LMFDB - Embedded newform 1075.6.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0141449 q^{2} -26.3066 q^{3} -31.9998 q^{4} +0.372106 q^{6} -217.673 q^{7} +0.905274 q^{8} +449.038 q^{9} +O(q^{10})$	\(q-0.0141449 q^{2} -26.3066 q^{3} -31.9998 q^{4} +0.372106 q^{6} -217.673 q^{7} +0.905274 q^{8} +449.038 q^{9} +593.318 q^{11} +841.806 q^{12} -42.0287 q^{13} +3.07897 q^{14} +1023.98 q^{16} +2087.41 q^{17} -6.35162 q^{18} -1521.82 q^{19} +5726.24 q^{21} -8.39244 q^{22} +3632.04 q^{23} -23.8147 q^{24} +0.594493 q^{26} -5420.17 q^{27} +6965.49 q^{28} +7548.81 q^{29} +3907.42 q^{31} -43.4529 q^{32} -15608.2 q^{33} -29.5263 q^{34} -14369.1 q^{36} -11131.6 q^{37} +21.5260 q^{38} +1105.63 q^{39} +3937.15 q^{41} -80.9973 q^{42} +1849.00 q^{43} -18986.0 q^{44} -51.3750 q^{46} -5615.94 q^{47} -26937.5 q^{48} +30574.5 q^{49} -54912.8 q^{51} +1344.91 q^{52} +32043.2 q^{53} +76.6679 q^{54} -197.054 q^{56} +40033.9 q^{57} -106.778 q^{58} +13422.4 q^{59} +5368.11 q^{61} -55.2702 q^{62} -97743.5 q^{63} -32766.8 q^{64} +220.777 q^{66} -5383.80 q^{67} -66796.8 q^{68} -95546.6 q^{69} +38877.8 q^{71} +406.502 q^{72} +9022.67 q^{73} +157.456 q^{74} +48697.9 q^{76} -129149. q^{77} -15.6391 q^{78} -30819.9 q^{79} +33470.0 q^{81} -55.6908 q^{82} +91009.7 q^{83} -183239. q^{84} -26.1540 q^{86} -198584. q^{87} +537.115 q^{88} -55880.5 q^{89} +9148.51 q^{91} -116224. q^{92} -102791. q^{93} +79.4372 q^{94} +1143.10 q^{96} +43246.2 q^{97} -432.475 q^{98} +266422. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9}+O(q^{10}) $ 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9} + 1206 q^{11} - 2175 q^{12} - 1942 q^{13} + 2531 q^{14} + 8851 q^{16} - 2470 q^{17} - 1279 q^{18} + 3020 q^{19} + 5632 q^{21} + 3227 q^{22} + 1326 q^{23} + 11040 q^{24} - 3415 q^{26} - 5156 q^{27} + 11489 q^{28} + 17906 q^{29} + 7982 q^{31} - 2427 q^{32} - 10100 q^{33} + 25248 q^{34} - 14813 q^{36} - 22640 q^{37} + 13695 q^{38} + 29048 q^{39} + 29112 q^{41} - 9163 q^{42} + 40678 q^{43} + 63924 q^{44} - 14944 q^{46} - 57080 q^{47} - 54894 q^{48} + 165560 q^{49} - 1576 q^{51} - 97639 q^{52} + 8054 q^{53} + 167379 q^{54} + 269326 q^{56} - 125424 q^{57} - 49485 q^{58} + 193484 q^{59} + 107466 q^{61} - 162441 q^{62} - 183778 q^{63} + 412603 q^{64} + 240489 q^{66} - 109764 q^{67} - 144300 q^{68} + 202444 q^{69} + 182964 q^{71} - 341504 q^{72} - 134468 q^{73} + 198067 q^{74} + 247729 q^{76} + 28416 q^{77} + 7286 q^{78} + 11148 q^{79} + 385246 q^{81} - 23657 q^{82} - 33850 q^{83} + 176749 q^{84} - 9245 q^{86} + 298280 q^{87} + 111354 q^{88} + 244912 q^{89} + 158092 q^{91} + 124762 q^{92} - 239860 q^{93} - 192166 q^{94} - 147719 q^{96} - 232826 q^{97} + 482463 q^{98} - 346894 q^{99}+O(q^{100}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9 + 1206 * q^11 - 2175 * q^12 - 1942 * q^13 + 2531 * q^14 + 8851 * q^16 - 2470 * q^17 - 1279 * q^18 + 3020 * q^19 + 5632 * q^21 + 3227 * q^22 + 1326 * q^23 + 11040 * q^24 - 3415 * q^26 - 5156 * q^27 + 11489 * q^28 + 17906 * q^29 + 7982 * q^31 - 2427 * q^32 - 10100 * q^33 + 25248 * q^34 - 14813 * q^36 - 22640 * q^37 + 13695 * q^38 + 29048 * q^39 + 29112 * q^41 - 9163 * q^42 + 40678 * q^43 + 63924 * q^44 - 14944 * q^46 - 57080 * q^47 - 54894 * q^48 + 165560 * q^49 - 1576 * q^51 - 97639 * q^52 + 8054 * q^53 + 167379 * q^54 + 269326 * q^56 - 125424 * q^57 - 49485 * q^58 + 193484 * q^59 + 107466 * q^61 - 162441 * q^62 - 183778 * q^63 + 412603 * q^64 + 240489 * q^66 - 109764 * q^67 - 144300 * q^68 + 202444 * q^69 + 182964 * q^71 - 341504 * q^72 - 134468 * q^73 + 198067 * q^74 + 247729 * q^76 + 28416 * q^77 + 7286 * q^78 + 11148 * q^79 + 385246 * q^81 - 23657 * q^82 - 33850 * q^83 + 176749 * q^84 - 9245 * q^86 + 298280 * q^87 + 111354 * q^88 + 244912 * q^89 + 158092 * q^91 + 124762 * q^92 - 239860 * q^93 - 192166 * q^94 - 147719 * q^96 - 232826 * q^97 + 482463 * q^98 - 346894 * 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 $

$2$	−0.0141449	−0.00250050	−0.00125025	−	0.999999i	$-0.500398\pi$
$2$	−0.0141449	−0.00250050	−0.00125025	+	0.999999i	$0.500398\pi$
$3$	−26.3066	−1.68757	−0.843785	−	0.536681i	$-0.819678\pi$
$3$	−26.3066	−1.68757	−0.843785	+	0.536681i	$0.819678\pi$
$4$	−31.9998	−0.999994
$5$	0	0
$5$	0	0
$6$	0.372106	0.00421976
$7$	−217.673	−1.67903	−0.839517	−	0.543334i	$-0.817162\pi$
$7$	−217.673	−1.67903	−0.839517	+	0.543334i	$0.817162\pi$
$8$	0.905274	0.00500098
$9$	449.038	1.84789
$10$	0	0
$11$	593.318	1.47845	0.739223	−	0.673461i	$-0.235193\pi$
$11$	593.318	1.47845	0.739223	+	0.673461i	$0.235193\pi$
$12$	841.806	1.68756
$13$	−42.0287	−0.0689743	−0.0344872	−	0.999405i	$-0.510980\pi$
$13$	−42.0287	−0.0689743	−0.0344872	+	0.999405i	$0.510980\pi$
$14$	3.07897	0.00419842
$15$	0	0
$16$	1023.98	0.999981
$17$	2087.41	1.75181	0.875903	−	0.482488i	$-0.160267\pi$
$17$	2087.41	1.75181	0.875903	+	0.482488i	$0.160267\pi$
$18$	−6.35162	−0.00462065
$19$	−1521.82	−0.967117	−0.483558	−	0.875312i	$-0.660656\pi$
$19$	−1521.82	−0.967117	−0.483558	+	0.875312i	$0.660656\pi$
$20$	0	0
$21$	5726.24	2.83349
$22$	−8.39244	−0.00369685
$23$	3632.04	1.43163	0.715815	−	0.698290i	$-0.246055\pi$
$23$	3632.04	1.43163	0.715815	+	0.698290i	$0.246055\pi$
$24$	−23.8147	−0.00843950
$25$	0	0
$26$	0.594493	0.000172470 0
$27$	−5420.17	−1.43088
$28$	6965.49	1.67902
$29$	7548.81	1.66680	0.833400	−	0.552670i	$-0.186391\pi$
$29$	7548.81	1.66680	0.833400	+	0.552670i	$0.186391\pi$
$30$	0	0
$31$	3907.42	0.730274	0.365137	−	0.930954i	$-0.381022\pi$
$31$	3907.42	0.730274	0.365137	+	0.930954i	$0.381022\pi$
$32$	−43.4529	−0.00750143
$33$	−15608.2	−2.49498
$34$	−29.5263	−0.00438038
$35$	0	0
$36$	−14369.1	−1.84788
$37$	−11131.6	−1.33676	−0.668380	−	0.743820i	$-0.733012\pi$
$37$	−11131.6	−1.33676	−0.668380	+	0.743820i	$0.733012\pi$
$38$	21.5260	0.00241827
$39$	1105.63	0.116399
$40$	0	0
$41$	3937.15	0.365782	0.182891	−	0.983133i	$-0.441454\pi$
$41$	3937.15	0.365782	0.182891	+	0.983133i	$0.441454\pi$
$42$	−80.9973	−0.00708513
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−18986.0	−1.47844
$45$	0	0
$46$	−51.3750	−0.00357979
$47$	−5615.94	−0.370833	−0.185416	−	0.982660i	$-0.559363\pi$
$47$	−5615.94	−0.370833	−0.185416	+	0.982660i	$0.559363\pi$
$48$	−26937.5	−1.68754
$49$	30574.5	1.81915
$50$	0	0
$51$	−54912.8	−2.95629
$52$	1344.91	0.0689739
$53$	32043.2	1.56692	0.783459	−	0.621443i	$-0.213453\pi$
$53$	32043.2	1.56692	0.783459	+	0.621443i	$0.213453\pi$
$54$	76.6679	0.00357791
$55$	0	0
$56$	−197.054	−0.00839681
$57$	40033.9	1.63208
$58$	−106.778	−0.00416783
$59$	13422.4	0.501996	0.250998	−	0.967988i	$-0.419241\pi$
$59$	13422.4	0.501996	0.250998	+	0.967988i	$0.419241\pi$
$60$	0	0
$61$	5368.11	0.184713	0.0923563	−	0.995726i	$-0.470560\pi$
$61$	5368.11	0.184713	0.0923563	+	0.995726i	$0.470560\pi$
$62$	−55.2702	−0.00182605
$63$	−97743.5	−3.10268
$64$	−32766.8	−0.999962
$65$	0	0
$66$	220.777	0.00623869
$67$	−5383.80	−0.146522	−0.0732609	−	0.997313i	$-0.523341\pi$
$67$	−5383.80	−0.146522	−0.0732609	+	0.997313i	$0.523341\pi$
$68$	−66796.8	−1.75179
$69$	−95546.6	−2.41598
$70$	0	0
$71$	38877.8	0.915284	0.457642	−	0.889137i	$-0.348694\pi$
$71$	38877.8	0.915284	0.457642	+	0.889137i	$0.348694\pi$
$72$	406.502	0.00924127
$73$	9022.67	0.198165	0.0990827	−	0.995079i	$-0.468409\pi$
$73$	9022.67	0.198165	0.0990827	+	0.995079i	$0.468409\pi$
$74$	157.456	0.00334256
$75$	0	0
$76$	48697.9	0.967111
$77$	−129149.	−2.48236
$78$	−15.6391	−0.000291055 0
$79$	−30819.9	−0.555602	−0.277801	−	0.960639i	$-0.589606\pi$
$79$	−30819.9	−0.555602	−0.277801	+	0.960639i	$0.589606\pi$
$80$	0	0
$81$	33470.0	0.566817
$82$	−55.6908	−0.000914637 0
$83$	91009.7	1.45008	0.725041	−	0.688706i	$-0.241821\pi$
$83$	91009.7	1.45008	0.725041	+	0.688706i	$0.241821\pi$
$84$	−183239.	−2.83347
$85$	0	0
$86$	−26.1540	−0.000381322 0
$87$	−198584.	−2.81284
$88$	537.115	0.00739368
$89$	−55880.5	−0.747800	−0.373900	−	0.927469i	$-0.621980\pi$
$89$	−55880.5	−0.747800	−0.373900	+	0.927469i	$0.621980\pi$
$90$	0	0
$91$	9148.51	0.115810
$92$	−116224.	−1.43162
$93$	−102791.	−1.23239
$94$	79.4372	0.000927266 0
$95$	0	0
$96$	1143.10	0.0126592
$97$	43246.2	0.466680	0.233340	−	0.972395i	$-0.425035\pi$
$97$	43246.2	0.466680	0.233340	+	0.972395i	$0.425035\pi$
$98$	−432.475	−0.00454879
$99$	266422.	2.73201
$100$	0	0
$101$	131220.	1.27996	0.639981	−	0.768391i	$-0.278942\pi$
$101$	131220.	1.27996	0.639981	+	0.768391i	$0.278942\pi$
$102$	776.738	0.00739221
$103$	−78262.1	−0.726873	−0.363436	−	0.931619i	$-0.618397\pi$
$103$	−78262.1	−0.726873	−0.363436	+	0.931619i	$0.618397\pi$
$104$	−38.0475	−0.000344939 0
$105$	0	0
$106$	−453.250	−0.00391808
$107$	−90998.8	−0.768380	−0.384190	−	0.923254i	$-0.625519\pi$
$107$	−90998.8	−0.768380	−0.384190	+	0.923254i	$0.625519\pi$
$108$	173444.	1.43087
$109$	−54611.5	−0.440269	−0.220135	−	0.975470i	$-0.570650\pi$
$109$	−54611.5	−0.440269	−0.220135	+	0.975470i	$0.570650\pi$
$110$	0	0
$111$	292835.	2.25588
$112$	−222893.	−1.67900
$113$	197093.	1.45203	0.726014	−	0.687680i	$-0.241371\pi$
$113$	197093.	1.45203	0.726014	+	0.687680i	$0.241371\pi$
$114$	−566.277	−0.00408100
$115$	0	0
$116$	−241560.	−1.66679
$117$	−18872.5	−0.127457
$118$	−189.859	−0.00125524
$119$	−454373.	−2.94134
$120$	0	0
$121$	190975.	1.18580
$122$	−75.9316	−0.000461873 0
$123$	−103573.	−0.617283
$124$	−125037.	−0.730269
$125$	0	0
$126$	1382.58	0.00775823
$127$	319843.	1.75966	0.879829	−	0.475291i	$-0.157657\pi$
$127$	319843.	1.75966	0.879829	+	0.475291i	$0.157657\pi$
$128$	1853.98	0.0100018
$129$	−48640.9	−0.257352
$130$	0	0
$131$	−89449.6	−0.455408	−0.227704	−	0.973730i	$-0.573122\pi$
$131$	−89449.6	−0.455408	−0.227704	+	0.973730i	$0.573122\pi$
$132$	499459.	2.49497
$133$	331259.	1.62382
$134$	76.1536	0.000366377 0
$135$	0	0
$136$	1889.68	0.00876074
$137$	−1796.89	−0.00817939	−0.00408970	−	0.999992i	$-0.501302\pi$
$137$	−1796.89	−0.00817939	−0.00408970	+	0.999992i	$0.501302\pi$
$138$	1351.50	0.00604114
$139$	−148553.	−0.652144	−0.326072	−	0.945345i	$-0.605725\pi$
$139$	−148553.	−0.652144	−0.326072	+	0.945345i	$0.605725\pi$
$140$	0	0
$141$	147736.	0.625806
$142$	−549.925	−0.00228867
$143$	−24936.3	−0.101975
$144$	459806.	1.84786
$145$	0	0
$146$	−127.625	−0.000495512 0
$147$	−804312.	−3.06995
$148$	356209.	1.33675
$149$	−54522.5	−0.201192	−0.100596	−	0.994927i	$-0.532075\pi$
$149$	−54522.5	−0.201192	−0.100596	+	0.994927i	$0.532075\pi$
$150$	0	0
$151$	104108.	0.371570	0.185785	−	0.982590i	$-0.440517\pi$
$151$	104108.	0.371570	0.185785	+	0.982590i	$0.440517\pi$
$152$	−1377.66	−0.00483653
$153$	937328.	3.23715
$154$	1826.81	0.00620713
$155$	0	0
$156$	−35380.0	−0.116398
$157$	591452.	1.91501	0.957504	−	0.288420i	$-0.0931301\pi$
$157$	591452.	1.91501	0.957504	+	0.288420i	$0.0931301\pi$
$158$	435.946	0.00138928
$159$	−842949.	−2.64429
$160$	0	0
$161$	−790596.	−2.40375
$162$	−473.431	−0.00141732
$163$	−443276.	−1.30679	−0.653394	−	0.757018i	$-0.726655\pi$
$163$	−443276.	−1.30679	−0.653394	+	0.757018i	$0.726655\pi$
$164$	−125988.	−0.365780
$165$	0	0
$166$	−1287.33	−0.00362592
$167$	116967.	0.324542	0.162271	−	0.986746i	$-0.448118\pi$
$167$	116967.	0.324542	0.162271	+	0.986746i	$0.448118\pi$
$168$	5183.81	0.0141702
$169$	−369527.	−0.995243
$170$	0	0
$171$	−683354.	−1.78713
$172$	−59167.6	−0.152498
$173$	200905.	0.510358	0.255179	−	0.966894i	$-0.417866\pi$
$173$	200905.	0.510358	0.255179	+	0.966894i	$0.417866\pi$
$174$	2808.96	0.00703350
$175$	0	0
$176$	607546.	1.47842
$177$	−353098.	−0.847154
$178$	790.427	0.00186987
$179$	691715.	1.61360	0.806798	−	0.590828i	$-0.201199\pi$
$179$	691715.	1.61360	0.806798	+	0.590828i	$0.201199\pi$
$180$	0	0
$181$	655143.	1.48641	0.743207	−	0.669062i	$-0.233304\pi$
$181$	655143.	1.48641	0.743207	+	0.669062i	$0.233304\pi$
$182$	−129.405	−0.000289583 0
$183$	−141217.	−0.311716
$184$	3287.99	0.00715955
$185$	0	0
$186$	1453.97	0.00308158
$187$	1.23850e6	2.58995
$188$	179709.	0.370830
$189$	1.17982e6	2.40250
$190$	0	0
$191$	−203063.	−0.402760	−0.201380	−	0.979513i	$-0.564543\pi$
$191$	−203063.	−0.402760	−0.201380	+	0.979513i	$0.564543\pi$
$192$	861983.	1.68751
$193$	−114967.	−0.222167	−0.111083	−	0.993811i	$-0.535432\pi$
$193$	−114967.	−0.222167	−0.111083	+	0.993811i	$0.535432\pi$
$194$	−611.715	−0.00116693
$195$	0	0
$196$	−978379.	−1.81914
$197$	−1.02159e6	−1.87547	−0.937733	−	0.347358i	$-0.887079\pi$
$197$	−1.02159e6	−1.87547	−0.937733	+	0.347358i	$0.887079\pi$
$198$	−3768.53	−0.00683138
$199$	259360.	0.464269	0.232135	−	0.972684i	$-0.425429\pi$
$199$	259360.	0.464269	0.232135	+	0.972684i	$0.425429\pi$
$200$	0	0
$201$	141630.	0.247266
$202$	−1856.10	−0.00320054
$203$	−1.64317e6	−2.79861
$204$	1.75720e6	2.95628
$205$	0	0
$206$	1107.01	0.00181754
$207$	1.63092e6	2.64550
$208$	−43036.6	−0.0689730
$209$	−902922.	−1.42983
$210$	0	0
$211$	−945525.	−1.46207	−0.731033	−	0.682342i	$-0.760961\pi$
$211$	−945525.	−1.46207	−0.731033	+	0.682342i	$0.760961\pi$
$212$	−1.02538e6	−1.56691
$213$	−1.02274e6	−1.54461
$214$	1287.17	0.00192133
$215$	0	0
$216$	−4906.73	−0.00715580
$217$	−850540.	−1.22615
$218$	772.477	0.00110089
$219$	−237356.	−0.334418
$220$	0	0
$221$	−87731.2	−0.120830
$222$	−4142.13	−0.00564081
$223$	244607.	0.329388	0.164694	−	0.986345i	$-0.447336\pi$
$223$	244607.	0.329388	0.164694	+	0.986345i	$0.447336\pi$
$224$	9458.52	0.0125951
$225$	0	0
$226$	−2787.87	−0.00363079
$227$	150549.	0.193916	0.0969580	−	0.995288i	$-0.469089\pi$
$227$	150549.	0.193916	0.0969580	+	0.995288i	$0.469089\pi$
$228$	−1.28108e6	−1.63207
$229$	−144699.	−0.182337	−0.0911686	−	0.995835i	$-0.529060\pi$
$229$	−144699.	−0.182337	−0.0911686	+	0.995835i	$0.529060\pi$
$230$	0	0
$231$	3.39748e6	4.18916
$232$	6833.74	0.00833563
$233$	1.26475e6	1.52622	0.763108	−	0.646270i	$-0.223672\pi$
$233$	1.26475e6	1.52622	0.763108	+	0.646270i	$0.223672\pi$
$234$	266.950	0.000318706 0
$235$	0	0
$236$	−429514.	−0.501993
$237$	810767.	0.937617
$238$	6427.08	0.00735481
$239$	−884403.	−1.00151	−0.500755	−	0.865589i	$-0.666944\pi$
$239$	−884403.	−1.00151	−0.500755	+	0.865589i	$0.666944\pi$
$240$	0	0
$241$	−127751.	−0.141684	−0.0708421	−	0.997488i	$-0.522569\pi$
$241$	−127751.	−0.141684	−0.0708421	+	0.997488i	$0.522569\pi$
$242$	−2701.33	−0.00296510
$243$	436619.	0.474337
$244$	−171778.	−0.184712
$245$	0	0
$246$	1465.04	0.00154351
$247$	63960.0	0.0667062
$248$	3537.28	0.00365208
$249$	−2.39416e6	−2.44711
$250$	0	0
$251$	1.07557e6	1.07759	0.538796	−	0.842436i	$-0.318879\pi$
$251$	1.07557e6	1.07759	0.538796	+	0.842436i	$0.318879\pi$
$252$	3.12777e6	3.10266
$253$	2.15495e6	2.11659
$254$	−4524.17	−0.00440002
$255$	0	0
$256$	1.04851e6	0.999937
$257$	962185.	0.908711	0.454356	−	0.890820i	$-0.349870\pi$
$257$	962185.	0.908711	0.454356	+	0.890820i	$0.349870\pi$
$258$	688.023	0.000643508 0
$259$	2.42305e6	2.24446
$260$	0	0
$261$	3.38970e6	3.08007
$262$	1265.26	0.00113875
$263$	−1.40731e6	−1.25458	−0.627292	−	0.778784i	$-0.715837\pi$
$263$	−1.40731e6	−1.25458	−0.627292	+	0.778784i	$0.715837\pi$
$264$	−14129.7	−0.0124773
$265$	0	0
$266$	−4685.64	−0.00406036
$267$	1.47003e6	1.26196
$268$	172281.	0.146521
$269$	−931075.	−0.784520	−0.392260	−	0.919854i	$-0.628307\pi$
$269$	−931075.	−0.784520	−0.392260	+	0.919854i	$0.628307\pi$
$270$	0	0
$271$	−744485.	−0.615790	−0.307895	−	0.951420i	$-0.599625\pi$
$271$	−744485.	−0.615790	−0.307895	+	0.951420i	$0.599625\pi$
$272$	2.13747e6	1.75177
$273$	−240666.	−0.195438
$274$	25.4170	2.04525e−5 0
$275$	0	0
$276$	3.05747e6	2.41596
$277$	1.72396e6	1.34998	0.674990	−	0.737827i	$-0.264148\pi$
$277$	1.72396e6	1.34998	0.674990	+	0.737827i	$0.264148\pi$
$278$	2101.27	0.00163068
$279$	1.75458e6	1.34947
$280$	0	0
$281$	−1.56346e6	−1.18119	−0.590596	−	0.806968i	$-0.701107\pi$
$281$	−1.56346e6	−1.18119	−0.590596	+	0.806968i	$0.701107\pi$
$282$	−2089.72	−0.00156483
$283$	−381520.	−0.283173	−0.141586	−	0.989926i	$-0.545220\pi$
$283$	−381520.	−0.283173	−0.141586	+	0.989926i	$0.545220\pi$
$284$	−1.24408e6	−0.915278
$285$	0	0
$286$	352.723	0.000254988 0
$287$	−857011.	−0.614160
$288$	−19512.0	−0.0138618
$289$	2.93743e6	2.06882
$290$	0	0
$291$	−1.13766e6	−0.787555
$292$	−288724.	−0.198164
$293$	1.43913e6	0.979338	0.489669	−	0.871908i	$-0.337118\pi$
$293$	1.43913e6	0.979338	0.489669	+	0.871908i	$0.337118\pi$
$294$	11377.0	0.00767640
$295$	0	0
$296$	−10077.1	−0.00668511
$297$	−3.21588e6	−2.11548
$298$	771.217	0.000503079 0
$299$	−152650.	−0.0987457
$300$	0	0
$301$	−402477.	−0.256050
$302$	−1472.60	−0.000929111 0
$303$	−3.45196e6	−2.16002
$304$	−1.55831e6	−0.967098
$305$	0	0
$306$	−13258.4	−0.00809448
$307$	−856617.	−0.518729	−0.259365	−	0.965779i	$-0.583513\pi$
$307$	−856617.	−0.518729	−0.259365	+	0.965779i	$0.583513\pi$
$308$	4.13275e6	2.48235
$309$	2.05881e6	1.22665
$310$	0	0
$311$	1.63870e6	0.960726	0.480363	−	0.877070i	$-0.340505\pi$
$311$	1.63870e6	0.960726	0.480363	+	0.877070i	$0.340505\pi$
$312$	1000.90	0.000582109 0
$313$	1.20869e6	0.697358	0.348679	−	0.937242i	$-0.386630\pi$
$313$	1.20869e6	0.697358	0.348679	+	0.937242i	$0.386630\pi$
$314$	−8366.06	−0.00478847
$315$	0	0
$316$	986231.	0.555598
$317$	2.15029e6	1.20185	0.600923	−	0.799307i	$-0.294800\pi$
$317$	2.15029e6	1.20185	0.600923	+	0.799307i	$0.294800\pi$
$318$	11923.5	0.00661203
$319$	4.47884e6	2.46427
$320$	0	0
$321$	2.39387e6	1.29670
$322$	11182.9	0.00601058
$323$	−3.17666e6	−1.69420
$324$	−1.07103e6	−0.566813
$325$	0	0
$326$	6270.11	0.00326762
$327$	1.43665e6	0.742985
$328$	3564.20	0.00182927
$329$	1.22244e6	0.622641
$330$	0	0
$331$	602222.	0.302125	0.151063	−	0.988524i	$-0.451731\pi$
$331$	602222.	0.302125	0.151063	+	0.988524i	$0.451731\pi$
$332$	−2.91229e6	−1.45007
$333$	−4.99851e6	−2.47019
$334$	−1654.49	−0.000811515 0
$335$	0	0
$336$	5.86356e6	2.83343
$337$	−2.77563e6	−1.33133	−0.665666	−	0.746250i	$-0.731852\pi$
$337$	−2.77563e6	−1.33133	−0.665666	+	0.746250i	$0.731852\pi$
$338$	5226.93	0.00248860
$339$	−5.18485e6	−2.45040
$340$	0	0
$341$	2.31834e6	1.07967
$342$	9666.01	0.00446871
$343$	−2.99682e6	−1.37539
$344$	1673.85	0.000762642 0
$345$	0	0
$346$	−2841.79	−0.00127615
$347$	164472.	0.0733276	0.0366638	−	0.999328i	$-0.488327\pi$
$347$	164472.	0.0733276	0.0366638	+	0.999328i	$0.488327\pi$
$348$	6.35464e6	2.81282
$349$	2.45036e6	1.07688	0.538438	−	0.842665i	$-0.319014\pi$
$349$	2.45036e6	1.07688	0.538438	+	0.842665i	$0.319014\pi$
$350$	0	0
$351$	227802.	0.0986939
$352$	−25781.4	−0.0110905
$353$	4.44171e6	1.89720	0.948601	−	0.316475i	$-0.102499\pi$
$353$	4.44171e6	1.89720	0.948601	+	0.316475i	$0.102499\pi$
$354$	4994.55	0.00211831
$355$	0	0
$356$	1.78817e6	0.747795
$357$	1.19530e7	4.96372
$358$	−9784.27	−0.00403479
$359$	−3.12063e6	−1.27793	−0.638964	−	0.769237i	$-0.720637\pi$
$359$	−3.12063e6	−1.27793	−0.638964	+	0.769237i	$0.720637\pi$
$360$	0	0
$361$	−160167.	−0.0646854
$362$	−9266.96	−0.00371677
$363$	−5.02390e6	−2.00113
$364$	−292750.	−0.115809
$365$	0	0
$366$	1997.50	0.000779444 0
$367$	−2.27184e6	−0.880464	−0.440232	−	0.897884i	$-0.645104\pi$
$367$	−2.27184e6	−0.880464	−0.440232	+	0.897884i	$0.645104\pi$
$368$	3.71914e6	1.43160
$369$	1.76793e6	0.675926
$370$	0	0
$371$	−6.97494e6	−2.63091
$372$	3.28929e6	1.23238
$373$	−4.22398e6	−1.57199	−0.785995	−	0.618233i	$-0.787849\pi$
$373$	−4.22398e6	−1.57199	−0.785995	+	0.618233i	$0.787849\pi$
$374$	−17518.5	−0.00647616
$375$	0	0
$376$	−5083.97	−0.00185453
$377$	−317266.	−0.114966
$378$	−16688.5	−0.00600743
$379$	841802.	0.301031	0.150516	−	0.988608i	$-0.451907\pi$
$379$	841802.	0.301031	0.150516	+	0.988608i	$0.451907\pi$
$380$	0	0
$381$	−8.41400e6	−2.96955
$382$	2872.31	0.00100710
$383$	2.01215e6	0.700911	0.350455	−	0.936579i	$-0.386027\pi$
$383$	2.01215e6	0.700911	0.350455	+	0.936579i	$0.386027\pi$
$384$	−48771.9	−0.0168788
$385$	0	0
$386$	1626.20	0.000555527 0
$387$	830271.	0.281801
$388$	−1.38387e6	−0.466677
$389$	−1.55677e6	−0.521617	−0.260809	−	0.965391i	$-0.583989\pi$
$389$	−1.55677e6	−0.521617	−0.260809	+	0.965391i	$0.583989\pi$
$390$	0	0
$391$	7.58156e6	2.50794
$392$	27678.3	0.00909755
$393$	2.35312e6	0.768532
$394$	14450.3	0.00468960
$395$	0	0
$396$	−8.52546e6	−2.73199
$397$	2.53771e6	0.808101	0.404050	−	0.914737i	$-0.367602\pi$
$397$	2.53771e6	0.808101	0.404050	+	0.914737i	$0.367602\pi$
$398$	−3668.63	−0.00116090
$399$	−8.71430e6	−2.74031
$400$	0	0
$401$	122931.	0.0381768	0.0190884	−	0.999818i	$-0.493924\pi$
$401$	122931.	0.0381768	0.0190884	+	0.999818i	$0.493924\pi$
$402$	−2003.34	−0.000618287 0
$403$	−164224.	−0.0503701
$404$	−4.19902e6	−1.27995
$405$	0	0
$406$	23242.6	0.00699792
$407$	−6.60458e6	−1.97633
$408$	−49711.1	−0.0147844
$409$	−2.81499e6	−0.832087	−0.416043	−	0.909345i	$-0.636584\pi$
$409$	−2.81499e6	−0.832087	−0.416043	+	0.909345i	$0.636584\pi$
$410$	0	0
$411$	47270.2	0.0138033
$412$	2.50437e6	0.726868
$413$	−2.92169e6	−0.842868
$414$	−23069.3	−0.00661506
$415$	0	0
$416$	1826.27	0.000517406 0
$417$	3.90792e6	1.10054
$418$	12771.8	0.00357528
$419$	−3.14290e6	−0.874572	−0.437286	−	0.899322i	$-0.644060\pi$
$419$	−3.14290e6	−0.874572	−0.437286	+	0.899322i	$0.644060\pi$
$420$	0	0
$421$	3.37805e6	0.928883	0.464442	−	0.885604i	$-0.346255\pi$
$421$	3.37805e6	0.928883	0.464442	+	0.885604i	$0.346255\pi$
$422$	13374.4	0.00365589
$423$	−2.52177e6	−0.685259
$424$	29007.9	0.00783613
$425$	0	0
$426$	14466.7	0.00386228
$427$	−1.16849e6	−0.310139
$428$	2.91194e6	0.768375
$429$	655991.	0.172090
$430$	0	0
$431$	−3.19749e6	−0.829117	−0.414558	−	0.910023i	$-0.636064\pi$
$431$	−3.19749e6	−0.829117	−0.414558	+	0.910023i	$0.636064\pi$
$432$	−5.55015e6	−1.43085
$433$	−2.96006e6	−0.758720	−0.379360	−	0.925249i	$-0.623856\pi$
$433$	−2.96006e6	−0.758720	−0.379360	+	0.925249i	$0.623856\pi$
$434$	12030.8	0.00306600
$435$	0	0
$436$	1.74756e6	0.440266
$437$	−5.52730e6	−1.38455
$438$	3357.39	0.000836212 0
$439$	−2.94173e6	−0.728519	−0.364260	−	0.931297i	$-0.618678\pi$
$439$	−2.94173e6	−0.728519	−0.364260	+	0.931297i	$0.618678\pi$
$440$	0	0
$441$	1.37291e7	3.36160
$442$	1240.95	0.000302134 0
$443$	−795150.	−0.192504	−0.0962520	−	0.995357i	$-0.530685\pi$
$443$	−795150.	−0.192504	−0.0962520	+	0.995357i	$0.530685\pi$
$444$	−9.37066e6	−2.25586
$445$	0	0
$446$	−3459.96	−0.000823633 0
$447$	1.43430e6	0.339525
$448$	7.13244e6	1.67897
$449$	−3.42184e6	−0.801022	−0.400511	−	0.916292i	$-0.631167\pi$
$449$	−3.42184e6	−0.801022	−0.400511	+	0.916292i	$0.631167\pi$
$450$	0	0
$451$	2.33598e6	0.540789
$452$	−6.30693e6	−1.45202
$453$	−2.73873e6	−0.627051
$454$	−2129.51	−0.000484886 0
$455$	0	0
$456$	36241.6	0.00816198
$457$	−4.18001e6	−0.936240	−0.468120	−	0.883665i	$-0.655068\pi$
$457$	−4.18001e6	−0.936240	−0.468120	+	0.883665i	$0.655068\pi$
$458$	2046.75	0.000455934 0
$459$	−1.13141e7	−2.50662
$460$	0	0
$461$	−4.84886e6	−1.06264	−0.531322	−	0.847170i	$-0.678304\pi$
$461$	−4.84886e6	−1.06264	−0.531322	+	0.847170i	$0.678304\pi$
$462$	−48057.1	−0.0104750
$463$	−706245.	−0.153110	−0.0765549	−	0.997065i	$-0.524392\pi$
$463$	−706245.	−0.153110	−0.0765549	+	0.997065i	$0.524392\pi$
$464$	7.72984e6	1.66677
$465$	0	0
$466$	−17889.9	−0.00381630
$467$	873901.	0.185426	0.0927129	−	0.995693i	$-0.470446\pi$
$467$	873901.	0.185426	0.0927129	+	0.995693i	$0.470446\pi$
$468$	603915.	0.127456
$469$	1.17191e6	0.246015
$470$	0	0
$471$	−1.55591e7	−3.23171
$472$	12151.0	0.00251047
$473$	1.09704e6	0.225461
$474$	−11468.3	−0.00234451
$475$	0	0
$476$	1.45399e7	2.94132
$477$	1.43886e7	2.89550
$478$	12509.8	0.00250427
$479$	−2.79347e6	−0.556295	−0.278147	−	0.960538i	$-0.589720\pi$
$479$	−2.79347e6	−0.556295	−0.278147	+	0.960538i	$0.589720\pi$
$480$	0	0
$481$	467846.	0.0922021
$482$	1807.03	0.000354281 0
$483$	2.07979e7	4.05651
$484$	−6.11115e6	−1.18580
$485$	0	0
$486$	−6175.95	−0.00118608
$487$	6.92295e6	1.32272	0.661361	−	0.750068i	$-0.269979\pi$
$487$	6.92295e6	1.32272	0.661361	+	0.750068i	$0.269979\pi$
$488$	4859.61	0.000923744 0
$489$	1.16611e7	2.20530
$490$	0	0
$491$	1.92374e6	0.360116	0.180058	−	0.983656i	$-0.442371\pi$
$491$	1.92374e6	0.360116	0.180058	+	0.983656i	$0.442371\pi$
$492$	3.31432e6	0.617279
$493$	1.57575e7	2.91991
$494$	−904.711	−0.000166799 0
$495$	0	0
$496$	4.00112e6	0.730260
$497$	−8.46265e6	−1.53679
$498$	33865.2	0.00611900
$499$	5.62275e6	1.01087	0.505437	−	0.862863i	$-0.331331\pi$
$499$	5.62275e6	1.01087	0.505437	+	0.862863i	$0.331331\pi$
$500$	0	0
$501$	−3.07699e6	−0.547687
$502$	−15213.9	−0.00269451
$503$	−1.01707e7	−1.79238	−0.896192	−	0.443667i	$-0.853677\pi$
$503$	−1.01707e7	−1.79238	−0.896192	+	0.443667i	$0.853677\pi$
$504$	−88484.6	−0.0155164
$505$	0	0
$506$	−30481.7	−0.00529252
$507$	9.72099e6	1.67954
$508$	−1.02349e7	−1.75965
$509$	1.98418e6	0.339458	0.169729	−	0.985491i	$-0.445711\pi$
$509$	1.98418e6	0.339458	0.169729	+	0.985491i	$0.445711\pi$
$510$	0	0
$511$	−1.96399e6	−0.332727
$512$	−74158.4	−0.0125022
$513$	8.24851e6	1.38383
$514$	−13610.1	−0.00227223
$515$	0	0
$516$	1.55650e6	0.257350
$517$	−3.33204e6	−0.548256
$518$	−34273.9	−0.00561228
$519$	−5.28513e6	−0.861266
$520$	0	0
$521$	8.70399e6	1.40483	0.702415	−	0.711767i	$-0.252105\pi$
$521$	8.70399e6	1.40483	0.702415	+	0.711767i	$0.252105\pi$
$522$	−47947.2	−0.00770170
$523$	−7.81219e6	−1.24887	−0.624437	−	0.781075i	$-0.714672\pi$
$523$	−7.81219e6	−1.24887	−0.624437	+	0.781075i	$0.714672\pi$
$524$	2.86237e6	0.455405
$525$	0	0
$526$	19906.3	0.00313708
$527$	8.15639e6	1.27930
$528$	−1.59825e7	−2.49493
$529$	6.75535e6	1.04956
$530$	0	0
$531$	6.02717e6	0.927635
$532$	−1.06002e7	−1.62381
$533$	−165473.	−0.0252296
$534$	−20793.5	−0.00315554
$535$	0	0
$536$	−4873.82	−0.000732752 0
$537$	−1.81967e7	−2.72306
$538$	13170.0	0.00196169
$539$	1.81404e7	2.68952
$540$	0	0
$541$	1.63240e6	0.239792	0.119896	−	0.992786i	$-0.461744\pi$
$541$	1.63240e6	0.239792	0.119896	+	0.992786i	$0.461744\pi$
$542$	10530.7	0.00153978
$543$	−1.72346e7	−2.50843
$544$	−90704.1	−0.0131410
$545$	0	0
$546$	3404.21	0.000488692 0
$547$	−2.12530e6	−0.303705	−0.151853	−	0.988403i	$-0.548524\pi$
$547$	−2.12530e6	−0.303705	−0.151853	+	0.988403i	$0.548524\pi$
$548$	57500.2	0.00817934
$549$	2.41049e6	0.341329
$550$	0	0
$551$	−1.14879e7	−1.61199
$552$	−86495.8	−0.0120822
$553$	6.70866e6	0.932874
$554$	−24385.3	−0.00337562
$555$	0	0
$556$	4.75365e6	0.652140
$557$	−2.68074e6	−0.366114	−0.183057	−	0.983102i	$-0.558599\pi$
$557$	−2.68074e6	−0.366114	−0.183057	+	0.983102i	$0.558599\pi$
$558$	−24818.4	−0.00337434
$559$	−77711.0	−0.0105185
$560$	0	0
$561$	−3.25807e7	−4.37072
$562$	22115.0	0.00295356
$563$	1.10346e7	1.46719	0.733593	−	0.679589i	$-0.237842\pi$
$563$	1.10346e7	1.46719	0.733593	+	0.679589i	$0.237842\pi$
$564$	−4.72754e6	−0.625802
$565$	0	0
$566$	5396.58	0.000708072 0
$567$	−7.28550e6	−0.951704
$568$	35195.1	0.00457732
$569$	−5.46407e6	−0.707514	−0.353757	−	0.935337i	$-0.615096\pi$
$569$	−5.46407e6	−0.707514	−0.353757	+	0.935337i	$0.615096\pi$
$570$	0	0
$571$	1.19722e7	1.53669	0.768343	−	0.640038i	$-0.221081\pi$
$571$	1.19722e7	1.53669	0.768343	+	0.640038i	$0.221081\pi$
$572$	797958.	0.101974
$573$	5.34189e6	0.679686
$574$	12122.4	0.00153571
$575$	0	0
$576$	−1.47135e7	−1.84782
$577$	7.62231e6	0.953119	0.476560	−	0.879142i	$-0.341884\pi$
$577$	7.62231e6	0.953119	0.476560	+	0.879142i	$0.341884\pi$
$578$	−41549.8	−0.00517308
$579$	3.02438e6	0.374922
$580$	0	0
$581$	−1.98103e7	−2.43473
$582$	16092.2	0.00196928
$583$	1.90118e7	2.31661
$584$	8167.99	0.000991021 0
$585$	0	0
$586$	−20356.5	−0.00244883
$587$	2.13823e6	0.256130	0.128065	−	0.991766i	$-0.459123\pi$
$587$	2.13823e6	0.256130	0.128065	+	0.991766i	$0.459123\pi$
$588$	2.57378e7	3.06993
$589$	−5.94638e6	−0.706260
$590$	0	0
$591$	2.68745e7	3.16498
$592$	−1.13985e7	−1.33673
$593$	−4.89924e6	−0.572127	−0.286063	−	0.958211i	$-0.592347\pi$
$593$	−4.89924e6	−0.572127	−0.286063	+	0.958211i	$0.592347\pi$
$594$	45488.4	0.00528975
$595$	0	0
$596$	1.74471e6	0.201190
$597$	−6.82288e6	−0.783487
$598$	2159.22	0.000246913 0
$599$	−1.27530e7	−1.45226	−0.726131	−	0.687557i	$-0.758683\pi$
$599$	−1.27530e7	−1.45226	−0.726131	+	0.687557i	$0.758683\pi$
$600$	0	0
$601$	7.96973e6	0.900031	0.450016	−	0.893021i	$-0.351418\pi$
$601$	7.96973e6	0.900031	0.450016	+	0.893021i	$0.351418\pi$
$602$	5693.02	0.000640253 0
$603$	−2.41753e6	−0.270757
$604$	−3.33143e6	−0.371568
$605$	0	0
$606$	48827.7	0.00540113
$607$	−9.92270e6	−1.09310	−0.546548	−	0.837428i	$-0.684058\pi$
$607$	−9.92270e6	−1.09310	−0.546548	+	0.837428i	$0.684058\pi$
$608$	66127.4	0.00725476
$609$	4.32263e7	4.72286
$610$	0	0
$611$	236031.	0.0255779
$612$	−2.99943e7	−3.23713
$613$	−7.69443e6	−0.827037	−0.413519	−	0.910496i	$-0.635700\pi$
$613$	−7.69443e6	−0.827037	−0.413519	+	0.910496i	$0.635700\pi$
$614$	12116.8	0.00129708
$615$	0	0
$616$	−116915.	−0.0124142
$617$	6.88604e6	0.728210	0.364105	−	0.931358i	$-0.381375\pi$
$617$	6.88604e6	0.728210	0.364105	+	0.931358i	$0.381375\pi$
$618$	−29121.8	−0.00306723
$619$	1.01357e7	1.06323	0.531617	−	0.846985i	$-0.321585\pi$
$619$	1.01357e7	1.06323	0.531617	+	0.846985i	$0.321585\pi$
$620$	0	0
$621$	−1.96862e7	−2.04849
$622$	−23179.4	−0.00240229
$623$	1.21637e7	1.25558
$624$	1.13215e6	0.116397
$625$	0	0
$626$	−17096.9	−0.00174374
$627$	2.37528e7	2.41294
$628$	−1.89264e7	−1.91500
$629$	−2.32362e7	−2.34174
$630$	0	0
$631$	−1.44410e7	−1.44385	−0.721927	−	0.691969i	$-0.756743\pi$
$631$	−1.44410e7	−1.44385	−0.721927	+	0.691969i	$0.756743\pi$
$632$	−27900.4	−0.00277855
$633$	2.48736e7	2.46734
$634$	−30415.7	−0.00300521
$635$	0	0
$636$	2.69742e7	2.64427
$637$	−1.28501e6	−0.125475
$638$	−63353.0	−0.00616191
$639$	1.74576e7	1.69135
$640$	0	0
$641$	1.09226e6	0.104998	0.0524990	−	0.998621i	$-0.483281\pi$
$641$	1.09226e6	0.104998	0.0524990	+	0.998621i	$0.483281\pi$
$642$	−33861.2	−0.00324238
$643$	−2.00469e7	−1.91214	−0.956069	−	0.293143i	$-0.905299\pi$
$643$	−2.00469e7	−1.91214	−0.956069	+	0.293143i	$0.905299\pi$
$644$	2.52989e7	2.40374
$645$	0	0
$646$	44933.7	0.00423634
$647$	−4.68232e6	−0.439744	−0.219872	−	0.975529i	$-0.570564\pi$
$647$	−4.68232e6	−0.439744	−0.219872	+	0.975529i	$0.570564\pi$
$648$	30299.5	0.00283464
$649$	7.96375e6	0.742174
$650$	0	0
$651$	2.23748e7	2.06922
$652$	1.41847e7	1.30678
$653$	−3.05303e6	−0.280187	−0.140094	−	0.990138i	$-0.544740\pi$
$653$	−3.05303e6	−0.280187	−0.140094	+	0.990138i	$0.544740\pi$
$654$	−20321.3	−0.00185783
$655$	0	0
$656$	4.03157e6	0.365775
$657$	4.05152e6	0.366189
$658$	−17291.3	−0.00155691
$659$	5.88921e6	0.528255	0.264127	−	0.964488i	$-0.414916\pi$
$659$	5.88921e6	0.528255	0.264127	+	0.964488i	$0.414916\pi$
$660$	0	0
$661$	−1.57513e7	−1.40221	−0.701106	−	0.713057i	$-0.747310\pi$
$661$	−1.57513e7	−1.40221	−0.701106	+	0.713057i	$0.747310\pi$
$662$	−8518.40	−0.000755463 0
$663$	2.30791e6	0.203908
$664$	82388.7	0.00725182
$665$	0	0
$666$	70703.7	0.00617670
$667$	2.74176e7	2.38624
$668$	−3.74291e6	−0.324540
$669$	−6.43480e6	−0.555865
$670$	0	0
$671$	3.18499e6	0.273088
$672$	−248822.	−0.0212552
$673$	−1.18294e7	−1.00675	−0.503377	−	0.864067i	$-0.667909\pi$
$673$	−1.18294e7	−1.00675	−0.503377	+	0.864067i	$0.667909\pi$
$674$	39261.1	0.00332899
$675$	0	0
$676$	1.18248e7	0.995236
$677$	4.32713e6	0.362851	0.181425	−	0.983405i	$-0.441929\pi$
$677$	4.32713e6	0.362851	0.181425	+	0.983405i	$0.441929\pi$
$678$	73339.4	0.00612721
$679$	−9.41353e6	−0.783571
$680$	0	0
$681$	−3.96044e6	−0.327247
$682$	−32792.8	−0.00269971
$683$	−8.52031e6	−0.698882	−0.349441	−	0.936958i	$-0.613628\pi$
$683$	−8.52031e6	−0.698882	−0.349441	+	0.936958i	$0.613628\pi$
$684$	2.18672e7	1.78712
$685$	0	0
$686$	42389.8	0.00343915
$687$	3.80653e6	0.307707
$688$	1.89334e6	0.152496
$689$	−1.34673e6	−0.108077
$690$	0	0
$691$	1.34884e7	1.07465	0.537323	−	0.843377i	$-0.319436\pi$
$691$	1.34884e7	1.07465	0.537323	+	0.843377i	$0.319436\pi$
$692$	−6.42892e6	−0.510355
$693$	−5.79929e7	−4.58714
$694$	−2326.44	−0.000183355 0
$695$	0	0
$696$	−179773.	−0.0140670
$697$	8.21846e6	0.640779
$698$	−34660.2	−0.00269273
$699$	−3.32714e7	−2.57560
$700$	0	0
$701$	−6.05253e6	−0.465202	−0.232601	−	0.972572i	$-0.574724\pi$
$701$	−6.05253e6	−0.465202	−0.232601	+	0.972572i	$0.574724\pi$
$702$	−3222.25	−0.000246784 0
$703$	1.69403e7	1.29280
$704$	−1.94411e7	−1.47839
$705$	0	0
$706$	−62827.7	−0.00474395
$707$	−2.85631e7	−2.14910
$708$	1.12991e7	0.847148
$709$	2.18329e7	1.63116	0.815580	−	0.578645i	$-0.196418\pi$
$709$	2.18329e7	1.63116	0.815580	+	0.578645i	$0.196418\pi$
$710$	0	0
$711$	−1.38393e7	−1.02669
$712$	−50587.2	−0.00373973
$713$	1.41919e7	1.04548
$714$	−169075.	−0.0124118
$715$	0	0
$716$	−2.21347e7	−1.61359
$717$	2.32656e7	1.69012
$718$	44141.2	0.00319545
$719$	369938.	0.0266875	0.0133437	−	0.999911i	$-0.495752\pi$
$719$	369938.	0.0266875	0.0133437	+	0.999911i	$0.495752\pi$
$720$	0	0
$721$	1.70355e7	1.22044
$722$	2265.56	0.000161746 0
$723$	3.36069e6	0.239102
$724$	−2.09644e7	−1.48640
$725$	0	0
$726$	71062.8	0.00500381
$727$	1.94850e7	1.36730	0.683651	−	0.729809i	$-0.260391\pi$
$727$	1.94850e7	1.36730	0.683651	+	0.729809i	$0.260391\pi$
$728$	8281.90	0.000579164 0
$729$	−1.96192e7	−1.36729
$730$	0	0
$731$	3.85963e6	0.267148
$732$	4.51891e6	0.311714
$733$	−1.59332e7	−1.09533	−0.547664	−	0.836698i	$-0.684483\pi$
$733$	−1.59332e7	−1.09533	−0.547664	+	0.836698i	$0.684483\pi$
$734$	32135.0	0.00220160
$735$	0	0
$736$	−157823.	−0.0107393
$737$	−3.19431e6	−0.216625
$738$	−25007.3	−0.00169015
$739$	−1.57162e7	−1.05861	−0.529306	−	0.848431i	$-0.677548\pi$
$739$	−1.57162e7	−1.05861	−0.529306	+	0.848431i	$0.677548\pi$
$740$	0	0
$741$	−1.68257e6	−0.112571
$742$	98660.2	0.00657858
$743$	−2.32347e7	−1.54406	−0.772030	−	0.635586i	$-0.780759\pi$
$743$	−2.32347e7	−1.54406	−0.772030	+	0.635586i	$0.780759\pi$
$744$	−93054.0	−0.00616315
$745$	0	0
$746$	59748.0	0.00393076
$747$	4.08668e7	2.67960
$748$	−3.96317e7	−2.58993
$749$	1.98080e7	1.29014
$750$	0	0
$751$	1.87298e7	1.21181	0.605905	−	0.795537i	$-0.292811\pi$
$751$	1.87298e7	1.21181	0.605905	+	0.795537i	$0.292811\pi$
$752$	−5.75062e6	−0.370826
$753$	−2.82946e7	−1.81851
$754$	4487.72	0.000287473 0
$755$	0	0
$756$	−3.77541e7	−2.40248
$757$	−2.36855e7	−1.50225	−0.751125	−	0.660160i	$-0.770488\pi$
$757$	−2.36855e7	−1.50225	−0.751125	+	0.660160i	$0.770488\pi$
$758$	−11907.2	−0.000752728 0
$759$	−5.66895e7	−3.57189
$760$	0	0
$761$	−1.01343e7	−0.634356	−0.317178	−	0.948366i	$-0.602735\pi$
$761$	−1.01343e7	−0.634356	−0.317178	+	0.948366i	$0.602735\pi$
$762$	119016.	0.00742534
$763$	1.18875e7	0.739227
$764$	6.49797e6	0.402758
$765$	0	0
$766$	−28461.7	−0.00175263
$767$	−564126.	−0.0346248
$768$	−2.75828e7	−1.68746
$769$	6.41840e6	0.391391	0.195695	−	0.980665i	$-0.437304\pi$
$769$	6.41840e6	0.391391	0.195695	+	0.980665i	$0.437304\pi$
$770$	0	0
$771$	−2.53118e7	−1.53351
$772$	3.67891e6	0.222165
$773$	−2.69221e6	−0.162054	−0.0810271	−	0.996712i	$-0.525820\pi$
$773$	−2.69221e6	−0.162054	−0.0810271	+	0.996712i	$0.525820\pi$
$774$	−11744.1	−0.000704643 0
$775$	0	0
$776$	39149.7	0.00233385
$777$	−6.37422e7	−3.78769
$778$	22020.5	0.00130430
$779$	−5.99163e6	−0.353754
$780$	0	0
$781$	2.30669e7	1.35320
$782$	−107241.	−0.00627109
$783$	−4.09158e7	−2.38499
$784$	3.13077e7	1.81912
$785$	0	0
$786$	−33284.7	−0.00192171
$787$	1.56582e7	0.901166	0.450583	−	0.892735i	$-0.351216\pi$
$787$	1.56582e7	0.901166	0.450583	+	0.892735i	$0.351216\pi$
$788$	3.26905e7	1.87545
$789$	3.70215e7	2.11720
$790$	0	0
$791$	−4.29018e7	−2.43800
$792$	241185.	0.0136627
$793$	−225614.	−0.0127404
$794$	−35895.7	−0.00202065
$795$	0	0
$796$	−8.29946e6	−0.464266
$797$	−1.55223e7	−0.865588	−0.432794	−	0.901493i	$-0.642472\pi$
$797$	−1.55223e7	−0.865588	−0.432794	+	0.901493i	$0.642472\pi$
$798$	123263.	0.00685214
$799$	−1.17228e7	−0.649627
$800$	0	0
$801$	−2.50925e7	−1.38185
$802$	−1738.85	−9.54610e−5 0
$803$	5.35331e6	0.292977
$804$	−4.53212e6	−0.247264
$805$	0	0
$806$	2322.93	0.000125950 0
$807$	2.44934e7	1.32393
$808$	118790.	0.00640106
$809$	3.19772e7	1.71778	0.858892	−	0.512156i	$-0.171153\pi$
$809$	3.19772e7	1.71778	0.858892	+	0.512156i	$0.171153\pi$
$810$	0	0
$811$	−1.65261e7	−0.882305	−0.441152	−	0.897432i	$-0.645430\pi$
$811$	−1.65261e7	−0.882305	−0.441152	+	0.897432i	$0.645430\pi$
$812$	5.25812e7	2.79860
$813$	1.95849e7	1.03919
$814$	93421.4	0.00494180
$815$	0	0
$816$	−5.62296e7	−2.95624
$817$	−2.81384e6	−0.147484
$818$	39817.9	0.00208063
$819$	4.10803e6	0.214005
$820$	0	0
$821$	−2.40597e7	−1.24576	−0.622878	−	0.782319i	$-0.714037\pi$
$821$	−2.40597e7	−1.24576	−0.622878	+	0.782319i	$0.714037\pi$
$822$	−668.634	−3.45151e−5 0
$823$	−2.71752e7	−1.39853	−0.699266	−	0.714862i	$-0.746490\pi$
$823$	−2.71752e7	−1.39853	−0.699266	+	0.714862i	$0.746490\pi$
$824$	−70848.6	−0.00363507
$825$	0	0
$826$	41327.2	0.00210759
$827$	−3.69354e7	−1.87793	−0.938965	−	0.344012i	$-0.888214\pi$
$827$	−3.69354e7	−1.87793	−0.938965	+	0.344012i	$0.888214\pi$
$828$	−5.21892e7	−2.64548
$829$	3.52396e6	0.178092	0.0890459	−	0.996028i	$-0.471618\pi$
$829$	3.52396e6	0.178092	0.0890459	+	0.996028i	$0.471618\pi$
$830$	0	0
$831$	−4.53515e7	−2.27819
$832$	1.37714e6	0.0689717
$833$	6.38216e7	3.18680
$834$	−55277.3	−0.00275189
$835$	0	0
$836$	2.88933e7	1.42982
$837$	−2.11789e7	−1.04493
$838$	44456.2	0.00218687
$839$	3.63309e7	1.78185	0.890926	−	0.454148i	$-0.150056\pi$
$839$	3.63309e7	1.78185	0.890926	+	0.454148i	$0.150056\pi$
$840$	0	0
$841$	3.64734e7	1.77822
$842$	−47782.4	−0.00232267
$843$	4.11293e7	1.99334
$844$	3.02566e7	1.46206
$845$	0	0
$846$	35670.3	0.00171349
$847$	−4.15700e7	−1.99100
$848$	3.28116e7	1.56689
$849$	1.00365e7	0.477874
$850$	0	0
$851$	−4.04304e7	−1.91375
$852$	3.27276e7	1.54460
$853$	3.10795e7	1.46252	0.731259	−	0.682100i	$-0.238933\pi$
$853$	3.10795e7	1.46252	0.731259	+	0.682100i	$0.238933\pi$
$854$	16528.3	0.000775501 0
$855$	0	0
$856$	−82378.8	−0.00384265
$857$	3.40203e7	1.58229	0.791146	−	0.611628i	$-0.209485\pi$
$857$	3.40203e7	1.58229	0.791146	+	0.611628i	$0.209485\pi$
$858$	−9278.96	−0.000430310 0
$859$	1.05637e7	0.488465	0.244232	−	0.969717i	$-0.421464\pi$
$859$	1.05637e7	0.488465	0.244232	+	0.969717i	$0.421464\pi$
$860$	0	0
$861$	2.25451e7	1.03644
$862$	45228.3	0.00207320
$863$	1.94863e7	0.890641	0.445321	−	0.895371i	$-0.353090\pi$
$863$	1.94863e7	0.890641	0.445321	+	0.895371i	$0.353090\pi$
$864$	235522.	0.0107336
$865$	0	0
$866$	41869.9	0.00189718
$867$	−7.72739e7	−3.49128
$868$	2.72171e7	1.22615
$869$	−1.82860e7	−0.821427
$870$	0	0
$871$	226274.	0.0101062
$872$	−49438.4	−0.00220178
$873$	1.94192e7	0.862374
$874$	78183.4	0.00346207
$875$	0	0
$876$	7.59534e6	0.334416
$877$	−1.59110e7	−0.698550	−0.349275	−	0.937020i	$-0.613572\pi$
$877$	−1.59110e7	−0.698550	−0.349275	+	0.937020i	$0.613572\pi$
$878$	41610.6	0.00182166
$879$	−3.78588e7	−1.65270
$880$	0	0
$881$	3.03991e7	1.31953	0.659767	−	0.751470i	$-0.270655\pi$
$881$	3.03991e7	1.31953	0.659767	+	0.751470i	$0.270655\pi$
$882$	−194198.	−0.00840568
$883$	2.33259e7	1.00679	0.503393	−	0.864058i	$-0.332085\pi$
$883$	2.33259e7	1.00679	0.503393	+	0.864058i	$0.332085\pi$
$884$	2.80738e6	0.120829
$885$	0	0
$886$	11247.4	0.000481356 0
$887$	7.42685e6	0.316953	0.158477	−	0.987363i	$-0.449342\pi$
$887$	7.42685e6	0.316953	0.158477	+	0.987363i	$0.449342\pi$
$888$	265096.	0.0112816
$889$	−6.96213e7	−2.95452
$890$	0	0
$891$	1.98583e7	0.838008
$892$	−7.82739e6	−0.329386
$893$	8.54645e6	0.358638
$894$	−20288.1	−0.000848981 0
$895$	0	0
$896$	−403561.	−0.0167934
$897$	4.01570e6	0.166640
$898$	48401.8	0.00200295
$899$	2.94964e7	1.21722
$900$	0	0
$901$	6.68874e7	2.74494
$902$	−33042.3	−0.00135224
$903$	1.05878e7	0.432103
$904$	178423.	0.00726156
$905$	0	0
$906$	38739.1	0.00156794
$907$	−3.11849e7	−1.25871	−0.629356	−	0.777117i	$-0.716681\pi$
$907$	−3.11849e7	−1.25871	−0.629356	+	0.777117i	$0.716681\pi$
$908$	−4.81754e6	−0.193915
$909$	5.89228e7	2.36523
$910$	0	0
$911$	−2.79813e7	−1.11705	−0.558525	−	0.829488i	$-0.688632\pi$
$911$	−2.79813e7	−1.11705	−0.558525	+	0.829488i	$0.688632\pi$
$912$	4.09939e7	1.63205
$913$	5.39976e7	2.14387
$914$	59126.1	0.00234107
$915$	0	0
$916$	4.63032e6	0.182336
$917$	1.94708e7	0.764645
$918$	160038.	0.00626780
$919$	1.16013e7	0.453125	0.226563	−	0.973997i	$-0.427251\pi$
$919$	1.16013e7	0.453125	0.226563	+	0.973997i	$0.427251\pi$
$920$	0	0
$921$	2.25347e7	0.875392
$922$	68586.9	0.00265714
$923$	−1.63398e6	−0.0631311
$924$	−1.08719e8	−4.18913
$925$	0	0
$926$	9989.80	0.000382851 0
$927$	−3.51427e7	−1.34318
$928$	−328018.	−0.0125034
$929$	1.32455e7	0.503533	0.251767	−	0.967788i	$-0.418988\pi$
$929$	1.32455e7	0.503533	0.251767	+	0.967788i	$0.418988\pi$
$930$	0	0
$931$	−4.65289e7	−1.75933
$932$	−4.04719e7	−1.52621
$933$	−4.31087e7	−1.62129
$934$	−12361.3	−0.000463656 0
$935$	0	0
$936$	−17084.8	−0.000637410 0
$937$	2.72917e7	1.01550	0.507752	−	0.861503i	$-0.330477\pi$
$937$	2.72917e7	1.01550	0.507752	+	0.861503i	$0.330477\pi$
$938$	−16576.6	−0.000615160 0
$939$	−3.17966e7	−1.17684
$940$	0	0
$941$	4.79112e7	1.76385	0.881927	−	0.471386i	$-0.156246\pi$
$941$	4.79112e7	1.76385	0.881927	+	0.471386i	$0.156246\pi$
$942$	220083.	0.00808088
$943$	1.42999e7	0.523664
$944$	1.37443e7	0.501987
$945$	0	0
$946$	−15517.6	−0.000563764 0
$947$	1.39269e7	0.504639	0.252320	−	0.967644i	$-0.418807\pi$
$947$	1.39269e7	0.504639	0.252320	+	0.967644i	$0.418807\pi$
$948$	−2.59444e7	−0.937611
$949$	−379211.	−0.0136683
$950$	0	0
$951$	−5.65669e7	−2.02820
$952$	−411332.	−0.0147096
$953$	2.89937e7	1.03412	0.517061	−	0.855948i	$-0.327026\pi$
$953$	2.89937e7	1.03412	0.517061	+	0.855948i	$0.327026\pi$
$954$	−203526.	−0.00724019
$955$	0	0
$956$	2.83007e7	1.00150
$957$	−1.17823e8	−4.15864
$958$	39513.4	0.00139101
$959$	391135.	0.0137335
$960$	0	0
$961$	−1.33612e7	−0.466700
$962$	−6617.66	−0.000230551 0
$963$	−4.08619e7	−1.41988
$964$	4.08800e6	0.141683
$965$	0	0
$966$	−294185.	−0.0101433
$967$	4.85479e7	1.66957	0.834784	−	0.550578i	$-0.185593\pi$
$967$	4.85479e7	1.66957	0.834784	+	0.550578i	$0.185593\pi$
$968$	172884.	0.00593017
$969$	8.35672e7	2.85908
$970$	0	0
$971$	−1.14183e7	−0.388646	−0.194323	−	0.980938i	$-0.562251\pi$
$971$	−1.14183e7	−0.388646	−0.194323	+	0.980938i	$0.562251\pi$
$972$	−1.39717e7	−0.474334
$973$	3.23359e7	1.09497
$974$	−97924.7	−0.00330746
$975$	0	0
$976$	5.49684e6	0.184709
$977$	−2.40381e7	−0.805684	−0.402842	−	0.915270i	$-0.631978\pi$
$977$	−2.40381e7	−0.805684	−0.402842	+	0.915270i	$0.631978\pi$
$978$	−164945.	−0.00551434
$979$	−3.31549e7	−1.10558
$980$	0	0
$981$	−2.45227e7	−0.813570
$982$	−27211.2	−0.000900469 0
$983$	4.39101e7	1.44937	0.724687	−	0.689078i	$-0.241984\pi$
$983$	4.39101e7	1.44937	0.724687	+	0.689078i	$0.241984\pi$
$984$	−93762.0	−0.00308702
$985$	0	0
$986$	−222889.	−0.00730122
$987$	−3.21582e7	−1.05075
$988$	−2.04671e6	−0.0667058
$989$	6.71564e6	0.218322
$990$	0	0
$991$	−2.86491e7	−0.926673	−0.463337	−	0.886182i	$-0.653348\pi$
$991$	−2.86491e7	−0.926673	−0.463337	+	0.886182i	$0.653348\pi$
$992$	−169789.	−0.00547810
$993$	−1.58424e7	−0.509857
$994$	119704.	0.00384275
$995$	0	0
$996$	7.66125e7	2.44710
$997$	−4.64759e7	−1.48078	−0.740389	−	0.672179i	$-0.765359\pi$
$997$	−4.64759e7	−1.48078	−0.740389	+	0.672179i	$0.765359\pi$
$998$	−79533.4	−0.00252769
$999$	6.03351e7	1.91274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.f.1.12		22
5.4	even	2		215.6.a.d.1.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.a.d.1.11	✓	22	5.4	even	2
1075.6.a.f.1.12		22	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0141449 q^{2} -26.3066 q^{3} -31.9998 q^{4} +0.372106 q^{6} -217.673 q^{7} +0.905274 q^{8} +449.038 q^{9} +O(q^{10})\)	\(q-0.0141449 q^{2} -26.3066 q^{3} -31.9998 q^{4} +0.372106 q^{6} -217.673 q^{7} +0.905274 q^{8} +449.038 q^{9} +593.318 q^{11} +841.806 q^{12} -42.0287 q^{13} +3.07897 q^{14} +1023.98 q^{16} +2087.41 q^{17} -6.35162 q^{18} -1521.82 q^{19} +5726.24 q^{21} -8.39244 q^{22} +3632.04 q^{23} -23.8147 q^{24} +0.594493 q^{26} -5420.17 q^{27} +6965.49 q^{28} +7548.81 q^{29} +3907.42 q^{31} -43.4529 q^{32} -15608.2 q^{33} -29.5263 q^{34} -14369.1 q^{36} -11131.6 q^{37} +21.5260 q^{38} +1105.63 q^{39} +3937.15 q^{41} -80.9973 q^{42} +1849.00 q^{43} -18986.0 q^{44} -51.3750 q^{46} -5615.94 q^{47} -26937.5 q^{48} +30574.5 q^{49} -54912.8 q^{51} +1344.91 q^{52} +32043.2 q^{53} +76.6679 q^{54} -197.054 q^{56} +40033.9 q^{57} -106.778 q^{58} +13422.4 q^{59} +5368.11 q^{61} -55.2702 q^{62} -97743.5 q^{63} -32766.8 q^{64} +220.777 q^{66} -5383.80 q^{67} -66796.8 q^{68} -95546.6 q^{69} +38877.8 q^{71} +406.502 q^{72} +9022.67 q^{73} +157.456 q^{74} +48697.9 q^{76} -129149. q^{77} -15.6391 q^{78} -30819.9 q^{79} +33470.0 q^{81} -55.6908 q^{82} +91009.7 q^{83} -183239. q^{84} -26.1540 q^{86} -198584. q^{87} +537.115 q^{88} -55880.5 q^{89} +9148.51 q^{91} -116224. q^{92} -102791. q^{93} +79.4372 q^{94} +1143.10 q^{96} +43246.2 q^{97} -432.475 q^{98} +266422. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9}+O(q^{10}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9} + 1206 q^{11} - 2175 q^{12} - 1942 q^{13} + 2531 q^{14} + 8851 q^{16} - 2470 q^{17} - 1279 q^{18} + 3020 q^{19} + 5632 q^{21} + 3227 q^{22} + 1326 q^{23} + 11040 q^{24} - 3415 q^{26} - 5156 q^{27} + 11489 q^{28} + 17906 q^{29} + 7982 q^{31} - 2427 q^{32} - 10100 q^{33} + 25248 q^{34} - 14813 q^{36} - 22640 q^{37} + 13695 q^{38} + 29048 q^{39} + 29112 q^{41} - 9163 q^{42} + 40678 q^{43} + 63924 q^{44} - 14944 q^{46} - 57080 q^{47} - 54894 q^{48} + 165560 q^{49} - 1576 q^{51} - 97639 q^{52} + 8054 q^{53} + 167379 q^{54} + 269326 q^{56} - 125424 q^{57} - 49485 q^{58} + 193484 q^{59} + 107466 q^{61} - 162441 q^{62} - 183778 q^{63} + 412603 q^{64} + 240489 q^{66} - 109764 q^{67} - 144300 q^{68} + 202444 q^{69} + 182964 q^{71} - 341504 q^{72} - 134468 q^{73} + 198067 q^{74} + 247729 q^{76} + 28416 q^{77} + 7286 q^{78} + 11148 q^{79} + 385246 q^{81} - 23657 q^{82} - 33850 q^{83} + 176749 q^{84} - 9245 q^{86} + 298280 q^{87} + 111354 q^{88} + 244912 q^{89} + 158092 q^{91} + 124762 q^{92} - 239860 q^{93} - 192166 q^{94} - 147719 q^{96} - 232826 q^{97} + 482463 q^{98} - 346894 q^{99}+O(q^{100}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9 + 1206 * q^11 - 2175 * q^12 - 1942 * q^13 + 2531 * q^14 + 8851 * q^16 - 2470 * q^17 - 1279 * q^18 + 3020 * q^19 + 5632 * q^21 + 3227 * q^22 + 1326 * q^23 + 11040 * q^24 - 3415 * q^26 - 5156 * q^27 + 11489 * q^28 + 17906 * q^29 + 7982 * q^31 - 2427 * q^32 - 10100 * q^33 + 25248 * q^34 - 14813 * q^36 - 22640 * q^37 + 13695 * q^38 + 29048 * q^39 + 29112 * q^41 - 9163 * q^42 + 40678 * q^43 + 63924 * q^44 - 14944 * q^46 - 57080 * q^47 - 54894 * q^48 + 165560 * q^49 - 1576 * q^51 - 97639 * q^52 + 8054 * q^53 + 167379 * q^54 + 269326 * q^56 - 125424 * q^57 - 49485 * q^58 + 193484 * q^59 + 107466 * q^61 - 162441 * q^62 - 183778 * q^63 + 412603 * q^64 + 240489 * q^66 - 109764 * q^67 - 144300 * q^68 + 202444 * q^69 + 182964 * q^71 - 341504 * q^72 - 134468 * q^73 + 198067 * q^74 + 247729 * q^76 + 28416 * q^77 + 7286 * q^78 + 11148 * q^79 + 385246 * q^81 - 23657 * q^82 - 33850 * q^83 + 176749 * q^84 - 9245 * q^86 + 298280 * q^87 + 111354 * q^88 + 244912 * q^89 + 158092 * q^91 + 124762 * q^92 - 239860 * q^93 - 192166 * q^94 - 147719 * q^96 - 232826 * q^97 + 482463 * q^98 - 346894 * q^99

Introduction

L-functions

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Varieties

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Database

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