LMFDB - Embedded newform 650.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,6,Mod(1,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, 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("650.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	650.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:	$104.249482878$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{10}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 10 $ x^2 - 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 130)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.16228$ of defining polynomial
Character	$\chi$	$=$	650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -13.8114 q^{3} +16.0000 q^{4} -55.2456 q^{6} -213.246 q^{7} +64.0000 q^{8} -52.2456 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -13.8114 q^{3} +16.0000 q^{4} -55.2456 q^{6} -213.246 q^{7} +64.0000 q^{8} -52.2456 q^{9} +587.285 q^{11} -220.982 q^{12} +169.000 q^{13} -852.982 q^{14} +256.000 q^{16} -162.605 q^{17} -208.982 q^{18} -81.3914 q^{19} +2945.22 q^{21} +2349.14 q^{22} +2948.84 q^{23} -883.929 q^{24} +676.000 q^{26} +4077.75 q^{27} -3411.93 q^{28} +6254.43 q^{29} -4034.62 q^{31} +1024.00 q^{32} -8111.22 q^{33} -650.420 q^{34} -835.929 q^{36} -7617.22 q^{37} -325.566 q^{38} -2334.12 q^{39} +958.121 q^{41} +11780.9 q^{42} -169.655 q^{43} +9396.56 q^{44} +11795.4 q^{46} -21612.6 q^{47} -3535.72 q^{48} +28666.7 q^{49} +2245.80 q^{51} +2704.00 q^{52} -24789.1 q^{53} +16311.0 q^{54} -13647.7 q^{56} +1124.13 q^{57} +25017.7 q^{58} +40109.2 q^{59} -16343.0 q^{61} -16138.5 q^{62} +11141.1 q^{63} +4096.00 q^{64} -32444.9 q^{66} -18362.1 q^{67} -2601.68 q^{68} -40727.6 q^{69} -77846.0 q^{71} -3343.72 q^{72} +62130.2 q^{73} -30468.9 q^{74} -1302.26 q^{76} -125236. q^{77} -9336.50 q^{78} -60599.1 q^{79} -43623.7 q^{81} +3832.48 q^{82} +2654.46 q^{83} +47123.5 q^{84} -678.619 q^{86} -86382.4 q^{87} +37586.2 q^{88} +8229.77 q^{89} -36038.5 q^{91} +47181.5 q^{92} +55723.7 q^{93} -86450.3 q^{94} -14142.9 q^{96} +53844.0 q^{97} +114667. q^{98} -30683.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 4 q^{3} + 32 q^{4} + 16 q^{6} - 300 q^{7} + 128 q^{8} + 22 q^{9}+O(q^{10}) $ 2 * q + 8 * q^2 + 4 * q^3 + 32 * q^4 + 16 * q^6 - 300 * q^7 + 128 * q^8 + 22 * q^9	\( 2 q + 8 q^{2} + 4 q^{3} + 32 q^{4} + 16 q^{6} - 300 q^{7} + 128 q^{8} + 22 q^{9} + 384 q^{11} + 64 q^{12} + 338 q^{13} - 1200 q^{14} + 512 q^{16} + 244 q^{17} + 88 q^{18} - 2408 q^{19} + 1400 q^{21} + 1536 q^{22} - 332 q^{23} + 256 q^{24} + 1352 q^{26} + 1072 q^{27} - 4800 q^{28} + 3528 q^{29} + 880 q^{31} + 2048 q^{32} - 11732 q^{33} + 976 q^{34} + 352 q^{36} - 10744 q^{37} - 9632 q^{38} + 676 q^{39} + 16020 q^{41} + 5600 q^{42} - 2964 q^{43} + 6144 q^{44} - 1328 q^{46} - 38292 q^{47} + 1024 q^{48} + 19386 q^{49} + 9488 q^{51} + 5408 q^{52} - 42052 q^{53} + 4288 q^{54} - 19200 q^{56} - 40316 q^{57} + 14112 q^{58} + 42872 q^{59} - 33192 q^{61} + 3520 q^{62} + 4700 q^{63} + 8192 q^{64} - 46928 q^{66} - 37420 q^{67} + 3904 q^{68} - 99164 q^{69} - 69520 q^{71} + 1408 q^{72} + 12632 q^{73} - 42976 q^{74} - 38528 q^{76} - 107600 q^{77} + 2704 q^{78} + 35208 q^{79} - 115202 q^{81} + 64080 q^{82} - 31500 q^{83} + 22400 q^{84} - 11856 q^{86} - 134944 q^{87} + 24576 q^{88} - 18452 q^{89} - 50700 q^{91} - 5312 q^{92} + 143260 q^{93} - 153168 q^{94} + 4096 q^{96} + 28884 q^{97} + 77544 q^{98} - 45776 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 4 * q^3 + 32 * q^4 + 16 * q^6 - 300 * q^7 + 128 * q^8 + 22 * q^9 + 384 * q^11 + 64 * q^12 + 338 * q^13 - 1200 * q^14 + 512 * q^16 + 244 * q^17 + 88 * q^18 - 2408 * q^19 + 1400 * q^21 + 1536 * q^22 - 332 * q^23 + 256 * q^24 + 1352 * q^26 + 1072 * q^27 - 4800 * q^28 + 3528 * q^29 + 880 * q^31 + 2048 * q^32 - 11732 * q^33 + 976 * q^34 + 352 * q^36 - 10744 * q^37 - 9632 * q^38 + 676 * q^39 + 16020 * q^41 + 5600 * q^42 - 2964 * q^43 + 6144 * q^44 - 1328 * q^46 - 38292 * q^47 + 1024 * q^48 + 19386 * q^49 + 9488 * q^51 + 5408 * q^52 - 42052 * q^53 + 4288 * q^54 - 19200 * q^56 - 40316 * q^57 + 14112 * q^58 + 42872 * q^59 - 33192 * q^61 + 3520 * q^62 + 4700 * q^63 + 8192 * q^64 - 46928 * q^66 - 37420 * q^67 + 3904 * q^68 - 99164 * q^69 - 69520 * q^71 + 1408 * q^72 + 12632 * q^73 - 42976 * q^74 - 38528 * q^76 - 107600 * q^77 + 2704 * q^78 + 35208 * q^79 - 115202 * q^81 + 64080 * q^82 - 31500 * q^83 + 22400 * q^84 - 11856 * q^86 - 134944 * q^87 + 24576 * q^88 - 18452 * q^89 - 50700 * q^91 - 5312 * q^92 + 143260 * q^93 - 153168 * q^94 + 4096 * q^96 + 28884 * q^97 + 77544 * q^98 - 45776 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−13.8114	−0.886001	−0.443000	−	0.896521i	$-0.646086\pi$
$3$	−13.8114	−0.886001	−0.443000	+	0.896521i	$0.646086\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−55.2456	−0.626497
$7$	−213.246	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$7$	−213.246	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$8$	64.0000	0.353553
$9$	−52.2456	−0.215002
$10$	0	0
$11$	587.285	1.46341	0.731707	−	0.681620i	$-0.238724\pi$
$11$	587.285	1.46341	0.731707	+	0.681620i	$0.238724\pi$
$12$	−220.982	−0.443000
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−852.982	−1.16311
$15$	0	0
$16$	256.000	0.250000
$17$	−162.605	−0.136462	−0.0682310	−	0.997670i	$-0.521735\pi$
$17$	−162.605	−0.136462	−0.0682310	+	0.997670i	$0.521735\pi$
$18$	−208.982	−0.152030
$19$	−81.3914	−0.0517243	−0.0258622	−	0.999666i	$-0.508233\pi$
$19$	−81.3914	−0.0517243	−0.0258622	+	0.999666i	$0.508233\pi$
$20$	0	0
$21$	2945.22	1.45737
$22$	2349.14	1.03479
$23$	2948.84	1.16234	0.581169	−	0.813783i	$-0.302596\pi$
$23$	2948.84	1.16234	0.581169	+	0.813783i	$0.302596\pi$
$24$	−883.929	−0.313249
$25$	0	0
$26$	676.000	0.196116
$27$	4077.75	1.07649
$28$	−3411.93	−0.822441
$29$	6254.43	1.38100	0.690499	−	0.723333i	$-0.257391\pi$
$29$	6254.43	1.38100	0.690499	+	0.723333i	$0.257391\pi$
$30$	0	0
$31$	−4034.62	−0.754048	−0.377024	−	0.926204i	$-0.623052\pi$
$31$	−4034.62	−0.754048	−0.377024	+	0.926204i	$0.623052\pi$
$32$	1024.00	0.176777
$33$	−8111.22	−1.29659
$34$	−650.420	−0.0964932
$35$	0	0
$36$	−835.929	−0.107501
$37$	−7617.22	−0.914728	−0.457364	−	0.889280i	$-0.651206\pi$
$37$	−7617.22	−0.914728	−0.457364	+	0.889280i	$0.651206\pi$
$38$	−325.566	−0.0365746
$39$	−2334.12	−0.245732
$40$	0	0
$41$	958.121	0.0890145	0.0445072	−	0.999009i	$-0.485828\pi$
$41$	958.121	0.0890145	0.0445072	+	0.999009i	$0.485828\pi$
$42$	11780.9	1.03051
$43$	−169.655	−0.0139925	−0.00699624	−	0.999976i	$-0.502227\pi$
$43$	−169.655	−0.0139925	−0.00699624	+	0.999976i	$0.502227\pi$
$44$	9396.56	0.731707
$45$	0	0
$46$	11795.4	0.821897
$47$	−21612.6	−1.42712	−0.713562	−	0.700592i	$-0.752919\pi$
$47$	−21612.6	−1.42712	−0.713562	+	0.700592i	$0.752919\pi$
$48$	−3535.72	−0.221500
$49$	28666.7	1.70564
$50$	0	0
$51$	2245.80	0.120905
$52$	2704.00	0.138675
$53$	−24789.1	−1.21219	−0.606096	−	0.795392i	$-0.707265\pi$
$53$	−24789.1	−1.21219	−0.606096	+	0.795392i	$0.707265\pi$
$54$	16311.0	0.761196
$55$	0	0
$56$	−13647.7	−0.581554
$57$	1124.13	0.0458278
$58$	25017.7	0.976513
$59$	40109.2	1.50008	0.750040	−	0.661392i	$-0.230034\pi$
$59$	40109.2	1.50008	0.750040	+	0.661392i	$0.230034\pi$
$60$	0	0
$61$	−16343.0	−0.562351	−0.281176	−	0.959656i	$-0.590724\pi$
$61$	−16343.0	−0.562351	−0.281176	+	0.959656i	$0.590724\pi$
$62$	−16138.5	−0.533192
$63$	11141.1	0.353653
$64$	4096.00	0.125000
$65$	0	0
$66$	−32444.9	−0.916824
$67$	−18362.1	−0.499731	−0.249866	−	0.968281i	$-0.580386\pi$
$67$	−18362.1	−0.499731	−0.249866	+	0.968281i	$0.580386\pi$
$68$	−2601.68	−0.0682310
$69$	−40727.6	−1.02983
$70$	0	0
$71$	−77846.0	−1.83270	−0.916348	−	0.400382i	$-0.868877\pi$
$71$	−77846.0	−1.83270	−0.916348	+	0.400382i	$0.868877\pi$
$72$	−3343.72	−0.0760148
$73$	62130.2	1.36457	0.682285	−	0.731087i	$-0.260986\pi$
$73$	62130.2	1.36457	0.682285	+	0.731087i	$0.260986\pi$
$74$	−30468.9	−0.646810
$75$	0	0
$76$	−1302.26	−0.0258622
$77$	−125236.	−2.40714
$78$	−9336.50	−0.173759
$79$	−60599.1	−1.09244	−0.546221	−	0.837641i	$-0.683934\pi$
$79$	−60599.1	−1.09244	−0.546221	+	0.837641i	$0.683934\pi$
$80$	0	0
$81$	−43623.7	−0.738772
$82$	3832.48	0.0629427
$83$	2654.46	0.0422941	0.0211471	−	0.999776i	$-0.493268\pi$
$83$	2654.46	0.0422941	0.0211471	+	0.999776i	$0.493268\pi$
$84$	47123.5	0.728684
$85$	0	0
$86$	−678.619	−0.00989418
$87$	−86382.4	−1.22357
$88$	37586.2	0.517395
$89$	8229.77	0.110132	0.0550659	−	0.998483i	$-0.482463\pi$
$89$	8229.77	0.110132	0.0550659	+	0.998483i	$0.482463\pi$
$90$	0	0
$91$	−36038.5	−0.456208
$92$	47181.5	0.581169
$93$	55723.7	0.668087
$94$	−86450.3	−1.00913
$95$	0	0
$96$	−14142.9	−0.156624
$97$	53844.0	0.581042	0.290521	−	0.956869i	$-0.406171\pi$
$97$	53844.0	0.581042	0.290521	+	0.956869i	$0.406171\pi$
$98$	114667.	1.20607
$99$	−30683.0	−0.314637
$100$	0	0
$101$	−167556.	−1.63439	−0.817196	−	0.576360i	$-0.804473\pi$
$101$	−167556.	−1.63439	−0.817196	+	0.576360i	$0.804473\pi$
$102$	8983.20	0.0854930
$103$	−30973.8	−0.287675	−0.143837	−	0.989601i	$-0.545944\pi$
$103$	−30973.8	−0.287675	−0.143837	+	0.989601i	$0.545944\pi$
$104$	10816.0	0.0980581
$105$	0	0
$106$	−99156.4	−0.857149
$107$	97343.8	0.821956	0.410978	−	0.911645i	$-0.365187\pi$
$107$	97343.8	0.821956	0.410978	+	0.911645i	$0.365187\pi$
$108$	65244.0	0.538247
$109$	16696.8	0.134607	0.0673035	−	0.997733i	$-0.478560\pi$
$109$	16696.8	0.134607	0.0673035	+	0.997733i	$0.478560\pi$
$110$	0	0
$111$	105204.	0.810450
$112$	−54590.9	−0.411221
$113$	−219357.	−1.61605	−0.808027	−	0.589145i	$-0.799465\pi$
$113$	−219357.	−1.61605	−0.808027	+	0.589145i	$0.799465\pi$
$114$	4496.51	0.0324051
$115$	0	0
$116$	100071.	0.690499
$117$	−8829.50	−0.0596309
$118$	160437.	1.06072
$119$	34674.8	0.224464
$120$	0	0
$121$	183852.	1.14158
$122$	−65372.1	−0.397642
$123$	−13233.0	−0.0788669
$124$	−64554.0	−0.377024
$125$	0	0
$126$	44564.5	0.250071
$127$	−158753.	−0.873399	−0.436700	−	0.899607i	$-0.643853\pi$
$127$	−158753.	−0.873399	−0.436700	+	0.899607i	$0.643853\pi$
$128$	16384.0	0.0883883
$129$	2343.17	0.0123974
$130$	0	0
$131$	160566.	0.817477	0.408739	−	0.912651i	$-0.365969\pi$
$131$	160566.	0.817477	0.408739	+	0.912651i	$0.365969\pi$
$132$	−129779.	−0.648293
$133$	17356.4	0.0850804
$134$	−73448.6	−0.353363
$135$	0	0
$136$	−10406.7	−0.0482466
$137$	295668.	1.34587	0.672934	−	0.739702i	$-0.265034\pi$
$137$	295668.	1.34587	0.672934	+	0.739702i	$0.265034\pi$
$138$	−162910.	−0.728201
$139$	6197.57	0.0272072	0.0136036	−	0.999907i	$-0.495670\pi$
$139$	6197.57	0.0272072	0.0136036	+	0.999907i	$0.495670\pi$
$140$	0	0
$141$	298500.	1.26443
$142$	−311384.	−1.29591
$143$	99251.1	0.405878
$144$	−13374.9	−0.0537506
$145$	0	0
$146$	248521.	0.964896
$147$	−395926.	−1.51120
$148$	−121875.	−0.457364
$149$	−371033.	−1.36914	−0.684569	−	0.728948i	$-0.740010\pi$
$149$	−371033.	−1.36914	−0.684569	+	0.728948i	$0.740010\pi$
$150$	0	0
$151$	−508361.	−1.81439	−0.907193	−	0.420714i	$-0.861780\pi$
$151$	−508361.	−1.81439	−0.907193	+	0.420714i	$0.861780\pi$
$152$	−5209.05	−0.0182873
$153$	8495.39	0.0293396
$154$	−500943.	−1.70211
$155$	0	0
$156$	−37346.0	−0.122866
$157$	−60014.9	−0.194317	−0.0971583	−	0.995269i	$-0.530975\pi$
$157$	−60014.9	−0.194317	−0.0971583	+	0.995269i	$0.530975\pi$
$158$	−242397.	−0.772474
$159$	342372.	1.07400
$160$	0	0
$161$	−628828.	−1.91191
$162$	−174495.	−0.522391
$163$	365913.	1.07872	0.539360	−	0.842075i	$-0.318666\pi$
$163$	365913.	1.07872	0.539360	+	0.842075i	$0.318666\pi$
$164$	15329.9	0.0445072
$165$	0	0
$166$	10617.8	0.0299065
$167$	−67392.0	−0.186990	−0.0934948	−	0.995620i	$-0.529804\pi$
$167$	−67392.0	−0.186990	−0.0934948	+	0.995620i	$0.529804\pi$
$168$	188494.	0.515257
$169$	28561.0	0.0769231
$170$	0	0
$171$	4252.34	0.0111208
$172$	−2714.48	−0.00699624
$173$	−518921.	−1.31821	−0.659107	−	0.752049i	$-0.729066\pi$
$173$	−518921.	−1.31821	−0.659107	+	0.752049i	$0.729066\pi$
$174$	−345530.	−0.865191
$175$	0	0
$176$	150345.	0.365853
$177$	−553964.	−1.32907
$178$	32919.1	0.0778750
$179$	−89728.6	−0.209314	−0.104657	−	0.994508i	$-0.533374\pi$
$179$	−89728.6	−0.209314	−0.104657	+	0.994508i	$0.533374\pi$
$180$	0	0
$181$	−376272.	−0.853700	−0.426850	−	0.904322i	$-0.640377\pi$
$181$	−376272.	−0.853700	−0.426850	+	0.904322i	$0.640377\pi$
$182$	−144154.	−0.322588
$183$	225720.	0.498244
$184$	188726.	0.410948
$185$	0	0
$186$	222895.	0.472409
$187$	−95495.4	−0.199700
$188$	−345801.	−0.713562
$189$	−869562.	−1.77070
$190$	0	0
$191$	206748.	0.410070	0.205035	−	0.978755i	$-0.434269\pi$
$191$	206748.	0.410070	0.205035	+	0.978755i	$0.434269\pi$
$192$	−56571.4	−0.110750
$193$	413088.	0.798269	0.399135	−	0.916892i	$-0.369311\pi$
$193$	413088.	0.798269	0.399135	+	0.916892i	$0.369311\pi$
$194$	215376.	0.410859
$195$	0	0
$196$	458667.	0.852819
$197$	−538825.	−0.989196	−0.494598	−	0.869122i	$-0.664685\pi$
$197$	−538825.	−0.989196	−0.494598	+	0.869122i	$0.664685\pi$
$198$	−122732.	−0.222482
$199$	−147336.	−0.263740	−0.131870	−	0.991267i	$-0.542098\pi$
$199$	−147336.	−0.263740	−0.131870	+	0.991267i	$0.542098\pi$
$200$	0	0
$201$	253607.	0.442762
$202$	−670223.	−1.15569
$203$	−1.33373e6	−2.27158
$204$	35932.8	0.0604527
$205$	0	0
$206$	−123895.	−0.203417
$207$	−154064.	−0.249905
$208$	43264.0	0.0693375
$209$	−47799.9	−0.0756940
$210$	0	0
$211$	−1.14921e6	−1.77703	−0.888515	−	0.458847i	$-0.848262\pi$
$211$	−1.14921e6	−1.77703	−0.888515	+	0.458847i	$0.848262\pi$
$212$	−396626.	−0.606096
$213$	1.07516e6	1.62377
$214$	389375.	0.581211
$215$	0	0
$216$	260976.	0.380598
$217$	860365.	1.24032
$218$	66787.3	0.0951815
$219$	−858104.	−1.20901
$220$	0	0
$221$	−27480.2	−0.0378477
$222$	420817.	0.573075
$223$	1.39430e6	1.87756	0.938782	−	0.344513i	$-0.111956\pi$
$223$	1.39430e6	1.87756	0.938782	+	0.344513i	$0.111956\pi$
$224$	−218363.	−0.290777
$225$	0	0
$226$	−877429.	−1.14272
$227$	−1.40291e6	−1.80703	−0.903515	−	0.428556i	$-0.859023\pi$
$227$	−1.40291e6	−1.80703	−0.903515	+	0.428556i	$0.859023\pi$
$228$	17986.1	0.0229139
$229$	−796626.	−1.00384	−0.501922	−	0.864913i	$-0.667373\pi$
$229$	−796626.	−1.00384	−0.501922	+	0.864913i	$0.667373\pi$
$230$	0	0
$231$	1.72968e6	2.13273
$232$	400284.	0.488257
$233$	−1.15975e6	−1.39951	−0.699753	−	0.714385i	$-0.746707\pi$
$233$	−1.15975e6	−1.39951	−0.699753	+	0.714385i	$0.746707\pi$
$234$	−35318.0	−0.0421654
$235$	0	0
$236$	641748.	0.750040
$237$	836958.	0.967905
$238$	138699.	0.158720
$239$	−687529.	−0.778568	−0.389284	−	0.921118i	$-0.627278\pi$
$239$	−687529.	−0.778568	−0.389284	+	0.921118i	$0.627278\pi$
$240$	0	0
$241$	−391345.	−0.434028	−0.217014	−	0.976169i	$-0.569632\pi$
$241$	−391345.	−0.434028	−0.217014	+	0.976169i	$0.569632\pi$
$242$	735409.	0.807218
$243$	−388389.	−0.421941
$244$	−261488.	−0.281176
$245$	0	0
$246$	−52931.9	−0.0557673
$247$	−13755.2	−0.0143457
$248$	−258216.	−0.266596
$249$	−36661.7	−0.0374727
$250$	0	0
$251$	944723.	0.946499	0.473249	−	0.880928i	$-0.343081\pi$
$251$	944723.	0.946499	0.473249	+	0.880928i	$0.343081\pi$
$252$	178258.	0.176827
$253$	1.73181e6	1.70098
$254$	−635012.	−0.617587
$255$	0	0
$256$	65536.0	0.0625000
$257$	−297219.	−0.280701	−0.140351	−	0.990102i	$-0.544823\pi$
$257$	−297219.	−0.280701	−0.140351	+	0.990102i	$0.544823\pi$
$258$	9372.67	0.00876626
$259$	1.62434e6	1.50462
$260$	0	0
$261$	−326766.	−0.296918
$262$	642264.	0.578044
$263$	1.53097e6	1.36483	0.682414	−	0.730966i	$-0.260930\pi$
$263$	1.53097e6	1.36483	0.682414	+	0.730966i	$0.260930\pi$
$264$	−519118.	−0.458412
$265$	0	0
$266$	69425.4	0.0601609
$267$	−113665.	−0.0975769
$268$	−293794.	−0.249866
$269$	−1.00878e6	−0.849994	−0.424997	−	0.905195i	$-0.639725\pi$
$269$	−1.00878e6	−0.849994	−0.424997	+	0.905195i	$0.639725\pi$
$270$	0	0
$271$	2.19122e6	1.81244	0.906220	−	0.422806i	$-0.138955\pi$
$271$	2.19122e6	1.81244	0.906220	+	0.422806i	$0.138955\pi$
$272$	−41626.9	−0.0341155
$273$	497742.	0.404201
$274$	1.18267e6	0.951673
$275$	0	0
$276$	−651642.	−0.514916
$277$	17924.0	0.0140357	0.00701786	−	0.999975i	$-0.497766\pi$
$277$	17924.0	0.0140357	0.00701786	+	0.999975i	$0.497766\pi$
$278$	24790.3	0.0192384
$279$	210791.	0.162122
$280$	0	0
$281$	−2.40663e6	−1.81821	−0.909106	−	0.416566i	$-0.863234\pi$
$281$	−2.40663e6	−1.81821	−0.909106	+	0.416566i	$0.863234\pi$
$282$	1.19400e6	0.894090
$283$	1.36921e6	1.01626	0.508128	−	0.861281i	$-0.330338\pi$
$283$	1.36921e6	1.01626	0.508128	+	0.861281i	$0.330338\pi$
$284$	−1.24554e6	−0.916348
$285$	0	0
$286$	397004.	0.286999
$287$	−204315.	−0.146418
$288$	−53499.4	−0.0380074
$289$	−1.39342e6	−0.981378
$290$	0	0
$291$	−743660.	−0.514804
$292$	994083.	0.682285
$293$	390649.	0.265838	0.132919	−	0.991127i	$-0.457565\pi$
$293$	390649.	0.265838	0.132919	+	0.991127i	$0.457565\pi$
$294$	−1.58371e6	−1.06858
$295$	0	0
$296$	−487502.	−0.323405
$297$	2.39480e6	1.57535
$298$	−1.48413e6	−0.968127
$299$	498355.	0.322374
$300$	0	0
$301$	36178.1	0.0230160
$302$	−2.03344e6	−1.28297
$303$	2.31418e6	1.44807
$304$	−20836.2	−0.0129311
$305$	0	0
$306$	33981.6	0.0207463
$307$	−566546.	−0.343075	−0.171537	−	0.985178i	$-0.554873\pi$
$307$	−566546.	−0.343075	−0.171537	+	0.985178i	$0.554873\pi$
$308$	−2.00377e6	−1.20357
$309$	427791.	0.254880
$310$	0	0
$311$	881239.	0.516646	0.258323	−	0.966059i	$-0.416830\pi$
$311$	881239.	0.516646	0.258323	+	0.966059i	$0.416830\pi$
$312$	−149384.	−0.0868795
$313$	916421.	0.528731	0.264365	−	0.964423i	$-0.414838\pi$
$313$	916421.	0.528731	0.264365	+	0.964423i	$0.414838\pi$
$314$	−240060.	−0.137403
$315$	0	0
$316$	−969586.	−0.546221
$317$	−2.01084e6	−1.12390	−0.561951	−	0.827170i	$-0.689949\pi$
$317$	−2.01084e6	−1.12390	−0.561951	+	0.827170i	$0.689949\pi$
$318$	1.36949e6	0.759435
$319$	3.67313e6	2.02097
$320$	0	0
$321$	−1.34445e6	−0.728254
$322$	−2.51531e6	−1.35192
$323$	13234.7	0.00705840
$324$	−697980.	−0.369386
$325$	0	0
$326$	1.46365e6	0.762770
$327$	−230606.	−0.119262
$328$	61319.7	0.0314714
$329$	4.60879e6	2.34745
$330$	0	0
$331$	2.47715e6	1.24275	0.621373	−	0.783515i	$-0.286575\pi$
$331$	2.47715e6	1.24275	0.621373	+	0.783515i	$0.286575\pi$
$332$	42471.3	0.0211471
$333$	397966.	0.196669
$334$	−269568.	−0.132222
$335$	0	0
$336$	753976.	0.364342
$337$	−2.55550e6	−1.22575	−0.612873	−	0.790181i	$-0.709986\pi$
$337$	−2.55550e6	−1.22575	−0.612873	+	0.790181i	$0.709986\pi$
$338$	114244.	0.0543928
$339$	3.02963e6	1.43183
$340$	0	0
$341$	−2.36947e6	−1.10348
$342$	17009.4	0.00786362
$343$	−2.52902e6	−1.16069
$344$	−10857.9	−0.00494709
$345$	0	0
$346$	−2.07568e6	−0.932118
$347$	475000.	0.211773	0.105886	−	0.994378i	$-0.466232\pi$
$347$	475000.	0.211773	0.105886	+	0.994378i	$0.466232\pi$
$348$	−1.38212e6	−0.611783
$349$	615277.	0.270400	0.135200	−	0.990818i	$-0.456832\pi$
$349$	615277.	0.270400	0.135200	+	0.990818i	$0.456832\pi$
$350$	0	0
$351$	689140.	0.298565
$352$	601380.	0.258697
$353$	4.37400e6	1.86828	0.934140	−	0.356908i	$-0.116169\pi$
$353$	4.37400e6	1.86828	0.934140	+	0.356908i	$0.116169\pi$
$354$	−2.21586e6	−0.939796
$355$	0	0
$356$	131676.	0.0550659
$357$	−478907.	−0.198875
$358$	−358914.	−0.148007
$359$	4.59562e6	1.88195	0.940975	−	0.338476i	$-0.109911\pi$
$359$	4.59562e6	1.88195	0.940975	+	0.338476i	$0.109911\pi$
$360$	0	0
$361$	−2.46947e6	−0.997325
$362$	−1.50509e6	−0.603657
$363$	−2.53926e6	−1.01144
$364$	−576616.	−0.228104
$365$	0	0
$366$	902879.	0.352312
$367$	4.59362e6	1.78029	0.890143	−	0.455681i	$-0.150604\pi$
$367$	4.59362e6	1.78029	0.890143	+	0.455681i	$0.150604\pi$
$368$	754904.	0.290584
$369$	−50057.6	−0.0191383
$370$	0	0
$371$	5.28617e6	1.99391
$372$	891580.	0.334043
$373$	−1.74314e6	−0.648724	−0.324362	−	0.945933i	$-0.605150\pi$
$373$	−1.74314e6	−0.648724	−0.324362	+	0.945933i	$0.605150\pi$
$374$	−381982.	−0.141209
$375$	0	0
$376$	−1.38320e6	−0.504565
$377$	1.05700e6	0.383020
$378$	−3.47825e6	−1.25208
$379$	−4.42529e6	−1.58250	−0.791250	−	0.611493i	$-0.790569\pi$
$379$	−4.42529e6	−1.58250	−0.791250	+	0.611493i	$0.790569\pi$
$380$	0	0
$381$	2.19260e6	0.773833
$382$	826992.	0.289963
$383$	−1.39773e6	−0.486884	−0.243442	−	0.969915i	$-0.578277\pi$
$383$	−1.39773e6	−0.486884	−0.243442	+	0.969915i	$0.578277\pi$
$384$	−226286.	−0.0783122
$385$	0	0
$386$	1.65235e6	0.564462
$387$	8863.71	0.00300842
$388$	861504.	0.290521
$389$	1.63535e6	0.547946	0.273973	−	0.961737i	$-0.411662\pi$
$389$	1.63535e6	0.547946	0.273973	+	0.961737i	$0.411662\pi$
$390$	0	0
$391$	−479497.	−0.158615
$392$	1.83467e6	0.603034
$393$	−2.21764e6	−0.724286
$394$	−2.15530e6	−0.699468
$395$	0	0
$396$	−490928.	−0.157319
$397$	−4.90653e6	−1.56242	−0.781210	−	0.624268i	$-0.785397\pi$
$397$	−4.90653e6	−1.56242	−0.781210	+	0.624268i	$0.785397\pi$
$398$	−589344.	−0.186493
$399$	−239715.	−0.0753813
$400$	0	0
$401$	−951184.	−0.295395	−0.147698	−	0.989033i	$-0.547186\pi$
$401$	−951184.	−0.295395	−0.147698	+	0.989033i	$0.547186\pi$
$402$	1.01443e6	0.313080
$403$	−681851.	−0.209135
$404$	−2.68089e6	−0.817196
$405$	0	0
$406$	−5.33492e6	−1.60625
$407$	−4.47348e6	−1.33863
$408$	143731.	0.0427465
$409$	4.49464e6	1.32858	0.664289	−	0.747476i	$-0.268735\pi$
$409$	4.49464e6	1.32858	0.664289	+	0.747476i	$0.268735\pi$
$410$	0	0
$411$	−4.08358e6	−1.19244
$412$	−495581.	−0.143837
$413$	−8.55312e6	−2.46746
$414$	−616256.	−0.176710
$415$	0	0
$416$	173056.	0.0490290
$417$	−85597.0	−0.0241056
$418$	−191200.	−0.0535238
$419$	−828906.	−0.230659	−0.115329	−	0.993327i	$-0.536792\pi$
$419$	−828906.	−0.230659	−0.115329	+	0.993327i	$0.536792\pi$
$420$	0	0
$421$	744813.	0.204806	0.102403	−	0.994743i	$-0.467347\pi$
$421$	744813.	0.204806	0.102403	+	0.994743i	$0.467347\pi$
$422$	−4.59686e6	−1.25655
$423$	1.12916e6	0.306835
$424$	−1.58650e6	−0.428574
$425$	0	0
$426$	4.30065e6	1.14818
$427$	3.48508e6	0.925002
$428$	1.55750e6	0.410978
$429$	−1.37080e6	−0.359608
$430$	0	0
$431$	−3.89529e6	−1.01006	−0.505030	−	0.863102i	$-0.668519\pi$
$431$	−3.89529e6	−1.01006	−0.505030	+	0.863102i	$0.668519\pi$
$432$	1.04390e6	0.269123
$433$	5.88297e6	1.50792	0.753958	−	0.656923i	$-0.228142\pi$
$433$	5.88297e6	1.50792	0.753958	+	0.656923i	$0.228142\pi$
$434$	3.44146e6	0.877038
$435$	0	0
$436$	267149.	0.0673035
$437$	−240011.	−0.0601211
$438$	−3.43242e6	−0.854899
$439$	1.73024e6	0.428495	0.214248	−	0.976779i	$-0.431270\pi$
$439$	1.73024e6	0.428495	0.214248	+	0.976779i	$0.431270\pi$
$440$	0	0
$441$	−1.49771e6	−0.366716
$442$	−109921.	−0.0267624
$443$	106432.	0.0257670	0.0128835	−	0.999917i	$-0.495899\pi$
$443$	106432.	0.0257670	0.0128835	+	0.999917i	$0.495899\pi$
$444$	1.68327e6	0.405225
$445$	0	0
$446$	5.57721e6	1.32764
$447$	5.12449e6	1.21306
$448$	−873454.	−0.205610
$449$	−4.89220e6	−1.14522	−0.572609	−	0.819828i	$-0.694069\pi$
$449$	−4.89220e6	−1.14522	−0.572609	+	0.819828i	$0.694069\pi$
$450$	0	0
$451$	562690.	0.130265
$452$	−3.50972e6	−0.808027
$453$	7.02117e6	1.60755
$454$	−5.61165e6	−1.27776
$455$	0	0
$456$	71944.2	0.0162026
$457$	−177252.	−0.0397008	−0.0198504	−	0.999803i	$-0.506319\pi$
$457$	−177252.	−0.0397008	−0.0198504	+	0.999803i	$0.506319\pi$
$458$	−3.18651e6	−0.709824
$459$	−663063.	−0.146900
$460$	0	0
$461$	7.15676e6	1.56843	0.784213	−	0.620491i	$-0.213067\pi$
$461$	7.15676e6	1.56843	0.784213	+	0.620491i	$0.213067\pi$
$462$	6.91872e6	1.50807
$463$	−3.44228e6	−0.746267	−0.373133	−	0.927778i	$-0.621717\pi$
$463$	−3.44228e6	−0.746267	−0.373133	+	0.927778i	$0.621717\pi$
$464$	1.60114e6	0.345249
$465$	0	0
$466$	−4.63900e6	−0.989600
$467$	9.22486e6	1.95735	0.978673	−	0.205423i	$-0.0658571\pi$
$467$	9.22486e6	1.95735	0.978673	+	0.205423i	$0.0658571\pi$
$468$	−141272.	−0.0298155
$469$	3.91565e6	0.821999
$470$	0	0
$471$	828889.	0.172165
$472$	2.56699e6	0.530358
$473$	−99635.7	−0.0204768
$474$	3.34783e6	0.684412
$475$	0	0
$476$	554797.	0.112232
$477$	1.29512e6	0.260624
$478$	−2.75012e6	−0.550531
$479$	1.23331e6	0.245602	0.122801	−	0.992431i	$-0.460812\pi$
$479$	1.23331e6	0.245602	0.122801	+	0.992431i	$0.460812\pi$
$480$	0	0
$481$	−1.28731e6	−0.253700
$482$	−1.56538e6	−0.306904
$483$	8.68498e6	1.69395
$484$	2.94164e6	0.570789
$485$	0	0
$486$	−1.55356e6	−0.298357
$487$	6.21276e6	1.18703	0.593516	−	0.804823i	$-0.297740\pi$
$487$	6.21276e6	1.18703	0.593516	+	0.804823i	$0.297740\pi$
$488$	−1.04595e6	−0.198821
$489$	−5.05376e6	−0.955747
$490$	0	0
$491$	−7.05221e6	−1.32014	−0.660072	−	0.751202i	$-0.729474\pi$
$491$	−7.05221e6	−1.32014	−0.660072	+	0.751202i	$0.729474\pi$
$492$	−211728.	−0.0394335
$493$	−1.01700e6	−0.188454
$494$	−55020.6	−0.0101440
$495$	0	0
$496$	−1.03286e6	−0.188512
$497$	1.66003e7	3.01457
$498$	−146647.	−0.0264972
$499$	5.63009e6	1.01220	0.506098	−	0.862476i	$-0.331088\pi$
$499$	5.63009e6	1.01220	0.506098	+	0.862476i	$0.331088\pi$
$500$	0	0
$501$	930778.	0.165673
$502$	3.77889e6	0.669276
$503$	−9.65803e6	−1.70204	−0.851018	−	0.525137i	$-0.824014\pi$
$503$	−9.65803e6	−1.70204	−0.851018	+	0.525137i	$0.824014\pi$
$504$	713032.	0.125035
$505$	0	0
$506$	6.92724e6	1.20277
$507$	−394467.	−0.0681539
$508$	−2.54005e6	−0.436700
$509$	−4.39209e6	−0.751409	−0.375705	−	0.926739i	$-0.622599\pi$
$509$	−4.39209e6	−0.751409	−0.375705	+	0.926739i	$0.622599\pi$
$510$	0	0
$511$	−1.32490e7	−2.24456
$512$	262144.	0.0441942
$513$	−331894.	−0.0556809
$514$	−1.18888e6	−0.198486
$515$	0	0
$516$	37490.7	0.00619868
$517$	−1.26927e7	−2.08847
$518$	6.49735e6	1.06393
$519$	7.16702e6	1.16794
$520$	0	0
$521$	−8.38443e6	−1.35325	−0.676627	−	0.736326i	$-0.736559\pi$
$521$	−8.38443e6	−1.35325	−0.676627	+	0.736326i	$0.736559\pi$
$522$	−1.30707e6	−0.209953
$523$	−2.54489e6	−0.406831	−0.203416	−	0.979092i	$-0.565204\pi$
$523$	−2.54489e6	−0.406831	−0.203416	+	0.979092i	$0.565204\pi$
$524$	2.56906e6	0.408739
$525$	0	0
$526$	6.12389e6	0.965080
$527$	656050.	0.102899
$528$	−2.07647e6	−0.324146
$529$	2.25933e6	0.351028
$530$	0	0
$531$	−2.09553e6	−0.322521
$532$	277702.	0.0425402
$533$	161922.	0.0246882
$534$	−454658.	−0.0689973
$535$	0	0
$536$	−1.17518e6	−0.176682
$537$	1.23928e6	0.185452
$538$	−4.03512e6	−0.601036
$539$	1.68355e7	2.49605
$540$	0	0
$541$	−3.83465e6	−0.563290	−0.281645	−	0.959519i	$-0.590880\pi$
$541$	−3.83465e6	−0.563290	−0.281645	+	0.959519i	$0.590880\pi$
$542$	8.76490e6	1.28159
$543$	5.19684e6	0.756379
$544$	−166508.	−0.0241233
$545$	0	0
$546$	1.99097e6	0.285813
$547$	2.61787e6	0.374093	0.187047	−	0.982351i	$-0.440108\pi$
$547$	2.61787e6	0.374093	0.187047	+	0.982351i	$0.440108\pi$
$548$	4.73068e6	0.672934
$549$	853850.	0.120907
$550$	0	0
$551$	−509057.	−0.0714312
$552$	−2.60657e6	−0.364101
$553$	1.29225e7	1.79694
$554$	71695.9	0.00992476
$555$	0	0
$556$	99161.1	0.0136036
$557$	−5.40419e6	−0.738061	−0.369031	−	0.929417i	$-0.620310\pi$
$557$	−5.40419e6	−0.738061	−0.369031	+	0.929417i	$0.620310\pi$
$558$	843164.	0.114638
$559$	−28671.7	−0.00388082
$560$	0	0
$561$	1.31892e6	0.176935
$562$	−9.62654e6	−1.28567
$563$	−904604.	−0.120278	−0.0601392	−	0.998190i	$-0.519154\pi$
$563$	−904604.	−0.120278	−0.0601392	+	0.998190i	$0.519154\pi$
$564$	4.77599e6	0.632217
$565$	0	0
$566$	5.47683e6	0.718602
$567$	9.30257e6	1.21519
$568$	−4.98215e6	−0.647956
$569$	−6.69355e6	−0.866714	−0.433357	−	0.901222i	$-0.642671\pi$
$569$	−6.69355e6	−0.866714	−0.433357	+	0.901222i	$0.642671\pi$
$570$	0	0
$571$	8.22981e6	1.05633	0.528165	−	0.849142i	$-0.322880\pi$
$571$	8.22981e6	1.05633	0.528165	+	0.849142i	$0.322880\pi$
$572$	1.58802e6	0.202939
$573$	−2.85548e6	−0.363322
$574$	−817260.	−0.103533
$575$	0	0
$576$	−213998.	−0.0268753
$577$	−3.07720e6	−0.384783	−0.192391	−	0.981318i	$-0.561624\pi$
$577$	−3.07720e6	−0.384783	−0.192391	+	0.981318i	$0.561624\pi$
$578$	−5.57367e6	−0.693939
$579$	−5.70532e6	−0.707267
$580$	0	0
$581$	−566051.	−0.0695689
$582$	−2.97464e6	−0.364021
$583$	−1.45583e7	−1.77394
$584$	3.97633e6	0.482448
$585$	0	0
$586$	1.56260e6	0.187976
$587$	−2.64175e6	−0.316443	−0.158222	−	0.987404i	$-0.550576\pi$
$587$	−2.64175e6	−0.316443	−0.158222	+	0.987404i	$0.550576\pi$
$588$	−6.33482e6	−0.755599
$589$	328384.	0.0390026
$590$	0	0
$591$	7.44193e6	0.876429
$592$	−1.95001e6	−0.228682
$593$	5.06641e6	0.591649	0.295824	−	0.955242i	$-0.404406\pi$
$593$	5.06641e6	0.591649	0.295824	+	0.955242i	$0.404406\pi$
$594$	9.57920e6	1.11394
$595$	0	0
$596$	−5.93654e6	−0.684569
$597$	2.03492e6	0.233674
$598$	1.99342e6	0.227953
$599$	1.31136e7	1.49332	0.746662	−	0.665204i	$-0.231655\pi$
$599$	1.31136e7	1.49332	0.746662	+	0.665204i	$0.231655\pi$
$600$	0	0
$601$	7.53425e6	0.850852	0.425426	−	0.904993i	$-0.360124\pi$
$601$	7.53425e6	0.850852	0.425426	+	0.904993i	$0.360124\pi$
$602$	144713.	0.0162748
$603$	959341.	0.107443
$604$	−8.13378e6	−0.907193
$605$	0	0
$606$	9.25672e6	1.02394
$607$	−8.76101e6	−0.965123	−0.482561	−	0.875862i	$-0.660293\pi$
$607$	−8.76101e6	−0.965123	−0.482561	+	0.875862i	$0.660293\pi$
$608$	−83344.8	−0.00914365
$609$	1.84207e7	2.01262
$610$	0	0
$611$	−3.65253e6	−0.395813
$612$	135926.	0.0146698
$613$	469316.	0.0504445	0.0252223	−	0.999682i	$-0.491971\pi$
$613$	469316.	0.0504445	0.0252223	+	0.999682i	$0.491971\pi$
$614$	−2.26618e6	−0.242591
$615$	0	0
$616$	−8.01509e6	−0.851054
$617$	4.14114e6	0.437933	0.218966	−	0.975732i	$-0.429732\pi$
$617$	4.14114e6	0.437933	0.218966	+	0.975732i	$0.429732\pi$
$618$	1.71116e6	0.180227
$619$	−1.31422e7	−1.37861	−0.689304	−	0.724472i	$-0.742084\pi$
$619$	−1.31422e7	−1.37861	−0.689304	+	0.724472i	$0.742084\pi$
$620$	0	0
$621$	1.20246e7	1.25125
$622$	3.52496e6	0.365324
$623$	−1.75496e6	−0.181154
$624$	−597536.	−0.0614331
$625$	0	0
$626$	3.66569e6	0.373869
$627$	660184.	0.0670650
$628$	−960239.	−0.0971583
$629$	1.23860e6	0.124826
$630$	0	0
$631$	9.79229e6	0.979063	0.489532	−	0.871986i	$-0.337168\pi$
$631$	9.79229e6	0.979063	0.489532	+	0.871986i	$0.337168\pi$
$632$	−3.87834e6	−0.386237
$633$	1.58722e7	1.57445
$634$	−8.04335e6	−0.794719
$635$	0	0
$636$	5.47795e6	0.537001
$637$	4.84467e6	0.473059
$638$	1.46925e7	1.42904
$639$	4.06711e6	0.394034
$640$	0	0
$641$	3.38154e6	0.325064	0.162532	−	0.986703i	$-0.448034\pi$
$641$	3.38154e6	0.325064	0.162532	+	0.986703i	$0.448034\pi$
$642$	−5.37781e6	−0.514953
$643$	3.04366e6	0.290314	0.145157	−	0.989409i	$-0.453631\pi$
$643$	3.04366e6	0.290314	0.145157	+	0.989409i	$0.453631\pi$
$644$	−1.00612e7	−0.955954
$645$	0	0
$646$	52938.6	0.00499104
$647$	−8.51735e6	−0.799915	−0.399957	−	0.916534i	$-0.630975\pi$
$647$	−8.51735e6	−0.799915	−0.399957	+	0.916534i	$0.630975\pi$
$648$	−2.79192e6	−0.261195
$649$	2.35555e7	2.19524
$650$	0	0
$651$	−1.18828e7	−1.09892
$652$	5.85461e6	0.539360
$653$	8.83998e6	0.811275	0.405638	−	0.914034i	$-0.367050\pi$
$653$	8.83998e6	0.811275	0.405638	+	0.914034i	$0.367050\pi$
$654$	−922425.	−0.0843309
$655$	0	0
$656$	245279.	0.0222536
$657$	−3.24603e6	−0.293386
$658$	1.84351e7	1.65990
$659$	−2.97807e6	−0.267129	−0.133564	−	0.991040i	$-0.542642\pi$
$659$	−2.97807e6	−0.267129	−0.133564	+	0.991040i	$0.542642\pi$
$660$	0	0
$661$	−7.90309e6	−0.703548	−0.351774	−	0.936085i	$-0.614421\pi$
$661$	−7.90309e6	−0.703548	−0.351774	+	0.936085i	$0.614421\pi$
$662$	9.90860e6	0.878754
$663$	379540.	0.0335331
$664$	169885.	0.0149532
$665$	0	0
$666$	1.59186e6	0.139066
$667$	1.84433e7	1.60519
$668$	−1.07827e6	−0.0934948
$669$	−1.92572e7	−1.66352
$670$	0	0
$671$	−9.59800e6	−0.822952
$672$	3.01590e6	0.257629
$673$	−1.82522e7	−1.55338	−0.776688	−	0.629885i	$-0.783102\pi$
$673$	−1.82522e7	−1.55338	−0.776688	+	0.629885i	$0.783102\pi$
$674$	−1.02220e7	−0.866734
$675$	0	0
$676$	456976.	0.0384615
$677$	−5.39380e6	−0.452296	−0.226148	−	0.974093i	$-0.572613\pi$
$677$	−5.39380e6	−0.452296	−0.226148	+	0.974093i	$0.572613\pi$
$678$	1.21185e7	1.01245
$679$	−1.14820e7	−0.955746
$680$	0	0
$681$	1.93762e7	1.60103
$682$	−9.47789e6	−0.780280
$683$	−2.30171e7	−1.88799	−0.943994	−	0.329963i	$-0.892964\pi$
$683$	−2.30171e7	−1.88799	−0.943994	+	0.329963i	$0.892964\pi$
$684$	68037.4	0.00556042
$685$	0	0
$686$	−1.01161e7	−0.820733
$687$	1.10025e7	0.889406
$688$	−43431.6	−0.00349812
$689$	−4.18936e6	−0.336201
$690$	0	0
$691$	4.87910e6	0.388727	0.194364	−	0.980930i	$-0.437736\pi$
$691$	4.87910e6	0.388727	0.194364	+	0.980930i	$0.437736\pi$
$692$	−8.30274e6	−0.659107
$693$	6.54302e6	0.517541
$694$	1.90000e6	0.149746
$695$	0	0
$696$	−5.52847e6	−0.432596
$697$	−155795.	−0.0121471
$698$	2.46111e6	0.191202
$699$	1.60178e7	1.23996
$700$	0	0
$701$	1.47820e7	1.13615	0.568077	−	0.822976i	$-0.307688\pi$
$701$	1.47820e7	1.13615	0.568077	+	0.822976i	$0.307688\pi$
$702$	2.75656e6	0.211118
$703$	619976.	0.0473137
$704$	2.40552e6	0.182927
$705$	0	0
$706$	1.74960e7	1.32107
$707$	3.57305e7	2.68838
$708$	−8.86343e6	−0.664536
$709$	−2.75364e6	−0.205727	−0.102863	−	0.994695i	$-0.532800\pi$
$709$	−2.75364e6	−0.205727	−0.102863	+	0.994695i	$0.532800\pi$
$710$	0	0
$711$	3.16603e6	0.234878
$712$	526705.	0.0389375
$713$	−1.18975e7	−0.876457
$714$	−1.91563e6	−0.140626
$715$	0	0
$716$	−1.43566e6	−0.104657
$717$	9.49574e6	0.689812
$718$	1.83825e7	1.33074
$719$	−2.10250e7	−1.51675	−0.758373	−	0.651820i	$-0.774006\pi$
$719$	−2.10250e7	−1.51675	−0.758373	+	0.651820i	$0.774006\pi$
$720$	0	0
$721$	6.60502e6	0.473191
$722$	−9.87790e6	−0.705215
$723$	5.40502e6	0.384549
$724$	−6.02035e6	−0.426850
$725$	0	0
$726$	−1.01570e7	−0.715196
$727$	−2.21381e7	−1.55347	−0.776737	−	0.629825i	$-0.783127\pi$
$727$	−2.21381e7	−1.55347	−0.776737	+	0.629825i	$0.783127\pi$
$728$	−2.30646e6	−0.161294
$729$	1.59648e7	1.11261
$730$	0	0
$731$	27586.7	0.00190944
$732$	3.61152e6	0.249122
$733$	−1.23177e7	−0.846775	−0.423388	−	0.905949i	$-0.639159\pi$
$733$	−1.23177e7	−0.846775	−0.423388	+	0.905949i	$0.639159\pi$
$734$	1.83745e7	1.25885
$735$	0	0
$736$	3.01962e6	0.205474
$737$	−1.07838e7	−0.731313
$738$	−200230.	−0.0135328
$739$	−1.79039e7	−1.20597	−0.602986	−	0.797752i	$-0.706023\pi$
$739$	−1.79039e7	−1.20597	−0.602986	+	0.797752i	$0.706023\pi$
$740$	0	0
$741$	189978.	0.0127103
$742$	2.11447e7	1.40991
$743$	9.82085e6	0.652645	0.326323	−	0.945258i	$-0.394190\pi$
$743$	9.82085e6	0.652645	0.326323	+	0.945258i	$0.394190\pi$
$744$	3.56632e6	0.236204
$745$	0	0
$746$	−6.97256e6	−0.458717
$747$	−138684.	−0.00909334
$748$	−1.52793e6	−0.0998501
$749$	−2.07581e7	−1.35202
$750$	0	0
$751$	1.04747e7	0.677705	0.338852	−	0.940840i	$-0.389961\pi$
$751$	1.04747e7	0.677705	0.338852	+	0.940840i	$0.389961\pi$
$752$	−5.53282e6	−0.356781
$753$	−1.30479e7	−0.838599
$754$	4.22800e6	0.270836
$755$	0	0
$756$	−1.39130e7	−0.885352
$757$	−2.20487e7	−1.39844	−0.699219	−	0.714908i	$-0.746469\pi$
$757$	−2.20487e7	−1.39844	−0.699219	+	0.714908i	$0.746469\pi$
$758$	−1.77012e7	−1.11900
$759$	−2.39187e7	−1.50707
$760$	0	0
$761$	−2.75293e7	−1.72319	−0.861596	−	0.507594i	$-0.830535\pi$
$761$	−2.75293e7	−1.72319	−0.861596	+	0.507594i	$0.830535\pi$
$762$	8.77040e6	0.547182
$763$	−3.56052e6	−0.221413
$764$	3.30797e6	0.205035
$765$	0	0
$766$	−5.59091e6	−0.344279
$767$	6.77846e6	0.416047
$768$	−905143.	−0.0553751
$769$	1.50464e7	0.917525	0.458763	−	0.888559i	$-0.348293\pi$
$769$	1.50464e7	0.917525	0.458763	+	0.888559i	$0.348293\pi$
$770$	0	0
$771$	4.10501e6	0.248701
$772$	6.60941e6	0.399135
$773$	−2.28606e6	−0.137606	−0.0688031	−	0.997630i	$-0.521918\pi$
$773$	−2.28606e6	−0.137606	−0.0688031	+	0.997630i	$0.521918\pi$
$774$	35454.8	0.00212727
$775$	0	0
$776$	3.44601e6	0.205430
$777$	−2.24344e7	−1.33310
$778$	6.54142e6	0.387456
$779$	−77982.8	−0.00460421
$780$	0	0
$781$	−4.57178e7	−2.68199
$782$	−1.91799e6	−0.112158
$783$	2.55040e7	1.48663
$784$	7.33867e6	0.426410
$785$	0	0
$786$	−8.87056e6	−0.512147
$787$	−9.89052e6	−0.569223	−0.284611	−	0.958643i	$-0.591865\pi$
$787$	−9.89052e6	−0.569223	−0.284611	+	0.958643i	$0.591865\pi$
$788$	−8.62121e6	−0.494598
$789$	−2.11449e7	−1.20924
$790$	0	0
$791$	4.67770e7	2.65822
$792$	−1.96371e6	−0.111241
$793$	−2.76197e6	−0.155968
$794$	−1.96261e7	−1.10480
$795$	0	0
$796$	−2.35738e6	−0.131870
$797$	−2.93049e7	−1.63416	−0.817080	−	0.576525i	$-0.804408\pi$
$797$	−2.93049e7	−1.63416	−0.817080	+	0.576525i	$0.804408\pi$
$798$	−958862.	−0.0533026
$799$	3.51431e6	0.194748
$800$	0	0
$801$	−429969.	−0.0236786
$802$	−3.80474e6	−0.208876
$803$	3.64881e7	1.99693
$804$	4.05771e6	0.221381
$805$	0	0
$806$	−2.72741e6	−0.147881
$807$	1.39327e7	0.753095
$808$	−1.07236e7	−0.577845
$809$	1.02027e7	0.548078	0.274039	−	0.961719i	$-0.411640\pi$
$809$	1.02027e7	0.548078	0.274039	+	0.961719i	$0.411640\pi$
$810$	0	0
$811$	−1.26432e7	−0.675001	−0.337501	−	0.941325i	$-0.609582\pi$
$811$	−1.26432e7	−0.675001	−0.337501	+	0.941325i	$0.609582\pi$
$812$	−2.13397e7	−1.13579
$813$	−3.02639e7	−1.60582
$814$	−1.78939e7	−0.946551
$815$	0	0
$816$	574925.	0.0302264
$817$	13808.4	0.000723752 0
$818$	1.79786e7	0.939446
$819$	1.88285e6	0.0980858
$820$	0	0
$821$	−1.56881e7	−0.812294	−0.406147	−	0.913808i	$-0.633128\pi$
$821$	−1.56881e7	−0.812294	−0.406147	+	0.913808i	$0.633128\pi$
$822$	−1.63343e7	−0.843183
$823$	−2.45799e7	−1.26497	−0.632487	−	0.774571i	$-0.717966\pi$
$823$	−2.45799e7	−1.26497	−0.632487	+	0.774571i	$0.717966\pi$
$824$	−1.98232e6	−0.101708
$825$	0	0
$826$	−3.42125e7	−1.74475
$827$	−3.62365e7	−1.84239	−0.921197	−	0.389098i	$-0.872787\pi$
$827$	−3.62365e7	−1.84239	−0.921197	+	0.389098i	$0.872787\pi$
$828$	−2.46502e6	−0.124953
$829$	−2.81815e7	−1.42422	−0.712110	−	0.702068i	$-0.752260\pi$
$829$	−2.81815e7	−1.42422	−0.712110	+	0.702068i	$0.752260\pi$
$830$	0	0
$831$	−247555.	−0.0124357
$832$	692224.	0.0346688
$833$	−4.66134e6	−0.232755
$834$	−342388.	−0.0170453
$835$	0	0
$836$	−764799.	−0.0378470
$837$	−1.64522e7	−0.811727
$838$	−3.31562e6	−0.163100
$839$	−8.42806e6	−0.413354	−0.206677	−	0.978409i	$-0.566265\pi$
$839$	−8.42806e6	−0.413354	−0.206677	+	0.978409i	$0.566265\pi$
$840$	0	0
$841$	1.86068e7	0.907155
$842$	2.97925e6	0.144820
$843$	3.32390e7	1.61094
$844$	−1.83874e7	−0.888515
$845$	0	0
$846$	4.51664e6	0.216965
$847$	−3.92057e7	−1.87776
$848$	−6.34601e6	−0.303048
$849$	−1.89107e7	−0.900404
$850$	0	0
$851$	−2.24620e7	−1.06322
$852$	1.72026e7	0.811886
$853$	3.10763e7	1.46237	0.731184	−	0.682180i	$-0.238968\pi$
$853$	3.10763e7	1.46237	0.731184	+	0.682180i	$0.238968\pi$
$854$	1.39403e7	0.654075
$855$	0	0
$856$	6.23000e6	0.290605
$857$	5.72064e6	0.266068	0.133034	−	0.991111i	$-0.457528\pi$
$857$	5.72064e6	0.266068	0.133034	+	0.991111i	$0.457528\pi$
$858$	−5.48318e6	−0.254281
$859$	−6.04140e6	−0.279354	−0.139677	−	0.990197i	$-0.544606\pi$
$859$	−6.04140e6	−0.279354	−0.139677	+	0.990197i	$0.544606\pi$
$860$	0	0
$861$	2.82187e6	0.129727
$862$	−1.55812e7	−0.714220
$863$	−2.09227e7	−0.956292	−0.478146	−	0.878280i	$-0.658691\pi$
$863$	−2.09227e7	−0.956292	−0.478146	+	0.878280i	$0.658691\pi$
$864$	4.17562e6	0.190299
$865$	0	0
$866$	2.35319e7	1.06626
$867$	1.92450e7	0.869502
$868$	1.37658e7	0.620160
$869$	−3.55889e7	−1.59869
$870$	0	0
$871$	−3.10320e6	−0.138601
$872$	1.06860e6	0.0475908
$873$	−2.81311e6	−0.124925
$874$	−960042.	−0.0425120
$875$	0	0
$876$	−1.37297e7	−0.604505
$877$	5.01539e6	0.220194	0.110097	−	0.993921i	$-0.464884\pi$
$877$	5.01539e6	0.220194	0.110097	+	0.993921i	$0.464884\pi$
$878$	6.92097e6	0.302992
$879$	−5.39541e6	−0.235533
$880$	0	0
$881$	−2.14791e7	−0.932346	−0.466173	−	0.884694i	$-0.654368\pi$
$881$	−2.14791e7	−0.932346	−0.466173	+	0.884694i	$0.654368\pi$
$882$	−5.99082e6	−0.259307
$883$	−996549.	−0.0430127	−0.0215064	−	0.999769i	$-0.506846\pi$
$883$	−996549.	−0.0430127	−0.0215064	+	0.999769i	$0.506846\pi$
$884$	−439684.	−0.0189239
$885$	0	0
$886$	425728.	0.0182200
$887$	−4.67336e6	−0.199444	−0.0997219	−	0.995015i	$-0.531795\pi$
$887$	−4.67336e6	−0.199444	−0.0997219	+	0.995015i	$0.531795\pi$
$888$	6.73308e6	0.286537
$889$	3.38534e7	1.43664
$890$	0	0
$891$	−2.56196e7	−1.08113
$892$	2.23088e7	0.938782
$893$	1.75908e6	0.0738170
$894$	2.04980e7	0.857762
$895$	0	0
$896$	−3.49382e6	−0.145388
$897$	−6.88297e6	−0.285624
$898$	−1.95688e7	−0.809792
$899$	−2.52343e7	−1.04134
$900$	0	0
$901$	4.03083e6	0.165418
$902$	2.25076e6	0.0921112
$903$	−499670.	−0.0203922
$904$	−1.40389e7	−0.571362
$905$	0	0
$906$	2.80847e7	1.13671
$907$	−1.18130e7	−0.476807	−0.238403	−	0.971166i	$-0.576624\pi$
$907$	−1.18130e7	−0.476807	−0.238403	+	0.971166i	$0.576624\pi$
$908$	−2.24466e7	−0.903515
$909$	8.75405e6	0.351398
$910$	0	0
$911$	3.55560e7	1.41944	0.709721	−	0.704483i	$-0.248821\pi$
$911$	3.55560e7	1.41944	0.709721	+	0.704483i	$0.248821\pi$
$912$	287777.	0.0114569
$913$	1.55892e6	0.0618938
$914$	−709006.	−0.0280727
$915$	0	0
$916$	−1.27460e7	−0.501922
$917$	−3.42400e7	−1.34465
$918$	−2.65225e6	−0.103874
$919$	2.66902e7	1.04247	0.521235	−	0.853413i	$-0.325472\pi$
$919$	2.66902e7	1.04247	0.521235	+	0.853413i	$0.325472\pi$
$920$	0	0
$921$	7.82478e6	0.303965
$922$	2.86270e7	1.10905
$923$	−1.31560e7	−0.508299
$924$	2.76749e7	1.06637
$925$	0	0
$926$	−1.37691e7	−0.527690
$927$	1.61824e6	0.0618507
$928$	6.40454e6	0.244128
$929$	−3.08229e7	−1.17175	−0.585874	−	0.810402i	$-0.699249\pi$
$929$	−3.08229e7	−1.17175	−0.585874	+	0.810402i	$0.699249\pi$
$930$	0	0
$931$	−2.33322e6	−0.0882230
$932$	−1.85560e7	−0.699753
$933$	−1.21711e7	−0.457749
$934$	3.68994e7	1.38405
$935$	0	0
$936$	−565088.	−0.0210827
$937$	−2.78462e7	−1.03613	−0.518067	−	0.855340i	$-0.673348\pi$
$937$	−2.78462e7	−1.03613	−0.518067	+	0.855340i	$0.673348\pi$
$938$	1.56626e7	0.581241
$939$	−1.26571e7	−0.468456
$940$	0	0
$941$	2.80836e7	1.03390	0.516950	−	0.856016i	$-0.327067\pi$
$941$	2.80836e7	1.03390	0.516950	+	0.856016i	$0.327067\pi$
$942$	3.31556e6	0.121739
$943$	2.82535e6	0.103465
$944$	1.02680e7	0.375020
$945$	0	0
$946$	−398543.	−0.0144793
$947$	4.49006e7	1.62696	0.813481	−	0.581592i	$-0.197570\pi$
$947$	4.49006e7	1.62696	0.813481	+	0.581592i	$0.197570\pi$
$948$	1.33913e7	0.483953
$949$	1.05000e7	0.378463
$950$	0	0
$951$	2.77724e7	0.995779
$952$	2.21919e6	0.0793600
$953$	1.13992e7	0.406577	0.203289	−	0.979119i	$-0.434837\pi$
$953$	1.13992e7	0.406577	0.203289	+	0.979119i	$0.434837\pi$
$954$	5.18048e6	0.184289
$955$	0	0
$956$	−1.10005e7	−0.389284
$957$	−5.07311e7	−1.79058
$958$	4.93322e6	0.173667
$959$	−6.30498e7	−2.21380
$960$	0	0
$961$	−1.23510e7	−0.431412
$962$	−5.14924e6	−0.179393
$963$	−5.08578e6	−0.176722
$964$	−6.26152e6	−0.217014
$965$	0	0
$966$	3.47399e7	1.19781
$967$	5.54751e7	1.90780	0.953898	−	0.300130i	$-0.0970300\pi$
$967$	5.54751e7	1.90780	0.953898	+	0.300130i	$0.0970300\pi$
$968$	1.17665e7	0.403609
$969$	−182789.	−0.00625375
$970$	0	0
$971$	−2.45562e6	−0.0835819	−0.0417910	−	0.999126i	$-0.513306\pi$
$971$	−2.45562e6	−0.0835819	−0.0417910	+	0.999126i	$0.513306\pi$
$972$	−6.21423e6	−0.210970
$973$	−1.32160e6	−0.0447527
$974$	2.48510e7	0.839358
$975$	0	0
$976$	−4.18381e6	−0.140588
$977$	−3.31344e7	−1.11056	−0.555280	−	0.831663i	$-0.687389\pi$
$977$	−3.31344e7	−1.11056	−0.555280	+	0.831663i	$0.687389\pi$
$978$	−2.02151e7	−0.675815
$979$	4.83322e6	0.161168
$980$	0	0
$981$	−872335.	−0.0289408
$982$	−2.82088e7	−0.933483
$983$	4.46461e7	1.47367	0.736834	−	0.676073i	$-0.236320\pi$
$983$	4.46461e7	1.47367	0.736834	+	0.676073i	$0.236320\pi$
$984$	−846911.	−0.0278837
$985$	0	0
$986$	−4.06801e6	−0.133257
$987$	−6.36537e7	−2.07985
$988$	−220082.	−0.00717287
$989$	−500285.	−0.0162640
$990$	0	0
$991$	4.99797e7	1.61662	0.808312	−	0.588754i	$-0.200381\pi$
$991$	4.99797e7	1.61662	0.808312	+	0.588754i	$0.200381\pi$
$992$	−4.13145e6	−0.133298
$993$	−3.42129e7	−1.10107
$994$	6.64013e7	2.13162
$995$	0	0
$996$	−586588.	−0.0187363
$997$	1.25647e7	0.400326	0.200163	−	0.979763i	$-0.435853\pi$
$997$	1.25647e7	0.400326	0.200163	+	0.979763i	$0.435853\pi$
$998$	2.25204e7	0.715730
$999$	−3.10611e7	−0.984699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.6.a.h.1.1		2
5.2	odd	4		650.6.b.g.599.4		4
5.3	odd	4		650.6.b.g.599.1		4
5.4	even	2		130.6.a.a.1.2	✓	2
20.19	odd	2		1040.6.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.a.1.2	✓	2	5.4	even	2
650.6.a.h.1.1		2	1.1	even	1	trivial
650.6.b.g.599.1		4	5.3	odd	4
650.6.b.g.599.4		4	5.2	odd	4
1040.6.a.e.1.1		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	650.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -13.8114 q^{3} +16.0000 q^{4} -55.2456 q^{6} -213.246 q^{7} +64.0000 q^{8} -52.2456 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -13.8114 q^{3} +16.0000 q^{4} -55.2456 q^{6} -213.246 q^{7} +64.0000 q^{8} -52.2456 q^{9} +587.285 q^{11} -220.982 q^{12} +169.000 q^{13} -852.982 q^{14} +256.000 q^{16} -162.605 q^{17} -208.982 q^{18} -81.3914 q^{19} +2945.22 q^{21} +2349.14 q^{22} +2948.84 q^{23} -883.929 q^{24} +676.000 q^{26} +4077.75 q^{27} -3411.93 q^{28} +6254.43 q^{29} -4034.62 q^{31} +1024.00 q^{32} -8111.22 q^{33} -650.420 q^{34} -835.929 q^{36} -7617.22 q^{37} -325.566 q^{38} -2334.12 q^{39} +958.121 q^{41} +11780.9 q^{42} -169.655 q^{43} +9396.56 q^{44} +11795.4 q^{46} -21612.6 q^{47} -3535.72 q^{48} +28666.7 q^{49} +2245.80 q^{51} +2704.00 q^{52} -24789.1 q^{53} +16311.0 q^{54} -13647.7 q^{56} +1124.13 q^{57} +25017.7 q^{58} +40109.2 q^{59} -16343.0 q^{61} -16138.5 q^{62} +11141.1 q^{63} +4096.00 q^{64} -32444.9 q^{66} -18362.1 q^{67} -2601.68 q^{68} -40727.6 q^{69} -77846.0 q^{71} -3343.72 q^{72} +62130.2 q^{73} -30468.9 q^{74} -1302.26 q^{76} -125236. q^{77} -9336.50 q^{78} -60599.1 q^{79} -43623.7 q^{81} +3832.48 q^{82} +2654.46 q^{83} +47123.5 q^{84} -678.619 q^{86} -86382.4 q^{87} +37586.2 q^{88} +8229.77 q^{89} -36038.5 q^{91} +47181.5 q^{92} +55723.7 q^{93} -86450.3 q^{94} -14142.9 q^{96} +53844.0 q^{97} +114667. q^{98} -30683.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 4 q^{3} + 32 q^{4} + 16 q^{6} - 300 q^{7} + 128 q^{8} + 22 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 + 4 * q^3 + 32 * q^4 + 16 * q^6 - 300 * q^7 + 128 * q^8 + 22 * q^9	\( 2 q + 8 q^{2} + 4 q^{3} + 32 q^{4} + 16 q^{6} - 300 q^{7} + 128 q^{8} + 22 q^{9} + 384 q^{11} + 64 q^{12} + 338 q^{13} - 1200 q^{14} + 512 q^{16} + 244 q^{17} + 88 q^{18} - 2408 q^{19} + 1400 q^{21} + 1536 q^{22} - 332 q^{23} + 256 q^{24} + 1352 q^{26} + 1072 q^{27} - 4800 q^{28} + 3528 q^{29} + 880 q^{31} + 2048 q^{32} - 11732 q^{33} + 976 q^{34} + 352 q^{36} - 10744 q^{37} - 9632 q^{38} + 676 q^{39} + 16020 q^{41} + 5600 q^{42} - 2964 q^{43} + 6144 q^{44} - 1328 q^{46} - 38292 q^{47} + 1024 q^{48} + 19386 q^{49} + 9488 q^{51} + 5408 q^{52} - 42052 q^{53} + 4288 q^{54} - 19200 q^{56} - 40316 q^{57} + 14112 q^{58} + 42872 q^{59} - 33192 q^{61} + 3520 q^{62} + 4700 q^{63} + 8192 q^{64} - 46928 q^{66} - 37420 q^{67} + 3904 q^{68} - 99164 q^{69} - 69520 q^{71} + 1408 q^{72} + 12632 q^{73} - 42976 q^{74} - 38528 q^{76} - 107600 q^{77} + 2704 q^{78} + 35208 q^{79} - 115202 q^{81} + 64080 q^{82} - 31500 q^{83} + 22400 q^{84} - 11856 q^{86} - 134944 q^{87} + 24576 q^{88} - 18452 q^{89} - 50700 q^{91} - 5312 q^{92} + 143260 q^{93} - 153168 q^{94} + 4096 q^{96} + 28884 q^{97} + 77544 q^{98} - 45776 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 4 * q^3 + 32 * q^4 + 16 * q^6 - 300 * q^7 + 128 * q^8 + 22 * q^9 + 384 * q^11 + 64 * q^12 + 338 * q^13 - 1200 * q^14 + 512 * q^16 + 244 * q^17 + 88 * q^18 - 2408 * q^19 + 1400 * q^21 + 1536 * q^22 - 332 * q^23 + 256 * q^24 + 1352 * q^26 + 1072 * q^27 - 4800 * q^28 + 3528 * q^29 + 880 * q^31 + 2048 * q^32 - 11732 * q^33 + 976 * q^34 + 352 * q^36 - 10744 * q^37 - 9632 * q^38 + 676 * q^39 + 16020 * q^41 + 5600 * q^42 - 2964 * q^43 + 6144 * q^44 - 1328 * q^46 - 38292 * q^47 + 1024 * q^48 + 19386 * q^49 + 9488 * q^51 + 5408 * q^52 - 42052 * q^53 + 4288 * q^54 - 19200 * q^56 - 40316 * q^57 + 14112 * q^58 + 42872 * q^59 - 33192 * q^61 + 3520 * q^62 + 4700 * q^63 + 8192 * q^64 - 46928 * q^66 - 37420 * q^67 + 3904 * q^68 - 99164 * q^69 - 69520 * q^71 + 1408 * q^72 + 12632 * q^73 - 42976 * q^74 - 38528 * q^76 - 107600 * q^77 + 2704 * q^78 + 35208 * q^79 - 115202 * q^81 + 64080 * q^82 - 31500 * q^83 + 22400 * q^84 - 11856 * q^86 - 134944 * q^87 + 24576 * q^88 - 18452 * q^89 - 50700 * q^91 - 5312 * q^92 + 143260 * q^93 - 153168 * q^94 + 4096 * q^96 + 28884 * q^97 + 77544 * q^98 - 45776 * q^99

Introduction

L-functions

Modular forms

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Database

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