LMFDB - Embedded newform 336.3.d.c.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(113,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("336.113");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.65856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 21 $ x^4 + 14*x^2 + 21
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.2
Root			$-3.50592i$ of defining polynomial
Character	$\chi$	$=$	336.113
Dual form			336.3.d.c.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.822876 + 2.88494i) q^{3} -1.24197i q^{5} -2.64575 q^{7} +(-7.64575 - 4.74789i) q^{9} +O(q^{10})$	\(q+(-0.822876 + 2.88494i) q^{3} -1.24197i q^{5} -2.64575 q^{7} +(-7.64575 - 4.74789i) q^{9} -7.01185i q^{11} -11.6458 q^{13} +(3.58301 + 1.02199i) q^{15} -4.52791i q^{17} -16.2288 q^{19} +(2.17712 - 7.63283i) q^{21} -25.5635i q^{23} +23.4575 q^{25} +(19.9889 - 18.1506i) q^{27} -9.49579i q^{29} -28.7085 q^{31} +(20.2288 + 5.76988i) q^{33} +3.28594i q^{35} -33.0405 q^{37} +(9.58301 - 33.5973i) q^{39} -67.1946i q^{41} +24.1255 q^{43} +(-5.89674 + 9.49579i) q^{45} -33.0153i q^{47} +7.00000 q^{49} +(13.0627 + 3.72591i) q^{51} +15.1877i q^{53} -8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +92.3960i q^{59} -57.5203 q^{61} +(20.2288 + 12.5617i) q^{63} +14.4637i q^{65} -15.1660 q^{67} +(73.7490 + 21.0355i) q^{69} -70.5584i q^{71} -76.7895 q^{73} +(-19.3026 + 67.6735i) q^{75} +18.5516i q^{77} -127.247 q^{79} +(35.9150 + 72.6024i) q^{81} +74.2844i q^{83} -5.62352 q^{85} +(27.3948 + 7.81385i) q^{87} +127.377i q^{89} +30.8118 q^{91} +(23.6235 - 82.8223i) q^{93} +20.1556i q^{95} -23.1660 q^{97} +(-33.2915 + 53.6108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 20 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 20 * q^9	$ 4 q + 2 q^{3} - 20 q^{9} - 36 q^{13} - 28 q^{15} - 12 q^{19} + 14 q^{21} - 12 q^{25} - 10 q^{27} - 136 q^{31} + 28 q^{33} + 16 q^{37} - 4 q^{39} + 160 q^{43} - 140 q^{45} + 28 q^{49} + 84 q^{51} - 56 q^{55} + 64 q^{57} - 156 q^{61} + 28 q^{63} + 24 q^{67} + 168 q^{69} - 32 q^{73} - 146 q^{75} - 128 q^{79} - 68 q^{81} + 168 q^{85} - 28 q^{87} + 28 q^{91} - 96 q^{93} - 8 q^{97} - 112 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 20 * q^9 - 36 * q^13 - 28 * q^15 - 12 * q^19 + 14 * q^21 - 12 * q^25 - 10 * q^27 - 136 * q^31 + 28 * q^33 + 16 * q^37 - 4 * q^39 + 160 * q^43 - 140 * q^45 + 28 * q^49 + 84 * q^51 - 56 * q^55 + 64 * q^57 - 156 * q^61 + 28 * q^63 + 24 * q^67 + 168 * q^69 - 32 * q^73 - 146 * q^75 - 128 * q^79 - 68 * q^81 + 168 * q^85 - 28 * q^87 + 28 * q^91 - 96 * q^93 - 8 * q^97 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.822876	+	2.88494i	−0.274292	+	0.961646i
$3$	−0.822876	+	2.88494i	−0.274292	+	0.961646i
$4$		0			0
$5$		−	1.24197i		−	0.248394i	−0.992258	−	0.124197i	$-0.960365\pi$
$5$		−	1.24197i		−	0.248394i	0.992258	−	0.124197i	$-0.0396354\pi$
$6$		0			0
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		0			0
$9$	−7.64575	−	4.74789i	−0.849528	−	0.527544i
$10$		0			0
$11$		−	7.01185i		−	0.637441i	−0.947849	−	0.318720i	$-0.896747\pi$
$11$		−	7.01185i		−	0.637441i	0.947849	−	0.318720i	$-0.103253\pi$
$12$		0			0
$13$	−11.6458			−0.895827			−0.447914	−	0.894077i	$-0.647833\pi$
$13$	−11.6458			−0.895827			−0.447914	+	0.894077i	$0.647833\pi$
$14$		0			0
$15$	3.58301	+	1.02199i	0.238867	+	0.0681324i
$16$		0			0
$17$		−	4.52791i		−	0.266348i	−0.991093	−	0.133174i	$-0.957483\pi$
$17$		−	4.52791i		−	0.266348i	0.991093	−	0.133174i	$-0.0425169\pi$
$18$		0			0
$19$	−16.2288			−0.854145			−0.427073	−	0.904217i	$-0.640455\pi$
$19$	−16.2288			−0.854145			−0.427073	+	0.904217i	$0.640455\pi$
$20$		0			0
$21$	2.17712	−	7.63283i	0.103673	−	0.363468i
$22$		0			0
$23$		−	25.5635i		−	1.11145i	−0.831365	−	0.555727i	$-0.812440\pi$
$23$		−	25.5635i		−	1.11145i	0.831365	−	0.555727i	$-0.187560\pi$
$24$		0			0
$25$	23.4575			0.938301
$26$		0			0
$27$	19.9889	−	18.1506i	0.740329	−	0.672245i
$28$		0			0
$29$		−	9.49579i		−	0.327441i	−0.986507	−	0.163720i	$-0.947650\pi$
$29$		−	9.49579i		−	0.327441i	0.986507	−	0.163720i	$-0.0523495\pi$
$30$		0			0
$31$	−28.7085			−0.926081			−0.463040	−	0.886337i	$-0.653241\pi$
$31$	−28.7085			−0.926081			−0.463040	+	0.886337i	$0.653241\pi$
$32$		0			0
$33$	20.2288	+	5.76988i	0.612993	+	0.174845i
$34$		0			0
$35$			3.28594i			0.0938840i
$36$		0			0
$37$	−33.0405			−0.892987			−0.446493	−	0.894787i	$-0.647327\pi$
$37$	−33.0405			−0.892987			−0.446493	+	0.894787i	$0.647327\pi$
$38$		0			0
$39$	9.58301	−	33.5973i	0.245718	−	0.861469i
$40$		0			0
$41$		−	67.1946i		−	1.63889i	−0.573156	−	0.819446i	$-0.694281\pi$
$41$		−	67.1946i		−	1.63889i	0.573156	−	0.819446i	$-0.305719\pi$
$42$		0			0
$43$	24.1255			0.561058			0.280529	−	0.959846i	$-0.409490\pi$
$43$	24.1255			0.561058			0.280529	+	0.959846i	$0.409490\pi$
$44$		0			0
$45$	−5.89674	+	9.49579i	−0.131039	+	0.211017i
$46$		0			0
$47$		−	33.0153i		−	0.702452i	−0.936291	−	0.351226i	$-0.885765\pi$
$47$		−	33.0153i		−	0.702452i	0.936291	−	0.351226i	$-0.114235\pi$
$48$		0			0
$49$	7.00000			0.142857
$50$		0			0
$51$	13.0627	+	3.72591i	0.256132	+	0.0730570i
$52$		0			0
$53$			15.1877i			0.286561i	0.989682	+	0.143281i	$0.0457651\pi$
$53$			15.1877i			0.286561i	−0.989682	+	0.143281i	$0.954235\pi$
$54$		0			0
$55$	−8.70850			−0.158336
$56$		0			0
$57$	13.3542	−	46.8190i	0.234285	−	0.821386i
$58$		0			0
$59$			92.3960i			1.56603i	0.622000	+	0.783017i	$0.286320\pi$
$59$			92.3960i			1.56603i	−0.622000	+	0.783017i	$0.713680\pi$
$60$		0			0
$61$	−57.5203			−0.942955			−0.471478	−	0.881878i	$-0.656279\pi$
$61$	−57.5203			−0.942955			−0.471478	+	0.881878i	$0.656279\pi$
$62$		0			0
$63$	20.2288	+	12.5617i	0.321091	+	0.199393i
$64$		0			0
$65$			14.4637i			0.222518i
$66$		0			0
$67$	−15.1660			−0.226358			−0.113179	−	0.993575i	$-0.536103\pi$
$67$	−15.1660			−0.226358			−0.113179	+	0.993575i	$0.536103\pi$
$68$		0			0
$69$	73.7490	+	21.0355i	1.06883	+	0.304863i
$70$		0			0
$71$		−	70.5584i		−	0.993781i	−0.867813	−	0.496890i	$-0.834475\pi$
$71$		−	70.5584i		−	0.993781i	0.867813	−	0.496890i	$-0.165525\pi$
$72$		0			0
$73$	−76.7895			−1.05191			−0.525956	−	0.850512i	$-0.676292\pi$
$73$	−76.7895			−1.05191			−0.525956	+	0.850512i	$0.676292\pi$
$74$		0			0
$75$	−19.3026	+	67.6735i	−0.257368	+	0.902313i
$76$		0			0
$77$			18.5516i			0.240930i
$78$		0			0
$79$	−127.247			−1.61072			−0.805361	−	0.592785i	$-0.798029\pi$
$79$	−127.247			−1.61072			−0.805361	+	0.592785i	$0.798029\pi$
$80$		0			0
$81$	35.9150	+	72.6024i	0.443395	+	0.896326i
$82$		0			0
$83$			74.2844i			0.894992i	0.894286	+	0.447496i	$0.147684\pi$
$83$			74.2844i			0.894992i	−0.894286	+	0.447496i	$0.852316\pi$
$84$		0			0
$85$	−5.62352			−0.0661591
$86$		0			0
$87$	27.3948	+	7.81385i	0.314882	+	0.0898144i
$88$		0			0
$89$			127.377i			1.43121i	0.698507	+	0.715603i	$0.253848\pi$
$89$			127.377i			1.43121i	−0.698507	+	0.715603i	$0.746152\pi$
$90$		0			0
$91$	30.8118			0.338591
$92$		0			0
$93$	23.6235	−	82.8223i	0.254016	−	0.890562i
$94$		0			0
$95$			20.1556i			0.212164i
$96$		0			0
$97$	−23.1660			−0.238825			−0.119412	−	0.992845i	$-0.538101\pi$
$97$	−23.1660			−0.238825			−0.119412	+	0.992845i	$0.538101\pi$
$98$		0			0
$99$	−33.2915	+	53.6108i	−0.336278	+	0.541524i
$100$		0			0
$101$			134.907i			1.33571i	0.744290	+	0.667857i	$0.232788\pi$
$101$			134.907i			1.33571i	−0.744290	+	0.667857i	$0.767212\pi$
$102$		0			0
$103$	119.749			1.16261			0.581306	−	0.813685i	$-0.302542\pi$
$103$	119.749			1.16261			0.581306	+	0.813685i	$0.302542\pi$
$104$		0			0
$105$	−9.47974	−	2.70392i	−0.0902832	−	0.0257516i
$106$		0			0
$107$		−	77.8544i		−	0.727611i	−0.931475	−	0.363806i	$-0.881477\pi$
$107$		−	77.8544i		−	0.727611i	0.931475	−	0.363806i	$-0.118523\pi$
$108$		0			0
$109$	−36.5385			−0.335216			−0.167608	−	0.985854i	$-0.553604\pi$
$109$	−36.5385			−0.335216			−0.167608	+	0.985854i	$0.553604\pi$
$110$		0			0
$111$	27.1882	−	95.3199i	0.244939	−	0.858738i
$112$		0			0
$113$		−	21.7596i		−	0.192563i	−0.995354	−	0.0962815i	$-0.969305\pi$
$113$		−	21.7596i		−	0.192563i	0.995354	−	0.0962815i	$-0.0306949\pi$
$114$		0			0
$115$	−31.7490			−0.276078
$116$		0			0
$117$	89.0405	+	55.2928i	0.761030	+	0.472588i
$118$		0			0
$119$			11.9797i			0.100670i
$120$		0			0
$121$	71.8340			0.593669
$122$		0			0
$123$	193.852	+	55.2928i	1.57603	+	0.449535i
$124$		0			0
$125$		−	60.1827i		−	0.481462i
$126$		0			0
$127$	15.4170			0.121394			0.0606968	−	0.998156i	$-0.480668\pi$
$127$	15.4170			0.121394			0.0606968	+	0.998156i	$0.480668\pi$
$128$		0			0
$129$	−19.8523	+	69.6006i	−0.153894	+	0.539539i
$130$		0			0
$131$			183.110i			1.39779i	0.715226	+	0.698893i	$0.246324\pi$
$131$			183.110i			1.39779i	−0.715226	+	0.698893i	$0.753676\pi$
$132$		0			0
$133$	42.9373			0.322836
$134$		0			0
$135$	−22.5425	−	24.8256i	−0.166981	−	0.183893i
$136$		0			0
$137$		−	33.0153i		−	0.240987i	−0.992714	−	0.120494i	$-0.961552\pi$
$137$		−	33.0153i		−	0.240987i	0.992714	−	0.120494i	$-0.0384477\pi$
$138$		0			0
$139$	−64.6418			−0.465049			−0.232525	−	0.972591i	$-0.574699\pi$
$139$	−64.6418			−0.465049			−0.232525	+	0.972591i	$0.574699\pi$
$140$		0			0
$141$	95.2470	+	27.1675i	0.675511	+	0.192677i
$142$		0			0
$143$			81.6582i			0.571037i
$144$		0			0
$145$	−11.7935			−0.0813343
$146$		0			0
$147$	−5.76013	+	20.1946i	−0.0391846	+	0.137378i
$148$		0			0
$149$		−	195.736i		−	1.31366i	−0.754037	−	0.656832i	$-0.771896\pi$
$149$		−	195.736i		−	1.31366i	0.754037	−	0.656832i	$-0.228104\pi$
$150$		0			0
$151$	−102.251			−0.677159			−0.338579	−	0.940938i	$-0.609946\pi$
$151$	−102.251			−0.677159			−0.338579	+	0.940938i	$0.609946\pi$
$152$		0			0
$153$	−21.4980	+	34.6193i	−0.140510	+	0.226270i
$154$		0			0
$155$			35.6551i			0.230033i
$156$		0			0
$157$	104.723			0.667025			0.333512	−	0.942746i	$-0.391766\pi$
$157$	104.723			0.667025			0.333512	+	0.942746i	$0.391766\pi$
$158$		0			0
$159$	−43.8157	−	12.4976i	−0.275570	−	0.0786014i
$160$		0			0
$161$			67.6345i			0.420090i
$162$		0			0
$163$	70.9595			0.435334			0.217667	−	0.976023i	$-0.430155\pi$
$163$	70.9595			0.435334			0.217667	+	0.976023i	$0.430155\pi$
$164$		0			0
$165$	7.16601	−	25.1235i	0.0434304	−	0.152264i
$166$		0			0
$167$		−	206.992i		−	1.23947i	−0.784811	−	0.619735i	$-0.787240\pi$
$167$		−	206.992i		−	1.23947i	0.784811	−	0.619735i	$-0.212760\pi$
$168$		0			0
$169$	−33.3765			−0.197494
$170$		0			0
$171$	124.081	+	77.0524i	0.725620	+	0.450599i
$172$		0			0
$173$		−	108.464i		−	0.626958i	−0.949595	−	0.313479i	$-0.898506\pi$
$173$		−	108.464i		−	0.626958i	0.949595	−	0.313479i	$-0.101494\pi$
$174$		0			0
$175$	−62.0627			−0.354644
$176$		0			0
$177$	−266.557	−	76.0304i	−1.50597	−	0.429550i
$178$		0			0
$179$			159.357i			0.890261i	0.895466	+	0.445131i	$0.146843\pi$
$179$			159.357i			0.890261i	−0.895466	+	0.445131i	$0.853157\pi$
$180$		0			0
$181$	−233.889			−1.29220			−0.646102	−	0.763251i	$-0.723602\pi$
$181$	−233.889			−1.29220			−0.646102	+	0.763251i	$0.723602\pi$
$182$		0			0
$183$	47.3320	−	165.942i	0.258645	−	0.906789i
$184$		0			0
$185$			41.0353i			0.221812i
$186$		0			0
$187$	−31.7490			−0.169781
$188$		0			0
$189$	−52.8856	+	48.0220i	−0.279818	+	0.254085i
$190$		0			0
$191$		−	288.210i		−	1.50895i	−0.656328	−	0.754476i	$-0.727891\pi$
$191$		−	288.210i		−	1.50895i	0.656328	−	0.754476i	$-0.272109\pi$
$192$		0			0
$193$	77.1216			0.399594			0.199797	−	0.979837i	$-0.435972\pi$
$193$	77.1216			0.399594			0.199797	+	0.979837i	$0.435972\pi$
$194$		0			0
$195$	−41.7268	−	11.9018i	−0.213984	−	0.0610348i
$196$		0			0
$197$			136.433i			0.692554i	0.938132	+	0.346277i	$0.112554\pi$
$197$			136.433i			0.692554i	−0.938132	+	0.346277i	$0.887446\pi$
$198$		0			0
$199$	−86.5830			−0.435090			−0.217545	−	0.976050i	$-0.569805\pi$
$199$	−86.5830			−0.435090			−0.217545	+	0.976050i	$0.569805\pi$
$200$		0			0
$201$	12.4797	−	43.7530i	0.0620883	−	0.217677i
$202$		0			0
$203$			25.1235i			0.123761i
$204$		0			0
$205$	−83.4536			−0.407091
$206$		0			0
$207$	−121.373	+	195.452i	−0.586341	+	0.944212i
$208$		0			0
$209$			113.794i			0.544467i
$210$		0			0
$211$	−19.4170			−0.0920237			−0.0460118	−	0.998941i	$-0.514651\pi$
$211$	−19.4170			−0.0920237			−0.0460118	+	0.998941i	$0.514651\pi$
$212$		0			0
$213$	203.557	+	58.0608i	0.955666	+	0.272586i
$214$		0			0
$215$		−	29.9631i		−	0.139363i
$216$		0			0
$217$	75.9555			0.350026
$218$		0			0
$219$	63.1882	−	221.533i	0.288531	−	1.01157i
$220$		0			0
$221$			52.7309i			0.238601i
$222$		0			0
$223$	−175.041			−0.784935			−0.392468	−	0.919766i	$-0.628378\pi$
$223$	−175.041			−0.784935			−0.392468	+	0.919766i	$0.628378\pi$
$224$		0			0
$225$	−179.350	−	111.374i	−0.797112	−	0.494994i
$226$		0			0
$227$		−	177.574i		−	0.782264i	−0.920335	−	0.391132i	$-0.872084\pi$
$227$		−	177.574i		−	0.782264i	0.920335	−	0.391132i	$-0.127916\pi$
$228$		0			0
$229$	40.8118			0.178217			0.0891087	−	0.996022i	$-0.471598\pi$
$229$	40.8118			0.178217			0.0891087	+	0.996022i	$0.471598\pi$
$230$		0			0
$231$	−53.5203	−	15.2657i	−0.231689	−	0.0660851i
$232$		0			0
$233$		−	387.696i		−	1.66393i	−0.554828	−	0.831965i	$-0.687216\pi$
$233$		−	387.696i		−	1.66393i	0.554828	−	0.831965i	$-0.312784\pi$
$234$		0			0
$235$	−41.0039			−0.174485
$236$		0			0
$237$	104.708	−	367.100i	0.441808	−	1.54895i
$238$		0			0
$239$		−	49.5229i		−	0.207209i	−0.994619	−	0.103604i	$-0.966962\pi$
$239$		−	49.5229i		−	0.207209i	0.994619	−	0.103604i	$-0.0330376\pi$
$240$		0			0
$241$	325.247			1.34957			0.674786	−	0.738013i	$-0.264236\pi$
$241$	325.247			1.34957			0.674786	+	0.738013i	$0.264236\pi$
$242$		0			0
$243$	−239.007	+	43.8699i	−0.983569	+	0.180535i
$244$		0			0
$245$		−	8.69378i		−	0.0354848i
$246$		0			0
$247$	188.996			0.765166
$248$		0			0
$249$	−214.306	−	61.1268i	−0.860666	−	0.245489i
$250$		0			0
$251$		−	263.732i		−	1.05073i	−0.850878	−	0.525364i	$-0.823929\pi$
$251$		−	263.732i		−	1.05073i	0.850878	−	0.525364i	$-0.176071\pi$
$252$		0			0
$253$	−179.247			−0.708486
$254$		0			0
$255$	4.62746	−	16.2235i	0.0181469	−	0.0636217i
$256$		0			0
$257$			151.181i			0.588252i	0.955767	+	0.294126i	$0.0950286\pi$
$257$			151.181i			0.588252i	−0.955767	+	0.294126i	$0.904971\pi$
$258$		0			0
$259$	87.4170			0.337517
$260$		0			0
$261$	−45.0850	+	72.6024i	−0.172739	+	0.278170i
$262$		0			0
$263$			114.389i			0.434941i	0.976067	+	0.217470i	$0.0697805\pi$
$263$			114.389i			0.434941i	−0.976067	+	0.217470i	$0.930219\pi$
$264$		0			0
$265$	18.8627			0.0711800
$266$		0			0
$267$	−367.476	−	104.816i	−1.37631	−	0.392568i
$268$		0			0
$269$		−	4.76170i		−	0.0177015i	−0.999961	−	0.00885074i	$-0.997183\pi$
$269$		−	4.76170i		−	0.0177015i	0.999961	−	0.00885074i	$-0.00281731\pi$
$270$		0			0
$271$	518.701			1.91402			0.957012	−	0.290048i	$-0.0936711\pi$
$271$	518.701			1.91402			0.957012	+	0.290048i	$0.0936711\pi$
$272$		0			0
$273$	−25.3542	+	88.8901i	−0.0928727	+	0.325605i
$274$		0			0
$275$		−	164.481i		−	0.598111i
$276$		0			0
$277$	−121.085			−0.437130			−0.218565	−	0.975822i	$-0.570138\pi$
$277$	−121.085			−0.437130			−0.218565	+	0.975822i	$0.570138\pi$
$278$		0			0
$279$	219.498	+	136.305i	0.786731	+	0.488548i
$280$		0			0
$281$		−	407.255i		−	1.44931i	−0.689113	−	0.724654i	$-0.742000\pi$
$281$		−	407.255i		−	1.44931i	0.689113	−	0.724654i	$-0.258000\pi$
$282$		0			0
$283$	398.634			1.40860			0.704300	−	0.709902i	$-0.251261\pi$
$283$	398.634			1.40860			0.704300	+	0.709902i	$0.251261\pi$
$284$		0			0
$285$	−58.1477	−	16.5856i	−0.204027	−	0.0581950i
$286$		0			0
$287$			177.780i			0.619443i
$288$		0			0
$289$	268.498			0.929059
$290$		0			0
$291$	19.0627	−	66.8325i	0.0655077	−	0.229665i
$292$		0			0
$293$		−	2.53426i		−	0.00864935i	−0.999991	−	0.00432468i	$-0.998623\pi$
$293$		−	2.53426i		−	0.00864935i	0.999991	−	0.00432468i	$-0.00137659\pi$
$294$		0			0
$295$	114.753			0.388993
$296$		0			0
$297$	−127.269	−	140.159i	−0.428516	−	0.471916i
$298$		0			0
$299$			297.706i			0.995671i
$300$		0			0
$301$	−63.8301			−0.212060
$302$		0			0
$303$	−389.199	−	111.012i	−1.28448	−	0.366375i
$304$		0			0
$305$			71.4384i			0.234224i
$306$		0			0
$307$	−86.2366			−0.280901			−0.140451	−	0.990088i	$-0.544855\pi$
$307$	−86.2366			−0.280901			−0.140451	+	0.990088i	$0.544855\pi$
$308$		0			0
$309$	−98.5385	+	345.469i	−0.318895	+	1.11802i
$310$		0			0
$311$			151.777i			0.488028i	0.969772	+	0.244014i	$0.0784643\pi$
$311$			151.777i			0.488028i	−0.969772	+	0.244014i	$0.921536\pi$
$312$		0			0
$313$	318.118			1.01635			0.508175	−	0.861254i	$-0.330320\pi$
$313$	318.118			1.01635			0.508175	+	0.861254i	$0.330320\pi$
$314$		0			0
$315$	15.6013	−	25.1235i	0.0495279	−	0.0797571i
$316$		0			0
$317$		−	364.020i		−	1.14833i	−0.818740	−	0.574164i	$-0.805327\pi$
$317$		−	364.020i		−	1.14833i	0.818740	−	0.574164i	$-0.194673\pi$
$318$		0			0
$319$	−66.5830			−0.208724
$320$		0			0
$321$	224.605	+	64.0645i	0.699705	+	0.199578i
$322$		0			0
$323$			73.4823i			0.227500i
$324$		0			0
$325$	−273.180			−0.840555
$326$		0			0
$327$	30.0667	−	105.412i	0.0919470	−	0.322359i
$328$		0			0
$329$			87.3502i			0.265502i
$330$		0			0
$331$	−154.369			−0.466370			−0.233185	−	0.972432i	$-0.574915\pi$
$331$	−154.369			−0.466370			−0.233185	+	0.972432i	$0.574915\pi$
$332$		0			0
$333$	252.620	+	156.873i	0.758617	+	0.471090i
$334$		0			0
$335$			18.8357i			0.0562260i
$336$		0			0
$337$	403.041			1.19597			0.597983	−	0.801509i	$-0.295969\pi$
$337$	403.041			1.19597			0.597983	+	0.801509i	$0.295969\pi$
$338$		0			0
$339$	62.7752	+	17.9055i	0.185178	+	0.0528185i
$340$		0			0
$341$			201.300i			0.590321i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$		0			0
$345$	26.1255	−	91.5940i	0.0757261	−	0.265490i
$346$		0			0
$347$		−	471.242i		−	1.35805i	−0.734117	−	0.679023i	$-0.762404\pi$
$347$		−	471.242i		−	1.35805i	0.734117	−	0.679023i	$-0.237596\pi$
$348$		0			0
$349$	−364.516			−1.04446			−0.522230	−	0.852805i	$-0.674900\pi$
$349$	−364.516			−1.04446			−0.522230	+	0.852805i	$0.674900\pi$
$350$		0			0
$351$	−232.786	+	211.377i	−0.663207	+	0.602215i
$352$		0			0
$353$			86.3420i			0.244595i	0.992493	+	0.122297i	$0.0390262\pi$
$353$			86.3420i			0.244595i	−0.992493	+	0.122297i	$0.960974\pi$
$354$		0			0
$355$	−87.6314			−0.246849
$356$		0			0
$357$	−34.5608	−	9.85782i	−0.0968089	−	0.0276129i
$358$		0			0
$359$			372.068i			1.03640i	0.855259	+	0.518200i	$0.173398\pi$
$359$			372.068i			1.03640i	−0.855259	+	0.518200i	$0.826602\pi$
$360$		0			0
$361$	−97.6275			−0.270436
$362$		0			0
$363$	−59.1104	+	207.237i	−0.162839	+	0.570900i
$364$		0			0
$365$			95.3702i			0.261288i
$366$		0			0
$367$	161.786			0.440833			0.220416	−	0.975406i	$-0.429258\pi$
$367$	161.786			0.440833			0.220416	+	0.975406i	$0.429258\pi$
$368$		0			0
$369$	−319.033	+	513.753i	−0.864587	+	1.39228i
$370$		0			0
$371$		−	40.1830i		−	0.108310i
$372$		0			0
$373$	378.251			1.01408			0.507039	−	0.861923i	$-0.330740\pi$
$373$	378.251			1.01408			0.507039	+	0.861923i	$0.330740\pi$
$374$		0			0
$375$	173.624	+	49.5229i	0.462996	+	0.132061i
$376$		0			0
$377$			110.586i			0.293330i
$378$		0			0
$379$	50.7974			0.134030			0.0670151	−	0.997752i	$-0.478652\pi$
$379$	50.7974			0.134030			0.0670151	+	0.997752i	$0.478652\pi$
$380$		0			0
$381$	−12.6863	+	44.4771i	−0.0332973	+	0.116738i
$382$		0			0
$383$			113.381i			0.296034i	0.988985	+	0.148017i	$0.0472891\pi$
$383$			113.381i			0.296034i	−0.988985	+	0.148017i	$0.952711\pi$
$384$		0			0
$385$	23.0405			0.0598455
$386$		0			0
$387$	−184.458	−	114.545i	−0.476634	−	0.295983i
$388$		0			0
$389$			725.584i			1.86526i	0.360841	+	0.932628i	$0.382490\pi$
$389$			725.584i			1.86526i	−0.360841	+	0.932628i	$0.617510\pi$
$390$		0			0
$391$	−115.749			−0.296033
$392$		0			0
$393$	−528.261	−	150.677i	−1.34418	−	0.383402i
$394$		0			0
$395$			158.037i			0.400093i
$396$		0			0
$397$	−94.3464			−0.237648			−0.118824	−	0.992915i	$-0.537912\pi$
$397$	−94.3464			−0.237648			−0.118824	+	0.992915i	$0.537912\pi$
$398$		0			0
$399$	−35.3320	+	123.871i	−0.0885514	+	0.310455i
$400$		0			0
$401$			677.665i			1.68994i	0.534815	+	0.844969i	$0.320381\pi$
$401$			677.665i			1.68994i	−0.534815	+	0.844969i	$0.679619\pi$
$402$		0			0
$403$	334.332			0.829608
$404$		0			0
$405$	90.1699	−	44.6053i	0.222642	−	0.110137i
$406$		0			0
$407$			231.675i			0.569226i
$408$		0			0
$409$	17.3647			0.0424564			0.0212282	−	0.999775i	$-0.493242\pi$
$409$	17.3647			0.0424564			0.0212282	+	0.999775i	$0.493242\pi$
$410$		0			0
$411$	95.2470	+	27.1675i	0.231745	+	0.0661009i
$412$		0			0
$413$		−	244.457i		−	0.591905i
$414$		0			0
$415$	92.2589			0.222311
$416$		0			0
$417$	53.1922	−	186.488i	0.127559	−	0.447213i
$418$		0			0
$419$			136.071i			0.324752i	0.986729	+	0.162376i	$0.0519157\pi$
$419$			136.071i			0.324752i	−0.986729	+	0.162376i	$0.948084\pi$
$420$		0			0
$421$	423.992			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$421$	423.992			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$422$		0			0
$423$	−156.753	+	252.427i	−0.370574	+	0.596753i
$424$		0			0
$425$		−	106.214i		−	0.249914i
$426$		0			0
$427$	152.184			0.356404
$428$		0			0
$429$	−235.579	−	67.1946i	−0.549135	−	0.156631i
$430$		0			0
$431$			340.244i			0.789430i	0.918804	+	0.394715i	$0.129157\pi$
$431$			340.244i			0.789430i	−0.918804	+	0.394715i	$0.870843\pi$
$432$		0			0
$433$	159.166			0.367589			0.183794	−	0.982965i	$-0.441162\pi$
$433$	159.166			0.367589			0.183794	+	0.982965i	$0.441162\pi$
$434$		0			0
$435$	9.70456	−	34.0235i	0.0223093	−	0.0782148i
$436$		0			0
$437$			414.863i			0.949343i
$438$		0			0
$439$	−128.073			−0.291738			−0.145869	−	0.989304i	$-0.546598\pi$
$439$	−128.073			−0.291738			−0.145869	+	0.989304i	$0.546598\pi$
$440$		0			0
$441$	−53.5203	−	33.2353i	−0.121361	−	0.0753634i
$442$		0			0
$443$		−	197.340i		−	0.445463i	−0.974880	−	0.222731i	$-0.928503\pi$
$443$		−	197.340i		−	0.445463i	0.974880	−	0.222731i	$-0.0714973\pi$
$444$		0			0
$445$	158.199			0.355503
$446$		0			0
$447$	564.686	+	161.066i	1.26328	+	0.360327i
$448$		0			0
$449$		−	148.101i		−	0.329847i	−0.986306	−	0.164923i	$-0.947262\pi$
$449$		−	148.101i		−	0.329847i	0.986306	−	0.164923i	$-0.0527377\pi$
$450$		0			0
$451$	−471.158			−1.04470
$452$		0			0
$453$	84.1398	−	294.988i	0.185739	−	0.651187i
$454$		0			0
$455$		−	38.2673i		−	0.0841038i
$456$		0			0
$457$	−122.214			−0.267428			−0.133714	−	0.991020i	$-0.542690\pi$
$457$	−122.214			−0.267428			−0.133714	+	0.991020i	$0.542690\pi$
$458$		0			0
$459$	−82.1843	−	90.5079i	−0.179051	−	0.197185i
$460$		0			0
$461$		−	602.089i		−	1.30605i	−0.757337	−	0.653025i	$-0.773500\pi$
$461$		−	602.089i		−	1.30605i	0.757337	−	0.653025i	$-0.226500\pi$
$462$		0			0
$463$	637.061			1.37594			0.687971	−	0.725738i	$-0.258502\pi$
$463$	637.061			1.37594			0.687971	+	0.725738i	$0.258502\pi$
$464$		0			0
$465$	−102.863	−	29.3397i	−0.221210	−	0.0630961i
$466$		0			0
$467$		−	767.706i		−	1.64391i	−0.569553	−	0.821955i	$-0.692884\pi$
$467$		−	767.706i		−	1.64391i	0.569553	−	0.821955i	$-0.307116\pi$
$468$		0			0
$469$	40.1255			0.0855554
$470$		0			0
$471$	−86.1739	+	302.119i	−0.182959	+	0.641442i
$472$		0			0
$473$		−	169.164i		−	0.357641i
$474$		0			0
$475$	−380.686			−0.801445
$476$		0			0
$477$	72.1097	−	116.122i	0.151173	−	0.243442i
$478$		0			0
$479$			393.855i			0.822245i	0.911580	+	0.411122i	$0.134863\pi$
$479$			393.855i			0.822245i	−0.911580	+	0.411122i	$0.865137\pi$
$480$		0			0
$481$	384.782			0.799962
$482$		0			0
$483$	−195.122	−	55.6548i	−0.403978	−	0.115227i
$484$		0			0
$485$			28.7715i			0.0593226i
$486$		0			0
$487$	−573.409			−1.17743			−0.588716	−	0.808340i	$-0.700366\pi$
$487$	−573.409			−1.17743			−0.588716	+	0.808340i	$0.700366\pi$
$488$		0			0
$489$	−58.3908	+	204.714i	−0.119409	+	0.418638i
$490$		0			0
$491$		−	170.796i		−	0.347853i	−0.984759	−	0.173927i	$-0.944354\pi$
$491$		−	170.796i		−	0.347853i	0.984759	−	0.173927i	$-0.0556455\pi$
$492$		0			0
$493$	−42.9961			−0.0872131
$494$		0			0
$495$	66.5830	+	41.3470i	0.134511	+	0.0835293i
$496$		0			0
$497$			186.680i			0.375614i
$498$		0			0
$499$	847.814			1.69903			0.849513	−	0.527567i	$-0.176896\pi$
$499$	847.814			1.69903			0.849513	+	0.527567i	$0.176896\pi$
$500$		0			0
$501$	597.158	+	170.328i	1.19193	+	0.339977i
$502$		0			0
$503$			197.624i			0.392891i	0.980515	+	0.196445i	$0.0629398\pi$
$503$			197.624i			0.392891i	−0.980515	+	0.196445i	$0.937060\pi$
$504$		0			0
$505$	167.550			0.331783
$506$		0			0
$507$	27.4647	−	96.2891i	0.0541710	−	0.189919i
$508$		0			0
$509$		−	491.448i		−	0.965516i	−0.875754	−	0.482758i	$-0.839635\pi$
$509$		−	491.448i		−	0.965516i	0.875754	−	0.482758i	$-0.160365\pi$
$510$		0			0
$511$	203.166			0.397585
$512$		0			0
$513$	−324.395	+	294.562i	−0.632348	+	0.574194i
$514$		0			0
$515$		−	148.725i		−	0.288786i
$516$		0			0
$517$	−231.498			−0.447772
$518$		0			0
$519$	312.911	+	89.2521i	0.602912	+	0.171969i
$520$		0			0
$521$		−	870.010i		−	1.66988i	−0.550338	−	0.834942i	$-0.685501\pi$
$521$		−	870.010i		−	1.66988i	0.550338	−	0.834942i	$-0.314499\pi$
$522$		0			0
$523$	−798.707			−1.52716			−0.763582	−	0.645710i	$-0.776561\pi$
$523$	−798.707			−1.52716			−0.763582	+	0.645710i	$0.776561\pi$
$524$		0			0
$525$	51.0699	−	179.047i	0.0972760	−	0.341042i
$526$		0			0
$527$			129.989i			0.246659i
$528$		0			0
$529$	−124.490			−0.235331
$530$		0			0
$531$	438.686	−	706.437i	0.826151	−	1.33039i
$532$		0			0
$533$			782.531i			1.46816i
$534$		0			0
$535$	−96.6927			−0.180734
$536$		0			0
$537$	−459.735	−	131.131i	−0.856117	−	0.244191i
$538$		0			0
$539$		−	49.0829i		−	0.0910630i
$540$		0			0
$541$	−736.243			−1.36089			−0.680446	−	0.732798i	$-0.738214\pi$
$541$	−736.243			−1.36089			−0.680446	+	0.732798i	$0.738214\pi$
$542$		0			0
$543$	192.461	−	674.755i	0.354441	−	1.24264i
$544$		0			0
$545$			45.3797i			0.0832656i
$546$		0			0
$547$	228.952			0.418559			0.209279	−	0.977856i	$-0.432888\pi$
$547$	228.952			0.418559			0.209279	+	0.977856i	$0.432888\pi$
$548$		0			0
$549$	439.786	+	273.100i	0.801067	+	0.497450i
$550$		0			0
$551$			154.105i			0.279682i
$552$		0			0
$553$	336.664			0.608796
$554$		0			0
$555$	−118.384	−	33.7669i	−0.213305	−	0.0608413i
$556$		0			0
$557$		−	906.288i		−	1.62709i	−0.581503	−	0.813544i	$-0.697535\pi$
$557$		−	906.288i		−	1.62709i	0.581503	−	0.813544i	$-0.302465\pi$
$558$		0			0
$559$	−280.959			−0.502611
$560$		0			0
$561$	26.1255	−	91.5940i	0.0465695	−	0.163269i
$562$		0			0
$563$		−	458.616i		−	0.814593i	−0.913296	−	0.407297i	$-0.866471\pi$
$563$		−	458.616i		−	0.814593i	0.913296	−	0.407297i	$-0.133529\pi$
$564$		0			0
$565$	−27.0248			−0.0478315
$566$		0			0
$567$	−95.0222	−	192.088i	−0.167588	−	0.338779i
$568$		0			0
$569$			577.428i			1.01481i	0.861707	+	0.507406i	$0.169395\pi$
$569$			577.428i			1.01481i	−0.861707	+	0.507406i	$0.830605\pi$
$570$		0			0
$571$	103.122			0.180598			0.0902991	−	0.995915i	$-0.471218\pi$
$571$	103.122			0.180598			0.0902991	+	0.995915i	$0.471218\pi$
$572$		0			0
$573$	831.468	+	237.161i	1.45108	+	0.413893i
$574$		0			0
$575$		−	599.655i		−	1.04288i
$576$		0			0
$577$	−676.583			−1.17259			−0.586294	−	0.810099i	$-0.699414\pi$
$577$	−676.583			−1.17259			−0.586294	+	0.810099i	$0.699414\pi$
$578$		0			0
$579$	−63.4615	+	222.491i	−0.109605	+	0.384268i
$580$		0			0
$581$		−	196.538i		−	0.338275i
$582$		0			0
$583$	106.494			0.182666
$584$		0			0
$585$	68.6719	−	110.586i	0.117388	−	0.189035i
$586$		0			0
$587$			158.683i			0.270329i	0.990823	+	0.135164i	$0.0431563\pi$
$587$			158.683i			0.270329i	−0.990823	+	0.135164i	$0.956844\pi$
$588$		0			0
$589$	465.903			0.791007
$590$		0			0
$591$	−393.601	−	112.267i	−0.665992	−	0.189962i
$592$		0			0
$593$			935.371i			1.57735i	0.614807	+	0.788677i	$0.289234\pi$
$593$			935.371i			1.57735i	−0.614807	+	0.788677i	$0.710766\pi$
$594$		0			0
$595$	14.8784			0.0250058
$596$		0			0
$597$	71.2470	−	249.787i	0.119342	−	0.418403i
$598$		0			0
$599$			73.7665i			0.123149i	0.998102	+	0.0615747i	$0.0196122\pi$
$599$			73.7665i			0.123149i	−0.998102	+	0.0615747i	$0.980388\pi$
$600$		0			0
$601$	−934.280			−1.55454			−0.777271	−	0.629166i	$-0.783397\pi$
$601$	−934.280			−1.55454			−0.777271	+	0.629166i	$0.783397\pi$
$602$		0			0
$603$	115.956	+	72.0066i	0.192298	+	0.119414i
$604$		0			0
$605$		−	89.2156i		−	0.147464i
$606$		0			0
$607$	181.608			0.299189			0.149595	−	0.988747i	$-0.452203\pi$
$607$	181.608			0.299189			0.149595	+	0.988747i	$0.452203\pi$
$608$		0			0
$609$	−72.4797	−	20.6735i	−0.119014	−	0.0339466i
$610$		0			0
$611$			384.488i			0.629276i
$612$		0			0
$613$	−897.940			−1.46483			−0.732414	−	0.680859i	$-0.761606\pi$
$613$	−897.940			−1.46483			−0.732414	+	0.680859i	$0.761606\pi$
$614$		0			0
$615$	68.6719	−	240.759i	0.111662	−	0.391477i
$616$		0			0
$617$		−	1169.69i		−	1.89576i	−0.318622	−	0.947882i	$-0.603220\pi$
$617$		−	1169.69i		−	1.89576i	0.318622	−	0.947882i	$-0.396780\pi$
$618$		0			0
$619$	−1208.97			−1.95310			−0.976548	−	0.215301i	$-0.930927\pi$
$619$	−1208.97			−1.95310			−0.976548	+	0.215301i	$0.930927\pi$
$620$		0			0
$621$	−463.992	−	510.985i	−0.747169	−	0.822842i
$622$		0			0
$623$		−	337.009i		−	0.540945i
$624$		0			0
$625$	511.693			0.818708
$626$		0			0
$627$	−328.288	−	93.6380i	−0.523585	−	0.149343i
$628$		0			0
$629$			149.604i			0.237845i
$630$		0			0
$631$	−901.223			−1.42825			−0.714123	−	0.700020i	$-0.753174\pi$
$631$	−901.223			−1.42825			−0.714123	+	0.700020i	$0.753174\pi$
$632$		0			0
$633$	15.9778	−	56.0169i	0.0252413	−	0.0884942i
$634$		0			0
$635$		−	19.1474i		−	0.0301534i
$636$		0			0
$637$	−81.5203			−0.127975
$638$		0			0
$639$	−335.004	+	539.472i	−0.524263	+	0.844245i
$640$		0			0
$641$		−	528.629i		−	0.824694i	−0.911027	−	0.412347i	$-0.864709\pi$
$641$		−	528.629i		−	0.824694i	0.911027	−	0.412347i	$-0.135291\pi$
$642$		0			0
$643$	−33.4392			−0.0520050			−0.0260025	−	0.999662i	$-0.508278\pi$
$643$	−33.4392			−0.0520050			−0.0260025	+	0.999662i	$0.508278\pi$
$644$		0			0
$645$	86.4418	+	24.6559i	0.134018	+	0.0382262i
$646$		0			0
$647$		−	786.308i		−	1.21531i	−0.794200	−	0.607657i	$-0.792110\pi$
$647$		−	786.308i		−	1.21531i	0.794200	−	0.607657i	$-0.207890\pi$
$648$		0			0
$649$	647.867			0.998254
$650$		0			0
$651$	−62.5020	+	219.127i	−0.0960092	+	0.336601i
$652$		0			0
$653$			385.807i			0.590823i	0.955370	+	0.295412i	$0.0954568\pi$
$653$			385.807i			0.590823i	−0.955370	+	0.295412i	$0.904543\pi$
$654$		0			0
$655$	227.417			0.347202
$656$		0			0
$657$	587.114	+	364.588i	0.893628	+	0.554929i
$658$		0			0
$659$		−	97.2583i		−	0.147585i	−0.997274	−	0.0737924i	$-0.976490\pi$
$659$		−	97.2583i		−	0.147585i	0.997274	−	0.0737924i	$-0.0235102\pi$
$660$		0			0
$661$	−961.505			−1.45462			−0.727311	−	0.686309i	$-0.759230\pi$
$661$	−961.505			−1.45462			−0.727311	+	0.686309i	$0.759230\pi$
$662$		0			0
$663$	−152.125	−	43.3910i	−0.229450	−	0.0654464i
$664$		0			0
$665$		−	53.3267i		−	0.0801906i
$666$		0			0
$667$	−242.745			−0.363936
$668$		0			0
$669$	144.037	−	504.981i	0.215301	−	0.754830i
$670$		0			0
$671$			403.323i			0.601078i
$672$		0			0
$673$	−1089.81			−1.61933			−0.809663	−	0.586895i	$-0.800350\pi$
$673$	−1089.81			−1.61933			−0.809663	+	0.586895i	$0.800350\pi$
$674$		0			0
$675$	468.890	−	425.768i	0.694651	−	0.630767i
$676$		0			0
$677$		−	1252.56i		−	1.85016i	−0.379771	−	0.925080i	$-0.623997\pi$
$677$		−	1252.56i		−	1.85016i	0.379771	−	0.925080i	$-0.376003\pi$
$678$		0			0
$679$	61.2915			0.0902673
$680$		0			0
$681$	512.290	+	146.121i	0.752262	+	0.214569i
$682$		0			0
$683$			341.097i			0.499409i	0.968322	+	0.249705i	$0.0803335\pi$
$683$			341.097i			0.499409i	−0.968322	+	0.249705i	$0.919666\pi$
$684$		0			0
$685$	−41.0039			−0.0598598
$686$		0			0
$687$	−33.5830	+	117.739i	−0.0488836	+	0.171382i
$688$		0			0
$689$		−	176.873i		−	0.256709i
$690$		0			0
$691$	783.667			1.13411			0.567053	−	0.823682i	$-0.308084\pi$
$691$	783.667			1.13411			0.567053	+	0.823682i	$0.308084\pi$
$692$		0			0
$693$	88.0810	−	141.841i	0.127101	−	0.204677i
$694$		0			0
$695$			80.2831i			0.115515i
$696$		0			0
$697$	−304.251			−0.436515
$698$		0			0
$699$	1118.48	+	319.025i	1.60011	+	0.456402i
$700$		0			0
$701$			1331.76i			1.89979i	0.312562	+	0.949897i	$0.398813\pi$
$701$			1331.76i			1.89979i	−0.312562	+	0.949897i	$0.601187\pi$
$702$		0			0
$703$	536.207			0.762740
$704$		0			0
$705$	33.7411	−	118.294i	0.0478598	−	0.167793i
$706$		0			0
$707$		−	356.930i		−	0.504852i
$708$		0			0
$709$	763.963			1.07752			0.538761	−	0.842459i	$-0.318893\pi$
$709$	763.963			1.07752			0.538761	+	0.842459i	$0.318893\pi$
$710$		0			0
$711$	972.899	+	604.155i	1.36835	+	0.849726i
$712$		0			0
$713$			733.888i			1.02930i
$714$		0			0
$715$	101.417			0.141842
$716$		0			0
$717$	142.871	+	40.7512i	0.199262	+	0.0568357i
$718$		0			0
$719$		−	623.715i		−	0.867476i	−0.901039	−	0.433738i	$-0.857194\pi$
$719$		−	623.715i		−	0.867476i	0.901039	−	0.433738i	$-0.142806\pi$
$720$		0			0
$721$	−316.826			−0.439426
$722$		0			0
$723$	−267.638	+	938.318i	−0.370177	+	1.29781i
$724$		0			0
$725$		−	222.748i		−	0.307238i
$726$		0			0
$727$	−678.494			−0.933279			−0.466640	−	0.884448i	$-0.654536\pi$
$727$	−678.494			−0.933279			−0.466640	+	0.884448i	$0.654536\pi$
$728$		0			0
$729$	70.1111	−	725.621i	0.0961744	−	0.995364i
$730$		0			0
$731$		−	109.238i		−	0.149436i
$732$		0			0
$733$	−394.966			−0.538835			−0.269417	−	0.963023i	$-0.586831\pi$
$733$	−394.966			−0.538835			−0.269417	+	0.963023i	$0.586831\pi$
$734$		0			0
$735$	25.0810	+	7.15390i	0.0341239	+	0.00973320i
$736$		0			0
$737$			106.342i			0.144290i
$738$		0			0
$739$	−292.199			−0.395397			−0.197699	−	0.980263i	$-0.563347\pi$
$739$	−292.199			−0.395397			−0.197699	+	0.980263i	$0.563347\pi$
$740$		0			0
$741$	−155.520	+	545.242i	−0.209879	+	0.735819i
$742$		0			0
$743$			383.452i			0.516086i	0.966133	+	0.258043i	$0.0830776\pi$
$743$			383.452i			0.516086i	−0.966133	+	0.258043i	$0.916922\pi$
$744$		0			0
$745$	−243.098			−0.326306
$746$		0			0
$747$	352.694	−	567.960i	0.472147	−	0.760321i
$748$		0			0
$749$			205.983i			0.275011i
$750$		0			0
$751$	696.332			0.927206			0.463603	−	0.886043i	$-0.346556\pi$
$751$	696.332			0.927206			0.463603	+	0.886043i	$0.346556\pi$
$752$		0			0
$753$	760.852	+	217.019i	1.01043	+	0.288206i
$754$		0			0
$755$			126.993i			0.168202i
$756$		0			0
$757$	967.357			1.27788			0.638941	−	0.769256i	$-0.279373\pi$
$757$	967.357			1.27788			0.638941	+	0.769256i	$0.279373\pi$
$758$		0			0
$759$	147.498	−	517.117i	0.194332	−	0.681313i
$760$		0			0
$761$		−	89.7059i		−	0.117879i	−0.998262	−	0.0589395i	$-0.981228\pi$
$761$		−	89.7059i		−	0.117879i	0.998262	−	0.0589395i	$-0.0187719\pi$
$762$		0			0
$763$	96.6719			0.126700
$764$		0			0
$765$	42.9961	+	26.6999i	0.0562040	+	0.0349018i
$766$		0			0
$767$		−	1076.02i		−	1.40290i
$768$		0			0
$769$	926.219			1.20445			0.602223	−	0.798328i	$-0.294282\pi$
$769$	926.219			1.20445			0.602223	+	0.798328i	$0.294282\pi$
$770$		0			0
$771$	−436.148	−	124.403i	−0.565691	−	0.161353i
$772$		0			0
$773$			424.125i			0.548674i	0.961634	+	0.274337i	$0.0884584\pi$
$773$			424.125i			0.548674i	−0.961634	+	0.274337i	$0.911542\pi$
$774$		0			0
$775$	−673.430			−0.868942
$776$		0			0
$777$	−71.9333	+	252.193i	−0.0925783	+	0.324572i
$778$		0			0
$779$			1090.48i			1.39985i
$780$		0			0
$781$	−494.745			−0.633476
$782$		0			0
$783$	−172.354	−	189.810i	−0.220120	−	0.242414i
$784$		0			0
$785$		−	130.063i		−	0.165685i
$786$		0			0
$787$	155.889			0.198080			0.0990399	−	0.995083i	$-0.468423\pi$
$787$	155.889			0.198080			0.0990399	+	0.995083i	$0.468423\pi$
$788$		0			0
$789$	−330.006	−	94.1282i	−0.418259	−	0.119301i
$790$		0			0
$791$			57.5705i			0.0727820i
$792$		0			0
$793$	669.867			0.844725
$794$		0			0
$795$	−15.5217	+	54.4177i	−0.0195241	+	0.0684500i
$796$		0			0
$797$		−	719.191i		−	0.902373i	−0.892430	−	0.451186i	$-0.851001\pi$
$797$		−	719.191i		−	0.902373i	0.892430	−	0.451186i	$-0.148999\pi$
$798$		0			0
$799$	−149.490			−0.187097
$800$		0			0
$801$	604.774	−	973.895i	0.755023	−	1.21585i
$802$		0			0
$803$			538.437i			0.670531i
$804$		0			0
$805$	84.0000			0.104348
$806$		0			0
$807$	13.7372	+	3.91828i	0.0170226	+	0.00485537i
$808$		0			0
$809$		−	212.244i		−	0.262353i	−0.991359	−	0.131176i	$-0.958125\pi$
$809$		−	212.244i		−	0.262353i	0.991359	−	0.131176i	$-0.0418755\pi$
$810$		0			0
$811$	−1058.66			−1.30538			−0.652690	−	0.757625i	$-0.726359\pi$
$811$	−1058.66			−1.30538			−0.652690	+	0.757625i	$0.726359\pi$
$812$		0			0
$813$	−426.826	+	1496.42i	−0.525001	+	1.84061i
$814$		0			0
$815$		−	88.1295i		−	0.108134i
$816$		0			0
$817$	−391.527			−0.479225
$818$		0			0
$819$	−235.579	−	146.291i	−0.287642	−	0.178621i
$820$		0			0
$821$			818.571i			0.997042i	0.866878	+	0.498521i	$0.166123\pi$
$821$			818.571i			0.997042i	−0.866878	+	0.498521i	$0.833877\pi$
$822$		0			0
$823$	−206.850			−0.251336			−0.125668	−	0.992072i	$-0.540107\pi$
$823$	−206.850			−0.251336			−0.125668	+	0.992072i	$0.540107\pi$
$824$		0			0
$825$	474.516	+	135.347i	0.575171	+	0.164057i
$826$		0			0
$827$			438.639i			0.530398i	0.964194	+	0.265199i	$0.0854376\pi$
$827$			438.639i			0.530398i	−0.964194	+	0.265199i	$0.914562\pi$
$828$		0			0
$829$	654.804			0.789872			0.394936	−	0.918709i	$-0.370767\pi$
$829$	654.804			0.789872			0.394936	+	0.918709i	$0.370767\pi$
$830$		0			0
$831$	99.6379	−	349.323i	0.119901	−	0.420364i
$832$		0			0
$833$		−	31.6954i		−	0.0380497i
$834$		0			0
$835$	−257.077			−0.307877
$836$		0			0
$837$	−573.851	+	521.077i	−0.685604	+	0.622553i
$838$		0			0
$839$		−	50.9710i		−	0.0607521i	−0.999539	−	0.0303761i	$-0.990330\pi$
$839$		−	50.9710i		−	0.0607521i	0.999539	−	0.0303761i	$-0.00967049\pi$
$840$		0			0
$841$	750.830			0.892782
$842$		0			0
$843$	1174.91	+	335.121i	1.39372	+	0.397533i
$844$		0			0
$845$			41.4525i			0.0490563i
$846$		0			0
$847$	−190.055			−0.224386
$848$		0			0
$849$	−328.026	+	1150.03i	−0.386368	+	1.35458i
$850$		0			0
$851$			844.630i			0.992514i
$852$		0			0
$853$	−883.941			−1.03627			−0.518137	−	0.855298i	$-0.673374\pi$
$853$	−883.941			−1.03627			−0.518137	+	0.855298i	$0.673374\pi$
$854$		0			0
$855$	95.6967	−	154.105i	0.111926	−	0.180240i
$856$		0			0
$857$		−	556.521i		−	0.649382i	−0.945820	−	0.324691i	$-0.894740\pi$
$857$		−	556.521i		−	0.649382i	0.945820	−	0.324691i	$-0.105260\pi$
$858$		0			0
$859$	643.078			0.748636			0.374318	−	0.927300i	$-0.377877\pi$
$859$	643.078			0.748636			0.374318	+	0.927300i	$0.377877\pi$
$860$		0			0
$861$	−512.885	−	146.291i	−0.595685	−	0.169908i
$862$		0			0
$863$			204.892i			0.237419i	0.992929	+	0.118709i	$0.0378757\pi$
$863$			204.892i			0.237419i	−0.992929	+	0.118709i	$0.962124\pi$
$864$		0			0
$865$	−134.708			−0.155732
$866$		0			0
$867$	−220.940	+	774.601i	−0.254833	+	0.893426i
$868$		0			0
$869$			892.237i			1.02674i
$870$		0			0
$871$	176.620			0.202778
$872$		0			0
$873$	177.122	+	109.990i	0.202888	+	0.125991i
$874$		0			0
$875$			159.229i			0.181975i
$876$		0			0
$877$	−207.210			−0.236272			−0.118136	−	0.992997i	$-0.537692\pi$
$877$	−207.210			−0.236272			−0.118136	+	0.992997i	$0.537692\pi$
$878$		0			0
$879$	7.31119	+	2.08538i	0.00831762	+	0.00237245i
$880$		0			0
$881$			1391.37i			1.57931i	0.613552	+	0.789654i	$0.289740\pi$
$881$			1391.37i			1.57931i	−0.613552	+	0.789654i	$0.710260\pi$
$882$		0			0
$883$	1091.99			1.23668			0.618342	−	0.785909i	$-0.287805\pi$
$883$	1091.99			1.23668			0.618342	+	0.785909i	$0.287805\pi$
$884$		0			0
$885$	−94.4274	+	331.055i	−0.106698	+	0.374074i
$886$		0			0
$887$			149.449i			0.168488i	0.996445	+	0.0842439i	$0.0268475\pi$
$887$			149.449i			0.168488i	−0.996445	+	0.0842439i	$0.973153\pi$
$888$		0			0
$889$	−40.7895			−0.0458825
$890$		0			0
$891$	509.077	−	251.831i	0.571355	−	0.282638i
$892$		0			0
$893$			535.797i			0.599996i
$894$		0			0
$895$	197.916			0.221135
$896$		0			0
$897$	−858.863	−	244.975i	−0.957483	−	0.273104i
$898$		0			0
$899$			272.610i			0.303237i
$900$		0			0
$901$	68.7687			0.0763249
$902$		0			0
$903$	52.5242	−	184.146i	0.0581663	−	0.203927i
$904$		0			0
$905$			290.483i			0.320975i
$906$		0			0
$907$	−593.718			−0.654595			−0.327297	−	0.944921i	$-0.606138\pi$
$907$	−593.718			−0.654595			−0.327297	+	0.944921i	$0.606138\pi$
$908$		0			0
$909$	640.524	−	1031.47i	0.704647	−	1.13473i
$910$		0			0
$911$			1133.75i			1.24451i	0.782815	+	0.622254i	$0.213783\pi$
$911$			1133.75i			1.24451i	−0.782815	+	0.622254i	$0.786217\pi$
$912$		0			0
$913$	520.871			0.570504
$914$		0			0
$915$	−206.095	−	58.7849i	−0.225241	−	0.0642458i
$916$		0			0
$917$		−	484.464i		−	0.528314i
$918$		0			0
$919$	684.988			0.745363			0.372681	−	0.927959i	$-0.378438\pi$
$919$	684.988			0.745363			0.372681	+	0.927959i	$0.378438\pi$
$920$		0			0
$921$	70.9620	−	248.787i	0.0770489	−	0.270128i
$922$		0			0
$923$			821.706i			0.890256i
$924$		0			0
$925$	−775.048			−0.837890
$926$		0			0
$927$	−915.571	−	568.556i	−0.987671	−	0.613328i
$928$		0			0
$929$			192.317i			0.207015i	0.994629	+	0.103507i	$0.0330066\pi$
$929$			192.317i			0.207015i	−0.994629	+	0.103507i	$0.966993\pi$
$930$		0			0
$931$	−113.601			−0.122021
$932$		0			0
$933$	−437.867	−	124.893i	−0.469310	−	0.133862i
$934$		0			0
$935$			39.4313i			0.0421725i
$936$		0			0
$937$	−1270.28			−1.35569			−0.677844	−	0.735206i	$-0.737086\pi$
$937$	−1270.28			−1.35569			−0.677844	+	0.735206i	$0.737086\pi$
$938$		0			0
$939$	−261.771	+	917.750i	−0.278777	+	0.977370i
$940$		0			0
$941$		−	156.951i		−	0.166791i	−0.996517	−	0.0833957i	$-0.973423\pi$
$941$		−	156.951i		−	0.166791i	0.996517	−	0.0833957i	$-0.0265766\pi$
$942$		0			0
$943$	−1717.73			−1.82155
$944$		0			0
$945$	59.6418	+	65.6823i	0.0631130	+	0.0695051i
$946$		0			0
$947$			879.945i			0.929193i	0.885523	+	0.464596i	$0.153801\pi$
$947$			879.945i			0.929193i	−0.885523	+	0.464596i	$0.846199\pi$
$948$		0			0
$949$	894.272			0.942331
$950$		0			0
$951$	1050.18	+	299.543i	1.10429	+	0.314977i
$952$		0			0
$953$		−	563.276i		−	0.591056i	−0.955334	−	0.295528i	$-0.904505\pi$
$953$		−	563.276i		−	0.591056i	0.955334	−	0.295528i	$-0.0954955\pi$
$954$		0			0
$955$	−357.948			−0.374814
$956$		0			0
$957$	54.7895	−	192.088i	0.0572513	−	0.200719i
$958$		0			0
$959$			87.3502i			0.0910847i
$960$		0			0
$961$	−136.822			−0.142375
$962$		0			0
$963$	−369.644	+	595.255i	−0.383847	+	0.618126i
$964$		0			0
$965$		−	95.7826i		−	0.0992566i
$966$		0			0
$967$	−237.676			−0.245787			−0.122893	−	0.992420i	$-0.539217\pi$
$967$	−237.676			−0.245787			−0.122893	+	0.992420i	$0.539217\pi$
$968$		0			0
$969$	−211.992	−	60.4668i	−0.218774	−	0.0624013i
$970$		0			0
$971$		−	1355.00i		−	1.39546i	−0.716359	−	0.697732i	$-0.754192\pi$
$971$		−	1355.00i		−	1.39546i	0.716359	−	0.697732i	$-0.245808\pi$
$972$		0			0
$973$	171.026			0.175772
$974$		0			0
$975$	224.793	−	788.109i	0.230557	−	0.808317i
$976$		0			0
$977$			493.726i			0.505349i	0.967551	+	0.252674i	$0.0813101\pi$
$977$			493.726i			0.505349i	−0.967551	+	0.252674i	$0.918690\pi$
$978$		0			0
$979$	893.150			0.912309
$980$		0			0
$981$	279.365	+	173.481i	0.284775	+	0.176841i
$982$		0			0
$983$		−	1538.05i		−	1.56465i	−0.622870	−	0.782325i	$-0.714034\pi$
$983$		−	1538.05i		−	1.56465i	0.622870	−	0.782325i	$-0.285966\pi$
$984$		0			0
$985$	169.446			0.172026
$986$		0			0
$987$	−252.000	−	71.8783i	−0.255319	−	0.0728251i
$988$		0			0
$989$		−	616.731i		−	0.623590i
$990$		0			0
$991$	−1514.73			−1.52849			−0.764243	−	0.644929i	$-0.776887\pi$
$991$	−1514.73			−1.52849			−0.764243	+	0.644929i	$0.776887\pi$
$992$		0			0
$993$	127.026	−	445.344i	0.127922	−	0.448483i
$994$		0			0
$995$			107.533i			0.108074i
$996$		0			0
$997$	1826.43			1.83193			0.915964	−	0.401260i	$-0.131428\pi$
$997$	1826.43			1.83193			0.915964	+	0.401260i	$0.131428\pi$
$998$		0			0
$999$	−660.443	+	599.705i	−0.661104	+	0.600306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.d.c.113.2		4
3.2	odd	2	inner	336.3.d.c.113.1		4
4.3	odd	2		21.3.b.a.8.4	yes	4
8.3	odd	2		1344.3.d.f.449.2		4
8.5	even	2		1344.3.d.b.449.3		4
12.11	even	2		21.3.b.a.8.1	✓	4
20.3	even	4		525.3.f.a.449.8		8
20.7	even	4		525.3.f.a.449.1		8
20.19	odd	2		525.3.c.a.176.1		4
24.5	odd	2		1344.3.d.b.449.4		4
24.11	even	2		1344.3.d.f.449.1		4
28.3	even	6		147.3.h.c.128.1		8
28.11	odd	6		147.3.h.e.128.1		8
28.19	even	6		147.3.h.c.116.4		8
28.23	odd	6		147.3.h.e.116.4		8
28.27	even	2		147.3.b.f.50.4		4
36.7	odd	6		567.3.r.c.134.4		8
36.11	even	6		567.3.r.c.134.1		8
36.23	even	6		567.3.r.c.512.4		8
36.31	odd	6		567.3.r.c.512.1		8
60.23	odd	4		525.3.f.a.449.2		8
60.47	odd	4		525.3.f.a.449.7		8
60.59	even	2		525.3.c.a.176.4		4
84.11	even	6		147.3.h.e.128.4		8
84.23	even	6		147.3.h.e.116.1		8
84.47	odd	6		147.3.h.c.116.1		8
84.59	odd	6		147.3.h.c.128.4		8
84.83	odd	2		147.3.b.f.50.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	12.11	even	2
21.3.b.a.8.4	yes	4	4.3	odd	2
147.3.b.f.50.1		4	84.83	odd	2
147.3.b.f.50.4		4	28.27	even	2
147.3.h.c.116.1		8	84.47	odd	6
147.3.h.c.116.4		8	28.19	even	6
147.3.h.c.128.1		8	28.3	even	6
147.3.h.c.128.4		8	84.59	odd	6
147.3.h.e.116.1		8	84.23	even	6
147.3.h.e.116.4		8	28.23	odd	6
147.3.h.e.128.1		8	28.11	odd	6
147.3.h.e.128.4		8	84.11	even	6
336.3.d.c.113.1		4	3.2	odd	2	inner
336.3.d.c.113.2		4	1.1	even	1	trivial
525.3.c.a.176.1		4	20.19	odd	2
525.3.c.a.176.4		4	60.59	even	2
525.3.f.a.449.1		8	20.7	even	4
525.3.f.a.449.2		8	60.23	odd	4
525.3.f.a.449.7		8	60.47	odd	4
525.3.f.a.449.8		8	20.3	even	4
567.3.r.c.134.1		8	36.11	even	6
567.3.r.c.134.4		8	36.7	odd	6
567.3.r.c.512.1		8	36.31	odd	6
567.3.r.c.512.4		8	36.23	even	6
1344.3.d.b.449.3		4	8.5	even	2
1344.3.d.b.449.4		4	24.5	odd	2
1344.3.d.f.449.1		4	24.11	even	2
1344.3.d.f.449.2		4	8.3	odd	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.822876 + 2.88494i) q^{3} -1.24197i q^{5} -2.64575 q^{7} +(-7.64575 - 4.74789i) q^{9} +O(q^{10})\)	\(q+(-0.822876 + 2.88494i) q^{3} -1.24197i q^{5} -2.64575 q^{7} +(-7.64575 - 4.74789i) q^{9} -7.01185i q^{11} -11.6458 q^{13} +(3.58301 + 1.02199i) q^{15} -4.52791i q^{17} -16.2288 q^{19} +(2.17712 - 7.63283i) q^{21} -25.5635i q^{23} +23.4575 q^{25} +(19.9889 - 18.1506i) q^{27} -9.49579i q^{29} -28.7085 q^{31} +(20.2288 + 5.76988i) q^{33} +3.28594i q^{35} -33.0405 q^{37} +(9.58301 - 33.5973i) q^{39} -67.1946i q^{41} +24.1255 q^{43} +(-5.89674 + 9.49579i) q^{45} -33.0153i q^{47} +7.00000 q^{49} +(13.0627 + 3.72591i) q^{51} +15.1877i q^{53} -8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +92.3960i q^{59} -57.5203 q^{61} +(20.2288 + 12.5617i) q^{63} +14.4637i q^{65} -15.1660 q^{67} +(73.7490 + 21.0355i) q^{69} -70.5584i q^{71} -76.7895 q^{73} +(-19.3026 + 67.6735i) q^{75} +18.5516i q^{77} -127.247 q^{79} +(35.9150 + 72.6024i) q^{81} +74.2844i q^{83} -5.62352 q^{85} +(27.3948 + 7.81385i) q^{87} +127.377i q^{89} +30.8118 q^{91} +(23.6235 - 82.8223i) q^{93} +20.1556i q^{95} -23.1660 q^{97} +(-33.2915 + 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 20 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 20 * q^9	\( 4 q + 2 q^{3} - 20 q^{9} - 36 q^{13} - 28 q^{15} - 12 q^{19} + 14 q^{21} - 12 q^{25} - 10 q^{27} - 136 q^{31} + 28 q^{33} + 16 q^{37} - 4 q^{39} + 160 q^{43} - 140 q^{45} + 28 q^{49} + 84 q^{51} - 56 q^{55} + 64 q^{57} - 156 q^{61} + 28 q^{63} + 24 q^{67} + 168 q^{69} - 32 q^{73} - 146 q^{75} - 128 q^{79} - 68 q^{81} + 168 q^{85} - 28 q^{87} + 28 q^{91} - 96 q^{93} - 8 q^{97} - 112 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 20 * q^9 - 36 * q^13 - 28 * q^15 - 12 * q^19 + 14 * q^21 - 12 * q^25 - 10 * q^27 - 136 * q^31 + 28 * q^33 + 16 * q^37 - 4 * q^39 + 160 * q^43 - 140 * q^45 + 28 * q^49 + 84 * q^51 - 56 * q^55 + 64 * q^57 - 156 * q^61 + 28 * q^63 + 24 * q^67 + 168 * q^69 - 32 * q^73 - 146 * q^75 - 128 * q^79 - 68 * q^81 + 168 * q^85 - 28 * q^87 + 28 * q^91 - 96 * q^93 - 8 * q^97 - 112 * q^99

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