LMFDB - Embedded newform 3381.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.a (trivial)

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:	yes
Analytic conductor:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.23607 q^{11} +0.618034 q^{12} +2.38197 q^{13} +0.618034 q^{15} -4.85410 q^{16} -6.70820 q^{17} -1.61803 q^{18} +3.47214 q^{19} +0.381966 q^{20} -3.61803 q^{22} -1.00000 q^{23} +2.23607 q^{24} -4.61803 q^{25} -3.85410 q^{26} +1.00000 q^{27} -8.23607 q^{29} -1.00000 q^{30} -6.70820 q^{31} +3.38197 q^{32} +2.23607 q^{33} +10.8541 q^{34} +0.618034 q^{36} -11.0000 q^{37} -5.61803 q^{38} +2.38197 q^{39} +1.38197 q^{40} +1.47214 q^{41} -1.61803 q^{43} +1.38197 q^{44} +0.618034 q^{45} +1.61803 q^{46} +7.23607 q^{47} -4.85410 q^{48} +7.47214 q^{50} -6.70820 q^{51} +1.47214 q^{52} -13.0902 q^{53} -1.61803 q^{54} +1.38197 q^{55} +3.47214 q^{57} +13.3262 q^{58} -9.38197 q^{59} +0.381966 q^{60} +4.85410 q^{61} +10.8541 q^{62} +4.23607 q^{64} +1.47214 q^{65} -3.61803 q^{66} -5.09017 q^{67} -4.14590 q^{68} -1.00000 q^{69} +4.38197 q^{71} +2.23607 q^{72} +12.7082 q^{73} +17.7984 q^{74} -4.61803 q^{75} +2.14590 q^{76} -3.85410 q^{78} -9.47214 q^{79} -3.00000 q^{80} +1.00000 q^{81} -2.38197 q^{82} +9.18034 q^{83} -4.14590 q^{85} +2.61803 q^{86} -8.23607 q^{87} +5.00000 q^{88} -11.6180 q^{89} -1.00000 q^{90} -0.618034 q^{92} -6.70820 q^{93} -11.7082 q^{94} +2.14590 q^{95} +3.38197 q^{96} -10.4164 q^{97} +2.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9} - 2 q^{10} - q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - q^{18} - 2 q^{19} + 3 q^{20} - 5 q^{22} - 2 q^{23} - 7 q^{25} - q^{26} + 2 q^{27} - 12 q^{29} - 2 q^{30} + 9 q^{32} + 15 q^{34} - q^{36} - 22 q^{37} - 9 q^{38} + 7 q^{39} + 5 q^{40} - 6 q^{41} - q^{43} + 5 q^{44} - q^{45} + q^{46} + 10 q^{47} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 15 q^{53} - q^{54} + 5 q^{55} - 2 q^{57} + 11 q^{58} - 21 q^{59} + 3 q^{60} + 3 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{65} - 5 q^{66} + q^{67} - 15 q^{68} - 2 q^{69} + 11 q^{71} + 12 q^{73} + 11 q^{74} - 7 q^{75} + 11 q^{76} - q^{78} - 10 q^{79} - 6 q^{80} + 2 q^{81} - 7 q^{82} - 4 q^{83} - 15 q^{85} + 3 q^{86} - 12 q^{87} + 10 q^{88} - 21 q^{89} - 2 q^{90} + q^{92} - 10 q^{94} + 11 q^{95} + 9 q^{96} + 6 q^{97}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9 - 2 * q^10 - q^12 + 7 * q^13 - q^15 - 3 * q^16 - q^18 - 2 * q^19 + 3 * q^20 - 5 * q^22 - 2 * q^23 - 7 * q^25 - q^26 + 2 * q^27 - 12 * q^29 - 2 * q^30 + 9 * q^32 + 15 * q^34 - q^36 - 22 * q^37 - 9 * q^38 + 7 * q^39 + 5 * q^40 - 6 * q^41 - q^43 + 5 * q^44 - q^45 + q^46 + 10 * q^47 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 15 * q^53 - q^54 + 5 * q^55 - 2 * q^57 + 11 * q^58 - 21 * q^59 + 3 * q^60 + 3 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^65 - 5 * q^66 + q^67 - 15 * q^68 - 2 * q^69 + 11 * q^71 + 12 * q^73 + 11 * q^74 - 7 * q^75 + 11 * q^76 - q^78 - 10 * q^79 - 6 * q^80 + 2 * q^81 - 7 * q^82 - 4 * q^83 - 15 * q^85 + 3 * q^86 - 12 * q^87 + 10 * q^88 - 21 * q^89 - 2 * q^90 + q^92 - 10 * q^94 + 11 * q^95 + 9 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.618034	0.309017
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	−1.61803	−0.660560
$7$	0	0
$7$	0	0
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	2.23607	0.674200	0.337100	−	0.941469i	$-0.390554\pi$
$11$	2.23607	0.674200	0.337100	+	0.941469i	$0.390554\pi$
$12$	0.618034	0.178411
$13$	2.38197	0.660639	0.330319	−	0.943869i	$-0.392844\pi$
$13$	2.38197	0.660639	0.330319	+	0.943869i	$0.392844\pi$
$14$	0	0
$15$	0.618034	0.159576
$16$	−4.85410	−1.21353
$17$	−6.70820	−1.62698	−0.813489	−	0.581580i	$-0.802435\pi$
$17$	−6.70820	−1.62698	−0.813489	+	0.581580i	$0.802435\pi$
$18$	−1.61803	−0.381374
$19$	3.47214	0.796563	0.398281	−	0.917263i	$-0.369607\pi$
$19$	3.47214	0.796563	0.398281	+	0.917263i	$0.369607\pi$
$20$	0.381966	0.0854102
$21$	0	0
$22$	−3.61803	−0.771367
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.23607	0.456435
$25$	−4.61803	−0.923607
$26$	−3.85410	−0.755852
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.23607	−1.52940	−0.764700	−	0.644387i	$-0.777113\pi$
$29$	−8.23607	−1.52940	−0.764700	+	0.644387i	$0.777113\pi$
$30$	−1.00000	−0.182574
$31$	−6.70820	−1.20483	−0.602414	−	0.798183i	$-0.705795\pi$
$31$	−6.70820	−1.20483	−0.602414	+	0.798183i	$0.705795\pi$
$32$	3.38197	0.597853
$33$	2.23607	0.389249
$34$	10.8541	1.86146
$35$	0	0
$36$	0.618034	0.103006
$37$	−11.0000	−1.80839	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−11.0000	−1.80839	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−5.61803	−0.911365
$39$	2.38197	0.381420
$40$	1.38197	0.218508
$41$	1.47214	0.229909	0.114955	−	0.993371i	$-0.463328\pi$
$41$	1.47214	0.229909	0.114955	+	0.993371i	$0.463328\pi$
$42$	0	0
$43$	−1.61803	−0.246748	−0.123374	−	0.992360i	$-0.539371\pi$
$43$	−1.61803	−0.246748	−0.123374	+	0.992360i	$0.539371\pi$
$44$	1.38197	0.208339
$45$	0.618034	0.0921311
$46$	1.61803	0.238566
$47$	7.23607	1.05549	0.527744	−	0.849403i	$-0.323038\pi$
$47$	7.23607	1.05549	0.527744	+	0.849403i	$0.323038\pi$
$48$	−4.85410	−0.700629
$49$	0	0
$50$	7.47214	1.05672
$51$	−6.70820	−0.939336
$52$	1.47214	0.204149
$53$	−13.0902	−1.79807	−0.899037	−	0.437874i	$-0.855732\pi$
$53$	−13.0902	−1.79807	−0.899037	+	0.437874i	$0.855732\pi$
$54$	−1.61803	−0.220187
$55$	1.38197	0.186344
$56$	0	0
$57$	3.47214	0.459896
$58$	13.3262	1.74982
$59$	−9.38197	−1.22143	−0.610714	−	0.791851i	$-0.709117\pi$
$59$	−9.38197	−1.22143	−0.610714	+	0.791851i	$0.709117\pi$
$60$	0.381966	0.0493116
$61$	4.85410	0.621504	0.310752	−	0.950491i	$-0.399419\pi$
$61$	4.85410	0.621504	0.310752	+	0.950491i	$0.399419\pi$
$62$	10.8541	1.37847
$63$	0	0
$64$	4.23607	0.529508
$65$	1.47214	0.182596
$66$	−3.61803	−0.445349
$67$	−5.09017	−0.621863	−0.310932	−	0.950432i	$-0.600641\pi$
$67$	−5.09017	−0.621863	−0.310932	+	0.950432i	$0.600641\pi$
$68$	−4.14590	−0.502764
$69$	−1.00000	−0.120386
$70$	0	0
$71$	4.38197	0.520044	0.260022	−	0.965603i	$-0.416270\pi$
$71$	4.38197	0.520044	0.260022	+	0.965603i	$0.416270\pi$
$72$	2.23607	0.263523
$73$	12.7082	1.48738	0.743691	−	0.668523i	$-0.233073\pi$
$73$	12.7082	1.48738	0.743691	+	0.668523i	$0.233073\pi$
$74$	17.7984	2.06902
$75$	−4.61803	−0.533245
$76$	2.14590	0.246151
$77$	0	0
$78$	−3.85410	−0.436391
$79$	−9.47214	−1.06570	−0.532849	−	0.846210i	$-0.678879\pi$
$79$	−9.47214	−1.06570	−0.532849	+	0.846210i	$0.678879\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	−2.38197	−0.263044
$83$	9.18034	1.00767	0.503837	−	0.863799i	$-0.331921\pi$
$83$	9.18034	1.00767	0.503837	+	0.863799i	$0.331921\pi$
$84$	0	0
$85$	−4.14590	−0.449686
$86$	2.61803	0.282310
$87$	−8.23607	−0.882999
$88$	5.00000	0.533002
$89$	−11.6180	−1.23151	−0.615755	−	0.787938i	$-0.711149\pi$
$89$	−11.6180	−1.23151	−0.615755	+	0.787938i	$0.711149\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−0.618034	−0.0644345
$93$	−6.70820	−0.695608
$94$	−11.7082	−1.20761
$95$	2.14590	0.220164
$96$	3.38197	0.345170
$97$	−10.4164	−1.05763	−0.528813	−	0.848738i	$-0.677363\pi$
$97$	−10.4164	−1.05763	−0.528813	+	0.848738i	$0.677363\pi$
$98$	0	0
$99$	2.23607	0.224733
$100$	−2.85410	−0.285410
$101$	−4.14590	−0.412532	−0.206266	−	0.978496i	$-0.566131\pi$
$101$	−4.14590	−0.412532	−0.206266	+	0.978496i	$0.566131\pi$
$102$	10.8541	1.07472
$103$	7.41641	0.730760	0.365380	−	0.930858i	$-0.380939\pi$
$103$	7.41641	0.730760	0.365380	+	0.930858i	$0.380939\pi$
$104$	5.32624	0.522281
$105$	0	0
$106$	21.1803	2.05722
$107$	3.32624	0.321560	0.160780	−	0.986990i	$-0.448599\pi$
$107$	3.32624	0.321560	0.160780	+	0.986990i	$0.448599\pi$
$108$	0.618034	0.0594703
$109$	19.2705	1.84578	0.922890	−	0.385064i	$-0.125820\pi$
$109$	19.2705	1.84578	0.922890	+	0.385064i	$0.125820\pi$
$110$	−2.23607	−0.213201
$111$	−11.0000	−1.04407
$112$	0	0
$113$	−0.909830	−0.0855896	−0.0427948	−	0.999084i	$-0.513626\pi$
$113$	−0.909830	−0.0855896	−0.0427948	+	0.999084i	$0.513626\pi$
$114$	−5.61803	−0.526177
$115$	−0.618034	−0.0576320
$116$	−5.09017	−0.472610
$117$	2.38197	0.220213
$118$	15.1803	1.39746
$119$	0	0
$120$	1.38197	0.126156
$121$	−6.00000	−0.545455
$122$	−7.85410	−0.711077
$123$	1.47214	0.132738
$124$	−4.14590	−0.372313
$125$	−5.94427	−0.531672
$126$	0	0
$127$	22.2705	1.97619	0.988094	−	0.153851i	$-0.0491675\pi$
$127$	22.2705	1.97619	0.988094	+	0.153851i	$0.0491675\pi$
$128$	−13.6180	−1.20368
$129$	−1.61803	−0.142460
$130$	−2.38197	−0.208912
$131$	−15.1803	−1.32631	−0.663156	−	0.748481i	$-0.730784\pi$
$131$	−15.1803	−1.32631	−0.663156	+	0.748481i	$0.730784\pi$
$132$	1.38197	0.120285
$133$	0	0
$134$	8.23607	0.711488
$135$	0.618034	0.0531919
$136$	−15.0000	−1.28624
$137$	−16.4164	−1.40255	−0.701274	−	0.712892i	$-0.747385\pi$
$137$	−16.4164	−1.40255	−0.701274	+	0.712892i	$0.747385\pi$
$138$	1.61803	0.137736
$139$	11.3820	0.965406	0.482703	−	0.875784i	$-0.339655\pi$
$139$	11.3820	0.965406	0.482703	+	0.875784i	$0.339655\pi$
$140$	0	0
$141$	7.23607	0.609387
$142$	−7.09017	−0.594994
$143$	5.32624	0.445402
$144$	−4.85410	−0.404508
$145$	−5.09017	−0.422716
$146$	−20.5623	−1.70175
$147$	0	0
$148$	−6.79837	−0.558823
$149$	−19.2361	−1.57588	−0.787940	−	0.615752i	$-0.788852\pi$
$149$	−19.2361	−1.57588	−0.787940	+	0.615752i	$0.788852\pi$
$150$	7.47214	0.610097
$151$	−15.2361	−1.23989	−0.619947	−	0.784644i	$-0.712846\pi$
$151$	−15.2361	−1.23989	−0.619947	+	0.784644i	$0.712846\pi$
$152$	7.76393	0.629738
$153$	−6.70820	−0.542326
$154$	0	0
$155$	−4.14590	−0.333007
$156$	1.47214	0.117865
$157$	0.291796	0.0232879	0.0116439	−	0.999932i	$-0.496294\pi$
$157$	0.291796	0.0232879	0.0116439	+	0.999932i	$0.496294\pi$
$158$	15.3262	1.21929
$159$	−13.0902	−1.03812
$160$	2.09017	0.165242
$161$	0	0
$162$	−1.61803	−0.127125
$163$	−0.618034	−0.0484082	−0.0242041	−	0.999707i	$-0.507705\pi$
$163$	−0.618034	−0.0484082	−0.0242041	+	0.999707i	$0.507705\pi$
$164$	0.909830	0.0710458
$165$	1.38197	0.107586
$166$	−14.8541	−1.15290
$167$	7.18034	0.555631	0.277816	−	0.960634i	$-0.410390\pi$
$167$	7.18034	0.555631	0.277816	+	0.960634i	$0.410390\pi$
$168$	0	0
$169$	−7.32624	−0.563557
$170$	6.70820	0.514496
$171$	3.47214	0.265521
$172$	−1.00000	−0.0762493
$173$	3.47214	0.263982	0.131991	−	0.991251i	$-0.457863\pi$
$173$	3.47214	0.263982	0.131991	+	0.991251i	$0.457863\pi$
$174$	13.3262	1.01026
$175$	0	0
$176$	−10.8541	−0.818159
$177$	−9.38197	−0.705192
$178$	18.7984	1.40900
$179$	1.85410	0.138582	0.0692910	−	0.997596i	$-0.477926\pi$
$179$	1.85410	0.138582	0.0692910	+	0.997596i	$0.477926\pi$
$180$	0.381966	0.0284701
$181$	1.94427	0.144517	0.0722583	−	0.997386i	$-0.476979\pi$
$181$	1.94427	0.144517	0.0722583	+	0.997386i	$0.476979\pi$
$182$	0	0
$183$	4.85410	0.358826
$184$	−2.23607	−0.164845
$185$	−6.79837	−0.499826
$186$	10.8541	0.795861
$187$	−15.0000	−1.09691
$188$	4.47214	0.326164
$189$	0	0
$190$	−3.47214	−0.251895
$191$	16.1803	1.17077	0.585384	−	0.810756i	$-0.300944\pi$
$191$	16.1803	1.17077	0.585384	+	0.810756i	$0.300944\pi$
$192$	4.23607	0.305712
$193$	8.29180	0.596857	0.298428	−	0.954432i	$-0.403538\pi$
$193$	8.29180	0.596857	0.298428	+	0.954432i	$0.403538\pi$
$194$	16.8541	1.21005
$195$	1.47214	0.105422
$196$	0	0
$197$	−25.5066	−1.81727	−0.908634	−	0.417593i	$-0.862874\pi$
$197$	−25.5066	−1.81727	−0.908634	+	0.417593i	$0.862874\pi$
$198$	−3.61803	−0.257122
$199$	6.90983	0.489825	0.244912	−	0.969545i	$-0.421241\pi$
$199$	6.90983	0.489825	0.244912	+	0.969545i	$0.421241\pi$
$200$	−10.3262	−0.730175
$201$	−5.09017	−0.359033
$202$	6.70820	0.471988
$203$	0	0
$204$	−4.14590	−0.290271
$205$	0.909830	0.0635453
$206$	−12.0000	−0.836080
$207$	−1.00000	−0.0695048
$208$	−11.5623	−0.801702
$209$	7.76393	0.537042
$210$	0	0
$211$	10.4164	0.717095	0.358548	−	0.933511i	$-0.383272\pi$
$211$	10.4164	0.717095	0.358548	+	0.933511i	$0.383272\pi$
$212$	−8.09017	−0.555635
$213$	4.38197	0.300247
$214$	−5.38197	−0.367904
$215$	−1.00000	−0.0681994
$216$	2.23607	0.152145
$217$	0	0
$218$	−31.1803	−2.11180
$219$	12.7082	0.858741
$220$	0.854102	0.0575835
$221$	−15.9787	−1.07484
$222$	17.7984	1.19455
$223$	17.8541	1.19560	0.597800	−	0.801646i	$-0.296042\pi$
$223$	17.8541	1.19560	0.597800	+	0.801646i	$0.296042\pi$
$224$	0	0
$225$	−4.61803	−0.307869
$226$	1.47214	0.0979250
$227$	−24.3262	−1.61459	−0.807295	−	0.590149i	$-0.799069\pi$
$227$	−24.3262	−1.61459	−0.807295	+	0.590149i	$0.799069\pi$
$228$	2.14590	0.142116
$229$	16.3262	1.07887	0.539434	−	0.842028i	$-0.318638\pi$
$229$	16.3262	1.07887	0.539434	+	0.842028i	$0.318638\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−18.4164	−1.20910
$233$	−11.0902	−0.726541	−0.363271	−	0.931684i	$-0.618340\pi$
$233$	−11.0902	−0.726541	−0.363271	+	0.931684i	$0.618340\pi$
$234$	−3.85410	−0.251951
$235$	4.47214	0.291730
$236$	−5.79837	−0.377442
$237$	−9.47214	−0.615281
$238$	0	0
$239$	−4.79837	−0.310381	−0.155191	−	0.987885i	$-0.549599\pi$
$239$	−4.79837	−0.310381	−0.155191	+	0.987885i	$0.549599\pi$
$240$	−3.00000	−0.193649
$241$	11.0000	0.708572	0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000	0.708572	0.354286	+	0.935137i	$0.384724\pi$
$242$	9.70820	0.624067
$243$	1.00000	0.0641500
$244$	3.00000	0.192055
$245$	0	0
$246$	−2.38197	−0.151869
$247$	8.27051	0.526240
$248$	−15.0000	−0.952501
$249$	9.18034	0.581780
$250$	9.61803	0.608298
$251$	−23.1246	−1.45961	−0.729806	−	0.683654i	$-0.760390\pi$
$251$	−23.1246	−1.45961	−0.729806	+	0.683654i	$0.760390\pi$
$252$	0	0
$253$	−2.23607	−0.140580
$254$	−36.0344	−2.26100
$255$	−4.14590	−0.259626
$256$	13.5623	0.847644
$257$	3.23607	0.201860	0.100930	−	0.994894i	$-0.467818\pi$
$257$	3.23607	0.201860	0.100930	+	0.994894i	$0.467818\pi$
$258$	2.61803	0.162992
$259$	0	0
$260$	0.909830	0.0564253
$261$	−8.23607	−0.509800
$262$	24.5623	1.51746
$263$	−0.0557281	−0.00343634	−0.00171817	−	0.999999i	$-0.500547\pi$
$263$	−0.0557281	−0.00343634	−0.00171817	+	0.999999i	$0.500547\pi$
$264$	5.00000	0.307729
$265$	−8.09017	−0.496975
$266$	0	0
$267$	−11.6180	−0.711012
$268$	−3.14590	−0.192166
$269$	32.0902	1.95657	0.978286	−	0.207259i	$-0.0664543\pi$
$269$	32.0902	1.95657	0.978286	+	0.207259i	$0.0664543\pi$
$270$	−1.00000	−0.0608581
$271$	−21.9443	−1.33302	−0.666510	−	0.745496i	$-0.732213\pi$
$271$	−21.9443	−1.33302	−0.666510	+	0.745496i	$0.732213\pi$
$272$	32.5623	1.97438
$273$	0	0
$274$	26.5623	1.60469
$275$	−10.3262	−0.622696
$276$	−0.618034	−0.0372013
$277$	4.27051	0.256590	0.128295	−	0.991736i	$-0.459050\pi$
$277$	4.27051	0.256590	0.128295	+	0.991736i	$0.459050\pi$
$278$	−18.4164	−1.10454
$279$	−6.70820	−0.401610
$280$	0	0
$281$	−3.70820	−0.221213	−0.110606	−	0.993864i	$-0.535279\pi$
$281$	−3.70820	−0.221213	−0.110606	+	0.993864i	$0.535279\pi$
$282$	−11.7082	−0.697213
$283$	26.2148	1.55831	0.779154	−	0.626833i	$-0.215649\pi$
$283$	26.2148	1.55831	0.779154	+	0.626833i	$0.215649\pi$
$284$	2.70820	0.160702
$285$	2.14590	0.127112
$286$	−8.61803	−0.509595
$287$	0	0
$288$	3.38197	0.199284
$289$	28.0000	1.64706
$290$	8.23607	0.483639
$291$	−10.4164	−0.610621
$292$	7.85410	0.459627
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	−5.79837	−0.337594
$296$	−24.5967	−1.42966
$297$	2.23607	0.129750
$298$	31.1246	1.80300
$299$	−2.38197	−0.137753
$300$	−2.85410	−0.164782
$301$	0	0
$302$	24.6525	1.41859
$303$	−4.14590	−0.238176
$304$	−16.8541	−0.966649
$305$	3.00000	0.171780
$306$	10.8541	0.620488
$307$	−16.1246	−0.920280	−0.460140	−	0.887846i	$-0.652201\pi$
$307$	−16.1246	−0.920280	−0.460140	+	0.887846i	$0.652201\pi$
$308$	0	0
$309$	7.41641	0.421905
$310$	6.70820	0.381000
$311$	−15.3262	−0.869071	−0.434536	−	0.900655i	$-0.643087\pi$
$311$	−15.3262	−0.869071	−0.434536	+	0.900655i	$0.643087\pi$
$312$	5.32624	0.301539
$313$	2.47214	0.139733	0.0698667	−	0.997556i	$-0.477743\pi$
$313$	2.47214	0.139733	0.0698667	+	0.997556i	$0.477743\pi$
$314$	−0.472136	−0.0266442
$315$	0	0
$316$	−5.85410	−0.329319
$317$	14.5066	0.814771	0.407385	−	0.913256i	$-0.366441\pi$
$317$	14.5066	0.814771	0.407385	+	0.913256i	$0.366441\pi$
$318$	21.1803	1.18773
$319$	−18.4164	−1.03112
$320$	2.61803	0.146353
$321$	3.32624	0.185652
$322$	0	0
$323$	−23.2918	−1.29599
$324$	0.618034	0.0343352
$325$	−11.0000	−0.610170
$326$	1.00000	0.0553849
$327$	19.2705	1.06566
$328$	3.29180	0.181759
$329$	0	0
$330$	−2.23607	−0.123091
$331$	−13.4164	−0.737432	−0.368716	−	0.929542i	$-0.620203\pi$
$331$	−13.4164	−0.737432	−0.368716	+	0.929542i	$0.620203\pi$
$332$	5.67376	0.311388
$333$	−11.0000	−0.602796
$334$	−11.6180	−0.635711
$335$	−3.14590	−0.171879
$336$	0	0
$337$	−7.50658	−0.408909	−0.204455	−	0.978876i	$-0.565542\pi$
$337$	−7.50658	−0.408909	−0.204455	+	0.978876i	$0.565542\pi$
$338$	11.8541	0.644778
$339$	−0.909830	−0.0494152
$340$	−2.56231	−0.138961
$341$	−15.0000	−0.812296
$342$	−5.61803	−0.303788
$343$	0	0
$344$	−3.61803	−0.195071
$345$	−0.618034	−0.0332738
$346$	−5.61803	−0.302027
$347$	5.18034	0.278095	0.139048	−	0.990286i	$-0.455596\pi$
$347$	5.18034	0.278095	0.139048	+	0.990286i	$0.455596\pi$
$348$	−5.09017	−0.272862
$349$	11.8541	0.634536	0.317268	−	0.948336i	$-0.397235\pi$
$349$	11.8541	0.634536	0.317268	+	0.948336i	$0.397235\pi$
$350$	0	0
$351$	2.38197	0.127140
$352$	7.56231	0.403072
$353$	−30.3050	−1.61297	−0.806485	−	0.591255i	$-0.798633\pi$
$353$	−30.3050	−1.61297	−0.806485	+	0.591255i	$0.798633\pi$
$354$	15.1803	0.806826
$355$	2.70820	0.143737
$356$	−7.18034	−0.380557
$357$	0	0
$358$	−3.00000	−0.158555
$359$	23.0902	1.21865	0.609326	−	0.792920i	$-0.291440\pi$
$359$	23.0902	1.21865	0.609326	+	0.792920i	$0.291440\pi$
$360$	1.38197	0.0728360
$361$	−6.94427	−0.365488
$362$	−3.14590	−0.165345
$363$	−6.00000	−0.314918
$364$	0	0
$365$	7.85410	0.411102
$366$	−7.85410	−0.410540
$367$	−10.8541	−0.566580	−0.283290	−	0.959034i	$-0.591426\pi$
$367$	−10.8541	−0.566580	−0.283290	+	0.959034i	$0.591426\pi$
$368$	4.85410	0.253038
$369$	1.47214	0.0766363
$370$	11.0000	0.571863
$371$	0	0
$372$	−4.14590	−0.214955
$373$	24.4164	1.26423	0.632117	−	0.774873i	$-0.282186\pi$
$373$	24.4164	1.26423	0.632117	+	0.774873i	$0.282186\pi$
$374$	24.2705	1.25500
$375$	−5.94427	−0.306961
$376$	16.1803	0.834437
$377$	−19.6180	−1.01038
$378$	0	0
$379$	7.41641	0.380955	0.190478	−	0.981692i	$-0.438996\pi$
$379$	7.41641	0.380955	0.190478	+	0.981692i	$0.438996\pi$
$380$	1.32624	0.0680346
$381$	22.2705	1.14095
$382$	−26.1803	−1.33950
$383$	0.708204	0.0361875	0.0180938	−	0.999836i	$-0.494240\pi$
$383$	0.708204	0.0361875	0.0180938	+	0.999836i	$0.494240\pi$
$384$	−13.6180	−0.694942
$385$	0	0
$386$	−13.4164	−0.682877
$387$	−1.61803	−0.0822493
$388$	−6.43769	−0.326824
$389$	5.29180	0.268305	0.134152	−	0.990961i	$-0.457169\pi$
$389$	5.29180	0.268305	0.134152	+	0.990961i	$0.457169\pi$
$390$	−2.38197	−0.120616
$391$	6.70820	0.339248
$392$	0	0
$393$	−15.1803	−0.765747
$394$	41.2705	2.07918
$395$	−5.85410	−0.294552
$396$	1.38197	0.0694464
$397$	−22.0689	−1.10761	−0.553803	−	0.832648i	$-0.686824\pi$
$397$	−22.0689	−1.10761	−0.553803	+	0.832648i	$0.686824\pi$
$398$	−11.1803	−0.560420
$399$	0	0
$400$	22.4164	1.12082
$401$	33.1803	1.65695	0.828474	−	0.560028i	$-0.189210\pi$
$401$	33.1803	1.65695	0.828474	+	0.560028i	$0.189210\pi$
$402$	8.23607	0.410778
$403$	−15.9787	−0.795956
$404$	−2.56231	−0.127479
$405$	0.618034	0.0307104
$406$	0	0
$407$	−24.5967	−1.21922
$408$	−15.0000	−0.742611
$409$	−6.41641	−0.317271	−0.158635	−	0.987337i	$-0.550709\pi$
$409$	−6.41641	−0.317271	−0.158635	+	0.987337i	$0.550709\pi$
$410$	−1.47214	−0.0727036
$411$	−16.4164	−0.809762
$412$	4.58359	0.225817
$413$	0	0
$414$	1.61803	0.0795220
$415$	5.67376	0.278514
$416$	8.05573	0.394965
$417$	11.3820	0.557377
$418$	−12.5623	−0.614442
$419$	−15.6738	−0.765713	−0.382857	−	0.923808i	$-0.625060\pi$
$419$	−15.6738	−0.765713	−0.382857	+	0.923808i	$0.625060\pi$
$420$	0	0
$421$	−10.2705	−0.500554	−0.250277	−	0.968174i	$-0.580522\pi$
$421$	−10.2705	−0.500554	−0.250277	+	0.968174i	$0.580522\pi$
$422$	−16.8541	−0.820445
$423$	7.23607	0.351830
$424$	−29.2705	−1.42150
$425$	30.9787	1.50269
$426$	−7.09017	−0.343520
$427$	0	0
$428$	2.05573	0.0993674
$429$	5.32624	0.257153
$430$	1.61803	0.0780285
$431$	0.673762	0.0324540	0.0162270	−	0.999868i	$-0.494835\pi$
$431$	0.673762	0.0324540	0.0162270	+	0.999868i	$0.494835\pi$
$432$	−4.85410	−0.233543
$433$	−19.1246	−0.919070	−0.459535	−	0.888160i	$-0.651984\pi$
$433$	−19.1246	−0.919070	−0.459535	+	0.888160i	$0.651984\pi$
$434$	0	0
$435$	−5.09017	−0.244055
$436$	11.9098	0.570377
$437$	−3.47214	−0.166095
$438$	−20.5623	−0.982505
$439$	−23.6525	−1.12887	−0.564436	−	0.825477i	$-0.690906\pi$
$439$	−23.6525	−1.12887	−0.564436	+	0.825477i	$0.690906\pi$
$440$	3.09017	0.147318
$441$	0	0
$442$	25.8541	1.22975
$443$	−9.52786	−0.452682	−0.226341	−	0.974048i	$-0.572676\pi$
$443$	−9.52786	−0.452682	−0.226341	+	0.974048i	$0.572676\pi$
$444$	−6.79837	−0.322637
$445$	−7.18034	−0.340381
$446$	−28.8885	−1.36791
$447$	−19.2361	−0.909835
$448$	0	0
$449$	−18.4377	−0.870129	−0.435064	−	0.900399i	$-0.643274\pi$
$449$	−18.4377	−0.870129	−0.435064	+	0.900399i	$0.643274\pi$
$450$	7.47214	0.352240
$451$	3.29180	0.155005
$452$	−0.562306	−0.0264486
$453$	−15.2361	−0.715853
$454$	39.3607	1.84729
$455$	0	0
$456$	7.76393	0.363579
$457$	−14.3262	−0.670153	−0.335077	−	0.942191i	$-0.608762\pi$
$457$	−14.3262	−0.670153	−0.335077	+	0.942191i	$0.608762\pi$
$458$	−26.4164	−1.23436
$459$	−6.70820	−0.313112
$460$	−0.381966	−0.0178093
$461$	−25.4508	−1.18536	−0.592682	−	0.805436i	$-0.701931\pi$
$461$	−25.4508	−1.18536	−0.592682	+	0.805436i	$0.701931\pi$
$462$	0	0
$463$	17.2918	0.803618	0.401809	−	0.915724i	$-0.368382\pi$
$463$	17.2918	0.803618	0.401809	+	0.915724i	$0.368382\pi$
$464$	39.9787	1.85597
$465$	−4.14590	−0.192261
$466$	17.9443	0.831252
$467$	15.1803	0.702462	0.351231	−	0.936289i	$-0.385763\pi$
$467$	15.1803	0.702462	0.351231	+	0.936289i	$0.385763\pi$
$468$	1.47214	0.0680495
$469$	0	0
$470$	−7.23607	−0.333775
$471$	0.291796	0.0134453
$472$	−20.9787	−0.965624
$473$	−3.61803	−0.166357
$474$	15.3262	0.703957
$475$	−16.0344	−0.735711
$476$	0	0
$477$	−13.0902	−0.599358
$478$	7.76393	0.355114
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	2.09017	0.0954028
$481$	−26.2016	−1.19469
$482$	−17.7984	−0.810694
$483$	0	0
$484$	−3.70820	−0.168555
$485$	−6.43769	−0.292321
$486$	−1.61803	−0.0733955
$487$	−29.2918	−1.32734	−0.663669	−	0.748026i	$-0.731002\pi$
$487$	−29.2918	−1.32734	−0.663669	+	0.748026i	$0.731002\pi$
$488$	10.8541	0.491342
$489$	−0.618034	−0.0279485
$490$	0	0
$491$	9.79837	0.442194	0.221097	−	0.975252i	$-0.429036\pi$
$491$	9.79837	0.442194	0.221097	+	0.975252i	$0.429036\pi$
$492$	0.909830	0.0410183
$493$	55.2492	2.48830
$494$	−13.3820	−0.602083
$495$	1.38197	0.0621148
$496$	32.5623	1.46209
$497$	0	0
$498$	−14.8541	−0.665628
$499$	−38.3951	−1.71880	−0.859401	−	0.511302i	$-0.829163\pi$
$499$	−38.3951	−1.71880	−0.859401	+	0.511302i	$0.829163\pi$
$500$	−3.67376	−0.164296
$501$	7.18034	0.320794
$502$	37.4164	1.66998
$503$	−36.3262	−1.61971	−0.809853	−	0.586632i	$-0.800453\pi$
$503$	−36.3262	−1.61971	−0.809853	+	0.586632i	$0.800453\pi$
$504$	0	0
$505$	−2.56231	−0.114021
$506$	3.61803	0.160841
$507$	−7.32624	−0.325370
$508$	13.7639	0.610676
$509$	15.5967	0.691314	0.345657	−	0.938361i	$-0.387656\pi$
$509$	15.5967	0.691314	0.345657	+	0.938361i	$0.387656\pi$
$510$	6.70820	0.297044
$511$	0	0
$512$	5.29180	0.233867
$513$	3.47214	0.153299
$514$	−5.23607	−0.230953
$515$	4.58359	0.201977
$516$	−1.00000	−0.0440225
$517$	16.1803	0.711611
$518$	0	0
$519$	3.47214	0.152410
$520$	3.29180	0.144355
$521$	−3.52786	−0.154559	−0.0772793	−	0.997009i	$-0.524623\pi$
$521$	−3.52786	−0.154559	−0.0772793	+	0.997009i	$0.524623\pi$
$522$	13.3262	0.583274
$523$	−21.4164	−0.936474	−0.468237	−	0.883603i	$-0.655111\pi$
$523$	−21.4164	−0.936474	−0.468237	+	0.883603i	$0.655111\pi$
$524$	−9.38197	−0.409853
$525$	0	0
$526$	0.0901699	0.00393160
$527$	45.0000	1.96023
$528$	−10.8541	−0.472364
$529$	1.00000	0.0434783
$530$	13.0902	0.568601
$531$	−9.38197	−0.407143
$532$	0	0
$533$	3.50658	0.151887
$534$	18.7984	0.813485
$535$	2.05573	0.0888769
$536$	−11.3820	−0.491626
$537$	1.85410	0.0800104
$538$	−51.9230	−2.23856
$539$	0	0
$540$	0.381966	0.0164372
$541$	−5.12461	−0.220324	−0.110162	−	0.993914i	$-0.535137\pi$
$541$	−5.12461	−0.220324	−0.110162	+	0.993914i	$0.535137\pi$
$542$	35.5066	1.52514
$543$	1.94427	0.0834367
$544$	−22.6869	−0.972694
$545$	11.9098	0.510161
$546$	0	0
$547$	12.7984	0.547219	0.273609	−	0.961841i	$-0.411782\pi$
$547$	12.7984	0.547219	0.273609	+	0.961841i	$0.411782\pi$
$548$	−10.1459	−0.433411
$549$	4.85410	0.207168
$550$	16.7082	0.712440
$551$	−28.5967	−1.21826
$552$	−2.23607	−0.0951734
$553$	0	0
$554$	−6.90983	−0.293571
$555$	−6.79837	−0.288575
$556$	7.03444	0.298327
$557$	−5.81966	−0.246587	−0.123293	−	0.992370i	$-0.539346\pi$
$557$	−5.81966	−0.246587	−0.123293	+	0.992370i	$0.539346\pi$
$558$	10.8541	0.459491
$559$	−3.85410	−0.163011
$560$	0	0
$561$	−15.0000	−0.633300
$562$	6.00000	0.253095
$563$	23.5066	0.990684	0.495342	−	0.868698i	$-0.335043\pi$
$563$	23.5066	0.990684	0.495342	+	0.868698i	$0.335043\pi$
$564$	4.47214	0.188311
$565$	−0.562306	−0.0236564
$566$	−42.4164	−1.78289
$567$	0	0
$568$	9.79837	0.411131
$569$	−16.3607	−0.685875	−0.342938	−	0.939358i	$-0.611422\pi$
$569$	−16.3607	−0.685875	−0.342938	+	0.939358i	$0.611422\pi$
$570$	−3.47214	−0.145432
$571$	−44.4164	−1.85877	−0.929384	−	0.369113i	$-0.879661\pi$
$571$	−44.4164	−1.85877	−0.929384	+	0.369113i	$0.879661\pi$
$572$	3.29180	0.137637
$573$	16.1803	0.675943
$574$	0	0
$575$	4.61803	0.192585
$576$	4.23607	0.176503
$577$	36.8328	1.53337	0.766685	−	0.642023i	$-0.221905\pi$
$577$	36.8328	1.53337	0.766685	+	0.642023i	$0.221905\pi$
$578$	−45.3050	−1.88444
$579$	8.29180	0.344595
$580$	−3.14590	−0.130626
$581$	0	0
$582$	16.8541	0.698625
$583$	−29.2705	−1.21226
$584$	28.4164	1.17588
$585$	1.47214	0.0608653
$586$	19.4164	0.802084
$587$	31.0344	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$587$	31.0344	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$588$	0	0
$589$	−23.2918	−0.959722
$590$	9.38197	0.386249
$591$	−25.5066	−1.04920
$592$	53.3951	2.19453
$593$	32.0689	1.31691	0.658456	−	0.752620i	$-0.271210\pi$
$593$	32.0689	1.31691	0.658456	+	0.752620i	$0.271210\pi$
$594$	−3.61803	−0.148450
$595$	0	0
$596$	−11.8885	−0.486974
$597$	6.90983	0.282801
$598$	3.85410	0.157606
$599$	−15.5066	−0.633582	−0.316791	−	0.948495i	$-0.602605\pi$
$599$	−15.5066	−0.633582	−0.316791	+	0.948495i	$0.602605\pi$
$600$	−10.3262	−0.421567
$601$	−0.909830	−0.0371127	−0.0185564	−	0.999828i	$-0.505907\pi$
$601$	−0.909830	−0.0371127	−0.0185564	+	0.999828i	$0.505907\pi$
$602$	0	0
$603$	−5.09017	−0.207288
$604$	−9.41641	−0.383148
$605$	−3.70820	−0.150760
$606$	6.70820	0.272502
$607$	33.7984	1.37183	0.685917	−	0.727680i	$-0.259401\pi$
$607$	33.7984	1.37183	0.685917	+	0.727680i	$0.259401\pi$
$608$	11.7426	0.476227
$609$	0	0
$610$	−4.85410	−0.196537
$611$	17.2361	0.697297
$612$	−4.14590	−0.167588
$613$	−11.6525	−0.470639	−0.235320	−	0.971918i	$-0.575614\pi$
$613$	−11.6525	−0.470639	−0.235320	+	0.971918i	$0.575614\pi$
$614$	26.0902	1.05291
$615$	0.909830	0.0366879
$616$	0	0
$617$	−2.67376	−0.107642	−0.0538208	−	0.998551i	$-0.517140\pi$
$617$	−2.67376	−0.107642	−0.0538208	+	0.998551i	$0.517140\pi$
$618$	−12.0000	−0.482711
$619$	19.6180	0.788515	0.394258	−	0.919000i	$-0.371002\pi$
$619$	19.6180	0.788515	0.394258	+	0.919000i	$0.371002\pi$
$620$	−2.56231	−0.102905
$621$	−1.00000	−0.0401286
$622$	24.7984	0.994324
$623$	0	0
$624$	−11.5623	−0.462863
$625$	19.4164	0.776656
$626$	−4.00000	−0.159872
$627$	7.76393	0.310062
$628$	0.180340	0.00719634
$629$	73.7902	2.94221
$630$	0	0
$631$	16.1246	0.641911	0.320955	−	0.947094i	$-0.395996\pi$
$631$	16.1246	0.641911	0.320955	+	0.947094i	$0.395996\pi$
$632$	−21.1803	−0.842509
$633$	10.4164	0.414015
$634$	−23.4721	−0.932198
$635$	13.7639	0.546205
$636$	−8.09017	−0.320796
$637$	0	0
$638$	29.7984	1.17973
$639$	4.38197	0.173348
$640$	−8.41641	−0.332688
$641$	17.7984	0.702994	0.351497	−	0.936189i	$-0.385673\pi$
$641$	17.7984	0.702994	0.351497	+	0.936189i	$0.385673\pi$
$642$	−5.38197	−0.212409
$643$	11.9787	0.472394	0.236197	−	0.971705i	$-0.424099\pi$
$643$	11.9787	0.472394	0.236197	+	0.971705i	$0.424099\pi$
$644$	0	0
$645$	−1.00000	−0.0393750
$646$	37.6869	1.48277
$647$	24.0344	0.944891	0.472446	−	0.881360i	$-0.343371\pi$
$647$	24.0344	0.944891	0.472446	+	0.881360i	$0.343371\pi$
$648$	2.23607	0.0878410
$649$	−20.9787	−0.823487
$650$	17.7984	0.698110
$651$	0	0
$652$	−0.381966	−0.0149589
$653$	27.7426	1.08565	0.542827	−	0.839845i	$-0.317354\pi$
$653$	27.7426	1.08565	0.542827	+	0.839845i	$0.317354\pi$
$654$	−31.1803	−1.21925
$655$	−9.38197	−0.366584
$656$	−7.14590	−0.279000
$657$	12.7082	0.495794
$658$	0	0
$659$	9.65248	0.376007	0.188004	−	0.982168i	$-0.439798\pi$
$659$	9.65248	0.376007	0.188004	+	0.982168i	$0.439798\pi$
$660$	0.854102	0.0332459
$661$	−14.4164	−0.560733	−0.280367	−	0.959893i	$-0.590456\pi$
$661$	−14.4164	−0.560733	−0.280367	+	0.959893i	$0.590456\pi$
$662$	21.7082	0.843713
$663$	−15.9787	−0.620562
$664$	20.5279	0.796636
$665$	0	0
$666$	17.7984	0.689673
$667$	8.23607	0.318902
$668$	4.43769	0.171700
$669$	17.8541	0.690279
$670$	5.09017	0.196650
$671$	10.8541	0.419018
$672$	0	0
$673$	12.4164	0.478617	0.239309	−	0.970944i	$-0.423079\pi$
$673$	12.4164	0.478617	0.239309	+	0.970944i	$0.423079\pi$
$674$	12.1459	0.467843
$675$	−4.61803	−0.177748
$676$	−4.52786	−0.174149
$677$	1.25735	0.0483240	0.0241620	−	0.999708i	$-0.492308\pi$
$677$	1.25735	0.0483240	0.0241620	+	0.999708i	$0.492308\pi$
$678$	1.47214	0.0565370
$679$	0	0
$680$	−9.27051	−0.355508
$681$	−24.3262	−0.932183
$682$	24.2705	0.929366
$683$	26.0132	0.995366	0.497683	−	0.867359i	$-0.334184\pi$
$683$	26.0132	0.995366	0.497683	+	0.867359i	$0.334184\pi$
$684$	2.14590	0.0820505
$685$	−10.1459	−0.387655
$686$	0	0
$687$	16.3262	0.622885
$688$	7.85410	0.299435
$689$	−31.1803	−1.18788
$690$	1.00000	0.0380693
$691$	7.72949	0.294044	0.147022	−	0.989133i	$-0.453031\pi$
$691$	7.72949	0.294044	0.147022	+	0.989133i	$0.453031\pi$
$692$	2.14590	0.0815748
$693$	0	0
$694$	−8.38197	−0.318175
$695$	7.03444	0.266832
$696$	−18.4164	−0.698072
$697$	−9.87539	−0.374057
$698$	−19.1803	−0.725987
$699$	−11.0902	−0.419469
$700$	0	0
$701$	37.4508	1.41450	0.707250	−	0.706964i	$-0.249936\pi$
$701$	37.4508	1.41450	0.707250	+	0.706964i	$0.249936\pi$
$702$	−3.85410	−0.145464
$703$	−38.1935	−1.44049
$704$	9.47214	0.356995
$705$	4.47214	0.168430
$706$	49.0344	1.84544
$707$	0	0
$708$	−5.79837	−0.217916
$709$	−2.56231	−0.0962294	−0.0481147	−	0.998842i	$-0.515321\pi$
$709$	−2.56231	−0.0962294	−0.0481147	+	0.998842i	$0.515321\pi$
$710$	−4.38197	−0.164452
$711$	−9.47214	−0.355233
$712$	−25.9787	−0.973593
$713$	6.70820	0.251224
$714$	0	0
$715$	3.29180	0.123106
$716$	1.14590	0.0428242
$717$	−4.79837	−0.179199
$718$	−37.3607	−1.39429
$719$	3.00000	0.111881	0.0559406	−	0.998434i	$-0.482184\pi$
$719$	3.00000	0.111881	0.0559406	+	0.998434i	$0.482184\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	11.2361	0.418163
$723$	11.0000	0.409094
$724$	1.20163	0.0446581
$725$	38.0344	1.41256
$726$	9.70820	0.360305
$727$	−18.8885	−0.700537	−0.350269	−	0.936649i	$-0.613910\pi$
$727$	−18.8885	−0.700537	−0.350269	+	0.936649i	$0.613910\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−12.7082	−0.470352
$731$	10.8541	0.401453
$732$	3.00000	0.110883
$733$	−25.5967	−0.945437	−0.472719	−	0.881213i	$-0.656727\pi$
$733$	−25.5967	−0.945437	−0.472719	+	0.881213i	$0.656727\pi$
$734$	17.5623	0.648237
$735$	0	0
$736$	−3.38197	−0.124661
$737$	−11.3820	−0.419260
$738$	−2.38197	−0.0876814
$739$	45.2492	1.66452	0.832260	−	0.554386i	$-0.187047\pi$
$739$	45.2492	1.66452	0.832260	+	0.554386i	$0.187047\pi$
$740$	−4.20163	−0.154455
$741$	8.27051	0.303825
$742$	0	0
$743$	11.6738	0.428269	0.214134	−	0.976804i	$-0.431307\pi$
$743$	11.6738	0.428269	0.214134	+	0.976804i	$0.431307\pi$
$744$	−15.0000	−0.549927
$745$	−11.8885	−0.435563
$746$	−39.5066	−1.44644
$747$	9.18034	0.335891
$748$	−9.27051	−0.338963
$749$	0	0
$750$	9.61803	0.351201
$751$	32.9787	1.20341	0.601705	−	0.798718i	$-0.294488\pi$
$751$	32.9787	1.20341	0.601705	+	0.798718i	$0.294488\pi$
$752$	−35.1246	−1.28086
$753$	−23.1246	−0.842708
$754$	31.7426	1.15600
$755$	−9.41641	−0.342698
$756$	0	0
$757$	−17.0000	−0.617876	−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000	−0.617876	−0.308938	+	0.951082i	$0.599973\pi$
$758$	−12.0000	−0.435860
$759$	−2.23607	−0.0811641
$760$	4.79837	0.174055
$761$	14.4721	0.524615	0.262307	−	0.964984i	$-0.415517\pi$
$761$	14.4721	0.524615	0.262307	+	0.964984i	$0.415517\pi$
$762$	−36.0344	−1.30539
$763$	0	0
$764$	10.0000	0.361787
$765$	−4.14590	−0.149895
$766$	−1.14590	−0.0414030
$767$	−22.3475	−0.806922
$768$	13.5623	0.489388
$769$	−33.2361	−1.19852	−0.599262	−	0.800553i	$-0.704539\pi$
$769$	−33.2361	−1.19852	−0.599262	+	0.800553i	$0.704539\pi$
$770$	0	0
$771$	3.23607	0.116544
$772$	5.12461	0.184439
$773$	19.9443	0.717346	0.358673	−	0.933463i	$-0.383229\pi$
$773$	19.9443	0.717346	0.358673	+	0.933463i	$0.383229\pi$
$774$	2.61803	0.0941033
$775$	30.9787	1.11279
$776$	−23.2918	−0.836127
$777$	0	0
$778$	−8.56231	−0.306974
$779$	5.11146	0.183137
$780$	0.909830	0.0325771
$781$	9.79837	0.350613
$782$	−10.8541	−0.388142
$783$	−8.23607	−0.294333
$784$	0	0
$785$	0.180340	0.00643661
$786$	24.5623	0.876108
$787$	48.5755	1.73153	0.865764	−	0.500452i	$-0.166833\pi$
$787$	48.5755	1.73153	0.865764	+	0.500452i	$0.166833\pi$
$788$	−15.7639	−0.561567
$789$	−0.0557281	−0.00198397
$790$	9.47214	0.337003
$791$	0	0
$792$	5.00000	0.177667
$793$	11.5623	0.410590
$794$	35.7082	1.26724
$795$	−8.09017	−0.286929
$796$	4.27051	0.151364
$797$	−44.1803	−1.56495	−0.782474	−	0.622683i	$-0.786043\pi$
$797$	−44.1803	−1.56495	−0.782474	+	0.622683i	$0.786043\pi$
$798$	0	0
$799$	−48.5410	−1.71726
$800$	−15.6180	−0.552181
$801$	−11.6180	−0.410503
$802$	−53.6869	−1.89575
$803$	28.4164	1.00279
$804$	−3.14590	−0.110947
$805$	0	0
$806$	25.8541	0.910672
$807$	32.0902	1.12963
$808$	−9.27051	−0.326135
$809$	−9.43769	−0.331812	−0.165906	−	0.986142i	$-0.553055\pi$
$809$	−9.43769	−0.331812	−0.165906	+	0.986142i	$0.553055\pi$
$810$	−1.00000	−0.0351364
$811$	−8.52786	−0.299454	−0.149727	−	0.988727i	$-0.547839\pi$
$811$	−8.52786	−0.299454	−0.149727	+	0.988727i	$0.547839\pi$
$812$	0	0
$813$	−21.9443	−0.769619
$814$	39.7984	1.39493
$815$	−0.381966	−0.0133797
$816$	32.5623	1.13991
$817$	−5.61803	−0.196550
$818$	10.3820	0.362997
$819$	0	0
$820$	0.562306	0.0196366
$821$	−29.1246	−1.01646	−0.508228	−	0.861223i	$-0.669699\pi$
$821$	−29.1246	−1.01646	−0.508228	+	0.861223i	$0.669699\pi$
$822$	26.5623	0.926467
$823$	−39.8541	−1.38923	−0.694613	−	0.719383i	$-0.744425\pi$
$823$	−39.8541	−1.38923	−0.694613	+	0.719383i	$0.744425\pi$
$824$	16.5836	0.577717
$825$	−10.3262	−0.359513
$826$	0	0
$827$	−28.2148	−0.981124	−0.490562	−	0.871406i	$-0.663208\pi$
$827$	−28.2148	−0.981124	−0.490562	+	0.871406i	$0.663208\pi$
$828$	−0.618034	−0.0214782
$829$	30.4164	1.05641	0.528203	−	0.849118i	$-0.322866\pi$
$829$	30.4164	1.05641	0.528203	+	0.849118i	$0.322866\pi$
$830$	−9.18034	−0.318654
$831$	4.27051	0.148142
$832$	10.0902	0.349814
$833$	0	0
$834$	−18.4164	−0.637708
$835$	4.43769	0.153573
$836$	4.79837	0.165955
$837$	−6.70820	−0.231869
$838$	25.3607	0.876070
$839$	−16.7426	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$839$	−16.7426	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$840$	0	0
$841$	38.8328	1.33906
$842$	16.6180	0.572695
$843$	−3.70820	−0.127717
$844$	6.43769	0.221595
$845$	−4.52786	−0.155763
$846$	−11.7082	−0.402536
$847$	0	0
$848$	63.5410	2.18201
$849$	26.2148	0.899689
$850$	−50.1246	−1.71926
$851$	11.0000	0.377075
$852$	2.70820	0.0927815
$853$	47.1246	1.61352	0.806758	−	0.590882i	$-0.201220\pi$
$853$	47.1246	1.61352	0.806758	+	0.590882i	$0.201220\pi$
$854$	0	0
$855$	2.14590	0.0733882
$856$	7.43769	0.254215
$857$	−39.7082	−1.35641	−0.678203	−	0.734874i	$-0.737241\pi$
$857$	−39.7082	−1.35641	−0.678203	+	0.734874i	$0.737241\pi$
$858$	−8.61803	−0.294215
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	−0.618034	−0.0210748
$861$	0	0
$862$	−1.09017	−0.0371313
$863$	−8.06888	−0.274668	−0.137334	−	0.990525i	$-0.543853\pi$
$863$	−8.06888	−0.274668	−0.137334	+	0.990525i	$0.543853\pi$
$864$	3.38197	0.115057
$865$	2.14590	0.0729627
$866$	30.9443	1.05153
$867$	28.0000	0.950930
$868$	0	0
$869$	−21.1803	−0.718494
$870$	8.23607	0.279229
$871$	−12.1246	−0.410827
$872$	43.0902	1.45922
$873$	−10.4164	−0.352542
$874$	5.61803	0.190033
$875$	0	0
$876$	7.85410	0.265366
$877$	16.5836	0.559988	0.279994	−	0.960002i	$-0.409667\pi$
$877$	16.5836	0.559988	0.279994	+	0.960002i	$0.409667\pi$
$878$	38.2705	1.29157
$879$	−12.0000	−0.404750
$880$	−6.70820	−0.226134
$881$	−1.81966	−0.0613059	−0.0306530	−	0.999530i	$-0.509759\pi$
$881$	−1.81966	−0.0613059	−0.0306530	+	0.999530i	$0.509759\pi$
$882$	0	0
$883$	−3.90983	−0.131576	−0.0657881	−	0.997834i	$-0.520956\pi$
$883$	−3.90983	−0.131576	−0.0657881	+	0.997834i	$0.520956\pi$
$884$	−9.87539	−0.332145
$885$	−5.79837	−0.194910
$886$	15.4164	0.517924
$887$	−9.79837	−0.328997	−0.164499	−	0.986377i	$-0.552601\pi$
$887$	−9.79837	−0.328997	−0.164499	+	0.986377i	$0.552601\pi$
$888$	−24.5967	−0.825413
$889$	0	0
$890$	11.6180	0.389437
$891$	2.23607	0.0749111
$892$	11.0344	0.369460
$893$	25.1246	0.840763
$894$	31.1246	1.04096
$895$	1.14590	0.0383031
$896$	0	0
$897$	−2.38197	−0.0795315
$898$	29.8328	0.995534
$899$	55.2492	1.84266
$900$	−2.85410	−0.0951367
$901$	87.8115	2.92543
$902$	−5.32624	−0.177344
$903$	0	0
$904$	−2.03444	−0.0676645
$905$	1.20163	0.0399434
$906$	24.6525	0.819024
$907$	48.9787	1.62631	0.813156	−	0.582046i	$-0.197748\pi$
$907$	48.9787	1.62631	0.813156	+	0.582046i	$0.197748\pi$
$908$	−15.0344	−0.498935
$909$	−4.14590	−0.137511
$910$	0	0
$911$	−7.59675	−0.251691	−0.125846	−	0.992050i	$-0.540164\pi$
$911$	−7.59675	−0.251691	−0.125846	+	0.992050i	$0.540164\pi$
$912$	−16.8541	−0.558095
$913$	20.5279	0.679373
$914$	23.1803	0.766737
$915$	3.00000	0.0991769
$916$	10.0902	0.333389
$917$	0	0
$918$	10.8541	0.358239
$919$	−50.1246	−1.65346	−0.826729	−	0.562600i	$-0.809801\pi$
$919$	−50.1246	−1.65346	−0.826729	+	0.562600i	$0.809801\pi$
$920$	−1.38197	−0.0455621
$921$	−16.1246	−0.531324
$922$	41.1803	1.35620
$923$	10.4377	0.343561
$924$	0	0
$925$	50.7984	1.67024
$926$	−27.9787	−0.919438
$927$	7.41641	0.243587
$928$	−27.8541	−0.914356
$929$	−28.9098	−0.948501	−0.474250	−	0.880390i	$-0.657281\pi$
$929$	−28.9098	−0.948501	−0.474250	+	0.880390i	$0.657281\pi$
$930$	6.70820	0.219971
$931$	0	0
$932$	−6.85410	−0.224514
$933$	−15.3262	−0.501759
$934$	−24.5623	−0.803703
$935$	−9.27051	−0.303178
$936$	5.32624	0.174094
$937$	−2.70820	−0.0884732	−0.0442366	−	0.999021i	$-0.514086\pi$
$937$	−2.70820	−0.0884732	−0.0442366	+	0.999021i	$0.514086\pi$
$938$	0	0
$939$	2.47214	0.0806751
$940$	2.76393	0.0901495
$941$	15.0557	0.490803	0.245401	−	0.969422i	$-0.421080\pi$
$941$	15.0557	0.490803	0.245401	+	0.969422i	$0.421080\pi$
$942$	−0.472136	−0.0153830
$943$	−1.47214	−0.0479393
$944$	45.5410	1.48223
$945$	0	0
$946$	5.85410	0.190333
$947$	−18.9443	−0.615606	−0.307803	−	0.951450i	$-0.599594\pi$
$947$	−18.9443	−0.615606	−0.307803	+	0.951450i	$0.599594\pi$
$948$	−5.85410	−0.190132
$949$	30.2705	0.982622
$950$	25.9443	0.841743
$951$	14.5066	0.470408
$952$	0	0
$953$	12.1591	0.393870	0.196935	−	0.980417i	$-0.436901\pi$
$953$	12.1591	0.393870	0.196935	+	0.980417i	$0.436901\pi$
$954$	21.1803	0.685739
$955$	10.0000	0.323592
$956$	−2.96556	−0.0959130
$957$	−18.4164	−0.595318
$958$	33.9787	1.09780
$959$	0	0
$960$	2.61803	0.0844967
$961$	14.0000	0.451613
$962$	42.3951	1.36687
$963$	3.32624	0.107187
$964$	6.79837	0.218961
$965$	5.12461	0.164967
$966$	0	0
$967$	50.3607	1.61949	0.809745	−	0.586782i	$-0.199605\pi$
$967$	50.3607	1.61949	0.809745	+	0.586782i	$0.199605\pi$
$968$	−13.4164	−0.431220
$969$	−23.2918	−0.748240
$970$	10.4164	0.334451
$971$	19.6869	0.631783	0.315892	−	0.948795i	$-0.397696\pi$
$971$	19.6869	0.631783	0.315892	+	0.948795i	$0.397696\pi$
$972$	0.618034	0.0198234
$973$	0	0
$974$	47.3951	1.51864
$975$	−11.0000	−0.352282
$976$	−23.5623	−0.754211
$977$	49.7984	1.59319	0.796596	−	0.604513i	$-0.206632\pi$
$977$	49.7984	1.59319	0.796596	+	0.604513i	$0.206632\pi$
$978$	1.00000	0.0319765
$979$	−25.9787	−0.830283
$980$	0	0
$981$	19.2705	0.615260
$982$	−15.8541	−0.505925
$983$	7.40325	0.236127	0.118064	−	0.993006i	$-0.462331\pi$
$983$	7.40325	0.236127	0.118064	+	0.993006i	$0.462331\pi$
$984$	3.29180	0.104939
$985$	−15.7639	−0.502281
$986$	−89.3951	−2.84692
$987$	0	0
$988$	5.11146	0.162617
$989$	1.61803	0.0514505
$990$	−2.23607	−0.0710669
$991$	−35.5755	−1.13009	−0.565046	−	0.825059i	$-0.691142\pi$
$991$	−35.5755	−1.13009	−0.565046	+	0.825059i	$0.691142\pi$
$992$	−22.6869	−0.720310
$993$	−13.4164	−0.425757
$994$	0	0
$995$	4.27051	0.135384
$996$	5.67376	0.179780
$997$	−57.7214	−1.82805	−0.914027	−	0.405654i	$-0.867044\pi$
$997$	−57.7214	−1.82805	−0.914027	+	0.405654i	$0.867044\pi$
$998$	62.1246	1.96652
$999$	−11.0000	−0.348025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.r.1.1		2
7.6	odd	2		483.2.a.d.1.1	✓	2
21.20	even	2		1449.2.a.h.1.2		2
28.27	even	2		7728.2.a.bn.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.d.1.1	✓	2	7.6	odd	2
1449.2.a.h.1.2		2	21.20	even	2
3381.2.a.r.1.1		2	1.1	even	1	trivial
7728.2.a.bn.1.1		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} +0.618034 q^{5} -1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.23607 q^{11} +0.618034 q^{12} +2.38197 q^{13} +0.618034 q^{15} -4.85410 q^{16} -6.70820 q^{17} -1.61803 q^{18} +3.47214 q^{19} +0.381966 q^{20} -3.61803 q^{22} -1.00000 q^{23} +2.23607 q^{24} -4.61803 q^{25} -3.85410 q^{26} +1.00000 q^{27} -8.23607 q^{29} -1.00000 q^{30} -6.70820 q^{31} +3.38197 q^{32} +2.23607 q^{33} +10.8541 q^{34} +0.618034 q^{36} -11.0000 q^{37} -5.61803 q^{38} +2.38197 q^{39} +1.38197 q^{40} +1.47214 q^{41} -1.61803 q^{43} +1.38197 q^{44} +0.618034 q^{45} +1.61803 q^{46} +7.23607 q^{47} -4.85410 q^{48} +7.47214 q^{50} -6.70820 q^{51} +1.47214 q^{52} -13.0902 q^{53} -1.61803 q^{54} +1.38197 q^{55} +3.47214 q^{57} +13.3262 q^{58} -9.38197 q^{59} +0.381966 q^{60} +4.85410 q^{61} +10.8541 q^{62} +4.23607 q^{64} +1.47214 q^{65} -3.61803 q^{66} -5.09017 q^{67} -4.14590 q^{68} -1.00000 q^{69} +4.38197 q^{71} +2.23607 q^{72} +12.7082 q^{73} +17.7984 q^{74} -4.61803 q^{75} +2.14590 q^{76} -3.85410 q^{78} -9.47214 q^{79} -3.00000 q^{80} +1.00000 q^{81} -2.38197 q^{82} +9.18034 q^{83} -4.14590 q^{85} +2.61803 q^{86} -8.23607 q^{87} +5.00000 q^{88} -11.6180 q^{89} -1.00000 q^{90} -0.618034 q^{92} -6.70820 q^{93} -11.7082 q^{94} +2.14590 q^{95} +3.38197 q^{96} -10.4164 q^{97} +2.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9} - 2 q^{10} - q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - q^{18} - 2 q^{19} + 3 q^{20} - 5 q^{22} - 2 q^{23} - 7 q^{25} - q^{26} + 2 q^{27} - 12 q^{29} - 2 q^{30} + 9 q^{32} + 15 q^{34} - q^{36} - 22 q^{37} - 9 q^{38} + 7 q^{39} + 5 q^{40} - 6 q^{41} - q^{43} + 5 q^{44} - q^{45} + q^{46} + 10 q^{47} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 15 q^{53} - q^{54} + 5 q^{55} - 2 q^{57} + 11 q^{58} - 21 q^{59} + 3 q^{60} + 3 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{65} - 5 q^{66} + q^{67} - 15 q^{68} - 2 q^{69} + 11 q^{71} + 12 q^{73} + 11 q^{74} - 7 q^{75} + 11 q^{76} - q^{78} - 10 q^{79} - 6 q^{80} + 2 q^{81} - 7 q^{82} - 4 q^{83} - 15 q^{85} + 3 q^{86} - 12 q^{87} + 10 q^{88} - 21 q^{89} - 2 q^{90} + q^{92} - 10 q^{94} + 11 q^{95} + 9 q^{96} + 6 q^{97}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9 - 2 * q^10 - q^12 + 7 * q^13 - q^15 - 3 * q^16 - q^18 - 2 * q^19 + 3 * q^20 - 5 * q^22 - 2 * q^23 - 7 * q^25 - q^26 + 2 * q^27 - 12 * q^29 - 2 * q^30 + 9 * q^32 + 15 * q^34 - q^36 - 22 * q^37 - 9 * q^38 + 7 * q^39 + 5 * q^40 - 6 * q^41 - q^43 + 5 * q^44 - q^45 + q^46 + 10 * q^47 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 15 * q^53 - q^54 + 5 * q^55 - 2 * q^57 + 11 * q^58 - 21 * q^59 + 3 * q^60 + 3 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^65 - 5 * q^66 + q^67 - 15 * q^68 - 2 * q^69 + 11 * q^71 + 12 * q^73 + 11 * q^74 - 7 * q^75 + 11 * q^76 - q^78 - 10 * q^79 - 6 * q^80 + 2 * q^81 - 7 * q^82 - 4 * q^83 - 15 * q^85 + 3 * q^86 - 12 * q^87 + 10 * q^88 - 21 * q^89 - 2 * q^90 + q^92 - 10 * q^94 + 11 * q^95 + 9 * q^96 + 6 * q^97

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