LMFDB - Embedded newform 1450.4.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,4,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1450.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:	$85.5527695083$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.19816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 42x - 54 $ x^3 - x^2 - 42*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$7.53003$ of defining polynomial
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +6.53003 q^{3} +4.00000 q^{4} -13.0601 q^{6} -8.55839 q^{7} -8.00000 q^{8} +15.6413 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +6.53003 q^{3} +4.00000 q^{4} -13.0601 q^{6} -8.55839 q^{7} -8.00000 q^{8} +15.6413 q^{9} +10.8092 q^{11} +26.1201 q^{12} -54.7046 q^{13} +17.1168 q^{14} +16.0000 q^{16} +106.127 q^{17} -31.2825 q^{18} -113.636 q^{19} -55.8865 q^{21} -21.6184 q^{22} +112.855 q^{23} -52.2402 q^{24} +109.409 q^{26} -74.1729 q^{27} -34.2336 q^{28} +29.0000 q^{29} -102.805 q^{31} -32.0000 q^{32} +70.5845 q^{33} -212.254 q^{34} +62.5650 q^{36} +105.665 q^{37} +227.272 q^{38} -357.223 q^{39} +216.958 q^{41} +111.773 q^{42} +102.230 q^{43} +43.2369 q^{44} -225.711 q^{46} -455.212 q^{47} +104.480 q^{48} -269.754 q^{49} +693.011 q^{51} -218.819 q^{52} +593.714 q^{53} +148.346 q^{54} +68.4671 q^{56} -742.048 q^{57} -58.0000 q^{58} -558.141 q^{59} -473.986 q^{61} +205.610 q^{62} -133.864 q^{63} +64.0000 q^{64} -141.169 q^{66} -193.132 q^{67} +424.507 q^{68} +736.949 q^{69} -2.38155 q^{71} -125.130 q^{72} -119.013 q^{73} -211.330 q^{74} -454.545 q^{76} -92.5096 q^{77} +714.446 q^{78} -964.306 q^{79} -906.665 q^{81} -433.915 q^{82} -1068.19 q^{83} -223.546 q^{84} -204.459 q^{86} +189.371 q^{87} -86.4738 q^{88} +772.544 q^{89} +468.184 q^{91} +451.421 q^{92} -671.318 q^{93} +910.423 q^{94} -208.961 q^{96} -1344.03 q^{97} +539.508 q^{98} +169.070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 4 q^{6} - 24 q^{7} - 24 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 4 * q^6 - 24 * q^7 - 24 * q^8 + 5 * q^9	$ 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 4 q^{6} - 24 q^{7} - 24 q^{8} + 5 q^{9} + 10 q^{11} - 8 q^{12} + 4 q^{13} + 48 q^{14} + 48 q^{16} + 66 q^{17} - 10 q^{18} - 164 q^{19} - 88 q^{21} - 20 q^{22} + 204 q^{23} + 16 q^{24} - 8 q^{26} + 142 q^{27} - 96 q^{28} + 87 q^{29} - 86 q^{31} - 96 q^{32} + 130 q^{33} - 132 q^{34} + 20 q^{36} + 42 q^{37} + 328 q^{38} - 394 q^{39} + 562 q^{41} + 176 q^{42} - 18 q^{43} + 40 q^{44} - 408 q^{46} - 654 q^{47} - 32 q^{48} + 539 q^{49} + 556 q^{51} + 16 q^{52} - 712 q^{53} - 284 q^{54} + 192 q^{56} - 828 q^{57} - 174 q^{58} + 184 q^{59} + 322 q^{61} + 172 q^{62} + 784 q^{63} + 192 q^{64} - 260 q^{66} + 228 q^{67} + 264 q^{68} + 684 q^{69} - 52 q^{71} - 40 q^{72} + 494 q^{73} - 84 q^{74} - 656 q^{76} - 872 q^{77} + 788 q^{78} - 2110 q^{79} - 1513 q^{81} - 1124 q^{82} + 288 q^{83} - 352 q^{84} + 36 q^{86} - 58 q^{87} - 80 q^{88} + 914 q^{89} - 2984 q^{91} + 816 q^{92} + 62 q^{93} + 1308 q^{94} + 64 q^{96} - 218 q^{97} - 1078 q^{98} - 304 q^{99}+O(q^{100}) $ 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 4 * q^6 - 24 * q^7 - 24 * q^8 + 5 * q^9 + 10 * q^11 - 8 * q^12 + 4 * q^13 + 48 * q^14 + 48 * q^16 + 66 * q^17 - 10 * q^18 - 164 * q^19 - 88 * q^21 - 20 * q^22 + 204 * q^23 + 16 * q^24 - 8 * q^26 + 142 * q^27 - 96 * q^28 + 87 * q^29 - 86 * q^31 - 96 * q^32 + 130 * q^33 - 132 * q^34 + 20 * q^36 + 42 * q^37 + 328 * q^38 - 394 * q^39 + 562 * q^41 + 176 * q^42 - 18 * q^43 + 40 * q^44 - 408 * q^46 - 654 * q^47 - 32 * q^48 + 539 * q^49 + 556 * q^51 + 16 * q^52 - 712 * q^53 - 284 * q^54 + 192 * q^56 - 828 * q^57 - 174 * q^58 + 184 * q^59 + 322 * q^61 + 172 * q^62 + 784 * q^63 + 192 * q^64 - 260 * q^66 + 228 * q^67 + 264 * q^68 + 684 * q^69 - 52 * q^71 - 40 * q^72 + 494 * q^73 - 84 * q^74 - 656 * q^76 - 872 * q^77 + 788 * q^78 - 2110 * q^79 - 1513 * q^81 - 1124 * q^82 + 288 * q^83 - 352 * q^84 + 36 * q^86 - 58 * q^87 - 80 * q^88 + 914 * q^89 - 2984 * q^91 + 816 * q^92 + 62 * q^93 + 1308 * q^94 + 64 * q^96 - 218 * q^97 - 1078 * q^98 - 304 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.53003	1.25670	0.628352	−	0.777929i	$-0.283730\pi$
$3$	6.53003	1.25670	0.628352	+	0.777929i	$0.283730\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−13.0601	−0.888624
$7$	−8.55839	−0.462110	−0.231055	−	0.972941i	$-0.574218\pi$
$7$	−8.55839	−0.462110	−0.231055	+	0.972941i	$0.574218\pi$
$8$	−8.00000	−0.353553
$9$	15.6413	0.579306
$10$	0	0
$11$	10.8092	0.296282	0.148141	−	0.988966i	$-0.452671\pi$
$11$	10.8092	0.296282	0.148141	+	0.988966i	$0.452671\pi$
$12$	26.1201	0.628352
$13$	−54.7046	−1.16710	−0.583551	−	0.812076i	$-0.698337\pi$
$13$	−54.7046	−1.16710	−0.583551	+	0.812076i	$0.698337\pi$
$14$	17.1168	0.326761
$15$	0	0
$16$	16.0000	0.250000
$17$	106.127	1.51409	0.757045	−	0.653363i	$-0.226642\pi$
$17$	106.127	1.51409	0.757045	+	0.653363i	$0.226642\pi$
$18$	−31.2825	−0.409631
$19$	−113.636	−1.37210	−0.686051	−	0.727554i	$-0.740657\pi$
$19$	−113.636	−1.37210	−0.686051	+	0.727554i	$0.740657\pi$
$20$	0	0
$21$	−55.8865	−0.580735
$22$	−21.6184	−0.209503
$23$	112.855	1.02313	0.511564	−	0.859245i	$-0.329066\pi$
$23$	112.855	1.02313	0.511564	+	0.859245i	$0.329066\pi$
$24$	−52.2402	−0.444312
$25$	0	0
$26$	109.409	0.825266
$27$	−74.1729	−0.528688
$28$	−34.2336	−0.231055
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−102.805	−0.595622	−0.297811	−	0.954625i	$-0.596257\pi$
$31$	−102.805	−0.595622	−0.297811	+	0.954625i	$0.596257\pi$
$32$	−32.0000	−0.176777
$33$	70.5845	0.372339
$34$	−212.254	−1.07062
$35$	0	0
$36$	62.5650	0.289653
$37$	105.665	0.469493	0.234746	−	0.972057i	$-0.424574\pi$
$37$	105.665	0.469493	0.234746	+	0.972057i	$0.424574\pi$
$38$	227.272	0.970222
$39$	−357.223	−1.46670
$40$	0	0
$41$	216.958	0.826417	0.413209	−	0.910636i	$-0.364408\pi$
$41$	216.958	0.826417	0.413209	+	0.910636i	$0.364408\pi$
$42$	111.773	0.410642
$43$	102.230	0.362555	0.181278	−	0.983432i	$-0.441977\pi$
$43$	102.230	0.362555	0.181278	+	0.983432i	$0.441977\pi$
$44$	43.2369	0.148141
$45$	0	0
$46$	−225.711	−0.723461
$47$	−455.212	−1.41275	−0.706377	−	0.707836i	$-0.749672\pi$
$47$	−455.212	−1.41275	−0.706377	+	0.707836i	$0.749672\pi$
$48$	104.480	0.314176
$49$	−269.754	−0.786455
$50$	0	0
$51$	693.011	1.90276
$52$	−218.819	−0.583551
$53$	593.714	1.53873	0.769367	−	0.638807i	$-0.220572\pi$
$53$	593.714	1.53873	0.769367	+	0.638807i	$0.220572\pi$
$54$	148.346	0.373839
$55$	0	0
$56$	68.4671	0.163380
$57$	−742.048	−1.72433
$58$	−58.0000	−0.131306
$59$	−558.141	−1.23159	−0.615794	−	0.787907i	$-0.711165\pi$
$59$	−558.141	−1.23159	−0.615794	+	0.787907i	$0.711165\pi$
$60$	0	0
$61$	−473.986	−0.994880	−0.497440	−	0.867498i	$-0.665727\pi$
$61$	−473.986	−0.994880	−0.497440	+	0.867498i	$0.665727\pi$
$62$	205.610	0.421168
$63$	−133.864	−0.267703
$64$	64.0000	0.125000
$65$	0	0
$66$	−141.169	−0.263283
$67$	−193.132	−0.352162	−0.176081	−	0.984376i	$-0.556342\pi$
$67$	−193.132	−0.352162	−0.176081	+	0.984376i	$0.556342\pi$
$68$	424.507	0.757045
$69$	736.949	1.28577
$70$	0	0
$71$	−2.38155	−0.00398082	−0.00199041	−	0.999998i	$-0.500634\pi$
$71$	−2.38155	−0.00398082	−0.00199041	+	0.999998i	$0.500634\pi$
$72$	−125.130	−0.204816
$73$	−119.013	−0.190814	−0.0954071	−	0.995438i	$-0.530415\pi$
$73$	−119.013	−0.190814	−0.0954071	+	0.995438i	$0.530415\pi$
$74$	−211.330	−0.331981
$75$	0	0
$76$	−454.545	−0.686051
$77$	−92.5096	−0.136915
$78$	714.446	1.03712
$79$	−964.306	−1.37333	−0.686664	−	0.726975i	$-0.740926\pi$
$79$	−964.306	−1.37333	−0.686664	+	0.726975i	$0.740926\pi$
$80$	0	0
$81$	−906.665	−1.24371
$82$	−433.915	−0.584365
$83$	−1068.19	−1.41264	−0.706319	−	0.707893i	$-0.749646\pi$
$83$	−1068.19	−1.41264	−0.706319	+	0.707893i	$0.749646\pi$
$84$	−223.546	−0.290368
$85$	0	0
$86$	−204.459	−0.256365
$87$	189.371	0.233364
$88$	−86.4738	−0.104752
$89$	772.544	0.920106	0.460053	−	0.887891i	$-0.347830\pi$
$89$	772.544	0.920106	0.460053	+	0.887891i	$0.347830\pi$
$90$	0	0
$91$	468.184	0.539330
$92$	451.421	0.511564
$93$	−671.318	−0.748521
$94$	910.423	0.998968
$95$	0	0
$96$	−208.961	−0.222156
$97$	−1344.03	−1.40686	−0.703431	−	0.710763i	$-0.748350\pi$
$97$	−1344.03	−1.40686	−0.703431	+	0.710763i	$0.748350\pi$
$98$	539.508	0.556107
$99$	169.070	0.171638
$100$	0	0
$101$	986.733	0.972115	0.486057	−	0.873927i	$-0.338435\pi$
$101$	986.733	0.972115	0.486057	+	0.873927i	$0.338435\pi$
$102$	−1386.02	−1.34546
$103$	−548.272	−0.524493	−0.262247	−	0.965001i	$-0.584463\pi$
$103$	−548.272	−0.524493	−0.262247	+	0.965001i	$0.584463\pi$
$104$	437.637	0.412633
$105$	0	0
$106$	−1187.43	−1.08805
$107$	−1387.51	−1.25361	−0.626803	−	0.779178i	$-0.715637\pi$
$107$	−1387.51	−1.25361	−0.626803	+	0.779178i	$0.715637\pi$
$108$	−296.692	−0.264344
$109$	−1293.32	−1.13649	−0.568246	−	0.822859i	$-0.692378\pi$
$109$	−1293.32	−1.13649	−0.568246	+	0.822859i	$0.692378\pi$
$110$	0	0
$111$	689.996	0.590014
$112$	−136.934	−0.115527
$113$	−302.883	−0.252149	−0.126075	−	0.992021i	$-0.540238\pi$
$113$	−302.883	−0.252149	−0.126075	+	0.992021i	$0.540238\pi$
$114$	1484.10	1.21928
$115$	0	0
$116$	116.000	0.0928477
$117$	−855.650	−0.676110
$118$	1116.28	0.870865
$119$	−908.274	−0.699676
$120$	0	0
$121$	−1214.16	−0.912217
$122$	947.972	0.703487
$123$	1416.74	1.03856
$124$	−411.219	−0.297811
$125$	0	0
$126$	267.728	0.189295
$127$	−2021.68	−1.41256	−0.706281	−	0.707931i	$-0.749629\pi$
$127$	−2021.68	−1.41256	−0.706281	+	0.707931i	$0.749629\pi$
$128$	−128.000	−0.0883883
$129$	667.562	0.455625
$130$	0	0
$131$	854.726	0.570059	0.285030	−	0.958519i	$-0.407997\pi$
$131$	854.726	0.570059	0.285030	+	0.958519i	$0.407997\pi$
$132$	282.338	0.186170
$133$	972.543	0.634062
$134$	386.264	0.249016
$135$	0	0
$136$	−849.014	−0.535311
$137$	−365.024	−0.227636	−0.113818	−	0.993502i	$-0.536308\pi$
$137$	−365.024	−0.227636	−0.113818	+	0.993502i	$0.536308\pi$
$138$	−1473.90	−0.909177
$139$	−1010.10	−0.616370	−0.308185	−	0.951326i	$-0.599722\pi$
$139$	−1010.10	−0.616370	−0.308185	+	0.951326i	$0.599722\pi$
$140$	0	0
$141$	−2972.55	−1.77541
$142$	4.76310	0.00281487
$143$	−591.315	−0.345792
$144$	250.260	0.144826
$145$	0	0
$146$	238.026	0.134926
$147$	−1761.50	−0.988341
$148$	422.660	0.234746
$149$	819.765	0.450723	0.225362	−	0.974275i	$-0.427644\pi$
$149$	819.765	0.450723	0.225362	+	0.974275i	$0.427644\pi$
$150$	0	0
$151$	1000.25	0.539068	0.269534	−	0.962991i	$-0.413130\pi$
$151$	1000.25	0.539068	0.269534	+	0.962991i	$0.413130\pi$
$152$	909.090	0.485111
$153$	1659.96	0.877121
$154$	185.019	0.0968134
$155$	0	0
$156$	−1428.89	−0.733352
$157$	1702.38	0.865382	0.432691	−	0.901542i	$-0.357564\pi$
$157$	1702.38	0.865382	0.432691	+	0.901542i	$0.357564\pi$
$158$	1928.61	0.971090
$159$	3876.97	1.93373
$160$	0	0
$161$	−965.860	−0.472798
$162$	1813.33	0.879436
$163$	3451.76	1.65867	0.829334	−	0.558753i	$-0.188720\pi$
$163$	3451.76	1.65867	0.829334	+	0.558753i	$0.188720\pi$
$164$	867.831	0.413209
$165$	0	0
$166$	2136.38	0.998886
$167$	−1409.23	−0.652990	−0.326495	−	0.945199i	$-0.605868\pi$
$167$	−1409.23	−0.652990	−0.326495	+	0.945199i	$0.605868\pi$
$168$	447.092	0.205321
$169$	795.598	0.362129
$170$	0	0
$171$	−1777.41	−0.794867
$172$	408.918	0.181278
$173$	−1358.39	−0.596973	−0.298487	−	0.954414i	$-0.596482\pi$
$173$	−1358.39	−0.596973	−0.298487	+	0.954414i	$0.596482\pi$
$174$	−378.742	−0.165013
$175$	0	0
$176$	172.948	0.0740705
$177$	−3644.67	−1.54774
$178$	−1545.09	−0.650614
$179$	−1702.56	−0.710924	−0.355462	−	0.934691i	$-0.615677\pi$
$179$	−1702.56	−0.710924	−0.355462	+	0.934691i	$0.615677\pi$
$180$	0	0
$181$	−7.33698	−0.00301300	−0.00150650	−	0.999999i	$-0.500480\pi$
$181$	−7.33698	−0.00301300	−0.00150650	+	0.999999i	$0.500480\pi$
$182$	−936.368	−0.381364
$183$	−3095.14	−1.25027
$184$	−902.843	−0.361731
$185$	0	0
$186$	1342.64	0.529284
$187$	1147.15	0.448598
$188$	−1820.85	−0.706377
$189$	634.801	0.244312
$190$	0	0
$191$	1324.78	0.501873	0.250936	−	0.968004i	$-0.419262\pi$
$191$	1324.78	0.501873	0.250936	+	0.968004i	$0.419262\pi$
$192$	417.922	0.157088
$193$	−1834.47	−0.684187	−0.342094	−	0.939666i	$-0.611136\pi$
$193$	−1834.47	−0.684187	−0.342094	+	0.939666i	$0.611136\pi$
$194$	2688.06	0.994802
$195$	0	0
$196$	−1079.02	−0.393227
$197$	4949.99	1.79021	0.895107	−	0.445851i	$-0.147099\pi$
$197$	4949.99	1.79021	0.895107	+	0.445851i	$0.147099\pi$
$198$	−338.140	−0.121366
$199$	3554.04	1.26603	0.633014	−	0.774140i	$-0.281818\pi$
$199$	3554.04	1.26603	0.633014	+	0.774140i	$0.281818\pi$
$200$	0	0
$201$	−1261.16	−0.442563
$202$	−1973.47	−0.687389
$203$	−248.193	−0.0858116
$204$	2772.04	0.951381
$205$	0	0
$206$	1096.54	0.370873
$207$	1765.20	0.592705
$208$	−875.274	−0.291776
$209$	−1228.32	−0.406529
$210$	0	0
$211$	2475.23	0.807590	0.403795	−	0.914849i	$-0.367691\pi$
$211$	2475.23	0.807590	0.403795	+	0.914849i	$0.367691\pi$
$212$	2374.86	0.769367
$213$	−15.5516	−0.00500271
$214$	2775.03	0.886434
$215$	0	0
$216$	593.383	0.186919
$217$	879.844	0.275243
$218$	2586.64	0.803622
$219$	−777.159	−0.239797
$220$	0	0
$221$	−5805.63	−1.76710
$222$	−1379.99	−0.417203
$223$	−2381.72	−0.715211	−0.357605	−	0.933873i	$-0.616407\pi$
$223$	−2381.72	−0.715211	−0.357605	+	0.933873i	$0.616407\pi$
$224$	273.869	0.0816902
$225$	0	0
$226$	605.767	0.178297
$227$	−5452.74	−1.59432	−0.797160	−	0.603768i	$-0.793666\pi$
$227$	−5452.74	−1.59432	−0.797160	+	0.603768i	$0.793666\pi$
$228$	−2968.19	−0.862163
$229$	596.232	0.172053	0.0860264	−	0.996293i	$-0.472583\pi$
$229$	596.232	0.172053	0.0860264	+	0.996293i	$0.472583\pi$
$230$	0	0
$231$	−604.090	−0.172062
$232$	−232.000	−0.0656532
$233$	5623.04	1.58102	0.790509	−	0.612450i	$-0.209816\pi$
$233$	5623.04	1.58102	0.790509	+	0.612450i	$0.209816\pi$
$234$	1711.30	0.478082
$235$	0	0
$236$	−2232.56	−0.615794
$237$	−6296.95	−1.72587
$238$	1816.55	0.494745
$239$	1564.27	0.423366	0.211683	−	0.977338i	$-0.432106\pi$
$239$	1564.27	0.423366	0.211683	+	0.977338i	$0.432106\pi$
$240$	0	0
$241$	−730.326	−0.195205	−0.0976026	−	0.995225i	$-0.531117\pi$
$241$	−730.326	−0.195205	−0.0976026	+	0.995225i	$0.531117\pi$
$242$	2428.32	0.645035
$243$	−3917.88	−1.03429
$244$	−1895.94	−0.497440
$245$	0	0
$246$	−2833.48	−0.734374
$247$	6216.43	1.60138
$248$	822.438	0.210584
$249$	−6975.31	−1.77527
$250$	0	0
$251$	−4244.39	−1.06735	−0.533673	−	0.845691i	$-0.679189\pi$
$251$	−4244.39	−1.06735	−0.533673	+	0.845691i	$0.679189\pi$
$252$	−535.456	−0.133851
$253$	1219.88	0.303135
$254$	4043.37	0.998833
$255$	0	0
$256$	256.000	0.0625000
$257$	235.374	0.0571292	0.0285646	−	0.999592i	$-0.490906\pi$
$257$	235.374	0.0571292	0.0285646	+	0.999592i	$0.490906\pi$
$258$	−1335.12	−0.322175
$259$	−904.323	−0.216957
$260$	0	0
$261$	453.597	0.107574
$262$	−1709.45	−0.403093
$263$	−3453.63	−0.809734	−0.404867	−	0.914376i	$-0.632682\pi$
$263$	−3453.63	−0.809734	−0.404867	+	0.914376i	$0.632682\pi$
$264$	−564.676	−0.131642
$265$	0	0
$266$	−1945.09	−0.448349
$267$	5044.73	1.15630
$268$	−772.528	−0.176081
$269$	−1921.31	−0.435481	−0.217741	−	0.976007i	$-0.569869\pi$
$269$	−1921.31	−0.435481	−0.217741	+	0.976007i	$0.569869\pi$
$270$	0	0
$271$	−2480.09	−0.555921	−0.277961	−	0.960592i	$-0.589658\pi$
$271$	−2480.09	−0.555921	−0.277961	+	0.960592i	$0.589658\pi$
$272$	1698.03	0.378522
$273$	3057.25	0.677778
$274$	730.048	0.160963
$275$	0	0
$276$	2947.79	0.642885
$277$	4766.90	1.03399	0.516995	−	0.855989i	$-0.327051\pi$
$277$	4766.90	1.03399	0.516995	+	0.855989i	$0.327051\pi$
$278$	2020.20	0.435840
$279$	−1608.00	−0.345047
$280$	0	0
$281$	194.329	0.0412552	0.0206276	−	0.999787i	$-0.493434\pi$
$281$	194.329	0.0412552	0.0206276	+	0.999787i	$0.493434\pi$
$282$	5945.09	1.25541
$283$	2817.42	0.591797	0.295898	−	0.955219i	$-0.404381\pi$
$283$	2817.42	0.591797	0.295898	+	0.955219i	$0.404381\pi$
$284$	−9.52621	−0.00199041
$285$	0	0
$286$	1182.63	0.244512
$287$	−1856.81	−0.381895
$288$	−500.520	−0.102408
$289$	6349.89	1.29247
$290$	0	0
$291$	−8776.56	−1.76801
$292$	−476.053	−0.0954071
$293$	−4059.12	−0.809339	−0.404670	−	0.914463i	$-0.632614\pi$
$293$	−4059.12	−0.809339	−0.404670	+	0.914463i	$0.632614\pi$
$294$	3523.00	0.698863
$295$	0	0
$296$	−845.320	−0.165991
$297$	−801.751	−0.156641
$298$	−1639.53	−0.318709
$299$	−6173.71	−1.19410
$300$	0	0
$301$	−874.921	−0.167540
$302$	−2000.50	−0.381178
$303$	6443.39	1.22166
$304$	−1818.18	−0.343025
$305$	0	0
$306$	−3319.91	−0.620218
$307$	131.572	0.0244600	0.0122300	−	0.999925i	$-0.496107\pi$
$307$	131.572	0.0244600	0.0122300	+	0.999925i	$0.496107\pi$
$308$	−370.038	−0.0684574
$309$	−3580.23	−0.659133
$310$	0	0
$311$	1517.84	0.276748	0.138374	−	0.990380i	$-0.455812\pi$
$311$	1517.84	0.276748	0.138374	+	0.990380i	$0.455812\pi$
$312$	2857.78	0.518558
$313$	−4244.17	−0.766436	−0.383218	−	0.923658i	$-0.625184\pi$
$313$	−4244.17	−0.766436	−0.383218	+	0.923658i	$0.625184\pi$
$314$	−3404.77	−0.611917
$315$	0	0
$316$	−3857.23	−0.686664
$317$	−5596.56	−0.991590	−0.495795	−	0.868439i	$-0.665123\pi$
$317$	−5596.56	−0.991590	−0.495795	+	0.868439i	$0.665123\pi$
$318$	−7753.94	−1.36736
$319$	313.467	0.0550182
$320$	0	0
$321$	−9060.50	−1.57541
$322$	1931.72	0.334319
$323$	−12059.8	−2.07748
$324$	−3626.66	−0.621855
$325$	0	0
$326$	−6903.53	−1.17286
$327$	−8445.42	−1.42824
$328$	−1735.66	−0.292183
$329$	3895.88	0.652848
$330$	0	0
$331$	−8383.85	−1.39220	−0.696100	−	0.717945i	$-0.745083\pi$
$331$	−8383.85	−1.39220	−0.696100	+	0.717945i	$0.745083\pi$
$332$	−4272.76	−0.706319
$333$	1652.73	0.271980
$334$	2818.45	0.461733
$335$	0	0
$336$	−894.185	−0.145184
$337$	−9887.12	−1.59818	−0.799089	−	0.601213i	$-0.794684\pi$
$337$	−9887.12	−1.59818	−0.799089	+	0.601213i	$0.794684\pi$
$338$	−1591.20	−0.256064
$339$	−1977.84	−0.316877
$340$	0	0
$341$	−1111.24	−0.176472
$342$	3554.83	0.562056
$343$	5244.19	0.825538
$344$	−817.837	−0.128183
$345$	0	0
$346$	2716.78	0.422124
$347$	−10678.8	−1.65206	−0.826032	−	0.563623i	$-0.809407\pi$
$347$	−10678.8	−1.65206	−0.826032	+	0.563623i	$0.809407\pi$
$348$	757.483	0.116682
$349$	−1457.88	−0.223605	−0.111803	−	0.993730i	$-0.535662\pi$
$349$	−1457.88	−0.223605	−0.111803	+	0.993730i	$0.535662\pi$
$350$	0	0
$351$	4057.60	0.617033
$352$	−345.895	−0.0523758
$353$	−6737.20	−1.01582	−0.507911	−	0.861410i	$-0.669582\pi$
$353$	−6737.20	−1.01582	−0.507911	+	0.861410i	$0.669582\pi$
$354$	7289.35	1.09442
$355$	0	0
$356$	3090.18	0.460053
$357$	−5931.06	−0.879285
$358$	3405.12	0.502699
$359$	−3539.85	−0.520407	−0.260204	−	0.965554i	$-0.583790\pi$
$359$	−3539.85	−0.520407	−0.260204	+	0.965554i	$0.583790\pi$
$360$	0	0
$361$	6054.19	0.882663
$362$	14.6740	0.00213051
$363$	−7928.50	−1.14639
$364$	1872.74	0.269665
$365$	0	0
$366$	6190.29	0.884075
$367$	4917.53	0.699436	0.349718	−	0.936855i	$-0.386277\pi$
$367$	4917.53	0.699436	0.349718	+	0.936855i	$0.386277\pi$
$368$	1805.69	0.255782
$369$	3393.49	0.478748
$370$	0	0
$371$	−5081.24	−0.711064
$372$	−2685.27	−0.374260
$373$	−2032.31	−0.282115	−0.141057	−	0.990001i	$-0.545050\pi$
$373$	−2032.31	−0.282115	−0.141057	+	0.990001i	$0.545050\pi$
$374$	−2294.30	−0.317206
$375$	0	0
$376$	3641.69	0.499484
$377$	−1586.43	−0.216726
$378$	−1269.60	−0.172755
$379$	−7051.47	−0.955699	−0.477849	−	0.878442i	$-0.658584\pi$
$379$	−7051.47	−0.955699	−0.477849	+	0.878442i	$0.658584\pi$
$380$	0	0
$381$	−13201.7	−1.77517
$382$	−2649.56	−0.354878
$383$	9334.72	1.24538	0.622691	−	0.782467i	$-0.286039\pi$
$383$	9334.72	1.24538	0.622691	+	0.782467i	$0.286039\pi$
$384$	−835.844	−0.111078
$385$	0	0
$386$	3668.94	0.483793
$387$	1599.00	0.210030
$388$	−5376.12	−0.703431
$389$	−1901.32	−0.247816	−0.123908	−	0.992294i	$-0.539543\pi$
$389$	−1901.32	−0.247816	−0.123908	+	0.992294i	$0.539543\pi$
$390$	0	0
$391$	11977.0	1.54911
$392$	2158.03	0.278054
$393$	5581.38	0.716396
$394$	−9899.98	−1.26587
$395$	0	0
$396$	676.280	0.0858190
$397$	−1995.81	−0.252309	−0.126155	−	0.992011i	$-0.540264\pi$
$397$	−1995.81	−0.252309	−0.126155	+	0.992011i	$0.540264\pi$
$398$	−7108.09	−0.895217
$399$	6350.73	0.796828
$400$	0	0
$401$	12920.6	1.60904	0.804520	−	0.593925i	$-0.202422\pi$
$401$	12920.6	1.60904	0.804520	+	0.593925i	$0.202422\pi$
$402$	2522.32	0.312939
$403$	5623.90	0.695152
$404$	3946.93	0.486057
$405$	0	0
$406$	496.387	0.0606780
$407$	1142.16	0.139102
$408$	−5544.09	−0.672728
$409$	−9713.54	−1.17434	−0.587168	−	0.809465i	$-0.699757\pi$
$409$	−9713.54	−1.17434	−0.587168	+	0.809465i	$0.699757\pi$
$410$	0	0
$411$	−2383.62	−0.286071
$412$	−2193.09	−0.262247
$413$	4776.79	0.569129
$414$	−3530.40	−0.419106
$415$	0	0
$416$	1750.55	0.206317
$417$	−6595.97	−0.774595
$418$	2456.64	0.287460
$419$	15925.4	1.85682	0.928411	−	0.371555i	$-0.121175\pi$
$419$	15925.4	1.85682	0.928411	+	0.371555i	$0.121175\pi$
$420$	0	0
$421$	10849.9	1.25604	0.628019	−	0.778198i	$-0.283866\pi$
$421$	10849.9	1.25604	0.628019	+	0.778198i	$0.283866\pi$
$422$	−4950.45	−0.571053
$423$	−7120.09	−0.818417
$424$	−4749.71	−0.544025
$425$	0	0
$426$	31.1032	0.00353745
$427$	4056.56	0.459744
$428$	−5550.05	−0.626803
$429$	−3861.30	−0.434558
$430$	0	0
$431$	−532.335	−0.0594934	−0.0297467	−	0.999557i	$-0.509470\pi$
$431$	−532.335	−0.0594934	−0.0297467	+	0.999557i	$0.509470\pi$
$432$	−1186.77	−0.132172
$433$	6995.94	0.776451	0.388225	−	0.921564i	$-0.373088\pi$
$433$	6995.94	0.776451	0.388225	+	0.921564i	$0.373088\pi$
$434$	−1759.69	−0.194626
$435$	0	0
$436$	−5173.28	−0.568246
$437$	−12824.5	−1.40384
$438$	1554.32	0.169562
$439$	3272.22	0.355750	0.177875	−	0.984053i	$-0.443078\pi$
$439$	3272.22	0.355750	0.177875	+	0.984053i	$0.443078\pi$
$440$	0	0
$441$	−4219.29	−0.455598
$442$	11611.3	1.24953
$443$	3818.14	0.409493	0.204746	−	0.978815i	$-0.434363\pi$
$443$	3818.14	0.409493	0.204746	+	0.978815i	$0.434363\pi$
$444$	2759.98	0.295007
$445$	0	0
$446$	4763.45	0.505731
$447$	5353.09	0.566426
$448$	−547.737	−0.0577637
$449$	−4323.19	−0.454396	−0.227198	−	0.973849i	$-0.572957\pi$
$449$	−4323.19	−0.454396	−0.227198	+	0.973849i	$0.572957\pi$
$450$	0	0
$451$	2345.14	0.244853
$452$	−1211.53	−0.126075
$453$	6531.66	0.677449
$454$	10905.5	1.12736
$455$	0	0
$456$	5936.38	0.609641
$457$	8367.43	0.856481	0.428240	−	0.903665i	$-0.359134\pi$
$457$	8367.43	0.856481	0.428240	+	0.903665i	$0.359134\pi$
$458$	−1192.46	−0.121660
$459$	−7871.73	−0.800481
$460$	0	0
$461$	−17249.0	−1.74266	−0.871328	−	0.490701i	$-0.836741\pi$
$461$	−17249.0	−1.74266	−0.871328	+	0.490701i	$0.836741\pi$
$462$	1208.18	0.121666
$463$	16774.3	1.68373	0.841864	−	0.539690i	$-0.181458\pi$
$463$	16774.3	1.68373	0.841864	+	0.539690i	$0.181458\pi$
$464$	464.000	0.0464238
$465$	0	0
$466$	−11246.1	−1.11795
$467$	−7701.05	−0.763088	−0.381544	−	0.924351i	$-0.624608\pi$
$467$	−7701.05	−0.763088	−0.381544	+	0.924351i	$0.624608\pi$
$468$	−3422.60	−0.338055
$469$	1652.90	0.162737
$470$	0	0
$471$	11116.6	1.08753
$472$	4465.13	0.435432
$473$	1105.02	0.107419
$474$	12593.9	1.22037
$475$	0	0
$476$	−3633.10	−0.349838
$477$	9286.44	0.891398
$478$	−3128.55	−0.299365
$479$	5988.77	0.571261	0.285630	−	0.958340i	$-0.407797\pi$
$479$	5988.77	0.571261	0.285630	+	0.958340i	$0.407797\pi$
$480$	0	0
$481$	−5780.37	−0.547946
$482$	1460.65	0.138031
$483$	−6307.09	−0.594167
$484$	−4856.64	−0.456108
$485$	0	0
$486$	7835.76	0.731352
$487$	−5790.34	−0.538779	−0.269390	−	0.963031i	$-0.586822\pi$
$487$	−5790.34	−0.538779	−0.269390	+	0.963031i	$0.586822\pi$
$488$	3791.89	0.351743
$489$	22540.1	2.08446
$490$	0	0
$491$	19228.8	1.76738	0.883692	−	0.468069i	$-0.155050\pi$
$491$	19228.8	1.76738	0.883692	+	0.468069i	$0.155050\pi$
$492$	5666.96	0.519281
$493$	3077.68	0.281159
$494$	−12432.9	−1.13235
$495$	0	0
$496$	−1644.88	−0.148905
$497$	20.3823	0.00183958
$498$	13950.6	1.25530
$499$	−7081.65	−0.635307	−0.317653	−	0.948207i	$-0.602895\pi$
$499$	−7081.65	−0.635307	−0.317653	+	0.948207i	$0.602895\pi$
$500$	0	0
$501$	−9202.29	−0.820615
$502$	8488.79	0.754727
$503$	5312.64	0.470932	0.235466	−	0.971883i	$-0.424338\pi$
$503$	5312.64	0.470932	0.235466	+	0.971883i	$0.424338\pi$
$504$	1070.91	0.0946473
$505$	0	0
$506$	−2439.76	−0.214349
$507$	5195.28	0.455089
$508$	−8086.74	−0.706281
$509$	−13862.7	−1.20717	−0.603587	−	0.797297i	$-0.706262\pi$
$509$	−13862.7	−1.20717	−0.603587	+	0.797297i	$0.706262\pi$
$510$	0	0
$511$	1018.56	0.0881771
$512$	−512.000	−0.0441942
$513$	8428.72	0.725414
$514$	−470.747	−0.0403965
$515$	0	0
$516$	2670.25	0.227812
$517$	−4920.49	−0.418574
$518$	1808.65	0.153412
$519$	−8870.32	−0.750219
$520$	0	0
$521$	15447.5	1.29897	0.649487	−	0.760373i	$-0.274984\pi$
$521$	15447.5	1.29897	0.649487	+	0.760373i	$0.274984\pi$
$522$	−907.193	−0.0760666
$523$	−4349.54	−0.363656	−0.181828	−	0.983330i	$-0.558201\pi$
$523$	−4349.54	−0.363656	−0.181828	+	0.983330i	$0.558201\pi$
$524$	3418.90	0.285030
$525$	0	0
$526$	6907.26	0.572568
$527$	−10910.3	−0.901825
$528$	1129.35	0.0930848
$529$	569.329	0.0467928
$530$	0	0
$531$	−8730.03	−0.713467
$532$	3890.17	0.317031
$533$	−11868.6	−0.964514
$534$	−10089.5	−0.817629
$535$	0	0
$536$	1545.06	0.124508
$537$	−11117.8	−0.893422
$538$	3842.62	0.307932
$539$	−2915.83	−0.233012
$540$	0	0
$541$	3206.84	0.254848	0.127424	−	0.991848i	$-0.459329\pi$
$541$	3206.84	0.254848	0.127424	+	0.991848i	$0.459329\pi$
$542$	4960.18	0.393096
$543$	−47.9107	−0.00378645
$544$	−3396.06	−0.267656
$545$	0	0
$546$	−6114.51	−0.479261
$547$	3289.81	0.257152	0.128576	−	0.991700i	$-0.458959\pi$
$547$	3289.81	0.257152	0.128576	+	0.991700i	$0.458959\pi$
$548$	−1460.10	−0.113818
$549$	−7413.74	−0.576340
$550$	0	0
$551$	−3295.45	−0.254793
$552$	−5895.59	−0.454589
$553$	8252.91	0.634628
$554$	−9533.79	−0.731141
$555$	0	0
$556$	−4040.40	−0.308185
$557$	313.140	0.0238207	0.0119104	−	0.999929i	$-0.496209\pi$
$557$	313.140	0.0238207	0.0119104	+	0.999929i	$0.496209\pi$
$558$	3215.99	0.243985
$559$	−5592.43	−0.423139
$560$	0	0
$561$	7490.91	0.563755
$562$	−388.659	−0.0291718
$563$	3425.84	0.256451	0.128225	−	0.991745i	$-0.459072\pi$
$563$	3425.84	0.256451	0.128225	+	0.991745i	$0.459072\pi$
$564$	−11890.2	−0.887707
$565$	0	0
$566$	−5634.85	−0.418463
$567$	7759.60	0.574731
$568$	19.0524	0.00140743
$569$	17763.8	1.30878	0.654390	−	0.756158i	$-0.272926\pi$
$569$	17763.8	1.30878	0.654390	+	0.756158i	$0.272926\pi$
$570$	0	0
$571$	5741.80	0.420818	0.210409	−	0.977613i	$-0.432520\pi$
$571$	5741.80	0.420818	0.210409	+	0.977613i	$0.432520\pi$
$572$	−2365.26	−0.172896
$573$	8650.85	0.630706
$574$	3713.62	0.270041
$575$	0	0
$576$	1001.04	0.0724132
$577$	−14477.5	−1.04455	−0.522275	−	0.852777i	$-0.674917\pi$
$577$	−14477.5	−1.04455	−0.522275	+	0.852777i	$0.674917\pi$
$578$	−12699.8	−0.913912
$579$	−11979.1	−0.859821
$580$	0	0
$581$	9141.98	0.652794
$582$	17553.1	1.25017
$583$	6417.59	0.455899
$584$	952.105	0.0674630
$585$	0	0
$586$	8118.24	0.572289
$587$	18082.8	1.27148	0.635738	−	0.771905i	$-0.280696\pi$
$587$	18082.8	1.27148	0.635738	+	0.771905i	$0.280696\pi$
$588$	−7046.00	−0.494170
$589$	11682.3	0.817254
$590$	0	0
$591$	32323.6	2.24977
$592$	1690.64	0.117373
$593$	−1731.57	−0.119911	−0.0599553	−	0.998201i	$-0.519096\pi$
$593$	−1731.57	−0.119911	−0.0599553	+	0.998201i	$0.519096\pi$
$594$	1603.50	0.110762
$595$	0	0
$596$	3279.06	0.225362
$597$	23208.0	1.59102
$598$	12347.4	0.844354
$599$	−11480.5	−0.783105	−0.391552	−	0.920156i	$-0.628062\pi$
$599$	−11480.5	−0.783105	−0.391552	+	0.920156i	$0.628062\pi$
$600$	0	0
$601$	2924.56	0.198495	0.0992474	−	0.995063i	$-0.468356\pi$
$601$	2924.56	0.198495	0.0992474	+	0.995063i	$0.468356\pi$
$602$	1749.84	0.118469
$603$	−3020.83	−0.204009
$604$	4001.00	0.269534
$605$	0	0
$606$	−12886.8	−0.863845
$607$	−3586.09	−0.239794	−0.119897	−	0.992786i	$-0.538256\pi$
$607$	−3586.09	−0.239794	−0.119897	+	0.992786i	$0.538256\pi$
$608$	3636.36	0.242556
$609$	−1620.71	−0.107840
$610$	0	0
$611$	24902.2	1.64883
$612$	6639.83	0.438561
$613$	11679.8	0.769561	0.384781	−	0.923008i	$-0.374277\pi$
$613$	11679.8	0.769561	0.384781	+	0.923008i	$0.374277\pi$
$614$	−263.145	−0.0172958
$615$	0	0
$616$	740.077	0.0484067
$617$	−11063.0	−0.721847	−0.360924	−	0.932595i	$-0.617539\pi$
$617$	−11063.0	−0.721847	−0.360924	+	0.932595i	$0.617539\pi$
$618$	7160.46	0.466078
$619$	−2463.60	−0.159969	−0.0799843	−	0.996796i	$-0.525487\pi$
$619$	−2463.60	−0.159969	−0.0799843	+	0.996796i	$0.525487\pi$
$620$	0	0
$621$	−8370.81	−0.540916
$622$	−3035.67	−0.195690
$623$	−6611.73	−0.425190
$624$	−5715.57	−0.366676
$625$	0	0
$626$	8488.34	0.541952
$627$	−8020.96	−0.510887
$628$	6809.53	0.432691
$629$	11213.9	0.710854
$630$	0	0
$631$	1032.43	0.0651352	0.0325676	−	0.999470i	$-0.489632\pi$
$631$	1032.43	0.0651352	0.0325676	+	0.999470i	$0.489632\pi$
$632$	7714.45	0.485545
$633$	16163.3	1.01490
$634$	11193.1	0.701160
$635$	0	0
$636$	15507.9	0.966867
$637$	14756.8	0.917873
$638$	−626.935	−0.0389038
$639$	−37.2505	−0.00230611
$640$	0	0
$641$	12841.6	0.791282	0.395641	−	0.918405i	$-0.370522\pi$
$641$	12841.6	0.791282	0.395641	+	0.918405i	$0.370522\pi$
$642$	18121.0	1.11399
$643$	−8449.14	−0.518198	−0.259099	−	0.965851i	$-0.583426\pi$
$643$	−8449.14	−0.518198	−0.259099	+	0.965851i	$0.583426\pi$
$644$	−3863.44	−0.236399
$645$	0	0
$646$	24119.7	1.46900
$647$	27036.8	1.64285	0.821426	−	0.570315i	$-0.193179\pi$
$647$	27036.8	1.64285	0.821426	+	0.570315i	$0.193179\pi$
$648$	7253.32	0.439718
$649$	−6033.07	−0.364898
$650$	0	0
$651$	5745.40	0.345899
$652$	13807.1	0.829334
$653$	27105.2	1.62436	0.812181	−	0.583405i	$-0.198280\pi$
$653$	27105.2	1.62436	0.812181	+	0.583405i	$0.198280\pi$
$654$	16890.8	1.00991
$655$	0	0
$656$	3471.32	0.206604
$657$	−1861.52	−0.110540
$658$	−7791.76	−0.461633
$659$	−22622.4	−1.33724	−0.668621	−	0.743603i	$-0.733115\pi$
$659$	−22622.4	−1.33724	−0.668621	+	0.743603i	$0.733115\pi$
$660$	0	0
$661$	−21000.2	−1.23572	−0.617862	−	0.786287i	$-0.712001\pi$
$661$	−21000.2	−1.23572	−0.617862	+	0.786287i	$0.712001\pi$
$662$	16767.7	0.984434
$663$	−37910.9	−2.22072
$664$	8545.51	0.499443
$665$	0	0
$666$	−3305.47	−0.192319
$667$	3272.80	0.189990
$668$	−5636.91	−0.326495
$669$	−15552.7	−0.898809
$670$	0	0
$671$	−5123.42	−0.294765
$672$	1788.37	0.102660
$673$	13691.2	0.784186	0.392093	−	0.919926i	$-0.371751\pi$
$673$	13691.2	0.784186	0.392093	+	0.919926i	$0.371751\pi$
$674$	19774.2	1.13008
$675$	0	0
$676$	3182.39	0.181065
$677$	−9694.60	−0.550360	−0.275180	−	0.961393i	$-0.588737\pi$
$677$	−9694.60	−0.550360	−0.275180	+	0.961393i	$0.588737\pi$
$678$	3955.68	0.224066
$679$	11502.7	0.650125
$680$	0	0
$681$	−35606.5	−2.00359
$682$	2222.48	0.124785
$683$	−6012.25	−0.336826	−0.168413	−	0.985717i	$-0.553864\pi$
$683$	−6012.25	−0.336826	−0.168413	+	0.985717i	$0.553864\pi$
$684$	−7109.65	−0.397433
$685$	0	0
$686$	−10488.4	−0.583744
$687$	3893.41	0.216220
$688$	1635.67	0.0906388
$689$	−32478.9	−1.79586
$690$	0	0
$691$	−10304.9	−0.567317	−0.283659	−	0.958925i	$-0.591548\pi$
$691$	−10304.9	−0.567317	−0.283659	+	0.958925i	$0.591548\pi$
$692$	−5433.55	−0.298487
$693$	−1446.97	−0.0793156
$694$	21357.5	1.16819
$695$	0	0
$696$	−1514.97	−0.0825067
$697$	23025.0	1.25127
$698$	2915.75	0.158113
$699$	36718.6	1.98687
$700$	0	0
$701$	11785.8	0.635011	0.317506	−	0.948256i	$-0.397155\pi$
$701$	11785.8	0.635011	0.317506	+	0.948256i	$0.397155\pi$
$702$	−8115.20	−0.436308
$703$	−12007.4	−0.644192
$704$	691.790	0.0370353
$705$	0	0
$706$	13474.4	0.718294
$707$	−8444.85	−0.449224
$708$	−14578.7	−0.773872
$709$	29226.1	1.54811	0.774054	−	0.633120i	$-0.218226\pi$
$709$	29226.1	1.54811	0.774054	+	0.633120i	$0.218226\pi$
$710$	0	0
$711$	−15083.0	−0.795577
$712$	−6180.35	−0.325307
$713$	−11602.1	−0.609398
$714$	11862.1	0.621749
$715$	0	0
$716$	−6810.25	−0.355462
$717$	10214.7	0.532045
$718$	7079.70	0.367983
$719$	14706.5	0.762809	0.381404	−	0.924408i	$-0.375441\pi$
$719$	14706.5	0.762809	0.381404	+	0.924408i	$0.375441\pi$
$720$	0	0
$721$	4692.32	0.242374
$722$	−12108.4	−0.624137
$723$	−4769.05	−0.245315
$724$	−29.3479	−0.00150650
$725$	0	0
$726$	15857.0	0.810618
$727$	35975.1	1.83527	0.917637	−	0.397419i	$-0.130094\pi$
$727$	35975.1	1.83527	0.917637	+	0.397419i	$0.130094\pi$
$728$	−3745.47	−0.190682
$729$	−1103.91	−0.0560843
$730$	0	0
$731$	10849.3	0.548941
$732$	−12380.6	−0.625135
$733$	−10872.8	−0.547879	−0.273939	−	0.961747i	$-0.588327\pi$
$733$	−10872.8	−0.547879	−0.273939	+	0.961747i	$0.588327\pi$
$734$	−9835.06	−0.494576
$735$	0	0
$736$	−3611.37	−0.180865
$737$	−2087.61	−0.104339
$738$	−6786.98	−0.338526
$739$	−1078.25	−0.0536727	−0.0268363	−	0.999640i	$-0.508543\pi$
$739$	−1078.25	−0.0536727	−0.0268363	+	0.999640i	$0.508543\pi$
$740$	0	0
$741$	40593.4	2.01247
$742$	10162.5	0.502798
$743$	23176.4	1.14436	0.572180	−	0.820128i	$-0.306098\pi$
$743$	23176.4	1.14436	0.572180	+	0.820128i	$0.306098\pi$
$744$	5370.54	0.264642
$745$	0	0
$746$	4064.61	0.199485
$747$	−16707.8	−0.818350
$748$	4588.59	0.224299
$749$	11874.9	0.579304
$750$	0	0
$751$	8738.85	0.424614	0.212307	−	0.977203i	$-0.431902\pi$
$751$	8738.85	0.424614	0.212307	+	0.977203i	$0.431902\pi$
$752$	−7283.39	−0.353189
$753$	−27716.0	−1.34134
$754$	3172.87	0.153248
$755$	0	0
$756$	2539.20	0.122156
$757$	−4121.15	−0.197868	−0.0989338	−	0.995094i	$-0.531543\pi$
$757$	−4121.15	−0.197868	−0.0989338	+	0.995094i	$0.531543\pi$
$758$	14102.9	0.675781
$759$	7965.84	0.380951
$760$	0	0
$761$	8706.54	0.414733	0.207367	−	0.978263i	$-0.433511\pi$
$761$	8706.54	0.414733	0.207367	+	0.978263i	$0.433511\pi$
$762$	26403.3	1.25524
$763$	11068.7	0.525184
$764$	5299.12	0.250936
$765$	0	0
$766$	−18669.4	−0.880619
$767$	30532.9	1.43739
$768$	1671.69	0.0785440
$769$	−32258.8	−1.51272	−0.756361	−	0.654154i	$-0.773025\pi$
$769$	−32258.8	−1.51272	−0.756361	+	0.654154i	$0.773025\pi$
$770$	0	0
$771$	1537.00	0.0717945
$772$	−7337.88	−0.342094
$773$	−24794.1	−1.15366	−0.576832	−	0.816863i	$-0.695711\pi$
$773$	−24794.1	−1.15366	−0.576832	+	0.816863i	$0.695711\pi$
$774$	−3198.00	−0.148514
$775$	0	0
$776$	10752.2	0.497401
$777$	−5905.25	−0.272651
$778$	3802.63	0.175233
$779$	−24654.2	−1.13393
$780$	0	0
$781$	−25.7427	−0.00117945
$782$	−23953.9	−1.09539
$783$	−2151.01	−0.0981749
$784$	−4316.06	−0.196614
$785$	0	0
$786$	−11162.8	−0.506568
$787$	11114.7	0.503427	0.251714	−	0.967802i	$-0.419006\pi$
$787$	11114.7	0.503427	0.251714	+	0.967802i	$0.419006\pi$
$788$	19800.0	0.895107
$789$	−22552.3	−1.01760
$790$	0	0
$791$	2592.20	0.116521
$792$	−1352.56	−0.0606832
$793$	25929.2	1.16113
$794$	3991.62	0.178410
$795$	0	0
$796$	14216.2	0.633014
$797$	12329.8	0.547986	0.273993	−	0.961732i	$-0.411656\pi$
$797$	12329.8	0.547986	0.273993	+	0.961732i	$0.411656\pi$
$798$	−12701.5	−0.563442
$799$	−48310.1	−2.13904
$800$	0	0
$801$	12083.6	0.533023
$802$	−25841.3	−1.13776
$803$	−1286.44	−0.0565348
$804$	−5044.63	−0.221282
$805$	0	0
$806$	−11247.8	−0.491547
$807$	−12546.2	−0.547271
$808$	−7893.86	−0.343695
$809$	−36175.5	−1.57214	−0.786070	−	0.618138i	$-0.787887\pi$
$809$	−36175.5	−1.57214	−0.786070	+	0.618138i	$0.787887\pi$
$810$	0	0
$811$	−26581.0	−1.15091	−0.575453	−	0.817835i	$-0.695174\pi$
$811$	−26581.0	−1.15091	−0.575453	+	0.817835i	$0.695174\pi$
$812$	−992.774	−0.0429058
$813$	−16195.0	−0.698629
$814$	−2284.31	−0.0983602
$815$	0	0
$816$	11088.2	0.475691
$817$	−11617.0	−0.497462
$818$	19427.1	0.830381
$819$	7322.98	0.312437
$820$	0	0
$821$	10811.1	0.459574	0.229787	−	0.973241i	$-0.426197\pi$
$821$	10811.1	0.459574	0.229787	+	0.973241i	$0.426197\pi$
$822$	4767.24	0.202283
$823$	−28625.1	−1.21240	−0.606202	−	0.795311i	$-0.707308\pi$
$823$	−28625.1	−1.21240	−0.606202	+	0.795311i	$0.707308\pi$
$824$	4386.17	0.185436
$825$	0	0
$826$	−9553.58	−0.402435
$827$	9970.68	0.419244	0.209622	−	0.977783i	$-0.432777\pi$
$827$	9970.68	0.419244	0.209622	+	0.977783i	$0.432777\pi$
$828$	7060.80	0.296352
$829$	20201.0	0.846334	0.423167	−	0.906052i	$-0.360918\pi$
$829$	20201.0	0.846334	0.423167	+	0.906052i	$0.360918\pi$
$830$	0	0
$831$	31128.0	1.29942
$832$	−3501.10	−0.145888
$833$	−28628.1	−1.19076
$834$	13191.9	0.547722
$835$	0	0
$836$	−4913.28	−0.203265
$837$	7625.33	0.314898
$838$	−31850.9	−1.31297
$839$	28023.4	1.15313	0.576564	−	0.817052i	$-0.304393\pi$
$839$	28023.4	1.15313	0.576564	+	0.817052i	$0.304393\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−21699.8	−0.888153
$843$	1268.98	0.0518456
$844$	9900.90	0.403795
$845$	0	0
$846$	14240.2	0.578708
$847$	10391.3	0.421544
$848$	9499.42	0.384683
$849$	18397.9	0.743714
$850$	0	0
$851$	11924.9	0.480352
$852$	−62.2064	−0.00250136
$853$	26333.8	1.05704	0.528518	−	0.848922i	$-0.322748\pi$
$853$	26333.8	1.05704	0.528518	+	0.848922i	$0.322748\pi$
$854$	−8113.12	−0.325088
$855$	0	0
$856$	11100.1	0.443217
$857$	−36388.6	−1.45042	−0.725211	−	0.688527i	$-0.758258\pi$
$857$	−36388.6	−1.45042	−0.725211	+	0.688527i	$0.758258\pi$
$858$	7722.60	0.307279
$859$	14974.0	0.594770	0.297385	−	0.954758i	$-0.403885\pi$
$859$	14974.0	0.594770	0.297385	+	0.954758i	$0.403885\pi$
$860$	0	0
$861$	−12125.0	−0.479930
$862$	1064.67	0.0420682
$863$	40168.2	1.58440	0.792202	−	0.610259i	$-0.208935\pi$
$863$	40168.2	1.58440	0.792202	+	0.610259i	$0.208935\pi$
$864$	2373.53	0.0934597
$865$	0	0
$866$	−13991.9	−0.549034
$867$	41465.0	1.62425
$868$	3519.37	0.137621
$869$	−10423.4	−0.406893
$870$	0	0
$871$	10565.2	0.411009
$872$	10346.6	0.401811
$873$	−21022.3	−0.815004
$874$	25648.9	0.992663
$875$	0	0
$876$	−3108.64	−0.119899
$877$	−32161.7	−1.23834	−0.619169	−	0.785258i	$-0.712531\pi$
$877$	−32161.7	−1.23834	−0.619169	+	0.785258i	$0.712531\pi$
$878$	−6544.43	−0.251553
$879$	−26506.2	−1.01710
$880$	0	0
$881$	−8870.49	−0.339222	−0.169611	−	0.985511i	$-0.554251\pi$
$881$	−8870.49	−0.339222	−0.169611	+	0.985511i	$0.554251\pi$
$882$	8438.58	0.322156
$883$	24647.3	0.939351	0.469675	−	0.882839i	$-0.344371\pi$
$883$	24647.3	0.939351	0.469675	+	0.882839i	$0.344371\pi$
$884$	−23222.5	−0.883549
$885$	0	0
$886$	−7636.28	−0.289555
$887$	−32371.7	−1.22541	−0.612703	−	0.790313i	$-0.709918\pi$
$887$	−32371.7	−1.22541	−0.612703	+	0.790313i	$0.709918\pi$
$888$	−5519.97	−0.208601
$889$	17302.4	0.652759
$890$	0	0
$891$	−9800.35	−0.368489
$892$	−9526.90	−0.357605
$893$	51728.5	1.93844
$894$	−10706.2	−0.400523
$895$	0	0
$896$	1095.47	0.0408451
$897$	−40314.5	−1.50063
$898$	8646.38	0.321307
$899$	−2981.34	−0.110604
$900$	0	0
$901$	63008.9	2.32978
$902$	−4690.29	−0.173137
$903$	−5713.26	−0.210549
$904$	2423.07	0.0891483
$905$	0	0
$906$	−13063.3	−0.479029
$907$	43728.0	1.60084	0.800422	−	0.599437i	$-0.204609\pi$
$907$	43728.0	1.60084	0.800422	+	0.599437i	$0.204609\pi$
$908$	−21810.9	−0.797160
$909$	15433.7	0.563152
$910$	0	0
$911$	16033.6	0.583115	0.291557	−	0.956553i	$-0.405827\pi$
$911$	16033.6	0.583115	0.291557	+	0.956553i	$0.405827\pi$
$912$	−11872.8	−0.431082
$913$	−11546.3	−0.418540
$914$	−16734.9	−0.605623
$915$	0	0
$916$	2384.93	0.0860264
$917$	−7315.08	−0.263430
$918$	15743.5	0.566026
$919$	29331.1	1.05282	0.526411	−	0.850230i	$-0.323537\pi$
$919$	29331.1	1.05282	0.526411	+	0.850230i	$0.323537\pi$
$920$	0	0
$921$	859.170	0.0307390
$922$	34497.9	1.23224
$923$	130.282	0.00464603
$924$	−2416.36	−0.0860308
$925$	0	0
$926$	−33548.5	−1.19058
$927$	−8575.66	−0.303842
$928$	−928.000	−0.0328266
$929$	−10024.6	−0.354034	−0.177017	−	0.984208i	$-0.556645\pi$
$929$	−10024.6	−0.354034	−0.177017	+	0.984208i	$0.556645\pi$
$930$	0	0
$931$	30653.8	1.07910
$932$	22492.1	0.790509
$933$	9911.51	0.347790
$934$	15402.1	0.539585
$935$	0	0
$936$	6845.20	0.239041
$937$	−21241.3	−0.740578	−0.370289	−	0.928917i	$-0.620741\pi$
$937$	−21241.3	−0.740578	−0.370289	+	0.928917i	$0.620741\pi$
$938$	−3305.80	−0.115073
$939$	−27714.5	−0.963184
$940$	0	0
$941$	11953.8	0.414115	0.207057	−	0.978329i	$-0.433611\pi$
$941$	11953.8	0.414115	0.207057	+	0.978329i	$0.433611\pi$
$942$	−22233.2	−0.768999
$943$	24484.8	0.845531
$944$	−8930.25	−0.307897
$945$	0	0
$946$	−2210.05	−0.0759564
$947$	31650.6	1.08607	0.543034	−	0.839711i	$-0.317275\pi$
$947$	31650.6	1.08607	0.543034	+	0.839711i	$0.317275\pi$
$948$	−25187.8	−0.862934
$949$	6510.57	0.222700
$950$	0	0
$951$	−36545.7	−1.24614
$952$	7266.20	0.247373
$953$	17373.5	0.590539	0.295269	−	0.955414i	$-0.404591\pi$
$953$	17373.5	0.590539	0.295269	+	0.955414i	$0.404591\pi$
$954$	−18572.9	−0.630313
$955$	0	0
$956$	6257.09	0.211683
$957$	2046.95	0.0691416
$958$	−11977.5	−0.403942
$959$	3124.02	0.105193
$960$	0	0
$961$	−19222.2	−0.645234
$962$	11560.7	0.387457
$963$	−21702.4	−0.726222
$964$	−2921.30	−0.0976026
$965$	0	0
$966$	12614.2	0.420140
$967$	11017.6	0.366394	0.183197	−	0.983076i	$-0.441355\pi$
$967$	11017.6	0.366394	0.183197	+	0.983076i	$0.441355\pi$
$968$	9713.29	0.322517
$969$	−78751.1	−2.61078
$970$	0	0
$971$	17365.0	0.573912	0.286956	−	0.957944i	$-0.407357\pi$
$971$	17365.0	0.573912	0.286956	+	0.957944i	$0.407357\pi$
$972$	−15671.5	−0.517144
$973$	8644.82	0.284831
$974$	11580.7	0.380975
$975$	0	0
$976$	−7583.78	−0.248720
$977$	29193.4	0.955967	0.477983	−	0.878369i	$-0.341368\pi$
$977$	29193.4	0.955967	0.477983	+	0.878369i	$0.341368\pi$
$978$	−45080.2	−1.47393
$979$	8350.60	0.272611
$980$	0	0
$981$	−20229.2	−0.658377
$982$	−38457.7	−1.24973
$983$	−50359.8	−1.63401	−0.817003	−	0.576634i	$-0.804366\pi$
$983$	−50359.8	−1.63401	−0.817003	+	0.576634i	$0.804366\pi$
$984$	−11333.9	−0.367187
$985$	0	0
$986$	−6155.35	−0.198810
$987$	25440.2	0.820436
$988$	24865.7	0.800692
$989$	11537.2	0.370941
$990$	0	0
$991$	−20823.5	−0.667488	−0.333744	−	0.942664i	$-0.608312\pi$
$991$	−20823.5	−0.667488	−0.333744	+	0.942664i	$0.608312\pi$
$992$	3289.75	0.105292
$993$	−54746.8	−1.74958
$994$	−40.7645	−0.00130078
$995$	0	0
$996$	−27901.2	−0.887635
$997$	27651.2	0.878356	0.439178	−	0.898400i	$-0.355270\pi$
$997$	27651.2	0.878356	0.439178	+	0.898400i	$0.355270\pi$
$998$	14163.3	0.449230
$999$	−7837.48	−0.248215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.4.a.h.1.3		3
5.4	even	2		58.4.a.d.1.1	✓	3
15.14	odd	2		522.4.a.k.1.1		3
20.19	odd	2		464.4.a.i.1.3		3
40.19	odd	2		1856.4.a.s.1.1		3
40.29	even	2		1856.4.a.r.1.3		3
145.144	even	2		1682.4.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.d.1.1	✓	3	5.4	even	2
464.4.a.i.1.3		3	20.19	odd	2
522.4.a.k.1.1		3	15.14	odd	2
1450.4.a.h.1.3		3	1.1	even	1	trivial
1682.4.a.d.1.3		3	145.144	even	2
1856.4.a.r.1.3		3	40.29	even	2
1856.4.a.s.1.1		3	40.19	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.53003 q^{3} +4.00000 q^{4} -13.0601 q^{6} -8.55839 q^{7} -8.00000 q^{8} +15.6413 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +6.53003 q^{3} +4.00000 q^{4} -13.0601 q^{6} -8.55839 q^{7} -8.00000 q^{8} +15.6413 q^{9} +10.8092 q^{11} +26.1201 q^{12} -54.7046 q^{13} +17.1168 q^{14} +16.0000 q^{16} +106.127 q^{17} -31.2825 q^{18} -113.636 q^{19} -55.8865 q^{21} -21.6184 q^{22} +112.855 q^{23} -52.2402 q^{24} +109.409 q^{26} -74.1729 q^{27} -34.2336 q^{28} +29.0000 q^{29} -102.805 q^{31} -32.0000 q^{32} +70.5845 q^{33} -212.254 q^{34} +62.5650 q^{36} +105.665 q^{37} +227.272 q^{38} -357.223 q^{39} +216.958 q^{41} +111.773 q^{42} +102.230 q^{43} +43.2369 q^{44} -225.711 q^{46} -455.212 q^{47} +104.480 q^{48} -269.754 q^{49} +693.011 q^{51} -218.819 q^{52} +593.714 q^{53} +148.346 q^{54} +68.4671 q^{56} -742.048 q^{57} -58.0000 q^{58} -558.141 q^{59} -473.986 q^{61} +205.610 q^{62} -133.864 q^{63} +64.0000 q^{64} -141.169 q^{66} -193.132 q^{67} +424.507 q^{68} +736.949 q^{69} -2.38155 q^{71} -125.130 q^{72} -119.013 q^{73} -211.330 q^{74} -454.545 q^{76} -92.5096 q^{77} +714.446 q^{78} -964.306 q^{79} -906.665 q^{81} -433.915 q^{82} -1068.19 q^{83} -223.546 q^{84} -204.459 q^{86} +189.371 q^{87} -86.4738 q^{88} +772.544 q^{89} +468.184 q^{91} +451.421 q^{92} -671.318 q^{93} +910.423 q^{94} -208.961 q^{96} -1344.03 q^{97} +539.508 q^{98} +169.070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 4 q^{6} - 24 q^{7} - 24 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 4 * q^6 - 24 * q^7 - 24 * q^8 + 5 * q^9	\( 3 q - 6 q^{2} - 2 q^{3} + 12 q^{4} + 4 q^{6} - 24 q^{7} - 24 q^{8} + 5 q^{9} + 10 q^{11} - 8 q^{12} + 4 q^{13} + 48 q^{14} + 48 q^{16} + 66 q^{17} - 10 q^{18} - 164 q^{19} - 88 q^{21} - 20 q^{22} + 204 q^{23} + 16 q^{24} - 8 q^{26} + 142 q^{27} - 96 q^{28} + 87 q^{29} - 86 q^{31} - 96 q^{32} + 130 q^{33} - 132 q^{34} + 20 q^{36} + 42 q^{37} + 328 q^{38} - 394 q^{39} + 562 q^{41} + 176 q^{42} - 18 q^{43} + 40 q^{44} - 408 q^{46} - 654 q^{47} - 32 q^{48} + 539 q^{49} + 556 q^{51} + 16 q^{52} - 712 q^{53} - 284 q^{54} + 192 q^{56} - 828 q^{57} - 174 q^{58} + 184 q^{59} + 322 q^{61} + 172 q^{62} + 784 q^{63} + 192 q^{64} - 260 q^{66} + 228 q^{67} + 264 q^{68} + 684 q^{69} - 52 q^{71} - 40 q^{72} + 494 q^{73} - 84 q^{74} - 656 q^{76} - 872 q^{77} + 788 q^{78} - 2110 q^{79} - 1513 q^{81} - 1124 q^{82} + 288 q^{83} - 352 q^{84} + 36 q^{86} - 58 q^{87} - 80 q^{88} + 914 q^{89} - 2984 q^{91} + 816 q^{92} + 62 q^{93} + 1308 q^{94} + 64 q^{96} - 218 q^{97} - 1078 q^{98} - 304 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 2 * q^3 + 12 * q^4 + 4 * q^6 - 24 * q^7 - 24 * q^8 + 5 * q^9 + 10 * q^11 - 8 * q^12 + 4 * q^13 + 48 * q^14 + 48 * q^16 + 66 * q^17 - 10 * q^18 - 164 * q^19 - 88 * q^21 - 20 * q^22 + 204 * q^23 + 16 * q^24 - 8 * q^26 + 142 * q^27 - 96 * q^28 + 87 * q^29 - 86 * q^31 - 96 * q^32 + 130 * q^33 - 132 * q^34 + 20 * q^36 + 42 * q^37 + 328 * q^38 - 394 * q^39 + 562 * q^41 + 176 * q^42 - 18 * q^43 + 40 * q^44 - 408 * q^46 - 654 * q^47 - 32 * q^48 + 539 * q^49 + 556 * q^51 + 16 * q^52 - 712 * q^53 - 284 * q^54 + 192 * q^56 - 828 * q^57 - 174 * q^58 + 184 * q^59 + 322 * q^61 + 172 * q^62 + 784 * q^63 + 192 * q^64 - 260 * q^66 + 228 * q^67 + 264 * q^68 + 684 * q^69 - 52 * q^71 - 40 * q^72 + 494 * q^73 - 84 * q^74 - 656 * q^76 - 872 * q^77 + 788 * q^78 - 2110 * q^79 - 1513 * q^81 - 1124 * q^82 + 288 * q^83 - 352 * q^84 + 36 * q^86 - 58 * q^87 - 80 * q^88 + 914 * q^89 - 2984 * q^91 + 816 * q^92 + 62 * q^93 + 1308 * q^94 + 64 * q^96 - 218 * q^97 - 1078 * q^98 - 304 * q^99

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