LMFDB - Embedded newform 3850.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -2.00000 q^{12} +4.74456 q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.74456 q^{17} -1.00000 q^{18} +4.74456 q^{19} +2.00000 q^{21} +1.00000 q^{22} -4.74456 q^{23} +2.00000 q^{24} -4.74456 q^{26} +4.00000 q^{27} -1.00000 q^{28} -2.74456 q^{29} -6.74456 q^{31} -1.00000 q^{32} +2.00000 q^{33} +4.74456 q^{34} +1.00000 q^{36} +10.7446 q^{37} -4.74456 q^{38} -9.48913 q^{39} -4.00000 q^{41} -2.00000 q^{42} -4.00000 q^{43} -1.00000 q^{44} +4.74456 q^{46} +6.74456 q^{47} -2.00000 q^{48} +1.00000 q^{49} +9.48913 q^{51} +4.74456 q^{52} +1.25544 q^{53} -4.00000 q^{54} +1.00000 q^{56} -9.48913 q^{57} +2.74456 q^{58} +2.74456 q^{59} +12.7446 q^{61} +6.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} +4.00000 q^{67} -4.74456 q^{68} +9.48913 q^{69} -4.00000 q^{71} -1.00000 q^{72} +0.744563 q^{73} -10.7446 q^{74} +4.74456 q^{76} +1.00000 q^{77} +9.48913 q^{78} -4.74456 q^{79} -11.0000 q^{81} +4.00000 q^{82} -8.00000 q^{83} +2.00000 q^{84} +4.00000 q^{86} +5.48913 q^{87} +1.00000 q^{88} -7.48913 q^{89} -4.74456 q^{91} -4.74456 q^{92} +13.4891 q^{93} -6.74456 q^{94} +2.00000 q^{96} +5.25544 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{11} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 2 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} + 4 q^{24} + 2 q^{26} + 8 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{31} - 2 q^{32} + 4 q^{33} - 2 q^{34} + 2 q^{36} + 10 q^{37} + 2 q^{38} + 4 q^{39} - 8 q^{41} - 4 q^{42} - 8 q^{43} - 2 q^{44} - 2 q^{46} + 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{51} - 2 q^{52} + 14 q^{53} - 8 q^{54} + 2 q^{56} + 4 q^{57} - 6 q^{58} - 6 q^{59} + 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{66} + 8 q^{67} + 2 q^{68} - 4 q^{69} - 8 q^{71} - 2 q^{72} - 10 q^{73} - 10 q^{74} - 2 q^{76} + 2 q^{77} - 4 q^{78} + 2 q^{79} - 22 q^{81} + 8 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{86} - 12 q^{87} + 2 q^{88} + 8 q^{89} + 2 q^{91} + 2 q^{92} + 4 q^{93} - 2 q^{94} + 4 q^{96} + 22 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^11 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 2 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 + 4 * q^24 + 2 * q^26 + 8 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^31 - 2 * q^32 + 4 * q^33 - 2 * q^34 + 2 * q^36 + 10 * q^37 + 2 * q^38 + 4 * q^39 - 8 * q^41 - 4 * q^42 - 8 * q^43 - 2 * q^44 - 2 * q^46 + 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^51 - 2 * q^52 + 14 * q^53 - 8 * q^54 + 2 * q^56 + 4 * q^57 - 6 * q^58 - 6 * q^59 + 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^66 + 8 * q^67 + 2 * q^68 - 4 * q^69 - 8 * q^71 - 2 * q^72 - 10 * q^73 - 10 * q^74 - 2 * q^76 + 2 * q^77 - 4 * q^78 + 2 * q^79 - 22 * q^81 + 8 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^86 - 12 * q^87 + 2 * q^88 + 8 * q^89 + 2 * q^91 + 2 * q^92 + 4 * q^93 - 2 * q^94 + 4 * q^96 + 22 * q^97 - 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.00000	−0.577350
$13$	4.74456	1.31590	0.657952	−	0.753059i	$-0.271423\pi$
$13$	4.74456	1.31590	0.657952	+	0.753059i	$0.271423\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.74456	−1.15073	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	−4.74456	−1.15073	−0.575363	+	0.817898i	$0.695139\pi$
$18$	−1.00000	−0.235702
$19$	4.74456	1.08848	0.544239	−	0.838930i	$-0.316819\pi$
$19$	4.74456	1.08848	0.544239	+	0.838930i	$0.316819\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	1.00000	0.213201
$23$	−4.74456	−0.989310	−0.494655	−	0.869090i	$-0.664706\pi$
$23$	−4.74456	−0.989310	−0.494655	+	0.869090i	$0.664706\pi$
$24$	2.00000	0.408248
$25$	0	0
$26$	−4.74456	−0.930485
$27$	4.00000	0.769800
$28$	−1.00000	−0.188982
$29$	−2.74456	−0.509652	−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456	−0.509652	−0.254826	+	0.966987i	$0.582018\pi$
$30$	0	0
$31$	−6.74456	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	4.74456	0.813686
$35$	0	0
$36$	1.00000	0.166667
$37$	10.7446	1.76640	0.883198	−	0.469001i	$-0.155386\pi$
$37$	10.7446	1.76640	0.883198	+	0.469001i	$0.155386\pi$
$38$	−4.74456	−0.769670
$39$	−9.48913	−1.51948
$40$	0	0
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	−2.00000	−0.308607
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	4.74456	0.699548
$47$	6.74456	0.983796	0.491898	−	0.870653i	$-0.336303\pi$
$47$	6.74456	0.983796	0.491898	+	0.870653i	$0.336303\pi$
$48$	−2.00000	−0.288675
$49$	1.00000	0.142857
$50$	0	0
$51$	9.48913	1.32874
$52$	4.74456	0.657952
$53$	1.25544	0.172448	0.0862238	−	0.996276i	$-0.472520\pi$
$53$	1.25544	0.172448	0.0862238	+	0.996276i	$0.472520\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	−9.48913	−1.25687
$58$	2.74456	0.360379
$59$	2.74456	0.357312	0.178656	−	0.983912i	$-0.442825\pi$
$59$	2.74456	0.357312	0.178656	+	0.983912i	$0.442825\pi$
$60$	0	0
$61$	12.7446	1.63177	0.815887	−	0.578211i	$-0.196249\pi$
$61$	12.7446	1.63177	0.815887	+	0.578211i	$0.196249\pi$
$62$	6.74456	0.856560
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−4.74456	−0.575363
$69$	9.48913	1.14236
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	−1.00000	−0.117851
$73$	0.744563	0.0871445	0.0435722	−	0.999050i	$-0.486126\pi$
$73$	0.744563	0.0871445	0.0435722	+	0.999050i	$0.486126\pi$
$74$	−10.7446	−1.24903
$75$	0	0
$76$	4.74456	0.544239
$77$	1.00000	0.113961
$78$	9.48913	1.07443
$79$	−4.74456	−0.533805	−0.266903	−	0.963724i	$-0.586000\pi$
$79$	−4.74456	−0.533805	−0.266903	+	0.963724i	$0.586000\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	4.00000	0.441726
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	4.00000	0.431331
$87$	5.48913	0.588496
$88$	1.00000	0.106600
$89$	−7.48913	−0.793846	−0.396923	−	0.917852i	$-0.629922\pi$
$89$	−7.48913	−0.793846	−0.396923	+	0.917852i	$0.629922\pi$
$90$	0	0
$91$	−4.74456	−0.497365
$92$	−4.74456	−0.494655
$93$	13.4891	1.39876
$94$	−6.74456	−0.695649
$95$	0	0
$96$	2.00000	0.204124
$97$	5.25544	0.533609	0.266804	−	0.963751i	$-0.414032\pi$
$97$	5.25544	0.533609	0.266804	+	0.963751i	$0.414032\pi$
$98$	−1.00000	−0.101015
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−8.74456	−0.870117	−0.435058	−	0.900402i	$-0.643272\pi$
$101$	−8.74456	−0.870117	−0.435058	+	0.900402i	$0.643272\pi$
$102$	−9.48913	−0.939563
$103$	−10.7446	−1.05869	−0.529347	−	0.848406i	$-0.677563\pi$
$103$	−10.7446	−1.05869	−0.529347	+	0.848406i	$0.677563\pi$
$104$	−4.74456	−0.465243
$105$	0	0
$106$	−1.25544	−0.121939
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	4.00000	0.384900
$109$	16.2337	1.55491	0.777453	−	0.628941i	$-0.216511\pi$
$109$	16.2337	1.55491	0.777453	+	0.628941i	$0.216511\pi$
$110$	0	0
$111$	−21.4891	−2.03966
$112$	−1.00000	−0.0944911
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	9.48913	0.888738
$115$	0	0
$116$	−2.74456	−0.254826
$117$	4.74456	0.438635
$118$	−2.74456	−0.252657
$119$	4.74456	0.434933
$120$	0	0
$121$	1.00000	0.0909091
$122$	−12.7446	−1.15384
$123$	8.00000	0.721336
$124$	−6.74456	−0.605680
$125$	0	0
$126$	1.00000	0.0890871
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	8.74456	0.764016	0.382008	−	0.924159i	$-0.375233\pi$
$131$	8.74456	0.764016	0.382008	+	0.924159i	$0.375233\pi$
$132$	2.00000	0.174078
$133$	−4.74456	−0.411406
$134$	−4.00000	−0.345547
$135$	0	0
$136$	4.74456	0.406843
$137$	19.4891	1.66507	0.832534	−	0.553974i	$-0.186889\pi$
$137$	19.4891	1.66507	0.832534	+	0.553974i	$0.186889\pi$
$138$	−9.48913	−0.807768
$139$	3.25544	0.276123	0.138061	−	0.990424i	$-0.455913\pi$
$139$	3.25544	0.276123	0.138061	+	0.990424i	$0.455913\pi$
$140$	0	0
$141$	−13.4891	−1.13599
$142$	4.00000	0.335673
$143$	−4.74456	−0.396760
$144$	1.00000	0.0833333
$145$	0	0
$146$	−0.744563	−0.0616204
$147$	−2.00000	−0.164957
$148$	10.7446	0.883198
$149$	10.7446	0.880229	0.440114	−	0.897942i	$-0.354938\pi$
$149$	10.7446	0.880229	0.440114	+	0.897942i	$0.354938\pi$
$150$	0	0
$151$	−20.7446	−1.68817	−0.844084	−	0.536211i	$-0.819855\pi$
$151$	−20.7446	−1.68817	−0.844084	+	0.536211i	$0.819855\pi$
$152$	−4.74456	−0.384835
$153$	−4.74456	−0.383575
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−9.48913	−0.759738
$157$	−23.4891	−1.87464	−0.937318	−	0.348475i	$-0.886700\pi$
$157$	−23.4891	−1.87464	−0.937318	+	0.348475i	$0.886700\pi$
$158$	4.74456	0.377457
$159$	−2.51087	−0.199125
$160$	0	0
$161$	4.74456	0.373924
$162$	11.0000	0.864242
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	8.00000	0.620920
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−2.00000	−0.154303
$169$	9.51087	0.731606
$170$	0	0
$171$	4.74456	0.362826
$172$	−4.00000	−0.304997
$173$	14.2337	1.08217	0.541084	−	0.840969i	$-0.318014\pi$
$173$	14.2337	1.08217	0.541084	+	0.840969i	$0.318014\pi$
$174$	−5.48913	−0.416130
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−5.48913	−0.412588
$178$	7.48913	0.561334
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	3.48913	0.259345	0.129672	−	0.991557i	$-0.458607\pi$
$181$	3.48913	0.259345	0.129672	+	0.991557i	$0.458607\pi$
$182$	4.74456	0.351690
$183$	−25.4891	−1.88421
$184$	4.74456	0.349774
$185$	0	0
$186$	−13.4891	−0.989071
$187$	4.74456	0.346957
$188$	6.74456	0.491898
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	−2.00000	−0.144338
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−5.25544	−0.377318
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	1.00000	0.0710669
$199$	14.7446	1.04521	0.522607	−	0.852574i	$-0.324959\pi$
$199$	14.7446	1.04521	0.522607	+	0.852574i	$0.324959\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	8.74456	0.615265
$203$	2.74456	0.192631
$204$	9.48913	0.664372
$205$	0	0
$206$	10.7446	0.748609
$207$	−4.74456	−0.329770
$208$	4.74456	0.328976
$209$	−4.74456	−0.328188
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	1.25544	0.0862238
$213$	8.00000	0.548151
$214$	−12.0000	−0.820303
$215$	0	0
$216$	−4.00000	−0.272166
$217$	6.74456	0.457851
$218$	−16.2337	−1.09948
$219$	−1.48913	−0.100626
$220$	0	0
$221$	−22.5109	−1.51425
$222$	21.4891	1.44226
$223$	−26.7446	−1.79095	−0.895474	−	0.445113i	$-0.853163\pi$
$223$	−26.7446	−1.79095	−0.895474	+	0.445113i	$0.853163\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	10.0000	0.665190
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	−9.48913	−0.628433
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	2.74456	0.180189
$233$	−20.9783	−1.37433	−0.687165	−	0.726501i	$-0.741145\pi$
$233$	−20.9783	−1.37433	−0.687165	+	0.726501i	$0.741145\pi$
$234$	−4.74456	−0.310162
$235$	0	0
$236$	2.74456	0.178656
$237$	9.48913	0.616385
$238$	−4.74456	−0.307544
$239$	−3.25544	−0.210577	−0.105288	−	0.994442i	$-0.533577\pi$
$239$	−3.25544	−0.210577	−0.105288	+	0.994442i	$0.533577\pi$
$240$	0	0
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	−1.00000	−0.0642824
$243$	10.0000	0.641500
$244$	12.7446	0.815887
$245$	0	0
$246$	−8.00000	−0.510061
$247$	22.5109	1.43233
$248$	6.74456	0.428280
$249$	16.0000	1.01396
$250$	0	0
$251$	8.23369	0.519706	0.259853	−	0.965648i	$-0.416326\pi$
$251$	8.23369	0.519706	0.259853	+	0.965648i	$0.416326\pi$
$252$	−1.00000	−0.0629941
$253$	4.74456	0.298288
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.2337	−1.51166	−0.755828	−	0.654770i	$-0.772765\pi$
$257$	−24.2337	−1.51166	−0.755828	+	0.654770i	$0.772765\pi$
$258$	−8.00000	−0.498058
$259$	−10.7446	−0.667635
$260$	0	0
$261$	−2.74456	−0.169884
$262$	−8.74456	−0.540241
$263$	18.9783	1.17025	0.585125	−	0.810943i	$-0.301046\pi$
$263$	18.9783	1.17025	0.585125	+	0.810943i	$0.301046\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	4.74456	0.290908
$267$	14.9783	0.916654
$268$	4.00000	0.244339
$269$	−24.9783	−1.52295	−0.761475	−	0.648194i	$-0.775525\pi$
$269$	−24.9783	−1.52295	−0.761475	+	0.648194i	$0.775525\pi$
$270$	0	0
$271$	−30.9783	−1.88179	−0.940897	−	0.338692i	$-0.890016\pi$
$271$	−30.9783	−1.88179	−0.940897	+	0.338692i	$0.890016\pi$
$272$	−4.74456	−0.287681
$273$	9.48913	0.574308
$274$	−19.4891	−1.17738
$275$	0	0
$276$	9.48913	0.571178
$277$	7.48913	0.449978	0.224989	−	0.974361i	$-0.427765\pi$
$277$	7.48913	0.449978	0.224989	+	0.974361i	$0.427765\pi$
$278$	−3.25544	−0.195248
$279$	−6.74456	−0.403786
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	13.4891	0.803266
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	−4.00000	−0.237356
$285$	0	0
$286$	4.74456	0.280552
$287$	4.00000	0.236113
$288$	−1.00000	−0.0589256
$289$	5.51087	0.324169
$290$	0	0
$291$	−10.5109	−0.616158
$292$	0.744563	0.0435722
$293$	−24.7446	−1.44559	−0.722796	−	0.691061i	$-0.757144\pi$
$293$	−24.7446	−1.44559	−0.722796	+	0.691061i	$0.757144\pi$
$294$	2.00000	0.116642
$295$	0	0
$296$	−10.7446	−0.624515
$297$	−4.00000	−0.232104
$298$	−10.7446	−0.622416
$299$	−22.5109	−1.30184
$300$	0	0
$301$	4.00000	0.230556
$302$	20.7446	1.19372
$303$	17.4891	1.00472
$304$	4.74456	0.272119
$305$	0	0
$306$	4.74456	0.271229
$307$	−21.4891	−1.22645	−0.613225	−	0.789909i	$-0.710128\pi$
$307$	−21.4891	−1.22645	−0.613225	+	0.789909i	$0.710128\pi$
$308$	1.00000	0.0569803
$309$	21.4891	1.22247
$310$	0	0
$311$	−9.25544	−0.524828	−0.262414	−	0.964955i	$-0.584519\pi$
$311$	−9.25544	−0.524828	−0.262414	+	0.964955i	$0.584519\pi$
$312$	9.48913	0.537216
$313$	−32.2337	−1.82196	−0.910978	−	0.412455i	$-0.864671\pi$
$313$	−32.2337	−1.82196	−0.910978	+	0.412455i	$0.864671\pi$
$314$	23.4891	1.32557
$315$	0	0
$316$	−4.74456	−0.266903
$317$	32.2337	1.81042	0.905212	−	0.424960i	$-0.139712\pi$
$317$	32.2337	1.81042	0.905212	+	0.424960i	$0.139712\pi$
$318$	2.51087	0.140803
$319$	2.74456	0.153666
$320$	0	0
$321$	−24.0000	−1.33955
$322$	−4.74456	−0.264404
$323$	−22.5109	−1.25254
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−32.4674	−1.79545
$328$	4.00000	0.220863
$329$	−6.74456	−0.371840
$330$	0	0
$331$	−30.9783	−1.70272	−0.851359	−	0.524583i	$-0.824221\pi$
$331$	−30.9783	−1.70272	−0.851359	+	0.524583i	$0.824221\pi$
$332$	−8.00000	−0.439057
$333$	10.7446	0.588798
$334$	0	0
$335$	0	0
$336$	2.00000	0.109109
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−9.51087	−0.517323
$339$	20.0000	1.08625
$340$	0	0
$341$	6.74456	0.365239
$342$	−4.74456	−0.256557
$343$	−1.00000	−0.0539949
$344$	4.00000	0.215666
$345$	0	0
$346$	−14.2337	−0.765208
$347$	−22.9783	−1.23354	−0.616769	−	0.787145i	$-0.711559\pi$
$347$	−22.9783	−1.23354	−0.616769	+	0.787145i	$0.711559\pi$
$348$	5.48913	0.294248
$349$	19.2554	1.03072	0.515360	−	0.856974i	$-0.327658\pi$
$349$	19.2554	1.03072	0.515360	+	0.856974i	$0.327658\pi$
$350$	0	0
$351$	18.9783	1.01298
$352$	1.00000	0.0533002
$353$	2.74456	0.146078	0.0730392	−	0.997329i	$-0.476730\pi$
$353$	2.74456	0.146078	0.0730392	+	0.997329i	$0.476730\pi$
$354$	5.48913	0.291744
$355$	0	0
$356$	−7.48913	−0.396923
$357$	−9.48913	−0.502218
$358$	4.00000	0.211407
$359$	−12.7446	−0.672632	−0.336316	−	0.941749i	$-0.609181\pi$
$359$	−12.7446	−0.672632	−0.336316	+	0.941749i	$0.609181\pi$
$360$	0	0
$361$	3.51087	0.184783
$362$	−3.48913	−0.183384
$363$	−2.00000	−0.104973
$364$	−4.74456	−0.248683
$365$	0	0
$366$	25.4891	1.33234
$367$	−2.74456	−0.143265	−0.0716325	−	0.997431i	$-0.522821\pi$
$367$	−2.74456	−0.143265	−0.0716325	+	0.997431i	$0.522821\pi$
$368$	−4.74456	−0.247327
$369$	−4.00000	−0.208232
$370$	0	0
$371$	−1.25544	−0.0651791
$372$	13.4891	0.699379
$373$	−28.9783	−1.50044	−0.750218	−	0.661190i	$-0.770052\pi$
$373$	−28.9783	−1.50044	−0.750218	+	0.661190i	$0.770052\pi$
$374$	−4.74456	−0.245335
$375$	0	0
$376$	−6.74456	−0.347824
$377$	−13.0217	−0.670654
$378$	4.00000	0.205738
$379$	−14.5109	−0.745374	−0.372687	−	0.927957i	$-0.621563\pi$
$379$	−14.5109	−0.745374	−0.372687	+	0.927957i	$0.621563\pi$
$380$	0	0
$381$	0	0
$382$	16.0000	0.818631
$383$	37.7228	1.92755	0.963773	−	0.266724i	$-0.0859413\pi$
$383$	37.7228	1.92755	0.963773	+	0.266724i	$0.0859413\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−2.00000	−0.101797
$387$	−4.00000	−0.203331
$388$	5.25544	0.266804
$389$	15.4891	0.785330	0.392665	−	0.919682i	$-0.371553\pi$
$389$	15.4891	0.785330	0.392665	+	0.919682i	$0.371553\pi$
$390$	0	0
$391$	22.5109	1.13842
$392$	−1.00000	−0.0505076
$393$	−17.4891	−0.882210
$394$	10.0000	0.503793
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	−12.5109	−0.627903	−0.313951	−	0.949439i	$-0.601653\pi$
$397$	−12.5109	−0.627903	−0.313951	+	0.949439i	$0.601653\pi$
$398$	−14.7446	−0.739078
$399$	9.48913	0.475050
$400$	0	0
$401$	0.510875	0.0255119	0.0127559	−	0.999919i	$-0.495940\pi$
$401$	0.510875	0.0255119	0.0127559	+	0.999919i	$0.495940\pi$
$402$	8.00000	0.399004
$403$	−32.0000	−1.59403
$404$	−8.74456	−0.435058
$405$	0	0
$406$	−2.74456	−0.136210
$407$	−10.7446	−0.532588
$408$	−9.48913	−0.469782
$409$	1.48913	0.0736325	0.0368163	−	0.999322i	$-0.488278\pi$
$409$	1.48913	0.0736325	0.0368163	+	0.999322i	$0.488278\pi$
$410$	0	0
$411$	−38.9783	−1.92266
$412$	−10.7446	−0.529347
$413$	−2.74456	−0.135051
$414$	4.74456	0.233183
$415$	0	0
$416$	−4.74456	−0.232621
$417$	−6.51087	−0.318839
$418$	4.74456	0.232064
$419$	10.7446	0.524906	0.262453	−	0.964945i	$-0.415468\pi$
$419$	10.7446	0.524906	0.262453	+	0.964945i	$0.415468\pi$
$420$	0	0
$421$	27.4891	1.33974	0.669869	−	0.742479i	$-0.266350\pi$
$421$	27.4891	1.33974	0.669869	+	0.742479i	$0.266350\pi$
$422$	12.0000	0.584151
$423$	6.74456	0.327932
$424$	−1.25544	−0.0609694
$425$	0	0
$426$	−8.00000	−0.387601
$427$	−12.7446	−0.616753
$428$	12.0000	0.580042
$429$	9.48913	0.458139
$430$	0	0
$431$	−28.7446	−1.38458	−0.692288	−	0.721621i	$-0.743397\pi$
$431$	−28.7446	−1.38458	−0.692288	+	0.721621i	$0.743397\pi$
$432$	4.00000	0.192450
$433$	−25.2554	−1.21370	−0.606849	−	0.794817i	$-0.707567\pi$
$433$	−25.2554	−1.21370	−0.606849	+	0.794817i	$0.707567\pi$
$434$	−6.74456	−0.323749
$435$	0	0
$436$	16.2337	0.777453
$437$	−22.5109	−1.07684
$438$	1.48913	0.0711532
$439$	−30.9783	−1.47851	−0.739256	−	0.673425i	$-0.764822\pi$
$439$	−30.9783	−1.47851	−0.739256	+	0.673425i	$0.764822\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	22.5109	1.07073
$443$	6.51087	0.309341	0.154670	−	0.987966i	$-0.450568\pi$
$443$	6.51087	0.309341	0.154670	+	0.987966i	$0.450568\pi$
$444$	−21.4891	−1.01983
$445$	0	0
$446$	26.7446	1.26639
$447$	−21.4891	−1.01640
$448$	−1.00000	−0.0472456
$449$	40.9783	1.93388	0.966942	−	0.254998i	$-0.0820748\pi$
$449$	40.9783	1.93388	0.966942	+	0.254998i	$0.0820748\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	−10.0000	−0.470360
$453$	41.4891	1.94933
$454$	20.0000	0.938647
$455$	0	0
$456$	9.48913	0.444369
$457$	19.4891	0.911663	0.455831	−	0.890066i	$-0.349342\pi$
$457$	19.4891	0.911663	0.455831	+	0.890066i	$0.349342\pi$
$458$	6.00000	0.280362
$459$	−18.9783	−0.885829
$460$	0	0
$461$	−23.7228	−1.10488	−0.552441	−	0.833552i	$-0.686303\pi$
$461$	−23.7228	−1.10488	−0.552441	+	0.833552i	$0.686303\pi$
$462$	2.00000	0.0930484
$463$	−12.7446	−0.592290	−0.296145	−	0.955143i	$-0.595701\pi$
$463$	−12.7446	−0.592290	−0.296145	+	0.955143i	$0.595701\pi$
$464$	−2.74456	−0.127413
$465$	0	0
$466$	20.9783	0.971799
$467$	28.9783	1.34095	0.670477	−	0.741931i	$-0.266090\pi$
$467$	28.9783	1.34095	0.670477	+	0.741931i	$0.266090\pi$
$468$	4.74456	0.219317
$469$	−4.00000	−0.184703
$470$	0	0
$471$	46.9783	2.16464
$472$	−2.74456	−0.126329
$473$	4.00000	0.183920
$474$	−9.48913	−0.435850
$475$	0	0
$476$	4.74456	0.217467
$477$	1.25544	0.0574825
$478$	3.25544	0.148900
$479$	−18.5109	−0.845783	−0.422892	−	0.906180i	$-0.638985\pi$
$479$	−18.5109	−0.845783	−0.422892	+	0.906180i	$0.638985\pi$
$480$	0	0
$481$	50.9783	2.32441
$482$	−20.0000	−0.910975
$483$	−9.48913	−0.431770
$484$	1.00000	0.0454545
$485$	0	0
$486$	−10.0000	−0.453609
$487$	−20.7446	−0.940026	−0.470013	−	0.882660i	$-0.655751\pi$
$487$	−20.7446	−0.940026	−0.470013	+	0.882660i	$0.655751\pi$
$488$	−12.7446	−0.576919
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−14.9783	−0.675959	−0.337979	−	0.941153i	$-0.609743\pi$
$491$	−14.9783	−0.675959	−0.337979	+	0.941153i	$0.609743\pi$
$492$	8.00000	0.360668
$493$	13.0217	0.586470
$494$	−22.5109	−1.01281
$495$	0	0
$496$	−6.74456	−0.302840
$497$	4.00000	0.179425
$498$	−16.0000	−0.716977
$499$	9.48913	0.424792	0.212396	−	0.977184i	$-0.431873\pi$
$499$	9.48913	0.424792	0.212396	+	0.977184i	$0.431873\pi$
$500$	0	0
$501$	0	0
$502$	−8.23369	−0.367487
$503$	−29.4891	−1.31486	−0.657428	−	0.753518i	$-0.728355\pi$
$503$	−29.4891	−1.31486	−0.657428	+	0.753518i	$0.728355\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−4.74456	−0.210922
$507$	−19.0217	−0.844786
$508$	0	0
$509$	−12.5109	−0.554535	−0.277267	−	0.960793i	$-0.589429\pi$
$509$	−12.5109	−0.554535	−0.277267	+	0.960793i	$0.589429\pi$
$510$	0	0
$511$	−0.744563	−0.0329375
$512$	−1.00000	−0.0441942
$513$	18.9783	0.837910
$514$	24.2337	1.06890
$515$	0	0
$516$	8.00000	0.352180
$517$	−6.74456	−0.296626
$518$	10.7446	0.472089
$519$	−28.4674	−1.24958
$520$	0	0
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	2.74456	0.120126
$523$	−5.48913	−0.240023	−0.120011	−	0.992773i	$-0.538293\pi$
$523$	−5.48913	−0.240023	−0.120011	+	0.992773i	$0.538293\pi$
$524$	8.74456	0.382008
$525$	0	0
$526$	−18.9783	−0.827491
$527$	32.0000	1.39394
$528$	2.00000	0.0870388
$529$	−0.489125	−0.0212663
$530$	0	0
$531$	2.74456	0.119104
$532$	−4.74456	−0.205703
$533$	−18.9783	−0.822039
$534$	−14.9783	−0.648172
$535$	0	0
$536$	−4.00000	−0.172774
$537$	8.00000	0.345225
$538$	24.9783	1.07689
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	36.2337	1.55781	0.778904	−	0.627143i	$-0.215776\pi$
$541$	36.2337	1.55781	0.778904	+	0.627143i	$0.215776\pi$
$542$	30.9783	1.33063
$543$	−6.97825	−0.299465
$544$	4.74456	0.203421
$545$	0	0
$546$	−9.48913	−0.406097
$547$	30.9783	1.32453	0.662267	−	0.749268i	$-0.269594\pi$
$547$	30.9783	1.32453	0.662267	+	0.749268i	$0.269594\pi$
$548$	19.4891	0.832534
$549$	12.7446	0.543925
$550$	0	0
$551$	−13.0217	−0.554745
$552$	−9.48913	−0.403884
$553$	4.74456	0.201759
$554$	−7.48913	−0.318182
$555$	0	0
$556$	3.25544	0.138061
$557$	−44.9783	−1.90579	−0.952895	−	0.303301i	$-0.901911\pi$
$557$	−44.9783	−1.90579	−0.952895	+	0.303301i	$0.901911\pi$
$558$	6.74456	0.285520
$559$	−18.9783	−0.802694
$560$	0	0
$561$	−9.48913	−0.400631
$562$	−14.0000	−0.590554
$563$	17.4891	0.737079	0.368539	−	0.929612i	$-0.379858\pi$
$563$	17.4891	0.737079	0.368539	+	0.929612i	$0.379858\pi$
$564$	−13.4891	−0.567995
$565$	0	0
$566$	28.0000	1.17693
$567$	11.0000	0.461957
$568$	4.00000	0.167836
$569$	39.4891	1.65547	0.827735	−	0.561119i	$-0.189629\pi$
$569$	39.4891	1.65547	0.827735	+	0.561119i	$0.189629\pi$
$570$	0	0
$571$	5.48913	0.229713	0.114856	−	0.993382i	$-0.463359\pi$
$571$	5.48913	0.229713	0.114856	+	0.993382i	$0.463359\pi$
$572$	−4.74456	−0.198380
$573$	32.0000	1.33682
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−2.74456	−0.114258	−0.0571288	−	0.998367i	$-0.518195\pi$
$577$	−2.74456	−0.114258	−0.0571288	+	0.998367i	$0.518195\pi$
$578$	−5.51087	−0.229222
$579$	−4.00000	−0.166234
$580$	0	0
$581$	8.00000	0.331896
$582$	10.5109	0.435690
$583$	−1.25544	−0.0519949
$584$	−0.744563	−0.0308102
$585$	0	0
$586$	24.7446	1.02219
$587$	−40.9783	−1.69135	−0.845677	−	0.533696i	$-0.820803\pi$
$587$	−40.9783	−1.69135	−0.845677	+	0.533696i	$0.820803\pi$
$588$	−2.00000	−0.0824786
$589$	−32.0000	−1.31854
$590$	0	0
$591$	20.0000	0.822690
$592$	10.7446	0.441599
$593$	5.76631	0.236794	0.118397	−	0.992966i	$-0.462224\pi$
$593$	5.76631	0.236794	0.118397	+	0.992966i	$0.462224\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	10.7446	0.440114
$597$	−29.4891	−1.20691
$598$	22.5109	0.920538
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	−10.5109	−0.428748	−0.214374	−	0.976752i	$-0.568771\pi$
$601$	−10.5109	−0.428748	−0.214374	+	0.976752i	$0.568771\pi$
$602$	−4.00000	−0.163028
$603$	4.00000	0.162893
$604$	−20.7446	−0.844084
$605$	0	0
$606$	−17.4891	−0.710447
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−4.74456	−0.192417
$609$	−5.48913	−0.222431
$610$	0	0
$611$	32.0000	1.29458
$612$	−4.74456	−0.191788
$613$	11.4891	0.464041	0.232021	−	0.972711i	$-0.425466\pi$
$613$	11.4891	0.464041	0.232021	+	0.972711i	$0.425466\pi$
$614$	21.4891	0.867231
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	−21.4891	−0.864419
$619$	−10.7446	−0.431860	−0.215930	−	0.976409i	$-0.569278\pi$
$619$	−10.7446	−0.431860	−0.215930	+	0.976409i	$0.569278\pi$
$620$	0	0
$621$	−18.9783	−0.761571
$622$	9.25544	0.371109
$623$	7.48913	0.300045
$624$	−9.48913	−0.379869
$625$	0	0
$626$	32.2337	1.28832
$627$	9.48913	0.378959
$628$	−23.4891	−0.937318
$629$	−50.9783	−2.03264
$630$	0	0
$631$	42.9783	1.71094	0.855469	−	0.517855i	$-0.173269\pi$
$631$	42.9783	1.71094	0.855469	+	0.517855i	$0.173269\pi$
$632$	4.74456	0.188729
$633$	24.0000	0.953914
$634$	−32.2337	−1.28016
$635$	0	0
$636$	−2.51087	−0.0995627
$637$	4.74456	0.187986
$638$	−2.74456	−0.108658
$639$	−4.00000	−0.158238
$640$	0	0
$641$	−11.4891	−0.453793	−0.226897	−	0.973919i	$-0.572858\pi$
$641$	−11.4891	−0.453793	−0.226897	+	0.973919i	$0.572858\pi$
$642$	24.0000	0.947204
$643$	22.4674	0.886027	0.443013	−	0.896515i	$-0.353909\pi$
$643$	22.4674	0.886027	0.443013	+	0.896515i	$0.353909\pi$
$644$	4.74456	0.186962
$645$	0	0
$646$	22.5109	0.885679
$647$	2.74456	0.107900	0.0539499	−	0.998544i	$-0.482819\pi$
$647$	2.74456	0.107900	0.0539499	+	0.998544i	$0.482819\pi$
$648$	11.0000	0.432121
$649$	−2.74456	−0.107734
$650$	0	0
$651$	−13.4891	−0.528681
$652$	4.00000	0.156652
$653$	41.7228	1.63274	0.816370	−	0.577529i	$-0.195983\pi$
$653$	41.7228	1.63274	0.816370	+	0.577529i	$0.195983\pi$
$654$	32.4674	1.26957
$655$	0	0
$656$	−4.00000	−0.156174
$657$	0.744563	0.0290482
$658$	6.74456	0.262930
$659$	−18.5109	−0.721081	−0.360541	−	0.932744i	$-0.617408\pi$
$659$	−18.5109	−0.721081	−0.360541	+	0.932744i	$0.617408\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	30.9783	1.20400
$663$	45.0217	1.74850
$664$	8.00000	0.310460
$665$	0	0
$666$	−10.7446	−0.416343
$667$	13.0217	0.504204
$668$	0	0
$669$	53.4891	2.06801
$670$	0	0
$671$	−12.7446	−0.491998
$672$	−2.00000	−0.0771517
$673$	24.9783	0.962841	0.481420	−	0.876490i	$-0.340121\pi$
$673$	24.9783	0.962841	0.481420	+	0.876490i	$0.340121\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	9.51087	0.365803
$677$	−1.76631	−0.0678849	−0.0339424	−	0.999424i	$-0.510806\pi$
$677$	−1.76631	−0.0678849	−0.0339424	+	0.999424i	$0.510806\pi$
$678$	−20.0000	−0.768095
$679$	−5.25544	−0.201685
$680$	0	0
$681$	40.0000	1.53280
$682$	−6.74456	−0.258263
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	4.74456	0.181413
$685$	0	0
$686$	1.00000	0.0381802
$687$	12.0000	0.457829
$688$	−4.00000	−0.152499
$689$	5.95650	0.226925
$690$	0	0
$691$	36.2337	1.37839	0.689197	−	0.724574i	$-0.257963\pi$
$691$	36.2337	1.37839	0.689197	+	0.724574i	$0.257963\pi$
$692$	14.2337	0.541084
$693$	1.00000	0.0379869
$694$	22.9783	0.872242
$695$	0	0
$696$	−5.48913	−0.208065
$697$	18.9783	0.718853
$698$	−19.2554	−0.728829
$699$	41.9565	1.58694
$700$	0	0
$701$	−12.2337	−0.462060	−0.231030	−	0.972947i	$-0.574210\pi$
$701$	−12.2337	−0.462060	−0.231030	+	0.972947i	$0.574210\pi$
$702$	−18.9783	−0.716288
$703$	50.9783	1.92268
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−2.74456	−0.103293
$707$	8.74456	0.328873
$708$	−5.48913	−0.206294
$709$	23.4891	0.882153	0.441076	−	0.897470i	$-0.354597\pi$
$709$	23.4891	0.882153	0.441076	+	0.897470i	$0.354597\pi$
$710$	0	0
$711$	−4.74456	−0.177935
$712$	7.48913	0.280667
$713$	32.0000	1.19841
$714$	9.48913	0.355122
$715$	0	0
$716$	−4.00000	−0.149487
$717$	6.51087	0.243153
$718$	12.7446	0.475623
$719$	−49.7228	−1.85435	−0.927174	−	0.374631i	$-0.877769\pi$
$719$	−49.7228	−1.85435	−0.927174	+	0.374631i	$0.877769\pi$
$720$	0	0
$721$	10.7446	0.400148
$722$	−3.51087	−0.130661
$723$	−40.0000	−1.48762
$724$	3.48913	0.129672
$725$	0	0
$726$	2.00000	0.0742270
$727$	20.2337	0.750426	0.375213	−	0.926939i	$-0.377570\pi$
$727$	20.2337	0.750426	0.375213	+	0.926939i	$0.377570\pi$
$728$	4.74456	0.175845
$729$	13.0000	0.481481
$730$	0	0
$731$	18.9783	0.701936
$732$	−25.4891	−0.942105
$733$	−18.2337	−0.673477	−0.336738	−	0.941598i	$-0.609324\pi$
$733$	−18.2337	−0.673477	−0.336738	+	0.941598i	$0.609324\pi$
$734$	2.74456	0.101304
$735$	0	0
$736$	4.74456	0.174887
$737$	−4.00000	−0.147342
$738$	4.00000	0.147242
$739$	14.9783	0.550984	0.275492	−	0.961303i	$-0.411159\pi$
$739$	14.9783	0.550984	0.275492	+	0.961303i	$0.411159\pi$
$740$	0	0
$741$	−45.0217	−1.65392
$742$	1.25544	0.0460886
$743$	18.9783	0.696244	0.348122	−	0.937449i	$-0.386819\pi$
$743$	18.9783	0.696244	0.348122	+	0.937449i	$0.386819\pi$
$744$	−13.4891	−0.494535
$745$	0	0
$746$	28.9783	1.06097
$747$	−8.00000	−0.292705
$748$	4.74456	0.173478
$749$	−12.0000	−0.438470
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	6.74456	0.245949
$753$	−16.4674	−0.600105
$754$	13.0217	0.474224
$755$	0	0
$756$	−4.00000	−0.145479
$757$	30.7446	1.11743	0.558715	−	0.829360i	$-0.311295\pi$
$757$	30.7446	1.11743	0.558715	+	0.829360i	$0.311295\pi$
$758$	14.5109	0.527059
$759$	−9.48913	−0.344433
$760$	0	0
$761$	−6.51087	−0.236019	−0.118010	−	0.993012i	$-0.537651\pi$
$761$	−6.51087	−0.236019	−0.118010	+	0.993012i	$0.537651\pi$
$762$	0	0
$763$	−16.2337	−0.587699
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−37.7228	−1.36298
$767$	13.0217	0.470188
$768$	−2.00000	−0.0721688
$769$	−8.00000	−0.288487	−0.144244	−	0.989542i	$-0.546075\pi$
$769$	−8.00000	−0.288487	−0.144244	+	0.989542i	$0.546075\pi$
$770$	0	0
$771$	48.4674	1.74551
$772$	2.00000	0.0719816
$773$	28.5109	1.02546	0.512732	−	0.858548i	$-0.328633\pi$
$773$	28.5109	1.02546	0.512732	+	0.858548i	$0.328633\pi$
$774$	4.00000	0.143777
$775$	0	0
$776$	−5.25544	−0.188659
$777$	21.4891	0.770918
$778$	−15.4891	−0.555312
$779$	−18.9783	−0.679966
$780$	0	0
$781$	4.00000	0.143131
$782$	−22.5109	−0.804987
$783$	−10.9783	−0.392331
$784$	1.00000	0.0357143
$785$	0	0
$786$	17.4891	0.623816
$787$	17.4891	0.623420	0.311710	−	0.950177i	$-0.399098\pi$
$787$	17.4891	0.623420	0.311710	+	0.950177i	$0.399098\pi$
$788$	−10.0000	−0.356235
$789$	−37.9565	−1.35129
$790$	0	0
$791$	10.0000	0.355559
$792$	1.00000	0.0355335
$793$	60.4674	2.14726
$794$	12.5109	0.443994
$795$	0	0
$796$	14.7446	0.522607
$797$	−26.4674	−0.937523	−0.468761	−	0.883325i	$-0.655300\pi$
$797$	−26.4674	−0.937523	−0.468761	+	0.883325i	$0.655300\pi$
$798$	−9.48913	−0.335911
$799$	−32.0000	−1.13208
$800$	0	0
$801$	−7.48913	−0.264615
$802$	−0.510875	−0.0180396
$803$	−0.744563	−0.0262750
$804$	−8.00000	−0.282138
$805$	0	0
$806$	32.0000	1.12715
$807$	49.9565	1.75855
$808$	8.74456	0.307633
$809$	−34.4674	−1.21181	−0.605904	−	0.795538i	$-0.707189\pi$
$809$	−34.4674	−1.21181	−0.605904	+	0.795538i	$0.707189\pi$
$810$	0	0
$811$	−7.25544	−0.254773	−0.127386	−	0.991853i	$-0.540659\pi$
$811$	−7.25544	−0.254773	−0.127386	+	0.991853i	$0.540659\pi$
$812$	2.74456	0.0963153
$813$	61.9565	2.17291
$814$	10.7446	0.376597
$815$	0	0
$816$	9.48913	0.332186
$817$	−18.9783	−0.663965
$818$	−1.48913	−0.0520660
$819$	−4.74456	−0.165788
$820$	0	0
$821$	−49.7228	−1.73534	−0.867669	−	0.497142i	$-0.834383\pi$
$821$	−49.7228	−1.73534	−0.867669	+	0.497142i	$0.834383\pi$
$822$	38.9783	1.35952
$823$	−42.2337	−1.47217	−0.736087	−	0.676887i	$-0.763329\pi$
$823$	−42.2337	−1.47217	−0.736087	+	0.676887i	$0.763329\pi$
$824$	10.7446	0.374305
$825$	0	0
$826$	2.74456	0.0954955
$827$	−4.00000	−0.139094	−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000	−0.139094	−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−4.74456	−0.164885
$829$	−54.4674	−1.89173	−0.945865	−	0.324560i	$-0.894784\pi$
$829$	−54.4674	−1.89173	−0.945865	+	0.324560i	$0.894784\pi$
$830$	0	0
$831$	−14.9783	−0.519590
$832$	4.74456	0.164488
$833$	−4.74456	−0.164389
$834$	6.51087	0.225453
$835$	0	0
$836$	−4.74456	−0.164094
$837$	−26.9783	−0.932505
$838$	−10.7446	−0.371165
$839$	−14.7446	−0.509039	−0.254519	−	0.967068i	$-0.581917\pi$
$839$	−14.7446	−0.509039	−0.254519	+	0.967068i	$0.581917\pi$
$840$	0	0
$841$	−21.4674	−0.740254
$842$	−27.4891	−0.947338
$843$	−28.0000	−0.964371
$844$	−12.0000	−0.413057
$845$	0	0
$846$	−6.74456	−0.231883
$847$	−1.00000	−0.0343604
$848$	1.25544	0.0431119
$849$	56.0000	1.92192
$850$	0	0
$851$	−50.9783	−1.74751
$852$	8.00000	0.274075
$853$	11.2554	0.385379	0.192689	−	0.981260i	$-0.438279\pi$
$853$	11.2554	0.385379	0.192689	+	0.981260i	$0.438279\pi$
$854$	12.7446	0.436110
$855$	0	0
$856$	−12.0000	−0.410152
$857$	−37.2119	−1.27114	−0.635568	−	0.772045i	$-0.719234\pi$
$857$	−37.2119	−1.27114	−0.635568	+	0.772045i	$0.719234\pi$
$858$	−9.48913	−0.323953
$859$	51.2119	1.74733	0.873664	−	0.486529i	$-0.161737\pi$
$859$	51.2119	1.74733	0.873664	+	0.486529i	$0.161737\pi$
$860$	0	0
$861$	−8.00000	−0.272639
$862$	28.7446	0.979044
$863$	5.76631	0.196288	0.0981438	−	0.995172i	$-0.468709\pi$
$863$	5.76631	0.196288	0.0981438	+	0.995172i	$0.468709\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	25.2554	0.858215
$867$	−11.0217	−0.374318
$868$	6.74456	0.228925
$869$	4.74456	0.160948
$870$	0	0
$871$	18.9783	0.643053
$872$	−16.2337	−0.549742
$873$	5.25544	0.177870
$874$	22.5109	0.761442
$875$	0	0
$876$	−1.48913	−0.0503129
$877$	−42.4674	−1.43402	−0.717011	−	0.697062i	$-0.754490\pi$
$877$	−42.4674	−1.43402	−0.717011	+	0.697062i	$0.754490\pi$
$878$	30.9783	1.04547
$879$	49.4891	1.66923
$880$	0	0
$881$	−32.5109	−1.09532	−0.547660	−	0.836701i	$-0.684481\pi$
$881$	−32.5109	−1.09532	−0.547660	+	0.836701i	$0.684481\pi$
$882$	−1.00000	−0.0336718
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	−22.5109	−0.757123
$885$	0	0
$886$	−6.51087	−0.218737
$887$	18.5109	0.621534	0.310767	−	0.950486i	$-0.399414\pi$
$887$	18.5109	0.621534	0.310767	+	0.950486i	$0.399414\pi$
$888$	21.4891	0.721128
$889$	0	0
$890$	0	0
$891$	11.0000	0.368514
$892$	−26.7446	−0.895474
$893$	32.0000	1.07084
$894$	21.4891	0.718704
$895$	0	0
$896$	1.00000	0.0334077
$897$	45.0217	1.50323
$898$	−40.9783	−1.36746
$899$	18.5109	0.617372
$900$	0	0
$901$	−5.95650	−0.198440
$902$	−4.00000	−0.133185
$903$	−8.00000	−0.266223
$904$	10.0000	0.332595
$905$	0	0
$906$	−41.4891	−1.37838
$907$	37.4891	1.24481	0.622403	−	0.782697i	$-0.286157\pi$
$907$	37.4891	1.24481	0.622403	+	0.782697i	$0.286157\pi$
$908$	−20.0000	−0.663723
$909$	−8.74456	−0.290039
$910$	0	0
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	−9.48913	−0.314216
$913$	8.00000	0.264761
$914$	−19.4891	−0.644643
$915$	0	0
$916$	−6.00000	−0.198246
$917$	−8.74456	−0.288771
$918$	18.9783	0.626376
$919$	25.2119	0.831665	0.415833	−	0.909441i	$-0.363490\pi$
$919$	25.2119	0.831665	0.415833	+	0.909441i	$0.363490\pi$
$920$	0	0
$921$	42.9783	1.41618
$922$	23.7228	0.781269
$923$	−18.9783	−0.624677
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	12.7446	0.418812
$927$	−10.7446	−0.352898
$928$	2.74456	0.0900947
$929$	16.9783	0.557038	0.278519	−	0.960431i	$-0.410156\pi$
$929$	16.9783	0.557038	0.278519	+	0.960431i	$0.410156\pi$
$930$	0	0
$931$	4.74456	0.155497
$932$	−20.9783	−0.687165
$933$	18.5109	0.606019
$934$	−28.9783	−0.948197
$935$	0	0
$936$	−4.74456	−0.155081
$937$	7.25544	0.237025	0.118512	−	0.992953i	$-0.462187\pi$
$937$	7.25544	0.237025	0.118512	+	0.992953i	$0.462187\pi$
$938$	4.00000	0.130605
$939$	64.4674	2.10381
$940$	0	0
$941$	−22.2337	−0.724798	−0.362399	−	0.932023i	$-0.618042\pi$
$941$	−22.2337	−0.724798	−0.362399	+	0.932023i	$0.618042\pi$
$942$	−46.9783	−1.53063
$943$	18.9783	0.618017
$944$	2.74456	0.0893279
$945$	0	0
$946$	−4.00000	−0.130051
$947$	8.00000	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$947$	8.00000	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$948$	9.48913	0.308192
$949$	3.53262	0.114674
$950$	0	0
$951$	−64.4674	−2.09050
$952$	−4.74456	−0.153772
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−1.25544	−0.0406463
$955$	0	0
$956$	−3.25544	−0.105288
$957$	−5.48913	−0.177438
$958$	18.5109	0.598059
$959$	−19.4891	−0.629337
$960$	0	0
$961$	14.4891	0.467391
$962$	−50.9783	−1.64360
$963$	12.0000	0.386695
$964$	20.0000	0.644157
$965$	0	0
$966$	9.48913	0.305308
$967$	5.02175	0.161489	0.0807443	−	0.996735i	$-0.474270\pi$
$967$	5.02175	0.161489	0.0807443	+	0.996735i	$0.474270\pi$
$968$	−1.00000	−0.0321412
$969$	45.0217	1.44631
$970$	0	0
$971$	−37.7228	−1.21058	−0.605291	−	0.796004i	$-0.706943\pi$
$971$	−37.7228	−1.21058	−0.605291	+	0.796004i	$0.706943\pi$
$972$	10.0000	0.320750
$973$	−3.25544	−0.104365
$974$	20.7446	0.664699
$975$	0	0
$976$	12.7446	0.407944
$977$	32.9783	1.05507	0.527534	−	0.849534i	$-0.323117\pi$
$977$	32.9783	1.05507	0.527534	+	0.849534i	$0.323117\pi$
$978$	8.00000	0.255812
$979$	7.48913	0.239353
$980$	0	0
$981$	16.2337	0.518302
$982$	14.9783	0.477975
$983$	32.2337	1.02809	0.514047	−	0.857762i	$-0.328146\pi$
$983$	32.2337	1.02809	0.514047	+	0.857762i	$0.328146\pi$
$984$	−8.00000	−0.255031
$985$	0	0
$986$	−13.0217	−0.414697
$987$	13.4891	0.429364
$988$	22.5109	0.716166
$989$	18.9783	0.603473
$990$	0	0
$991$	−21.4891	−0.682625	−0.341312	−	0.939950i	$-0.610871\pi$
$991$	−21.4891	−0.682625	−0.341312	+	0.939950i	$0.610871\pi$
$992$	6.74456	0.214140
$993$	61.9565	1.96613
$994$	−4.00000	−0.126872
$995$	0	0
$996$	16.0000	0.506979
$997$	41.2119	1.30520	0.652598	−	0.757705i	$-0.273679\pi$
$997$	41.2119	1.30520	0.652598	+	0.757705i	$0.273679\pi$
$998$	−9.48913	−0.300373
$999$	42.9783	1.35977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.bc.1.2		2
5.2	odd	4		3850.2.c.y.1849.1		4
5.3	odd	4		3850.2.c.y.1849.4		4
5.4	even	2		770.2.a.k.1.1	✓	2
15.14	odd	2		6930.2.a.bo.1.1		2
20.19	odd	2		6160.2.a.r.1.1		2
35.34	odd	2		5390.2.a.bq.1.2		2
55.54	odd	2		8470.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.k.1.1	✓	2	5.4	even	2
3850.2.a.bc.1.2		2	1.1	even	1	trivial
3850.2.c.y.1849.1		4	5.2	odd	4
3850.2.c.y.1849.4		4	5.3	odd	4
5390.2.a.bq.1.2		2	35.34	odd	2
6160.2.a.r.1.1		2	20.19	odd	2
6930.2.a.bo.1.1		2	15.14	odd	2
8470.2.a.bu.1.2		2	55.54	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -2.00000 q^{12} +4.74456 q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.74456 q^{17} -1.00000 q^{18} +4.74456 q^{19} +2.00000 q^{21} +1.00000 q^{22} -4.74456 q^{23} +2.00000 q^{24} -4.74456 q^{26} +4.00000 q^{27} -1.00000 q^{28} -2.74456 q^{29} -6.74456 q^{31} -1.00000 q^{32} +2.00000 q^{33} +4.74456 q^{34} +1.00000 q^{36} +10.7446 q^{37} -4.74456 q^{38} -9.48913 q^{39} -4.00000 q^{41} -2.00000 q^{42} -4.00000 q^{43} -1.00000 q^{44} +4.74456 q^{46} +6.74456 q^{47} -2.00000 q^{48} +1.00000 q^{49} +9.48913 q^{51} +4.74456 q^{52} +1.25544 q^{53} -4.00000 q^{54} +1.00000 q^{56} -9.48913 q^{57} +2.74456 q^{58} +2.74456 q^{59} +12.7446 q^{61} +6.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} +4.00000 q^{67} -4.74456 q^{68} +9.48913 q^{69} -4.00000 q^{71} -1.00000 q^{72} +0.744563 q^{73} -10.7446 q^{74} +4.74456 q^{76} +1.00000 q^{77} +9.48913 q^{78} -4.74456 q^{79} -11.0000 q^{81} +4.00000 q^{82} -8.00000 q^{83} +2.00000 q^{84} +4.00000 q^{86} +5.48913 q^{87} +1.00000 q^{88} -7.48913 q^{89} -4.74456 q^{91} -4.74456 q^{92} +13.4891 q^{93} -6.74456 q^{94} +2.00000 q^{96} +5.25544 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{11} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 2 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} + 4 q^{24} + 2 q^{26} + 8 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{31} - 2 q^{32} + 4 q^{33} - 2 q^{34} + 2 q^{36} + 10 q^{37} + 2 q^{38} + 4 q^{39} - 8 q^{41} - 4 q^{42} - 8 q^{43} - 2 q^{44} - 2 q^{46} + 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{51} - 2 q^{52} + 14 q^{53} - 8 q^{54} + 2 q^{56} + 4 q^{57} - 6 q^{58} - 6 q^{59} + 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{66} + 8 q^{67} + 2 q^{68} - 4 q^{69} - 8 q^{71} - 2 q^{72} - 10 q^{73} - 10 q^{74} - 2 q^{76} + 2 q^{77} - 4 q^{78} + 2 q^{79} - 22 q^{81} + 8 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{86} - 12 q^{87} + 2 q^{88} + 8 q^{89} + 2 q^{91} + 2 q^{92} + 4 q^{93} - 2 q^{94} + 4 q^{96} + 22 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^11 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 2 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 + 4 * q^24 + 2 * q^26 + 8 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^31 - 2 * q^32 + 4 * q^33 - 2 * q^34 + 2 * q^36 + 10 * q^37 + 2 * q^38 + 4 * q^39 - 8 * q^41 - 4 * q^42 - 8 * q^43 - 2 * q^44 - 2 * q^46 + 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^51 - 2 * q^52 + 14 * q^53 - 8 * q^54 + 2 * q^56 + 4 * q^57 - 6 * q^58 - 6 * q^59 + 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^66 + 8 * q^67 + 2 * q^68 - 4 * q^69 - 8 * q^71 - 2 * q^72 - 10 * q^73 - 10 * q^74 - 2 * q^76 + 2 * q^77 - 4 * q^78 + 2 * q^79 - 22 * q^81 + 8 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^86 - 12 * q^87 + 2 * q^88 + 8 * q^89 + 2 * q^91 + 2 * q^92 + 4 * q^93 - 2 * q^94 + 4 * q^96 + 22 * q^97 - 2 * q^98 - 2 * q^99

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