LMFDB - Embedded newform 1725.2.a.bi.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1725,2,Mod(1,1725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1725, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1725 = 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1725.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:	$13.7741943487$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	1725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} -2.34292 q^{6} -4.48929 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} -2.34292 q^{6} -4.48929 q^{7} +3.48929 q^{8} +1.00000 q^{9} -1.14637 q^{11} -3.48929 q^{12} -0.853635 q^{13} -10.5181 q^{14} +1.19656 q^{16} -1.34292 q^{17} +2.34292 q^{18} -3.83221 q^{19} +4.48929 q^{21} -2.68585 q^{22} -1.00000 q^{23} -3.48929 q^{24} -2.00000 q^{26} -1.00000 q^{27} -15.6644 q^{28} -8.02877 q^{29} +2.19656 q^{31} -4.17513 q^{32} +1.14637 q^{33} -3.14637 q^{34} +3.48929 q^{36} +2.48929 q^{37} -8.97858 q^{38} +0.853635 q^{39} +11.3001 q^{41} +10.5181 q^{42} -10.6858 q^{43} -4.00000 q^{44} -2.34292 q^{46} -1.53948 q^{47} -1.19656 q^{48} +13.1537 q^{49} +1.34292 q^{51} -2.97858 q^{52} -4.02877 q^{53} -2.34292 q^{54} -15.6644 q^{56} +3.83221 q^{57} -18.8108 q^{58} -15.0073 q^{59} -5.83221 q^{61} +5.14637 q^{62} -4.48929 q^{63} -12.1751 q^{64} +2.68585 q^{66} +11.5682 q^{67} -4.68585 q^{68} +1.00000 q^{69} +4.32150 q^{71} +3.48929 q^{72} +13.1035 q^{73} +5.83221 q^{74} -13.3717 q^{76} +5.14637 q^{77} +2.00000 q^{78} +0.585462 q^{79} +1.00000 q^{81} +26.4752 q^{82} -5.63565 q^{83} +15.6644 q^{84} -25.0361 q^{86} +8.02877 q^{87} -4.00000 q^{88} -0.100384 q^{89} +3.83221 q^{91} -3.48929 q^{92} -2.19656 q^{93} -3.60688 q^{94} +4.17513 q^{96} -11.5640 q^{97} +30.8181 q^{98} -1.14637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 3 q^{3} + 3 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 - 3 * q^3 + 3 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} - 3 q^{3} + 3 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 2 q^{11} - 3 q^{12} - 4 q^{13} - 6 q^{14} - q^{16} + 2 q^{17} + q^{18} + 2 q^{19} + 6 q^{21} + 4 q^{22} - 3 q^{23} - 3 q^{24} - 6 q^{26} - 3 q^{27} - 20 q^{28} - 6 q^{29} + 2 q^{31} + 7 q^{32} + 2 q^{33} - 8 q^{34} + 3 q^{36} - 12 q^{38} + 4 q^{39} - 2 q^{41} + 6 q^{42} - 20 q^{43} - 12 q^{44} - q^{46} + 6 q^{47} + q^{48} + 5 q^{49} - 2 q^{51} + 6 q^{52} + 6 q^{53} - q^{54} - 20 q^{56} - 2 q^{57} - 28 q^{58} - 12 q^{59} - 4 q^{61} + 14 q^{62} - 6 q^{63} - 17 q^{64} - 4 q^{66} + 6 q^{67} - 2 q^{68} + 3 q^{69} - 8 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} - 16 q^{76} + 14 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{81} + 24 q^{82} - 8 q^{83} + 20 q^{84} - 24 q^{86} + 6 q^{87} - 12 q^{88} + 6 q^{89} - 2 q^{91} - 3 q^{92} - 2 q^{93} - 20 q^{94} - 7 q^{96} - 14 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q + q^2 - 3 * q^3 + 3 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 2 * q^11 - 3 * q^12 - 4 * q^13 - 6 * q^14 - q^16 + 2 * q^17 + q^18 + 2 * q^19 + 6 * q^21 + 4 * q^22 - 3 * q^23 - 3 * q^24 - 6 * q^26 - 3 * q^27 - 20 * q^28 - 6 * q^29 + 2 * q^31 + 7 * q^32 + 2 * q^33 - 8 * q^34 + 3 * q^36 - 12 * q^38 + 4 * q^39 - 2 * q^41 + 6 * q^42 - 20 * q^43 - 12 * q^44 - q^46 + 6 * q^47 + q^48 + 5 * q^49 - 2 * q^51 + 6 * q^52 + 6 * q^53 - q^54 - 20 * q^56 - 2 * q^57 - 28 * q^58 - 12 * q^59 - 4 * q^61 + 14 * q^62 - 6 * q^63 - 17 * q^64 - 4 * q^66 + 6 * q^67 - 2 * q^68 + 3 * q^69 - 8 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 - 16 * q^76 + 14 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^81 + 24 * q^82 - 8 * q^83 + 20 * q^84 - 24 * q^86 + 6 * q^87 - 12 * q^88 + 6 * q^89 - 2 * q^91 - 3 * q^92 - 2 * q^93 - 20 * q^94 - 7 * q^96 - 14 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.34292	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$2$	2.34292	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.48929	1.74464
$5$	0	0
$5$	0	0
$6$	−2.34292	−0.956494
$7$	−4.48929	−1.69679	−0.848396	−	0.529362i	$-0.822431\pi$
$7$	−4.48929	−1.69679	−0.848396	+	0.529362i	$0.822431\pi$
$8$	3.48929	1.23365
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.14637	−0.345642	−0.172821	−	0.984953i	$-0.555288\pi$
$11$	−1.14637	−0.345642	−0.172821	+	0.984953i	$0.555288\pi$
$12$	−3.48929	−1.00727
$13$	−0.853635	−0.236756	−0.118378	−	0.992969i	$-0.537769\pi$
$13$	−0.853635	−0.236756	−0.118378	+	0.992969i	$0.537769\pi$
$14$	−10.5181	−2.81107
$15$	0	0
$16$	1.19656	0.299139
$17$	−1.34292	−0.325707	−0.162853	−	0.986650i	$-0.552070\pi$
$17$	−1.34292	−0.325707	−0.162853	+	0.986650i	$0.552070\pi$
$18$	2.34292	0.552232
$19$	−3.83221	−0.879170	−0.439585	−	0.898201i	$-0.644874\pi$
$19$	−3.83221	−0.879170	−0.439585	+	0.898201i	$0.644874\pi$
$20$	0	0
$21$	4.48929	0.979643
$22$	−2.68585	−0.572624
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.48929	−0.712248
$25$	0	0
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	−15.6644	−2.96030
$29$	−8.02877	−1.49091	−0.745453	−	0.666559i	$-0.767767\pi$
$29$	−8.02877	−1.49091	−0.745453	+	0.666559i	$0.767767\pi$
$30$	0	0
$31$	2.19656	0.394513	0.197257	−	0.980352i	$-0.436797\pi$
$31$	2.19656	0.394513	0.197257	+	0.980352i	$0.436797\pi$
$32$	−4.17513	−0.738067
$33$	1.14637	0.199557
$34$	−3.14637	−0.539597
$35$	0	0
$36$	3.48929	0.581548
$37$	2.48929	0.409237	0.204618	−	0.978842i	$-0.434405\pi$
$37$	2.48929	0.409237	0.204618	+	0.978842i	$0.434405\pi$
$38$	−8.97858	−1.45652
$39$	0.853635	0.136691
$40$	0	0
$41$	11.3001	1.76478	0.882388	−	0.470523i	$-0.155935\pi$
$41$	11.3001	1.76478	0.882388	+	0.470523i	$0.155935\pi$
$42$	10.5181	1.62297
$43$	−10.6858	−1.62958	−0.814788	−	0.579759i	$-0.803147\pi$
$43$	−10.6858	−1.62958	−0.814788	+	0.579759i	$0.803147\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	−2.34292	−0.345445
$47$	−1.53948	−0.224556	−0.112278	−	0.993677i	$-0.535815\pi$
$47$	−1.53948	−0.224556	−0.112278	+	0.993677i	$0.535815\pi$
$48$	−1.19656	−0.172708
$49$	13.1537	1.87910
$50$	0	0
$51$	1.34292	0.188047
$52$	−2.97858	−0.413054
$53$	−4.02877	−0.553394	−0.276697	−	0.960957i	$-0.589240\pi$
$53$	−4.02877	−0.553394	−0.276697	+	0.960957i	$0.589240\pi$
$54$	−2.34292	−0.318831
$55$	0	0
$56$	−15.6644	−2.09325
$57$	3.83221	0.507589
$58$	−18.8108	−2.46998
$59$	−15.0073	−1.95379	−0.976895	−	0.213720i	$-0.931442\pi$
$59$	−15.0073	−1.95379	−0.976895	+	0.213720i	$0.931442\pi$
$60$	0	0
$61$	−5.83221	−0.746738	−0.373369	−	0.927683i	$-0.621797\pi$
$61$	−5.83221	−0.746738	−0.373369	+	0.927683i	$0.621797\pi$
$62$	5.14637	0.653589
$63$	−4.48929	−0.565597
$64$	−12.1751	−1.52189
$65$	0	0
$66$	2.68585	0.330605
$67$	11.5682	1.41329	0.706643	−	0.707570i	$-0.250209\pi$
$67$	11.5682	1.41329	0.706643	+	0.707570i	$0.250209\pi$
$68$	−4.68585	−0.568242
$69$	1.00000	0.120386
$70$	0	0
$71$	4.32150	0.512868	0.256434	−	0.966562i	$-0.417452\pi$
$71$	4.32150	0.512868	0.256434	+	0.966562i	$0.417452\pi$
$72$	3.48929	0.411217
$73$	13.1035	1.53365	0.766825	−	0.641856i	$-0.221835\pi$
$73$	13.1035	1.53365	0.766825	+	0.641856i	$0.221835\pi$
$74$	5.83221	0.677981
$75$	0	0
$76$	−13.3717	−1.53384
$77$	5.14637	0.586483
$78$	2.00000	0.226455
$79$	0.585462	0.0658696	0.0329348	−	0.999458i	$-0.489515\pi$
$79$	0.585462	0.0658696	0.0329348	+	0.999458i	$0.489515\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	26.4752	2.92370
$83$	−5.63565	−0.618593	−0.309297	−	0.950966i	$-0.600094\pi$
$83$	−5.63565	−0.618593	−0.309297	+	0.950966i	$0.600094\pi$
$84$	15.6644	1.70913
$85$	0	0
$86$	−25.0361	−2.69971
$87$	8.02877	0.860774
$88$	−4.00000	−0.426401
$89$	−0.100384	−0.0106407	−0.00532035	−	0.999986i	$-0.501694\pi$
$89$	−0.100384	−0.0106407	−0.00532035	+	0.999986i	$0.501694\pi$
$90$	0	0
$91$	3.83221	0.401725
$92$	−3.48929	−0.363783
$93$	−2.19656	−0.227772
$94$	−3.60688	−0.372022
$95$	0	0
$96$	4.17513	0.426123
$97$	−11.5640	−1.17415	−0.587075	−	0.809532i	$-0.699721\pi$
$97$	−11.5640	−1.17415	−0.587075	+	0.809532i	$0.699721\pi$
$98$	30.8181	3.11310
$99$	−1.14637	−0.115214
$100$	0	0
$101$	11.6932	1.16352	0.581758	−	0.813362i	$-0.302365\pi$
$101$	11.6932	1.16352	0.581758	+	0.813362i	$0.302365\pi$
$102$	3.14637	0.311537
$103$	19.7220	1.94326	0.971631	−	0.236501i	$-0.0760006\pi$
$103$	19.7220	1.94326	0.971631	+	0.236501i	$0.0760006\pi$
$104$	−2.97858	−0.292074
$105$	0	0
$106$	−9.43910	−0.916806
$107$	−5.44331	−0.526224	−0.263112	−	0.964765i	$-0.584749\pi$
$107$	−5.44331	−0.526224	−0.263112	+	0.964765i	$0.584749\pi$
$108$	−3.48929	−0.335757
$109$	−12.5181	−1.19901	−0.599506	−	0.800370i	$-0.704636\pi$
$109$	−12.5181	−1.19901	−0.599506	+	0.800370i	$0.704636\pi$
$110$	0	0
$111$	−2.48929	−0.236273
$112$	−5.37169	−0.507577
$113$	14.1292	1.32916	0.664579	−	0.747218i	$-0.268611\pi$
$113$	14.1292	1.32916	0.664579	+	0.747218i	$0.268611\pi$
$114$	8.97858	0.840921
$115$	0	0
$116$	−28.0147	−2.60110
$117$	−0.853635	−0.0789185
$118$	−35.1611	−3.23684
$119$	6.02877	0.552656
$120$	0	0
$121$	−9.68585	−0.880531
$122$	−13.6644	−1.23712
$123$	−11.3001	−1.01889
$124$	7.66442	0.688286
$125$	0	0
$126$	−10.5181	−0.937023
$127$	−5.48194	−0.486444	−0.243222	−	0.969971i	$-0.578204\pi$
$127$	−5.48194	−0.486444	−0.243222	+	0.969971i	$0.578204\pi$
$128$	−20.1751	−1.78325
$129$	10.6858	0.940836
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	4.00000	0.348155
$133$	17.2039	1.49177
$134$	27.1035	2.34139
$135$	0	0
$136$	−4.68585	−0.401808
$137$	−11.7648	−1.00514	−0.502568	−	0.864538i	$-0.667611\pi$
$137$	−11.7648	−1.00514	−0.502568	+	0.864538i	$0.667611\pi$
$138$	2.34292	0.199443
$139$	8.15371	0.691589	0.345794	−	0.938310i	$-0.387609\pi$
$139$	8.15371	0.691589	0.345794	+	0.938310i	$0.387609\pi$
$140$	0	0
$141$	1.53948	0.129648
$142$	10.1249	0.849666
$143$	0.978577	0.0818327
$144$	1.19656	0.0997131
$145$	0	0
$146$	30.7005	2.54079
$147$	−13.1537	−1.08490
$148$	8.68585	0.713972
$149$	−3.73183	−0.305723	−0.152862	−	0.988248i	$-0.548849\pi$
$149$	−3.73183	−0.305723	−0.152862	+	0.988248i	$0.548849\pi$
$150$	0	0
$151$	16.6430	1.35439	0.677194	−	0.735804i	$-0.263196\pi$
$151$	16.6430	1.35439	0.677194	+	0.735804i	$0.263196\pi$
$152$	−13.3717	−1.08459
$153$	−1.34292	−0.108569
$154$	12.0575	0.971624
$155$	0	0
$156$	2.97858	0.238477
$157$	13.2327	1.05608	0.528041	−	0.849219i	$-0.322927\pi$
$157$	13.2327	1.05608	0.528041	+	0.849219i	$0.322927\pi$
$158$	1.37169	0.109126
$159$	4.02877	0.319502
$160$	0	0
$161$	4.48929	0.353806
$162$	2.34292	0.184077
$163$	−16.3931	−1.28401	−0.642004	−	0.766701i	$-0.721897\pi$
$163$	−16.3931	−1.28401	−0.642004	+	0.766701i	$0.721897\pi$
$164$	39.4292	3.07891
$165$	0	0
$166$	−13.2039	−1.02482
$167$	−3.04598	−0.235705	−0.117853	−	0.993031i	$-0.537601\pi$
$167$	−3.04598	−0.235705	−0.117853	+	0.993031i	$0.537601\pi$
$168$	15.6644	1.20854
$169$	−12.2713	−0.943947
$170$	0	0
$171$	−3.83221	−0.293057
$172$	−37.2860	−2.84303
$173$	24.9357	1.89583	0.947914	−	0.318526i	$-0.103188\pi$
$173$	24.9357	1.89583	0.947914	+	0.318526i	$0.103188\pi$
$174$	18.8108	1.42604
$175$	0	0
$176$	−1.37169	−0.103395
$177$	15.0073	1.12802
$178$	−0.235192	−0.0176284
$179$	−6.68585	−0.499724	−0.249862	−	0.968282i	$-0.580385\pi$
$179$	−6.68585	−0.499724	−0.249862	+	0.968282i	$0.580385\pi$
$180$	0	0
$181$	−20.6002	−1.53120	−0.765599	−	0.643318i	$-0.777557\pi$
$181$	−20.6002	−1.53120	−0.765599	+	0.643318i	$0.777557\pi$
$182$	8.97858	0.665536
$183$	5.83221	0.431129
$184$	−3.48929	−0.257234
$185$	0	0
$186$	−5.14637	−0.377350
$187$	1.53948	0.112578
$188$	−5.37169	−0.391771
$189$	4.48929	0.326548
$190$	0	0
$191$	4.95402	0.358460	0.179230	−	0.983807i	$-0.442639\pi$
$191$	4.95402	0.358460	0.179230	+	0.983807i	$0.442639\pi$
$192$	12.1751	0.878665
$193$	−6.05754	−0.436031	−0.218016	−	0.975945i	$-0.569958\pi$
$193$	−6.05754	−0.436031	−0.218016	+	0.975945i	$0.569958\pi$
$194$	−27.0937	−1.94521
$195$	0	0
$196$	45.8971	3.27836
$197$	24.4078	1.73898	0.869492	−	0.493947i	$-0.164446\pi$
$197$	24.4078	1.73898	0.869492	+	0.493947i	$0.164446\pi$
$198$	−2.68585	−0.190875
$199$	−3.85677	−0.273399	−0.136700	−	0.990613i	$-0.543650\pi$
$199$	−3.85677	−0.273399	−0.136700	+	0.990613i	$0.543650\pi$
$200$	0	0
$201$	−11.5682	−0.815961
$202$	27.3963	1.92759
$203$	36.0435	2.52976
$204$	4.68585	0.328075
$205$	0	0
$206$	46.2070	3.21940
$207$	−1.00000	−0.0695048
$208$	−1.02142	−0.0708229
$209$	4.39312	0.303878
$210$	0	0
$211$	−0.824865	−0.0567861	−0.0283930	−	0.999597i	$-0.509039\pi$
$211$	−0.824865	−0.0567861	−0.0283930	+	0.999597i	$0.509039\pi$
$212$	−14.0575	−0.965476
$213$	−4.32150	−0.296104
$214$	−12.7533	−0.871794
$215$	0	0
$216$	−3.48929	−0.237416
$217$	−9.86098	−0.669407
$218$	−29.3288	−1.98640
$219$	−13.1035	−0.885454
$220$	0	0
$221$	1.14637	0.0771129
$222$	−5.83221	−0.391432
$223$	−5.56404	−0.372596	−0.186298	−	0.982493i	$-0.559649\pi$
$223$	−5.56404	−0.372596	−0.186298	+	0.982493i	$0.559649\pi$
$224$	18.7434	1.25235
$225$	0	0
$226$	33.1035	2.20201
$227$	−16.5855	−1.10082	−0.550408	−	0.834896i	$-0.685528\pi$
$227$	−16.5855	−1.10082	−0.550408	+	0.834896i	$0.685528\pi$
$228$	13.3717	0.885562
$229$	6.64300	0.438982	0.219491	−	0.975615i	$-0.429560\pi$
$229$	6.64300	0.438982	0.219491	+	0.975615i	$0.429560\pi$
$230$	0	0
$231$	−5.14637	−0.338606
$232$	−28.0147	−1.83925
$233$	14.3931	0.942924	0.471462	−	0.881886i	$-0.343726\pi$
$233$	14.3931	0.942924	0.471462	+	0.881886i	$0.343726\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−52.3650	−3.40867
$237$	−0.585462	−0.0380298
$238$	14.1249	0.915584
$239$	−13.1077	−0.847869	−0.423934	−	0.905693i	$-0.639351\pi$
$239$	−13.1077	−0.847869	−0.423934	+	0.905693i	$0.639351\pi$
$240$	0	0
$241$	12.5181	0.806359	0.403179	−	0.915121i	$-0.367905\pi$
$241$	12.5181	0.806359	0.403179	+	0.915121i	$0.367905\pi$
$242$	−22.6932	−1.45877
$243$	−1.00000	−0.0641500
$244$	−20.3503	−1.30279
$245$	0	0
$246$	−26.4752	−1.68800
$247$	3.27131	0.208148
$248$	7.66442	0.486691
$249$	5.63565	0.357145
$250$	0	0
$251$	−26.3503	−1.66321	−0.831607	−	0.555364i	$-0.812579\pi$
$251$	−26.3503	−1.66321	−0.831607	+	0.555364i	$0.812579\pi$
$252$	−15.6644	−0.986766
$253$	1.14637	0.0720714
$254$	−12.8438	−0.805890
$255$	0	0
$256$	−22.9185	−1.43241
$257$	27.0116	1.68493	0.842467	−	0.538747i	$-0.181102\pi$
$257$	27.0116	1.68493	0.842467	+	0.538747i	$0.181102\pi$
$258$	25.0361	1.55868
$259$	−11.1751	−0.694389
$260$	0	0
$261$	−8.02877	−0.496968
$262$	0	0
$263$	−21.8855	−1.34952	−0.674760	−	0.738037i	$-0.735753\pi$
$263$	−21.8855	−1.34952	−0.674760	+	0.738037i	$0.735753\pi$
$264$	4.00000	0.246183
$265$	0	0
$266$	40.3074	2.47141
$267$	0.100384	0.00614341
$268$	40.3650	2.46568
$269$	3.69319	0.225178	0.112589	−	0.993642i	$-0.464086\pi$
$269$	3.69319	0.225178	0.112589	+	0.993642i	$0.464086\pi$
$270$	0	0
$271$	0.288520	0.0175264	0.00876318	−	0.999962i	$-0.497211\pi$
$271$	0.288520	0.0175264	0.00876318	+	0.999962i	$0.497211\pi$
$272$	−1.60688	−0.0974317
$273$	−3.83221	−0.231936
$274$	−27.5640	−1.66520
$275$	0	0
$276$	3.48929	0.210030
$277$	−21.3288	−1.28153	−0.640763	−	0.767739i	$-0.721382\pi$
$277$	−21.3288	−1.28153	−0.640763	+	0.767739i	$0.721382\pi$
$278$	19.1035	1.14575
$279$	2.19656	0.131504
$280$	0	0
$281$	−26.6676	−1.59085	−0.795427	−	0.606050i	$-0.792753\pi$
$281$	−26.6676	−1.59085	−0.795427	+	0.606050i	$0.792753\pi$
$282$	3.60688	0.214787
$283$	−25.9185	−1.54070	−0.770348	−	0.637624i	$-0.779918\pi$
$283$	−25.9185	−1.54070	−0.770348	+	0.637624i	$0.779918\pi$
$284$	15.0790	0.894772
$285$	0	0
$286$	2.29273	0.135572
$287$	−50.7293	−2.99446
$288$	−4.17513	−0.246022
$289$	−15.1966	−0.893915
$290$	0	0
$291$	11.5640	0.677896
$292$	45.7220	2.67568
$293$	−13.6503	−0.797462	−0.398731	−	0.917068i	$-0.630549\pi$
$293$	−13.6503	−0.797462	−0.398731	+	0.917068i	$0.630549\pi$
$294$	−30.8181	−1.79735
$295$	0	0
$296$	8.68585	0.504855
$297$	1.14637	0.0665189
$298$	−8.74338	−0.506491
$299$	0.853635	0.0493670
$300$	0	0
$301$	47.9718	2.76505
$302$	38.9933	2.24381
$303$	−11.6932	−0.671756
$304$	−4.58546	−0.262994
$305$	0	0
$306$	−3.14637	−0.179866
$307$	9.78937	0.558709	0.279354	−	0.960188i	$-0.409880\pi$
$307$	9.78937	0.558709	0.279354	+	0.960188i	$0.409880\pi$
$308$	17.9572	1.02320
$309$	−19.7220	−1.12194
$310$	0	0
$311$	−3.32885	−0.188762	−0.0943808	−	0.995536i	$-0.530087\pi$
$311$	−3.32885	−0.188762	−0.0943808	+	0.995536i	$0.530087\pi$
$312$	2.97858	0.168629
$313$	18.8824	1.06730	0.533648	−	0.845707i	$-0.320821\pi$
$313$	18.8824	1.06730	0.533648	+	0.845707i	$0.320821\pi$
$314$	31.0031	1.74961
$315$	0	0
$316$	2.04285	0.114919
$317$	8.06740	0.453111	0.226555	−	0.973998i	$-0.427254\pi$
$317$	8.06740	0.453111	0.226555	+	0.973998i	$0.427254\pi$
$318$	9.43910	0.529318
$319$	9.20390	0.515320
$320$	0	0
$321$	5.44331	0.303816
$322$	10.5181	0.586148
$323$	5.14637	0.286351
$324$	3.48929	0.193849
$325$	0	0
$326$	−38.4078	−2.12721
$327$	12.5181	0.692250
$328$	39.4292	2.17712
$329$	6.91117	0.381025
$330$	0	0
$331$	−26.6388	−1.46420	−0.732100	−	0.681197i	$-0.761460\pi$
$331$	−26.6388	−1.46420	−0.732100	+	0.681197i	$0.761460\pi$
$332$	−19.6644	−1.07923
$333$	2.48929	0.136412
$334$	−7.13650	−0.390492
$335$	0	0
$336$	5.37169	0.293050
$337$	8.54262	0.465346	0.232673	−	0.972555i	$-0.425253\pi$
$337$	8.54262	0.465346	0.232673	+	0.972555i	$0.425253\pi$
$338$	−28.7507	−1.56383
$339$	−14.1292	−0.767390
$340$	0	0
$341$	−2.51806	−0.136360
$342$	−8.97858	−0.485506
$343$	−27.6258	−1.49165
$344$	−37.2860	−2.01033
$345$	0	0
$346$	58.4225	3.14081
$347$	16.2499	0.872340	0.436170	−	0.899864i	$-0.356335\pi$
$347$	16.2499	0.872340	0.436170	+	0.899864i	$0.356335\pi$
$348$	28.0147	1.50175
$349$	23.1898	1.24132	0.620662	−	0.784079i	$-0.286864\pi$
$349$	23.1898	1.24132	0.620662	+	0.784079i	$0.286864\pi$
$350$	0	0
$351$	0.853635	0.0455636
$352$	4.78623	0.255107
$353$	7.48194	0.398224	0.199112	−	0.979977i	$-0.436194\pi$
$353$	7.48194	0.398224	0.199112	+	0.979977i	$0.436194\pi$
$354$	35.1611	1.86879
$355$	0	0
$356$	−0.350269	−0.0185642
$357$	−6.02877	−0.319076
$358$	−15.6644	−0.827890
$359$	1.87506	0.0989617	0.0494809	−	0.998775i	$-0.484243\pi$
$359$	1.87506	0.0989617	0.0494809	+	0.998775i	$0.484243\pi$
$360$	0	0
$361$	−4.31415	−0.227061
$362$	−48.2646	−2.53673
$363$	9.68585	0.508375
$364$	13.3717	0.700867
$365$	0	0
$366$	13.6644	0.714251
$367$	4.68164	0.244379	0.122190	−	0.992507i	$-0.461008\pi$
$367$	4.68164	0.244379	0.122190	+	0.992507i	$0.461008\pi$
$368$	−1.19656	−0.0623749
$369$	11.3001	0.588259
$370$	0	0
$371$	18.0863	0.938994
$372$	−7.66442	−0.397382
$373$	−18.6430	−0.965298	−0.482649	−	0.875814i	$-0.660325\pi$
$373$	−18.6430	−0.965298	−0.482649	+	0.875814i	$0.660325\pi$
$374$	3.60688	0.186508
$375$	0	0
$376$	−5.37169	−0.277024
$377$	6.85363	0.352980
$378$	10.5181	0.540991
$379$	29.8715	1.53439	0.767197	−	0.641412i	$-0.221651\pi$
$379$	29.8715	1.53439	0.767197	+	0.641412i	$0.221651\pi$
$380$	0	0
$381$	5.48194	0.280848
$382$	11.6069	0.593860
$383$	−20.5714	−1.05115	−0.525574	−	0.850748i	$-0.676150\pi$
$383$	−20.5714	−1.05115	−0.525574	+	0.850748i	$0.676150\pi$
$384$	20.1751	1.02956
$385$	0	0
$386$	−14.1923	−0.722371
$387$	−10.6858	−0.543192
$388$	−40.3503	−2.04847
$389$	−2.33558	−0.118418	−0.0592092	−	0.998246i	$-0.518858\pi$
$389$	−2.33558	−0.118418	−0.0592092	+	0.998246i	$0.518858\pi$
$390$	0	0
$391$	1.34292	0.0679145
$392$	45.8971	2.31815
$393$	0	0
$394$	57.1856	2.88097
$395$	0	0
$396$	−4.00000	−0.201008
$397$	−29.1365	−1.46232	−0.731160	−	0.682207i	$-0.761020\pi$
$397$	−29.1365	−1.46232	−0.731160	+	0.682207i	$0.761020\pi$
$398$	−9.03612	−0.452940
$399$	−17.2039	−0.861272
$400$	0	0
$401$	−14.8353	−0.740842	−0.370421	−	0.928864i	$-0.620787\pi$
$401$	−14.8353	−0.740842	−0.370421	+	0.928864i	$0.620787\pi$
$402$	−27.1035	−1.35180
$403$	−1.87506	−0.0934033
$404$	40.8009	2.02992
$405$	0	0
$406$	84.4471	4.19104
$407$	−2.85363	−0.141449
$408$	4.68585	0.231984
$409$	−38.0189	−1.87991	−0.939957	−	0.341293i	$-0.889135\pi$
$409$	−38.0189	−1.87991	−0.939957	+	0.341293i	$0.889135\pi$
$410$	0	0
$411$	11.7648	0.580315
$412$	68.8156	3.39030
$413$	67.3723	3.31517
$414$	−2.34292	−0.115148
$415$	0	0
$416$	3.56404	0.174741
$417$	−8.15371	−0.399289
$418$	10.2927	0.503434
$419$	21.8469	1.06729	0.533646	−	0.845708i	$-0.320822\pi$
$419$	21.8469	1.06729	0.533646	+	0.845708i	$0.320822\pi$
$420$	0	0
$421$	21.4391	1.04488	0.522439	−	0.852677i	$-0.325022\pi$
$421$	21.4391	1.04488	0.522439	+	0.852677i	$0.325022\pi$
$422$	−1.93260	−0.0940773
$423$	−1.53948	−0.0748521
$424$	−14.0575	−0.682694
$425$	0	0
$426$	−10.1249	−0.490555
$427$	26.1825	1.26706
$428$	−18.9933	−0.918074
$429$	−0.978577	−0.0472461
$430$	0	0
$431$	29.8223	1.43649	0.718246	−	0.695789i	$-0.244945\pi$
$431$	29.8223	1.43649	0.718246	+	0.695789i	$0.244945\pi$
$432$	−1.19656	−0.0575694
$433$	0.925249	0.0444647	0.0222323	−	0.999753i	$-0.492923\pi$
$433$	0.925249	0.0444647	0.0222323	+	0.999753i	$0.492923\pi$
$434$	−23.1035	−1.10900
$435$	0	0
$436$	−43.6791	−2.09185
$437$	3.83221	0.183320
$438$	−30.7005	−1.46693
$439$	−21.6791	−1.03469	−0.517344	−	0.855778i	$-0.673079\pi$
$439$	−21.6791	−1.03469	−0.517344	+	0.855778i	$0.673079\pi$
$440$	0	0
$441$	13.1537	0.626367
$442$	2.68585	0.127753
$443$	−5.20390	−0.247245	−0.123622	−	0.992329i	$-0.539451\pi$
$443$	−5.20390	−0.247245	−0.123622	+	0.992329i	$0.539451\pi$
$444$	−8.68585	−0.412212
$445$	0	0
$446$	−13.0361	−0.617278
$447$	3.73183	0.176509
$448$	54.6577	2.58233
$449$	−10.8578	−0.512413	−0.256207	−	0.966622i	$-0.582473\pi$
$449$	−10.8578	−0.512413	−0.256207	+	0.966622i	$0.582473\pi$
$450$	0	0
$451$	−12.9540	−0.609981
$452$	49.3007	2.31891
$453$	−16.6430	−0.781956
$454$	−38.8585	−1.82372
$455$	0	0
$456$	13.3717	0.626187
$457$	−27.2755	−1.27589	−0.637947	−	0.770080i	$-0.720216\pi$
$457$	−27.2755	−1.27589	−0.637947	+	0.770080i	$0.720216\pi$
$458$	15.5640	0.727260
$459$	1.34292	0.0626823
$460$	0	0
$461$	20.2070	0.941136	0.470568	−	0.882364i	$-0.344049\pi$
$461$	20.2070	0.941136	0.470568	+	0.882364i	$0.344049\pi$
$462$	−12.0575	−0.560967
$463$	−8.03298	−0.373324	−0.186662	−	0.982424i	$-0.559767\pi$
$463$	−8.03298	−0.373324	−0.186662	+	0.982424i	$0.559767\pi$
$464$	−9.60688	−0.445988
$465$	0	0
$466$	33.7220	1.56214
$467$	19.4580	0.900409	0.450204	−	0.892926i	$-0.351351\pi$
$467$	19.4580	0.900409	0.450204	+	0.892926i	$0.351351\pi$
$468$	−2.97858	−0.137685
$469$	−51.9332	−2.39805
$470$	0	0
$471$	−13.2327	−0.609729
$472$	−52.3650	−2.41029
$473$	12.2499	0.563250
$474$	−1.37169	−0.0630039
$475$	0	0
$476$	21.0361	0.964189
$477$	−4.02877	−0.184465
$478$	−30.7104	−1.40466
$479$	28.9540	1.32294	0.661471	−	0.749970i	$-0.269932\pi$
$479$	28.9540	1.32294	0.661471	+	0.749970i	$0.269932\pi$
$480$	0	0
$481$	−2.12494	−0.0968890
$482$	29.3288	1.33589
$483$	−4.48929	−0.204270
$484$	−33.7967	−1.53621
$485$	0	0
$486$	−2.34292	−0.106277
$487$	−20.8108	−0.943027	−0.471513	−	0.881859i	$-0.656292\pi$
$487$	−20.8108	−0.943027	−0.471513	+	0.881859i	$0.656292\pi$
$488$	−20.3503	−0.921213
$489$	16.3931	0.741322
$490$	0	0
$491$	35.1140	1.58467	0.792336	−	0.610084i	$-0.208865\pi$
$491$	35.1140	1.58467	0.792336	+	0.610084i	$0.208865\pi$
$492$	−39.4292	−1.77761
$493$	10.7820	0.485598
$494$	7.66442	0.344839
$495$	0	0
$496$	2.62831	0.118014
$497$	−19.4005	−0.870230
$498$	13.2039	0.591681
$499$	−7.31836	−0.327615	−0.163807	−	0.986492i	$-0.552378\pi$
$499$	−7.31836	−0.327615	−0.163807	+	0.986492i	$0.552378\pi$
$500$	0	0
$501$	3.04598	0.136084
$502$	−61.7367	−2.75544
$503$	22.0006	0.980959	0.490479	−	0.871453i	$-0.336822\pi$
$503$	22.0006	0.980959	0.490479	+	0.871453i	$0.336822\pi$
$504$	−15.6644	−0.697749
$505$	0	0
$506$	2.68585	0.119400
$507$	12.2713	0.544988
$508$	−19.1281	−0.848671
$509$	−35.4783	−1.57255	−0.786275	−	0.617877i	$-0.787993\pi$
$509$	−35.4783	−1.57255	−0.786275	+	0.617877i	$0.787993\pi$
$510$	0	0
$511$	−58.8255	−2.60229
$512$	−13.3461	−0.589818
$513$	3.83221	0.169196
$514$	63.2860	2.79143
$515$	0	0
$516$	37.2860	1.64142
$517$	1.76481	0.0776161
$518$	−26.1825	−1.15039
$519$	−24.9357	−1.09456
$520$	0	0
$521$	21.4966	0.941785	0.470892	−	0.882191i	$-0.343932\pi$
$521$	21.4966	0.941785	0.470892	+	0.882191i	$0.343932\pi$
$522$	−18.8108	−0.823326
$523$	11.3288	0.495376	0.247688	−	0.968840i	$-0.420329\pi$
$523$	11.3288	0.495376	0.247688	+	0.968840i	$0.420329\pi$
$524$	0	0
$525$	0	0
$526$	−51.2761	−2.23575
$527$	−2.94981	−0.128496
$528$	1.37169	0.0596952
$529$	1.00000	0.0434783
$530$	0	0
$531$	−15.0073	−0.651263
$532$	60.0294	2.60260
$533$	−9.64614	−0.417821
$534$	0.235192	0.0101778
$535$	0	0
$536$	40.3650	1.74350
$537$	6.68585	0.288516
$538$	8.65287	0.373052
$539$	−15.0790	−0.649497
$540$	0	0
$541$	−7.67912	−0.330151	−0.165075	−	0.986281i	$-0.552787\pi$
$541$	−7.67912	−0.330151	−0.165075	+	0.986281i	$0.552787\pi$
$542$	0.675981	0.0290358
$543$	20.6002	0.884037
$544$	5.60688	0.240393
$545$	0	0
$546$	−8.97858	−0.384248
$547$	−31.5296	−1.34811	−0.674054	−	0.738682i	$-0.735449\pi$
$547$	−31.5296	−1.34811	−0.674054	+	0.738682i	$0.735449\pi$
$548$	−41.0508	−1.75360
$549$	−5.83221	−0.248913
$550$	0	0
$551$	30.7679	1.31076
$552$	3.48929	0.148514
$553$	−2.62831	−0.111767
$554$	−49.9718	−2.12310
$555$	0	0
$556$	28.4507	1.20658
$557$	10.1292	0.429186	0.214593	−	0.976704i	$-0.431157\pi$
$557$	10.1292	0.429186	0.214593	+	0.976704i	$0.431157\pi$
$558$	5.14637	0.217863
$559$	9.12181	0.385811
$560$	0	0
$561$	−1.53948	−0.0649969
$562$	−62.4800	−2.63556
$563$	−40.7146	−1.71592	−0.857958	−	0.513719i	$-0.828267\pi$
$563$	−40.7146	−1.71592	−0.857958	+	0.513719i	$0.828267\pi$
$564$	5.37169	0.226189
$565$	0	0
$566$	−60.7251	−2.55247
$567$	−4.48929	−0.188532
$568$	15.0790	0.632699
$569$	1.66442	0.0697763	0.0348881	−	0.999391i	$-0.488893\pi$
$569$	1.66442	0.0697763	0.0348881	+	0.999391i	$0.488893\pi$
$570$	0	0
$571$	−41.8469	−1.75124	−0.875619	−	0.483002i	$-0.839546\pi$
$571$	−41.8469	−1.75124	−0.875619	+	0.483002i	$0.839546\pi$
$572$	3.41454	0.142769
$573$	−4.95402	−0.206957
$574$	−118.855	−4.96091
$575$	0	0
$576$	−12.1751	−0.507297
$577$	−21.6069	−0.899506	−0.449753	−	0.893153i	$-0.648488\pi$
$577$	−21.6069	−0.899506	−0.449753	+	0.893153i	$0.648488\pi$
$578$	−35.6044	−1.48095
$579$	6.05754	0.251743
$580$	0	0
$581$	25.3001	1.04962
$582$	27.0937	1.12307
$583$	4.61844	0.191276
$584$	45.7220	1.89199
$585$	0	0
$586$	−31.9817	−1.32115
$587$	−0.393115	−0.0162256	−0.00811280	−	0.999967i	$-0.502582\pi$
$587$	−0.393115	−0.0162256	−0.00811280	+	0.999967i	$0.502582\pi$
$588$	−45.8971	−1.89276
$589$	−8.41767	−0.346844
$590$	0	0
$591$	−24.4078	−1.00400
$592$	2.97858	0.122419
$593$	8.31729	0.341550	0.170775	−	0.985310i	$-0.445373\pi$
$593$	8.31729	0.341550	0.170775	+	0.985310i	$0.445373\pi$
$594$	2.68585	0.110202
$595$	0	0
$596$	−13.0214	−0.533378
$597$	3.85677	0.157847
$598$	2.00000	0.0817861
$599$	9.03612	0.369206	0.184603	−	0.982813i	$-0.440900\pi$
$599$	9.03612	0.369206	0.184603	+	0.982813i	$0.440900\pi$
$600$	0	0
$601$	−27.6602	−1.12828	−0.564142	−	0.825678i	$-0.690793\pi$
$601$	−27.6602	−1.12828	−0.564142	+	0.825678i	$0.690793\pi$
$602$	112.394	4.58085
$603$	11.5682	0.471096
$604$	58.0722	2.36293
$605$	0	0
$606$	−27.3963	−1.11290
$607$	−29.6461	−1.20330	−0.601650	−	0.798760i	$-0.705490\pi$
$607$	−29.6461	−1.20330	−0.601650	+	0.798760i	$0.705490\pi$
$608$	16.0000	0.648886
$609$	−36.0435	−1.46055
$610$	0	0
$611$	1.31415	0.0531650
$612$	−4.68585	−0.189414
$613$	−39.4868	−1.59486	−0.797428	−	0.603414i	$-0.793807\pi$
$613$	−39.4868	−1.59486	−0.797428	+	0.603414i	$0.793807\pi$
$614$	22.9357	0.925611
$615$	0	0
$616$	17.9572	0.723514
$617$	−16.8641	−0.678924	−0.339462	−	0.940620i	$-0.610245\pi$
$617$	−16.8641	−0.678924	−0.339462	+	0.940620i	$0.610245\pi$
$618$	−46.2070	−1.85872
$619$	2.74338	0.110266	0.0551330	−	0.998479i	$-0.482442\pi$
$619$	2.74338	0.110266	0.0551330	+	0.998479i	$0.482442\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	−7.79923	−0.312721
$623$	0.450654	0.0180551
$624$	1.02142	0.0408896
$625$	0	0
$626$	44.2400	1.76819
$627$	−4.39312	−0.175444
$628$	46.1726	1.84249
$629$	−3.34292	−0.133291
$630$	0	0
$631$	−9.93260	−0.395410	−0.197705	−	0.980262i	$-0.563349\pi$
$631$	−9.93260	−0.395410	−0.197705	+	0.980262i	$0.563349\pi$
$632$	2.04285	0.0812600
$633$	0.824865	0.0327855
$634$	18.9013	0.750667
$635$	0	0
$636$	14.0575	0.557418
$637$	−11.2285	−0.444888
$638$	21.5640	0.853728
$639$	4.32150	0.170956
$640$	0	0
$641$	−10.6184	−0.419403	−0.209702	−	0.977765i	$-0.567249\pi$
$641$	−10.6184	−0.419403	−0.209702	+	0.977765i	$0.567249\pi$
$642$	12.7533	0.503331
$643$	−20.5959	−0.812225	−0.406112	−	0.913823i	$-0.633116\pi$
$643$	−20.5959	−0.812225	−0.406112	+	0.913823i	$0.633116\pi$
$644$	15.6644	0.617265
$645$	0	0
$646$	12.0575	0.474398
$647$	6.71883	0.264144	0.132072	−	0.991240i	$-0.457837\pi$
$647$	6.71883	0.264144	0.132072	+	0.991240i	$0.457837\pi$
$648$	3.48929	0.137072
$649$	17.2039	0.675312
$650$	0	0
$651$	9.86098	0.386482
$652$	−57.2003	−2.24014
$653$	4.07583	0.159499	0.0797497	−	0.996815i	$-0.474588\pi$
$653$	4.07583	0.159499	0.0797497	+	0.996815i	$0.474588\pi$
$654$	29.3288	1.14685
$655$	0	0
$656$	13.5212	0.527914
$657$	13.1035	0.511217
$658$	16.1923	0.631243
$659$	−29.0607	−1.13204	−0.566022	−	0.824390i	$-0.691518\pi$
$659$	−29.0607	−1.13204	−0.566022	+	0.824390i	$0.691518\pi$
$660$	0	0
$661$	31.2369	1.21497	0.607487	−	0.794330i	$-0.292178\pi$
$661$	31.2369	1.21497	0.607487	+	0.794330i	$0.292178\pi$
$662$	−62.4126	−2.42574
$663$	−1.14637	−0.0445211
$664$	−19.6644	−0.763128
$665$	0	0
$666$	5.83221	0.225994
$667$	8.02877	0.310875
$668$	−10.6283	−0.411222
$669$	5.56404	0.215118
$670$	0	0
$671$	6.68585	0.258104
$672$	−18.7434	−0.723042
$673$	−9.74652	−0.375701	−0.187850	−	0.982198i	$-0.560152\pi$
$673$	−9.74652	−0.375701	−0.187850	+	0.982198i	$0.560152\pi$
$674$	20.0147	0.770937
$675$	0	0
$676$	−42.8181	−1.64685
$677$	−6.80031	−0.261357	−0.130679	−	0.991425i	$-0.541716\pi$
$677$	−6.80031	−0.261357	−0.130679	+	0.991425i	$0.541716\pi$
$678$	−33.1035	−1.27133
$679$	51.9143	1.99229
$680$	0	0
$681$	16.5855	0.635556
$682$	−5.89962	−0.225908
$683$	41.5029	1.58806	0.794032	−	0.607876i	$-0.207978\pi$
$683$	41.5029	1.58806	0.794032	+	0.607876i	$0.207978\pi$
$684$	−13.3717	−0.511279
$685$	0	0
$686$	−64.7251	−2.47122
$687$	−6.64300	−0.253446
$688$	−12.7862	−0.487470
$689$	3.43910	0.131019
$690$	0	0
$691$	−31.2713	−1.18962	−0.594808	−	0.803868i	$-0.702772\pi$
$691$	−31.2713	−1.18962	−0.594808	+	0.803868i	$0.702772\pi$
$692$	87.0080	3.30755
$693$	5.14637	0.195494
$694$	38.0722	1.44520
$695$	0	0
$696$	28.0147	1.06189
$697$	−15.1751	−0.574799
$698$	54.3320	2.05650
$699$	−14.3931	−0.544398
$700$	0	0
$701$	−6.02456	−0.227544	−0.113772	−	0.993507i	$-0.536293\pi$
$701$	−6.02456	−0.227544	−0.113772	+	0.993507i	$0.536293\pi$
$702$	2.00000	0.0754851
$703$	−9.53948	−0.359788
$704$	13.9572	0.526030
$705$	0	0
$706$	17.5296	0.659736
$707$	−52.4941	−1.97424
$708$	52.3650	1.96800
$709$	37.6974	1.41576	0.707878	−	0.706335i	$-0.249653\pi$
$709$	37.6974	1.41576	0.707878	+	0.706335i	$0.249653\pi$
$710$	0	0
$711$	0.585462	0.0219565
$712$	−0.350269	−0.0131269
$713$	−2.19656	−0.0822617
$714$	−14.1249	−0.528613
$715$	0	0
$716$	−23.3288	−0.871840
$717$	13.1077	0.489517
$718$	4.39312	0.163950
$719$	19.8708	0.741058	0.370529	−	0.928821i	$-0.379176\pi$
$719$	19.8708	0.741058	0.370529	+	0.928821i	$0.379176\pi$
$720$	0	0
$721$	−88.5376	−3.29731
$722$	−10.1077	−0.376171
$723$	−12.5181	−0.465552
$724$	−71.8799	−2.67139
$725$	0	0
$726$	22.6932	0.842223
$727$	−15.8757	−0.588796	−0.294398	−	0.955683i	$-0.595119\pi$
$727$	−15.8757	−0.588796	−0.294398	+	0.955683i	$0.595119\pi$
$728$	13.3717	0.495588
$729$	1.00000	0.0370370
$730$	0	0
$731$	14.3503	0.530764
$732$	20.3503	0.752168
$733$	−37.1751	−1.37309	−0.686547	−	0.727085i	$-0.740875\pi$
$733$	−37.1751	−1.37309	−0.686547	+	0.727085i	$0.740875\pi$
$734$	10.9687	0.404863
$735$	0	0
$736$	4.17513	0.153898
$737$	−13.2614	−0.488492
$738$	26.4752	0.974566
$739$	44.0189	1.61926	0.809631	−	0.586940i	$-0.199667\pi$
$739$	44.0189	1.61926	0.809631	+	0.586940i	$0.199667\pi$
$740$	0	0
$741$	−3.27131	−0.120175
$742$	42.3748	1.55563
$743$	−51.5296	−1.89044	−0.945219	−	0.326437i	$-0.894152\pi$
$743$	−51.5296	−1.89044	−0.945219	+	0.326437i	$0.894152\pi$
$744$	−7.66442	−0.280991
$745$	0	0
$746$	−43.6791	−1.59921
$747$	−5.63565	−0.206198
$748$	5.37169	0.196409
$749$	24.4366	0.892893
$750$	0	0
$751$	−3.91790	−0.142966	−0.0714832	−	0.997442i	$-0.522773\pi$
$751$	−3.91790	−0.142966	−0.0714832	+	0.997442i	$0.522773\pi$
$752$	−1.84208	−0.0671736
$753$	26.3503	0.960257
$754$	16.0575	0.584781
$755$	0	0
$756$	15.6644	0.569710
$757$	−25.7606	−0.936285	−0.468142	−	0.883653i	$-0.655077\pi$
$757$	−25.7606	−0.936285	−0.468142	+	0.883653i	$0.655077\pi$
$758$	69.9865	2.54203
$759$	−1.14637	−0.0416104
$760$	0	0
$761$	−15.7507	−0.570964	−0.285482	−	0.958384i	$-0.592154\pi$
$761$	−15.7507	−0.570964	−0.285482	+	0.958384i	$0.592154\pi$
$762$	12.8438	0.465281
$763$	56.1972	2.03447
$764$	17.2860	0.625386
$765$	0	0
$766$	−48.1972	−1.74143
$767$	12.8108	0.462571
$768$	22.9185	0.827001
$769$	−19.0031	−0.685271	−0.342635	−	0.939468i	$-0.611320\pi$
$769$	−19.0031	−0.685271	−0.342635	+	0.939468i	$0.611320\pi$
$770$	0	0
$771$	−27.0116	−0.972797
$772$	−21.1365	−0.760719
$773$	41.7795	1.50270	0.751352	−	0.659902i	$-0.229402\pi$
$773$	41.7795	1.50270	0.751352	+	0.659902i	$0.229402\pi$
$774$	−25.0361	−0.899905
$775$	0	0
$776$	−40.3503	−1.44849
$777$	11.1751	0.400906
$778$	−5.47208	−0.196183
$779$	−43.3043	−1.55154
$780$	0	0
$781$	−4.95402	−0.177269
$782$	3.14637	0.112514
$783$	8.02877	0.286925
$784$	15.7392	0.562113
$785$	0	0
$786$	0	0
$787$	21.8610	0.779260	0.389630	−	0.920972i	$-0.372603\pi$
$787$	21.8610	0.779260	0.389630	+	0.920972i	$0.372603\pi$
$788$	85.1659	3.03391
$789$	21.8855	0.779146
$790$	0	0
$791$	−63.4298	−2.25531
$792$	−4.00000	−0.142134
$793$	4.97858	0.176794
$794$	−68.2646	−2.42262
$795$	0	0
$796$	−13.4574	−0.476984
$797$	27.8280	0.985718	0.492859	−	0.870109i	$-0.335952\pi$
$797$	27.8280	0.985718	0.492859	+	0.870109i	$0.335952\pi$
$798$	−40.3074	−1.42687
$799$	2.06740	0.0731395
$800$	0	0
$801$	−0.100384	−0.00354690
$802$	−34.7581	−1.22735
$803$	−15.0214	−0.530095
$804$	−40.3650	−1.42356
$805$	0	0
$806$	−4.39312	−0.154741
$807$	−3.69319	−0.130007
$808$	40.8009	1.43537
$809$	−21.0565	−0.740306	−0.370153	−	0.928971i	$-0.620695\pi$
$809$	−21.0565	−0.740306	−0.370153	+	0.928971i	$0.620695\pi$
$810$	0	0
$811$	−16.8249	−0.590801	−0.295400	−	0.955374i	$-0.595453\pi$
$811$	−16.8249	−0.590801	−0.295400	+	0.955374i	$0.595453\pi$
$812$	125.766	4.41352
$813$	−0.288520	−0.0101188
$814$	−6.68585	−0.234339
$815$	0	0
$816$	1.60688	0.0562522
$817$	40.9504	1.43267
$818$	−89.0754	−3.11445
$819$	3.83221	0.133908
$820$	0	0
$821$	−2.59388	−0.0905272	−0.0452636	−	0.998975i	$-0.514413\pi$
$821$	−2.59388	−0.0905272	−0.0452636	+	0.998975i	$0.514413\pi$
$822$	27.5640	0.961406
$823$	−0.786230	−0.0274063	−0.0137031	−	0.999906i	$-0.504362\pi$
$823$	−0.786230	−0.0274063	−0.0137031	+	0.999906i	$0.504362\pi$
$824$	68.8156	2.39731
$825$	0	0
$826$	157.848	5.49224
$827$	−10.2211	−0.355423	−0.177712	−	0.984083i	$-0.556869\pi$
$827$	−10.2211	−0.355423	−0.177712	+	0.984083i	$0.556869\pi$
$828$	−3.48929	−0.121261
$829$	−8.97437	−0.311693	−0.155846	−	0.987781i	$-0.549810\pi$
$829$	−8.97437	−0.311693	−0.155846	+	0.987781i	$0.549810\pi$
$830$	0	0
$831$	21.3288	0.739889
$832$	10.3931	0.360316
$833$	−17.6644	−0.612036
$834$	−19.1035	−0.661501
$835$	0	0
$836$	15.3288	0.530159
$837$	−2.19656	−0.0759241
$838$	51.1856	1.76818
$839$	19.6069	0.676905	0.338452	−	0.940984i	$-0.390097\pi$
$839$	19.6069	0.676905	0.338452	+	0.940984i	$0.390097\pi$
$840$	0	0
$841$	35.4611	1.22280
$842$	50.2302	1.73105
$843$	26.6676	0.918480
$844$	−2.87819	−0.0990715
$845$	0	0
$846$	−3.60688	−0.124007
$847$	43.4826	1.49408
$848$	−4.82065	−0.165542
$849$	25.9185	0.889521
$850$	0	0
$851$	−2.48929	−0.0853317
$852$	−15.0790	−0.516597
$853$	14.3650	0.491847	0.245923	−	0.969289i	$-0.420909\pi$
$853$	14.3650	0.491847	0.245923	+	0.969289i	$0.420909\pi$
$854$	61.3435	2.09913
$855$	0	0
$856$	−18.9933	−0.649177
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	−2.29273	−0.0782725
$859$	−4.85425	−0.165625	−0.0828125	−	0.996565i	$-0.526390\pi$
$859$	−4.85425	−0.165625	−0.0828125	+	0.996565i	$0.526390\pi$
$860$	0	0
$861$	50.7293	1.72885
$862$	69.8715	2.37983
$863$	−41.8139	−1.42336	−0.711681	−	0.702503i	$-0.752066\pi$
$863$	−41.8139	−1.42336	−0.711681	+	0.702503i	$0.752066\pi$
$864$	4.17513	0.142041
$865$	0	0
$866$	2.16779	0.0736644
$867$	15.1966	0.516102
$868$	−34.4078	−1.16788
$869$	−0.671153	−0.0227673
$870$	0	0
$871$	−9.87506	−0.334604
$872$	−43.6791	−1.47916
$873$	−11.5640	−0.391383
$874$	8.97858	0.303705
$875$	0	0
$876$	−45.7220	−1.54480
$877$	1.27973	0.0432134	0.0216067	−	0.999767i	$-0.493122\pi$
$877$	1.27973	0.0432134	0.0216067	+	0.999767i	$0.493122\pi$
$878$	−50.7925	−1.71416
$879$	13.6503	0.460415
$880$	0	0
$881$	52.9687	1.78456	0.892281	−	0.451481i	$-0.149104\pi$
$881$	52.9687	1.78456	0.892281	+	0.451481i	$0.149104\pi$
$882$	30.8181	1.03770
$883$	17.5479	0.590534	0.295267	−	0.955415i	$-0.404591\pi$
$883$	17.5479	0.590534	0.295267	+	0.955415i	$0.404591\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	−12.1923	−0.409610
$887$	11.2713	0.378453	0.189227	−	0.981933i	$-0.439402\pi$
$887$	11.2713	0.378453	0.189227	+	0.981933i	$0.439402\pi$
$888$	−8.68585	−0.291478
$889$	24.6100	0.825394
$890$	0	0
$891$	−1.14637	−0.0384047
$892$	−19.4145	−0.650047
$893$	5.89962	0.197423
$894$	8.74338	0.292423
$895$	0	0
$896$	90.5720	3.02580
$897$	−0.853635	−0.0285020
$898$	−25.4391	−0.848914
$899$	−17.6357	−0.588182
$900$	0	0
$901$	5.41033	0.180244
$902$	−30.3503	−1.01055
$903$	−47.9718	−1.59640
$904$	49.3007	1.63972
$905$	0	0
$906$	−38.9933	−1.29546
$907$	−27.2045	−0.903311	−0.451656	−	0.892192i	$-0.649166\pi$
$907$	−27.2045	−0.903311	−0.451656	+	0.892192i	$0.649166\pi$
$908$	−57.8715	−1.92053
$909$	11.6932	0.387839
$910$	0	0
$911$	−3.41454	−0.113129	−0.0565643	−	0.998399i	$-0.518015\pi$
$911$	−3.41454	−0.113129	−0.0565643	+	0.998399i	$0.518015\pi$
$912$	4.58546	0.151840
$913$	6.46052	0.213812
$914$	−63.9044	−2.11377
$915$	0	0
$916$	23.1793	0.765867
$917$	0	0
$918$	3.14637	0.103846
$919$	20.4998	0.676225	0.338113	−	0.941106i	$-0.390212\pi$
$919$	20.4998	0.676225	0.338113	+	0.941106i	$0.390212\pi$
$920$	0	0
$921$	−9.78937	−0.322571
$922$	47.3435	1.55918
$923$	−3.68898	−0.121424
$924$	−17.9572	−0.590747
$925$	0	0
$926$	−18.8207	−0.618485
$927$	19.7220	0.647754
$928$	33.5212	1.10039
$929$	38.2640	1.25540	0.627700	−	0.778455i	$-0.283996\pi$
$929$	38.2640	1.25540	0.627700	+	0.778455i	$0.283996\pi$
$930$	0	0
$931$	−50.4078	−1.65205
$932$	50.2217	1.64507
$933$	3.32885	0.108982
$934$	45.5886	1.49170
$935$	0	0
$936$	−2.97858	−0.0973578
$937$	−35.6791	−1.16559	−0.582793	−	0.812621i	$-0.698040\pi$
$937$	−35.6791	−1.16559	−0.582793	+	0.812621i	$0.698040\pi$
$938$	−121.676	−3.97285
$939$	−18.8824	−0.616204
$940$	0	0
$941$	15.2321	0.496551	0.248275	−	0.968689i	$-0.420136\pi$
$941$	15.2321	0.496551	0.248275	+	0.968689i	$0.420136\pi$
$942$	−31.0031	−1.01014
$943$	−11.3001	−0.367981
$944$	−17.9572	−0.584456
$945$	0	0
$946$	28.7005	0.933135
$947$	−6.29273	−0.204486	−0.102243	−	0.994759i	$-0.532602\pi$
$947$	−6.29273	−0.204486	−0.102243	+	0.994759i	$0.532602\pi$
$948$	−2.04285	−0.0663485
$949$	−11.1856	−0.363100
$950$	0	0
$951$	−8.06740	−0.261604
$952$	21.0361	0.681784
$953$	−20.3418	−0.658937	−0.329469	−	0.944167i	$-0.606870\pi$
$953$	−20.3418	−0.658937	−0.329469	+	0.944167i	$0.606870\pi$
$954$	−9.43910	−0.305602
$955$	0	0
$956$	−45.7367	−1.47923
$957$	−9.20390	−0.297520
$958$	67.8370	2.19172
$959$	52.8156	1.70551
$960$	0	0
$961$	−26.1751	−0.844359
$962$	−4.97858	−0.160516
$963$	−5.44331	−0.175408
$964$	43.6791	1.40681
$965$	0	0
$966$	−10.5181	−0.338413
$967$	37.6461	1.21062	0.605309	−	0.795991i	$-0.293050\pi$
$967$	37.6461	1.21062	0.605309	+	0.795991i	$0.293050\pi$
$968$	−33.7967	−1.08627
$969$	−5.14637	−0.165325
$970$	0	0
$971$	−29.6216	−0.950602	−0.475301	−	0.879823i	$-0.657661\pi$
$971$	−29.6216	−0.950602	−0.475301	+	0.879823i	$0.657661\pi$
$972$	−3.48929	−0.111919
$973$	−36.6044	−1.17348
$974$	−48.7581	−1.56231
$975$	0	0
$976$	−6.97858	−0.223379
$977$	−21.0158	−0.672354	−0.336177	−	0.941799i	$-0.609134\pi$
$977$	−21.0158	−0.672354	−0.336177	+	0.941799i	$0.609134\pi$
$978$	38.4078	1.22815
$979$	0.115077	0.00367788
$980$	0	0
$981$	−12.5181	−0.399671
$982$	82.2694	2.62532
$983$	27.5647	0.879176	0.439588	−	0.898200i	$-0.355124\pi$
$983$	27.5647	0.879176	0.439588	+	0.898200i	$0.355124\pi$
$984$	−39.4292	−1.25696
$985$	0	0
$986$	25.2614	0.804488
$987$	−6.91117	−0.219985
$988$	11.4145	0.363145
$989$	10.6858	0.339790
$990$	0	0
$991$	−20.1537	−0.640204	−0.320102	−	0.947383i	$-0.603717\pi$
$991$	−20.1537	−0.640204	−0.320102	+	0.947383i	$0.603717\pi$
$992$	−9.17092	−0.291177
$993$	26.6388	0.845356
$994$	−45.4538	−1.44171
$995$	0	0
$996$	19.6644	0.623091
$997$	−14.9295	−0.472821	−0.236410	−	0.971653i	$-0.575971\pi$
$997$	−14.9295	−0.472821	−0.236410	+	0.971653i	$0.575971\pi$
$998$	−17.1464	−0.542759
$999$	−2.48929	−0.0787576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1725.2.a.bi.1.3		3
3.2	odd	2		5175.2.a.br.1.1		3
5.2	odd	4		1725.2.b.u.1174.6		6
5.3	odd	4		1725.2.b.u.1174.1		6
5.4	even	2		345.2.a.j.1.1	✓	3
15.14	odd	2		1035.2.a.n.1.3		3
20.19	odd	2		5520.2.a.by.1.1		3
115.114	odd	2		7935.2.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.a.j.1.1	✓	3	5.4	even	2
1035.2.a.n.1.3		3	15.14	odd	2
1725.2.a.bi.1.3		3	1.1	even	1	trivial
1725.2.b.u.1174.1		6	5.3	odd	4
1725.2.b.u.1174.6		6	5.2	odd	4
5175.2.a.br.1.1		3	3.2	odd	2
5520.2.a.by.1.1		3	20.19	odd	2
7935.2.a.u.1.1		3	115.114	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:	\( N \)	\(=\)	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1725.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} -2.34292 q^{6} -4.48929 q^{7} +3.48929 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.34292 q^{2} -1.00000 q^{3} +3.48929 q^{4} -2.34292 q^{6} -4.48929 q^{7} +3.48929 q^{8} +1.00000 q^{9} -1.14637 q^{11} -3.48929 q^{12} -0.853635 q^{13} -10.5181 q^{14} +1.19656 q^{16} -1.34292 q^{17} +2.34292 q^{18} -3.83221 q^{19} +4.48929 q^{21} -2.68585 q^{22} -1.00000 q^{23} -3.48929 q^{24} -2.00000 q^{26} -1.00000 q^{27} -15.6644 q^{28} -8.02877 q^{29} +2.19656 q^{31} -4.17513 q^{32} +1.14637 q^{33} -3.14637 q^{34} +3.48929 q^{36} +2.48929 q^{37} -8.97858 q^{38} +0.853635 q^{39} +11.3001 q^{41} +10.5181 q^{42} -10.6858 q^{43} -4.00000 q^{44} -2.34292 q^{46} -1.53948 q^{47} -1.19656 q^{48} +13.1537 q^{49} +1.34292 q^{51} -2.97858 q^{52} -4.02877 q^{53} -2.34292 q^{54} -15.6644 q^{56} +3.83221 q^{57} -18.8108 q^{58} -15.0073 q^{59} -5.83221 q^{61} +5.14637 q^{62} -4.48929 q^{63} -12.1751 q^{64} +2.68585 q^{66} +11.5682 q^{67} -4.68585 q^{68} +1.00000 q^{69} +4.32150 q^{71} +3.48929 q^{72} +13.1035 q^{73} +5.83221 q^{74} -13.3717 q^{76} +5.14637 q^{77} +2.00000 q^{78} +0.585462 q^{79} +1.00000 q^{81} +26.4752 q^{82} -5.63565 q^{83} +15.6644 q^{84} -25.0361 q^{86} +8.02877 q^{87} -4.00000 q^{88} -0.100384 q^{89} +3.83221 q^{91} -3.48929 q^{92} -2.19656 q^{93} -3.60688 q^{94} +4.17513 q^{96} -11.5640 q^{97} +30.8181 q^{98} -1.14637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 2 q^{11} - 3 q^{12} - 4 q^{13} - 6 q^{14} - q^{16} + 2 q^{17} + q^{18} + 2 q^{19} + 6 q^{21} + 4 q^{22} - 3 q^{23} - 3 q^{24} - 6 q^{26} - 3 q^{27} - 20 q^{28} - 6 q^{29} + 2 q^{31} + 7 q^{32} + 2 q^{33} - 8 q^{34} + 3 q^{36} - 12 q^{38} + 4 q^{39} - 2 q^{41} + 6 q^{42} - 20 q^{43} - 12 q^{44} - q^{46} + 6 q^{47} + q^{48} + 5 q^{49} - 2 q^{51} + 6 q^{52} + 6 q^{53} - q^{54} - 20 q^{56} - 2 q^{57} - 28 q^{58} - 12 q^{59} - 4 q^{61} + 14 q^{62} - 6 q^{63} - 17 q^{64} - 4 q^{66} + 6 q^{67} - 2 q^{68} + 3 q^{69} - 8 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} - 16 q^{76} + 14 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{81} + 24 q^{82} - 8 q^{83} + 20 q^{84} - 24 q^{86} + 6 q^{87} - 12 q^{88} + 6 q^{89} - 2 q^{91} - 3 q^{92} - 2 q^{93} - 20 q^{94} - 7 q^{96} - 14 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 2 * q^11 - 3 * q^12 - 4 * q^13 - 6 * q^14 - q^16 + 2 * q^17 + q^18 + 2 * q^19 + 6 * q^21 + 4 * q^22 - 3 * q^23 - 3 * q^24 - 6 * q^26 - 3 * q^27 - 20 * q^28 - 6 * q^29 + 2 * q^31 + 7 * q^32 + 2 * q^33 - 8 * q^34 + 3 * q^36 - 12 * q^38 + 4 * q^39 - 2 * q^41 + 6 * q^42 - 20 * q^43 - 12 * q^44 - q^46 + 6 * q^47 + q^48 + 5 * q^49 - 2 * q^51 + 6 * q^52 + 6 * q^53 - q^54 - 20 * q^56 - 2 * q^57 - 28 * q^58 - 12 * q^59 - 4 * q^61 + 14 * q^62 - 6 * q^63 - 17 * q^64 - 4 * q^66 + 6 * q^67 - 2 * q^68 + 3 * q^69 - 8 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 - 16 * q^76 + 14 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^81 + 24 * q^82 - 8 * q^83 + 20 * q^84 - 24 * q^86 + 6 * q^87 - 12 * q^88 + 6 * q^89 - 2 * q^91 - 3 * q^92 - 2 * q^93 - 20 * q^94 - 7 * q^96 - 14 * q^97 + 31 * q^98 - 2 * q^99

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