LMFDB - Embedded newform 1250.4.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,4,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1250.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:	$73.7523875072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 125 x^{14} + 990 x^{13} + 6166 x^{12} - 47880 x^{11} - 151199 x^{10} + \cdots - 45086320 $ x^16 - 8x^15 - 125x^14 + 990x^13 + 6166x^12 - 47880x^11 - 151199x^10 + 1143340x^9 + 1899751x^8 - 14035110x^7 - 11070230x^6 + 83435508x^5 + 14900696x^4 - 193725880x^3 + 78433160x^2 + 82757040*x - 45086320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{15} $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.18615$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +2.01244 q^{3} +4.00000 q^{4} +4.02487 q^{6} +29.3318 q^{7} +8.00000 q^{8} -22.9501 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +2.01244 q^{3} +4.00000 q^{4} +4.02487 q^{6} +29.3318 q^{7} +8.00000 q^{8} -22.9501 q^{9} +7.09626 q^{11} +8.04975 q^{12} +70.3489 q^{13} +58.6636 q^{14} +16.0000 q^{16} -32.6275 q^{17} -45.9002 q^{18} +153.540 q^{19} +59.0284 q^{21} +14.1925 q^{22} -143.329 q^{23} +16.0995 q^{24} +140.698 q^{26} -100.521 q^{27} +117.327 q^{28} +135.045 q^{29} +99.6761 q^{31} +32.0000 q^{32} +14.2808 q^{33} -65.2550 q^{34} -91.8004 q^{36} -336.162 q^{37} +307.081 q^{38} +141.573 q^{39} -162.629 q^{41} +118.057 q^{42} -85.9689 q^{43} +28.3850 q^{44} -286.658 q^{46} +367.891 q^{47} +32.1990 q^{48} +517.356 q^{49} -65.6608 q^{51} +281.396 q^{52} +349.173 q^{53} -201.043 q^{54} +234.655 q^{56} +308.990 q^{57} +270.089 q^{58} -130.418 q^{59} -334.503 q^{61} +199.352 q^{62} -673.168 q^{63} +64.0000 q^{64} +28.5616 q^{66} +473.135 q^{67} -130.510 q^{68} -288.441 q^{69} +306.296 q^{71} -183.601 q^{72} +377.380 q^{73} -672.323 q^{74} +614.162 q^{76} +208.146 q^{77} +283.145 q^{78} +320.938 q^{79} +417.360 q^{81} -325.258 q^{82} +509.786 q^{83} +236.114 q^{84} -171.938 q^{86} +271.769 q^{87} +56.7701 q^{88} -472.671 q^{89} +2063.46 q^{91} -573.316 q^{92} +200.592 q^{93} +735.782 q^{94} +64.3980 q^{96} -85.4778 q^{97} +1034.71 q^{98} -162.860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) $ 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	2.01244	0.387294	0.193647	−	0.981071i	$-0.437968\pi$
$3$	2.01244	0.387294	0.193647	+	0.981071i	$0.437968\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	4.02487	0.273858
$7$	29.3318	1.58377	0.791885	−	0.610670i	$-0.209100\pi$
$7$	29.3318	1.58377	0.791885	+	0.610670i	$0.209100\pi$
$8$	8.00000	0.353553
$9$	−22.9501	−0.850004
$10$	0	0
$11$	7.09626	0.194509	0.0972547	−	0.995260i	$-0.468994\pi$
$11$	7.09626	0.194509	0.0972547	+	0.995260i	$0.468994\pi$
$12$	8.04975	0.193647
$13$	70.3489	1.50087	0.750434	−	0.660946i	$-0.229845\pi$
$13$	70.3489	1.50087	0.750434	+	0.660946i	$0.229845\pi$
$14$	58.6636	1.11989
$15$	0	0
$16$	16.0000	0.250000
$17$	−32.6275	−0.465490	−0.232745	−	0.972538i	$-0.574771\pi$
$17$	−32.6275	−0.465490	−0.232745	+	0.972538i	$0.574771\pi$
$18$	−45.9002	−0.601043
$19$	153.540	1.85393	0.926963	−	0.375153i	$-0.122410\pi$
$19$	153.540	1.85393	0.926963	+	0.375153i	$0.122410\pi$
$20$	0	0
$21$	59.0284	0.613384
$22$	14.1925	0.137539
$23$	−143.329	−1.29940	−0.649699	−	0.760191i	$-0.725105\pi$
$23$	−143.329	−1.29940	−0.649699	+	0.760191i	$0.725105\pi$
$24$	16.0995	0.136929
$25$	0	0
$26$	140.698	1.06127
$27$	−100.521	−0.716495
$28$	117.327	0.791885
$29$	135.045	0.864730	0.432365	−	0.901699i	$-0.357679\pi$
$29$	135.045	0.864730	0.432365	+	0.901699i	$0.357679\pi$
$30$	0	0
$31$	99.6761	0.577495	0.288748	−	0.957405i	$-0.406761\pi$
$31$	99.6761	0.577495	0.288748	+	0.957405i	$0.406761\pi$
$32$	32.0000	0.176777
$33$	14.2808	0.0753322
$34$	−65.2550	−0.329151
$35$	0	0
$36$	−91.8004	−0.425002
$37$	−336.162	−1.49364	−0.746820	−	0.665027i	$-0.768420\pi$
$37$	−336.162	−1.49364	−0.746820	+	0.665027i	$0.768420\pi$
$38$	307.081	1.31092
$39$	141.573	0.581276
$40$	0	0
$41$	−162.629	−0.619473	−0.309736	−	0.950823i	$-0.600241\pi$
$41$	−162.629	−0.619473	−0.309736	+	0.950823i	$0.600241\pi$
$42$	118.057	0.433728
$43$	−85.9689	−0.304887	−0.152443	−	0.988312i	$-0.548714\pi$
$43$	−85.9689	−0.304887	−0.152443	+	0.988312i	$0.548714\pi$
$44$	28.3850	0.0972547
$45$	0	0
$46$	−286.658	−0.918813
$47$	367.891	1.14175	0.570877	−	0.821036i	$-0.306603\pi$
$47$	367.891	1.14175	0.570877	+	0.821036i	$0.306603\pi$
$48$	32.1990	0.0968234
$49$	517.356	1.50833
$50$	0	0
$51$	−65.6608	−0.180281
$52$	281.396	0.750434
$53$	349.173	0.904955	0.452477	−	0.891776i	$-0.350540\pi$
$53$	349.173	0.904955	0.452477	+	0.891776i	$0.350540\pi$
$54$	−201.043	−0.506638
$55$	0	0
$56$	234.655	0.559947
$57$	308.990	0.718014
$58$	270.089	0.611456
$59$	−130.418	−0.287779	−0.143889	−	0.989594i	$-0.545961\pi$
$59$	−130.418	−0.287779	−0.143889	+	0.989594i	$0.545961\pi$
$60$	0	0
$61$	−334.503	−0.702111	−0.351055	−	0.936355i	$-0.614177\pi$
$61$	−334.503	−0.702111	−0.351055	+	0.936355i	$0.614177\pi$
$62$	199.352	0.408351
$63$	−673.168	−1.34621
$64$	64.0000	0.125000
$65$	0	0
$66$	28.5616	0.0532679
$67$	473.135	0.862726	0.431363	−	0.902178i	$-0.358033\pi$
$67$	473.135	0.862726	0.431363	+	0.902178i	$0.358033\pi$
$68$	−130.510	−0.232745
$69$	−288.441	−0.503249
$70$	0	0
$71$	306.296	0.511980	0.255990	−	0.966679i	$-0.417599\pi$
$71$	306.296	0.511980	0.255990	+	0.966679i	$0.417599\pi$
$72$	−183.601	−0.300522
$73$	377.380	0.605055	0.302527	−	0.953141i	$-0.402170\pi$
$73$	377.380	0.605055	0.302527	+	0.953141i	$0.402170\pi$
$74$	−672.323	−1.05616
$75$	0	0
$76$	614.162	0.926963
$77$	208.146	0.308058
$78$	283.145	0.411024
$79$	320.938	0.457068	0.228534	−	0.973536i	$-0.426607\pi$
$79$	320.938	0.457068	0.228534	+	0.973536i	$0.426607\pi$
$80$	0	0
$81$	417.360	0.572510
$82$	−325.258	−0.438033
$83$	509.786	0.674172	0.337086	−	0.941474i	$-0.390559\pi$
$83$	509.786	0.674172	0.337086	+	0.941474i	$0.390559\pi$
$84$	236.114	0.306692
$85$	0	0
$86$	−171.938	−0.215587
$87$	271.769	0.334904
$88$	56.7701	0.0687694
$89$	−472.671	−0.562956	−0.281478	−	0.959568i	$-0.590825\pi$
$89$	−472.671	−0.562956	−0.281478	+	0.959568i	$0.590825\pi$
$90$	0	0
$91$	2063.46	2.37703
$92$	−573.316	−0.649699
$93$	200.592	0.223660
$94$	735.782	0.807342
$95$	0	0
$96$	64.3980	0.0684645
$97$	−85.4778	−0.0894737	−0.0447369	−	0.998999i	$-0.514245\pi$
$97$	−85.4778	−0.0894737	−0.0447369	+	0.998999i	$0.514245\pi$
$98$	1034.71	1.06655
$99$	−162.860	−0.165334
$100$	0	0
$101$	−1894.25	−1.86619	−0.933093	−	0.359634i	$-0.882901\pi$
$101$	−1894.25	−1.86619	−0.933093	+	0.359634i	$0.882901\pi$
$102$	−131.322	−0.127478
$103$	750.752	0.718192	0.359096	−	0.933301i	$-0.383085\pi$
$103$	750.752	0.718192	0.359096	+	0.933301i	$0.383085\pi$
$104$	562.791	0.530637
$105$	0	0
$106$	698.346	0.639900
$107$	−922.049	−0.833064	−0.416532	−	0.909121i	$-0.636755\pi$
$107$	−922.049	−0.833064	−0.416532	+	0.909121i	$0.636755\pi$
$108$	−402.086	−0.358247
$109$	1001.72	0.880256	0.440128	−	0.897935i	$-0.354933\pi$
$109$	1001.72	0.880256	0.440128	+	0.897935i	$0.354933\pi$
$110$	0	0
$111$	−676.504	−0.578477
$112$	469.309	0.395942
$113$	431.582	0.359290	0.179645	−	0.983731i	$-0.442505\pi$
$113$	431.582	0.359290	0.179645	+	0.983731i	$0.442505\pi$
$114$	617.981	0.507712
$115$	0	0
$116$	540.178	0.432365
$117$	−1614.51	−1.27574
$118$	−260.836	−0.203490
$119$	−957.024	−0.737229
$120$	0	0
$121$	−1280.64	−0.962166
$122$	−669.007	−0.496467
$123$	−327.280	−0.239918
$124$	398.704	0.288748
$125$	0	0
$126$	−1346.34	−0.951914
$127$	−428.279	−0.299241	−0.149621	−	0.988743i	$-0.547805\pi$
$127$	−428.279	−0.299241	−0.149621	+	0.988743i	$0.547805\pi$
$128$	128.000	0.0883883
$129$	−173.007	−0.118081
$130$	0	0
$131$	−567.185	−0.378284	−0.189142	−	0.981950i	$-0.560571\pi$
$131$	−567.185	−0.378284	−0.189142	+	0.981950i	$0.560571\pi$
$132$	57.1231	0.0376661
$133$	4503.62	2.93619
$134$	946.270	0.610040
$135$	0	0
$136$	−261.020	−0.164576
$137$	−1298.47	−0.809753	−0.404876	−	0.914371i	$-0.632685\pi$
$137$	−1298.47	−0.809753	−0.404876	+	0.914371i	$0.632685\pi$
$138$	−576.881	−0.355851
$139$	1520.14	0.927603	0.463802	−	0.885939i	$-0.346485\pi$
$139$	1520.14	0.927603	0.463802	+	0.885939i	$0.346485\pi$
$140$	0	0
$141$	740.358	0.442194
$142$	612.591	0.362025
$143$	499.214	0.291933
$144$	−367.202	−0.212501
$145$	0	0
$146$	754.760	0.427838
$147$	1041.15	0.584165
$148$	−1344.65	−0.746820
$149$	1270.42	0.698504	0.349252	−	0.937029i	$-0.386436\pi$
$149$	1270.42	0.698504	0.349252	+	0.937029i	$0.386436\pi$
$150$	0	0
$151$	1355.51	0.730531	0.365265	−	0.930903i	$-0.380978\pi$
$151$	1355.51	0.730531	0.365265	+	0.930903i	$0.380978\pi$
$152$	1228.32	0.655462
$153$	748.804	0.395668
$154$	416.293	0.217830
$155$	0	0
$156$	566.291	0.290638
$157$	−2574.17	−1.30854	−0.654272	−	0.756260i	$-0.727025\pi$
$157$	−2574.17	−1.30854	−0.654272	+	0.756260i	$0.727025\pi$
$158$	641.877	0.323196
$159$	702.689	0.350483
$160$	0	0
$161$	−4204.10	−2.05795
$162$	834.719	0.404826
$163$	3796.26	1.82421	0.912106	−	0.409955i	$-0.134456\pi$
$163$	3796.26	1.82421	0.912106	+	0.409955i	$0.134456\pi$
$164$	−650.516	−0.309736
$165$	0	0
$166$	1019.57	0.476712
$167$	1219.11	0.564894	0.282447	−	0.959283i	$-0.408854\pi$
$167$	1219.11	0.564894	0.282447	+	0.959283i	$0.408854\pi$
$168$	472.228	0.216864
$169$	2751.97	1.25260
$170$	0	0
$171$	−3523.77	−1.57584
$172$	−343.875	−0.152443
$173$	1864.82	0.819537	0.409768	−	0.912190i	$-0.365610\pi$
$173$	1864.82	0.819537	0.409768	+	0.912190i	$0.365610\pi$
$174$	543.538	0.236813
$175$	0	0
$176$	113.540	0.0486273
$177$	−262.458	−0.111455
$178$	−945.343	−0.398070
$179$	598.457	0.249892	0.124946	−	0.992164i	$-0.460124\pi$
$179$	598.457	0.249892	0.124946	+	0.992164i	$0.460124\pi$
$180$	0	0
$181$	3970.19	1.63040	0.815198	−	0.579183i	$-0.196628\pi$
$181$	3970.19	1.63040	0.815198	+	0.579183i	$0.196628\pi$
$182$	4126.92	1.68081
$183$	−673.167	−0.271923
$184$	−1146.63	−0.459407
$185$	0	0
$186$	401.184	0.158152
$187$	−231.533	−0.0905422
$188$	1471.56	0.570877
$189$	−2948.48	−1.13476
$190$	0	0
$191$	1047.99	0.397015	0.198508	−	0.980099i	$-0.436391\pi$
$191$	1047.99	0.397015	0.198508	+	0.980099i	$0.436391\pi$
$192$	128.796	0.0484117
$193$	1488.28	0.555071	0.277536	−	0.960715i	$-0.410482\pi$
$193$	1488.28	0.555071	0.277536	+	0.960715i	$0.410482\pi$
$194$	−170.956	−0.0632675
$195$	0	0
$196$	2069.42	0.754163
$197$	−4149.23	−1.50061	−0.750306	−	0.661091i	$-0.770094\pi$
$197$	−4149.23	−1.50061	−0.750306	+	0.661091i	$0.770094\pi$
$198$	−325.720	−0.116909
$199$	−1419.93	−0.505809	−0.252905	−	0.967491i	$-0.581386\pi$
$199$	−1419.93	−0.505809	−0.252905	+	0.967491i	$0.581386\pi$
$200$	0	0
$201$	952.155	0.334128
$202$	−3788.50	−1.31959
$203$	3961.10	1.36953
$204$	−262.643	−0.0901407
$205$	0	0
$206$	1501.50	0.507839
$207$	3289.41	1.10449
$208$	1125.58	0.375217
$209$	1089.56	0.360606
$210$	0	0
$211$	−4406.80	−1.43780	−0.718901	−	0.695112i	$-0.755355\pi$
$211$	−4406.80	−1.43780	−0.718901	+	0.695112i	$0.755355\pi$
$212$	1396.69	0.452477
$213$	616.401	0.198287
$214$	−1844.10	−0.589065
$215$	0	0
$216$	−804.171	−0.253319
$217$	2923.68	0.914620
$218$	2003.45	0.622435
$219$	759.454	0.234334
$220$	0	0
$221$	−2295.31	−0.698639
$222$	−1353.01	−0.409045
$223$	3996.36	1.20007	0.600036	−	0.799973i	$-0.295153\pi$
$223$	3996.36	1.20007	0.600036	+	0.799973i	$0.295153\pi$
$224$	938.618	0.279974
$225$	0	0
$226$	863.163	0.254057
$227$	964.552	0.282025	0.141012	−	0.990008i	$-0.454964\pi$
$227$	964.552	0.282025	0.141012	+	0.990008i	$0.454964\pi$
$228$	1235.96	0.359007
$229$	−5270.96	−1.52102	−0.760512	−	0.649323i	$-0.775052\pi$
$229$	−5270.96	−1.52102	−0.760512	+	0.649323i	$0.775052\pi$
$230$	0	0
$231$	418.881	0.119309
$232$	1080.36	0.305728
$233$	−6618.97	−1.86104	−0.930522	−	0.366235i	$-0.880646\pi$
$233$	−6618.97	−1.86104	−0.930522	+	0.366235i	$0.880646\pi$
$234$	−3229.03	−0.902086
$235$	0	0
$236$	−521.671	−0.143889
$237$	645.868	0.177020
$238$	−1914.05	−0.521300
$239$	5826.24	1.57685	0.788427	−	0.615128i	$-0.210896\pi$
$239$	5826.24	1.57685	0.788427	+	0.615128i	$0.210896\pi$
$240$	0	0
$241$	−3345.06	−0.894084	−0.447042	−	0.894513i	$-0.647523\pi$
$241$	−3345.06	−0.894084	−0.447042	+	0.894513i	$0.647523\pi$
$242$	−2561.29	−0.680354
$243$	3553.99	0.938224
$244$	−1338.01	−0.351055
$245$	0	0
$246$	−654.561	−0.169647
$247$	10801.4	2.78250
$248$	797.409	0.204175
$249$	1025.91	0.261103
$250$	0	0
$251$	−3597.34	−0.904630	−0.452315	−	0.891858i	$-0.649402\pi$
$251$	−3597.34	−0.904630	−0.452315	+	0.891858i	$0.649402\pi$
$252$	−2692.67	−0.673105
$253$	−1017.10	−0.252745
$254$	−856.559	−0.211596
$255$	0	0
$256$	256.000	0.0625000
$257$	−4644.81	−1.12738	−0.563688	−	0.825988i	$-0.690618\pi$
$257$	−4644.81	−1.12738	−0.563688	+	0.825988i	$0.690618\pi$
$258$	−346.014	−0.0834957
$259$	−9860.24	−2.36558
$260$	0	0
$261$	−3099.29	−0.735023
$262$	−1134.37	−0.267487
$263$	5421.31	1.27107	0.635536	−	0.772071i	$-0.280779\pi$
$263$	5421.31	1.27107	0.635536	+	0.772071i	$0.280779\pi$
$264$	114.246	0.0266340
$265$	0	0
$266$	9007.24	2.07620
$267$	−951.221	−0.218029
$268$	1892.54	0.431363
$269$	−6711.15	−1.52114	−0.760569	−	0.649257i	$-0.775080\pi$
$269$	−6711.15	−1.52114	−0.760569	+	0.649257i	$0.775080\pi$
$270$	0	0
$271$	1375.06	0.308225	0.154112	−	0.988053i	$-0.450748\pi$
$271$	1375.06	0.308225	0.154112	+	0.988053i	$0.450748\pi$
$272$	−522.040	−0.116373
$273$	4152.59	0.920608
$274$	−2596.95	−0.572582
$275$	0	0
$276$	−1153.76	−0.251624
$277$	2099.06	0.455307	0.227654	−	0.973742i	$-0.426895\pi$
$277$	2099.06	0.455307	0.227654	+	0.973742i	$0.426895\pi$
$278$	3040.29	0.655915
$279$	−2287.58	−0.490873
$280$	0	0
$281$	1672.42	0.355048	0.177524	−	0.984116i	$-0.443191\pi$
$281$	1672.42	0.355048	0.177524	+	0.984116i	$0.443191\pi$
$282$	1480.72	0.312678
$283$	−4055.49	−0.851851	−0.425925	−	0.904758i	$-0.640051\pi$
$283$	−4055.49	−0.851851	−0.425925	+	0.904758i	$0.640051\pi$
$284$	1225.18	0.255990
$285$	0	0
$286$	998.428	0.206428
$287$	−4770.20	−0.981102
$288$	−734.403	−0.150261
$289$	−3848.45	−0.783319
$290$	0	0
$291$	−172.019	−0.0346526
$292$	1509.52	0.302527
$293$	−1373.72	−0.273904	−0.136952	−	0.990578i	$-0.543731\pi$
$293$	−1373.72	−0.273904	−0.136952	+	0.990578i	$0.543731\pi$
$294$	2082.29	0.413067
$295$	0	0
$296$	−2689.29	−0.528081
$297$	−713.326	−0.139365
$298$	2540.85	0.493917
$299$	−10083.0	−1.95022
$300$	0	0
$301$	−2521.62	−0.482870
$302$	2711.03	0.516563
$303$	−3812.06	−0.722762
$304$	2456.65	0.463481
$305$	0	0
$306$	1497.61	0.279780
$307$	−4275.19	−0.794782	−0.397391	−	0.917649i	$-0.630084\pi$
$307$	−4275.19	−0.794782	−0.397391	+	0.917649i	$0.630084\pi$
$308$	832.585	0.154029
$309$	1510.84	0.278151
$310$	0	0
$311$	−5511.39	−1.00489	−0.502447	−	0.864608i	$-0.667567\pi$
$311$	−5511.39	−1.00489	−0.502447	+	0.864608i	$0.667567\pi$
$312$	1132.58	0.205512
$313$	−6698.78	−1.20970	−0.604852	−	0.796338i	$-0.706768\pi$
$313$	−6698.78	−1.20970	−0.604852	+	0.796338i	$0.706768\pi$
$314$	−5148.34	−0.925280
$315$	0	0
$316$	1283.75	0.228534
$317$	1618.21	0.286712	0.143356	−	0.989671i	$-0.454211\pi$
$317$	1618.21	0.286712	0.143356	+	0.989671i	$0.454211\pi$
$318$	1405.38	0.247829
$319$	958.312	0.168198
$320$	0	0
$321$	−1855.57	−0.322640
$322$	−8408.20	−1.45519
$323$	−5009.64	−0.862984
$324$	1669.44	0.286255
$325$	0	0
$326$	7592.53	1.28991
$327$	2015.91	0.340917
$328$	−1301.03	−0.219017
$329$	10790.9	1.80828
$330$	0	0
$331$	−1886.73	−0.313305	−0.156653	−	0.987654i	$-0.550070\pi$
$331$	−1886.73	−0.313305	−0.156653	+	0.987654i	$0.550070\pi$
$332$	2039.14	0.337086
$333$	7714.94	1.26960
$334$	2438.21	0.399440
$335$	0	0
$336$	944.455	0.153346
$337$	865.877	0.139962	0.0699812	−	0.997548i	$-0.477706\pi$
$337$	865.877	0.139962	0.0699812	+	0.997548i	$0.477706\pi$
$338$	5503.94	0.885724
$339$	868.531	0.139151
$340$	0	0
$341$	707.328	0.112328
$342$	−7047.53	−1.11429
$343$	5114.18	0.805072
$344$	−687.751	−0.107794
$345$	0	0
$346$	3729.65	0.579500
$347$	363.143	0.0561802	0.0280901	−	0.999605i	$-0.491057\pi$
$347$	363.143	0.0561802	0.0280901	+	0.999605i	$0.491057\pi$
$348$	1087.08	0.167452
$349$	1648.78	0.252886	0.126443	−	0.991974i	$-0.459644\pi$
$349$	1648.78	0.252886	0.126443	+	0.991974i	$0.459644\pi$
$350$	0	0
$351$	−7071.57	−1.07536
$352$	227.080	0.0343847
$353$	−11219.6	−1.69167	−0.845837	−	0.533442i	$-0.820898\pi$
$353$	−11219.6	−1.69167	−0.845837	+	0.533442i	$0.820898\pi$
$354$	−524.915	−0.0788106
$355$	0	0
$356$	−1890.69	−0.281478
$357$	−1925.95	−0.285524
$358$	1196.91	0.176701
$359$	6915.67	1.01670	0.508350	−	0.861151i	$-0.330256\pi$
$359$	6915.67	1.01670	0.508350	+	0.861151i	$0.330256\pi$
$360$	0	0
$361$	16715.7	2.43704
$362$	7940.37	1.15286
$363$	−2577.21	−0.372641
$364$	8253.85	1.18851
$365$	0	0
$366$	−1346.33	−0.192279
$367$	383.295	0.0545172	0.0272586	−	0.999628i	$-0.491322\pi$
$367$	383.295	0.0545172	0.0272586	+	0.999628i	$0.491322\pi$
$368$	−2293.26	−0.324850
$369$	3732.35	0.526554
$370$	0	0
$371$	10241.9	1.43324
$372$	802.367	0.111830
$373$	−3194.72	−0.443475	−0.221738	−	0.975106i	$-0.571173\pi$
$373$	−3194.72	−0.443475	−0.221738	+	0.975106i	$0.571173\pi$
$374$	−463.066	−0.0640230
$375$	0	0
$376$	2943.13	0.403671
$377$	9500.24	1.29784
$378$	−5896.95	−0.802398
$379$	337.684	0.0457670	0.0228835	−	0.999738i	$-0.492715\pi$
$379$	337.684	0.0457670	0.0228835	+	0.999738i	$0.492715\pi$
$380$	0	0
$381$	−861.885	−0.115894
$382$	2095.98	0.280732
$383$	7110.60	0.948655	0.474327	−	0.880349i	$-0.342691\pi$
$383$	7110.60	0.948655	0.474327	+	0.880349i	$0.342691\pi$
$384$	257.592	0.0342322
$385$	0	0
$386$	2976.56	0.392495
$387$	1972.99	0.259155
$388$	−341.911	−0.0447369
$389$	−3727.24	−0.485806	−0.242903	−	0.970051i	$-0.578100\pi$
$389$	−3727.24	−0.485806	−0.242903	+	0.970051i	$0.578100\pi$
$390$	0	0
$391$	4676.47	0.604857
$392$	4138.85	0.533274
$393$	−1141.42	−0.146507
$394$	−8298.46	−1.06109
$395$	0	0
$396$	−651.440	−0.0826668
$397$	10734.1	1.35700	0.678499	−	0.734602i	$-0.262631\pi$
$397$	10734.1	1.35700	0.678499	+	0.734602i	$0.262631\pi$
$398$	−2839.86	−0.357661
$399$	9063.25	1.13717
$400$	0	0
$401$	1298.60	0.161718	0.0808589	−	0.996726i	$-0.474234\pi$
$401$	1298.60	0.161718	0.0808589	+	0.996726i	$0.474234\pi$
$402$	1904.31	0.236264
$403$	7012.10	0.866744
$404$	−7577.00	−0.933093
$405$	0	0
$406$	7922.21	0.968406
$407$	−2385.49	−0.290527
$408$	−525.286	−0.0637391
$409$	5201.71	0.628870	0.314435	−	0.949279i	$-0.398185\pi$
$409$	5201.71	0.628870	0.314435	+	0.949279i	$0.398185\pi$
$410$	0	0
$411$	−2613.10	−0.313612
$412$	3003.01	0.359096
$413$	−3825.39	−0.455776
$414$	6578.83	0.780995
$415$	0	0
$416$	2251.16	0.265318
$417$	3059.19	0.359255
$418$	2179.13	0.254987
$419$	−6810.05	−0.794017	−0.397008	−	0.917815i	$-0.629952\pi$
$419$	−6810.05	−0.794017	−0.397008	+	0.917815i	$0.629952\pi$
$420$	0	0
$421$	−12128.7	−1.40408	−0.702040	−	0.712137i	$-0.747727\pi$
$421$	−12128.7	−1.40408	−0.702040	+	0.712137i	$0.747727\pi$
$422$	−8813.59	−1.01668
$423$	−8443.14	−0.970495
$424$	2793.38	0.319950
$425$	0	0
$426$	1232.80	0.140210
$427$	−9811.59	−1.11198
$428$	−3688.20	−0.416532
$429$	1004.64	0.113064
$430$	0	0
$431$	−14041.5	−1.56927	−0.784636	−	0.619957i	$-0.787150\pi$
$431$	−14041.5	−1.56927	−0.784636	+	0.619957i	$0.787150\pi$
$432$	−1608.34	−0.179124
$433$	−371.807	−0.0412654	−0.0206327	−	0.999787i	$-0.506568\pi$
$433$	−371.807	−0.0412654	−0.0206327	+	0.999787i	$0.506568\pi$
$434$	5847.36	0.646734
$435$	0	0
$436$	4006.90	0.440128
$437$	−22006.8	−2.40899
$438$	1518.91	0.165699
$439$	−12898.1	−1.40226	−0.701132	−	0.713031i	$-0.747322\pi$
$439$	−12898.1	−1.40226	−0.701132	+	0.713031i	$0.747322\pi$
$440$	0	0
$441$	−11873.4	−1.28208
$442$	−4590.62	−0.494012
$443$	−10257.2	−1.10007	−0.550037	−	0.835141i	$-0.685386\pi$
$443$	−10257.2	−1.10007	−0.550037	+	0.835141i	$0.685386\pi$
$444$	−2706.02	−0.289238
$445$	0	0
$446$	7992.72	0.848579
$447$	2556.65	0.270526
$448$	1877.24	0.197971
$449$	4725.49	0.496680	0.248340	−	0.968673i	$-0.420115\pi$
$449$	4725.49	0.496680	0.248340	+	0.968673i	$0.420115\pi$
$450$	0	0
$451$	−1154.06	−0.120493
$452$	1726.33	0.179645
$453$	2727.89	0.282930
$454$	1929.10	0.199422
$455$	0	0
$456$	2471.92	0.253856
$457$	−4393.74	−0.449739	−0.224869	−	0.974389i	$-0.572196\pi$
$457$	−4393.74	−0.449739	−0.224869	+	0.974389i	$0.572196\pi$
$458$	−10541.9	−1.07553
$459$	3279.76	0.333521
$460$	0	0
$461$	−5370.32	−0.542561	−0.271280	−	0.962500i	$-0.587447\pi$
$461$	−5370.32	−0.542561	−0.271280	+	0.962500i	$0.587447\pi$
$462$	837.762	0.0843641
$463$	6924.94	0.695095	0.347548	−	0.937662i	$-0.387014\pi$
$463$	6924.94	0.695095	0.347548	+	0.937662i	$0.387014\pi$
$464$	2160.71	0.216182
$465$	0	0
$466$	−13237.9	−1.31596
$467$	−4541.69	−0.450031	−0.225015	−	0.974355i	$-0.572243\pi$
$467$	−4541.69	−0.450031	−0.225015	+	0.974355i	$0.572243\pi$
$468$	−6458.06	−0.637871
$469$	13877.9	1.36636
$470$	0	0
$471$	−5180.36	−0.506791
$472$	−1043.34	−0.101745
$473$	−610.058	−0.0593033
$474$	1291.74	0.125172
$475$	0	0
$476$	−3828.10	−0.368615
$477$	−8013.56	−0.769215
$478$	11652.5	1.11500
$479$	−12108.8	−1.15504	−0.577522	−	0.816375i	$-0.695980\pi$
$479$	−12108.8	−1.15504	−0.577522	+	0.816375i	$0.695980\pi$
$480$	0	0
$481$	−23648.6	−2.24175
$482$	−6690.12	−0.632213
$483$	−8460.49	−0.797030
$484$	−5122.57	−0.481083
$485$	0	0
$486$	7107.98	0.663425
$487$	3448.88	0.320911	0.160455	−	0.987043i	$-0.448704\pi$
$487$	3448.88	0.320911	0.160455	+	0.987043i	$0.448704\pi$
$488$	−2676.03	−0.248234
$489$	7639.74	0.706505
$490$	0	0
$491$	−6214.56	−0.571199	−0.285600	−	0.958349i	$-0.592193\pi$
$491$	−6214.56	−0.571199	−0.285600	+	0.958349i	$0.592193\pi$
$492$	−1309.12	−0.119959
$493$	−4406.17	−0.402523
$494$	21602.8	1.96752
$495$	0	0
$496$	1594.82	0.144374
$497$	8984.21	0.810859
$498$	2051.82	0.184627
$499$	−16134.7	−1.44747	−0.723734	−	0.690079i	$-0.757576\pi$
$499$	−16134.7	−1.44747	−0.723734	+	0.690079i	$0.757576\pi$
$500$	0	0
$501$	2453.37	0.218780
$502$	−7194.68	−0.639670
$503$	1193.42	0.105789	0.0528947	−	0.998600i	$-0.483155\pi$
$503$	1193.42	0.105789	0.0528947	+	0.998600i	$0.483155\pi$
$504$	−5385.35	−0.475957
$505$	0	0
$506$	−2034.20	−0.178718
$507$	5538.16	0.485125
$508$	−1713.12	−0.149621
$509$	−19958.4	−1.73800	−0.869000	−	0.494813i	$-0.835237\pi$
$509$	−19958.4	−1.73800	−0.869000	+	0.494813i	$0.835237\pi$
$510$	0	0
$511$	11069.2	0.958267
$512$	512.000	0.0441942
$513$	−15434.1	−1.32833
$514$	−9289.62	−0.797175
$515$	0	0
$516$	−692.028	−0.0590403
$517$	2610.65	0.222082
$518$	−19720.5	−1.67272
$519$	3752.84	0.317401
$520$	0	0
$521$	17162.2	1.44316	0.721582	−	0.692329i	$-0.243415\pi$
$521$	17162.2	1.44316	0.721582	+	0.692329i	$0.243415\pi$
$522$	−6198.57	−0.519740
$523$	2330.43	0.194843	0.0974214	−	0.995243i	$-0.468941\pi$
$523$	2330.43	0.194843	0.0974214	+	0.995243i	$0.468941\pi$
$524$	−2268.74	−0.189142
$525$	0	0
$526$	10842.6	0.898784
$527$	−3252.18	−0.268818
$528$	228.492	0.0188331
$529$	8376.21	0.688436
$530$	0	0
$531$	2993.10	0.244613
$532$	18014.5	1.46810
$533$	−11440.8	−0.929746
$534$	−1902.44	−0.154170
$535$	0	0
$536$	3785.08	0.305020
$537$	1204.36	0.0967818
$538$	−13422.3	−1.07561
$539$	3671.29	0.293384
$540$	0	0
$541$	−11442.8	−0.909359	−0.454680	−	0.890655i	$-0.650246\pi$
$541$	−11442.8	−0.909359	−0.454680	+	0.890655i	$0.650246\pi$
$542$	2750.12	0.217948
$543$	7989.75	0.631442
$544$	−1044.08	−0.0822878
$545$	0	0
$546$	8305.17	0.650968
$547$	−4362.52	−0.341002	−0.170501	−	0.985358i	$-0.554539\pi$
$547$	−4362.52	−0.341002	−0.170501	+	0.985358i	$0.554539\pi$
$548$	−5193.90	−0.404876
$549$	7676.88	0.596797
$550$	0	0
$551$	20734.8	1.60314
$552$	−2307.52	−0.177925
$553$	9413.71	0.723891
$554$	4198.11	0.321951
$555$	0	0
$556$	6080.57	0.463802
$557$	−284.989	−0.0216793	−0.0108397	−	0.999941i	$-0.503450\pi$
$557$	−284.989	−0.0216793	−0.0108397	+	0.999941i	$0.503450\pi$
$558$	−4575.15	−0.347100
$559$	−6047.82	−0.457595
$560$	0	0
$561$	−465.946	−0.0350664
$562$	3344.85	0.251057
$563$	−4472.73	−0.334819	−0.167409	−	0.985887i	$-0.553540\pi$
$563$	−4472.73	−0.334819	−0.167409	+	0.985887i	$0.553540\pi$
$564$	2961.43	0.221097
$565$	0	0
$566$	−8110.98	−0.602349
$567$	12241.9	0.906724
$568$	2450.37	0.181012
$569$	−15821.2	−1.16565	−0.582827	−	0.812596i	$-0.698054\pi$
$569$	−15821.2	−1.16565	−0.582827	+	0.812596i	$0.698054\pi$
$570$	0	0
$571$	−22008.8	−1.61303	−0.806515	−	0.591214i	$-0.798649\pi$
$571$	−22008.8	−1.61303	−0.806515	+	0.591214i	$0.798649\pi$
$572$	1996.86	0.145966
$573$	2109.01	0.153761
$574$	−9540.41	−0.693744
$575$	0	0
$576$	−1468.81	−0.106250
$577$	6896.15	0.497557	0.248779	−	0.968560i	$-0.419971\pi$
$577$	6896.15	0.497557	0.248779	+	0.968560i	$0.419971\pi$
$578$	−7696.89	−0.553890
$579$	2995.07	0.214975
$580$	0	0
$581$	14953.0	1.06773
$582$	−344.037	−0.0245031
$583$	2477.82	0.176022
$584$	3019.04	0.213919
$585$	0	0
$586$	−2747.45	−0.193679
$587$	−14815.2	−1.04172	−0.520860	−	0.853642i	$-0.674389\pi$
$587$	−14815.2	−1.04172	−0.520860	+	0.853642i	$0.674389\pi$
$588$	4164.58	0.292083
$589$	15304.3	1.07063
$590$	0	0
$591$	−8350.06	−0.581177
$592$	−5378.59	−0.373410
$593$	−17515.7	−1.21296	−0.606478	−	0.795100i	$-0.707418\pi$
$593$	−17515.7	−1.21296	−0.606478	+	0.795100i	$0.707418\pi$
$594$	−1426.65	−0.0985459
$595$	0	0
$596$	5081.69	0.349252
$597$	−2857.52	−0.195897
$598$	−20166.1	−1.37902
$599$	27650.4	1.88609	0.943044	−	0.332669i	$-0.107949\pi$
$599$	27650.4	1.88609	0.943044	+	0.332669i	$0.107949\pi$
$600$	0	0
$601$	−9564.79	−0.649178	−0.324589	−	0.945855i	$-0.605226\pi$
$601$	−9564.79	−0.649178	−0.324589	+	0.945855i	$0.605226\pi$
$602$	−5043.25	−0.341441
$603$	−10858.5	−0.733320
$604$	5422.06	0.365265
$605$	0	0
$606$	−7624.11	−0.511070
$607$	18556.9	1.24086	0.620430	−	0.784262i	$-0.286958\pi$
$607$	18556.9	1.24086	0.620430	+	0.784262i	$0.286958\pi$
$608$	4913.29	0.327731
$609$	7971.47	0.530411
$610$	0	0
$611$	25880.7	1.71362
$612$	2995.22	0.197834
$613$	911.504	0.0600576	0.0300288	−	0.999549i	$-0.490440\pi$
$613$	911.504	0.0600576	0.0300288	+	0.999549i	$0.490440\pi$
$614$	−8550.38	−0.561996
$615$	0	0
$616$	1665.17	0.108915
$617$	3984.51	0.259984	0.129992	−	0.991515i	$-0.458505\pi$
$617$	3984.51	0.259984	0.129992	+	0.991515i	$0.458505\pi$
$618$	3021.68	0.196683
$619$	13583.3	0.882003	0.441001	−	0.897506i	$-0.354623\pi$
$619$	13583.3	0.882003	0.441001	+	0.897506i	$0.354623\pi$
$620$	0	0
$621$	14407.6	0.931012
$622$	−11022.8	−0.710568
$623$	−13864.3	−0.891592
$624$	2265.16	0.145319
$625$	0	0
$626$	−13397.6	−0.855390
$627$	2192.68	0.139660
$628$	−10296.7	−0.654272
$629$	10968.1	0.695274
$630$	0	0
$631$	−27719.1	−1.74878	−0.874389	−	0.485226i	$-0.838738\pi$
$631$	−27719.1	−1.74878	−0.874389	+	0.485226i	$0.838738\pi$
$632$	2567.51	0.161598
$633$	−8868.40	−0.556852
$634$	3236.42	0.202736
$635$	0	0
$636$	2810.75	0.175242
$637$	36395.4	2.26380
$638$	1916.62	0.118934
$639$	−7029.52	−0.435185
$640$	0	0
$641$	−10101.0	−0.622409	−0.311205	−	0.950343i	$-0.600732\pi$
$641$	−10101.0	−0.622409	−0.311205	+	0.950343i	$0.600732\pi$
$642$	−3711.13	−0.228141
$643$	−25425.7	−1.55940	−0.779699	−	0.626154i	$-0.784628\pi$
$643$	−25425.7	−1.55940	−0.779699	+	0.626154i	$0.784628\pi$
$644$	−16816.4	−1.02897
$645$	0	0
$646$	−10019.3	−0.610222
$647$	−7012.31	−0.426093	−0.213047	−	0.977042i	$-0.568339\pi$
$647$	−7012.31	−0.426093	−0.213047	+	0.977042i	$0.568339\pi$
$648$	3338.88	0.202413
$649$	−925.479	−0.0559757
$650$	0	0
$651$	5883.72	0.354226
$652$	15185.1	0.912106
$653$	14918.5	0.894036	0.447018	−	0.894525i	$-0.352486\pi$
$653$	14918.5	0.894036	0.447018	+	0.894525i	$0.352486\pi$
$654$	4031.82	0.241065
$655$	0	0
$656$	−2602.06	−0.154868
$657$	−8660.91	−0.514299
$658$	21581.8	1.27864
$659$	26076.4	1.54142	0.770709	−	0.637188i	$-0.219902\pi$
$659$	26076.4	1.54142	0.770709	+	0.637188i	$0.219902\pi$
$660$	0	0
$661$	−8574.94	−0.504579	−0.252289	−	0.967652i	$-0.581184\pi$
$661$	−8574.94	−0.504579	−0.252289	+	0.967652i	$0.581184\pi$
$662$	−3773.46	−0.221540
$663$	−4619.16	−0.270578
$664$	4078.29	0.238356
$665$	0	0
$666$	15429.9	0.897742
$667$	−19355.8	−1.12363
$668$	4876.42	0.282447
$669$	8042.42	0.464780
$670$	0	0
$671$	−2373.72	−0.136567
$672$	1888.91	0.108432
$673$	−17068.9	−0.977648	−0.488824	−	0.872382i	$-0.662574\pi$
$673$	−17068.9	−0.977648	−0.488824	+	0.872382i	$0.662574\pi$
$674$	1731.75	0.0989684
$675$	0	0
$676$	11007.9	0.626301
$677$	4759.38	0.270189	0.135094	−	0.990833i	$-0.456866\pi$
$677$	4759.38	0.270189	0.135094	+	0.990833i	$0.456866\pi$
$678$	1737.06	0.0983945
$679$	−2507.22	−0.141706
$680$	0	0
$681$	1941.10	0.109226
$682$	1414.66	0.0794281
$683$	19220.1	1.07677	0.538386	−	0.842698i	$-0.319034\pi$
$683$	19220.1	1.07677	0.538386	+	0.842698i	$0.319034\pi$
$684$	−14095.1	−0.787922
$685$	0	0
$686$	10228.4	0.569272
$687$	−10607.5	−0.589083
$688$	−1375.50	−0.0762217
$689$	24563.9	1.35822
$690$	0	0
$691$	−27838.7	−1.53261	−0.766305	−	0.642477i	$-0.777907\pi$
$691$	−27838.7	−1.53261	−0.766305	+	0.642477i	$0.777907\pi$
$692$	7459.29	0.409768
$693$	−4776.98	−0.261850
$694$	726.286	0.0397254
$695$	0	0
$696$	2174.15	0.118407
$697$	5306.18	0.288358
$698$	3297.56	0.178817
$699$	−13320.3	−0.720771
$700$	0	0
$701$	−9708.28	−0.523077	−0.261538	−	0.965193i	$-0.584230\pi$
$701$	−9708.28	−0.523077	−0.261538	+	0.965193i	$0.584230\pi$
$702$	−14143.1	−0.760397
$703$	−51614.4	−2.76910
$704$	454.161	0.0243137
$705$	0	0
$706$	−22439.3	−1.19619
$707$	−55561.8	−2.95561
$708$	−1049.83	−0.0557275
$709$	15845.5	0.839340	0.419670	−	0.907677i	$-0.362146\pi$
$709$	15845.5	0.839340	0.419670	+	0.907677i	$0.362146\pi$
$710$	0	0
$711$	−7365.57	−0.388510
$712$	−3781.37	−0.199035
$713$	−14286.5	−0.750397
$714$	−3851.90	−0.201896
$715$	0	0
$716$	2393.83	0.124946
$717$	11724.9	0.610706
$718$	13831.3	0.718915
$719$	−13377.2	−0.693860	−0.346930	−	0.937891i	$-0.612776\pi$
$719$	−13377.2	−0.693860	−0.346930	+	0.937891i	$0.612776\pi$
$720$	0	0
$721$	22020.9	1.13745
$722$	33431.3	1.72325
$723$	−6731.72	−0.346273
$724$	15880.7	0.815198
$725$	0	0
$726$	−5154.43	−0.263497
$727$	20609.6	1.05140	0.525701	−	0.850669i	$-0.323803\pi$
$727$	20609.6	1.05140	0.525701	+	0.850669i	$0.323803\pi$
$728$	16507.7	0.840406
$729$	−4116.53	−0.209142
$730$	0	0
$731$	2804.95	0.141922
$732$	−2692.67	−0.135962
$733$	1757.24	0.0885474	0.0442737	−	0.999019i	$-0.485903\pi$
$733$	1757.24	0.0885474	0.0442737	+	0.999019i	$0.485903\pi$
$734$	766.590	0.0385495
$735$	0	0
$736$	−4586.53	−0.229703
$737$	3357.49	0.167808
$738$	7464.70	0.372330
$739$	−7927.26	−0.394599	−0.197300	−	0.980343i	$-0.563217\pi$
$739$	−7927.26	−0.394599	−0.197300	+	0.980343i	$0.563217\pi$
$740$	0	0
$741$	21737.1	1.07764
$742$	20483.8	1.01345
$743$	22921.8	1.13179	0.565895	−	0.824477i	$-0.308531\pi$
$743$	22921.8	1.13179	0.565895	+	0.824477i	$0.308531\pi$
$744$	1604.73	0.0790758
$745$	0	0
$746$	−6389.44	−0.313584
$747$	−11699.6	−0.573049
$748$	−926.133	−0.0452711
$749$	−27045.4	−1.31938
$750$	0	0
$751$	−31048.1	−1.50861	−0.754303	−	0.656527i	$-0.772025\pi$
$751$	−31048.1	−1.50861	−0.754303	+	0.656527i	$0.772025\pi$
$752$	5886.26	0.285438
$753$	−7239.42	−0.350358
$754$	19000.5	0.917714
$755$	0	0
$756$	−11793.9	−0.567381
$757$	24419.8	1.17246	0.586230	−	0.810144i	$-0.300611\pi$
$757$	24419.8	1.17246	0.586230	+	0.810144i	$0.300611\pi$
$758$	675.369	0.0323621
$759$	−2046.85	−0.0978866
$760$	0	0
$761$	40840.2	1.94541	0.972704	−	0.232050i	$-0.0745431\pi$
$761$	40840.2	1.94541	0.972704	+	0.232050i	$0.0745431\pi$
$762$	−1723.77	−0.0819496
$763$	29382.4	1.39412
$764$	4191.96	0.198508
$765$	0	0
$766$	14221.2	0.670800
$767$	−9174.75	−0.431918
$768$	515.184	0.0242059
$769$	7911.62	0.371002	0.185501	−	0.982644i	$-0.440609\pi$
$769$	7911.62	0.371002	0.185501	+	0.982644i	$0.440609\pi$
$770$	0	0
$771$	−9347.39	−0.436625
$772$	5953.12	0.277536
$773$	32034.9	1.49058	0.745288	−	0.666743i	$-0.232312\pi$
$773$	32034.9	1.49058	0.745288	+	0.666743i	$0.232312\pi$
$774$	3945.99	0.183250
$775$	0	0
$776$	−683.822	−0.0316337
$777$	−19843.1	−0.916174
$778$	−7454.48	−0.343517
$779$	−24970.1	−1.14846
$780$	0	0
$781$	2173.55	0.0995850
$782$	9352.93	0.427699
$783$	−13574.9	−0.619574
$784$	8277.70	0.377082
$785$	0	0
$786$	−2282.85	−0.103596
$787$	28373.2	1.28513	0.642563	−	0.766233i	$-0.277871\pi$
$787$	28373.2	1.28513	0.642563	+	0.766233i	$0.277871\pi$
$788$	−16596.9	−0.750306
$789$	10910.0	0.492278
$790$	0	0
$791$	12659.1	0.569033
$792$	−1302.88	−0.0584543
$793$	−23531.9	−1.05378
$794$	21468.2	0.959542
$795$	0	0
$796$	−5679.71	−0.252905
$797$	11191.9	0.497412	0.248706	−	0.968579i	$-0.419995\pi$
$797$	11191.9	0.497412	0.248706	+	0.968579i	$0.419995\pi$
$798$	18126.5	0.804099
$799$	−12003.4	−0.531475
$800$	0	0
$801$	10847.9	0.478514
$802$	2597.20	0.114352
$803$	2677.99	0.117689
$804$	3808.62	0.167064
$805$	0	0
$806$	14024.2	0.612880
$807$	−13505.8	−0.589127
$808$	−15154.0	−0.659797
$809$	−40350.8	−1.75359	−0.876797	−	0.480860i	$-0.840324\pi$
$809$	−40350.8	−1.75359	−0.876797	+	0.480860i	$0.840324\pi$
$810$	0	0
$811$	−11049.4	−0.478420	−0.239210	−	0.970968i	$-0.576888\pi$
$811$	−11049.4	−0.478420	−0.239210	+	0.970968i	$0.576888\pi$
$812$	15844.4	0.684766
$813$	2767.22	0.119374
$814$	−4770.98	−0.205433
$815$	0	0
$816$	−1050.57	−0.0450703
$817$	−13199.7	−0.565237
$818$	10403.4	0.444678
$819$	−47356.6	−2.02048
$820$	0	0
$821$	1236.69	0.0525712	0.0262856	−	0.999654i	$-0.491632\pi$
$821$	1236.69	0.0525712	0.0262856	+	0.999654i	$0.491632\pi$
$822$	−5226.19	−0.221757
$823$	−8386.12	−0.355190	−0.177595	−	0.984104i	$-0.556832\pi$
$823$	−8386.12	−0.355190	−0.177595	+	0.984104i	$0.556832\pi$
$824$	6006.02	0.253919
$825$	0	0
$826$	−7650.79	−0.322282
$827$	10689.4	0.449464	0.224732	−	0.974421i	$-0.427849\pi$
$827$	10689.4	0.449464	0.224732	+	0.974421i	$0.427849\pi$
$828$	13157.7	0.552247
$829$	10378.7	0.434820	0.217410	−	0.976080i	$-0.430239\pi$
$829$	10378.7	0.434820	0.217410	+	0.976080i	$0.430239\pi$
$830$	0	0
$831$	4224.22	0.176338
$832$	4502.33	0.187608
$833$	−16880.0	−0.702111
$834$	6118.38	0.254032
$835$	0	0
$836$	4358.25	0.180303
$837$	−10019.6	−0.413772
$838$	−13620.1	−0.561454
$839$	−40157.9	−1.65245	−0.826224	−	0.563342i	$-0.809515\pi$
$839$	−40157.9	−1.65245	−0.826224	+	0.563342i	$0.809515\pi$
$840$	0	0
$841$	−6151.95	−0.252243
$842$	−24257.4	−0.992835
$843$	3365.65	0.137508
$844$	−17627.2	−0.718901
$845$	0	0
$846$	−16886.3	−0.686244
$847$	−37563.6	−1.52385
$848$	5586.77	0.226239
$849$	−8161.41	−0.329916
$850$	0	0
$851$	48181.7	1.94083
$852$	2465.60	0.0991434
$853$	27968.8	1.12267	0.561333	−	0.827590i	$-0.310289\pi$
$853$	27968.8	1.12267	0.561333	+	0.827590i	$0.310289\pi$
$854$	−19623.2	−0.786290
$855$	0	0
$856$	−7376.39	−0.294533
$857$	29403.0	1.17198	0.585990	−	0.810318i	$-0.300706\pi$
$857$	29403.0	1.17198	0.585990	+	0.810318i	$0.300706\pi$
$858$	2009.27	0.0799481
$859$	−24573.8	−0.976073	−0.488036	−	0.872823i	$-0.662287\pi$
$859$	−24573.8	−0.976073	−0.488036	+	0.872823i	$0.662287\pi$
$860$	0	0
$861$	−9599.73	−0.379975
$862$	−28083.0	−1.10964
$863$	−11773.9	−0.464414	−0.232207	−	0.972666i	$-0.574595\pi$
$863$	−11773.9	−0.464414	−0.232207	+	0.972666i	$0.574595\pi$
$864$	−3216.69	−0.126660
$865$	0	0
$866$	−743.614	−0.0291790
$867$	−7744.75	−0.303374
$868$	11694.7	0.457310
$869$	2277.46	0.0889041
$870$	0	0
$871$	33284.5	1.29484
$872$	8013.80	0.311217
$873$	1961.72	0.0760530
$874$	−44013.6	−1.70341
$875$	0	0
$876$	3037.81	0.117167
$877$	−5031.55	−0.193732	−0.0968662	−	0.995297i	$-0.530882\pi$
$877$	−5031.55	−0.193732	−0.0968662	+	0.995297i	$0.530882\pi$
$878$	−25796.3	−0.991551
$879$	−2764.53	−0.106081
$880$	0	0
$881$	7693.29	0.294204	0.147102	−	0.989121i	$-0.453005\pi$
$881$	7693.29	0.294204	0.147102	+	0.989121i	$0.453005\pi$
$882$	−23746.7	−0.906570
$883$	−19812.1	−0.755072	−0.377536	−	0.925995i	$-0.623229\pi$
$883$	−19812.1	−0.755072	−0.377536	+	0.925995i	$0.623229\pi$
$884$	−9181.23	−0.349319
$885$	0	0
$886$	−20514.3	−0.777869
$887$	−41414.0	−1.56769	−0.783847	−	0.620954i	$-0.786746\pi$
$887$	−41414.0	−1.56769	−0.783847	+	0.620954i	$0.786746\pi$
$888$	−5412.03	−0.204522
$889$	−12562.2	−0.473929
$890$	0	0
$891$	2961.69	0.111359
$892$	15985.4	0.600036
$893$	56486.2	2.11673
$894$	5113.29	0.191291
$895$	0	0
$896$	3754.47	0.139987
$897$	−20291.5	−0.755310
$898$	9450.97	0.351206
$899$	13460.7	0.499377
$900$	0	0
$901$	−11392.6	−0.421247
$902$	−2308.11	−0.0852016
$903$	−5074.61	−0.187013
$904$	3452.65	0.127028
$905$	0	0
$906$	5455.77	0.200062
$907$	8776.67	0.321306	0.160653	−	0.987011i	$-0.448640\pi$
$907$	8776.67	0.321306	0.160653	+	0.987011i	$0.448640\pi$
$908$	3858.21	0.141012
$909$	43473.2	1.58627
$910$	0	0
$911$	−11633.7	−0.423097	−0.211549	−	0.977367i	$-0.567851\pi$
$911$	−11633.7	−0.423097	−0.211549	+	0.977367i	$0.567851\pi$
$912$	4943.85	0.179503
$913$	3617.57	0.131133
$914$	−8787.48	−0.318013
$915$	0	0
$916$	−21083.8	−0.760512
$917$	−16636.6	−0.599114
$918$	6559.52	0.235835
$919$	24405.7	0.876029	0.438014	−	0.898968i	$-0.355682\pi$
$919$	24405.7	0.876029	0.438014	+	0.898968i	$0.355682\pi$
$920$	0	0
$921$	−8603.55	−0.307814
$922$	−10740.6	−0.383648
$923$	21547.6	0.768415
$924$	1675.52	0.0596545
$925$	0	0
$926$	13849.9	0.491507
$927$	−17229.8	−0.610466
$928$	4321.43	0.152864
$929$	−43554.1	−1.53818	−0.769088	−	0.639143i	$-0.779289\pi$
$929$	−43554.1	−1.53818	−0.769088	+	0.639143i	$0.779289\pi$
$930$	0	0
$931$	79435.0	2.79632
$932$	−26475.9	−0.930522
$933$	−11091.3	−0.389189
$934$	−9083.38	−0.318220
$935$	0	0
$936$	−12916.1	−0.451043
$937$	−9843.58	−0.343197	−0.171599	−	0.985167i	$-0.554893\pi$
$937$	−9843.58	−0.343197	−0.171599	+	0.985167i	$0.554893\pi$
$938$	27755.8	0.966162
$939$	−13480.9	−0.468511
$940$	0	0
$941$	34395.2	1.19155	0.595777	−	0.803150i	$-0.296844\pi$
$941$	34395.2	1.19155	0.595777	+	0.803150i	$0.296844\pi$
$942$	−10360.7	−0.358355
$943$	23309.4	0.804942
$944$	−2086.69	−0.0719447
$945$	0	0
$946$	−1220.12	−0.0419338
$947$	28801.8	0.988314	0.494157	−	0.869373i	$-0.335477\pi$
$947$	28801.8	0.988314	0.494157	+	0.869373i	$0.335477\pi$
$948$	2583.47	0.0885098
$949$	26548.3	0.908107
$950$	0	0
$951$	3256.54	0.111042
$952$	−7656.19	−0.260650
$953$	21392.1	0.727134	0.363567	−	0.931568i	$-0.381559\pi$
$953$	21392.1	0.727134	0.363567	+	0.931568i	$0.381559\pi$
$954$	−16027.1	−0.543917
$955$	0	0
$956$	23305.0	0.788427
$957$	1928.54	0.0651420
$958$	−24217.7	−0.816740
$959$	−38086.6	−1.28246
$960$	0	0
$961$	−19855.7	−0.666499
$962$	−47297.2	−1.58516
$963$	21161.1	0.708108
$964$	−13380.2	−0.447042
$965$	0	0
$966$	−16921.0	−0.563585
$967$	50524.8	1.68021	0.840107	−	0.542421i	$-0.182492\pi$
$967$	50524.8	1.68021	0.840107	+	0.542421i	$0.182492\pi$
$968$	−10245.1	−0.340177
$969$	−10081.6	−0.334228
$970$	0	0
$971$	−32155.4	−1.06273	−0.531367	−	0.847142i	$-0.678322\pi$
$971$	−32155.4	−1.06273	−0.531367	+	0.847142i	$0.678322\pi$
$972$	14216.0	0.469112
$973$	44588.6	1.46911
$974$	6897.76	0.226918
$975$	0	0
$976$	−5352.05	−0.175528
$977$	−24346.0	−0.797234	−0.398617	−	0.917117i	$-0.630510\pi$
$977$	−24346.0	−0.797234	−0.398617	+	0.917117i	$0.630510\pi$
$978$	15279.5	0.499575
$979$	−3354.20	−0.109500
$980$	0	0
$981$	−22989.7	−0.748220
$982$	−12429.1	−0.403899
$983$	48277.3	1.56644	0.783219	−	0.621746i	$-0.213577\pi$
$983$	48277.3	1.56644	0.783219	+	0.621746i	$0.213577\pi$
$984$	−2618.24	−0.0848237
$985$	0	0
$986$	−8812.34	−0.284627
$987$	21716.0	0.700333
$988$	43205.6	1.39125
$989$	12321.8	0.396169
$990$	0	0
$991$	38089.1	1.22093	0.610464	−	0.792044i	$-0.290983\pi$
$991$	38089.1	1.22093	0.610464	+	0.792044i	$0.290983\pi$
$992$	3189.64	0.102088
$993$	−3796.93	−0.121341
$994$	17968.4	0.573364
$995$	0	0
$996$	4103.65	0.130551
$997$	8030.02	0.255079	0.127539	−	0.991834i	$-0.459292\pi$
$997$	8030.02	0.255079	0.127539	+	0.991834i	$0.459292\pi$
$998$	−32269.3	−1.02351
$999$	33791.5	1.07018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.4.a.n.1.9		16
5.4	even	2		1250.4.a.m.1.8		16
25.3	odd	20		50.4.e.a.9.2	✓	32
25.4	even	10		250.4.d.d.201.4		32
25.6	even	5		250.4.d.c.51.5		32
25.8	odd	20		250.4.e.b.199.7		32
25.17	odd	20		50.4.e.a.39.2	yes	32
25.19	even	10		250.4.d.d.51.4		32
25.21	even	5		250.4.d.c.201.5		32
25.22	odd	20		250.4.e.b.49.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.2	✓	32	25.3	odd	20
50.4.e.a.39.2	yes	32	25.17	odd	20
250.4.d.c.51.5		32	25.6	even	5
250.4.d.c.201.5		32	25.21	even	5
250.4.d.d.51.4		32	25.19	even	10
250.4.d.d.201.4		32	25.4	even	10
250.4.e.b.49.7		32	25.22	odd	20
250.4.e.b.199.7		32	25.8	odd	20
1250.4.a.m.1.8		16	5.4	even	2
1250.4.a.n.1.9		16	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:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +2.01244 q^{3} +4.00000 q^{4} +4.02487 q^{6} +29.3318 q^{7} +8.00000 q^{8} -22.9501 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +2.01244 q^{3} +4.00000 q^{4} +4.02487 q^{6} +29.3318 q^{7} +8.00000 q^{8} -22.9501 q^{9} +7.09626 q^{11} +8.04975 q^{12} +70.3489 q^{13} +58.6636 q^{14} +16.0000 q^{16} -32.6275 q^{17} -45.9002 q^{18} +153.540 q^{19} +59.0284 q^{21} +14.1925 q^{22} -143.329 q^{23} +16.0995 q^{24} +140.698 q^{26} -100.521 q^{27} +117.327 q^{28} +135.045 q^{29} +99.6761 q^{31} +32.0000 q^{32} +14.2808 q^{33} -65.2550 q^{34} -91.8004 q^{36} -336.162 q^{37} +307.081 q^{38} +141.573 q^{39} -162.629 q^{41} +118.057 q^{42} -85.9689 q^{43} +28.3850 q^{44} -286.658 q^{46} +367.891 q^{47} +32.1990 q^{48} +517.356 q^{49} -65.6608 q^{51} +281.396 q^{52} +349.173 q^{53} -201.043 q^{54} +234.655 q^{56} +308.990 q^{57} +270.089 q^{58} -130.418 q^{59} -334.503 q^{61} +199.352 q^{62} -673.168 q^{63} +64.0000 q^{64} +28.5616 q^{66} +473.135 q^{67} -130.510 q^{68} -288.441 q^{69} +306.296 q^{71} -183.601 q^{72} +377.380 q^{73} -672.323 q^{74} +614.162 q^{76} +208.146 q^{77} +283.145 q^{78} +320.938 q^{79} +417.360 q^{81} -325.258 q^{82} +509.786 q^{83} +236.114 q^{84} -171.938 q^{86} +271.769 q^{87} +56.7701 q^{88} -472.671 q^{89} +2063.46 q^{91} -573.316 q^{92} +200.592 q^{93} +735.782 q^{94} +64.3980 q^{96} -85.4778 q^{97} +1034.71 q^{98} -162.860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * q^99

Introduction

L-functions

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Database

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