$
$229$	7054.63	+	21711.9i	0.00888967	+	0.0273596i	−0.946513	+	0.322665i	$0.895421\pi$
$230$	764993.			0.953537
$231$		0			0
$232$	−131653.			−0.160587
$233$	−171179.	−	526834.i	−0.206567	−	0.635747i	−0.999645	−	0.0266278i	$-0.991523\pi$
$233$	−171179.	−	526834.i	−0.206567	−	0.635747i	0.793079	−	0.609119i	$-0.208477\pi$
$234$		0			0
$235$	−738779.	+	536754.i	−0.872659	+	0.634024i
$236$	−290512.	−	94393.2i	−0.339535	−	0.110322i
$237$		0			0
$238$	1.31574e6	+	1.81096e6i	1.50566	+	2.07237i
$239$	993999.	+	722182.i	1.12562	+	0.817810i	0.985051	−	0.172262i	$-0.0551075\pi$
$239$	993999.	+	722182.i	1.12562	+	0.817810i	0.140567	+	0.990071i	$0.455107\pi$
$240$		0			0
$241$		−	195450.i		−	0.216767i	−0.994109	−	0.108383i	$-0.965433\pi$
$241$		−	195450.i		−	0.216767i	0.994109	−	0.108383i	$-0.0345674\pi$
$242$	414618.	−	493042.i	0.455103	−	0.541185i
$243$		0			0
$244$	198355.	−	64449.6i	0.213289	−	0.0693019i
$245$	2.09538e6	−	2.88404e6i	2.23021	−	3.06963i
$246$		0			0
$247$	134396.	−	413627.i	0.140166	−	0.431387i
$248$	−140290.	+	431768.i	−0.144843	+	0.445781i
$249$		0			0
$250$	194323.	−	267463.i	0.196642	−	0.270654i
$251$	−417217.	+	135562.i	−0.418001	+	0.135817i	−0.510464	−	0.859899i	$-0.670526\pi$
$251$	−417217.	+	135562.i	−0.418001	+	0.135817i	0.0924625	+	0.995716i	$0.470526\pi$
$252$		0			0
$253$	−521963.	+	940452.i	−0.512671	+	0.923709i
$254$			1.29859e6i			1.26296i
$255$		0			0
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	116713.	+	160642.i	0.110227	+	0.151715i	0.860566	−	0.509338i	$-0.170110\pi$
$257$	116713.	+	160642.i	0.110227	+	0.151715i	−0.750339	+	0.661053i	$0.770110\pi$
$258$		0			0
$259$	651079.	+	211548.i	0.603093	+	0.195957i
$260$	−437540.	+	317891.i	−0.401406	+	0.291639i
$261$		0			0
$262$	319392.	+	982987.i	0.287455	+	0.884697i
$263$	1.23851e6			1.10411			0.552053	−	0.833809i	$-0.313844\pi$
$263$	1.23851e6			1.10411			0.552053	+	0.833809i	$0.313844\pi$
$264$		0			0
$265$	−2.18294e6			−1.90953
$266$	−293234.	−	902481.i	−0.254103	−	0.782049i
$267$		0			0
$268$	−14947.6	+	10860.0i	−0.0127126	+	0.00923622i
$269$	−137990.	−	44835.6i	−0.116270	−	0.0377783i	0.250304	−	0.968167i	$-0.419469\pi$
$269$	−137990.	−	44835.6i	−0.116270	−	0.0377783i	−0.366574	+	0.930389i	$0.619469\pi$
$270$		0			0
$271$	708537.	+	975218.i	0.586056	+	0.806638i	0.994343	−	0.106216i	$-0.0338736\pi$
$271$	708537.	+	975218.i	0.586056	+	0.806638i	−0.408287	+	0.912854i	$0.633874\pi$
$272$	−448552.	−	325892.i	−0.367613	−	0.267086i
$273$		0			0
$274$			763337.i			0.614242i
$275$	−333173.	−	715498.i	−0.265667	−	0.570528i
$276$		0			0
$277$	425777.	−	138343.i	0.333413	−	0.108333i	−0.137526	−	0.990498i	$-0.543915\pi$
$277$	425777.	−	138343.i	0.333413	−	0.108333i	0.470939	+	0.882166i	$0.343915\pi$
$278$	−552014.	+	759783.i	−0.428389	+	0.589627i
$279$		0			0
$280$	−364646.	+	1.12226e6i	−0.277956	+	0.855461i
$281$	−38265.1	+	117768.i	−0.0289093	+	0.0889737i	−0.964470	−	0.264192i	$-0.914895\pi$
$281$	−38265.1	+	117768.i	−0.0289093	+	0.0889737i	0.935561	+	0.353166i	$0.114895\pi$
$282$		0			0
$283$	−1.17764e6	+	1.62088e6i	−0.874068	+	1.20305i	0.103960	+	0.994581i	$0.466848\pi$
$283$	−1.17764e6	+	1.62088e6i	−0.874068	+	1.20305i	−0.978029	+	0.208470i	$0.933152\pi$
$284$	−115105.	+	37399.8i	−0.0846833	+	0.0275153i
$285$		0			0
$286$	−92264.4	−	754795.i	−0.0666990	−	0.545650i
$287$			2.10743e6i			1.51025i
$288$		0			0
$289$	−2.64610e6	−	1.92251e6i	−1.86364	−	1.35401i
$290$	−345113.	−	475008.i	−0.240972	−	0.331670i
$291$		0			0
$292$	805319.	+	261664.i	0.552727	+	0.179592i
$293$	1.88308e6	−	1.36814e6i	1.28145	−	0.931026i	0.281852	−	0.959458i	$-0.409051\pi$
$293$	1.88308e6	−	1.36814e6i	1.28145	−	0.931026i	0.999596	+	0.0284318i	$0.00905134\pi$
$294$		0			0
$295$	−420972.	−	1.29562e6i	−0.281642	−	0.866806i
$296$	−169563.			−0.112487
$297$		0			0
$298$	472754.			0.308386
$299$	392334.	+	1.20748e6i	0.253792	+	0.781091i
$300$		0			0
$301$	−1.52328e6	+	1.10673e6i	−0.969087	+	0.704083i
$302$	−471945.	−	153344.i	−0.297765	−	0.0967497i
$303$		0			0
$304$	138151.	+	190148.i	0.0857373	+	0.118007i
$305$	752502.	+	546724.i	0.463189	+	0.336526i
$306$		0			0
$307$		−	923870.i		−	0.559455i	−0.960079	−	0.279727i	$-0.909756\pi$
$307$		−	923870.i		−	0.559455i	0.960079	−	0.279727i	$-0.0902441\pi$
$308$	−1.13086e6	−	1.21401e6i	−0.679257	−	0.729201i
$309$		0			0
$310$	−1.92558e6	+	625660.i	−1.13804	+	0.369772i
$311$	−340519.	+	468684.i	−0.199636	+	0.274776i	−0.897084	−	0.441860i	$-0.854319\pi$
$311$	−340519.	+	468684.i	−0.199636	+	0.274776i	0.697448	+	0.716636i	$0.254319\pi$
$312$		0			0
$313$	−383934.	+	1.18163e6i	−0.221511	+	0.681742i	0.777116	+	0.629358i	$0.216682\pi$
$313$	−383934.	+	1.18163e6i	−0.221511	+	0.681742i	−0.998627	+	0.0523839i	$0.983318\pi$
$314$	−282077.	+	868144.i	−0.161452	+	0.496899i
$315$		0			0
$316$	−615172.	+	846712.i	−0.346561	+	0.477000i
$317$	967449.	−	314343.i	0.540729	−	0.175694i	−0.0259028	−	0.999664i	$-0.508246\pi$
$317$	967449.	−	314343.i	0.540729	−	0.175694i	0.566632	+	0.823971i	$0.308246\pi$
$318$		0			0
$319$	819430.	−	100165.i	0.450853	−	0.0551113i
$320$		−	292275.i		−	0.159557i
$321$		0			0
$322$	2.24109e6	+	1.62825e6i	1.20454	+	0.875147i
$323$	1.16877e6	+	1.60867e6i	0.623337	+	0.857949i
$324$		0			0
$325$	−886046.	−	287894.i	−0.465316	−	0.151190i
$326$	2.06225e6	−	1.49831e6i	1.07473	−	0.780834i
$327$		0			0
$328$	−161302.	−	496435.i	−0.0827855	−	0.254788i
$329$	−3.30675e6			−1.68427
$330$		0			0
$331$	2.58246e6			1.29558			0.647788	−	0.761820i	$-0.275694\pi$
$331$	2.58246e6			1.29558			0.647788	+	0.761820i	$0.275694\pi$
$332$	−203127.	−	625162.i	−0.101140	−	0.311277i
$333$		0			0
$334$	432347.	−	314119.i	0.212064	−	0.154073i
$335$	−78366.6	−	25462.9i	−0.0381522	−	0.0123964i
$336$		0			0
$337$	−62148.1	−	85539.5i	−0.0298094	−	0.0410291i	0.793852	−	0.608111i	$-0.208072\pi$
$337$	−62148.1	−	85539.5i	−0.0298094	−	0.0410291i	−0.823662	+	0.567082i	$0.808072\pi$
$338$	475368.	+	345375.i	0.226328	+	0.164437i
$339$		0			0
$340$		−	2.47268e6i		−	1.16003i
$341$	544686.	−	2.79413e6i	0.253665	−	1.30125i
$342$		0			0
$343$	8.14683e6	−	2.64707e6i	3.73898	−	1.21487i
$344$	274122.	−	377296.i	0.124896	−	0.171904i
$345$		0			0
$346$	−92197.0	+	283753.i	−0.0414025	+	0.127424i
$347$	311289.	−	958049.i	0.138784	−	0.427134i	−0.857375	−	0.514692i	$-0.827906\pi$
$347$	311289.	−	958049.i	0.138784	−	0.427134i	0.996159	+	0.0875580i	$0.0279063\pi$
$348$		0			0
$349$	2.29525e6	−	3.15914e6i	1.00871	−	1.38837i	0.0888841	−	0.996042i	$-0.471670\pi$
$349$	2.29525e6	−	3.15914e6i	1.00871	−	1.38837i	0.919825	−	0.392328i	$-0.128330\pi$
$350$	−1.93324e6	+	628147.i	−0.843558	+	0.274089i
$351$		0			0
$352$	359312.	+	199423.i	0.154566	+	0.0857863i
$353$			2.01468e6i			0.860535i	0.902701	+	0.430268i	$0.141581\pi$
$353$			2.01468e6i			0.860535i	−0.902701	+	0.430268i	$0.858419\pi$
$354$		0			0
$355$	−436674.	−	317262.i	−0.183902	−	0.133613i
$356$	1.14400e6	+	1.57458e6i	0.478410	+	0.658475i
$357$		0			0
$358$	−1.32586e6	−	430798.i	−0.546751	−	0.177650i
$359$	1.85907e6	−	1.35069e6i	0.761305	−	0.553120i	−0.138005	−	0.990431i	$-0.544069\pi$
$359$	1.85907e6	−	1.35069e6i	0.761305	−	0.553120i	0.899310	+	0.437311i	$0.144069\pi$
$360$		0			0
$361$	504678.	+	1.55324e6i	0.203820	+	0.627293i
$362$	−2.70895e6			−1.08650
$363$		0			0
$364$	−1.95841e6			−0.774731
$365$	1.16696e6	+	3.59154e6i	0.458484	+	1.41107i
$366$		0			0
$367$	−546660.	+	397172.i	−0.211862	+	0.153927i	−0.688656	−	0.725089i	$-0.741799\pi$
$367$	−546660.	+	397172.i	−0.211862	+	0.153927i	0.476794	+	0.879015i	$0.341799\pi$
$368$	−652547.	−	212025.i	−0.251184	−	0.0816146i
$369$		0			0
$370$	−444490.	−	611787.i	−0.168794	−	0.232325i
$371$	−6.39504e6	−	4.64627e6i	−2.41218	−	1.75255i
$372$		0			0
$373$		−	4.87197e6i		−	1.81314i	−0.422051	−	0.906572i	$-0.638690\pi$
$373$		−	4.87197e6i		−	1.81314i	0.422051	−	0.906572i	$-0.361310\pi$
$374$	3.03981e6	+	1.68714e6i	1.12374	+	0.623693i
$375$		0			0
$376$	778952.	−	253097.i	0.284146	−	0.0923246i
$377$	572766.	−	788345.i	0.207551	−	0.285669i
$378$		0			0
$379$	−1.15000e6	+	3.53933e6i	−0.411243	+	1.26568i	0.504325	+	0.863514i	$0.331741\pi$
$379$	−1.15000e6	+	3.53933e6i	−0.411243	+	1.26568i	−0.915568	+	0.402163i	$0.868259\pi$
$380$	−323914.	+	996904.i	−0.115072	+	0.354156i
$381$		0			0
$382$	−42837.9	+	58961.4i	−0.0150200	+	0.0206733i
$383$	−2.86626e6	+	931306.i	−0.998434	+	0.324411i	−0.762240	−	0.647295i	$-0.775900\pi$
$383$	−2.86626e6	+	931306.i	−0.998434	+	0.324411i	−0.236194	+	0.971706i	$0.575900\pi$
$384$		0			0
$385$	1.41577e6	−	7.26259e6i	0.486788	−	2.49712i
$386$			1.70665e6i			0.583012i
$387$		0			0
$388$	802235.	+	582858.i	0.270534	+	0.196555i
$389$	692239.	+	952785.i	0.231943	+	0.319243i	0.909085	−	0.416610i	$-0.136782\pi$
$389$	692239.	+	952785.i	0.231943	+	0.319243i	−0.677142	+	0.735852i	$0.736782\pi$
$390$		0			0
$391$	−5.52061e6	−	1.79375e6i	−1.82619	−	0.593364i
$392$	−2.58672e6	+	1.87936e6i	−0.850224	+	0.617724i
$393$		0			0
$394$	617410.	+	1.90019e6i	0.200370	+	0.616676i
$395$	−4.66756e6			−1.50521
$396$		0			0
$397$	−5.65578e6			−1.80101			−0.900505	−	0.434846i	$-0.856803\pi$
$397$	−5.65578e6			−1.80101			−0.900505	+	0.434846i	$0.856803\pi$
$398$	−420016.	−	1.29268e6i	−0.132910	−	0.409056i
$399$		0			0
$400$	407324.	−	295938.i	0.127289	−	0.0924806i
$401$	−5.11372e6	−	1.66155e6i	−1.58809	−	0.516003i	−0.623969	−	0.781449i	$-0.714481\pi$
$401$	−5.11372e6	−	1.66155e6i	−1.58809	−	0.516003i	−0.964126	+	0.265446i	$0.914481\pi$
$402$		0			0
$403$	−1.97511e6	−	2.71850e6i	−0.605798	−	0.833810i
$404$	−380158.	−	276201.i	−0.115880	−	0.0841921i
$405$		0			0
$406$		−	2.12612e6i		−	0.640136i
$407$	1.05539e6	−	129008.i	0.315810	−	0.0386039i
$408$		0			0
$409$	−2.47293e6	+	803503.i	−0.730976	+	0.237508i	−0.650775	−	0.759270i	$-0.725556\pi$
$409$	−2.47293e6	+	803503.i	−0.730976	+	0.237508i	−0.0802004	+	0.996779i	$0.525556\pi$
$410$	1.36832e6	−	1.88333e6i	0.402001	−	0.553308i
$411$		0			0
$412$	−783074.	+	2.41005e6i	−0.227279	+	0.699494i
$413$	1.52439e6	−	4.69160e6i	0.439767	−	1.35346i
$414$		0			0
$415$	1.72312e6	−	2.37168e6i	0.491130	−	0.675983i
$416$	461333.	−	149896.i	0.130702	−	0.0424675i
$417$		0			0
$418$	−1.00454e6	−	1.07841e6i	−0.281208	−	0.301885i
$419$			897462.i			0.249736i	0.992173	+	0.124868i	$0.0398507\pi$
$419$			897462.i			0.249736i	−0.992173	+	0.124868i	$0.960149\pi$
$420$		0			0
$421$	2.67094e6	+	1.94055e6i	0.734444	+	0.533605i	0.890966	−	0.454070i	$-0.150028\pi$
$421$	2.67094e6	+	1.94055e6i	0.734444	+	0.533605i	−0.156522	+	0.987674i	$0.550028\pi$
$422$	−18247.2	−	25115.1i	−0.00498787	−	0.00686521i
$423$		0			0
$424$	1.86207e6	+	605023.i	0.503015	+	0.163439i
$425$	3.44600e6	−	2.50366e6i	0.925428	−	0.672363i
$426$		0			0
$427$	1.04082e6	+	3.20332e6i	0.276253	+	0.850219i
$428$	2.81696e6			0.743311
$429$		0			0
$430$	2.07987e6			0.542457
$431$	1.16933e6	+	3.59883e6i	0.303211	+	0.933187i	0.980339	+	0.197322i	$0.0632244\pi$
$431$	1.16933e6	+	3.59883e6i	0.303211	+	0.933187i	−0.677128	+	0.735865i	$0.736776\pi$
$432$		0			0
$433$	4.20063e6	−	3.05194e6i	1.07670	−	0.782269i	0.0995957	−	0.995028i	$-0.468245\pi$
$433$	4.20063e6	−	3.05194e6i	1.07670	−	0.782269i	0.977105	+	0.212759i	$0.0682451\pi$
$434$	−6.97280e6	−	2.26560e6i	−1.77698	−	0.577376i
$435$		0			0
$436$	−1.53886e6	−	2.11806e6i	−0.387689	−	0.533609i
$437$	1.99076e6	+	1.44637e6i	0.498671	+	0.362306i
$438$		0			0
$439$			5.12357e6i			1.26885i	0.772983	+	0.634427i	$0.218764\pi$
$439$			5.12357e6i			1.26885i	−0.772983	+	0.634427i	$0.781236\pi$
$440$	222371.	+	1.81917e6i	0.0547579	+	0.447962i
$441$		0			0
$442$	3.90292e6	−	1.26813e6i	0.950241	−	0.308752i
$443$	−3.07073e6	+	4.22650e6i	−0.743418	+	1.02323i	0.254997	+	0.966942i	$0.417925\pi$
$443$	−3.07073e6	+	4.22650e6i	−0.743418	+	1.02323i	−0.998415	+	0.0562848i	$0.982075\pi$
$444$		0			0
$445$	−2.68226e6	+	8.25515e6i	−0.642098	+	1.97617i
$446$	1.26846e6	−	3.90391e6i	0.301953	−	0.929315i
$447$		0			0
$448$	622093.	−	856238.i	0.146440	−	0.201558i
$449$	331272.	−	107637.i	0.0775476	−	0.0251968i	−0.269986	−	0.962864i	$-0.587019\pi$
$449$	331272.	−	107637.i	0.0775476	−	0.0251968i	0.347534	+	0.937667i	$0.387019\pi$
$450$		0			0
$451$	1.38167e6	+	2.96717e6i	0.319862	+	0.686913i
$452$			1.69805e6i			0.390934i
$453$		0			0
$454$	563520.	+	409422.i	0.128313	+	0.0932247i
$455$	−5.13376e6	−	7.06601e6i	−1.16254	−	1.60010i
$456$		0			0
$457$	−800964.	−	260249.i	−0.179400	−	0.0582906i	0.217939	−	0.975962i	$-0.430066\pi$
$457$	−800964.	−	260249.i	−0.179400	−	0.0582906i	−0.397340	+	0.917672i	$0.630066\pi$
$458$	73877.0	−	53674.8i	0.0164568	−	0.0119566i
$459$		0			0
$460$	−945583.	−	2.91021e6i	−0.208356	−	0.641253i
$461$	6.10022e6			1.33688			0.668441	−	0.743765i	$-0.266962\pi$
$461$	6.10022e6			1.33688			0.668441	+	0.743765i	$0.266962\pi$
$462$		0			0
$463$	4.33845e6			0.940550			0.470275	−	0.882520i	$-0.344155\pi$
$463$	4.33845e6			0.940550			0.470275	+	0.882520i	$0.344155\pi$
$464$	162732.	+	500838.i	0.0350896	+	0.107995i
$465$		0			0
$466$	−1.79261e6	+	1.30241e6i	−0.382402	+	0.277832i
$467$	636395.	+	206777.i	0.135031	+	0.0438743i	0.375753	−	0.926720i	$-0.377384\pi$
$467$	636395.	+	206777.i	0.135031	+	0.0438743i	−0.240722	+	0.970594i	$0.577384\pi$
$468$		0			0
$469$	−175383.	−	241394.i	−0.0368176	−	0.0506751i
$470$	2.95511e6	+	2.14702e6i	0.617063	+	0.448323i
$471$		0			0
$472$			1.22185e6i			0.252443i
$473$	−1.41912e6	+	2.55691e6i	−0.291653	+	0.525488i
$474$		0			0
$475$	−1.71729e6	+	557981.i	−0.349228	+	0.113471i
$476$	5.26297e6	−	7.24385e6i	1.06467	−	1.46539i
$477$		0			0
$478$	1.51870e6	−	4.67406e6i	0.304019	−	0.935675i
$479$	−1.90484e6	+	5.86249e6i	−0.379332	+	1.16746i	0.561178	+	0.827695i	$0.310348\pi$
$479$	−1.90484e6	+	5.86249e6i	−0.379332	+	1.16746i	−0.940509	+	0.339768i	$0.889652\pi$
$480$		0			0
$481$	737696.	−	1.01535e6i	0.145383	−	0.200103i
$482$	−743536.	+	241589.i	−0.145775	+	0.0473653i
$483$		0			0
$484$	−2.38814e6	−	967866.i	−0.463390	−	0.187803i
$485$			4.42238e6i			0.853693i
$486$		0			0
$487$	1.56467e6	+	1.13680e6i	0.298951	+	0.217200i	0.727141	−	0.686488i	$-0.240849\pi$
$487$	1.56467e6	+	1.13680e6i	0.298951	+	0.217200i	−0.428190	+	0.903689i	$0.640849\pi$
$488$	−490361.	−	674925.i	−0.0932109	−	0.128294i
$489$		0			0
$490$	−1.35616e7	−	4.40642e6i	−2.55164	−	0.829078i
$491$	−6.08545e6	+	4.42134e6i	−1.13917	+	0.827657i	−0.987004	−	0.160698i	$-0.948626\pi$
$491$	−6.08545e6	+	4.42134e6i	−1.13917	+	0.827657i	−0.152168	+	0.988355i	$0.548626\pi$
$492$		0			0
$493$	1.37673e6	+	4.23714e6i	0.255112	+	0.785154i
$494$	−1.73965e6			−0.320734
$495$		0			0
$496$	1.81595e6			0.331436
$497$	−603985.	−	1.85888e6i	−0.109682	−	0.337567i
$498$		0			0
$499$	−2.08052e6	+	1.51158e6i	−0.374041	+	0.271757i	−0.758885	−	0.651225i	$-0.774255\pi$
$499$	−2.08052e6	+	1.51158e6i	−0.374041	+	0.271757i	0.384843	+	0.922982i	$0.374255\pi$
$500$	−1.25769e6	−	408648.i	−0.224982	−	0.0731011i
$501$		0			0
$502$	1.03142e6	+	1.41962e6i	0.182673	+	0.251428i
$503$	−5.81131e6	−	4.22216e6i	−1.02413	−	0.744072i	−0.0570024	−	0.998374i	$-0.518154\pi$
$503$	−5.81131e6	−	4.22216e6i	−1.02413	−	0.744072i	−0.967125	+	0.254302i	$0.918154\pi$
$504$		0			0
$505$		−	2.09565e6i		−	0.365670i
$506$	4.22287e6	+	823204.i	0.733216	+	0.142933i
$507$		0			0
$508$	4.94014e6	−	1.60515e6i	0.849336	−	0.275966i
$509$	−3.26831e6	+	4.49844e6i	−0.559151	+	0.769605i	−0.991218	−	0.132236i	$-0.957784\pi$
$509$	−3.26831e6	+	4.49844e6i	−0.559151	+	0.769605i	0.432067	+	0.901841i	$0.357784\pi$
$510$		0			0
$511$	−4.22572e6	+	1.30054e7i	−0.715894	+	2.20329i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	466854.	−	642569.i	0.0779423	−	0.107278i
$515$	−1.07483e7	+	3.49233e6i	−1.78575	+	0.580226i
$516$		0			0
$517$	−4.65576e6	+	2.16797e6i	−0.766063	+	0.356719i
$518$		−	2.73834e6i		−	0.448397i
$519$		0			0
$520$	1.75016e6	+	1.27157e6i	0.283837	+	0.206220i
$521$	45725.3	+	62935.5i	0.00738010	+	0.0101578i	0.812691	−	0.582695i	$-0.198002\pi$
$521$	45725.3	+	62935.5i	0.00738010	+	0.0101578i	−0.805311	+	0.592853i	$0.798002\pi$
$522$		0			0
$523$	1.03220e6	+	335383.i	0.165010	+	0.0536150i	0.390357	−	0.920664i	$-0.372352\pi$
$523$	1.03220e6	+	335383.i	0.165010	+	0.0536150i	−0.225347	+	0.974279i	$0.572352\pi$
$524$	3.34471e6	−	2.43008e6i	0.532146	−	0.386627i
$525$		0			0
$526$	−1.53089e6	−	4.71158e6i	−0.241256	−	0.742510i
$527$	1.53631e7			2.40964
$528$		0			0
$529$	−747063.			−0.116069
$530$	2.69826e6	+	8.30439e6i	0.417248	+	1.28416i
$531$		0			0
$532$	−3.07078e6	+	2.23106e6i	−0.470403	+	0.341768i
$533$	3.67444e6	+	1.19390e6i	0.560238	+	0.182032i
$534$		0			0
$535$	7.38433e6	+	1.01637e7i	1.11539	+	1.53520i
$536$	59790.2	+	43440.1i	0.00898914	+	0.00653099i
$537$		0			0
$538$			580364.i			0.0864459i
$539$	1.46703e7	−	1.36655e7i	2.17504	−	2.02606i
$540$		0			0
$541$	8.01701e6	−	2.60488e6i	1.17766	−	0.382644i	0.346162	−	0.938175i	$-0.387485\pi$
$541$	8.01701e6	−	2.60488e6i	1.17766	−	0.382644i	0.831496	+	0.555530i	$0.187485\pi$
$542$	2.83415e6	−	3.90087e6i	0.414405	−	0.570379i
$543$		0			0
$544$	−685327.	+	2.10922e6i	−0.0992888	+	0.305580i
$545$	3.60808e6	−	1.11045e7i	0.520337	−	1.60143i
$546$		0			0
$547$	5.75806e6	−	7.92529e6i	0.822826	−	1.13252i	−0.166390	−	0.986060i	$-0.553211\pi$
$547$	5.75806e6	−	7.92529e6i	0.822826	−	1.13252i	0.989216	−	0.146463i	$-0.0467890\pi$
$548$	2.90390e6	−	943536.i	0.413077	−	0.134217i
$549$		0			0
$550$	−2.31009e6	+	2.15187e6i	−0.325629	+	0.303326i
$551$		−	1.88863e6i		−	0.265013i
$552$		0			0
$553$	−1.36739e7	−	9.93467e6i	−1.90143	−	1.38147i
$554$	−1.05258e6	−	1.44875e6i	−0.145707	−	0.200549i
$555$		0			0
$556$	3.57271e6	+	1.16084e6i	0.490130	+	0.159253i
$557$	−1.49145e6	+	1.08360e6i	−0.203690	+	0.147990i	−0.684954	−	0.728586i	$-0.740178\pi$
$557$	−1.49145e6	+	1.08360e6i	−0.203690	+	0.147990i	0.481264	+	0.876576i	$0.340178\pi$
$558$		0			0
$559$	1.06668e6	+	3.28291e6i	0.144379	+	0.444354i
$560$	4.72007e6			0.636032
$561$		0			0
$562$	495314.			0.0661516
$563$	1.90652e6	+	5.86765e6i	0.253495	+	0.780178i	0.994122	+	0.108262i	$0.0345284\pi$
$563$	1.90652e6	+	5.86765e6i	0.253495	+	0.780178i	−0.740627	+	0.671916i	$0.765472\pi$
$564$		0			0
$565$	−6.12660e6	+	4.45124e6i	−0.807418	+	0.586624i
$566$	7.62183e6	+	2.47648e6i	1.00004	+	0.324933i
$567$		0			0
$568$	284555.	+	391656.i	0.0370080	+	0.0509371i
$569$	3.81349e6	+	2.77067e6i	0.493790	+	0.358760i	0.806640	−	0.591043i	$-0.201284\pi$
$569$	3.81349e6	+	2.77067e6i	0.493790	+	0.358760i	−0.312850	+	0.949803i	$0.601284\pi$
$570$		0			0
$571$			4.53393e6i			0.581949i	0.956731	+	0.290974i	$0.0939795\pi$
$571$			4.53393e6i			0.581949i	−0.956731	+	0.290974i	$0.906021\pi$
$572$	−2.75737e6	+	1.28397e6i	−0.352374	+	0.164084i
$573$		0			0
$574$	8.01714e6	−	2.60493e6i	1.01564	−	0.330001i
$575$	3.09832e6	−	4.26447e6i	0.390802	−	0.537892i
$576$		0			0
$577$	−3.58123e6	+	1.10219e7i	−0.447809	+	1.37821i	0.431564	+	0.902082i	$0.357962\pi$
$577$	−3.58123e6	+	1.10219e7i	−0.447809	+	1.37821i	−0.879374	+	0.476133i	$0.842038\pi$
$578$	−4.04289e6	+	1.24427e7i	−0.503352	+	1.54916i
$579$		0			0
$580$	−1.38045e6	+	1.90003e6i	−0.170393	+	0.234526i
$581$	1.00960e7	−	3.28039e6i	1.24082	−	0.403167i
$582$		0			0
$583$	−1.20501e7	−	2.34905e6i	−1.46832	−	0.286233i
$584$		−	3.38705e6i		−	0.410951i
$585$		0			0
$586$	−7.53234e6	−	5.47256e6i	−0.906120	−	0.658335i
$587$	8.73832e6	+	1.20273e7i	1.04673	+	1.44069i	0.891613	+	0.452797i	$0.149574\pi$
$587$	8.73832e6	+	1.20273e7i	1.04673	+	1.44069i	0.155112	+	0.987897i	$0.450426\pi$
$588$		0			0
$589$	−6.19392e6	−	2.01253e6i	−0.735660	−	0.239030i
$590$	−4.40847e6	+	3.20294e6i	−0.521384	+	0.378808i
$591$		0			0
$592$	209591.	+	645055.i	0.0245793	+	0.0756472i
$593$	−5.79067e6			−0.676227			−0.338113	−	0.941105i	$-0.609789\pi$
$593$	−5.79067e6			−0.676227			−0.338113	+	0.941105i	$0.609789\pi$
$594$		0			0
$595$	3.99323e7			4.62415
$596$	−584357.	−	1.79846e6i	−0.0673849	−	0.207389i
$597$		0			0
$598$	4.10857e6	−	2.98505e6i	0.469827	−	0.341349i
$599$	−2.97611e6	−	966996.i	−0.338908	−	0.110118i	0.134618	−	0.990898i	$-0.457019\pi$
$599$	−2.97611e6	−	966996.i	−0.338908	−	0.110118i	−0.473526	+	0.880780i	$0.657019\pi$
$600$		0			0
$601$	6.77072e6	+	9.31910e6i	0.764626	+	1.05242i	0.996815	+	0.0797466i	$0.0254111\pi$
$601$	6.77072e6	+	9.31910e6i	0.764626	+	1.05242i	−0.232189	+	0.972671i	$0.574589\pi$
$602$	6.09311e6	+	4.42690e6i	0.685248	+	0.497862i
$603$		0			0
$604$			1.98493e6i			0.221387i
$605$	−2.76815e6	−	1.11536e7i	−0.307469	−	1.23888i
$606$		0			0
$607$	−1.26501e7	+	4.11027e6i	−1.39355	+	0.452792i	−0.907099	−	0.420916i	$-0.861709\pi$
$607$	−1.26501e7	+	4.11027e6i	−1.39355	+	0.452792i	−0.486450	+	0.873708i	$0.661709\pi$
$608$	552604.	−	760594.i	0.0606254	−	0.0834437i
$609$		0			0
$610$	1.14972e6	−	3.53847e6i	0.125103	−	0.385027i
$611$	−1.87333e6	+	5.76552e6i	−0.203007	+	0.624792i
$612$		0			0
$613$	−910575.	+	1.25330e6i	−0.0978734	+	0.134711i	−0.855145	−	0.518389i	$-0.826532\pi$
$613$	−910575.	+	1.25330e6i	−0.0978734	+	0.134711i	0.757272	+	0.653100i	$0.226532\pi$
$614$	−3.51461e6	+	1.14197e6i	−0.376233	+	0.122245i
$615$		0			0
$616$	−3.22056e6	+	5.80267e6i	−0.341963	+	0.616135i
$617$		−	6.33722e6i		−	0.670172i	−0.942188	−	0.335086i	$-0.891235\pi$
$617$		−	6.33722e6i		−	0.670172i	0.942188	−	0.335086i	$-0.108765\pi$
$618$		0			0
$619$	−8.61010e6	−	6.25560e6i	−0.903195	−	0.656210i	0.0360894	−	0.999349i	$-0.488510\pi$
$619$	−8.61010e6	−	6.25560e6i	−0.903195	−	0.656210i	−0.939285	+	0.343139i	$0.888510\pi$
$620$	4.76031e6	+	6.55200e6i	0.497343	+	0.684533i
$621$		0			0
$622$	2.20388e6	+	716085.i	0.228409	+	0.0742145i
$623$	−2.54285e7	+	1.84749e7i	−2.62483	+	1.90705i
$624$		0			0
$625$	−3.72169e6	−	1.14542e7i	−0.381101	−	1.17291i
$626$	4.96975e6			0.506872
$627$		0			0
$628$	3.65128e6			0.369442
$629$	1.77316e6	+	5.45723e6i	0.178699	+	0.549978i
$630$		0			0
$631$	5.04906e6	−	3.66836e6i	0.504821	−	0.366774i	−0.306035	−	0.952020i	$-0.599002\pi$
$631$	5.04906e6	−	3.66836e6i	0.504821	−	0.366774i	0.810855	+	0.585247i	$0.199002\pi$
$632$	3.98148e6	+	1.29366e6i	0.396508	+	0.128833i
$633$		0			0
$634$	−2.39167e6	−	3.29185e6i	−0.236307	−	0.325249i
$635$	1.87414e7	+	1.36164e7i	1.84446	+	1.34008i
$636$		0			0
$637$		−	2.36657e7i		−	2.31084i
$638$	−1.39392e6	−	2.99349e6i	−0.135577	−	0.291156i
$639$		0			0
$640$	−1.11188e6	+	361272.i	−0.107302	+	0.0348646i
$641$	4.12248e6	−	5.67411e6i	0.396291	−	0.545447i	−0.563518	−	0.826104i	$-0.690552\pi$
$641$	4.12248e6	−	5.67411e6i	0.396291	−	0.545447i	0.959808	+	0.280657i	$0.0905523\pi$
$642$		0			0
$643$	−1.29187e6	+	3.97595e6i	−0.123222	+	0.379240i	−0.993573	−	0.113193i	$-0.963892\pi$
$643$	−1.29187e6	+	3.97595e6i	−0.123222	+	0.379240i	0.870351	+	0.492433i	$0.163892\pi$
$644$	3.42408e6	−	1.05382e7i	0.325334	−	1.00128i
$645$		0			0
$646$	4.67508e6	−	6.43469e6i	0.440766	−	0.606662i
$647$	−1.10906e7	+	3.60354e6i	−1.04158	+	0.338430i	−0.779359	−	0.626578i	$-0.784455\pi$
$647$	−1.10906e7	+	3.60354e6i	−1.04158	+	0.338430i	−0.262221	+	0.965008i	$0.584455\pi$
$648$		0			0
$649$	−929619.	−	7.60500e6i	−0.0866349	−	0.708741i
$650$			3.72658e6i			0.345960i
$651$		0			0
$652$	−8.24901e6	−	5.99326e6i	−0.759946	−	0.552133i
$653$	−3.14993e6	−	4.33551e6i	−0.289080	−	0.397885i	0.639635	−	0.768679i	$-0.279086\pi$
$653$	−3.14993e6	−	4.33551e6i	−0.289080	−	0.397885i	−0.928715	+	0.370794i	$0.879086\pi$
$654$		0			0
$655$	1.75356e7	+	5.69765e6i	1.59704	+	0.518911i
$656$	−1.68917e6	+	1.22726e6i	−0.153255	+	0.111346i
$657$		0			0
$658$	4.08737e6	+	1.25796e7i	0.368026	+	1.13267i
$659$	8.42117e6			0.755368			0.377684	−	0.925934i	$-0.376720\pi$
$659$	8.42117e6			0.755368			0.377684	+	0.925934i	$0.376720\pi$
$660$		0			0
$661$	969922.			0.0863442			0.0431721	−	0.999068i	$-0.486254\pi$
$661$	969922.			0.0863442			0.0431721	+	0.999068i	$0.486254\pi$
$662$	−3.19209e6	−	9.82425e6i	−0.283094	−	0.871273i
$663$		0			0
$664$	−2.12718e6	+	1.54548e6i	−0.187233	+	0.136033i
$665$	−1.60994e7	−	5.23102e6i	−1.41174	−	0.458704i
$666$		0			0
$667$	3.24067e6	+	4.46040e6i	0.282046	+	0.388203i
$668$	−1.72939e6	−	1.25647e6i	−0.149952	−	0.108946i
$669$		0			0
$670$			329598.i			0.0283660i
$671$	3.56559e6	+	3.82776e6i	0.305721	+	0.328200i
$672$		0			0
$673$	2.31724e6	−	752916.i	0.197212	−	0.0640779i	−0.208746	−	0.977970i	$-0.566938\pi$
$673$	2.31724e6	−	752916.i	0.197212	−	0.0640779i	0.405957	+	0.913892i	$0.366938\pi$
$674$	−248592.	+	342158.i	−0.0210784	+	0.0290119i
$675$		0			0
$676$	726297.	−	2.23531e6i	0.0611290	−	0.188136i
$677$	4.55021e6	−	1.40041e7i	0.381557	−	1.17431i	−0.557390	−	0.830251i	$-0.688197\pi$
$677$	4.55021e6	−	1.40041e7i	0.381557	−	1.17431i	0.938947	−	0.344061i	$-0.111803\pi$
$678$		0			0
$679$	−9.41281e6	+	1.29556e7i	−0.783510	+	1.07841i
$680$	−9.40662e6	+	3.05640e6i	−0.780120	+	0.253476i
$681$		0			0
$682$	−1.13028e7	+	1.38163e6i	−0.930517	+	0.113744i
$683$		−	1.09957e7i		−	0.901925i	−0.892543	−	0.450962i	$-0.851081\pi$
$683$		−	1.09957e7i		−	0.901925i	0.892543	−	0.450962i	$-0.148919\pi$
$684$		0			0
$685$	1.10166e7	+	8.00400e6i	0.897056	+	0.651749i
$686$	−2.01401e7	−	2.77204e7i	−1.63400	−	2.24900i
$687$		0			0
$688$	−1.77415e6	−	576457.i	−0.142896	−	0.0464297i
$689$	−1.17240e7	+	8.51796e6i	−0.940864	+	0.683578i
$690$		0			0
$691$	1.47381e6	+	4.53593e6i	0.117421	+	0.361386i	0.992444	−	0.122696i	$-0.0391539\pi$
$691$	1.47381e6	+	4.53593e6i	0.117421	+	0.361386i	−0.875023	+	0.484081i	$0.839154\pi$
$692$	1.19342e6			0.0947390
$693$		0			0
$694$	−4.02941e6			−0.317572
$695$	5.17710e6	+	1.59335e7i	0.406560	+	1.25126i
$696$		0			0
$697$	−1.42906e7	+	1.03827e7i	−1.11421	+	0.809521i
$698$	−1.48552e7	−	4.82673e6i	−1.15409	−	0.374986i
$699$		0			0
$700$	4.77922e6	+	6.57804e6i	0.368648	+	0.507401i
$701$	−2.02363e7	−	1.47025e7i	−1.55538	−	1.13005i	−0.939674	−	0.342070i	$-0.888872\pi$
$701$	−2.02363e7	−	1.47025e7i	−1.55538	−	1.13005i	−0.615703	−	0.787978i	$-0.711128\pi$
$702$		0			0
$703$		−	2.43246e6i		−	0.185634i
$704$	314516.	−	1.61340e6i	0.0239172	−	0.122691i
$705$		0			0
$706$	7.66429e6	−	2.49028e6i	0.578709	−	0.188034i
$707$	4.46048e6	−	6.13932e6i	0.335608	−	0.461925i
$708$		0			0
$709$	4.95675e6	−	1.52553e7i	0.370324	−	1.13974i	−0.576256	−	0.817269i	$-0.695487\pi$
$709$	4.95675e6	−	1.52553e7i	0.370324	−	1.13974i	0.946580	−	0.322470i	$-0.104513\pi$
$710$	−667178.	+	2.05336e6i	−0.0496702	+	0.152869i
$711$		0			0
$712$	4.57599e6	−	6.29831e6i	0.338287	−	0.465612i
$713$	1.80815e7	−	5.87505e6i	1.33202	−	0.432801i
$714$		0			0
$715$	−1.18607e7	−	6.58286e6i	−0.867653	−	0.481559i
$716$			5.57636e6i			0.406508i
$717$		0			0
$718$	−7.43626e6	−	5.40276e6i	−0.538324	−	0.391115i
$719$	−4.83050e6	−	6.64862e6i	−0.348474	−	0.479633i	0.598419	−	0.801184i	$-0.295796\pi$
$719$	−4.83050e6	−	6.64862e6i	−0.348474	−	0.479633i	−0.946892	+	0.321551i	$0.895796\pi$
$720$		0			0
$721$	−3.89210e7	−	1.26462e7i	−2.78834	−	0.905986i
$722$	5.28505e6	−	3.83982e6i	0.377317	−	0.274137i
$723$		0			0
$724$	3.34845e6	+	1.03055e7i	0.237409	+	0.730671i
$725$	−4.04569e6			−0.285856
$726$		0			0
$727$	4.38252e6			0.307530			0.153765	−	0.988107i	$-0.450860\pi$
$727$	4.38252e6			0.307530			0.153765	+	0.988107i	$0.450860\pi$
$728$	2.42073e6	+	7.45025e6i	0.169285	+	0.521006i
$729$		0			0
$730$	1.22206e7	−	8.87877e6i	0.848759	−	0.616659i
$731$	−1.50095e7	−	4.87688e6i	−1.03890	−	0.337558i
$732$		0			0
$733$	5.55292e6	+	7.64294e6i	0.381735	+	0.525413i	0.956043	−	0.293226i	$-0.0947290\pi$
$733$	5.55292e6	+	7.64294e6i	0.381735	+	0.525413i	−0.574308	+	0.818639i	$0.694729\pi$
$734$	2.18664e6	+	1.58869e6i	0.149809	+	0.108842i
$735$		0			0
$736$			2.74451e6i			0.186754i
$737$	−405195.	−	224889.i	−0.0274786	−	0.0152510i
$738$		0			0
$739$	−2.30933e6	+	750346.i	−0.155552	+	0.0505418i	−0.385758	−	0.922600i	$-0.626060\pi$
$739$	−2.30933e6	+	750346.i	−0.155552	+	0.0505418i	0.230206	+	0.973142i	$0.426060\pi$
$740$	−1.77796e6	+	2.44715e6i	−0.119355	+	0.164279i
$741$		0			0
$742$	−9.77076e6	+	3.00713e7i	−0.651506	+	2.00513i
$743$	5.33891e6	−	1.64315e7i	0.354798	−	1.09195i	−0.601329	−	0.799001i	$-0.705362\pi$
$743$	5.33891e6	−	1.64315e7i	0.354798	−	1.09195i	0.956127	−	0.292953i	$-0.0946380\pi$
$744$		0			0
$745$	4.95709e6	−	6.82284e6i	0.327217	−	0.450376i
$746$	−1.85341e7	+	6.02208e6i	−1.21934	+	0.396186i
$747$		0			0
$748$	2.66083e6	−	1.36495e7i	0.173886	−	0.891998i
$749$			4.54922e7i			2.96300i
$750$		0			0
$751$	−1.49310e7	−	1.08480e7i	−0.966026	−	0.701859i	−0.0114838	−	0.999934i	$-0.503655\pi$
$751$	−1.49310e7	−	1.08480e7i	−0.966026	−	0.701859i	−0.954542	+	0.298075i	$0.903655\pi$
$752$	−1.92568e6	−	2.65047e6i	−0.124176	−	0.170914i
$753$		0			0
$754$	−3.70702e6	−	1.20448e6i	−0.237463	−	0.0771565i
$755$	−7.16167e6	+	5.20326e6i	−0.457243	+	0.332207i
$756$		0			0
$757$	−644512.	−	1.98361e6i	−0.0408782	−	0.125810i	0.928535	−	0.371245i	$-0.121069\pi$
$757$	−644512.	−	1.98361e6i	−0.0408782	−	0.125810i	−0.969413	+	0.245435i	$0.921069\pi$
$758$	1.48859e7			0.941026
$759$		0			0
$760$	4.19283e6			0.263314
$761$	−4.13851e6	−	1.27370e7i	−0.259050	−	0.797273i	−0.993005	−	0.118075i	$-0.962328\pi$
$761$	−4.13851e6	−	1.27370e7i	−0.259050	−	0.797273i	0.733955	−	0.679198i	$-0.237672\pi$
$762$		0			0
$763$	3.42055e7	−	2.48517e7i	2.12708	−	1.54542i
$764$	277253.	+	90084.9i	0.0171847	+	0.00558366i
$765$		0			0
$766$	7.08579e6	+	9.75276e6i	0.436332	+	0.600559i
$767$	−7.31651e6	−	5.31575e6i	−0.449071	−	0.326269i
$768$		0			0
$769$		−	2.60043e7i		−	1.58573i	−0.609397	−	0.792866i	$-0.708588\pi$
$769$		−	2.60043e7i		−	1.58573i	0.609397	−	0.792866i	$-0.291412\pi$
$770$	−2.93785e7	+	3.59116e6i	−1.78568	+	0.218277i
$771$		0			0
$772$	6.49250e6	−	2.10954e6i	0.392075	−	0.127393i
$773$	−4.88790e6	+	6.72762e6i	−0.294221	+	0.404960i	−0.930379	−	0.366598i	$-0.880522\pi$
$773$	−4.88790e6	+	6.72762e6i	−0.294221	+	0.404960i	0.636159	+	0.771558i	$0.280522\pi$
$774$		0			0
$775$	−4.31110e6	+	1.32682e7i	−0.257830	+	0.793521i
$776$	1.22571e6	−	3.77233e6i	0.0730688	−	0.224883i
$777$		0			0
$778$	2.76895e6	−	3.81114e6i	0.164009	−	0.225739i
$779$	7.12160e6	−	2.31395e6i	0.420469	−	0.136619i
$780$		0			0
$781$	−2.06910e6	−	2.22124e6i	−0.121382	−	0.130307i
$782$			2.32188e7i			1.35776i
$783$		0			0
$784$	1.03469e7	+	7.51744e6i	0.601199	+	0.436797i
$785$	9.57142e6	+	1.31739e7i	0.554373	+	0.763029i
$786$		0			0
$787$	−1.97423e7	−	6.41467e6i	−1.13622	−	0.369179i	−0.320282	−	0.947322i	$-0.603778\pi$
$787$	−1.97423e7	−	6.41467e6i	−1.13622	−	0.369179i	−0.815936	+	0.578143i	$0.803778\pi$
$788$	6.46561e6	−	4.69754e6i	0.370931	−	0.269497i
$789$		0			0
$790$	5.76943e6	+	1.77565e7i	0.328901	+	1.01225i
$791$	−2.74225e7			−1.55835
$792$		0			0
$793$	6.17484e6			0.348692
$794$	6.99093e6	+	2.15159e7i	0.393535	+	1.21118i
$795$		0			0
$796$	−4.39847e6	+	3.19567e6i	−0.246047	+	0.178764i
$797$	−3.23899e7	−	1.05241e7i	−1.80619	−	0.586868i	−0.806205	−	0.591637i	$-0.798482\pi$
$797$	−3.23899e7	−	1.05241e7i	−1.80619	−	0.586868i	−0.999989	+	0.00476922i	$0.998482\pi$
$798$		0			0
$799$	−1.62914e7	−	2.24232e7i	−0.902800	−	1.24260i
$800$	−1.62929e6	−	1.18375e6i	−0.0900067	−	0.0653937i
$801$		0			0
$802$			2.15075e7i			1.18074i
$803$	2.57696e6	+	2.10816e7i	0.141033	+	1.15376i
$804$		0			0
$805$	4.69981e7	−	1.52706e7i	2.55618	−	0.830552i
$806$	−7.90043e6	+	1.08740e7i	−0.428364	+	0.589593i
$807$		0			0
$808$	−580829.	+	1.78761e6i	−0.0312982	+	0.0963261i
$809$	1.02918e7	−	3.16749e7i	0.552866	−	1.70155i	−0.148647	−	0.988890i	$-0.547492\pi$
$809$	1.02918e7	−	3.16749e7i	0.552866	−	1.70155i	0.701513	−	0.712657i	$-0.252508\pi$
$810$		0			0
$811$	−3.06344e6	+	4.21647e6i	−0.163553	+	0.225111i	−0.882925	−	0.469513i	$-0.844429\pi$
$811$	−3.06344e6	+	4.21647e6i	−0.163553	+	0.225111i	0.719373	+	0.694624i	$0.244429\pi$
$812$	−8.08823e6	+	2.62803e6i	−0.430491	+	0.139875i
$813$		0			0
$814$	−1.79531e6	−	3.85547e6i	−0.0949681	−	0.203946i
$815$		−	4.54733e7i		−	2.39807i
$816$		0			0
$817$	5.41249e6	+	3.93241e6i	0.283689	+	0.206112i
$818$	6.11341e6	+	8.41439e6i	0.319448	+	0.439683i
$819$		0			0
$820$	−8.85594e6	−	2.87747e6i	−0.459939	−	0.149443i
$821$	2.11670e7	−	1.53787e7i	1.09598	−	0.796275i	0.115579	−	0.993298i	$-0.463128\pi$
$821$	2.11670e7	−	1.53787e7i	1.09598	−	0.796275i	0.980399	+	0.197023i	$0.0631275\pi$
$822$		0			0
$823$	2.53586e6	+	7.80456e6i	0.130504	+	0.401651i	0.994864	−	0.101224i	$-0.0322757\pi$
$823$	2.53586e6	+	7.80456e6i	0.130504	+	0.401651i	−0.864359	+	0.502875i	$0.832276\pi$
$824$	1.01363e7			0.520071
$825$		0			0
$826$	−1.97322e7			−1.00629
$827$	17273.8	+	53163.3i	0.000878262	+	0.00270301i	0.951495	−	0.307665i	$-0.0995477\pi$
$827$	17273.8	+	53163.3i	0.000878262	+	0.00270301i	−0.950616	+	0.310368i	$0.899548\pi$
$828$		0			0
$829$	−4.77435e6	+	3.46877e6i	−0.241283	+	0.175303i	−0.701855	−	0.712320i	$-0.747645\pi$
$829$	−4.77435e6	+	3.46877e6i	−0.241283	+	0.175303i	0.460571	+	0.887623i	$0.347645\pi$
$830$	−1.11523e7	−	3.62360e6i	−0.561913	−	0.182577i
$831$		0			0
$832$	−1.14048e6	−	1.56973e6i	−0.0571187	−	0.0786171i
$833$	8.75354e7	+	6.35982e7i	4.37091	+	3.17565i
$834$		0			0
$835$		−	9.53338e6i		−	0.473185i
$836$	−2.86081e6	+	5.15450e6i	−0.141571	+	0.255077i
$837$		0			0
$838$	3.41415e6	−	1.10932e6i	0.167947	−	0.0545693i
$839$	1.17537e7	−	1.61775e7i	0.576458	−	0.793427i	−0.416843	−	0.908978i	$-0.636864\pi$
$839$	1.17537e7	−	1.61775e7i	0.576458	−	0.793427i	0.993301	+	0.115552i	$0.0368636\pi$
$840$		0			0
$841$	−5.03067e6	+	1.54828e7i	−0.245265	+	0.754848i
$842$	4.08083e6	−	1.25595e7i	0.198366	−	0.610509i
$843$		0			0
$844$	−72988.8	+	100460.i	−0.00352695	+	0.00485444i
$845$	9.96897e6	−	3.23912e6i	0.480296	−	0.156058i
$846$		0			0
$847$	1.56305e7	−	3.85671e7i	0.748623	−	1.84718i
$848$		−	7.83158e6i		−	0.373990i
$849$		0			0
$850$	−1.37840e7	−	1.00147e7i	−0.654376	−	0.475432i
$851$	4.17383e6	+	5.74478e6i	0.197565	+	0.271925i
$852$		0			0
$853$	−2.75982e6	−	896721.i	−0.129870	−	0.0421973i	0.243361	−	0.969936i	$-0.421750\pi$
$853$	−2.75982e6	−	896721.i	−0.129870	−	0.0421973i	−0.373231	+	0.927738i	$0.621750\pi$
$854$	1.08996e7	−	7.91905e6i	0.511408	−	0.371559i
$855$		0			0
$856$	−3.48195e6	−	1.07163e7i	−0.162419	−	0.499876i
$857$	−6.23878e6			−0.290167			−0.145083	−	0.989419i	$-0.546345\pi$
$857$	−6.23878e6			−0.290167			−0.145083	+	0.989419i	$0.546345\pi$
$858$		0			0
$859$	1.78074e7			0.823413			0.411706	−	0.911317i	$-0.364933\pi$
$859$	1.78074e7			0.823413			0.411706	+	0.911317i	$0.364933\pi$
$860$	−2.57086e6	−	7.91231e6i	−0.118531	−	0.364802i
$861$		0			0
$862$	1.22454e7	−	8.89681e6i	0.561313	−	0.407818i
$863$	2.55057e6	+	828730.i	0.116576	+	0.0378779i	0.366724	−	0.930330i	$-0.380479\pi$
$863$	2.55057e6	+	828730.i	0.116576	+	0.0378779i	−0.250148	+	0.968208i	$0.580479\pi$
$864$		0			0
$865$	3.12842e6	+	4.30590e6i	0.142162	+	0.195670i
$866$	−1.68025e7	−	1.22077e7i	−0.761342	−	0.553147i
$867$		0			0
$868$			2.93265e7i			1.32118i
$869$	−2.57656e7	−	5.02274e6i	−1.15742	−	0.225627i
$870$		0			0
$871$	−520244.	+	169037.i	−0.0232360	+	0.00754984i
$872$	−6.15545e6	+	8.47225e6i	−0.274138	+	0.377318i
$873$		0			0
$874$	3.04160e6	−	9.36109e6i	0.134686	−	0.414522i
$875$	6.59942e6	−	2.03109e7i	0.291397	−	0.896829i
$876$		0			0
$877$	−1.51775e7	+	2.08901e7i	−0.666350	+	0.917153i	−0.999671	−	0.0256611i	$-0.991831\pi$
$877$	−1.51775e7	+	2.08901e7i	−0.666350	+	0.917153i	0.333320	+	0.942814i	$0.391831\pi$
$878$	1.94912e7	−	6.33309e6i	0.853302	−	0.277255i
$879$		0			0
$880$	6.64567e6	−	3.09457e6i	0.289289	−	0.134708i
$881$		−	1.08548e7i		−	0.471176i	−0.971853	−	0.235588i	$-0.924298\pi$
$881$		−	1.08548e7i		−	0.471176i	0.971853	−	0.235588i	$-0.0757016\pi$
$882$		0			0
$883$	−1.75273e7	−	1.27343e7i	−0.756506	−	0.549634i	0.141331	−	0.989962i	$-0.454862\pi$
$883$	−1.75273e7	−	1.27343e7i	−0.756506	−	0.549634i	−0.897837	+	0.440329i	$0.854862\pi$
$884$	−9.64854e6	−	1.32801e7i	−0.415271	−	0.571571i
$885$		0			0
$886$	1.98742e7	+	6.45752e6i	0.850561	+	0.276364i
$887$	1.63471e6	−	1.18768e6i	0.0697639	−	0.0506865i	−0.552357	−	0.833608i	$-0.686271\pi$
$887$	1.63471e6	−	1.18768e6i	0.0697639	−	0.0506865i	0.622121	+	0.782921i	$0.286271\pi$
$888$		0			0
$889$	2.59222e7	+	7.97803e7i	1.10006	+	3.38564i
$890$	3.47199e7			1.46928
$891$		0			0
$892$	−1.64193e7			−0.690942
$893$	3.63080e6	+	1.11744e7i	0.152361	+	0.468918i
$894$		0			0
$895$	−2.01197e7	+	1.46178e7i	−0.839583	+	0.609992i
$896$	−4.02627e6	−	1.30821e6i	−0.167546	−	0.0544389i
$897$		0			0
$898$	−818949.	−	1.12719e6i	−0.0338896	−	0.0466450i
$899$	−1.18052e7	−	8.57696e6i	−0.487162	−	0.353944i
$900$		0			0
$901$		−	6.62559e7i		−	2.71902i
$902$	9.57996e6	−	8.92381e6i	0.392055	−	0.365203i
$903$		0			0
$904$	6.45976e6	−	2.09890e6i	0.262903	−	0.0854223i
$905$	−2.84049e7	+	3.90959e7i	−1.15285	+	1.58676i
$906$		0			0
$907$	−9.76893e6	+	3.00657e7i	−0.394302	+	1.21354i	0.535202	+	0.844724i	$0.320235\pi$
$907$	−9.76893e6	+	3.00657e7i	−0.394302	+	1.21354i	−0.929504	+	0.368812i	$0.879765\pi$
$908$	860983.	−	2.64983e6i	0.0346561	−	0.106661i
$909$		0			0
$910$	−2.05350e7	+	2.82640e7i	−0.822038	+	1.13144i
$911$	−2.41105e7	+	7.83397e6i	−0.962521	+	0.312742i	−0.747793	−	0.663932i	$-0.768886\pi$
$911$	−2.41105e7	+	7.83397e6i	−0.962521	+	0.312742i	−0.214728	+	0.976674i	$0.568886\pi$
$912$		0			0
$913$	1.20641e7	−	1.12378e7i	0.478979	−	0.446173i
$914$			3.36873e6i			0.133383i
$915$		0			0
$916$	−295508.	−	214699.i	−0.0116367	−	0.00845457i
$917$	3.92443e7	+	5.40152e7i	1.54118	+	2.12125i
$918$		0			0
$919$	1.63759e6	+	532084.i	0.0639610	+	0.0207822i	0.340823	−	0.940128i	$-0.389294\pi$
$919$	1.63759e6	+	532084.i	0.0639610	+	0.0207822i	−0.276862	+	0.960910i	$0.589294\pi$
$920$	−9.90228e6	+	7.19442e6i	−0.385714	+	0.280238i
$921$		0			0
$922$	−7.54029e6	−	2.32066e7i	−0.292120	−	0.899052i
$923$	−3.58323e6			−0.138443
$924$		0			0
$925$	−5.21066e6			−0.200234
$926$	−5.36262e6	−	1.65044e7i	−0.205518	−	0.632518i
$927$		0			0
$928$	1.70415e6	−	1.23814e6i	0.0649589	−	0.0471954i
$929$	−1.51057e7	−	4.90815e6i	−0.574252	−	0.186586i	0.00747203	−	0.999972i	$-0.497622\pi$
$929$	−1.51057e7	−	4.90815e6i	−0.574252	−	0.186586i	−0.581724	+	0.813386i	$0.697622\pi$
$930$		0			0
$931$	−2.69603e7	−	3.71077e7i	−1.01941	−	1.40310i
$932$	7.17043e6	+	5.20962e6i	0.270399	+	0.196457i
$933$		0			0
$934$		−	2.67658e6i		−	0.100395i
$935$	5.62230e7	−	2.61803e7i	2.10322	−	0.979369i
$936$		0			0
$937$	−4.23043e6	+	1.37455e6i	−0.157411	+	0.0511460i	−0.386663	−	0.922221i	$-0.626372\pi$
$937$	−4.23043e6	+	1.37455e6i	−0.157411	+	0.0511460i	0.229251	+	0.973367i	$0.426372\pi$
$938$	−701533.	+	965577.i	−0.0260340	+	0.0358327i
$939$		0			0
$940$	4.51501e6	−	1.38958e7i	0.166663	−	0.512936i
$941$	−1.57581e6	+	4.84986e6i	−0.0580138	+	0.178548i	−0.975864	−	0.218379i	$-0.929923\pi$
$941$	−1.57581e6	+	4.84986e6i	−0.0580138	+	0.178548i	0.917850	+	0.396927i	$0.129923\pi$
$942$		0			0
$943$	−1.28487e7	+	1.76848e7i	−0.470523	+	0.647620i
$944$	4.64820e6	−	1.51029e6i	0.169768	−	0.0551608i
$945$		0			0
$946$	1.14812e7	+	2.23814e6i	0.417119	+	0.0813128i
$947$			2.70977e7i			0.981879i	0.871194	+	0.490940i	$0.163346\pi$
$947$			2.70977e7i			0.981879i	−0.871194	+	0.490940i	$0.836654\pi$
$948$		0			0
$949$	2.02818e7	+	1.47356e7i	0.731041	+	0.531132i
$950$	4.24537e6	+	5.84325e6i	0.152618	+	0.210061i
$951$		0			0
$952$	−3.40626e7	−	1.10676e7i	−1.21811	−	0.395787i
$953$	2.71601e7	−	1.97329e7i	0.968721	−	0.703817i	0.0135611	−	0.999908i	$-0.495683\pi$
$953$	2.71601e7	−	1.97329e7i	0.968721	−	0.703817i	0.955160	+	0.296091i	$0.0956832\pi$
$954$		0			0
$955$	401758.	+	1.23648e6i	0.0142546	+	0.0438712i
$956$	−1.96584e7			−0.695670
$957$		0			0
$958$	2.46567e7			0.868004
$959$	1.52375e7	+	4.68964e7i	0.535018	+	1.64662i
$960$		0			0
$961$	−1.75471e7	+	1.27487e7i	−0.612910	+	0.445305i
$962$	−4.77447e6	−	1.55132e6i	−0.166336	−	0.0540460i
$963$		0			0
$964$	1.83812e6	+	2.52996e6i	0.0637062	+	0.0876840i
$965$	2.46306e7	+	1.78952e7i	0.851446	+	0.618612i
$966$		0			0
$967$			2.89932e6i			0.0997079i	0.998757	+	0.0498539i	$0.0158756\pi$
$967$			2.89932e6i			0.0997079i	−0.998757	+	0.0498539i	$0.984124\pi$
$968$	−730076.	+	1.02814e7i	−0.0250426	+	0.352665i
$969$		0			0
$970$	1.68237e7	−	5.46636e6i	0.574107	−	0.186539i
$971$	2.51164e7	−	3.45698e7i	0.854890	−	1.17665i	−0.127874	−	0.991790i	$-0.540815\pi$
$971$	2.51164e7	−	3.45698e7i	0.854890	−	1.17665i	0.982764	−	0.184865i	$-0.0591846\pi$
$972$		0			0
$973$	−1.87470e7	+	5.76972e7i	−0.634817	+	1.95377i
$974$	2.39060e6	−	7.35751e6i	0.0807438	−	0.248504i
$975$		0			0
$976$	−1.96145e6	+	2.69970e6i	−0.0659101	+	0.0907174i
$977$	3.02089e7	−	9.81547e6i	1.01251	−	0.328984i	0.244656	−	0.969610i	$-0.421325\pi$
$977$	3.02089e7	−	9.81547e6i	1.01251	−	0.328984i	0.767853	+	0.640626i	$0.221325\pi$
$978$		0			0
$979$	−2.36898e7	+	4.26833e7i	−0.789959	+	1.42332i
$980$			5.70379e7i			1.89713i
$981$		0			0
$982$	2.43418e7	+	1.76854e7i	0.805516	+	0.585242i
$983$	1.76278e7	+	2.42626e7i	0.581854	+	0.800853i	0.993897	−	0.110311i	$-0.0351847\pi$
$983$	1.76278e7	+	2.42626e7i	0.581854	+	0.800853i	−0.412043	+	0.911164i	$0.635185\pi$
$984$		0			0
$985$	3.38977e7	+	1.10140e7i	1.11322	+	0.361706i
$986$	1.44173e7	−	1.04748e7i	0.472271	−	0.343125i
$987$		0			0
$988$	2.15033e6	+	6.61804e6i	0.0700830	+	0.215693i
$989$	−1.95303e7			−0.634920
$990$		0			0
$991$	3.32414e7			1.07521			0.537607	−	0.843195i	$-0.319328\pi$
$991$	3.32414e7			1.07521			0.537607	+	0.843195i	$0.319328\pi$
$992$	−2.24464e6	−	6.90829e6i	−0.0724215	−	0.222890i
$993$		0			0
$994$	−6.32502e6	+	4.59539e6i	−0.203047	+	0.147522i
$995$	−2.30602e7	−	7.49270e6i	−0.738422	−	0.239928i
$996$		0			0
$997$	1.47189e7	+	2.02589e7i	0.468962	+	0.645471i	0.976337	−	0.216254i	$-0.0693840\pi$
$997$	1.47189e7	+	2.02589e7i	0.468962	+	0.645471i	−0.507375	+	0.861726i	$0.669384\pi$
$998$	8.32206e6	+	6.04633e6i	0.264487	+	0.192161i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.l.b.17.2	yes	40
3.2	odd	2		198.6.l.a.17.9	✓	40
11.2	odd	10		198.6.l.a.35.9	yes	40
33.2	even	10	inner	198.6.l.b.35.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.l.a.17.9	✓	40	3.2	odd	2
198.6.l.a.35.9	yes	40	11.2	odd	10
198.6.l.b.17.2	yes	40	1.1	even	1	trivial
198.6.l.b.35.2	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-67.8638 - 22.0503i) q^{5} +(-151.878 - 209.042i) q^{7} +(51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-12.9443 + 9.40456i) q^{4} +(-67.8638 - 22.0503i) q^{5} +(-151.878 - 209.042i) q^{7} +(51.7771 + 37.6183i) q^{8} +285.425i q^{10} +(-350.890 - 194.749i) q^{11} +(-450.520 + 146.383i) q^{13} +(-607.513 + 836.169i) q^{14} +(79.1084 - 243.470i) q^{16} +(669.264 - 2059.78i) q^{17} +(-539.652 + 742.767i) q^{19} +(1085.82 - 352.805i) q^{20} +(-307.144 + 1575.59i) q^{22} -2680.19i q^{23} +(1591.11 + 1156.01i) q^{25} +(1113.75 + 1532.94i) q^{26} +(3931.90 + 1277.55i) q^{28} +(-1664.21 + 1209.12i) q^{29} +(2192.03 + 6746.37i) q^{31} -1024.00 q^{32} -8663.14 q^{34} +(5697.59 + 17535.4i) q^{35} +(-2143.43 + 1557.29i) q^{37} +(3492.70 + 1134.85i) q^{38} +(-2684.30 - 3694.62i) q^{40} +(-6598.33 - 4793.97i) q^{41} -7286.93i q^{43} +(6373.55 - 779.088i) q^{44} +(-10196.0 + 3312.89i) q^{46} +(7522.17 - 10353.4i) q^{47} +(-15438.1 + 47513.5i) q^{49} +(2431.00 - 7481.84i) q^{50} +(4454.99 - 6131.76i) q^{52} +(29094.8 - 9453.48i) q^{53} +(19518.5 + 20953.6i) q^{55} -16537.0i q^{56} +(6656.84 + 4836.48i) q^{58} +(11221.7 + 15445.3i) q^{59} +(-12397.2 - 4028.10i) q^{61} +(22955.2 - 16678.0i) q^{62} +(1265.73 + 3895.53i) q^{64} +33801.8 q^{65} +1154.76 q^{67} +(10708.2 + 32956.5i) q^{68} +(59665.9 - 43349.8i) q^{70} +(7194.05 + 2337.49i) q^{71} +(-31107.2 - 42815.3i) q^{73} +(8573.70 + 6229.16i) q^{74} -14689.8i q^{76} +(12581.8 + 102929. i) q^{77} +(62210.6 - 20213.5i) q^{79} +(-10737.2 + 14778.5i) q^{80} +(-10081.4 + 31027.2i) q^{82} +(-12695.5 + 39072.6i) q^{83} +(-90837.7 + 125027. i) q^{85} +(-27721.1 + 9007.14i) q^{86} +(-10842.0 - 23283.4i) q^{88} -121643. i q^{89} +(99024.4 + 71945.4i) q^{91} +(25206.0 + 34693.1i) q^{92} +(-48684.5 - 15818.6i) q^{94} +(53001.1 - 38507.6i) q^{95} +(-19151.6 - 58942.7i) q^{97} +199835. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 160 q^{4} + 640 q^{8}+O(q^{10}) \) 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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