LMFDB - Embedded newform 5775.2.a.bp.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5775,2,Mod(1,5775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5775.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:	$46.1136071673$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	5775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} -1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} -1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} -1.00000 q^{11} -1.74590 q^{12} +3.17313 q^{13} +1.93543 q^{14} -4.44364 q^{16} -6.85446 q^{17} +1.93543 q^{18} -0.318669 q^{19} -1.00000 q^{21} -1.93543 q^{22} +1.87086 q^{23} +0.491797 q^{24} +6.14137 q^{26} -1.00000 q^{27} +1.74590 q^{28} -3.17313 q^{29} +9.23353 q^{31} -7.61676 q^{32} +1.00000 q^{33} -13.2663 q^{34} +1.74590 q^{36} +7.55220 q^{37} -0.616763 q^{38} -3.17313 q^{39} +9.36266 q^{41} -1.93543 q^{42} +10.8873 q^{43} -1.74590 q^{44} +3.62093 q^{46} +8.06040 q^{47} +4.44364 q^{48} +1.00000 q^{49} +6.85446 q^{51} +5.53996 q^{52} -0.508203 q^{53} -1.93543 q^{54} -0.491797 q^{56} +0.318669 q^{57} -6.14137 q^{58} -7.04399 q^{59} -2.00000 q^{61} +17.8709 q^{62} +1.00000 q^{63} -5.85446 q^{64} +1.93543 q^{66} +2.66492 q^{67} -11.9672 q^{68} -1.87086 q^{69} -5.01641 q^{71} -0.491797 q^{72} +4.82687 q^{73} +14.6168 q^{74} -0.556364 q^{76} -1.00000 q^{77} -6.14137 q^{78} +5.01641 q^{79} +1.00000 q^{81} +18.1208 q^{82} -3.52461 q^{83} -1.74590 q^{84} +21.0716 q^{86} +3.17313 q^{87} +0.491797 q^{88} -1.74173 q^{89} +3.17313 q^{91} +3.26634 q^{92} -9.23353 q^{93} +15.6004 q^{94} +7.61676 q^{96} +12.2499 q^{97} +1.93543 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} - 3 q^{21} + 2 q^{22} - 10 q^{23} + 3 q^{24} - q^{26} - 3 q^{27} + 6 q^{28} - 4 q^{29} - 2 q^{31} - 8 q^{32} + 3 q^{33} - 4 q^{34} + 6 q^{36} + 13 q^{38} - 4 q^{39} + 14 q^{41} + 2 q^{42} + 14 q^{43} - 6 q^{44} + 28 q^{46} + 4 q^{48} + 3 q^{49} + 8 q^{51} + 29 q^{52} + 2 q^{54} - 3 q^{56} + 8 q^{57} + q^{58} - 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 2 q^{66} + 4 q^{67} - 42 q^{68} + 10 q^{69} - 12 q^{71} - 3 q^{72} + 20 q^{73} + 29 q^{74} - 11 q^{76} - 3 q^{77} + q^{78} + 12 q^{79} + 3 q^{81} + 6 q^{82} - 6 q^{83} - 6 q^{84} + 24 q^{86} + 4 q^{87} + 3 q^{88} + 26 q^{89} + 4 q^{91} - 26 q^{92} + 2 q^{93} + 35 q^{94} + 8 q^{96} + 4 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 - 3 * q^21 + 2 * q^22 - 10 * q^23 + 3 * q^24 - q^26 - 3 * q^27 + 6 * q^28 - 4 * q^29 - 2 * q^31 - 8 * q^32 + 3 * q^33 - 4 * q^34 + 6 * q^36 + 13 * q^38 - 4 * q^39 + 14 * q^41 + 2 * q^42 + 14 * q^43 - 6 * q^44 + 28 * q^46 + 4 * q^48 + 3 * q^49 + 8 * q^51 + 29 * q^52 + 2 * q^54 - 3 * q^56 + 8 * q^57 + q^58 - 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 2 * q^66 + 4 * q^67 - 42 * q^68 + 10 * q^69 - 12 * q^71 - 3 * q^72 + 20 * q^73 + 29 * q^74 - 11 * q^76 - 3 * q^77 + q^78 + 12 * q^79 + 3 * q^81 + 6 * q^82 - 6 * q^83 - 6 * q^84 + 24 * q^86 + 4 * q^87 + 3 * q^88 + 26 * q^89 + 4 * q^91 - 26 * q^92 + 2 * q^93 + 35 * q^94 + 8 * q^96 + 4 * q^97 - 2 * 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 $

$2$	1.93543	1.36856	0.684279	−	0.729221i	$-0.260117\pi$
$2$	1.93543	1.36856	0.684279	+	0.729221i	$0.260117\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.74590	0.872949
$5$	0	0
$5$	0	0
$6$	−1.93543	−0.790137
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.491797	−0.173876
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.74590	−0.503997
$13$	3.17313	0.880067	0.440034	−	0.897981i	$-0.354967\pi$
$13$	3.17313	0.880067	0.440034	+	0.897981i	$0.354967\pi$
$14$	1.93543	0.517266
$15$	0	0
$16$	−4.44364	−1.11091
$17$	−6.85446	−1.66245	−0.831225	−	0.555936i	$-0.812360\pi$
$17$	−6.85446	−1.66245	−0.831225	+	0.555936i	$0.812360\pi$
$18$	1.93543	0.456186
$19$	−0.318669	−0.0731078	−0.0365539	−	0.999332i	$-0.511638\pi$
$19$	−0.318669	−0.0731078	−0.0365539	+	0.999332i	$0.511638\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−1.93543	−0.412636
$23$	1.87086	0.390102	0.195051	−	0.980793i	$-0.437513\pi$
$23$	1.87086	0.390102	0.195051	+	0.980793i	$0.437513\pi$
$24$	0.491797	0.100388
$25$	0	0
$26$	6.14137	1.20442
$27$	−1.00000	−0.192450
$28$	1.74590	0.329944
$29$	−3.17313	−0.589235	−0.294617	−	0.955615i	$-0.595192\pi$
$29$	−3.17313	−0.589235	−0.294617	+	0.955615i	$0.595192\pi$
$30$	0	0
$31$	9.23353	1.65839	0.829195	−	0.558959i	$-0.188799\pi$
$31$	9.23353	1.65839	0.829195	+	0.558959i	$0.188799\pi$
$32$	−7.61676	−1.34647
$33$	1.00000	0.174078
$34$	−13.2663	−2.27516
$35$	0	0
$36$	1.74590	0.290983
$37$	7.55220	1.24157	0.620787	−	0.783980i	$-0.286813\pi$
$37$	7.55220	1.24157	0.620787	+	0.783980i	$0.286813\pi$
$38$	−0.616763	−0.100052
$39$	−3.17313	−0.508107
$40$	0	0
$41$	9.36266	1.46220	0.731101	−	0.682269i	$-0.239007\pi$
$41$	9.36266	1.46220	0.731101	+	0.682269i	$0.239007\pi$
$42$	−1.93543	−0.298644
$43$	10.8873	1.66029	0.830147	−	0.557545i	$-0.188257\pi$
$43$	10.8873	1.66029	0.830147	+	0.557545i	$0.188257\pi$
$44$	−1.74590	−0.263204
$45$	0	0
$46$	3.62093	0.533877
$47$	8.06040	1.17573	0.587865	−	0.808959i	$-0.299969\pi$
$47$	8.06040	1.17573	0.587865	+	0.808959i	$0.299969\pi$
$48$	4.44364	0.641384
$49$	1.00000	0.142857
$50$	0	0
$51$	6.85446	0.959816
$52$	5.53996	0.768254
$53$	−0.508203	−0.0698071	−0.0349036	−	0.999391i	$-0.511112\pi$
$53$	−0.508203	−0.0698071	−0.0349036	+	0.999391i	$0.511112\pi$
$54$	−1.93543	−0.263379
$55$	0	0
$56$	−0.491797	−0.0657191
$57$	0.318669	0.0422088
$58$	−6.14137	−0.806402
$59$	−7.04399	−0.917050	−0.458525	−	0.888682i	$-0.651622\pi$
$59$	−7.04399	−0.917050	−0.458525	+	0.888682i	$0.651622\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	17.8709	2.26960
$63$	1.00000	0.125988
$64$	−5.85446	−0.731807
$65$	0	0
$66$	1.93543	0.238235
$67$	2.66492	0.325572	0.162786	−	0.986661i	$-0.447952\pi$
$67$	2.66492	0.325572	0.162786	+	0.986661i	$0.447952\pi$
$68$	−11.9672	−1.45123
$69$	−1.87086	−0.225226
$70$	0	0
$71$	−5.01641	−0.595338	−0.297669	−	0.954669i	$-0.596209\pi$
$71$	−5.01641	−0.595338	−0.297669	+	0.954669i	$0.596209\pi$
$72$	−0.491797	−0.0579588
$73$	4.82687	0.564943	0.282471	−	0.959276i	$-0.408846\pi$
$73$	4.82687	0.564943	0.282471	+	0.959276i	$0.408846\pi$
$74$	14.6168	1.69916
$75$	0	0
$76$	−0.556364	−0.0638194
$77$	−1.00000	−0.113961
$78$	−6.14137	−0.695374
$79$	5.01641	0.564390	0.282195	−	0.959357i	$-0.408938\pi$
$79$	5.01641	0.564390	0.282195	+	0.959357i	$0.408938\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	18.1208	2.00111
$83$	−3.52461	−0.386876	−0.193438	−	0.981112i	$-0.561964\pi$
$83$	−3.52461	−0.386876	−0.193438	+	0.981112i	$0.561964\pi$
$84$	−1.74590	−0.190493
$85$	0	0
$86$	21.0716	2.27221
$87$	3.17313	0.340195
$88$	0.491797	0.0524257
$89$	−1.74173	−0.184623	−0.0923115	−	0.995730i	$-0.529426\pi$
$89$	−1.74173	−0.184623	−0.0923115	+	0.995730i	$0.529426\pi$
$90$	0	0
$91$	3.17313	0.332634
$92$	3.26634	0.340539
$93$	−9.23353	−0.957472
$94$	15.6004	1.60905
$95$	0	0
$96$	7.61676	0.777383
$97$	12.2499	1.24379	0.621896	−	0.783100i	$-0.286363\pi$
$97$	12.2499	1.24379	0.621896	+	0.783100i	$0.286363\pi$
$98$	1.93543	0.195508
$99$	−1.00000	−0.100504
$100$	0	0
$101$	4.88727	0.486302	0.243151	−	0.969988i	$-0.421819\pi$
$101$	4.88727	0.486302	0.243151	+	0.969988i	$0.421819\pi$
$102$	13.2663	1.31356
$103$	0.637339	0.0627988	0.0313994	−	0.999507i	$-0.490004\pi$
$103$	0.637339	0.0627988	0.0313994	+	0.999507i	$0.490004\pi$
$104$	−1.56053	−0.153023
$105$	0	0
$106$	−0.983593	−0.0955350
$107$	−0.956008	−0.0924208	−0.0462104	−	0.998932i	$-0.514714\pi$
$107$	−0.956008	−0.0924208	−0.0462104	+	0.998932i	$0.514714\pi$
$108$	−1.74590	−0.167999
$109$	−7.61259	−0.729154	−0.364577	−	0.931173i	$-0.618786\pi$
$109$	−7.61259	−0.729154	−0.364577	+	0.931173i	$0.618786\pi$
$110$	0	0
$111$	−7.55220	−0.716823
$112$	−4.44364	−0.419884
$113$	7.70892	0.725194	0.362597	−	0.931946i	$-0.381890\pi$
$113$	7.70892	0.725194	0.362597	+	0.931946i	$0.381890\pi$
$114$	0.616763	0.0577651
$115$	0	0
$116$	−5.53996	−0.514372
$117$	3.17313	0.293356
$118$	−13.6332	−1.25504
$119$	−6.85446	−0.628347
$120$	0	0
$121$	1.00000	0.0909091
$122$	−3.87086	−0.350452
$123$	−9.36266	−0.844203
$124$	16.1208	1.44769
$125$	0	0
$126$	1.93543	0.172422
$127$	5.49180	0.487318	0.243659	−	0.969861i	$-0.421652\pi$
$127$	5.49180	0.487318	0.243659	+	0.969861i	$0.421652\pi$
$128$	3.90262	0.344946
$129$	−10.8873	−0.958571
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	1.74590	0.151961
$133$	−0.318669	−0.0276321
$134$	5.15778	0.445564
$135$	0	0
$136$	3.37100	0.289061
$137$	−15.6126	−1.33387	−0.666937	−	0.745114i	$-0.732395\pi$
$137$	−15.6126	−1.33387	−0.666937	+	0.745114i	$0.732395\pi$
$138$	−3.62093	−0.308234
$139$	−9.01641	−0.764762	−0.382381	−	0.924005i	$-0.624896\pi$
$139$	−9.01641	−0.764762	−0.382381	+	0.924005i	$0.624896\pi$
$140$	0	0
$141$	−8.06040	−0.678808
$142$	−9.70892	−0.814754
$143$	−3.17313	−0.265350
$144$	−4.44364	−0.370303
$145$	0	0
$146$	9.34209	0.773157
$147$	−1.00000	−0.0824786
$148$	13.1854	1.08383
$149$	−5.20594	−0.426487	−0.213244	−	0.976999i	$-0.568403\pi$
$149$	−5.20594	−0.426487	−0.213244	+	0.976999i	$0.568403\pi$
$150$	0	0
$151$	6.24993	0.508612	0.254306	−	0.967124i	$-0.418153\pi$
$151$	6.24993	0.508612	0.254306	+	0.967124i	$0.418153\pi$
$152$	0.156721	0.0127117
$153$	−6.85446	−0.554150
$154$	−1.93543	−0.155962
$155$	0	0
$156$	−5.53996	−0.443552
$157$	18.1208	1.44620	0.723099	−	0.690745i	$-0.242717\pi$
$157$	18.1208	1.44620	0.723099	+	0.690745i	$0.242717\pi$
$158$	9.70892	0.772400
$159$	0.508203	0.0403031
$160$	0	0
$161$	1.87086	0.147445
$162$	1.93543	0.152062
$163$	2.66492	0.208733	0.104366	−	0.994539i	$-0.466719\pi$
$163$	2.66492	0.208733	0.104366	+	0.994539i	$0.466719\pi$
$164$	16.3463	1.27643
$165$	0	0
$166$	−6.82164	−0.529462
$167$	11.1455	0.862468	0.431234	−	0.902240i	$-0.358078\pi$
$167$	11.1455	0.862468	0.431234	+	0.902240i	$0.358078\pi$
$168$	0.491797	0.0379429
$169$	−2.93126	−0.225482
$170$	0	0
$171$	−0.318669	−0.0243693
$172$	19.0081	1.44935
$173$	24.8461	1.88902	0.944508	−	0.328489i	$-0.106539\pi$
$173$	24.8461	1.88902	0.944508	+	0.328489i	$0.106539\pi$
$174$	6.14137	0.465576
$175$	0	0
$176$	4.44364	0.334952
$177$	7.04399	0.529459
$178$	−3.37100	−0.252667
$179$	−12.7581	−0.953588	−0.476794	−	0.879015i	$-0.658201\pi$
$179$	−12.7581	−0.953588	−0.476794	+	0.879015i	$0.658201\pi$
$180$	0	0
$181$	−3.23353	−0.240346	−0.120173	−	0.992753i	$-0.538345\pi$
$181$	−3.23353	−0.240346	−0.120173	+	0.992753i	$0.538345\pi$
$182$	6.14137	0.455229
$183$	2.00000	0.147844
$184$	−0.920085	−0.0678296
$185$	0	0
$186$	−17.8709	−1.31036
$187$	6.85446	0.501248
$188$	14.0726	1.02635
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	20.9753	1.51772	0.758858	−	0.651256i	$-0.225758\pi$
$191$	20.9753	1.51772	0.758858	+	0.651256i	$0.225758\pi$
$192$	5.85446	0.422509
$193$	−0.249933	−0.0179905	−0.00899527	−	0.999960i	$-0.502863\pi$
$193$	−0.249933	−0.0179905	−0.00899527	+	0.999960i	$0.502863\pi$
$194$	23.7089	1.70220
$195$	0	0
$196$	1.74590	0.124707
$197$	−18.4999	−1.31806	−0.659030	−	0.752116i	$-0.729033\pi$
$197$	−18.4999	−1.31806	−0.659030	+	0.752116i	$0.729033\pi$
$198$	−1.93543	−0.137545
$199$	9.87086	0.699727	0.349864	−	0.936801i	$-0.386228\pi$
$199$	9.87086	0.699727	0.349864	+	0.936801i	$0.386228\pi$
$200$	0	0
$201$	−2.66492	−0.187969
$202$	9.45898	0.665532
$203$	−3.17313	−0.222710
$204$	11.9672	0.837871
$205$	0	0
$206$	1.23353	0.0859438
$207$	1.87086	0.130034
$208$	−14.1002	−0.977674
$209$	0.318669	0.0220428
$210$	0	0
$211$	−4.63734	−0.319248	−0.159624	−	0.987178i	$-0.551028\pi$
$211$	−4.63734	−0.319248	−0.159624	+	0.987178i	$0.551028\pi$
$212$	−0.887271	−0.0609381
$213$	5.01641	0.343719
$214$	−1.85029	−0.126483
$215$	0	0
$216$	0.491797	0.0334625
$217$	9.23353	0.626813
$218$	−14.7337	−0.997889
$219$	−4.82687	−0.326170
$220$	0	0
$221$	−21.7501	−1.46307
$222$	−14.6168	−0.981013
$223$	18.3463	1.22856	0.614278	−	0.789090i	$-0.289447\pi$
$223$	18.3463	1.22856	0.614278	+	0.789090i	$0.289447\pi$
$224$	−7.61676	−0.508916
$225$	0	0
$226$	14.9201	0.992469
$227$	−0.379068	−0.0251596	−0.0125798	−	0.999921i	$-0.504004\pi$
$227$	−0.379068	−0.0251596	−0.0125798	+	0.999921i	$0.504004\pi$
$228$	0.556364	0.0368461
$229$	24.9424	1.64824	0.824121	−	0.566413i	$-0.191669\pi$
$229$	24.9424	1.64824	0.824121	+	0.566413i	$0.191669\pi$
$230$	0	0
$231$	1.00000	0.0657952
$232$	1.56053	0.102454
$233$	−23.4506	−1.53630	−0.768151	−	0.640268i	$-0.778823\pi$
$233$	−23.4506	−1.53630	−0.768151	+	0.640268i	$0.778823\pi$
$234$	6.14137	0.401474
$235$	0	0
$236$	−12.2981	−0.800538
$237$	−5.01641	−0.325851
$238$	−13.2663	−0.859929
$239$	5.07681	0.328391	0.164196	−	0.986428i	$-0.447497\pi$
$239$	5.07681	0.328391	0.164196	+	0.986428i	$0.447497\pi$
$240$	0	0
$241$	19.2939	1.24283	0.621415	−	0.783481i	$-0.286558\pi$
$241$	19.2939	1.24283	0.621415	+	0.783481i	$0.286558\pi$
$242$	1.93543	0.124414
$243$	−1.00000	−0.0641500
$244$	−3.49180	−0.223539
$245$	0	0
$246$	−18.1208	−1.15534
$247$	−1.01118	−0.0643397
$248$	−4.54102	−0.288355
$249$	3.52461	0.223363
$250$	0	0
$251$	23.8021	1.50238	0.751188	−	0.660088i	$-0.229481\pi$
$251$	23.8021	1.50238	0.751188	+	0.660088i	$0.229481\pi$
$252$	1.74590	0.109981
$253$	−1.87086	−0.117620
$254$	10.6290	0.666923
$255$	0	0
$256$	19.2622	1.20389
$257$	−14.9149	−0.930363	−0.465182	−	0.885215i	$-0.654011\pi$
$257$	−14.9149	−0.930363	−0.465182	+	0.885215i	$0.654011\pi$
$258$	−21.0716	−1.31186
$259$	7.55220	0.469271
$260$	0	0
$261$	−3.17313	−0.196412
$262$	7.74173	0.478286
$263$	−2.92319	−0.180252	−0.0901259	−	0.995930i	$-0.528727\pi$
$263$	−2.92319	−0.180252	−0.0901259	+	0.995930i	$0.528727\pi$
$264$	−0.491797	−0.0302680
$265$	0	0
$266$	−0.616763	−0.0378162
$267$	1.74173	0.106592
$268$	4.65269	0.284208
$269$	11.9672	0.729652	0.364826	−	0.931076i	$-0.381128\pi$
$269$	11.9672	0.729652	0.364826	+	0.931076i	$0.381128\pi$
$270$	0	0
$271$	−20.3187	−1.23427	−0.617136	−	0.786857i	$-0.711707\pi$
$271$	−20.3187	−1.23427	−0.617136	+	0.786857i	$0.711707\pi$
$272$	30.4587	1.84683
$273$	−3.17313	−0.192046
$274$	−30.2171	−1.82548
$275$	0	0
$276$	−3.26634	−0.196611
$277$	−18.0552	−1.08483	−0.542415	−	0.840111i	$-0.682490\pi$
$277$	−18.0552	−1.08483	−0.542415	+	0.840111i	$0.682490\pi$
$278$	−17.4506	−1.04662
$279$	9.23353	0.552797
$280$	0	0
$281$	27.2939	1.62822	0.814110	−	0.580711i	$-0.197226\pi$
$281$	27.2939	1.62822	0.814110	+	0.580711i	$0.197226\pi$
$282$	−15.6004	−0.928988
$283$	−29.8901	−1.77678	−0.888391	−	0.459087i	$-0.848177\pi$
$283$	−29.8901	−1.77678	−0.888391	+	0.459087i	$0.848177\pi$
$284$	−8.75814	−0.519700
$285$	0	0
$286$	−6.14137	−0.363147
$287$	9.36266	0.552660
$288$	−7.61676	−0.448822
$289$	29.9836	1.76374
$290$	0	0
$291$	−12.2499	−0.718104
$292$	8.42723	0.493166
$293$	4.34625	0.253911	0.126955	−	0.991908i	$-0.459479\pi$
$293$	4.34625	0.253911	0.126955	+	0.991908i	$0.459479\pi$
$294$	−1.93543	−0.112877
$295$	0	0
$296$	−3.71414	−0.215880
$297$	1.00000	0.0580259
$298$	−10.0757	−0.583672
$299$	5.93649	0.343316
$300$	0	0
$301$	10.8873	0.627532
$302$	12.0963	0.696065
$303$	−4.88727	−0.280766
$304$	1.41605	0.0812161
$305$	0	0
$306$	−13.2663	−0.758386
$307$	20.7581	1.18473	0.592365	−	0.805670i	$-0.298194\pi$
$307$	20.7581	1.18473	0.592365	+	0.805670i	$0.298194\pi$
$308$	−1.74590	−0.0994818
$309$	−0.637339	−0.0362569
$310$	0	0
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	1.56053	0.0883478
$313$	−8.12914	−0.459486	−0.229743	−	0.973251i	$-0.573789\pi$
$313$	−8.12914	−0.459486	−0.229743	+	0.973251i	$0.573789\pi$
$314$	35.0716	1.97920
$315$	0	0
$316$	8.75814	0.492684
$317$	19.9917	1.12284	0.561422	−	0.827530i	$-0.310255\pi$
$317$	19.9917	1.12284	0.561422	+	0.827530i	$0.310255\pi$
$318$	0.983593	0.0551572
$319$	3.17313	0.177661
$320$	0	0
$321$	0.956008	0.0533592
$322$	3.62093	0.201787
$323$	2.18431	0.121538
$324$	1.74590	0.0969944
$325$	0	0
$326$	5.15778	0.285663
$327$	7.61259	0.420977
$328$	−4.60453	−0.254242
$329$	8.06040	0.444384
$330$	0	0
$331$	17.0164	0.935306	0.467653	−	0.883912i	$-0.345100\pi$
$331$	17.0164	0.935306	0.467653	+	0.883912i	$0.345100\pi$
$332$	−6.15361	−0.337723
$333$	7.55220	0.413858
$334$	21.5714	1.18034
$335$	0	0
$336$	4.44364	0.242420
$337$	−1.52461	−0.0830508	−0.0415254	−	0.999137i	$-0.513222\pi$
$337$	−1.52461	−0.0830508	−0.0415254	+	0.999137i	$0.513222\pi$
$338$	−5.67326	−0.308585
$339$	−7.70892	−0.418691
$340$	0	0
$341$	−9.23353	−0.500023
$342$	−0.616763	−0.0333507
$343$	1.00000	0.0539949
$344$	−5.35432	−0.288686
$345$	0	0
$346$	48.0880	2.58523
$347$	−17.4506	−0.936800	−0.468400	−	0.883517i	$-0.655169\pi$
$347$	−17.4506	−0.936800	−0.468400	+	0.883517i	$0.655169\pi$
$348$	5.53996	0.296973
$349$	6.85969	0.367191	0.183595	−	0.983002i	$-0.441226\pi$
$349$	6.85969	0.367191	0.183595	+	0.983002i	$0.441226\pi$
$350$	0	0
$351$	−3.17313	−0.169369
$352$	7.61676	0.405975
$353$	31.9313	1.69953	0.849765	−	0.527162i	$-0.176744\pi$
$353$	31.9313	1.69953	0.849765	+	0.527162i	$0.176744\pi$
$354$	13.6332	0.724595
$355$	0	0
$356$	−3.04088	−0.161166
$357$	6.85446	0.362776
$358$	−24.6925	−1.30504
$359$	−24.4342	−1.28959	−0.644795	−	0.764356i	$-0.723057\pi$
$359$	−24.4342	−1.28959	−0.644795	+	0.764356i	$0.723057\pi$
$360$	0	0
$361$	−18.8984	−0.994655
$362$	−6.25827	−0.328927
$363$	−1.00000	−0.0524864
$364$	5.53996	0.290373
$365$	0	0
$366$	3.87086	0.202333
$367$	−17.0716	−0.891129	−0.445565	−	0.895250i	$-0.646997\pi$
$367$	−17.0716	−0.891129	−0.445565	+	0.895250i	$0.646997\pi$
$368$	−8.31344	−0.433368
$369$	9.36266	0.487401
$370$	0	0
$371$	−0.508203	−0.0263846
$372$	−16.1208	−0.835824
$373$	−3.17836	−0.164569	−0.0822845	−	0.996609i	$-0.526222\pi$
$373$	−3.17836	−0.164569	−0.0822845	+	0.996609i	$0.526222\pi$
$374$	13.2663	0.685986
$375$	0	0
$376$	−3.96408	−0.204432
$377$	−10.0687	−0.518566
$378$	−1.93543	−0.0995479
$379$	3.93960	0.202364	0.101182	−	0.994868i	$-0.467738\pi$
$379$	3.93960	0.202364	0.101182	+	0.994868i	$0.467738\pi$
$380$	0	0
$381$	−5.49180	−0.281353
$382$	40.5962	2.07708
$383$	24.7581	1.26508	0.632541	−	0.774527i	$-0.282012\pi$
$383$	24.7581	1.26508	0.632541	+	0.774527i	$0.282012\pi$
$384$	−3.90262	−0.199155
$385$	0	0
$386$	−0.483728	−0.0246211
$387$	10.8873	0.553431
$388$	21.3871	1.08577
$389$	3.65375	0.185252	0.0926261	−	0.995701i	$-0.470474\pi$
$389$	3.65375	0.185252	0.0926261	+	0.995701i	$0.470474\pi$
$390$	0	0
$391$	−12.8238	−0.648526
$392$	−0.491797	−0.0248395
$393$	−4.00000	−0.201773
$394$	−35.8052	−1.80384
$395$	0	0
$396$	−1.74590	−0.0877347
$397$	−4.56337	−0.229029	−0.114515	−	0.993422i	$-0.536531\pi$
$397$	−4.56337	−0.229029	−0.114515	+	0.993422i	$0.536531\pi$
$398$	19.1044	0.957617
$399$	0.318669	0.0159534
$400$	0	0
$401$	−7.23353	−0.361225	−0.180613	−	0.983554i	$-0.557808\pi$
$401$	−7.23353	−0.361225	−0.180613	+	0.983554i	$0.557808\pi$
$402$	−5.15778	−0.257247
$403$	29.2992	1.45949
$404$	8.53268	0.424517
$405$	0	0
$406$	−6.14137	−0.304791
$407$	−7.55220	−0.374348
$408$	−3.37100	−0.166889
$409$	5.30749	0.262439	0.131219	−	0.991353i	$-0.458111\pi$
$409$	5.30749	0.262439	0.131219	+	0.991353i	$0.458111\pi$
$410$	0	0
$411$	15.6126	0.770112
$412$	1.11273	0.0548202
$413$	−7.04399	−0.346612
$414$	3.62093	0.177959
$415$	0	0
$416$	−24.1690	−1.18498
$417$	9.01641	0.441535
$418$	0.616763	0.0301669
$419$	−11.4231	−0.558053	−0.279026	−	0.960283i	$-0.590012\pi$
$419$	−11.4231	−0.558053	−0.279026	+	0.960283i	$0.590012\pi$
$420$	0	0
$421$	−27.4147	−1.33611	−0.668056	−	0.744111i	$-0.732873\pi$
$421$	−27.4147	−1.33611	−0.668056	+	0.744111i	$0.732873\pi$
$422$	−8.97526	−0.436909
$423$	8.06040	0.391910
$424$	0.249933	0.0121378
$425$	0	0
$426$	9.70892	0.470399
$427$	−2.00000	−0.0967868
$428$	−1.66909	−0.0806786
$429$	3.17313	0.153200
$430$	0	0
$431$	−2.28586	−0.110106	−0.0550529	−	0.998483i	$-0.517533\pi$
$431$	−2.28586	−0.110106	−0.0550529	+	0.998483i	$0.517533\pi$
$432$	4.44364	0.213795
$433$	−31.5714	−1.51723	−0.758613	−	0.651541i	$-0.774123\pi$
$433$	−31.5714	−1.51723	−0.758613	+	0.651541i	$0.774123\pi$
$434$	17.8709	0.857829
$435$	0	0
$436$	−13.2908	−0.636515
$437$	−0.596187	−0.0285195
$438$	−9.34209	−0.446382
$439$	−18.5275	−0.884267	−0.442133	−	0.896949i	$-0.645778\pi$
$439$	−18.5275	−0.884267	−0.442133	+	0.896949i	$0.645778\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−42.0958	−2.00229
$443$	−28.4342	−1.35095	−0.675476	−	0.737382i	$-0.736062\pi$
$443$	−28.4342	−1.35095	−0.675476	+	0.737382i	$0.736062\pi$
$444$	−13.1854	−0.625750
$445$	0	0
$446$	35.5079	1.68135
$447$	5.20594	0.246233
$448$	−5.85446	−0.276597
$449$	−5.68656	−0.268365	−0.134183	−	0.990957i	$-0.542841\pi$
$449$	−5.68656	−0.268365	−0.134183	+	0.990957i	$0.542841\pi$
$450$	0	0
$451$	−9.36266	−0.440871
$452$	13.4590	0.633057
$453$	−6.24993	−0.293647
$454$	−0.733661	−0.0344324
$455$	0	0
$456$	−0.156721	−0.00733911
$457$	13.0081	0.608492	0.304246	−	0.952594i	$-0.401596\pi$
$457$	13.0081	0.608492	0.304246	+	0.952594i	$0.401596\pi$
$458$	48.2744	2.25571
$459$	6.85446	0.319939
$460$	0	0
$461$	−6.37907	−0.297103	−0.148551	−	0.988905i	$-0.547461\pi$
$461$	−6.37907	−0.297103	−0.148551	+	0.988905i	$0.547461\pi$
$462$	1.93543	0.0900445
$463$	−34.0932	−1.58445	−0.792223	−	0.610232i	$-0.791076\pi$
$463$	−34.0932	−1.58445	−0.792223	+	0.610232i	$0.791076\pi$
$464$	14.1002	0.654586
$465$	0	0
$466$	−45.3871	−2.10252
$467$	−18.1484	−0.839807	−0.419903	−	0.907569i	$-0.637936\pi$
$467$	−18.1484	−0.839807	−0.419903	+	0.907569i	$0.637936\pi$
$468$	5.53996	0.256085
$469$	2.66492	0.123055
$470$	0	0
$471$	−18.1208	−0.834962
$472$	3.46421	0.159453
$473$	−10.8873	−0.500597
$474$	−9.70892	−0.445945
$475$	0	0
$476$	−11.9672	−0.548515
$477$	−0.508203	−0.0232690
$478$	9.82581	0.449422
$479$	−42.7498	−1.95329	−0.976644	−	0.214864i	$-0.931069\pi$
$479$	−42.7498	−1.95329	−0.976644	+	0.214864i	$0.931069\pi$
$480$	0	0
$481$	23.9641	1.09267
$482$	37.3421	1.70089
$483$	−1.87086	−0.0851273
$484$	1.74590	0.0793590
$485$	0	0
$486$	−1.93543	−0.0877930
$487$	−26.7909	−1.21401	−0.607007	−	0.794697i	$-0.707630\pi$
$487$	−26.7909	−1.21401	−0.607007	+	0.794697i	$0.707630\pi$
$488$	0.983593	0.0445252
$489$	−2.66492	−0.120512
$490$	0	0
$491$	31.6813	1.42976	0.714879	−	0.699248i	$-0.246482\pi$
$491$	31.6813	1.42976	0.714879	+	0.699248i	$0.246482\pi$
$492$	−16.3463	−0.736946
$493$	21.7501	0.979574
$494$	−1.95707	−0.0880526
$495$	0	0
$496$	−41.0304	−1.84232
$497$	−5.01641	−0.225017
$498$	6.82164	0.305685
$499$	−24.1260	−1.08003	−0.540015	−	0.841656i	$-0.681581\pi$
$499$	−24.1260	−1.08003	−0.540015	+	0.841656i	$0.681581\pi$
$500$	0	0
$501$	−11.1455	−0.497946
$502$	46.0674	2.05609
$503$	−30.8873	−1.37720	−0.688598	−	0.725144i	$-0.741773\pi$
$503$	−30.8873	−1.37720	−0.688598	+	0.725144i	$0.741773\pi$
$504$	−0.491797	−0.0219064
$505$	0	0
$506$	−3.62093	−0.160970
$507$	2.93126	0.130182
$508$	9.58812	0.425404
$509$	28.2088	1.25033	0.625166	−	0.780492i	$-0.285031\pi$
$509$	28.2088	1.25033	0.625166	+	0.780492i	$0.285031\pi$
$510$	0	0
$511$	4.82687	0.213528
$512$	29.4754	1.30264
$513$	0.318669	0.0140696
$514$	−28.8667	−1.27326
$515$	0	0
$516$	−19.0081	−0.836784
$517$	−8.06040	−0.354496
$518$	14.6168	0.642224
$519$	−24.8461	−1.09062
$520$	0	0
$521$	−33.7610	−1.47910	−0.739548	−	0.673104i	$-0.764961\pi$
$521$	−33.7610	−1.47910	−0.739548	+	0.673104i	$0.764961\pi$
$522$	−6.14137	−0.268801
$523$	−12.8185	−0.560515	−0.280258	−	0.959925i	$-0.590420\pi$
$523$	−12.8185	−0.560515	−0.280258	+	0.959925i	$0.590420\pi$
$524$	6.98359	0.305080
$525$	0	0
$526$	−5.65765	−0.246685
$527$	−63.2908	−2.75699
$528$	−4.44364	−0.193384
$529$	−19.4999	−0.847820
$530$	0	0
$531$	−7.04399	−0.305683
$532$	−0.556364	−0.0241215
$533$	29.7089	1.28684
$534$	3.37100	0.145877
$535$	0	0
$536$	−1.31060	−0.0566093
$537$	12.7581	0.550554
$538$	23.1617	0.998571
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−21.8625	−0.939943	−0.469972	−	0.882681i	$-0.655736\pi$
$541$	−21.8625	−0.939943	−0.469972	+	0.882681i	$0.655736\pi$
$542$	−39.3254	−1.68917
$543$	3.23353	0.138764
$544$	52.2088	2.23843
$545$	0	0
$546$	−6.14137	−0.262827
$547$	−23.4178	−1.00127	−0.500637	−	0.865657i	$-0.666901\pi$
$547$	−23.4178	−1.00127	−0.500637	+	0.865657i	$0.666901\pi$
$548$	−27.2580	−1.16440
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	1.01118	0.0430776
$552$	0.920085	0.0391614
$553$	5.01641	0.213319
$554$	−34.9446	−1.48465
$555$	0	0
$556$	−15.7417	−0.667598
$557$	6.91486	0.292992	0.146496	−	0.989211i	$-0.453200\pi$
$557$	6.91486	0.292992	0.146496	+	0.989211i	$0.453200\pi$
$558$	17.8709	0.756534
$559$	34.5467	1.46117
$560$	0	0
$561$	−6.85446	−0.289395
$562$	52.8255	2.22831
$563$	−11.8381	−0.498914	−0.249457	−	0.968386i	$-0.580252\pi$
$563$	−11.8381	−0.498914	−0.249457	+	0.968386i	$0.580252\pi$
$564$	−14.0726	−0.592565
$565$	0	0
$566$	−57.8503	−2.43163
$567$	1.00000	0.0419961
$568$	2.46705	0.103515
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	−15.2252	−0.637154	−0.318577	−	0.947897i	$-0.603205\pi$
$571$	−15.2252	−0.637154	−0.318577	+	0.947897i	$0.603205\pi$
$572$	−5.53996	−0.231637
$573$	−20.9753	−0.876254
$574$	18.1208	0.756347
$575$	0	0
$576$	−5.85446	−0.243936
$577$	−17.3215	−0.721104	−0.360552	−	0.932739i	$-0.617412\pi$
$577$	−17.3215	−0.721104	−0.360552	+	0.932739i	$0.617412\pi$
$578$	58.0312	2.41378
$579$	0.249933	0.0103868
$580$	0	0
$581$	−3.52461	−0.146225
$582$	−23.7089	−0.982766
$583$	0.508203	0.0210476
$584$	−2.37384	−0.0982302
$585$	0	0
$586$	8.41188	0.347492
$587$	−27.8678	−1.15023	−0.575113	−	0.818074i	$-0.695042\pi$
$587$	−27.8678	−1.15023	−0.575113	+	0.818074i	$0.695042\pi$
$588$	−1.74590	−0.0719996
$589$	−2.94244	−0.121241
$590$	0	0
$591$	18.4999	0.760983
$592$	−33.5592	−1.37927
$593$	24.3463	0.999781	0.499890	−	0.866089i	$-0.333374\pi$
$593$	24.3463	0.999781	0.499890	+	0.866089i	$0.333374\pi$
$594$	1.93543	0.0794118
$595$	0	0
$596$	−9.08904	−0.372302
$597$	−9.87086	−0.403988
$598$	11.4897	0.469848
$599$	21.0164	0.858707	0.429354	−	0.903136i	$-0.358741\pi$
$599$	21.0164	0.858707	0.429354	+	0.903136i	$0.358741\pi$
$600$	0	0
$601$	40.9477	1.67029	0.835145	−	0.550030i	$-0.185384\pi$
$601$	40.9477	1.67029	0.835145	+	0.550030i	$0.185384\pi$
$602$	21.0716	0.858813
$603$	2.66492	0.108524
$604$	10.9117	0.443993
$605$	0	0
$606$	−9.45898	−0.384245
$607$	14.0276	0.569362	0.284681	−	0.958622i	$-0.408112\pi$
$607$	14.0276	0.569362	0.284681	+	0.958622i	$0.408112\pi$
$608$	2.42723	0.0984371
$609$	3.17313	0.128582
$610$	0	0
$611$	25.5767	1.03472
$612$	−11.9672	−0.483745
$613$	−18.5306	−0.748442	−0.374221	−	0.927339i	$-0.622090\pi$
$613$	−18.5306	−0.748442	−0.374221	+	0.927339i	$0.622090\pi$
$614$	40.1760	1.62137
$615$	0	0
$616$	0.491797	0.0198151
$617$	−2.43424	−0.0979987	−0.0489994	−	0.998799i	$-0.515603\pi$
$617$	−2.43424	−0.0979987	−0.0489994	+	0.998799i	$0.515603\pi$
$618$	−1.23353	−0.0496197
$619$	−30.4259	−1.22292	−0.611460	−	0.791275i	$-0.709418\pi$
$619$	−30.4259	−1.22292	−0.611460	+	0.791275i	$0.709418\pi$
$620$	0	0
$621$	−1.87086	−0.0750752
$622$	15.4835	0.620830
$623$	−1.74173	−0.0697809
$624$	14.1002	0.564461
$625$	0	0
$626$	−15.7334	−0.628833
$627$	−0.318669	−0.0127264
$628$	31.6371	1.26246
$629$	−51.7662	−2.06405
$630$	0	0
$631$	34.9836	1.39267	0.696337	−	0.717715i	$-0.254812\pi$
$631$	34.9836	1.39267	0.696337	+	0.717715i	$0.254812\pi$
$632$	−2.46705	−0.0981341
$633$	4.63734	0.184318
$634$	38.6925	1.53668
$635$	0	0
$636$	0.887271	0.0351826
$637$	3.17313	0.125724
$638$	6.14137	0.243139
$639$	−5.01641	−0.198446
$640$	0	0
$641$	8.56337	0.338233	0.169116	−	0.985596i	$-0.445909\pi$
$641$	8.56337	0.338233	0.169116	+	0.985596i	$0.445909\pi$
$642$	1.85029	0.0730251
$643$	5.11273	0.201626	0.100813	−	0.994905i	$-0.467856\pi$
$643$	5.11273	0.201626	0.100813	+	0.994905i	$0.467856\pi$
$644$	3.26634	0.128712
$645$	0	0
$646$	4.22758	0.166332
$647$	−25.7693	−1.01310	−0.506548	−	0.862212i	$-0.669079\pi$
$647$	−25.7693	−1.01310	−0.506548	+	0.862212i	$0.669079\pi$
$648$	−0.491797	−0.0193196
$649$	7.04399	0.276501
$650$	0	0
$651$	−9.23353	−0.361890
$652$	4.65269	0.182213
$653$	47.8953	1.87429	0.937145	−	0.348941i	$-0.113459\pi$
$653$	47.8953	1.87429	0.937145	+	0.348941i	$0.113459\pi$
$654$	14.7337	0.576132
$655$	0	0
$656$	−41.6043	−1.62437
$657$	4.82687	0.188314
$658$	15.6004	0.608165
$659$	8.95601	0.348877	0.174438	−	0.984668i	$-0.444189\pi$
$659$	8.95601	0.348877	0.174438	+	0.984668i	$0.444189\pi$
$660$	0	0
$661$	−10.7993	−0.420044	−0.210022	−	0.977697i	$-0.567353\pi$
$661$	−10.7993	−0.420044	−0.210022	+	0.977697i	$0.567353\pi$
$662$	32.9341	1.28002
$663$	21.7501	0.844703
$664$	1.73339	0.0672686
$665$	0	0
$666$	14.6168	0.566388
$667$	−5.93649	−0.229862
$668$	19.4590	0.752891
$669$	−18.3463	−0.709307
$670$	0	0
$671$	2.00000	0.0772091
$672$	7.61676	0.293823
$673$	−32.2499	−1.24314	−0.621572	−	0.783357i	$-0.713506\pi$
$673$	−32.2499	−1.24314	−0.621572	+	0.783357i	$0.713506\pi$
$674$	−2.95078	−0.113660
$675$	0	0
$676$	−5.11769	−0.196834
$677$	27.7089	1.06494	0.532470	−	0.846449i	$-0.321264\pi$
$677$	27.7089	1.06494	0.532470	+	0.846449i	$0.321264\pi$
$678$	−14.9201	−0.573002
$679$	12.2499	0.470109
$680$	0	0
$681$	0.379068	0.0145259
$682$	−17.8709	−0.684311
$683$	−22.3156	−0.853881	−0.426941	−	0.904280i	$-0.640409\pi$
$683$	−22.3156	−0.853881	−0.426941	+	0.904280i	$0.640409\pi$
$684$	−0.556364	−0.0212731
$685$	0	0
$686$	1.93543	0.0738951
$687$	−24.9424	−0.951614
$688$	−48.3791	−1.84443
$689$	−1.61259	−0.0614349
$690$	0	0
$691$	25.1372	0.956264	0.478132	−	0.878288i	$-0.341314\pi$
$691$	25.1372	0.956264	0.478132	+	0.878288i	$0.341314\pi$
$692$	43.3788	1.64901
$693$	−1.00000	−0.0379869
$694$	−33.7745	−1.28206
$695$	0	0
$696$	−1.56053	−0.0591519
$697$	−64.1760	−2.43084
$698$	13.2765	0.502521
$699$	23.4506	0.886985
$700$	0	0
$701$	−19.2747	−0.727995	−0.363997	−	0.931400i	$-0.618588\pi$
$701$	−19.2747	−0.727995	−0.363997	+	0.931400i	$0.618588\pi$
$702$	−6.14137	−0.231791
$703$	−2.40665	−0.0907686
$704$	5.85446	0.220648
$705$	0	0
$706$	61.8008	2.32590
$707$	4.88727	0.183805
$708$	12.2981	0.462191
$709$	9.76098	0.366581	0.183291	−	0.983059i	$-0.441325\pi$
$709$	9.76098	0.366581	0.183291	+	0.983059i	$0.441325\pi$
$710$	0	0
$711$	5.01641	0.188130
$712$	0.856577	0.0321016
$713$	17.2747	0.646942
$714$	13.2663	0.496480
$715$	0	0
$716$	−22.2744	−0.832434
$717$	−5.07681	−0.189597
$718$	−47.2908	−1.76488
$719$	14.0276	0.523141	0.261570	−	0.965184i	$-0.415760\pi$
$719$	14.0276	0.523141	0.261570	+	0.965184i	$0.415760\pi$
$720$	0	0
$721$	0.637339	0.0237357
$722$	−36.5767	−1.36124
$723$	−19.2939	−0.717549
$724$	−5.64541	−0.209810
$725$	0	0
$726$	−1.93543	−0.0718306
$727$	34.3051	1.27231	0.636153	−	0.771563i	$-0.280525\pi$
$727$	34.3051	1.27231	0.636153	+	0.771563i	$0.280525\pi$
$728$	−1.56053	−0.0578372
$729$	1.00000	0.0370370
$730$	0	0
$731$	−74.6263	−2.76016
$732$	3.49180	0.129061
$733$	10.7581	0.397361	0.198680	−	0.980064i	$-0.436334\pi$
$733$	10.7581	0.397361	0.198680	+	0.980064i	$0.436334\pi$
$734$	−33.0409	−1.21956
$735$	0	0
$736$	−14.2499	−0.525259
$737$	−2.66492	−0.0981637
$738$	18.1208	0.667036
$739$	−6.38741	−0.234965	−0.117482	−	0.993075i	$-0.537482\pi$
$739$	−6.38741	−0.234965	−0.117482	+	0.993075i	$0.537482\pi$
$740$	0	0
$741$	1.01118	0.0371466
$742$	−0.983593	−0.0361088
$743$	23.1096	0.847810	0.423905	−	0.905707i	$-0.360659\pi$
$743$	23.1096	0.847810	0.423905	+	0.905707i	$0.360659\pi$
$744$	4.54102	0.166482
$745$	0	0
$746$	−6.15149	−0.225222
$747$	−3.52461	−0.128959
$748$	11.9672	0.437564
$749$	−0.956008	−0.0349318
$750$	0	0
$751$	31.8678	1.16287	0.581435	−	0.813593i	$-0.302491\pi$
$751$	31.8678	1.16287	0.581435	+	0.813593i	$0.302491\pi$
$752$	−35.8175	−1.30613
$753$	−23.8021	−0.867398
$754$	−19.4874	−0.709688
$755$	0	0
$756$	−1.74590	−0.0634977
$757$	48.3103	1.75587	0.877934	−	0.478781i	$-0.158921\pi$
$757$	48.3103	1.75587	0.877934	+	0.478781i	$0.158921\pi$
$758$	7.62483	0.276946
$759$	1.87086	0.0679081
$760$	0	0
$761$	−17.8625	−0.647516	−0.323758	−	0.946140i	$-0.604946\pi$
$761$	−17.8625	−0.647516	−0.323758	+	0.946140i	$0.604946\pi$
$762$	−10.6290	−0.385048
$763$	−7.61259	−0.275594
$764$	36.6207	1.32489
$765$	0	0
$766$	47.9177	1.73134
$767$	−22.3515	−0.807065
$768$	−19.2622	−0.695064
$769$	−24.8820	−0.897269	−0.448635	−	0.893715i	$-0.648090\pi$
$769$	−24.8820	−0.897269	−0.448635	+	0.893715i	$0.648090\pi$
$770$	0	0
$771$	14.9149	0.537145
$772$	−0.436357	−0.0157048
$773$	34.9700	1.25778	0.628892	−	0.777492i	$-0.283509\pi$
$773$	34.9700	1.25778	0.628892	+	0.777492i	$0.283509\pi$
$774$	21.0716	0.757402
$775$	0	0
$776$	−6.02448	−0.216266
$777$	−7.55220	−0.270933
$778$	7.07158	0.253528
$779$	−2.98359	−0.106898
$780$	0	0
$781$	5.01641	0.179501
$782$	−24.8195	−0.887544
$783$	3.17313	0.113398
$784$	−4.44364	−0.158701
$785$	0	0
$786$	−7.74173	−0.276138
$787$	15.1648	0.540566	0.270283	−	0.962781i	$-0.412883\pi$
$787$	15.1648	0.540566	0.270283	+	0.962781i	$0.412883\pi$
$788$	−32.2989	−1.15060
$789$	2.92319	0.104068
$790$	0	0
$791$	7.70892	0.274097
$792$	0.491797	0.0174752
$793$	−6.34625	−0.225362
$794$	−8.83210	−0.313440
$795$	0	0
$796$	17.2335	0.610826
$797$	−8.24470	−0.292042	−0.146021	−	0.989281i	$-0.546647\pi$
$797$	−8.24470	−0.292042	−0.146021	+	0.989281i	$0.546647\pi$
$798$	0.616763	0.0218332
$799$	−55.2497	−1.95459
$800$	0	0
$801$	−1.74173	−0.0615410
$802$	−14.0000	−0.494357
$803$	−4.82687	−0.170337
$804$	−4.65269	−0.164088
$805$	0	0
$806$	56.7065	1.99740
$807$	−11.9672	−0.421265
$808$	−2.40354	−0.0845564
$809$	29.8433	1.04923	0.524617	−	0.851338i	$-0.324209\pi$
$809$	29.8433	1.04923	0.524617	+	0.851338i	$0.324209\pi$
$810$	0	0
$811$	−16.6321	−0.584032	−0.292016	−	0.956413i	$-0.594326\pi$
$811$	−16.6321	−0.584032	−0.292016	+	0.956413i	$0.594326\pi$
$812$	−5.53996	−0.194414
$813$	20.3187	0.712607
$814$	−14.6168	−0.512317
$815$	0	0
$816$	−30.4587	−1.06627
$817$	−3.46944	−0.121380
$818$	10.2723	0.359162
$819$	3.17313	0.110878
$820$	0	0
$821$	30.3327	1.05862	0.529309	−	0.848429i	$-0.322451\pi$
$821$	30.3327	1.05862	0.529309	+	0.848429i	$0.322451\pi$
$822$	30.2171	1.05394
$823$	18.4067	0.641616	0.320808	−	0.947144i	$-0.396046\pi$
$823$	18.4067	0.641616	0.320808	+	0.947144i	$0.396046\pi$
$824$	−0.313441	−0.0109192
$825$	0	0
$826$	−13.6332	−0.474359
$827$	−45.4559	−1.58066	−0.790328	−	0.612684i	$-0.790090\pi$
$827$	−45.4559	−1.58066	−0.790328	+	0.612684i	$0.790090\pi$
$828$	3.26634	0.113513
$829$	−20.3463	−0.706655	−0.353327	−	0.935500i	$-0.614950\pi$
$829$	−20.3463	−0.706655	−0.353327	+	0.935500i	$0.614950\pi$
$830$	0	0
$831$	18.0552	0.626327
$832$	−18.5769	−0.644040
$833$	−6.85446	−0.237493
$834$	17.4506	0.604266
$835$	0	0
$836$	0.556364	0.0192423
$837$	−9.23353	−0.319157
$838$	−22.1086	−0.763728
$839$	16.1812	0.558637	0.279318	−	0.960199i	$-0.409891\pi$
$839$	16.1812	0.558637	0.279318	+	0.960199i	$0.409891\pi$
$840$	0	0
$841$	−18.9313	−0.652802
$842$	−53.0593	−1.82855
$843$	−27.2939	−0.940053
$844$	−8.09632	−0.278687
$845$	0	0
$846$	15.6004	0.536351
$847$	1.00000	0.0343604
$848$	2.25827	0.0775493
$849$	29.8901	1.02583
$850$	0	0
$851$	14.1291	0.484341
$852$	8.75814	0.300049
$853$	20.9836	0.718465	0.359232	−	0.933248i	$-0.383039\pi$
$853$	20.9836	0.718465	0.359232	+	0.933248i	$0.383039\pi$
$854$	−3.87086	−0.132458
$855$	0	0
$856$	0.470162	0.0160698
$857$	−4.79095	−0.163656	−0.0818279	−	0.996646i	$-0.526076\pi$
$857$	−4.79095	−0.163656	−0.0818279	+	0.996646i	$0.526076\pi$
$858$	6.14137	0.209663
$859$	−9.96719	−0.340076	−0.170038	−	0.985438i	$-0.554389\pi$
$859$	−9.96719	−0.340076	−0.170038	+	0.985438i	$0.554389\pi$
$860$	0	0
$861$	−9.36266	−0.319079
$862$	−4.42412	−0.150686
$863$	−25.5470	−0.869629	−0.434814	−	0.900520i	$-0.643186\pi$
$863$	−25.5470	−0.869629	−0.434814	+	0.900520i	$0.643186\pi$
$864$	7.61676	0.259128
$865$	0	0
$866$	−61.1044	−2.07641
$867$	−29.9836	−1.01830
$868$	16.1208	0.547176
$869$	−5.01641	−0.170170
$870$	0	0
$871$	8.45614	0.286525
$872$	3.74385	0.126783
$873$	12.2499	0.414597
$874$	−1.15388	−0.0390306
$875$	0	0
$876$	−8.42723	−0.284730
$877$	50.9893	1.72179	0.860893	−	0.508787i	$-0.169906\pi$
$877$	50.9893	1.72179	0.860893	+	0.508787i	$0.169906\pi$
$878$	−35.8586	−1.21017
$879$	−4.34625	−0.146596
$880$	0	0
$881$	32.1895	1.08449	0.542246	−	0.840219i	$-0.317574\pi$
$881$	32.1895	1.08449	0.542246	+	0.840219i	$0.317574\pi$
$882$	1.93543	0.0651694
$883$	−36.6154	−1.23221	−0.616104	−	0.787665i	$-0.711290\pi$
$883$	−36.6154	−1.23221	−0.616104	+	0.787665i	$0.711290\pi$
$884$	−37.9734	−1.27718
$885$	0	0
$886$	−55.0325	−1.84885
$887$	48.2004	1.61841	0.809206	−	0.587525i	$-0.199897\pi$
$887$	48.2004	1.61841	0.809206	+	0.587525i	$0.199897\pi$
$888$	3.71414	0.124639
$889$	5.49180	0.184189
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	32.0307	1.07247
$893$	−2.56860	−0.0859550
$894$	10.0757	0.336983
$895$	0	0
$896$	3.90262	0.130377
$897$	−5.93649	−0.198214
$898$	−11.0060	−0.367273
$899$	−29.2992	−0.977181
$900$	0	0
$901$	3.48346	0.116051
$902$	−18.1208	−0.603357
$903$	−10.8873	−0.362306
$904$	−3.79122	−0.126094
$905$	0	0
$906$	−12.0963	−0.401873
$907$	−22.9013	−0.760425	−0.380212	−	0.924899i	$-0.624149\pi$
$907$	−22.9013	−0.760425	−0.380212	+	0.924899i	$0.624149\pi$
$908$	−0.661814	−0.0219631
$909$	4.88727	0.162101
$910$	0	0
$911$	−36.0552	−1.19456	−0.597281	−	0.802032i	$-0.703752\pi$
$911$	−36.0552	−1.19456	−0.597281	+	0.802032i	$0.703752\pi$
$912$	−1.41605	−0.0468901
$913$	3.52461	0.116648
$914$	25.1762	0.832756
$915$	0	0
$916$	43.5470	1.43883
$917$	4.00000	0.132092
$918$	13.2663	0.437854
$919$	−28.3379	−0.934782	−0.467391	−	0.884051i	$-0.654806\pi$
$919$	−28.3379	−0.934782	−0.467391	+	0.884051i	$0.654806\pi$
$920$	0	0
$921$	−20.7581	−0.684004
$922$	−12.3463	−0.406602
$923$	−15.9177	−0.523937
$924$	1.74590	0.0574358
$925$	0	0
$926$	−65.9851	−2.16841
$927$	0.637339	0.0209329
$928$	24.1690	0.793385
$929$	5.08514	0.166838	0.0834191	−	0.996515i	$-0.473416\pi$
$929$	5.08514	0.166838	0.0834191	+	0.996515i	$0.473416\pi$
$930$	0	0
$931$	−0.318669	−0.0104440
$932$	−40.9424	−1.34111
$933$	−8.00000	−0.261908
$934$	−35.1250	−1.14932
$935$	0	0
$936$	−1.56053	−0.0510076
$937$	−32.2088	−1.05222	−0.526108	−	0.850418i	$-0.676349\pi$
$937$	−32.2088	−1.05222	−0.526108	+	0.850418i	$0.676349\pi$
$938$	5.15778	0.168407
$939$	8.12914	0.265284
$940$	0	0
$941$	32.7805	1.06861	0.534307	−	0.845291i	$-0.320573\pi$
$941$	32.7805	1.06861	0.534307	+	0.845291i	$0.320573\pi$
$942$	−35.0716	−1.14269
$943$	17.5163	0.570408
$944$	31.3009	1.01876
$945$	0	0
$946$	−21.0716	−0.685096
$947$	27.3627	0.889167	0.444584	−	0.895737i	$-0.353352\pi$
$947$	27.3627	0.889167	0.444584	+	0.895737i	$0.353352\pi$
$948$	−8.75814	−0.284451
$949$	15.3163	0.497188
$950$	0	0
$951$	−19.9917	−0.648274
$952$	3.37100	0.109255
$953$	24.6894	0.799768	0.399884	−	0.916566i	$-0.369050\pi$
$953$	24.6894	0.799768	0.399884	+	0.916566i	$0.369050\pi$
$954$	−0.983593	−0.0318450
$955$	0	0
$956$	8.86359	0.286669
$957$	−3.17313	−0.102573
$958$	−82.7393	−2.67319
$959$	−15.6126	−0.504157
$960$	0	0
$961$	54.2580	1.75026
$962$	46.3808	1.49538
$963$	−0.956008	−0.0308069
$964$	33.6852	1.08493
$965$	0	0
$966$	−3.62093	−0.116502
$967$	−21.3298	−0.685922	−0.342961	−	0.939350i	$-0.611430\pi$
$967$	−21.3298	−0.685922	−0.342961	+	0.939350i	$0.611430\pi$
$968$	−0.491797	−0.0158069
$969$	−2.18431	−0.0701700
$970$	0	0
$971$	28.4946	0.914436	0.457218	−	0.889355i	$-0.348846\pi$
$971$	28.4946	0.914436	0.457218	+	0.889355i	$0.348846\pi$
$972$	−1.74590	−0.0559997
$973$	−9.01641	−0.289053
$974$	−51.8521	−1.66145
$975$	0	0
$976$	8.88727	0.284475
$977$	19.8157	0.633960	0.316980	−	0.948432i	$-0.397331\pi$
$977$	19.8157	0.633960	0.316980	+	0.948432i	$0.397331\pi$
$978$	−5.15778	−0.164928
$979$	1.74173	0.0556659
$980$	0	0
$981$	−7.61259	−0.243051
$982$	61.3171	1.95671
$983$	53.7745	1.71514	0.857571	−	0.514366i	$-0.171973\pi$
$983$	53.7745	1.71514	0.857571	+	0.514366i	$0.171973\pi$
$984$	4.60453	0.146787
$985$	0	0
$986$	42.0958	1.34060
$987$	−8.06040	−0.256565
$988$	−1.76541	−0.0561653
$989$	20.3686	0.647684
$990$	0	0
$991$	49.7693	1.58097	0.790487	−	0.612479i	$-0.209827\pi$
$991$	49.7693	1.58097	0.790487	+	0.612479i	$0.209827\pi$
$992$	−70.3296	−2.23297
$993$	−17.0164	−0.539999
$994$	−9.70892	−0.307948
$995$	0	0
$996$	6.15361	0.194985
$997$	−0.659696	−0.0208928	−0.0104464	−	0.999945i	$-0.503325\pi$
$997$	−0.659696	−0.0208928	−0.0104464	+	0.999945i	$0.503325\pi$
$998$	−46.6943	−1.47808
$999$	−7.55220	−0.238941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5775.2.a.bp.1.3		3
5.4	even	2		231.2.a.e.1.1	✓	3
15.14	odd	2		693.2.a.l.1.3		3
20.19	odd	2		3696.2.a.bo.1.3		3
35.34	odd	2		1617.2.a.t.1.1		3
55.54	odd	2		2541.2.a.bg.1.3		3
105.104	even	2		4851.2.a.bi.1.3		3
165.164	even	2		7623.2.a.cd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.a.e.1.1	✓	3	5.4	even	2
693.2.a.l.1.3		3	15.14	odd	2
1617.2.a.t.1.1		3	35.34	odd	2
2541.2.a.bg.1.3		3	55.54	odd	2
3696.2.a.bo.1.3		3	20.19	odd	2
4851.2.a.bi.1.3		3	105.104	even	2
5775.2.a.bp.1.3		3	1.1	even	1	trivial
7623.2.a.cd.1.1		3	165.164	even	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:	\( N \)	\(=\)	\( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5775.a (trivial)

\(f(q)\)	\(=\)	\(q+1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} -1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.93543 q^{2} -1.00000 q^{3} +1.74590 q^{4} -1.93543 q^{6} +1.00000 q^{7} -0.491797 q^{8} +1.00000 q^{9} -1.00000 q^{11} -1.74590 q^{12} +3.17313 q^{13} +1.93543 q^{14} -4.44364 q^{16} -6.85446 q^{17} +1.93543 q^{18} -0.318669 q^{19} -1.00000 q^{21} -1.93543 q^{22} +1.87086 q^{23} +0.491797 q^{24} +6.14137 q^{26} -1.00000 q^{27} +1.74590 q^{28} -3.17313 q^{29} +9.23353 q^{31} -7.61676 q^{32} +1.00000 q^{33} -13.2663 q^{34} +1.74590 q^{36} +7.55220 q^{37} -0.616763 q^{38} -3.17313 q^{39} +9.36266 q^{41} -1.93543 q^{42} +10.8873 q^{43} -1.74590 q^{44} +3.62093 q^{46} +8.06040 q^{47} +4.44364 q^{48} +1.00000 q^{49} +6.85446 q^{51} +5.53996 q^{52} -0.508203 q^{53} -1.93543 q^{54} -0.491797 q^{56} +0.318669 q^{57} -6.14137 q^{58} -7.04399 q^{59} -2.00000 q^{61} +17.8709 q^{62} +1.00000 q^{63} -5.85446 q^{64} +1.93543 q^{66} +2.66492 q^{67} -11.9672 q^{68} -1.87086 q^{69} -5.01641 q^{71} -0.491797 q^{72} +4.82687 q^{73} +14.6168 q^{74} -0.556364 q^{76} -1.00000 q^{77} -6.14137 q^{78} +5.01641 q^{79} +1.00000 q^{81} +18.1208 q^{82} -3.52461 q^{83} -1.74590 q^{84} +21.0716 q^{86} +3.17313 q^{87} +0.491797 q^{88} -1.74173 q^{89} +3.17313 q^{91} +3.26634 q^{92} -9.23353 q^{93} +15.6004 q^{94} +7.61676 q^{96} +12.2499 q^{97} +1.93543 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} - 3 q^{21} + 2 q^{22} - 10 q^{23} + 3 q^{24} - q^{26} - 3 q^{27} + 6 q^{28} - 4 q^{29} - 2 q^{31} - 8 q^{32} + 3 q^{33} - 4 q^{34} + 6 q^{36} + 13 q^{38} - 4 q^{39} + 14 q^{41} + 2 q^{42} + 14 q^{43} - 6 q^{44} + 28 q^{46} + 4 q^{48} + 3 q^{49} + 8 q^{51} + 29 q^{52} + 2 q^{54} - 3 q^{56} + 8 q^{57} + q^{58} - 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 2 q^{66} + 4 q^{67} - 42 q^{68} + 10 q^{69} - 12 q^{71} - 3 q^{72} + 20 q^{73} + 29 q^{74} - 11 q^{76} - 3 q^{77} + q^{78} + 12 q^{79} + 3 q^{81} + 6 q^{82} - 6 q^{83} - 6 q^{84} + 24 q^{86} + 4 q^{87} + 3 q^{88} + 26 q^{89} + 4 q^{91} - 26 q^{92} + 2 q^{93} + 35 q^{94} + 8 q^{96} + 4 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 - 3 * q^21 + 2 * q^22 - 10 * q^23 + 3 * q^24 - q^26 - 3 * q^27 + 6 * q^28 - 4 * q^29 - 2 * q^31 - 8 * q^32 + 3 * q^33 - 4 * q^34 + 6 * q^36 + 13 * q^38 - 4 * q^39 + 14 * q^41 + 2 * q^42 + 14 * q^43 - 6 * q^44 + 28 * q^46 + 4 * q^48 + 3 * q^49 + 8 * q^51 + 29 * q^52 + 2 * q^54 - 3 * q^56 + 8 * q^57 + q^58 - 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 2 * q^66 + 4 * q^67 - 42 * q^68 + 10 * q^69 - 12 * q^71 - 3 * q^72 + 20 * q^73 + 29 * q^74 - 11 * q^76 - 3 * q^77 + q^78 + 12 * q^79 + 3 * q^81 + 6 * q^82 - 6 * q^83 - 6 * q^84 + 24 * q^86 + 4 * q^87 + 3 * q^88 + 26 * q^89 + 4 * q^91 - 26 * q^92 + 2 * q^93 + 35 * q^94 + 8 * q^96 + 4 * q^97 - 2 * q^98 - 3 * q^99

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