LMFDB - Embedded newform 17.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.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:	$1.00303247010$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.87707$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} +4.29415 q^{6} -7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} +O(q^{10})$	\(q+1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} +4.29415 q^{6} -7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} +4.12682 q^{10} +27.6161 q^{11} -19.3918 q^{12} +58.1117 q^{13} -10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} -17.0000 q^{17} -23.2065 q^{18} +89.1688 q^{19} -18.6361 q^{20} -25.0493 q^{21} +37.5916 q^{22} -115.269 q^{23} -60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} -138.956 q^{27} +48.8108 q^{28} -128.558 q^{29} +13.0186 q^{30} +273.460 q^{31} +185.316 q^{32} +87.1187 q^{33} -23.1408 q^{34} -24.0732 q^{35} +104.797 q^{36} -132.351 q^{37} +121.379 q^{38} +183.321 q^{39} -58.3825 q^{40} -470.559 q^{41} -34.0977 q^{42} +352.642 q^{43} -169.758 q^{44} -51.6854 q^{45} -156.907 q^{46} +152.598 q^{47} +72.4403 q^{48} -279.949 q^{49} -157.641 q^{50} -53.6287 q^{51} -357.217 q^{52} +527.614 q^{53} -189.150 q^{54} +83.7239 q^{55} +152.912 q^{56} +281.295 q^{57} -174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} -53.8962 q^{61} +372.239 q^{62} +135.372 q^{63} +68.5514 q^{64} +176.178 q^{65} +118.588 q^{66} +52.9572 q^{67} +104.500 q^{68} -363.632 q^{69} -32.7690 q^{70} +788.400 q^{71} +328.304 q^{72} +295.780 q^{73} -180.159 q^{74} -365.334 q^{75} -548.127 q^{76} -219.285 q^{77} +249.541 q^{78} -720.325 q^{79} +69.6175 q^{80} +21.9487 q^{81} -640.535 q^{82} -116.051 q^{83} +153.980 q^{84} -51.5390 q^{85} +480.024 q^{86} -405.552 q^{87} -531.812 q^{88} -813.329 q^{89} -70.3553 q^{90} -461.435 q^{91} +708.569 q^{92} +862.664 q^{93} +207.720 q^{94} +270.334 q^{95} +584.605 q^{96} +794.693 q^{97} -381.072 q^{98} -470.808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q + q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} - 74 q^{6} + 22 q^{7} - 39 q^{8} + 59 q^{9} - 56 q^{10} - 28 q^{11} + 22 q^{12} + 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} - 51 q^{17} - 103 q^{18} + 80 q^{19} - 168 q^{20} - 192 q^{21} + 286 q^{22} + 142 q^{23} - 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} + 476 q^{28} - 456 q^{29} + 400 q^{30} + 230 q^{31} - 71 q^{32} - 332 q^{33} - 17 q^{34} - 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} + 268 q^{39} - 424 q^{40} - 294 q^{41} - 1128 q^{42} + 556 q^{43} - 1122 q^{44} - 384 q^{45} - 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} + 547 q^{50} - 68 q^{51} - 774 q^{52} + 302 q^{53} - 1100 q^{54} + 76 q^{55} + 684 q^{56} - 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} - 84 q^{61} + 508 q^{62} + 1122 q^{63} - 919 q^{64} + 408 q^{65} + 2468 q^{66} + 1008 q^{67} - 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} - 927 q^{72} + 838 q^{73} + 836 q^{74} - 1548 q^{75} - 908 q^{76} - 504 q^{77} + 1308 q^{78} - 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} - 2396 q^{83} - 2040 q^{84} + 136 q^{85} - 1264 q^{86} + 1428 q^{87} + 1838 q^{88} - 170 q^{89} - 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} - 2016 q^{94} - 472 q^{95} + 678 q^{96} - 270 q^{97} + 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 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 - 28 * q^11 + 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 + 286 * q^22 + 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 - 332 * q^33 - 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 - 1122 * q^44 - 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 + 76 * q^55 + 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 + 2468 * q^66 + 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 - 504 * q^77 + 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 + 1838 * q^88 - 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 - 2920 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.36122	0.481264	0.240632	−	0.970616i	$-0.422645\pi$
$2$	1.36122	0.481264	0.240632	+	0.970616i	$0.422645\pi$
$3$	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	$-0.568771\pi$
$7$	−7.94049	−0.428746	−0.214373	+	0.976752i	$0.568771\pi$
$8$	−19.2573	−0.851061
$9$	−17.0483	−0.631419
$10$	4.12682	0.130502
$11$	27.6161	0.756961	0.378481	−	0.925609i	$-0.376447\pi$
$11$	27.6161	0.756961	0.378481	+	0.925609i	$0.376447\pi$
$12$	−19.3918	−0.466493
$13$	58.1117	1.23979	0.619896	−	0.784684i	$-0.287175\pi$
$13$	58.1117	1.23979	0.619896	+	0.784684i	$0.287175\pi$
$14$	−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	$-0.319054\pi$
$19$	89.1688	1.07667	0.538335	+	0.842731i	$0.319054\pi$
$20$	−18.6361	−0.208358
$21$	−25.0493	−0.260296
$22$	37.5916	0.364298
$23$	−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	$-0.635028\pi$
$29$	−128.558	−0.823191	−0.411596	+	0.911367i	$0.635028\pi$
$30$	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
$33$	87.1187	0.459558
$34$	−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	$-0.853688\pi$
$41$	−470.559	−1.79241	−0.896207	+	0.443636i	$0.853688\pi$
$42$	−34.0977	−0.125271
$43$	352.642	1.25064	0.625318	−	0.780370i	$-0.284969\pi$
$43$	352.642	1.25064	0.625318	+	0.780370i	$0.284969\pi$
$44$	−169.758	−0.581637
$45$	−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
$55$	83.7239	0.205261
$56$	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	$-0.518014\pi$
$61$	−53.8962	−0.113126	−0.0565632	+	0.998399i	$0.518014\pi$
$62$	372.239	0.762490
$63$	135.372	0.270718
$64$	68.5514	0.133889
$65$	176.178	0.336187
$66$	118.588	0.221169
$67$	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	$-0.423799\pi$
$73$	295.780	0.474224	0.237112	+	0.971482i	$0.423799\pi$
$74$	−180.159	−0.283014
$75$	−365.334	−0.562468
$76$	−548.127	−0.827296
$77$	−219.285	−0.324544
$78$	249.541	0.362242
$79$	−720.325	−1.02586	−0.512930	−	0.858430i	$-0.671440\pi$
$79$	−720.325	−1.02586	−0.512930	+	0.858430i	$0.671440\pi$
$80$	69.6175	0.0972934
$81$	21.9487	0.0301079
$82$	−640.535	−0.862625
$83$	−116.051	−0.153473	−0.0767363	−	0.997051i	$-0.524450\pi$
$83$	−116.051	−0.153473	−0.0767363	+	0.997051i	$0.524450\pi$
$84$	153.980	0.200007
$85$	−51.5390	−0.0657669
$86$	480.024	0.601887
$87$	−405.552	−0.499767
$88$	−531.812	−0.644220
$89$	−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
$99$	−470.808	−0.477959
$100$	711.885	0.711885
$101$	265.513	0.261579	0.130790	−	0.991410i	$-0.458249\pi$
$101$	265.513	0.261579	0.130790	+	0.991410i	$0.458249\pi$
$102$	−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	$-0.646952\pi$
$107$	−986.039	−0.890878	−0.445439	+	0.895312i	$0.646952\pi$
$108$	854.174	0.761046
$109$	1814.39	1.59438	0.797188	−	0.603732i	$-0.206320\pi$
$109$	1814.39	1.59438	0.797188	+	0.603732i	$0.206320\pi$
$110$	113.967	0.0987846
$111$	−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
$121$	−568.350	−0.427010
$122$	−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	$-0.123938\pi$
$127$	2648.18	1.85030	0.925151	+	0.379600i	$0.123938\pi$
$128$	−1389.22	−0.959302
$129$	1112.46	0.759273
$130$	239.817	0.161795
$131$	−1979.08	−1.31995	−0.659974	−	0.751289i	$-0.729433\pi$
$131$	−1979.08	−1.31995	−0.659974	+	0.751289i	$0.729433\pi$
$132$	−535.525	−0.353117
$133$	−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	$-0.352167\pi$
$139$	1468.07	0.895830	0.447915	+	0.894076i	$0.352167\pi$
$140$	147.980	0.0893327
$141$	481.390	0.287520
$142$	1073.19	0.634224
$143$	1604.82	0.938474
$144$	−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	$-0.525055\pi$
$149$	−286.027	−0.157263	−0.0786316	+	0.996904i	$0.525055\pi$
$150$	−497.300	−0.270696
$151$	−669.626	−0.360883	−0.180442	−	0.983586i	$-0.557753\pi$
$151$	−669.626	−0.360883	−0.180442	+	0.983586i	$0.557753\pi$
$152$	−1717.15	−0.916311
$153$	289.821	0.153141
$154$	−298.496	−0.156191
$155$	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
$165$	264.118	0.124616
$166$	−157.971	−0.0738609
$167$	−2835.67	−1.31396	−0.656979	−	0.753909i	$-0.728166\pi$
$167$	−2835.67	−1.31396	−0.656979	+	0.753909i	$0.728166\pi$
$168$	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	$-0.512405\pi$
$173$	−177.314	−0.0779243	−0.0389621	+	0.999241i	$0.512405\pi$
$174$	−552.046	−0.240520
$175$	919.578	0.397220
$176$	634.153	0.271597
$177$	−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
$187$	−469.474	−0.183590
$188$	−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	$-0.730200\pi$
$193$	−3548.80	−1.32357	−0.661783	+	0.749696i	$0.730200\pi$
$194$	1081.75	0.400337
$195$	555.775	0.204102
$196$	1720.87	0.627138
$197$	1363.15	0.492996	0.246498	−	0.969143i	$-0.420720\pi$
$197$	1363.15	0.492996	0.246498	+	0.969143i	$0.420720\pi$
$198$	−640.874	−0.230025
$199$	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
$209$	2462.50	0.814997
$210$	−103.374	−0.0339690
$211$	−5266.12	−1.71817	−0.859087	−	0.511829i	$-0.828968\pi$
$211$	−5266.12	−1.71817	−0.859087	+	0.511829i	$0.828968\pi$
$212$	−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
$220$	−514.657	−0.157719
$221$	−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	$-0.601838\pi$
$227$	−2151.26	−0.629006	−0.314503	+	0.949256i	$0.601838\pi$
$228$	−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
$231$	−691.764	−0.197034
$232$	2475.67	0.700586
$233$	−5192.74	−1.46003	−0.730017	−	0.683429i	$-0.760488\pi$
$233$	−5192.74	−1.46003	−0.730017	+	0.683429i	$0.760488\pi$
$234$	−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	$-0.485595\pi$
$239$	334.305	0.0904786	0.0452393	+	0.998976i	$0.485595\pi$
$240$	219.618	0.0590677
$241$	−1918.45	−0.512773	−0.256386	−	0.966574i	$-0.582532\pi$
$241$	−1918.45	−0.512773	−0.256386	+	0.966574i	$0.582532\pi$
$242$	−773.651	−0.205505
$243$	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
$253$	−3183.29	−0.791035
$254$	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	$-0.347420\pi$
$263$	3934.15	0.922396	0.461198	+	0.887297i	$0.347420\pi$
$264$	−1677.67	−0.391112
$265$	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	$-0.480401\pi$
$271$	549.034	0.123068	0.0615340	+	0.998105i	$0.480401\pi$
$272$	−390.374	−0.0870216
$273$	−1455.66	−0.322712
$274$	4276.85	0.942970
$275$	−3198.19	−0.701302
$276$	2235.27	0.487492
$277$	5203.65	1.12873	0.564363	−	0.825527i	$-0.309122\pi$
$277$	5203.65	1.12873	0.564363	+	0.825527i	$0.309122\pi$
$278$	1998.37	0.431131
$279$	−4662.02	−1.00039
$280$	463.585	0.0989447
$281$	−1986.73	−0.421774	−0.210887	−	0.977510i	$-0.567635\pi$
$281$	−1986.73	−0.421774	−0.210887	+	0.977510i	$0.567635\pi$
$282$	655.279	0.138373
$283$	753.696	0.158313	0.0791565	−	0.996862i	$-0.474777\pi$
$283$	753.696	0.158313	0.0791565	+	0.996862i	$0.474777\pi$
$284$	−4846.36	−1.01260
$285$	852.803	0.177248
$286$	2184.51	0.451654
$287$	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	$-0.754950\pi$
$293$	−7202.22	−1.43603	−0.718017	+	0.696025i	$0.754950\pi$
$294$	−1202.14	−0.238471
$295$	−885.318	−0.174729
$296$	2548.72	0.500477
$297$	−3837.43	−0.749731
$298$	−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	$-0.427606\pi$
$307$	2425.71	0.450953	0.225477	+	0.974249i	$0.427606\pi$
$308$	1347.96	0.249375
$309$	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
$319$	−3550.26	−0.623124
$320$	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
$330$	359.523	0.0599730
$331$	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	$-0.550860\pi$
$337$	−1968.57	−0.318204	−0.159102	+	0.987262i	$0.550860\pi$
$338$	1606.20	0.258479
$339$	−2231.39	−0.357501
$340$	316.814	0.0505343
$341$	7551.89	1.19929
$342$	−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	$-0.400306\pi$
$347$	3983.10	0.616207	0.308104	+	0.951353i	$0.400306\pi$
$348$	2492.96	0.384013
$349$	1495.61	0.229393	0.114697	−	0.993401i	$-0.463410\pi$
$349$	1495.61	0.229393	0.114697	+	0.993401i	$0.463410\pi$
$350$	1251.75	0.191168
$351$	−8074.98	−1.22795
$352$	5117.72	0.774930
$353$	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	$-0.618376\pi$
$359$	−4943.42	−0.726751	−0.363376	+	0.931643i	$0.618376\pi$
$360$	995.322	0.145717
$361$	1092.08	0.159218
$362$	−4696.50	−0.681886
$363$	−1792.94	−0.259242
$364$	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	$-0.457384\pi$
$373$	1923.18	0.266966	0.133483	+	0.991051i	$0.457384\pi$
$374$	−639.058	−0.0883554
$375$	−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
$385$	−664.809	−0.0880046
$386$	−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
$396$	2894.09	0.367256
$397$	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
$407$	−3655.01	−0.445141
$408$	1032.74	0.125315
$409$	−9505.94	−1.14924	−0.574619	−	0.818421i	$-0.694850\pi$
$409$	−9505.94	−1.14924	−0.574619	+	0.818421i	$0.694850\pi$
$410$	−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
$418$	3352.00	0.392229
$419$	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
$429$	5062.61	0.569756
$430$	1455.29	0.163210
$431$	2970.58	0.331990	0.165995	−	0.986127i	$-0.446916\pi$
$431$	2970.58	0.331990	0.165995	+	0.986127i	$0.446916\pi$
$432$	−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	$-0.544176\pi$
$439$	−2544.91	−0.276679	−0.138339	+	0.990385i	$0.544176\pi$
$440$	−1612.30	−0.174689
$441$	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
$451$	−12995.0	−1.35679
$452$	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	$-0.619334\pi$
$457$	−7154.78	−0.732356	−0.366178	+	0.930545i	$0.619334\pi$
$458$	−5331.82	−0.543973
$459$	2362.25	0.240219
$460$	2148.17	0.217737
$461$	−7263.06	−0.733784	−0.366892	−	0.930264i	$-0.619578\pi$
$461$	−7263.06	−0.733784	−0.366892	+	0.930264i	$0.619578\pi$
$462$	−941.645	−0.0948253
$463$	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
$473$	9738.60	0.946683
$474$	−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	$-0.658084\pi$
$479$	−9990.10	−0.952942	−0.476471	+	0.879190i	$0.658084\pi$
$480$	1772.35	0.168534
$481$	−7691.13	−0.729075
$482$	−2611.44	−0.246779
$483$	2887.42	0.272012
$484$	3493.69	0.328108
$485$	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	$-0.168689\pi$
$491$	18774.9	1.72566	0.862832	+	0.505491i	$0.168689\pi$
$492$	9124.97	0.836149
$493$	2185.48	0.199653
$494$	7053.51	0.642414
$495$	−1427.35	−0.129605
$496$	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	$-0.874712\pi$
$503$	−20837.0	−1.84707	−0.923533	+	0.383518i	$0.874712\pi$
$504$	−2606.90	−0.230398
$505$	804.957	0.0709309
$506$	−4333.16	−0.380697
$507$	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
$517$	4214.16	0.358489
$518$	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	$-0.340724\pi$
$523$	11476.4	0.959518	0.479759	+	0.877400i	$0.340724\pi$
$524$	12165.6	1.01423
$525$	2900.93	0.241156
$526$	5355.25	0.443916
$527$	−4648.81	−0.384261
$528$	2000.52	0.164889
$529$	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
$539$	−7731.09	−0.617814
$540$	2589.60	0.206368
$541$	−546.481	−0.0434289	−0.0217145	−	0.999764i	$-0.506912\pi$
$541$	−546.481	−0.0434289	−0.0217145	+	0.999764i	$0.506912\pi$
$542$	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	$-0.393560\pi$
$547$	8397.33	0.656388	0.328194	+	0.944610i	$0.393560\pi$
$548$	−19313.6	−1.50554
$549$	918.839	0.0714301
$550$	−4353.44	−0.337512
$551$	−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	$-0.559447\pi$
$557$	−4881.65	−0.371350	−0.185675	+	0.982611i	$0.559447\pi$
$558$	−6346.04	−0.481451
$559$	20492.6	1.55053
$560$	−552.797	−0.0417142
$561$	−1481.02	−0.111459
$562$	−2704.38	−0.202985
$563$	7198.57	0.538870	0.269435	−	0.963019i	$-0.413163\pi$
$563$	7198.57	0.538870	0.269435	+	0.963019i	$0.413163\pi$
$564$	−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	$-0.843916\pi$
$569$	−23946.9	−1.76433	−0.882167	+	0.470937i	$0.843916\pi$
$570$	1160.85	0.0853032
$571$	1593.15	0.116763	0.0583813	−	0.998294i	$-0.481406\pi$
$571$	1593.15	0.116763	0.0583813	+	0.998294i	$0.481406\pi$
$572$	−9864.95	−0.721109
$573$	−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
$583$	14570.6	1.03508
$584$	−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	$-0.451794\pi$
$593$	4357.13	0.301730	0.150865	+	0.988554i	$0.451794\pi$
$594$	−5223.59	−0.360819
$595$	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	$-0.472622\pi$
$601$	2531.41	0.171811	0.0859056	+	0.996303i	$0.472622\pi$
$602$	−3811.62	−0.258057
$603$	−902.830	−0.0609720
$604$	4116.24	0.277297
$605$	−1723.07	−0.115790
$606$	1140.15	0.0764283
$607$	185.004	0.0123708	0.00618540	−	0.999981i	$-0.498031\pi$
$607$	185.004	0.0123708	0.00618540	+	0.999981i	$0.498031\pi$
$608$	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	$-0.698254\pi$
$613$	−17706.9	−1.16668	−0.583339	+	0.812228i	$0.698254\pi$
$614$	3301.93	0.217028
$615$	−4500.39	−0.295078
$616$	4222.84	0.276207
$617$	−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
$627$	7768.27	0.494792
$628$	−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
$638$	−4832.69	−0.299887
$639$	−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
$649$	−8064.45	−0.487762
$650$	−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	$-0.544458\pi$
$659$	−4710.22	−0.278428	−0.139214	+	0.990262i	$0.544458\pi$
$660$	−1623.55	−0.0957527
$661$	−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
$671$	−1488.40	−0.0856322
$672$	−4642.05	−0.266474
$673$	11723.0	0.671454	0.335727	−	0.941959i	$-0.391018\pi$
$673$	11723.0	0.671454	0.335727	+	0.941959i	$0.391018\pi$
$674$	−2679.65	−0.153140
$675$	16092.3	0.917621
$676$	−7253.37	−0.412686
$677$	−289.531	−0.0164366	−0.00821829	−	0.999966i	$-0.502616\pi$
$677$	−289.531	−0.0164366	−0.00821829	+	0.999966i	$0.502616\pi$
$678$	−3037.42	−0.172052
$679$	−6310.25	−0.356650
$680$	992.502	0.0559716
$681$	−6786.45	−0.381875
$682$	10279.8	0.577175
$683$	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
$693$	3738.44	0.204923
$694$	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	$-0.276423\pi$
$701$	23981.1	1.29209	0.646043	+	0.763301i	$0.276423\pi$
$702$	−10991.8	−0.590969
$703$	−11801.6	−0.633150
$704$	1893.12	0.101349
$705$	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
$715$	4865.34	0.254480
$716$	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
$726$	−2440.58	−0.124764
$727$	−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	$-0.702386\pi$
$733$	−23569.5	−1.18767	−0.593833	+	0.804588i	$0.702386\pi$
$734$	−20.2646	−0.00101905
$735$	−2677.41	−0.134364
$736$	−21361.3	−1.06982
$737$	1462.47	0.0730948
$738$	10920.0	0.544678
$739$	10149.1	0.505199	0.252599	−	0.967571i	$-0.418715\pi$
$739$	10149.1	0.505199	0.252599	+	0.967571i	$0.418715\pi$
$740$	2466.50	0.122528
$741$	16346.5	0.810397
$742$	−5702.85	−0.282154
$743$	27758.0	1.37058	0.685291	−	0.728269i	$-0.259675\pi$
$743$	27758.0	1.37058	0.685291	+	0.728269i	$0.259675\pi$
$744$	−16612.6	−0.818611
$745$	−867.148	−0.0426441
$746$	2617.87	0.128481
$747$	1978.47	0.0969054
$748$	2885.89	0.141068
$749$	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
$759$	−10042.1	−0.480244
$760$	−5205.90	−0.248471
$761$	−11028.2	−0.525324	−0.262662	−	0.964888i	$-0.584600\pi$
$761$	−11028.2	−0.525324	−0.262662	+	0.964888i	$0.584600\pi$
$762$	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	$-0.646313\pi$
$769$	−18921.2	−0.887277	−0.443639	+	0.896206i	$0.646313\pi$
$770$	−904.952	−0.0423535
$771$	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
$781$	21772.5	0.997545
$782$	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	$-0.654391\pi$
$787$	−20587.3	−0.932477	−0.466239	+	0.884659i	$0.654391\pi$
$788$	−8379.37	−0.378811
$789$	12410.8	0.559995
$790$	−2972.66	−0.133876
$791$	5616.62	0.252470
$792$	9066.49	0.406772
$793$	−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
$803$	8168.28	0.358969
$804$	−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	$-0.169248\pi$
$809$	39667.1	1.72388	0.861942	+	0.507007i	$0.169248\pi$
$810$	90.5783	0.00392913
$811$	8003.87	0.346552	0.173276	−	0.984873i	$-0.444565\pi$
$811$	8003.87	0.346552	0.173276	+	0.984873i	$0.444565\pi$
$812$	−6275.00	−0.271194
$813$	1732.00	0.0747157
$814$	−4975.28	−0.214230
$815$	−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	$-0.591079\pi$
$821$	−13279.1	−0.564489	−0.282244	+	0.959343i	$0.591079\pi$
$822$	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
$825$	−10089.1	−0.425767
$826$	3156.37	0.132959
$827$	−13679.6	−0.575193	−0.287597	−	0.957752i	$-0.592856\pi$
$827$	−13679.6	−0.575193	−0.287597	+	0.957752i	$0.592856\pi$
$828$	−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
$836$	−15137.1	−0.626231
$837$	−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
$847$	4512.98	0.183079
$848$	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	$-0.447615\pi$
$853$	8162.96	0.327660	0.163830	+	0.986489i	$0.447615\pi$
$854$	582.551	0.0233425
$855$	−4608.73	−0.184345
$856$	18988.4	0.758191
$857$	18724.9	0.746361	0.373181	−	0.927759i	$-0.378267\pi$
$857$	18724.9	0.746361	0.373181	+	0.927759i	$0.378267\pi$
$858$	6891.34	0.274203
$859$	−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
$869$	−19892.6	−0.776536
$870$	−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	$-0.228143\pi$
$877$	39163.0	1.50791	0.753957	+	0.656924i	$0.228143\pi$
$878$	−3464.19	−0.133156
$879$	−22720.3	−0.871830
$880$	1922.57	0.0736473
$881$	−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	$-0.419025\pi$
$887$	13296.0	0.503309	0.251654	+	0.967817i	$0.419025\pi$
$888$	8040.27	0.303844
$889$	−21027.9	−0.793309
$890$	−3356.46	−0.126415
$891$	606.137	0.0227905
$892$	−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
$902$	−17689.1	−0.652974
$903$	−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
$913$	−3204.87	−0.116173
$914$	−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	$-0.291399\pi$
$919$	33956.8	1.21886	0.609429	+	0.792841i	$0.291399\pi$
$920$	6729.71	0.241165
$921$	7652.23	0.273778
$922$	−9886.63	−0.353144
$923$	45815.3	1.63383
$924$	4252.33	0.151398
$925$	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
$935$	−1423.31	−0.0497830
$936$	19078.3	0.666234
$937$	7990.62	0.278593	0.139297	−	0.990251i	$-0.455516\pi$
$937$	7990.62	0.278593	0.139297	+	0.990251i	$0.455516\pi$
$938$	−572.402	−0.0199249
$939$	1856.12	0.0645071
$940$	−2843.83	−0.0986762
$941$	24385.9	0.844799	0.422400	−	0.906410i	$-0.361188\pi$
$941$	24385.9	0.844799	0.422400	+	0.906410i	$0.361188\pi$
$942$	3095.26	0.107058
$943$	54241.0	1.87310
$944$	−6705.69	−0.231199
$945$	3345.12	0.115150
$946$	13256.4	0.455605
$947$	−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	$-0.693112\pi$
$953$	−33546.9	−1.14029	−0.570143	+	0.821546i	$0.693112\pi$
$954$	−12244.1	−0.415531
$955$	−1488.25	−0.0504277
$956$	−2055.00	−0.0695224
$957$	−11199.8	−0.378304
$958$	−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	$-0.364896\pi$
$967$	24766.8	0.823625	0.411813	+	0.911269i	$0.364896\pi$
$968$	10944.9	0.363411
$969$	−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
$979$	−22461.0	−0.733254
$980$	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
$990$	−1942.94	−0.0623744
$991$	−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	$-0.837216\pi$
$997$	−54905.9	−1.74412	−0.872060	+	0.489398i	$0.837216\pi$
$998$	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	17.4.a.b.1.2	✓	3
3.2	odd	2		153.4.a.g.1.2		3
4.3	odd	2		272.4.a.h.1.2		3
5.2	odd	4		425.4.b.f.324.4		6
5.3	odd	4		425.4.b.f.324.3		6
5.4	even	2		425.4.a.g.1.2		3
7.6	odd	2		833.4.a.d.1.2		3
8.3	odd	2		1088.4.a.x.1.2		3
8.5	even	2		1088.4.a.v.1.2		3
11.10	odd	2		2057.4.a.e.1.2		3
12.11	even	2		2448.4.a.bi.1.1		3
17.4	even	4		289.4.b.b.288.3		6
17.13	even	4		289.4.b.b.288.4		6
17.16	even	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	1.1	even	1	trivial
153.4.a.g.1.2		3	3.2	odd	2
272.4.a.h.1.2		3	4.3	odd	2
289.4.a.b.1.2		3	17.16	even	2
289.4.b.b.288.3		6	17.4	even	4
289.4.b.b.288.4		6	17.13	even	4
425.4.a.g.1.2		3	5.4	even	2
425.4.b.f.324.3		6	5.3	odd	4
425.4.b.f.324.4		6	5.2	odd	4
833.4.a.d.1.2		3	7.6	odd	2
1088.4.a.v.1.2		3	8.5	even	2
1088.4.a.x.1.2		3	8.3	odd	2
2057.4.a.e.1.2		3	11.10	odd	2
2448.4.a.bi.1.1		3	12.11	even	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} +4.29415 q^{6} -7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} +O(q^{10})\)	\(q+1.36122 q^{2} +3.15463 q^{3} -6.14708 q^{4} +3.03171 q^{5} +4.29415 q^{6} -7.94049 q^{7} -19.2573 q^{8} -17.0483 q^{9} +4.12682 q^{10} +27.6161 q^{11} -19.3918 q^{12} +58.1117 q^{13} -10.8088 q^{14} +9.56391 q^{15} +22.9632 q^{16} -17.0000 q^{17} -23.2065 q^{18} +89.1688 q^{19} -18.6361 q^{20} -25.0493 q^{21} +37.5916 q^{22} -115.269 q^{23} -60.7497 q^{24} -115.809 q^{25} +79.1029 q^{26} -138.956 q^{27} +48.8108 q^{28} -128.558 q^{29} +13.0186 q^{30} +273.460 q^{31} +185.316 q^{32} +87.1187 q^{33} -23.1408 q^{34} -24.0732 q^{35} +104.797 q^{36} -132.351 q^{37} +121.379 q^{38} +183.321 q^{39} -58.3825 q^{40} -470.559 q^{41} -34.0977 q^{42} +352.642 q^{43} -169.758 q^{44} -51.6854 q^{45} -156.907 q^{46} +152.598 q^{47} +72.4403 q^{48} -279.949 q^{49} -157.641 q^{50} -53.6287 q^{51} -357.217 q^{52} +527.614 q^{53} -189.150 q^{54} +83.7239 q^{55} +152.912 q^{56} +281.295 q^{57} -174.995 q^{58} -292.020 q^{59} -58.7901 q^{60} -53.8962 q^{61} +372.239 q^{62} +135.372 q^{63} +68.5514 q^{64} +176.178 q^{65} +118.588 q^{66} +52.9572 q^{67} +104.500 q^{68} -363.632 q^{69} -32.7690 q^{70} +788.400 q^{71} +328.304 q^{72} +295.780 q^{73} -180.159 q^{74} -365.334 q^{75} -548.127 q^{76} -219.285 q^{77} +249.541 q^{78} -720.325 q^{79} +69.6175 q^{80} +21.9487 q^{81} -640.535 q^{82} -116.051 q^{83} +153.980 q^{84} -51.5390 q^{85} +480.024 q^{86} -405.552 q^{87} -531.812 q^{88} -813.329 q^{89} -70.3553 q^{90} -461.435 q^{91} +708.569 q^{92} +862.664 q^{93} +207.720 q^{94} +270.334 q^{95} +584.605 q^{96} +794.693 q^{97} -381.072 q^{98} -470.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} - 74 q^{6} + 22 q^{7} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) 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	\( 3 q + q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} - 74 q^{6} + 22 q^{7} - 39 q^{8} + 59 q^{9} - 56 q^{10} - 28 q^{11} + 22 q^{12} + 30 q^{13} + 92 q^{14} + 108 q^{15} + 137 q^{16} - 51 q^{17} - 103 q^{18} + 80 q^{19} - 168 q^{20} - 192 q^{21} + 286 q^{22} + 142 q^{23} - 666 q^{24} - 223 q^{25} + 26 q^{26} - 20 q^{27} + 476 q^{28} - 456 q^{29} + 400 q^{30} + 230 q^{31} - 71 q^{32} - 332 q^{33} - 17 q^{34} - 332 q^{35} + 1313 q^{36} + 356 q^{37} + 724 q^{38} + 268 q^{39} - 424 q^{40} - 294 q^{41} - 1128 q^{42} + 556 q^{43} - 1122 q^{44} - 384 q^{45} - 704 q^{46} + 640 q^{47} + 774 q^{48} - 269 q^{49} + 547 q^{50} - 68 q^{51} - 774 q^{52} + 302 q^{53} - 1100 q^{54} + 76 q^{55} + 684 q^{56} - 720 q^{57} - 1304 q^{58} + 636 q^{59} + 1328 q^{60} - 84 q^{61} + 508 q^{62} + 1122 q^{63} - 919 q^{64} + 408 q^{65} + 2468 q^{66} + 1008 q^{67} - 425 q^{68} + 576 q^{69} - 1504 q^{70} - 402 q^{71} - 927 q^{72} + 838 q^{73} + 836 q^{74} - 1548 q^{75} - 908 q^{76} - 504 q^{77} + 1308 q^{78} - 594 q^{79} - 40 q^{80} - 505 q^{81} + 358 q^{82} - 2396 q^{83} - 2040 q^{84} + 136 q^{85} - 1264 q^{86} + 1428 q^{87} + 1838 q^{88} - 170 q^{89} - 2008 q^{90} - 1016 q^{91} + 4896 q^{92} + 632 q^{93} - 2016 q^{94} - 472 q^{95} + 678 q^{96} - 270 q^{97} + 2857 q^{98} - 2920 q^{99}+O(q^{100}) \) 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 - 28 * q^11 + 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 + 286 * q^22 + 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 - 332 * q^33 - 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 - 1122 * q^44 - 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 + 76 * q^55 + 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 + 2468 * q^66 + 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 - 504 * q^77 + 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 + 1838 * q^88 - 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 - 2920 * q^99

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