LMFDB - Embedded newform 363.2.f.c.215.2

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			215.2
Root			$-0.570223 + 1.63550i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.c.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.570223 - 1.63550i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-3.15430 - 1.02489i) q^{5} +(-2.34969 - 1.86519i) q^{9} +O(q^{10})$	$q+(0.570223 - 1.63550i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-3.15430 - 1.02489i) q^{5} +(-2.34969 - 1.86519i) q^{9} +(-1.00000 - 3.31662i) q^{12} +(-3.47486 + 4.57442i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-6.30860 + 2.04979i) q^{20} -3.31662i q^{23} +(4.85410 + 3.52671i) q^{25} +(-4.39037 + 2.77933i) q^{27} +(1.54508 + 4.75528i) q^{31} +(-5.99455 - 0.255720i) q^{36} +(5.66312 - 4.11450i) q^{37} +(5.50000 + 8.29156i) q^{45} +(3.89893 - 5.36641i) q^{47} +(-5.51696 - 4.19084i) q^{48} +(2.16312 - 6.65740i) q^{49} +(12.6172 - 4.09957i) q^{53} +(1.94946 + 2.68321i) q^{59} +(-0.244889 + 11.4865i) q^{60} +(-2.47214 - 7.60845i) q^{64} -13.0000 q^{67} +(-5.42433 - 1.89122i) q^{69} +(15.7715 + 5.12447i) q^{71} +(8.53584 - 5.92785i) q^{75} +(-7.79785 + 10.7328i) q^{80} +(2.04210 + 8.76526i) q^{81} +16.5831i q^{89} +(-3.89893 - 5.36641i) q^{92} +(8.65829 + 0.184592i) q^{93} +(5.25329 + 16.1680i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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		0.951057	−	0.309017i	$-0.100000\pi$
$2$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$3$	0.570223	−	1.63550i	0.329218	−	0.944254i
$3$	0.570223	−	1.63550i	0.329218	−	0.944254i
$4$	1.61803	−	1.17557i	0.809017	−	0.587785i
$5$	−3.15430	−	1.02489i	−1.41064	−	0.458346i	−0.498027	−	0.867161i	$-0.665942\pi$
$5$	−3.15430	−	1.02489i	−1.41064	−	0.458346i	−0.912617	+	0.408815i	$0.865942\pi$
$6$		0			0
$7$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$7$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$8$		0			0
$9$	−2.34969	−	1.86519i	−0.783230	−	0.621732i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−1.00000	−	3.31662i	−0.288675	−	0.957427i
$13$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$13$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$14$		0			0
$15$	−3.47486	+	4.57442i	−0.897205	+	1.18111i
$16$	1.23607	−	3.80423i	0.309017	−	0.951057i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$		0			0
$19$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$19$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$20$	−6.30860	+	2.04979i	−1.41064	+	0.458346i
$21$		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
$25$	4.85410	+	3.52671i	0.970820	+	0.705342i
$26$		0			0
$27$	−4.39037	+	2.77933i	−0.844926	+	0.534883i
$28$		0			0
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$		0			0
$31$	1.54508	+	4.75528i	0.277505	+	0.854074i	0.988546	+	0.150923i	$0.0482244\pi$
$31$	1.54508	+	4.75528i	0.277505	+	0.854074i	−0.711040	+	0.703151i	$0.751776\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−5.99455	−	0.255720i	−0.999091	−	0.0426201i
$37$	5.66312	−	4.11450i	0.931011	−	0.676419i	−0.0152291	−	0.999884i	$-0.504848\pi$
$37$	5.66312	−	4.11450i	0.931011	−	0.676419i	0.946240	+	0.323465i	$0.104848\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$		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
$47$	3.89893	−	5.36641i	0.568717	−	0.782772i	−0.423685	−	0.905810i	$-0.639264\pi$
$47$	3.89893	−	5.36641i	0.568717	−	0.782772i	0.992402	+	0.123038i	$0.0392637\pi$
$48$	−5.51696	−	4.19084i	−0.796305	−	0.604896i
$49$	2.16312	−	6.65740i	0.309017	−	0.951057i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	12.6172	−	4.09957i	1.73310	−	0.563120i	0.739212	−	0.673473i	$-0.235198\pi$
$53$	12.6172	−	4.09957i	1.73310	−	0.563120i	0.993892	+	0.110353i	$0.0351982\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.94946	+	2.68321i	0.253798	+	0.349324i	0.916837	−	0.399262i	$-0.130733\pi$
$59$	1.94946	+	2.68321i	0.253798	+	0.349324i	−0.663039	+	0.748585i	$0.730733\pi$
$60$	−0.244889	+	11.4865i	−0.0316151	+	1.48290i
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$		0			0
$63$		0			0
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$		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
$69$	−5.42433	−	1.89122i	−0.653012	−	0.227676i
$70$		0			0
$71$	15.7715	+	5.12447i	1.87173	+	0.608162i	0.990876	+	0.134777i	$0.0430317\pi$
$71$	15.7715	+	5.12447i	1.87173	+	0.608162i	0.880855	+	0.473386i	$0.156968\pi$
$72$		0			0
$73$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$73$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$74$		0			0
$75$	8.53584	−	5.92785i	0.985634	−	0.684489i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$79$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$80$	−7.79785	+	10.7328i	−0.871826	+	1.19997i
$81$	2.04210	+	8.76526i	0.226900	+	0.973918i
$82$		0			0
$83$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$83$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$84$		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
$92$	−3.89893	−	5.36641i	−0.406491	−	0.559487i
$93$	8.65829	+	0.184592i	0.897822	+	0.0191413i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.25329	+	16.1680i	0.533391	+	1.64161i	0.747101	+	0.664711i	$0.231445\pi$
$97$	5.25329	+	16.1680i	0.533391	+	1.64161i	−0.213710	+	0.976897i	$0.568555\pi$
$98$		0			0
$99$		0			0
$100$	12.0000			1.20000
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	−0.416829	−	0.908985i	$-0.636859\pi$
$103$	3.23607	−	2.35114i	0.318859	−	0.231665i	0.735689	+	0.677320i	$0.236859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$107$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$108$	−3.83646	+	9.65824i	−0.369163	+	0.929364i
$109$		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
$113$	−1.94946	+	2.68321i	−0.183390	+	0.252415i	−0.890807	−	0.454382i	$-0.849860\pi$
$113$	−1.94946	+	2.68321i	−0.183390	+	0.252415i	0.707417	+	0.706796i	$0.249860\pi$
$114$		0			0
$115$	−3.39919	+	10.4616i	−0.316976	+	0.975551i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	8.09017	+	5.87785i	0.726519	+	0.527847i
$125$	−1.94946	−	2.68321i	−0.174365	−	0.239993i
$126$		0			0
$127$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$127$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$128$		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
$135$	16.6970	−	4.26719i	1.43705	−	0.367261i
$136$		0			0
$137$	−22.0801	−	7.17425i	−1.88643	−	0.612938i	−0.982816	−	0.184588i	$-0.940905\pi$
$137$	−22.0801	−	7.17425i	−1.88643	−	0.612938i	−0.903613	−	0.428350i	$-0.859095\pi$
$138$		0			0
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$	−6.55348	−	9.43673i	−0.551903	−	0.794716i
$142$		0			0
$143$		0			0
$144$	−10.0000	+	6.63325i	−0.833333	+	0.552771i
$145$		0			0
$146$		0			0
$147$	−9.65468	−	7.33397i	−0.796305	−	0.604896i
$148$	4.32624	−	13.3148i	0.355615	−	1.09447i
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$		0			0
$151$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$151$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	16.5831i		−	1.33199i
$156$		0			0
$157$	−18.6074	−	13.5191i	−1.48503	−	1.07894i	−0.975892	−	0.218255i	$-0.929964\pi$
$157$	−18.6074	−	13.5191i	−1.48503	−	1.07894i	−0.509140	−	0.860684i	$-0.670036\pi$
$158$		0			0
$159$	0.489779	−	22.9730i	0.0388420	−	1.82188i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.94427	−	15.2169i	−0.387265	−	1.19188i	−0.934824	−	0.355112i	$-0.884443\pi$
$163$	−4.94427	−	15.2169i	−0.387265	−	1.19188i	0.547558	−	0.836768i	$-0.315557\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$		0			0
$169$	−10.5172	+	7.64121i	−0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$173$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.50000	−	1.65831i	0.413405	−	0.124646i
$178$		0			0
$179$	9.74732	−	13.4160i	0.728549	−	1.00276i	−0.270648	−	0.962678i	$-0.587238\pi$
$179$	9.74732	−	13.4160i	0.728549	−	1.00276i	0.999196	−	0.0400827i	$-0.0127621\pi$
$180$	18.6465	+	6.95039i	1.38983	+	0.518052i
$181$	−7.72542	+	23.7764i	−0.574226	+	1.76729i	0.0645725	+	0.997913i	$0.479432\pi$
$181$	−7.72542	+	23.7764i	−0.574226	+	1.76729i	−0.638799	+	0.769374i	$0.720568\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−22.0801	+	7.17425i	−1.62336	+	0.527462i
$186$		0			0
$187$		0			0
$188$		−	13.2665i		−	0.967559i
$189$		0			0
$190$		0			0
$191$	13.6462	+	18.7824i	0.987407	+	1.35905i	0.932742	+	0.360545i	$0.117409\pi$
$191$	13.6462	+	18.7824i	0.987407	+	1.35905i	0.0546656	+	0.998505i	$0.482591\pi$
$192$	−13.8533	−	0.295348i	−0.999773	−	0.0213149i
$193$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$193$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$194$		0			0
$195$		0			0
$196$	−4.32624	−	13.3148i	−0.309017	−	0.951057i
$197$		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
$201$	−7.41290	+	21.2614i	−0.522866	+	1.49967i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.18615	+	7.79304i	−0.429967	+	0.541654i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$	15.5957	−	21.4656i	1.07112	−	1.47427i
$213$	17.3743	−	22.8721i	1.19047	−	1.56717i
$214$		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
$223$	0.809017	+	0.587785i	0.0541758	+	0.0393610i	0.614544	−	0.788883i	$-0.289340\pi$
$223$	0.809017	+	0.587785i	0.0541758	+	0.0393610i	−0.560368	+	0.828244i	$0.689340\pi$
$224$		0			0
$225$	−4.82764	−	17.3405i	−0.321843	−	1.15604i
$226$		0			0
$227$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$227$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$228$		0			0
$229$	1.54508	+	4.75528i	0.102102	+	0.314238i	0.989039	−	0.147652i	$-0.0471715\pi$
$229$	1.54508	+	4.75528i	0.102102	+	0.314238i	−0.886937	+	0.461890i	$0.847172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$233$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$234$		0			0
$235$	−17.7984	+	12.9313i	−1.16104	+	0.843543i
$236$	6.30860	+	2.04979i	0.410655	+	0.133430i
$237$		0			0
$238$		0			0
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$	13.1070	+	18.8735i	0.846051	+	1.21828i
$241$		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
$245$	−13.6462	+	18.7824i	−0.871826	+	1.19997i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.7715	+	5.12447i	−0.995488	+	0.323453i	−0.761061	−	0.648680i	$-0.775321\pi$
$251$	−15.7715	+	5.12447i	−0.995488	+	0.323453i	−0.234427	+	0.972134i	$0.575321\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	−15.5957	−	21.4656i	−0.972833	−	1.33899i	−0.940603	−	0.339510i	$-0.889739\pi$
$257$	−15.5957	−	21.4656i	−0.972833	−	1.33899i	−0.0322308	−	0.999480i	$-0.510261\pi$
$258$		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
$267$	27.1216	+	9.45608i	1.65982	+	0.578703i
$268$	−21.0344	+	15.2824i	−1.28488	+	0.933522i
$269$	−12.6172	−	4.09957i	−0.769284	−	0.249955i	−0.102025	−	0.994782i	$-0.532532\pi$
$269$	−12.6172	−	4.09957i	−0.769284	−	0.249955i	−0.667258	+	0.744826i	$0.732532\pi$
$270$		0			0
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−11.0000	+	3.31662i	−0.662122	+	0.199637i
$277$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$277$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$278$		0			0
$279$	5.23905	−	14.0553i	0.313654	−	0.841471i
$280$		0			0
$281$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$281$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$282$		0			0
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	31.5430	−	10.2489i	1.87173	−	0.608162i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$	29.4382	+	0.627614i	1.72570	+	0.0367914i
$292$		0			0
$293$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$293$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$294$		0			0
$295$	−3.39919	−	10.4616i	−0.197908	−	0.609099i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	6.84268	−	19.6259i	0.395062	−	1.13310i
$301$		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
$311$	−19.4946	+	26.8321i	−1.10544	+	1.52151i	−0.277469	+	0.960735i	$0.589495\pi$
$311$	−19.4946	+	26.8321i	−1.10544	+	1.52151i	−0.827970	+	0.560772i	$0.810505\pi$
$312$		0			0
$313$	−5.87132	+	18.0701i	−0.331867	+	1.02138i	0.636378	+	0.771377i	$0.280432\pi$
$313$	−5.87132	+	18.0701i	−0.331867	+	1.02138i	−0.968245	+	0.250004i	$0.919568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.0801	−	7.17425i	1.24014	−	0.402946i	0.385763	−	0.922598i	$-0.373938\pi$
$317$	22.0801	−	7.17425i	1.24014	−	0.402946i	0.854378	+	0.519652i	$0.173938\pi$
$318$		0			0
$319$		0			0
$320$			26.5330i			1.48324i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	13.6084	+	11.7819i	0.756021	+	0.654548i
$325$		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
$333$	−20.9809	−	0.895022i	−1.14975	−	0.0490469i
$334$		0			0
$335$	41.0059	+	13.3236i	2.24039	+	0.727947i
$336$		0			0
$337$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$337$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$338$		0			0
$339$	3.27674	+	4.71836i	0.177968	+	0.256266i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	15.1716	+	11.5248i	0.816814	+	0.620475i
$346$		0			0
$347$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$347$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$348$		0			0
$349$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$349$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$350$		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
$355$	−44.4959	−	32.3282i	−2.36160	−	1.71580i
$356$	19.4946	+	26.8321i	1.03321	+	1.42210i
$357$		0			0
$358$		0			0
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$		0			0
$361$	5.87132	+	18.0701i	0.309017	+	0.951057i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	29.9336	−	21.7481i	1.56252	−	1.13524i	0.628620	−	0.777713i	$-0.283620\pi$
$367$	29.9336	−	21.7481i	1.56252	−	1.13524i	0.933903	−	0.357526i	$-0.116380\pi$
$368$	−12.6172	−	4.09957i	−0.657717	−	0.213705i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	14.2264	−	9.87975i	0.737605	−	0.512241i
$373$		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
$379$	−7.72542	+	23.7764i	−0.396828	+	1.22131i	0.530700	+	0.847560i	$0.321929\pi$
$379$	−7.72542	+	23.7764i	−0.396828	+	1.22131i	−0.927528	+	0.373753i	$0.878071\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.15430	−	1.02489i	0.161177	−	0.0523696i	−0.227317	−	0.973821i	$-0.572995\pi$
$383$	3.15430	−	1.02489i	0.161177	−	0.0523696i	0.388494	+	0.921451i	$0.372995\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	27.5066	+	19.9847i	1.39643	+	1.01457i
$389$	−21.4441	−	29.5153i	−1.08726	−	1.49648i	−0.851270	−	0.524727i	$-0.824167\pi$
$389$	−21.4441	−	29.5153i	−1.08726	−	1.49648i	−0.235988	−	0.971756i	$-0.575833\pi$
$390$		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
$400$	19.4164	−	14.1068i	0.970820	−	0.705342i
$401$	25.2344	+	8.19915i	1.26014	+	0.409446i	0.861546	−	0.507679i	$-0.169497\pi$
$401$	25.2344	+	8.19915i	1.26014	+	0.409446i	0.398599	+	0.917125i	$0.369497\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	2.54207	−	29.7412i	0.126317	−	1.47785i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$409$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$410$		0			0
$411$	−24.3240	+	32.0210i	−1.19982	+	1.57948i
$412$	2.47214	−	7.60845i	0.121793	−	0.374842i
$413$		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
$421$	8.09017	+	5.87785i	0.394291	+	0.286469i	0.767211	−	0.641394i	$-0.221644\pi$
$421$	8.09017	+	5.87785i	0.394291	+	0.286469i	−0.372921	+	0.927863i	$0.621644\pi$
$422$		0			0
$423$	−19.1707	+	5.33715i	−0.932110	+	0.259501i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$431$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$432$	5.14642	+	20.1374i	0.247607	+	0.968860i
$433$	−23.4615	+	17.0458i	−1.12749	+	0.819168i	−0.985327	−	0.170676i	$-0.945405\pi$
$433$	−23.4615	+	17.0458i	−1.12749	+	0.819168i	−0.142160	+	0.989844i	$0.545405\pi$
$434$		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
$443$	21.4441	−	29.5153i	1.01884	−	1.40231i	0.105825	−	0.994385i	$-0.466252\pi$
$443$	21.4441	−	29.5153i	1.01884	−	1.40231i	0.913014	−	0.407928i	$-0.133748\pi$
$444$	−19.3094	−	14.6679i	−0.916382	−	0.696110i
$445$	16.9959	−	52.3081i	0.805685	−	2.47964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−15.7715	+	5.12447i	−0.744303	+	0.241839i	−0.656528	−	0.754302i	$-0.727976\pi$
$449$	−15.7715	+	5.12447i	−0.744303	+	0.241839i	−0.0877747	+	0.996140i	$0.527976\pi$
$450$		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		0.309017	−	0.951057i	$-0.400000\pi$
$457$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$458$		0			0
$459$		0			0
$460$	6.79837	+	20.9232i	0.316976	+	0.975551i
$461$		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
$465$	−27.1216	−	9.45608i	−1.25774	−	0.438515i
$466$		0			0
$467$	−41.0059	−	13.3236i	−1.89753	−	0.616543i	−0.970212	−	0.242257i	$-0.922112\pi$
$467$	−41.0059	−	13.3236i	−1.89753	−	0.616543i	−0.927313	−	0.374286i	$-0.877888\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−32.7207	+	22.7234i	−1.50769	+	1.04704i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−37.2930	−	13.9008i	−1.70753	−	0.636473i
$478$		0			0
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	56.3826i		−	2.56020i
$486$		0			0
$487$	34.7877	+	25.2748i	1.57638	+	1.14531i	0.920699	+	0.390273i	$0.127619\pi$
$487$	34.7877	+	25.2748i	1.57638	+	1.14531i	0.655683	+	0.755036i	$0.272381\pi$
$488$		0			0
$489$	−27.7065	−	0.590695i	−1.25293	−	0.0267122i
$490$		0			0
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	20.0000			0.898027
$497$		0			0
$498$		0			0
$499$	32.3607	−	23.5114i	1.44866	−	1.05252i	0.462522	−	0.886608i	$-0.346945\pi$
$499$	32.3607	−	23.5114i	1.44866	−	1.05252i	0.986141	−	0.165907i	$-0.0530552\pi$
$500$	−6.30860	−	2.04979i	−0.282129	−	0.0916693i
$501$		0			0
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.50000	+	21.5581i	0.288675	+	0.957427i
$508$		0			0
$509$	−1.94946	+	2.68321i	−0.0864084	+	0.118931i	−0.850033	−	0.526730i	$-0.823418\pi$
$509$	−1.94946	+	2.68321i	−0.0864084	+	0.118931i	0.763624	+	0.645661i	$0.223418\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.6172	+	4.09957i	−0.555980	+	0.180649i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	25.3430	+	34.8817i	1.11030	+	1.52819i	0.820977	+	0.570962i	$0.193430\pi$
$521$	25.3430	+	34.8817i	1.11030	+	1.52819i	0.289321	+	0.957232i	$0.406570\pi$
$522$		0			0
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	12.0000			0.521739
$530$		0			0
$531$	0.424064	−	9.94083i	0.0184028	−	0.431395i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−16.3837	−	23.5918i	−0.707009	−	1.01806i
$538$		0			0
$539$		0			0
$540$	22.0000	−	26.5330i	0.946729	−	1.14180i
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$		0			0
$543$	34.4810	+	26.1928i	1.47972	+	1.12404i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$547$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$548$	−44.1602	+	14.3485i	−1.88643	+	0.612938i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.857113	+	40.2028i	−0.0363824	+	1.70651i
$556$		0			0
$557$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$557$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$	−21.6973	−	7.56486i	−0.913621	−	0.318538i
$565$	8.89919	−	6.46564i	0.374392	−	0.272011i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		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
$575$	11.6968	−	16.0992i	0.487789	−	0.671385i
$576$	−8.38249	+	22.4885i	−0.349270	+	0.937022i
$577$	14.5238	−	44.6997i	0.604634	−	1.86087i	0.105344	−	0.994436i	$-0.466406\pi$
$577$	14.5238	−	44.6997i	0.604634	−	1.86087i	0.499290	−	0.866435i	$-0.333594\pi$
$578$		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
$587$	−3.89893	−	5.36641i	−0.160926	−	0.221496i	0.720938	−	0.693000i	$-0.243711\pi$
$587$	−3.89893	−	5.36641i	−0.160926	−	0.221496i	−0.881864	+	0.471504i	$0.843711\pi$
$588$	−24.2432	−	0.516858i	−0.999773	−	0.0213149i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−8.65248	−	26.6296i	−0.355615	−	1.09447i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.4045	−	32.7099i	0.466754	−	1.33873i
$598$		0			0
$599$	−31.5430	−	10.2489i	−1.28881	−	0.418760i	−0.417136	−	0.908844i	$-0.636966\pi$
$599$	−31.5430	−	10.2489i	−1.28881	−	0.418760i	−0.871675	+	0.490084i	$0.836966\pi$
$600$		0			0
$601$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$601$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$602$		0			0
$603$	30.5460	+	24.2475i	1.24393	+	0.987436i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$607$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$613$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$614$		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
$619$	0.809017	+	0.587785i	0.0325171	+	0.0236251i	0.603925	−	0.797041i	$-0.293603\pi$
$619$	0.809017	+	0.587785i	0.0325171	+	0.0236251i	−0.571408	+	0.820666i	$0.693603\pi$
$620$	−19.4946	−	26.8321i	−0.782923	−	1.07760i
$621$	9.21800	+	14.5612i	0.369906	+	0.584321i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.87132	−	18.0701i	−0.234853	−	0.722803i
$626$		0			0
$627$		0			0
$628$	−46.0000			−1.83560
$629$		0			0
$630$		0			0
$631$	5.66312	−	4.11450i	0.225445	−	0.163796i	−0.469329	−	0.883023i	$-0.655504\pi$
$631$	5.66312	−	4.11450i	0.225445	−	0.163796i	0.694774	+	0.719228i	$0.255504\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−26.2139	−	37.7469i	−1.03945	−	1.49676i
$637$		0			0
$638$		0			0
$639$	−27.5000	−	41.4578i	−1.08788	−	1.64005i
$640$		0			0
$641$	−13.6462	+	18.7824i	−0.538994	+	0.741862i	−0.988468	−	0.151432i	$-0.951612\pi$
$641$	−13.6462	+	18.7824i	−0.538994	+	0.741862i	0.449474	+	0.893294i	$0.351612\pi$
$642$		0			0
$643$	12.6697	−	38.9933i	0.499644	−	1.53775i	−0.309948	−	0.950753i	$-0.600312\pi$
$643$	12.6697	−	38.9933i	0.499644	−	1.53775i	0.809592	−	0.586993i	$-0.199688\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	41.0059	−	13.3236i	1.61211	−	0.523805i	0.642046	−	0.766666i	$-0.278086\pi$
$647$	41.0059	−	13.3236i	1.61211	−	0.523805i	0.970061	+	0.242861i	$0.0780858\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−25.8885	−	18.8091i	−1.01387	−	0.736622i
$653$	1.94946	+	2.68321i	0.0762884	+	0.105002i	0.845456	−	0.534045i	$-0.179329\pi$
$653$	1.94946	+	2.68321i	0.0762884	+	0.105002i	−0.769167	+	0.639047i	$0.779329\pi$
$654$		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
$669$	1.42264	−	0.987975i	0.0550025	−	0.0381973i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$673$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$674$		0			0
$675$	−31.1132	−	1.99239i	−1.19755	−	0.0766871i
$676$	−8.03444	+	24.7275i	−0.309017	+	0.951057i
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		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
$685$	62.2943	+	45.2595i	2.38014	+	1.72928i
$686$		0			0
$687$	8.65829	+	0.184592i	0.330334	+	0.00704263i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	5.25329	+	16.1680i	0.199845	+	0.615058i	0.999886	+	0.0151132i	$0.00481087\pi$
$691$	5.25329	+	16.1680i	0.199845	+	0.615058i	−0.800041	+	0.599945i	$0.795189\pi$
$692$		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		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	11.0000	+	36.4829i	0.414284	+	1.37402i
$706$		0			0
$707$		0			0
$708$	6.94972	−	9.14884i	0.261187	−	0.343835i
$709$	−5.87132	+	18.0701i	−0.220502	+	0.678636i	0.778215	+	0.627998i	$0.216125\pi$
$709$	−5.87132	+	18.0701i	−0.220502	+	0.678636i	−0.998717	+	0.0506378i	$0.983875\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.7715	−	5.12447i	0.590647	−	0.191913i
$714$		0			0
$715$		0			0
$716$		−	33.1662i		−	1.23948i
$717$		0			0
$718$		0			0
$719$	−9.74732	−	13.4160i	−0.363514	−	0.500333i	0.587610	−	0.809144i	$-0.300069\pi$
$719$	−9.74732	−	13.4160i	−0.363514	−	0.500333i	−0.951123	+	0.308811i	$0.900069\pi$
$720$	38.3414	−	10.6743i	1.42890	−	0.397808i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	15.4508	+	47.5528i	0.574226	+	1.76729i
$725$		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
$729$	11.5506	−	24.4046i	0.427801	−	0.903873i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$	22.9372	+	33.0285i	0.846051	+	1.21828i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$	−27.2925	+	37.5649i	−1.00329	+	1.38091i
$741$		0			0
$742$		0			0
$743$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$743$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−18.6074	−	13.5191i	−0.678993	−	0.493318i	0.194030	−	0.980996i	$-0.437844\pi$
$751$	−18.6074	−	13.5191i	−0.678993	−	0.493318i	−0.873024	+	0.487678i	$0.837844\pi$
$752$	−15.5957	−	21.4656i	−0.568717	−	0.782772i
$753$	−0.612223	+	28.7163i	−0.0223107	+	1.04648i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.7426	+	36.1401i	0.426794	+	1.31354i	0.901266	+	0.433266i	$0.142639\pi$
$757$	11.7426	+	36.1401i	0.426794	+	1.31354i	−0.474473	+	0.880270i	$0.657361\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$		0			0
$764$	44.1602	+	14.3485i	1.59766	+	0.519111i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−22.7622	+	15.8076i	−0.821362	+	0.570408i
$769$		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
$773$	−7.79785	+	10.7328i	−0.280469	+	0.386033i	−0.925889	−	0.377795i	$-0.876682\pi$
$773$	−7.79785	+	10.7328i	−0.280469	+	0.386033i	0.645420	+	0.763828i	$0.276682\pi$
$774$		0			0
$775$	−9.27051	+	28.5317i	−0.333007	+	1.02489i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−22.6525	−	16.4580i	−0.809017	−	0.587785i
$785$	44.8377	+	61.7137i	1.60032	+	2.20266i
$786$		0			0
$787$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$787$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−25.0898	+	71.9618i	−0.889844	+	2.55222i
$796$	32.3607	−	23.5114i	1.14699	−	0.833340i
$797$	53.6231	+	17.4232i	1.89943	+	0.617161i	0.966132	+	0.258048i	$0.0830794\pi$
$797$	53.6231	+	17.4232i	1.89943	+	0.617161i	0.933294	+	0.359113i	$0.116921\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	30.9308	−	38.9652i	1.09288	−	1.37677i
$802$		0			0
$803$		0			0
$804$	13.0000	+	43.1161i	0.458475	+	1.52059i
$805$		0			0
$806$		0			0
$807$	−13.8994	+	18.2977i	−0.489284	+	0.644109i
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$		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		−0.587785	−	0.809017i	$-0.700000\pi$
$821$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$	−15.1418	−	46.6018i	−0.527811	−	1.62444i	−0.758689	−	0.651453i	$-0.774160\pi$
$823$	−15.1418	−	46.6018i	−0.527811	−	1.62444i	0.230878	−	0.972983i	$-0.425840\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$827$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$828$	−0.848129	+	19.8817i	−0.0294745	+	0.690936i
$829$	−23.4615	+	17.0458i	−0.814851	+	0.592024i	−0.915233	−	0.402925i	$-0.867994\pi$
$829$	−23.4615	+	17.0458i	−0.814851	+	0.592024i	0.100382	+	0.994949i	$0.467994\pi$
$830$		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
$839$	21.4441	−	29.5153i	0.740332	−	1.01898i	−0.258267	−	0.966074i	$-0.583151\pi$
$839$	21.4441	−	29.5153i	0.740332	−	1.01898i	0.998599	−	0.0529065i	$-0.0168485\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	41.0059	−	13.3236i	1.41064	−	0.458346i
$846$		0			0
$847$		0			0
$848$		−	53.0660i		−	1.82229i
$849$		0			0
$850$		0			0
$851$	−13.6462	−	18.7824i	−0.467787	−	0.643854i
$852$	1.22445	−	57.4326i	0.0419488	−	1.96761i
$853$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$853$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$854$		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
$863$	44.1602	+	14.3485i	1.50323	+	0.488429i	0.940958	−	0.338524i	$-0.109928\pi$
$863$	44.1602	+	14.3485i	1.50323	+	0.488429i	0.562272	+	0.826953i	$0.309928\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	24.1849	−	16.7956i	0.821362	−	0.570408i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	17.8128	−	47.7881i	0.602871	−	1.61738i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$877$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$878$		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
$883$	−45.3050	−	32.9160i	−1.52463	−	1.10771i	−0.959130	−	0.282964i	$-0.908682\pi$
$883$	−45.3050	−	32.9160i	−1.52463	−	1.10771i	−0.565503	−	0.824747i	$-0.691318\pi$
$884$		0			0
$885$	−19.0482	−	0.406103i	−0.640299	−	0.0136510i
$886$		0			0
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	2.00000			0.0669650
$893$		0			0
$894$		0			0
$895$	−44.4959	+	32.3282i	−1.48734	+	1.08061i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−28.1963	−	22.3823i	−0.939877	−	0.746078i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	48.7366	−	67.0801i	1.62006	−	2.22982i
$906$		0			0
$907$	2.47214	−	7.60845i	0.0820859	−	0.252635i	−0.901588	−	0.432597i	$-0.857597\pi$
$907$	2.47214	−	7.60845i	0.0820859	−	0.252635i	0.983674	+	0.179962i	$0.0575975\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.30860	+	2.04979i	−0.209013	+	0.0679125i	−0.411652	−	0.911341i	$-0.635048\pi$
$911$	−6.30860	+	2.04979i	−0.209013	+	0.0679125i	0.202639	+	0.979253i	$0.435048\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	8.09017	+	5.87785i	0.267307	+	0.194210i
$917$		0			0
$918$		0			0
$919$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$919$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	42.0000			1.38095
$926$		0			0
$927$	−11.9891	−	0.511441i	−0.393774	−	0.0167979i
$928$		0			0
$929$	−50.4688	−	16.3983i	−1.65583	−	0.538011i	−0.675835	−	0.737053i	$-0.736217\pi$
$929$	−50.4688	−	16.3983i	−1.65583	−	0.538011i	−0.979991	+	0.199042i	$0.936217\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	32.7674	+	47.1836i	1.07276	+	1.54472i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$937$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$	26.2056	+	19.9065i	0.855186	+	0.649624i
$940$	−13.5967	+	41.8465i	−0.443477	+	1.36488i
$941$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$941$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$942$		0			0
$943$		0			0
$944$	12.6172	−	4.09957i	0.410655	−	0.133430i
$945$		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
$951$	0.857113	−	40.2028i	0.0277938	−	1.30367i
$952$		0			0
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$		0			0
$955$	−23.7943	−	73.2314i	−0.769966	−	2.36971i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	43.3946	+	15.1297i	1.40055	+	0.488310i
$961$	4.85410	−	3.52671i	0.156584	−	0.113765i
$962$		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
$971$	−25.3430	+	34.8817i	−0.813296	+	1.11941i	0.177510	+	0.984119i	$0.443196\pi$
$971$	−25.3430	+	34.8817i	−0.813296	+	1.11941i	−0.990806	+	0.135287i	$0.956804\pi$
$972$	27.0290	−	15.5381i	0.866955	−	0.498386i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−53.6231	+	17.4232i	−1.71555	+	0.557417i	−0.991242	−	0.132056i	$-0.957842\pi$
$977$	−53.6231	+	17.4232i	−1.71555	+	0.557417i	−0.724311	+	0.689473i	$0.757842\pi$
$978$		0			0
$979$		0			0
$980$			46.4327i			1.48324i
$981$		0			0
$982$		0			0
$983$	−21.4441	−	29.5153i	−0.683960	−	0.941391i	0.316012	−	0.948755i	$-0.397656\pi$
$983$	−21.4441	−	29.5153i	−0.683960	−	0.941391i	−0.999973	+	0.00736431i	$0.997656\pi$
$984$		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
$993$	19.9578	−	57.2423i	0.633342	−	1.81653i
$994$		0			0
$995$	−63.0860	−	20.4979i	−1.99996	−	0.649826i
$996$		0			0
$997$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$997$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$998$		0			0
$999$	−13.4276	+	33.8038i	−0.424831	+	1.06951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.c.215.2		8
3.2	odd	2	inner	363.2.f.c.215.1		8
11.2	odd	10	inner	363.2.f.c.233.1		8
11.3	even	5		33.2.d.a.32.2	yes	2
11.4	even	5	inner	363.2.f.c.239.1		8
11.5	even	5	inner	363.2.f.c.161.2		8
11.6	odd	10	inner	363.2.f.c.161.2		8
11.7	odd	10	inner	363.2.f.c.239.1		8
11.8	odd	10		33.2.d.a.32.2	yes	2
11.9	even	5	inner	363.2.f.c.233.1		8
11.10	odd	2	CM	363.2.f.c.215.2		8
33.2	even	10	inner	363.2.f.c.233.2		8
33.5	odd	10	inner	363.2.f.c.161.1		8
33.8	even	10		33.2.d.a.32.1	✓	2
33.14	odd	10		33.2.d.a.32.1	✓	2
33.17	even	10	inner	363.2.f.c.161.1		8
33.20	odd	10	inner	363.2.f.c.233.2		8
33.26	odd	10	inner	363.2.f.c.239.2		8
33.29	even	10	inner	363.2.f.c.239.2		8
33.32	even	2	inner	363.2.f.c.215.1		8
44.3	odd	10		528.2.b.a.65.1		2
44.19	even	10		528.2.b.a.65.1		2
55.3	odd	20		825.2.d.a.824.2		4
55.8	even	20		825.2.d.a.824.2		4
55.14	even	10		825.2.f.a.626.1		2
55.19	odd	10		825.2.f.a.626.1		2
55.47	odd	20		825.2.d.a.824.3		4
55.52	even	20		825.2.d.a.824.3		4
88.3	odd	10		2112.2.b.f.65.2		2
88.19	even	10		2112.2.b.f.65.2		2
88.69	even	10		2112.2.b.e.65.1		2
88.85	odd	10		2112.2.b.e.65.1		2
99.14	odd	30		891.2.g.a.593.2		4
99.25	even	15		891.2.g.a.296.2		4
99.41	even	30		891.2.g.a.593.2		4
99.47	odd	30		891.2.g.a.296.1		4
99.52	odd	30		891.2.g.a.296.2		4
99.58	even	15		891.2.g.a.593.1		4
99.74	even	30		891.2.g.a.296.1		4
99.85	odd	30		891.2.g.a.593.1		4
132.47	even	10		528.2.b.a.65.2		2
132.107	odd	10		528.2.b.a.65.2		2
165.8	odd	20		825.2.d.a.824.4		4
165.14	odd	10		825.2.f.a.626.2		2
165.47	even	20		825.2.d.a.824.1		4
165.74	even	10		825.2.f.a.626.2		2
165.107	odd	20		825.2.d.a.824.1		4
165.113	even	20		825.2.d.a.824.4		4
264.107	odd	10		2112.2.b.f.65.1		2
264.173	even	10		2112.2.b.e.65.2		2
264.179	even	10		2112.2.b.f.65.1		2
264.245	odd	10		2112.2.b.e.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.d.a.32.1	✓	2	33.8	even	10
33.2.d.a.32.1	✓	2	33.14	odd	10
33.2.d.a.32.2	yes	2	11.3	even	5
33.2.d.a.32.2	yes	2	11.8	odd	10
363.2.f.c.161.1		8	33.5	odd	10	inner
363.2.f.c.161.1		8	33.17	even	10	inner
363.2.f.c.161.2		8	11.5	even	5	inner
363.2.f.c.161.2		8	11.6	odd	10	inner
363.2.f.c.215.1		8	3.2	odd	2	inner
363.2.f.c.215.1		8	33.32	even	2	inner
363.2.f.c.215.2		8	1.1	even	1	trivial
363.2.f.c.215.2		8	11.10	odd	2	CM
363.2.f.c.233.1		8	11.2	odd	10	inner
363.2.f.c.233.1		8	11.9	even	5	inner
363.2.f.c.233.2		8	33.2	even	10	inner
363.2.f.c.233.2		8	33.20	odd	10	inner
363.2.f.c.239.1		8	11.4	even	5	inner
363.2.f.c.239.1		8	11.7	odd	10	inner
363.2.f.c.239.2		8	33.26	odd	10	inner
363.2.f.c.239.2		8	33.29	even	10	inner
528.2.b.a.65.1		2	44.3	odd	10
528.2.b.a.65.1		2	44.19	even	10
528.2.b.a.65.2		2	132.47	even	10
528.2.b.a.65.2		2	132.107	odd	10
825.2.d.a.824.1		4	165.47	even	20
825.2.d.a.824.1		4	165.107	odd	20
825.2.d.a.824.2		4	55.3	odd	20
825.2.d.a.824.2		4	55.8	even	20
825.2.d.a.824.3		4	55.47	odd	20
825.2.d.a.824.3		4	55.52	even	20
825.2.d.a.824.4		4	165.8	odd	20
825.2.d.a.824.4		4	165.113	even	20
825.2.f.a.626.1		2	55.14	even	10
825.2.f.a.626.1		2	55.19	odd	10
825.2.f.a.626.2		2	165.14	odd	10
825.2.f.a.626.2		2	165.74	even	10
891.2.g.a.296.1		4	99.47	odd	30
891.2.g.a.296.1		4	99.74	even	30
891.2.g.a.296.2		4	99.25	even	15
891.2.g.a.296.2		4	99.52	odd	30
891.2.g.a.593.1		4	99.58	even	15
891.2.g.a.593.1		4	99.85	odd	30
891.2.g.a.593.2		4	99.14	odd	30
891.2.g.a.593.2		4	99.41	even	30
2112.2.b.e.65.1		2	88.69	even	10
2112.2.b.e.65.1		2	88.85	odd	10
2112.2.b.e.65.2		2	264.173	even	10
2112.2.b.e.65.2		2	264.245	odd	10
2112.2.b.f.65.1		2	264.107	odd	10
2112.2.b.f.65.1		2	264.179	even	10
2112.2.b.f.65.2		2	88.3	odd	10
2112.2.b.f.65.2		2	88.19	even	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)

\(f(q)\)	\(=\)	\(q+(0.570223 - 1.63550i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-3.15430 - 1.02489i) q^{5} +(-2.34969 - 1.86519i) q^{9} +O(q^{10})\)	\(q+(0.570223 - 1.63550i) q^{3} +(1.61803 - 1.17557i) q^{4} +(-3.15430 - 1.02489i) q^{5} +(-2.34969 - 1.86519i) q^{9} +(-1.00000 - 3.31662i) q^{12} +(-3.47486 + 4.57442i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-6.30860 + 2.04979i) q^{20} -3.31662i q^{23} +(4.85410 + 3.52671i) q^{25} +(-4.39037 + 2.77933i) q^{27} +(1.54508 + 4.75528i) q^{31} +(-5.99455 - 0.255720i) q^{36} +(5.66312 - 4.11450i) q^{37} +(5.50000 + 8.29156i) q^{45} +(3.89893 - 5.36641i) q^{47} +(-5.51696 - 4.19084i) q^{48} +(2.16312 - 6.65740i) q^{49} +(12.6172 - 4.09957i) q^{53} +(1.94946 + 2.68321i) q^{59} +(-0.244889 + 11.4865i) q^{60} +(-2.47214 - 7.60845i) q^{64} -13.0000 q^{67} +(-5.42433 - 1.89122i) q^{69} +(15.7715 + 5.12447i) q^{71} +(8.53584 - 5.92785i) q^{75} +(-7.79785 + 10.7328i) q^{80} +(2.04210 + 8.76526i) q^{81} +16.5831i q^{89} +(-3.89893 - 5.36641i) q^{92} +(8.65829 + 0.184592i) q^{93} +(5.25329 + 16.1680i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} + 4 q^{4} + 5 q^{9}+O(q^{10}) \) 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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