LMFDB - Embedded newform 1250.4.a.n.1.13

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			1.13
Root			$-5.52002$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +7.10721 q^{3} +4.00000 q^{4} +14.2144 q^{6} +25.2037 q^{7} +8.00000 q^{8} +23.5124 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +7.10721 q^{3} +4.00000 q^{4} +14.2144 q^{6} +25.2037 q^{7} +8.00000 q^{8} +23.5124 q^{9} -41.1467 q^{11} +28.4288 q^{12} -50.7429 q^{13} +50.4075 q^{14} +16.0000 q^{16} +79.2312 q^{17} +47.0247 q^{18} +42.4778 q^{19} +179.128 q^{21} -82.2934 q^{22} +79.4015 q^{23} +56.8576 q^{24} -101.486 q^{26} -24.7873 q^{27} +100.815 q^{28} +227.164 q^{29} -39.2434 q^{31} +32.0000 q^{32} -292.438 q^{33} +158.462 q^{34} +94.0495 q^{36} +163.017 q^{37} +84.9555 q^{38} -360.640 q^{39} +492.906 q^{41} +358.256 q^{42} +496.241 q^{43} -164.587 q^{44} +158.803 q^{46} -431.291 q^{47} +113.715 q^{48} +292.228 q^{49} +563.113 q^{51} -202.972 q^{52} +268.063 q^{53} -49.5747 q^{54} +201.630 q^{56} +301.898 q^{57} +454.328 q^{58} +12.7818 q^{59} +494.198 q^{61} -78.4869 q^{62} +592.600 q^{63} +64.0000 q^{64} -584.876 q^{66} -410.522 q^{67} +316.925 q^{68} +564.323 q^{69} +141.116 q^{71} +188.099 q^{72} -650.000 q^{73} +326.033 q^{74} +169.911 q^{76} -1037.05 q^{77} -721.280 q^{78} -597.485 q^{79} -811.003 q^{81} +985.811 q^{82} -322.790 q^{83} +716.513 q^{84} +992.482 q^{86} +1614.50 q^{87} -329.173 q^{88} +883.404 q^{89} -1278.91 q^{91} +317.606 q^{92} -278.911 q^{93} -862.583 q^{94} +227.431 q^{96} -1088.57 q^{97} +584.457 q^{98} -967.456 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7.10721	1.36778	0.683891	−	0.729584i	$-0.260286\pi$
$3$	7.10721	1.36778	0.683891	+	0.729584i	$0.260286\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	14.2144	0.967168
$7$	25.2037	1.36087	0.680437	−	0.732807i	$-0.261790\pi$
$7$	25.2037	1.36087	0.680437	+	0.732807i	$0.261790\pi$
$8$	8.00000	0.353553
$9$	23.5124	0.870828
$10$	0	0
$11$	−41.1467	−1.12784	−0.563918	−	0.825831i	$-0.690707\pi$
$11$	−41.1467	−1.12784	−0.563918	+	0.825831i	$0.690707\pi$
$12$	28.4288	0.683891
$13$	−50.7429	−1.08258	−0.541290	−	0.840836i	$-0.682064\pi$
$13$	−50.7429	−1.08258	−0.541290	+	0.840836i	$0.682064\pi$
$14$	50.4075	0.962283
$15$	0	0
$16$	16.0000	0.250000
$17$	79.2312	1.13038	0.565188	−	0.824962i	$-0.308804\pi$
$17$	79.2312	1.13038	0.565188	+	0.824962i	$0.308804\pi$
$18$	47.0247	0.615769
$19$	42.4778	0.512898	0.256449	−	0.966558i	$-0.417447\pi$
$19$	42.4778	0.512898	0.256449	+	0.966558i	$0.417447\pi$
$20$	0	0
$21$	179.128	1.86138
$22$	−82.2934	−0.797500
$23$	79.4015	0.719842	0.359921	−	0.932983i	$-0.382804\pi$
$23$	79.4015	0.719842	0.359921	+	0.932983i	$0.382804\pi$
$24$	56.8576	0.483584
$25$	0	0
$26$	−101.486	−0.765500
$27$	−24.7873	−0.176679
$28$	100.815	0.680437
$29$	227.164	1.45460	0.727298	−	0.686321i	$-0.240776\pi$
$29$	227.164	1.45460	0.727298	+	0.686321i	$0.240776\pi$
$30$	0	0
$31$	−39.2434	−0.227365	−0.113683	−	0.993517i	$-0.536265\pi$
$31$	−39.2434	−0.227365	−0.113683	+	0.993517i	$0.536265\pi$
$32$	32.0000	0.176777
$33$	−292.438	−1.54263
$34$	158.462	0.799297
$35$	0	0
$36$	94.0495	0.435414
$37$	163.017	0.724318	0.362159	−	0.932116i	$-0.382040\pi$
$37$	163.017	0.724318	0.362159	+	0.932116i	$0.382040\pi$
$38$	84.9555	0.362674
$39$	−360.640	−1.48073
$40$	0	0
$41$	492.906	1.87753	0.938767	−	0.344552i	$-0.111969\pi$
$41$	492.906	1.87753	0.938767	+	0.344552i	$0.111969\pi$
$42$	358.256	1.31619
$43$	496.241	1.75991	0.879954	−	0.475059i	$-0.157573\pi$
$43$	496.241	1.75991	0.879954	+	0.475059i	$0.157573\pi$
$44$	−164.587	−0.563918
$45$	0	0
$46$	158.803	0.509005
$47$	−431.291	−1.33852	−0.669259	−	0.743029i	$-0.733388\pi$
$47$	−431.291	−1.33852	−0.669259	+	0.743029i	$0.733388\pi$
$48$	113.715	0.341946
$49$	292.228	0.851978
$50$	0	0
$51$	563.113	1.54611
$52$	−202.972	−0.541290
$53$	268.063	0.694740	0.347370	−	0.937728i	$-0.387075\pi$
$53$	268.063	0.694740	0.347370	+	0.937728i	$0.387075\pi$
$54$	−49.5747	−0.124931
$55$	0	0
$56$	201.630	0.481142
$57$	301.898	0.701533
$58$	454.328	1.02856
$59$	12.7818	0.0282043	0.0141021	−	0.999901i	$-0.495511\pi$
$59$	12.7818	0.0282043	0.0141021	+	0.999901i	$0.495511\pi$
$60$	0	0
$61$	494.198	1.03730	0.518652	−	0.854985i	$-0.326434\pi$
$61$	494.198	1.03730	0.518652	+	0.854985i	$0.326434\pi$
$62$	−78.4869	−0.160772
$63$	592.600	1.18509
$64$	64.0000	0.125000
$65$	0	0
$66$	−584.876	−1.09081
$67$	−410.522	−0.748555	−0.374278	−	0.927317i	$-0.622109\pi$
$67$	−410.522	−0.748555	−0.374278	+	0.927317i	$0.622109\pi$
$68$	316.925	0.565188
$69$	564.323	0.984587
$70$	0	0
$71$	141.116	0.235878	0.117939	−	0.993021i	$-0.462371\pi$
$71$	141.116	0.235878	0.117939	+	0.993021i	$0.462371\pi$
$72$	188.099	0.307884
$73$	−650.000	−1.04215	−0.521074	−	0.853512i	$-0.674468\pi$
$73$	−650.000	−1.04215	−0.521074	+	0.853512i	$0.674468\pi$
$74$	326.033	0.512170
$75$	0	0
$76$	169.911	0.256449
$77$	−1037.05	−1.53484
$78$	−721.280	−1.04704
$79$	−597.485	−0.850915	−0.425458	−	0.904978i	$-0.639887\pi$
$79$	−597.485	−0.850915	−0.425458	+	0.904978i	$0.639887\pi$
$80$	0	0
$81$	−811.003	−1.11249
$82$	985.811	1.32762
$83$	−322.790	−0.426877	−0.213439	−	0.976956i	$-0.568466\pi$
$83$	−322.790	−0.426877	−0.213439	+	0.976956i	$0.568466\pi$
$84$	716.513	0.930690
$85$	0	0
$86$	992.482	1.24444
$87$	1614.50	1.98957
$88$	−329.173	−0.398750
$89$	883.404	1.05214	0.526071	−	0.850441i	$-0.323665\pi$
$89$	883.404	1.05214	0.526071	+	0.850441i	$0.323665\pi$
$90$	0	0
$91$	−1278.91	−1.47326
$92$	317.606	0.359921
$93$	−278.911	−0.310986
$94$	−862.583	−0.946475
$95$	0	0
$96$	227.431	0.241792
$97$	−1088.57	−1.13946	−0.569728	−	0.821833i	$-0.692951\pi$
$97$	−1088.57	−1.13946	−0.569728	+	0.821833i	$0.692951\pi$
$98$	584.457	0.602439
$99$	−967.456	−0.982151
$100$	0	0
$101$	−90.1130	−0.0887780	−0.0443890	−	0.999014i	$-0.514134\pi$
$101$	−90.1130	−0.0887780	−0.0443890	+	0.999014i	$0.514134\pi$
$102$	1126.23	1.09326
$103$	−1114.71	−1.06636	−0.533182	−	0.846000i	$-0.679004\pi$
$103$	−1114.71	−1.06636	−0.533182	+	0.846000i	$0.679004\pi$
$104$	−405.943	−0.382750
$105$	0	0
$106$	536.125	0.491255
$107$	−2041.47	−1.84445	−0.922227	−	0.386649i	$-0.873633\pi$
$107$	−2041.47	−1.84445	−0.922227	+	0.386649i	$0.873633\pi$
$108$	−99.1493	−0.0883393
$109$	−1007.34	−0.885189	−0.442595	−	0.896722i	$-0.645942\pi$
$109$	−1007.34	−0.885189	−0.442595	+	0.896722i	$0.645942\pi$
$110$	0	0
$111$	1158.59	0.990709
$112$	403.260	0.340218
$113$	816.191	0.679476	0.339738	−	0.940520i	$-0.389662\pi$
$113$	816.191	0.679476	0.339738	+	0.940520i	$0.389662\pi$
$114$	603.797	0.496059
$115$	0	0
$116$	908.656	0.727298
$117$	−1193.09	−0.942742
$118$	25.5636	0.0199434
$119$	1996.92	1.53830
$120$	0	0
$121$	362.049	0.272013
$122$	988.396	0.733485
$123$	3503.18	2.56806
$124$	−156.974	−0.113683
$125$	0	0
$126$	1185.20	0.837984
$127$	−93.7816	−0.0655258	−0.0327629	−	0.999463i	$-0.510431\pi$
$127$	−93.7816	−0.0655258	−0.0327629	+	0.999463i	$0.510431\pi$
$128$	128.000	0.0883883
$129$	3526.89	2.40717
$130$	0	0
$131$	−1565.24	−1.04393	−0.521966	−	0.852966i	$-0.674801\pi$
$131$	−1565.24	−1.04393	−0.521966	+	0.852966i	$0.674801\pi$
$132$	−1169.75	−0.771317
$133$	1070.60	0.697990
$134$	−821.043	−0.529308
$135$	0	0
$136$	633.850	0.399648
$137$	−1846.97	−1.15181	−0.575903	−	0.817518i	$-0.695350\pi$
$137$	−1846.97	−1.15181	−0.575903	+	0.817518i	$0.695350\pi$
$138$	1128.65	0.696208
$139$	163.910	0.100019	0.0500094	−	0.998749i	$-0.484075\pi$
$139$	163.910	0.100019	0.0500094	+	0.998749i	$0.484075\pi$
$140$	0	0
$141$	−3065.28	−1.83080
$142$	282.231	0.166791
$143$	2087.90	1.22097
$144$	376.198	0.217707
$145$	0	0
$146$	−1300.00	−0.736909
$147$	2076.93	1.16532
$148$	652.066	0.362159
$149$	−368.277	−0.202486	−0.101243	−	0.994862i	$-0.532282\pi$
$149$	−368.277	−0.202486	−0.101243	+	0.994862i	$0.532282\pi$
$150$	0	0
$151$	−337.000	−0.181620	−0.0908101	−	0.995868i	$-0.528946\pi$
$151$	−337.000	−0.181620	−0.0908101	+	0.995868i	$0.528946\pi$
$152$	339.822	0.181337
$153$	1862.91	0.984364
$154$	−2074.10	−1.08530
$155$	0	0
$156$	−1442.56	−0.740367
$157$	2345.46	1.19228	0.596141	−	0.802880i	$-0.296700\pi$
$157$	2345.46	1.19228	0.596141	+	0.802880i	$0.296700\pi$
$158$	−1194.97	−0.601688
$159$	1905.18	0.950253
$160$	0	0
$161$	2001.22	0.979614
$162$	−1622.01	−0.786647
$163$	926.598	0.445256	0.222628	−	0.974903i	$-0.428536\pi$
$163$	926.598	0.445256	0.222628	+	0.974903i	$0.428536\pi$
$164$	1971.62	0.938767
$165$	0	0
$166$	−645.580	−0.301848
$167$	−505.851	−0.234395	−0.117197	−	0.993109i	$-0.537391\pi$
$167$	−505.851	−0.234395	−0.117197	+	0.993109i	$0.537391\pi$
$168$	1433.03	0.658097
$169$	377.840	0.171980
$170$	0	0
$171$	998.753	0.446646
$172$	1984.96	0.879954
$173$	−75.3093	−0.0330963	−0.0165481	−	0.999863i	$-0.505268\pi$
$173$	−75.3093	−0.0330963	−0.0165481	+	0.999863i	$0.505268\pi$
$174$	3229.00	1.40684
$175$	0	0
$176$	−658.347	−0.281959
$177$	90.8431	0.0385773
$178$	1766.81	0.743977
$179$	−539.698	−0.225357	−0.112679	−	0.993631i	$-0.535943\pi$
$179$	−539.698	−0.225357	−0.112679	+	0.993631i	$0.535943\pi$
$180$	0	0
$181$	−533.768	−0.219197	−0.109599	−	0.993976i	$-0.534957\pi$
$181$	−533.768	−0.219197	−0.109599	+	0.993976i	$0.534957\pi$
$182$	−2557.82	−1.04175
$183$	3512.37	1.41881
$184$	635.212	0.254503
$185$	0	0
$186$	−557.822	−0.219901
$187$	−3260.10	−1.27488
$188$	−1725.17	−0.669259
$189$	−624.733	−0.240437
$190$	0	0
$191$	−4764.37	−1.80491	−0.902455	−	0.430784i	$-0.858237\pi$
$191$	−4764.37	−1.80491	−0.902455	+	0.430784i	$0.858237\pi$
$192$	454.861	0.170973
$193$	4796.58	1.78894	0.894471	−	0.447127i	$-0.147553\pi$
$193$	4796.58	1.78894	0.894471	+	0.447127i	$0.147553\pi$
$194$	−2177.13	−0.805717
$195$	0	0
$196$	1168.91	0.425989
$197$	−3692.41	−1.33540	−0.667700	−	0.744431i	$-0.732721\pi$
$197$	−3692.41	−1.33540	−0.667700	+	0.744431i	$0.732721\pi$
$198$	−1934.91	−0.694486
$199$	−438.597	−0.156238	−0.0781189	−	0.996944i	$-0.524891\pi$
$199$	−438.597	−0.156238	−0.0781189	+	0.996944i	$0.524891\pi$
$200$	0	0
$201$	−2917.66	−1.02386
$202$	−180.226	−0.0627755
$203$	5725.38	1.97952
$204$	2252.45	0.773054
$205$	0	0
$206$	−2229.42	−0.754033
$207$	1866.92	0.626859
$208$	−811.886	−0.270645
$209$	−1747.82	−0.578465
$210$	0	0
$211$	−2521.99	−0.822850	−0.411425	−	0.911444i	$-0.634969\pi$
$211$	−2521.99	−0.822850	−0.411425	+	0.911444i	$0.634969\pi$
$212$	1072.25	0.347370
$213$	1002.94	0.322630
$214$	−4082.94	−1.30423
$215$	0	0
$216$	−198.299	−0.0624653
$217$	−989.081	−0.309416
$218$	−2014.68	−0.625923
$219$	−4619.68	−1.42543
$220$	0	0
$221$	−4020.42	−1.22372
$222$	2317.18	0.700537
$223$	3098.75	0.930528	0.465264	−	0.885172i	$-0.345959\pi$
$223$	3098.75	0.930528	0.465264	+	0.885172i	$0.345959\pi$
$224$	806.520	0.240571
$225$	0	0
$226$	1632.38	0.480462
$227$	4898.42	1.43224	0.716122	−	0.697975i	$-0.245915\pi$
$227$	4898.42	1.43224	0.716122	+	0.697975i	$0.245915\pi$
$228$	1207.59	0.350767
$229$	−1863.47	−0.537736	−0.268868	−	0.963177i	$-0.586649\pi$
$229$	−1863.47	−0.537736	−0.268868	+	0.963177i	$0.586649\pi$
$230$	0	0
$231$	−7370.53	−2.09933
$232$	1817.31	0.514278
$233$	331.995	0.0933465	0.0466732	−	0.998910i	$-0.485138\pi$
$233$	331.995	0.0933465	0.0466732	+	0.998910i	$0.485138\pi$
$234$	−2386.17	−0.666619
$235$	0	0
$236$	51.1273	0.0141021
$237$	−4246.45	−1.16387
$238$	3993.85	1.08774
$239$	−4355.17	−1.17871	−0.589356	−	0.807873i	$-0.700618\pi$
$239$	−4355.17	−1.17871	−0.589356	+	0.807873i	$0.700618\pi$
$240$	0	0
$241$	2069.99	0.553277	0.276638	−	0.960974i	$-0.410780\pi$
$241$	2069.99	0.553277	0.276638	+	0.960974i	$0.410780\pi$
$242$	724.099	0.192342
$243$	−5094.70	−1.34496
$244$	1976.79	0.518652
$245$	0	0
$246$	7006.36	1.81589
$247$	−2155.44	−0.555254
$248$	−313.947	−0.0803858
$249$	−2294.13	−0.583875
$250$	0	0
$251$	−4608.75	−1.15897	−0.579486	−	0.814982i	$-0.696747\pi$
$251$	−4608.75	−1.15897	−0.579486	+	0.814982i	$0.696747\pi$
$252$	2370.40	0.592544
$253$	−3267.11	−0.811863
$254$	−187.563	−0.0463337
$255$	0	0
$256$	256.000	0.0625000
$257$	−2208.39	−0.536013	−0.268007	−	0.963417i	$-0.586365\pi$
$257$	−2208.39	−0.536013	−0.268007	+	0.963417i	$0.586365\pi$
$258$	7053.77	1.70213
$259$	4108.63	0.985705
$260$	0	0
$261$	5341.16	1.26670
$262$	−3130.47	−0.738172
$263$	1595.49	0.374076	0.187038	−	0.982353i	$-0.440111\pi$
$263$	1595.49	0.374076	0.187038	+	0.982353i	$0.440111\pi$
$264$	−2339.50	−0.545403
$265$	0	0
$266$	2141.20	0.493554
$267$	6278.53	1.43910
$268$	−1642.09	−0.374278
$269$	−703.949	−0.159556	−0.0797779	−	0.996813i	$-0.525421\pi$
$269$	−703.949	−0.159556	−0.0797779	+	0.996813i	$0.525421\pi$
$270$	0	0
$271$	5600.74	1.25543	0.627713	−	0.778445i	$-0.283991\pi$
$271$	5600.74	1.25543	0.627713	+	0.778445i	$0.283991\pi$
$272$	1267.70	0.282594
$273$	−9089.48	−2.01509
$274$	−3693.95	−0.814450
$275$	0	0
$276$	2257.29	0.492294
$277$	−1682.49	−0.364949	−0.182475	−	0.983211i	$-0.558411\pi$
$277$	−1682.49	−0.364949	−0.182475	+	0.983211i	$0.558411\pi$
$278$	327.819	0.0707240
$279$	−922.706	−0.197996
$280$	0	0
$281$	−2598.27	−0.551601	−0.275801	−	0.961215i	$-0.588943\pi$
$281$	−2598.27	−0.551601	−0.275801	+	0.961215i	$0.588943\pi$
$282$	−6130.55	−1.29457
$283$	3682.47	0.773498	0.386749	−	0.922185i	$-0.373598\pi$
$283$	3682.47	0.773498	0.386749	+	0.922185i	$0.373598\pi$
$284$	564.463	0.117939
$285$	0	0
$286$	4175.80	0.863358
$287$	12423.1	2.55509
$288$	752.396	0.153942
$289$	1364.59	0.277751
$290$	0	0
$291$	−7736.67	−1.55853
$292$	−2600.00	−0.521074
$293$	−1789.63	−0.356829	−0.178415	−	0.983955i	$-0.557097\pi$
$293$	−1789.63	−0.356829	−0.178415	+	0.983955i	$0.557097\pi$
$294$	4153.85	0.824006
$295$	0	0
$296$	1304.13	0.256085
$297$	1019.92	0.199264
$298$	−736.553	−0.143179
$299$	−4029.06	−0.779287
$300$	0	0
$301$	12507.1	2.39501
$302$	−674.000	−0.128425
$303$	−640.451	−0.121429
$304$	679.644	0.128225
$305$	0	0
$306$	3725.83	0.696050
$307$	8282.23	1.53971	0.769857	−	0.638217i	$-0.220328\pi$
$307$	8282.23	1.53971	0.769857	+	0.638217i	$0.220328\pi$
$308$	−4148.20	−0.767421
$309$	−7922.46	−1.45855
$310$	0	0
$311$	4699.43	0.856850	0.428425	−	0.903577i	$-0.359069\pi$
$311$	4699.43	0.856850	0.428425	+	0.903577i	$0.359069\pi$
$312$	−2885.12	−0.523519
$313$	−7754.24	−1.40030	−0.700152	−	0.713994i	$-0.746885\pi$
$313$	−7754.24	−1.40030	−0.700152	+	0.713994i	$0.746885\pi$
$314$	4690.92	0.843070
$315$	0	0
$316$	−2389.94	−0.425458
$317$	−2212.01	−0.391920	−0.195960	−	0.980612i	$-0.562782\pi$
$317$	−2212.01	−0.391920	−0.195960	+	0.980612i	$0.562782\pi$
$318$	3810.35	0.671931
$319$	−9347.05	−1.64055
$320$	0	0
$321$	−14509.2	−2.52281
$322$	4002.43	0.692692
$323$	3365.57	0.579768
$324$	−3244.01	−0.556243
$325$	0	0
$326$	1853.20	0.314844
$327$	−7159.37	−1.21075
$328$	3943.24	0.663809
$329$	−10870.2	−1.82155
$330$	0	0
$331$	3913.92	0.649936	0.324968	−	0.945725i	$-0.394646\pi$
$331$	3913.92	0.649936	0.324968	+	0.945725i	$0.394646\pi$
$332$	−1291.16	−0.213439
$333$	3832.91	0.630757
$334$	−1011.70	−0.165742
$335$	0	0
$336$	2866.05	0.465345
$337$	11652.7	1.88358	0.941788	−	0.336208i	$-0.109144\pi$
$337$	11652.7	1.88358	0.941788	+	0.336208i	$0.109144\pi$
$338$	755.680	0.121608
$339$	5800.84	0.929376
$340$	0	0
$341$	1614.74	0.256431
$342$	1997.51	0.315827
$343$	−1279.63	−0.201439
$344$	3969.93	0.622222
$345$	0	0
$346$	−150.619	−0.0234026
$347$	−7419.90	−1.14790	−0.573950	−	0.818891i	$-0.694589\pi$
$347$	−7419.90	−1.14790	−0.573950	+	0.818891i	$0.694589\pi$
$348$	6458.01	0.994786
$349$	12550.2	1.92492	0.962460	−	0.271424i	$-0.0874946\pi$
$349$	12550.2	1.92492	0.962460	+	0.271424i	$0.0874946\pi$
$350$	0	0
$351$	1257.78	0.191269
$352$	−1316.69	−0.199375
$353$	273.792	0.0412818	0.0206409	−	0.999787i	$-0.493429\pi$
$353$	273.792	0.0412818	0.0206409	+	0.999787i	$0.493429\pi$
$354$	181.686	0.0272783
$355$	0	0
$356$	3533.62	0.526071
$357$	14192.5	2.10406
$358$	−1079.40	−0.159352
$359$	5821.23	0.855802	0.427901	−	0.903826i	$-0.359253\pi$
$359$	5821.23	0.855802	0.427901	+	0.903826i	$0.359253\pi$
$360$	0	0
$361$	−5054.64	−0.736935
$362$	−1067.54	−0.154996
$363$	2573.16	0.372055
$364$	−5115.64	−0.736628
$365$	0	0
$366$	7024.73	1.00325
$367$	−5230.36	−0.743931	−0.371965	−	0.928247i	$-0.621316\pi$
$367$	−5230.36	−0.743931	−0.371965	+	0.928247i	$0.621316\pi$
$368$	1270.42	0.179960
$369$	11589.4	1.63501
$370$	0	0
$371$	6756.18	0.945454
$372$	−1115.64	−0.155493
$373$	13574.8	1.88439	0.942195	−	0.335065i	$-0.108758\pi$
$373$	13574.8	1.88439	0.942195	+	0.335065i	$0.108758\pi$
$374$	−6520.21	−0.901475
$375$	0	0
$376$	−3450.33	−0.473237
$377$	−11527.0	−1.57472
$378$	−1249.47	−0.170015
$379$	837.225	0.113471	0.0567353	−	0.998389i	$-0.481931\pi$
$379$	837.225	0.113471	0.0567353	+	0.998389i	$0.481931\pi$
$380$	0	0
$381$	−666.525	−0.0896250
$382$	−9528.74	−1.27626
$383$	−8239.02	−1.09920	−0.549601	−	0.835427i	$-0.685220\pi$
$383$	−8239.02	−1.09920	−0.549601	+	0.835427i	$0.685220\pi$
$384$	909.722	0.120896
$385$	0	0
$386$	9593.17	1.26497
$387$	11667.8	1.53258
$388$	−4354.27	−0.569728
$389$	−2440.39	−0.318079	−0.159039	−	0.987272i	$-0.550840\pi$
$389$	−2440.39	−0.318079	−0.159039	+	0.987272i	$0.550840\pi$
$390$	0	0
$391$	6291.08	0.813692
$392$	2337.83	0.301220
$393$	−11124.4	−1.42787
$394$	−7384.83	−0.944270
$395$	0	0
$396$	−3869.82	−0.491076
$397$	−5227.49	−0.660857	−0.330429	−	0.943831i	$-0.607193\pi$
$397$	−5227.49	−0.660857	−0.330429	+	0.943831i	$0.607193\pi$
$398$	−877.194	−0.110477
$399$	7608.96	0.954698
$400$	0	0
$401$	−3347.34	−0.416853	−0.208427	−	0.978038i	$-0.566834\pi$
$401$	−3347.34	−0.416853	−0.208427	+	0.978038i	$0.566834\pi$
$402$	−5835.32	−0.723979
$403$	1991.32	0.246141
$404$	−360.452	−0.0443890
$405$	0	0
$406$	11450.8	1.39973
$407$	−6707.59	−0.816911
$408$	4504.90	0.546632
$409$	1609.83	0.194624	0.0973119	−	0.995254i	$-0.468976\pi$
$409$	1609.83	0.194624	0.0973119	+	0.995254i	$0.468976\pi$
$410$	0	0
$411$	−13126.8	−1.57542
$412$	−4458.84	−0.533182
$413$	322.150	0.0383825
$414$	3733.84	0.443256
$415$	0	0
$416$	−1623.77	−0.191375
$417$	1164.94	0.136804
$418$	−3495.64	−0.409037
$419$	4682.04	0.545901	0.272950	−	0.962028i	$-0.412001\pi$
$419$	4682.04	0.545901	0.272950	+	0.962028i	$0.412001\pi$
$420$	0	0
$421$	−2581.51	−0.298848	−0.149424	−	0.988773i	$-0.547742\pi$
$421$	−2581.51	−0.298848	−0.149424	+	0.988773i	$0.547742\pi$
$422$	−5043.99	−0.581843
$423$	−10140.7	−1.16562
$424$	2144.50	0.245628
$425$	0	0
$426$	2005.88	0.228134
$427$	12455.6	1.41164
$428$	−8165.89	−0.922227
$429$	14839.1	1.67002
$430$	0	0
$431$	15712.7	1.75604	0.878020	−	0.478624i	$-0.158864\pi$
$431$	15712.7	1.75604	0.878020	+	0.478624i	$0.158864\pi$
$432$	−396.597	−0.0441697
$433$	−10885.3	−1.20812	−0.604061	−	0.796938i	$-0.706451\pi$
$433$	−10885.3	−1.20812	−0.604061	+	0.796938i	$0.706451\pi$
$434$	−1978.16	−0.218790
$435$	0	0
$436$	−4029.36	−0.442595
$437$	3372.80	0.369206
$438$	−9239.37	−1.00793
$439$	3948.05	0.429226	0.214613	−	0.976699i	$-0.431151\pi$
$439$	3948.05	0.429226	0.214613	+	0.976699i	$0.431151\pi$
$440$	0	0
$441$	6870.98	0.741927
$442$	−8040.84	−0.865303
$443$	4648.92	0.498593	0.249297	−	0.968427i	$-0.419801\pi$
$443$	4648.92	0.498593	0.249297	+	0.968427i	$0.419801\pi$
$444$	4634.37	0.495355
$445$	0	0
$446$	6197.50	0.657983
$447$	−2617.42	−0.276957
$448$	1613.04	0.170109
$449$	386.675	0.0406421	0.0203211	−	0.999794i	$-0.493531\pi$
$449$	386.675	0.0406421	0.0203211	+	0.999794i	$0.493531\pi$
$450$	0	0
$451$	−20281.4	−2.11755
$452$	3264.77	0.339738
$453$	−2395.13	−0.248417
$454$	9796.83	1.01275
$455$	0	0
$456$	2415.19	0.248029
$457$	−4982.46	−0.510000	−0.255000	−	0.966941i	$-0.582075\pi$
$457$	−4982.46	−0.510000	−0.255000	+	0.966941i	$0.582075\pi$
$458$	−3726.94	−0.380236
$459$	−1963.93	−0.199713
$460$	0	0
$461$	−5299.45	−0.535401	−0.267700	−	0.963502i	$-0.586264\pi$
$461$	−5299.45	−0.535401	−0.267700	+	0.963502i	$0.586264\pi$
$462$	−14741.1	−1.48445
$463$	6268.68	0.629223	0.314612	−	0.949220i	$-0.398126\pi$
$463$	6268.68	0.629223	0.314612	+	0.949220i	$0.398126\pi$
$464$	3634.62	0.363649
$465$	0	0
$466$	663.991	0.0660059
$467$	−10824.8	−1.07262	−0.536308	−	0.844022i	$-0.680181\pi$
$467$	−10824.8	−1.07262	−0.536308	+	0.844022i	$0.680181\pi$
$468$	−4772.34	−0.471371
$469$	−10346.7	−1.01869
$470$	0	0
$471$	16669.7	1.63078
$472$	102.255	0.00997171
$473$	−20418.7	−1.98489
$474$	−8492.89	−0.822978
$475$	0	0
$476$	7987.69	0.769150
$477$	6302.79	0.604999
$478$	−8710.33	−0.833475
$479$	−15604.8	−1.48852	−0.744260	−	0.667890i	$-0.767198\pi$
$479$	−15604.8	−1.48852	−0.744260	+	0.667890i	$0.767198\pi$
$480$	0	0
$481$	−8271.93	−0.784132
$482$	4139.98	0.391226
$483$	14223.1	1.33990
$484$	1448.20	0.136006
$485$	0	0
$486$	−10189.4	−0.951031
$487$	−7996.16	−0.744026	−0.372013	−	0.928228i	$-0.621332\pi$
$487$	−7996.16	−0.744026	−0.372013	+	0.928228i	$0.621332\pi$
$488$	3953.58	0.366743
$489$	6585.52	0.609014
$490$	0	0
$491$	5652.29	0.519519	0.259760	−	0.965673i	$-0.416357\pi$
$491$	5652.29	0.519519	0.259760	+	0.965673i	$0.416357\pi$
$492$	14012.7	1.28403
$493$	17998.5	1.64424
$494$	−4310.89	−0.392624
$495$	0	0
$496$	−627.895	−0.0568414
$497$	3556.64	0.321000
$498$	−4588.27	−0.412862
$499$	−9200.89	−0.825428	−0.412714	−	0.910861i	$-0.635419\pi$
$499$	−9200.89	−0.825428	−0.412714	+	0.910861i	$0.635419\pi$
$500$	0	0
$501$	−3595.19	−0.320601
$502$	−9217.50	−0.819516
$503$	4486.68	0.397716	0.198858	−	0.980028i	$-0.436277\pi$
$503$	4486.68	0.397716	0.198858	+	0.980028i	$0.436277\pi$
$504$	4740.80	0.418992
$505$	0	0
$506$	−6534.22	−0.574074
$507$	2685.39	0.235231
$508$	−375.126	−0.0327629
$509$	−3763.74	−0.327750	−0.163875	−	0.986481i	$-0.552399\pi$
$509$	−3763.74	−0.327750	−0.163875	+	0.986481i	$0.552399\pi$
$510$	0	0
$511$	−16382.4	−1.41823
$512$	512.000	0.0441942
$513$	−1052.91	−0.0906182
$514$	−4416.77	−0.379019
$515$	0	0
$516$	14107.5	1.20359
$517$	17746.2	1.50963
$518$	8217.25	0.696999
$519$	−535.238	−0.0452685
$520$	0	0
$521$	−15634.9	−1.31474	−0.657368	−	0.753570i	$-0.728330\pi$
$521$	−15634.9	−1.31474	−0.657368	+	0.753570i	$0.728330\pi$
$522$	10682.3	0.895695
$523$	16628.5	1.39027	0.695137	−	0.718877i	$-0.255344\pi$
$523$	16628.5	1.39027	0.695137	+	0.718877i	$0.255344\pi$
$524$	−6260.94	−0.521966
$525$	0	0
$526$	3190.97	0.264511
$527$	−3109.31	−0.257009
$528$	−4679.01	−0.385658
$529$	−5862.40	−0.481828
$530$	0	0
$531$	300.531	0.0245611
$532$	4282.39	0.348995
$533$	−25011.4	−2.03258
$534$	12557.1	1.01760
$535$	0	0
$536$	−3284.17	−0.264654
$537$	−3835.75	−0.308240
$538$	−1407.90	−0.112823
$539$	−12024.2	−0.960891
$540$	0	0
$541$	6884.17	0.547086	0.273543	−	0.961860i	$-0.411804\pi$
$541$	6884.17	0.547086	0.273543	+	0.961860i	$0.411804\pi$
$542$	11201.5	0.887721
$543$	−3793.60	−0.299814
$544$	2535.40	0.199824
$545$	0	0
$546$	−18179.0	−1.42489
$547$	−277.190	−0.0216669	−0.0108334	−	0.999941i	$-0.503448\pi$
$547$	−277.190	−0.0216669	−0.0108334	+	0.999941i	$0.503448\pi$
$548$	−7387.89	−0.575903
$549$	11619.8	0.903314
$550$	0	0
$551$	9649.42	0.746060
$552$	4514.58	0.348104
$553$	−15058.8	−1.15799
$554$	−3364.98	−0.258058
$555$	0	0
$556$	655.638	0.0500094
$557$	13894.9	1.05700	0.528499	−	0.848934i	$-0.322755\pi$
$557$	13894.9	1.05700	0.528499	+	0.848934i	$0.322755\pi$
$558$	−1845.41	−0.140005
$559$	−25180.7	−1.90524
$560$	0	0
$561$	−23170.2	−1.74376
$562$	−5196.55	−0.390041
$563$	−7705.84	−0.576843	−0.288421	−	0.957504i	$-0.593130\pi$
$563$	−7705.84	−0.576843	−0.288421	+	0.957504i	$0.593130\pi$
$564$	−12261.1	−0.915400
$565$	0	0
$566$	7364.93	0.546945
$567$	−20440.3	−1.51395
$568$	1128.93	0.0833955
$569$	−8562.88	−0.630887	−0.315443	−	0.948944i	$-0.602153\pi$
$569$	−8562.88	−0.630887	−0.315443	+	0.948944i	$0.602153\pi$
$570$	0	0
$571$	−7476.26	−0.547937	−0.273968	−	0.961739i	$-0.588336\pi$
$571$	−7476.26	−0.547937	−0.273968	+	0.961739i	$0.588336\pi$
$572$	8351.60	0.610486
$573$	−33861.4	−2.46872
$574$	24846.1	1.80672
$575$	0	0
$576$	1504.79	0.108854
$577$	19680.4	1.41994	0.709971	−	0.704231i	$-0.248708\pi$
$577$	19680.4	1.41994	0.709971	+	0.704231i	$0.248708\pi$
$578$	2729.18	0.196400
$579$	34090.3	2.44688
$580$	0	0
$581$	−8135.51	−0.580926
$582$	−15473.3	−1.10205
$583$	−11029.9	−0.783553
$584$	−5200.00	−0.368455
$585$	0	0
$586$	−3579.25	−0.252317
$587$	−12204.1	−0.858119	−0.429060	−	0.903276i	$-0.641155\pi$
$587$	−12204.1	−0.858119	−0.429060	+	0.903276i	$0.641155\pi$
$588$	8307.71	0.582660
$589$	−1666.97	−0.116615
$590$	0	0
$591$	−26242.8	−1.82654
$592$	2608.27	0.181079
$593$	−677.527	−0.0469185	−0.0234593	−	0.999725i	$-0.507468\pi$
$593$	−677.527	−0.0469185	−0.0234593	+	0.999725i	$0.507468\pi$
$594$	2039.83	0.140901
$595$	0	0
$596$	−1473.11	−0.101243
$597$	−3117.20	−0.213699
$598$	−8058.13	−0.551039
$599$	−1463.93	−0.0998574	−0.0499287	−	0.998753i	$-0.515899\pi$
$599$	−1463.93	−0.0998574	−0.0499287	+	0.998753i	$0.515899\pi$
$600$	0	0
$601$	−20284.9	−1.37677	−0.688386	−	0.725345i	$-0.741680\pi$
$601$	−20284.9	−1.37677	−0.688386	+	0.725345i	$0.741680\pi$
$602$	25014.3	1.69353
$603$	−9652.34	−0.651863
$604$	−1348.00	−0.0908101
$605$	0	0
$606$	−1280.90	−0.0858632
$607$	−488.395	−0.0326579	−0.0163289	−	0.999867i	$-0.505198\pi$
$607$	−488.395	−0.0326579	−0.0163289	+	0.999867i	$0.505198\pi$
$608$	1359.29	0.0906685
$609$	40691.5	2.70756
$610$	0	0
$611$	21885.0	1.44905
$612$	7451.66	0.492182
$613$	−630.885	−0.0415680	−0.0207840	−	0.999784i	$-0.506616\pi$
$613$	−630.885	−0.0415680	−0.0207840	+	0.999784i	$0.506616\pi$
$614$	16564.5	1.08874
$615$	0	0
$616$	−8296.40	−0.542649
$617$	5924.72	0.386581	0.193290	−	0.981142i	$-0.438084\pi$
$617$	5924.72	0.386581	0.193290	+	0.981142i	$0.438084\pi$
$618$	−15844.9	−1.03135
$619$	10863.6	0.705406	0.352703	−	0.935735i	$-0.385263\pi$
$619$	10863.6	0.705406	0.352703	+	0.935735i	$0.385263\pi$
$620$	0	0
$621$	−1968.15	−0.127181
$622$	9398.86	0.605884
$623$	22265.1	1.43183
$624$	−5770.24	−0.370184
$625$	0	0
$626$	−15508.5	−0.990165
$627$	−12422.1	−0.791214
$628$	9381.85	0.596141
$629$	12916.0	0.818752
$630$	0	0
$631$	−12643.3	−0.797657	−0.398828	−	0.917026i	$-0.630583\pi$
$631$	−12643.3	−0.797657	−0.398828	+	0.917026i	$0.630583\pi$
$632$	−4779.88	−0.300844
$633$	−17924.3	−1.12548
$634$	−4424.02	−0.277130
$635$	0	0
$636$	7620.70	0.475127
$637$	−14828.5	−0.922335
$638$	−18694.1	−1.16004
$639$	3317.96	0.205409
$640$	0	0
$641$	27852.7	1.71625	0.858124	−	0.513443i	$-0.171630\pi$
$641$	27852.7	1.71625	0.858124	+	0.513443i	$0.171630\pi$
$642$	−29018.3	−1.78390
$643$	−8898.64	−0.545767	−0.272884	−	0.962047i	$-0.587977\pi$
$643$	−8898.64	−0.545767	−0.272884	+	0.962047i	$0.587977\pi$
$644$	8004.86	0.489807
$645$	0	0
$646$	6731.13	0.409958
$647$	−7669.43	−0.466022	−0.233011	−	0.972474i	$-0.574858\pi$
$647$	−7669.43	−0.466022	−0.233011	+	0.972474i	$0.574858\pi$
$648$	−6488.02	−0.393323
$649$	−525.930	−0.0318098
$650$	0	0
$651$	−7029.60	−0.423213
$652$	3706.39	0.222628
$653$	−22399.9	−1.34238	−0.671190	−	0.741285i	$-0.734217\pi$
$653$	−22399.9	−1.34238	−0.671190	+	0.741285i	$0.734217\pi$
$654$	−14318.7	−0.856127
$655$	0	0
$656$	7886.49	0.469384
$657$	−15283.0	−0.907531
$658$	−21740.3	−1.28803
$659$	4654.26	0.275120	0.137560	−	0.990493i	$-0.456074\pi$
$659$	4654.26	0.275120	0.137560	+	0.990493i	$0.456074\pi$
$660$	0	0
$661$	−21716.2	−1.27786	−0.638929	−	0.769266i	$-0.720622\pi$
$661$	−21716.2	−1.27786	−0.638929	+	0.769266i	$0.720622\pi$
$662$	7827.85	0.459574
$663$	−28574.0	−1.67379
$664$	−2582.32	−0.150924
$665$	0	0
$666$	7665.81	0.446012
$667$	18037.2	1.04708
$668$	−2023.40	−0.117197
$669$	22023.5	1.27276
$670$	0	0
$671$	−20334.6	−1.16991
$672$	5732.10	0.329048
$673$	4002.40	0.229244	0.114622	−	0.993409i	$-0.463434\pi$
$673$	4002.40	0.229244	0.114622	+	0.993409i	$0.463434\pi$
$674$	23305.5	1.33189
$675$	0	0
$676$	1511.36	0.0859900
$677$	−23499.4	−1.33406	−0.667028	−	0.745032i	$-0.732434\pi$
$677$	−23499.4	−1.33406	−0.667028	+	0.745032i	$0.732434\pi$
$678$	11601.7	0.657168
$679$	−27435.9	−1.55066
$680$	0	0
$681$	34814.1	1.95900
$682$	3229.47	0.181324
$683$	6203.41	0.347536	0.173768	−	0.984787i	$-0.444406\pi$
$683$	6203.41	0.347536	0.173768	+	0.984787i	$0.444406\pi$
$684$	3995.01	0.223323
$685$	0	0
$686$	−2559.27	−0.142439
$687$	−13244.1	−0.735505
$688$	7939.86	0.439977
$689$	−13602.3	−0.752112
$690$	0	0
$691$	−5052.55	−0.278159	−0.139080	−	0.990281i	$-0.544414\pi$
$691$	−5052.55	−0.278159	−0.139080	+	0.990281i	$0.544414\pi$
$692$	−301.237	−0.0165481
$693$	−24383.5	−1.33658
$694$	−14839.8	−0.811687
$695$	0	0
$696$	12916.0	0.703420
$697$	39053.5	2.12232
$698$	25100.4	1.36112
$699$	2359.56	0.127678
$700$	0	0
$701$	24514.5	1.32083	0.660413	−	0.750903i	$-0.270381\pi$
$701$	24514.5	1.32083	0.660413	+	0.750903i	$0.270381\pi$
$702$	2515.56	0.135247
$703$	6924.58	0.371501
$704$	−2633.39	−0.140979
$705$	0	0
$706$	547.584	0.0291907
$707$	−2271.18	−0.120816
$708$	363.372	0.0192886
$709$	21767.8	1.15304	0.576521	−	0.817082i	$-0.304410\pi$
$709$	21767.8	1.15304	0.576521	+	0.817082i	$0.304410\pi$
$710$	0	0
$711$	−14048.3	−0.741001
$712$	7067.23	0.371988
$713$	−3115.99	−0.163667
$714$	28385.1	1.48779
$715$	0	0
$716$	−2158.79	−0.112679
$717$	−30953.1	−1.61222
$718$	11642.5	0.605143
$719$	13833.1	0.717508	0.358754	−	0.933432i	$-0.383202\pi$
$719$	13833.1	0.717508	0.358754	+	0.933432i	$0.383202\pi$
$720$	0	0
$721$	−28094.8	−1.45119
$722$	−10109.3	−0.521092
$723$	14711.8	0.756762
$724$	−2135.07	−0.109599
$725$	0	0
$726$	5146.32	0.263082
$727$	−1875.77	−0.0956925	−0.0478463	−	0.998855i	$-0.515236\pi$
$727$	−1875.77	−0.0956925	−0.0478463	+	0.998855i	$0.515236\pi$
$728$	−10231.3	−0.520874
$729$	−14312.0	−0.727127
$730$	0	0
$731$	39317.8	1.98936
$732$	14049.5	0.709403
$733$	34502.1	1.73856	0.869279	−	0.494321i	$-0.164583\pi$
$733$	34502.1	1.73856	0.869279	+	0.494321i	$0.164583\pi$
$734$	−10460.7	−0.526039
$735$	0	0
$736$	2540.85	0.127251
$737$	16891.6	0.844247
$738$	23178.8	1.15613
$739$	26249.7	1.30664	0.653321	−	0.757081i	$-0.273375\pi$
$739$	26249.7	1.30664	0.653321	+	0.757081i	$0.273375\pi$
$740$	0	0
$741$	−15319.2	−0.759466
$742$	13512.4	0.668537
$743$	28826.6	1.42334	0.711672	−	0.702512i	$-0.247938\pi$
$743$	28826.6	1.42334	0.711672	+	0.702512i	$0.247938\pi$
$744$	−2231.29	−0.109950
$745$	0	0
$746$	27149.6	1.33247
$747$	−7589.56	−0.371737
$748$	−13040.4	−0.637439
$749$	−51452.7	−2.51007
$750$	0	0
$751$	−19821.9	−0.963132	−0.481566	−	0.876410i	$-0.659932\pi$
$751$	−19821.9	−0.963132	−0.481566	+	0.876410i	$0.659932\pi$
$752$	−6900.66	−0.334629
$753$	−32755.3	−1.58522
$754$	−23053.9	−1.11349
$755$	0	0
$756$	−2498.93	−0.120219
$757$	−15983.2	−0.767395	−0.383697	−	0.923459i	$-0.625349\pi$
$757$	−15983.2	−0.767395	−0.383697	+	0.923459i	$0.625349\pi$
$758$	1674.45	0.0802358
$759$	−23220.0	−1.11045
$760$	0	0
$761$	−17687.6	−0.842544	−0.421272	−	0.906934i	$-0.638416\pi$
$761$	−17687.6	−0.842544	−0.421272	+	0.906934i	$0.638416\pi$
$762$	−1333.05	−0.0633744
$763$	−25388.7	−1.20463
$764$	−19057.5	−0.902455
$765$	0	0
$766$	−16478.0	−0.777253
$767$	−648.587	−0.0305334
$768$	1819.44	0.0854864
$769$	673.328	0.0315745	0.0157873	−	0.999875i	$-0.494975\pi$
$769$	673.328	0.0315745	0.0157873	+	0.999875i	$0.494975\pi$
$770$	0	0
$771$	−15695.5	−0.733149
$772$	19186.3	0.894471
$773$	13528.1	0.629458	0.314729	−	0.949182i	$-0.398086\pi$
$773$	13528.1	0.629458	0.314729	+	0.949182i	$0.398086\pi$
$774$	23335.6	1.08370
$775$	0	0
$776$	−8708.53	−0.402858
$777$	29200.9	1.34823
$778$	−4880.78	−0.224916
$779$	20937.5	0.962984
$780$	0	0
$781$	−5806.44	−0.266032
$782$	12582.2	0.575367
$783$	−5630.79	−0.256996
$784$	4675.66	0.212994
$785$	0	0
$786$	−22248.9	−1.00966
$787$	21469.2	0.972418	0.486209	−	0.873842i	$-0.338379\pi$
$787$	21469.2	0.972418	0.486209	+	0.873842i	$0.338379\pi$
$788$	−14769.7	−0.667700
$789$	11339.4	0.511654
$790$	0	0
$791$	20571.1	0.924682
$792$	−7739.65	−0.347243
$793$	−25077.0	−1.12297
$794$	−10455.0	−0.467297
$795$	0	0
$796$	−1754.39	−0.0781189
$797$	−40056.9	−1.78029	−0.890144	−	0.455680i	$-0.849396\pi$
$797$	−40056.9	−1.78029	−0.890144	+	0.455680i	$0.849396\pi$
$798$	15217.9	0.675074
$799$	−34171.8	−1.51303
$800$	0	0
$801$	20770.9	0.916235
$802$	−6694.68	−0.294760
$803$	26745.3	1.17537
$804$	−11670.6	−0.511930
$805$	0	0
$806$	3982.65	0.174048
$807$	−5003.11	−0.218238
$808$	−720.904	−0.0313878
$809$	−12752.8	−0.554219	−0.277109	−	0.960838i	$-0.589376\pi$
$809$	−12752.8	−0.554219	−0.277109	+	0.960838i	$0.589376\pi$
$810$	0	0
$811$	41080.3	1.77870	0.889349	−	0.457229i	$-0.151158\pi$
$811$	41080.3	1.77870	0.889349	+	0.457229i	$0.151158\pi$
$812$	22901.5	0.989761
$813$	39805.6	1.71715
$814$	−13415.2	−0.577644
$815$	0	0
$816$	9009.80	0.386527
$817$	21079.2	0.902654
$818$	3219.67	0.137620
$819$	−30070.2	−1.28295
$820$	0	0
$821$	34727.0	1.47622	0.738111	−	0.674679i	$-0.235718\pi$
$821$	34727.0	1.47622	0.738111	+	0.674679i	$0.235718\pi$
$822$	−26253.6	−1.11399
$823$	−33902.8	−1.43594	−0.717969	−	0.696076i	$-0.754928\pi$
$823$	−33902.8	−1.43594	−0.717969	+	0.696076i	$0.754928\pi$
$824$	−8917.67	−0.377017
$825$	0	0
$826$	644.300	0.0271405
$827$	−19718.8	−0.829128	−0.414564	−	0.910020i	$-0.636066\pi$
$827$	−19718.8	−0.829128	−0.414564	+	0.910020i	$0.636066\pi$
$828$	7467.67	0.313429
$829$	3091.78	0.129532	0.0647659	−	0.997900i	$-0.479370\pi$
$829$	3091.78	0.129532	0.0647659	+	0.997900i	$0.479370\pi$
$830$	0	0
$831$	−11957.8	−0.499171
$832$	−3247.54	−0.135323
$833$	23153.6	0.963056
$834$	2329.88	0.0967351
$835$	0	0
$836$	−6991.28	−0.289233
$837$	972.740	0.0401706
$838$	9364.07	0.386010
$839$	−23024.0	−0.947409	−0.473704	−	0.880684i	$-0.657083\pi$
$839$	−23024.0	−0.947409	−0.473704	+	0.880684i	$0.657083\pi$
$840$	0	0
$841$	27214.5	1.11585
$842$	−5163.02	−0.211318
$843$	−18466.5	−0.754471
$844$	−10088.0	−0.411425
$845$	0	0
$846$	−20281.4	−0.824217
$847$	9125.00	0.370175
$848$	4289.00	0.173685
$849$	26172.0	1.05798
$850$	0	0
$851$	12943.8	0.521394
$852$	4011.75	0.161315
$853$	7531.49	0.302313	0.151157	−	0.988510i	$-0.451700\pi$
$853$	7531.49	0.302313	0.151157	+	0.988510i	$0.451700\pi$
$854$	24911.3	0.998181
$855$	0	0
$856$	−16331.8	−0.652113
$857$	35659.6	1.42137	0.710683	−	0.703513i	$-0.248386\pi$
$857$	35659.6	1.42137	0.710683	+	0.703513i	$0.248386\pi$
$858$	29678.3	1.18089
$859$	−19314.4	−0.767169	−0.383585	−	0.923506i	$-0.625311\pi$
$859$	−19314.4	−0.767169	−0.383585	+	0.923506i	$0.625311\pi$
$860$	0	0
$861$	88293.3	3.49480
$862$	31425.4	1.24171
$863$	36893.6	1.45524	0.727619	−	0.685981i	$-0.240627\pi$
$863$	36893.6	1.45524	0.727619	+	0.685981i	$0.240627\pi$
$864$	−793.194	−0.0312327
$865$	0	0
$866$	−21770.7	−0.854271
$867$	9698.43	0.379903
$868$	−3956.32	−0.154708
$869$	24584.5	0.959692
$870$	0	0
$871$	20831.1	0.810371
$872$	−8058.72	−0.312962
$873$	−25594.8	−0.992270
$874$	6745.60	0.261068
$875$	0	0
$876$	−18478.7	−0.712715
$877$	1677.42	0.0645865	0.0322933	−	0.999478i	$-0.489719\pi$
$877$	1677.42	0.0645865	0.0322933	+	0.999478i	$0.489719\pi$
$878$	7896.11	0.303509
$879$	−12719.2	−0.488065
$880$	0	0
$881$	−4231.80	−0.161831	−0.0809154	−	0.996721i	$-0.525784\pi$
$881$	−4231.80	−0.161831	−0.0809154	+	0.996721i	$0.525784\pi$
$882$	13742.0	0.524621
$883$	4566.21	0.174026	0.0870131	−	0.996207i	$-0.472268\pi$
$883$	4566.21	0.174026	0.0870131	+	0.996207i	$0.472268\pi$
$884$	−16081.7	−0.611862
$885$	0	0
$886$	9297.84	0.352559
$887$	−13273.7	−0.502465	−0.251232	−	0.967927i	$-0.580836\pi$
$887$	−13273.7	−0.502465	−0.251232	+	0.967927i	$0.580836\pi$
$888$	9268.74	0.350269
$889$	−2363.65	−0.0891723
$890$	0	0
$891$	33370.1	1.25470
$892$	12395.0	0.465264
$893$	−18320.3	−0.686524
$894$	−5234.84	−0.195838
$895$	0	0
$896$	3226.08	0.120285
$897$	−28635.4	−1.06589
$898$	773.349	0.0287383
$899$	−8914.70	−0.330725
$900$	0	0
$901$	21238.9	0.785318
$902$	−40562.9	−1.49733
$903$	88890.7	3.27586
$904$	6529.53	0.240231
$905$	0	0
$906$	−4790.25	−0.175657
$907$	7912.72	0.289678	0.144839	−	0.989455i	$-0.453734\pi$
$907$	7912.72	0.289678	0.144839	+	0.989455i	$0.453734\pi$
$908$	19593.7	0.716122
$909$	−2118.77	−0.0773104
$910$	0	0
$911$	−29943.3	−1.08898	−0.544492	−	0.838766i	$-0.683278\pi$
$911$	−29943.3	−1.08898	−0.544492	+	0.838766i	$0.683278\pi$
$912$	4830.37	0.175383
$913$	13281.7	0.481447
$914$	−9964.93	−0.360624
$915$	0	0
$916$	−7453.87	−0.268868
$917$	−39449.8	−1.42066
$918$	−3927.86	−0.141219
$919$	−35150.1	−1.26169	−0.630846	−	0.775908i	$-0.717292\pi$
$919$	−35150.1	−1.26169	−0.630846	+	0.775908i	$0.717292\pi$
$920$	0	0
$921$	58863.5	2.10599
$922$	−10598.9	−0.378586
$923$	−7160.62	−0.255357
$924$	−29482.1	−1.04966
$925$	0	0
$926$	12537.4	0.444928
$927$	−26209.4	−0.928620
$928$	7269.25	0.257139
$929$	52039.9	1.83786	0.918930	−	0.394420i	$-0.129054\pi$
$929$	52039.9	1.83786	0.918930	+	0.394420i	$0.129054\pi$
$930$	0	0
$931$	12413.2	0.436978
$932$	1327.98	0.0466732
$933$	33399.8	1.17198
$934$	−21649.6	−0.758454
$935$	0	0
$936$	−9544.68	−0.333310
$937$	6823.94	0.237917	0.118959	−	0.992899i	$-0.462044\pi$
$937$	6823.94	0.237917	0.118959	+	0.992899i	$0.462044\pi$
$938$	−20693.4	−0.720322
$939$	−55110.9	−1.91531
$940$	0	0
$941$	−32439.4	−1.12380	−0.561899	−	0.827206i	$-0.689929\pi$
$941$	−32439.4	−1.12380	−0.561899	+	0.827206i	$0.689929\pi$
$942$	33339.4	1.15314
$943$	39137.5	1.35153
$944$	204.509	0.00705107
$945$	0	0
$946$	−40837.3	−1.40353
$947$	−16948.0	−0.581560	−0.290780	−	0.956790i	$-0.593915\pi$
$947$	−16948.0	−0.581560	−0.290780	+	0.956790i	$0.593915\pi$
$948$	−16985.8	−0.581933
$949$	32982.9	1.12821
$950$	0	0
$951$	−15721.2	−0.536062
$952$	15975.4	0.543871
$953$	−31457.8	−1.06927	−0.534637	−	0.845082i	$-0.679552\pi$
$953$	−31457.8	−1.06927	−0.534637	+	0.845082i	$0.679552\pi$
$954$	12605.6	0.427799
$955$	0	0
$956$	−17420.7	−0.589356
$957$	−66431.4	−2.24391
$958$	−31209.6	−1.05254
$959$	−46550.6	−1.56746
$960$	0	0
$961$	−28251.0	−0.948305
$962$	−16543.9	−0.554465
$963$	−47999.8	−1.60620
$964$	8279.96	0.276638
$965$	0	0
$966$	28446.1	0.947452
$967$	32983.4	1.09687	0.548436	−	0.836192i	$-0.315223\pi$
$967$	32983.4	1.09687	0.548436	+	0.836192i	$0.315223\pi$
$968$	2896.39	0.0961711
$969$	23919.8	0.792997
$970$	0	0
$971$	21727.5	0.718094	0.359047	−	0.933319i	$-0.383102\pi$
$971$	21727.5	0.718094	0.359047	+	0.933319i	$0.383102\pi$
$972$	−20378.8	−0.672480
$973$	4131.13	0.136113
$974$	−15992.3	−0.526106
$975$	0	0
$976$	7907.17	0.259326
$977$	−46517.1	−1.52325	−0.761624	−	0.648019i	$-0.775598\pi$
$977$	−46517.1	−1.52325	−0.761624	+	0.648019i	$0.775598\pi$
$978$	13171.0	0.430638
$979$	−36349.1	−1.18664
$980$	0	0
$981$	−23684.9	−0.770848
$982$	11304.6	0.367356
$983$	−22906.3	−0.743232	−0.371616	−	0.928387i	$-0.621196\pi$
$983$	−22906.3	−0.743232	−0.371616	+	0.928387i	$0.621196\pi$
$984$	28025.4	0.907946
$985$	0	0
$986$	35997.0	1.16265
$987$	−77256.4	−2.49149
$988$	−8621.78	−0.277627
$989$	39402.3	1.26686
$990$	0	0
$991$	−34920.8	−1.11937	−0.559685	−	0.828705i	$-0.689078\pi$
$991$	−34920.8	−1.11937	−0.559685	+	0.828705i	$0.689078\pi$
$992$	−1255.79	−0.0401929
$993$	27817.1	0.888971
$994$	7113.28	0.226982
$995$	0	0
$996$	−9176.54	−0.291937
$997$	30169.3	0.958345	0.479173	−	0.877721i	$-0.340937\pi$
$997$	30169.3	0.958345	0.479173	+	0.877721i	$0.340937\pi$
$998$	−18401.8	−0.583666
$999$	−4040.75	−0.127971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.4.a.n.1.13		16
5.4	even	2		1250.4.a.m.1.4		16
25.3	odd	20		250.4.e.b.49.1		32
25.4	even	10		250.4.d.d.201.2		32
25.6	even	5		250.4.d.c.51.7		32
25.8	odd	20		50.4.e.a.39.8	yes	32
25.17	odd	20		250.4.e.b.199.1		32
25.19	even	10		250.4.d.d.51.2		32
25.21	even	5		250.4.d.c.201.7		32
25.22	odd	20		50.4.e.a.9.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.8	✓	32	25.22	odd	20
50.4.e.a.39.8	yes	32	25.8	odd	20
250.4.d.c.51.7		32	25.6	even	5
250.4.d.c.201.7		32	25.21	even	5
250.4.d.d.51.2		32	25.19	even	10
250.4.d.d.201.2		32	25.4	even	10
250.4.e.b.49.1		32	25.3	odd	20
250.4.e.b.199.1		32	25.17	odd	20
1250.4.a.m.1.4		16	5.4	even	2
1250.4.a.n.1.13		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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +7.10721 q^{3} +4.00000 q^{4} +14.2144 q^{6} +25.2037 q^{7} +8.00000 q^{8} +23.5124 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +7.10721 q^{3} +4.00000 q^{4} +14.2144 q^{6} +25.2037 q^{7} +8.00000 q^{8} +23.5124 q^{9} -41.1467 q^{11} +28.4288 q^{12} -50.7429 q^{13} +50.4075 q^{14} +16.0000 q^{16} +79.2312 q^{17} +47.0247 q^{18} +42.4778 q^{19} +179.128 q^{21} -82.2934 q^{22} +79.4015 q^{23} +56.8576 q^{24} -101.486 q^{26} -24.7873 q^{27} +100.815 q^{28} +227.164 q^{29} -39.2434 q^{31} +32.0000 q^{32} -292.438 q^{33} +158.462 q^{34} +94.0495 q^{36} +163.017 q^{37} +84.9555 q^{38} -360.640 q^{39} +492.906 q^{41} +358.256 q^{42} +496.241 q^{43} -164.587 q^{44} +158.803 q^{46} -431.291 q^{47} +113.715 q^{48} +292.228 q^{49} +563.113 q^{51} -202.972 q^{52} +268.063 q^{53} -49.5747 q^{54} +201.630 q^{56} +301.898 q^{57} +454.328 q^{58} +12.7818 q^{59} +494.198 q^{61} -78.4869 q^{62} +592.600 q^{63} +64.0000 q^{64} -584.876 q^{66} -410.522 q^{67} +316.925 q^{68} +564.323 q^{69} +141.116 q^{71} +188.099 q^{72} -650.000 q^{73} +326.033 q^{74} +169.911 q^{76} -1037.05 q^{77} -721.280 q^{78} -597.485 q^{79} -811.003 q^{81} +985.811 q^{82} -322.790 q^{83} +716.513 q^{84} +992.482 q^{86} +1614.50 q^{87} -329.173 q^{88} +883.404 q^{89} -1278.91 q^{91} +317.606 q^{92} -278.911 q^{93} -862.583 q^{94} +227.431 q^{96} -1088.57 q^{97} +584.457 q^{98} -967.456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) \) 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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