LMFDB - Embedded newform 575.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,4,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	575.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:	$33.9260982533$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 34x^{3} - 9x^{2} + 260x + 60 $ x^5 - 34x^3 - 9x^2 + 260*x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.98640$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.98640 q^{2} +7.39409 q^{3} +7.89136 q^{4} -29.4758 q^{6} +3.57544 q^{7} +0.433099 q^{8} +27.6726 q^{9} +O(q^{10})$	\(q-3.98640 q^{2} +7.39409 q^{3} +7.89136 q^{4} -29.4758 q^{6} +3.57544 q^{7} +0.433099 q^{8} +27.6726 q^{9} -43.8100 q^{11} +58.3494 q^{12} +65.2647 q^{13} -14.2531 q^{14} -64.8574 q^{16} -25.0257 q^{17} -110.314 q^{18} +93.1311 q^{19} +26.4371 q^{21} +174.644 q^{22} -23.0000 q^{23} +3.20238 q^{24} -260.171 q^{26} +4.97335 q^{27} +28.2151 q^{28} -84.6447 q^{29} +275.951 q^{31} +255.082 q^{32} -323.935 q^{33} +99.7625 q^{34} +218.374 q^{36} +270.136 q^{37} -371.257 q^{38} +482.574 q^{39} +178.492 q^{41} -105.389 q^{42} +46.0544 q^{43} -345.720 q^{44} +91.6871 q^{46} +390.733 q^{47} -479.561 q^{48} -330.216 q^{49} -185.043 q^{51} +515.027 q^{52} +460.760 q^{53} -19.8257 q^{54} +1.54852 q^{56} +688.620 q^{57} +337.427 q^{58} -171.714 q^{59} -432.337 q^{61} -1100.05 q^{62} +98.9417 q^{63} -498.000 q^{64} +1291.33 q^{66} -234.236 q^{67} -197.487 q^{68} -170.064 q^{69} -465.620 q^{71} +11.9850 q^{72} -363.534 q^{73} -1076.87 q^{74} +734.930 q^{76} -156.640 q^{77} -1923.73 q^{78} +430.514 q^{79} -710.387 q^{81} -711.541 q^{82} -318.020 q^{83} +208.625 q^{84} -183.591 q^{86} -625.871 q^{87} -18.9741 q^{88} +1453.20 q^{89} +233.350 q^{91} -181.501 q^{92} +2040.41 q^{93} -1557.62 q^{94} +1886.10 q^{96} +919.515 q^{97} +1316.37 q^{98} -1212.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 6 q^{3} + 33 q^{4} - 36 q^{6} + 15 q^{7} + 102 q^{8} + 79 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 6 * q^3 + 33 * q^4 - 36 * q^6 + 15 * q^7 + 102 * q^8 + 79 * q^9	\( 5 q + 5 q^{2} + 6 q^{3} + 33 q^{4} - 36 q^{6} + 15 q^{7} + 102 q^{8} + 79 q^{9} - 153 q^{11} + 30 q^{12} - 28 q^{13} + 69 q^{14} + 145 q^{16} + 341 q^{17} + 409 q^{18} + 3 q^{19} - 212 q^{21} - 11 q^{22} - 115 q^{23} - 243 q^{24} - 266 q^{26} + 243 q^{27} + 709 q^{28} - 583 q^{29} + 662 q^{31} + 681 q^{32} + 457 q^{33} + 799 q^{34} + 2047 q^{36} + 172 q^{37} - 511 q^{38} + 83 q^{39} + 344 q^{41} - 1668 q^{42} + 230 q^{43} - 503 q^{44} - 115 q^{46} + 337 q^{47} - 2050 q^{48} - 4 q^{49} - 205 q^{51} - 130 q^{52} + 942 q^{53} + 783 q^{54} + 2621 q^{56} + 890 q^{57} - 2039 q^{58} - 1166 q^{59} + 499 q^{61} + 1768 q^{62} + 1228 q^{63} + 388 q^{64} + 4627 q^{66} + 972 q^{67} + 2433 q^{68} - 138 q^{69} - 14 q^{71} + 4023 q^{72} + 229 q^{73} - 1004 q^{74} + 1529 q^{76} - 312 q^{77} - 3161 q^{78} - 88 q^{79} + 897 q^{81} - 114 q^{82} + 72 q^{83} - 6302 q^{84} + 2490 q^{86} - 1157 q^{87} - 1789 q^{88} - 90 q^{89} - 1309 q^{91} - 759 q^{92} + 3071 q^{93} - 1827 q^{94} - 4160 q^{96} + 1765 q^{97} + 4006 q^{98} - 91 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 6 * q^3 + 33 * q^4 - 36 * q^6 + 15 * q^7 + 102 * q^8 + 79 * q^9 - 153 * q^11 + 30 * q^12 - 28 * q^13 + 69 * q^14 + 145 * q^16 + 341 * q^17 + 409 * q^18 + 3 * q^19 - 212 * q^21 - 11 * q^22 - 115 * q^23 - 243 * q^24 - 266 * q^26 + 243 * q^27 + 709 * q^28 - 583 * q^29 + 662 * q^31 + 681 * q^32 + 457 * q^33 + 799 * q^34 + 2047 * q^36 + 172 * q^37 - 511 * q^38 + 83 * q^39 + 344 * q^41 - 1668 * q^42 + 230 * q^43 - 503 * q^44 - 115 * q^46 + 337 * q^47 - 2050 * q^48 - 4 * q^49 - 205 * q^51 - 130 * q^52 + 942 * q^53 + 783 * q^54 + 2621 * q^56 + 890 * q^57 - 2039 * q^58 - 1166 * q^59 + 499 * q^61 + 1768 * q^62 + 1228 * q^63 + 388 * q^64 + 4627 * q^66 + 972 * q^67 + 2433 * q^68 - 138 * q^69 - 14 * q^71 + 4023 * q^72 + 229 * q^73 - 1004 * q^74 + 1529 * q^76 - 312 * q^77 - 3161 * q^78 - 88 * q^79 + 897 * q^81 - 114 * q^82 + 72 * q^83 - 6302 * q^84 + 2490 * q^86 - 1157 * q^87 - 1789 * q^88 - 90 * q^89 - 1309 * q^91 - 759 * q^92 + 3071 * q^93 - 1827 * q^94 - 4160 * q^96 + 1765 * q^97 + 4006 * q^98 - 91 * 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 $

$2$	−3.98640	−1.40940	−0.704702	−	0.709503i	$-0.748919\pi$
$2$	−3.98640	−1.40940	−0.704702	+	0.709503i	$0.748919\pi$
$3$	7.39409	1.42299	0.711497	−	0.702689i	$-0.248018\pi$
$3$	7.39409	1.42299	0.711497	+	0.702689i	$0.248018\pi$
$4$	7.89136	0.986419
$5$	0	0
$5$	0	0
$6$	−29.4758	−2.00557
$7$	3.57544	0.193056	0.0965278	−	0.995330i	$-0.469226\pi$
$7$	3.57544	0.193056	0.0965278	+	0.995330i	$0.469226\pi$
$8$	0.433099	0.0191405
$9$	27.6726	1.02491
$10$	0	0
$11$	−43.8100	−1.20084	−0.600419	−	0.799686i	$-0.705000\pi$
$11$	−43.8100	−1.20084	−0.600419	+	0.799686i	$0.705000\pi$
$12$	58.3494	1.40367
$13$	65.2647	1.39240	0.696199	−	0.717848i	$-0.254873\pi$
$13$	65.2647	1.39240	0.696199	+	0.717848i	$0.254873\pi$
$14$	−14.2531	−0.272093
$15$	0	0
$16$	−64.8574	−1.01340
$17$	−25.0257	−0.357037	−0.178519	−	0.983937i	$-0.557130\pi$
$17$	−25.0257	−0.357037	−0.178519	+	0.983937i	$0.557130\pi$
$18$	−110.314	−1.44451
$19$	93.1311	1.12451	0.562256	−	0.826963i	$-0.309934\pi$
$19$	93.1311	1.12451	0.562256	+	0.826963i	$0.309934\pi$
$20$	0	0
$21$	26.4371	0.274717
$22$	174.644	1.69247
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	3.20238	0.0272368
$25$	0	0
$26$	−260.171	−1.96245
$27$	4.97335	0.0354490
$28$	28.2151	0.190434
$29$	−84.6447	−0.542004	−0.271002	−	0.962579i	$-0.587355\pi$
$29$	−84.6447	−0.542004	−0.271002	+	0.962579i	$0.587355\pi$
$30$	0	0
$31$	275.951	1.59879	0.799393	−	0.600809i	$-0.205155\pi$
$31$	275.951	1.59879	0.799393	+	0.600809i	$0.205155\pi$
$32$	255.082	1.40914
$33$	−323.935	−1.70879
$34$	99.7625	0.503209
$35$	0	0
$36$	218.374	1.01099
$37$	270.136	1.20027	0.600137	−	0.799897i	$-0.295113\pi$
$37$	270.136	1.20027	0.600137	+	0.799897i	$0.295113\pi$
$38$	−371.257	−1.58489
$39$	482.574	1.98137
$40$	0	0
$41$	178.492	0.679898	0.339949	−	0.940444i	$-0.389590\pi$
$41$	178.492	0.679898	0.339949	+	0.940444i	$0.389590\pi$
$42$	−105.389	−0.387187
$43$	46.0544	0.163331	0.0816654	−	0.996660i	$-0.473976\pi$
$43$	46.0544	0.163331	0.0816654	+	0.996660i	$0.473976\pi$
$44$	−345.720	−1.18453
$45$	0	0
$46$	91.6871	0.293881
$47$	390.733	1.21265	0.606323	−	0.795219i	$-0.292644\pi$
$47$	390.733	1.21265	0.606323	+	0.795219i	$0.292644\pi$
$48$	−479.561	−1.44206
$49$	−330.216	−0.962730
$50$	0	0
$51$	−185.043	−0.508062
$52$	515.027	1.37349
$53$	460.760	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$53$	460.760	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$54$	−19.8257	−0.0499619
$55$	0	0
$56$	1.54852	0.00369517
$57$	688.620	1.60017
$58$	337.427	0.763903
$59$	−171.714	−0.378902	−0.189451	−	0.981890i	$-0.560671\pi$
$59$	−171.714	−0.378902	−0.189451	+	0.981890i	$0.560671\pi$
$60$	0	0
$61$	−432.337	−0.907460	−0.453730	−	0.891139i	$-0.649907\pi$
$61$	−432.337	−0.907460	−0.453730	+	0.891139i	$0.649907\pi$
$62$	−1100.05	−2.25333
$63$	98.9417	0.197865
$64$	−498.000	−0.972657
$65$	0	0
$66$	1291.33	2.40837
$67$	−234.236	−0.427112	−0.213556	−	0.976931i	$-0.568505\pi$
$67$	−234.236	−0.427112	−0.213556	+	0.976931i	$0.568505\pi$
$68$	−197.487	−0.352188
$69$	−170.064	−0.296715
$70$	0	0
$71$	−465.620	−0.778295	−0.389147	−	0.921176i	$-0.627230\pi$
$71$	−465.620	−0.778295	−0.389147	+	0.921176i	$0.627230\pi$
$72$	11.9850	0.0196173
$73$	−363.534	−0.582856	−0.291428	−	0.956593i	$-0.594130\pi$
$73$	−363.534	−0.582856	−0.291428	+	0.956593i	$0.594130\pi$
$74$	−1076.87	−1.69167
$75$	0	0
$76$	734.930	1.10924
$77$	−156.640	−0.231828
$78$	−1923.73	−2.79256
$79$	430.514	0.613122	0.306561	−	0.951851i	$-0.400822\pi$
$79$	430.514	0.613122	0.306561	+	0.951851i	$0.400822\pi$
$80$	0	0
$81$	−710.387	−0.974468
$82$	−711.541	−0.958250
$83$	−318.020	−0.420569	−0.210285	−	0.977640i	$-0.567439\pi$
$83$	−318.020	−0.420569	−0.210285	+	0.977640i	$0.567439\pi$
$84$	208.625	0.270986
$85$	0	0
$86$	−183.591	−0.230199
$87$	−625.871	−0.771269
$88$	−18.9741	−0.0229846
$89$	1453.20	1.73077	0.865385	−	0.501108i	$-0.167074\pi$
$89$	1453.20	1.73077	0.865385	+	0.501108i	$0.167074\pi$
$90$	0	0
$91$	233.350	0.268810
$92$	−181.501	−0.205683
$93$	2040.41	2.27506
$94$	−1557.62	−1.70911
$95$	0	0
$96$	1886.10	2.00520
$97$	919.515	0.962501	0.481250	−	0.876583i	$-0.340183\pi$
$97$	919.515	0.962501	0.481250	+	0.876583i	$0.340183\pi$
$98$	1316.37	1.35687
$99$	−1212.34	−1.23075
$100$	0	0
$101$	773.116	0.761662	0.380831	−	0.924645i	$-0.375638\pi$
$101$	773.116	0.761662	0.380831	+	0.924645i	$0.375638\pi$
$102$	737.653	0.716064
$103$	2025.62	1.93776	0.968882	−	0.247521i	$-0.0796160\pi$
$103$	2025.62	1.93776	0.968882	+	0.247521i	$0.0796160\pi$
$104$	28.2661	0.0266512
$105$	0	0
$106$	−1836.77	−1.68305
$107$	−456.342	−0.412302	−0.206151	−	0.978520i	$-0.566094\pi$
$107$	−456.342	−0.412302	−0.206151	+	0.978520i	$0.566094\pi$
$108$	39.2465	0.0349675
$109$	287.101	0.252287	0.126144	−	0.992012i	$-0.459740\pi$
$109$	287.101	0.252287	0.126144	+	0.992012i	$0.459740\pi$
$110$	0	0
$111$	1997.41	1.70798
$112$	−231.894	−0.195642
$113$	1519.75	1.26519	0.632595	−	0.774483i	$-0.281990\pi$
$113$	1519.75	1.26519	0.632595	+	0.774483i	$0.281990\pi$
$114$	−2745.11	−2.25529
$115$	0	0
$116$	−667.962	−0.534644
$117$	1806.05	1.42709
$118$	684.519	0.534026
$119$	−89.4780	−0.0689280
$120$	0	0
$121$	588.318	0.442012
$122$	1723.47	1.27898
$123$	1319.79	0.967490
$124$	2177.63	1.57707
$125$	0	0
$126$	−394.421	−0.278872
$127$	−130.296	−0.0910385	−0.0455193	−	0.998963i	$-0.514494\pi$
$127$	−130.296	−0.0910385	−0.0455193	+	0.998963i	$0.514494\pi$
$128$	−55.4316	−0.0382774
$129$	340.530	0.232419
$130$	0	0
$131$	−1380.44	−0.920682	−0.460341	−	0.887742i	$-0.652273\pi$
$131$	−1380.44	−0.920682	−0.460341	+	0.887742i	$0.652273\pi$
$132$	−2556.29	−1.68558
$133$	332.984	0.217093
$134$	933.759	0.601974
$135$	0	0
$136$	−10.8386	−0.00683386
$137$	975.666	0.608444	0.304222	−	0.952601i	$-0.401604\pi$
$137$	975.666	0.608444	0.304222	+	0.952601i	$0.401604\pi$
$138$	677.943	0.418191
$139$	2733.61	1.66807	0.834034	−	0.551713i	$-0.186026\pi$
$139$	2733.61	1.66807	0.834034	+	0.551713i	$0.186026\pi$
$140$	0	0
$141$	2889.12	1.72559
$142$	1856.15	1.09693
$143$	−2859.25	−1.67205
$144$	−1794.77	−1.03864
$145$	0	0
$146$	1449.19	0.821479
$147$	−2441.65	−1.36996
$148$	2131.74	1.18397
$149$	−1040.01	−0.571820	−0.285910	−	0.958256i	$-0.592296\pi$
$149$	−1040.01	−0.571820	−0.285910	+	0.958256i	$0.592296\pi$
$150$	0	0
$151$	2822.72	1.52125	0.760627	−	0.649189i	$-0.224892\pi$
$151$	2822.72	1.52125	0.760627	+	0.649189i	$0.224892\pi$
$152$	40.3350	0.0215237
$153$	−692.527	−0.365931
$154$	624.429	0.326740
$155$	0	0
$156$	3808.16	1.95447
$157$	3318.49	1.68691	0.843454	−	0.537202i	$-0.180519\pi$
$157$	3318.49	1.68691	0.843454	+	0.537202i	$0.180519\pi$
$158$	−1716.20	−0.864137
$159$	3406.90	1.69927
$160$	0	0
$161$	−82.2351	−0.0402549
$162$	2831.88	1.37342
$163$	−954.290	−0.458563	−0.229282	−	0.973360i	$-0.573638\pi$
$163$	−954.290	−0.458563	−0.229282	+	0.973360i	$0.573638\pi$
$164$	1408.55	0.670664
$165$	0	0
$166$	1267.75	0.592752
$167$	−1137.20	−0.526942	−0.263471	−	0.964667i	$-0.584867\pi$
$167$	−1137.20	−0.526942	−0.263471	+	0.964667i	$0.584867\pi$
$168$	11.4499	0.00525821
$169$	2062.49	0.938774
$170$	0	0
$171$	2577.18	1.15253
$172$	363.431	0.161113
$173$	4348.83	1.91119	0.955593	−	0.294689i	$-0.0952160\pi$
$173$	4348.83	1.91119	0.955593	+	0.294689i	$0.0952160\pi$
$174$	2494.97	1.08703
$175$	0	0
$176$	2841.40	1.21692
$177$	−1269.67	−0.539175
$178$	−5793.02	−2.43935
$179$	−2627.76	−1.09725	−0.548625	−	0.836069i	$-0.684848\pi$
$179$	−2627.76	−1.09725	−0.548625	+	0.836069i	$0.684848\pi$
$180$	0	0
$181$	−1985.85	−0.815507	−0.407754	−	0.913092i	$-0.633688\pi$
$181$	−1985.85	−0.815507	−0.407754	+	0.913092i	$0.633688\pi$
$182$	−930.226	−0.378862
$183$	−3196.74	−1.29131
$184$	−9.96128	−0.00399106
$185$	0	0
$186$	−8133.89	−3.20648
$187$	1096.38	0.428744
$188$	3083.42	1.19618
$189$	17.7819	0.00684362
$190$	0	0
$191$	−4129.34	−1.56434	−0.782169	−	0.623066i	$-0.785887\pi$
$191$	−4129.34	−1.56434	−0.782169	+	0.623066i	$0.785887\pi$
$192$	−3682.26	−1.38408
$193$	−2623.33	−0.978401	−0.489201	−	0.872171i	$-0.662711\pi$
$193$	−2623.33	−0.978401	−0.489201	+	0.872171i	$0.662711\pi$
$194$	−3665.55	−1.35655
$195$	0	0
$196$	−2605.85	−0.949655
$197$	−3297.25	−1.19248	−0.596242	−	0.802805i	$-0.703340\pi$
$197$	−3297.25	−1.19248	−0.596242	+	0.802805i	$0.703340\pi$
$198$	4832.86	1.73463
$199$	3608.58	1.28545	0.642726	−	0.766096i	$-0.277803\pi$
$199$	3608.58	1.28545	0.642726	+	0.766096i	$0.277803\pi$
$200$	0	0
$201$	−1731.97	−0.607778
$202$	−3081.95	−1.07349
$203$	−302.642	−0.104637
$204$	−1460.24	−0.501162
$205$	0	0
$206$	−8074.90	−2.73109
$207$	−636.470	−0.213709
$208$	−4232.90	−1.41105
$209$	−4080.07	−1.35036
$210$	0	0
$211$	4486.91	1.46394	0.731971	−	0.681336i	$-0.238601\pi$
$211$	4486.91	1.46394	0.731971	+	0.681336i	$0.238601\pi$
$212$	3636.02	1.17794
$213$	−3442.84	−1.10751
$214$	1819.16	0.581100
$215$	0	0
$216$	2.15395	0.000678509 0
$217$	986.648	0.308654
$218$	−1144.50	−0.355575
$219$	−2688.01	−0.829400
$220$	0	0
$221$	−1633.30	−0.497138
$222$	−7962.48	−2.40724
$223$	−5279.87	−1.58550	−0.792749	−	0.609548i	$-0.791351\pi$
$223$	−5279.87	−1.58550	−0.792749	+	0.609548i	$0.791351\pi$
$224$	912.031	0.272043
$225$	0	0
$226$	−6058.34	−1.78316
$227$	1784.77	0.521846	0.260923	−	0.965360i	$-0.415973\pi$
$227$	1784.77	0.521846	0.260923	+	0.965360i	$0.415973\pi$
$228$	5434.14	1.57844
$229$	3938.09	1.13640	0.568201	−	0.822890i	$-0.307640\pi$
$229$	3938.09	1.13640	0.568201	+	0.822890i	$0.307640\pi$
$230$	0	0
$231$	−1158.21	−0.329890
$232$	−36.6596	−0.0103742
$233$	991.889	0.278888	0.139444	−	0.990230i	$-0.455469\pi$
$233$	991.889	0.278888	0.139444	+	0.990230i	$0.455469\pi$
$234$	−7199.62	−2.01134
$235$	0	0
$236$	−1355.05	−0.373756
$237$	3183.26	0.872469
$238$	356.695	0.0971474
$239$	4989.81	1.35048	0.675239	−	0.737599i	$-0.264041\pi$
$239$	4989.81	1.35048	0.675239	+	0.737599i	$0.264041\pi$
$240$	0	0
$241$	3317.95	0.886838	0.443419	−	0.896314i	$-0.353765\pi$
$241$	3317.95	0.886838	0.443419	+	0.896314i	$0.353765\pi$
$242$	−2345.27	−0.622973
$243$	−5386.95	−1.42211
$244$	−3411.73	−0.895137
$245$	0	0
$246$	−5261.20	−1.36358
$247$	6078.18	1.56577
$248$	119.514	0.0306015
$249$	−2351.47	−0.598467
$250$	0	0
$251$	−3640.41	−0.915460	−0.457730	−	0.889091i	$-0.651337\pi$
$251$	−3640.41	−0.915460	−0.457730	+	0.889091i	$0.651337\pi$
$252$	780.784	0.195178
$253$	1007.63	0.250392
$254$	519.411	0.128310
$255$	0	0
$256$	4204.98	1.02661
$257$	−7166.41	−1.73941	−0.869705	−	0.493571i	$-0.835691\pi$
$257$	−7166.41	−1.73941	−0.869705	+	0.493571i	$0.835691\pi$
$258$	−1357.49	−0.327572
$259$	965.856	0.231719
$260$	0	0
$261$	−2342.34	−0.555507
$262$	5502.97	1.29761
$263$	8092.80	1.89743	0.948714	−	0.316137i	$-0.102386\pi$
$263$	8092.80	1.89743	0.948714	+	0.316137i	$0.102386\pi$
$264$	−140.296	−0.0327069
$265$	0	0
$266$	−1327.41	−0.305972
$267$	10745.1	2.46288
$268$	−1848.44	−0.421312
$269$	−1356.94	−0.307562	−0.153781	−	0.988105i	$-0.549145\pi$
$269$	−1356.94	−0.307562	−0.153781	+	0.988105i	$0.549145\pi$
$270$	0	0
$271$	−6907.18	−1.54827	−0.774135	−	0.633021i	$-0.781815\pi$
$271$	−6907.18	−1.54827	−0.774135	+	0.633021i	$0.781815\pi$
$272$	1623.10	0.361820
$273$	1725.41	0.382515
$274$	−3889.39	−0.857543
$275$	0	0
$276$	−1342.04	−0.292685
$277$	−7889.76	−1.71137	−0.855685	−	0.517497i	$-0.826864\pi$
$277$	−7889.76	−1.71137	−0.855685	+	0.517497i	$0.826864\pi$
$278$	−10897.2	−2.35098
$279$	7636.30	1.63861
$280$	0	0
$281$	−7569.89	−1.60705	−0.803527	−	0.595269i	$-0.797046\pi$
$281$	−7569.89	−1.60705	−0.803527	+	0.595269i	$0.797046\pi$
$282$	−11517.2	−2.43205
$283$	−2541.02	−0.533739	−0.266869	−	0.963733i	$-0.585989\pi$
$283$	−2541.02	−0.533739	−0.266869	+	0.963733i	$0.585989\pi$
$284$	−3674.37	−0.767725
$285$	0	0
$286$	11398.1	2.35659
$287$	638.188	0.131258
$288$	7058.79	1.44425
$289$	−4286.71	−0.872525
$290$	0	0
$291$	6798.98	1.36963
$292$	−2868.78	−0.574940
$293$	1187.01	0.236676	0.118338	−	0.992973i	$-0.462243\pi$
$293$	1187.01	0.236676	0.118338	+	0.992973i	$0.462243\pi$
$294$	9733.38	1.93082
$295$	0	0
$296$	116.996	0.0229738
$297$	−217.883	−0.0425684
$298$	4145.91	0.805926
$299$	−1501.09	−0.290335
$300$	0	0
$301$	164.665	0.0315319
$302$	−11252.5	−2.14406
$303$	5716.49	1.08384
$304$	−6040.23	−1.13958
$305$	0	0
$306$	2760.69	0.515745
$307$	2865.01	0.532621	0.266310	−	0.963887i	$-0.414195\pi$
$307$	2865.01	0.532621	0.266310	+	0.963887i	$0.414195\pi$
$308$	−1236.10	−0.228680
$309$	14977.6	2.75743
$310$	0	0
$311$	−952.727	−0.173711	−0.0868556	−	0.996221i	$-0.527682\pi$
$311$	−952.727	−0.173711	−0.0868556	+	0.996221i	$0.527682\pi$
$312$	209.002	0.0379244
$313$	708.750	0.127990	0.0639951	−	0.997950i	$-0.479616\pi$
$313$	708.750	0.127990	0.0639951	+	0.997950i	$0.479616\pi$
$314$	−13228.8	−2.37753
$315$	0	0
$316$	3397.34	0.604795
$317$	−4406.36	−0.780712	−0.390356	−	0.920664i	$-0.627648\pi$
$317$	−4406.36	−0.780712	−0.390356	+	0.920664i	$0.627648\pi$
$318$	−13581.3	−2.39496
$319$	3708.29	0.650860
$320$	0	0
$321$	−3374.24	−0.586703
$322$	327.822	0.0567354
$323$	−2330.67	−0.401493
$324$	−5605.92	−0.961234
$325$	0	0
$326$	3804.18	0.646301
$327$	2122.85	0.359003
$328$	77.3049	0.0130136
$329$	1397.04	0.234108
$330$	0	0
$331$	−10068.7	−1.67198	−0.835990	−	0.548744i	$-0.815106\pi$
$331$	−10068.7	−1.67198	−0.835990	+	0.548744i	$0.815106\pi$
$332$	−2509.61	−0.414858
$333$	7475.37	1.23017
$334$	4533.34	0.742674
$335$	0	0
$336$	−1714.64	−0.278397
$337$	5782.71	0.934732	0.467366	−	0.884064i	$-0.345203\pi$
$337$	5782.71	0.934732	0.467366	+	0.884064i	$0.345203\pi$
$338$	−8221.89	−1.32311
$339$	11237.2	1.80036
$340$	0	0
$341$	−12089.4	−1.91988
$342$	−10273.7	−1.62437
$343$	−2407.04	−0.378916
$344$	19.9461	0.00312623
$345$	0	0
$346$	−17336.2	−2.69363
$347$	2808.27	0.434454	0.217227	−	0.976121i	$-0.430299\pi$
$347$	2808.27	0.434454	0.217227	+	0.976121i	$0.430299\pi$
$348$	−4938.97	−0.760795
$349$	−1990.62	−0.305316	−0.152658	−	0.988279i	$-0.548783\pi$
$349$	−1990.62	−0.305316	−0.152658	+	0.988279i	$0.548783\pi$
$350$	0	0
$351$	324.584	0.0493591
$352$	−11175.2	−1.69215
$353$	9719.18	1.46544	0.732719	−	0.680531i	$-0.238251\pi$
$353$	9719.18	1.46544	0.732719	+	0.680531i	$0.238251\pi$
$354$	5061.40	0.759916
$355$	0	0
$356$	11467.7	1.70727
$357$	−661.608	−0.0980841
$358$	10475.3	1.54647
$359$	−3571.57	−0.525070	−0.262535	−	0.964922i	$-0.584559\pi$
$359$	−3571.57	−0.525070	−0.262535	+	0.964922i	$0.584559\pi$
$360$	0	0
$361$	1814.39	0.264528
$362$	7916.37	1.14938
$363$	4350.08	0.628980
$364$	1841.45	0.265160
$365$	0	0
$366$	12743.5	1.81998
$367$	−6150.13	−0.874752	−0.437376	−	0.899279i	$-0.644092\pi$
$367$	−6150.13	−0.874752	−0.437376	+	0.899279i	$0.644092\pi$
$368$	1491.72	0.211308
$369$	4939.35	0.696835
$370$	0	0
$371$	1647.42	0.230538
$372$	16101.6	2.24417
$373$	2039.11	0.283059	0.141529	−	0.989934i	$-0.454798\pi$
$373$	2039.11	0.283059	0.141529	+	0.989934i	$0.454798\pi$
$374$	−4370.60	−0.604273
$375$	0	0
$376$	169.226	0.0232106
$377$	−5524.32	−0.754686
$378$	−70.8857	−0.00964542
$379$	4989.43	0.676227	0.338113	−	0.941105i	$-0.390211\pi$
$379$	4989.43	0.676227	0.338113	+	0.941105i	$0.390211\pi$
$380$	0	0
$381$	−963.420	−0.129547
$382$	16461.2	2.20479
$383$	−10033.8	−1.33865	−0.669323	−	0.742972i	$-0.733416\pi$
$383$	−10033.8	−1.33865	−0.669323	+	0.742972i	$0.733416\pi$
$384$	−409.866	−0.0544685
$385$	0	0
$386$	10457.6	1.37896
$387$	1274.44	0.167400
$388$	7256.22	0.949430
$389$	−9316.20	−1.21427	−0.607134	−	0.794599i	$-0.707681\pi$
$389$	−9316.20	−1.21427	−0.607134	+	0.794599i	$0.707681\pi$
$390$	0	0
$391$	575.592	0.0744474
$392$	−143.016	−0.0184271
$393$	−10207.1	−1.31013
$394$	13144.2	1.68069
$395$	0	0
$396$	−9566.99	−1.21404
$397$	−5744.41	−0.726205	−0.363103	−	0.931749i	$-0.618283\pi$
$397$	−5744.41	−0.726205	−0.363103	+	0.931749i	$0.618283\pi$
$398$	−14385.2	−1.81172
$399$	2462.12	0.308922
$400$	0	0
$401$	9605.68	1.19622	0.598111	−	0.801414i	$-0.295918\pi$
$401$	9605.68	1.19622	0.598111	+	0.801414i	$0.295918\pi$
$402$	6904.30	0.856605
$403$	18009.9	2.22615
$404$	6100.93	0.751319
$405$	0	0
$406$	1206.45	0.147476
$407$	−11834.7	−1.44133
$408$	−80.1418	−0.00972454
$409$	−10013.5	−1.21060	−0.605298	−	0.795999i	$-0.706946\pi$
$409$	−10013.5	−1.21060	−0.605298	+	0.795999i	$0.706946\pi$
$410$	0	0
$411$	7214.16	0.865811
$412$	15984.8	1.91145
$413$	−613.952	−0.0731491
$414$	2537.22	0.301202
$415$	0	0
$416$	16647.9	1.96209
$417$	20212.5	2.37365
$418$	16264.8	1.90320
$419$	−674.948	−0.0786954	−0.0393477	−	0.999226i	$-0.512528\pi$
$419$	−674.948	−0.0786954	−0.0393477	+	0.999226i	$0.512528\pi$
$420$	0	0
$421$	900.392	0.104234	0.0521169	−	0.998641i	$-0.483403\pi$
$421$	900.392	0.104234	0.0521169	+	0.998641i	$0.483403\pi$
$422$	−17886.6	−2.06328
$423$	10812.6	1.24285
$424$	199.555	0.0228567
$425$	0	0
$426$	13724.5	1.56093
$427$	−1545.79	−0.175190
$428$	−3601.16	−0.406702
$429$	−21141.6	−2.37931
$430$	0	0
$431$	−10830.3	−1.21039	−0.605193	−	0.796079i	$-0.706904\pi$
$431$	−10830.3	−1.21039	−0.605193	+	0.796079i	$0.706904\pi$
$432$	−322.558	−0.0359238
$433$	−11231.0	−1.24649	−0.623243	−	0.782029i	$-0.714185\pi$
$433$	−11231.0	−1.24649	−0.623243	+	0.782029i	$0.714185\pi$
$434$	−3933.17	−0.435019
$435$	0	0
$436$	2265.62	0.248861
$437$	−2142.01	−0.234477
$438$	10715.5	1.16896
$439$	13988.9	1.52085	0.760425	−	0.649426i	$-0.224991\pi$
$439$	13988.9	1.52085	0.760425	+	0.649426i	$0.224991\pi$
$440$	0	0
$441$	−9137.95	−0.986713
$442$	6510.97	0.700668
$443$	−298.267	−0.0319890	−0.0159945	−	0.999872i	$-0.505091\pi$
$443$	−298.267	−0.0319890	−0.0159945	+	0.999872i	$0.505091\pi$
$444$	15762.3	1.68479
$445$	0	0
$446$	21047.6	2.23461
$447$	−7689.96	−0.813697
$448$	−1780.57	−0.187777
$449$	−13606.7	−1.43016	−0.715079	−	0.699044i	$-0.753609\pi$
$449$	−13606.7	−1.43016	−0.715079	+	0.699044i	$0.753609\pi$
$450$	0	0
$451$	−7819.75	−0.816447
$452$	11992.9	1.24801
$453$	20871.4	2.16474
$454$	−7114.79	−0.735492
$455$	0	0
$456$	298.241	0.0306281
$457$	−4374.49	−0.447768	−0.223884	−	0.974616i	$-0.571874\pi$
$457$	−4374.49	−0.447768	−0.223884	+	0.974616i	$0.571874\pi$
$458$	−15698.8	−1.60165
$459$	−124.462	−0.0126566
$460$	0	0
$461$	1026.64	0.103721	0.0518604	−	0.998654i	$-0.483485\pi$
$461$	1026.64	0.103721	0.0518604	+	0.998654i	$0.483485\pi$
$462$	4617.09	0.464949
$463$	−10398.6	−1.04377	−0.521884	−	0.853016i	$-0.674771\pi$
$463$	−10398.6	−1.04377	−0.521884	+	0.853016i	$0.674771\pi$
$464$	5489.83	0.549265
$465$	0	0
$466$	−3954.06	−0.393065
$467$	5755.27	0.570282	0.285141	−	0.958486i	$-0.407959\pi$
$467$	5755.27	0.570282	0.285141	+	0.958486i	$0.407959\pi$
$468$	14252.2	1.40771
$469$	−837.498	−0.0824564
$470$	0	0
$471$	24537.2	2.40046
$472$	−74.3691	−0.00725236
$473$	−2017.64	−0.196134
$474$	−12689.7	−1.22966
$475$	0	0
$476$	−706.102	−0.0679919
$477$	12750.4	1.22390
$478$	−19891.4	−1.90337
$479$	−7944.26	−0.757793	−0.378896	−	0.925439i	$-0.623696\pi$
$479$	−7944.26	−0.757793	−0.378896	+	0.925439i	$0.623696\pi$
$480$	0	0
$481$	17630.4	1.67126
$482$	−13226.7	−1.24991
$483$	−608.054	−0.0572824
$484$	4642.63	0.436009
$485$	0	0
$486$	21474.5	2.00433
$487$	13904.3	1.29376	0.646881	−	0.762591i	$-0.276073\pi$
$487$	13904.3	1.29376	0.646881	+	0.762591i	$0.276073\pi$
$488$	−187.245	−0.0173692
$489$	−7056.11	−0.652532
$490$	0	0
$491$	3935.58	0.361731	0.180866	−	0.983508i	$-0.442110\pi$
$491$	3935.58	0.361731	0.180866	+	0.983508i	$0.442110\pi$
$492$	10414.9	0.954351
$493$	2118.30	0.193516
$494$	−24230.0	−2.20680
$495$	0	0
$496$	−17897.5	−1.62020
$497$	−1664.80	−0.150254
$498$	9373.89	0.843482
$499$	−7865.34	−0.705613	−0.352807	−	0.935696i	$-0.614773\pi$
$499$	−7865.34	−0.705613	−0.352807	+	0.935696i	$0.614773\pi$
$500$	0	0
$501$	−8408.58	−0.749835
$502$	14512.1	1.29025
$503$	−2435.58	−0.215899	−0.107950	−	0.994156i	$-0.534429\pi$
$503$	−2435.58	−0.215899	−0.107950	+	0.994156i	$0.534429\pi$
$504$	42.8516	0.00378723
$505$	0	0
$506$	−4016.81	−0.352904
$507$	15250.2	1.33587
$508$	−1028.21	−0.0898022
$509$	−19061.4	−1.65988	−0.829942	−	0.557850i	$-0.811627\pi$
$509$	−19061.4	−1.65988	−0.829942	+	0.557850i	$0.811627\pi$
$510$	0	0
$511$	−1299.79	−0.112524
$512$	−16319.2	−1.40862
$513$	463.173	0.0398628
$514$	28568.2	2.45153
$515$	0	0
$516$	2687.25	0.229262
$517$	−17118.0	−1.45619
$518$	−3850.28	−0.326586
$519$	32155.6	2.71961
$520$	0	0
$521$	8446.00	0.710222	0.355111	−	0.934824i	$-0.384443\pi$
$521$	8446.00	0.710222	0.355111	+	0.934824i	$0.384443\pi$
$522$	9337.50	0.782933
$523$	20207.4	1.68950	0.844749	−	0.535162i	$-0.179749\pi$
$523$	20207.4	1.68950	0.844749	+	0.535162i	$0.179749\pi$
$524$	−10893.5	−0.908179
$525$	0	0
$526$	−32261.1	−2.67424
$527$	−6905.89	−0.570826
$528$	21009.6	1.73168
$529$	529.000	0.0434783
$530$	0	0
$531$	−4751.77	−0.388341
$532$	2627.70	0.214145
$533$	11649.3	0.946689
$534$	−42834.1	−3.47119
$535$	0	0
$536$	−101.448	−0.00817513
$537$	−19429.9	−1.56138
$538$	5409.30	0.433478
$539$	14466.8	1.15608
$540$	0	0
$541$	14298.5	1.13631	0.568153	−	0.822923i	$-0.307658\pi$
$541$	14298.5	1.13631	0.568153	+	0.822923i	$0.307658\pi$
$542$	27534.7	2.18214
$543$	−14683.5	−1.16046
$544$	−6383.62	−0.503117
$545$	0	0
$546$	−6878.18	−0.539119
$547$	1820.52	0.142303	0.0711515	−	0.997466i	$-0.477333\pi$
$547$	1820.52	0.142303	0.0711515	+	0.997466i	$0.477333\pi$
$548$	7699.33	0.600181
$549$	−11963.9	−0.930067
$550$	0	0
$551$	−7883.05	−0.609491
$552$	−73.6547	−0.00567926
$553$	1539.28	0.118367
$554$	31451.7	2.41201
$555$	0	0
$556$	21571.9	1.64542
$557$	−19947.4	−1.51741	−0.758707	−	0.651432i	$-0.774168\pi$
$557$	−19947.4	−1.51741	−0.758707	+	0.651432i	$0.774168\pi$
$558$	−30441.3	−2.30947
$559$	3005.73	0.227422
$560$	0	0
$561$	8106.72	0.610100
$562$	30176.6	2.26499
$563$	−6202.95	−0.464339	−0.232170	−	0.972675i	$-0.574582\pi$
$563$	−6202.95	−0.464339	−0.232170	+	0.972675i	$0.574582\pi$
$564$	22799.1	1.70215
$565$	0	0
$566$	10129.5	0.752253
$567$	−2539.95	−0.188126
$568$	−201.660	−0.0148969
$569$	15907.6	1.17203	0.586013	−	0.810302i	$-0.300697\pi$
$569$	15907.6	1.17203	0.586013	+	0.810302i	$0.300697\pi$
$570$	0	0
$571$	−4501.17	−0.329892	−0.164946	−	0.986303i	$-0.552745\pi$
$571$	−4501.17	−0.329892	−0.164946	+	0.986303i	$0.552745\pi$
$572$	−22563.4	−1.64934
$573$	−30532.7	−2.22604
$574$	−2544.07	−0.184996
$575$	0	0
$576$	−13781.0	−0.996887
$577$	−8735.09	−0.630237	−0.315119	−	0.949052i	$-0.602044\pi$
$577$	−8735.09	−0.630237	−0.315119	+	0.949052i	$0.602044\pi$
$578$	17088.5	1.22974
$579$	−19397.1	−1.39226
$580$	0	0
$581$	−1137.06	−0.0811932
$582$	−27103.4	−1.93037
$583$	−20185.9	−1.43399
$584$	−157.446	−0.0111561
$585$	0	0
$586$	−4731.91	−0.333572
$587$	−17132.8	−1.20468	−0.602340	−	0.798240i	$-0.705765\pi$
$587$	−17132.8	−1.20468	−0.602340	+	0.798240i	$0.705765\pi$
$588$	−19267.9	−1.35135
$589$	25699.7	1.79785
$590$	0	0
$591$	−24380.2	−1.69690
$592$	−17520.3	−1.21635
$593$	7756.71	0.537150	0.268575	−	0.963259i	$-0.413447\pi$
$593$	7756.71	0.537150	0.268575	+	0.963259i	$0.413447\pi$
$594$	868.566	0.0599961
$595$	0	0
$596$	−8207.12	−0.564055
$597$	26682.1	1.82919
$598$	5983.94	0.409200
$599$	11689.1	0.797338	0.398669	−	0.917095i	$-0.369472\pi$
$599$	11689.1	0.797338	0.398669	+	0.917095i	$0.369472\pi$
$600$	0	0
$601$	−5361.70	−0.363907	−0.181954	−	0.983307i	$-0.558242\pi$
$601$	−5361.70	−0.363907	−0.181954	+	0.983307i	$0.558242\pi$
$602$	−656.418	−0.0444412
$603$	−6481.93	−0.437752
$604$	22275.1	1.50060
$605$	0	0
$606$	−22788.2	−1.52757
$607$	−6585.62	−0.440366	−0.220183	−	0.975459i	$-0.570665\pi$
$607$	−6585.62	−0.440366	−0.220183	+	0.975459i	$0.570665\pi$
$608$	23756.1	1.58460
$609$	−2237.76	−0.148898
$610$	0	0
$611$	25501.1	1.68849
$612$	−5464.98	−0.360962
$613$	10187.9	0.671265	0.335633	−	0.941993i	$-0.391050\pi$
$613$	10187.9	0.671265	0.335633	+	0.941993i	$0.391050\pi$
$614$	−11421.1	−0.750678
$615$	0	0
$616$	−67.8407	−0.00443731
$617$	14025.9	0.915174	0.457587	−	0.889165i	$-0.348714\pi$
$617$	14025.9	0.915174	0.457587	+	0.889165i	$0.348714\pi$
$618$	−59706.6	−3.88633
$619$	−23123.6	−1.50148	−0.750741	−	0.660597i	$-0.770303\pi$
$619$	−23123.6	−1.50148	−0.750741	+	0.660597i	$0.770303\pi$
$620$	0	0
$621$	−114.387	−0.00739162
$622$	3797.95	0.244829
$623$	5195.82	0.334135
$624$	−31298.4	−2.00792
$625$	0	0
$626$	−2825.36	−0.180390
$627$	−30168.4	−1.92155
$628$	26187.4	1.66400
$629$	−6760.35	−0.428542
$630$	0	0
$631$	−21569.0	−1.36078	−0.680389	−	0.732852i	$-0.738189\pi$
$631$	−21569.0	−1.36078	−0.680389	+	0.732852i	$0.738189\pi$
$632$	186.455	0.0117354
$633$	33176.6	2.08318
$634$	17565.5	1.10034
$635$	0	0
$636$	26885.1	1.67620
$637$	−21551.5	−1.34050
$638$	−14782.7	−0.917324
$639$	−12884.9	−0.797683
$640$	0	0
$641$	−14908.3	−0.918633	−0.459317	−	0.888273i	$-0.651906\pi$
$641$	−14908.3	−0.918633	−0.459317	+	0.888273i	$0.651906\pi$
$642$	13451.0	0.826901
$643$	−20215.7	−1.23986	−0.619930	−	0.784657i	$-0.712839\pi$
$643$	−20215.7	−1.23986	−0.619930	+	0.784657i	$0.712839\pi$
$644$	−648.946	−0.0397082
$645$	0	0
$646$	9290.98	0.565865
$647$	2941.45	0.178733	0.0893666	−	0.995999i	$-0.471516\pi$
$647$	2941.45	0.178733	0.0893666	+	0.995999i	$0.471516\pi$
$648$	−307.668	−0.0186518
$649$	7522.78	0.455000
$650$	0	0
$651$	7295.36	0.439213
$652$	−7530.64	−0.452335
$653$	−5575.27	−0.334115	−0.167058	−	0.985947i	$-0.553427\pi$
$653$	−5575.27	−0.334115	−0.167058	+	0.985947i	$0.553427\pi$
$654$	−8462.54	−0.505981
$655$	0	0
$656$	−11576.5	−0.689006
$657$	−10059.9	−0.597376
$658$	−5569.17	−0.329953
$659$	−20945.0	−1.23809	−0.619046	−	0.785354i	$-0.712481\pi$
$659$	−20945.0	−1.23809	−0.619046	+	0.785354i	$0.712481\pi$
$660$	0	0
$661$	−18339.9	−1.07919	−0.539593	−	0.841926i	$-0.681422\pi$
$661$	−18339.9	−1.07919	−0.539593	+	0.841926i	$0.681422\pi$
$662$	40137.8	2.35650
$663$	−12076.8	−0.707424
$664$	−137.734	−0.00804989
$665$	0	0
$666$	−29799.8	−1.73381
$667$	1946.83	0.113016
$668$	−8974.06	−0.519786
$669$	−39039.8	−2.25615
$670$	0	0
$671$	18940.7	1.08971
$672$	6743.64	0.387116
$673$	−8682.73	−0.497318	−0.248659	−	0.968591i	$-0.579990\pi$
$673$	−8682.73	−0.497318	−0.248659	+	0.968591i	$0.579990\pi$
$674$	−23052.2	−1.31741
$675$	0	0
$676$	16275.8	0.926025
$677$	24621.6	1.39776	0.698880	−	0.715238i	$-0.253682\pi$
$677$	24621.6	1.39776	0.698880	+	0.715238i	$0.253682\pi$
$678$	−44795.9	−2.53743
$679$	3287.67	0.185816
$680$	0	0
$681$	13196.7	0.742584
$682$	48193.3	2.70589
$683$	12701.5	0.711582	0.355791	−	0.934565i	$-0.384211\pi$
$683$	12701.5	0.711582	0.355791	+	0.934565i	$0.384211\pi$
$684$	20337.4	1.13687
$685$	0	0
$686$	9595.43	0.534046
$687$	29118.6	1.61709
$688$	−2986.96	−0.165519
$689$	30071.4	1.66274
$690$	0	0
$691$	−12914.2	−0.710968	−0.355484	−	0.934682i	$-0.615684\pi$
$691$	−12914.2	−0.710968	−0.355484	+	0.934682i	$0.615684\pi$
$692$	34318.1	1.88523
$693$	−4334.64	−0.237604
$694$	−11194.9	−0.612322
$695$	0	0
$696$	−271.064	−0.0147624
$697$	−4466.90	−0.242749
$698$	7935.38	0.430313
$699$	7334.12	0.396855
$700$	0	0
$701$	13188.4	0.710581	0.355290	−	0.934756i	$-0.384382\pi$
$701$	13188.4	0.710581	0.355290	+	0.934756i	$0.384382\pi$
$702$	−1293.92	−0.0695669
$703$	25158.1	1.34972
$704$	21817.4	1.16800
$705$	0	0
$706$	−38744.5	−2.06539
$707$	2764.23	0.147043
$708$	−10019.4	−0.531853
$709$	−13435.5	−0.711680	−0.355840	−	0.934547i	$-0.615805\pi$
$709$	−13435.5	−0.711680	−0.355840	+	0.934547i	$0.615805\pi$
$710$	0	0
$711$	11913.5	0.628396
$712$	629.378	0.0331277
$713$	−6346.88	−0.333370
$714$	2637.43	0.138240
$715$	0	0
$716$	−20736.6	−1.08235
$717$	36895.1	1.92172
$718$	14237.7	0.740036
$719$	−17486.8	−0.907020	−0.453510	−	0.891251i	$-0.649828\pi$
$719$	−17486.8	−0.907020	−0.453510	+	0.891251i	$0.649828\pi$
$720$	0	0
$721$	7242.46	0.374096
$722$	−7232.89	−0.372826
$723$	24533.2	1.26197
$724$	−15671.0	−0.804432
$725$	0	0
$726$	−17341.1	−0.886487
$727$	13036.5	0.665060	0.332530	−	0.943093i	$-0.392098\pi$
$727$	13036.5	0.665060	0.332530	+	0.943093i	$0.392098\pi$
$728$	101.064	0.00514516
$729$	−20651.1	−1.04919
$730$	0	0
$731$	−1152.54	−0.0583152
$732$	−25226.6	−1.27377
$733$	35051.0	1.76622	0.883108	−	0.469169i	$-0.155446\pi$
$733$	35051.0	1.76622	0.883108	+	0.469169i	$0.155446\pi$
$734$	24516.9	1.23288
$735$	0	0
$736$	−5866.89	−0.293827
$737$	10261.9	0.512893
$738$	−19690.2	−0.982122
$739$	25898.2	1.28915	0.644575	−	0.764541i	$-0.277035\pi$
$739$	25898.2	1.28915	0.644575	+	0.764541i	$0.277035\pi$
$740$	0	0
$741$	44942.6	2.22808
$742$	−6567.26	−0.324922
$743$	25133.5	1.24100	0.620498	−	0.784208i	$-0.286931\pi$
$743$	25133.5	1.24100	0.620498	+	0.784208i	$0.286931\pi$
$744$	883.701	0.0435457
$745$	0	0
$746$	−8128.68	−0.398944
$747$	−8800.45	−0.431046
$748$	8651.91	0.422921
$749$	−1631.62	−0.0795971
$750$	0	0
$751$	20368.0	0.989667	0.494833	−	0.868988i	$-0.335229\pi$
$751$	20368.0	0.989667	0.494833	+	0.868988i	$0.335229\pi$
$752$	−25341.9	−1.22889
$753$	−26917.5	−1.30269
$754$	22022.1	1.06366
$755$	0	0
$756$	140.323	0.00675068
$757$	−25262.7	−1.21293	−0.606465	−	0.795110i	$-0.707413\pi$
$757$	−25262.7	−1.21293	−0.606465	+	0.795110i	$0.707413\pi$
$758$	−19889.9	−0.953077
$759$	7450.51	0.356306
$760$	0	0
$761$	14926.1	0.711001	0.355500	−	0.934676i	$-0.384310\pi$
$761$	14926.1	0.711001	0.355500	+	0.934676i	$0.384310\pi$
$762$	3840.57	0.182584
$763$	1026.51	0.0487055
$764$	−32586.1	−1.54309
$765$	0	0
$766$	39998.6	1.88669
$767$	−11206.9	−0.527583
$768$	31092.0	1.46085
$769$	32390.7	1.51891	0.759453	−	0.650562i	$-0.225467\pi$
$769$	32390.7	1.51891	0.759453	+	0.650562i	$0.225467\pi$
$770$	0	0
$771$	−52989.1	−2.47517
$772$	−20701.6	−0.965114
$773$	28163.3	1.31043	0.655215	−	0.755443i	$-0.272578\pi$
$773$	28163.3	1.31043	0.655215	+	0.755443i	$0.272578\pi$
$774$	−5080.44	−0.235934
$775$	0	0
$776$	398.241	0.0184227
$777$	7141.63	0.329735
$778$	37138.1	1.71139
$779$	16623.2	0.764553
$780$	0	0
$781$	20398.8	0.934606
$782$	−2294.54	−0.104926
$783$	−420.968	−0.0192135
$784$	21417.0	0.975626
$785$	0	0
$786$	40689.5	1.84650
$787$	−34922.9	−1.58179	−0.790893	−	0.611954i	$-0.790384\pi$
$787$	−34922.9	−1.58179	−0.790893	+	0.611954i	$0.790384\pi$
$788$	−26019.8	−1.17629
$789$	59838.9	2.70003
$790$	0	0
$791$	5433.79	0.244252
$792$	−525.063	−0.0235572
$793$	−28216.4	−1.26355
$794$	22899.5	1.02352
$795$	0	0
$796$	28476.6	1.26800
$797$	−26096.8	−1.15985	−0.579923	−	0.814671i	$-0.696917\pi$
$797$	−26096.8	−1.15985	−0.579923	+	0.814671i	$0.696917\pi$
$798$	−9814.98	−0.435397
$799$	−9778.39	−0.432959
$800$	0	0
$801$	40213.7	1.77389
$802$	−38292.0	−1.68596
$803$	15926.4	0.699915
$804$	−13667.6	−0.599524
$805$	0	0
$806$	−71794.6	−3.13754
$807$	−10033.3	−0.437658
$808$	334.836	0.0145786
$809$	−236.848	−0.0102931	−0.00514656	−	0.999987i	$-0.501638\pi$
$809$	−236.848	−0.0102931	−0.00514656	+	0.999987i	$0.501638\pi$
$810$	0	0
$811$	−36386.9	−1.57548	−0.787742	−	0.616005i	$-0.788750\pi$
$811$	−36386.9	−1.57548	−0.787742	+	0.616005i	$0.788750\pi$
$812$	−2388.26	−0.103216
$813$	−51072.3	−2.20318
$814$	47177.7	2.03142
$815$	0	0
$816$	12001.4	0.514868
$817$	4289.09	0.183668
$818$	39917.6	1.70622
$819$	6457.41	0.275507
$820$	0	0
$821$	−27347.7	−1.16254	−0.581268	−	0.813712i	$-0.697443\pi$
$821$	−27347.7	−1.16254	−0.581268	+	0.813712i	$0.697443\pi$
$822$	−28758.5	−1.22028
$823$	−2368.01	−0.100296	−0.0501480	−	0.998742i	$-0.515969\pi$
$823$	−2368.01	−0.100296	−0.0501480	+	0.998742i	$0.515969\pi$
$824$	877.292	0.0370897
$825$	0	0
$826$	2447.46	0.103097
$827$	−19465.1	−0.818463	−0.409231	−	0.912431i	$-0.634203\pi$
$827$	−19465.1	−0.818463	−0.409231	+	0.912431i	$0.634203\pi$
$828$	−5022.61	−0.210807
$829$	33035.4	1.38404	0.692020	−	0.721879i	$-0.256721\pi$
$829$	33035.4	1.38404	0.692020	+	0.721879i	$0.256721\pi$
$830$	0	0
$831$	−58337.6	−2.43527
$832$	−32501.9	−1.35433
$833$	8263.90	0.343730
$834$	−80575.2	−3.34543
$835$	0	0
$836$	−32197.3	−1.33202
$837$	1372.40	0.0566753
$838$	2690.61	0.110914
$839$	−36015.4	−1.48199	−0.740995	−	0.671511i	$-0.765646\pi$
$839$	−36015.4	−1.48199	−0.740995	+	0.671511i	$0.765646\pi$
$840$	0	0
$841$	−17224.3	−0.706231
$842$	−3589.32	−0.146908
$843$	−55972.5	−2.28683
$844$	35407.8	1.44406
$845$	0	0
$846$	−43103.4	−1.75168
$847$	2103.50	0.0853329
$848$	−29883.7	−1.21015
$849$	−18788.6	−0.759507
$850$	0	0
$851$	−6213.13	−0.250274
$852$	−27168.6	−1.09247
$853$	−9941.26	−0.399041	−0.199521	−	0.979894i	$-0.563938\pi$
$853$	−9941.26	−0.399041	−0.199521	+	0.979894i	$0.563938\pi$
$854$	6162.15	0.246914
$855$	0	0
$856$	−197.642	−0.00789165
$857$	11884.7	0.473716	0.236858	−	0.971544i	$-0.423882\pi$
$857$	11884.7	0.473716	0.236858	+	0.971544i	$0.423882\pi$
$858$	84278.6	3.35341
$859$	24824.3	0.986022	0.493011	−	0.870023i	$-0.335896\pi$
$859$	24824.3	0.986022	0.493011	+	0.870023i	$0.335896\pi$
$860$	0	0
$861$	4718.82	0.186779
$862$	43173.8	1.70592
$863$	18701.1	0.737653	0.368826	−	0.929498i	$-0.379760\pi$
$863$	18701.1	0.737653	0.368826	+	0.929498i	$0.379760\pi$
$864$	1268.61	0.0499527
$865$	0	0
$866$	44771.3	1.75680
$867$	−31696.4	−1.24160
$868$	7785.99	0.304463
$869$	−18860.8	−0.736260
$870$	0	0
$871$	−15287.4	−0.594711
$872$	124.343	0.00482890
$873$	25445.4	0.986478
$874$	8538.92	0.330473
$875$	0	0
$876$	−21212.0	−0.818137
$877$	2743.01	0.105615	0.0528077	−	0.998605i	$-0.483183\pi$
$877$	2743.01	0.105615	0.0528077	+	0.998605i	$0.483183\pi$
$878$	−55765.2	−2.14349
$879$	8776.90	0.336789
$880$	0	0
$881$	39165.3	1.49774	0.748872	−	0.662715i	$-0.230596\pi$
$881$	39165.3	1.49774	0.748872	+	0.662715i	$0.230596\pi$
$882$	36427.5	1.39068
$883$	27421.4	1.04508	0.522539	−	0.852615i	$-0.324985\pi$
$883$	27421.4	1.04508	0.522539	+	0.852615i	$0.324985\pi$
$884$	−12888.9	−0.490387
$885$	0	0
$886$	1189.01	0.0450854
$887$	22388.7	0.847509	0.423754	−	0.905777i	$-0.360712\pi$
$887$	22388.7	0.847509	0.423754	+	0.905777i	$0.360712\pi$
$888$	865.078	0.0326916
$889$	−465.865	−0.0175755
$890$	0	0
$891$	31122.1	1.17018
$892$	−41665.3	−1.56397
$893$	36389.4	1.36363
$894$	30655.2	1.14683
$895$	0	0
$896$	−198.192	−0.00738967
$897$	−11099.2	−0.413145
$898$	54241.8	2.01567
$899$	−23357.8	−0.866549
$900$	0	0
$901$	−11530.8	−0.426358
$902$	31172.6	1.15070
$903$	1217.55	0.0448697
$904$	658.205	0.0242163
$905$	0	0
$906$	−83201.8	−3.05099
$907$	8406.44	0.307752	0.153876	−	0.988090i	$-0.450824\pi$
$907$	8406.44	0.307752	0.153876	+	0.988090i	$0.450824\pi$
$908$	14084.2	0.514759
$909$	21394.1	0.780636
$910$	0	0
$911$	−23147.0	−0.841816	−0.420908	−	0.907103i	$-0.638288\pi$
$911$	−23147.0	−0.841816	−0.420908	+	0.907103i	$0.638288\pi$
$912$	−44662.1	−1.62161
$913$	13932.5	0.505036
$914$	17438.4	0.631086
$915$	0	0
$916$	31076.8	1.12097
$917$	−4935.67	−0.177743
$918$	496.154	0.0178382
$919$	−8915.09	−0.320002	−0.160001	−	0.987117i	$-0.551150\pi$
$919$	−8915.09	−0.320002	−0.160001	+	0.987117i	$0.551150\pi$
$920$	0	0
$921$	21184.1	0.757916
$922$	−4092.58	−0.146184
$923$	−30388.6	−1.08370
$924$	−9139.86	−0.325410
$925$	0	0
$926$	41453.0	1.47109
$927$	56054.1	1.98604
$928$	−21591.4	−0.763762
$929$	29110.6	1.02808	0.514041	−	0.857766i	$-0.328148\pi$
$929$	29110.6	1.02808	0.514041	+	0.857766i	$0.328148\pi$
$930$	0	0
$931$	−30753.4	−1.08260
$932$	7827.35	0.275100
$933$	−7044.55	−0.247190
$934$	−22942.8	−0.803758
$935$	0	0
$936$	782.197	0.0273151
$937$	−47055.8	−1.64061	−0.820303	−	0.571930i	$-0.806195\pi$
$937$	−47055.8	−1.64061	−0.820303	+	0.571930i	$0.806195\pi$
$938$	3338.60	0.116214
$939$	5240.56	0.182129
$940$	0	0
$941$	36217.3	1.25468	0.627339	−	0.778747i	$-0.284144\pi$
$941$	36217.3	1.25468	0.627339	+	0.778747i	$0.284144\pi$
$942$	−97815.1	−3.38322
$943$	−4105.32	−0.141768
$944$	11136.9	0.383978
$945$	0	0
$946$	8043.13	0.276432
$947$	−13445.6	−0.461376	−0.230688	−	0.973028i	$-0.574098\pi$
$947$	−13445.6	−0.461376	−0.230688	+	0.973028i	$0.574098\pi$
$948$	25120.3	0.860620
$949$	−23726.0	−0.811568
$950$	0	0
$951$	−32581.0	−1.11095
$952$	−38.7528	−0.00131931
$953$	−25975.6	−0.882929	−0.441465	−	0.897279i	$-0.645541\pi$
$953$	−25975.6	−0.882929	−0.441465	+	0.897279i	$0.645541\pi$
$954$	−50828.2	−1.72497
$955$	0	0
$956$	39376.4	1.33214
$957$	27419.4	0.926169
$958$	31669.0	1.06804
$959$	3488.43	0.117463
$960$	0	0
$961$	46358.2	1.55611
$962$	−70281.6	−2.35548
$963$	−12628.2	−0.422573
$964$	26183.1	0.874795
$965$	0	0
$966$	2423.94	0.0807341
$967$	7598.70	0.252697	0.126348	−	0.991986i	$-0.459674\pi$
$967$	7598.70	0.252697	0.126348	+	0.991986i	$0.459674\pi$
$968$	254.800	0.00846032
$969$	−17233.2	−0.571321
$970$	0	0
$971$	11186.0	0.369696	0.184848	−	0.982767i	$-0.440821\pi$
$971$	11186.0	0.369696	0.184848	+	0.982767i	$0.440821\pi$
$972$	−42510.3	−1.40280
$973$	9773.84	0.322030
$974$	−55427.9	−1.82343
$975$	0	0
$976$	28040.2	0.919617
$977$	2597.14	0.0850460	0.0425230	−	0.999095i	$-0.486460\pi$
$977$	2597.14	0.0850460	0.0425230	+	0.999095i	$0.486460\pi$
$978$	28128.5	0.919682
$979$	−63664.6	−2.07837
$980$	0	0
$981$	7944.84	0.258572
$982$	−15688.8	−0.509826
$983$	33005.1	1.07090	0.535452	−	0.844566i	$-0.320141\pi$
$983$	33005.1	1.07090	0.535452	+	0.844566i	$0.320141\pi$
$984$	571.599	0.0185182
$985$	0	0
$986$	−8444.37	−0.272742
$987$	10329.9	0.333134
$988$	47965.0	1.54451
$989$	−1059.25	−0.0340568
$990$	0	0
$991$	4986.74	0.159848	0.0799239	−	0.996801i	$-0.474532\pi$
$991$	4986.74	0.159848	0.0799239	+	0.996801i	$0.474532\pi$
$992$	70390.3	2.25292
$993$	−74448.9	−2.37922
$994$	6636.53	0.211769
$995$	0	0
$996$	−18556.3	−0.590340
$997$	58754.2	1.86636	0.933182	−	0.359405i	$-0.117020\pi$
$997$	58754.2	1.86636	0.933182	+	0.359405i	$0.117020\pi$
$998$	31354.4	0.994494
$999$	1343.48	0.0425484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.4.a.k.1.1		5
5.2	odd	4		575.4.b.h.24.3		10
5.3	odd	4		575.4.b.h.24.8		10
5.4	even	2		115.4.a.d.1.5	✓	5
15.14	odd	2		1035.4.a.m.1.1		5
20.19	odd	2		1840.4.a.p.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.a.d.1.5	✓	5	5.4	even	2
575.4.a.k.1.1		5	1.1	even	1	trivial
575.4.b.h.24.3		10	5.2	odd	4
575.4.b.h.24.8		10	5.3	odd	4
1035.4.a.m.1.1		5	15.14	odd	2
1840.4.a.p.1.4		5	20.19	odd	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-3.98640 q^{2} +7.39409 q^{3} +7.89136 q^{4} -29.4758 q^{6} +3.57544 q^{7} +0.433099 q^{8} +27.6726 q^{9} +O(q^{10})\)	\(q-3.98640 q^{2} +7.39409 q^{3} +7.89136 q^{4} -29.4758 q^{6} +3.57544 q^{7} +0.433099 q^{8} +27.6726 q^{9} -43.8100 q^{11} +58.3494 q^{12} +65.2647 q^{13} -14.2531 q^{14} -64.8574 q^{16} -25.0257 q^{17} -110.314 q^{18} +93.1311 q^{19} +26.4371 q^{21} +174.644 q^{22} -23.0000 q^{23} +3.20238 q^{24} -260.171 q^{26} +4.97335 q^{27} +28.2151 q^{28} -84.6447 q^{29} +275.951 q^{31} +255.082 q^{32} -323.935 q^{33} +99.7625 q^{34} +218.374 q^{36} +270.136 q^{37} -371.257 q^{38} +482.574 q^{39} +178.492 q^{41} -105.389 q^{42} +46.0544 q^{43} -345.720 q^{44} +91.6871 q^{46} +390.733 q^{47} -479.561 q^{48} -330.216 q^{49} -185.043 q^{51} +515.027 q^{52} +460.760 q^{53} -19.8257 q^{54} +1.54852 q^{56} +688.620 q^{57} +337.427 q^{58} -171.714 q^{59} -432.337 q^{61} -1100.05 q^{62} +98.9417 q^{63} -498.000 q^{64} +1291.33 q^{66} -234.236 q^{67} -197.487 q^{68} -170.064 q^{69} -465.620 q^{71} +11.9850 q^{72} -363.534 q^{73} -1076.87 q^{74} +734.930 q^{76} -156.640 q^{77} -1923.73 q^{78} +430.514 q^{79} -710.387 q^{81} -711.541 q^{82} -318.020 q^{83} +208.625 q^{84} -183.591 q^{86} -625.871 q^{87} -18.9741 q^{88} +1453.20 q^{89} +233.350 q^{91} -181.501 q^{92} +2040.41 q^{93} -1557.62 q^{94} +1886.10 q^{96} +919.515 q^{97} +1316.37 q^{98} -1212.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 6 q^{3} + 33 q^{4} - 36 q^{6} + 15 q^{7} + 102 q^{8} + 79 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 6 * q^3 + 33 * q^4 - 36 * q^6 + 15 * q^7 + 102 * q^8 + 79 * q^9	\( 5 q + 5 q^{2} + 6 q^{3} + 33 q^{4} - 36 q^{6} + 15 q^{7} + 102 q^{8} + 79 q^{9} - 153 q^{11} + 30 q^{12} - 28 q^{13} + 69 q^{14} + 145 q^{16} + 341 q^{17} + 409 q^{18} + 3 q^{19} - 212 q^{21} - 11 q^{22} - 115 q^{23} - 243 q^{24} - 266 q^{26} + 243 q^{27} + 709 q^{28} - 583 q^{29} + 662 q^{31} + 681 q^{32} + 457 q^{33} + 799 q^{34} + 2047 q^{36} + 172 q^{37} - 511 q^{38} + 83 q^{39} + 344 q^{41} - 1668 q^{42} + 230 q^{43} - 503 q^{44} - 115 q^{46} + 337 q^{47} - 2050 q^{48} - 4 q^{49} - 205 q^{51} - 130 q^{52} + 942 q^{53} + 783 q^{54} + 2621 q^{56} + 890 q^{57} - 2039 q^{58} - 1166 q^{59} + 499 q^{61} + 1768 q^{62} + 1228 q^{63} + 388 q^{64} + 4627 q^{66} + 972 q^{67} + 2433 q^{68} - 138 q^{69} - 14 q^{71} + 4023 q^{72} + 229 q^{73} - 1004 q^{74} + 1529 q^{76} - 312 q^{77} - 3161 q^{78} - 88 q^{79} + 897 q^{81} - 114 q^{82} + 72 q^{83} - 6302 q^{84} + 2490 q^{86} - 1157 q^{87} - 1789 q^{88} - 90 q^{89} - 1309 q^{91} - 759 q^{92} + 3071 q^{93} - 1827 q^{94} - 4160 q^{96} + 1765 q^{97} + 4006 q^{98} - 91 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 6 * q^3 + 33 * q^4 - 36 * q^6 + 15 * q^7 + 102 * q^8 + 79 * q^9 - 153 * q^11 + 30 * q^12 - 28 * q^13 + 69 * q^14 + 145 * q^16 + 341 * q^17 + 409 * q^18 + 3 * q^19 - 212 * q^21 - 11 * q^22 - 115 * q^23 - 243 * q^24 - 266 * q^26 + 243 * q^27 + 709 * q^28 - 583 * q^29 + 662 * q^31 + 681 * q^32 + 457 * q^33 + 799 * q^34 + 2047 * q^36 + 172 * q^37 - 511 * q^38 + 83 * q^39 + 344 * q^41 - 1668 * q^42 + 230 * q^43 - 503 * q^44 - 115 * q^46 + 337 * q^47 - 2050 * q^48 - 4 * q^49 - 205 * q^51 - 130 * q^52 + 942 * q^53 + 783 * q^54 + 2621 * q^56 + 890 * q^57 - 2039 * q^58 - 1166 * q^59 + 499 * q^61 + 1768 * q^62 + 1228 * q^63 + 388 * q^64 + 4627 * q^66 + 972 * q^67 + 2433 * q^68 - 138 * q^69 - 14 * q^71 + 4023 * q^72 + 229 * q^73 - 1004 * q^74 + 1529 * q^76 - 312 * q^77 - 3161 * q^78 - 88 * q^79 + 897 * q^81 - 114 * q^82 + 72 * q^83 - 6302 * q^84 + 2490 * q^86 - 1157 * q^87 - 1789 * q^88 - 90 * q^89 - 1309 * q^91 - 759 * q^92 + 3071 * q^93 - 1827 * q^94 - 4160 * q^96 + 1765 * q^97 + 4006 * q^98 - 91 * q^99

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