LMFDB - Embedded newform 414.3.k.b.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

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

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	414.71
Dual form			414.3.k.b.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(0.404235 - 1.37670i) q^{5} +(-1.64257 + 1.89563i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(0.404235 - 1.37670i) q^{5} +(-1.64257 + 1.89563i) q^{7} +(2.79964 + 0.402527i) q^{8} +(1.32880 + 1.53352i) q^{10} +(5.25149 + 8.17148i) q^{11} +(-7.25236 - 8.36967i) q^{13} +(-0.999372 - 3.40355i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(13.6824 + 6.24852i) q^{17} +(-5.06198 - 11.0842i) q^{19} +(-2.84043 + 0.408392i) q^{20} -13.7369 q^{22} +(10.9611 + 20.2202i) q^{23} +(19.2994 + 12.4030i) q^{25} +(15.5025 - 2.22893i) q^{26} +(4.81335 + 1.41333i) q^{28} +(47.2529 + 21.5797i) q^{29} +(-1.03516 + 7.19967i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-17.8952 + 11.5006i) q^{34} +(1.94572 + 3.02760i) q^{35} +(-3.01096 + 0.884098i) q^{37} +(17.0573 + 2.45247i) q^{38} +(1.68587 - 3.69154i) q^{40} +(-2.24129 + 7.63313i) q^{41} +(5.87432 + 40.8568i) q^{43} +(10.5030 - 16.3430i) q^{44} +(-32.4368 - 2.41945i) q^{46} +2.35511i q^{47} +(6.07806 + 42.2738i) q^{49} +(-29.5120 + 13.4777i) q^{50} +(-9.20116 + 20.1477i) q^{52} +(23.7885 + 20.6128i) q^{53} +(13.3725 - 3.92652i) q^{55} +(-5.36165 + 4.64589i) q^{56} +(-61.8023 + 39.7179i) q^{58} +(-10.3021 + 8.92680i) q^{59} +(7.14418 - 49.6889i) q^{61} +(-7.77407 - 6.73627i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-14.4542 + 6.60100i) q^{65} +(-12.0190 - 7.72413i) q^{67} -30.0833i q^{68} -5.08964 q^{70} +(-35.7687 + 55.6572i) q^{71} +(-4.40508 - 9.64578i) q^{73} +(1.25030 - 4.25814i) q^{74} +(-15.9594 + 18.4182i) q^{76} +(-24.1160 - 3.46736i) q^{77} +(69.3272 + 80.0078i) q^{79} +(3.10289 + 4.82818i) q^{80} +(-7.36758 - 8.50264i) q^{82} +(14.9238 + 50.8257i) q^{83} +(14.1332 - 16.3106i) q^{85} +(-53.0993 - 24.2496i) q^{86} +(11.4130 + 24.9911i) q^{88} +(43.0814 - 6.19417i) q^{89} +27.7783 q^{91} +(27.6790 - 36.7406i) q^{92} +(-2.80191 - 1.80068i) q^{94} +(-17.3058 + 2.48820i) q^{95} +(-87.4033 - 25.6639i) q^{97} +(-54.9409 - 25.0907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 + 16 * q^7	$ 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	−	1.81926i	−0.207708	−	0.454816i
$5$	0.404235	−	1.37670i	0.0808470	−	0.275340i	−0.909142	−	0.416487i	$-0.863261\pi$
$5$	0.404235	−	1.37670i	0.0808470	−	0.275340i	0.989989	+	0.141148i	$0.0450792\pi$
$6$		0			0
$7$	−1.64257	+	1.89563i	−0.234653	+	0.270804i	−0.860848	−	0.508863i	$-0.830066\pi$
$7$	−1.64257	+	1.89563i	−0.234653	+	0.270804i	0.626195	+	0.779667i	$0.284612\pi$
$8$	2.79964	+	0.402527i	0.349955	+	0.0503159i
$9$		0			0
$10$	1.32880	+	1.53352i	0.132880	+	0.153352i
$11$	5.25149	+	8.17148i	0.477409	+	0.742862i	0.993520	−	0.113659i	$-0.0362573\pi$
$11$	5.25149	+	8.17148i	0.477409	+	0.742862i	−0.516111	+	0.856522i	$0.672621\pi$
$12$		0			0
$13$	−7.25236	−	8.36967i	−0.557874	−	0.643821i	0.404826	−	0.914394i	$-0.367332\pi$
$13$	−7.25236	−	8.36967i	−0.557874	−	0.643821i	−0.962699	+	0.270573i	$0.912787\pi$
$14$	−0.999372	−	3.40355i	−0.0713837	−	0.243111i
$15$		0			0
$16$	−2.61944	+	3.02300i	−0.163715	+	0.188937i
$17$	13.6824	+	6.24852i	0.804844	+	0.367560i	0.774973	−	0.631994i	$-0.217763\pi$
$17$	13.6824	+	6.24852i	0.804844	+	0.367560i	0.0298707	+	0.999554i	$0.490490\pi$
$18$		0			0
$19$	−5.06198	−	11.0842i	−0.266420	−	0.583378i	0.728386	−	0.685167i	$-0.240271\pi$
$19$	−5.06198	−	11.0842i	−0.266420	−	0.583378i	−0.994806	+	0.101789i	$0.967543\pi$
$20$	−2.84043	+	0.408392i	−0.142021	+	0.0204196i
$21$		0			0
$22$	−13.7369			−0.624405
$23$	10.9611	+	20.2202i	0.476568	+	0.879138i
$23$	10.9611	+	20.2202i	0.476568	+	0.879138i
$24$		0			0
$25$	19.2994	+	12.4030i	0.771978	+	0.496120i
$26$	15.5025	−	2.22893i	0.596251	−	0.0857279i
$27$		0			0
$28$	4.81335	+	1.41333i	0.171905	+	0.0504759i
$29$	47.2529	+	21.5797i	1.62941	+	0.744127i	0.999471	−	0.0325173i	$-0.0103524\pi$
$29$	47.2529	+	21.5797i	1.62941	+	0.744127i	0.629939	+	0.776644i	$0.283080\pi$
$30$		0			0
$31$	−1.03516	+	7.19967i	−0.0333921	+	0.232247i	−0.999682	−	0.0252084i	$-0.991975\pi$
$31$	−1.03516	+	7.19967i	−0.0333921	+	0.232247i	0.966290	+	0.257456i	$0.0828842\pi$
$32$	−1.59372	−	5.42771i	−0.0498038	−	0.169616i
$33$		0			0
$34$	−17.8952	+	11.5006i	−0.526330	+	0.338252i
$35$	1.94572	+	3.02760i	0.0555921	+	0.0865030i
$36$		0			0
$37$	−3.01096	+	0.884098i	−0.0813774	+	0.0238946i	−0.322168	−	0.946683i	$-0.604412\pi$
$37$	−3.01096	+	0.884098i	−0.0813774	+	0.0238946i	0.240790	+	0.970577i	$0.422593\pi$
$38$	17.0573	+	2.45247i	0.448876	+	0.0645386i
$39$		0			0
$40$	1.68587	−	3.69154i	0.0421468	−	0.0922885i
$41$	−2.24129	+	7.63313i	−0.0546656	+	0.186174i	−0.982300	−	0.187317i	$-0.940021\pi$
$41$	−2.24129	+	7.63313i	−0.0546656	+	0.186174i	0.927634	+	0.373491i	$0.121839\pi$
$42$		0			0
$43$	5.87432	+	40.8568i	0.136612	+	0.950159i	0.936664	+	0.350228i	$0.113896\pi$
$43$	5.87432	+	40.8568i	0.136612	+	0.950159i	−0.800052	+	0.599930i	$0.795195\pi$
$44$	10.5030	−	16.3430i	0.238704	−	0.371431i
$45$		0			0
$46$	−32.4368	−	2.41945i	−0.705148	−	0.0525967i
$47$			2.35511i			0.0501088i	0.999686	+	0.0250544i	$0.00797590\pi$
$47$			2.35511i			0.0501088i	−0.999686	+	0.0250544i	$0.992024\pi$
$48$		0			0
$49$	6.07806	+	42.2738i	0.124042	+	0.862731i
$50$	−29.5120	+	13.4777i	−0.590240	+	0.269554i
$51$		0			0
$52$	−9.20116	+	20.1477i	−0.176945	+	0.387456i
$53$	23.7885	+	20.6128i	0.448839	+	0.388921i	0.849742	−	0.527199i	$-0.176758\pi$
$53$	23.7885	+	20.6128i	0.448839	+	0.388921i	−0.400902	+	0.916121i	$0.631303\pi$
$54$		0			0
$55$	13.3725	−	3.92652i	0.243136	−	0.0713913i
$56$	−5.36165	+	4.64589i	−0.0957437	+	0.0829624i
$57$		0			0
$58$	−61.8023	+	39.7179i	−1.06556	+	0.684792i
$59$	−10.3021	+	8.92680i	−0.174612	+	0.151302i	−0.737782	−	0.675039i	$-0.764127\pi$
$59$	−10.3021	+	8.92680i	−0.174612	+	0.151302i	0.563171	+	0.826341i	$0.309581\pi$
$60$		0			0
$61$	7.14418	−	49.6889i	0.117118	−	0.814572i	−0.843586	−	0.536995i	$-0.819560\pi$
$61$	7.14418	−	49.6889i	0.117118	−	0.814572i	0.960703	−	0.277577i	$-0.0895314\pi$
$62$	−7.77407	−	6.73627i	−0.125388	−	0.108650i
$63$		0			0
$64$	7.67594	+	2.25386i	0.119937	+	0.0352166i
$65$	−14.4542	+	6.60100i	−0.222372	+	0.101554i
$66$		0			0
$67$	−12.0190	−	7.72413i	−0.179388	−	0.115286i	0.447865	−	0.894101i	$-0.352184\pi$
$67$	−12.0190	−	7.72413i	−0.179388	−	0.115286i	−0.627253	+	0.778816i	$0.715821\pi$
$68$		−	30.0833i		−	0.442401i
$69$		0			0
$70$	−5.08964			−0.0727092
$71$	−35.7687	+	55.6572i	−0.503785	+	0.783904i	−0.996259	−	0.0864229i	$-0.972456\pi$
$71$	−35.7687	+	55.6572i	−0.503785	+	0.783904i	0.492474	+	0.870327i	$0.336093\pi$
$72$		0			0
$73$	−4.40508	−	9.64578i	−0.0603436	−	0.132134i	0.877058	−	0.480385i	$-0.159503\pi$
$73$	−4.40508	−	9.64578i	−0.0603436	−	0.132134i	−0.937401	+	0.348251i	$0.886776\pi$
$74$	1.25030	−	4.25814i	0.0168960	−	0.0575425i
$75$		0			0
$76$	−15.9594	+	18.4182i	−0.209992	+	0.242344i
$77$	−24.1160	−	3.46736i	−0.313195	−	0.0450307i
$78$		0			0
$79$	69.3272	+	80.0078i	0.877559	+	1.01276i	0.999795	+	0.0202564i	$0.00644826\pi$
$79$	69.3272	+	80.0078i	0.877559	+	1.01276i	−0.122235	+	0.992501i	$0.539006\pi$
$80$	3.10289	+	4.82818i	0.0387861	+	0.0603523i
$81$		0			0
$82$	−7.36758	−	8.50264i	−0.0898486	−	0.103691i
$83$	14.9238	+	50.8257i	0.179804	+	0.612358i	0.999232	+	0.0391755i	$0.0124731\pi$
$83$	14.9238	+	50.8257i	0.179804	+	0.612358i	−0.819428	+	0.573182i	$0.805709\pi$
$84$		0			0
$85$	14.1332	−	16.3106i	0.166273	−	0.191889i
$86$	−53.0993	−	24.2496i	−0.617433	−	0.281972i
$87$		0			0
$88$	11.4130	+	24.9911i	0.129694	+	0.283989i
$89$	43.0814	−	6.19417i	0.484060	−	0.0695974i	0.104035	−	0.994574i	$-0.466824\pi$
$89$	43.0814	−	6.19417i	0.484060	−	0.0695974i	0.380025	+	0.924976i	$0.375915\pi$
$90$		0			0
$91$	27.7783			0.305256
$92$	27.6790	−	36.7406i	0.300859	−	0.399354i
$93$		0			0
$94$	−2.80191	−	1.80068i	−0.0298075	−	0.0191561i
$95$	−17.3058	+	2.48820i	−0.182166	+	0.0261916i
$96$		0			0
$97$	−87.4033	−	25.6639i	−0.901065	−	0.264577i	−0.201790	−	0.979429i	$-0.564676\pi$
$97$	−87.4033	−	25.6639i	−0.901065	−	0.264577i	−0.699275	+	0.714852i	$0.746494\pi$
$98$	−54.9409	−	25.0907i	−0.560621	−	0.256027i
$99$		0			0
$100$	6.52977	−	45.4156i	0.0652977	−	0.454156i
$101$	−51.3919	−	175.025i	−0.508831	−	1.73292i	−0.666574	−	0.745438i	$-0.732240\pi$
$101$	−51.3919	−	175.025i	−0.508831	−	1.73292i	0.157744	−	0.987480i	$-0.449578\pi$
$102$		0			0
$103$	104.120	−	66.9139i	1.01087	−	0.649649i	0.0732546	−	0.997313i	$-0.476661\pi$
$103$	104.120	−	66.9139i	1.01087	−	0.649649i	0.937619	+	0.347664i	$0.113025\pi$
$104$	−16.9350	−	26.3513i	−0.162836	−	0.253378i
$105$		0			0
$106$	−42.7116	+	12.5412i	−0.402939	+	0.118314i
$107$	3.58386	+	0.515281i	0.0334940	+	0.00481571i	0.159041	−	0.987272i	$-0.449160\pi$
$107$	3.58386	+	0.515281i	0.0334940	+	0.00481571i	−0.125547	+	0.992088i	$0.540069\pi$
$108$		0			0
$109$	45.1666	−	98.9010i	0.414372	−	0.907349i	−0.581236	−	0.813735i	$-0.697431\pi$
$109$	45.1666	−	98.9010i	0.414372	−	0.907349i	0.995609	−	0.0936141i	$-0.0298420\pi$
$110$	−5.55294	+	18.9116i	−0.0504813	+	0.171923i
$111$		0			0
$112$	−1.42786	−	9.93098i	−0.0127487	−	0.0886695i
$113$	−58.7412	+	91.4030i	−0.519833	+	0.808876i	−0.997573	−	0.0696249i	$-0.977820\pi$
$113$	−58.7412	+	91.4030i	−0.519833	+	0.808876i	0.477740	+	0.878501i	$0.341456\pi$
$114$		0			0
$115$	32.2679	−	6.91638i	0.280591	−	0.0601425i
$116$		−	103.895i		−	0.895643i
$117$		0			0
$118$	−2.74355	−	19.0818i	−0.0232504	−	0.161710i
$119$	−34.3191	+	15.6730i	−0.288396	+	0.131706i
$120$		0			0
$121$	11.0703	−	24.2405i	0.0914897	−	0.200335i
$122$	53.6532	+	46.4907i	0.439780	+	0.381071i
$123$		0			0
$124$	13.9581	−	4.09848i	0.112566	−	0.0330522i
$125$	51.9858	−	45.0459i	0.415886	−	0.360368i
$126$		0			0
$127$	87.9935	−	56.5500i	0.692863	−	0.445276i	−0.146240	−	0.989249i	$-0.546717\pi$
$127$	87.9935	−	56.5500i	0.692863	−	0.445276i	0.839102	+	0.543973i	$0.183081\pi$
$128$	−8.55033	+	7.40890i	−0.0667995	+	0.0578821i
$129$		0			0
$130$	3.19810	−	22.2433i	0.0246008	−	0.171102i
$131$	−14.5238	−	12.5850i	−0.110869	−	0.0960685i	0.597662	−	0.801748i	$-0.296096\pi$
$131$	−14.5238	−	12.5850i	−0.110869	−	0.0960685i	−0.708531	+	0.705680i	$0.750642\pi$
$132$		0			0
$133$	29.3262	+	8.61094i	0.220497	+	0.0647439i
$134$	18.3790	−	8.39340i	0.137157	−	0.0626373i
$135$		0			0
$136$	35.7904	+	23.0011i	0.263165	+	0.169126i
$137$		−	88.3939i		−	0.645211i	−0.946534	−	0.322605i	$-0.895441\pi$
$137$		−	88.3939i		−	0.645211i	0.946534	−	0.322605i	$-0.104559\pi$
$138$		0			0
$139$	12.2451			0.0880946			0.0440473	−	0.999029i	$-0.485975\pi$
$139$	12.2451			0.0880946			0.0440473	+	0.999029i	$0.485975\pi$
$140$	3.89145	−	6.05521i	0.0277960	−	0.0432515i
$141$		0			0
$142$	−38.8680	−	85.1090i	−0.273718	−	0.599359i
$143$	30.3069	−	103.216i	0.211936	−	0.721789i
$144$		0			0
$145$	48.8100	−	56.3297i	0.336621	−	0.388481i
$146$	14.8437	+	2.13421i	0.101670	+	0.0146179i
$147$		0			0
$148$	4.11001	+	4.74320i	0.0277703	+	0.0320487i
$149$	33.9162	+	52.7746i	0.227625	+	0.354192i	0.936214	−	0.351430i	$-0.114304\pi$
$149$	33.9162	+	52.7746i	0.227625	+	0.354192i	−0.708589	+	0.705621i	$0.750668\pi$
$150$		0			0
$151$	51.3724	+	59.2869i	0.340214	+	0.392628i	0.899914	−	0.436067i	$-0.143629\pi$
$151$	51.3724	+	59.2869i	0.340214	+	0.392628i	−0.559700	+	0.828695i	$0.689084\pi$
$152$	−9.71002	−	33.0693i	−0.0638817	−	0.217561i
$153$		0			0
$154$	22.5638	−	26.0401i	0.146519	−	0.169091i
$155$	9.49332	+	4.33546i	0.0612473	+	0.0279707i
$156$		0			0
$157$	−55.2251	−	120.926i	−0.351752	−	0.770229i	−0.999962	−	0.00876747i	$-0.997209\pi$
$157$	−55.2251	−	120.926i	−0.351752	−	0.770229i	0.648210	−	0.761462i	$-0.275518\pi$
$158$	−148.193	+	21.3069i	−0.937928	+	0.134854i
$159$		0			0
$160$	−8.11656			−0.0507285
$161$	−56.3342	−	12.4349i	−0.349902	−	0.0772357i
$162$		0			0
$163$	−96.3602	−	61.9269i	−0.591167	−	0.379920i	0.210586	−	0.977575i	$-0.432463\pi$
$163$	−96.3602	−	61.9269i	−0.591167	−	0.379920i	−0.801753	+	0.597655i	$0.796099\pi$
$164$	15.7488	−	2.26434i	0.0960294	−	0.0138069i
$165$		0			0
$166$	−71.8784	−	21.1054i	−0.433002	−	0.127141i
$167$	−224.232	−	102.403i	−1.34271	−	0.613193i	−0.391053	−	0.920368i	$-0.627889\pi$
$167$	−224.232	−	102.403i	−1.34271	−	0.613193i	−0.951653	+	0.307175i	$0.900616\pi$
$168$		0			0
$169$	6.59657	−	45.8802i	0.0390330	−	0.271480i
$170$	8.59892	+	29.2852i	0.0505819	+	0.172266i
$171$		0			0
$172$	69.4488	−	44.6320i	0.403772	−	0.259488i
$173$	−19.6730	−	30.6118i	−0.113717	−	0.176947i	0.779730	−	0.626116i	$-0.215356\pi$
$173$	−19.6730	−	30.6118i	−0.113717	−	0.176947i	−0.893447	+	0.449169i	$0.851720\pi$
$174$		0			0
$175$	−55.2122	+	16.2118i	−0.315498	+	0.0926386i
$176$	−38.4584	−	5.52948i	−0.218513	−	0.0314175i
$177$		0			0
$178$	−25.5700	+	55.9904i	−0.143651	+	0.314553i
$179$	−9.72077	+	33.1059i	−0.0543060	+	0.184949i	−0.982179	−	0.187946i	$-0.939817\pi$
$179$	−9.72077	+	33.1059i	−0.0543060	+	0.184949i	0.927873	+	0.372896i	$0.121635\pi$
$180$		0			0
$181$	−15.8069	−	109.939i	−0.0873307	−	0.607399i	−0.985745	−	0.168249i	$-0.946189\pi$
$181$	−15.8069	−	109.939i	−0.0873307	−	0.607399i	0.898414	−	0.439150i	$-0.144720\pi$
$182$	−21.2388	+	33.0482i	−0.116697	+	0.181583i
$183$		0			0
$184$	22.5479	+	61.0213i	0.122543	+	0.331637i
$185$			4.50257i			0.0243382i
$186$		0			0
$187$	20.7931	+	144.619i	0.111193	+	0.773365i
$188$	4.28457	−	1.95670i	0.0227903	−	0.0104080i
$189$		0			0
$190$	10.2715	−	22.4914i	0.0540603	−	0.118376i
$191$	76.7088	+	66.4686i	0.401617	+	0.348003i	0.832129	−	0.554582i	$-0.187122\pi$
$191$	76.7088	+	66.4686i	0.401617	+	0.348003i	−0.430512	+	0.902585i	$0.641667\pi$
$192$		0			0
$193$	−74.4912	+	21.8726i	−0.385965	+	0.113329i	−0.468958	−	0.883221i	$-0.655370\pi$
$193$	−74.4912	+	21.8726i	−0.385965	+	0.113329i	0.0829930	+	0.996550i	$0.473552\pi$
$194$	97.3596	−	84.3626i	0.501854	−	0.434859i
$195$		0			0
$196$	71.8574	−	46.1800i	0.366620	−	0.235612i
$197$	−59.4230	+	51.4904i	−0.301640	+	0.261372i	−0.792508	−	0.609861i	$-0.791225\pi$
$197$	−59.4230	+	51.4904i	−0.301640	+	0.261372i	0.490868	+	0.871234i	$0.336680\pi$
$198$		0			0
$199$	46.7375	−	325.067i	0.234862	−	1.63350i	−0.441734	−	0.897146i	$-0.645636\pi$
$199$	46.7375	−	325.067i	0.234862	−	1.63350i	0.676596	−	0.736355i	$-0.263454\pi$
$200$	49.0389	+	42.4925i	0.245195	+	0.212462i
$201$		0			0
$202$	247.522	+	72.6791i	1.22536	+	0.359798i
$203$	−118.523	+	54.1278i	−0.583859	+	0.266639i
$204$		0			0
$205$	9.60252	+	6.17116i	0.0468415	+	0.0301032i
$206$			175.034i			0.849679i
$207$		0			0
$208$	44.2986			0.212974
$209$	63.9913	−	99.5724i	0.306179	−	0.476423i
$210$		0			0
$211$	161.213	+	353.008i	0.764044	+	1.67302i	0.739343	+	0.673329i	$0.235136\pi$
$211$	161.213	+	353.008i	0.764044	+	1.67302i	0.0247011	+	0.999695i	$0.492137\pi$
$212$	17.7360	−	60.4033i	0.0836604	−	0.284921i
$213$		0			0
$214$	−3.35319	+	3.86979i	−0.0156691	+	0.0180831i
$215$	58.6221	+	8.42859i	0.272661	+	0.0392027i
$216$		0			0
$217$	−11.9476	−	13.7882i	−0.0550579	−	0.0635403i
$218$	83.1302	+	129.353i	0.381331	+	0.593363i
$219$		0			0
$220$	−18.2537	−	21.0658i	−0.0829712	−	0.0957538i
$221$	−46.9313	−	159.833i	−0.212359	−	0.723227i
$222$		0			0
$223$	−247.681	+	285.840i	−1.11068	+	1.28179i	−0.154828	+	0.987941i	$0.549482\pi$
$223$	−247.681	+	285.840i	−1.11068	+	1.28179i	−0.955851	+	0.293850i	$0.905063\pi$
$224$	12.9067	+	5.89430i	0.0576193	+	0.0263138i
$225$		0			0
$226$	−63.8309	−	139.770i	−0.282438	−	0.618452i
$227$	−113.873	+	16.3725i	−0.501644	+	0.0721255i	−0.388492	−	0.921452i	$-0.627004\pi$
$227$	−113.873	+	16.3725i	−0.501644	+	0.0721255i	−0.113152	+	0.993578i	$0.536095\pi$
$228$		0			0
$229$	−268.333			−1.17176			−0.585881	−	0.810397i	$-0.699251\pi$
$229$	−268.333			−1.17176			−0.585881	+	0.810397i	$0.699251\pi$
$230$	−16.4429	+	43.6777i	−0.0714911	+	0.189903i
$231$		0			0
$232$	123.605	+	79.4359i	0.532779	+	0.342396i
$233$	350.806	−	50.4383i	1.50560	−	0.216473i	0.660399	−	0.750915i	$-0.270387\pi$
$233$	350.806	−	50.4383i	1.50560	−	0.216473i	0.845206	+	0.534441i	$0.179478\pi$
$234$		0			0
$235$	3.24228	+	0.952019i	0.0137969	+	0.00405115i
$236$	24.7995	+	11.3255i	0.105083	+	0.0479896i
$237$		0			0
$238$	7.59338	−	52.8132i	0.0319050	−	0.221904i
$239$	−49.0286	−	166.976i	−0.205141	−	0.698645i	−0.996215	−	0.0869249i	$-0.972296\pi$
$239$	−49.0286	−	166.976i	−0.205141	−	0.698645i	0.791074	−	0.611720i	$-0.209522\pi$
$240$		0			0
$241$	−389.353	+	250.222i	−1.61557	+	1.03826i	−0.656809	+	0.754057i	$0.728094\pi$
$241$	−389.353	+	250.222i	−1.61557	+	1.03826i	−0.958763	+	0.284208i	$0.908269\pi$
$242$	20.3751	+	31.7042i	0.0841945	+	0.131009i
$243$		0			0
$244$	−96.3328	+	28.2859i	−0.394807	+	0.115926i
$245$	60.6553	+	8.72091i	0.247573	+	0.0355956i
$246$		0			0
$247$	−56.0597	+	122.754i	−0.226962	+	0.496978i
$248$	−5.79612	+	19.7398i	−0.0233715	+	0.0795959i
$249$		0			0
$250$	13.8443	+	96.2894i	0.0553773	+	0.385158i
$251$	−43.7765	+	68.1175i	−0.174408	+	0.271385i	−0.917442	−	0.397869i	$-0.869750\pi$
$251$	−43.7765	+	68.1175i	−0.174408	+	0.271385i	0.743034	+	0.669254i	$0.233386\pi$
$252$		0			0
$253$	−107.667	+	195.754i	−0.425560	+	0.773732i
$254$			147.924i			0.582378i
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.00889468	−	0.0618638i
$257$	−6.40347	+	2.92436i	−0.0249162	+	0.0113789i	−0.427834	−	0.903857i	$-0.640723\pi$
$257$	−6.40347	+	2.92436i	−0.0249162	+	0.0113789i	0.402918	+	0.915236i	$0.367996\pi$
$258$		0			0
$259$	3.26980	−	7.15986i	0.0126247	−	0.0276442i
$260$	24.0179	+	20.8116i	0.0923766	+	0.0800448i
$261$		0			0
$262$	26.0772	−	7.65694i	0.0995311	−	0.0292250i
$263$	−214.095	+	185.514i	−0.814050	+	0.705378i	−0.958798	−	0.284090i	$-0.908308\pi$
$263$	−214.095	+	185.514i	−0.814050	+	0.705378i	0.144748	+	0.989469i	$0.453763\pi$
$264$		0			0
$265$	37.9938	−	24.4171i	0.143373	−	0.0921401i
$266$	−32.6668	+	28.3059i	−0.122807	+	0.106413i
$267$		0			0
$268$	−4.06650	+	28.2831i	−0.0151735	+	0.105534i
$269$	289.636	+	250.971i	1.07671	+	0.932977i	0.997955	−	0.0639169i	$-0.0203593\pi$
$269$	289.636	+	250.971i	1.07671	+	0.932977i	0.0787575	+	0.996894i	$0.474905\pi$
$270$		0			0
$271$	398.403	+	116.982i	1.47012	+	0.431666i	0.916138	−	0.400862i	$-0.131289\pi$
$271$	398.403	+	116.982i	1.47012	+	0.431666i	0.553982	+	0.832529i	$0.313108\pi$
$272$	−54.7294	+	24.9941i	−0.201211	+	0.0918900i
$273$		0			0
$274$	105.163	+	67.5843i	0.383808	+	0.246658i
$275$			222.839i			0.810325i
$276$		0			0
$277$	−83.8924			−0.302860			−0.151430	−	0.988468i	$-0.548388\pi$
$277$	−83.8924			−0.302860			−0.151430	+	0.988468i	$0.548388\pi$
$278$	−9.36241	+	14.5682i	−0.0336777	+	0.0524036i
$279$		0			0
$280$	4.22863	+	9.25940i	0.0151022	+	0.0330693i
$281$	128.472	−	437.536i	0.457196	−	1.55707i	−0.332216	−	0.943203i	$-0.607796\pi$
$281$	128.472	−	437.536i	0.457196	−	1.55707i	0.789412	−	0.613864i	$-0.210386\pi$
$282$		0			0
$283$	−199.164	+	229.848i	−0.703760	+	0.812183i	−0.989255	−	0.146197i	$-0.953297\pi$
$283$	−199.164	+	229.848i	−0.703760	+	0.812183i	0.285495	+	0.958380i	$0.407842\pi$
$284$	130.973	+	18.8311i	0.461172	+	0.0663065i
$285$		0			0
$286$	99.6250	+	114.973i	0.348339	+	0.402005i
$287$	−10.7881	−	16.7866i	−0.0375892	−	0.0584900i
$288$		0			0
$289$	−41.0920	−	47.4227i	−0.142187	−	0.164093i
$290$	29.6969	+	101.139i	0.102403	+	0.348754i
$291$		0			0
$292$	−13.8884	+	16.0280i	−0.0475628	+	0.0548905i
$293$	228.771	+	104.476i	0.780790	+	0.356575i	0.765606	−	0.643310i	$-0.222439\pi$
$293$	228.771	+	104.476i	0.780790	+	0.356575i	0.0151839	+	0.999885i	$0.495167\pi$
$294$		0			0
$295$	8.12505	+	17.7914i	0.0275426	+	0.0603098i
$296$	−8.78548	+	1.26316i	−0.0296807	+	0.00426744i
$297$		0			0
$298$	−88.7182			−0.297712
$299$	89.7425	−	238.384i	0.300142	−	0.797272i
$300$		0			0
$301$	−87.0983	−	55.9747i	−0.289363	−	0.185962i
$302$	−109.813	+	15.7887i	−0.363618	+	0.0522804i
$303$		0			0
$304$	46.7670	+	13.7320i	0.153839	+	0.0451712i
$305$	−65.5187	−	29.9214i	−0.214815	−	0.0981029i
$306$		0			0
$307$	1.74531	−	12.1389i	0.00568505	−	0.0395404i	−0.986781	−	0.162057i	$-0.948187\pi$
$307$	1.74531	−	12.1389i	0.00568505	−	0.0395404i	0.992467	+	0.122516i	$0.0390964\pi$
$308$	13.7283	+	46.7542i	0.0445724	+	0.151799i
$309$		0			0
$310$	−12.4164	+	7.97951i	−0.0400528	+	0.0257404i
$311$	309.179	+	481.092i	0.994146	+	1.54692i	0.827930	+	0.560831i	$0.189518\pi$
$311$	309.179	+	481.092i	0.994146	+	1.54692i	0.166215	+	0.986089i	$0.446845\pi$
$312$		0			0
$313$	−502.012	+	147.404i	−1.60387	+	0.470939i	−0.956621	−	0.291337i	$-0.905900\pi$
$313$	−502.012	+	147.404i	−1.60387	+	0.470939i	−0.647252	+	0.762276i	$0.724082\pi$
$314$	186.091	+	26.7559i	0.592647	+	0.0852098i
$315$		0			0
$316$	87.9563	−	192.597i	0.278343	−	0.609485i
$317$	−43.9426	+	149.655i	−0.138620	+	0.472097i	−0.999314	−	0.0370254i	$-0.988212\pi$
$317$	−43.9426	+	149.655i	−0.138620	+	0.472097i	0.860694	+	0.509122i	$0.170030\pi$
$318$		0			0
$319$	71.8103	+	499.452i	0.225111	+	1.56568i
$320$	6.20577	−	9.65637i	0.0193930	−	0.0301762i
$321$		0			0
$322$	57.8661	−	57.5140i	0.179708	−	0.178615i
$323$		−	183.288i		−	0.567454i
$324$		0			0
$325$	−36.1575	−	251.481i	−0.111254	−	0.773788i
$326$	147.350	−	67.2927i	0.451995	−	0.206419i
$327$		0			0
$328$	−9.34735	+	20.4678i	−0.0284980	+	0.0624019i
$329$	−4.46442	−	3.86844i	−0.0135697	−	0.0117582i
$330$		0			0
$331$	29.2276	−	8.58201i	0.0883010	−	0.0259275i	−0.237284	−	0.971440i	$-0.576257\pi$
$331$	29.2276	−	8.58201i	0.0883010	−	0.0259275i	0.325585	+	0.945513i	$0.394439\pi$
$332$	80.0662	−	69.3778i	0.241163	−	0.208969i
$333$		0			0
$334$	293.274	−	188.476i	0.878066	−	0.564299i
$335$	−15.4923	+	13.4242i	−0.0462457	+	0.0400721i
$336$		0			0
$337$	40.4870	−	281.593i	0.120140	−	0.835589i	−0.837256	−	0.546810i	$-0.815842\pi$
$337$	40.4870	−	281.593i	0.120140	−	0.835589i	0.957396	−	0.288778i	$-0.0932491\pi$
$338$	49.5406	+	42.9271i	0.146570	+	0.127003i
$339$		0			0
$340$	−41.4156	−	12.1607i	−0.121811	−	0.0357668i
$341$	−64.2681	+	29.3502i	−0.188469	+	0.0860711i
$342$		0			0
$343$	−193.514	−	124.364i	−0.564180	−	0.362577i
$344$			116.749i			0.339386i
$345$		0			0
$346$	51.4609			0.148731
$347$	−57.1260	+	88.8897i	−0.164628	+	0.256166i	−0.913760	−	0.406255i	$-0.866835\pi$
$347$	−57.1260	+	88.8897i	−0.164628	+	0.256166i	0.749132	+	0.662421i	$0.230471\pi$
$348$		0			0
$349$	−111.134	−	243.350i	−0.318436	−	0.697278i	0.680949	−	0.732331i	$-0.261567\pi$
$349$	−111.134	−	243.350i	−0.318436	−	0.697278i	−0.999385	+	0.0350523i	$0.988840\pi$
$350$	22.9269	−	78.0818i	0.0655054	−	0.223091i
$351$		0			0
$352$	35.9830	−	41.5267i	0.102225	−	0.117973i
$353$	−233.071	−	33.5106i	−0.660258	−	0.0949308i	−0.195963	−	0.980611i	$-0.562783\pi$
$353$	−233.071	−	33.5106i	−0.660258	−	0.0949308i	−0.464295	+	0.885680i	$0.653692\pi$
$354$		0			0
$355$	62.1642	+	71.7413i	0.175110	+	0.202088i
$356$	−47.0621	−	73.2301i	−0.132197	−	0.205703i
$357$		0			0
$358$	−31.9542	−	36.8771i	−0.0892575	−	0.103009i
$359$	75.0765	+	255.687i	0.209127	+	0.712220i	0.995525	+	0.0945001i	$0.0301253\pi$
$359$	75.0765	+	255.687i	0.209127	+	0.712220i	−0.786398	+	0.617720i	$0.788057\pi$
$360$		0			0
$361$	139.169	−	160.610i	0.385510	−	0.444902i
$362$	142.882	+	65.2518i	0.394701	+	0.180254i
$363$		0			0
$364$	−23.0790	−	50.5360i	−0.0634040	−	0.138835i
$365$	−15.0600	+	2.16530i	−0.0412603	+	0.00593234i
$366$		0			0
$367$	−290.122			−0.790523			−0.395261	−	0.918569i	$-0.629346\pi$
$367$	−290.122			−0.790523			−0.395261	+	0.918569i	$0.629346\pi$
$368$	−89.8374	−	19.8303i	−0.244123	−	0.0538866i
$369$		0			0
$370$	−5.35676	−	3.44258i	−0.0144777	−	0.00930428i
$371$	−78.1485	+	11.2361i	−0.210643	+	0.0302859i
$372$		0			0
$373$	−309.875	−	90.9874i	−0.830763	−	0.243934i	−0.161418	−	0.986886i	$-0.551607\pi$
$373$	−309.875	−	90.9874i	−0.830763	−	0.243934i	−0.669345	+	0.742952i	$0.733425\pi$
$374$	−187.953	−	85.8354i	−0.502549	−	0.229506i
$375$		0			0
$376$	−0.947997	+	6.59346i	−0.00252127	+	0.0175358i
$377$	−162.080	−	551.995i	−0.429921	−	1.46418i
$378$		0			0
$379$	384.623	−	247.182i	1.01484	−	0.652196i	0.0761967	−	0.997093i	$-0.475722\pi$
$379$	384.623	−	247.182i	1.01484	−	0.652196i	0.938641	+	0.344896i	$0.112086\pi$
$380$	18.9049	+	29.4166i	0.0497497	+	0.0774120i
$381$		0			0
$382$	−137.729	+	40.4408i	−0.360546	+	0.105866i
$383$	472.154	+	67.8856i	1.23278	+	0.177247i	0.727742	−	0.685851i	$-0.240570\pi$
$383$	472.154	+	67.8856i	1.23278	+	0.177247i	0.505037	+	0.863098i	$0.331479\pi$
$384$		0			0
$385$	−14.5221	+	31.7989i	−0.0377197	+	0.0825945i
$386$	30.9325	−	105.346i	0.0801360	−	0.272918i
$387$		0			0
$388$	25.9278	+	180.332i	0.0668243	+	0.464773i
$389$	18.9893	−	29.5480i	0.0488157	−	0.0759588i	−0.815988	−	0.578069i	$-0.803806\pi$
$389$	18.9893	−	29.5480i	0.0488157	−	0.0759588i	0.864804	+	0.502110i	$0.167443\pi$
$390$		0			0
$391$	23.6271	+	345.150i	0.0604273	+	0.882736i
$392$			120.798i			0.308158i
$393$		0			0
$394$	−15.8249	−	110.065i	−0.0401648	−	0.279352i
$395$	138.171	−	63.1007i	0.349800	−	0.159748i
$396$		0			0
$397$	198.254	−	434.116i	0.499380	−	1.09349i	−0.477290	−	0.878746i	$-0.658381\pi$
$397$	198.254	−	434.116i	0.499380	−	1.09349i	0.976670	−	0.214745i	$-0.0688919\pi$
$398$	351.001	+	304.144i	0.881912	+	0.764181i
$399$		0			0
$400$	−88.0480	+	25.8532i	−0.220120	+	0.0646331i
$401$	76.4891	−	66.2782i	0.190746	−	0.165282i	−0.554252	−	0.832349i	$-0.686996\pi$
$401$	76.4891	−	66.2782i	0.190746	−	0.165282i	0.744998	+	0.667066i	$0.232450\pi$
$402$		0			0
$403$	67.7661	−	43.5507i	0.168154	−	0.108066i
$404$	−275.718	+	238.911i	−0.682471	+	0.591365i
$405$		0			0
$406$	26.2243	−	182.394i	0.0645918	−	0.449246i
$407$	−23.0364	−	19.9612i	−0.0566006	−	0.0490447i
$408$		0			0
$409$	245.923	+	72.2094i	0.601278	+	0.176551i	0.568184	−	0.822901i	$-0.307646\pi$
$409$	245.923	+	72.2094i	0.601278	+	0.176551i	0.0330932	+	0.999452i	$0.489464\pi$
$410$	−14.6838	+	6.70587i	−0.0358142	+	0.0163558i
$411$		0			0
$412$	−208.240	−	133.828i	−0.505437	−	0.324825i
$413$		−	34.1918i		−	0.0827889i
$414$		0			0
$415$	76.0044			0.183143
$416$	−33.8699	+	52.7026i	−0.0814181	+	0.126689i
$417$		0			0
$418$	69.5359	+	152.262i	0.166354	+	0.364264i
$419$	28.1458	−	95.8559i	0.0671739	−	0.228773i	−0.919063	−	0.394110i	$-0.871053\pi$
$419$	28.1458	−	95.8559i	0.0671739	−	0.228773i	0.986237	+	0.165337i	$0.0528711\pi$
$420$		0			0
$421$	434.470	−	501.405i	1.03199	−	1.19099i	0.0506524	−	0.998716i	$-0.483870\pi$
$421$	434.470	−	501.405i	1.03199	−	1.19099i	0.981342	−	0.192269i	$-0.0615846\pi$
$422$	−543.239	−	78.1059i	−1.28730	−	0.185085i
$423$		0			0
$424$	58.3019	+	67.2840i	0.137504	+	0.158689i
$425$	186.561	+	290.295i	0.438968	+	0.683048i
$426$		0			0
$427$	82.4568	+	95.1602i	0.193107	+	0.222858i
$428$	−2.04015	−	6.94810i	−0.00476670	−	0.0162339i
$429$		0			0
$430$	−54.8490	+	63.2991i	−0.127556	+	0.147207i
$431$	−493.845	−	225.531i	−1.14581	−	0.523274i	−0.250236	−	0.968185i	$-0.580508\pi$
$431$	−493.845	−	225.531i	−1.14581	−	0.523274i	−0.895575	+	0.444910i	$0.853236\pi$
$432$		0			0
$433$	−103.757	−	227.196i	−0.239623	−	0.524701i	0.751166	−	0.660113i	$-0.229492\pi$
$433$	−103.757	−	227.196i	−0.239623	−	0.524701i	−0.990789	+	0.135412i	$0.956764\pi$
$434$	25.5389	−	3.67194i	0.0588455	−	0.00846070i
$435$		0			0
$436$	−217.453			−0.498745
$437$	168.639	−	223.849i	0.385903	−	0.512239i
$438$		0			0
$439$	369.633	+	237.548i	0.841988	+	0.541113i	0.889066	−	0.457779i	$-0.151355\pi$
$439$	369.633	+	237.548i	0.841988	+	0.541113i	−0.0470786	+	0.998891i	$0.514991\pi$
$440$	39.0187	−	5.61004i	0.0886789	−	0.0127501i
$441$		0			0
$442$	226.038	+	66.3708i	0.511399	+	0.150160i
$443$	−607.498	−	277.435i	−1.37133	−	0.626264i	−0.412684	−	0.910874i	$-0.635409\pi$
$443$	−607.498	−	277.435i	−1.37133	−	0.626264i	−0.958643	+	0.284610i	$0.908136\pi$
$444$		0			0
$445$	8.88751	−	61.8140i	0.0199719	−	0.138908i
$446$	−150.694	−	513.217i	−0.337879	−	1.15071i
$447$		0			0
$448$	−16.8808	+	10.8486i	−0.0376803	+	0.0242156i
$449$	197.292	+	306.993i	0.439404	+	0.683726i	0.988361	−	0.152124i	$-0.0486115\pi$
$449$	197.292	+	306.993i	0.439404	+	0.683726i	−0.548957	+	0.835850i	$0.684975\pi$
$450$		0			0
$451$	−74.1442	+	21.7707i	−0.164399	+	0.0482720i
$452$	215.090	+	30.9253i	0.475863	+	0.0684188i
$453$		0			0
$454$	67.5868	−	147.994i	0.148870	−	0.325979i
$455$	11.2290	−	38.2423i	0.0246790	−	0.0840491i
$456$		0			0
$457$	83.4698	+	580.545i	0.182647	+	1.27034i	0.850472	+	0.526021i	$0.176317\pi$
$457$	83.4698	+	580.545i	0.182647	+	1.27034i	−0.667825	+	0.744319i	$0.732774\pi$
$458$	205.163	−	319.240i	0.447954	−	0.697029i
$459$		0			0
$460$	−39.3919	−	52.9575i	−0.0856345	−	0.115125i
$461$		−	610.720i		−	1.32477i	−0.749163	−	0.662386i	$-0.769544\pi$
$461$		−	610.720i		−	1.32477i	0.749163	−	0.662386i	$-0.230456\pi$
$462$		0			0
$463$	−32.9509	−	229.179i	−0.0711683	−	0.494986i	−0.993965	−	0.109699i	$-0.965011\pi$
$463$	−32.9509	−	229.179i	−0.0711683	−	0.494986i	0.922797	−	0.385287i	$-0.125898\pi$
$464$	−189.012	+	86.3187i	−0.407353	+	0.186032i
$465$		0			0
$466$	−208.213	+	455.922i	−0.446808	+	0.978374i
$467$	−24.3225	−	21.0755i	−0.0520824	−	0.0451297i	0.628431	−	0.777866i	$-0.283698\pi$
$467$	−24.3225	−	21.0755i	−0.0520824	−	0.0451297i	−0.680513	+	0.732736i	$0.738243\pi$
$468$		0			0
$469$	34.3841	−	10.0961i	0.0733137	−	0.0215268i
$470$	−3.61162	+	3.12948i	−0.00768429	+	0.00665848i
$471$		0			0
$472$	−32.4354	+	20.8450i	−0.0687190	+	0.0441630i
$473$	−303.012	+	262.561i	−0.640617	+	0.555098i
$474$		0			0
$475$	39.7838	−	276.702i	0.0837554	−	0.582531i
$476$	57.0267	+	49.4139i	0.119804	+	0.103811i
$477$		0			0
$478$	236.140	+	69.3370i	0.494017	+	0.145056i
$479$	−665.264	+	303.816i	−1.38886	+	0.634272i	−0.962748	−	0.270399i	$-0.912845\pi$
$479$	−665.264	+	303.816i	−1.38886	+	0.634272i	−0.426113	+	0.904670i	$0.640117\pi$
$480$		0			0
$481$	29.2362	+	18.7890i	0.0607821	+	0.0390623i
$482$		−	654.533i		−	1.35795i
$483$		0			0
$484$	−53.2973			−0.110118
$485$	−70.6630	+	109.954i	−0.145697	+	0.226709i
$486$		0			0
$487$	−211.625	−	463.394i	−0.434548	−	0.951528i	−0.992567	−	0.121699i	$-0.961166\pi$
$487$	−211.625	−	463.394i	−0.434548	−	0.951528i	0.558019	−	0.829828i	$-0.311562\pi$
$488$	40.0022	−	136.235i	0.0819718	−	0.279170i
$489$		0			0
$490$	−56.7513	+	65.4945i	−0.115819	+	0.133662i
$491$	−413.779	−	59.4924i	−0.842726	−	0.121166i	−0.292587	−	0.956239i	$-0.594516\pi$
$491$	−413.779	−	59.4924i	−0.842726	−	0.121166i	−0.550139	+	0.835073i	$0.685425\pi$
$492$		0			0
$493$	511.690	+	590.522i	1.03791	+	1.19781i
$494$	−103.179	−	160.550i	−0.208865	−	0.325000i
$495$		0			0
$496$	−19.0531	−	21.9884i	−0.0384134	−	0.0443314i
$497$	−46.7527	−	159.225i	−0.0940698	−	0.320372i
$498$		0			0
$499$	373.325	−	430.840i	0.748147	−	0.863407i	−0.246240	−	0.969209i	$-0.579195\pi$
$499$	373.325	−	430.840i	0.748147	−	0.863407i	0.994387	+	0.105801i	$0.0337408\pi$
$500$	−125.142	−	57.1504i	−0.250284	−	0.114301i
$501$		0			0
$502$	−47.5696	−	104.163i	−0.0947601	−	0.207496i
$503$	−155.746	+	22.3929i	−0.309635	+	0.0445188i	−0.295381	−	0.955380i	$-0.595446\pi$
$503$	−155.746	+	22.3929i	−0.309635	+	0.0445188i	−0.0142541	+	0.999898i	$0.504537\pi$
$504$		0			0
$505$	−261.731			−0.518279
$506$	−150.571	−	277.763i	−0.297572	−	0.548938i
$507$		0			0
$508$	−175.987	−	113.100i	−0.346431	−	0.222638i
$509$	677.996	−	97.4811i	1.33202	−	0.191515i	0.560727	−	0.828001i	$-0.310522\pi$
$509$	677.996	−	97.4811i	1.33202	−	0.191515i	0.771288	+	0.636486i	$0.219613\pi$
$510$		0			0
$511$	25.5205	+	7.49349i	0.0499422	+	0.0146644i
$512$	20.5826	+	9.39977i	0.0402004	+	0.0183589i
$513$		0			0
$514$	1.41682	−	9.85420i	0.00275646	−	0.0191716i
$515$	−50.0312	−	170.391i	−0.0971480	−	0.330856i
$516$		0			0
$517$	−19.2448	+	12.3679i	−0.0372239	+	0.0239224i
$518$	6.01815	+	9.36442i	0.0116180	+	0.0180780i
$519$		0			0
$520$	−43.1235	+	12.6622i	−0.0829298	+	0.0243504i
$521$	−561.406	−	80.7179i	−1.07755	−	0.154929i	−0.419392	−	0.907805i	$-0.637757\pi$
$521$	−561.406	−	80.7179i	−1.07755	−	0.154929i	−0.658162	+	0.752876i	$0.728666\pi$
$522$		0			0
$523$	−75.0532	+	164.344i	−0.143505	+	0.314232i	−0.967713	−	0.252055i	$-0.918894\pi$
$523$	−75.0532	+	164.344i	−0.143505	+	0.314232i	0.824208	+	0.566288i	$0.191621\pi$
$524$	−10.8286	+	36.8787i	−0.0206652	+	0.0703791i
$525$		0			0
$526$	−57.0156	−	396.553i	−0.108395	−	0.753902i
$527$	−59.1506	+	92.0402i	−0.112240	+	0.174649i
$528$		0			0
$529$	−288.710	+	443.269i	−0.545766	+	0.837938i
$530$			63.8706i			0.120510i
$531$		0			0
$532$	−8.69949	−	60.5063i	−0.0163524	−	0.113734i
$533$	80.1414	−	36.5994i	0.150359	−	0.0686667i
$534$		0			0
$535$	2.15811	−	4.72560i	0.00403385	−	0.00883289i
$536$	−30.5396	−	26.4627i	−0.0569769	−	0.0493708i
$537$		0			0
$538$	−520.033	+	152.696i	−0.966604	+	0.283821i
$539$	−313.521	+	271.668i	−0.581672	+	0.504022i
$540$		0			0
$541$	618.419	−	397.434i	1.14310	−	0.734628i	0.174849	−	0.984595i	$-0.444056\pi$
$541$	618.419	−	397.434i	1.14310	−	0.734628i	0.968254	+	0.249968i	$0.0804200\pi$
$542$	−443.786	+	384.542i	−0.818793	+	0.709488i
$543$		0			0
$544$	12.1093	−	84.2223i	0.0222598	−	0.154820i
$545$	−117.899	−	102.160i	−0.216328	−	0.187450i
$546$		0			0
$547$	1016.01	+	298.328i	1.85742	+	0.545389i	0.999500	+	0.0316100i	$0.0100635\pi$
$547$	1016.01	+	298.328i	1.85742	+	0.545389i	0.857923	+	0.513779i	$0.171755\pi$
$548$	−160.812	+	73.4403i	−0.293452	+	0.134015i
$549$		0			0
$550$	−265.115	−	170.379i	−0.482027	−	0.309780i
$551$		−	632.996i		−	1.14881i
$552$		0			0
$553$	−265.540			−0.480181
$554$	64.1425	−	99.8077i	0.115781	−	0.180158i
$555$		0			0
$556$	−10.1736	−	22.2771i	−0.0182979	−	0.0400668i
$557$	−26.6197	+	90.6583i	−0.0477912	+	0.162762i	−0.979931	−	0.199336i	$-0.936121\pi$
$557$	−26.6197	+	90.6583i	−0.0477912	+	0.162762i	0.932140	+	0.362098i	$0.117940\pi$
$558$		0			0
$559$	299.355	−	345.474i	0.535519	−	0.618022i
$560$	−14.2492	−	2.04872i	−0.0254449	−	0.00365843i
$561$		0			0
$562$	422.314	+	487.377i	0.751449	+	0.867218i
$563$	575.322	+	895.219i	1.02189	+	1.59009i	0.785923	+	0.618324i	$0.212188\pi$
$563$	575.322	+	895.219i	1.02189	+	1.59009i	0.235963	+	0.971762i	$0.424176\pi$
$564$		0			0
$565$	102.089	+	117.817i	0.180689	+	0.208526i
$566$	−121.175	−	412.685i	−0.214091	−	0.729126i
$567$		0			0
$568$	−122.543	+	141.422i	−0.215745	+	0.248983i
$569$	79.9703	+	36.5212i	0.140545	+	0.0641849i	0.484446	−	0.874821i	$-0.339021\pi$
$569$	79.9703	+	36.5212i	0.140545	+	0.0641849i	−0.343901	+	0.939006i	$0.611748\pi$
$570$		0			0
$571$	−142.751	−	312.582i	−0.250002	−	0.547429i	0.742473	−	0.669876i	$-0.233653\pi$
$571$	−142.751	−	312.582i	−0.250002	−	0.547429i	−0.992475	+	0.122448i	$0.960926\pi$
$572$	−212.957	+	30.6185i	−0.372302	+	0.0535289i
$573$		0			0
$574$	28.2196			0.0491631
$575$	−39.2482	+	526.188i	−0.0682577	+	0.915110i
$576$		0			0
$577$	88.4919	+	56.8703i	0.153365	+	0.0985620i	0.615073	−	0.788470i	$-0.289127\pi$
$577$	88.4919	+	56.8703i	0.153365	+	0.0985620i	−0.461707	+	0.887032i	$0.652763\pi$
$578$	87.8376	−	12.6291i	0.151968	−	0.0218497i
$579$		0			0
$580$	−143.031	−	41.9978i	−0.246606	−	0.0724101i
$581$	−120.860	−	55.1949i	−0.208021	−	0.0949998i
$582$		0			0
$583$	−43.5124	+	302.635i	−0.0746353	+	0.519100i
$584$	−8.44994	−	28.7779i	−0.0144691	−	0.0492772i
$585$		0			0
$586$	−299.211	+	192.291i	−0.510599	+	0.328142i
$587$	−70.3514	−	109.469i	−0.119849	−	0.186489i	0.776145	−	0.630554i	$-0.217172\pi$
$587$	−70.3514	−	109.469i	−0.119849	−	0.186489i	−0.895994	+	0.444065i	$0.853536\pi$
$588$		0			0
$589$	85.0424	−	24.9707i	0.144384	−	0.0423951i
$590$	−27.3789	−	3.93649i	−0.0464049	−	0.00667202i
$591$		0			0
$592$	5.21442	−	11.4180i	0.00880814	−	0.0192871i
$593$	−242.666	+	826.444i	−0.409217	+	1.39367i	0.454974	+	0.890504i	$0.349648\pi$
$593$	−242.666	+	826.444i	−0.409217	+	1.39367i	−0.864192	+	0.503162i	$0.832170\pi$
$594$		0			0
$595$	7.70402	+	53.5826i	0.0129479	+	0.0900548i
$596$	67.8323	−	105.549i	0.113813	−	0.177096i
$597$		0			0
$598$	214.993	+	289.032i	0.359521	+	0.483331i
$599$		−	125.083i		−	0.208819i	−0.994534	−	0.104410i	$-0.966705\pi$
$599$		−	125.083i		−	0.208819i	0.994534	−	0.104410i	$-0.0332953\pi$
$600$		0			0
$601$	−45.7290	−	318.052i	−0.0760882	−	0.529205i	−0.991843	−	0.127467i	$-0.959315\pi$
$601$	−45.7290	−	318.052i	−0.0760882	−	0.529205i	0.915755	−	0.401738i	$-0.131594\pi$
$602$	133.188	−	60.8247i	0.221242	−	0.101038i
$603$		0			0
$604$	65.1768	−	142.717i	0.107909	−	0.236287i
$605$	−28.8968	−	25.0393i	−0.0477634	−	0.0413872i
$606$		0			0
$607$	133.483	−	39.1940i	0.219905	−	0.0645701i	−0.169924	−	0.985457i	$-0.554352\pi$
$607$	133.483	−	39.1940i	0.219905	−	0.0645701i	0.389829	+	0.920887i	$0.372534\pi$
$608$	−52.0944	+	45.1401i	−0.0856816	+	0.0742435i
$609$		0			0
$610$	85.6922	−	55.0710i	0.140479	−	0.0902804i
$611$	19.7115	−	17.0801i	0.0322611	−	0.0279544i
$612$		0			0
$613$	106.715	−	742.217i	0.174086	−	1.21079i	−0.696054	−	0.717989i	$-0.745063\pi$
$613$	106.715	−	742.217i	0.174086	−	1.21079i	0.870140	−	0.492805i	$-0.164028\pi$
$614$	13.1074	+	11.3576i	0.0213475	+	0.0184977i
$615$		0			0
$616$	−66.1205	−	19.4147i	−0.107338	−	0.0315174i
$617$	344.135	−	157.161i	0.557755	−	0.254718i	−0.116533	−	0.993187i	$-0.537178\pi$
$617$	344.135	−	157.161i	0.557755	−	0.254718i	0.674288	+	0.738469i	$0.264451\pi$
$618$		0			0
$619$	−938.274	−	602.992i	−1.51579	−	0.974139i	−0.992535	−	0.121963i	$-0.961081\pi$
$619$	−938.274	−	602.992i	−1.51579	−	0.974139i	−0.523255	−	0.852176i	$-0.675283\pi$
$620$		−	20.8729i		−	0.0336660i
$621$		0			0
$622$	−808.754			−1.30025
$623$	−59.0224	+	91.8406i	−0.0947390	+	0.147417i
$624$		0			0
$625$	197.254	+	431.926i	0.315606	+	0.691081i
$626$	208.461	−	709.952i	0.333005	−	1.13411i
$627$		0			0
$628$	−174.114	+	200.938i	−0.277251	+	0.319965i
$629$	−46.7214	−	6.71752i	−0.0742788	−	0.0106797i
$630$		0			0
$631$	274.418	+	316.696i	0.434894	+	0.501895i	0.930317	−	0.366758i	$-0.119532\pi$
$631$	274.418	+	316.696i	0.434894	+	0.501895i	−0.495422	+	0.868652i	$0.664987\pi$
$632$	161.886	+	251.899i	0.256148	+	0.398574i
$633$		0			0
$634$	−144.448	−	166.702i	−0.227837	−	0.262937i
$635$	−42.2822	−	144.000i	−0.0665862	−	0.226772i
$636$		0			0
$637$	309.738	−	357.456i	0.486244	−	0.561156i
$638$	−649.109	−	296.438i	−1.01741	−	0.464637i
$639$		0			0
$640$	6.74348	+	14.7662i	0.0105367	+	0.0230721i
$641$	−565.007	+	81.2358i	−0.881447	+	0.126733i	−0.568153	−	0.822923i	$-0.692342\pi$
$641$	−565.007	+	81.2358i	−0.881447	+	0.126733i	−0.313294	+	0.949656i	$0.601433\pi$
$642$		0			0
$643$	−367.731			−0.571899			−0.285950	−	0.958245i	$-0.592309\pi$
$643$	−367.731			−0.571899			−0.285950	+	0.958245i	$0.592309\pi$
$644$	24.1817	+	112.818i	0.0375493	+	0.175184i
$645$		0			0
$646$	218.060	+	140.138i	0.337553	+	0.216932i
$647$	1099.89	−	158.140i	1.69998	−	0.244420i	0.777062	−	0.629424i	$-0.216709\pi$
$647$	1099.89	−	158.140i	1.69998	−	0.244420i	0.922915	+	0.385004i	$0.125800\pi$
$648$		0			0
$649$	−127.047	−	37.3042i	−0.195757	−	0.0574796i
$650$	326.835	+	149.261i	0.502824	+	0.229632i
$651$		0			0
$652$	−32.6025	+	226.755i	−0.0500038	+	0.347784i
$653$	1.19378	+	4.06564i	0.00182815	+	0.00622610i	0.960402	−	0.278618i	$-0.0898763\pi$
$653$	1.19378	+	4.06564i	0.00182815	+	0.00622610i	−0.958574	+	0.284844i	$0.908058\pi$
$654$		0			0
$655$	−23.1968	+	14.9076i	−0.0354149	+	0.0227598i
$656$	−17.2040	−	26.7700i	−0.0262256	−	0.0408079i
$657$		0			0
$658$	8.01574	−	2.35363i	0.0121820	−	0.00357695i
$659$	948.015	+	136.304i	1.43857	+	0.206835i	0.817050	−	0.576567i	$-0.195608\pi$
$659$	948.015	+	136.304i	1.43857	+	0.206835i	0.621516	+	0.783401i	$0.286517\pi$
$660$		0			0
$661$	21.1540	−	46.3208i	0.0320030	−	0.0700769i	−0.892955	−	0.450145i	$-0.851372\pi$
$661$	21.1540	−	46.3208i	0.0320030	−	0.0700769i	0.924958	+	0.380068i	$0.124100\pi$
$662$	−12.1368	+	41.3341i	−0.0183335	+	0.0624383i
$663$		0			0
$664$	21.3224	+	148.301i	0.0321121	+	0.223345i
$665$	23.7093	−	36.8924i	0.0356531	−	0.0554773i
$666$		0			0
$667$	81.5977	+	1192.00i	0.122335	+	1.78710i
$668$			493.017i			0.738049i
$669$		0			0
$670$	−4.12575	−	28.6952i	−0.00615784	−	0.0428287i
$671$	443.549	−	202.562i	0.661028	−	0.301881i
$672$		0			0
$673$	−289.728	+	634.416i	−0.430502	+	0.942669i	0.562743	+	0.826632i	$0.309746\pi$
$673$	−289.728	+	634.416i	−0.430502	+	0.942669i	−0.993245	+	0.116036i	$0.962981\pi$
$674$	304.059	+	263.469i	0.451127	+	0.390904i
$675$		0			0
$676$	−88.9488	+	26.1177i	−0.131581	+	0.0386357i
$677$	256.763	−	222.486i	0.379266	−	0.328636i	−0.444277	−	0.895889i	$-0.646539\pi$
$677$	256.763	−	222.486i	0.379266	−	0.328636i	0.823543	+	0.567254i	$0.191994\pi$
$678$		0			0
$679$	192.215	−	123.529i	0.283086	−	0.181928i
$680$	46.1333	−	39.9748i	0.0678431	−	0.0587864i
$681$		0			0
$682$	14.2198	−	98.9012i	0.0208502	−	0.145016i
$683$	680.355	+	589.531i	0.996127	+	0.863149i	0.990594	−	0.136835i	$-0.0436931\pi$
$683$	680.355	+	589.531i	0.996127	+	0.863149i	0.00553364	+	0.999985i	$0.498239\pi$
$684$		0			0
$685$	−121.692	−	35.7319i	−0.177652	−	0.0521634i
$686$	295.914	−	135.139i	0.431362	−	0.196996i
$687$		0			0
$688$	−138.898	−	89.2640i	−0.201886	−	0.129744i
$689$		−	348.593i		−	0.505941i
$690$		0			0
$691$	926.610			1.34097			0.670485	−	0.741923i	$-0.266086\pi$
$691$	926.610			1.34097			0.670485	+	0.741923i	$0.266086\pi$
$692$	−39.3460	+	61.2236i	−0.0568584	+	0.0884734i
$693$		0			0
$694$	−62.0757	−	135.927i	−0.0894463	−	0.195860i
$695$	4.94992	−	16.8579i	0.00712218	−	0.0242559i
$696$		0			0
$697$	−78.3619	+	90.4345i	−0.112427	+	0.129748i
$698$	374.488	+	53.8432i	0.536516	+	0.0771393i
$699$		0			0
$700$	75.3654	+	86.9763i	0.107665	+	0.124252i
$701$	253.709	+	394.779i	0.361924	+	0.563165i	0.973691	−	0.227873i	$-0.0731772\pi$
$701$	253.709	+	394.779i	0.361924	+	0.563165i	−0.611767	+	0.791038i	$0.709541\pi$
$702$		0			0
$703$	25.0409	+	28.8988i	0.0356201	+	0.0411078i
$704$	21.8928	+	74.5600i	0.0310977	+	0.105909i
$705$		0			0
$706$	218.070	−	251.666i	0.308881	−	0.356467i
$707$	416.197	+	190.071i	0.588680	+	0.268841i
$708$		0			0
$709$	−528.022	−	1156.21i	−0.744742	−	1.63076i	−0.775593	−	0.631233i	$-0.782549\pi$
$709$	−528.022	−	1156.21i	−0.744742	−	1.63076i	0.0308519	−	0.999524i	$-0.490178\pi$
$710$	−132.881	+	19.1054i	−0.187157	+	0.0269091i
$711$		0			0
$712$	123.106			0.172901
$713$	−156.925	+	57.9850i	−0.220091	+	0.0813254i
$714$		0			0
$715$	−129.846	−	83.4469i	−0.181603	−	0.116709i
$716$	68.3047	−	9.82073i	0.0953976	−	0.0137161i
$717$		0			0
$718$	−361.596	−	106.174i	−0.503616	−	0.147875i
$719$	−466.434	−	213.013i	−0.648726	−	0.296263i	0.0637434	−	0.997966i	$-0.479696\pi$
$719$	−466.434	−	213.013i	−0.648726	−	0.296263i	−0.712470	+	0.701703i	$0.752423\pi$
$720$		0			0
$721$	−44.1807	+	307.284i	−0.0612770	+	0.426191i
$722$	84.6732	+	288.370i	0.117276	+	0.399405i
$723$		0			0
$724$	−186.876	+	120.098i	−0.258115	+	0.165881i
$725$	644.302	+	1002.55i	0.888693	+	1.38283i
$726$		0			0
$727$	−733.776	+	215.456i	−1.00932	+	0.296363i	−0.744275	−	0.667873i	$-0.767205\pi$
$727$	−733.776	+	215.456i	−1.00932	+	0.296363i	−0.265045	+	0.964236i	$0.585387\pi$
$728$	77.7692	+	11.1815i	0.106826	+	0.0153592i
$729$		0			0
$730$	8.93853	−	19.5726i	0.0122446	−	0.0268118i
$731$	−174.920	+	595.723i	−0.239289	+	0.814943i
$732$		0			0
$733$	154.457	+	1074.27i	0.210719	+	1.46558i	0.770763	+	0.637122i	$0.219875\pi$
$733$	154.457	+	1074.27i	0.210719	+	1.46558i	−0.560044	+	0.828463i	$0.689216\pi$
$734$	221.822	−	345.162i	0.302210	−	0.470247i
$735$		0			0
$736$	92.2803	−	91.7188i	0.125381	−	0.124618i
$737$		−	138.776i		−	0.188299i
$738$		0			0
$739$	−57.6373	−	400.876i	−0.0779937	−	0.542458i	−0.990932	−	0.134361i	$-0.957102\pi$
$739$	−57.6373	−	400.876i	−0.0779937	−	0.542458i	0.912939	−	0.408097i	$-0.133807\pi$
$740$	8.19137	−	3.74087i	0.0110694	−	0.00505523i
$741$		0			0
$742$	46.3832	−	101.565i	0.0625111	−	0.136880i
$743$	92.3311	+	80.0054i	0.124268	+	0.107679i	0.714778	−	0.699352i	$-0.246528\pi$
$743$	92.3311	+	80.0054i	0.124268	+	0.107679i	−0.590510	+	0.807030i	$0.701073\pi$
$744$		0			0
$745$	86.3648	−	25.3590i	0.115926	−	0.0340389i
$746$	345.173	−	299.094i	0.462699	−	0.400931i
$747$		0			0
$748$	245.825	−	157.982i	0.328643	−	0.211206i
$749$	−6.86353	+	5.94728i	−0.00916359	+	0.00794029i
$750$		0			0
$751$	172.294	−	1198.33i	0.229419	−	1.59564i	−0.471147	−	0.882055i	$-0.656160\pi$
$751$	172.294	−	1198.33i	0.229419	−	1.59564i	0.700565	−	0.713588i	$-0.252931\pi$
$752$	−7.11950	−	6.16908i	−0.00946742	−	0.00820357i
$753$		0			0
$754$	780.638	+	229.216i	1.03533	+	0.304000i
$755$	102.387	−	46.7584i	0.135611	−	0.0619317i
$756$		0			0
$757$	−28.5282	−	18.3339i	−0.0376858	−	0.0242192i	0.521662	−	0.853152i	$-0.325312\pi$
$757$	−28.5282	−	18.3339i	−0.0376858	−	0.0242192i	−0.559348	+	0.828933i	$0.688948\pi$
$758$			646.582i			0.853011i
$759$		0			0
$760$	−49.4516			−0.0650679
$761$	−133.040	+	207.014i	−0.174822	+	0.272028i	−0.917596	−	0.397514i	$-0.869873\pi$
$761$	−133.040	+	207.014i	−0.174822	+	0.272028i	0.742774	+	0.669542i	$0.233510\pi$
$762$		0			0
$763$	113.290	+	248.071i	0.148480	+	0.325126i
$764$	57.1919	−	194.778i	0.0748585	−	0.254945i
$765$		0			0
$766$	−441.765	+	509.824i	−0.576716	+	0.665566i
$767$	149.429	+	21.4846i	0.194822	+	0.0280112i
$768$		0			0
$769$	386.110	+	445.595i	0.502094	+	0.579447i	0.949057	−	0.315105i	$-0.102040\pi$
$769$	386.110	+	445.595i	0.502094	+	0.579447i	−0.446963	+	0.894553i	$0.647494\pi$
$770$	−26.7282	−	41.5899i	−0.0347120	−	0.0540129i
$771$		0			0
$772$	101.681	+	117.347i	0.131712	+	0.152003i
$773$	196.734	+	670.014i	0.254507	+	0.866771i	0.983293	+	0.182029i	$0.0582666\pi$
$773$	196.734	+	670.014i	0.254507	+	0.866771i	−0.728786	+	0.684741i	$0.759915\pi$
$774$		0			0
$775$	−109.275	+	126.111i	−0.141001	+	0.162723i
$776$	−234.367	−	107.032i	−0.302020	−	0.137928i
$777$		0			0
$778$	20.6347	+	45.1836i	0.0265227	+	0.0580767i
$779$	95.9525	−	13.7959i	0.123174	−	0.0177097i
$780$		0			0
$781$	−642.641			−0.822844
$782$	−428.694	−	235.786i	−0.548202	−	0.301516i
$783$		0			0
$784$	−143.715	−	92.3600i	−0.183310	−	0.117806i
$785$	−188.803	+	27.1457i	−0.240513	+	0.0345805i
$786$		0			0
$787$	−963.580	−	282.933i	−1.22437	−	0.359508i	−0.395248	−	0.918574i	$-0.629341\pi$
$787$	−963.580	−	282.933i	−1.22437	−	0.359508i	−0.829123	+	0.559067i	$0.811160\pi$
$788$	143.045	+	65.3265i	0.181529	+	0.0829016i
$789$		0			0
$790$	−30.5715	+	212.629i	−0.0386981	+	0.269151i
$791$	−76.7796	−	261.487i	−0.0970665	−	0.330578i
$792$		0			0
$793$	−467.692	+	300.567i	−0.589775	+	0.379025i
$794$	364.891	+	567.782i	0.459561	+	0.715091i
$795$		0			0
$796$	−630.213	+	185.047i	−0.791725	+	0.232471i
$797$	781.401	+	112.348i	0.980428	+	0.140964i	0.613849	−	0.789423i	$-0.289620\pi$
$797$	781.401	+	112.348i	0.980428	+	0.140964i	0.366578	+	0.930387i	$0.380529\pi$
$798$		0			0
$799$	−14.7160	+	32.2235i	−0.0184180	+	0.0403298i
$800$	36.5620	−	124.519i	0.0457025	−	0.155648i
$801$		0			0
$802$	20.3698	+	141.675i	0.0253988	+	0.176652i
$803$	55.6871	−	86.6508i	0.0693488	−	0.107909i
$804$		0			0
$805$	−39.8915	+	72.5286i	−0.0495546	+	0.0900977i
$806$			113.920i			0.141340i
$807$		0			0
$808$	−73.4265	−	510.693i	−0.0908744	−	0.632045i
$809$	297.399	−	135.818i	0.367613	−	0.167883i	−0.223039	−	0.974809i	$-0.571598\pi$
$809$	297.399	−	135.818i	0.367613	−	0.167883i	0.590652	+	0.806926i	$0.298871\pi$
$810$		0			0
$811$	−287.417	+	629.355i	−0.354398	+	0.776023i	0.645527	+	0.763738i	$0.276638\pi$
$811$	−287.417	+	629.355i	−0.354398	+	0.776023i	−0.999925	+	0.0122855i	$0.996089\pi$
$812$	196.945	+	170.654i	0.242544	+	0.210165i
$813$		0			0
$814$	41.3613	−	12.1448i	0.0508124	−	0.0149199i
$815$	−124.207	+	107.626i	−0.152401	+	0.132056i
$816$		0			0
$817$	423.129	−	271.928i	0.517906	−	0.332838i
$818$	−273.936	+	237.367i	−0.334885	+	0.290180i
$819$		0			0
$820$	3.24891	−	22.5967i	0.00396209	−	0.0275569i
$821$	799.452	+	692.729i	0.973754	+	0.843762i	0.987735	−	0.156140i	$-0.0499050\pi$
$821$	799.452	+	692.729i	0.973754	+	0.843762i	−0.0139812	+	0.999902i	$0.504450\pi$
$822$		0			0
$823$	−587.001	−	172.359i	−0.713246	−	0.209428i	−0.0950734	−	0.995470i	$-0.530309\pi$
$823$	−587.001	−	172.359i	−0.713246	−	0.209428i	−0.618173	+	0.786042i	$0.712127\pi$
$824$	318.433	−	145.423i	0.386448	−	0.176485i
$825$		0			0
$826$	40.6784	+	26.1424i	0.0492475	+	0.0316494i
$827$		−	1319.77i		−	1.59585i	−0.602754	−	0.797927i	$-0.705930\pi$
$827$		−	1319.77i		−	1.59585i	0.602754	−	0.797927i	$-0.294070\pi$
$828$		0			0
$829$	384.494			0.463805			0.231902	−	0.972739i	$-0.425505\pi$
$829$	384.494			0.463805			0.231902	+	0.972739i	$0.425505\pi$
$830$	−58.1115	+	90.4233i	−0.0700139	+	0.108944i
$831$		0			0
$832$	−36.8046	−	80.5909i	−0.0442363	−	0.0968641i
$833$	−180.987	+	616.384i	−0.217271	+	0.739957i
$834$		0			0
$835$	−231.621	+	267.305i	−0.277390	+	0.320125i
$836$	−234.314	−	33.6893i	−0.280280	−	0.0402982i
$837$		0			0
$838$	92.5212	+	106.775i	0.110407	+	0.127417i
$839$	−821.282	−	1277.94i	−0.978882	−	1.52317i	−0.846786	−	0.531934i	$-0.821465\pi$
$839$	−821.282	−	1277.94i	−0.978882	−	1.52317i	−0.132097	−	0.991237i	$-0.542171\pi$
$840$		0			0
$841$	1216.42	+	1403.82i	1.44639	+	1.66923i
$842$	264.340	+	900.259i	0.313943	+	1.06919i
$843$		0			0
$844$	508.274	−	586.579i	0.602220	−	0.694999i
$845$	−60.4966	−	27.6279i	−0.0715936	−	0.0326957i
$846$		0			0
$847$	27.7673	+	60.8018i	0.0327831	+	0.0717849i
$848$	−124.625	+	17.9184i	−0.146964	+	0.0211302i
$849$		0			0
$850$	−488.009			−0.574128
$851$	−50.8800	−	51.1915i	−0.0597885	−	0.0601545i
$852$		0			0
$853$	198.492	+	127.563i	0.232699	+	0.149546i	0.651794	−	0.758396i	$-0.274016\pi$
$853$	198.492	+	127.563i	0.232699	+	0.149546i	−0.419096	+	0.907942i	$0.637653\pi$
$854$	−176.258	+	25.3421i	−0.206391	+	0.0296746i
$855$		0			0
$856$	9.82609	+	2.88520i	0.0114791	+	0.00337056i
$857$	−1524.31	−	696.128i	−1.77866	−	0.812285i	−0.976609	−	0.215024i	$-0.931017\pi$
$857$	−1524.31	−	696.128i	−1.77866	−	0.812285i	−0.802047	−	0.597261i	$-0.796256\pi$
$858$		0			0
$859$	−3.66601	+	25.4976i	−0.00426776	+	0.0296829i	−0.991844	−	0.127457i	$-0.959318\pi$
$859$	−3.66601	+	25.4976i	−0.00426776	+	0.0296829i	0.987576	+	0.157140i	$0.0502275\pi$
$860$	−33.3712	−	113.652i	−0.0388037	−	0.132153i
$861$		0			0
$862$	645.902	−	415.096i	0.749306	−	0.481550i
$863$	437.661	+	681.014i	0.507139	+	0.789124i	0.996556	−	0.0829265i	$-0.0264267\pi$
$863$	437.661	+	681.014i	0.507139	+	0.789124i	−0.489417	+	0.872050i	$0.662790\pi$
$864$		0			0
$865$	−50.0957	+	14.7094i	−0.0579141	+	0.0170051i
$866$	349.628	+	50.2689i	0.403728	+	0.0580473i
$867$		0			0
$868$	−15.1580	+	33.1915i	−0.0174632	+	0.0382390i
$869$	−289.711	+	986.667i	−0.333385	+	1.13540i
$870$		0			0
$871$	22.5176	+	156.613i	0.0258525	+	0.179808i
$872$	166.260	−	258.706i	0.190666	−	0.296682i
$873$		0			0
$874$	137.377	+	371.783i	0.157182	+	0.425381i
$875$			172.537i			0.197185i
$876$		0			0
$877$	−235.111	−	1635.23i	−0.268085	−	1.86457i	−0.466592	−	0.884473i	$-0.654518\pi$
$877$	−235.111	−	1635.23i	−0.268085	−	1.86457i	0.198507	−	0.980100i	$-0.436391\pi$
$878$	−565.228	+	258.131i	−0.643768	+	0.293999i
$879$		0			0
$880$	−23.1586	+	50.7104i	−0.0263166	+	0.0576254i
$881$	−867.447	−	751.647i	−0.984616	−	0.853175i	0.00454808	−	0.999990i	$-0.498552\pi$
$881$	−867.447	−	751.647i	−0.984616	−	0.853175i	−0.989164	+	0.146815i	$0.953098\pi$
$882$		0			0
$883$	−1264.04	+	371.154i	−1.43152	+	0.420333i	−0.903387	−	0.428826i	$-0.858927\pi$
$883$	−1264.04	+	371.154i	−1.43152	+	0.420333i	−0.528137	+	0.849159i	$0.677109\pi$
$884$	−251.787	+	218.175i	−0.284827	+	0.246804i
$885$		0			0
$886$	794.549	−	510.626i	0.896783	−	0.576327i
$887$	160.651	−	139.205i	0.181117	−	0.156939i	−0.559584	−	0.828774i	$-0.689039\pi$
$887$	160.651	−	139.205i	0.181117	−	0.156939i	0.740701	+	0.671835i	$0.234494\pi$
$888$		0			0
$889$	−37.3379	+	259.690i	−0.0419998	+	0.292115i
$890$	66.7456	+	57.8354i	0.0749951	+	0.0649836i
$891$		0			0
$892$	725.799	+	213.114i	0.813676	+	0.238917i
$893$	26.1045	−	11.9215i	0.0292324	−	0.0133500i
$894$		0			0
$895$	41.6474	+	26.7651i	0.0465334	+	0.0299052i
$896$		−	28.3779i		−	0.0316718i
$897$		0			0
$898$	−516.079			−0.574699
$899$	−204.281	+	317.867i	−0.227231	+	0.353578i
$900$		0			0
$901$	196.683	+	430.675i	0.218294	+	0.477996i
$902$	30.7884	−	104.856i	0.0341335	−	0.116248i
$903$		0			0
$904$	−201.246	+	232.250i	−0.222617	+	0.256914i
$905$	−157.743	−	22.6800i	−0.174301	−	0.0250608i
$906$		0			0
$907$	−598.058	−	690.196i	−0.659380	−	0.760966i	0.323295	−	0.946298i	$-0.395209\pi$
$907$	−598.058	−	690.196i	−0.659380	−	0.760966i	−0.982676	+	0.185332i	$0.940664\pi$
$908$	124.395	+	193.563i	0.136999	+	0.213175i
$909$		0			0
$910$	36.9119	+	42.5986i	0.0405625	+	0.0468117i
$911$	−425.493	−	1449.10i	−0.467061	−	1.59067i	−0.770255	−	0.637736i	$-0.779871\pi$
$911$	−425.493	−	1449.10i	−0.467061	−	1.59067i	0.303193	−	0.952929i	$-0.401947\pi$
$912$		0			0
$913$	−336.949	+	388.860i	−0.369057	+	0.425915i
$914$	−754.501	−	344.569i	−0.825493	−	0.376990i
$915$		0			0
$916$	222.939	+	488.169i	0.243384	+	0.532936i
$917$	47.7129	−	6.86007i	0.0520315	−	0.00748100i
$918$		0			0
$919$	−520.488			−0.566363			−0.283182	−	0.959066i	$-0.591390\pi$
$919$	−520.488			−0.566363			−0.283182	+	0.959066i	$0.591390\pi$
$920$	93.1225	−	6.37466i	0.101220	−	0.00692898i
$921$		0			0
$922$	726.581	+	466.945i	0.788048	+	0.506448i
$923$	725.240	−	104.274i	0.785742	−	0.112973i
$924$		0			0
$925$	−69.0754	−	20.2824i	−0.0746761	−	0.0219269i
$926$	297.850	+	136.024i	0.321653	+	0.146894i
$927$		0			0
$928$	41.8204	−	290.867i	0.0450651	−	0.313434i
$929$	−398.476	−	1357.08i	−0.428930	−	1.46080i	−0.836673	−	0.547703i	$-0.815502\pi$
$929$	−398.476	−	1357.08i	−0.428930	−	1.46080i	0.407743	−	0.913097i	$-0.366316\pi$
$930$		0			0
$931$	437.804	−	281.360i	0.470252	−	0.302212i
$932$	−383.221	−	596.303i	−0.411181	−	0.639810i
$933$		0			0
$934$	43.6704	−	12.8228i	0.0467563	−	0.0137289i
$935$	207.502	+	29.8343i	0.221928	+	0.0319084i
$936$		0			0
$937$	−524.755	+	1149.05i	−0.560037	+	1.22631i	0.391897	+	0.920009i	$0.371819\pi$
$937$	−524.755	+	1149.05i	−0.560037	+	1.22631i	−0.951935	+	0.306302i	$0.900908\pi$
$938$	−14.2780	+	48.6265i	−0.0152218	+	0.0518406i
$939$		0			0
$940$	−0.961809	−	6.68953i	−0.00102320	−	0.00711652i
$941$	82.3090	−	128.075i	0.0874697	−	0.136105i	−0.794762	−	0.606922i	$-0.792404\pi$
$941$	82.3090	−	128.075i	0.0874697	−	0.136105i	0.882231	+	0.470816i	$0.156041\pi$
$942$		0			0
$943$	−178.910	+	38.3480i	−0.189724	+	0.0406660i
$944$		−	54.5264i		−	0.0577610i
$945$		0			0
$946$	−80.6951	−	561.246i	−0.0853013	−	0.593284i
$947$	−916.232	+	418.429i	−0.967510	+	0.441847i	−0.835554	−	0.549409i	$-0.814853\pi$
$947$	−916.232	+	418.429i	−0.967510	+	0.441847i	−0.131956	+	0.991256i	$0.542126\pi$
$948$		0			0
$949$	−48.7848	+	106.824i	−0.0514065	+	0.112565i
$950$	298.778	+	258.893i	0.314503	+	0.272519i
$951$		0			0
$952$	−102.390	+	30.0644i	−0.107552	+	0.0315802i
$953$	−1005.52	+	871.292i	−1.05511	+	0.914262i	−0.996464	−	0.0840166i	$-0.973225\pi$
$953$	−1005.52	+	871.292i	−1.05511	+	0.914262i	−0.0586503	+	0.998279i	$0.518680\pi$
$954$		0			0
$955$	122.516	−	78.7360i	0.128289	−	0.0824461i
$956$	−263.039	+	227.925i	−0.275146	+	0.238415i
$957$		0			0
$958$	147.195	−	1023.77i	0.153648	−	1.06865i
$959$	167.562	+	145.193i	0.174726	+	0.151401i
$960$		0			0
$961$	871.309	+	255.839i	0.906669	+	0.266222i
$962$	−44.7069	+	20.4170i	−0.0464729	+	0.0212235i
$963$		0			0
$964$	778.706	+	500.444i	0.807786	+	0.519132i
$965$			111.394i			0.115434i
$966$		0			0
$967$	−745.368			−0.770804			−0.385402	−	0.922749i	$-0.625937\pi$
$967$	−745.368			−0.770804			−0.385402	+	0.922749i	$0.625937\pi$
$968$	40.7502	−	63.4085i	0.0420973	−	0.0655046i
$969$		0			0
$970$	−76.7857	−	168.137i	−0.0791605	−	0.173337i
$971$	441.628	−	1504.05i	0.454818	−	1.54897i	−0.338985	−	0.940792i	$-0.610084\pi$
$971$	441.628	−	1504.05i	0.454818	−	1.54897i	0.793803	−	0.608175i	$-0.208098\pi$
$972$		0			0
$973$	−20.1135	+	23.2122i	−0.0206717	+	0.0238564i
$974$	713.110	+	102.530i	0.732146	+	0.105267i
$975$		0			0
$976$	131.496	+	151.754i	0.134729	+	0.155486i
$977$	−371.839	−	578.592i	−0.380592	−	0.592213i	0.597123	−	0.802150i	$-0.296311\pi$
$977$	−371.839	−	578.592i	−0.380592	−	0.592213i	−0.977715	+	0.209937i	$0.932674\pi$
$978$		0			0
$979$	276.857	+	319.510i	0.282796	+	0.326364i
$980$	−34.5286	−	117.594i	−0.0352333	−	0.119993i
$981$		0			0
$982$	387.146	−	446.791i	0.394243	−	0.454980i
$983$	553.885	+	252.951i	0.563464	+	0.257325i	0.676720	−	0.736241i	$-0.263401\pi$
$983$	553.885	+	252.951i	0.563464	+	0.257325i	−0.113256	+	0.993566i	$0.536128\pi$
$984$		0			0
$985$	46.8658	+	102.622i	0.0475795	+	0.104185i
$986$	−1093.78	+	157.262i	−1.10931	+	0.159495i
$987$		0			0
$988$	269.897			0.273175
$989$	−761.743	+	566.614i	−0.770215	+	0.572916i
$990$		0			0
$991$	440.625	+	283.172i	0.444627	+	0.285744i	0.743734	−	0.668475i	$-0.233053\pi$
$991$	440.625	+	283.172i	0.444627	+	0.285744i	−0.299108	+	0.954219i	$0.596689\pi$
$992$	40.7275	−	5.85573i	0.0410559	−	0.00590295i
$993$		0			0
$994$	225.178	+	66.1183i	0.226538	+	0.0665174i
$995$	−428.626	−	195.747i	−0.430780	−	0.196730i
$996$		0			0
$997$	35.5525	−	247.273i	0.0356595	−	0.248017i	−0.964193	−	0.265202i	$-0.914561\pi$
$997$	35.5525	−	247.273i	0.0356595	−	0.248017i	0.999852	+	0.0171849i	$0.00547038\pi$
$998$	227.138	+	773.562i	0.227594	+	0.775112i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.b.71.3	yes	80
3.2	odd	2	inner	414.3.k.b.71.6	yes	80
23.12	even	11	inner	414.3.k.b.35.6	yes	80
69.35	odd	22	inner	414.3.k.b.35.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.3	✓	80	69.35	odd	22	inner
414.3.k.b.35.6	yes	80	23.12	even	11	inner
414.3.k.b.71.3	yes	80	1.1	even	1	trivial
414.3.k.b.71.6	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(0.404235 - 1.37670i) q^{5} +(-1.64257 + 1.89563i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(0.404235 - 1.37670i) q^{5} +(-1.64257 + 1.89563i) q^{7} +(2.79964 + 0.402527i) q^{8} +(1.32880 + 1.53352i) q^{10} +(5.25149 + 8.17148i) q^{11} +(-7.25236 - 8.36967i) q^{13} +(-0.999372 - 3.40355i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(13.6824 + 6.24852i) q^{17} +(-5.06198 - 11.0842i) q^{19} +(-2.84043 + 0.408392i) q^{20} -13.7369 q^{22} +(10.9611 + 20.2202i) q^{23} +(19.2994 + 12.4030i) q^{25} +(15.5025 - 2.22893i) q^{26} +(4.81335 + 1.41333i) q^{28} +(47.2529 + 21.5797i) q^{29} +(-1.03516 + 7.19967i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-17.8952 + 11.5006i) q^{34} +(1.94572 + 3.02760i) q^{35} +(-3.01096 + 0.884098i) q^{37} +(17.0573 + 2.45247i) q^{38} +(1.68587 - 3.69154i) q^{40} +(-2.24129 + 7.63313i) q^{41} +(5.87432 + 40.8568i) q^{43} +(10.5030 - 16.3430i) q^{44} +(-32.4368 - 2.41945i) q^{46} +2.35511i q^{47} +(6.07806 + 42.2738i) q^{49} +(-29.5120 + 13.4777i) q^{50} +(-9.20116 + 20.1477i) q^{52} +(23.7885 + 20.6128i) q^{53} +(13.3725 - 3.92652i) q^{55} +(-5.36165 + 4.64589i) q^{56} +(-61.8023 + 39.7179i) q^{58} +(-10.3021 + 8.92680i) q^{59} +(7.14418 - 49.6889i) q^{61} +(-7.77407 - 6.73627i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-14.4542 + 6.60100i) q^{65} +(-12.0190 - 7.72413i) q^{67} -30.0833i q^{68} -5.08964 q^{70} +(-35.7687 + 55.6572i) q^{71} +(-4.40508 - 9.64578i) q^{73} +(1.25030 - 4.25814i) q^{74} +(-15.9594 + 18.4182i) q^{76} +(-24.1160 - 3.46736i) q^{77} +(69.3272 + 80.0078i) q^{79} +(3.10289 + 4.82818i) q^{80} +(-7.36758 - 8.50264i) q^{82} +(14.9238 + 50.8257i) q^{83} +(14.1332 - 16.3106i) q^{85} +(-53.0993 - 24.2496i) q^{86} +(11.4130 + 24.9911i) q^{88} +(43.0814 - 6.19417i) q^{89} +27.7783 q^{91} +(27.6790 - 36.7406i) q^{92} +(-2.80191 - 1.80068i) q^{94} +(-17.3058 + 2.48820i) q^{95} +(-87.4033 - 25.6639i) q^{97} +(-54.9409 - 25.0907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 + 16 * q^7	\( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

Introduction

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