LMFDB - Embedded newform 3525.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} - 15x^{2} + 1 $ x^7 - 3x^6 - 5x^5 + 18x^4 - 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.29479$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.29479 q^{2} +1.00000 q^{3} +3.26608 q^{4} +2.29479 q^{6} +4.13749 q^{7} +2.90540 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.29479 q^{2} +1.00000 q^{3} +3.26608 q^{4} +2.29479 q^{6} +4.13749 q^{7} +2.90540 q^{8} +1.00000 q^{9} -1.15116 q^{11} +3.26608 q^{12} -1.65535 q^{13} +9.49470 q^{14} +0.135126 q^{16} -1.91044 q^{17} +2.29479 q^{18} +1.91125 q^{19} +4.13749 q^{21} -2.64168 q^{22} +7.97869 q^{23} +2.90540 q^{24} -3.79869 q^{26} +1.00000 q^{27} +13.5134 q^{28} +5.49233 q^{29} -2.62677 q^{31} -5.50071 q^{32} -1.15116 q^{33} -4.38406 q^{34} +3.26608 q^{36} -0.593596 q^{37} +4.38592 q^{38} -1.65535 q^{39} +4.60898 q^{41} +9.49470 q^{42} +4.74023 q^{43} -3.75979 q^{44} +18.3095 q^{46} -1.00000 q^{47} +0.135126 q^{48} +10.1188 q^{49} -1.91044 q^{51} -5.40651 q^{52} -11.0099 q^{53} +2.29479 q^{54} +12.0211 q^{56} +1.91125 q^{57} +12.6038 q^{58} +9.87905 q^{59} -2.94523 q^{61} -6.02789 q^{62} +4.13749 q^{63} -12.8932 q^{64} -2.64168 q^{66} -1.04903 q^{67} -6.23965 q^{68} +7.97869 q^{69} -7.46017 q^{71} +2.90540 q^{72} -5.46152 q^{73} -1.36218 q^{74} +6.24228 q^{76} -4.76293 q^{77} -3.79869 q^{78} -15.6092 q^{79} +1.00000 q^{81} +10.5767 q^{82} +0.0744327 q^{83} +13.5134 q^{84} +10.8778 q^{86} +5.49233 q^{87} -3.34459 q^{88} -4.82156 q^{89} -6.84901 q^{91} +26.0591 q^{92} -2.62677 q^{93} -2.29479 q^{94} -5.50071 q^{96} +0.130495 q^{97} +23.2207 q^{98} -1.15116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

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 $

$2$	2.29479	1.62266	0.811332	−	0.584585i	$-0.198743\pi$
$2$	2.29479	1.62266	0.811332	+	0.584585i	$0.198743\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.26608	1.63304
$5$	0	0
$5$	0	0
$6$	2.29479	0.936846
$7$	4.13749	1.56383	0.781913	−	0.623388i	$-0.214244\pi$
$7$	4.13749	1.56383	0.781913	+	0.623388i	$0.214244\pi$
$8$	2.90540	1.02721
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.15116	−0.347089	−0.173544	−	0.984826i	$-0.555522\pi$
$11$	−1.15116	−0.347089	−0.173544	+	0.984826i	$0.555522\pi$
$12$	3.26608	0.942837
$13$	−1.65535	−0.459112	−0.229556	−	0.973295i	$-0.573727\pi$
$13$	−1.65535	−0.459112	−0.229556	+	0.973295i	$0.573727\pi$
$14$	9.49470	2.53756
$15$	0	0
$16$	0.135126	0.0337816
$17$	−1.91044	−0.463349	−0.231675	−	0.972793i	$-0.574421\pi$
$17$	−1.91044	−0.463349	−0.231675	+	0.972793i	$0.574421\pi$
$18$	2.29479	0.540888
$19$	1.91125	0.438470	0.219235	−	0.975672i	$-0.429644\pi$
$19$	1.91125	0.438470	0.219235	+	0.975672i	$0.429644\pi$
$20$	0	0
$21$	4.13749	0.902875
$22$	−2.64168	−0.563208
$23$	7.97869	1.66367	0.831836	−	0.555021i	$-0.187290\pi$
$23$	7.97869	1.66367	0.831836	+	0.555021i	$0.187290\pi$
$24$	2.90540	0.593062
$25$	0	0
$26$	−3.79869	−0.744985
$27$	1.00000	0.192450
$28$	13.5134	2.55379
$29$	5.49233	1.01990	0.509950	−	0.860204i	$-0.329664\pi$
$29$	5.49233	1.01990	0.509950	+	0.860204i	$0.329664\pi$
$30$	0	0
$31$	−2.62677	−0.471781	−0.235891	−	0.971780i	$-0.575801\pi$
$31$	−2.62677	−0.471781	−0.235891	+	0.971780i	$0.575801\pi$
$32$	−5.50071	−0.972397
$33$	−1.15116	−0.200392
$34$	−4.38406	−0.751861
$35$	0	0
$36$	3.26608	0.544347
$37$	−0.593596	−0.0975865	−0.0487933	−	0.998809i	$-0.515538\pi$
$37$	−0.593596	−0.0975865	−0.0487933	+	0.998809i	$0.515538\pi$
$38$	4.38592	0.711489
$39$	−1.65535	−0.265068
$40$	0	0
$41$	4.60898	0.719802	0.359901	−	0.932991i	$-0.382811\pi$
$41$	4.60898	0.719802	0.359901	+	0.932991i	$0.382811\pi$
$42$	9.49470	1.46506
$43$	4.74023	0.722878	0.361439	−	0.932396i	$-0.382286\pi$
$43$	4.74023	0.722878	0.361439	+	0.932396i	$0.382286\pi$
$44$	−3.75979	−0.566810
$45$	0	0
$46$	18.3095	2.69958
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	0.135126	0.0195038
$49$	10.1188	1.44555
$50$	0	0
$51$	−1.91044	−0.267515
$52$	−5.40651	−0.749749
$53$	−11.0099	−1.51232	−0.756162	−	0.654385i	$-0.772928\pi$
$53$	−11.0099	−1.51232	−0.756162	+	0.654385i	$0.772928\pi$
$54$	2.29479	0.312282
$55$	0	0
$56$	12.0211	1.60638
$57$	1.91125	0.253151
$58$	12.6038	1.65496
$59$	9.87905	1.28614	0.643071	−	0.765806i	$-0.277660\pi$
$59$	9.87905	1.28614	0.643071	+	0.765806i	$0.277660\pi$
$60$	0	0
$61$	−2.94523	−0.377098	−0.188549	−	0.982064i	$-0.560378\pi$
$61$	−2.94523	−0.377098	−0.188549	+	0.982064i	$0.560378\pi$
$62$	−6.02789	−0.765543
$63$	4.13749	0.521275
$64$	−12.8932	−1.61166
$65$	0	0
$66$	−2.64168	−0.325169
$67$	−1.04903	−0.128159	−0.0640797	−	0.997945i	$-0.520411\pi$
$67$	−1.04903	−0.128159	−0.0640797	+	0.997945i	$0.520411\pi$
$68$	−6.23965	−0.756669
$69$	7.97869	0.960522
$70$	0	0
$71$	−7.46017	−0.885359	−0.442679	−	0.896680i	$-0.645972\pi$
$71$	−7.46017	−0.885359	−0.442679	+	0.896680i	$0.645972\pi$
$72$	2.90540	0.342404
$73$	−5.46152	−0.639222	−0.319611	−	0.947549i	$-0.603552\pi$
$73$	−5.46152	−0.639222	−0.319611	+	0.947549i	$0.603552\pi$
$74$	−1.36218	−0.158350
$75$	0	0
$76$	6.24228	0.716039
$77$	−4.76293	−0.542786
$78$	−3.79869	−0.430117
$79$	−15.6092	−1.75617	−0.878086	−	0.478503i	$-0.841180\pi$
$79$	−15.6092	−1.75617	−0.878086	+	0.478503i	$0.841180\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.5767	1.16800
$83$	0.0744327	0.00817005	0.00408503	−	0.999992i	$-0.498700\pi$
$83$	0.0744327	0.00817005	0.00408503	+	0.999992i	$0.498700\pi$
$84$	13.5134	1.47443
$85$	0	0
$86$	10.8778	1.17299
$87$	5.49233	0.588839
$88$	−3.34459	−0.356534
$89$	−4.82156	−0.511084	−0.255542	−	0.966798i	$-0.582254\pi$
$89$	−4.82156	−0.511084	−0.255542	+	0.966798i	$0.582254\pi$
$90$	0	0
$91$	−6.84901	−0.717971
$92$	26.0591	2.71685
$93$	−2.62677	−0.272383
$94$	−2.29479	−0.236690
$95$	0	0
$96$	−5.50071	−0.561414
$97$	0.130495	0.0132498	0.00662488	−	0.999978i	$-0.497891\pi$
$97$	0.130495	0.0132498	0.00662488	+	0.999978i	$0.497891\pi$
$98$	23.2207	2.34564
$99$	−1.15116	−0.115696
$100$	0	0
$101$	12.8291	1.27654	0.638271	−	0.769812i	$-0.279650\pi$
$101$	12.8291	1.27654	0.638271	+	0.769812i	$0.279650\pi$
$102$	−4.38406	−0.434087
$103$	0.690290	0.0680163	0.0340081	−	0.999422i	$-0.489173\pi$
$103$	0.690290	0.0680163	0.0340081	+	0.999422i	$0.489173\pi$
$104$	−4.80946	−0.471606
$105$	0	0
$106$	−25.2654	−2.45399
$107$	−16.1099	−1.55740	−0.778700	−	0.627397i	$-0.784120\pi$
$107$	−16.1099	−1.55740	−0.778700	+	0.627397i	$0.784120\pi$
$108$	3.26608	0.314279
$109$	8.82586	0.845364	0.422682	−	0.906278i	$-0.361089\pi$
$109$	8.82586	0.845364	0.422682	+	0.906278i	$0.361089\pi$
$110$	0	0
$111$	−0.593596	−0.0563416
$112$	0.559084	0.0528285
$113$	16.1288	1.51727	0.758637	−	0.651513i	$-0.225866\pi$
$113$	16.1288	1.51727	0.758637	+	0.651513i	$0.225866\pi$
$114$	4.38592	0.410779
$115$	0	0
$116$	17.9384	1.66554
$117$	−1.65535	−0.153037
$118$	22.6704	2.08698
$119$	−7.90443	−0.724598
$120$	0	0
$121$	−9.67482	−0.879529
$122$	−6.75870	−0.611904
$123$	4.60898	0.415578
$124$	−8.57923	−0.770438
$125$	0	0
$126$	9.49470	0.845855
$127$	−7.58953	−0.673462	−0.336731	−	0.941601i	$-0.609321\pi$
$127$	−7.58953	−0.673462	−0.336731	+	0.941601i	$0.609321\pi$
$128$	−18.5859	−1.64278
$129$	4.74023	0.417354
$130$	0	0
$131$	3.76878	0.329279	0.164640	−	0.986354i	$-0.447354\pi$
$131$	3.76878	0.329279	0.164640	+	0.986354i	$0.447354\pi$
$132$	−3.75979	−0.327248
$133$	7.90776	0.685690
$134$	−2.40731	−0.207960
$135$	0	0
$136$	−5.55058	−0.475959
$137$	−4.49146	−0.383732	−0.191866	−	0.981421i	$-0.561454\pi$
$137$	−4.49146	−0.383732	−0.191866	+	0.981421i	$0.561454\pi$
$138$	18.3095	1.55861
$139$	−4.04243	−0.342874	−0.171437	−	0.985195i	$-0.554841\pi$
$139$	−4.04243	−0.342874	−0.171437	+	0.985195i	$0.554841\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−17.1195	−1.43664
$143$	1.90558	0.159353
$144$	0.135126	0.0112605
$145$	0	0
$146$	−12.5331	−1.03724
$147$	10.1188	0.834588
$148$	−1.93873	−0.159363
$149$	7.67156	0.628479	0.314239	−	0.949344i	$-0.398251\pi$
$149$	7.67156	0.628479	0.314239	+	0.949344i	$0.398251\pi$
$150$	0	0
$151$	−11.7425	−0.955589	−0.477795	−	0.878472i	$-0.658564\pi$
$151$	−11.7425	−0.955589	−0.477795	+	0.878472i	$0.658564\pi$
$152$	5.55293	0.450402
$153$	−1.91044	−0.154450
$154$	−10.9299	−0.880760
$155$	0	0
$156$	−5.40651	−0.432868
$157$	−19.0132	−1.51742	−0.758708	−	0.651431i	$-0.774169\pi$
$157$	−19.0132	−1.51742	−0.758708	+	0.651431i	$0.774169\pi$
$158$	−35.8199	−2.84968
$159$	−11.0099	−0.873140
$160$	0	0
$161$	33.0118	2.60169
$162$	2.29479	0.180296
$163$	−7.46253	−0.584511	−0.292255	−	0.956340i	$-0.594406\pi$
$163$	−7.46253	−0.584511	−0.292255	+	0.956340i	$0.594406\pi$
$164$	15.0533	1.17547
$165$	0	0
$166$	0.170808	0.0132573
$167$	−14.8517	−1.14926	−0.574631	−	0.818413i	$-0.694854\pi$
$167$	−14.8517	−1.14926	−0.574631	+	0.818413i	$0.694854\pi$
$168$	12.0211	0.927445
$169$	−10.2598	−0.789216
$170$	0	0
$171$	1.91125	0.146157
$172$	15.4820	1.18049
$173$	−6.57287	−0.499726	−0.249863	−	0.968281i	$-0.580386\pi$
$173$	−6.57287	−0.499726	−0.249863	+	0.968281i	$0.580386\pi$
$174$	12.6038	0.955489
$175$	0	0
$176$	−0.155552	−0.0117252
$177$	9.87905	0.742555
$178$	−11.0645	−0.829318
$179$	−16.5288	−1.23542	−0.617712	−	0.786405i	$-0.711940\pi$
$179$	−16.5288	−1.23542	−0.617712	+	0.786405i	$0.711940\pi$
$180$	0	0
$181$	−20.3114	−1.50973	−0.754867	−	0.655878i	$-0.772299\pi$
$181$	−20.3114	−1.50973	−0.754867	+	0.655878i	$0.772299\pi$
$182$	−15.7171	−1.16503
$183$	−2.94523	−0.217718
$184$	23.1813	1.70895
$185$	0	0
$186$	−6.02789	−0.441986
$187$	2.19923	0.160823
$188$	−3.26608	−0.238203
$189$	4.13749	0.300958
$190$	0	0
$191$	22.4408	1.62376	0.811880	−	0.583824i	$-0.198444\pi$
$191$	22.4408	1.62376	0.811880	+	0.583824i	$0.198444\pi$
$192$	−12.8932	−0.930490
$193$	16.9425	1.21955	0.609775	−	0.792575i	$-0.291260\pi$
$193$	16.9425	1.21955	0.609775	+	0.792575i	$0.291260\pi$
$194$	0.299459	0.0214999
$195$	0	0
$196$	33.0490	2.36064
$197$	2.54134	0.181063	0.0905315	−	0.995894i	$-0.471143\pi$
$197$	2.54134	0.181063	0.0905315	+	0.995894i	$0.471143\pi$
$198$	−2.64168	−0.187736
$199$	15.0637	1.06783	0.533917	−	0.845537i	$-0.320719\pi$
$199$	15.0637	1.06783	0.533917	+	0.845537i	$0.320719\pi$
$200$	0	0
$201$	−1.04903	−0.0739928
$202$	29.4401	2.07140
$203$	22.7245	1.59495
$204$	−6.23965	−0.436863
$205$	0	0
$206$	1.58407	0.110368
$207$	7.97869	0.554558
$208$	−0.223682	−0.0155095
$209$	−2.20015	−0.152188
$210$	0	0
$211$	−7.60248	−0.523377	−0.261688	−	0.965152i	$-0.584279\pi$
$211$	−7.60248	−0.523377	−0.261688	+	0.965152i	$0.584279\pi$
$212$	−35.9592	−2.46969
$213$	−7.46017	−0.511162
$214$	−36.9688	−2.52714
$215$	0	0
$216$	2.90540	0.197687
$217$	−10.8682	−0.737783
$218$	20.2535	1.37174
$219$	−5.46152	−0.369055
$220$	0	0
$221$	3.16245	0.212729
$222$	−1.36218	−0.0914235
$223$	−0.674989	−0.0452006	−0.0226003	−	0.999745i	$-0.507195\pi$
$223$	−0.674989	−0.0452006	−0.0226003	+	0.999745i	$0.507195\pi$
$224$	−22.7591	−1.52066
$225$	0	0
$226$	37.0124	2.46203
$227$	18.2609	1.21202	0.606010	−	0.795457i	$-0.292769\pi$
$227$	18.2609	1.21202	0.606010	+	0.795457i	$0.292769\pi$
$228$	6.24228	0.413405
$229$	13.5615	0.896172	0.448086	−	0.893990i	$-0.352106\pi$
$229$	13.5615	0.896172	0.448086	+	0.893990i	$0.352106\pi$
$230$	0	0
$231$	−4.76293	−0.313378
$232$	15.9574	1.04765
$233$	13.1243	0.859799	0.429899	−	0.902877i	$-0.358549\pi$
$233$	13.1243	0.859799	0.429899	+	0.902877i	$0.358549\pi$
$234$	−3.79869	−0.248328
$235$	0	0
$236$	32.2658	2.10032
$237$	−15.6092	−1.01393
$238$	−18.1390	−1.17578
$239$	0.864929	0.0559476	0.0279738	−	0.999609i	$-0.491095\pi$
$239$	0.864929	0.0559476	0.0279738	+	0.999609i	$0.491095\pi$
$240$	0	0
$241$	−25.8090	−1.66251	−0.831253	−	0.555895i	$-0.812376\pi$
$241$	−25.8090	−1.66251	−0.831253	+	0.555895i	$0.812376\pi$
$242$	−22.2017	−1.42718
$243$	1.00000	0.0641500
$244$	−9.61937	−0.615817
$245$	0	0
$246$	10.5767	0.674343
$247$	−3.16378	−0.201307
$248$	−7.63180	−0.484620
$249$	0.0744327	0.00471698
$250$	0	0
$251$	18.7792	1.18533	0.592665	−	0.805449i	$-0.298076\pi$
$251$	18.7792	1.18533	0.592665	+	0.805449i	$0.298076\pi$
$252$	13.5134	0.851263
$253$	−9.18478	−0.577442
$254$	−17.4164	−1.09280
$255$	0	0
$256$	−16.8644	−1.05403
$257$	−13.4433	−0.838568	−0.419284	−	0.907855i	$-0.637719\pi$
$257$	−13.4433	−0.838568	−0.419284	+	0.907855i	$0.637719\pi$
$258$	10.8778	0.677225
$259$	−2.45600	−0.152608
$260$	0	0
$261$	5.49233	0.339967
$262$	8.64856	0.534310
$263$	−4.71811	−0.290931	−0.145466	−	0.989363i	$-0.546468\pi$
$263$	−4.71811	−0.290931	−0.145466	+	0.989363i	$0.546468\pi$
$264$	−3.34459	−0.205845
$265$	0	0
$266$	18.1467	1.11265
$267$	−4.82156	−0.295075
$268$	−3.42621	−0.209289
$269$	1.03149	0.0628914	0.0314457	−	0.999505i	$-0.489989\pi$
$269$	1.03149	0.0628914	0.0314457	+	0.999505i	$0.489989\pi$
$270$	0	0
$271$	−11.9508	−0.725961	−0.362981	−	0.931797i	$-0.618241\pi$
$271$	−11.9508	−0.725961	−0.362981	+	0.931797i	$0.618241\pi$
$272$	−0.258151	−0.0156527
$273$	−6.84901	−0.414521
$274$	−10.3070	−0.622668
$275$	0	0
$276$	26.0591	1.56857
$277$	10.5209	0.632140	0.316070	−	0.948736i	$-0.397637\pi$
$277$	10.5209	0.632140	0.316070	+	0.948736i	$0.397637\pi$
$278$	−9.27654	−0.556370
$279$	−2.62677	−0.157260
$280$	0	0
$281$	−14.6406	−0.873385	−0.436692	−	0.899611i	$-0.643850\pi$
$281$	−14.6406	−0.873385	−0.436692	+	0.899611i	$0.643850\pi$
$282$	−2.29479	−0.136653
$283$	13.2603	0.788245	0.394123	−	0.919058i	$-0.371049\pi$
$283$	13.2603	0.788245	0.394123	+	0.919058i	$0.371049\pi$
$284$	−24.3655	−1.44583
$285$	0	0
$286$	4.37291	0.258576
$287$	19.0696	1.12564
$288$	−5.50071	−0.324132
$289$	−13.3502	−0.785307
$290$	0	0
$291$	0.130495	0.00764975
$292$	−17.8378	−1.04388
$293$	29.3890	1.71692	0.858462	−	0.512877i	$-0.171420\pi$
$293$	29.3890	1.71692	0.858462	+	0.512877i	$0.171420\pi$
$294$	23.2207	1.35426
$295$	0	0
$296$	−1.72463	−0.100242
$297$	−1.15116	−0.0667972
$298$	17.6047	1.01981
$299$	−13.2075	−0.763812
$300$	0	0
$301$	19.6127	1.13045
$302$	−26.9466	−1.55060
$303$	12.8291	0.737012
$304$	0.258260	0.0148122
$305$	0	0
$306$	−4.38406	−0.250620
$307$	−10.9311	−0.623873	−0.311936	−	0.950103i	$-0.600978\pi$
$307$	−10.9311	−0.623873	−0.311936	+	0.950103i	$0.600978\pi$
$308$	−15.5561	−0.886392
$309$	0.690290	0.0392692
$310$	0	0
$311$	1.95767	0.111009	0.0555047	−	0.998458i	$-0.482323\pi$
$311$	1.95767	0.111009	0.0555047	+	0.998458i	$0.482323\pi$
$312$	−4.80946	−0.272282
$313$	18.5888	1.05070	0.525352	−	0.850885i	$-0.323934\pi$
$313$	18.5888	1.05070	0.525352	+	0.850885i	$0.323934\pi$
$314$	−43.6313	−2.46226
$315$	0	0
$316$	−50.9809	−2.86790
$317$	20.4255	1.14721	0.573604	−	0.819133i	$-0.305545\pi$
$317$	20.4255	1.14721	0.573604	+	0.819133i	$0.305545\pi$
$318$	−25.2654	−1.41681
$319$	−6.32256	−0.353996
$320$	0	0
$321$	−16.1099	−0.899165
$322$	75.7553	4.22168
$323$	−3.65132	−0.203165
$324$	3.26608	0.181449
$325$	0	0
$326$	−17.1250	−0.948465
$327$	8.82586	0.488071
$328$	13.3909	0.739390
$329$	−4.13749	−0.228107
$330$	0	0
$331$	−15.8647	−0.872001	−0.436000	−	0.899946i	$-0.643605\pi$
$331$	−15.8647	−0.872001	−0.436000	+	0.899946i	$0.643605\pi$
$332$	0.243103	0.0133420
$333$	−0.593596	−0.0325288
$334$	−34.0817	−1.86487
$335$	0	0
$336$	0.559084	0.0305005
$337$	33.8640	1.84469	0.922345	−	0.386366i	$-0.126270\pi$
$337$	33.8640	1.84469	0.922345	+	0.386366i	$0.126270\pi$
$338$	−23.5442	−1.28063
$339$	16.1288	0.875999
$340$	0	0
$341$	3.02384	0.163750
$342$	4.38592	0.237163
$343$	12.9042	0.696761
$344$	13.7722	0.742550
$345$	0	0
$346$	−15.0834	−0.810888
$347$	−3.95468	−0.212298	−0.106149	−	0.994350i	$-0.533852\pi$
$347$	−3.95468	−0.212298	−0.106149	+	0.994350i	$0.533852\pi$
$348$	17.9384	0.961599
$349$	24.6725	1.32069	0.660343	−	0.750964i	$-0.270411\pi$
$349$	24.6725	1.32069	0.660343	+	0.750964i	$0.270411\pi$
$350$	0	0
$351$	−1.65535	−0.0883562
$352$	6.33221	0.337508
$353$	17.5879	0.936111	0.468056	−	0.883699i	$-0.344955\pi$
$353$	17.5879	0.936111	0.468056	+	0.883699i	$0.344955\pi$
$354$	22.6704	1.20492
$355$	0	0
$356$	−15.7476	−0.834621
$357$	−7.90443	−0.418347
$358$	−37.9303	−2.00468
$359$	−15.8948	−0.838893	−0.419446	−	0.907780i	$-0.637776\pi$
$359$	−15.8948	−0.838893	−0.419446	+	0.907780i	$0.637776\pi$
$360$	0	0
$361$	−15.3471	−0.807744
$362$	−46.6105	−2.44979
$363$	−9.67482	−0.507797
$364$	−22.3694	−1.17248
$365$	0	0
$366$	−6.75870	−0.353283
$367$	35.8929	1.87360	0.936798	−	0.349871i	$-0.113775\pi$
$367$	35.8929	1.87360	0.936798	+	0.349871i	$0.113775\pi$
$368$	1.07813	0.0562015
$369$	4.60898	0.239934
$370$	0	0
$371$	−45.5533	−2.36501
$372$	−8.57923	−0.444812
$373$	−20.8693	−1.08057	−0.540286	−	0.841481i	$-0.681684\pi$
$373$	−20.8693	−1.08057	−0.540286	+	0.841481i	$0.681684\pi$
$374$	5.04677	0.260962
$375$	0	0
$376$	−2.90540	−0.149834
$377$	−9.09174	−0.468248
$378$	9.49470	0.488354
$379$	−32.9750	−1.69381	−0.846905	−	0.531744i	$-0.821537\pi$
$379$	−32.9750	−1.69381	−0.846905	+	0.531744i	$0.821537\pi$
$380$	0	0
$381$	−7.58953	−0.388823
$382$	51.4971	2.63482
$383$	−6.66448	−0.340539	−0.170270	−	0.985398i	$-0.554464\pi$
$383$	−6.66448	−0.340539	−0.170270	+	0.985398i	$0.554464\pi$
$384$	−18.5859	−0.948460
$385$	0	0
$386$	38.8796	1.97892
$387$	4.74023	0.240959
$388$	0.426207	0.0216374
$389$	17.5033	0.887454	0.443727	−	0.896162i	$-0.353656\pi$
$389$	17.5033	0.887454	0.443727	+	0.896162i	$0.353656\pi$
$390$	0	0
$391$	−15.2428	−0.770862
$392$	29.3993	1.48489
$393$	3.76878	0.190110
$394$	5.83186	0.293805
$395$	0	0
$396$	−3.75979	−0.188937
$397$	8.77499	0.440404	0.220202	−	0.975454i	$-0.429328\pi$
$397$	8.77499	0.440404	0.220202	+	0.975454i	$0.429328\pi$
$398$	34.5680	1.73274
$399$	7.90776	0.395883
$400$	0	0
$401$	−16.8348	−0.840688	−0.420344	−	0.907365i	$-0.638091\pi$
$401$	−16.8348	−0.840688	−0.420344	+	0.907365i	$0.638091\pi$
$402$	−2.40731	−0.120066
$403$	4.34822	0.216600
$404$	41.9009	2.08465
$405$	0	0
$406$	52.1480	2.58806
$407$	0.683325	0.0338712
$408$	−5.55058	−0.274795
$409$	28.8799	1.42802	0.714010	−	0.700136i	$-0.246877\pi$
$409$	28.8799	1.42802	0.714010	+	0.700136i	$0.246877\pi$
$410$	0	0
$411$	−4.49146	−0.221547
$412$	2.25454	0.111073
$413$	40.8745	2.01130
$414$	18.3095	0.899861
$415$	0	0
$416$	9.10561	0.446439
$417$	−4.04243	−0.197959
$418$	−5.04890	−0.246950
$419$	12.1564	0.593880	0.296940	−	0.954896i	$-0.404034\pi$
$419$	12.1564	0.593880	0.296940	+	0.954896i	$0.404034\pi$
$420$	0	0
$421$	−24.1097	−1.17504	−0.587518	−	0.809211i	$-0.699895\pi$
$421$	−24.1097	−1.17504	−0.587518	+	0.809211i	$0.699895\pi$
$422$	−17.4461	−0.849265
$423$	−1.00000	−0.0486217
$424$	−31.9881	−1.55348
$425$	0	0
$426$	−17.1195	−0.829445
$427$	−12.1859	−0.589716
$428$	−52.6161	−2.54330
$429$	1.90558	0.0920022
$430$	0	0
$431$	−32.5833	−1.56948	−0.784740	−	0.619825i	$-0.787204\pi$
$431$	−32.5833	−1.56948	−0.784740	+	0.619825i	$0.787204\pi$
$432$	0.135126	0.00650127
$433$	−14.9966	−0.720689	−0.360345	−	0.932819i	$-0.617341\pi$
$433$	−14.9966	−0.720689	−0.360345	+	0.932819i	$0.617341\pi$
$434$	−24.9403	−1.19717
$435$	0	0
$436$	28.8260	1.38051
$437$	15.2492	0.729470
$438$	−12.5331	−0.598853
$439$	10.8565	0.518154	0.259077	−	0.965857i	$-0.416582\pi$
$439$	10.8565	0.518154	0.259077	+	0.965857i	$0.416582\pi$
$440$	0	0
$441$	10.1188	0.481850
$442$	7.25717	0.345188
$443$	1.51860	0.0721507	0.0360754	−	0.999349i	$-0.488514\pi$
$443$	1.51860	0.0721507	0.0360754	+	0.999349i	$0.488514\pi$
$444$	−1.93873	−0.0920081
$445$	0	0
$446$	−1.54896	−0.0733454
$447$	7.67156	0.362852
$448$	−53.3457	−2.52035
$449$	−25.9022	−1.22240	−0.611200	−	0.791476i	$-0.709313\pi$
$449$	−25.9022	−1.22240	−0.611200	+	0.791476i	$0.709313\pi$
$450$	0	0
$451$	−5.30569	−0.249835
$452$	52.6781	2.47777
$453$	−11.7425	−0.551710
$454$	41.9051	1.96670
$455$	0	0
$456$	5.55293	0.260040
$457$	5.36133	0.250792	0.125396	−	0.992107i	$-0.459980\pi$
$457$	5.36133	0.250792	0.125396	+	0.992107i	$0.459980\pi$
$458$	31.1210	1.45419
$459$	−1.91044	−0.0891716
$460$	0	0
$461$	−40.0912	−1.86723	−0.933616	−	0.358276i	$-0.883365\pi$
$461$	−40.0912	−1.86723	−0.933616	+	0.358276i	$0.883365\pi$
$462$	−10.9299	−0.508507
$463$	−7.21087	−0.335117	−0.167559	−	0.985862i	$-0.553588\pi$
$463$	−7.21087	−0.335117	−0.167559	+	0.985862i	$0.553588\pi$
$464$	0.742158	0.0344538
$465$	0	0
$466$	30.1175	1.39517
$467$	27.0558	1.25199	0.625996	−	0.779826i	$-0.284692\pi$
$467$	27.0558	1.25199	0.625996	+	0.779826i	$0.284692\pi$
$468$	−5.40651	−0.249916
$469$	−4.34035	−0.200419
$470$	0	0
$471$	−19.0132	−0.876081
$472$	28.7026	1.32114
$473$	−5.45677	−0.250903
$474$	−35.8199	−1.64526
$475$	0	0
$476$	−25.8165	−1.18330
$477$	−11.0099	−0.504108
$478$	1.98483	0.0907842
$479$	−17.7240	−0.809832	−0.404916	−	0.914354i	$-0.632699\pi$
$479$	−17.7240	−0.809832	−0.404916	+	0.914354i	$0.632699\pi$
$480$	0	0
$481$	0.982610	0.0448032
$482$	−59.2264	−2.69769
$483$	33.0118	1.50209
$484$	−31.5988	−1.43631
$485$	0	0
$486$	2.29479	0.104094
$487$	−28.7334	−1.30203	−0.651017	−	0.759063i	$-0.725657\pi$
$487$	−28.7334	−1.30203	−0.651017	+	0.759063i	$0.725657\pi$
$488$	−8.55707	−0.387360
$489$	−7.46253	−0.337467
$490$	0	0
$491$	−16.5412	−0.746496	−0.373248	−	0.927732i	$-0.621756\pi$
$491$	−16.5412	−0.746496	−0.373248	+	0.927732i	$0.621756\pi$
$492$	15.0533	0.678655
$493$	−10.4928	−0.472570
$494$	−7.26023	−0.326653
$495$	0	0
$496$	−0.354945	−0.0159375
$497$	−30.8664	−1.38455
$498$	0.170808	0.00765408
$499$	9.30401	0.416505	0.208252	−	0.978075i	$-0.433222\pi$
$499$	9.30401	0.416505	0.208252	+	0.978075i	$0.433222\pi$
$500$	0	0
$501$	−14.8517	−0.663526
$502$	43.0943	1.92339
$503$	−0.402288	−0.0179371	−0.00896857	−	0.999960i	$-0.502855\pi$
$503$	−0.402288	−0.0179371	−0.00896857	+	0.999960i	$0.502855\pi$
$504$	12.0211	0.535461
$505$	0	0
$506$	−21.0772	−0.936995
$507$	−10.2598	−0.455654
$508$	−24.7880	−1.09979
$509$	−17.6735	−0.783364	−0.391682	−	0.920101i	$-0.628107\pi$
$509$	−17.6735	−0.783364	−0.391682	+	0.920101i	$0.628107\pi$
$510$	0	0
$511$	−22.5970	−0.999631
$512$	−1.52848	−0.0675500
$513$	1.91125	0.0843835
$514$	−30.8495	−1.36071
$515$	0	0
$516$	15.4820	0.681556
$517$	1.15116	0.0506281
$518$	−5.63601	−0.247632
$519$	−6.57287	−0.288517
$520$	0	0
$521$	−32.9012	−1.44143	−0.720714	−	0.693232i	$-0.756186\pi$
$521$	−32.9012	−1.44143	−0.720714	+	0.693232i	$0.756186\pi$
$522$	12.6038	0.551652
$523$	−17.8755	−0.781639	−0.390820	−	0.920467i	$-0.627808\pi$
$523$	−17.8755	−0.781639	−0.390820	+	0.920467i	$0.627808\pi$
$524$	12.3091	0.537727
$525$	0	0
$526$	−10.8271	−0.472084
$527$	5.01828	0.218600
$528$	−0.155552	−0.00676955
$529$	40.6596	1.76781
$530$	0	0
$531$	9.87905	0.428714
$532$	25.8274	1.11976
$533$	−7.62948	−0.330470
$534$	−11.0645	−0.478807
$535$	0	0
$536$	−3.04785	−0.131647
$537$	−16.5288	−0.713272
$538$	2.36707	0.102052
$539$	−11.6484	−0.501734
$540$	0	0
$541$	32.3233	1.38969	0.694844	−	0.719161i	$-0.255474\pi$
$541$	32.3233	1.38969	0.694844	+	0.719161i	$0.255474\pi$
$542$	−27.4247	−1.17799
$543$	−20.3114	−0.871646
$544$	10.5088	0.450560
$545$	0	0
$546$	−15.7171	−0.672628
$547$	−20.1941	−0.863436	−0.431718	−	0.902009i	$-0.642092\pi$
$547$	−20.1941	−0.863436	−0.431718	+	0.902009i	$0.642092\pi$
$548$	−14.6695	−0.626649
$549$	−2.94523	−0.125699
$550$	0	0
$551$	10.4972	0.447195
$552$	23.1813	0.986661
$553$	−64.5829	−2.74635
$554$	24.1433	1.02575
$555$	0	0
$556$	−13.2029	−0.559928
$557$	−6.14902	−0.260542	−0.130271	−	0.991478i	$-0.541585\pi$
$557$	−6.14902	−0.260542	−0.130271	+	0.991478i	$0.541585\pi$
$558$	−6.02789	−0.255181
$559$	−7.84674	−0.331882
$560$	0	0
$561$	2.19923	0.0928514
$562$	−33.5972	−1.41721
$563$	7.39249	0.311556	0.155778	−	0.987792i	$-0.450212\pi$
$563$	7.39249	0.311556	0.155778	+	0.987792i	$0.450212\pi$
$564$	−3.26608	−0.137527
$565$	0	0
$566$	30.4297	1.27906
$567$	4.13749	0.173758
$568$	−21.6747	−0.909452
$569$	−1.58287	−0.0663574	−0.0331787	−	0.999449i	$-0.510563\pi$
$569$	−1.58287	−0.0663574	−0.0331787	+	0.999449i	$0.510563\pi$
$570$	0	0
$571$	−26.7402	−1.11904	−0.559522	−	0.828815i	$-0.689015\pi$
$571$	−26.7402	−1.11904	−0.559522	+	0.828815i	$0.689015\pi$
$572$	6.22378	0.260229
$573$	22.4408	0.937479
$574$	43.7609	1.82654
$575$	0	0
$576$	−12.8932	−0.537219
$577$	39.1583	1.63018	0.815090	−	0.579334i	$-0.196687\pi$
$577$	39.1583	1.63018	0.815090	+	0.579334i	$0.196687\pi$
$578$	−30.6360	−1.27429
$579$	16.9425	0.704107
$580$	0	0
$581$	0.307965	0.0127765
$582$	0.299459	0.0124130
$583$	12.6742	0.524910
$584$	−15.8679	−0.656617
$585$	0	0
$586$	67.4417	2.78599
$587$	16.2055	0.668873	0.334437	−	0.942418i	$-0.391454\pi$
$587$	16.2055	0.668873	0.334437	+	0.942418i	$0.391454\pi$
$588$	33.0490	1.36292
$589$	−5.02039	−0.206862
$590$	0	0
$591$	2.54134	0.104537
$592$	−0.0802104	−0.00329663
$593$	7.42723	0.305000	0.152500	−	0.988304i	$-0.451268\pi$
$593$	7.42723	0.305000	0.152500	+	0.988304i	$0.451268\pi$
$594$	−2.64168	−0.108390
$595$	0	0
$596$	25.0559	1.02633
$597$	15.0637	0.616515
$598$	−30.3086	−1.23941
$599$	35.4456	1.44827	0.724135	−	0.689659i	$-0.242239\pi$
$599$	35.4456	1.44827	0.724135	+	0.689659i	$0.242239\pi$
$600$	0	0
$601$	−43.0383	−1.75557	−0.877784	−	0.479057i	$-0.840979\pi$
$601$	−43.0383	−1.75557	−0.877784	+	0.479057i	$0.840979\pi$
$602$	45.0070	1.83435
$603$	−1.04903	−0.0427198
$604$	−38.3519	−1.56052
$605$	0	0
$606$	29.4401	1.19592
$607$	−17.7735	−0.721406	−0.360703	−	0.932681i	$-0.617463\pi$
$607$	−17.7735	−0.721406	−0.360703	+	0.932681i	$0.617463\pi$
$608$	−10.5132	−0.426367
$609$	22.7245	0.920842
$610$	0	0
$611$	1.65535	0.0669684
$612$	−6.23965	−0.252223
$613$	15.8293	0.639339	0.319669	−	0.947529i	$-0.396428\pi$
$613$	15.8293	0.639339	0.319669	+	0.947529i	$0.396428\pi$
$614$	−25.0847	−1.01234
$615$	0	0
$616$	−13.8382	−0.557557
$617$	3.52239	0.141806	0.0709031	−	0.997483i	$-0.477412\pi$
$617$	3.52239	0.141806	0.0709031	+	0.997483i	$0.477412\pi$
$618$	1.58407	0.0637208
$619$	−37.2163	−1.49585	−0.747925	−	0.663784i	$-0.768950\pi$
$619$	−37.2163	−1.49585	−0.747925	+	0.663784i	$0.768950\pi$
$620$	0	0
$621$	7.97869	0.320174
$622$	4.49245	0.180131
$623$	−19.9492	−0.799246
$624$	−0.223682	−0.00895443
$625$	0	0
$626$	42.6576	1.70494
$627$	−2.20015	−0.0878657
$628$	−62.0986	−2.47800
$629$	1.13403	0.0452167
$630$	0	0
$631$	37.5194	1.49362	0.746812	−	0.665035i	$-0.231583\pi$
$631$	37.5194	1.49362	0.746812	+	0.665035i	$0.231583\pi$
$632$	−45.3509	−1.80396
$633$	−7.60248	−0.302172
$634$	46.8722	1.86153
$635$	0	0
$636$	−35.9592	−1.42587
$637$	−16.7503	−0.663669
$638$	−14.5090	−0.574416
$639$	−7.46017	−0.295120
$640$	0	0
$641$	21.6908	0.856736	0.428368	−	0.903604i	$-0.359089\pi$
$641$	21.6908	0.856736	0.428368	+	0.903604i	$0.359089\pi$
$642$	−36.9688	−1.45904
$643$	−12.1633	−0.479673	−0.239837	−	0.970813i	$-0.577094\pi$
$643$	−12.1633	−0.479673	−0.239837	+	0.970813i	$0.577094\pi$
$644$	107.819	4.24867
$645$	0	0
$646$	−8.37902	−0.329668
$647$	22.9665	0.902905	0.451452	−	0.892295i	$-0.350906\pi$
$647$	22.9665	0.902905	0.451452	+	0.892295i	$0.350906\pi$
$648$	2.90540	0.114135
$649$	−11.3724	−0.446406
$650$	0	0
$651$	−10.8682	−0.425959
$652$	−24.3732	−0.954530
$653$	−10.4950	−0.410699	−0.205350	−	0.978689i	$-0.565833\pi$
$653$	−10.4950	−0.410699	−0.205350	+	0.978689i	$0.565833\pi$
$654$	20.2535	0.791976
$655$	0	0
$656$	0.622795	0.0243160
$657$	−5.46152	−0.213074
$658$	−9.49470	−0.370142
$659$	24.8914	0.969630	0.484815	−	0.874617i	$-0.338887\pi$
$659$	24.8914	0.969630	0.484815	+	0.874617i	$0.338887\pi$
$660$	0	0
$661$	18.0898	0.703613	0.351806	−	0.936073i	$-0.385568\pi$
$661$	18.0898	0.703613	0.351806	+	0.936073i	$0.385568\pi$
$662$	−36.4061	−1.41497
$663$	3.16245	0.122819
$664$	0.216257	0.00839238
$665$	0	0
$666$	−1.36218	−0.0527834
$667$	43.8216	1.69678
$668$	−48.5070	−1.87679
$669$	−0.674989	−0.0260966
$670$	0	0
$671$	3.39044	0.130887
$672$	−22.7591	−0.877953
$673$	12.5814	0.484976	0.242488	−	0.970154i	$-0.422036\pi$
$673$	12.5814	0.484976	0.242488	+	0.970154i	$0.422036\pi$
$674$	77.7110	2.99331
$675$	0	0
$676$	−33.5094	−1.28882
$677$	41.1854	1.58289	0.791443	−	0.611243i	$-0.209330\pi$
$677$	41.1854	1.58289	0.791443	+	0.611243i	$0.209330\pi$
$678$	37.0124	1.42145
$679$	0.539922	0.0207203
$680$	0	0
$681$	18.2609	0.699760
$682$	6.93908	0.265711
$683$	22.3779	0.856268	0.428134	−	0.903715i	$-0.359171\pi$
$683$	22.3779	0.856268	0.428134	+	0.903715i	$0.359171\pi$
$684$	6.24228	0.238680
$685$	0	0
$686$	29.6125	1.13061
$687$	13.5615	0.517405
$688$	0.640530	0.0244200
$689$	18.2252	0.694326
$690$	0	0
$691$	18.5766	0.706687	0.353343	−	0.935494i	$-0.385045\pi$
$691$	18.5766	0.706687	0.353343	+	0.935494i	$0.385045\pi$
$692$	−21.4675	−0.816074
$693$	−4.76293	−0.180929
$694$	−9.07518	−0.344489
$695$	0	0
$696$	15.9574	0.604864
$697$	−8.80517	−0.333520
$698$	56.6182	2.14303
$699$	13.1243	0.496405
$700$	0	0
$701$	−20.5743	−0.777081	−0.388541	−	0.921432i	$-0.627021\pi$
$701$	−20.5743	−0.777081	−0.388541	+	0.921432i	$0.627021\pi$
$702$	−3.79869	−0.143372
$703$	−1.13451	−0.0427887
$704$	14.8422	0.559387
$705$	0	0
$706$	40.3607	1.51899
$707$	53.0803	1.99629
$708$	32.2658	1.21262
$709$	29.9691	1.12551	0.562756	−	0.826623i	$-0.309741\pi$
$709$	29.9691	1.12551	0.562756	+	0.826623i	$0.309741\pi$
$710$	0	0
$711$	−15.6092	−0.585391
$712$	−14.0085	−0.524992
$713$	−20.9582	−0.784889
$714$	−18.1390	−0.678836
$715$	0	0
$716$	−53.9845	−2.01750
$717$	0.864929	0.0323014
$718$	−36.4752	−1.36124
$719$	−12.7285	−0.474691	−0.237346	−	0.971425i	$-0.576277\pi$
$719$	−12.7285	−0.474691	−0.237346	+	0.971425i	$0.576277\pi$
$720$	0	0
$721$	2.85607	0.106366
$722$	−35.2185	−1.31070
$723$	−25.8090	−0.959848
$724$	−66.3387	−2.46546
$725$	0	0
$726$	−22.2017	−0.823984
$727$	−3.96783	−0.147159	−0.0735794	−	0.997289i	$-0.523442\pi$
$727$	−3.96783	−0.147159	−0.0735794	+	0.997289i	$0.523442\pi$
$728$	−19.8991	−0.737509
$729$	1.00000	0.0370370
$730$	0	0
$731$	−9.05591	−0.334945
$732$	−9.61937	−0.355542
$733$	40.1181	1.48179	0.740897	−	0.671618i	$-0.234401\pi$
$733$	40.1181	1.48179	0.740897	+	0.671618i	$0.234401\pi$
$734$	82.3669	3.04022
$735$	0	0
$736$	−43.8885	−1.61775
$737$	1.20760	0.0444826
$738$	10.5767	0.389332
$739$	25.6902	0.945030	0.472515	−	0.881323i	$-0.343346\pi$
$739$	25.6902	0.945030	0.472515	+	0.881323i	$0.343346\pi$
$740$	0	0
$741$	−3.16378	−0.116225
$742$	−104.535	−3.83762
$743$	27.4318	1.00637	0.503187	−	0.864178i	$-0.332161\pi$
$743$	27.4318	1.00637	0.503187	+	0.864178i	$0.332161\pi$
$744$	−7.63180	−0.279795
$745$	0	0
$746$	−47.8908	−1.75341
$747$	0.0744327	0.00272335
$748$	7.18285	0.262631
$749$	−66.6544	−2.43550
$750$	0	0
$751$	−14.4235	−0.526319	−0.263160	−	0.964752i	$-0.584765\pi$
$751$	−14.4235	−0.526319	−0.263160	+	0.964752i	$0.584765\pi$
$752$	−0.135126	−0.00492755
$753$	18.7792	0.684351
$754$	−20.8637	−0.759810
$755$	0	0
$756$	13.5134	0.491477
$757$	4.31642	0.156883	0.0784415	−	0.996919i	$-0.475006\pi$
$757$	4.31642	0.156883	0.0784415	+	0.996919i	$0.475006\pi$
$758$	−75.6708	−2.74849
$759$	−9.18478	−0.333386
$760$	0	0
$761$	31.2004	1.13101	0.565506	−	0.824744i	$-0.308681\pi$
$761$	31.2004	1.13101	0.565506	+	0.824744i	$0.308681\pi$
$762$	−17.4164	−0.630930
$763$	36.5169	1.32200
$764$	73.2935	2.65167
$765$	0	0
$766$	−15.2936	−0.552581
$767$	−16.3533	−0.590484
$768$	−16.8644	−0.608542
$769$	−52.4304	−1.89069	−0.945344	−	0.326076i	$-0.894274\pi$
$769$	−52.4304	−1.89069	−0.945344	+	0.326076i	$0.894274\pi$
$770$	0	0
$771$	−13.4433	−0.484148
$772$	55.3357	1.99157
$773$	−43.2526	−1.55569	−0.777844	−	0.628458i	$-0.783686\pi$
$773$	−43.2526	−1.55569	−0.777844	+	0.628458i	$0.783686\pi$
$774$	10.8778	0.390996
$775$	0	0
$776$	0.379140	0.0136103
$777$	−2.45600	−0.0881084
$778$	40.1666	1.44004
$779$	8.80889	0.315611
$780$	0	0
$781$	8.58786	0.307298
$782$	−34.9791	−1.25085
$783$	5.49233	0.196280
$784$	1.36732	0.0488330
$785$	0	0
$786$	8.64856	0.308484
$787$	−34.4149	−1.22676	−0.613380	−	0.789788i	$-0.710191\pi$
$787$	−34.4149	−1.22676	−0.613380	+	0.789788i	$0.710191\pi$
$788$	8.30023	0.295683
$789$	−4.71811	−0.167969
$790$	0	0
$791$	66.7330	2.37275
$792$	−3.34459	−0.118845
$793$	4.87540	0.173130
$794$	20.1368	0.714628
$795$	0	0
$796$	49.1991	1.74382
$797$	−28.6653	−1.01538	−0.507688	−	0.861541i	$-0.669500\pi$
$797$	−28.6653	−1.01538	−0.507688	+	0.861541i	$0.669500\pi$
$798$	18.1467	0.642386
$799$	1.91044	0.0675865
$800$	0	0
$801$	−4.82156	−0.170361
$802$	−38.6323	−1.36416
$803$	6.28709	0.221867
$804$	−3.42621	−0.120833
$805$	0	0
$806$	9.97828	0.351470
$807$	1.03149	0.0363103
$808$	37.2736	1.31128
$809$	53.1347	1.86812	0.934058	−	0.357121i	$-0.116242\pi$
$809$	53.1347	1.86812	0.934058	+	0.357121i	$0.116242\pi$
$810$	0	0
$811$	47.8425	1.67998	0.839988	−	0.542604i	$-0.182562\pi$
$811$	47.8425	1.67998	0.839988	+	0.542604i	$0.182562\pi$
$812$	74.2200	2.60461
$813$	−11.9508	−0.419134
$814$	1.56809	0.0549616
$815$	0	0
$816$	−0.258151	−0.00903708
$817$	9.05974	0.316960
$818$	66.2735	2.31720
$819$	−6.84901	−0.239324
$820$	0	0
$821$	17.2192	0.600956	0.300478	−	0.953789i	$-0.402854\pi$
$821$	17.2192	0.600956	0.300478	+	0.953789i	$0.402854\pi$
$822$	−10.3070	−0.359497
$823$	−36.0984	−1.25831	−0.629156	−	0.777279i	$-0.716599\pi$
$823$	−36.0984	−1.25831	−0.629156	+	0.777279i	$0.716599\pi$
$824$	2.00557	0.0698672
$825$	0	0
$826$	93.7986	3.26367
$827$	26.5149	0.922012	0.461006	−	0.887397i	$-0.347489\pi$
$827$	26.5149	0.922012	0.461006	+	0.887397i	$0.347489\pi$
$828$	26.0591	0.905615
$829$	48.2733	1.67660	0.838301	−	0.545207i	$-0.183549\pi$
$829$	48.2733	1.67660	0.838301	+	0.545207i	$0.183549\pi$
$830$	0	0
$831$	10.5209	0.364966
$832$	21.3429	0.739931
$833$	−19.3314	−0.669795
$834$	−9.27654	−0.321220
$835$	0	0
$836$	−7.18588	−0.248529
$837$	−2.62677	−0.0907943
$838$	27.8965	0.963668
$839$	−41.8728	−1.44561	−0.722804	−	0.691053i	$-0.757147\pi$
$839$	−41.8728	−1.44561	−0.722804	+	0.691053i	$0.757147\pi$
$840$	0	0
$841$	1.16568	0.0401958
$842$	−55.3269	−1.90669
$843$	−14.6406	−0.504249
$844$	−24.8303	−0.854695
$845$	0	0
$846$	−2.29479	−0.0788967
$847$	−40.0295	−1.37543
$848$	−1.48772	−0.0510887
$849$	13.2603	0.455094
$850$	0	0
$851$	−4.73612	−0.162352
$852$	−24.3655	−0.834749
$853$	7.97003	0.272889	0.136444	−	0.990648i	$-0.456433\pi$
$853$	7.97003	0.272889	0.136444	+	0.990648i	$0.456433\pi$
$854$	−27.9641	−0.956911
$855$	0	0
$856$	−46.8055	−1.59978
$857$	−45.2426	−1.54546	−0.772728	−	0.634737i	$-0.781108\pi$
$857$	−45.2426	−1.54546	−0.772728	+	0.634737i	$0.781108\pi$
$858$	4.37291	0.149289
$859$	24.3937	0.832302	0.416151	−	0.909295i	$-0.363379\pi$
$859$	24.3937	0.832302	0.416151	+	0.909295i	$0.363379\pi$
$860$	0	0
$861$	19.0696	0.649891
$862$	−74.7719	−2.54674
$863$	13.9191	0.473810	0.236905	−	0.971533i	$-0.423867\pi$
$863$	13.9191	0.473810	0.236905	+	0.971533i	$0.423867\pi$
$864$	−5.50071	−0.187138
$865$	0	0
$866$	−34.4140	−1.16944
$867$	−13.3502	−0.453397
$868$	−35.4965	−1.20483
$869$	17.9687	0.609547
$870$	0	0
$871$	1.73651	0.0588395
$872$	25.6426	0.868369
$873$	0.130495	0.00441658
$874$	34.9939	1.18369
$875$	0	0
$876$	−17.8378	−0.602682
$877$	5.43752	0.183612	0.0918060	−	0.995777i	$-0.470736\pi$
$877$	5.43752	0.183612	0.0918060	+	0.995777i	$0.470736\pi$
$878$	24.9135	0.840791
$879$	29.3890	0.991267
$880$	0	0
$881$	−29.5850	−0.996743	−0.498372	−	0.866964i	$-0.666068\pi$
$881$	−29.5850	−0.996743	−0.498372	+	0.866964i	$0.666068\pi$
$882$	23.2207	0.781881
$883$	58.2594	1.96058	0.980292	−	0.197553i	$-0.0632996\pi$
$883$	58.2594	1.96058	0.980292	+	0.197553i	$0.0632996\pi$
$884$	10.3288	0.347396
$885$	0	0
$886$	3.48487	0.117076
$887$	−10.5636	−0.354690	−0.177345	−	0.984149i	$-0.556751\pi$
$887$	−10.5636	−0.354690	−0.177345	+	0.984149i	$0.556751\pi$
$888$	−1.72463	−0.0578748
$889$	−31.4016	−1.05318
$890$	0	0
$891$	−1.15116	−0.0385654
$892$	−2.20457	−0.0738144
$893$	−1.91125	−0.0639574
$894$	17.6047	0.588788
$895$	0	0
$896$	−76.8992	−2.56902
$897$	−13.2075	−0.440987
$898$	−59.4402	−1.98355
$899$	−14.4271	−0.481170
$900$	0	0
$901$	21.0337	0.700734
$902$	−12.1755	−0.405398
$903$	19.6127	0.652668
$904$	46.8607	1.55856
$905$	0	0
$906$	−26.9466	−0.895240
$907$	−45.3730	−1.50658	−0.753292	−	0.657686i	$-0.771536\pi$
$907$	−45.3730	−1.50658	−0.753292	+	0.657686i	$0.771536\pi$
$908$	59.6417	1.97928
$909$	12.8291	0.425514
$910$	0	0
$911$	14.7511	0.488727	0.244364	−	0.969684i	$-0.421421\pi$
$911$	14.7511	0.488727	0.244364	+	0.969684i	$0.421421\pi$
$912$	0.258260	0.00855183
$913$	−0.0856842	−0.00283573
$914$	12.3031	0.406952
$915$	0	0
$916$	44.2931	1.46349
$917$	15.5933	0.514935
$918$	−4.38406	−0.144696
$919$	43.5027	1.43502	0.717511	−	0.696548i	$-0.245282\pi$
$919$	43.5027	1.43502	0.717511	+	0.696548i	$0.245282\pi$
$920$	0	0
$921$	−10.9311	−0.360193
$922$	−92.0010	−3.02989
$923$	12.3492	0.406479
$924$	−15.5561	−0.511758
$925$	0	0
$926$	−16.5475	−0.543783
$927$	0.690290	0.0226721
$928$	−30.2117	−0.991747
$929$	−18.6044	−0.610392	−0.305196	−	0.952290i	$-0.598722\pi$
$929$	−18.6044	−0.610392	−0.305196	+	0.952290i	$0.598722\pi$
$930$	0	0
$931$	19.3396	0.633830
$932$	42.8649	1.40409
$933$	1.95767	0.0640913
$934$	62.0875	2.03156
$935$	0	0
$936$	−4.80946	−0.157202
$937$	−45.3256	−1.48072	−0.740361	−	0.672209i	$-0.765346\pi$
$937$	−45.3256	−1.48072	−0.740361	+	0.672209i	$0.765346\pi$
$938$	−9.96021	−0.325212
$939$	18.5888	0.606624
$940$	0	0
$941$	14.8235	0.483233	0.241617	−	0.970372i	$-0.422322\pi$
$941$	14.8235	0.483233	0.241617	+	0.970372i	$0.422322\pi$
$942$	−43.6313	−1.42159
$943$	36.7736	1.19751
$944$	1.33492	0.0434479
$945$	0	0
$946$	−12.5222	−0.407131
$947$	−0.122012	−0.00396485	−0.00198242	−	0.999998i	$-0.500631\pi$
$947$	−0.122012	−0.00396485	−0.00198242	+	0.999998i	$0.500631\pi$
$948$	−50.9809	−1.65578
$949$	9.04073	0.293475
$950$	0	0
$951$	20.4255	0.662341
$952$	−22.9655	−0.744316
$953$	25.7086	0.832782	0.416391	−	0.909186i	$-0.363295\pi$
$953$	25.7086	0.832782	0.416391	+	0.909186i	$0.363295\pi$
$954$	−25.2654	−0.817998
$955$	0	0
$956$	2.82493	0.0913647
$957$	−6.32256	−0.204379
$958$	−40.6730	−1.31409
$959$	−18.5834	−0.600089
$960$	0	0
$961$	−24.1001	−0.777423
$962$	2.25489	0.0727005
$963$	−16.1099	−0.519133
$964$	−84.2944	−2.71494
$965$	0	0
$966$	75.7553	2.43739
$967$	45.8238	1.47359	0.736796	−	0.676115i	$-0.236338\pi$
$967$	45.8238	1.47359	0.736796	+	0.676115i	$0.236338\pi$
$968$	−28.1092	−0.903464
$969$	−3.65132	−0.117297
$970$	0	0
$971$	−6.12848	−0.196672	−0.0983362	−	0.995153i	$-0.531352\pi$
$971$	−6.12848	−0.196672	−0.0983362	+	0.995153i	$0.531352\pi$
$972$	3.26608	0.104760
$973$	−16.7255	−0.536196
$974$	−65.9372	−2.11276
$975$	0	0
$976$	−0.397978	−0.0127390
$977$	49.5272	1.58452	0.792258	−	0.610186i	$-0.208905\pi$
$977$	49.5272	1.58452	0.792258	+	0.610186i	$0.208905\pi$
$978$	−17.1250	−0.547596
$979$	5.55040	0.177391
$980$	0	0
$981$	8.82586	0.281788
$982$	−37.9587	−1.21131
$983$	27.7280	0.884387	0.442193	−	0.896920i	$-0.354201\pi$
$983$	27.7280	0.884387	0.442193	+	0.896920i	$0.354201\pi$
$984$	13.3909	0.426887
$985$	0	0
$986$	−24.0787	−0.766823
$987$	−4.13749	−0.131698
$988$	−10.3332	−0.328742
$989$	37.8208	1.20263
$990$	0	0
$991$	−11.6003	−0.368496	−0.184248	−	0.982880i	$-0.558985\pi$
$991$	−11.6003	−0.368496	−0.184248	+	0.982880i	$0.558985\pi$
$992$	14.4491	0.458758
$993$	−15.8647	−0.503450
$994$	−70.8320	−2.24665
$995$	0	0
$996$	0.243103	0.00770302
$997$	24.3181	0.770163	0.385082	−	0.922883i	$-0.374173\pi$
$997$	24.3181	0.770163	0.385082	+	0.922883i	$0.374173\pi$
$998$	21.3508	0.675848
$999$	−0.593596	−0.0187805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bc.1.6	yes	7
5.4	even	2		3525.2.a.x.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.2	✓	7	5.4	even	2
3525.2.a.bc.1.6	yes	7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.29479 q^{2} +1.00000 q^{3} +3.26608 q^{4} +2.29479 q^{6} +4.13749 q^{7} +2.90540 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.29479 q^{2} +1.00000 q^{3} +3.26608 q^{4} +2.29479 q^{6} +4.13749 q^{7} +2.90540 q^{8} +1.00000 q^{9} -1.15116 q^{11} +3.26608 q^{12} -1.65535 q^{13} +9.49470 q^{14} +0.135126 q^{16} -1.91044 q^{17} +2.29479 q^{18} +1.91125 q^{19} +4.13749 q^{21} -2.64168 q^{22} +7.97869 q^{23} +2.90540 q^{24} -3.79869 q^{26} +1.00000 q^{27} +13.5134 q^{28} +5.49233 q^{29} -2.62677 q^{31} -5.50071 q^{32} -1.15116 q^{33} -4.38406 q^{34} +3.26608 q^{36} -0.593596 q^{37} +4.38592 q^{38} -1.65535 q^{39} +4.60898 q^{41} +9.49470 q^{42} +4.74023 q^{43} -3.75979 q^{44} +18.3095 q^{46} -1.00000 q^{47} +0.135126 q^{48} +10.1188 q^{49} -1.91044 q^{51} -5.40651 q^{52} -11.0099 q^{53} +2.29479 q^{54} +12.0211 q^{56} +1.91125 q^{57} +12.6038 q^{58} +9.87905 q^{59} -2.94523 q^{61} -6.02789 q^{62} +4.13749 q^{63} -12.8932 q^{64} -2.64168 q^{66} -1.04903 q^{67} -6.23965 q^{68} +7.97869 q^{69} -7.46017 q^{71} +2.90540 q^{72} -5.46152 q^{73} -1.36218 q^{74} +6.24228 q^{76} -4.76293 q^{77} -3.79869 q^{78} -15.6092 q^{79} +1.00000 q^{81} +10.5767 q^{82} +0.0744327 q^{83} +13.5134 q^{84} +10.8778 q^{86} +5.49233 q^{87} -3.34459 q^{88} -4.82156 q^{89} -6.84901 q^{91} +26.0591 q^{92} -2.62677 q^{93} -2.29479 q^{94} -5.50071 q^{96} +0.130495 q^{97} +23.2207 q^{98} -1.15116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Introduction

L-functions

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