LMFDB - Embedded newform 2057.4.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2057,4,Mod(1,2057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2057, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2057.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2057 = 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2057.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:	$121.366928882$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.2636.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 14x - 4 $ x^3 - 14*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.87707$ of defining polynomial
Character	$\chi$	$=$	2057.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +O(q^{10})$	\(q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} -4.12682 q^{10} -19.3918 q^{12} -58.1117 q^{13} -10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} +17.0000 q^{17} +23.2065 q^{18} -89.1688 q^{19} -18.6361 q^{20} +25.0493 q^{21} -115.269 q^{23} +60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} -138.956 q^{27} -48.8108 q^{28} +128.558 q^{29} -13.0186 q^{30} +273.460 q^{31} -185.316 q^{32} -23.1408 q^{34} +24.0732 q^{35} +104.797 q^{36} -132.351 q^{37} +121.379 q^{38} -183.321 q^{39} +58.3825 q^{40} +470.559 q^{41} -34.0977 q^{42} -352.642 q^{43} -51.6854 q^{45} +156.907 q^{46} +152.598 q^{47} +72.4403 q^{48} -279.949 q^{49} +157.641 q^{50} +53.6287 q^{51} +357.217 q^{52} +527.614 q^{53} +189.150 q^{54} +152.912 q^{56} -281.295 q^{57} -174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} +53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} -176.178 q^{65} +52.9572 q^{67} -104.500 q^{68} -363.632 q^{69} -32.7690 q^{70} +788.400 q^{71} -328.304 q^{72} -295.780 q^{73} +180.159 q^{74} -365.334 q^{75} +548.127 q^{76} +249.541 q^{78} +720.325 q^{79} +69.6175 q^{80} +21.9487 q^{81} -640.535 q^{82} +116.051 q^{83} -153.980 q^{84} +51.5390 q^{85} +480.024 q^{86} +405.552 q^{87} -813.329 q^{89} +70.3553 q^{90} -461.435 q^{91} +708.569 q^{92} +862.664 q^{93} -207.720 q^{94} -270.334 q^{95} -584.605 q^{96} +794.693 q^{97} +381.072 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) $ 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} + 56 q^{10} + 22 q^{12} - 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} + 51 q^{17} + 103 q^{18} - 80 q^{19} - 168 q^{20} + 192 q^{21} + 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} - 476 q^{28} + 456 q^{29} - 400 q^{30} + 230 q^{31} + 71 q^{32} - 17 q^{34} + 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} - 556 q^{43} - 384 q^{45} + 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} - 547 q^{50} + 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} + 684 q^{56} + 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 1008 q^{67} + 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} + 927 q^{72} - 838 q^{73} - 836 q^{74} - 1548 q^{75} + 908 q^{76} + 1308 q^{78} + 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} + 2396 q^{83} + 2040 q^{84} - 136 q^{85} - 1264 q^{86} - 1428 q^{87} - 170 q^{89} + 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} + 472 q^{95} - 678 q^{96} - 270 q^{97} - 2857 q^{98}+O(q^{100}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 + 56 * q^10 + 22 * q^12 - 30 * q^13 + 92 * q^14 + 108 * q^15 + 137 * q^16 + 51 * q^17 + 103 * q^18 - 80 * q^19 - 168 * q^20 + 192 * q^21 + 142 * q^23 + 666 * q^24 - 223 * q^25 + 26 * q^26 - 20 * q^27 - 476 * q^28 + 456 * q^29 - 400 * q^30 + 230 * q^31 + 71 * q^32 - 17 * q^34 + 332 * q^35 + 1313 * q^36 + 356 * q^37 + 724 * q^38 - 268 * q^39 + 424 * q^40 + 294 * q^41 - 1128 * q^42 - 556 * q^43 - 384 * q^45 + 704 * q^46 + 640 * q^47 + 774 * q^48 - 269 * q^49 - 547 * q^50 + 68 * q^51 + 774 * q^52 + 302 * q^53 + 1100 * q^54 + 684 * q^56 + 720 * q^57 - 1304 * q^58 + 636 * q^59 + 1328 * q^60 + 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 - 408 * q^65 + 1008 * q^67 + 425 * q^68 + 576 * q^69 - 1504 * q^70 - 402 * q^71 + 927 * q^72 - 838 * q^73 - 836 * q^74 - 1548 * q^75 + 908 * q^76 + 1308 * q^78 + 594 * q^79 - 40 * q^80 - 505 * q^81 + 358 * q^82 + 2396 * q^83 + 2040 * q^84 - 136 * q^85 - 1264 * q^86 - 1428 * q^87 - 170 * q^89 + 2008 * q^90 - 1016 * q^91 + 4896 * q^92 + 632 * q^93 + 2016 * q^94 + 472 * q^95 - 678 * q^96 - 270 * q^97 - 2857 * q^98

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 $

$2$	−1.36122	−0.481264	−0.240632	−	0.970616i	$-0.577355\pi$
$2$	−1.36122	−0.481264	−0.240632	+	0.970616i	$0.577355\pi$
$3$	3.15463	0.607109	0.303555	−	0.952814i	$-0.401827\pi$
$3$	3.15463	0.607109	0.303555	+	0.952814i	$0.401827\pi$
$4$	−6.14708	−0.768385
$5$	3.03171	0.271164	0.135582	−	0.990766i	$-0.456710\pi$
$5$	3.03171	0.271164	0.135582	+	0.990766i	$0.456710\pi$
$6$	−4.29415	−0.292180
$7$	7.94049	0.428746	0.214373	−	0.976752i	$-0.431229\pi$
$7$	7.94049	0.428746	0.214373	+	0.976752i	$0.431229\pi$
$8$	19.2573	0.851061
$9$	−17.0483	−0.631419
$10$	−4.12682	−0.130502
$11$	0	0
$11$	0	0
$12$	−19.3918	−0.466493
$13$	−58.1117	−1.23979	−0.619896	−	0.784684i	$-0.712825\pi$
$13$	−58.1117	−1.23979	−0.619896	+	0.784684i	$0.712825\pi$
$14$	−10.8088	−0.206340
$15$	9.56391	0.164626
$16$	22.9632	0.358799
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	23.2065	0.303879
$19$	−89.1688	−1.07667	−0.538335	−	0.842731i	$-0.680946\pi$
$19$	−89.1688	−1.07667	−0.538335	+	0.842731i	$0.680946\pi$
$20$	−18.6361	−0.208358
$21$	25.0493	0.260296
$22$	0	0
$23$	−115.269	−1.04501	−0.522507	−	0.852635i	$-0.675003\pi$
$23$	−115.269	−1.04501	−0.522507	+	0.852635i	$0.675003\pi$
$24$	60.7497	0.516687
$25$	−115.809	−0.926470
$26$	79.1029	0.596668
$27$	−138.956	−0.990449
$28$	−48.8108	−0.329442
$29$	128.558	0.823191	0.411596	−	0.911367i	$-0.364972\pi$
$29$	128.558	0.823191	0.411596	+	0.911367i	$0.364972\pi$
$30$	−13.0186	−0.0792287
$31$	273.460	1.58435	0.792174	−	0.610295i	$-0.208949\pi$
$31$	273.460	1.58435	0.792174	+	0.610295i	$0.208949\pi$
$32$	−185.316	−1.02374
$33$	0	0
$34$	−23.1408	−0.116724
$35$	24.0732	0.116260
$36$	104.797	0.485172
$37$	−132.351	−0.588063	−0.294031	−	0.955796i	$-0.594997\pi$
$37$	−132.351	−0.588063	−0.294031	+	0.955796i	$0.594997\pi$
$38$	121.379	0.518163
$39$	−183.321	−0.752689
$40$	58.3825	0.230777
$41$	470.559	1.79241	0.896207	−	0.443636i	$-0.146312\pi$
$41$	470.559	1.79241	0.896207	+	0.443636i	$0.146312\pi$
$42$	−34.0977	−0.125271
$43$	−352.642	−1.25064	−0.625318	−	0.780370i	$-0.715031\pi$
$43$	−352.642	−1.25064	−0.625318	+	0.780370i	$0.715031\pi$
$44$	0	0
$45$	−51.6854	−0.171218
$46$	156.907	0.502928
$47$	152.598	0.473589	0.236795	−	0.971560i	$-0.423903\pi$
$47$	152.598	0.473589	0.236795	+	0.971560i	$0.423903\pi$
$48$	72.4403	0.217830
$49$	−279.949	−0.816177
$50$	157.641	0.445877
$51$	53.6287	0.147246
$52$	357.217	0.952637
$53$	527.614	1.36742	0.683711	−	0.729753i	$-0.260365\pi$
$53$	527.614	1.36742	0.683711	+	0.729753i	$0.260365\pi$
$54$	189.150	0.476668
$55$	0	0
$56$	152.912	0.364889
$57$	−281.295	−0.653656
$58$	−174.995	−0.396173
$59$	−292.020	−0.644368	−0.322184	−	0.946677i	$-0.604417\pi$
$59$	−292.020	−0.644368	−0.322184	+	0.946677i	$0.604417\pi$
$60$	−58.7901	−0.126496
$61$	53.8962	0.113126	0.0565632	−	0.998399i	$-0.481986\pi$
$61$	53.8962	0.113126	0.0565632	+	0.998399i	$0.481986\pi$
$62$	−372.239	−0.762490
$63$	−135.372	−0.270718
$64$	68.5514	0.133889
$65$	−176.178	−0.336187
$66$	0	0
$67$	52.9572	0.0965635	0.0482817	−	0.998834i	$-0.484625\pi$
$67$	52.9572	0.0965635	0.0482817	+	0.998834i	$0.484625\pi$
$68$	−104.500	−0.186361
$69$	−363.632	−0.634437
$70$	−32.7690	−0.0559520
$71$	788.400	1.31783	0.658915	−	0.752218i	$-0.271016\pi$
$71$	788.400	1.31783	0.658915	+	0.752218i	$0.271016\pi$
$72$	−328.304	−0.537375
$73$	−295.780	−0.474224	−0.237112	−	0.971482i	$-0.576201\pi$
$73$	−295.780	−0.474224	−0.237112	+	0.971482i	$0.576201\pi$
$74$	180.159	0.283014
$75$	−365.334	−0.562468
$76$	548.127	0.827296
$77$	0	0
$78$	249.541	0.362242
$79$	720.325	1.02586	0.512930	−	0.858430i	$-0.328560\pi$
$79$	720.325	1.02586	0.512930	+	0.858430i	$0.328560\pi$
$80$	69.6175	0.0972934
$81$	21.9487	0.0301079
$82$	−640.535	−0.862625
$83$	116.051	0.153473	0.0767363	−	0.997051i	$-0.475550\pi$
$83$	116.051	0.153473	0.0767363	+	0.997051i	$0.475550\pi$
$84$	−153.980	−0.200007
$85$	51.5390	0.0657669
$86$	480.024	0.601887
$87$	405.552	0.499767
$88$	0	0
$89$	−813.329	−0.968682	−0.484341	−	0.874879i	$-0.660941\pi$
$89$	−813.329	−0.968682	−0.484341	+	0.874879i	$0.660941\pi$
$90$	70.3553	0.0824011
$91$	−461.435	−0.531556
$92$	708.569	0.802972
$93$	862.664	0.961872
$94$	−207.720	−0.227922
$95$	−270.334	−0.291954
$96$	−584.605	−0.621521
$97$	794.693	0.831844	0.415922	−	0.909400i	$-0.363459\pi$
$97$	794.693	0.831844	0.415922	+	0.909400i	$0.363459\pi$
$98$	381.072	0.392797
$99$	0	0
$100$	711.885	0.711885
$101$	−265.513	−0.261579	−0.130790	−	0.991410i	$-0.541751\pi$
$101$	−265.513	−0.261579	−0.130790	+	0.991410i	$0.541751\pi$
$102$	−73.0006	−0.0708641
$103$	523.107	0.500420	0.250210	−	0.968192i	$-0.419500\pi$
$103$	523.107	0.500420	0.250210	+	0.968192i	$0.419500\pi$
$104$	−1119.07	−1.05514
$105$	75.9421	0.0705828
$106$	−718.199	−0.658091
$107$	986.039	0.890878	0.445439	−	0.895312i	$-0.353048\pi$
$107$	986.039	0.890878	0.445439	+	0.895312i	$0.353048\pi$
$108$	854.174	0.761046
$109$	−1814.39	−1.59438	−0.797188	−	0.603732i	$-0.793680\pi$
$109$	−1814.39	−1.59438	−0.797188	+	0.603732i	$0.793680\pi$
$110$	0	0
$111$	−417.518	−0.357018
$112$	182.339	0.153834
$113$	−707.339	−0.588857	−0.294429	−	0.955673i	$-0.595129\pi$
$113$	−707.339	−0.588857	−0.294429	+	0.955673i	$0.595129\pi$
$114$	382.904	0.314581
$115$	−349.463	−0.283370
$116$	−790.253	−0.632527
$117$	990.706	0.782827
$118$	397.503	0.310112
$119$	134.988	0.103986
$120$	184.175	0.140107
$121$	0	0
$122$	−73.3647	−0.0544437
$123$	1484.44	1.08819
$124$	−1680.98	−1.21739
$125$	−730.061	−0.522389
$126$	184.271	0.130287
$127$	−2648.18	−1.85030	−0.925151	−	0.379600i	$-0.876062\pi$
$127$	−2648.18	−1.85030	−0.925151	+	0.379600i	$0.876062\pi$
$128$	1389.22	0.959302
$129$	−1112.46	−0.759273
$130$	239.817	0.161795
$131$	1979.08	1.31995	0.659974	−	0.751289i	$-0.270567\pi$
$131$	1979.08	1.31995	0.659974	+	0.751289i	$0.270567\pi$
$132$	0	0
$133$	−708.044	−0.461618
$134$	−72.0865	−0.0464726
$135$	−421.274	−0.268574
$136$	327.374	0.206413
$137$	3141.92	1.95936	0.979679	−	0.200570i	$-0.0642794\pi$
$137$	3141.92	1.95936	0.979679	+	0.200570i	$0.0642794\pi$
$138$	494.984	0.305332
$139$	−1468.07	−0.895830	−0.447915	−	0.894076i	$-0.647833\pi$
$139$	−1468.07	−0.895830	−0.447915	+	0.894076i	$0.647833\pi$
$140$	−147.980	−0.0893327
$141$	481.390	0.287520
$142$	−1073.19	−0.634224
$143$	0	0
$144$	−391.483	−0.226553
$145$	389.749	0.223220
$146$	402.621	0.228227
$147$	−883.135	−0.495508
$148$	813.570	0.451858
$149$	286.027	0.157263	0.0786316	−	0.996904i	$-0.474945\pi$
$149$	286.027	0.157263	0.0786316	+	0.996904i	$0.474945\pi$
$150$	497.300	0.270696
$151$	669.626	0.360883	0.180442	−	0.983586i	$-0.442247\pi$
$151$	669.626	0.360883	0.180442	+	0.983586i	$0.442247\pi$
$152$	−1717.15	−0.916311
$153$	−289.821	−0.153141
$154$	0	0
$155$	829.049	0.429618
$156$	1126.89	0.578354
$157$	720.809	0.366413	0.183206	−	0.983074i	$-0.441352\pi$
$157$	720.809	0.366413	0.183206	+	0.983074i	$0.441352\pi$
$158$	−980.522	−0.493710
$159$	1664.43	0.830174
$160$	−561.825	−0.277601
$161$	−915.294	−0.448045
$162$	−29.8770	−0.0144899
$163$	−676.599	−0.325125	−0.162562	−	0.986698i	$-0.551976\pi$
$163$	−676.599	−0.325125	−0.162562	+	0.986698i	$0.551976\pi$
$164$	−2892.56	−1.37726
$165$	0	0
$166$	−157.971	−0.0738609
$167$	2835.67	1.31396	0.656979	−	0.753909i	$-0.271834\pi$
$167$	2835.67	1.31396	0.656979	+	0.753909i	$0.271834\pi$
$168$	482.382	0.221527
$169$	1179.97	0.537083
$170$	−70.1560	−0.0316513
$171$	1520.18	0.679829
$172$	2167.72	0.960970
$173$	177.314	0.0779243	0.0389621	−	0.999241i	$-0.487595\pi$
$173$	177.314	0.0779243	0.0389621	+	0.999241i	$0.487595\pi$
$174$	−552.046	−0.240520
$175$	−919.578	−0.397220
$176$	0	0
$177$	−921.214	−0.391202
$178$	1107.12	0.466192
$179$	−1023.76	−0.427483	−0.213741	−	0.976890i	$-0.568565\pi$
$179$	−1023.76	−0.427483	−0.213741	+	0.976890i	$0.568565\pi$
$180$	317.714	0.131561
$181$	−3450.21	−1.41686	−0.708432	−	0.705779i	$-0.750597\pi$
$181$	−3450.21	−1.41686	−0.708432	+	0.705779i	$0.750597\pi$
$182$	628.116	0.255819
$183$	170.023	0.0686800
$184$	−2219.78	−0.889370
$185$	−401.248	−0.159461
$186$	−1174.28	−0.462915
$187$	0	0
$188$	−938.031	−0.363899
$189$	−1103.38	−0.424651
$190$	367.984	0.140507
$191$	−490.894	−0.185968	−0.0929839	−	0.995668i	$-0.529640\pi$
$191$	−490.894	−0.185968	−0.0929839	+	0.995668i	$0.529640\pi$
$192$	216.254	0.0812855
$193$	3548.80	1.32357	0.661783	−	0.749696i	$-0.269800\pi$
$193$	3548.80	1.32357	0.661783	+	0.749696i	$0.269800\pi$
$194$	−1081.75	−0.400337
$195$	−555.775	−0.204102
$196$	1720.87	0.627138
$197$	−1363.15	−0.492996	−0.246498	−	0.969143i	$-0.579280\pi$
$197$	−1363.15	−0.492996	−0.246498	+	0.969143i	$0.579280\pi$
$198$	0	0
$199$	3737.46	1.33137	0.665683	−	0.746235i	$-0.268140\pi$
$199$	3737.46	1.33137	0.665683	+	0.746235i	$0.268140\pi$
$200$	−2230.16	−0.788482
$201$	167.060	0.0586246
$202$	361.422	0.125889
$203$	1020.81	0.352940
$204$	−329.660	−0.113141
$205$	1426.60	0.486038
$206$	−712.064	−0.240834
$207$	1965.15	0.659841
$208$	−1334.43	−0.444836
$209$	0	0
$210$	−103.374	−0.0339690
$211$	5266.12	1.71817	0.859087	−	0.511829i	$-0.171032\pi$
$211$	5266.12	1.71817	0.859087	+	0.511829i	$0.171032\pi$
$212$	−3243.28	−1.05071
$213$	2487.11	0.800066
$214$	−1342.22	−0.428748
$215$	−1069.11	−0.339128
$216$	−2675.92	−0.842932
$217$	2171.40	0.679283
$218$	2469.78	0.767316
$219$	−933.075	−0.287906
$220$	0	0
$221$	−987.899	−0.300694
$222$	568.334	0.171820
$223$	704.546	0.211569	0.105785	−	0.994389i	$-0.466265\pi$
$223$	704.546	0.211569	0.105785	+	0.994389i	$0.466265\pi$
$224$	−1471.50	−0.438923
$225$	1974.34	0.584990
$226$	962.845	0.283396
$227$	2151.26	0.629006	0.314503	−	0.949256i	$-0.398162\pi$
$227$	2151.26	0.629006	0.314503	+	0.949256i	$0.398162\pi$
$228$	1729.14	0.502259
$229$	−3916.94	−1.13030	−0.565149	−	0.824989i	$-0.691181\pi$
$229$	−3916.94	−1.13030	−0.565149	+	0.824989i	$0.691181\pi$
$230$	475.696	0.136376
$231$	0	0
$232$	2475.67	0.700586
$233$	5192.74	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$233$	5192.74	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$234$	−1348.57	−0.376747
$235$	462.632	0.128420
$236$	1795.07	0.495123
$237$	2272.36	0.622809
$238$	−183.749	−0.0500448
$239$	−334.305	−0.0904786	−0.0452393	−	0.998976i	$-0.514405\pi$
$239$	−334.305	−0.0904786	−0.0452393	+	0.998976i	$0.514405\pi$
$240$	219.618	0.0590677
$241$	1918.45	0.512773	0.256386	−	0.966574i	$-0.417468\pi$
$241$	1918.45	0.512773	0.256386	+	0.966574i	$0.417468\pi$
$242$	0	0
$243$	3821.06	1.00873
$244$	−331.304	−0.0869245
$245$	−848.722	−0.221318
$246$	−2020.65	−0.523708
$247$	5181.75	1.33485
$248$	5266.09	1.34838
$249$	366.097	0.0931746
$250$	993.775	0.251407
$251$	7695.71	1.93525	0.967627	−	0.252385i	$-0.0812148\pi$
$251$	7695.71	1.93525	0.967627	+	0.252385i	$0.0812148\pi$
$252$	832.141	0.208016
$253$	0	0
$254$	3604.76	0.890484
$255$	162.587	0.0399277
$256$	−2439.44	−0.595567
$257$	5335.10	1.29492	0.647460	−	0.762099i	$-0.275831\pi$
$257$	5335.10	1.29492	0.647460	+	0.762099i	$0.275831\pi$
$258$	1514.30	0.365411
$259$	−1050.93	−0.252130
$260$	1082.98	0.258321
$261$	−2191.69	−0.519778
$262$	−2693.97	−0.635244
$263$	−3934.15	−0.922396	−0.461198	−	0.887297i	$-0.652580\pi$
$263$	−3934.15	−0.922396	−0.461198	+	0.887297i	$0.652580\pi$
$264$	0	0
$265$	1599.57	0.370795
$266$	963.804	0.222160
$267$	−2565.75	−0.588095
$268$	−325.532	−0.0741979
$269$	3424.04	0.776088	0.388044	−	0.921641i	$-0.373151\pi$
$269$	3424.04	0.776088	0.388044	+	0.921641i	$0.373151\pi$
$270$	573.447	0.129255
$271$	−549.034	−0.123068	−0.0615340	−	0.998105i	$-0.519599\pi$
$271$	−549.034	−0.123068	−0.0615340	+	0.998105i	$0.519599\pi$
$272$	390.374	0.0870216
$273$	−1455.66	−0.322712
$274$	−4276.85	−0.942970
$275$	0	0
$276$	2235.27	0.487492
$277$	−5203.65	−1.12873	−0.564363	−	0.825527i	$-0.690878\pi$
$277$	−5203.65	−1.12873	−0.564363	+	0.825527i	$0.690878\pi$
$278$	1998.37	0.431131
$279$	−4662.02	−1.00039
$280$	463.585	0.0989447
$281$	1986.73	0.421774	0.210887	−	0.977510i	$-0.432365\pi$
$281$	1986.73	0.421774	0.210887	+	0.977510i	$0.432365\pi$
$282$	−655.279	−0.138373
$283$	−753.696	−0.158313	−0.0791565	−	0.996862i	$-0.525223\pi$
$283$	−753.696	−0.158313	−0.0791565	+	0.996862i	$0.525223\pi$
$284$	−4846.36	−1.01260
$285$	−852.803	−0.177248
$286$	0	0
$287$	3736.47	0.768490
$288$	3159.33	0.646407
$289$	289.000	0.0588235
$290$	−530.534	−0.107428
$291$	2506.96	0.505020
$292$	1818.18	0.364387
$293$	7202.22	1.43603	0.718017	−	0.696025i	$-0.245050\pi$
$293$	7202.22	1.43603	0.718017	+	0.696025i	$0.245050\pi$
$294$	1202.14	0.238471
$295$	−885.318	−0.174729
$296$	−2548.72	−0.500477
$297$	0	0
$298$	−389.345	−0.0756852
$299$	6698.50	1.29560
$300$	2245.74	0.432192
$301$	−2800.15	−0.536205
$302$	−911.509	−0.173680
$303$	−837.595	−0.158807
$304$	−2047.60	−0.386308
$305$	163.398	0.0306758
$306$	394.511	0.0737016
$307$	−2425.71	−0.450953	−0.225477	−	0.974249i	$-0.572394\pi$
$307$	−2425.71	−0.450953	−0.225477	+	0.974249i	$0.572394\pi$
$308$	0	0
$309$	1650.21	0.303809
$310$	−1128.52	−0.206760
$311$	−9544.94	−1.74033	−0.870167	−	0.492757i	$-0.835989\pi$
$311$	−9544.94	−1.74033	−0.870167	+	0.492757i	$0.835989\pi$
$312$	−3530.27	−0.640584
$313$	588.379	0.106253	0.0531264	−	0.998588i	$-0.483081\pi$
$313$	588.379	0.106253	0.0531264	+	0.998588i	$0.483081\pi$
$314$	−981.180	−0.176341
$315$	−410.407	−0.0734090
$316$	−4427.89	−0.788255
$317$	7653.31	1.35600	0.678001	−	0.735061i	$-0.262846\pi$
$317$	7653.31	1.35600	0.678001	+	0.735061i	$0.262846\pi$
$318$	−2265.65	−0.399533
$319$	0	0
$320$	207.828	0.0363060
$321$	3110.59	0.540860
$322$	1245.92	0.215628
$323$	−1515.87	−0.261131
$324$	−134.920	−0.0231345
$325$	6729.85	1.14863
$326$	921.001	0.156471
$327$	−5723.73	−0.967960
$328$	9061.70	1.52545
$329$	1211.70	0.203050
$330$	0	0
$331$	752.266	0.124919	0.0624597	−	0.998047i	$-0.480106\pi$
$331$	752.266	0.124919	0.0624597	+	0.998047i	$0.480106\pi$
$332$	−713.373	−0.117926
$333$	2256.36	0.371314
$334$	−3859.98	−0.632361
$335$	160.551	0.0261845
$336$	575.211	0.0933939
$337$	1968.57	0.318204	0.159102	−	0.987262i	$-0.449140\pi$
$337$	1968.57	0.318204	0.159102	+	0.987262i	$0.449140\pi$
$338$	−1606.20	−0.258479
$339$	−2231.39	−0.357501
$340$	−316.814	−0.0505343
$341$	0	0
$342$	−2069.30	−0.327178
$343$	−4946.52	−0.778678
$344$	−6790.93	−1.06437
$345$	−1102.43	−0.172037
$346$	−241.363	−0.0375022
$347$	−3983.10	−0.616207	−0.308104	−	0.951353i	$-0.599694\pi$
$347$	−3983.10	−0.616207	−0.308104	+	0.951353i	$0.599694\pi$
$348$	−2492.96	−0.384013
$349$	−1495.61	−0.229393	−0.114697	−	0.993401i	$-0.536590\pi$
$349$	−1495.61	−0.229393	−0.114697	+	0.993401i	$0.536590\pi$
$350$	1251.75	0.191168
$351$	8074.98	1.22795
$352$	0	0
$353$	6482.49	0.977417	0.488708	−	0.872447i	$-0.337468\pi$
$353$	6482.49	0.977417	0.488708	+	0.872447i	$0.337468\pi$
$354$	1253.98	0.188272
$355$	2390.20	0.357348
$356$	4999.59	0.744320
$357$	425.838	0.0631309
$358$	1393.56	0.205732
$359$	4943.42	0.726751	0.363376	−	0.931643i	$-0.381624\pi$
$359$	4943.42	0.726751	0.363376	+	0.931643i	$0.381624\pi$
$360$	−995.322	−0.145717
$361$	1092.08	0.159218
$362$	4696.50	0.681886
$363$	0	0
$364$	2836.48	0.408439
$365$	−896.717	−0.128593
$366$	−231.439	−0.0330533
$367$	−14.8871	−0.00211743	−0.00105872	−	0.999999i	$-0.500337\pi$
$367$	−14.8871	−0.00211743	−0.00105872	+	0.999999i	$0.500337\pi$
$368$	−2646.95	−0.374950
$369$	−8022.23	−1.13176
$370$	546.188	0.0767431
$371$	4189.51	0.586276
$372$	−5302.86	−0.739088
$373$	−1923.18	−0.266966	−0.133483	−	0.991051i	$-0.542616\pi$
$373$	−1923.18	−0.266966	−0.133483	+	0.991051i	$0.542616\pi$
$374$	0	0
$375$	−2303.07	−0.317147
$376$	2938.63	0.403053
$377$	−7470.70	−1.02059
$378$	1501.94	0.204369
$379$	−9592.87	−1.30014	−0.650069	−	0.759875i	$-0.725260\pi$
$379$	−9592.87	−1.30014	−0.650069	+	0.759875i	$0.725260\pi$
$380$	1661.76	0.224333
$381$	−8354.04	−1.12333
$382$	668.215	0.0894996
$383$	−9083.77	−1.21190	−0.605951	−	0.795502i	$-0.707207\pi$
$383$	−9083.77	−1.21190	−0.605951	+	0.795502i	$0.707207\pi$
$384$	4382.47	0.582401
$385$	0	0
$386$	−4830.70	−0.636985
$387$	6011.95	0.789675
$388$	−4885.04	−0.639176
$389$	−1143.78	−0.149079	−0.0745396	−	0.997218i	$-0.523749\pi$
$389$	−1143.78	−0.149079	−0.0745396	+	0.997218i	$0.523749\pi$
$390$	756.533	0.0982271
$391$	−1959.58	−0.253453
$392$	−5391.06	−0.694616
$393$	6243.27	0.801352
$394$	1855.55	0.237262
$395$	2183.81	0.278176
$396$	0	0
$397$	10604.5	1.34061	0.670307	−	0.742084i	$-0.266162\pi$
$397$	10604.5	1.34061	0.670307	+	0.742084i	$0.266162\pi$
$398$	−5087.51	−0.640739
$399$	−2233.62	−0.280252
$400$	−2659.33	−0.332417
$401$	13785.4	1.71674	0.858368	−	0.513035i	$-0.171479\pi$
$401$	13785.4	1.71674	0.858368	+	0.513035i	$0.171479\pi$
$402$	−227.406	−0.0282139
$403$	−15891.2	−1.96426
$404$	1632.13	0.200993
$405$	66.5420	0.00816419
$406$	−1389.55	−0.169857
$407$	0	0
$408$	1032.74	0.125315
$409$	9505.94	1.14924	0.574619	−	0.818421i	$-0.305150\pi$
$409$	9505.94	1.14924	0.574619	+	0.818421i	$0.305150\pi$
$410$	−1941.91	−0.233913
$411$	9911.59	1.18954
$412$	−3215.58	−0.384515
$413$	−2318.78	−0.276270
$414$	−2675.00	−0.317558
$415$	351.832	0.0416162
$416$	10769.1	1.26922
$417$	−4631.23	−0.543866
$418$	0	0
$419$	9680.86	1.12874	0.564369	−	0.825523i	$-0.309120\pi$
$419$	9680.86	1.12874	0.564369	+	0.825523i	$0.309120\pi$
$420$	−466.822	−0.0542347
$421$	−12360.3	−1.43089	−0.715444	−	0.698671i	$-0.753775\pi$
$421$	−12360.3	−1.43089	−0.715444	+	0.698671i	$0.753775\pi$
$422$	−7168.36	−0.826897
$423$	−2601.54	−0.299033
$424$	10160.4	1.16376
$425$	−1968.75	−0.224702
$426$	−3385.51	−0.385043
$427$	427.962	0.0485025
$428$	−6061.25	−0.684537
$429$	0	0
$430$	1455.29	0.163210
$431$	−2970.58	−0.331990	−0.165995	−	0.986127i	$-0.553084\pi$
$431$	−2970.58	−0.331990	−0.165995	+	0.986127i	$0.553084\pi$
$432$	−3190.87	−0.355372
$433$	6131.50	0.680510	0.340255	−	0.940333i	$-0.389487\pi$
$433$	6131.50	0.680510	0.340255	+	0.940333i	$0.389487\pi$
$434$	−2955.76	−0.326915
$435$	1229.51	0.135519
$436$	11153.2	1.22509
$437$	10278.4	1.12513
$438$	1270.12	0.138559
$439$	2544.91	0.276679	0.138339	−	0.990385i	$-0.455824\pi$
$439$	2544.91	0.276679	0.138339	+	0.990385i	$0.455824\pi$
$440$	0	0
$441$	4772.65	0.515349
$442$	1344.75	0.144713
$443$	8529.82	0.914817	0.457408	−	0.889257i	$-0.348778\pi$
$443$	8529.82	0.914817	0.457408	+	0.889257i	$0.348778\pi$
$444$	2566.51	0.274327
$445$	−2465.77	−0.262672
$446$	−959.043	−0.101821
$447$	902.308	0.0954759
$448$	544.331	0.0574046
$449$	8855.74	0.930798	0.465399	−	0.885101i	$-0.345911\pi$
$449$	8855.74	0.930798	0.465399	+	0.885101i	$0.345911\pi$
$450$	−2687.52	−0.281535
$451$	0	0
$452$	4348.07	0.452469
$453$	2112.42	0.219095
$454$	−2928.35	−0.302718
$455$	−1398.94	−0.144139
$456$	−5416.98	−0.556301
$457$	7154.78	0.732356	0.366178	−	0.930545i	$-0.380666\pi$
$457$	7154.78	0.732356	0.366178	+	0.930545i	$0.380666\pi$
$458$	5331.82	0.543973
$459$	−2362.25	−0.240219
$460$	2148.17	0.217737
$461$	7263.06	0.733784	0.366892	−	0.930264i	$-0.380422\pi$
$461$	7263.06	0.733784	0.366892	+	0.930264i	$0.380422\pi$
$462$	0	0
$463$	352.898	0.0354224	0.0177112	−	0.999843i	$-0.494362\pi$
$463$	352.898	0.0354224	0.0177112	+	0.999843i	$0.494362\pi$
$464$	2952.09	0.295360
$465$	2615.34	0.260825
$466$	−7068.47	−0.702662
$467$	1483.02	0.146951	0.0734753	−	0.997297i	$-0.476591\pi$
$467$	1483.02	0.146951	0.0734753	+	0.997297i	$0.476591\pi$
$468$	−6089.94	−0.601512
$469$	420.506	0.0414012
$470$	−629.745	−0.0618042
$471$	2273.89	0.222452
$472$	−5623.51	−0.548396
$473$	0	0
$474$	−3093.19	−0.299736
$475$	10326.5	0.997502
$476$	−829.783	−0.0799014
$477$	−8994.92	−0.863415
$478$	455.063	0.0435441
$479$	9990.10	0.952942	0.476471	−	0.879190i	$-0.341916\pi$
$479$	9990.10	0.952942	0.476471	+	0.879190i	$0.341916\pi$
$480$	−1772.35	−0.168534
$481$	7691.13	0.729075
$482$	−2611.44	−0.246779
$483$	−2887.42	−0.272012
$484$	0	0
$485$	2409.27	0.225566
$486$	−5201.30	−0.485465
$487$	−1129.88	−0.105133	−0.0525663	−	0.998617i	$-0.516740\pi$
$487$	−1129.88	−0.105133	−0.0525663	+	0.998617i	$0.516740\pi$
$488$	1037.90	0.0962774
$489$	−2134.42	−0.197386
$490$	1155.30	0.106512
$491$	−18774.9	−1.72566	−0.862832	−	0.505491i	$-0.831311\pi$
$491$	−18774.9	−1.72566	−0.862832	+	0.505491i	$0.831311\pi$
$492$	−9124.97	−0.836149
$493$	2185.48	0.199653
$494$	−7053.51	−0.642414
$495$	0	0
$496$	6279.49	0.568463
$497$	6260.28	0.565014
$498$	−498.339	−0.0448416
$499$	17329.1	1.55462	0.777310	−	0.629118i	$-0.216584\pi$
$499$	17329.1	1.55462	0.777310	+	0.629118i	$0.216584\pi$
$500$	4487.74	0.401396
$501$	8945.50	0.797716
$502$	−10475.6	−0.931369
$503$	20837.0	1.84707	0.923533	−	0.383518i	$-0.125288\pi$
$503$	20837.0	1.84707	0.923533	+	0.383518i	$0.125288\pi$
$504$	−2606.90	−0.230398
$505$	−804.957	−0.0709309
$506$	0	0
$507$	3722.37	0.326068
$508$	16278.6	1.42174
$509$	11835.0	1.03060	0.515301	−	0.857009i	$-0.327680\pi$
$509$	11835.0	1.03060	0.515301	+	0.857009i	$0.327680\pi$
$510$	−221.316	−0.0192158
$511$	−2348.63	−0.203322
$512$	−7793.12	−0.672676
$513$	12390.6	1.06639
$514$	−7262.26	−0.623199
$515$	1585.91	0.135696
$516$	6838.35	0.583414
$517$	0	0
$518$	1430.55	0.121341
$519$	559.359	0.0473086
$520$	−3392.71	−0.286115
$521$	7686.37	0.646346	0.323173	−	0.946340i	$-0.395250\pi$
$521$	7686.37	0.646346	0.323173	+	0.946340i	$0.395250\pi$
$522$	2983.37	0.250151
$523$	−11476.4	−0.959518	−0.479759	−	0.877400i	$-0.659276\pi$
$523$	−11476.4	−0.959518	−0.479759	+	0.877400i	$0.659276\pi$
$524$	−12165.6	−1.01423
$525$	−2900.93	−0.241156
$526$	5355.25	0.443916
$527$	4648.81	0.384261
$528$	0	0
$529$	1120.01	0.0920535
$530$	−2177.37	−0.178451
$531$	4978.44	0.406866
$532$	4352.40	0.354700
$533$	−27345.0	−2.22222
$534$	3492.56	0.283029
$535$	2989.38	0.241574
$536$	1019.81	0.0821814
$537$	−3229.59	−0.259529
$538$	−4660.88	−0.373504
$539$	0	0
$540$	2589.60	0.206368
$541$	546.481	0.0434289	0.0217145	−	0.999764i	$-0.493088\pi$
$541$	546.481	0.0434289	0.0217145	+	0.999764i	$0.493088\pi$
$542$	747.357	0.0592283
$543$	−10884.1	−0.860191
$544$	−3150.38	−0.248293
$545$	−5500.69	−0.432337
$546$	1981.47	0.155310
$547$	−8397.33	−0.656388	−0.328194	−	0.944610i	$-0.606440\pi$
$547$	−8397.33	−0.656388	−0.328194	+	0.944610i	$0.606440\pi$
$548$	−19313.6	−1.50554
$549$	−918.839	−0.0714301
$550$	0	0
$551$	−11463.3	−0.886305
$552$	−7002.58	−0.539945
$553$	5719.73	0.439833
$554$	7083.32	0.543215
$555$	−1265.79	−0.0968105
$556$	9024.36	0.688342
$557$	4881.65	0.371350	0.185675	−	0.982611i	$-0.440553\pi$
$557$	4881.65	0.371350	0.185675	+	0.982611i	$0.440553\pi$
$558$	6346.04	0.481451
$559$	20492.6	1.55053
$560$	552.797	0.0417142
$561$	0	0
$562$	−2704.38	−0.202985
$563$	−7198.57	−0.538870	−0.269435	−	0.963019i	$-0.586837\pi$
$563$	−7198.57	−0.538870	−0.269435	+	0.963019i	$0.586837\pi$
$564$	−2959.14	−0.220926
$565$	−2144.44	−0.159677
$566$	1025.95	0.0761904
$567$	174.283	0.0129087
$568$	15182.5	1.12155
$569$	23946.9	1.76433	0.882167	−	0.470937i	$-0.156084\pi$
$569$	23946.9	1.76433	0.882167	+	0.470937i	$0.156084\pi$
$570$	1160.85	0.0853032
$571$	−1593.15	−0.116763	−0.0583813	−	0.998294i	$-0.518594\pi$
$571$	−1593.15	−0.116763	−0.0583813	+	0.998294i	$0.518594\pi$
$572$	0	0
$573$	−1548.59	−0.112903
$574$	−5086.16	−0.369847
$575$	13349.2	0.968174
$576$	−1168.69	−0.0845403
$577$	12937.4	0.933435	0.466717	−	0.884406i	$-0.345436\pi$
$577$	12937.4	0.933435	0.466717	+	0.884406i	$0.345436\pi$
$578$	−393.393	−0.0283097
$579$	11195.2	0.803549
$580$	−2395.82	−0.171519
$581$	921.499	0.0658007
$582$	−3412.53	−0.243048
$583$	0	0
$584$	−5695.92	−0.403594
$585$	3003.53	0.212275
$586$	−9803.82	−0.691112
$587$	−12899.2	−0.906998	−0.453499	−	0.891257i	$-0.649824\pi$
$587$	−12899.2	−0.906998	−0.453499	+	0.891257i	$0.649824\pi$
$588$	5428.70	0.380741
$589$	−24384.1	−1.70582
$590$	1205.11	0.0840911
$591$	−4300.23	−0.299302
$592$	−3039.19	−0.210997
$593$	−4357.13	−0.301730	−0.150865	−	0.988554i	$-0.548206\pi$
$593$	−4357.13	−0.301730	−0.150865	+	0.988554i	$0.548206\pi$
$594$	0	0
$595$	409.245	0.0281973
$596$	−1758.23	−0.120839
$597$	11790.3	0.808284
$598$	−9118.14	−0.623526
$599$	13726.8	0.936328	0.468164	−	0.883642i	$-0.344916\pi$
$599$	13726.8	0.936328	0.468164	+	0.883642i	$0.344916\pi$
$600$	−7035.35	−0.478695
$601$	−2531.41	−0.171811	−0.0859056	−	0.996303i	$-0.527378\pi$
$601$	−2531.41	−0.171811	−0.0859056	+	0.996303i	$0.527378\pi$
$602$	3811.62	0.258057
$603$	−902.830	−0.0609720
$604$	−4116.24	−0.277297
$605$	0	0
$606$	1140.15	0.0764283
$607$	−185.004	−0.0123708	−0.00618540	−	0.999981i	$-0.501969\pi$
$607$	−185.004	−0.0123708	−0.00618540	+	0.999981i	$0.501969\pi$
$608$	16524.4	1.10223
$609$	3220.28	0.214273
$610$	−222.420	−0.0147632
$611$	−8867.73	−0.587152
$612$	1781.55	0.117672
$613$	17706.9	1.16668	0.583339	−	0.812228i	$-0.301746\pi$
$613$	17706.9	1.16668	0.583339	+	0.812228i	$0.301746\pi$
$614$	3301.93	0.217028
$615$	4500.39	0.295078
$616$	0	0
$617$	−6183.89	−0.403491	−0.201746	−	0.979438i	$-0.564661\pi$
$617$	−6183.89	−0.403491	−0.201746	+	0.979438i	$0.564661\pi$
$618$	−2246.30	−0.146213
$619$	−1247.51	−0.0810046	−0.0405023	−	0.999179i	$-0.512896\pi$
$619$	−1247.51	−0.0810046	−0.0405023	+	0.999179i	$0.512896\pi$
$620$	−5096.23	−0.330112
$621$	16017.4	1.03503
$622$	12992.8	0.837561
$623$	−6458.23	−0.415318
$624$	−4209.63	−0.270064
$625$	12262.8	0.784817
$626$	−800.914	−0.0511357
$627$	0	0
$628$	−4430.87	−0.281546
$629$	−2249.96	−0.142626
$630$	558.655	0.0353292
$631$	24053.3	1.51750	0.758752	−	0.651379i	$-0.225809\pi$
$631$	24053.3	1.51750	0.758752	+	0.651379i	$0.225809\pi$
$632$	13871.5	0.873069
$633$	16612.7	1.04312
$634$	−10417.8	−0.652596
$635$	−8028.51	−0.501735
$636$	−10231.4	−0.637893
$637$	16268.3	1.01189
$638$	0	0
$639$	−13440.9	−0.832102
$640$	4211.70	0.260128
$641$	−21286.8	−1.31167	−0.655834	−	0.754905i	$-0.727683\pi$
$641$	−21286.8	−1.31167	−0.655834	+	0.754905i	$0.727683\pi$
$642$	−4234.20	−0.260297
$643$	−1789.41	−0.109747	−0.0548736	−	0.998493i	$-0.517476\pi$
$643$	−1789.41	−0.109747	−0.0548736	+	0.998493i	$0.517476\pi$
$644$	5626.38	0.344271
$645$	−3372.64	−0.205888
$646$	2063.43	0.125673
$647$	−4378.61	−0.266060	−0.133030	−	0.991112i	$-0.542471\pi$
$647$	−4378.61	−0.266060	−0.133030	+	0.991112i	$0.542471\pi$
$648$	422.672	0.0256237
$649$	0	0
$650$	−9160.81	−0.552795
$651$	6849.97	0.412399
$652$	4159.11	0.249821
$653$	−7665.15	−0.459358	−0.229679	−	0.973266i	$-0.573768\pi$
$653$	−7665.15	−0.459358	−0.229679	+	0.973266i	$0.573768\pi$
$654$	7791.26	0.465845
$655$	5999.99	0.357922
$656$	10805.5	0.643117
$657$	5042.54	0.299434
$658$	−1649.39	−0.0977205
$659$	4710.22	0.278428	0.139214	−	0.990262i	$-0.455542\pi$
$659$	4710.22	0.278428	0.139214	+	0.990262i	$0.455542\pi$
$660$	0	0
$661$	−31266.6	−1.83983	−0.919916	−	0.392116i	$-0.871743\pi$
$661$	−31266.6	−1.83983	−0.919916	+	0.392116i	$0.871743\pi$
$662$	−1024.00	−0.0601192
$663$	−3116.46	−0.182554
$664$	2234.82	0.130614
$665$	−2146.58	−0.125174
$666$	−3071.40	−0.178700
$667$	−14818.7	−0.860246
$668$	−17431.1	−1.00962
$669$	2222.58	0.128446
$670$	−218.545	−0.0126017
$671$	0	0
$672$	−4642.05	−0.266474
$673$	−11723.0	−0.671454	−0.335727	−	0.941959i	$-0.608982\pi$
$673$	−11723.0	−0.671454	−0.335727	+	0.941959i	$0.608982\pi$
$674$	−2679.65	−0.153140
$675$	16092.3	0.917621
$676$	−7253.37	−0.412686
$677$	289.531	0.0164366	0.00821829	−	0.999966i	$-0.497384\pi$
$677$	289.531	0.0164366	0.00821829	+	0.999966i	$0.497384\pi$
$678$	3037.42	0.172052
$679$	6310.25	0.356650
$680$	992.502	0.0559716
$681$	6786.45	0.381875
$682$	0	0
$683$	1720.10	0.0963660	0.0481830	−	0.998839i	$-0.484657\pi$
$683$	1720.10	0.0963660	0.0481830	+	0.998839i	$0.484657\pi$
$684$	−9344.64	−0.522370
$685$	9525.37	0.531308
$686$	6733.30	0.374750
$687$	−12356.5	−0.686215
$688$	−8097.77	−0.448728
$689$	−30660.5	−1.69532
$690$	1500.65	0.0827951
$691$	−16777.7	−0.923665	−0.461832	−	0.886967i	$-0.652808\pi$
$691$	−16777.7	−0.923665	−0.461832	+	0.886967i	$0.652808\pi$
$692$	−1089.96	−0.0598758
$693$	0	0
$694$	5421.88	0.296559
$695$	−4450.77	−0.242917
$696$	7809.84	0.425332
$697$	7999.50	0.434724
$698$	2035.86	0.110399
$699$	16381.2	0.886400
$700$	5652.71	0.305218
$701$	−23981.1	−1.29209	−0.646043	−	0.763301i	$-0.723577\pi$
$701$	−23981.1	−1.29209	−0.646043	+	0.763301i	$0.723577\pi$
$702$	−10991.8	−0.590969
$703$	11801.6	0.633150
$704$	0	0
$705$	1459.43	0.0779652
$706$	−8824.10	−0.470396
$707$	−2108.30	−0.112151
$708$	5662.78	0.300593
$709$	−7709.28	−0.408361	−0.204181	−	0.978933i	$-0.565453\pi$
$709$	−7709.28	−0.408361	−0.204181	+	0.978933i	$0.565453\pi$
$710$	−3253.59	−0.171979
$711$	−12280.3	−0.647747
$712$	−15662.5	−0.824407
$713$	−31521.5	−1.65567
$714$	−579.660	−0.0303827
$715$	0	0
$716$	6293.13	0.328471
$717$	−1054.61	−0.0549304
$718$	−6729.09	−0.349760
$719$	−11976.5	−0.621209	−0.310605	−	0.950539i	$-0.600532\pi$
$719$	−11976.5	−0.621209	−0.310605	+	0.950539i	$0.600532\pi$
$720$	−1186.86	−0.0614329
$721$	4153.72	0.214553
$722$	−1486.56	−0.0766260
$723$	6052.00	0.311309
$724$	21208.7	1.08870
$725$	−14888.1	−0.762662
$726$	0	0
$727$	−18597.3	−0.948745	−0.474372	−	0.880324i	$-0.657325\pi$
$727$	−18597.3	−0.948745	−0.474372	+	0.880324i	$0.657325\pi$
$728$	−8886.00	−0.452386
$729$	11461.4	0.582300
$730$	1220.63	0.0618870
$731$	−5994.91	−0.303324
$732$	−1045.14	−0.0527727
$733$	23569.5	1.18767	0.593833	−	0.804588i	$-0.297614\pi$
$733$	23569.5	1.18767	0.593833	+	0.804588i	$0.297614\pi$
$734$	20.2646	0.00101905
$735$	−2677.41	−0.134364
$736$	21361.3	1.06982
$737$	0	0
$738$	10920.0	0.544678
$739$	−10149.1	−0.505199	−0.252599	−	0.967571i	$-0.581285\pi$
$739$	−10149.1	−0.505199	−0.252599	+	0.967571i	$0.581285\pi$
$740$	2466.50	0.122528
$741$	16346.5	0.810397
$742$	−5702.85	−0.282154
$743$	−27758.0	−1.37058	−0.685291	−	0.728269i	$-0.740325\pi$
$743$	−27758.0	−1.37058	−0.685291	+	0.728269i	$0.740325\pi$
$744$	16612.6	0.818611
$745$	867.148	0.0426441
$746$	2617.87	0.128481
$747$	−1978.47	−0.0969054
$748$	0	0
$749$	7829.63	0.381960
$750$	3134.99	0.152632
$751$	−815.225	−0.0396112	−0.0198056	−	0.999804i	$-0.506305\pi$
$751$	−815.225	−0.0396112	−0.0198056	+	0.999804i	$0.506305\pi$
$752$	3504.13	0.169924
$753$	24277.1	1.17491
$754$	10169.3	0.491172
$755$	2030.11	0.0978585
$756$	6782.56	0.326295
$757$	−13239.4	−0.635659	−0.317829	−	0.948148i	$-0.602954\pi$
$757$	−13239.4	−0.635659	−0.317829	+	0.948148i	$0.602954\pi$
$758$	13058.0	0.625710
$759$	0	0
$760$	−5205.90	−0.248471
$761$	11028.2	0.525324	0.262662	−	0.964888i	$-0.415400\pi$
$761$	11028.2	0.525324	0.262662	+	0.964888i	$0.415400\pi$
$762$	11371.7	0.540621
$763$	−14407.1	−0.683582
$764$	3017.56	0.142895
$765$	−878.652	−0.0415265
$766$	12365.0	0.583246
$767$	16969.8	0.798882
$768$	−7695.55	−0.361574
$769$	18921.2	0.887277	0.443639	−	0.896206i	$-0.353687\pi$
$769$	18921.2	0.887277	0.443639	+	0.896206i	$0.353687\pi$
$770$	0	0
$771$	16830.3	0.786158
$772$	−21814.7	−1.01701
$773$	38728.6	1.80203	0.901016	−	0.433786i	$-0.142823\pi$
$773$	38728.6	1.80203	0.901016	+	0.433786i	$0.142823\pi$
$774$	−8183.59	−0.380043
$775$	−31669.0	−1.46785
$776$	15303.6	0.707949
$777$	−3315.29	−0.153070
$778$	1556.93	0.0717465
$779$	−41959.2	−1.92984
$780$	3416.39	0.156829
$781$	0	0
$782$	2667.42	0.121978
$783$	−17863.9	−0.815329
$784$	−6428.50	−0.292844
$785$	2185.28	0.0993579
$786$	−8498.47	−0.385662
$787$	20587.3	0.932477	0.466239	−	0.884659i	$-0.345609\pi$
$787$	20587.3	0.932477	0.466239	+	0.884659i	$0.345609\pi$
$788$	8379.37	0.378811
$789$	−12410.8	−0.559995
$790$	−2972.66	−0.133876
$791$	−5616.62	−0.252470
$792$	0	0
$793$	−3132.00	−0.140253
$794$	−14435.0	−0.645190
$795$	5046.05	0.225113
$796$	−22974.5	−1.02300
$797$	−15871.4	−0.705385	−0.352693	−	0.935739i	$-0.614734\pi$
$797$	−15871.4	−0.705385	−0.352693	+	0.935739i	$0.614734\pi$
$798$	3040.45	0.134876
$799$	2594.17	0.114862
$800$	21461.3	0.948463
$801$	13865.9	0.611644
$802$	−18765.0	−0.826204
$803$	0	0
$804$	−1026.93	−0.0450462
$805$	−2774.90	−0.121494
$806$	21631.4	0.945329
$807$	10801.6	0.471170
$808$	−5113.06	−0.222620
$809$	−39667.1	−1.72388	−0.861942	−	0.507007i	$-0.830752\pi$
$809$	−39667.1	−1.72388	−0.861942	+	0.507007i	$0.830752\pi$
$810$	−90.5783	−0.00392913
$811$	−8003.87	−0.346552	−0.173276	−	0.984873i	$-0.555435\pi$
$811$	−8003.87	−0.346552	−0.173276	+	0.984873i	$0.555435\pi$
$812$	−6275.00	−0.271194
$813$	−1732.00	−0.0747157
$814$	0	0
$815$	−2051.25	−0.0881621
$816$	1231.48	0.0528316
$817$	31444.7	1.34652
$818$	−12939.7	−0.553088
$819$	7866.69	0.335634
$820$	−8769.40	−0.373464
$821$	13279.1	0.564489	0.282244	−	0.959343i	$-0.408921\pi$
$821$	13279.1	0.564489	0.282244	+	0.959343i	$0.408921\pi$
$822$	−13491.9	−0.572486
$823$	28934.0	1.22549	0.612745	−	0.790281i	$-0.290065\pi$
$823$	28934.0	1.22549	0.612745	+	0.790281i	$0.290065\pi$
$824$	10073.6	0.425887
$825$	0	0
$826$	3156.37	0.132959
$827$	13679.6	0.575193	0.287597	−	0.957752i	$-0.407144\pi$
$827$	13679.6	0.575193	0.287597	+	0.957752i	$0.407144\pi$
$828$	−12079.9	−0.507012
$829$	16514.5	0.691886	0.345943	−	0.938256i	$-0.387559\pi$
$829$	16514.5	0.691886	0.345943	+	0.938256i	$0.387559\pi$
$830$	−478.921	−0.0200284
$831$	−16415.6	−0.685260
$832$	−3983.64	−0.165995
$833$	−4759.13	−0.197952
$834$	6304.13	0.261744
$835$	8596.93	0.356298
$836$	0	0
$837$	−37998.9	−1.56922
$838$	−13177.8	−0.543221
$839$	−87.9839	−0.00362043	−0.00181022	−	0.999998i	$-0.500576\pi$
$839$	−87.9839	−0.00362043	−0.00181022	+	0.999998i	$0.500576\pi$
$840$	1462.44	0.0600702
$841$	−7861.94	−0.322356
$842$	16825.1	0.688635
$843$	6267.41	0.256063
$844$	−32371.3	−1.32022
$845$	3577.33	0.145638
$846$	3541.27	0.143914
$847$	0	0
$848$	12115.7	0.490630
$849$	−2377.63	−0.0961133
$850$	2679.90	0.108141
$851$	15256.0	0.614534
$852$	−15288.5	−0.614758
$853$	−8162.96	−0.327660	−0.163830	−	0.986489i	$-0.552385\pi$
$853$	−8162.96	−0.327660	−0.163830	+	0.986489i	$0.552385\pi$
$854$	−582.551	−0.0233425
$855$	4608.73	0.184345
$856$	18988.4	0.758191
$857$	−18724.9	−0.746361	−0.373181	−	0.927759i	$-0.621733\pi$
$857$	−18724.9	−0.746361	−0.373181	+	0.927759i	$0.621733\pi$
$858$	0	0
$859$	−46422.5	−1.84391	−0.921953	−	0.387301i	$-0.873407\pi$
$859$	−46422.5	−1.84391	−0.921953	+	0.387301i	$0.873407\pi$
$860$	6571.88	0.260580
$861$	11787.2	0.466557
$862$	4043.61	0.159775
$863$	29112.3	1.14831	0.574157	−	0.818746i	$-0.305330\pi$
$863$	29112.3	1.14831	0.574157	+	0.818746i	$0.305330\pi$
$864$	25750.8	1.01396
$865$	537.563	0.0211303
$866$	−8346.33	−0.327505
$867$	911.688	0.0357123
$868$	−13347.8	−0.521950
$869$	0	0
$870$	−1673.64	−0.0652204
$871$	−3077.43	−0.119719
$872$	−34940.2	−1.35691
$873$	−13548.2	−0.525241
$874$	−13991.2	−0.541487
$875$	−5797.04	−0.223972
$876$	5735.69	0.221222
$877$	−39163.0	−1.50791	−0.753957	−	0.656924i	$-0.771857\pi$
$877$	−39163.0	−1.50791	−0.753957	+	0.656924i	$0.771857\pi$
$878$	−3464.19	−0.133156
$879$	22720.3	0.871830
$880$	0	0
$881$	−35073.2	−1.34125	−0.670627	−	0.741795i	$-0.733975\pi$
$881$	−35073.2	−1.34125	−0.670627	+	0.741795i	$0.733975\pi$
$882$	−6496.63	−0.248019
$883$	−48775.7	−1.85893	−0.929463	−	0.368915i	$-0.879729\pi$
$883$	−48775.7	−1.85893	−0.929463	+	0.368915i	$0.879729\pi$
$884$	6072.69	0.231048
$885$	−2792.85	−0.106080
$886$	−11611.0	−0.440269
$887$	−13296.0	−0.503309	−0.251654	−	0.967817i	$-0.580975\pi$
$887$	−13296.0	−0.503309	−0.251654	+	0.967817i	$0.580975\pi$
$888$	−8040.27	−0.303844
$889$	−21027.9	−0.793309
$890$	3356.46	0.126415
$891$	0	0
$892$	−4330.90	−0.162566
$893$	−13607.0	−0.509899
$894$	−1228.24	−0.0459492
$895$	−3103.74	−0.115918
$896$	11031.1	0.411297
$897$	21131.3	0.786570
$898$	−12054.6	−0.447960
$899$	35155.3	1.30422
$900$	−12136.4	−0.449498
$901$	8969.43	0.331648
$902$	0	0
$903$	−8833.44	−0.325535
$904$	−13621.4	−0.501153
$905$	−10460.0	−0.384202
$906$	−2875.47	−0.105443
$907$	−11675.0	−0.427410	−0.213705	−	0.976898i	$-0.568553\pi$
$907$	−11675.0	−0.427410	−0.213705	+	0.976898i	$0.568553\pi$
$908$	−13224.0	−0.483319
$909$	4526.54	0.165166
$910$	1904.26	0.0693689
$911$	18552.9	0.674738	0.337369	−	0.941372i	$-0.390463\pi$
$911$	18552.9	0.674738	0.337369	+	0.941372i	$0.390463\pi$
$912$	−6459.41	−0.234531
$913$	0	0
$914$	−9739.24	−0.352457
$915$	515.459	0.0186235
$916$	24077.7	0.868504
$917$	15714.9	0.565922
$918$	3215.55	0.115609
$919$	−33956.8	−1.21886	−0.609429	−	0.792841i	$-0.708601\pi$
$919$	−33956.8	−1.21886	−0.609429	+	0.792841i	$0.708601\pi$
$920$	−6729.71	−0.241165
$921$	−7652.23	−0.273778
$922$	−9886.63	−0.353144
$923$	−45815.3	−1.63383
$924$	0	0
$925$	15327.4	0.544823
$926$	−480.372	−0.0170475
$927$	−8918.08	−0.315974
$928$	−23823.8	−0.842732
$929$	−23695.3	−0.836832	−0.418416	−	0.908256i	$-0.637415\pi$
$929$	−23695.3	−0.836832	−0.418416	+	0.908256i	$0.637415\pi$
$930$	−3560.06	−0.125526
$931$	24962.7	0.878753
$932$	−31920.2	−1.12187
$933$	−30110.8	−1.05657
$934$	−2018.72	−0.0707221
$935$	0	0
$936$	19078.3	0.666234
$937$	−7990.62	−0.278593	−0.139297	−	0.990251i	$-0.544484\pi$
$937$	−7990.62	−0.278593	−0.139297	+	0.990251i	$0.544484\pi$
$938$	−572.402	−0.0199249
$939$	1856.12	0.0645071
$940$	−2843.83	−0.0986762
$941$	−24385.9	−0.844799	−0.422400	−	0.906410i	$-0.638812\pi$
$941$	−24385.9	−0.844799	−0.422400	+	0.906410i	$0.638812\pi$
$942$	−3095.26	−0.107058
$943$	−54241.0	−1.87310
$944$	−6705.69	−0.231199
$945$	−3345.12	−0.115150
$946$	0	0
$947$	−1174.62	−0.0403064	−0.0201532	−	0.999797i	$-0.506415\pi$
$947$	−1174.62	−0.0403064	−0.0201532	+	0.999797i	$0.506415\pi$
$948$	−13968.4	−0.478557
$949$	17188.3	0.587939
$950$	−14056.7	−0.480063
$951$	24143.4	0.823241
$952$	2599.51	0.0884985
$953$	33546.9	1.14029	0.570143	−	0.821546i	$-0.306888\pi$
$953$	33546.9	1.14029	0.570143	+	0.821546i	$0.306888\pi$
$954$	12244.1	0.415531
$955$	−1488.25	−0.0504277
$956$	2055.00	0.0695224
$957$	0	0
$958$	−13598.7	−0.458617
$959$	24948.4	0.840067
$960$	655.620	0.0220417
$961$	44989.1	1.51016
$962$	−10469.3	−0.350878
$963$	−16810.3	−0.562517
$964$	−11792.9	−0.394007
$965$	10758.9	0.358903
$966$	3930.41	0.130910
$967$	−24766.8	−0.823625	−0.411813	−	0.911269i	$-0.635104\pi$
$967$	−24766.8	−0.823625	−0.411813	+	0.911269i	$0.635104\pi$
$968$	0	0
$969$	−4782.01	−0.158535
$970$	−3279.56	−0.108557
$971$	42324.3	1.39882	0.699409	−	0.714721i	$-0.253447\pi$
$971$	42324.3	1.39882	0.699409	+	0.714721i	$0.253447\pi$
$972$	−23488.3	−0.775091
$973$	−11657.2	−0.384083
$974$	1538.01	0.0505966
$975$	21230.2	0.697344
$976$	1237.63	0.0405896
$977$	−11320.4	−0.370698	−0.185349	−	0.982673i	$-0.559342\pi$
$977$	−11320.4	−0.370698	−0.185349	+	0.982673i	$0.559342\pi$
$978$	2905.42	0.0949949
$979$	0	0
$980$	5217.16	0.170057
$981$	30932.2	1.00672
$982$	25556.8	0.830500
$983$	−11311.9	−0.367032	−0.183516	−	0.983017i	$-0.558748\pi$
$983$	−11311.9	−0.367032	−0.183516	+	0.983017i	$0.558748\pi$
$984$	28586.3	0.926116
$985$	−4132.66	−0.133683
$986$	−2974.92	−0.0960860
$987$	3822.47	0.123273
$988$	−31852.6	−1.02568
$989$	40648.8	1.30693
$990$	0	0
$991$	−29405.5	−0.942580	−0.471290	−	0.881978i	$-0.656212\pi$
$991$	−29405.5	−0.942580	−0.471290	+	0.881978i	$0.656212\pi$
$992$	−50676.5	−1.62196
$993$	2373.12	0.0758397
$994$	−8521.63	−0.271921
$995$	11330.9	0.361018
$996$	−2250.43	−0.0715939
$997$	54905.9	1.74412	0.872060	−	0.489398i	$-0.162784\pi$
$997$	54905.9	1.74412	0.872060	+	0.489398i	$0.162784\pi$
$998$	−23588.7	−0.748183
$999$	18390.9	0.582446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.4.a.e.1.2		3
11.10	odd	2		17.4.a.b.1.2	✓	3
33.32	even	2		153.4.a.g.1.2		3
44.43	even	2		272.4.a.h.1.2		3
55.32	even	4		425.4.b.f.324.4		6
55.43	even	4		425.4.b.f.324.3		6
55.54	odd	2		425.4.a.g.1.2		3
77.76	even	2		833.4.a.d.1.2		3
88.21	odd	2		1088.4.a.v.1.2		3
88.43	even	2		1088.4.a.x.1.2		3
132.131	odd	2		2448.4.a.bi.1.1		3
187.21	odd	4		289.4.b.b.288.3		6
187.98	odd	4		289.4.b.b.288.4		6
187.186	odd	2		289.4.a.b.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.2	✓	3	11.10	odd	2
153.4.a.g.1.2		3	33.32	even	2
272.4.a.h.1.2		3	44.43	even	2
289.4.a.b.1.2		3	187.186	odd	2
289.4.b.b.288.3		6	187.21	odd	4
289.4.b.b.288.4		6	187.98	odd	4
425.4.a.g.1.2		3	55.54	odd	2
425.4.b.f.324.3		6	55.43	even	4
425.4.b.f.324.4		6	55.32	even	4
833.4.a.d.1.2		3	77.76	even	2
1088.4.a.v.1.2		3	88.21	odd	2
1088.4.a.x.1.2		3	88.43	even	2
2057.4.a.e.1.2		3	1.1	even	1	trivial
2448.4.a.bi.1.1		3	132.131	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:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\)	\(q-1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} -4.29415 q^{6} +7.94049 q^{7} +19.2573 q^{8} -17.0483 q^{9} -4.12682 q^{10} -19.3918 q^{12} -58.1117 q^{13} -10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} +17.0000 q^{17} +23.2065 q^{18} -89.1688 q^{19} -18.6361 q^{20} +25.0493 q^{21} -115.269 q^{23} +60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} -138.956 q^{27} -48.8108 q^{28} +128.558 q^{29} -13.0186 q^{30} +273.460 q^{31} -185.316 q^{32} -23.1408 q^{34} +24.0732 q^{35} +104.797 q^{36} -132.351 q^{37} +121.379 q^{38} -183.321 q^{39} +58.3825 q^{40} +470.559 q^{41} -34.0977 q^{42} -352.642 q^{43} -51.6854 q^{45} +156.907 q^{46} +152.598 q^{47} +72.4403 q^{48} -279.949 q^{49} +157.641 q^{50} +53.6287 q^{51} +357.217 q^{52} +527.614 q^{53} +189.150 q^{54} +152.912 q^{56} -281.295 q^{57} -174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} +53.8962 q^{61} -372.239 q^{62} -135.372 q^{63} +68.5514 q^{64} -176.178 q^{65} +52.9572 q^{67} -104.500 q^{68} -363.632 q^{69} -32.7690 q^{70} +788.400 q^{71} -328.304 q^{72} -295.780 q^{73} +180.159 q^{74} -365.334 q^{75} +548.127 q^{76} +249.541 q^{78} +720.325 q^{79} +69.6175 q^{80} +21.9487 q^{81} -640.535 q^{82} +116.051 q^{83} -153.980 q^{84} +51.5390 q^{85} +480.024 q^{86} +405.552 q^{87} -813.329 q^{89} +70.3553 q^{90} -461.435 q^{91} +708.569 q^{92} +862.664 q^{93} -207.720 q^{94} -270.334 q^{95} -584.605 q^{96} +794.693 q^{97} +381.072 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9}+O(q^{10}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9	\( 3 q - q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} + 74 q^{6} - 22 q^{7} + 39 q^{8} + 59 q^{9} + 56 q^{10} + 22 q^{12} - 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} + 51 q^{17} + 103 q^{18} - 80 q^{19} - 168 q^{20} + 192 q^{21} + 142 q^{23} + 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} - 476 q^{28} + 456 q^{29} - 400 q^{30} + 230 q^{31} + 71 q^{32} - 17 q^{34} + 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} - 268 q^{39} + 424 q^{40} + 294 q^{41} - 1128 q^{42} - 556 q^{43} - 384 q^{45} + 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} - 547 q^{50} + 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} + 684 q^{56} + 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 1122 q^{63} - 919 q^{64} - 408 q^{65} + 1008 q^{67} + 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} + 927 q^{72} - 838 q^{73} - 836 q^{74} - 1548 q^{75} + 908 q^{76} + 1308 q^{78} + 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} + 2396 q^{83} + 2040 q^{84} - 136 q^{85} - 1264 q^{86} - 1428 q^{87} - 170 q^{89} + 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} + 472 q^{95} - 678 q^{96} - 270 q^{97} - 2857 q^{98}+O(q^{100}) \) 3 * q - q^2 + 4 * q^3 + 25 * q^4 - 8 * q^5 + 74 * q^6 - 22 * q^7 + 39 * q^8 + 59 * q^9 + 56 * q^10 + 22 * q^12 - 30 * q^13 + 92 * q^14 + 108 * q^15 + 137 * q^16 + 51 * q^17 + 103 * q^18 - 80 * q^19 - 168 * q^20 + 192 * q^21 + 142 * q^23 + 666 * q^24 - 223 * q^25 + 26 * q^26 - 20 * q^27 - 476 * q^28 + 456 * q^29 - 400 * q^30 + 230 * q^31 + 71 * q^32 - 17 * q^34 + 332 * q^35 + 1313 * q^36 + 356 * q^37 + 724 * q^38 - 268 * q^39 + 424 * q^40 + 294 * q^41 - 1128 * q^42 - 556 * q^43 - 384 * q^45 + 704 * q^46 + 640 * q^47 + 774 * q^48 - 269 * q^49 - 547 * q^50 + 68 * q^51 + 774 * q^52 + 302 * q^53 + 1100 * q^54 + 684 * q^56 + 720 * q^57 - 1304 * q^58 + 636 * q^59 + 1328 * q^60 + 84 * q^61 - 508 * q^62 - 1122 * q^63 - 919 * q^64 - 408 * q^65 + 1008 * q^67 + 425 * q^68 + 576 * q^69 - 1504 * q^70 - 402 * q^71 + 927 * q^72 - 838 * q^73 - 836 * q^74 - 1548 * q^75 + 908 * q^76 + 1308 * q^78 + 594 * q^79 - 40 * q^80 - 505 * q^81 + 358 * q^82 + 2396 * q^83 + 2040 * q^84 - 136 * q^85 - 1264 * q^86 - 1428 * q^87 - 170 * q^89 + 2008 * q^90 - 1016 * q^91 + 4896 * q^92 + 632 * q^93 + 2016 * q^94 + 472 * q^95 - 678 * q^96 - 270 * q^97 - 2857 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more