LMFDB - Embedded newform 1150.2.a.r.1.4

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.13448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 2 $ x^4 - 7*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.546295$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.40815 q^{3} +1.00000 q^{4} -2.40815 q^{6} -0.706585 q^{7} -1.00000 q^{8} +2.79917 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.40815 q^{3} +1.00000 q^{4} -2.40815 q^{6} -0.706585 q^{7} -1.00000 q^{8} +2.79917 q^{9} +0.747120 q^{11} +2.40815 q^{12} -1.29341 q^{13} +0.706585 q^{14} +1.00000 q^{16} +5.50074 q^{17} -2.79917 q^{18} +2.44868 q^{19} -1.70156 q^{21} -0.747120 q^{22} -1.00000 q^{23} -2.40815 q^{24} +1.29341 q^{26} -0.483617 q^{27} -0.706585 q^{28} +5.72371 q^{29} +7.52288 q^{31} -1.00000 q^{32} +1.79917 q^{33} -5.50074 q^{34} +2.79917 q^{36} +5.07420 q^{37} -2.44868 q^{38} -3.11473 q^{39} +10.0876 q^{41} +1.70156 q^{42} +5.34045 q^{43} +0.747120 q^{44} +1.00000 q^{46} -7.90888 q^{47} +2.40815 q^{48} -6.50074 q^{49} +13.2466 q^{51} -1.29341 q^{52} -5.84621 q^{53} +0.483617 q^{54} +0.706585 q^{56} +5.89679 q^{57} -5.72371 q^{58} +12.4146 q^{59} +1.57346 q^{61} -7.52288 q^{62} -1.97786 q^{63} +1.00000 q^{64} -1.79917 q^{66} -5.25938 q^{67} +5.50074 q^{68} -2.40815 q^{69} +2.68444 q^{71} -2.79917 q^{72} -10.4589 q^{73} -5.07420 q^{74} +2.44868 q^{76} -0.527904 q^{77} +3.11473 q^{78} -6.55005 q^{79} -9.56214 q^{81} -10.0876 q^{82} -12.7068 q^{83} -1.70156 q^{84} -5.34045 q^{86} +13.7835 q^{87} -0.747120 q^{88} +13.6426 q^{89} +0.913908 q^{91} -1.00000 q^{92} +18.1162 q^{93} +7.90888 q^{94} -2.40815 q^{96} -1.50074 q^{97} +6.50074 q^{98} +2.09132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9	$ 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9} + 5 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{14} + 4 q^{16} + 5 q^{17} - 7 q^{18} - q^{19} + 6 q^{21} - 5 q^{22} - 4 q^{23} + 3 q^{24} + 5 q^{26} - 6 q^{27} - 3 q^{28} + 2 q^{29} + 5 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{34} + 7 q^{36} + 6 q^{37} + q^{38} + 23 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 4 q^{46} - 2 q^{47} - 3 q^{48} - 9 q^{49} + 7 q^{51} - 5 q^{52} + 6 q^{54} + 3 q^{56} + 28 q^{57} - 2 q^{58} + 16 q^{59} + 9 q^{61} - 5 q^{62} - 16 q^{63} + 4 q^{64} - 3 q^{66} + 2 q^{67} + 5 q^{68} + 3 q^{69} + 19 q^{71} - 7 q^{72} + 8 q^{73} - 6 q^{74} - q^{76} + 10 q^{77} - 6 q^{79} + 16 q^{81} - 23 q^{82} + 14 q^{83} + 6 q^{84} - 2 q^{86} + 38 q^{87} - 5 q^{88} + 30 q^{89} - 13 q^{91} - 4 q^{92} + 26 q^{93} + 2 q^{94} + 3 q^{96} + 11 q^{97} + 9 q^{98} - 27 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9 + 5 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^14 + 4 * q^16 + 5 * q^17 - 7 * q^18 - q^19 + 6 * q^21 - 5 * q^22 - 4 * q^23 + 3 * q^24 + 5 * q^26 - 6 * q^27 - 3 * q^28 + 2 * q^29 + 5 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^34 + 7 * q^36 + 6 * q^37 + q^38 + 23 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 4 * q^46 - 2 * q^47 - 3 * q^48 - 9 * q^49 + 7 * q^51 - 5 * q^52 + 6 * q^54 + 3 * q^56 + 28 * q^57 - 2 * q^58 + 16 * q^59 + 9 * q^61 - 5 * q^62 - 16 * q^63 + 4 * q^64 - 3 * q^66 + 2 * q^67 + 5 * q^68 + 3 * q^69 + 19 * q^71 - 7 * q^72 + 8 * q^73 - 6 * q^74 - q^76 + 10 * q^77 - 6 * q^79 + 16 * q^81 - 23 * q^82 + 14 * q^83 + 6 * q^84 - 2 * q^86 + 38 * q^87 - 5 * q^88 + 30 * q^89 - 13 * q^91 - 4 * q^92 + 26 * q^93 + 2 * q^94 + 3 * q^96 + 11 * q^97 + 9 * q^98 - 27 * 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
$3$	2.40815	1.39034	0.695172	−	0.718843i	$-0.255328\pi$
$3$	2.40815	1.39034	0.695172	+	0.718843i	$0.255328\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.40815	−0.983122
$7$	−0.706585	−0.267064	−0.133532	−	0.991044i	$-0.542632\pi$
$7$	−0.706585	−0.267064	−0.133532	+	0.991044i	$0.542632\pi$
$8$	−1.00000	−0.353553
$9$	2.79917	0.933058
$10$	0	0
$11$	0.747120	0.225265	0.112633	−	0.993637i	$-0.464072\pi$
$11$	0.747120	0.225265	0.112633	+	0.993637i	$0.464072\pi$
$12$	2.40815	0.695172
$13$	−1.29341	−0.358729	−0.179364	−	0.983783i	$-0.557404\pi$
$13$	−1.29341	−0.358729	−0.179364	+	0.983783i	$0.557404\pi$
$14$	0.706585	0.188843
$15$	0	0
$16$	1.00000	0.250000
$17$	5.50074	1.33412	0.667062	−	0.745002i	$-0.267551\pi$
$17$	5.50074	1.33412	0.667062	+	0.745002i	$0.267551\pi$
$18$	−2.79917	−0.659772
$19$	2.44868	0.561766	0.280883	−	0.959742i	$-0.409373\pi$
$19$	2.44868	0.561766	0.280883	+	0.959742i	$0.409373\pi$
$20$	0	0
$21$	−1.70156	−0.371311
$22$	−0.747120	−0.159286
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.40815	−0.491561
$25$	0	0
$26$	1.29341	0.253659
$27$	−0.483617	−0.0930721
$28$	−0.706585	−0.133532
$29$	5.72371	1.06287	0.531433	−	0.847100i	$-0.321654\pi$
$29$	5.72371	1.06287	0.531433	+	0.847100i	$0.321654\pi$
$30$	0	0
$31$	7.52288	1.35115	0.675575	−	0.737292i	$-0.263896\pi$
$31$	7.52288	1.35115	0.675575	+	0.737292i	$0.263896\pi$
$32$	−1.00000	−0.176777
$33$	1.79917	0.313196
$34$	−5.50074	−0.943369
$35$	0	0
$36$	2.79917	0.466529
$37$	5.07420	0.834193	0.417097	−	0.908862i	$-0.363048\pi$
$37$	5.07420	0.834193	0.417097	+	0.908862i	$0.363048\pi$
$38$	−2.44868	−0.397229
$39$	−3.11473	−0.498756
$40$	0	0
$41$	10.0876	1.57541	0.787707	−	0.616051i	$-0.211268\pi$
$41$	10.0876	1.57541	0.787707	+	0.616051i	$0.211268\pi$
$42$	1.70156	0.262557
$43$	5.34045	0.814410	0.407205	−	0.913337i	$-0.366503\pi$
$43$	5.34045	0.814410	0.407205	+	0.913337i	$0.366503\pi$
$44$	0.747120	0.112633
$45$	0	0
$46$	1.00000	0.147442
$47$	−7.90888	−1.15363	−0.576815	−	0.816875i	$-0.695705\pi$
$47$	−7.90888	−1.15363	−0.576815	+	0.816875i	$0.695705\pi$
$48$	2.40815	0.347586
$49$	−6.50074	−0.928677
$50$	0	0
$51$	13.2466	1.85489
$52$	−1.29341	−0.179364
$53$	−5.84621	−0.803038	−0.401519	−	0.915851i	$-0.631518\pi$
$53$	−5.84621	−0.803038	−0.401519	+	0.915851i	$0.631518\pi$
$54$	0.483617	0.0658119
$55$	0	0
$56$	0.706585	0.0944215
$57$	5.89679	0.781049
$58$	−5.72371	−0.751559
$59$	12.4146	1.61625	0.808125	−	0.589012i	$-0.200483\pi$
$59$	12.4146	1.61625	0.808125	+	0.589012i	$0.200483\pi$
$60$	0	0
$61$	1.57346	0.201461	0.100731	−	0.994914i	$-0.467882\pi$
$61$	1.57346	0.201461	0.100731	+	0.994914i	$0.467882\pi$
$62$	−7.52288	−0.955407
$63$	−1.97786	−0.249186
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.79917	−0.221463
$67$	−5.25938	−0.642535	−0.321268	−	0.946988i	$-0.604109\pi$
$67$	−5.25938	−0.642535	−0.321268	+	0.946988i	$0.604109\pi$
$68$	5.50074	0.667062
$69$	−2.40815	−0.289907
$70$	0	0
$71$	2.68444	0.318585	0.159292	−	0.987231i	$-0.449079\pi$
$71$	2.68444	0.318585	0.159292	+	0.987231i	$0.449079\pi$
$72$	−2.79917	−0.329886
$73$	−10.4589	−1.22413	−0.612063	−	0.790809i	$-0.709660\pi$
$73$	−10.4589	−1.22413	−0.612063	+	0.790809i	$0.709660\pi$
$74$	−5.07420	−0.589864
$75$	0	0
$76$	2.44868	0.280883
$77$	−0.527904	−0.0601602
$78$	3.11473	0.352674
$79$	−6.55005	−0.736938	−0.368469	−	0.929640i	$-0.620118\pi$
$79$	−6.55005	−0.736938	−0.368469	+	0.929640i	$0.620118\pi$
$80$	0	0
$81$	−9.56214	−1.06246
$82$	−10.0876	−1.11399
$83$	−12.7068	−1.39475	−0.697376	−	0.716706i	$-0.745649\pi$
$83$	−12.7068	−1.39475	−0.697376	+	0.716706i	$0.745649\pi$
$84$	−1.70156	−0.185656
$85$	0	0
$86$	−5.34045	−0.575875
$87$	13.7835	1.47775
$88$	−0.747120	−0.0796432
$89$	13.6426	1.44612	0.723058	−	0.690787i	$-0.242736\pi$
$89$	13.6426	1.44612	0.723058	+	0.690787i	$0.242736\pi$
$90$	0	0
$91$	0.913908	0.0958036
$92$	−1.00000	−0.104257
$93$	18.1162	1.87856
$94$	7.90888	0.815739
$95$	0	0
$96$	−2.40815	−0.245781
$97$	−1.50074	−0.152377	−0.0761884	−	0.997093i	$-0.524275\pi$
$97$	−1.50074	−0.152377	−0.0761884	+	0.997093i	$0.524275\pi$
$98$	6.50074	0.656674
$99$	2.09132	0.210185
$100$	0	0
$101$	−16.0472	−1.59676	−0.798380	−	0.602154i	$-0.794309\pi$
$101$	−16.0472	−1.59676	−0.798380	+	0.602154i	$0.794309\pi$
$102$	−13.2466	−1.31161
$103$	−9.49069	−0.935145	−0.467573	−	0.883955i	$-0.654871\pi$
$103$	−9.49069	−0.935145	−0.467573	+	0.883955i	$0.654871\pi$
$104$	1.29341	0.126830
$105$	0	0
$106$	5.84621	0.567834
$107$	−1.38473	−0.133867	−0.0669336	−	0.997757i	$-0.521322\pi$
$107$	−1.38473	−0.133867	−0.0669336	+	0.997757i	$0.521322\pi$
$108$	−0.483617	−0.0465360
$109$	−14.0370	−1.34450	−0.672250	−	0.740325i	$-0.734672\pi$
$109$	−14.0370	−1.34450	−0.672250	+	0.740325i	$0.734672\pi$
$110$	0	0
$111$	12.2194	1.15982
$112$	−0.706585	−0.0667661
$113$	16.3105	1.53437	0.767183	−	0.641428i	$-0.221658\pi$
$113$	16.3105	1.53437	0.767183	+	0.641428i	$0.221658\pi$
$114$	−5.89679	−0.552285
$115$	0	0
$116$	5.72371	0.531433
$117$	−3.62049	−0.334715
$118$	−12.4146	−1.14286
$119$	−3.88674	−0.356297
$120$	0	0
$121$	−10.4418	−0.949256
$122$	−1.57346	−0.142455
$123$	24.2923	2.19037
$124$	7.52288	0.675575
$125$	0	0
$126$	1.97786	0.176201
$127$	2.73523	0.242712	0.121356	−	0.992609i	$-0.461276\pi$
$127$	2.73523	0.242712	0.121356	+	0.992609i	$0.461276\pi$
$128$	−1.00000	−0.0883883
$129$	12.8606	1.13231
$130$	0	0
$131$	−8.21942	−0.718134	−0.359067	−	0.933312i	$-0.616905\pi$
$131$	−8.21942	−0.718134	−0.359067	+	0.933312i	$0.616905\pi$
$132$	1.79917	0.156598
$133$	−1.73020	−0.150028
$134$	5.25938	0.454341
$135$	0	0
$136$	−5.50074	−0.471684
$137$	22.8449	1.95177	0.975887	−	0.218275i	$-0.0700430\pi$
$137$	22.8449	1.95177	0.975887	+	0.218275i	$0.0700430\pi$
$138$	2.40815	0.204995
$139$	3.76049	0.318960	0.159480	−	0.987201i	$-0.449018\pi$
$139$	3.76049	0.318960	0.159480	+	0.987201i	$0.449018\pi$
$140$	0	0
$141$	−19.0458	−1.60394
$142$	−2.68444	−0.225273
$143$	−0.966336	−0.0808090
$144$	2.79917	0.233265
$145$	0	0
$146$	10.4589	0.865587
$147$	−15.6547	−1.29118
$148$	5.07420	0.417097
$149$	−1.90614	−0.156157	−0.0780785	−	0.996947i	$-0.524878\pi$
$149$	−1.90614	−0.156157	−0.0780785	+	0.996947i	$0.524878\pi$
$150$	0	0
$151$	−9.41967	−0.766562	−0.383281	−	0.923632i	$-0.625206\pi$
$151$	−9.41967	−0.766562	−0.383281	+	0.923632i	$0.625206\pi$
$152$	−2.44868	−0.198614
$153$	15.3975	1.24482
$154$	0.527904	0.0425397
$155$	0	0
$156$	−3.11473	−0.249378
$157$	−4.43304	−0.353795	−0.176897	−	0.984229i	$-0.556606\pi$
$157$	−4.43304	−0.353795	−0.176897	+	0.984229i	$0.556606\pi$
$158$	6.55005	0.521094
$159$	−14.0785	−1.11650
$160$	0	0
$161$	0.706585	0.0556867
$162$	9.56214	0.751273
$163$	−9.92453	−0.777349	−0.388675	−	0.921375i	$-0.627067\pi$
$163$	−9.92453	−0.777349	−0.388675	+	0.921375i	$0.627067\pi$
$164$	10.0876	0.787707
$165$	0	0
$166$	12.7068	0.986238
$167$	11.9089	0.921537	0.460769	−	0.887520i	$-0.347574\pi$
$167$	11.9089	0.921537	0.460769	+	0.887520i	$0.347574\pi$
$168$	1.70156	0.131278
$169$	−11.3271	−0.871314
$170$	0	0
$171$	6.85429	0.524161
$172$	5.34045	0.407205
$173$	−2.91391	−0.221540	−0.110770	−	0.993846i	$-0.535332\pi$
$173$	−2.91391	−0.221540	−0.110770	+	0.993846i	$0.535332\pi$
$174$	−13.7835	−1.04493
$175$	0	0
$176$	0.747120	0.0563163
$177$	29.8963	2.24714
$178$	−13.6426	−1.02256
$179$	19.3663	1.44751	0.723754	−	0.690058i	$-0.242415\pi$
$179$	19.3663	1.44751	0.723754	+	0.690058i	$0.242415\pi$
$180$	0	0
$181$	17.5986	1.30809	0.654045	−	0.756456i	$-0.273071\pi$
$181$	17.5986	1.30809	0.654045	+	0.756456i	$0.273071\pi$
$182$	−0.913908	−0.0677434
$183$	3.78913	0.280100
$184$	1.00000	0.0737210
$185$	0	0
$186$	−18.1162	−1.32834
$187$	4.10971	0.300532
$188$	−7.90888	−0.576815
$189$	0.341716	0.0248562
$190$	0	0
$191$	20.3578	1.47304	0.736518	−	0.676418i	$-0.236469\pi$
$191$	20.3578	1.47304	0.736518	+	0.676418i	$0.236469\pi$
$192$	2.40815	0.173793
$193$	1.41317	0.101722	0.0508611	−	0.998706i	$-0.483803\pi$
$193$	1.41317	0.101722	0.0508611	+	0.998706i	$0.483803\pi$
$194$	1.50074	0.107747
$195$	0	0
$196$	−6.50074	−0.464338
$197$	−4.92395	−0.350817	−0.175409	−	0.984496i	$-0.556125\pi$
$197$	−4.92395	−0.350817	−0.175409	+	0.984496i	$0.556125\pi$
$198$	−2.09132	−0.148624
$199$	−10.3105	−0.730894	−0.365447	−	0.930832i	$-0.619084\pi$
$199$	−10.3105	−0.730894	−0.365447	+	0.930832i	$0.619084\pi$
$200$	0	0
$201$	−12.6654	−0.893345
$202$	16.0472	1.12908
$203$	−4.04429	−0.283853
$204$	13.2466	0.927447
$205$	0	0
$206$	9.49069	0.661248
$207$	−2.79917	−0.194556
$208$	−1.29341	−0.0896822
$209$	1.82946	0.126546
$210$	0	0
$211$	11.4161	0.785918	0.392959	−	0.919556i	$-0.371451\pi$
$211$	11.4161	0.785918	0.392959	+	0.919556i	$0.371451\pi$
$212$	−5.84621	−0.401519
$213$	6.46453	0.442942
$214$	1.38473	0.0946584
$215$	0	0
$216$	0.483617	0.0329059
$217$	−5.31556	−0.360844
$218$	14.0370	0.950705
$219$	−25.1867	−1.70196
$220$	0	0
$221$	−7.11473	−0.478589
$222$	−12.2194	−0.820114
$223$	18.2094	1.21939	0.609695	−	0.792636i	$-0.291292\pi$
$223$	18.2094	1.21939	0.609695	+	0.792636i	$0.291292\pi$
$224$	0.706585	0.0472107
$225$	0	0
$226$	−16.3105	−1.08496
$227$	18.9363	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$227$	18.9363	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$228$	5.89679	0.390524
$229$	−8.46433	−0.559339	−0.279669	−	0.960096i	$-0.590225\pi$
$229$	−8.46433	−0.559339	−0.279669	+	0.960096i	$0.590225\pi$
$230$	0	0
$231$	−1.27127	−0.0836435
$232$	−5.72371	−0.375780
$233$	−16.6341	−1.08973	−0.544867	−	0.838523i	$-0.683420\pi$
$233$	−16.6341	−1.08973	−0.544867	+	0.838523i	$0.683420\pi$
$234$	3.62049	0.236679
$235$	0	0
$236$	12.4146	0.808125
$237$	−15.7735	−1.02460
$238$	3.88674	0.251940
$239$	−16.0840	−1.04039	−0.520194	−	0.854048i	$-0.674140\pi$
$239$	−16.0840	−1.04039	−0.520194	+	0.854048i	$0.674140\pi$
$240$	0	0
$241$	−28.1283	−1.81190	−0.905952	−	0.423381i	$-0.860843\pi$
$241$	−28.1283	−1.81190	−0.905952	+	0.423381i	$0.860843\pi$
$242$	10.4418	0.671225
$243$	−21.5762	−1.38411
$244$	1.57346	0.100731
$245$	0	0
$246$	−24.2923	−1.54882
$247$	−3.16716	−0.201522
$248$	−7.52288	−0.477703
$249$	−30.5998	−1.93919
$250$	0	0
$251$	−20.5770	−1.29881	−0.649404	−	0.760444i	$-0.724982\pi$
$251$	−20.5770	−1.29881	−0.649404	+	0.760444i	$0.724982\pi$
$252$	−1.97786	−0.124593
$253$	−0.747120	−0.0469710
$254$	−2.73523	−0.171623
$255$	0	0
$256$	1.00000	0.0625000
$257$	−16.8505	−1.05111	−0.525554	−	0.850760i	$-0.676142\pi$
$257$	−16.8505	−1.05111	−0.525554	+	0.850760i	$0.676142\pi$
$258$	−12.8606	−0.800665
$259$	−3.58536	−0.222783
$260$	0	0
$261$	16.0217	0.991715
$262$	8.21942	0.507797
$263$	−24.7630	−1.52695	−0.763475	−	0.645837i	$-0.776508\pi$
$263$	−24.7630	−1.52695	−0.763475	+	0.645837i	$0.776508\pi$
$264$	−1.79917	−0.110732
$265$	0	0
$266$	1.73020	0.106086
$267$	32.8535	2.01060
$268$	−5.25938	−0.321268
$269$	−3.55152	−0.216540	−0.108270	−	0.994122i	$-0.534531\pi$
$269$	−3.55152	−0.216540	−0.108270	+	0.994122i	$0.534531\pi$
$270$	0	0
$271$	−27.4761	−1.66905	−0.834526	−	0.550969i	$-0.814258\pi$
$271$	−27.4761	−1.66905	−0.834526	+	0.550969i	$0.814258\pi$
$272$	5.50074	0.333531
$273$	2.20083	0.133200
$274$	−22.8449	−1.38011
$275$	0	0
$276$	−2.40815	−0.144953
$277$	−11.1001	−0.666940	−0.333470	−	0.942761i	$-0.608220\pi$
$277$	−11.1001	−0.666940	−0.333470	+	0.942761i	$0.608220\pi$
$278$	−3.76049	−0.225539
$279$	21.0579	1.26070
$280$	0	0
$281$	13.0458	0.778245	0.389122	−	0.921186i	$-0.372778\pi$
$281$	13.0458	0.778245	0.389122	+	0.921186i	$0.372778\pi$
$282$	19.0458	1.13416
$283$	3.35049	0.199166	0.0995831	−	0.995029i	$-0.468249\pi$
$283$	3.35049	0.199166	0.0995831	+	0.995029i	$0.468249\pi$
$284$	2.68444	0.159292
$285$	0	0
$286$	0.966336	0.0571406
$287$	−7.12773	−0.420736
$288$	−2.79917	−0.164943
$289$	13.2581	0.779889
$290$	0	0
$291$	−3.61400	−0.211856
$292$	−10.4589	−0.612063
$293$	8.89197	0.519474	0.259737	−	0.965679i	$-0.416364\pi$
$293$	8.89197	0.519474	0.259737	+	0.965679i	$0.416364\pi$
$294$	15.6547	0.913003
$295$	0	0
$296$	−5.07420	−0.294932
$297$	−0.361320	−0.0209659
$298$	1.90614	0.110420
$299$	1.29341	0.0748001
$300$	0	0
$301$	−3.77348	−0.217500
$302$	9.41967	0.542041
$303$	−38.6441	−2.22005
$304$	2.44868	0.140442
$305$	0	0
$306$	−15.3975	−0.880218
$307$	−28.4111	−1.62151	−0.810753	−	0.585388i	$-0.800942\pi$
$307$	−28.4111	−1.62151	−0.810753	+	0.585388i	$0.800942\pi$
$308$	−0.527904	−0.0300801
$309$	−22.8550	−1.30017
$310$	0	0
$311$	−28.0105	−1.58833	−0.794164	−	0.607704i	$-0.792091\pi$
$311$	−28.0105	−1.58833	−0.794164	+	0.607704i	$0.792091\pi$
$312$	3.11473	0.176337
$313$	7.42882	0.419902	0.209951	−	0.977712i	$-0.432670\pi$
$313$	7.42882	0.419902	0.209951	+	0.977712i	$0.432670\pi$
$314$	4.43304	0.250171
$315$	0	0
$316$	−6.55005	−0.368469
$317$	−13.1480	−0.738463	−0.369232	−	0.929337i	$-0.620379\pi$
$317$	−13.1480	−0.738463	−0.369232	+	0.929337i	$0.620379\pi$
$318$	14.0785	0.789485
$319$	4.27629	0.239427
$320$	0	0
$321$	−3.33464	−0.186122
$322$	−0.706585	−0.0393765
$323$	13.4696	0.749466
$324$	−9.56214	−0.531230
$325$	0	0
$326$	9.92453	0.549669
$327$	−33.8031	−1.86932
$328$	−10.0876	−0.556993
$329$	5.58830	0.308093
$330$	0	0
$331$	−15.6225	−0.858693	−0.429346	−	0.903140i	$-0.641256\pi$
$331$	−15.6225	−0.858693	−0.429346	+	0.903140i	$0.641256\pi$
$332$	−12.7068	−0.697376
$333$	14.2036	0.778351
$334$	−11.9089	−0.651625
$335$	0	0
$336$	−1.70156	−0.0928278
$337$	16.6965	0.909518	0.454759	−	0.890614i	$-0.349725\pi$
$337$	16.6965	0.909518	0.454759	+	0.890614i	$0.349725\pi$
$338$	11.3271	0.616112
$339$	39.2782	2.13330
$340$	0	0
$341$	5.62049	0.304367
$342$	−6.85429	−0.370637
$343$	9.53942	0.515081
$344$	−5.34045	−0.287938
$345$	0	0
$346$	2.91391	0.156653
$347$	−16.3981	−0.880296	−0.440148	−	0.897925i	$-0.645074\pi$
$347$	−16.3981	−0.880296	−0.440148	+	0.897925i	$0.645074\pi$
$348$	13.7835	0.738875
$349$	−1.86165	−0.0996518	−0.0498259	−	0.998758i	$-0.515867\pi$
$349$	−1.86165	−0.0996518	−0.0498259	+	0.998758i	$0.515867\pi$
$350$	0	0
$351$	0.625517	0.0333876
$352$	−0.747120	−0.0398216
$353$	25.8408	1.37537	0.687684	−	0.726010i	$-0.258628\pi$
$353$	25.8408	1.37537	0.687684	+	0.726010i	$0.258628\pi$
$354$	−29.8963	−1.58897
$355$	0	0
$356$	13.6426	0.723058
$357$	−9.35985	−0.495376
$358$	−19.3663	−1.02354
$359$	8.72223	0.460342	0.230171	−	0.973150i	$-0.426071\pi$
$359$	8.72223	0.460342	0.230171	+	0.973150i	$0.426071\pi$
$360$	0	0
$361$	−13.0040	−0.684419
$362$	−17.5986	−0.924959
$363$	−25.1454	−1.31979
$364$	0.913908	0.0479018
$365$	0	0
$366$	−3.78913	−0.198061
$367$	−25.5958	−1.33609	−0.668045	−	0.744121i	$-0.732869\pi$
$367$	−25.5958	−1.33609	−0.668045	+	0.744121i	$0.732869\pi$
$368$	−1.00000	−0.0521286
$369$	28.2369	1.46995
$370$	0	0
$371$	4.13084	0.214463
$372$	18.1162	0.939282
$373$	17.2125	0.891232	0.445616	−	0.895224i	$-0.352985\pi$
$373$	17.2125	0.891232	0.445616	+	0.895224i	$0.352985\pi$
$374$	−4.10971	−0.212508
$375$	0	0
$376$	7.90888	0.407870
$377$	−7.40312	−0.381280
$378$	−0.341716	−0.0175760
$379$	23.0339	1.18317	0.591585	−	0.806243i	$-0.298502\pi$
$379$	23.0339	1.18317	0.591585	+	0.806243i	$0.298502\pi$
$380$	0	0
$381$	6.58683	0.337453
$382$	−20.3578	−1.04159
$383$	−3.81777	−0.195079	−0.0975394	−	0.995232i	$-0.531097\pi$
$383$	−3.81777	−0.195079	−0.0975394	+	0.995232i	$0.531097\pi$
$384$	−2.40815	−0.122890
$385$	0	0
$386$	−1.41317	−0.0719285
$387$	14.9488	0.759892
$388$	−1.50074	−0.0761884
$389$	−8.25435	−0.418512	−0.209256	−	0.977861i	$-0.567104\pi$
$389$	−8.25435	−0.418512	−0.209256	+	0.977861i	$0.567104\pi$
$390$	0	0
$391$	−5.50074	−0.278184
$392$	6.50074	0.328337
$393$	−19.7936	−0.998454
$394$	4.92395	0.248065
$395$	0	0
$396$	2.09132	0.105093
$397$	−12.4967	−0.627193	−0.313596	−	0.949556i	$-0.601534\pi$
$397$	−12.4967	−0.627193	−0.313596	+	0.949556i	$0.601534\pi$
$398$	10.3105	0.516820
$399$	−4.16658	−0.208590
$400$	0	0
$401$	34.5660	1.72614	0.863072	−	0.505082i	$-0.168538\pi$
$401$	34.5660	1.72614	0.863072	+	0.505082i	$0.168538\pi$
$402$	12.6654	0.631691
$403$	−9.73020	−0.484696
$404$	−16.0472	−0.798380
$405$	0	0
$406$	4.04429	0.200715
$407$	3.79103	0.187915
$408$	−13.2466	−0.655804
$409$	12.0499	0.595829	0.297914	−	0.954593i	$-0.403709\pi$
$409$	12.0499	0.595829	0.297914	+	0.954593i	$0.403709\pi$
$410$	0	0
$411$	55.0140	2.71364
$412$	−9.49069	−0.467573
$413$	−8.77201	−0.431642
$414$	2.79917	0.137572
$415$	0	0
$416$	1.29341	0.0634149
$417$	9.05581	0.443465
$418$	−1.82946	−0.0894818
$419$	38.6157	1.88650	0.943250	−	0.332085i	$-0.107752\pi$
$419$	38.6157	1.88650	0.943250	+	0.332085i	$0.107752\pi$
$420$	0	0
$421$	32.7384	1.59557	0.797785	−	0.602941i	$-0.206005\pi$
$421$	32.7384	1.59557	0.797785	+	0.602941i	$0.206005\pi$
$422$	−11.4161	−0.555728
$423$	−22.1384	−1.07640
$424$	5.84621	0.283917
$425$	0	0
$426$	−6.46453	−0.313208
$427$	−1.11179	−0.0538031
$428$	−1.38473	−0.0669336
$429$	−2.32708	−0.112352
$430$	0	0
$431$	−35.7739	−1.72317	−0.861584	−	0.507615i	$-0.830527\pi$
$431$	−35.7739	−1.72317	−0.861584	+	0.507615i	$0.830527\pi$
$432$	−0.483617	−0.0232680
$433$	10.5682	0.507877	0.253938	−	0.967220i	$-0.418274\pi$
$433$	10.5682	0.507877	0.253938	+	0.967220i	$0.418274\pi$
$434$	5.31556	0.255155
$435$	0	0
$436$	−14.0370	−0.672250
$437$	−2.44868	−0.117136
$438$	25.1867	1.20346
$439$	−27.6642	−1.32034	−0.660170	−	0.751117i	$-0.729516\pi$
$439$	−27.6642	−1.32034	−0.660170	+	0.751117i	$0.729516\pi$
$440$	0	0
$441$	−18.1967	−0.866509
$442$	7.11473	0.338413
$443$	−36.8082	−1.74881	−0.874404	−	0.485198i	$-0.838747\pi$
$443$	−36.8082	−1.74881	−0.874404	+	0.485198i	$0.838747\pi$
$444$	12.2194	0.579908
$445$	0	0
$446$	−18.2094	−0.862239
$447$	−4.59027	−0.217112
$448$	−0.706585	−0.0333830
$449$	18.2711	0.862267	0.431133	−	0.902288i	$-0.358114\pi$
$449$	18.2711	0.862267	0.431133	+	0.902288i	$0.358114\pi$
$450$	0	0
$451$	7.53662	0.354886
$452$	16.3105	0.767183
$453$	−22.6840	−1.06579
$454$	−18.9363	−0.888722
$455$	0	0
$456$	−5.89679	−0.276142
$457$	27.6326	1.29260	0.646299	−	0.763084i	$-0.276316\pi$
$457$	27.6326	1.29260	0.646299	+	0.763084i	$0.276316\pi$
$458$	8.46433	0.395512
$459$	−2.66025	−0.124170
$460$	0	0
$461$	35.5515	1.65580	0.827900	−	0.560876i	$-0.189536\pi$
$461$	35.5515	1.65580	0.827900	+	0.560876i	$0.189536\pi$
$462$	1.27127	0.0591449
$463$	23.9331	1.11226	0.556132	−	0.831094i	$-0.312285\pi$
$463$	23.9331	1.11226	0.556132	+	0.831094i	$0.312285\pi$
$464$	5.72371	0.265716
$465$	0	0
$466$	16.6341	0.770558
$467$	19.9035	0.921024	0.460512	−	0.887654i	$-0.347666\pi$
$467$	19.9035	0.921024	0.460512	+	0.887654i	$0.347666\pi$
$468$	−3.62049	−0.167357
$469$	3.71620	0.171598
$470$	0	0
$471$	−10.6754	−0.491897
$472$	−12.4146	−0.571430
$473$	3.98995	0.183458
$474$	15.7735	0.724500
$475$	0	0
$476$	−3.88674	−0.178148
$477$	−16.3646	−0.749281
$478$	16.0840	0.735666
$479$	−3.86206	−0.176462	−0.0882309	−	0.996100i	$-0.528121\pi$
$479$	−3.86206	−0.176462	−0.0882309	+	0.996100i	$0.528121\pi$
$480$	0	0
$481$	−6.56304	−0.299249
$482$	28.1283	1.28121
$483$	1.70156	0.0774238
$484$	−10.4418	−0.474628
$485$	0	0
$486$	21.5762	0.978717
$487$	15.1499	0.686506	0.343253	−	0.939243i	$-0.388471\pi$
$487$	15.1499	0.686506	0.343253	+	0.939243i	$0.388471\pi$
$488$	−1.57346	−0.0712273
$489$	−23.8997	−1.08078
$490$	0	0
$491$	−6.86312	−0.309728	−0.154864	−	0.987936i	$-0.549494\pi$
$491$	−6.86312	−0.309728	−0.154864	+	0.987936i	$0.549494\pi$
$492$	24.2923	1.09518
$493$	31.4846	1.41800
$494$	3.16716	0.142497
$495$	0	0
$496$	7.52288	0.337787
$497$	−1.89679	−0.0850826
$498$	30.5998	1.37121
$499$	−18.6809	−0.836272	−0.418136	−	0.908385i	$-0.637316\pi$
$499$	−18.6809	−0.836272	−0.418136	+	0.908385i	$0.637316\pi$
$500$	0	0
$501$	28.6784	1.28125
$502$	20.5770	0.918396
$503$	−23.1886	−1.03393	−0.516963	−	0.856008i	$-0.672938\pi$
$503$	−23.1886	−1.03393	−0.516963	+	0.856008i	$0.672938\pi$
$504$	1.97786	0.0881007
$505$	0	0
$506$	0.747120	0.0332135
$507$	−27.2773	−1.21143
$508$	2.73523	0.121356
$509$	11.5385	0.511436	0.255718	−	0.966751i	$-0.417688\pi$
$509$	11.5385	0.511436	0.255718	+	0.966751i	$0.417688\pi$
$510$	0	0
$511$	7.39013	0.326920
$512$	−1.00000	−0.0441942
$513$	−1.18422	−0.0522847
$514$	16.8505	0.743245
$515$	0	0
$516$	12.8606	0.566156
$517$	−5.90888	−0.259872
$518$	3.58536	0.157531
$519$	−7.01712	−0.308017
$520$	0	0
$521$	−16.2792	−0.713207	−0.356603	−	0.934256i	$-0.616065\pi$
$521$	−16.2792	−0.713207	−0.356603	+	0.934256i	$0.616065\pi$
$522$	−16.0217	−0.701249
$523$	−30.8347	−1.34831	−0.674153	−	0.738591i	$-0.735491\pi$
$523$	−30.8347	−1.34831	−0.674153	+	0.738591i	$0.735491\pi$
$524$	−8.21942	−0.359067
$525$	0	0
$526$	24.7630	1.07972
$527$	41.3814	1.80260
$528$	1.79917	0.0782990
$529$	1.00000	0.0434783
$530$	0	0
$531$	34.7508	1.50805
$532$	−1.73020	−0.0750138
$533$	−13.0474	−0.565146
$534$	−32.8535	−1.42171
$535$	0	0
$536$	5.25938	0.227171
$537$	46.6370	2.01254
$538$	3.55152	0.153117
$539$	−4.85683	−0.209198
$540$	0	0
$541$	−30.5199	−1.31215	−0.656077	−	0.754694i	$-0.727785\pi$
$541$	−30.5199	−1.31215	−0.656077	+	0.754694i	$0.727785\pi$
$542$	27.4761	1.18020
$543$	42.3799	1.81870
$544$	−5.50074	−0.235842
$545$	0	0
$546$	−2.20083	−0.0941866
$547$	−28.0416	−1.19897	−0.599487	−	0.800385i	$-0.704629\pi$
$547$	−28.0416	−1.19897	−0.599487	+	0.800385i	$0.704629\pi$
$548$	22.8449	0.975887
$549$	4.40439	0.187975
$550$	0	0
$551$	14.0155	0.597082
$552$	2.40815	0.102498
$553$	4.62817	0.196810
$554$	11.1001	0.471598
$555$	0	0
$556$	3.76049	0.159480
$557$	4.15674	0.176127	0.0880634	−	0.996115i	$-0.471932\pi$
$557$	4.15674	0.176127	0.0880634	+	0.996115i	$0.471932\pi$
$558$	−21.0579	−0.891450
$559$	−6.90741	−0.292152
$560$	0	0
$561$	9.89679	0.417843
$562$	−13.0458	−0.550302
$563$	21.3480	0.899709	0.449854	−	0.893102i	$-0.351476\pi$
$563$	21.3480	0.899709	0.449854	+	0.893102i	$0.351476\pi$
$564$	−19.0458	−0.801971
$565$	0	0
$566$	−3.35049	−0.140832
$567$	6.75647	0.283745
$568$	−2.68444	−0.112637
$569$	−25.6430	−1.07501	−0.537506	−	0.843260i	$-0.680634\pi$
$569$	−25.6430	−1.07501	−0.537506	+	0.843260i	$0.680634\pi$
$570$	0	0
$571$	−7.10743	−0.297437	−0.148718	−	0.988880i	$-0.547515\pi$
$571$	−7.10743	−0.297437	−0.148718	+	0.988880i	$0.547515\pi$
$572$	−0.966336	−0.0404045
$573$	49.0245	2.04803
$574$	7.12773	0.297506
$575$	0	0
$576$	2.79917	0.116632
$577$	22.7226	0.945956	0.472978	−	0.881074i	$-0.343179\pi$
$577$	22.7226	0.945956	0.472978	+	0.881074i	$0.343179\pi$
$578$	−13.2581	−0.551465
$579$	3.40312	0.141429
$580$	0	0
$581$	8.97843	0.372488
$582$	3.61400	0.149805
$583$	−4.36782	−0.180896
$584$	10.4589	0.432794
$585$	0	0
$586$	−8.89197	−0.367324
$587$	7.06600	0.291645	0.145822	−	0.989311i	$-0.453417\pi$
$587$	7.06600	0.291645	0.145822	+	0.989311i	$0.453417\pi$
$588$	−15.6547	−0.645590
$589$	18.4211	0.759030
$590$	0	0
$591$	−11.8576	−0.487757
$592$	5.07420	0.208548
$593$	14.9914	0.615624	0.307812	−	0.951447i	$-0.400403\pi$
$593$	14.9914	0.615624	0.307812	+	0.951447i	$0.400403\pi$
$594$	0.361320	0.0148251
$595$	0	0
$596$	−1.90614	−0.0780785
$597$	−24.8293	−1.01620
$598$	−1.29341	−0.0528917
$599$	−4.03069	−0.164690	−0.0823448	−	0.996604i	$-0.526241\pi$
$599$	−4.03069	−0.164690	−0.0823448	+	0.996604i	$0.526241\pi$
$600$	0	0
$601$	13.9320	0.568300	0.284150	−	0.958780i	$-0.408289\pi$
$601$	13.9320	0.568300	0.284150	+	0.958780i	$0.408289\pi$
$602$	3.77348	0.153796
$603$	−14.7219	−0.599523
$604$	−9.41967	−0.383281
$605$	0	0
$606$	38.6441	1.56981
$607$	−31.0588	−1.26064	−0.630318	−	0.776337i	$-0.717075\pi$
$607$	−31.0588	−1.26064	−0.630318	+	0.776337i	$0.717075\pi$
$608$	−2.44868	−0.0993072
$609$	−9.73924	−0.394654
$610$	0	0
$611$	10.2295	0.413840
$612$	15.3975	0.622408
$613$	19.6722	0.794554	0.397277	−	0.917699i	$-0.369955\pi$
$613$	19.6722	0.794554	0.397277	+	0.917699i	$0.369955\pi$
$614$	28.4111	1.14658
$615$	0	0
$616$	0.527904	0.0212699
$617$	−40.9043	−1.64674	−0.823372	−	0.567502i	$-0.807910\pi$
$617$	−40.9043	−1.64674	−0.823372	+	0.567502i	$0.807910\pi$
$618$	22.8550	0.919362
$619$	−3.58556	−0.144116	−0.0720579	−	0.997400i	$-0.522957\pi$
$619$	−3.58556	−0.144116	−0.0720579	+	0.997400i	$0.522957\pi$
$620$	0	0
$621$	0.483617	0.0194069
$622$	28.0105	1.12312
$623$	−9.63969	−0.386206
$624$	−3.11473	−0.124689
$625$	0	0
$626$	−7.42882	−0.296915
$627$	4.40561	0.175943
$628$	−4.43304	−0.176897
$629$	27.9118	1.11292
$630$	0	0
$631$	−7.19670	−0.286496	−0.143248	−	0.989687i	$-0.545755\pi$
$631$	−7.19670	−0.286496	−0.143248	+	0.989687i	$0.545755\pi$
$632$	6.55005	0.260547
$633$	27.4917	1.09270
$634$	13.1480	0.522172
$635$	0	0
$636$	−14.0785	−0.558250
$637$	8.40815	0.333143
$638$	−4.27629	−0.169300
$639$	7.51422	0.297258
$640$	0	0
$641$	−16.3436	−0.645534	−0.322767	−	0.946478i	$-0.604613\pi$
$641$	−16.3436	−0.645534	−0.322767	+	0.946478i	$0.604613\pi$
$642$	3.33464	0.131608
$643$	−6.55839	−0.258638	−0.129319	−	0.991603i	$-0.541279\pi$
$643$	−6.55839	−0.258638	−0.129319	+	0.991603i	$0.541279\pi$
$644$	0.706585	0.0278434
$645$	0	0
$646$	−13.4696	−0.529953
$647$	16.5455	0.650470	0.325235	−	0.945633i	$-0.394557\pi$
$647$	16.5455	0.650470	0.325235	+	0.945633i	$0.394557\pi$
$648$	9.56214	0.375637
$649$	9.27523	0.364085
$650$	0	0
$651$	−12.8006	−0.501697
$652$	−9.92453	−0.388675
$653$	−12.7408	−0.498587	−0.249294	−	0.968428i	$-0.580198\pi$
$653$	−12.7408	−0.498587	−0.249294	+	0.968428i	$0.580198\pi$
$654$	33.8031	1.32181
$655$	0	0
$656$	10.0876	0.393853
$657$	−29.2764	−1.14218
$658$	−5.58830	−0.217855
$659$	−23.8094	−0.927484	−0.463742	−	0.885970i	$-0.653493\pi$
$659$	−23.8094	−0.927484	−0.463742	+	0.885970i	$0.653493\pi$
$660$	0	0
$661$	24.9323	0.969754	0.484877	−	0.874582i	$-0.338864\pi$
$661$	24.9323	0.969754	0.484877	+	0.874582i	$0.338864\pi$
$662$	15.6225	0.607187
$663$	−17.1333	−0.665403
$664$	12.7068	0.493119
$665$	0	0
$666$	−14.2036	−0.550377
$667$	−5.72371	−0.221623
$668$	11.9089	0.460769
$669$	43.8509	1.69537
$670$	0	0
$671$	1.17556	0.0453822
$672$	1.70156	0.0656392
$673$	5.48050	0.211258	0.105629	−	0.994406i	$-0.466314\pi$
$673$	5.48050	0.211258	0.105629	+	0.994406i	$0.466314\pi$
$674$	−16.6965	−0.643127
$675$	0	0
$676$	−11.3271	−0.435657
$677$	1.75255	0.0673560	0.0336780	−	0.999433i	$-0.489278\pi$
$677$	1.75255	0.0673560	0.0336780	+	0.999433i	$0.489278\pi$
$678$	−39.2782	−1.50847
$679$	1.06040	0.0406944
$680$	0	0
$681$	45.6013	1.74745
$682$	−5.62049	−0.215220
$683$	23.5091	0.899552	0.449776	−	0.893141i	$-0.351504\pi$
$683$	23.5091	0.899552	0.449776	+	0.893141i	$0.351504\pi$
$684$	6.85429	0.262080
$685$	0	0
$686$	−9.53942	−0.364217
$687$	−20.3834	−0.777673
$688$	5.34045	0.203603
$689$	7.56157	0.288073
$690$	0	0
$691$	−21.4834	−0.817269	−0.408634	−	0.912698i	$-0.633995\pi$
$691$	−21.4834	−0.817269	−0.408634	+	0.912698i	$0.633995\pi$
$692$	−2.91391	−0.110770
$693$	−1.47770	−0.0561330
$694$	16.3981	0.622463
$695$	0	0
$696$	−13.7835	−0.522463
$697$	55.4890	2.10180
$698$	1.86165	0.0704645
$699$	−40.0573	−1.51511
$700$	0	0
$701$	9.62985	0.363714	0.181857	−	0.983325i	$-0.441789\pi$
$701$	9.62985	0.363714	0.181857	+	0.983325i	$0.441789\pi$
$702$	−0.625517	−0.0236086
$703$	12.4251	0.468621
$704$	0.747120	0.0281581
$705$	0	0
$706$	−25.8408	−0.972532
$707$	11.3387	0.426437
$708$	29.8963	1.12357
$709$	11.8970	0.446801	0.223400	−	0.974727i	$-0.428284\pi$
$709$	11.8970	0.446801	0.223400	+	0.974727i	$0.428284\pi$
$710$	0	0
$711$	−18.3347	−0.687606
$712$	−13.6426	−0.511279
$713$	−7.52288	−0.281734
$714$	9.35985	0.350283
$715$	0	0
$716$	19.3663	0.723754
$717$	−38.7327	−1.44650
$718$	−8.72223	−0.325511
$719$	24.2949	0.906046	0.453023	−	0.891499i	$-0.350345\pi$
$719$	24.2949	0.906046	0.453023	+	0.891499i	$0.350345\pi$
$720$	0	0
$721$	6.70598	0.249744
$722$	13.0040	0.483957
$723$	−67.7371	−2.51917
$724$	17.5986	0.654045
$725$	0	0
$726$	25.1454	0.933234
$727$	−6.25721	−0.232067	−0.116034	−	0.993245i	$-0.537018\pi$
$727$	−6.25721	−0.232067	−0.116034	+	0.993245i	$0.537018\pi$
$728$	−0.913908	−0.0338717
$729$	−23.2723	−0.861935
$730$	0	0
$731$	29.3764	1.08653
$732$	3.78913	0.140050
$733$	37.3304	1.37883	0.689415	−	0.724367i	$-0.257868\pi$
$733$	37.3304	1.37883	0.689415	+	0.724367i	$0.257868\pi$
$734$	25.5958	0.944759
$735$	0	0
$736$	1.00000	0.0368605
$737$	−3.92939	−0.144741
$738$	−28.2369	−1.03941
$739$	−26.9889	−0.992802	−0.496401	−	0.868093i	$-0.665345\pi$
$739$	−26.9889	−0.992802	−0.496401	+	0.868093i	$0.665345\pi$
$740$	0	0
$741$	−7.62699	−0.280185
$742$	−4.13084	−0.151648
$743$	32.1544	1.17963	0.589815	−	0.807538i	$-0.299201\pi$
$743$	32.1544	1.17963	0.589815	+	0.807538i	$0.299201\pi$
$744$	−18.1162	−0.664172
$745$	0	0
$746$	−17.2125	−0.630196
$747$	−35.5685	−1.30138
$748$	4.10971	0.150266
$749$	0.978433	0.0357512
$750$	0	0
$751$	39.7865	1.45183	0.725915	−	0.687785i	$-0.241417\pi$
$751$	39.7865	1.45183	0.725915	+	0.687785i	$0.241417\pi$
$752$	−7.90888	−0.288407
$753$	−49.5524	−1.80579
$754$	7.40312	0.269606
$755$	0	0
$756$	0.341716	0.0124281
$757$	26.9961	0.981189	0.490595	−	0.871388i	$-0.336780\pi$
$757$	26.9961	0.981189	0.490595	+	0.871388i	$0.336780\pi$
$758$	−23.0339	−0.836628
$759$	−1.79917	−0.0653059
$760$	0	0
$761$	−7.21529	−0.261554	−0.130777	−	0.991412i	$-0.541747\pi$
$761$	−7.21529	−0.261554	−0.130777	+	0.991412i	$0.541747\pi$
$762$	−6.58683	−0.238616
$763$	9.91833	0.359068
$764$	20.3578	0.736518
$765$	0	0
$766$	3.81777	0.137942
$767$	−16.0573	−0.579795
$768$	2.40815	0.0868965
$769$	6.40916	0.231120	0.115560	−	0.993300i	$-0.463134\pi$
$769$	6.40916	0.231120	0.115560	+	0.993300i	$0.463134\pi$
$770$	0	0
$771$	−40.5786	−1.46140
$772$	1.41317	0.0508611
$773$	50.2483	1.80730	0.903652	−	0.428267i	$-0.140876\pi$
$773$	50.2483	1.80730	0.903652	+	0.428267i	$0.140876\pi$
$774$	−14.9488	−0.537325
$775$	0	0
$776$	1.50074	0.0538733
$777$	−8.63406	−0.309745
$778$	8.25435	0.295933
$779$	24.7012	0.885014
$780$	0	0
$781$	2.00560	0.0717660
$782$	5.50074	0.196706
$783$	−2.76808	−0.0989231
$784$	−6.50074	−0.232169
$785$	0	0
$786$	19.7936	0.706013
$787$	2.70933	0.0965772	0.0482886	−	0.998833i	$-0.484623\pi$
$787$	2.70933	0.0965772	0.0482886	+	0.998833i	$0.484623\pi$
$788$	−4.92395	−0.175409
$789$	−59.6329	−2.12299
$790$	0	0
$791$	−11.5248	−0.409774
$792$	−2.09132	−0.0743118
$793$	−2.03514	−0.0722699
$794$	12.4967	0.443492
$795$	0	0
$796$	−10.3105	−0.365447
$797$	−15.1452	−0.536471	−0.268236	−	0.963353i	$-0.586441\pi$
$797$	−15.1452	−0.536471	−0.268236	+	0.963353i	$0.586441\pi$
$798$	4.16658	0.147495
$799$	−43.5047	−1.53909
$800$	0	0
$801$	38.1881	1.34931
$802$	−34.5660	−1.22057
$803$	−7.81408	−0.275753
$804$	−12.6654	−0.446673
$805$	0	0
$806$	9.73020	0.342732
$807$	−8.55259	−0.301065
$808$	16.0472	0.564540
$809$	−3.94373	−0.138654	−0.0693270	−	0.997594i	$-0.522085\pi$
$809$	−3.94373	−0.138654	−0.0693270	+	0.997594i	$0.522085\pi$
$810$	0	0
$811$	−14.1521	−0.496947	−0.248474	−	0.968639i	$-0.579929\pi$
$811$	−14.1521	−0.496947	−0.248474	+	0.968639i	$0.579929\pi$
$812$	−4.04429	−0.141927
$813$	−66.1664	−2.32056
$814$	−3.79103	−0.132876
$815$	0	0
$816$	13.2466	0.463723
$817$	13.0771	0.457508
$818$	−12.0499	−0.421314
$819$	2.55819	0.0893903
$820$	0	0
$821$	37.0094	1.29164	0.645818	−	0.763491i	$-0.276516\pi$
$821$	37.0094	1.29164	0.645818	+	0.763491i	$0.276516\pi$
$822$	−55.0140	−1.91883
$823$	−18.1208	−0.631651	−0.315826	−	0.948817i	$-0.602281\pi$
$823$	−18.1208	−0.631651	−0.315826	+	0.948817i	$0.602281\pi$
$824$	9.49069	0.330624
$825$	0	0
$826$	8.77201	0.305217
$827$	−41.5398	−1.44448	−0.722240	−	0.691643i	$-0.756887\pi$
$827$	−41.5398	−1.44448	−0.722240	+	0.691643i	$0.756887\pi$
$828$	−2.79917	−0.0972781
$829$	21.3976	0.743171	0.371585	−	0.928399i	$-0.378814\pi$
$829$	21.3976	0.743171	0.371585	+	0.928399i	$0.378814\pi$
$830$	0	0
$831$	−26.7307	−0.927277
$832$	−1.29341	−0.0448411
$833$	−35.7588	−1.23897
$834$	−9.05581	−0.313577
$835$	0	0
$836$	1.82946	0.0632732
$837$	−3.63819	−0.125754
$838$	−38.6157	−1.33396
$839$	−41.3437	−1.42734	−0.713672	−	0.700480i	$-0.752969\pi$
$839$	−41.3437	−1.42734	−0.713672	+	0.700480i	$0.752969\pi$
$840$	0	0
$841$	3.76081	0.129683
$842$	−32.7384	−1.12824
$843$	31.4161	1.08203
$844$	11.4161	0.392959
$845$	0	0
$846$	22.1384	0.761132
$847$	7.37803	0.253512
$848$	−5.84621	−0.200760
$849$	8.06848	0.276910
$850$	0	0
$851$	−5.07420	−0.173941
$852$	6.46453	0.221471
$853$	−56.0373	−1.91868	−0.959340	−	0.282252i	$-0.908919\pi$
$853$	−56.0373	−1.91868	−0.959340	+	0.282252i	$0.908919\pi$
$854$	1.11179	0.0380445
$855$	0	0
$856$	1.38473	0.0473292
$857$	−43.4734	−1.48502	−0.742512	−	0.669833i	$-0.766366\pi$
$857$	−43.4734	−1.48502	−0.742512	+	0.669833i	$0.766366\pi$
$858$	2.32708	0.0794452
$859$	11.1599	0.380771	0.190386	−	0.981709i	$-0.439026\pi$
$859$	11.1599	0.380771	0.190386	+	0.981709i	$0.439026\pi$
$860$	0	0
$861$	−17.1646	−0.584969
$862$	35.7739	1.21846
$863$	32.2767	1.09871	0.549356	−	0.835589i	$-0.314873\pi$
$863$	32.2767	1.09871	0.549356	+	0.835589i	$0.314873\pi$
$864$	0.483617	0.0164530
$865$	0	0
$866$	−10.5682	−0.359123
$867$	31.9275	1.08431
$868$	−5.31556	−0.180422
$869$	−4.89367	−0.166006
$870$	0	0
$871$	6.80256	0.230496
$872$	14.0370	0.475352
$873$	−4.20083	−0.142176
$874$	2.44868	0.0828279
$875$	0	0
$876$	−25.1867	−0.850978
$877$	−9.52493	−0.321634	−0.160817	−	0.986984i	$-0.551413\pi$
$877$	−9.52493	−0.321634	−0.160817	+	0.986984i	$0.551413\pi$
$878$	27.6642	0.933621
$879$	21.4132	0.722248
$880$	0	0
$881$	49.1585	1.65619	0.828096	−	0.560586i	$-0.189424\pi$
$881$	49.1585	1.65619	0.828096	+	0.560586i	$0.189424\pi$
$882$	18.1967	0.612715
$883$	33.1379	1.11518	0.557590	−	0.830117i	$-0.311726\pi$
$883$	33.1379	1.11518	0.557590	+	0.830117i	$0.311726\pi$
$884$	−7.11473	−0.239294
$885$	0	0
$886$	36.8082	1.23659
$887$	−1.59084	−0.0534153	−0.0267076	−	0.999643i	$-0.508502\pi$
$887$	−1.59084	−0.0534153	−0.0267076	+	0.999643i	$0.508502\pi$
$888$	−12.2194	−0.410057
$889$	−1.93267	−0.0648197
$890$	0	0
$891$	−7.14407	−0.239335
$892$	18.2094	0.609695
$893$	−19.3663	−0.648070
$894$	4.59027	0.153522
$895$	0	0
$896$	0.706585	0.0236054
$897$	3.11473	0.103998
$898$	−18.2711	−0.609715
$899$	43.0588	1.43609
$900$	0	0
$901$	−32.1584	−1.07135
$902$	−7.53662	−0.250942
$903$	−9.08710	−0.302400
$904$	−16.3105	−0.542480
$905$	0	0
$906$	22.6840	0.753624
$907$	17.4658	0.579942	0.289971	−	0.957035i	$-0.406354\pi$
$907$	17.4658	0.579942	0.289971	+	0.957035i	$0.406354\pi$
$908$	18.9363	0.628422
$909$	−44.9190	−1.48987
$910$	0	0
$911$	−21.6050	−0.715805	−0.357903	−	0.933759i	$-0.616508\pi$
$911$	−21.6050	−0.715805	−0.357903	+	0.933759i	$0.616508\pi$
$912$	5.89679	0.195262
$913$	−9.49349	−0.314189
$914$	−27.6326	−0.914005
$915$	0	0
$916$	−8.46433	−0.279669
$917$	5.80772	0.191788
$918$	2.66025	0.0878013
$919$	−41.7396	−1.37686	−0.688432	−	0.725301i	$-0.741701\pi$
$919$	−41.7396	−1.37686	−0.688432	+	0.725301i	$0.741701\pi$
$920$	0	0
$921$	−68.4181	−2.25445
$922$	−35.5515	−1.17083
$923$	−3.47210	−0.114285
$924$	−1.27127	−0.0418217
$925$	0	0
$926$	−23.9331	−0.786490
$927$	−26.5661	−0.872545
$928$	−5.72371	−0.187890
$929$	38.8505	1.27464	0.637322	−	0.770597i	$-0.280042\pi$
$929$	38.8505	1.27464	0.637322	+	0.770597i	$0.280042\pi$
$930$	0	0
$931$	−15.9182	−0.521699
$932$	−16.6341	−0.544867
$933$	−67.4533	−2.20832
$934$	−19.9035	−0.651262
$935$	0	0
$936$	3.62049	0.118340
$937$	33.1555	1.08314	0.541571	−	0.840655i	$-0.317830\pi$
$937$	33.1555	1.08314	0.541571	+	0.840655i	$0.317830\pi$
$938$	−3.71620	−0.121338
$939$	17.8897	0.583808
$940$	0	0
$941$	−33.8004	−1.10186	−0.550931	−	0.834551i	$-0.685727\pi$
$941$	−33.8004	−1.10186	−0.550931	+	0.834551i	$0.685727\pi$
$942$	10.6754	0.347823
$943$	−10.0876	−0.328496
$944$	12.4146	0.404062
$945$	0	0
$946$	−3.98995	−0.129725
$947$	−20.2406	−0.657730	−0.328865	−	0.944377i	$-0.606666\pi$
$947$	−20.2406	−0.657730	−0.328865	+	0.944377i	$0.606666\pi$
$948$	−15.7735	−0.512299
$949$	13.5277	0.439129
$950$	0	0
$951$	−31.6622	−1.02672
$952$	3.88674	0.125970
$953$	28.3885	0.919592	0.459796	−	0.888024i	$-0.347922\pi$
$953$	28.3885	0.919592	0.459796	+	0.888024i	$0.347922\pi$
$954$	16.3646	0.529822
$955$	0	0
$956$	−16.0840	−0.520194
$957$	10.2979	0.332885
$958$	3.86206	0.124777
$959$	−16.1419	−0.521249
$960$	0	0
$961$	25.5937	0.825604
$962$	6.56304	0.211601
$963$	−3.87611	−0.124906
$964$	−28.1283	−0.905952
$965$	0	0
$966$	−1.70156	−0.0547469
$967$	57.6163	1.85282	0.926408	−	0.376522i	$-0.122880\pi$
$967$	57.6163	1.85282	0.926408	+	0.376522i	$0.122880\pi$
$968$	10.4418	0.335613
$969$	32.4367	1.04202
$970$	0	0
$971$	−1.47686	−0.0473946	−0.0236973	−	0.999719i	$-0.507544\pi$
$971$	−1.47686	−0.0473946	−0.0236973	+	0.999719i	$0.507544\pi$
$972$	−21.5762	−0.692057
$973$	−2.65711	−0.0851829
$974$	−15.1499	−0.485433
$975$	0	0
$976$	1.57346	0.0503653
$977$	11.5709	0.370185	0.185092	−	0.982721i	$-0.440742\pi$
$977$	11.5709	0.370185	0.185092	+	0.982721i	$0.440742\pi$
$978$	23.8997	0.764229
$979$	10.1927	0.325760
$980$	0	0
$981$	−39.2920	−1.25450
$982$	6.86312	0.219011
$983$	−37.5275	−1.19694	−0.598470	−	0.801145i	$-0.704225\pi$
$983$	−37.5275	−1.19694	−0.598470	+	0.801145i	$0.704225\pi$
$984$	−24.2923	−0.774412
$985$	0	0
$986$	−31.4846	−1.00267
$987$	13.4575	0.428356
$988$	−3.16716	−0.100761
$989$	−5.34045	−0.169816
$990$	0	0
$991$	9.87860	0.313804	0.156902	−	0.987614i	$-0.449849\pi$
$991$	9.87860	0.313804	0.156902	+	0.987614i	$0.449849\pi$
$992$	−7.52288	−0.238852
$993$	−37.6214	−1.19388
$994$	1.89679	0.0601624
$995$	0	0
$996$	−30.5998	−0.969593
$997$	53.6506	1.69913	0.849565	−	0.527484i	$-0.176865\pi$
$997$	53.6506	1.69913	0.849565	+	0.527484i	$0.176865\pi$
$998$	18.6809	0.591333
$999$	−2.45397	−0.0776401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.r.1.4		4
4.3	odd	2		9200.2.a.cr.1.1		4
5.2	odd	4		230.2.b.b.139.1	✓	8
5.3	odd	4		230.2.b.b.139.8	yes	8
5.4	even	2		1150.2.a.s.1.1		4
15.2	even	4		2070.2.d.f.829.5		8
15.8	even	4		2070.2.d.f.829.1		8
20.3	even	4		1840.2.e.e.369.2		8
20.7	even	4		1840.2.e.e.369.7		8
20.19	odd	2		9200.2.a.cj.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.1	✓	8	5.2	odd	4
230.2.b.b.139.8	yes	8	5.3	odd	4
1150.2.a.r.1.4		4	1.1	even	1	trivial
1150.2.a.s.1.1		4	5.4	even	2
1840.2.e.e.369.2		8	20.3	even	4
1840.2.e.e.369.7		8	20.7	even	4
2070.2.d.f.829.1		8	15.8	even	4
2070.2.d.f.829.5		8	15.2	even	4
9200.2.a.cj.1.4		4	20.19	odd	2
9200.2.a.cr.1.1		4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.40815 q^{3} +1.00000 q^{4} -2.40815 q^{6} -0.706585 q^{7} -1.00000 q^{8} +2.79917 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.40815 q^{3} +1.00000 q^{4} -2.40815 q^{6} -0.706585 q^{7} -1.00000 q^{8} +2.79917 q^{9} +0.747120 q^{11} +2.40815 q^{12} -1.29341 q^{13} +0.706585 q^{14} +1.00000 q^{16} +5.50074 q^{17} -2.79917 q^{18} +2.44868 q^{19} -1.70156 q^{21} -0.747120 q^{22} -1.00000 q^{23} -2.40815 q^{24} +1.29341 q^{26} -0.483617 q^{27} -0.706585 q^{28} +5.72371 q^{29} +7.52288 q^{31} -1.00000 q^{32} +1.79917 q^{33} -5.50074 q^{34} +2.79917 q^{36} +5.07420 q^{37} -2.44868 q^{38} -3.11473 q^{39} +10.0876 q^{41} +1.70156 q^{42} +5.34045 q^{43} +0.747120 q^{44} +1.00000 q^{46} -7.90888 q^{47} +2.40815 q^{48} -6.50074 q^{49} +13.2466 q^{51} -1.29341 q^{52} -5.84621 q^{53} +0.483617 q^{54} +0.706585 q^{56} +5.89679 q^{57} -5.72371 q^{58} +12.4146 q^{59} +1.57346 q^{61} -7.52288 q^{62} -1.97786 q^{63} +1.00000 q^{64} -1.79917 q^{66} -5.25938 q^{67} +5.50074 q^{68} -2.40815 q^{69} +2.68444 q^{71} -2.79917 q^{72} -10.4589 q^{73} -5.07420 q^{74} +2.44868 q^{76} -0.527904 q^{77} +3.11473 q^{78} -6.55005 q^{79} -9.56214 q^{81} -10.0876 q^{82} -12.7068 q^{83} -1.70156 q^{84} -5.34045 q^{86} +13.7835 q^{87} -0.747120 q^{88} +13.6426 q^{89} +0.913908 q^{91} -1.00000 q^{92} +18.1162 q^{93} +7.90888 q^{94} -2.40815 q^{96} -1.50074 q^{97} +6.50074 q^{98} +2.09132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9	\( 4 q - 4 q^{2} - 3 q^{3} + 4 q^{4} + 3 q^{6} - 3 q^{7} - 4 q^{8} + 7 q^{9} + 5 q^{11} - 3 q^{12} - 5 q^{13} + 3 q^{14} + 4 q^{16} + 5 q^{17} - 7 q^{18} - q^{19} + 6 q^{21} - 5 q^{22} - 4 q^{23} + 3 q^{24} + 5 q^{26} - 6 q^{27} - 3 q^{28} + 2 q^{29} + 5 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{34} + 7 q^{36} + 6 q^{37} + q^{38} + 23 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 4 q^{46} - 2 q^{47} - 3 q^{48} - 9 q^{49} + 7 q^{51} - 5 q^{52} + 6 q^{54} + 3 q^{56} + 28 q^{57} - 2 q^{58} + 16 q^{59} + 9 q^{61} - 5 q^{62} - 16 q^{63} + 4 q^{64} - 3 q^{66} + 2 q^{67} + 5 q^{68} + 3 q^{69} + 19 q^{71} - 7 q^{72} + 8 q^{73} - 6 q^{74} - q^{76} + 10 q^{77} - 6 q^{79} + 16 q^{81} - 23 q^{82} + 14 q^{83} + 6 q^{84} - 2 q^{86} + 38 q^{87} - 5 q^{88} + 30 q^{89} - 13 q^{91} - 4 q^{92} + 26 q^{93} + 2 q^{94} + 3 q^{96} + 11 q^{97} + 9 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 3 * q^3 + 4 * q^4 + 3 * q^6 - 3 * q^7 - 4 * q^8 + 7 * q^9 + 5 * q^11 - 3 * q^12 - 5 * q^13 + 3 * q^14 + 4 * q^16 + 5 * q^17 - 7 * q^18 - q^19 + 6 * q^21 - 5 * q^22 - 4 * q^23 + 3 * q^24 + 5 * q^26 - 6 * q^27 - 3 * q^28 + 2 * q^29 + 5 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^34 + 7 * q^36 + 6 * q^37 + q^38 + 23 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 4 * q^46 - 2 * q^47 - 3 * q^48 - 9 * q^49 + 7 * q^51 - 5 * q^52 + 6 * q^54 + 3 * q^56 + 28 * q^57 - 2 * q^58 + 16 * q^59 + 9 * q^61 - 5 * q^62 - 16 * q^63 + 4 * q^64 - 3 * q^66 + 2 * q^67 + 5 * q^68 + 3 * q^69 + 19 * q^71 - 7 * q^72 + 8 * q^73 - 6 * q^74 - q^76 + 10 * q^77 - 6 * q^79 + 16 * q^81 - 23 * q^82 + 14 * q^83 + 6 * q^84 - 2 * q^86 + 38 * q^87 - 5 * q^88 + 30 * q^89 - 13 * q^91 - 4 * q^92 + 26 * q^93 + 2 * q^94 + 3 * q^96 + 11 * q^97 + 9 * q^98 - 27 * q^99

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