LMFDB - Embedded newform 289.4.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + 38476 x^{4} - 32336 x^{3} - 57024 x^{2} - 15776 x + 1156 $ x^12 - 4x^11 - 58x^10 + 204x^9 + 1191x^8 - 3456x^7 - 10364x^6 + 21448x^5 + 38476x^4 - 32336x^3 - 57024x^2 - 15776*x + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.34747$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.49971 q^{2} -2.82539 q^{3} +4.24796 q^{4} -8.71933 q^{5} +9.88806 q^{6} -6.85501 q^{7} +13.1311 q^{8} -19.0171 q^{9} +O(q^{10})$	\(q-3.49971 q^{2} -2.82539 q^{3} +4.24796 q^{4} -8.71933 q^{5} +9.88806 q^{6} -6.85501 q^{7} +13.1311 q^{8} -19.0171 q^{9} +30.5151 q^{10} +61.7928 q^{11} -12.0022 q^{12} -5.37363 q^{13} +23.9905 q^{14} +24.6355 q^{15} -79.9385 q^{16} +66.5545 q^{18} +96.7877 q^{19} -37.0393 q^{20} +19.3681 q^{21} -216.257 q^{22} +116.525 q^{23} -37.1004 q^{24} -48.9733 q^{25} +18.8061 q^{26} +130.017 q^{27} -29.1198 q^{28} -197.375 q^{29} -86.2172 q^{30} +138.070 q^{31} +174.713 q^{32} -174.589 q^{33} +59.7710 q^{35} -80.7840 q^{36} +111.428 q^{37} -338.729 q^{38} +15.1826 q^{39} -114.494 q^{40} -166.487 q^{41} -67.7827 q^{42} +165.887 q^{43} +262.493 q^{44} +165.817 q^{45} -407.804 q^{46} -130.994 q^{47} +225.858 q^{48} -296.009 q^{49} +171.392 q^{50} -22.8269 q^{52} -714.232 q^{53} -455.020 q^{54} -538.792 q^{55} -90.0135 q^{56} -273.463 q^{57} +690.754 q^{58} -846.216 q^{59} +104.651 q^{60} -4.99209 q^{61} -483.205 q^{62} +130.363 q^{63} +28.0634 q^{64} +46.8544 q^{65} +611.011 q^{66} -314.069 q^{67} -329.230 q^{69} -209.181 q^{70} -118.468 q^{71} -249.715 q^{72} +650.548 q^{73} -389.965 q^{74} +138.369 q^{75} +411.150 q^{76} -423.590 q^{77} -53.1347 q^{78} +208.405 q^{79} +697.010 q^{80} +146.115 q^{81} +582.655 q^{82} -742.430 q^{83} +82.2749 q^{84} -580.555 q^{86} +557.662 q^{87} +811.405 q^{88} +215.527 q^{89} -580.310 q^{90} +36.8362 q^{91} +494.994 q^{92} -390.102 q^{93} +458.441 q^{94} -843.923 q^{95} -493.633 q^{96} -705.690 q^{97} +1035.94 q^{98} -1175.12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.49971	−1.23733	−0.618667	−	0.785653i	$-0.712327\pi$
$2$	−3.49971	−1.23733	−0.618667	+	0.785653i	$0.712327\pi$
$3$	−2.82539	−0.543747	−0.271874	−	0.962333i	$-0.587643\pi$
$3$	−2.82539	−0.543747	−0.271874	+	0.962333i	$0.587643\pi$
$4$	4.24796	0.530995
$5$	−8.71933	−0.779880	−0.389940	−	0.920840i	$-0.627504\pi$
$5$	−8.71933	−0.779880	−0.389940	+	0.920840i	$0.627504\pi$
$6$	9.88806	0.672797
$7$	−6.85501	−0.370136	−0.185068	−	0.982726i	$-0.559250\pi$
$7$	−6.85501	−0.370136	−0.185068	+	0.982726i	$0.559250\pi$
$8$	13.1311	0.580316
$9$	−19.0171	−0.704339
$10$	30.5151	0.964972
$11$	61.7928	1.69375	0.846875	−	0.531793i	$-0.178481\pi$
$11$	61.7928	1.69375	0.846875	+	0.531793i	$0.178481\pi$
$12$	−12.0022	−0.288727
$13$	−5.37363	−0.114644	−0.0573221	−	0.998356i	$-0.518256\pi$
$13$	−5.37363	−0.114644	−0.0573221	+	0.998356i	$0.518256\pi$
$14$	23.9905	0.457981
$15$	24.6355	0.424058
$16$	−79.9385	−1.24904
$17$	0	0
$17$	0	0
$18$	66.5545	0.871502
$19$	96.7877	1.16866	0.584332	−	0.811515i	$-0.301357\pi$
$19$	96.7877	1.16866	0.584332	+	0.811515i	$0.301357\pi$
$20$	−37.0393	−0.414112
$21$	19.3681	0.201260
$22$	−216.257	−2.09573
$23$	116.525	1.05640	0.528200	−	0.849120i	$-0.322867\pi$
$23$	116.525	1.05640	0.528200	+	0.849120i	$0.322867\pi$
$24$	−37.1004	−0.315545
$25$	−48.9733	−0.391787
$26$	18.8061	0.141853
$27$	130.017	0.926730
$28$	−29.1198	−0.196540
$29$	−197.375	−1.26385	−0.631924	−	0.775031i	$-0.717734\pi$
$29$	−197.375	−1.26385	−0.631924	+	0.775031i	$0.717734\pi$
$30$	−86.2172	−0.524701
$31$	138.070	0.799939	0.399970	−	0.916528i	$-0.369021\pi$
$31$	138.070	0.799939	0.399970	+	0.916528i	$0.369021\pi$
$32$	174.713	0.965162
$33$	−174.589	−0.920972
$34$	0	0
$35$	59.7710	0.288661
$36$	−80.7840	−0.374000
$37$	111.428	0.495098	0.247549	−	0.968875i	$-0.420375\pi$
$37$	111.428	0.495098	0.247549	+	0.968875i	$0.420375\pi$
$38$	−338.729	−1.44603
$39$	15.1826	0.0623375
$40$	−114.494	−0.452577
$41$	−166.487	−0.634167	−0.317084	−	0.948398i	$-0.602704\pi$
$41$	−166.487	−0.634167	−0.317084	+	0.948398i	$0.602704\pi$
$42$	−67.7827	−0.249026
$43$	165.887	0.588314	0.294157	−	0.955757i	$-0.404961\pi$
$43$	165.887	0.588314	0.294157	+	0.955757i	$0.404961\pi$
$44$	262.493	0.899372
$45$	165.817	0.549300
$46$	−407.804	−1.30712
$47$	−130.994	−0.406541	−0.203271	−	0.979123i	$-0.565157\pi$
$47$	−130.994	−0.406541	−0.203271	+	0.979123i	$0.565157\pi$
$48$	225.858	0.679162
$49$	−296.009	−0.863000
$50$	171.392	0.484771
$51$	0	0
$52$	−22.8269	−0.0608755
$53$	−714.232	−1.85108	−0.925541	−	0.378648i	$-0.876389\pi$
$53$	−714.232	−1.85108	−0.925541	+	0.378648i	$0.876389\pi$
$54$	−455.020	−1.14667
$55$	−538.792	−1.32092
$56$	−90.0135	−0.214796
$57$	−273.463	−0.635458
$58$	690.754	1.56380
$59$	−846.216	−1.86725	−0.933627	−	0.358247i	$-0.883375\pi$
$59$	−846.216	−1.86725	−0.933627	+	0.358247i	$0.883375\pi$
$60$	104.651	0.225172
$61$	−4.99209	−0.0104782	−0.00523911	−	0.999986i	$-0.501668\pi$
$61$	−4.99209	−0.0104782	−0.00523911	+	0.999986i	$0.501668\pi$
$62$	−483.205	−0.989792
$63$	130.363	0.260701
$64$	28.0634	0.0548113
$65$	46.8544	0.0894088
$66$	611.011	1.13955
$67$	−314.069	−0.572681	−0.286341	−	0.958128i	$-0.592439\pi$
$67$	−314.069	−0.572681	−0.286341	+	0.958128i	$0.592439\pi$
$68$	0	0
$69$	−329.230	−0.574415
$70$	−209.181	−0.357171
$71$	−118.468	−0.198022	−0.0990108	−	0.995086i	$-0.531568\pi$
$71$	−118.468	−0.198022	−0.0990108	+	0.995086i	$0.531568\pi$
$72$	−249.715	−0.408739
$73$	650.548	1.04303	0.521513	−	0.853243i	$-0.325368\pi$
$73$	650.548	1.04303	0.521513	+	0.853243i	$0.325368\pi$
$74$	−389.965	−0.612601
$75$	138.369	0.213033
$76$	411.150	0.620554
$77$	−423.590	−0.626917
$78$	−53.1347	−0.0771323
$79$	208.405	0.296803	0.148402	−	0.988927i	$-0.452587\pi$
$79$	208.405	0.296803	0.148402	+	0.988927i	$0.452587\pi$
$80$	697.010	0.974101
$81$	146.115	0.200432
$82$	582.655	0.784677
$83$	−742.430	−0.981834	−0.490917	−	0.871206i	$-0.663338\pi$
$83$	−742.430	−0.981834	−0.490917	+	0.871206i	$0.663338\pi$
$84$	82.2749	0.106868
$85$	0	0
$86$	−580.555	−0.727940
$87$	557.662	0.687214
$88$	811.405	0.982910
$89$	215.527	0.256695	0.128348	−	0.991729i	$-0.459033\pi$
$89$	215.527	0.256695	0.128348	+	0.991729i	$0.459033\pi$
$90$	−580.310	−0.679667
$91$	36.8362	0.0424339
$92$	494.994	0.560943
$93$	−390.102	−0.434965
$94$	458.441	0.503027
$95$	−843.923	−0.911418
$96$	−493.633	−0.524805
$97$	−705.690	−0.738680	−0.369340	−	0.929294i	$-0.620416\pi$
$97$	−705.690	−0.738680	−0.369340	+	0.929294i	$0.620416\pi$
$98$	1035.94	1.06782
$99$	−1175.12	−1.19297
$100$	−208.037	−0.208037
$101$	−546.988	−0.538884	−0.269442	−	0.963017i	$-0.586839\pi$
$101$	−546.988	−0.538884	−0.269442	+	0.963017i	$0.586839\pi$
$102$	0	0
$103$	1550.96	1.48369	0.741846	−	0.670570i	$-0.233950\pi$
$103$	1550.96	1.48369	0.741846	+	0.670570i	$0.233950\pi$
$104$	−70.5614	−0.0665299
$105$	−168.877	−0.156959
$106$	2499.60	2.29041
$107$	245.779	0.222059	0.111029	−	0.993817i	$-0.464585\pi$
$107$	245.779	0.222059	0.111029	+	0.993817i	$0.464585\pi$
$108$	552.305	0.492089
$109$	−1993.39	−1.75167	−0.875834	−	0.482612i	$-0.839688\pi$
$109$	−1993.39	−1.75167	−0.875834	+	0.482612i	$0.839688\pi$
$110$	1885.61	1.63442
$111$	−314.827	−0.269208
$112$	547.979	0.462314
$113$	1082.75	0.901387	0.450693	−	0.892679i	$-0.351177\pi$
$113$	1082.75	0.901387	0.450693	+	0.892679i	$0.351177\pi$
$114$	957.042	0.786273
$115$	−1016.02	−0.823865
$116$	−838.440	−0.671096
$117$	102.191	0.0807484
$118$	2961.51	2.31042
$119$	0	0
$120$	323.491	0.246088
$121$	2487.35	1.86879
$122$	17.4708	0.0129651
$123$	470.391	0.344827
$124$	586.516	0.424764
$125$	1516.93	1.08543
$126$	−456.231	−0.322574
$127$	1016.07	0.709932	0.354966	−	0.934879i	$-0.384492\pi$
$127$	1016.07	0.709932	0.354966	+	0.934879i	$0.384492\pi$
$128$	−1495.92	−1.03298
$129$	−468.695	−0.319894
$130$	−163.977	−0.110629
$131$	1108.85	0.739550	0.369775	−	0.929121i	$-0.379435\pi$
$131$	1108.85	0.739550	0.369775	+	0.929121i	$0.379435\pi$
$132$	−741.647	−0.489031
$133$	−663.480	−0.432564
$134$	1099.15	0.708598
$135$	−1133.66	−0.722738
$136$	0	0
$137$	−1975.27	−1.23182	−0.615909	−	0.787818i	$-0.711211\pi$
$137$	−1975.27	−1.23182	−0.615909	+	0.787818i	$0.711211\pi$
$138$	1152.21	0.710743
$139$	1038.50	0.633702	0.316851	−	0.948475i	$-0.397374\pi$
$139$	1038.50	0.633702	0.316851	+	0.948475i	$0.397374\pi$
$140$	253.905	0.153278
$141$	370.110	0.221056
$142$	414.603	0.245019
$143$	−332.052	−0.194179
$144$	1520.20	0.879747
$145$	1720.97	0.985650
$146$	−2276.73	−1.29057
$147$	836.342	0.469254
$148$	473.340	0.262894
$149$	119.562	0.0657377	0.0328689	−	0.999460i	$-0.489536\pi$
$149$	119.562	0.0657377	0.0328689	+	0.999460i	$0.489536\pi$
$150$	−484.251	−0.263593
$151$	−1567.85	−0.844966	−0.422483	−	0.906371i	$-0.638841\pi$
$151$	−1567.85	−0.844966	−0.422483	+	0.906371i	$0.638841\pi$
$152$	1270.92	0.678194
$153$	0	0
$154$	1482.44	0.775705
$155$	−1203.88	−0.623857
$156$	64.4951	0.0331009
$157$	2121.62	1.07850	0.539248	−	0.842147i	$-0.318709\pi$
$157$	2121.62	1.07850	0.539248	+	0.842147i	$0.318709\pi$
$158$	−729.358	−0.367245
$159$	2017.99	1.00652
$160$	−1523.38	−0.752711
$161$	−798.782	−0.391011
$162$	−511.359	−0.248001
$163$	−443.287	−0.213012	−0.106506	−	0.994312i	$-0.533966\pi$
$163$	−443.287	−0.213012	−0.106506	+	0.994312i	$0.533966\pi$
$164$	−707.229	−0.336740
$165$	1522.30	0.718248
$166$	2598.29	1.21486
$167$	−2352.44	−1.09005	−0.545023	−	0.838421i	$-0.683479\pi$
$167$	−2352.44	−1.09005	−0.545023	+	0.838421i	$0.683479\pi$
$168$	254.324	0.116795
$169$	−2168.12	−0.986857
$170$	0	0
$171$	−1840.63	−0.823135
$172$	704.680	0.312391
$173$	−1900.27	−0.835116	−0.417558	−	0.908650i	$-0.637114\pi$
$173$	−1900.27	−0.835116	−0.417558	+	0.908650i	$0.637114\pi$
$174$	−1951.65	−0.850313
$175$	335.713	0.145014
$176$	−4939.63	−2.11556
$177$	2390.89	1.01531
$178$	−754.283	−0.317617
$179$	99.7302	0.0416435	0.0208217	−	0.999783i	$-0.493372\pi$
$179$	99.7302	0.0416435	0.0208217	+	0.999783i	$0.493372\pi$
$180$	704.382	0.291675
$181$	−3878.82	−1.59287	−0.796437	−	0.604721i	$-0.793285\pi$
$181$	−3878.82	−1.59287	−0.796437	+	0.604721i	$0.793285\pi$
$182$	−128.916	−0.0525049
$183$	14.1046	0.00569750
$184$	1530.10	0.613046
$185$	−971.575	−0.386117
$186$	1365.24	0.538197
$187$	0	0
$188$	−556.457	−0.215871
$189$	−891.265	−0.343016
$190$	2953.48	1.12773
$191$	−2326.90	−0.881511	−0.440756	−	0.897627i	$-0.645289\pi$
$191$	−2326.90	−0.881511	−0.440756	+	0.897627i	$0.645289\pi$
$192$	−79.2901	−0.0298035
$193$	−1396.48	−0.520835	−0.260418	−	0.965496i	$-0.583860\pi$
$193$	−1396.48	−0.520835	−0.260418	+	0.965496i	$0.583860\pi$
$194$	2469.71	0.913994
$195$	−132.382	−0.0486158
$196$	−1257.43	−0.458248
$197$	2023.83	0.731939	0.365969	−	0.930627i	$-0.380738\pi$
$197$	2023.83	0.731939	0.365969	+	0.930627i	$0.380738\pi$
$198$	4112.59	1.47611
$199$	−4143.34	−1.47595	−0.737973	−	0.674830i	$-0.764217\pi$
$199$	−4143.34	−1.47595	−0.737973	+	0.674830i	$0.764217\pi$
$200$	−643.072	−0.227360
$201$	887.369	0.311394
$202$	1914.30	0.666780
$203$	1353.01	0.467795
$204$	0	0
$205$	1451.65	0.494575
$206$	−5427.90	−1.83582
$207$	−2215.98	−0.744063
$208$	429.560	0.143195
$209$	5980.78	1.97942
$210$	591.019	0.194211
$211$	2350.55	0.766912	0.383456	−	0.923559i	$-0.374734\pi$
$211$	2350.55	0.766912	0.383456	+	0.923559i	$0.374734\pi$
$212$	−3034.03	−0.982914
$213$	334.718	0.107674
$214$	−860.153	−0.274761
$215$	−1446.42	−0.458814
$216$	1707.25	0.537796
$217$	−946.471	−0.296086
$218$	6976.27	2.16740
$219$	−1838.05	−0.567143
$220$	−2288.77	−0.701402
$221$	0	0
$222$	1101.80	0.333100
$223$	412.388	0.123837	0.0619183	−	0.998081i	$-0.480278\pi$
$223$	412.388	0.123837	0.0619183	+	0.998081i	$0.480278\pi$
$224$	−1197.66	−0.357241
$225$	931.333	0.275951
$226$	−3789.31	−1.11532
$227$	−1915.89	−0.560186	−0.280093	−	0.959973i	$-0.590365\pi$
$227$	−1915.89	−0.560186	−0.280093	+	0.959973i	$0.590365\pi$
$228$	−1161.66	−0.337425
$229$	−4863.54	−1.40346	−0.701729	−	0.712444i	$-0.747588\pi$
$229$	−4863.54	−1.40346	−0.701729	+	0.712444i	$0.747588\pi$
$230$	3555.78	1.01940
$231$	1196.81	0.340884
$232$	−2591.74	−0.733431
$233$	−555.672	−0.156237	−0.0781186	−	0.996944i	$-0.524891\pi$
$233$	−555.672	−0.156237	−0.0781186	+	0.996944i	$0.524891\pi$
$234$	−357.639	−0.0999127
$235$	1142.18	0.317053
$236$	−3594.69	−0.991502
$237$	−588.828	−0.161386
$238$	0	0
$239$	−3205.56	−0.867575	−0.433787	−	0.901015i	$-0.642823\pi$
$239$	−3205.56	−0.867575	−0.433787	+	0.901015i	$0.642823\pi$
$240$	−1969.33	−0.529665
$241$	−893.396	−0.238791	−0.119396	−	0.992847i	$-0.538096\pi$
$241$	−893.396	−0.238791	−0.119396	+	0.992847i	$0.538096\pi$
$242$	−8705.02	−2.31231
$243$	−3923.28	−1.03571
$244$	−21.2062	−0.00556388
$245$	2581.00	0.673036
$246$	−1646.23	−0.426666
$247$	−520.101	−0.133981
$248$	1813.01	0.464218
$249$	2097.66	0.533870
$250$	−5308.81	−1.34304
$251$	−2431.39	−0.611427	−0.305713	−	0.952124i	$-0.598895\pi$
$251$	−2431.39	−0.611427	−0.305713	+	0.952124i	$0.598895\pi$
$252$	553.775	0.138431
$253$	7200.43	1.78928
$254$	−3555.94	−0.878422
$255$	0	0
$256$	5010.77	1.22333
$257$	−3215.44	−0.780442	−0.390221	−	0.920721i	$-0.627601\pi$
$257$	−3215.44	−0.780442	−0.390221	+	0.920721i	$0.627601\pi$
$258$	1640.30	0.395816
$259$	−763.838	−0.183253
$260$	199.035	0.0474756
$261$	3753.50	0.890177
$262$	−3880.67	−0.915070
$263$	2659.16	0.623464	0.311732	−	0.950170i	$-0.399091\pi$
$263$	2659.16	0.623464	0.311732	+	0.950170i	$0.399091\pi$
$264$	−2292.54	−0.534455
$265$	6227.62	1.44362
$266$	2321.99	0.535226
$267$	−608.950	−0.139577
$268$	−1334.15	−0.304091
$269$	−5712.40	−1.29476	−0.647381	−	0.762166i	$-0.724136\pi$
$269$	−5712.40	−1.29476	−0.647381	+	0.762166i	$0.724136\pi$
$270$	3967.47	0.894268
$271$	−250.885	−0.0562369	−0.0281185	−	0.999605i	$-0.508952\pi$
$271$	−250.885	−0.0562369	−0.0281185	+	0.999605i	$0.508952\pi$
$272$	0	0
$273$	−104.077	−0.0230733
$274$	6912.88	1.52417
$275$	−3026.20	−0.663589
$276$	−1398.55	−0.305011
$277$	−3688.27	−0.800024	−0.400012	−	0.916510i	$-0.630994\pi$
$277$	−3688.27	−0.800024	−0.400012	+	0.916510i	$0.630994\pi$
$278$	−3634.46	−0.784101
$279$	−2625.70	−0.563428
$280$	784.857	0.167515
$281$	3532.00	0.749827	0.374914	−	0.927060i	$-0.377672\pi$
$281$	3532.00	0.749827	0.374914	+	0.927060i	$0.377672\pi$
$282$	−1295.28	−0.273520
$283$	788.220	0.165565	0.0827824	−	0.996568i	$-0.473619\pi$
$283$	788.220	0.165565	0.0827824	+	0.996568i	$0.473619\pi$
$284$	−503.246	−0.105148
$285$	2384.42	0.495581
$286$	1162.08	0.240264
$287$	1141.27	0.234728
$288$	−3322.54	−0.679801
$289$	0	0
$290$	−6022.91	−1.21958
$291$	1993.85	0.401656
$292$	2763.50	0.553841
$293$	−1413.82	−0.281899	−0.140949	−	0.990017i	$-0.545015\pi$
$293$	−1413.82	−0.281899	−0.140949	+	0.990017i	$0.545015\pi$
$294$	−2926.95	−0.580624
$295$	7378.44	1.45623
$296$	1463.16	0.287313
$297$	8034.09	1.56965
$298$	−418.433	−0.0813395
$299$	−626.163	−0.121110
$300$	587.786	0.113119
$301$	−1137.15	−0.217756
$302$	5487.02	1.04551
$303$	1545.46	0.293017
$304$	−7737.06	−1.45971
$305$	43.5276	0.00817175
$306$	0	0
$307$	4499.58	0.836498	0.418249	−	0.908333i	$-0.362644\pi$
$307$	4499.58	0.836498	0.418249	+	0.908333i	$0.362644\pi$
$308$	−1799.39	−0.332890
$309$	−4382.06	−0.806754
$310$	4213.22	0.771919
$311$	−4716.79	−0.860014	−0.430007	−	0.902825i	$-0.641489\pi$
$311$	−4716.79	−0.860014	−0.430007	+	0.902825i	$0.641489\pi$
$312$	199.364	0.0361755
$313$	−6171.31	−1.11445	−0.557225	−	0.830361i	$-0.688134\pi$
$313$	−6171.31	−1.11445	−0.557225	+	0.830361i	$0.688134\pi$
$314$	−7425.05	−1.33446
$315$	−1136.67	−0.203315
$316$	885.298	0.157601
$317$	−1186.87	−0.210287	−0.105144	−	0.994457i	$-0.533530\pi$
$317$	−1186.87	−0.210287	−0.105144	+	0.994457i	$0.533530\pi$
$318$	−7062.37	−1.24540
$319$	−12196.3	−2.14064
$320$	−244.694	−0.0427462
$321$	−694.421	−0.120744
$322$	2795.50	0.483811
$323$	0	0
$324$	620.690	0.106428
$325$	263.164	0.0449161
$326$	1551.37	0.263567
$327$	5632.10	0.952465
$328$	−2186.15	−0.368018
$329$	897.965	0.150475
$330$	−5327.60	−0.888712
$331$	3070.09	0.509811	0.254905	−	0.966966i	$-0.417956\pi$
$331$	3070.09	0.509811	0.254905	+	0.966966i	$0.417956\pi$
$332$	−3153.81	−0.521349
$333$	−2119.04	−0.348716
$334$	8232.87	1.34875
$335$	2738.47	0.446623
$336$	−1548.26	−0.251382
$337$	4437.46	0.717281	0.358640	−	0.933476i	$-0.383240\pi$
$337$	4437.46	0.717281	0.358640	+	0.933476i	$0.383240\pi$
$338$	7587.80	1.22107
$339$	−3059.20	−0.490127
$340$	0	0
$341$	8531.74	1.35490
$342$	6441.65	1.01849
$343$	4380.41	0.689563
$344$	2178.27	0.341408
$345$	2870.66	0.447975
$346$	6650.40	1.03332
$347$	8714.21	1.34814	0.674068	−	0.738669i	$-0.264545\pi$
$347$	8714.21	1.34814	0.674068	+	0.738669i	$0.264545\pi$
$348$	2368.92	0.364907
$349$	−100.929	−0.0154803	−0.00774014	−	0.999970i	$-0.502464\pi$
$349$	−100.929	−0.0154803	−0.00774014	+	0.999970i	$0.502464\pi$
$350$	−1174.90	−0.179431
$351$	−698.660	−0.106244
$352$	10796.0	1.63474
$353$	8688.88	1.31009	0.655046	−	0.755589i	$-0.272649\pi$
$353$	8688.88	1.31009	0.655046	+	0.755589i	$0.272649\pi$
$354$	−8367.43	−1.25628
$355$	1032.96	0.154433
$356$	915.551	0.136304
$357$	0	0
$358$	−349.026	−0.0515269
$359$	2411.52	0.354526	0.177263	−	0.984163i	$-0.443276\pi$
$359$	2411.52	0.354526	0.177263	+	0.984163i	$0.443276\pi$
$360$	2177.35	0.318768
$361$	2508.85	0.365775
$362$	13574.7	1.97092
$363$	−7027.76	−1.01615
$364$	156.479	0.0225322
$365$	−5672.34	−0.813435
$366$	−49.3620	−0.00704971
$367$	2274.20	0.323467	0.161734	−	0.986834i	$-0.448291\pi$
$367$	2274.20	0.323467	0.161734	+	0.986834i	$0.448291\pi$
$368$	−9314.86	−1.31948
$369$	3166.10	0.446669
$370$	3400.23	0.477755
$371$	4896.07	0.685151
$372$	−1657.14	−0.230964
$373$	9493.93	1.31790	0.658951	−	0.752186i	$-0.271001\pi$
$373$	9493.93	1.31790	0.658951	+	0.752186i	$0.271001\pi$
$374$	0	0
$375$	−4285.93	−0.590198
$376$	−1720.09	−0.235922
$377$	1060.62	0.144893
$378$	3119.17	0.424425
$379$	5337.70	0.723428	0.361714	−	0.932289i	$-0.382192\pi$
$379$	5337.70	0.723428	0.361714	+	0.932289i	$0.382192\pi$
$380$	−3584.95	−0.483958
$381$	−2870.79	−0.386024
$382$	8143.47	1.09072
$383$	−779.426	−0.103986	−0.0519932	−	0.998647i	$-0.516557\pi$
$383$	−779.426	−0.103986	−0.0519932	+	0.998647i	$0.516557\pi$
$384$	4226.56	0.561681
$385$	3693.42	0.488920
$386$	4887.29	0.644447
$387$	−3154.69	−0.414372
$388$	−2997.74	−0.392235
$389$	−10826.1	−1.41106	−0.705532	−	0.708679i	$-0.749292\pi$
$389$	−10826.1	−1.41106	−0.705532	+	0.708679i	$0.749292\pi$
$390$	463.299	0.0601540
$391$	0	0
$392$	−3886.91	−0.500813
$393$	−3132.95	−0.402128
$394$	−7082.81	−0.905652
$395$	−1817.16	−0.231471
$396$	−4991.88	−0.633463
$397$	−6106.87	−0.772027	−0.386014	−	0.922493i	$-0.626148\pi$
$397$	−6106.87	−0.772027	−0.386014	+	0.922493i	$0.626148\pi$
$398$	14500.5	1.82624
$399$	1874.59	0.235206
$400$	3914.86	0.489357
$401$	−11451.6	−1.42609	−0.713047	−	0.701116i	$-0.752686\pi$
$401$	−11451.6	−1.42609	−0.713047	+	0.701116i	$0.752686\pi$
$402$	−3105.53	−0.385298
$403$	−741.937	−0.0917085
$404$	−2323.58	−0.286145
$405$	−1274.02	−0.156313
$406$	−4735.12	−0.578818
$407$	6885.44	0.838571
$408$	0	0
$409$	−7597.11	−0.918466	−0.459233	−	0.888316i	$-0.651876\pi$
$409$	−7597.11	−0.918466	−0.459233	+	0.888316i	$0.651876\pi$
$410$	−5080.36	−0.611954
$411$	5580.93	0.669798
$412$	6588.40	0.787833
$413$	5800.82	0.691137
$414$	7755.28	0.920655
$415$	6473.49	0.765713
$416$	−938.843	−0.110650
$417$	−2934.18	−0.344574
$418$	−20931.0	−2.44921
$419$	−6887.55	−0.803052	−0.401526	−	0.915848i	$-0.631520\pi$
$419$	−6887.55	−0.803052	−0.401526	+	0.915848i	$0.631520\pi$
$420$	−717.381	−0.0833444
$421$	13586.7	1.57286	0.786431	−	0.617678i	$-0.211927\pi$
$421$	13586.7	1.57286	0.786431	+	0.617678i	$0.211927\pi$
$422$	−8226.24	−0.948926
$423$	2491.13	0.286343
$424$	−9378.62	−1.07421
$425$	0	0
$426$	−1171.42	−0.133228
$427$	34.2208	0.00387836
$428$	1044.06	0.117912
$429$	938.177	0.105584
$430$	5062.05	0.567706
$431$	−16814.5	−1.87917	−0.939587	−	0.342311i	$-0.888790\pi$
$431$	−16814.5	−1.87917	−0.939587	+	0.342311i	$0.888790\pi$
$432$	−10393.3	−1.15752
$433$	−248.824	−0.0276159	−0.0138080	−	0.999905i	$-0.504395\pi$
$433$	−248.824	−0.0276159	−0.0138080	+	0.999905i	$0.504395\pi$
$434$	3312.37	0.366357
$435$	−4862.43	−0.535944
$436$	−8467.82	−0.930127
$437$	11278.2	1.23458
$438$	6432.66	0.701745
$439$	−9870.05	−1.07306	−0.536528	−	0.843882i	$-0.680265\pi$
$439$	−9870.05	−1.07306	−0.536528	+	0.843882i	$0.680265\pi$
$440$	−7074.91	−0.766552
$441$	5629.24	0.607844
$442$	0	0
$443$	−10000.3	−1.07253	−0.536264	−	0.844051i	$-0.680165\pi$
$443$	−10000.3	−1.07253	−0.536264	+	0.844051i	$0.680165\pi$
$444$	−1337.37	−0.142948
$445$	−1879.25	−0.200191
$446$	−1443.24	−0.153227
$447$	−337.810	−0.0357447
$448$	−192.375	−0.0202876
$449$	−8580.38	−0.901856	−0.450928	−	0.892560i	$-0.648907\pi$
$449$	−8580.38	−0.901856	−0.450928	+	0.892560i	$0.648907\pi$
$450$	−3259.39	−0.341443
$451$	−10287.7	−1.07412
$452$	4599.48	0.478632
$453$	4429.80	0.459448
$454$	6705.07	0.693137
$455$	−321.187	−0.0330934
$456$	−3590.86	−0.368766
$457$	8345.86	0.854273	0.427137	−	0.904187i	$-0.359522\pi$
$457$	8345.86	0.854273	0.427137	+	0.904187i	$0.359522\pi$
$458$	17021.0	1.73655
$459$	0	0
$460$	−4316.02	−0.437468
$461$	−8600.87	−0.868942	−0.434471	−	0.900686i	$-0.643065\pi$
$461$	−8600.87	−0.868942	−0.434471	+	0.900686i	$0.643065\pi$
$462$	−4188.48	−0.421788
$463$	−15888.5	−1.59482	−0.797408	−	0.603440i	$-0.793796\pi$
$463$	−15888.5	−1.59482	−0.797408	+	0.603440i	$0.793796\pi$
$464$	15777.8	1.57860
$465$	3401.43	0.339221
$466$	1944.69	0.193318
$467$	−5941.71	−0.588757	−0.294378	−	0.955689i	$-0.595113\pi$
$467$	−5941.71	−0.588757	−0.294378	+	0.955689i	$0.595113\pi$
$468$	434.103	0.0428770
$469$	2152.95	0.211970
$470$	−3997.29	−0.392301
$471$	−5994.41	−0.586429
$472$	−11111.7	−1.08360
$473$	10250.6	0.996456
$474$	2060.72	0.199688
$475$	−4740.02	−0.457867
$476$	0	0
$477$	13582.7	1.30379
$478$	11218.5	1.07348
$479$	14915.1	1.42273	0.711366	−	0.702822i	$-0.248077\pi$
$479$	14915.1	1.42273	0.711366	+	0.702822i	$0.248077\pi$
$480$	4304.15	0.409285
$481$	−598.771	−0.0567601
$482$	3126.63	0.295465
$483$	2256.87	0.212611
$484$	10566.2	0.992316
$485$	6153.15	0.576082
$486$	13730.3	1.28152
$487$	8222.85	0.765119	0.382559	−	0.923931i	$-0.375043\pi$
$487$	8222.85	0.765119	0.382559	+	0.923931i	$0.375043\pi$
$488$	−65.5514	−0.00608068
$489$	1252.46	0.115825
$490$	−9032.74	−0.832771
$491$	−2635.62	−0.242248	−0.121124	−	0.992637i	$-0.538650\pi$
$491$	−2635.62	−0.242248	−0.121124	+	0.992637i	$0.538650\pi$
$492$	1998.20	0.183101
$493$	0	0
$494$	1820.20	0.165779
$495$	10246.3	0.930376
$496$	−11037.1	−0.999156
$497$	812.097	0.0732949
$498$	−7341.19	−0.660575
$499$	12763.9	1.14507	0.572537	−	0.819879i	$-0.305959\pi$
$499$	12763.9	1.14507	0.572537	+	0.819879i	$0.305959\pi$
$500$	6443.86	0.576356
$501$	6646.58	0.592709
$502$	8509.16	0.756539
$503$	−6403.16	−0.567600	−0.283800	−	0.958884i	$-0.591595\pi$
$503$	−6403.16	−0.567600	−0.283800	+	0.958884i	$0.591595\pi$
$504$	1711.80	0.151289
$505$	4769.36	0.420265
$506$	−25199.4	−2.21393
$507$	6125.81	0.536601
$508$	4316.21	0.376970
$509$	−7892.36	−0.687274	−0.343637	−	0.939103i	$-0.611659\pi$
$509$	−7892.36	−0.687274	−0.343637	+	0.939103i	$0.611659\pi$
$510$	0	0
$511$	−4459.51	−0.386061
$512$	−5568.89	−0.480688
$513$	12584.0	1.08304
$514$	11253.1	0.965667
$515$	−13523.3	−1.15710
$516$	−1991.00	−0.169862
$517$	−8094.49	−0.688579
$518$	2673.21	0.226745
$519$	5369.02	0.454092
$520$	615.248	0.0518854
$521$	−8506.79	−0.715335	−0.357667	−	0.933849i	$-0.616428\pi$
$521$	−8506.79	−0.715335	−0.357667	+	0.933849i	$0.616428\pi$
$522$	−13136.2	−1.10145
$523$	18757.8	1.56830	0.784150	−	0.620571i	$-0.213099\pi$
$523$	18757.8	1.56830	0.784150	+	0.620571i	$0.213099\pi$
$524$	4710.37	0.392697
$525$	−948.521	−0.0788511
$526$	−9306.30	−0.771433
$527$	0	0
$528$	13956.4	1.15033
$529$	1411.14	0.115981
$530$	−21794.9	−1.78624
$531$	16092.6	1.31518
$532$	−2818.44	−0.229689
$533$	894.638	0.0727037
$534$	2131.15	0.172704
$535$	−2143.02	−0.173179
$536$	−4124.06	−0.332336
$537$	−281.777	−0.0226435
$538$	19991.7	1.60205
$539$	−18291.2	−1.46170
$540$	−4815.73	−0.383770
$541$	13399.5	1.06486	0.532429	−	0.846475i	$-0.321279\pi$
$541$	13399.5	1.06486	0.532429	+	0.846475i	$0.321279\pi$
$542$	878.026	0.0695838
$543$	10959.2	0.866121
$544$	0	0
$545$	17381.0	1.36609
$546$	364.239	0.0285494
$547$	7133.73	0.557616	0.278808	−	0.960347i	$-0.410061\pi$
$547$	7133.73	0.557616	0.278808	+	0.960347i	$0.410061\pi$
$548$	−8390.88	−0.654089
$549$	94.9352	0.00738021
$550$	10590.8	0.821080
$551$	−19103.4	−1.47701
$552$	−4323.13	−0.333342
$553$	−1428.62	−0.109857
$554$	12907.9	0.989897
$555$	2745.08	0.209950
$556$	4411.52	0.336493
$557$	5175.60	0.393712	0.196856	−	0.980432i	$-0.436927\pi$
$557$	5175.60	0.393712	0.196856	+	0.980432i	$0.436927\pi$
$558$	9189.18	0.697149
$559$	−891.413	−0.0674468
$560$	−4778.01	−0.360550
$561$	0	0
$562$	−12361.0	−0.927787
$563$	5569.32	0.416907	0.208454	−	0.978032i	$-0.433157\pi$
$563$	5569.32	0.416907	0.208454	+	0.978032i	$0.433157\pi$
$564$	1572.21	0.117379
$565$	−9440.87	−0.702974
$566$	−2758.54	−0.204859
$567$	−1001.62	−0.0741870
$568$	−1555.61	−0.114915
$569$	−15330.1	−1.12948	−0.564738	−	0.825270i	$-0.691023\pi$
$569$	−15330.1	−1.12948	−0.564738	+	0.825270i	$0.691023\pi$
$570$	−8344.76	−0.613199
$571$	22285.0	1.63327	0.816636	−	0.577153i	$-0.195836\pi$
$571$	22285.0	1.63327	0.816636	+	0.577153i	$0.195836\pi$
$572$	−1410.54	−0.103108
$573$	6574.41	0.479319
$574$	−3994.11	−0.290437
$575$	−5706.63	−0.413883
$576$	−533.686	−0.0386057
$577$	−19321.1	−1.39401	−0.697007	−	0.717064i	$-0.745485\pi$
$577$	−19321.1	−1.39401	−0.697007	+	0.717064i	$0.745485\pi$
$578$	0	0
$579$	3945.62	0.283203
$580$	7310.63	0.523375
$581$	5089.36	0.363412
$582$	−6977.91	−0.496982
$583$	−44134.4	−3.13527
$584$	8542.38	0.605285
$585$	−891.037	−0.0629741
$586$	4947.96	0.348803
$587$	−23571.2	−1.65739	−0.828696	−	0.559699i	$-0.810917\pi$
$587$	−23571.2	−1.65739	−0.828696	+	0.559699i	$0.810917\pi$
$588$	3552.74	0.249171
$589$	13363.5	0.934860
$590$	−25822.4	−1.80185
$591$	−5718.12	−0.397990
$592$	−8907.37	−0.618396
$593$	27338.0	1.89315	0.946576	−	0.322481i	$-0.104517\pi$
$593$	27338.0	1.89315	0.946576	+	0.322481i	$0.104517\pi$
$594$	−28117.0	−1.94218
$595$	0	0
$596$	507.895	0.0349064
$597$	11706.6	0.802542
$598$	2191.39	0.149854
$599$	−3930.83	−0.268129	−0.134064	−	0.990973i	$-0.542803\pi$
$599$	−3930.83	−0.268129	−0.134064	+	0.990973i	$0.542803\pi$
$600$	1816.93	0.123626
$601$	−22459.9	−1.52439	−0.762196	−	0.647347i	$-0.775879\pi$
$601$	−22459.9	−1.52439	−0.762196	+	0.647347i	$0.775879\pi$
$602$	3979.71	0.269437
$603$	5972.70	0.403362
$604$	−6660.16	−0.448673
$605$	−21688.1	−1.45743
$606$	−5408.64	−0.362560
$607$	−2227.26	−0.148932	−0.0744660	−	0.997224i	$-0.523725\pi$
$607$	−2227.26	−0.148932	−0.0744660	+	0.997224i	$0.523725\pi$
$608$	16910.1	1.12795
$609$	−3822.77	−0.254362
$610$	−152.334	−0.0101112
$611$	703.913	0.0466076
$612$	0	0
$613$	721.642	0.0475479	0.0237739	−	0.999717i	$-0.492432\pi$
$613$	721.642	0.0475479	0.0237739	+	0.999717i	$0.492432\pi$
$614$	−15747.2	−1.03503
$615$	−4101.49	−0.268924
$616$	−5562.19	−0.363810
$617$	6831.58	0.445752	0.222876	−	0.974847i	$-0.428455\pi$
$617$	6831.58	0.445752	0.222876	+	0.974847i	$0.428455\pi$
$618$	15335.9	0.998224
$619$	16094.9	1.04509	0.522544	−	0.852612i	$-0.324983\pi$
$619$	16094.9	1.04509	0.522544	+	0.852612i	$0.324983\pi$
$620$	−5114.02	−0.331265
$621$	15150.2	0.978997
$622$	16507.4	1.06412
$623$	−1477.44	−0.0950120
$624$	−1213.68	−0.0778620
$625$	−7104.94	−0.454716
$626$	21597.8	1.37895
$627$	−16898.1	−1.07631
$628$	9012.55	0.572675
$629$	0	0
$630$	3978.03	0.251569
$631$	−27131.0	−1.71168	−0.855838	−	0.517245i	$-0.826958\pi$
$631$	−27131.0	−1.71168	−0.855838	+	0.517245i	$0.826958\pi$
$632$	2736.58	0.172240
$633$	−6641.23	−0.417007
$634$	4153.69	0.260196
$635$	−8859.42	−0.553662
$636$	8572.32	0.534457
$637$	1590.64	0.0989380
$638$	42683.7	2.64869
$639$	2252.92	0.139474
$640$	13043.4	0.805603
$641$	13901.7	0.856606	0.428303	−	0.903635i	$-0.359112\pi$
$641$	13901.7	0.856606	0.428303	+	0.903635i	$0.359112\pi$
$642$	2430.27	0.149401
$643$	8827.31	0.541392	0.270696	−	0.962665i	$-0.412746\pi$
$643$	8827.31	0.541392	0.270696	+	0.962665i	$0.412746\pi$
$644$	−3393.19	−0.207625
$645$	4086.71	0.249479
$646$	0	0
$647$	−14695.4	−0.892946	−0.446473	−	0.894797i	$-0.647320\pi$
$647$	−14695.4	−0.892946	−0.446473	+	0.894797i	$0.647320\pi$
$648$	1918.64	0.116314
$649$	−52290.1	−3.16266
$650$	−920.999	−0.0555762
$651$	2674.15	0.160996
$652$	−1883.06	−0.113108
$653$	6942.30	0.416039	0.208019	−	0.978125i	$-0.433298\pi$
$653$	6942.30	0.416039	0.208019	+	0.978125i	$0.433298\pi$
$654$	−19710.7	−1.17852
$655$	−9668.47	−0.576761
$656$	13308.7	0.792100
$657$	−12371.6	−0.734644
$658$	−3142.61	−0.186188
$659$	−11804.8	−0.697800	−0.348900	−	0.937160i	$-0.613445\pi$
$659$	−11804.8	−0.697800	−0.348900	+	0.937160i	$0.613445\pi$
$660$	6466.66	0.381386
$661$	3863.35	0.227333	0.113666	−	0.993519i	$-0.463741\pi$
$661$	3863.35	0.227333	0.113666	+	0.993519i	$0.463741\pi$
$662$	−10744.4	−0.630806
$663$	0	0
$664$	−9748.88	−0.569774
$665$	5785.10	0.337348
$666$	7416.01	0.431479
$667$	−22999.1	−1.33513
$668$	−9993.08	−0.578808
$669$	−1165.16	−0.0673358
$670$	−9583.85	−0.552622
$671$	−308.475	−0.0177475
$672$	3383.86	0.194249
$673$	−876.547	−0.0502057	−0.0251028	−	0.999685i	$-0.507991\pi$
$673$	−876.547	−0.0502057	−0.0251028	+	0.999685i	$0.507991\pi$
$674$	−15529.8	−0.887516
$675$	−6367.35	−0.363080
$676$	−9210.10	−0.524016
$677$	20341.1	1.15476	0.577378	−	0.816477i	$-0.304076\pi$
$677$	20341.1	1.15476	0.577378	+	0.816477i	$0.304076\pi$
$678$	10706.3	0.606450
$679$	4837.51	0.273412
$680$	0	0
$681$	5413.15	0.304600
$682$	−29858.6	−1.67646
$683$	30034.8	1.68265	0.841324	−	0.540531i	$-0.181777\pi$
$683$	30034.8	1.68265	0.841324	+	0.540531i	$0.181777\pi$
$684$	−7818.90	−0.437080
$685$	17223.1	0.960670
$686$	−15330.2	−0.853219
$687$	13741.4	0.763126
$688$	−13260.7	−0.734827
$689$	3838.02	0.212216
$690$	−10046.5	−0.554294
$691$	−10797.7	−0.594450	−0.297225	−	0.954807i	$-0.596061\pi$
$691$	−10797.7	−0.594450	−0.297225	+	0.954807i	$0.596061\pi$
$692$	−8072.28	−0.443442
$693$	8055.48	0.441562
$694$	−30497.2	−1.66810
$695$	−9055.04	−0.494212
$696$	7322.68	0.398801
$697$	0	0
$698$	353.223	0.0191543
$699$	1569.99	0.0849536
$700$	1426.09	0.0770018
$701$	−328.897	−0.0177208	−0.00886039	−	0.999961i	$-0.502820\pi$
$701$	−328.897	−0.0177208	−0.00886039	+	0.999961i	$0.502820\pi$
$702$	2445.11	0.131460
$703$	10784.8	0.578603
$704$	1734.12	0.0928366
$705$	−3227.11	−0.172397
$706$	−30408.6	−1.62102
$707$	3749.60	0.199460
$708$	10156.4	0.539127
$709$	−4850.17	−0.256914	−0.128457	−	0.991715i	$-0.541002\pi$
$709$	−4850.17	−0.256914	−0.128457	+	0.991715i	$0.541002\pi$
$710$	−3615.06	−0.191085
$711$	−3963.28	−0.209050
$712$	2830.10	0.148964
$713$	16088.7	0.845056
$714$	0	0
$715$	2895.27	0.151436
$716$	423.650	0.0221125
$717$	9056.97	0.471741
$718$	−8439.60	−0.438667
$719$	32883.0	1.70560	0.852801	−	0.522236i	$-0.174902\pi$
$719$	32883.0	1.70560	0.852801	+	0.522236i	$0.174902\pi$
$720$	−13255.1	−0.686097
$721$	−10631.8	−0.549167
$722$	−8780.24	−0.452586
$723$	2524.20	0.129842
$724$	−16477.1	−0.845808
$725$	9666.10	0.495159
$726$	24595.1	1.25731
$727$	−16213.2	−0.827116	−0.413558	−	0.910478i	$-0.635714\pi$
$727$	−16213.2	−0.827116	−0.413558	+	0.910478i	$0.635714\pi$
$728$	483.699	0.0246251
$729$	7139.71	0.362735
$730$	19851.5	1.00649
$731$	0	0
$732$	59.9158	0.00302534
$733$	−24861.1	−1.25275	−0.626374	−	0.779523i	$-0.715462\pi$
$733$	−24861.1	−1.25275	−0.626374	+	0.779523i	$0.715462\pi$
$734$	−7959.05	−0.400237
$735$	−7292.34	−0.365962
$736$	20358.5	1.01960
$737$	−19407.2	−0.969979
$738$	−11080.4	−0.552678
$739$	1024.01	0.0509727	0.0254863	−	0.999675i	$-0.491887\pi$
$739$	1024.01	0.0509727	0.0254863	+	0.999675i	$0.491887\pi$
$740$	−4127.21	−0.205026
$741$	1469.49	0.0728516
$742$	−17134.8	−0.847761
$743$	−6870.67	−0.339247	−0.169623	−	0.985509i	$-0.554255\pi$
$743$	−6870.67	−0.339247	−0.169623	+	0.985509i	$0.554255\pi$
$744$	−5122.45	−0.252417
$745$	−1042.50	−0.0512676
$746$	−33226.0	−1.63068
$747$	14118.9	0.691544
$748$	0	0
$749$	−1684.81	−0.0821919
$750$	14999.5	0.730272
$751$	12169.0	0.591284	0.295642	−	0.955299i	$-0.404466\pi$
$751$	12169.0	0.591284	0.295642	+	0.955299i	$0.404466\pi$
$752$	10471.5	0.507786
$753$	6869.64	0.332462
$754$	−3711.85	−0.179281
$755$	13670.6	0.658972
$756$	−3786.05	−0.182140
$757$	28243.4	1.35604	0.678021	−	0.735043i	$-0.262838\pi$
$757$	28243.4	1.35604	0.678021	+	0.735043i	$0.262838\pi$
$758$	−18680.4	−0.895121
$759$	−20344.0	−0.972914
$760$	−11081.6	−0.528910
$761$	30505.2	1.45310	0.726552	−	0.687112i	$-0.241122\pi$
$761$	30505.2	1.45310	0.726552	+	0.687112i	$0.241122\pi$
$762$	10046.9	0.477640
$763$	13664.7	0.648355
$764$	−9884.58	−0.468078
$765$	0	0
$766$	2727.76	0.128666
$767$	4547.25	0.214070
$768$	−14157.4	−0.665184
$769$	20404.5	0.956834	0.478417	−	0.878133i	$-0.341211\pi$
$769$	20404.5	0.956834	0.478417	+	0.878133i	$0.341211\pi$
$770$	−12925.9	−0.604957
$771$	9084.89	0.424363
$772$	−5932.21	−0.276561
$773$	30606.6	1.42412	0.712059	−	0.702119i	$-0.247763\pi$
$773$	30606.6	1.42412	0.712059	+	0.702119i	$0.247763\pi$
$774$	11040.5	0.512716
$775$	−6761.75	−0.313406
$776$	−9266.46	−0.428668
$777$	2158.14	0.0996435
$778$	37888.1	1.74596
$779$	−16113.9	−0.741129
$780$	−562.354	−0.0258147
$781$	−7320.46	−0.335399
$782$	0	0
$783$	−25662.0	−1.17124
$784$	23662.5	1.07792
$785$	−18499.1	−0.841097
$786$	10964.4	0.497567
$787$	−36091.5	−1.63472	−0.817360	−	0.576127i	$-0.804563\pi$
$787$	−36091.5	−1.63472	−0.817360	+	0.576127i	$0.804563\pi$
$788$	8597.14	0.388656
$789$	−7513.19	−0.339007
$790$	6359.51	0.286407
$791$	−7422.27	−0.333635
$792$	−15430.6	−0.692302
$793$	26.8256	0.00120127
$794$	21372.3	0.955255
$795$	−17595.5	−0.784966
$796$	−17600.7	−0.783720
$797$	−21357.2	−0.949199	−0.474599	−	0.880202i	$-0.657407\pi$
$797$	−21357.2	−0.949199	−0.474599	+	0.880202i	$0.657407\pi$
$798$	−6560.53	−0.291028
$799$	0	0
$800$	−8556.28	−0.378138
$801$	−4098.72	−0.180800
$802$	40077.1	1.76455
$803$	40199.2	1.76662
$804$	3769.51	0.165349
$805$	6964.84	0.304942
$806$	2596.56	0.113474
$807$	16139.8	0.704024
$808$	−7182.52	−0.312723
$809$	26168.9	1.13727	0.568633	−	0.822591i	$-0.307473\pi$
$809$	26168.9	1.13727	0.568633	+	0.822591i	$0.307473\pi$
$810$	4458.71	0.193411
$811$	20028.2	0.867185	0.433592	−	0.901109i	$-0.357246\pi$
$811$	20028.2	0.867185	0.433592	+	0.901109i	$0.357246\pi$
$812$	5747.51	0.248397
$813$	708.850	0.0305787
$814$	−24097.0	−1.03759
$815$	3865.16	0.166124
$816$	0	0
$817$	16055.8	0.687541
$818$	26587.7	1.13645
$819$	−700.520	−0.0298879
$820$	6166.56	0.262617
$821$	2162.08	0.0919087	0.0459544	−	0.998944i	$-0.485367\pi$
$821$	2162.08	0.0919087	0.0459544	+	0.998944i	$0.485367\pi$
$822$	−19531.6	−0.828763
$823$	39375.6	1.66773	0.833867	−	0.551965i	$-0.186122\pi$
$823$	39375.6	1.66773	0.833867	+	0.551965i	$0.186122\pi$
$824$	20365.7	0.861011
$825$	8550.21	0.360825
$826$	−20301.2	−0.855167
$827$	22589.8	0.949849	0.474925	−	0.880026i	$-0.342475\pi$
$827$	22589.8	0.949849	0.474925	+	0.880026i	$0.342475\pi$
$828$	−9413.38	−0.395094
$829$	−10977.3	−0.459898	−0.229949	−	0.973203i	$-0.573856\pi$
$829$	−10977.3	−0.459898	−0.229949	+	0.973203i	$0.573856\pi$
$830$	−22655.3	−0.947443
$831$	10420.8	0.435011
$832$	−150.802	−0.00628380
$833$	0	0
$834$	10268.8	0.426353
$835$	20511.7	0.850105
$836$	25406.1	1.05106
$837$	17951.4	0.741327
$838$	24104.4	0.993643
$839$	44593.9	1.83499	0.917493	−	0.397752i	$-0.130210\pi$
$839$	44593.9	1.83499	0.917493	+	0.397752i	$0.130210\pi$
$840$	−2217.53	−0.0910858
$841$	14567.8	0.597310
$842$	−47549.4	−1.94615
$843$	−9979.30	−0.407717
$844$	9985.03	0.407226
$845$	18904.6	0.769630
$846$	−8718.23	−0.354301
$847$	−17050.8	−0.691704
$848$	57094.6	2.31207
$849$	−2227.03	−0.0900254
$850$	0	0
$851$	12984.1	0.523021
$852$	1421.87	0.0571742
$853$	−37075.9	−1.48822	−0.744112	−	0.668055i	$-0.767127\pi$
$853$	−37075.9	−1.48822	−0.744112	+	0.668055i	$0.767127\pi$
$854$	−119.763	−0.00479883
$855$	16049.0	0.641947
$856$	3227.33	0.128864
$857$	−45571.5	−1.81645	−0.908223	−	0.418487i	$-0.862560\pi$
$857$	−45571.5	−1.81645	−0.908223	+	0.418487i	$0.862560\pi$
$858$	−3283.34	−0.130643
$859$	68.5340	0.00272218	0.00136109	−	0.999999i	$-0.499567\pi$
$859$	68.5340	0.00272218	0.00136109	+	0.999999i	$0.499567\pi$
$860$	−6144.33	−0.243628
$861$	−3224.53	−0.127633
$862$	58845.7	2.32516
$863$	−5064.23	−0.199755	−0.0998774	−	0.995000i	$-0.531845\pi$
$863$	−5064.23	−0.199755	−0.0998774	+	0.995000i	$0.531845\pi$
$864$	22715.6	0.894445
$865$	16569.1	0.651291
$866$	870.810	0.0341701
$867$	0	0
$868$	−4020.57	−0.157220
$869$	12878.0	0.502710
$870$	17017.1	0.663142
$871$	1687.69	0.0656546
$872$	−26175.3	−1.01652
$873$	13420.2	0.520281
$874$	−39470.4	−1.52758
$875$	−10398.6	−0.401755
$876$	−7807.98	−0.301150
$877$	3826.86	0.147348	0.0736738	−	0.997282i	$-0.476528\pi$
$877$	3826.86	0.147348	0.0736738	+	0.997282i	$0.476528\pi$
$878$	34542.3	1.32773
$879$	3994.60	0.153282
$880$	43070.2	1.64988
$881$	−41015.0	−1.56848	−0.784240	−	0.620457i	$-0.786947\pi$
$881$	−41015.0	−1.56848	−0.784240	+	0.620457i	$0.786947\pi$
$882$	−19700.7	−0.752106
$883$	7085.32	0.270034	0.135017	−	0.990843i	$-0.456891\pi$
$883$	7085.32	0.270034	0.135017	+	0.990843i	$0.456891\pi$
$884$	0	0
$885$	−20847.0	−0.791824
$886$	34998.2	1.32707
$887$	−17254.1	−0.653141	−0.326570	−	0.945173i	$-0.605893\pi$
$887$	−17254.1	−0.653141	−0.326570	+	0.945173i	$0.605893\pi$
$888$	−4134.01	−0.156226
$889$	−6965.14	−0.262771
$890$	6576.84	0.247704
$891$	9028.85	0.339481
$892$	1751.81	0.0657566
$893$	−12678.6	−0.475110
$894$	1182.24	0.0442281
$895$	−869.580	−0.0324769
$896$	10254.5	0.382344
$897$	1769.16	0.0658534
$898$	30028.8	1.11590
$899$	−27251.5	−1.01100
$900$	3956.26	0.146528
$901$	0	0
$902$	36003.9	1.32905
$903$	3212.91	0.118404
$904$	14217.7	0.523089
$905$	33820.7	1.24225
$906$	−15503.0	−0.568491
$907$	18106.5	0.662861	0.331431	−	0.943480i	$-0.392469\pi$
$907$	18106.5	0.662861	0.331431	+	0.943480i	$0.392469\pi$
$908$	−8138.63	−0.297456
$909$	10402.1	0.379557
$910$	1124.06	0.0409476
$911$	19160.7	0.696840	0.348420	−	0.937339i	$-0.386718\pi$
$911$	19160.7	0.696840	0.348420	+	0.937339i	$0.386718\pi$
$912$	21860.2	0.793712
$913$	−45876.8	−1.66298
$914$	−29208.1	−1.05702
$915$	−122.983	−0.00444337
$916$	−20660.1	−0.745229
$917$	−7601.21	−0.273734
$918$	0	0
$919$	−13214.6	−0.474329	−0.237165	−	0.971469i	$-0.576218\pi$
$919$	−13214.6	−0.474329	−0.237165	+	0.971469i	$0.576218\pi$
$920$	−13341.4	−0.478102
$921$	−12713.1	−0.454843
$922$	30100.5	1.07517
$923$	636.601	0.0227020
$924$	5084.00	0.181008
$925$	−5456.99	−0.193973
$926$	55605.0	1.97332
$927$	−29494.8	−1.04502
$928$	−34483.9	−1.21982
$929$	8124.36	0.286923	0.143462	−	0.989656i	$-0.454177\pi$
$929$	8124.36	0.286923	0.143462	+	0.989656i	$0.454177\pi$
$930$	−11904.0	−0.419729
$931$	−28650.0	−1.00856
$932$	−2360.47	−0.0829612
$933$	13326.8	0.467631
$934$	20794.2	0.728489
$935$	0	0
$936$	1341.88	0.0468596
$937$	−11617.7	−0.405053	−0.202526	−	0.979277i	$-0.564915\pi$
$937$	−11617.7	−0.405053	−0.202526	+	0.979277i	$0.564915\pi$
$938$	−7534.68	−0.262277
$939$	17436.4	0.605980
$940$	4851.93	0.168354
$941$	12810.7	0.443801	0.221901	−	0.975069i	$-0.428774\pi$
$941$	12810.7	0.443801	0.221901	+	0.975069i	$0.428774\pi$
$942$	20978.7	0.725608
$943$	−19399.9	−0.669934
$944$	67645.3	2.33227
$945$	7771.23	0.267511
$946$	−35874.1	−1.23295
$947$	−21469.3	−0.736703	−0.368351	−	0.929687i	$-0.620078\pi$
$947$	−21469.3	−0.736703	−0.368351	+	0.929687i	$0.620078\pi$
$948$	−2501.31	−0.0856951
$949$	−3495.80	−0.119577
$950$	16588.7	0.566534
$951$	3353.37	0.114343
$952$	0	0
$953$	15897.5	0.540369	0.270184	−	0.962809i	$-0.412915\pi$
$953$	15897.5	0.540369	0.270184	+	0.962809i	$0.412915\pi$
$954$	−47535.3	−1.61322
$955$	20289.0	0.687473
$956$	−13617.1	−0.460678
$957$	34459.5	1.16397
$958$	−52198.5	−1.76039
$959$	13540.5	0.455940
$960$	691.356	0.0232432
$961$	−10727.7	−0.360097
$962$	2095.52	0.0702312
$963$	−4674.01	−0.156405
$964$	−3795.11	−0.126797
$965$	12176.4	0.406189
$966$	−7898.40	−0.263071
$967$	−33191.2	−1.10378	−0.551891	−	0.833916i	$-0.686094\pi$
$967$	−33191.2	−1.10378	−0.551891	+	0.833916i	$0.686094\pi$
$968$	32661.6	1.08449
$969$	0	0
$970$	−21534.2	−0.712806
$971$	31834.5	1.05213	0.526065	−	0.850445i	$-0.323667\pi$
$971$	31834.5	1.05213	0.526065	+	0.850445i	$0.323667\pi$
$972$	−16665.9	−0.549959
$973$	−7118.94	−0.234556
$974$	−28777.6	−0.946708
$975$	−743.543	−0.0244230
$976$	399.060	0.0130877
$977$	−14447.7	−0.473105	−0.236552	−	0.971619i	$-0.576018\pi$
$977$	−14447.7	−0.473105	−0.236552	+	0.971619i	$0.576018\pi$
$978$	−4383.24	−0.143314
$979$	13318.0	0.434777
$980$	10964.0	0.357379
$981$	37908.5	1.23377
$982$	9223.90	0.299742
$983$	−7830.90	−0.254086	−0.127043	−	0.991897i	$-0.540549\pi$
$983$	−7830.90	−0.254086	−0.127043	+	0.991897i	$0.540549\pi$
$984$	6176.73	0.200109
$985$	−17646.4	−0.570824
$986$	0	0
$987$	−2537.10	−0.0818206
$988$	−2209.37	−0.0711430
$989$	19330.0	0.621494
$990$	−35859.0	−1.15119
$991$	14647.7	0.469526	0.234763	−	0.972053i	$-0.424569\pi$
$991$	14647.7	0.469526	0.234763	+	0.972053i	$0.424569\pi$
$992$	24122.6	0.772071
$993$	−8674.21	−0.277208
$994$	−2842.10	−0.0906902
$995$	36127.1	1.15106
$996$	8910.76	0.283482
$997$	−49174.6	−1.56206	−0.781031	−	0.624492i	$-0.785306\pi$
$997$	−49174.6	−1.56206	−0.781031	+	0.624492i	$0.785306\pi$
$998$	−44670.1	−1.41684
$999$	14487.5	0.458822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.g.1.3		12
17.4	even	4		289.4.b.e.288.10		12
17.10	odd	16		17.4.d.a.15.3	yes	12
17.12	odd	16		17.4.d.a.8.3	✓	12
17.13	even	4		289.4.b.e.288.9		12
17.16	even	2	inner	289.4.a.g.1.4		12
51.29	even	16		153.4.l.a.127.1		12
51.44	even	16		153.4.l.a.100.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.3	✓	12	17.12	odd	16
17.4.d.a.15.3	yes	12	17.10	odd	16
153.4.l.a.100.1		12	51.44	even	16
153.4.l.a.127.1		12	51.29	even	16
289.4.a.g.1.3		12	1.1	even	1	trivial
289.4.a.g.1.4		12	17.16	even	2	inner
289.4.b.e.288.9		12	17.13	even	4
289.4.b.e.288.10		12	17.4	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-3.49971 q^{2} -2.82539 q^{3} +4.24796 q^{4} -8.71933 q^{5} +9.88806 q^{6} -6.85501 q^{7} +13.1311 q^{8} -19.0171 q^{9} +O(q^{10})\)	\(q-3.49971 q^{2} -2.82539 q^{3} +4.24796 q^{4} -8.71933 q^{5} +9.88806 q^{6} -6.85501 q^{7} +13.1311 q^{8} -19.0171 q^{9} +30.5151 q^{10} +61.7928 q^{11} -12.0022 q^{12} -5.37363 q^{13} +23.9905 q^{14} +24.6355 q^{15} -79.9385 q^{16} +66.5545 q^{18} +96.7877 q^{19} -37.0393 q^{20} +19.3681 q^{21} -216.257 q^{22} +116.525 q^{23} -37.1004 q^{24} -48.9733 q^{25} +18.8061 q^{26} +130.017 q^{27} -29.1198 q^{28} -197.375 q^{29} -86.2172 q^{30} +138.070 q^{31} +174.713 q^{32} -174.589 q^{33} +59.7710 q^{35} -80.7840 q^{36} +111.428 q^{37} -338.729 q^{38} +15.1826 q^{39} -114.494 q^{40} -166.487 q^{41} -67.7827 q^{42} +165.887 q^{43} +262.493 q^{44} +165.817 q^{45} -407.804 q^{46} -130.994 q^{47} +225.858 q^{48} -296.009 q^{49} +171.392 q^{50} -22.8269 q^{52} -714.232 q^{53} -455.020 q^{54} -538.792 q^{55} -90.0135 q^{56} -273.463 q^{57} +690.754 q^{58} -846.216 q^{59} +104.651 q^{60} -4.99209 q^{61} -483.205 q^{62} +130.363 q^{63} +28.0634 q^{64} +46.8544 q^{65} +611.011 q^{66} -314.069 q^{67} -329.230 q^{69} -209.181 q^{70} -118.468 q^{71} -249.715 q^{72} +650.548 q^{73} -389.965 q^{74} +138.369 q^{75} +411.150 q^{76} -423.590 q^{77} -53.1347 q^{78} +208.405 q^{79} +697.010 q^{80} +146.115 q^{81} +582.655 q^{82} -742.430 q^{83} +82.2749 q^{84} -580.555 q^{86} +557.662 q^{87} +811.405 q^{88} +215.527 q^{89} -580.310 q^{90} +36.8362 q^{91} +494.994 q^{92} -390.102 q^{93} +458.441 q^{94} -843.923 q^{95} -493.633 q^{96} -705.690 q^{97} +1035.94 q^{98} -1175.12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Introduction

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