LMFDB - Embedded newform 1150.4.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 68x^{2} - 111x + 342 $ x^4 - 68x^2 - 111x + 342
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-6.57209$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +7.57209 q^{3} +4.00000 q^{4} +15.1442 q^{6} +35.4229 q^{7} +8.00000 q^{8} +30.3365 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +7.57209 q^{3} +4.00000 q^{4} +15.1442 q^{6} +35.4229 q^{7} +8.00000 q^{8} +30.3365 q^{9} -16.6298 q^{11} +30.2883 q^{12} +79.9132 q^{13} +70.8458 q^{14} +16.0000 q^{16} +46.8219 q^{17} +60.6730 q^{18} -110.653 q^{19} +268.225 q^{21} -33.2597 q^{22} +23.0000 q^{23} +60.5767 q^{24} +159.826 q^{26} +25.2641 q^{27} +141.692 q^{28} -0.836422 q^{29} -119.836 q^{31} +32.0000 q^{32} -125.923 q^{33} +93.6438 q^{34} +121.346 q^{36} -368.201 q^{37} -221.307 q^{38} +605.109 q^{39} -95.7927 q^{41} +536.450 q^{42} -331.961 q^{43} -66.5193 q^{44} +46.0000 q^{46} +535.037 q^{47} +121.153 q^{48} +911.782 q^{49} +354.539 q^{51} +319.653 q^{52} -409.345 q^{53} +50.5282 q^{54} +283.383 q^{56} -837.876 q^{57} -1.67284 q^{58} -352.950 q^{59} -507.223 q^{61} -239.672 q^{62} +1074.61 q^{63} +64.0000 q^{64} -251.845 q^{66} +820.056 q^{67} +187.288 q^{68} +174.158 q^{69} -733.770 q^{71} +242.692 q^{72} +91.4599 q^{73} -736.402 q^{74} -442.613 q^{76} -589.077 q^{77} +1210.22 q^{78} +329.381 q^{79} -627.783 q^{81} -191.585 q^{82} +753.834 q^{83} +1072.90 q^{84} -663.922 q^{86} -6.33346 q^{87} -133.039 q^{88} -1050.14 q^{89} +2830.76 q^{91} +92.0000 q^{92} -907.407 q^{93} +1070.07 q^{94} +242.307 q^{96} +271.928 q^{97} +1823.56 q^{98} -504.491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9	$ 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9} - 39 q^{11} + 16 q^{12} + 20 q^{13} + 2 q^{14} + 64 q^{16} + 23 q^{17} + 64 q^{18} + 53 q^{19} + 300 q^{21} - 78 q^{22} + 92 q^{23} + 32 q^{24} + 40 q^{26} - 137 q^{27} + 4 q^{28} + 161 q^{29} + 388 q^{31} + 128 q^{32} - 87 q^{33} + 46 q^{34} + 128 q^{36} - 466 q^{37} + 106 q^{38} + 1047 q^{39} + 484 q^{41} + 600 q^{42} - 894 q^{43} - 156 q^{44} + 184 q^{46} + 265 q^{47} + 64 q^{48} + 1643 q^{49} + 1825 q^{51} + 80 q^{52} - 576 q^{53} - 274 q^{54} + 8 q^{56} - 178 q^{57} + 322 q^{58} - 94 q^{59} + 1153 q^{61} + 776 q^{62} - 60 q^{63} + 256 q^{64} - 174 q^{66} + 1472 q^{67} + 92 q^{68} + 92 q^{69} + 200 q^{71} + 256 q^{72} - 1147 q^{73} - 932 q^{74} + 212 q^{76} + 2176 q^{77} + 2094 q^{78} - 908 q^{79} - 1056 q^{81} + 968 q^{82} + 1048 q^{83} + 1200 q^{84} - 1788 q^{86} + 2167 q^{87} - 312 q^{88} - 1784 q^{89} + 2329 q^{91} + 368 q^{92} - 1483 q^{93} + 530 q^{94} + 128 q^{96} + 2047 q^{97} + 3286 q^{98} - 2665 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9 - 39 * q^11 + 16 * q^12 + 20 * q^13 + 2 * q^14 + 64 * q^16 + 23 * q^17 + 64 * q^18 + 53 * q^19 + 300 * q^21 - 78 * q^22 + 92 * q^23 + 32 * q^24 + 40 * q^26 - 137 * q^27 + 4 * q^28 + 161 * q^29 + 388 * q^31 + 128 * q^32 - 87 * q^33 + 46 * q^34 + 128 * q^36 - 466 * q^37 + 106 * q^38 + 1047 * q^39 + 484 * q^41 + 600 * q^42 - 894 * q^43 - 156 * q^44 + 184 * q^46 + 265 * q^47 + 64 * q^48 + 1643 * q^49 + 1825 * q^51 + 80 * q^52 - 576 * q^53 - 274 * q^54 + 8 * q^56 - 178 * q^57 + 322 * q^58 - 94 * q^59 + 1153 * q^61 + 776 * q^62 - 60 * q^63 + 256 * q^64 - 174 * q^66 + 1472 * q^67 + 92 * q^68 + 92 * q^69 + 200 * q^71 + 256 * q^72 - 1147 * q^73 - 932 * q^74 + 212 * q^76 + 2176 * q^77 + 2094 * q^78 - 908 * q^79 - 1056 * q^81 + 968 * q^82 + 1048 * q^83 + 1200 * q^84 - 1788 * q^86 + 2167 * q^87 - 312 * q^88 - 1784 * q^89 + 2329 * q^91 + 368 * q^92 - 1483 * q^93 + 530 * q^94 + 128 * q^96 + 2047 * q^97 + 3286 * q^98 - 2665 * 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
$3$	7.57209	1.45725	0.728624	−	0.684914i	$-0.240160\pi$
$3$	7.57209	1.45725	0.728624	+	0.684914i	$0.240160\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	15.1442	1.03043
$7$	35.4229	1.91266	0.956328	−	0.292294i	$-0.0944187\pi$
$7$	35.4229	1.91266	0.956328	+	0.292294i	$0.0944187\pi$
$8$	8.00000	0.353553
$9$	30.3365	1.12357
$10$	0	0
$11$	−16.6298	−0.455826	−0.227913	−	0.973682i	$-0.573190\pi$
$11$	−16.6298	−0.455826	−0.227913	+	0.973682i	$0.573190\pi$
$12$	30.2883	0.728624
$13$	79.9132	1.70492	0.852459	−	0.522795i	$-0.175111\pi$
$13$	79.9132	1.70492	0.852459	+	0.522795i	$0.175111\pi$
$14$	70.8458	1.35245
$15$	0	0
$16$	16.0000	0.250000
$17$	46.8219	0.667999	0.333999	−	0.942573i	$-0.391602\pi$
$17$	46.8219	0.667999	0.333999	+	0.942573i	$0.391602\pi$
$18$	60.6730	0.794486
$19$	−110.653	−1.33608	−0.668042	−	0.744123i	$-0.732868\pi$
$19$	−110.653	−1.33608	−0.668042	+	0.744123i	$0.732868\pi$
$20$	0	0
$21$	268.225	2.78722
$22$	−33.2597	−0.322318
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	60.5767	0.515215
$25$	0	0
$26$	159.826	1.20556
$27$	25.2641	0.180077
$28$	141.692	0.956328
$29$	−0.836422	−0.00535585	−0.00267793	−	0.999996i	$-0.500852\pi$
$29$	−0.836422	−0.00535585	−0.00267793	+	0.999996i	$0.500852\pi$
$30$	0	0
$31$	−119.836	−0.694295	−0.347147	−	0.937811i	$-0.612850\pi$
$31$	−119.836	−0.694295	−0.347147	+	0.937811i	$0.612850\pi$
$32$	32.0000	0.176777
$33$	−125.923	−0.664252
$34$	93.6438	0.472346
$35$	0	0
$36$	121.346	0.561787
$37$	−368.201	−1.63600	−0.817998	−	0.575221i	$-0.804916\pi$
$37$	−368.201	−1.63600	−0.817998	+	0.575221i	$0.804916\pi$
$38$	−221.307	−0.944755
$39$	605.109	2.48449
$40$	0	0
$41$	−95.7927	−0.364886	−0.182443	−	0.983216i	$-0.558400\pi$
$41$	−95.7927	−0.364886	−0.182443	+	0.983216i	$0.558400\pi$
$42$	536.450	1.97086
$43$	−331.961	−1.17729	−0.588647	−	0.808390i	$-0.700339\pi$
$43$	−331.961	−1.17729	−0.588647	+	0.808390i	$0.700339\pi$
$44$	−66.5193	−0.227913
$45$	0	0
$46$	46.0000	0.147442
$47$	535.037	1.66049	0.830246	−	0.557397i	$-0.188200\pi$
$47$	535.037	1.66049	0.830246	+	0.557397i	$0.188200\pi$
$48$	121.153	0.364312
$49$	911.782	2.65826
$50$	0	0
$51$	354.539	0.973440
$52$	319.653	0.852459
$53$	−409.345	−1.06090	−0.530452	−	0.847715i	$-0.677978\pi$
$53$	−409.345	−1.06090	−0.530452	+	0.847715i	$0.677978\pi$
$54$	50.5282	0.127334
$55$	0	0
$56$	283.383	0.676226
$57$	−837.876	−1.94701
$58$	−1.67284	−0.00378716
$59$	−352.950	−0.778817	−0.389408	−	0.921065i	$-0.627321\pi$
$59$	−352.950	−0.778817	−0.389408	+	0.921065i	$0.627321\pi$
$60$	0	0
$61$	−507.223	−1.06464	−0.532322	−	0.846542i	$-0.678680\pi$
$61$	−507.223	−1.06464	−0.532322	+	0.846542i	$0.678680\pi$
$62$	−239.672	−0.490941
$63$	1074.61	2.14901
$64$	64.0000	0.125000
$65$	0	0
$66$	−251.845	−0.469697
$67$	820.056	1.49531	0.747655	−	0.664087i	$-0.231180\pi$
$67$	820.056	1.49531	0.747655	+	0.664087i	$0.231180\pi$
$68$	187.288	0.333999
$69$	174.158	0.303857
$70$	0	0
$71$	−733.770	−1.22651	−0.613257	−	0.789884i	$-0.710141\pi$
$71$	−733.770	−1.22651	−0.613257	+	0.789884i	$0.710141\pi$
$72$	242.692	0.397243
$73$	91.4599	0.146638	0.0733190	−	0.997309i	$-0.476641\pi$
$73$	91.4599	0.146638	0.0733190	+	0.997309i	$0.476641\pi$
$74$	−736.402	−1.15682
$75$	0	0
$76$	−442.613	−0.668042
$77$	−589.077	−0.871838
$78$	1210.22	1.75680
$79$	329.381	0.469092	0.234546	−	0.972105i	$-0.424640\pi$
$79$	329.381	0.469092	0.234546	+	0.972105i	$0.424640\pi$
$80$	0	0
$81$	−627.783	−0.861156
$82$	−191.585	−0.258013
$83$	753.834	0.996916	0.498458	−	0.866914i	$-0.333900\pi$
$83$	753.834	0.996916	0.498458	+	0.866914i	$0.333900\pi$
$84$	1072.90	1.39361
$85$	0	0
$86$	−663.922	−0.832472
$87$	−6.33346	−0.00780481
$88$	−133.039	−0.161159
$89$	−1050.14	−1.25073	−0.625365	−	0.780332i	$-0.715050\pi$
$89$	−1050.14	−1.25073	−0.625365	+	0.780332i	$0.715050\pi$
$90$	0	0
$91$	2830.76	3.26092
$92$	92.0000	0.104257
$93$	−907.407	−1.01176
$94$	1070.07	1.17415
$95$	0	0
$96$	242.307	0.257608
$97$	271.928	0.284641	0.142320	−	0.989821i	$-0.454544\pi$
$97$	271.928	0.284641	0.142320	+	0.989821i	$0.454544\pi$
$98$	1823.56	1.87967
$99$	−504.491	−0.512154
$100$	0	0
$101$	1658.68	1.63410	0.817052	−	0.576563i	$-0.195607\pi$
$101$	1658.68	1.63410	0.817052	+	0.576563i	$0.195607\pi$
$102$	709.079	0.688326
$103$	−1735.52	−1.66025	−0.830123	−	0.557580i	$-0.811730\pi$
$103$	−1735.52	−1.66025	−0.830123	+	0.557580i	$0.811730\pi$
$104$	639.305	0.602779
$105$	0	0
$106$	−818.691	−0.750172
$107$	1629.88	1.47258	0.736292	−	0.676664i	$-0.236575\pi$
$107$	1629.88	1.47258	0.736292	+	0.676664i	$0.236575\pi$
$108$	101.056	0.0900385
$109$	−432.151	−0.379748	−0.189874	−	0.981808i	$-0.560808\pi$
$109$	−432.151	−0.379748	−0.189874	+	0.981808i	$0.560808\pi$
$110$	0	0
$111$	−2788.05	−2.38405
$112$	566.766	0.478164
$113$	240.115	0.199895	0.0999476	−	0.994993i	$-0.468132\pi$
$113$	240.115	0.199895	0.0999476	+	0.994993i	$0.468132\pi$
$114$	−1675.75	−1.37674
$115$	0	0
$116$	−3.34569	−0.00267793
$117$	2424.28	1.91560
$118$	−705.900	−0.550707
$119$	1658.57	1.27765
$120$	0	0
$121$	−1054.45	−0.792223
$122$	−1014.45	−0.752817
$123$	−725.350	−0.531729
$124$	−479.343	−0.347147
$125$	0	0
$126$	2149.21	1.51958
$127$	210.993	0.147422	0.0737110	−	0.997280i	$-0.476516\pi$
$127$	210.993	0.147422	0.0737110	+	0.997280i	$0.476516\pi$
$128$	128.000	0.0883883
$129$	−2513.64	−1.71561
$130$	0	0
$131$	−746.178	−0.497663	−0.248832	−	0.968547i	$-0.580047\pi$
$131$	−746.178	−0.497663	−0.248832	+	0.968547i	$0.580047\pi$
$132$	−503.690	−0.332126
$133$	−3919.66	−2.55547
$134$	1640.11	1.05734
$135$	0	0
$136$	374.575	0.236173
$137$	2420.07	1.50920	0.754601	−	0.656184i	$-0.227830\pi$
$137$	2420.07	1.50920	0.754601	+	0.656184i	$0.227830\pi$
$138$	348.316	0.214860
$139$	924.030	0.563850	0.281925	−	0.959436i	$-0.409027\pi$
$139$	924.030	0.563850	0.281925	+	0.959436i	$0.409027\pi$
$140$	0	0
$141$	4051.34	2.41975
$142$	−1467.54	−0.867276
$143$	−1328.94	−0.777145
$144$	485.384	0.280893
$145$	0	0
$146$	182.920	0.103689
$147$	6904.09	3.87374
$148$	−1472.80	−0.817998
$149$	430.614	0.236760	0.118380	−	0.992968i	$-0.462230\pi$
$149$	430.614	0.236760	0.118380	+	0.992968i	$0.462230\pi$
$150$	0	0
$151$	−25.4118	−0.0136953	−0.00684763	−	0.999977i	$-0.502180\pi$
$151$	−25.4118	−0.0136953	−0.00684763	+	0.999977i	$0.502180\pi$
$152$	−885.226	−0.472377
$153$	1420.41	0.750546
$154$	−1178.15	−0.616483
$155$	0	0
$156$	2420.44	1.24224
$157$	1580.29	0.803317	0.401658	−	0.915790i	$-0.368434\pi$
$157$	1580.29	0.803317	0.401658	+	0.915790i	$0.368434\pi$
$158$	658.762	0.331698
$159$	−3099.60	−1.54600
$160$	0	0
$161$	814.727	0.398817
$162$	−1255.57	−0.608930
$163$	−458.739	−0.220437	−0.110218	−	0.993907i	$-0.535155\pi$
$163$	−458.739	−0.220437	−0.110218	+	0.993907i	$0.535155\pi$
$164$	−383.171	−0.182443
$165$	0	0
$166$	1507.67	0.704926
$167$	561.275	0.260076	0.130038	−	0.991509i	$-0.458490\pi$
$167$	561.275	0.260076	0.130038	+	0.991509i	$0.458490\pi$
$168$	2145.80	0.985430
$169$	4189.11	1.90674
$170$	0	0
$171$	−3356.83	−1.50119
$172$	−1327.84	−0.588647
$173$	−1573.95	−0.691705	−0.345852	−	0.938289i	$-0.612410\pi$
$173$	−1573.95	−0.691705	−0.345852	+	0.938289i	$0.612410\pi$
$174$	−12.6669	−0.00551883
$175$	0	0
$176$	−266.077	−0.113956
$177$	−2672.57	−1.13493
$178$	−2100.29	−0.884400
$179$	2215.59	0.925145	0.462572	−	0.886581i	$-0.346927\pi$
$179$	2215.59	0.925145	0.462572	+	0.886581i	$0.346927\pi$
$180$	0	0
$181$	873.497	0.358710	0.179355	−	0.983784i	$-0.442599\pi$
$181$	873.497	0.358710	0.179355	+	0.983784i	$0.442599\pi$
$182$	5661.51	2.30582
$183$	−3840.74	−1.55145
$184$	184.000	0.0737210
$185$	0	0
$186$	−1814.81	−0.715422
$187$	−778.641	−0.304491
$188$	2140.15	0.830246
$189$	894.928	0.344425
$190$	0	0
$191$	−2497.74	−0.946230	−0.473115	−	0.881001i	$-0.656870\pi$
$191$	−2497.74	−0.946230	−0.473115	+	0.881001i	$0.656870\pi$
$192$	484.613	0.182156
$193$	−909.155	−0.339080	−0.169540	−	0.985523i	$-0.554228\pi$
$193$	−909.155	−0.339080	−0.169540	+	0.985523i	$0.554228\pi$
$194$	543.857	0.201271
$195$	0	0
$196$	3647.13	1.32913
$197$	−608.627	−0.220116	−0.110058	−	0.993925i	$-0.535104\pi$
$197$	−608.627	−0.220116	−0.110058	+	0.993925i	$0.535104\pi$
$198$	−1008.98	−0.362147
$199$	−2304.98	−0.821083	−0.410542	−	0.911842i	$-0.634660\pi$
$199$	−2304.98	−0.821083	−0.410542	+	0.911842i	$0.634660\pi$
$200$	0	0
$201$	6209.54	2.17904
$202$	3317.36	1.15549
$203$	−29.6285	−0.0102439
$204$	1418.16	0.486720
$205$	0	0
$206$	−3471.03	−1.17397
$207$	697.739	0.234281
$208$	1278.61	0.426229
$209$	1840.15	0.609022
$210$	0	0
$211$	−4373.37	−1.42690	−0.713448	−	0.700708i	$-0.752868\pi$
$211$	−4373.37	−1.42690	−0.713448	+	0.700708i	$0.752868\pi$
$212$	−1637.38	−0.530452
$213$	−5556.17	−1.78733
$214$	3259.76	1.04127
$215$	0	0
$216$	202.113	0.0636668
$217$	−4244.93	−1.32795
$218$	−864.303	−0.268523
$219$	692.542	0.213688
$220$	0	0
$221$	3741.69	1.13888
$222$	−5576.10	−1.68578
$223$	−5439.50	−1.63343	−0.816717	−	0.577038i	$-0.804208\pi$
$223$	−5439.50	−1.63343	−0.816717	+	0.577038i	$0.804208\pi$
$224$	1133.53	0.338113
$225$	0	0
$226$	480.231	0.141347
$227$	−216.498	−0.0633017	−0.0316508	−	0.999499i	$-0.510076\pi$
$227$	−216.498	−0.0633017	−0.0316508	+	0.999499i	$0.510076\pi$
$228$	−3351.51	−0.973504
$229$	−924.664	−0.266828	−0.133414	−	0.991060i	$-0.542594\pi$
$229$	−924.664	−0.266828	−0.133414	+	0.991060i	$0.542594\pi$
$230$	0	0
$231$	−4460.54	−1.27049
$232$	−6.69138	−0.00189358
$233$	2369.69	0.666280	0.333140	−	0.942877i	$-0.391892\pi$
$233$	2369.69	0.666280	0.333140	+	0.942877i	$0.391892\pi$
$234$	4848.57	1.35453
$235$	0	0
$236$	−1411.80	−0.389408
$237$	2494.10	0.683584
$238$	3317.14	0.903437
$239$	−2769.60	−0.749583	−0.374791	−	0.927109i	$-0.622286\pi$
$239$	−2769.60	−0.749583	−0.374791	+	0.927109i	$0.622286\pi$
$240$	0	0
$241$	−5334.10	−1.42572	−0.712862	−	0.701305i	$-0.752601\pi$
$241$	−5334.10	−1.42572	−0.712862	+	0.701305i	$0.752601\pi$
$242$	−2108.90	−0.560186
$243$	−5435.76	−1.43500
$244$	−2028.89	−0.532322
$245$	0	0
$246$	−1450.70	−0.375989
$247$	−8842.66	−2.27791
$248$	−958.686	−0.245470
$249$	5708.10	1.45275
$250$	0	0
$251$	4677.13	1.17617	0.588084	−	0.808800i	$-0.299882\pi$
$251$	4677.13	1.17617	0.588084	+	0.808800i	$0.299882\pi$
$252$	4298.42	1.07451
$253$	−382.486	−0.0950463
$254$	421.986	0.104243
$255$	0	0
$256$	256.000	0.0625000
$257$	2602.99	0.631789	0.315895	−	0.948794i	$-0.397695\pi$
$257$	2602.99	0.631789	0.315895	+	0.948794i	$0.397695\pi$
$258$	−5027.28	−1.21312
$259$	−13042.7	−3.12910
$260$	0	0
$261$	−25.3741	−0.00601769
$262$	−1492.36	−0.351901
$263$	3411.30	0.799809	0.399904	−	0.916557i	$-0.369043\pi$
$263$	3411.30	0.799809	0.399904	+	0.916557i	$0.369043\pi$
$264$	−1007.38	−0.234848
$265$	0	0
$266$	−7839.32	−1.80699
$267$	−7951.77	−1.82262
$268$	3280.22	0.747655
$269$	4366.56	0.989718	0.494859	−	0.868973i	$-0.335220\pi$
$269$	4366.56	0.989718	0.494859	+	0.868973i	$0.335220\pi$
$270$	0	0
$271$	5682.45	1.27374	0.636872	−	0.770970i	$-0.280228\pi$
$271$	5682.45	1.27374	0.636872	+	0.770970i	$0.280228\pi$
$272$	749.150	0.167000
$273$	21434.7	4.75197
$274$	4840.14	1.06717
$275$	0	0
$276$	696.632	0.151929
$277$	1884.62	0.408794	0.204397	−	0.978888i	$-0.434477\pi$
$277$	1884.62	0.408794	0.204397	+	0.978888i	$0.434477\pi$
$278$	1848.06	0.398702
$279$	−3635.39	−0.780091
$280$	0	0
$281$	−2706.42	−0.574561	−0.287281	−	0.957846i	$-0.592751\pi$
$281$	−2706.42	−0.574561	−0.287281	+	0.957846i	$0.592751\pi$
$282$	8102.69	1.71102
$283$	5963.64	1.25266	0.626328	−	0.779560i	$-0.284557\pi$
$283$	5963.64	1.25266	0.626328	+	0.779560i	$0.284557\pi$
$284$	−2935.08	−0.613257
$285$	0	0
$286$	−2657.89	−0.549525
$287$	−3393.26	−0.697901
$288$	970.767	0.198622
$289$	−2720.71	−0.553778
$290$	0	0
$291$	2059.06	0.414792
$292$	365.840	0.0733190
$293$	4735.85	0.944272	0.472136	−	0.881526i	$-0.343483\pi$
$293$	4735.85	0.944272	0.472136	+	0.881526i	$0.343483\pi$
$294$	13808.2	2.73915
$295$	0	0
$296$	−2945.61	−0.578412
$297$	−420.138	−0.0820837
$298$	861.227	0.167415
$299$	1838.00	0.355500
$300$	0	0
$301$	−11759.0	−2.25176
$302$	−50.8236	−0.00968401
$303$	12559.6	2.38130
$304$	−1770.45	−0.334021
$305$	0	0
$306$	2840.82	0.530716
$307$	769.241	0.143006	0.0715031	−	0.997440i	$-0.477220\pi$
$307$	769.241	0.143006	0.0715031	+	0.997440i	$0.477220\pi$
$308$	−2356.31	−0.435919
$309$	−13141.5	−2.41939
$310$	0	0
$311$	−5592.71	−1.01972	−0.509861	−	0.860257i	$-0.670303\pi$
$311$	−5592.71	−1.01972	−0.509861	+	0.860257i	$0.670303\pi$
$312$	4840.87	0.878399
$313$	−9777.19	−1.76562	−0.882811	−	0.469729i	$-0.844352\pi$
$313$	−9777.19	−1.76562	−0.882811	+	0.469729i	$0.844352\pi$
$314$	3160.58	0.568031
$315$	0	0
$316$	1317.52	0.234546
$317$	−1868.51	−0.331060	−0.165530	−	0.986205i	$-0.552934\pi$
$317$	−1868.51	−0.331060	−0.165530	+	0.986205i	$0.552934\pi$
$318$	−6199.20	−1.09319
$319$	13.9096	0.00244134
$320$	0	0
$321$	12341.6	2.14592
$322$	1629.45	0.282006
$323$	−5181.00	−0.892503
$324$	−2511.13	−0.430578
$325$	0	0
$326$	−917.477	−0.155872
$327$	−3272.29	−0.553388
$328$	−766.342	−0.129007
$329$	18952.6	3.17595
$330$	0	0
$331$	6966.91	1.15691	0.578454	−	0.815715i	$-0.303656\pi$
$331$	6966.91	1.15691	0.578454	+	0.815715i	$0.303656\pi$
$332$	3015.34	0.498458
$333$	−11169.9	−1.83816
$334$	1122.55	0.183902
$335$	0	0
$336$	4291.60	0.696804
$337$	17.5487	0.00283661	0.00141830	−	0.999999i	$-0.499549\pi$
$337$	17.5487	0.00283661	0.00141830	+	0.999999i	$0.499549\pi$
$338$	8378.23	1.34827
$339$	1818.17	0.291297
$340$	0	0
$341$	1992.85	0.316477
$342$	−6713.66	−1.06150
$343$	20147.9	3.17167
$344$	−2655.69	−0.416236
$345$	0	0
$346$	−3147.89	−0.489109
$347$	9859.30	1.52529	0.762644	−	0.646818i	$-0.223901\pi$
$347$	9859.30	1.52529	0.762644	+	0.646818i	$0.223901\pi$
$348$	−25.3338	−0.00390240
$349$	7200.25	1.10436	0.552178	−	0.833726i	$-0.313797\pi$
$349$	7200.25	1.10436	0.552178	+	0.833726i	$0.313797\pi$
$350$	0	0
$351$	2018.93	0.307016
$352$	−532.155	−0.0805794
$353$	6054.58	0.912897	0.456449	−	0.889750i	$-0.349121\pi$
$353$	6054.58	0.912897	0.456449	+	0.889750i	$0.349121\pi$
$354$	−5345.14	−0.802516
$355$	0	0
$356$	−4200.57	−0.625365
$357$	12558.8	1.86186
$358$	4431.18	0.654176
$359$	2734.26	0.401974	0.200987	−	0.979594i	$-0.435585\pi$
$359$	2734.26	0.401974	0.200987	+	0.979594i	$0.435585\pi$
$360$	0	0
$361$	5385.16	0.785123
$362$	1746.99	0.253646
$363$	−7984.37	−1.15447
$364$	11323.0	1.63046
$365$	0	0
$366$	−7681.47	−1.09704
$367$	2465.50	0.350676	0.175338	−	0.984508i	$-0.443898\pi$
$367$	2465.50	0.350676	0.175338	+	0.984508i	$0.443898\pi$
$368$	368.000	0.0521286
$369$	−2906.01	−0.409976
$370$	0	0
$371$	−14500.2	−2.02915
$372$	−3629.63	−0.505880
$373$	−5704.45	−0.791863	−0.395932	−	0.918280i	$-0.629578\pi$
$373$	−5704.45	−0.791863	−0.395932	+	0.918280i	$0.629578\pi$
$374$	−1557.28	−0.215308
$375$	0	0
$376$	4280.29	0.587073
$377$	−66.8411	−0.00913128
$378$	1789.86	0.243546
$379$	10231.9	1.38675	0.693376	−	0.720576i	$-0.256122\pi$
$379$	10231.9	1.38675	0.693376	+	0.720576i	$0.256122\pi$
$380$	0	0
$381$	1597.66	0.214830
$382$	−4995.47	−0.669086
$383$	−6321.34	−0.843356	−0.421678	−	0.906746i	$-0.638559\pi$
$383$	−6321.34	−0.843356	−0.421678	+	0.906746i	$0.638559\pi$
$384$	969.227	0.128804
$385$	0	0
$386$	−1818.31	−0.239766
$387$	−10070.5	−1.32278
$388$	1087.71	0.142320
$389$	−925.594	−0.120641	−0.0603207	−	0.998179i	$-0.519212\pi$
$389$	−925.594	−0.120641	−0.0603207	+	0.998179i	$0.519212\pi$
$390$	0	0
$391$	1076.90	0.139287
$392$	7294.25	0.939835
$393$	−5650.13	−0.725219
$394$	−1217.25	−0.155646
$395$	0	0
$396$	−2017.96	−0.256077
$397$	2706.75	0.342187	0.171093	−	0.985255i	$-0.445270\pi$
$397$	2706.75	0.342187	0.171093	+	0.985255i	$0.445270\pi$
$398$	−4609.96	−0.580594
$399$	−29680.0	−3.72396
$400$	0	0
$401$	−14095.3	−1.75532	−0.877661	−	0.479281i	$-0.840897\pi$
$401$	−14095.3	−1.75532	−0.877661	+	0.479281i	$0.840897\pi$
$402$	12419.1	1.54081
$403$	−9576.45	−1.18372
$404$	6634.71	0.817052
$405$	0	0
$406$	−59.2570	−0.00724353
$407$	6123.12	0.745729
$408$	2836.32	0.344163
$409$	−10846.0	−1.31125	−0.655625	−	0.755087i	$-0.727595\pi$
$409$	−10846.0	−1.31125	−0.655625	+	0.755087i	$0.727595\pi$
$410$	0	0
$411$	18325.0	2.19928
$412$	−6942.06	−0.830123
$413$	−12502.5	−1.48961
$414$	1395.48	0.165662
$415$	0	0
$416$	2557.22	0.301390
$417$	6996.84	0.821670
$418$	3680.29	0.430644
$419$	−5626.55	−0.656026	−0.328013	−	0.944673i	$-0.606379\pi$
$419$	−5626.55	−0.656026	−0.328013	+	0.944673i	$0.606379\pi$
$420$	0	0
$421$	−7109.09	−0.822983	−0.411491	−	0.911414i	$-0.634992\pi$
$421$	−7109.09	−0.822983	−0.411491	+	0.911414i	$0.634992\pi$
$422$	−8746.74	−1.00897
$423$	16231.1	1.86568
$424$	−3274.76	−0.375086
$425$	0	0
$426$	−11112.3	−1.26384
$427$	−17967.3	−2.03630
$428$	6519.52	0.736292
$429$	−10062.9	−1.13249
$430$	0	0
$431$	4464.14	0.498909	0.249455	−	0.968387i	$-0.419749\pi$
$431$	4464.14	0.498909	0.249455	+	0.968387i	$0.419749\pi$
$432$	404.226	0.0450192
$433$	−11009.4	−1.22189	−0.610947	−	0.791672i	$-0.709211\pi$
$433$	−11009.4	−1.22189	−0.610947	+	0.791672i	$0.709211\pi$
$434$	−8489.86	−0.939001
$435$	0	0
$436$	−1728.61	−0.189874
$437$	−2545.03	−0.278593
$438$	1385.08	0.151100
$439$	−3052.70	−0.331885	−0.165943	−	0.986135i	$-0.553067\pi$
$439$	−3052.70	−0.331885	−0.165943	+	0.986135i	$0.553067\pi$
$440$	0	0
$441$	27660.2	2.98675
$442$	7483.37	0.805312
$443$	4465.82	0.478956	0.239478	−	0.970902i	$-0.423024\pi$
$443$	4465.82	0.478956	0.239478	+	0.970902i	$0.423024\pi$
$444$	−11152.2	−1.19203
$445$	0	0
$446$	−10879.0	−1.15501
$447$	3260.64	0.345018
$448$	2267.07	0.239082
$449$	9040.14	0.950179	0.475090	−	0.879937i	$-0.342416\pi$
$449$	9040.14	0.950179	0.475090	+	0.879937i	$0.342416\pi$
$450$	0	0
$451$	1593.02	0.166324
$452$	960.462	0.0999476
$453$	−192.420	−0.0199574
$454$	−432.996	−0.0447610
$455$	0	0
$456$	−6703.01	−0.688371
$457$	−7756.88	−0.793986	−0.396993	−	0.917822i	$-0.629946\pi$
$457$	−7756.88	−0.793986	−0.396993	+	0.917822i	$0.629946\pi$
$458$	−1849.33	−0.188676
$459$	1182.91	0.120291
$460$	0	0
$461$	7064.19	0.713692	0.356846	−	0.934163i	$-0.383852\pi$
$461$	7064.19	0.713692	0.356846	+	0.934163i	$0.383852\pi$
$462$	−8921.08	−0.898369
$463$	−12599.7	−1.26470	−0.632350	−	0.774682i	$-0.717910\pi$
$463$	−12599.7	−1.26470	−0.632350	+	0.774682i	$0.717910\pi$
$464$	−13.3828	−0.00133896
$465$	0	0
$466$	4739.37	0.471131
$467$	−14746.0	−1.46117	−0.730583	−	0.682824i	$-0.760751\pi$
$467$	−14746.0	−1.46117	−0.730583	+	0.682824i	$0.760751\pi$
$468$	9697.14	0.957800
$469$	29048.8	2.86002
$470$	0	0
$471$	11966.1	1.17063
$472$	−2823.60	−0.275353
$473$	5520.46	0.536641
$474$	4988.20	0.483367
$475$	0	0
$476$	6634.27	0.638826
$477$	−12418.1	−1.19200
$478$	−5539.19	−0.530035
$479$	−17411.2	−1.66084	−0.830418	−	0.557141i	$-0.811898\pi$
$479$	−17411.2	−1.66084	−0.830418	+	0.557141i	$0.811898\pi$
$480$	0	0
$481$	−29424.1	−2.78924
$482$	−10668.2	−1.00814
$483$	6169.18	0.581175
$484$	−4217.79	−0.396111
$485$	0	0
$486$	−10871.5	−1.01470
$487$	−1320.34	−0.122855	−0.0614276	−	0.998112i	$-0.519565\pi$
$487$	−1320.34	−0.122855	−0.0614276	+	0.998112i	$0.519565\pi$
$488$	−4057.78	−0.376408
$489$	−3473.61	−0.321231
$490$	0	0
$491$	17115.8	1.57317	0.786583	−	0.617485i	$-0.211848\pi$
$491$	17115.8	1.57317	0.786583	+	0.617485i	$0.211848\pi$
$492$	−2901.40	−0.265864
$493$	−39.1629	−0.00357770
$494$	−17685.3	−1.61073
$495$	0	0
$496$	−1917.37	−0.173574
$497$	−25992.3	−2.34590
$498$	11416.2	1.02725
$499$	17540.6	1.57360	0.786798	−	0.617210i	$-0.211737\pi$
$499$	17540.6	1.57360	0.786798	+	0.617210i	$0.211737\pi$
$500$	0	0
$501$	4250.02	0.378996
$502$	9354.27	0.831676
$503$	4934.98	0.437455	0.218727	−	0.975786i	$-0.429809\pi$
$503$	4934.98	0.437455	0.218727	+	0.975786i	$0.429809\pi$
$504$	8596.85	0.759790
$505$	0	0
$506$	−764.972	−0.0672079
$507$	31720.3	2.77860
$508$	843.972	0.0737110
$509$	11927.3	1.03865	0.519323	−	0.854578i	$-0.326184\pi$
$509$	11927.3	1.03865	0.519323	+	0.854578i	$0.326184\pi$
$510$	0	0
$511$	3239.78	0.280468
$512$	512.000	0.0441942
$513$	−2795.56	−0.240598
$514$	5205.97	0.446743
$515$	0	0
$516$	−10054.6	−0.857804
$517$	−8897.57	−0.756895
$518$	−26085.5	−2.21261
$519$	−11918.1	−1.00799
$520$	0	0
$521$	−9592.76	−0.806653	−0.403327	−	0.915056i	$-0.632146\pi$
$521$	−9592.76	−0.806653	−0.403327	+	0.915056i	$0.632146\pi$
$522$	−50.7482	−0.00425515
$523$	−6525.20	−0.545558	−0.272779	−	0.962077i	$-0.587943\pi$
$523$	−6525.20	−0.545558	−0.272779	+	0.962077i	$0.587943\pi$
$524$	−2984.71	−0.248832
$525$	0	0
$526$	6822.60	0.565550
$527$	−5610.94	−0.463788
$528$	−2014.76	−0.166063
$529$	529.000	0.0434783
$530$	0	0
$531$	−10707.3	−0.875058
$532$	−15678.6	−1.27774
$533$	−7655.10	−0.622100
$534$	−15903.5	−1.28879
$535$	0	0
$536$	6560.45	0.528672
$537$	16776.6	1.34817
$538$	8733.13	0.699836
$539$	−15162.8	−1.21170
$540$	0	0
$541$	5634.05	0.447739	0.223870	−	0.974619i	$-0.428131\pi$
$541$	5634.05	0.447739	0.223870	+	0.974619i	$0.428131\pi$
$542$	11364.9	0.900673
$543$	6614.19	0.522729
$544$	1498.30	0.118087
$545$	0	0
$546$	42869.5	3.36015
$547$	−6093.08	−0.476273	−0.238136	−	0.971232i	$-0.576537\pi$
$547$	−6093.08	−0.476273	−0.238136	+	0.971232i	$0.576537\pi$
$548$	9680.29	0.754601
$549$	−15387.4	−1.19620
$550$	0	0
$551$	92.5529	0.00715587
$552$	1393.26	0.107430
$553$	11667.6	0.897212
$554$	3769.24	0.289061
$555$	0	0
$556$	3696.12	0.281925
$557$	−21461.9	−1.63262	−0.816311	−	0.577612i	$-0.803985\pi$
$557$	−21461.9	−1.63262	−0.816311	+	0.577612i	$0.803985\pi$
$558$	−7270.79	−0.551608
$559$	−26528.1	−2.00719
$560$	0	0
$561$	−5895.93	−0.443719
$562$	−5412.85	−0.406276
$563$	11038.5	0.826316	0.413158	−	0.910659i	$-0.364426\pi$
$563$	11038.5	0.826316	0.413158	+	0.910659i	$0.364426\pi$
$564$	16205.4	1.20988
$565$	0	0
$566$	11927.3	0.885761
$567$	−22237.9	−1.64710
$568$	−5870.16	−0.433638
$569$	−19210.3	−1.41535	−0.707677	−	0.706536i	$-0.750257\pi$
$569$	−19210.3	−1.41535	−0.707677	+	0.706536i	$0.750257\pi$
$570$	0	0
$571$	−11967.0	−0.877066	−0.438533	−	0.898715i	$-0.644502\pi$
$571$	−11967.0	−0.877066	−0.438533	+	0.898715i	$0.644502\pi$
$572$	−5315.77	−0.388573
$573$	−18913.1	−1.37889
$574$	−6786.51	−0.493490
$575$	0	0
$576$	1941.53	0.140447
$577$	14982.3	1.08097	0.540487	−	0.841352i	$-0.318240\pi$
$577$	14982.3	1.08097	0.540487	+	0.841352i	$0.318240\pi$
$578$	−5441.42	−0.391580
$579$	−6884.20	−0.494124
$580$	0	0
$581$	26703.0	1.90676
$582$	4118.13	0.293302
$583$	6807.35	0.483587
$584$	731.679	0.0518444
$585$	0	0
$586$	9471.71	0.667701
$587$	−24002.9	−1.68774	−0.843871	−	0.536547i	$-0.819729\pi$
$587$	−24002.9	−1.68774	−0.843871	+	0.536547i	$0.819729\pi$
$588$	27616.4	1.93687
$589$	13260.2	0.927637
$590$	0	0
$591$	−4608.58	−0.320764
$592$	−5891.21	−0.408999
$593$	−5124.67	−0.354882	−0.177441	−	0.984131i	$-0.556782\pi$
$593$	−5124.67	−0.354882	−0.177441	+	0.984131i	$0.556782\pi$
$594$	−840.276	−0.0580420
$595$	0	0
$596$	1722.45	0.118380
$597$	−17453.5	−1.19652
$598$	3676.01	0.251376
$599$	−23776.8	−1.62186	−0.810928	−	0.585146i	$-0.801037\pi$
$599$	−23776.8	−1.62186	−0.810928	+	0.585146i	$0.801037\pi$
$600$	0	0
$601$	−25435.3	−1.72633	−0.863166	−	0.504920i	$-0.831522\pi$
$601$	−25435.3	−1.72633	−0.863166	+	0.504920i	$0.831522\pi$
$602$	−23518.1	−1.59223
$603$	24877.6	1.68009
$604$	−101.647	−0.00684763
$605$	0	0
$606$	25119.3	1.68383
$607$	7445.94	0.497894	0.248947	−	0.968517i	$-0.419916\pi$
$607$	7445.94	0.497894	0.248947	+	0.968517i	$0.419916\pi$
$608$	−3540.91	−0.236189
$609$	−224.349	−0.0149279
$610$	0	0
$611$	42756.5	2.83100
$612$	5681.65	0.375273
$613$	12874.4	0.848275	0.424138	−	0.905598i	$-0.360577\pi$
$613$	12874.4	0.848275	0.424138	+	0.905598i	$0.360577\pi$
$614$	1538.48	0.101121
$615$	0	0
$616$	−4712.62	−0.308241
$617$	19247.2	1.25585	0.627927	−	0.778272i	$-0.283904\pi$
$617$	19247.2	1.25585	0.627927	+	0.778272i	$0.283904\pi$
$618$	−26282.9	−1.71077
$619$	−14496.4	−0.941293	−0.470647	−	0.882322i	$-0.655979\pi$
$619$	−14496.4	−0.941293	−0.470647	+	0.882322i	$0.655979\pi$
$620$	0	0
$621$	581.074	0.0375486
$622$	−11185.4	−0.721052
$623$	−37199.1	−2.39222
$624$	9681.75	0.621122
$625$	0	0
$626$	−19554.4	−1.24848
$627$	13933.7	0.887496
$628$	6321.15	0.401658
$629$	−17239.9	−1.09284
$630$	0	0
$631$	−18030.9	−1.13756	−0.568779	−	0.822490i	$-0.692584\pi$
$631$	−18030.9	−1.13756	−0.568779	+	0.822490i	$0.692584\pi$
$632$	2635.05	0.165849
$633$	−33115.5	−2.07934
$634$	−3737.03	−0.234095
$635$	0	0
$636$	−12398.4	−0.773000
$637$	72863.4	4.53211
$638$	27.8191	0.00172628
$639$	−22260.0	−1.37808
$640$	0	0
$641$	11776.4	0.725646	0.362823	−	0.931858i	$-0.381813\pi$
$641$	11776.4	0.725646	0.362823	+	0.931858i	$0.381813\pi$
$642$	24683.2	1.51740
$643$	−20207.4	−1.23935	−0.619676	−	0.784858i	$-0.712736\pi$
$643$	−20207.4	−1.23935	−0.619676	+	0.784858i	$0.712736\pi$
$644$	3258.91	0.199408
$645$	0	0
$646$	−10362.0	−0.631095
$647$	−21452.8	−1.30355	−0.651776	−	0.758412i	$-0.725976\pi$
$647$	−21452.8	−1.30355	−0.651776	+	0.758412i	$0.725976\pi$
$648$	−5022.26	−0.304465
$649$	5869.50	0.355005
$650$	0	0
$651$	−32143.0	−1.93515
$652$	−1834.95	−0.110218
$653$	15095.2	0.904624	0.452312	−	0.891860i	$-0.350599\pi$
$653$	15095.2	0.904624	0.452312	+	0.891860i	$0.350599\pi$
$654$	−6544.57	−0.391304
$655$	0	0
$656$	−1532.68	−0.0912214
$657$	2774.57	0.164759
$658$	37905.1	2.24574
$659$	6964.68	0.411693	0.205846	−	0.978584i	$-0.434005\pi$
$659$	6964.68	0.411693	0.205846	+	0.978584i	$0.434005\pi$
$660$	0	0
$661$	−17380.4	−1.02272	−0.511361	−	0.859366i	$-0.670858\pi$
$661$	−17380.4	−1.02272	−0.511361	+	0.859366i	$0.670858\pi$
$662$	13933.8	0.818057
$663$	28332.4	1.65964
$664$	6030.67	0.352463
$665$	0	0
$666$	−22339.8	−1.29978
$667$	−19.2377	−0.00111677
$668$	2245.10	0.130038
$669$	−41188.3	−2.38032
$670$	0	0
$671$	8435.04	0.485292
$672$	8583.21	0.492715
$673$	−12383.2	−0.709271	−0.354635	−	0.935005i	$-0.615395\pi$
$673$	−12383.2	−0.709271	−0.354635	+	0.935005i	$0.615395\pi$
$674$	35.0973	0.00200578
$675$	0	0
$676$	16756.5	0.953371
$677$	8375.74	0.475489	0.237744	−	0.971328i	$-0.423592\pi$
$677$	8375.74	0.475489	0.237744	+	0.971328i	$0.423592\pi$
$678$	3636.35	0.205978
$679$	9632.49	0.544420
$680$	0	0
$681$	−1639.34	−0.0922463
$682$	3985.70	0.223783
$683$	4434.66	0.248444	0.124222	−	0.992254i	$-0.460356\pi$
$683$	4434.66	0.248444	0.124222	+	0.992254i	$0.460356\pi$
$684$	−13427.3	−0.750595
$685$	0	0
$686$	40295.8	2.24271
$687$	−7001.64	−0.388834
$688$	−5311.38	−0.294323
$689$	−32712.1	−1.80875
$690$	0	0
$691$	11032.8	0.607389	0.303694	−	0.952770i	$-0.401780\pi$
$691$	11032.8	0.607389	0.303694	+	0.952770i	$0.401780\pi$
$692$	−6295.79	−0.345852
$693$	−17870.5	−0.979574
$694$	19718.6	1.07854
$695$	0	0
$696$	−50.6677	−0.00275942
$697$	−4485.20	−0.243743
$698$	14400.5	0.780898
$699$	17943.5	0.970936
$700$	0	0
$701$	3708.40	0.199806	0.0999032	−	0.994997i	$-0.468147\pi$
$701$	3708.40	0.199806	0.0999032	+	0.994997i	$0.468147\pi$
$702$	4037.87	0.217093
$703$	40742.6	2.18583
$704$	−1064.31	−0.0569782
$705$	0	0
$706$	12109.2	0.645516
$707$	58755.2	3.12548
$708$	−10690.3	−0.567465
$709$	−6315.04	−0.334508	−0.167254	−	0.985914i	$-0.553490\pi$
$709$	−6315.04	−0.334508	−0.167254	+	0.985914i	$0.553490\pi$
$710$	0	0
$711$	9992.26	0.527059
$712$	−8401.15	−0.442200
$713$	−2756.22	−0.144770
$714$	25117.6	1.31653
$715$	0	0
$716$	8862.36	0.462572
$717$	−20971.6	−1.09233
$718$	5468.52	0.284239
$719$	24736.9	1.28307	0.641536	−	0.767093i	$-0.278297\pi$
$719$	24736.9	1.28307	0.641536	+	0.767093i	$0.278297\pi$
$720$	0	0
$721$	−61477.0	−3.17548
$722$	10770.3	0.555165
$723$	−40390.2	−2.07763
$724$	3493.99	0.179355
$725$	0	0
$726$	−15968.7	−0.816330
$727$	−33283.6	−1.69797	−0.848983	−	0.528420i	$-0.822785\pi$
$727$	−33283.6	−1.69797	−0.848983	+	0.528420i	$0.822785\pi$
$728$	22646.0	1.15291
$729$	−24209.9	−1.22999
$730$	0	0
$731$	−15543.1	−0.786430
$732$	−15362.9	−0.775725
$733$	33636.5	1.69494	0.847471	−	0.530841i	$-0.178124\pi$
$733$	33636.5	1.69494	0.847471	+	0.530841i	$0.178124\pi$
$734$	4931.00	0.247965
$735$	0	0
$736$	736.000	0.0368605
$737$	−13637.4	−0.681601
$738$	−5812.03	−0.289897
$739$	36575.5	1.82064	0.910319	−	0.413907i	$-0.135836\pi$
$739$	36575.5	1.82064	0.910319	+	0.413907i	$0.135836\pi$
$740$	0	0
$741$	−66957.3	−3.31949
$742$	−29000.4	−1.43482
$743$	17704.7	0.874190	0.437095	−	0.899415i	$-0.356007\pi$
$743$	17704.7	0.874190	0.437095	+	0.899415i	$0.356007\pi$
$744$	−7259.25	−0.357711
$745$	0	0
$746$	−11408.9	−0.559932
$747$	22868.7	1.12011
$748$	−3114.56	−0.152246
$749$	57735.1	2.81655
$750$	0	0
$751$	8858.37	0.430421	0.215211	−	0.976568i	$-0.430956\pi$
$751$	8858.37	0.430421	0.215211	+	0.976568i	$0.430956\pi$
$752$	8560.59	0.415123
$753$	35415.7	1.71397
$754$	−133.682	−0.00645679
$755$	0	0
$756$	3579.71	0.172213
$757$	−7899.26	−0.379265	−0.189633	−	0.981855i	$-0.560730\pi$
$757$	−7899.26	−0.379265	−0.189633	+	0.981855i	$0.560730\pi$
$758$	20463.9	0.980582
$759$	−2896.22	−0.138506
$760$	0	0
$761$	23437.4	1.11643	0.558216	−	0.829696i	$-0.311486\pi$
$761$	23437.4	1.11643	0.558216	+	0.829696i	$0.311486\pi$
$762$	3195.31	0.151908
$763$	−15308.1	−0.726329
$764$	−9990.95	−0.473115
$765$	0	0
$766$	−12642.7	−0.596343
$767$	−28205.4	−1.32782
$768$	1938.45	0.0910780
$769$	31447.7	1.47468	0.737342	−	0.675519i	$-0.236081\pi$
$769$	31447.7	1.47468	0.737342	+	0.675519i	$0.236081\pi$
$770$	0	0
$771$	19710.0	0.920674
$772$	−3636.62	−0.169540
$773$	−2397.42	−0.111551	−0.0557756	−	0.998443i	$-0.517763\pi$
$773$	−2397.42	−0.111551	−0.0557756	+	0.998443i	$0.517763\pi$
$774$	−20141.1	−0.935343
$775$	0	0
$776$	2175.43	0.100636
$777$	−98760.8	−4.55987
$778$	−1851.19	−0.0853063
$779$	10599.8	0.487518
$780$	0	0
$781$	12202.5	0.559077
$782$	2153.81	0.0984911
$783$	−21.1314	−0.000964465 0
$784$	14588.5	0.664564
$785$	0	0
$786$	−11300.3	−0.512807
$787$	19407.0	0.879014	0.439507	−	0.898239i	$-0.355153\pi$
$787$	19407.0	0.879014	0.439507	+	0.898239i	$0.355153\pi$
$788$	−2434.51	−0.110058
$789$	25830.7	1.16552
$790$	0	0
$791$	8505.58	0.382331
$792$	−4035.93	−0.181074
$793$	−40533.8	−1.81513
$794$	5413.51	0.241962
$795$	0	0
$796$	−9219.91	−0.410542
$797$	28631.1	1.27248	0.636240	−	0.771491i	$-0.280489\pi$
$797$	28631.1	1.27248	0.636240	+	0.771491i	$0.280489\pi$
$798$	−59360.0	−2.63324
$799$	25051.4	1.10921
$800$	0	0
$801$	−31857.6	−1.40529
$802$	−28190.6	−1.24120
$803$	−1520.96	−0.0668414
$804$	24838.1	1.08952
$805$	0	0
$806$	−19152.9	−0.837013
$807$	33064.0	1.44227
$808$	13269.4	0.577743
$809$	−9191.25	−0.399440	−0.199720	−	0.979853i	$-0.564003\pi$
$809$	−9191.25	−0.399440	−0.199720	+	0.979853i	$0.564003\pi$
$810$	0	0
$811$	−567.477	−0.0245706	−0.0122853	−	0.999925i	$-0.503911\pi$
$811$	−567.477	−0.0245706	−0.0122853	+	0.999925i	$0.503911\pi$
$812$	−118.514	−0.00512195
$813$	43028.0	1.85616
$814$	12246.2	0.527310
$815$	0	0
$816$	5672.63	0.243360
$817$	36732.6	1.57296
$818$	−21692.0	−0.927193
$819$	85875.2	3.66388
$820$	0	0
$821$	−6057.35	−0.257494	−0.128747	−	0.991677i	$-0.541096\pi$
$821$	−6057.35	−0.257494	−0.128747	+	0.991677i	$0.541096\pi$
$822$	36650.0	1.55513
$823$	21327.0	0.903294	0.451647	−	0.892197i	$-0.350837\pi$
$823$	21327.0	0.903294	0.451647	+	0.892197i	$0.350837\pi$
$824$	−13884.1	−0.586986
$825$	0	0
$826$	−25005.0	−1.05331
$827$	27553.8	1.15857	0.579286	−	0.815124i	$-0.303332\pi$
$827$	27553.8	1.15857	0.579286	+	0.815124i	$0.303332\pi$
$828$	2790.96	0.117141
$829$	11181.6	0.468461	0.234231	−	0.972181i	$-0.424743\pi$
$829$	11181.6	0.468461	0.234231	+	0.972181i	$0.424743\pi$
$830$	0	0
$831$	14270.5	0.595715
$832$	5114.44	0.213115
$833$	42691.4	1.77571
$834$	13993.7	0.581009
$835$	0	0
$836$	7360.59	0.304511
$837$	−3027.54	−0.125026
$838$	−11253.1	−0.463881
$839$	9811.83	0.403745	0.201872	−	0.979412i	$-0.435297\pi$
$839$	9811.83	0.403745	0.201872	+	0.979412i	$0.435297\pi$
$840$	0	0
$841$	−24388.3	−0.999971
$842$	−14218.2	−0.581937
$843$	−20493.3	−0.837279
$844$	−17493.5	−0.713448
$845$	0	0
$846$	32462.3	1.31924
$847$	−37351.6	−1.51525
$848$	−6549.53	−0.265226
$849$	45157.2	1.82543
$850$	0	0
$851$	−8468.62	−0.341129
$852$	−22224.7	−0.893667
$853$	24030.8	0.964594	0.482297	−	0.876008i	$-0.339803\pi$
$853$	24030.8	0.964594	0.482297	+	0.876008i	$0.339803\pi$
$854$	−35934.6	−1.43988
$855$	0	0
$856$	13039.0	0.520637
$857$	16934.8	0.675008	0.337504	−	0.941324i	$-0.390417\pi$
$857$	16934.8	0.675008	0.337504	+	0.941324i	$0.390417\pi$
$858$	−20125.7	−0.800794
$859$	−31057.0	−1.23359	−0.616793	−	0.787125i	$-0.711568\pi$
$859$	−31057.0	−1.23359	−0.616793	+	0.787125i	$0.711568\pi$
$860$	0	0
$861$	−25694.0	−1.01701
$862$	8928.27	0.352782
$863$	16157.8	0.637332	0.318666	−	0.947867i	$-0.396765\pi$
$863$	16157.8	0.637332	0.318666	+	0.947867i	$0.396765\pi$
$864$	808.451	0.0318334
$865$	0	0
$866$	−22018.9	−0.864009
$867$	−20601.4	−0.806992
$868$	−16979.7	−0.663974
$869$	−5477.55	−0.213824
$870$	0	0
$871$	65533.3	2.54938
$872$	−3457.21	−0.134261
$873$	8249.35	0.319815
$874$	−5090.05	−0.196995
$875$	0	0
$876$	2770.17	0.106844
$877$	32473.9	1.25036	0.625180	−	0.780480i	$-0.285025\pi$
$877$	32473.9	1.25036	0.625180	+	0.780480i	$0.285025\pi$
$878$	−6105.41	−0.234678
$879$	35860.3	1.37604
$880$	0	0
$881$	−15703.2	−0.600517	−0.300258	−	0.953858i	$-0.597073\pi$
$881$	−15703.2	−0.600517	−0.300258	+	0.953858i	$0.597073\pi$
$882$	55320.5	2.11195
$883$	14330.4	0.546155	0.273078	−	0.961992i	$-0.411958\pi$
$883$	14330.4	0.546155	0.273078	+	0.961992i	$0.411958\pi$
$884$	14966.7	0.569441
$885$	0	0
$886$	8931.65	0.338673
$887$	−23238.2	−0.879664	−0.439832	−	0.898080i	$-0.644962\pi$
$887$	−23238.2	−0.879664	−0.439832	+	0.898080i	$0.644962\pi$
$888$	−22304.4	−0.842890
$889$	7473.98	0.281968
$890$	0	0
$891$	10439.9	0.392537
$892$	−21758.0	−0.816717
$893$	−59203.6	−2.21856
$894$	6521.29	0.243965
$895$	0	0
$896$	4534.13	0.169057
$897$	13917.5	0.518052
$898$	18080.3	0.671878
$899$	100.233	0.00371854
$900$	0	0
$901$	−19166.3	−0.708683
$902$	3186.03	0.117609
$903$	−89040.4	−3.28137
$904$	1920.92	0.0706736
$905$	0	0
$906$	−384.841	−0.0141120
$907$	3667.46	0.134263	0.0671313	−	0.997744i	$-0.478615\pi$
$907$	3667.46	0.134263	0.0671313	+	0.997744i	$0.478615\pi$
$908$	−865.992	−0.0316508
$909$	50318.4	1.83604
$910$	0	0
$911$	21457.9	0.780385	0.390192	−	0.920733i	$-0.372409\pi$
$911$	21457.9	0.780385	0.390192	+	0.920733i	$0.372409\pi$
$912$	−13406.0	−0.486752
$913$	−12536.1	−0.454420
$914$	−15513.8	−0.561433
$915$	0	0
$916$	−3698.66	−0.133414
$917$	−26431.8	−0.951859
$918$	2365.83	0.0850587
$919$	−11109.3	−0.398762	−0.199381	−	0.979922i	$-0.563893\pi$
$919$	−11109.3	−0.398762	−0.199381	+	0.979922i	$0.563893\pi$
$920$	0	0
$921$	5824.76	0.208396
$922$	14128.4	0.504657
$923$	−58637.9	−2.09110
$924$	−17842.2	−0.635243
$925$	0	0
$926$	−25199.3	−0.894279
$927$	−52649.4	−1.86541
$928$	−26.7655	−0.000946790 0
$929$	−20804.3	−0.734732	−0.367366	−	0.930076i	$-0.619740\pi$
$929$	−20804.3	−0.734732	−0.367366	+	0.930076i	$0.619740\pi$
$930$	0	0
$931$	−100892.	−3.55166
$932$	9478.75	0.333140
$933$	−42348.5	−1.48599
$934$	−29492.0	−1.03320
$935$	0	0
$936$	19394.3	0.677267
$937$	35550.5	1.23947	0.619735	−	0.784811i	$-0.287240\pi$
$937$	35550.5	1.23947	0.619735	+	0.784811i	$0.287240\pi$
$938$	58097.5	2.02234
$939$	−74033.7	−2.57295
$940$	0	0
$941$	49674.4	1.72087	0.860436	−	0.509558i	$-0.170191\pi$
$941$	49674.4	1.72087	0.860436	+	0.509558i	$0.170191\pi$
$942$	23932.2	0.827762
$943$	−2203.23	−0.0760839
$944$	−5647.20	−0.194704
$945$	0	0
$946$	11040.9	0.379462
$947$	−33466.2	−1.14837	−0.574184	−	0.818726i	$-0.694681\pi$
$947$	−33466.2	−1.14837	−0.574184	+	0.818726i	$0.694681\pi$
$948$	9976.41	0.341792
$949$	7308.85	0.250006
$950$	0	0
$951$	−14148.5	−0.482437
$952$	13268.5	0.451718
$953$	17298.4	0.587984	0.293992	−	0.955808i	$-0.405016\pi$
$953$	17298.4	0.587984	0.293992	+	0.955808i	$0.405016\pi$
$954$	−24836.2	−0.842874
$955$	0	0
$956$	−11078.4	−0.374791
$957$	105.324	0.00355763
$958$	−34822.5	−1.17439
$959$	85726.0	2.88659
$960$	0	0
$961$	−15430.4	−0.517955
$962$	−58848.2	−1.97229
$963$	49444.8	1.65456
$964$	−21336.4	−0.712862
$965$	0	0
$966$	12338.4	0.410953
$967$	14869.7	0.494495	0.247248	−	0.968952i	$-0.420474\pi$
$967$	14869.7	0.494495	0.247248	+	0.968952i	$0.420474\pi$
$968$	−8435.59	−0.280093
$969$	−39231.0	−1.30060
$970$	0	0
$971$	26634.9	0.880283	0.440142	−	0.897928i	$-0.354928\pi$
$971$	26634.9	0.880283	0.440142	+	0.897928i	$0.354928\pi$
$972$	−21743.0	−0.717498
$973$	32731.8	1.07845
$974$	−2640.69	−0.0868717
$975$	0	0
$976$	−8115.57	−0.266161
$977$	−40803.6	−1.33615	−0.668077	−	0.744092i	$-0.732882\pi$
$977$	−40803.6	−1.33615	−0.668077	+	0.744092i	$0.732882\pi$
$978$	−6947.22	−0.227145
$979$	17463.7	0.570115
$980$	0	0
$981$	−13109.9	−0.426675
$982$	34231.6	1.11240
$983$	18615.8	0.604021	0.302011	−	0.953305i	$-0.402342\pi$
$983$	18615.8	0.604021	0.302011	+	0.953305i	$0.402342\pi$
$984$	−5802.80	−0.187995
$985$	0	0
$986$	−78.3257	−0.00252982
$987$	143510.	4.62815
$988$	−35370.6	−1.13896
$989$	−7635.11	−0.245483
$990$	0	0
$991$	46185.1	1.48044	0.740220	−	0.672364i	$-0.234721\pi$
$991$	46185.1	1.48044	0.740220	+	0.672364i	$0.234721\pi$
$992$	−3834.74	−0.122735
$993$	52754.1	1.68590
$994$	−51984.5	−1.65880
$995$	0	0
$996$	22832.4	0.726377
$997$	−16544.3	−0.525541	−0.262771	−	0.964858i	$-0.584636\pi$
$997$	−16544.3	−0.525541	−0.262771	+	0.964858i	$0.584636\pi$
$998$	35081.2	1.11270
$999$	−9302.26	−0.294605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.p.1.4		4
5.2	odd	4		1150.4.b.n.599.5		8
5.3	odd	4		1150.4.b.n.599.4		8
5.4	even	2		230.4.a.h.1.1	✓	4
15.14	odd	2		2070.4.a.bj.1.1		4
20.19	odd	2		1840.4.a.m.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.1	✓	4	5.4	even	2
1150.4.a.p.1.4		4	1.1	even	1	trivial
1150.4.b.n.599.4		8	5.3	odd	4
1150.4.b.n.599.5		8	5.2	odd	4
1840.4.a.m.1.4		4	20.19	odd	2
2070.4.a.bj.1.1		4	15.14	odd	2

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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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +7.57209 q^{3} +4.00000 q^{4} +15.1442 q^{6} +35.4229 q^{7} +8.00000 q^{8} +30.3365 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +7.57209 q^{3} +4.00000 q^{4} +15.1442 q^{6} +35.4229 q^{7} +8.00000 q^{8} +30.3365 q^{9} -16.6298 q^{11} +30.2883 q^{12} +79.9132 q^{13} +70.8458 q^{14} +16.0000 q^{16} +46.8219 q^{17} +60.6730 q^{18} -110.653 q^{19} +268.225 q^{21} -33.2597 q^{22} +23.0000 q^{23} +60.5767 q^{24} +159.826 q^{26} +25.2641 q^{27} +141.692 q^{28} -0.836422 q^{29} -119.836 q^{31} +32.0000 q^{32} -125.923 q^{33} +93.6438 q^{34} +121.346 q^{36} -368.201 q^{37} -221.307 q^{38} +605.109 q^{39} -95.7927 q^{41} +536.450 q^{42} -331.961 q^{43} -66.5193 q^{44} +46.0000 q^{46} +535.037 q^{47} +121.153 q^{48} +911.782 q^{49} +354.539 q^{51} +319.653 q^{52} -409.345 q^{53} +50.5282 q^{54} +283.383 q^{56} -837.876 q^{57} -1.67284 q^{58} -352.950 q^{59} -507.223 q^{61} -239.672 q^{62} +1074.61 q^{63} +64.0000 q^{64} -251.845 q^{66} +820.056 q^{67} +187.288 q^{68} +174.158 q^{69} -733.770 q^{71} +242.692 q^{72} +91.4599 q^{73} -736.402 q^{74} -442.613 q^{76} -589.077 q^{77} +1210.22 q^{78} +329.381 q^{79} -627.783 q^{81} -191.585 q^{82} +753.834 q^{83} +1072.90 q^{84} -663.922 q^{86} -6.33346 q^{87} -133.039 q^{88} -1050.14 q^{89} +2830.76 q^{91} +92.0000 q^{92} -907.407 q^{93} +1070.07 q^{94} +242.307 q^{96} +271.928 q^{97} +1823.56 q^{98} -504.491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9	\( 4 q + 8 q^{2} + 4 q^{3} + 16 q^{4} + 8 q^{6} + q^{7} + 32 q^{8} + 32 q^{9} - 39 q^{11} + 16 q^{12} + 20 q^{13} + 2 q^{14} + 64 q^{16} + 23 q^{17} + 64 q^{18} + 53 q^{19} + 300 q^{21} - 78 q^{22} + 92 q^{23} + 32 q^{24} + 40 q^{26} - 137 q^{27} + 4 q^{28} + 161 q^{29} + 388 q^{31} + 128 q^{32} - 87 q^{33} + 46 q^{34} + 128 q^{36} - 466 q^{37} + 106 q^{38} + 1047 q^{39} + 484 q^{41} + 600 q^{42} - 894 q^{43} - 156 q^{44} + 184 q^{46} + 265 q^{47} + 64 q^{48} + 1643 q^{49} + 1825 q^{51} + 80 q^{52} - 576 q^{53} - 274 q^{54} + 8 q^{56} - 178 q^{57} + 322 q^{58} - 94 q^{59} + 1153 q^{61} + 776 q^{62} - 60 q^{63} + 256 q^{64} - 174 q^{66} + 1472 q^{67} + 92 q^{68} + 92 q^{69} + 200 q^{71} + 256 q^{72} - 1147 q^{73} - 932 q^{74} + 212 q^{76} + 2176 q^{77} + 2094 q^{78} - 908 q^{79} - 1056 q^{81} + 968 q^{82} + 1048 q^{83} + 1200 q^{84} - 1788 q^{86} + 2167 q^{87} - 312 q^{88} - 1784 q^{89} + 2329 q^{91} + 368 q^{92} - 1483 q^{93} + 530 q^{94} + 128 q^{96} + 2047 q^{97} + 3286 q^{98} - 2665 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 4 * q^3 + 16 * q^4 + 8 * q^6 + q^7 + 32 * q^8 + 32 * q^9 - 39 * q^11 + 16 * q^12 + 20 * q^13 + 2 * q^14 + 64 * q^16 + 23 * q^17 + 64 * q^18 + 53 * q^19 + 300 * q^21 - 78 * q^22 + 92 * q^23 + 32 * q^24 + 40 * q^26 - 137 * q^27 + 4 * q^28 + 161 * q^29 + 388 * q^31 + 128 * q^32 - 87 * q^33 + 46 * q^34 + 128 * q^36 - 466 * q^37 + 106 * q^38 + 1047 * q^39 + 484 * q^41 + 600 * q^42 - 894 * q^43 - 156 * q^44 + 184 * q^46 + 265 * q^47 + 64 * q^48 + 1643 * q^49 + 1825 * q^51 + 80 * q^52 - 576 * q^53 - 274 * q^54 + 8 * q^56 - 178 * q^57 + 322 * q^58 - 94 * q^59 + 1153 * q^61 + 776 * q^62 - 60 * q^63 + 256 * q^64 - 174 * q^66 + 1472 * q^67 + 92 * q^68 + 92 * q^69 + 200 * q^71 + 256 * q^72 - 1147 * q^73 - 932 * q^74 + 212 * q^76 + 2176 * q^77 + 2094 * q^78 - 908 * q^79 - 1056 * q^81 + 968 * q^82 + 1048 * q^83 + 1200 * q^84 - 1788 * q^86 + 2167 * q^87 - 312 * q^88 - 1784 * q^89 + 2329 * q^91 + 368 * q^92 - 1483 * q^93 + 530 * q^94 + 128 * q^96 + 2047 * q^97 + 3286 * q^98 - 2665 * q^99

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