LMFDB - Embedded newform 6025.2.a.m.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14986 q^{2} +1.70160 q^{3} +2.62188 q^{4} -3.65820 q^{6} +3.86024 q^{7} -1.33695 q^{8} -0.104549 q^{9} +O(q^{10})$	\(q-2.14986 q^{2} +1.70160 q^{3} +2.62188 q^{4} -3.65820 q^{6} +3.86024 q^{7} -1.33695 q^{8} -0.104549 q^{9} -3.36727 q^{11} +4.46140 q^{12} +3.60241 q^{13} -8.29896 q^{14} -2.36950 q^{16} -4.80509 q^{17} +0.224765 q^{18} +0.226945 q^{19} +6.56859 q^{21} +7.23915 q^{22} -1.91949 q^{23} -2.27496 q^{24} -7.74467 q^{26} -5.28271 q^{27} +10.1211 q^{28} -4.83459 q^{29} +3.43781 q^{31} +7.76800 q^{32} -5.72976 q^{33} +10.3303 q^{34} -0.274114 q^{36} -1.65269 q^{37} -0.487900 q^{38} +6.12988 q^{39} -5.01238 q^{41} -14.1215 q^{42} +1.20938 q^{43} -8.82859 q^{44} +4.12663 q^{46} -1.14233 q^{47} -4.03195 q^{48} +7.90145 q^{49} -8.17636 q^{51} +9.44510 q^{52} -4.03982 q^{53} +11.3571 q^{54} -5.16096 q^{56} +0.386171 q^{57} +10.3937 q^{58} +9.59775 q^{59} -14.7276 q^{61} -7.39079 q^{62} -0.403583 q^{63} -11.9611 q^{64} +12.3182 q^{66} +2.12724 q^{67} -12.5984 q^{68} -3.26621 q^{69} -2.50693 q^{71} +0.139777 q^{72} -5.03915 q^{73} +3.55305 q^{74} +0.595023 q^{76} -12.9985 q^{77} -13.1784 q^{78} +13.6737 q^{79} -8.67542 q^{81} +10.7759 q^{82} -5.82936 q^{83} +17.2221 q^{84} -2.59998 q^{86} -8.22655 q^{87} +4.50189 q^{88} -1.13959 q^{89} +13.9062 q^{91} -5.03268 q^{92} +5.84978 q^{93} +2.45584 q^{94} +13.2180 q^{96} -13.2097 q^{97} -16.9870 q^{98} +0.352044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * 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 $

$2$	−2.14986	−1.52018	−0.760089	−	0.649819i	$-0.774845\pi$
$2$	−2.14986	−1.52018	−0.760089	+	0.649819i	$0.774845\pi$
$3$	1.70160	0.982421	0.491210	−	0.871041i	$-0.336555\pi$
$3$	1.70160	0.982421	0.491210	+	0.871041i	$0.336555\pi$
$4$	2.62188	1.31094
$5$	0	0
$5$	0	0
$6$	−3.65820	−1.49345
$7$	3.86024	1.45903	0.729517	−	0.683963i	$-0.239745\pi$
$7$	3.86024	1.45903	0.729517	+	0.683963i	$0.239745\pi$
$8$	−1.33695	−0.472684
$9$	−0.104549	−0.0348496
$10$	0	0
$11$	−3.36727	−1.01527	−0.507636	−	0.861572i	$-0.669480\pi$
$11$	−3.36727	−1.01527	−0.507636	+	0.861572i	$0.669480\pi$
$12$	4.46140	1.28789
$13$	3.60241	0.999130	0.499565	−	0.866276i	$-0.333493\pi$
$13$	3.60241	0.999130	0.499565	+	0.866276i	$0.333493\pi$
$14$	−8.29896	−2.21799
$15$	0	0
$16$	−2.36950	−0.592376
$17$	−4.80509	−1.16541	−0.582703	−	0.812685i	$-0.698005\pi$
$17$	−4.80509	−1.16541	−0.582703	+	0.812685i	$0.698005\pi$
$18$	0.224765	0.0529775
$19$	0.226945	0.0520648	0.0260324	−	0.999661i	$-0.491713\pi$
$19$	0.226945	0.0520648	0.0260324	+	0.999661i	$0.491713\pi$
$20$	0	0
$21$	6.56859	1.43338
$22$	7.23915	1.54339
$23$	−1.91949	−0.400242	−0.200121	−	0.979771i	$-0.564133\pi$
$23$	−1.91949	−0.400242	−0.200121	+	0.979771i	$0.564133\pi$
$24$	−2.27496	−0.464375
$25$	0	0
$26$	−7.74467	−1.51885
$27$	−5.28271	−1.01666
$28$	10.1211	1.91271
$29$	−4.83459	−0.897761	−0.448880	−	0.893592i	$-0.648177\pi$
$29$	−4.83459	−0.897761	−0.448880	+	0.893592i	$0.648177\pi$
$30$	0	0
$31$	3.43781	0.617448	0.308724	−	0.951152i	$-0.400098\pi$
$31$	3.43781	0.617448	0.308724	+	0.951152i	$0.400098\pi$
$32$	7.76800	1.37320
$33$	−5.72976	−0.997423
$34$	10.3303	1.77162
$35$	0	0
$36$	−0.274114	−0.0456857
$37$	−1.65269	−0.271701	−0.135851	−	0.990729i	$-0.543377\pi$
$37$	−1.65269	−0.271701	−0.135851	+	0.990729i	$0.543377\pi$
$38$	−0.487900	−0.0791478
$39$	6.12988	0.981566
$40$	0	0
$41$	−5.01238	−0.782803	−0.391401	−	0.920220i	$-0.628010\pi$
$41$	−5.01238	−0.782803	−0.391401	+	0.920220i	$0.628010\pi$
$42$	−14.1215	−2.17900
$43$	1.20938	0.184428	0.0922141	−	0.995739i	$-0.470606\pi$
$43$	1.20938	0.184428	0.0922141	+	0.995739i	$0.470606\pi$
$44$	−8.82859	−1.33096
$45$	0	0
$46$	4.12663	0.608438
$47$	−1.14233	−0.166626	−0.0833130	−	0.996523i	$-0.526550\pi$
$47$	−1.14233	−0.166626	−0.0833130	+	0.996523i	$0.526550\pi$
$48$	−4.03195	−0.581963
$49$	7.90145	1.12878
$50$	0	0
$51$	−8.17636	−1.14492
$52$	9.44510	1.30980
$53$	−4.03982	−0.554912	−0.277456	−	0.960738i	$-0.589491\pi$
$53$	−4.03982	−0.554912	−0.277456	+	0.960738i	$0.589491\pi$
$54$	11.3571	1.54550
$55$	0	0
$56$	−5.16096	−0.689662
$57$	0.386171	0.0511496
$58$	10.3937	1.36476
$59$	9.59775	1.24952	0.624760	−	0.780817i	$-0.285197\pi$
$59$	9.59775	1.24952	0.624760	+	0.780817i	$0.285197\pi$
$60$	0	0
$61$	−14.7276	−1.88567	−0.942837	−	0.333255i	$-0.891853\pi$
$61$	−14.7276	−1.88567	−0.942837	+	0.333255i	$0.891853\pi$
$62$	−7.39079	−0.938631
$63$	−0.403583	−0.0508467
$64$	−11.9611	−1.49513
$65$	0	0
$66$	12.3182	1.51626
$67$	2.12724	0.259883	0.129942	−	0.991522i	$-0.458521\pi$
$67$	2.12724	0.259883	0.129942	+	0.991522i	$0.458521\pi$
$68$	−12.5984	−1.52778
$69$	−3.26621	−0.393206
$70$	0	0
$71$	−2.50693	−0.297518	−0.148759	−	0.988873i	$-0.547528\pi$
$71$	−2.50693	−0.297518	−0.148759	+	0.988873i	$0.547528\pi$
$72$	0.139777	0.0164728
$73$	−5.03915	−0.589787	−0.294894	−	0.955530i	$-0.595284\pi$
$73$	−5.03915	−0.589787	−0.294894	+	0.955530i	$0.595284\pi$
$74$	3.55305	0.413034
$75$	0	0
$76$	0.595023	0.0682539
$77$	−12.9985	−1.48131
$78$	−13.1784	−1.49215
$79$	13.6737	1.53841	0.769207	−	0.639000i	$-0.220651\pi$
$79$	13.6737	1.53841	0.769207	+	0.639000i	$0.220651\pi$
$80$	0	0
$81$	−8.67542	−0.963936
$82$	10.7759	1.19000
$83$	−5.82936	−0.639855	−0.319928	−	0.947442i	$-0.603659\pi$
$83$	−5.82936	−0.639855	−0.319928	+	0.947442i	$0.603659\pi$
$84$	17.2221	1.87908
$85$	0	0
$86$	−2.59998	−0.280364
$87$	−8.22655	−0.881979
$88$	4.50189	0.479903
$89$	−1.13959	−0.120797	−0.0603984	−	0.998174i	$-0.519237\pi$
$89$	−1.13959	−0.120797	−0.0603984	+	0.998174i	$0.519237\pi$
$90$	0	0
$91$	13.9062	1.45776
$92$	−5.03268	−0.524693
$93$	5.84978	0.606594
$94$	2.45584	0.253301
$95$	0	0
$96$	13.2180	1.34906
$97$	−13.2097	−1.34124	−0.670620	−	0.741801i	$-0.733972\pi$
$97$	−13.2097	−1.34124	−0.670620	+	0.741801i	$0.733972\pi$
$98$	−16.9870	−1.71594
$99$	0.352044	0.0353817
$100$	0	0
$101$	−7.43809	−0.740118	−0.370059	−	0.929008i	$-0.620663\pi$
$101$	−7.43809	−0.740118	−0.370059	+	0.929008i	$0.620663\pi$
$102$	17.5780	1.74048
$103$	−14.5631	−1.43494	−0.717472	−	0.696587i	$-0.754701\pi$
$103$	−14.5631	−1.43494	−0.717472	+	0.696587i	$0.754701\pi$
$104$	−4.81626	−0.472273
$105$	0	0
$106$	8.68503	0.843565
$107$	−9.50646	−0.919024	−0.459512	−	0.888172i	$-0.651976\pi$
$107$	−9.50646	−0.919024	−0.459512	+	0.888172i	$0.651976\pi$
$108$	−13.8506	−1.33278
$109$	16.0398	1.53633	0.768165	−	0.640252i	$-0.221170\pi$
$109$	16.0398	1.53633	0.768165	+	0.640252i	$0.221170\pi$
$110$	0	0
$111$	−2.81223	−0.266925
$112$	−9.14685	−0.864296
$113$	−13.4925	−1.26927	−0.634634	−	0.772813i	$-0.718849\pi$
$113$	−13.4925	−1.26927	−0.634634	+	0.772813i	$0.718849\pi$
$114$	−0.830211	−0.0777564
$115$	0	0
$116$	−12.6757	−1.17691
$117$	−0.376628	−0.0348192
$118$	−20.6338	−1.89949
$119$	−18.5488	−1.70037
$120$	0	0
$121$	0.338528	0.0307753
$122$	31.6622	2.86656
$123$	−8.52908	−0.769042
$124$	9.01352	0.809438
$125$	0	0
$126$	0.867645	0.0772960
$127$	7.52355	0.667607	0.333803	−	0.942643i	$-0.391668\pi$
$127$	7.52355	0.667607	0.333803	+	0.942643i	$0.391668\pi$
$128$	10.1786	0.899668
$129$	2.05788	0.181186
$130$	0	0
$131$	7.02682	0.613936	0.306968	−	0.951720i	$-0.400686\pi$
$131$	7.02682	0.613936	0.306968	+	0.951720i	$0.400686\pi$
$132$	−15.0227	−1.30756
$133$	0.876063	0.0759643
$134$	−4.57325	−0.395069
$135$	0	0
$136$	6.42418	0.550869
$137$	−5.86157	−0.500788	−0.250394	−	0.968144i	$-0.580560\pi$
$137$	−5.86157	−0.500788	−0.250394	+	0.968144i	$0.580560\pi$
$138$	7.02188	0.597743
$139$	−13.2572	−1.12446	−0.562231	−	0.826980i	$-0.690057\pi$
$139$	−13.2572	−1.12446	−0.562231	+	0.826980i	$0.690057\pi$
$140$	0	0
$141$	−1.94379	−0.163697
$142$	5.38954	0.452280
$143$	−12.1303	−1.01439
$144$	0.247729	0.0206440
$145$	0	0
$146$	10.8334	0.896582
$147$	13.4451	1.10894
$148$	−4.33316	−0.356184
$149$	−0.0486387	−0.00398463	−0.00199232	−	0.999998i	$-0.500634\pi$
$149$	−0.0486387	−0.00398463	−0.00199232	+	0.999998i	$0.500634\pi$
$150$	0	0
$151$	2.43809	0.198409	0.0992045	−	0.995067i	$-0.468370\pi$
$151$	2.43809	0.198409	0.0992045	+	0.995067i	$0.468370\pi$
$152$	−0.303415	−0.0246102
$153$	0.502366	0.0406139
$154$	27.9449	2.25186
$155$	0	0
$156$	16.0718	1.28677
$157$	−7.69109	−0.613815	−0.306908	−	0.951739i	$-0.599294\pi$
$157$	−7.69109	−0.613815	−0.306908	+	0.951739i	$0.599294\pi$
$158$	−29.3965	−2.33866
$159$	−6.87417	−0.545157
$160$	0	0
$161$	−7.40970	−0.583966
$162$	18.6509	1.46535
$163$	16.6059	1.30067	0.650336	−	0.759646i	$-0.274628\pi$
$163$	16.6059	1.30067	0.650336	+	0.759646i	$0.274628\pi$
$164$	−13.1419	−1.02621
$165$	0	0
$166$	12.5323	0.972694
$167$	15.1961	1.17591	0.587953	−	0.808895i	$-0.299934\pi$
$167$	15.1961	1.17591	0.587953	+	0.808895i	$0.299934\pi$
$168$	−8.78190	−0.677538
$169$	−0.0226134	−0.00173949
$170$	0	0
$171$	−0.0237268	−0.00181444
$172$	3.17084	0.241774
$173$	−9.72441	−0.739333	−0.369667	−	0.929164i	$-0.620528\pi$
$173$	−9.72441	−0.739333	−0.369667	+	0.929164i	$0.620528\pi$
$174$	17.6859	1.34076
$175$	0	0
$176$	7.97877	0.601422
$177$	16.3316	1.22755
$178$	2.44996	0.183633
$179$	−13.2615	−0.991208	−0.495604	−	0.868549i	$-0.665053\pi$
$179$	−13.2615	−0.991208	−0.495604	+	0.868549i	$0.665053\pi$
$180$	0	0
$181$	−7.09939	−0.527694	−0.263847	−	0.964565i	$-0.584991\pi$
$181$	−7.09939	−0.527694	−0.263847	+	0.964565i	$0.584991\pi$
$182$	−29.8963	−2.21606
$183$	−25.0605	−1.85252
$184$	2.56627	0.189188
$185$	0	0
$186$	−12.5762	−0.922131
$187$	16.1801	1.18320
$188$	−2.99505	−0.218437
$189$	−20.3925	−1.48334
$190$	0	0
$191$	15.2427	1.10293	0.551463	−	0.834200i	$-0.314070\pi$
$191$	15.2427	1.10293	0.551463	+	0.834200i	$0.314070\pi$
$192$	−20.3530	−1.46885
$193$	−5.71316	−0.411242	−0.205621	−	0.978632i	$-0.565921\pi$
$193$	−5.71316	−0.411242	−0.205621	+	0.978632i	$0.565921\pi$
$194$	28.3989	2.03892
$195$	0	0
$196$	20.7166	1.47976
$197$	15.5073	1.10485	0.552426	−	0.833562i	$-0.313702\pi$
$197$	15.5073	1.10485	0.552426	+	0.833562i	$0.313702\pi$
$198$	−0.756844	−0.0537865
$199$	−2.50728	−0.177736	−0.0888681	−	0.996043i	$-0.528325\pi$
$199$	−2.50728	−0.177736	−0.0888681	+	0.996043i	$0.528325\pi$
$200$	0	0
$201$	3.61971	0.255315
$202$	15.9908	1.12511
$203$	−18.6627	−1.30986
$204$	−21.4374	−1.50092
$205$	0	0
$206$	31.3085	2.18137
$207$	0.200680	0.0139482
$208$	−8.53594	−0.591861
$209$	−0.764187	−0.0528599
$210$	0	0
$211$	−22.8809	−1.57519	−0.787593	−	0.616196i	$-0.788673\pi$
$211$	−22.8809	−1.57519	−0.787593	+	0.616196i	$0.788673\pi$
$212$	−10.5919	−0.727456
$213$	−4.26580	−0.292288
$214$	20.4375	1.39708
$215$	0	0
$216$	7.06273	0.480558
$217$	13.2708	0.900878
$218$	−34.4832	−2.33549
$219$	−8.57462	−0.579419
$220$	0	0
$221$	−17.3099	−1.16439
$222$	6.04588	0.405773
$223$	−0.134785	−0.00902590	−0.00451295	−	0.999990i	$-0.501437\pi$
$223$	−0.134785	−0.00902590	−0.00451295	+	0.999990i	$0.501437\pi$
$224$	29.9863	2.00355
$225$	0	0
$226$	29.0069	1.92951
$227$	−10.8306	−0.718849	−0.359425	−	0.933174i	$-0.617027\pi$
$227$	−10.8306	−0.718849	−0.359425	+	0.933174i	$0.617027\pi$
$228$	1.01249	0.0670540
$229$	7.89246	0.521548	0.260774	−	0.965400i	$-0.416022\pi$
$229$	7.89246	0.521548	0.260774	+	0.965400i	$0.416022\pi$
$230$	0	0
$231$	−22.1182	−1.45527
$232$	6.46362	0.424357
$233$	−8.69503	−0.569631	−0.284815	−	0.958582i	$-0.591932\pi$
$233$	−8.69503	−0.569631	−0.284815	+	0.958582i	$0.591932\pi$
$234$	0.809695	0.0529314
$235$	0	0
$236$	25.1641	1.63805
$237$	23.2672	1.51137
$238$	39.8772	2.58486
$239$	−3.13922	−0.203059	−0.101529	−	0.994833i	$-0.532374\pi$
$239$	−3.13922	−0.203059	−0.101529	+	0.994833i	$0.532374\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−0.727787	−0.0467839
$243$	1.08600	0.0696670
$244$	−38.6140	−2.47201
$245$	0	0
$246$	18.3363	1.16908
$247$	0.817551	0.0520195
$248$	−4.59619	−0.291858
$249$	−9.91925	−0.628607
$250$	0	0
$251$	21.4720	1.35530	0.677649	−	0.735385i	$-0.262999\pi$
$251$	21.4720	1.35530	0.677649	+	0.735385i	$0.262999\pi$
$252$	−1.05815	−0.0666569
$253$	6.46345	0.406354
$254$	−16.1745	−1.01488
$255$	0	0
$256$	2.03967	0.127479
$257$	26.5355	1.65524	0.827619	−	0.561291i	$-0.189695\pi$
$257$	26.5355	1.65524	0.827619	+	0.561291i	$0.189695\pi$
$258$	−4.42414	−0.275435
$259$	−6.37979	−0.396421
$260$	0	0
$261$	0.505450	0.0312866
$262$	−15.1066	−0.933291
$263$	−10.2585	−0.632567	−0.316283	−	0.948665i	$-0.602435\pi$
$263$	−10.2585	−0.632567	−0.316283	+	0.948665i	$0.602435\pi$
$264$	7.66042	0.471466
$265$	0	0
$266$	−1.88341	−0.115479
$267$	−1.93914	−0.118673
$268$	5.57736	0.340692
$269$	−0.0604403	−0.00368511	−0.00184256	−	0.999998i	$-0.500587\pi$
$269$	−0.0604403	−0.00368511	−0.00184256	+	0.999998i	$0.500587\pi$
$270$	0	0
$271$	21.5869	1.31131	0.655654	−	0.755062i	$-0.272393\pi$
$271$	21.5869	1.31131	0.655654	+	0.755062i	$0.272393\pi$
$272$	11.3857	0.690359
$273$	23.6628	1.43214
$274$	12.6015	0.761287
$275$	0	0
$276$	−8.56362	−0.515469
$277$	−22.3807	−1.34473	−0.672363	−	0.740221i	$-0.734721\pi$
$277$	−22.3807	−1.34473	−0.672363	+	0.740221i	$0.734721\pi$
$278$	28.5011	1.70938
$279$	−0.359418	−0.0215178
$280$	0	0
$281$	−30.8057	−1.83771	−0.918856	−	0.394594i	$-0.870885\pi$
$281$	−30.8057	−1.83771	−0.918856	+	0.394594i	$0.870885\pi$
$282$	4.17887	0.248848
$283$	−29.8883	−1.77668	−0.888338	−	0.459189i	$-0.848140\pi$
$283$	−29.8883	−1.77668	−0.888338	+	0.459189i	$0.848140\pi$
$284$	−6.57287	−0.390028
$285$	0	0
$286$	26.0784	1.54205
$287$	−19.3490	−1.14214
$288$	−0.812134	−0.0478555
$289$	6.08890	0.358170
$290$	0	0
$291$	−22.4776	−1.31766
$292$	−13.2120	−0.773176
$293$	19.2209	1.12289	0.561447	−	0.827513i	$-0.310245\pi$
$293$	19.2209	1.12289	0.561447	+	0.827513i	$0.310245\pi$
$294$	−28.9051	−1.68578
$295$	0	0
$296$	2.20957	0.128429
$297$	17.7883	1.03218
$298$	0.104566	0.00605735
$299$	−6.91480	−0.399893
$300$	0	0
$301$	4.66848	0.269087
$302$	−5.24154	−0.301617
$303$	−12.6567	−0.727107
$304$	−0.537748	−0.0308420
$305$	0	0
$306$	−1.08001	−0.0617403
$307$	5.35829	0.305814	0.152907	−	0.988241i	$-0.451137\pi$
$307$	5.35829	0.305814	0.152907	+	0.988241i	$0.451137\pi$
$308$	−34.0805	−1.94191
$309$	−24.7806	−1.40972
$310$	0	0
$311$	14.7195	0.834666	0.417333	−	0.908754i	$-0.362965\pi$
$311$	14.7195	0.834666	0.417333	+	0.908754i	$0.362965\pi$
$312$	−8.19536	−0.463971
$313$	10.4175	0.588832	0.294416	−	0.955677i	$-0.404875\pi$
$313$	10.4175	0.588832	0.294416	+	0.955677i	$0.404875\pi$
$314$	16.5347	0.933109
$315$	0	0
$316$	35.8509	2.01677
$317$	6.26700	0.351990	0.175995	−	0.984391i	$-0.443686\pi$
$317$	6.26700	0.351990	0.175995	+	0.984391i	$0.443686\pi$
$318$	14.7785	0.828735
$319$	16.2794	0.911471
$320$	0	0
$321$	−16.1762	−0.902868
$322$	15.9298	0.887732
$323$	−1.09049	−0.0606766
$324$	−22.7459	−1.26366
$325$	0	0
$326$	−35.7002	−1.97725
$327$	27.2933	1.50932
$328$	6.70132	0.370019
$329$	−4.40967	−0.243113
$330$	0	0
$331$	−15.6686	−0.861226	−0.430613	−	0.902537i	$-0.641703\pi$
$331$	−15.6686	−0.861226	−0.430613	+	0.902537i	$0.641703\pi$
$332$	−15.2839	−0.838812
$333$	0.172787	0.00946867
$334$	−32.6693	−1.78759
$335$	0	0
$336$	−15.5643	−0.849103
$337$	−7.22408	−0.393521	−0.196760	−	0.980452i	$-0.563042\pi$
$337$	−7.22408	−0.393521	−0.196760	+	0.980452i	$0.563042\pi$
$338$	0.0486156	0.00264434
$339$	−22.9589	−1.24695
$340$	0	0
$341$	−11.5760	−0.626877
$342$	0.0510093	0.00275826
$343$	3.47980	0.187892
$344$	−1.61688	−0.0871763
$345$	0	0
$346$	20.9061	1.12392
$347$	1.93577	0.103917	0.0519587	−	0.998649i	$-0.483454\pi$
$347$	1.93577	0.103917	0.0519587	+	0.998649i	$0.483454\pi$
$348$	−21.5690	−1.15622
$349$	−10.3941	−0.556385	−0.278192	−	0.960525i	$-0.589735\pi$
$349$	−10.3941	−0.556385	−0.278192	+	0.960525i	$0.589735\pi$
$350$	0	0
$351$	−19.0305	−1.01577
$352$	−26.1570	−1.39417
$353$	14.4634	0.769809	0.384905	−	0.922956i	$-0.374234\pi$
$353$	14.4634	0.769809	0.384905	+	0.922956i	$0.374234\pi$
$354$	−35.1105	−1.86610
$355$	0	0
$356$	−2.98788	−0.158357
$357$	−31.5627	−1.67047
$358$	28.5102	1.50681
$359$	31.9938	1.68857	0.844284	−	0.535896i	$-0.180026\pi$
$359$	31.9938	1.68857	0.844284	+	0.535896i	$0.180026\pi$
$360$	0	0
$361$	−18.9485	−0.997289
$362$	15.2627	0.802188
$363$	0.576041	0.0302343
$364$	36.4603	1.91104
$365$	0	0
$366$	53.8764	2.81617
$367$	−17.0688	−0.890982	−0.445491	−	0.895286i	$-0.646971\pi$
$367$	−17.0688	−0.890982	−0.445491	+	0.895286i	$0.646971\pi$
$368$	4.54824	0.237094
$369$	0.524038	0.0272803
$370$	0	0
$371$	−15.5947	−0.809635
$372$	15.3374	0.795209
$373$	23.2843	1.20562	0.602808	−	0.797886i	$-0.294048\pi$
$373$	23.2843	1.20562	0.602808	+	0.797886i	$0.294048\pi$
$374$	−34.7848	−1.79868
$375$	0	0
$376$	1.52724	0.0787615
$377$	−17.4162	−0.896980
$378$	43.8410	2.25494
$379$	33.0919	1.69982	0.849908	−	0.526931i	$-0.176657\pi$
$379$	33.0919	1.69982	0.849908	+	0.526931i	$0.176657\pi$
$380$	0	0
$381$	12.8021	0.655871
$382$	−32.7697	−1.67664
$383$	−12.2692	−0.626926	−0.313463	−	0.949600i	$-0.601489\pi$
$383$	−12.2692	−0.626926	−0.313463	+	0.949600i	$0.601489\pi$
$384$	17.3199	0.883852
$385$	0	0
$386$	12.2825	0.625161
$387$	−0.126439	−0.00642724
$388$	−34.6342	−1.75828
$389$	8.65132	0.438639	0.219320	−	0.975653i	$-0.429616\pi$
$389$	8.65132	0.438639	0.219320	+	0.975653i	$0.429616\pi$
$390$	0	0
$391$	9.22333	0.466444
$392$	−10.5639	−0.533556
$393$	11.9568	0.603143
$394$	−33.3385	−1.67957
$395$	0	0
$396$	0.923017	0.0463834
$397$	10.8717	0.545637	0.272819	−	0.962065i	$-0.412044\pi$
$397$	10.8717	0.545637	0.272819	+	0.962065i	$0.412044\pi$
$398$	5.39028	0.270191
$399$	1.49071	0.0746289
$400$	0	0
$401$	−13.1654	−0.657447	−0.328724	−	0.944426i	$-0.606618\pi$
$401$	−13.1654	−0.657447	−0.328724	+	0.944426i	$0.606618\pi$
$402$	−7.78186	−0.388124
$403$	12.3844	0.616911
$404$	−19.5018	−0.970250
$405$	0	0
$406$	40.1221	1.99122
$407$	5.56507	0.275850
$408$	10.9314	0.541185
$409$	18.4576	0.912670	0.456335	−	0.889808i	$-0.349162\pi$
$409$	18.4576	0.912670	0.456335	+	0.889808i	$0.349162\pi$
$410$	0	0
$411$	−9.97407	−0.491984
$412$	−38.1827	−1.88113
$413$	37.0496	1.82309
$414$	−0.431434	−0.0212038
$415$	0	0
$416$	27.9835	1.37201
$417$	−22.5585	−1.10470
$418$	1.64289	0.0803564
$419$	7.30445	0.356846	0.178423	−	0.983954i	$-0.442901\pi$
$419$	7.30445	0.356846	0.178423	+	0.983954i	$0.442901\pi$
$420$	0	0
$421$	25.0861	1.22262	0.611310	−	0.791391i	$-0.290643\pi$
$421$	25.0861	1.22262	0.611310	+	0.791391i	$0.290643\pi$
$422$	49.1906	2.39456
$423$	0.119429	0.00580684
$424$	5.40105	0.262298
$425$	0	0
$426$	9.17085	0.444329
$427$	−56.8520	−2.75126
$428$	−24.9248	−1.20479
$429$	−20.6410	−0.996555
$430$	0	0
$431$	33.5910	1.61802	0.809011	−	0.587794i	$-0.200003\pi$
$431$	33.5910	1.61802	0.809011	+	0.587794i	$0.200003\pi$
$432$	12.5174	0.602244
$433$	−12.6008	−0.605557	−0.302778	−	0.953061i	$-0.597914\pi$
$433$	−12.6008	−0.605557	−0.302778	+	0.953061i	$0.597914\pi$
$434$	−28.5302	−1.36949
$435$	0	0
$436$	42.0543	2.01404
$437$	−0.435620	−0.0208385
$438$	18.4342	0.880820
$439$	16.4897	0.787011	0.393506	−	0.919322i	$-0.371262\pi$
$439$	16.4897	0.787011	0.393506	+	0.919322i	$0.371262\pi$
$440$	0	0
$441$	−0.826086	−0.0393374
$442$	37.2138	1.77008
$443$	−4.44054	−0.210976	−0.105488	−	0.994421i	$-0.533641\pi$
$443$	−4.44054	−0.210976	−0.105488	+	0.994421i	$0.533641\pi$
$444$	−7.37332	−0.349922
$445$	0	0
$446$	0.289769	0.0137210
$447$	−0.0827637	−0.00391459
$448$	−46.1726	−2.18145
$449$	−35.0886	−1.65593	−0.827967	−	0.560776i	$-0.810503\pi$
$449$	−35.0886	−1.65593	−0.827967	+	0.560776i	$0.810503\pi$
$450$	0	0
$451$	16.8781	0.794757
$452$	−35.3757	−1.66393
$453$	4.14866	0.194921
$454$	23.2841	1.09278
$455$	0	0
$456$	−0.516292	−0.0241776
$457$	−24.1907	−1.13159	−0.565797	−	0.824544i	$-0.691432\pi$
$457$	−24.1907	−1.13159	−0.565797	+	0.824544i	$0.691432\pi$
$458$	−16.9677	−0.792846
$459$	25.3839	1.18482
$460$	0	0
$461$	−11.4172	−0.531753	−0.265876	−	0.964007i	$-0.585661\pi$
$461$	−11.4172	−0.531753	−0.265876	+	0.964007i	$0.585661\pi$
$462$	47.5510	2.21227
$463$	−3.69770	−0.171847	−0.0859235	−	0.996302i	$-0.527384\pi$
$463$	−3.69770	−0.171847	−0.0859235	+	0.996302i	$0.527384\pi$
$464$	11.4556	0.531812
$465$	0	0
$466$	18.6931	0.865940
$467$	25.9384	1.20028	0.600142	−	0.799893i	$-0.295111\pi$
$467$	25.9384	1.20028	0.600142	+	0.799893i	$0.295111\pi$
$468$	−0.987473	−0.0456459
$469$	8.21164	0.379178
$470$	0	0
$471$	−13.0872	−0.603025
$472$	−12.8317	−0.590629
$473$	−4.07230	−0.187245
$474$	−50.0212	−2.29755
$475$	0	0
$476$	−48.6327	−2.22908
$477$	0.422358	0.0193384
$478$	6.74886	0.308686
$479$	−15.9509	−0.728817	−0.364408	−	0.931239i	$-0.618729\pi$
$479$	−15.9509	−0.728817	−0.364408	+	0.931239i	$0.618729\pi$
$480$	0	0
$481$	−5.95369	−0.271465
$482$	−2.14986	−0.0979233
$483$	−12.6084	−0.573700
$484$	0.887581	0.0403446
$485$	0	0
$486$	−2.33475	−0.105906
$487$	−2.85926	−0.129565	−0.0647826	−	0.997899i	$-0.520635\pi$
$487$	−2.85926	−0.129565	−0.0647826	+	0.997899i	$0.520635\pi$
$488$	19.6901	0.891328
$489$	28.2566	1.27781
$490$	0	0
$491$	−34.7086	−1.56638	−0.783189	−	0.621783i	$-0.786409\pi$
$491$	−34.7086	−1.56638	−0.783189	+	0.621783i	$0.786409\pi$
$492$	−22.3622	−1.00817
$493$	23.2306	1.04626
$494$	−1.75762	−0.0790789
$495$	0	0
$496$	−8.14590	−0.365762
$497$	−9.67735	−0.434089
$498$	21.3250	0.955595
$499$	32.6502	1.46162	0.730812	−	0.682579i	$-0.239142\pi$
$499$	32.6502	1.46162	0.730812	+	0.682579i	$0.239142\pi$
$500$	0	0
$501$	25.8577	1.15523
$502$	−46.1616	−2.06029
$503$	1.74843	0.0779587	0.0389793	−	0.999240i	$-0.487589\pi$
$503$	1.74843	0.0779587	0.0389793	+	0.999240i	$0.487589\pi$
$504$	0.539571	0.0240344
$505$	0	0
$506$	−13.8955	−0.617730
$507$	−0.0384790	−0.00170891
$508$	19.7258	0.875193
$509$	22.7486	1.00832	0.504158	−	0.863612i	$-0.331803\pi$
$509$	22.7486	1.00832	0.504158	+	0.863612i	$0.331803\pi$
$510$	0	0
$511$	−19.4523	−0.860519
$512$	−24.7421	−1.09346
$513$	−1.19889	−0.0529321
$514$	−57.0474	−2.51625
$515$	0	0
$516$	5.39551	0.237524
$517$	3.84654	0.169170
$518$	13.7156	0.602630
$519$	−16.5471	−0.726336
$520$	0	0
$521$	−11.8373	−0.518603	−0.259301	−	0.965796i	$-0.583492\pi$
$521$	−11.8373	−0.518603	−0.259301	+	0.965796i	$0.583492\pi$
$522$	−1.08664	−0.0475611
$523$	−18.3947	−0.804344	−0.402172	−	0.915564i	$-0.631745\pi$
$523$	−18.3947	−0.804344	−0.402172	+	0.915564i	$0.631745\pi$
$524$	18.4235	0.804833
$525$	0	0
$526$	22.0543	0.961614
$527$	−16.5190	−0.719578
$528$	13.5767	0.590850
$529$	−19.3156	−0.839807
$530$	0	0
$531$	−1.00343	−0.0435452
$532$	2.29693	0.0995846
$533$	−18.0567	−0.782122
$534$	4.16887	0.180404
$535$	0	0
$536$	−2.84402	−0.122843
$537$	−22.5657	−0.973783
$538$	0.129938	0.00560203
$539$	−26.6063	−1.14602
$540$	0	0
$541$	−10.8842	−0.467948	−0.233974	−	0.972243i	$-0.575173\pi$
$541$	−10.8842	−0.467948	−0.233974	+	0.972243i	$0.575173\pi$
$542$	−46.4086	−1.99342
$543$	−12.0803	−0.518417
$544$	−37.3259	−1.60034
$545$	0	0
$546$	−50.8716	−2.17710
$547$	−41.3630	−1.76855	−0.884277	−	0.466962i	$-0.845348\pi$
$547$	−41.3630	−1.76855	−0.884277	+	0.466962i	$0.845348\pi$
$548$	−15.3683	−0.656503
$549$	1.53975	0.0657149
$550$	0	0
$551$	−1.09719	−0.0467418
$552$	4.36677	0.185862
$553$	52.7838	2.24460
$554$	48.1153	2.04422
$555$	0	0
$556$	−34.7588	−1.47410
$557$	11.7230	0.496720	0.248360	−	0.968668i	$-0.420108\pi$
$557$	11.7230	0.496720	0.248360	+	0.968668i	$0.420108\pi$
$558$	0.772697	0.0327109
$559$	4.35667	0.184268
$560$	0	0
$561$	27.5320	1.16240
$562$	66.2277	2.79365
$563$	19.6865	0.829689	0.414844	−	0.909892i	$-0.363836\pi$
$563$	19.6865	0.829689	0.414844	+	0.909892i	$0.363836\pi$
$564$	−5.09639	−0.214597
$565$	0	0
$566$	64.2556	2.70086
$567$	−33.4892	−1.40641
$568$	3.35165	0.140632
$569$	44.1961	1.85280	0.926399	−	0.376542i	$-0.122887\pi$
$569$	44.1961	1.85280	0.926399	+	0.376542i	$0.122887\pi$
$570$	0	0
$571$	−42.2447	−1.76789	−0.883943	−	0.467595i	$-0.845121\pi$
$571$	−42.2447	−1.76789	−0.883943	+	0.467595i	$0.845121\pi$
$572$	−31.8042	−1.32980
$573$	25.9371	1.08354
$574$	41.5976	1.73625
$575$	0	0
$576$	1.25051	0.0521047
$577$	−17.0708	−0.710668	−0.355334	−	0.934739i	$-0.615633\pi$
$577$	−17.0708	−0.710668	−0.355334	+	0.934739i	$0.615633\pi$
$578$	−13.0903	−0.544483
$579$	−9.72153	−0.404013
$580$	0	0
$581$	−22.5027	−0.933570
$582$	48.3236	2.00308
$583$	13.6032	0.563386
$584$	6.73710	0.278783
$585$	0	0
$586$	−41.3221	−1.70700
$587$	25.8807	1.06821	0.534105	−	0.845418i	$-0.320649\pi$
$587$	25.8807	1.06821	0.534105	+	0.845418i	$0.320649\pi$
$588$	35.2515	1.45375
$589$	0.780194	0.0321473
$590$	0	0
$591$	26.3873	1.08543
$592$	3.91606	0.160949
$593$	−21.0088	−0.862729	−0.431364	−	0.902178i	$-0.641968\pi$
$593$	−21.0088	−0.862729	−0.431364	+	0.902178i	$0.641968\pi$
$594$	−38.2423	−1.56910
$595$	0	0
$596$	−0.127525	−0.00522362
$597$	−4.26639	−0.174612
$598$	14.8658	0.607909
$599$	8.72823	0.356626	0.178313	−	0.983974i	$-0.442936\pi$
$599$	8.72823	0.356626	0.178313	+	0.983974i	$0.442936\pi$
$600$	0	0
$601$	−22.4335	−0.915080	−0.457540	−	0.889189i	$-0.651269\pi$
$601$	−22.4335	−0.915080	−0.457540	+	0.889189i	$0.651269\pi$
$602$	−10.0366	−0.409060
$603$	−0.222400	−0.00905682
$604$	6.39238	0.260102
$605$	0	0
$606$	27.2100	1.10533
$607$	27.7266	1.12539	0.562693	−	0.826666i	$-0.309765\pi$
$607$	27.7266	1.12539	0.562693	+	0.826666i	$0.309765\pi$
$608$	1.76291	0.0714955
$609$	−31.7565	−1.28684
$610$	0	0
$611$	−4.11515	−0.166481
$612$	1.31714	0.0532424
$613$	6.18419	0.249777	0.124888	−	0.992171i	$-0.460143\pi$
$613$	6.18419	0.249777	0.124888	+	0.992171i	$0.460143\pi$
$614$	−11.5196	−0.464892
$615$	0	0
$616$	17.3784	0.700194
$617$	−11.7107	−0.471456	−0.235728	−	0.971819i	$-0.575747\pi$
$617$	−11.7107	−0.471456	−0.235728	+	0.971819i	$0.575747\pi$
$618$	53.2747	2.14302
$619$	24.6950	0.992575	0.496288	−	0.868158i	$-0.334696\pi$
$619$	24.6950	0.992575	0.496288	+	0.868158i	$0.334696\pi$
$620$	0	0
$621$	10.1401	0.406909
$622$	−31.6448	−1.26884
$623$	−4.39911	−0.176247
$624$	−14.5248	−0.581456
$625$	0	0
$626$	−22.3961	−0.895129
$627$	−1.30034	−0.0519307
$628$	−20.1651	−0.804675
$629$	7.94134	0.316642
$630$	0	0
$631$	8.11033	0.322867	0.161434	−	0.986884i	$-0.448388\pi$
$631$	8.11033	0.322867	0.161434	+	0.986884i	$0.448388\pi$
$632$	−18.2811	−0.727184
$633$	−38.9342	−1.54750
$634$	−13.4732	−0.535087
$635$	0	0
$636$	−18.0232	−0.714668
$637$	28.4643	1.12780
$638$	−34.9983	−1.38560
$639$	0.262096	0.0103684
$640$	0	0
$641$	5.59199	0.220870	0.110435	−	0.993883i	$-0.464776\pi$
$641$	5.59199	0.220870	0.110435	+	0.993883i	$0.464776\pi$
$642$	34.7765	1.37252
$643$	27.6688	1.09115	0.545575	−	0.838062i	$-0.316311\pi$
$643$	27.6688	1.09115	0.545575	+	0.838062i	$0.316311\pi$
$644$	−19.4273	−0.765544
$645$	0	0
$646$	2.34440	0.0922393
$647$	36.5140	1.43551	0.717757	−	0.696294i	$-0.245169\pi$
$647$	36.5140	1.43551	0.717757	+	0.696294i	$0.245169\pi$
$648$	11.5986	0.455637
$649$	−32.3182	−1.26860
$650$	0	0
$651$	22.5816	0.885041
$652$	43.5386	1.70510
$653$	−25.4592	−0.996296	−0.498148	−	0.867092i	$-0.665986\pi$
$653$	−25.4592	−0.996296	−0.498148	+	0.867092i	$0.665986\pi$
$654$	−58.6766	−2.29444
$655$	0	0
$656$	11.8769	0.463714
$657$	0.526836	0.0205538
$658$	9.48015	0.369575
$659$	−24.6793	−0.961369	−0.480684	−	0.876894i	$-0.659612\pi$
$659$	−24.6793	−0.961369	−0.480684	+	0.876894i	$0.659612\pi$
$660$	0	0
$661$	−22.3577	−0.869615	−0.434808	−	0.900523i	$-0.643184\pi$
$661$	−22.3577	−0.869615	−0.434808	+	0.900523i	$0.643184\pi$
$662$	33.6853	1.30922
$663$	−29.4546	−1.14392
$664$	7.79358	0.302450
$665$	0	0
$666$	−0.371467	−0.0143941
$667$	9.27996	0.359321
$668$	39.8423	1.54154
$669$	−0.229351	−0.00886723
$670$	0	0
$671$	49.5918	1.91447
$672$	51.0248	1.96833
$673$	−28.8997	−1.11400	−0.557001	−	0.830512i	$-0.688048\pi$
$673$	−28.8997	−1.11400	−0.557001	+	0.830512i	$0.688048\pi$
$674$	15.5307	0.598221
$675$	0	0
$676$	−0.0592896	−0.00228037
$677$	−3.14192	−0.120754	−0.0603769	−	0.998176i	$-0.519230\pi$
$677$	−3.14192	−0.120754	−0.0603769	+	0.998176i	$0.519230\pi$
$678$	49.3582	1.89559
$679$	−50.9925	−1.95691
$680$	0	0
$681$	−18.4293	−0.706212
$682$	24.8868	0.952965
$683$	−12.9423	−0.495224	−0.247612	−	0.968859i	$-0.579646\pi$
$683$	−12.9423	−0.495224	−0.247612	+	0.968859i	$0.579646\pi$
$684$	−0.0622089	−0.00237862
$685$	0	0
$686$	−7.48107	−0.285629
$687$	13.4298	0.512380
$688$	−2.86562	−0.109251
$689$	−14.5531	−0.554429
$690$	0	0
$691$	−35.5562	−1.35262	−0.676311	−	0.736616i	$-0.736422\pi$
$691$	−35.5562	−1.35262	−0.676311	+	0.736616i	$0.736422\pi$
$692$	−25.4962	−0.969222
$693$	1.35897	0.0516231
$694$	−4.16162	−0.157973
$695$	0	0
$696$	10.9985	0.416897
$697$	24.0850	0.912283
$698$	22.3459	0.845803
$699$	−14.7955	−0.559617
$700$	0	0
$701$	15.7109	0.593393	0.296697	−	0.954972i	$-0.404115\pi$
$701$	15.7109	0.593393	0.296697	+	0.954972i	$0.404115\pi$
$702$	40.9128	1.54416
$703$	−0.375071	−0.0141461
$704$	40.2762	1.51797
$705$	0	0
$706$	−31.0942	−1.17025
$707$	−28.7128	−1.07986
$708$	42.8194	1.60925
$709$	−11.3414	−0.425936	−0.212968	−	0.977059i	$-0.568313\pi$
$709$	−11.3414	−0.425936	−0.212968	+	0.977059i	$0.568313\pi$
$710$	0	0
$711$	−1.42957	−0.0536131
$712$	1.52358	0.0570987
$713$	−6.59884	−0.247129
$714$	67.8552	2.53942
$715$	0	0
$716$	−34.7700	−1.29941
$717$	−5.34170	−0.199489
$718$	−68.7821	−2.56692
$719$	−27.4225	−1.02269	−0.511343	−	0.859377i	$-0.670852\pi$
$719$	−27.4225	−1.02269	−0.511343	+	0.859377i	$0.670852\pi$
$720$	0	0
$721$	−56.2170	−2.09363
$722$	40.7365	1.51606
$723$	1.70160	0.0632833
$724$	−18.6138	−0.691775
$725$	0	0
$726$	−1.23840	−0.0459615
$727$	−26.3265	−0.976396	−0.488198	−	0.872733i	$-0.662346\pi$
$727$	−26.3265	−0.976396	−0.488198	+	0.872733i	$0.662346\pi$
$728$	−18.5919	−0.689062
$729$	27.8742	1.03238
$730$	0	0
$731$	−5.81116	−0.214934
$732$	−65.7056	−2.42855
$733$	17.1782	0.634490	0.317245	−	0.948344i	$-0.397242\pi$
$733$	17.1782	0.634490	0.317245	+	0.948344i	$0.397242\pi$
$734$	36.6954	1.35445
$735$	0	0
$736$	−14.9106	−0.549612
$737$	−7.16299	−0.263852
$738$	−1.12661	−0.0414710
$739$	45.5581	1.67588	0.837940	−	0.545762i	$-0.183760\pi$
$739$	45.5581	1.67588	0.837940	+	0.545762i	$0.183760\pi$
$740$	0	0
$741$	1.39115	0.0511050
$742$	33.5263	1.23079
$743$	−27.3015	−1.00160	−0.500798	−	0.865564i	$-0.666960\pi$
$743$	−27.3015	−1.00160	−0.500798	+	0.865564i	$0.666960\pi$
$744$	−7.82088	−0.286727
$745$	0	0
$746$	−50.0579	−1.83275
$747$	0.609452	0.0222987
$748$	42.4222	1.55111
$749$	−36.6972	−1.34089
$750$	0	0
$751$	36.3189	1.32530	0.662648	−	0.748931i	$-0.269433\pi$
$751$	36.3189	1.32530	0.662648	+	0.748931i	$0.269433\pi$
$752$	2.70676	0.0987052
$753$	36.5368	1.33147
$754$	37.4423	1.36357
$755$	0	0
$756$	−53.4667	−1.94457
$757$	−26.8976	−0.977611	−0.488806	−	0.872393i	$-0.662567\pi$
$757$	−26.8976	−0.977611	−0.488806	+	0.872393i	$0.662567\pi$
$758$	−71.1428	−2.58402
$759$	10.9982	0.399210
$760$	0	0
$761$	−47.1591	−1.70951	−0.854757	−	0.519028i	$-0.826294\pi$
$761$	−47.1591	−1.70951	−0.854757	+	0.519028i	$0.826294\pi$
$762$	−27.5226	−0.997040
$763$	61.9173	2.24156
$764$	39.9646	1.44587
$765$	0	0
$766$	26.3770	0.953038
$767$	34.5751	1.24843
$768$	3.47070	0.125238
$769$	−6.84252	−0.246747	−0.123374	−	0.992360i	$-0.539371\pi$
$769$	−6.84252	−0.246747	−0.123374	+	0.992360i	$0.539371\pi$
$770$	0	0
$771$	45.1528	1.62614
$772$	−14.9792	−0.539114
$773$	19.6772	0.707740	0.353870	−	0.935295i	$-0.384866\pi$
$773$	19.6772	0.707740	0.353870	+	0.935295i	$0.384866\pi$
$774$	0.271825	0.00977054
$775$	0	0
$776$	17.6607	0.633983
$777$	−10.8559	−0.389452
$778$	−18.5991	−0.666810
$779$	−1.13754	−0.0407565
$780$	0	0
$781$	8.44152	0.302061
$782$	−19.8288	−0.709078
$783$	25.5397	0.912715
$784$	−18.7225	−0.668661
$785$	0	0
$786$	−25.7055	−0.916885
$787$	−26.7410	−0.953213	−0.476607	−	0.879117i	$-0.658133\pi$
$787$	−26.7410	−0.953213	−0.476607	+	0.879117i	$0.658133\pi$
$788$	40.6584	1.44839
$789$	−17.4559	−0.621447
$790$	0	0
$791$	−52.0843	−1.85190
$792$	−0.470666	−0.0167244
$793$	−53.0549	−1.88403
$794$	−23.3727	−0.829466
$795$	0	0
$796$	−6.57378	−0.233001
$797$	−54.6670	−1.93640	−0.968202	−	0.250171i	$-0.919513\pi$
$797$	−54.6670	−1.93640	−0.968202	+	0.250171i	$0.919513\pi$
$798$	−3.20481	−0.113449
$799$	5.48900	0.194187
$800$	0	0
$801$	0.119143	0.00420972
$802$	28.3036	0.999437
$803$	16.9682	0.598794
$804$	9.49045	0.334702
$805$	0	0
$806$	−26.6247	−0.937815
$807$	−0.102845	−0.00362033
$808$	9.94438	0.349842
$809$	−20.5992	−0.724230	−0.362115	−	0.932133i	$-0.617945\pi$
$809$	−20.5992	−0.724230	−0.362115	+	0.932133i	$0.617945\pi$
$810$	0	0
$811$	53.0273	1.86204	0.931020	−	0.364968i	$-0.118920\pi$
$811$	53.0273	1.86204	0.931020	+	0.364968i	$0.118920\pi$
$812$	−48.9313	−1.71715
$813$	36.7322	1.28826
$814$	−11.9641	−0.419342
$815$	0	0
$816$	19.3739	0.678222
$817$	0.274462	0.00960222
$818$	−39.6812	−1.38742
$819$	−1.45387	−0.0508024
$820$	0	0
$821$	−17.4856	−0.610250	−0.305125	−	0.952312i	$-0.598698\pi$
$821$	−17.4856	−0.610250	−0.305125	+	0.952312i	$0.598698\pi$
$822$	21.4428	0.747904
$823$	−3.94292	−0.137442	−0.0687208	−	0.997636i	$-0.521892\pi$
$823$	−3.94292	−0.137442	−0.0687208	+	0.997636i	$0.521892\pi$
$824$	19.4702	0.678275
$825$	0	0
$826$	−79.6513	−2.77142
$827$	−46.4685	−1.61587	−0.807934	−	0.589274i	$-0.799414\pi$
$827$	−46.4685	−1.61587	−0.807934	+	0.589274i	$0.799414\pi$
$828$	0.526160	0.0182853
$829$	−5.50401	−0.191162	−0.0955811	−	0.995422i	$-0.530471\pi$
$829$	−5.50401	−0.191162	−0.0955811	+	0.995422i	$0.530471\pi$
$830$	0	0
$831$	−38.0831	−1.32109
$832$	−43.0887	−1.49383
$833$	−37.9672	−1.31548
$834$	48.4976	1.67933
$835$	0	0
$836$	−2.00361	−0.0692962
$837$	−18.1609	−0.627734
$838$	−15.7035	−0.542469
$839$	−41.1331	−1.42007	−0.710037	−	0.704165i	$-0.751322\pi$
$839$	−41.1331	−1.42007	−0.710037	+	0.704165i	$0.751322\pi$
$840$	0	0
$841$	−5.62674	−0.194025
$842$	−53.9314	−1.85860
$843$	−52.4190	−1.80541
$844$	−59.9910	−2.06498
$845$	0	0
$846$	−0.256755	−0.00882743
$847$	1.30680	0.0449022
$848$	9.57237	0.328716
$849$	−50.8581	−1.74544
$850$	0	0
$851$	3.17233	0.108746
$852$	−11.1844	−0.383172
$853$	12.6606	0.433491	0.216746	−	0.976228i	$-0.430456\pi$
$853$	12.6606	0.433491	0.216746	+	0.976228i	$0.430456\pi$
$854$	122.224	4.18241
$855$	0	0
$856$	12.7097	0.434408
$857$	−29.3491	−1.00255	−0.501273	−	0.865289i	$-0.667135\pi$
$857$	−29.3491	−1.00255	−0.501273	+	0.865289i	$0.667135\pi$
$858$	44.3751	1.51494
$859$	−16.5376	−0.564256	−0.282128	−	0.959377i	$-0.591040\pi$
$859$	−16.5376	−0.564256	−0.282128	+	0.959377i	$0.591040\pi$
$860$	0	0
$861$	−32.9243	−1.12206
$862$	−72.2158	−2.45968
$863$	−50.4538	−1.71747	−0.858734	−	0.512421i	$-0.828749\pi$
$863$	−50.4538	−1.71747	−0.858734	+	0.512421i	$0.828749\pi$
$864$	−41.0361	−1.39608
$865$	0	0
$866$	27.0899	0.920554
$867$	10.3609	0.351874
$868$	34.7943	1.18100
$869$	−46.0432	−1.56191
$870$	0	0
$871$	7.66319	0.259657
$872$	−21.4444	−0.726199
$873$	1.38105	0.0467416
$874$	0.936519	0.0316782
$875$	0	0
$876$	−22.4816	−0.759584
$877$	−23.3907	−0.789847	−0.394924	−	0.918714i	$-0.629229\pi$
$877$	−23.3907	−0.789847	−0.394924	+	0.918714i	$0.629229\pi$
$878$	−35.4505	−1.19640
$879$	32.7063	1.10315
$880$	0	0
$881$	−9.95967	−0.335550	−0.167775	−	0.985825i	$-0.553658\pi$
$881$	−9.95967	−0.335550	−0.167775	+	0.985825i	$0.553658\pi$
$882$	1.77597	0.0597999
$883$	−26.5158	−0.892329	−0.446165	−	0.894951i	$-0.647210\pi$
$883$	−26.5158	−0.892329	−0.446165	+	0.894951i	$0.647210\pi$
$884$	−45.3846	−1.52645
$885$	0	0
$886$	9.54652	0.320722
$887$	−54.2449	−1.82137	−0.910683	−	0.413105i	$-0.864444\pi$
$887$	−54.2449	−1.82137	−0.910683	+	0.413105i	$0.864444\pi$
$888$	3.75982	0.126171
$889$	29.0427	0.974061
$890$	0	0
$891$	29.2125	0.978656
$892$	−0.353391	−0.0118324
$893$	−0.259246	−0.00867535
$894$	0.177930	0.00595087
$895$	0	0
$896$	39.2917	1.31264
$897$	−11.7662	−0.392864
$898$	75.4355	2.51731
$899$	−16.6204	−0.554321
$900$	0	0
$901$	19.4117	0.646697
$902$	−36.2854	−1.20817
$903$	7.94390	0.264356
$904$	18.0388	0.599963
$905$	0	0
$906$	−8.91902	−0.296315
$907$	−33.0947	−1.09889	−0.549447	−	0.835529i	$-0.685161\pi$
$907$	−33.0947	−1.09889	−0.549447	+	0.835529i	$0.685161\pi$
$908$	−28.3964	−0.942368
$909$	0.777643	0.0257928
$910$	0	0
$911$	20.2776	0.671828	0.335914	−	0.941893i	$-0.390955\pi$
$911$	20.2776	0.671828	0.335914	+	0.941893i	$0.390955\pi$
$912$	−0.915033	−0.0302998
$913$	19.6290	0.649627
$914$	52.0066	1.72023
$915$	0	0
$916$	20.6931	0.683719
$917$	27.1252	0.895753
$918$	−54.5717	−1.80113
$919$	38.1612	1.25882	0.629412	−	0.777072i	$-0.283296\pi$
$919$	38.1612	1.25882	0.629412	+	0.777072i	$0.283296\pi$
$920$	0	0
$921$	9.11769	0.300438
$922$	24.5454	0.808359
$923$	−9.03100	−0.297259
$924$	−57.9914	−1.90778
$925$	0	0
$926$	7.94953	0.261238
$927$	1.52255	0.0500072
$928$	−37.5551	−1.23281
$929$	19.1236	0.627425	0.313712	−	0.949518i	$-0.398427\pi$
$929$	19.1236	0.627425	0.313712	+	0.949518i	$0.398427\pi$
$930$	0	0
$931$	1.79320	0.0587696
$932$	−22.7973	−0.746752
$933$	25.0467	0.819994
$934$	−55.7637	−1.82465
$935$	0	0
$936$	0.503533	0.0164585
$937$	40.2441	1.31472	0.657359	−	0.753578i	$-0.271674\pi$
$937$	40.2441	1.31472	0.657359	+	0.753578i	$0.271674\pi$
$938$	−17.6538	−0.576419
$939$	17.7265	0.578481
$940$	0	0
$941$	25.7799	0.840399	0.420200	−	0.907432i	$-0.361960\pi$
$941$	25.7799	0.840399	0.420200	+	0.907432i	$0.361960\pi$
$942$	28.1355	0.916705
$943$	9.62123	0.313310
$944$	−22.7419	−0.740186
$945$	0	0
$946$	8.75486	0.284645
$947$	40.7917	1.32555	0.662776	−	0.748818i	$-0.269378\pi$
$947$	40.7917	1.32555	0.662776	+	0.748818i	$0.269378\pi$
$948$	61.0039	1.98132
$949$	−18.1531	−0.589274
$950$	0	0
$951$	10.6640	0.345802
$952$	24.7989	0.803736
$953$	−36.8213	−1.19276	−0.596379	−	0.802703i	$-0.703395\pi$
$953$	−36.8213	−1.19276	−0.596379	+	0.802703i	$0.703395\pi$
$954$	−0.908008	−0.0293979
$955$	0	0
$956$	−8.23065	−0.266198
$957$	27.7010	0.895448
$958$	34.2922	1.10793
$959$	−22.6271	−0.730666
$960$	0	0
$961$	−19.1815	−0.618757
$962$	12.7996	0.412675
$963$	0.993888	0.0320276
$964$	2.62188	0.0844451
$965$	0	0
$966$	27.1062	0.872126
$967$	−8.04134	−0.258592	−0.129296	−	0.991606i	$-0.541272\pi$
$967$	−8.04134	−0.258592	−0.129296	+	0.991606i	$0.541272\pi$
$968$	−0.452596	−0.0145470
$969$	−1.85559	−0.0596100
$970$	0	0
$971$	−29.7266	−0.953972	−0.476986	−	0.878911i	$-0.658271\pi$
$971$	−29.7266	−0.953972	−0.476986	+	0.878911i	$0.658271\pi$
$972$	2.84736	0.0913293
$973$	−51.1760	−1.64063
$974$	6.14699	0.196962
$975$	0	0
$976$	34.8971	1.11703
$977$	−37.3788	−1.19586	−0.597928	−	0.801550i	$-0.704009\pi$
$977$	−37.3788	−1.19586	−0.597928	+	0.801550i	$0.704009\pi$
$978$	−60.7476	−1.94249
$979$	3.83733	0.122641
$980$	0	0
$981$	−1.67693	−0.0535404
$982$	74.6186	2.38117
$983$	29.0852	0.927672	0.463836	−	0.885921i	$-0.346473\pi$
$983$	29.0852	0.927672	0.463836	+	0.885921i	$0.346473\pi$
$984$	11.4030	0.363514
$985$	0	0
$986$	−49.9425	−1.59049
$987$	−7.50350	−0.238839
$988$	2.14352	0.0681945
$989$	−2.32139	−0.0738158
$990$	0	0
$991$	−11.1607	−0.354532	−0.177266	−	0.984163i	$-0.556725\pi$
$991$	−11.1607	−0.354532	−0.177266	+	0.984163i	$0.556725\pi$
$992$	26.7049	0.847881
$993$	−26.6618	−0.846087
$994$	20.8049	0.659892
$995$	0	0
$996$	−26.0071	−0.824066
$997$	−9.75783	−0.309034	−0.154517	−	0.987990i	$-0.549382\pi$
$997$	−9.75783	−0.309034	−0.154517	+	0.987990i	$0.549382\pi$
$998$	−70.1933	−2.22193
$999$	8.73070	0.276227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.9	✓	40
5.4	even	2		6025.2.a.n.1.32	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.9	✓	40	1.1	even	1	trivial
6025.2.a.n.1.32	yes	40	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14986 q^{2} +1.70160 q^{3} +2.62188 q^{4} -3.65820 q^{6} +3.86024 q^{7} -1.33695 q^{8} -0.104549 q^{9} +O(q^{10})\)	\(q-2.14986 q^{2} +1.70160 q^{3} +2.62188 q^{4} -3.65820 q^{6} +3.86024 q^{7} -1.33695 q^{8} -0.104549 q^{9} -3.36727 q^{11} +4.46140 q^{12} +3.60241 q^{13} -8.29896 q^{14} -2.36950 q^{16} -4.80509 q^{17} +0.224765 q^{18} +0.226945 q^{19} +6.56859 q^{21} +7.23915 q^{22} -1.91949 q^{23} -2.27496 q^{24} -7.74467 q^{26} -5.28271 q^{27} +10.1211 q^{28} -4.83459 q^{29} +3.43781 q^{31} +7.76800 q^{32} -5.72976 q^{33} +10.3303 q^{34} -0.274114 q^{36} -1.65269 q^{37} -0.487900 q^{38} +6.12988 q^{39} -5.01238 q^{41} -14.1215 q^{42} +1.20938 q^{43} -8.82859 q^{44} +4.12663 q^{46} -1.14233 q^{47} -4.03195 q^{48} +7.90145 q^{49} -8.17636 q^{51} +9.44510 q^{52} -4.03982 q^{53} +11.3571 q^{54} -5.16096 q^{56} +0.386171 q^{57} +10.3937 q^{58} +9.59775 q^{59} -14.7276 q^{61} -7.39079 q^{62} -0.403583 q^{63} -11.9611 q^{64} +12.3182 q^{66} +2.12724 q^{67} -12.5984 q^{68} -3.26621 q^{69} -2.50693 q^{71} +0.139777 q^{72} -5.03915 q^{73} +3.55305 q^{74} +0.595023 q^{76} -12.9985 q^{77} -13.1784 q^{78} +13.6737 q^{79} -8.67542 q^{81} +10.7759 q^{82} -5.82936 q^{83} +17.2221 q^{84} -2.59998 q^{86} -8.22655 q^{87} +4.50189 q^{88} -1.13959 q^{89} +13.9062 q^{91} -5.03268 q^{92} +5.84978 q^{93} +2.45584 q^{94} +13.2180 q^{96} -13.2097 q^{97} -16.9870 q^{98} +0.352044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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