LMFDB - Embedded newform 725.4.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} +1.82843 q^{6} +22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} +1.82843 q^{6} +22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +39.3259 q^{11} -1.64466 q^{12} -23.7696 q^{13} +53.4558 q^{14} -41.9117 q^{16} -4.54416 q^{17} -63.7990 q^{18} -155.255 q^{19} +16.7696 q^{21} +94.9411 q^{22} +41.8823 q^{23} -18.5980 q^{24} -57.3848 q^{26} -40.4630 q^{27} -48.0833 q^{28} +29.0000 q^{29} -57.9045 q^{31} +95.2670 q^{32} +29.7838 q^{33} -10.9706 q^{34} +57.3869 q^{36} -235.196 q^{37} -374.818 q^{38} -18.0021 q^{39} -175.161 q^{41} +40.4853 q^{42} +402.831 q^{43} -85.3991 q^{44} +101.113 q^{46} -227.742 q^{47} -31.7422 q^{48} +147.274 q^{49} -3.44156 q^{51} +51.6173 q^{52} -673.534 q^{53} -97.6863 q^{54} -543.730 q^{56} -117.584 q^{57} +70.0122 q^{58} -800.725 q^{59} -222.270 q^{61} -139.794 q^{62} -585.137 q^{63} +565.288 q^{64} +71.9045 q^{66} +524.479 q^{67} +9.86797 q^{68} +31.7199 q^{69} -281.917 q^{71} +648.936 q^{72} -1229.10 q^{73} -567.813 q^{74} +337.147 q^{76} +870.759 q^{77} -43.4609 q^{78} +611.247 q^{79} +682.868 q^{81} -422.877 q^{82} -515.490 q^{83} -36.4163 q^{84} +972.519 q^{86} +21.9634 q^{87} -965.701 q^{88} -358.219 q^{89} -526.309 q^{91} -90.9504 q^{92} -43.8545 q^{93} -549.818 q^{94} +72.1514 q^{96} -829.415 q^{97} +355.551 q^{98} -1039.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.41421	0.853553	0.426777	−	0.904357i	$-0.359649\pi$
$2$	2.41421	0.853553	0.426777	+	0.904357i	$0.359649\pi$
$3$	0.757359	0.145754	0.0728769	−	0.997341i	$-0.476782\pi$
$3$	0.757359	0.145754	0.0728769	+	0.997341i	$0.476782\pi$
$4$	−2.17157	−0.271447
$5$	0	0
$5$	0	0
$6$	1.82843	0.124409
$7$	22.1421	1.19556	0.597781	−	0.801659i	$-0.296049\pi$
$7$	22.1421	1.19556	0.597781	+	0.801659i	$0.296049\pi$
$8$	−24.5563	−1.08525
$9$	−26.4264	−0.978756
$10$	0	0
$11$	39.3259	1.07793	0.538964	−	0.842329i	$-0.318816\pi$
$11$	39.3259	1.07793	0.538964	+	0.842329i	$0.318816\pi$
$12$	−1.64466	−0.0395644
$13$	−23.7696	−0.507114	−0.253557	−	0.967320i	$-0.581601\pi$
$13$	−23.7696	−0.507114	−0.253557	+	0.967320i	$0.581601\pi$
$14$	53.4558	1.02048
$15$	0	0
$16$	−41.9117	−0.654870
$17$	−4.54416	−0.0648306	−0.0324153	−	0.999474i	$-0.510320\pi$
$17$	−4.54416	−0.0648306	−0.0324153	+	0.999474i	$0.510320\pi$
$18$	−63.7990	−0.835420
$19$	−155.255	−1.87463	−0.937313	−	0.348488i	$-0.886695\pi$
$19$	−155.255	−1.87463	−0.937313	+	0.348488i	$0.886695\pi$
$20$	0	0
$21$	16.7696	0.174258
$22$	94.9411	0.920069
$23$	41.8823	0.379698	0.189849	−	0.981813i	$-0.439200\pi$
$23$	41.8823	0.379698	0.189849	+	0.981813i	$0.439200\pi$
$24$	−18.5980	−0.158179
$25$	0	0
$26$	−57.3848	−0.432849
$27$	−40.4630	−0.288411
$28$	−48.0833	−0.324532
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−57.9045	−0.335483	−0.167741	−	0.985831i	$-0.553647\pi$
$31$	−57.9045	−0.335483	−0.167741	+	0.985831i	$0.553647\pi$
$32$	95.2670	0.526281
$33$	29.7838	0.157112
$34$	−10.9706	−0.0553364
$35$	0	0
$36$	57.3869	0.265680
$37$	−235.196	−1.04503	−0.522513	−	0.852631i	$-0.675005\pi$
$37$	−235.196	−1.04503	−0.522513	+	0.852631i	$0.675005\pi$
$38$	−374.818	−1.60009
$39$	−18.0021	−0.0739139
$40$	0	0
$41$	−175.161	−0.667210	−0.333605	−	0.942713i	$-0.608265\pi$
$41$	−175.161	−0.667210	−0.333605	+	0.942713i	$0.608265\pi$
$42$	40.4853	0.148738
$43$	402.831	1.42863	0.714315	−	0.699824i	$-0.246738\pi$
$43$	402.831	1.42863	0.714315	+	0.699824i	$0.246738\pi$
$44$	−85.3991	−0.292600
$45$	0	0
$46$	101.113	0.324092
$47$	−227.742	−0.706800	−0.353400	−	0.935472i	$-0.614975\pi$
$47$	−227.742	−0.706800	−0.353400	+	0.935472i	$0.614975\pi$
$48$	−31.7422	−0.0954499
$49$	147.274	0.429371
$50$	0	0
$51$	−3.44156	−0.00944931
$52$	51.6173	0.137654
$53$	−673.534	−1.74560	−0.872802	−	0.488074i	$-0.837699\pi$
$53$	−673.534	−1.74560	−0.872802	+	0.488074i	$0.837699\pi$
$54$	−97.6863	−0.246174
$55$	0	0
$56$	−543.730	−1.29748
$57$	−117.584	−0.273234
$58$	70.0122	0.158501
$59$	−800.725	−1.76687	−0.883437	−	0.468551i	$-0.844776\pi$
$59$	−800.725	−1.76687	−0.883437	+	0.468551i	$0.844776\pi$
$60$	0	0
$61$	−222.270	−0.466537	−0.233268	−	0.972412i	$-0.574942\pi$
$61$	−222.270	−0.466537	−0.233268	+	0.972412i	$0.574942\pi$
$62$	−139.794	−0.286352
$63$	−585.137	−1.17016
$64$	565.288	1.10408
$65$	0	0
$66$	71.9045	0.134104
$67$	524.479	0.956349	0.478174	−	0.878265i	$-0.341299\pi$
$67$	524.479	0.956349	0.478174	+	0.878265i	$0.341299\pi$
$68$	9.86797	0.0175980
$69$	31.7199	0.0553424
$70$	0	0
$71$	−281.917	−0.471230	−0.235615	−	0.971846i	$-0.575711\pi$
$71$	−281.917	−0.471230	−0.235615	+	0.971846i	$0.575711\pi$
$72$	648.936	1.06219
$73$	−1229.10	−1.97061	−0.985307	−	0.170790i	$-0.945368\pi$
$73$	−1229.10	−1.97061	−0.985307	+	0.170790i	$0.945368\pi$
$74$	−567.813	−0.891986
$75$	0	0
$76$	337.147	0.508861
$77$	870.759	1.28873
$78$	−43.4609	−0.0630895
$79$	611.247	0.870514	0.435257	−	0.900306i	$-0.356657\pi$
$79$	611.247	0.870514	0.435257	+	0.900306i	$0.356657\pi$
$80$	0	0
$81$	682.868	0.936719
$82$	−422.877	−0.569500
$83$	−515.490	−0.681716	−0.340858	−	0.940115i	$-0.610718\pi$
$83$	−515.490	−0.681716	−0.340858	+	0.940115i	$0.610718\pi$
$84$	−36.4163	−0.0473017
$85$	0	0
$86$	972.519	1.21941
$87$	21.9634	0.0270658
$88$	−965.701	−1.16982
$89$	−358.219	−0.426643	−0.213321	−	0.976982i	$-0.568428\pi$
$89$	−358.219	−0.426643	−0.213321	+	0.976982i	$0.568428\pi$
$90$	0	0
$91$	−526.309	−0.606287
$92$	−90.9504	−0.103068
$93$	−43.8545	−0.0488979
$94$	−549.818	−0.603292
$95$	0	0
$96$	72.1514	0.0767075
$97$	−829.415	−0.868189	−0.434095	−	0.900867i	$-0.642932\pi$
$97$	−829.415	−0.868189	−0.434095	+	0.900867i	$0.642932\pi$
$98$	355.551	0.366491
$99$	−1039.24	−1.05503
$100$	0	0
$101$	−978.010	−0.963521	−0.481761	−	0.876303i	$-0.660003\pi$
$101$	−978.010	−0.963521	−0.481761	+	0.876303i	$0.660003\pi$
$102$	−8.30866	−0.00806549
$103$	1217.33	1.16453	0.582266	−	0.812998i	$-0.302166\pi$
$103$	1217.33	1.16453	0.582266	+	0.812998i	$0.302166\pi$
$104$	583.693	0.550345
$105$	0	0
$106$	−1626.06	−1.48997
$107$	707.044	0.638808	0.319404	−	0.947619i	$-0.396517\pi$
$107$	707.044	0.638808	0.319404	+	0.947619i	$0.396517\pi$
$108$	87.8683	0.0782883
$109$	−1496.14	−1.31471	−0.657357	−	0.753580i	$-0.728326\pi$
$109$	−1496.14	−1.31471	−0.657357	+	0.753580i	$0.728326\pi$
$110$	0	0
$111$	−178.128	−0.152317
$112$	−928.014	−0.782938
$113$	1067.23	0.888469	0.444234	−	0.895911i	$-0.353476\pi$
$113$	1067.23	0.888469	0.444234	+	0.895911i	$0.353476\pi$
$114$	−283.872	−0.233220
$115$	0	0
$116$	−62.9756	−0.0504064
$117$	628.144	0.496341
$118$	−1933.12	−1.50812
$119$	−100.617	−0.0775090
$120$	0	0
$121$	215.527	0.161928
$122$	−536.607	−0.398214
$123$	−132.660	−0.0972485
$124$	125.744	0.0910656
$125$	0	0
$126$	−1412.65	−0.998798
$127$	1179.58	0.824177	0.412088	−	0.911144i	$-0.364799\pi$
$127$	1179.58	0.824177	0.412088	+	0.911144i	$0.364799\pi$
$128$	602.591	0.416109
$129$	305.087	0.208228
$130$	0	0
$131$	−2357.47	−1.57231	−0.786156	−	0.618028i	$-0.787932\pi$
$131$	−2357.47	−1.57231	−0.786156	+	0.618028i	$0.787932\pi$
$132$	−64.6778	−0.0426476
$133$	−3437.67	−2.24123
$134$	1266.21	0.816295
$135$	0	0
$136$	111.588	0.0703572
$137$	−722.489	−0.450558	−0.225279	−	0.974294i	$-0.572329\pi$
$137$	−722.489	−0.450558	−0.225279	+	0.974294i	$0.572329\pi$
$138$	76.5786	0.0472377
$139$	1398.24	0.853219	0.426610	−	0.904436i	$-0.359708\pi$
$139$	1398.24	0.853219	0.426610	+	0.904436i	$0.359708\pi$
$140$	0	0
$141$	−172.483	−0.103019
$142$	−680.607	−0.402220
$143$	−934.759	−0.546633
$144$	1107.58	0.640958
$145$	0	0
$146$	−2967.30	−1.68203
$147$	111.539	0.0625824
$148$	510.745	0.283669
$149$	2830.63	1.55634	0.778168	−	0.628056i	$-0.216149\pi$
$149$	2830.63	1.55634	0.778168	+	0.628056i	$0.216149\pi$
$150$	0	0
$151$	1705.58	0.919194	0.459597	−	0.888128i	$-0.347994\pi$
$151$	1705.58	0.919194	0.459597	+	0.888128i	$0.347994\pi$
$152$	3812.49	2.03443
$153$	120.086	0.0634533
$154$	2102.20	1.10000
$155$	0	0
$156$	39.0929	0.0200637
$157$	2670.84	1.35768	0.678841	−	0.734286i	$-0.262483\pi$
$157$	2670.84	1.35768	0.678841	+	0.734286i	$0.262483\pi$
$158$	1475.68	0.743031
$159$	−510.107	−0.254429
$160$	0	0
$161$	927.362	0.453953
$162$	1648.59	0.799539
$163$	2151.92	1.03406	0.517028	−	0.855968i	$-0.327038\pi$
$163$	2151.92	1.03406	0.517028	+	0.855968i	$0.327038\pi$
$164$	380.376	0.181112
$165$	0	0
$166$	−1244.50	−0.581881
$167$	−999.387	−0.463083	−0.231542	−	0.972825i	$-0.574377\pi$
$167$	−999.387	−0.463083	−0.231542	+	0.972825i	$0.574377\pi$
$168$	−411.799	−0.189113
$169$	−1632.01	−0.742835
$170$	0	0
$171$	4102.83	1.83480
$172$	−874.776	−0.387797
$173$	2534.30	1.11375	0.556877	−	0.830595i	$-0.311999\pi$
$173$	2534.30	1.11375	0.556877	+	0.830595i	$0.311999\pi$
$174$	53.0244	0.0231021
$175$	0	0
$176$	−1648.21	−0.705903
$177$	−606.437	−0.257529
$178$	−864.818	−0.364162
$179$	3550.27	1.48245	0.741227	−	0.671254i	$-0.234244\pi$
$179$	3550.27	1.48245	0.741227	+	0.671254i	$0.234244\pi$
$180$	0	0
$181$	−3034.68	−1.24622	−0.623110	−	0.782135i	$-0.714131\pi$
$181$	−3034.68	−1.24622	−0.623110	+	0.782135i	$0.714131\pi$
$182$	−1270.62	−0.517499
$183$	−168.338	−0.0679996
$184$	−1028.48	−0.412066
$185$	0	0
$186$	−105.874	−0.0417370
$187$	−178.703	−0.0698827
$188$	494.559	0.191859
$189$	−895.937	−0.344814
$190$	0	0
$191$	2224.00	0.842529	0.421265	−	0.906938i	$-0.361586\pi$
$191$	2224.00	0.842529	0.421265	+	0.906938i	$0.361586\pi$
$192$	428.126	0.160924
$193$	632.830	0.236021	0.118011	−	0.993012i	$-0.462348\pi$
$193$	632.830	0.236021	0.118011	+	0.993012i	$0.462348\pi$
$194$	−2002.39	−0.741046
$195$	0	0
$196$	−319.817	−0.116551
$197$	−1369.80	−0.495404	−0.247702	−	0.968836i	$-0.579675\pi$
$197$	−1369.80	−0.495404	−0.247702	+	0.968836i	$0.579675\pi$
$198$	−2508.95	−0.900523
$199$	1416.38	0.504544	0.252272	−	0.967656i	$-0.418822\pi$
$199$	1416.38	0.504544	0.252272	+	0.967656i	$0.418822\pi$
$200$	0	0
$201$	397.219	0.139391
$202$	−2361.13	−0.822417
$203$	642.122	0.222010
$204$	7.47360	0.00256498
$205$	0	0
$206$	2938.89	0.993991
$207$	−1106.80	−0.371632
$208$	996.222	0.332094
$209$	−6105.54	−2.02071
$210$	0	0
$211$	−896.432	−0.292478	−0.146239	−	0.989249i	$-0.546717\pi$
$211$	−896.432	−0.292478	−0.146239	+	0.989249i	$0.546717\pi$
$212$	1462.63	0.473838
$213$	−213.512	−0.0686837
$214$	1706.95	0.545257
$215$	0	0
$216$	993.623	0.312998
$217$	−1282.13	−0.401091
$218$	−3611.99	−1.12218
$219$	−930.868	−0.287225
$220$	0	0
$221$	108.013	0.0328765
$222$	−430.039	−0.130010
$223$	2268.94	0.681344	0.340672	−	0.940182i	$-0.389345\pi$
$223$	2268.94	0.681344	0.340672	+	0.940182i	$0.389345\pi$
$224$	2109.42	0.629202
$225$	0	0
$226$	2576.53	0.758356
$227$	2078.09	0.607610	0.303805	−	0.952734i	$-0.401743\pi$
$227$	2078.09	0.607610	0.303805	+	0.952734i	$0.401743\pi$
$228$	255.342	0.0741685
$229$	−3715.05	−1.07204	−0.536020	−	0.844205i	$-0.680073\pi$
$229$	−3715.05	−1.07204	−0.536020	+	0.844205i	$0.680073\pi$
$230$	0	0
$231$	659.478	0.187837
$232$	−712.134	−0.201525
$233$	−2521.35	−0.708923	−0.354461	−	0.935071i	$-0.615336\pi$
$233$	−2521.35	−0.708923	−0.354461	+	0.935071i	$0.615336\pi$
$234$	1516.47	0.423654
$235$	0	0
$236$	1738.83	0.479612
$237$	462.933	0.126881
$238$	−242.912	−0.0661581
$239$	3940.04	1.06636	0.533179	−	0.846002i	$-0.320997\pi$
$239$	3940.04	1.06636	0.533179	+	0.846002i	$0.320997\pi$
$240$	0	0
$241$	−1973.06	−0.527369	−0.263684	−	0.964609i	$-0.584938\pi$
$241$	−1973.06	−0.527369	−0.263684	+	0.964609i	$0.584938\pi$
$242$	520.327	0.138214
$243$	1609.68	0.424942
$244$	482.675	0.126640
$245$	0	0
$246$	−320.270	−0.0830068
$247$	3690.34	0.950650
$248$	1421.92	0.364082
$249$	−390.411	−0.0993627
$250$	0	0
$251$	−1236.65	−0.310982	−0.155491	−	0.987837i	$-0.549696\pi$
$251$	−1236.65	−0.310982	−0.155491	+	0.987837i	$0.549696\pi$
$252$	1270.67	0.317637
$253$	1647.06	0.409287
$254$	2847.75	0.703479
$255$	0	0
$256$	−3067.52	−0.748907
$257$	−2918.10	−0.708272	−0.354136	−	0.935194i	$-0.615225\pi$
$257$	−2918.10	−0.708272	−0.354136	+	0.935194i	$0.615225\pi$
$258$	736.546	0.177734
$259$	−5207.74	−1.24939
$260$	0	0
$261$	−766.366	−0.181750
$262$	−5691.43	−1.34205
$263$	310.789	0.0728673	0.0364336	−	0.999336i	$-0.488400\pi$
$263$	310.789	0.0728673	0.0364336	+	0.999336i	$0.488400\pi$
$264$	−731.382	−0.170506
$265$	0	0
$266$	−8299.28	−1.91301
$267$	−271.301	−0.0621848
$268$	−1138.95	−0.259598
$269$	−1839.98	−0.417047	−0.208523	−	0.978017i	$-0.566866\pi$
$269$	−1839.98	−0.417047	−0.208523	+	0.978017i	$0.566866\pi$
$270$	0	0
$271$	5187.35	1.16277	0.581383	−	0.813630i	$-0.302512\pi$
$271$	5187.35	1.16277	0.581383	+	0.813630i	$0.302512\pi$
$272$	190.453	0.0424556
$273$	−398.605	−0.0883687
$274$	−1744.24	−0.384575
$275$	0	0
$276$	−68.8821	−0.0150225
$277$	−8666.41	−1.87983	−0.939917	−	0.341403i	$-0.889098\pi$
$277$	−8666.41	−1.87983	−0.939917	+	0.341403i	$0.889098\pi$
$278$	3375.66	0.728268
$279$	1530.21	0.328356
$280$	0	0
$281$	7856.96	1.66800	0.833998	−	0.551767i	$-0.186046\pi$
$281$	7856.96	1.66800	0.833998	+	0.551767i	$0.186046\pi$
$282$	−416.410	−0.0879321
$283$	3054.71	0.641638	0.320819	−	0.947141i	$-0.396042\pi$
$283$	3054.71	0.641638	0.320819	+	0.947141i	$0.396042\pi$
$284$	612.203	0.127914
$285$	0	0
$286$	−2256.71	−0.466580
$287$	−3878.45	−0.797692
$288$	−2517.57	−0.515101
$289$	−4892.35	−0.995797
$290$	0	0
$291$	−628.166	−0.126542
$292$	2669.07	0.534917
$293$	−2847.83	−0.567822	−0.283911	−	0.958851i	$-0.591632\pi$
$293$	−2847.83	−0.567822	−0.283911	+	0.958851i	$0.591632\pi$
$294$	269.280	0.0534175
$295$	0	0
$296$	5775.55	1.13411
$297$	−1591.24	−0.310887
$298$	6833.74	1.32842
$299$	−995.522	−0.192550
$300$	0	0
$301$	8919.53	1.70802
$302$	4117.64	0.784581
$303$	−740.705	−0.140437
$304$	6506.99	1.22764
$305$	0	0
$306$	289.913	0.0541608
$307$	2470.79	0.459334	0.229667	−	0.973269i	$-0.426236\pi$
$307$	2470.79	0.459334	0.229667	+	0.973269i	$0.426236\pi$
$308$	−1890.92	−0.349822
$309$	921.955	0.169735
$310$	0	0
$311$	−5653.29	−1.03077	−0.515384	−	0.856959i	$-0.672351\pi$
$311$	−5653.29	−1.03077	−0.515384	+	0.856959i	$0.672351\pi$
$312$	442.066	0.0802149
$313$	8289.72	1.49701	0.748503	−	0.663132i	$-0.230773\pi$
$313$	8289.72	1.49701	0.748503	+	0.663132i	$0.230773\pi$
$314$	6447.97	1.15885
$315$	0	0
$316$	−1327.37	−0.236298
$317$	−2577.06	−0.456600	−0.228300	−	0.973591i	$-0.573317\pi$
$317$	−2577.06	−0.456600	−0.228300	+	0.973591i	$0.573317\pi$
$318$	−1231.51	−0.217168
$319$	1140.45	0.200166
$320$	0	0
$321$	535.486	0.0931088
$322$	2238.85	0.387473
$323$	705.502	0.121533
$324$	−1482.90	−0.254269
$325$	0	0
$326$	5195.19	0.882622
$327$	−1133.11	−0.191625
$328$	4301.33	0.724088
$329$	−5042.70	−0.845024
$330$	0	0
$331$	7672.12	1.27401	0.637006	−	0.770859i	$-0.280173\pi$
$331$	7672.12	1.27401	0.637006	+	0.770859i	$0.280173\pi$
$332$	1119.42	0.185049
$333$	6215.38	1.02283
$334$	−2412.73	−0.395266
$335$	0	0
$336$	−702.840	−0.114116
$337$	−3650.77	−0.590120	−0.295060	−	0.955479i	$-0.595340\pi$
$337$	−3650.77	−0.590120	−0.295060	+	0.955479i	$0.595340\pi$
$338$	−3940.02	−0.634049
$339$	808.280	0.129498
$340$	0	0
$341$	−2277.15	−0.361626
$342$	9905.10	1.56610
$343$	−4333.79	−0.682223
$344$	−9892.05	−1.55042
$345$	0	0
$346$	6118.35	0.950649
$347$	8737.06	1.35167	0.675835	−	0.737053i	$-0.263783\pi$
$347$	8737.06	1.35167	0.675835	+	0.737053i	$0.263783\pi$
$348$	−47.6952	−0.00734692
$349$	−2143.83	−0.328816	−0.164408	−	0.986392i	$-0.552571\pi$
$349$	−2143.83	−0.328816	−0.164408	+	0.986392i	$0.552571\pi$
$350$	0	0
$351$	961.787	0.146258
$352$	3746.46	0.567293
$353$	5111.17	0.770651	0.385326	−	0.922781i	$-0.374089\pi$
$353$	5111.17	0.770651	0.385326	+	0.922781i	$0.374089\pi$
$354$	−1464.07	−0.219814
$355$	0	0
$356$	777.900	0.115811
$357$	−76.2035	−0.0112972
$358$	8571.10	1.26535
$359$	4520.87	0.664630	0.332315	−	0.943168i	$-0.392170\pi$
$359$	4520.87	0.664630	0.332315	+	0.943168i	$0.392170\pi$
$360$	0	0
$361$	17245.1	2.51422
$362$	−7326.35	−1.06371
$363$	163.231	0.0236017
$364$	1142.92	0.164575
$365$	0	0
$366$	−406.404	−0.0580413
$367$	486.272	0.0691641	0.0345820	−	0.999402i	$-0.488990\pi$
$367$	486.272	0.0691641	0.0345820	+	0.999402i	$0.488990\pi$
$368$	−1755.36	−0.248653
$369$	4628.89	0.653036
$370$	0	0
$371$	−14913.5	−2.08698
$372$	95.2333	0.0132732
$373$	−10053.1	−1.39552	−0.697758	−	0.716333i	$-0.745819\pi$
$373$	−10053.1	−1.39552	−0.697758	+	0.716333i	$0.745819\pi$
$374$	−431.427	−0.0596486
$375$	0	0
$376$	5592.52	0.767053
$377$	−689.317	−0.0941688
$378$	−2162.98	−0.294317
$379$	−11602.8	−1.57255	−0.786273	−	0.617879i	$-0.787992\pi$
$379$	−11602.8	−1.57255	−0.786273	+	0.617879i	$0.787992\pi$
$380$	0	0
$381$	893.363	0.120127
$382$	5369.22	0.719144
$383$	4161.38	0.555187	0.277593	−	0.960699i	$-0.410463\pi$
$383$	4161.38	0.555187	0.277593	+	0.960699i	$0.410463\pi$
$384$	456.378	0.0606496
$385$	0	0
$386$	1527.79	0.201457
$387$	−10645.4	−1.39828
$388$	1801.14	0.235667
$389$	−6843.95	−0.892036	−0.446018	−	0.895024i	$-0.647158\pi$
$389$	−6843.95	−0.892036	−0.446018	+	0.895024i	$0.647158\pi$
$390$	0	0
$391$	−190.319	−0.0246160
$392$	−3616.52	−0.465974
$393$	−1785.45	−0.229171
$394$	−3307.00	−0.422854
$395$	0	0
$396$	2256.79	0.286384
$397$	−5474.73	−0.692112	−0.346056	−	0.938214i	$-0.612479\pi$
$397$	−5474.73	−0.692112	−0.346056	+	0.938214i	$0.612479\pi$
$398$	3419.43	0.430655
$399$	−2603.55	−0.326669
$400$	0	0
$401$	890.013	0.110836	0.0554178	−	0.998463i	$-0.482351\pi$
$401$	890.013	0.110836	0.0554178	+	0.998463i	$0.482351\pi$
$402$	958.972	0.118978
$403$	1376.37	0.170128
$404$	2123.82	0.261545
$405$	0	0
$406$	1550.22	0.189498
$407$	−9249.29	−1.12646
$408$	84.5121	0.0102548
$409$	8107.81	0.980209	0.490104	−	0.871664i	$-0.336959\pi$
$409$	8107.81	0.980209	0.490104	+	0.871664i	$0.336959\pi$
$410$	0	0
$411$	−547.184	−0.0656706
$412$	−2643.52	−0.316109
$413$	−17729.8	−2.11241
$414$	−2672.05	−0.317207
$415$	0	0
$416$	−2264.45	−0.266885
$417$	1058.97	0.124360
$418$	−14740.1	−1.72479
$419$	4237.59	0.494080	0.247040	−	0.969005i	$-0.420542\pi$
$419$	4237.59	0.494080	0.247040	+	0.969005i	$0.420542\pi$
$420$	0	0
$421$	−953.634	−0.110397	−0.0551987	−	0.998475i	$-0.517579\pi$
$421$	−953.634	−0.110397	−0.0551987	+	0.998475i	$0.517579\pi$
$422$	−2164.18	−0.249646
$423$	6018.41	0.691785
$424$	16539.5	1.89441
$425$	0	0
$426$	−515.464	−0.0586252
$427$	−4921.53	−0.557774
$428$	−1535.40	−0.173402
$429$	−707.949	−0.0796738
$430$	0	0
$431$	−10098.8	−1.12864	−0.564318	−	0.825557i	$-0.690861\pi$
$431$	−10098.8	−1.12864	−0.564318	+	0.825557i	$0.690861\pi$
$432$	1695.87	0.188872
$433$	12833.1	1.42430	0.712148	−	0.702029i	$-0.247722\pi$
$433$	12833.1	1.42430	0.712148	+	0.702029i	$0.247722\pi$
$434$	−3095.34	−0.342352
$435$	0	0
$436$	3248.97	0.356875
$437$	−6502.42	−0.711792
$438$	−2247.31	−0.245162
$439$	−14434.8	−1.56932	−0.784662	−	0.619924i	$-0.787164\pi$
$439$	−14434.8	−1.56932	−0.784662	+	0.619924i	$0.787164\pi$
$440$	0	0
$441$	−3891.93	−0.420249
$442$	260.765	0.0280619
$443$	7020.65	0.752959	0.376480	−	0.926425i	$-0.377134\pi$
$443$	7020.65	0.752959	0.376480	+	0.926425i	$0.377134\pi$
$444$	386.818	0.0413458
$445$	0	0
$446$	5477.71	0.581563
$447$	2143.80	0.226842
$448$	12516.7	1.32000
$449$	13210.5	1.38851	0.694254	−	0.719730i	$-0.255735\pi$
$449$	13210.5	1.38851	0.694254	+	0.719730i	$0.255735\pi$
$450$	0	0
$451$	−6888.38	−0.719205
$452$	−2317.58	−0.241172
$453$	1291.74	0.133976
$454$	5016.95	0.518628
$455$	0	0
$456$	2887.43	0.296527
$457$	2811.18	0.287749	0.143875	−	0.989596i	$-0.454044\pi$
$457$	2811.18	0.287749	0.143875	+	0.989596i	$0.454044\pi$
$458$	−8968.92	−0.915044
$459$	183.870	0.0186979
$460$	0	0
$461$	−9645.10	−0.974441	−0.487220	−	0.873279i	$-0.661989\pi$
$461$	−9645.10	−0.974441	−0.487220	+	0.873279i	$0.661989\pi$
$462$	1592.12	0.160329
$463$	−6923.23	−0.694924	−0.347462	−	0.937694i	$-0.612956\pi$
$463$	−6923.23	−0.694924	−0.347462	+	0.937694i	$0.612956\pi$
$464$	−1215.44	−0.121606
$465$	0	0
$466$	−6087.07	−0.605103
$467$	124.351	0.0123218	0.00616089	−	0.999981i	$-0.498039\pi$
$467$	124.351	0.0123218	0.00616089	+	0.999981i	$0.498039\pi$
$468$	−1364.06	−0.134730
$469$	11613.1	1.14337
$470$	0	0
$471$	2022.78	0.197887
$472$	19662.9	1.91749
$473$	15841.7	1.53996
$474$	1117.62	0.108300
$475$	0	0
$476$	218.498	0.0210396
$477$	17799.1	1.70852
$478$	9512.09	0.910194
$479$	−4461.48	−0.425575	−0.212788	−	0.977098i	$-0.568254\pi$
$479$	−4461.48	−0.425575	−0.212788	+	0.977098i	$0.568254\pi$
$480$	0	0
$481$	5590.50	0.529948
$482$	−4763.39	−0.450137
$483$	702.347	0.0661654
$484$	−468.032	−0.0439549
$485$	0	0
$486$	3886.10	0.362710
$487$	5660.72	0.526718	0.263359	−	0.964698i	$-0.415170\pi$
$487$	5660.72	0.526718	0.263359	+	0.964698i	$0.415170\pi$
$488$	5458.14	0.506308
$489$	1629.77	0.150718
$490$	0	0
$491$	5587.50	0.513565	0.256782	−	0.966469i	$-0.417338\pi$
$491$	5587.50	0.513565	0.256782	+	0.966469i	$0.417338\pi$
$492$	288.081	0.0263978
$493$	−131.781	−0.0120387
$494$	8909.26	0.811431
$495$	0	0
$496$	2426.88	0.219698
$497$	−6242.24	−0.563386
$498$	−942.537	−0.0848114
$499$	−4210.19	−0.377703	−0.188851	−	0.982006i	$-0.560476\pi$
$499$	−4210.19	−0.377703	−0.188851	+	0.982006i	$0.560476\pi$
$500$	0	0
$501$	−756.895	−0.0674962
$502$	−2985.53	−0.265440
$503$	−10796.7	−0.957063	−0.478532	−	0.878070i	$-0.658831\pi$
$503$	−10796.7	−0.957063	−0.478532	+	0.878070i	$0.658831\pi$
$504$	14368.8	1.26992
$505$	0	0
$506$	3976.35	0.349348
$507$	−1236.02	−0.108271
$508$	−2561.54	−0.223720
$509$	14983.6	1.30479	0.652395	−	0.757879i	$-0.273764\pi$
$509$	14983.6	1.30479	0.652395	+	0.757879i	$0.273764\pi$
$510$	0	0
$511$	−27214.8	−2.35599
$512$	−12226.4	−1.05534
$513$	6282.07	0.540663
$514$	−7044.91	−0.604548
$515$	0	0
$516$	−662.520	−0.0565229
$517$	−8956.17	−0.761880
$518$	−12572.6	−1.06643
$519$	1919.38	0.162334
$520$	0	0
$521$	−10770.3	−0.905671	−0.452836	−	0.891594i	$-0.649588\pi$
$521$	−10770.3	−0.905671	−0.452836	+	0.891594i	$0.649588\pi$
$522$	−1850.17	−0.155134
$523$	7538.93	0.630314	0.315157	−	0.949040i	$-0.397943\pi$
$523$	7538.93	0.630314	0.315157	+	0.949040i	$0.397943\pi$
$524$	5119.41	0.426799
$525$	0	0
$526$	750.312	0.0621961
$527$	263.127	0.0217495
$528$	−1248.29	−0.102888
$529$	−10412.9	−0.855829
$530$	0	0
$531$	21160.3	1.72934
$532$	7465.16	0.608375
$533$	4163.51	0.338352
$534$	−654.978	−0.0530781
$535$	0	0
$536$	−12879.3	−1.03787
$537$	2688.83	0.216073
$538$	−4442.11	−0.355972
$539$	5791.69	0.462831
$540$	0	0
$541$	595.816	0.0473496	0.0236748	−	0.999720i	$-0.492463\pi$
$541$	595.816	0.0473496	0.0236748	+	0.999720i	$0.492463\pi$
$542$	12523.4	0.992482
$543$	−2298.34	−0.181641
$544$	−432.908	−0.0341191
$545$	0	0
$546$	−962.317	−0.0754274
$547$	−12703.4	−0.992978	−0.496489	−	0.868043i	$-0.665378\pi$
$547$	−12703.4	−0.992978	−0.496489	+	0.868043i	$0.665378\pi$
$548$	1568.94	0.122302
$549$	5873.80	0.456626
$550$	0	0
$551$	−4502.39	−0.348109
$552$	−778.925	−0.0600603
$553$	13534.3	1.04075
$554$	−20922.6	−1.60454
$555$	0	0
$556$	−3036.39	−0.231604
$557$	14973.0	1.13901	0.569503	−	0.821990i	$-0.307136\pi$
$557$	14973.0	1.13901	0.569503	+	0.821990i	$0.307136\pi$
$558$	3694.25	0.280269
$559$	−9575.10	−0.724479
$560$	0	0
$561$	−135.342	−0.0101857
$562$	18968.4	1.42372
$563$	10439.3	0.781466	0.390733	−	0.920504i	$-0.372222\pi$
$563$	10439.3	0.781466	0.390733	+	0.920504i	$0.372222\pi$
$564$	374.559	0.0279641
$565$	0	0
$566$	7374.71	0.547672
$567$	15120.2	1.11991
$568$	6922.85	0.511402
$569$	−8859.72	−0.652757	−0.326379	−	0.945239i	$-0.605828\pi$
$569$	−8859.72	−0.652757	−0.326379	+	0.945239i	$0.605828\pi$
$570$	0	0
$571$	−5078.17	−0.372180	−0.186090	−	0.982533i	$-0.559582\pi$
$571$	−5078.17	−0.372180	−0.186090	+	0.982533i	$0.559582\pi$
$572$	2029.90	0.148382
$573$	1684.37	0.122802
$574$	−9363.40	−0.680873
$575$	0	0
$576$	−14938.5	−1.08062
$577$	−20457.2	−1.47599	−0.737994	−	0.674808i	$-0.764227\pi$
$577$	−20457.2	−1.47599	−0.737994	+	0.674808i	$0.764227\pi$
$578$	−11811.2	−0.849966
$579$	479.280	0.0344010
$580$	0	0
$581$	−11414.1	−0.815034
$582$	−1516.53	−0.108010
$583$	−26487.3	−1.88164
$584$	30182.1	2.13860
$585$	0	0
$586$	−6875.27	−0.484667
$587$	−4355.22	−0.306234	−0.153117	−	0.988208i	$-0.548931\pi$
$587$	−4355.22	−0.306234	−0.153117	+	0.988208i	$0.548931\pi$
$588$	−242.216	−0.0169878
$589$	8989.96	0.628905
$590$	0	0
$591$	−1037.43	−0.0722070
$592$	9857.46	0.684357
$593$	−4342.49	−0.300716	−0.150358	−	0.988632i	$-0.548043\pi$
$593$	−4342.49	−0.300716	−0.150358	+	0.988632i	$0.548043\pi$
$594$	−3841.60	−0.265358
$595$	0	0
$596$	−6146.92	−0.422462
$597$	1072.71	0.0735392
$598$	−2403.40	−0.164352
$599$	−12761.8	−0.870506	−0.435253	−	0.900308i	$-0.643341\pi$
$599$	−12761.8	−0.870506	−0.435253	+	0.900308i	$0.643341\pi$
$600$	0	0
$601$	−2804.87	−0.190371	−0.0951857	−	0.995460i	$-0.530344\pi$
$601$	−2804.87	−0.190371	−0.0951857	+	0.995460i	$0.530344\pi$
$602$	21533.6	1.45788
$603$	−13860.1	−0.936032
$604$	−3703.80	−0.249512
$605$	0	0
$606$	−1788.22	−0.119870
$607$	−12033.5	−0.804654	−0.402327	−	0.915496i	$-0.631798\pi$
$607$	−12033.5	−0.804654	−0.402327	+	0.915496i	$0.631798\pi$
$608$	−14790.7	−0.986580
$609$	486.317	0.0323589
$610$	0	0
$611$	5413.33	0.358429
$612$	−260.775	−0.0172242
$613$	−7993.67	−0.526690	−0.263345	−	0.964702i	$-0.584826\pi$
$613$	−7993.67	−0.526690	−0.263345	+	0.964702i	$0.584826\pi$
$614$	5965.02	0.392066
$615$	0	0
$616$	−21382.7	−1.39859
$617$	−9922.51	−0.647432	−0.323716	−	0.946154i	$-0.604932\pi$
$617$	−9922.51	−0.647432	−0.323716	+	0.946154i	$0.604932\pi$
$618$	2225.80	0.144878
$619$	−15401.4	−1.00005	−0.500027	−	0.866010i	$-0.666676\pi$
$619$	−15401.4	−1.00005	−0.500027	+	0.866010i	$0.666676\pi$
$620$	0	0
$621$	−1694.68	−0.109509
$622$	−13648.3	−0.879816
$623$	−7931.74	−0.510078
$624$	754.498	0.0484040
$625$	0	0
$626$	20013.2	1.27777
$627$	−4624.08	−0.294527
$628$	−5799.92	−0.368538
$629$	1068.77	0.0677497
$630$	0	0
$631$	−3776.97	−0.238287	−0.119143	−	0.992877i	$-0.538015\pi$
$631$	−3776.97	−0.238287	−0.119143	+	0.992877i	$0.538015\pi$
$632$	−15010.0	−0.944724
$633$	−678.921	−0.0426298
$634$	−6221.57	−0.389732
$635$	0	0
$636$	1107.74	0.0690638
$637$	−3500.64	−0.217740
$638$	2753.29	0.170853
$639$	7450.05	0.461220
$640$	0	0
$641$	464.125	0.0285988	0.0142994	−	0.999898i	$-0.495448\pi$
$641$	464.125	0.0285988	0.0142994	+	0.999898i	$0.495448\pi$
$642$	1292.78	0.0794733
$643$	−7607.61	−0.466586	−0.233293	−	0.972406i	$-0.574950\pi$
$643$	−7607.61	−0.466586	−0.233293	+	0.972406i	$0.574950\pi$
$644$	−2013.84	−0.123224
$645$	0	0
$646$	1703.23	0.103735
$647$	−7776.85	−0.472550	−0.236275	−	0.971686i	$-0.575927\pi$
$647$	−7776.85	−0.472550	−0.236275	+	0.971686i	$0.575927\pi$
$648$	−16768.7	−1.01657
$649$	−31489.2	−1.90456
$650$	0	0
$651$	−971.033	−0.0584605
$652$	−4673.04	−0.280691
$653$	24486.1	1.46740	0.733702	−	0.679471i	$-0.237791\pi$
$653$	24486.1	1.46740	0.733702	+	0.679471i	$0.237791\pi$
$654$	−2735.57	−0.163562
$655$	0	0
$656$	7341.31	0.436936
$657$	32480.6	1.92875
$658$	−12174.2	−0.721273
$659$	910.966	0.0538486	0.0269243	−	0.999637i	$-0.491429\pi$
$659$	910.966	0.0538486	0.0269243	+	0.999637i	$0.491429\pi$
$660$	0	0
$661$	5826.64	0.342859	0.171430	−	0.985196i	$-0.445161\pi$
$661$	5826.64	0.342859	0.171430	+	0.985196i	$0.445161\pi$
$662$	18522.1	1.08744
$663$	81.8043	0.00479188
$664$	12658.6	0.739830
$665$	0	0
$666$	15005.3	0.873036
$667$	1214.59	0.0705081
$668$	2170.24	0.125702
$669$	1718.40	0.0993085
$670$	0	0
$671$	−8740.97	−0.502893
$672$	1597.59	0.0917086
$673$	−27236.0	−1.55999	−0.779994	−	0.625788i	$-0.784778\pi$
$673$	−27236.0	−1.55999	−0.779994	+	0.625788i	$0.784778\pi$
$674$	−8813.75	−0.503699
$675$	0	0
$676$	3544.03	0.201640
$677$	−8989.70	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$677$	−8989.70	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$678$	1951.36	0.110533
$679$	−18365.0	−1.03798
$680$	0	0
$681$	1573.86	0.0885616
$682$	−5497.52	−0.308667
$683$	−6934.65	−0.388502	−0.194251	−	0.980952i	$-0.562228\pi$
$683$	−6934.65	−0.388502	−0.194251	+	0.980952i	$0.562228\pi$
$684$	−8909.59	−0.498051
$685$	0	0
$686$	−10462.7	−0.582314
$687$	−2813.63	−0.156254
$688$	−16883.3	−0.935567
$689$	16009.6	0.885221
$690$	0	0
$691$	5234.54	0.288178	0.144089	−	0.989565i	$-0.453975\pi$
$691$	5234.54	0.288178	0.144089	+	0.989565i	$0.453975\pi$
$692$	−5503.43	−0.302325
$693$	−23011.0	−1.26135
$694$	21093.1	1.15372
$695$	0	0
$696$	−539.341	−0.0293731
$697$	795.961	0.0432556
$698$	−5175.67	−0.280662
$699$	−1909.57	−0.103328
$700$	0	0
$701$	−33713.7	−1.81647	−0.908237	−	0.418457i	$-0.862571\pi$
$701$	−33713.7	−1.81647	−0.908237	+	0.418457i	$0.862571\pi$
$702$	2321.96	0.124839
$703$	36515.3	1.95903
$704$	22230.5	1.19012
$705$	0	0
$706$	12339.4	0.657792
$707$	−21655.2	−1.15195
$708$	1316.92	0.0699053
$709$	−12687.3	−0.672049	−0.336025	−	0.941853i	$-0.609083\pi$
$709$	−12687.3	−0.672049	−0.336025	+	0.941853i	$0.609083\pi$
$710$	0	0
$711$	−16153.1	−0.852021
$712$	8796.56	0.463013
$713$	−2425.17	−0.127382
$714$	−183.971	−0.00964280
$715$	0	0
$716$	−7709.66	−0.402407
$717$	2984.02	0.155426
$718$	10914.3	0.567297
$719$	30604.9	1.58744	0.793720	−	0.608283i	$-0.208141\pi$
$719$	30604.9	1.58744	0.793720	+	0.608283i	$0.208141\pi$
$720$	0	0
$721$	26954.2	1.39227
$722$	41633.3	2.14602
$723$	−1494.31	−0.0768661
$724$	6590.02	0.338282
$725$	0	0
$726$	394.075	0.0201453
$727$	−3727.96	−0.190182	−0.0950911	−	0.995469i	$-0.530314\pi$
$727$	−3727.96	−0.190182	−0.0950911	+	0.995469i	$0.530314\pi$
$728$	12924.2	0.657972
$729$	−17218.3	−0.874782
$730$	0	0
$731$	−1830.52	−0.0926189
$732$	365.559	0.0184583
$733$	−1107.21	−0.0557921	−0.0278960	−	0.999611i	$-0.508881\pi$
$733$	−1107.21	−0.0557921	−0.0278960	+	0.999611i	$0.508881\pi$
$734$	1173.97	0.0590352
$735$	0	0
$736$	3990.00	0.199828
$737$	20625.6	1.03087
$738$	11175.1	0.557401
$739$	−29127.7	−1.44991	−0.724953	−	0.688798i	$-0.758139\pi$
$739$	−29127.7	−1.44991	−0.724953	+	0.688798i	$0.758139\pi$
$740$	0	0
$741$	2794.91	0.138561
$742$	−36004.3	−1.78135
$743$	−12162.8	−0.600552	−0.300276	−	0.953852i	$-0.597079\pi$
$743$	−12162.8	−0.600552	−0.300276	+	0.953852i	$0.597079\pi$
$744$	1076.91	0.0530663
$745$	0	0
$746$	−24270.2	−1.19115
$747$	13622.6	0.667233
$748$	388.067	0.0189694
$749$	15655.5	0.763736
$750$	0	0
$751$	−25067.6	−1.21802	−0.609008	−	0.793164i	$-0.708432\pi$
$751$	−25067.6	−1.21802	−0.609008	+	0.793164i	$0.708432\pi$
$752$	9545.06	0.462862
$753$	−936.587	−0.0453269
$754$	−1664.16	−0.0803781
$755$	0	0
$756$	1945.59	0.0935986
$757$	12020.6	0.577140	0.288570	−	0.957459i	$-0.406820\pi$
$757$	12020.6	0.577140	0.288570	+	0.957459i	$0.406820\pi$
$758$	−28011.6	−1.34225
$759$	1247.41	0.0596552
$760$	0	0
$761$	9255.42	0.440879	0.220439	−	0.975401i	$-0.429251\pi$
$761$	9255.42	0.440879	0.220439	+	0.975401i	$0.429251\pi$
$762$	2156.77	0.102535
$763$	−33127.6	−1.57182
$764$	−4829.58	−0.228702
$765$	0	0
$766$	10046.5	0.473881
$767$	19032.9	0.896007
$768$	−2323.22	−0.109156
$769$	28690.1	1.34537	0.672687	−	0.739928i	$-0.265140\pi$
$769$	28690.1	1.34537	0.672687	+	0.739928i	$0.265140\pi$
$770$	0	0
$771$	−2210.05	−0.103233
$772$	−1374.24	−0.0640672
$773$	8984.36	0.418040	0.209020	−	0.977911i	$-0.432973\pi$
$773$	8984.36	0.418040	0.209020	+	0.977911i	$0.432973\pi$
$774$	−25700.2	−1.19351
$775$	0	0
$776$	20367.4	0.942201
$777$	−3944.13	−0.182104
$778$	−16522.8	−0.761400
$779$	27194.7	1.25077
$780$	0	0
$781$	−11086.6	−0.507952
$782$	−459.472	−0.0210111
$783$	−1173.43	−0.0535566
$784$	−6172.51	−0.281182
$785$	0	0
$786$	−4310.46	−0.195609
$787$	5257.13	0.238115	0.119058	−	0.992887i	$-0.462013\pi$
$787$	5257.13	0.238115	0.119058	+	0.992887i	$0.462013\pi$
$788$	2974.63	0.134476
$789$	235.379	0.0106207
$790$	0	0
$791$	23630.9	1.06222
$792$	25520.0	1.14497
$793$	5283.26	0.236588
$794$	−13217.2	−0.590755
$795$	0	0
$796$	−3075.76	−0.136957
$797$	−7623.92	−0.338837	−0.169419	−	0.985544i	$-0.554189\pi$
$797$	−7623.92	−0.338837	−0.169419	+	0.985544i	$0.554189\pi$
$798$	−6285.54	−0.278829
$799$	1034.90	0.0458223
$800$	0	0
$801$	9466.45	0.417579
$802$	2148.68	0.0946042
$803$	−48335.3	−2.12418
$804$	−862.591	−0.0378373
$805$	0	0
$806$	3322.84	0.145213
$807$	−1393.53	−0.0607862
$808$	24016.4	1.04566
$809$	−28238.7	−1.22722	−0.613609	−	0.789610i	$-0.710283\pi$
$809$	−28238.7	−1.22722	−0.613609	+	0.789610i	$0.710283\pi$
$810$	0	0
$811$	29851.2	1.29250	0.646251	−	0.763125i	$-0.276336\pi$
$811$	29851.2	1.29250	0.646251	+	0.763125i	$0.276336\pi$
$812$	−1394.41	−0.0602640
$813$	3928.69	0.169478
$814$	−22329.8	−0.961496
$815$	0	0
$816$	144.242	0.00618807
$817$	−62541.4	−2.67815
$818$	19574.0	0.836661
$819$	13908.4	0.593407
$820$	0	0
$821$	2043.20	0.0868552	0.0434276	−	0.999057i	$-0.486172\pi$
$821$	2043.20	0.0868552	0.0434276	+	0.999057i	$0.486172\pi$
$822$	−1321.02	−0.0560533
$823$	−123.242	−0.00521988	−0.00260994	−	0.999997i	$-0.500831\pi$
$823$	−123.242	−0.00521988	−0.00260994	+	0.999997i	$0.500831\pi$
$824$	−29893.1	−1.26381
$825$	0	0
$826$	−42803.4	−1.80305
$827$	−34335.2	−1.44371	−0.721857	−	0.692043i	$-0.756711\pi$
$827$	−34335.2	−1.44371	−0.721857	+	0.692043i	$0.756711\pi$
$828$	2403.49	0.100878
$829$	−14705.0	−0.616073	−0.308037	−	0.951375i	$-0.599672\pi$
$829$	−14705.0	−0.616073	−0.308037	+	0.951375i	$0.599672\pi$
$830$	0	0
$831$	−6563.58	−0.273993
$832$	−13436.7	−0.559894
$833$	−669.237	−0.0278364
$834$	2556.59	0.106148
$835$	0	0
$836$	13258.6	0.548515
$837$	2342.99	0.0967570
$838$	10230.4	0.421724
$839$	−22204.3	−0.913679	−0.456840	−	0.889549i	$-0.651019\pi$
$839$	−22204.3	−0.913679	−0.456840	+	0.889549i	$0.651019\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−2302.28	−0.0942300
$843$	5950.54	0.243117
$844$	1946.67	0.0793922
$845$	0	0
$846$	14529.7	0.590475
$847$	4772.22	0.193595
$848$	28228.9	1.14314
$849$	2313.51	0.0935212
$850$	0	0
$851$	−9850.54	−0.396794
$852$	463.657	0.0186439
$853$	40095.2	1.60942	0.804710	−	0.593669i	$-0.202321\pi$
$853$	40095.2	1.60942	0.804710	+	0.593669i	$0.202321\pi$
$854$	−11881.6	−0.476090
$855$	0	0
$856$	−17362.4	−0.693265
$857$	12883.7	0.513536	0.256768	−	0.966473i	$-0.417342\pi$
$857$	12883.7	0.513536	0.256768	+	0.966473i	$0.417342\pi$
$858$	−1709.14	−0.0680059
$859$	−34336.9	−1.36386	−0.681932	−	0.731416i	$-0.738860\pi$
$859$	−34336.9	−1.36386	−0.681932	+	0.731416i	$0.738860\pi$
$860$	0	0
$861$	−2937.38	−0.116267
$862$	−24380.7	−0.963351
$863$	−10864.2	−0.428531	−0.214266	−	0.976775i	$-0.568736\pi$
$863$	−10864.2	−0.428531	−0.214266	+	0.976775i	$0.568736\pi$
$864$	−3854.79	−0.151785
$865$	0	0
$866$	30981.9	1.21571
$867$	−3705.27	−0.145141
$868$	2784.24	0.108875
$869$	24037.8	0.938352
$870$	0	0
$871$	−12466.6	−0.484978
$872$	36739.6	1.42679
$873$	21918.5	0.849745
$874$	−15698.2	−0.607552
$875$	0	0
$876$	2021.45	0.0779662
$877$	−4818.40	−0.185525	−0.0927626	−	0.995688i	$-0.529570\pi$
$877$	−4818.40	−0.185525	−0.0927626	+	0.995688i	$0.529570\pi$
$878$	−34848.6	−1.33950
$879$	−2156.83	−0.0827623
$880$	0	0
$881$	−30195.7	−1.15473	−0.577366	−	0.816485i	$-0.695920\pi$
$881$	−30195.7	−1.15473	−0.577366	+	0.816485i	$0.695920\pi$
$882$	−9395.94	−0.358705
$883$	−30734.0	−1.17133	−0.585663	−	0.810555i	$-0.699166\pi$
$883$	−30734.0	−1.17133	−0.585663	+	0.810555i	$0.699166\pi$
$884$	−234.557	−0.00892422
$885$	0	0
$886$	16949.3	0.642691
$887$	43409.3	1.64323	0.821614	−	0.570045i	$-0.193074\pi$
$887$	43409.3	1.64323	0.821614	+	0.570045i	$0.193074\pi$
$888$	4374.17	0.165301
$889$	26118.3	0.985355
$890$	0	0
$891$	26854.4	1.00972
$892$	−4927.17	−0.184948
$893$	35358.1	1.32499
$894$	5175.60	0.193622
$895$	0	0
$896$	13342.6	0.497485
$897$	−753.968	−0.0280650
$898$	31892.9	1.18517
$899$	−1679.23	−0.0622976
$900$	0	0
$901$	3060.64	0.113169
$902$	−16630.0	−0.613880
$903$	6755.29	0.248950
$904$	−26207.4	−0.964209
$905$	0	0
$906$	3118.53	0.114356
$907$	7991.51	0.292562	0.146281	−	0.989243i	$-0.453270\pi$
$907$	7991.51	0.292562	0.146281	+	0.989243i	$0.453270\pi$
$908$	−4512.72	−0.164934
$909$	25845.3	0.943052
$910$	0	0
$911$	24188.5	0.879694	0.439847	−	0.898073i	$-0.355033\pi$
$911$	24188.5	0.879694	0.439847	+	0.898073i	$0.355033\pi$
$912$	4928.13	0.178933
$913$	−20272.1	−0.734840
$914$	6786.79	0.245609
$915$	0	0
$916$	8067.50	0.291002
$917$	−52199.4	−1.87980
$918$	443.902	0.0159596
$919$	27421.3	0.984273	0.492136	−	0.870518i	$-0.336216\pi$
$919$	27421.3	0.984273	0.492136	+	0.870518i	$0.336216\pi$
$920$	0	0
$921$	1871.28	0.0669497
$922$	−23285.3	−0.831737
$923$	6701.03	0.238968
$924$	−1432.10	−0.0509878
$925$	0	0
$926$	−16714.1	−0.593154
$927$	−32169.6	−1.13979
$928$	2762.74	0.0977279
$929$	−9284.12	−0.327882	−0.163941	−	0.986470i	$-0.552421\pi$
$929$	−9284.12	−0.327882	−0.163941	+	0.986470i	$0.552421\pi$
$930$	0	0
$931$	−22865.0	−0.804910
$932$	5475.29	0.192435
$933$	−4281.57	−0.150238
$934$	300.210	0.0105173
$935$	0	0
$936$	−15424.9	−0.538653
$937$	1891.00	0.0659297	0.0329649	−	0.999457i	$-0.489505\pi$
$937$	1891.00	0.0659297	0.0329649	+	0.999457i	$0.489505\pi$
$938$	28036.5	0.975932
$939$	6278.30	0.218194
$940$	0	0
$941$	15163.9	0.525322	0.262661	−	0.964888i	$-0.415400\pi$
$941$	15163.9	0.525322	0.262661	+	0.964888i	$0.415400\pi$
$942$	4883.43	0.168907
$943$	−7336.16	−0.253338
$944$	33559.7	1.15707
$945$	0	0
$946$	38245.2	1.31444
$947$	31251.8	1.07238	0.536192	−	0.844096i	$-0.319862\pi$
$947$	31251.8	1.07238	0.536192	+	0.844096i	$0.319862\pi$
$948$	−1005.29	−0.0344414
$949$	29215.1	0.999327
$950$	0	0
$951$	−1951.76	−0.0665512
$952$	2470.79	0.0841165
$953$	12521.4	0.425612	0.212806	−	0.977094i	$-0.431740\pi$
$953$	12521.4	0.425612	0.212806	+	0.977094i	$0.431740\pi$
$954$	42970.8	1.45831
$955$	0	0
$956$	−8556.07	−0.289459
$957$	863.731	0.0291750
$958$	−10771.0	−0.363251
$959$	−15997.5	−0.538670
$960$	0	0
$961$	−26438.1	−0.887451
$962$	13496.7	0.452339
$963$	−18684.6	−0.625237
$964$	4284.64	0.143152
$965$	0	0
$966$	1695.61	0.0564757
$967$	18348.5	0.610183	0.305091	−	0.952323i	$-0.401313\pi$
$967$	18348.5	0.610183	0.305091	+	0.952323i	$0.401313\pi$
$968$	−5292.55	−0.175732
$969$	534.319	0.0177139
$970$	0	0
$971$	27188.0	0.898564	0.449282	−	0.893390i	$-0.351680\pi$
$971$	27188.0	0.898564	0.449282	+	0.893390i	$0.351680\pi$
$972$	−3495.53	−0.115349
$973$	30960.1	1.02008
$974$	13666.2	0.449582
$975$	0	0
$976$	9315.71	0.305521
$977$	−4733.67	−0.155009	−0.0775044	−	0.996992i	$-0.524695\pi$
$977$	−4733.67	−0.155009	−0.0775044	+	0.996992i	$0.524695\pi$
$978$	3934.62	0.128646
$979$	−14087.3	−0.459890
$980$	0	0
$981$	39537.5	1.28678
$982$	13489.4	0.438355
$983$	43971.5	1.42673	0.713363	−	0.700795i	$-0.247171\pi$
$983$	43971.5	1.42673	0.713363	+	0.700795i	$0.247171\pi$
$984$	3257.65	0.105539
$985$	0	0
$986$	−318.146	−0.0102757
$987$	−3819.13	−0.123166
$988$	−8013.84	−0.258051
$989$	16871.4	0.542448
$990$	0	0
$991$	−14031.4	−0.449769	−0.224885	−	0.974385i	$-0.572201\pi$
$991$	−14031.4	−0.449769	−0.224885	+	0.974385i	$0.572201\pi$
$992$	−5516.39	−0.176558
$993$	5810.56	0.185692
$994$	−15070.1	−0.480880
$995$	0	0
$996$	847.807	0.0269717
$997$	−43177.4	−1.37156	−0.685779	−	0.727810i	$-0.740538\pi$
$997$	−43177.4	−1.37156	−0.685779	+	0.727810i	$0.740538\pi$
$998$	−10164.3	−0.322390
$999$	9516.73	0.301397

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} +1.82843 q^{6} +22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} +1.82843 q^{6} +22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +39.3259 q^{11} -1.64466 q^{12} -23.7696 q^{13} +53.4558 q^{14} -41.9117 q^{16} -4.54416 q^{17} -63.7990 q^{18} -155.255 q^{19} +16.7696 q^{21} +94.9411 q^{22} +41.8823 q^{23} -18.5980 q^{24} -57.3848 q^{26} -40.4630 q^{27} -48.0833 q^{28} +29.0000 q^{29} -57.9045 q^{31} +95.2670 q^{32} +29.7838 q^{33} -10.9706 q^{34} +57.3869 q^{36} -235.196 q^{37} -374.818 q^{38} -18.0021 q^{39} -175.161 q^{41} +40.4853 q^{42} +402.831 q^{43} -85.3991 q^{44} +101.113 q^{46} -227.742 q^{47} -31.7422 q^{48} +147.274 q^{49} -3.44156 q^{51} +51.6173 q^{52} -673.534 q^{53} -97.6863 q^{54} -543.730 q^{56} -117.584 q^{57} +70.0122 q^{58} -800.725 q^{59} -222.270 q^{61} -139.794 q^{62} -585.137 q^{63} +565.288 q^{64} +71.9045 q^{66} +524.479 q^{67} +9.86797 q^{68} +31.7199 q^{69} -281.917 q^{71} +648.936 q^{72} -1229.10 q^{73} -567.813 q^{74} +337.147 q^{76} +870.759 q^{77} -43.4609 q^{78} +611.247 q^{79} +682.868 q^{81} -422.877 q^{82} -515.490 q^{83} -36.4163 q^{84} +972.519 q^{86} +21.9634 q^{87} -965.701 q^{88} -358.219 q^{89} -526.309 q^{91} -90.9504 q^{92} -43.8545 q^{93} -549.818 q^{94} +72.1514 q^{96} -829.415 q^{97} +355.551 q^{98} -1039.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 2 q^{6} + 16 q^{7} - 18 q^{8} + 32 q^{9}+O(q^{10}) \) 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

Introduction

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