LMFDB - Embedded newform 1150.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,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, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
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:	$9.18279623245$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} -0.561553 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{11} +1.56155 q^{12} +0.561553 q^{13} +2.56155 q^{14} +1.00000 q^{16} -5.56155 q^{17} +0.561553 q^{18} +3.00000 q^{19} -4.00000 q^{21} +1.00000 q^{22} -1.00000 q^{23} -1.56155 q^{24} -0.561553 q^{26} -5.56155 q^{27} -2.56155 q^{28} +1.43845 q^{29} -5.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} +5.56155 q^{34} -0.561553 q^{36} -3.12311 q^{37} -3.00000 q^{38} +0.876894 q^{39} -1.87689 q^{41} +4.00000 q^{42} -7.68466 q^{43} -1.00000 q^{44} +1.00000 q^{46} -6.00000 q^{47} +1.56155 q^{48} -0.438447 q^{49} -8.68466 q^{51} +0.561553 q^{52} -9.12311 q^{53} +5.56155 q^{54} +2.56155 q^{56} +4.68466 q^{57} -1.43845 q^{58} +4.00000 q^{59} +2.24621 q^{61} +5.12311 q^{62} +1.43845 q^{63} +1.00000 q^{64} +1.56155 q^{66} +5.56155 q^{67} -5.56155 q^{68} -1.56155 q^{69} +1.12311 q^{71} +0.561553 q^{72} +6.12311 q^{73} +3.12311 q^{74} +3.00000 q^{76} +2.56155 q^{77} -0.876894 q^{78} +15.9309 q^{79} -7.00000 q^{81} +1.87689 q^{82} -6.12311 q^{83} -4.00000 q^{84} +7.68466 q^{86} +2.24621 q^{87} +1.00000 q^{88} -8.43845 q^{89} -1.43845 q^{91} -1.00000 q^{92} -8.00000 q^{93} +6.00000 q^{94} -1.56155 q^{96} -8.24621 q^{97} +0.438447 q^{98} +0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 + 3 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{11} - q^{12} - 3 q^{13} + q^{14} + 2 q^{16} - 7 q^{17} - 3 q^{18} + 6 q^{19} - 8 q^{21} + 2 q^{22} - 2 q^{23} + q^{24} + 3 q^{26} - 7 q^{27} - q^{28} + 7 q^{29} - 2 q^{31} - 2 q^{32} + q^{33} + 7 q^{34} + 3 q^{36} + 2 q^{37} - 6 q^{38} + 10 q^{39} - 12 q^{41} + 8 q^{42} - 3 q^{43} - 2 q^{44} + 2 q^{46} - 12 q^{47} - q^{48} - 5 q^{49} - 5 q^{51} - 3 q^{52} - 10 q^{53} + 7 q^{54} + q^{56} - 3 q^{57} - 7 q^{58} + 8 q^{59} - 12 q^{61} + 2 q^{62} + 7 q^{63} + 2 q^{64} - q^{66} + 7 q^{67} - 7 q^{68} + q^{69} - 6 q^{71} - 3 q^{72} + 4 q^{73} - 2 q^{74} + 6 q^{76} + q^{77} - 10 q^{78} + 3 q^{79} - 14 q^{81} + 12 q^{82} - 4 q^{83} - 8 q^{84} + 3 q^{86} - 12 q^{87} + 2 q^{88} - 21 q^{89} - 7 q^{91} - 2 q^{92} - 16 q^{93} + 12 q^{94} + q^{96} + 5 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 + 3 * q^9 - 2 * q^11 - q^12 - 3 * q^13 + q^14 + 2 * q^16 - 7 * q^17 - 3 * q^18 + 6 * q^19 - 8 * q^21 + 2 * q^22 - 2 * q^23 + q^24 + 3 * q^26 - 7 * q^27 - q^28 + 7 * q^29 - 2 * q^31 - 2 * q^32 + q^33 + 7 * q^34 + 3 * q^36 + 2 * q^37 - 6 * q^38 + 10 * q^39 - 12 * q^41 + 8 * q^42 - 3 * q^43 - 2 * q^44 + 2 * q^46 - 12 * q^47 - q^48 - 5 * q^49 - 5 * q^51 - 3 * q^52 - 10 * q^53 + 7 * q^54 + q^56 - 3 * q^57 - 7 * q^58 + 8 * q^59 - 12 * q^61 + 2 * q^62 + 7 * q^63 + 2 * q^64 - q^66 + 7 * q^67 - 7 * q^68 + q^69 - 6 * q^71 - 3 * q^72 + 4 * q^73 - 2 * q^74 + 6 * q^76 + q^77 - 10 * q^78 + 3 * q^79 - 14 * q^81 + 12 * q^82 - 4 * q^83 - 8 * q^84 + 3 * q^86 - 12 * q^87 + 2 * q^88 - 21 * q^89 - 7 * q^91 - 2 * q^92 - 16 * q^93 + 12 * q^94 + q^96 + 5 * q^98 - 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.56155	0.901563	0.450781	−	0.892634i	$-0.351145\pi$
$3$	1.56155	0.901563	0.450781	+	0.892634i	$0.351145\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.56155	−0.637501
$7$	−2.56155	−0.968176	−0.484088	−	0.875019i	$-0.660849\pi$
$7$	−2.56155	−0.968176	−0.484088	+	0.875019i	$0.660849\pi$
$8$	−1.00000	−0.353553
$9$	−0.561553	−0.187184
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	1.56155	0.450781
$13$	0.561553	0.155747	0.0778734	−	0.996963i	$-0.475187\pi$
$13$	0.561553	0.155747	0.0778734	+	0.996963i	$0.475187\pi$
$14$	2.56155	0.684604
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.56155	−1.34887	−0.674437	−	0.738332i	$-0.735614\pi$
$17$	−5.56155	−1.34887	−0.674437	+	0.738332i	$0.735614\pi$
$18$	0.561553	0.132359
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	1.00000	0.213201
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.56155	−0.318751
$25$	0	0
$26$	−0.561553	−0.110130
$27$	−5.56155	−1.07032
$28$	−2.56155	−0.484088
$29$	1.43845	0.267113	0.133556	−	0.991041i	$-0.457360\pi$
$29$	1.43845	0.267113	0.133556	+	0.991041i	$0.457360\pi$
$30$	0	0
$31$	−5.12311	−0.920137	−0.460068	−	0.887883i	$-0.652175\pi$
$31$	−5.12311	−0.920137	−0.460068	+	0.887883i	$0.652175\pi$
$32$	−1.00000	−0.176777
$33$	−1.56155	−0.271831
$34$	5.56155	0.953798
$35$	0	0
$36$	−0.561553	−0.0935921
$37$	−3.12311	−0.513435	−0.256718	−	0.966486i	$-0.582641\pi$
$37$	−3.12311	−0.513435	−0.256718	+	0.966486i	$0.582641\pi$
$38$	−3.00000	−0.486664
$39$	0.876894	0.140415
$40$	0	0
$41$	−1.87689	−0.293122	−0.146561	−	0.989202i	$-0.546820\pi$
$41$	−1.87689	−0.293122	−0.146561	+	0.989202i	$0.546820\pi$
$42$	4.00000	0.617213
$43$	−7.68466	−1.17190	−0.585950	−	0.810347i	$-0.699278\pi$
$43$	−7.68466	−1.17190	−0.585950	+	0.810347i	$0.699278\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	1.00000	0.147442
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.56155	0.225391
$49$	−0.438447	−0.0626353
$50$	0	0
$51$	−8.68466	−1.21610
$52$	0.561553	0.0778734
$53$	−9.12311	−1.25315	−0.626577	−	0.779359i	$-0.715545\pi$
$53$	−9.12311	−1.25315	−0.626577	+	0.779359i	$0.715545\pi$
$54$	5.56155	0.756831
$55$	0	0
$56$	2.56155	0.342302
$57$	4.68466	0.620498
$58$	−1.43845	−0.188877
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	2.24621	0.287598	0.143799	−	0.989607i	$-0.454068\pi$
$61$	2.24621	0.287598	0.143799	+	0.989607i	$0.454068\pi$
$62$	5.12311	0.650635
$63$	1.43845	0.181227
$64$	1.00000	0.125000
$65$	0	0
$66$	1.56155	0.192214
$67$	5.56155	0.679452	0.339726	−	0.940524i	$-0.389666\pi$
$67$	5.56155	0.679452	0.339726	+	0.940524i	$0.389666\pi$
$68$	−5.56155	−0.674437
$69$	−1.56155	−0.187989
$70$	0	0
$71$	1.12311	0.133288	0.0666441	−	0.997777i	$-0.478771\pi$
$71$	1.12311	0.133288	0.0666441	+	0.997777i	$0.478771\pi$
$72$	0.561553	0.0661796
$73$	6.12311	0.716655	0.358328	−	0.933596i	$-0.383347\pi$
$73$	6.12311	0.716655	0.358328	+	0.933596i	$0.383347\pi$
$74$	3.12311	0.363054
$75$	0	0
$76$	3.00000	0.344124
$77$	2.56155	0.291916
$78$	−0.876894	−0.0992887
$79$	15.9309	1.79236	0.896181	−	0.443688i	$-0.146330\pi$
$79$	15.9309	1.79236	0.896181	+	0.443688i	$0.146330\pi$
$80$	0	0
$81$	−7.00000	−0.777778
$82$	1.87689	0.207268
$83$	−6.12311	−0.672098	−0.336049	−	0.941844i	$-0.609091\pi$
$83$	−6.12311	−0.672098	−0.336049	+	0.941844i	$0.609091\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	7.68466	0.828658
$87$	2.24621	0.240819
$88$	1.00000	0.106600
$89$	−8.43845	−0.894474	−0.447237	−	0.894416i	$-0.647592\pi$
$89$	−8.43845	−0.894474	−0.447237	+	0.894416i	$0.647592\pi$
$90$	0	0
$91$	−1.43845	−0.150790
$92$	−1.00000	−0.104257
$93$	−8.00000	−0.829561
$94$	6.00000	0.618853
$95$	0	0
$96$	−1.56155	−0.159375
$97$	−8.24621	−0.837276	−0.418638	−	0.908153i	$-0.637492\pi$
$97$	−8.24621	−0.837276	−0.418638	+	0.908153i	$0.637492\pi$
$98$	0.438447	0.0442899
$99$	0.561553	0.0564382
$100$	0	0
$101$	11.3693	1.13129	0.565645	−	0.824649i	$-0.308627\pi$
$101$	11.3693	1.13129	0.565645	+	0.824649i	$0.308627\pi$
$102$	8.68466	0.859909
$103$	5.68466	0.560126	0.280063	−	0.959982i	$-0.409645\pi$
$103$	5.68466	0.560126	0.280063	+	0.959982i	$0.409645\pi$
$104$	−0.561553	−0.0550648
$105$	0	0
$106$	9.12311	0.886114
$107$	−15.8078	−1.52819	−0.764097	−	0.645101i	$-0.776815\pi$
$107$	−15.8078	−1.52819	−0.764097	+	0.645101i	$0.776815\pi$
$108$	−5.56155	−0.535161
$109$	−9.36932	−0.897418	−0.448709	−	0.893678i	$-0.648116\pi$
$109$	−9.36932	−0.897418	−0.448709	+	0.893678i	$0.648116\pi$
$110$	0	0
$111$	−4.87689	−0.462894
$112$	−2.56155	−0.242044
$113$	8.93087	0.840146	0.420073	−	0.907490i	$-0.362005\pi$
$113$	8.93087	0.840146	0.420073	+	0.907490i	$0.362005\pi$
$114$	−4.68466	−0.438758
$115$	0	0
$116$	1.43845	0.133556
$117$	−0.315342	−0.0291533
$118$	−4.00000	−0.368230
$119$	14.2462	1.30595
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−2.24621	−0.203362
$123$	−2.93087	−0.264268
$124$	−5.12311	−0.460068
$125$	0	0
$126$	−1.43845	−0.128147
$127$	18.2462	1.61909	0.809545	−	0.587058i	$-0.199714\pi$
$127$	18.2462	1.61909	0.809545	+	0.587058i	$0.199714\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0000	−1.05654
$130$	0	0
$131$	−1.12311	−0.0981262	−0.0490631	−	0.998796i	$-0.515624\pi$
$131$	−1.12311	−0.0981262	−0.0490631	+	0.998796i	$0.515624\pi$
$132$	−1.56155	−0.135916
$133$	−7.68466	−0.666344
$134$	−5.56155	−0.480445
$135$	0	0
$136$	5.56155	0.476899
$137$	9.80776	0.837934	0.418967	−	0.908001i	$-0.362392\pi$
$137$	9.80776	0.837934	0.418967	+	0.908001i	$0.362392\pi$
$138$	1.56155	0.132928
$139$	−9.56155	−0.811000	−0.405500	−	0.914095i	$-0.632903\pi$
$139$	−9.56155	−0.811000	−0.405500	+	0.914095i	$0.632903\pi$
$140$	0	0
$141$	−9.36932	−0.789039
$142$	−1.12311	−0.0942489
$143$	−0.561553	−0.0469594
$144$	−0.561553	−0.0467961
$145$	0	0
$146$	−6.12311	−0.506752
$147$	−0.684658	−0.0564697
$148$	−3.12311	−0.256718
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−3.36932	−0.274191	−0.137096	−	0.990558i	$-0.543777\pi$
$151$	−3.36932	−0.274191	−0.137096	+	0.990558i	$0.543777\pi$
$152$	−3.00000	−0.243332
$153$	3.12311	0.252488
$154$	−2.56155	−0.206416
$155$	0	0
$156$	0.876894	0.0702077
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	−15.9309	−1.26739
$159$	−14.2462	−1.12980
$160$	0	0
$161$	2.56155	0.201879
$162$	7.00000	0.549972
$163$	13.8078	1.08151	0.540754	−	0.841181i	$-0.318139\pi$
$163$	13.8078	1.08151	0.540754	+	0.841181i	$0.318139\pi$
$164$	−1.87689	−0.146561
$165$	0	0
$166$	6.12311	0.475245
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	4.00000	0.308607
$169$	−12.6847	−0.975743
$170$	0	0
$171$	−1.68466	−0.128829
$172$	−7.68466	−0.585950
$173$	15.0540	1.14453	0.572266	−	0.820068i	$-0.306064\pi$
$173$	15.0540	1.14453	0.572266	+	0.820068i	$0.306064\pi$
$174$	−2.24621	−0.170285
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	6.24621	0.469494
$178$	8.43845	0.632488
$179$	5.80776	0.434093	0.217046	−	0.976161i	$-0.430358\pi$
$179$	5.80776	0.434093	0.217046	+	0.976161i	$0.430358\pi$
$180$	0	0
$181$	−5.36932	−0.399098	−0.199549	−	0.979888i	$-0.563948\pi$
$181$	−5.36932	−0.399098	−0.199549	+	0.979888i	$0.563948\pi$
$182$	1.43845	0.106625
$183$	3.50758	0.259288
$184$	1.00000	0.0737210
$185$	0	0
$186$	8.00000	0.586588
$187$	5.56155	0.406701
$188$	−6.00000	−0.437595
$189$	14.2462	1.03626
$190$	0	0
$191$	−15.0540	−1.08927	−0.544634	−	0.838674i	$-0.683331\pi$
$191$	−15.0540	−1.08927	−0.544634	+	0.838674i	$0.683331\pi$
$192$	1.56155	0.112695
$193$	12.9309	0.930784	0.465392	−	0.885105i	$-0.345913\pi$
$193$	12.9309	0.930784	0.465392	+	0.885105i	$0.345913\pi$
$194$	8.24621	0.592043
$195$	0	0
$196$	−0.438447	−0.0313177
$197$	−11.6847	−0.832497	−0.416249	−	0.909251i	$-0.636655\pi$
$197$	−11.6847	−0.832497	−0.416249	+	0.909251i	$0.636655\pi$
$198$	−0.561553	−0.0399078
$199$	−2.31534	−0.164130	−0.0820651	−	0.996627i	$-0.526152\pi$
$199$	−2.31534	−0.164130	−0.0820651	+	0.996627i	$0.526152\pi$
$200$	0	0
$201$	8.68466	0.612569
$202$	−11.3693	−0.799942
$203$	−3.68466	−0.258612
$204$	−8.68466	−0.608048
$205$	0	0
$206$	−5.68466	−0.396069
$207$	0.561553	0.0390306
$208$	0.561553	0.0389367
$209$	−3.00000	−0.207514
$210$	0	0
$211$	18.6847	1.28630	0.643152	−	0.765738i	$-0.277626\pi$
$211$	18.6847	1.28630	0.643152	+	0.765738i	$0.277626\pi$
$212$	−9.12311	−0.626577
$213$	1.75379	0.120168
$214$	15.8078	1.08060
$215$	0	0
$216$	5.56155	0.378416
$217$	13.1231	0.890854
$218$	9.36932	0.634570
$219$	9.56155	0.646110
$220$	0	0
$221$	−3.12311	−0.210083
$222$	4.87689	0.327316
$223$	17.6155	1.17962	0.589812	−	0.807541i	$-0.299202\pi$
$223$	17.6155	1.17962	0.589812	+	0.807541i	$0.299202\pi$
$224$	2.56155	0.171151
$225$	0	0
$226$	−8.93087	−0.594073
$227$	−26.2462	−1.74202	−0.871011	−	0.491263i	$-0.836535\pi$
$227$	−26.2462	−1.74202	−0.871011	+	0.491263i	$0.836535\pi$
$228$	4.68466	0.310249
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	−1.43845	−0.0944387
$233$	21.6847	1.42061	0.710305	−	0.703894i	$-0.248557\pi$
$233$	21.6847	1.42061	0.710305	+	0.703894i	$0.248557\pi$
$234$	0.315342	0.0206145
$235$	0	0
$236$	4.00000	0.260378
$237$	24.8769	1.61593
$238$	−14.2462	−0.923445
$239$	−0.246211	−0.0159261	−0.00796304	−	0.999968i	$-0.502535\pi$
$239$	−0.246211	−0.0159261	−0.00796304	+	0.999968i	$0.502535\pi$
$240$	0	0
$241$	−1.31534	−0.0847286	−0.0423643	−	0.999102i	$-0.513489\pi$
$241$	−1.31534	−0.0847286	−0.0423643	+	0.999102i	$0.513489\pi$
$242$	10.0000	0.642824
$243$	5.75379	0.369106
$244$	2.24621	0.143799
$245$	0	0
$246$	2.93087	0.186865
$247$	1.68466	0.107192
$248$	5.12311	0.325318
$249$	−9.56155	−0.605939
$250$	0	0
$251$	0.684658	0.0432153	0.0216076	−	0.999767i	$-0.493122\pi$
$251$	0.684658	0.0432153	0.0216076	+	0.999767i	$0.493122\pi$
$252$	1.43845	0.0906137
$253$	1.00000	0.0628695
$254$	−18.2462	−1.14487
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.4924	−1.15353	−0.576763	−	0.816912i	$-0.695684\pi$
$257$	−18.4924	−1.15353	−0.576763	+	0.816912i	$0.695684\pi$
$258$	12.0000	0.747087
$259$	8.00000	0.497096
$260$	0	0
$261$	−0.807764	−0.0499993
$262$	1.12311	0.0693857
$263$	22.2462	1.37176	0.685880	−	0.727715i	$-0.259417\pi$
$263$	22.2462	1.37176	0.685880	+	0.727715i	$0.259417\pi$
$264$	1.56155	0.0961069
$265$	0	0
$266$	7.68466	0.471177
$267$	−13.1771	−0.806424
$268$	5.56155	0.339726
$269$	−30.1771	−1.83993	−0.919965	−	0.392002i	$-0.871783\pi$
$269$	−30.1771	−1.83993	−0.919965	+	0.392002i	$0.871783\pi$
$270$	0	0
$271$	20.2462	1.22987	0.614935	−	0.788578i	$-0.289182\pi$
$271$	20.2462	1.22987	0.614935	+	0.788578i	$0.289182\pi$
$272$	−5.56155	−0.337219
$273$	−2.24621	−0.135947
$274$	−9.80776	−0.592509
$275$	0	0
$276$	−1.56155	−0.0939944
$277$	31.0540	1.86585	0.932926	−	0.360067i	$-0.117246\pi$
$277$	31.0540	1.86585	0.932926	+	0.360067i	$0.117246\pi$
$278$	9.56155	0.573464
$279$	2.87689	0.172235
$280$	0	0
$281$	7.75379	0.462552	0.231276	−	0.972888i	$-0.425710\pi$
$281$	7.75379	0.462552	0.231276	+	0.972888i	$0.425710\pi$
$282$	9.36932	0.557935
$283$	−21.1771	−1.25885	−0.629423	−	0.777063i	$-0.716709\pi$
$283$	−21.1771	−1.25885	−0.629423	+	0.777063i	$0.716709\pi$
$284$	1.12311	0.0666441
$285$	0	0
$286$	0.561553	0.0332053
$287$	4.80776	0.283793
$288$	0.561553	0.0330898
$289$	13.9309	0.819463
$290$	0	0
$291$	−12.8769	−0.754857
$292$	6.12311	0.358328
$293$	12.4924	0.729815	0.364908	−	0.931044i	$-0.381101\pi$
$293$	12.4924	0.729815	0.364908	+	0.931044i	$0.381101\pi$
$294$	0.684658	0.0399301
$295$	0	0
$296$	3.12311	0.181527
$297$	5.56155	0.322714
$298$	18.0000	1.04271
$299$	−0.561553	−0.0324754
$300$	0	0
$301$	19.6847	1.13460
$302$	3.36932	0.193882
$303$	17.7538	1.01993
$304$	3.00000	0.172062
$305$	0	0
$306$	−3.12311	−0.178536
$307$	1.06913	0.0610185	0.0305092	−	0.999534i	$-0.490287\pi$
$307$	1.06913	0.0610185	0.0305092	+	0.999534i	$0.490287\pi$
$308$	2.56155	0.145958
$309$	8.87689	0.504989
$310$	0	0
$311$	25.3693	1.43856	0.719281	−	0.694719i	$-0.244471\pi$
$311$	25.3693	1.43856	0.719281	+	0.694719i	$0.244471\pi$
$312$	−0.876894	−0.0496444
$313$	−12.8769	−0.727845	−0.363923	−	0.931429i	$-0.618563\pi$
$313$	−12.8769	−0.727845	−0.363923	+	0.931429i	$0.618563\pi$
$314$	−6.00000	−0.338600
$315$	0	0
$316$	15.9309	0.896181
$317$	−13.4384	−0.754778	−0.377389	−	0.926055i	$-0.623178\pi$
$317$	−13.4384	−0.754778	−0.377389	+	0.926055i	$0.623178\pi$
$318$	14.2462	0.798888
$319$	−1.43845	−0.0805376
$320$	0	0
$321$	−24.6847	−1.37776
$322$	−2.56155	−0.142750
$323$	−16.6847	−0.928359
$324$	−7.00000	−0.388889
$325$	0	0
$326$	−13.8078	−0.764741
$327$	−14.6307	−0.809079
$328$	1.87689	0.103634
$329$	15.3693	0.847338
$330$	0	0
$331$	30.3002	1.66545	0.832724	−	0.553688i	$-0.186780\pi$
$331$	30.3002	1.66545	0.832724	+	0.553688i	$0.186780\pi$
$332$	−6.12311	−0.336049
$333$	1.75379	0.0961070
$334$	10.0000	0.547176
$335$	0	0
$336$	−4.00000	−0.218218
$337$	24.4384	1.33125	0.665624	−	0.746288i	$-0.268166\pi$
$337$	24.4384	1.33125	0.665624	+	0.746288i	$0.268166\pi$
$338$	12.6847	0.689954
$339$	13.9460	0.757444
$340$	0	0
$341$	5.12311	0.277432
$342$	1.68466	0.0910959
$343$	19.0540	1.02882
$344$	7.68466	0.414329
$345$	0	0
$346$	−15.0540	−0.809307
$347$	−26.4384	−1.41929	−0.709645	−	0.704559i	$-0.751145\pi$
$347$	−26.4384	−1.41929	−0.709645	+	0.704559i	$0.751145\pi$
$348$	2.24621	0.120410
$349$	21.0540	1.12699	0.563497	−	0.826118i	$-0.309456\pi$
$349$	21.0540	1.12699	0.563497	+	0.826118i	$0.309456\pi$
$350$	0	0
$351$	−3.12311	−0.166699
$352$	1.00000	0.0533002
$353$	−32.4233	−1.72572	−0.862859	−	0.505445i	$-0.831328\pi$
$353$	−32.4233	−1.72572	−0.862859	+	0.505445i	$0.831328\pi$
$354$	−6.24621	−0.331982
$355$	0	0
$356$	−8.43845	−0.447237
$357$	22.2462	1.17739
$358$	−5.80776	−0.306950
$359$	−13.4384	−0.709254	−0.354627	−	0.935008i	$-0.615392\pi$
$359$	−13.4384	−0.709254	−0.354627	+	0.935008i	$0.615392\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	5.36932	0.282205
$363$	−15.6155	−0.819603
$364$	−1.43845	−0.0753951
$365$	0	0
$366$	−3.50758	−0.183344
$367$	16.5616	0.864506	0.432253	−	0.901752i	$-0.357719\pi$
$367$	16.5616	0.864506	0.432253	+	0.901752i	$0.357719\pi$
$368$	−1.00000	−0.0521286
$369$	1.05398	0.0548678
$370$	0	0
$371$	23.3693	1.21327
$372$	−8.00000	−0.414781
$373$	−16.4924	−0.853945	−0.426973	−	0.904265i	$-0.640420\pi$
$373$	−16.4924	−0.853945	−0.426973	+	0.904265i	$0.640420\pi$
$374$	−5.56155	−0.287581
$375$	0	0
$376$	6.00000	0.309426
$377$	0.807764	0.0416020
$378$	−14.2462	−0.732746
$379$	−7.80776	−0.401058	−0.200529	−	0.979688i	$-0.564266\pi$
$379$	−7.80776	−0.401058	−0.200529	+	0.979688i	$0.564266\pi$
$380$	0	0
$381$	28.4924	1.45971
$382$	15.0540	0.770228
$383$	2.80776	0.143470	0.0717350	−	0.997424i	$-0.477146\pi$
$383$	2.80776	0.143470	0.0717350	+	0.997424i	$0.477146\pi$
$384$	−1.56155	−0.0796877
$385$	0	0
$386$	−12.9309	−0.658164
$387$	4.31534	0.219361
$388$	−8.24621	−0.418638
$389$	−22.8769	−1.15990	−0.579952	−	0.814650i	$-0.696929\pi$
$389$	−22.8769	−1.15990	−0.579952	+	0.814650i	$0.696929\pi$
$390$	0	0
$391$	5.56155	0.281260
$392$	0.438447	0.0221449
$393$	−1.75379	−0.0884669
$394$	11.6847	0.588665
$395$	0	0
$396$	0.561553	0.0282191
$397$	6.87689	0.345141	0.172571	−	0.984997i	$-0.444793\pi$
$397$	6.87689	0.345141	0.172571	+	0.984997i	$0.444793\pi$
$398$	2.31534	0.116058
$399$	−12.0000	−0.600751
$400$	0	0
$401$	3.31534	0.165560	0.0827801	−	0.996568i	$-0.473620\pi$
$401$	3.31534	0.165560	0.0827801	+	0.996568i	$0.473620\pi$
$402$	−8.68466	−0.433151
$403$	−2.87689	−0.143308
$404$	11.3693	0.565645
$405$	0	0
$406$	3.68466	0.182867
$407$	3.12311	0.154807
$408$	8.68466	0.429955
$409$	−29.2462	−1.44613	−0.723066	−	0.690779i	$-0.757268\pi$
$409$	−29.2462	−1.44613	−0.723066	+	0.690779i	$0.757268\pi$
$410$	0	0
$411$	15.3153	0.755450
$412$	5.68466	0.280063
$413$	−10.2462	−0.504183
$414$	−0.561553	−0.0275988
$415$	0	0
$416$	−0.561553	−0.0275324
$417$	−14.9309	−0.731168
$418$	3.00000	0.146735
$419$	20.1231	0.983078	0.491539	−	0.870856i	$-0.336435\pi$
$419$	20.1231	0.983078	0.491539	+	0.870856i	$0.336435\pi$
$420$	0	0
$421$	−32.2462	−1.57158	−0.785792	−	0.618491i	$-0.787744\pi$
$421$	−32.2462	−1.57158	−0.785792	+	0.618491i	$0.787744\pi$
$422$	−18.6847	−0.909555
$423$	3.36932	0.163822
$424$	9.12311	0.443057
$425$	0	0
$426$	−1.75379	−0.0849713
$427$	−5.75379	−0.278445
$428$	−15.8078	−0.764097
$429$	−0.876894	−0.0423369
$430$	0	0
$431$	1.75379	0.0844770	0.0422385	−	0.999108i	$-0.486551\pi$
$431$	1.75379	0.0844770	0.0422385	+	0.999108i	$0.486551\pi$
$432$	−5.56155	−0.267580
$433$	−28.3002	−1.36002	−0.680010	−	0.733203i	$-0.738025\pi$
$433$	−28.3002	−1.36002	−0.680010	+	0.733203i	$0.738025\pi$
$434$	−13.1231	−0.629929
$435$	0	0
$436$	−9.36932	−0.448709
$437$	−3.00000	−0.143509
$438$	−9.56155	−0.456869
$439$	39.1231	1.86724	0.933622	−	0.358260i	$-0.116630\pi$
$439$	39.1231	1.86724	0.933622	+	0.358260i	$0.116630\pi$
$440$	0	0
$441$	0.246211	0.0117243
$442$	3.12311	0.148551
$443$	17.8078	0.846072	0.423036	−	0.906113i	$-0.360964\pi$
$443$	17.8078	0.846072	0.423036	+	0.906113i	$0.360964\pi$
$444$	−4.87689	−0.231447
$445$	0	0
$446$	−17.6155	−0.834119
$447$	−28.1080	−1.32946
$448$	−2.56155	−0.121022
$449$	−37.4233	−1.76611	−0.883057	−	0.469265i	$-0.844519\pi$
$449$	−37.4233	−1.76611	−0.883057	+	0.469265i	$0.844519\pi$
$450$	0	0
$451$	1.87689	0.0883795
$452$	8.93087	0.420073
$453$	−5.26137	−0.247201
$454$	26.2462	1.23180
$455$	0	0
$456$	−4.68466	−0.219379
$457$	−19.1771	−0.897066	−0.448533	−	0.893766i	$-0.648053\pi$
$457$	−19.1771	−0.897066	−0.448533	+	0.893766i	$0.648053\pi$
$458$	−10.0000	−0.467269
$459$	30.9309	1.44373
$460$	0	0
$461$	32.1771	1.49864	0.749318	−	0.662210i	$-0.230381\pi$
$461$	32.1771	1.49864	0.749318	+	0.662210i	$0.230381\pi$
$462$	−4.00000	−0.186097
$463$	−29.3693	−1.36491	−0.682454	−	0.730929i	$-0.739087\pi$
$463$	−29.3693	−1.36491	−0.682454	+	0.730929i	$0.739087\pi$
$464$	1.43845	0.0667782
$465$	0	0
$466$	−21.6847	−1.00452
$467$	7.68466	0.355604	0.177802	−	0.984066i	$-0.443101\pi$
$467$	7.68466	0.355604	0.177802	+	0.984066i	$0.443101\pi$
$468$	−0.315342	−0.0145767
$469$	−14.2462	−0.657829
$470$	0	0
$471$	9.36932	0.431715
$472$	−4.00000	−0.184115
$473$	7.68466	0.353341
$474$	−24.8769	−1.14263
$475$	0	0
$476$	14.2462	0.652974
$477$	5.12311	0.234571
$478$	0.246211	0.0112614
$479$	25.9309	1.18481	0.592406	−	0.805640i	$-0.298178\pi$
$479$	25.9309	1.18481	0.592406	+	0.805640i	$0.298178\pi$
$480$	0	0
$481$	−1.75379	−0.0799659
$482$	1.31534	0.0599122
$483$	4.00000	0.182006
$484$	−10.0000	−0.454545
$485$	0	0
$486$	−5.75379	−0.260997
$487$	12.2462	0.554929	0.277464	−	0.960736i	$-0.410506\pi$
$487$	12.2462	0.554929	0.277464	+	0.960736i	$0.410506\pi$
$488$	−2.24621	−0.101681
$489$	21.5616	0.975047
$490$	0	0
$491$	−10.2462	−0.462405	−0.231203	−	0.972906i	$-0.574266\pi$
$491$	−10.2462	−0.462405	−0.231203	+	0.972906i	$0.574266\pi$
$492$	−2.93087	−0.132134
$493$	−8.00000	−0.360302
$494$	−1.68466	−0.0757964
$495$	0	0
$496$	−5.12311	−0.230034
$497$	−2.87689	−0.129046
$498$	9.56155	0.428463
$499$	−23.8617	−1.06820	−0.534099	−	0.845422i	$-0.679349\pi$
$499$	−23.8617	−1.06820	−0.534099	+	0.845422i	$0.679349\pi$
$500$	0	0
$501$	−15.6155	−0.697650
$502$	−0.684658	−0.0305578
$503$	−17.4384	−0.777542	−0.388771	−	0.921334i	$-0.627100\pi$
$503$	−17.4384	−0.777542	−0.388771	+	0.921334i	$0.627100\pi$
$504$	−1.43845	−0.0640735
$505$	0	0
$506$	−1.00000	−0.0444554
$507$	−19.8078	−0.879694
$508$	18.2462	0.809545
$509$	−25.1231	−1.11356	−0.556781	−	0.830659i	$-0.687964\pi$
$509$	−25.1231	−1.11356	−0.556781	+	0.830659i	$0.687964\pi$
$510$	0	0
$511$	−15.6847	−0.693848
$512$	−1.00000	−0.0441942
$513$	−16.6847	−0.736646
$514$	18.4924	0.815666
$515$	0	0
$516$	−12.0000	−0.528271
$517$	6.00000	0.263880
$518$	−8.00000	−0.351500
$519$	23.5076	1.03187
$520$	0	0
$521$	−26.9309	−1.17986	−0.589931	−	0.807453i	$-0.700845\pi$
$521$	−26.9309	−1.17986	−0.589931	+	0.807453i	$0.700845\pi$
$522$	0.807764	0.0353549
$523$	39.1080	1.71007	0.855036	−	0.518569i	$-0.173535\pi$
$523$	39.1080	1.71007	0.855036	+	0.518569i	$0.173535\pi$
$524$	−1.12311	−0.0490631
$525$	0	0
$526$	−22.2462	−0.969981
$527$	28.4924	1.24115
$528$	−1.56155	−0.0679579
$529$	1.00000	0.0434783
$530$	0	0
$531$	−2.24621	−0.0974773
$532$	−7.68466	−0.333172
$533$	−1.05398	−0.0456527
$534$	13.1771	0.570228
$535$	0	0
$536$	−5.56155	−0.240222
$537$	9.06913	0.391362
$538$	30.1771	1.30103
$539$	0.438447	0.0188853
$540$	0	0
$541$	3.68466	0.158416	0.0792079	−	0.996858i	$-0.474761\pi$
$541$	3.68466	0.158416	0.0792079	+	0.996858i	$0.474761\pi$
$542$	−20.2462	−0.869649
$543$	−8.38447	−0.359812
$544$	5.56155	0.238450
$545$	0	0
$546$	2.24621	0.0961290
$547$	8.43845	0.360802	0.180401	−	0.983593i	$-0.442260\pi$
$547$	8.43845	0.360802	0.180401	+	0.983593i	$0.442260\pi$
$548$	9.80776	0.418967
$549$	−1.26137	−0.0538338
$550$	0	0
$551$	4.31534	0.183840
$552$	1.56155	0.0664641
$553$	−40.8078	−1.73532
$554$	−31.0540	−1.31936
$555$	0	0
$556$	−9.56155	−0.405500
$557$	−13.3693	−0.566476	−0.283238	−	0.959050i	$-0.591409\pi$
$557$	−13.3693	−0.566476	−0.283238	+	0.959050i	$0.591409\pi$
$558$	−2.87689	−0.121789
$559$	−4.31534	−0.182520
$560$	0	0
$561$	8.68466	0.366667
$562$	−7.75379	−0.327074
$563$	4.80776	0.202623	0.101312	−	0.994855i	$-0.467696\pi$
$563$	4.80776	0.202623	0.101312	+	0.994855i	$0.467696\pi$
$564$	−9.36932	−0.394519
$565$	0	0
$566$	21.1771	0.890139
$567$	17.9309	0.753026
$568$	−1.12311	−0.0471245
$569$	23.3153	0.977430	0.488715	−	0.872444i	$-0.337466\pi$
$569$	23.3153	0.977430	0.488715	+	0.872444i	$0.337466\pi$
$570$	0	0
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−0.561553	−0.0234797
$573$	−23.5076	−0.982043
$574$	−4.80776	−0.200672
$575$	0	0
$576$	−0.561553	−0.0233980
$577$	−44.1231	−1.83687	−0.918434	−	0.395573i	$-0.870546\pi$
$577$	−44.1231	−1.83687	−0.918434	+	0.395573i	$0.870546\pi$
$578$	−13.9309	−0.579448
$579$	20.1922	0.839161
$580$	0	0
$581$	15.6847	0.650709
$582$	12.8769	0.533764
$583$	9.12311	0.377840
$584$	−6.12311	−0.253376
$585$	0	0
$586$	−12.4924	−0.516057
$587$	16.1922	0.668325	0.334163	−	0.942515i	$-0.391547\pi$
$587$	16.1922	0.668325	0.334163	+	0.942515i	$0.391547\pi$
$588$	−0.684658	−0.0282348
$589$	−15.3693	−0.633282
$590$	0	0
$591$	−18.2462	−0.750549
$592$	−3.12311	−0.128359
$593$	−21.2462	−0.872477	−0.436239	−	0.899831i	$-0.643690\pi$
$593$	−21.2462	−0.872477	−0.436239	+	0.899831i	$0.643690\pi$
$594$	−5.56155	−0.228193
$595$	0	0
$596$	−18.0000	−0.737309
$597$	−3.61553	−0.147974
$598$	0.561553	0.0229636
$599$	−22.8769	−0.934725	−0.467362	−	0.884066i	$-0.654796\pi$
$599$	−22.8769	−0.934725	−0.467362	+	0.884066i	$0.654796\pi$
$600$	0	0
$601$	−13.3153	−0.543144	−0.271572	−	0.962418i	$-0.587544\pi$
$601$	−13.3153	−0.543144	−0.271572	+	0.962418i	$0.587544\pi$
$602$	−19.6847	−0.802287
$603$	−3.12311	−0.127183
$604$	−3.36932	−0.137096
$605$	0	0
$606$	−17.7538	−0.721198
$607$	34.9848	1.41999	0.709996	−	0.704206i	$-0.248697\pi$
$607$	34.9848	1.41999	0.709996	+	0.704206i	$0.248697\pi$
$608$	−3.00000	−0.121666
$609$	−5.75379	−0.233155
$610$	0	0
$611$	−3.36932	−0.136308
$612$	3.12311	0.126244
$613$	−28.4924	−1.15080	−0.575399	−	0.817873i	$-0.695153\pi$
$613$	−28.4924	−1.15080	−0.575399	+	0.817873i	$0.695153\pi$
$614$	−1.06913	−0.0431466
$615$	0	0
$616$	−2.56155	−0.103208
$617$	25.8617	1.04115	0.520577	−	0.853815i	$-0.325717\pi$
$617$	25.8617	1.04115	0.520577	+	0.853815i	$0.325717\pi$
$618$	−8.87689	−0.357081
$619$	−36.9848	−1.48655	−0.743273	−	0.668988i	$-0.766728\pi$
$619$	−36.9848	−1.48655	−0.743273	+	0.668988i	$0.766728\pi$
$620$	0	0
$621$	5.56155	0.223177
$622$	−25.3693	−1.01722
$623$	21.6155	0.866008
$624$	0.876894	0.0351039
$625$	0	0
$626$	12.8769	0.514664
$627$	−4.68466	−0.187087
$628$	6.00000	0.239426
$629$	17.3693	0.692560
$630$	0	0
$631$	−2.17708	−0.0866682	−0.0433341	−	0.999061i	$-0.513798\pi$
$631$	−2.17708	−0.0866682	−0.0433341	+	0.999061i	$0.513798\pi$
$632$	−15.9309	−0.633696
$633$	29.1771	1.15968
$634$	13.4384	0.533709
$635$	0	0
$636$	−14.2462	−0.564899
$637$	−0.246211	−0.00975524
$638$	1.43845	0.0569487
$639$	−0.630683	−0.0249494
$640$	0	0
$641$	−29.8617	−1.17947	−0.589734	−	0.807598i	$-0.700767\pi$
$641$	−29.8617	−1.17947	−0.589734	+	0.807598i	$0.700767\pi$
$642$	24.6847	0.974226
$643$	−12.9460	−0.510541	−0.255271	−	0.966870i	$-0.582165\pi$
$643$	−12.9460	−0.510541	−0.255271	+	0.966870i	$0.582165\pi$
$644$	2.56155	0.100939
$645$	0	0
$646$	16.6847	0.656449
$647$	−12.6307	−0.496563	−0.248282	−	0.968688i	$-0.579866\pi$
$647$	−12.6307	−0.496563	−0.248282	+	0.968688i	$0.579866\pi$
$648$	7.00000	0.274986
$649$	−4.00000	−0.157014
$650$	0	0
$651$	20.4924	0.803161
$652$	13.8078	0.540754
$653$	−47.9309	−1.87568	−0.937840	−	0.347068i	$-0.887177\pi$
$653$	−47.9309	−1.87568	−0.937840	+	0.347068i	$0.887177\pi$
$654$	14.6307	0.572105
$655$	0	0
$656$	−1.87689	−0.0732804
$657$	−3.43845	−0.134147
$658$	−15.3693	−0.599158
$659$	−21.7386	−0.846817	−0.423408	−	0.905939i	$-0.639166\pi$
$659$	−21.7386	−0.846817	−0.423408	+	0.905939i	$0.639166\pi$
$660$	0	0
$661$	−27.8617	−1.08370	−0.541848	−	0.840476i	$-0.682275\pi$
$661$	−27.8617	−1.08370	−0.541848	+	0.840476i	$0.682275\pi$
$662$	−30.3002	−1.17765
$663$	−4.87689	−0.189403
$664$	6.12311	0.237623
$665$	0	0
$666$	−1.75379	−0.0679579
$667$	−1.43845	−0.0556969
$668$	−10.0000	−0.386912
$669$	27.5076	1.06350
$670$	0	0
$671$	−2.24621	−0.0867140
$672$	4.00000	0.154303
$673$	17.1922	0.662712	0.331356	−	0.943506i	$-0.392494\pi$
$673$	17.1922	0.662712	0.331356	+	0.943506i	$0.392494\pi$
$674$	−24.4384	−0.941334
$675$	0	0
$676$	−12.6847	−0.487871
$677$	4.87689	0.187434	0.0937171	−	0.995599i	$-0.470125\pi$
$677$	4.87689	0.187434	0.0937171	+	0.995599i	$0.470125\pi$
$678$	−13.9460	−0.535594
$679$	21.1231	0.810630
$680$	0	0
$681$	−40.9848	−1.57054
$682$	−5.12311	−0.196174
$683$	6.68466	0.255781	0.127891	−	0.991788i	$-0.459179\pi$
$683$	6.68466	0.255781	0.127891	+	0.991788i	$0.459179\pi$
$684$	−1.68466	−0.0644145
$685$	0	0
$686$	−19.0540	−0.727484
$687$	15.6155	0.595770
$688$	−7.68466	−0.292975
$689$	−5.12311	−0.195175
$690$	0	0
$691$	−9.56155	−0.363739	−0.181869	−	0.983323i	$-0.558215\pi$
$691$	−9.56155	−0.363739	−0.181869	+	0.983323i	$0.558215\pi$
$692$	15.0540	0.572266
$693$	−1.43845	−0.0546421
$694$	26.4384	1.00359
$695$	0	0
$696$	−2.24621	−0.0851424
$697$	10.4384	0.395384
$698$	−21.0540	−0.796905
$699$	33.8617	1.28077
$700$	0	0
$701$	34.2462	1.29346	0.646731	−	0.762718i	$-0.276136\pi$
$701$	34.2462	1.29346	0.646731	+	0.762718i	$0.276136\pi$
$702$	3.12311	0.117874
$703$	−9.36932	−0.353370
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	32.4233	1.22027
$707$	−29.1231	−1.09529
$708$	6.24621	0.234747
$709$	27.8617	1.04637	0.523185	−	0.852219i	$-0.324744\pi$
$709$	27.8617	1.04637	0.523185	+	0.852219i	$0.324744\pi$
$710$	0	0
$711$	−8.94602	−0.335502
$712$	8.43845	0.316244
$713$	5.12311	0.191862
$714$	−22.2462	−0.832544
$715$	0	0
$716$	5.80776	0.217046
$717$	−0.384472	−0.0143584
$718$	13.4384	0.501518
$719$	38.7386	1.44471	0.722354	−	0.691524i	$-0.243060\pi$
$719$	38.7386	1.44471	0.722354	+	0.691524i	$0.243060\pi$
$720$	0	0
$721$	−14.5616	−0.542301
$722$	10.0000	0.372161
$723$	−2.05398	−0.0763882
$724$	−5.36932	−0.199549
$725$	0	0
$726$	15.6155	0.579547
$727$	14.2462	0.528363	0.264181	−	0.964473i	$-0.414898\pi$
$727$	14.2462	0.528363	0.264181	+	0.964473i	$0.414898\pi$
$728$	1.43845	0.0533124
$729$	29.9848	1.11055
$730$	0	0
$731$	42.7386	1.58075
$732$	3.50758	0.129644
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−16.5616	−0.611298
$735$	0	0
$736$	1.00000	0.0368605
$737$	−5.56155	−0.204862
$738$	−1.05398	−0.0387974
$739$	−33.1231	−1.21845	−0.609227	−	0.792996i	$-0.708520\pi$
$739$	−33.1231	−1.21845	−0.609227	+	0.792996i	$0.708520\pi$
$740$	0	0
$741$	2.63068	0.0966406
$742$	−23.3693	−0.857915
$743$	−42.6695	−1.56539	−0.782696	−	0.622404i	$-0.786156\pi$
$743$	−42.6695	−1.56539	−0.782696	+	0.622404i	$0.786156\pi$
$744$	8.00000	0.293294
$745$	0	0
$746$	16.4924	0.603830
$747$	3.43845	0.125806
$748$	5.56155	0.203351
$749$	40.4924	1.47956
$750$	0	0
$751$	−8.80776	−0.321400	−0.160700	−	0.987003i	$-0.551375\pi$
$751$	−8.80776	−0.321400	−0.160700	+	0.987003i	$0.551375\pi$
$752$	−6.00000	−0.218797
$753$	1.06913	0.0389613
$754$	−0.807764	−0.0294170
$755$	0	0
$756$	14.2462	0.518130
$757$	21.7538	0.790655	0.395327	−	0.918540i	$-0.370631\pi$
$757$	21.7538	0.790655	0.395327	+	0.918540i	$0.370631\pi$
$758$	7.80776	0.283591
$759$	1.56155	0.0566808
$760$	0	0
$761$	29.4924	1.06910	0.534550	−	0.845137i	$-0.320481\pi$
$761$	29.4924	1.06910	0.534550	+	0.845137i	$0.320481\pi$
$762$	−28.4924	−1.03217
$763$	24.0000	0.868858
$764$	−15.0540	−0.544634
$765$	0	0
$766$	−2.80776	−0.101449
$767$	2.24621	0.0811060
$768$	1.56155	0.0563477
$769$	−19.4233	−0.700422	−0.350211	−	0.936671i	$-0.613890\pi$
$769$	−19.4233	−0.700422	−0.350211	+	0.936671i	$0.613890\pi$
$770$	0	0
$771$	−28.8769	−1.03998
$772$	12.9309	0.465392
$773$	−22.2462	−0.800141	−0.400070	−	0.916484i	$-0.631014\pi$
$773$	−22.2462	−0.800141	−0.400070	+	0.916484i	$0.631014\pi$
$774$	−4.31534	−0.155112
$775$	0	0
$776$	8.24621	0.296022
$777$	12.4924	0.448163
$778$	22.8769	0.820176
$779$	−5.63068	−0.201740
$780$	0	0
$781$	−1.12311	−0.0401879
$782$	−5.56155	−0.198881
$783$	−8.00000	−0.285897
$784$	−0.438447	−0.0156588
$785$	0	0
$786$	1.75379	0.0625556
$787$	−39.0540	−1.39212	−0.696062	−	0.717982i	$-0.745066\pi$
$787$	−39.0540	−1.39212	−0.696062	+	0.717982i	$0.745066\pi$
$788$	−11.6847	−0.416249
$789$	34.7386	1.23673
$790$	0	0
$791$	−22.8769	−0.813409
$792$	−0.561553	−0.0199539
$793$	1.26137	0.0447924
$794$	−6.87689	−0.244052
$795$	0	0
$796$	−2.31534	−0.0820651
$797$	29.3693	1.04031	0.520157	−	0.854070i	$-0.325873\pi$
$797$	29.3693	1.04031	0.520157	+	0.854070i	$0.325873\pi$
$798$	12.0000	0.424795
$799$	33.3693	1.18052
$800$	0	0
$801$	4.73863	0.167431
$802$	−3.31534	−0.117069
$803$	−6.12311	−0.216080
$804$	8.68466	0.306284
$805$	0	0
$806$	2.87689	0.101334
$807$	−47.1231	−1.65881
$808$	−11.3693	−0.399971
$809$	39.9309	1.40389	0.701947	−	0.712229i	$-0.252314\pi$
$809$	39.9309	1.40389	0.701947	+	0.712229i	$0.252314\pi$
$810$	0	0
$811$	44.9848	1.57963	0.789816	−	0.613344i	$-0.210176\pi$
$811$	44.9848	1.57963	0.789816	+	0.613344i	$0.210176\pi$
$812$	−3.68466	−0.129306
$813$	31.6155	1.10880
$814$	−3.12311	−0.109465
$815$	0	0
$816$	−8.68466	−0.304024
$817$	−23.0540	−0.806557
$818$	29.2462	1.02257
$819$	0.807764	0.0282256
$820$	0	0
$821$	37.3002	1.30179	0.650893	−	0.759170i	$-0.274395\pi$
$821$	37.3002	1.30179	0.650893	+	0.759170i	$0.274395\pi$
$822$	−15.3153	−0.534184
$823$	−2.63068	−0.0916998	−0.0458499	−	0.998948i	$-0.514600\pi$
$823$	−2.63068	−0.0916998	−0.0458499	+	0.998948i	$0.514600\pi$
$824$	−5.68466	−0.198034
$825$	0	0
$826$	10.2462	0.356511
$827$	−21.0000	−0.730242	−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000	−0.730242	−0.365121	+	0.930960i	$0.618972\pi$
$828$	0.561553	0.0195153
$829$	−40.8078	−1.41731	−0.708656	−	0.705554i	$-0.750698\pi$
$829$	−40.8078	−1.41731	−0.708656	+	0.705554i	$0.750698\pi$
$830$	0	0
$831$	48.4924	1.68218
$832$	0.561553	0.0194683
$833$	2.43845	0.0844872
$834$	14.9309	0.517014
$835$	0	0
$836$	−3.00000	−0.103757
$837$	28.4924	0.984842
$838$	−20.1231	−0.695141
$839$	−11.9309	−0.411899	−0.205950	−	0.978563i	$-0.566028\pi$
$839$	−11.9309	−0.411899	−0.205950	+	0.978563i	$0.566028\pi$
$840$	0	0
$841$	−26.9309	−0.928651
$842$	32.2462	1.11128
$843$	12.1080	0.417020
$844$	18.6847	0.643152
$845$	0	0
$846$	−3.36932	−0.115840
$847$	25.6155	0.880160
$848$	−9.12311	−0.313289
$849$	−33.0691	−1.13493
$850$	0	0
$851$	3.12311	0.107059
$852$	1.75379	0.0600838
$853$	−20.8078	−0.712444	−0.356222	−	0.934401i	$-0.615935\pi$
$853$	−20.8078	−0.712444	−0.356222	+	0.934401i	$0.615935\pi$
$854$	5.75379	0.196891
$855$	0	0
$856$	15.8078	0.540298
$857$	−48.0540	−1.64149	−0.820746	−	0.571293i	$-0.806442\pi$
$857$	−48.0540	−1.64149	−0.820746	+	0.571293i	$0.806442\pi$
$858$	0.876894	0.0299367
$859$	5.17708	0.176640	0.0883199	−	0.996092i	$-0.471850\pi$
$859$	5.17708	0.176640	0.0883199	+	0.996092i	$0.471850\pi$
$860$	0	0
$861$	7.50758	0.255858
$862$	−1.75379	−0.0597343
$863$	26.8769	0.914900	0.457450	−	0.889235i	$-0.348763\pi$
$863$	26.8769	0.914900	0.457450	+	0.889235i	$0.348763\pi$
$864$	5.56155	0.189208
$865$	0	0
$866$	28.3002	0.961679
$867$	21.7538	0.738797
$868$	13.1231	0.445427
$869$	−15.9309	−0.540418
$870$	0	0
$871$	3.12311	0.105822
$872$	9.36932	0.317285
$873$	4.63068	0.156725
$874$	3.00000	0.101477
$875$	0	0
$876$	9.56155	0.323055
$877$	−30.4924	−1.02966	−0.514828	−	0.857294i	$-0.672144\pi$
$877$	−30.4924	−1.02966	−0.514828	+	0.857294i	$0.672144\pi$
$878$	−39.1231	−1.32034
$879$	19.5076	0.657974
$880$	0	0
$881$	−22.6307	−0.762447	−0.381224	−	0.924483i	$-0.624497\pi$
$881$	−22.6307	−0.762447	−0.381224	+	0.924483i	$0.624497\pi$
$882$	−0.246211	−0.00829036
$883$	39.3153	1.32307	0.661533	−	0.749916i	$-0.269906\pi$
$883$	39.3153	1.32307	0.661533	+	0.749916i	$0.269906\pi$
$884$	−3.12311	−0.105041
$885$	0	0
$886$	−17.8078	−0.598264
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	4.87689	0.163658
$889$	−46.7386	−1.56756
$890$	0	0
$891$	7.00000	0.234509
$892$	17.6155	0.589812
$893$	−18.0000	−0.602347
$894$	28.1080	0.940070
$895$	0	0
$896$	2.56155	0.0855755
$897$	−0.876894	−0.0292787
$898$	37.4233	1.24883
$899$	−7.36932	−0.245780
$900$	0	0
$901$	50.7386	1.69035
$902$	−1.87689	−0.0624937
$903$	30.7386	1.02292
$904$	−8.93087	−0.297036
$905$	0	0
$906$	5.26137	0.174797
$907$	−0.315342	−0.0104707	−0.00523537	−	0.999986i	$-0.501666\pi$
$907$	−0.315342	−0.0104707	−0.00523537	+	0.999986i	$0.501666\pi$
$908$	−26.2462	−0.871011
$909$	−6.38447	−0.211760
$910$	0	0
$911$	−17.5464	−0.581338	−0.290669	−	0.956824i	$-0.593878\pi$
$911$	−17.5464	−0.581338	−0.290669	+	0.956824i	$0.593878\pi$
$912$	4.68466	0.155125
$913$	6.12311	0.202645
$914$	19.1771	0.634321
$915$	0	0
$916$	10.0000	0.330409
$917$	2.87689	0.0950034
$918$	−30.9309	−1.02087
$919$	34.7386	1.14592	0.572961	−	0.819583i	$-0.305795\pi$
$919$	34.7386	1.14592	0.572961	+	0.819583i	$0.305795\pi$
$920$	0	0
$921$	1.66950	0.0550120
$922$	−32.1771	−1.05970
$923$	0.630683	0.0207592
$924$	4.00000	0.131590
$925$	0	0
$926$	29.3693	0.965136
$927$	−3.19224	−0.104847
$928$	−1.43845	−0.0472193
$929$	12.0691	0.395975	0.197988	−	0.980205i	$-0.436559\pi$
$929$	12.0691	0.395975	0.197988	+	0.980205i	$0.436559\pi$
$930$	0	0
$931$	−1.31534	−0.0431086
$932$	21.6847	0.710305
$933$	39.6155	1.29695
$934$	−7.68466	−0.251450
$935$	0	0
$936$	0.315342	0.0103073
$937$	−15.0691	−0.492287	−0.246144	−	0.969233i	$-0.579163\pi$
$937$	−15.0691	−0.492287	−0.246144	+	0.969233i	$0.579163\pi$
$938$	14.2462	0.465155
$939$	−20.1080	−0.656198
$940$	0	0
$941$	−23.8617	−0.777870	−0.388935	−	0.921265i	$-0.627157\pi$
$941$	−23.8617	−0.777870	−0.388935	+	0.921265i	$0.627157\pi$
$942$	−9.36932	−0.305269
$943$	1.87689	0.0611201
$944$	4.00000	0.130189
$945$	0	0
$946$	−7.68466	−0.249850
$947$	18.1080	0.588429	0.294215	−	0.955739i	$-0.404942\pi$
$947$	18.1080	0.588429	0.294215	+	0.955739i	$0.404942\pi$
$948$	24.8769	0.807964
$949$	3.43845	0.111617
$950$	0	0
$951$	−20.9848	−0.680480
$952$	−14.2462	−0.461722
$953$	42.4384	1.37472	0.687358	−	0.726319i	$-0.258770\pi$
$953$	42.4384	1.37472	0.687358	+	0.726319i	$0.258770\pi$
$954$	−5.12311	−0.165867
$955$	0	0
$956$	−0.246211	−0.00796304
$957$	−2.24621	−0.0726097
$958$	−25.9309	−0.837788
$959$	−25.1231	−0.811267
$960$	0	0
$961$	−4.75379	−0.153348
$962$	1.75379	0.0565444
$963$	8.87689	0.286054
$964$	−1.31534	−0.0423643
$965$	0	0
$966$	−4.00000	−0.128698
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	10.0000	0.321412
$969$	−26.0540	−0.836974
$970$	0	0
$971$	34.3693	1.10296	0.551482	−	0.834187i	$-0.314063\pi$
$971$	34.3693	1.10296	0.551482	+	0.834187i	$0.314063\pi$
$972$	5.75379	0.184553
$973$	24.4924	0.785191
$974$	−12.2462	−0.392394
$975$	0	0
$976$	2.24621	0.0718995
$977$	32.0540	1.02550	0.512749	−	0.858539i	$-0.328627\pi$
$977$	32.0540	1.02550	0.512749	+	0.858539i	$0.328627\pi$
$978$	−21.5616	−0.689462
$979$	8.43845	0.269694
$980$	0	0
$981$	5.26137	0.167982
$982$	10.2462	0.326970
$983$	21.6847	0.691633	0.345817	−	0.938302i	$-0.387602\pi$
$983$	21.6847	0.691633	0.345817	+	0.938302i	$0.387602\pi$
$984$	2.93087	0.0934327
$985$	0	0
$986$	8.00000	0.254772
$987$	24.0000	0.763928
$988$	1.68466	0.0535961
$989$	7.68466	0.244358
$990$	0	0
$991$	12.2462	0.389014	0.194507	−	0.980901i	$-0.437689\pi$
$991$	12.2462	0.389014	0.194507	+	0.980901i	$0.437689\pi$
$992$	5.12311	0.162659
$993$	47.3153	1.50151
$994$	2.87689	0.0912495
$995$	0	0
$996$	−9.56155	−0.302969
$997$	46.1771	1.46244	0.731221	−	0.682140i	$-0.238951\pi$
$997$	46.1771	1.46244	0.731221	+	0.682140i	$0.238951\pi$
$998$	23.8617	0.755330
$999$	17.3693	0.549541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.k.1.2	✓	2
4.3	odd	2		9200.2.a.bw.1.1		2
5.2	odd	4		1150.2.b.h.599.1		4
5.3	odd	4		1150.2.b.h.599.4		4
5.4	even	2		1150.2.a.p.1.1	yes	2
20.19	odd	2		9200.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.a.k.1.2	✓	2	1.1	even	1	trivial
1150.2.a.p.1.1	yes	2	5.4	even	2
1150.2.b.h.599.1		4	5.2	odd	4
1150.2.b.h.599.4		4	5.3	odd	4
9200.2.a.bp.1.2		2	20.19	odd	2
9200.2.a.bw.1.1		2	4.3	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} -0.561553 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{11} +1.56155 q^{12} +0.561553 q^{13} +2.56155 q^{14} +1.00000 q^{16} -5.56155 q^{17} +0.561553 q^{18} +3.00000 q^{19} -4.00000 q^{21} +1.00000 q^{22} -1.00000 q^{23} -1.56155 q^{24} -0.561553 q^{26} -5.56155 q^{27} -2.56155 q^{28} +1.43845 q^{29} -5.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} +5.56155 q^{34} -0.561553 q^{36} -3.12311 q^{37} -3.00000 q^{38} +0.876894 q^{39} -1.87689 q^{41} +4.00000 q^{42} -7.68466 q^{43} -1.00000 q^{44} +1.00000 q^{46} -6.00000 q^{47} +1.56155 q^{48} -0.438447 q^{49} -8.68466 q^{51} +0.561553 q^{52} -9.12311 q^{53} +5.56155 q^{54} +2.56155 q^{56} +4.68466 q^{57} -1.43845 q^{58} +4.00000 q^{59} +2.24621 q^{61} +5.12311 q^{62} +1.43845 q^{63} +1.00000 q^{64} +1.56155 q^{66} +5.56155 q^{67} -5.56155 q^{68} -1.56155 q^{69} +1.12311 q^{71} +0.561553 q^{72} +6.12311 q^{73} +3.12311 q^{74} +3.00000 q^{76} +2.56155 q^{77} -0.876894 q^{78} +15.9309 q^{79} -7.00000 q^{81} +1.87689 q^{82} -6.12311 q^{83} -4.00000 q^{84} +7.68466 q^{86} +2.24621 q^{87} +1.00000 q^{88} -8.43845 q^{89} -1.43845 q^{91} -1.00000 q^{92} -8.00000 q^{93} +6.00000 q^{94} -1.56155 q^{96} -8.24621 q^{97} +0.438447 q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{11} - q^{12} - 3 q^{13} + q^{14} + 2 q^{16} - 7 q^{17} - 3 q^{18} + 6 q^{19} - 8 q^{21} + 2 q^{22} - 2 q^{23} + q^{24} + 3 q^{26} - 7 q^{27} - q^{28} + 7 q^{29} - 2 q^{31} - 2 q^{32} + q^{33} + 7 q^{34} + 3 q^{36} + 2 q^{37} - 6 q^{38} + 10 q^{39} - 12 q^{41} + 8 q^{42} - 3 q^{43} - 2 q^{44} + 2 q^{46} - 12 q^{47} - q^{48} - 5 q^{49} - 5 q^{51} - 3 q^{52} - 10 q^{53} + 7 q^{54} + q^{56} - 3 q^{57} - 7 q^{58} + 8 q^{59} - 12 q^{61} + 2 q^{62} + 7 q^{63} + 2 q^{64} - q^{66} + 7 q^{67} - 7 q^{68} + q^{69} - 6 q^{71} - 3 q^{72} + 4 q^{73} - 2 q^{74} + 6 q^{76} + q^{77} - 10 q^{78} + 3 q^{79} - 14 q^{81} + 12 q^{82} - 4 q^{83} - 8 q^{84} + 3 q^{86} - 12 q^{87} + 2 q^{88} - 21 q^{89} - 7 q^{91} - 2 q^{92} - 16 q^{93} + 12 q^{94} + q^{96} + 5 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^6 - q^7 - 2 * q^8 + 3 * q^9 - 2 * q^11 - q^12 - 3 * q^13 + q^14 + 2 * q^16 - 7 * q^17 - 3 * q^18 + 6 * q^19 - 8 * q^21 + 2 * q^22 - 2 * q^23 + q^24 + 3 * q^26 - 7 * q^27 - q^28 + 7 * q^29 - 2 * q^31 - 2 * q^32 + q^33 + 7 * q^34 + 3 * q^36 + 2 * q^37 - 6 * q^38 + 10 * q^39 - 12 * q^41 + 8 * q^42 - 3 * q^43 - 2 * q^44 + 2 * q^46 - 12 * q^47 - q^48 - 5 * q^49 - 5 * q^51 - 3 * q^52 - 10 * q^53 + 7 * q^54 + q^56 - 3 * q^57 - 7 * q^58 + 8 * q^59 - 12 * q^61 + 2 * q^62 + 7 * q^63 + 2 * q^64 - q^66 + 7 * q^67 - 7 * q^68 + q^69 - 6 * q^71 - 3 * q^72 + 4 * q^73 - 2 * q^74 + 6 * q^76 + q^77 - 10 * q^78 + 3 * q^79 - 14 * q^81 + 12 * q^82 - 4 * q^83 - 8 * q^84 + 3 * q^86 - 12 * q^87 + 2 * q^88 - 21 * q^89 - 7 * q^91 - 2 * q^92 - 16 * q^93 + 12 * q^94 + q^96 + 5 * q^98 - 3 * q^99

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