LMFDB - Embedded newform 4025.2.a.w.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 19x^{5} + 12x^{4} - 34x^{3} - 12x^{2} + 17x + 7 $ x^8 - 3x^7 - 6x^6 + 19x^5 + 12x^4 - 34x^3 - 12x^2 + 17*x + 7
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			1.5
Root			$1.07669$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.07669 q^{2} +0.452781 q^{3} -0.840734 q^{4} +0.487505 q^{6} -1.00000 q^{7} -3.05860 q^{8} -2.79499 q^{9} +O(q^{10})$	\(q+1.07669 q^{2} +0.452781 q^{3} -0.840734 q^{4} +0.487505 q^{6} -1.00000 q^{7} -3.05860 q^{8} -2.79499 q^{9} -3.82971 q^{11} -0.380668 q^{12} +0.602656 q^{13} -1.07669 q^{14} -1.61170 q^{16} +1.96757 q^{17} -3.00934 q^{18} +6.94375 q^{19} -0.452781 q^{21} -4.12342 q^{22} -1.00000 q^{23} -1.38487 q^{24} +0.648875 q^{26} -2.62386 q^{27} +0.840734 q^{28} +8.21503 q^{29} -9.00220 q^{31} +4.38189 q^{32} -1.73402 q^{33} +2.11847 q^{34} +2.34984 q^{36} -1.08337 q^{37} +7.47628 q^{38} +0.272871 q^{39} +2.84151 q^{41} -0.487505 q^{42} -4.32461 q^{43} +3.21977 q^{44} -1.07669 q^{46} -2.72760 q^{47} -0.729745 q^{48} +1.00000 q^{49} +0.890877 q^{51} -0.506674 q^{52} +11.2864 q^{53} -2.82509 q^{54} +3.05860 q^{56} +3.14399 q^{57} +8.84506 q^{58} +11.5660 q^{59} -9.60958 q^{61} -9.69259 q^{62} +2.79499 q^{63} +7.94134 q^{64} -1.86701 q^{66} +13.0701 q^{67} -1.65420 q^{68} -0.452781 q^{69} +11.2197 q^{71} +8.54874 q^{72} -14.5431 q^{73} -1.16645 q^{74} -5.83785 q^{76} +3.82971 q^{77} +0.293798 q^{78} +2.63634 q^{79} +7.19694 q^{81} +3.05943 q^{82} +11.0866 q^{83} +0.380668 q^{84} -4.65627 q^{86} +3.71961 q^{87} +11.7135 q^{88} -2.00455 q^{89} -0.602656 q^{91} +0.840734 q^{92} -4.07602 q^{93} -2.93678 q^{94} +1.98404 q^{96} +7.93551 q^{97} +1.07669 q^{98} +10.7040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8	$ 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8} - 5 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} - q^{16} - q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{21} - 5 q^{22} - 8 q^{23} + 16 q^{24} + 22 q^{26} - q^{27} - 5 q^{28} - 5 q^{29} - q^{31} + 2 q^{32} + 12 q^{33} - 2 q^{34} + 16 q^{36} + 18 q^{37} + 14 q^{38} + 14 q^{39} - q^{41} + q^{42} + 20 q^{43} - 3 q^{46} + 10 q^{47} + 31 q^{48} + 8 q^{49} - 4 q^{51} + 11 q^{52} + 11 q^{53} + 29 q^{54} - 12 q^{56} + 8 q^{57} + 24 q^{58} + 20 q^{59} - 6 q^{61} + 2 q^{62} + 8 q^{64} - 37 q^{66} + 23 q^{67} + 9 q^{68} - 2 q^{69} + 3 q^{71} + 29 q^{72} - 8 q^{73} + 35 q^{74} - 29 q^{76} + 5 q^{77} + 31 q^{78} + 4 q^{79} - 44 q^{81} + 27 q^{82} + 4 q^{83} - 3 q^{84} - 18 q^{86} + 27 q^{87} - 4 q^{88} - 17 q^{89} - 9 q^{91} - 5 q^{92} - 7 q^{93} + 13 q^{94} + 22 q^{96} + 41 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8 - 5 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 - q^16 - q^17 + 6 * q^18 - 4 * q^19 - 2 * q^21 - 5 * q^22 - 8 * q^23 + 16 * q^24 + 22 * q^26 - q^27 - 5 * q^28 - 5 * q^29 - q^31 + 2 * q^32 + 12 * q^33 - 2 * q^34 + 16 * q^36 + 18 * q^37 + 14 * q^38 + 14 * q^39 - q^41 + q^42 + 20 * q^43 - 3 * q^46 + 10 * q^47 + 31 * q^48 + 8 * q^49 - 4 * q^51 + 11 * q^52 + 11 * q^53 + 29 * q^54 - 12 * q^56 + 8 * q^57 + 24 * q^58 + 20 * q^59 - 6 * q^61 + 2 * q^62 + 8 * q^64 - 37 * q^66 + 23 * q^67 + 9 * q^68 - 2 * q^69 + 3 * q^71 + 29 * q^72 - 8 * q^73 + 35 * q^74 - 29 * q^76 + 5 * q^77 + 31 * q^78 + 4 * q^79 - 44 * q^81 + 27 * q^82 + 4 * q^83 - 3 * q^84 - 18 * q^86 + 27 * q^87 - 4 * q^88 - 17 * q^89 - 9 * q^91 - 5 * q^92 - 7 * q^93 + 13 * q^94 + 22 * q^96 + 41 * q^97 + 3 * q^98 + 7 * 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 $

$2$	1.07669	0.761336	0.380668	−	0.924712i	$-0.375694\pi$
$2$	1.07669	0.761336	0.380668	+	0.924712i	$0.375694\pi$
$3$	0.452781	0.261413	0.130707	−	0.991421i	$-0.458275\pi$
$3$	0.452781	0.261413	0.130707	+	0.991421i	$0.458275\pi$
$4$	−0.840734	−0.420367
$5$	0	0
$5$	0	0
$6$	0.487505	0.199023
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.05860	−1.08138
$9$	−2.79499	−0.931663
$10$	0	0
$11$	−3.82971	−1.15470	−0.577351	−	0.816496i	$-0.695914\pi$
$11$	−3.82971	−1.15470	−0.577351	+	0.816496i	$0.695914\pi$
$12$	−0.380668	−0.109889
$13$	0.602656	0.167147	0.0835734	−	0.996502i	$-0.473367\pi$
$13$	0.602656	0.167147	0.0835734	+	0.996502i	$0.473367\pi$
$14$	−1.07669	−0.287758
$15$	0	0
$16$	−1.61170	−0.402924
$17$	1.96757	0.477206	0.238603	−	0.971117i	$-0.423311\pi$
$17$	1.96757	0.477206	0.238603	+	0.971117i	$0.423311\pi$
$18$	−3.00934	−0.709309
$19$	6.94375	1.59300	0.796502	−	0.604635i	$-0.206681\pi$
$19$	6.94375	1.59300	0.796502	+	0.604635i	$0.206681\pi$
$20$	0	0
$21$	−0.452781	−0.0988048
$22$	−4.12342	−0.879117
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.38487	−0.282686
$25$	0	0
$26$	0.648875	0.127255
$27$	−2.62386	−0.504962
$28$	0.840734	0.158884
$29$	8.21503	1.52549	0.762747	−	0.646697i	$-0.223850\pi$
$29$	8.21503	1.52549	0.762747	+	0.646697i	$0.223850\pi$
$30$	0	0
$31$	−9.00220	−1.61684	−0.808421	−	0.588605i	$-0.799678\pi$
$31$	−9.00220	−1.61684	−0.808421	+	0.588605i	$0.799678\pi$
$32$	4.38189	0.774616
$33$	−1.73402	−0.301854
$34$	2.11847	0.363314
$35$	0	0
$36$	2.34984	0.391641
$37$	−1.08337	−0.178104	−0.0890522	−	0.996027i	$-0.528384\pi$
$37$	−1.08337	−0.178104	−0.0890522	+	0.996027i	$0.528384\pi$
$38$	7.47628	1.21281
$39$	0.272871	0.0436943
$40$	0	0
$41$	2.84151	0.443769	0.221885	−	0.975073i	$-0.428779\pi$
$41$	2.84151	0.443769	0.221885	+	0.975073i	$0.428779\pi$
$42$	−0.487505	−0.0752237
$43$	−4.32461	−0.659497	−0.329748	−	0.944069i	$-0.606964\pi$
$43$	−4.32461	−0.659497	−0.329748	+	0.944069i	$0.606964\pi$
$44$	3.21977	0.485399
$45$	0	0
$46$	−1.07669	−0.158750
$47$	−2.72760	−0.397861	−0.198930	−	0.980014i	$-0.563747\pi$
$47$	−2.72760	−0.397861	−0.198930	+	0.980014i	$0.563747\pi$
$48$	−0.729745	−0.105330
$49$	1.00000	0.142857
$50$	0	0
$51$	0.890877	0.124748
$52$	−0.506674	−0.0702630
$53$	11.2864	1.55031	0.775155	−	0.631771i	$-0.217672\pi$
$53$	11.2864	1.55031	0.775155	+	0.631771i	$0.217672\pi$
$54$	−2.82509	−0.384446
$55$	0	0
$56$	3.05860	0.408722
$57$	3.14399	0.416432
$58$	8.84506	1.16141
$59$	11.5660	1.50577	0.752884	−	0.658153i	$-0.228662\pi$
$59$	11.5660	1.50577	0.752884	+	0.658153i	$0.228662\pi$
$60$	0	0
$61$	−9.60958	−1.23038	−0.615190	−	0.788379i	$-0.710921\pi$
$61$	−9.60958	−1.23038	−0.615190	+	0.788379i	$0.710921\pi$
$62$	−9.69259	−1.23096
$63$	2.79499	0.352136
$64$	7.94134	0.992668
$65$	0	0
$66$	−1.86701	−0.229813
$67$	13.0701	1.59677	0.798383	−	0.602150i	$-0.205689\pi$
$67$	13.0701	1.59677	0.798383	+	0.602150i	$0.205689\pi$
$68$	−1.65420	−0.200602
$69$	−0.452781	−0.0545084
$70$	0	0
$71$	11.2197	1.33153	0.665766	−	0.746160i	$-0.268105\pi$
$71$	11.2197	1.33153	0.665766	+	0.746160i	$0.268105\pi$
$72$	8.54874	1.00748
$73$	−14.5431	−1.70214	−0.851070	−	0.525052i	$-0.824046\pi$
$73$	−14.5431	−1.70214	−0.851070	+	0.525052i	$0.824046\pi$
$74$	−1.16645	−0.135597
$75$	0	0
$76$	−5.83785	−0.669647
$77$	3.82971	0.436436
$78$	0.293798	0.0332661
$79$	2.63634	0.296611	0.148305	−	0.988942i	$-0.452618\pi$
$79$	2.63634	0.296611	0.148305	+	0.988942i	$0.452618\pi$
$80$	0	0
$81$	7.19694	0.799660
$82$	3.05943	0.337858
$83$	11.0866	1.21691	0.608456	−	0.793588i	$-0.291789\pi$
$83$	11.0866	1.21691	0.608456	+	0.793588i	$0.291789\pi$
$84$	0.380668	0.0415343
$85$	0	0
$86$	−4.65627	−0.502099
$87$	3.71961	0.398784
$88$	11.7135	1.24867
$89$	−2.00455	−0.212482	−0.106241	−	0.994340i	$-0.533882\pi$
$89$	−2.00455	−0.212482	−0.106241	+	0.994340i	$0.533882\pi$
$90$	0	0
$91$	−0.602656	−0.0631755
$92$	0.840734	0.0876526
$93$	−4.07602	−0.422664
$94$	−2.93678	−0.302906
$95$	0	0
$96$	1.98404	0.202495
$97$	7.93551	0.805729	0.402865	−	0.915260i	$-0.368015\pi$
$97$	7.93551	0.805729	0.402865	+	0.915260i	$0.368015\pi$
$98$	1.07669	0.108762
$99$	10.7040	1.07579
$100$	0	0
$101$	1.66465	0.165639	0.0828195	−	0.996565i	$-0.473608\pi$
$101$	1.66465	0.165639	0.0828195	+	0.996565i	$0.473608\pi$
$102$	0.959200	0.0949750
$103$	5.47244	0.539215	0.269608	−	0.962970i	$-0.413106\pi$
$103$	5.47244	0.539215	0.269608	+	0.962970i	$0.413106\pi$
$104$	−1.84328	−0.180749
$105$	0	0
$106$	12.1520	1.18031
$107$	−0.409092	−0.0395484	−0.0197742	−	0.999804i	$-0.506295\pi$
$107$	−0.409092	−0.0395484	−0.0197742	+	0.999804i	$0.506295\pi$
$108$	2.20597	0.212269
$109$	−0.0524029	−0.00501929	−0.00250965	−	0.999997i	$-0.500799\pi$
$109$	−0.0524029	−0.00501929	−0.00250965	+	0.999997i	$0.500799\pi$
$110$	0	0
$111$	−0.490527	−0.0465588
$112$	1.61170	0.152291
$113$	8.09587	0.761595	0.380798	−	0.924658i	$-0.375649\pi$
$113$	8.09587	0.761595	0.380798	+	0.924658i	$0.375649\pi$
$114$	3.38511	0.317045
$115$	0	0
$116$	−6.90666	−0.641267
$117$	−1.68442	−0.155725
$118$	12.4530	1.14640
$119$	−1.96757	−0.180367
$120$	0	0
$121$	3.66671	0.333337
$122$	−10.3466	−0.936734
$123$	1.28658	0.116007
$124$	7.56846	0.679667
$125$	0	0
$126$	3.00934	0.268094
$127$	14.4800	1.28489	0.642447	−	0.766330i	$-0.277919\pi$
$127$	14.4800	1.28489	0.642447	+	0.766330i	$0.277919\pi$
$128$	−0.213404	−0.0188624
$129$	−1.95810	−0.172401
$130$	0	0
$131$	0.768275	0.0671245	0.0335622	−	0.999437i	$-0.489315\pi$
$131$	0.768275	0.0671245	0.0335622	+	0.999437i	$0.489315\pi$
$132$	1.45785	0.126890
$133$	−6.94375	−0.602099
$134$	14.0725	1.21568
$135$	0	0
$136$	−6.01800	−0.516039
$137$	−8.59602	−0.734407	−0.367204	−	0.930141i	$-0.619685\pi$
$137$	−8.59602	−0.734407	−0.367204	+	0.930141i	$0.619685\pi$
$138$	−0.487505	−0.0414992
$139$	10.9403	0.927946	0.463973	−	0.885849i	$-0.346424\pi$
$139$	10.9403	0.927946	0.463973	+	0.885849i	$0.346424\pi$
$140$	0	0
$141$	−1.23500	−0.104006
$142$	12.0802	1.01374
$143$	−2.30800	−0.193005
$144$	4.50468	0.375390
$145$	0	0
$146$	−15.6584	−1.29590
$147$	0.452781	0.0373447
$148$	0.910823	0.0748692
$149$	−7.27412	−0.595919	−0.297959	−	0.954579i	$-0.596306\pi$
$149$	−7.27412	−0.595919	−0.297959	+	0.954579i	$0.596306\pi$
$150$	0	0
$151$	9.36427	0.762054	0.381027	−	0.924564i	$-0.375571\pi$
$151$	9.36427	0.762054	0.381027	+	0.924564i	$0.375571\pi$
$152$	−21.2381	−1.72264
$153$	−5.49934	−0.444595
$154$	4.12342	0.332275
$155$	0	0
$156$	−0.229412	−0.0183677
$157$	20.2884	1.61919	0.809597	−	0.586986i	$-0.199686\pi$
$157$	20.2884	1.61919	0.809597	+	0.586986i	$0.199686\pi$
$158$	2.83852	0.225821
$159$	5.11028	0.405271
$160$	0	0
$161$	1.00000	0.0788110
$162$	7.74888	0.608810
$163$	−3.76561	−0.294945	−0.147473	−	0.989066i	$-0.547114\pi$
$163$	−3.76561	−0.294945	−0.147473	+	0.989066i	$0.547114\pi$
$164$	−2.38896	−0.186546
$165$	0	0
$166$	11.9368	0.926479
$167$	0.602450	0.0466190	0.0233095	−	0.999728i	$-0.492580\pi$
$167$	0.602450	0.0466190	0.0233095	+	0.999728i	$0.492580\pi$
$168$	1.38487	0.106845
$169$	−12.6368	−0.972062
$170$	0	0
$171$	−19.4077	−1.48414
$172$	3.63585	0.277231
$173$	−2.66511	−0.202624	−0.101312	−	0.994855i	$-0.532304\pi$
$173$	−2.66511	−0.202624	−0.101312	+	0.994855i	$0.532304\pi$
$174$	4.00487	0.303609
$175$	0	0
$176$	6.17234	0.465258
$177$	5.23687	0.393627
$178$	−2.15829	−0.161770
$179$	19.6354	1.46762	0.733809	−	0.679356i	$-0.237741\pi$
$179$	19.6354	1.46762	0.733809	+	0.679356i	$0.237741\pi$
$180$	0	0
$181$	5.01185	0.372528	0.186264	−	0.982500i	$-0.440362\pi$
$181$	5.01185	0.372528	0.186264	+	0.982500i	$0.440362\pi$
$182$	−0.648875	−0.0480978
$183$	−4.35103	−0.321638
$184$	3.05860	0.225483
$185$	0	0
$186$	−4.38862	−0.321789
$187$	−7.53523	−0.551030
$188$	2.29318	0.167248
$189$	2.62386	0.190858
$190$	0	0
$191$	4.37482	0.316551	0.158275	−	0.987395i	$-0.449407\pi$
$191$	4.37482	0.316551	0.158275	+	0.987395i	$0.449407\pi$
$192$	3.59568	0.259496
$193$	−4.89963	−0.352683	−0.176342	−	0.984329i	$-0.556426\pi$
$193$	−4.89963	−0.352683	−0.176342	+	0.984329i	$0.556426\pi$
$194$	8.54410	0.613431
$195$	0	0
$196$	−0.840734	−0.0600525
$197$	−19.6206	−1.39791	−0.698956	−	0.715165i	$-0.746352\pi$
$197$	−19.6206	−1.39791	−0.698956	+	0.715165i	$0.746352\pi$
$198$	11.5249	0.819041
$199$	−8.18751	−0.580397	−0.290198	−	0.956966i	$-0.593721\pi$
$199$	−8.18751	−0.580397	−0.290198	+	0.956966i	$0.593721\pi$
$200$	0	0
$201$	5.91789	0.417415
$202$	1.79232	0.126107
$203$	−8.21503	−0.576582
$204$	−0.748991	−0.0524399
$205$	0	0
$206$	5.89213	0.410524
$207$	2.79499	0.194265
$208$	−0.971299	−0.0673475
$209$	−26.5926	−1.83945
$210$	0	0
$211$	−23.6163	−1.62581	−0.812906	−	0.582394i	$-0.802116\pi$
$211$	−23.6163	−1.62581	−0.812906	+	0.582394i	$0.802116\pi$
$212$	−9.48889	−0.651700
$213$	5.08006	0.348080
$214$	−0.440466	−0.0301096
$215$	0	0
$216$	8.02532	0.546054
$217$	9.00220	0.611109
$218$	−0.0564218	−0.00382137
$219$	−6.58483	−0.444962
$220$	0	0
$221$	1.18577	0.0797634
$222$	−0.528147	−0.0354469
$223$	26.0027	1.74127	0.870636	−	0.491929i	$-0.163708\pi$
$223$	26.0027	1.74127	0.870636	+	0.491929i	$0.163708\pi$
$224$	−4.38189	−0.292777
$225$	0	0
$226$	8.71676	0.579830
$227$	9.71308	0.644680	0.322340	−	0.946624i	$-0.395531\pi$
$227$	9.71308	0.644680	0.322340	+	0.946624i	$0.395531\pi$
$228$	−2.64326	−0.175054
$229$	9.02301	0.596258	0.298129	−	0.954526i	$-0.403638\pi$
$229$	9.02301	0.596258	0.298129	+	0.954526i	$0.403638\pi$
$230$	0	0
$231$	1.73402	0.114090
$232$	−25.1265	−1.64963
$233$	−24.4999	−1.60504	−0.802521	−	0.596623i	$-0.796509\pi$
$233$	−24.4999	−1.60504	−0.802521	+	0.596623i	$0.796509\pi$
$234$	−1.81360	−0.118559
$235$	0	0
$236$	−9.72396	−0.632976
$237$	1.19368	0.0775379
$238$	−2.11847	−0.137320
$239$	−8.06261	−0.521527	−0.260764	−	0.965403i	$-0.583974\pi$
$239$	−8.06261	−0.521527	−0.260764	+	0.965403i	$0.583974\pi$
$240$	0	0
$241$	−7.12826	−0.459172	−0.229586	−	0.973288i	$-0.573737\pi$
$241$	−7.12826	−0.459172	−0.229586	+	0.973288i	$0.573737\pi$
$242$	3.94792	0.253782
$243$	11.1302	0.714003
$244$	8.07911	0.517212
$245$	0	0
$246$	1.38525	0.0883204
$247$	4.18469	0.266266
$248$	27.5341	1.74842
$249$	5.01979	0.318117
$250$	0	0
$251$	−27.0997	−1.71052	−0.855258	−	0.518203i	$-0.826601\pi$
$251$	−27.0997	−1.71052	−0.855258	+	0.518203i	$0.826601\pi$
$252$	−2.34984	−0.148026
$253$	3.82971	0.240772
$254$	15.5905	0.978237
$255$	0	0
$256$	−16.1125	−1.00703
$257$	−4.97036	−0.310042	−0.155021	−	0.987911i	$-0.549545\pi$
$257$	−4.97036	−0.310042	−0.155021	+	0.987911i	$0.549545\pi$
$258$	−2.10827	−0.131255
$259$	1.08337	0.0673171
$260$	0	0
$261$	−22.9609	−1.42125
$262$	0.827195	0.0511043
$263$	7.45249	0.459540	0.229770	−	0.973245i	$-0.426203\pi$
$263$	7.45249	0.459540	0.229770	+	0.973245i	$0.426203\pi$
$264$	5.30367	0.326418
$265$	0	0
$266$	−7.47628	−0.458400
$267$	−0.907623	−0.0555456
$268$	−10.9885	−0.671228
$269$	−30.3991	−1.85347	−0.926734	−	0.375719i	$-0.877396\pi$
$269$	−30.3991	−1.85347	−0.926734	+	0.375719i	$0.877396\pi$
$270$	0	0
$271$	−13.5771	−0.824749	−0.412375	−	0.911014i	$-0.635301\pi$
$271$	−13.5771	−0.824749	−0.412375	+	0.911014i	$0.635301\pi$
$272$	−3.17113	−0.192278
$273$	−0.272871	−0.0165149
$274$	−9.25526	−0.559131
$275$	0	0
$276$	0.380668	0.0229135
$277$	22.5026	1.35205	0.676026	−	0.736878i	$-0.263701\pi$
$277$	22.5026	1.35205	0.676026	+	0.736878i	$0.263701\pi$
$278$	11.7794	0.706479
$279$	25.1610	1.50635
$280$	0	0
$281$	−22.6147	−1.34908	−0.674541	−	0.738237i	$-0.735659\pi$
$281$	−22.6147	−1.34908	−0.674541	+	0.738237i	$0.735659\pi$
$282$	−1.32972	−0.0791835
$283$	−4.84386	−0.287937	−0.143969	−	0.989582i	$-0.545986\pi$
$283$	−4.84386	−0.287937	−0.143969	+	0.989582i	$0.545986\pi$
$284$	−9.43278	−0.559732
$285$	0	0
$286$	−2.48501	−0.146942
$287$	−2.84151	−0.167729
$288$	−12.2473	−0.721681
$289$	−13.1287	−0.772275
$290$	0	0
$291$	3.59305	0.210628
$292$	12.2269	0.715524
$293$	32.8714	1.92037	0.960185	−	0.279366i	$-0.0901242\pi$
$293$	32.8714	1.92037	0.960185	+	0.279366i	$0.0901242\pi$
$294$	0.487505	0.0284319
$295$	0	0
$296$	3.31358	0.192598
$297$	10.0486	0.583081
$298$	−7.83198	−0.453695
$299$	−0.602656	−0.0348525
$300$	0	0
$301$	4.32461	0.249266
$302$	10.0824	0.580179
$303$	0.753722	0.0433002
$304$	−11.1912	−0.641860
$305$	0	0
$306$	−5.92109	−0.338486
$307$	14.1539	0.807805	0.403903	−	0.914802i	$-0.367653\pi$
$307$	14.1539	0.807805	0.403903	+	0.914802i	$0.367653\pi$
$308$	−3.21977	−0.183464
$309$	2.47781	0.140958
$310$	0	0
$311$	−19.8544	−1.12584	−0.562920	−	0.826511i	$-0.690322\pi$
$311$	−19.8544	−1.12584	−0.562920	+	0.826511i	$0.690322\pi$
$312$	−0.834602	−0.0472501
$313$	21.7754	1.23082	0.615408	−	0.788209i	$-0.288991\pi$
$313$	21.7754	1.23082	0.615408	+	0.788209i	$0.288991\pi$
$314$	21.8444	1.23275
$315$	0	0
$316$	−2.21646	−0.124685
$317$	30.8982	1.73542	0.867709	−	0.497073i	$-0.165592\pi$
$317$	30.8982	1.73542	0.867709	+	0.497073i	$0.165592\pi$
$318$	5.50219	0.308548
$319$	−31.4612	−1.76149
$320$	0	0
$321$	−0.185229	−0.0103385
$322$	1.07669	0.0600017
$323$	13.6623	0.760191
$324$	−6.05071	−0.336151
$325$	0	0
$326$	−4.05440	−0.224552
$327$	−0.0237270	−0.00131211
$328$	−8.69103	−0.479882
$329$	2.72760	0.150377
$330$	0	0
$331$	20.7948	1.14298	0.571492	−	0.820607i	$-0.306365\pi$
$331$	20.7948	1.14298	0.571492	+	0.820607i	$0.306365\pi$
$332$	−9.32088	−0.511550
$333$	3.02800	0.165933
$334$	0.648653	0.0354927
$335$	0	0
$336$	0.729745	0.0398109
$337$	−27.0381	−1.47286	−0.736431	−	0.676513i	$-0.763490\pi$
$337$	−27.0381	−1.47286	−0.736431	+	0.676513i	$0.763490\pi$
$338$	−13.6059	−0.740066
$339$	3.66565	0.199091
$340$	0	0
$341$	34.4758	1.86697
$342$	−20.8961	−1.12993
$343$	−1.00000	−0.0539949
$344$	13.2272	0.713165
$345$	0	0
$346$	−2.86950	−0.154265
$347$	19.3139	1.03682	0.518411	−	0.855132i	$-0.326524\pi$
$347$	19.3139	1.03682	0.518411	+	0.855132i	$0.326524\pi$
$348$	−3.12720	−0.167636
$349$	6.20644	0.332223	0.166112	−	0.986107i	$-0.446879\pi$
$349$	6.20644	0.332223	0.166112	+	0.986107i	$0.446879\pi$
$350$	0	0
$351$	−1.58129	−0.0844028
$352$	−16.7814	−0.894451
$353$	1.43451	0.0763514	0.0381757	−	0.999271i	$-0.487845\pi$
$353$	1.43451	0.0763514	0.0381757	+	0.999271i	$0.487845\pi$
$354$	5.63850	0.299683
$355$	0	0
$356$	1.68530	0.0893206
$357$	−0.890877	−0.0471502
$358$	21.1413	1.11735
$359$	−3.33730	−0.176136	−0.0880681	−	0.996114i	$-0.528069\pi$
$359$	−3.33730	−0.176136	−0.0880681	+	0.996114i	$0.528069\pi$
$360$	0	0
$361$	29.2156	1.53766
$362$	5.39622	0.283619
$363$	1.66022	0.0871387
$364$	0.506674	0.0265569
$365$	0	0
$366$	−4.68472	−0.244874
$367$	−12.9543	−0.676209	−0.338105	−	0.941109i	$-0.609786\pi$
$367$	−12.9543	−0.676209	−0.338105	+	0.941109i	$0.609786\pi$
$368$	1.61170	0.0840155
$369$	−7.94199	−0.413444
$370$	0	0
$371$	−11.2864	−0.585962
$372$	3.42685	0.177674
$373$	33.9121	1.75590	0.877951	−	0.478750i	$-0.158910\pi$
$373$	33.9121	1.75590	0.877951	+	0.478750i	$0.158910\pi$
$374$	−8.11312	−0.419519
$375$	0	0
$376$	8.34261	0.430238
$377$	4.95084	0.254981
$378$	2.82509	0.145307
$379$	−5.74760	−0.295234	−0.147617	−	0.989045i	$-0.547160\pi$
$379$	−5.74760	−0.295234	−0.147617	+	0.989045i	$0.547160\pi$
$380$	0	0
$381$	6.55627	0.335888
$382$	4.71033	0.241002
$383$	−12.0897	−0.617757	−0.308879	−	0.951101i	$-0.599954\pi$
$383$	−12.0897	−0.617757	−0.308879	+	0.951101i	$0.599954\pi$
$384$	−0.0966250	−0.00493087
$385$	0	0
$386$	−5.27540	−0.268511
$387$	12.0872	0.614429
$388$	−6.67166	−0.338702
$389$	3.43699	0.174262	0.0871311	−	0.996197i	$-0.472230\pi$
$389$	3.43699	0.174262	0.0871311	+	0.996197i	$0.472230\pi$
$390$	0	0
$391$	−1.96757	−0.0995042
$392$	−3.05860	−0.154482
$393$	0.347860	0.0175472
$394$	−21.1254	−1.06428
$395$	0	0
$396$	−8.99923	−0.452228
$397$	15.0161	0.753636	0.376818	−	0.926287i	$-0.377018\pi$
$397$	15.0161	0.753636	0.376818	+	0.926287i	$0.377018\pi$
$398$	−8.81542	−0.441877
$399$	−3.14399	−0.157397
$400$	0	0
$401$	−21.5566	−1.07649	−0.538243	−	0.842790i	$-0.680912\pi$
$401$	−21.5566	−1.07649	−0.538243	+	0.842790i	$0.680912\pi$
$402$	6.37174	0.317794
$403$	−5.42523	−0.270250
$404$	−1.39953	−0.0696292
$405$	0	0
$406$	−8.84506	−0.438973
$407$	4.14898	0.205657
$408$	−2.72483	−0.134899
$409$	29.0106	1.43448	0.717241	−	0.696826i	$-0.245405\pi$
$409$	29.0106	1.43448	0.717241	+	0.696826i	$0.245405\pi$
$410$	0	0
$411$	−3.89211	−0.191984
$412$	−4.60087	−0.226668
$413$	−11.5660	−0.569127
$414$	3.00934	0.147901
$415$	0	0
$416$	2.64077	0.129475
$417$	4.95356	0.242577
$418$	−28.6320	−1.40044
$419$	33.3657	1.63002	0.815010	−	0.579446i	$-0.196731\pi$
$419$	33.3657	1.63002	0.815010	+	0.579446i	$0.196731\pi$
$420$	0	0
$421$	32.3224	1.57530	0.787650	−	0.616124i	$-0.211298\pi$
$421$	32.3224	1.57530	0.787650	+	0.616124i	$0.211298\pi$
$422$	−25.4275	−1.23779
$423$	7.62360	0.370672
$424$	−34.5206	−1.67647
$425$	0	0
$426$	5.46966	0.265006
$427$	9.60958	0.465040
$428$	0.343937	0.0166248
$429$	−1.04502	−0.0504540
$430$	0	0
$431$	−34.2395	−1.64926	−0.824630	−	0.565673i	$-0.808616\pi$
$431$	−34.2395	−1.64926	−0.824630	+	0.565673i	$0.808616\pi$
$432$	4.22887	0.203461
$433$	9.56285	0.459561	0.229781	−	0.973242i	$-0.426199\pi$
$433$	9.56285	0.459561	0.229781	+	0.973242i	$0.426199\pi$
$434$	9.69259	0.465259
$435$	0	0
$436$	0.0440570	0.00210995
$437$	−6.94375	−0.332164
$438$	−7.08983	−0.338765
$439$	−18.3043	−0.873616	−0.436808	−	0.899555i	$-0.643891\pi$
$439$	−18.3043	−0.873616	−0.436808	+	0.899555i	$0.643891\pi$
$440$	0	0
$441$	−2.79499	−0.133095
$442$	1.27671	0.0607268
$443$	13.6727	0.649608	0.324804	−	0.945781i	$-0.394702\pi$
$443$	13.6727	0.649608	0.324804	+	0.945781i	$0.394702\pi$
$444$	0.412403	0.0195718
$445$	0	0
$446$	27.9969	1.32569
$447$	−3.29358	−0.155781
$448$	−7.94134	−0.375193
$449$	−9.10509	−0.429696	−0.214848	−	0.976648i	$-0.568926\pi$
$449$	−9.10509	−0.429696	−0.214848	+	0.976648i	$0.568926\pi$
$450$	0	0
$451$	−10.8822	−0.512422
$452$	−6.80647	−0.320150
$453$	4.23996	0.199211
$454$	10.4580	0.490818
$455$	0	0
$456$	−9.61621	−0.450320
$457$	15.0444	0.703749	0.351874	−	0.936047i	$-0.385544\pi$
$457$	15.0444	0.703749	0.351874	+	0.936047i	$0.385544\pi$
$458$	9.71501	0.453952
$459$	−5.16262	−0.240971
$460$	0	0
$461$	9.98078	0.464851	0.232426	−	0.972614i	$-0.425334\pi$
$461$	9.98078	0.464851	0.232426	+	0.972614i	$0.425334\pi$
$462$	1.86701	0.0868610
$463$	−4.79903	−0.223030	−0.111515	−	0.993763i	$-0.535570\pi$
$463$	−4.79903	−0.223030	−0.111515	+	0.993763i	$0.535570\pi$
$464$	−13.2401	−0.614658
$465$	0	0
$466$	−26.3789	−1.22198
$467$	−35.0930	−1.62391	−0.811956	−	0.583719i	$-0.801597\pi$
$467$	−35.0930	−1.62391	−0.811956	+	0.583719i	$0.801597\pi$
$468$	1.41615	0.0654615
$469$	−13.0701	−0.603521
$470$	0	0
$471$	9.18621	0.423278
$472$	−35.3758	−1.62830
$473$	16.5620	0.761522
$474$	1.28523	0.0590324
$475$	0	0
$476$	1.65420	0.0758203
$477$	−31.5455	−1.44437
$478$	−8.68095	−0.397057
$479$	−6.78573	−0.310048	−0.155024	−	0.987911i	$-0.549545\pi$
$479$	−6.78573	−0.310048	−0.155024	+	0.987911i	$0.549545\pi$
$480$	0	0
$481$	−0.652898	−0.0297696
$482$	−7.67494	−0.349584
$483$	0.452781	0.0206022
$484$	−3.08273	−0.140124
$485$	0	0
$486$	11.9838	0.543597
$487$	12.8417	0.581915	0.290958	−	0.956736i	$-0.406026\pi$
$487$	12.8417	0.581915	0.290958	+	0.956736i	$0.406026\pi$
$488$	29.3918	1.33051
$489$	−1.70499	−0.0771025
$490$	0	0
$491$	39.2039	1.76925	0.884625	−	0.466304i	$-0.154415\pi$
$491$	39.2039	1.76925	0.884625	+	0.466304i	$0.154415\pi$
$492$	−1.08167	−0.0487656
$493$	16.1636	0.727974
$494$	4.50563	0.202718
$495$	0	0
$496$	14.5088	0.651465
$497$	−11.2197	−0.503272
$498$	5.40477	0.242194
$499$	6.99793	0.313270	0.156635	−	0.987657i	$-0.449935\pi$
$499$	6.99793	0.313270	0.156635	+	0.987657i	$0.449935\pi$
$500$	0	0
$501$	0.272778	0.0121868
$502$	−29.1780	−1.30228
$503$	4.68125	0.208727	0.104363	−	0.994539i	$-0.466720\pi$
$503$	4.68125	0.208727	0.104363	+	0.994539i	$0.466720\pi$
$504$	−8.54874	−0.380791
$505$	0	0
$506$	4.12342	0.183309
$507$	−5.72170	−0.254110
$508$	−12.1739	−0.540127
$509$	−8.52869	−0.378028	−0.189014	−	0.981974i	$-0.560529\pi$
$509$	−8.52869	−0.378028	−0.189014	+	0.981974i	$0.560529\pi$
$510$	0	0
$511$	14.5431	0.643349
$512$	−16.9213	−0.747825
$513$	−18.2194	−0.804407
$514$	−5.35155	−0.236047
$515$	0	0
$516$	1.64624	0.0724717
$517$	10.4459	0.459411
$518$	1.16645	0.0512510
$519$	−1.20671	−0.0529687
$520$	0	0
$521$	33.3521	1.46118	0.730591	−	0.682816i	$-0.239245\pi$
$521$	33.3521	1.46118	0.730591	+	0.682816i	$0.239245\pi$
$522$	−24.7219	−1.08205
$523$	17.2023	0.752202	0.376101	−	0.926579i	$-0.377265\pi$
$523$	17.2023	0.752202	0.376101	+	0.926579i	$0.377265\pi$
$524$	−0.645915	−0.0282169
$525$	0	0
$526$	8.02404	0.349865
$527$	−17.7124	−0.771566
$528$	2.79472	0.121624
$529$	1.00000	0.0434783
$530$	0	0
$531$	−32.3269	−1.40287
$532$	5.83785	0.253103
$533$	1.71245	0.0741746
$534$	−0.977231	−0.0422889
$535$	0	0
$536$	−39.9761	−1.72671
$537$	8.89052	0.383654
$538$	−32.7305	−1.41111
$539$	−3.82971	−0.164957
$540$	0	0
$541$	−14.7166	−0.632718	−0.316359	−	0.948640i	$-0.602460\pi$
$541$	−14.7166	−0.632718	−0.316359	+	0.948640i	$0.602460\pi$
$542$	−14.6183	−0.627911
$543$	2.26927	0.0973837
$544$	8.62167	0.369651
$545$	0	0
$546$	−0.293798	−0.0125734
$547$	20.1802	0.862845	0.431423	−	0.902150i	$-0.358012\pi$
$547$	20.1802	0.862845	0.431423	+	0.902150i	$0.358012\pi$
$548$	7.22697	0.308721
$549$	26.8587	1.14630
$550$	0	0
$551$	57.0431	2.43012
$552$	1.38487	0.0589441
$553$	−2.63634	−0.112108
$554$	24.2284	1.02937
$555$	0	0
$556$	−9.19790	−0.390078
$557$	9.36643	0.396868	0.198434	−	0.980114i	$-0.436414\pi$
$557$	9.36643	0.396868	0.198434	+	0.980114i	$0.436414\pi$
$558$	27.0907	1.14684
$559$	−2.60625	−0.110233
$560$	0	0
$561$	−3.41180	−0.144047
$562$	−24.3491	−1.02711
$563$	26.0729	1.09884	0.549420	−	0.835546i	$-0.314849\pi$
$563$	26.0729	1.09884	0.549420	+	0.835546i	$0.314849\pi$
$564$	1.03831	0.0437207
$565$	0	0
$566$	−5.21534	−0.219217
$567$	−7.19694	−0.302243
$568$	−34.3165	−1.43989
$569$	−19.7922	−0.829732	−0.414866	−	0.909882i	$-0.636172\pi$
$569$	−19.7922	−0.829732	−0.414866	+	0.909882i	$0.636172\pi$
$570$	0	0
$571$	−30.5525	−1.27858	−0.639291	−	0.768965i	$-0.720772\pi$
$571$	−30.5525	−1.27858	−0.639291	+	0.768965i	$0.720772\pi$
$572$	1.94042	0.0811329
$573$	1.98083	0.0827505
$574$	−3.05943	−0.127698
$575$	0	0
$576$	−22.1960	−0.924832
$577$	−2.66307	−0.110865	−0.0554325	−	0.998462i	$-0.517654\pi$
$577$	−2.66307	−0.110865	−0.0554325	+	0.998462i	$0.517654\pi$
$578$	−14.1355	−0.587961
$579$	−2.21846	−0.0921960
$580$	0	0
$581$	−11.0866	−0.459949
$582$	3.86860	0.160359
$583$	−43.2238	−1.79015
$584$	44.4814	1.84066
$585$	0	0
$586$	35.3924	1.46205
$587$	19.0325	0.785556	0.392778	−	0.919633i	$-0.371514\pi$
$587$	19.0325	0.785556	0.392778	+	0.919633i	$0.371514\pi$
$588$	−0.380668	−0.0156985
$589$	−62.5090	−2.57564
$590$	0	0
$591$	−8.88384	−0.365432
$592$	1.74606	0.0717626
$593$	−36.1102	−1.48287	−0.741434	−	0.671026i	$-0.765854\pi$
$593$	−36.1102	−1.48287	−0.741434	+	0.671026i	$0.765854\pi$
$594$	10.8193	0.443920
$595$	0	0
$596$	6.11560	0.250505
$597$	−3.70714	−0.151723
$598$	−0.648875	−0.0265345
$599$	−1.63915	−0.0669739	−0.0334869	−	0.999439i	$-0.510661\pi$
$599$	−1.63915	−0.0669739	−0.0334869	+	0.999439i	$0.510661\pi$
$600$	0	0
$601$	26.3313	1.07407	0.537037	−	0.843558i	$-0.319543\pi$
$601$	26.3313	1.07407	0.537037	+	0.843558i	$0.319543\pi$
$602$	4.65627	0.189775
$603$	−36.5308	−1.48765
$604$	−7.87287	−0.320342
$605$	0	0
$606$	0.811526	0.0329660
$607$	−4.46421	−0.181197	−0.0905984	−	0.995888i	$-0.528878\pi$
$607$	−4.46421	−0.181197	−0.0905984	+	0.995888i	$0.528878\pi$
$608$	30.4267	1.23397
$609$	−3.71961	−0.150726
$610$	0	0
$611$	−1.64380	−0.0665012
$612$	4.62348	0.186893
$613$	−5.09327	−0.205715	−0.102858	−	0.994696i	$-0.532799\pi$
$613$	−5.09327	−0.205715	−0.102858	+	0.994696i	$0.532799\pi$
$614$	15.2394	0.615012
$615$	0	0
$616$	−11.7135	−0.471952
$617$	32.0023	1.28836	0.644182	−	0.764872i	$-0.277198\pi$
$617$	32.0023	1.28836	0.644182	+	0.764872i	$0.277198\pi$
$618$	2.66784	0.107316
$619$	−39.3608	−1.58204	−0.791021	−	0.611789i	$-0.790450\pi$
$619$	−39.3608	−1.58204	−0.791021	+	0.611789i	$0.790450\pi$
$620$	0	0
$621$	2.62386	0.105292
$622$	−21.3771	−0.857143
$623$	2.00455	0.0803108
$624$	−0.439786	−0.0176055
$625$	0	0
$626$	23.4454	0.937065
$627$	−12.0406	−0.480855
$628$	−17.0572	−0.680656
$629$	−2.13160	−0.0849924
$630$	0	0
$631$	29.9410	1.19193	0.595966	−	0.803009i	$-0.296769\pi$
$631$	29.9410	1.19193	0.595966	+	0.803009i	$0.296769\pi$
$632$	−8.06348	−0.320748
$633$	−10.6930	−0.425009
$634$	33.2679	1.32124
$635$	0	0
$636$	−4.29638	−0.170363
$637$	0.602656	0.0238781
$638$	−33.8741	−1.34109
$639$	−31.3589	−1.24054
$640$	0	0
$641$	−0.304663	−0.0120335	−0.00601674	−	0.999982i	$-0.501915\pi$
$641$	−0.304663	−0.0120335	−0.00601674	+	0.999982i	$0.501915\pi$
$642$	−0.199434	−0.00787105
$643$	−2.99658	−0.118174	−0.0590868	−	0.998253i	$-0.518819\pi$
$643$	−2.99658	−0.118174	−0.0590868	+	0.998253i	$0.518819\pi$
$644$	−0.840734	−0.0331296
$645$	0	0
$646$	14.7101	0.578761
$647$	−23.5778	−0.926937	−0.463469	−	0.886113i	$-0.653395\pi$
$647$	−23.5778	−0.926937	−0.463469	+	0.886113i	$0.653395\pi$
$648$	−22.0125	−0.864734
$649$	−44.2946	−1.73871
$650$	0	0
$651$	4.07602	0.159752
$652$	3.16588	0.123985
$653$	−41.8757	−1.63872	−0.819361	−	0.573278i	$-0.805672\pi$
$653$	−41.8757	−1.63872	−0.819361	+	0.573278i	$0.805672\pi$
$654$	−0.0255467	−0.000998956 0
$655$	0	0
$656$	−4.57965	−0.178805
$657$	40.6478	1.58582
$658$	2.93678	0.114488
$659$	13.2397	0.515745	0.257873	−	0.966179i	$-0.416979\pi$
$659$	13.2397	0.515745	0.257873	+	0.966179i	$0.416979\pi$
$660$	0	0
$661$	−45.4386	−1.76736	−0.883678	−	0.468096i	$-0.844940\pi$
$661$	−45.4386	−1.76736	−0.883678	+	0.468096i	$0.844940\pi$
$662$	22.3896	0.870195
$663$	0.536893	0.0208512
$664$	−33.9094	−1.31594
$665$	0	0
$666$	3.26022	0.126331
$667$	−8.21503	−0.318087
$668$	−0.506501	−0.0195971
$669$	11.7735	0.455191
$670$	0	0
$671$	36.8020	1.42072
$672$	−1.98404	−0.0765358
$673$	23.7532	0.915618	0.457809	−	0.889051i	$-0.348634\pi$
$673$	23.7532	0.915618	0.457809	+	0.889051i	$0.348634\pi$
$674$	−29.1118	−1.12134
$675$	0	0
$676$	10.6242	0.408623
$677$	−5.90017	−0.226762	−0.113381	−	0.993552i	$-0.536168\pi$
$677$	−5.90017	−0.226762	−0.113381	+	0.993552i	$0.536168\pi$
$678$	3.94678	0.151575
$679$	−7.93551	−0.304537
$680$	0	0
$681$	4.39789	0.168528
$682$	37.1199	1.42139
$683$	−13.3383	−0.510375	−0.255187	−	0.966892i	$-0.582137\pi$
$683$	−13.3383	−0.510375	−0.255187	+	0.966892i	$0.582137\pi$
$684$	16.3167	0.623885
$685$	0	0
$686$	−1.07669	−0.0411083
$687$	4.08545	0.155869
$688$	6.96996	0.265727
$689$	6.80184	0.259129
$690$	0	0
$691$	28.1892	1.07237	0.536183	−	0.844102i	$-0.319866\pi$
$691$	28.1892	1.07237	0.536183	+	0.844102i	$0.319866\pi$
$692$	2.24065	0.0851767
$693$	−10.7040	−0.406612
$694$	20.7951	0.789370
$695$	0	0
$696$	−11.3768	−0.431236
$697$	5.59087	0.211769
$698$	6.68243	0.252934
$699$	−11.0931	−0.419579
$700$	0	0
$701$	−2.98153	−0.112611	−0.0563055	−	0.998414i	$-0.517932\pi$
$701$	−2.98153	−0.112611	−0.0563055	+	0.998414i	$0.517932\pi$
$702$	−1.70256	−0.0642589
$703$	−7.52262	−0.283721
$704$	−30.4131	−1.14624
$705$	0	0
$706$	1.54453	0.0581291
$707$	−1.66465	−0.0626057
$708$	−4.40282	−0.165468
$709$	11.6837	0.438790	0.219395	−	0.975636i	$-0.429592\pi$
$709$	11.6837	0.438790	0.219395	+	0.975636i	$0.429592\pi$
$710$	0	0
$711$	−7.36853	−0.276341
$712$	6.13112	0.229773
$713$	9.00220	0.337135
$714$	−0.959200	−0.0358972
$715$	0	0
$716$	−16.5081	−0.616938
$717$	−3.65059	−0.136334
$718$	−3.59325	−0.134099
$719$	−3.94459	−0.147109	−0.0735543	−	0.997291i	$-0.523434\pi$
$719$	−3.94459	−0.147109	−0.0735543	+	0.997291i	$0.523434\pi$
$720$	0	0
$721$	−5.47244	−0.203804
$722$	31.4562	1.17068
$723$	−3.22754	−0.120033
$724$	−4.21364	−0.156599
$725$	0	0
$726$	1.78754	0.0663419
$727$	17.3714	0.644269	0.322134	−	0.946694i	$-0.395600\pi$
$727$	17.3714	0.644269	0.322134	+	0.946694i	$0.395600\pi$
$728$	1.84328	0.0683166
$729$	−16.5513	−0.613010
$730$	0	0
$731$	−8.50897	−0.314716
$732$	3.65806	0.135206
$733$	11.2160	0.414273	0.207137	−	0.978312i	$-0.433586\pi$
$733$	11.2160	0.414273	0.207137	+	0.978312i	$0.433586\pi$
$734$	−13.9478	−0.514822
$735$	0	0
$736$	−4.38189	−0.161519
$737$	−50.0547	−1.84379
$738$	−8.55108	−0.314770
$739$	39.0600	1.43685	0.718423	−	0.695606i	$-0.244864\pi$
$739$	39.0600	1.43685	0.718423	+	0.695606i	$0.244864\pi$
$740$	0	0
$741$	1.89475	0.0696053
$742$	−12.1520	−0.446114
$743$	6.83018	0.250575	0.125288	−	0.992120i	$-0.460015\pi$
$743$	6.83018	0.250575	0.125288	+	0.992120i	$0.460015\pi$
$744$	12.4669	0.457059
$745$	0	0
$746$	36.5129	1.33683
$747$	−30.9869	−1.13375
$748$	6.33512	0.231635
$749$	0.409092	0.0149479
$750$	0	0
$751$	−24.1906	−0.882729	−0.441364	−	0.897328i	$-0.645505\pi$
$751$	−24.1906	−0.882729	−0.441364	+	0.897328i	$0.645505\pi$
$752$	4.39606	0.160308
$753$	−12.2702	−0.447151
$754$	5.33053	0.194127
$755$	0	0
$756$	−2.20597	−0.0802303
$757$	−22.6812	−0.824363	−0.412182	−	0.911102i	$-0.635233\pi$
$757$	−22.6812	−0.824363	−0.412182	+	0.911102i	$0.635233\pi$
$758$	−6.18839	−0.224772
$759$	1.73402	0.0629410
$760$	0	0
$761$	29.2806	1.06142	0.530710	−	0.847554i	$-0.321925\pi$
$761$	29.2806	1.06142	0.530710	+	0.847554i	$0.321925\pi$
$762$	7.05909	0.255724
$763$	0.0524029	0.00189711
$764$	−3.67806	−0.133068
$765$	0	0
$766$	−13.0169	−0.470321
$767$	6.97034	0.251684
$768$	−7.29541	−0.263250
$769$	35.9413	1.29608	0.648038	−	0.761608i	$-0.275590\pi$
$769$	35.9413	1.29608	0.648038	+	0.761608i	$0.275590\pi$
$770$	0	0
$771$	−2.25048	−0.0810491
$772$	4.11929	0.148256
$773$	−53.3906	−1.92033	−0.960164	−	0.279437i	$-0.909852\pi$
$773$	−53.3906	−1.92033	−0.960164	+	0.279437i	$0.909852\pi$
$774$	13.0142	0.467787
$775$	0	0
$776$	−24.2715	−0.871297
$777$	0.490527	0.0175976
$778$	3.70058	0.132672
$779$	19.7307	0.706927
$780$	0	0
$781$	−42.9682	−1.53752
$782$	−2.11847	−0.0757562
$783$	−21.5551	−0.770316
$784$	−1.61170	−0.0575606
$785$	0	0
$786$	0.374538	0.0133593
$787$	53.1835	1.89579	0.947893	−	0.318589i	$-0.103209\pi$
$787$	53.1835	1.89579	0.947893	+	0.318589i	$0.103209\pi$
$788$	16.4957	0.587636
$789$	3.37434	0.120130
$790$	0	0
$791$	−8.09587	−0.287856
$792$	−32.7392	−1.16334
$793$	−5.79128	−0.205654
$794$	16.1677	0.573770
$795$	0	0
$796$	6.88352	0.243980
$797$	−44.1446	−1.56368	−0.781841	−	0.623478i	$-0.785719\pi$
$797$	−44.1446	−1.56368	−0.781841	+	0.623478i	$0.785719\pi$
$798$	−3.38511	−0.119832
$799$	−5.36673	−0.189861
$800$	0	0
$801$	5.60271	0.197962
$802$	−23.2098	−0.819568
$803$	55.6959	1.96547
$804$	−4.97537	−0.175468
$805$	0	0
$806$	−5.84130	−0.205751
$807$	−13.7641	−0.484520
$808$	−5.09150	−0.179118
$809$	−9.50890	−0.334315	−0.167158	−	0.985930i	$-0.553459\pi$
$809$	−9.50890	−0.334315	−0.167158	+	0.985930i	$0.553459\pi$
$810$	0	0
$811$	−18.2498	−0.640837	−0.320418	−	0.947276i	$-0.603824\pi$
$811$	−18.2498	−0.640837	−0.320418	+	0.947276i	$0.603824\pi$
$812$	6.90666	0.242376
$813$	−6.14744	−0.215600
$814$	4.46718	0.156574
$815$	0	0
$816$	−1.43582	−0.0502639
$817$	−30.0290	−1.05058
$818$	31.2355	1.09212
$819$	1.68442	0.0588583
$820$	0	0
$821$	2.40246	0.0838464	0.0419232	−	0.999121i	$-0.486652\pi$
$821$	2.40246	0.0838464	0.0419232	+	0.999121i	$0.486652\pi$
$822$	−4.19060	−0.146164
$823$	0.596098	0.0207787	0.0103893	−	0.999946i	$-0.496693\pi$
$823$	0.596098	0.0207787	0.0103893	+	0.999946i	$0.496693\pi$
$824$	−16.7380	−0.583095
$825$	0	0
$826$	−12.4530	−0.433297
$827$	2.06267	0.0717260	0.0358630	−	0.999357i	$-0.488582\pi$
$827$	2.06267	0.0717260	0.0358630	+	0.999357i	$0.488582\pi$
$828$	−2.34984	−0.0816627
$829$	50.1105	1.74041	0.870205	−	0.492691i	$-0.163987\pi$
$829$	50.1105	1.74041	0.870205	+	0.492691i	$0.163987\pi$
$830$	0	0
$831$	10.1888	0.353444
$832$	4.78590	0.165921
$833$	1.96757	0.0681722
$834$	5.33346	0.184683
$835$	0	0
$836$	22.3573	0.773243
$837$	23.6205	0.816444
$838$	35.9246	1.24099
$839$	35.2397	1.21661	0.608305	−	0.793703i	$-0.291850\pi$
$839$	35.2397	1.21661	0.608305	+	0.793703i	$0.291850\pi$
$840$	0	0
$841$	38.4868	1.32713
$842$	34.8013	1.19933
$843$	−10.2395	−0.352668
$844$	19.8550	0.683438
$845$	0	0
$846$	8.20827	0.282206
$847$	−3.66671	−0.125990
$848$	−18.1903	−0.624658
$849$	−2.19320	−0.0752706
$850$	0	0
$851$	1.08337	0.0371373
$852$	−4.27098	−0.146321
$853$	−44.2291	−1.51438	−0.757188	−	0.653197i	$-0.773427\pi$
$853$	−44.2291	−1.51438	−0.757188	+	0.653197i	$0.773427\pi$
$854$	10.3466	0.354052
$855$	0	0
$856$	1.25125	0.0427667
$857$	−14.8630	−0.507711	−0.253855	−	0.967242i	$-0.581699\pi$
$857$	−14.8630	−0.507711	−0.253855	+	0.967242i	$0.581699\pi$
$858$	−1.12516	−0.0384124
$859$	−54.9799	−1.87589	−0.937944	−	0.346786i	$-0.887273\pi$
$859$	−54.9799	−1.87589	−0.937944	+	0.346786i	$0.887273\pi$
$860$	0	0
$861$	−1.28658	−0.0438466
$862$	−36.8654	−1.25564
$863$	9.32277	0.317351	0.158675	−	0.987331i	$-0.449278\pi$
$863$	9.32277	0.317351	0.158675	+	0.987331i	$0.449278\pi$
$864$	−11.4975	−0.391152
$865$	0	0
$866$	10.2962	0.349881
$867$	−5.94441	−0.201883
$868$	−7.56846	−0.256890
$869$	−10.0964	−0.342497
$870$	0	0
$871$	7.87678	0.266894
$872$	0.160279	0.00542775
$873$	−22.1797	−0.750668
$874$	−7.47628	−0.252889
$875$	0	0
$876$	5.53609	0.187047
$877$	5.98210	0.202001	0.101001	−	0.994886i	$-0.467796\pi$
$877$	5.98210	0.202001	0.101001	+	0.994886i	$0.467796\pi$
$878$	−19.7081	−0.665116
$879$	14.8835	0.502010
$880$	0	0
$881$	−46.9444	−1.58160	−0.790799	−	0.612076i	$-0.790335\pi$
$881$	−46.9444	−1.58160	−0.790799	+	0.612076i	$0.790335\pi$
$882$	−3.00934	−0.101330
$883$	48.8803	1.64495	0.822477	−	0.568799i	$-0.192592\pi$
$883$	48.8803	1.64495	0.822477	+	0.568799i	$0.192592\pi$
$884$	−0.996916	−0.0335299
$885$	0	0
$886$	14.7213	0.494570
$887$	18.0865	0.607286	0.303643	−	0.952786i	$-0.401797\pi$
$887$	18.0865	0.607286	0.303643	+	0.952786i	$0.401797\pi$
$888$	1.50032	0.0503476
$889$	−14.4800	−0.485644
$890$	0	0
$891$	−27.5622	−0.923369
$892$	−21.8614	−0.731973
$893$	−18.9397	−0.633794
$894$	−3.54617	−0.118602
$895$	0	0
$896$	0.213404	0.00712931
$897$	−0.272871	−0.00911090
$898$	−9.80338	−0.327143
$899$	−73.9533	−2.46648
$900$	0	0
$901$	22.2068	0.739817
$902$	−11.7168	−0.390125
$903$	1.95810	0.0651615
$904$	−24.7620	−0.823572
$905$	0	0
$906$	4.56513	0.151666
$907$	45.7684	1.51971	0.759857	−	0.650090i	$-0.225269\pi$
$907$	45.7684	1.51971	0.759857	+	0.650090i	$0.225269\pi$
$908$	−8.16612	−0.271002
$909$	−4.65268	−0.154320
$910$	0	0
$911$	20.7898	0.688797	0.344398	−	0.938824i	$-0.388083\pi$
$911$	20.7898	0.688797	0.344398	+	0.938824i	$0.388083\pi$
$912$	−5.06717	−0.167791
$913$	−42.4585	−1.40517
$914$	16.1982	0.535790
$915$	0	0
$916$	−7.58596	−0.250647
$917$	−0.768275	−0.0253707
$918$	−5.55856	−0.183460
$919$	−6.48749	−0.214003	−0.107001	−	0.994259i	$-0.534125\pi$
$919$	−6.48749	−0.214003	−0.107001	+	0.994259i	$0.534125\pi$
$920$	0	0
$921$	6.40861	0.211171
$922$	10.7462	0.353908
$923$	6.76162	0.222561
$924$	−1.45785	−0.0479598
$925$	0	0
$926$	−5.16707	−0.169801
$927$	−15.2954	−0.502367
$928$	35.9974	1.18167
$929$	−8.06990	−0.264765	−0.132382	−	0.991199i	$-0.542263\pi$
$929$	−8.06990	−0.264765	−0.132382	+	0.991199i	$0.542263\pi$
$930$	0	0
$931$	6.94375	0.227572
$932$	20.5979	0.674707
$933$	−8.98970	−0.294309
$934$	−37.7844	−1.23634
$935$	0	0
$936$	5.15195	0.168397
$937$	0.224265	0.00732643	0.00366321	−	0.999993i	$-0.498834\pi$
$937$	0.224265	0.00732643	0.00366321	+	0.999993i	$0.498834\pi$
$938$	−14.0725	−0.459482
$939$	9.85946	0.321751
$940$	0	0
$941$	24.3369	0.793361	0.396680	−	0.917957i	$-0.370162\pi$
$941$	24.3369	0.793361	0.396680	+	0.917957i	$0.370162\pi$
$942$	9.89072	0.322257
$943$	−2.84151	−0.0925323
$944$	−18.6409	−0.606711
$945$	0	0
$946$	17.8322	0.579775
$947$	28.6986	0.932578	0.466289	−	0.884632i	$-0.345591\pi$
$947$	28.6986	0.932578	0.466289	+	0.884632i	$0.345591\pi$
$948$	−1.00357	−0.0325944
$949$	−8.76449	−0.284507
$950$	0	0
$951$	13.9901	0.453661
$952$	6.01800	0.195044
$953$	−33.1622	−1.07423	−0.537114	−	0.843510i	$-0.680485\pi$
$953$	−33.1622	−1.07423	−0.537114	+	0.843510i	$0.680485\pi$
$954$	−33.9647	−1.09965
$955$	0	0
$956$	6.77852	0.219233
$957$	−14.2450	−0.460477
$958$	−7.30614	−0.236051
$959$	8.59602	0.277580
$960$	0	0
$961$	50.0395	1.61418
$962$	−0.702970	−0.0226646
$963$	1.14341	0.0368458
$964$	5.99297	0.193021
$965$	0	0
$966$	0.487505	0.0156852
$967$	50.2696	1.61656	0.808281	−	0.588797i	$-0.200398\pi$
$967$	50.2696	1.61656	0.808281	+	0.588797i	$0.200398\pi$
$968$	−11.2150	−0.360463
$969$	6.18603	0.198724
$970$	0	0
$971$	29.1232	0.934608	0.467304	−	0.884097i	$-0.345225\pi$
$971$	29.1232	0.934608	0.467304	+	0.884097i	$0.345225\pi$
$972$	−9.35755	−0.300144
$973$	−10.9403	−0.350731
$974$	13.8266	0.443033
$975$	0	0
$976$	15.4877	0.495750
$977$	−27.1512	−0.868645	−0.434322	−	0.900758i	$-0.643012\pi$
$977$	−27.1512	−0.868645	−0.434322	+	0.900758i	$0.643012\pi$
$978$	−1.83575	−0.0587009
$979$	7.67687	0.245354
$980$	0	0
$981$	0.146466	0.00467629
$982$	42.2106	1.34699
$983$	−59.7377	−1.90534	−0.952668	−	0.304013i	$-0.901673\pi$
$983$	−59.7377	−1.90534	−0.952668	+	0.304013i	$0.901673\pi$
$984$	−3.93513	−0.125447
$985$	0	0
$986$	17.4033	0.554233
$987$	1.23500	0.0393106
$988$	−3.51822	−0.111929
$989$	4.32461	0.137515
$990$	0	0
$991$	−9.02607	−0.286723	−0.143361	−	0.989670i	$-0.545791\pi$
$991$	−9.02607	−0.286723	−0.143361	+	0.989670i	$0.545791\pi$
$992$	−39.4466	−1.25243
$993$	9.41547	0.298791
$994$	−12.0802	−0.383159
$995$	0	0
$996$	−4.22031	−0.133726
$997$	40.2503	1.27474	0.637370	−	0.770558i	$-0.280022\pi$
$997$	40.2503	1.27474	0.637370	+	0.770558i	$0.280022\pi$
$998$	7.53462	0.238504
$999$	2.84260	0.0899359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.w.1.5	yes	8
5.4	even	2		4025.2.a.s.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.s.1.4	✓	8	5.4	even	2
4025.2.a.w.1.5	yes	8	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.07669 q^{2} +0.452781 q^{3} -0.840734 q^{4} +0.487505 q^{6} -1.00000 q^{7} -3.05860 q^{8} -2.79499 q^{9} +O(q^{10})\)	\(q+1.07669 q^{2} +0.452781 q^{3} -0.840734 q^{4} +0.487505 q^{6} -1.00000 q^{7} -3.05860 q^{8} -2.79499 q^{9} -3.82971 q^{11} -0.380668 q^{12} +0.602656 q^{13} -1.07669 q^{14} -1.61170 q^{16} +1.96757 q^{17} -3.00934 q^{18} +6.94375 q^{19} -0.452781 q^{21} -4.12342 q^{22} -1.00000 q^{23} -1.38487 q^{24} +0.648875 q^{26} -2.62386 q^{27} +0.840734 q^{28} +8.21503 q^{29} -9.00220 q^{31} +4.38189 q^{32} -1.73402 q^{33} +2.11847 q^{34} +2.34984 q^{36} -1.08337 q^{37} +7.47628 q^{38} +0.272871 q^{39} +2.84151 q^{41} -0.487505 q^{42} -4.32461 q^{43} +3.21977 q^{44} -1.07669 q^{46} -2.72760 q^{47} -0.729745 q^{48} +1.00000 q^{49} +0.890877 q^{51} -0.506674 q^{52} +11.2864 q^{53} -2.82509 q^{54} +3.05860 q^{56} +3.14399 q^{57} +8.84506 q^{58} +11.5660 q^{59} -9.60958 q^{61} -9.69259 q^{62} +2.79499 q^{63} +7.94134 q^{64} -1.86701 q^{66} +13.0701 q^{67} -1.65420 q^{68} -0.452781 q^{69} +11.2197 q^{71} +8.54874 q^{72} -14.5431 q^{73} -1.16645 q^{74} -5.83785 q^{76} +3.82971 q^{77} +0.293798 q^{78} +2.63634 q^{79} +7.19694 q^{81} +3.05943 q^{82} +11.0866 q^{83} +0.380668 q^{84} -4.65627 q^{86} +3.71961 q^{87} +11.7135 q^{88} -2.00455 q^{89} -0.602656 q^{91} +0.840734 q^{92} -4.07602 q^{93} -2.93678 q^{94} +1.98404 q^{96} +7.93551 q^{97} +1.07669 q^{98} +10.7040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8	\( 8 q + 3 q^{2} + 2 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 12 q^{8} - 5 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} - q^{16} - q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{21} - 5 q^{22} - 8 q^{23} + 16 q^{24} + 22 q^{26} - q^{27} - 5 q^{28} - 5 q^{29} - q^{31} + 2 q^{32} + 12 q^{33} - 2 q^{34} + 16 q^{36} + 18 q^{37} + 14 q^{38} + 14 q^{39} - q^{41} + q^{42} + 20 q^{43} - 3 q^{46} + 10 q^{47} + 31 q^{48} + 8 q^{49} - 4 q^{51} + 11 q^{52} + 11 q^{53} + 29 q^{54} - 12 q^{56} + 8 q^{57} + 24 q^{58} + 20 q^{59} - 6 q^{61} + 2 q^{62} + 8 q^{64} - 37 q^{66} + 23 q^{67} + 9 q^{68} - 2 q^{69} + 3 q^{71} + 29 q^{72} - 8 q^{73} + 35 q^{74} - 29 q^{76} + 5 q^{77} + 31 q^{78} + 4 q^{79} - 44 q^{81} + 27 q^{82} + 4 q^{83} - 3 q^{84} - 18 q^{86} + 27 q^{87} - 4 q^{88} - 17 q^{89} - 9 q^{91} - 5 q^{92} - 7 q^{93} + 13 q^{94} + 22 q^{96} + 41 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 12 * q^8 - 5 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 - q^16 - q^17 + 6 * q^18 - 4 * q^19 - 2 * q^21 - 5 * q^22 - 8 * q^23 + 16 * q^24 + 22 * q^26 - q^27 - 5 * q^28 - 5 * q^29 - q^31 + 2 * q^32 + 12 * q^33 - 2 * q^34 + 16 * q^36 + 18 * q^37 + 14 * q^38 + 14 * q^39 - q^41 + q^42 + 20 * q^43 - 3 * q^46 + 10 * q^47 + 31 * q^48 + 8 * q^49 - 4 * q^51 + 11 * q^52 + 11 * q^53 + 29 * q^54 - 12 * q^56 + 8 * q^57 + 24 * q^58 + 20 * q^59 - 6 * q^61 + 2 * q^62 + 8 * q^64 - 37 * q^66 + 23 * q^67 + 9 * q^68 - 2 * q^69 + 3 * q^71 + 29 * q^72 - 8 * q^73 + 35 * q^74 - 29 * q^76 + 5 * q^77 + 31 * q^78 + 4 * q^79 - 44 * q^81 + 27 * q^82 + 4 * q^83 - 3 * q^84 - 18 * q^86 + 27 * q^87 - 4 * q^88 - 17 * q^89 - 9 * q^91 - 5 * q^92 - 7 * q^93 + 13 * q^94 + 22 * q^96 + 41 * q^97 + 3 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

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Database

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