LMFDB - Embedded newform 3450.2.a.bj.1.1

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{73}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 18 $ x^2 - x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.77200$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.77200 q^{11} -1.00000 q^{12} -4.77200 q^{13} +3.00000 q^{14} +1.00000 q^{16} +7.77200 q^{17} +1.00000 q^{18} -0.772002 q^{19} -3.00000 q^{21} -2.77200 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.77200 q^{26} -1.00000 q^{27} +3.00000 q^{28} +3.00000 q^{29} +7.54400 q^{31} +1.00000 q^{32} +2.77200 q^{33} +7.77200 q^{34} +1.00000 q^{36} +1.77200 q^{37} -0.772002 q^{38} +4.77200 q^{39} +2.77200 q^{41} -3.00000 q^{42} +0.772002 q^{43} -2.77200 q^{44} -1.00000 q^{46} +0.227998 q^{47} -1.00000 q^{48} +2.00000 q^{49} -7.77200 q^{51} -4.77200 q^{52} -4.00000 q^{53} -1.00000 q^{54} +3.00000 q^{56} +0.772002 q^{57} +3.00000 q^{58} +6.00000 q^{59} +7.54400 q^{61} +7.54400 q^{62} +3.00000 q^{63} +1.00000 q^{64} +2.77200 q^{66} -7.54400 q^{67} +7.77200 q^{68} +1.00000 q^{69} +3.77200 q^{71} +1.00000 q^{72} +10.5440 q^{73} +1.77200 q^{74} -0.772002 q^{76} -8.31601 q^{77} +4.77200 q^{78} +10.7720 q^{79} +1.00000 q^{81} +2.77200 q^{82} +1.00000 q^{83} -3.00000 q^{84} +0.772002 q^{86} -3.00000 q^{87} -2.77200 q^{88} +8.22800 q^{89} -14.3160 q^{91} -1.00000 q^{92} -7.54400 q^{93} +0.227998 q^{94} -1.00000 q^{96} -0.455996 q^{97} +2.00000 q^{98} -2.77200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 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 + 6 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{11} - 2 q^{12} - q^{13} + 6 q^{14} + 2 q^{16} + 7 q^{17} + 2 q^{18} + 7 q^{19} - 6 q^{21} + 3 q^{22} - 2 q^{23} - 2 q^{24} - q^{26} - 2 q^{27} + 6 q^{28} + 6 q^{29} - 2 q^{31} + 2 q^{32} - 3 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 7 q^{38} + q^{39} - 3 q^{41} - 6 q^{42} - 7 q^{43} + 3 q^{44} - 2 q^{46} + 9 q^{47} - 2 q^{48} + 4 q^{49} - 7 q^{51} - q^{52} - 8 q^{53} - 2 q^{54} + 6 q^{56} - 7 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{61} - 2 q^{62} + 6 q^{63} + 2 q^{64} - 3 q^{66} + 2 q^{67} + 7 q^{68} + 2 q^{69} - q^{71} + 2 q^{72} + 4 q^{73} - 5 q^{74} + 7 q^{76} + 9 q^{77} + q^{78} + 13 q^{79} + 2 q^{81} - 3 q^{82} + 2 q^{83} - 6 q^{84} - 7 q^{86} - 6 q^{87} + 3 q^{88} + 25 q^{89} - 3 q^{91} - 2 q^{92} + 2 q^{93} + 9 q^{94} - 2 q^{96} - 18 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^11 - 2 * q^12 - q^13 + 6 * q^14 + 2 * q^16 + 7 * q^17 + 2 * q^18 + 7 * q^19 - 6 * q^21 + 3 * q^22 - 2 * q^23 - 2 * q^24 - q^26 - 2 * q^27 + 6 * q^28 + 6 * q^29 - 2 * q^31 + 2 * q^32 - 3 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 7 * q^38 + q^39 - 3 * q^41 - 6 * q^42 - 7 * q^43 + 3 * q^44 - 2 * q^46 + 9 * q^47 - 2 * q^48 + 4 * q^49 - 7 * q^51 - q^52 - 8 * q^53 - 2 * q^54 + 6 * q^56 - 7 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^61 - 2 * q^62 + 6 * q^63 + 2 * q^64 - 3 * q^66 + 2 * q^67 + 7 * q^68 + 2 * q^69 - q^71 + 2 * q^72 + 4 * q^73 - 5 * q^74 + 7 * q^76 + 9 * q^77 + q^78 + 13 * q^79 + 2 * q^81 - 3 * q^82 + 2 * q^83 - 6 * q^84 - 7 * q^86 - 6 * q^87 + 3 * q^88 + 25 * q^89 - 3 * q^91 - 2 * q^92 + 2 * q^93 + 9 * q^94 - 2 * q^96 - 18 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	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
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.77200	−0.835790	−0.417895	−	0.908495i	$-0.637232\pi$
$11$	−2.77200	−0.835790	−0.417895	+	0.908495i	$0.637232\pi$
$12$	−1.00000	−0.288675
$13$	−4.77200	−1.32352	−0.661758	−	0.749718i	$-0.730189\pi$
$13$	−4.77200	−1.32352	−0.661758	+	0.749718i	$0.730189\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	7.77200	1.88499	0.942494	−	0.334224i	$-0.108474\pi$
$17$	7.77200	1.88499	0.942494	+	0.334224i	$0.108474\pi$
$18$	1.00000	0.235702
$19$	−0.772002	−0.177109	−0.0885547	−	0.996071i	$-0.528225\pi$
$19$	−0.772002	−0.177109	−0.0885547	+	0.996071i	$0.528225\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	−2.77200	−0.590993
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−4.77200	−0.935867
$27$	−1.00000	−0.192450
$28$	3.00000	0.566947
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	7.54400	1.35494	0.677472	−	0.735549i	$-0.263076\pi$
$31$	7.54400	1.35494	0.677472	+	0.735549i	$0.263076\pi$
$32$	1.00000	0.176777
$33$	2.77200	0.482544
$34$	7.77200	1.33289
$35$	0	0
$36$	1.00000	0.166667
$37$	1.77200	0.291315	0.145658	−	0.989335i	$-0.453470\pi$
$37$	1.77200	0.291315	0.145658	+	0.989335i	$0.453470\pi$
$38$	−0.772002	−0.125235
$39$	4.77200	0.764132
$40$	0	0
$41$	2.77200	0.432914	0.216457	−	0.976292i	$-0.430550\pi$
$41$	2.77200	0.432914	0.216457	+	0.976292i	$0.430550\pi$
$42$	−3.00000	−0.462910
$43$	0.772002	0.117729	0.0588646	−	0.998266i	$-0.481252\pi$
$43$	0.772002	0.117729	0.0588646	+	0.998266i	$0.481252\pi$
$44$	−2.77200	−0.417895
$45$	0	0
$46$	−1.00000	−0.147442
$47$	0.227998	0.0332569	0.0166285	−	0.999862i	$-0.494707\pi$
$47$	0.227998	0.0332569	0.0166285	+	0.999862i	$0.494707\pi$
$48$	−1.00000	−0.144338
$49$	2.00000	0.285714
$50$	0	0
$51$	−7.77200	−1.08830
$52$	−4.77200	−0.661758
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	0.772002	0.102254
$58$	3.00000	0.393919
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	7.54400	0.965911	0.482955	−	0.875645i	$-0.339563\pi$
$61$	7.54400	0.965911	0.482955	+	0.875645i	$0.339563\pi$
$62$	7.54400	0.958089
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	2.77200	0.341210
$67$	−7.54400	−0.921647	−0.460823	−	0.887492i	$-0.652446\pi$
$67$	−7.54400	−0.921647	−0.460823	+	0.887492i	$0.652446\pi$
$68$	7.77200	0.942494
$69$	1.00000	0.120386
$70$	0	0
$71$	3.77200	0.447654	0.223827	−	0.974629i	$-0.428145\pi$
$71$	3.77200	0.447654	0.223827	+	0.974629i	$0.428145\pi$
$72$	1.00000	0.117851
$73$	10.5440	1.23408	0.617041	−	0.786931i	$-0.288331\pi$
$73$	10.5440	1.23408	0.617041	+	0.786931i	$0.288331\pi$
$74$	1.77200	0.205991
$75$	0	0
$76$	−0.772002	−0.0885547
$77$	−8.31601	−0.947697
$78$	4.77200	0.540323
$79$	10.7720	1.21194	0.605972	−	0.795486i	$-0.292784\pi$
$79$	10.7720	1.21194	0.605972	+	0.795486i	$0.292784\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.77200	0.306116
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	−3.00000	−0.327327
$85$	0	0
$86$	0.772002	0.0832471
$87$	−3.00000	−0.321634
$88$	−2.77200	−0.295496
$89$	8.22800	0.872166	0.436083	−	0.899906i	$-0.356365\pi$
$89$	8.22800	0.872166	0.436083	+	0.899906i	$0.356365\pi$
$90$	0	0
$91$	−14.3160	−1.50073
$92$	−1.00000	−0.104257
$93$	−7.54400	−0.782277
$94$	0.227998	0.0235162
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−0.455996	−0.0462994	−0.0231497	−	0.999732i	$-0.507369\pi$
$97$	−0.455996	−0.0462994	−0.0231497	+	0.999732i	$0.507369\pi$
$98$	2.00000	0.202031
$99$	−2.77200	−0.278597
$100$	0	0
$101$	−11.3160	−1.12598	−0.562992	−	0.826462i	$-0.690350\pi$
$101$	−11.3160	−1.12598	−0.562992	+	0.826462i	$0.690350\pi$
$102$	−7.77200	−0.769543
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	−4.77200	−0.467933
$105$	0	0
$106$	−4.00000	−0.388514
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−1.00000	−0.0962250
$109$	6.22800	0.596534	0.298267	−	0.954482i	$-0.403591\pi$
$109$	6.22800	0.596534	0.298267	+	0.954482i	$0.403591\pi$
$110$	0	0
$111$	−1.77200	−0.168191
$112$	3.00000	0.283473
$113$	3.77200	0.354840	0.177420	−	0.984135i	$-0.443225\pi$
$113$	3.77200	0.354840	0.177420	+	0.984135i	$0.443225\pi$
$114$	0.772002	0.0723046
$115$	0	0
$116$	3.00000	0.278543
$117$	−4.77200	−0.441172
$118$	6.00000	0.552345
$119$	23.3160	2.13737
$120$	0	0
$121$	−3.31601	−0.301455
$122$	7.54400	0.683002
$123$	−2.77200	−0.249943
$124$	7.54400	0.677472
$125$	0	0
$126$	3.00000	0.267261
$127$	−21.5440	−1.91172	−0.955861	−	0.293821i	$-0.905073\pi$
$127$	−21.5440	−1.91172	−0.955861	+	0.293821i	$0.905073\pi$
$128$	1.00000	0.0883883
$129$	−0.772002	−0.0679710
$130$	0	0
$131$	15.0880	1.31825	0.659123	−	0.752035i	$-0.270928\pi$
$131$	15.0880	1.31825	0.659123	+	0.752035i	$0.270928\pi$
$132$	2.77200	0.241272
$133$	−2.31601	−0.200823
$134$	−7.54400	−0.651703
$135$	0	0
$136$	7.77200	0.666444
$137$	−6.22800	−0.532094	−0.266047	−	0.963960i	$-0.585718\pi$
$137$	−6.22800	−0.532094	−0.266047	+	0.963960i	$0.585718\pi$
$138$	1.00000	0.0851257
$139$	7.77200	0.659213	0.329606	−	0.944118i	$-0.393084\pi$
$139$	7.77200	0.659213	0.329606	+	0.944118i	$0.393084\pi$
$140$	0	0
$141$	−0.227998	−0.0192009
$142$	3.77200	0.316539
$143$	13.2280	1.10618
$144$	1.00000	0.0833333
$145$	0	0
$146$	10.5440	0.872628
$147$	−2.00000	−0.164957
$148$	1.77200	0.145658
$149$	23.0880	1.89144	0.945722	−	0.324978i	$-0.105357\pi$
$149$	23.0880	1.89144	0.945722	+	0.324978i	$0.105357\pi$
$150$	0	0
$151$	6.45600	0.525382	0.262691	−	0.964880i	$-0.415390\pi$
$151$	6.45600	0.525382	0.262691	+	0.964880i	$0.415390\pi$
$152$	−0.772002	−0.0626176
$153$	7.77200	0.628329
$154$	−8.31601	−0.670123
$155$	0	0
$156$	4.77200	0.382066
$157$	3.54400	0.282842	0.141421	−	0.989950i	$-0.454833\pi$
$157$	3.54400	0.282842	0.141421	+	0.989950i	$0.454833\pi$
$158$	10.7720	0.856974
$159$	4.00000	0.317221
$160$	0	0
$161$	−3.00000	−0.236433
$162$	1.00000	0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	2.77200	0.216457
$165$	0	0
$166$	1.00000	0.0776151
$167$	9.31601	0.720894	0.360447	−	0.932780i	$-0.382624\pi$
$167$	9.31601	0.720894	0.360447	+	0.932780i	$0.382624\pi$
$168$	−3.00000	−0.231455
$169$	9.77200	0.751692
$170$	0	0
$171$	−0.772002	−0.0590365
$172$	0.772002	0.0588646
$173$	7.22800	0.549535	0.274767	−	0.961511i	$-0.411399\pi$
$173$	7.22800	0.549535	0.274767	+	0.961511i	$0.411399\pi$
$174$	−3.00000	−0.227429
$175$	0	0
$176$	−2.77200	−0.208948
$177$	−6.00000	−0.450988
$178$	8.22800	0.616715
$179$	−9.54400	−0.713352	−0.356676	−	0.934228i	$-0.616090\pi$
$179$	−9.54400	−0.713352	−0.356676	+	0.934228i	$0.616090\pi$
$180$	0	0
$181$	−11.3160	−0.841112	−0.420556	−	0.907267i	$-0.638165\pi$
$181$	−11.3160	−0.841112	−0.420556	+	0.907267i	$0.638165\pi$
$182$	−14.3160	−1.06117
$183$	−7.54400	−0.557669
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−7.54400	−0.553153
$187$	−21.5440	−1.57545
$188$	0.227998	0.0166285
$189$	−3.00000	−0.218218
$190$	0	0
$191$	18.3160	1.32530	0.662650	−	0.748929i	$-0.269432\pi$
$191$	18.3160	1.32530	0.662650	+	0.748929i	$0.269432\pi$
$192$	−1.00000	−0.0721688
$193$	3.77200	0.271515	0.135757	−	0.990742i	$-0.456653\pi$
$193$	3.77200	0.271515	0.135757	+	0.990742i	$0.456653\pi$
$194$	−0.455996	−0.0327386
$195$	0	0
$196$	2.00000	0.142857
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	−2.77200	−0.196998
$199$	−22.0880	−1.56578	−0.782889	−	0.622162i	$-0.786255\pi$
$199$	−22.0880	−1.56578	−0.782889	+	0.622162i	$0.786255\pi$
$200$	0	0
$201$	7.54400	0.532113
$202$	−11.3160	−0.796191
$203$	9.00000	0.631676
$204$	−7.77200	−0.544149
$205$	0	0
$206$	−11.0000	−0.766406
$207$	−1.00000	−0.0695048
$208$	−4.77200	−0.330879
$209$	2.13999	0.148026
$210$	0	0
$211$	15.3160	1.05440	0.527199	−	0.849742i	$-0.323242\pi$
$211$	15.3160	1.05440	0.527199	+	0.849742i	$0.323242\pi$
$212$	−4.00000	−0.274721
$213$	−3.77200	−0.258453
$214$	4.00000	0.273434
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	22.6320	1.53636
$218$	6.22800	0.421813
$219$	−10.5440	−0.712498
$220$	0	0
$221$	−37.0880	−2.49481
$222$	−1.77200	−0.118929
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	3.77200	0.250910
$227$	2.22800	0.147877	0.0739387	−	0.997263i	$-0.476443\pi$
$227$	2.22800	0.147877	0.0739387	+	0.997263i	$0.476443\pi$
$228$	0.772002	0.0511271
$229$	−23.5440	−1.55583	−0.777916	−	0.628369i	$-0.783723\pi$
$229$	−23.5440	−1.55583	−0.777916	+	0.628369i	$0.783723\pi$
$230$	0	0
$231$	8.31601	0.547153
$232$	3.00000	0.196960
$233$	28.3160	1.85504	0.927522	−	0.373770i	$-0.121935\pi$
$233$	28.3160	1.85504	0.927522	+	0.373770i	$0.121935\pi$
$234$	−4.77200	−0.311956
$235$	0	0
$236$	6.00000	0.390567
$237$	−10.7720	−0.699717
$238$	23.3160	1.51135
$239$	14.2280	0.920333	0.460166	−	0.887833i	$-0.347790\pi$
$239$	14.2280	0.920333	0.460166	+	0.887833i	$0.347790\pi$
$240$	0	0
$241$	24.6320	1.58669	0.793344	−	0.608774i	$-0.208338\pi$
$241$	24.6320	1.58669	0.793344	+	0.608774i	$0.208338\pi$
$242$	−3.31601	−0.213161
$243$	−1.00000	−0.0641500
$244$	7.54400	0.482955
$245$	0	0
$246$	−2.77200	−0.176736
$247$	3.68399	0.234407
$248$	7.54400	0.479045
$249$	−1.00000	−0.0633724
$250$	0	0
$251$	−29.3160	−1.85041	−0.925205	−	0.379468i	$-0.876107\pi$
$251$	−29.3160	−1.85041	−0.925205	+	0.379468i	$0.876107\pi$
$252$	3.00000	0.188982
$253$	2.77200	0.174274
$254$	−21.5440	−1.35179
$255$	0	0
$256$	1.00000	0.0625000
$257$	−25.0880	−1.56495	−0.782473	−	0.622684i	$-0.786042\pi$
$257$	−25.0880	−1.56495	−0.782473	+	0.622684i	$0.786042\pi$
$258$	−0.772002	−0.0480627
$259$	5.31601	0.330321
$260$	0	0
$261$	3.00000	0.185695
$262$	15.0880	0.932140
$263$	23.5440	1.45179	0.725893	−	0.687808i	$-0.241427\pi$
$263$	23.5440	1.45179	0.725893	+	0.687808i	$0.241427\pi$
$264$	2.77200	0.170605
$265$	0	0
$266$	−2.31601	−0.142003
$267$	−8.22800	−0.503545
$268$	−7.54400	−0.460823
$269$	15.8600	0.967002	0.483501	−	0.875344i	$-0.339365\pi$
$269$	15.8600	0.967002	0.483501	+	0.875344i	$0.339365\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	7.77200	0.471247
$273$	14.3160	0.866444
$274$	−6.22800	−0.376247
$275$	0	0
$276$	1.00000	0.0601929
$277$	16.7720	1.00773	0.503866	−	0.863782i	$-0.331911\pi$
$277$	16.7720	1.00773	0.503866	+	0.863782i	$0.331911\pi$
$278$	7.77200	0.466134
$279$	7.54400	0.451648
$280$	0	0
$281$	−26.8600	−1.60233	−0.801167	−	0.598441i	$-0.795787\pi$
$281$	−26.8600	−1.60233	−0.801167	+	0.598441i	$0.795787\pi$
$282$	−0.227998	−0.0135771
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	3.77200	0.223827
$285$	0	0
$286$	13.2280	0.782188
$287$	8.31601	0.490878
$288$	1.00000	0.0589256
$289$	43.4040	2.55318
$290$	0	0
$291$	0.455996	0.0267310
$292$	10.5440	0.617041
$293$	−7.54400	−0.440725	−0.220363	−	0.975418i	$-0.570724\pi$
$293$	−7.54400	−0.440725	−0.220363	+	0.975418i	$0.570724\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	1.77200	0.102996
$297$	2.77200	0.160848
$298$	23.0880	1.33745
$299$	4.77200	0.275972
$300$	0	0
$301$	2.31601	0.133492
$302$	6.45600	0.371501
$303$	11.3160	0.650088
$304$	−0.772002	−0.0442773
$305$	0	0
$306$	7.77200	0.444296
$307$	−5.31601	−0.303400	−0.151700	−	0.988427i	$-0.548475\pi$
$307$	−5.31601	−0.303400	−0.151700	+	0.988427i	$0.548475\pi$
$308$	−8.31601	−0.473848
$309$	11.0000	0.625768
$310$	0	0
$311$	24.8600	1.40968	0.704841	−	0.709365i	$-0.251018\pi$
$311$	24.8600	1.40968	0.704841	+	0.709365i	$0.251018\pi$
$312$	4.77200	0.270161
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	3.54400	0.200000
$315$	0	0
$316$	10.7720	0.605972
$317$	9.00000	0.505490	0.252745	−	0.967533i	$-0.418667\pi$
$317$	9.00000	0.505490	0.252745	+	0.967533i	$0.418667\pi$
$318$	4.00000	0.224309
$319$	−8.31601	−0.465607
$320$	0	0
$321$	−4.00000	−0.223258
$322$	−3.00000	−0.167183
$323$	−6.00000	−0.333849
$324$	1.00000	0.0555556
$325$	0	0
$326$	−16.0000	−0.886158
$327$	−6.22800	−0.344409
$328$	2.77200	0.153058
$329$	0.683994	0.0377098
$330$	0	0
$331$	26.2280	1.44162	0.720811	−	0.693132i	$-0.243770\pi$
$331$	26.2280	1.44162	0.720811	+	0.693132i	$0.243770\pi$
$332$	1.00000	0.0548821
$333$	1.77200	0.0971051
$334$	9.31601	0.509749
$335$	0	0
$336$	−3.00000	−0.163663
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	9.77200	0.531527
$339$	−3.77200	−0.204867
$340$	0	0
$341$	−20.9120	−1.13245
$342$	−0.772002	−0.0417451
$343$	−15.0000	−0.809924
$344$	0.772002	0.0416236
$345$	0	0
$346$	7.22800	0.388580
$347$	7.54400	0.404983	0.202492	−	0.979284i	$-0.435096\pi$
$347$	7.54400	0.404983	0.202492	+	0.979284i	$0.435096\pi$
$348$	−3.00000	−0.160817
$349$	−8.77200	−0.469554	−0.234777	−	0.972049i	$-0.575436\pi$
$349$	−8.77200	−0.469554	−0.234777	+	0.972049i	$0.575436\pi$
$350$	0	0
$351$	4.77200	0.254711
$352$	−2.77200	−0.147748
$353$	−23.8600	−1.26994	−0.634970	−	0.772537i	$-0.718988\pi$
$353$	−23.8600	−1.26994	−0.634970	+	0.772537i	$0.718988\pi$
$354$	−6.00000	−0.318896
$355$	0	0
$356$	8.22800	0.436083
$357$	−23.3160	−1.23401
$358$	−9.54400	−0.504416
$359$	−18.7720	−0.990748	−0.495374	−	0.868680i	$-0.664969\pi$
$359$	−18.7720	−0.990748	−0.495374	+	0.868680i	$0.664969\pi$
$360$	0	0
$361$	−18.4040	−0.968632
$362$	−11.3160	−0.594756
$363$	3.31601	0.174045
$364$	−14.3160	−0.750363
$365$	0	0
$366$	−7.54400	−0.394331
$367$	−7.68399	−0.401101	−0.200551	−	0.979683i	$-0.564273\pi$
$367$	−7.68399	−0.401101	−0.200551	+	0.979683i	$0.564273\pi$
$368$	−1.00000	−0.0521286
$369$	2.77200	0.144305
$370$	0	0
$371$	−12.0000	−0.623009
$372$	−7.54400	−0.391138
$373$	4.22800	0.218917	0.109459	−	0.993991i	$-0.465088\pi$
$373$	4.22800	0.218917	0.109459	+	0.993991i	$0.465088\pi$
$374$	−21.5440	−1.11401
$375$	0	0
$376$	0.227998	0.0117581
$377$	−14.3160	−0.737312
$378$	−3.00000	−0.154303
$379$	11.0880	0.569553	0.284776	−	0.958594i	$-0.408081\pi$
$379$	11.0880	0.569553	0.284776	+	0.958594i	$0.408081\pi$
$380$	0	0
$381$	21.5440	1.10373
$382$	18.3160	0.937128
$383$	−5.22800	−0.267138	−0.133569	−	0.991040i	$-0.542644\pi$
$383$	−5.22800	−0.267138	−0.133569	+	0.991040i	$0.542644\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	3.77200	0.191990
$387$	0.772002	0.0392431
$388$	−0.455996	−0.0231497
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−7.77200	−0.393047
$392$	2.00000	0.101015
$393$	−15.0880	−0.761089
$394$	13.0000	0.654931
$395$	0	0
$396$	−2.77200	−0.139298
$397$	−36.6320	−1.83851	−0.919254	−	0.393665i	$-0.871207\pi$
$397$	−36.6320	−1.83851	−0.919254	+	0.393665i	$0.871207\pi$
$398$	−22.0880	−1.10717
$399$	2.31601	0.115945
$400$	0	0
$401$	22.6320	1.13019	0.565094	−	0.825026i	$-0.308840\pi$
$401$	22.6320	1.13019	0.565094	+	0.825026i	$0.308840\pi$
$402$	7.54400	0.376261
$403$	−36.0000	−1.79329
$404$	−11.3160	−0.562992
$405$	0	0
$406$	9.00000	0.446663
$407$	−4.91199	−0.243478
$408$	−7.77200	−0.384771
$409$	−23.0000	−1.13728	−0.568638	−	0.822588i	$-0.692530\pi$
$409$	−23.0000	−1.13728	−0.568638	+	0.822588i	$0.692530\pi$
$410$	0	0
$411$	6.22800	0.307204
$412$	−11.0000	−0.541931
$413$	18.0000	0.885722
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−4.77200	−0.233967
$417$	−7.77200	−0.380597
$418$	2.13999	0.104670
$419$	−25.6320	−1.25221	−0.626103	−	0.779740i	$-0.715351\pi$
$419$	−25.6320	−1.25221	−0.626103	+	0.779740i	$0.715351\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	15.3160	0.745571
$423$	0.227998	0.0110856
$424$	−4.00000	−0.194257
$425$	0	0
$426$	−3.77200	−0.182754
$427$	22.6320	1.09524
$428$	4.00000	0.193347
$429$	−13.2280	−0.638654
$430$	0	0
$431$	−26.6320	−1.28282	−0.641409	−	0.767199i	$-0.721650\pi$
$431$	−26.6320	−1.28282	−0.641409	+	0.767199i	$0.721650\pi$
$432$	−1.00000	−0.0481125
$433$	−23.5440	−1.13145	−0.565726	−	0.824593i	$-0.691404\pi$
$433$	−23.5440	−1.13145	−0.565726	+	0.824593i	$0.691404\pi$
$434$	22.6320	1.08637
$435$	0	0
$436$	6.22800	0.298267
$437$	0.772002	0.0369299
$438$	−10.5440	−0.503812
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	−37.0880	−1.76410
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−1.77200	−0.0840955
$445$	0	0
$446$	−10.0000	−0.473514
$447$	−23.0880	−1.09203
$448$	3.00000	0.141737
$449$	−2.00000	−0.0943858	−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000	−0.0943858	−0.0471929	+	0.998886i	$0.515028\pi$
$450$	0	0
$451$	−7.68399	−0.361825
$452$	3.77200	0.177420
$453$	−6.45600	−0.303329
$454$	2.22800	0.104565
$455$	0	0
$456$	0.772002	0.0361523
$457$	−20.6320	−0.965125	−0.482562	−	0.875862i	$-0.660294\pi$
$457$	−20.6320	−0.965125	−0.482562	+	0.875862i	$0.660294\pi$
$458$	−23.5440	−1.10014
$459$	−7.77200	−0.362766
$460$	0	0
$461$	−4.54400	−0.211635	−0.105818	−	0.994386i	$-0.533746\pi$
$461$	−4.54400	−0.211635	−0.105818	+	0.994386i	$0.533746\pi$
$462$	8.31601	0.386896
$463$	−35.0880	−1.63068	−0.815339	−	0.578984i	$-0.803449\pi$
$463$	−35.0880	−1.63068	−0.815339	+	0.578984i	$0.803449\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	28.3160	1.31171
$467$	−1.45600	−0.0673755	−0.0336877	−	0.999432i	$-0.510725\pi$
$467$	−1.45600	−0.0673755	−0.0336877	+	0.999432i	$0.510725\pi$
$468$	−4.77200	−0.220586
$469$	−22.6320	−1.04505
$470$	0	0
$471$	−3.54400	−0.163299
$472$	6.00000	0.276172
$473$	−2.13999	−0.0983969
$474$	−10.7720	−0.494774
$475$	0	0
$476$	23.3160	1.06869
$477$	−4.00000	−0.183147
$478$	14.2280	0.650773
$479$	−9.68399	−0.442473	−0.221236	−	0.975220i	$-0.571009\pi$
$479$	−9.68399	−0.442473	−0.221236	+	0.975220i	$0.571009\pi$
$480$	0	0
$481$	−8.45600	−0.385560
$482$	24.6320	1.12196
$483$	3.00000	0.136505
$484$	−3.31601	−0.150728
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−29.5440	−1.33877	−0.669383	−	0.742917i	$-0.733442\pi$
$487$	−29.5440	−1.33877	−0.669383	+	0.742917i	$0.733442\pi$
$488$	7.54400	0.341501
$489$	16.0000	0.723545
$490$	0	0
$491$	−27.5440	−1.24304	−0.621522	−	0.783397i	$-0.713485\pi$
$491$	−27.5440	−1.24304	−0.621522	+	0.783397i	$0.713485\pi$
$492$	−2.77200	−0.124971
$493$	23.3160	1.05010
$494$	3.68399	0.165751
$495$	0	0
$496$	7.54400	0.338736
$497$	11.3160	0.507592
$498$	−1.00000	−0.0448111
$499$	−35.3160	−1.58096	−0.790481	−	0.612487i	$-0.790169\pi$
$499$	−35.3160	−1.58096	−0.790481	+	0.612487i	$0.790169\pi$
$500$	0	0
$501$	−9.31601	−0.416208
$502$	−29.3160	−1.30844
$503$	−36.9480	−1.64743	−0.823715	−	0.567004i	$-0.808103\pi$
$503$	−36.9480	−1.64743	−0.823715	+	0.567004i	$0.808103\pi$
$504$	3.00000	0.133631
$505$	0	0
$506$	2.77200	0.123231
$507$	−9.77200	−0.433990
$508$	−21.5440	−0.955861
$509$	−14.8600	−0.658658	−0.329329	−	0.944215i	$-0.606823\pi$
$509$	−14.8600	−0.658658	−0.329329	+	0.944215i	$0.606823\pi$
$510$	0	0
$511$	31.6320	1.39932
$512$	1.00000	0.0441942
$513$	0.772002	0.0340847
$514$	−25.0880	−1.10658
$515$	0	0
$516$	−0.772002	−0.0339855
$517$	−0.632011	−0.0277958
$518$	5.31601	0.233572
$519$	−7.22800	−0.317274
$520$	0	0
$521$	−1.77200	−0.0776328	−0.0388164	−	0.999246i	$-0.512359\pi$
$521$	−1.77200	−0.0776328	−0.0388164	+	0.999246i	$0.512359\pi$
$522$	3.00000	0.131306
$523$	−12.3160	−0.538541	−0.269271	−	0.963065i	$-0.586783\pi$
$523$	−12.3160	−0.538541	−0.269271	+	0.963065i	$0.586783\pi$
$524$	15.0880	0.659123
$525$	0	0
$526$	23.5440	1.02657
$527$	58.6320	2.55405
$528$	2.77200	0.120636
$529$	1.00000	0.0434783
$530$	0	0
$531$	6.00000	0.260378
$532$	−2.31601	−0.100412
$533$	−13.2280	−0.572968
$534$	−8.22800	−0.356060
$535$	0	0
$536$	−7.54400	−0.325851
$537$	9.54400	0.411854
$538$	15.8600	0.683774
$539$	−5.54400	−0.238797
$540$	0	0
$541$	−36.3160	−1.56135	−0.780674	−	0.624939i	$-0.785124\pi$
$541$	−36.3160	−1.56135	−0.780674	+	0.624939i	$0.785124\pi$
$542$	16.0000	0.687259
$543$	11.3160	0.485616
$544$	7.77200	0.333222
$545$	0	0
$546$	14.3160	0.612668
$547$	30.8600	1.31948	0.659739	−	0.751494i	$-0.270667\pi$
$547$	30.8600	1.31948	0.659739	+	0.751494i	$0.270667\pi$
$548$	−6.22800	−0.266047
$549$	7.54400	0.321970
$550$	0	0
$551$	−2.31601	−0.0986652
$552$	1.00000	0.0425628
$553$	32.3160	1.37422
$554$	16.7720	0.712574
$555$	0	0
$556$	7.77200	0.329606
$557$	−13.0880	−0.554557	−0.277278	−	0.960790i	$-0.589432\pi$
$557$	−13.0880	−0.554557	−0.277278	+	0.960790i	$0.589432\pi$
$558$	7.54400	0.319363
$559$	−3.68399	−0.155816
$560$	0	0
$561$	21.5440	0.909589
$562$	−26.8600	−1.13302
$563$	32.9480	1.38859	0.694297	−	0.719689i	$-0.255716\pi$
$563$	32.9480	1.38859	0.694297	+	0.719689i	$0.255716\pi$
$564$	−0.227998	−0.00960045
$565$	0	0
$566$	−28.0000	−1.17693
$567$	3.00000	0.125988
$568$	3.77200	0.158270
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	−38.6320	−1.61670	−0.808350	−	0.588703i	$-0.799639\pi$
$571$	−38.6320	−1.61670	−0.808350	+	0.588703i	$0.799639\pi$
$572$	13.2280	0.553090
$573$	−18.3160	−0.765162
$574$	8.31601	0.347103
$575$	0	0
$576$	1.00000	0.0416667
$577$	5.68399	0.236628	0.118314	−	0.992976i	$-0.462251\pi$
$577$	5.68399	0.236628	0.118314	+	0.992976i	$0.462251\pi$
$578$	43.4040	1.80537
$579$	−3.77200	−0.156759
$580$	0	0
$581$	3.00000	0.124461
$582$	0.455996	0.0189017
$583$	11.0880	0.459218
$584$	10.5440	0.436314
$585$	0	0
$586$	−7.54400	−0.311640
$587$	−41.5440	−1.71470	−0.857352	−	0.514730i	$-0.827892\pi$
$587$	−41.5440	−1.71470	−0.857352	+	0.514730i	$0.827892\pi$
$588$	−2.00000	−0.0824786
$589$	−5.82399	−0.239973
$590$	0	0
$591$	−13.0000	−0.534749
$592$	1.77200	0.0728288
$593$	−15.6840	−0.644064	−0.322032	−	0.946729i	$-0.604366\pi$
$593$	−15.6840	−0.644064	−0.322032	+	0.946729i	$0.604366\pi$
$594$	2.77200	0.113737
$595$	0	0
$596$	23.0880	0.945722
$597$	22.0880	0.904002
$598$	4.77200	0.195142
$599$	8.00000	0.326871	0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000	0.326871	0.163436	+	0.986554i	$0.447742\pi$
$600$	0	0
$601$	−24.2280	−0.988281	−0.494140	−	0.869382i	$-0.664517\pi$
$601$	−24.2280	−0.988281	−0.494140	+	0.869382i	$0.664517\pi$
$602$	2.31601	0.0943933
$603$	−7.54400	−0.307216
$604$	6.45600	0.262691
$605$	0	0
$606$	11.3160	0.459681
$607$	29.0880	1.18065	0.590323	−	0.807167i	$-0.299000\pi$
$607$	29.0880	1.18065	0.590323	+	0.807167i	$0.299000\pi$
$608$	−0.772002	−0.0313088
$609$	−9.00000	−0.364698
$610$	0	0
$611$	−1.08801	−0.0440161
$612$	7.77200	0.314165
$613$	−12.2280	−0.493884	−0.246942	−	0.969030i	$-0.579426\pi$
$613$	−12.2280	−0.493884	−0.246942	+	0.969030i	$0.579426\pi$
$614$	−5.31601	−0.214537
$615$	0	0
$616$	−8.31601	−0.335061
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	11.0000	0.442485
$619$	−35.0880	−1.41031	−0.705153	−	0.709055i	$-0.749122\pi$
$619$	−35.0880	−1.41031	−0.705153	+	0.709055i	$0.749122\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	24.8600	0.996796
$623$	24.6840	0.988943
$624$	4.77200	0.191033
$625$	0	0
$626$	8.00000	0.319744
$627$	−2.13999	−0.0854630
$628$	3.54400	0.141421
$629$	13.7720	0.549126
$630$	0	0
$631$	−20.0880	−0.799691	−0.399845	−	0.916583i	$-0.630936\pi$
$631$	−20.0880	−0.799691	−0.399845	+	0.916583i	$0.630936\pi$
$632$	10.7720	0.428487
$633$	−15.3160	−0.608757
$634$	9.00000	0.357436
$635$	0	0
$636$	4.00000	0.158610
$637$	−9.54400	−0.378147
$638$	−8.31601	−0.329234
$639$	3.77200	0.149218
$640$	0	0
$641$	24.8600	0.981911	0.490956	−	0.871185i	$-0.336648\pi$
$641$	24.8600	0.981911	0.490956	+	0.871185i	$0.336648\pi$
$642$	−4.00000	−0.157867
$643$	−6.31601	−0.249079	−0.124539	−	0.992215i	$-0.539745\pi$
$643$	−6.31601	−0.249079	−0.124539	+	0.992215i	$0.539745\pi$
$644$	−3.00000	−0.118217
$645$	0	0
$646$	−6.00000	−0.236067
$647$	22.2280	0.873873	0.436936	−	0.899492i	$-0.356063\pi$
$647$	22.2280	0.873873	0.436936	+	0.899492i	$0.356063\pi$
$648$	1.00000	0.0392837
$649$	−16.6320	−0.652864
$650$	0	0
$651$	−22.6320	−0.887018
$652$	−16.0000	−0.626608
$653$	−40.5440	−1.58661	−0.793305	−	0.608825i	$-0.791641\pi$
$653$	−40.5440	−1.58661	−0.793305	+	0.608825i	$0.791641\pi$
$654$	−6.22800	−0.243534
$655$	0	0
$656$	2.77200	0.108228
$657$	10.5440	0.411361
$658$	0.683994	0.0266649
$659$	7.63201	0.297301	0.148650	−	0.988890i	$-0.452507\pi$
$659$	7.63201	0.297301	0.148650	+	0.988890i	$0.452507\pi$
$660$	0	0
$661$	24.8600	0.966942	0.483471	−	0.875360i	$-0.339376\pi$
$661$	24.8600	0.966942	0.483471	+	0.875360i	$0.339376\pi$
$662$	26.2280	1.01938
$663$	37.0880	1.44038
$664$	1.00000	0.0388075
$665$	0	0
$666$	1.77200	0.0686637
$667$	−3.00000	−0.116160
$668$	9.31601	0.360447
$669$	10.0000	0.386622
$670$	0	0
$671$	−20.9120	−0.807299
$672$	−3.00000	−0.115728
$673$	9.45600	0.364502	0.182251	−	0.983252i	$-0.441662\pi$
$673$	9.45600	0.364502	0.182251	+	0.983252i	$0.441662\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	9.77200	0.375846
$677$	48.0000	1.84479	0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000	1.84479	0.922395	+	0.386248i	$0.126229\pi$
$678$	−3.77200	−0.144863
$679$	−1.36799	−0.0524986
$680$	0	0
$681$	−2.22800	−0.0853771
$682$	−20.9120	−0.800762
$683$	−24.6320	−0.942518	−0.471259	−	0.881995i	$-0.656200\pi$
$683$	−24.6320	−0.942518	−0.471259	+	0.881995i	$0.656200\pi$
$684$	−0.772002	−0.0295182
$685$	0	0
$686$	−15.0000	−0.572703
$687$	23.5440	0.898260
$688$	0.772002	0.0294323
$689$	19.0880	0.727195
$690$	0	0
$691$	−47.7720	−1.81733	−0.908666	−	0.417523i	$-0.862898\pi$
$691$	−47.7720	−1.81733	−0.908666	+	0.417523i	$0.862898\pi$
$692$	7.22800	0.274767
$693$	−8.31601	−0.315899
$694$	7.54400	0.286366
$695$	0	0
$696$	−3.00000	−0.113715
$697$	21.5440	0.816037
$698$	−8.77200	−0.332025
$699$	−28.3160	−1.07101
$700$	0	0
$701$	−15.5440	−0.587089	−0.293544	−	0.955945i	$-0.594835\pi$
$701$	−15.5440	−0.587089	−0.293544	+	0.955945i	$0.594835\pi$
$702$	4.77200	0.180108
$703$	−1.36799	−0.0515947
$704$	−2.77200	−0.104474
$705$	0	0
$706$	−23.8600	−0.897983
$707$	−33.9480	−1.27675
$708$	−6.00000	−0.225494
$709$	−1.31601	−0.0494236	−0.0247118	−	0.999695i	$-0.507867\pi$
$709$	−1.31601	−0.0494236	−0.0247118	+	0.999695i	$0.507867\pi$
$710$	0	0
$711$	10.7720	0.403982
$712$	8.22800	0.308357
$713$	−7.54400	−0.282525
$714$	−23.3160	−0.872580
$715$	0	0
$716$	−9.54400	−0.356676
$717$	−14.2280	−0.531354
$718$	−18.7720	−0.700565
$719$	−4.68399	−0.174684	−0.0873418	−	0.996178i	$-0.527837\pi$
$719$	−4.68399	−0.174684	−0.0873418	+	0.996178i	$0.527837\pi$
$720$	0	0
$721$	−33.0000	−1.22898
$722$	−18.4040	−0.684926
$723$	−24.6320	−0.916074
$724$	−11.3160	−0.420556
$725$	0	0
$726$	3.31601	0.123069
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−14.3160	−0.530586
$729$	1.00000	0.0370370
$730$	0	0
$731$	6.00000	0.221918
$732$	−7.54400	−0.278834
$733$	−25.7720	−0.951911	−0.475955	−	0.879469i	$-0.657898\pi$
$733$	−25.7720	−0.951911	−0.475955	+	0.879469i	$0.657898\pi$
$734$	−7.68399	−0.283621
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	20.9120	0.770303
$738$	2.77200	0.102039
$739$	25.7720	0.948038	0.474019	−	0.880515i	$-0.342803\pi$
$739$	25.7720	0.948038	0.474019	+	0.880515i	$0.342803\pi$
$740$	0	0
$741$	−3.68399	−0.135335
$742$	−12.0000	−0.440534
$743$	−28.7720	−1.05554	−0.527771	−	0.849387i	$-0.676972\pi$
$743$	−28.7720	−1.05554	−0.527771	+	0.849387i	$0.676972\pi$
$744$	−7.54400	−0.276577
$745$	0	0
$746$	4.22800	0.154798
$747$	1.00000	0.0365881
$748$	−21.5440	−0.787727
$749$	12.0000	0.438470
$750$	0	0
$751$	−9.45600	−0.345054	−0.172527	−	0.985005i	$-0.555193\pi$
$751$	−9.45600	−0.345054	−0.172527	+	0.985005i	$0.555193\pi$
$752$	0.227998	0.00831424
$753$	29.3160	1.06833
$754$	−14.3160	−0.521358
$755$	0	0
$756$	−3.00000	−0.109109
$757$	49.7720	1.80899	0.904497	−	0.426480i	$-0.140246\pi$
$757$	49.7720	1.80899	0.904497	+	0.426480i	$0.140246\pi$
$758$	11.0880	0.402735
$759$	−2.77200	−0.100617
$760$	0	0
$761$	27.8600	1.00992	0.504962	−	0.863141i	$-0.331506\pi$
$761$	27.8600	1.00992	0.504962	+	0.863141i	$0.331506\pi$
$762$	21.5440	0.780457
$763$	18.6840	0.676406
$764$	18.3160	0.662650
$765$	0	0
$766$	−5.22800	−0.188895
$767$	−28.6320	−1.03384
$768$	−1.00000	−0.0360844
$769$	25.0880	0.904697	0.452348	−	0.891841i	$-0.350586\pi$
$769$	25.0880	0.904697	0.452348	+	0.891841i	$0.350586\pi$
$770$	0	0
$771$	25.0880	0.903523
$772$	3.77200	0.135757
$773$	31.5440	1.13456	0.567279	−	0.823525i	$-0.307996\pi$
$773$	31.5440	1.13456	0.567279	+	0.823525i	$0.307996\pi$
$774$	0.772002	0.0277490
$775$	0	0
$776$	−0.455996	−0.0163693
$777$	−5.31601	−0.190711
$778$	18.0000	0.645331
$779$	−2.13999	−0.0766731
$780$	0	0
$781$	−10.4560	−0.374145
$782$	−7.77200	−0.277926
$783$	−3.00000	−0.107211
$784$	2.00000	0.0714286
$785$	0	0
$786$	−15.0880	−0.538171
$787$	−13.2280	−0.471527	−0.235764	−	0.971810i	$-0.575759\pi$
$787$	−13.2280	−0.471527	−0.235764	+	0.971810i	$0.575759\pi$
$788$	13.0000	0.463106
$789$	−23.5440	−0.838189
$790$	0	0
$791$	11.3160	0.402351
$792$	−2.77200	−0.0984988
$793$	−36.0000	−1.27840
$794$	−36.6320	−1.30002
$795$	0	0
$796$	−22.0880	−0.782889
$797$	37.0880	1.31372	0.656862	−	0.754011i	$-0.271883\pi$
$797$	37.0880	1.31372	0.656862	+	0.754011i	$0.271883\pi$
$798$	2.31601	0.0819857
$799$	1.77200	0.0626889
$800$	0	0
$801$	8.22800	0.290722
$802$	22.6320	0.799164
$803$	−29.2280	−1.03143
$804$	7.54400	0.266056
$805$	0	0
$806$	−36.0000	−1.26805
$807$	−15.8600	−0.558299
$808$	−11.3160	−0.398096
$809$	21.6840	0.762369	0.381184	−	0.924499i	$-0.375516\pi$
$809$	21.6840	0.762369	0.381184	+	0.924499i	$0.375516\pi$
$810$	0	0
$811$	12.6320	0.443570	0.221785	−	0.975096i	$-0.428812\pi$
$811$	12.6320	0.443570	0.221785	+	0.975096i	$0.428812\pi$
$812$	9.00000	0.315838
$813$	−16.0000	−0.561144
$814$	−4.91199	−0.172165
$815$	0	0
$816$	−7.77200	−0.272074
$817$	−0.595987	−0.0208509
$818$	−23.0000	−0.804176
$819$	−14.3160	−0.500242
$820$	0	0
$821$	−20.7720	−0.724948	−0.362474	−	0.931994i	$-0.618068\pi$
$821$	−20.7720	−0.724948	−0.362474	+	0.931994i	$0.618068\pi$
$822$	6.22800	0.217226
$823$	6.45600	0.225042	0.112521	−	0.993649i	$-0.464107\pi$
$823$	6.45600	0.225042	0.112521	+	0.993649i	$0.464107\pi$
$824$	−11.0000	−0.383203
$825$	0	0
$826$	18.0000	0.626300
$827$	0.367989	0.0127962	0.00639811	−	0.999980i	$-0.497963\pi$
$827$	0.367989	0.0127962	0.00639811	+	0.999980i	$0.497963\pi$
$828$	−1.00000	−0.0347524
$829$	21.4040	0.743392	0.371696	−	0.928354i	$-0.378776\pi$
$829$	21.4040	0.743392	0.371696	+	0.928354i	$0.378776\pi$
$830$	0	0
$831$	−16.7720	−0.581814
$832$	−4.77200	−0.165439
$833$	15.5440	0.538568
$834$	−7.77200	−0.269122
$835$	0	0
$836$	2.13999	0.0740131
$837$	−7.54400	−0.260759
$838$	−25.6320	−0.885443
$839$	−27.4040	−0.946092	−0.473046	−	0.881038i	$-0.656845\pi$
$839$	−27.4040	−0.946092	−0.473046	+	0.881038i	$0.656845\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	22.0000	0.758170
$843$	26.8600	0.925108
$844$	15.3160	0.527199
$845$	0	0
$846$	0.227998	0.00783874
$847$	−9.94802	−0.341818
$848$	−4.00000	−0.137361
$849$	28.0000	0.960958
$850$	0	0
$851$	−1.77200	−0.0607434
$852$	−3.77200	−0.129227
$853$	33.8600	1.15934	0.579672	−	0.814850i	$-0.303181\pi$
$853$	33.8600	1.15934	0.579672	+	0.814850i	$0.303181\pi$
$854$	22.6320	0.774451
$855$	0	0
$856$	4.00000	0.136717
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	−13.2280	−0.451596
$859$	−41.5440	−1.41746	−0.708732	−	0.705478i	$-0.750732\pi$
$859$	−41.5440	−1.41746	−0.708732	+	0.705478i	$0.750732\pi$
$860$	0	0
$861$	−8.31601	−0.283409
$862$	−26.6320	−0.907090
$863$	23.3160	0.793686	0.396843	−	0.917886i	$-0.370106\pi$
$863$	23.3160	0.793686	0.396843	+	0.917886i	$0.370106\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−23.5440	−0.800058
$867$	−43.4040	−1.47408
$868$	22.6320	0.768181
$869$	−29.8600	−1.01293
$870$	0	0
$871$	36.0000	1.21981
$872$	6.22800	0.210907
$873$	−0.455996	−0.0154331
$874$	0.772002	0.0261134
$875$	0	0
$876$	−10.5440	−0.356249
$877$	55.2640	1.86613	0.933067	−	0.359703i	$-0.117122\pi$
$877$	55.2640	1.86613	0.933067	+	0.359703i	$0.117122\pi$
$878$	−12.0000	−0.404980
$879$	7.54400	0.254453
$880$	0	0
$881$	27.5440	0.927981	0.463991	−	0.885840i	$-0.346417\pi$
$881$	27.5440	0.927981	0.463991	+	0.885840i	$0.346417\pi$
$882$	2.00000	0.0673435
$883$	2.22800	0.0749781	0.0374891	−	0.999297i	$-0.488064\pi$
$883$	2.22800	0.0749781	0.0374891	+	0.999297i	$0.488064\pi$
$884$	−37.0880	−1.24740
$885$	0	0
$886$	−24.0000	−0.806296
$887$	−29.9480	−1.00556	−0.502778	−	0.864416i	$-0.667689\pi$
$887$	−29.9480	−1.00556	−0.502778	+	0.864416i	$0.667689\pi$
$888$	−1.77200	−0.0594645
$889$	−64.6320	−2.16769
$890$	0	0
$891$	−2.77200	−0.0928656
$892$	−10.0000	−0.334825
$893$	−0.176015	−0.00589012
$894$	−23.0880	−0.772178
$895$	0	0
$896$	3.00000	0.100223
$897$	−4.77200	−0.159333
$898$	−2.00000	−0.0667409
$899$	22.6320	0.754820
$900$	0	0
$901$	−31.0880	−1.03569
$902$	−7.68399	−0.255849
$903$	−2.31601	−0.0770718
$904$	3.77200	0.125455
$905$	0	0
$906$	−6.45600	−0.214486
$907$	25.4040	0.843526	0.421763	−	0.906706i	$-0.361411\pi$
$907$	25.4040	0.843526	0.421763	+	0.906706i	$0.361411\pi$
$908$	2.22800	0.0739387
$909$	−11.3160	−0.375328
$910$	0	0
$911$	−2.77200	−0.0918405	−0.0459203	−	0.998945i	$-0.514622\pi$
$911$	−2.77200	−0.0918405	−0.0459203	+	0.998945i	$0.514622\pi$
$912$	0.772002	0.0255635
$913$	−2.77200	−0.0917399
$914$	−20.6320	−0.682446
$915$	0	0
$916$	−23.5440	−0.777916
$917$	45.2640	1.49475
$918$	−7.77200	−0.256514
$919$	−5.31601	−0.175359	−0.0876794	−	0.996149i	$-0.527945\pi$
$919$	−5.31601	−0.175359	−0.0876794	+	0.996149i	$0.527945\pi$
$920$	0	0
$921$	5.31601	0.175168
$922$	−4.54400	−0.149649
$923$	−18.0000	−0.592477
$924$	8.31601	0.273576
$925$	0	0
$926$	−35.0880	−1.15306
$927$	−11.0000	−0.361287
$928$	3.00000	0.0984798
$929$	50.3160	1.65081	0.825407	−	0.564538i	$-0.190946\pi$
$929$	50.3160	1.65081	0.825407	+	0.564538i	$0.190946\pi$
$930$	0	0
$931$	−1.54400	−0.0506027
$932$	28.3160	0.927522
$933$	−24.8600	−0.813880
$934$	−1.45600	−0.0476417
$935$	0	0
$936$	−4.77200	−0.155978
$937$	42.6320	1.39273	0.696364	−	0.717689i	$-0.254800\pi$
$937$	42.6320	1.39273	0.696364	+	0.717689i	$0.254800\pi$
$938$	−22.6320	−0.738961
$939$	−8.00000	−0.261070
$940$	0	0
$941$	−30.6320	−0.998575	−0.499288	−	0.866436i	$-0.666405\pi$
$941$	−30.6320	−0.998575	−0.499288	+	0.866436i	$0.666405\pi$
$942$	−3.54400	−0.115470
$943$	−2.77200	−0.0902688
$944$	6.00000	0.195283
$945$	0	0
$946$	−2.13999	−0.0695771
$947$	3.08801	0.100347	0.0501734	−	0.998741i	$-0.484023\pi$
$947$	3.08801	0.100347	0.0501734	+	0.998741i	$0.484023\pi$
$948$	−10.7720	−0.349858
$949$	−50.3160	−1.63333
$950$	0	0
$951$	−9.00000	−0.291845
$952$	23.3160	0.755676
$953$	38.2280	1.23833	0.619163	−	0.785262i	$-0.287472\pi$
$953$	38.2280	1.23833	0.619163	+	0.785262i	$0.287472\pi$
$954$	−4.00000	−0.129505
$955$	0	0
$956$	14.2280	0.460166
$957$	8.31601	0.268818
$958$	−9.68399	−0.312876
$959$	−18.6840	−0.603338
$960$	0	0
$961$	25.9120	0.835871
$962$	−8.45600	−0.272632
$963$	4.00000	0.128898
$964$	24.6320	0.793344
$965$	0	0
$966$	3.00000	0.0965234
$967$	42.6320	1.37095	0.685477	−	0.728095i	$-0.259594\pi$
$967$	42.6320	1.37095	0.685477	+	0.728095i	$0.259594\pi$
$968$	−3.31601	−0.106580
$969$	6.00000	0.192748
$970$	0	0
$971$	19.6320	0.630021	0.315011	−	0.949088i	$-0.397992\pi$
$971$	19.6320	0.630021	0.315011	+	0.949088i	$0.397992\pi$
$972$	−1.00000	−0.0320750
$973$	23.3160	0.747477
$974$	−29.5440	−0.946651
$975$	0	0
$976$	7.54400	0.241478
$977$	34.6840	1.10964	0.554820	−	0.831971i	$-0.312787\pi$
$977$	34.6840	1.10964	0.554820	+	0.831971i	$0.312787\pi$
$978$	16.0000	0.511624
$979$	−22.8080	−0.728948
$980$	0	0
$981$	6.22800	0.198845
$982$	−27.5440	−0.878964
$983$	51.4040	1.63953	0.819767	−	0.572698i	$-0.194103\pi$
$983$	51.4040	1.63953	0.819767	+	0.572698i	$0.194103\pi$
$984$	−2.77200	−0.0883682
$985$	0	0
$986$	23.3160	0.742533
$987$	−0.683994	−0.0217718
$988$	3.68399	0.117203
$989$	−0.772002	−0.0245482
$990$	0	0
$991$	−38.1760	−1.21270	−0.606351	−	0.795197i	$-0.707367\pi$
$991$	−38.1760	−1.21270	−0.606351	+	0.795197i	$0.707367\pi$
$992$	7.54400	0.239522
$993$	−26.2280	−0.832320
$994$	11.3160	0.358922
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	8.77200	0.277812	0.138906	−	0.990306i	$-0.455641\pi$
$997$	8.77200	0.277812	0.138906	+	0.990306i	$0.455641\pi$
$998$	−35.3160	−1.11791
$999$	−1.77200	−0.0560637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.a.bj.1.1	yes	2
5.2	odd	4		3450.2.d.w.2899.3		4
5.3	odd	4		3450.2.d.w.2899.1		4
5.4	even	2		3450.2.a.bh.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bh.1.1	✓	2	5.4	even	2
3450.2.a.bj.1.1	yes	2	1.1	even	1	trivial
3450.2.d.w.2899.1		4	5.3	odd	4
3450.2.d.w.2899.3		4	5.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.77200 q^{11} -1.00000 q^{12} -4.77200 q^{13} +3.00000 q^{14} +1.00000 q^{16} +7.77200 q^{17} +1.00000 q^{18} -0.772002 q^{19} -3.00000 q^{21} -2.77200 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.77200 q^{26} -1.00000 q^{27} +3.00000 q^{28} +3.00000 q^{29} +7.54400 q^{31} +1.00000 q^{32} +2.77200 q^{33} +7.77200 q^{34} +1.00000 q^{36} +1.77200 q^{37} -0.772002 q^{38} +4.77200 q^{39} +2.77200 q^{41} -3.00000 q^{42} +0.772002 q^{43} -2.77200 q^{44} -1.00000 q^{46} +0.227998 q^{47} -1.00000 q^{48} +2.00000 q^{49} -7.77200 q^{51} -4.77200 q^{52} -4.00000 q^{53} -1.00000 q^{54} +3.00000 q^{56} +0.772002 q^{57} +3.00000 q^{58} +6.00000 q^{59} +7.54400 q^{61} +7.54400 q^{62} +3.00000 q^{63} +1.00000 q^{64} +2.77200 q^{66} -7.54400 q^{67} +7.77200 q^{68} +1.00000 q^{69} +3.77200 q^{71} +1.00000 q^{72} +10.5440 q^{73} +1.77200 q^{74} -0.772002 q^{76} -8.31601 q^{77} +4.77200 q^{78} +10.7720 q^{79} +1.00000 q^{81} +2.77200 q^{82} +1.00000 q^{83} -3.00000 q^{84} +0.772002 q^{86} -3.00000 q^{87} -2.77200 q^{88} +8.22800 q^{89} -14.3160 q^{91} -1.00000 q^{92} -7.54400 q^{93} +0.227998 q^{94} -1.00000 q^{96} -0.455996 q^{97} +2.00000 q^{98} -2.77200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{11} - 2 q^{12} - q^{13} + 6 q^{14} + 2 q^{16} + 7 q^{17} + 2 q^{18} + 7 q^{19} - 6 q^{21} + 3 q^{22} - 2 q^{23} - 2 q^{24} - q^{26} - 2 q^{27} + 6 q^{28} + 6 q^{29} - 2 q^{31} + 2 q^{32} - 3 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 7 q^{38} + q^{39} - 3 q^{41} - 6 q^{42} - 7 q^{43} + 3 q^{44} - 2 q^{46} + 9 q^{47} - 2 q^{48} + 4 q^{49} - 7 q^{51} - q^{52} - 8 q^{53} - 2 q^{54} + 6 q^{56} - 7 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{61} - 2 q^{62} + 6 q^{63} + 2 q^{64} - 3 q^{66} + 2 q^{67} + 7 q^{68} + 2 q^{69} - q^{71} + 2 q^{72} + 4 q^{73} - 5 q^{74} + 7 q^{76} + 9 q^{77} + q^{78} + 13 q^{79} + 2 q^{81} - 3 q^{82} + 2 q^{83} - 6 q^{84} - 7 q^{86} - 6 q^{87} + 3 q^{88} + 25 q^{89} - 3 q^{91} - 2 q^{92} + 2 q^{93} + 9 q^{94} - 2 q^{96} - 18 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^11 - 2 * q^12 - q^13 + 6 * q^14 + 2 * q^16 + 7 * q^17 + 2 * q^18 + 7 * q^19 - 6 * q^21 + 3 * q^22 - 2 * q^23 - 2 * q^24 - q^26 - 2 * q^27 + 6 * q^28 + 6 * q^29 - 2 * q^31 + 2 * q^32 - 3 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 7 * q^38 + q^39 - 3 * q^41 - 6 * q^42 - 7 * q^43 + 3 * q^44 - 2 * q^46 + 9 * q^47 - 2 * q^48 + 4 * q^49 - 7 * q^51 - q^52 - 8 * q^53 - 2 * q^54 + 6 * q^56 - 7 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^61 - 2 * q^62 + 6 * q^63 + 2 * q^64 - 3 * q^66 + 2 * q^67 + 7 * q^68 + 2 * q^69 - q^71 + 2 * q^72 + 4 * q^73 - 5 * q^74 + 7 * q^76 + 9 * q^77 + q^78 + 13 * q^79 + 2 * q^81 - 3 * q^82 + 2 * q^83 - 6 * q^84 - 7 * q^86 - 6 * q^87 + 3 * q^88 + 25 * q^89 - 3 * q^91 - 2 * q^92 + 2 * q^93 + 9 * q^94 - 2 * q^96 - 18 * q^97 + 4 * q^98 + 3 * q^99

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