LMFDB - Embedded newform 528.3.i.d.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,3,Mod(353,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))

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

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

chi := DirichletCharacter("528.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	528.i (of order $2$, degree $1$, not 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:	$14.3869579582$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.3
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	528.353
Dual form			528.3.i.d.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68614 - 1.33591i) q^{3} +0.792287i q^{5} -6.74456 q^{7} +(5.43070 - 7.17687i) q^{9} +O(q^{10})$	\(q+(2.68614 - 1.33591i) q^{3} +0.792287i q^{5} -6.74456 q^{7} +(5.43070 - 7.17687i) q^{9} +3.31662i q^{11} +9.48913 q^{13} +(1.05842 + 2.12819i) q^{15} -29.2974i q^{17} +26.2337 q^{19} +(-18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +24.3723 q^{25} +(5.00000 - 26.5330i) q^{27} -25.9431i q^{29} +2.86141 q^{31} +(4.43070 + 8.90892i) q^{33} -5.34363i q^{35} -2.39403 q^{37} +(25.4891 - 12.6766i) q^{39} -17.6155i q^{41} -12.5109 q^{43} +(5.68614 + 4.30268i) q^{45} +41.6790i q^{47} -3.51087 q^{49} +(-39.1386 - 78.6969i) q^{51} +89.5865i q^{53} -2.62772 q^{55} +(70.4674 - 35.0458i) q^{57} -14.7585i q^{59} -63.4456 q^{61} +(-36.6277 + 48.4048i) q^{63} +7.51811i q^{65} +63.3288 q^{67} +(-35.9633 - 72.3123i) q^{69} +4.55134i q^{71} -53.7663 q^{73} +(65.4674 - 32.5591i) q^{75} -22.3692i q^{77} -55.6793 q^{79} +(-22.0149 - 77.9509i) q^{81} +65.3378i q^{83} +23.2119 q^{85} +(-34.6576 - 69.6868i) q^{87} -14.1341i q^{89} -64.0000 q^{91} +(7.68614 - 3.82257i) q^{93} +20.7846i q^{95} +149.285 q^{97} +(23.8030 + 18.0116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{3} - 4 q^{7} - 7 q^{9}+O(q^{10}) $ 4 * q + 5 * q^3 - 4 * q^7 - 7 * q^9	$ 4 q + 5 q^{3} - 4 q^{7} - 7 q^{9} - 8 q^{13} - 13 q^{15} + 36 q^{19} - 38 q^{21} + 86 q^{25} + 20 q^{27} - 46 q^{31} - 11 q^{33} - 90 q^{37} + 56 q^{39} - 96 q^{43} + 17 q^{45} - 60 q^{49} - 214 q^{51} - 22 q^{55} + 144 q^{57} - 24 q^{61} - 158 q^{63} + 58 q^{67} - 253 q^{69} - 284 q^{73} + 124 q^{75} + 76 q^{79} + 113 q^{81} - 68 q^{85} + 252 q^{87} - 256 q^{91} + 25 q^{93} + 218 q^{97} + 55 q^{99}+O(q^{100}) $ 4 * q + 5 * q^3 - 4 * q^7 - 7 * q^9 - 8 * q^13 - 13 * q^15 + 36 * q^19 - 38 * q^21 + 86 * q^25 + 20 * q^27 - 46 * q^31 - 11 * q^33 - 90 * q^37 + 56 * q^39 - 96 * q^43 + 17 * q^45 - 60 * q^49 - 214 * q^51 - 22 * q^55 + 144 * q^57 - 24 * q^61 - 158 * q^63 + 58 * q^67 - 253 * q^69 - 284 * q^73 + 124 * q^75 + 76 * q^79 + 113 * q^81 - 68 * q^85 + 252 * q^87 - 256 * q^91 + 25 * q^93 + 218 * q^97 + 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.68614	−	1.33591i	0.895380	−	0.445302i
$3$	2.68614	−	1.33591i	0.895380	−	0.445302i
$4$		0			0
$5$			0.792287i			0.158457i	0.996856	+	0.0792287i	$0.0252457\pi$
$5$			0.792287i			0.158457i	−0.996856	+	0.0792287i	$0.974754\pi$
$6$		0			0
$7$	−6.74456			−0.963509			−0.481754	−	0.876306i	$-0.660000\pi$
$7$	−6.74456			−0.963509			−0.481754	+	0.876306i	$0.660000\pi$
$8$		0			0
$9$	5.43070	−	7.17687i	0.603411	−	0.797430i
$10$		0			0
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$		0			0
$13$	9.48913			0.729933			0.364966	−	0.931021i	$-0.381080\pi$
$13$	9.48913			0.729933			0.364966	+	0.931021i	$0.381080\pi$
$14$		0			0
$15$	1.05842	+	2.12819i	0.0705615	+	0.141880i
$16$		0			0
$17$		−	29.2974i		−	1.72338i	−0.507439	−	0.861688i	$-0.669408\pi$
$17$		−	29.2974i		−	1.72338i	0.507439	−	0.861688i	$-0.330592\pi$
$18$		0			0
$19$	26.2337			1.38072			0.690360	−	0.723466i	$-0.257452\pi$
$19$	26.2337			1.38072			0.690360	+	0.723466i	$0.257452\pi$
$20$		0			0
$21$	−18.1168	+	9.01011i	−0.862707	+	0.429053i
$22$		0			0
$23$		−	26.9205i		−	1.17046i	−0.810868	−	0.585229i	$-0.801005\pi$
$23$		−	26.9205i		−	1.17046i	0.810868	−	0.585229i	$-0.198995\pi$
$24$		0			0
$25$	24.3723			0.974891
$26$		0			0
$27$	5.00000	−	26.5330i	0.185185	−	0.982704i
$28$		0			0
$29$		−	25.9431i		−	0.894589i	−0.894387	−	0.447295i	$-0.852388\pi$
$29$		−	25.9431i		−	0.894589i	0.894387	−	0.447295i	$-0.147612\pi$
$30$		0			0
$31$	2.86141			0.0923034			0.0461517	−	0.998934i	$-0.485304\pi$
$31$	2.86141			0.0923034			0.0461517	+	0.998934i	$0.485304\pi$
$32$		0			0
$33$	4.43070	+	8.90892i	0.134264	+	0.269967i
$34$		0			0
$35$		−	5.34363i		−	0.152675i
$36$		0			0
$37$	−2.39403			−0.0647035			−0.0323518	−	0.999477i	$-0.510300\pi$
$37$	−2.39403			−0.0647035			−0.0323518	+	0.999477i	$0.510300\pi$
$38$		0			0
$39$	25.4891	−	12.6766i	0.653567	−	0.325041i
$40$		0			0
$41$		−	17.6155i		−	0.429645i	−0.976653	−	0.214823i	$-0.931083\pi$
$41$		−	17.6155i		−	0.429645i	0.976653	−	0.214823i	$-0.0689174\pi$
$42$		0			0
$43$	−12.5109			−0.290951			−0.145475	−	0.989362i	$-0.546471\pi$
$43$	−12.5109			−0.290951			−0.145475	+	0.989362i	$0.546471\pi$
$44$		0			0
$45$	5.68614	+	4.30268i	0.126359	+	0.0956150i
$46$		0			0
$47$			41.6790i			0.886788i	0.896327	+	0.443394i	$0.146226\pi$
$47$			41.6790i			0.886788i	−0.896327	+	0.443394i	$0.853774\pi$
$48$		0			0
$49$	−3.51087			−0.0716505
$50$		0			0
$51$	−39.1386	−	78.6969i	−0.767423	−	1.54308i
$52$		0			0
$53$			89.5865i			1.69031i	0.534520	+	0.845156i	$0.320493\pi$
$53$			89.5865i			1.69031i	−0.534520	+	0.845156i	$0.679507\pi$
$54$		0			0
$55$	−2.62772			−0.0477767
$56$		0			0
$57$	70.4674	−	35.0458i	1.23627	−	0.614838i
$58$		0			0
$59$		−	14.7585i		−	0.250144i	−0.992148	−	0.125072i	$-0.960084\pi$
$59$		−	14.7585i		−	0.250144i	0.992148	−	0.125072i	$-0.0399162\pi$
$60$		0			0
$61$	−63.4456			−1.04009			−0.520046	−	0.854138i	$-0.674085\pi$
$61$	−63.4456			−1.04009			−0.520046	+	0.854138i	$0.674085\pi$
$62$		0			0
$63$	−36.6277	+	48.4048i	−0.581392	+	0.768331i
$64$		0			0
$65$			7.51811i			0.115663i
$66$		0			0
$67$	63.3288			0.945206			0.472603	−	0.881276i	$-0.343315\pi$
$67$	63.3288			0.945206			0.472603	+	0.881276i	$0.343315\pi$
$68$		0			0
$69$	−35.9633	−	72.3123i	−0.521208	−	1.04800i
$70$		0			0
$71$			4.55134i			0.0641034i	0.999486	+	0.0320517i	$0.0102041\pi$
$71$			4.55134i			0.0641034i	−0.999486	+	0.0320517i	$0.989796\pi$
$72$		0			0
$73$	−53.7663			−0.736525			−0.368262	−	0.929722i	$-0.620047\pi$
$73$	−53.7663			−0.736525			−0.368262	+	0.929722i	$0.620047\pi$
$74$		0			0
$75$	65.4674	−	32.5591i	0.872898	−	0.434121i
$76$		0			0
$77$		−	22.3692i		−	0.290509i
$78$		0			0
$79$	−55.6793			−0.704801			−0.352401	−	0.935849i	$-0.614635\pi$
$79$	−55.6793			−0.704801			−0.352401	+	0.935849i	$0.614635\pi$
$80$		0			0
$81$	−22.0149	−	77.9509i	−0.271789	−	0.962357i
$82$		0			0
$83$			65.3378i			0.787203i	0.919281	+	0.393601i	$0.128771\pi$
$83$			65.3378i			0.787203i	−0.919281	+	0.393601i	$0.871229\pi$
$84$		0			0
$85$	23.2119			0.273082
$86$		0			0
$87$	−34.6576	−	69.6868i	−0.398363	−	0.800998i
$88$		0			0
$89$		−	14.1341i		−	0.158810i	−0.996842	−	0.0794052i	$-0.974698\pi$
$89$		−	14.1341i		−	0.158810i	0.996842	−	0.0794052i	$-0.0253021\pi$
$90$		0			0
$91$	−64.0000			−0.703297
$92$		0			0
$93$	7.68614	−	3.82257i	0.0826467	−	0.0411029i
$94$		0			0
$95$			20.7846i			0.218785i
$96$		0			0
$97$	149.285			1.53902			0.769512	−	0.638633i	$-0.220500\pi$
$97$	149.285			1.53902			0.769512	+	0.638633i	$0.220500\pi$
$98$		0			0
$99$	23.8030	+	18.0116i	0.240434	+	0.181935i
$100$		0			0
$101$		−	20.0096i		−	0.198114i	−0.995082	−	0.0990572i	$-0.968417\pi$
$101$		−	20.0096i		−	0.198114i	0.995082	−	0.0990572i	$-0.0315827\pi$
$102$		0			0
$103$	180.424			1.75169			0.875844	−	0.482594i	$-0.160305\pi$
$103$	180.424			1.75169			0.875844	+	0.482594i	$0.160305\pi$
$104$		0			0
$105$	−7.13859	−	14.3537i	−0.0679866	−	0.136702i
$106$		0			0
$107$		−	64.5283i		−	0.603068i	−0.953455	−	0.301534i	$-0.902501\pi$
$107$		−	64.5283i		−	0.603068i	0.953455	−	0.301534i	$-0.0974987\pi$
$108$		0			0
$109$	110.277			1.01172			0.505859	−	0.862616i	$-0.331176\pi$
$109$	110.277			1.01172			0.505859	+	0.862616i	$0.331176\pi$
$110$		0			0
$111$	−6.43070	+	3.19820i	−0.0579343	+	0.0288126i
$112$		0			0
$113$			125.239i			1.10831i	0.832412	+	0.554157i	$0.186959\pi$
$113$			125.239i			1.10831i	−0.832412	+	0.554157i	$0.813041\pi$
$114$		0			0
$115$	21.3288			0.185468
$116$		0			0
$117$	51.5326	−	68.1022i	0.440450	−	0.582070i
$118$		0			0
$119$			197.598i			1.66049i
$120$		0			0
$121$	−11.0000			−0.0909091
$122$		0			0
$123$	−23.5326	−	47.3176i	−0.191322	−	0.384696i
$124$		0			0
$125$			39.1170i			0.312936i
$126$		0			0
$127$	−192.848			−1.51849			−0.759243	−	0.650807i	$-0.774431\pi$
$127$	−192.848			−1.51849			−0.759243	+	0.650807i	$0.774431\pi$
$128$		0			0
$129$	−33.6060	+	16.7134i	−0.260511	+	0.129561i
$130$		0			0
$131$		−	106.098i		−	0.809905i	−0.914338	−	0.404952i	$-0.867288\pi$
$131$		−	106.098i		−	0.809905i	0.914338	−	0.404952i	$-0.132712\pi$
$132$		0			0
$133$	−176.935			−1.33034
$134$		0			0
$135$	21.0217	+	3.96143i	0.155717	+	0.0293440i
$136$		0			0
$137$			195.297i			1.42552i	0.701407	+	0.712761i	$0.252556\pi$
$137$			195.297i			1.42552i	−0.701407	+	0.712761i	$0.747444\pi$
$138$		0			0
$139$	−6.93475			−0.0498903			−0.0249452	−	0.999689i	$-0.507941\pi$
$139$	−6.93475			−0.0498903			−0.0249452	+	0.999689i	$0.507941\pi$
$140$		0			0
$141$	55.6793	+	111.956i	0.394889	+	0.794012i
$142$		0			0
$143$			31.4719i			0.220083i
$144$		0			0
$145$	20.5544			0.141754
$146$		0			0
$147$	−9.43070	+	4.69020i	−0.0641544	+	0.0319061i
$148$		0			0
$149$		−	67.6975i		−	0.454345i	−0.973854	−	0.227173i	$-0.927052\pi$
$149$		−	67.6975i		−	0.454345i	0.973854	−	0.227173i	$-0.0729482\pi$
$150$		0			0
$151$	−28.2337			−0.186978			−0.0934890	−	0.995620i	$-0.529802\pi$
$151$	−28.2337			−0.186978			−0.0934890	+	0.995620i	$0.529802\pi$
$152$		0			0
$153$	−210.264	−	159.105i	−1.37427	−	1.03990i
$154$		0			0
$155$			2.26706i			0.0146262i
$156$		0			0
$157$	−67.7962			−0.431823			−0.215911	−	0.976413i	$-0.569272\pi$
$157$	−67.7962			−0.431823			−0.215911	+	0.976413i	$0.569272\pi$
$158$		0			0
$159$	119.679	+	240.642i	0.752700	+	1.51347i
$160$		0			0
$161$			181.567i			1.12775i
$162$		0			0
$163$	67.8695			0.416377			0.208189	−	0.978089i	$-0.433243\pi$
$163$	67.8695			0.416377			0.208189	+	0.978089i	$0.433243\pi$
$164$		0			0
$165$	−7.05842	+	3.51039i	−0.0427783	+	0.0212751i
$166$		0			0
$167$			56.2351i			0.336737i	0.985724	+	0.168369i	$0.0538499\pi$
$167$			56.2351i			0.336737i	−0.985724	+	0.168369i	$0.946150\pi$
$168$		0			0
$169$	−78.9565			−0.467198
$170$		0			0
$171$	142.467	−	188.276i	0.833143	−	1.10103i
$172$		0			0
$173$			224.536i			1.29789i	0.760833	+	0.648947i	$0.224791\pi$
$173$			224.536i			1.29789i	−0.760833	+	0.648947i	$0.775209\pi$
$174$		0			0
$175$	−164.380			−0.939316
$176$		0			0
$177$	−19.7160	−	39.6434i	−0.111390	−	0.223974i
$178$		0			0
$179$		−	140.461i		−	0.784697i	−0.919817	−	0.392349i	$-0.871663\pi$
$179$		−	140.461i		−	0.784697i	0.919817	−	0.392349i	$-0.128337\pi$
$180$		0			0
$181$	130.861			0.722991			0.361496	−	0.932374i	$-0.382266\pi$
$181$	130.861			0.722991			0.361496	+	0.932374i	$0.382266\pi$
$182$		0			0
$183$	−170.424	+	84.7575i	−0.931278	+	0.463156i
$184$		0			0
$185$		−	1.89676i		−	0.0102528i
$186$		0			0
$187$	97.1684			0.519617
$188$		0			0
$189$	−33.7228	+	178.953i	−0.178428	+	0.946844i
$190$		0			0
$191$			351.401i			1.83979i	0.392160	+	0.919897i	$0.371728\pi$
$191$			351.401i			1.83979i	−0.392160	+	0.919897i	$0.628272\pi$
$192$		0			0
$193$	−245.505			−1.27205			−0.636024	−	0.771669i	$-0.719422\pi$
$193$	−245.505			−1.27205			−0.636024	+	0.771669i	$0.719422\pi$
$194$		0			0
$195$	10.0435	+	20.1947i	0.0515051	+	0.103563i
$196$		0			0
$197$			6.15315i			0.0312343i	0.999878	+	0.0156171i	$0.00497129\pi$
$197$			6.15315i			0.0312343i	−0.999878	+	0.0156171i	$0.995029\pi$
$198$		0			0
$199$	−193.272			−0.971214			−0.485607	−	0.874177i	$-0.661401\pi$
$199$	−193.272			−0.971214			−0.485607	+	0.874177i	$0.661401\pi$
$200$		0			0
$201$	170.110	−	84.6014i	0.846318	−	0.420902i
$202$		0			0
$203$			174.975i			0.861945i
$204$		0			0
$205$	13.9565			0.0680805
$206$		0			0
$207$	−193.205	−	146.197i	−0.933358	−	0.706268i
$208$		0			0
$209$			87.0073i			0.416303i
$210$		0			0
$211$	106.788			0.506105			0.253052	−	0.967453i	$-0.418566\pi$
$211$	106.788			0.506105			0.253052	+	0.967453i	$0.418566\pi$
$212$		0			0
$213$	6.08017	+	12.2255i	0.0285454	+	0.0573969i
$214$		0			0
$215$		−	9.91220i		−	0.0461033i
$216$		0			0
$217$	−19.2989			−0.0889352
$218$		0			0
$219$	−144.424	+	71.8268i	−0.659470	+	0.327976i
$220$		0			0
$221$		−	278.007i		−	1.25795i
$222$		0			0
$223$	−76.7309			−0.344085			−0.172042	−	0.985090i	$-0.555037\pi$
$223$	−76.7309			−0.344085			−0.172042	+	0.985090i	$0.555037\pi$
$224$		0			0
$225$	132.359	−	174.917i	0.588261	−	0.777408i
$226$		0			0
$227$		−	48.2433i		−	0.212526i	−0.994338	−	0.106263i	$-0.966111\pi$
$227$		−	48.2433i		−	0.212526i	0.994338	−	0.106263i	$-0.0338885\pi$
$228$		0			0
$229$	−15.4158			−0.0673178			−0.0336589	−	0.999433i	$-0.510716\pi$
$229$	−15.4158			−0.0673178			−0.0336589	+	0.999433i	$0.510716\pi$
$230$		0			0
$231$	−29.8832	−	60.0868i	−0.129364	−	0.260116i
$232$		0			0
$233$			173.205i			0.743369i	0.928359	+	0.371685i	$0.121220\pi$
$233$			173.205i			0.743369i	−0.928359	+	0.371685i	$0.878780\pi$
$234$		0			0
$235$	−33.0217			−0.140518
$236$		0			0
$237$	−149.562	+	74.3824i	−0.631065	+	0.313850i
$238$		0			0
$239$			296.397i			1.24016i	0.784540	+	0.620078i	$0.212899\pi$
$239$			296.397i			1.24016i	−0.784540	+	0.620078i	$0.787101\pi$
$240$		0			0
$241$	46.7011			0.193780			0.0968902	−	0.995295i	$-0.469110\pi$
$241$	46.7011			0.193780			0.0968902	+	0.995295i	$0.469110\pi$
$242$		0			0
$243$	−163.270	−	179.977i	−0.671894	−	0.740647i
$244$		0			0
$245$		−	2.78162i		−	0.0113536i
$246$		0			0
$247$	248.935			1.00783
$248$		0			0
$249$	87.2853	+	175.507i	0.350543	+	0.704846i
$250$		0			0
$251$			207.788i			0.827841i	0.910313	+	0.413920i	$0.135841\pi$
$251$			207.788i			0.827841i	−0.910313	+	0.413920i	$0.864159\pi$
$252$		0			0
$253$	89.2853			0.352906
$254$		0			0
$255$	62.3505	−	31.0090i	0.244512	−	0.121604i
$256$		0			0
$257$			199.738i			0.777191i	0.921408	+	0.388595i	$0.127040\pi$
$257$			199.738i			0.777191i	−0.921408	+	0.388595i	$0.872960\pi$
$258$		0			0
$259$	16.1467			0.0623424
$260$		0			0
$261$	−186.190	−	140.889i	−0.713372	−	0.539805i
$262$		0			0
$263$			99.7592i			0.379313i	0.981851	+	0.189656i	$0.0607374\pi$
$263$			99.7592i			0.379313i	−0.981851	+	0.189656i	$0.939263\pi$
$264$		0			0
$265$	−70.9783			−0.267842
$266$		0			0
$267$	−18.8819	−	37.9663i	−0.0707187	−	0.142196i
$268$		0			0
$269$			50.3770i			0.187275i	0.995606	+	0.0936375i	$0.0298495\pi$
$269$			50.3770i			0.187275i	−0.995606	+	0.0936375i	$0.970151\pi$
$270$		0			0
$271$	124.380			0.458968			0.229484	−	0.973312i	$-0.426296\pi$
$271$	124.380			0.458968			0.229484	+	0.973312i	$0.426296\pi$
$272$		0			0
$273$	−171.913	+	85.4981i	−0.629718	+	0.313180i
$274$		0			0
$275$			80.8337i			0.293941i
$276$		0			0
$277$	293.723			1.06037			0.530186	−	0.847882i	$-0.322122\pi$
$277$	293.723			1.06037			0.530186	+	0.847882i	$0.322122\pi$
$278$		0			0
$279$	15.5395	−	20.5359i	0.0556970	−	0.0736055i
$280$		0			0
$281$		−	263.676i		−	0.938350i	−0.883105	−	0.469175i	$-0.844551\pi$
$281$		−	263.676i		−	0.938350i	0.883105	−	0.469175i	$-0.155449\pi$
$282$		0			0
$283$	−398.788			−1.40915			−0.704573	−	0.709632i	$-0.748861\pi$
$283$	−398.788			−1.40915			−0.704573	+	0.709632i	$0.748861\pi$
$284$		0			0
$285$	27.7663	+	55.8304i	0.0974257	+	0.195896i
$286$		0			0
$287$			118.809i			0.413967i
$288$		0			0
$289$	−569.337			−1.97002
$290$		0			0
$291$	401.001	−	199.431i	1.37801	−	0.685331i
$292$		0			0
$293$		−	348.839i		−	1.19058i	−0.803512	−	0.595288i	$-0.797038\pi$
$293$		−	348.839i		−	1.19058i	0.803512	−	0.595288i	$-0.202962\pi$
$294$		0			0
$295$	11.6930			0.0396372
$296$		0			0
$297$	88.0000	+	16.5831i	0.296296	+	0.0558354i
$298$		0			0
$299$		−	255.452i		−	0.854355i
$300$		0			0
$301$	84.3804			0.280333
$302$		0			0
$303$	−26.7309	−	53.7485i	−0.0882208	−	0.177388i
$304$		0			0
$305$		−	50.2671i		−	0.164810i
$306$		0			0
$307$	398.527			1.29813			0.649067	−	0.760731i	$-0.275160\pi$
$307$	398.527			1.29813			0.649067	+	0.760731i	$0.275160\pi$
$308$		0			0
$309$	484.644	−	241.030i	1.56843	−	0.780031i
$310$		0			0
$311$		−	440.346i		−	1.41590i	−0.706261	−	0.707951i	$-0.749620\pi$
$311$		−	440.346i		−	1.41590i	0.706261	−	0.707951i	$-0.250380\pi$
$312$		0			0
$313$	529.899			1.69297			0.846485	−	0.532413i	$-0.178715\pi$
$313$	529.899			1.69297			0.846485	+	0.532413i	$0.178715\pi$
$314$		0			0
$315$	−38.3505	−	29.0197i	−0.121748	−	0.0921259i
$316$		0			0
$317$		−	368.426i		−	1.16223i	−0.813822	−	0.581114i	$-0.802617\pi$
$317$		−	368.426i		−	1.16223i	0.813822	−	0.581114i	$-0.197383\pi$
$318$		0			0
$319$	86.0435			0.269729
$320$		0			0
$321$	−86.2038	−	173.332i	−0.268548	−	0.539975i
$322$		0			0
$323$		−	768.579i		−	2.37950i
$324$		0			0
$325$	231.272			0.711605
$326$		0			0
$327$	296.220	−	147.320i	0.905872	−	0.450520i
$328$		0			0
$329$		−	281.107i		−	0.854428i
$330$		0			0
$331$	115.649			0.349394			0.174697	−	0.984622i	$-0.444105\pi$
$331$	115.649			0.349394			0.174697	+	0.984622i	$0.444105\pi$
$332$		0			0
$333$	−13.0013	+	17.1816i	−0.0390429	+	0.0515965i
$334$		0			0
$335$			50.1746i			0.149775i
$336$		0			0
$337$	−53.2716			−0.158076			−0.0790380	−	0.996872i	$-0.525185\pi$
$337$	−53.2716			−0.158076			−0.0790380	+	0.996872i	$0.525185\pi$
$338$		0			0
$339$	167.308	+	336.411i	0.493535	+	0.992362i
$340$		0			0
$341$			9.49021i			0.0278305i
$342$		0			0
$343$	354.163			1.03254
$344$		0			0
$345$	57.2921	−	28.4933i	0.166064	−	0.0825892i
$346$		0			0
$347$		−	11.2082i		−	0.0323004i	−0.999870	−	0.0161502i	$-0.994859\pi$
$347$		−	11.2082i		−	0.0323004i	0.999870	−	0.0161502i	$-0.00514099\pi$
$348$		0			0
$349$	−214.016			−0.613227			−0.306613	−	0.951834i	$-0.599196\pi$
$349$	−214.016			−0.613227			−0.306613	+	0.951834i	$0.599196\pi$
$350$		0			0
$351$	47.4456	−	251.775i	0.135173	−	0.717308i
$352$		0			0
$353$			531.528i			1.50574i	0.658167	+	0.752872i	$0.271332\pi$
$353$			531.528i			1.50574i	−0.658167	+	0.752872i	$0.728668\pi$
$354$		0			0
$355$	−3.60597			−0.0101577
$356$		0			0
$357$	263.973	+	530.776i	0.739419	+	1.48677i
$358$		0			0
$359$			175.194i			0.488007i	0.969774	+	0.244003i	$0.0784608\pi$
$359$			175.194i			0.488007i	−0.969774	+	0.244003i	$0.921539\pi$
$360$		0			0
$361$	327.206			0.906389
$362$		0			0
$363$	−29.5475	+	14.6950i	−0.0813982	+	0.0404820i
$364$		0			0
$365$		−	42.5983i		−	0.116708i
$366$		0			0
$367$	−139.035			−0.378843			−0.189422	−	0.981896i	$-0.560661\pi$
$367$	−139.035			−0.378843			−0.189422	+	0.981896i	$0.560661\pi$
$368$		0			0
$369$	−126.424	−	95.6643i	−0.342612	−	0.259253i
$370$		0			0
$371$		−	604.222i		−	1.62863i
$372$		0			0
$373$	149.081			0.399682			0.199841	−	0.979828i	$-0.435957\pi$
$373$	149.081			0.399682			0.199841	+	0.979828i	$0.435957\pi$
$374$		0			0
$375$	52.2567	+	105.074i	0.139351	+	0.280197i
$376$		0			0
$377$		−	246.177i		−	0.652990i
$378$		0			0
$379$	−270.394			−0.713441			−0.356720	−	0.934211i	$-0.616105\pi$
$379$	−270.394			−0.713441			−0.356720	+	0.934211i	$0.616105\pi$
$380$		0			0
$381$	−518.016	+	257.627i	−1.35962	+	0.676186i
$382$		0			0
$383$		−	631.801i		−	1.64961i	−0.565416	−	0.824806i	$-0.691284\pi$
$383$		−	631.801i		−	1.64961i	0.565416	−	0.824806i	$-0.308716\pi$
$384$		0			0
$385$	17.7228			0.0460333
$386$		0			0
$387$	−67.9428	+	89.7889i	−0.175563	+	0.232013i
$388$		0			0
$389$		−	459.996i		−	1.18251i	−0.806485	−	0.591254i	$-0.798633\pi$
$389$		−	459.996i		−	1.18251i	0.806485	−	0.591254i	$-0.201367\pi$
$390$		0			0
$391$	−788.701			−2.01714
$392$		0			0
$393$	−141.736	−	284.993i	−0.360653	−	0.725173i
$394$		0			0
$395$		−	44.1140i		−	0.111681i
$396$		0			0
$397$	−561.272			−1.41378			−0.706891	−	0.707322i	$-0.749903\pi$
$397$	−561.272			−1.41378			−0.706891	+	0.707322i	$0.749903\pi$
$398$		0			0
$399$	−475.272	+	236.368i	−1.19116	+	0.592402i
$400$		0			0
$401$			179.845i			0.448491i	0.974533	+	0.224245i	$0.0719917\pi$
$401$			179.845i			0.448491i	−0.974533	+	0.224245i	$0.928008\pi$
$402$		0			0
$403$	27.1522			0.0673753
$404$		0			0
$405$	61.7595	−	17.4421i	0.152493	−	0.0430670i
$406$		0			0
$407$		−	7.94010i		−	0.0195088i
$408$		0			0
$409$	135.696			0.331774			0.165887	−	0.986145i	$-0.446951\pi$
$409$	135.696			0.331774			0.165887	+	0.986145i	$0.446951\pi$
$410$		0			0
$411$	260.898	+	524.594i	0.634789	+	1.27638i
$412$		0			0
$413$			99.5396i			0.241016i
$414$		0			0
$415$	−51.7663			−0.124738
$416$		0			0
$417$	−18.6277	+	9.26419i	−0.0446708	+	0.0222163i
$418$		0			0
$419$		−	50.3361i		−	0.120134i	−0.998194	−	0.0600669i	$-0.980869\pi$
$419$		−	50.3361i		−	0.120134i	0.998194	−	0.0600669i	$-0.0191314\pi$
$420$		0			0
$421$	−52.6849			−0.125142			−0.0625711	−	0.998041i	$-0.519930\pi$
$421$	−52.6849			−0.125142			−0.0625711	+	0.998041i	$0.519930\pi$
$422$		0			0
$423$	299.125	+	226.346i	0.707151	+	0.535098i
$424$		0			0
$425$		−	714.044i		−	1.68010i
$426$		0			0
$427$	427.913			1.00214
$428$		0			0
$429$	42.0435	+	84.5379i	0.0980035	+	0.197058i
$430$		0			0
$431$			496.807i			1.15268i	0.817209	+	0.576342i	$0.195520\pi$
$431$			496.807i			1.15268i	−0.817209	+	0.576342i	$0.804480\pi$
$432$		0			0
$433$	515.622			1.19081			0.595407	−	0.803424i	$-0.296991\pi$
$433$	515.622			1.19081			0.595407	+	0.803424i	$0.296991\pi$
$434$		0			0
$435$	55.2119	−	27.4587i	0.126924	−	0.0631235i
$436$		0			0
$437$		−	706.225i		−	1.61607i
$438$		0			0
$439$	25.1087			0.0571953			0.0285977	−	0.999591i	$-0.490896\pi$
$439$	25.1087			0.0571953			0.0285977	+	0.999591i	$0.490896\pi$
$440$		0			0
$441$	−19.0665	+	25.1971i	−0.0432347	+	0.0571363i
$442$		0			0
$443$			870.420i			1.96483i	0.186711	+	0.982415i	$0.440217\pi$
$443$			870.420i			1.96483i	−0.186711	+	0.982415i	$0.559783\pi$
$444$		0			0
$445$	11.1983			0.0251647
$446$		0			0
$447$	−90.4375	−	181.845i	−0.202321	−	0.406812i
$448$		0			0
$449$			575.642i			1.28205i	0.767519	+	0.641026i	$0.221491\pi$
$449$			575.642i			1.28205i	−0.767519	+	0.641026i	$0.778509\pi$
$450$		0			0
$451$	58.4239			0.129543
$452$		0			0
$453$	−75.8397	+	37.7176i	−0.167416	+	0.0832618i
$454$		0			0
$455$		−	50.7064i		−	0.111443i
$456$		0			0
$457$	25.5923			0.0560007			0.0280003	−	0.999608i	$-0.491086\pi$
$457$	25.5923			0.0560007			0.0280003	+	0.999608i	$0.491086\pi$
$458$		0			0
$459$	−777.348	−	146.487i	−1.69357	−	0.319144i
$460$		0			0
$461$			289.365i			0.627691i	0.949474	+	0.313845i	$0.101617\pi$
$461$			289.365i			0.627691i	−0.949474	+	0.313845i	$0.898383\pi$
$462$		0			0
$463$	201.052			0.434237			0.217118	−	0.976145i	$-0.430334\pi$
$463$	201.052			0.434237			0.217118	+	0.976145i	$0.430334\pi$
$464$		0			0
$465$	3.02858	+	6.08963i	0.00651307	+	0.0130960i
$466$		0			0
$467$			110.319i			0.236230i	0.993000	+	0.118115i	$0.0376852\pi$
$467$			110.319i			0.236230i	−0.993000	+	0.118115i	$0.962315\pi$
$468$		0			0
$469$	−427.125			−0.910714
$470$		0			0
$471$	−182.110	+	90.5694i	−0.386645	+	0.192292i
$472$		0			0
$473$		−	41.4939i		−	0.0877249i
$474$		0			0
$475$	639.375			1.34605
$476$		0			0
$477$	642.951	+	486.518i	1.34791	+	1.01995i
$478$		0			0
$479$		−	683.532i		−	1.42700i	−0.700656	−	0.713499i	$-0.747109\pi$
$479$		−	683.532i		−	1.42700i	0.700656	−	0.713499i	$-0.252891\pi$
$480$		0			0
$481$	−22.7173			−0.0472292
$482$		0			0
$483$	242.557	+	487.715i	0.502188	+	1.00976i
$484$		0			0
$485$			118.277i			0.243870i
$486$		0			0
$487$	130.101			0.267147			0.133574	−	0.991039i	$-0.457355\pi$
$487$	130.101			0.267147			0.133574	+	0.991039i	$0.457355\pi$
$488$		0			0
$489$	182.307	−	90.6674i	0.372816	−	0.185414i
$490$		0			0
$491$		−	796.580i		−	1.62236i	−0.584795	−	0.811181i	$-0.698825\pi$
$491$		−	796.580i		−	1.62236i	0.584795	−	0.811181i	$-0.301175\pi$
$492$		0			0
$493$	−760.065			−1.54171
$494$		0			0
$495$	−14.2704	+	18.8588i	−0.0288290	+	0.0380986i
$496$		0			0
$497$		−	30.6968i		−	0.0617642i
$498$		0			0
$499$	−490.032			−0.982029			−0.491014	−	0.871151i	$-0.663374\pi$
$499$	−490.032			−0.982029			−0.491014	+	0.871151i	$0.663374\pi$
$500$		0			0
$501$	75.1249	+	151.056i	0.149950	+	0.301508i
$502$		0			0
$503$		−	283.281i		−	0.563183i	−0.959534	−	0.281592i	$-0.909138\pi$
$503$		−	283.281i		−	0.563183i	0.959534	−	0.281592i	$-0.0908624\pi$
$504$		0			0
$505$	15.8533			0.0313927
$506$		0			0
$507$	−212.088	+	105.479i	−0.418320	+	0.208045i
$508$		0			0
$509$		−	243.650i		−	0.478683i	−0.970935	−	0.239342i	$-0.923068\pi$
$509$		−	243.650i		−	0.478683i	0.970935	−	0.239342i	$-0.0769316\pi$
$510$		0			0
$511$	362.630			0.709648
$512$		0			0
$513$	131.168	−	696.058i	0.255689	−	1.35684i
$514$		0			0
$515$			142.947i			0.277568i
$516$		0			0
$517$	−138.234			−0.267377
$518$		0			0
$519$	299.959	+	603.135i	0.577956	+	1.16211i
$520$		0			0
$521$			376.274i			0.722215i	0.932524	+	0.361107i	$0.117601\pi$
$521$			376.274i			0.722215i	−0.932524	+	0.361107i	$0.882399\pi$
$522$		0			0
$523$	−555.842			−1.06280			−0.531398	−	0.847122i	$-0.678333\pi$
$523$	−555.842			−1.06280			−0.531398	+	0.847122i	$0.678333\pi$
$524$		0			0
$525$	−441.549	+	219.597i	−0.841045	+	0.418280i
$526$		0			0
$527$		−	83.8317i		−	0.159074i
$528$		0			0
$529$	−195.715			−0.369971
$530$		0			0
$531$	−105.920	−	80.1490i	−0.199472	−	0.150940i
$532$		0			0
$533$		−	167.155i		−	0.313612i
$534$		0			0
$535$	51.1249			0.0955606
$536$		0			0
$537$	−187.643	−	377.298i	−0.349428	−	0.702602i
$538$		0			0
$539$		−	11.6443i		−	0.0216034i
$540$		0			0
$541$	932.206			1.72312			0.861559	−	0.507658i	$-0.169489\pi$
$541$	932.206			1.72312			0.861559	+	0.507658i	$0.169489\pi$
$542$		0			0
$543$	351.512	−	174.819i	0.647352	−	0.321950i
$544$		0			0
$545$			87.3712i			0.160314i
$546$		0			0
$547$	−736.983			−1.34732			−0.673659	−	0.739042i	$-0.735278\pi$
$547$	−736.983			−1.34732			−0.673659	+	0.739042i	$0.735278\pi$
$548$		0			0
$549$	−344.554	+	455.341i	−0.627604	+	0.829401i
$550$		0			0
$551$		−	680.583i		−	1.23518i
$552$		0			0
$553$	375.533			0.679083
$554$		0			0
$555$	−2.53389	−	5.09496i	−0.00456558	−	0.00918011i
$556$		0			0
$557$			635.659i			1.14122i	0.821221	+	0.570610i	$0.193293\pi$
$557$			635.659i			1.14122i	−0.821221	+	0.570610i	$0.806707\pi$
$558$		0			0
$559$	−118.717			−0.212374
$560$		0			0
$561$	261.008	−	129.808i	0.465255	−	0.231387i
$562$		0			0
$563$			800.352i			1.42158i	0.703402	+	0.710792i	$0.251663\pi$
$563$			800.352i			1.42158i	−0.703402	+	0.710792i	$0.748337\pi$
$564$		0			0
$565$	−99.2256			−0.175621
$566$		0			0
$567$	148.481	+	525.745i	0.261871	+	0.927239i
$568$		0			0
$569$			52.5450i			0.0923463i	0.998933	+	0.0461731i	$0.0147026\pi$
$569$			52.5450i			0.0923463i	−0.998933	+	0.0461731i	$0.985297\pi$
$570$		0			0
$571$	−10.1143			−0.0177133			−0.00885666	−	0.999961i	$-0.502819\pi$
$571$	−10.1143			−0.0177133			−0.00885666	+	0.999961i	$0.502819\pi$
$572$		0			0
$573$	469.439	+	943.912i	0.819265	+	1.64732i
$574$		0			0
$575$		−	656.115i		−	1.14107i
$576$		0			0
$577$	−88.2959			−0.153026			−0.0765129	−	0.997069i	$-0.524379\pi$
$577$	−88.2959			−0.153026			−0.0765129	+	0.997069i	$0.524379\pi$
$578$		0			0
$579$	−659.462	+	327.972i	−1.13897	+	0.566446i
$580$		0			0
$581$		−	440.675i		−	0.758477i
$582$		0			0
$583$	−297.125			−0.509648
$584$		0			0
$585$	53.9565	+	40.8286i	0.0922333	+	0.0697925i
$586$		0			0
$587$			752.212i			1.28145i	0.767770	+	0.640726i	$0.221366\pi$
$587$			752.212i			1.28145i	−0.767770	+	0.640726i	$0.778634\pi$
$588$		0			0
$589$	75.0652			0.127445
$590$		0			0
$591$	8.22004	+	16.5282i	0.0139087	+	0.0279665i
$592$		0			0
$593$			656.836i			1.10765i	0.832633	+	0.553825i	$0.186832\pi$
$593$			656.836i			1.10765i	−0.832633	+	0.553825i	$0.813168\pi$
$594$		0			0
$595$	−156.554			−0.263117
$596$		0			0
$597$	−519.155	+	258.193i	−0.869606	+	0.432484i
$598$		0			0
$599$		−	403.922i		−	0.674327i	−0.941446	−	0.337164i	$-0.890532\pi$
$599$		−	403.922i		−	0.674327i	0.941446	−	0.337164i	$-0.109468\pi$
$600$		0			0
$601$	−826.761			−1.37564			−0.687821	−	0.725880i	$-0.741433\pi$
$601$	−826.761			−1.37564			−0.687821	+	0.725880i	$0.741433\pi$
$602$		0			0
$603$	343.920	−	454.502i	0.570348	−	0.753735i
$604$		0			0
$605$		−	8.71516i		−	0.0144052i
$606$		0			0
$607$	1156.44			1.90517			0.952587	−	0.304268i	$-0.0984118\pi$
$607$	1156.44			1.90517			0.952587	+	0.304268i	$0.0984118\pi$
$608$		0			0
$609$	233.750	+	470.007i	0.383826	+	0.771768i
$610$		0			0
$611$			395.497i			0.647295i
$612$		0			0
$613$	−898.250			−1.46533			−0.732667	−	0.680587i	$-0.761725\pi$
$613$	−898.250			−1.46533			−0.732667	+	0.680587i	$0.761725\pi$
$614$		0			0
$615$	37.4891	−	18.6446i	0.0609579	−	0.0303164i
$616$		0			0
$617$		−	713.002i		−	1.15560i	−0.816180	−	0.577798i	$-0.803912\pi$
$617$		−	713.002i		−	1.15560i	0.816180	−	0.577798i	$-0.196088\pi$
$618$		0			0
$619$	40.4102			0.0652831			0.0326415	−	0.999467i	$-0.489608\pi$
$619$	40.4102			0.0652831			0.0326415	+	0.999467i	$0.489608\pi$
$620$		0			0
$621$	−714.282	−	134.603i	−1.15021	−	0.216751i
$622$		0			0
$623$			95.3285i			0.153015i
$624$		0			0
$625$	578.315			0.925304
$626$		0			0
$627$	116.234	+	233.714i	0.185381	+	0.372749i
$628$		0			0
$629$			70.1388i			0.111508i
$630$		0			0
$631$	748.502			1.18622			0.593108	−	0.805123i	$-0.297901\pi$
$631$	748.502			1.18622			0.593108	+	0.805123i	$0.297901\pi$
$632$		0			0
$633$	286.848	−	142.659i	0.453156	−	0.225370i
$634$		0			0
$635$		−	152.791i		−	0.240615i
$636$		0			0
$637$	−33.3151			−0.0523000
$638$		0			0
$639$	32.6644	+	24.7170i	0.0511180	+	0.0386807i
$640$		0			0
$641$			122.303i			0.190800i	0.995439	+	0.0954000i	$0.0304130\pi$
$641$			122.303i			0.190800i	−0.995439	+	0.0954000i	$0.969587\pi$
$642$		0			0
$643$	629.313			0.978713			0.489357	−	0.872084i	$-0.337232\pi$
$643$	629.313			0.978713			0.489357	+	0.872084i	$0.337232\pi$
$644$		0			0
$645$	−13.2418	−	26.6256i	−0.0205299	−	0.0412800i
$646$		0			0
$647$			185.830i			0.287218i	0.989635	+	0.143609i	$0.0458707\pi$
$647$			185.830i			0.287218i	−0.989635	+	0.143609i	$0.954129\pi$
$648$		0			0
$649$	48.9484			0.0754213
$650$		0			0
$651$	−51.8397	+	25.7816i	−0.0796308	+	0.0396031i
$652$		0			0
$653$			202.416i			0.309979i	0.987916	+	0.154990i	$0.0495344\pi$
$653$			202.416i			0.309979i	−0.987916	+	0.154990i	$0.950466\pi$
$654$		0			0
$655$	84.0597			0.128335
$656$		0			0
$657$	−291.989	+	385.874i	−0.444428	+	0.587327i
$658$		0			0
$659$			1094.02i			1.66012i	0.557674	+	0.830060i	$0.311694\pi$
$659$			1094.02i			1.66012i	−0.557674	+	0.830060i	$0.688306\pi$
$660$		0			0
$661$	1024.53			1.54997			0.774985	−	0.631980i	$-0.217758\pi$
$661$	1024.53			1.54997			0.774985	+	0.631980i	$0.217758\pi$
$662$		0			0
$663$	−371.391	−	746.765i	−0.560167	−	1.12634i
$664$		0			0
$665$		−	140.183i		−	0.210802i
$666$		0			0
$667$	−698.402			−1.04708
$668$		0			0
$669$	−206.110	+	102.505i	−0.308087	+	0.153222i
$670$		0			0
$671$		−	210.425i		−	0.313600i
$672$		0			0
$673$	259.489			0.385571			0.192785	−	0.981241i	$-0.438248\pi$
$673$	259.489			0.385571			0.192785	+	0.981241i	$0.438248\pi$
$674$		0			0
$675$	121.861	−	646.670i	0.180535	−	0.958029i
$676$		0			0
$677$		−	116.565i		−	0.172179i	−0.996287	−	0.0860895i	$-0.972563\pi$
$677$		−	116.565i		−	0.172179i	0.996287	−	0.0860895i	$-0.0274371\pi$
$678$		0			0
$679$	−1006.86			−1.48286
$680$		0			0
$681$	−64.4486	−	129.588i	−0.0946382	−	0.190291i
$682$		0			0
$683$			739.385i			1.08255i	0.840844	+	0.541277i	$0.182059\pi$
$683$			739.385i			1.08255i	−0.840844	+	0.541277i	$0.817941\pi$
$684$		0			0
$685$	−154.731			−0.225885
$686$		0			0
$687$	−41.4090	+	20.5941i	−0.0602750	+	0.0299768i
$688$		0			0
$689$			850.098i			1.23381i
$690$		0			0
$691$	−389.024			−0.562987			−0.281494	−	0.959563i	$-0.590830\pi$
$691$	−389.024			−0.562987			−0.281494	+	0.959563i	$0.590830\pi$
$692$		0			0
$693$	−160.541	−	121.480i	−0.231660	−	0.175296i
$694$		0			0
$695$		−	5.49431i		−	0.00790549i
$696$		0			0
$697$	−516.087			−0.740440
$698$		0			0
$699$	231.386	+	465.253i	0.331024	+	0.665598i
$700$		0			0
$701$		−	1164.12i		−	1.66066i	−0.557271	−	0.830330i	$-0.688152\pi$
$701$		−	1164.12i		−	1.66066i	0.557271	−	0.830330i	$-0.311848\pi$
$702$		0			0
$703$	−62.8043			−0.0893375
$704$		0			0
$705$	−88.7011	+	44.1140i	−0.125817	+	0.0625730i
$706$		0			0
$707$			134.956i			0.190885i
$708$		0			0
$709$	1329.93			1.87579			0.937893	−	0.346926i	$-0.112774\pi$
$709$	1329.93			1.87579			0.937893	+	0.346926i	$0.112774\pi$
$710$		0			0
$711$	−302.378	+	399.603i	−0.425285	+	0.562030i
$712$		0			0
$713$		−	77.0306i		−	0.108037i
$714$		0			0
$715$	−24.9348			−0.0348738
$716$		0			0
$717$	395.959	+	796.164i	0.552244	+	1.11041i
$718$		0			0
$719$			838.618i			1.16637i	0.812340	+	0.583184i	$0.198193\pi$
$719$			838.618i			1.16637i	−0.812340	+	0.583184i	$0.801807\pi$
$720$		0			0
$721$	−1216.88			−1.68777
$722$		0			0
$723$	125.446	−	62.3883i	0.173507	−	0.0862909i
$724$		0			0
$725$		−	632.292i		−	0.872127i
$726$		0			0
$727$	−154.628			−0.212693			−0.106346	−	0.994329i	$-0.533915\pi$
$727$	−154.628			−0.212693			−0.106346	+	0.994329i	$0.533915\pi$
$728$		0			0
$729$	−679.000	−	265.330i	−0.931413	−	0.363964i
$730$		0			0
$731$			366.536i			0.501417i
$732$		0			0
$733$	445.022			0.607124			0.303562	−	0.952812i	$-0.401824\pi$
$733$	445.022			0.607124			0.303562	+	0.952812i	$0.401824\pi$
$734$		0			0
$735$	−3.71599	−	7.47182i	−0.00505576	−	0.0101657i
$736$		0			0
$737$			210.038i			0.284990i
$738$		0			0
$739$	−61.3586			−0.0830293			−0.0415146	−	0.999138i	$-0.513218\pi$
$739$	−61.3586			−0.0830293			−0.0415146	+	0.999138i	$0.513218\pi$
$740$		0			0
$741$	668.674	−	332.554i	0.902394	−	0.448790i
$742$		0			0
$743$		−	723.250i		−	0.973419i	−0.873564	−	0.486709i	$-0.838197\pi$
$743$		−	723.250i		−	0.973419i	0.873564	−	0.486709i	$-0.161803\pi$
$744$		0			0
$745$	53.6358			0.0719944
$746$		0			0
$747$	468.921	+	354.830i	0.627739	+	0.475007i
$748$		0			0
$749$			435.215i			0.581062i
$750$		0			0
$751$	−1286.37			−1.71287			−0.856436	−	0.516253i	$-0.827326\pi$
$751$	−1286.37			−1.71287			−0.856436	+	0.516253i	$0.827326\pi$
$752$		0			0
$753$	277.585	+	558.148i	0.368639	+	0.741232i
$754$		0			0
$755$		−	22.3692i		−	0.0296281i
$756$		0			0
$757$	−272.717			−0.360261			−0.180130	−	0.983643i	$-0.557652\pi$
$757$	−272.717			−0.360261			−0.180130	+	0.983643i	$0.557652\pi$
$758$		0			0
$759$	239.833	−	119.277i	0.315985	−	0.157150i
$760$		0			0
$761$			476.634i			0.626326i	0.949699	+	0.313163i	$0.101389\pi$
$761$			476.634i			0.626326i	−0.949699	+	0.313163i	$0.898611\pi$
$762$		0			0
$763$	−743.771			−0.974799
$764$		0			0
$765$	126.057	−	166.589i	0.164781	−	0.217763i
$766$		0			0
$767$		−	140.045i		−	0.182588i
$768$		0			0
$769$	−22.4401			−0.0291808			−0.0145904	−	0.999894i	$-0.504644\pi$
$769$	−22.4401			−0.0291808			−0.0145904	+	0.999894i	$0.504644\pi$
$770$		0			0
$771$	266.832	+	536.525i	0.346085	+	0.695881i
$772$		0			0
$773$		−	1227.79i		−	1.58834i	−0.607694	−	0.794171i	$-0.707905\pi$
$773$		−	1227.79i		−	1.58834i	0.607694	−	0.794171i	$-0.292095\pi$
$774$		0			0
$775$	69.7390			0.0899858
$776$		0			0
$777$	43.3723	−	21.5705i	0.0558202	−	0.0277612i
$778$		0			0
$779$		−	462.119i		−	0.593220i
$780$		0			0
$781$	−15.0951			−0.0193279
$782$		0			0
$783$	−688.348	−	129.715i	−0.879116	−	0.165665i
$784$		0			0
$785$		−	53.7140i		−	0.0684255i
$786$		0			0
$787$	−872.277			−1.10836			−0.554179	−	0.832398i	$-0.686968\pi$
$787$	−872.277			−1.10836			−0.554179	+	0.832398i	$0.686968\pi$
$788$		0			0
$789$	133.269	+	267.967i	0.168909	+	0.339629i
$790$		0			0
$791$		−	844.685i		−	1.06787i
$792$		0			0
$793$	−602.043			−0.759197
$794$		0			0
$795$	−190.658	+	94.8204i	−0.239821	+	0.119271i
$796$		0			0
$797$		−	55.7659i		−	0.0699697i	−0.999388	−	0.0349849i	$-0.988862\pi$
$797$		−	55.7659i		−	0.0699697i	0.999388	−	0.0349849i	$-0.0111383\pi$
$798$		0			0
$799$	1221.09			1.52827
$800$		0			0
$801$	−101.439	−	76.7583i	−0.126640	−	0.0958280i
$802$		0			0
$803$		−	178.323i		−	0.222071i
$804$		0			0
$805$	−143.853			−0.178700
$806$		0			0
$807$	67.2989	+	135.320i	0.0833940	+	0.167682i
$808$		0			0
$809$			1325.11i			1.63796i	0.573819	+	0.818982i	$0.305461\pi$
$809$			1325.11i			1.63796i	−0.573819	+	0.818982i	$0.694539\pi$
$810$		0			0
$811$	1028.13			1.26773			0.633866	−	0.773443i	$-0.281467\pi$
$811$	1028.13			1.26773			0.633866	+	0.773443i	$0.281467\pi$
$812$		0			0
$813$	334.103	−	166.161i	0.410951	−	0.204380i
$814$		0			0
$815$			53.7721i			0.0659781i
$816$		0			0
$817$	−328.206			−0.401721
$818$		0			0
$819$	−347.565	+	459.320i	−0.424377	+	0.560830i
$820$		0			0
$821$		−	892.085i		−	1.08658i	−0.839544	−	0.543292i	$-0.817178\pi$
$821$		−	892.085i		−	1.08658i	0.839544	−	0.543292i	$-0.182822\pi$
$822$		0			0
$823$	415.301			0.504619			0.252310	−	0.967647i	$-0.418810\pi$
$823$	415.301			0.504619			0.252310	+	0.967647i	$0.418810\pi$
$824$		0			0
$825$	107.986	+	217.131i	0.130893	+	0.263189i
$826$		0			0
$827$		−	464.560i		−	0.561741i	−0.959746	−	0.280871i	$-0.909377\pi$
$827$		−	464.560i		−	0.561741i	0.959746	−	0.280871i	$-0.0906232\pi$
$828$		0			0
$829$	−886.193			−1.06899			−0.534495	−	0.845172i	$-0.679498\pi$
$829$	−886.193			−1.06899			−0.534495	+	0.845172i	$0.679498\pi$
$830$		0			0
$831$	788.981	−	392.386i	0.949435	−	0.472186i
$832$		0			0
$833$			102.859i			0.123481i
$834$		0			0
$835$	−44.5544			−0.0533585
$836$		0			0
$837$	14.3070	−	75.9217i	0.0170932	−	0.0907069i
$838$		0			0
$839$		−	163.482i		−	0.194854i	−0.995243	−	0.0974270i	$-0.968939\pi$
$839$		−	163.482i		−	0.194854i	0.995243	−	0.0974270i	$-0.0310612\pi$
$840$		0			0
$841$	167.956			0.199710
$842$		0			0
$843$	−352.247	−	708.272i	−0.417850	−	0.840180i
$844$		0			0
$845$		−	62.5562i		−	0.0740310i
$846$		0			0
$847$	74.1902			0.0875917
$848$		0			0
$849$	−1071.20	+	532.744i	−1.26172	+	0.627496i
$850$		0			0
$851$			64.4486i			0.0757327i
$852$		0			0
$853$	−451.647			−0.529481			−0.264740	−	0.964320i	$-0.585286\pi$
$853$	−451.647			−0.529481			−0.264740	+	0.964320i	$0.585286\pi$
$854$		0			0
$855$	149.168	+	112.875i	0.174466	+	0.132018i
$856$		0			0
$857$		−	233.720i		−	0.272719i	−0.990659	−	0.136360i	$-0.956460\pi$
$857$		−	233.720i		−	0.272719i	0.990659	−	0.136360i	$-0.0435402\pi$
$858$		0			0
$859$	694.225			0.808178			0.404089	−	0.914720i	$-0.367589\pi$
$859$	694.225			0.808178			0.404089	+	0.914720i	$0.367589\pi$
$860$		0			0
$861$	158.717	+	319.137i	0.184341	+	0.370658i
$862$		0			0
$863$			1143.39i			1.32490i	0.749106	+	0.662450i	$0.230483\pi$
$863$			1143.39i			1.32490i	−0.749106	+	0.662450i	$0.769517\pi$
$864$		0			0
$865$	−177.897			−0.205661
$866$		0			0
$867$	−1529.32	+	760.581i	−1.76392	+	0.877256i
$868$		0			0
$869$		−	184.667i		−	0.212506i
$870$		0			0
$871$	600.935			0.689937
$872$		0			0
$873$	810.724	−	1071.40i	0.928664	−	1.22726i
$874$		0			0
$875$		−	263.827i		−	0.301517i
$876$		0			0
$877$	−1080.36			−1.23188			−0.615940	−	0.787793i	$-0.711223\pi$
$877$	−1080.36			−1.23188			−0.615940	+	0.787793i	$0.711223\pi$
$878$		0			0
$879$	−466.016	−	937.030i	−0.530166	−	1.06602i
$880$		0			0
$881$		−	638.008i		−	0.724186i	−0.932142	−	0.362093i	$-0.882062\pi$
$881$		−	638.008i		−	0.724186i	0.932142	−	0.362093i	$-0.117938\pi$
$882$		0			0
$883$	972.195			1.10101			0.550507	−	0.834831i	$-0.314434\pi$
$883$	972.195			1.10101			0.550507	+	0.834831i	$0.314434\pi$
$884$		0			0
$885$	31.4090	−	15.6207i	0.0354903	−	0.0176505i
$886$		0			0
$887$			525.975i			0.592982i	0.955036	+	0.296491i	$0.0958165\pi$
$887$			525.975i			0.592982i	−0.955036	+	0.296491i	$0.904183\pi$
$888$		0			0
$889$	1300.67			1.46308
$890$		0			0
$891$	258.534	−	73.0152i	0.290161	−	0.0819475i
$892$		0			0
$893$			1093.39i			1.22441i
$894$		0			0
$895$	111.285			0.124341
$896$		0			0
$897$	−341.261	−	686.181i	−0.380447	−	0.764973i
$898$		0			0
$899$		−	74.2337i		−	0.0825737i
$900$		0			0
$901$	2624.65			2.91304
$902$		0			0
$903$	226.658	−	112.724i	0.251005	−	0.124833i
$904$		0			0
$905$			103.680i			0.114563i
$906$		0			0
$907$	574.706			0.633634			0.316817	−	0.948487i	$-0.397386\pi$
$907$	574.706			0.633634			0.316817	+	0.948487i	$0.397386\pi$
$908$		0			0
$909$	−143.606	−	108.666i	−0.157982	−	0.119545i
$910$		0			0
$911$		−	1279.17i		−	1.40413i	−0.712111	−	0.702067i	$-0.752261\pi$
$911$		−	1279.17i		−	1.40413i	0.712111	−	0.702067i	$-0.247739\pi$
$912$		0			0
$913$	−216.701			−0.237351
$914$		0			0
$915$	−67.1522	−	135.025i	−0.0733904	−	0.147568i
$916$		0			0
$917$			715.581i			0.780351i
$918$		0			0
$919$	481.929			0.524406			0.262203	−	0.965013i	$-0.415551\pi$
$919$	481.929			0.524406			0.262203	+	0.965013i	$0.415551\pi$
$920$		0			0
$921$	1070.50	−	532.395i	1.16232	−	0.578062i
$922$		0			0
$923$			43.1883i			0.0467912i
$924$		0			0
$925$	−58.3480			−0.0630789
$926$		0			0
$927$	979.829	−	1294.88i	1.05699	−	1.39685i
$928$		0			0
$929$			1112.26i			1.19726i	0.801024	+	0.598632i	$0.204289\pi$
$929$			1112.26i			1.19726i	−0.801024	+	0.598632i	$0.795711\pi$
$930$		0			0
$931$	−92.1032			−0.0989293
$932$		0			0
$933$	−588.261	−	1182.83i	−0.630505	−	1.26777i
$934$		0			0
$935$			76.9853i			0.0823372i
$936$		0			0
$937$	1743.58			1.86081			0.930406	−	0.366530i	$-0.119454\pi$
$937$	1743.58			1.86081			0.930406	+	0.366530i	$0.119454\pi$
$938$		0			0
$939$	1423.38	−	707.896i	1.51585	−	0.753883i
$940$		0			0
$941$		−	836.194i		−	0.888623i	−0.895872	−	0.444311i	$-0.853448\pi$
$941$		−	836.194i		−	0.888623i	0.895872	−	0.444311i	$-0.146552\pi$
$942$		0			0
$943$	−474.217			−0.502882
$944$		0			0
$945$	−141.783	−	26.7181i	−0.150034	−	0.0282732i
$946$		0			0
$947$		−	114.725i		−	0.121145i	−0.998164	−	0.0605726i	$-0.980707\pi$
$947$		−	114.725i		−	0.121145i	0.998164	−	0.0605726i	$-0.0192927\pi$
$948$		0			0
$949$	−510.195			−0.537614
$950$		0			0
$951$	−492.183	−	989.645i	−0.517543	−	1.04064i
$952$		0			0
$953$		−	327.059i		−	0.343189i	−0.985168	−	0.171595i	$-0.945108\pi$
$953$		−	327.059i		−	0.343189i	0.985168	−	0.171595i	$-0.0548919\pi$
$954$		0			0
$955$	−278.410			−0.291529
$956$		0			0
$957$	231.125	−	114.946i	0.241510	−	0.120111i
$958$		0			0
$959$		−	1317.19i		−	1.37350i
$960$		0			0
$961$	−952.812			−0.991480
$962$		0			0
$963$	−463.111	−	350.434i	−0.480905	−	0.363898i
$964$		0			0
$965$		−	194.511i		−	0.201565i
$966$		0			0
$967$	−168.674			−0.174430			−0.0872150	−	0.996190i	$-0.527797\pi$
$967$	−168.674			−0.174430			−0.0872150	+	0.996190i	$0.527797\pi$
$968$		0			0
$969$	−1026.75	−	2064.51i	−1.05960	−	2.13056i
$970$		0			0
$971$			81.7370i			0.0841782i	0.999114	+	0.0420891i	$0.0134013\pi$
$971$			81.7370i			0.0841782i	−0.999114	+	0.0420891i	$0.986599\pi$
$972$		0			0
$973$	46.7719			0.0480698
$974$		0			0
$975$	621.228	−	308.957i	0.637157	−	0.316879i
$976$		0			0
$977$		−	20.3562i		−	0.0208354i	−0.999946	−	0.0104177i	$-0.996684\pi$
$977$		−	20.3562i		−	0.0208354i	0.999946	−	0.0104177i	$-0.00331612\pi$
$978$		0			0
$979$	46.8776			0.0478831
$980$		0			0
$981$	598.883	−	791.445i	0.610482	−	0.806774i
$982$		0			0
$983$		−	797.407i		−	0.811197i	−0.914051	−	0.405598i	$-0.867063\pi$
$983$		−	797.407i		−	0.811197i	0.914051	−	0.405598i	$-0.132937\pi$
$984$		0			0
$985$	−4.87506			−0.00494930
$986$		0			0
$987$	−375.533	−	755.092i	−0.380479	−	0.765038i
$988$		0			0
$989$			336.799i			0.340545i
$990$		0			0
$991$	−609.620			−0.615156			−0.307578	−	0.951523i	$-0.599519\pi$
$991$	−609.620			−0.615156			−0.307578	+	0.951523i	$0.599519\pi$
$992$		0			0
$993$	310.651	−	154.497i	0.312841	−	0.155586i
$994$		0			0
$995$		−	153.127i		−	0.153896i
$996$		0			0
$997$	1771.28			1.77661			0.888303	−	0.459257i	$-0.151884\pi$
$997$	1771.28			1.77661			0.888303	+	0.459257i	$0.151884\pi$
$998$		0			0
$999$	−11.9702	+	63.5208i	−0.0119821	+	0.0635844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.3.i.d.353.3		4
3.2	odd	2	inner	528.3.i.d.353.4		4
4.3	odd	2		33.3.b.b.23.4	yes	4
12.11	even	2		33.3.b.b.23.1	✓	4
44.3	odd	10		363.3.h.m.251.4		16
44.7	even	10		363.3.h.l.269.4		16
44.15	odd	10		363.3.h.m.269.1		16
44.19	even	10		363.3.h.l.251.1		16
44.27	odd	10		363.3.h.m.245.1		16
44.31	odd	10		363.3.h.m.323.4		16
44.35	even	10		363.3.h.l.323.1		16
44.39	even	10		363.3.h.l.245.4		16
44.43	even	2		363.3.b.h.122.1		4
132.35	odd	10		363.3.h.l.323.4		16
132.47	even	10		363.3.h.m.251.1		16
132.59	even	10		363.3.h.m.269.4		16
132.71	even	10		363.3.h.m.245.4		16
132.83	odd	10		363.3.h.l.245.1		16
132.95	odd	10		363.3.h.l.269.1		16
132.107	odd	10		363.3.h.l.251.4		16
132.119	even	10		363.3.h.m.323.1		16
132.131	odd	2		363.3.b.h.122.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.1	✓	4	12.11	even	2
33.3.b.b.23.4	yes	4	4.3	odd	2
363.3.b.h.122.1		4	44.43	even	2
363.3.b.h.122.4		4	132.131	odd	2
363.3.h.l.245.1		16	132.83	odd	10
363.3.h.l.245.4		16	44.39	even	10
363.3.h.l.251.1		16	44.19	even	10
363.3.h.l.251.4		16	132.107	odd	10
363.3.h.l.269.1		16	132.95	odd	10
363.3.h.l.269.4		16	44.7	even	10
363.3.h.l.323.1		16	44.35	even	10
363.3.h.l.323.4		16	132.35	odd	10
363.3.h.m.245.1		16	44.27	odd	10
363.3.h.m.245.4		16	132.71	even	10
363.3.h.m.251.1		16	132.47	even	10
363.3.h.m.251.4		16	44.3	odd	10
363.3.h.m.269.1		16	44.15	odd	10
363.3.h.m.269.4		16	132.59	even	10
363.3.h.m.323.1		16	132.119	even	10
363.3.h.m.323.4		16	44.31	odd	10
528.3.i.d.353.3		4	1.1	even	1	trivial
528.3.i.d.353.4		4	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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	528.i (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.68614 - 1.33591i) q^{3} +0.792287i q^{5} -6.74456 q^{7} +(5.43070 - 7.17687i) q^{9} +O(q^{10})\)	\(q+(2.68614 - 1.33591i) q^{3} +0.792287i q^{5} -6.74456 q^{7} +(5.43070 - 7.17687i) q^{9} +3.31662i q^{11} +9.48913 q^{13} +(1.05842 + 2.12819i) q^{15} -29.2974i q^{17} +26.2337 q^{19} +(-18.1168 + 9.01011i) q^{21} -26.9205i q^{23} +24.3723 q^{25} +(5.00000 - 26.5330i) q^{27} -25.9431i q^{29} +2.86141 q^{31} +(4.43070 + 8.90892i) q^{33} -5.34363i q^{35} -2.39403 q^{37} +(25.4891 - 12.6766i) q^{39} -17.6155i q^{41} -12.5109 q^{43} +(5.68614 + 4.30268i) q^{45} +41.6790i q^{47} -3.51087 q^{49} +(-39.1386 - 78.6969i) q^{51} +89.5865i q^{53} -2.62772 q^{55} +(70.4674 - 35.0458i) q^{57} -14.7585i q^{59} -63.4456 q^{61} +(-36.6277 + 48.4048i) q^{63} +7.51811i q^{65} +63.3288 q^{67} +(-35.9633 - 72.3123i) q^{69} +4.55134i q^{71} -53.7663 q^{73} +(65.4674 - 32.5591i) q^{75} -22.3692i q^{77} -55.6793 q^{79} +(-22.0149 - 77.9509i) q^{81} +65.3378i q^{83} +23.2119 q^{85} +(-34.6576 - 69.6868i) q^{87} -14.1341i q^{89} -64.0000 q^{91} +(7.68614 - 3.82257i) q^{93} +20.7846i q^{95} +149.285 q^{97} +(23.8030 + 18.0116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{3} - 4 q^{7} - 7 q^{9}+O(q^{10}) \) 4 * q + 5 * q^3 - 4 * q^7 - 7 * q^9	\( 4 q + 5 q^{3} - 4 q^{7} - 7 q^{9} - 8 q^{13} - 13 q^{15} + 36 q^{19} - 38 q^{21} + 86 q^{25} + 20 q^{27} - 46 q^{31} - 11 q^{33} - 90 q^{37} + 56 q^{39} - 96 q^{43} + 17 q^{45} - 60 q^{49} - 214 q^{51} - 22 q^{55} + 144 q^{57} - 24 q^{61} - 158 q^{63} + 58 q^{67} - 253 q^{69} - 284 q^{73} + 124 q^{75} + 76 q^{79} + 113 q^{81} - 68 q^{85} + 252 q^{87} - 256 q^{91} + 25 q^{93} + 218 q^{97} + 55 q^{99}+O(q^{100}) \) 4 * q + 5 * q^3 - 4 * q^7 - 7 * q^9 - 8 * q^13 - 13 * q^15 + 36 * q^19 - 38 * q^21 + 86 * q^25 + 20 * q^27 - 46 * q^31 - 11 * q^33 - 90 * q^37 + 56 * q^39 - 96 * q^43 + 17 * q^45 - 60 * q^49 - 214 * q^51 - 22 * q^55 + 144 * q^57 - 24 * q^61 - 158 * q^63 + 58 * q^67 - 253 * q^69 - 284 * q^73 + 124 * q^75 + 76 * q^79 + 113 * q^81 - 68 * q^85 + 252 * q^87 - 256 * q^91 + 25 * q^93 + 218 * q^97 + 55 * q^99

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