LMFDB - Embedded newform 3750.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.763932 q^{11} +1.00000 q^{12} -1.85410 q^{13} -2.00000 q^{14} +1.00000 q^{16} -1.14590 q^{17} +1.00000 q^{18} -7.23607 q^{19} -2.00000 q^{21} -0.763932 q^{22} -6.00000 q^{23} +1.00000 q^{24} -1.85410 q^{26} +1.00000 q^{27} -2.00000 q^{28} -3.61803 q^{29} -9.70820 q^{31} +1.00000 q^{32} -0.763932 q^{33} -1.14590 q^{34} +1.00000 q^{36} +8.85410 q^{37} -7.23607 q^{38} -1.85410 q^{39} +5.09017 q^{41} -2.00000 q^{42} -3.23607 q^{43} -0.763932 q^{44} -6.00000 q^{46} -9.23607 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.14590 q^{51} -1.85410 q^{52} +11.5623 q^{53} +1.00000 q^{54} -2.00000 q^{56} -7.23607 q^{57} -3.61803 q^{58} -8.94427 q^{59} -2.14590 q^{61} -9.70820 q^{62} -2.00000 q^{63} +1.00000 q^{64} -0.763932 q^{66} -3.70820 q^{67} -1.14590 q^{68} -6.00000 q^{69} +8.18034 q^{71} +1.00000 q^{72} +9.85410 q^{73} +8.85410 q^{74} -7.23607 q^{76} +1.52786 q^{77} -1.85410 q^{78} +1.00000 q^{81} +5.09017 q^{82} -6.00000 q^{83} -2.00000 q^{84} -3.23607 q^{86} -3.61803 q^{87} -0.763932 q^{88} +3.61803 q^{89} +3.70820 q^{91} -6.00000 q^{92} -9.70820 q^{93} -9.23607 q^{94} +1.00000 q^{96} +7.14590 q^{97} -3.00000 q^{98} -0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} + 2 q^{12} + 3 q^{13} - 4 q^{14} + 2 q^{16} - 9 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} - 4 q^{28} - 5 q^{29} - 6 q^{31} + 2 q^{32} - 6 q^{33} - 9 q^{34} + 2 q^{36} + 11 q^{37} - 10 q^{38} + 3 q^{39} - q^{41} - 4 q^{42} - 2 q^{43} - 6 q^{44} - 12 q^{46} - 14 q^{47} + 2 q^{48} - 6 q^{49} - 9 q^{51} + 3 q^{52} + 3 q^{53} + 2 q^{54} - 4 q^{56} - 10 q^{57} - 5 q^{58} - 11 q^{61} - 6 q^{62} - 4 q^{63} + 2 q^{64} - 6 q^{66} + 6 q^{67} - 9 q^{68} - 12 q^{69} - 6 q^{71} + 2 q^{72} + 13 q^{73} + 11 q^{74} - 10 q^{76} + 12 q^{77} + 3 q^{78} + 2 q^{81} - q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{86} - 5 q^{87} - 6 q^{88} + 5 q^{89} - 6 q^{91} - 12 q^{92} - 6 q^{93} - 14 q^{94} + 2 q^{96} + 21 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 + 2 * q^12 + 3 * q^13 - 4 * q^14 + 2 * q^16 - 9 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 - 4 * q^28 - 5 * q^29 - 6 * q^31 + 2 * q^32 - 6 * q^33 - 9 * q^34 + 2 * q^36 + 11 * q^37 - 10 * q^38 + 3 * q^39 - q^41 - 4 * q^42 - 2 * q^43 - 6 * q^44 - 12 * q^46 - 14 * q^47 + 2 * q^48 - 6 * q^49 - 9 * q^51 + 3 * q^52 + 3 * q^53 + 2 * q^54 - 4 * q^56 - 10 * q^57 - 5 * q^58 - 11 * q^61 - 6 * q^62 - 4 * q^63 + 2 * q^64 - 6 * q^66 + 6 * q^67 - 9 * q^68 - 12 * q^69 - 6 * q^71 + 2 * q^72 + 13 * q^73 + 11 * q^74 - 10 * q^76 + 12 * q^77 + 3 * q^78 + 2 * q^81 - q^82 - 12 * q^83 - 4 * q^84 - 2 * q^86 - 5 * q^87 - 6 * q^88 + 5 * q^89 - 6 * q^91 - 12 * q^92 - 6 * q^93 - 14 * q^94 + 2 * q^96 + 21 * q^97 - 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.763932	−0.230334	−0.115167	−	0.993346i	$-0.536740\pi$
$11$	−0.763932	−0.230334	−0.115167	+	0.993346i	$0.536740\pi$
$12$	1.00000	0.288675
$13$	−1.85410	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$13$	−1.85410	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.14590	−0.277921	−0.138961	−	0.990298i	$-0.544376\pi$
$17$	−1.14590	−0.277921	−0.138961	+	0.990298i	$0.544376\pi$
$18$	1.00000	0.235702
$19$	−7.23607	−1.66007	−0.830034	−	0.557713i	$-0.811679\pi$
$19$	−7.23607	−1.66007	−0.830034	+	0.557713i	$0.811679\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	−0.763932	−0.162871
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.85410	−0.363619
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	−3.61803	−0.671852	−0.335926	−	0.941888i	$-0.609049\pi$
$29$	−3.61803	−0.671852	−0.335926	+	0.941888i	$0.609049\pi$
$30$	0	0
$31$	−9.70820	−1.74364	−0.871822	−	0.489822i	$-0.837062\pi$
$31$	−9.70820	−1.74364	−0.871822	+	0.489822i	$0.837062\pi$
$32$	1.00000	0.176777
$33$	−0.763932	−0.132983
$34$	−1.14590	−0.196520
$35$	0	0
$36$	1.00000	0.166667
$37$	8.85410	1.45561	0.727803	−	0.685787i	$-0.240542\pi$
$37$	8.85410	1.45561	0.727803	+	0.685787i	$0.240542\pi$
$38$	−7.23607	−1.17385
$39$	−1.85410	−0.296894
$40$	0	0
$41$	5.09017	0.794951	0.397475	−	0.917613i	$-0.369886\pi$
$41$	5.09017	0.794951	0.397475	+	0.917613i	$0.369886\pi$
$42$	−2.00000	−0.308607
$43$	−3.23607	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$44$	−0.763932	−0.115167
$45$	0	0
$46$	−6.00000	−0.884652
$47$	−9.23607	−1.34722	−0.673609	−	0.739087i	$-0.735257\pi$
$47$	−9.23607	−1.34722	−0.673609	+	0.739087i	$0.735257\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−1.14590	−0.160458
$52$	−1.85410	−0.257118
$53$	11.5623	1.58820	0.794102	−	0.607784i	$-0.207941\pi$
$53$	11.5623	1.58820	0.794102	+	0.607784i	$0.207941\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	−7.23607	−0.958441
$58$	−3.61803	−0.475071
$59$	−8.94427	−1.16445	−0.582223	−	0.813029i	$-0.697817\pi$
$59$	−8.94427	−1.16445	−0.582223	+	0.813029i	$0.697817\pi$
$60$	0	0
$61$	−2.14590	−0.274754	−0.137377	−	0.990519i	$-0.543867\pi$
$61$	−2.14590	−0.274754	−0.137377	+	0.990519i	$0.543867\pi$
$62$	−9.70820	−1.23294
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.763932	−0.0940335
$67$	−3.70820	−0.453029	−0.226515	−	0.974008i	$-0.572733\pi$
$67$	−3.70820	−0.453029	−0.226515	+	0.974008i	$0.572733\pi$
$68$	−1.14590	−0.138961
$69$	−6.00000	−0.722315
$70$	0	0
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	1.00000	0.117851
$73$	9.85410	1.15334	0.576668	−	0.816979i	$-0.304353\pi$
$73$	9.85410	1.15334	0.576668	+	0.816979i	$0.304353\pi$
$74$	8.85410	1.02927
$75$	0	0
$76$	−7.23607	−0.830034
$77$	1.52786	0.174116
$78$	−1.85410	−0.209936
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.09017	0.562115
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−3.23607	−0.348954
$87$	−3.61803	−0.387894
$88$	−0.763932	−0.0814354
$89$	3.61803	0.383511	0.191755	−	0.981443i	$-0.438582\pi$
$89$	3.61803	0.383511	0.191755	+	0.981443i	$0.438582\pi$
$90$	0	0
$91$	3.70820	0.388725
$92$	−6.00000	−0.625543
$93$	−9.70820	−1.00669
$94$	−9.23607	−0.952628
$95$	0	0
$96$	1.00000	0.102062
$97$	7.14590	0.725556	0.362778	−	0.931876i	$-0.381828\pi$
$97$	7.14590	0.725556	0.362778	+	0.931876i	$0.381828\pi$
$98$	−3.00000	−0.303046
$99$	−0.763932	−0.0767781
$100$	0	0
$101$	17.3262	1.72403	0.862013	−	0.506887i	$-0.169204\pi$
$101$	17.3262	1.72403	0.862013	+	0.506887i	$0.169204\pi$
$102$	−1.14590	−0.113461
$103$	15.7082	1.54778	0.773888	−	0.633323i	$-0.218309\pi$
$103$	15.7082	1.54778	0.773888	+	0.633323i	$0.218309\pi$
$104$	−1.85410	−0.181810
$105$	0	0
$106$	11.5623	1.12303
$107$	6.94427	0.671328	0.335664	−	0.941982i	$-0.391039\pi$
$107$	6.94427	0.671328	0.335664	+	0.941982i	$0.391039\pi$
$108$	1.00000	0.0962250
$109$	−17.5623	−1.68216	−0.841082	−	0.540908i	$-0.818081\pi$
$109$	−17.5623	−1.68216	−0.841082	+	0.540908i	$0.818081\pi$
$110$	0	0
$111$	8.85410	0.840394
$112$	−2.00000	−0.188982
$113$	−8.56231	−0.805474	−0.402737	−	0.915316i	$-0.631941\pi$
$113$	−8.56231	−0.805474	−0.402737	+	0.915316i	$0.631941\pi$
$114$	−7.23607	−0.677720
$115$	0	0
$116$	−3.61803	−0.335926
$117$	−1.85410	−0.171412
$118$	−8.94427	−0.823387
$119$	2.29180	0.210089
$120$	0	0
$121$	−10.4164	−0.946946
$122$	−2.14590	−0.194280
$123$	5.09017	0.458965
$124$	−9.70820	−0.871822
$125$	0	0
$126$	−2.00000	−0.178174
$127$	−13.7082	−1.21641	−0.608203	−	0.793781i	$-0.708109\pi$
$127$	−13.7082	−1.21641	−0.608203	+	0.793781i	$0.708109\pi$
$128$	1.00000	0.0883883
$129$	−3.23607	−0.284920
$130$	0	0
$131$	−5.23607	−0.457477	−0.228739	−	0.973488i	$-0.573460\pi$
$131$	−5.23607	−0.457477	−0.228739	+	0.973488i	$0.573460\pi$
$132$	−0.763932	−0.0664917
$133$	14.4721	1.25489
$134$	−3.70820	−0.320340
$135$	0	0
$136$	−1.14590	−0.0982599
$137$	−14.0344	−1.19904	−0.599522	−	0.800359i	$-0.704642\pi$
$137$	−14.0344	−1.19904	−0.599522	+	0.800359i	$0.704642\pi$
$138$	−6.00000	−0.510754
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	0	0
$141$	−9.23607	−0.777817
$142$	8.18034	0.686479
$143$	1.41641	0.118446
$144$	1.00000	0.0833333
$145$	0	0
$146$	9.85410	0.815531
$147$	−3.00000	−0.247436
$148$	8.85410	0.727803
$149$	−22.0344	−1.80513	−0.902566	−	0.430552i	$-0.858319\pi$
$149$	−22.0344	−1.80513	−0.902566	+	0.430552i	$0.858319\pi$
$150$	0	0
$151$	10.9443	0.890632	0.445316	−	0.895373i	$-0.353091\pi$
$151$	10.9443	0.890632	0.445316	+	0.895373i	$0.353091\pi$
$152$	−7.23607	−0.586923
$153$	−1.14590	−0.0926404
$154$	1.52786	0.123119
$155$	0	0
$156$	−1.85410	−0.148447
$157$	−11.1459	−0.889540	−0.444770	−	0.895645i	$-0.646714\pi$
$157$	−11.1459	−0.889540	−0.444770	+	0.895645i	$0.646714\pi$
$158$	0	0
$159$	11.5623	0.916951
$160$	0	0
$161$	12.0000	0.945732
$162$	1.00000	0.0785674
$163$	−11.5279	−0.902932	−0.451466	−	0.892288i	$-0.649099\pi$
$163$	−11.5279	−0.902932	−0.451466	+	0.892288i	$0.649099\pi$
$164$	5.09017	0.397475
$165$	0	0
$166$	−6.00000	−0.465690
$167$	2.47214	0.191300	0.0956498	−	0.995415i	$-0.469507\pi$
$167$	2.47214	0.191300	0.0956498	+	0.995415i	$0.469507\pi$
$168$	−2.00000	−0.154303
$169$	−9.56231	−0.735562
$170$	0	0
$171$	−7.23607	−0.553356
$172$	−3.23607	−0.246748
$173$	22.0902	1.67948	0.839742	−	0.542985i	$-0.182706\pi$
$173$	22.0902	1.67948	0.839742	+	0.542985i	$0.182706\pi$
$174$	−3.61803	−0.274282
$175$	0	0
$176$	−0.763932	−0.0575835
$177$	−8.94427	−0.672293
$178$	3.61803	0.271183
$179$	−26.1803	−1.95681	−0.978405	−	0.206696i	$-0.933729\pi$
$179$	−26.1803	−1.95681	−0.978405	+	0.206696i	$0.933729\pi$
$180$	0	0
$181$	9.03444	0.671525	0.335762	−	0.941947i	$-0.391006\pi$
$181$	9.03444	0.671525	0.335762	+	0.941947i	$0.391006\pi$
$182$	3.70820	0.274870
$183$	−2.14590	−0.158629
$184$	−6.00000	−0.442326
$185$	0	0
$186$	−9.70820	−0.711840
$187$	0.875388	0.0640147
$188$	−9.23607	−0.673609
$189$	−2.00000	−0.145479
$190$	0	0
$191$	−5.23607	−0.378869	−0.189434	−	0.981893i	$-0.560665\pi$
$191$	−5.23607	−0.378869	−0.189434	+	0.981893i	$0.560665\pi$
$192$	1.00000	0.0721688
$193$	−4.61803	−0.332413	−0.166207	−	0.986091i	$-0.553152\pi$
$193$	−4.61803	−0.332413	−0.166207	+	0.986091i	$0.553152\pi$
$194$	7.14590	0.513046
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−2.32624	−0.165738	−0.0828688	−	0.996560i	$-0.526408\pi$
$197$	−2.32624	−0.165738	−0.0828688	+	0.996560i	$0.526408\pi$
$198$	−0.763932	−0.0542903
$199$	16.1803	1.14699	0.573497	−	0.819208i	$-0.305586\pi$
$199$	16.1803	1.14699	0.573497	+	0.819208i	$0.305586\pi$
$200$	0	0
$201$	−3.70820	−0.261557
$202$	17.3262	1.21907
$203$	7.23607	0.507872
$204$	−1.14590	−0.0802289
$205$	0	0
$206$	15.7082	1.09444
$207$	−6.00000	−0.417029
$208$	−1.85410	−0.128559
$209$	5.52786	0.382370
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	11.5623	0.794102
$213$	8.18034	0.560508
$214$	6.94427	0.474701
$215$	0	0
$216$	1.00000	0.0680414
$217$	19.4164	1.31807
$218$	−17.5623	−1.18947
$219$	9.85410	0.665879
$220$	0	0
$221$	2.12461	0.142917
$222$	8.85410	0.594248
$223$	15.7082	1.05190	0.525950	−	0.850516i	$-0.323710\pi$
$223$	15.7082	1.05190	0.525950	+	0.850516i	$0.323710\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	−8.56231	−0.569556
$227$	−0.944272	−0.0626735	−0.0313368	−	0.999509i	$-0.509976\pi$
$227$	−0.944272	−0.0626735	−0.0313368	+	0.999509i	$0.509976\pi$
$228$	−7.23607	−0.479220
$229$	9.27051	0.612613	0.306306	−	0.951933i	$-0.400907\pi$
$229$	9.27051	0.612613	0.306306	+	0.951933i	$0.400907\pi$
$230$	0	0
$231$	1.52786	0.100526
$232$	−3.61803	−0.237536
$233$	10.9098	0.714727	0.357363	−	0.933965i	$-0.383676\pi$
$233$	10.9098	0.714727	0.357363	+	0.933965i	$0.383676\pi$
$234$	−1.85410	−0.121206
$235$	0	0
$236$	−8.94427	−0.582223
$237$	0	0
$238$	2.29180	0.148555
$239$	−26.8328	−1.73567	−0.867835	−	0.496852i	$-0.834489\pi$
$239$	−26.8328	−1.73567	−0.867835	+	0.496852i	$0.834489\pi$
$240$	0	0
$241$	−7.14590	−0.460308	−0.230154	−	0.973154i	$-0.573923\pi$
$241$	−7.14590	−0.460308	−0.230154	+	0.973154i	$0.573923\pi$
$242$	−10.4164	−0.669592
$243$	1.00000	0.0641500
$244$	−2.14590	−0.137377
$245$	0	0
$246$	5.09017	0.324537
$247$	13.4164	0.853666
$248$	−9.70820	−0.616472
$249$	−6.00000	−0.380235
$250$	0	0
$251$	−3.52786	−0.222677	−0.111338	−	0.993783i	$-0.535514\pi$
$251$	−3.52786	−0.222677	−0.111338	+	0.993783i	$0.535514\pi$
$252$	−2.00000	−0.125988
$253$	4.58359	0.288168
$254$	−13.7082	−0.860129
$255$	0	0
$256$	1.00000	0.0625000
$257$	9.38197	0.585231	0.292615	−	0.956230i	$-0.405474\pi$
$257$	9.38197	0.585231	0.292615	+	0.956230i	$0.405474\pi$
$258$	−3.23607	−0.201469
$259$	−17.7082	−1.10033
$260$	0	0
$261$	−3.61803	−0.223951
$262$	−5.23607	−0.323485
$263$	8.47214	0.522414	0.261207	−	0.965283i	$-0.415879\pi$
$263$	8.47214	0.522414	0.261207	+	0.965283i	$0.415879\pi$
$264$	−0.763932	−0.0470168
$265$	0	0
$266$	14.4721	0.887344
$267$	3.61803	0.221420
$268$	−3.70820	−0.226515
$269$	−13.0902	−0.798122	−0.399061	−	0.916924i	$-0.630664\pi$
$269$	−13.0902	−0.798122	−0.399061	+	0.916924i	$0.630664\pi$
$270$	0	0
$271$	5.81966	0.353519	0.176760	−	0.984254i	$-0.443438\pi$
$271$	5.81966	0.353519	0.176760	+	0.984254i	$0.443438\pi$
$272$	−1.14590	−0.0694803
$273$	3.70820	0.224431
$274$	−14.0344	−0.847852
$275$	0	0
$276$	−6.00000	−0.361158
$277$	28.8541	1.73367	0.866837	−	0.498591i	$-0.166149\pi$
$277$	28.8541	1.73367	0.866837	+	0.498591i	$0.166149\pi$
$278$	13.4164	0.804663
$279$	−9.70820	−0.581215
$280$	0	0
$281$	5.09017	0.303654	0.151827	−	0.988407i	$-0.451484\pi$
$281$	5.09017	0.303654	0.151827	+	0.988407i	$0.451484\pi$
$282$	−9.23607	−0.550000
$283$	1.23607	0.0734766	0.0367383	−	0.999325i	$-0.488303\pi$
$283$	1.23607	0.0734766	0.0367383	+	0.999325i	$0.488303\pi$
$284$	8.18034	0.485414
$285$	0	0
$286$	1.41641	0.0837540
$287$	−10.1803	−0.600926
$288$	1.00000	0.0589256
$289$	−15.6869	−0.922760
$290$	0	0
$291$	7.14590	0.418900
$292$	9.85410	0.576668
$293$	4.20163	0.245462	0.122731	−	0.992440i	$-0.460835\pi$
$293$	4.20163	0.245462	0.122731	+	0.992440i	$0.460835\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	8.85410	0.514634
$297$	−0.763932	−0.0443278
$298$	−22.0344	−1.27642
$299$	11.1246	0.643353
$300$	0	0
$301$	6.47214	0.373048
$302$	10.9443	0.629772
$303$	17.3262	0.995366
$304$	−7.23607	−0.415017
$305$	0	0
$306$	−1.14590	−0.0655066
$307$	29.7082	1.69554	0.847768	−	0.530367i	$-0.177946\pi$
$307$	29.7082	1.69554	0.847768	+	0.530367i	$0.177946\pi$
$308$	1.52786	0.0870581
$309$	15.7082	0.893609
$310$	0	0
$311$	12.6525	0.717456	0.358728	−	0.933442i	$-0.383211\pi$
$311$	12.6525	0.717456	0.358728	+	0.933442i	$0.383211\pi$
$312$	−1.85410	−0.104968
$313$	−18.3607	−1.03781	−0.518903	−	0.854833i	$-0.673660\pi$
$313$	−18.3607	−1.03781	−0.518903	+	0.854833i	$0.673660\pi$
$314$	−11.1459	−0.628999
$315$	0	0
$316$	0	0
$317$	−10.9443	−0.614692	−0.307346	−	0.951598i	$-0.599441\pi$
$317$	−10.9443	−0.614692	−0.307346	+	0.951598i	$0.599441\pi$
$318$	11.5623	0.648382
$319$	2.76393	0.154750
$320$	0	0
$321$	6.94427	0.387591
$322$	12.0000	0.668734
$323$	8.29180	0.461368
$324$	1.00000	0.0555556
$325$	0	0
$326$	−11.5279	−0.638469
$327$	−17.5623	−0.971198
$328$	5.09017	0.281058
$329$	18.4721	1.01840
$330$	0	0
$331$	−23.5279	−1.29321	−0.646604	−	0.762826i	$-0.723811\pi$
$331$	−23.5279	−1.29321	−0.646604	+	0.762826i	$0.723811\pi$
$332$	−6.00000	−0.329293
$333$	8.85410	0.485202
$334$	2.47214	0.135269
$335$	0	0
$336$	−2.00000	−0.109109
$337$	24.8328	1.35273	0.676365	−	0.736567i	$-0.263554\pi$
$337$	24.8328	1.35273	0.676365	+	0.736567i	$0.263554\pi$
$338$	−9.56231	−0.520121
$339$	−8.56231	−0.465041
$340$	0	0
$341$	7.41641	0.401621
$342$	−7.23607	−0.391282
$343$	20.0000	1.07990
$344$	−3.23607	−0.174477
$345$	0	0
$346$	22.0902	1.18757
$347$	0.763932	0.0410100	0.0205050	−	0.999790i	$-0.493473\pi$
$347$	0.763932	0.0410100	0.0205050	+	0.999790i	$0.493473\pi$
$348$	−3.61803	−0.193947
$349$	−9.79837	−0.524495	−0.262247	−	0.965001i	$-0.584464\pi$
$349$	−9.79837	−0.524495	−0.262247	+	0.965001i	$0.584464\pi$
$350$	0	0
$351$	−1.85410	−0.0989646
$352$	−0.763932	−0.0407177
$353$	−11.5279	−0.613566	−0.306783	−	0.951779i	$-0.599253\pi$
$353$	−11.5279	−0.613566	−0.306783	+	0.951779i	$0.599253\pi$
$354$	−8.94427	−0.475383
$355$	0	0
$356$	3.61803	0.191755
$357$	2.29180	0.121295
$358$	−26.1803	−1.38367
$359$	7.88854	0.416341	0.208171	−	0.978093i	$-0.433249\pi$
$359$	7.88854	0.416341	0.208171	+	0.978093i	$0.433249\pi$
$360$	0	0
$361$	33.3607	1.75583
$362$	9.03444	0.474840
$363$	−10.4164	−0.546720
$364$	3.70820	0.194363
$365$	0	0
$366$	−2.14590	−0.112168
$367$	3.52786	0.184153	0.0920765	−	0.995752i	$-0.470650\pi$
$367$	3.52786	0.184153	0.0920765	+	0.995752i	$0.470650\pi$
$368$	−6.00000	−0.312772
$369$	5.09017	0.264984
$370$	0	0
$371$	−23.1246	−1.20057
$372$	−9.70820	−0.503347
$373$	−29.4164	−1.52312	−0.761562	−	0.648092i	$-0.775567\pi$
$373$	−29.4164	−1.52312	−0.761562	+	0.648092i	$0.775567\pi$
$374$	0.875388	0.0452652
$375$	0	0
$376$	−9.23607	−0.476314
$377$	6.70820	0.345490
$378$	−2.00000	−0.102869
$379$	23.4164	1.20282	0.601410	−	0.798941i	$-0.294606\pi$
$379$	23.4164	1.20282	0.601410	+	0.798941i	$0.294606\pi$
$380$	0	0
$381$	−13.7082	−0.702293
$382$	−5.23607	−0.267901
$383$	−11.5279	−0.589046	−0.294523	−	0.955644i	$-0.595161\pi$
$383$	−11.5279	−0.589046	−0.294523	+	0.955644i	$0.595161\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−4.61803	−0.235052
$387$	−3.23607	−0.164499
$388$	7.14590	0.362778
$389$	−30.9787	−1.57068	−0.785342	−	0.619063i	$-0.787513\pi$
$389$	−30.9787	−1.57068	−0.785342	+	0.619063i	$0.787513\pi$
$390$	0	0
$391$	6.87539	0.347703
$392$	−3.00000	−0.151523
$393$	−5.23607	−0.264125
$394$	−2.32624	−0.117194
$395$	0	0
$396$	−0.763932	−0.0383890
$397$	24.8328	1.24632	0.623162	−	0.782093i	$-0.285848\pi$
$397$	24.8328	1.24632	0.623162	+	0.782093i	$0.285848\pi$
$398$	16.1803	0.811047
$399$	14.4721	0.724513
$400$	0	0
$401$	−14.9098	−0.744561	−0.372281	−	0.928120i	$-0.621424\pi$
$401$	−14.9098	−0.744561	−0.372281	+	0.928120i	$0.621424\pi$
$402$	−3.70820	−0.184948
$403$	18.0000	0.896644
$404$	17.3262	0.862013
$405$	0	0
$406$	7.23607	0.359120
$407$	−6.76393	−0.335276
$408$	−1.14590	−0.0567304
$409$	−25.9787	−1.28456	−0.642282	−	0.766468i	$-0.722012\pi$
$409$	−25.9787	−1.28456	−0.642282	+	0.766468i	$0.722012\pi$
$410$	0	0
$411$	−14.0344	−0.692268
$412$	15.7082	0.773888
$413$	17.8885	0.880238
$414$	−6.00000	−0.294884
$415$	0	0
$416$	−1.85410	−0.0909048
$417$	13.4164	0.657004
$418$	5.52786	0.270377
$419$	−2.11146	−0.103151	−0.0515757	−	0.998669i	$-0.516424\pi$
$419$	−2.11146	−0.103151	−0.0515757	+	0.998669i	$0.516424\pi$
$420$	0	0
$421$	0.0901699	0.00439461	0.00219731	−	0.999998i	$-0.499301\pi$
$421$	0.0901699	0.00439461	0.00219731	+	0.999998i	$0.499301\pi$
$422$	−8.00000	−0.389434
$423$	−9.23607	−0.449073
$424$	11.5623	0.561515
$425$	0	0
$426$	8.18034	0.396339
$427$	4.29180	0.207695
$428$	6.94427	0.335664
$429$	1.41641	0.0683848
$430$	0	0
$431$	−9.70820	−0.467628	−0.233814	−	0.972281i	$-0.575121\pi$
$431$	−9.70820	−0.467628	−0.233814	+	0.972281i	$0.575121\pi$
$432$	1.00000	0.0481125
$433$	29.8541	1.43470	0.717348	−	0.696715i	$-0.245356\pi$
$433$	29.8541	1.43470	0.717348	+	0.696715i	$0.245356\pi$
$434$	19.4164	0.932017
$435$	0	0
$436$	−17.5623	−0.841082
$437$	43.4164	2.07689
$438$	9.85410	0.470847
$439$	15.1246	0.721858	0.360929	−	0.932593i	$-0.382460\pi$
$439$	15.1246	0.721858	0.360929	+	0.932593i	$0.382460\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	2.12461	0.101057
$443$	28.0689	1.33359	0.666796	−	0.745240i	$-0.267665\pi$
$443$	28.0689	1.33359	0.666796	+	0.745240i	$0.267665\pi$
$444$	8.85410	0.420197
$445$	0	0
$446$	15.7082	0.743805
$447$	−22.0344	−1.04219
$448$	−2.00000	−0.0944911
$449$	−19.7984	−0.934343	−0.467172	−	0.884167i	$-0.654727\pi$
$449$	−19.7984	−0.934343	−0.467172	+	0.884167i	$0.654727\pi$
$450$	0	0
$451$	−3.88854	−0.183104
$452$	−8.56231	−0.402737
$453$	10.9443	0.514207
$454$	−0.944272	−0.0443169
$455$	0	0
$456$	−7.23607	−0.338860
$457$	3.52786	0.165027	0.0825133	−	0.996590i	$-0.473705\pi$
$457$	3.52786	0.165027	0.0825133	+	0.996590i	$0.473705\pi$
$458$	9.27051	0.433182
$459$	−1.14590	−0.0534859
$460$	0	0
$461$	13.9098	0.647845	0.323923	−	0.946084i	$-0.394998\pi$
$461$	13.9098	0.647845	0.323923	+	0.946084i	$0.394998\pi$
$462$	1.52786	0.0710827
$463$	25.7082	1.19476	0.597381	−	0.801958i	$-0.296208\pi$
$463$	25.7082	1.19476	0.597381	+	0.801958i	$0.296208\pi$
$464$	−3.61803	−0.167963
$465$	0	0
$466$	10.9098	0.505388
$467$	−38.1803	−1.76678	−0.883388	−	0.468643i	$-0.844743\pi$
$467$	−38.1803	−1.76678	−0.883388	+	0.468643i	$0.844743\pi$
$468$	−1.85410	−0.0857059
$469$	7.41641	0.342458
$470$	0	0
$471$	−11.1459	−0.513576
$472$	−8.94427	−0.411693
$473$	2.47214	0.113669
$474$	0	0
$475$	0	0
$476$	2.29180	0.105044
$477$	11.5623	0.529402
$478$	−26.8328	−1.22730
$479$	−4.47214	−0.204337	−0.102169	−	0.994767i	$-0.532578\pi$
$479$	−4.47214	−0.204337	−0.102169	+	0.994767i	$0.532578\pi$
$480$	0	0
$481$	−16.4164	−0.748524
$482$	−7.14590	−0.325487
$483$	12.0000	0.546019
$484$	−10.4164	−0.473473
$485$	0	0
$486$	1.00000	0.0453609
$487$	−23.7082	−1.07432	−0.537161	−	0.843480i	$-0.680503\pi$
$487$	−23.7082	−1.07432	−0.537161	+	0.843480i	$0.680503\pi$
$488$	−2.14590	−0.0971402
$489$	−11.5279	−0.521308
$490$	0	0
$491$	−5.88854	−0.265746	−0.132873	−	0.991133i	$-0.542420\pi$
$491$	−5.88854	−0.265746	−0.132873	+	0.991133i	$0.542420\pi$
$492$	5.09017	0.229483
$493$	4.14590	0.186722
$494$	13.4164	0.603633
$495$	0	0
$496$	−9.70820	−0.435911
$497$	−16.3607	−0.733877
$498$	−6.00000	−0.268866
$499$	−6.58359	−0.294722	−0.147361	−	0.989083i	$-0.547078\pi$
$499$	−6.58359	−0.294722	−0.147361	+	0.989083i	$0.547078\pi$
$500$	0	0
$501$	2.47214	0.110447
$502$	−3.52786	−0.157456
$503$	−30.4721	−1.35869	−0.679343	−	0.733821i	$-0.737735\pi$
$503$	−30.4721	−1.35869	−0.679343	+	0.733821i	$0.737735\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	4.58359	0.203766
$507$	−9.56231	−0.424677
$508$	−13.7082	−0.608203
$509$	28.7426	1.27400	0.636998	−	0.770866i	$-0.280176\pi$
$509$	28.7426	1.27400	0.636998	+	0.770866i	$0.280176\pi$
$510$	0	0
$511$	−19.7082	−0.871840
$512$	1.00000	0.0441942
$513$	−7.23607	−0.319480
$514$	9.38197	0.413821
$515$	0	0
$516$	−3.23607	−0.142460
$517$	7.05573	0.310311
$518$	−17.7082	−0.778054
$519$	22.0902	0.969651
$520$	0	0
$521$	−27.2705	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$521$	−27.2705	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$522$	−3.61803	−0.158357
$523$	15.7082	0.686872	0.343436	−	0.939176i	$-0.388409\pi$
$523$	15.7082	0.686872	0.343436	+	0.939176i	$0.388409\pi$
$524$	−5.23607	−0.228739
$525$	0	0
$526$	8.47214	0.369403
$527$	11.1246	0.484596
$528$	−0.763932	−0.0332459
$529$	13.0000	0.565217
$530$	0	0
$531$	−8.94427	−0.388148
$532$	14.4721	0.627447
$533$	−9.43769	−0.408792
$534$	3.61803	0.156568
$535$	0	0
$536$	−3.70820	−0.160170
$537$	−26.1803	−1.12977
$538$	−13.0902	−0.564357
$539$	2.29180	0.0987146
$540$	0	0
$541$	−12.2705	−0.527550	−0.263775	−	0.964584i	$-0.584968\pi$
$541$	−12.2705	−0.527550	−0.263775	+	0.964584i	$0.584968\pi$
$542$	5.81966	0.249976
$543$	9.03444	0.387705
$544$	−1.14590	−0.0491300
$545$	0	0
$546$	3.70820	0.158696
$547$	−2.00000	−0.0855138	−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000	−0.0855138	−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−14.0344	−0.599522
$549$	−2.14590	−0.0915847
$550$	0	0
$551$	26.1803	1.11532
$552$	−6.00000	−0.255377
$553$	0	0
$554$	28.8541	1.22589
$555$	0	0
$556$	13.4164	0.568982
$557$	−6.27051	−0.265690	−0.132845	−	0.991137i	$-0.542411\pi$
$557$	−6.27051	−0.265690	−0.132845	+	0.991137i	$0.542411\pi$
$558$	−9.70820	−0.410981
$559$	6.00000	0.253773
$560$	0	0
$561$	0.875388	0.0369589
$562$	5.09017	0.214716
$563$	−1.52786	−0.0643918	−0.0321959	−	0.999482i	$-0.510250\pi$
$563$	−1.52786	−0.0643918	−0.0321959	+	0.999482i	$0.510250\pi$
$564$	−9.23607	−0.388909
$565$	0	0
$566$	1.23607	0.0519558
$567$	−2.00000	−0.0839921
$568$	8.18034	0.343239
$569$	23.6180	0.990119	0.495060	−	0.868859i	$-0.335146\pi$
$569$	23.6180	0.990119	0.495060	+	0.868859i	$0.335146\pi$
$570$	0	0
$571$	20.2918	0.849185	0.424593	−	0.905385i	$-0.360417\pi$
$571$	20.2918	0.849185	0.424593	+	0.905385i	$0.360417\pi$
$572$	1.41641	0.0592230
$573$	−5.23607	−0.218740
$574$	−10.1803	−0.424919
$575$	0	0
$576$	1.00000	0.0416667
$577$	24.8328	1.03380	0.516902	−	0.856045i	$-0.327085\pi$
$577$	24.8328	1.03380	0.516902	+	0.856045i	$0.327085\pi$
$578$	−15.6869	−0.652490
$579$	−4.61803	−0.191919
$580$	0	0
$581$	12.0000	0.497844
$582$	7.14590	0.296207
$583$	−8.83282	−0.365818
$584$	9.85410	0.407766
$585$	0	0
$586$	4.20163	0.173568
$587$	−19.8885	−0.820888	−0.410444	−	0.911886i	$-0.634626\pi$
$587$	−19.8885	−0.820888	−0.410444	+	0.911886i	$0.634626\pi$
$588$	−3.00000	−0.123718
$589$	70.2492	2.89457
$590$	0	0
$591$	−2.32624	−0.0956886
$592$	8.85410	0.363901
$593$	−23.0344	−0.945911	−0.472956	−	0.881086i	$-0.656813\pi$
$593$	−23.0344	−0.945911	−0.472956	+	0.881086i	$0.656813\pi$
$594$	−0.763932	−0.0313445
$595$	0	0
$596$	−22.0344	−0.902566
$597$	16.1803	0.662217
$598$	11.1246	0.454919
$599$	18.9443	0.774042	0.387021	−	0.922071i	$-0.373504\pi$
$599$	18.9443	0.774042	0.387021	+	0.922071i	$0.373504\pi$
$600$	0	0
$601$	−8.32624	−0.339634	−0.169817	−	0.985476i	$-0.554318\pi$
$601$	−8.32624	−0.339634	−0.169817	+	0.985476i	$0.554318\pi$
$602$	6.47214	0.263785
$603$	−3.70820	−0.151010
$604$	10.9443	0.445316
$605$	0	0
$606$	17.3262	0.703830
$607$	24.1803	0.981450	0.490725	−	0.871315i	$-0.336732\pi$
$607$	24.1803	0.981450	0.490725	+	0.871315i	$0.336732\pi$
$608$	−7.23607	−0.293461
$609$	7.23607	0.293220
$610$	0	0
$611$	17.1246	0.692788
$612$	−1.14590	−0.0463202
$613$	1.43769	0.0580679	0.0290340	−	0.999578i	$-0.490757\pi$
$613$	1.43769	0.0580679	0.0290340	+	0.999578i	$0.490757\pi$
$614$	29.7082	1.19893
$615$	0	0
$616$	1.52786	0.0615594
$617$	−10.6180	−0.427466	−0.213733	−	0.976892i	$-0.568562\pi$
$617$	−10.6180	−0.427466	−0.213733	+	0.976892i	$0.568562\pi$
$618$	15.7082	0.631877
$619$	−23.4164	−0.941185	−0.470592	−	0.882351i	$-0.655960\pi$
$619$	−23.4164	−0.941185	−0.470592	+	0.882351i	$0.655960\pi$
$620$	0	0
$621$	−6.00000	−0.240772
$622$	12.6525	0.507318
$623$	−7.23607	−0.289907
$624$	−1.85410	−0.0742235
$625$	0	0
$626$	−18.3607	−0.733840
$627$	5.52786	0.220762
$628$	−11.1459	−0.444770
$629$	−10.1459	−0.404543
$630$	0	0
$631$	−2.87539	−0.114467	−0.0572337	−	0.998361i	$-0.518228\pi$
$631$	−2.87539	−0.114467	−0.0572337	+	0.998361i	$0.518228\pi$
$632$	0	0
$633$	−8.00000	−0.317971
$634$	−10.9443	−0.434653
$635$	0	0
$636$	11.5623	0.458475
$637$	5.56231	0.220387
$638$	2.76393	0.109425
$639$	8.18034	0.323609
$640$	0	0
$641$	−9.05573	−0.357680	−0.178840	−	0.983878i	$-0.557234\pi$
$641$	−9.05573	−0.357680	−0.178840	+	0.983878i	$0.557234\pi$
$642$	6.94427	0.274069
$643$	−31.7771	−1.25317	−0.626583	−	0.779355i	$-0.715547\pi$
$643$	−31.7771	−1.25317	−0.626583	+	0.779355i	$0.715547\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	8.29180	0.326236
$647$	0.111456	0.00438179	0.00219090	−	0.999998i	$-0.499303\pi$
$647$	0.111456	0.00438179	0.00219090	+	0.999998i	$0.499303\pi$
$648$	1.00000	0.0392837
$649$	6.83282	0.268211
$650$	0	0
$651$	19.4164	0.760989
$652$	−11.5279	−0.451466
$653$	−19.2148	−0.751933	−0.375966	−	0.926633i	$-0.622689\pi$
$653$	−19.2148	−0.751933	−0.375966	+	0.926633i	$0.622689\pi$
$654$	−17.5623	−0.686741
$655$	0	0
$656$	5.09017	0.198738
$657$	9.85410	0.384445
$658$	18.4721	0.720119
$659$	21.0557	0.820215	0.410107	−	0.912037i	$-0.365491\pi$
$659$	21.0557	0.820215	0.410107	+	0.912037i	$0.365491\pi$
$660$	0	0
$661$	−32.4721	−1.26302	−0.631510	−	0.775368i	$-0.717564\pi$
$661$	−32.4721	−1.26302	−0.631510	+	0.775368i	$0.717564\pi$
$662$	−23.5279	−0.914436
$663$	2.12461	0.0825131
$664$	−6.00000	−0.232845
$665$	0	0
$666$	8.85410	0.343089
$667$	21.7082	0.840545
$668$	2.47214	0.0956498
$669$	15.7082	0.607314
$670$	0	0
$671$	1.63932	0.0632853
$672$	−2.00000	−0.0771517
$673$	−5.79837	−0.223511	−0.111755	−	0.993736i	$-0.535647\pi$
$673$	−5.79837	−0.223511	−0.111755	+	0.993736i	$0.535647\pi$
$674$	24.8328	0.956524
$675$	0	0
$676$	−9.56231	−0.367781
$677$	−27.5279	−1.05798	−0.528991	−	0.848628i	$-0.677429\pi$
$677$	−27.5279	−1.05798	−0.528991	+	0.848628i	$0.677429\pi$
$678$	−8.56231	−0.328833
$679$	−14.2918	−0.548469
$680$	0	0
$681$	−0.944272	−0.0361846
$682$	7.41641	0.283989
$683$	7.41641	0.283781	0.141890	−	0.989882i	$-0.454682\pi$
$683$	7.41641	0.283781	0.141890	+	0.989882i	$0.454682\pi$
$684$	−7.23607	−0.276678
$685$	0	0
$686$	20.0000	0.763604
$687$	9.27051	0.353692
$688$	−3.23607	−0.123374
$689$	−21.4377	−0.816711
$690$	0	0
$691$	−1.81966	−0.0692231	−0.0346116	−	0.999401i	$-0.511019\pi$
$691$	−1.81966	−0.0692231	−0.0346116	+	0.999401i	$0.511019\pi$
$692$	22.0902	0.839742
$693$	1.52786	0.0580388
$694$	0.763932	0.0289985
$695$	0	0
$696$	−3.61803	−0.137141
$697$	−5.83282	−0.220934
$698$	−9.79837	−0.370874
$699$	10.9098	0.412648
$700$	0	0
$701$	49.1591	1.85671	0.928356	−	0.371692i	$-0.121222\pi$
$701$	49.1591	1.85671	0.928356	+	0.371692i	$0.121222\pi$
$702$	−1.85410	−0.0699786
$703$	−64.0689	−2.41640
$704$	−0.763932	−0.0287918
$705$	0	0
$706$	−11.5279	−0.433857
$707$	−34.6525	−1.30324
$708$	−8.94427	−0.336146
$709$	−5.20163	−0.195351	−0.0976756	−	0.995218i	$-0.531141\pi$
$709$	−5.20163	−0.195351	−0.0976756	+	0.995218i	$0.531141\pi$
$710$	0	0
$711$	0	0
$712$	3.61803	0.135592
$713$	58.2492	2.18145
$714$	2.29180	0.0857683
$715$	0	0
$716$	−26.1803	−0.978405
$717$	−26.8328	−1.00209
$718$	7.88854	0.294398
$719$	−22.3607	−0.833913	−0.416956	−	0.908927i	$-0.636903\pi$
$719$	−22.3607	−0.833913	−0.416956	+	0.908927i	$0.636903\pi$
$720$	0	0
$721$	−31.4164	−1.17001
$722$	33.3607	1.24156
$723$	−7.14590	−0.265759
$724$	9.03444	0.335762
$725$	0	0
$726$	−10.4164	−0.386589
$727$	−23.7082	−0.879289	−0.439644	−	0.898172i	$-0.644895\pi$
$727$	−23.7082	−0.879289	−0.439644	+	0.898172i	$0.644895\pi$
$728$	3.70820	0.137435
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.70820	0.137153
$732$	−2.14590	−0.0793147
$733$	−38.3607	−1.41688	−0.708442	−	0.705769i	$-0.750602\pi$
$733$	−38.3607	−1.41688	−0.708442	+	0.705769i	$0.750602\pi$
$734$	3.52786	0.130216
$735$	0	0
$736$	−6.00000	−0.221163
$737$	2.83282	0.104348
$738$	5.09017	0.187372
$739$	21.7082	0.798549	0.399275	−	0.916831i	$-0.369262\pi$
$739$	21.7082	0.798549	0.399275	+	0.916831i	$0.369262\pi$
$740$	0	0
$741$	13.4164	0.492864
$742$	−23.1246	−0.848931
$743$	24.6525	0.904412	0.452206	−	0.891914i	$-0.350637\pi$
$743$	24.6525	0.904412	0.452206	+	0.891914i	$0.350637\pi$
$744$	−9.70820	−0.355920
$745$	0	0
$746$	−29.4164	−1.07701
$747$	−6.00000	−0.219529
$748$	0.875388	0.0320074
$749$	−13.8885	−0.507476
$750$	0	0
$751$	19.2361	0.701934	0.350967	−	0.936388i	$-0.385853\pi$
$751$	19.2361	0.701934	0.350967	+	0.936388i	$0.385853\pi$
$752$	−9.23607	−0.336805
$753$	−3.52786	−0.128563
$754$	6.70820	0.244298
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	22.1459	0.804906	0.402453	−	0.915441i	$-0.368158\pi$
$757$	22.1459	0.804906	0.402453	+	0.915441i	$0.368158\pi$
$758$	23.4164	0.850522
$759$	4.58359	0.166374
$760$	0	0
$761$	−45.1591	−1.63701	−0.818507	−	0.574496i	$-0.805198\pi$
$761$	−45.1591	−1.63701	−0.818507	+	0.574496i	$0.805198\pi$
$762$	−13.7082	−0.496596
$763$	35.1246	1.27160
$764$	−5.23607	−0.189434
$765$	0	0
$766$	−11.5279	−0.416519
$767$	16.5836	0.598799
$768$	1.00000	0.0360844
$769$	42.3607	1.52757	0.763783	−	0.645474i	$-0.223340\pi$
$769$	42.3607	1.52757	0.763783	+	0.645474i	$0.223340\pi$
$770$	0	0
$771$	9.38197	0.337883
$772$	−4.61803	−0.166207
$773$	−2.90983	−0.104659	−0.0523297	−	0.998630i	$-0.516665\pi$
$773$	−2.90983	−0.104659	−0.0523297	+	0.998630i	$0.516665\pi$
$774$	−3.23607	−0.116318
$775$	0	0
$776$	7.14590	0.256523
$777$	−17.7082	−0.635278
$778$	−30.9787	−1.11064
$779$	−36.8328	−1.31967
$780$	0	0
$781$	−6.24922	−0.223615
$782$	6.87539	0.245863
$783$	−3.61803	−0.129298
$784$	−3.00000	−0.107143
$785$	0	0
$786$	−5.23607	−0.186764
$787$	36.5410	1.30255	0.651273	−	0.758843i	$-0.274235\pi$
$787$	36.5410	1.30255	0.651273	+	0.758843i	$0.274235\pi$
$788$	−2.32624	−0.0828688
$789$	8.47214	0.301616
$790$	0	0
$791$	17.1246	0.608881
$792$	−0.763932	−0.0271451
$793$	3.97871	0.141288
$794$	24.8328	0.881284
$795$	0	0
$796$	16.1803	0.573497
$797$	−2.32624	−0.0823996	−0.0411998	−	0.999151i	$-0.513118\pi$
$797$	−2.32624	−0.0823996	−0.0411998	+	0.999151i	$0.513118\pi$
$798$	14.4721	0.512308
$799$	10.5836	0.374421
$800$	0	0
$801$	3.61803	0.127837
$802$	−14.9098	−0.526484
$803$	−7.52786	−0.265653
$804$	−3.70820	−0.130778
$805$	0	0
$806$	18.0000	0.634023
$807$	−13.0902	−0.460796
$808$	17.3262	0.609535
$809$	−43.2148	−1.51935	−0.759675	−	0.650302i	$-0.774642\pi$
$809$	−43.2148	−1.51935	−0.759675	+	0.650302i	$0.774642\pi$
$810$	0	0
$811$	23.7082	0.832508	0.416254	−	0.909248i	$-0.363343\pi$
$811$	23.7082	0.832508	0.416254	+	0.909248i	$0.363343\pi$
$812$	7.23607	0.253936
$813$	5.81966	0.204104
$814$	−6.76393	−0.237076
$815$	0	0
$816$	−1.14590	−0.0401145
$817$	23.4164	0.819236
$818$	−25.9787	−0.908324
$819$	3.70820	0.129575
$820$	0	0
$821$	8.83282	0.308267	0.154134	−	0.988050i	$-0.450741\pi$
$821$	8.83282	0.308267	0.154134	+	0.988050i	$0.450741\pi$
$822$	−14.0344	−0.489507
$823$	−25.5967	−0.892247	−0.446123	−	0.894972i	$-0.647196\pi$
$823$	−25.5967	−0.892247	−0.446123	+	0.894972i	$0.647196\pi$
$824$	15.7082	0.547221
$825$	0	0
$826$	17.8885	0.622422
$827$	−19.2361	−0.668904	−0.334452	−	0.942413i	$-0.608551\pi$
$827$	−19.2361	−0.668904	−0.334452	+	0.942413i	$0.608551\pi$
$828$	−6.00000	−0.208514
$829$	45.8541	1.59258	0.796289	−	0.604916i	$-0.206793\pi$
$829$	45.8541	1.59258	0.796289	+	0.604916i	$0.206793\pi$
$830$	0	0
$831$	28.8541	1.00094
$832$	−1.85410	−0.0642794
$833$	3.43769	0.119109
$834$	13.4164	0.464572
$835$	0	0
$836$	5.52786	0.191185
$837$	−9.70820	−0.335565
$838$	−2.11146	−0.0729390
$839$	35.1246	1.21264	0.606318	−	0.795222i	$-0.292646\pi$
$839$	35.1246	1.21264	0.606318	+	0.795222i	$0.292646\pi$
$840$	0	0
$841$	−15.9098	−0.548615
$842$	0.0901699	0.00310746
$843$	5.09017	0.175315
$844$	−8.00000	−0.275371
$845$	0	0
$846$	−9.23607	−0.317543
$847$	20.8328	0.715824
$848$	11.5623	0.397051
$849$	1.23607	0.0424217
$850$	0	0
$851$	−53.1246	−1.82109
$852$	8.18034	0.280254
$853$	39.4508	1.35077	0.675386	−	0.737465i	$-0.263977\pi$
$853$	39.4508	1.35077	0.675386	+	0.737465i	$0.263977\pi$
$854$	4.29180	0.146862
$855$	0	0
$856$	6.94427	0.237350
$857$	39.3050	1.34263	0.671316	−	0.741171i	$-0.265729\pi$
$857$	39.3050	1.34263	0.671316	+	0.741171i	$0.265729\pi$
$858$	1.41641	0.0483554
$859$	54.4721	1.85857	0.929283	−	0.369369i	$-0.120426\pi$
$859$	54.4721	1.85857	0.929283	+	0.369369i	$0.120426\pi$
$860$	0	0
$861$	−10.1803	−0.346945
$862$	−9.70820	−0.330663
$863$	10.1803	0.346543	0.173271	−	0.984874i	$-0.444566\pi$
$863$	10.1803	0.346543	0.173271	+	0.984874i	$0.444566\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	29.8541	1.01448
$867$	−15.6869	−0.532756
$868$	19.4164	0.659036
$869$	0	0
$870$	0	0
$871$	6.87539	0.232964
$872$	−17.5623	−0.594735
$873$	7.14590	0.241852
$874$	43.4164	1.46858
$875$	0	0
$876$	9.85410	0.332939
$877$	28.9787	0.978542	0.489271	−	0.872132i	$-0.337263\pi$
$877$	28.9787	0.978542	0.489271	+	0.872132i	$0.337263\pi$
$878$	15.1246	0.510431
$879$	4.20163	0.141717
$880$	0	0
$881$	−42.7214	−1.43932	−0.719660	−	0.694327i	$-0.755702\pi$
$881$	−42.7214	−1.43932	−0.719660	+	0.694327i	$0.755702\pi$
$882$	−3.00000	−0.101015
$883$	−19.8197	−0.666985	−0.333492	−	0.942753i	$-0.608227\pi$
$883$	−19.8197	−0.666985	−0.333492	+	0.942753i	$0.608227\pi$
$884$	2.12461	0.0714584
$885$	0	0
$886$	28.0689	0.942993
$887$	−48.1803	−1.61774	−0.808869	−	0.587989i	$-0.799920\pi$
$887$	−48.1803	−1.61774	−0.808869	+	0.587989i	$0.799920\pi$
$888$	8.85410	0.297124
$889$	27.4164	0.919517
$890$	0	0
$891$	−0.763932	−0.0255927
$892$	15.7082	0.525950
$893$	66.8328	2.23647
$894$	−22.0344	−0.736942
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	11.1246	0.371440
$898$	−19.7984	−0.660680
$899$	35.1246	1.17147
$900$	0	0
$901$	−13.2492	−0.441396
$902$	−3.88854	−0.129474
$903$	6.47214	0.215379
$904$	−8.56231	−0.284778
$905$	0	0
$906$	10.9443	0.363599
$907$	−33.7082	−1.11926	−0.559631	−	0.828742i	$-0.689057\pi$
$907$	−33.7082	−1.11926	−0.559631	+	0.828742i	$0.689057\pi$
$908$	−0.944272	−0.0313368
$909$	17.3262	0.574675
$910$	0	0
$911$	−2.06888	−0.0685452	−0.0342726	−	0.999413i	$-0.510911\pi$
$911$	−2.06888	−0.0685452	−0.0342726	+	0.999413i	$0.510911\pi$
$912$	−7.23607	−0.239610
$913$	4.58359	0.151695
$914$	3.52786	0.116691
$915$	0	0
$916$	9.27051	0.306306
$917$	10.4721	0.345820
$918$	−1.14590	−0.0378203
$919$	−18.9443	−0.624914	−0.312457	−	0.949932i	$-0.601152\pi$
$919$	−18.9443	−0.624914	−0.312457	+	0.949932i	$0.601152\pi$
$920$	0	0
$921$	29.7082	0.978919
$922$	13.9098	0.458096
$923$	−15.1672	−0.499234
$924$	1.52786	0.0502630
$925$	0	0
$926$	25.7082	0.844824
$927$	15.7082	0.515925
$928$	−3.61803	−0.118768
$929$	15.9787	0.524245	0.262122	−	0.965035i	$-0.415578\pi$
$929$	15.9787	0.524245	0.262122	+	0.965035i	$0.415578\pi$
$930$	0	0
$931$	21.7082	0.711458
$932$	10.9098	0.357363
$933$	12.6525	0.414223
$934$	−38.1803	−1.24930
$935$	0	0
$936$	−1.85410	−0.0606032
$937$	−23.9098	−0.781100	−0.390550	−	0.920582i	$-0.627715\pi$
$937$	−23.9098	−0.781100	−0.390550	+	0.920582i	$0.627715\pi$
$938$	7.41641	0.242154
$939$	−18.3607	−0.599178
$940$	0	0
$941$	37.3262	1.21680	0.608400	−	0.793630i	$-0.291812\pi$
$941$	37.3262	1.21680	0.608400	+	0.793630i	$0.291812\pi$
$942$	−11.1459	−0.363153
$943$	−30.5410	−0.994552
$944$	−8.94427	−0.291111
$945$	0	0
$946$	2.47214	0.0803761
$947$	6.94427	0.225659	0.112829	−	0.993614i	$-0.464009\pi$
$947$	6.94427	0.225659	0.112829	+	0.993614i	$0.464009\pi$
$948$	0	0
$949$	−18.2705	−0.593086
$950$	0	0
$951$	−10.9443	−0.354892
$952$	2.29180	0.0742775
$953$	−49.8673	−1.61536	−0.807679	−	0.589622i	$-0.799277\pi$
$953$	−49.8673	−1.61536	−0.807679	+	0.589622i	$0.799277\pi$
$954$	11.5623	0.374343
$955$	0	0
$956$	−26.8328	−0.867835
$957$	2.76393	0.0893452
$958$	−4.47214	−0.144488
$959$	28.0689	0.906392
$960$	0	0
$961$	63.2492	2.04030
$962$	−16.4164	−0.529286
$963$	6.94427	0.223776
$964$	−7.14590	−0.230154
$965$	0	0
$966$	12.0000	0.386094
$967$	−23.0557	−0.741422	−0.370711	−	0.928748i	$-0.620886\pi$
$967$	−23.0557	−0.741422	−0.370711	+	0.928748i	$0.620886\pi$
$968$	−10.4164	−0.334796
$969$	8.29180	0.266371
$970$	0	0
$971$	37.7771	1.21232	0.606162	−	0.795341i	$-0.292708\pi$
$971$	37.7771	1.21232	0.606162	+	0.795341i	$0.292708\pi$
$972$	1.00000	0.0320750
$973$	−26.8328	−0.860221
$974$	−23.7082	−0.759660
$975$	0	0
$976$	−2.14590	−0.0686885
$977$	0.437694	0.0140031	0.00700154	−	0.999975i	$-0.497771\pi$
$977$	0.437694	0.0140031	0.00700154	+	0.999975i	$0.497771\pi$
$978$	−11.5279	−0.368620
$979$	−2.76393	−0.0883357
$980$	0	0
$981$	−17.5623	−0.560721
$982$	−5.88854	−0.187911
$983$	−24.5410	−0.782737	−0.391368	−	0.920234i	$-0.627998\pi$
$983$	−24.5410	−0.782737	−0.391368	+	0.920234i	$0.627998\pi$
$984$	5.09017	0.162269
$985$	0	0
$986$	4.14590	0.132032
$987$	18.4721	0.587975
$988$	13.4164	0.426833
$989$	19.4164	0.617406
$990$	0	0
$991$	−6.54102	−0.207782	−0.103891	−	0.994589i	$-0.533129\pi$
$991$	−6.54102	−0.207782	−0.103891	+	0.994589i	$0.533129\pi$
$992$	−9.70820	−0.308236
$993$	−23.5279	−0.746634
$994$	−16.3607	−0.518929
$995$	0	0
$996$	−6.00000	−0.190117
$997$	−25.4164	−0.804946	−0.402473	−	0.915432i	$-0.631849\pi$
$997$	−25.4164	−0.804946	−0.402473	+	0.915432i	$0.631849\pi$
$998$	−6.58359	−0.208400
$999$	8.85410	0.280131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.g.1.2		2
5.2	odd	4		3750.2.c.c.1249.4		4
5.3	odd	4		3750.2.c.c.1249.2		4
5.4	even	2		3750.2.a.b.1.2		2
25.3	odd	20		750.2.h.a.49.1		8
25.4	even	10		150.2.g.b.91.1	yes	4
25.6	even	5		750.2.g.a.301.1		4
25.8	odd	20		750.2.h.a.199.2		8
25.17	odd	20		750.2.h.a.199.1		8
25.19	even	10		150.2.g.b.61.1	✓	4
25.21	even	5		750.2.g.a.451.1		4
25.22	odd	20		750.2.h.a.49.2		8
75.29	odd	10		450.2.h.b.91.1		4
75.44	odd	10		450.2.h.b.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.61.1	✓	4	25.19	even	10
150.2.g.b.91.1	yes	4	25.4	even	10
450.2.h.b.91.1		4	75.29	odd	10
450.2.h.b.361.1		4	75.44	odd	10
750.2.g.a.301.1		4	25.6	even	5
750.2.g.a.451.1		4	25.21	even	5
750.2.h.a.49.1		8	25.3	odd	20
750.2.h.a.49.2		8	25.22	odd	20
750.2.h.a.199.1		8	25.17	odd	20
750.2.h.a.199.2		8	25.8	odd	20
3750.2.a.b.1.2		2	5.4	even	2
3750.2.a.g.1.2		2	1.1	even	1	trivial
3750.2.c.c.1249.2		4	5.3	odd	4
3750.2.c.c.1249.4		4	5.2	odd	4

Overview	Random
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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.763932 q^{11} +1.00000 q^{12} -1.85410 q^{13} -2.00000 q^{14} +1.00000 q^{16} -1.14590 q^{17} +1.00000 q^{18} -7.23607 q^{19} -2.00000 q^{21} -0.763932 q^{22} -6.00000 q^{23} +1.00000 q^{24} -1.85410 q^{26} +1.00000 q^{27} -2.00000 q^{28} -3.61803 q^{29} -9.70820 q^{31} +1.00000 q^{32} -0.763932 q^{33} -1.14590 q^{34} +1.00000 q^{36} +8.85410 q^{37} -7.23607 q^{38} -1.85410 q^{39} +5.09017 q^{41} -2.00000 q^{42} -3.23607 q^{43} -0.763932 q^{44} -6.00000 q^{46} -9.23607 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.14590 q^{51} -1.85410 q^{52} +11.5623 q^{53} +1.00000 q^{54} -2.00000 q^{56} -7.23607 q^{57} -3.61803 q^{58} -8.94427 q^{59} -2.14590 q^{61} -9.70820 q^{62} -2.00000 q^{63} +1.00000 q^{64} -0.763932 q^{66} -3.70820 q^{67} -1.14590 q^{68} -6.00000 q^{69} +8.18034 q^{71} +1.00000 q^{72} +9.85410 q^{73} +8.85410 q^{74} -7.23607 q^{76} +1.52786 q^{77} -1.85410 q^{78} +1.00000 q^{81} +5.09017 q^{82} -6.00000 q^{83} -2.00000 q^{84} -3.23607 q^{86} -3.61803 q^{87} -0.763932 q^{88} +3.61803 q^{89} +3.70820 q^{91} -6.00000 q^{92} -9.70820 q^{93} -9.23607 q^{94} +1.00000 q^{96} +7.14590 q^{97} -3.00000 q^{98} -0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} + 2 q^{12} + 3 q^{13} - 4 q^{14} + 2 q^{16} - 9 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} - 4 q^{28} - 5 q^{29} - 6 q^{31} + 2 q^{32} - 6 q^{33} - 9 q^{34} + 2 q^{36} + 11 q^{37} - 10 q^{38} + 3 q^{39} - q^{41} - 4 q^{42} - 2 q^{43} - 6 q^{44} - 12 q^{46} - 14 q^{47} + 2 q^{48} - 6 q^{49} - 9 q^{51} + 3 q^{52} + 3 q^{53} + 2 q^{54} - 4 q^{56} - 10 q^{57} - 5 q^{58} - 11 q^{61} - 6 q^{62} - 4 q^{63} + 2 q^{64} - 6 q^{66} + 6 q^{67} - 9 q^{68} - 12 q^{69} - 6 q^{71} + 2 q^{72} + 13 q^{73} + 11 q^{74} - 10 q^{76} + 12 q^{77} + 3 q^{78} + 2 q^{81} - q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{86} - 5 q^{87} - 6 q^{88} + 5 q^{89} - 6 q^{91} - 12 q^{92} - 6 q^{93} - 14 q^{94} + 2 q^{96} + 21 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 + 2 * q^12 + 3 * q^13 - 4 * q^14 + 2 * q^16 - 9 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 - 4 * q^28 - 5 * q^29 - 6 * q^31 + 2 * q^32 - 6 * q^33 - 9 * q^34 + 2 * q^36 + 11 * q^37 - 10 * q^38 + 3 * q^39 - q^41 - 4 * q^42 - 2 * q^43 - 6 * q^44 - 12 * q^46 - 14 * q^47 + 2 * q^48 - 6 * q^49 - 9 * q^51 + 3 * q^52 + 3 * q^53 + 2 * q^54 - 4 * q^56 - 10 * q^57 - 5 * q^58 - 11 * q^61 - 6 * q^62 - 4 * q^63 + 2 * q^64 - 6 * q^66 + 6 * q^67 - 9 * q^68 - 12 * q^69 - 6 * q^71 + 2 * q^72 + 13 * q^73 + 11 * q^74 - 10 * q^76 + 12 * q^77 + 3 * q^78 + 2 * q^81 - q^82 - 12 * q^83 - 4 * q^84 - 2 * q^86 - 5 * q^87 - 6 * q^88 + 5 * q^89 - 6 * q^91 - 12 * q^92 - 6 * q^93 - 14 * q^94 + 2 * q^96 + 21 * q^97 - 6 * q^98 - 6 * q^99

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