LMFDB - Embedded newform 950.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,4,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	950.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:	$56.0518145055$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{73}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 18 $ x^2 - x - 18
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.77200$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -8.77200 q^{3} +4.00000 q^{4} +17.5440 q^{6} +26.0880 q^{7} -8.00000 q^{8} +49.9480 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -8.77200 q^{3} +4.00000 q^{4} +17.5440 q^{6} +26.0880 q^{7} -8.00000 q^{8} +49.9480 q^{9} -4.22800 q^{11} -35.0880 q^{12} -64.0360 q^{13} -52.1760 q^{14} +16.0000 q^{16} +48.5440 q^{17} -99.8960 q^{18} +19.0000 q^{19} -228.844 q^{21} +8.45600 q^{22} -92.0360 q^{23} +70.1760 q^{24} +128.072 q^{26} -201.300 q^{27} +104.352 q^{28} -88.2120 q^{29} -81.9681 q^{31} -32.0000 q^{32} +37.0880 q^{33} -97.0880 q^{34} +199.792 q^{36} +23.6161 q^{37} -38.0000 q^{38} +561.724 q^{39} +17.7200 q^{41} +457.688 q^{42} -368.404 q^{43} -16.9120 q^{44} +184.072 q^{46} +497.812 q^{47} -140.352 q^{48} +337.584 q^{49} -425.828 q^{51} -256.144 q^{52} +536.876 q^{53} +402.600 q^{54} -208.704 q^{56} -166.668 q^{57} +176.424 q^{58} -36.7000 q^{59} +630.692 q^{61} +163.936 q^{62} +1303.04 q^{63} +64.0000 q^{64} -74.1760 q^{66} -282.556 q^{67} +194.176 q^{68} +807.340 q^{69} +595.552 q^{71} -399.584 q^{72} +597.048 q^{73} -47.2321 q^{74} +76.0000 q^{76} -110.300 q^{77} -1123.45 q^{78} +427.224 q^{79} +417.208 q^{81} -35.4400 q^{82} -493.768 q^{83} -915.376 q^{84} +736.808 q^{86} +773.796 q^{87} +33.8240 q^{88} -921.136 q^{89} -1670.57 q^{91} -368.144 q^{92} +719.024 q^{93} -995.624 q^{94} +280.704 q^{96} -1082.74 q^{97} -675.168 q^{98} -211.180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 9 q^{3} + 8 q^{4} + 18 q^{6} + 18 q^{7} - 16 q^{8} + 23 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 9 * q^3 + 8 * q^4 + 18 * q^6 + 18 * q^7 - 16 * q^8 + 23 * q^9	$ 2 q - 4 q^{2} - 9 q^{3} + 8 q^{4} + 18 q^{6} + 18 q^{7} - 16 q^{8} + 23 q^{9} - 17 q^{11} - 36 q^{12} - 17 q^{13} - 36 q^{14} + 32 q^{16} + 80 q^{17} - 46 q^{18} + 38 q^{19} - 227 q^{21} + 34 q^{22} - 73 q^{23} + 72 q^{24} + 34 q^{26} - 189 q^{27} + 72 q^{28} + 3 q^{29} + 212 q^{31} - 64 q^{32} + 40 q^{33} - 160 q^{34} + 92 q^{36} - 192 q^{37} - 76 q^{38} + 551 q^{39} - 50 q^{41} + 454 q^{42} - 677 q^{43} - 68 q^{44} + 146 q^{46} + 389 q^{47} - 144 q^{48} + 60 q^{49} - 433 q^{51} - 68 q^{52} + 1219 q^{53} + 378 q^{54} - 144 q^{56} - 171 q^{57} - 6 q^{58} - 287 q^{59} + 313 q^{61} - 424 q^{62} + 1521 q^{63} + 128 q^{64} - 80 q^{66} - 1223 q^{67} + 320 q^{68} + 803 q^{69} + 200 q^{71} - 184 q^{72} - 378 q^{73} + 384 q^{74} + 152 q^{76} - 7 q^{77} - 1102 q^{78} + 1350 q^{79} + 1142 q^{81} + 100 q^{82} + 670 q^{83} - 908 q^{84} + 1354 q^{86} + 753 q^{87} + 136 q^{88} - 236 q^{89} - 2051 q^{91} - 292 q^{92} + 652 q^{93} - 778 q^{94} + 288 q^{96} - 1294 q^{97} - 120 q^{98} + 133 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 - 9 * q^3 + 8 * q^4 + 18 * q^6 + 18 * q^7 - 16 * q^8 + 23 * q^9 - 17 * q^11 - 36 * q^12 - 17 * q^13 - 36 * q^14 + 32 * q^16 + 80 * q^17 - 46 * q^18 + 38 * q^19 - 227 * q^21 + 34 * q^22 - 73 * q^23 + 72 * q^24 + 34 * q^26 - 189 * q^27 + 72 * q^28 + 3 * q^29 + 212 * q^31 - 64 * q^32 + 40 * q^33 - 160 * q^34 + 92 * q^36 - 192 * q^37 - 76 * q^38 + 551 * q^39 - 50 * q^41 + 454 * q^42 - 677 * q^43 - 68 * q^44 + 146 * q^46 + 389 * q^47 - 144 * q^48 + 60 * q^49 - 433 * q^51 - 68 * q^52 + 1219 * q^53 + 378 * q^54 - 144 * q^56 - 171 * q^57 - 6 * q^58 - 287 * q^59 + 313 * q^61 - 424 * q^62 + 1521 * q^63 + 128 * q^64 - 80 * q^66 - 1223 * q^67 + 320 * q^68 + 803 * q^69 + 200 * q^71 - 184 * q^72 - 378 * q^73 + 384 * q^74 + 152 * q^76 - 7 * q^77 - 1102 * q^78 + 1350 * q^79 + 1142 * q^81 + 100 * q^82 + 670 * q^83 - 908 * q^84 + 1354 * q^86 + 753 * q^87 + 136 * q^88 - 236 * q^89 - 2051 * q^91 - 292 * q^92 + 652 * q^93 - 778 * q^94 + 288 * q^96 - 1294 * q^97 - 120 * q^98 + 133 * 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
$3$	−8.77200	−1.68817	−0.844086	−	0.536207i	$-0.819856\pi$
$3$	−8.77200	−1.68817	−0.844086	+	0.536207i	$0.819856\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	17.5440	1.19372
$7$	26.0880	1.40862	0.704310	−	0.709893i	$-0.251257\pi$
$7$	26.0880	1.40862	0.704310	+	0.709893i	$0.251257\pi$
$8$	−8.00000	−0.353553
$9$	49.9480	1.84993
$10$	0	0
$11$	−4.22800	−0.115890	−0.0579450	−	0.998320i	$-0.518455\pi$
$11$	−4.22800	−0.115890	−0.0579450	+	0.998320i	$0.518455\pi$
$12$	−35.0880	−0.844086
$13$	−64.0360	−1.36618	−0.683092	−	0.730332i	$-0.739365\pi$
$13$	−64.0360	−1.36618	−0.683092	+	0.730332i	$0.739365\pi$
$14$	−52.1760	−0.996045
$15$	0	0
$16$	16.0000	0.250000
$17$	48.5440	0.692568	0.346284	−	0.938130i	$-0.387443\pi$
$17$	48.5440	0.692568	0.346284	+	0.938130i	$0.387443\pi$
$18$	−99.8960	−1.30810
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	0	0
$21$	−228.844	−2.37799
$22$	8.45600	0.0819466
$23$	−92.0360	−0.834384	−0.417192	−	0.908818i	$-0.636986\pi$
$23$	−92.0360	−0.834384	−0.417192	+	0.908818i	$0.636986\pi$
$24$	70.1760	0.596859
$25$	0	0
$26$	128.072	0.966038
$27$	−201.300	−1.43482
$28$	104.352	0.704310
$29$	−88.2120	−0.564847	−0.282424	−	0.959290i	$-0.591138\pi$
$29$	−88.2120	−0.564847	−0.282424	+	0.959290i	$0.591138\pi$
$30$	0	0
$31$	−81.9681	−0.474900	−0.237450	−	0.971400i	$-0.576312\pi$
$31$	−81.9681	−0.474900	−0.237450	+	0.971400i	$0.576312\pi$
$32$	−32.0000	−0.176777
$33$	37.0880	0.195642
$34$	−97.0880	−0.489719
$35$	0	0
$36$	199.792	0.924963
$37$	23.6161	0.104931	0.0524656	−	0.998623i	$-0.483292\pi$
$37$	23.6161	0.104931	0.0524656	+	0.998623i	$0.483292\pi$
$38$	−38.0000	−0.162221
$39$	561.724	2.30636
$40$	0	0
$41$	17.7200	0.0674976	0.0337488	−	0.999430i	$-0.489255\pi$
$41$	17.7200	0.0674976	0.0337488	+	0.999430i	$0.489255\pi$
$42$	457.688	1.68150
$43$	−368.404	−1.30654	−0.653268	−	0.757126i	$-0.726603\pi$
$43$	−368.404	−1.30654	−0.653268	+	0.757126i	$0.726603\pi$
$44$	−16.9120	−0.0579450
$45$	0	0
$46$	184.072	0.589999
$47$	497.812	1.54497	0.772483	−	0.635036i	$-0.219015\pi$
$47$	497.812	1.54497	0.772483	+	0.635036i	$0.219015\pi$
$48$	−140.352	−0.422043
$49$	337.584	0.984210
$50$	0	0
$51$	−425.828	−1.16917
$52$	−256.144	−0.683092
$53$	536.876	1.39143	0.695713	−	0.718320i	$-0.255089\pi$
$53$	536.876	1.39143	0.695713	+	0.718320i	$0.255089\pi$
$54$	402.600	1.01457
$55$	0	0
$56$	−208.704	−0.498022
$57$	−166.668	−0.387293
$58$	176.424	0.399407
$59$	−36.7000	−0.0809818	−0.0404909	−	0.999180i	$-0.512892\pi$
$59$	−36.7000	−0.0809818	−0.0404909	+	0.999180i	$0.512892\pi$
$60$	0	0
$61$	630.692	1.32380	0.661901	−	0.749592i	$-0.269750\pi$
$61$	630.692	1.32380	0.661901	+	0.749592i	$0.269750\pi$
$62$	163.936	0.335805
$63$	1303.04	2.60584
$64$	64.0000	0.125000
$65$	0	0
$66$	−74.1760	−0.138340
$67$	−282.556	−0.515219	−0.257610	−	0.966249i	$-0.582935\pi$
$67$	−282.556	−0.515219	−0.257610	+	0.966249i	$0.582935\pi$
$68$	194.176	0.346284
$69$	807.340	1.40858
$70$	0	0
$71$	595.552	0.995480	0.497740	−	0.867326i	$-0.334163\pi$
$71$	595.552	0.995480	0.497740	+	0.867326i	$0.334163\pi$
$72$	−399.584	−0.654048
$73$	597.048	0.957250	0.478625	−	0.878020i	$-0.341135\pi$
$73$	597.048	0.957250	0.478625	+	0.878020i	$0.341135\pi$
$74$	−47.2321	−0.0741976
$75$	0	0
$76$	76.0000	0.114708
$77$	−110.300	−0.163245
$78$	−1123.45	−1.63084
$79$	427.224	0.608436	0.304218	−	0.952602i	$-0.401605\pi$
$79$	427.224	0.608436	0.304218	+	0.952602i	$0.401605\pi$
$80$	0	0
$81$	417.208	0.572302
$82$	−35.4400	−0.0477280
$83$	−493.768	−0.652989	−0.326495	−	0.945199i	$-0.605868\pi$
$83$	−493.768	−0.652989	−0.326495	+	0.945199i	$0.605868\pi$
$84$	−915.376	−1.18900
$85$	0	0
$86$	736.808	0.923861
$87$	773.796	0.953559
$88$	33.8240	0.0409733
$89$	−921.136	−1.09708	−0.548541	−	0.836124i	$-0.684816\pi$
$89$	−921.136	−1.09708	−0.548541	+	0.836124i	$0.684816\pi$
$90$	0	0
$91$	−1670.57	−1.92443
$92$	−368.144	−0.417192
$93$	719.024	0.801713
$94$	−995.624	−1.09246
$95$	0	0
$96$	280.704	0.298430
$97$	−1082.74	−1.13336	−0.566680	−	0.823938i	$-0.691773\pi$
$97$	−1082.74	−1.13336	−0.566680	+	0.823938i	$0.691773\pi$
$98$	−675.168	−0.695942
$99$	−211.180	−0.214388
$100$	0	0
$101$	−712.448	−0.701893	−0.350947	−	0.936395i	$-0.614140\pi$
$101$	−712.448	−0.701893	−0.350947	+	0.936395i	$0.614140\pi$
$102$	851.656	0.826731
$103$	26.4797	0.0253313	0.0126656	−	0.999920i	$-0.495968\pi$
$103$	26.4797	0.0253313	0.0126656	+	0.999920i	$0.495968\pi$
$104$	512.288	0.483019
$105$	0	0
$106$	−1073.75	−0.983887
$107$	740.996	0.669484	0.334742	−	0.942310i	$-0.391351\pi$
$107$	740.996	0.669484	0.334742	+	0.942310i	$0.391351\pi$
$108$	−805.200	−0.717411
$109$	−1983.08	−1.74261	−0.871304	−	0.490744i	$-0.836725\pi$
$109$	−1983.08	−1.74261	−0.871304	+	0.490744i	$0.836725\pi$
$110$	0	0
$111$	−207.160	−0.177142
$112$	417.408	0.352155
$113$	718.720	0.598332	0.299166	−	0.954201i	$-0.403292\pi$
$113$	718.720	0.598332	0.299166	+	0.954201i	$0.403292\pi$
$114$	333.336	0.273858
$115$	0	0
$116$	−352.848	−0.282424
$117$	−3198.47	−2.52734
$118$	73.3999	0.0572628
$119$	1266.42	0.975565
$120$	0	0
$121$	−1313.12	−0.986570
$122$	−1261.38	−0.936069
$123$	−155.440	−0.113948
$124$	−327.872	−0.237450
$125$	0	0
$126$	−2606.09	−1.84261
$127$	−2610.72	−1.82413	−0.912063	−	0.410050i	$-0.865511\pi$
$127$	−2610.72	−1.82413	−0.912063	+	0.410050i	$0.865511\pi$
$128$	−128.000	−0.0883883
$129$	3231.64	2.20566
$130$	0	0
$131$	−1216.69	−0.811472	−0.405736	−	0.913990i	$-0.632985\pi$
$131$	−1216.69	−0.811472	−0.405736	+	0.913990i	$0.632985\pi$
$132$	148.352	0.0978211
$133$	495.672	0.323160
$134$	565.112	0.364315
$135$	0	0
$136$	−388.352	−0.244860
$137$	−1170.67	−0.730053	−0.365026	−	0.930997i	$-0.618940\pi$
$137$	−1170.67	−0.730053	−0.365026	+	0.930997i	$0.618940\pi$
$138$	−1614.68	−0.996020
$139$	−271.083	−0.165417	−0.0827086	−	0.996574i	$-0.526357\pi$
$139$	−271.083	−0.165417	−0.0827086	+	0.996574i	$0.526357\pi$
$140$	0	0
$141$	−4366.81	−2.60817
$142$	−1191.10	−0.703910
$143$	270.744	0.158327
$144$	799.168	0.462482
$145$	0	0
$146$	−1194.10	−0.676878
$147$	−2961.29	−1.66152
$148$	94.4642	0.0524656
$149$	1841.19	1.01232	0.506161	−	0.862439i	$-0.331064\pi$
$149$	1841.19	1.01232	0.506161	+	0.862439i	$0.331064\pi$
$150$	0	0
$151$	3322.32	1.79051	0.895254	−	0.445557i	$-0.146994\pi$
$151$	3322.32	1.79051	0.895254	+	0.445557i	$0.146994\pi$
$152$	−152.000	−0.0811107
$153$	2424.68	1.28120
$154$	220.600	0.115432
$155$	0	0
$156$	2246.90	1.15318
$157$	−243.616	−0.123839	−0.0619194	−	0.998081i	$-0.519722\pi$
$157$	−243.616	−0.123839	−0.0619194	+	0.998081i	$0.519722\pi$
$158$	−854.448	−0.430229
$159$	−4709.48	−2.34897
$160$	0	0
$161$	−2401.04	−1.17533
$162$	−834.416	−0.404678
$163$	2598.11	1.24847	0.624233	−	0.781238i	$-0.285412\pi$
$163$	2598.11	1.24847	0.624233	+	0.781238i	$0.285412\pi$
$164$	70.8801	0.0337488
$165$	0	0
$166$	987.537	0.461733
$167$	491.064	0.227543	0.113772	−	0.993507i	$-0.463707\pi$
$167$	491.064	0.227543	0.113772	+	0.993507i	$0.463707\pi$
$168$	1830.75	0.840748
$169$	1903.61	0.866460
$170$	0	0
$171$	949.012	0.424402
$172$	−1473.62	−0.653268
$173$	−1648.56	−0.724496	−0.362248	−	0.932082i	$-0.617991\pi$
$173$	−1648.56	−0.724496	−0.362248	+	0.932082i	$0.617991\pi$
$174$	−1547.59	−0.674268
$175$	0	0
$176$	−67.6480	−0.0289725
$177$	321.932	0.136711
$178$	1842.27	0.775754
$179$	2326.81	0.971586	0.485793	−	0.874074i	$-0.338531\pi$
$179$	2326.81	0.971586	0.485793	+	0.874074i	$0.338531\pi$
$180$	0	0
$181$	−4637.46	−1.90442	−0.952208	−	0.305449i	$-0.901193\pi$
$181$	−4637.46	−1.90442	−0.952208	+	0.305449i	$0.901193\pi$
$182$	3341.14	1.36078
$183$	−5532.43	−2.23480
$184$	736.288	0.294999
$185$	0	0
$186$	−1438.05	−0.566897
$187$	−205.244	−0.0802616
$188$	1991.25	0.772483
$189$	−5251.52	−2.02112
$190$	0	0
$191$	5260.38	1.99281	0.996407	−	0.0846903i	$-0.0269901\pi$
$191$	5260.38	1.99281	0.996407	+	0.0846903i	$0.0269901\pi$
$192$	−561.408	−0.211022
$193$	−16.1833	−0.00603575	−0.00301787	−	0.999995i	$-0.500961\pi$
$193$	−16.1833	−0.00603575	−0.00301787	+	0.999995i	$0.500961\pi$
$194$	2165.49	0.801407
$195$	0	0
$196$	1350.34	0.492105
$197$	−3784.71	−1.36878	−0.684390	−	0.729116i	$-0.739931\pi$
$197$	−3784.71	−1.36878	−0.684390	+	0.729116i	$0.739931\pi$
$198$	422.360	0.151595
$199$	73.2079	0.0260783	0.0130391	−	0.999915i	$-0.495849\pi$
$199$	73.2079	0.0260783	0.0130391	+	0.999915i	$0.495849\pi$
$200$	0	0
$201$	2478.58	0.869779
$202$	1424.90	0.496313
$203$	−2301.28	−0.795655
$204$	−1703.31	−0.584587
$205$	0	0
$206$	−52.9594	−0.0179119
$207$	−4597.02	−1.54355
$208$	−1024.58	−0.341546
$209$	−80.3320	−0.0265870
$210$	0	0
$211$	−2945.44	−0.961006	−0.480503	−	0.876993i	$-0.659546\pi$
$211$	−2945.44	−0.961006	−0.480503	+	0.876993i	$0.659546\pi$
$212$	2147.50	0.695713
$213$	−5224.19	−1.68054
$214$	−1481.99	−0.473397
$215$	0	0
$216$	1610.40	0.507286
$217$	−2138.38	−0.668954
$218$	3966.15	1.23221
$219$	−5237.31	−1.61600
$220$	0	0
$221$	−3108.57	−0.946175
$222$	414.320	0.125258
$223$	−3125.30	−0.938499	−0.469250	−	0.883066i	$-0.655476\pi$
$223$	−3125.30	−0.938499	−0.469250	+	0.883066i	$0.655476\pi$
$224$	−834.816	−0.249011
$225$	0	0
$226$	−1437.44	−0.423085
$227$	3577.80	1.04611	0.523055	−	0.852299i	$-0.324792\pi$
$227$	3577.80	1.04611	0.523055	+	0.852299i	$0.324792\pi$
$228$	−666.672	−0.193647
$229$	−4802.00	−1.38570	−0.692850	−	0.721082i	$-0.743645\pi$
$229$	−4802.00	−1.38570	−0.692850	+	0.721082i	$0.743645\pi$
$230$	0	0
$231$	967.552	0.275586
$232$	705.696	0.199704
$233$	−5829.49	−1.63907	−0.819534	−	0.573031i	$-0.805768\pi$
$233$	−5829.49	−1.63907	−0.819534	+	0.573031i	$0.805768\pi$
$234$	6396.94	1.78710
$235$	0	0
$236$	−146.800	−0.0404909
$237$	−3747.61	−1.02714
$238$	−2532.83	−0.689828
$239$	1364.33	0.369251	0.184625	−	0.982809i	$-0.440893\pi$
$239$	1364.33	0.369251	0.184625	+	0.982809i	$0.440893\pi$
$240$	0	0
$241$	−2647.22	−0.707563	−0.353782	−	0.935328i	$-0.615104\pi$
$241$	−2647.22	−0.707563	−0.353782	+	0.935328i	$0.615104\pi$
$242$	2626.25	0.697610
$243$	1775.35	0.468679
$244$	2522.77	0.661901
$245$	0	0
$246$	310.880	0.0805731
$247$	−1216.68	−0.313424
$248$	655.745	0.167903
$249$	4331.34	1.10236
$250$	0	0
$251$	1970.73	0.495582	0.247791	−	0.968814i	$-0.420295\pi$
$251$	1970.73	0.495582	0.247791	+	0.968814i	$0.420295\pi$
$252$	5212.18	1.30292
$253$	389.128	0.0966967
$254$	5221.44	1.28985
$255$	0	0
$256$	256.000	0.0625000
$257$	7915.82	1.92131	0.960653	−	0.277752i	$-0.0895892\pi$
$257$	7915.82	1.92131	0.960653	+	0.277752i	$0.0895892\pi$
$258$	−6463.28	−1.55964
$259$	616.096	0.147808
$260$	0	0
$261$	−4406.02	−1.04493
$262$	2433.38	0.573798
$263$	−3287.96	−0.770892	−0.385446	−	0.922730i	$-0.625952\pi$
$263$	−3287.96	−0.770892	−0.385446	+	0.922730i	$0.625952\pi$
$264$	−296.704	−0.0691700
$265$	0	0
$266$	−991.344	−0.228508
$267$	8080.21	1.85206
$268$	−1130.22	−0.257610
$269$	−4749.61	−1.07654	−0.538269	−	0.842773i	$-0.680922\pi$
$269$	−4749.61	−1.07654	−0.538269	+	0.842773i	$0.680922\pi$
$270$	0	0
$271$	242.661	0.0543933	0.0271967	−	0.999630i	$-0.491342\pi$
$271$	242.661	0.0543933	0.0271967	+	0.999630i	$0.491342\pi$
$272$	776.704	0.173142
$273$	14654.3	3.24878
$274$	2341.34	0.516225
$275$	0	0
$276$	3229.36	0.704292
$277$	4131.13	0.896086	0.448043	−	0.894012i	$-0.352121\pi$
$277$	4131.13	0.896086	0.448043	+	0.894012i	$0.352121\pi$
$278$	542.167	0.116968
$279$	−4094.14	−0.878530
$280$	0	0
$281$	1007.19	0.213822	0.106911	−	0.994269i	$-0.465904\pi$
$281$	1007.19	0.213822	0.106911	+	0.994269i	$0.465904\pi$
$282$	8733.62	1.84425
$283$	−2333.63	−0.490176	−0.245088	−	0.969501i	$-0.578817\pi$
$283$	−2333.63	−0.490176	−0.245088	+	0.969501i	$0.578817\pi$
$284$	2382.21	0.497740
$285$	0	0
$286$	−541.488	−0.111954
$287$	462.280	0.0950785
$288$	−1598.34	−0.327024
$289$	−2556.48	−0.520350
$290$	0	0
$291$	9497.83	1.91331
$292$	2388.19	0.478625
$293$	1588.68	0.316763	0.158381	−	0.987378i	$-0.449372\pi$
$293$	1588.68	0.316763	0.158381	+	0.987378i	$0.449372\pi$
$294$	5922.58	1.17487
$295$	0	0
$296$	−188.928	−0.0370988
$297$	851.096	0.166282
$298$	−3682.38	−0.715820
$299$	5893.62	1.13992
$300$	0	0
$301$	−9610.93	−1.84041
$302$	−6644.64	−1.26608
$303$	6249.59	1.18492
$304$	304.000	0.0573539
$305$	0	0
$306$	−4849.35	−0.905945
$307$	−4057.46	−0.754304	−0.377152	−	0.926151i	$-0.623097\pi$
$307$	−4057.46	−0.754304	−0.377152	+	0.926151i	$0.623097\pi$
$308$	−441.200	−0.0816224
$309$	−232.280	−0.0427636
$310$	0	0
$311$	2871.92	0.523638	0.261819	−	0.965117i	$-0.415678\pi$
$311$	2871.92	0.523638	0.261819	+	0.965117i	$0.415678\pi$
$312$	−4493.79	−0.815420
$313$	−4322.67	−0.780612	−0.390306	−	0.920685i	$-0.627631\pi$
$313$	−4322.67	−0.780612	−0.390306	+	0.920685i	$0.627631\pi$
$314$	487.232	0.0875672
$315$	0	0
$316$	1708.90	0.304218
$317$	−2513.56	−0.445349	−0.222674	−	0.974893i	$-0.571479\pi$
$317$	−2513.56	−0.445349	−0.222674	+	0.974893i	$0.571479\pi$
$318$	9418.95	1.66097
$319$	372.960	0.0654601
$320$	0	0
$321$	−6500.02	−1.13021
$322$	4802.07	0.831084
$323$	922.336	0.158886
$324$	1668.83	0.286151
$325$	0	0
$326$	−5196.22	−0.882798
$327$	17395.6	2.94182
$328$	−141.760	−0.0238640
$329$	12986.9	2.17627
$330$	0	0
$331$	−4573.78	−0.759509	−0.379754	−	0.925087i	$-0.623992\pi$
$331$	−4573.78	−0.759509	−0.379754	+	0.925087i	$0.623992\pi$
$332$	−1975.07	−0.326495
$333$	1179.57	0.194115
$334$	−982.129	−0.160897
$335$	0	0
$336$	−3661.50	−0.594498
$337$	−9001.71	−1.45506	−0.727529	−	0.686077i	$-0.759331\pi$
$337$	−9001.71	−1.45506	−0.727529	+	0.686077i	$0.759331\pi$
$338$	−3807.22	−0.612680
$339$	−6304.62	−1.01009
$340$	0	0
$341$	346.561	0.0550361
$342$	−1898.02	−0.300098
$343$	−141.289	−0.0222417
$344$	2947.23	0.461931
$345$	0	0
$346$	3297.12	0.512296
$347$	−9358.68	−1.44784	−0.723920	−	0.689884i	$-0.757661\pi$
$347$	−9358.68	−1.44784	−0.723920	+	0.689884i	$0.757661\pi$
$348$	3095.18	0.476780
$349$	5787.76	0.887712	0.443856	−	0.896098i	$-0.353610\pi$
$349$	5787.76	0.887712	0.443856	+	0.896098i	$0.353610\pi$
$350$	0	0
$351$	12890.5	1.96023
$352$	135.296	0.0204866
$353$	−5784.59	−0.872188	−0.436094	−	0.899901i	$-0.643639\pi$
$353$	−5784.59	−0.872188	−0.436094	+	0.899901i	$0.643639\pi$
$354$	−643.864	−0.0966695
$355$	0	0
$356$	−3684.55	−0.548541
$357$	−11109.0	−1.64692
$358$	−4653.62	−0.687015
$359$	−10132.3	−1.48959	−0.744796	−	0.667292i	$-0.767453\pi$
$359$	−10132.3	−1.48959	−0.744796	+	0.667292i	$0.767453\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	9274.91	1.34663
$363$	11518.7	1.66550
$364$	−6682.29	−0.962217
$365$	0	0
$366$	11064.9	1.58025
$367$	6993.81	0.994752	0.497376	−	0.867535i	$-0.334297\pi$
$367$	6993.81	0.994752	0.497376	+	0.867535i	$0.334297\pi$
$368$	−1472.58	−0.208596
$369$	885.080	0.124866
$370$	0	0
$371$	14006.0	1.95999
$372$	2876.10	0.400857
$373$	−6523.15	−0.905512	−0.452756	−	0.891634i	$-0.649559\pi$
$373$	−6523.15	−0.905512	−0.452756	+	0.891634i	$0.649559\pi$
$374$	410.488	0.0567535
$375$	0	0
$376$	−3982.50	−0.546228
$377$	5648.75	0.771685
$378$	10503.0	1.42915
$379$	−9782.00	−1.32577	−0.662886	−	0.748720i	$-0.730669\pi$
$379$	−9782.00	−1.32577	−0.662886	+	0.748720i	$0.730669\pi$
$380$	0	0
$381$	22901.2	3.07944
$382$	−10520.8	−1.40913
$383$	−9878.11	−1.31788	−0.658940	−	0.752196i	$-0.728995\pi$
$383$	−9878.11	−1.31788	−0.658940	+	0.752196i	$0.728995\pi$
$384$	1122.82	0.149215
$385$	0	0
$386$	32.3666	0.00426792
$387$	−18401.0	−2.41700
$388$	−4330.98	−0.566680
$389$	−7891.25	−1.02854	−0.514270	−	0.857628i	$-0.671937\pi$
$389$	−7891.25	−1.02854	−0.514270	+	0.857628i	$0.671937\pi$
$390$	0	0
$391$	−4467.80	−0.577868
$392$	−2700.67	−0.347971
$393$	10672.8	1.36991
$394$	7569.43	0.967874
$395$	0	0
$396$	−844.720	−0.107194
$397$	2787.84	0.352437	0.176219	−	0.984351i	$-0.443613\pi$
$397$	2787.84	0.352437	0.176219	+	0.984351i	$0.443613\pi$
$398$	−146.416	−0.0184401
$399$	−4348.04	−0.545549
$400$	0	0
$401$	1264.42	0.157461	0.0787306	−	0.996896i	$-0.474913\pi$
$401$	1264.42	0.157461	0.0787306	+	0.996896i	$0.474913\pi$
$402$	−4957.16	−0.615027
$403$	5248.91	0.648801
$404$	−2849.79	−0.350947
$405$	0	0
$406$	4602.55	0.562613
$407$	−99.8486	−0.0121605
$408$	3406.62	0.413365
$409$	−8140.55	−0.984166	−0.492083	−	0.870548i	$-0.663764\pi$
$409$	−8140.55	−0.984166	−0.492083	+	0.870548i	$0.663764\pi$
$410$	0	0
$411$	10269.1	1.23246
$412$	105.919	0.0126656
$413$	−957.429	−0.114073
$414$	9194.03	1.09145
$415$	0	0
$416$	2049.15	0.241510
$417$	2377.94	0.279253
$418$	160.664	0.0187998
$419$	−9601.15	−1.11944	−0.559722	−	0.828680i	$-0.689092\pi$
$419$	−9601.15	−1.11944	−0.559722	+	0.828680i	$0.689092\pi$
$420$	0	0
$421$	5702.48	0.660147	0.330074	−	0.943955i	$-0.392926\pi$
$421$	5702.48	0.660147	0.330074	+	0.943955i	$0.392926\pi$
$422$	5890.87	0.679534
$423$	24864.7	2.85807
$424$	−4295.01	−0.491943
$425$	0	0
$426$	10448.4	1.18832
$427$	16453.5	1.86473
$428$	2963.99	0.334742
$429$	−2374.97	−0.267283
$430$	0	0
$431$	−4025.72	−0.449912	−0.224956	−	0.974369i	$-0.572224\pi$
$431$	−4025.72	−0.449912	−0.224956	+	0.974369i	$0.572224\pi$
$432$	−3220.80	−0.358706
$433$	1347.10	0.149510	0.0747548	−	0.997202i	$-0.476183\pi$
$433$	1347.10	0.149510	0.0747548	+	0.997202i	$0.476183\pi$
$434$	4276.77	0.473022
$435$	0	0
$436$	−7932.31	−0.871304
$437$	−1748.68	−0.191421
$438$	10474.6	1.14269
$439$	4109.36	0.446763	0.223381	−	0.974731i	$-0.428290\pi$
$439$	4109.36	0.446763	0.223381	+	0.974731i	$0.428290\pi$
$440$	0	0
$441$	16861.7	1.82072
$442$	6217.13	0.669047
$443$	−6964.84	−0.746974	−0.373487	−	0.927635i	$-0.621838\pi$
$443$	−6964.84	−0.746974	−0.373487	+	0.927635i	$0.621838\pi$
$444$	−828.640	−0.0885710
$445$	0	0
$446$	6250.59	0.663619
$447$	−16150.9	−1.70897
$448$	1669.63	0.176078
$449$	3041.21	0.319652	0.159826	−	0.987145i	$-0.448907\pi$
$449$	3041.21	0.319652	0.159826	+	0.987145i	$0.448907\pi$
$450$	0	0
$451$	−74.9202	−0.00782229
$452$	2874.88	0.299166
$453$	−29143.4	−3.02269
$454$	−7155.60	−0.739711
$455$	0	0
$456$	1333.34	0.136929
$457$	−11984.3	−1.22670	−0.613352	−	0.789810i	$-0.710179\pi$
$457$	−11984.3	−1.22670	−0.613352	+	0.789810i	$0.710179\pi$
$458$	9604.01	0.979838
$459$	−9771.91	−0.993712
$460$	0	0
$461$	−12126.7	−1.22515	−0.612577	−	0.790411i	$-0.709867\pi$
$461$	−12126.7	−1.22515	−0.612577	+	0.790411i	$0.709867\pi$
$462$	−1935.10	−0.194868
$463$	6399.19	0.642323	0.321162	−	0.947024i	$-0.395927\pi$
$463$	6399.19	0.642323	0.321162	+	0.947024i	$0.395927\pi$
$464$	−1411.39	−0.141212
$465$	0	0
$466$	11659.0	1.15900
$467$	−993.366	−0.0984315	−0.0492157	−	0.998788i	$-0.515672\pi$
$467$	−993.366	−0.0984315	−0.0492157	+	0.998788i	$0.515672\pi$
$468$	−12793.9	−1.26367
$469$	−7371.32	−0.725748
$470$	0	0
$471$	2137.00	0.209061
$472$	293.600	0.0286314
$473$	1557.61	0.151414
$474$	7495.22	0.726301
$475$	0	0
$476$	5065.67	0.487782
$477$	26815.9	2.57404
$478$	−2728.65	−0.261100
$479$	6639.36	0.633320	0.316660	−	0.948539i	$-0.397439\pi$
$479$	6639.36	0.633320	0.316660	+	0.948539i	$0.397439\pi$
$480$	0	0
$481$	−1512.28	−0.143355
$482$	5294.45	0.500323
$483$	21061.9	1.98416
$484$	−5252.50	−0.493285
$485$	0	0
$486$	−3550.70	−0.331406
$487$	11088.8	1.03179	0.515894	−	0.856652i	$-0.327460\pi$
$487$	11088.8	1.03179	0.515894	+	0.856652i	$0.327460\pi$
$488$	−5045.54	−0.468034
$489$	−22790.6	−2.10762
$490$	0	0
$491$	−13215.2	−1.21465	−0.607324	−	0.794454i	$-0.707757\pi$
$491$	−13215.2	−1.21465	−0.607324	+	0.794454i	$0.707757\pi$
$492$	−621.760	−0.0569738
$493$	−4282.17	−0.391195
$494$	2433.37	0.221624
$495$	0	0
$496$	−1311.49	−0.118725
$497$	15536.8	1.40225
$498$	−8662.67	−0.779485
$499$	410.640	0.0368393	0.0184196	−	0.999830i	$-0.494137\pi$
$499$	410.640	0.0368393	0.0184196	+	0.999830i	$0.494137\pi$
$500$	0	0
$501$	−4307.62	−0.384132
$502$	−3941.45	−0.350429
$503$	9407.88	0.833950	0.416975	−	0.908918i	$-0.363090\pi$
$503$	9407.88	0.833950	0.416975	+	0.908918i	$0.363090\pi$
$504$	−10424.4	−0.921305
$505$	0	0
$506$	−778.256	−0.0683749
$507$	−16698.5	−1.46273
$508$	−10442.9	−0.912063
$509$	10482.2	0.912803	0.456402	−	0.889774i	$-0.349138\pi$
$509$	10482.2	0.912803	0.456402	+	0.889774i	$0.349138\pi$
$510$	0	0
$511$	15575.8	1.34840
$512$	−512.000	−0.0441942
$513$	−3824.70	−0.329171
$514$	−15831.6	−1.35857
$515$	0	0
$516$	12926.6	1.10283
$517$	−2104.75	−0.179046
$518$	−1232.19	−0.104516
$519$	14461.2	1.22307
$520$	0	0
$521$	−3181.02	−0.267492	−0.133746	−	0.991016i	$-0.542701\pi$
$521$	−3181.02	−0.267492	−0.133746	+	0.991016i	$0.542701\pi$
$522$	8812.03	0.738874
$523$	4360.12	0.364541	0.182270	−	0.983248i	$-0.441655\pi$
$523$	4360.12	0.364541	0.182270	+	0.983248i	$0.441655\pi$
$524$	−4866.77	−0.405736
$525$	0	0
$526$	6575.93	0.545103
$527$	−3979.06	−0.328900
$528$	593.408	0.0489106
$529$	−3696.37	−0.303803
$530$	0	0
$531$	−1833.09	−0.149810
$532$	1982.69	0.161580
$533$	−1134.72	−0.0922142
$534$	−16160.4	−1.30961
$535$	0	0
$536$	2260.45	0.182158
$537$	−20410.8	−1.64020
$538$	9499.22	0.761227
$539$	−1427.31	−0.114060
$540$	0	0
$541$	−23681.2	−1.88195	−0.940973	−	0.338481i	$-0.890087\pi$
$541$	−23681.2	−1.88195	−0.940973	+	0.338481i	$0.890087\pi$
$542$	−485.322	−0.0384619
$543$	40679.8	3.21498
$544$	−1553.41	−0.122430
$545$	0	0
$546$	−29308.5	−2.29723
$547$	7373.25	0.576339	0.288169	−	0.957579i	$-0.406953\pi$
$547$	7373.25	0.576339	0.288169	+	0.957579i	$0.406953\pi$
$548$	−4682.69	−0.365026
$549$	31501.8	2.44893
$550$	0	0
$551$	−1676.03	−0.129585
$552$	−6458.72	−0.498010
$553$	11145.4	0.857055
$554$	−8262.27	−0.633628
$555$	0	0
$556$	−1084.33	−0.0827086
$557$	−4772.14	−0.363020	−0.181510	−	0.983389i	$-0.558098\pi$
$557$	−4772.14	−0.363020	−0.181510	+	0.983389i	$0.558098\pi$
$558$	8188.29	0.621215
$559$	23591.1	1.78497
$560$	0	0
$561$	1800.40	0.135495
$562$	−2014.38	−0.151195
$563$	−7276.49	−0.544702	−0.272351	−	0.962198i	$-0.587801\pi$
$563$	−7276.49	−0.544702	−0.272351	+	0.962198i	$0.587801\pi$
$564$	−17467.2	−1.30408
$565$	0	0
$566$	4667.26	0.346607
$567$	10884.1	0.806156
$568$	−4764.42	−0.351955
$569$	−10685.1	−0.787245	−0.393622	−	0.919272i	$-0.628778\pi$
$569$	−10685.1	−0.787245	−0.393622	+	0.919272i	$0.628778\pi$
$570$	0	0
$571$	14856.1	1.08881	0.544404	−	0.838823i	$-0.316756\pi$
$571$	14856.1	1.08881	0.544404	+	0.838823i	$0.316756\pi$
$572$	1082.98	0.0791635
$573$	−46144.0	−3.36421
$574$	−924.560	−0.0672306
$575$	0	0
$576$	3196.67	0.231241
$577$	−3212.67	−0.231794	−0.115897	−	0.993261i	$-0.536974\pi$
$577$	−3212.67	−0.231794	−0.115897	+	0.993261i	$0.536974\pi$
$578$	5112.96	0.367943
$579$	141.960	0.0101894
$580$	0	0
$581$	−12881.4	−0.919814
$582$	−18995.7	−1.35291
$583$	−2269.91	−0.161252
$584$	−4776.39	−0.338439
$585$	0	0
$586$	−3177.35	−0.223985
$587$	22321.1	1.56949	0.784745	−	0.619818i	$-0.212794\pi$
$587$	22321.1	1.56949	0.784745	+	0.619818i	$0.212794\pi$
$588$	−11845.2	−0.830758
$589$	−1557.39	−0.108950
$590$	0	0
$591$	33199.5	2.31074
$592$	377.857	0.0262328
$593$	8202.50	0.568021	0.284010	−	0.958821i	$-0.408335\pi$
$593$	8202.50	0.568021	0.284010	+	0.958821i	$0.408335\pi$
$594$	−1702.19	−0.117579
$595$	0	0
$596$	7364.75	0.506161
$597$	−642.180	−0.0440246
$598$	−11787.2	−0.806047
$599$	10583.3	0.721906	0.360953	−	0.932584i	$-0.382452\pi$
$599$	10583.3	0.721906	0.360953	+	0.932584i	$0.382452\pi$
$600$	0	0
$601$	−9051.94	−0.614370	−0.307185	−	0.951650i	$-0.599387\pi$
$601$	−9051.94	−0.614370	−0.307185	+	0.951650i	$0.599387\pi$
$602$	19221.9	1.30137
$603$	−14113.1	−0.953118
$604$	13289.3	0.895254
$605$	0	0
$606$	−12499.2	−0.837863
$607$	−8123.48	−0.543199	−0.271599	−	0.962410i	$-0.587553\pi$
$607$	−8123.48	−0.543199	−0.271599	+	0.962410i	$0.587553\pi$
$608$	−608.000	−0.0405554
$609$	20186.8	1.34320
$610$	0	0
$611$	−31877.9	−2.11071
$612$	9698.71	0.640600
$613$	−22384.7	−1.47490	−0.737448	−	0.675404i	$-0.763969\pi$
$613$	−22384.7	−1.47490	−0.737448	+	0.675404i	$0.763969\pi$
$614$	8114.91	0.533373
$615$	0	0
$616$	882.400	0.0577158
$617$	−11349.1	−0.740517	−0.370259	−	0.928929i	$-0.620731\pi$
$617$	−11349.1	−0.740517	−0.370259	+	0.928929i	$0.620731\pi$
$618$	464.560	0.0302384
$619$	−9106.25	−0.591294	−0.295647	−	0.955297i	$-0.595535\pi$
$619$	−9106.25	−0.591294	−0.295647	+	0.955297i	$0.595535\pi$
$620$	0	0
$621$	18526.9	1.19719
$622$	−5743.84	−0.370268
$623$	−24030.6	−1.54537
$624$	8987.59	0.576589
$625$	0	0
$626$	8645.34	0.551976
$627$	704.672	0.0448834
$628$	−974.464	−0.0619194
$629$	1146.42	0.0726720
$630$	0	0
$631$	−27784.2	−1.75289	−0.876444	−	0.481505i	$-0.840090\pi$
$631$	−27784.2	−1.75289	−0.876444	+	0.481505i	$0.840090\pi$
$632$	−3417.79	−0.215115
$633$	25837.4	1.62234
$634$	5027.12	0.314909
$635$	0	0
$636$	−18837.9	−1.17448
$637$	−21617.5	−1.34461
$638$	−745.921	−0.0462873
$639$	29746.7	1.84156
$640$	0	0
$641$	−16958.3	−1.04495	−0.522476	−	0.852654i	$-0.674992\pi$
$641$	−16958.3	−1.04495	−0.522476	+	0.852654i	$0.674992\pi$
$642$	13000.0	0.799176
$643$	−4754.37	−0.291592	−0.145796	−	0.989315i	$-0.546574\pi$
$643$	−4754.37	−0.291592	−0.145796	+	0.989315i	$0.546574\pi$
$644$	−9604.15	−0.587665
$645$	0	0
$646$	−1844.67	−0.112349
$647$	11254.0	0.683831	0.341916	−	0.939731i	$-0.388924\pi$
$647$	11254.0	0.683831	0.341916	+	0.939731i	$0.388924\pi$
$648$	−3337.66	−0.202339
$649$	155.167	0.00938498
$650$	0	0
$651$	18757.9	1.12931
$652$	10392.4	0.624233
$653$	15515.1	0.929793	0.464896	−	0.885365i	$-0.346092\pi$
$653$	15515.1	0.929793	0.464896	+	0.885365i	$0.346092\pi$
$654$	−34791.1	−2.08018
$655$	0	0
$656$	283.520	0.0168744
$657$	29821.4	1.77084
$658$	−25973.9	−1.53885
$659$	17203.2	1.01691	0.508453	−	0.861090i	$-0.330217\pi$
$659$	17203.2	1.01691	0.508453	+	0.861090i	$0.330217\pi$
$660$	0	0
$661$	2305.65	0.135672	0.0678361	−	0.997696i	$-0.478390\pi$
$661$	2305.65	0.135672	0.0678361	+	0.997696i	$0.478390\pi$
$662$	9147.55	0.537054
$663$	27268.3	1.59731
$664$	3950.15	0.230867
$665$	0	0
$666$	−2359.15	−0.137260
$667$	8118.69	0.471299
$668$	1964.26	0.113772
$669$	27415.1	1.58435
$670$	0	0
$671$	−2666.57	−0.153415
$672$	7323.01	0.420374
$673$	14242.8	0.815782	0.407891	−	0.913031i	$-0.366264\pi$
$673$	14242.8	0.815782	0.407891	+	0.913031i	$0.366264\pi$
$674$	18003.4	1.02888
$675$	0	0
$676$	7614.45	0.433230
$677$	13480.0	0.765256	0.382628	−	0.923902i	$-0.375019\pi$
$677$	13480.0	0.765256	0.382628	+	0.923902i	$0.375019\pi$
$678$	12609.2	0.714240
$679$	−28246.6	−1.59647
$680$	0	0
$681$	−31384.5	−1.76601
$682$	−693.122	−0.0389164
$683$	−27626.1	−1.54771	−0.773854	−	0.633365i	$-0.781673\pi$
$683$	−27626.1	−1.54771	−0.773854	+	0.633365i	$0.781673\pi$
$684$	3796.05	0.212201
$685$	0	0
$686$	282.578	0.0157272
$687$	42123.2	2.33930
$688$	−5894.46	−0.326634
$689$	−34379.4	−1.90094
$690$	0	0
$691$	17419.7	0.959009	0.479505	−	0.877539i	$-0.340816\pi$
$691$	17419.7	0.959009	0.479505	+	0.877539i	$0.340816\pi$
$692$	−6594.24	−0.362248
$693$	−5509.27	−0.301991
$694$	18717.4	1.02378
$695$	0	0
$696$	−6190.37	−0.337134
$697$	860.201	0.0467467
$698$	−11575.5	−0.627707
$699$	51136.3	2.76703
$700$	0	0
$701$	5069.39	0.273136	0.136568	−	0.990631i	$-0.456393\pi$
$701$	5069.39	0.273136	0.136568	+	0.990631i	$0.456393\pi$
$702$	−25780.9	−1.38609
$703$	448.705	0.0240729
$704$	−270.592	−0.0144862
$705$	0	0
$706$	11569.2	0.616730
$707$	−18586.3	−0.988701
$708$	1287.73	0.0683556
$709$	−16758.9	−0.887719	−0.443860	−	0.896096i	$-0.646391\pi$
$709$	−16758.9	−0.887719	−0.443860	+	0.896096i	$0.646391\pi$
$710$	0	0
$711$	21339.0	1.12556
$712$	7369.09	0.387877
$713$	7544.02	0.396249
$714$	22218.0	1.16455
$715$	0	0
$716$	9307.24	0.485793
$717$	−11967.9	−0.623359
$718$	20264.6	1.05330
$719$	−3885.84	−0.201554	−0.100777	−	0.994909i	$-0.532133\pi$
$719$	−3885.84	−0.201554	−0.100777	+	0.994909i	$0.532133\pi$
$720$	0	0
$721$	690.803	0.0356822
$722$	−722.000	−0.0372161
$723$	23221.5	1.19449
$724$	−18549.8	−0.952208
$725$	0	0
$726$	−23037.5	−1.17769
$727$	−6468.37	−0.329984	−0.164992	−	0.986295i	$-0.552760\pi$
$727$	−6468.37	−0.329984	−0.164992	+	0.986295i	$0.552760\pi$
$728$	13364.6	0.680390
$729$	−26838.0	−1.36351
$730$	0	0
$731$	−17883.8	−0.904865
$732$	−22129.7	−1.11740
$733$	−25245.5	−1.27212	−0.636059	−	0.771640i	$-0.719437\pi$
$733$	−25245.5	−1.27212	−0.636059	+	0.771640i	$0.719437\pi$
$734$	−13987.6	−0.703396
$735$	0	0
$736$	2945.15	0.147500
$737$	1194.65	0.0597087
$738$	−1770.16	−0.0882933
$739$	3229.28	0.160746	0.0803728	−	0.996765i	$-0.474389\pi$
$739$	3229.28	0.160746	0.0803728	+	0.996765i	$0.474389\pi$
$740$	0	0
$741$	10672.8	0.529114
$742$	−28012.0	−1.38592
$743$	−18876.2	−0.932033	−0.466016	−	0.884776i	$-0.654311\pi$
$743$	−18876.2	−0.932033	−0.466016	+	0.884776i	$0.654311\pi$
$744$	−5752.19	−0.283448
$745$	0	0
$746$	13046.3	0.640294
$747$	−24662.8	−1.20798
$748$	−820.976	−0.0401308
$749$	19331.1	0.943049
$750$	0	0
$751$	24895.8	1.20967	0.604833	−	0.796352i	$-0.293240\pi$
$751$	24895.8	1.20967	0.604833	+	0.796352i	$0.293240\pi$
$752$	7964.99	0.386241
$753$	−17287.2	−0.836628
$754$	−11297.5	−0.545664
$755$	0	0
$756$	−21006.1	−1.01056
$757$	36203.2	1.73821	0.869107	−	0.494624i	$-0.164694\pi$
$757$	36203.2	1.73821	0.869107	+	0.494624i	$0.164694\pi$
$758$	19564.0	0.937462
$759$	−3413.43	−0.163241
$760$	0	0
$761$	11417.5	0.543868	0.271934	−	0.962316i	$-0.412337\pi$
$761$	11417.5	0.543868	0.271934	+	0.962316i	$0.412337\pi$
$762$	−45802.5	−2.17749
$763$	−51734.5	−2.45467
$764$	21041.5	0.996407
$765$	0	0
$766$	19756.2	0.931881
$767$	2350.12	0.110636
$768$	−2245.63	−0.105511
$769$	39414.5	1.84828	0.924138	−	0.382058i	$-0.124785\pi$
$769$	39414.5	1.84828	0.924138	+	0.382058i	$0.124785\pi$
$770$	0	0
$771$	−69437.6	−3.24350
$772$	−64.7332	−0.00301787
$773$	14268.5	0.663910	0.331955	−	0.943295i	$-0.392292\pi$
$773$	14268.5	0.663910	0.331955	+	0.943295i	$0.392292\pi$
$774$	36802.1	1.70908
$775$	0	0
$776$	8661.95	0.400704
$777$	−5404.39	−0.249526
$778$	15782.5	0.727288
$779$	336.680	0.0154850
$780$	0	0
$781$	−2517.99	−0.115366
$782$	8935.59	0.408614
$783$	17757.1	0.810455
$784$	5401.35	0.246053
$785$	0	0
$786$	−21345.7	−0.968669
$787$	2922.28	0.132361	0.0661804	−	0.997808i	$-0.478919\pi$
$787$	2922.28	0.132361	0.0661804	+	0.997808i	$0.478919\pi$
$788$	−15138.9	−0.684390
$789$	28842.0	1.30140
$790$	0	0
$791$	18750.0	0.842823
$792$	1689.44	0.0757976
$793$	−40387.0	−1.80856
$794$	−5575.67	−0.249211
$795$	0	0
$796$	292.832	0.0130391
$797$	7724.25	0.343296	0.171648	−	0.985158i	$-0.445091\pi$
$797$	7724.25	0.343296	0.171648	+	0.985158i	$0.445091\pi$
$798$	8696.07	0.385762
$799$	24165.8	1.06999
$800$	0	0
$801$	−46008.9	−2.02952
$802$	−2528.83	−0.111342
$803$	−2524.32	−0.110936
$804$	9914.32	0.434890
$805$	0	0
$806$	−10497.8	−0.458772
$807$	41663.6	1.81738
$808$	5699.58	0.248157
$809$	42980.8	1.86789	0.933947	−	0.357412i	$-0.116341\pi$
$809$	42980.8	1.86789	0.933947	+	0.357412i	$0.116341\pi$
$810$	0	0
$811$	28749.5	1.24480	0.622398	−	0.782701i	$-0.286158\pi$
$811$	28749.5	1.24480	0.622398	+	0.782701i	$0.286158\pi$
$812$	−9205.11	−0.397827
$813$	−2128.62	−0.0918253
$814$	199.697	0.00859875
$815$	0	0
$816$	−6813.25	−0.292293
$817$	−6999.68	−0.299740
$818$	16281.1	0.695911
$819$	−83441.8	−3.56006
$820$	0	0
$821$	−30274.8	−1.28696	−0.643482	−	0.765461i	$-0.722511\pi$
$821$	−30274.8	−1.28696	−0.643482	+	0.765461i	$0.722511\pi$
$822$	−20538.3	−0.871477
$823$	−17296.1	−0.732568	−0.366284	−	0.930503i	$-0.619370\pi$
$823$	−17296.1	−0.732568	−0.366284	+	0.930503i	$0.619370\pi$
$824$	−211.838	−0.00895596
$825$	0	0
$826$	1914.86	0.0806615
$827$	2022.80	0.0850541	0.0425271	−	0.999095i	$-0.486459\pi$
$827$	2022.80	0.0850541	0.0425271	+	0.999095i	$0.486459\pi$
$828$	−18388.1	−0.771775
$829$	−43239.0	−1.81152	−0.905762	−	0.423786i	$-0.860701\pi$
$829$	−43239.0	−1.81152	−0.905762	+	0.423786i	$0.860701\pi$
$830$	0	0
$831$	−36238.3	−1.51275
$832$	−4098.31	−0.170773
$833$	16387.7	0.681632
$834$	−4755.89	−0.197462
$835$	0	0
$836$	−321.328	−0.0132935
$837$	16500.2	0.681397
$838$	19202.3	0.791567
$839$	27435.9	1.12895	0.564477	−	0.825449i	$-0.309078\pi$
$839$	27435.9	1.12895	0.564477	+	0.825449i	$0.309078\pi$
$840$	0	0
$841$	−16607.6	−0.680948
$842$	−11405.0	−0.466795
$843$	−8835.09	−0.360969
$844$	−11781.7	−0.480503
$845$	0	0
$846$	−49729.5	−2.02096
$847$	−34256.8	−1.38970
$848$	8590.02	0.347857
$849$	20470.6	0.827502
$850$	0	0
$851$	−2173.53	−0.0875530
$852$	−20896.7	−0.840271
$853$	20978.4	0.842071	0.421035	−	0.907044i	$-0.361667\pi$
$853$	20978.4	0.842071	0.421035	+	0.907044i	$0.361667\pi$
$854$	−32907.0	−1.31857
$855$	0	0
$856$	−5927.97	−0.236698
$857$	30822.4	1.22856	0.614279	−	0.789089i	$-0.289447\pi$
$857$	30822.4	1.22856	0.614279	+	0.789089i	$0.289447\pi$
$858$	4749.94	0.188998
$859$	−39267.6	−1.55971	−0.779856	−	0.625959i	$-0.784708\pi$
$859$	−39267.6	−1.55971	−0.779856	+	0.625959i	$0.784708\pi$
$860$	0	0
$861$	−4055.12	−0.160509
$862$	8051.45	0.318136
$863$	24131.3	0.951842	0.475921	−	0.879488i	$-0.342115\pi$
$863$	24131.3	0.951842	0.475921	+	0.879488i	$0.342115\pi$
$864$	6441.60	0.253643
$865$	0	0
$866$	−2694.21	−0.105719
$867$	22425.4	0.878441
$868$	−8553.54	−0.334477
$869$	−1806.30	−0.0705116
$870$	0	0
$871$	18093.8	0.703885
$872$	15864.6	0.616105
$873$	−54080.9	−2.09663
$874$	3497.37	0.135355
$875$	0	0
$876$	−20949.2	−0.808001
$877$	−39380.6	−1.51629	−0.758147	−	0.652084i	$-0.773895\pi$
$877$	−39380.6	−1.51629	−0.758147	+	0.652084i	$0.773895\pi$
$878$	−8218.71	−0.315909
$879$	−13935.9	−0.534750
$880$	0	0
$881$	30887.5	1.18119	0.590595	−	0.806968i	$-0.298893\pi$
$881$	30887.5	1.18119	0.590595	+	0.806968i	$0.298893\pi$
$882$	−33723.3	−1.28744
$883$	−28191.9	−1.07444	−0.537221	−	0.843441i	$-0.680526\pi$
$883$	−28191.9	−1.07444	−0.537221	+	0.843441i	$0.680526\pi$
$884$	−12434.3	−0.473088
$885$	0	0
$886$	13929.7	0.528190
$887$	−2760.58	−0.104500	−0.0522498	−	0.998634i	$-0.516639\pi$
$887$	−2760.58	−0.104500	−0.0522498	+	0.998634i	$0.516639\pi$
$888$	1657.28	0.0626292
$889$	−68108.5	−2.56950
$890$	0	0
$891$	−1763.95	−0.0663240
$892$	−12501.2	−0.469250
$893$	9458.43	0.354439
$894$	32301.8	1.20843
$895$	0	0
$896$	−3339.26	−0.124506
$897$	−51698.9	−1.92439
$898$	−6082.42	−0.226028
$899$	7230.57	0.268246
$900$	0	0
$901$	26062.1	0.963657
$902$	149.840	0.00553120
$903$	84307.1	3.10694
$904$	−5749.76	−0.211542
$905$	0	0
$906$	58286.8	2.13736
$907$	18969.1	0.694443	0.347222	−	0.937783i	$-0.387125\pi$
$907$	18969.1	0.694443	0.347222	+	0.937783i	$0.387125\pi$
$908$	14311.2	0.523055
$909$	−35585.4	−1.29845
$910$	0	0
$911$	−48732.9	−1.77233	−0.886164	−	0.463371i	$-0.846640\pi$
$911$	−48732.9	−1.77233	−0.886164	+	0.463371i	$0.846640\pi$
$912$	−2666.69	−0.0968233
$913$	2087.65	0.0756749
$914$	23968.7	0.867411
$915$	0	0
$916$	−19208.0	−0.692850
$917$	−31741.1	−1.14306
$918$	19543.8	0.702660
$919$	−35850.4	−1.28683	−0.643414	−	0.765518i	$-0.722483\pi$
$919$	−35850.4	−1.28683	−0.643414	+	0.765518i	$0.722483\pi$
$920$	0	0
$921$	35592.0	1.27340
$922$	24253.4	0.866315
$923$	−38136.8	−1.36001
$924$	3870.21	0.137793
$925$	0	0
$926$	−12798.4	−0.454191
$927$	1322.61	0.0468610
$928$	2822.79	0.0998518
$929$	22936.8	0.810044	0.405022	−	0.914307i	$-0.367264\pi$
$929$	22936.8	0.810044	0.405022	+	0.914307i	$0.367264\pi$
$930$	0	0
$931$	6414.10	0.225793
$932$	−23318.0	−0.819534
$933$	−25192.5	−0.883992
$934$	1986.73	0.0696016
$935$	0	0
$936$	25587.8	0.893550
$937$	−47925.4	−1.67092	−0.835462	−	0.549548i	$-0.814800\pi$
$937$	−47925.4	−1.67092	−0.835462	+	0.549548i	$0.814800\pi$
$938$	14742.6	0.513181
$939$	37918.5	1.31781
$940$	0	0
$941$	−25842.2	−0.895251	−0.447626	−	0.894221i	$-0.647730\pi$
$941$	−25842.2	−0.895251	−0.447626	+	0.894221i	$0.647730\pi$
$942$	−4274.00	−0.147829
$943$	−1630.88	−0.0563189
$944$	−587.199	−0.0202455
$945$	0	0
$946$	−3115.22	−0.107066
$947$	−36562.8	−1.25463	−0.627314	−	0.778766i	$-0.715846\pi$
$947$	−36562.8	−1.25463	−0.627314	+	0.778766i	$0.715846\pi$
$948$	−14990.4	−0.513572
$949$	−38232.6	−1.30778
$950$	0	0
$951$	22048.9	0.751825
$952$	−10131.3	−0.344914
$953$	−29813.1	−1.01337	−0.506684	−	0.862132i	$-0.669129\pi$
$953$	−29813.1	−1.01337	−0.506684	+	0.862132i	$0.669129\pi$
$954$	−53631.8	−1.82012
$955$	0	0
$956$	5457.31	0.184625
$957$	−3271.61	−0.110508
$958$	−13278.7	−0.447825
$959$	−30540.5	−1.02837
$960$	0	0
$961$	−23072.2	−0.774470
$962$	3024.56	0.101368
$963$	37011.3	1.23850
$964$	−10588.9	−0.353782
$965$	0	0
$966$	−42123.8	−1.40301
$967$	−30315.5	−1.00815	−0.504075	−	0.863660i	$-0.668167\pi$
$967$	−30315.5	−1.00815	−0.504075	+	0.863660i	$0.668167\pi$
$968$	10505.0	0.348805
$969$	−8090.73	−0.268227
$970$	0	0
$971$	26455.6	0.874357	0.437178	−	0.899375i	$-0.355978\pi$
$971$	26455.6	0.874357	0.437178	+	0.899375i	$0.355978\pi$
$972$	7101.41	0.234339
$973$	−7072.03	−0.233010
$974$	−22177.6	−0.729584
$975$	0	0
$976$	10091.1	0.330950
$977$	−30207.7	−0.989183	−0.494591	−	0.869126i	$-0.664682\pi$
$977$	−30207.7	−0.989183	−0.494591	+	0.869126i	$0.664682\pi$
$978$	45581.3	1.49032
$979$	3894.56	0.127141
$980$	0	0
$981$	−99050.7	−3.22370
$982$	26430.3	0.858886
$983$	5878.48	0.190737	0.0953685	−	0.995442i	$-0.469597\pi$
$983$	5878.48	0.190737	0.0953685	+	0.995442i	$0.469597\pi$
$984$	1243.52	0.0402866
$985$	0	0
$986$	8564.33	0.276616
$987$	−113921.	−3.67392
$988$	−4866.74	−0.156712
$989$	33906.4	1.09015
$990$	0	0
$991$	−42532.3	−1.36335	−0.681676	−	0.731654i	$-0.738749\pi$
$991$	−42532.3	−1.36335	−0.681676	+	0.731654i	$0.738749\pi$
$992$	2622.98	0.0839513
$993$	40121.2	1.28218
$994$	−31073.5	−0.991542
$995$	0	0
$996$	17325.3	0.551179
$997$	−6320.28	−0.200767	−0.100384	−	0.994949i	$-0.532007\pi$
$997$	−6320.28	−0.200767	−0.100384	+	0.994949i	$0.532007\pi$
$998$	−821.281	−0.0260493
$999$	−4753.91	−0.150558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.4.a.e.1.1		2
5.2	odd	4		950.4.b.i.799.2		4
5.3	odd	4		950.4.b.i.799.3		4
5.4	even	2		38.4.a.c.1.2	✓	2
15.14	odd	2		342.4.a.h.1.2		2
20.19	odd	2		304.4.a.c.1.1		2
35.34	odd	2		1862.4.a.e.1.1		2
40.19	odd	2		1216.4.a.p.1.2		2
40.29	even	2		1216.4.a.g.1.1		2
95.94	odd	2		722.4.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.a.c.1.2	✓	2	5.4	even	2
304.4.a.c.1.1		2	20.19	odd	2
342.4.a.h.1.2		2	15.14	odd	2
722.4.a.f.1.1		2	95.94	odd	2
950.4.a.e.1.1		2	1.1	even	1	trivial
950.4.b.i.799.2		4	5.2	odd	4
950.4.b.i.799.3		4	5.3	odd	4
1216.4.a.g.1.1		2	40.29	even	2
1216.4.a.p.1.2		2	40.19	odd	2
1862.4.a.e.1.1		2	35.34	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -8.77200 q^{3} +4.00000 q^{4} +17.5440 q^{6} +26.0880 q^{7} -8.00000 q^{8} +49.9480 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -8.77200 q^{3} +4.00000 q^{4} +17.5440 q^{6} +26.0880 q^{7} -8.00000 q^{8} +49.9480 q^{9} -4.22800 q^{11} -35.0880 q^{12} -64.0360 q^{13} -52.1760 q^{14} +16.0000 q^{16} +48.5440 q^{17} -99.8960 q^{18} +19.0000 q^{19} -228.844 q^{21} +8.45600 q^{22} -92.0360 q^{23} +70.1760 q^{24} +128.072 q^{26} -201.300 q^{27} +104.352 q^{28} -88.2120 q^{29} -81.9681 q^{31} -32.0000 q^{32} +37.0880 q^{33} -97.0880 q^{34} +199.792 q^{36} +23.6161 q^{37} -38.0000 q^{38} +561.724 q^{39} +17.7200 q^{41} +457.688 q^{42} -368.404 q^{43} -16.9120 q^{44} +184.072 q^{46} +497.812 q^{47} -140.352 q^{48} +337.584 q^{49} -425.828 q^{51} -256.144 q^{52} +536.876 q^{53} +402.600 q^{54} -208.704 q^{56} -166.668 q^{57} +176.424 q^{58} -36.7000 q^{59} +630.692 q^{61} +163.936 q^{62} +1303.04 q^{63} +64.0000 q^{64} -74.1760 q^{66} -282.556 q^{67} +194.176 q^{68} +807.340 q^{69} +595.552 q^{71} -399.584 q^{72} +597.048 q^{73} -47.2321 q^{74} +76.0000 q^{76} -110.300 q^{77} -1123.45 q^{78} +427.224 q^{79} +417.208 q^{81} -35.4400 q^{82} -493.768 q^{83} -915.376 q^{84} +736.808 q^{86} +773.796 q^{87} +33.8240 q^{88} -921.136 q^{89} -1670.57 q^{91} -368.144 q^{92} +719.024 q^{93} -995.624 q^{94} +280.704 q^{96} -1082.74 q^{97} -675.168 q^{98} -211.180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 9 q^{3} + 8 q^{4} + 18 q^{6} + 18 q^{7} - 16 q^{8} + 23 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 9 * q^3 + 8 * q^4 + 18 * q^6 + 18 * q^7 - 16 * q^8 + 23 * q^9	\( 2 q - 4 q^{2} - 9 q^{3} + 8 q^{4} + 18 q^{6} + 18 q^{7} - 16 q^{8} + 23 q^{9} - 17 q^{11} - 36 q^{12} - 17 q^{13} - 36 q^{14} + 32 q^{16} + 80 q^{17} - 46 q^{18} + 38 q^{19} - 227 q^{21} + 34 q^{22} - 73 q^{23} + 72 q^{24} + 34 q^{26} - 189 q^{27} + 72 q^{28} + 3 q^{29} + 212 q^{31} - 64 q^{32} + 40 q^{33} - 160 q^{34} + 92 q^{36} - 192 q^{37} - 76 q^{38} + 551 q^{39} - 50 q^{41} + 454 q^{42} - 677 q^{43} - 68 q^{44} + 146 q^{46} + 389 q^{47} - 144 q^{48} + 60 q^{49} - 433 q^{51} - 68 q^{52} + 1219 q^{53} + 378 q^{54} - 144 q^{56} - 171 q^{57} - 6 q^{58} - 287 q^{59} + 313 q^{61} - 424 q^{62} + 1521 q^{63} + 128 q^{64} - 80 q^{66} - 1223 q^{67} + 320 q^{68} + 803 q^{69} + 200 q^{71} - 184 q^{72} - 378 q^{73} + 384 q^{74} + 152 q^{76} - 7 q^{77} - 1102 q^{78} + 1350 q^{79} + 1142 q^{81} + 100 q^{82} + 670 q^{83} - 908 q^{84} + 1354 q^{86} + 753 q^{87} + 136 q^{88} - 236 q^{89} - 2051 q^{91} - 292 q^{92} + 652 q^{93} - 778 q^{94} + 288 q^{96} - 1294 q^{97} - 120 q^{98} + 133 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 9 * q^3 + 8 * q^4 + 18 * q^6 + 18 * q^7 - 16 * q^8 + 23 * q^9 - 17 * q^11 - 36 * q^12 - 17 * q^13 - 36 * q^14 + 32 * q^16 + 80 * q^17 - 46 * q^18 + 38 * q^19 - 227 * q^21 + 34 * q^22 - 73 * q^23 + 72 * q^24 + 34 * q^26 - 189 * q^27 + 72 * q^28 + 3 * q^29 + 212 * q^31 - 64 * q^32 + 40 * q^33 - 160 * q^34 + 92 * q^36 - 192 * q^37 - 76 * q^38 + 551 * q^39 - 50 * q^41 + 454 * q^42 - 677 * q^43 - 68 * q^44 + 146 * q^46 + 389 * q^47 - 144 * q^48 + 60 * q^49 - 433 * q^51 - 68 * q^52 + 1219 * q^53 + 378 * q^54 - 144 * q^56 - 171 * q^57 - 6 * q^58 - 287 * q^59 + 313 * q^61 - 424 * q^62 + 1521 * q^63 + 128 * q^64 - 80 * q^66 - 1223 * q^67 + 320 * q^68 + 803 * q^69 + 200 * q^71 - 184 * q^72 - 378 * q^73 + 384 * q^74 + 152 * q^76 - 7 * q^77 - 1102 * q^78 + 1350 * q^79 + 1142 * q^81 + 100 * q^82 + 670 * q^83 - 908 * q^84 + 1354 * q^86 + 753 * q^87 + 136 * q^88 - 236 * q^89 - 2051 * q^91 - 292 * q^92 + 652 * q^93 - 778 * q^94 + 288 * q^96 - 1294 * q^97 - 120 * q^98 + 133 * q^99

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