LMFDB - Embedded newform 975.2.c.i.274.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(274,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("975.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.5
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	975.274
Dual form			975.2.c.i.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48929i q^{2} -1.00000i q^{3} -4.19656 q^{4} +2.48929 q^{6} +1.19656i q^{7} -5.46787i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.48929i q^{2} -1.00000i q^{3} -4.19656 q^{4} +2.48929 q^{6} +1.19656i q^{7} -5.46787i q^{8} -1.00000 q^{9} -1.19656 q^{11} +4.19656i q^{12} +1.00000i q^{13} -2.97858 q^{14} +5.21798 q^{16} -6.17513i q^{17} -2.48929i q^{18} -6.97858 q^{19} +1.19656 q^{21} -2.97858i q^{22} +4.17513i q^{23} -5.46787 q^{24} -2.48929 q^{26} +1.00000i q^{27} -5.02142i q^{28} -6.00000 q^{29} -2.97858 q^{31} +2.05333i q^{32} +1.19656i q^{33} +15.3717 q^{34} +4.19656 q^{36} -7.78202i q^{37} -17.3717i q^{38} +1.00000 q^{39} -6.17513 q^{41} +2.97858i q^{42} -9.95715i q^{43} +5.02142 q^{44} -10.3931 q^{46} +1.02142i q^{47} -5.21798i q^{48} +5.56825 q^{49} -6.17513 q^{51} -4.19656i q^{52} +10.1751i q^{53} -2.48929 q^{54} +6.54262 q^{56} +6.97858i q^{57} -14.9357i q^{58} -5.37169 q^{59} +12.5682 q^{61} -7.41454i q^{62} -1.19656i q^{63} +5.32464 q^{64} -2.97858 q^{66} -9.37169i q^{67} +25.9143i q^{68} +4.17513 q^{69} -5.19656 q^{71} +5.46787i q^{72} -11.9572i q^{73} +19.3717 q^{74} +29.2860 q^{76} -1.43175i q^{77} +2.48929i q^{78} +1.78202 q^{79} +1.00000 q^{81} -15.3717i q^{82} -5.37169i q^{83} -5.02142 q^{84} +24.7862 q^{86} +6.00000i q^{87} +6.54262i q^{88} -10.1751 q^{89} -1.19656 q^{91} -17.5212i q^{92} +2.97858i q^{93} -2.54262 q^{94} +2.05333 q^{96} +1.82487i q^{97} +13.8610i q^{98} +1.19656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16 q^{4} - 6 q^{9}+O(q^{10}) $ 6 * q - 16 * q^4 - 6 * q^9	$ 6 q - 16 q^{4} - 6 q^{9} + 2 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} - 2 q^{21} + 12 q^{24} - 36 q^{29} + 12 q^{31} + 44 q^{34} + 16 q^{36} + 6 q^{39} + 2 q^{41} + 60 q^{44} - 44 q^{46} - 24 q^{49} + 2 q^{51} - 32 q^{56} + 16 q^{59} + 18 q^{61} - 60 q^{64} + 12 q^{66} - 14 q^{69} - 22 q^{71} + 68 q^{74} + 8 q^{76} - 10 q^{79} + 6 q^{81} - 60 q^{84} + 112 q^{86} - 22 q^{89} + 2 q^{91} + 56 q^{94} - 44 q^{96} - 2 q^{99}+O(q^{100}) $ 6 * q - 16 * q^4 - 6 * q^9 + 2 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 - 2 * q^21 + 12 * q^24 - 36 * q^29 + 12 * q^31 + 44 * q^34 + 16 * q^36 + 6 * q^39 + 2 * q^41 + 60 * q^44 - 44 * q^46 - 24 * q^49 + 2 * q^51 - 32 * q^56 + 16 * q^59 + 18 * q^61 - 60 * q^64 + 12 * q^66 - 14 * q^69 - 22 * q^71 + 68 * q^74 + 8 * q^76 - 10 * q^79 + 6 * q^81 - 60 * q^84 + 112 * q^86 - 22 * q^89 + 2 * q^91 + 56 * q^94 - 44 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.48929i	1.76019i	0.474795	+	0.880096i	$0.342522\pi$
$2$	2.48929i	1.76019i	−0.474795	+	0.880096i	$0.657478\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−4.19656	−2.09828
$5$	0	0
$5$	0	0
$6$	2.48929	1.01625
$7$	1.19656i	0.452256i	0.974098	+	0.226128i	$0.0726068\pi$
$7$	1.19656i	0.452256i	−0.974098	+	0.226128i	$0.927393\pi$
$8$	− 5.46787i	− 1.93318i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.19656	−0.360776	−0.180388	−	0.983596i	$-0.557735\pi$
$11$	−1.19656	−0.360776	−0.180388	+	0.983596i	$0.557735\pi$
$12$	4.19656i	1.21144i
$13$	1.00000i	0.277350i
$13$	1.00000i	0.277350i
$14$	−2.97858	−0.796058
$15$	0	0
$16$	5.21798	1.30450
$17$	− 6.17513i	− 1.49769i	−0.662745	−	0.748845i	$-0.730609\pi$
$17$	− 6.17513i	− 1.49769i	0.662745	−	0.748845i	$-0.269391\pi$
$18$	− 2.48929i	− 0.586731i
$19$	−6.97858	−1.60100	−0.800498	−	0.599336i	$-0.795431\pi$
$19$	−6.97858	−1.60100	−0.800498	+	0.599336i	$0.795431\pi$
$20$	0	0
$21$	1.19656	0.261110
$22$	− 2.97858i	− 0.635035i
$23$	4.17513i	0.870576i	0.900291	+	0.435288i	$0.143353\pi$
$23$	4.17513i	0.870576i	−0.900291	+	0.435288i	$0.856647\pi$
$24$	−5.46787	−1.11612
$25$	0	0
$26$	−2.48929	−0.488190
$27$	1.00000i	0.192450i
$28$	− 5.02142i	− 0.948960i
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−2.97858	−0.534968	−0.267484	−	0.963562i	$-0.586192\pi$
$31$	−2.97858	−0.534968	−0.267484	+	0.963562i	$0.586192\pi$
$32$	2.05333i	0.362980i
$33$	1.19656i	0.208294i
$34$	15.3717	2.63622
$35$	0	0
$36$	4.19656	0.699426
$37$	− 7.78202i	− 1.27936i	−0.768643	−	0.639678i	$-0.779068\pi$
$37$	− 7.78202i	− 1.27936i	0.768643	−	0.639678i	$-0.220932\pi$
$38$	− 17.3717i	− 2.81806i
$39$	1.00000	0.160128
$40$	0	0
$41$	−6.17513	−0.964394	−0.482197	−	0.876063i	$-0.660161\pi$
$41$	−6.17513	−0.964394	−0.482197	+	0.876063i	$0.660161\pi$
$42$	2.97858i	0.459604i
$43$	− 9.95715i	− 1.51845i	−0.650827	−	0.759226i	$-0.725578\pi$
$43$	− 9.95715i	− 1.51845i	0.650827	−	0.759226i	$-0.274422\pi$
$44$	5.02142	0.757008
$45$	0	0
$46$	−10.3931	−1.53238
$47$	1.02142i	0.148990i	0.997221	+	0.0744949i	$0.0237345\pi$
$47$	1.02142i	0.148990i	−0.997221	+	0.0744949i	$0.976266\pi$
$48$	− 5.21798i	− 0.753151i
$49$	5.56825	0.795464
$50$	0	0
$51$	−6.17513	−0.864692
$52$	− 4.19656i	− 0.581958i
$53$	10.1751i	1.39766i	0.715287	+	0.698831i	$0.246296\pi$
$53$	10.1751i	1.39766i	−0.715287	+	0.698831i	$0.753704\pi$
$54$	−2.48929	−0.338749
$55$	0	0
$56$	6.54262	0.874294
$57$	6.97858i	0.924335i
$58$	− 14.9357i	− 1.96116i
$59$	−5.37169	−0.699335	−0.349667	−	0.936874i	$-0.613705\pi$
$59$	−5.37169	−0.699335	−0.349667	+	0.936874i	$0.613705\pi$
$60$	0	0
$61$	12.5682	1.60920	0.804600	−	0.593818i	$-0.202380\pi$
$61$	12.5682	1.60920	0.804600	+	0.593818i	$0.202380\pi$
$62$	− 7.41454i	− 0.941647i
$63$	− 1.19656i	− 0.150752i
$64$	5.32464	0.665579
$65$	0	0
$66$	−2.97858	−0.366638
$67$	− 9.37169i	− 1.14493i	−0.819928	−	0.572467i	$-0.805986\pi$
$67$	− 9.37169i	− 1.14493i	0.819928	−	0.572467i	$-0.194014\pi$
$68$	25.9143i	3.14257i
$69$	4.17513	0.502627
$70$	0	0
$71$	−5.19656	−0.616718	−0.308359	−	0.951270i	$-0.599780\pi$
$71$	−5.19656	−0.616718	−0.308359	+	0.951270i	$0.599780\pi$
$72$	5.46787i	0.644394i
$73$	− 11.9572i	− 1.39948i	−0.714398	−	0.699740i	$-0.753299\pi$
$73$	− 11.9572i	− 1.39948i	0.714398	−	0.699740i	$-0.246701\pi$
$74$	19.3717	2.25191
$75$	0	0
$76$	29.2860	3.35933
$77$	− 1.43175i	− 0.163163i
$78$	2.48929i	0.281856i
$79$	1.78202	0.200493	0.100246	−	0.994963i	$-0.468037\pi$
$79$	1.78202	0.200493	0.100246	+	0.994963i	$0.468037\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 15.3717i	− 1.69752i
$83$	− 5.37169i	− 0.589620i	−0.955556	−	0.294810i	$-0.904744\pi$
$83$	− 5.37169i	− 0.589620i	0.955556	−	0.294810i	$-0.0952563\pi$
$84$	−5.02142	−0.547882
$85$	0	0
$86$	24.7862	2.67277
$87$	6.00000i	0.643268i
$88$	6.54262i	0.697445i
$89$	−10.1751	−1.07856	−0.539281	−	0.842126i	$-0.681304\pi$
$89$	−10.1751	−1.07856	−0.539281	+	0.842126i	$0.681304\pi$
$90$	0	0
$91$	−1.19656	−0.125433
$92$	− 17.5212i	− 1.82671i
$93$	2.97858i	0.308864i
$94$	−2.54262	−0.262251
$95$	0	0
$96$	2.05333	0.209567
$97$	1.82487i	0.185287i	0.995699	+	0.0926435i	$0.0295317\pi$
$97$	1.82487i	0.185287i	−0.995699	+	0.0926435i	$0.970468\pi$
$98$	13.8610i	1.40017i
$99$	1.19656	0.120259
$100$	0	0
$101$	−10.3503	−1.02989	−0.514945	−	0.857223i	$-0.672188\pi$
$101$	−10.3503	−1.02989	−0.514945	+	0.857223i	$0.672188\pi$
$102$	− 15.3717i	− 1.52202i
$103$	18.7434i	1.84684i	0.383790	+	0.923420i	$0.374619\pi$
$103$	18.7434i	1.84684i	−0.383790	+	0.923420i	$0.625381\pi$
$104$	5.46787	0.536168
$105$	0	0
$106$	−25.3288	−2.46016
$107$	18.5682i	1.79506i	0.440953	+	0.897530i	$0.354641\pi$
$107$	18.5682i	1.79506i	−0.440953	+	0.897530i	$0.645359\pi$
$108$	− 4.19656i	− 0.403814i
$109$	−8.39312	−0.803915	−0.401957	−	0.915658i	$-0.631670\pi$
$109$	−8.39312	−0.803915	−0.401957	+	0.915658i	$0.631670\pi$
$110$	0	0
$111$	−7.78202	−0.738637
$112$	6.24361i	0.589966i
$113$	7.95715i	0.748546i	0.927319	+	0.374273i	$0.122108\pi$
$113$	7.95715i	0.748546i	−0.927319	+	0.374273i	$0.877892\pi$
$114$	−17.3717	−1.62701
$115$	0	0
$116$	25.1793	2.33784
$117$	− 1.00000i	− 0.0924500i
$118$	− 13.3717i	− 1.23096i
$119$	7.38890	0.677340
$120$	0	0
$121$	−9.56825	−0.869841
$122$	31.2860i	2.83250i
$123$	6.17513i	0.556793i
$124$	12.4998	1.12251
$125$	0	0
$126$	2.97858	0.265353
$127$	10.3931i	0.922240i	0.887338	+	0.461120i	$0.152552\pi$
$127$	10.3931i	0.922240i	−0.887338	+	0.461120i	$0.847448\pi$
$128$	17.3612i	1.53453i
$129$	−9.95715	−0.876679
$130$	0	0
$131$	−6.39312	−0.558569	−0.279285	−	0.960208i	$-0.590097\pi$
$131$	−6.39312	−0.558569	−0.279285	+	0.960208i	$0.590097\pi$
$132$	− 5.02142i	− 0.437059i
$133$	− 8.35027i	− 0.724060i
$134$	23.3288	2.01531
$135$	0	0
$136$	−33.7648	−2.89531
$137$	− 16.7434i	− 1.43048i	−0.698877	−	0.715242i	$-0.746316\pi$
$137$	− 16.7434i	− 1.43048i	0.698877	−	0.715242i	$-0.253684\pi$
$138$	10.3931i	0.884721i
$139$	−5.78202	−0.490424	−0.245212	−	0.969469i	$-0.578858\pi$
$139$	−5.78202	−0.490424	−0.245212	+	0.969469i	$0.578858\pi$
$140$	0	0
$141$	1.02142	0.0860193
$142$	− 12.9357i	− 1.08554i
$143$	− 1.19656i	− 0.100061i
$144$	−5.21798	−0.434832
$145$	0	0
$146$	29.7648	2.46335
$147$	− 5.56825i	− 0.459262i
$148$	32.6577i	2.68445i
$149$	−15.3461	−1.25720	−0.628599	−	0.777730i	$-0.716371\pi$
$149$	−15.3461	−1.25720	−0.628599	+	0.777730i	$0.716371\pi$
$150$	0	0
$151$	−8.58546	−0.698675	−0.349337	−	0.936997i	$-0.613593\pi$
$151$	−8.58546	−0.698675	−0.349337	+	0.936997i	$0.613593\pi$
$152$	38.1579i	3.09502i
$153$	6.17513i	0.499230i
$154$	3.56404	0.287198
$155$	0	0
$156$	−4.19656	−0.335994
$157$	− 2.78623i	− 0.222365i	−0.993800	−	0.111183i	$-0.964536\pi$
$157$	− 2.78623i	− 0.222365i	0.993800	−	0.111183i	$-0.0354639\pi$
$158$	4.43596i	0.352906i
$159$	10.1751	0.806941
$160$	0	0
$161$	−4.99579	−0.393723
$162$	2.48929i	0.195577i
$163$	8.76060i	0.686183i	0.939302	+	0.343091i	$0.111474\pi$
$163$	8.76060i	0.686183i	−0.939302	+	0.343091i	$0.888526\pi$
$164$	25.9143	2.02357
$165$	0	0
$166$	13.3717	1.03784
$167$	17.3717i	1.34426i	0.740432	+	0.672131i	$0.234621\pi$
$167$	17.3717i	1.34426i	−0.740432	+	0.672131i	$0.765379\pi$
$168$	− 6.54262i	− 0.504774i
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	6.97858	0.533665
$172$	41.7858i	3.18614i
$173$	− 7.95715i	− 0.604971i	−0.953154	−	0.302486i	$-0.902184\pi$
$173$	− 7.95715i	− 0.604971i	0.953154	−	0.302486i	$-0.0978164\pi$
$174$	−14.9357	−1.13227
$175$	0	0
$176$	−6.24361	−0.470630
$177$	5.37169i	0.403761i
$178$	− 25.3288i	− 1.89848i
$179$	15.5640	1.16331	0.581655	−	0.813435i	$-0.302405\pi$
$179$	15.5640	1.16331	0.581655	+	0.813435i	$0.302405\pi$
$180$	0	0
$181$	15.7820	1.17307	0.586534	−	0.809925i	$-0.300492\pi$
$181$	15.7820	1.17307	0.586534	+	0.809925i	$0.300492\pi$
$182$	− 2.97858i	− 0.220787i
$183$	− 12.5682i	− 0.929072i
$184$	22.8291	1.68298
$185$	0	0
$186$	−7.41454	−0.543660
$187$	7.38890i	0.540330i
$188$	− 4.28646i	− 0.312622i
$189$	−1.19656	−0.0870368
$190$	0	0
$191$	10.7434	0.777364	0.388682	−	0.921372i	$-0.372930\pi$
$191$	10.7434	0.777364	0.388682	+	0.921372i	$0.372930\pi$
$192$	− 5.32464i	− 0.384272i
$193$	9.73917i	0.701041i	0.936555	+	0.350521i	$0.113995\pi$
$193$	9.73917i	0.701041i	−0.936555	+	0.350521i	$0.886005\pi$
$194$	−4.54262	−0.326141
$195$	0	0
$196$	−23.3675	−1.66911
$197$	9.56404i	0.681410i	0.940170	+	0.340705i	$0.110666\pi$
$197$	9.56404i	0.681410i	−0.940170	+	0.340705i	$0.889334\pi$
$198$	2.97858i	0.211678i
$199$	−5.95715	−0.422291	−0.211146	−	0.977455i	$-0.567719\pi$
$199$	−5.95715	−0.422291	−0.211146	+	0.977455i	$0.567719\pi$
$200$	0	0
$201$	−9.37169	−0.661028
$202$	− 25.7648i	− 1.81281i
$203$	− 7.17935i	− 0.503891i
$204$	25.9143	1.81436
$205$	0	0
$206$	−46.6577	−3.25080
$207$	− 4.17513i	− 0.290192i
$208$	5.21798i	0.361802i
$209$	8.35027	0.577600
$210$	0	0
$211$	23.9143	1.64633	0.823164	−	0.567803i	$-0.192206\pi$
$211$	23.9143	1.64633	0.823164	+	0.567803i	$0.192206\pi$
$212$	− 42.7005i	− 2.93269i
$213$	5.19656i	0.356062i
$214$	−46.2217	−3.15965
$215$	0	0
$216$	5.46787	0.372041
$217$	− 3.56404i	− 0.241943i
$218$	− 20.8929i	− 1.41504i
$219$	−11.9572	−0.807990
$220$	0	0
$221$	6.17513	0.415385
$222$	− 19.3717i	− 1.30014i
$223$	2.62831i	0.176004i	0.996120	+	0.0880022i	$0.0280483\pi$
$223$	2.62831i	0.176004i	−0.996120	+	0.0880022i	$0.971952\pi$
$224$	−2.45692	−0.164160
$225$	0	0
$226$	−19.8077	−1.31759
$227$	− 15.7648i	− 1.04635i	−0.852226	−	0.523174i	$-0.824748\pi$
$227$	− 15.7648i	− 1.04635i	0.852226	−	0.523174i	$-0.175252\pi$
$228$	− 29.2860i	− 1.93951i
$229$	−8.74338	−0.577779	−0.288890	−	0.957362i	$-0.593286\pi$
$229$	−8.74338	−0.577779	−0.288890	+	0.957362i	$0.593286\pi$
$230$	0	0
$231$	−1.43175	−0.0942022
$232$	32.8072i	2.15390i
$233$	− 2.17513i	− 0.142498i	−0.997459	−	0.0712489i	$-0.977302\pi$
$233$	− 2.17513i	− 0.142498i	0.997459	−	0.0712489i	$-0.0226985\pi$
$234$	2.48929	0.162730
$235$	0	0
$236$	22.5426	1.46740
$237$	− 1.78202i	− 0.115755i
$238$	18.3931i	1.19225i
$239$	−2.80344	−0.181340	−0.0906698	−	0.995881i	$-0.528901\pi$
$239$	−2.80344	−0.181340	−0.0906698	+	0.995881i	$0.528901\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	− 23.8181i	− 1.53109i
$243$	− 1.00000i	− 0.0641500i
$244$	−52.7434	−3.37655
$245$	0	0
$246$	−15.3717	−0.980063
$247$	− 6.97858i	− 0.444036i
$248$	16.2865i	1.03419i
$249$	−5.37169	−0.340417
$250$	0	0
$251$	−23.9143	−1.50946	−0.754729	−	0.656037i	$-0.772232\pi$
$251$	−23.9143	−1.50946	−0.754729	+	0.656037i	$0.772232\pi$
$252$	5.02142i	0.316320i
$253$	− 4.99579i	− 0.314083i
$254$	−25.8715	−1.62332
$255$	0	0
$256$	−32.5678	−2.03549
$257$	19.9572i	1.24489i	0.782662	+	0.622447i	$0.213861\pi$
$257$	19.9572i	1.24489i	−0.782662	+	0.622447i	$0.786139\pi$
$258$	− 24.7862i	− 1.54312i
$259$	9.31163	0.578597
$260$	0	0
$261$	6.00000	0.371391
$262$	− 15.9143i	− 0.983189i
$263$	8.00000i	0.493301i	0.969104	+	0.246651i	$0.0793300\pi$
$263$	8.00000i	0.493301i	−0.969104	+	0.246651i	$0.920670\pi$
$264$	6.54262	0.402670
$265$	0	0
$266$	20.7862	1.27449
$267$	10.1751i	0.622708i
$268$	39.3288i	2.40239i
$269$	2.35027	0.143298	0.0716492	−	0.997430i	$-0.477174\pi$
$269$	2.35027	0.143298	0.0716492	+	0.997430i	$0.477174\pi$
$270$	0	0
$271$	10.9786	0.666901	0.333451	−	0.942768i	$-0.391787\pi$
$271$	10.9786	0.666901	0.333451	+	0.942768i	$0.391787\pi$
$272$	− 32.2217i	− 1.95373i
$273$	1.19656i	0.0724190i
$274$	41.6791	2.51793
$275$	0	0
$276$	−17.5212	−1.05465
$277$	− 1.21377i	− 0.0729283i	−0.999335	−	0.0364642i	$-0.988391\pi$
$277$	− 1.21377i	− 0.0729283i	0.999335	−	0.0364642i	$-0.0116095\pi$
$278$	− 14.3931i	− 0.863242i
$279$	2.97858	0.178323
$280$	0	0
$281$	11.9572	0.713304	0.356652	−	0.934237i	$-0.383918\pi$
$281$	11.9572	0.713304	0.356652	+	0.934237i	$0.383918\pi$
$282$	2.54262i	0.151411i
$283$	− 29.8715i	− 1.77567i	−0.460158	−	0.887837i	$-0.652207\pi$
$283$	− 29.8715i	− 1.77567i	0.460158	−	0.887837i	$-0.347793\pi$
$284$	21.8077	1.29405
$285$	0	0
$286$	2.97858	0.176127
$287$	− 7.38890i	− 0.436153i
$288$	− 2.05333i	− 0.120993i
$289$	−21.1323	−1.24308
$290$	0	0
$291$	1.82487	0.106975
$292$	50.1789i	2.93650i
$293$	0.777809i	0.0454401i	0.999742	+	0.0227200i	$0.00723263\pi$
$293$	0.777809i	0.0454401i	−0.999742	+	0.0227200i	$0.992767\pi$
$294$	13.8610	0.808389
$295$	0	0
$296$	−42.5510	−2.47323
$297$	− 1.19656i	− 0.0694313i
$298$	− 38.2008i	− 2.21291i
$299$	−4.17513	−0.241454
$300$	0	0
$301$	11.9143	0.686729
$302$	− 21.3717i	− 1.22980i
$303$	10.3503i	0.594607i
$304$	−36.4141	−2.08849
$305$	0	0
$306$	−15.3717	−0.878741
$307$	− 0.760597i	− 0.0434095i	−0.999764	−	0.0217048i	$-0.993091\pi$
$307$	− 0.760597i	− 0.0434095i	0.999764	−	0.0217048i	$-0.00690939\pi$
$308$	6.00842i	0.342362i
$309$	18.7434	1.06627
$310$	0	0
$311$	−23.1281	−1.31147	−0.655736	−	0.754990i	$-0.727642\pi$
$311$	−23.1281	−1.31147	−0.655736	+	0.754990i	$0.727642\pi$
$312$	− 5.46787i	− 0.309557i
$313$	− 33.9143i	− 1.91695i	−0.285176	−	0.958475i	$-0.592052\pi$
$313$	− 33.9143i	− 1.91695i	0.285176	−	0.958475i	$-0.407948\pi$
$314$	6.93573	0.391406
$315$	0	0
$316$	−7.47835	−0.420690
$317$	− 9.64973i	− 0.541983i	−0.962582	−	0.270991i	$-0.912648\pi$
$317$	− 9.64973i	− 0.541983i	0.962582	−	0.270991i	$-0.0873515\pi$
$318$	25.3288i	1.42037i
$319$	7.17935	0.401966
$320$	0	0
$321$	18.5682	1.03638
$322$	− 12.4360i	− 0.693029i
$323$	43.0937i	2.39780i
$324$	−4.19656	−0.233142
$325$	0	0
$326$	−21.8077	−1.20781
$327$	8.39312i	0.464140i
$328$	33.7648i	1.86435i
$329$	−1.22219	−0.0673816
$330$	0	0
$331$	15.3288	0.842550	0.421275	−	0.906933i	$-0.361583\pi$
$331$	15.3288	0.842550	0.421275	+	0.906933i	$0.361583\pi$
$332$	22.5426i	1.23719i
$333$	7.78202i	0.426452i
$334$	−43.2432	−2.36616
$335$	0	0
$336$	6.24361	0.340617
$337$	22.3503i	1.21750i	0.793363	+	0.608748i	$0.208328\pi$
$337$	22.3503i	1.21750i	−0.793363	+	0.608748i	$0.791672\pi$
$338$	− 2.48929i	− 0.135399i
$339$	7.95715	0.432173
$340$	0	0
$341$	3.56404	0.193004
$342$	17.3717i	0.939354i
$343$	15.0386i	0.812010i
$344$	−54.4444	−2.93544
$345$	0	0
$346$	19.8077	1.06487
$347$	5.78202i	0.310395i	0.987883	+	0.155198i	$0.0496014\pi$
$347$	5.78202i	0.310395i	−0.987883	+	0.155198i	$0.950399\pi$
$348$	− 25.1793i	− 1.34975i
$349$	27.5212	1.47318	0.736588	−	0.676342i	$-0.236436\pi$
$349$	27.5212	1.47318	0.736588	+	0.676342i	$0.236436\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	− 2.45692i	− 0.130955i
$353$	− 28.7434i	− 1.52986i	−0.644116	−	0.764928i	$-0.722775\pi$
$353$	− 28.7434i	− 1.52986i	0.644116	−	0.764928i	$-0.277225\pi$
$354$	−13.3717	−0.710697
$355$	0	0
$356$	42.7005	2.26312
$357$	− 7.38890i	− 0.391062i
$358$	38.7434i	2.04765i
$359$	12.5855	0.664235	0.332118	−	0.943238i	$-0.392237\pi$
$359$	12.5855	0.664235	0.332118	+	0.943238i	$0.392237\pi$
$360$	0	0
$361$	29.7005	1.56319
$362$	39.2860i	2.06483i
$363$	9.56825i	0.502203i
$364$	5.02142	0.263194
$365$	0	0
$366$	31.2860	1.63535
$367$	27.9143i	1.45712i	0.684985	+	0.728558i	$0.259809\pi$
$367$	27.9143i	1.45712i	−0.684985	+	0.728558i	$0.740191\pi$
$368$	21.7858i	1.13566i
$369$	6.17513	0.321465
$370$	0	0
$371$	−12.1751	−0.632102
$372$	− 12.4998i	− 0.648083i
$373$	− 2.35027i	− 0.121692i	−0.998147	−	0.0608462i	$-0.980620\pi$
$373$	− 2.35027i	− 0.121692i	0.998147	−	0.0608462i	$-0.0193799\pi$
$374$	−18.3931	−0.951085
$375$	0	0
$376$	5.58500	0.288025
$377$	− 6.00000i	− 0.309016i
$378$	− 2.97858i	− 0.153201i
$379$	−24.5510	−1.26110	−0.630551	−	0.776148i	$-0.717171\pi$
$379$	−24.5510	−1.26110	−0.630551	+	0.776148i	$0.717171\pi$
$380$	0	0
$381$	10.3931	0.532455
$382$	26.7434i	1.36831i
$383$	5.80765i	0.296757i	0.988931	+	0.148379i	$0.0474054\pi$
$383$	5.80765i	0.296757i	−0.988931	+	0.148379i	$0.952595\pi$
$384$	17.3612	0.885961
$385$	0	0
$386$	−24.2436	−1.23397
$387$	9.95715i	0.506151i
$388$	− 7.65815i	− 0.388784i
$389$	−13.6497	−0.692069	−0.346034	−	0.938222i	$-0.612472\pi$
$389$	−13.6497	−0.692069	−0.346034	+	0.938222i	$0.612472\pi$
$390$	0	0
$391$	25.7820	1.30385
$392$	− 30.4464i	− 1.53778i
$393$	6.39312i	0.322490i
$394$	−23.8077	−1.19941
$395$	0	0
$396$	−5.02142	−0.252336
$397$	12.1323i	0.608902i	0.952528	+	0.304451i	$0.0984730\pi$
$397$	12.1323i	0.608902i	−0.952528	+	0.304451i	$0.901527\pi$
$398$	− 14.8291i	− 0.743314i
$399$	−8.35027	−0.418036
$400$	0	0
$401$	−37.4439	−1.86986	−0.934930	−	0.354832i	$-0.884538\pi$
$401$	−37.4439	−1.86986	−0.934930	+	0.354832i	$0.884538\pi$
$402$	− 23.3288i	− 1.16354i
$403$	− 2.97858i	− 0.148373i
$404$	43.4355	2.16100
$405$	0	0
$406$	17.8715	0.886946
$407$	9.31163i	0.461561i
$408$	33.7648i	1.67161i
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	0	0
$411$	−16.7434	−0.825890
$412$	− 78.6577i	− 3.87519i
$413$	− 6.42754i	− 0.316279i
$414$	10.3931	0.510794
$415$	0	0
$416$	−2.05333	−0.100673
$417$	5.78202i	0.283147i
$418$	20.7862i	1.01669i
$419$	−3.17935	−0.155321	−0.0776606	−	0.996980i	$-0.524745\pi$
$419$	−3.17935	−0.155321	−0.0776606	+	0.996980i	$0.524745\pi$
$420$	0	0
$421$	−16.3074	−0.794775	−0.397388	−	0.917651i	$-0.630083\pi$
$421$	−16.3074	−0.794775	−0.397388	+	0.917651i	$0.630083\pi$
$422$	59.5296i	2.89786i
$423$	− 1.02142i	− 0.0496633i
$424$	55.6363	2.70194
$425$	0	0
$426$	−12.9357	−0.626738
$427$	15.0386i	0.727771i
$428$	− 77.9227i	− 3.76654i
$429$	−1.19656	−0.0577703
$430$	0	0
$431$	4.58546	0.220874	0.110437	−	0.993883i	$-0.464775\pi$
$431$	4.58546	0.220874	0.110437	+	0.993883i	$0.464775\pi$
$432$	5.21798i	0.251050i
$433$	− 38.3503i	− 1.84300i	−0.388383	−	0.921498i	$-0.626966\pi$
$433$	− 38.3503i	− 1.84300i	0.388383	−	0.921498i	$-0.373034\pi$
$434$	8.87192	0.425866
$435$	0	0
$436$	35.2222	1.68684
$437$	− 29.1365i	− 1.39379i
$438$	− 29.7648i	− 1.42222i
$439$	−7.73917	−0.369371	−0.184685	−	0.982798i	$-0.559127\pi$
$439$	−7.73917	−0.369371	−0.184685	+	0.982798i	$0.559127\pi$
$440$	0	0
$441$	−5.56825	−0.265155
$442$	15.3717i	0.731157i
$443$	34.9185i	1.65903i	0.558485	+	0.829514i	$0.311383\pi$
$443$	34.9185i	1.65903i	−0.558485	+	0.829514i	$0.688617\pi$
$444$	32.6577	1.54987
$445$	0	0
$446$	−6.54262	−0.309802
$447$	15.3461i	0.725844i
$448$	6.37123i	0.301012i
$449$	6.17513	0.291423	0.145711	−	0.989327i	$-0.453453\pi$
$449$	6.17513	0.291423	0.145711	+	0.989327i	$0.453453\pi$
$450$	0	0
$451$	7.38890	0.347930
$452$	− 33.3927i	− 1.57066i
$453$	8.58546i	0.403380i
$454$	39.2432	1.84177
$455$	0	0
$456$	38.1579	1.78691
$457$	− 1.38890i	− 0.0649702i	−0.999472	−	0.0324851i	$-0.989658\pi$
$457$	− 1.38890i	− 0.0649702i	0.999472	−	0.0324851i	$-0.0103421\pi$
$458$	− 21.7648i	− 1.01700i
$459$	6.17513	0.288231
$460$	0	0
$461$	28.4826	1.32657	0.663283	−	0.748369i	$-0.269163\pi$
$461$	28.4826	1.32657	0.663283	+	0.748369i	$0.269163\pi$
$462$	− 3.56404i	− 0.165814i
$463$	16.3759i	0.761053i	0.924770	+	0.380526i	$0.124257\pi$
$463$	16.3759i	0.761053i	−0.924770	+	0.380526i	$0.875743\pi$
$464$	−31.3079	−1.45343
$465$	0	0
$466$	5.41454	0.250824
$467$	− 25.7476i	− 1.19146i	−0.803186	−	0.595728i	$-0.796864\pi$
$467$	− 25.7476i	− 1.19146i	0.803186	−	0.595728i	$-0.203136\pi$
$468$	4.19656i	0.193986i
$469$	11.2138	0.517804
$470$	0	0
$471$	−2.78623	−0.128383
$472$	29.3717i	1.35194i
$473$	11.9143i	0.547820i
$474$	4.43596	0.203750
$475$	0	0
$476$	−31.0080	−1.42125
$477$	− 10.1751i	− 0.465887i
$478$	− 6.97858i	− 0.319193i
$479$	7.58967	0.346781	0.173391	−	0.984853i	$-0.444528\pi$
$479$	7.58967	0.346781	0.173391	+	0.984853i	$0.444528\pi$
$480$	0	0
$481$	7.78202	0.354830
$482$	− 14.9357i	− 0.680304i
$483$	4.99579i	0.227316i
$484$	40.1537	1.82517
$485$	0	0
$486$	2.48929	0.112916
$487$	− 4.41033i	− 0.199851i	−0.994995	−	0.0999255i	$-0.968140\pi$
$487$	− 4.41033i	− 0.199851i	0.994995	−	0.0999255i	$-0.0318604\pi$
$488$	− 68.7215i	− 3.11088i
$489$	8.76060	0.396168
$490$	0	0
$491$	−0.0856914	−0.00386720	−0.00193360	−	0.999998i	$-0.500615\pi$
$491$	−0.0856914	−0.00386720	−0.00193360	+	0.999998i	$0.500615\pi$
$492$	− 25.9143i	− 1.16831i
$493$	37.0508i	1.66868i
$494$	17.3717	0.781589
$495$	0	0
$496$	−15.5422	−0.697863
$497$	− 6.21798i	− 0.278915i
$498$	− 13.3717i	− 0.599200i
$499$	17.7220	0.793344	0.396672	−	0.917960i	$-0.370165\pi$
$499$	17.7220	0.793344	0.396672	+	0.917960i	$0.370165\pi$
$500$	0	0
$501$	17.3717	0.776110
$502$	− 59.5296i	− 2.65694i
$503$	− 8.70054i	− 0.387938i	−0.981008	−	0.193969i	$-0.937864\pi$
$503$	− 8.70054i	− 0.387938i	0.981008	−	0.193969i	$-0.0621361\pi$
$504$	−6.54262	−0.291431
$505$	0	0
$506$	12.4360	0.552846
$507$	1.00000i	0.0444116i
$508$	− 43.6153i	− 1.93512i
$509$	33.3545	1.47841	0.739206	−	0.673480i	$-0.235201\pi$
$509$	33.3545	1.47841	0.739206	+	0.673480i	$0.235201\pi$
$510$	0	0
$511$	14.3074	0.632923
$512$	− 46.3482i	− 2.04832i
$513$	− 6.97858i	− 0.308112i
$514$	−49.6791	−2.19125
$515$	0	0
$516$	41.7858	1.83952
$517$	− 1.22219i	− 0.0537519i
$518$	23.1793i	1.01844i
$519$	−7.95715	−0.349280
$520$	0	0
$521$	18.7005	0.819285	0.409643	−	0.912246i	$-0.365653\pi$
$521$	18.7005	0.819285	0.409643	+	0.912246i	$0.365653\pi$
$522$	14.9357i	0.653719i
$523$	− 4.00000i	− 0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$	− 4.00000i	− 0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	26.8291	1.17203
$525$	0	0
$526$	−19.9143	−0.868305
$527$	18.3931i	0.801217i
$528$	6.24361i	0.271718i
$529$	5.56825	0.242098
$530$	0	0
$531$	5.37169	0.233112
$532$	35.0424i	1.51928i
$533$	− 6.17513i	− 0.267475i
$534$	−25.3288	−1.09609
$535$	0	0
$536$	−51.2432	−2.21337
$537$	− 15.5640i	− 0.671638i
$538$	5.85050i	0.252233i
$539$	−6.66273	−0.286984
$540$	0	0
$541$	−41.5296	−1.78550	−0.892749	−	0.450555i	$-0.851226\pi$
$541$	−41.5296	−1.78550	−0.892749	+	0.450555i	$0.851226\pi$
$542$	27.3288i	1.17387i
$543$	− 15.7820i	− 0.677271i
$544$	12.6796	0.543632
$545$	0	0
$546$	−2.97858	−0.127471
$547$	7.91431i	0.338391i	0.985582	+	0.169196i	$0.0541170\pi$
$547$	7.91431i	0.338391i	−0.985582	+	0.169196i	$0.945883\pi$
$548$	70.2646i	3.00155i
$549$	−12.5682	−0.536400
$550$	0	0
$551$	41.8715	1.78378
$552$	− 22.8291i	− 0.971670i
$553$	2.13229i	0.0906742i
$554$	3.02142	0.128368
$555$	0	0
$556$	24.2646	1.02905
$557$	− 42.7005i	− 1.80928i	−0.426177	−	0.904640i	$-0.640140\pi$
$557$	− 42.7005i	− 1.80928i	0.426177	−	0.904640i	$-0.359860\pi$
$558$	7.41454i	0.313882i
$559$	9.95715	0.421143
$560$	0	0
$561$	7.38890	0.311960
$562$	29.7648i	1.25555i
$563$	1.04706i	0.0441282i	0.999757	+	0.0220641i	$0.00702379\pi$
$563$	1.04706i	0.0441282i	−0.999757	+	0.0220641i	$0.992976\pi$
$564$	−4.28646	−0.180493
$565$	0	0
$566$	74.3587	3.12553
$567$	1.19656i	0.0502507i
$568$	28.4141i	1.19223i
$569$	−16.7778	−0.703362	−0.351681	−	0.936120i	$-0.614390\pi$
$569$	−16.7778	−0.703362	−0.351681	+	0.936120i	$0.614390\pi$
$570$	0	0
$571$	−20.6111	−0.862548	−0.431274	−	0.902221i	$-0.641936\pi$
$571$	−20.6111	−0.862548	−0.431274	+	0.902221i	$0.641936\pi$
$572$	5.02142i	0.209956i
$573$	− 10.7434i	− 0.448811i
$574$	18.3931	0.767714
$575$	0	0
$576$	−5.32464	−0.221860
$577$	− 1.38890i	− 0.0578208i	−0.999582	−	0.0289104i	$-0.990796\pi$
$577$	− 1.38890i	− 0.0578208i	0.999582	−	0.0289104i	$-0.00920376\pi$
$578$	− 52.6044i	− 2.18805i
$579$	9.73917	0.404746
$580$	0	0
$581$	6.42754	0.266659
$582$	4.54262i	0.188298i
$583$	− 12.1751i	− 0.504243i
$584$	−65.3801	−2.70545
$585$	0	0
$586$	−1.93619	−0.0799833
$587$	0.935731i	0.0386218i	0.999814	+	0.0193109i	$0.00614723\pi$
$587$	0.935731i	0.0386218i	−0.999814	+	0.0193109i	$0.993853\pi$
$588$	23.3675i	0.963659i
$589$	20.7862	0.856482
$590$	0	0
$591$	9.56404	0.393412
$592$	− 40.6064i	− 1.66891i
$593$	− 0.478807i	− 0.0196622i	−0.999952	−	0.00983112i	$-0.996871\pi$
$593$	− 0.478807i	− 0.0196622i	0.999952	−	0.00983112i	$-0.00312939\pi$
$594$	2.97858	0.122213
$595$	0	0
$596$	64.4006	2.63795
$597$	5.95715i	0.243810i
$598$	− 10.3931i	− 0.425006i
$599$	−29.0852	−1.18839	−0.594195	−	0.804321i	$-0.702529\pi$
$599$	−29.0852	−1.18839	−0.594195	+	0.804321i	$0.702529\pi$
$600$	0	0
$601$	11.4318	0.466311	0.233155	−	0.972439i	$-0.425095\pi$
$601$	11.4318	0.466311	0.233155	+	0.972439i	$0.425095\pi$
$602$	29.6582i	1.20878i
$603$	9.37169i	0.381645i
$604$	36.0294	1.46601
$605$	0	0
$606$	−25.7648	−1.04662
$607$	− 27.9143i	− 1.13301i	−0.824059	−	0.566503i	$-0.808296\pi$
$607$	− 27.9143i	− 1.13301i	0.824059	−	0.566503i	$-0.191704\pi$
$608$	− 14.3293i	− 0.581130i
$609$	−7.17935	−0.290922
$610$	0	0
$611$	−1.02142	−0.0413223
$612$	− 25.9143i	− 1.04752i
$613$	− 4.65394i	− 0.187971i	−0.995574	−	0.0939855i	$-0.970039\pi$
$613$	− 4.65394i	− 0.187971i	0.995574	−	0.0939855i	$-0.0299607\pi$
$614$	1.89334	0.0764092
$615$	0	0
$616$	−7.82862	−0.315424
$617$	15.9572i	0.642411i	0.947010	+	0.321205i	$0.104088\pi$
$617$	15.9572i	0.642411i	−0.947010	+	0.321205i	$0.895912\pi$
$618$	46.6577i	1.87685i
$619$	−1.02142	−0.0410545	−0.0205272	−	0.999789i	$-0.506534\pi$
$619$	−1.02142	−0.0410545	−0.0205272	+	0.999789i	$0.506534\pi$
$620$	0	0
$621$	−4.17513	−0.167542
$622$	− 57.5725i	− 2.30845i
$623$	− 12.1751i	− 0.487786i
$624$	5.21798	0.208886
$625$	0	0
$626$	84.4225	3.37420
$627$	− 8.35027i	− 0.333478i
$628$	11.6926i	0.466585i
$629$	−48.0550	−1.91608
$630$	0	0
$631$	−20.4998	−0.816083	−0.408041	−	0.912963i	$-0.633788\pi$
$631$	−20.4998	−0.816083	−0.408041	+	0.912963i	$0.633788\pi$
$632$	− 9.74384i	− 0.387589i
$633$	− 23.9143i	− 0.950508i
$634$	24.0210	0.953994
$635$	0	0
$636$	−42.7005	−1.69319
$637$	5.56825i	0.220622i
$638$	17.8715i	0.707538i
$639$	5.19656	0.205573
$640$	0	0
$641$	38.2646	1.51136	0.755680	−	0.654941i	$-0.227307\pi$
$641$	38.2646	1.51136	0.755680	+	0.654941i	$0.227307\pi$
$642$	46.2217i	1.82423i
$643$	− 33.1109i	− 1.30577i	−0.757459	−	0.652883i	$-0.773560\pi$
$643$	− 33.1109i	− 1.30577i	0.757459	−	0.652883i	$-0.226440\pi$
$644$	20.9651	0.826141
$645$	0	0
$646$	−107.273	−4.22058
$647$	16.9614i	0.666820i	0.942782	+	0.333410i	$0.108199\pi$
$647$	16.9614i	0.666820i	−0.942782	+	0.333410i	$0.891801\pi$
$648$	− 5.46787i	− 0.214798i
$649$	6.42754	0.252303
$650$	0	0
$651$	−3.56404	−0.139686
$652$	− 36.7643i	− 1.43980i
$653$	− 19.1709i	− 0.750216i	−0.926981	−	0.375108i	$-0.877606\pi$
$653$	− 19.1709i	− 0.750216i	0.926981	−	0.375108i	$-0.122394\pi$
$654$	−20.8929	−0.816976
$655$	0	0
$656$	−32.2217	−1.25805
$657$	11.9572i	0.466493i
$658$	− 3.04239i	− 0.118605i
$659$	−37.8715	−1.47526	−0.737631	−	0.675204i	$-0.764056\pi$
$659$	−37.8715	−1.47526	−0.737631	+	0.675204i	$0.764056\pi$
$660$	0	0
$661$	24.3931	0.948782	0.474391	−	0.880314i	$-0.342668\pi$
$661$	24.3931	0.948782	0.474391	+	0.880314i	$0.342668\pi$
$662$	38.1579i	1.48305i
$663$	− 6.17513i	− 0.239822i
$664$	−29.3717	−1.13984
$665$	0	0
$666$	−19.3717	−0.750638
$667$	− 25.0508i	− 0.969971i
$668$	− 72.9013i	− 2.82064i
$669$	2.62831	0.101616
$670$	0	0
$671$	−15.0386	−0.580560
$672$	2.45692i	0.0947779i
$673$	− 21.1281i	− 0.814428i	−0.913333	−	0.407214i	$-0.866500\pi$
$673$	− 21.1281i	− 0.814428i	0.913333	−	0.407214i	$-0.133500\pi$
$674$	−55.6363	−2.14303
$675$	0	0
$676$	4.19656	0.161406
$677$	15.3973i	0.591767i	0.955224	+	0.295884i	$0.0956141\pi$
$677$	15.3973i	0.591767i	−0.955224	+	0.295884i	$0.904386\pi$
$678$	19.8077i	0.760708i
$679$	−2.18356	−0.0837972
$680$	0	0
$681$	−15.7648	−0.604109
$682$	8.87192i	0.339723i
$683$	30.0722i	1.15068i	0.817914	+	0.575341i	$0.195131\pi$
$683$	30.0722i	1.15068i	−0.817914	+	0.575341i	$0.804869\pi$
$684$	−29.2860	−1.11978
$685$	0	0
$686$	−37.4355	−1.42929
$687$	8.74338i	0.333581i
$688$	− 51.9562i	− 1.98081i
$689$	−10.1751	−0.387642
$690$	0	0
$691$	−8.14950	−0.310022	−0.155011	−	0.987913i	$-0.549541\pi$
$691$	−8.14950	−0.310022	−0.155011	+	0.987913i	$0.549541\pi$
$692$	33.3927i	1.26940i
$693$	1.43175i	0.0543877i
$694$	−14.3931	−0.546355
$695$	0	0
$696$	32.8072	1.24355
$697$	38.1323i	1.44436i
$698$	68.5082i	2.59307i
$699$	−2.17513	−0.0822712
$700$	0	0
$701$	−28.6921	−1.08369	−0.541843	−	0.840480i	$-0.682273\pi$
$701$	−28.6921	−1.08369	−0.541843	+	0.840480i	$0.682273\pi$
$702$	− 2.48929i	− 0.0939521i
$703$	54.3074i	2.04824i
$704$	−6.37123	−0.240125
$705$	0	0
$706$	71.5506	2.69284
$707$	− 12.3847i	− 0.465774i
$708$	− 22.5426i	− 0.847203i
$709$	−12.3074	−0.462215	−0.231108	−	0.972928i	$-0.574235\pi$
$709$	−12.3074	−0.462215	−0.231108	+	0.972928i	$0.574235\pi$
$710$	0	0
$711$	−1.78202	−0.0668310
$712$	55.6363i	2.08506i
$713$	− 12.4360i	− 0.465730i
$714$	18.3931	0.688345
$715$	0	0
$716$	−65.3154	−2.44095
$717$	2.80344i	0.104696i
$718$	31.3288i	1.16918i
$719$	28.7862	1.07355	0.536773	−	0.843727i	$-0.319643\pi$
$719$	28.7862	1.07355	0.536773	+	0.843727i	$0.319643\pi$
$720$	0	0
$721$	−22.4275	−0.835245
$722$	73.9332i	2.75151i
$723$	6.00000i	0.223142i
$724$	−66.2302	−2.46142
$725$	0	0
$726$	−23.8181	−0.883974
$727$	− 34.3931i	− 1.27557i	−0.770214	−	0.637785i	$-0.779851\pi$
$727$	− 34.3931i	− 1.27557i	0.770214	−	0.637785i	$-0.220149\pi$
$728$	6.54262i	0.242485i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−61.4868	−2.27417
$732$	52.7434i	1.94945i
$733$	− 29.0042i	− 1.07129i	−0.844442	−	0.535647i	$-0.820068\pi$
$733$	− 29.0042i	− 1.07129i	0.844442	−	0.535647i	$-0.179932\pi$
$734$	−69.4868	−2.56480
$735$	0	0
$736$	−8.57292	−0.316002
$737$	11.2138i	0.413065i
$738$	15.3717i	0.565840i
$739$	6.27804	0.230941	0.115471	−	0.993311i	$-0.463162\pi$
$739$	6.27804	0.230941	0.115471	+	0.993311i	$0.463162\pi$
$740$	0	0
$741$	−6.97858	−0.256364
$742$	− 30.3074i	− 1.11262i
$743$	12.2352i	0.448866i	0.974490	+	0.224433i	$0.0720529\pi$
$743$	12.2352i	0.448866i	−0.974490	+	0.224433i	$0.927947\pi$
$744$	16.2865	0.597091
$745$	0	0
$746$	5.85050	0.214202
$747$	5.37169i	0.196540i
$748$	− 31.0080i	− 1.13376i
$749$	−22.2180	−0.811827
$750$	0	0
$751$	−28.8757	−1.05369	−0.526844	−	0.849962i	$-0.676625\pi$
$751$	−28.8757	−1.05369	−0.526844	+	0.849962i	$0.676625\pi$
$752$	5.32976i	0.194357i
$753$	23.9143i	0.871486i
$754$	14.9357	0.543927
$755$	0	0
$756$	5.02142	0.182627
$757$	− 30.3503i	− 1.10310i	−0.834142	−	0.551550i	$-0.814037\pi$
$757$	− 30.3503i	− 1.10310i	0.834142	−	0.551550i	$-0.185963\pi$
$758$	− 61.1146i	− 2.21978i
$759$	−4.99579	−0.181336
$760$	0	0
$761$	−27.1709	−0.984945	−0.492473	−	0.870328i	$-0.663907\pi$
$761$	−27.1709	−0.984945	−0.492473	+	0.870328i	$0.663907\pi$
$762$	25.8715i	0.937224i
$763$	− 10.0428i	− 0.363575i
$764$	−45.0852	−1.63113
$765$	0	0
$766$	−14.4569	−0.522350
$767$	− 5.37169i	− 0.193961i
$768$	32.5678i	1.17519i
$769$	38.3503	1.38295	0.691473	−	0.722402i	$-0.256962\pi$
$769$	38.3503	1.38295	0.691473	+	0.722402i	$0.256962\pi$
$770$	0	0
$771$	19.9572	0.718739
$772$	− 40.8710i	− 1.47098i
$773$	− 50.2646i	− 1.80789i	−0.427647	−	0.903946i	$-0.640658\pi$
$773$	− 50.2646i	− 1.80789i	0.427647	−	0.903946i	$-0.359342\pi$
$774$	−24.7862	−0.890923
$775$	0	0
$776$	9.97812	0.358194
$777$	− 9.31163i	− 0.334053i
$778$	− 33.9781i	− 1.21817i
$779$	43.0937	1.54399
$780$	0	0
$781$	6.21798	0.222497
$782$	64.1789i	2.29503i
$783$	− 6.00000i	− 0.214423i
$784$	29.0550	1.03768
$785$	0	0
$786$	−15.9143	−0.567645
$787$	13.2860i	0.473595i	0.971559	+	0.236797i	$0.0760978\pi$
$787$	13.2860i	0.473595i	−0.971559	+	0.236797i	$0.923902\pi$
$788$	− 40.1360i	− 1.42979i
$789$	8.00000	0.284808
$790$	0	0
$791$	−9.52119	−0.338535
$792$	− 6.54262i	− 0.232482i
$793$	12.5682i	0.446312i
$794$	−30.2008	−1.07179
$795$	0	0
$796$	24.9995	0.886085
$797$	− 9.82487i	− 0.348015i	−0.984744	−	0.174007i	$-0.944328\pi$
$797$	− 9.82487i	− 0.348015i	0.984744	−	0.174007i	$-0.0556716\pi$
$798$	− 20.7862i	− 0.735825i
$799$	6.30742	0.223141
$800$	0	0
$801$	10.1751	0.359521
$802$	− 93.2087i	− 3.29131i
$803$	14.3074i	0.504898i
$804$	39.3288	1.38702
$805$	0	0
$806$	7.41454	0.261166
$807$	− 2.35027i	− 0.0827334i
$808$	56.5939i	1.99097i
$809$	9.91431	0.348569	0.174284	−	0.984695i	$-0.444239\pi$
$809$	9.91431	0.348569	0.174284	+	0.984695i	$0.444239\pi$
$810$	0	0
$811$	−36.5855	−1.28469	−0.642345	−	0.766416i	$-0.722038\pi$
$811$	−36.5855	−1.28469	−0.642345	+	0.766416i	$0.722038\pi$
$812$	30.1285i	1.05730i
$813$	− 10.9786i	− 0.385036i
$814$	−23.1793	−0.812436
$815$	0	0
$816$	−32.2217	−1.12799
$817$	69.4868i	2.43103i
$818$	34.8500i	1.21850i
$819$	1.19656	0.0418111
$820$	0	0
$821$	−34.4741	−1.20316	−0.601578	−	0.798814i	$-0.705461\pi$
$821$	−34.4741	−1.20316	−0.601578	+	0.798814i	$0.705461\pi$
$822$	− 41.6791i	− 1.45373i
$823$	13.2566i	0.462097i	0.972942	+	0.231048i	$0.0742155\pi$
$823$	13.2566i	0.462097i	−0.972942	+	0.231048i	$0.925784\pi$
$824$	102.486	3.57028
$825$	0	0
$826$	16.0000	0.556711
$827$	− 28.1495i	− 0.978854i	−0.872044	−	0.489427i	$-0.837206\pi$
$827$	− 28.1495i	− 0.978854i	0.872044	−	0.489427i	$-0.162794\pi$
$828$	17.5212i	0.608904i
$829$	−16.3418	−0.567576	−0.283788	−	0.958887i	$-0.591591\pi$
$829$	−16.3418	−0.567576	−0.283788	+	0.958887i	$0.591591\pi$
$830$	0	0
$831$	−1.21377	−0.0421052
$832$	5.32464i	0.184599i
$833$	− 34.3847i	− 1.19136i
$834$	−14.3931	−0.498393
$835$	0	0
$836$	−35.0424	−1.21197
$837$	− 2.97858i	− 0.102955i
$838$	− 7.91431i	− 0.273395i
$839$	30.3675	1.04840	0.524201	−	0.851595i	$-0.324364\pi$
$839$	30.3675	1.04840	0.524201	+	0.851595i	$0.324364\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	− 40.5939i	− 1.39896i
$843$	− 11.9572i	− 0.411826i
$844$	−100.358	−3.45446
$845$	0	0
$846$	2.54262	0.0874169
$847$	− 11.4490i	− 0.393391i
$848$	53.0937i	1.82324i
$849$	−29.8715	−1.02519
$850$	0	0
$851$	32.4910	1.11378
$852$	− 21.8077i	− 0.747118i
$853$	− 42.1407i	− 1.44287i	−0.692482	−	0.721435i	$-0.743483\pi$
$853$	− 42.1407i	− 1.44287i	0.692482	−	0.721435i	$-0.256517\pi$
$854$	−37.4355	−1.28102
$855$	0	0
$856$	101.529	3.47018
$857$	2.17513i	0.0743012i	0.999310	+	0.0371506i	$0.0118281\pi$
$857$	2.17513i	0.0743012i	−0.999310	+	0.0371506i	$0.988172\pi$
$858$	− 2.97858i	− 0.101687i
$859$	−18.5682	−0.633541	−0.316770	−	0.948502i	$-0.602598\pi$
$859$	−18.5682	−0.633541	−0.316770	+	0.948502i	$0.602598\pi$
$860$	0	0
$861$	−7.38890	−0.251813
$862$	11.4145i	0.388781i
$863$	33.7220i	1.14791i	0.818887	+	0.573954i	$0.194591\pi$
$863$	33.7220i	1.14791i	−0.818887	+	0.573954i	$0.805409\pi$
$864$	−2.05333	−0.0698556
$865$	0	0
$866$	95.4649	3.24403
$867$	21.1323i	0.717690i
$868$	14.9567i	0.507663i
$869$	−2.13229	−0.0723330
$870$	0	0
$871$	9.37169	0.317548
$872$	45.8924i	1.55411i
$873$	− 1.82487i	− 0.0617623i
$874$	72.5292	2.45334
$875$	0	0
$876$	50.1789	1.69539
$877$	− 43.4868i	− 1.46844i	−0.678910	−	0.734222i	$-0.737547\pi$
$877$	− 43.4868i	− 1.46844i	0.678910	−	0.734222i	$-0.262453\pi$
$878$	− 19.2650i	− 0.650164i
$879$	0.777809	0.0262348
$880$	0	0
$881$	26.7005	0.899564	0.449782	−	0.893138i	$-0.351502\pi$
$881$	26.7005	0.899564	0.449782	+	0.893138i	$0.351502\pi$
$882$	− 13.8610i	− 0.466724i
$883$	20.2990i	0.683116i	0.939861	+	0.341558i	$0.110955\pi$
$883$	20.2990i	0.683116i	−0.939861	+	0.341558i	$0.889045\pi$
$884$	−25.9143	−0.871593
$885$	0	0
$886$	−86.9223	−2.92021
$887$	− 36.0550i	− 1.21061i	−0.795994	−	0.605305i	$-0.793051\pi$
$887$	− 36.0550i	− 1.21061i	0.795994	−	0.605305i	$-0.206949\pi$
$888$	42.5510i	1.42792i
$889$	−12.4360	−0.417089
$890$	0	0
$891$	−1.19656	−0.0400862
$892$	− 11.0298i	− 0.369307i
$893$	− 7.12808i	− 0.238532i
$894$	−38.2008	−1.27762
$895$	0	0
$896$	−20.7737	−0.694000
$897$	4.17513i	0.139404i
$898$	15.3717i	0.512960i
$899$	17.8715	0.596047
$900$	0	0
$901$	62.8328	2.09326
$902$	18.3931i	0.612424i
$903$	− 11.9143i	− 0.396483i
$904$	43.5087	1.44708
$905$	0	0
$906$	−21.3717	−0.710027
$907$	7.26504i	0.241232i	0.992699	+	0.120616i	$0.0384869\pi$
$907$	7.26504i	0.241232i	−0.992699	+	0.120616i	$0.961513\pi$
$908$	66.1579i	2.19553i
$909$	10.3503	0.343297
$910$	0	0
$911$	−6.65769	−0.220579	−0.110290	−	0.993899i	$-0.535178\pi$
$911$	−6.65769	−0.220579	−0.110290	+	0.993899i	$0.535178\pi$
$912$	36.4141i	1.20579i
$913$	6.42754i	0.212721i
$914$	3.45738	0.114360
$915$	0	0
$916$	36.6921	1.21234
$917$	− 7.64973i	− 0.252616i
$918$	15.3717i	0.507341i
$919$	27.1831	0.896688	0.448344	−	0.893861i	$-0.352014\pi$
$919$	27.1831	0.896688	0.448344	+	0.893861i	$0.352014\pi$
$920$	0	0
$921$	−0.760597	−0.0250625
$922$	70.9013i	2.33501i
$923$	− 5.19656i	− 0.171047i
$924$	6.00842	0.197663
$925$	0	0
$926$	−40.7643	−1.33960
$927$	− 18.7434i	− 0.615614i
$928$	− 12.3200i	− 0.404423i
$929$	15.3973	0.505170	0.252585	−	0.967575i	$-0.418719\pi$
$929$	15.3973	0.505170	0.252585	+	0.967575i	$0.418719\pi$
$930$	0	0
$931$	−38.8585	−1.27353
$932$	9.12808i	0.299000i
$933$	23.1281i	0.757179i
$934$	64.0932	2.09719
$935$	0	0
$936$	−5.46787	−0.178723
$937$	− 1.12808i	− 0.0368527i	−0.999830	−	0.0184264i	$-0.994134\pi$
$937$	− 1.12808i	− 0.0368527i	0.999830	−	0.0184264i	$-0.00586562\pi$
$938$	27.9143i	0.911434i
$939$	−33.9143	−1.10675
$940$	0	0
$941$	−30.1407	−0.982559	−0.491280	−	0.871002i	$-0.663471\pi$
$941$	−30.1407	−0.982559	−0.491280	+	0.871002i	$0.663471\pi$
$942$	− 6.93573i	− 0.225978i
$943$	− 25.7820i	− 0.839578i
$944$	−28.0294	−0.912279
$945$	0	0
$946$	−29.6582	−0.964270
$947$	20.0294i	0.650868i	0.945565	+	0.325434i	$0.105510\pi$
$947$	20.0294i	0.650868i	−0.945565	+	0.325434i	$0.894490\pi$
$948$	7.47835i	0.242885i
$949$	11.9572	0.388146
$950$	0	0
$951$	−9.64973	−0.312914
$952$	− 40.4015i	− 1.30942i
$953$	− 43.2259i	− 1.40023i	−0.714032	−	0.700113i	$-0.753133\pi$
$953$	− 43.2259i	− 1.40023i	0.714032	−	0.700113i	$-0.246867\pi$
$954$	25.3288	0.820052
$955$	0	0
$956$	11.7648	0.380501
$957$	− 7.17935i	− 0.232075i
$958$	18.8929i	0.610401i
$959$	20.0344	0.646945
$960$	0	0
$961$	−22.1281	−0.713809
$962$	19.3717i	0.624568i
$963$	− 18.5682i	− 0.598353i
$964$	25.1793	0.810972
$965$	0	0
$966$	−12.4360	−0.400120
$967$	− 57.6875i	− 1.85511i	−0.373691	−	0.927553i	$-0.621908\pi$
$967$	− 57.6875i	− 1.85511i	0.373691	−	0.927553i	$-0.378092\pi$
$968$	52.3179i	1.68156i
$969$	43.0937	1.38437
$970$	0	0
$971$	−19.5296	−0.626735	−0.313368	−	0.949632i	$-0.601457\pi$
$971$	−19.5296	−0.626735	−0.313368	+	0.949632i	$0.601457\pi$
$972$	4.19656i	0.134605i
$973$	− 6.91852i	− 0.221798i
$974$	10.9786	0.351776
$975$	0	0
$976$	65.5809	2.09919
$977$	40.3074i	1.28955i	0.764373	+	0.644774i	$0.223049\pi$
$977$	40.3074i	1.28955i	−0.764373	+	0.644774i	$0.776951\pi$
$978$	21.8077i	0.697332i
$979$	12.1751	0.389119
$980$	0	0
$981$	8.39312	0.267972
$982$	− 0.213311i	− 0.00680702i
$983$	32.2008i	1.02705i	0.858076	+	0.513523i	$0.171660\pi$
$983$	32.2008i	1.02705i	−0.858076	+	0.513523i	$0.828340\pi$
$984$	33.7648	1.07638
$985$	0	0
$986$	−92.2302	−2.93721
$987$	1.22219i	0.0389028i
$988$	29.2860i	0.931712i
$989$	41.5725	1.32193
$990$	0	0
$991$	26.4826	0.841246	0.420623	−	0.907235i	$-0.361811\pi$
$991$	26.4826	0.841246	0.420623	+	0.907235i	$0.361811\pi$
$992$	− 6.11599i	− 0.194183i
$993$	− 15.3288i	− 0.486446i
$994$	15.4783	0.490943
$995$	0	0
$996$	22.5426	0.714290
$997$	− 35.1365i	− 1.11278i	−0.830920	−	0.556392i	$-0.812185\pi$
$997$	− 35.1365i	− 1.11278i	0.830920	−	0.556392i	$-0.187815\pi$
$998$	44.1151i	1.39644i
$999$	7.78202	0.246212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.c.i.274.5		6
3.2	odd	2		2925.2.c.w.2224.2		6
5.2	odd	4		195.2.a.e.1.1	✓	3
5.3	odd	4		975.2.a.o.1.3		3
5.4	even	2	inner	975.2.c.i.274.2		6
15.2	even	4		585.2.a.n.1.3		3
15.8	even	4		2925.2.a.bh.1.1		3
15.14	odd	2		2925.2.c.w.2224.5		6
20.7	even	4		3120.2.a.bj.1.2		3
35.27	even	4		9555.2.a.bq.1.1		3
60.47	odd	4		9360.2.a.dd.1.2		3
65.12	odd	4		2535.2.a.bc.1.3		3
195.77	even	4		7605.2.a.bx.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.1	✓	3	5.2	odd	4
585.2.a.n.1.3		3	15.2	even	4
975.2.a.o.1.3		3	5.3	odd	4
975.2.c.i.274.2		6	5.4	even	2	inner
975.2.c.i.274.5		6	1.1	even	1	trivial
2535.2.a.bc.1.3		3	65.12	odd	4
2925.2.a.bh.1.1		3	15.8	even	4
2925.2.c.w.2224.2		6	3.2	odd	2
2925.2.c.w.2224.5		6	15.14	odd	2
3120.2.a.bj.1.2		3	20.7	even	4
7605.2.a.bx.1.1		3	195.77	even	4
9360.2.a.dd.1.2		3	60.47	odd	4
9555.2.a.bq.1.1		3	35.27	even	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.48929i q^{2} -1.00000i q^{3} -4.19656 q^{4} +2.48929 q^{6} +1.19656i q^{7} -5.46787i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.48929i q^{2} -1.00000i q^{3} -4.19656 q^{4} +2.48929 q^{6} +1.19656i q^{7} -5.46787i q^{8} -1.00000 q^{9} -1.19656 q^{11} +4.19656i q^{12} +1.00000i q^{13} -2.97858 q^{14} +5.21798 q^{16} -6.17513i q^{17} -2.48929i q^{18} -6.97858 q^{19} +1.19656 q^{21} -2.97858i q^{22} +4.17513i q^{23} -5.46787 q^{24} -2.48929 q^{26} +1.00000i q^{27} -5.02142i q^{28} -6.00000 q^{29} -2.97858 q^{31} +2.05333i q^{32} +1.19656i q^{33} +15.3717 q^{34} +4.19656 q^{36} -7.78202i q^{37} -17.3717i q^{38} +1.00000 q^{39} -6.17513 q^{41} +2.97858i q^{42} -9.95715i q^{43} +5.02142 q^{44} -10.3931 q^{46} +1.02142i q^{47} -5.21798i q^{48} +5.56825 q^{49} -6.17513 q^{51} -4.19656i q^{52} +10.1751i q^{53} -2.48929 q^{54} +6.54262 q^{56} +6.97858i q^{57} -14.9357i q^{58} -5.37169 q^{59} +12.5682 q^{61} -7.41454i q^{62} -1.19656i q^{63} +5.32464 q^{64} -2.97858 q^{66} -9.37169i q^{67} +25.9143i q^{68} +4.17513 q^{69} -5.19656 q^{71} +5.46787i q^{72} -11.9572i q^{73} +19.3717 q^{74} +29.2860 q^{76} -1.43175i q^{77} +2.48929i q^{78} +1.78202 q^{79} +1.00000 q^{81} -15.3717i q^{82} -5.37169i q^{83} -5.02142 q^{84} +24.7862 q^{86} +6.00000i q^{87} +6.54262i q^{88} -10.1751 q^{89} -1.19656 q^{91} -17.5212i q^{92} +2.97858i q^{93} -2.54262 q^{94} +2.05333 q^{96} +1.82487i q^{97} +13.8610i q^{98} +1.19656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16 q^{4} - 6 q^{9}+O(q^{10}) \) 6 * q - 16 * q^4 - 6 * q^9	\( 6 q - 16 q^{4} - 6 q^{9} + 2 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} - 2 q^{21} + 12 q^{24} - 36 q^{29} + 12 q^{31} + 44 q^{34} + 16 q^{36} + 6 q^{39} + 2 q^{41} + 60 q^{44} - 44 q^{46} - 24 q^{49} + 2 q^{51} - 32 q^{56} + 16 q^{59} + 18 q^{61} - 60 q^{64} + 12 q^{66} - 14 q^{69} - 22 q^{71} + 68 q^{74} + 8 q^{76} - 10 q^{79} + 6 q^{81} - 60 q^{84} + 112 q^{86} - 22 q^{89} + 2 q^{91} + 56 q^{94} - 44 q^{96} - 2 q^{99}+O(q^{100}) \) 6 * q - 16 * q^4 - 6 * q^9 + 2 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 - 2 * q^21 + 12 * q^24 - 36 * q^29 + 12 * q^31 + 44 * q^34 + 16 * q^36 + 6 * q^39 + 2 * q^41 + 60 * q^44 - 44 * q^46 - 24 * q^49 + 2 * q^51 - 32 * q^56 + 16 * q^59 + 18 * q^61 - 60 * q^64 + 12 * q^66 - 14 * q^69 - 22 * q^71 + 68 * q^74 + 8 * q^76 - 10 * q^79 + 6 * q^81 - 60 * q^84 + 112 * q^86 - 22 * q^89 + 2 * q^91 + 56 * q^94 - 44 * q^96 - 2 * q^99

Introduction

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