LMFDB - Embedded newform 725.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,4,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("725.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	725.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:	$42.7763847542$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} +9.24264 q^{3} -7.82843 q^{4} -3.82843 q^{6} -6.14214 q^{7} +6.55635 q^{8} +58.4264 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} +9.24264 q^{3} -7.82843 q^{4} -3.82843 q^{6} -6.14214 q^{7} +6.55635 q^{8} +58.4264 q^{9} -65.3259 q^{11} -72.3553 q^{12} +49.7696 q^{13} +2.54416 q^{14} +59.9117 q^{16} -55.4558 q^{17} -24.2010 q^{18} -64.7452 q^{19} -56.7696 q^{21} +27.0589 q^{22} -93.8823 q^{23} +60.5980 q^{24} -20.6152 q^{26} +290.463 q^{27} +48.0833 q^{28} +29.0000 q^{29} -236.095 q^{31} -77.2670 q^{32} -603.784 q^{33} +22.9706 q^{34} -457.387 q^{36} -76.8040 q^{37} +26.8183 q^{38} +460.002 q^{39} +215.161 q^{41} +23.5147 q^{42} -80.8305 q^{43} +511.399 q^{44} +38.8873 q^{46} +357.742 q^{47} +553.742 q^{48} -305.274 q^{49} -512.558 q^{51} -389.617 q^{52} -328.466 q^{53} -120.314 q^{54} -40.2700 q^{56} -598.416 q^{57} -12.0122 q^{58} -99.2750 q^{59} -725.730 q^{61} +97.7939 q^{62} -358.863 q^{63} -447.288 q^{64} +250.095 q^{66} -844.479 q^{67} +434.132 q^{68} -867.720 q^{69} -378.083 q^{71} +383.064 q^{72} +581.097 q^{73} +31.8133 q^{74} +506.853 q^{76} +401.241 q^{77} -190.539 q^{78} -353.247 q^{79} +1107.13 q^{81} -89.1228 q^{82} -696.510 q^{83} +444.416 q^{84} +33.4811 q^{86} +268.037 q^{87} -428.299 q^{88} +1118.22 q^{89} -305.691 q^{91} +734.950 q^{92} -2182.15 q^{93} -148.182 q^{94} -714.151 q^{96} +805.415 q^{97} +126.449 q^{98} -3816.76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 2 q^{6} + 16 q^{7} - 18 q^{8} + 32 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 2 * q^6 + 16 * q^7 - 18 * q^8 + 32 * q^9	$ 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 2 q^{6} + 16 q^{7} - 18 q^{8} + 32 q^{9} - 26 q^{11} - 74 q^{12} + 26 q^{13} + 56 q^{14} + 18 q^{16} - 60 q^{17} - 88 q^{18} - 220 q^{19} - 40 q^{21} + 122 q^{22} - 52 q^{23} + 42 q^{24} - 78 q^{26} + 250 q^{27} + 58 q^{29} - 294 q^{31} + 18 q^{32} - 574 q^{33} + 12 q^{34} - 400 q^{36} - 312 q^{37} - 348 q^{38} + 442 q^{39} + 40 q^{41} + 64 q^{42} + 322 q^{43} + 426 q^{44} + 140 q^{46} + 130 q^{47} + 522 q^{48} - 158 q^{49} - 516 q^{51} - 338 q^{52} - 1002 q^{53} - 218 q^{54} - 584 q^{56} - 716 q^{57} + 58 q^{58} - 900 q^{59} - 948 q^{61} - 42 q^{62} - 944 q^{63} + 118 q^{64} + 322 q^{66} - 320 q^{67} + 444 q^{68} - 836 q^{69} - 660 q^{71} + 1032 q^{72} - 648 q^{73} - 536 q^{74} + 844 q^{76} + 1272 q^{77} - 234 q^{78} + 258 q^{79} + 1790 q^{81} - 512 q^{82} - 1212 q^{83} + 408 q^{84} + 1006 q^{86} + 290 q^{87} - 1394 q^{88} + 760 q^{89} - 832 q^{91} + 644 q^{92} - 2226 q^{93} - 698 q^{94} - 642 q^{96} - 24 q^{97} + 482 q^{98} - 4856 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 2 * q^6 + 16 * q^7 - 18 * q^8 + 32 * q^9 - 26 * q^11 - 74 * q^12 + 26 * q^13 + 56 * q^14 + 18 * q^16 - 60 * q^17 - 88 * q^18 - 220 * q^19 - 40 * q^21 + 122 * q^22 - 52 * q^23 + 42 * q^24 - 78 * q^26 + 250 * q^27 + 58 * q^29 - 294 * q^31 + 18 * q^32 - 574 * q^33 + 12 * q^34 - 400 * q^36 - 312 * q^37 - 348 * q^38 + 442 * q^39 + 40 * q^41 + 64 * q^42 + 322 * q^43 + 426 * q^44 + 140 * q^46 + 130 * q^47 + 522 * q^48 - 158 * q^49 - 516 * q^51 - 338 * q^52 - 1002 * q^53 - 218 * q^54 - 584 * q^56 - 716 * q^57 + 58 * q^58 - 900 * q^59 - 948 * q^61 - 42 * q^62 - 944 * q^63 + 118 * q^64 + 322 * q^66 - 320 * q^67 + 444 * q^68 - 836 * q^69 - 660 * q^71 + 1032 * q^72 - 648 * q^73 - 536 * q^74 + 844 * q^76 + 1272 * q^77 - 234 * q^78 + 258 * q^79 + 1790 * q^81 - 512 * q^82 - 1212 * q^83 + 408 * q^84 + 1006 * q^86 + 290 * q^87 - 1394 * q^88 + 760 * q^89 - 832 * q^91 + 644 * q^92 - 2226 * q^93 - 698 * q^94 - 642 * q^96 - 24 * q^97 + 482 * q^98 - 4856 * 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 $

$2$	−0.414214	−0.146447	−0.0732233	−	0.997316i	$-0.523329\pi$
$2$	−0.414214	−0.146447	−0.0732233	+	0.997316i	$0.523329\pi$
$3$	9.24264	1.77875	0.889374	−	0.457181i	$-0.151141\pi$
$3$	9.24264	1.77875	0.889374	+	0.457181i	$0.151141\pi$
$4$	−7.82843	−0.978553
$5$	0	0
$5$	0	0
$6$	−3.82843	−0.260491
$7$	−6.14214	−0.331644	−0.165822	−	0.986156i	$-0.553028\pi$
$7$	−6.14214	−0.331644	−0.165822	+	0.986156i	$0.553028\pi$
$8$	6.55635	0.289752
$9$	58.4264	2.16394
$10$	0	0
$11$	−65.3259	−1.79059	−0.895295	−	0.445473i	$-0.853036\pi$
$11$	−65.3259	−1.79059	−0.895295	+	0.445473i	$0.853036\pi$
$12$	−72.3553	−1.74060
$13$	49.7696	1.06181	0.530907	−	0.847430i	$-0.321851\pi$
$13$	49.7696	1.06181	0.530907	+	0.847430i	$0.321851\pi$
$14$	2.54416	0.0485682
$15$	0	0
$16$	59.9117	0.936120
$17$	−55.4558	−0.791178	−0.395589	−	0.918428i	$-0.629459\pi$
$17$	−55.4558	−0.791178	−0.395589	+	0.918428i	$0.629459\pi$
$18$	−24.2010	−0.316902
$19$	−64.7452	−0.781766	−0.390883	−	0.920440i	$-0.627830\pi$
$19$	−64.7452	−0.781766	−0.390883	+	0.920440i	$0.627830\pi$
$20$	0	0
$21$	−56.7696	−0.589911
$22$	27.0589	0.262226
$23$	−93.8823	−0.851122	−0.425561	−	0.904930i	$-0.639923\pi$
$23$	−93.8823	−0.851122	−0.425561	+	0.904930i	$0.639923\pi$
$24$	60.5980	0.515396
$25$	0	0
$26$	−20.6152	−0.155499
$27$	290.463	2.07036
$28$	48.0833	0.324532
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−236.095	−1.36787	−0.683935	−	0.729543i	$-0.739733\pi$
$31$	−236.095	−1.36787	−0.683935	+	0.729543i	$0.739733\pi$
$32$	−77.2670	−0.426844
$33$	−603.784	−3.18501
$34$	22.9706	0.115865
$35$	0	0
$36$	−457.387	−2.11753
$37$	−76.8040	−0.341257	−0.170628	−	0.985335i	$-0.554580\pi$
$37$	−76.8040	−0.341257	−0.170628	+	0.985335i	$0.554580\pi$
$38$	26.8183	0.114487
$39$	460.002	1.88870
$40$	0	0
$41$	215.161	0.819575	0.409788	−	0.912181i	$-0.365603\pi$
$41$	215.161	0.819575	0.409788	+	0.912181i	$0.365603\pi$
$42$	23.5147	0.0863905
$43$	−80.8305	−0.286664	−0.143332	−	0.989675i	$-0.545782\pi$
$43$	−80.8305	−0.286664	−0.143332	+	0.989675i	$0.545782\pi$
$44$	511.399	1.75219
$45$	0	0
$46$	38.8873	0.124644
$47$	357.742	1.11026	0.555128	−	0.831765i	$-0.312669\pi$
$47$	357.742	1.11026	0.555128	+	0.831765i	$0.312669\pi$
$48$	553.742	1.66512
$49$	−305.274	−0.890012
$50$	0	0
$51$	−512.558	−1.40730
$52$	−389.617	−1.03904
$53$	−328.466	−0.851288	−0.425644	−	0.904891i	$-0.639952\pi$
$53$	−328.466	−0.851288	−0.425644	+	0.904891i	$0.639952\pi$
$54$	−120.314	−0.303197
$55$	0	0
$56$	−40.2700	−0.0960947
$57$	−598.416	−1.39056
$58$	−12.0122	−0.0271945
$59$	−99.2750	−0.219059	−0.109530	−	0.993984i	$-0.534934\pi$
$59$	−99.2750	−0.219059	−0.109530	+	0.993984i	$0.534934\pi$
$60$	0	0
$61$	−725.730	−1.52328	−0.761641	−	0.647999i	$-0.775606\pi$
$61$	−725.730	−1.52328	−0.761641	+	0.647999i	$0.775606\pi$
$62$	97.7939	0.200320
$63$	−358.863	−0.717658
$64$	−447.288	−0.873610
$65$	0	0
$66$	250.095	0.466434
$67$	−844.479	−1.53984	−0.769922	−	0.638138i	$-0.779705\pi$
$67$	−844.479	−1.53984	−0.769922	+	0.638138i	$0.779705\pi$
$68$	434.132	0.774209
$69$	−867.720	−1.51393
$70$	0	0
$71$	−378.083	−0.631975	−0.315988	−	0.948763i	$-0.602336\pi$
$71$	−378.083	−0.631975	−0.315988	+	0.948763i	$0.602336\pi$
$72$	383.064	0.627007
$73$	581.097	0.931674	0.465837	−	0.884870i	$-0.345753\pi$
$73$	581.097	0.931674	0.465837	+	0.884870i	$0.345753\pi$
$74$	31.8133	0.0499759
$75$	0	0
$76$	506.853	0.765000
$77$	401.241	0.593839
$78$	−190.539	−0.276594
$79$	−353.247	−0.503081	−0.251540	−	0.967847i	$-0.580937\pi$
$79$	−353.247	−0.503081	−0.251540	+	0.967847i	$0.580937\pi$
$80$	0	0
$81$	1107.13	1.51870
$82$	−89.1228	−0.120024
$83$	−696.510	−0.921107	−0.460553	−	0.887632i	$-0.652349\pi$
$83$	−696.510	−0.921107	−0.460553	+	0.887632i	$0.652349\pi$
$84$	444.416	0.577259
$85$	0	0
$86$	33.4811	0.0419809
$87$	268.037	0.330305
$88$	−428.299	−0.518828
$89$	1118.22	1.33181	0.665905	−	0.746037i	$-0.268046\pi$
$89$	1118.22	1.33181	0.665905	+	0.746037i	$0.268046\pi$
$90$	0	0
$91$	−305.691	−0.352145
$92$	734.950	0.832868
$93$	−2182.15	−2.43310
$94$	−148.182	−0.162593
$95$	0	0
$96$	−714.151	−0.759248
$97$	805.415	0.843068	0.421534	−	0.906813i	$-0.361492\pi$
$97$	805.415	0.843068	0.421534	+	0.906813i	$0.361492\pi$
$98$	126.449	0.130339
$99$	−3816.76	−3.87473
$100$	0	0
$101$	−1373.99	−1.35363	−0.676817	−	0.736151i	$-0.736641\pi$
$101$	−1373.99	−1.35363	−0.676817	+	0.736151i	$0.736641\pi$
$102$	212.309	0.206095
$103$	634.672	0.607147	0.303573	−	0.952808i	$-0.401820\pi$
$103$	634.672	0.607147	0.303573	+	0.952808i	$0.401820\pi$
$104$	326.307	0.307663
$105$	0	0
$106$	136.055	0.124668
$107$	180.956	0.163493	0.0817463	−	0.996653i	$-0.473950\pi$
$107$	180.956	0.163493	0.0817463	+	0.996653i	$0.473950\pi$
$108$	−2273.87	−2.02595
$109$	1038.14	0.912251	0.456125	−	0.889916i	$-0.349237\pi$
$109$	1038.14	0.912251	0.456125	+	0.889916i	$0.349237\pi$
$110$	0	0
$111$	−709.872	−0.607010
$112$	−367.986	−0.310459
$113$	184.765	0.153816	0.0769082	−	0.997038i	$-0.475495\pi$
$113$	184.765	0.153816	0.0769082	+	0.997038i	$0.475495\pi$
$114$	247.872	0.203643
$115$	0	0
$116$	−227.024	−0.181713
$117$	2907.86	2.29770
$118$	41.1211	0.0320805
$119$	340.617	0.262389
$120$	0	0
$121$	2936.47	2.20622
$122$	300.607	0.223079
$123$	1988.66	1.45782
$124$	1848.26	1.33853
$125$	0	0
$126$	148.646	0.105099
$127$	−1999.58	−1.39712	−0.698558	−	0.715554i	$-0.746175\pi$
$127$	−1999.58	−1.39712	−0.698558	+	0.715554i	$0.746175\pi$
$128$	803.409	0.554781
$129$	−747.087	−0.509902
$130$	0	0
$131$	561.468	0.374471	0.187236	−	0.982315i	$-0.440047\pi$
$131$	561.468	0.374471	0.187236	+	0.982315i	$0.440047\pi$
$132$	4726.68	3.11670
$133$	397.674	0.259268
$134$	349.795	0.225505
$135$	0	0
$136$	−363.588	−0.229246
$137$	250.489	0.156210	0.0781050	−	0.996945i	$-0.475113\pi$
$137$	250.489	0.156210	0.0781050	+	0.996945i	$0.475113\pi$
$138$	359.421	0.221710
$139$	−242.244	−0.147819	−0.0739096	−	0.997265i	$-0.523548\pi$
$139$	−242.244	−0.147819	−0.0739096	+	0.997265i	$0.523548\pi$
$140$	0	0
$141$	3306.48	1.97487
$142$	156.607	0.0925506
$143$	−3251.24	−1.90128
$144$	3500.42	2.02571
$145$	0	0
$146$	−240.698	−0.136441
$147$	−2821.54	−1.58311
$148$	601.255	0.333938
$149$	−1632.63	−0.897652	−0.448826	−	0.893619i	$-0.648158\pi$
$149$	−1632.63	−0.897652	−0.448826	+	0.893619i	$0.648158\pi$
$150$	0	0
$151$	−121.582	−0.0655245	−0.0327623	−	0.999463i	$-0.510430\pi$
$151$	−121.582	−0.0655245	−0.0327623	+	0.999463i	$0.510430\pi$
$152$	−424.492	−0.226519
$153$	−3240.09	−1.71206
$154$	−166.199	−0.0869657
$155$	0	0
$156$	−3601.09	−1.84819
$157$	753.163	0.382860	0.191430	−	0.981506i	$-0.438688\pi$
$157$	753.163	0.382860	0.191430	+	0.981506i	$0.438688\pi$
$158$	146.320	0.0736745
$159$	−3035.89	−1.51423
$160$	0	0
$161$	576.638	0.282270
$162$	−458.589	−0.222408
$163$	−537.917	−0.258484	−0.129242	−	0.991613i	$-0.541254\pi$
$163$	−537.917	−0.258484	−0.129242	+	0.991613i	$0.541254\pi$
$164$	−1684.38	−0.801998
$165$	0	0
$166$	288.504	0.134893
$167$	−484.613	−0.224554	−0.112277	−	0.993677i	$-0.535814\pi$
$167$	−484.613	−0.224554	−0.112277	+	0.993677i	$0.535814\pi$
$168$	−372.201	−0.170928
$169$	280.008	0.127450
$170$	0	0
$171$	−3782.83	−1.69170
$172$	632.776	0.280516
$173$	3269.70	1.43694	0.718469	−	0.695559i	$-0.244843\pi$
$173$	3269.70	1.43694	0.718469	+	0.695559i	$0.244843\pi$
$174$	−111.024	−0.0483721
$175$	0	0
$176$	−3913.79	−1.67621
$177$	−917.563	−0.389651
$178$	−463.182	−0.195039
$179$	−562.267	−0.234781	−0.117390	−	0.993086i	$-0.537453\pi$
$179$	−562.267	−0.234781	−0.117390	+	0.993086i	$0.537453\pi$
$180$	0	0
$181$	−1507.32	−0.618998	−0.309499	−	0.950900i	$-0.600161\pi$
$181$	−1507.32	−0.618998	−0.309499	+	0.950900i	$0.600161\pi$
$182$	126.621	0.0515704
$183$	−6707.66	−2.70953
$184$	−615.525	−0.246615
$185$	0	0
$186$	903.874	0.356319
$187$	3622.70	1.41668
$188$	−2800.56	−1.08645
$189$	−1784.06	−0.686622
$190$	0	0
$191$	4532.00	1.71688	0.858439	−	0.512915i	$-0.171434\pi$
$191$	4532.00	1.71688	0.858439	+	0.512915i	$0.171434\pi$
$192$	−4134.13	−1.55393
$193$	2935.17	1.09471	0.547353	−	0.836902i	$-0.315636\pi$
$193$	2935.17	1.09471	0.547353	+	0.836902i	$0.315636\pi$
$194$	−333.614	−0.123464
$195$	0	0
$196$	2389.82	0.870924
$197$	−2682.20	−0.970043	−0.485022	−	0.874502i	$-0.661188\pi$
$197$	−2682.20	−0.970043	−0.485022	+	0.874502i	$0.661188\pi$
$198$	1580.95	0.567442
$199$	−648.376	−0.230966	−0.115483	−	0.993309i	$-0.536842\pi$
$199$	−648.376	−0.230966	−0.115483	+	0.993309i	$0.536842\pi$
$200$	0	0
$201$	−7805.22	−2.73899
$202$	569.125	0.198235
$203$	−178.122	−0.0615848
$204$	4012.53	1.37712
$205$	0	0
$206$	−262.890	−0.0889145
$207$	−5485.20	−1.84178
$208$	2981.78	0.993986
$209$	4229.54	1.39982
$210$	0	0
$211$	−4949.57	−1.61489	−0.807446	−	0.589941i	$-0.799151\pi$
$211$	−4949.57	−1.61489	−0.807446	+	0.589941i	$0.799151\pi$
$212$	2571.37	0.833031
$213$	−3494.49	−1.12412
$214$	−74.9545	−0.0239429
$215$	0	0
$216$	1904.38	0.599891
$217$	1450.13	0.453646
$218$	−430.010	−0.133596
$219$	5370.87	1.65721
$220$	0	0
$221$	−2760.01	−0.840084
$222$	294.039	0.0888945
$223$	−2216.94	−0.665729	−0.332864	−	0.942975i	$-0.608015\pi$
$223$	−2216.94	−0.665729	−0.332864	+	0.942975i	$0.608015\pi$
$224$	474.585	0.141560
$225$	0	0
$226$	−76.5323	−0.0225259
$227$	−4546.09	−1.32923	−0.664613	−	0.747187i	$-0.731404\pi$
$227$	−4546.09	−1.32923	−0.664613	+	0.747187i	$0.731404\pi$
$228$	4684.66	1.36074
$229$	3339.05	0.963539	0.481770	−	0.876298i	$-0.339994\pi$
$229$	3339.05	0.963539	0.481770	+	0.876298i	$0.339994\pi$
$230$	0	0
$231$	3708.52	1.05629
$232$	190.134	0.0538057
$233$	3995.35	1.12336	0.561682	−	0.827353i	$-0.310154\pi$
$233$	3995.35	1.12336	0.561682	+	0.827353i	$0.310154\pi$
$234$	−1204.47	−0.336491
$235$	0	0
$236$	777.167	0.214361
$237$	−3264.93	−0.894853
$238$	−141.088	−0.0384260
$239$	−1400.04	−0.378915	−0.189458	−	0.981889i	$-0.560673\pi$
$239$	−1400.04	−0.378915	−0.189458	+	0.981889i	$0.560673\pi$
$240$	0	0
$241$	−2040.94	−0.545513	−0.272756	−	0.962083i	$-0.587935\pi$
$241$	−2040.94	−0.545513	−0.272756	+	0.962083i	$0.587935\pi$
$242$	−1216.33	−0.323093
$243$	2390.32	0.631026
$244$	5681.32	1.49061
$245$	0	0
$246$	−823.730	−0.213492
$247$	−3222.34	−0.830091
$248$	−1547.92	−0.396344
$249$	−6437.59	−1.63842
$250$	0	0
$251$	802.648	0.201843	0.100922	−	0.994894i	$-0.467821\pi$
$251$	802.648	0.201843	0.100922	+	0.994894i	$0.467821\pi$
$252$	2809.33	0.702267
$253$	6132.94	1.52401
$254$	828.252	0.204603
$255$	0	0
$256$	3245.52	0.792364
$257$	4464.10	1.08351	0.541756	−	0.840536i	$-0.317760\pi$
$257$	4464.10	1.08351	0.541756	+	0.840536i	$0.317760\pi$
$258$	309.454	0.0746734
$259$	471.741	0.113176
$260$	0	0
$261$	1694.37	0.401834
$262$	−232.568	−0.0548400
$263$	3815.21	0.894509	0.447255	−	0.894407i	$-0.352402\pi$
$263$	3815.21	0.894509	0.447255	+	0.894407i	$0.352402\pi$
$264$	−3958.62	−0.922864
$265$	0	0
$266$	−164.722	−0.0379690
$267$	10335.3	2.36895
$268$	6610.95	1.50682
$269$	4523.98	1.02540	0.512699	−	0.858569i	$-0.328646\pi$
$269$	4523.98	1.02540	0.512699	+	0.858569i	$0.328646\pi$
$270$	0	0
$271$	3962.65	0.888242	0.444121	−	0.895967i	$-0.353516\pi$
$271$	3962.65	0.888242	0.444121	+	0.895967i	$0.353516\pi$
$272$	−3322.45	−0.740637
$273$	−2825.40	−0.626376
$274$	−103.756	−0.0228764
$275$	0	0
$276$	6792.88	1.48146
$277$	−2217.59	−0.481019	−0.240509	−	0.970647i	$-0.577315\pi$
$277$	−2217.59	−0.481019	−0.240509	+	0.970647i	$0.577315\pi$
$278$	100.341	0.0216476
$279$	−13794.2	−2.95999
$280$	0	0
$281$	−2562.96	−0.544105	−0.272053	−	0.962282i	$-0.587702\pi$
$281$	−2562.96	−0.544105	−0.272053	+	0.962282i	$0.587702\pi$
$282$	−1369.59	−0.289212
$283$	3869.29	0.812741	0.406370	−	0.913708i	$-0.366794\pi$
$283$	3869.29	0.812741	0.406370	+	0.913708i	$0.366794\pi$
$284$	2959.80	0.618421
$285$	0	0
$286$	1346.71	0.278435
$287$	−1321.55	−0.271807
$288$	−4514.43	−0.923665
$289$	−1837.65	−0.374038
$290$	0	0
$291$	7444.17	1.49960
$292$	−4549.07	−0.911693
$293$	3883.83	0.774388	0.387194	−	0.921998i	$-0.373444\pi$
$293$	3883.83	0.774388	0.387194	+	0.921998i	$0.373444\pi$
$294$	1168.72	0.231841
$295$	0	0
$296$	−503.554	−0.0988800
$297$	−18974.8	−3.70716
$298$	676.257	0.131458
$299$	−4672.48	−0.903734
$300$	0	0
$301$	496.472	0.0950703
$302$	50.3609	0.00959584
$303$	−12699.3	−2.40777
$304$	−3878.99	−0.731827
$305$	0	0
$306$	1342.09	0.250726
$307$	403.210	0.0749590	0.0374795	−	0.999297i	$-0.488067\pi$
$307$	403.210	0.0749590	0.0374795	+	0.999297i	$0.488067\pi$
$308$	−3141.08	−0.581103
$309$	5866.05	1.07996
$310$	0	0
$311$	−4838.71	−0.882244	−0.441122	−	0.897447i	$-0.645419\pi$
$311$	−4838.71	−0.882244	−0.441122	+	0.897447i	$0.645419\pi$
$312$	3015.93	0.547255
$313$	8544.28	1.54298	0.771488	−	0.636244i	$-0.219513\pi$
$313$	8544.28	1.54298	0.771488	+	0.636244i	$0.219513\pi$
$314$	−311.970	−0.0560685
$315$	0	0
$316$	2765.37	0.492291
$317$	1773.06	0.314148	0.157074	−	0.987587i	$-0.449794\pi$
$317$	1773.06	0.314148	0.157074	+	0.987587i	$0.449794\pi$
$318$	1257.51	0.221753
$319$	−1894.45	−0.332504
$320$	0	0
$321$	1672.51	0.290812
$322$	−238.851	−0.0413374
$323$	3590.50	0.618516
$324$	−8667.10	−1.48613
$325$	0	0
$326$	222.813	0.0378541
$327$	9595.11	1.62266
$328$	1410.67	0.237474
$329$	−2197.30	−0.368210
$330$	0	0
$331$	801.875	0.133157	0.0665786	−	0.997781i	$-0.478792\pi$
$331$	801.875	0.133157	0.0665786	+	0.997781i	$0.478792\pi$
$332$	5452.58	0.901352
$333$	−4487.38	−0.738460
$334$	200.733	0.0328851
$335$	0	0
$336$	−3401.16	−0.552228
$337$	−8193.23	−1.32437	−0.662186	−	0.749339i	$-0.730371\pi$
$337$	−8193.23	−1.32437	−0.662186	+	0.749339i	$0.730371\pi$
$338$	−115.983	−0.0186647
$339$	1707.72	0.273601
$340$	0	0
$341$	15423.1	2.44930
$342$	1566.90	0.247743
$343$	3981.79	0.626811
$344$	−529.953	−0.0830615
$345$	0	0
$346$	−1354.35	−0.210435
$347$	10914.9	1.68860	0.844301	−	0.535869i	$-0.180016\pi$
$347$	10914.9	1.68860	0.844301	+	0.535869i	$0.180016\pi$
$348$	−2098.30	−0.323221
$349$	6697.83	1.02730	0.513649	−	0.858001i	$-0.328294\pi$
$349$	6697.83	1.02730	0.513649	+	0.858001i	$0.328294\pi$
$350$	0	0
$351$	14456.2	2.19833
$352$	5047.54	0.764303
$353$	3764.83	0.567654	0.283827	−	0.958875i	$-0.408396\pi$
$353$	3764.83	0.567654	0.283827	+	0.958875i	$0.408396\pi$
$354$	380.067	0.0570631
$355$	0	0
$356$	−8753.90	−1.30325
$357$	3148.20	0.466724
$358$	232.898	0.0343829
$359$	6577.13	0.966930	0.483465	−	0.875364i	$-0.339378\pi$
$359$	6577.13	0.966930	0.483465	+	0.875364i	$0.339378\pi$
$360$	0	0
$361$	−2667.06	−0.388841
$362$	624.354	0.0906501
$363$	27140.8	3.92430
$364$	2393.08	0.344592
$365$	0	0
$366$	2778.40	0.396802
$367$	−2274.27	−0.323477	−0.161738	−	0.986834i	$-0.551710\pi$
$367$	−2274.27	−0.323477	−0.161738	+	0.986834i	$0.551710\pi$
$368$	−5624.64	−0.796752
$369$	12571.1	1.77351
$370$	0	0
$371$	2017.48	0.282325
$372$	17082.8	2.38091
$373$	−1284.94	−0.178369	−0.0891844	−	0.996015i	$-0.528426\pi$
$373$	−1284.94	−0.178369	−0.0891844	+	0.996015i	$0.528426\pi$
$374$	−1500.57	−0.207467
$375$	0	0
$376$	2345.48	0.321700
$377$	1443.32	0.197174
$378$	738.983	0.100553
$379$	174.785	0.0236890	0.0118445	−	0.999930i	$-0.496230\pi$
$379$	174.785	0.0236890	0.0118445	+	0.999930i	$0.496230\pi$
$380$	0	0
$381$	−18481.4	−2.48512
$382$	−1877.22	−0.251431
$383$	5558.62	0.741599	0.370799	−	0.928713i	$-0.379084\pi$
$383$	5558.62	0.741599	0.370799	+	0.928713i	$0.379084\pi$
$384$	7425.62	0.986816
$385$	0	0
$386$	−1215.79	−0.160316
$387$	−4722.64	−0.620323
$388$	−6305.14	−0.824987
$389$	−2556.05	−0.333154	−0.166577	−	0.986028i	$-0.553271\pi$
$389$	−2556.05	−0.333154	−0.166577	+	0.986028i	$0.553271\pi$
$390$	0	0
$391$	5206.32	0.673388
$392$	−2001.48	−0.257883
$393$	5189.45	0.666089
$394$	1111.00	0.142060
$395$	0	0
$396$	29879.2	3.79163
$397$	−5927.27	−0.749323	−0.374662	−	0.927162i	$-0.622241\pi$
$397$	−5927.27	−0.749323	−0.374662	+	0.927162i	$0.622241\pi$
$398$	268.566	0.0338241
$399$	3675.55	0.461173
$400$	0	0
$401$	4747.99	0.591280	0.295640	−	0.955299i	$-0.404467\pi$
$401$	4747.99	0.591280	0.295640	+	0.955299i	$0.404467\pi$
$402$	3233.03	0.401116
$403$	−11750.4	−1.45243
$404$	10756.2	1.32460
$405$	0	0
$406$	73.7805	0.00901888
$407$	5017.29	0.611052
$408$	−3360.51	−0.407770
$409$	5200.19	0.628686	0.314343	−	0.949309i	$-0.398216\pi$
$409$	5200.19	0.628686	0.314343	+	0.949309i	$0.398216\pi$
$410$	0	0
$411$	2315.18	0.277858
$412$	−4968.48	−0.594125
$413$	609.761	0.0726498
$414$	2272.05	0.269722
$415$	0	0
$416$	−3845.55	−0.453229
$417$	−2238.97	−0.262933
$418$	−1751.93	−0.204999
$419$	−6425.59	−0.749189	−0.374595	−	0.927189i	$-0.622218\pi$
$419$	−6425.59	−0.749189	−0.374595	+	0.927189i	$0.622218\pi$
$420$	0	0
$421$	10037.6	1.16201	0.581003	−	0.813902i	$-0.302661\pi$
$421$	10037.6	1.16201	0.581003	+	0.813902i	$0.302661\pi$
$422$	2050.18	0.236496
$423$	20901.6	2.40253
$424$	−2153.54	−0.246663
$425$	0	0
$426$	1447.46	0.164624
$427$	4457.53	0.505188
$428$	−1416.60	−0.159986
$429$	−30050.1	−3.38189
$430$	0	0
$431$	16646.8	1.86044	0.930218	−	0.367006i	$-0.119617\pi$
$431$	16646.8	1.86044	0.930218	+	0.367006i	$0.119617\pi$
$432$	17402.1	1.93810
$433$	−15089.1	−1.67468	−0.837340	−	0.546682i	$-0.815891\pi$
$433$	−15089.1	−1.67468	−0.837340	+	0.546682i	$0.815891\pi$
$434$	−600.664	−0.0664350
$435$	0	0
$436$	−8126.97	−0.892686
$437$	6078.42	0.665378
$438$	−2224.69	−0.242693
$439$	−3777.24	−0.410656	−0.205328	−	0.978693i	$-0.565826\pi$
$439$	−3777.24	−0.410656	−0.205328	+	0.978693i	$0.565826\pi$
$440$	0	0
$441$	−17836.1	−1.92593
$442$	1143.23	0.123027
$443$	−7992.65	−0.857206	−0.428603	−	0.903493i	$-0.640994\pi$
$443$	−7992.65	−0.857206	−0.428603	+	0.903493i	$0.640994\pi$
$444$	5557.18	0.593991
$445$	0	0
$446$	918.288	0.0974937
$447$	−15089.8	−1.59670
$448$	2747.31	0.289728
$449$	6433.54	0.676209	0.338104	−	0.941109i	$-0.390214\pi$
$449$	6433.54	0.676209	0.338104	+	0.941109i	$0.390214\pi$
$450$	0	0
$451$	−14055.6	−1.46752
$452$	−1446.42	−0.150518
$453$	−1123.74	−0.116552
$454$	1883.05	0.194661
$455$	0	0
$456$	−3923.43	−0.402919
$457$	−6975.18	−0.713972	−0.356986	−	0.934110i	$-0.616196\pi$
$457$	−6975.18	−0.713972	−0.356986	+	0.934110i	$0.616196\pi$
$458$	−1383.08	−0.141107
$459$	−16107.9	−1.63802
$460$	0	0
$461$	−14758.9	−1.49109	−0.745543	−	0.666458i	$-0.767810\pi$
$461$	−14758.9	−1.49109	−0.745543	+	0.666458i	$0.767810\pi$
$462$	−1536.12	−0.154690
$463$	18951.2	1.90224	0.951121	−	0.308818i	$-0.0999334\pi$
$463$	18951.2	1.90224	0.951121	+	0.308818i	$0.0999334\pi$
$464$	1737.44	0.173833
$465$	0	0
$466$	−1654.93	−0.164513
$467$	−12442.4	−1.23290	−0.616449	−	0.787395i	$-0.711429\pi$
$467$	−12442.4	−1.23290	−0.616449	+	0.787395i	$0.711429\pi$
$468$	−22763.9	−2.24843
$469$	5186.91	0.510680
$470$	0	0
$471$	6961.22	0.681010
$472$	−650.882	−0.0634730
$473$	5280.33	0.513297
$474$	1352.38	0.131048
$475$	0	0
$476$	−2666.50	−0.256762
$477$	−19191.1	−1.84214
$478$	579.914	0.0554909
$479$	12947.5	1.23504	0.617522	−	0.786554i	$-0.288137\pi$
$479$	12947.5	1.23504	0.617522	+	0.786554i	$0.288137\pi$
$480$	0	0
$481$	−3822.50	−0.362352
$482$	845.385	0.0798885
$483$	5329.65	0.502086
$484$	−22988.0	−2.15890
$485$	0	0
$486$	−990.104	−0.0924116
$487$	−9844.72	−0.916030	−0.458015	−	0.888944i	$-0.651439\pi$
$487$	−9844.72	−0.916030	−0.458015	+	0.888944i	$0.651439\pi$
$488$	−4758.14	−0.441375
$489$	−4971.77	−0.459778
$490$	0	0
$491$	−6809.50	−0.625883	−0.312941	−	0.949772i	$-0.601314\pi$
$491$	−6809.50	−0.625883	−0.312941	+	0.949772i	$0.601314\pi$
$492$	−15568.1	−1.42655
$493$	−1608.22	−0.146918
$494$	1334.74	0.121564
$495$	0	0
$496$	−14144.9	−1.28049
$497$	2322.24	0.209591
$498$	2666.54	0.239940
$499$	−15953.8	−1.43124	−0.715622	−	0.698488i	$-0.753857\pi$
$499$	−15953.8	−1.43124	−0.715622	+	0.698488i	$0.753857\pi$
$500$	0	0
$501$	−4479.11	−0.399424
$502$	−332.468	−0.0295593
$503$	14582.7	1.29267	0.646334	−	0.763054i	$-0.276301\pi$
$503$	14582.7	1.29267	0.646334	+	0.763054i	$0.276301\pi$
$504$	−2352.83	−0.207943
$505$	0	0
$506$	−2540.35	−0.223186
$507$	2588.02	0.226702
$508$	15653.5	1.36715
$509$	20906.4	1.82055	0.910273	−	0.414008i	$-0.135871\pi$
$509$	20906.4	1.82055	0.910273	+	0.414008i	$0.135871\pi$
$510$	0	0
$511$	−3569.17	−0.308984
$512$	−7771.61	−0.670820
$513$	−18806.1	−1.61854
$514$	−1849.09	−0.158677
$515$	0	0
$516$	5848.52	0.498967
$517$	−23369.8	−1.98802
$518$	−195.401	−0.0165742
$519$	30220.6	2.55595
$520$	0	0
$521$	−15131.7	−1.27242	−0.636212	−	0.771515i	$-0.719500\pi$
$521$	−15131.7	−1.27242	−0.636212	+	0.771515i	$0.719500\pi$
$522$	−701.829	−0.0588472
$523$	−12146.9	−1.01558	−0.507790	−	0.861481i	$-0.669537\pi$
$523$	−12146.9	−1.01558	−0.507790	+	0.861481i	$0.669537\pi$
$524$	−4395.41	−0.366440
$525$	0	0
$526$	−1580.31	−0.130998
$527$	13092.9	1.08223
$528$	−36173.7	−2.98155
$529$	−3353.12	−0.275592
$530$	0	0
$531$	−5800.28	−0.474032
$532$	−3113.16	−0.253708
$533$	10708.5	0.870237
$534$	−4281.02	−0.346925
$535$	0	0
$536$	−5536.70	−0.446174
$537$	−5196.83	−0.417616
$538$	−1873.89	−0.150166
$539$	19942.3	1.59365
$540$	0	0
$541$	−22291.8	−1.77153	−0.885767	−	0.464130i	$-0.846367\pi$
$541$	−22291.8	−1.77153	−0.885767	+	0.464130i	$0.846367\pi$
$542$	−1641.38	−0.130080
$543$	−13931.7	−1.10104
$544$	4284.91	0.337709
$545$	0	0
$546$	1170.32	0.0917307
$547$	15439.4	1.20684	0.603421	−	0.797423i	$-0.293804\pi$
$547$	15439.4	1.20684	0.603421	+	0.797423i	$0.293804\pi$
$548$	−1960.94	−0.152860
$549$	−42401.8	−3.29629
$550$	0	0
$551$	−1877.61	−0.145170
$552$	−5689.07	−0.438665
$553$	2169.69	0.166844
$554$	918.557	0.0704436
$555$	0	0
$556$	1896.39	0.144649
$557$	−2336.99	−0.177776	−0.0888881	−	0.996042i	$-0.528331\pi$
$557$	−2336.99	−0.177776	−0.0888881	+	0.996042i	$0.528331\pi$
$558$	5713.75	0.433481
$559$	−4022.90	−0.304384
$560$	0	0
$561$	33483.3	2.51991
$562$	1061.61	0.0796824
$563$	−19833.3	−1.48468	−0.742340	−	0.670023i	$-0.766284\pi$
$563$	−19833.3	−1.48468	−0.742340	+	0.670023i	$0.766284\pi$
$564$	−25884.6	−1.93251
$565$	0	0
$566$	−1602.71	−0.119023
$567$	−6800.16	−0.503668
$568$	−2478.85	−0.183116
$569$	11063.7	0.815141	0.407571	−	0.913174i	$-0.366376\pi$
$569$	11063.7	0.815141	0.407571	+	0.913174i	$0.366376\pi$
$570$	0	0
$571$	−665.827	−0.0487986	−0.0243993	−	0.999702i	$-0.507767\pi$
$571$	−665.827	−0.0487986	−0.0243993	+	0.999702i	$0.507767\pi$
$572$	25452.1	1.86050
$573$	41887.6	3.05389
$574$	547.404	0.0398053
$575$	0	0
$576$	−26133.5	−1.89044
$577$	7165.21	0.516970	0.258485	−	0.966015i	$-0.416777\pi$
$577$	7165.21	0.516970	0.258485	+	0.966015i	$0.416777\pi$
$578$	761.179	0.0547766
$579$	27128.7	1.94720
$580$	0	0
$581$	4278.06	0.305480
$582$	−3083.47	−0.219612
$583$	21457.3	1.52431
$584$	3809.87	0.269955
$585$	0	0
$586$	−1608.73	−0.113406
$587$	10375.2	0.729525	0.364763	−	0.931101i	$-0.381150\pi$
$587$	10375.2	0.729525	0.364763	+	0.931101i	$0.381150\pi$
$588$	22088.2	1.54915
$589$	15286.0	1.06936
$590$	0	0
$591$	−24790.6	−1.72546
$592$	−4601.46	−0.319457
$593$	−18931.5	−1.31100	−0.655501	−	0.755194i	$-0.727542\pi$
$593$	−18931.5	−1.31100	−0.655501	+	0.755194i	$0.727542\pi$
$594$	7859.60	0.542901
$595$	0	0
$596$	12780.9	0.878401
$597$	−5992.71	−0.410829
$598$	1935.40	0.132349
$599$	−12244.2	−0.835199	−0.417600	−	0.908631i	$-0.637129\pi$
$599$	−12244.2	−0.835199	−0.417600	+	0.908631i	$0.637129\pi$
$600$	0	0
$601$	15596.9	1.05859	0.529293	−	0.848439i	$-0.322457\pi$
$601$	15596.9	1.05859	0.529293	+	0.848439i	$0.322457\pi$
$602$	−205.645	−0.0139227
$603$	−49339.9	−3.33213
$604$	951.796	0.0641192
$605$	0	0
$606$	5260.22	0.352610
$607$	10155.5	0.679076	0.339538	−	0.940592i	$-0.389729\pi$
$607$	10155.5	0.679076	0.339538	+	0.940592i	$0.389729\pi$
$608$	5002.67	0.333692
$609$	−1646.32	−0.109544
$610$	0	0
$611$	17804.7	1.17889
$612$	25364.8	1.67534
$613$	6227.67	0.410331	0.205166	−	0.978727i	$-0.434227\pi$
$613$	6227.67	0.410331	0.205166	+	0.978727i	$0.434227\pi$
$614$	−167.015	−0.0109775
$615$	0	0
$616$	2630.67	0.172066
$617$	−14357.5	−0.936808	−0.468404	−	0.883514i	$-0.655171\pi$
$617$	−14357.5	−0.936808	−0.468404	+	0.883514i	$0.655171\pi$
$618$	−2429.80	−0.158156
$619$	−13220.6	−0.858453	−0.429227	−	0.903197i	$-0.641214\pi$
$619$	−13220.6	−0.858453	−0.429227	+	0.903197i	$0.641214\pi$
$620$	0	0
$621$	−27269.3	−1.76213
$622$	2004.26	0.129202
$623$	−6868.26	−0.441687
$624$	27559.5	1.76805
$625$	0	0
$626$	−3539.16	−0.225963
$627$	39092.1	2.48993
$628$	−5896.08	−0.374649
$629$	4259.23	0.269995
$630$	0	0
$631$	1828.97	0.115389	0.0576943	−	0.998334i	$-0.481625\pi$
$631$	1828.97	0.115389	0.0576943	+	0.998334i	$0.481625\pi$
$632$	−2316.01	−0.145769
$633$	−45747.1	−2.87249
$634$	−734.426	−0.0460059
$635$	0	0
$636$	23766.3	1.48175
$637$	−15193.4	−0.945028
$638$	784.707	0.0486941
$639$	−22090.0	−1.36756
$640$	0	0
$641$	−22644.1	−1.39530	−0.697651	−	0.716437i	$-0.745772\pi$
$641$	−22644.1	−1.39530	−0.697651	+	0.716437i	$0.745772\pi$
$642$	−692.778	−0.0425884
$643$	−22728.4	−1.39397	−0.696983	−	0.717088i	$-0.745475\pi$
$643$	−22728.4	−1.39397	−0.696983	+	0.717088i	$0.745475\pi$
$644$	−4514.16	−0.276216
$645$	0	0
$646$	−1487.23	−0.0905796
$647$	5844.85	0.355154	0.177577	−	0.984107i	$-0.443174\pi$
$647$	5844.85	0.355154	0.177577	+	0.984107i	$0.443174\pi$
$648$	7258.74	0.440047
$649$	6485.23	0.392246
$650$	0	0
$651$	13403.0	0.806922
$652$	4211.04	0.252941
$653$	−15174.1	−0.909355	−0.454677	−	0.890656i	$-0.650245\pi$
$653$	−15174.1	−0.909355	−0.454677	+	0.890656i	$0.650245\pi$
$654$	−3974.43	−0.237634
$655$	0	0
$656$	12890.7	0.767221
$657$	33951.4	2.01609
$658$	910.152	0.0539231
$659$	−27857.0	−1.64667	−0.823333	−	0.567558i	$-0.807888\pi$
$659$	−27857.0	−1.64667	−0.823333	+	0.567558i	$0.807888\pi$
$660$	0	0
$661$	−4966.64	−0.292254	−0.146127	−	0.989266i	$-0.546681\pi$
$661$	−4966.64	−0.292254	−0.146127	+	0.989266i	$0.546681\pi$
$662$	−332.148	−0.0195004
$663$	−25509.8	−1.49430
$664$	−4566.56	−0.266893
$665$	0	0
$666$	1858.74	0.108145
$667$	−2722.59	−0.158049
$668$	3793.76	0.219738
$669$	−20490.4	−1.18416
$670$	0	0
$671$	47409.0	2.72758
$672$	4386.41	0.251800
$673$	2338.02	0.133914	0.0669569	−	0.997756i	$-0.478671\pi$
$673$	2338.02	0.133914	0.0669569	+	0.997756i	$0.478671\pi$
$674$	3393.75	0.193950
$675$	0	0
$676$	−2192.03	−0.124717
$677$	−6342.30	−0.360051	−0.180025	−	0.983662i	$-0.557618\pi$
$677$	−6342.30	−0.360051	−0.180025	+	0.983662i	$0.557618\pi$
$678$	−707.361	−0.0400679
$679$	−4946.97	−0.279598
$680$	0	0
$681$	−42017.9	−2.36436
$682$	−6388.48	−0.358691
$683$	30366.6	1.70124	0.850620	−	0.525780i	$-0.176227\pi$
$683$	30366.6	1.70124	0.850620	+	0.525780i	$0.176227\pi$
$684$	29613.6	1.65542
$685$	0	0
$686$	−1649.31	−0.0917944
$687$	30861.6	1.71389
$688$	−4842.69	−0.268352
$689$	−16347.6	−0.903910
$690$	0	0
$691$	−11826.5	−0.651089	−0.325545	−	0.945527i	$-0.605548\pi$
$691$	−11826.5	−0.651089	−0.325545	+	0.945527i	$0.605548\pi$
$692$	−25596.6	−1.40612
$693$	23443.0	1.28503
$694$	−4521.12	−0.247290
$695$	0	0
$696$	1757.34	0.0957067
$697$	−11932.0	−0.648429
$698$	−2774.33	−0.150444
$699$	36927.6	1.99818
$700$	0	0
$701$	−2776.33	−0.149587	−0.0747936	−	0.997199i	$-0.523830\pi$
$701$	−2776.33	−0.149587	−0.0747936	+	0.997199i	$0.523830\pi$
$702$	−5987.96	−0.321939
$703$	4972.69	0.266783
$704$	29219.5	1.56428
$705$	0	0
$706$	−1559.45	−0.0831310
$707$	8439.23	0.448925
$708$	7183.08	0.381295
$709$	−15962.7	−0.845543	−0.422772	−	0.906236i	$-0.638943\pi$
$709$	−15962.7	−0.845543	−0.422772	+	0.906236i	$0.638943\pi$
$710$	0	0
$711$	−20638.9	−1.08864
$712$	7331.44	0.385895
$713$	22165.2	1.16422
$714$	−1304.03	−0.0683502
$715$	0	0
$716$	4401.66	0.229746
$717$	−12940.0	−0.673994
$718$	−2724.34	−0.141604
$719$	−20832.9	−1.08058	−0.540289	−	0.841480i	$-0.681685\pi$
$719$	−20832.9	−1.08058	−0.540289	+	0.841480i	$0.681685\pi$
$720$	0	0
$721$	−3898.24	−0.201357
$722$	1104.73	0.0569445
$723$	−18863.7	−0.970329
$724$	11800.0	0.605722
$725$	0	0
$726$	−11242.1	−0.574700
$727$	−4452.04	−0.227121	−0.113561	−	0.993531i	$-0.536226\pi$
$727$	−4452.04	−0.227121	−0.113561	+	0.993531i	$0.536226\pi$
$728$	−2004.22	−0.102035
$729$	−7799.67	−0.396264
$730$	0	0
$731$	4482.52	0.226802
$732$	52510.4	2.65142
$733$	12107.2	0.610082	0.305041	−	0.952339i	$-0.401330\pi$
$733$	12107.2	0.610082	0.305041	+	0.952339i	$0.401330\pi$
$734$	942.034	0.0473721
$735$	0	0
$736$	7254.00	0.363296
$737$	55166.4	2.75723
$738$	−5207.12	−0.259725
$739$	−4506.27	−0.224311	−0.112156	−	0.993691i	$-0.535775\pi$
$739$	−4506.27	−0.224311	−0.112156	+	0.993691i	$0.535775\pi$
$740$	0	0
$741$	−29782.9	−1.47652
$742$	−835.669	−0.0413455
$743$	−1177.19	−0.0581253	−0.0290626	−	0.999578i	$-0.509252\pi$
$743$	−1177.19	−0.0581253	−0.0290626	+	0.999578i	$0.509252\pi$
$744$	−14306.9	−0.704996
$745$	0	0
$746$	532.239	0.0261215
$747$	−40694.6	−1.99322
$748$	−28360.1	−1.38629
$749$	−1111.46	−0.0542214
$750$	0	0
$751$	27631.6	1.34260	0.671300	−	0.741186i	$-0.265736\pi$
$751$	27631.6	1.34260	0.671300	+	0.741186i	$0.265736\pi$
$752$	21432.9	1.03933
$753$	7418.59	0.359028
$754$	−597.841	−0.0288755
$755$	0	0
$756$	13966.4	0.671896
$757$	−11336.6	−0.544300	−0.272150	−	0.962255i	$-0.587735\pi$
$757$	−11336.6	−0.544300	−0.272150	+	0.962255i	$0.587735\pi$
$758$	−72.3984	−0.00346917
$759$	56684.6	2.71083
$760$	0	0
$761$	4356.58	0.207524	0.103762	−	0.994602i	$-0.466912\pi$
$761$	4356.58	0.207524	0.103762	+	0.994602i	$0.466912\pi$
$762$	7655.23	0.363937
$763$	−6376.37	−0.302543
$764$	−35478.4	−1.68006
$765$	0	0
$766$	−2302.46	−0.108605
$767$	−4940.87	−0.232601
$768$	29997.2	1.40942
$769$	−21718.1	−1.01843	−0.509217	−	0.860638i	$-0.670065\pi$
$769$	−21718.1	−1.01843	−0.509217	+	0.860638i	$0.670065\pi$
$770$	0	0
$771$	41260.0	1.92729
$772$	−22977.8	−1.07123
$773$	−22688.4	−1.05568	−0.527842	−	0.849343i	$-0.676999\pi$
$773$	−22688.4	−1.05568	−0.527842	+	0.849343i	$0.676999\pi$
$774$	1956.18	0.0908442
$775$	0	0
$776$	5280.58	0.244281
$777$	4360.13	0.201311
$778$	1058.75	0.0487893
$779$	−13930.7	−0.640716
$780$	0	0
$781$	24698.6	1.13161
$782$	−2156.53	−0.0986155
$783$	8423.43	0.384456
$784$	−18289.5	−0.833158
$785$	0	0
$786$	−2149.54	−0.0975465
$787$	32890.9	1.48975	0.744875	−	0.667204i	$-0.232509\pi$
$787$	32890.9	1.48975	0.744875	+	0.667204i	$0.232509\pi$
$788$	20997.4	0.949239
$789$	35262.6	1.59111
$790$	0	0
$791$	−1134.85	−0.0510123
$792$	−25024.0	−1.12271
$793$	−36119.3	−1.61744
$794$	2455.16	0.109736
$795$	0	0
$796$	5075.76	0.226012
$797$	−30404.1	−1.35128	−0.675638	−	0.737233i	$-0.736132\pi$
$797$	−30404.1	−1.35128	−0.675638	+	0.737233i	$0.736132\pi$
$798$	−1522.46	−0.0675372
$799$	−19838.9	−0.878410
$800$	0	0
$801$	65333.5	2.88196
$802$	−1966.68	−0.0865909
$803$	−37960.7	−1.66825
$804$	61102.6	2.68025
$805$	0	0
$806$	4867.16	0.212703
$807$	41813.5	1.82392
$808$	−9008.36	−0.392219
$809$	−37889.3	−1.64662	−0.823311	−	0.567591i	$-0.807876\pi$
$809$	−37889.3	−1.64662	−0.823311	+	0.567591i	$0.807876\pi$
$810$	0	0
$811$	−8123.23	−0.351720	−0.175860	−	0.984415i	$-0.556271\pi$
$811$	−8123.23	−0.351720	−0.175860	+	0.984415i	$0.556271\pi$
$812$	1394.41	0.0602640
$813$	36625.3	1.57996
$814$	−2078.23	−0.0894864
$815$	0	0
$816$	−30708.2	−1.31741
$817$	5233.39	0.224104
$818$	−2153.99	−0.0920690
$819$	−17860.4	−0.762020
$820$	0	0
$821$	13226.8	0.562264	0.281132	−	0.959669i	$-0.409290\pi$
$821$	13226.8	0.562264	0.281132	+	0.959669i	$0.409290\pi$
$822$	−958.981	−0.0406914
$823$	29575.2	1.25265	0.626323	−	0.779563i	$-0.284559\pi$
$823$	29575.2	1.25265	0.626323	+	0.779563i	$0.284559\pi$
$824$	4161.13	0.175922
$825$	0	0
$826$	−252.571	−0.0106393
$827$	36661.2	1.54152	0.770758	−	0.637128i	$-0.219878\pi$
$827$	36661.2	1.54152	0.770758	+	0.637128i	$0.219878\pi$
$828$	42940.5	1.80228
$829$	11277.0	0.472455	0.236228	−	0.971698i	$-0.424089\pi$
$829$	11277.0	0.472455	0.236228	+	0.971698i	$0.424089\pi$
$830$	0	0
$831$	−20496.4	−0.855611
$832$	−22261.3	−0.927612
$833$	16929.2	0.704158
$834$	927.413	0.0385056
$835$	0	0
$836$	−33110.6	−1.36980
$837$	−68577.0	−2.83198
$838$	2661.56	0.109716
$839$	−18965.7	−0.780417	−0.390208	−	0.920727i	$-0.627597\pi$
$839$	−18965.7	−0.780417	−0.390208	+	0.920727i	$0.627597\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−4157.72	−0.170172
$843$	−23688.5	−0.967825
$844$	38747.3	1.58026
$845$	0	0
$846$	−8657.72	−0.351842
$847$	−18036.2	−0.731679
$848$	−19678.9	−0.796908
$849$	35762.5	1.44566
$850$	0	0
$851$	7210.54	0.290451
$852$	27356.3	1.10002
$853$	−8067.23	−0.323818	−0.161909	−	0.986806i	$-0.551765\pi$
$853$	−8067.23	−0.323818	−0.161909	+	0.986806i	$0.551765\pi$
$854$	−1846.37	−0.0739830
$855$	0	0
$856$	1186.41	0.0473724
$857$	−15281.7	−0.609118	−0.304559	−	0.952493i	$-0.598509\pi$
$857$	−15281.7	−0.609118	−0.304559	+	0.952493i	$0.598509\pi$
$858$	12447.1	0.495266
$859$	−36789.1	−1.46127	−0.730634	−	0.682770i	$-0.760775\pi$
$859$	−36789.1	−1.46127	−0.730634	+	0.682770i	$0.760775\pi$
$860$	0	0
$861$	−12214.6	−0.483476
$862$	−6895.33	−0.272455
$863$	−40907.8	−1.61358	−0.806788	−	0.590840i	$-0.798796\pi$
$863$	−40907.8	−1.61358	−0.806788	+	0.590840i	$0.798796\pi$
$864$	−22443.2	−0.883719
$865$	0	0
$866$	6250.12	0.245251
$867$	−16984.7	−0.665319
$868$	−11352.2	−0.443917
$869$	23076.2	0.900812
$870$	0	0
$871$	−42029.4	−1.63503
$872$	6806.38	0.264327
$873$	47057.5	1.82435
$874$	−2517.76	−0.0974424
$875$	0	0
$876$	−42045.4	−1.62167
$877$	−2391.60	−0.0920852	−0.0460426	−	0.998939i	$-0.514661\pi$
$877$	−2391.60	−0.0920852	−0.0460426	+	0.998939i	$0.514661\pi$
$878$	1564.59	0.0601392
$879$	35896.8	1.37744
$880$	0	0
$881$	5487.72	0.209859	0.104930	−	0.994480i	$-0.466538\pi$
$881$	5487.72	0.209859	0.104930	+	0.994480i	$0.466538\pi$
$882$	7387.94	0.282046
$883$	−170.008	−0.00647931	−0.00323966	−	0.999995i	$-0.501031\pi$
$883$	−170.008	−0.00647931	−0.00323966	+	0.999995i	$0.501031\pi$
$884$	21606.6	0.822067
$885$	0	0
$886$	3310.66	0.125535
$887$	−25867.3	−0.979188	−0.489594	−	0.871950i	$-0.662855\pi$
$887$	−25867.3	−0.979188	−0.489594	+	0.871950i	$0.662855\pi$
$888$	−4654.17	−0.175883
$889$	12281.7	0.463345
$890$	0	0
$891$	−72324.4	−2.71937
$892$	17355.2	0.651451
$893$	−23162.1	−0.867961
$894$	6250.40	0.233831
$895$	0	0
$896$	−4934.65	−0.183990
$897$	−43186.0	−1.60751
$898$	−2664.86	−0.0990285
$899$	−6846.77	−0.254007
$900$	0	0
$901$	18215.4	0.673520
$902$	5822.03	0.214914
$903$	4588.71	0.169106
$904$	1211.39	0.0445687
$905$	0	0
$906$	465.468	0.0170686
$907$	−11411.5	−0.417765	−0.208882	−	0.977941i	$-0.566983\pi$
$907$	−11411.5	−0.417765	−0.208882	+	0.977941i	$0.566983\pi$
$908$	35588.7	1.30072
$909$	−80277.3	−2.92919
$910$	0	0
$911$	−38718.5	−1.40813	−0.704063	−	0.710138i	$-0.748633\pi$
$911$	−38718.5	−1.40813	−0.704063	+	0.710138i	$0.748633\pi$
$912$	−35852.1	−1.30174
$913$	45500.1	1.64933
$914$	2889.21	0.104559
$915$	0	0
$916$	−26139.5	−0.942875
$917$	−3448.62	−0.124191
$918$	6672.10	0.239882
$919$	−48465.3	−1.73963	−0.869817	−	0.493374i	$-0.835763\pi$
$919$	−48465.3	−1.73963	−0.869817	+	0.493374i	$0.835763\pi$
$920$	0	0
$921$	3726.72	0.133333
$922$	6113.34	0.218364
$923$	−18817.0	−0.671040
$924$	−29031.9	−1.03364
$925$	0	0
$926$	−7849.85	−0.278577
$927$	37081.6	1.31383
$928$	−2240.74	−0.0792630
$929$	10560.1	0.372946	0.186473	−	0.982460i	$-0.440294\pi$
$929$	10560.1	0.372946	0.186473	+	0.982460i	$0.440294\pi$
$930$	0	0
$931$	19765.0	0.695782
$932$	−31277.3	−1.09927
$933$	−44722.4	−1.56929
$934$	5153.79	0.180554
$935$	0	0
$936$	19064.9	0.665765
$937$	23025.0	0.802769	0.401384	−	0.915910i	$-0.368529\pi$
$937$	23025.0	0.802769	0.401384	+	0.915910i	$0.368529\pi$
$938$	−2148.49	−0.0747874
$939$	78971.7	2.74456
$940$	0	0
$941$	40778.1	1.41268	0.706338	−	0.707874i	$-0.250346\pi$
$941$	40778.1	1.41268	0.706338	+	0.707874i	$0.250346\pi$
$942$	−2883.43	−0.0997317
$943$	−20199.8	−0.697558
$944$	−5947.74	−0.205066
$945$	0	0
$946$	−2187.18	−0.0751707
$947$	−36129.8	−1.23977	−0.619884	−	0.784693i	$-0.712821\pi$
$947$	−36129.8	−1.23977	−0.619884	+	0.784693i	$0.712821\pi$
$948$	25559.3	0.875662
$949$	28920.9	0.989265
$950$	0	0
$951$	16387.8	0.558790
$952$	2233.21	0.0760280
$953$	−20831.4	−0.708075	−0.354037	−	0.935231i	$-0.615191\pi$
$953$	−20831.4	−0.708075	−0.354037	+	0.935231i	$0.615191\pi$
$954$	7949.21	0.269775
$955$	0	0
$956$	10960.1	0.370789
$957$	−17509.7	−0.591441
$958$	−5363.02	−0.180868
$959$	−1538.54	−0.0518061
$960$	0	0
$961$	25950.1	0.871071
$962$	1583.33	0.0530652
$963$	10572.6	0.353788
$964$	15977.4	0.533813
$965$	0	0
$966$	−2207.61	−0.0735288
$967$	−49242.5	−1.63757	−0.818785	−	0.574100i	$-0.805352\pi$
$967$	−49242.5	−1.63757	−0.818785	+	0.574100i	$0.805352\pi$
$968$	19252.5	0.639256
$969$	33185.7	1.10018
$970$	0	0
$971$	−2352.05	−0.0777351	−0.0388675	−	0.999244i	$-0.512375\pi$
$971$	−2352.05	−0.0777351	−0.0388675	+	0.999244i	$0.512375\pi$
$972$	−18712.5	−0.617493
$973$	1487.89	0.0490233
$974$	4077.82	0.134150
$975$	0	0
$976$	−43479.7	−1.42598
$977$	−18768.3	−0.614588	−0.307294	−	0.951615i	$-0.599423\pi$
$977$	−18768.3	−0.614588	−0.307294	+	0.951615i	$0.599423\pi$
$978$	2059.38	0.0673329
$979$	−73048.7	−2.38473
$980$	0	0
$981$	60654.5	1.97406
$982$	2820.59	0.0916584
$983$	49014.5	1.59036	0.795179	−	0.606375i	$-0.207377\pi$
$983$	49014.5	1.59036	0.795179	+	0.606375i	$0.207377\pi$
$984$	13038.4	0.422406
$985$	0	0
$986$	666.146	0.0215156
$987$	−20308.9	−0.654953
$988$	25225.8	0.812288
$989$	7588.55	0.243986
$990$	0	0
$991$	−48860.6	−1.56620	−0.783102	−	0.621893i	$-0.786364\pi$
$991$	−48860.6	−1.56620	−0.783102	+	0.621893i	$0.786364\pi$
$992$	18242.4	0.583868
$993$	7411.44	0.236853
$994$	−961.903	−0.0306939
$995$	0	0
$996$	50396.2	1.60328
$997$	−2934.57	−0.0932184	−0.0466092	−	0.998913i	$-0.514842\pi$
$997$	−2934.57	−0.0932184	−0.0466092	+	0.998913i	$0.514842\pi$
$998$	6608.29	0.209601
$999$	−22308.7	−0.706524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.4.a.b.1.1		2
5.4	even	2		29.4.a.a.1.2	✓	2
15.14	odd	2		261.4.a.b.1.1		2
20.19	odd	2		464.4.a.f.1.2		2
35.34	odd	2		1421.4.a.c.1.2		2
40.19	odd	2		1856.4.a.h.1.1		2
40.29	even	2		1856.4.a.n.1.2		2
145.144	even	2		841.4.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.a.1.2	✓	2	5.4	even	2
261.4.a.b.1.1		2	15.14	odd	2
464.4.a.f.1.2		2	20.19	odd	2
725.4.a.b.1.1		2	1.1	even	1	trivial
841.4.a.a.1.1		2	145.144	even	2
1421.4.a.c.1.2		2	35.34	odd	2
1856.4.a.h.1.1		2	40.19	odd	2
1856.4.a.n.1.2		2	40.29	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} +9.24264 q^{3} -7.82843 q^{4} -3.82843 q^{6} -6.14214 q^{7} +6.55635 q^{8} +58.4264 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} +9.24264 q^{3} -7.82843 q^{4} -3.82843 q^{6} -6.14214 q^{7} +6.55635 q^{8} +58.4264 q^{9} -65.3259 q^{11} -72.3553 q^{12} +49.7696 q^{13} +2.54416 q^{14} +59.9117 q^{16} -55.4558 q^{17} -24.2010 q^{18} -64.7452 q^{19} -56.7696 q^{21} +27.0589 q^{22} -93.8823 q^{23} +60.5980 q^{24} -20.6152 q^{26} +290.463 q^{27} +48.0833 q^{28} +29.0000 q^{29} -236.095 q^{31} -77.2670 q^{32} -603.784 q^{33} +22.9706 q^{34} -457.387 q^{36} -76.8040 q^{37} +26.8183 q^{38} +460.002 q^{39} +215.161 q^{41} +23.5147 q^{42} -80.8305 q^{43} +511.399 q^{44} +38.8873 q^{46} +357.742 q^{47} +553.742 q^{48} -305.274 q^{49} -512.558 q^{51} -389.617 q^{52} -328.466 q^{53} -120.314 q^{54} -40.2700 q^{56} -598.416 q^{57} -12.0122 q^{58} -99.2750 q^{59} -725.730 q^{61} +97.7939 q^{62} -358.863 q^{63} -447.288 q^{64} +250.095 q^{66} -844.479 q^{67} +434.132 q^{68} -867.720 q^{69} -378.083 q^{71} +383.064 q^{72} +581.097 q^{73} +31.8133 q^{74} +506.853 q^{76} +401.241 q^{77} -190.539 q^{78} -353.247 q^{79} +1107.13 q^{81} -89.1228 q^{82} -696.510 q^{83} +444.416 q^{84} +33.4811 q^{86} +268.037 q^{87} -428.299 q^{88} +1118.22 q^{89} -305.691 q^{91} +734.950 q^{92} -2182.15 q^{93} -148.182 q^{94} -714.151 q^{96} +805.415 q^{97} +126.449 q^{98} -3816.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 2 q^{6} + 16 q^{7} - 18 q^{8} + 32 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 2 * q^6 + 16 * q^7 - 18 * q^8 + 32 * q^9	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 2 q^{6} + 16 q^{7} - 18 q^{8} + 32 q^{9} - 26 q^{11} - 74 q^{12} + 26 q^{13} + 56 q^{14} + 18 q^{16} - 60 q^{17} - 88 q^{18} - 220 q^{19} - 40 q^{21} + 122 q^{22} - 52 q^{23} + 42 q^{24} - 78 q^{26} + 250 q^{27} + 58 q^{29} - 294 q^{31} + 18 q^{32} - 574 q^{33} + 12 q^{34} - 400 q^{36} - 312 q^{37} - 348 q^{38} + 442 q^{39} + 40 q^{41} + 64 q^{42} + 322 q^{43} + 426 q^{44} + 140 q^{46} + 130 q^{47} + 522 q^{48} - 158 q^{49} - 516 q^{51} - 338 q^{52} - 1002 q^{53} - 218 q^{54} - 584 q^{56} - 716 q^{57} + 58 q^{58} - 900 q^{59} - 948 q^{61} - 42 q^{62} - 944 q^{63} + 118 q^{64} + 322 q^{66} - 320 q^{67} + 444 q^{68} - 836 q^{69} - 660 q^{71} + 1032 q^{72} - 648 q^{73} - 536 q^{74} + 844 q^{76} + 1272 q^{77} - 234 q^{78} + 258 q^{79} + 1790 q^{81} - 512 q^{82} - 1212 q^{83} + 408 q^{84} + 1006 q^{86} + 290 q^{87} - 1394 q^{88} + 760 q^{89} - 832 q^{91} + 644 q^{92} - 2226 q^{93} - 698 q^{94} - 642 q^{96} - 24 q^{97} + 482 q^{98} - 4856 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 2 * q^6 + 16 * q^7 - 18 * q^8 + 32 * q^9 - 26 * q^11 - 74 * q^12 + 26 * q^13 + 56 * q^14 + 18 * q^16 - 60 * q^17 - 88 * q^18 - 220 * q^19 - 40 * q^21 + 122 * q^22 - 52 * q^23 + 42 * q^24 - 78 * q^26 + 250 * q^27 + 58 * q^29 - 294 * q^31 + 18 * q^32 - 574 * q^33 + 12 * q^34 - 400 * q^36 - 312 * q^37 - 348 * q^38 + 442 * q^39 + 40 * q^41 + 64 * q^42 + 322 * q^43 + 426 * q^44 + 140 * q^46 + 130 * q^47 + 522 * q^48 - 158 * q^49 - 516 * q^51 - 338 * q^52 - 1002 * q^53 - 218 * q^54 - 584 * q^56 - 716 * q^57 + 58 * q^58 - 900 * q^59 - 948 * q^61 - 42 * q^62 - 944 * q^63 + 118 * q^64 + 322 * q^66 - 320 * q^67 + 444 * q^68 - 836 * q^69 - 660 * q^71 + 1032 * q^72 - 648 * q^73 - 536 * q^74 + 844 * q^76 + 1272 * q^77 - 234 * q^78 + 258 * q^79 + 1790 * q^81 - 512 * q^82 - 1212 * q^83 + 408 * q^84 + 1006 * q^86 + 290 * q^87 - 1394 * q^88 + 760 * q^89 - 832 * q^91 + 644 * q^92 - 2226 * q^93 - 698 * q^94 - 642 * q^96 - 24 * q^97 + 482 * q^98 - 4856 * q^99

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