LMFDB - Embedded newform 333.6.c.d.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,6,Mod(73,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("333.73");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	333.c (of order $2$, degree $1$, 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:	$53.4078119977$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 $ x^16 + 390x^14 + 60701x^12 + 4799932x^10 + 203487156x^8 + 4519465040x^6 + 48993644736x^4 + 211923220224*x^2 + 178006118400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.6
Root			$-4.32146i$ of defining polynomial
Character	$\chi$	$=$	333.73
Dual form			333.6.c.d.73.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.32146i q^{2} +13.3250 q^{4} +61.4962i q^{5} +41.8425 q^{7} -195.870i q^{8} +O(q^{10})$	\(q-4.32146i q^{2} +13.3250 q^{4} +61.4962i q^{5} +41.8425 q^{7} -195.870i q^{8} +265.753 q^{10} -646.924 q^{11} -842.206i q^{13} -180.821i q^{14} -420.045 q^{16} +1320.32i q^{17} +328.490i q^{19} +819.436i q^{20} +2795.66i q^{22} +3115.93i q^{23} -656.781 q^{25} -3639.56 q^{26} +557.551 q^{28} -6648.96i q^{29} -3324.21i q^{31} -4452.64i q^{32} +5705.72 q^{34} +2573.16i q^{35} +(-8234.35 - 1240.75i) q^{37} +1419.56 q^{38} +12045.3 q^{40} -7567.06 q^{41} -8904.72i q^{43} -8620.26 q^{44} +13465.4 q^{46} -20029.7 q^{47} -15056.2 q^{49} +2838.25i q^{50} -11222.4i q^{52} +1283.48 q^{53} -39783.4i q^{55} -8195.70i q^{56} -28733.2 q^{58} -34840.5i q^{59} +14462.2i q^{61} -14365.5 q^{62} -32683.3 q^{64} +51792.5 q^{65} -2238.65 q^{67} +17593.3i q^{68} +11119.8 q^{70} -57203.4 q^{71} -5228.09 q^{73} +(-5361.86 + 35584.4i) q^{74} +4377.13i q^{76} -27068.9 q^{77} -53995.0i q^{79} -25831.2i q^{80} +32700.8i q^{82} +74351.1 q^{83} -81194.8 q^{85} -38481.4 q^{86} +126713. i q^{88} +64976.2i q^{89} -35240.0i q^{91} +41519.8i q^{92} +86557.3i q^{94} -20200.9 q^{95} -21428.1i q^{97} +65064.8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 268 q^{4} + 190 q^{7}+O(q^{10}) $ 16 * q - 268 * q^4 + 190 * q^7	$ 16 q - 268 q^{4} + 190 q^{7} - 74 q^{10} + 1110 q^{11} + 2900 q^{16} - 12052 q^{25} - 4902 q^{26} - 16824 q^{28} + 20556 q^{34} - 11400 q^{37} - 12108 q^{38} + 16966 q^{40} - 3918 q^{41} - 125394 q^{44} + 17470 q^{46} - 3822 q^{47} - 32618 q^{49} + 24126 q^{53} - 164718 q^{58} + 81426 q^{62} + 158076 q^{64} - 98976 q^{65} + 23560 q^{67} - 222404 q^{70} + 50046 q^{71} - 196274 q^{73} - 141216 q^{74} + 239574 q^{77} + 215814 q^{83} - 346472 q^{85} - 197640 q^{86} + 132504 q^{95}+O(q^{100}) $ 16 * q - 268 * q^4 + 190 * q^7 - 74 * q^10 + 1110 * q^11 + 2900 * q^16 - 12052 * q^25 - 4902 * q^26 - 16824 * q^28 + 20556 * q^34 - 11400 * q^37 - 12108 * q^38 + 16966 * q^40 - 3918 * q^41 - 125394 * q^44 + 17470 * q^46 - 3822 * q^47 - 32618 * q^49 + 24126 * q^53 - 164718 * q^58 + 81426 * q^62 + 158076 * q^64 - 98976 * q^65 + 23560 * q^67 - 222404 * q^70 + 50046 * q^71 - 196274 * q^73 - 141216 * q^74 + 239574 * q^77 + 215814 * q^83 - 346472 * q^85 - 197640 * q^86 + 132504 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	4.32146i		−	0.763933i	−0.924176	−	0.381967i	$-0.875247\pi$
$2$		−	4.32146i		−	0.763933i	0.924176	−	0.381967i	$-0.124753\pi$
$3$		0			0
$3$		0			0
$4$	13.3250			0.416406
$5$			61.4962i			1.10008i	0.835139	+	0.550039i	$0.185387\pi$
$5$			61.4962i			1.10008i	−0.835139	+	0.550039i	$0.814613\pi$
$6$		0			0
$7$	41.8425			0.322755			0.161377	−	0.986893i	$-0.448406\pi$
$7$	41.8425			0.322755			0.161377	+	0.986893i	$0.448406\pi$
$8$		−	195.870i		−	1.08204i
$9$		0			0
$10$	265.753			0.840386
$11$	−646.924			−1.61203			−0.806013	−	0.591899i	$-0.798379\pi$
$11$	−646.924			−1.61203			−0.806013	+	0.591899i	$0.798379\pi$
$12$		0			0
$13$		−	842.206i		−	1.38217i	−0.722776	−	0.691083i	$-0.757134\pi$
$13$		−	842.206i		−	1.38217i	0.722776	−	0.691083i	$-0.242866\pi$
$14$		−	180.821i		−	0.246563i
$15$		0			0
$16$	−420.045			−0.410200
$17$			1320.32i			1.10805i	0.832502	+	0.554023i	$0.186908\pi$
$17$			1320.32i			1.10805i	−0.832502	+	0.554023i	$0.813092\pi$
$18$		0			0
$19$			328.490i			0.208756i	0.994538	+	0.104378i	$0.0332851\pi$
$19$			328.490i			0.208756i	−0.994538	+	0.104378i	$0.966715\pi$
$20$			819.436i			0.458079i
$21$		0			0
$22$			2795.66i			1.23148i
$23$			3115.93i			1.22820i	0.789229	+	0.614099i	$0.210480\pi$
$23$			3115.93i			1.22820i	−0.789229	+	0.614099i	$0.789520\pi$
$24$		0			0
$25$	−656.781			−0.210170
$26$	−3639.56			−1.05588
$27$		0			0
$28$	557.551			0.134397
$29$		−	6648.96i		−	1.46811i	−0.679089	−	0.734056i	$-0.737625\pi$
$29$		−	6648.96i		−	1.46811i	0.679089	−	0.734056i	$-0.262375\pi$
$30$		0			0
$31$		−	3324.21i		−	0.621276i	−0.950528	−	0.310638i	$-0.899457\pi$
$31$		−	3324.21i		−	0.621276i	0.950528	−	0.310638i	$-0.100543\pi$
$32$		−	4452.64i		−	0.768674i
$33$		0			0
$34$	5705.72			0.846473
$35$			2573.16i			0.355055i
$36$		0			0
$37$	−8234.35	−	1240.75i	−0.988837	−	0.148998i
$37$	−8234.35	−	1240.75i	−0.988837	−	0.148998i
$38$	1419.56			0.159475
$39$		0			0
$40$	12045.3			1.19033
$41$	−7567.06			−0.703020			−0.351510	−	0.936184i	$-0.614332\pi$
$41$	−7567.06			−0.703020			−0.351510	+	0.936184i	$0.614332\pi$
$42$		0			0
$43$		−	8904.72i		−	0.734428i	−0.930137	−	0.367214i	$-0.880312\pi$
$43$		−	8904.72i		−	0.734428i	0.930137	−	0.367214i	$-0.119688\pi$
$44$	−8620.26			−0.671257
$45$		0			0
$46$	13465.4			0.938261
$47$	−20029.7			−1.32260			−0.661301	−	0.750121i	$-0.729995\pi$
$47$	−20029.7			−1.32260			−0.661301	+	0.750121i	$0.729995\pi$
$48$		0			0
$49$	−15056.2			−0.895829
$50$			2838.25i			0.160556i
$51$		0			0
$52$		−	11222.4i		−	0.575542i
$53$	1283.48			0.0627624			0.0313812	−	0.999507i	$-0.490009\pi$
$53$	1283.48			0.0627624			0.0313812	+	0.999507i	$0.490009\pi$
$54$		0			0
$55$		−	39783.4i		−	1.77335i
$56$		−	8195.70i		−	0.349234i
$57$		0			0
$58$	−28733.2			−1.12154
$59$		−	34840.5i		−	1.30303i	−0.758635	−	0.651516i	$-0.774133\pi$
$59$		−	34840.5i		−	1.30303i	0.758635	−	0.651516i	$-0.225867\pi$
$60$		0			0
$61$			14462.2i			0.497634i	0.968551	+	0.248817i	$0.0800418\pi$
$61$			14462.2i			0.497634i	−0.968551	+	0.248817i	$0.919958\pi$
$62$	−14365.5			−0.474614
$63$		0			0
$64$	−32683.3			−0.997416
$65$	51792.5			1.52049
$66$		0			0
$67$	−2238.65			−0.0609254			−0.0304627	−	0.999536i	$-0.509698\pi$
$67$	−2238.65			−0.0609254			−0.0304627	+	0.999536i	$0.509698\pi$
$68$			17593.3i			0.461397i
$69$		0			0
$70$	11119.8			0.271239
$71$	−57203.4			−1.34672			−0.673358	−	0.739317i	$-0.735149\pi$
$71$	−57203.4			−1.34672			−0.673358	+	0.739317i	$0.735149\pi$
$72$		0			0
$73$	−5228.09			−0.114825			−0.0574124	−	0.998351i	$-0.518285\pi$
$73$	−5228.09			−0.114825			−0.0574124	+	0.998351i	$0.518285\pi$
$74$	−5361.86	+	35584.4i	−0.113825	+	0.755406i
$75$		0			0
$76$			4377.13i			0.0869271i
$77$	−27068.9			−0.520289
$78$		0			0
$79$		−	53995.0i		−	0.973387i	−0.873573	−	0.486694i	$-0.838203\pi$
$79$		−	53995.0i		−	0.973387i	0.873573	−	0.486694i	$-0.161797\pi$
$80$		−	25831.2i		−	0.451252i
$81$		0			0
$82$			32700.8i			0.537060i
$83$	74351.1			1.18466			0.592328	−	0.805697i	$-0.298209\pi$
$83$	74351.1			1.18466			0.592328	+	0.805697i	$0.298209\pi$
$84$		0			0
$85$	−81194.8			−1.21894
$86$	−38481.4			−0.561054
$87$		0			0
$88$			126713.i			1.74427i
$89$			64976.2i			0.869520i	0.900546	+	0.434760i	$0.143167\pi$
$89$			64976.2i			0.869520i	−0.900546	+	0.434760i	$0.856833\pi$
$90$		0			0
$91$		−	35240.0i		−	0.446101i
$92$			41519.8i			0.511429i
$93$		0			0
$94$			86557.3i			1.01038i
$95$	−20200.9			−0.229647
$96$		0			0
$97$		−	21428.1i		−	0.231235i	−0.993294	−	0.115618i	$-0.963115\pi$
$97$		−	21428.1i		−	0.231235i	0.993294	−	0.115618i	$-0.0368847\pi$
$98$			65064.8i			0.684354i
$99$		0			0
$100$	−8751.60			−0.0875160
$101$	74940.2			0.730990			0.365495	−	0.930813i	$-0.380900\pi$
$101$	74940.2			0.730990			0.365495	+	0.930813i	$0.380900\pi$
$102$		0			0
$103$			155725.i			1.44633i	0.690677	+	0.723163i	$0.257313\pi$
$103$			155725.i			1.44633i	−0.690677	+	0.723163i	$0.742687\pi$
$104$	−164963.			−1.49556
$105$		0			0
$106$		−	5546.51i		−	0.0479463i
$107$	−180616.			−1.52509			−0.762546	−	0.646934i	$-0.776051\pi$
$107$	−180616.			−1.52509			−0.762546	+	0.646934i	$0.776051\pi$
$108$		0			0
$109$		−	78536.9i		−	0.633152i	−0.948567	−	0.316576i	$-0.897467\pi$
$109$		−	78536.9i		−	0.633152i	0.948567	−	0.316576i	$-0.102533\pi$
$110$	−171922.			−1.35472
$111$		0			0
$112$	−17575.7			−0.132394
$113$		−	209531.i		−	1.54366i	−0.635829	−	0.771830i	$-0.719342\pi$
$113$		−	209531.i		−	1.54366i	0.635829	−	0.771830i	$-0.280658\pi$
$114$		0			0
$115$	−191618.			−1.35111
$116$		−	88597.4i		−	0.611330i
$117$		0			0
$118$	−150562.			−0.995429
$119$			55245.6i			0.357627i
$120$		0			0
$121$	257460.			1.59862
$122$	62497.8			0.380159
$123$		0			0
$124$		−	44295.1i		−	0.258703i
$125$			151786.i			0.868874i
$126$		0			0
$127$	−174859.			−0.962008			−0.481004	−	0.876718i	$-0.659728\pi$
$127$	−174859.			−0.962008			−0.481004	+	0.876718i	$0.659728\pi$
$128$		−	1244.74i		−	0.00671514i
$129$		0			0
$130$		−	223819.i		−	1.16155i
$131$		−	188117.i		−	0.957746i	−0.877884	−	0.478873i	$-0.841045\pi$
$131$		−	188117.i		−	0.957746i	0.877884	−	0.478873i	$-0.158955\pi$
$132$		0			0
$133$			13744.9i			0.0673769i
$134$			9674.22i			0.0465430i
$135$		0			0
$136$	258612.			1.19895
$137$	−308591.			−1.40469			−0.702347	−	0.711835i	$-0.747865\pi$
$137$	−308591.			−1.40469			−0.702347	+	0.711835i	$0.747865\pi$
$138$		0			0
$139$	−167532.			−0.735464			−0.367732	−	0.929932i	$-0.619866\pi$
$139$	−167532.			−0.735464			−0.367732	+	0.929932i	$0.619866\pi$
$140$			34287.3i			0.147847i
$141$		0			0
$142$			247202.i			1.02880i
$143$			544844.i			2.22809i
$144$		0			0
$145$	408886.			1.61504
$146$			22593.0i			0.0877185i
$147$		0			0
$148$	−109723.	−	16533.0i	−0.411758	−	0.0620437i
$149$	−56048.7			−0.206823			−0.103412	−	0.994639i	$-0.532976\pi$
$149$	−56048.7			−0.206823			−0.103412	+	0.994639i	$0.532976\pi$
$150$		0			0
$151$	147310.			0.525764			0.262882	−	0.964828i	$-0.415327\pi$
$151$	147310.			0.525764			0.262882	+	0.964828i	$0.415327\pi$
$152$	64341.4			0.225882
$153$		0			0
$154$			116977.i			0.397466i
$155$	204427.			0.683452
$156$		0			0
$157$	−241023.			−0.780385			−0.390192	−	0.920733i	$-0.627592\pi$
$157$	−241023.			−0.780385			−0.390192	+	0.920733i	$0.627592\pi$
$158$	−233337.			−0.743603
$159$		0			0
$160$	273820.			0.845601
$161$			130378.i			0.396407i
$162$		0			0
$163$			575493.i			1.69657i	0.529542	+	0.848283i	$0.322364\pi$
$163$			575493.i			1.69657i	−0.529542	+	0.848283i	$0.677636\pi$
$164$	−100831.			−0.292742
$165$		0			0
$166$		−	321305.i		−	0.904998i
$167$		−	648076.i		−	1.79819i	−0.437757	−	0.899093i	$-0.644227\pi$
$167$		−	648076.i		−	1.79819i	0.437757	−	0.899093i	$-0.355773\pi$
$168$		0			0
$169$	−338018.			−0.910381
$170$			350880.i			0.931185i
$171$		0			0
$172$		−	118655.i		−	0.305820i
$173$	−32850.9			−0.0834510			−0.0417255	−	0.999129i	$-0.513285\pi$
$173$	−32850.9			−0.0834510			−0.0417255	+	0.999129i	$0.513285\pi$
$174$		0			0
$175$	−27481.4			−0.0678334
$176$	271737.			0.661253
$177$		0			0
$178$	280792.			0.664255
$179$			199299.i			0.464913i	0.972607	+	0.232457i	$0.0746764\pi$
$179$			199299.i			0.464913i	−0.972607	+	0.232457i	$0.925324\pi$
$180$		0			0
$181$	−483878.			−1.09784			−0.548920	−	0.835875i	$-0.684961\pi$
$181$	−483878.			−1.09784			−0.548920	+	0.835875i	$0.684961\pi$
$182$	−152288.			−0.340791
$183$		0			0
$184$	610318.			1.32896
$185$	76301.5	−	506381.i	0.163909	−	1.08780i
$186$		0			0
$187$		−	854148.i		−	1.78620i
$188$	−266895.			−0.550739
$189$		0			0
$190$			87297.3i			0.175435i
$191$			90595.6i			0.179690i	0.995956	+	0.0898450i	$0.0286372\pi$
$191$			90595.6i			0.179690i	−0.995956	+	0.0898450i	$0.971363\pi$
$192$		0			0
$193$			92217.7i			0.178206i	0.996022	+	0.0891028i	$0.0284000\pi$
$193$			92217.7i			0.178206i	−0.996022	+	0.0891028i	$0.971600\pi$
$194$	−92600.7			−0.176648
$195$		0			0
$196$	−200624.			−0.373029
$197$	905450.			1.66226			0.831130	−	0.556078i	$-0.187694\pi$
$197$	905450.			1.66226			0.831130	+	0.556078i	$0.187694\pi$
$198$		0			0
$199$			604369.i			1.08186i	0.841069	+	0.540928i	$0.181927\pi$
$199$			604369.i			1.08186i	−0.841069	+	0.540928i	$0.818073\pi$
$200$			128644.i			0.227412i
$201$		0			0
$202$		−	323851.i		−	0.558428i
$203$		−	278209.i		−	0.473840i
$204$		0			0
$205$		−	465346.i		−	0.773377i
$206$	672961.			1.10490
$207$		0			0
$208$			353764.i			0.566964i
$209$		−	212508.i		−	0.336519i
$210$		0			0
$211$	115864.			0.179161			0.0895806	−	0.995980i	$-0.471447\pi$
$211$	115864.			0.179161			0.0895806	+	0.995980i	$0.471447\pi$
$212$	17102.4			0.0261347
$213$		0			0
$214$			780523.i			1.16507i
$215$	547606.			0.807927
$216$		0			0
$217$		−	139094.i		−	0.200520i
$218$	−339394.			−0.483686
$219$		0			0
$220$		−	530113.i		−	0.738434i
$221$	1.11198e6			1.53150
$222$		0			0
$223$	155524.			0.209428			0.104714	−	0.994502i	$-0.466607\pi$
$223$	155524.			0.209428			0.104714	+	0.994502i	$0.466607\pi$
$224$		−	186310.i		−	0.248093i
$225$		0			0
$226$	−905478.			−1.17925
$227$		−	1.20036e6i		−	1.54613i	−0.634328	−	0.773064i	$-0.718723\pi$
$227$		−	1.20036e6i		−	1.54613i	0.634328	−	0.773064i	$-0.281277\pi$
$228$		0			0
$229$	1.29594e6			1.63304			0.816518	−	0.577320i	$-0.195902\pi$
$229$	1.29594e6			1.63304			0.816518	+	0.577320i	$0.195902\pi$
$230$			828069.i			1.03216i
$231$		0			0
$232$	−1.30233e6			−1.58855
$233$	331887.			0.400499			0.200249	−	0.979745i	$-0.435825\pi$
$233$	331887.			0.400499			0.200249	+	0.979745i	$0.435825\pi$
$234$		0			0
$235$		−	1.23175e6i		−	1.45496i
$236$		−	464250.i		−	0.542590i
$237$		0			0
$238$	238742.			0.273203
$239$			644624.i			0.729981i	0.931011	+	0.364991i	$0.118928\pi$
$239$			644624.i			0.729981i	−0.931011	+	0.364991i	$0.881072\pi$
$240$		0			0
$241$			376830.i			0.417929i	0.977923	+	0.208965i	$0.0670093\pi$
$241$			376830.i			0.417929i	−0.977923	+	0.208965i	$0.932991\pi$
$242$		−	1.11260e6i		−	1.22124i
$243$		0			0
$244$			192709.i			0.207218i
$245$		−	925899.i		−	0.985481i
$246$		0			0
$247$	276656.			0.288535
$248$	−651114.			−0.672246
$249$		0			0
$250$	655937.			0.663762
$251$			611157.i			0.612306i	0.951982	+	0.306153i	$0.0990418\pi$
$251$			611157.i			0.612306i	−0.951982	+	0.306153i	$0.900958\pi$
$252$		0			0
$253$		−	2.01577e6i		−	1.97989i
$254$			755646.i			0.734910i
$255$		0			0
$256$	−1.05125e6			−1.00255
$257$			1.47145e6i			1.38967i	0.719168	+	0.694836i	$0.244523\pi$
$257$			1.47145e6i			1.38967i	−0.719168	+	0.694836i	$0.755477\pi$
$258$		0			0
$259$	−344546.	−	51916.2i	−0.319152	−	0.0480899i
$260$	690134.			0.633141
$261$		0			0
$262$	−812941.			−0.731654
$263$	636455.			0.567385			0.283693	−	0.958915i	$-0.408440\pi$
$263$	636455.			0.567385			0.283693	+	0.958915i	$0.408440\pi$
$264$		0			0
$265$			78929.2i			0.0690435i
$266$	59397.8			0.0514714
$267$		0			0
$268$	−29830.0			−0.0253697
$269$	−327392.			−0.275860			−0.137930	−	0.990442i	$-0.544045\pi$
$269$	−327392.			−0.275860			−0.137930	+	0.990442i	$0.544045\pi$
$270$		0			0
$271$	1.60097e6			1.32422			0.662108	−	0.749408i	$-0.269662\pi$
$271$	1.60097e6			1.32422			0.662108	+	0.749408i	$0.269662\pi$
$272$		−	554594.i		−	0.454520i
$273$		0			0
$274$			1.33356e6i			1.07309i
$275$	424888.			0.338799
$276$		0			0
$277$		−	448286.i		−	0.351039i	−0.984476	−	0.175520i	$-0.943839\pi$
$277$		−	448286.i		−	0.351039i	0.984476	−	0.175520i	$-0.0561605\pi$
$278$			723984.i			0.561845i
$279$		0			0
$280$	504004.			0.384184
$281$		−	1.28712e6i		−	0.972418i	−0.873843	−	0.486209i	$-0.838379\pi$
$281$		−	1.28712e6i		−	0.972418i	0.873843	−	0.486209i	$-0.161621\pi$
$282$		0			0
$283$			397374.i			0.294939i	0.989067	+	0.147470i	$0.0471129\pi$
$283$			397374.i			0.294939i	−0.989067	+	0.147470i	$0.952887\pi$
$284$	−762234.			−0.560780
$285$		0			0
$286$	2.35452e6			1.70211
$287$	−316625.			−0.226903
$288$		0			0
$289$	−323393.			−0.227764
$290$		−	1.76698e6i		−	1.23378i
$291$		0			0
$292$	−69664.3			−0.0478138
$293$	2.88093e6			1.96049			0.980243	−	0.197799i	$-0.0633794\pi$
$293$	2.88093e6			1.96049			0.980243	+	0.197799i	$0.0633794\pi$
$294$		0			0
$295$	2.14256e6			1.43344
$296$	−243026.	+	1.61286e6i	−0.161222	+	1.06996i
$297$		0			0
$298$			242212.i			0.157999i
$299$	2.62426e6			1.69757
$300$		0			0
$301$		−	372596.i		−	0.237040i
$302$		−	636595.i		−	0.401648i
$303$		0			0
$304$		−	137981.i		−	0.0856315i
$305$	−889371.			−0.547436
$306$		0			0
$307$	837734.			0.507295			0.253647	−	0.967297i	$-0.418370\pi$
$307$	837734.			0.507295			0.253647	+	0.967297i	$0.418370\pi$
$308$	−360694.			−0.216651
$309$		0			0
$310$		−	883421.i		−	0.522112i
$311$			2.53759e6i			1.48772i	0.668338	+	0.743858i	$0.267006\pi$
$311$			2.53759e6i			1.48772i	−0.668338	+	0.743858i	$0.732994\pi$
$312$		0			0
$313$		−	40805.7i		−	0.0235429i	−0.999931	−	0.0117714i	$-0.996253\pi$
$313$		−	40805.7i		−	0.0235429i	0.999931	−	0.0117714i	$-0.00374705\pi$
$314$			1.04157e6i			0.596162i
$315$		0			0
$316$		−	719483.i		−	0.405324i
$317$	−3.05190e6			−1.70577			−0.852887	−	0.522095i	$-0.825151\pi$
$317$	−3.05190e6			−1.70577			−0.852887	+	0.522095i	$0.825151\pi$
$318$		0			0
$319$			4.30138e6i			2.36663i
$320$		−	2.00990e6i		−	1.09723i
$321$		0			0
$322$	563425.			0.302828
$323$	−433712.			−0.231311
$324$		0			0
$325$			553145.i			0.290490i
$326$	2.48697e6			1.29606
$327$		0			0
$328$			1.48216e6i			0.760696i
$329$	−838091.			−0.426876
$330$		0			0
$331$			1.61763e6i			0.811541i	0.913975	+	0.405770i	$0.132997\pi$
$331$			1.61763e6i			0.811541i	−0.913975	+	0.405770i	$0.867003\pi$
$332$	990728.			0.493298
$333$		0			0
$334$	−2.80063e6			−1.37369
$335$		−	137668.i		−	0.0670227i
$336$		0			0
$337$	481991.			0.231187			0.115594	−	0.993297i	$-0.463123\pi$
$337$	481991.			0.231187			0.115594	+	0.993297i	$0.463123\pi$
$338$			1.46073e6i			0.695470i
$339$		0			0
$340$	−1.08192e6			−0.507572
$341$			2.15052e6i			1.00151i
$342$		0			0
$343$	−1.33324e6			−0.611888
$344$	−1.74417e6			−0.794680
$345$		0			0
$346$			141964.i			0.0637510i
$347$		−	2.41283e6i		−	1.07573i	−0.843032	−	0.537864i	$-0.819231\pi$
$347$		−	2.41283e6i		−	1.07573i	0.843032	−	0.537864i	$-0.180769\pi$
$348$		0			0
$349$	1.58139e6			0.694987			0.347494	−	0.937682i	$-0.387033\pi$
$349$	1.58139e6			0.694987			0.347494	+	0.937682i	$0.387033\pi$
$350$			118760.i			0.0518202i
$351$		0			0
$352$			2.88052e6i			1.23912i
$353$		−	1.49851e6i		−	0.640061i	−0.947407	−	0.320031i	$-0.896307\pi$
$353$		−	1.49851e6i		−	0.640061i	0.947407	−	0.320031i	$-0.103693\pi$
$354$		0			0
$355$		−	3.51779e6i		−	1.48149i
$356$			865808.i			0.362073i
$357$		0			0
$358$	861261.			0.355163
$359$	−1.31212e6			−0.537324			−0.268662	−	0.963234i	$-0.586582\pi$
$359$	−1.31212e6			−0.537324			−0.268662	+	0.963234i	$0.586582\pi$
$360$		0			0
$361$	2.36819e6			0.956421
$362$			2.09106e6i			0.838677i
$363$		0			0
$364$		−	469573.i		−	0.185759i
$365$		−	321508.i		−	0.126316i
$366$		0			0
$367$	2478.13			0.000960417			0.000480208	−	1.00000i	$-0.499847\pi$
$367$	2478.13			0.000960417			0.000480208		1.00000i	$0.499847\pi$
$368$		−	1.30883e6i		−	0.503807i
$369$		0			0
$370$	−2.18830e6	−	329734.i	−0.831005	−	0.125216i
$371$	53704.1			0.0202569
$372$		0			0
$373$	−3.52163e6			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$373$	−3.52163e6			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$374$	−3.69117e6			−1.36454
$375$		0			0
$376$			3.92321e6i			1.43111i
$377$	−5.59980e6			−2.02917
$378$		0			0
$379$	−54249.9			−0.0194000			−0.00969998	−	0.999953i	$-0.503088\pi$
$379$	−54249.9			−0.0194000			−0.00969998	+	0.999953i	$0.503088\pi$
$380$	−269177.			−0.0956265
$381$		0			0
$382$	391505.			0.137271
$383$			335097.i			0.116728i	0.998295	+	0.0583639i	$0.0185884\pi$
$383$			335097.i			0.116728i	−0.998295	+	0.0583639i	$0.981412\pi$
$384$		0			0
$385$		−	1.66464e6i		−	0.572358i
$386$	398515.			0.136137
$387$		0			0
$388$		−	285529.i		−	0.0962878i
$389$		−	455081.i		−	0.152481i	−0.997089	−	0.0762403i	$-0.975708\pi$
$389$		−	455081.i		−	0.152481i	0.997089	−	0.0762403i	$-0.0242916\pi$
$390$		0			0
$391$	−4.11403e6			−1.36090
$392$			2.94906e6i			0.969323i
$393$		0			0
$394$		−	3.91287e6i		−	1.26986i
$395$	3.32049e6			1.07080
$396$		0			0
$397$	4.78706e6			1.52438			0.762189	−	0.647354i	$-0.224125\pi$
$397$	4.78706e6			1.52438			0.762189	+	0.647354i	$0.224125\pi$
$398$	2.61176e6			0.826466
$399$		0			0
$400$	275877.			0.0862117
$401$		−	1.69791e6i		−	0.527296i	−0.964619	−	0.263648i	$-0.915074\pi$
$401$		−	1.69791e6i		−	0.527296i	0.964619	−	0.263648i	$-0.0849257\pi$
$402$		0			0
$403$	−2.79967e6			−0.858707
$404$	998578.			0.304389
$405$		0			0
$406$	−1.20227e6			−0.361982
$407$	5.32700e6	+	802673.i	1.59403	+	0.240189i
$408$		0			0
$409$		−	5.43824e6i		−	1.60750i	−0.594969	−	0.803749i	$-0.702836\pi$
$409$		−	5.43824e6i		−	1.60750i	0.594969	−	0.803749i	$-0.297164\pi$
$410$	−2.01097e6			−0.590808
$411$		0			0
$412$			2.07504e6i			0.602259i
$413$		−	1.45782e6i		−	0.420560i
$414$		0			0
$415$			4.57231e6i			1.30321i
$416$	−3.75004e6			−1.06243
$417$		0			0
$418$	−918345.			−0.257078
$419$	2.38118e6			0.662609			0.331305	−	0.943524i	$-0.392511\pi$
$419$	2.38118e6			0.662609			0.331305	+	0.943524i	$0.392511\pi$
$420$		0			0
$421$		−	6.37474e6i		−	1.75290i	−0.481493	−	0.876450i	$-0.659905\pi$
$421$		−	6.37474e6i		−	1.75290i	0.481493	−	0.876450i	$-0.340095\pi$
$422$		−	500703.i		−	0.136867i
$423$		0			0
$424$		−	251396.i		−	0.0679115i
$425$		−	867162.i		−	0.232878i
$426$		0			0
$427$			605135.i			0.160614i
$428$	−2.40670e6			−0.635057
$429$		0			0
$430$		−	2.36646e6i		−	0.617202i
$431$			2.95930e6i			0.767353i	0.923468	+	0.383676i	$0.125342\pi$
$431$			2.95930e6i			0.767353i	−0.923468	+	0.383676i	$0.874658\pi$
$432$		0			0
$433$	−3.48491e6			−0.893248			−0.446624	−	0.894722i	$-0.647374\pi$
$433$	−3.48491e6			−0.893248			−0.446624	+	0.894722i	$0.647374\pi$
$434$	−601087.			−0.153184
$435$		0			0
$436$		−	1.04650e6i		−	0.263648i
$437$	−1.02355e6			−0.256393
$438$		0			0
$439$			824442.i			0.204173i	0.994776	+	0.102087i	$0.0325519\pi$
$439$			824442.i			0.204173i	−0.994776	+	0.102087i	$0.967448\pi$
$440$	−7.79237e6			−1.91884
$441$		0			0
$442$		−	4.80539e6i		−	1.16997i
$443$	−86934.7			−0.0210467			−0.0105233	−	0.999945i	$-0.503350\pi$
$443$	−86934.7			−0.0210467			−0.0105233	+	0.999945i	$0.503350\pi$
$444$		0			0
$445$	−3.99579e6			−0.956539
$446$		−	672091.i		−	0.159989i
$447$		0			0
$448$	−1.36755e6			−0.321921
$449$		−	2.36098e6i		−	0.552683i	−0.961060	−	0.276341i	$-0.910878\pi$
$449$		−	2.36098e6i		−	0.552683i	0.961060	−	0.276341i	$-0.0891220\pi$
$450$		0			0
$451$	4.89532e6			1.13329
$452$		−	2.79199e6i		−	0.642789i
$453$		0			0
$454$	−5.18729e6			−1.18114
$455$	2.16713e6			0.490745
$456$		0			0
$457$			7.72701e6i			1.73070i	0.501171	+	0.865348i	$0.332903\pi$
$457$			7.72701e6i			1.73070i	−0.501171	+	0.865348i	$0.667097\pi$
$458$		−	5.60034e6i		−	1.24753i
$459$		0			0
$460$	−2.55331e6			−0.562612
$461$		−	3.96398e6i		−	0.868718i	−0.900740	−	0.434359i	$-0.856975\pi$
$461$		−	3.96398e6i		−	0.868718i	0.900740	−	0.434359i	$-0.143025\pi$
$462$		0			0
$463$			292922.i			0.0635037i	0.999496	+	0.0317519i	$0.0101086\pi$
$463$			292922.i			0.0635037i	−0.999496	+	0.0317519i	$0.989891\pi$
$464$			2.79286e6i			0.602219i
$465$		0			0
$466$		−	1.43424e6i		−	0.305954i
$467$			3.37447e6i			0.716000i	0.933722	+	0.358000i	$0.116541\pi$
$467$			3.37447e6i			0.716000i	−0.933722	+	0.358000i	$0.883459\pi$
$468$		0			0
$469$	−93670.7			−0.0196640
$470$	−5.32295e6			−1.11149
$471$		0			0
$472$	−6.82422e6			−1.40993
$473$			5.76068e6i			1.18392i
$474$		0			0
$475$		−	215746.i		−	0.0438742i
$476$			736147.i			0.148918i
$477$		0			0
$478$	2.78572e6			0.557657
$479$		−	180336.i		−	0.0359123i	−0.999839	−	0.0179561i	$-0.994284\pi$
$479$		−	180336.i		−	0.0359123i	0.999839	−	0.0179561i	$-0.00571593\pi$
$480$		0			0
$481$	−1.04497e6	+	6.93502e6i	−0.205940	+	1.36674i
$482$	1.62845e6			0.319270
$483$		0			0
$484$	3.43065e6			0.665677
$485$	1.31775e6			0.254377
$486$		0			0
$487$		−	2.54645e6i		−	0.486534i	−0.969959	−	0.243267i	$-0.921781\pi$
$487$		−	2.54645e6i		−	0.486534i	0.969959	−	0.243267i	$-0.0782191\pi$
$488$	2.83271e6			0.538460
$489$		0			0
$490$	−4.00123e6			−0.752842
$491$	−6.90340e6			−1.29229			−0.646144	−	0.763216i	$-0.723619\pi$
$491$	−6.90340e6			−1.29229			−0.646144	+	0.763216i	$0.723619\pi$
$492$		0			0
$493$	8.77877e6			1.62673
$494$		−	1.19556e6i		−	0.220421i
$495$		0			0
$496$			1.39632e6i			0.254848i
$497$	−2.39353e6			−0.434659
$498$		0			0
$499$			8.49860e6i			1.52790i	0.645273	+	0.763952i	$0.276744\pi$
$499$			8.49860e6i			1.52790i	−0.645273	+	0.763952i	$0.723256\pi$
$500$			2.02255e6i			0.361804i
$501$		0			0
$502$	2.64109e6			0.467761
$503$		−	1.99714e6i		−	0.351956i	−0.984394	−	0.175978i	$-0.943691\pi$
$503$		−	1.99714e6i		−	0.351956i	0.984394	−	0.175978i	$-0.0563088\pi$
$504$		0			0
$505$			4.60854e6i			0.804146i
$506$	−8.71108e6			−1.51250
$507$		0			0
$508$	−2.33000e6			−0.400586
$509$	760830.			0.130165			0.0650824	−	0.997880i	$-0.479269\pi$
$509$	760830.			0.130165			0.0650824	+	0.997880i	$0.479269\pi$
$510$		0			0
$511$	−218756.			−0.0370603
$512$			4.50308e6i			0.759163i
$513$		0			0
$514$	6.35881e6			1.06162
$515$	−9.57652e6			−1.59107
$516$		0			0
$517$	1.29577e7			2.13207
$518$	−224354.	+	1.48894e6i	−0.0367375	+	0.243811i
$519$		0			0
$520$		−	1.01446e7i		−	1.64523i
$521$	6.12915e6			0.989251			0.494625	−	0.869106i	$-0.335305\pi$
$521$	6.12915e6			0.989251			0.494625	+	0.869106i	$0.335305\pi$
$522$		0			0
$523$		−	2.39336e6i		−	0.382608i	−0.981531	−	0.191304i	$-0.938728\pi$
$523$		−	2.39336e6i		−	0.382608i	0.981531	−	0.191304i	$-0.0612716\pi$
$524$		−	2.50666e6i		−	0.398811i
$525$		0			0
$526$		−	2.75041e6i		−	0.433445i
$527$	4.38903e6			0.688402
$528$		0			0
$529$	−3.27269e6			−0.508471
$530$	341089.			0.0527447
$531$		0			0
$532$			183150.i			0.0280561i
$533$			6.37303e6i			0.971690i
$534$		0			0
$535$		−	1.11072e7i		−	1.67772i
$536$			438484.i			0.0659237i
$537$		0			0
$538$			1.41481e6i			0.210738i
$539$	9.74022e6			1.44410
$540$		0			0
$541$			1.33289e6i			0.195795i	0.995197	+	0.0978975i	$0.0312117\pi$
$541$			1.33289e6i			0.195795i	−0.995197	+	0.0978975i	$0.968788\pi$
$542$		−	6.91851e6i		−	1.01161i
$543$		0			0
$544$	5.87891e6			0.851726
$545$	4.82972e6			0.696516
$546$		0			0
$547$			3.62910e6i			0.518598i	0.965797	+	0.259299i	$0.0834914\pi$
$547$			3.62910e6i			0.518598i	−0.965797	+	0.259299i	$0.916509\pi$
$548$	−4.11197e6			−0.584923
$549$		0			0
$550$		−	1.83613e6i		−	0.258820i
$551$	2.18412e6			0.306476
$552$		0			0
$553$		−	2.25929e6i		−	0.314166i
$554$	−1.93725e6			−0.268171
$555$		0			0
$556$	−2.23237e6			−0.306252
$557$			2.68324e6i			0.366456i	0.983070	+	0.183228i	$0.0586546\pi$
$557$			2.68324e6i			0.366456i	−0.983070	+	0.183228i	$0.941345\pi$
$558$		0			0
$559$	−7.49961e6			−1.01510
$560$		−	1.08084e6i		−	0.145644i
$561$		0			0
$562$	−5.56223e6			−0.742862
$563$		−	8.91127e6i		−	1.18486i	−0.805620	−	0.592432i	$-0.798168\pi$
$563$		−	8.91127e6i		−	1.18486i	0.805620	−	0.592432i	$-0.201832\pi$
$564$		0			0
$565$	1.28853e7			1.69814
$566$	1.71723e6			0.225314
$567$		0			0
$568$			1.12044e7i			1.45720i
$569$			1.82414e6i			0.236199i	0.993002	+	0.118100i	$0.0376802\pi$
$569$			1.82414e6i			0.236199i	−0.993002	+	0.118100i	$0.962320\pi$
$570$		0			0
$571$	−1.44646e7			−1.85659			−0.928296	−	0.371843i	$-0.878726\pi$
$571$	−1.44646e7			−1.85659			−0.928296	+	0.371843i	$0.878726\pi$
$572$			7.26004e6i			0.927788i
$573$		0			0
$574$			1.36828e6i			0.173339i
$575$		−	2.04649e6i		−	0.258130i
$576$		0			0
$577$		−	9.87667e6i		−	1.23501i	−0.786566	−	0.617506i	$-0.788143\pi$
$577$		−	9.87667e6i		−	1.23501i	0.786566	−	0.617506i	$-0.211857\pi$
$578$			1.39753e6i			0.173997i
$579$		0			0
$580$	5.44840e6			0.672511
$581$	3.11104e6			0.382354
$582$		0			0
$583$	−830315.			−0.101175
$584$			1.02403e6i			0.124245i
$585$		0			0
$586$		−	1.24498e7i		−	1.49768i
$587$		−	1.32330e7i		−	1.58512i	−0.609792	−	0.792562i	$-0.708747\pi$
$587$		−	1.32330e7i		−	1.58512i	0.609792	−	0.792562i	$-0.291253\pi$
$588$		0			0
$589$	1.09197e6			0.129695
$590$		−	9.25899e6i		−	1.09505i
$591$		0			0
$592$	3.45880e6	+	521172.i	0.405621	+	0.0611190i
$593$	−2.94423e6			−0.343823			−0.171911	−	0.985112i	$-0.554994\pi$
$593$	−2.94423e6			−0.343823			−0.171911	+	0.985112i	$0.554994\pi$
$594$		0			0
$595$	−3.39739e6			−0.393417
$596$	−746848.			−0.0861225
$597$		0			0
$598$		−	1.13406e7i		−	1.29683i
$599$	−2.83285e6			−0.322594			−0.161297	−	0.986906i	$-0.551568\pi$
$599$	−2.83285e6			−0.322594			−0.161297	+	0.986906i	$0.551568\pi$
$600$		0			0
$601$	−6.31969e6			−0.713690			−0.356845	−	0.934164i	$-0.616148\pi$
$601$	−6.31969e6			−0.713690			−0.356845	+	0.934164i	$0.616148\pi$
$602$	−1.61016e6			−0.181083
$603$		0			0
$604$	1.96291e6			0.218931
$605$			1.58328e7i			1.75861i
$606$		0			0
$607$			1.08691e7i			1.19735i	0.800993	+	0.598674i	$0.204306\pi$
$607$			1.08691e7i			1.19735i	−0.800993	+	0.598674i	$0.795694\pi$
$608$	1.46265e6			0.160465
$609$		0			0
$610$			3.84338e6i			0.418204i
$611$			1.68691e7i			1.82805i
$612$		0			0
$613$	1.21710e7			1.30820			0.654100	−	0.756408i	$-0.273047\pi$
$613$	1.21710e7			1.30820			0.654100	+	0.756408i	$0.273047\pi$
$614$		−	3.62023e6i		−	0.387539i
$615$		0			0
$616$			5.30200e6i			0.562973i
$617$	4.97705e6			0.526331			0.263165	−	0.964751i	$-0.415234\pi$
$617$	4.97705e6			0.526331			0.263165	+	0.964751i	$0.415234\pi$
$618$		0			0
$619$	−1.30866e7			−1.37278			−0.686388	−	0.727235i	$-0.740805\pi$
$619$	−1.30866e7			−1.37278			−0.686388	+	0.727235i	$0.740805\pi$
$620$	2.72398e6			0.284593
$621$		0			0
$622$	1.09661e7			1.13652
$623$			2.71877e6i			0.280642i
$624$		0			0
$625$	−1.13867e7			−1.16600
$626$	−176340.			−0.0179852
$627$		0			0
$628$	−3.21163e6			−0.324957
$629$	1.63819e6	−	1.08720e7i	0.165097	−	1.09568i
$630$		0			0
$631$		−	3.35117e6i		−	0.335060i	−0.985867	−	0.167530i	$-0.946421\pi$
$631$		−	3.35117e6i		−	0.335060i	0.985867	−	0.167530i	$-0.0535791\pi$
$632$	−1.05760e7			−1.05324
$633$		0			0
$634$			1.31886e7i			1.30310i
$635$		−	1.07532e7i		−	1.05828i
$636$		0			0
$637$			1.26804e7i			1.23818i
$638$	1.85882e7			1.80795
$639$		0			0
$640$	76547.0			0.00738717
$641$	1.14208e7			1.09787			0.548936	−	0.835864i	$-0.315033\pi$
$641$	1.14208e7			1.09787			0.548936	+	0.835864i	$0.315033\pi$
$642$		0			0
$643$		−	3.69497e6i		−	0.352438i	−0.984351	−	0.176219i	$-0.943613\pi$
$643$		−	3.69497e6i		−	0.352438i	0.984351	−	0.176219i	$-0.0563867\pi$
$644$			1.73729e6i			0.165066i
$645$		0			0
$646$			1.87427e6i			0.176706i
$647$			1.92498e7i			1.80786i	0.427680	+	0.903930i	$0.359331\pi$
$647$			1.92498e7i			1.80786i	−0.427680	+	0.903930i	$0.640669\pi$
$648$		0			0
$649$			2.25392e7i			2.10052i
$650$	2.39039e6			0.221915
$651$		0			0
$652$			7.66844e6i			0.706461i
$653$			6.42777e6i			0.589898i	0.955513	+	0.294949i	$0.0953027\pi$
$653$			6.42777e6i			0.589898i	−0.955513	+	0.294949i	$0.904697\pi$
$654$		0			0
$655$	1.15685e7			1.05359
$656$	3.17851e6			0.288379
$657$		0			0
$658$			3.62178e6i			0.326105i
$659$	1.61323e7			1.44705			0.723525	−	0.690298i	$-0.242521\pi$
$659$	1.61323e7			1.44705			0.723525	+	0.690298i	$0.242521\pi$
$660$		0			0
$661$			1.46494e7i			1.30412i	0.758168	+	0.652059i	$0.226095\pi$
$661$			1.46494e7i			1.30412i	−0.758168	+	0.652059i	$0.773905\pi$
$662$	6.99054e6			0.619963
$663$		0			0
$664$		−	1.45632e7i		−	1.28184i
$665$	−845256.			−0.0741198
$666$		0			0
$667$	2.07177e7			1.80313
$668$		−	8.63561e6i		−	0.748776i
$669$		0			0
$670$	−594928.			−0.0512009
$671$		−	9.35595e6i		−	0.802198i
$672$		0			0
$673$	1.29525e7			1.10234			0.551169	−	0.834394i	$-0.314182\pi$
$673$	1.29525e7			1.10234			0.551169	+	0.834394i	$0.314182\pi$
$674$		−	2.08290e6i		−	0.176612i
$675$		0			0
$676$	−4.50409e6			−0.379088
$677$	7.27861e6			0.610347			0.305174	−	0.952297i	$-0.401286\pi$
$677$	7.27861e6			0.610347			0.305174	+	0.952297i	$0.401286\pi$
$678$		0			0
$679$		−	896606.i		−	0.0746324i
$680$			1.59036e7i			1.31894i
$681$		0			0
$682$	9.29336e6			0.765089
$683$		−	1.85212e6i		−	0.151921i	−0.997111	−	0.0759604i	$-0.975798\pi$
$683$		−	1.85212e6i		−	0.151921i	0.997111	−	0.0759604i	$-0.0242022\pi$
$684$		0			0
$685$		−	1.89772e7i		−	1.54527i
$686$			5.76153e6i			0.467442i
$687$		0			0
$688$			3.74038e6i			0.301262i
$689$		−	1.08096e6i		−	0.0867481i
$690$		0			0
$691$	5.70051e6			0.454170			0.227085	−	0.973875i	$-0.427081\pi$
$691$	5.70051e6			0.454170			0.227085	+	0.973875i	$0.427081\pi$
$692$	−437737.			−0.0347495
$693$		0			0
$694$	−1.04269e7			−0.821785
$695$		−	1.03026e7i		−	0.809067i
$696$		0			0
$697$		−	9.99096e6i		−	0.778978i
$698$		−	6.83393e6i		−	0.530924i
$699$		0			0
$700$	−366189.			−0.0282462
$701$		−	1.41728e7i		−	1.08933i	−0.838653	−	0.544666i	$-0.816656\pi$
$701$		−	1.41728e7i		−	1.08933i	0.838653	−	0.544666i	$-0.183344\pi$
$702$		0			0
$703$	407575.	−	2.70490e6i	0.0311042	−	0.206425i
$704$	2.11436e7			1.60786
$705$		0			0
$706$	−6.47573e6			−0.488964
$707$	3.13569e6			0.235931
$708$		0			0
$709$		−	1.92333e6i		−	0.143694i	−0.997416	−	0.0718468i	$-0.977111\pi$
$709$		−	1.92333e6i		−	0.143694i	0.997416	−	0.0718468i	$-0.0228893\pi$
$710$	−1.52020e7			−1.13176
$711$		0			0
$712$	1.27269e7			0.940855
$713$	1.03580e7			0.763050
$714$		0			0
$715$	−3.35058e7			−2.45107
$716$			2.65565e6i			0.193593i
$717$		0			0
$718$			5.67026e6i			0.410480i
$719$	−465638.			−0.0335913			−0.0167956	−	0.999859i	$-0.505346\pi$
$719$	−465638.			−0.0335913			−0.0167956	+	0.999859i	$0.505346\pi$
$720$		0			0
$721$			6.51594e6i			0.466809i
$722$		−	1.02341e7i		−	0.730642i
$723$		0			0
$724$	−6.44767e6			−0.457147
$725$			4.36691e6i			0.308553i
$726$		0			0
$727$		−	1.43963e7i		−	1.01022i	−0.863056	−	0.505108i	$-0.831453\pi$
$727$		−	1.43963e7i		−	1.01022i	0.863056	−	0.505108i	$-0.168547\pi$
$728$	−6.90247e6			−0.482699
$729$		0			0
$730$	−1.38938e6			−0.0964971
$731$	1.17571e7			0.813779
$732$		0			0
$733$	−3.84437e6			−0.264281			−0.132140	−	0.991231i	$-0.542185\pi$
$733$	−3.84437e6			−0.264281			−0.132140	+	0.991231i	$0.542185\pi$
$734$		−	10709.2i		−	0.000733694i
$735$		0			0
$736$	1.38741e7			0.944084
$737$	1.44824e6			0.0982133
$738$		0			0
$739$	−1.75279e7			−1.18064			−0.590321	−	0.807169i	$-0.700999\pi$
$739$	−1.75279e7			−1.18064			−0.590321	+	0.807169i	$0.700999\pi$
$740$	1.01672e6	−	6.74752e6i	0.0682529	−	0.452965i
$741$		0			0
$742$		−	232080.i		−	0.0154749i
$743$	3.23769e6			0.215161			0.107580	−	0.994196i	$-0.465690\pi$
$743$	3.23769e6			0.215161			0.107580	+	0.994196i	$0.465690\pi$
$744$		0			0
$745$		−	3.44678e6i		−	0.227522i
$746$			1.52186e7i			1.00121i
$747$		0			0
$748$		−	1.13815e7i		−	0.743783i
$749$	−7.55742e6			−0.492231
$750$		0			0
$751$	5.90153e6			0.381825			0.190913	−	0.981607i	$-0.438855\pi$
$751$	5.90153e6			0.381825			0.190913	+	0.981607i	$0.438855\pi$
$752$	8.41335e6			0.542531
$753$		0			0
$754$			2.41993e7i			1.55015i
$755$			9.05902e6i			0.578381i
$756$		0			0
$757$		−	1.35235e7i		−	0.857729i	−0.903369	−	0.428865i	$-0.858914\pi$
$757$		−	1.35235e7i		−	0.857729i	0.903369	−	0.428865i	$-0.141086\pi$
$758$			234439.i			0.0148203i
$759$		0			0
$760$			3.95675e6i			0.248487i
$761$	−1.77191e7			−1.10913			−0.554563	−	0.832142i	$-0.687115\pi$
$761$	−1.77191e7			−1.10913			−0.554563	+	0.832142i	$0.687115\pi$
$762$		0			0
$763$		−	3.28618e6i		−	0.204353i
$764$			1.20719e6i			0.0748240i
$765$		0			0
$766$	1.44811e6			0.0891722
$767$	−2.93429e7			−1.80100
$768$		0			0
$769$		−	2.88272e7i		−	1.75787i	−0.476945	−	0.878933i	$-0.658256\pi$
$769$		−	2.88272e7i		−	1.75787i	0.476945	−	0.878933i	$-0.341744\pi$
$770$	−7.19366e6			−0.437243
$771$		0			0
$772$			1.22880e6i			0.0742059i
$773$	1.64694e7			0.991354			0.495677	−	0.868507i	$-0.334920\pi$
$773$	1.64694e7			0.991354			0.495677	+	0.868507i	$0.334920\pi$
$774$		0			0
$775$			2.18328e6i			0.130574i
$776$	−4.19712e6			−0.250206
$777$		0			0
$778$	−1.96661e6			−0.116485
$779$		−	2.48570e6i		−	0.146759i
$780$		0			0
$781$	3.70062e7			2.17094
$782$			1.77786e7i			1.03964i
$783$		0			0
$784$	6.32428e6			0.367469
$785$		−	1.48220e7i		−	0.858484i
$786$		0			0
$787$	1.70192e6			0.0979498			0.0489749	−	0.998800i	$-0.484405\pi$
$787$	1.70192e6			0.0979498			0.0489749	+	0.998800i	$0.484405\pi$
$788$	1.20651e7			0.692175
$789$		0			0
$790$		−	1.43493e7i		−	0.818021i
$791$		−	8.76729e6i		−	0.498224i
$792$		0			0
$793$	1.21802e7			0.687812
$794$		−	2.06871e7i		−	1.16452i
$795$		0			0
$796$			8.05322e6i			0.450492i
$797$			139708.i			0.00779068i	0.999992	+	0.00389534i	$0.00123993\pi$
$797$			139708.i			0.00779068i	−0.999992	+	0.00389534i	$0.998760\pi$
$798$		0			0
$799$		−	2.64456e7i		−	1.46550i
$800$			2.92441e6i			0.161552i
$801$		0			0
$802$	−7.33746e6			−0.402819
$803$	3.38218e6			0.185101
$804$		0			0
$805$	−8.01778e6			−0.436078
$806$			1.20987e7i			0.655995i
$807$		0			0
$808$		−	1.46786e7i		−	0.790960i
$809$			1.90144e7i			1.02144i	0.859747	+	0.510719i	$0.170621\pi$
$809$			1.90144e7i			1.02144i	−0.859747	+	0.510719i	$0.829379\pi$
$810$		0			0
$811$	−1.76552e7			−0.942583			−0.471291	−	0.881978i	$-0.656212\pi$
$811$	−1.76552e7			−0.942583			−0.471291	+	0.881978i	$0.656212\pi$
$812$		−	3.70714e6i		−	0.197310i
$813$		0			0
$814$	3.46872e6	−	2.30204e7i	0.183488	−	1.21773i
$815$	−3.53906e7			−1.86635
$816$		0			0
$817$	2.92511e6			0.153316
$818$	−2.35011e7			−1.22802
$819$		0			0
$820$		−	6.20073e6i		−	0.322039i
$821$	−9.66364e6			−0.500360			−0.250180	−	0.968199i	$-0.580490\pi$
$821$	−9.66364e6			−0.500360			−0.250180	+	0.968199i	$0.580490\pi$
$822$		0			0
$823$	−5.50924e6			−0.283525			−0.141763	−	0.989901i	$-0.545277\pi$
$823$	−5.50924e6			−0.283525			−0.141763	+	0.989901i	$0.545277\pi$
$824$	3.05019e7			1.56498
$825$		0			0
$826$	−6.29989e6			−0.321280
$827$		−	7.14304e6i		−	0.363178i	−0.983375	−	0.181589i	$-0.941876\pi$
$827$		−	7.14304e6i		−	0.363178i	0.983375	−	0.181589i	$-0.0581240\pi$
$828$		0			0
$829$			1.06660e7i			0.539035i	0.962996	+	0.269517i	$0.0868642\pi$
$829$			1.06660e7i			0.539035i	−0.962996	+	0.269517i	$0.913136\pi$
$830$	1.97591e7			0.995568
$831$		0			0
$832$			2.75261e7i			1.37859i
$833$		−	1.98790e7i		−	0.992619i
$834$		0			0
$835$	3.98542e7			1.97814
$836$		−	2.83167e6i		−	0.140129i
$837$		0			0
$838$		−	1.02902e7i		−	0.506189i
$839$	−2.40901e7			−1.18150			−0.590751	−	0.806854i	$-0.701168\pi$
$839$	−2.40901e7			−1.18150			−0.590751	+	0.806854i	$0.701168\pi$
$840$		0			0
$841$	−2.36976e7			−1.15535
$842$	−2.75482e7			−1.33910
$843$		0			0
$844$	1.54389e6			0.0746038
$845$		−	2.07868e7i		−	1.00149i
$846$		0			0
$847$	1.07728e7			0.515964
$848$	−539120.			−0.0257452
$849$		0			0
$850$	−3.74741e6			−0.177903
$851$	3.86610e6	−	2.56577e7i	0.182999	−	1.21449i
$852$		0			0
$853$		−	6.97130e6i		−	0.328051i	−0.986456	−	0.164025i	$-0.947552\pi$
$853$		−	6.97130e6i		−	0.328051i	0.986456	−	0.164025i	$-0.0524479\pi$
$854$	2.61507e6			0.122698
$855$		0			0
$856$			3.53772e7i			1.65021i
$857$			9.63784e6i			0.448258i	0.974560	+	0.224129i	$0.0719536\pi$
$857$			9.63784e6i			0.448258i	−0.974560	+	0.224129i	$0.928046\pi$
$858$		0			0
$859$			9.01647e6i			0.416921i	0.978031	+	0.208461i	$0.0668453\pi$
$859$			9.01647e6i			0.416921i	−0.978031	+	0.208461i	$0.933155\pi$
$860$	7.29685e6			0.336426
$861$		0			0
$862$	1.27885e7			0.586206
$863$	−2.16670e7			−0.990312			−0.495156	−	0.868804i	$-0.664889\pi$
$863$	−2.16670e7			−0.990312			−0.495156	+	0.868804i	$0.664889\pi$
$864$		0			0
$865$		−	2.02020e6i		−	0.0918025i
$866$			1.50599e7i			0.682382i
$867$		0			0
$868$		−	1.85342e6i		−	0.0834977i
$869$			3.49307e7i			1.56912i
$870$		0			0
$871$			1.88540e6i			0.0842090i
$872$	−1.53830e7			−0.685095
$873$		0			0
$874$			4.42324e6i			0.195867i
$875$			6.35111e6i			0.280433i
$876$		0			0
$877$	−2.19642e7			−0.964308			−0.482154	−	0.876086i	$-0.660146\pi$
$877$	−2.19642e7			−0.964308			−0.482154	+	0.876086i	$0.660146\pi$
$878$	3.56279e6			0.155975
$879$		0			0
$880$			1.67108e7i			0.727429i
$881$	−2.50710e7			−1.08826			−0.544130	−	0.839001i	$-0.683140\pi$
$881$	−2.50710e7			−1.08826			−0.544130	+	0.839001i	$0.683140\pi$
$882$		0			0
$883$			1.63882e7i			0.707343i	0.935370	+	0.353672i	$0.115067\pi$
$883$			1.63882e7i			0.707343i	−0.935370	+	0.353672i	$0.884933\pi$
$884$	1.48172e7			0.637727
$885$		0			0
$886$			375685.i			0.0160783i
$887$	−3.48007e7			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$887$	−3.48007e7			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$888$		0			0
$889$	−7.31654e6			−0.310493
$890$			1.72676e7i			0.730732i
$891$		0			0
$892$	2.07236e6			0.0872072
$893$		−	6.57954e6i		−	0.276100i
$894$		0			0
$895$	−1.22561e7			−0.511440
$896$		−	52083.2i		−	0.00216734i
$897$		0			0
$898$	−1.02029e7			−0.422213
$899$	−2.21026e7			−0.912103
$900$		0			0
$901$			1.69461e6i			0.0695436i
$902$		−	2.11549e7i		−	0.865755i
$903$		0			0
$904$	−4.10408e7			−1.67030
$905$		−	2.97566e7i		−	1.20771i
$906$		0			0
$907$			4.68436e7i			1.89074i	0.325998	+	0.945370i	$0.394300\pi$
$907$			4.68436e7i			1.89074i	−0.325998	+	0.945370i	$0.605700\pi$
$908$		−	1.59947e7i		−	0.643817i
$909$		0			0
$910$		−	9.36515e6i		−	0.374897i
$911$			2.25403e7i			0.899836i	0.893070	+	0.449918i	$0.148547\pi$
$911$			2.25403e7i			0.899836i	−0.893070	+	0.449918i	$0.851453\pi$
$912$		0			0
$913$	−4.80995e7			−1.90970
$914$	3.33919e7			1.32214
$915$		0			0
$916$	1.72684e7			0.680006
$917$		−	7.87130e6i		−	0.309117i
$918$		0			0
$919$		−	3.10604e6i		−	0.121316i	−0.998159	−	0.0606580i	$-0.980680\pi$
$919$		−	3.10604e6i		−	0.121316i	0.998159	−	0.0606580i	$-0.0193199\pi$
$920$			3.75322e7i			1.46196i
$921$		0			0
$922$	−1.71302e7			−0.663643
$923$			4.81770e7i			1.86138i
$924$		0			0
$925$	5.40816e6	+	814903.i	0.207824	+	0.0313149i
$926$	1.26585e6			0.0485126
$927$		0			0
$928$	−2.96054e7			−1.12850
$929$	−4.01231e7			−1.52530			−0.762651	−	0.646811i	$-0.776102\pi$
$929$	−4.01231e7			−1.52530			−0.762651	+	0.646811i	$0.776102\pi$
$930$		0			0
$931$		−	4.94581e6i		−	0.187009i
$932$	4.42240e6			0.166770
$933$		0			0
$934$	1.45826e7			0.546976
$935$	5.25269e7			1.96495
$936$		0			0
$937$	−1.11839e7			−0.416146			−0.208073	−	0.978113i	$-0.566719\pi$
$937$	−1.11839e7			−0.416146			−0.208073	+	0.978113i	$0.566719\pi$
$938$			404794.i			0.0150220i
$939$		0			0
$940$		−	1.64130e7i		−	0.605855i
$941$	6.06029e6			0.223110			0.111555	−	0.993758i	$-0.464417\pi$
$941$	6.06029e6			0.223110			0.111555	+	0.993758i	$0.464417\pi$
$942$		0			0
$943$		−	2.35785e7i		−	0.863448i
$944$			1.46346e7i			0.534504i
$945$		0			0
$946$	2.48945e7			0.904433
$947$			1.03024e7i			0.373305i	0.982426	+	0.186652i	$0.0597638\pi$
$947$			1.03024e7i			0.373305i	−0.982426	+	0.186652i	$0.940236\pi$
$948$		0			0
$949$			4.40313e6i			0.158707i
$950$	−932337.			−0.0335169
$951$		0			0
$952$	1.08210e7			0.386967
$953$	−4.09791e6			−0.146160			−0.0730802	−	0.997326i	$-0.523283\pi$
$953$	−4.09791e6			−0.146160			−0.0730802	+	0.997326i	$0.523283\pi$
$954$		0			0
$955$	−5.57129e6			−0.197673
$956$			8.58961e6i			0.303969i
$957$		0			0
$958$	−779314.			−0.0274346
$959$	−1.29122e7			−0.453372
$960$		0			0
$961$	1.75787e7			0.614016
$962$	2.99694e7	+	4.51579e6i	1.04410	+	0.157324i
$963$		0			0
$964$			5.02125e6i			0.174028i
$965$	−5.67104e6			−0.196040
$966$		0			0
$967$		−	3.24582e7i		−	1.11624i	−0.829759	−	0.558122i	$-0.811522\pi$
$967$		−	3.24582e7i		−	1.11624i	0.829759	−	0.558122i	$-0.188478\pi$
$968$		−	5.04287e7i		−	1.72978i
$969$		0			0
$970$		−	5.69459e6i		−	0.194327i
$971$	−8.02053e6			−0.272995			−0.136498	−	0.990640i	$-0.543585\pi$
$971$	−8.02053e6			−0.272995			−0.136498	+	0.990640i	$0.543585\pi$
$972$		0			0
$973$	−7.00997e6			−0.237375
$974$	−1.10044e7			−0.371679
$975$		0			0
$976$		−	6.07478e6i		−	0.204129i
$977$		−	1.02996e7i		−	0.345209i	−0.984991	−	0.172605i	$-0.944782\pi$
$977$		−	1.02996e7i		−	0.345209i	0.984991	−	0.172605i	$-0.0552183\pi$
$978$		0			0
$979$		−	4.20347e7i		−	1.40169i
$980$		−	1.23376e7i		−	0.410360i
$981$		0			0
$982$			2.98328e7i			0.987221i
$983$	−860199.			−0.0283933			−0.0141966	−	0.999899i	$-0.504519\pi$
$983$	−860199.			−0.0283933			−0.0141966	+	0.999899i	$0.504519\pi$
$984$		0			0
$985$			5.56817e7i			1.82861i
$986$		−	3.79371e7i		−	1.24272i
$987$		0			0
$988$	3.68644e6			0.120148
$989$	2.77465e7			0.902023
$990$		0			0
$991$			2.70808e7i			0.875946i	0.898988	+	0.437973i	$0.144303\pi$
$991$			2.70808e7i			0.875946i	−0.898988	+	0.437973i	$0.855697\pi$
$992$	−1.48015e7			−0.477559
$993$		0			0
$994$			1.03436e7i			0.332050i
$995$	−3.71664e7			−1.19013
$996$		0			0
$997$			3.74240e7i			1.19237i	0.802846	+	0.596187i	$0.203318\pi$
$997$			3.74240e7i			1.19237i	−0.802846	+	0.596187i	$0.796682\pi$
$998$	3.67263e7			1.16722
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.6.c.d.73.6		16
3.2	odd	2		37.6.b.a.36.11	yes	16
12.11	even	2		592.6.g.c.369.13		16
37.36	even	2	inner	333.6.c.d.73.11		16
111.110	odd	2		37.6.b.a.36.6	✓	16
444.443	even	2		592.6.g.c.369.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.b.a.36.6	✓	16	111.110	odd	2
37.6.b.a.36.11	yes	16	3.2	odd	2
333.6.c.d.73.6		16	1.1	even	1	trivial
333.6.c.d.73.11		16	37.36	even	2	inner
592.6.g.c.369.13		16	12.11	even	2
592.6.g.c.369.14		16	444.443	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	333.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.32146i q^{2} +13.3250 q^{4} +61.4962i q^{5} +41.8425 q^{7} -195.870i q^{8} +O(q^{10})\)	\(q-4.32146i q^{2} +13.3250 q^{4} +61.4962i q^{5} +41.8425 q^{7} -195.870i q^{8} +265.753 q^{10} -646.924 q^{11} -842.206i q^{13} -180.821i q^{14} -420.045 q^{16} +1320.32i q^{17} +328.490i q^{19} +819.436i q^{20} +2795.66i q^{22} +3115.93i q^{23} -656.781 q^{25} -3639.56 q^{26} +557.551 q^{28} -6648.96i q^{29} -3324.21i q^{31} -4452.64i q^{32} +5705.72 q^{34} +2573.16i q^{35} +(-8234.35 - 1240.75i) q^{37} +1419.56 q^{38} +12045.3 q^{40} -7567.06 q^{41} -8904.72i q^{43} -8620.26 q^{44} +13465.4 q^{46} -20029.7 q^{47} -15056.2 q^{49} +2838.25i q^{50} -11222.4i q^{52} +1283.48 q^{53} -39783.4i q^{55} -8195.70i q^{56} -28733.2 q^{58} -34840.5i q^{59} +14462.2i q^{61} -14365.5 q^{62} -32683.3 q^{64} +51792.5 q^{65} -2238.65 q^{67} +17593.3i q^{68} +11119.8 q^{70} -57203.4 q^{71} -5228.09 q^{73} +(-5361.86 + 35584.4i) q^{74} +4377.13i q^{76} -27068.9 q^{77} -53995.0i q^{79} -25831.2i q^{80} +32700.8i q^{82} +74351.1 q^{83} -81194.8 q^{85} -38481.4 q^{86} +126713. i q^{88} +64976.2i q^{89} -35240.0i q^{91} +41519.8i q^{92} +86557.3i q^{94} -20200.9 q^{95} -21428.1i q^{97} +65064.8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 268 q^{4} + 190 q^{7}+O(q^{10}) \) 16 * q - 268 * q^4 + 190 * q^7	\( 16 q - 268 q^{4} + 190 q^{7} - 74 q^{10} + 1110 q^{11} + 2900 q^{16} - 12052 q^{25} - 4902 q^{26} - 16824 q^{28} + 20556 q^{34} - 11400 q^{37} - 12108 q^{38} + 16966 q^{40} - 3918 q^{41} - 125394 q^{44} + 17470 q^{46} - 3822 q^{47} - 32618 q^{49} + 24126 q^{53} - 164718 q^{58} + 81426 q^{62} + 158076 q^{64} - 98976 q^{65} + 23560 q^{67} - 222404 q^{70} + 50046 q^{71} - 196274 q^{73} - 141216 q^{74} + 239574 q^{77} + 215814 q^{83} - 346472 q^{85} - 197640 q^{86} + 132504 q^{95}+O(q^{100}) \) 16 * q - 268 * q^4 + 190 * q^7 - 74 * q^10 + 1110 * q^11 + 2900 * q^16 - 12052 * q^25 - 4902 * q^26 - 16824 * q^28 + 20556 * q^34 - 11400 * q^37 - 12108 * q^38 + 16966 * q^40 - 3918 * q^41 - 125394 * q^44 + 17470 * q^46 - 3822 * q^47 - 32618 * q^49 + 24126 * q^53 - 164718 * q^58 + 81426 * q^62 + 158076 * q^64 - 98976 * q^65 + 23560 * q^67 - 222404 * q^70 + 50046 * q^71 - 196274 * q^73 - 141216 * q^74 + 239574 * q^77 + 215814 * q^83 - 346472 * q^85 - 197640 * q^86 + 132504 * q^95

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