LMFDB - Embedded newform 3450.2.a.bf.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(1,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, 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("3450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.44949$ of defining polynomial
Character	$\chi$	$=$	3450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} -6.89898 q^{13} -3.44949 q^{14} +1.00000 q^{16} +0.550510 q^{17} -1.00000 q^{18} -2.89898 q^{19} -3.44949 q^{21} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +6.89898 q^{26} -1.00000 q^{27} +3.44949 q^{28} +5.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} -0.550510 q^{34} +1.00000 q^{36} +6.34847 q^{37} +2.89898 q^{38} +6.89898 q^{39} +4.89898 q^{41} +3.44949 q^{42} -1.10102 q^{43} +2.00000 q^{44} +1.00000 q^{46} -5.89898 q^{47} -1.00000 q^{48} +4.89898 q^{49} -0.550510 q^{51} -6.89898 q^{52} +8.89898 q^{53} +1.00000 q^{54} -3.44949 q^{56} +2.89898 q^{57} -5.00000 q^{58} +10.0000 q^{59} +4.89898 q^{61} -2.00000 q^{62} +3.44949 q^{63} +1.00000 q^{64} +2.00000 q^{66} +2.00000 q^{67} +0.550510 q^{68} +1.00000 q^{69} -8.79796 q^{71} -1.00000 q^{72} -11.8990 q^{73} -6.34847 q^{74} -2.89898 q^{76} +6.89898 q^{77} -6.89898 q^{78} +10.0000 q^{79} +1.00000 q^{81} -4.89898 q^{82} +7.44949 q^{83} -3.44949 q^{84} +1.10102 q^{86} -5.00000 q^{87} -2.00000 q^{88} +4.34847 q^{89} -23.7980 q^{91} -1.00000 q^{92} -2.00000 q^{93} +5.89898 q^{94} +1.00000 q^{96} -16.6969 q^{97} -4.89898 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 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 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} - 2 q^{18} + 4 q^{19} - 2 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{26} - 2 q^{27} + 2 q^{28} + 10 q^{29} + 4 q^{31} - 2 q^{32} - 4 q^{33} - 6 q^{34} + 2 q^{36} - 2 q^{37} - 4 q^{38} + 4 q^{39} + 2 q^{42} - 12 q^{43} + 4 q^{44} + 2 q^{46} - 2 q^{47} - 2 q^{48} - 6 q^{51} - 4 q^{52} + 8 q^{53} + 2 q^{54} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 20 q^{59} - 4 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{66} + 4 q^{67} + 6 q^{68} + 2 q^{69} + 2 q^{71} - 2 q^{72} - 14 q^{73} + 2 q^{74} + 4 q^{76} + 4 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{81} + 10 q^{83} - 2 q^{84} + 12 q^{86} - 10 q^{87} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 2 q^{92} - 4 q^{93} + 2 q^{94} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 4 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 - 2 * q^18 + 4 * q^19 - 2 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^26 - 2 * q^27 + 2 * q^28 + 10 * q^29 + 4 * q^31 - 2 * q^32 - 4 * q^33 - 6 * q^34 + 2 * q^36 - 2 * q^37 - 4 * q^38 + 4 * q^39 + 2 * q^42 - 12 * q^43 + 4 * q^44 + 2 * q^46 - 2 * q^47 - 2 * q^48 - 6 * q^51 - 4 * q^52 + 8 * q^53 + 2 * q^54 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 20 * q^59 - 4 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^66 + 4 * q^67 + 6 * q^68 + 2 * q^69 + 2 * q^71 - 2 * q^72 - 14 * q^73 + 2 * q^74 + 4 * q^76 + 4 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^81 + 10 * q^83 - 2 * q^84 + 12 * q^86 - 10 * q^87 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 2 * q^92 - 4 * q^93 + 2 * q^94 + 2 * q^96 - 4 * q^97 + 4 * 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
$7$	3.44949	1.30378	0.651892	−	0.758312i	$-0.273975\pi$
$7$	3.44949	1.30378	0.651892	+	0.758312i	$0.273975\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	−6.89898	−1.91343	−0.956716	−	0.291022i	$-0.906005\pi$
$13$	−6.89898	−1.91343	−0.956716	+	0.291022i	$0.906005\pi$
$14$	−3.44949	−0.921915
$15$	0	0
$16$	1.00000	0.250000
$17$	0.550510	0.133518	0.0667592	−	0.997769i	$-0.478734\pi$
$17$	0.550510	0.133518	0.0667592	+	0.997769i	$0.478734\pi$
$18$	−1.00000	−0.235702
$19$	−2.89898	−0.665072	−0.332536	−	0.943091i	$-0.607904\pi$
$19$	−2.89898	−0.665072	−0.332536	+	0.943091i	$0.607904\pi$
$20$	0	0
$21$	−3.44949	−0.752740
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	0	0
$26$	6.89898	1.35300
$27$	−1.00000	−0.192450
$28$	3.44949	0.651892
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−0.550510	−0.0944117
$35$	0	0
$36$	1.00000	0.166667
$37$	6.34847	1.04368	0.521841	−	0.853043i	$-0.325245\pi$
$37$	6.34847	1.04368	0.521841	+	0.853043i	$0.325245\pi$
$38$	2.89898	0.470277
$39$	6.89898	1.10472
$40$	0	0
$41$	4.89898	0.765092	0.382546	−	0.923936i	$-0.375047\pi$
$41$	4.89898	0.765092	0.382546	+	0.923936i	$0.375047\pi$
$42$	3.44949	0.532268
$43$	−1.10102	−0.167904	−0.0839520	−	0.996470i	$-0.526754\pi$
$43$	−1.10102	−0.167904	−0.0839520	+	0.996470i	$0.526754\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	1.00000	0.147442
$47$	−5.89898	−0.860455	−0.430227	−	0.902721i	$-0.641567\pi$
$47$	−5.89898	−0.860455	−0.430227	+	0.902721i	$0.641567\pi$
$48$	−1.00000	−0.144338
$49$	4.89898	0.699854
$50$	0	0
$51$	−0.550510	−0.0770869
$52$	−6.89898	−0.956716
$53$	8.89898	1.22237	0.611184	−	0.791488i	$-0.290693\pi$
$53$	8.89898	1.22237	0.611184	+	0.791488i	$0.290693\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−3.44949	−0.460957
$57$	2.89898	0.383979
$58$	−5.00000	−0.656532
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	4.89898	0.627250	0.313625	−	0.949547i	$-0.398457\pi$
$61$	4.89898	0.627250	0.313625	+	0.949547i	$0.398457\pi$
$62$	−2.00000	−0.254000
$63$	3.44949	0.434595
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	0.550510	0.0667592
$69$	1.00000	0.120386
$70$	0	0
$71$	−8.79796	−1.04413	−0.522063	−	0.852907i	$-0.674837\pi$
$71$	−8.79796	−1.04413	−0.522063	+	0.852907i	$0.674837\pi$
$72$	−1.00000	−0.117851
$73$	−11.8990	−1.39267	−0.696335	−	0.717717i	$-0.745187\pi$
$73$	−11.8990	−1.39267	−0.696335	+	0.717717i	$0.745187\pi$
$74$	−6.34847	−0.737995
$75$	0	0
$76$	−2.89898	−0.332536
$77$	6.89898	0.786212
$78$	−6.89898	−0.781156
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−4.89898	−0.541002
$83$	7.44949	0.817688	0.408844	−	0.912604i	$-0.365932\pi$
$83$	7.44949	0.817688	0.408844	+	0.912604i	$0.365932\pi$
$84$	−3.44949	−0.376370
$85$	0	0
$86$	1.10102	0.118726
$87$	−5.00000	−0.536056
$88$	−2.00000	−0.213201
$89$	4.34847	0.460937	0.230468	−	0.973080i	$-0.425974\pi$
$89$	4.34847	0.460937	0.230468	+	0.973080i	$0.425974\pi$
$90$	0	0
$91$	−23.7980	−2.49470
$92$	−1.00000	−0.104257
$93$	−2.00000	−0.207390
$94$	5.89898	0.608433
$95$	0	0
$96$	1.00000	0.102062
$97$	−16.6969	−1.69532	−0.847659	−	0.530542i	$-0.821988\pi$
$97$	−16.6969	−1.69532	−0.847659	+	0.530542i	$0.821988\pi$
$98$	−4.89898	−0.494872
$99$	2.00000	0.201008
$100$	0	0
$101$	15.6969	1.56190	0.780952	−	0.624591i	$-0.214734\pi$
$101$	15.6969	1.56190	0.780952	+	0.624591i	$0.214734\pi$
$102$	0.550510	0.0545086
$103$	−11.2474	−1.10824	−0.554122	−	0.832435i	$-0.686946\pi$
$103$	−11.2474	−1.10824	−0.554122	+	0.832435i	$0.686946\pi$
$104$	6.89898	0.676501
$105$	0	0
$106$	−8.89898	−0.864345
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	−1.00000	−0.0962250
$109$	−1.44949	−0.138836	−0.0694180	−	0.997588i	$-0.522114\pi$
$109$	−1.44949	−0.138836	−0.0694180	+	0.997588i	$0.522114\pi$
$110$	0	0
$111$	−6.34847	−0.602570
$112$	3.44949	0.325946
$113$	0.348469	0.0327812	0.0163906	−	0.999866i	$-0.494782\pi$
$113$	0.348469	0.0327812	0.0163906	+	0.999866i	$0.494782\pi$
$114$	−2.89898	−0.271514
$115$	0	0
$116$	5.00000	0.464238
$117$	−6.89898	−0.637811
$118$	−10.0000	−0.920575
$119$	1.89898	0.174079
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−4.89898	−0.443533
$123$	−4.89898	−0.441726
$124$	2.00000	0.179605
$125$	0	0
$126$	−3.44949	−0.307305
$127$	17.7980	1.57931	0.789657	−	0.613549i	$-0.210259\pi$
$127$	17.7980	1.57931	0.789657	+	0.613549i	$0.210259\pi$
$128$	−1.00000	−0.0883883
$129$	1.10102	0.0969395
$130$	0	0
$131$	−0.898979	−0.0785442	−0.0392721	−	0.999229i	$-0.512504\pi$
$131$	−0.898979	−0.0785442	−0.0392721	+	0.999229i	$0.512504\pi$
$132$	−2.00000	−0.174078
$133$	−10.0000	−0.867110
$134$	−2.00000	−0.172774
$135$	0	0
$136$	−0.550510	−0.0472059
$137$	7.65153	0.653714	0.326857	−	0.945074i	$-0.394010\pi$
$137$	7.65153	0.653714	0.326857	+	0.945074i	$0.394010\pi$
$138$	−1.00000	−0.0851257
$139$	−13.6969	−1.16176	−0.580880	−	0.813990i	$-0.697291\pi$
$139$	−13.6969	−1.16176	−0.580880	+	0.813990i	$0.697291\pi$
$140$	0	0
$141$	5.89898	0.496784
$142$	8.79796	0.738308
$143$	−13.7980	−1.15384
$144$	1.00000	0.0833333
$145$	0	0
$146$	11.8990	0.984767
$147$	−4.89898	−0.404061
$148$	6.34847	0.521841
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	10.6969	0.870505	0.435252	−	0.900309i	$-0.356659\pi$
$151$	10.6969	0.870505	0.435252	+	0.900309i	$0.356659\pi$
$152$	2.89898	0.235138
$153$	0.550510	0.0445061
$154$	−6.89898	−0.555936
$155$	0	0
$156$	6.89898	0.552360
$157$	−0.898979	−0.0717464	−0.0358732	−	0.999356i	$-0.511421\pi$
$157$	−0.898979	−0.0717464	−0.0358732	+	0.999356i	$0.511421\pi$
$158$	−10.0000	−0.795557
$159$	−8.89898	−0.705735
$160$	0	0
$161$	−3.44949	−0.271858
$162$	−1.00000	−0.0785674
$163$	1.79796	0.140827	0.0704135	−	0.997518i	$-0.477568\pi$
$163$	1.79796	0.140827	0.0704135	+	0.997518i	$0.477568\pi$
$164$	4.89898	0.382546
$165$	0	0
$166$	−7.44949	−0.578193
$167$	7.00000	0.541676	0.270838	−	0.962625i	$-0.412699\pi$
$167$	7.00000	0.541676	0.270838	+	0.962625i	$0.412699\pi$
$168$	3.44949	0.266134
$169$	34.5959	2.66122
$170$	0	0
$171$	−2.89898	−0.221691
$172$	−1.10102	−0.0839520
$173$	0.202041	0.0153609	0.00768045	−	0.999971i	$-0.497555\pi$
$173$	0.202041	0.0153609	0.00768045	+	0.999971i	$0.497555\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	−10.0000	−0.751646
$178$	−4.34847	−0.325932
$179$	12.8990	0.964115	0.482057	−	0.876140i	$-0.339890\pi$
$179$	12.8990	0.964115	0.482057	+	0.876140i	$0.339890\pi$
$180$	0	0
$181$	−3.65153	−0.271416	−0.135708	−	0.990749i	$-0.543331\pi$
$181$	−3.65153	−0.271416	−0.135708	+	0.990749i	$0.543331\pi$
$182$	23.7980	1.76402
$183$	−4.89898	−0.362143
$184$	1.00000	0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	1.10102	0.0805146
$188$	−5.89898	−0.430227
$189$	−3.44949	−0.250913
$190$	0	0
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	−1.00000	−0.0721688
$193$	19.6969	1.41782	0.708908	−	0.705301i	$-0.249188\pi$
$193$	19.6969	1.41782	0.708908	+	0.705301i	$0.249188\pi$
$194$	16.6969	1.19877
$195$	0	0
$196$	4.89898	0.349927
$197$	−5.89898	−0.420285	−0.210142	−	0.977671i	$-0.567393\pi$
$197$	−5.89898	−0.420285	−0.210142	+	0.977671i	$0.567393\pi$
$198$	−2.00000	−0.142134
$199$	−10.1464	−0.719261	−0.359631	−	0.933095i	$-0.617097\pi$
$199$	−10.1464	−0.719261	−0.359631	+	0.933095i	$0.617097\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	−15.6969	−1.10443
$203$	17.2474	1.21053
$204$	−0.550510	−0.0385434
$205$	0	0
$206$	11.2474	0.783647
$207$	−1.00000	−0.0695048
$208$	−6.89898	−0.478358
$209$	−5.79796	−0.401053
$210$	0	0
$211$	−8.79796	−0.605676	−0.302838	−	0.953042i	$-0.597934\pi$
$211$	−8.79796	−0.605676	−0.302838	+	0.953042i	$0.597934\pi$
$212$	8.89898	0.611184
$213$	8.79796	0.602826
$214$	−2.00000	−0.136717
$215$	0	0
$216$	1.00000	0.0680414
$217$	6.89898	0.468333
$218$	1.44949	0.0981718
$219$	11.8990	0.804059
$220$	0	0
$221$	−3.79796	−0.255478
$222$	6.34847	0.426081
$223$	4.69694	0.314530	0.157265	−	0.987556i	$-0.449732\pi$
$223$	4.69694	0.314530	0.157265	+	0.987556i	$0.449732\pi$
$224$	−3.44949	−0.230479
$225$	0	0
$226$	−0.348469	−0.0231798
$227$	29.2474	1.94122	0.970611	−	0.240655i	$-0.0773623\pi$
$227$	29.2474	1.94122	0.970611	+	0.240655i	$0.0773623\pi$
$228$	2.89898	0.191990
$229$	12.8990	0.852389	0.426194	−	0.904632i	$-0.359854\pi$
$229$	12.8990	0.852389	0.426194	+	0.904632i	$0.359854\pi$
$230$	0	0
$231$	−6.89898	−0.453920
$232$	−5.00000	−0.328266
$233$	−2.69694	−0.176682	−0.0883412	−	0.996090i	$-0.528157\pi$
$233$	−2.69694	−0.176682	−0.0883412	+	0.996090i	$0.528157\pi$
$234$	6.89898	0.451000
$235$	0	0
$236$	10.0000	0.650945
$237$	−10.0000	−0.649570
$238$	−1.89898	−0.123093
$239$	−17.8990	−1.15779	−0.578894	−	0.815403i	$-0.696516\pi$
$239$	−17.8990	−1.15779	−0.578894	+	0.815403i	$0.696516\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	4.89898	0.313625
$245$	0	0
$246$	4.89898	0.312348
$247$	20.0000	1.27257
$248$	−2.00000	−0.127000
$249$	−7.44949	−0.472092
$250$	0	0
$251$	19.2474	1.21489	0.607444	−	0.794362i	$-0.292195\pi$
$251$	19.2474	1.21489	0.607444	+	0.794362i	$0.292195\pi$
$252$	3.44949	0.217297
$253$	−2.00000	−0.125739
$254$	−17.7980	−1.11674
$255$	0	0
$256$	1.00000	0.0625000
$257$	27.7980	1.73399	0.866995	−	0.498318i	$-0.166049\pi$
$257$	27.7980	1.73399	0.866995	+	0.498318i	$0.166049\pi$
$258$	−1.10102	−0.0685465
$259$	21.8990	1.36074
$260$	0	0
$261$	5.00000	0.309492
$262$	0.898979	0.0555391
$263$	0.202041	0.0124584	0.00622919	−	0.999981i	$-0.498017\pi$
$263$	0.202041	0.0124584	0.00622919	+	0.999981i	$0.498017\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	10.0000	0.613139
$267$	−4.34847	−0.266122
$268$	2.00000	0.122169
$269$	−15.7980	−0.963219	−0.481609	−	0.876386i	$-0.659948\pi$
$269$	−15.7980	−0.963219	−0.481609	+	0.876386i	$0.659948\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	0.550510	0.0333796
$273$	23.7980	1.44032
$274$	−7.65153	−0.462246
$275$	0	0
$276$	1.00000	0.0601929
$277$	13.5959	0.816900	0.408450	−	0.912781i	$-0.366070\pi$
$277$	13.5959	0.816900	0.408450	+	0.912781i	$0.366070\pi$
$278$	13.6969	0.821488
$279$	2.00000	0.119737
$280$	0	0
$281$	−25.2474	−1.50614	−0.753068	−	0.657942i	$-0.771427\pi$
$281$	−25.2474	−1.50614	−0.753068	+	0.657942i	$0.771427\pi$
$282$	−5.89898	−0.351279
$283$	27.5959	1.64041	0.820204	−	0.572072i	$-0.193860\pi$
$283$	27.5959	1.64041	0.820204	+	0.572072i	$0.193860\pi$
$284$	−8.79796	−0.522063
$285$	0	0
$286$	13.7980	0.815890
$287$	16.8990	0.997515
$288$	−1.00000	−0.0589256
$289$	−16.6969	−0.982173
$290$	0	0
$291$	16.6969	0.978792
$292$	−11.8990	−0.696335
$293$	11.7980	0.689244	0.344622	−	0.938742i	$-0.388007\pi$
$293$	11.7980	0.689244	0.344622	+	0.938742i	$0.388007\pi$
$294$	4.89898	0.285714
$295$	0	0
$296$	−6.34847	−0.368997
$297$	−2.00000	−0.116052
$298$	−20.0000	−1.15857
$299$	6.89898	0.398978
$300$	0	0
$301$	−3.79796	−0.218911
$302$	−10.6969	−0.615540
$303$	−15.6969	−0.901766
$304$	−2.89898	−0.166268
$305$	0	0
$306$	−0.550510	−0.0314706
$307$	29.8990	1.70642	0.853212	−	0.521564i	$-0.174651\pi$
$307$	29.8990	1.70642	0.853212	+	0.521564i	$0.174651\pi$
$308$	6.89898	0.393106
$309$	11.2474	0.639845
$310$	0	0
$311$	−24.5959	−1.39471	−0.697353	−	0.716728i	$-0.745639\pi$
$311$	−24.5959	−1.39471	−0.697353	+	0.716728i	$0.745639\pi$
$312$	−6.89898	−0.390578
$313$	3.10102	0.175280	0.0876400	−	0.996152i	$-0.472067\pi$
$313$	3.10102	0.175280	0.0876400	+	0.996152i	$0.472067\pi$
$314$	0.898979	0.0507323
$315$	0	0
$316$	10.0000	0.562544
$317$	28.5959	1.60611	0.803053	−	0.595907i	$-0.203207\pi$
$317$	28.5959	1.60611	0.803053	+	0.595907i	$0.203207\pi$
$318$	8.89898	0.499030
$319$	10.0000	0.559893
$320$	0	0
$321$	−2.00000	−0.111629
$322$	3.44949	0.192233
$323$	−1.59592	−0.0887992
$324$	1.00000	0.0555556
$325$	0	0
$326$	−1.79796	−0.0995797
$327$	1.44949	0.0801570
$328$	−4.89898	−0.270501
$329$	−20.3485	−1.12185
$330$	0	0
$331$	12.7980	0.703439	0.351720	−	0.936105i	$-0.385597\pi$
$331$	12.7980	0.703439	0.351720	+	0.936105i	$0.385597\pi$
$332$	7.44949	0.408844
$333$	6.34847	0.347894
$334$	−7.00000	−0.383023
$335$	0	0
$336$	−3.44949	−0.188185
$337$	−32.4949	−1.77011	−0.885055	−	0.465487i	$-0.845879\pi$
$337$	−32.4949	−1.77011	−0.885055	+	0.465487i	$0.845879\pi$
$338$	−34.5959	−1.88177
$339$	−0.348469	−0.0189263
$340$	0	0
$341$	4.00000	0.216612
$342$	2.89898	0.156759
$343$	−7.24745	−0.391325
$344$	1.10102	0.0593630
$345$	0	0
$346$	−0.202041	−0.0108618
$347$	3.30306	0.177318	0.0886588	−	0.996062i	$-0.471742\pi$
$347$	3.30306	0.177318	0.0886588	+	0.996062i	$0.471742\pi$
$348$	−5.00000	−0.268028
$349$	22.8990	1.22575	0.612877	−	0.790178i	$-0.290012\pi$
$349$	22.8990	1.22575	0.612877	+	0.790178i	$0.290012\pi$
$350$	0	0
$351$	6.89898	0.368240
$352$	−2.00000	−0.106600
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	10.0000	0.531494
$355$	0	0
$356$	4.34847	0.230468
$357$	−1.89898	−0.100505
$358$	−12.8990	−0.681732
$359$	−25.7980	−1.36156	−0.680782	−	0.732486i	$-0.738360\pi$
$359$	−25.7980	−1.36156	−0.680782	+	0.732486i	$0.738360\pi$
$360$	0	0
$361$	−10.5959	−0.557680
$362$	3.65153	0.191920
$363$	7.00000	0.367405
$364$	−23.7980	−1.24735
$365$	0	0
$366$	4.89898	0.256074
$367$	27.7980	1.45104	0.725521	−	0.688200i	$-0.241599\pi$
$367$	27.7980	1.45104	0.725521	+	0.688200i	$0.241599\pi$
$368$	−1.00000	−0.0521286
$369$	4.89898	0.255031
$370$	0	0
$371$	30.6969	1.59371
$372$	−2.00000	−0.103695
$373$	−21.2474	−1.10015	−0.550076	−	0.835115i	$-0.685401\pi$
$373$	−21.2474	−1.10015	−0.550076	+	0.835115i	$0.685401\pi$
$374$	−1.10102	−0.0569324
$375$	0	0
$376$	5.89898	0.304217
$377$	−34.4949	−1.77658
$378$	3.44949	0.177423
$379$	30.2929	1.55604	0.778020	−	0.628240i	$-0.216224\pi$
$379$	30.2929	1.55604	0.778020	+	0.628240i	$0.216224\pi$
$380$	0	0
$381$	−17.7980	−0.911817
$382$	−2.00000	−0.102329
$383$	−9.79796	−0.500652	−0.250326	−	0.968162i	$-0.580538\pi$
$383$	−9.79796	−0.500652	−0.250326	+	0.968162i	$0.580538\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−19.6969	−1.00255
$387$	−1.10102	−0.0559680
$388$	−16.6969	−0.847659
$389$	−4.20204	−0.213052	−0.106526	−	0.994310i	$-0.533973\pi$
$389$	−4.20204	−0.213052	−0.106526	+	0.994310i	$0.533973\pi$
$390$	0	0
$391$	−0.550510	−0.0278405
$392$	−4.89898	−0.247436
$393$	0.898979	0.0453475
$394$	5.89898	0.297186
$395$	0	0
$396$	2.00000	0.100504
$397$	−28.0000	−1.40528	−0.702640	−	0.711546i	$-0.747995\pi$
$397$	−28.0000	−1.40528	−0.702640	+	0.711546i	$0.747995\pi$
$398$	10.1464	0.508594
$399$	10.0000	0.500626
$400$	0	0
$401$	10.6969	0.534180	0.267090	−	0.963672i	$-0.413938\pi$
$401$	10.6969	0.534180	0.267090	+	0.963672i	$0.413938\pi$
$402$	2.00000	0.0997509
$403$	−13.7980	−0.687325
$404$	15.6969	0.780952
$405$	0	0
$406$	−17.2474	−0.855977
$407$	12.6969	0.629364
$408$	0.550510	0.0272543
$409$	−3.69694	−0.182802	−0.0914009	−	0.995814i	$-0.529134\pi$
$409$	−3.69694	−0.182802	−0.0914009	+	0.995814i	$0.529134\pi$
$410$	0	0
$411$	−7.65153	−0.377422
$412$	−11.2474	−0.554122
$413$	34.4949	1.69738
$414$	1.00000	0.0491473
$415$	0	0
$416$	6.89898	0.338250
$417$	13.6969	0.670742
$418$	5.79796	0.283587
$419$	−20.1464	−0.984217	−0.492109	−	0.870534i	$-0.663774\pi$
$419$	−20.1464	−0.984217	−0.492109	+	0.870534i	$0.663774\pi$
$420$	0	0
$421$	36.4949	1.77865	0.889326	−	0.457273i	$-0.151174\pi$
$421$	36.4949	1.77865	0.889326	+	0.457273i	$0.151174\pi$
$422$	8.79796	0.428278
$423$	−5.89898	−0.286818
$424$	−8.89898	−0.432173
$425$	0	0
$426$	−8.79796	−0.426263
$427$	16.8990	0.817799
$428$	2.00000	0.0966736
$429$	13.7980	0.666172
$430$	0	0
$431$	40.6969	1.96030	0.980151	−	0.198251i	$-0.0635261\pi$
$431$	40.6969	1.96030	0.980151	+	0.198251i	$0.0635261\pi$
$432$	−1.00000	−0.0481125
$433$	−12.6969	−0.610176	−0.305088	−	0.952324i	$-0.598686\pi$
$433$	−12.6969	−0.610176	−0.305088	+	0.952324i	$0.598686\pi$
$434$	−6.89898	−0.331162
$435$	0	0
$436$	−1.44949	−0.0694180
$437$	2.89898	0.138677
$438$	−11.8990	−0.568555
$439$	18.6969	0.892356	0.446178	−	0.894944i	$-0.352785\pi$
$439$	18.6969	0.892356	0.446178	+	0.894944i	$0.352785\pi$
$440$	0	0
$441$	4.89898	0.233285
$442$	3.79796	0.180650
$443$	34.6969	1.64850	0.824251	−	0.566225i	$-0.191597\pi$
$443$	34.6969	1.64850	0.824251	+	0.566225i	$0.191597\pi$
$444$	−6.34847	−0.301285
$445$	0	0
$446$	−4.69694	−0.222406
$447$	−20.0000	−0.945968
$448$	3.44949	0.162973
$449$	−15.7980	−0.745552	−0.372776	−	0.927921i	$-0.621594\pi$
$449$	−15.7980	−0.745552	−0.372776	+	0.927921i	$0.621594\pi$
$450$	0	0
$451$	9.79796	0.461368
$452$	0.348469	0.0163906
$453$	−10.6969	−0.502586
$454$	−29.2474	−1.37265
$455$	0	0
$456$	−2.89898	−0.135757
$457$	−39.5959	−1.85222	−0.926109	−	0.377255i	$-0.876868\pi$
$457$	−39.5959	−1.85222	−0.926109	+	0.377255i	$0.876868\pi$
$458$	−12.8990	−0.602730
$459$	−0.550510	−0.0256956
$460$	0	0
$461$	−27.4949	−1.28057	−0.640283	−	0.768140i	$-0.721183\pi$
$461$	−27.4949	−1.28057	−0.640283	+	0.768140i	$0.721183\pi$
$462$	6.89898	0.320970
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	2.69694	0.124933
$467$	−23.9444	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$467$	−23.9444	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$468$	−6.89898	−0.318905
$469$	6.89898	0.318565
$470$	0	0
$471$	0.898979	0.0414228
$472$	−10.0000	−0.460287
$473$	−2.20204	−0.101250
$474$	10.0000	0.459315
$475$	0	0
$476$	1.89898	0.0870396
$477$	8.89898	0.407456
$478$	17.8990	0.818680
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	0	0
$481$	−43.7980	−1.99702
$482$	8.00000	0.364390
$483$	3.44949	0.156957
$484$	−7.00000	−0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	24.8990	1.12828	0.564140	−	0.825679i	$-0.309208\pi$
$487$	24.8990	1.12828	0.564140	+	0.825679i	$0.309208\pi$
$488$	−4.89898	−0.221766
$489$	−1.79796	−0.0813065
$490$	0	0
$491$	34.8990	1.57497	0.787484	−	0.616335i	$-0.211383\pi$
$491$	34.8990	1.57497	0.787484	+	0.616335i	$0.211383\pi$
$492$	−4.89898	−0.220863
$493$	2.75255	0.123969
$494$	−20.0000	−0.899843
$495$	0	0
$496$	2.00000	0.0898027
$497$	−30.3485	−1.36131
$498$	7.44949	0.333820
$499$	12.1010	0.541716	0.270858	−	0.962619i	$-0.412693\pi$
$499$	12.1010	0.541716	0.270858	+	0.962619i	$0.412693\pi$
$500$	0	0
$501$	−7.00000	−0.312737
$502$	−19.2474	−0.859056
$503$	14.6969	0.655304	0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969	0.655304	0.327652	+	0.944798i	$0.393743\pi$
$504$	−3.44949	−0.153652
$505$	0	0
$506$	2.00000	0.0889108
$507$	−34.5959	−1.53646
$508$	17.7980	0.789657
$509$	−15.0000	−0.664863	−0.332432	−	0.943127i	$-0.607869\pi$
$509$	−15.0000	−0.664863	−0.332432	+	0.943127i	$0.607869\pi$
$510$	0	0
$511$	−41.0454	−1.81574
$512$	−1.00000	−0.0441942
$513$	2.89898	0.127993
$514$	−27.7980	−1.22612
$515$	0	0
$516$	1.10102	0.0484697
$517$	−11.7980	−0.518874
$518$	−21.8990	−0.962186
$519$	−0.202041	−0.00886862
$520$	0	0
$521$	−8.14643	−0.356901	−0.178451	−	0.983949i	$-0.557109\pi$
$521$	−8.14643	−0.356901	−0.178451	+	0.983949i	$0.557109\pi$
$522$	−5.00000	−0.218844
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−0.898979	−0.0392721
$525$	0	0
$526$	−0.202041	−0.00880941
$527$	1.10102	0.0479612
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	0	0
$531$	10.0000	0.433963
$532$	−10.0000	−0.433555
$533$	−33.7980	−1.46395
$534$	4.34847	0.188177
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	−12.8990	−0.556632
$538$	15.7980	0.681098
$539$	9.79796	0.422028
$540$	0	0
$541$	23.5959	1.01447	0.507234	−	0.861808i	$-0.330668\pi$
$541$	23.5959	1.01447	0.507234	+	0.861808i	$0.330668\pi$
$542$	8.00000	0.343629
$543$	3.65153	0.156702
$544$	−0.550510	−0.0236029
$545$	0	0
$546$	−23.7980	−1.01846
$547$	−8.79796	−0.376174	−0.188087	−	0.982152i	$-0.560229\pi$
$547$	−8.79796	−0.376174	−0.188087	+	0.982152i	$0.560229\pi$
$548$	7.65153	0.326857
$549$	4.89898	0.209083
$550$	0	0
$551$	−14.4949	−0.617503
$552$	−1.00000	−0.0425628
$553$	34.4949	1.46687
$554$	−13.5959	−0.577635
$555$	0	0
$556$	−13.6969	−0.580880
$557$	0.696938	0.0295302	0.0147651	−	0.999891i	$-0.495300\pi$
$557$	0.696938	0.0295302	0.0147651	+	0.999891i	$0.495300\pi$
$558$	−2.00000	−0.0846668
$559$	7.59592	0.321273
$560$	0	0
$561$	−1.10102	−0.0464851
$562$	25.2474	1.06500
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	5.89898	0.248392
$565$	0	0
$566$	−27.5959	−1.15994
$567$	3.44949	0.144865
$568$	8.79796	0.369154
$569$	4.49490	0.188436	0.0942180	−	0.995552i	$-0.469965\pi$
$569$	4.49490	0.188436	0.0942180	+	0.995552i	$0.469965\pi$
$570$	0	0
$571$	3.30306	0.138229	0.0691144	−	0.997609i	$-0.477983\pi$
$571$	3.30306	0.138229	0.0691144	+	0.997609i	$0.477983\pi$
$572$	−13.7980	−0.576922
$573$	−2.00000	−0.0835512
$574$	−16.8990	−0.705350
$575$	0	0
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	16.6969	0.694501
$579$	−19.6969	−0.818577
$580$	0	0
$581$	25.6969	1.06609
$582$	−16.6969	−0.692110
$583$	17.7980	0.737116
$584$	11.8990	0.492383
$585$	0	0
$586$	−11.7980	−0.487369
$587$	4.89898	0.202203	0.101101	−	0.994876i	$-0.467763\pi$
$587$	4.89898	0.202203	0.101101	+	0.994876i	$0.467763\pi$
$588$	−4.89898	−0.202031
$589$	−5.79796	−0.238901
$590$	0	0
$591$	5.89898	0.242652
$592$	6.34847	0.260920
$593$	4.40408	0.180854	0.0904270	−	0.995903i	$-0.471177\pi$
$593$	4.40408	0.180854	0.0904270	+	0.995903i	$0.471177\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	20.0000	0.819232
$597$	10.1464	0.415266
$598$	−6.89898	−0.282120
$599$	37.3939	1.52787	0.763936	−	0.645292i	$-0.223264\pi$
$599$	37.3939	1.52787	0.763936	+	0.645292i	$0.223264\pi$
$600$	0	0
$601$	37.0000	1.50926	0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000	1.50926	0.754631	+	0.656150i	$0.227816\pi$
$602$	3.79796	0.154793
$603$	2.00000	0.0814463
$604$	10.6969	0.435252
$605$	0	0
$606$	15.6969	0.637645
$607$	−18.0000	−0.730597	−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000	−0.730597	−0.365299	+	0.930890i	$0.619033\pi$
$608$	2.89898	0.117569
$609$	−17.2474	−0.698902
$610$	0	0
$611$	40.6969	1.64642
$612$	0.550510	0.0222531
$613$	−34.1464	−1.37916	−0.689581	−	0.724209i	$-0.742205\pi$
$613$	−34.1464	−1.37916	−0.689581	+	0.724209i	$0.742205\pi$
$614$	−29.8990	−1.20662
$615$	0	0
$616$	−6.89898	−0.277968
$617$	36.4949	1.46923	0.734615	−	0.678485i	$-0.237363\pi$
$617$	36.4949	1.46923	0.734615	+	0.678485i	$0.237363\pi$
$618$	−11.2474	−0.452439
$619$	4.49490	0.180665	0.0903326	−	0.995912i	$-0.471207\pi$
$619$	4.49490	0.180665	0.0903326	+	0.995912i	$0.471207\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	24.5959	0.986206
$623$	15.0000	0.600962
$624$	6.89898	0.276180
$625$	0	0
$626$	−3.10102	−0.123942
$627$	5.79796	0.231548
$628$	−0.898979	−0.0358732
$629$	3.49490	0.139351
$630$	0	0
$631$	10.5505	0.420009	0.210005	−	0.977700i	$-0.432652\pi$
$631$	10.5505	0.420009	0.210005	+	0.977700i	$0.432652\pi$
$632$	−10.0000	−0.397779
$633$	8.79796	0.349687
$634$	−28.5959	−1.13569
$635$	0	0
$636$	−8.89898	−0.352867
$637$	−33.7980	−1.33912
$638$	−10.0000	−0.395904
$639$	−8.79796	−0.348042
$640$	0	0
$641$	−29.4495	−1.16318	−0.581592	−	0.813480i	$-0.697570\pi$
$641$	−29.4495	−1.16318	−0.581592	+	0.813480i	$0.697570\pi$
$642$	2.00000	0.0789337
$643$	0.202041	0.00796772	0.00398386	−	0.999992i	$-0.498732\pi$
$643$	0.202041	0.00796772	0.00398386	+	0.999992i	$0.498732\pi$
$644$	−3.44949	−0.135929
$645$	0	0
$646$	1.59592	0.0627906
$647$	18.5959	0.731081	0.365540	−	0.930795i	$-0.380884\pi$
$647$	18.5959	0.731081	0.365540	+	0.930795i	$0.380884\pi$
$648$	−1.00000	−0.0392837
$649$	20.0000	0.785069
$650$	0	0
$651$	−6.89898	−0.270392
$652$	1.79796	0.0704135
$653$	29.6969	1.16213	0.581066	−	0.813857i	$-0.302636\pi$
$653$	29.6969	1.16213	0.581066	+	0.813857i	$0.302636\pi$
$654$	−1.44949	−0.0566795
$655$	0	0
$656$	4.89898	0.191273
$657$	−11.8990	−0.464223
$658$	20.3485	0.793266
$659$	−18.5505	−0.722625	−0.361313	−	0.932445i	$-0.617671\pi$
$659$	−18.5505	−0.722625	−0.361313	+	0.932445i	$0.617671\pi$
$660$	0	0
$661$	−16.5505	−0.643740	−0.321870	−	0.946784i	$-0.604311\pi$
$661$	−16.5505	−0.643740	−0.321870	+	0.946784i	$0.604311\pi$
$662$	−12.7980	−0.497407
$663$	3.79796	0.147501
$664$	−7.44949	−0.289096
$665$	0	0
$666$	−6.34847	−0.245998
$667$	−5.00000	−0.193601
$668$	7.00000	0.270838
$669$	−4.69694	−0.181594
$670$	0	0
$671$	9.79796	0.378246
$672$	3.44949	0.133067
$673$	12.5959	0.485537	0.242768	−	0.970084i	$-0.421944\pi$
$673$	12.5959	0.485537	0.242768	+	0.970084i	$0.421944\pi$
$674$	32.4949	1.25166
$675$	0	0
$676$	34.5959	1.33061
$677$	−25.3939	−0.975966	−0.487983	−	0.872853i	$-0.662267\pi$
$677$	−25.3939	−0.975966	−0.487983	+	0.872853i	$0.662267\pi$
$678$	0.348469	0.0133829
$679$	−57.5959	−2.21033
$680$	0	0
$681$	−29.2474	−1.12076
$682$	−4.00000	−0.153168
$683$	−16.8990	−0.646621	−0.323311	−	0.946293i	$-0.604796\pi$
$683$	−16.8990	−0.646621	−0.323311	+	0.946293i	$0.604796\pi$
$684$	−2.89898	−0.110845
$685$	0	0
$686$	7.24745	0.276709
$687$	−12.8990	−0.492127
$688$	−1.10102	−0.0419760
$689$	−61.3939	−2.33892
$690$	0	0
$691$	−28.7980	−1.09553	−0.547763	−	0.836634i	$-0.684520\pi$
$691$	−28.7980	−1.09553	−0.547763	+	0.836634i	$0.684520\pi$
$692$	0.202041	0.00768045
$693$	6.89898	0.262071
$694$	−3.30306	−0.125383
$695$	0	0
$696$	5.00000	0.189525
$697$	2.69694	0.102154
$698$	−22.8990	−0.866739
$699$	2.69694	0.102008
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	−6.89898	−0.260385
$703$	−18.4041	−0.694123
$704$	2.00000	0.0753778
$705$	0	0
$706$	−26.0000	−0.978523
$707$	54.1464	2.03639
$708$	−10.0000	−0.375823
$709$	−25.9444	−0.974362	−0.487181	−	0.873301i	$-0.661975\pi$
$709$	−25.9444	−0.974362	−0.487181	+	0.873301i	$0.661975\pi$
$710$	0	0
$711$	10.0000	0.375029
$712$	−4.34847	−0.162966
$713$	−2.00000	−0.0749006
$714$	1.89898	0.0710675
$715$	0	0
$716$	12.8990	0.482057
$717$	17.8990	0.668450
$718$	25.7980	0.962771
$719$	9.20204	0.343178	0.171589	−	0.985169i	$-0.445110\pi$
$719$	9.20204	0.343178	0.171589	+	0.985169i	$0.445110\pi$
$720$	0	0
$721$	−38.7980	−1.44491
$722$	10.5959	0.394339
$723$	8.00000	0.297523
$724$	−3.65153	−0.135708
$725$	0	0
$726$	−7.00000	−0.259794
$727$	19.3939	0.719279	0.359640	−	0.933091i	$-0.382900\pi$
$727$	19.3939	0.719279	0.359640	+	0.933091i	$0.382900\pi$
$728$	23.7980	0.882011
$729$	1.00000	0.0370370
$730$	0	0
$731$	−0.606123	−0.0224183
$732$	−4.89898	−0.181071
$733$	5.85357	0.216207	0.108103	−	0.994140i	$-0.465522\pi$
$733$	5.85357	0.216207	0.108103	+	0.994140i	$0.465522\pi$
$734$	−27.7980	−1.02604
$735$	0	0
$736$	1.00000	0.0368605
$737$	4.00000	0.147342
$738$	−4.89898	−0.180334
$739$	−26.5959	−0.978347	−0.489173	−	0.872187i	$-0.662701\pi$
$739$	−26.5959	−0.978347	−0.489173	+	0.872187i	$0.662701\pi$
$740$	0	0
$741$	−20.0000	−0.734718
$742$	−30.6969	−1.12692
$743$	−44.2929	−1.62495	−0.812474	−	0.582998i	$-0.801880\pi$
$743$	−44.2929	−1.62495	−0.812474	+	0.582998i	$0.801880\pi$
$744$	2.00000	0.0733236
$745$	0	0
$746$	21.2474	0.777924
$747$	7.44949	0.272563
$748$	1.10102	0.0402573
$749$	6.89898	0.252083
$750$	0	0
$751$	−0.752551	−0.0274610	−0.0137305	−	0.999906i	$-0.504371\pi$
$751$	−0.752551	−0.0274610	−0.0137305	+	0.999906i	$0.504371\pi$
$752$	−5.89898	−0.215114
$753$	−19.2474	−0.701416
$754$	34.4949	1.25623
$755$	0	0
$756$	−3.44949	−0.125457
$757$	−35.2474	−1.28109	−0.640545	−	0.767921i	$-0.721292\pi$
$757$	−35.2474	−1.28109	−0.640545	+	0.767921i	$0.721292\pi$
$758$	−30.2929	−1.10029
$759$	2.00000	0.0725954
$760$	0	0
$761$	38.0908	1.38079	0.690395	−	0.723432i	$-0.257437\pi$
$761$	38.0908	1.38079	0.690395	+	0.723432i	$0.257437\pi$
$762$	17.7980	0.644752
$763$	−5.00000	−0.181012
$764$	2.00000	0.0723575
$765$	0	0
$766$	9.79796	0.354015
$767$	−68.9898	−2.49108
$768$	−1.00000	−0.0360844
$769$	−20.2929	−0.731779	−0.365890	−	0.930658i	$-0.619235\pi$
$769$	−20.2929	−0.731779	−0.365890	+	0.930658i	$0.619235\pi$
$770$	0	0
$771$	−27.7980	−1.00112
$772$	19.6969	0.708908
$773$	−1.10102	−0.0396010	−0.0198005	−	0.999804i	$-0.506303\pi$
$773$	−1.10102	−0.0396010	−0.0198005	+	0.999804i	$0.506303\pi$
$774$	1.10102	0.0395754
$775$	0	0
$776$	16.6969	0.599385
$777$	−21.8990	−0.785622
$778$	4.20204	0.150650
$779$	−14.2020	−0.508841
$780$	0	0
$781$	−17.5959	−0.629631
$782$	0.550510	0.0196862
$783$	−5.00000	−0.178685
$784$	4.89898	0.174964
$785$	0	0
$786$	−0.898979	−0.0320655
$787$	−28.0000	−0.998092	−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000	−0.998092	−0.499046	+	0.866575i	$0.666316\pi$
$788$	−5.89898	−0.210142
$789$	−0.202041	−0.00719285
$790$	0	0
$791$	1.20204	0.0427397
$792$	−2.00000	−0.0710669
$793$	−33.7980	−1.20020
$794$	28.0000	0.993683
$795$	0	0
$796$	−10.1464	−0.359631
$797$	−25.1010	−0.889124	−0.444562	−	0.895748i	$-0.646641\pi$
$797$	−25.1010	−0.889124	−0.444562	+	0.895748i	$0.646641\pi$
$798$	−10.0000	−0.353996
$799$	−3.24745	−0.114886
$800$	0	0
$801$	4.34847	0.153646
$802$	−10.6969	−0.377722
$803$	−23.7980	−0.839812
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	13.7980	0.486012
$807$	15.7980	0.556114
$808$	−15.6969	−0.552216
$809$	−47.3939	−1.66628	−0.833140	−	0.553062i	$-0.813459\pi$
$809$	−47.3939	−1.66628	−0.833140	+	0.553062i	$0.813459\pi$
$810$	0	0
$811$	26.2020	0.920078	0.460039	−	0.887899i	$-0.347835\pi$
$811$	26.2020	0.920078	0.460039	+	0.887899i	$0.347835\pi$
$812$	17.2474	0.605267
$813$	8.00000	0.280572
$814$	−12.6969	−0.445027
$815$	0	0
$816$	−0.550510	−0.0192717
$817$	3.19184	0.111668
$818$	3.69694	0.129260
$819$	−23.7980	−0.831568
$820$	0	0
$821$	−32.2020	−1.12386	−0.561929	−	0.827185i	$-0.689941\pi$
$821$	−32.2020	−1.12386	−0.561929	+	0.827185i	$0.689941\pi$
$822$	7.65153	0.266878
$823$	32.0908	1.11862	0.559308	−	0.828960i	$-0.311067\pi$
$823$	32.0908	1.11862	0.559308	+	0.828960i	$0.311067\pi$
$824$	11.2474	0.391823
$825$	0	0
$826$	−34.4949	−1.20023
$827$	39.2474	1.36477	0.682384	−	0.730994i	$-0.260943\pi$
$827$	39.2474	1.36477	0.682384	+	0.730994i	$0.260943\pi$
$828$	−1.00000	−0.0347524
$829$	−42.8990	−1.48994	−0.744972	−	0.667096i	$-0.767537\pi$
$829$	−42.8990	−1.48994	−0.744972	+	0.667096i	$0.767537\pi$
$830$	0	0
$831$	−13.5959	−0.471637
$832$	−6.89898	−0.239179
$833$	2.69694	0.0934434
$834$	−13.6969	−0.474286
$835$	0	0
$836$	−5.79796	−0.200527
$837$	−2.00000	−0.0691301
$838$	20.1464	0.695947
$839$	−38.6969	−1.33597	−0.667983	−	0.744176i	$-0.732842\pi$
$839$	−38.6969	−1.33597	−0.667983	+	0.744176i	$0.732842\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−36.4949	−1.25770
$843$	25.2474	0.869568
$844$	−8.79796	−0.302838
$845$	0	0
$846$	5.89898	0.202811
$847$	−24.1464	−0.829681
$848$	8.89898	0.305592
$849$	−27.5959	−0.947089
$850$	0	0
$851$	−6.34847	−0.217623
$852$	8.79796	0.301413
$853$	−52.9898	−1.81434	−0.907168	−	0.420769i	$-0.861760\pi$
$853$	−52.9898	−1.81434	−0.907168	+	0.420769i	$0.861760\pi$
$854$	−16.8990	−0.578271
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	6.49490	0.221861	0.110931	−	0.993828i	$-0.464617\pi$
$857$	6.49490	0.221861	0.110931	+	0.993828i	$0.464617\pi$
$858$	−13.7980	−0.471055
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	−16.8990	−0.575916
$862$	−40.6969	−1.38614
$863$	38.3939	1.30694	0.653471	−	0.756951i	$-0.273312\pi$
$863$	38.3939	1.30694	0.653471	+	0.756951i	$0.273312\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	12.6969	0.431460
$867$	16.6969	0.567058
$868$	6.89898	0.234167
$869$	20.0000	0.678454
$870$	0	0
$871$	−13.7980	−0.467526
$872$	1.44949	0.0490859
$873$	−16.6969	−0.565106
$874$	−2.89898	−0.0980594
$875$	0	0
$876$	11.8990	0.402029
$877$	−29.5959	−0.999383	−0.499692	−	0.866203i	$-0.666553\pi$
$877$	−29.5959	−0.999383	−0.499692	+	0.866203i	$0.666553\pi$
$878$	−18.6969	−0.630991
$879$	−11.7980	−0.397935
$880$	0	0
$881$	−40.8990	−1.37792	−0.688961	−	0.724799i	$-0.741933\pi$
$881$	−40.8990	−1.37792	−0.688961	+	0.724799i	$0.741933\pi$
$882$	−4.89898	−0.164957
$883$	9.40408	0.316473	0.158236	−	0.987401i	$-0.449419\pi$
$883$	9.40408	0.316473	0.158236	+	0.987401i	$0.449419\pi$
$884$	−3.79796	−0.127739
$885$	0	0
$886$	−34.6969	−1.16567
$887$	19.8990	0.668142	0.334071	−	0.942548i	$-0.391577\pi$
$887$	19.8990	0.668142	0.334071	+	0.942548i	$0.391577\pi$
$888$	6.34847	0.213041
$889$	61.3939	2.05908
$890$	0	0
$891$	2.00000	0.0670025
$892$	4.69694	0.157265
$893$	17.1010	0.572264
$894$	20.0000	0.668900
$895$	0	0
$896$	−3.44949	−0.115239
$897$	−6.89898	−0.230350
$898$	15.7980	0.527185
$899$	10.0000	0.333519
$900$	0	0
$901$	4.89898	0.163209
$902$	−9.79796	−0.326236
$903$	3.79796	0.126388
$904$	−0.348469	−0.0115899
$905$	0	0
$906$	10.6969	0.355382
$907$	46.4949	1.54384	0.771919	−	0.635721i	$-0.219297\pi$
$907$	46.4949	1.54384	0.771919	+	0.635721i	$0.219297\pi$
$908$	29.2474	0.970611
$909$	15.6969	0.520635
$910$	0	0
$911$	50.6969	1.67966	0.839832	−	0.542846i	$-0.182653\pi$
$911$	50.6969	1.67966	0.839832	+	0.542846i	$0.182653\pi$
$912$	2.89898	0.0959948
$913$	14.8990	0.493084
$914$	39.5959	1.30972
$915$	0	0
$916$	12.8990	0.426194
$917$	−3.10102	−0.102405
$918$	0.550510	0.0181695
$919$	25.9444	0.855826	0.427913	−	0.903820i	$-0.359249\pi$
$919$	25.9444	0.855826	0.427913	+	0.903820i	$0.359249\pi$
$920$	0	0
$921$	−29.8990	−0.985205
$922$	27.4949	0.905496
$923$	60.6969	1.99786
$924$	−6.89898	−0.226960
$925$	0	0
$926$	4.00000	0.131448
$927$	−11.2474	−0.369415
$928$	−5.00000	−0.164133
$929$	15.7980	0.518314	0.259157	−	0.965835i	$-0.416555\pi$
$929$	15.7980	0.518314	0.259157	+	0.965835i	$0.416555\pi$
$930$	0	0
$931$	−14.2020	−0.465453
$932$	−2.69694	−0.0883412
$933$	24.5959	0.805234
$934$	23.9444	0.783484
$935$	0	0
$936$	6.89898	0.225500
$937$	−3.79796	−0.124074	−0.0620370	−	0.998074i	$-0.519760\pi$
$937$	−3.79796	−0.124074	−0.0620370	+	0.998074i	$0.519760\pi$
$938$	−6.89898	−0.225260
$939$	−3.10102	−0.101198
$940$	0	0
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	−0.898979	−0.0292903
$943$	−4.89898	−0.159533
$944$	10.0000	0.325472
$945$	0	0
$946$	2.20204	0.0715945
$947$	−39.5959	−1.28669	−0.643347	−	0.765575i	$-0.722455\pi$
$947$	−39.5959	−1.28669	−0.643347	+	0.765575i	$0.722455\pi$
$948$	−10.0000	−0.324785
$949$	82.0908	2.66478
$950$	0	0
$951$	−28.5959	−0.927286
$952$	−1.89898	−0.0615463
$953$	−32.8434	−1.06390	−0.531951	−	0.846775i	$-0.678541\pi$
$953$	−32.8434	−1.06390	−0.531951	+	0.846775i	$0.678541\pi$
$954$	−8.89898	−0.288115
$955$	0	0
$956$	−17.8990	−0.578894
$957$	−10.0000	−0.323254
$958$	30.0000	0.969256
$959$	26.3939	0.852303
$960$	0	0
$961$	−27.0000	−0.870968
$962$	43.7980	1.41210
$963$	2.00000	0.0644491
$964$	−8.00000	−0.257663
$965$	0	0
$966$	−3.44949	−0.110986
$967$	−9.59592	−0.308584	−0.154292	−	0.988025i	$-0.549310\pi$
$967$	−9.59592	−0.308584	−0.154292	+	0.988025i	$0.549310\pi$
$968$	7.00000	0.224989
$969$	1.59592	0.0512683
$970$	0	0
$971$	−8.14643	−0.261431	−0.130716	−	0.991420i	$-0.541727\pi$
$971$	−8.14643	−0.261431	−0.130716	+	0.991420i	$0.541727\pi$
$972$	−1.00000	−0.0320750
$973$	−47.2474	−1.51468
$974$	−24.8990	−0.797815
$975$	0	0
$976$	4.89898	0.156813
$977$	49.2474	1.57557	0.787783	−	0.615953i	$-0.211229\pi$
$977$	49.2474	1.57557	0.787783	+	0.615953i	$0.211229\pi$
$978$	1.79796	0.0574924
$979$	8.69694	0.277955
$980$	0	0
$981$	−1.44949	−0.0462786
$982$	−34.8990	−1.11367
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	4.89898	0.156174
$985$	0	0
$986$	−2.75255	−0.0876591
$987$	20.3485	0.647699
$988$	20.0000	0.636285
$989$	1.10102	0.0350104
$990$	0	0
$991$	37.7980	1.20069	0.600346	−	0.799740i	$-0.295030\pi$
$991$	37.7980	1.20069	0.600346	+	0.799740i	$0.295030\pi$
$992$	−2.00000	−0.0635001
$993$	−12.7980	−0.406131
$994$	30.3485	0.962595
$995$	0	0
$996$	−7.44949	−0.236046
$997$	−30.8990	−0.978580	−0.489290	−	0.872121i	$-0.662744\pi$
$997$	−30.8990	−0.978580	−0.489290	+	0.872121i	$0.662744\pi$
$998$	−12.1010	−0.383051
$999$	−6.34847	−0.200857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.a.bf.1.2	✓	2
5.2	odd	4		3450.2.d.y.2899.2		4
5.3	odd	4		3450.2.d.y.2899.3		4
5.4	even	2		3450.2.a.bl.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bf.1.2	✓	2	1.1	even	1	trivial
3450.2.a.bl.1.1	yes	2	5.4	even	2
3450.2.d.y.2899.2		4	5.2	odd	4
3450.2.d.y.2899.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +3.44949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} -6.89898 q^{13} -3.44949 q^{14} +1.00000 q^{16} +0.550510 q^{17} -1.00000 q^{18} -2.89898 q^{19} -3.44949 q^{21} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +6.89898 q^{26} -1.00000 q^{27} +3.44949 q^{28} +5.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} -0.550510 q^{34} +1.00000 q^{36} +6.34847 q^{37} +2.89898 q^{38} +6.89898 q^{39} +4.89898 q^{41} +3.44949 q^{42} -1.10102 q^{43} +2.00000 q^{44} +1.00000 q^{46} -5.89898 q^{47} -1.00000 q^{48} +4.89898 q^{49} -0.550510 q^{51} -6.89898 q^{52} +8.89898 q^{53} +1.00000 q^{54} -3.44949 q^{56} +2.89898 q^{57} -5.00000 q^{58} +10.0000 q^{59} +4.89898 q^{61} -2.00000 q^{62} +3.44949 q^{63} +1.00000 q^{64} +2.00000 q^{66} +2.00000 q^{67} +0.550510 q^{68} +1.00000 q^{69} -8.79796 q^{71} -1.00000 q^{72} -11.8990 q^{73} -6.34847 q^{74} -2.89898 q^{76} +6.89898 q^{77} -6.89898 q^{78} +10.0000 q^{79} +1.00000 q^{81} -4.89898 q^{82} +7.44949 q^{83} -3.44949 q^{84} +1.10102 q^{86} -5.00000 q^{87} -2.00000 q^{88} +4.34847 q^{89} -23.7980 q^{91} -1.00000 q^{92} -2.00000 q^{93} +5.89898 q^{94} +1.00000 q^{96} -16.6969 q^{97} -4.89898 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} - 2 q^{18} + 4 q^{19} - 2 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{26} - 2 q^{27} + 2 q^{28} + 10 q^{29} + 4 q^{31} - 2 q^{32} - 4 q^{33} - 6 q^{34} + 2 q^{36} - 2 q^{37} - 4 q^{38} + 4 q^{39} + 2 q^{42} - 12 q^{43} + 4 q^{44} + 2 q^{46} - 2 q^{47} - 2 q^{48} - 6 q^{51} - 4 q^{52} + 8 q^{53} + 2 q^{54} - 2 q^{56} - 4 q^{57} - 10 q^{58} + 20 q^{59} - 4 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{66} + 4 q^{67} + 6 q^{68} + 2 q^{69} + 2 q^{71} - 2 q^{72} - 14 q^{73} + 2 q^{74} + 4 q^{76} + 4 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{81} + 10 q^{83} - 2 q^{84} + 12 q^{86} - 10 q^{87} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 2 q^{92} - 4 q^{93} + 2 q^{94} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 4 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 - 2 * q^18 + 4 * q^19 - 2 * q^21 - 4 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^26 - 2 * q^27 + 2 * q^28 + 10 * q^29 + 4 * q^31 - 2 * q^32 - 4 * q^33 - 6 * q^34 + 2 * q^36 - 2 * q^37 - 4 * q^38 + 4 * q^39 + 2 * q^42 - 12 * q^43 + 4 * q^44 + 2 * q^46 - 2 * q^47 - 2 * q^48 - 6 * q^51 - 4 * q^52 + 8 * q^53 + 2 * q^54 - 2 * q^56 - 4 * q^57 - 10 * q^58 + 20 * q^59 - 4 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^66 + 4 * q^67 + 6 * q^68 + 2 * q^69 + 2 * q^71 - 2 * q^72 - 14 * q^73 + 2 * q^74 + 4 * q^76 + 4 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^81 + 10 * q^83 - 2 * q^84 + 12 * q^86 - 10 * q^87 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 2 * q^92 - 4 * q^93 + 2 * q^94 + 2 * q^96 - 4 * q^97 + 4 * q^99

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