LMFDB - Embedded newform 245.6.a.m.1.2

Error: no document with id 225285568 found in table mf_hecke_traces.

Error: table True does not exist

Error: no document with id 209186782 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,6,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,10,58] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 $ x^10 - 246x^8 - 192x^7 + 20336x^6 + 25380x^5 - 639206x^4 - 722920x^3 + 7583055x^2 + 5935300x - 22888100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 7^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$10.2693$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-9.26930 q^{2} +1.27429 q^{3} +53.9199 q^{4} +25.0000 q^{5} -11.8118 q^{6} -203.182 q^{8} -241.376 q^{9} -231.732 q^{10} +478.980 q^{11} +68.7096 q^{12} -203.039 q^{13} +31.8573 q^{15} +157.917 q^{16} +854.151 q^{17} +2237.39 q^{18} +1385.35 q^{19} +1348.00 q^{20} -4439.81 q^{22} +2414.39 q^{23} -258.913 q^{24} +625.000 q^{25} +1882.03 q^{26} -617.236 q^{27} -4207.61 q^{29} -295.295 q^{30} -7478.19 q^{31} +5038.04 q^{32} +610.360 q^{33} -7917.38 q^{34} -13015.0 q^{36} +9593.09 q^{37} -12841.2 q^{38} -258.731 q^{39} -5079.55 q^{40} -5503.30 q^{41} -5020.82 q^{43} +25826.5 q^{44} -6034.40 q^{45} -22379.7 q^{46} -23703.5 q^{47} +201.232 q^{48} -5793.31 q^{50} +1088.44 q^{51} -10947.9 q^{52} -10841.4 q^{53} +5721.35 q^{54} +11974.5 q^{55} +1765.34 q^{57} +39001.6 q^{58} +10487.3 q^{59} +1717.74 q^{60} +44185.5 q^{61} +69317.5 q^{62} -51752.4 q^{64} -5075.99 q^{65} -5657.61 q^{66} +53131.2 q^{67} +46055.7 q^{68} +3076.64 q^{69} +15897.1 q^{71} +49043.3 q^{72} +77627.1 q^{73} -88921.2 q^{74} +796.432 q^{75} +74697.8 q^{76} +2398.26 q^{78} -86136.0 q^{79} +3947.92 q^{80} +57867.9 q^{81} +51011.7 q^{82} -52126.2 q^{83} +21353.8 q^{85} +46539.5 q^{86} -5361.72 q^{87} -97320.0 q^{88} +23299.1 q^{89} +55934.7 q^{90} +130184. q^{92} -9529.38 q^{93} +219715. q^{94} +34633.7 q^{95} +6419.93 q^{96} +180093. q^{97} -115614. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19}+ \cdots + 109024 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * q^99

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 $

$2$	−9.26930	−1.63860	−0.819298	−	0.573368i	$-0.805637\pi$
$2$	−9.26930	−1.63860	−0.819298	+	0.573368i	$0.805637\pi$
$3$	1.27429	0.0817458	0.0408729	−	0.999164i	$-0.486986\pi$
$3$	1.27429	0.0817458	0.0408729	+	0.999164i	$0.486986\pi$
$4$	53.9199	1.68500
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−11.8118	−0.133948
$7$	0	0
$7$	0	0
$8$	−203.182	−1.12243
$9$	−241.376	−0.993318
$10$	−231.732	−0.732802
$11$	478.980	1.19354	0.596768	−	0.802414i	$-0.296451\pi$
$11$	478.980	1.19354	0.596768	+	0.802414i	$0.296451\pi$
$12$	68.7096	0.137741
$13$	−203.039	−0.333213	−0.166607	−	0.986023i	$-0.553281\pi$
$13$	−203.039	−0.333213	−0.166607	+	0.986023i	$0.553281\pi$
$14$	0	0
$15$	31.8573	0.0365578
$16$	157.917	0.154216
$17$	854.151	0.716824	0.358412	−	0.933564i	$-0.383318\pi$
$17$	854.151	0.716824	0.358412	+	0.933564i	$0.383318\pi$
$18$	2237.39	1.62765
$19$	1385.35	0.880389	0.440195	−	0.897902i	$-0.354909\pi$
$19$	1385.35	0.880389	0.440195	+	0.897902i	$0.354909\pi$
$20$	1348.00	0.753553
$21$	0	0
$22$	−4439.81	−1.95572
$23$	2414.39	0.951674	0.475837	−	0.879533i	$-0.342145\pi$
$23$	2414.39	0.951674	0.475837	+	0.879533i	$0.342145\pi$
$24$	−258.913	−0.0917541
$25$	625.000	0.200000
$26$	1882.03	0.546002
$27$	−617.236	−0.162945
$28$	0	0
$29$	−4207.61	−0.929053	−0.464526	−	0.885559i	$-0.653775\pi$
$29$	−4207.61	−0.929053	−0.464526	+	0.885559i	$0.653775\pi$
$30$	−295.295	−0.0599035
$31$	−7478.19	−1.39763	−0.698815	−	0.715303i	$-0.746289\pi$
$31$	−7478.19	−1.39763	−0.698815	+	0.715303i	$0.746289\pi$
$32$	5038.04	0.869734
$33$	610.360	0.0975666
$34$	−7917.38	−1.17458
$35$	0	0
$36$	−13015.0	−1.67374
$37$	9593.09	1.15200	0.576002	−	0.817448i	$-0.304612\pi$
$37$	9593.09	1.15200	0.576002	+	0.817448i	$0.304612\pi$
$38$	−12841.2	−1.44260
$39$	−258.731	−0.0272388
$40$	−5079.55	−0.501967
$41$	−5503.30	−0.511285	−0.255643	−	0.966771i	$-0.582287\pi$
$41$	−5503.30	−0.511285	−0.255643	+	0.966771i	$0.582287\pi$
$42$	0	0
$43$	−5020.82	−0.414099	−0.207049	−	0.978331i	$-0.566386\pi$
$43$	−5020.82	−0.414099	−0.207049	+	0.978331i	$0.566386\pi$
$44$	25826.5	2.01110
$45$	−6034.40	−0.444225
$46$	−22379.7	−1.55941
$47$	−23703.5	−1.56520	−0.782598	−	0.622527i	$-0.786106\pi$
$47$	−23703.5	−1.56520	−0.782598	+	0.622527i	$0.786106\pi$
$48$	201.232	0.0126065
$49$	0	0
$50$	−5793.31	−0.327719
$51$	1088.44	0.0585973
$52$	−10947.9	−0.561463
$53$	−10841.4	−0.530144	−0.265072	−	0.964229i	$-0.585396\pi$
$53$	−10841.4	−0.530144	−0.265072	+	0.964229i	$0.585396\pi$
$54$	5721.35	0.267002
$55$	11974.5	0.533766
$56$	0	0
$57$	1765.34	0.0719681
$58$	39001.6	1.52234
$59$	10487.3	0.392224	0.196112	−	0.980582i	$-0.437168\pi$
$59$	10487.3	0.392224	0.196112	+	0.980582i	$0.437168\pi$
$60$	1717.74	0.0615998
$61$	44185.5	1.52039	0.760196	−	0.649694i	$-0.225103\pi$
$61$	44185.5	1.52039	0.760196	+	0.649694i	$0.225103\pi$
$62$	69317.5	2.29015
$63$	0	0
$64$	−51752.4	−1.57936
$65$	−5075.99	−0.149017
$66$	−5657.61	−0.159872
$67$	53131.2	1.44598	0.722991	−	0.690857i	$-0.242767\pi$
$67$	53131.2	1.44598	0.722991	+	0.690857i	$0.242767\pi$
$68$	46055.7	1.20785
$69$	3076.64	0.0777954
$70$	0	0
$71$	15897.1	0.374258	0.187129	−	0.982335i	$-0.440082\pi$
$71$	15897.1	0.374258	0.187129	+	0.982335i	$0.440082\pi$
$72$	49043.3	1.11493
$73$	77627.1	1.70493	0.852464	−	0.522786i	$-0.175107\pi$
$73$	77627.1	1.70493	0.852464	+	0.522786i	$0.175107\pi$
$74$	−88921.2	−1.88767
$75$	796.432	0.0163492
$76$	74697.8	1.48345
$77$	0	0
$78$	2398.26	0.0446333
$79$	−86136.0	−1.55280	−0.776402	−	0.630238i	$-0.782957\pi$
$79$	−86136.0	−1.55280	−0.776402	+	0.630238i	$0.782957\pi$
$80$	3947.92	0.0689674
$81$	57867.9	0.979998
$82$	51011.7	0.837790
$83$	−52126.2	−0.830541	−0.415271	−	0.909698i	$-0.636313\pi$
$83$	−52126.2	−0.830541	−0.415271	+	0.909698i	$0.636313\pi$
$84$	0	0
$85$	21353.8	0.320573
$86$	46539.5	0.678540
$87$	−5361.72	−0.0759461
$88$	−97320.0	−1.33966
$89$	23299.1	0.311791	0.155896	−	0.987774i	$-0.450174\pi$
$89$	23299.1	0.311791	0.155896	+	0.987774i	$0.450174\pi$
$90$	55934.7	0.727905
$91$	0	0
$92$	130184.	1.60357
$93$	−9529.38	−0.114250
$94$	219715.	2.56472
$95$	34633.7	0.393722
$96$	6419.93	0.0710971
$97$	180093.	1.94343	0.971714	−	0.236161i	$-0.0758893\pi$
$97$	180093.	1.94343	0.971714	+	0.236161i	$0.0758893\pi$
$98$	0	0
$99$	−115614.	−1.18556
$100$	33699.9	0.336999
$101$	107548.	1.04906	0.524531	−	0.851392i	$-0.324241\pi$
$101$	107548.	1.04906	0.524531	+	0.851392i	$0.324241\pi$
$102$	−10089.0	−0.0960173
$103$	172551.	1.60259	0.801297	−	0.598266i	$-0.204144\pi$
$103$	172551.	1.60259	0.801297	+	0.598266i	$0.204144\pi$
$104$	41253.9	0.374009
$105$	0	0
$106$	100492.	0.868691
$107$	14341.5	0.121098	0.0605488	−	0.998165i	$-0.480715\pi$
$107$	14341.5	0.121098	0.0605488	+	0.998165i	$0.480715\pi$
$108$	−33281.3	−0.274562
$109$	−190351.	−1.53458	−0.767290	−	0.641300i	$-0.778395\pi$
$109$	−190351.	−1.53458	−0.767290	+	0.641300i	$0.778395\pi$
$110$	−110995.	−0.874626
$111$	12224.4	0.0941715
$112$	0	0
$113$	66701.8	0.491407	0.245704	−	0.969345i	$-0.420981\pi$
$113$	66701.8	0.491407	0.245704	+	0.969345i	$0.420981\pi$
$114$	−16363.4	−0.117927
$115$	60359.8	0.425602
$116$	−226874.	−1.56545
$117$	49008.9	0.330986
$118$	−97209.9	−0.642696
$119$	0	0
$120$	−6472.82	−0.0410337
$121$	68370.8	0.424529
$122$	−409569.	−2.49131
$123$	−7012.80	−0.0417954
$124$	−403223.	−2.35500
$125$	15625.0	0.0894427
$126$	0	0
$127$	156626.	0.861698	0.430849	−	0.902424i	$-0.358214\pi$
$127$	156626.	0.861698	0.430849	+	0.902424i	$0.358214\pi$
$128$	318491.	1.71820
$129$	−6397.99	−0.0338508
$130$	47050.8	0.244179
$131$	71582.9	0.364444	0.182222	−	0.983257i	$-0.441671\pi$
$131$	71582.9	0.364444	0.182222	+	0.983257i	$0.441671\pi$
$132$	32910.5	0.164399
$133$	0	0
$134$	−492489.	−2.36938
$135$	−15430.9	−0.0728714
$136$	−173548.	−0.804586
$137$	299786.	1.36462	0.682308	−	0.731065i	$-0.260976\pi$
$137$	299786.	1.36462	0.682308	+	0.731065i	$0.260976\pi$
$138$	−28518.3	−0.127475
$139$	52166.8	0.229012	0.114506	−	0.993423i	$-0.463472\pi$
$139$	52166.8	0.229012	0.114506	+	0.993423i	$0.463472\pi$
$140$	0	0
$141$	−30205.2	−0.127948
$142$	−147355.	−0.613258
$143$	−97251.8	−0.397702
$144$	−38117.4	−0.153185
$145$	−105190.	−0.415485
$146$	−719549.	−2.79369
$147$	0	0
$148$	517258.	1.94112
$149$	−432166.	−1.59472	−0.797361	−	0.603502i	$-0.793772\pi$
$149$	−432166.	−1.59472	−0.797361	+	0.603502i	$0.793772\pi$
$150$	−7382.36	−0.0267897
$151$	224235.	0.800315	0.400157	−	0.916446i	$-0.368955\pi$
$151$	224235.	0.800315	0.400157	+	0.916446i	$0.368955\pi$
$152$	−281477.	−0.988177
$153$	−206172.	−0.712034
$154$	0	0
$155$	−186955.	−0.625039
$156$	−13950.8	−0.0458972
$157$	235433.	0.762287	0.381143	−	0.924516i	$-0.375530\pi$
$157$	235433.	0.762287	0.381143	+	0.924516i	$0.375530\pi$
$158$	798420.	2.54442
$159$	−13815.0	−0.0433370
$160$	125951.	0.388957
$161$	0	0
$162$	−536395.	−1.60582
$163$	2875.40	0.00847675	0.00423837	−	0.999991i	$-0.498651\pi$
$163$	2875.40	0.00847675	0.00423837	+	0.999991i	$0.498651\pi$
$164$	−296737.	−0.861513
$165$	15259.0	0.0436331
$166$	483174.	1.36092
$167$	−402505.	−1.11681	−0.558406	−	0.829568i	$-0.688587\pi$
$167$	−402505.	−1.11681	−0.558406	+	0.829568i	$0.688587\pi$
$168$	0	0
$169$	−330068.	−0.888969
$170$	−197935.	−0.525290
$171$	−334390.	−0.874506
$172$	−270722.	−0.697755
$173$	599804.	1.52368	0.761841	−	0.647764i	$-0.224296\pi$
$173$	599804.	1.52368	0.761841	+	0.647764i	$0.224296\pi$
$174$	49699.3	0.124445
$175$	0	0
$176$	75639.0	0.184062
$177$	13363.9	0.0320626
$178$	−215966.	−0.510900
$179$	640796.	1.49481	0.747407	−	0.664366i	$-0.231298\pi$
$179$	640796.	1.49481	0.747407	+	0.664366i	$0.231298\pi$
$180$	−325374.	−0.748518
$181$	640997.	1.45432	0.727160	−	0.686468i	$-0.240840\pi$
$181$	640997.	1.45432	0.727160	+	0.686468i	$0.240840\pi$
$182$	0	0
$183$	56305.2	0.124286
$184$	−490561.	−1.06819
$185$	239827.	0.515192
$186$	88330.7	0.187210
$187$	409121.	0.855555
$188$	−1.27809e6	−2.63735
$189$	0	0
$190$	−321030.	−0.645151
$191$	−795460.	−1.57774	−0.788870	−	0.614561i	$-0.789333\pi$
$191$	−795460.	−1.57774	−0.788870	+	0.614561i	$0.789333\pi$
$192$	−65947.7	−0.129106
$193$	164019.	0.316958	0.158479	−	0.987362i	$-0.449341\pi$
$193$	164019.	0.316958	0.158479	+	0.987362i	$0.449341\pi$
$194$	−1.66934e6	−3.18449
$195$	−6468.28	−0.0121816
$196$	0	0
$197$	−79137.4	−0.145283	−0.0726417	−	0.997358i	$-0.523143\pi$
$197$	−79137.4	−0.145283	−0.0726417	+	0.997358i	$0.523143\pi$
$198$	1.07166e6	1.94265
$199$	990048.	1.77224	0.886122	−	0.463451i	$-0.153389\pi$
$199$	990048.	1.77224	0.886122	+	0.463451i	$0.153389\pi$
$200$	−126989.	−0.224486
$201$	67704.6	0.118203
$202$	−996899.	−1.71899
$203$	0	0
$204$	58688.4	0.0987363
$205$	−137582.	−0.228654
$206$	−1.59942e6	−2.62600
$207$	−582777.	−0.945315
$208$	−32063.4	−0.0513867
$209$	663554.	1.05078
$210$	0	0
$211$	983192.	1.52031	0.760155	−	0.649742i	$-0.225123\pi$
$211$	983192.	1.52031	0.760155	+	0.649742i	$0.225123\pi$
$212$	−584564.	−0.893290
$213$	20257.5	0.0305940
$214$	−132936.	−0.198430
$215$	−125521.	−0.185191
$216$	125411.	0.182895
$217$	0	0
$218$	1.76442e6	2.51456
$219$	98919.5	0.139371
$220$	645663.	0.899393
$221$	−173426.	−0.238855
$222$	−113311.	−0.154309
$223$	285245.	0.384110	0.192055	−	0.981384i	$-0.438485\pi$
$223$	285245.	0.384110	0.192055	+	0.981384i	$0.438485\pi$
$224$	0	0
$225$	−150860.	−0.198664
$226$	−618279.	−0.805218
$227$	949950.	1.22359	0.611795	−	0.791016i	$-0.290448\pi$
$227$	949950.	1.22359	0.611795	+	0.791016i	$0.290448\pi$
$228$	95186.7	0.121266
$229$	−1.05143e6	−1.32493	−0.662463	−	0.749094i	$-0.730489\pi$
$229$	−1.05143e6	−1.32493	−0.662463	+	0.749094i	$0.730489\pi$
$230$	−559493.	−0.697389
$231$	0	0
$232$	854910.	1.04280
$233$	−168689.	−0.203562	−0.101781	−	0.994807i	$-0.532454\pi$
$233$	−168689.	−0.203562	−0.101781	+	0.994807i	$0.532454\pi$
$234$	−454278.	−0.542353
$235$	−592589.	−0.699977
$236$	565474.	0.660895
$237$	−109762.	−0.126935
$238$	0	0
$239$	658618.	0.745829	0.372914	−	0.927866i	$-0.378359\pi$
$239$	658618.	0.745829	0.372914	+	0.927866i	$0.378359\pi$
$240$	5030.80	0.00563779
$241$	314422.	0.348715	0.174358	−	0.984682i	$-0.444215\pi$
$241$	314422.	0.348715	0.174358	+	0.984682i	$0.444215\pi$
$242$	−633749.	−0.695631
$243$	223729.	0.243056
$244$	2.38248e6	2.56185
$245$	0	0
$246$	65003.7	0.0684858
$247$	−281280.	−0.293357
$248$	1.51943e6	1.56874
$249$	−66424.0	−0.0678932
$250$	−144833.	−0.146560
$251$	−18719.5	−0.0187547	−0.00937736	−	0.999956i	$-0.502985\pi$
$251$	−18719.5	−0.0187547	−0.00937736	+	0.999956i	$0.502985\pi$
$252$	0	0
$253$	1.15645e6	1.13586
$254$	−1.45181e6	−1.41197
$255$	27210.9	0.0262055
$256$	−1.29611e6	−1.23607
$257$	638749.	0.603251	0.301625	−	0.953427i	$-0.402471\pi$
$257$	638749.	0.603251	0.301625	+	0.953427i	$0.402471\pi$
$258$	59304.9	0.0554678
$259$	0	0
$260$	−273697.	−0.251094
$261$	1.01562e6	0.922844
$262$	−663524.	−0.597177
$263$	32605.9	0.0290674	0.0145337	−	0.999894i	$-0.495374\pi$
$263$	32605.9	0.0290674	0.0145337	+	0.999894i	$0.495374\pi$
$264$	−124014.	−0.109512
$265$	−271034.	−0.237088
$266$	0	0
$267$	29689.8	0.0254876
$268$	2.86483e6	2.43647
$269$	−137381.	−0.115757	−0.0578785	−	0.998324i	$-0.518434\pi$
$269$	−137381.	−0.115757	−0.0578785	+	0.998324i	$0.518434\pi$
$270$	143034.	0.119407
$271$	1.08503e6	0.897467	0.448733	−	0.893666i	$-0.351875\pi$
$271$	1.08503e6	0.897467	0.448733	+	0.893666i	$0.351875\pi$
$272$	134885.	0.110545
$273$	0	0
$274$	−2.77881e6	−2.23605
$275$	299362.	0.238707
$276$	165892.	0.131085
$277$	−1.19753e6	−0.937753	−0.468877	−	0.883264i	$-0.655341\pi$
$277$	−1.19753e6	−0.937753	−0.468877	+	0.883264i	$0.655341\pi$
$278$	−483550.	−0.375257
$279$	1.80506e6	1.38829
$280$	0	0
$281$	864879.	0.653415	0.326708	−	0.945125i	$-0.394061\pi$
$281$	864879.	0.653415	0.326708	+	0.945125i	$0.394061\pi$
$282$	279981.	0.209655
$283$	1.34159e6	0.995757	0.497879	−	0.867247i	$-0.334112\pi$
$283$	1.34159e6	0.995757	0.497879	+	0.867247i	$0.334112\pi$
$284$	857168.	0.630623
$285$	44133.4	0.0321851
$286$	901456.	0.651673
$287$	0	0
$288$	−1.21606e6	−0.863923
$289$	−690283.	−0.486164
$290$	975039.	0.680812
$291$	229491.	0.158867
$292$	4.18564e6	2.87280
$293$	−669371.	−0.455510	−0.227755	−	0.973718i	$-0.573139\pi$
$293$	−669371.	−0.455510	−0.227755	+	0.973718i	$0.573139\pi$
$294$	0	0
$295$	262183.	0.175408
$296$	−1.94914e6	−1.29305
$297$	−295644.	−0.194481
$298$	4.00588e6	2.61311
$299$	−490217.	−0.317110
$300$	42943.5	0.0275483
$301$	0	0
$302$	−2.07850e6	−1.31139
$303$	137048.	0.0857563
$304$	218770.	0.135770
$305$	1.10464e6	0.679940
$306$	1.91107e6	1.16674
$307$	134224.	0.0812804	0.0406402	−	0.999174i	$-0.487060\pi$
$307$	134224.	0.0812804	0.0406402	+	0.999174i	$0.487060\pi$
$308$	0	0
$309$	219880.	0.131005
$310$	1.73294e6	1.02419
$311$	−395022.	−0.231590	−0.115795	−	0.993273i	$-0.536942\pi$
$311$	−395022.	−0.231590	−0.115795	+	0.993273i	$0.536942\pi$
$312$	52569.5	0.0305737
$313$	−1.37654e6	−0.794195	−0.397098	−	0.917776i	$-0.629983\pi$
$313$	−1.37654e6	−0.794195	−0.397098	+	0.917776i	$0.629983\pi$
$314$	−2.18230e6	−1.24908
$315$	0	0
$316$	−4.64444e6	−2.61647
$317$	−1.68888e6	−0.943951	−0.471976	−	0.881612i	$-0.656459\pi$
$317$	−1.68888e6	−0.943951	−0.471976	+	0.881612i	$0.656459\pi$
$318$	128056.	0.0710119
$319$	−2.01536e6	−1.10886
$320$	−1.29381e6	−0.706311
$321$	18275.3	0.00989922
$322$	0	0
$323$	1.18330e6	0.631084
$324$	3.12023e6	1.65129
$325$	−126900.	−0.0666426
$326$	−26652.9	−0.0138900
$327$	−242563.	−0.125445
$328$	1.11817e6	0.573883
$329$	0	0
$330$	−141440.	−0.0714970
$331$	1.59017e6	0.797760	0.398880	−	0.917003i	$-0.369399\pi$
$331$	1.59017e6	0.797760	0.398880	+	0.917003i	$0.369399\pi$
$332$	−2.81064e6	−1.39946
$333$	−2.31554e6	−1.14431
$334$	3.73094e6	1.83000
$335$	1.32828e6	0.646663
$336$	0	0
$337$	−823436.	−0.394962	−0.197481	−	0.980307i	$-0.563276\pi$
$337$	−823436.	−0.394962	−0.197481	+	0.980307i	$0.563276\pi$
$338$	3.05950e6	1.45666
$339$	84997.5	0.0401705
$340$	1.15139e6	0.540165
$341$	−3.58190e6	−1.66812
$342$	3.09956e6	1.43296
$343$	0	0
$344$	1.02014e6	0.464797
$345$	76915.9	0.0347911
$346$	−5.55977e6	−2.49670
$347$	−2.62964e6	−1.17239	−0.586195	−	0.810170i	$-0.699375\pi$
$347$	−2.62964e6	−1.17239	−0.586195	+	0.810170i	$0.699375\pi$
$348$	−289103.	−0.127969
$349$	−3.26813e6	−1.43627	−0.718134	−	0.695905i	$-0.755003\pi$
$349$	−3.26813e6	−1.43627	−0.718134	+	0.695905i	$0.755003\pi$
$350$	0	0
$351$	125323.	0.0542955
$352$	2.41312e6	1.03806
$353$	−621440.	−0.265438	−0.132719	−	0.991154i	$-0.542371\pi$
$353$	−621440.	−0.265438	−0.132719	+	0.991154i	$0.542371\pi$
$354$	−123874.	−0.0525377
$355$	397427.	0.167373
$356$	1.25628e6	0.525367
$357$	0	0
$358$	−5.93973e6	−2.44940
$359$	1.34486e6	0.550734	0.275367	−	0.961339i	$-0.411201\pi$
$359$	1.34486e6	0.550734	0.275367	+	0.961339i	$0.411201\pi$
$360$	1.22608e6	0.498612
$361$	−556911.	−0.224915
$362$	−5.94159e6	−2.38304
$363$	87124.3	0.0347034
$364$	0	0
$365$	1.94068e6	0.762467
$366$	−521910.	−0.203654
$367$	−2.75801e6	−1.06888	−0.534442	−	0.845205i	$-0.679478\pi$
$367$	−2.75801e6	−1.06888	−0.534442	+	0.845205i	$0.679478\pi$
$368$	381273.	0.146763
$369$	1.32836e6	0.507869
$370$	−2.22303e6	−0.844192
$371$	0	0
$372$	−513823.	−0.192511
$373$	3.29037e6	1.22454	0.612269	−	0.790649i	$-0.290257\pi$
$373$	3.29037e6	1.22454	0.612269	+	0.790649i	$0.290257\pi$
$374$	−3.79227e6	−1.40191
$375$	19910.8	0.00731157
$376$	4.81613e6	1.75683
$377$	854311.	0.309573
$378$	0	0
$379$	−1.33527e6	−0.477496	−0.238748	−	0.971081i	$-0.576737\pi$
$379$	−1.33527e6	−0.477496	−0.238748	+	0.971081i	$0.576737\pi$
$380$	1.86744e6	0.663420
$381$	199587.	0.0704402
$382$	7.37336e6	2.58528
$383$	−3.37282e6	−1.17489	−0.587443	−	0.809266i	$-0.699865\pi$
$383$	−3.37282e6	−1.17489	−0.587443	+	0.809266i	$0.699865\pi$
$384$	405851.	0.140455
$385$	0	0
$386$	−1.52034e6	−0.519366
$387$	1.21191e6	0.411332
$388$	9.71061e6	3.27467
$389$	−3.46519e6	−1.16105	−0.580527	−	0.814241i	$-0.697154\pi$
$389$	−3.46519e6	−1.16105	−0.580527	+	0.814241i	$0.697154\pi$
$390$	59956.4	0.0199606
$391$	2.06226e6	0.682183
$392$	0	0
$393$	91217.5	0.0297918
$394$	733548.	0.238061
$395$	−2.15340e6	−0.694435
$396$	−6.23391e6	−1.99766
$397$	−1.75508e6	−0.558882	−0.279441	−	0.960163i	$-0.590149\pi$
$397$	−1.75508e6	−0.558882	−0.279441	+	0.960163i	$0.590149\pi$
$398$	−9.17705e6	−2.90399
$399$	0	0
$400$	98698.0	0.0308431
$401$	−5.12451e6	−1.59145	−0.795723	−	0.605661i	$-0.792909\pi$
$401$	−5.12451e6	−1.59145	−0.795723	+	0.605661i	$0.792909\pi$
$402$	−627574.	−0.193687
$403$	1.51837e6	0.465708
$404$	5.79900e6	1.76766
$405$	1.44670e6	0.438268
$406$	0	0
$407$	4.59490e6	1.37496
$408$	−221151.	−0.0657715
$409$	879358.	0.259931	0.129965	−	0.991519i	$-0.458513\pi$
$409$	879358.	0.259931	0.129965	+	0.991519i	$0.458513\pi$
$410$	1.27529e6	0.374671
$411$	382015.	0.111552
$412$	9.30391e6	2.70037
$413$	0	0
$414$	5.40193e6	1.54899
$415$	−1.30316e6	−0.371429
$416$	−1.02292e6	−0.289807
$417$	66475.7	0.0187207
$418$	−6.15068e6	−1.72180
$419$	−5.68610e6	−1.58227	−0.791133	−	0.611644i	$-0.790508\pi$
$419$	−5.68610e6	−1.58227	−0.791133	+	0.611644i	$0.790508\pi$
$420$	0	0
$421$	627448.	0.172533	0.0862666	−	0.996272i	$-0.472506\pi$
$421$	627448.	0.172533	0.0862666	+	0.996272i	$0.472506\pi$
$422$	−9.11350e6	−2.49117
$423$	5.72147e6	1.55474
$424$	2.20277e6	0.595050
$425$	533844.	0.143365
$426$	−187773.	−0.0501312
$427$	0	0
$428$	773292.	0.204049
$429$	−123927.	−0.0325105
$430$	1.16349e6	0.303452
$431$	−953877.	−0.247343	−0.123671	−	0.992323i	$-0.539467\pi$
$431$	−953877.	−0.247343	−0.123671	+	0.992323i	$0.539467\pi$
$432$	−97472.0	−0.0251287
$433$	4.52050e6	1.15869	0.579344	−	0.815083i	$-0.303309\pi$
$433$	4.52050e6	1.15869	0.579344	+	0.815083i	$0.303309\pi$
$434$	0	0
$435$	−134043.	−0.0339641
$436$	−1.02637e7	−2.58576
$437$	3.34477e6	0.837844
$438$	−916914.	−0.228372
$439$	6.99034e6	1.73116	0.865579	−	0.500772i	$-0.166950\pi$
$439$	6.99034e6	1.73116	0.865579	+	0.500772i	$0.166950\pi$
$440$	−2.43300e6	−0.599115
$441$	0	0
$442$	1.60754e6	0.391387
$443$	−4.66063e6	−1.12833	−0.564164	−	0.825663i	$-0.690801\pi$
$443$	−4.66063e6	−1.12833	−0.564164	+	0.825663i	$0.690801\pi$
$444$	659137.	0.158679
$445$	582478.	0.139437
$446$	−2.64402e6	−0.629401
$447$	−550706.	−0.130362
$448$	0	0
$449$	6.40084e6	1.49838	0.749189	−	0.662357i	$-0.230444\pi$
$449$	6.40084e6	1.49838	0.749189	+	0.662357i	$0.230444\pi$
$450$	1.39837e6	0.325529
$451$	−2.63597e6	−0.610237
$452$	3.59655e6	0.828020
$453$	285740.	0.0654224
$454$	−8.80537e6	−2.00497
$455$	0	0
$456$	−358684.	−0.0807793
$457$	4.09410e6	0.916997	0.458498	−	0.888695i	$-0.348387\pi$
$457$	4.09410e6	0.916997	0.458498	+	0.888695i	$0.348387\pi$
$458$	9.74602e6	2.17102
$459$	−527213.	−0.116803
$460$	3.25459e6	0.717137
$461$	7.91448e6	1.73448	0.867242	−	0.497887i	$-0.165891\pi$
$461$	7.91448e6	1.73448	0.867242	+	0.497887i	$0.165891\pi$
$462$	0	0
$463$	−4.60789e6	−0.998963	−0.499482	−	0.866324i	$-0.666476\pi$
$463$	−4.60789e6	−0.998963	−0.499482	+	0.866324i	$0.666476\pi$
$464$	−664452.	−0.143275
$465$	−238235.	−0.0510943
$466$	1.56363e6	0.333555
$467$	3.90317e6	0.828181	0.414090	−	0.910236i	$-0.364100\pi$
$467$	3.90317e6	0.828181	0.414090	+	0.910236i	$0.364100\pi$
$468$	2.64255e6	0.557711
$469$	0	0
$470$	5.49288e6	1.14698
$471$	300010.	0.0623137
$472$	−2.13083e6	−0.440244
$473$	−2.40487e6	−0.494242
$474$	1.01742e6	0.207996
$475$	865842.	0.176078
$476$	0	0
$477$	2.61684e6	0.526601
$478$	−6.10493e6	−1.22211
$479$	4.42629e6	0.881457	0.440728	−	0.897640i	$-0.354720\pi$
$479$	4.42629e6	0.881457	0.440728	+	0.897640i	$0.354720\pi$
$480$	160498.	0.0317956
$481$	−1.94778e6	−0.383863
$482$	−2.91447e6	−0.571403
$483$	0	0
$484$	3.68654e6	0.715329
$485$	4.50233e6	0.869127
$486$	−2.07381e6	−0.398271
$487$	−2.22924e6	−0.425926	−0.212963	−	0.977060i	$-0.568311\pi$
$487$	−2.22924e6	−0.425926	−0.212963	+	0.977060i	$0.568311\pi$
$488$	−8.97770e6	−1.70654
$489$	3664.10	0.000692939 0
$490$	0	0
$491$	627714.	0.117505	0.0587527	−	0.998273i	$-0.481288\pi$
$491$	627714.	0.117505	0.0587527	+	0.998273i	$0.481288\pi$
$492$	−378129.	−0.0704251
$493$	−3.59393e6	−0.665967
$494$	2.60727e6	0.480694
$495$	−2.89036e6	−0.530199
$496$	−1.18093e6	−0.215536
$497$	0	0
$498$	615704.	0.111250
$499$	1.00327e6	0.180370	0.0901850	−	0.995925i	$-0.471254\pi$
$499$	1.00327e6	0.180370	0.0901850	+	0.995925i	$0.471254\pi$
$500$	842498.	0.150711
$501$	−512908.	−0.0912946
$502$	173517.	0.0307314
$503$	−904051.	−0.159321	−0.0796605	−	0.996822i	$-0.525384\pi$
$503$	−904051.	−0.159321	−0.0796605	+	0.996822i	$0.525384\pi$
$504$	0	0
$505$	2.68871e6	0.469154
$506$	−1.07194e7	−1.86121
$507$	−420603.	−0.0726695
$508$	8.44526e6	1.45196
$509$	−3.02145e6	−0.516917	−0.258458	−	0.966022i	$-0.583215\pi$
$509$	−3.02145e6	−0.516917	−0.258458	+	0.966022i	$0.583215\pi$
$510$	−252226.	−0.0429403
$511$	0	0
$512$	1.82234e6	0.307223
$513$	−855087.	−0.143455
$514$	−5.92076e6	−0.988484
$515$	4.31377e6	0.716702
$516$	−344979.	−0.0570385
$517$	−1.13535e7	−1.86812
$518$	0	0
$519$	764325.	0.124555
$520$	1.03135e6	0.167262
$521$	8882.28	0.00143361	0.000716804	−	1.00000i	$-0.499772\pi$
$521$	8882.28	0.00143361	0.000716804		1.00000i	$0.499772\pi$
$522$	−9.41405e6	−1.51217
$523$	−9.60588e6	−1.53562	−0.767809	−	0.640679i	$-0.778653\pi$
$523$	−9.60588e6	−1.53562	−0.767809	+	0.640679i	$0.778653\pi$
$524$	3.85974e6	0.614087
$525$	0	0
$526$	−302234.	−0.0476298
$527$	−6.38750e6	−1.00185
$528$	96386.1	0.0150463
$529$	−607053.	−0.0943165
$530$	2.51229e6	0.388491
$531$	−2.53138e6	−0.389603
$532$	0	0
$533$	1.11739e6	0.170367
$534$	−275204.	−0.0417639
$535$	358538.	0.0541565
$536$	−1.07953e7	−1.62302
$537$	816561.	0.122195
$538$	1.27343e6	0.189679
$539$	0	0
$540$	−832032.	−0.122788
$541$	2.47643e6	0.363775	0.181887	−	0.983319i	$-0.441779\pi$
$541$	2.47643e6	0.363775	0.181887	+	0.983319i	$0.441779\pi$
$542$	−1.00575e7	−1.47058
$543$	816817.	0.118884
$544$	4.30325e6	0.623446
$545$	−4.75878e6	−0.686285
$546$	0	0
$547$	−1.10660e7	−1.58132	−0.790662	−	0.612253i	$-0.790263\pi$
$547$	−1.10660e7	−1.58132	−0.790662	+	0.612253i	$0.790263\pi$
$548$	1.61644e7	2.29937
$549$	−1.06653e7	−1.51023
$550$	−2.77488e6	−0.391145
$551$	−5.82900e6	−0.817928
$552$	−625117.	−0.0873200
$553$	0	0
$554$	1.11003e7	1.53660
$555$	305610.	0.0421148
$556$	2.81283e6	0.385884
$557$	−4.36913e6	−0.596702	−0.298351	−	0.954456i	$-0.596437\pi$
$557$	−4.36913e6	−0.596702	−0.298351	+	0.954456i	$0.596437\pi$
$558$	−1.67316e7	−2.27485
$559$	1.01943e6	0.137983
$560$	0	0
$561$	521339.	0.0699380
$562$	−8.01682e6	−1.07068
$563$	−5.02223e6	−0.667768	−0.333884	−	0.942614i	$-0.608359\pi$
$563$	−5.02223e6	−0.667768	−0.333884	+	0.942614i	$0.608359\pi$
$564$	−1.62866e6	−0.215592
$565$	1.66755e6	0.219764
$566$	−1.24356e7	−1.63164
$567$	0	0
$568$	−3.23000e6	−0.420079
$569$	−348871.	−0.0451735	−0.0225868	−	0.999745i	$-0.507190\pi$
$569$	−348871.	−0.0451735	−0.0225868	+	0.999745i	$0.507190\pi$
$570$	−409086.	−0.0527384
$571$	1.53588e7	1.97136	0.985680	−	0.168627i	$-0.0539334\pi$
$571$	1.53588e7	1.97136	0.985680	+	0.168627i	$0.0539334\pi$
$572$	−5.24381e6	−0.670126
$573$	−1.01365e6	−0.128974
$574$	0	0
$575$	1.50900e6	0.190335
$576$	1.24918e7	1.56881
$577$	1.05696e7	1.32166	0.660830	−	0.750536i	$-0.270204\pi$
$577$	1.05696e7	1.32166	0.660830	+	0.750536i	$0.270204\pi$
$578$	6.39844e6	0.796626
$579$	209008.	0.0259100
$580$	−5.67184e6	−0.700091
$581$	0	0
$582$	−2.12722e6	−0.260319
$583$	−5.19279e6	−0.632746
$584$	−1.57724e7	−1.91367
$585$	1.22522e6	0.148022
$586$	6.20460e6	0.746397
$587$	−4.57417e6	−0.547920	−0.273960	−	0.961741i	$-0.588334\pi$
$587$	−4.57417e6	−0.547920	−0.273960	+	0.961741i	$0.588334\pi$
$588$	0	0
$589$	−1.03599e7	−1.23046
$590$	−2.43025e6	−0.287422
$591$	−100844.	−0.0118763
$592$	1.51491e6	0.177657
$593$	1.46686e7	1.71297	0.856487	−	0.516169i	$-0.172642\pi$
$593$	1.46686e7	1.71297	0.856487	+	0.516169i	$0.172642\pi$
$594$	2.74041e6	0.318676
$595$	0	0
$596$	−2.33024e7	−2.68710
$597$	1.26161e6	0.144874
$598$	4.54397e6	0.519616
$599$	1.42374e7	1.62130	0.810649	−	0.585532i	$-0.199114\pi$
$599$	1.42374e7	1.62130	0.810649	+	0.585532i	$0.199114\pi$
$600$	−161820.	−0.0183508
$601$	8.21658e6	0.927908	0.463954	−	0.885859i	$-0.346430\pi$
$601$	8.21658e6	0.927908	0.463954	+	0.885859i	$0.346430\pi$
$602$	0	0
$603$	−1.28246e7	−1.43632
$604$	1.20907e7	1.34853
$605$	1.70927e6	0.189855
$606$	−1.27034e6	−0.140520
$607$	1.69772e7	1.87023	0.935114	−	0.354348i	$-0.115297\pi$
$607$	1.69772e7	1.87023	0.935114	+	0.354348i	$0.115297\pi$
$608$	6.97944e6	0.765705
$609$	0	0
$610$	−1.02392e7	−1.11415
$611$	4.81276e6	0.521544
$612$	−1.11168e7	−1.19977
$613$	5.22841e6	0.561977	0.280988	−	0.959711i	$-0.409338\pi$
$613$	5.22841e6	0.561977	0.280988	+	0.959711i	$0.409338\pi$
$614$	−1.24417e6	−0.133186
$615$	−175320.	−0.0186915
$616$	0	0
$617$	−1.71179e7	−1.81025	−0.905123	−	0.425150i	$-0.860221\pi$
$617$	−1.71179e7	−1.81025	−0.905123	+	0.425150i	$0.860221\pi$
$618$	−2.03813e6	−0.214665
$619$	7.20377e6	0.755672	0.377836	−	0.925872i	$-0.376668\pi$
$619$	7.20377e6	0.755672	0.377836	+	0.925872i	$0.376668\pi$
$620$	−1.00806e7	−1.05319
$621$	−1.49025e6	−0.155071
$622$	3.66158e6	0.379483
$623$	0	0
$624$	−40858.0	−0.00420065
$625$	390625.	0.0400000
$626$	1.27595e7	1.30136
$627$	845560.	0.0858966
$628$	1.26945e7	1.28445
$629$	8.19395e6	0.825784
$630$	0	0
$631$	8.56923e6	0.856779	0.428389	−	0.903594i	$-0.359081\pi$
$631$	8.56923e6	0.856779	0.428389	+	0.903594i	$0.359081\pi$
$632$	1.75013e7	1.74292
$633$	1.25287e6	0.124279
$634$	1.56547e7	1.54675
$635$	3.91565e6	0.385363
$636$	−744905.	−0.0730227
$637$	0	0
$638$	1.86810e7	1.81697
$639$	−3.83717e6	−0.371757
$640$	7.96229e6	0.768401
$641$	9.91653e6	0.953267	0.476633	−	0.879102i	$-0.341857\pi$
$641$	9.91653e6	0.953267	0.476633	+	0.879102i	$0.341857\pi$
$642$	−169399.	−0.0162208
$643$	3.70762e6	0.353645	0.176822	−	0.984243i	$-0.443418\pi$
$643$	3.70762e6	0.353645	0.176822	+	0.984243i	$0.443418\pi$
$644$	0	0
$645$	−159950.	−0.0151385
$646$	−1.09683e7	−1.03409
$647$	6.36378e6	0.597660	0.298830	−	0.954306i	$-0.403404\pi$
$647$	6.36378e6	0.597660	0.298830	+	0.954306i	$0.403404\pi$
$648$	−1.17577e7	−1.09998
$649$	5.02321e6	0.468133
$650$	1.17627e6	0.109200
$651$	0	0
$652$	155041.	0.0142833
$653$	7.58179e6	0.695807	0.347903	−	0.937530i	$-0.386894\pi$
$653$	7.58179e6	0.695807	0.347903	+	0.937530i	$0.386894\pi$
$654$	2.24839e6	0.205554
$655$	1.78957e6	0.162984
$656$	−869063.	−0.0788482
$657$	−1.87373e7	−1.69354
$658$	0	0
$659$	−9.44484e6	−0.847191	−0.423595	−	0.905851i	$-0.639232\pi$
$659$	−9.44484e6	−0.847191	−0.423595	+	0.905851i	$0.639232\pi$
$660$	822763.	0.0735216
$661$	−2.23762e7	−1.99197	−0.995985	−	0.0895192i	$-0.971467\pi$
$661$	−2.23762e7	−1.99197	−0.995985	+	0.0895192i	$0.971467\pi$
$662$	−1.47397e7	−1.30721
$663$	−220996.	−0.0195254
$664$	1.05911e7	0.932226
$665$	0	0
$666$	2.14635e7	1.87506
$667$	−1.01588e7	−0.884155
$668$	−2.17030e7	−1.88182
$669$	363485.	0.0313994
$670$	−1.23122e7	−1.05962
$671$	2.11640e7	1.81464
$672$	0	0
$673$	121935.	0.0103775	0.00518875	−	0.999987i	$-0.498348\pi$
$673$	121935.	0.0103775	0.00518875	+	0.999987i	$0.498348\pi$
$674$	7.63267e6	0.647183
$675$	−385773.	−0.0325891
$676$	−1.77972e7	−1.49791
$677$	−4.12171e6	−0.345625	−0.172813	−	0.984955i	$-0.555286\pi$
$677$	−4.12171e6	−0.345625	−0.172813	+	0.984955i	$0.555286\pi$
$678$	−787868.	−0.0658232
$679$	0	0
$680$	−4.33870e6	−0.359822
$681$	1.21051e6	0.100023
$682$	3.32017e7	2.73338
$683$	−4.30505e6	−0.353123	−0.176562	−	0.984290i	$-0.556497\pi$
$683$	−4.30505e6	−0.353123	−0.176562	+	0.984290i	$0.556497\pi$
$684$	−1.80303e7	−1.47354
$685$	7.49466e6	0.610275
$686$	0	0
$687$	−1.33983e6	−0.108307
$688$	−792873.	−0.0638605
$689$	2.20122e6	0.176651
$690$	−712957.	−0.0570086
$691$	1.54709e7	1.23260	0.616298	−	0.787513i	$-0.288632\pi$
$691$	1.54709e7	1.23260	0.616298	+	0.787513i	$0.288632\pi$
$692$	3.23414e7	2.56740
$693$	0	0
$694$	2.43749e7	1.92107
$695$	1.30417e6	0.102417
$696$	1.08940e6	0.0852444
$697$	−4.70065e6	−0.366501
$698$	3.02932e7	2.35346
$699$	−214958.	−0.0166403
$700$	0	0
$701$	631976.	0.0485742	0.0242871	−	0.999705i	$-0.492268\pi$
$701$	631976.	0.0485742	0.0242871	+	0.999705i	$0.492268\pi$
$702$	−1.16166e6	−0.0889684
$703$	1.32898e7	1.01421
$704$	−2.47884e7	−1.88502
$705$	−755130.	−0.0572202
$706$	5.76032e6	0.434945
$707$	0	0
$708$	720578.	0.0540254
$709$	−1.13182e7	−0.845594	−0.422797	−	0.906224i	$-0.638952\pi$
$709$	−1.13182e7	−0.845594	−0.422797	+	0.906224i	$0.638952\pi$
$710$	−3.68387e6	−0.274257
$711$	2.07912e7	1.54243
$712$	−4.73396e6	−0.349965
$713$	−1.80553e7	−1.33009
$714$	0	0
$715$	−2.43130e6	−0.177858
$716$	3.45516e7	2.51876
$717$	839271.	0.0609684
$718$	−1.24659e7	−0.902431
$719$	−1.35453e7	−0.977162	−0.488581	−	0.872519i	$-0.662485\pi$
$719$	−1.35453e7	−0.977162	−0.488581	+	0.872519i	$0.662485\pi$
$720$	−952934.	−0.0685065
$721$	0	0
$722$	5.16218e6	0.368545
$723$	400666.	0.0285060
$724$	3.45625e7	2.45052
$725$	−2.62976e6	−0.185811
$726$	−807581.	−0.0568649
$727$	−1.41927e7	−0.995932	−0.497966	−	0.867197i	$-0.665920\pi$
$727$	−1.41927e7	−0.995932	−0.497966	+	0.867197i	$0.665920\pi$
$728$	0	0
$729$	−1.37768e7	−0.960129
$730$	−1.79887e7	−1.24938
$731$	−4.28854e6	−0.296836
$732$	3.03597e6	0.209421
$733$	−1.55238e6	−0.106718	−0.0533591	−	0.998575i	$-0.516993\pi$
$733$	−1.55238e6	−0.106718	−0.0533591	+	0.998575i	$0.516993\pi$
$734$	2.55648e7	1.75147
$735$	0	0
$736$	1.21638e7	0.827704
$737$	2.54488e7	1.72583
$738$	−1.23130e7	−0.832191
$739$	−1.20108e7	−0.809026	−0.404513	−	0.914532i	$-0.632559\pi$
$739$	−1.20108e7	−0.809026	−0.404513	+	0.914532i	$0.632559\pi$
$740$	1.29315e7	0.868097
$741$	−358433.	−0.0239807
$742$	0	0
$743$	7.84220e6	0.521154	0.260577	−	0.965453i	$-0.416087\pi$
$743$	7.84220e6	0.521154	0.260577	+	0.965453i	$0.416087\pi$
$744$	1.93620e6	0.128238
$745$	−1.08042e7	−0.713182
$746$	−3.04994e7	−2.00652
$747$	1.25820e7	0.824991
$748$	2.20598e7	1.44161
$749$	0	0
$750$	−184559.	−0.0119807
$751$	−3.95564e6	−0.255927	−0.127964	−	0.991779i	$-0.540844\pi$
$751$	−3.95564e6	−0.255927	−0.127964	+	0.991779i	$0.540844\pi$
$752$	−3.74319e6	−0.241378
$753$	−23854.1	−0.00153312
$754$	−7.91886e6	−0.507264
$755$	5.60587e6	0.357912
$756$	0	0
$757$	2.28287e7	1.44791	0.723956	−	0.689846i	$-0.242322\pi$
$757$	2.28287e7	1.44791	0.723956	+	0.689846i	$0.242322\pi$
$758$	1.23770e7	0.782424
$759$	1.47365e6	0.0928516
$760$	−7.03694e6	−0.441926
$761$	−2.59221e7	−1.62259	−0.811295	−	0.584638i	$-0.801237\pi$
$761$	−2.59221e7	−1.62259	−0.811295	+	0.584638i	$0.801237\pi$
$762$	−1.85003e6	−0.115423
$763$	0	0
$764$	−4.28911e7	−2.65848
$765$	−5.15429e6	−0.318431
$766$	3.12636e7	1.92516
$767$	−2.12934e6	−0.130694
$768$	−1.65163e6	−0.101044
$769$	−381532.	−0.0232656	−0.0116328	−	0.999932i	$-0.503703\pi$
$769$	−381532.	−0.0232656	−0.0116328	+	0.999932i	$0.503703\pi$
$770$	0	0
$771$	813953.	0.0493132
$772$	8.84390e6	0.534073
$773$	−9.18755e6	−0.553033	−0.276516	−	0.961009i	$-0.589180\pi$
$773$	−9.18755e6	−0.553033	−0.276516	+	0.961009i	$0.589180\pi$
$774$	−1.12335e7	−0.674006
$775$	−4.67387e6	−0.279526
$776$	−3.65917e7	−2.18136
$777$	0	0
$778$	3.21198e7	1.90250
$779$	−7.62398e6	−0.450130
$780$	−348769.	−0.0205259
$781$	7.61438e6	0.446691
$782$	−1.91157e7	−1.11782
$783$	2.59709e6	0.151385
$784$	0	0
$785$	5.88583e6	0.340905
$786$	−845522.	−0.0488167
$787$	−6.94528e6	−0.399717	−0.199859	−	0.979825i	$-0.564048\pi$
$787$	−6.94528e6	−0.399717	−0.199859	+	0.979825i	$0.564048\pi$
$788$	−4.26708e6	−0.244802
$789$	41549.4	0.00237614
$790$	1.99605e7	1.13790
$791$	0	0
$792$	2.34907e7	1.33071
$793$	−8.97141e6	−0.506614
$794$	1.62683e7	0.915782
$795$	−345376.	−0.0193809
$796$	5.33833e7	2.98623
$797$	5.81421e6	0.324224	0.162112	−	0.986772i	$-0.448169\pi$
$797$	5.81421e6	0.324224	0.162112	+	0.986772i	$0.448169\pi$
$798$	0	0
$799$	−2.02464e7	−1.12197
$800$	3.14878e6	0.173947
$801$	−5.62385e6	−0.309708
$802$	4.75007e7	2.60774
$803$	3.71818e7	2.03489
$804$	3.65063e6	0.199172
$805$	0	0
$806$	−1.40742e7	−0.763108
$807$	−175064.	−0.00946265
$808$	−2.18519e7	−1.17750
$809$	−2.76000e7	−1.48265	−0.741324	−	0.671147i	$-0.765802\pi$
$809$	−2.76000e7	−1.48265	−0.741324	+	0.671147i	$0.765802\pi$
$810$	−1.34099e7	−0.718144
$811$	−5.51268e6	−0.294314	−0.147157	−	0.989113i	$-0.547012\pi$
$811$	−5.51268e6	−0.294314	−0.147157	+	0.989113i	$0.547012\pi$
$812$	0	0
$813$	1.38264e6	0.0733641
$814$	−4.25915e7	−2.25300
$815$	71885.0	0.00379092
$816$	171883.	0.00903663
$817$	−6.95559e6	−0.364568
$818$	−8.15103e6	−0.425921
$819$	0	0
$820$	−7.41842e6	−0.385281
$821$	4.69730e6	0.243215	0.121607	−	0.992578i	$-0.461195\pi$
$821$	4.69730e6	0.243215	0.121607	+	0.992578i	$0.461195\pi$
$822$	−3.54101e6	−0.182788
$823$	1.68012e7	0.864652	0.432326	−	0.901717i	$-0.357693\pi$
$823$	1.68012e7	0.864652	0.432326	+	0.901717i	$0.357693\pi$
$824$	−3.50592e7	−1.79880
$825$	381475.	0.0195133
$826$	0	0
$827$	1.91479e6	0.0973548	0.0486774	−	0.998815i	$-0.484499\pi$
$827$	1.91479e6	0.0973548	0.0486774	+	0.998815i	$0.484499\pi$
$828$	−3.14233e7	−1.59285
$829$	7.32861e6	0.370369	0.185185	−	0.982704i	$-0.440712\pi$
$829$	7.32861e6	0.370369	0.185185	+	0.982704i	$0.440712\pi$
$830$	1.20793e7	0.608622
$831$	−1.52601e6	−0.0766574
$832$	1.05078e7	0.526263
$833$	0	0
$834$	−616183.	−0.0306757
$835$	−1.00626e7	−0.499453
$836$	3.57787e7	1.77055
$837$	4.61581e6	0.227737
$838$	5.27062e7	2.59269
$839$	−1.77241e7	−0.869281	−0.434641	−	0.900604i	$-0.643125\pi$
$839$	−1.77241e7	−0.869281	−0.434641	+	0.900604i	$0.643125\pi$
$840$	0	0
$841$	−2.80718e6	−0.136861
$842$	−5.81601e6	−0.282712
$843$	1.10211e6	0.0534140
$844$	5.30136e7	2.56172
$845$	−8.25170e6	−0.397559
$846$	−5.30340e7	−2.54759
$847$	0	0
$848$	−1.71203e6	−0.0817565
$849$	1.70958e6	0.0813990
$850$	−4.94836e6	−0.234917
$851$	2.31615e7	1.09633
$852$	1.09228e6	0.0515508
$853$	−2.61947e7	−1.23265	−0.616327	−	0.787490i	$-0.711380\pi$
$853$	−2.61947e7	−1.23265	−0.616327	+	0.787490i	$0.711380\pi$
$854$	0	0
$855$	−8.35975e6	−0.391091
$856$	−2.91393e6	−0.135924
$857$	−3.21925e7	−1.49728	−0.748639	−	0.662977i	$-0.769293\pi$
$857$	−3.21925e7	−1.49728	−0.748639	+	0.662977i	$0.769293\pi$
$858$	1.14872e6	0.0532715
$859$	−2.22096e7	−1.02697	−0.513485	−	0.858098i	$-0.671646\pi$
$859$	−2.22096e7	−1.02697	−0.513485	+	0.858098i	$0.671646\pi$
$860$	−6.76805e6	−0.312045
$861$	0	0
$862$	8.84177e6	0.405295
$863$	2.10546e7	0.962322	0.481161	−	0.876632i	$-0.340215\pi$
$863$	2.10546e7	0.962322	0.481161	+	0.876632i	$0.340215\pi$
$864$	−3.10966e6	−0.141719
$865$	1.49951e7	0.681411
$866$	−4.19018e7	−1.89862
$867$	−879621.	−0.0397418
$868$	0	0
$869$	−4.12574e7	−1.85333
$870$	1.24248e6	0.0556535
$871$	−1.07877e7	−0.481820
$872$	3.86759e7	1.72246
$873$	−4.34703e7	−1.93044
$874$	−3.10037e7	−1.37289
$875$	0	0
$876$	5.33373e6	0.234839
$877$	1.49233e7	0.655189	0.327594	−	0.944818i	$-0.393762\pi$
$877$	1.49233e7	0.655189	0.327594	+	0.944818i	$0.393762\pi$
$878$	−6.47955e7	−2.83667
$879$	−852974.	−0.0372360
$880$	1.89098e6	0.0823150
$881$	3.85987e7	1.67546	0.837729	−	0.546087i	$-0.183883\pi$
$881$	3.85987e7	1.67546	0.837729	+	0.546087i	$0.183883\pi$
$882$	0	0
$883$	−3.35117e7	−1.44642	−0.723210	−	0.690628i	$-0.757334\pi$
$883$	−3.35117e7	−1.44642	−0.723210	+	0.690628i	$0.757334\pi$
$884$	−9.35113e6	−0.402470
$885$	334097.	0.0143388
$886$	4.32008e7	1.84887
$887$	4.18929e7	1.78785	0.893927	−	0.448213i	$-0.147939\pi$
$887$	4.18929e7	1.78785	0.893927	+	0.448213i	$0.147939\pi$
$888$	−2.48377e6	−0.105701
$889$	0	0
$890$	−5.39916e6	−0.228482
$891$	2.77176e7	1.16966
$892$	1.53804e7	0.647224
$893$	−3.28377e7	−1.37798
$894$	5.10465e6	0.213610
$895$	1.60199e7	0.668501
$896$	0	0
$897$	−624679.	−0.0259224
$898$	−5.93313e7	−2.45524
$899$	3.14653e7	1.29847
$900$	−8.13436e6	−0.334747
$901$	−9.26015e6	−0.380020
$902$	2.44336e7	0.999932
$903$	0	0
$904$	−1.35526e7	−0.551571
$905$	1.60249e7	0.650391
$906$	−2.64861e6	−0.107201
$907$	2.30904e6	0.0931993	0.0465997	−	0.998914i	$-0.485161\pi$
$907$	2.30904e6	0.0931993	0.0465997	+	0.998914i	$0.485161\pi$
$908$	5.12212e7	2.06175
$909$	−2.59596e7	−1.04205
$910$	0	0
$911$	1.48503e7	0.592843	0.296421	−	0.955057i	$-0.404207\pi$
$911$	1.48503e7	0.592843	0.296421	+	0.955057i	$0.404207\pi$
$912$	278776.	0.0110986
$913$	−2.49674e7	−0.991281
$914$	−3.79494e7	−1.50259
$915$	1.40763e6	0.0555822
$916$	−5.66930e7	−2.23250
$917$	0	0
$918$	4.88689e6	0.191393
$919$	1.02358e7	0.399793	0.199896	−	0.979817i	$-0.435939\pi$
$919$	1.02358e7	0.399793	0.199896	+	0.979817i	$0.435939\pi$
$920$	−1.22640e7	−0.477709
$921$	171041.	0.00664433
$922$	−7.33617e7	−2.84212
$923$	−3.22773e6	−0.124708
$924$	0	0
$925$	5.99568e6	0.230401
$926$	4.27119e7	1.63690
$927$	−4.16496e7	−1.59189
$928$	−2.11981e7	−0.808029
$929$	−2.00459e7	−0.762054	−0.381027	−	0.924564i	$-0.624429\pi$
$929$	−2.00459e7	−0.762054	−0.381027	+	0.924564i	$0.624429\pi$
$930$	2.20827e6	0.0837229
$931$	0	0
$932$	−9.09567e6	−0.343001
$933$	−503373.	−0.0189315
$934$	−3.61796e7	−1.35705
$935$	1.02280e7	0.382616
$936$	−9.95772e6	−0.371510
$937$	−3.63602e7	−1.35293	−0.676467	−	0.736473i	$-0.736490\pi$
$937$	−3.63602e7	−1.35293	−0.676467	+	0.736473i	$0.736490\pi$
$938$	0	0
$939$	−1.75411e6	−0.0649221
$940$	−3.19523e7	−1.17946
$941$	1.57487e7	0.579789	0.289895	−	0.957059i	$-0.406380\pi$
$941$	1.57487e7	0.579789	0.289895	+	0.957059i	$0.406380\pi$
$942$	−2.78088e6	−0.102107
$943$	−1.32871e7	−0.486577
$944$	1.65612e6	0.0604870
$945$	0	0
$946$	2.22915e7	0.809862
$947$	−2.19938e7	−0.796938	−0.398469	−	0.917182i	$-0.630458\pi$
$947$	−2.19938e7	−0.796938	−0.398469	+	0.917182i	$0.630458\pi$
$948$	−5.91837e6	−0.213885
$949$	−1.57614e7	−0.568105
$950$	−8.02575e6	−0.288520
$951$	−2.15212e6	−0.0771640
$952$	0	0
$953$	3.79156e7	1.35234	0.676170	−	0.736746i	$-0.263639\pi$
$953$	3.79156e7	1.35234	0.676170	+	0.736746i	$0.263639\pi$
$954$	−2.42563e7	−0.862887
$955$	−1.98865e7	−0.705586
$956$	3.55126e7	1.25672
$957$	−2.56815e6	−0.0906445
$958$	−4.10286e7	−1.44435
$959$	0	0
$960$	−1.64869e6	−0.0577379
$961$	2.72941e7	0.953368
$962$	1.80545e7	0.628996
$963$	−3.46170e6	−0.120288
$964$	1.69536e7	0.587584
$965$	4.10048e6	0.141748
$966$	0	0
$967$	−2.20041e7	−0.756724	−0.378362	−	0.925658i	$-0.623513\pi$
$967$	−2.20041e7	−0.756724	−0.378362	+	0.925658i	$0.623513\pi$
$968$	−1.38917e7	−0.476505
$969$	1.50786e6	0.0515885
$970$	−4.17335e7	−1.42415
$971$	−3.57397e7	−1.21647	−0.608237	−	0.793755i	$-0.708123\pi$
$971$	−3.57397e7	−1.21647	−0.608237	+	0.793755i	$0.708123\pi$
$972$	1.20634e7	0.409548
$973$	0	0
$974$	2.06635e7	0.697921
$975$	−161707.	−0.00544775
$976$	6.97764e6	0.234468
$977$	−5.52739e7	−1.85261	−0.926305	−	0.376774i	$-0.877033\pi$
$977$	−5.52739e7	−1.85261	−0.926305	+	0.376774i	$0.877033\pi$
$978$	−33963.6	−0.00113545
$979$	1.11598e7	0.372134
$980$	0	0
$981$	4.59463e7	1.52433
$982$	−5.81847e6	−0.192544
$983$	−22923.2	−0.000756644 0	−0.000378322	−	1.00000i	$-0.500120\pi$
$983$	−22923.2	−0.000756644 0	−0.000378322		1.00000i	$0.500120\pi$
$984$	1.42487e6	0.0469125
$985$	−1.97843e6	−0.0649727
$986$	3.33132e7	1.09125
$987$	0	0
$988$	−1.51666e7	−0.494306
$989$	−1.21222e7	−0.394087
$990$	2.67916e7	0.868782
$991$	−8.30772e6	−0.268719	−0.134359	−	0.990933i	$-0.542898\pi$
$991$	−8.30772e6	−0.268719	−0.134359	+	0.990933i	$0.542898\pi$
$992$	−3.76754e7	−1.21557
$993$	2.02633e6	0.0652136
$994$	0	0
$995$	2.47512e7	0.792572
$996$	−3.58157e6	−0.114400
$997$	3.35426e7	1.06871	0.534353	−	0.845261i	$-0.320555\pi$
$997$	3.35426e7	1.06871	0.534353	+	0.845261i	$0.320555\pi$
$998$	−9.29956e6	−0.295554
$999$	−5.92120e6	−0.187714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.m.1.2	yes	10
7.6	odd	2		245.6.a.l.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.2	✓	10	7.6	odd	2
245.6.a.m.1.2	yes	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-9.26930 q^{2} +1.27429 q^{3} +53.9199 q^{4} +25.0000 q^{5} -11.8118 q^{6} -203.182 q^{8} -241.376 q^{9} -231.732 q^{10} +478.980 q^{11} +68.7096 q^{12} -203.039 q^{13} +31.8573 q^{15} +157.917 q^{16} +854.151 q^{17} +2237.39 q^{18} +1385.35 q^{19} +1348.00 q^{20} -4439.81 q^{22} +2414.39 q^{23} -258.913 q^{24} +625.000 q^{25} +1882.03 q^{26} -617.236 q^{27} -4207.61 q^{29} -295.295 q^{30} -7478.19 q^{31} +5038.04 q^{32} +610.360 q^{33} -7917.38 q^{34} -13015.0 q^{36} +9593.09 q^{37} -12841.2 q^{38} -258.731 q^{39} -5079.55 q^{40} -5503.30 q^{41} -5020.82 q^{43} +25826.5 q^{44} -6034.40 q^{45} -22379.7 q^{46} -23703.5 q^{47} +201.232 q^{48} -5793.31 q^{50} +1088.44 q^{51} -10947.9 q^{52} -10841.4 q^{53} +5721.35 q^{54} +11974.5 q^{55} +1765.34 q^{57} +39001.6 q^{58} +10487.3 q^{59} +1717.74 q^{60} +44185.5 q^{61} +69317.5 q^{62} -51752.4 q^{64} -5075.99 q^{65} -5657.61 q^{66} +53131.2 q^{67} +46055.7 q^{68} +3076.64 q^{69} +15897.1 q^{71} +49043.3 q^{72} +77627.1 q^{73} -88921.2 q^{74} +796.432 q^{75} +74697.8 q^{76} +2398.26 q^{78} -86136.0 q^{79} +3947.92 q^{80} +57867.9 q^{81} +51011.7 q^{82} -52126.2 q^{83} +21353.8 q^{85} +46539.5 q^{86} -5361.72 q^{87} -97320.0 q^{88} +23299.1 q^{89} +55934.7 q^{90} +130184. q^{92} -9529.38 q^{93} +219715. q^{94} +34633.7 q^{95} +6419.93 q^{96} +180093. q^{97} -115614. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19}+ \cdots + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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