LMFDB - Embedded newform 363.2.f.c.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.228765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 $ x^8 - x^7 - 2x^6 + 5x^5 + x^4 + 15x^3 - 18x^2 - 27*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			239.1
Root			$1.42264 - 0.987975i$ of defining polynomial
Character	$\chi$	$=$	363.239
Dual form			363.2.f.c.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42264 + 0.987975i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(1.04781 - 2.81107i) q^{9} +O(q^{10})$	$q+(-1.42264 + 0.987975i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(1.04781 - 2.81107i) q^{9} +(-1.00000 - 3.31662i) q^{12} +(0.122445 - 5.74326i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-3.89893 - 5.36641i) q^{20} -3.31662i q^{23} +(-1.85410 - 5.70634i) q^{25} +(1.28660 + 5.03435i) q^{27} +(-4.04508 + 2.93893i) q^{31} +(4.69938 + 3.73039i) q^{36} +(-2.16312 + 6.65740i) q^{37} +(5.50000 + 8.29156i) q^{45} +(-6.30860 + 2.04979i) q^{47} +(6.92663 + 0.147674i) q^{48} +(-5.66312 - 4.11450i) q^{49} +(7.79785 + 10.7328i) q^{53} +(-3.15430 - 1.02489i) q^{59} +(10.8487 + 3.78243i) q^{60} +(6.47214 - 4.70228i) q^{64} -13.0000 q^{67} +(3.27674 + 4.71836i) q^{69} +(9.74732 - 13.4160i) q^{71} +(8.27544 + 6.28626i) q^{75} +(12.6172 - 4.09957i) q^{80} +(-6.80418 - 5.89093i) q^{81} +16.5831i q^{89} +(6.30860 + 2.04979i) q^{92} +(2.85112 - 8.17748i) q^{93} +(-13.7533 + 9.99235i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} + 4 q^{4} + 5 q^{9}+O(q^{10}) $ 8 * q - q^3 + 4 * q^4 + 5 * q^9	$ 8 q - q^{3} + 4 q^{4} + 5 q^{9} - 8 q^{12} - 11 q^{15} - 8 q^{16} + 12 q^{25} + 8 q^{27} - 10 q^{31} - 10 q^{36} + 14 q^{37} + 44 q^{45} - 4 q^{48} - 14 q^{49} + 22 q^{60} + 16 q^{64} - 104 q^{67} - 11 q^{69} + 6 q^{75} - 7 q^{81} - 5 q^{93} - 34 q^{97}+O(q^{100}) $ 8 * q - q^3 + 4 * q^4 + 5 * q^9 - 8 * q^12 - 11 * q^15 - 8 * q^16 + 12 * q^25 + 8 * q^27 - 10 * q^31 - 10 * q^36 + 14 * q^37 + 44 * q^45 - 4 * q^48 - 14 * q^49 + 22 * q^60 + 16 * q^64 - 104 * q^67 - 11 * q^69 + 6 * q^75 - 7 * q^81 - 5 * q^93 - 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$2$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$3$	−1.42264	+	0.987975i	−0.821362	+	0.570408i
$3$	−1.42264	+	0.987975i	−0.821362	+	0.570408i
$4$	−0.618034	+	1.90211i	−0.309017	+	0.951057i
$5$	−1.94946	+	2.68321i	−0.871826	+	1.19997i	0.106792	+	0.994281i	$0.465942\pi$
$5$	−1.94946	+	2.68321i	−0.871826	+	1.19997i	−0.978618	+	0.205685i	$0.934058\pi$
$6$		0			0
$7$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$7$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$8$		0			0
$9$	1.04781	−	2.81107i	0.349270	−	0.937022i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−1.00000	−	3.31662i	−0.288675	−	0.957427i
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$		0			0
$15$	0.122445	−	5.74326i	0.0316151	−	1.48290i
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$		0			0
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$	−3.89893	−	5.36641i	−0.871826	−	1.19997i
$21$		0			0
$22$		0			0
$23$		−	3.31662i		−	0.691564i	−0.938315	−	0.345782i	$-0.887614\pi$
$23$		−	3.31662i		−	0.691564i	0.938315	−	0.345782i	$-0.112386\pi$
$24$		0			0
$25$	−1.85410	−	5.70634i	−0.370820	−	1.14127i
$26$		0			0
$27$	1.28660	+	5.03435i	0.247607	+	0.968860i
$28$		0			0
$29$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$29$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$30$		0			0
$31$	−4.04508	+	2.93893i	−0.726519	+	0.527847i	−0.888460	−	0.458954i	$-0.848224\pi$
$31$	−4.04508	+	2.93893i	−0.726519	+	0.527847i	0.161942	+	0.986800i	$0.448224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	4.69938	+	3.73039i	0.783230	+	0.621732i
$37$	−2.16312	+	6.65740i	−0.355615	+	1.09447i	0.600038	+	0.799972i	$0.295152\pi$
$37$	−2.16312	+	6.65740i	−0.355615	+	1.09447i	−0.955652	+	0.294497i	$0.904848\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	5.50000	+	8.29156i	0.819892	+	1.23603i
$46$		0			0
$47$	−6.30860	+	2.04979i	−0.920203	+	0.298992i	−0.730550	−	0.682859i	$-0.760736\pi$
$47$	−6.30860	+	2.04979i	−0.920203	+	0.298992i	−0.189653	+	0.981851i	$0.560736\pi$
$48$	6.92663	+	0.147674i	0.999773	+	0.0213149i
$49$	−5.66312	−	4.11450i	−0.809017	−	0.587785i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.79785	+	10.7328i	1.07112	+	1.47427i	0.868940	+	0.494918i	$0.164802\pi$
$53$	7.79785	+	10.7328i	1.07112	+	1.47427i	0.202178	+	0.979349i	$0.435198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.15430	−	1.02489i	−0.410655	−	0.133430i	0.0964021	−	0.995342i	$-0.469267\pi$
$59$	−3.15430	−	1.02489i	−0.410655	−	0.133430i	−0.507057	+	0.861913i	$0.669267\pi$
$60$	10.8487	+	3.78243i	1.40055	+	0.488310i
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$		0			0
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$		0			0
$66$		0			0
$67$	−13.0000			−1.58820			−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000			−1.58820			−0.794101	+	0.607785i	$0.792058\pi$
$68$		0			0
$69$	3.27674	+	4.71836i	0.394473	+	0.568024i
$70$		0			0
$71$	9.74732	−	13.4160i	1.15679	−	1.59219i	0.434378	−	0.900731i	$-0.356968\pi$
$71$	9.74732	−	13.4160i	1.15679	−	1.59219i	0.722416	−	0.691459i	$-0.243032\pi$
$72$		0			0
$73$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$73$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$74$		0			0
$75$	8.27544	+	6.28626i	0.955566	+	0.725875i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$79$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$80$	12.6172	−	4.09957i	1.41064	−	0.458346i
$81$	−6.80418	−	5.89093i	−0.756021	−	0.654548i
$82$		0			0
$83$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$83$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$			16.5831i			1.75781i	0.476999	+	0.878904i	$0.341725\pi$
$89$			16.5831i			1.75781i	−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$		0			0
$92$	6.30860	+	2.04979i	0.657717	+	0.213705i
$93$	2.85112	−	8.17748i	0.295647	−	0.847965i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.7533	+	9.99235i	−1.39643	+	1.01457i	−0.401310	+	0.915942i	$0.631445\pi$
$97$	−13.7533	+	9.99235i	−1.39643	+	1.01457i	−0.995124	+	0.0986273i	$0.968555\pi$
$98$		0			0
$99$		0			0
$100$	12.0000			1.20000
$101$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$101$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$102$		0			0
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	−0.993303	−	0.115536i	$-0.963141\pi$
$103$	−1.23607	+	3.80423i	−0.121793	+	0.374842i	0.871510	+	0.490378i	$0.163141\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$107$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$108$	−10.3711	−	0.664130i	−0.997956	−	0.0639059i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$	−3.50000	−	11.6082i	−0.332205	−	1.10180i
$112$		0			0
$113$	3.15430	−	1.02489i	0.296731	−	0.0964139i	−0.156868	−	0.987620i	$-0.550140\pi$
$113$	3.15430	−	1.02489i	0.296731	−	0.0964139i	0.453599	+	0.891206i	$0.350140\pi$
$114$		0			0
$115$	8.89919	+	6.46564i	0.829853	+	0.602924i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	−3.09017	−	9.51057i	−0.277505	−	0.854074i
$125$	3.15430	+	1.02489i	0.282129	+	0.0916693i
$126$		0			0
$127$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$127$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−16.0164	−	6.36205i	−1.37847	−	0.547558i
$136$		0			0
$137$	−13.6462	+	18.7824i	−1.16588	+	1.60469i	−0.479260	+	0.877673i	$0.659095\pi$
$137$	−13.6462	+	18.7824i	−1.16588	+	1.60469i	−0.686617	+	0.727019i	$0.740905\pi$
$138$		0			0
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$		0			0
$141$	6.94972	−	9.14884i	0.585272	−	0.770472i
$142$		0			0
$143$		0			0
$144$	−10.0000	+	6.63325i	−0.833333	+	0.552771i
$145$		0			0
$146$		0			0
$147$	12.1216	+	0.258429i	0.999773	+	0.0213149i
$148$	−11.3262	−	8.22899i	−0.931011	−	0.676419i
$149$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$149$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$150$		0			0
$151$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$151$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	16.5831i		−	1.33199i
$156$		0			0
$157$	7.10739	+	21.8743i	0.567232	+	1.74576i	0.661226	+	0.750186i	$0.270036\pi$
$157$	7.10739	+	21.8743i	0.567232	+	1.74576i	−0.0939948	+	0.995573i	$0.529964\pi$
$158$		0			0
$159$	−21.6973	−	7.56486i	−1.72071	−	0.599933i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	12.9443	−	9.40456i	1.01387	−	0.736622i	0.0488556	−	0.998806i	$-0.484443\pi$
$163$	12.9443	−	9.40456i	1.01387	−	0.736622i	0.965018	+	0.262184i	$0.0844426\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$167$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$168$		0			0
$169$	4.01722	−	12.3637i	0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.50000	−	1.65831i	0.413405	−	0.124646i
$178$		0			0
$179$	−15.7715	+	5.12447i	−1.17882	+	0.383021i	−0.831927	−	0.554885i	$-0.812762\pi$
$179$	−15.7715	+	5.12447i	−1.17882	+	0.383021i	−0.346890	+	0.937906i	$0.612762\pi$
$180$	−19.1707	+	5.33715i	−1.42890	+	0.397808i
$181$	20.2254	+	14.6946i	1.50334	+	1.09224i	0.969026	+	0.246960i	$0.0794316\pi$
$181$	20.2254	+	14.6946i	1.50334	+	1.09224i	0.534318	+	0.845283i	$0.320568\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−13.6462	−	18.7824i	−1.00329	−	1.38091i
$186$		0			0
$187$		0			0
$188$		−	13.2665i		−	0.967559i
$189$		0			0
$190$		0			0
$191$	−22.0801	−	7.17425i	−1.59766	−	0.519111i	−0.631132	−	0.775676i	$-0.717409\pi$
$191$	−22.0801	−	7.17425i	−1.59766	−	0.519111i	−0.966527	+	0.256565i	$0.917409\pi$
$192$	−4.56178	+	13.0840i	−0.329218	+	0.944254i
$193$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$193$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$194$		0			0
$195$		0			0
$196$	11.3262	−	8.22899i	0.809017	−	0.587785i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$		0			0
$201$	18.4943	−	12.8437i	1.30449	−	0.905923i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−9.32325	−	3.47520i	−0.648011	−	0.241543i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	−25.2344	+	8.19915i	−1.73310	+	0.563120i
$213$	−0.612223	+	28.7163i	−0.0419488	+	1.96761i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.309017	−	0.951057i	−0.0206933	−	0.0636875i	0.940177	−	0.340687i	$-0.110660\pi$
$223$	−0.309017	−	0.951057i	−0.0206933	−	0.0636875i	−0.960870	+	0.277000i	$0.910660\pi$
$224$		0			0
$225$	−17.9836	−	0.767161i	−1.19891	−	0.0511441i
$226$		0			0
$227$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$227$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$228$		0			0
$229$	−4.04508	+	2.93893i	−0.267307	+	0.194210i	−0.713362	−	0.700796i	$-0.752828\pi$
$229$	−4.04508	+	2.93893i	−0.267307	+	0.194210i	0.446055	+	0.895005i	$0.352828\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$233$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$234$		0			0
$235$	6.79837	−	20.9232i	0.443477	−	1.36488i
$236$	3.89893	−	5.36641i	0.253798	−	0.349324i
$237$		0			0
$238$		0			0
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$	−13.8994	+	18.2977i	−0.897205	+	1.18111i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$		0			0
$243$	15.5000	+	1.65831i	0.994325	+	0.106381i
$244$		0			0
$245$	22.0801	−	7.17425i	1.41064	−	0.458346i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.74732	−	13.4160i	−0.615245	−	0.846812i	0.381751	−	0.924265i	$-0.375321\pi$
$251$	−9.74732	−	13.4160i	−0.615245	−	0.846812i	−0.996996	+	0.0774530i	$0.975321\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	25.2344	+	8.19915i	1.57408	+	0.511449i	0.960522	−	0.278203i	$-0.0897388\pi$
$257$	25.2344	+	8.19915i	1.57408	+	0.511449i	0.613555	+	0.789652i	$0.289739\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−44.0000			−2.70290
$266$		0			0
$267$	−16.3837	−	23.5918i	−1.00267	−	1.44380i
$268$	8.03444	−	24.7275i	0.490782	−	1.51047i
$269$	−7.79785	+	10.7328i	−0.475443	+	0.654392i	−0.977621	−	0.210373i	$-0.932532\pi$
$269$	−7.79785	+	10.7328i	−0.475443	+	0.654392i	0.502178	+	0.864764i	$0.332532\pi$
$270$		0			0
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−11.0000	+	3.31662i	−0.662122	+	0.199637i
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$		0			0
$279$	4.02303	+	14.4504i	0.240853	+	0.865125i
$280$		0			0
$281$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$281$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	19.4946	+	26.8321i	1.15679	+	1.59219i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5.25329	−	16.1680i	−0.309017	−	0.951057i
$290$		0			0
$291$	9.69379	−	27.8034i	0.568260	−	1.62987i
$292$		0			0
$293$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$293$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$294$		0			0
$295$	8.89919	−	6.46564i	0.518131	−	0.376444i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−17.0717	+	11.8557i	−0.985634	+	0.684489i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	−2.00000	−	6.63325i	−0.113776	−	0.377352i
$310$		0			0
$311$	31.5430	−	10.2489i	1.78864	−	0.581164i	0.789183	−	0.614159i	$-0.210505\pi$
$311$	31.5430	−	10.2489i	1.78864	−	0.581164i	0.999456	+	0.0329949i	$0.0105045\pi$
$312$		0			0
$313$	15.3713	+	11.1679i	0.868839	+	0.631248i	0.930275	−	0.366863i	$-0.119568\pi$
$313$	15.3713	+	11.1679i	0.868839	+	0.631248i	−0.0614365	+	0.998111i	$0.519568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.6462	+	18.7824i	0.766449	+	1.05493i	0.996650	+	0.0817838i	$0.0260617\pi$
$317$	13.6462	+	18.7824i	0.766449	+	1.05493i	−0.230201	+	0.973143i	$0.573938\pi$
$318$		0			0
$319$		0			0
$320$			26.5330i			1.48324i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	15.4104	−	9.30153i	0.856135	−	0.516752i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	35.0000			1.92377			0.961887	−	0.273447i	$-0.0881639\pi$
$331$	35.0000			1.92377			0.961887	+	0.273447i	$0.0881639\pi$
$332$		0			0
$333$	16.4478	+	13.0564i	0.901336	+	0.715484i
$334$		0			0
$335$	25.3430	−	34.8817i	1.38464	−	1.90579i
$336$		0			0
$337$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$337$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$338$		0			0
$339$	−3.47486	+	4.57442i	−0.188729	+	0.248448i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−19.0482	−	0.406103i	−1.02552	−	0.0218639i
$346$		0			0
$347$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$347$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$348$		0			0
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			36.4829i			1.94179i	0.239511	+	0.970894i	$0.423013\pi$
$353$			36.4829i			1.94179i	−0.239511	+	0.970894i	$0.576987\pi$
$354$		0			0
$355$	16.9959	+	52.3081i	0.902051	+	2.77623i
$356$	−31.5430	−	10.2489i	−1.67177	−	0.543192i
$357$		0			0
$358$		0			0
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$		0			0
$361$	−15.3713	+	11.1679i	−0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.4336	+	35.1891i	−0.596831	+	1.83686i	−0.0514358	+	0.998676i	$0.516380\pi$
$367$	−11.4336	+	35.1891i	−0.596831	+	1.83686i	−0.545395	+	0.838179i	$0.683620\pi$
$368$	−7.79785	+	10.7328i	−0.406491	+	0.559487i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	13.7924	+	10.4771i	0.715103	+	0.543212i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	−5.50000	+	1.65831i	−0.284019	+	0.0856349i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	20.2254	+	14.6946i	1.03891	+	0.754813i	0.970073	−	0.242815i	$-0.0780709\pi$
$379$	20.2254	+	14.6946i	1.03891	+	0.754813i	0.0688378	+	0.997628i	$0.478071\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.94946	+	2.68321i	0.0996129	+	0.137105i	0.855914	−	0.517119i	$-0.172995\pi$
$383$	1.94946	+	2.68321i	0.0996129	+	0.137105i	−0.756301	+	0.654224i	$0.772995\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−10.5066	−	32.3359i	−0.533391	−	1.64161i
$389$	34.6973	+	11.2738i	1.75922	+	0.571606i	0.997119	−	0.0758507i	$-0.0241672\pi$
$389$	34.6973	+	11.2738i	1.75922	+	0.571606i	0.762102	+	0.647456i	$0.224167\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$		0			0
$400$	−7.41641	+	22.8254i	−0.370820	+	1.14127i
$401$	15.5957	−	21.4656i	0.778812	−	1.07194i	−0.216600	−	0.976261i	$-0.569497\pi$
$401$	15.5957	−	21.4656i	0.778812	−	1.07194i	0.995412	−	0.0956827i	$-0.0305034\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	29.0711	−	6.77287i	1.44455	−	0.336547i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$409$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$	0.857113	−	40.2028i	0.0422782	−	1.98306i
$412$	−6.47214	−	4.70228i	−0.318859	−	0.231665i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	33.1662i		−	1.62028i	−0.586238	−	0.810139i	$-0.699392\pi$
$419$		−	33.1662i		−	1.62028i	0.586238	−	0.810139i	$-0.300608\pi$
$420$		0			0
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	0.847084	−	0.531460i	$-0.178356\pi$
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	−0.997689	+	0.0679432i	$0.978356\pi$
$422$		0			0
$423$	−0.848129	+	19.8817i	−0.0412374	+	0.966680i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$	7.67292	−	19.3165i	0.369163	−	0.929364i
$433$	8.96149	−	27.5806i	0.430662	−	1.32544i	−0.466805	−	0.884360i	$-0.654595\pi$
$433$	8.96149	−	27.5806i	0.430662	−	1.32544i	0.897467	−	0.441081i	$-0.145405\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−17.5000	+	11.6082i	−0.833333	+	0.552771i
$442$		0			0
$443$	−34.6973	+	11.2738i	−1.64852	+	0.535636i	−0.978418	−	0.206636i	$-0.933748\pi$
$443$	−34.6973	+	11.2738i	−1.64852	+	0.535636i	−0.670099	+	0.742271i	$0.733748\pi$
$444$	24.2432	+	0.516858i	1.15053	+	0.0245290i
$445$	−44.4959	−	32.3282i	−2.10931	−	1.53250i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.74732	−	13.4160i	−0.460004	−	0.633142i	0.514505	−	0.857487i	$-0.327976\pi$
$449$	−9.74732	−	13.4160i	−0.460004	−	0.633142i	−0.974510	+	0.224346i	$0.927976\pi$
$450$		0			0
$451$		0			0
$452$			6.63325i			0.312002i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$457$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$458$		0			0
$459$		0			0
$460$	−17.7984	+	12.9313i	−0.829853	+	0.602924i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$		0			0
$465$	16.3837	+	23.5918i	0.759776	+	1.09404i
$466$		0			0
$467$	−25.3430	+	34.8817i	−1.17274	+	1.61413i	−0.530212	+	0.847865i	$0.677888\pi$
$467$	−25.3430	+	34.8817i	−1.17274	+	1.61413i	−0.642523	+	0.766267i	$0.722112\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−31.7225	−	24.0973i	−1.46170	−	1.11035i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	38.3414	−	10.6743i	1.75553	−	0.488743i
$478$		0			0
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	56.3826i		−	2.56020i
$486$		0			0
$487$	−13.2877	−	40.8954i	−0.602125	−	1.85315i	−0.515465	−	0.856911i	$-0.672381\pi$
$487$	−13.2877	−	40.8954i	−0.602125	−	1.85315i	−0.0866600	−	0.996238i	$-0.527619\pi$
$488$		0			0
$489$	−9.12357	+	26.1679i	−0.412582	+	1.18335i
$490$		0			0
$491$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$491$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$		0			0
$498$		0			0
$499$	−12.3607	+	38.0423i	−0.553340	+	1.70301i	0.146947	+	0.989144i	$0.453055\pi$
$499$	−12.3607	+	38.0423i	−0.553340	+	1.70301i	−0.700287	+	0.713861i	$0.746945\pi$
$500$	−3.89893	+	5.36641i	−0.174365	+	0.239993i
$501$		0			0
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.50000	+	21.5581i	0.288675	+	0.957427i
$508$		0			0
$509$	3.15430	−	1.02489i	0.139812	−	0.0454276i	−0.238275	−	0.971198i	$-0.576582\pi$
$509$	3.15430	−	1.02489i	0.139812	−	0.0454276i	0.378087	+	0.925770i	$0.376582\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.79785	−	10.7328i	−0.343614	−	0.472945i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−41.0059	−	13.3236i	−1.79650	−	0.583718i	−0.796713	−	0.604358i	$-0.793430\pi$
$521$	−41.0059	−	13.3236i	−1.79650	−	0.583718i	−0.999787	+	0.0206400i	$0.993430\pi$
$522$		0			0
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	12.0000			0.521739
$530$		0			0
$531$	−6.18615	+	7.79304i	−0.268456	+	0.338189i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	17.3743	−	22.8721i	0.749757	−	0.987004i
$538$		0			0
$539$		0			0
$540$	22.0000	−	26.5330i	0.946729	−	1.14180i
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$		0			0
$543$	−43.2914	−	0.922961i	−1.85781	−	0.0396081i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$547$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$548$	−27.2925	−	37.5649i	−1.16588	−	1.60469i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	37.9703	+	13.2385i	1.61175	+	0.561944i
$556$		0			0
$557$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$557$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$563$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$564$	13.1070	+	18.8735i	0.551903	+	0.794716i
$565$	−3.39919	+	10.4616i	−0.143005	+	0.440124i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	38.5000	−	11.6082i	1.60836	−	0.484939i
$574$		0			0
$575$	−18.9258	+	6.14936i	−0.789260	+	0.256446i
$576$	−6.43685	−	23.1207i	−0.268202	−	0.963363i
$577$	−38.0238	−	27.6259i	−1.58295	−	1.15008i	−0.913212	−	0.407486i	$-0.866406\pi$
$577$	−38.0238	−	27.6259i	−1.58295	−	1.15008i	−0.669740	−	0.742596i	$-0.733594\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.30860	+	2.04979i	0.260384	+	0.0846038i	0.436300	−	0.899801i	$-0.356289\pi$
$587$	6.30860	+	2.04979i	0.260384	+	0.0846038i	−0.175916	+	0.984405i	$0.556289\pi$
$588$	−7.98312	+	22.8969i	−0.329218	+	0.944254i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	22.6525	−	16.4580i	0.931011	−	0.676419i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−28.4528	+	19.7595i	−1.16450	+	0.808702i
$598$		0			0
$599$	−19.4946	+	26.8321i	−0.796529	+	1.09633i	0.196735	+	0.980457i	$0.436966\pi$
$599$	−19.4946	+	26.8321i	−0.796529	+	1.09633i	−0.993264	+	0.115872i	$0.963034\pi$
$600$		0			0
$601$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$601$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$602$		0			0
$603$	−13.6215	+	36.5439i	−0.554712	+	1.48818i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$607$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$613$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			26.5330i			1.06818i	0.845428	+	0.534089i	$0.179345\pi$
$617$			26.5330i			1.06818i	−0.845428	+	0.534089i	$0.820655\pi$
$618$		0			0
$619$	−0.309017	−	0.951057i	−0.0124204	−	0.0382262i	0.944654	−	0.328068i	$-0.106397\pi$
$619$	−0.309017	−	0.951057i	−0.0124204	−	0.0382262i	−0.957075	+	0.289841i	$0.906397\pi$
$620$	31.5430	+	10.2489i	1.26680	+	0.411607i
$621$	16.6970	−	4.26719i	0.670029	−	0.171236i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$		0			0
$627$		0			0
$628$	−46.0000			−1.83560
$629$		0			0
$630$		0			0
$631$	−2.16312	+	6.65740i	−0.0861124	+	0.265027i	−0.984836	−	0.173489i	$-0.944496\pi$
$631$	−2.16312	+	6.65740i	−0.0861124	+	0.265027i	0.898723	+	0.438516i	$0.144496\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	27.7989	−	36.5954i	1.10230	−	1.45110i
$637$		0			0
$638$		0			0
$639$	−27.5000	−	41.4578i	−1.08788	−	1.64005i
$640$		0			0
$641$	22.0801	−	7.17425i	0.872111	−	0.283366i	0.161433	−	0.986884i	$-0.448388\pi$
$641$	22.0801	−	7.17425i	0.872111	−	0.283366i	0.710678	+	0.703518i	$0.248388\pi$
$642$		0			0
$643$	−33.1697	−	24.0992i	−1.30809	−	0.950379i	−0.308086	−	0.951359i	$-0.599688\pi$
$643$	−33.1697	−	24.0992i	−1.30809	−	0.950379i	−1.00000		0.000979141i	$0.999688\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	25.3430	+	34.8817i	0.996337	+	1.37134i	0.927546	+	0.373709i	$0.121914\pi$
$647$	25.3430	+	34.8817i	0.996337	+	1.37134i	0.0687910	+	0.997631i	$0.478086\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	9.88854	+	30.4338i	0.387265	+	1.19188i
$653$	−3.15430	−	1.02489i	−0.123437	−	0.0401072i	0.246647	−	0.969105i	$-0.420671\pi$
$653$	−3.15430	−	1.02489i	−0.123437	−	0.0401072i	−0.370084	+	0.928998i	$0.620671\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−13.0000			−0.505641			−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000			−0.505641			−0.252821	+	0.967513i	$0.581358\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.37924	+	1.04771i	0.0533245	+	0.0405068i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$		0			0
$675$	26.3422	−	16.6760i	1.01391	−	0.641859i
$676$	21.0344	+	15.2824i	0.809017	+	0.587785i
$677$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$677$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			46.4327i			1.77670i	0.459167	+	0.888350i	$0.348148\pi$
$683$			46.4327i			1.77670i	−0.459167	+	0.888350i	$0.651852\pi$
$684$		0			0
$685$	−23.7943	−	73.2314i	−0.909134	−	2.79803i
$686$		0			0
$687$	2.85112	−	8.17748i	0.108777	−	0.311990i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−13.7533	+	9.99235i	−0.523200	+	0.380127i	−0.817808	−	0.575491i	$-0.804811\pi$
$691$	−13.7533	+	9.99235i	−0.523200	+	0.380127i	0.294608	+	0.955618i	$0.404811\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$701$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	11.0000	+	36.4829i	0.414284	+	1.37402i
$706$		0			0
$707$		0			0
$708$	−0.244889	+	11.4865i	−0.00920350	+	0.431690i
$709$	15.3713	+	11.1679i	0.577282	+	0.419420i	0.837743	−	0.546064i	$-0.183875\pi$
$709$	15.3713	+	11.1679i	0.577282	+	0.419420i	−0.260461	+	0.965484i	$0.583875\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.74732	+	13.4160i	0.365040	+	0.502434i
$714$		0			0
$715$		0			0
$716$		−	33.1662i		−	1.23948i
$717$		0			0
$718$		0			0
$719$	15.7715	+	5.12447i	0.588177	+	0.191110i	0.587961	−	0.808890i	$-0.299931\pi$
$719$	15.7715	+	5.12447i	0.588177	+	0.191110i	0.000216702		1.00000i	$0.499931\pi$
$720$	1.69626	−	39.7633i	0.0632158	−	1.48189i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−40.4508	+	29.3893i	−1.50334	+	1.09224i
$725$		0			0
$726$		0			0
$727$	53.0000			1.96566			0.982831	−	0.184510i	$-0.0590699\pi$
$727$	53.0000			1.96566			0.982831	+	0.184510i	$0.0590699\pi$
$728$		0			0
$729$	−23.6893	+	12.9544i	−0.877381	+	0.479794i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$	−24.3240	+	32.0210i	−0.897205	+	1.18111i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$	44.1602	−	14.3485i	1.62336	−	0.527462i
$741$		0			0
$742$		0			0
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.10739	+	21.8743i	0.259352	+	0.798205i	0.992941	+	0.118611i	$0.0378440\pi$
$751$	7.10739	+	21.8743i	0.259352	+	0.798205i	−0.733588	+	0.679594i	$0.762156\pi$
$752$	25.2344	+	8.19915i	0.920203	+	0.298992i
$753$	27.1216	+	9.45608i	0.988367	+	0.344599i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.133554	+	0.991042i	$0.542639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$761$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$762$		0			0
$763$		0			0
$764$	27.2925	−	37.5649i	0.987407	−	1.35905i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−22.0678	−	16.7634i	−0.796305	−	0.604896i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	−44.0000	+	13.2665i	−1.58462	+	0.477781i
$772$		0			0
$773$	12.6172	−	4.09957i	0.453809	−	0.147451i	−0.0731890	−	0.997318i	$-0.523318\pi$
$773$	12.6172	−	4.09957i	0.453809	−	0.147451i	0.526998	+	0.849867i	$0.323318\pi$
$774$		0			0
$775$	24.2705	+	17.6336i	0.871822	+	0.633416i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	8.65248	+	26.6296i	0.309017	+	0.951057i
$785$	−72.5488	−	23.5725i	−2.58938	−	0.841340i
$786$		0			0
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	62.5962	−	43.4709i	2.22006	−	1.54175i
$796$	−12.3607	+	38.0423i	−0.438113	+	1.34837i
$797$	33.1409	−	45.6145i	1.17391	−	1.61575i	0.543970	−	0.839105i	$-0.316921\pi$
$797$	33.1409	−	45.6145i	1.17391	−	1.61575i	0.629940	−	0.776644i	$-0.283079\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	46.6163	+	17.3760i	1.64710	+	0.613950i
$802$		0			0
$803$		0			0
$804$	13.0000	+	43.1161i	0.458475	+	1.52059i
$805$		0			0
$806$		0			0
$807$	0.489779	−	22.9730i	0.0172410	−	0.808689i
$808$		0			0
$809$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$809$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			53.0660i			1.85882i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$821$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$822$		0			0
$823$	39.6418	−	28.8015i	1.38183	−	1.00396i	0.385121	−	0.922866i	$-0.374160\pi$
$823$	39.6418	−	28.8015i	1.38183	−	1.00396i	0.996707	−	0.0810902i	$-0.0258402\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$827$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$828$	12.3723	−	15.5861i	0.429967	−	0.541654i
$829$	8.96149	−	27.5806i	0.311246	−	0.957915i	−0.666027	−	0.745928i	$-0.732006\pi$
$829$	8.96149	−	27.5806i	0.311246	−	0.957915i	0.977272	−	0.211987i	$-0.0679936\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−20.0000	−	16.5831i	−0.691301	−	0.573197i
$838$		0			0
$839$	−34.6973	+	11.2738i	−1.19788	+	0.389216i	−0.838982	−	0.544160i	$-0.816849\pi$
$839$	−34.6973	+	11.2738i	−1.19788	+	0.389216i	−0.358901	+	0.933376i	$0.616849\pi$
$840$		0			0
$841$	23.4615	+	17.0458i	0.809017	+	0.587785i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	25.3430	+	34.8817i	0.871826	+	1.19997i
$846$		0			0
$847$		0			0
$848$		−	53.0660i		−	1.82229i
$849$		0			0
$850$		0			0
$851$	22.0801	+	7.17425i	0.756896	+	0.245930i
$852$	−54.2433	−	18.9122i	−1.85834	−	0.647920i
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−31.0000			−1.05771			−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000			−1.05771			−0.528853	+	0.848713i	$0.677378\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.2925	−	37.5649i	0.929047	−	1.27872i	−0.0311832	−	0.999514i	$-0.509928\pi$
$863$	27.2925	−	37.5649i	0.929047	−	1.27872i	0.960230	−	0.279210i	$-0.0900725\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	23.4471	+	17.8111i	0.796305	+	0.604896i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	13.6783	+	49.1315i	0.462941	+	1.66285i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			16.5831i			0.558700i	0.960189	+	0.279350i	$0.0901189\pi$
$881$			16.5831i			0.558700i	−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	17.3050	+	53.2592i	0.582358	+	1.79231i	0.609631	+	0.792686i	$0.291318\pi$
$883$	17.3050	+	53.2592i	0.582358	+	1.79231i	−0.0272727	+	0.999628i	$0.508682\pi$
$884$		0			0
$885$	−6.27245	+	17.9905i	−0.210846	+	0.604742i
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	2.00000			0.0669650
$893$		0			0
$894$		0			0
$895$	16.9959	−	52.3081i	0.568111	−	1.74847i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	12.5737	−	33.7328i	0.419124	−	1.12443i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−78.8574	+	25.6223i	−2.62131	+	0.851715i
$906$		0			0
$907$	−6.47214	−	4.70228i	−0.214904	−	0.156137i	0.475126	−	0.879918i	$-0.342403\pi$
$907$	−6.47214	−	4.70228i	−0.214904	−	0.156137i	−0.690030	+	0.723781i	$0.742403\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.89893	−	5.36641i	−0.129177	−	0.177797i	0.739529	−	0.673124i	$-0.235048\pi$
$911$	−3.89893	−	5.36641i	−0.129177	−	0.177797i	−0.868706	+	0.495327i	$0.835048\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−3.09017	−	9.51057i	−0.102102	−	0.314238i
$917$		0			0
$918$		0			0
$919$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$919$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	42.0000			1.38095
$926$		0			0
$927$	9.39877	+	7.46078i	0.308696	+	0.245044i
$928$		0			0
$929$	−31.1914	+	42.9313i	−1.02336	+	1.40853i	−0.113534	+	0.993534i	$0.536217\pi$
$929$	−31.1914	+	42.9313i	−1.02336	+	1.40853i	−0.909823	+	0.414996i	$0.863783\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−34.7486	+	45.7442i	−1.13762	+	1.49760i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$	−32.9015	−	0.701451i	−1.07370	−	0.0228910i
$940$	35.5967	+	25.8626i	1.16104	+	0.843543i
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$		0			0
$944$	7.79785	+	10.7328i	0.253798	+	0.349324i
$945$		0			0
$946$		0			0
$947$		−	23.2164i		−	0.754431i	−0.926126	−	0.377215i	$-0.876882\pi$
$947$		−	23.2164i		−	0.754431i	0.926126	−	0.377215i	$-0.123118\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−37.9703	−	13.2385i	−1.23127	−	0.429288i
$952$		0			0
$953$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$953$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$954$		0			0
$955$	62.2943	−	45.2595i	2.01580	−	1.46456i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−26.2139	−	37.7469i	−0.846051	−	1.21828i
$961$	−1.85410	+	5.70634i	−0.0598097	+	0.184075i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	41.0059	−	13.3236i	1.31594	−	0.427575i	0.434842	−	0.900507i	$-0.356804\pi$
$971$	41.0059	−	13.3236i	1.31594	−	0.427575i	0.881099	+	0.472932i	$0.156804\pi$
$972$	−12.7338	+	28.4579i	−0.408438	+	0.912786i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.1409	−	45.6145i	−1.06027	−	1.45934i	−0.879552	−	0.475802i	$-0.842158\pi$
$977$	−33.1409	−	45.6145i	−1.06027	−	1.45934i	−0.180718	−	0.983535i	$-0.557842\pi$
$978$		0			0
$979$		0			0
$980$			46.4327i			1.48324i
$981$		0			0
$982$		0			0
$983$	34.6973	+	11.2738i	1.10667	+	0.359579i	0.804666	−	0.593727i	$-0.202344\pi$
$983$	34.6973	+	11.2738i	1.10667	+	0.359579i	0.302005	+	0.953306i	$0.402344\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$		0			0
$993$	−49.7924	+	34.5791i	−1.58011	+	1.09734i
$994$		0			0
$995$	−38.9893	+	53.6641i	−1.23604	+	1.70127i
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$		0			0
$999$	−36.2987	−	2.32445i	−1.14844	−	0.0735425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.c.239.1		8
3.2	odd	2	inner	363.2.f.c.239.2		8
11.2	odd	10		33.2.d.a.32.2	yes	2
11.3	even	5	inner	363.2.f.c.215.2		8
11.4	even	5	inner	363.2.f.c.161.2		8
11.5	even	5	inner	363.2.f.c.233.1		8
11.6	odd	10	inner	363.2.f.c.233.1		8
11.7	odd	10	inner	363.2.f.c.161.2		8
11.8	odd	10	inner	363.2.f.c.215.2		8
11.9	even	5		33.2.d.a.32.2	yes	2
11.10	odd	2	CM	363.2.f.c.239.1		8
33.2	even	10		33.2.d.a.32.1	✓	2
33.5	odd	10	inner	363.2.f.c.233.2		8
33.8	even	10	inner	363.2.f.c.215.1		8
33.14	odd	10	inner	363.2.f.c.215.1		8
33.17	even	10	inner	363.2.f.c.233.2		8
33.20	odd	10		33.2.d.a.32.1	✓	2
33.26	odd	10	inner	363.2.f.c.161.1		8
33.29	even	10	inner	363.2.f.c.161.1		8
33.32	even	2	inner	363.2.f.c.239.2		8
44.31	odd	10		528.2.b.a.65.1		2
44.35	even	10		528.2.b.a.65.1		2
55.2	even	20		825.2.d.a.824.3		4
55.9	even	10		825.2.f.a.626.1		2
55.13	even	20		825.2.d.a.824.2		4
55.24	odd	10		825.2.f.a.626.1		2
55.42	odd	20		825.2.d.a.824.3		4
55.53	odd	20		825.2.d.a.824.2		4
88.13	odd	10		2112.2.b.e.65.1		2
88.35	even	10		2112.2.b.f.65.2		2
88.53	even	10		2112.2.b.e.65.1		2
88.75	odd	10		2112.2.b.f.65.2		2
99.2	even	30		891.2.g.a.296.1		4
99.13	odd	30		891.2.g.a.593.1		4
99.20	odd	30		891.2.g.a.296.1		4
99.31	even	15		891.2.g.a.593.1		4
99.68	even	30		891.2.g.a.593.2		4
99.79	odd	30		891.2.g.a.296.2		4
99.86	odd	30		891.2.g.a.593.2		4
99.97	even	15		891.2.g.a.296.2		4
132.35	odd	10		528.2.b.a.65.2		2
132.119	even	10		528.2.b.a.65.2		2
165.2	odd	20		825.2.d.a.824.1		4
165.53	even	20		825.2.d.a.824.4		4
165.68	odd	20		825.2.d.a.824.4		4
165.119	odd	10		825.2.f.a.626.2		2
165.134	even	10		825.2.f.a.626.2		2
165.152	even	20		825.2.d.a.824.1		4
264.35	odd	10		2112.2.b.f.65.1		2
264.53	odd	10		2112.2.b.e.65.2		2
264.101	even	10		2112.2.b.e.65.2		2
264.251	even	10		2112.2.b.f.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.d.a.32.1	✓	2	33.2	even	10
33.2.d.a.32.1	✓	2	33.20	odd	10
33.2.d.a.32.2	yes	2	11.2	odd	10
33.2.d.a.32.2	yes	2	11.9	even	5
363.2.f.c.161.1		8	33.26	odd	10	inner
363.2.f.c.161.1		8	33.29	even	10	inner
363.2.f.c.161.2		8	11.4	even	5	inner
363.2.f.c.161.2		8	11.7	odd	10	inner
363.2.f.c.215.1		8	33.8	even	10	inner
363.2.f.c.215.1		8	33.14	odd	10	inner
363.2.f.c.215.2		8	11.3	even	5	inner
363.2.f.c.215.2		8	11.8	odd	10	inner
363.2.f.c.233.1		8	11.5	even	5	inner
363.2.f.c.233.1		8	11.6	odd	10	inner
363.2.f.c.233.2		8	33.5	odd	10	inner
363.2.f.c.233.2		8	33.17	even	10	inner
363.2.f.c.239.1		8	1.1	even	1	trivial
363.2.f.c.239.1		8	11.10	odd	2	CM
363.2.f.c.239.2		8	3.2	odd	2	inner
363.2.f.c.239.2		8	33.32	even	2	inner
528.2.b.a.65.1		2	44.31	odd	10
528.2.b.a.65.1		2	44.35	even	10
528.2.b.a.65.2		2	132.35	odd	10
528.2.b.a.65.2		2	132.119	even	10
825.2.d.a.824.1		4	165.2	odd	20
825.2.d.a.824.1		4	165.152	even	20
825.2.d.a.824.2		4	55.13	even	20
825.2.d.a.824.2		4	55.53	odd	20
825.2.d.a.824.3		4	55.2	even	20
825.2.d.a.824.3		4	55.42	odd	20
825.2.d.a.824.4		4	165.53	even	20
825.2.d.a.824.4		4	165.68	odd	20
825.2.f.a.626.1		2	55.9	even	10
825.2.f.a.626.1		2	55.24	odd	10
825.2.f.a.626.2		2	165.119	odd	10
825.2.f.a.626.2		2	165.134	even	10
891.2.g.a.296.1		4	99.2	even	30
891.2.g.a.296.1		4	99.20	odd	30
891.2.g.a.296.2		4	99.79	odd	30
891.2.g.a.296.2		4	99.97	even	15
891.2.g.a.593.1		4	99.13	odd	30
891.2.g.a.593.1		4	99.31	even	15
891.2.g.a.593.2		4	99.68	even	30
891.2.g.a.593.2		4	99.86	odd	30
2112.2.b.e.65.1		2	88.13	odd	10
2112.2.b.e.65.1		2	88.53	even	10
2112.2.b.e.65.2		2	264.53	odd	10
2112.2.b.e.65.2		2	264.101	even	10
2112.2.b.f.65.1		2	264.35	odd	10
2112.2.b.f.65.1		2	264.251	even	10
2112.2.b.f.65.2		2	88.35	even	10
2112.2.b.f.65.2		2	88.75	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42264 + 0.987975i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(1.04781 - 2.81107i) q^{9} +O(q^{10})\)	\(q+(-1.42264 + 0.987975i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-1.94946 + 2.68321i) q^{5} +(1.04781 - 2.81107i) q^{9} +(-1.00000 - 3.31662i) q^{12} +(0.122445 - 5.74326i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-3.89893 - 5.36641i) q^{20} -3.31662i q^{23} +(-1.85410 - 5.70634i) q^{25} +(1.28660 + 5.03435i) q^{27} +(-4.04508 + 2.93893i) q^{31} +(4.69938 + 3.73039i) q^{36} +(-2.16312 + 6.65740i) q^{37} +(5.50000 + 8.29156i) q^{45} +(-6.30860 + 2.04979i) q^{47} +(6.92663 + 0.147674i) q^{48} +(-5.66312 - 4.11450i) q^{49} +(7.79785 + 10.7328i) q^{53} +(-3.15430 - 1.02489i) q^{59} +(10.8487 + 3.78243i) q^{60} +(6.47214 - 4.70228i) q^{64} -13.0000 q^{67} +(3.27674 + 4.71836i) q^{69} +(9.74732 - 13.4160i) q^{71} +(8.27544 + 6.28626i) q^{75} +(12.6172 - 4.09957i) q^{80} +(-6.80418 - 5.89093i) q^{81} +16.5831i q^{89} +(6.30860 + 2.04979i) q^{92} +(2.85112 - 8.17748i) q^{93} +(-13.7533 + 9.99235i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 4 q^{4} + 5 q^{9}+O(q^{10}) \) 8 * q - q^3 + 4 * q^4 + 5 * q^9	\( 8 q - q^{3} + 4 q^{4} + 5 q^{9} - 8 q^{12} - 11 q^{15} - 8 q^{16} + 12 q^{25} + 8 q^{27} - 10 q^{31} - 10 q^{36} + 14 q^{37} + 44 q^{45} - 4 q^{48} - 14 q^{49} + 22 q^{60} + 16 q^{64} - 104 q^{67} - 11 q^{69} + 6 q^{75} - 7 q^{81} - 5 q^{93} - 34 q^{97}+O(q^{100}) \) 8 * q - q^3 + 4 * q^4 + 5 * q^9 - 8 * q^12 - 11 * q^15 - 8 * q^16 + 12 * q^25 + 8 * q^27 - 10 * q^31 - 10 * q^36 + 14 * q^37 + 44 * q^45 - 4 * q^48 - 14 * q^49 + 22 * q^60 + 16 * q^64 - 104 * q^67 - 11 * q^69 + 6 * q^75 - 7 * q^81 - 5 * q^93 - 34 * q^97

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