LMFDB - Embedded newform 333.3.bu.c.55.5

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			55.5
Character	$\chi$	$=$	333.55
Dual form			333.3.bu.c.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.135828 + 1.55252i) q^{2} +(1.54735 - 0.272840i) q^{4} +(-3.79373 + 1.76905i) q^{5} +(3.40196 + 1.23821i) q^{7} +(2.24719 + 8.38664i) q^{8} +O(q^{10})$	\(q+(0.135828 + 1.55252i) q^{2} +(1.54735 - 0.272840i) q^{4} +(-3.79373 + 1.76905i) q^{5} +(3.40196 + 1.23821i) q^{7} +(2.24719 + 8.38664i) q^{8} +(-3.26178 - 5.64957i) q^{10} +(4.53915 + 2.62068i) q^{11} +(-2.94875 - 2.06473i) q^{13} +(-1.46027 + 5.44980i) q^{14} +(-6.80935 + 2.47840i) q^{16} +(9.96208 + 14.2273i) q^{17} +(-1.21516 + 13.8894i) q^{19} +(-5.38758 + 3.77243i) q^{20} +(-3.45212 + 7.40309i) q^{22} +(-31.6712 - 8.48627i) q^{23} +(-4.80680 + 5.72852i) q^{25} +(2.80502 - 4.85844i) q^{26} +(5.60187 + 0.987760i) q^{28} +(2.50460 - 0.671105i) q^{29} +(33.7821 + 33.7821i) q^{31} +(9.90485 + 21.2410i) q^{32} +(-20.7351 + 17.3988i) q^{34} +(-15.0966 + 1.32078i) q^{35} +(17.8177 + 32.4273i) q^{37} -21.7286 q^{38} +(-23.3616 - 27.8413i) q^{40} +(-23.9533 + 4.22361i) q^{41} +(8.38771 - 8.38771i) q^{43} +(7.73869 + 2.81665i) q^{44} +(8.87329 - 50.3229i) q^{46} +(-14.9928 - 25.9682i) q^{47} +(-27.4960 - 23.0719i) q^{49} +(-9.54656 - 6.68457i) q^{50} +(-5.12610 - 2.39034i) q^{52} +(15.4429 - 5.62074i) q^{53} +(-21.8564 - 1.91219i) q^{55} +(-2.73958 + 31.3135i) q^{56} +(1.38210 + 3.79729i) q^{58} +(31.6273 - 67.8249i) q^{59} +(-22.4275 + 32.0298i) q^{61} +(-47.8589 + 57.0360i) q^{62} +(-56.7339 + 32.7553i) q^{64} +(14.8394 + 2.61658i) q^{65} +(9.59191 - 26.3536i) q^{67} +(19.2966 + 19.2966i) q^{68} +(-4.10108 - 23.2584i) q^{70} +(50.4301 - 42.3159i) q^{71} -43.5704i q^{73} +(-47.9240 + 32.0669i) q^{74} +(1.90929 + 21.8233i) q^{76} +(12.1970 + 14.5359i) q^{77} +(104.359 - 48.6636i) q^{79} +(21.4484 - 21.4484i) q^{80} +(-9.81078 - 36.6143i) q^{82} +(-9.46921 + 53.7026i) q^{83} +(-62.9623 - 36.3513i) q^{85} +(14.1614 + 11.8828i) q^{86} +(-11.7783 + 43.9574i) q^{88} +(116.687 + 54.4119i) q^{89} +(-7.47493 - 10.6753i) q^{91} +(-51.3220 - 4.49009i) q^{92} +(38.2798 - 26.8038i) q^{94} +(-19.9609 - 54.8422i) q^{95} +(49.4781 + 13.2576i) q^{97} +(32.0849 - 45.8220i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{17}{36}\right)$

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 $

$2$	0.135828	+	1.55252i	0.0679141	+	0.776261i	0.951431	+	0.307862i	$0.0996135\pi$
$2$	0.135828	+	1.55252i	0.0679141	+	0.776261i	−0.883517	+	0.468399i	$0.844831\pi$
$3$		0			0
$3$		0			0
$4$	1.54735	−	0.272840i	0.386839	−	0.0682101i
$5$	−3.79373	+	1.76905i	−0.758747	+	0.353809i	−0.763184	−	0.646181i	$-0.776365\pi$
$5$	−3.79373	+	1.76905i	−0.758747	+	0.353809i	0.00443764	+	0.999990i	$0.498587\pi$
$6$		0			0
$7$	3.40196	+	1.23821i	0.485994	+	0.176887i	0.573384	−	0.819287i	$-0.305630\pi$
$7$	3.40196	+	1.23821i	0.485994	+	0.176887i	−0.0873900	+	0.996174i	$0.527853\pi$
$8$	2.24719	+	8.38664i	0.280899	+	1.04833i
$9$		0			0
$10$	−3.26178	−	5.64957i	−0.326178	−	0.564957i
$11$	4.53915	+	2.62068i	0.412650	+	0.238243i	0.691928	−	0.721967i	$-0.256762\pi$
$11$	4.53915	+	2.62068i	0.412650	+	0.238243i	−0.279278	+	0.960210i	$0.590095\pi$
$12$		0			0
$13$	−2.94875	−	2.06473i	−0.226827	−	0.158826i	0.454639	−	0.890676i	$-0.349768\pi$
$13$	−2.94875	−	2.06473i	−0.226827	−	0.158826i	−0.681466	+	0.731850i	$0.738657\pi$
$14$	−1.46027	+	5.44980i	−0.104305	+	0.389271i
$15$		0			0
$16$	−6.80935	+	2.47840i	−0.425584	+	0.154900i
$17$	9.96208	+	14.2273i	0.586005	+	0.836901i	0.997210	−	0.0746412i	$-0.0237811\pi$
$17$	9.96208	+	14.2273i	0.586005	+	0.836901i	−0.411206	+	0.911543i	$0.634892\pi$
$18$		0			0
$19$	−1.21516	+	13.8894i	−0.0639559	+	0.731019i	0.894740	+	0.446587i	$0.147361\pi$
$19$	−1.21516	+	13.8894i	−0.0639559	+	0.731019i	−0.958696	+	0.284432i	$0.908195\pi$
$20$	−5.38758	+	3.77243i	−0.269379	+	0.188621i
$21$		0			0
$22$	−3.45212	+	7.40309i	−0.156914	+	0.336504i
$23$	−31.6712	−	8.48627i	−1.37701	−	0.368968i	−0.506975	−	0.861961i	$-0.669236\pi$
$23$	−31.6712	−	8.48627i	−1.37701	−	0.368968i	−0.870034	+	0.492992i	$0.835903\pi$
$24$		0			0
$25$	−4.80680	+	5.72852i	−0.192272	+	0.229141i
$26$	2.80502	−	4.85844i	0.107886	−	0.186863i
$27$		0			0
$28$	5.60187	+	0.987760i	0.200067	+	0.0352771i
$29$	2.50460	−	0.671105i	0.0863655	−	0.0231416i	−0.215378	−	0.976531i	$-0.569098\pi$
$29$	2.50460	−	0.671105i	0.0863655	−	0.0231416i	0.301743	+	0.953389i	$0.402432\pi$
$30$		0			0
$31$	33.7821	+	33.7821i	1.08975	+	1.08975i	0.995554	+	0.0941910i	$0.0300264\pi$
$31$	33.7821	+	33.7821i	1.08975	+	1.08975i	0.0941910	+	0.995554i	$0.469974\pi$
$32$	9.90485	+	21.2410i	0.309526	+	0.663782i
$33$		0			0
$34$	−20.7351	+	17.3988i	−0.609856	+	0.511730i
$35$	−15.0966	+	1.32078i	−0.431331	+	0.0377365i
$36$		0			0
$37$	17.8177	+	32.4273i	0.481560	+	0.876413i
$37$	17.8177	+	32.4273i	0.481560	+	0.876413i
$38$	−21.7286			−0.571805
$39$		0			0
$40$	−23.3616	−	27.8413i	−0.584041	−	0.696032i
$41$	−23.9533	+	4.22361i	−0.584226	+	0.103015i	−0.457946	−	0.888980i	$-0.651415\pi$
$41$	−23.9533	+	4.22361i	−0.584226	+	0.103015i	−0.126280	+	0.991995i	$0.540304\pi$
$42$		0			0
$43$	8.38771	−	8.38771i	0.195063	−	0.195063i	−0.602817	−	0.797880i	$-0.705955\pi$
$43$	8.38771	−	8.38771i	0.195063	−	0.195063i	0.797880	+	0.602817i	$0.205955\pi$
$44$	7.73869	+	2.81665i	0.175879	+	0.0640149i
$45$		0			0
$46$	8.87329	−	50.3229i	0.192898	−	1.09398i
$47$	−14.9928	−	25.9682i	−0.318995	−	0.552515i	0.661284	−	0.750136i	$-0.270012\pi$
$47$	−14.9928	−	25.9682i	−0.318995	−	0.552515i	−0.980279	+	0.197621i	$0.936679\pi$
$48$		0			0
$49$	−27.4960	−	23.0719i	−0.561144	−	0.470855i
$50$	−9.54656	−	6.68457i	−0.190931	−	0.133691i
$51$		0			0
$52$	−5.12610	−	2.39034i	−0.0985788	−	0.0459680i
$53$	15.4429	−	5.62074i	0.291375	−	0.106052i	−0.192197	−	0.981356i	$-0.561561\pi$
$53$	15.4429	−	5.62074i	0.291375	−	0.106052i	0.483572	+	0.875305i	$0.339339\pi$
$54$		0			0
$55$	−21.8564	−	1.91219i	−0.397389	−	0.0347671i
$56$	−2.73958	+	31.3135i	−0.0489210	+	0.559170i
$57$		0			0
$58$	1.38210	+	3.79729i	0.0238293	+	0.0654705i
$59$	31.6273	−	67.8249i	0.536055	−	1.14957i	−0.432696	−	0.901540i	$-0.642438\pi$
$59$	31.6273	−	67.8249i	0.536055	−	1.14957i	0.968751	−	0.248034i	$-0.0797845\pi$
$60$		0			0
$61$	−22.4275	+	32.0298i	−0.367664	+	0.525078i	−0.959772	−	0.280780i	$-0.909407\pi$
$61$	−22.4275	+	32.0298i	−0.367664	+	0.525078i	0.592108	+	0.805858i	$0.298296\pi$
$62$	−47.8589	+	57.0360i	−0.771918	+	0.919936i
$63$		0			0
$64$	−56.7339	+	32.7553i	−0.886467	+	0.511802i
$65$	14.8394	+	2.61658i	0.228298	+	0.0402551i
$66$		0			0
$67$	9.59191	−	26.3536i	0.143163	−	0.393337i	−0.847300	−	0.531114i	$-0.821774\pi$
$67$	9.59191	−	26.3536i	0.143163	−	0.393337i	0.990463	+	0.137777i	$0.0439958\pi$
$68$	19.2966	+	19.2966i	0.283774	+	0.283774i
$69$		0			0
$70$	−4.10108	−	23.2584i	−0.0585868	−	0.332262i
$71$	50.4301	−	42.3159i	0.710283	−	0.595998i	−0.214396	−	0.976747i	$-0.568778\pi$
$71$	50.4301	−	42.3159i	0.710283	−	0.595998i	0.924679	+	0.380749i	$0.124334\pi$
$72$		0			0
$73$		−	43.5704i		−	0.596854i	−0.954432	−	0.298427i	$-0.903538\pi$
$73$		−	43.5704i		−	0.596854i	0.954432	−	0.298427i	$-0.0964620\pi$
$74$	−47.9240	+	32.0669i	−0.647621	+	0.433337i
$75$		0			0
$76$	1.90929	+	21.8233i	0.0251223	+	0.287149i
$77$	12.1970	+	14.5359i	0.158403	+	0.188777i
$78$		0			0
$79$	104.359	−	48.6636i	1.32101	−	0.615995i	0.371118	−	0.928586i	$-0.378975\pi$
$79$	104.359	−	48.6636i	1.32101	−	0.615995i	0.949888	+	0.312590i	$0.101197\pi$
$80$	21.4484	−	21.4484i	0.268106	−	0.268106i
$81$		0			0
$82$	−9.81078	−	36.6143i	−0.119644	−	0.446516i
$83$	−9.46921	+	53.7026i	−0.114087	+	0.647019i	0.873111	+	0.487521i	$0.162099\pi$
$83$	−9.46921	+	53.7026i	−0.114087	+	0.647019i	−0.987198	+	0.159498i	$0.949012\pi$
$84$		0			0
$85$	−62.9623	−	36.3513i	−0.740733	−	0.427662i
$86$	14.1614	+	11.8828i	0.164667	+	0.138172i
$87$		0			0
$88$	−11.7783	+	43.9574i	−0.133845	+	0.499516i
$89$	116.687	+	54.4119i	1.31109	+	0.611370i	0.947370	−	0.320140i	$-0.103730\pi$
$89$	116.687	+	54.4119i	1.31109	+	0.611370i	0.363716	+	0.931510i	$0.381508\pi$
$90$		0			0
$91$	−7.47493	−	10.6753i	−0.0821421	−	0.117311i
$92$	−51.3220	−	4.49009i	−0.557847	−	0.0488053i
$93$		0			0
$94$	38.2798	−	26.8038i	0.407232	−	0.285147i
$95$	−19.9609	−	54.8422i	−0.210115	−	0.577287i
$96$		0			0
$97$	49.4781	+	13.2576i	0.510084	+	0.136677i	0.504676	−	0.863309i	$-0.331612\pi$
$97$	49.4781	+	13.2576i	0.510084	+	0.136677i	0.00540791	+	0.999985i	$0.498279\pi$
$98$	32.0849	−	45.8220i	0.327397	−	0.467572i
$99$		0			0
$100$	−5.87485	+	10.1755i	−0.0587485	+	0.101755i
$101$	55.2810	−	31.9165i	0.547337	−	0.316005i	−0.200710	−	0.979651i	$-0.564325\pi$
$101$	55.2810	−	31.9165i	0.547337	−	0.316005i	0.748047	+	0.663646i	$0.230992\pi$
$102$		0			0
$103$	−18.9480	+	5.07709i	−0.183961	+	0.0492922i	−0.349623	−	0.936890i	$-0.613690\pi$
$103$	−18.9480	+	5.07709i	−0.183961	+	0.0492922i	0.165662	+	0.986183i	$0.447024\pi$
$104$	10.6898	−	29.3699i	0.102786	−	0.282403i
$105$		0			0
$106$	10.8239	+	23.2119i	0.102112	+	0.218981i
$107$	−17.6627	−	100.170i	−0.165072	−	0.936170i	−0.948990	−	0.315306i	$-0.897893\pi$
$107$	−17.6627	−	100.170i	−0.165072	−	0.936170i	0.783918	−	0.620864i	$-0.213218\pi$
$108$		0			0
$109$	86.5751	−	7.57434i	0.794267	−	0.0694894i	0.317203	−	0.948358i	$-0.397256\pi$
$109$	86.5751	−	7.57434i	0.794267	−	0.0694894i	0.477064	+	0.878868i	$0.341701\pi$
$110$		−	34.1923i		−	0.310839i
$111$		0			0
$112$	−26.2339			−0.234231
$113$	−8.04608	−	91.9671i	−0.0712042	−	0.813868i	−0.944892	−	0.327382i	$-0.893834\pi$
$113$	−8.04608	−	91.9671i	−0.0712042	−	0.813868i	0.873688	−	0.486487i	$-0.161722\pi$
$114$		0			0
$115$	135.165	−	23.8332i	1.17535	−	0.207245i
$116$	3.69240	−	1.72179i	0.0318310	−	0.0148430i
$117$		0			0
$118$	109.596	+	39.8895i	0.928775	+	0.338047i
$119$	16.2741	+	60.7359i	0.136757	+	0.510386i
$120$		0			0
$121$	−46.7641	−	80.9978i	−0.386480	−	0.669403i
$122$	−52.7732	−	30.4686i	−0.432568	−	0.249743i
$123$		0			0
$124$	61.4900	+	43.0558i	0.495887	+	0.347224i
$125$	35.1866	−	131.318i	0.281493	−	1.05055i
$126$		0			0
$127$	106.262	−	38.6761i	0.836706	−	0.304536i	0.112098	−	0.993697i	$-0.464243\pi$
$127$	106.262	−	38.6761i	0.836706	−	0.304536i	0.724608	+	0.689161i	$0.242021\pi$
$128$	−4.78813	−	6.83815i	−0.0374072	−	0.0534231i
$129$		0			0
$130$	−2.04670	+	23.3939i	−0.0157438	+	0.179953i
$131$	159.000	−	111.333i	1.21374	−	0.849870i	0.221616	−	0.975134i	$-0.428867\pi$
$131$	159.000	−	111.333i	1.21374	−	0.849870i	0.992123	+	0.125264i	$0.0399779\pi$
$132$		0			0
$133$	−21.3319	+	45.7464i	−0.160390	+	0.343958i
$134$	42.2173	+	11.3121i	0.315055	+	0.0844187i
$135$		0			0
$136$	−96.9327	+	115.520i	−0.712741	+	0.849411i
$137$	−39.7084	+	68.7769i	−0.289842	+	0.502021i	−0.973772	−	0.227527i	$-0.926936\pi$
$137$	−39.7084	+	68.7769i	−0.289842	+	0.502021i	0.683930	+	0.729548i	$0.260269\pi$
$138$		0			0
$139$	−184.366	−	32.5086i	−1.32637	−	0.233875i	−0.534814	−	0.844970i	$-0.679618\pi$
$139$	−184.366	−	32.5086i	−1.32637	−	0.233875i	−0.791557	+	0.611095i	$0.790729\pi$
$140$	−22.9994	+	6.16267i	−0.164281	+	0.0440190i
$141$		0			0
$142$	72.5462	+	72.5462i	0.510889	+	0.510889i
$143$	−7.97379	−	17.0998i	−0.0557607	−	0.119579i
$144$		0			0
$145$	−8.31457	+	6.97675i	−0.0573418	+	0.0481155i
$146$	67.6440	−	5.91808i	0.463315	−	0.0405348i
$147$		0			0
$148$	36.4178	+	45.3151i	0.246066	+	0.306183i
$149$	194.988			1.30865			0.654323	−	0.756215i	$-0.272954\pi$
$149$	194.988			1.30865			0.654323	+	0.756215i	$0.272954\pi$
$150$		0			0
$151$	169.747	+	202.297i	1.12415	+	1.33971i	0.933716	+	0.358014i	$0.116546\pi$
$151$	169.747	+	202.297i	1.12415	+	1.33971i	0.190437	+	0.981699i	$0.439010\pi$
$152$	−119.216	+	21.0210i	−0.784315	+	0.138296i
$153$		0			0
$154$	−20.9105	+	20.9105i	−0.135783	+	0.135783i
$155$	−187.922	−	68.3982i	−1.21240	−	0.441279i
$156$		0			0
$157$	1.59290	−	9.03381i	0.0101459	−	0.0575402i	−0.979314	−	0.202344i	$-0.935144\pi$
$157$	1.59290	−	9.03381i	0.0101459	−	0.0575402i	0.989460	+	0.144804i	$0.0462552\pi$
$158$	89.7263	+	155.411i	0.567888	+	0.983611i
$159$		0			0
$160$	−75.1527	−	63.0606i	−0.469704	−	0.394129i
$161$	−97.2363	−	68.0856i	−0.603952	−	0.422892i
$162$		0			0
$163$	−203.082	−	94.6987i	−1.24590	−	0.580973i	−0.315992	−	0.948762i	$-0.602337\pi$
$163$	−203.082	−	94.6987i	−1.24590	−	0.580973i	−0.929909	+	0.367789i	$0.880115\pi$
$164$	−35.9118	+	13.0708i	−0.218975	+	0.0797002i
$165$		0			0
$166$	−84.6606	−	7.40685i	−0.510004	−	0.0446196i
$167$	−21.7386	+	248.473i	−0.130171	+	1.48786i	0.597463	+	0.801896i	$0.296175\pi$
$167$	−21.7386	+	248.473i	−0.130171	+	1.48786i	−0.727634	+	0.685965i	$0.759380\pi$
$168$		0			0
$169$	−53.3694	−	146.631i	−0.315795	−	0.867641i
$170$	47.8841	−	102.688i	0.281671	−	0.604046i
$171$		0			0
$172$	10.6902	−	15.2673i	0.0621526	−	0.0887631i
$173$	−114.601	+	136.576i	−0.662434	+	0.789458i	−0.987733	−	0.156154i	$-0.950091\pi$
$173$	−114.601	+	136.576i	−0.662434	+	0.789458i	0.325299	+	0.945611i	$0.394535\pi$
$174$		0			0
$175$	−23.4456	+	13.5364i	−0.133975	+	0.0773506i
$176$	−37.4037	−	6.59528i	−0.212521	−	0.0374732i
$177$		0			0
$178$	−68.6264	+	188.549i	−0.385541	+	1.05927i
$179$	82.9520	+	82.9520i	0.463419	+	0.463419i	0.899774	−	0.436355i	$-0.143731\pi$
$179$	82.9520	+	82.9520i	0.463419	+	0.463419i	−0.436355	+	0.899774i	$0.643731\pi$
$180$		0			0
$181$	−39.4274	−	223.604i	−0.217831	−	1.23538i	−0.875926	−	0.482446i	$-0.839748\pi$
$181$	−39.4274	−	223.604i	−0.217831	−	1.23538i	0.658095	−	0.752935i	$-0.271363\pi$
$182$	15.5583	−	13.0550i	0.0854854	−	0.0717308i
$183$		0			0
$184$		−	284.685i		−	1.54720i
$185$	−124.961	−	91.5002i	−0.675465	−	0.494595i
$186$		0			0
$187$	7.93411	+	90.6873i	0.0424284	+	0.484959i
$188$	−30.2843	−	36.0914i	−0.161087	−	0.191975i
$189$		0			0
$190$	82.4326	−	38.4389i	0.433856	−	0.202310i
$191$	−125.816	+	125.816i	−0.658724	+	0.658724i	−0.955078	−	0.296354i	$-0.904229\pi$
$191$	−125.816	+	125.816i	−0.658724	+	0.658724i	0.296354	+	0.955078i	$0.404229\pi$
$192$		0			0
$193$	−85.2379	−	318.112i	−0.441647	−	1.64825i	−0.724640	−	0.689128i	$-0.757994\pi$
$193$	−85.2379	−	318.112i	−0.441647	−	1.64825i	0.282993	−	0.959122i	$-0.408673\pi$
$194$	−13.8622	+	78.6167i	−0.0714549	+	0.405241i
$195$		0			0
$196$	−48.8410	−	28.1984i	−0.249189	−	0.143869i
$197$	−18.7068	−	15.6968i	−0.0949581	−	0.0796793i	0.594073	−	0.804411i	$-0.297519\pi$
$197$	−18.7068	−	15.6968i	−0.0949581	−	0.0796793i	−0.689031	+	0.724732i	$0.741964\pi$
$198$		0			0
$199$	−93.8256	+	350.162i	−0.471486	+	1.75961i	0.162952	+	0.986634i	$0.447899\pi$
$199$	−93.8256	+	350.162i	−0.471486	+	1.75961i	−0.634437	+	0.772974i	$0.718768\pi$
$200$	−58.8449	−	27.4398i	−0.294224	−	0.137199i
$201$		0			0
$202$	57.0598	+	81.4899i	0.282474	+	0.403415i
$203$	9.35151	+	0.818151i	0.0460665	+	0.00403030i
$204$		0			0
$205$	83.4006	−	58.3977i	0.406832	−	0.284867i
$206$	−10.4560	−	28.7275i	−0.0507571	−	0.139454i
$207$		0			0
$208$	25.1963	+	6.75132i	0.121136	+	0.0324583i
$209$	−41.9153	+	59.8613i	−0.200552	+	0.286418i
$210$		0			0
$211$	118.380	−	205.040i	0.561042	−	0.971753i	−0.436364	−	0.899770i	$-0.643734\pi$
$211$	118.380	−	205.040i	0.561042	−	0.971753i	0.997406	−	0.0719830i	$-0.0229327\pi$
$212$	22.3620	−	12.9107i	0.105481	−	0.0608996i
$213$		0			0
$214$	153.117	−	41.0277i	0.715502	−	0.191718i
$215$	−16.9825	+	46.6590i	−0.0789883	+	0.217019i
$216$		0			0
$217$	73.0959	+	156.755i	0.336847	+	0.722371i
$218$	23.5187	+	133.381i	0.107884	+	0.611840i
$219$		0			0
$220$	−34.3413	+	3.00448i	−0.156097	+	0.0136567i
$221$		−	62.5218i		−	0.282904i
$222$		0			0
$223$	−340.025			−1.52477			−0.762387	−	0.647121i	$-0.775973\pi$
$223$	−340.025			−1.52477			−0.762387	+	0.647121i	$0.775973\pi$
$224$	7.39500	+	84.5253i	0.0330134	+	0.377345i
$225$		0			0
$226$	141.688	−	24.9834i	0.626939	−	0.110546i
$227$	14.2180	−	6.62998i	0.0626346	−	0.0292070i	−0.391049	−	0.920370i	$-0.627888\pi$
$227$	14.2180	−	6.62998i	0.0626346	−	0.0292070i	0.453683	+	0.891163i	$0.350110\pi$
$228$		0			0
$229$	−323.581	−	117.774i	−1.41302	−	0.514297i	−0.481005	−	0.876718i	$-0.659728\pi$
$229$	−323.581	−	117.774i	−1.41302	−	0.514297i	−0.932014	+	0.362421i	$0.881950\pi$
$230$	55.3607	+	206.609i	0.240699	+	0.898300i
$231$		0			0
$232$	11.2566	+	19.4971i	0.0485200	+	0.0840391i
$233$	252.704	+	145.899i	1.08457	+	0.626174i	0.932124	−	0.362138i	$-0.117953\pi$
$233$	252.704	+	145.899i	1.08457	+	0.626174i	0.152441	+	0.988313i	$0.451287\pi$
$234$		0			0
$235$	102.817	+	71.9936i	0.437521	+	0.306356i
$236$	30.4332	−	113.578i	0.128954	−	0.481264i
$237$		0			0
$238$	−92.0834	+	33.5156i	−0.386905	+	0.140822i
$239$	−84.8179	−	121.132i	−0.354886	−	0.506830i	0.601525	−	0.798854i	$-0.294560\pi$
$239$	−84.8179	−	121.132i	−0.354886	−	0.506830i	−0.956411	+	0.292024i	$0.905671\pi$
$240$		0			0
$241$	−17.2639	+	197.327i	−0.0716342	+	0.818783i	0.872369	+	0.488848i	$0.162583\pi$
$241$	−17.2639	+	197.327i	−0.0716342	+	0.818783i	−0.944003	+	0.329936i	$0.892973\pi$
$242$	119.399	−	83.6041i	0.493384	−	0.345471i
$243$		0			0
$244$	−25.9643	+	55.6805i	−0.106411	+	0.228199i
$245$	145.128	+	38.8869i	0.592359	+	0.158722i
$246$		0			0
$247$	32.2610	−	38.4472i	0.130612	−	0.155657i
$248$	−207.403	+	359.233i	−0.836304	+	1.44852i
$249$		0			0
$250$	208.654	+	36.7913i	0.834615	+	0.147165i
$251$	−103.370	+	27.6979i	−0.411833	+	0.110350i	−0.458786	−	0.888547i	$-0.651716\pi$
$251$	−103.370	+	27.6979i	−0.411833	+	0.110350i	0.0469531	+	0.998897i	$0.485049\pi$
$252$		0			0
$253$	−121.520	−	121.520i	−0.480318	−	0.480318i
$254$	74.4788	+	159.720i	0.293224	+	0.628820i
$255$		0			0
$256$	−190.770	+	160.075i	−0.745196	+	0.625294i
$257$	−220.026	+	19.2498i	−0.856134	+	0.0749020i	−0.506766	−	0.862084i	$-0.669159\pi$
$257$	−220.026	+	19.2498i	−0.856134	+	0.0749020i	−0.349368	+	0.936986i	$0.613604\pi$
$258$		0			0
$259$	20.4632	+	132.378i	0.0790086	+	0.511113i
$260$	23.6757			0.0910603
$261$		0			0
$262$	194.443	+	231.729i	0.742151	+	0.884461i
$263$	−77.0501	+	13.5860i	−0.292966	+	0.0516578i	−0.318199	−	0.948024i	$-0.603078\pi$
$263$	−77.0501	+	13.5860i	−0.292966	+	0.0516578i	0.0252335	+	0.999682i	$0.491967\pi$
$264$		0			0
$265$	−48.6427	+	48.6427i	−0.183558	+	0.183558i
$266$	−73.9198	−	26.9046i	−0.277894	−	0.101145i
$267$		0			0
$268$	7.65177	−	43.3954i	0.0285514	−	0.161923i
$269$	−117.601	−	203.691i	−0.437179	−	0.757216i	0.560292	−	0.828295i	$-0.310689\pi$
$269$	−117.601	−	203.691i	−0.437179	−	0.757216i	−0.997471	+	0.0710793i	$0.977356\pi$
$270$		0			0
$271$	94.7307	+	79.4885i	0.349560	+	0.293315i	0.800613	−	0.599182i	$-0.204507\pi$
$271$	94.7307	+	79.4885i	0.349560	+	0.293315i	−0.451054	+	0.892497i	$0.648952\pi$
$272$	−103.096	−	72.1888i	−0.379030	−	0.265400i
$273$		0			0
$274$	−112.171	−	52.3063i	−0.409384	−	0.190899i
$275$	−36.8314	+	13.4055i	−0.133932	+	0.0487474i
$276$		0			0
$277$	215.163	+	18.8243i	0.776761	+	0.0679578i	0.468640	−	0.883389i	$-0.344744\pi$
$277$	215.163	+	18.8243i	0.776761	+	0.0679578i	0.308121	+	0.951347i	$0.400300\pi$
$278$	25.4283	−	290.647i	0.0914689	−	1.04549i
$279$		0			0
$280$	−45.0018	−	123.642i	−0.160721	−	0.441577i
$281$	166.904	−	357.927i	0.593964	−	1.27376i	−0.347826	−	0.937559i	$-0.613080\pi$
$281$	166.904	−	357.927i	0.593964	−	1.27376i	0.941790	−	0.336201i	$-0.109142\pi$
$282$		0			0
$283$	−218.200	+	311.622i	−0.771026	+	1.10114i	0.221021	+	0.975269i	$0.429061\pi$
$283$	−218.200	+	311.622i	−0.771026	+	1.10114i	−0.992047	+	0.125870i	$0.959828\pi$
$284$	66.4877	−	79.2370i	0.234112	−	0.279004i
$285$		0			0
$286$	25.4648	−	14.7021i	0.0890378	−	0.0514060i
$287$	−86.7178	−	15.2907i	−0.302152	−	0.0532776i
$288$		0			0
$289$	−4.32987	+	11.8962i	−0.0149823	+	0.0411634i
$290$	−11.9609	−	11.9609i	−0.0412445	−	0.0412445i
$291$		0			0
$292$	−11.8878	−	67.4188i	−0.0407115	−	0.230886i
$293$	−60.4669	+	50.7378i	−0.206372	+	0.173166i	−0.740115	−	0.672480i	$-0.765229\pi$
$293$	−60.4669	+	50.7378i	−0.206372	+	0.173166i	0.533744	+	0.845646i	$0.320785\pi$
$294$		0			0
$295$			313.260i			1.06190i
$296$	−231.916	+	222.301i	−0.783501	+	0.751017i
$297$		0			0
$298$	26.4849	+	302.724i	0.0888755	+	1.01585i
$299$	75.8684	+	90.4165i	0.253741	+	0.302396i
$300$		0			0
$301$	38.9204	−	18.1489i	0.129304	−	0.0602952i
$302$	−291.014	+	291.014i	−0.963622	+	0.963622i
$303$		0			0
$304$	−26.1489	−	97.5892i	−0.0860162	−	0.321017i
$305$	28.4218	−	161.188i	0.0931861	−	0.528484i
$306$		0			0
$307$	173.214	+	100.005i	0.564215	+	0.325750i	0.754836	−	0.655914i	$-0.227717\pi$
$307$	173.214	+	100.005i	0.564215	+	0.325750i	−0.190620	+	0.981664i	$0.561050\pi$
$308$	22.8391	+	19.1643i	0.0741529	+	0.0622217i
$309$		0			0
$310$	80.6645	−	301.044i	0.260208	−	0.971110i
$311$	127.675	+	59.5357i	0.410530	+	0.191433i	0.616901	−	0.787041i	$-0.288388\pi$
$311$	127.675	+	59.5357i	0.410530	+	0.191433i	−0.206372	+	0.978474i	$0.566166\pi$
$312$		0			0
$313$	208.427	+	297.664i	0.665900	+	0.951003i	0.999964	+	0.00845326i	$0.00269079\pi$
$313$	208.427	+	297.664i	0.665900	+	0.951003i	−0.334064	+	0.942550i	$0.608420\pi$
$314$	14.2416	+	1.24597i	0.0453553	+	0.00396807i
$315$		0			0
$316$	148.204	−	103.773i	0.468999	−	0.328397i
$317$	89.3478	+	245.481i	0.281854	+	0.774388i	0.997141	+	0.0755573i	$0.0240736\pi$
$317$	89.3478	+	245.481i	0.281854	+	0.774388i	−0.715287	+	0.698830i	$0.753704\pi$
$318$		0			0
$319$	13.1275	+	3.51750i	0.0411520	+	0.0110266i
$320$	157.288	−	224.630i	0.491524	−	0.701969i
$321$		0			0
$322$	92.4970	−	160.209i	0.287258	−	0.497545i
$323$	−209.714	+	121.078i	−0.649269	+	0.374856i
$324$		0			0
$325$	26.0019	−	6.96719i	0.0800059	−	0.0214375i
$326$	119.438	−	328.152i	0.366373	−	1.00660i
$327$		0			0
$328$	−89.2496	−	191.396i	−0.272102	−	0.583525i
$329$	−18.8506	−	106.907i	−0.0572966	−	0.324945i
$330$		0			0
$331$	516.476	−	45.1858i	1.56035	−	0.136513i	0.725980	−	0.687716i	$-0.241387\pi$
$331$	516.476	−	45.1858i	1.56035	−	0.136513i	0.834371	+	0.551203i	$0.185831\pi$
$332$			85.6805i			0.258074i
$333$		0			0
$334$	−388.712			−1.16381
$335$	10.2315	+	116.947i	0.0305419	+	0.349095i
$336$		0			0
$337$	528.783	−	93.2388i	1.56909	−	0.276673i	0.679584	−	0.733597i	$-0.262160\pi$
$337$	528.783	−	93.2388i	1.56909	−	0.276673i	0.889506	+	0.456924i	$0.151049\pi$
$338$	220.399	−	102.774i	0.652069	−	0.304065i
$339$		0			0
$340$	−107.343	−	39.0697i	−0.315715	−	0.114911i
$341$	64.8099	+	241.874i	0.190058	+	0.709308i
$342$		0			0
$343$	−153.669	−	266.163i	−0.448016	−	0.775986i
$344$	89.1935	+	51.4959i	0.259283	+	0.149697i
$345$		0			0
$346$	−227.604	−	159.370i	−0.657814	−	0.460606i
$347$	122.867	−	458.546i	0.354084	−	1.32146i	−0.527550	−	0.849524i	$-0.676889\pi$
$347$	122.867	−	458.546i	0.354084	−	1.32146i	0.881634	−	0.471935i	$-0.156444\pi$
$348$		0			0
$349$	−22.7380	+	8.27597i	−0.0651520	+	0.0237134i	−0.374391	−	0.927271i	$-0.622148\pi$
$349$	−22.7380	+	8.27597i	−0.0651520	+	0.0237134i	0.309239	+	0.950984i	$0.399926\pi$
$350$	−24.2001	−	34.5613i	−0.0691430	−	0.0987465i
$351$		0			0
$352$	−10.7063	+	122.373i	−0.0304156	+	0.347652i
$353$	441.321	−	309.016i	1.25020	−	0.875400i	0.254413	−	0.967096i	$-0.418118\pi$
$353$	441.321	−	309.016i	1.25020	−	0.875400i	0.995787	+	0.0916961i	$0.0292288\pi$
$354$		0			0
$355$	−116.460	+	249.748i	−0.328055	+	0.703517i
$356$	195.401	+	52.3577i	0.548880	+	0.147072i
$357$		0			0
$358$	−117.518	+	140.052i	−0.328262	+	0.391207i
$359$	−189.657	+	328.496i	−0.528293	+	0.915031i	0.471162	+	0.882046i	$0.343835\pi$
$359$	−189.657	+	328.496i	−0.528293	+	0.915031i	−0.999456	+	0.0329846i	$0.989499\pi$
$360$		0			0
$361$	164.078	+	28.9313i	0.454509	+	0.0801422i
$362$	341.795	−	91.5837i	0.944185	−	0.252994i
$363$		0			0
$364$	−14.4790	−	14.4790i	−0.0397775	−	0.0397775i
$365$	77.0780	+	165.294i	0.211173	+	0.452861i
$366$		0			0
$367$	−222.265	+	186.503i	−0.605627	+	0.508181i	−0.893249	−	0.449563i	$-0.851580\pi$
$367$	−222.265	+	186.503i	−0.605627	+	0.508181i	0.287622	+	0.957744i	$0.407135\pi$
$368$	236.693	−	20.7079i	0.643186	−	0.0562715i
$369$		0			0
$370$	125.083	−	206.433i	0.338062	−	0.557927i
$371$	59.4956			0.160366
$372$		0			0
$373$	−308.346	−	367.472i	−0.826664	−	0.985180i	−1.00000		0.000317533i	$-0.999899\pi$
$373$	−308.346	−	367.472i	−0.826664	−	0.985180i	0.173335	−	0.984863i	$-0.444546\pi$
$374$	−139.716	+	24.6358i	−0.373573	+	0.0658710i
$375$		0			0
$376$	184.094	−	184.094i	0.489613	−	0.489613i
$377$	−8.77108	−	3.19241i	−0.0232655	−	0.00846793i
$378$		0			0
$379$	72.9695	−	413.831i	0.192532	−	1.09190i	−0.723358	−	0.690473i	$-0.757403\pi$
$379$	72.9695	−	413.831i	0.192532	−	1.09190i	0.915890	−	0.401429i	$-0.131486\pi$
$380$	−45.8498	−	79.4142i	−0.120657	−	0.208985i
$381$		0			0
$382$	−212.422	−	178.243i	−0.556079	−	0.466606i
$383$	−70.4063	−	49.2990i	−0.183828	−	0.128718i	0.478040	−	0.878338i	$-0.341347\pi$
$383$	−70.4063	−	49.2990i	−0.183828	−	0.128718i	−0.661868	+	0.749620i	$0.730236\pi$
$384$		0			0
$385$	−71.9869	−	33.5680i	−0.186979	−	0.0871897i
$386$	482.299	−	175.542i	1.24948	−	0.454773i
$387$		0			0
$388$	80.1774	+	7.01462i	0.206643	+	0.0180789i
$389$	37.4995	−	428.621i	0.0963998	−	1.10185i	−0.781790	−	0.623542i	$-0.785693\pi$
$389$	37.4995	−	428.621i	0.0963998	−	1.10185i	0.878190	−	0.478313i	$-0.158751\pi$
$390$		0			0
$391$	−194.774	−	535.137i	−0.498143	−	1.36864i
$392$	131.707	−	282.446i	0.335987	−	0.720527i
$393$		0			0
$394$	21.8288	−	31.1747i	0.0554030	−	0.0791237i
$395$	−309.824	+	369.234i	−0.784364	+	0.934769i
$396$		0			0
$397$	157.353	−	90.8476i	0.396354	−	0.228835i	−0.288555	−	0.957463i	$-0.593175\pi$
$397$	157.353	−	90.8476i	0.396354	−	0.228835i	0.684910	+	0.728628i	$0.259842\pi$
$398$	−556.379	−	98.1046i	−1.39794	−	0.246494i
$399$		0			0
$400$	18.5336	−	50.9207i	0.0463340	−	0.127302i
$401$	−373.727	−	373.727i	−0.931988	−	0.931988i	0.0658420	−	0.997830i	$-0.479027\pi$
$401$	−373.727	−	373.727i	−0.931988	−	0.931988i	−0.997830	+	0.0658420i	$0.979027\pi$
$402$		0			0
$403$	−29.8638	−	169.366i	−0.0741036	−	0.420263i
$404$	76.8312	−	64.4690i	0.190176	−	0.159577i
$405$		0			0
$406$			14.6296i			0.0360334i
$407$	−4.10430	+	193.887i	−0.0100843	+	0.476380i
$408$		0			0
$409$	13.6429	+	155.939i	0.0333568	+	0.381270i	0.994463	+	0.105090i	$0.0335130\pi$
$409$	13.6429	+	155.939i	0.0333568	+	0.381270i	−0.961106	+	0.276180i	$0.910931\pi$
$410$	101.992	+	121.549i	0.248761	+	0.296462i
$411$		0			0
$412$	−27.9340	+	13.0258i	−0.0678009	+	0.0316161i
$413$	191.576	−	191.576i	0.463865	−	0.463865i
$414$		0			0
$415$	−59.0787	−	220.485i	−0.142358	−	0.531289i
$416$	14.6502	−	83.0852i	0.0352167	−	0.199724i
$417$		0			0
$418$	−98.6293	−	56.9437i	−0.235955	−	0.136229i
$419$	377.896	+	317.092i	0.901900	+	0.756784i	0.970561	−	0.240856i	$-0.0774282\pi$
$419$	377.896	+	317.092i	0.901900	+	0.756784i	−0.0686608	+	0.997640i	$0.521873\pi$
$420$		0			0
$421$	171.299	−	639.296i	0.406885	−	1.51852i	−0.393666	−	0.919253i	$-0.628793\pi$
$421$	171.299	−	639.296i	0.406885	−	1.51852i	0.800552	−	0.599264i	$-0.204540\pi$
$422$	334.408	+	155.937i	0.792437	+	0.369519i
$423$		0			0
$424$	81.8423	+	116.883i	0.193024	+	0.275667i
$425$	−129.387	−	11.3199i	−0.304441	−	0.0266351i
$426$		0			0
$427$	−115.957	+	81.1940i	−0.271562	+	0.190150i
$428$	−54.6609	−	150.180i	−0.127712	−	0.350887i
$429$		0			0
$430$	−74.7458	−	20.0281i	−0.173827	−	0.0465769i
$431$	−396.596	+	566.398i	−0.920177	+	1.31415i	0.0290572	+	0.999578i	$0.490750\pi$
$431$	−396.596	+	566.398i	−0.920177	+	1.31415i	−0.949234	+	0.314571i	$0.898139\pi$
$432$		0			0
$433$	−285.627	+	494.721i	−0.659648	+	1.14254i	0.321059	+	0.947059i	$0.395961\pi$
$433$	−285.627	+	494.721i	−0.659648	+	1.14254i	−0.980707	+	0.195484i	$0.937372\pi$
$434$	−233.437	+	134.775i	−0.537872	+	0.310541i
$435$		0			0
$436$	131.896	−	35.3414i	0.302513	−	0.0810582i
$437$	156.355	−	429.581i	0.357791	−	0.983022i
$438$		0			0
$439$	232.947	+	499.557i	0.530631	+	1.13794i	0.970770	+	0.240012i	$0.0771515\pi$
$439$	232.947	+	499.557i	0.530631	+	1.13794i	−0.440139	+	0.897930i	$0.645071\pi$
$440$	−33.0788	−	187.599i	−0.0751790	−	0.426361i
$441$		0			0
$442$	97.0665	−	8.49222i	0.219607	−	0.0192132i
$443$			362.606i			0.818524i	0.912417	+	0.409262i	$0.134214\pi$
$443$			362.606i			0.818524i	−0.912417	+	0.409262i	$0.865786\pi$
$444$		0			0
$445$	−538.936			−1.21109
$446$	−46.1849	−	527.896i	−0.103554	−	1.18362i
$447$		0			0
$448$	−233.564	+	41.1837i	−0.521349	+	0.0919279i
$449$	−613.884	+	286.259i	−1.36722	+	0.637547i	−0.961082	−	0.276263i	$-0.910904\pi$
$449$	−613.884	+	286.259i	−1.36722	+	0.637547i	−0.406142	+	0.913810i	$0.633126\pi$
$450$		0			0
$451$	−119.796	−	43.6022i	−0.265623	−	0.0966790i
$452$	−37.5425	−	140.110i	−0.0830585	−	0.309979i
$453$		0			0
$454$	12.2244	+	21.1733i	0.0269260	+	0.0466372i
$455$	47.2430	+	27.2758i	0.103831	+	0.0599467i
$456$		0			0
$457$	660.433	+	462.440i	1.44515	+	1.01190i	0.992764	+	0.120080i	$0.0383152\pi$
$457$	660.433	+	462.440i	1.44515	+	1.01190i	0.452384	+	0.891823i	$0.350574\pi$
$458$	138.895	−	518.364i	0.303265	−	1.13180i
$459$		0			0
$460$	202.645	−	73.7568i	0.440533	−	0.160341i
$461$	−364.237	−	520.184i	−0.790102	−	1.12838i	−0.988935	−	0.148349i	$-0.952604\pi$
$461$	−364.237	−	520.184i	−0.790102	−	1.12838i	0.198833	−	0.980033i	$-0.436285\pi$
$462$		0			0
$463$	−33.4114	+	381.894i	−0.0721628	+	0.824824i	0.870737	+	0.491748i	$0.163642\pi$
$463$	−33.4114	+	381.894i	−0.0721628	+	0.824824i	−0.942900	+	0.333076i	$0.891914\pi$
$464$	−15.3914	+	10.7772i	−0.0331712	+	0.0232267i
$465$		0			0
$466$	−192.187	+	412.145i	−0.412418	+	0.884432i
$467$	437.597	+	117.254i	0.937039	+	0.251079i	0.694854	−	0.719151i	$-0.255469\pi$
$467$	437.597	+	117.254i	0.937039	+	0.251079i	0.242185	+	0.970230i	$0.422136\pi$
$468$		0			0
$469$	65.2625	−	77.7769i	0.139153	−	0.165836i
$470$	−97.8062	+	169.405i	−0.208098	+	0.360437i
$471$		0			0
$472$	639.895	+	112.831i	1.35571	+	0.239048i
$473$	60.0545	−	16.0916i	0.126965	−	0.0340202i
$474$		0			0
$475$	−73.7245	−	73.7245i	−0.155209	−	0.155209i
$476$	41.7530	+	89.5397i	0.0877165	+	0.188109i
$477$		0			0
$478$	176.540	−	148.135i	0.369331	−	0.309906i
$479$	477.725	−	41.7955i	0.997337	−	0.0872557i	0.423219	−	0.906028i	$-0.360900\pi$
$479$	477.725	−	41.7955i	0.997337	−	0.0872557i	0.574119	+	0.818772i	$0.305345\pi$
$480$		0			0
$481$	14.4138	−	132.409i	0.0299664	−	0.275278i
$482$	−308.699			−0.640455
$483$		0			0
$484$	−94.4601	−	112.573i	−0.195165	−	0.232589i
$485$	−211.160	+	37.2333i	−0.435382	+	0.0767696i
$486$		0			0
$487$	−374.276	+	374.276i	−0.768534	+	0.768534i	−0.977848	−	0.209315i	$-0.932877\pi$
$487$	−374.276	+	374.276i	−0.768534	+	0.768534i	0.209315	+	0.977848i	$0.432877\pi$
$488$	−319.021	−	116.114i	−0.653732	−	0.237939i
$489$		0			0
$490$	−40.6604	+	230.596i	−0.0829803	+	0.470605i
$491$	−211.141	−	365.707i	−0.430022	−	0.744821i	0.566852	−	0.823819i	$-0.308161\pi$
$491$	−211.141	−	365.707i	−0.430022	−	0.744821i	−0.996875	+	0.0789988i	$0.974828\pi$
$492$		0			0
$493$	34.4990	+	28.9481i	0.0699778	+	0.0587183i
$494$	64.0721	+	44.8638i	0.129701	+	0.0908174i
$495$		0			0
$496$	−313.760	−	146.308i	−0.632580	−	0.294977i
$497$	223.957	−	81.5137i	0.450618	−	0.164011i
$498$		0			0
$499$	81.2231	+	7.10610i	0.162772	+	0.0142407i	0.168250	−	0.985744i	$-0.446188\pi$
$499$	81.2231	+	7.10610i	0.162772	+	0.0142407i	−0.00547854	+	0.999985i	$0.501744\pi$
$500$	18.6172	−	212.796i	0.0372345	−	0.425592i
$501$		0			0
$502$	−57.0422	−	156.722i	−0.113630	−	0.312196i
$503$	−275.370	+	590.532i	−0.547455	+	1.17402i	0.416789	+	0.909003i	$0.363155\pi$
$503$	−275.370	+	590.532i	−0.547455	+	1.17402i	−0.964244	+	0.265017i	$0.914622\pi$
$504$		0			0
$505$	−153.260	+	218.877i	−0.303484	+	0.433421i
$506$	172.157	−	205.169i	0.340232	−	0.405473i
$507$		0			0
$508$	153.872	−	88.8381i	0.302898	−	0.174878i
$509$	889.021	+	156.758i	1.74660	+	0.307973i	0.953562	−	0.301196i	$-0.0973859\pi$
$509$	889.021	+	156.758i	1.74660	+	0.307973i	0.793040	+	0.609169i	$0.208497\pi$
$510$		0			0
$511$	53.9493	−	148.225i	0.105576	−	0.290068i
$512$	−298.044	−	298.044i	−0.582117	−	0.582117i
$513$		0			0
$514$	−59.7715	−	338.981i	−0.116287	−	0.659496i
$515$	62.9019	−	52.7810i	0.122140	−	0.102487i
$516$		0			0
$517$		−	157.165i		−	0.303994i
$518$	−202.741	+	49.7503i	−0.391392	+	0.0960431i
$519$		0			0
$520$	11.4026	+	130.332i	0.0219281	+	0.250639i
$521$	4.26421	+	5.08189i	0.00818467	+	0.00975411i	0.770121	−	0.637898i	$-0.220196\pi$
$521$	4.26421	+	5.08189i	0.00818467	+	0.00975411i	−0.761937	+	0.647652i	$0.775751\pi$
$522$		0			0
$523$	−95.5687	+	44.5644i	−0.182732	+	0.0852092i	−0.511831	−	0.859086i	$-0.671033\pi$
$523$	−95.5687	+	44.5644i	−0.182732	+	0.0852092i	0.329099	+	0.944295i	$0.393255\pi$
$524$	215.653	−	215.653i	0.411552	−	0.411552i
$525$		0			0
$526$	−31.5581	−	117.777i	−0.0599965	−	0.223910i
$527$	−144.089	+	817.169i	−0.273413	+	1.55060i
$528$		0			0
$529$	472.921	+	273.041i	0.893990	+	0.516145i
$530$	−82.1260	−	68.9119i	−0.154955	−	0.130022i
$531$		0			0
$532$	−20.5265	+	76.6061i	−0.0385837	+	0.143996i
$533$	79.3528	+	37.0028i	0.148879	+	0.0694236i
$534$		0			0
$535$	244.213	+	348.773i	0.456474	+	0.651912i
$536$	242.573	+	21.2224i	0.452561	+	0.0395940i
$537$		0			0
$538$	300.261	−	210.245i	0.558107	−	0.390791i
$539$	−64.3445	−	176.785i	−0.119378	−	0.327987i
$540$		0			0
$541$	−445.980	−	119.500i	−0.824363	−	0.220887i	−0.178110	−	0.984011i	$-0.556998\pi$
$541$	−445.980	−	119.500i	−0.824363	−	0.220887i	−0.646253	+	0.763123i	$0.723665\pi$
$542$	−110.541	+	157.868i	−0.203949	+	0.291270i
$543$		0			0
$544$	−203.530	+	352.524i	−0.374136	+	0.648022i
$545$	−315.044	+	181.891i	−0.578062	+	0.333744i
$546$		0			0
$547$	−852.126	+	228.326i	−1.55782	+	0.417416i	−0.931971	−	0.362532i	$-0.881912\pi$
$547$	−852.126	+	228.326i	−1.55782	+	0.417416i	−0.625845	+	0.779947i	$0.715246\pi$
$548$	−42.6778	+	117.256i	−0.0778792	+	0.213971i
$549$		0			0
$550$	−25.8151	−	55.3607i	−0.0469366	−	0.100656i
$551$	6.27773	+	35.6028i	0.0113933	+	0.0646149i
$552$		0			0
$553$	415.282	−	36.3325i	0.750963	−	0.0657007i
$554$			336.602i			0.607585i
$555$		0			0
$556$	−294.148			−0.529044
$557$	55.1800	+	630.710i	0.0990664	+	1.13233i	0.869203	+	0.494455i	$0.164632\pi$
$557$	55.1800	+	630.710i	0.0990664	+	1.13233i	−0.770137	+	0.637879i	$0.779812\pi$
$558$		0			0
$559$	−42.0516	+	7.41483i	−0.0752265	+	0.0132645i
$560$	99.5244	−	46.4090i	0.177722	−	0.0828732i
$561$		0			0
$562$	578.360	+	210.506i	1.02911	+	0.374565i
$563$	186.193	+	694.883i	0.330716	+	1.23425i	0.908439	+	0.418018i	$0.137275\pi$
$563$	186.193	+	694.883i	0.330716	+	1.23425i	−0.577722	+	0.816233i	$0.696058\pi$
$564$		0			0
$565$	193.219	+	334.665i	0.341980	+	0.592327i
$566$	−513.438	−	296.434i	−0.907135	−	0.523735i
$567$		0			0
$568$	468.214	+	327.847i	0.824321	+	0.577196i
$569$	16.9175	−	63.1369i	0.0297319	−	0.110961i	−0.949465	−	0.313872i	$-0.898374\pi$
$569$	16.9175	−	63.1369i	0.0297319	−	0.110961i	0.979197	+	0.202911i	$0.0650403\pi$
$570$		0			0
$571$	890.852	−	324.243i	1.56016	−	0.567852i	0.589387	−	0.807851i	$-0.299369\pi$
$571$	890.852	−	324.243i	1.56016	−	0.567852i	0.970773	+	0.239999i	$0.0771471\pi$
$572$	−17.0038	−	24.2839i	−0.0297269	−	0.0424544i
$573$		0			0
$574$	11.9604	−	136.708i	0.0208370	−	0.238168i
$575$	200.851	−	140.637i	0.349306	−	0.244587i
$576$		0			0
$577$	−93.0663	+	199.581i	−0.161293	+	0.345895i	−0.970300	−	0.241905i	$-0.922228\pi$
$577$	−93.0663	+	199.581i	−0.161293	+	0.345895i	0.809007	+	0.587800i	$0.200006\pi$
$578$	−19.0573	−	5.10639i	−0.0329711	−	0.00883458i
$579$		0			0
$580$	−10.9620	+	13.0640i	−0.0189001	+	0.0225242i
$581$	−98.7090	+	170.969i	−0.169895	+	0.294267i
$582$		0			0
$583$	84.8276	+	14.9574i	0.145502	+	0.0256559i
$584$	365.409	−	97.9111i	0.625701	−	0.167656i
$585$		0			0
$586$	−86.9846	−	86.9846i	−0.148438	−	0.148438i
$587$	235.510	+	505.053i	0.401210	+	0.860398i	0.998303	+	0.0582259i	$0.0185444\pi$
$587$	235.510	+	505.053i	0.401210	+	0.860398i	−0.597093	+	0.802172i	$0.703678\pi$
$588$		0			0
$589$	−510.263	+	428.161i	−0.866320	+	0.726929i
$590$	−486.343	+	42.5495i	−0.824309	+	0.0721177i
$591$		0			0
$592$	−201.695	−	176.649i	−0.340701	−	0.298394i
$593$	65.5846			0.110598			0.0552990	−	0.998470i	$-0.482389\pi$
$593$	65.5846			0.110598			0.0552990	+	0.998470i	$0.482389\pi$
$594$		0			0
$595$	−169.184	−	201.626i	−0.284344	−	0.338867i
$596$	301.716	−	53.2007i	0.506235	−	0.0892629i
$597$		0			0
$598$	−130.069	+	130.069i	−0.217506	+	0.217506i
$599$	−252.396	−	91.8648i	−0.421363	−	0.153364i	0.122632	−	0.992452i	$-0.460867\pi$
$599$	−252.396	−	91.8648i	−0.421363	−	0.153364i	−0.543995	+	0.839089i	$0.683089\pi$
$600$		0			0
$601$	109.346	−	620.131i	0.181940	−	1.03183i	−0.747885	−	0.663829i	$-0.768930\pi$
$601$	109.346	−	620.131i	0.181940	−	1.03183i	0.929824	−	0.368003i	$-0.119959\pi$
$602$	33.4630	+	57.9596i	0.0555864	+	0.0962785i
$603$		0			0
$604$	317.854	+	266.711i	0.526248	+	0.441574i
$605$	320.699	+	224.556i	0.530082	+	0.371167i
$606$		0			0
$607$	−561.140	−	261.664i	−0.924447	−	0.431077i	−0.0987001	−	0.995117i	$-0.531468\pi$
$607$	−561.140	−	261.664i	−0.924447	−	0.431077i	−0.825747	+	0.564040i	$0.809246\pi$
$608$	−307.060	+	111.761i	−0.505033	+	0.183817i
$609$		0			0
$610$	254.108	+	22.2316i	0.416571	+	0.0364452i
$611$	−9.40763	+	107.530i	−0.0153971	+	0.175990i
$612$		0			0
$613$	−195.687	−	537.647i	−0.319229	−	0.877075i	−0.990703	−	0.136046i	$-0.956561\pi$
$613$	−195.687	−	537.647i	−0.319229	−	0.877075i	0.671473	−	0.741029i	$-0.265662\pi$
$614$	−131.733	+	282.502i	−0.214549	+	0.460101i
$615$		0			0
$616$	−94.4979	+	134.957i	−0.153406	+	0.219086i
$617$	242.800	−	289.358i	0.393517	−	0.468976i	−0.532515	−	0.846421i	$-0.678753\pi$
$617$	242.800	−	289.358i	0.393517	−	0.468976i	0.926032	+	0.377445i	$0.123197\pi$
$618$		0			0
$619$	91.3370	−	52.7334i	0.147556	−	0.0851913i	−0.424404	−	0.905473i	$-0.639517\pi$
$619$	91.3370	−	52.7334i	0.147556	−	0.0851913i	0.571960	+	0.820281i	$0.306183\pi$
$620$	−309.444	−	54.5634i	−0.499104	−	0.0880055i
$621$		0			0
$622$	−75.0887	+	206.305i	−0.120721	+	0.331679i
$623$	329.590	+	329.590i	0.529036	+	0.529036i
$624$		0			0
$625$	66.3557	+	376.322i	0.106169	+	0.602115i
$626$	−433.820	+	364.018i	−0.693003	+	0.581499i
$627$		0			0
$628$		−	14.4131i		−	0.0229508i
$629$	−283.852	+	576.541i	−0.451275	+	0.916600i
$630$		0			0
$631$	−37.5520	−	429.222i	−0.0595119	−	0.680224i	−0.966093	−	0.258193i	$-0.916873\pi$
$631$	−37.5520	−	429.222i	−0.0595119	−	0.680224i	0.906581	−	0.422031i	$-0.138683\pi$
$632$	642.640	+	765.869i	1.01684	+	1.21182i
$633$		0			0
$634$	−368.979	+	172.058i	−0.581985	+	0.271384i
$635$	−334.709	+	334.709i	−0.527101	+	0.527101i
$636$		0			0
$637$	33.4414	+	124.805i	0.0524984	+	0.195927i
$638$	−3.67792	+	20.8585i	−0.00576476	+	0.0326936i
$639$		0			0
$640$	30.2619	+	17.4717i	0.0472842	+	0.0272996i
$641$	−766.425	−	643.107i	−1.19567	−	1.00329i	−0.999743	−	0.0226693i	$-0.992784\pi$
$641$	−766.425	−	643.107i	−1.19567	−	1.00329i	−0.195928	−	0.980618i	$-0.562772\pi$
$642$		0			0
$643$	140.259	−	523.454i	0.218132	−	0.814080i	−0.766908	−	0.641757i	$-0.778206\pi$
$643$	140.259	−	523.454i	0.218132	−	0.814080i	0.985040	−	0.172323i	$-0.0551274\pi$
$644$	−169.035	−	78.8225i	−0.262477	−	0.122395i
$645$		0			0
$646$	−216.462	−	309.140i	−0.335081	−	0.478545i
$647$	−583.680	−	51.0654i	−0.902132	−	0.0789264i	−0.373357	−	0.927688i	$-0.621793\pi$
$647$	−583.680	−	51.0654i	−0.902132	−	0.0789264i	−0.528776	+	0.848762i	$0.677349\pi$
$648$		0			0
$649$	321.308	−	224.982i	0.495081	−	0.346660i
$650$	14.3485	+	39.4222i	0.0220746	+	0.0606495i
$651$		0			0
$652$	−340.077	−	91.1234i	−0.521591	−	0.139760i
$653$	−259.040	+	369.947i	−0.396692	+	0.566535i	−0.966961	−	0.254923i	$-0.917950\pi$
$653$	−259.040	+	369.947i	−0.396692	+	0.566535i	0.570270	+	0.821458i	$0.306839\pi$
$654$		0			0
$655$	−406.250	+	703.646i	−0.620229	+	1.07427i
$656$	152.638	−	88.1258i	0.232681	−	0.134338i
$657$		0			0
$658$	163.415	−	43.7869i	0.248351	−	0.0665454i
$659$	155.852	−	428.200i	0.236498	−	0.649772i	−0.763495	−	0.645814i	$-0.776518\pi$
$659$	155.852	−	428.200i	0.236498	−	0.649772i	0.999992	−	0.00395756i	$-0.00125973\pi$
$660$		0			0
$661$	171.921	+	368.685i	0.260092	+	0.557769i	0.992378	−	0.123228i	$-0.0393246\pi$
$661$	171.921	+	368.685i	0.260092	+	0.557769i	−0.732287	+	0.680997i	$0.761547\pi$
$662$	140.304	+	795.703i	0.211940	+	1.20197i
$663$		0			0
$664$	−471.663	+	41.2652i	−0.710337	+	0.0621464i
$665$		−	211.287i		−	0.317724i
$666$		0			0
$667$	−85.0188			−0.127465
$668$	34.1562	+	390.407i	0.0511320	+	0.584441i
$669$		0			0
$670$	−180.173	+	31.7694i	−0.268915	+	0.0474170i
$671$	−185.741	+	86.6126i	−0.276813	+	0.129080i
$672$		0			0
$673$	112.396	+	40.9089i	0.167008	+	0.0607859i	0.424171	−	0.905582i	$-0.360566\pi$
$673$	112.396	+	40.9089i	0.167008	+	0.0607859i	−0.257163	+	0.966368i	$0.582788\pi$
$674$	216.579	+	808.284i	0.321334	+	1.19923i
$675$		0			0
$676$	−122.588	−	212.329i	−0.181344	−	0.314096i
$677$	−369.764	−	213.483i	−0.546180	−	0.315337i	0.201400	−	0.979509i	$-0.435451\pi$
$677$	−369.764	−	213.483i	−0.546180	−	0.315337i	−0.747580	+	0.664172i	$0.768784\pi$
$678$		0			0
$679$	151.907	+	106.366i	0.223721	+	0.156651i
$680$	163.377	−	609.731i	0.240260	−	0.896663i
$681$		0			0
$682$	−366.712	+	133.472i	−0.537700	+	0.195707i
$683$	−603.540	−	861.944i	−0.883660	−	1.26200i	−0.964181	−	0.265244i	$-0.914547\pi$
$683$	−603.540	−	861.944i	−0.883660	−	1.26200i	0.0805214	−	0.996753i	$-0.474341\pi$
$684$		0			0
$685$	28.9734	−	331.167i	0.0422969	−	0.483456i
$686$	392.352	−	274.728i	0.571942	−	0.400478i
$687$		0			0
$688$	−36.3267	+	77.9029i	−0.0528005	+	0.113231i
$689$	−57.1424	−	15.3113i	−0.0829353	−	0.0222224i
$690$		0			0
$691$	369.831	−	440.747i	0.535211	−	0.637839i	−0.428896	−	0.903354i	$-0.641097\pi$
$691$	369.831	−	440.747i	0.535211	−	0.637839i	0.964107	+	0.265515i	$0.0855418\pi$
$692$	−140.065	+	242.599i	−0.202406	+	0.350577i
$693$		0			0
$694$	728.592	+	128.470i	1.04984	+	0.185116i
$695$	756.943	−	202.822i	1.08913	−	0.291831i
$696$		0			0
$697$	−298.715	−	298.715i	−0.428573	−	0.428573i
$698$	−15.9371	−	34.1772i	−0.0228325	−	0.0489645i
$699$		0			0
$700$	−32.5855	+	27.3424i	−0.0465507	+	0.0390606i
$701$	307.418	−	26.8956i	0.438543	−	0.0383675i	0.134253	−	0.990947i	$-0.457136\pi$
$701$	307.418	−	26.8956i	0.438543	−	0.0383675i	0.304290	+	0.952580i	$0.401581\pi$
$702$		0			0
$703$	−472.046	+	208.072i	−0.671474	+	0.295978i
$704$	−343.365			−0.487734
$705$		0			0
$706$	539.698	+	643.187i	0.764445	+	0.911030i
$707$	227.583	−	40.1290i	0.321900	−	0.0567596i
$708$		0			0
$709$	−402.806	+	402.806i	−0.568133	+	0.568133i	−0.931605	−	0.363472i	$-0.881591\pi$
$709$	−402.806	+	402.806i	−0.568133	+	0.568133i	0.363472	+	0.931605i	$0.381591\pi$
$710$	−403.558	−	146.883i	−0.568392	−	0.206878i
$711$		0			0
$712$	−194.116	+	1100.88i	−0.272634	+	1.54619i
$713$	−783.236	−	1356.60i	−1.09851	−	1.90267i
$714$		0			0
$715$	60.5008	+	50.7662i	0.0846166	+	0.0710017i
$716$	150.989	+	105.723i	0.210878	+	0.147659i
$717$		0			0
$718$	−535.758	−	249.828i	−0.746182	−	0.347950i
$719$	862.184	−	313.809i	1.19914	−	0.436452i	0.336218	−	0.941784i	$-0.390852\pi$
$719$	862.184	−	313.809i	1.19914	−	0.436452i	0.862925	+	0.505332i	$0.168630\pi$
$720$		0			0
$721$	−70.7467	−	6.18953i	−0.0981230	−	0.00858465i
$722$	−22.6302	+	258.664i	−0.0313437	+	0.358260i
$723$		0			0
$724$	−122.016	−	335.237i	−0.168531	−	0.463035i
$725$	−8.19467	+	17.5735i	−0.0113030	+	0.0242393i
$726$		0			0
$727$	269.223	−	384.491i	0.370321	−	0.528873i	−0.590135	−	0.807304i	$-0.700926\pi$
$727$	269.223	−	384.491i	0.370321	−	0.528873i	0.960456	+	0.278431i	$0.0898145\pi$
$728$	72.7323	−	86.6790i	0.0999071	−	0.119065i
$729$		0			0
$730$	−246.154	+	142.117i	−0.337197	+	0.194681i
$731$	202.894	+	35.7756i	0.277556	+	0.0489407i
$732$		0			0
$733$	9.47712	−	26.0382i	0.0129292	−	0.0355227i	−0.933060	−	0.359720i	$-0.882872\pi$
$733$	9.47712	−	26.0382i	0.0129292	−	0.0355227i	0.945989	+	0.324198i	$0.105094\pi$
$734$	−319.739	−	319.739i	−0.435612	−	0.435612i
$735$		0			0
$736$	−133.441	−	756.784i	−0.181306	−	1.02824i
$737$	112.603	−	94.4854i	0.152786	−	0.128203i
$738$		0			0
$739$		−	352.038i		−	0.476371i	−0.971220	−	0.238185i	$-0.923447\pi$
$739$		−	352.038i		−	0.476371i	0.971220	−	0.238185i	$-0.0765525\pi$
$740$	−218.324	−	107.489i	−0.295032	−	0.145255i
$741$		0			0
$742$	8.08118	+	92.3683i	0.0108911	+	0.124486i
$743$	494.990	+	589.906i	0.666204	+	0.793951i	0.988262	−	0.152769i	$-0.0488190\pi$
$743$	494.990	+	589.906i	0.666204	+	0.793951i	−0.322058	+	0.946720i	$0.604375\pi$
$744$		0			0
$745$	−739.734	+	344.944i	−0.992931	+	0.463012i
$746$	528.627	−	528.627i	0.708615	−	0.708615i
$747$		0			0
$748$	37.0200	+	138.161i	0.0494920	+	0.184707i
$749$	63.9441	−	362.645i	0.0853726	−	0.484172i
$750$		0			0
$751$	739.427	+	426.908i	0.984589	+	0.568453i	0.903653	−	0.428266i	$-0.140875\pi$
$751$	739.427	+	426.908i	0.984589	+	0.568453i	0.0809368	+	0.996719i	$0.474209\pi$
$752$	166.450	+	139.669i	0.221344	+	0.185729i
$753$		0			0
$754$	3.76493	−	14.0509i	0.00499328	−	0.0186352i
$755$	−1001.85	−	467.169i	−1.32695	−	0.618767i
$756$		0			0
$757$	−129.469	−	184.901i	−0.171029	−	0.244254i	0.724483	−	0.689293i	$-0.242079\pi$
$757$	−129.469	−	184.901i	−0.171029	−	0.244254i	−0.895511	+	0.445039i	$0.853190\pi$
$758$	652.393	+	57.0770i	0.860676	+	0.0752994i
$759$		0			0
$760$	415.086	−	290.646i	0.546166	−	0.382430i
$761$	−347.116	−	953.693i	−0.456131	−	1.25321i	−0.928343	−	0.371725i	$-0.878766\pi$
$761$	−347.116	−	953.693i	−0.456131	−	1.25321i	0.472211	−	0.881485i	$-0.343456\pi$
$762$		0			0
$763$	303.903	+	81.4307i	0.398301	+	0.106724i
$764$	−160.355	+	229.010i	−0.209888	+	0.299752i
$765$		0			0
$766$	66.9747	−	116.004i	0.0874343	−	0.151441i
$767$	−233.301	+	134.696i	−0.304173	+	0.175615i
$768$		0			0
$769$	748.127	−	200.460i	0.972857	−	0.260676i	0.262823	−	0.964844i	$-0.415346\pi$
$769$	748.127	−	200.460i	0.972857	−	0.260676i	0.710034	+	0.704168i	$0.248680\pi$
$770$	42.3373	−	116.321i	0.0549835	−	0.151066i
$771$		0			0
$772$	−218.687	−	468.976i	−0.283273	−	0.607482i
$773$	−128.594	−	729.291i	−0.166357	−	0.943456i	−0.947655	−	0.319297i	$-0.896553\pi$
$773$	−128.594	−	729.291i	−0.166357	−	0.943456i	0.781298	−	0.624158i	$-0.214558\pi$
$774$		0			0
$775$	−355.905	+	31.1377i	−0.459233	+	0.0401777i
$776$			444.748i			0.573129i
$777$		0			0
$778$	670.538			0.861874
$779$	−29.5561	−	337.828i	−0.0379411	−	0.433669i
$780$		0			0
$781$	339.806	−	59.9169i	0.435091	−	0.0767182i
$782$	804.357	−	375.078i	1.02859	−	0.479639i
$783$		0			0
$784$	244.411	+	88.9585i	0.311749	+	0.113467i
$785$	9.93818	+	37.0898i	0.0126601	+	0.0472481i
$786$		0			0
$787$	−327.734	−	567.653i	−0.416435	−	0.721287i	0.579143	−	0.815226i	$-0.303387\pi$
$787$	−327.734	−	567.653i	−0.416435	−	0.721287i	−0.995578	+	0.0939395i	$0.970054\pi$
$788$	−33.2287	−	19.1846i	−0.0421684	−	0.0243459i
$789$		0			0
$790$	−615.326	−	430.856i	−0.778894	−	0.545388i
$791$	86.5023	−	322.831i	0.109358	−	0.408130i
$792$		0			0
$793$	132.266	−	48.1409i	0.166792	−	0.0607073i
$794$	162.416	+	231.954i	0.204554	+	0.292133i
$795$		0			0
$796$	−49.6432	+	567.424i	−0.0623658	+	0.712844i
$797$	357.019	−	249.987i	0.447953	−	0.313660i	−0.327743	−	0.944767i	$-0.606288\pi$
$797$	357.019	−	249.987i	0.447953	−	0.313660i	0.775696	+	0.631107i	$0.217399\pi$
$798$		0			0
$799$	220.099	−	472.004i	0.275468	−	0.590743i
$800$	−169.290	−	45.3612i	−0.211613	−	0.0567015i
$801$		0			0
$802$	529.457	−	630.983i	0.660171	−	0.786761i
$803$	114.184	−	197.772i	0.142197	−	0.246292i
$804$		0			0
$805$	489.335	+	86.2830i	0.607870	+	0.107184i
$806$	258.888	−	69.3688i	0.321201	−	0.0860655i
$807$		0			0
$808$	391.899	+	391.899i	0.485024	+	0.485024i
$809$	−143.007	−	306.679i	−0.176770	−	0.379085i	0.797881	−	0.602815i	$-0.205954\pi$
$809$	−143.007	−	306.679i	−0.176770	−	0.379085i	−0.974651	+	0.223730i	$0.928176\pi$
$810$		0			0
$811$	−902.976	+	757.687i	−1.11341	+	0.934262i	−0.998253	−	0.0590847i	$-0.981182\pi$
$811$	−902.976	+	757.687i	−1.11341	+	0.934262i	−0.115158	+	0.993347i	$0.536737\pi$
$812$	14.6933	−	1.28550i	0.0180952	−	0.00158313i
$813$		0			0
$814$	−301.571	+	19.9632i	−0.370480	+	0.0245249i
$815$	937.965			1.15088
$816$		0			0
$817$	106.308	+	126.692i	0.130119	+	0.155070i
$818$	−240.246	+	42.3619i	−0.293700	+	0.0517872i
$819$		0			0
$820$	113.117	−	113.117i	0.137948	−	0.137948i
$821$	−637.845	−	232.157i	−0.776913	−	0.282773i	−0.0770279	−	0.997029i	$-0.524543\pi$
$821$	−637.845	−	232.157i	−0.776913	−	0.282773i	−0.699885	+	0.714256i	$0.746765\pi$
$822$		0			0
$823$	−58.5172	+	331.868i	−0.0711023	+	0.403241i	0.928397	+	0.371591i	$0.121188\pi$
$823$	−58.5172	+	331.868i	−0.0711023	+	0.403241i	−0.999499	+	0.0316507i	$0.989924\pi$
$824$	−85.1595	−	147.501i	−0.103349	−	0.179006i
$825$		0			0
$826$	323.448	+	271.405i	0.391583	+	0.328577i
$827$	593.536	+	415.599i	0.717698	+	0.502538i	0.874459	−	0.485099i	$-0.161216\pi$
$827$	593.536	+	415.599i	0.717698	+	0.502538i	−0.156761	+	0.987637i	$0.550105\pi$
$828$		0			0
$829$	1473.13	+	686.930i	1.77699	+	0.828625i	0.971871	+	0.235514i	$0.0756775\pi$
$829$	1473.13	+	686.930i	1.77699	+	0.828625i	0.805121	+	0.593111i	$0.202100\pi$
$830$	334.283	−	121.669i	0.402751	−	0.146589i
$831$		0			0
$832$	234.925	+	20.5533i	0.282362	+	0.0247034i
$833$	54.3339	−	621.039i	0.0652268	−	0.745545i
$834$		0			0
$835$	−357.090	−	981.096i	−0.427653	−	1.17497i
$836$	−48.5253	+	104.063i	−0.0580446	+	0.124477i
$837$		0			0
$838$	−440.964	+	629.762i	−0.526210	+	0.751506i
$839$	−917.987	+	1094.01i	−1.09414	+	1.30395i	−0.144888	+	0.989448i	$0.546282\pi$
$839$	−917.987	+	1094.01i	−1.09414	+	1.30395i	−0.949257	+	0.314502i	$0.898162\pi$
$840$		0			0
$841$	−722.505	+	417.138i	−0.859102	+	0.496003i
$842$	1015.79	+	179.111i	1.20640	+	0.212721i
$843$		0			0
$844$	127.232	−	349.568i	0.150749	−	0.414180i
$845$	461.867	+	461.867i	0.546588	+	0.546588i
$846$		0			0
$847$	−58.7971	−	333.455i	−0.0694180	−	0.393689i
$848$	−91.2254	+	76.5472i	−0.107577	+	0.0902679i
$849$		0			0
$850$		−	202.414i		−	0.238134i
$851$	−289.121	−	1178.22i	−0.339743	−	1.38451i
$852$		0			0
$853$	−138.570	−	1583.86i	−0.162450	−	1.85681i	−0.442427	−	0.896805i	$-0.645882\pi$
$853$	−138.570	−	1583.86i	−0.162450	−	1.85681i	0.279977	−	0.960007i	$-0.409673\pi$
$854$	−141.806	−	168.997i	−0.166049	−	0.197889i
$855$		0			0
$856$	800.400	−	373.233i	0.935047	−	0.436019i
$857$	−689.027	+	689.027i	−0.803999	+	0.803999i	−0.983718	−	0.179719i	$-0.942481\pi$
$857$	−689.027	+	689.027i	−0.803999	+	0.803999i	0.179719	+	0.983718i	$0.442481\pi$
$858$		0			0
$859$	231.562	+	864.202i	0.269572	+	1.00606i	0.959392	+	0.282076i	$0.0910229\pi$
$859$	231.562	+	864.202i	0.269572	+	1.00606i	−0.689820	+	0.723981i	$0.742310\pi$
$860$	−13.5475	+	76.8315i	−0.0157529	+	0.0893389i
$861$		0			0
$862$	−933.215	−	538.792i	−1.08262	−	0.625048i
$863$	−42.6683	−	35.8030i	−0.0494419	−	0.0414866i	0.617732	−	0.786389i	$-0.288052\pi$
$863$	−42.6683	−	35.8030i	−0.0494419	−	0.0414866i	−0.667174	+	0.744902i	$0.732496\pi$
$864$		0			0
$865$	193.156	−	720.868i	0.223302	−	0.833374i
$866$	−806.862	−	376.246i	−0.931711	−	0.434464i
$867$		0			0
$868$	155.874	+	222.611i	0.179579	+	0.256465i
$869$	601.235	+	52.6012i	0.691870	+	0.0605307i
$870$		0			0
$871$	−82.6972	+	57.9052i	−0.0949451	+	0.0664813i
$872$	258.074	+	709.054i	0.295957	+	0.813135i
$873$		0			0
$874$	688.171	+	184.395i	0.787381	+	0.210978i
$875$	282.303	−	403.170i	0.322632	−	0.460766i
$876$		0			0
$877$	−588.611	+	1019.50i	−0.671164	+	1.16249i	0.306410	+	0.951900i	$0.400872\pi$
$877$	−588.611	+	1019.50i	−0.671164	+	1.16249i	−0.977574	+	0.210591i	$0.932461\pi$
$878$	−743.932	+	429.509i	−0.847303	+	0.489191i
$879$		0			0
$880$	153.567	−	41.1482i	0.174508	−	0.0467593i
$881$	252.014	−	692.403i	0.286055	−	0.785929i	−0.710554	−	0.703643i	$-0.751556\pi$
$881$	252.014	−	692.403i	0.286055	−	0.785929i	0.996609	−	0.0822860i	$-0.0262221\pi$
$882$		0			0
$883$	−145.126	−	311.223i	−0.164355	−	0.352461i	0.806831	−	0.590782i	$-0.201181\pi$
$883$	−145.126	−	311.223i	−0.164355	−	0.352461i	−0.971186	+	0.238321i	$0.923403\pi$
$884$	−17.0585	−	96.7434i	−0.0192969	−	0.109438i
$885$		0			0
$886$	−562.954	+	49.2521i	−0.635389	+	0.0555893i
$887$			714.434i			0.805450i	0.915321	+	0.402725i	$0.131937\pi$
$887$			714.434i			0.805450i	−0.915321	+	0.402725i	$0.868063\pi$
$888$		0			0
$889$	409.387			0.460503
$890$	−73.2026	−	836.710i	−0.0822501	−	0.940123i
$891$		0			0
$892$	−526.139	+	92.7725i	−0.589842	+	0.104005i
$893$	378.901	−	176.684i	0.424301	−	0.197855i
$894$		0			0
$895$	−461.444	−	167.952i	−0.515580	−	0.187656i
$896$	−7.82192	−	29.1918i	−0.00872983	−	0.0325802i
$897$		0			0
$898$	−527.806	−	914.186i	−0.587757	−	1.01803i
$899$	107.282	+	61.9393i	0.119335	+	0.0688980i
$900$		0			0
$901$	233.811	+	163.716i	0.259502	+	0.181705i
$902$	51.4218	−	191.909i	0.0570086	−	0.212759i
$903$		0			0
$904$	753.214	−	274.148i	0.833201	−	0.303261i
$905$	545.143	+	778.545i	0.602368	+	0.860271i
$906$		0			0
$907$	−16.8021	+	192.049i	−0.0185249	+	0.211741i	0.981291	+	0.192532i	$0.0616701\pi$
$907$	−16.8021	+	192.049i	−0.0185249	+	0.211741i	−0.999816	+	0.0192081i	$0.993885\pi$
$908$	20.1914	−	14.1382i	0.0222372	−	0.0155707i
$909$		0			0
$910$	−35.9293	+	77.0507i	−0.0394828	+	0.0846710i
$911$	898.331	+	240.707i	0.986093	+	0.264223i	0.715609	−	0.698501i	$-0.246149\pi$
$911$	898.331	+	240.707i	0.986093	+	0.264223i	0.270485	+	0.962724i	$0.412816\pi$
$912$		0			0
$913$	−183.719	+	218.948i	−0.201226	+	0.239812i
$914$	−628.243	+	1088.15i	−0.687356	+	1.19053i
$915$		0			0
$916$	−532.828	−	93.9520i	−0.581690	−	0.102568i
$917$	678.764	−	181.874i	0.740201	−	0.198336i
$918$		0			0
$919$	−0.000375323	0	0.000375323i	−4.08403e−7	0	4.08403e-7i	0.707107	−	0.707107i	$-0.250000\pi$
$919$	−0.000375323	0	0.000375323i	−4.08403e−7	0	4.08403e-7i	−0.707107	+	0.707107i	$0.750000\pi$
$920$	503.622	+	1080.02i	0.547415	+	1.17394i
$921$		0			0
$922$	758.124	−	636.142i	0.822261	−	0.689959i
$923$	−236.077	+	20.6540i	−0.255771	+	0.0223771i
$924$		0			0
$925$	−271.407	−	53.8024i	−0.293413	−	0.0581648i
$926$	−597.437			−0.645180
$927$		0			0
$928$	39.0626	+	46.5530i	0.0420933	+	0.0501649i
$929$	−891.478	+	157.192i	−0.959610	+	0.169205i	−0.631450	−	0.775417i	$-0.717540\pi$
$929$	−891.478	+	157.192i	−0.959610	+	0.169205i	−0.328160	+	0.944622i	$0.606429\pi$
$930$		0			0
$931$	353.866	−	353.866i	0.380093	−	0.380093i
$932$	430.829	+	156.809i	0.462263	+	0.168250i
$933$		0			0
$934$	−122.601	+	695.306i	−0.131265	+	0.744439i
$935$	−190.530	−	330.008i	−0.203775	−	0.352949i
$936$		0			0
$937$	−593.300	−	497.838i	−0.633191	−	0.531311i	0.268727	−	0.963216i	$-0.413397\pi$
$937$	−593.300	−	497.838i	−0.633191	−	0.531311i	−0.901919	+	0.431906i	$0.857841\pi$
$938$	129.615	+	90.7573i	0.138182	+	0.0967562i
$939$		0			0
$940$	178.738	+	83.3468i	0.190147	+	0.0886668i
$941$	1508.69	−	549.117i	1.60328	−	0.583547i	0.623186	−	0.782074i	$-0.285838\pi$
$941$	1508.69	−	549.117i	1.60328	−	0.583547i	0.980095	+	0.198527i	$0.0636159\pi$
$942$		0			0
$943$	794.472	+	69.5073i	0.842494	+	0.0737087i
$944$	−47.2638	+	540.228i	−0.0500676	+	0.572275i
$945$		0			0
$946$	33.1396	+	91.0503i	0.0350313	+	0.0962477i
$947$	−284.260	+	609.597i	−0.300168	+	0.643713i	−0.997316	−	0.0732141i	$-0.976674\pi$
$947$	−284.260	+	609.597i	−0.300168	+	0.643713i	0.697148	+	0.716927i	$0.254452\pi$
$948$		0			0
$949$	−89.9612	+	128.478i	−0.0947958	+	0.135382i
$950$	104.445	−	124.473i	0.109942	−	0.131024i
$951$		0			0
$952$	−472.799	+	272.971i	−0.496638	+	0.286734i
$953$	1719.28	+	303.155i	1.80407	+	0.318106i	0.971718	−	0.236143i	$-0.0758833\pi$
$953$	1719.28	+	303.155i	1.80407	+	0.318106i	0.832351	+	0.554249i	$0.186994\pi$
$954$		0			0
$955$	254.739	−	699.889i	0.266742	−	0.732868i
$956$	−164.293	−	164.293i	−0.171855	−	0.171855i
$957$		0			0
$958$	129.777	+	736.001i	0.135466	+	0.768269i
$959$	−220.246	+	184.809i	−0.229663	+	0.192710i
$960$		0			0
$961$			1321.46i			1.37509i
$962$	207.525	+	4.39301i	0.215723	+	0.00456653i
$963$		0			0
$964$	27.1254	+	310.045i	0.0281384	+	0.321623i
$965$	886.125	+	1056.04i	0.918265	+	1.09435i
$966$		0			0
$967$	888.461	−	414.296i	0.918781	−	0.428434i	0.0950866	−	0.995469i	$-0.469687\pi$
$967$	888.461	−	414.296i	0.918781	−	0.428434i	0.823694	+	0.567035i	$0.191909\pi$
$968$	574.212	−	574.212i	0.593194	−	0.593194i
$969$		0			0
$970$	−86.4870	−	322.774i	−0.0891618	−	0.332756i
$971$	117.810	−	668.134i	0.121329	−	0.688089i	−0.862092	−	0.506751i	$-0.830846\pi$
$971$	117.810	−	668.134i	0.121329	−	0.688089i	0.983421	−	0.181338i	$-0.0580427\pi$
$972$		0			0
$973$	−586.951	−	338.876i	−0.603239	−	0.348280i
$974$	−631.909	−	530.234i	−0.648777	−	0.544389i
$975$		0			0
$976$	73.3340	−	273.686i	0.0751373	−	0.280416i
$977$	−1078.24	−	502.790i	−1.10362	−	0.514627i	−0.216555	−	0.976270i	$-0.569482\pi$
$977$	−1078.24	−	502.790i	−1.10362	−	0.514627i	−0.887066	+	0.461644i	$0.847260\pi$
$978$		0			0
$979$	387.062	+	552.782i	0.395365	+	0.564639i
$980$	235.174	+	20.5751i	0.239974	+	0.0209950i
$981$		0			0
$982$	539.089	−	377.474i	0.548971	−	0.384394i
$983$	−601.402	−	1652.34i	−0.611803	−	1.68091i	−0.726204	−	0.687480i	$-0.758717\pi$
$983$	−601.402	−	1652.34i	−0.611803	−	1.68091i	0.114401	−	0.993435i	$-0.463505\pi$
$984$		0			0
$985$	98.7369	+	26.4565i	0.100240	+	0.0268594i
$986$	−40.2567	+	57.4925i	−0.0408283	+	0.0583088i
$987$		0			0
$988$	39.4293	−	68.2936i	0.0399082	−	0.0691231i
$989$	−336.829	+	194.468i	−0.340576	+	0.196631i
$990$		0			0
$991$	−1150.22	+	308.201i	−1.16067	+	0.311000i	−0.787233	−	0.616656i	$-0.788487\pi$
$991$	−1150.22	+	308.201i	−1.16067	+	0.311000i	−0.373435	+	0.927656i	$0.621820\pi$
$992$	−382.959	+	1052.17i	−0.386048	+	1.06066i
$993$		0			0
$994$	156.971	+	336.626i	0.157919	+	0.338658i
$995$	−263.504	−	1494.40i	−0.264828	−	1.50191i
$996$		0			0
$997$	−233.054	+	20.3896i	−0.233755	+	0.0204509i	−0.203431	−	0.979089i	$-0.565209\pi$
$997$	−233.054	+	20.3896i	−0.233755	+	0.0204509i	−0.0303237	+	0.999540i	$0.509654\pi$
$998$			127.066i			0.127321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bu.c.55.5		72
3.2	odd	2		111.3.r.a.55.2	✓	72
37.35	odd	36	inner	333.3.bu.c.109.5		72
111.35	even	36		111.3.r.a.109.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.r.a.55.2	✓	72	3.2	odd	2
111.3.r.a.109.2	yes	72	111.35	even	36
333.3.bu.c.55.5		72	1.1	even	1	trivial
333.3.bu.c.109.5		72	37.35	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)

\(f(q)\)	\(=\)	\(q+(0.135828 + 1.55252i) q^{2} +(1.54735 - 0.272840i) q^{4} +(-3.79373 + 1.76905i) q^{5} +(3.40196 + 1.23821i) q^{7} +(2.24719 + 8.38664i) q^{8} +O(q^{10})\)	\(q+(0.135828 + 1.55252i) q^{2} +(1.54735 - 0.272840i) q^{4} +(-3.79373 + 1.76905i) q^{5} +(3.40196 + 1.23821i) q^{7} +(2.24719 + 8.38664i) q^{8} +(-3.26178 - 5.64957i) q^{10} +(4.53915 + 2.62068i) q^{11} +(-2.94875 - 2.06473i) q^{13} +(-1.46027 + 5.44980i) q^{14} +(-6.80935 + 2.47840i) q^{16} +(9.96208 + 14.2273i) q^{17} +(-1.21516 + 13.8894i) q^{19} +(-5.38758 + 3.77243i) q^{20} +(-3.45212 + 7.40309i) q^{22} +(-31.6712 - 8.48627i) q^{23} +(-4.80680 + 5.72852i) q^{25} +(2.80502 - 4.85844i) q^{26} +(5.60187 + 0.987760i) q^{28} +(2.50460 - 0.671105i) q^{29} +(33.7821 + 33.7821i) q^{31} +(9.90485 + 21.2410i) q^{32} +(-20.7351 + 17.3988i) q^{34} +(-15.0966 + 1.32078i) q^{35} +(17.8177 + 32.4273i) q^{37} -21.7286 q^{38} +(-23.3616 - 27.8413i) q^{40} +(-23.9533 + 4.22361i) q^{41} +(8.38771 - 8.38771i) q^{43} +(7.73869 + 2.81665i) q^{44} +(8.87329 - 50.3229i) q^{46} +(-14.9928 - 25.9682i) q^{47} +(-27.4960 - 23.0719i) q^{49} +(-9.54656 - 6.68457i) q^{50} +(-5.12610 - 2.39034i) q^{52} +(15.4429 - 5.62074i) q^{53} +(-21.8564 - 1.91219i) q^{55} +(-2.73958 + 31.3135i) q^{56} +(1.38210 + 3.79729i) q^{58} +(31.6273 - 67.8249i) q^{59} +(-22.4275 + 32.0298i) q^{61} +(-47.8589 + 57.0360i) q^{62} +(-56.7339 + 32.7553i) q^{64} +(14.8394 + 2.61658i) q^{65} +(9.59191 - 26.3536i) q^{67} +(19.2966 + 19.2966i) q^{68} +(-4.10108 - 23.2584i) q^{70} +(50.4301 - 42.3159i) q^{71} -43.5704i q^{73} +(-47.9240 + 32.0669i) q^{74} +(1.90929 + 21.8233i) q^{76} +(12.1970 + 14.5359i) q^{77} +(104.359 - 48.6636i) q^{79} +(21.4484 - 21.4484i) q^{80} +(-9.81078 - 36.6143i) q^{82} +(-9.46921 + 53.7026i) q^{83} +(-62.9623 - 36.3513i) q^{85} +(14.1614 + 11.8828i) q^{86} +(-11.7783 + 43.9574i) q^{88} +(116.687 + 54.4119i) q^{89} +(-7.47493 - 10.6753i) q^{91} +(-51.3220 - 4.49009i) q^{92} +(38.2798 - 26.8038i) q^{94} +(-19.9609 - 54.8422i) q^{95} +(49.4781 + 13.2576i) q^{97} +(32.0849 - 45.8220i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8}+O(q^{10}) \) 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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