LMFDB - Embedded newform 396.3.s.a.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,3,Mod(91,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("396.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	396.s (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:	$10.7902184687$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			235.4
Character	$\chi$	$=$	396.235
Dual form			396.3.s.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844007 - 1.81319i) q^{2} +(-2.57530 + 3.06069i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(3.68852 - 1.19847i) q^{7} +(7.72318 + 2.08627i) q^{8} +O(q^{10})$	\(q+(-0.844007 - 1.81319i) q^{2} +(-2.57530 + 3.06069i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(3.68852 - 1.19847i) q^{7} +(7.72318 + 2.08627i) q^{8} +(1.30826 + 0.726338i) q^{10} +(-10.4619 + 3.39827i) q^{11} +(-2.78472 - 2.02322i) q^{13} +(-5.28619 - 5.67646i) q^{14} +(-2.73563 - 15.7644i) q^{16} +(-6.28791 + 4.56843i) q^{17} +(-18.2467 - 5.92872i) q^{19} +(0.212810 - 2.98515i) q^{20} +(14.9916 + 16.1013i) q^{22} -15.0061i q^{23} +(-7.55245 + 23.2440i) q^{25} +(-1.31815 + 6.75684i) q^{26} +(-5.83090 + 14.3758i) q^{28} +(-4.31911 - 13.2929i) q^{29} +(-32.6981 + 45.0051i) q^{31} +(-26.2749 + 18.2655i) q^{32} +(13.5905 + 7.54537i) q^{34} +(-1.70557 + 2.34752i) q^{35} +(11.3339 + 34.8823i) q^{37} +(4.65049 + 38.0886i) q^{38} +(-5.59225 + 2.13362i) q^{40} +(-17.0545 + 52.4884i) q^{41} -43.0444i q^{43} +(16.5416 - 40.7723i) q^{44} +(-27.2090 + 12.6653i) q^{46} +(-46.1847 - 15.0063i) q^{47} +(-27.4730 + 19.9603i) q^{49} +(48.5201 - 5.92413i) q^{50} +(13.3640 - 3.31277i) q^{52} +(74.7736 + 54.3262i) q^{53} +(4.83805 - 6.65778i) q^{55} +(30.9874 - 1.56078i) q^{56} +(-20.4571 + 19.0506i) q^{58} +(-76.2995 + 24.7912i) q^{59} +(62.8898 - 45.6921i) q^{61} +(109.200 + 21.3032i) q^{62} +(55.2950 + 32.2252i) q^{64} +2.57532 q^{65} -57.7376i q^{67} +(2.21072 - 31.0104i) q^{68} +(5.69602 + 1.11120i) q^{70} +(-57.7740 - 79.5191i) q^{71} +(23.1219 + 71.1618i) q^{73} +(53.6822 - 49.9914i) q^{74} +(65.1368 - 40.5793i) q^{76} +(-34.5162 + 25.0729i) q^{77} +(-44.4641 + 61.1996i) q^{79} +(8.58856 + 8.33900i) q^{80} +(109.565 - 13.3775i) q^{82} +(38.8192 + 53.4301i) q^{83} +(1.79696 - 5.53046i) q^{85} +(-78.0477 + 36.3298i) q^{86} +(-87.8890 + 4.41910i) q^{88} -46.7420 q^{89} +(-12.6963 - 4.12527i) q^{91} +(45.9291 + 38.6454i) q^{92} +(11.7709 + 96.4070i) q^{94} +(13.6519 - 4.43576i) q^{95} +(-86.8069 - 63.0689i) q^{97} +(59.3792 + 32.9671i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8	$ 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8} - 8 q^{10} - 6 q^{13} + 36 q^{14} - 65 q^{16} + 30 q^{17} - 34 q^{20} + 25 q^{22} - 156 q^{26} + 130 q^{28} + 38 q^{29} - 20 q^{32} + 258 q^{34} - 150 q^{37} - 80 q^{38} + 112 q^{40} + 150 q^{41} - 4 q^{44} + 40 q^{46} + 132 q^{49} + 177 q^{50} - 314 q^{52} - 290 q^{53} + 856 q^{56} - 476 q^{58} + 42 q^{61} + 364 q^{62} + 303 q^{64} - 164 q^{65} - 14 q^{68} + 576 q^{70} + 186 q^{73} - 588 q^{74} + 366 q^{76} - 190 q^{77} - 1100 q^{80} + 365 q^{82} + 286 q^{85} + 501 q^{86} + 47 q^{88} + 88 q^{89} + 702 q^{92} - 678 q^{94} - 130 q^{97} + 652 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8 - 8 * q^10 - 6 * q^13 + 36 * q^14 - 65 * q^16 + 30 * q^17 - 34 * q^20 + 25 * q^22 - 156 * q^26 + 130 * q^28 + 38 * q^29 - 20 * q^32 + 258 * q^34 - 150 * q^37 - 80 * q^38 + 112 * q^40 + 150 * q^41 - 4 * q^44 + 40 * q^46 + 132 * q^49 + 177 * q^50 - 314 * q^52 - 290 * q^53 + 856 * q^56 - 476 * q^58 + 42 * q^61 + 364 * q^62 + 303 * q^64 - 164 * q^65 - 14 * q^68 + 576 * q^70 + 186 * q^73 - 588 * q^74 + 366 * q^76 - 190 * q^77 - 1100 * q^80 + 365 * q^82 + 286 * q^85 + 501 * q^86 + 47 * q^88 + 88 * q^89 + 702 * q^92 - 678 * q^94 - 130 * q^97 + 652 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.844007	−	1.81319i	−0.422004	−	0.906594i
$2$	−0.844007	−	1.81319i	−0.422004	−	0.906594i
$3$		0			0
$3$		0			0
$4$	−2.57530	+	3.06069i	−0.643826	+	0.765172i
$5$	−0.605291	+	0.439770i	−0.121058	+	0.0879539i	−0.646667	−	0.762773i	$-0.723838\pi$
$5$	−0.605291	+	0.439770i	−0.121058	+	0.0879539i	0.525609	+	0.850726i	$0.323838\pi$
$6$		0			0
$7$	3.68852	−	1.19847i	0.526931	−	0.171210i	−0.0334574	−	0.999440i	$-0.510652\pi$
$7$	3.68852	−	1.19847i	0.526931	−	0.171210i	0.560389	+	0.828230i	$0.310652\pi$
$8$	7.72318	+	2.08627i	0.965397	+	0.260783i
$9$		0			0
$10$	1.30826	+	0.726338i	0.130826	+	0.0726338i
$11$	−10.4619	+	3.39827i	−0.951084	+	0.308934i
$11$	−10.4619	+	3.39827i	−0.951084	+	0.308934i
$12$		0			0
$13$	−2.78472	−	2.02322i	−0.214210	−	0.155632i	0.475507	−	0.879712i	$-0.342265\pi$
$13$	−2.78472	−	2.02322i	−0.214210	−	0.155632i	−0.689716	+	0.724080i	$0.742265\pi$
$14$	−5.28619	−	5.67646i	−0.377585	−	0.405461i
$15$		0			0
$16$	−2.73563	−	15.7644i	−0.170977	−	0.985275i
$17$	−6.28791	+	4.56843i	−0.369877	+	0.268731i	−0.757160	−	0.653230i	$-0.773414\pi$
$17$	−6.28791	+	4.56843i	−0.369877	+	0.268731i	0.387283	+	0.921961i	$0.373414\pi$
$18$		0			0
$19$	−18.2467	−	5.92872i	−0.960354	−	0.312038i	−0.213438	−	0.976957i	$-0.568466\pi$
$19$	−18.2467	−	5.92872i	−0.960354	−	0.312038i	−0.746916	+	0.664919i	$0.768466\pi$
$20$	0.212810	−	2.98515i	0.0106405	−	0.149257i
$21$		0			0
$22$	14.9916	+	16.1013i	0.681438	+	0.731876i
$23$		−	15.0061i		−	0.652441i	−0.945294	−	0.326220i	$-0.894225\pi$
$23$		−	15.0061i		−	0.652441i	0.945294	−	0.326220i	$-0.105775\pi$
$24$		0			0
$25$	−7.55245	+	23.2440i	−0.302098	+	0.929761i
$26$	−1.31815	+	6.75684i	−0.0506982	+	0.259879i
$27$		0			0
$28$	−5.83090	+	14.3758i	−0.208247	+	0.513423i
$29$	−4.31911	−	13.2929i	−0.148935	−	0.458374i	0.848561	−	0.529097i	$-0.177469\pi$
$29$	−4.31911	−	13.2929i	−0.148935	−	0.458374i	−0.997496	+	0.0707231i	$0.977469\pi$
$30$		0			0
$31$	−32.6981	+	45.0051i	−1.05478	+	1.45178i	−0.170185	+	0.985412i	$0.554436\pi$
$31$	−32.6981	+	45.0051i	−1.05478	+	1.45178i	−0.884593	+	0.466364i	$0.845564\pi$
$32$	−26.2749	+	18.2655i	−0.821092	+	0.570796i
$33$		0			0
$34$	13.5905	+	7.54537i	0.399720	+	0.221923i
$35$	−1.70557	+	2.34752i	−0.0487307	+	0.0670721i
$36$		0			0
$37$	11.3339	+	34.8823i	0.306323	+	0.942764i	0.979180	+	0.202992i	$0.0650666\pi$
$37$	11.3339	+	34.8823i	0.306323	+	0.942764i	−0.672858	+	0.739772i	$0.734933\pi$
$38$	4.65049	+	38.0886i	0.122381	+	1.00233i
$39$		0			0
$40$	−5.59225	+	2.13362i	−0.139806	+	0.0533405i
$41$	−17.0545	+	52.4884i	−0.415964	+	1.28020i	0.495422	+	0.868652i	$0.335013\pi$
$41$	−17.0545	+	52.4884i	−0.415964	+	1.28020i	−0.911386	+	0.411553i	$0.864987\pi$
$42$		0			0
$43$		−	43.0444i		−	1.00103i	−0.865727	−	0.500517i	$-0.833143\pi$
$43$		−	43.0444i		−	1.00103i	0.865727	−	0.500517i	$-0.166857\pi$
$44$	16.5416	−	40.7723i	0.375945	−	0.926642i
$45$		0			0
$46$	−27.2090	+	12.6653i	−0.591499	+	0.275332i
$47$	−46.1847	−	15.0063i	−0.982653	−	0.319283i	−0.226740	−	0.973955i	$-0.572807\pi$
$47$	−46.1847	−	15.0063i	−0.982653	−	0.319283i	−0.755913	+	0.654672i	$0.772807\pi$
$48$		0			0
$49$	−27.4730	+	19.9603i	−0.560674	+	0.407353i
$50$	48.5201	−	5.92413i	0.970403	−	0.118483i
$51$		0			0
$52$	13.3640	−	3.31277i	0.256999	−	0.0637071i
$53$	74.7736	+	54.3262i	1.41082	+	1.02502i	0.993202	+	0.116402i	$0.0371361\pi$
$53$	74.7736	+	54.3262i	1.41082	+	1.02502i	0.417621	+	0.908621i	$0.362864\pi$
$54$		0			0
$55$	4.83805	−	6.65778i	0.0879645	−	0.121050i
$56$	30.9874	−	1.56078i	0.553347	−	0.0278712i
$57$		0			0
$58$	−20.4571	+	19.0506i	−0.352708	+	0.328459i
$59$	−76.2995	+	24.7912i	−1.29321	+	0.420190i	−0.873215	−	0.487335i	$-0.837969\pi$
$59$	−76.2995	+	24.7912i	−1.29321	+	0.420190i	−0.419997	+	0.907525i	$0.637969\pi$
$60$		0			0
$61$	62.8898	−	45.6921i	1.03098	−	0.749052i	0.0624763	−	0.998046i	$-0.480100\pi$
$61$	62.8898	−	45.6921i	1.03098	−	0.749052i	0.968505	+	0.248995i	$0.0801002\pi$
$62$	109.200	+	21.3032i	1.76129	+	0.343600i
$63$		0			0
$64$	55.2950	+	32.2252i	0.863984	+	0.503519i
$65$	2.57532			0.0396203
$66$		0			0
$67$		−	57.7376i		−	0.861755i	−0.902411	−	0.430877i	$-0.858204\pi$
$67$		−	57.7376i		−	0.861755i	0.902411	−	0.430877i	$-0.141796\pi$
$68$	2.21072	−	31.0104i	0.0325106	−	0.456036i
$69$		0			0
$70$	5.69602	+	1.11120i	0.0813717	+	0.0158743i
$71$	−57.7740	−	79.5191i	−0.813719	−	1.11999i	−0.990739	−	0.135780i	$-0.956646\pi$
$71$	−57.7740	−	79.5191i	−0.813719	−	1.11999i	0.177020	−	0.984207i	$-0.443354\pi$
$72$		0			0
$73$	23.1219	+	71.1618i	0.316738	+	0.974820i	0.975033	+	0.222060i	$0.0712780\pi$
$73$	23.1219	+	71.1618i	0.316738	+	0.974820i	−0.658295	+	0.752760i	$0.728722\pi$
$74$	53.6822	−	49.9914i	0.725435	−	0.675560i
$75$		0			0
$76$	65.1368	−	40.5793i	0.857064	−	0.533938i
$77$	−34.5162	+	25.0729i	−0.448263	+	0.325622i
$78$		0			0
$79$	−44.4641	+	61.1996i	−0.562837	+	0.774678i	−0.991684	−	0.128699i	$-0.958920\pi$
$79$	−44.4641	+	61.1996i	−0.562837	+	0.774678i	0.428847	+	0.903377i	$0.358920\pi$
$80$	8.58856	+	8.33900i	0.107357	+	0.104238i
$81$		0			0
$82$	109.565	−	13.3775i	1.33616	−	0.163141i
$83$	38.8192	+	53.4301i	0.467701	+	0.643736i	0.976084	−	0.217396i	$-0.0697562\pi$
$83$	38.8192	+	53.4301i	0.467701	+	0.643736i	−0.508382	+	0.861132i	$0.669756\pi$
$84$		0			0
$85$	1.79696	−	5.53046i	0.0211407	−	0.0650643i
$86$	−78.0477	+	36.3298i	−0.907531	+	0.422440i
$87$		0			0
$88$	−87.8890	+	4.41910i	−0.998738	+	0.0502171i
$89$	−46.7420			−0.525191			−0.262596	−	0.964906i	$-0.584579\pi$
$89$	−46.7420			−0.525191			−0.262596	+	0.964906i	$0.584579\pi$
$90$		0			0
$91$	−12.6963	−	4.12527i	−0.139520	−	0.0453327i
$92$	45.9291	+	38.6454i	0.499229	+	0.420058i
$93$		0			0
$94$	11.7709	+	96.4070i	0.125223	+	1.02561i
$95$	13.6519	−	4.43576i	0.143704	−	0.0466922i
$96$		0			0
$97$	−86.8069	−	63.0689i	−0.894916	−	0.650195i	0.0422389	−	0.999108i	$-0.486551\pi$
$97$	−86.8069	−	63.0689i	−0.894916	−	0.650195i	−0.937155	+	0.348913i	$0.886551\pi$
$98$	59.3792	+	32.9671i	0.605910	+	0.336399i
$99$		0			0
$100$	−51.6929	−	82.9761i	−0.516929	−	0.829761i
$101$	−58.6040	−	42.5783i	−0.580238	−	0.421568i	0.258572	−	0.965992i	$-0.416748\pi$
$101$	−58.6040	−	42.5783i	−0.580238	−	0.421568i	−0.838810	+	0.544424i	$0.816748\pi$
$102$		0			0
$103$	−19.9403	+	6.47899i	−0.193595	+	0.0629029i	−0.404210	−	0.914666i	$-0.632453\pi$
$103$	−19.9403	+	6.47899i	−0.193595	+	0.0629029i	0.210615	+	0.977569i	$0.432453\pi$
$104$	−17.2859	−	21.4354i	−0.166211	−	0.206109i
$105$		0			0
$106$	35.3942	−	181.430i	0.333907	−	1.71161i
$107$	24.9694	+	8.11306i	0.233359	+	0.0758230i	0.423362	−	0.905961i	$-0.360850\pi$
$107$	24.9694	+	8.11306i	0.233359	+	0.0758230i	−0.190003	+	0.981783i	$0.560850\pi$
$108$		0			0
$109$	−79.3568			−0.728044			−0.364022	−	0.931390i	$-0.618597\pi$
$109$	−79.3568			−0.728044			−0.364022	+	0.931390i	$0.618597\pi$
$110$	−16.1552	−	3.15308i	−0.146865	−	0.0286644i
$111$		0			0
$112$	−28.9836	−	54.8687i	−0.258782	−	0.489899i
$113$	7.02958	−	21.6348i	0.0622087	−	0.191459i	−0.915122	−	0.403177i	$-0.867906\pi$
$113$	7.02958	−	21.6348i	0.0622087	−	0.191459i	0.977331	+	0.211718i	$0.0679059\pi$
$114$		0			0
$115$	6.59924	+	9.08308i	0.0573847	+	0.0789833i
$116$	51.8083	+	21.0137i	0.446623	+	0.181152i
$117$		0			0
$118$	109.348	+	117.421i	0.926682	+	0.995097i
$119$	−17.7179	+	24.3866i	−0.148890	+	0.204930i
$120$		0			0
$121$	97.9035	−	71.1049i	0.809120	−	0.587644i
$122$	−135.928	−	75.4666i	−1.11416	−	0.618579i
$123$		0			0
$124$	−53.5390	−	215.980i	−0.431766	−	1.74178i
$125$	−11.4306	−	35.1798i	−0.0914449	−	0.281438i
$126$		0			0
$127$	−52.1961	−	71.8418i	−0.410993	−	0.565683i	0.552467	−	0.833535i	$-0.313686\pi$
$127$	−52.1961	−	71.8418i	−0.410993	−	0.565683i	−0.963460	+	0.267851i	$0.913686\pi$
$128$	11.7610	−	127.459i	0.0918828	−	0.995770i
$129$		0			0
$130$	−2.17359	−	4.66954i	−0.0167199	−	0.0359195i
$131$		−	170.654i		−	1.30271i	−0.758775	−	0.651353i	$-0.774202\pi$
$131$		−	170.654i		−	1.30271i	0.758775	−	0.651353i	$-0.225798\pi$
$132$		0			0
$133$	−74.4088			−0.559465
$134$	−104.689	+	48.7309i	−0.781262	+	0.363664i
$135$		0			0
$136$	−58.0936	+	22.1646i	−0.427159	+	0.162975i
$137$	72.1395	−	52.4124i	0.526565	−	0.382572i	−0.292506	−	0.956264i	$-0.594489\pi$
$137$	72.1395	−	52.4124i	0.526565	−	0.382572i	0.819071	+	0.573692i	$0.194489\pi$
$138$		0			0
$139$	170.380	−	55.3599i	1.22576	−	0.398273i	0.376582	−	0.926383i	$-0.377099\pi$
$139$	170.380	−	55.3599i	1.22576	−	0.398273i	0.849176	+	0.528111i	$0.177099\pi$
$140$	−2.79266	−	11.2658i	−0.0199476	−	0.0804701i
$141$		0			0
$142$	−95.4214	+	171.870i	−0.671982	+	1.21035i
$143$	36.0090	+	11.7035i	0.251811	+	0.0818428i
$144$		0			0
$145$	8.46011	+	6.14663i	0.0583456	+	0.0423906i
$146$	109.515	−	101.985i	0.750101	−	0.698530i
$147$		0			0
$148$	−135.952	−	55.1428i	−0.918595	−	0.372586i
$149$	−95.8450	+	69.6355i	−0.643255	+	0.467352i	−0.860967	−	0.508661i	$-0.830141\pi$
$149$	−95.8450	+	69.6355i	−0.643255	+	0.467352i	0.217712	+	0.976013i	$0.430141\pi$
$150$		0			0
$151$	138.124	+	44.8793i	0.914731	+	0.297214i	0.728303	−	0.685255i	$-0.240309\pi$
$151$	138.124	+	44.8793i	0.914731	+	0.297214i	0.186427	+	0.982469i	$0.440309\pi$
$152$	−128.554	−	83.8561i	−0.845749	−	0.551685i
$153$		0			0
$154$	74.5939	+	41.4227i	0.484376	+	0.268979i
$155$		−	41.6208i		−	0.268521i
$156$		0			0
$157$	27.4296	−	84.4196i	0.174711	−	0.537705i	−0.824909	−	0.565265i	$-0.808774\pi$
$157$	27.4296	−	84.4196i	0.174711	−	0.537705i	0.999620	+	0.0275605i	$0.00877388\pi$
$158$	148.494	+	28.9689i	0.939838	+	0.183347i
$159$		0			0
$160$	7.87138	−	22.6108i	0.0491961	−	0.141318i
$161$	−17.9844	−	55.3504i	−0.111705	−	0.343791i
$162$		0			0
$163$	−13.3585	+	18.3864i	−0.0819539	+	0.112800i	−0.848026	−	0.529955i	$-0.822209\pi$
$163$	−13.3585	+	18.3864i	−0.0819539	+	0.112800i	0.766072	+	0.642755i	$0.222209\pi$
$164$	−116.730	−	187.372i	−0.711769	−	1.14251i
$165$		0			0
$166$	64.1151	−	115.482i	0.386235	−	0.695674i
$167$	−175.977	+	242.212i	−1.05376	+	1.45037i	−0.168247	+	0.985745i	$0.553811\pi$
$167$	−175.977	+	242.212i	−1.05376	+	1.45037i	−0.885508	+	0.464624i	$0.846189\pi$
$168$		0			0
$169$	−48.5626	−	149.460i	−0.287353	−	0.884381i
$170$	−11.5444	+	1.40953i	−0.0679083	+	0.00829136i
$171$		0			0
$172$	131.746	+	110.852i	0.765963	+	0.644491i
$173$	14.5428	−	44.7583i	0.0840627	−	0.258718i	−0.900187	−	0.435504i	$-0.856570\pi$
$173$	14.5428	−	44.7583i	0.0840627	−	0.258718i	0.984249	+	0.176786i	$0.0565700\pi$
$174$		0			0
$175$			94.7874i			0.541642i
$176$	82.1916	+	155.629i	0.466998	+	0.884258i
$177$		0			0
$178$	39.4506	+	84.7521i	0.221633	+	0.476135i
$179$	86.7866	+	28.1987i	0.484842	+	0.157535i	0.541230	−	0.840874i	$-0.317959\pi$
$179$	86.7866	+	28.1987i	0.484842	+	0.157535i	−0.0563889	+	0.998409i	$0.517959\pi$
$180$		0			0
$181$	16.1873	−	11.7607i	0.0894324	−	0.0649764i	−0.542171	−	0.840268i	$-0.682397\pi$
$181$	16.1873	−	11.7607i	0.0894324	−	0.0649764i	0.631603	+	0.775292i	$0.282397\pi$
$182$	3.23586	+	26.5025i	0.0177795	+	0.145618i
$183$		0			0
$184$	31.3068	−	115.895i	0.170146	−	0.629865i
$185$	−22.2005	−	16.1296i	−0.120003	−	0.0871870i
$186$		0			0
$187$	50.2588	−	69.1626i	0.268764	−	0.369854i
$188$	164.869	−	102.711i	0.876964	−	0.546336i
$189$		0			0
$190$	−19.5651	−	21.0096i	−0.102974	−	0.110577i
$191$	208.998	−	67.9075i	1.09423	−	0.355537i	0.294350	−	0.955698i	$-0.404897\pi$
$191$	208.998	−	67.9075i	1.09423	−	0.355537i	0.799879	+	0.600161i	$0.204897\pi$
$192$		0			0
$193$	−72.6595	+	52.7902i	−0.376474	+	0.273524i	−0.759890	−	0.650051i	$-0.774747\pi$
$193$	−72.6595	+	52.7902i	−0.376474	+	0.273524i	0.383416	+	0.923576i	$0.374747\pi$
$194$	−41.0901	+	210.628i	−0.211805	+	1.08571i
$195$		0			0
$196$	9.65904	−	135.490i	0.0492808	−	0.691276i
$197$	113.348			0.575370			0.287685	−	0.957725i	$-0.407114\pi$
$197$	113.348			0.575370			0.287685	+	0.957725i	$0.407114\pi$
$198$		0			0
$199$		−	128.213i		−	0.644289i	−0.946691	−	0.322144i	$-0.895596\pi$
$199$		−	128.213i		−	0.644289i	0.946691	−	0.322144i	$-0.104404\pi$
$200$	−106.822	+	163.761i	−0.534111	+	0.818807i
$201$		0			0
$202$	−27.7403	+	142.197i	−0.137328	+	0.703943i
$203$	−31.8622	−	43.8546i	−0.156957	−	0.216032i
$204$		0			0
$205$	−12.7599	−	39.2708i	−0.0622432	−	0.191565i
$206$	28.5774	+	30.6872i	0.138725	+	0.148967i
$207$		0			0
$208$	−24.2769	+	49.4343i	−0.116716	+	0.237665i
$209$	211.043	+	0.0184845i	1.00978	+	8.84427e-5i
$210$		0			0
$211$	−169.233	+	232.929i	−0.802053	+	1.10393i	0.190449	+	0.981697i	$0.439006\pi$
$211$	−169.233	+	232.929i	−0.802053	+	1.10393i	−0.992501	+	0.122234i	$0.960994\pi$
$212$	−358.840	+	88.9523i	−1.69264	+	0.419586i
$213$		0			0
$214$	−6.36388	−	52.1217i	−0.0297377	−	0.243560i
$215$	18.9296	+	26.0544i	0.0880448	+	0.121183i
$216$		0			0
$217$	−66.6702	+	205.190i	−0.307236	+	0.945575i
$218$	66.9777	+	143.889i	0.307237	+	0.660040i
$219$		0			0
$220$	7.91794	+	31.9536i	0.0359906	+	0.145243i
$221$	26.7530			0.121055
$222$		0			0
$223$	−146.310	−	47.5389i	−0.656097	−	0.213179i	−0.0379966	−	0.999278i	$-0.512098\pi$
$223$	−146.310	−	47.5389i	−0.656097	−	0.213179i	−0.618101	+	0.786099i	$0.712098\pi$
$224$	−75.0249	+	98.8623i	−0.334933	+	0.441350i
$225$		0			0
$226$	−45.1610	+	5.51400i	−0.199827	+	0.0243982i
$227$	307.232	−	99.8258i	1.35345	−	0.439761i	0.459596	−	0.888128i	$-0.347994\pi$
$227$	307.232	−	99.8258i	1.35345	−	0.439761i	0.893850	+	0.448367i	$0.147994\pi$
$228$		0			0
$229$	230.677	+	167.597i	1.00732	+	0.731864i	0.963646	−	0.267181i	$-0.0860922\pi$
$229$	230.677	+	167.597i	1.00732	+	0.731864i	0.0436787	+	0.999046i	$0.486092\pi$
$230$	10.8995	−	19.6319i	0.0473892	−	0.0853559i
$231$		0			0
$232$	−5.62483	−	111.674i	−0.0242450	−	0.481353i
$233$	−157.782	−	114.636i	−0.677178	−	0.491999i	0.195242	−	0.980755i	$-0.437451\pi$
$233$	−157.782	−	114.636i	−0.677178	−	0.491999i	−0.872420	+	0.488756i	$0.837451\pi$
$234$		0			0
$235$	34.5545	−	11.2274i	0.147040	−	0.0477763i
$236$	120.616	−	297.374i	0.511086	−	1.26006i
$237$		0			0
$238$	59.1716	+	11.5434i	0.248620	+	0.0485018i
$239$	200.985	+	65.3040i	0.840941	+	0.273238i	0.697647	−	0.716442i	$-0.254230\pi$
$239$	200.985	+	65.3040i	0.840941	+	0.273238i	0.143294	+	0.989680i	$0.454230\pi$
$240$		0			0
$241$	328.286			1.36218			0.681092	−	0.732198i	$-0.261505\pi$
$241$	328.286			1.36218			0.681092	+	0.732198i	$0.261505\pi$
$242$	−211.558	−	117.504i	−0.874206	−	0.485556i
$243$		0			0
$244$	−22.1110	+	310.157i	−0.0906188	+	1.27114i
$245$	7.85123	−	24.1636i	0.0320458	−	0.0986269i
$246$		0			0
$247$	38.8170	+	53.4270i	0.157154	+	0.216304i
$248$	−346.426	+	279.365i	−1.39688	+	1.12647i
$249$		0			0
$250$	−54.1401	+	50.4179i	−0.216560	+	0.201671i
$251$	−49.3072	+	67.8655i	−0.196443	+	0.270380i	−0.895863	−	0.444330i	$-0.853442\pi$
$251$	−49.3072	+	67.8655i	−0.196443	+	0.270380i	0.699420	+	0.714711i	$0.253442\pi$
$252$		0			0
$253$	50.9949	+	156.993i	0.201561	+	0.620526i
$254$	−86.2088	+	155.276i	−0.339405	+	0.611324i
$255$		0			0
$256$	−241.033	+	86.2510i	−0.941534	+	0.336918i
$257$	50.0346	+	153.991i	0.194687	+	0.599185i	0.999980	+	0.00630817i	$0.00200797\pi$
$257$	50.0346	+	153.991i	0.194687	+	0.599185i	−0.805293	+	0.592877i	$0.797992\pi$
$258$		0			0
$259$	83.6108	+	115.080i	0.322822	+	0.444326i
$260$	−6.63223	+	7.88225i	−0.0255086	+	0.0303164i
$261$		0			0
$262$	−309.429	+	144.034i	−1.18103	+	0.549747i
$263$			399.263i			1.51811i	0.651027	+	0.759055i	$0.274339\pi$
$263$			399.263i			1.51811i	−0.651027	+	0.759055i	$0.725661\pi$
$264$		0			0
$265$	−69.1508			−0.260947
$266$	62.8016	+	134.917i	0.236096	+	0.507207i
$267$		0			0
$268$	176.717	+	148.692i	0.659391	+	0.554820i
$269$	−51.6076	+	37.4951i	−0.191850	+	0.139387i	−0.679564	−	0.733617i	$-0.737831\pi$
$269$	−51.6076	+	37.4951i	−0.191850	+	0.139387i	0.487714	+	0.873003i	$0.337831\pi$
$270$		0			0
$271$	−162.436	+	52.7786i	−0.599394	+	0.194755i	−0.592970	−	0.805225i	$-0.702045\pi$
$271$	−162.436	+	52.7786i	−0.599394	+	0.194755i	−0.00642369	+	0.999979i	$0.502045\pi$
$272$	89.2200	+	86.6276i	0.328015	+	0.318484i
$273$		0			0
$274$	−155.920	−	86.5660i	−0.569050	−	0.315934i
$275$	0.0235469	−	268.842i	8.56253e−5	−	0.977609i
$276$		0			0
$277$	−261.885	−	190.270i	−0.945432	−	0.686897i	0.00428992	−	0.999991i	$-0.498634\pi$
$277$	−261.885	−	190.270i	−0.945432	−	0.686897i	−0.949722	+	0.313094i	$0.898634\pi$
$278$	−244.180	−	262.207i	−0.878346	−	0.943192i
$279$		0			0
$280$	−18.0700	+	14.5721i	−0.0645358	+	0.0520430i
$281$	309.396	−	224.789i	1.10105	−	0.799961i	0.119821	−	0.992796i	$-0.461768\pi$
$281$	309.396	−	224.789i	1.10105	−	0.799961i	0.981231	+	0.192834i	$0.0617680\pi$
$282$		0			0
$283$	419.260	+	136.226i	1.48148	+	0.481364i	0.934556	−	0.355816i	$-0.115797\pi$
$283$	419.260	+	136.226i	1.48148	+	0.481364i	0.546928	+	0.837179i	$0.315797\pi$
$284$	392.169	+	27.9576i	1.38088	+	0.0984421i
$285$		0			0
$286$	−9.17118	−	75.1690i	−0.0320671	−	0.262829i
$287$			214.044i			0.745797i
$288$		0			0
$289$	−70.6387	+	217.404i	−0.244425	+	0.752261i
$290$	4.00460	−	20.5276i	0.0138090	−	0.0707847i
$291$		0			0
$292$	−277.350	−	112.494i	−0.949829	−	0.385255i
$293$	161.544	+	497.182i	0.551345	+	1.69687i	0.705404	+	0.708805i	$0.250765\pi$
$293$	161.544	+	497.182i	0.551345	+	1.69687i	−0.154059	+	0.988062i	$0.549235\pi$
$294$		0			0
$295$	35.2810	−	48.5601i	0.119597	−	0.164611i
$296$	14.7603	+	293.048i	0.0498659	+	0.990026i
$297$		0			0
$298$	207.156	+	115.012i	0.695155	+	0.385947i
$299$	−30.3607	+	41.7880i	−0.101541	+	0.139759i
$300$		0			0
$301$	−51.5875	−	158.770i	−0.171387	−	0.527476i
$302$	−35.2033	−	288.324i	−0.116567	−	0.954715i
$303$		0			0
$304$	−43.5465	+	303.868i	−0.143245	+	0.999564i
$305$	−17.9726	+	55.3141i	−0.0589267	+	0.181358i
$306$		0			0
$307$		−	528.080i		−	1.72013i	−0.510183	−	0.860066i	$-0.670422\pi$
$307$		−	528.080i		−	1.72013i	0.510183	−	0.860066i	$-0.329578\pi$
$308$	12.1495	−	170.214i	0.0394463	−	0.552642i
$309$		0			0
$310$	−75.4663	+	35.1283i	−0.243440	+	0.113317i
$311$	−303.245	−	98.5302i	−0.975064	−	0.316817i	−0.222205	−	0.975000i	$-0.571326\pi$
$311$	−303.245	−	98.5302i	−0.975064	−	0.316817i	−0.752859	+	0.658182i	$0.771326\pi$
$312$		0			0
$313$	260.815	−	189.493i	0.833274	−	0.605409i	−0.0872100	−	0.996190i	$-0.527795\pi$
$313$	260.815	−	189.493i	0.833274	−	0.605409i	0.920484	+	0.390781i	$0.127795\pi$
$314$	−176.219	+	21.5158i	−0.561208	+	0.0685215i
$315$		0			0
$316$	−72.8043	−	293.698i	−0.230393	−	0.929425i
$317$	−293.298	−	213.093i	−0.925230	−	0.672219i	0.0195904	−	0.999808i	$-0.493764\pi$
$317$	−293.298	−	213.093i	−0.925230	−	0.672219i	−0.944820	+	0.327589i	$0.893764\pi$
$318$		0			0
$319$	90.3589	+	124.391i	0.283257	+	0.389941i
$320$	−47.6412	+	4.81143i	−0.148879	+	0.0150357i
$321$		0			0
$322$	−85.1817	+	79.3253i	−0.264539	+	0.246352i
$323$	141.819	−	46.0797i	0.439067	−	0.142662i
$324$		0			0
$325$	68.0593	−	49.4480i	0.209413	−	0.152148i
$326$	44.6126	+	8.70321i	0.136848	+	0.0266970i
$327$		0			0
$328$	−241.220	+	369.797i	−0.735426	+	1.12743i
$329$	−188.338			−0.572455
$330$		0			0
$331$			88.0333i			0.265962i	0.991119	+	0.132981i	$0.0424549\pi$
$331$			88.0333i			0.265962i	−0.991119	+	0.132981i	$0.957545\pi$
$332$	−263.504	−	18.7851i	−0.793687	−	0.0565816i
$333$		0			0
$334$	587.701	+	114.651i	1.75958	+	0.343267i
$335$	25.3912	+	34.9480i	0.0757947	+	0.104322i
$336$		0			0
$337$	−3.58012	−	11.0185i	−0.0106235	−	0.0326957i	0.945604	−	0.325319i	$-0.105472\pi$
$337$	−3.58012	−	11.0185i	−0.0106235	−	0.0326957i	−0.956228	+	0.292623i	$0.905472\pi$
$338$	−230.013	+	214.199i	−0.680510	+	0.633724i
$339$		0			0
$340$	12.2993	+	19.7425i	0.0361745	+	0.0580663i
$341$	189.145	−	581.956i	0.554679	−	1.70662i
$342$		0			0
$343$	−189.115	+	260.294i	−0.551355	+	0.758875i
$344$	89.8021	−	332.440i	0.261053	−	0.966395i
$345$		0			0
$346$	−93.4295	+	11.4074i	−0.270027	+	0.0329694i
$347$	−15.5579	−	21.4136i	−0.0448355	−	0.0617108i	0.786011	−	0.618213i	$-0.212143\pi$
$347$	−15.5579	−	21.4136i	−0.0448355	−	0.0617108i	−0.830846	+	0.556502i	$0.812143\pi$
$348$		0			0
$349$	−89.5402	+	275.576i	−0.256562	+	0.789617i	0.736956	+	0.675941i	$0.236263\pi$
$349$	−89.5402	+	275.576i	−0.256562	+	0.789617i	−0.993518	+	0.113676i	$0.963737\pi$
$350$	171.867	−	80.0013i	0.491050	−	0.228575i
$351$		0			0
$352$	212.815	−	280.381i	0.604589	−	0.796538i
$353$	−217.033			−0.614825			−0.307413	−	0.951576i	$-0.599463\pi$
$353$	−217.033			−0.614825			−0.307413	+	0.951576i	$0.599463\pi$
$354$		0			0
$355$	69.9402	+	22.7249i	0.197015	+	0.0640139i
$356$	120.375	−	143.063i	0.338132	−	0.401862i
$357$		0			0
$358$	−22.1190	−	181.160i	−0.0617850	−	0.506035i
$359$	222.876	−	72.4169i	0.620825	−	0.201718i	0.0183184	−	0.999832i	$-0.494169\pi$
$359$	222.876	−	72.4169i	0.620825	−	0.201718i	0.602507	+	0.798114i	$0.294169\pi$
$360$		0			0
$361$	5.73832	+	4.16913i	0.0158956	+	0.0115488i
$362$	−34.9866	−	19.4244i	−0.0966480	−	0.0536586i
$363$		0			0
$364$	45.3229	−	28.2355i	0.124514	−	0.0775701i
$365$	−45.2903	−	32.9053i	−0.124083	−	0.0901516i
$366$		0			0
$367$	−269.892	+	87.6932i	−0.735400	+	0.238946i	−0.652687	−	0.757627i	$-0.726358\pi$
$367$	−269.892	+	87.6932i	−0.735400	+	0.238946i	−0.0827128	+	0.996573i	$0.526358\pi$
$368$	−236.563	+	41.0512i	−0.642834	+	0.111552i
$369$		0			0
$370$	−10.5086	+	53.8672i	−0.0284017	+	0.145587i
$371$	340.912	+	110.769i	0.918901	+	0.298569i
$372$		0			0
$373$	377.208			1.01128			0.505640	−	0.862744i	$-0.331256\pi$
$373$	377.208			1.01128			0.505640	+	0.862744i	$0.331256\pi$
$374$	−167.824	−	32.7550i	−0.448726	−	0.0875801i
$375$		0			0
$376$	−325.385	−	212.250i	−0.865387	−	0.564495i
$377$	−14.8668	+	45.7554i	−0.0394346	+	0.121367i
$378$		0			0
$379$	−237.957	−	327.520i	−0.627855	−	0.864168i	0.370040	−	0.929016i	$-0.379344\pi$
$379$	−237.957	−	327.520i	−0.627855	−	0.864168i	−0.997895	+	0.0648476i	$0.979344\pi$
$380$	−21.5812	+	53.2075i	−0.0567926	+	0.140020i
$381$		0			0
$382$	−299.525	−	321.638i	−0.784097	−	0.841985i
$383$	106.026	−	145.932i	0.276830	−	0.381023i	−0.647851	−	0.761767i	$-0.724332\pi$
$383$	106.026	−	145.932i	0.276830	−	0.381023i	0.924681	+	0.380744i	$0.124332\pi$
$384$		0			0
$385$	9.86607	−	30.3556i	0.0256262	−	0.0788457i
$386$	157.044	+	87.1900i	0.406849	+	0.225881i
$387$		0			0
$388$	416.588	−	103.267i	1.07368	−	0.266153i
$389$	−65.7531	−	202.367i	−0.169031	−	0.520224i	0.830280	−	0.557347i	$-0.188181\pi$
$389$	−65.7531	−	202.367i	−0.169031	−	0.520224i	−0.999311	+	0.0371228i	$0.988181\pi$
$390$		0			0
$391$	68.5545	+	94.3572i	0.175331	+	0.241323i
$392$	−253.821	+	96.8410i	−0.647504	+	0.247043i
$393$		0			0
$394$	−95.6664	−	205.521i	−0.242808	−	0.521627i
$395$		−	56.5975i		−	0.143285i
$396$		0			0
$397$	−510.883			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$397$	−510.883			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$398$	−232.475	+	108.213i	−0.584108	+	0.271892i
$399$		0			0
$400$	387.089	+	55.4728i	0.967722	+	0.138682i
$401$	−22.1925	+	16.1238i	−0.0553429	+	0.0402090i	−0.615113	−	0.788439i	$-0.710890\pi$
$401$	−22.1925	+	16.1238i	−0.0553429	+	0.0402090i	0.559770	+	0.828648i	$0.310890\pi$
$402$		0			0
$403$	182.110	−	59.1713i	0.451887	−	0.146827i
$404$	281.242	−	69.7166i	0.696144	−	0.172566i
$405$		0			0
$406$	−52.6247	+	94.7858i	−0.129617	+	0.233463i
$407$	−237.114	−	326.420i	−0.582590	−	0.802014i
$408$		0			0
$409$	−107.946	−	78.4274i	−0.263927	−	0.191754i	0.447950	−	0.894059i	$-0.352154\pi$
$409$	−107.946	−	78.4274i	−0.263927	−	0.191754i	−0.711876	+	0.702305i	$0.752154\pi$
$410$	−60.4360	+	56.2809i	−0.147405	+	0.137270i
$411$		0			0
$412$	31.5221	−	77.7164i	0.0765100	−	0.188632i
$413$	−251.721	+	182.886i	−0.609493	+	0.442822i
$414$		0			0
$415$	−46.9938	−	15.2692i	−0.113238	−	0.0367933i
$416$	110.124	+	2.29568i	0.264720	+	0.00551847i
$417$		0			0
$418$	−178.089	−	382.677i	−0.426049	−	0.915495i
$419$			302.402i			0.721723i	0.932619	+	0.360861i	$0.117517\pi$
$419$			302.402i			0.721723i	−0.932619	+	0.360861i	$0.882483\pi$
$420$		0			0
$421$	−32.1608	+	98.9806i	−0.0763914	+	0.235108i	−0.981959	−	0.189093i	$-0.939445\pi$
$421$	−32.1608	+	98.9806i	−0.0763914	+	0.235108i	0.905568	+	0.424202i	$0.139445\pi$
$422$	565.179	+	110.257i	1.33929	+	0.261273i
$423$		0			0
$424$	464.151	+	575.569i	1.09470	+	1.35747i
$425$	−58.6997	−	180.659i	−0.138117	−	0.425081i
$426$		0			0
$427$	177.210	−	243.908i	0.415011	−	0.571213i
$428$	−89.1354	+	55.5300i	−0.208260	+	0.129743i
$429$		0			0
$430$	31.2648	−	56.3131i	0.0727088	−	0.130961i
$431$	−197.345	+	271.622i	−0.457876	+	0.630213i	−0.974067	−	0.226261i	$-0.927350\pi$
$431$	−197.345	+	271.622i	−0.457876	+	0.630213i	0.516190	+	0.856474i	$0.327350\pi$
$432$		0			0
$433$	−197.554	−	608.008i	−0.456244	−	1.40418i	−0.869668	−	0.493637i	$-0.835667\pi$
$433$	−197.554	−	608.008i	−0.456244	−	1.40418i	0.413424	−	0.910539i	$-0.364333\pi$
$434$	428.318	−	52.2961i	0.986907	−	0.120498i
$435$		0			0
$436$	204.368	−	242.886i	0.468733	−	0.557079i
$437$	−88.9672	+	273.813i	−0.203586	+	0.626574i
$438$		0			0
$439$			419.823i			0.956317i	0.878273	+	0.478159i	$0.158696\pi$
$439$			419.823i			0.956317i	−0.878273	+	0.478159i	$0.841304\pi$
$440$	51.2550	−	41.3257i	0.116489	−	0.0939221i
$441$		0			0
$442$	−22.5798	−	48.5083i	−0.0510855	−	0.109747i
$443$	−238.218	−	77.4017i	−0.537738	−	0.174722i	0.0275424	−	0.999621i	$-0.491232\pi$
$443$	−238.218	−	77.4017i	−0.537738	−	0.174722i	−0.565280	+	0.824899i	$0.691232\pi$
$444$		0			0
$445$	28.2925	−	20.5557i	0.0635787	−	0.0461926i
$446$	37.2895	+	305.410i	0.0836087	+	0.684776i
$447$		0			0
$448$	242.578	+	52.5938i	0.541468	+	0.117397i
$449$	88.8032	+	64.5193i	0.197780	+	0.143695i	0.682268	−	0.731103i	$-0.260994\pi$
$449$	88.8032	+	64.5193i	0.197780	+	0.143695i	−0.484488	+	0.874798i	$0.660994\pi$
$450$		0			0
$451$	0.0531724	−	607.085i	0.000117899	−	1.34609i
$452$	48.1141	+	77.2316i	0.106447	+	0.170866i
$453$		0			0
$454$	−440.309	−	472.816i	−0.969844	−	1.04145i
$455$	9.49911	−	3.08645i	0.0208772	−	0.00678340i
$456$		0			0
$457$	−258.376	+	187.721i	−0.565375	+	0.410769i	−0.833422	−	0.552637i	$-0.813622\pi$
$457$	−258.376	+	187.721i	−0.565375	+	0.410769i	0.268047	+	0.963406i	$0.413622\pi$
$458$	109.191	−	559.715i	0.238409	−	1.22208i
$459$		0			0
$460$	−44.7955	−	3.19346i	−0.0973816	−	0.00694230i
$461$	635.144			1.37775			0.688876	−	0.724879i	$-0.258104\pi$
$461$	635.144			1.37775			0.688876	+	0.724879i	$0.258104\pi$
$462$		0			0
$463$			735.608i			1.58879i	0.607404	+	0.794393i	$0.292211\pi$
$463$			735.608i			1.58879i	−0.607404	+	0.794393i	$0.707789\pi$
$464$	−197.738	+	104.452i	−0.426160	+	0.225113i
$465$		0			0
$466$	−74.6865	+	382.843i	−0.160271	+	0.821551i
$467$	−172.418	−	237.313i	−0.369204	−	0.508166i	0.583480	−	0.812127i	$-0.301691\pi$
$467$	−172.418	−	237.313i	−0.369204	−	0.508166i	−0.952684	+	0.303962i	$0.901691\pi$
$468$		0			0
$469$	−69.1969	−	212.966i	−0.147541	−	0.454085i
$470$	−49.5217	−	53.1778i	−0.105365	−	0.113144i
$471$		0			0
$472$	−640.996	+	32.2859i	−1.35804	+	0.0684023i
$473$	146.277	+	450.327i	0.309253	+	0.952066i
$474$		0			0
$475$	275.615	−	379.351i	0.580242	−	0.798634i
$476$	−29.0109	−	117.032i	−0.0609472	−	0.245866i
$477$		0			0
$478$	−51.2244	−	419.541i	−0.107164	−	0.877700i
$479$	−59.1076	−	81.3546i	−0.123398	−	0.169843i	0.742849	−	0.669459i	$-0.233474\pi$
$479$	−59.1076	−	81.3546i	−0.123398	−	0.169843i	−0.866247	+	0.499617i	$0.833474\pi$
$480$		0			0
$481$	39.0126	−	120.069i	0.0811074	−	0.249623i
$482$	−277.076	−	595.245i	−0.574847	−	1.23495i
$483$		0			0
$484$	−34.5014	+	482.769i	−0.0712839	+	0.997456i
$485$	80.2792			0.165524
$486$		0			0
$487$	−113.789	−	36.9723i	−0.233653	−	0.0759186i	0.189850	−	0.981813i	$-0.439200\pi$
$487$	−113.789	−	36.9723i	−0.233653	−	0.0759186i	−0.423503	+	0.905895i	$0.639200\pi$
$488$	581.036	−	221.684i	1.19065	−	0.454270i
$489$		0			0
$490$	−50.4396	+	6.15849i	−0.102938	+	0.0125684i
$491$	−265.485	+	86.2615i	−0.540704	+	0.175685i	−0.566621	−	0.823979i	$-0.691749\pi$
$491$	−265.485	+	86.2615i	−0.540704	+	0.175685i	0.0259170	+	0.999664i	$0.491749\pi$
$492$		0			0
$493$	87.8857	+	63.8527i	0.178267	+	0.129519i
$494$	64.1114	−	115.475i	0.129780	−	0.233756i
$495$		0			0
$496$	798.928	+	392.349i	1.61074	+	0.791026i
$497$	−308.402	−	224.067i	−0.620527	−	0.450839i
$498$		0			0
$499$	160.821	−	52.2540i	0.322287	−	0.104717i	−0.143405	−	0.989664i	$-0.545805\pi$
$499$	160.821	−	52.2540i	0.322287	−	0.104717i	0.465693	+	0.884947i	$0.345805\pi$
$500$	137.112	+	55.6131i	0.274223	+	0.111226i
$501$		0			0
$502$	164.668	+	32.1242i	0.328025	+	0.0639924i
$503$	−591.543	−	192.204i	−1.17603	−	0.382115i	−0.345139	−	0.938552i	$-0.612168\pi$
$503$	−591.543	−	192.204i	−1.17603	−	0.382115i	−0.830890	+	0.556436i	$0.812168\pi$
$504$		0			0
$505$	54.1971			0.107321
$506$	241.618	−	224.967i	0.477505	−	0.444598i
$507$		0			0
$508$	354.306	+	25.2583i	0.697453	+	0.0497212i
$509$	−97.9151	+	301.352i	−0.192367	+	0.592046i	0.807630	+	0.589690i	$0.200750\pi$
$509$	−97.9151	+	301.352i	−0.192367	+	0.592046i	−0.999997	+	0.00235633i	$0.999250\pi$
$510$		0			0
$511$	170.571	+	234.771i	0.333798	+	0.459434i
$512$	359.823	+	364.241i	0.702779	+	0.711408i
$513$		0			0
$514$	236.984	−	220.691i	0.461059	−	0.429360i
$515$	9.22042	−	12.6908i	0.0179037	−	0.0246424i
$516$		0			0
$517$	534.176	+	0.0467866i	1.03322	+	9.04962e-5i
$518$	138.094	−	248.731i	0.266591	−	0.480176i
$519$		0			0
$520$	19.8897	+	5.37280i	0.0382493	+	0.0103323i
$521$	108.271	+	333.223i	0.207814	+	0.639584i	0.999586	+	0.0287683i	$0.00915850\pi$
$521$	108.271	+	333.223i	0.207814	+	0.639584i	−0.791773	+	0.610816i	$0.790842\pi$
$522$		0			0
$523$	−397.190	−	546.685i	−0.759445	−	1.04529i	−0.997260	−	0.0739759i	$-0.976431\pi$
$523$	−397.190	−	546.685i	−0.759445	−	1.04529i	0.237815	−	0.971310i	$-0.423569\pi$
$524$	522.320	+	439.487i	0.996794	+	0.838716i
$525$		0			0
$526$	723.939	−	336.981i	1.37631	−	0.640648i
$527$		−	432.367i		−	0.820431i
$528$		0			0
$529$	303.816			0.574321
$530$	58.3638	+	125.383i	0.110120	+	0.236573i
$531$		0			0
$532$	191.625	−	227.742i	0.360198	−	0.428087i
$533$	153.688	−	111.661i	0.288345	−	0.209495i
$534$		0			0
$535$	−18.6816	+	6.07003i	−0.0349190	+	0.0113459i
$536$	120.456	−	445.917i	0.224731	−	0.831936i
$537$		0			0
$538$	111.543	+	61.9281i	0.207329	+	0.115108i
$539$	219.590	−	302.184i	0.407402	−	0.560638i
$540$		0			0
$541$	−307.422	−	223.355i	−0.568247	−	0.412856i	0.266221	−	0.963912i	$-0.414225\pi$
$541$	−307.422	−	223.355i	−0.568247	−	0.412856i	−0.834468	+	0.551056i	$0.814225\pi$
$542$	232.794	+	249.981i	0.429510	+	0.461220i
$543$		0			0
$544$	81.7698	−	234.887i	0.150312	−	0.431778i
$545$	48.0339	−	34.8987i	0.0881357	−	0.0640343i
$546$		0			0
$547$	222.878	+	72.4175i	0.407455	+	0.132390i	0.505571	−	0.862785i	$-0.331282\pi$
$547$	222.878	+	72.4175i	0.407455	+	0.132390i	−0.0981162	+	0.995175i	$0.531282\pi$
$548$	−25.3630	+	355.774i	−0.0462829	+	0.649223i
$549$		0			0
$550$	−487.482	+	226.862i	−0.886331	+	0.412477i
$551$			268.158i			0.486675i
$552$		0			0
$553$	−90.6606	+	279.025i	−0.163943	+	0.504566i
$554$	−123.963	+	635.436i	−0.223761	+	1.14700i
$555$		0			0
$556$	−269.341	+	664.049i	−0.484427	+	1.19433i
$557$	15.6464	+	48.1548i	0.0280906	+	0.0864539i	0.964119	−	0.265471i	$-0.0855274\pi$
$557$	15.6464	+	48.1548i	0.0280906	+	0.0864539i	−0.936028	+	0.351925i	$0.885527\pi$
$558$		0			0
$559$	−87.0884	+	119.867i	−0.155793	+	0.214431i
$560$	41.6731	+	20.4654i	0.0744163	+	0.0365454i
$561$		0			0
$562$	−668.717	−	371.269i	−1.18989	−	0.660621i
$563$	−306.745	+	422.198i	−0.544840	+	0.749908i	−0.989301	−	0.145890i	$-0.953395\pi$
$563$	−306.745	+	422.198i	−0.544840	+	0.749908i	0.444460	+	0.895798i	$0.353395\pi$
$564$		0			0
$565$	5.25940	+	16.1868i	0.00930866	+	0.0286491i
$566$	−106.855	−	875.173i	−0.188791	−	1.54624i
$567$		0			0
$568$	−280.301	−	734.672i	−0.493488	−	1.29344i
$569$	−87.5395	+	269.419i	−0.153848	+	0.473495i	−0.998042	−	0.0625419i	$-0.980079\pi$
$569$	−87.5395	+	269.419i	−0.153848	+	0.473495i	0.844194	+	0.536037i	$0.180079\pi$
$570$		0			0
$571$		−	187.846i		−	0.328977i	−0.986379	−	0.164488i	$-0.947403\pi$
$571$		−	187.846i		−	0.328977i	0.986379	−	0.164488i	$-0.0525973\pi$
$572$	−128.555	+	80.0723i	−0.224746	+	0.139986i
$573$		0			0
$574$	388.102	−	180.655i	0.676135	−	0.314729i
$575$	348.803	+	113.333i	0.606614	+	0.197101i
$576$		0			0
$577$	−762.773	+	554.187i	−1.32196	+	0.960463i	−0.322058	+	0.946720i	$0.604374\pi$
$577$	−762.773	+	554.187i	−1.32196	+	0.960463i	−0.999906	+	0.0137424i	$0.995626\pi$
$578$	453.813	−	55.4089i	0.785144	−	0.0958632i
$579$		0			0
$580$	−40.6003	+	10.0643i	−0.0700005	+	0.0173523i
$581$	207.220	+	150.554i	0.356661	+	0.259129i
$582$		0			0
$583$	−966.891	−	314.256i	−1.65848	−	0.539032i
$584$	30.1119	+	597.834i	0.0515615	+	1.02369i
$585$		0			0
$586$	765.140	−	712.535i	1.30570	−	1.21593i
$587$	−29.3693	+	9.54266i	−0.0500329	+	0.0162567i	−0.333927	−	0.942599i	$-0.608374\pi$
$587$	−29.3693	+	9.54266i	−0.0500329	+	0.0162567i	0.283894	+	0.958856i	$0.408374\pi$
$588$		0			0
$589$	863.456	−	627.337i	1.46597	−	1.06509i
$590$	−117.826	−	22.9860i	−0.199705	−	0.0389593i
$591$		0			0
$592$	518.893	−	274.098i	0.876508	−	0.463003i
$593$	313.027			0.527870			0.263935	−	0.964540i	$-0.414980\pi$
$593$	313.027			0.527870			0.263935	+	0.964540i	$0.414980\pi$
$594$		0			0
$595$		−	22.5528i		−	0.0379039i
$596$	33.6975	−	472.684i	0.0565394	−	0.793094i
$597$		0			0
$598$	101.394	+	19.7804i	0.169555	+	0.0330776i
$599$	−533.190	−	733.872i	−0.890133	−	1.22516i	−0.973510	−	0.228645i	$-0.926571\pi$
$599$	−533.190	−	733.872i	−0.890133	−	1.22516i	0.0833771	−	0.996518i	$-0.473429\pi$
$600$		0			0
$601$	320.006	+	984.877i	0.532456	+	1.63873i	0.749083	+	0.662477i	$0.230495\pi$
$601$	320.006	+	984.877i	0.532456	+	1.63873i	−0.216627	+	0.976255i	$0.569505\pi$
$602$	−244.340	+	227.541i	−0.405880	+	0.377975i
$603$		0			0
$604$	−493.074	+	307.178i	−0.816347	+	0.508572i
$605$	−27.9904	+	86.0941i	−0.0462650	+	0.142304i
$606$		0			0
$607$	−290.604	+	399.983i	−0.478755	+	0.658950i	−0.978265	−	0.207358i	$-0.933513\pi$
$607$	−290.604	+	399.983i	−0.478755	+	0.658950i	0.499510	+	0.866308i	$0.333513\pi$
$608$	587.723	−	177.508i	0.966649	−	0.291955i
$609$		0			0
$610$	115.464	−	14.0977i	0.189285	−	0.0231110i
$611$	98.2505	+	135.230i	0.160803	+	0.221326i
$612$		0			0
$613$	−252.174	+	776.112i	−0.411377	+	1.26609i	0.504075	+	0.863660i	$0.331834\pi$
$613$	−252.174	+	776.112i	−0.411377	+	1.26609i	−0.915452	+	0.402428i	$0.868166\pi$
$614$	−957.509	+	445.704i	−1.55946	+	0.725902i
$615$		0			0
$616$	−318.884	+	121.632i	−0.517669	+	0.197455i
$617$	−965.796			−1.56531			−0.782654	−	0.622457i	$-0.786135\pi$
$617$	−965.796			−1.56531			−0.782654	+	0.622457i	$0.786135\pi$
$618$		0			0
$619$	−1.84967	−	0.600994i	−0.00298816	−	0.000970911i	0.307523	−	0.951541i	$-0.400500\pi$
$619$	−1.84967	−	0.600994i	−0.00298816	−	0.000970911i	−0.310511	+	0.950570i	$0.600500\pi$
$620$	127.388	+	107.186i	0.205465	+	0.172881i
$621$		0			0
$622$	77.2870	+	633.000i	0.124256	+	1.01769i
$623$	−172.409	+	56.0190i	−0.276740	+	0.0899182i
$624$		0			0
$625$	−471.924	−	342.873i	−0.755079	−	0.548597i
$626$	−563.716	−	312.973i	−0.900504	−	0.499956i
$627$		0			0
$628$	187.743	+	301.360i	0.298953	+	0.479872i
$629$	−230.624	−	167.558i	−0.366652	−	0.266388i
$630$		0			0
$631$	−408.093	+	132.598i	−0.646740	+	0.210139i	−0.613976	−	0.789324i	$-0.710431\pi$
$631$	−408.093	+	132.598i	−0.646740	+	0.210139i	−0.0327641	+	0.999463i	$0.510431\pi$
$632$	−471.083	+	379.891i	−0.745384	+	0.601094i
$633$		0			0
$634$	−138.833	+	711.657i	−0.218979	+	1.12249i
$635$	63.1877	+	20.5309i	0.0995081	+	0.0323322i
$636$		0			0
$637$	116.889			0.183499
$638$	149.281	−	268.825i	0.233983	−	0.421355i
$639$		0			0
$640$	48.9336	+	82.3216i	0.0764587	+	0.128628i
$641$	86.8750	−	267.374i	0.135530	−	0.417120i	−0.860142	−	0.510055i	$-0.829625\pi$
$641$	86.8750	−	267.374i	0.135530	−	0.417120i	0.995672	+	0.0929354i	$0.0296250\pi$
$642$		0			0
$643$	367.425	+	505.717i	0.571422	+	0.786495i	0.992722	−	0.120426i	$-0.0384260\pi$
$643$	367.425	+	505.717i	0.571422	+	0.786495i	−0.421300	+	0.906921i	$0.638426\pi$
$644$	215.726	+	87.4993i	0.334978	+	0.135869i
$645$		0			0
$646$	−203.247	−	218.253i	−0.314624	−	0.337852i
$647$	4.40525	−	6.06331i	0.00680874	−	0.00937142i	−0.805599	−	0.592461i	$-0.798156\pi$
$647$	4.40525	−	6.06331i	0.00680874	−	0.00937142i	0.812408	+	0.583090i	$0.198156\pi$
$648$		0			0
$649$	713.992	−	518.650i	1.10014	−	0.799153i
$650$	−147.101	−	81.6699i	−0.226309	−	0.125646i
$651$		0			0
$652$	−21.8728	−	88.2366i	−0.0335473	−	0.135332i
$653$	−338.138	−	1040.68i	−0.517823	−	1.59369i	−0.778087	−	0.628157i	$-0.783810\pi$
$653$	−338.138	−	1040.68i	−0.517823	−	1.59369i	0.260264	−	0.965538i	$-0.416190\pi$
$654$		0			0
$655$	75.0487	+	103.296i	0.114578	+	0.157703i
$656$	874.103	+	125.266i	1.33247	+	0.190954i
$657$		0			0
$658$	158.958	+	341.492i	0.241578	+	0.518984i
$659$		−	690.561i		−	1.04789i	−0.851752	−	0.523946i	$-0.824459\pi$
$659$		−	690.561i		−	1.04789i	0.851752	−	0.523946i	$-0.175541\pi$
$660$		0			0
$661$	−981.006			−1.48412			−0.742062	−	0.670331i	$-0.766152\pi$
$661$	−981.006			−1.48412			−0.742062	+	0.670331i	$0.766152\pi$
$662$	159.621	−	74.3008i	0.241119	−	0.112237i
$663$		0			0
$664$	188.338	+	493.637i	0.283642	+	0.743429i
$665$	45.0390	−	32.7227i	0.0677278	−	0.0492071i
$666$		0			0
$667$	−199.474	+	64.8132i	−0.299062	+	0.0971711i
$668$	−288.140	−	1162.38i	−0.431347	−	1.74009i
$669$		0			0
$670$	41.9370	−	75.5355i	0.0625925	−	0.112739i
$671$	−502.674	+	691.744i	−0.749142	+	1.03092i
$672$		0			0
$673$	173.221	+	125.852i	0.257386	+	0.187002i	0.708994	−	0.705214i	$-0.249149\pi$
$673$	173.221	+	125.852i	0.257386	+	0.187002i	−0.451608	+	0.892217i	$0.649149\pi$
$674$	−16.9569	+	15.7911i	−0.0251586	+	0.0234289i
$675$		0			0
$676$	582.515	+	236.271i	0.861708	+	0.349513i
$677$	−909.036	+	660.454i	−1.34274	+	0.975559i	−0.343404	+	0.939188i	$0.611580\pi$
$677$	−909.036	+	660.454i	−1.34274	+	0.975559i	−0.999338	+	0.0363712i	$0.988420\pi$
$678$		0			0
$679$	−395.775	−	128.595i	−0.582879	−	0.189389i
$680$	25.4162	−	38.9638i	0.0373768	−	0.0572998i
$681$		0			0
$682$	−1214.84	+	148.219i	−1.78129	+	0.217330i
$683$		−	87.6213i		−	0.128289i	−0.997941	−	0.0641445i	$-0.979568\pi$
$683$		−	87.6213i		−	0.128289i	0.997941	−	0.0641445i	$-0.0204318\pi$
$684$		0			0
$685$	−20.6160	+	63.4495i	−0.0300963	+	0.0926270i
$686$	631.576	+	123.210i	0.920665	+	0.179607i
$687$		0			0
$688$	−678.570	+	117.753i	−0.986293	+	0.171153i
$689$	−98.3100	−	302.567i	−0.142685	−	0.439140i
$690$		0			0
$691$	316.481	−	435.598i	0.458004	−	0.630388i	−0.516090	−	0.856535i	$-0.672613\pi$
$691$	316.481	−	435.598i	0.458004	−	0.630388i	0.974093	+	0.226147i	$0.0726129\pi$
$692$	99.5389	+	159.777i	0.143842	+	0.230892i
$693$		0			0
$694$	−25.6960	+	46.2827i	−0.0370259	+	0.0666898i
$695$	−78.7840	+	108.437i	−0.113358	+	0.156024i
$696$		0			0
$697$	−132.553	−	407.955i	−0.190176	−	0.585301i
$698$	575.244	−	70.2352i	0.824132	−	0.100624i
$699$		0			0
$700$	−290.115	−	244.106i	−0.414450	−	0.348723i
$701$	−253.827	+	781.200i	−0.362093	+	1.11441i	0.589688	+	0.807631i	$0.299251\pi$
$701$	−253.827	+	781.200i	−0.362093	+	1.11441i	−0.951781	+	0.306777i	$0.900749\pi$
$702$		0			0
$703$		−	703.683i		−	1.00097i
$704$	−688.002	−	149.230i	−0.977275	−	0.211975i
$705$		0			0
$706$	183.178	+	393.522i	0.259459	+	0.557397i
$707$	−267.191	−	86.8156i	−0.377922	−	0.122794i
$708$		0			0
$709$	−574.514	+	417.409i	−0.810315	+	0.588729i	−0.913922	−	0.405890i	$-0.866962\pi$
$709$	−574.514	+	417.409i	−0.810315	+	0.588729i	0.103607	+	0.994618i	$0.466962\pi$
$710$	−17.8254	−	145.995i	−0.0251062	−	0.205626i
$711$		0			0
$712$	−360.997	−	97.5163i	−0.507018	−	0.136961i
$713$	675.352	+	490.672i	0.947198	+	0.688180i
$714$		0			0
$715$	−26.9428	+	8.75163i	−0.0376822	+	0.0122400i
$716$	−309.809	+	193.007i	−0.432695	+	0.269562i
$717$		0			0
$718$	−319.415	−	342.996i	−0.444867	−	0.477710i
$719$	−878.206	+	285.347i	−1.22143	+	0.396866i	−0.847602	−	0.530633i	$-0.821954\pi$
$719$	−878.206	+	285.347i	−1.22143	+	0.396866i	−0.373826	+	0.927499i	$0.621954\pi$
$720$		0			0
$721$	−65.7852	+	47.7958i	−0.0912417	+	0.0662909i
$722$	2.71624	−	13.9234i	0.00376210	−	0.0192845i
$723$		0			0
$724$	−5.69117	+	79.8316i	−0.00786073	+	0.110265i
$725$	341.599			0.471172
$726$		0			0
$727$			824.285i			1.13382i	0.823781	+	0.566909i	$0.191861\pi$
$727$			824.285i			1.13382i	−0.823781	+	0.566909i	$0.808139\pi$
$728$	−89.4492	−	58.3480i	−0.122870	−	0.0801484i
$729$		0			0
$730$	−21.4382	+	109.892i	−0.0293674	+	0.150537i
$731$	196.646	+	270.659i	0.269009	+	0.370259i
$732$		0			0
$733$	−0.267616	−	0.823639i	−0.000365098	−	0.00112365i	0.950874	−	0.309579i	$-0.100188\pi$
$733$	−0.267616	−	0.823639i	−0.000365098	−	0.00112365i	−0.951239	+	0.308455i	$0.900188\pi$
$734$	386.795	+	415.351i	0.526968	+	0.565873i
$735$		0			0
$736$	274.094	+	394.285i	0.372411	+	0.535714i
$737$	196.208	+	604.046i	0.266225	+	0.819601i
$738$		0			0
$739$	247.106	−	340.112i	0.334378	−	0.460232i	−0.608411	−	0.793622i	$-0.708193\pi$
$739$	247.106	−	340.112i	0.334378	−	0.460232i	0.942789	+	0.333390i	$0.108193\pi$
$740$	106.541	−	26.4102i	0.143974	−	0.0356894i
$741$		0			0
$742$	−86.8872	−	711.628i	−0.117099	−	0.959068i
$743$	814.385	+	1120.90i	1.09608	+	1.50862i	0.840485	+	0.541835i	$0.182270\pi$
$743$	814.385	+	1120.90i	1.09608	+	1.50862i	0.255591	+	0.966785i	$0.417730\pi$
$744$		0			0
$745$	27.3905	−	84.2994i	0.0367658	−	0.113154i
$746$	−318.366	−	683.948i	−0.426764	−	0.916821i
$747$		0			0
$748$	82.2535	+	331.941i	0.109965	+	0.443772i
$749$	101.823			0.135946
$750$		0			0
$751$	1243.83	+	404.146i	1.65624	+	0.538144i	0.980078	−	0.198612i	$-0.0636434\pi$
$751$	1243.83	+	404.146i	1.65624	+	0.538144i	0.676159	+	0.736756i	$0.263643\pi$
$752$	−110.222	+	769.126i	−0.146571	+	1.02277i
$753$		0			0
$754$	95.5110	−	11.6615i	0.126672	−	0.0154662i
$755$	−103.342	+	33.5778i	−0.136877	+	0.0444740i
$756$		0			0
$757$	27.1049	+	19.6929i	0.0358057	+	0.0260143i	0.605544	−	0.795812i	$-0.292956\pi$
$757$	27.1049	+	19.6929i	0.0358057	+	0.0260143i	−0.569738	+	0.821826i	$0.692956\pi$
$758$	−393.017	+	707.890i	−0.518493	+	0.933892i
$759$		0			0
$760$	114.690	−	5.77674i	0.150908	−	0.00760097i
$761$	53.4377	+	38.8247i	0.0702203	+	0.0510181i	0.622342	−	0.782746i	$-0.286181\pi$
$761$	53.4377	+	38.8247i	0.0702203	+	0.0510181i	−0.552121	+	0.833764i	$0.686181\pi$
$762$		0			0
$763$	−292.709	+	95.1069i	−0.383629	+	0.124649i
$764$	−330.389	+	814.560i	−0.432447	+	1.06618i
$765$		0			0
$766$	−354.089	−	69.0771i	−0.462257	−	0.0901789i
$767$	262.631	+	85.3341i	0.342414	+	0.111257i
$768$		0			0
$769$	1115.14			1.45012			0.725062	−	0.688684i	$-0.241811\pi$
$769$	1115.14			1.45012			0.725062	+	0.688684i	$0.241811\pi$
$770$	−63.3674	+	7.73130i	−0.0822954	+	0.0100407i
$771$		0			0
$772$	25.5458	−	358.339i	0.0330905	−	0.464170i
$773$	52.6568	−	162.061i	0.0681200	−	0.209652i	−0.911202	−	0.411960i	$-0.864844\pi$
$773$	52.6568	−	162.061i	0.0681200	−	0.209652i	0.979322	+	0.202308i	$0.0648443\pi$
$774$		0			0
$775$	−799.149	−	1099.93i	−1.03116	−	1.41927i
$776$	−538.847	−	668.195i	−0.694390	−	0.861075i
$777$		0			0
$778$	−311.434	+	290.022i	−0.400301	+	0.372779i
$779$	622.378	−	856.630i	0.798945	−	1.09965i
$780$		0			0
$781$	874.655	+	635.591i	1.11992	+	0.813817i
$782$	113.227	−	203.940i	0.144791	−	0.260793i
$783$		0			0
$784$	389.818	+	378.492i	0.497217	+	0.482770i
$785$	20.5223	+	63.1611i	0.0261431	+	0.0804601i
$786$		0			0
$787$	306.107	+	421.320i	0.388954	+	0.535350i	0.957929	−	0.287005i	$-0.0926598\pi$
$787$	306.107	+	421.320i	0.388954	+	0.535350i	−0.568975	+	0.822355i	$0.692660\pi$
$788$	−291.905	+	346.922i	−0.370438	+	0.440257i
$789$		0			0
$790$	−102.622	+	47.7687i	−0.129901	+	0.0604667i
$791$		−	88.2252i		−	0.111536i
$792$		0			0
$793$	−267.576			−0.337423
$794$	431.189	+	926.327i	0.543059	+	1.16666i
$795$		0			0
$796$	392.421	+	330.189i	0.492992	+	0.414810i
$797$	332.100	−	241.285i	0.416688	−	0.302742i	−0.359616	−	0.933100i	$-0.617092\pi$
$797$	332.100	−	241.285i	0.416688	−	0.302742i	0.776304	+	0.630359i	$0.217092\pi$
$798$		0			0
$799$	358.960	−	116.633i	0.449262	−	0.145974i
$800$	−226.123	−	748.685i	−0.282654	−	0.935856i
$801$		0			0
$802$	47.9662	+	26.6306i	0.0598082	+	0.0332052i
$803$	−483.727	−	665.915i	−0.602399	−	0.829284i
$804$		0			0
$805$	35.2272	+	25.5941i	0.0437606	+	0.0317939i
$806$	−260.991	−	280.259i	−0.323810	−	0.347716i
$807$		0			0
$808$	−363.780	−	451.104i	−0.450222	−	0.558297i
$809$	1064.09	−	773.105i	1.31531	−	0.955630i	0.315334	−	0.948981i	$-0.397883\pi$
$809$	1064.09	−	773.105i	1.31531	−	0.955630i	0.999978	−	0.00664931i	$-0.00211656\pi$
$810$		0			0
$811$	−967.742	−	314.438i	−1.19327	−	0.387717i	−0.355989	−	0.934490i	$-0.615856\pi$
$811$	−967.742	−	314.438i	−1.19327	−	0.387717i	−0.837281	+	0.546773i	$0.815856\pi$
$812$	216.280	+	15.4185i	0.266355	+	0.0189883i
$813$		0			0
$814$	−391.734	+	705.433i	−0.481246	+	0.866625i
$815$		−	17.0038i		−	0.0208635i
$816$		0			0
$817$	−255.198	+	785.420i	−0.312360	+	0.961347i
$818$	−51.0964	+	261.920i	−0.0624650	+	0.320195i
$819$		0			0
$820$	153.056	+	62.0803i	0.186654	+	0.0757077i
$821$	−1.01822	−	3.13376i	−0.00124022	−	0.00381700i	0.950434	−	0.310925i	$-0.100639\pi$
$821$	−1.01822	−	3.13376i	−0.00124022	−	0.00381700i	−0.951675	+	0.307108i	$0.900639\pi$
$822$		0			0
$823$	−686.883	+	945.413i	−0.834608	+	1.14874i	0.152440	+	0.988313i	$0.451287\pi$
$823$	−686.883	+	945.413i	−0.834608	+	1.14874i	−0.987048	+	0.160427i	$0.948713\pi$
$824$	−167.519	+	8.43767i	−0.203300	+	0.0102399i
$825$		0			0
$826$	544.060	+	302.060i	0.658668	+	0.365690i
$827$	629.832	−	866.889i	0.761586	−	1.04823i	−0.235494	−	0.971876i	$-0.575671\pi$
$827$	629.832	−	866.889i	0.761586	−	1.04823i	0.997080	−	0.0763576i	$-0.0243291\pi$
$828$		0			0
$829$	74.0327	+	227.849i	0.0893036	+	0.274848i	0.985727	−	0.168350i	$-0.0538438\pi$
$829$	74.0327	+	227.849i	0.0893036	+	0.274848i	−0.896424	+	0.443198i	$0.853844\pi$
$830$	11.9772	+	98.0960i	0.0144303	+	0.118188i
$831$		0			0
$832$	−88.7826	−	201.612i	−0.106710	−	0.242323i
$833$	81.5604	−	251.017i	0.0979117	−	0.301341i
$834$		0			0
$835$		−	223.998i		−	0.268261i
$836$	−543.557	+	645.890i	−0.650188	+	0.772596i
$837$		0			0
$838$	548.311	−	255.229i	0.654309	−	0.304570i
$839$	826.516	+	268.551i	0.985120	+	0.320085i	0.756904	−	0.653526i	$-0.226711\pi$
$839$	826.516	+	268.551i	0.985120	+	0.320085i	0.228216	+	0.973611i	$0.426711\pi$
$840$		0			0
$841$	522.338	−	379.501i	0.621092	−	0.451249i
$842$	206.614	−	25.2269i	0.245385	−	0.0299607i
$843$		0			0
$844$	−277.098	−	1117.83i	−0.328315	−	1.32445i
$845$	95.1226	+	69.1106i	0.112571	+	0.0817877i
$846$		0			0
$847$	275.902	−	379.606i	0.325740	−	0.448177i
$848$	651.868	−	1327.38i	0.768712	−	1.56530i
$849$		0			0
$850$	−278.026	+	258.911i	−0.327090	+	0.304602i
$851$	523.448	−	170.079i	0.615098	−	0.199857i
$852$		0			0
$853$	1053.49	−	765.403i	1.23504	−	0.897307i	0.237780	−	0.971319i	$-0.423580\pi$
$853$	1053.49	−	765.403i	1.23504	−	0.897307i	0.997257	+	0.0740115i	$0.0235802\pi$
$854$	−591.817	−	115.454i	−0.692995	−	0.135192i
$855$		0			0
$856$	175.917	+	114.751i	0.205511	+	0.134055i
$857$	−676.267			−0.789110			−0.394555	−	0.918872i	$-0.629101\pi$
$857$	−676.267			−0.789110			−0.394555	+	0.918872i	$0.629101\pi$
$858$		0			0
$859$			745.506i			0.867877i	0.900943	+	0.433938i	$0.142876\pi$
$859$			745.506i			0.867877i	−0.900943	+	0.433938i	$0.857124\pi$
$860$	−128.494	−	9.16028i	−0.149412	−	0.0106515i
$861$		0			0
$862$	659.062	+	128.572i	0.764573	+	0.149156i
$863$	783.896	+	1078.94i	0.908338	+	1.25022i	0.967731	+	0.251986i	$0.0810836\pi$
$863$	783.896	+	1078.94i	0.908338	+	1.25022i	−0.0593926	+	0.998235i	$0.518916\pi$
$864$		0			0
$865$	10.8807	+	33.4873i	0.0125788	+	0.0387136i
$866$	−935.696	+	871.365i	−1.08048	+	1.00620i
$867$		0			0
$868$	−456.326	−	732.483i	−0.525721	−	0.843874i
$869$	257.207	−	791.366i	0.295981	−	0.910663i
$870$		0			0
$871$	−116.816	+	160.783i	−0.134117	+	0.184596i
$872$	−612.887	−	165.559i	−0.702852	−	0.189862i
$873$		0			0
$874$	571.563	−	69.7858i	0.653963	−	0.0798465i
$875$	−84.3240	−	116.062i	−0.0963703	−	0.132642i
$876$		0			0
$877$	−122.743	+	377.764i	−0.139958	+	0.430746i	−0.996328	−	0.0856163i	$-0.972714\pi$
$877$	−122.743	+	377.764i	−0.139958	+	0.430746i	0.856370	+	0.516362i	$0.172714\pi$
$878$	761.219	−	354.334i	0.866992	−	0.403569i
$879$		0			0
$880$	−118.191	−	58.0558i	−0.134308	−	0.0659725i
$881$	−473.383			−0.537325			−0.268662	−	0.963234i	$-0.586582\pi$
$881$	−473.383			−0.537325			−0.268662	+	0.963234i	$0.586582\pi$
$882$		0			0
$883$	1305.74	+	424.260i	1.47875	+	0.480475i	0.933739	−	0.357954i	$-0.116525\pi$
$883$	1305.74	+	424.260i	1.47875	+	0.480475i	0.545011	+	0.838429i	$0.316525\pi$
$884$	−68.8972	+	81.8827i	−0.0779380	+	0.0926275i
$885$		0			0
$886$	60.7138	+	497.261i	0.0685257	+	0.561243i
$887$	266.937	−	86.7330i	0.300943	−	0.0977824i	−0.154653	−	0.987969i	$-0.549426\pi$
$887$	266.937	−	86.7330i	0.300943	−	0.0977824i	0.455597	+	0.890186i	$0.349426\pi$
$888$		0			0
$889$	−278.627	−	202.434i	−0.313416	−	0.227710i
$890$	−61.1505	−	33.9505i	−0.0687084	−	0.0381466i
$891$		0			0
$892$	522.294	−	325.381i	0.585531	−	0.364777i
$893$	753.751	+	547.632i	0.844066	+	0.613250i
$894$		0			0
$895$	−64.9321	+	21.0977i	−0.0725498	+	0.0235729i
$896$	−109.375	−	484.228i	−0.122070	−	0.540433i
$897$		0			0
$898$	42.0351	−	215.472i	0.0468097	−	0.239946i
$899$	739.472	+	240.269i	0.822550	+	0.267263i
$900$		0			0
$901$	−718.356			−0.797287
$902$	−1100.80	+	512.288i	−1.22040	+	0.567947i
$903$		0			0
$904$	99.4267	−	152.424i	0.109985	−	0.168611i
$905$	−4.62599	+	14.2373i	−0.00511159	+	0.0157319i
$906$		0			0
$907$	286.376	+	394.163i	0.315740	+	0.434578i	0.937160	−	0.348899i	$-0.113444\pi$
$907$	286.376	+	394.163i	0.315740	+	0.434578i	−0.621421	+	0.783477i	$0.713444\pi$
$908$	−485.680	+	1197.42i	−0.534890	+	1.31875i
$909$		0			0
$910$	−13.6136	−	14.6187i	−0.0149600	−	0.0160645i
$911$	−627.748	+	864.021i	−0.689076	+	0.948431i	−0.999998	−	0.00200421i	$-0.999362\pi$
$911$	−627.748	+	864.021i	−0.689076	+	0.948431i	0.310922	+	0.950435i	$0.399362\pi$
$912$		0			0
$913$	−587.693	−	427.063i	−0.643695	−	0.467758i
$914$	558.446	+	310.047i	0.610991	+	0.339219i
$915$		0			0
$916$	−1107.03	+	274.419i	−1.20854	+	0.299584i
$917$	−204.525	−	629.462i	−0.223037	−	0.686436i
$918$		0			0
$919$	170.812	+	235.102i	0.185867	+	0.255824i	0.891774	−	0.452480i	$-0.149461\pi$
$919$	170.812	+	235.102i	0.185867	+	0.255824i	−0.705908	+	0.708304i	$0.749461\pi$
$920$	32.0174	+	83.9180i	0.0348015	+	0.0912152i
$921$		0			0
$922$	−536.066	−	1151.64i	−0.581417	−	1.24906i
$923$			338.328i			0.366553i
$924$		0			0
$925$	−896.403			−0.969085
$926$	1333.80	−	620.859i	1.44038	−	0.670474i
$927$		0			0
$928$	356.285	+	270.378i	0.383927	+	0.291356i
$929$	−139.029	+	101.011i	−0.149655	+	0.108731i	−0.660093	−	0.751184i	$-0.729483\pi$
$929$	−139.029	+	101.011i	−0.149655	+	0.108731i	0.510438	+	0.859914i	$0.329483\pi$
$930$		0			0
$931$	619.632	−	201.331i	0.665555	−	0.216252i
$932$	757.202	−	187.701i	0.812448	−	0.201396i
$933$		0			0
$934$	−284.772	+	512.921i	−0.304895	+	0.549166i
$935$	−0.00560254	+	63.9658i	−5.99202e−6	+	0.0684126i
$936$		0			0
$937$	−694.695	−	504.726i	−0.741404	−	0.538661i	0.151747	−	0.988419i	$-0.451510\pi$
$937$	−694.695	−	504.726i	−0.741404	−	0.538661i	−0.893150	+	0.449758i	$0.851510\pi$
$938$	−327.745	+	305.212i	−0.349408	+	0.325386i
$939$		0			0
$940$	−54.6246	+	134.675i	−0.0581113	+	0.143271i
$941$	755.437	−	548.857i	0.802802	−	0.583270i	−0.108932	−	0.994049i	$-0.534743\pi$
$941$	755.437	−	548.857i	0.802802	−	0.583270i	0.911735	+	0.410779i	$0.134743\pi$
$942$		0			0
$943$	787.648	+	255.922i	0.835258	+	0.271392i
$944$	599.546	+	1135.00i	0.635112	+	1.20233i
$945$		0			0
$946$	693.070	−	645.307i	0.732632	−	0.682142i
$947$			588.592i			0.621533i	0.950486	+	0.310767i	$0.100586\pi$
$947$			588.592i			0.621533i	−0.950486	+	0.310767i	$0.899414\pi$
$948$		0			0
$949$	79.5881	−	244.947i	0.0838652	−	0.258110i
$950$	−920.456	−	179.566i	−0.968901	−	0.189017i
$951$		0			0
$952$	−187.716	+	151.378i	−0.197180	+	0.159011i
$953$	4.59701	+	14.1481i	0.00482373	+	0.0148459i	0.953439	−	0.301585i	$-0.0975156\pi$
$953$	4.59701	+	14.1481i	0.00482373	+	0.0148459i	−0.948616	+	0.316431i	$0.897516\pi$
$954$		0			0
$955$	−96.6409	+	133.015i	−0.101195	+	0.139282i
$956$	−717.473	+	446.975i	−0.750494	+	0.467547i
$957$		0			0
$958$	−97.6240	+	175.837i	−0.101904	+	0.183546i
$959$	203.273	−	279.781i	0.211963	−	0.291743i
$960$		0			0
$961$	−659.325	−	2029.19i	−0.686083	−	2.11155i
$962$	−250.634	+	30.6015i	−0.260534	+	0.0318103i
$963$		0			0
$964$	−845.437	+	1004.78i	−0.877009	+	1.04231i
$965$	20.7646	−	63.9069i	0.0215177	−	0.0662248i
$966$		0			0
$967$		−	974.002i		−	1.00724i	−0.863925	−	0.503621i	$-0.832001\pi$
$967$		−	974.002i		−	1.00724i	0.863925	−	0.503621i	$-0.167999\pi$
$968$	904.470	−	344.903i	0.934370	−	0.356305i
$969$		0			0
$970$	−67.7562	−	145.561i	−0.0698518	−	0.150063i
$971$	408.637	+	132.774i	0.420841	+	0.136740i	0.511779	−	0.859117i	$-0.328987\pi$
$971$	408.637	+	132.774i	0.420841	+	0.136740i	−0.0909380	+	0.995857i	$0.528987\pi$
$972$		0			0
$973$	562.103	−	408.392i	0.577701	−	0.419725i
$974$	29.0011	+	237.526i	0.0297752	+	0.243867i
$975$		0			0
$976$	−892.353	−	866.424i	−0.914296	−	0.887730i
$977$	−258.647	−	187.918i	−0.264736	−	0.192342i	0.447496	−	0.894286i	$-0.352316\pi$
$977$	−258.647	−	187.918i	−0.264736	−	0.192342i	−0.712232	+	0.701944i	$0.752316\pi$
$978$		0			0
$979$	489.011	−	158.842i	0.499501	−	0.162249i
$980$	53.7379	+	86.2587i	0.0548346	+	0.0880191i
$981$		0			0
$982$	380.480	+	408.570i	0.387454	+	0.416059i
$983$	−281.950	+	91.6112i	−0.286826	+	0.0931955i	−0.448897	−	0.893584i	$-0.648183\pi$
$983$	−281.950	+	91.6112i	−0.286826	+	0.0931955i	0.162070	+	0.986779i	$0.448183\pi$
$984$		0			0
$985$	−68.6084	+	49.8469i	−0.0696532	+	0.0506060i
$986$	41.6008	−	213.245i	0.0421915	−	0.216273i
$987$		0			0
$988$	−263.489	−	18.7840i	−0.266689	−	0.0190122i
$989$	−645.931			−0.653115
$990$		0			0
$991$		−	418.812i		−	0.422616i	−0.977420	−	0.211308i	$-0.932228\pi$
$991$		−	418.812i		−	0.422616i	0.977420	−	0.211308i	$-0.0677723\pi$
$992$	37.1014	−	1779.75i	0.0374006	−	1.79410i
$993$		0			0
$994$	−145.982	+	748.305i	−0.146864	+	0.752822i
$995$	56.3844	+	77.6065i	0.0566677	+	0.0779964i
$996$		0			0
$997$	−474.883	−	1461.54i	−0.476312	−	1.46594i	−0.844180	−	0.536059i	$-0.819912\pi$
$997$	−474.883	−	1461.54i	−0.476312	−	1.46594i	0.367868	−	0.929878i	$-0.380088\pi$
$998$	−230.481	−	247.496i	−0.230943	−	0.247992i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.3.s.a.235.4		40
3.2	odd	2		44.3.h.a.15.7	yes	40
4.3	odd	2	inner	396.3.s.a.235.1		40
11.3	even	5	inner	396.3.s.a.91.1		40
12.11	even	2		44.3.h.a.15.10	yes	40
33.5	odd	10		484.3.b.j.243.3		20
33.14	odd	10		44.3.h.a.3.10	yes	40
33.17	even	10		484.3.b.k.243.18		20
44.3	odd	10	inner	396.3.s.a.91.4		40
132.47	even	10		44.3.h.a.3.7	✓	40
132.71	even	10		484.3.b.j.243.4		20
132.83	odd	10		484.3.b.k.243.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.h.a.3.7	✓	40	132.47	even	10
44.3.h.a.3.10	yes	40	33.14	odd	10
44.3.h.a.15.7	yes	40	3.2	odd	2
44.3.h.a.15.10	yes	40	12.11	even	2
396.3.s.a.91.1		40	11.3	even	5	inner
396.3.s.a.91.4		40	44.3	odd	10	inner
396.3.s.a.235.1		40	4.3	odd	2	inner
396.3.s.a.235.4		40	1.1	even	1	trivial
484.3.b.j.243.3		20	33.5	odd	10
484.3.b.j.243.4		20	132.71	even	10
484.3.b.k.243.17		20	132.83	odd	10
484.3.b.k.243.18		20	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	396.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844007 - 1.81319i) q^{2} +(-2.57530 + 3.06069i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(3.68852 - 1.19847i) q^{7} +(7.72318 + 2.08627i) q^{8} +O(q^{10})\)	\(q+(-0.844007 - 1.81319i) q^{2} +(-2.57530 + 3.06069i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(3.68852 - 1.19847i) q^{7} +(7.72318 + 2.08627i) q^{8} +(1.30826 + 0.726338i) q^{10} +(-10.4619 + 3.39827i) q^{11} +(-2.78472 - 2.02322i) q^{13} +(-5.28619 - 5.67646i) q^{14} +(-2.73563 - 15.7644i) q^{16} +(-6.28791 + 4.56843i) q^{17} +(-18.2467 - 5.92872i) q^{19} +(0.212810 - 2.98515i) q^{20} +(14.9916 + 16.1013i) q^{22} -15.0061i q^{23} +(-7.55245 + 23.2440i) q^{25} +(-1.31815 + 6.75684i) q^{26} +(-5.83090 + 14.3758i) q^{28} +(-4.31911 - 13.2929i) q^{29} +(-32.6981 + 45.0051i) q^{31} +(-26.2749 + 18.2655i) q^{32} +(13.5905 + 7.54537i) q^{34} +(-1.70557 + 2.34752i) q^{35} +(11.3339 + 34.8823i) q^{37} +(4.65049 + 38.0886i) q^{38} +(-5.59225 + 2.13362i) q^{40} +(-17.0545 + 52.4884i) q^{41} -43.0444i q^{43} +(16.5416 - 40.7723i) q^{44} +(-27.2090 + 12.6653i) q^{46} +(-46.1847 - 15.0063i) q^{47} +(-27.4730 + 19.9603i) q^{49} +(48.5201 - 5.92413i) q^{50} +(13.3640 - 3.31277i) q^{52} +(74.7736 + 54.3262i) q^{53} +(4.83805 - 6.65778i) q^{55} +(30.9874 - 1.56078i) q^{56} +(-20.4571 + 19.0506i) q^{58} +(-76.2995 + 24.7912i) q^{59} +(62.8898 - 45.6921i) q^{61} +(109.200 + 21.3032i) q^{62} +(55.2950 + 32.2252i) q^{64} +2.57532 q^{65} -57.7376i q^{67} +(2.21072 - 31.0104i) q^{68} +(5.69602 + 1.11120i) q^{70} +(-57.7740 - 79.5191i) q^{71} +(23.1219 + 71.1618i) q^{73} +(53.6822 - 49.9914i) q^{74} +(65.1368 - 40.5793i) q^{76} +(-34.5162 + 25.0729i) q^{77} +(-44.4641 + 61.1996i) q^{79} +(8.58856 + 8.33900i) q^{80} +(109.565 - 13.3775i) q^{82} +(38.8192 + 53.4301i) q^{83} +(1.79696 - 5.53046i) q^{85} +(-78.0477 + 36.3298i) q^{86} +(-87.8890 + 4.41910i) q^{88} -46.7420 q^{89} +(-12.6963 - 4.12527i) q^{91} +(45.9291 + 38.6454i) q^{92} +(11.7709 + 96.4070i) q^{94} +(13.6519 - 4.43576i) q^{95} +(-86.8069 - 63.0689i) q^{97} +(59.3792 + 32.9671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8	\( 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8} - 8 q^{10} - 6 q^{13} + 36 q^{14} - 65 q^{16} + 30 q^{17} - 34 q^{20} + 25 q^{22} - 156 q^{26} + 130 q^{28} + 38 q^{29} - 20 q^{32} + 258 q^{34} - 150 q^{37} - 80 q^{38} + 112 q^{40} + 150 q^{41} - 4 q^{44} + 40 q^{46} + 132 q^{49} + 177 q^{50} - 314 q^{52} - 290 q^{53} + 856 q^{56} - 476 q^{58} + 42 q^{61} + 364 q^{62} + 303 q^{64} - 164 q^{65} - 14 q^{68} + 576 q^{70} + 186 q^{73} - 588 q^{74} + 366 q^{76} - 190 q^{77} - 1100 q^{80} + 365 q^{82} + 286 q^{85} + 501 q^{86} + 47 q^{88} + 88 q^{89} + 702 q^{92} - 678 q^{94} - 130 q^{97} + 652 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8 - 8 * q^10 - 6 * q^13 + 36 * q^14 - 65 * q^16 + 30 * q^17 - 34 * q^20 + 25 * q^22 - 156 * q^26 + 130 * q^28 + 38 * q^29 - 20 * q^32 + 258 * q^34 - 150 * q^37 - 80 * q^38 + 112 * q^40 + 150 * q^41 - 4 * q^44 + 40 * q^46 + 132 * q^49 + 177 * q^50 - 314 * q^52 - 290 * q^53 + 856 * q^56 - 476 * q^58 + 42 * q^61 + 364 * q^62 + 303 * q^64 - 164 * q^65 - 14 * q^68 + 576 * q^70 + 186 * q^73 - 588 * q^74 + 366 * q^76 - 190 * q^77 - 1100 * q^80 + 365 * q^82 + 286 * q^85 + 501 * q^86 + 47 * q^88 + 88 * q^89 + 702 * q^92 - 678 * q^94 - 130 * q^97 + 652 * q^98

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