LMFDB - Embedded newform 432.4.i.b.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,4,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, 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:	$25.4888251225$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} - 9x + 81 $ x^4 - x^3 - 8x^2 - 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.2
Root			$-2.31174 + 1.91203i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.4.i.b.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.43521 - 9.41407i) q^{5} +(12.4352 + 21.5384i) q^{7} +O(q^{10})$	$q+(5.43521 - 9.41407i) q^{5} +(12.4352 + 21.5384i) q^{7} +(21.3704 + 37.0147i) q^{11} +(-7.56479 + 13.1026i) q^{13} +13.8704 q^{17} -143.352 q^{19} +(-9.56479 + 16.5667i) q^{23} +(3.41692 + 5.91828i) q^{25} +(113.046 + 195.802i) q^{29} +(29.6944 - 51.4321i) q^{31} +270.352 q^{35} -84.1860 q^{37} +(101.630 - 176.028i) q^{41} +(162.945 + 282.229i) q^{43} +(-5.47180 - 9.47744i) q^{47} +(-137.769 + 238.623i) q^{49} +140.186 q^{53} +464.611 q^{55} +(-57.3704 + 99.3685i) q^{59} +(377.528 + 653.898i) q^{61} +(82.2325 + 142.431i) q^{65} +(-383.723 + 664.627i) q^{67} +335.854 q^{71} +167.279 q^{73} +(-531.492 + 920.570i) q^{77} +(-12.6578 - 21.9239i) q^{79} +(-143.861 - 249.174i) q^{83} +(75.3887 - 130.577i) q^{85} +860.817 q^{89} -376.279 q^{91} +(-779.149 + 1349.53i) q^{95} +(201.075 + 348.272i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{5} + 19 q^{7}+O(q^{10}) $ 4 * q - 9 * q^5 + 19 * q^7	$ 4 q - 9 q^{5} + 19 q^{7} + 24 q^{11} - 61 q^{13} - 6 q^{17} - 266 q^{19} - 69 q^{23} - 263 q^{25} + 237 q^{29} + 211 q^{31} + 774 q^{35} + 524 q^{37} + 468 q^{41} - 86 q^{43} - 483 q^{47} + 33 q^{49} - 300 q^{53} + 1674 q^{55} - 168 q^{59} + 1049 q^{61} - 747 q^{65} - 1166 q^{67} - 624 q^{71} - 622 q^{73} - 1173 q^{77} + 349 q^{79} - 1221 q^{83} + 486 q^{85} + 984 q^{89} - 214 q^{91} - 1764 q^{95} + 128 q^{97}+O(q^{100}) $ 4 * q - 9 * q^5 + 19 * q^7 + 24 * q^11 - 61 * q^13 - 6 * q^17 - 266 * q^19 - 69 * q^23 - 263 * q^25 + 237 * q^29 + 211 * q^31 + 774 * q^35 + 524 * q^37 + 468 * q^41 - 86 * q^43 - 483 * q^47 + 33 * q^49 - 300 * q^53 + 1674 * q^55 - 168 * q^59 + 1049 * q^61 - 747 * q^65 - 1166 * q^67 - 624 * q^71 - 622 * q^73 - 1173 * q^77 + 349 * q^79 - 1221 * q^83 + 486 * q^85 + 984 * q^89 - 214 * q^91 - 1764 * q^95 + 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	5.43521	−	9.41407i	0.486140	−	0.842020i	−0.513733	−	0.857950i	$-0.671738\pi$
$5$	5.43521	−	9.41407i	0.486140	−	0.842020i	0.999873	+	0.0159306i	$0.00507109\pi$
$6$		0			0
$7$	12.4352	+	21.5384i	0.671438	+	1.16297i	0.977496	+	0.210953i	$0.0676565\pi$
$7$	12.4352	+	21.5384i	0.671438	+	1.16297i	−0.306058	+	0.952013i	$0.599010\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	21.3704	+	37.0147i	0.585766	+	1.01458i	0.994779	+	0.102048i	$0.0325396\pi$
$11$	21.3704	+	37.0147i	0.585766	+	1.01458i	−0.409013	+	0.912528i	$0.634127\pi$
$12$		0			0
$13$	−7.56479	+	13.1026i	−0.161392	+	0.279539i	−0.935368	−	0.353676i	$-0.884932\pi$
$13$	−7.56479	+	13.1026i	−0.161392	+	0.279539i	0.773976	+	0.633215i	$0.218265\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	13.8704			0.197887			0.0989433	−	0.995093i	$-0.468454\pi$
$17$	13.8704			0.197887			0.0989433	+	0.995093i	$0.468454\pi$
$18$		0			0
$19$	−143.352			−1.73091			−0.865454	−	0.500989i	$-0.832970\pi$
$19$	−143.352			−1.73091			−0.865454	+	0.500989i	$0.832970\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−9.56479	+	16.5667i	−0.0867129	+	0.150191i	−0.906120	−	0.423021i	$-0.860970\pi$
$23$	−9.56479	+	16.5667i	−0.0867129	+	0.150191i	0.819407	+	0.573212i	$0.194303\pi$
$24$		0			0
$25$	3.41692	+	5.91828i	0.0273353	+	0.0473462i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	113.046	+	195.802i	0.723869	+	1.25378i	0.959438	+	0.281920i	$0.0909714\pi$
$29$	113.046	+	195.802i	0.723869	+	1.25378i	−0.235569	+	0.971858i	$0.575695\pi$
$30$		0			0
$31$	29.6944	−	51.4321i	0.172041	−	0.297983i	−0.767092	−	0.641537i	$-0.778297\pi$
$31$	29.6944	−	51.4321i	0.172041	−	0.297983i	0.939133	+	0.343553i	$0.111631\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	270.352			1.30565
$36$		0			0
$37$	−84.1860			−0.374056			−0.187028	−	0.982355i	$-0.559886\pi$
$37$	−84.1860			−0.374056			−0.187028	+	0.982355i	$0.559886\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	101.630	−	176.028i	0.387119	−	0.670510i	−0.604942	−	0.796270i	$-0.706804\pi$
$41$	101.630	−	176.028i	0.387119	−	0.670510i	0.992061	+	0.125760i	$0.0401370\pi$
$42$		0			0
$43$	162.945	+	282.229i	0.577881	+	1.00092i	0.995722	+	0.0923995i	$0.0294537\pi$
$43$	162.945	+	282.229i	0.577881	+	1.00092i	−0.417841	+	0.908520i	$0.637213\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.47180	−	9.47744i	−0.0169818	−	0.0294133i	0.857410	−	0.514635i	$-0.172072\pi$
$47$	−5.47180	−	9.47744i	−0.0169818	−	0.0294133i	−0.874391	+	0.485221i	$0.838739\pi$
$48$		0			0
$49$	−137.769	+	238.623i	−0.401659	+	0.695694i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	140.186			0.363321			0.181661	−	0.983361i	$-0.441853\pi$
$53$	140.186			0.363321			0.181661	+	0.983361i	$0.441853\pi$
$54$		0			0
$55$	464.611			1.13906
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−57.3704	+	99.3685i	−0.126593	+	0.219266i	−0.922355	−	0.386345i	$-0.873738\pi$
$59$	−57.3704	+	99.3685i	−0.126593	+	0.219266i	0.795761	+	0.605610i	$0.207071\pi$
$60$		0			0
$61$	377.528	+	653.898i	0.792419	+	1.37251i	0.924465	+	0.381266i	$0.124512\pi$
$61$	377.528	+	653.898i	0.792419	+	1.37251i	−0.132047	+	0.991243i	$0.542155\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	82.2325	+	142.431i	0.156918	+	0.271790i
$66$		0			0
$67$	−383.723	+	664.627i	−0.699689	+	1.21190i	0.268885	+	0.963172i	$0.413345\pi$
$67$	−383.723	+	664.627i	−0.699689	+	1.21190i	−0.968574	+	0.248725i	$0.919989\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	335.854			0.561387			0.280694	−	0.959797i	$-0.409436\pi$
$71$	335.854			0.561387			0.280694	+	0.959797i	$0.409436\pi$
$72$		0			0
$73$	167.279			0.268199			0.134099	−	0.990968i	$-0.457186\pi$
$73$	167.279			0.268199			0.134099	+	0.990968i	$0.457186\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−531.492	+	920.570i	−0.786612	+	1.36245i
$78$		0			0
$79$	−12.6578	−	21.9239i	−0.0180267	−	0.0312232i	0.856871	−	0.515530i	$-0.172405\pi$
$79$	−12.6578	−	21.9239i	−0.0180267	−	0.0312232i	−0.874898	+	0.484307i	$0.839072\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−143.861	−	249.174i	−0.190250	−	0.329523i	0.755083	−	0.655629i	$-0.227597\pi$
$83$	−143.861	−	249.174i	−0.190250	−	0.329523i	−0.945333	+	0.326107i	$0.894263\pi$
$84$		0			0
$85$	75.3887	−	130.577i	0.0962006	−	0.166624i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	860.817			1.02524			0.512620	−	0.858615i	$-0.328675\pi$
$89$	860.817			1.02524			0.512620	+	0.858615i	$0.328675\pi$
$90$		0			0
$91$	−376.279			−0.433459
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−779.149	+	1349.53i	−0.841464	+	1.45746i
$96$		0			0
$97$	201.075	+	348.272i	0.210475	+	0.364553i	0.951863	−	0.306523i	$-0.0991657\pi$
$97$	201.075	+	348.272i	0.210475	+	0.364553i	−0.741389	+	0.671076i	$0.765832\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−665.714	−	1153.05i	−0.655852	−	1.13597i	−0.981680	−	0.190540i	$-0.938976\pi$
$101$	−665.714	−	1153.05i	−0.655852	−	1.13597i	0.325828	−	0.945429i	$-0.394357\pi$
$102$		0			0
$103$	−259.252	+	449.038i	−0.248009	+	0.429563i	−0.962973	−	0.269597i	$-0.913109\pi$
$103$	−259.252	+	449.038i	−0.248009	+	0.429563i	0.714965	+	0.699161i	$0.246443\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1471.87			1.32982			0.664912	−	0.746922i	$-0.268469\pi$
$107$	1471.87			1.32982			0.664912	+	0.746922i	$0.268469\pi$
$108$		0			0
$109$	−643.668			−0.565616			−0.282808	−	0.959176i	$-0.591266\pi$
$109$	−643.668			−0.565616			−0.282808	+	0.959176i	$0.591266\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	511.864	−	886.574i	0.426125	−	0.738069i	−0.570400	−	0.821367i	$-0.693212\pi$
$113$	511.864	−	886.574i	0.426125	−	0.738069i	0.996525	+	0.0832976i	$0.0265452\pi$
$114$		0			0
$115$	103.973	+	180.087i	0.0843092	+	0.146028i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	172.482	+	298.747i	0.132869	+	0.230135i
$120$		0			0
$121$	−247.890	+	429.358i	−0.186244	+	0.322583i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1433.09			1.02544
$126$		0			0
$127$	31.4481			0.0219730			0.0109865	−	0.999940i	$-0.496503\pi$
$127$	31.4481			0.0219730			0.0109865	+	0.999940i	$0.496503\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	968.678	−	1677.80i	0.646059	−	1.11901i	−0.337997	−	0.941147i	$-0.609749\pi$
$131$	968.678	−	1677.80i	0.646059	−	1.11901i	0.984056	−	0.177860i	$-0.0569174\pi$
$132$		0			0
$133$	−1782.61	−	3087.58i	−1.16220	−	2.01299i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	579.297	+	1003.37i	0.361261	+	0.625722i	0.988169	−	0.153372i	$-0.0490131\pi$
$137$	579.297	+	1003.37i	0.361261	+	0.625722i	−0.626908	+	0.779093i	$0.715680\pi$
$138$		0			0
$139$	1155.80	−	2001.90i	0.705277	−	1.22158i	−0.261314	−	0.965254i	$-0.584156\pi$
$139$	1155.80	−	2001.90i	0.705277	−	1.22158i	0.966591	−	0.256323i	$-0.0825109\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−646.651			−0.378151
$144$		0			0
$145$	2457.73			1.40761
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1475.11	+	2554.96i	−0.811043	+	1.40477i	0.101092	+	0.994877i	$0.467766\pi$
$149$	−1475.11	+	2554.96i	−0.811043	+	1.40477i	−0.912135	+	0.409890i	$0.865567\pi$
$150$		0			0
$151$	−863.199	−	1495.10i	−0.465206	−	0.805761i	0.534005	−	0.845482i	$-0.320686\pi$
$151$	−863.199	−	1495.10i	−0.465206	−	0.805761i	−0.999211	+	0.0397208i	$0.987353\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−322.790	−	559.089i	−0.167272	−	0.289723i
$156$		0			0
$157$	−641.694	+	1111.45i	−0.326196	+	0.564988i	−0.981754	−	0.190157i	$-0.939100\pi$
$157$	−641.694	+	1111.45i	−0.326196	+	0.564988i	0.655558	+	0.755145i	$0.272434\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−475.761			−0.232889
$162$		0			0
$163$	−1033.93			−0.496831			−0.248415	−	0.968654i	$-0.579910\pi$
$163$	−1033.93			−0.496831			−0.248415	+	0.968654i	$0.579910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	141.309	−	244.754i	0.0654778	−	0.113411i	−0.831428	−	0.555632i	$-0.812476\pi$
$167$	141.309	−	244.754i	0.0654778	−	0.113411i	0.896906	+	0.442222i	$0.145810\pi$
$168$		0			0
$169$	984.048	+	1704.42i	0.447905	+	0.775795i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1766.36	−	3059.43i	−0.776266	−	1.34453i	−0.934080	−	0.357063i	$-0.883778\pi$
$173$	−1766.36	−	3059.43i	−0.776266	−	1.34453i	0.157814	−	0.987469i	$-0.449555\pi$
$174$		0			0
$175$	−84.9802	+	147.190i	−0.0367080	+	0.0635801i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4052.74			−1.69227			−0.846135	−	0.532969i	$-0.821076\pi$
$179$	−4052.74			−1.69227			−0.846135	+	0.532969i	$0.821076\pi$
$180$		0			0
$181$	−2830.97			−1.16257			−0.581283	−	0.813702i	$-0.697449\pi$
$181$	−2830.97			−1.16257			−0.581283	+	0.813702i	$0.697449\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−457.569	+	792.532i	−0.181844	+	0.314963i
$186$		0			0
$187$	296.417	+	513.409i	0.115915	+	0.200771i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2254.62	−	3905.12i	−0.854129	−	1.47940i	−0.877451	−	0.479667i	$-0.840757\pi$
$191$	−2254.62	−	3905.12i	−0.854129	−	1.47940i	0.0233215	−	0.999728i	$-0.492576\pi$
$192$		0			0
$193$	1610.56	−	2789.58i	0.600678	−	1.04040i	−0.392041	−	0.919948i	$-0.628231\pi$
$193$	1610.56	−	2789.58i	0.600678	−	1.04040i	0.992719	−	0.120457i	$-0.0384359\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3784.20			−1.36859			−0.684297	−	0.729204i	$-0.739891\pi$
$197$	−3784.20			−1.36859			−0.684297	+	0.729204i	$0.739891\pi$
$198$		0			0
$199$	2926.27			1.04240			0.521200	−	0.853435i	$-0.325485\pi$
$199$	2926.27			1.04240			0.521200	+	0.853435i	$0.325485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2811.51	+	4869.69i	−0.972067	+	1.68367i
$204$		0			0
$205$	−1104.76	−	1913.49i	−0.376388	−	0.651923i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3063.50	−	5306.13i	−1.01391	−	1.75614i
$210$		0			0
$211$	156.737	−	271.476i	0.0511385	−	0.0885744i	−0.839323	−	0.543633i	$-0.817048\pi$
$211$	156.737	−	271.476i	0.0511385	−	0.0885744i	0.890462	+	0.455059i	$0.150382\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3542.57			1.12373
$216$		0			0
$217$	1477.02			0.462059
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−104.927	+	181.739i	−0.0319373	+	0.0553170i
$222$		0			0
$223$	−355.193	−	615.212i	−0.106661	−	0.184743i	0.807754	−	0.589519i	$-0.200683\pi$
$223$	−355.193	−	615.212i	−0.106661	−	0.184743i	−0.914416	+	0.404776i	$0.867349\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.3308	−	28.2858i	−0.00477496	−	0.00827046i	0.863628	−	0.504130i	$-0.168187\pi$
$227$	−16.3308	−	28.2858i	−0.00477496	−	0.00827046i	−0.868403	+	0.495859i	$0.834853\pi$
$228$		0			0
$229$	2751.92	−	4766.47i	0.794114	−	1.37545i	−0.129286	−	0.991607i	$-0.541268\pi$
$229$	2751.92	−	4766.47i	0.794114	−	1.37545i	0.923400	−	0.383839i	$-0.125398\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6788.81			1.90880			0.954399	−	0.298534i	$-0.0964977\pi$
$233$	6788.81			1.90880			0.954399	+	0.298534i	$0.0964977\pi$
$234$		0			0
$235$	−118.962			−0.0330221
$236$		0			0
$237$		0			0
$238$		0			0
$239$	214.694	−	371.862i	0.0581064	−	0.100643i	−0.835509	−	0.549477i	$-0.814827\pi$
$239$	214.694	−	371.862i	0.0581064	−	0.100643i	0.893615	+	0.448834i	$0.148160\pi$
$240$		0			0
$241$	2421.82	+	4194.72i	0.647317	+	1.12119i	0.983761	+	0.179483i	$0.0574424\pi$
$241$	2421.82	+	4194.72i	0.647317	+	1.12119i	−0.336444	+	0.941703i	$0.609224\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1497.61	+	2593.93i	0.390525	+	0.676410i
$246$		0			0
$247$	1084.43	−	1878.28i	0.279354	−	0.483856i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2400.87			0.603752			0.301876	−	0.953347i	$-0.402387\pi$
$251$	2400.87			0.603752			0.301876	+	0.953347i	$0.402387\pi$
$252$		0			0
$253$	−817.614			−0.203174
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1490.50	−	2581.62i	0.361769	−	0.626602i	−0.626483	−	0.779435i	$-0.715506\pi$
$257$	1490.50	−	2581.62i	0.361769	−	0.626602i	0.988252	+	0.152833i	$0.0488396\pi$
$258$		0			0
$259$	−1046.87	−	1813.23i	−0.251156	−	0.435015i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2780.41	−	4815.81i	−0.651891	−	1.12911i	−0.982664	−	0.185398i	$-0.940643\pi$
$263$	−2780.41	−	4815.81i	−0.651891	−	1.12911i	0.330773	−	0.943710i	$-0.392691\pi$
$264$		0			0
$265$	761.941	−	1319.72i	0.176625	−	0.305924i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6288.50			−1.42534			−0.712671	−	0.701499i	$-0.752515\pi$
$269$	−6288.50			−1.42534			−0.712671	+	0.701499i	$0.752515\pi$
$270$		0			0
$271$	−6854.90			−1.53655			−0.768275	−	0.640119i	$-0.778885\pi$
$271$	−6854.90			−1.53655			−0.768275	+	0.640119i	$0.778885\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−146.042	+	252.952i	−0.0320242	+	0.0554676i
$276$		0			0
$277$	−449.086	−	777.840i	−0.0974114	−	0.168722i	0.813201	−	0.581983i	$-0.197723\pi$
$277$	−449.086	−	777.840i	−0.0974114	−	0.168722i	−0.910612	+	0.413261i	$0.864390\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	119.385	+	206.781i	0.0253448	+	0.0438986i	0.878420	−	0.477890i	$-0.158598\pi$
$281$	119.385	+	206.781i	0.0253448	+	0.0438986i	−0.853075	+	0.521789i	$0.825265\pi$
$282$		0			0
$283$	1035.58	−	1793.68i	0.217523	−	0.376760i	−0.736527	−	0.676408i	$-0.763536\pi$
$283$	1035.58	−	1793.68i	0.217523	−	0.376760i	0.954050	+	0.299647i	$0.0968690\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5055.14			1.03971
$288$		0			0
$289$	−4720.61			−0.960841
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3288.88	+	5696.51i	−0.655763	+	1.13581i	0.325939	+	0.945391i	$0.394319\pi$
$293$	−3288.88	+	5696.51i	−0.655763	+	1.13581i	−0.981702	+	0.190423i	$0.939014\pi$
$294$		0			0
$295$	623.641	+	1080.18i	0.123084	+	0.213188i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−144.711	−	250.647i	−0.0279895	−	0.0484792i
$300$		0			0
$301$	−4052.51	+	7019.16i	−0.776023	+	1.34411i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8207.78			1.54091
$306$		0			0
$307$	5237.30			0.973644			0.486822	−	0.873501i	$-0.338156\pi$
$307$	5237.30			0.973644			0.486822	+	0.873501i	$0.338156\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2852.49	+	4940.67i	−0.520097	+	0.900834i	0.479630	+	0.877471i	$0.340771\pi$
$311$	−2852.49	+	4940.67i	−0.520097	+	0.900834i	−0.999727	+	0.0233635i	$0.992562\pi$
$312$		0			0
$313$	−2538.74	−	4397.23i	−0.458460	−	0.794076i	0.540420	−	0.841396i	$-0.318265\pi$
$313$	−2538.74	−	4397.23i	−0.458460	−	0.794076i	−0.998880	+	0.0473193i	$0.984932\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1434.46	+	2484.55i	0.254155	+	0.440209i	0.964666	−	0.263477i	$-0.0848694\pi$
$317$	1434.46	+	2484.55i	0.254155	+	0.440209i	−0.710511	+	0.703686i	$0.751536\pi$
$318$		0			0
$319$	−4831.70	+	8368.76i	−0.848036	+	1.46884i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1988.36			−0.342523
$324$		0			0
$325$	−103.393			−0.0176468
$326$		0			0
$327$		0			0
$328$		0			0
$329$	136.086	−	235.708i	0.0228045	−	0.0394985i
$330$		0			0
$331$	1015.67	+	1759.20i	0.168660	+	0.292128i	0.937949	−	0.346773i	$-0.112723\pi$
$331$	1015.67	+	1759.20i	0.168660	+	0.292128i	−0.769289	+	0.638901i	$0.779389\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4171.23	+	7224.78i	0.680294	+	1.17830i
$336$		0			0
$337$	−4899.14	+	8485.56i	−0.791909	+	1.37163i	0.132875	+	0.991133i	$0.457579\pi$
$337$	−4899.14	+	8485.56i	−0.791909	+	1.37163i	−0.924784	+	0.380493i	$0.875754\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2538.32			0.403103
$342$		0			0
$343$	1677.81			0.264120
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2278.28	−	3946.10i	0.352463	−	0.610483i	−0.634218	−	0.773154i	$-0.718678\pi$
$347$	2278.28	−	3946.10i	0.352463	−	0.610483i	0.986680	+	0.162671i	$0.0520111\pi$
$348$		0			0
$349$	−1674.44	−	2900.22i	−0.256822	−	0.444829i	0.708567	−	0.705644i	$-0.249342\pi$
$349$	−1674.44	−	2900.22i	−0.256822	−	0.444829i	−0.965389	+	0.260815i	$0.916009\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	931.134	+	1612.77i	0.140395	+	0.243170i	0.927645	−	0.373463i	$-0.121830\pi$
$353$	931.134	+	1612.77i	0.140395	+	0.243170i	−0.787251	+	0.616633i	$0.788496\pi$
$354$		0			0
$355$	1825.44	−	3161.75i	0.272913	−	0.472699i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6179.46			0.908466			0.454233	−	0.890883i	$-0.349913\pi$
$359$	6179.46			0.908466			0.454233	+	0.890883i	$0.349913\pi$
$360$		0			0
$361$	13690.8			1.99604
$362$		0			0
$363$		0			0
$364$		0			0
$365$	909.197	−	1574.77i	0.130382	−	0.225829i
$366$		0			0
$367$	3436.98	+	5953.02i	0.488852	+	0.846717i	0.999918	−	0.0128251i	$-0.00408245\pi$
$367$	3436.98	+	5953.02i	0.488852	+	0.846717i	−0.511066	+	0.859542i	$0.670749\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1743.24	+	3019.38i	0.243948	+	0.422530i
$372$		0			0
$373$	−635.013	+	1099.87i	−0.0881494	+	0.152679i	−0.906729	−	0.421714i	$-0.861429\pi$
$373$	−635.013	+	1099.87i	−0.0881494	+	0.152679i	0.818580	+	0.574393i	$0.194762\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3420.69			−0.467306
$378$		0			0
$379$	−2490.54			−0.337548			−0.168774	−	0.985655i	$-0.553981\pi$
$379$	−2490.54			−0.337548			−0.168774	+	0.985655i	$0.553981\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−156.213	+	270.568i	−0.0208410	+	0.0360976i	−0.876258	−	0.481843i	$-0.839968\pi$
$383$	−156.213	+	270.568i	−0.0208410	+	0.0360976i	0.855417	+	0.517940i	$0.173301\pi$
$384$		0			0
$385$	5777.54	+	10007.0i	0.764807	+	1.32468i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4821.58	+	8351.23i	0.628442	+	1.08849i	0.987864	+	0.155319i	$0.0496404\pi$
$389$	4821.58	+	8351.23i	0.628442	+	1.08849i	−0.359422	+	0.933175i	$0.617026\pi$
$390$		0			0
$391$	−132.668	+	229.787i	−0.0171593	+	0.0297208i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−275.191			−0.0350540
$396$		0			0
$397$	−2260.32			−0.285749			−0.142874	−	0.989741i	$-0.545634\pi$
$397$	−2260.32			−0.285749			−0.142874	+	0.989741i	$0.545634\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5084.64	−	8806.85i	0.633204	−	1.09674i	−0.353689	−	0.935363i	$-0.615073\pi$
$401$	5084.64	−	8806.85i	0.633204	−	1.09674i	0.986893	−	0.161378i	$-0.0515938\pi$
$402$		0			0
$403$	449.263	+	778.146i	0.0555320	+	0.0961842i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1799.09	−	3116.12i	−0.219110	−	0.379509i
$408$		0			0
$409$	474.916	−	822.579i	0.0574159	−	0.0994472i	−0.835889	−	0.548899i	$-0.815047\pi$
$409$	474.916	−	822.579i	0.0574159	−	0.0994472i	0.893305	+	0.449452i	$0.148381\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2853.65			−0.339998
$414$		0			0
$415$	−3127.65			−0.369953
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5899.63	−	10218.5i	0.687866	−	1.19142i	−0.284660	−	0.958628i	$-0.591881\pi$
$419$	5899.63	−	10218.5i	0.687866	−	1.19142i	0.972527	−	0.232791i	$-0.0747859\pi$
$420$		0			0
$421$	3206.46	+	5553.76i	0.371196	+	0.642930i	0.989750	−	0.142812i	$-0.0456145\pi$
$421$	3206.46	+	5553.76i	0.371196	+	0.642930i	−0.618554	+	0.785742i	$0.712281\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	47.3941	+	82.0890i	0.00540930	+	0.00936918i
$426$		0			0
$427$	−9389.29	+	16262.7i	−1.06412	+	1.84311i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12042.7			−1.34589			−0.672945	−	0.739693i	$-0.734971\pi$
$431$	−12042.7			−1.34589			−0.672945	+	0.739693i	$0.734971\pi$
$432$		0			0
$433$	7279.83			0.807959			0.403980	−	0.914768i	$-0.367627\pi$
$433$	7279.83			0.807959			0.403980	+	0.914768i	$0.367627\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1371.13	−	2374.87i	0.150092	−	0.259967i
$438$		0			0
$439$	−1799.35	−	3116.57i	−0.195623	−	0.338828i	0.751482	−	0.659754i	$-0.229339\pi$
$439$	−1799.35	−	3116.57i	−0.195623	−	0.338828i	−0.947104	+	0.320926i	$0.896006\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7393.18	+	12805.4i	0.792913	+	1.37337i	0.924156	+	0.382016i	$0.124770\pi$
$443$	7393.18	+	12805.4i	0.792913	+	1.37337i	−0.131243	+	0.991350i	$0.541897\pi$
$444$		0			0
$445$	4678.72	−	8103.79i	0.498411	−	0.863273i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−114.489			−0.0120336			−0.00601681	−	0.999982i	$-0.501915\pi$
$449$	−114.489			−0.0120336			−0.00601681	+	0.999982i	$0.501915\pi$
$450$		0			0
$451$	8687.47			0.907044
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2045.16	+	3542.31i	−0.210722	+	0.364981i
$456$		0			0
$457$	−3155.57	−	5465.60i	−0.323001	−	0.559453i	0.658105	−	0.752926i	$-0.271358\pi$
$457$	−3155.57	−	5465.60i	−0.323001	−	0.559453i	−0.981106	+	0.193473i	$0.938025\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6872.41	−	11903.4i	−0.694317	−	1.20259i	−0.970411	−	0.241461i	$-0.922373\pi$
$461$	−6872.41	−	11903.4i	−0.694317	−	1.20259i	0.276094	−	0.961131i	$-0.410960\pi$
$462$		0			0
$463$	7824.30	−	13552.1i	0.785369	−	1.36030i	−0.143409	−	0.989664i	$-0.545806\pi$
$463$	7824.30	−	13552.1i	0.785369	−	1.36030i	0.928778	−	0.370636i	$-0.120860\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7395.79			−0.732840			−0.366420	−	0.930450i	$-0.619417\pi$
$467$	−7395.79			−0.732840			−0.366420	+	0.930450i	$0.619417\pi$
$468$		0			0
$469$	−19086.7			−1.87919
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6964.41	+	12062.7i	−0.677006	+	1.17261i
$474$		0			0
$475$	−489.822	−	848.397i	−0.0473149	−	0.0819519i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3130.53	+	5422.24i	0.298617	+	0.517221i	0.975820	−	0.218576i	$-0.0701412\pi$
$479$	3130.53	+	5422.24i	0.298617	+	0.517221i	−0.677202	+	0.735797i	$0.736808\pi$
$480$		0			0
$481$	636.849	−	1103.05i	0.0603697	−	0.104563i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4371.54			0.409281
$486$		0			0
$487$	10314.7			0.959763			0.479881	−	0.877333i	$-0.340680\pi$
$487$	10314.7			0.959763			0.479881	+	0.877333i	$0.340680\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1380.45	−	2391.01i	0.126881	−	0.219765i	−0.795585	−	0.605841i	$-0.792837\pi$
$491$	1380.45	−	2391.01i	0.126881	−	0.219765i	0.922467	+	0.386076i	$0.126170\pi$
$492$		0			0
$493$	1568.00	+	2715.86i	0.143244	+	0.248106i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4176.41	+	7233.76i	0.376937	+	0.652874i
$498$		0			0
$499$	−4793.00	+	8301.71i	−0.429988	+	0.744761i	−0.996872	−	0.0790369i	$-0.974816\pi$
$499$	−4793.00	+	8301.71i	−0.429988	+	0.744761i	0.566884	+	0.823798i	$0.308149\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8829.60			0.782689			0.391344	−	0.920244i	$-0.372010\pi$
$503$	8829.60			0.782689			0.391344	+	0.920244i	$0.372010\pi$
$504$		0			0
$505$	−14473.2			−1.27534
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2370.87	−	4106.47i	0.206458	−	0.357595i	−0.744138	−	0.668025i	$-0.767140\pi$
$509$	2370.87	−	4106.47i	0.206458	−	0.357595i	0.950596	+	0.310430i	$0.100473\pi$
$510$		0			0
$511$	2080.15	+	3602.92i	0.180079	+	0.311906i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2818.18	+	4881.24i	0.241134	+	0.417656i
$516$		0			0
$517$	233.870	−	405.074i	0.0198947	−	0.0344587i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2753.22			0.231518			0.115759	−	0.993277i	$-0.463070\pi$
$521$	2753.22			0.231518			0.115759	+	0.993277i	$0.463070\pi$
$522$		0			0
$523$	−17115.3			−1.43098			−0.715489	−	0.698624i	$-0.753796\pi$
$523$	−17115.3			−1.43098			−0.715489	+	0.698624i	$0.753796\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	411.873	−	713.386i	0.0340446	−	0.0589669i
$528$		0			0
$529$	5900.53	+	10220.0i	0.484962	+	0.839978i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1537.61	+	2663.22i	0.124956	+	0.216430i
$534$		0			0
$535$	7999.93	−	13856.3i	0.646481	−	1.11974i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11776.7			−0.941113
$540$		0			0
$541$	17880.1			1.42093			0.710467	−	0.703731i	$-0.248484\pi$
$541$	17880.1			1.42093			0.710467	+	0.703731i	$0.248484\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3498.47	+	6059.53i	−0.274969	+	0.476260i
$546$		0			0
$547$	−6534.73	−	11318.5i	−0.510795	−	0.884723i	−0.999922	−	0.0125101i	$-0.996018\pi$
$547$	−6534.73	−	11318.5i	−0.510795	−	0.884723i	0.489127	−	0.872213i	$-0.337316\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−16205.5	−	28068.7i	−1.25295	−	2.17017i
$552$		0			0
$553$	314.804	−	545.257i	0.0242077	−	0.0419289i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9507.62			−0.723251			−0.361626	−	0.932323i	$-0.617778\pi$
$557$	−9507.62			−0.723251			−0.361626	+	0.932323i	$0.617778\pi$
$558$		0			0
$559$	−4930.58			−0.373061
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10222.3	−	17705.6i	0.765221	−	1.32540i	−0.174909	−	0.984585i	$-0.555963\pi$
$563$	10222.3	−	17705.6i	0.765221	−	1.32540i	0.940130	−	0.340817i	$-0.110704\pi$
$564$		0			0
$565$	−5564.17	−	9637.43i	−0.414313	−	0.717610i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1323.03	+	2291.56i	0.0974770	+	0.168835i	0.910640	−	0.413201i	$-0.135589\pi$
$569$	1323.03	+	2291.56i	0.0974770	+	0.168835i	−0.813163	+	0.582036i	$0.802256\pi$
$570$		0			0
$571$	878.514	−	1521.63i	0.0643864	−	0.111521i	−0.832035	−	0.554723i	$-0.812824\pi$
$571$	878.514	−	1521.63i	0.0643864	−	0.111521i	0.896422	+	0.443202i	$0.146158\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−130.728			−0.00948130
$576$		0			0
$577$	−7515.43			−0.542238			−0.271119	−	0.962546i	$-0.587394\pi$
$577$	−7515.43			−0.542238			−0.271119	+	0.962546i	$0.587394\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3577.87	−	6197.06i	0.255482	−	0.442508i
$582$		0			0
$583$	2995.83	+	5188.94i	0.212821	+	0.368617i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2476.24	+	4288.98i	0.174115	+	0.301576i	0.939855	−	0.341575i	$-0.110960\pi$
$587$	2476.24	+	4288.98i	0.174115	+	0.301576i	−0.765740	+	0.643151i	$0.777627\pi$
$588$		0			0
$589$	−4256.75	+	7372.91i	−0.297787	+	0.515782i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17115.3			−1.18523			−0.592613	−	0.805487i	$-0.701904\pi$
$593$	−17115.3			−1.18523			−0.592613	+	0.805487i	$0.701904\pi$
$594$		0			0
$595$	3749.90			0.258371
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4207.06	+	7286.85i	−0.286972	+	0.497049i	−0.973085	−	0.230445i	$-0.925982\pi$
$599$	−4207.06	+	7286.85i	−0.286972	+	0.497049i	0.686114	+	0.727494i	$0.259315\pi$
$600$		0			0
$601$	−14047.1	−	24330.3i	−0.953399	−	1.65134i	−0.737990	−	0.674812i	$-0.764225\pi$
$601$	−14047.1	−	24330.3i	−0.953399	−	1.65134i	−0.215409	−	0.976524i	$-0.569108\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2694.67	+	4667.31i	0.181081	+	0.313642i
$606$		0			0
$607$	715.423	−	1239.15i	0.0478388	−	0.0828592i	−0.841114	−	0.540857i	$-0.818100\pi$
$607$	715.423	−	1239.15i	0.0478388	−	0.0828592i	0.888953	+	0.457998i	$0.151433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	165.572			0.0109629
$612$		0			0
$613$	14438.1			0.951306			0.475653	−	0.879633i	$-0.342212\pi$
$613$	14438.1			0.951306			0.475653	+	0.879633i	$0.342212\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12722.5	−	22036.0i	0.830125	−	1.43782i	−0.0678130	−	0.997698i	$-0.521602\pi$
$617$	12722.5	−	22036.0i	0.830125	−	1.43782i	0.897938	−	0.440121i	$-0.145065\pi$
$618$		0			0
$619$	−1739.73	−	3013.30i	−0.112966	−	0.195662i	0.803999	−	0.594631i	$-0.202702\pi$
$619$	−1739.73	−	3013.30i	−0.112966	−	0.195662i	−0.916965	+	0.398968i	$0.869368\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10704.4	+	18540.6i	0.688386	+	1.19232i
$624$		0			0
$625$	7362.03	−	12751.4i	0.471170	−	0.816091i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1167.70			−0.0740208
$630$		0			0
$631$	−11151.7			−0.703552			−0.351776	−	0.936084i	$-0.614422\pi$
$631$	−11151.7			−0.703552			−0.351776	+	0.936084i	$0.614422\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	170.927	−	296.055i	0.0106820	−	0.0185017i
$636$		0			0
$637$	−2084.39	−	3610.26i	−0.129649	−	0.224559i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−546.388	−	946.373i	−0.0336678	−	0.0583143i	0.848701	−	0.528874i	$-0.177385\pi$
$641$	−546.388	−	946.373i	−0.0336678	−	0.0583143i	−0.882368	+	0.470559i	$0.844052\pi$
$642$		0			0
$643$	15847.0	−	27447.8i	0.971922	−	1.68342i	0.282181	−	0.959361i	$-0.408942\pi$
$643$	15847.0	−	27447.8i	0.971922	−	1.68342i	0.689741	−	0.724056i	$-0.257724\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13719.9			−0.833672			−0.416836	−	0.908982i	$-0.636861\pi$
$647$	−13719.9			−0.833672			−0.416836	+	0.908982i	$0.636861\pi$
$648$		0			0
$649$	−4904.12			−0.296616
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6642.59	−	11505.3i	0.398078	−	0.689491i	−0.595411	−	0.803421i	$-0.703011\pi$
$653$	6642.59	−	11505.3i	0.398078	−	0.689491i	0.993489	+	0.113930i	$0.0363441\pi$
$654$		0			0
$655$	−10529.9	−	18238.4i	−0.628151	−	1.08799i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1296.99	+	2246.45i	0.0766670	+	0.132791i	0.901810	−	0.432133i	$-0.142239\pi$
$659$	1296.99	+	2246.45i	0.0766670	+	0.132791i	−0.825143	+	0.564924i	$0.808905\pi$
$660$		0			0
$661$	7937.67	−	13748.4i	0.467079	−	0.809005i	−0.532213	−	0.846610i	$-0.678640\pi$
$661$	7937.67	−	13748.4i	0.467079	−	0.809005i	0.999293	+	0.0376052i	$0.0119729\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−38755.6			−2.25996
$666$		0			0
$667$	−4325.06			−0.251075
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−16135.9	+	27948.2i	−0.928344	+	1.60794i
$672$		0			0
$673$	−10717.3	−	18563.0i	−0.613853	−	1.06323i	−0.990585	−	0.136903i	$-0.956285\pi$
$673$	−10717.3	−	18563.0i	−0.613853	−	1.06323i	0.376731	−	0.926323i	$-0.377048\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10166.5	−	17608.9i	−0.577150	−	0.999653i	−0.995804	−	0.0915074i	$-0.970832\pi$
$677$	−10166.5	−	17608.9i	−0.577150	−	0.999653i	0.418655	−	0.908146i	$-0.362502\pi$
$678$		0			0
$679$	−5000.81	+	8661.66i	−0.282642	+	0.489549i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−27149.0			−1.52097			−0.760487	−	0.649353i	$-0.775040\pi$
$683$	−27149.0			−1.52097			−0.760487	+	0.649353i	$0.775040\pi$
$684$		0			0
$685$	12594.4			0.702493
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1060.48	+	1836.80i	−0.0586371	+	0.101562i
$690$		0			0
$691$	11355.1	+	19667.6i	0.625134	+	1.08276i	0.988515	+	0.151123i	$0.0482891\pi$
$691$	11355.1	+	19667.6i	0.625134	+	1.08276i	−0.363381	+	0.931641i	$0.618378\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12564.0	−	21761.5i	−0.685728	−	1.18771i
$696$		0			0
$697$	1409.65	−	2441.58i	0.0766056	−	0.132685i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	20079.5			1.08187			0.540936	−	0.841064i	$-0.318070\pi$
$701$	20079.5			1.08187			0.540936	+	0.841064i	$0.318070\pi$
$702$		0			0
$703$	12068.2			0.647457
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16556.6	−	28676.9i	0.880728	−	1.52547i
$708$		0			0
$709$	14491.8	+	25100.6i	0.767634	+	1.32958i	0.938843	+	0.344346i	$0.111899\pi$
$709$	14491.8	+	25100.6i	0.767634	+	1.32958i	−0.171209	+	0.985235i	$0.554767\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	568.040	+	983.875i	0.0298363	+	0.0516780i
$714$		0			0
$715$	−3514.69	+	6087.61i	−0.183835	+	0.318411i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14496.2			0.751901			0.375951	−	0.926640i	$-0.377316\pi$
$719$	14496.2			0.751901			0.375951	+	0.926640i	$0.377316\pi$
$720$		0			0
$721$	−12895.4			−0.666090
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−772.541	+	1338.08i	−0.0395744	+	0.0685449i
$726$		0			0
$727$	2500.25	+	4330.56i	0.127550	+	0.220924i	0.922727	−	0.385454i	$-0.125955\pi$
$727$	2500.25	+	4330.56i	0.127550	+	0.220924i	−0.795177	+	0.606378i	$0.792622\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2260.12	+	3914.64i	0.114355	+	0.198069i
$732$		0			0
$733$	−8757.79	+	15168.9i	−0.441305	+	0.764362i	−0.997787	−	0.0664977i	$-0.978817\pi$
$733$	−8757.79	+	15168.9i	−0.441305	+	0.764362i	0.556482	+	0.830860i	$0.312151\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32801.3			−1.63942
$738$		0			0
$739$	20169.2			1.00397			0.501985	−	0.864876i	$-0.332603\pi$
$739$	20169.2			1.00397			0.501985	+	0.864876i	$0.332603\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18351.3	−	31785.4i	0.906116	−	1.56944i	0.0867044	−	0.996234i	$-0.472366\pi$
$743$	18351.3	−	31785.4i	0.906116	−	1.56944i	0.819412	−	0.573205i	$-0.194300\pi$
$744$		0			0
$745$	16035.0	+	27773.5i	0.788561	+	1.36583i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	18303.0	+	31701.8i	0.892894	+	1.54654i
$750$		0			0
$751$	−16660.0	+	28856.0i	−0.809499	+	1.40209i	0.103713	+	0.994607i	$0.466928\pi$
$751$	−16660.0	+	28856.0i	−0.809499	+	1.40209i	−0.913212	+	0.407485i	$0.866406\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18766.7			−0.904622
$756$		0			0
$757$	26515.6			1.27309			0.636543	−	0.771241i	$-0.280364\pi$
$757$	26515.6			1.27309			0.636543	+	0.771241i	$0.280364\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2842.17	+	4922.79i	−0.135386	+	0.234495i	−0.925745	−	0.378149i	$-0.876561\pi$
$761$	−2842.17	+	4922.79i	−0.135386	+	0.234495i	0.790359	+	0.612644i	$0.209894\pi$
$762$		0			0
$763$	−8004.14	−	13863.6i	−0.379777	−	0.657792i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−867.990	−	1503.40i	−0.0408622	−	0.0707754i
$768$		0			0
$769$	199.189	−	345.005i	0.00934060	−	0.0161784i	−0.861317	−	0.508067i	$-0.830360\pi$
$769$	199.189	−	345.005i	0.00934060	−	0.0161784i	0.870658	+	0.491889i	$0.163693\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8437.17			0.392579			0.196290	−	0.980546i	$-0.437111\pi$
$773$	8437.17			0.392579			0.196290	+	0.980546i	$0.437111\pi$
$774$		0			0
$775$	405.853			0.0188112
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14568.8	+	25233.9i	−0.670067	+	1.16059i
$780$		0			0
$781$	7177.34	+	12431.5i	0.328842	+	0.569570i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6975.49	+	12081.9i	0.317154	+	0.549327i
$786$		0			0
$787$	8138.94	−	14097.1i	0.368643	−	0.638508i	−0.620711	−	0.784040i	$-0.713156\pi$
$787$	8138.94	−	14097.1i	0.368643	−	0.638508i	0.989354	+	0.145531i	$0.0464892\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	25460.5			1.14447
$792$		0			0
$793$	−11423.7			−0.511560
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2556.06	−	4427.22i	0.113601	−	0.196763i	−0.803619	−	0.595145i	$-0.797095\pi$
$797$	2556.06	−	4427.22i	0.113601	−	0.196763i	0.917220	+	0.398382i	$0.130428\pi$
$798$		0			0
$799$	−75.8963	−	131.456i	−0.00336047	−	0.00582051i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3574.82	+	6191.77i	0.157102	+	0.272108i
$804$		0			0
$805$	−2585.86	+	4478.84i	−0.113217	+	0.196097i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	13141.2			0.571100			0.285550	−	0.958364i	$-0.407824\pi$
$809$	13141.2			0.571100			0.285550	+	0.958364i	$0.407824\pi$
$810$		0			0
$811$	18614.2			0.805957			0.402979	−	0.915209i	$-0.367975\pi$
$811$	18614.2			0.805957			0.402979	+	0.915209i	$0.367975\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5619.61	+	9733.45i	−0.241529	+	0.418341i
$816$		0			0
$817$	−23358.5	−	40458.2i	−1.00026	−	1.73250i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5660.01	−	9803.43i	−0.240604	−	0.416738i	0.720283	−	0.693681i	$-0.244012\pi$
$821$	−5660.01	−	9803.43i	−0.240604	−	0.416738i	−0.960886	+	0.276943i	$0.910679\pi$
$822$		0			0
$823$	5433.29	−	9410.73i	0.230125	−	0.398587i	−0.727720	−	0.685874i	$-0.759420\pi$
$823$	5433.29	−	9410.73i	0.230125	−	0.398587i	0.957845	+	0.287287i	$0.0927533\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13059.3			−0.549114			−0.274557	−	0.961571i	$-0.588531\pi$
$827$	−13059.3			−0.549114			−0.274557	+	0.961571i	$0.588531\pi$
$828$		0			0
$829$	−21203.7			−0.888341			−0.444171	−	0.895942i	$-0.646502\pi$
$829$	−21203.7			−0.888341			−0.444171	+	0.895942i	$0.646502\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1910.92	+	3309.80i	−0.0794829	+	0.137669i
$834$		0			0
$835$	−1536.09	−	2660.58i	−0.0636628	−	0.110267i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7240.28	+	12540.5i	0.297929	+	0.516028i	0.975662	−	0.219280i	$-0.0703708\pi$
$839$	7240.28	+	12540.5i	0.297929	+	0.516028i	−0.677733	+	0.735308i	$0.737038\pi$
$840$		0			0
$841$	−13364.5	+	23148.0i	−0.547973	+	0.949117i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21394.0			0.870979
$846$		0			0
$847$	−12330.3			−0.500204
$848$		0			0
$849$		0			0
$850$		0			0
$851$	805.221	−	1394.68i	0.0324355	−	0.0561799i
$852$		0			0
$853$	3233.61	+	5600.78i	0.129797	+	0.224815i	0.923598	−	0.383363i	$-0.125234\pi$
$853$	3233.61	+	5600.78i	0.129797	+	0.224815i	−0.793801	+	0.608178i	$0.791901\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1947.32	+	3372.85i	0.0776186	+	0.134439i	0.902222	−	0.431272i	$-0.141935\pi$
$857$	1947.32	+	3372.85i	0.0776186	+	0.134439i	−0.824603	+	0.565711i	$0.808602\pi$
$858$		0			0
$859$	−18826.9	+	32609.1i	−0.747805	+	1.29524i	0.201067	+	0.979577i	$0.435559\pi$
$859$	−18826.9	+	32609.1i	−0.747805	+	1.29524i	−0.948873	+	0.315659i	$0.897774\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	47067.5			1.85654			0.928271	−	0.371905i	$-0.121295\pi$
$863$	47067.5			1.85654			0.928271	+	0.371905i	$0.121295\pi$
$864$		0			0
$865$	−38402.2			−1.50950
$866$		0			0
$867$		0			0
$868$		0			0
$869$	541.004	−	937.046i	0.0211189	−	0.0365790i
$870$		0			0
$871$	−5805.56	−	10055.5i	−0.225848	−	0.391181i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	17820.8	+	30866.5i	0.688517	+	1.19255i
$876$		0			0
$877$	3721.77	−	6446.29i	0.143301	−	0.248205i	−0.785437	−	0.618942i	$-0.787562\pi$
$877$	3721.77	−	6446.29i	0.143301	−	0.248205i	0.928738	+	0.370737i	$0.120895\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13781.9			0.527040			0.263520	−	0.964654i	$-0.415116\pi$
$881$	13781.9			0.527040			0.263520	+	0.964654i	$0.415116\pi$
$882$		0			0
$883$	−12230.3			−0.466119			−0.233060	−	0.972462i	$-0.574874\pi$
$883$	−12230.3			−0.466119			−0.233060	+	0.972462i	$0.574874\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	837.437	−	1450.48i	0.0317005	−	0.0549069i	−0.849740	−	0.527202i	$-0.823241\pi$
$887$	837.437	−	1450.48i	0.0317005	−	0.0549069i	0.881440	+	0.472295i	$0.156574\pi$
$888$		0			0
$889$	391.064	+	677.343i	0.0147535	+	0.0255538i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	784.395	+	1358.61i	0.0293939	+	0.0509118i
$894$		0			0
$895$	−22027.5	+	38152.8i	−0.822680	+	1.42492i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	13427.4			0.498140
$900$		0			0
$901$	1944.44			0.0718964
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−15386.9	+	26650.9i	−0.565170	+	0.978903i
$906$		0			0
$907$	8544.04	+	14798.7i	0.312790	+	0.541768i	0.978965	−	0.204027i	$-0.0654031\pi$
$907$	8544.04	+	14798.7i	0.312790	+	0.541768i	−0.666175	+	0.745795i	$0.732070\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10644.2	−	18436.3i	−0.387111	−	0.670496i	0.604949	−	0.796264i	$-0.293194\pi$
$911$	−10644.2	−	18436.3i	−0.387111	−	0.670496i	−0.992060	+	0.125769i	$0.959860\pi$
$912$		0			0
$913$	6148.72	−	10649.9i	0.222884	−	0.386046i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	48182.8			1.73516
$918$		0			0
$919$	10413.4			0.373784			0.186892	−	0.982380i	$-0.440159\pi$
$919$	10413.4			0.373784			0.186892	+	0.982380i	$0.440159\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2540.66	+	4400.55i	−0.0906033	+	0.156930i
$924$		0			0
$925$	−287.657	−	498.236i	−0.0102250	−	0.0177102i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3411.72	−	5909.26i	−0.120490	−	0.208694i	0.799471	−	0.600704i	$-0.205113\pi$
$929$	−3411.72	−	5909.26i	−0.120490	−	0.208694i	−0.919961	+	0.392010i	$0.871780\pi$
$930$		0			0
$931$	19749.5	−	34207.1i	0.695234	−	1.20418i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6444.36			0.225404
$936$		0			0
$937$	41049.8			1.43120			0.715602	−	0.698508i	$-0.246152\pi$
$937$	41049.8			1.43120			0.715602	+	0.698508i	$0.246152\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1208.06	−	2092.42i	0.0418508	−	0.0724878i	−0.844341	−	0.535806i	$-0.820008\pi$
$941$	1208.06	−	2092.42i	0.0418508	−	0.0724878i	0.886192	+	0.463318i	$0.153341\pi$
$942$		0			0
$943$	1944.13	+	3367.33i	0.0671364	+	0.116284i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1197.04	+	2073.33i	0.0410755	+	0.0711448i	0.885832	−	0.464006i	$-0.153588\pi$
$947$	1197.04	+	2073.33i	0.0410755	+	0.0711448i	−0.844757	+	0.535150i	$0.820255\pi$
$948$		0			0
$949$	−1265.43	+	2191.79i	−0.0432851	+	0.0749720i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	50651.3			1.72168			0.860838	−	0.508879i	$-0.169940\pi$
$953$	50651.3			1.72168			0.860838	+	0.508879i	$0.169940\pi$
$954$		0			0
$955$	−49017.4			−1.66091
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14407.4	+	24954.3i	−0.485128	+	0.840267i
$960$		0			0
$961$	13132.0	+	22745.3i	0.440804	+	0.763495i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17507.5	−	30323.9i	−0.584027	−	1.01156i
$966$		0			0
$967$	12517.5	−	21680.9i	0.416271	−	0.721003i	−0.579290	−	0.815122i	$-0.696670\pi$
$967$	12517.5	−	21680.9i	0.416271	−	0.721003i	0.995561	+	0.0941189i	$0.0300034\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	49553.7			1.63775			0.818875	−	0.573972i	$-0.194598\pi$
$971$	49553.7			1.63775			0.818875	+	0.573972i	$0.194598\pi$
$972$		0			0
$973$	57490.4			1.89420
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17588.1	+	30463.5i	−0.575939	+	0.997556i	0.419999	+	0.907524i	$0.362030\pi$
$977$	−17588.1	+	30463.5i	−0.575939	+	0.997556i	−0.995939	+	0.0900320i	$0.971303\pi$
$978$		0			0
$979$	18396.0	+	31862.9i	0.600551	+	1.04019i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16674.6	−	28881.3i	−0.541036	−	0.937102i	−0.998845	−	0.0480511i	$-0.984699\pi$
$983$	−16674.6	−	28881.3i	−0.541036	−	0.937102i	0.457809	−	0.889051i	$-0.348634\pi$
$984$		0			0
$985$	−20567.9	+	35624.7i	−0.665328	+	1.15238i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6234.14			−0.200439
$990$		0			0
$991$	−23066.3			−0.739378			−0.369689	−	0.929156i	$-0.620536\pi$
$991$	−23066.3			−0.739378			−0.369689	+	0.929156i	$0.620536\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15904.9	−	27548.1i	0.506752	−	0.877721i
$996$		0			0
$997$	27884.9	+	48298.1i	0.885782	+	1.53422i	0.844815	+	0.535059i	$0.179711\pi$
$997$	27884.9	+	48298.1i	0.885782	+	1.53422i	0.0409671	+	0.999160i	$0.486956\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.4.i.b.145.2		4
3.2	odd	2		144.4.i.b.49.1		4
4.3	odd	2		54.4.c.b.37.2		4
9.2	odd	6		144.4.i.b.97.1		4
9.4	even	3		1296.4.a.r.1.1		2
9.5	odd	6		1296.4.a.l.1.2		2
9.7	even	3	inner	432.4.i.b.289.2		4
12.11	even	2		18.4.c.b.13.2	yes	4
36.7	odd	6		54.4.c.b.19.2		4
36.11	even	6		18.4.c.b.7.2	✓	4
36.23	even	6		162.4.a.f.1.2		2
36.31	odd	6		162.4.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.4.c.b.7.2	✓	4	36.11	even	6
18.4.c.b.13.2	yes	4	12.11	even	2
54.4.c.b.19.2		4	36.7	odd	6
54.4.c.b.37.2		4	4.3	odd	2
144.4.i.b.49.1		4	3.2	odd	2
144.4.i.b.97.1		4	9.2	odd	6
162.4.a.f.1.2		2	36.23	even	6
162.4.a.g.1.1		2	36.31	odd	6
432.4.i.b.145.2		4	1.1	even	1	trivial
432.4.i.b.289.2		4	9.7	even	3	inner
1296.4.a.l.1.2		2	9.5	odd	6
1296.4.a.r.1.1		2	9.4	even	3

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.43521 - 9.41407i) q^{5} +(12.4352 + 21.5384i) q^{7} +O(q^{10})\)	\(q+(5.43521 - 9.41407i) q^{5} +(12.4352 + 21.5384i) q^{7} +(21.3704 + 37.0147i) q^{11} +(-7.56479 + 13.1026i) q^{13} +13.8704 q^{17} -143.352 q^{19} +(-9.56479 + 16.5667i) q^{23} +(3.41692 + 5.91828i) q^{25} +(113.046 + 195.802i) q^{29} +(29.6944 - 51.4321i) q^{31} +270.352 q^{35} -84.1860 q^{37} +(101.630 - 176.028i) q^{41} +(162.945 + 282.229i) q^{43} +(-5.47180 - 9.47744i) q^{47} +(-137.769 + 238.623i) q^{49} +140.186 q^{53} +464.611 q^{55} +(-57.3704 + 99.3685i) q^{59} +(377.528 + 653.898i) q^{61} +(82.2325 + 142.431i) q^{65} +(-383.723 + 664.627i) q^{67} +335.854 q^{71} +167.279 q^{73} +(-531.492 + 920.570i) q^{77} +(-12.6578 - 21.9239i) q^{79} +(-143.861 - 249.174i) q^{83} +(75.3887 - 130.577i) q^{85} +860.817 q^{89} -376.279 q^{91} +(-779.149 + 1349.53i) q^{95} +(201.075 + 348.272i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{5} + 19 q^{7}+O(q^{10}) \) 4 * q - 9 * q^5 + 19 * q^7	\( 4 q - 9 q^{5} + 19 q^{7} + 24 q^{11} - 61 q^{13} - 6 q^{17} - 266 q^{19} - 69 q^{23} - 263 q^{25} + 237 q^{29} + 211 q^{31} + 774 q^{35} + 524 q^{37} + 468 q^{41} - 86 q^{43} - 483 q^{47} + 33 q^{49} - 300 q^{53} + 1674 q^{55} - 168 q^{59} + 1049 q^{61} - 747 q^{65} - 1166 q^{67} - 624 q^{71} - 622 q^{73} - 1173 q^{77} + 349 q^{79} - 1221 q^{83} + 486 q^{85} + 984 q^{89} - 214 q^{91} - 1764 q^{95} + 128 q^{97}+O(q^{100}) \) 4 * q - 9 * q^5 + 19 * q^7 + 24 * q^11 - 61 * q^13 - 6 * q^17 - 266 * q^19 - 69 * q^23 - 263 * q^25 + 237 * q^29 + 211 * q^31 + 774 * q^35 + 524 * q^37 + 468 * q^41 - 86 * q^43 - 483 * q^47 + 33 * q^49 - 300 * q^53 + 1674 * q^55 - 168 * q^59 + 1049 * q^61 - 747 * q^65 - 1166 * q^67 - 624 * q^71 - 622 * q^73 - 1173 * q^77 + 349 * q^79 - 1221 * q^83 + 486 * q^85 + 984 * q^89 - 214 * q^91 - 1764 * q^95 + 128 * q^97

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