LMFDB - Embedded newform 333.3.bu.c.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(19,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 35]))

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

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

chi := DirichletCharacter("333.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bu (of order $36$, degree $12$, 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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	333.91
Dual form			333.3.bu.c.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918684 - 0.643270i) q^{2} +(-0.937895 - 2.57685i) q^{4} +(-0.0665498 - 0.760667i) q^{5} +(8.60985 + 7.22452i) q^{7} +(-1.95705 + 7.30380i) q^{8} +O(q^{10})$	\(q+(-0.918684 - 0.643270i) q^{2} +(-0.937895 - 2.57685i) q^{4} +(-0.0665498 - 0.760667i) q^{5} +(8.60985 + 7.22452i) q^{7} +(-1.95705 + 7.30380i) q^{8} +(-0.428176 + 0.741623i) q^{10} +(-6.75804 + 3.90176i) q^{11} +(-1.02592 - 0.478396i) q^{13} +(-3.26242 - 12.1755i) q^{14} +(-1.90644 + 1.59969i) q^{16} +(7.60116 + 16.3007i) q^{17} +(-26.5585 + 18.5965i) q^{19} +(-1.89771 + 0.884915i) q^{20} +(8.71839 + 0.762760i) q^{22} +(40.1171 - 10.7493i) q^{23} +(24.0460 - 4.23996i) q^{25} +(0.634762 + 1.09944i) q^{26} +(10.5413 - 28.9621i) q^{28} +(5.98657 + 1.60410i) q^{29} +(13.1478 - 13.1478i) q^{31} +(32.9111 - 2.87935i) q^{32} +(3.50271 - 19.8648i) q^{34} +(4.92247 - 7.03002i) q^{35} +(-23.2685 + 28.7676i) q^{37} +36.3614 q^{38} +(5.68600 + 1.00260i) q^{40} +(21.1432 + 58.0906i) q^{41} +(15.5474 + 15.5474i) q^{43} +(16.3926 + 13.7550i) q^{44} +(-43.7696 - 15.9308i) q^{46} +(0.753031 - 1.30429i) q^{47} +(13.4270 + 76.1485i) q^{49} +(-24.8181 - 11.5729i) q^{50} +(-0.270544 + 3.09233i) q^{52} +(43.3876 - 36.4065i) q^{53} +(3.41768 + 4.88096i) q^{55} +(-69.6163 + 48.7459i) q^{56} +(-4.46790 - 5.32464i) q^{58} +(-80.4298 - 7.03669i) q^{59} +(33.3617 - 71.5444i) q^{61} +(-20.5363 + 3.62110i) q^{62} +(-23.4661 - 13.5482i) q^{64} +(-0.295625 + 0.812224i) q^{65} +(49.7451 - 59.2839i) q^{67} +(34.8754 - 34.8754i) q^{68} +(-9.04440 + 3.29189i) q^{70} +(2.29618 - 13.0223i) q^{71} +88.1001i q^{73} +(39.8818 - 11.4604i) q^{74} +(72.8293 + 50.9956i) q^{76} +(-86.3740 - 15.2301i) q^{77} +(3.55184 + 40.5977i) q^{79} +(1.34371 + 1.34371i) q^{80} +(17.9439 - 66.9677i) q^{82} +(-4.62098 - 1.68190i) q^{83} +(11.8936 - 6.86676i) q^{85} +(-4.28199 - 24.2844i) q^{86} +(-15.2718 - 56.9953i) q^{88} +(-6.89035 + 78.7571i) q^{89} +(-5.37686 - 11.5307i) q^{91} +(-65.3250 - 93.2938i) q^{92} +(-1.53081 + 0.713827i) q^{94} +(15.9132 + 18.9646i) q^{95} +(-75.0980 + 20.1225i) q^{97} +(36.6488 - 78.5936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8}+O(q^{10}) $ 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8	$ 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8} - 72 q^{13} - 42 q^{14} - 6 q^{16} + 24 q^{17} + 108 q^{19} + 354 q^{20} + 18 q^{25} + 30 q^{26} + 48 q^{28} + 156 q^{29} - 60 q^{31} + 192 q^{32} - 90 q^{34} - 24 q^{35} - 294 q^{37} + 120 q^{38} + 612 q^{40} - 300 q^{41} - 60 q^{43} - 174 q^{44} + 234 q^{46} - 66 q^{47} - 144 q^{49} + 252 q^{50} + 912 q^{52} - 234 q^{53} + 234 q^{55} - 312 q^{56} - 1014 q^{58} + 18 q^{59} - 720 q^{61} + 1092 q^{62} + 54 q^{64} + 54 q^{65} - 708 q^{67} + 408 q^{68} - 228 q^{70} - 234 q^{74} + 90 q^{76} + 18 q^{77} + 360 q^{79} - 924 q^{80} + 1134 q^{82} - 438 q^{83} - 756 q^{85} - 396 q^{86} + 684 q^{88} - 1470 q^{89} + 1170 q^{91} - 1602 q^{92} - 1008 q^{94} + 984 q^{95} - 774 q^{97} + 1038 q^{98}+O(q^{100}) $ 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8 - 72 * q^13 - 42 * q^14 - 6 * q^16 + 24 * q^17 + 108 * q^19 + 354 * q^20 + 18 * q^25 + 30 * q^26 + 48 * q^28 + 156 * q^29 - 60 * q^31 + 192 * q^32 - 90 * q^34 - 24 * q^35 - 294 * q^37 + 120 * q^38 + 612 * q^40 - 300 * q^41 - 60 * q^43 - 174 * q^44 + 234 * q^46 - 66 * q^47 - 144 * q^49 + 252 * q^50 + 912 * q^52 - 234 * q^53 + 234 * q^55 - 312 * q^56 - 1014 * q^58 + 18 * q^59 - 720 * q^61 + 1092 * q^62 + 54 * q^64 + 54 * q^65 - 708 * q^67 + 408 * q^68 - 228 * q^70 - 234 * q^74 + 90 * q^76 + 18 * q^77 + 360 * q^79 - 924 * q^80 + 1134 * q^82 - 438 * q^83 - 756 * q^85 - 396 * q^86 + 684 * q^88 - 1470 * q^89 + 1170 * q^91 - 1602 * q^92 - 1008 * q^94 + 984 * q^95 - 774 * q^97 + 1038 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{7}{36}\right)$

Coefficient data

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

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

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

$2$	−0.918684	−	0.643270i	−0.459342	−	0.321635i	0.320899	−	0.947113i	$-0.396015\pi$
$2$	−0.918684	−	0.643270i	−0.459342	−	0.321635i	−0.780241	+	0.625478i	$0.784904\pi$
$3$		0			0
$3$		0			0
$4$	−0.937895	−	2.57685i	−0.234474	−	0.644212i
$5$	−0.0665498	−	0.760667i	−0.0133100	−	0.152133i	0.986631	−	0.162968i	$-0.0521067\pi$
$5$	−0.0665498	−	0.760667i	−0.0133100	−	0.152133i	−0.999941	+	0.0108346i	$0.996551\pi$
$6$		0			0
$7$	8.60985	+	7.22452i	1.22998	+	1.03207i	0.998240	+	0.0592962i	$0.0188856\pi$
$7$	8.60985	+	7.22452i	1.22998	+	1.03207i	0.231738	+	0.972778i	$0.425559\pi$
$8$	−1.95705	+	7.30380i	−0.244631	+	0.912975i
$9$		0			0
$10$	−0.428176	+	0.741623i	−0.0428176	+	0.0741623i
$11$	−6.75804	+	3.90176i	−0.614367	+	0.354705i	−0.774673	−	0.632362i	$-0.782085\pi$
$11$	−6.75804	+	3.90176i	−0.614367	+	0.354705i	0.160305	+	0.987067i	$0.448752\pi$
$12$		0			0
$13$	−1.02592	−	0.478396i	−0.0789172	−	0.0367997i	0.382759	−	0.923848i	$-0.374974\pi$
$13$	−1.02592	−	0.478396i	−0.0789172	−	0.0367997i	−0.461676	+	0.887049i	$0.652752\pi$
$14$	−3.26242	−	12.1755i	−0.233030	−	0.869679i
$15$		0			0
$16$	−1.90644	+	1.59969i	−0.119152	+	0.0999807i
$17$	7.60116	+	16.3007i	0.447127	+	0.958867i	0.992678	+	0.120789i	$0.0385426\pi$
$17$	7.60116	+	16.3007i	0.447127	+	0.958867i	−0.545551	+	0.838078i	$0.683680\pi$
$18$		0			0
$19$	−26.5585	+	18.5965i	−1.39782	+	0.978761i	−0.399748	+	0.916625i	$0.630902\pi$
$19$	−26.5585	+	18.5965i	−1.39782	+	0.978761i	−0.998068	+	0.0621357i	$0.980209\pi$
$20$	−1.89771	+	0.884915i	−0.0948853	+	0.0442457i
$21$		0			0
$22$	8.71839	+	0.762760i	0.396290	+	0.0346709i
$23$	40.1171	−	10.7493i	1.74422	−	0.467362i	0.760843	−	0.648936i	$-0.224786\pi$
$23$	40.1171	−	10.7493i	1.74422	−	0.467362i	0.983377	+	0.181574i	$0.0581191\pi$
$24$		0			0
$25$	24.0460	−	4.23996i	0.961840	−	0.169598i
$26$	0.634762	+	1.09944i	0.0244139	+	0.0422862i
$27$		0			0
$28$	10.5413	−	28.9621i	0.376477	−	1.03436i
$29$	5.98657	+	1.60410i	0.206434	+	0.0553137i	0.360554	−	0.932738i	$-0.382588\pi$
$29$	5.98657	+	1.60410i	0.206434	+	0.0553137i	−0.154120	+	0.988052i	$0.549254\pi$
$30$		0			0
$31$	13.1478	−	13.1478i	0.424123	−	0.424123i	−0.462497	−	0.886621i	$-0.653047\pi$
$31$	13.1478	−	13.1478i	0.424123	−	0.424123i	0.886621	+	0.462497i	$0.153047\pi$
$32$	32.9111	−	2.87935i	1.02847	−	0.0899798i
$33$		0			0
$34$	3.50271	−	19.8648i	0.103021	−	0.584260i
$35$	4.92247	−	7.03002i	0.140642	−	0.200858i
$36$		0			0
$37$	−23.2685	+	28.7676i	−0.628880	+	0.777503i
$37$	−23.2685	+	28.7676i	−0.628880	+	0.777503i
$38$	36.3614			0.956879
$39$		0			0
$40$	5.68600	+	1.00260i	0.142150	+	0.0250649i
$41$	21.1432	+	58.0906i	0.515689	+	1.41684i	0.875227	+	0.483713i	$0.160712\pi$
$41$	21.1432	+	58.0906i	0.515689	+	1.41684i	−0.359538	+	0.933130i	$0.617066\pi$
$42$		0			0
$43$	15.5474	+	15.5474i	0.361568	+	0.361568i	0.864390	−	0.502822i	$-0.167705\pi$
$43$	15.5474	+	15.5474i	0.361568	+	0.361568i	−0.502822	+	0.864390i	$0.667705\pi$
$44$	16.3926	+	13.7550i	0.372558	+	0.312614i
$45$		0			0
$46$	−43.7696	−	15.9308i	−0.951514	−	0.346323i
$47$	0.753031	−	1.30429i	0.0160219	−	0.0277508i	−0.857903	−	0.513811i	$-0.828233\pi$
$47$	0.753031	−	1.30429i	0.0160219	−	0.0277508i	0.873925	+	0.486060i	$0.161567\pi$
$48$		0			0
$49$	13.4270	+	76.1485i	0.274021	+	1.55405i
$50$	−24.8181	−	11.5729i	−0.496363	−	0.231458i
$51$		0			0
$52$	−0.270544	+	3.09233i	−0.00520277	+	0.0594679i
$53$	43.3876	−	36.4065i	0.818634	−	0.686916i	−0.134018	−	0.990979i	$-0.542788\pi$
$53$	43.3876	−	36.4065i	0.818634	−	0.686916i	0.952652	+	0.304063i	$0.0983434\pi$
$54$		0			0
$55$	3.41768	+	4.88096i	0.0621397	+	0.0887447i
$56$	−69.6163	+	48.7459i	−1.24315	+	0.870462i
$57$		0			0
$58$	−4.46790	−	5.32464i	−0.0770328	−	0.0918042i
$59$	−80.4298	−	7.03669i	−1.36322	−	0.119266i	−0.618047	−	0.786141i	$-0.712076\pi$
$59$	−80.4298	−	7.03669i	−1.36322	−	0.119266i	−0.745170	+	0.666875i	$0.767631\pi$
$60$		0			0
$61$	33.3617	−	71.5444i	0.546913	−	1.17286i	−0.417553	−	0.908652i	$-0.637112\pi$
$61$	33.3617	−	71.5444i	0.546913	−	1.17286i	0.964466	−	0.264206i	$-0.0851100\pi$
$62$	−20.5363	+	3.62110i	−0.331231	+	0.0584049i
$63$		0			0
$64$	−23.4661	−	13.5482i	−0.366658	−	0.211690i
$65$	−0.295625	+	0.812224i	−0.00454808	+	0.0124957i
$66$		0			0
$67$	49.7451	−	59.2839i	0.742464	−	0.884834i	−0.254141	−	0.967167i	$-0.581793\pi$
$67$	49.7451	−	59.2839i	0.742464	−	0.884834i	0.996605	+	0.0823334i	$0.0262372\pi$
$68$	34.8754	−	34.8754i	0.512874	−	0.512874i
$69$		0			0
$70$	−9.04440	+	3.29189i	−0.129206	+	0.0470270i
$71$	2.29618	−	13.0223i	0.0323405	−	0.183412i	−0.964358	−	0.264600i	$-0.914760\pi$
$71$	2.29618	−	13.0223i	0.0323405	−	0.183412i	0.996699	+	0.0811876i	$0.0258713\pi$
$72$		0			0
$73$			88.1001i			1.20685i	0.797419	+	0.603426i	$0.206198\pi$
$73$			88.1001i			1.20685i	−0.797419	+	0.603426i	$0.793802\pi$
$74$	39.8818	−	11.4604i	0.538943	−	0.154870i
$75$		0			0
$76$	72.8293	+	50.9956i	0.958280	+	0.670995i
$77$	−86.3740	−	15.2301i	−1.12174	−	0.197793i
$78$		0			0
$79$	3.55184	+	40.5977i	0.0449600	+	0.513895i	0.984967	+	0.172741i	$0.0552622\pi$
$79$	3.55184	+	40.5977i	0.0449600	+	0.513895i	−0.940007	+	0.341154i	$0.889182\pi$
$80$	1.34371	+	1.34371i	0.0167963	+	0.0167963i
$81$		0			0
$82$	17.9439	−	66.9677i	0.218829	−	0.816679i
$83$	−4.62098	−	1.68190i	−0.0556745	−	0.0202639i	0.314033	−	0.949412i	$-0.398320\pi$
$83$	−4.62098	−	1.68190i	−0.0556745	−	0.0202639i	−0.369707	+	0.929148i	$0.620542\pi$
$84$		0			0
$85$	11.8936	−	6.86676i	0.139925	−	0.0807854i
$86$	−4.28199	−	24.2844i	−0.0497906	−	0.282376i
$87$		0			0
$88$	−15.2718	−	56.9953i	−0.173544	−	0.647674i
$89$	−6.89035	+	78.7571i	−0.0774197	+	0.884911i	0.853835	+	0.520543i	$0.174271\pi$
$89$	−6.89035	+	78.7571i	−0.0774197	+	0.884911i	−0.931255	+	0.364368i	$0.881285\pi$
$90$		0			0
$91$	−5.37686	−	11.5307i	−0.0590864	−	0.126711i
$92$	−65.3250	−	93.2938i	−0.710054	−	1.01406i
$93$		0			0
$94$	−1.53081	+	0.713827i	−0.0162852	+	0.00759390i
$95$	15.9132	+	18.9646i	0.167507	+	0.199627i
$96$		0			0
$97$	−75.0980	+	20.1225i	−0.774207	+	0.207448i	−0.624229	−	0.781241i	$-0.714587\pi$
$97$	−75.0980	+	20.1225i	−0.774207	+	0.207448i	−0.149978	+	0.988689i	$0.547920\pi$
$98$	36.6488	−	78.5936i	0.373967	−	0.801976i
$99$		0			0
$100$	−33.4784	−	57.9862i	−0.334784	−	0.579862i
$101$	−141.541	−	81.7188i	−1.40140	−	0.809097i	−0.406861	−	0.913490i	$-0.633377\pi$
$101$	−141.541	−	81.7188i	−1.40140	−	0.809097i	−0.994536	+	0.104393i	$0.966710\pi$
$102$		0			0
$103$	−31.6433	−	8.47879i	−0.307216	−	0.0823183i	0.101917	−	0.994793i	$-0.467502\pi$
$103$	−31.6433	−	8.47879i	−0.307216	−	0.0823183i	−0.409133	+	0.912475i	$0.634169\pi$
$104$	5.50189	−	6.55689i	0.0529028	−	0.0630471i
$105$		0			0
$106$	−63.2787	+	5.53617i	−0.596969	+	0.0522280i
$107$	−31.7962	+	11.5729i	−0.297161	+	0.108158i	−0.486298	−	0.873793i	$-0.661653\pi$
$107$	−31.7962	+	11.5729i	−0.297161	+	0.108158i	0.189137	+	0.981951i	$0.439431\pi$
$108$		0			0
$109$	−32.7259	+	46.7375i	−0.300238	+	0.428784i	−0.940718	−	0.339191i	$-0.889847\pi$
$109$	−32.7259	+	46.7375i	−0.300238	+	0.428784i	0.640480	+	0.767975i	$0.278736\pi$
$110$		−	6.68256i		−	0.0607505i
$111$		0			0
$112$	−27.9711			−0.249742
$113$	58.3238	+	40.8387i	0.516139	+	0.361405i	0.802438	−	0.596736i	$-0.203536\pi$
$113$	58.3238	+	40.8387i	0.516139	+	0.361405i	−0.286298	+	0.958141i	$0.592425\pi$
$114$		0			0
$115$	−10.8464	−	29.8004i	−0.0943169	−	0.259134i
$116$	−1.48127	−	16.9310i	−0.0127695	−	0.145957i
$117$		0			0
$118$	69.3631	+	58.2026i	0.587823	+	0.493242i
$119$	−52.3202	+	195.262i	−0.439666	+	1.64085i
$120$		0			0
$121$	−30.0526	+	52.0526i	−0.248368	+	0.430187i
$122$	−76.6712	+	44.2661i	−0.628452	+	0.362837i
$123$		0			0
$124$	−46.2112	−	21.5486i	−0.372671	−	0.173779i
$125$	−9.76613	−	36.4477i	−0.0781291	−	0.291582i
$126$		0			0
$127$	53.2531	−	44.6847i	0.419316	−	0.351848i	−0.408587	−	0.912719i	$-0.633978\pi$
$127$	53.2531	−	44.6847i	0.419316	−	0.351848i	0.827903	+	0.560872i	$0.189534\pi$
$128$	−43.0051	−	92.2247i	−0.335977	−	0.720506i
$129$		0			0
$130$	0.794065	−	0.556010i	0.00610819	−	0.00427700i
$131$	−37.1279	+	17.3130i	−0.283419	+	0.132160i	−0.559130	−	0.829080i	$-0.688865\pi$
$131$	−37.1279	+	17.3130i	−0.283419	+	0.132160i	0.275711	+	0.961241i	$0.411087\pi$
$132$		0			0
$133$	−363.015	−	31.7597i	−2.72944	−	0.238795i
$134$	−83.8355	+	22.4637i	−0.625638	+	0.167639i
$135$		0			0
$136$	−133.933	+	23.6160i	−0.984802	+	0.173647i
$137$	40.9707	+	70.9633i	0.299056	+	0.517980i	0.975920	−	0.218128i	$-0.0699949\pi$
$137$	40.9707	+	70.9633i	0.299056	+	0.517980i	−0.676864	+	0.736108i	$0.736662\pi$
$138$		0			0
$139$	31.8599	−	87.5344i	0.229208	−	0.629744i	−0.770765	−	0.637120i	$-0.780126\pi$
$139$	31.8599	−	87.5344i	0.229208	−	0.629744i	0.999973	+	0.00737578i	$0.00234781\pi$
$140$	−22.7320	−	6.09103i	−0.162372	−	0.0435074i
$141$		0			0
$142$	−10.4863	+	10.4863i	−0.0738471	+	0.0738471i
$143$	8.79982	−	0.769884i	0.0615372	−	0.00538381i
$144$		0			0
$145$	0.821779	−	4.66054i	0.00566744	−	0.0321417i
$146$	56.6722	−	80.9362i	0.388165	−	0.554358i
$147$		0			0
$148$	95.9532	+	32.9785i	0.648332	+	0.222827i
$149$	239.457			1.60709			0.803546	−	0.595242i	$-0.202944\pi$
$149$	239.457			1.60709			0.803546	+	0.595242i	$0.202944\pi$
$150$		0			0
$151$	−67.5741	−	11.9151i	−0.447511	−	0.0789082i	−0.0546487	−	0.998506i	$-0.517404\pi$
$151$	−67.5741	−	11.9151i	−0.447511	−	0.0789082i	−0.392862	+	0.919597i	$0.628515\pi$
$152$	−83.8485	−	230.372i	−0.551635	−	1.51561i
$153$		0			0
$154$	69.5534	+	69.5534i	0.451646	+	0.451646i
$155$	−10.8761	−	9.12614i	−0.0701684	−	0.0588783i
$156$		0			0
$157$	128.561	+	46.7923i	0.818858	+	0.298040i	0.717278	−	0.696788i	$-0.245388\pi$
$157$	128.561	+	46.7923i	0.818858	+	0.298040i	0.101580	+	0.994827i	$0.467610\pi$
$158$	22.8522	−	39.5812i	0.144634	−	0.250514i
$159$		0			0
$160$	−4.38046	−	24.8428i	−0.0273779	−	0.155268i
$161$	423.061	+	197.276i	2.62771	+	1.22532i
$162$		0			0
$163$	2.38596	−	27.2717i	0.0146378	−	0.167311i	−0.985357	−	0.170503i	$-0.945461\pi$
$163$	2.38596	−	27.2717i	0.0146378	−	0.167311i	0.999995	+	0.00319241i	$0.00101618\pi$
$164$	129.860	−	108.966i	0.791831	−	0.664425i
$165$		0			0
$166$	3.16331	+	4.51767i	0.0190561	+	0.0272149i
$167$	−154.546	+	108.214i	−0.925426	+	0.647990i	−0.936017	−	0.351954i	$-0.885517\pi$
$167$	−154.546	+	108.214i	−0.925426	+	0.647990i	0.0105914	+	0.999944i	$0.496629\pi$
$168$		0			0
$169$	−107.807	−	128.480i	−0.637914	−	0.760236i
$170$	−15.3436	−	1.34239i	−0.0902567	−	0.00789643i
$171$		0			0
$172$	25.4815	−	54.6452i	0.148148	−	0.317705i
$173$	−145.690	+	25.6891i	−0.842139	+	0.148492i	−0.578045	−	0.816005i	$-0.696184\pi$
$173$	−145.690	+	25.6891i	−0.842139	+	0.148492i	−0.264094	+	0.964497i	$0.585073\pi$
$174$		0			0
$175$	237.664	+	137.215i	1.35808	+	0.784088i
$176$	6.64218	−	18.2492i	0.0377397	−	0.103689i
$177$		0			0
$178$	56.9921	−	67.9206i	0.320180	−	0.381576i
$179$	−230.359	+	230.359i	−1.28692	+	1.28692i	−0.350277	+	0.936646i	$0.613912\pi$
$179$	−230.359	+	230.359i	−1.28692	+	1.28692i	−0.936646	+	0.350277i	$0.886088\pi$
$180$		0			0
$181$	310.909	−	113.162i	1.71773	−	0.625203i	0.720091	−	0.693879i	$-0.244100\pi$
$181$	310.909	−	113.162i	1.71773	−	0.625203i	0.997639	+	0.0686766i	$0.0218777\pi$
$182$	−2.47772	+	14.0519i	−0.0136139	+	0.0772081i
$183$		0			0
$184$			314.044i			1.70676i
$185$	23.4311	+	15.7851i	0.126655	+	0.0853251i
$186$		0			0
$187$	−114.970	−	80.5032i	−0.614815	−	0.430498i
$188$	−4.06721	−	0.717160i	−0.0216341	−	0.00381468i
$189$		0			0
$190$	−2.41984	−	27.6589i	−0.0127360	−	0.145573i
$191$	−163.185	−	163.185i	−0.854372	−	0.854372i	0.136296	−	0.990668i	$-0.456480\pi$
$191$	−163.185	−	163.185i	−0.854372	−	0.854372i	−0.990668	+	0.136296i	$0.956480\pi$
$192$		0			0
$193$	−15.9326	+	59.4613i	−0.0825523	+	0.308090i	−0.994839	−	0.101462i	$-0.967648\pi$
$193$	−15.9326	+	59.4613i	−0.0825523	+	0.308090i	0.912287	+	0.409551i	$0.134315\pi$
$194$	81.9356	+	29.8221i	0.422348	+	0.153722i
$195$		0			0
$196$	183.630	−	106.019i	0.936887	−	0.540912i
$197$	−20.9517	−	118.823i	−0.106354	−	0.603161i	−0.990671	−	0.136275i	$-0.956487\pi$
$197$	−20.9517	−	118.823i	−0.106354	−	0.603161i	0.884317	−	0.466886i	$-0.154624\pi$
$198$		0			0
$199$	−15.5832	−	58.1571i	−0.0783073	−	0.292247i	0.915656	−	0.401964i	$-0.131672\pi$
$199$	−15.5832	−	58.1571i	−0.0783073	−	0.292247i	−0.993963	+	0.109717i	$0.965006\pi$
$200$	−16.0914	+	183.925i	−0.0804568	+	0.919625i
$201$		0			0
$202$	77.4644	+	166.123i	0.383487	+	0.822391i
$203$	39.9547	+	57.0612i	0.196821	+	0.281089i
$204$		0			0
$205$	42.7805	−	19.9489i	0.208685	−	0.0973116i
$206$	23.6160	+	28.1445i	0.114641	+	0.136624i
$207$		0			0
$208$	2.72115	−	0.729129i	0.0130824	−	0.00350543i
$209$	106.925	−	229.300i	0.511601	−	1.09713i
$210$		0			0
$211$	171.809	+	297.582i	0.814261	+	1.41034i	0.909857	+	0.414922i	$0.136191\pi$
$211$	171.809	+	297.582i	0.814261	+	1.41034i	−0.0955956	+	0.995420i	$0.530476\pi$
$212$	−134.507	−	77.6577i	−0.634467	−	0.366310i
$213$		0			0
$214$	36.6552	+	9.82173i	0.171286	+	0.0458959i
$215$	10.7917	−	12.8611i	0.0501941	−	0.0598190i
$216$		0			0
$217$	208.188	−	18.2140i	0.959390	−	0.0839357i
$218$	60.1296	−	21.8854i	0.275824	−	0.100392i
$219$		0			0
$220$	9.37205	−	13.3847i	0.0426002	−	0.0608395i
$221$		−	20.3597i		−	0.0921252i
$222$		0			0
$223$	94.5510			0.423996			0.211998	−	0.977270i	$-0.432003\pi$
$223$	94.5510			0.423996			0.211998	+	0.977270i	$0.432003\pi$
$224$	304.162	+	212.976i	1.35787	+	0.950788i
$225$		0			0
$226$	−27.3108	−	75.0358i	−0.120844	−	0.332017i
$227$	11.6367	+	133.008i	0.0512628	+	0.585936i	0.977773	+	0.209667i	$0.0672379\pi$
$227$	11.6367	+	133.008i	0.0512628	+	0.585936i	−0.926510	+	0.376270i	$0.877207\pi$
$228$		0			0
$229$	−300.337	−	252.013i	−1.31152	−	1.10049i	−0.988030	−	0.154260i	$-0.950701\pi$
$229$	−300.337	−	252.013i	−1.31152	−	1.10049i	−0.323486	−	0.946233i	$-0.604855\pi$
$230$	−9.20522	+	34.3543i	−0.0400227	+	0.149367i
$231$		0			0
$232$	−23.4320	+	40.5854i	−0.101000	+	0.174937i
$233$	216.381	−	124.928i	0.928674	−	0.536170i	0.0422822	−	0.999106i	$-0.486537\pi$
$233$	216.381	−	124.928i	0.928674	−	0.536170i	0.886392	+	0.462935i	$0.153204\pi$
$234$		0			0
$235$	−1.04224	−	0.486006i	−0.00443508	−	0.00206811i
$236$	57.3023	+	213.855i	0.242806	+	0.906165i
$237$		0			0
$238$	173.672	−	145.728i	0.729713	−	0.612302i
$239$	−147.845	−	317.055i	−0.618599	−	1.32659i	−0.926903	−	0.375302i	$-0.877539\pi$
$239$	−147.845	−	317.055i	−0.618599	−	1.32659i	0.308303	−	0.951288i	$-0.400239\pi$
$240$		0			0
$241$	179.956	−	126.006i	0.746704	−	0.522847i	−0.137185	−	0.990545i	$-0.543805\pi$
$241$	179.956	−	126.006i	0.746704	−	0.522847i	0.883888	+	0.467698i	$0.154917\pi$
$242$	61.0927	−	28.4880i	0.252449	−	0.117719i
$243$		0			0
$244$	−215.649	−	18.8668i	−0.883806	−	0.0773230i
$245$	57.0301	−	15.2812i	0.232776	−	0.0623721i
$246$		0			0
$247$	36.1435	−	6.37307i	0.146330	−	0.0258019i
$248$	70.2981	+	121.760i	0.283460	+	0.490968i
$249$		0			0
$250$	−14.4737	+	39.7662i	−0.0578949	+	0.159065i
$251$	211.570	+	56.6901i	0.842910	+	0.225857i	0.654338	−	0.756202i	$-0.272947\pi$
$251$	211.570	+	56.6901i	0.842910	+	0.225857i	0.188572	+	0.982059i	$0.439614\pi$
$252$		0			0
$253$	−229.171	+	229.171i	−0.905816	+	0.905816i
$254$	−77.6671	+	6.79499i	−0.305776	+	0.0267519i
$255$		0			0
$256$	−38.6382	+	219.128i	−0.150930	+	0.855969i
$257$	203.166	−	290.151i	0.790530	−	1.12899i	−0.198329	−	0.980136i	$-0.563551\pi$
$257$	203.166	−	290.151i	0.790530	−	1.12899i	0.988859	−	0.148858i	$-0.0475598\pi$
$258$		0			0
$259$	−408.171	+	79.5806i	−1.57595	+	0.307261i
$260$	2.37024			0.00911631
$261$		0			0
$262$	45.2458	+	7.97805i	0.172694	+	0.0304506i
$263$	109.398	+	300.568i	0.415962	+	1.14285i	0.953969	+	0.299905i	$0.0969550\pi$
$263$	109.398	+	300.568i	0.415962	+	1.14285i	−0.538007	+	0.842940i	$0.680823\pi$
$264$		0			0
$265$	−30.5807	−	30.5807i	−0.115399	−	0.115399i
$266$	313.066	+	262.694i	1.17694	+	0.987571i
$267$		0			0
$268$	−199.421	−	72.5833i	−0.744108	−	0.270833i
$269$	208.625	−	361.349i	0.775557	−	1.34330i	−0.158923	−	0.987291i	$-0.550802\pi$
$269$	208.625	−	361.349i	0.775557	−	1.34330i	0.934481	−	0.356014i	$-0.115864\pi$
$270$		0			0
$271$	−37.4418	−	212.343i	−0.138162	−	0.783554i	−0.972606	−	0.232461i	$-0.925322\pi$
$271$	−37.4418	−	212.343i	−0.138162	−	0.783554i	0.834444	−	0.551093i	$-0.185789\pi$
$272$	−40.5673	−	18.9168i	−0.149144	−	0.0695472i
$273$		0			0
$274$	8.00942	−	91.5481i	0.0292315	−	0.334117i
$275$	−145.961	+	122.476i	−0.530766	+	0.445365i
$276$		0			0
$277$	287.147	+	410.089i	1.03663	+	1.48046i	0.869124	+	0.494594i	$0.164683\pi$
$277$	287.147	+	410.089i	1.03663	+	1.48046i	0.167508	+	0.985871i	$0.446428\pi$
$278$	−85.5775	+	59.9220i	−0.307833	+	0.215547i
$279$		0			0
$280$	41.7123	+	49.7108i	0.148973	+	0.177539i
$281$	73.2792	+	6.41110i	0.260780	+	0.0228153i	0.216796	−	0.976217i	$-0.430439\pi$
$281$	73.2792	+	6.41110i	0.260780	+	0.0228153i	0.0439842	+	0.999032i	$0.485995\pi$
$282$		0			0
$283$	19.2687	−	41.3219i	0.0680874	−	0.146014i	−0.869319	−	0.494252i	$-0.835442\pi$
$283$	19.2687	−	41.3219i	0.0680874	−	0.146014i	0.937406	+	0.348238i	$0.113220\pi$
$284$	−35.7099	+	6.29662i	−0.125739	+	0.0221712i
$285$		0			0
$286$	−8.57950	−	4.95338i	−0.0299982	−	0.0173195i
$287$	−237.636	+	652.901i	−0.828002	+	2.27492i
$288$		0			0
$289$	−22.1708	+	26.4222i	−0.0767157	+	0.0914262i
$290$	−3.75294	+	3.75294i	−0.0129412	+	0.0129412i
$291$		0			0
$292$	227.021	−	82.6287i	0.777468	−	0.282975i
$293$	−19.9534	+	113.162i	−0.0681004	+	0.386217i	0.931639	+	0.363385i	$0.118379\pi$
$293$	−19.9534	+	113.162i	−0.0681004	+	0.386217i	−0.999739	+	0.0228313i	$0.992732\pi$
$294$		0			0
$295$			61.6486i			0.208978i
$296$	−164.575	−	226.248i	−0.555997	−	0.764352i
$297$		0			0
$298$	−219.985	−	154.035i	−0.738206	−	0.516897i
$299$	−46.2995	−	8.16385i	−0.154848	−	0.0273038i
$300$		0			0
$301$	21.5383	+	246.184i	0.0715558	+	0.817886i
$302$	54.4147	+	54.4147i	0.180181	+	0.180181i
$303$		0			0
$304$	20.8835	−	77.9384i	0.0686958	−	0.256376i
$305$	−56.6417	−	20.6159i	−0.185710	−	0.0675931i
$306$		0			0
$307$	−213.445	+	123.232i	−0.695260	+	0.401408i	−0.805579	−	0.592488i	$-0.798146\pi$
$307$	−213.445	+	123.232i	−0.695260	+	0.401408i	0.110320	+	0.993896i	$0.464812\pi$
$308$	41.7643	+	236.857i	0.135598	+	0.769016i
$309$		0			0
$310$	4.12114	+	15.3803i	0.0132940	+	0.0496139i
$311$	27.6345	−	315.864i	0.0888570	−	1.01564i	−0.812614	−	0.582802i	$-0.801956\pi$
$311$	27.6345	−	315.864i	0.0888570	−	1.01564i	0.901471	−	0.432839i	$-0.142488\pi$
$312$		0			0
$313$	−110.182	−	236.285i	−0.352018	−	0.754904i	0.647959	−	0.761675i	$-0.275623\pi$
$313$	−110.182	−	236.285i	−0.352018	−	0.754904i	−0.999977	+	0.00677055i	$0.997845\pi$
$314$	−88.0066	−	125.687i	−0.280276	−	0.400276i
$315$		0			0
$316$	101.283	−	47.2289i	0.320515	−	0.149459i
$317$	−164.647	−	196.219i	−0.519391	−	0.618987i	0.441045	−	0.897485i	$-0.354608\pi$
$317$	−164.647	−	196.219i	−0.519391	−	0.618987i	−0.960437	+	0.278498i	$0.910163\pi$
$318$		0			0
$319$	−46.7163	+	12.5176i	−0.146446	+	0.0392401i
$320$	−8.74399	+	18.7515i	−0.0273250	+	0.0585986i
$321$		0			0
$322$	−261.757	−	453.377i	−0.812911	−	1.40800i
$323$	−505.011	−	291.568i	−1.56350	−	0.902689i
$324$		0			0
$325$	−26.6977	−	7.15364i	−0.0821469	−	0.0220112i
$326$	−19.7350	+	23.5193i	−0.0605368	+	0.0721450i
$327$		0			0
$328$	−465.660	+	40.7400i	−1.41970	+	0.124207i
$329$	15.9063	−	5.78943i	0.0483475	−	0.0175971i
$330$		0			0
$331$	−24.4044	+	34.8531i	−0.0737293	+	0.105296i	−0.854323	−	0.519742i	$-0.826028\pi$
$331$	−24.4044	+	34.8531i	−0.0737293	+	0.105296i	0.780594	+	0.625039i	$0.214917\pi$
$332$			13.4850i			0.0406175i
$333$		0			0
$334$	211.590			0.633504
$335$	−48.4058	−	33.8941i	−0.144495	−	0.101176i
$336$		0			0
$337$	105.120	+	288.815i	0.311929	+	0.857019i	0.992267	+	0.124120i	$0.0396108\pi$
$337$	105.120	+	288.815i	0.311929	+	0.857019i	−0.680338	+	0.732899i	$0.738167\pi$
$338$	16.3938	+	187.382i	0.0485023	+	0.554384i
$339$		0			0
$340$	−28.8495	−	24.2076i	−0.0848516	−	0.0711989i
$341$	−37.5539	+	140.153i	−0.110129	+	0.411006i
$342$		0			0
$343$	−159.167	+	275.686i	−0.464045	+	0.803749i
$344$	−143.982	+	83.1282i	−0.418553	+	0.241652i
$345$		0			0
$346$	150.368	+	70.1178i	0.434590	+	0.202653i
$347$	−66.5814	−	248.485i	−0.191877	−	0.716096i	−0.993053	−	0.117667i	$-0.962458\pi$
$347$	−66.5814	−	248.485i	−0.191877	−	0.716096i	0.801176	−	0.598429i	$-0.204208\pi$
$348$		0			0
$349$	41.2440	−	34.6078i	0.118178	−	0.0991627i	−0.581784	−	0.813344i	$-0.697645\pi$
$349$	41.2440	−	34.6078i	0.118178	−	0.0991627i	0.699961	+	0.714181i	$0.253201\pi$
$350$	−130.072	−	278.940i	−0.371634	−	0.796971i
$351$		0			0
$352$	−211.180	+	147.870i	−0.599944	+	0.420085i
$353$	−68.3037	+	31.8505i	−0.193495	+	0.0902281i	−0.516951	−	0.856015i	$-0.672933\pi$
$353$	−68.3037	+	31.8505i	−0.193495	+	0.0902281i	0.323456	+	0.946243i	$0.395155\pi$
$354$		0			0
$355$	−10.0584	−	0.879997i	−0.0283336	−	0.00247887i
$356$	209.407	−	56.1105i	0.588223	−	0.157614i
$357$		0			0
$358$	359.811	−	63.4443i	1.00506	−	0.177219i
$359$	−36.2953	−	62.8652i	−0.101101	−	0.175112i	0.811038	−	0.584994i	$-0.198903\pi$
$359$	−36.2953	−	62.8652i	−0.101101	−	0.175112i	−0.912139	+	0.409882i	$0.865570\pi$
$360$		0			0
$361$	236.056	−	648.559i	0.653895	−	1.79656i
$362$	−358.421	−	96.0386i	−0.990113	−	0.265300i
$363$		0			0
$364$	−24.6700	+	24.6700i	−0.0677746	+	0.0677746i
$365$	67.0149	−	5.86304i	0.183602	−	0.0160631i
$366$		0			0
$367$	98.9394	−	561.113i	0.269590	−	1.52892i	−0.486050	−	0.873931i	$-0.661563\pi$
$367$	98.9394	−	561.113i	0.269590	−	1.52892i	0.755639	−	0.654988i	$-0.227326\pi$
$368$	−59.2851	+	84.6679i	−0.161101	+	0.230076i
$369$		0			0
$370$	−11.3717	−	29.5741i	−0.0307342	−	0.0799299i
$371$	636.581			1.71585
$372$		0			0
$373$	446.564	+	78.7413i	1.19722	+	0.211103i	0.736498	−	0.676440i	$-0.236478\pi$
$373$	446.564	+	78.7413i	1.19722	+	0.211103i	0.460726	+	0.887543i	$0.347589\pi$
$374$	53.8363	+	147.914i	0.143947	+	0.395492i
$375$		0			0
$376$	8.05254	+	8.05254i	0.0214163	+	0.0214163i
$377$	−5.37437	−	4.50963i	−0.0142556	−	0.0119619i
$378$		0			0
$379$	−483.173	−	175.860i	−1.27486	−	0.464012i	−0.386132	−	0.922443i	$-0.626189\pi$
$379$	−483.173	−	175.860i	−1.27486	−	0.464012i	−0.888730	+	0.458432i	$0.848411\pi$
$380$	33.9439	−	58.7926i	0.0893261	−	0.154717i
$381$		0			0
$382$	44.9436	+	254.888i	0.117653	+	0.667245i
$383$	−562.992	−	262.527i	−1.46995	−	0.685450i	−0.487700	−	0.873011i	$-0.662164\pi$
$383$	−562.992	−	262.527i	−1.46995	−	0.685450i	−0.982253	+	0.187561i	$0.939942\pi$
$384$		0			0
$385$	−5.83685	+	66.7155i	−0.0151606	+	0.173287i
$386$	52.8867	−	44.3772i	0.137012	−	0.114967i
$387$		0			0
$388$	122.287	+	174.643i	0.315172	+	0.450112i
$389$	170.184	−	119.164i	0.437491	−	0.306334i	−0.334002	−	0.942572i	$-0.608399\pi$
$389$	170.184	−	119.164i	0.437491	−	0.306334i	0.771493	+	0.636238i	$0.219510\pi$
$390$		0			0
$391$	480.158	+	572.230i	1.22803	+	1.46350i
$392$	−582.450	−	50.9578i	−1.48584	−	0.129994i
$393$		0			0
$394$	−57.1871	+	122.638i	−0.145145	+	0.311265i
$395$	30.6449	−	5.40353i	0.0775822	−	0.0136798i
$396$		0			0
$397$	107.765	+	62.2180i	0.271448	+	0.156720i	0.629545	−	0.776964i	$-0.283241\pi$
$397$	107.765	+	62.2180i	0.271448	+	0.156720i	−0.358098	+	0.933684i	$0.616575\pi$
$398$	−23.0947	+	63.4522i	−0.0580269	+	0.159428i
$399$		0			0
$400$	−39.0596	+	46.5494i	−0.0976490	+	0.116374i
$401$	536.149	−	536.149i	1.33703	−	1.33703i	0.438108	−	0.898922i	$-0.355649\pi$
$401$	536.149	−	536.149i	1.33703	−	1.33703i	0.898922	−	0.438108i	$-0.144351\pi$
$402$		0			0
$403$	−19.7785	+	7.19880i	−0.0490782	+	0.0178630i
$404$	−77.8261	+	441.374i	−0.192639	+	1.09251i
$405$		0			0
$406$		−	78.1228i		−	0.192421i
$407$	45.0056	−	285.201i	0.110579	−	0.700739i
$408$		0			0
$409$	−309.025	−	216.381i	−0.755562	−	0.529050i	0.131156	−	0.991362i	$-0.458131\pi$
$409$	−309.025	−	216.381i	−0.755562	−	0.529050i	−0.886717	+	0.462312i	$0.847020\pi$
$410$	−52.1343	−	9.19269i	−0.127157	−	0.0224212i
$411$		0			0
$412$	7.82954	+	89.4921i	0.0190037	+	0.217214i
$413$	−641.652	−	641.652i	−1.55364	−	1.55364i
$414$		0			0
$415$	−0.971841	+	3.62696i	−0.00234179	+	0.00873966i
$416$	−35.1418	−	12.7906i	−0.0844754	−	0.0307465i
$417$		0			0
$418$	−245.732	+	141.873i	−0.587875	+	0.339410i
$419$	68.0276	+	385.804i	0.162357	+	0.920773i	0.951748	+	0.306882i	$0.0992856\pi$
$419$	68.0276	+	385.804i	0.162357	+	0.920773i	−0.789391	+	0.613891i	$0.789603\pi$
$420$		0			0
$421$	−42.3100	−	157.903i	−0.100499	−	0.375067i	0.897297	−	0.441428i	$-0.145528\pi$
$421$	−42.3100	−	157.903i	−0.100499	−	0.375067i	−0.997796	+	0.0663608i	$0.978861\pi$
$422$	33.5872	−	383.904i	0.0795906	−	0.909725i
$423$		0			0
$424$	180.994	+	388.144i	0.426873	+	0.915433i
$425$	251.892	+	359.739i	0.592687	+	0.846445i
$426$		0			0
$427$	804.113	−	374.964i	1.88317	−	0.878136i
$428$	59.6431	+	71.0799i	0.139353	+	0.166074i
$429$		0			0
$430$	−18.1874	+	4.87329i	−0.0422962	+	0.0113332i
$431$	−133.398	+	286.074i	−0.309509	+	0.663744i	−0.998114	−	0.0613927i	$-0.980446\pi$
$431$	−133.398	+	286.074i	−0.309509	+	0.663744i	0.688605	+	0.725137i	$0.258224\pi$
$432$		0			0
$433$	−175.690	−	304.305i	−0.405752	−	0.702782i	0.588657	−	0.808383i	$-0.299657\pi$
$433$	−175.690	−	304.305i	−0.405752	−	0.702782i	−0.994409	+	0.105601i	$0.966324\pi$
$434$	−202.975	−	117.188i	−0.467685	−	0.270018i
$435$		0			0
$436$	151.129	+	40.4948i	0.346626	+	0.0928781i
$437$	−865.549	+	1031.52i	−1.98066	+	2.36046i
$438$		0			0
$439$	−397.888	+	34.8107i	−0.906350	+	0.0792953i	−0.530791	−	0.847503i	$-0.678105\pi$
$439$	−397.888	+	34.8107i	−0.906350	+	0.0792953i	−0.375559	+	0.926798i	$0.622549\pi$
$440$	−42.3381	+	15.4098i	−0.0962230	+	0.0350223i
$441$		0			0
$442$	−13.0968	+	18.7041i	−0.0296307	+	0.0423170i
$443$		−	804.906i		−	1.81694i	−0.417947	−	0.908472i	$-0.637250\pi$
$443$		−	804.906i		−	1.81694i	0.417947	−	0.908472i	$-0.362750\pi$
$444$		0			0
$445$	60.3665			0.135655
$446$	−86.8626	−	60.8218i	−0.194759	−	0.136372i
$447$		0			0
$448$	−104.161	−	286.179i	−0.232502	−	0.638793i
$449$	47.0403	+	537.673i	0.104767	+	1.19749i	0.848567	+	0.529088i	$0.177466\pi$
$449$	47.0403	+	537.673i	0.104767	+	1.19749i	−0.743800	+	0.668402i	$0.766979\pi$
$450$		0			0
$451$	−369.542	−	310.083i	−0.819384	−	0.687545i
$452$	50.5336	−	188.594i	0.111800	−	0.417243i
$453$		0			0
$454$	74.8693	−	129.677i	0.164910	−	0.285633i
$455$	−8.41321	+	4.85737i	−0.0184906	+	0.0106755i
$456$		0			0
$457$	−507.004	−	236.420i	−1.10942	−	0.517330i	−0.220495	−	0.975388i	$-0.570767\pi$
$457$	−507.004	−	236.420i	−1.10942	−	0.517330i	−0.888922	+	0.458058i	$0.848545\pi$
$458$	113.803	+	424.718i	0.248478	+	0.927332i
$459$		0			0
$460$	−66.6182	+	55.8993i	−0.144822	+	0.121520i
$461$	51.0346	+	109.444i	0.110704	+	0.237406i	0.953853	−	0.300275i	$-0.0970784\pi$
$461$	51.0346	+	109.444i	0.110704	+	0.237406i	−0.843149	+	0.537681i	$0.819301\pi$
$462$		0			0
$463$	−263.051	+	184.190i	−0.568145	+	0.397819i	−0.822055	−	0.569409i	$-0.807172\pi$
$463$	−263.051	+	184.190i	−0.568145	+	0.397819i	0.253910	+	0.967228i	$0.418283\pi$
$464$	−13.9791	+	6.51856i	−0.0301274	+	0.0140486i
$465$		0			0
$466$	−279.148	−	24.4223i	−0.599030	−	0.0524084i
$467$	−222.657	+	59.6608i	−0.476782	+	0.127753i	−0.489204	−	0.872169i	$-0.662713\pi$
$467$	−222.657	+	59.6608i	−0.476782	+	0.127753i	0.0124218	+	0.999923i	$0.496046\pi$
$468$		0			0
$469$	856.595	−	151.041i	1.82643	−	0.322049i
$470$	0.644860	+	1.11693i	0.00137204	+	0.00237645i
$471$		0			0
$472$	208.799	−	573.672i	0.442372	−	1.21541i
$473$	−165.732	−	44.4079i	−0.350386	−	0.0938856i
$474$		0			0
$475$	−559.778	+	559.778i	−1.17848	+	1.17848i
$476$	552.230	−	48.3139i	1.16015	−	0.101500i
$477$		0			0
$478$	−68.1289	+	386.378i	−0.142529	+	0.808322i
$479$	176.950	−	252.711i	0.369416	−	0.527581i	−0.590808	−	0.806812i	$-0.701191\pi$
$479$	176.950	−	252.711i	0.369416	−	0.527581i	0.960224	+	0.279232i	$0.0900797\pi$
$480$		0			0
$481$	37.6341	−	18.3818i	0.0782413	−	0.0382158i
$482$	−246.378			−0.511158
$483$		0			0
$484$	162.318	+	28.6210i	0.335367	+	0.0591343i
$485$	20.3043	+	55.7855i	0.0418644	+	0.115022i
$486$		0			0
$487$	63.4569	+	63.4569i	0.130302	+	0.130302i	0.769250	−	0.638948i	$-0.220630\pi$
$487$	63.4569	+	63.4569i	0.130302	+	0.130302i	−0.638948	+	0.769250i	$0.720630\pi$
$488$	457.255	+	383.683i	0.936999	+	0.786235i
$489$		0			0
$490$	−62.2226	−	22.6472i	−0.126985	−	0.0462187i
$491$	323.843	−	560.913i	0.659559	−	1.14239i	−0.321171	−	0.947021i	$-0.604077\pi$
$491$	323.843	−	560.913i	0.659559	−	1.14239i	0.980730	−	0.195368i	$-0.0625901\pi$
$492$		0			0
$493$	19.3569	+	109.779i	0.0392635	+	0.222675i
$494$	−37.3040	−	17.3952i	−0.0755142	−	0.0352129i
$495$		0			0
$496$	−4.03305	+	46.0980i	−0.00813115	+	0.0929395i
$497$	113.849	−	95.5309i	0.229073	−	0.192215i
$498$		0			0
$499$	−273.177	−	390.137i	−0.547448	−	0.781837i	0.446132	−	0.894967i	$-0.352801\pi$
$499$	−273.177	−	390.137i	−0.547448	−	0.781837i	−0.993580	+	0.113130i	$0.963912\pi$
$500$	−84.7605	+	59.3500i	−0.169521	+	0.118700i
$501$		0			0
$502$	−157.899	−	188.177i	−0.314541	−	0.374855i
$503$	101.277	+	8.86060i	0.201346	+	0.0176155i	0.187383	−	0.982287i	$-0.440000\pi$
$503$	101.277	+	8.86060i	0.201346	+	0.0176155i	0.0139635	+	0.999903i	$0.495555\pi$
$504$		0			0
$505$	−52.7413	+	113.104i	−0.104438	+	0.223968i
$506$	357.955	−	63.1172i	0.707422	−	0.124738i
$507$		0			0
$508$	−165.091	−	95.3156i	−0.324983	−	0.187629i
$509$	102.536	−	281.714i	0.201445	−	0.553466i	−0.797298	−	0.603586i	$-0.793738\pi$
$509$	102.536	−	281.714i	0.201445	−	0.553466i	0.998743	+	0.0501197i	$0.0159603\pi$
$510$		0			0
$511$	−636.481	+	758.529i	−1.24556	+	1.48440i
$512$	−111.362	+	111.362i	−0.217505	+	0.217505i
$513$		0			0
$514$	−373.291	+	135.867i	−0.726248	+	0.264332i
$515$	−4.34368	+	24.6343i	−0.00843434	+	0.0478335i
$516$		0			0
$517$			11.7526i			0.0227323i
$518$	426.172	+	189.454i	0.822726	+	0.365742i
$519$		0			0
$520$	−5.35376	−	3.74875i	−0.0102957	−	0.00720913i
$521$	767.711	+	135.368i	1.47353	+	0.259824i	0.851991	−	0.523557i	$-0.175395\pi$
$521$	767.711	+	135.368i	1.47353	+	0.259824i	0.621543	+	0.783380i	$0.286506\pi$
$522$		0			0
$523$	−26.1874	−	299.324i	−0.0500715	−	0.572320i	−0.979246	−	0.202678i	$-0.935036\pi$
$523$	−26.1874	−	299.324i	−0.0500715	−	0.572320i	0.929174	−	0.369643i	$-0.120520\pi$
$524$	79.4351	+	79.4351i	0.151594	+	0.151594i
$525$		0			0
$526$	92.8443	−	346.500i	0.176510	−	0.658745i
$527$	314.258	+	114.381i	0.596315	+	0.217041i
$528$		0			0
$529$	1035.70	−	597.964i	1.95785	−	1.13037i
$530$	8.42237	+	47.7656i	0.0158913	+	0.0901238i
$531$		0			0
$532$	258.630	+	965.222i	0.486147	+	1.81433i
$533$	6.09895	−	69.7113i	0.0114427	−	0.130790i
$534$		0			0
$535$	10.9191	+	23.4162i	0.0204096	+	0.0437686i
$536$	335.644	+	479.349i	0.626201	+	0.894308i
$537$		0			0
$538$	−424.105	+	197.764i	−0.788300	+	0.367590i
$539$	−387.853	−	462.226i	−0.719579	−	0.857561i
$540$		0			0
$541$	528.163	−	141.521i	0.976272	−	0.261591i	0.264798	−	0.964304i	$-0.414695\pi$
$541$	528.163	−	141.521i	0.976272	−	0.261591i	0.711474	+	0.702713i	$0.248028\pi$
$542$	−102.197	+	219.161i	−0.188555	+	0.404357i
$543$		0			0
$544$	297.098	+	514.590i	0.546137	+	0.945937i
$545$	37.7296	+	21.7832i	0.0692286	+	0.0399691i
$546$		0			0
$547$	168.099	+	45.0420i	0.307311	+	0.0823437i	0.409179	−	0.912454i	$-0.365815\pi$
$547$	168.099	+	45.0420i	0.307311	+	0.0823437i	−0.101868	+	0.994798i	$0.532482\pi$
$548$	144.435	−	172.131i	0.263568	−	0.314108i
$549$		0			0
$550$	212.877	−	18.6243i	0.387048	−	0.0338623i
$551$	−188.825	+	68.7266i	−0.342695	+	0.124731i
$552$		0			0
$553$	−262.718	+	375.200i	−0.475078	+	0.678481i
$554$		−	561.455i		−	1.01346i
$555$		0			0
$556$	−255.444			−0.459432
$557$	−42.6906	−	29.8923i	−0.0766438	−	0.0536666i	0.534627	−	0.845088i	$-0.320452\pi$
$557$	−42.6906	−	29.8923i	−0.0766438	−	0.0536666i	−0.611270	+	0.791422i	$0.709341\pi$
$558$		0			0
$559$	−8.51264	−	23.3883i	−0.0152283	−	0.0418395i
$560$	1.86147	+	21.2767i	0.00332406	+	0.0379942i
$561$		0			0
$562$	−63.1964	−	53.0281i	−0.112449	−	0.0943560i
$563$	−145.749	+	543.942i	−0.258879	+	0.966150i	0.707012	+	0.707201i	$0.250043\pi$
$563$	−145.749	+	543.942i	−0.258879	+	0.966150i	−0.965891	+	0.258948i	$0.916624\pi$
$564$		0			0
$565$	27.1833	−	47.0828i	0.0481120	−	0.0833324i
$566$	−44.2830	+	25.5668i	−0.0782386	+	0.0451711i
$567$		0			0
$568$	90.6182	+	42.2560i	0.159539	+	0.0743943i
$569$	147.832	+	551.716i	0.259810	+	0.969624i	0.965351	+	0.260955i	$0.0840374\pi$
$569$	147.832	+	551.716i	0.259810	+	0.969624i	−0.705541	+	0.708669i	$0.749296\pi$
$570$		0			0
$571$	380.377	−	319.174i	0.666159	−	0.558974i	−0.245767	−	0.969329i	$-0.579040\pi$
$571$	380.377	−	319.174i	0.666159	−	0.558974i	0.911926	+	0.410355i	$0.134595\pi$
$572$	−10.2372	−	21.9537i	−0.0178972	−	0.0383806i
$573$		0			0
$574$	638.304	−	446.945i	1.11203	−	0.778651i
$575$	919.079	−	428.573i	1.59840	−	0.745345i
$576$		0			0
$577$	−710.154	−	62.1304i	−1.23077	−	0.107678i	−0.546847	−	0.837233i	$-0.684172\pi$
$577$	−710.154	−	62.1304i	−1.23077	−	0.107678i	−0.683923	+	0.729554i	$0.739727\pi$
$578$	37.3646	−	10.0118i	0.0646446	−	0.0173215i
$579$		0			0
$580$	−12.7802	+	2.25350i	−0.0220349	+	0.00388535i
$581$	−27.6350	−	47.8653i	−0.0475646	−	0.0823843i
$582$		0			0
$583$	−151.166	+	415.325i	−0.259290	+	0.712392i
$584$	−643.466	−	172.416i	−1.10182	−	0.295233i
$585$		0			0
$586$	91.1243	−	91.1243i	0.155502	−	0.155502i
$587$	145.820	−	12.7576i	0.248416	−	0.0217336i	0.0377324	−	0.999288i	$-0.487987\pi$
$587$	145.820	−	12.7576i	0.248416	−	0.0217336i	0.210684	+	0.977554i	$0.432431\pi$
$588$		0			0
$589$	−104.683	+	593.689i	−0.177731	+	1.00796i
$590$	39.6567	−	56.6356i	0.0672147	−	0.0959926i
$591$		0			0
$592$	−1.65925	−	92.0661i	−0.00280278	−	0.155517i
$593$	−878.514			−1.48147			−0.740737	−	0.671795i	$-0.765524\pi$
$593$	−878.514			−1.48147			−0.740737	+	0.671795i	$0.765524\pi$
$594$		0			0
$595$	152.011	+	26.8036i	0.255481	+	0.0450481i
$596$	−224.585	−	617.043i	−0.376821	−	1.03531i
$597$		0			0
$598$	37.2831	+	37.2831i	0.0623462	+	0.0623462i
$599$	375.256	+	314.877i	0.626470	+	0.525671i	0.899830	−	0.436241i	$-0.143690\pi$
$599$	375.256	+	314.877i	0.626470	+	0.525671i	−0.273360	+	0.961912i	$0.588135\pi$
$600$		0			0
$601$	340.770	+	124.030i	0.567005	+	0.206373i	0.609586	−	0.792720i	$-0.291336\pi$
$601$	340.770	+	124.030i	0.567005	+	0.206373i	−0.0425807	+	0.999093i	$0.513558\pi$
$602$	138.576	−	240.020i	0.230192	−	0.398704i
$603$		0			0
$604$	32.6740	+	185.303i	0.0540960	+	0.306794i
$605$	41.5947	+	19.3959i	0.0687516	+	0.0320594i
$606$		0			0
$607$	81.5269	−	931.857i	0.134311	−	1.53518i	−0.567830	−	0.823146i	$-0.692217\pi$
$607$	81.5269	−	931.857i	0.134311	−	1.53518i	0.702141	−	0.712038i	$-0.252228\pi$
$608$	−820.525	+	688.502i	−1.34955	+	1.13240i
$609$		0			0
$610$	38.7743	+	55.3754i	0.0635644	+	0.0907793i
$611$	−1.39652	+	0.977853i	−0.00228563	+	0.00160041i
$612$		0			0
$613$	−189.889	−	226.301i	−0.309770	−	0.369169i	0.588589	−	0.808433i	$-0.299684\pi$
$613$	−189.889	−	226.301i	−0.309770	−	0.369169i	−0.898358	+	0.439264i	$0.855239\pi$
$614$	275.360	+	24.0909i	0.448469	+	0.0392360i
$615$		0			0
$616$	280.275	−	601.053i	0.454993	−	0.975735i
$617$	593.342	−	104.622i	0.961656	−	0.169566i	0.329284	−	0.944231i	$-0.393193\pi$
$617$	593.342	−	104.622i	0.961656	−	0.169566i	0.632372	+	0.774665i	$0.282081\pi$
$618$		0			0
$619$	81.5373	+	47.0756i	0.131724	+	0.0760510i	0.564414	−	0.825492i	$-0.309102\pi$
$619$	81.5373	+	47.0756i	0.131724	+	0.0760510i	−0.432690	+	0.901543i	$0.642435\pi$
$620$	−13.3160	+	36.5854i	−0.0214774	+	0.0590087i
$621$		0			0
$622$	−228.573	+	272.403i	−0.367481	+	0.437947i
$623$	−628.307	+	628.307i	−1.00852	+	1.00852i
$624$		0			0
$625$	546.536	−	198.923i	0.874458	−	0.318277i
$626$	−50.7730	+	287.948i	−0.0811070	+	0.459981i
$627$		0			0
$628$		−	375.167i		−	0.597400i
$629$	−645.801	−	160.627i	−1.02671	−	0.255369i
$630$		0			0
$631$	3.36919	+	2.35913i	0.00533945	+	0.00373872i	0.576243	−	0.817278i	$-0.304518\pi$
$631$	3.36919	+	2.35913i	0.00533945	+	0.00373872i	−0.570904	+	0.821017i	$0.693407\pi$
$632$	−303.468	−	53.5097i	−0.480171	−	0.0846672i
$633$		0			0
$634$	25.0371	+	286.176i	0.0394907	+	0.451381i
$635$	−37.5341	−	37.5341i	−0.0591089	−	0.0591089i
$636$		0			0
$637$	22.6540	−	84.5460i	0.0355636	−	0.132725i
$638$	50.9697	+	18.5515i	0.0798899	+	0.0290775i
$639$		0			0
$640$	−67.2903	+	38.8501i	−0.105141	+	0.0607033i
$641$	147.524	+	836.648i	0.230146	+	1.30522i	0.852599	+	0.522566i	$0.175025\pi$
$641$	147.524	+	836.648i	0.230146	+	1.30522i	−0.622453	+	0.782657i	$0.713864\pi$
$642$		0			0
$643$	263.500	+	983.396i	0.409798	+	1.52939i	0.795032	+	0.606568i	$0.207454\pi$
$643$	263.500	+	983.396i	0.409798	+	1.52939i	−0.385233	+	0.922819i	$0.625879\pi$
$644$	111.564	−	1275.19i	0.173237	−	1.98010i
$645$		0			0
$646$	276.389	+	592.718i	0.427847	+	0.917520i
$647$	389.066	+	555.643i	0.601338	+	0.858800i	0.998255	−	0.0590548i	$-0.0188087\pi$
$647$	389.066	+	555.643i	0.601338	+	0.858800i	−0.396917	+	0.917855i	$0.629920\pi$
$648$		0			0
$649$	571.003	−	266.263i	0.879820	−	0.410267i
$650$	19.9251	+	23.7458i	0.0306540	+	0.0365320i
$651$		0			0
$652$	−72.5127	+	19.4297i	−0.111216	+	0.0298002i
$653$	421.445	−	903.792i	0.645399	−	1.38406i	−0.262525	−	0.964925i	$-0.584555\pi$
$653$	421.445	−	903.792i	0.645399	−	1.38406i	0.907923	−	0.419136i	$-0.137667\pi$
$654$		0			0
$655$	15.6403	+	27.0898i	0.0238783	+	0.0413585i
$656$	−133.235	−	76.9234i	−0.203103	−	0.117261i
$657$		0			0
$658$	−18.3371	−	4.91340i	−0.0278679	−	0.00746718i
$659$	−666.840	+	794.709i	−1.01190	+	1.20593i	−0.0334483	+	0.999440i	$0.510649\pi$
$659$	−666.840	+	794.709i	−1.01190	+	1.20593i	−0.978448	+	0.206491i	$0.933796\pi$
$660$		0			0
$661$	−299.719	+	26.2220i	−0.453433	+	0.0396703i	−0.311585	−	0.950218i	$-0.600860\pi$
$661$	−299.719	+	26.2220i	−0.453433	+	0.0396703i	−0.141848	+	0.989888i	$0.545304\pi$
$662$	44.8399	−	16.3204i	0.0677340	−	0.0246531i
$663$		0			0
$664$	21.3277	−	30.4592i	0.0321201	−	0.0458722i
$665$			278.247i			0.418417i
$666$		0			0
$667$	257.407			0.385917
$668$	423.800	+	296.748i	0.634431	+	0.444233i
$669$		0			0
$670$	22.6666	+	62.2760i	0.0338308	+	0.0929492i
$671$	53.6891	+	613.669i	0.0800135	+	0.914559i
$672$		0			0
$673$	627.858	+	526.835i	0.932924	+	0.782816i	0.976340	−	0.216241i	$-0.0693797\pi$
$673$	627.858	+	526.835i	0.932924	+	0.782816i	−0.0434163	+	0.999057i	$0.513824\pi$
$674$	89.2139	−	332.951i	0.132365	−	0.493992i
$675$		0			0
$676$	−229.961	+	398.304i	−0.340179	+	0.589207i
$677$	1053.12	−	608.017i	1.55556	−	0.898104i	0.557890	−	0.829915i	$-0.311611\pi$
$677$	1053.12	−	608.017i	1.55556	−	0.898104i	0.997672	−	0.0681897i	$-0.0217223\pi$
$678$		0			0
$679$	−791.958	−	369.296i	−1.16636	−	0.543882i
$680$	26.8772	+	100.307i	0.0395252	+	0.147510i
$681$		0			0
$682$	124.657	−	104.599i	0.182781	−	0.153371i
$683$	125.650	+	269.458i	0.183968	+	0.394521i	0.976564	−	0.215226i	$-0.0690488\pi$
$683$	125.650	+	269.458i	0.183968	+	0.394521i	−0.792596	+	0.609747i	$0.791271\pi$
$684$		0			0
$685$	51.2529	−	35.8876i	0.0748217	−	0.0523907i
$686$	323.565	−	150.881i	0.471669	−	0.219943i
$687$		0			0
$688$	−54.5113	−	4.76912i	−0.0792315	−	0.00693186i
$689$	−61.9291	+	16.5939i	−0.0898826	+	0.0240840i
$690$		0			0
$691$	108.780	−	19.1809i	0.157424	−	0.0277581i	−0.0943806	−	0.995536i	$-0.530087\pi$
$691$	108.780	−	19.1809i	0.157424	−	0.0277581i	0.251805	+	0.967778i	$0.418976\pi$
$692$	202.839	+	351.327i	0.293120	+	0.507698i
$693$		0			0
$694$	−98.6758	+	271.109i	−0.142184	+	0.390648i
$695$	−68.7049	−	18.4094i	−0.0988559	−	0.0264884i
$696$		0			0
$697$	−786.206	+	786.206i	−1.12799	+	1.12799i
$698$	−60.1523	+	5.26265i	−0.0861781	+	0.00753961i
$699$		0			0
$700$	130.679	−	741.118i	0.186684	−	1.05874i
$701$	−261.688	+	373.729i	−0.373307	+	0.533137i	−0.961219	−	0.275788i	$-0.911061\pi$
$701$	−261.688	+	373.729i	−0.373307	+	0.533137i	0.587912	+	0.808925i	$0.299950\pi$
$702$		0			0
$703$	83.0020	−	1196.74i	0.118068	−	1.70233i
$704$	211.447			0.300350
$705$		0			0
$706$	83.2380	+	14.6771i	0.117901	+	0.0207891i
$707$	−628.269	−	1726.15i	−0.888640	−	2.44152i
$708$		0			0
$709$	589.364	+	589.364i	0.831260	+	0.831260i	0.987689	−	0.156429i	$-0.0499982\pi$
$709$	589.364	+	589.364i	0.831260	+	0.831260i	−0.156429	+	0.987689i	$0.549998\pi$
$710$	8.67443	+	7.27871i	0.0122175	+	0.0102517i
$711$		0			0
$712$	−561.741	−	204.457i	−0.788962	−	0.287159i
$713$	386.122	−	668.783i	0.541545	−	0.937984i
$714$		0			0
$715$	−1.17125	−	6.64250i	−0.00163811	−	0.00929021i
$716$	809.653	+	377.547i	1.13080	+	0.527301i
$717$		0			0
$718$	−7.09541	+	81.1010i	−0.00988219	+	0.112954i
$719$	566.148	−	475.054i	0.787410	−	0.660715i	−0.157693	−	0.987488i	$-0.550406\pi$
$719$	566.148	−	475.054i	0.787410	−	0.660715i	0.945103	+	0.326773i	$0.105961\pi$
$720$		0			0
$721$	−211.189	−	301.609i	−0.292911	−	0.418320i
$722$	−634.059	+	443.973i	−0.878198	+	0.614921i
$723$		0			0
$724$	−583.201	−	695.031i	−0.805526	−	0.959988i
$725$	150.755	+	13.1893i	0.207937	+	0.0181922i
$726$		0			0
$727$	−472.747	+	1013.81i	−0.650271	+	1.39451i	0.253854	+	0.967243i	$0.418302\pi$
$727$	−472.747	+	1013.81i	−0.650271	+	1.39451i	−0.904125	+	0.427268i	$0.859476\pi$
$728$	94.7408	−	16.7054i	0.130139	−	0.0229469i
$729$		0			0
$730$	−65.3371	−	37.7224i	−0.0895028	−	0.0516745i
$731$	−135.256	+	371.613i	−0.185029	+	0.508362i
$732$		0			0
$733$	124.826	−	148.762i	0.170294	−	0.202949i	−0.674147	−	0.738598i	$-0.735488\pi$
$733$	124.826	−	148.762i	0.170294	−	0.202949i	0.844441	+	0.535649i	$0.179933\pi$
$734$	−451.841	+	451.841i	−0.615588	+	0.615588i
$735$		0			0
$736$	1289.35	−	469.284i	1.75183	−	0.637614i
$737$	−104.868	+	594.736i	−0.142290	+	0.806969i
$738$		0			0
$739$			387.267i			0.524042i	0.965062	+	0.262021i	$0.0843890\pi$
$739$			387.267i			0.524042i	−0.965062	+	0.262021i	$0.915611\pi$
$740$	18.7000	−	75.1831i	0.0252702	−	0.101599i
$741$		0			0
$742$	−584.817	−	409.493i	−0.788163	−	0.551877i
$743$	1399.14	+	246.707i	1.88310	+	0.332041i	0.992450	−	0.122649i	$-0.0391388\pi$
$743$	1399.14	+	246.707i	1.88310	+	0.332041i	0.890650	+	0.454690i	$0.150250\pi$
$744$		0			0
$745$	−15.9358	−	182.147i	−0.0213903	−	0.244493i
$746$	−359.600	−	359.600i	−0.482037	−	0.482037i
$747$		0			0
$748$	−99.6141	+	371.765i	−0.133174	+	0.497012i
$749$	−357.369	−	130.072i	−0.477129	−	0.173661i
$750$		0			0
$751$	522.746	−	301.808i	0.696067	−	0.401875i	−0.109814	−	0.993952i	$-0.535025\pi$
$751$	522.746	−	301.808i	0.696067	−	0.401875i	0.805881	+	0.592078i	$0.201692\pi$
$752$	0.650851	+	3.69116i	0.000865494	+	0.00490846i
$753$		0			0
$754$	2.03644	+	7.60010i	0.00270085	+	0.0100797i
$755$	−4.56642	+	52.1944i	−0.00604823	+	0.0691316i
$756$		0			0
$757$	−226.439	−	485.601i	−0.299127	−	0.641480i	0.698092	−	0.716008i	$-0.254033\pi$
$757$	−226.439	−	485.601i	−0.299127	−	0.641480i	−0.997219	+	0.0745280i	$0.976255\pi$
$758$	330.757	+	472.371i	0.436355	+	0.623180i
$759$		0			0
$760$	−169.656	+	79.1120i	−0.223232	+	0.104095i
$761$	−57.5792	−	68.6202i	−0.0756625	−	0.0901711i	0.726885	−	0.686759i	$-0.240967\pi$
$761$	−57.5792	−	68.6202i	−0.0756625	−	0.0901711i	−0.802548	+	0.596588i	$0.796523\pi$
$762$		0			0
$763$	−619.421	+	165.973i	−0.811823	+	0.217527i
$764$	−267.452	+	573.553i	−0.350069	+	0.750724i
$765$		0			0
$766$	348.336	+	603.336i	0.454747	+	0.787644i
$767$	79.1485	+	45.6964i	0.103192	+	0.0595781i
$768$		0			0
$769$	−1010.03	−	270.636i	−1.31343	−	0.351932i	−0.466916	−	0.884302i	$-0.654635\pi$
$769$	−1010.03	−	270.636i	−1.31343	−	0.351932i	−0.846512	+	0.532369i	$0.821302\pi$
$770$	48.2783	−	57.5358i	0.0626990	−	0.0747218i
$771$		0			0
$772$	168.166	−	14.7126i	0.217831	−	0.0190578i
$773$	715.894	−	260.564i	0.926124	−	0.337082i	0.165452	−	0.986218i	$-0.447092\pi$
$773$	715.894	−	260.564i	0.926124	−	0.337082i	0.760672	+	0.649136i	$0.224870\pi$
$774$		0			0
$775$	260.406	−	371.899i	0.336008	−	0.479870i
$776$		−	587.882i		−	0.757579i
$777$		0			0
$778$	−233.000			−0.299486
$779$	−1641.81	−	1149.61i	−2.10759	−	1.47575i
$780$		0			0
$781$	35.2920	+	96.9641i	0.0451883	+	0.124154i
$782$	−73.0155	−	834.570i	−0.0933701	−	1.06723i
$783$		0			0
$784$	−147.412	−	123.693i	−0.188025	−	0.157772i
$785$	27.0377	−	100.906i	0.0344429	−	0.128543i
$786$		0			0
$787$	334.968	−	580.181i	0.425626	−	0.737206i	−0.570853	−	0.821053i	$-0.693387\pi$
$787$	334.968	−	580.181i	0.425626	−	0.737206i	0.996479	+	0.0838466i	$0.0267206\pi$
$788$	−286.538	+	165.433i	−0.363626	+	0.209940i
$789$		0			0
$790$	−31.6290	−	14.7488i	−0.0400367	−	0.0186694i
$791$	207.118	+	772.976i	0.261844	+	0.977214i
$792$		0			0
$793$	−68.4531	+	57.4390i	−0.0863217	+	0.0724325i
$794$	−58.9788	−	126.480i	−0.0742806	−	0.159295i
$795$		0			0
$796$	−135.247	+	94.7007i	−0.169908	+	0.118971i
$797$	−19.5765	+	9.12868i	−0.0245628	+	0.0114538i	−0.434861	−	0.900498i	$-0.643202\pi$
$797$	−19.5765	+	9.12868i	−0.0245628	+	0.0114538i	0.410298	+	0.911951i	$0.365425\pi$
$798$		0			0
$799$	26.9848	+	2.36086i	0.0337732	+	0.00295477i
$800$	779.173	−	208.779i	0.973967	−	0.260974i
$801$		0			0
$802$	−837.441	+	147.663i	−1.04419	+	0.184119i
$803$	−343.745	−	595.384i	−0.428076	−	0.741450i
$804$		0			0
$805$	121.907	−	334.937i	0.151437	−	0.416071i
$806$	22.8010	+	6.10951i	0.0282891	+	0.00758004i
$807$		0			0
$808$	873.860	−	873.860i	1.08151	−	1.08151i
$809$	383.140	−	33.5204i	0.473598	−	0.0414344i	0.152141	−	0.988359i	$-0.451383\pi$
$809$	383.140	−	33.5204i	0.473598	−	0.0414344i	0.321456	+	0.946924i	$0.395828\pi$
$810$		0			0
$811$	−189.283	+	1073.48i	−0.233395	+	1.32365i	0.612573	+	0.790414i	$0.290135\pi$
$811$	−189.283	+	1073.48i	−0.233395	+	1.32365i	−0.845968	+	0.533234i	$0.820976\pi$
$812$	109.565	−	156.474i	0.134932	−	0.192702i
$813$		0			0
$814$	−224.807	+	233.059i	−0.276176	+	0.286313i
$815$	−20.9035			−0.0256484
$816$		0			0
$817$	−702.043	−	123.789i	−0.859294	−	0.151517i
$818$	144.705	+	397.572i	0.176900	+	0.486030i
$819$		0			0
$820$	−91.5289	−	91.5289i	−0.111621	−	0.111621i
$821$	−523.226	−	439.039i	−0.637303	−	0.534761i	0.265885	−	0.964005i	$-0.414336\pi$
$821$	−523.226	−	439.039i	−0.637303	−	0.534761i	−0.903189	+	0.429244i	$0.858780\pi$
$822$		0			0
$823$	−592.383	−	215.610i	−0.719785	−	0.261980i	−0.0439502	−	0.999034i	$-0.513994\pi$
$823$	−592.383	−	215.610i	−0.719785	−	0.261980i	−0.675834	+	0.737054i	$0.736217\pi$
$824$	123.855	−	214.523i	0.150309	−	0.260343i
$825$		0			0
$826$	176.720	+	1002.23i	0.213947	+	1.21335i
$827$	−449.744	−	209.719i	−0.543826	−	0.253590i	0.131236	−	0.991351i	$-0.458105\pi$
$827$	−449.744	−	209.719i	−0.543826	−	0.253590i	−0.675062	+	0.737761i	$0.735883\pi$
$828$		0			0
$829$	−0.0785947	+	0.898341i	−9.48066e−5	+	0.00108364i	−0.996242	−	0.0866139i	$-0.972395\pi$
$829$	−0.0785947	+	0.898341i	−9.48066e−5	+	0.00108364i	0.996147	+	0.0876976i	$0.0279509\pi$
$830$	3.22593	−	2.70688i	0.00388666	−	0.00326130i
$831$		0			0
$832$	17.5931	+	25.1255i	0.0211455	+	0.0301989i
$833$	−1139.22	+	797.687i	−1.36761	+	0.957608i
$834$		0			0
$835$	92.6001	+	110.357i	0.110898	+	0.132164i
$836$	−691.156	−	60.4683i	−0.826742	−	0.0723305i
$837$		0			0
$838$	185.680	−	398.192i	0.221575	−	0.475170i
$839$	−899.002	+	158.518i	−1.07152	+	0.188937i	−0.681461	−	0.731854i	$-0.738655\pi$
$839$	−899.002	+	158.518i	−1.07152	+	0.188937i	−0.390055	+	0.920792i	$0.627544\pi$
$840$		0			0
$841$	−695.061	−	401.294i	−0.826470	−	0.477163i
$842$	−62.7048	+	172.280i	−0.0744712	+	0.204608i
$843$		0			0
$844$	605.685	−	721.827i	0.717636	−	0.855245i
$845$	−90.5559	+	90.5559i	−0.107167	+	0.107167i
$846$		0			0
$847$	−634.803	+	231.050i	−0.749473	+	0.272786i
$848$	−24.4766	+	138.814i	−0.0288639	+	0.163695i
$849$		0			0
$850$		−	492.521i		−	0.579437i
$851$	−624.233	+	1404.19i	−0.733529	+	1.65005i
$852$		0			0
$853$	1308.68	+	916.351i	1.53421	+	1.07427i	0.968296	+	0.249807i	$0.0803673\pi$
$853$	1308.68	+	916.351i	1.53421	+	1.07427i	0.565919	+	0.824461i	$0.308522\pi$
$854$	−979.929	−	172.788i	−1.14746	−	0.202328i
$855$		0			0
$856$	−22.2993	−	254.882i	−0.0260506	−	0.297759i
$857$	−986.620	−	986.620i	−1.15125	−	1.15125i	−0.986303	−	0.164946i	$-0.947255\pi$
$857$	−986.620	−	986.620i	−1.15125	−	1.15125i	−0.164946	−	0.986303i	$-0.552745\pi$
$858$		0			0
$859$	−135.208	+	504.602i	−0.157401	+	0.587430i	0.841486	+	0.540278i	$0.181681\pi$
$859$	−135.208	+	504.602i	−0.157401	+	0.587430i	−0.998888	+	0.0471517i	$0.984986\pi$
$860$	−43.2626	−	15.7463i	−0.0503053	−	0.0183096i
$861$		0			0
$862$	306.574	−	177.000i	0.355654	−	0.205337i
$863$	−276.896	−	1570.36i	−0.320853	−	1.81965i	−0.537345	−	0.843362i	$-0.680573\pi$
$863$	−276.896	−	1570.36i	−0.320853	−	1.81965i	0.216492	−	0.976284i	$-0.430538\pi$
$864$		0			0
$865$	29.2365	+	109.112i	0.0337994	+	0.126141i
$866$	−34.3460	+	392.576i	−0.0396605	+	0.453321i
$867$		0			0
$868$	−242.193	−	519.384i	−0.279024	−	0.598369i
$869$	−182.406	−	260.502i	−0.209903	−	0.299773i
$870$		0			0
$871$	−79.3958	+	37.0229i	−0.0911547	+	0.0425062i
$872$	−277.315	−	330.491i	−0.318022	−	0.379003i
$873$		0			0
$874$	1458.71	−	390.861i	1.66901	−	0.447209i
$875$	179.232	−	384.365i	0.204837	−	0.439274i
$876$		0			0
$877$	−267.699	−	463.668i	−0.305244	−	0.528697i	0.672072	−	0.740486i	$-0.265405\pi$
$877$	−267.699	−	463.668i	−0.305244	−	0.528697i	−0.977316	+	0.211789i	$0.932071\pi$
$878$	387.926	+	223.969i	0.441829	+	0.255090i
$879$		0			0
$880$	−14.3236	−	3.83801i	−0.0162769	−	0.00436137i
$881$	−255.657	+	304.681i	−0.290190	+	0.345835i	−0.891368	−	0.453280i	$-0.850254\pi$
$881$	−255.657	+	304.681i	−0.290190	+	0.345835i	0.601178	+	0.799115i	$0.294698\pi$
$882$		0			0
$883$	556.720	−	48.7066i	0.630486	−	0.0551604i	0.232566	−	0.972581i	$-0.425288\pi$
$883$	556.720	−	48.7066i	0.630486	−	0.0551604i	0.397920	+	0.917420i	$0.369732\pi$
$884$	−52.4638	+	19.0952i	−0.0593481	+	0.0216010i
$885$		0			0
$886$	−517.772	+	739.454i	−0.584392	+	0.834599i
$887$			1446.76i			1.63108i	0.578704	+	0.815538i	$0.303559\pi$
$887$			1446.76i			1.63108i	−0.578704	+	0.815538i	$0.696441\pi$
$888$		0			0
$889$	781.327			0.878882
$890$	−55.4578	−	38.8319i	−0.0623121	−	0.0436314i
$891$		0			0
$892$	−88.6790	−	243.644i	−0.0994159	−	0.273143i
$893$	4.25577	+	48.6436i	0.00476570	+	0.0544721i
$894$		0			0
$895$	190.557	+	159.896i	0.212913	+	0.178655i
$896$	296.012	−	1104.73i	0.330371	−	1.23296i
$897$		0			0
$898$	302.654	−	524.212i	0.337031	−	0.583754i
$899$	99.8008	−	57.6200i	0.111013	−	0.0640935i
$900$		0			0
$901$	923.250	+	430.518i	1.02469	+	0.477823i
$902$	140.026	+	522.583i	0.155239	+	0.579361i
$903$		0			0
$904$	−412.420	+	346.062i	−0.456217	+	0.382811i
$905$	−106.769	−	228.968i	−0.117977	−	0.253003i
$906$		0			0
$907$	−1313.26	+	919.556i	−1.44792	+	1.01384i	−0.455593	+	0.890188i	$0.650573\pi$
$907$	−1313.26	+	919.556i	−1.44792	+	1.01384i	−0.992325	+	0.123655i	$0.960538\pi$
$908$	331.826	−	154.733i	0.365447	−	0.170411i
$909$		0			0
$910$	10.8537	+	0.949575i	0.0119271	+	0.00104349i
$911$	895.763	−	240.019i	0.983275	−	0.263468i	0.268851	−	0.963182i	$-0.413356\pi$
$911$	895.763	−	240.019i	0.983275	−	0.263468i	0.714423	+	0.699714i	$0.246689\pi$
$912$		0			0
$913$	37.7911	−	6.66360i	0.0413923	−	0.00729857i
$914$	313.695	+	543.335i	0.343211	+	0.594459i
$915$		0			0
$916$	−367.713	+	1010.28i	−0.401434	+	1.10293i
$917$	−444.744	−	119.169i	−0.484999	−	0.129955i
$918$		0			0
$919$	−143.858	+	143.858i	−0.156537	+	0.156537i	−0.781030	−	0.624493i	$-0.785306\pi$
$919$	−143.858	+	143.858i	−0.156537	+	0.156537i	0.624493	+	0.781030i	$0.285306\pi$
$920$	238.883	−	20.8995i	0.259655	−	0.0227169i
$921$		0			0
$922$	23.5174	−	133.374i	0.0255069	−	0.144657i
$923$	−8.58550	+	12.2614i	−0.00930173	+	0.0132842i
$924$		0			0
$925$	−437.542	+	790.404i	−0.473019	+	0.854490i
$926$	360.145			0.388925
$927$		0			0
$928$	201.644	+	35.5552i	0.217289	+	0.0383138i
$929$	241.158	+	662.577i	0.259589	+	0.713215i	0.999193	+	0.0401725i	$0.0127908\pi$
$929$	241.158	+	662.577i	0.259589	+	0.713215i	−0.739604	+	0.673043i	$0.764987\pi$
$930$		0			0
$931$	−1772.69	−	1772.69i	−1.90407	−	1.90407i
$932$	−524.862	−	440.412i	−0.563157	−	0.472545i
$933$		0			0
$934$	242.930	+	88.4192i	0.260096	+	0.0946672i
$935$	−53.5849	+	92.8117i	−0.0573100	+	0.0992639i
$936$		0			0
$937$	−239.844	−	1360.22i	−0.255970	−	1.45168i	−0.793570	−	0.608478i	$-0.791780\pi$
$937$	−239.844	−	1360.22i	−0.255970	−	1.45168i	0.537600	−	0.843200i	$-0.319331\pi$
$938$	−884.100	−	412.263i	−0.942538	−	0.439513i
$939$		0			0
$940$	−0.274848	+	3.14152i	−0.000292391	+	0.00334205i
$941$	295.650	−	248.080i	0.314187	−	0.263634i	−0.472033	−	0.881581i	$-0.656480\pi$
$941$	295.650	−	248.080i	0.314187	−	0.263634i	0.786220	+	0.617947i	$0.212035\pi$
$942$		0			0
$943$	1472.64	+	2103.15i	1.56165	+	2.23027i
$944$	164.591	−	115.248i	0.174355	−	0.122085i
$945$		0			0
$946$	123.690	+	147.407i	0.130750	+	0.155822i
$947$	−1154.36	−	100.994i	−1.21897	−	0.106646i	−0.540544	−	0.841316i	$-0.681782\pi$
$947$	−1154.36	−	100.994i	−1.21897	−	0.106646i	−0.678425	+	0.734670i	$0.737337\pi$
$948$		0			0
$949$	42.1467	−	90.3840i	0.0444117	−	0.0952413i
$950$	874.347	−	154.171i	0.920365	−	0.162285i
$951$		0			0
$952$	−1323.76	−	764.272i	−1.39050	−	0.802807i
$953$	290.638	−	798.520i	0.304971	−	0.837901i	−0.688646	−	0.725098i	$-0.741795\pi$
$953$	290.638	−	798.520i	0.304971	−	0.837901i	0.993617	−	0.112804i	$-0.0359831\pi$
$954$		0			0
$955$	−113.270	+	134.989i	−0.118607	+	0.141350i
$956$	−678.339	+	678.339i	−0.709560	+	0.709560i
$957$		0			0
$958$	−325.123	+	118.335i	−0.339377	+	0.123523i
$959$	−159.924	+	906.977i	−0.166762	+	0.945753i
$960$		0			0
$961$			615.269i			0.640239i
$962$	−46.3983	−	7.32179i	−0.0482310	−	0.00761101i
$963$		0			0
$964$	−493.478	−	345.537i	−0.511907	−	0.358441i
$965$	46.2906	+	8.16228i	0.0479695	+	0.00845832i
$966$		0			0
$967$	36.5924	+	418.253i	0.0378412	+	0.432527i	0.991358	+	0.131186i	$0.0418785\pi$
$967$	36.5924	+	418.253i	0.0378412	+	0.432527i	−0.953517	+	0.301340i	$0.902566\pi$
$968$	−321.367	−	321.367i	−0.331991	−	0.331991i
$969$		0			0
$970$	17.2319	−	64.3104i	0.0177649	−	0.0662993i
$971$	−369.424	−	134.459i	−0.380457	−	0.138475i	0.144710	−	0.989474i	$-0.453775\pi$
$971$	−369.424	−	134.459i	−0.380457	−	0.138475i	−0.525167	+	0.850999i	$0.675997\pi$
$972$		0			0
$973$	906.704	−	523.486i	0.931864	−	0.538012i
$974$	−17.4770	−	99.1167i	−0.0179435	−	0.101763i
$975$		0			0
$976$	50.8469	+	189.763i	0.0520973	+	0.194430i
$977$	−16.0456	+	183.402i	−0.0164234	+	0.187720i	0.983551	+	0.180628i	$0.0578130\pi$
$977$	−16.0456	+	183.402i	−0.0164234	+	0.187720i	−0.999975	+	0.00709188i	$0.997743\pi$
$978$		0			0
$979$	−260.726	−	559.128i	−0.266318	−	0.571122i
$980$	−92.8655	−	132.626i	−0.0947607	−	0.135332i
$981$		0			0
$982$	−658.328	+	306.983i	−0.670395	+	0.312610i
$983$	−1155.93	−	1377.58i	−1.17592	−	1.40141i	−0.897538	−	0.440936i	$-0.854647\pi$
$983$	−1155.93	−	1377.58i	−1.17592	−	1.40141i	−0.278381	−	0.960471i	$-0.589798\pi$
$984$		0			0
$985$	−88.9903	+	23.8449i	−0.0903455	+	0.0242080i
$986$	52.8343	−	113.304i	0.0535845	−	0.114912i
$987$		0			0
$988$	−50.3212	−	87.1589i	−0.0509324	−	0.0882175i
$989$	790.842	+	456.593i	0.799638	+	0.461671i
$990$		0			0
$991$	269.600	+	72.2392i	0.272049	+	0.0728952i	0.392264	−	0.919853i	$-0.371692\pi$
$991$	269.600	+	72.2392i	0.272049	+	0.0728952i	−0.120216	+	0.992748i	$0.538359\pi$
$992$	394.853	−	470.567i	0.398037	−	0.474362i
$993$		0			0
$994$	−166.044	+	14.5269i	−0.167046	+	0.0146146i
$995$	−43.2012	+	15.7239i	−0.0434183	+	0.0158030i
$996$		0			0
$997$	−781.381	+	1115.93i	−0.783732	+	1.11929i	0.206306	+	0.978487i	$0.433856\pi$
$997$	−781.381	+	1115.93i	−0.783732	+	1.11929i	−0.990038	+	0.140798i	$0.955033\pi$
$998$			534.139i			0.535209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bu.c.91.3		72
3.2	odd	2		111.3.r.a.91.4	yes	72
37.24	odd	36	inner	333.3.bu.c.172.3		72
111.98	even	36		111.3.r.a.61.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.r.a.61.4	✓	72	111.98	even	36
111.3.r.a.91.4	yes	72	3.2	odd	2
333.3.bu.c.91.3		72	1.1	even	1	trivial
333.3.bu.c.172.3		72	37.24	odd	36	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bu (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.918684 - 0.643270i) q^{2} +(-0.937895 - 2.57685i) q^{4} +(-0.0665498 - 0.760667i) q^{5} +(8.60985 + 7.22452i) q^{7} +(-1.95705 + 7.30380i) q^{8} +O(q^{10})\)	\(q+(-0.918684 - 0.643270i) q^{2} +(-0.937895 - 2.57685i) q^{4} +(-0.0665498 - 0.760667i) q^{5} +(8.60985 + 7.22452i) q^{7} +(-1.95705 + 7.30380i) q^{8} +(-0.428176 + 0.741623i) q^{10} +(-6.75804 + 3.90176i) q^{11} +(-1.02592 - 0.478396i) q^{13} +(-3.26242 - 12.1755i) q^{14} +(-1.90644 + 1.59969i) q^{16} +(7.60116 + 16.3007i) q^{17} +(-26.5585 + 18.5965i) q^{19} +(-1.89771 + 0.884915i) q^{20} +(8.71839 + 0.762760i) q^{22} +(40.1171 - 10.7493i) q^{23} +(24.0460 - 4.23996i) q^{25} +(0.634762 + 1.09944i) q^{26} +(10.5413 - 28.9621i) q^{28} +(5.98657 + 1.60410i) q^{29} +(13.1478 - 13.1478i) q^{31} +(32.9111 - 2.87935i) q^{32} +(3.50271 - 19.8648i) q^{34} +(4.92247 - 7.03002i) q^{35} +(-23.2685 + 28.7676i) q^{37} +36.3614 q^{38} +(5.68600 + 1.00260i) q^{40} +(21.1432 + 58.0906i) q^{41} +(15.5474 + 15.5474i) q^{43} +(16.3926 + 13.7550i) q^{44} +(-43.7696 - 15.9308i) q^{46} +(0.753031 - 1.30429i) q^{47} +(13.4270 + 76.1485i) q^{49} +(-24.8181 - 11.5729i) q^{50} +(-0.270544 + 3.09233i) q^{52} +(43.3876 - 36.4065i) q^{53} +(3.41768 + 4.88096i) q^{55} +(-69.6163 + 48.7459i) q^{56} +(-4.46790 - 5.32464i) q^{58} +(-80.4298 - 7.03669i) q^{59} +(33.3617 - 71.5444i) q^{61} +(-20.5363 + 3.62110i) q^{62} +(-23.4661 - 13.5482i) q^{64} +(-0.295625 + 0.812224i) q^{65} +(49.7451 - 59.2839i) q^{67} +(34.8754 - 34.8754i) q^{68} +(-9.04440 + 3.29189i) q^{70} +(2.29618 - 13.0223i) q^{71} +88.1001i q^{73} +(39.8818 - 11.4604i) q^{74} +(72.8293 + 50.9956i) q^{76} +(-86.3740 - 15.2301i) q^{77} +(3.55184 + 40.5977i) q^{79} +(1.34371 + 1.34371i) q^{80} +(17.9439 - 66.9677i) q^{82} +(-4.62098 - 1.68190i) q^{83} +(11.8936 - 6.86676i) q^{85} +(-4.28199 - 24.2844i) q^{86} +(-15.2718 - 56.9953i) q^{88} +(-6.89035 + 78.7571i) q^{89} +(-5.37686 - 11.5307i) q^{91} +(-65.3250 - 93.2938i) q^{92} +(-1.53081 + 0.713827i) q^{94} +(15.9132 + 18.9646i) q^{95} +(-75.0980 + 20.1225i) q^{97} +(36.6488 - 78.5936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8}+O(q^{10}) \) 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8	\( 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8} - 72 q^{13} - 42 q^{14} - 6 q^{16} + 24 q^{17} + 108 q^{19} + 354 q^{20} + 18 q^{25} + 30 q^{26} + 48 q^{28} + 156 q^{29} - 60 q^{31} + 192 q^{32} - 90 q^{34} - 24 q^{35} - 294 q^{37} + 120 q^{38} + 612 q^{40} - 300 q^{41} - 60 q^{43} - 174 q^{44} + 234 q^{46} - 66 q^{47} - 144 q^{49} + 252 q^{50} + 912 q^{52} - 234 q^{53} + 234 q^{55} - 312 q^{56} - 1014 q^{58} + 18 q^{59} - 720 q^{61} + 1092 q^{62} + 54 q^{64} + 54 q^{65} - 708 q^{67} + 408 q^{68} - 228 q^{70} - 234 q^{74} + 90 q^{76} + 18 q^{77} + 360 q^{79} - 924 q^{80} + 1134 q^{82} - 438 q^{83} - 756 q^{85} - 396 q^{86} + 684 q^{88} - 1470 q^{89} + 1170 q^{91} - 1602 q^{92} - 1008 q^{94} + 984 q^{95} - 774 q^{97} + 1038 q^{98}+O(q^{100}) \) 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8 - 72 * q^13 - 42 * q^14 - 6 * q^16 + 24 * q^17 + 108 * q^19 + 354 * q^20 + 18 * q^25 + 30 * q^26 + 48 * q^28 + 156 * q^29 - 60 * q^31 + 192 * q^32 - 90 * q^34 - 24 * q^35 - 294 * q^37 + 120 * q^38 + 612 * q^40 - 300 * q^41 - 60 * q^43 - 174 * q^44 + 234 * q^46 - 66 * q^47 - 144 * q^49 + 252 * q^50 + 912 * q^52 - 234 * q^53 + 234 * q^55 - 312 * q^56 - 1014 * q^58 + 18 * q^59 - 720 * q^61 + 1092 * q^62 + 54 * q^64 + 54 * q^65 - 708 * q^67 + 408 * q^68 - 228 * q^70 - 234 * q^74 + 90 * q^76 + 18 * q^77 + 360 * q^79 - 924 * q^80 + 1134 * q^82 - 438 * q^83 - 756 * q^85 - 396 * q^86 + 684 * q^88 - 1470 * q^89 + 1170 * q^91 - 1602 * q^92 - 1008 * q^94 + 984 * q^95 - 774 * q^97 + 1038 * q^98

Introduction

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