LMFDB - Embedded newform 288.3.u.a.235.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			235.7
Character	$\chi$	$=$	288.235
Dual form			288.3.u.a.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96275 - 0.384217i) q^{2} +(3.70475 - 1.50824i) q^{4} +(-2.95565 + 7.13556i) q^{5} +(-4.18452 + 4.18452i) q^{7} +(6.69200 - 4.38373i) q^{8} +O(q^{10})$	\(q+(1.96275 - 0.384217i) q^{2} +(3.70475 - 1.50824i) q^{4} +(-2.95565 + 7.13556i) q^{5} +(-4.18452 + 4.18452i) q^{7} +(6.69200 - 4.38373i) q^{8} +(-3.05958 + 15.1409i) q^{10} +(-1.42655 + 3.44399i) q^{11} +(8.39996 + 20.2793i) q^{13} +(-6.60538 + 9.82091i) q^{14} +(11.4504 - 11.1753i) q^{16} +1.73115i q^{17} +(14.2459 - 5.90085i) q^{19} +(-0.187785 + 30.8933i) q^{20} +(-1.47671 + 7.30779i) q^{22} +(-15.1565 - 15.1565i) q^{23} +(-24.5027 - 24.5027i) q^{25} +(24.2787 + 36.5757i) q^{26} +(-9.19134 + 21.8139i) q^{28} +(6.74107 - 2.79224i) q^{29} +31.1695i q^{31} +(18.1805 - 26.3338i) q^{32} +(0.665136 + 3.39780i) q^{34} +(-17.4909 - 42.2268i) q^{35} +(5.30038 - 12.7962i) q^{37} +(25.6939 - 17.0554i) q^{38} +(11.5012 + 60.7079i) q^{40} +(18.5776 - 18.5776i) q^{41} +(31.0691 - 75.0074i) q^{43} +(-0.0906349 + 14.9107i) q^{44} +(-35.5718 - 23.9250i) q^{46} +16.2824 q^{47} +13.9797i q^{49} +(-57.5069 - 38.6782i) q^{50} +(61.7059 + 62.4607i) q^{52} +(29.0670 + 12.0399i) q^{53} +(-20.3584 - 20.3584i) q^{55} +(-9.65901 + 46.3466i) q^{56} +(12.1582 - 8.07050i) q^{58} +(-34.1002 - 14.1248i) q^{59} +(-68.7647 + 28.4833i) q^{61} +(11.9758 + 61.1778i) q^{62} +(25.5658 - 58.6719i) q^{64} -169.531 q^{65} +(10.5147 + 25.3846i) q^{67} +(2.61099 + 6.41347i) q^{68} +(-50.5545 - 76.1602i) q^{70} +(32.2012 - 32.2012i) q^{71} +(-28.5494 + 28.5494i) q^{73} +(5.48676 - 27.1523i) q^{74} +(43.8777 - 43.3475i) q^{76} +(-8.44203 - 20.3809i) q^{77} +22.4049 q^{79} +(45.8989 + 114.735i) q^{80} +(29.3252 - 43.6009i) q^{82} +(123.286 - 51.0669i) q^{83} +(-12.3527 - 5.11665i) q^{85} +(32.1616 - 159.158i) q^{86} +(5.55106 + 29.3008i) q^{88} +(-61.0281 - 61.0281i) q^{89} +(-120.009 - 49.7093i) q^{91} +(-79.0109 - 33.2915i) q^{92} +(31.9583 - 6.25599i) q^{94} +119.093i q^{95} -69.9064 q^{97} +(5.37122 + 27.4385i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.96275	−	0.384217i	0.981374	−	0.192109i
$2$	1.96275	−	0.384217i	0.981374	−	0.192109i
$3$		0			0
$3$		0			0
$4$	3.70475	−	1.50824i	0.926189	−	0.377061i
$5$	−2.95565	+	7.13556i	−0.591129	+	1.42711i	0.291284	+	0.956637i	$0.405917\pi$
$5$	−2.95565	+	7.13556i	−0.591129	+	1.42711i	−0.882413	+	0.470475i	$0.844083\pi$
$6$		0			0
$7$	−4.18452	+	4.18452i	−0.597788	+	0.597788i	−0.939723	−	0.341935i	$-0.888918\pi$
$7$	−4.18452	+	4.18452i	−0.597788	+	0.597788i	0.341935	+	0.939723i	$0.388918\pi$
$8$	6.69200	−	4.38373i	0.836500	−	0.547966i
$9$		0			0
$10$	−3.05958	+	15.1409i	−0.305958	+	1.51409i
$11$	−1.42655	+	3.44399i	−0.129686	+	0.313090i	−0.975363	−	0.220605i	$-0.929197\pi$
$11$	−1.42655	+	3.44399i	−0.129686	+	0.313090i	0.845677	+	0.533695i	$0.179197\pi$
$12$		0			0
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	0.818247	+	0.574866i	$0.194946\pi$
$13$	8.39996	+	20.2793i	0.646151	+	1.55995i	−0.172096	+	0.985080i	$0.555054\pi$
$14$	−6.60538	+	9.82091i	−0.471813	+	0.701494i
$15$		0			0
$16$	11.4504	−	11.1753i	0.715651	−	0.698459i
$17$			1.73115i			0.101832i	0.998703	+	0.0509161i	$0.0162141\pi$
$17$			1.73115i			0.101832i	−0.998703	+	0.0509161i	$0.983786\pi$
$18$		0			0
$19$	14.2459	−	5.90085i	0.749785	−	0.310571i	0.0251314	−	0.999684i	$-0.492000\pi$
$19$	14.2459	−	5.90085i	0.749785	−	0.310571i	0.724654	+	0.689113i	$0.242000\pi$
$20$	−0.187785	+	30.8933i	−0.00938926	+	1.54467i
$21$		0			0
$22$	−1.47671	+	7.30779i	−0.0671233	+	0.332172i
$23$	−15.1565	−	15.1565i	−0.658979	−	0.658979i	0.296159	−	0.955139i	$-0.404294\pi$
$23$	−15.1565	−	15.1565i	−0.658979	−	0.658979i	−0.955139	+	0.296159i	$0.904294\pi$
$24$		0			0
$25$	−24.5027	−	24.5027i	−0.980107	−	0.980107i
$26$	24.2787	+	36.5757i	0.933795	+	1.40676i
$27$		0			0
$28$	−9.19134	+	21.8139i	−0.328262	+	0.779067i
$29$	6.74107	−	2.79224i	0.232451	−	0.0962842i	−0.263418	−	0.964682i	$-0.584850\pi$
$29$	6.74107	−	2.79224i	0.232451	−	0.0962842i	0.495869	+	0.868398i	$0.334850\pi$
$30$		0			0
$31$			31.1695i			1.00547i	0.864442	+	0.502733i	$0.167672\pi$
$31$			31.1695i			1.00547i	−0.864442	+	0.502733i	$0.832328\pi$
$32$	18.1805	−	26.3338i	0.568141	−	0.822931i
$33$		0			0
$34$	0.665136	+	3.39780i	0.0195628	+	0.0999354i
$35$	−17.4909	−	42.2268i	−0.499740	−	1.20648i
$36$		0			0
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	−0.835926	−	0.548843i	$-0.815069\pi$
$37$	5.30038	−	12.7962i	0.143253	−	0.345844i	0.979179	+	0.202998i	$0.0650686\pi$
$38$	25.6939	−	17.0554i	0.676156	−	0.448827i
$39$		0			0
$40$	11.5012	+	60.7079i	0.287529	+	1.51770i
$41$	18.5776	−	18.5776i	0.453111	−	0.453111i	−0.443275	−	0.896386i	$-0.646183\pi$
$41$	18.5776	−	18.5776i	0.453111	−	0.453111i	0.896386	+	0.443275i	$0.146183\pi$
$42$		0			0
$43$	31.0691	−	75.0074i	0.722537	−	1.74436i	0.0565443	−	0.998400i	$-0.481992\pi$
$43$	31.0691	−	75.0074i	0.722537	−	1.74436i	0.665993	−	0.745958i	$-0.268008\pi$
$44$	−0.0906349	+	14.9107i	−0.00205988	+	0.338880i
$45$		0			0
$46$	−35.5718	−	23.9250i	−0.773301	−	0.520109i
$47$	16.2824			0.346435			0.173217	−	0.984884i	$-0.444584\pi$
$47$	16.2824			0.346435			0.173217	+	0.984884i	$0.444584\pi$
$48$		0			0
$49$			13.9797i			0.285299i
$50$	−57.5069	−	38.6782i	−1.15014	−	0.773565i
$51$		0			0
$52$	61.7059	+	62.4607i	1.18665	+	1.20117i
$53$	29.0670	+	12.0399i	0.548434	+	0.227169i	0.639655	−	0.768662i	$-0.279077\pi$
$53$	29.0670	+	12.0399i	0.548434	+	0.227169i	−0.0912216	+	0.995831i	$0.529077\pi$
$54$		0			0
$55$	−20.3584	−	20.3584i	−0.370153	−	0.370153i
$56$	−9.65901	+	46.3466i	−0.172482	+	0.827618i
$57$		0			0
$58$	12.1582	−	8.07050i	0.209624	−	0.139147i
$59$	−34.1002	−	14.1248i	−0.577969	−	0.239403i	0.0744962	−	0.997221i	$-0.476265\pi$
$59$	−34.1002	−	14.1248i	−0.577969	−	0.239403i	−0.652465	+	0.757819i	$0.726265\pi$
$60$		0			0
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.866859	−	0.498553i	$-0.833865\pi$
$61$	−68.7647	+	28.4833i	−1.12729	+	0.466939i	−0.260432	+	0.965492i	$0.583865\pi$
$62$	11.9758	+	61.1778i	0.193159	+	0.986739i
$63$		0			0
$64$	25.5658	−	58.6719i	0.399466	−	0.916748i
$65$	−169.531			−2.60818
$66$		0			0
$67$	10.5147	+	25.3846i	0.156935	+	0.378875i	0.982717	−	0.185115i	$-0.0592657\pi$
$67$	10.5147	+	25.3846i	0.156935	+	0.378875i	−0.825782	+	0.563990i	$0.809266\pi$
$68$	2.61099	+	6.41347i	0.0383969	+	0.0943158i
$69$		0			0
$70$	−50.5545	−	76.1602i	−0.722207	−	1.08800i
$71$	32.2012	−	32.2012i	0.453538	−	0.453538i	−0.442989	−	0.896527i	$-0.646082\pi$
$71$	32.2012	−	32.2012i	0.453538	−	0.453538i	0.896527	+	0.442989i	$0.146082\pi$
$72$		0			0
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	−0.875075	−	0.483987i	$-0.839188\pi$
$73$	−28.5494	+	28.5494i	−0.391088	+	0.391088i	0.483987	+	0.875075i	$0.339188\pi$
$74$	5.48676	−	27.1523i	0.0741455	−	0.366923i
$75$		0			0
$76$	43.8777	−	43.3475i	0.577338	−	0.570362i
$77$	−8.44203	−	20.3809i	−0.109637	−	0.264686i
$78$		0			0
$79$	22.4049			0.283606			0.141803	−	0.989895i	$-0.454710\pi$
$79$	22.4049			0.283606			0.141803	+	0.989895i	$0.454710\pi$
$80$	45.8989	+	114.735i	0.573737	+	1.43419i
$81$		0			0
$82$	29.3252	−	43.6009i	0.357625	−	0.531718i
$83$	123.286	−	51.0669i	1.48538	−	0.615264i	0.515073	−	0.857146i	$-0.327765\pi$
$83$	123.286	−	51.0669i	1.48538	−	0.615264i	0.970306	+	0.241882i	$0.0777648\pi$
$84$		0			0
$85$	−12.3527	−	5.11665i	−0.145326	−	0.0601959i
$86$	32.1616	−	159.158i	0.373972	−	1.85067i
$87$		0			0
$88$	5.55106	+	29.3008i	0.0630803	+	0.332964i
$89$	−61.0281	−	61.0281i	−0.685709	−	0.685709i	0.275572	−	0.961280i	$-0.411133\pi$
$89$	−61.0281	−	61.0281i	−0.685709	−	0.685709i	−0.961280	+	0.275572i	$0.911133\pi$
$90$		0			0
$91$	−120.009	−	49.7093i	−1.31878	−	0.546256i
$92$	−79.0109	−	33.2915i	−0.858814	−	0.361864i
$93$		0			0
$94$	31.9583	−	6.25599i	0.339982	−	0.0665531i
$95$			119.093i			1.25362i
$96$		0			0
$97$	−69.9064			−0.720684			−0.360342	−	0.932820i	$-0.617340\pi$
$97$	−69.9064			−0.720684			−0.360342	+	0.932820i	$0.617340\pi$
$98$	5.37122	+	27.4385i	0.0548084	+	0.279985i
$99$		0			0
$100$	−127.732	−	53.8204i	−1.27732	−	0.538204i
$101$	10.4825	−	25.3069i	0.103787	−	0.250564i	−0.863452	−	0.504431i	$-0.831702\pi$
$101$	10.4825	−	25.3069i	0.103787	−	0.250564i	0.967239	+	0.253867i	$0.0817025\pi$
$102$		0			0
$103$	116.721	−	116.721i	1.13322	−	1.13322i	0.143579	−	0.989639i	$-0.454139\pi$
$103$	116.721	−	116.721i	1.13322	−	1.13322i	0.989639	−	0.143579i	$-0.0458612\pi$
$104$	145.112	+	98.8860i	1.39530	+	0.950827i
$105$		0			0
$106$	61.6771	+	12.4633i	0.581859	+	0.117579i
$107$	21.6236	−	52.2039i	0.202090	−	0.487887i	−0.790047	−	0.613046i	$-0.789944\pi$
$107$	21.6236	−	52.2039i	0.202090	−	0.487887i	0.992137	+	0.125159i	$0.0399440\pi$
$108$		0			0
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	0.734725	−	0.678366i	$-0.237311\pi$
$109$	−28.8284	−	69.5980i	−0.264481	−	0.638514i	−0.999206	+	0.0398518i	$0.987311\pi$
$110$	−47.7805	−	32.1364i	−0.434369	−	0.292149i
$111$		0			0
$112$	−1.15104	+	94.6778i	−0.0102772	+	0.845337i
$113$			130.141i			1.15169i	0.817559	+	0.575845i	$0.195327\pi$
$113$			130.141i			1.15169i	−0.817559	+	0.575845i	$0.804673\pi$
$114$		0			0
$115$	152.948	−	63.3530i	1.32998	−	0.550895i
$116$	20.7626	−	20.5117i	0.178988	−	0.176825i
$117$		0			0
$118$	−72.3570	−	14.6214i	−0.613195	−	0.123911i
$119$	−7.24401	−	7.24401i	−0.0608740	−	0.0608740i
$120$		0			0
$121$	75.7339	+	75.7339i	0.625900	+	0.625900i
$122$	−124.024	+	82.3261i	−1.01659	+	0.674804i
$123$		0			0
$124$	47.0111	+	115.475i	0.379122	+	0.931252i
$125$	68.8726	−	28.5280i	0.550981	−	0.228224i
$126$		0			0
$127$			56.3580i			0.443764i	0.975074	+	0.221882i	$0.0712200\pi$
$127$			56.3580i			0.443764i	−0.975074	+	0.221882i	$0.928780\pi$
$128$	27.6365	−	124.981i	0.215910	−	0.976413i
$129$		0			0
$130$	−332.747	+	65.1369i	−2.55960	+	0.501053i
$131$	39.2631	+	94.7895i	0.299718	+	0.723584i	0.999953	+	0.00967128i	$0.00307851\pi$
$131$	39.2631	+	94.7895i	0.299718	+	0.723584i	−0.700235	+	0.713912i	$0.746921\pi$
$132$		0			0
$133$	−34.9201	+	84.3045i	−0.262557	+	0.633868i
$134$	30.3908	+	45.7837i	0.226797	+	0.341670i
$135$		0			0
$136$	7.58888	+	11.5848i	0.0558006	+	0.0851826i
$137$	−62.6423	+	62.6423i	−0.457243	+	0.457243i	−0.897750	−	0.440506i	$-0.854799\pi$
$137$	−62.6423	+	62.6423i	−0.457243	+	0.457243i	0.440506	+	0.897750i	$0.354799\pi$
$138$		0			0
$139$	11.6343	−	28.0877i	0.0837000	−	0.202070i	−0.876488	−	0.481423i	$-0.840120\pi$
$139$	11.6343	−	28.0877i	0.0837000	−	0.202070i	0.960188	+	0.279353i	$0.0901201\pi$
$140$	−128.488	−	130.059i	−0.917770	−	0.928996i
$141$		0			0
$142$	50.8306	−	75.5751i	0.357962	−	0.532219i
$143$	−81.8247			−0.572201
$144$		0			0
$145$			56.3542i			0.388649i
$146$	−45.0661	+	67.0044i	−0.308672	+	0.458935i
$147$		0			0
$148$	0.336756	−	55.4012i	0.00227538	−	0.374332i
$149$	52.6977	+	21.8281i	0.353676	+	0.146497i	0.552446	−	0.833549i	$-0.313695\pi$
$149$	52.6977	+	21.8281i	0.353676	+	0.146497i	−0.198770	+	0.980046i	$0.563695\pi$
$150$		0			0
$151$	−48.5998	−	48.5998i	−0.321853	−	0.321853i	0.527625	−	0.849478i	$-0.323083\pi$
$151$	−48.5998	−	48.5998i	−0.321853	−	0.321853i	−0.849478	+	0.527625i	$0.823083\pi$
$152$	69.4660	−	101.939i	0.457013	−	0.670650i
$153$		0			0
$154$	−24.4002	−	36.7589i	−0.158443	−	0.238694i
$155$	−222.412	−	92.1259i	−1.43491	−	0.594361i
$156$		0			0
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.0399023	−	0.999204i	$-0.487295\pi$
$157$	121.622	−	50.3774i	0.774661	−	0.320875i	0.734759	+	0.678328i	$0.237295\pi$
$158$	43.9751	−	8.60834i	0.278323	−	0.0544832i
$159$		0			0
$160$	134.171	+	207.561i	0.838571	+	1.29726i
$161$	126.845			0.787860
$162$		0			0
$163$	−13.0161	−	31.4236i	−0.0798533	−	0.192783i	0.878911	−	0.476986i	$-0.158271\pi$
$163$	−13.0161	−	31.4236i	−0.0798533	−	0.192783i	−0.958764	+	0.284203i	$0.908271\pi$
$164$	40.8058	−	96.8448i	0.248816	−	0.590517i
$165$		0			0
$166$	222.359	−	147.600i	1.33951	−	0.889158i
$167$	138.734	−	138.734i	0.830744	−	0.830744i	−0.156875	−	0.987619i	$-0.550142\pi$
$167$	138.734	−	138.734i	0.830744	−	0.830744i	0.987619	+	0.156875i	$0.0501419\pi$
$168$		0			0
$169$	−221.190	+	221.190i	−1.30881	+	1.30881i
$170$	−26.2111	−	5.29658i	−0.154183	−	0.0311564i
$171$		0			0
$172$	1.97396	−	324.744i	0.0114765	−	1.88805i
$173$	69.7574	+	168.409i	0.403222	+	0.973464i	0.986879	+	0.161464i	$0.0516215\pi$
$173$	69.7574	+	168.409i	0.403222	+	0.973464i	−0.583656	+	0.812001i	$0.698379\pi$
$174$		0			0
$175$	205.064			1.17179
$176$	22.1532	+	55.3773i	0.125871	+	0.314644i
$177$		0			0
$178$	−143.231	−	96.3346i	−0.804667	−	0.541206i
$179$	−45.0027	+	18.6407i	−0.251411	+	0.104138i	−0.504830	−	0.863219i	$-0.668445\pi$
$179$	−45.0027	+	18.6407i	−0.251411	+	0.104138i	0.253419	+	0.967357i	$0.418445\pi$
$180$		0			0
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	0.686201	−	0.727412i	$-0.259277\pi$
$181$	118.928	+	49.2615i	0.657060	+	0.272163i	−0.0291408	+	0.999575i	$0.509277\pi$
$182$	−254.646	−	51.4573i	−1.39915	−	0.282732i
$183$		0			0
$184$	−167.870	−	34.9854i	−0.912335	−	0.190138i
$185$	75.6423	+	75.6423i	0.408877	+	0.408877i
$186$		0			0
$187$	−5.96206	−	2.46956i	−0.0318827	−	0.0132062i
$188$	60.3224	−	24.5579i	0.320864	−	0.130627i
$189$		0			0
$190$	45.7577	+	233.750i	0.240830	+	1.23026i
$191$			179.282i			0.938649i	0.883026	+	0.469325i	$0.155503\pi$
$191$			179.282i			0.938649i	−0.883026	+	0.469325i	$0.844497\pi$
$192$		0			0
$193$	179.924			0.932249			0.466125	−	0.884719i	$-0.345650\pi$
$193$	179.924			0.932249			0.466125	+	0.884719i	$0.345650\pi$
$194$	−137.209	+	26.8592i	−0.707260	+	0.138450i
$195$		0			0
$196$	21.0847	+	51.7912i	0.107575	+	0.264241i
$197$	93.2938	−	225.231i	0.473573	−	1.14331i	−0.489000	−	0.872284i	$-0.662638\pi$
$197$	93.2938	−	225.231i	0.473573	−	1.14331i	0.962573	−	0.271022i	$-0.0873617\pi$
$198$		0			0
$199$	−131.782	+	131.782i	−0.662220	+	0.662220i	−0.955903	−	0.293683i	$-0.905119\pi$
$199$	−131.782	+	131.782i	−0.662220	+	0.662220i	0.293683	+	0.955903i	$0.405119\pi$
$200$	−271.385	−	56.5589i	−1.35693	−	0.282795i
$201$		0			0
$202$	10.8511	−	53.6987i	0.0537183	−	0.265835i
$203$	−16.5239	+	39.8923i	−0.0813987	+	0.196514i
$204$		0			0
$205$	77.6526	+	187.470i	0.378793	+	0.914487i
$206$	184.248	−	273.941i	0.894409	−	1.32981i
$207$		0			0
$208$	322.811	+	138.334i	1.55198	+	0.665067i
$209$			57.4807i			0.275027i
$210$		0			0
$211$	−182.694	+	75.6743i	−0.865848	+	0.358646i	−0.770992	−	0.636845i	$-0.780239\pi$
$211$	−182.694	+	75.6743i	−0.865848	+	0.358646i	−0.0948559	+	0.995491i	$0.530239\pi$
$212$	125.845	+	0.764951i	0.593609	+	0.00360826i
$213$		0			0
$214$	22.3840	−	110.771i	0.104598	−	0.517623i
$215$	443.391	+	443.391i	2.06228	+	2.06228i
$216$		0			0
$217$	−130.429	−	130.429i	−0.601056	−	0.601056i
$218$	−83.3237	−	125.527i	−0.382219	−	0.575812i
$219$		0			0
$220$	−106.128	−	44.7176i	−0.482402	−	0.203262i
$221$	−35.1064	+	14.5416i	−0.158853	+	0.0657989i
$222$		0			0
$223$			175.414i			0.786612i	0.919408	+	0.393306i	$0.128669\pi$
$223$			175.414i			0.786612i	−0.919408	+	0.393306i	$0.871331\pi$
$224$	34.1176	+	186.271i	0.152311	+	0.831566i
$225$		0			0
$226$	50.0024	+	255.434i	0.221250	+	1.13024i
$227$	−157.825	−	381.024i	−0.695265	−	1.67852i	−0.733893	−	0.679265i	$-0.762299\pi$
$227$	−157.825	−	381.024i	−0.695265	−	1.67852i	0.0386277	−	0.999254i	$-0.487701\pi$
$228$		0			0
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	−0.748965	−	0.662610i	$-0.769449\pi$
$229$	57.0597	−	137.754i	0.249169	−	0.601547i	0.998134	+	0.0610623i	$0.0194488\pi$
$230$	275.856	−	183.111i	1.19937	−	0.796135i
$231$		0			0
$232$	32.8708	−	48.2367i	0.141685	−	0.207917i
$233$	−275.512	+	275.512i	−1.18246	+	1.18246i	−0.203349	+	0.979106i	$0.565183\pi$
$233$	−275.512	+	275.512i	−1.18246	+	1.18246i	−0.979106	+	0.203349i	$0.934817\pi$
$234$		0			0
$235$	−48.1251	+	116.184i	−0.204788	+	0.494401i
$236$	−147.636	−	0.897408i	−0.625578	−	0.00380258i
$237$		0			0
$238$	−17.0014	−	11.4349i	−0.0714346	−	0.0480457i
$239$	63.0374			0.263755			0.131877	−	0.991266i	$-0.457899\pi$
$239$	63.0374			0.263755			0.131877	+	0.991266i	$0.457899\pi$
$240$		0			0
$241$		−	194.368i		−	0.806507i	−0.915088	−	0.403253i	$-0.867879\pi$
$241$		−	194.368i		−	0.806507i	0.915088	−	0.403253i	$-0.132121\pi$
$242$	177.745	+	119.548i	0.734482	+	0.494001i
$243$		0			0
$244$	−211.797	+	209.238i	−0.868020	+	0.857531i
$245$	−99.7526	−	41.3189i	−0.407154	−	0.168649i
$246$		0			0
$247$	239.330	+	239.330i	0.968949	+	0.968949i
$248$	136.639	+	208.586i	0.550962	+	0.841073i
$249$		0			0
$250$	124.219	−	82.4553i	0.496875	−	0.329821i
$251$	317.091	+	131.343i	1.26331	+	0.523281i	0.910924	−	0.412574i	$-0.135370\pi$
$251$	317.091	+	131.343i	1.26331	+	0.523281i	0.352387	+	0.935854i	$0.385370\pi$
$252$		0			0
$253$	73.8205	−	30.5774i	0.291781	−	0.120859i
$254$	21.6537	+	110.617i	0.0852509	+	0.435498i
$255$		0			0
$256$	6.22370	−	255.924i	0.0243113	−	0.999704i
$257$	180.756			0.703330			0.351665	−	0.936126i	$-0.385616\pi$
$257$	180.756			0.703330			0.351665	+	0.936126i	$0.385616\pi$
$258$		0			0
$259$	31.3666	+	75.7256i	0.121106	+	0.292377i
$260$	−628.072	+	255.695i	−2.41566	+	0.983441i
$261$		0			0
$262$	113.483	+	170.962i	0.433142	+	0.652527i
$263$	−266.626	+	266.626i	−1.01379	+	1.01379i	−0.0138830	+	0.999904i	$0.504419\pi$
$263$	−266.626	+	266.626i	−1.01379	+	1.01379i	−0.999904	+	0.0138830i	$0.995581\pi$
$264$		0			0
$265$	−171.823	+	171.823i	−0.648390	+	0.648390i
$266$	−36.1480	+	178.885i	−0.135895	+	0.672501i
$267$		0			0
$268$	77.2404	+	78.1852i	0.288211	+	0.291736i
$269$	156.911	+	378.816i	0.583311	+	1.40824i	0.889794	+	0.456362i	$0.150848\pi$
$269$	156.911	+	378.816i	0.583311	+	1.40824i	−0.306483	+	0.951876i	$0.599152\pi$
$270$		0			0
$271$	−323.931			−1.19532			−0.597659	−	0.801750i	$-0.703902\pi$
$271$	−323.931			−1.19532			−0.597659	+	0.801750i	$0.703902\pi$
$272$	19.3461	+	19.8223i	0.0711255	+	0.0728762i
$273$		0			0
$274$	−98.8828	+	147.019i	−0.360886	+	0.536567i
$275$	119.341	−	49.4328i	0.433969	−	0.179756i
$276$		0			0
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.207864	−	0.978158i	$-0.566651\pi$
$277$	−289.883	−	120.073i	−1.04651	−	0.433478i	−0.838644	+	0.544680i	$0.816651\pi$
$278$	12.0434	−	59.5991i	0.0433216	−	0.214385i
$279$		0			0
$280$	−302.160	−	205.906i	−1.07914	−	0.735380i
$281$	−297.826	−	297.826i	−1.05988	−	1.05988i	−0.998089	−	0.0617901i	$-0.980319\pi$
$281$	−297.826	−	297.826i	−1.05988	−	1.05988i	−0.0617901	−	0.998089i	$-0.519681\pi$
$282$		0			0
$283$	−132.389	−	54.8372i	−0.467804	−	0.193771i	0.136314	−	0.990666i	$-0.456474\pi$
$283$	−132.389	−	54.8372i	−0.467804	−	0.193771i	−0.604118	+	0.796895i	$0.706474\pi$
$284$	70.7303	−	167.865i	0.249050	−	0.591073i
$285$		0			0
$286$	−160.601	+	31.4385i	−0.561543	+	0.109925i
$287$			155.476i			0.541729i
$288$		0			0
$289$	286.003			0.989630
$290$	21.6522	+	110.609i	0.0746629	+	0.381410i
$291$		0			0
$292$	−62.7091	+	148.828i	−0.214757	+	0.509685i
$293$	−18.1180	+	43.7407i	−0.0618361	+	0.149286i	−0.951777	−	0.306790i	$-0.900745\pi$
$293$	−18.1180	+	43.7407i	−0.0618361	+	0.149286i	0.889941	+	0.456075i	$0.150745\pi$
$294$		0			0
$295$	201.576	−	201.576i	0.683309	−	0.683309i
$296$	−20.6251	−	108.868i	−0.0696795	−	0.367797i
$297$		0			0
$298$	111.819	+	22.5957i	0.375231	+	0.0758244i
$299$	180.050	−	434.678i	0.602172	−	1.45377i
$300$		0			0
$301$	183.861	+	443.879i	0.610833	+	1.47468i
$302$	−114.062	−	76.7162i	−0.377689	−	0.254027i
$303$		0			0
$304$	97.1776	−	226.770i	0.319663	−	0.745954i
$305$		−	574.861i		−	1.88479i
$306$		0			0
$307$	532.332	−	220.499i	1.73398	−	0.718239i	0.734779	−	0.678307i	$-0.237286\pi$
$307$	532.332	−	220.499i	1.73398	−	0.718239i	0.999202	−	0.0399320i	$-0.0127141\pi$
$308$	−62.0149	−	62.7734i	−0.201347	−	0.203810i
$309$		0			0
$310$	−471.934	−	95.3655i	−1.52237	−	0.307631i
$311$	−383.582	−	383.582i	−1.23338	−	1.23338i	−0.962657	−	0.270725i	$-0.912737\pi$
$311$	−383.582	−	383.582i	−1.23338	−	1.23338i	−0.270725	−	0.962657i	$-0.587263\pi$
$312$		0			0
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.985101	−	0.171974i	$-0.944985\pi$
$313$	−362.165	−	362.165i	−1.15708	−	1.15708i	−0.171974	−	0.985101i	$-0.555015\pi$
$314$	219.357	−	145.607i	0.698589	−	0.463718i
$315$		0			0
$316$	83.0046	−	33.7920i	0.262673	−	0.106937i
$317$	487.277	−	201.837i	1.53715	−	0.636709i	0.556215	−	0.831038i	$-0.312253\pi$
$317$	487.277	−	201.837i	1.53715	−	0.636709i	0.980936	+	0.194329i	$0.0622529\pi$
$318$		0			0
$319$			27.1995i			0.0852648i
$320$	343.093	+	355.840i	1.07217	+	1.11200i
$321$		0			0
$322$	248.966	−	48.7362i	0.773185	−	0.151355i
$323$	10.2152	+	24.6618i	0.0316261	+	0.0763523i
$324$		0			0
$325$	291.076	−	702.719i	0.895618	−	2.16221i
$326$	−37.6208	−	56.6756i	−0.115401	−	0.173852i
$327$		0			0
$328$	42.8821	−	205.760i	0.130738	−	0.627317i
$329$	−68.1341	+	68.1341i	−0.207095	+	0.207095i
$330$		0			0
$331$	20.5475	−	49.6062i	0.0620772	−	0.149868i	−0.889797	−	0.456356i	$-0.849154\pi$
$331$	20.5475	−	49.6062i	0.0620772	−	0.149868i	0.951874	+	0.306489i	$0.0991542\pi$
$332$	379.725	−	375.136i	1.14375	−	1.12993i
$333$		0			0
$334$	218.996	−	325.604i	0.655677	−	0.974863i
$335$	−212.211			−0.633466
$336$		0			0
$337$		−	627.680i		−	1.86255i	−0.364315	−	0.931276i	$-0.618697\pi$
$337$		−	627.680i		−	1.86255i	0.364315	−	0.931276i	$-0.381303\pi$
$338$	−349.155	+	519.124i	−1.03300	+	1.53587i
$339$		0			0
$340$	−53.4809	−	0.325084i	−0.157297	−	0.000956128i
$341$	−107.347	−	44.4648i	−0.314802	−	0.130395i
$342$		0			0
$343$	−263.539	−	263.539i	−0.768336	−	0.768336i
$344$	−120.898	−	638.148i	−0.351447	−	1.85508i
$345$		0			0
$346$	201.622	+	303.743i	0.582722	+	0.877870i
$347$	−320.625	−	132.807i	−0.923992	−	0.382730i	−0.130596	−	0.991436i	$-0.541689\pi$
$347$	−320.625	−	132.807i	−0.923992	−	0.382730i	−0.793396	+	0.608706i	$0.791689\pi$
$348$		0			0
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	−0.361741	−	0.932279i	$-0.617818\pi$
$349$	14.5498	−	6.02674i	0.0416901	−	0.0172686i	0.403431	+	0.915010i	$0.367818\pi$
$350$	402.488	−	78.7890i	1.14997	−	0.225112i
$351$		0			0
$352$	64.7581	+	100.180i	0.183972	+	0.284602i
$353$	−283.828			−0.804045			−0.402023	−	0.915630i	$-0.631693\pi$
$353$	−283.828			−0.804045			−0.402023	+	0.915630i	$0.631693\pi$
$354$		0			0
$355$	134.598	+	324.949i	0.379150	+	0.915349i
$356$	−318.139	−	134.049i	−0.893649	−	0.376542i
$357$		0			0
$358$	−81.1668	+	53.8778i	−0.226723	+	0.150497i
$359$	−388.417	+	388.417i	−1.08194	+	1.08194i	−0.0856121	+	0.996329i	$0.527285\pi$
$359$	−388.417	+	388.417i	−1.08194	+	1.08194i	−0.996329	+	0.0856121i	$0.972715\pi$
$360$		0			0
$361$	−87.1393	+	87.1393i	−0.241383	+	0.241383i
$362$	252.352	+	50.9938i	0.697106	+	0.140867i
$363$		0			0
$364$	−519.577	−	3.15825i	−1.42741	−	0.00867651i
$365$	−119.334	−	288.098i	−0.326943	−	0.789309i
$366$		0			0
$367$	−529.617			−1.44310			−0.721548	−	0.692364i	$-0.756569\pi$
$367$	−529.617			−1.44310			−0.721548	+	0.692364i	$0.756569\pi$
$368$	−342.928	−	4.16913i	−0.931869	−	0.0113292i
$369$		0			0
$370$	177.530	+	119.404i	0.479810	+	0.322713i
$371$	−172.013	+	71.2499i	−0.463646	+	0.192048i
$372$		0			0
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	0.332737	−	0.943020i	$-0.392028\pi$
$373$	−36.8515	−	15.2644i	−0.0987975	−	0.0409233i	−0.431535	+	0.902096i	$0.642028\pi$
$374$	−12.6509	−	2.55641i	−0.0338258	−	0.00683531i
$375$		0			0
$376$	108.962	−	71.3778i	0.289793	−	0.189835i
$377$	113.249	+	113.249i	0.300396	+	0.300396i
$378$		0			0
$379$	−463.955	−	192.176i	−1.22415	−	0.507061i	−0.325426	−	0.945567i	$-0.605508\pi$
$379$	−463.955	−	192.176i	−1.22415	−	0.507061i	−0.898728	+	0.438506i	$0.855508\pi$
$380$	179.622	+	441.212i	0.472689	+	1.16108i
$381$		0			0
$382$	68.8832	+	351.885i	0.180323	+	0.921165i
$383$		−	304.650i		−	0.795432i	−0.917509	−	0.397716i	$-0.869803\pi$
$383$		−	304.650i		−	0.795432i	0.917509	−	0.397716i	$-0.130197\pi$
$384$		0			0
$385$	170.380			0.442547
$386$	353.145	−	69.1299i	0.914885	−	0.179093i
$387$		0			0
$388$	−258.986	+	105.436i	−0.667489	+	0.271742i
$389$	72.6039	−	175.281i	0.186642	−	0.450594i	−0.802667	−	0.596428i	$-0.796586\pi$
$389$	72.6039	−	175.281i	0.186642	−	0.450594i	0.989309	+	0.145833i	$0.0465863\pi$
$390$		0			0
$391$	26.2382	−	26.2382i	0.0671053	−	0.0671053i
$392$	61.2830	+	93.5519i	0.156334	+	0.238653i
$393$		0			0
$394$	96.5745	−	477.917i	0.245113	−	1.21299i
$395$	−66.2209	+	159.871i	−0.167648	+	0.404737i
$396$		0			0
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	0.991796	−	0.127829i	$-0.0408007\pi$
$397$	79.4405	+	191.786i	0.200102	+	0.483089i	−0.791694	+	0.610917i	$0.790801\pi$
$398$	−208.021	+	309.287i	−0.522667	+	0.777103i
$399$		0			0
$400$	−554.392	−	6.73999i	−1.38598	−	0.0168500i
$401$		−	58.9969i		−	0.147124i	−0.997291	−	0.0735622i	$-0.976563\pi$
$401$		−	58.9969i		−	0.147124i	0.997291	−	0.0735622i	$-0.0234368\pi$
$402$		0			0
$403$	−632.095	+	261.822i	−1.56847	+	0.649683i
$404$	0.665998	−	109.566i	0.00164851	−	0.271203i
$405$		0			0
$406$	−17.1050	+	84.6473i	−0.0421305	+	0.208491i
$407$	36.5089	+	36.5089i	0.0897025	+	0.0897025i
$408$		0			0
$409$	110.309	+	110.309i	0.269704	+	0.269704i	0.828981	−	0.559277i	$-0.188921\pi$
$409$	110.309	+	110.309i	0.269704	+	0.269704i	−0.559277	+	0.828981i	$0.688921\pi$
$410$	224.442	+	338.121i	0.547418	+	0.824685i
$411$		0			0
$412$	256.380	−	608.469i	0.622282	−	1.47687i
$413$	201.798	−	83.5875i	0.488615	−	0.202391i
$414$		0			0
$415$			1030.65i			2.48350i
$416$	686.747	+	147.485i	1.65083	+	0.354531i
$417$		0			0
$418$	22.0851	+	112.820i	0.0528351	+	0.269905i
$419$	−4.61960	−	11.1527i	−0.0110253	−	0.0266174i	0.918271	−	0.395952i	$-0.129585\pi$
$419$	−4.61960	−	11.1527i	−0.0110253	−	0.0266174i	−0.929296	+	0.369335i	$0.879585\pi$
$420$		0			0
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	−0.880506	−	0.474036i	$-0.842797\pi$
$421$	32.5432	−	78.5662i	0.0772998	−	0.186618i	0.957805	+	0.287418i	$0.0927967\pi$
$422$	−329.506	+	218.724i	−0.780821	+	0.518302i
$423$		0			0
$424$	247.296	−	46.8505i	0.583246	−	0.110496i
$425$	42.4177	−	42.4177i	0.0998064	−	0.0998064i
$426$		0			0
$427$	168.558	−	406.936i	0.394750	−	0.953012i
$428$	1.37384	−	226.016i	0.00320991	−	0.528076i
$429$		0			0
$430$	1040.62	+	699.905i	2.42005	+	1.62769i
$431$	201.982			0.468636			0.234318	−	0.972160i	$-0.424714\pi$
$431$	201.982			0.468636			0.234318	+	0.972160i	$0.424714\pi$
$432$		0			0
$433$			643.404i			1.48592i	0.669334	+	0.742961i	$0.266579\pi$
$433$			643.404i			1.48592i	−0.669334	+	0.742961i	$0.733421\pi$
$434$	−306.113	−	205.886i	−0.705328	−	0.474392i
$435$		0			0
$436$	−211.773	−	214.363i	−0.485718	−	0.491659i
$437$	−305.355	−	126.482i	−0.698753	−	0.289433i
$438$		0			0
$439$	−218.953	−	218.953i	−0.498753	−	0.498753i	0.412296	−	0.911050i	$-0.364727\pi$
$439$	−218.953	−	218.953i	−0.498753	−	0.498753i	−0.911050	+	0.412296i	$0.864727\pi$
$440$	−225.485	−	46.9929i	−0.512465	−	0.106802i
$441$		0			0
$442$	−63.3180	+	42.0299i	−0.143253	+	0.0950903i
$443$	−275.767	−	114.227i	−0.622499	−	0.257848i	0.0490630	−	0.998796i	$-0.484376\pi$
$443$	−275.767	−	114.227i	−0.622499	−	0.257848i	−0.671562	+	0.740948i	$0.734376\pi$
$444$		0			0
$445$	615.847	−	255.092i	1.38392	−	0.573240i
$446$	67.3972	+	344.294i	0.151115	+	0.771960i
$447$		0			0
$448$	138.533	+	352.494i	0.309225	+	0.786817i
$449$	264.162			0.588334			0.294167	−	0.955754i	$-0.404958\pi$
$449$	264.162			0.588334			0.294167	+	0.955754i	$0.404958\pi$
$450$		0			0
$451$	37.4792	+	90.4828i	0.0831024	+	0.200627i
$452$	196.284	+	482.140i	0.434257	+	1.06668i
$453$		0			0
$454$	−456.167	−	687.214i	−1.00477	−	1.51369i
$455$	709.407	−	709.407i	1.55914	−	1.55914i
$456$		0			0
$457$	324.484	−	324.484i	0.710030	−	0.710030i	−0.256511	−	0.966541i	$-0.582573\pi$
$457$	324.484	−	324.484i	0.710030	−	0.710030i	0.966541	+	0.256511i	$0.0825731\pi$
$458$	59.0662	−	292.300i	0.128966	−	0.638210i
$459$		0			0
$460$	471.082	−	465.389i	1.02409	−	1.01172i
$461$	46.5472	+	112.375i	0.100970	+	0.243763i	0.966290	−	0.257457i	$-0.0828846\pi$
$461$	46.5472	+	112.375i	0.100970	+	0.243763i	−0.865320	+	0.501220i	$0.832885\pi$
$462$		0			0
$463$	−602.217			−1.30069			−0.650343	−	0.759641i	$-0.725375\pi$
$463$	−602.217			−1.30069			−0.650343	+	0.759641i	$0.725375\pi$
$464$	45.9837	−	107.306i	0.0991029	−	0.231263i
$465$		0			0
$466$	−434.904	+	646.617i	−0.933271	+	1.38759i
$467$	−327.171	+	135.519i	−0.700580	+	0.290190i	−0.704400	−	0.709803i	$-0.748784\pi$
$467$	−327.171	+	135.519i	−0.700580	+	0.290190i	0.00382006	+	0.999993i	$0.498784\pi$
$468$		0			0
$469$	−150.221	−	62.2237i	−0.320301	−	0.132673i
$470$	−49.8174	+	246.531i	−0.105995	+	0.524534i
$471$		0			0
$472$	−290.118	+	54.9630i	−0.614656	+	0.116447i
$473$	214.003	+	214.003i	0.452439	+	0.452439i
$474$		0			0
$475$	−493.650	−	204.477i	−1.03926	−	0.430477i
$476$	−37.7630	−	15.9116i	−0.0793340	−	0.0334276i
$477$		0			0
$478$	123.726	−	24.2201i	0.258842	−	0.0506696i
$479$			151.023i			0.315289i	0.987496	+	0.157644i	$0.0503900\pi$
$479$			151.023i			0.315289i	−0.987496	+	0.157644i	$0.949610\pi$
$480$		0			0
$481$	304.022			0.632062
$482$	−74.6796	−	381.495i	−0.154937	−	0.791484i
$483$		0			0
$484$	394.800	+	166.350i	0.815703	+	0.343699i
$485$	206.618	−	498.821i	0.426017	−	1.02850i
$486$		0			0
$487$	382.894	−	382.894i	0.786231	−	0.786231i	−0.194643	−	0.980874i	$-0.562355\pi$
$487$	382.894	−	382.894i	0.786231	−	0.786231i	0.980874	+	0.194643i	$0.0623549\pi$
$488$	−335.311	+	492.056i	−0.687112	+	1.00831i
$489$		0			0
$490$	−211.665	−	42.7719i	−0.431969	−	0.0872895i
$491$	−205.776	+	496.786i	−0.419095	+	1.01178i	0.563516	+	0.826105i	$0.309448\pi$
$491$	−205.776	+	496.786i	−0.419095	+	1.01178i	−0.982610	+	0.185679i	$0.940552\pi$
$492$		0			0
$493$	4.83378	+	11.6698i	0.00980483	+	0.0236709i
$494$	561.700	+	377.790i	1.13704	+	0.764758i
$495$		0			0
$496$	348.329	+	356.903i	0.702277	+	0.719563i
$497$			269.493i			0.542239i
$498$		0			0
$499$	604.867	−	250.544i	1.21216	−	0.502093i	0.317250	−	0.948342i	$-0.397240\pi$
$499$	604.867	−	250.544i	1.21216	−	0.502093i	0.894909	+	0.446249i	$0.147240\pi$
$500$	212.129	−	209.566i	0.424258	−	0.419132i
$501$		0			0
$502$	672.834	+	135.962i	1.34031	+	0.270841i
$503$	−324.203	−	324.203i	−0.644539	−	0.644539i	0.307129	−	0.951668i	$-0.400632\pi$
$503$	−324.203	−	324.203i	−0.644539	−	0.644539i	−0.951668	+	0.307129i	$0.900632\pi$
$504$		0			0
$505$	149.597	+	149.597i	0.296231	+	0.296231i
$506$	133.143	−	88.3789i	0.263128	−	0.174662i
$507$		0			0
$508$	85.0016	+	208.793i	0.167326	+	0.411009i
$509$	−734.614	+	304.287i	−1.44325	+	0.597813i	−0.960584	−	0.277991i	$-0.910331\pi$
$509$	−734.614	+	304.287i	−1.44325	+	0.597813i	−0.482666	+	0.875805i	$0.660331\pi$
$510$		0			0
$511$		−	238.931i		−	0.467575i
$512$	−86.1150	−	504.706i	−0.168193	−	0.985754i
$513$		0			0
$514$	354.778	−	69.4495i	0.690229	−	0.135116i
$515$	487.886	+	1177.86i	0.947351	+	2.28711i
$516$		0			0
$517$	−23.2277	+	56.0766i	−0.0449278	+	0.108465i
$518$	90.6597	+	136.579i	0.175019	+	0.263665i
$519$		0			0
$520$	−1134.51	+	743.180i	−2.18174	+	1.42919i
$521$	16.7805	−	16.7805i	0.0322082	−	0.0322082i	−0.690819	−	0.723027i	$-0.742750\pi$
$521$	16.7805	−	16.7805i	0.0322082	−	0.0322082i	0.723027	+	0.690819i	$0.242750\pi$
$522$		0			0
$523$	−250.400	+	604.519i	−0.478776	+	1.15587i	0.481407	+	0.876497i	$0.340126\pi$
$523$	−250.400	+	604.519i	−0.478776	+	1.15587i	−0.960183	+	0.279371i	$0.909874\pi$
$524$	288.426	+	291.953i	0.550430	+	0.557163i
$525$		0			0
$526$	−420.877	+	625.762i	−0.800146	+	1.18966i
$527$	−53.9589			−0.102389
$528$		0			0
$529$		−	69.5595i		−	0.131492i
$530$	−271.228	+	403.263i	−0.511752	+	0.760874i
$531$		0			0
$532$	−2.21863	+	364.995i	−0.00417035	+	0.686082i
$533$	532.791	+	220.689i	0.999607	+	0.414051i
$534$		0			0
$535$	308.593	+	308.593i	0.576809	+	0.576809i
$536$	181.644	+	123.781i	0.338887	+	0.230934i
$537$		0			0
$538$	453.524	+	683.232i	0.842981	+	1.26995i
$539$	−48.1458	−	19.9427i	−0.0893244	−	0.0369994i
$540$		0			0
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.992781	−	0.119939i	$-0.961730\pi$
$541$	−870.996	+	360.778i	−1.60997	+	0.666873i	−0.617192	+	0.786812i	$0.711730\pi$
$542$	−635.795	+	124.460i	−1.17305	+	0.229631i
$543$		0			0
$544$	45.5877	+	31.4731i	0.0838009	+	0.0578550i
$545$	581.827			1.06757
$546$		0			0
$547$	36.1835	+	87.3546i	0.0661489	+	0.159698i	0.953497	−	0.301403i	$-0.0974548\pi$
$547$	36.1835	+	87.3546i	0.0661489	+	0.159698i	−0.887348	+	0.461100i	$0.847455\pi$
$548$	−137.595	+	326.554i	−0.251085	+	0.595902i
$549$		0			0
$550$	215.244	−	142.877i	0.391353	−	0.259777i
$551$	79.5561	−	79.5561i	0.144385	−	0.144385i
$552$		0			0
$553$	−93.7536	+	93.7536i	−0.169536	+	0.169536i
$554$	−615.101	−	124.296i	−1.11029	−	0.224360i
$555$		0			0
$556$	0.739178	−	121.605i	0.00132946	−	0.218715i
$557$	−288.342	−	696.118i	−0.517669	−	1.24976i	−0.939332	−	0.343010i	$-0.888553\pi$
$557$	−288.342	−	696.118i	−0.517669	−	1.24976i	0.421663	−	0.906753i	$-0.361447\pi$
$558$		0			0
$559$	1782.08			3.18797
$560$	−672.177	−	288.047i	−1.20032	−	0.514370i
$561$		0			0
$562$	−698.987	−	470.127i	−1.24375	−	0.836526i
$563$	609.320	−	252.389i	1.08227	−	0.448293i	0.230968	−	0.972961i	$-0.425811\pi$
$563$	609.320	−	252.389i	1.08227	−	0.448293i	0.851306	+	0.524669i	$0.175811\pi$
$564$		0			0
$565$	−928.629	−	384.651i	−1.64359	−	0.680797i
$566$	−280.915	−	56.7655i	−0.496316	−	0.100292i
$567$		0			0
$568$	74.3292	−	356.652i	0.130861	−	0.627908i
$569$	−256.311	−	256.311i	−0.450459	−	0.450459i	0.445047	−	0.895507i	$-0.353187\pi$
$569$	−256.311	−	256.311i	−0.450459	−	0.450459i	−0.895507	+	0.445047i	$0.853187\pi$
$570$		0			0
$571$	346.136	+	143.374i	0.606193	+	0.251094i	0.664600	−	0.747199i	$-0.268602\pi$
$571$	346.136	+	143.374i	0.606193	+	0.251094i	−0.0584066	+	0.998293i	$0.518602\pi$
$572$	−303.141	+	123.412i	−0.529966	+	0.215754i
$573$		0			0
$574$	59.7366	+	305.160i	0.104071	+	0.531638i
$575$			742.751i			1.29174i
$576$		0			0
$577$	−354.659			−0.614661			−0.307330	−	0.951603i	$-0.599436\pi$
$577$	−354.659			−0.614661			−0.307330	+	0.951603i	$0.599436\pi$
$578$	561.352	−	109.887i	0.971197	−	0.190116i
$579$		0			0
$580$	84.9958	+	208.778i	0.146544	+	0.359963i
$581$	−302.204	+	729.584i	−0.520144	+	1.25574i
$582$		0			0
$583$	−82.9309	+	82.9309i	−0.142249	+	0.142249i
$584$	−65.8999	+	316.206i	−0.112842	+	0.541448i
$585$		0			0
$586$	−18.7551	+	92.8132i	−0.0320053	+	0.158384i
$587$	230.018	−	555.312i	0.391853	−	0.946018i	−0.597683	−	0.801733i	$-0.703912\pi$
$587$	230.018	−	555.312i	0.391853	−	0.946018i	0.989536	−	0.144285i	$-0.0460882\pi$
$588$		0			0
$589$	183.926	+	444.038i	0.312269	+	0.753884i
$590$	318.194	−	473.092i	0.539312	−	0.801850i
$591$		0			0
$592$	−82.3108	−	205.756i	−0.139039	−	0.347560i
$593$		−	458.661i		−	0.773460i	−0.922193	−	0.386730i	$-0.873605\pi$
$593$		−	458.661i		−	0.773460i	0.922193	−	0.386730i	$-0.126395\pi$
$594$		0			0
$595$	73.1008	−	30.2793i	0.122858	−	0.0508896i
$596$	228.154	+	1.38683i	0.382809	+	0.00232690i
$597$		0			0
$598$	186.381	−	922.341i	0.311674	−	1.54238i
$599$	−265.583	−	265.583i	−0.443377	−	0.443377i	0.449768	−	0.893145i	$-0.351507\pi$
$599$	−265.583	−	265.583i	−0.443377	−	0.443377i	−0.893145	+	0.449768i	$0.851507\pi$
$600$		0			0
$601$	466.600	+	466.600i	0.776373	+	0.776373i	0.979212	−	0.202839i	$-0.0650168\pi$
$601$	466.600	+	466.600i	0.776373	+	0.776373i	−0.202839	+	0.979212i	$0.565017\pi$
$602$	531.418	+	800.579i	0.882754	+	1.32987i
$603$		0			0
$604$	−253.351	−	106.750i	−0.419455	−	0.176738i
$605$	−764.246	+	316.561i	−1.26322	+	0.523241i
$606$		0			0
$607$		−	90.4302i		−	0.148979i	−0.997222	−	0.0744894i	$-0.976267\pi$
$607$		−	90.4302i		−	0.148979i	0.997222	−	0.0744894i	$-0.0237327\pi$
$608$	103.606	−	482.430i	0.170405	−	0.793470i
$609$		0			0
$610$	−220.872	−	1128.31i	−0.362085	−	1.84968i
$611$	136.772	+	330.197i	0.223849	+	0.540420i
$612$		0			0
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	−0.863542	−	0.504277i	$-0.831759\pi$
$613$	63.5389	−	153.397i	0.103652	−	0.250239i	0.967194	+	0.254038i	$0.0817589\pi$
$614$	960.114	−	637.316i	1.56370	−	1.03797i
$615$		0			0
$616$	−145.838	−	99.3812i	−0.236750	−	0.161333i
$617$	−181.842	+	181.842i	−0.294720	+	0.294720i	−0.838942	−	0.544221i	$-0.816825\pi$
$617$	−181.842	+	181.842i	−0.294720	+	0.294720i	0.544221	+	0.838942i	$0.316825\pi$
$618$		0			0
$619$	−388.636	+	938.250i	−0.627844	+	1.51575i	0.214451	+	0.976735i	$0.431204\pi$
$619$	−388.636	+	938.250i	−0.627844	+	1.51575i	−0.842296	+	0.539016i	$0.818796\pi$
$620$	−962.928	−	5.85316i	−1.55311	−	0.00944059i
$621$		0			0
$622$	−900.253	−	605.495i	−1.44735	−	0.973465i
$623$	510.746			0.819817
$624$		0			0
$625$		−	290.538i		−	0.464860i
$626$	−849.988	−	571.688i	−1.35781	−	0.913239i
$627$		0			0
$628$	374.598	−	370.071i	0.596493	−	0.589285i
$629$	22.1522	+	9.17573i	0.0352181	+	0.0145878i
$630$		0			0
$631$	−241.593	−	241.593i	−0.382873	−	0.382873i	0.489263	−	0.872136i	$-0.337266\pi$
$631$	−241.593	−	241.593i	−0.382873	−	0.382873i	−0.872136	+	0.489263i	$0.837266\pi$
$632$	149.934	−	98.2169i	0.237237	−	0.155407i
$633$		0			0
$634$	878.853	−	583.375i	1.38620	−	0.920150i
$635$	−402.146	−	166.574i	−0.633301	−	0.262322i
$636$		0			0
$637$	−283.498	+	117.429i	−0.445051	+	0.184346i
$638$	10.4505	+	53.3857i	0.0163801	+	0.0836766i
$639$		0			0
$640$	810.125	+	566.601i	1.26582	+	0.885314i
$641$	385.038			0.600684			0.300342	−	0.953832i	$-0.402899\pi$
$641$	385.038			0.600684			0.300342	+	0.953832i	$0.402899\pi$
$642$		0			0
$643$	144.485	+	348.818i	0.224705	+	0.542486i	0.995518	−	0.0945760i	$-0.0301495\pi$
$643$	144.485	+	348.818i	0.224705	+	0.542486i	−0.770813	+	0.637062i	$0.780150\pi$
$644$	469.931	−	191.314i	0.729707	−	0.297071i
$645$		0			0
$646$	29.5254	+	44.4800i	0.0457050	+	0.0688544i
$647$	580.537	−	580.537i	0.897276	−	0.897276i	−0.0979186	−	0.995194i	$-0.531218\pi$
$647$	580.537	−	580.537i	0.897276	−	0.897276i	0.995194	+	0.0979186i	$0.0312185\pi$
$648$		0			0
$649$	97.2911	−	97.2911i	0.149909	−	0.149909i
$650$	301.311	−	1491.10i	0.463556	−	2.29399i
$651$		0			0
$652$	−95.6158	−	96.7853i	−0.146650	−	0.148444i
$653$	467.055	+	1127.57i	0.715246	+	1.72676i	0.686457	+	0.727170i	$0.259165\pi$
$653$	467.055	+	1127.57i	0.715246	+	1.72676i	0.0287882	+	0.999586i	$0.490835\pi$
$654$		0			0
$655$	−792.423			−1.20981
$656$	5.11016	−	420.331i	0.00778988	−	0.640749i
$657$		0			0
$658$	−107.552	+	159.908i	−0.163453	+	0.243022i
$659$	287.435	−	119.060i	0.436169	−	0.180667i	−0.153784	−	0.988104i	$-0.549146\pi$
$659$	287.435	−	119.060i	0.436169	−	0.180667i	0.589953	+	0.807437i	$0.299146\pi$
$660$		0			0
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.00997082	−	0.999950i	$-0.503174\pi$
$661$	−478.625	−	198.253i	−0.724093	−	0.299929i	−0.714122	+	0.700021i	$0.753174\pi$
$662$	21.2701	−	105.259i	0.0321301	−	0.159002i
$663$		0			0
$664$	601.170	−	882.194i	0.905376	−	1.32861i
$665$	−498.348	−	498.348i	−0.749396	−	0.749396i
$666$		0			0
$667$	−144.492	−	59.8505i	−0.216629	−	0.0897309i
$668$	304.731	−	723.221i	0.456185	−	1.08267i
$669$		0			0
$670$	−416.517	+	81.5352i	−0.621667	+	0.121694i
$671$		−	277.458i		−	0.413499i
$672$		0			0
$673$	831.026			1.23481			0.617405	−	0.786646i	$-0.288184\pi$
$673$	831.026			1.23481			0.617405	+	0.786646i	$0.288184\pi$
$674$	−241.165	−	1231.98i	−0.357812	−	1.82786i
$675$		0			0
$676$	−485.846	+	1153.06i	−0.718707	+	1.70571i
$677$	16.6301	−	40.1487i	0.0245644	−	0.0593038i	−0.911121	−	0.412138i	$-0.864782\pi$
$677$	16.6301	−	40.1487i	0.0245644	−	0.0593038i	0.935686	+	0.352834i	$0.114782\pi$
$678$		0			0
$679$	292.524	−	292.524i	0.430816	−	0.430816i
$680$	−105.094	+	19.9102i	−0.154550	+	0.0292797i
$681$		0			0
$682$	−227.780	−	46.0284i	−0.333988	−	0.0674903i
$683$	−411.955	+	994.547i	−0.603155	+	1.45614i	0.267162	+	0.963652i	$0.413914\pi$
$683$	−411.955	+	994.547i	−0.603155	+	1.45614i	−0.870317	+	0.492493i	$0.836086\pi$
$684$		0			0
$685$	−261.839	−	632.136i	−0.382247	−	0.922827i
$686$	−618.518	−	416.005i	−0.901629	−	0.606421i
$687$		0			0
$688$	−482.479	−	1206.07i	−0.701278	−	1.75301i
$689$			690.593i			1.00231i
$690$		0			0
$691$	657.136	−	272.195i	0.950993	−	0.393914i	0.147389	−	0.989079i	$-0.452913\pi$
$691$	657.136	−	272.195i	0.950993	−	0.393914i	0.803604	+	0.595164i	$0.202913\pi$
$692$	512.436	+	518.704i	0.740515	+	0.749572i
$693$		0			0
$694$	−680.333	−	137.478i	−0.980307	−	0.198094i
$695$	166.034	+	166.034i	0.238898	+	0.238898i
$696$		0			0
$697$	32.1605	+	32.1605i	0.0461413	+	0.0461413i
$698$	26.2421	−	17.4193i	0.0375961	−	0.0249560i
$699$		0			0
$700$	759.711	−	309.286i	1.08530	−	0.441837i
$701$	−57.0623	+	23.6360i	−0.0814012	+	0.0337175i	−0.423013	−	0.906124i	$-0.639027\pi$
$701$	−57.0623	+	23.6360i	−0.0814012	+	0.0337175i	0.341611	+	0.939841i	$0.389027\pi$
$702$		0			0
$703$		−	213.571i		−	0.303799i
$704$	165.595	+	171.747i	0.235220	+	0.243959i
$705$		0			0
$706$	−557.083	+	109.052i	−0.789069	+	0.154464i
$707$	62.0332	+	149.761i	0.0877414	+	0.211827i
$708$		0			0
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	−0.996930	−	0.0783041i	$-0.975049\pi$
$709$	−167.767	+	405.025i	−0.236625	+	0.571262i	0.760305	+	0.649566i	$0.225049\pi$
$710$	389.033	+	586.078i	0.547934	+	0.825461i
$711$		0			0
$712$	−675.931	−	140.869i	−0.949341	−	0.197850i
$713$	472.421	−	472.421i	0.662582	−	0.662582i
$714$		0			0
$715$	241.845	−	583.865i	0.338245	−	0.816595i
$716$	−138.609	+	136.934i	−0.193588	+	0.191249i
$717$		0			0
$718$	−613.127	+	911.600i	−0.853938	+	1.26964i
$719$	−1154.30			−1.60542			−0.802712	−	0.596367i	$-0.796610\pi$
$719$	−1154.30			−1.60542			−0.802712	+	0.596367i	$0.796610\pi$
$720$		0			0
$721$			976.846i			1.35485i
$722$	−137.552	+	204.513i	−0.190515	+	0.283259i
$723$		0			0
$724$	514.897	+	3.12980i	0.711183	+	0.00432293i
$725$	−233.592	−	96.7569i	−0.322195	−	0.133458i
$726$		0			0
$727$	−644.722	−	644.722i	−0.886825	−	0.886825i	0.107392	−	0.994217i	$-0.465750\pi$
$727$	−644.722	−	644.722i	−0.886825	−	0.886825i	−0.994217	+	0.107392i	$0.965750\pi$
$728$	−1021.01	+	193.432i	−1.40249	+	0.265703i
$729$		0			0
$730$	−344.915	−	519.613i	−0.472486	−	0.711799i
$731$	129.849	+	53.7851i	0.177632	+	0.0735775i
$732$		0			0
$733$	508.297	−	210.544i	0.693448	−	0.287235i	−0.00798801	−	0.999968i	$-0.502543\pi$
$733$	508.297	−	210.544i	0.693448	−	0.287235i	0.701436	+	0.712733i	$0.252543\pi$
$734$	−1039.50	+	203.488i	−1.41622	+	0.277231i
$735$		0			0
$736$	−674.682	+	123.576i	−0.916688	+	0.167902i
$737$	−102.424			−0.138974
$738$		0			0
$739$	−479.243	−	1157.00i	−0.648503	−	1.56562i	−0.814923	−	0.579569i	$-0.803221\pi$
$739$	−479.243	−	1157.00i	−0.648503	−	1.56562i	0.166421	−	0.986055i	$-0.446779\pi$
$740$	394.323	+	166.149i	0.532869	+	0.224526i
$741$		0			0
$742$	−310.242	+	205.936i	−0.418116	+	0.277542i
$743$	106.350	−	106.350i	0.143136	−	0.143136i	−0.631908	−	0.775044i	$-0.717728\pi$
$743$	106.350	−	106.350i	0.143136	−	0.143136i	0.775044	+	0.631908i	$0.217728\pi$
$744$		0			0
$745$	−311.511	+	311.511i	−0.418136	+	0.418136i
$746$	−78.1950	−	15.8012i	−0.104819	−	0.0211812i
$747$		0			0
$748$	−25.8127	−	0.156902i	−0.0345089	−	0.000209762i
$749$	127.964	+	308.932i	0.170846	+	0.412460i
$750$		0			0
$751$	−186.540			−0.248389			−0.124195	−	0.992258i	$-0.539635\pi$
$751$	−186.540			−0.248389			−0.124195	+	0.992258i	$0.539635\pi$
$752$	186.441	−	181.962i	0.247926	−	0.241970i
$753$		0			0
$754$	265.792	+	178.768i	0.352510	+	0.237092i
$755$	490.430	−	203.143i	0.649577	−	0.269064i
$756$		0			0
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.987244	−	0.159214i	$-0.0508959\pi$
$757$	1190.57	+	493.151i	1.57275	+	0.651454i	0.585506	+	0.810668i	$0.300896\pi$
$758$	−984.463	−	198.934i	−1.29876	−	0.262446i
$759$		0			0
$760$	522.073	+	796.974i	0.686939	+	1.04865i
$761$	1042.65	+	1042.65i	1.37010	+	1.37010i	0.860279	+	0.509823i	$0.170289\pi$
$761$	1042.65	+	1042.65i	1.37010	+	1.37010i	0.509823	+	0.860279i	$0.329711\pi$
$762$		0			0
$763$	411.867	+	170.601i	0.539800	+	0.223592i
$764$	270.401	+	664.196i	0.353928	+	0.869366i
$765$		0			0
$766$	−117.052	−	597.952i	−0.152809	−	0.780616i
$767$		−	810.175i		−	1.05629i
$768$		0			0
$769$	362.542			0.471446			0.235723	−	0.971820i	$-0.424254\pi$
$769$	362.542			0.471446			0.235723	+	0.971820i	$0.424254\pi$
$770$	334.414	−	65.4631i	0.434304	−	0.0850170i
$771$		0			0
$772$	666.574	−	271.369i	0.863438	−	0.351514i
$773$	−259.669	+	626.896i	−0.335924	+	0.810991i	0.662175	+	0.749350i	$0.269634\pi$
$773$	−259.669	+	626.896i	−0.335924	+	0.810991i	−0.998098	+	0.0616419i	$0.980366\pi$
$774$		0			0
$775$	763.736	−	763.736i	0.985465	−	0.985465i
$776$	−467.814	+	306.451i	−0.602853	+	0.394910i
$777$		0			0
$778$	75.1570	−	371.928i	0.0966028	−	0.478057i
$779$	155.031	−	374.278i	0.199013	−	0.480459i
$780$		0			0
$781$	64.9641	+	156.837i	0.0831807	+	0.200816i
$782$	41.4177	−	61.5800i	0.0529639	−	0.0787469i
$783$		0			0
$784$	156.227	+	160.073i	0.199270	+	0.204174i
$785$			1016.74i			1.29521i
$786$		0			0
$787$	−148.037	+	61.3188i	−0.188103	+	0.0779147i	−0.474747	−	0.880122i	$-0.657460\pi$
$787$	−148.037	+	61.3188i	−0.188103	+	0.0779147i	0.286644	+	0.958037i	$0.407460\pi$
$788$	5.92737	−	975.136i	0.00752204	−	1.23748i
$789$		0			0
$790$	−68.5495	+	339.230i	−0.0867715	+	0.429405i
$791$	−544.577	−	544.577i	−0.688466	−	0.688466i
$792$		0			0
$793$	−1155.24	−	1155.24i	−1.45680	−	1.45680i
$794$	229.609	+	345.906i	0.289180	+	0.435649i
$795$		0			0
$796$	−289.460	+	686.978i	−0.363643	+	0.863037i
$797$	173.793	−	71.9875i	0.218059	−	0.0903231i	−0.270980	−	0.962585i	$-0.587348\pi$
$797$	173.793	−	71.9875i	0.218059	−	0.0903231i	0.489039	+	0.872262i	$0.337348\pi$
$798$		0			0
$799$			28.1873i			0.0352782i
$800$	−1090.72	+	199.778i	−1.36340	+	0.249722i
$801$		0			0
$802$	−22.6676	−	115.796i	−0.0282639	−	0.144384i
$803$	−57.5968	−	139.051i	−0.0717271	−	0.173164i
$804$		0			0
$805$	−374.910	+	905.113i	−0.465727	+	1.12436i
$806$	−1140.05	+	756.753i	−1.41445	+	0.938899i
$807$		0			0
$808$	−40.7900	−	215.307i	−0.0504827	−	0.266468i
$809$	679.446	−	679.446i	0.839859	−	0.839859i	−0.148981	−	0.988840i	$-0.547599\pi$
$809$	679.446	−	679.446i	0.839859	−	0.839859i	0.988840	+	0.148981i	$0.0475993\pi$
$810$		0			0
$811$	4.19630	−	10.1308i	0.00517422	−	0.0124917i	−0.921271	−	0.388921i	$-0.872848\pi$
$811$	4.19630	−	10.1308i	0.00517422	−	0.0124917i	0.926446	+	0.376429i	$0.122848\pi$
$812$	−1.04984	+	172.713i	−0.00129290	+	0.212701i
$813$		0			0
$814$	85.6851	+	57.6304i	0.105264	+	0.0707990i
$815$	262.696			0.322326
$816$		0			0
$817$		−	1251.88i		−	1.53229i
$818$	258.891	+	174.126i	0.316493	+	0.212868i
$819$		0			0
$820$	570.434	+	577.411i	0.695651	+	0.704160i
$821$	−114.507	−	47.4303i	−0.139472	−	0.0577714i	0.311855	−	0.950130i	$-0.399050\pi$
$821$	−114.507	−	47.4303i	−0.139472	−	0.0577714i	−0.451328	+	0.892358i	$0.649050\pi$
$822$		0			0
$823$	701.981	+	701.981i	0.852954	+	0.852954i	0.990496	−	0.137542i	$-0.0439202\pi$
$823$	701.981	+	701.981i	0.852954	+	0.852954i	−0.137542	+	0.990496i	$0.543920\pi$
$824$	269.425	−	1292.78i	0.326972	−	1.56890i
$825$		0			0
$826$	363.963	−	241.595i	0.440633	−	0.292488i
$827$	420.620	+	174.226i	0.508609	+	0.210673i	0.622205	−	0.782854i	$-0.286237\pi$
$827$	420.620	+	174.226i	0.508609	+	0.210673i	−0.113596	+	0.993527i	$0.536237\pi$
$828$		0			0
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.859893	−	0.510475i	$-0.829470\pi$
$829$	−917.677	+	380.114i	−1.10697	+	0.458521i	−0.247076	+	0.968996i	$0.579470\pi$
$830$	395.995	+	2022.91i	0.477102	+	2.43724i
$831$		0			0
$832$	1404.58	+	25.6157i	1.68819	+	0.0307881i
$833$	−24.2008			−0.0290526
$834$		0			0
$835$	579.897	+	1400.00i	0.694487	+	1.67664i
$836$	86.6949	+	212.952i	0.103702	+	0.254727i
$837$		0			0
$838$	−13.3522	−	20.1150i	−0.0159334	−	0.0240036i
$839$	−125.592	+	125.592i	−0.149693	+	0.149693i	−0.777981	−	0.628288i	$-0.783756\pi$
$839$	−125.592	+	125.592i	−0.149693	+	0.149693i	0.628288	+	0.777981i	$0.283756\pi$
$840$		0			0
$841$	−557.031	+	557.031i	−0.662344	+	0.662344i
$842$	33.6876	−	166.709i	0.0400090	−	0.197992i
$843$		0			0
$844$	−562.701	+	555.901i	−0.666707	+	0.658651i
$845$	−924.554	−	2232.07i	−1.09415	−	2.64150i
$846$		0			0
$847$	−633.819			−0.748311
$848$	467.379	−	186.971i	0.551155	−	0.220485i
$849$		0			0
$850$	66.9577	−	99.5529i	0.0787737	−	0.117121i
$851$	−274.282	+	113.611i	−0.322305	+	0.133503i
$852$		0			0
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.827659	−	0.561232i	$-0.189672\pi$
$853$	866.692	+	358.995i	1.01605	+	0.420862i	0.188392	+	0.982094i	$0.439672\pi$
$854$	174.486	−	863.475i	0.204316	−	1.01110i
$855$		0			0
$856$	−84.1429	−	444.141i	−0.0982977	−	0.518856i
$857$	559.264	+	559.264i	0.652584	+	0.652584i	0.953614	−	0.301031i	$-0.0973307\pi$
$857$	559.264	+	559.264i	0.652584	+	0.652584i	−0.301031	+	0.953614i	$0.597331\pi$
$858$		0			0
$859$	552.858	+	229.001i	0.643607	+	0.266591i	0.680522	−	0.732728i	$-0.261753\pi$
$859$	552.858	+	229.001i	0.643607	+	0.266591i	−0.0369150	+	0.999318i	$0.511753\pi$
$860$	2311.39	+	973.913i	2.68767	+	1.13246i
$861$		0			0
$862$	396.440	−	77.6051i	0.459907	−	0.0900291i
$863$			106.004i			0.122833i	0.998112	+	0.0614163i	$0.0195617\pi$
$863$			106.004i			0.122833i	−0.998112	+	0.0614163i	$0.980438\pi$
$864$		0			0
$865$	−1407.87			−1.62760
$866$	247.207	+	1262.84i	0.285458	+	1.45825i
$867$		0			0
$868$	−679.927	−	286.489i	−0.783326	−	0.330057i
$869$	−31.9616	+	77.1622i	−0.0367798	+	0.0887943i
$870$		0			0
$871$	−426.460	+	426.460i	−0.489621	+	0.489621i
$872$	−498.019	−	339.374i	−0.571123	−	0.389190i
$873$		0			0
$874$	−647.932	−	130.930i	−0.741340	−	0.149805i
$875$	−168.823	+	407.574i	−0.192940	+	0.465799i
$876$		0			0
$877$	135.124	+	326.217i	0.154075	+	0.371969i	0.982003	−	0.188864i	$-0.0604807\pi$
$877$	135.124	+	326.217i	0.154075	+	0.371969i	−0.827928	+	0.560834i	$0.810481\pi$
$878$	−513.874	−	345.623i	−0.585278	−	0.393649i
$879$		0			0
$880$	−460.625	−	5.60003i	−0.523437	−	0.00636367i
$881$		−	628.648i		−	0.713562i	−0.934188	−	0.356781i	$-0.883874\pi$
$881$		−	628.648i		−	0.713562i	0.934188	−	0.356781i	$-0.116126\pi$
$882$		0			0
$883$	816.843	−	338.347i	0.925077	−	0.383179i	0.131268	−	0.991347i	$-0.458095\pi$
$883$	816.843	−	338.347i	0.925077	−	0.383179i	0.793809	+	0.608167i	$0.208095\pi$
$884$	−108.129	+	106.822i	−0.122317	+	0.120839i
$885$		0			0
$886$	−585.149	−	118.243i	−0.660439	−	0.133457i
$887$	−22.4622	−	22.4622i	−0.0253238	−	0.0253238i	0.694332	−	0.719655i	$-0.255700\pi$
$887$	−22.4622	−	22.4622i	−0.0253238	−	0.0253238i	−0.719655	+	0.694332i	$0.755700\pi$
$888$		0			0
$889$	−235.831	−	235.831i	−0.265277	−	0.265277i
$890$	1110.74	−	737.300i	1.24802	−	0.828427i
$891$		0			0
$892$	264.568	+	649.867i	0.296600	+	0.728551i
$893$	231.958	−	96.0803i	0.259752	−	0.107593i
$894$		0			0
$895$		−	376.214i		−	0.420351i
$896$	407.339	+	638.630i	0.454619	+	0.712757i
$897$		0			0
$898$	518.483	−	101.496i	0.577376	−	0.113024i
$899$	87.0327	+	210.116i	0.0968106	+	0.233721i
$900$		0			0
$901$	−20.8429	+	50.3192i	−0.0231331	+	0.0558482i
$902$	108.327	+	163.195i	0.120097	+	0.180925i
$903$		0			0
$904$	570.503	+	870.904i	0.631087	+	0.963389i
$905$	−703.017	+	703.017i	−0.776814	+	0.776814i
$906$		0			0
$907$	554.178	−	1337.90i	0.611001	−	1.47509i	−0.250902	−	0.968012i	$-0.580727\pi$
$907$	554.178	−	1337.90i	0.611001	−	1.47509i	0.861903	−	0.507074i	$-0.169273\pi$
$908$	−1159.38	−	1173.56i	−1.27685	−	1.29247i
$909$		0			0
$910$	1119.82	−	1664.95i	1.23057	−	1.82962i
$911$	267.709			0.293863			0.146931	−	0.989147i	$-0.453060\pi$
$911$	267.709			0.293863			0.146931	+	0.989147i	$0.453060\pi$
$912$		0			0
$913$			497.447i			0.544849i
$914$	512.207	−	761.551i	0.560402	−	0.833207i
$915$		0			0
$916$	3.62526	−	596.406i	0.00395770	−	0.651098i
$917$	−560.945	−	232.351i	−0.611717	−	0.253382i
$918$		0			0
$919$	−191.361	−	191.361i	−0.208227	−	0.208227i	0.595286	−	0.803514i	$-0.297039\pi$
$919$	−191.361	−	191.361i	−0.208227	−	0.208227i	−0.803514	+	0.595286i	$0.797039\pi$
$920$	745.803	−	1094.44i	0.810656	−	1.18961i
$921$		0			0
$922$	134.537	+	202.679i	0.145918	+	0.219826i
$923$	923.507	+	382.529i	1.00055	+	0.414441i
$924$		0			0
$925$	−443.416	+	183.669i	−0.479368	+	0.198561i
$926$	−1182.00	+	231.382i	−1.27646	+	0.249873i
$927$		0			0
$928$	49.0256	−	228.282i	0.0528294	−	0.245994i
$929$	459.352			0.494458			0.247229	−	0.968957i	$-0.420480\pi$
$929$	459.352			0.494458			0.247229	+	0.968957i	$0.420480\pi$
$930$		0			0
$931$	82.4919	+	199.153i	0.0886057	+	0.213913i
$932$	−605.165	+	1436.24i	−0.649319	+	1.54103i
$933$		0			0
$934$	−590.085	+	391.694i	−0.631783	+	0.419372i
$935$	35.2434	−	35.2434i	0.0376935	−	0.0376935i
$936$		0			0
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	−0.775796	−	0.630984i	$-0.782651\pi$
$937$	−135.689	+	135.689i	−0.144812	+	0.144812i	0.630984	+	0.775796i	$0.282651\pi$
$938$	−318.754	−	64.4118i	−0.339823	−	0.0686692i
$939$		0			0
$940$	−3.05760	+	503.019i	−0.00325277	+	0.535126i
$941$	471.321	+	1137.87i	0.500873	+	1.20921i	0.949009	+	0.315249i	$0.102088\pi$
$941$	471.321	+	1137.87i	0.500873	+	1.20921i	−0.448136	+	0.893965i	$0.647912\pi$
$942$		0			0
$943$	−563.142			−0.597182
$944$	−548.310	+	219.347i	−0.580837	+	0.232359i
$945$		0			0
$946$	502.258	+	337.811i	0.530929	+	0.357094i
$947$	−300.223	+	124.357i	−0.317026	+	0.131316i	−0.535522	−	0.844521i	$-0.679885\pi$
$947$	−300.223	+	124.357i	−0.317026	+	0.131316i	0.218496	+	0.975838i	$0.429885\pi$
$948$		0			0
$949$	−818.776	−	339.148i	−0.862778	−	0.357374i
$950$	−1047.47	−	211.667i	−1.10260	−	0.222807i
$951$		0			0
$952$	−80.2327	−	16.7212i	−0.0842781	−	0.0175642i
$953$	−362.517	−	362.517i	−0.380395	−	0.380395i	0.490849	−	0.871245i	$-0.336687\pi$
$953$	−362.517	−	362.517i	−0.380395	−	0.380395i	−0.871245	+	0.490849i	$0.836687\pi$
$954$		0			0
$955$	−1279.28	−	529.894i	−1.33956	−	0.554863i
$956$	233.538	−	95.0757i	0.244287	−	0.0994516i
$957$		0			0
$958$	58.0258	+	296.421i	0.0605697	+	0.309416i
$959$		−	524.256i		−	0.546669i
$960$		0			0
$961$	−10.5357			−0.0109633
$962$	596.718	−	116.810i	0.620289	−	0.121425i
$963$		0			0
$964$	−293.154	−	720.086i	−0.304102	−	0.746977i
$965$	−531.792	+	1283.86i	−0.551079	+	1.33042i
$966$		0			0
$967$	642.315	−	642.315i	0.664235	−	0.664235i	−0.292141	−	0.956375i	$-0.594368\pi$
$967$	642.315	−	642.315i	0.664235	−	0.664235i	0.956375	+	0.292141i	$0.0943675\pi$
$968$	838.808	+	174.815i	0.866537	+	0.180594i
$969$		0			0
$970$	213.884	−	1058.45i	0.220499	−	1.09118i
$971$	−114.682	+	276.867i	−0.118107	+	0.285136i	−0.971867	−	0.235532i	$-0.924317\pi$
$971$	−114.682	+	276.867i	−0.118107	+	0.285136i	0.853760	+	0.520667i	$0.174317\pi$
$972$		0			0
$973$	68.8494	+	166.217i	0.0707599	+	0.170830i
$974$	604.410	−	898.640i	0.620545	−	0.922628i
$975$		0			0
$976$	−469.074	+	1094.61i	−0.480609	+	1.12153i
$977$		−	1952.32i		−	1.99828i	−0.0414975	−	0.999139i	$-0.513213\pi$
$977$		−	1952.32i		−	1.99828i	0.0414975	−	0.999139i	$-0.486787\pi$
$978$		0			0
$979$	297.240	−	123.121i	0.303616	−	0.125762i
$980$	−431.878	−	2.62517i	−0.440692	−	0.00267875i
$981$		0			0
$982$	−213.012	+	1054.13i	−0.216916	+	1.07345i
$983$	−437.102	−	437.102i	−0.444661	−	0.444661i	0.448914	−	0.893575i	$-0.351811\pi$
$983$	−437.102	−	437.102i	−0.444661	−	0.444661i	−0.893575	+	0.448914i	$0.851811\pi$
$984$		0			0
$985$	1331.41	+	1331.41i	1.35168	+	1.35168i
$986$	13.9712	+	21.0476i	0.0141696	+	0.0213465i
$987$		0			0
$988$	1247.63	+	525.692i	1.26278	+	0.532077i
$989$	−1607.75	+	665.952i	−1.62563	+	0.673359i
$990$		0			0
$991$			238.251i			0.240415i	0.992749	+	0.120208i	$0.0383560\pi$
$991$			238.251i			0.240415i	−0.992749	+	0.120208i	$0.961644\pi$
$992$	820.811	+	566.677i	0.827430	+	0.571247i
$993$		0			0
$994$	103.544	+	528.946i	0.104169	+	0.532139i
$995$	−550.836	−	1329.84i	−0.553604	−	1.33652i
$996$		0			0
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	−0.999161	−	0.0409509i	$-0.986961\pi$
$997$	−262.900	+	634.696i	−0.263691	+	0.636606i	0.735470	+	0.677557i	$0.236961\pi$
$998$	1090.94	−	724.156i	1.09312	−	0.725607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.235.7		28
3.2	odd	2		32.3.h.a.11.1	yes	28
12.11	even	2		128.3.h.a.79.5		28
24.5	odd	2		256.3.h.b.159.5		28
24.11	even	2		256.3.h.a.159.3		28
32.3	odd	8	inner	288.3.u.a.163.7		28
96.29	odd	8		128.3.h.a.47.5		28
96.35	even	8		32.3.h.a.3.1	✓	28
96.77	odd	8		256.3.h.a.95.3		28
96.83	even	8		256.3.h.b.95.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.1	✓	28	96.35	even	8
32.3.h.a.11.1	yes	28	3.2	odd	2
128.3.h.a.47.5		28	96.29	odd	8
128.3.h.a.79.5		28	12.11	even	2
256.3.h.a.95.3		28	96.77	odd	8
256.3.h.a.159.3		28	24.11	even	2
256.3.h.b.95.5		28	96.83	even	8
256.3.h.b.159.5		28	24.5	odd	2
288.3.u.a.163.7		28	32.3	odd	8	inner
288.3.u.a.235.7		28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.96275 - 0.384217i) q^{2} +(3.70475 - 1.50824i) q^{4} +(-2.95565 + 7.13556i) q^{5} +(-4.18452 + 4.18452i) q^{7} +(6.69200 - 4.38373i) q^{8} +O(q^{10})\)	\(q+(1.96275 - 0.384217i) q^{2} +(3.70475 - 1.50824i) q^{4} +(-2.95565 + 7.13556i) q^{5} +(-4.18452 + 4.18452i) q^{7} +(6.69200 - 4.38373i) q^{8} +(-3.05958 + 15.1409i) q^{10} +(-1.42655 + 3.44399i) q^{11} +(8.39996 + 20.2793i) q^{13} +(-6.60538 + 9.82091i) q^{14} +(11.4504 - 11.1753i) q^{16} +1.73115i q^{17} +(14.2459 - 5.90085i) q^{19} +(-0.187785 + 30.8933i) q^{20} +(-1.47671 + 7.30779i) q^{22} +(-15.1565 - 15.1565i) q^{23} +(-24.5027 - 24.5027i) q^{25} +(24.2787 + 36.5757i) q^{26} +(-9.19134 + 21.8139i) q^{28} +(6.74107 - 2.79224i) q^{29} +31.1695i q^{31} +(18.1805 - 26.3338i) q^{32} +(0.665136 + 3.39780i) q^{34} +(-17.4909 - 42.2268i) q^{35} +(5.30038 - 12.7962i) q^{37} +(25.6939 - 17.0554i) q^{38} +(11.5012 + 60.7079i) q^{40} +(18.5776 - 18.5776i) q^{41} +(31.0691 - 75.0074i) q^{43} +(-0.0906349 + 14.9107i) q^{44} +(-35.5718 - 23.9250i) q^{46} +16.2824 q^{47} +13.9797i q^{49} +(-57.5069 - 38.6782i) q^{50} +(61.7059 + 62.4607i) q^{52} +(29.0670 + 12.0399i) q^{53} +(-20.3584 - 20.3584i) q^{55} +(-9.65901 + 46.3466i) q^{56} +(12.1582 - 8.07050i) q^{58} +(-34.1002 - 14.1248i) q^{59} +(-68.7647 + 28.4833i) q^{61} +(11.9758 + 61.1778i) q^{62} +(25.5658 - 58.6719i) q^{64} -169.531 q^{65} +(10.5147 + 25.3846i) q^{67} +(2.61099 + 6.41347i) q^{68} +(-50.5545 - 76.1602i) q^{70} +(32.2012 - 32.2012i) q^{71} +(-28.5494 + 28.5494i) q^{73} +(5.48676 - 27.1523i) q^{74} +(43.8777 - 43.3475i) q^{76} +(-8.44203 - 20.3809i) q^{77} +22.4049 q^{79} +(45.8989 + 114.735i) q^{80} +(29.3252 - 43.6009i) q^{82} +(123.286 - 51.0669i) q^{83} +(-12.3527 - 5.11665i) q^{85} +(32.1616 - 159.158i) q^{86} +(5.55106 + 29.3008i) q^{88} +(-61.0281 - 61.0281i) q^{89} +(-120.009 - 49.7093i) q^{91} +(-79.0109 - 33.2915i) q^{92} +(31.9583 - 6.25599i) q^{94} +119.093i q^{95} -69.9064 q^{97} +(5.37122 + 27.4385i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

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