LMFDB - Embedded newform 17.4.a.b.1.1

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			1.1
Root			$-3.58966$ 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)

$f(q)$	$=$	$q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} +O(q^{10})$	\(q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} -4.45724 q^{10} -52.3720 q^{11} +146.845 q^{12} -8.06025 q^{13} -19.2156 q^{14} +7.50653 q^{15} +97.5862 q^{16} -17.0000 q^{17} -225.616 q^{18} -66.5154 q^{19} +15.3456 q^{20} +32.3613 q^{21} +263.563 q^{22} +180.226 q^{23} -397.782 q^{24} -124.216 q^{25} +40.5633 q^{26} +151.129 q^{27} +66.1562 q^{28} -41.2800 q^{29} -37.7767 q^{30} -34.9114 q^{31} -115.632 q^{32} -443.871 q^{33} +85.5527 q^{34} +3.38182 q^{35} +776.759 q^{36} +130.368 q^{37} +334.739 q^{38} -68.3134 q^{39} -41.5689 q^{40} -17.9081 q^{41} -162.859 q^{42} +277.620 q^{43} -907.405 q^{44} +39.7069 q^{45} -906.987 q^{46} +463.789 q^{47} +827.078 q^{48} -328.421 q^{49} +625.116 q^{50} -144.081 q^{51} -139.653 q^{52} -329.944 q^{53} -760.560 q^{54} -46.3853 q^{55} -179.207 q^{56} -563.741 q^{57} +207.742 q^{58} +678.656 q^{59} +130.059 q^{60} +340.280 q^{61} +175.692 q^{62} +171.180 q^{63} -198.770 q^{64} -7.13888 q^{65} +2233.79 q^{66} +15.3925 q^{67} -294.545 q^{68} +1527.48 q^{69} -17.0190 q^{70} -670.203 q^{71} -2104.12 q^{72} +193.480 q^{73} -656.080 q^{74} -1052.77 q^{75} -1152.46 q^{76} -199.971 q^{77} +343.788 q^{78} +1080.15 q^{79} +86.4311 q^{80} +70.4207 q^{81} +90.1229 q^{82} -865.668 q^{83} +560.697 q^{84} -15.0567 q^{85} -1397.13 q^{86} -349.863 q^{87} +2458.02 q^{88} +1129.46 q^{89} -199.825 q^{90} -30.7763 q^{91} +3122.61 q^{92} -295.886 q^{93} -2334.02 q^{94} -58.9120 q^{95} -980.023 q^{96} -379.412 q^{97} +1652.78 q^{98} -2347.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.03251	−1.77926	−0.889630	−	0.456681i	$-0.849038\pi$
$2$	−5.03251	−1.77926	−0.889630	+	0.456681i	$0.849038\pi$
$3$	8.47535	1.63108	0.815541	−	0.578699i	$-0.196439\pi$
$3$	8.47535	1.63108	0.815541	+	0.578699i	$0.196439\pi$
$4$	17.3261	2.16577
$5$	0.885690	0.0792185	0.0396092	−	0.999215i	$-0.487389\pi$
$5$	0.885690	0.0792185	0.0396092	+	0.999215i	$0.487389\pi$
$6$	−42.6523	−2.90212
$7$	3.81828	0.206168	0.103084	−	0.994673i	$-0.467129\pi$
$7$	3.81828	0.206168	0.103084	+	0.994673i	$0.467129\pi$
$8$	−46.9339	−2.07421
$9$	44.8316	1.66043
$10$	−4.45724	−0.140950
$11$	−52.3720	−1.43552	−0.717761	−	0.696289i	$-0.754833\pi$
$11$	−52.3720	−1.43552	−0.717761	+	0.696289i	$0.754833\pi$
$12$	146.845	3.53255
$13$	−8.06025	−0.171962	−0.0859811	−	0.996297i	$-0.527402\pi$
$13$	−8.06025	−0.171962	−0.0859811	+	0.996297i	$0.527402\pi$
$14$	−19.2156	−0.366827
$15$	7.50653	0.129212
$16$	97.5862	1.52478
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	−225.616	−2.95434
$19$	−66.5154	−0.803141	−0.401570	−	0.915828i	$-0.631535\pi$
$19$	−66.5154	−0.803141	−0.401570	+	0.915828i	$0.631535\pi$
$20$	15.3456	0.171569
$21$	32.3613	0.336277
$22$	263.563	2.55417
$23$	180.226	1.63390	0.816948	−	0.576711i	$-0.195664\pi$
$23$	180.226	1.63390	0.816948	+	0.576711i	$0.195664\pi$
$24$	−397.782	−3.38320
$25$	−124.216	−0.993724
$26$	40.5633	0.305966
$27$	151.129	1.07722
$28$	66.1562	0.446512
$29$	−41.2800	−0.264328	−0.132164	−	0.991228i	$-0.542193\pi$
$29$	−41.2800	−0.264328	−0.132164	+	0.991228i	$0.542193\pi$
$30$	−37.7767	−0.229902
$31$	−34.9114	−0.202267	−0.101133	−	0.994873i	$-0.532247\pi$
$31$	−34.9114	−0.202267	−0.101133	+	0.994873i	$0.532247\pi$
$32$	−115.632	−0.638783
$33$	−443.871	−2.34146
$34$	85.5527	0.431534
$35$	3.38182	0.0163323
$36$	776.759	3.59611
$37$	130.368	0.579255	0.289627	−	0.957139i	$-0.406469\pi$
$37$	130.368	0.579255	0.289627	+	0.957139i	$0.406469\pi$
$38$	334.739	1.42900
$39$	−68.3134	−0.280485
$40$	−41.5689	−0.164315
$41$	−17.9081	−0.0682142	−0.0341071	−	0.999418i	$-0.510859\pi$
$41$	−17.9081	−0.0682142	−0.0341071	+	0.999418i	$0.510859\pi$
$42$	−162.859	−0.598325
$43$	277.620	0.984573	0.492287	−	0.870433i	$-0.336161\pi$
$43$	277.620	0.984573	0.492287	+	0.870433i	$0.336161\pi$
$44$	−907.405	−3.10901
$45$	39.7069	0.131537
$46$	−906.987	−2.90713
$47$	463.789	1.43937	0.719687	−	0.694299i	$-0.244285\pi$
$47$	463.789	1.43937	0.719687	+	0.694299i	$0.244285\pi$
$48$	827.078	2.48705
$49$	−328.421	−0.957495
$50$	625.116	1.76809
$51$	−144.081	−0.395596
$52$	−139.653	−0.372431
$53$	−329.944	−0.855118	−0.427559	−	0.903987i	$-0.640626\pi$
$53$	−329.944	−0.855118	−0.427559	+	0.903987i	$0.640626\pi$
$54$	−760.560	−1.91665
$55$	−46.3853	−0.113720
$56$	−179.207	−0.427635
$57$	−563.741	−1.30999
$58$	207.742	0.470308
$59$	678.656	1.49752	0.748759	−	0.662843i	$-0.230650\pi$
$59$	678.656	1.49752	0.748759	+	0.662843i	$0.230650\pi$
$60$	130.059	0.279843
$61$	340.280	0.714237	0.357118	−	0.934059i	$-0.383759\pi$
$61$	340.280	0.714237	0.357118	+	0.934059i	$0.383759\pi$
$62$	175.692	0.359885
$63$	171.180	0.342328
$64$	−198.770	−0.388223
$65$	−7.13888	−0.0136226
$66$	2233.79	4.16606
$67$	15.3925	0.0280671	0.0140336	−	0.999902i	$-0.495533\pi$
$67$	15.3925	0.0280671	0.0140336	+	0.999902i	$0.495533\pi$
$68$	−294.545	−0.525276
$69$	1527.48	2.66502
$70$	−17.0190	−0.0290595
$71$	−670.203	−1.12026	−0.560130	−	0.828405i	$-0.689249\pi$
$71$	−670.203	−1.12026	−0.560130	+	0.828405i	$0.689249\pi$
$72$	−2104.12	−3.44408
$73$	193.480	0.310207	0.155103	−	0.987898i	$-0.450429\pi$
$73$	193.480	0.310207	0.155103	+	0.987898i	$0.450429\pi$
$74$	−656.080	−1.03065
$75$	−1052.77	−1.62085
$76$	−1152.46	−1.73942
$77$	−199.971	−0.295959
$78$	343.788	0.499055
$79$	1080.15	1.53831	0.769156	−	0.639061i	$-0.220677\pi$
$79$	1080.15	1.53831	0.769156	+	0.639061i	$0.220677\pi$
$80$	86.4311	0.120791
$81$	70.4207	0.0965990
$82$	90.1229	0.121371
$83$	−865.668	−1.14481	−0.572406	−	0.819970i	$-0.693990\pi$
$83$	−865.668	−1.14481	−0.572406	+	0.819970i	$0.693990\pi$
$84$	560.697	0.728298
$85$	−15.0567	−0.0192133
$86$	−1397.13	−1.75181
$87$	−349.863	−0.431141
$88$	2458.02	2.97757
$89$	1129.46	1.34520	0.672599	−	0.740008i	$-0.265178\pi$
$89$	1129.46	1.34520	0.672599	+	0.740008i	$0.265178\pi$
$90$	−199.825	−0.234038
$91$	−30.7763	−0.0354531
$92$	3122.61	3.53864
$93$	−295.886	−0.329914
$94$	−2334.02	−2.56102
$95$	−58.9120	−0.0636236
$96$	−980.023	−1.04191
$97$	−379.412	−0.397149	−0.198574	−	0.980086i	$-0.563631\pi$
$97$	−379.412	−0.397149	−0.198574	+	0.980086i	$0.563631\pi$
$98$	1652.78	1.70363
$99$	−2347.92	−2.38359
$100$	−2152.18	−2.15218
$101$	131.732	0.129780	0.0648902	−	0.997892i	$-0.479330\pi$
$101$	131.732	0.129780	0.0648902	+	0.997892i	$0.479330\pi$
$102$	725.089	0.703868
$103$	195.988	0.187488	0.0937442	−	0.995596i	$-0.470116\pi$
$103$	195.988	0.187488	0.0937442	+	0.995596i	$0.470116\pi$
$104$	378.299	0.356685
$105$	28.6621	0.0266394
$106$	1660.45	1.52148
$107$	−485.147	−0.438326	−0.219163	−	0.975688i	$-0.570333\pi$
$107$	−485.147	−0.438326	−0.219163	+	0.975688i	$0.570333\pi$
$108$	2618.49	2.33300
$109$	−1255.12	−1.10292	−0.551460	−	0.834201i	$-0.685929\pi$
$109$	−1255.12	−1.10292	−0.551460	+	0.834201i	$0.685929\pi$
$110$	233.435	0.202337
$111$	1104.92	0.944812
$112$	372.612	0.314362
$113$	−1013.35	−0.843612	−0.421806	−	0.906686i	$-0.638604\pi$
$113$	−1013.35	−0.843612	−0.421806	+	0.906686i	$0.638604\pi$
$114$	2837.03	2.33081
$115$	159.624	0.129435
$116$	−715.224	−0.572473
$117$	−361.354	−0.285531
$118$	−3415.34	−2.66447
$119$	−64.9108	−0.0500031
$120$	−352.311	−0.268012
$121$	1411.83	1.06073
$122$	−1712.46	−1.27081
$123$	−151.778	−0.111263
$124$	−604.880	−0.438063
$125$	−220.728	−0.157940
$126$	−861.464	−0.609090
$127$	1927.72	1.34691	0.673456	−	0.739227i	$-0.264809\pi$
$127$	1927.72	1.34691	0.673456	+	0.739227i	$0.264809\pi$
$128$	1925.37	1.32953
$129$	2352.93	1.60592
$130$	35.9265	0.0242381
$131$	−406.738	−0.271274	−0.135637	−	0.990759i	$-0.543308\pi$
$131$	−406.738	−0.271274	−0.135637	+	0.990759i	$0.543308\pi$
$132$	−7690.58	−5.07105
$133$	−253.975	−0.165582
$134$	−77.4631	−0.0499387
$135$	133.854	0.0853355
$136$	797.877	0.503069
$137$	−130.552	−0.0814149	−0.0407074	−	0.999171i	$-0.512961\pi$
$137$	−130.552	−0.0814149	−0.0407074	+	0.999171i	$0.512961\pi$
$138$	−7687.03	−4.74177
$139$	2073.54	1.26529	0.632644	−	0.774443i	$-0.281970\pi$
$139$	2073.54	1.26529	0.632644	+	0.774443i	$0.281970\pi$
$140$	58.5938	0.0353720
$141$	3930.78	2.34774
$142$	3372.80	1.99323
$143$	422.131	0.246856
$144$	4374.95	2.53180
$145$	−36.5613	−0.0209397
$146$	−973.689	−0.551939
$147$	−2783.48	−1.56175
$148$	2258.78	1.25453
$149$	−1852.73	−1.01867	−0.509334	−	0.860569i	$-0.670108\pi$
$149$	−1852.73	−1.01867	−0.509334	+	0.860569i	$0.670108\pi$
$150$	5298.08	2.88391
$151$	2050.86	1.10527	0.552637	−	0.833422i	$-0.313622\pi$
$151$	2050.86	1.10527	0.552637	+	0.833422i	$0.313622\pi$
$152$	3121.83	1.66588
$153$	−762.138	−0.402714
$154$	1006.36	0.526588
$155$	−30.9207	−0.0160233
$156$	−1183.61	−0.607465
$157$	−262.991	−0.133688	−0.0668438	−	0.997763i	$-0.521293\pi$
$157$	−262.991	−0.133688	−0.0668438	+	0.997763i	$0.521293\pi$
$158$	−5435.88	−2.73706
$159$	−2796.39	−1.39477
$160$	−102.414	−0.0506035
$161$	688.152	0.336857
$162$	−354.393	−0.171875
$163$	−1444.98	−0.694354	−0.347177	−	0.937800i	$-0.612860\pi$
$163$	−1444.98	−0.694354	−0.347177	+	0.937800i	$0.612860\pi$
$164$	−310.279	−0.147736
$165$	−393.132	−0.185487
$166$	4356.48	2.03692
$167$	−501.565	−0.232409	−0.116204	−	0.993225i	$-0.537073\pi$
$167$	−501.565	−0.232409	−0.116204	+	0.993225i	$0.537073\pi$
$168$	−1518.84	−0.697508
$169$	−2132.03	−0.970429
$170$	75.7731	0.0341855
$171$	−2981.99	−1.33356
$172$	4810.08	2.13236
$173$	−2590.14	−1.13829	−0.569146	−	0.822237i	$-0.692726\pi$
$173$	−2590.14	−1.13829	−0.569146	+	0.822237i	$0.692726\pi$
$174$	1760.69	0.767112
$175$	−474.290	−0.204874
$176$	−5110.79	−2.18886
$177$	5751.85	2.44257
$178$	−5684.02	−2.39346
$179$	2165.65	0.904294	0.452147	−	0.891943i	$-0.350658\pi$
$179$	2165.65	0.904294	0.452147	+	0.891943i	$0.350658\pi$
$180$	687.968	0.284878
$181$	−1925.56	−0.790750	−0.395375	−	0.918520i	$-0.629385\pi$
$181$	−1925.56	−0.790750	−0.395375	+	0.918520i	$0.629385\pi$
$182$	154.882	0.0630803
$183$	2884.00	1.16498
$184$	−8458.69	−3.38904
$185$	115.466	0.0458877
$186$	1489.05	0.587003
$187$	890.324	0.348165
$188$	8035.68	3.11735
$189$	577.055	0.222088
$190$	296.475	0.113203
$191$	−2783.52	−1.05449	−0.527247	−	0.849712i	$-0.676776\pi$
$191$	−2783.52	−1.05449	−0.527247	+	0.849712i	$0.676776\pi$
$192$	−1684.65	−0.633223
$193$	2258.27	0.842246	0.421123	−	0.907004i	$-0.361636\pi$
$193$	2258.27	0.842246	0.421123	+	0.907004i	$0.361636\pi$
$194$	1909.39	0.706631
$195$	−60.5045	−0.0222196
$196$	−5690.27	−2.07371
$197$	−1270.70	−0.459560	−0.229780	−	0.973243i	$-0.573801\pi$
$197$	−1270.70	−0.459560	−0.229780	+	0.973243i	$0.573801\pi$
$198$	11815.9	4.24102
$199$	−4794.36	−1.70786	−0.853928	−	0.520392i	$-0.825786\pi$
$199$	−4794.36	−1.70786	−0.853928	+	0.520392i	$0.825786\pi$
$200$	5829.92	2.06119
$201$	130.457	0.0457798
$202$	−662.942	−0.230913
$203$	−157.619	−0.0544960
$204$	−2496.37	−0.856769
$205$	−15.8611	−0.00540383
$206$	−986.313	−0.333591
$207$	8079.80	2.71297
$208$	−786.569	−0.262205
$209$	3483.54	1.15293
$210$	−144.242	−0.0473984
$211$	−2807.00	−0.915837	−0.457918	−	0.888994i	$-0.651405\pi$
$211$	−2807.00	−0.915837	−0.457918	+	0.888994i	$0.651405\pi$
$212$	−5716.66	−1.85199
$213$	−5680.21	−1.82724
$214$	2441.50	0.779896
$215$	245.885	0.0779964
$216$	−7093.09	−2.23437
$217$	−133.302	−0.0417009
$218$	6316.38	1.96238
$219$	1639.81	0.505973
$220$	−803.679	−0.246291
$221$	137.024	0.0417070
$222$	−5560.51	−1.68107
$223$	4684.30	1.40665	0.703327	−	0.710866i	$-0.251697\pi$
$223$	4684.30	1.40665	0.703327	+	0.710866i	$0.251697\pi$
$224$	−441.516	−0.131697
$225$	−5568.79	−1.65001
$226$	5099.70	1.50101
$227$	−1395.72	−0.408095	−0.204047	−	0.978961i	$-0.565410\pi$
$227$	−1395.72	−0.408095	−0.204047	+	0.978961i	$0.565410\pi$
$228$	−9767.47	−2.83713
$229$	894.638	0.258163	0.129082	−	0.991634i	$-0.458797\pi$
$229$	894.638	0.258163	0.129082	+	0.991634i	$0.458797\pi$
$230$	−803.309	−0.230298
$231$	−1694.83	−0.482733
$232$	1937.43	0.548270
$233$	1196.13	0.336313	0.168156	−	0.985760i	$-0.446219\pi$
$233$	1196.13	0.336313	0.168156	+	0.985760i	$0.446219\pi$
$234$	1818.52	0.508035
$235$	410.773	0.114025
$236$	11758.5	3.24328
$237$	9154.67	2.50911
$238$	326.664	0.0889685
$239$	4948.82	1.33938	0.669691	−	0.742639i	$-0.266426\pi$
$239$	4948.82	1.33938	0.669691	+	0.742639i	$0.266426\pi$
$240$	732.534	0.197020
$241$	−6702.73	−1.79154	−0.895770	−	0.444518i	$-0.853375\pi$
$241$	−6702.73	−1.79154	−0.895770	+	0.444518i	$0.853375\pi$
$242$	−7105.03	−1.88731
$243$	−3483.65	−0.919656
$244$	5895.75	1.54687
$245$	−290.879	−0.0758513
$246$	763.824	0.197966
$247$	536.130	0.138110
$248$	1638.53	0.419543
$249$	−7336.85	−1.86728
$250$	1110.81	0.281016
$251$	−4756.08	−1.19602	−0.598010	−	0.801489i	$-0.704042\pi$
$251$	−4756.08	−1.19602	−0.598010	+	0.801489i	$0.704042\pi$
$252$	2965.89	0.741402
$253$	−9438.77	−2.34550
$254$	−9701.29	−2.39651
$255$	−127.611	−0.0313385
$256$	−8099.28	−1.97736
$257$	2892.84	0.702143	0.351071	−	0.936349i	$-0.385817\pi$
$257$	2892.84	0.702143	0.351071	+	0.936349i	$0.385817\pi$
$258$	−11841.1	−2.85735
$259$	497.784	0.119424
$260$	−123.689	−0.0295034
$261$	−1850.65	−0.438898
$262$	2046.92	0.482667
$263$	5415.48	1.26971	0.634853	−	0.772633i	$-0.281061\pi$
$263$	5415.48	1.26971	0.634853	+	0.772633i	$0.281061\pi$
$264$	20832.6	4.85666
$265$	−292.228	−0.0677412
$266$	1278.13	0.294613
$267$	9572.58	2.19413
$268$	266.693	0.0607869
$269$	5787.00	1.31167	0.655835	−	0.754904i	$-0.272317\pi$
$269$	5787.00	1.31167	0.655835	+	0.754904i	$0.272317\pi$
$270$	−673.620	−0.151834
$271$	5465.13	1.22503	0.612515	−	0.790459i	$-0.290158\pi$
$271$	5465.13	1.22503	0.612515	+	0.790459i	$0.290158\pi$
$272$	−1658.97	−0.369815
$273$	−260.840	−0.0578270
$274$	657.006	0.144858
$275$	6505.42	1.42651
$276$	26465.3	5.77182
$277$	−1207.65	−0.261952	−0.130976	−	0.991386i	$-0.541811\pi$
$277$	−1207.65	−0.261952	−0.130976	+	0.991386i	$0.541811\pi$
$278$	−10435.1	−2.25128
$279$	−1565.13	−0.335850
$280$	−158.722	−0.0338766
$281$	−1197.18	−0.254155	−0.127077	−	0.991893i	$-0.540560\pi$
$281$	−1197.18	−0.254155	−0.127077	+	0.991893i	$0.540560\pi$
$282$	−19781.7	−4.17724
$283$	3164.73	0.664748	0.332374	−	0.943148i	$-0.392150\pi$
$283$	3164.73	0.664748	0.332374	+	0.943148i	$0.392150\pi$
$284$	−11612.0	−2.42622
$285$	−499.300	−0.103775
$286$	−2124.38	−0.439221
$287$	−68.3784	−0.0140636
$288$	−5183.98	−1.06066
$289$	289.000	0.0588235
$290$	183.995	0.0372571
$291$	−3215.65	−0.647782
$292$	3352.26	0.671836
$293$	7456.21	1.48668	0.743339	−	0.668915i	$-0.233241\pi$
$293$	7456.21	1.48668	0.743339	+	0.668915i	$0.233241\pi$
$294$	14007.9	2.77877
$295$	601.079	0.118631
$296$	−6118.70	−1.20149
$297$	−7914.94	−1.54637
$298$	9323.89	1.81248
$299$	−1452.66	−0.280969
$300$	−18240.5	−3.51038
$301$	1060.03	0.202988
$302$	−10321.0	−1.96657
$303$	1116.47	0.211683
$304$	−6490.98	−1.22462
$305$	301.383	0.0565808
$306$	3835.46	0.716532
$307$	−6535.48	−1.21498	−0.607491	−	0.794327i	$-0.707824\pi$
$307$	−6535.48	−1.21498	−0.607491	+	0.794327i	$0.707824\pi$
$308$	−3464.73	−0.640978
$309$	1661.07	0.305809
$310$	155.608	0.0285096
$311$	−8935.89	−1.62928	−0.814642	−	0.579963i	$-0.803067\pi$
$311$	−8935.89	−1.62928	−0.814642	+	0.579963i	$0.803067\pi$
$312$	3206.22	0.581783
$313$	−2628.71	−0.474707	−0.237353	−	0.971423i	$-0.576280\pi$
$313$	−2628.71	−0.474707	−0.237353	+	0.971423i	$0.576280\pi$
$314$	1323.50	0.237865
$315$	151.612	0.0271187
$316$	18714.9	3.33163
$317$	4268.54	0.756293	0.378147	−	0.925746i	$-0.376562\pi$
$317$	4268.54	0.756293	0.378147	+	0.925746i	$0.376562\pi$
$318$	14072.9	2.48166
$319$	2161.92	0.379449
$320$	−176.048	−0.0307544
$321$	−4111.79	−0.714946
$322$	−3463.13	−0.599357
$323$	1130.76	0.194790
$324$	1220.12	0.209211
$325$	1001.21	0.170883
$326$	7271.89	1.23544
$327$	−10637.5	−1.79895
$328$	840.500	0.141490
$329$	1770.88	0.296753
$330$	1978.44	0.330029
$331$	992.298	0.164778	0.0823892	−	0.996600i	$-0.473745\pi$
$331$	992.298	0.164778	0.0823892	+	0.996600i	$0.473745\pi$
$332$	−14998.7	−2.47940
$333$	5844.63	0.961812
$334$	2524.13	0.413516
$335$	13.6330	0.00222344
$336$	3158.02	0.512750
$337$	8042.26	1.29997	0.649985	−	0.759947i	$-0.274775\pi$
$337$	8042.26	1.29997	0.649985	+	0.759947i	$0.274775\pi$
$338$	10729.5	1.72665
$339$	−8588.52	−1.37600
$340$	−260.875	−0.0416116
$341$	1828.38	0.290359
$342$	15006.9	2.37275
$343$	−2563.68	−0.403573
$344$	−13029.8	−2.04221
$345$	1352.87	0.211119
$346$	13034.9	2.02532
$347$	−7414.16	−1.14701	−0.573506	−	0.819202i	$-0.694417\pi$
$347$	−7414.16	−1.14701	−0.573506	+	0.819202i	$0.694417\pi$
$348$	−6061.78	−0.933751
$349$	−859.194	−0.131781	−0.0658905	−	0.997827i	$-0.520989\pi$
$349$	−859.194	−0.131781	−0.0658905	+	0.997827i	$0.520989\pi$
$350$	2386.87	0.364525
$351$	−1218.14	−0.185241
$352$	6055.89	0.916988
$353$	569.084	0.0858053	0.0429027	−	0.999079i	$-0.486339\pi$
$353$	569.084	0.0858053	0.0429027	+	0.999079i	$0.486339\pi$
$354$	−28946.3	−4.34598
$355$	−593.592	−0.0887453
$356$	19569.2	2.91339
$357$	−550.142	−0.0815592
$358$	−10898.7	−1.60897
$359$	−5005.21	−0.735835	−0.367918	−	0.929858i	$-0.619929\pi$
$359$	−5005.21	−0.735835	−0.367918	+	0.929858i	$0.619929\pi$
$360$	−1863.60	−0.272834
$361$	−2434.71	−0.354965
$362$	9690.40	1.40695
$363$	11965.7	1.73013
$364$	−533.235	−0.0767833
$365$	171.363	0.0245741
$366$	−14513.7	−2.07280
$367$	−10975.3	−1.56105	−0.780523	−	0.625127i	$-0.785047\pi$
$367$	−10975.3	−1.56105	−0.780523	+	0.625127i	$0.785047\pi$
$368$	17587.5	2.49134
$369$	−802.851	−0.113265
$370$	−581.083	−0.0816462
$371$	−1259.82	−0.176298
$372$	−5126.57	−0.714517
$373$	−3211.72	−0.445835	−0.222918	−	0.974837i	$-0.571558\pi$
$373$	−3211.72	−0.445835	−0.222918	+	0.974837i	$0.571558\pi$
$374$	−4480.56	−0.619477
$375$	−1870.74	−0.257613
$376$	−21767.4	−2.98556
$377$	332.727	0.0454544
$378$	−2904.03	−0.395152
$379$	8051.48	1.09123	0.545616	−	0.838035i	$-0.316296\pi$
$379$	8051.48	1.09123	0.545616	+	0.838035i	$0.316296\pi$
$380$	−1020.72	−0.137794
$381$	16338.1	2.19692
$382$	14008.1	1.87622
$383$	−2584.16	−0.344763	−0.172382	−	0.985030i	$-0.555146\pi$
$383$	−2584.16	−0.344763	−0.172382	+	0.985030i	$0.555146\pi$
$384$	16318.2	2.16858
$385$	−177.112	−0.0234454
$386$	−11364.7	−1.49858
$387$	12446.2	1.63482
$388$	−6573.74	−0.860132
$389$	−5174.31	−0.674417	−0.337208	−	0.941430i	$-0.609483\pi$
$389$	−5174.31	−0.674417	−0.337208	+	0.941430i	$0.609483\pi$
$390$	304.489	0.0395344
$391$	−3063.83	−0.396278
$392$	15414.1	1.98604
$393$	−3447.25	−0.442470
$394$	6394.79	0.817677
$395$	956.680	0.121863
$396$	−40680.4	−5.16230
$397$	−5149.36	−0.650980	−0.325490	−	0.945545i	$-0.605529\pi$
$397$	−5149.36	−0.650980	−0.325490	+	0.945545i	$0.605529\pi$
$398$	24127.7	3.03872
$399$	−2152.53	−0.270078
$400$	−12121.7	−1.51522
$401$	8700.49	1.08350	0.541748	−	0.840541i	$-0.317763\pi$
$401$	8700.49	1.08350	0.541748	+	0.840541i	$0.317763\pi$
$402$	−656.527	−0.0814542
$403$	281.394	0.0347823
$404$	2282.41	0.281074
$405$	62.3709	0.00765243
$406$	793.219	0.0969625
$407$	−6827.65	−0.831533
$408$	6762.29	0.820547
$409$	12346.0	1.49260	0.746299	−	0.665611i	$-0.231829\pi$
$409$	12346.0	1.49260	0.746299	+	0.665611i	$0.231829\pi$
$410$	79.8209	0.00961482
$411$	−1106.48	−0.132794
$412$	3395.72	0.406056
$413$	2591.30	0.308740
$414$	−40661.7	−4.82708
$415$	−766.713	−0.0906903
$416$	932.023	0.109847
$417$	17574.0	2.06379
$418$	−17531.0	−2.05136
$419$	−5763.33	−0.671974	−0.335987	−	0.941867i	$-0.609070\pi$
$419$	−5763.33	−0.671974	−0.335987	+	0.941867i	$0.609070\pi$
$420$	496.604	0.0576947
$421$	−1876.12	−0.217188	−0.108594	−	0.994086i	$-0.534635\pi$
$421$	−1876.12	−0.217188	−0.108594	+	0.994086i	$0.534635\pi$
$422$	14126.2	1.62951
$423$	20792.4	2.38998
$424$	15485.6	1.77369
$425$	2111.66	0.241014
$426$	28585.7	3.25113
$427$	1299.29	0.147253
$428$	−8405.72	−0.949313
$429$	3577.71	0.402642
$430$	−1237.42	−0.138776
$431$	83.9299	0.00937996	0.00468998	−	0.999989i	$-0.498507\pi$
$431$	83.9299	0.00937996	0.00468998	+	0.999989i	$0.498507\pi$
$432$	14748.1	1.64252
$433$	−15345.0	−1.70308	−0.851539	−	0.524291i	$-0.824331\pi$
$433$	−15345.0	−1.70308	−0.851539	+	0.524291i	$0.824331\pi$
$434$	670.842	0.0741968
$435$	−309.870	−0.0341543
$436$	−21746.3	−2.38867
$437$	−11987.8	−1.31225
$438$	−8252.36	−0.900258
$439$	3064.74	0.333194	0.166597	−	0.986025i	$-0.446722\pi$
$439$	3064.74	0.333194	0.166597	+	0.986025i	$0.446722\pi$
$440$	2177.05	0.235879
$441$	−14723.6	−1.58985
$442$	−689.575	−0.0742076
$443$	−1792.97	−0.192295	−0.0961474	−	0.995367i	$-0.530652\pi$
$443$	−1792.97	−0.192295	−0.0961474	+	0.995367i	$0.530652\pi$
$444$	19144.0	2.04624
$445$	1000.35	0.106564
$446$	−23573.8	−2.50281
$447$	−15702.6	−1.66153
$448$	−758.960	−0.0800391
$449$	2499.19	0.262681	0.131341	−	0.991337i	$-0.458072\pi$
$449$	2499.19	0.262681	0.131341	+	0.991337i	$0.458072\pi$
$450$	28025.0	2.93580
$451$	937.885	0.0979231
$452$	−17557.5	−1.82707
$453$	17381.7	1.80279
$454$	7024.00	0.726107
$455$	−27.2583	−0.00280854
$456$	26458.6	2.71719
$457$	14784.4	1.51331	0.756656	−	0.653813i	$-0.226832\pi$
$457$	14784.4	1.51331	0.756656	+	0.653813i	$0.226832\pi$
$458$	−4502.28	−0.459340
$459$	−2569.20	−0.261263
$460$	2765.67	0.280326
$461$	−17746.9	−1.79297	−0.896483	−	0.443078i	$-0.853887\pi$
$461$	−17746.9	−1.79297	−0.896483	+	0.443078i	$0.853887\pi$
$462$	8529.23	0.858909
$463$	18486.4	1.85559	0.927793	−	0.373096i	$-0.121704\pi$
$463$	18486.4	1.85559	0.927793	+	0.373096i	$0.121704\pi$
$464$	−4028.36	−0.403043
$465$	−262.064	−0.0261353
$466$	−6019.52	−0.598388
$467$	7406.57	0.733908	0.366954	−	0.930239i	$-0.380401\pi$
$467$	7406.57	0.733908	0.366954	+	0.930239i	$0.380401\pi$
$468$	−6260.87	−0.618395
$469$	58.7731	0.00578655
$470$	−2067.22	−0.202880
$471$	−2228.94	−0.218055
$472$	−31852.0	−3.10616
$473$	−14539.5	−1.41338
$474$	−46071.0	−4.46437
$475$	8262.24	0.798101
$476$	−1124.65	−0.108295
$477$	−14791.9	−1.41986
$478$	−24905.0	−2.38311
$479$	−18550.9	−1.76955	−0.884775	−	0.466019i	$-0.845688\pi$
$479$	−18550.9	−1.76955	−0.884775	+	0.466019i	$0.845688\pi$
$480$	−867.997	−0.0825384
$481$	−1050.80	−0.0996100
$482$	33731.6	3.18762
$483$	5832.34	0.549442
$484$	24461.5	2.29729
$485$	−336.041	−0.0314615
$486$	17531.5	1.63631
$487$	10203.4	0.949406	0.474703	−	0.880146i	$-0.342556\pi$
$487$	10203.4	0.949406	0.474703	+	0.880146i	$0.342556\pi$
$488$	−15970.7	−1.48147
$489$	−12246.7	−1.13255
$490$	1463.85	0.134959
$491$	−1247.46	−0.114658	−0.0573290	−	0.998355i	$-0.518258\pi$
$491$	−1247.46	−0.114658	−0.0573290	+	0.998355i	$0.518258\pi$
$492$	−2629.73	−0.240970
$493$	701.760	0.0641089
$494$	−2698.08	−0.245734
$495$	−2079.53	−0.188824
$496$	−3406.87	−0.308413
$497$	−2559.03	−0.230962
$498$	36922.7	3.32238
$499$	70.0303	0.00628254	0.00314127	−	0.999995i	$-0.499000\pi$
$499$	70.0303	0.00628254	0.00314127	+	0.999995i	$0.499000\pi$
$500$	−3824.36	−0.342061
$501$	−4250.94	−0.379078
$502$	23935.0	2.12803
$503$	1444.29	0.128028	0.0640138	−	0.997949i	$-0.479610\pi$
$503$	1444.29	0.128028	0.0640138	+	0.997949i	$0.479610\pi$
$504$	−8034.15	−0.710058
$505$	116.674	0.0102810
$506$	47500.7	4.17325
$507$	−18069.7	−1.58285
$508$	33400.0	2.91710
$509$	14272.8	1.24289	0.621445	−	0.783458i	$-0.286546\pi$
$509$	14272.8	1.24289	0.621445	+	0.783458i	$0.286546\pi$
$510$	642.204	0.0557593
$511$	738.761	0.0639547
$512$	25356.7	2.18871
$513$	−10052.4	−0.865157
$514$	−14558.3	−1.24929
$515$	173.585	0.0148525
$516$	40767.2	3.47805
$517$	−24289.6	−2.06625
$518$	−2505.10	−0.212486
$519$	−21952.3	−1.85665
$520$	335.055	0.0282561
$521$	14874.0	1.25075	0.625376	−	0.780324i	$-0.284946\pi$
$521$	14874.0	1.25075	0.625376	+	0.780324i	$0.284946\pi$
$522$	9313.42	0.780914
$523$	−8142.90	−0.680811	−0.340406	−	0.940279i	$-0.610564\pi$
$523$	−8142.90	−0.680811	−0.340406	+	0.940279i	$0.610564\pi$
$524$	−7047.21	−0.587517
$525$	−4019.78	−0.334167
$526$	−27253.4	−2.25914
$527$	593.494	0.0490569
$528$	−43315.7	−3.57022
$529$	20314.2	1.66962
$530$	1470.64	0.120529
$531$	30425.3	2.48652
$532$	−4400.40	−0.358612
$533$	144.344	0.0117303
$534$	−48174.1	−3.90393
$535$	−429.689	−0.0347235
$536$	−722.432	−0.0582170
$537$	18354.7	1.47498
$538$	−29123.1	−2.33380
$539$	17200.0	1.37451
$540$	2319.17	0.184817
$541$	3179.67	0.252689	0.126344	−	0.991986i	$-0.459676\pi$
$541$	3179.67	0.252689	0.126344	+	0.991986i	$0.459676\pi$
$542$	−27503.3	−2.17965
$543$	−16319.8	−1.28978
$544$	1965.75	0.154928
$545$	−1111.64	−0.0873716
$546$	1312.68	0.102889
$547$	2107.07	0.164702	0.0823509	−	0.996603i	$-0.473757\pi$
$547$	2107.07	0.164702	0.0823509	+	0.996603i	$0.473757\pi$
$548$	−2261.97	−0.176326
$549$	15255.3	1.18594
$550$	−32738.6	−2.53814
$551$	2745.76	0.212292
$552$	−71690.4	−5.52780
$553$	4124.33	0.317151
$554$	6077.51	0.466081
$555$	978.614	0.0748466
$556$	35926.4	2.74032
$557$	467.382	0.0355540	0.0177770	−	0.999842i	$-0.494341\pi$
$557$	467.382	0.0355540	0.0177770	+	0.999842i	$0.494341\pi$
$558$	7876.55	0.597565
$559$	−2237.69	−0.169309
$560$	330.019	0.0249033
$561$	7545.81	0.567887
$562$	6024.80	0.452208
$563$	14612.6	1.09387	0.546935	−	0.837175i	$-0.315794\pi$
$563$	14612.6	1.09387	0.546935	+	0.837175i	$0.315794\pi$
$564$	68105.2	5.08466
$565$	−897.515	−0.0668297
$566$	−15926.5	−1.18276
$567$	268.886	0.0199156
$568$	31455.3	2.32365
$569$	11602.3	0.854821	0.427410	−	0.904058i	$-0.359426\pi$
$569$	11602.3	0.854821	0.427410	+	0.904058i	$0.359426\pi$
$570$	2512.73	0.184643
$571$	−10534.9	−0.772104	−0.386052	−	0.922477i	$-0.626161\pi$
$571$	−10534.9	−0.772104	−0.386052	+	0.922477i	$0.626161\pi$
$572$	7313.91	0.534633
$573$	−23591.3	−1.71997
$574$	344.115	0.0250228
$575$	−22386.8	−1.62364
$576$	−8911.18	−0.644617
$577$	14404.7	1.03930	0.519650	−	0.854379i	$-0.326062\pi$
$577$	14404.7	1.03930	0.519650	+	0.854379i	$0.326062\pi$
$578$	−1454.40	−0.104662
$579$	19139.6	1.37377
$580$	−633.466	−0.0453504
$581$	−3305.37	−0.236024
$582$	16182.8	1.15257
$583$	17279.8	1.22754
$584$	−9080.77	−0.643433
$585$	−320.047	−0.0226194
$586$	−37523.5	−2.64519
$587$	−11004.9	−0.773799	−0.386900	−	0.922122i	$-0.626454\pi$
$587$	−11004.9	−0.773799	−0.386900	+	0.922122i	$0.626454\pi$
$588$	−48227.0	−3.38240
$589$	2322.14	0.162449
$590$	−3024.94	−0.211076
$591$	−10769.6	−0.749581
$592$	12722.2	0.883239
$593$	1853.59	0.128361	0.0641804	−	0.997938i	$-0.479557\pi$
$593$	1853.59	0.128361	0.0641804	+	0.997938i	$0.479557\pi$
$594$	39832.0	2.75139
$595$	−57.4909	−0.00396117
$596$	−32100.7	−2.20620
$597$	−40633.9	−2.78565
$598$	7310.53	0.499916
$599$	19074.7	1.30112	0.650559	−	0.759456i	$-0.274535\pi$
$599$	19074.7	1.30112	0.650559	+	0.759456i	$0.274535\pi$
$600$	49410.7	3.36197
$601$	−27776.0	−1.88520	−0.942600	−	0.333923i	$-0.891627\pi$
$601$	−27776.0	−1.88520	−0.942600	+	0.333923i	$0.891627\pi$
$602$	−5334.62	−0.361168
$603$	690.073	0.0466035
$604$	35533.4	2.39377
$605$	1250.44	0.0840291
$606$	−5618.67	−0.376638
$607$	18728.3	1.25232	0.626159	−	0.779695i	$-0.284626\pi$
$607$	18728.3	1.25232	0.626159	+	0.779695i	$0.284626\pi$
$608$	7691.32	0.513033
$609$	−1335.88	−0.0888874
$610$	−1516.71	−0.100672
$611$	−3738.25	−0.247518
$612$	−13204.9	−0.872184
$613$	−24405.3	−1.60802	−0.804012	−	0.594613i	$-0.797305\pi$
$613$	−24405.3	−1.60802	−0.804012	+	0.594613i	$0.797305\pi$
$614$	32889.8	2.16177
$615$	−134.428	−0.00881409
$616$	9385.43	0.613880
$617$	−22516.4	−1.46917	−0.734584	−	0.678518i	$-0.762623\pi$
$617$	−22516.4	−1.46917	−0.734584	+	0.678518i	$0.762623\pi$
$618$	−8359.35	−0.544114
$619$	−5146.53	−0.334179	−0.167089	−	0.985942i	$-0.553437\pi$
$619$	−5146.53	−0.334179	−0.167089	+	0.985942i	$0.553437\pi$
$620$	−535.736	−0.0347027
$621$	27237.4	1.76006
$622$	44969.9	2.89892
$623$	4312.60	0.277337
$624$	−6666.45	−0.427679
$625$	15331.4	0.981213
$626$	13229.0	0.844627
$627$	29524.3	1.88052
$628$	−4556.62	−0.289536
$629$	−2216.26	−0.140490
$630$	−762.990	−0.0482512
$631$	−3858.77	−0.243447	−0.121724	−	0.992564i	$-0.538842\pi$
$631$	−3858.77	−0.243447	−0.121724	+	0.992564i	$0.538842\pi$
$632$	−50695.8	−3.19078
$633$	−23790.3	−1.49381
$634$	−21481.5	−1.34564
$635$	1707.36	0.106700
$636$	−48450.7	−3.02075
$637$	2647.15	0.164653
$638$	−10879.9	−0.675138
$639$	−30046.3	−1.86011
$640$	1705.28	0.105324
$641$	18689.3	1.15161	0.575805	−	0.817587i	$-0.304689\pi$
$641$	18689.3	1.15161	0.575805	+	0.817587i	$0.304689\pi$
$642$	20692.6	1.27208
$643$	26473.5	1.62366	0.811831	−	0.583893i	$-0.198471\pi$
$643$	26473.5	1.62366	0.811831	+	0.583893i	$0.198471\pi$
$644$	11923.0	0.729555
$645$	2083.96	0.127219
$646$	−5690.57	−0.346583
$647$	14397.7	0.874855	0.437427	−	0.899254i	$-0.355890\pi$
$647$	14397.7	0.874855	0.437427	+	0.899254i	$0.355890\pi$
$648$	−3305.12	−0.200366
$649$	−35542.6	−2.14972
$650$	−5038.59	−0.304046
$651$	−1129.78	−0.0680177
$652$	−25036.0	−1.50381
$653$	20939.5	1.25486	0.627431	−	0.778672i	$-0.284107\pi$
$653$	20939.5	1.25486	0.627431	+	0.778672i	$0.284107\pi$
$654$	53533.6	3.20081
$655$	−360.244	−0.0214899
$656$	−1747.59	−0.104012
$657$	8674.02	0.515077
$658$	−8911.96	−0.528001
$659$	4031.76	0.238323	0.119162	−	0.992875i	$-0.461979\pi$
$659$	4031.76	0.238323	0.119162	+	0.992875i	$0.461979\pi$
$660$	−6811.47	−0.401721
$661$	6691.52	0.393752	0.196876	−	0.980428i	$-0.436920\pi$
$661$	6691.52	0.393752	0.196876	+	0.980428i	$0.436920\pi$
$662$	−4993.75	−0.293184
$663$	1161.33	0.0680275
$664$	40629.2	2.37458
$665$	−224.943	−0.0131171
$666$	−29413.1	−1.71131
$667$	−7439.71	−0.431884
$668$	−8690.19	−0.503344
$669$	39701.1	2.29437
$670$	−68.6083	−0.00395607
$671$	−17821.2	−1.02530
$672$	−3742.01	−0.214808
$673$	10319.2	0.591048	0.295524	−	0.955335i	$-0.404506\pi$
$673$	10319.2	0.591048	0.295524	+	0.955335i	$0.404506\pi$
$674$	−40472.7	−2.31298
$675$	−18772.6	−1.07046
$676$	−36939.9	−2.10172
$677$	−19813.3	−1.12480	−0.562398	−	0.826866i	$-0.690121\pi$
$677$	−19813.3	−1.12480	−0.562398	+	0.826866i	$0.690121\pi$
$678$	43221.8	2.44826
$679$	−1448.70	−0.0818793
$680$	706.671	0.0398524
$681$	−11829.3	−0.665636
$682$	−9201.33	−0.516624
$683$	5924.61	0.331916	0.165958	−	0.986133i	$-0.446928\pi$
$683$	5924.61	0.331916	0.165958	+	0.986133i	$0.446928\pi$
$684$	−51666.4	−2.88818
$685$	−115.629	−0.00644957
$686$	12901.7	0.718061
$687$	7582.38	0.421085
$688$	27091.9	1.50126
$689$	2659.43	0.147048
$690$	−6808.33	−0.375636
$691$	1973.16	0.108629	0.0543143	−	0.998524i	$-0.482703\pi$
$691$	1973.16	0.108629	0.0543143	+	0.998524i	$0.482703\pi$
$692$	−44877.1	−2.46528
$693$	−8965.03	−0.491419
$694$	37311.8	2.04083
$695$	1836.51	0.100234
$696$	16420.4	0.894274
$697$	304.439	0.0165444
$698$	4323.90	0.234473
$699$	10137.6	0.548554
$700$	−8217.63	−0.443710
$701$	−12840.1	−0.691815	−0.345907	−	0.938269i	$-0.612429\pi$
$701$	−12840.1	−0.691815	−0.345907	+	0.938269i	$0.612429\pi$
$702$	6130.30	0.329591
$703$	−8671.50	−0.465223
$704$	10410.0	0.557302
$705$	3481.45	0.185984
$706$	−2863.92	−0.152670
$707$	502.990	0.0267566
$708$	99657.5	5.29005
$709$	−27749.7	−1.46990	−0.734952	−	0.678119i	$-0.762796\pi$
$709$	−27749.7	−1.46990	−0.734952	+	0.678119i	$0.762796\pi$
$710$	2987.26	0.157901
$711$	48425.0	2.55426
$712$	−53010.0	−2.79022
$713$	−6291.92	−0.330483
$714$	2768.60	0.145115
$715$	373.877	0.0195555
$716$	37522.4	1.95849
$717$	41943.0	2.18464
$718$	25188.8	1.30924
$719$	16888.3	0.875979	0.437989	−	0.898980i	$-0.355691\pi$
$719$	16888.3	0.875979	0.437989	+	0.898980i	$0.355691\pi$
$720$	3874.85	0.200565
$721$	748.339	0.0386541
$722$	12252.7	0.631575
$723$	−56808.0	−2.92215
$724$	−33362.6	−1.71258
$725$	5127.62	0.262669
$726$	−60217.6	−3.07835
$727$	2135.25	0.108930	0.0544649	−	0.998516i	$-0.482655\pi$
$727$	2135.25	0.108930	0.0544649	+	0.998516i	$0.482655\pi$
$728$	1444.45	0.0735371
$729$	−31426.5	−1.59663
$730$	−862.386	−0.0437238
$731$	−4719.54	−0.238794
$732$	49968.6	2.52308
$733$	4795.27	0.241633	0.120817	−	0.992675i	$-0.461449\pi$
$733$	4795.27	0.241633	0.120817	+	0.992675i	$0.461449\pi$
$734$	55233.1	2.77751
$735$	−2465.30	−0.123720
$736$	−20839.9	−1.04371
$737$	−806.138	−0.0402910
$738$	4040.36	0.201528
$739$	−32747.6	−1.63010	−0.815048	−	0.579393i	$-0.803290\pi$
$739$	−32747.6	−1.63010	−0.815048	+	0.579393i	$0.803290\pi$
$740$	2000.58	0.0993821
$741$	4543.89	0.225269
$742$	6340.05	0.313680
$743$	12299.4	0.607298	0.303649	−	0.952784i	$-0.401795\pi$
$743$	12299.4	0.607298	0.303649	+	0.952784i	$0.401795\pi$
$744$	13887.1	0.684309
$745$	−1640.94	−0.0806974
$746$	16163.0	0.793257
$747$	−38809.3	−1.90088
$748$	15425.9	0.754046
$749$	−1852.43	−0.0903688
$750$	9414.54	0.458361
$751$	30102.6	1.46266	0.731332	−	0.682021i	$-0.238899\pi$
$751$	30102.6	1.46266	0.731332	+	0.682021i	$0.238899\pi$
$752$	45259.4	2.19474
$753$	−40309.4	−1.95081
$754$	−1674.45	−0.0808753
$755$	1816.42	0.0875581
$756$	9998.14	0.480990
$757$	38826.3	1.86416	0.932078	−	0.362257i	$-0.117994\pi$
$757$	38826.3	1.86416	0.932078	+	0.362257i	$0.117994\pi$
$758$	−40519.2	−1.94159
$759$	−79996.9	−3.82570
$760$	2764.97	0.131968
$761$	19981.6	0.951815	0.475907	−	0.879495i	$-0.342120\pi$
$761$	19981.6	0.951815	0.475907	+	0.879495i	$0.342120\pi$
$762$	−82221.8	−3.90890
$763$	−4792.39	−0.227387
$764$	−48227.7	−2.28379
$765$	−675.017	−0.0319024
$766$	13004.8	0.613424
$767$	−5470.14	−0.257517
$768$	−68644.2	−3.22524
$769$	−22407.7	−1.05077	−0.525384	−	0.850865i	$-0.676078\pi$
$769$	−22407.7	−1.05077	−0.525384	+	0.850865i	$0.676078\pi$
$770$	891.320	0.0417155
$771$	24517.9	1.14525
$772$	39127.0	1.82411
$773$	−6902.77	−0.321184	−0.160592	−	0.987021i	$-0.551340\pi$
$773$	−6902.77	−0.321184	−0.160592	+	0.987021i	$0.551340\pi$
$774$	−62635.4	−2.90876
$775$	4336.54	0.200997
$776$	17807.3	0.823768
$777$	4218.89	0.194790
$778$	26039.8	1.19996
$779$	1191.17	0.0547856
$780$	−1048.31	−0.0481225
$781$	35099.9	1.60816
$782$	15418.8	0.705082
$783$	−6238.62	−0.284738
$784$	−32049.3	−1.45997
$785$	−232.928	−0.0105905
$786$	17348.3	0.787270
$787$	−22185.9	−1.00488	−0.502442	−	0.864611i	$-0.667565\pi$
$787$	−22185.9	−1.00488	−0.502442	+	0.864611i	$0.667565\pi$
$788$	−22016.3	−0.995301
$789$	45898.1	2.07099
$790$	−4814.50	−0.216826
$791$	−3869.27	−0.173926
$792$	110197.	4.94405
$793$	−2742.74	−0.122822
$794$	25914.2	1.15826
$795$	−2476.73	−0.110491
$796$	−83067.8	−3.69882
$797$	−16291.1	−0.724040	−0.362020	−	0.932170i	$-0.617913\pi$
$797$	−16291.1	−0.724040	−0.362020	+	0.932170i	$0.617913\pi$
$798$	10832.6	0.480539
$799$	−7884.41	−0.349100
$800$	14363.3	0.634775
$801$	50635.5	2.23361
$802$	−43785.3	−1.92782
$803$	−10132.9	−0.445309
$804$	2260.32	0.0991485
$805$	609.489	0.0266853
$806$	−1416.12	−0.0618867
$807$	49046.8	2.13944
$808$	−6182.70	−0.269191
$809$	17696.8	0.769082	0.384541	−	0.923108i	$-0.374360\pi$
$809$	17696.8	0.769082	0.384541	+	0.923108i	$0.374360\pi$
$810$	−313.882	−0.0136157
$811$	−3095.34	−0.134022	−0.0670111	−	0.997752i	$-0.521346\pi$
$811$	−3095.34	−0.134022	−0.0670111	+	0.997752i	$0.521346\pi$
$812$	−2730.93	−0.118026
$813$	46318.9	1.99812
$814$	34360.2	1.47951
$815$	−1279.81	−0.0550057
$816$	−14060.3	−0.603198
$817$	−18466.0	−0.790751
$818$	−62131.5	−2.65572
$819$	−1379.75	−0.0588674
$820$	−274.811	−0.0117034
$821$	12323.5	0.523864	0.261932	−	0.965086i	$-0.415640\pi$
$821$	12323.5	0.523864	0.261932	+	0.965086i	$0.415640\pi$
$822$	5568.36	0.236276
$823$	−34436.5	−1.45854	−0.729271	−	0.684225i	$-0.760140\pi$
$823$	−34436.5	−1.45854	−0.729271	+	0.684225i	$0.760140\pi$
$824$	−9198.50	−0.388889
$825$	55135.7	2.32676
$826$	−13040.8	−0.549329
$827$	18761.6	0.788880	0.394440	−	0.918922i	$-0.370939\pi$
$827$	18761.6	0.788880	0.394440	+	0.918922i	$0.370939\pi$
$828$	139992.	5.87567
$829$	22423.8	0.939457	0.469728	−	0.882811i	$-0.344352\pi$
$829$	22423.8	0.939457	0.469728	+	0.882811i	$0.344352\pi$
$830$	3858.49	0.161362
$831$	−10235.3	−0.427265
$832$	1602.13	0.0667596
$833$	5583.15	0.232227
$834$	−88441.1	−3.67202
$835$	−444.231	−0.0184111
$836$	60356.4	2.49697
$837$	−5276.13	−0.217885
$838$	29004.0	1.19562
$839$	9128.63	0.375632	0.187816	−	0.982204i	$-0.439859\pi$
$839$	9128.63	0.375632	0.187816	+	0.982204i	$0.439859\pi$
$840$	−1345.22	−0.0552555
$841$	−22685.0	−0.930131
$842$	9441.58	0.386435
$843$	−10146.5	−0.414547
$844$	−48634.4	−1.98349
$845$	−1888.32	−0.0768759
$846$	−104638.	−4.25240
$847$	5390.75	0.218688
$848$	−32198.0	−1.30387
$849$	26822.2	1.08426
$850$	−10627.0	−0.428826
$851$	23495.7	0.946442
$852$	−98416.1	−3.95737
$853$	27204.8	1.09200	0.545999	−	0.837786i	$-0.316150\pi$
$853$	27204.8	1.09200	0.545999	+	0.837786i	$0.316150\pi$
$854$	−6538.68	−0.262001
$855$	−2641.12	−0.105643
$856$	22769.8	0.909179
$857$	−38060.0	−1.51704	−0.758520	−	0.651649i	$-0.774077\pi$
$857$	−38060.0	−1.51704	−0.758520	+	0.651649i	$0.774077\pi$
$858$	−18004.9	−0.716405
$859$	−33326.2	−1.32372	−0.661860	−	0.749627i	$-0.730233\pi$
$859$	−33326.2	−1.32372	−0.661860	+	0.749627i	$0.730233\pi$
$860$	4260.24	0.168922
$861$	−579.531	−0.0229389
$862$	−422.378	−0.0166894
$863$	−41724.2	−1.64578	−0.822890	−	0.568201i	$-0.807640\pi$
$863$	−41724.2	−1.64578	−0.822890	+	0.568201i	$0.807640\pi$
$864$	−17475.4	−0.688108
$865$	−2294.06	−0.0901737
$866$	77223.8	3.03022
$867$	2449.38	0.0959460
$868$	−2309.60	−0.0903146
$869$	−56569.7	−2.20828
$870$	1559.42	0.0607694
$871$	−124.068	−0.00482649
$872$	58907.5	2.28768
$873$	−17009.6	−0.659438
$874$	60328.6	2.33483
$875$	−842.801	−0.0325621
$876$	28411.6	1.09582
$877$	−49337.3	−1.89966	−0.949830	−	0.312767i	$-0.898744\pi$
$877$	−49337.3	−1.89966	−0.949830	+	0.312767i	$0.898744\pi$
$878$	−15423.3	−0.592838
$879$	63194.0	2.42489
$880$	−4526.57	−0.173398
$881$	8845.46	0.338265	0.169132	−	0.985593i	$-0.445903\pi$
$881$	8845.46	0.338265	0.169132	+	0.985593i	$0.445903\pi$
$882$	74096.8	2.82876
$883$	14724.2	0.561165	0.280582	−	0.959830i	$-0.409472\pi$
$883$	14724.2	0.561165	0.280582	+	0.959830i	$0.409472\pi$
$884$	2374.10	0.0903277
$885$	5094.36	0.193497
$886$	9023.14	0.342143
$887$	3864.38	0.146283	0.0731415	−	0.997322i	$-0.476698\pi$
$887$	3864.38	0.146283	0.0731415	+	0.997322i	$0.476698\pi$
$888$	−51858.1	−1.95974
$889$	7360.60	0.277690
$890$	−5034.28	−0.189606
$891$	−3688.07	−0.138670
$892$	81160.9	3.04649
$893$	−30849.1	−1.15602
$894$	79023.2	2.95630
$895$	1918.10	0.0716368
$896$	7351.61	0.274107
$897$	−12311.8	−0.458283
$898$	−12577.2	−0.467379
$899$	1441.14	0.0534648
$900$	−96485.6	−3.57354
$901$	5609.04	0.207397
$902$	−4719.92	−0.174231
$903$	8984.15	0.331089
$904$	47560.6	1.74982
$905$	−1705.45	−0.0626421
$906$	−87473.7	−3.20764
$907$	−743.409	−0.0272155	−0.0136078	−	0.999907i	$-0.504332\pi$
$907$	−743.409	−0.0272155	−0.0136078	+	0.999907i	$0.504332\pi$
$908$	−24182.5	−0.883839
$909$	5905.76	0.215491
$910$	137.177	0.00499713
$911$	16291.0	0.592475	0.296238	−	0.955114i	$-0.404268\pi$
$911$	16291.0	0.592475	0.296238	+	0.955114i	$0.404268\pi$
$912$	−55013.4	−1.99745
$913$	45336.8	1.64340
$914$	−74402.5	−2.69258
$915$	2554.33	0.0922879
$916$	15500.6	0.559122
$917$	−1553.04	−0.0559280
$918$	12929.5	0.464856
$919$	−6188.99	−0.222150	−0.111075	−	0.993812i	$-0.535429\pi$
$919$	−6188.99	−0.222150	−0.111075	+	0.993812i	$0.535429\pi$
$920$	−7491.78	−0.268474
$921$	−55390.5	−1.98174
$922$	89311.6	3.19015
$923$	5402.00	0.192643
$924$	−29364.8	−1.04549
$925$	−16193.8	−0.575620
$926$	−93033.0	−3.30157
$927$	8786.47	0.311311
$928$	4773.30	0.168848
$929$	−31661.7	−1.11818	−0.559089	−	0.829108i	$-0.688849\pi$
$929$	−31661.7	−1.11818	−0.559089	+	0.829108i	$0.688849\pi$
$930$	1318.84	0.0465015
$931$	21845.0	0.769003
$932$	20724.3	0.728376
$933$	−75734.8	−2.65750
$934$	−37273.6	−1.30581
$935$	788.551	0.0275811
$936$	16959.8	0.592251
$937$	35010.5	1.22064	0.610322	−	0.792153i	$-0.291040\pi$
$937$	35010.5	1.22064	0.610322	+	0.792153i	$0.291040\pi$
$938$	−295.776	−0.0102958
$939$	−22279.2	−0.774286
$940$	7117.12	0.246952
$941$	−45625.8	−1.58061	−0.790307	−	0.612711i	$-0.790079\pi$
$941$	−45625.8	−1.58061	−0.790307	+	0.612711i	$0.790079\pi$
$942$	11217.2	0.387977
$943$	−3227.51	−0.111455
$944$	66227.5	2.28339
$945$	511.092	0.0175934
$946$	73170.2	2.51477
$947$	−21508.4	−0.738044	−0.369022	−	0.929421i	$-0.620307\pi$
$947$	−21508.4	−0.738044	−0.369022	+	0.929421i	$0.620307\pi$
$948$	158615.	5.43416
$949$	−1559.50	−0.0533439
$950$	−41579.8	−1.42003
$951$	36177.4	1.23358
$952$	3046.52	0.103717
$953$	35686.7	1.21302	0.606509	−	0.795076i	$-0.292569\pi$
$953$	35686.7	1.21302	0.606509	+	0.795076i	$0.292569\pi$
$954$	74440.5	2.52631
$955$	−2465.34	−0.0835355
$956$	85744.0	2.90079
$957$	18323.0	0.618912
$958$	93357.8	3.14849
$959$	−498.486	−0.0167851
$960$	−1492.07	−0.0501630
$961$	−28572.2	−0.959088
$962$	5288.17	0.177232
$963$	−21749.9	−0.727810
$964$	−116133.	−3.88006
$965$	2000.12	0.0667215
$966$	−29351.3	−0.977600
$967$	−3731.33	−0.124086	−0.0620432	−	0.998073i	$-0.519762\pi$
$967$	−3731.33	−0.124086	−0.0620432	+	0.998073i	$0.519762\pi$
$968$	−66262.5	−2.20016
$969$	9583.60	0.317719
$970$	1691.13	0.0559782
$971$	17645.1	0.583171	0.291585	−	0.956545i	$-0.405817\pi$
$971$	17645.1	0.583171	0.291585	+	0.956545i	$0.405817\pi$
$972$	−60358.3	−1.99176
$973$	7917.35	0.260862
$974$	−51348.7	−1.68924
$975$	8485.59	0.278725
$976$	33206.7	1.08906
$977$	24941.2	0.816723	0.408362	−	0.912820i	$-0.366100\pi$
$977$	24941.2	0.816723	0.408362	+	0.912820i	$0.366100\pi$
$978$	61631.8	2.01510
$979$	−59152.1	−1.93106
$980$	−5039.81	−0.164276
$981$	−56268.9	−1.83132
$982$	6277.85	0.204006
$983$	−22506.2	−0.730252	−0.365126	−	0.930958i	$-0.618974\pi$
$983$	−22506.2	−0.730252	−0.365126	+	0.930958i	$0.618974\pi$
$984$	7123.53	0.230782
$985$	−1125.44	−0.0364057
$986$	−3531.62	−0.114066
$987$	15008.8	0.484029
$988$	9289.07	0.299114
$989$	50034.2	1.60869
$990$	10465.3	0.335967
$991$	32694.1	1.04799	0.523997	−	0.851720i	$-0.324440\pi$
$991$	32694.1	1.04799	0.523997	+	0.851720i	$0.324440\pi$
$992$	4036.88	0.129205
$993$	8410.08	0.268767
$994$	12878.3	0.410941
$995$	−4246.32	−0.135294
$996$	−127119.	−4.04410
$997$	18248.8	0.579686	0.289843	−	0.957074i	$-0.406397\pi$
$997$	18248.8	0.579686	0.289843	+	0.957074i	$0.406397\pi$
$998$	−352.428	−0.0111783
$999$	19702.5	0.623983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.a.b.1.1	✓	3
3.2	odd	2		153.4.a.g.1.3		3
4.3	odd	2		272.4.a.h.1.1		3
5.2	odd	4		425.4.b.f.324.1		6
5.3	odd	4		425.4.b.f.324.6		6
5.4	even	2		425.4.a.g.1.3		3
7.6	odd	2		833.4.a.d.1.1		3
8.3	odd	2		1088.4.a.x.1.3		3
8.5	even	2		1088.4.a.v.1.1		3
11.10	odd	2		2057.4.a.e.1.3		3
12.11	even	2		2448.4.a.bi.1.2		3
17.4	even	4		289.4.b.b.288.5		6
17.13	even	4		289.4.b.b.288.6		6
17.16	even	2		289.4.a.b.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.1	✓	3	1.1	even	1	trivial
153.4.a.g.1.3		3	3.2	odd	2
272.4.a.h.1.1		3	4.3	odd	2
289.4.a.b.1.1		3	17.16	even	2
289.4.b.b.288.5		6	17.4	even	4
289.4.b.b.288.6		6	17.13	even	4
425.4.a.g.1.3		3	5.4	even	2
425.4.b.f.324.1		6	5.2	odd	4
425.4.b.f.324.6		6	5.3	odd	4
833.4.a.d.1.1		3	7.6	odd	2
1088.4.a.v.1.1		3	8.5	even	2
1088.4.a.x.1.3		3	8.3	odd	2
2057.4.a.e.1.3		3	11.10	odd	2
2448.4.a.bi.1.2		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)

\(f(q)\)	\(=\)	\(q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} +O(q^{10})\)	\(q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} -4.45724 q^{10} -52.3720 q^{11} +146.845 q^{12} -8.06025 q^{13} -19.2156 q^{14} +7.50653 q^{15} +97.5862 q^{16} -17.0000 q^{17} -225.616 q^{18} -66.5154 q^{19} +15.3456 q^{20} +32.3613 q^{21} +263.563 q^{22} +180.226 q^{23} -397.782 q^{24} -124.216 q^{25} +40.5633 q^{26} +151.129 q^{27} +66.1562 q^{28} -41.2800 q^{29} -37.7767 q^{30} -34.9114 q^{31} -115.632 q^{32} -443.871 q^{33} +85.5527 q^{34} +3.38182 q^{35} +776.759 q^{36} +130.368 q^{37} +334.739 q^{38} -68.3134 q^{39} -41.5689 q^{40} -17.9081 q^{41} -162.859 q^{42} +277.620 q^{43} -907.405 q^{44} +39.7069 q^{45} -906.987 q^{46} +463.789 q^{47} +827.078 q^{48} -328.421 q^{49} +625.116 q^{50} -144.081 q^{51} -139.653 q^{52} -329.944 q^{53} -760.560 q^{54} -46.3853 q^{55} -179.207 q^{56} -563.741 q^{57} +207.742 q^{58} +678.656 q^{59} +130.059 q^{60} +340.280 q^{61} +175.692 q^{62} +171.180 q^{63} -198.770 q^{64} -7.13888 q^{65} +2233.79 q^{66} +15.3925 q^{67} -294.545 q^{68} +1527.48 q^{69} -17.0190 q^{70} -670.203 q^{71} -2104.12 q^{72} +193.480 q^{73} -656.080 q^{74} -1052.77 q^{75} -1152.46 q^{76} -199.971 q^{77} +343.788 q^{78} +1080.15 q^{79} +86.4311 q^{80} +70.4207 q^{81} +90.1229 q^{82} -865.668 q^{83} +560.697 q^{84} -15.0567 q^{85} -1397.13 q^{86} -349.863 q^{87} +2458.02 q^{88} +1129.46 q^{89} -199.825 q^{90} -30.7763 q^{91} +3122.61 q^{92} -295.886 q^{93} -2334.02 q^{94} -58.9120 q^{95} -980.023 q^{96} -379.412 q^{97} +1652.78 q^{98} -2347.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 4 q^{3} + 25 q^{4} - 8 q^{5} - 74 q^{6} + 22 q^{7} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more