LMFDB - Embedded newform 8085.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} +1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} -2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41421 q^{2} +1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} -2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} -1.00000 q^{11} +3.82843 q^{12} +5.65685 q^{13} +1.00000 q^{15} +3.00000 q^{16} +1.17157 q^{17} -2.41421 q^{18} +6.82843 q^{19} +3.82843 q^{20} +2.41421 q^{22} -4.00000 q^{23} -4.41421 q^{24} +1.00000 q^{25} -13.6569 q^{26} +1.00000 q^{27} -4.82843 q^{29} -2.41421 q^{30} +1.58579 q^{32} -1.00000 q^{33} -2.82843 q^{34} +3.82843 q^{36} +11.6569 q^{37} -16.4853 q^{38} +5.65685 q^{39} -4.41421 q^{40} -4.82843 q^{41} -8.82843 q^{43} -3.82843 q^{44} +1.00000 q^{45} +9.65685 q^{46} +4.00000 q^{47} +3.00000 q^{48} -2.41421 q^{50} +1.17157 q^{51} +21.6569 q^{52} +9.31371 q^{53} -2.41421 q^{54} -1.00000 q^{55} +6.82843 q^{57} +11.6569 q^{58} +4.00000 q^{59} +3.82843 q^{60} +11.6569 q^{61} -9.82843 q^{64} +5.65685 q^{65} +2.41421 q^{66} -5.65685 q^{67} +4.48528 q^{68} -4.00000 q^{69} +2.34315 q^{71} -4.41421 q^{72} -11.3137 q^{73} -28.1421 q^{74} +1.00000 q^{75} +26.1421 q^{76} -13.6569 q^{78} +8.48528 q^{79} +3.00000 q^{80} +1.00000 q^{81} +11.6569 q^{82} +10.0000 q^{83} +1.17157 q^{85} +21.3137 q^{86} -4.82843 q^{87} +4.41421 q^{88} -3.65685 q^{89} -2.41421 q^{90} -15.3137 q^{92} -9.65685 q^{94} +6.82843 q^{95} +1.58579 q^{96} -11.6569 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} - 6 q^{24} + 2 q^{25} - 16 q^{26} + 2 q^{27} - 4 q^{29} - 2 q^{30} + 6 q^{32} - 2 q^{33} + 2 q^{36} + 12 q^{37} - 16 q^{38} - 6 q^{40} - 4 q^{41} - 12 q^{43} - 2 q^{44} + 2 q^{45} + 8 q^{46} + 8 q^{47} + 6 q^{48} - 2 q^{50} + 8 q^{51} + 32 q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} + 8 q^{57} + 12 q^{58} + 8 q^{59} + 2 q^{60} + 12 q^{61} - 14 q^{64} + 2 q^{66} - 8 q^{68} - 8 q^{69} + 16 q^{71} - 6 q^{72} - 28 q^{74} + 2 q^{75} + 24 q^{76} - 16 q^{78} + 6 q^{80} + 2 q^{81} + 12 q^{82} + 20 q^{83} + 8 q^{85} + 20 q^{86} - 4 q^{87} + 6 q^{88} + 4 q^{89} - 2 q^{90} - 8 q^{92} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 12 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 + 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 - 6 * q^24 + 2 * q^25 - 16 * q^26 + 2 * q^27 - 4 * q^29 - 2 * q^30 + 6 * q^32 - 2 * q^33 + 2 * q^36 + 12 * q^37 - 16 * q^38 - 6 * q^40 - 4 * q^41 - 12 * q^43 - 2 * q^44 + 2 * q^45 + 8 * q^46 + 8 * q^47 + 6 * q^48 - 2 * q^50 + 8 * q^51 + 32 * q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 + 8 * q^57 + 12 * q^58 + 8 * q^59 + 2 * q^60 + 12 * q^61 - 14 * q^64 + 2 * q^66 - 8 * q^68 - 8 * q^69 + 16 * q^71 - 6 * q^72 - 28 * q^74 + 2 * q^75 + 24 * q^76 - 16 * q^78 + 6 * q^80 + 2 * q^81 + 12 * q^82 + 20 * q^83 + 8 * q^85 + 20 * q^86 - 4 * q^87 + 6 * q^88 + 4 * q^89 - 2 * q^90 - 8 * q^92 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 12 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.41421	−1.70711	−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421	−1.70711	−0.853553	+	0.521005i	$0.825557\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.82843	1.91421
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.41421	−0.985599
$7$	0	0
$7$	0	0
$8$	−4.41421	−1.56066
$9$	1.00000	0.333333
$10$	−2.41421	−0.763441
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.82843	1.10517
$13$	5.65685	1.56893	0.784465	−	0.620174i	$-0.212938\pi$
$13$	5.65685	1.56893	0.784465	+	0.620174i	$0.212938\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	3.00000	0.750000
$17$	1.17157	0.284148	0.142074	−	0.989856i	$-0.454623\pi$
$17$	1.17157	0.284148	0.142074	+	0.989856i	$0.454623\pi$
$18$	−2.41421	−0.569036
$19$	6.82843	1.56655	0.783274	−	0.621676i	$-0.213548\pi$
$19$	6.82843	1.56655	0.783274	+	0.621676i	$0.213548\pi$
$20$	3.82843	0.856062
$21$	0	0
$22$	2.41421	0.514712
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−4.41421	−0.901048
$25$	1.00000	0.200000
$26$	−13.6569	−2.67833
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.82843	−0.896616	−0.448308	−	0.893879i	$-0.647973\pi$
$29$	−4.82843	−0.896616	−0.448308	+	0.893879i	$0.647973\pi$
$30$	−2.41421	−0.440773
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.58579	0.280330
$33$	−1.00000	−0.174078
$34$	−2.82843	−0.485071
$35$	0	0
$36$	3.82843	0.638071
$37$	11.6569	1.91638	0.958188	−	0.286141i	$-0.0923726\pi$
$37$	11.6569	1.91638	0.958188	+	0.286141i	$0.0923726\pi$
$38$	−16.4853	−2.67427
$39$	5.65685	0.905822
$40$	−4.41421	−0.697948
$41$	−4.82843	−0.754074	−0.377037	−	0.926198i	$-0.623057\pi$
$41$	−4.82843	−0.754074	−0.377037	+	0.926198i	$0.623057\pi$
$42$	0	0
$43$	−8.82843	−1.34632	−0.673161	−	0.739496i	$-0.735064\pi$
$43$	−8.82843	−1.34632	−0.673161	+	0.739496i	$0.735064\pi$
$44$	−3.82843	−0.577157
$45$	1.00000	0.149071
$46$	9.65685	1.42383
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	3.00000	0.433013
$49$	0	0
$50$	−2.41421	−0.341421
$51$	1.17157	0.164053
$52$	21.6569	3.00327
$53$	9.31371	1.27934	0.639668	−	0.768651i	$-0.279072\pi$
$53$	9.31371	1.27934	0.639668	+	0.768651i	$0.279072\pi$
$54$	−2.41421	−0.328533
$55$	−1.00000	−0.134840
$56$	0	0
$57$	6.82843	0.904447
$58$	11.6569	1.53062
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	3.82843	0.494248
$61$	11.6569	1.49251	0.746254	−	0.665662i	$-0.231851\pi$
$61$	11.6569	1.49251	0.746254	+	0.665662i	$0.231851\pi$
$62$	0	0
$63$	0	0
$64$	−9.82843	−1.22855
$65$	5.65685	0.701646
$66$	2.41421	0.297169
$67$	−5.65685	−0.691095	−0.345547	−	0.938401i	$-0.612307\pi$
$67$	−5.65685	−0.691095	−0.345547	+	0.938401i	$0.612307\pi$
$68$	4.48528	0.543920
$69$	−4.00000	−0.481543
$70$	0	0
$71$	2.34315	0.278080	0.139040	−	0.990287i	$-0.455598\pi$
$71$	2.34315	0.278080	0.139040	+	0.990287i	$0.455598\pi$
$72$	−4.41421	−0.520220
$73$	−11.3137	−1.32417	−0.662085	−	0.749429i	$-0.730328\pi$
$73$	−11.3137	−1.32417	−0.662085	+	0.749429i	$0.730328\pi$
$74$	−28.1421	−3.27146
$75$	1.00000	0.115470
$76$	26.1421	2.99871
$77$	0	0
$78$	−13.6569	−1.54633
$79$	8.48528	0.954669	0.477334	−	0.878722i	$-0.341603\pi$
$79$	8.48528	0.954669	0.477334	+	0.878722i	$0.341603\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	11.6569	1.28728
$83$	10.0000	1.09764	0.548821	−	0.835940i	$-0.315077\pi$
$83$	10.0000	1.09764	0.548821	+	0.835940i	$0.315077\pi$
$84$	0	0
$85$	1.17157	0.127075
$86$	21.3137	2.29832
$87$	−4.82843	−0.517662
$88$	4.41421	0.470557
$89$	−3.65685	−0.387626	−0.193813	−	0.981039i	$-0.562085\pi$
$89$	−3.65685	−0.387626	−0.193813	+	0.981039i	$0.562085\pi$
$90$	−2.41421	−0.254480
$91$	0	0
$92$	−15.3137	−1.59656
$93$	0	0
$94$	−9.65685	−0.996028
$95$	6.82843	0.700582
$96$	1.58579	0.161849
$97$	−11.6569	−1.18357	−0.591787	−	0.806094i	$-0.701577\pi$
$97$	−11.6569	−1.18357	−0.591787	+	0.806094i	$0.701577\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	3.82843	0.382843
$101$	0.828427	0.0824316	0.0412158	−	0.999150i	$-0.486877\pi$
$101$	0.828427	0.0824316	0.0412158	+	0.999150i	$0.486877\pi$
$102$	−2.82843	−0.280056
$103$	3.31371	0.326509	0.163255	−	0.986584i	$-0.447801\pi$
$103$	3.31371	0.326509	0.163255	+	0.986584i	$0.447801\pi$
$104$	−24.9706	−2.44857
$105$	0	0
$106$	−22.4853	−2.18396
$107$	17.3137	1.67378	0.836890	−	0.547372i	$-0.184372\pi$
$107$	17.3137	1.67378	0.836890	+	0.547372i	$0.184372\pi$
$108$	3.82843	0.368391
$109$	17.3137	1.65835	0.829176	−	0.558987i	$-0.188810\pi$
$109$	17.3137	1.65835	0.829176	+	0.558987i	$0.188810\pi$
$110$	2.41421	0.230186
$111$	11.6569	1.10642
$112$	0	0
$113$	−18.9706	−1.78460	−0.892300	−	0.451442i	$-0.850910\pi$
$113$	−18.9706	−1.78460	−0.892300	+	0.451442i	$0.850910\pi$
$114$	−16.4853	−1.54399
$115$	−4.00000	−0.373002
$116$	−18.4853	−1.71632
$117$	5.65685	0.522976
$118$	−9.65685	−0.888985
$119$	0	0
$120$	−4.41421	−0.402961
$121$	1.00000	0.0909091
$122$	−28.1421	−2.54787
$123$	−4.82843	−0.435365
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−14.4853	−1.28536	−0.642680	−	0.766134i	$-0.722178\pi$
$127$	−14.4853	−1.28536	−0.642680	+	0.766134i	$0.722178\pi$
$128$	20.5563	1.81694
$129$	−8.82843	−0.777300
$130$	−13.6569	−1.19779
$131$	−3.31371	−0.289520	−0.144760	−	0.989467i	$-0.546241\pi$
$131$	−3.31371	−0.289520	−0.144760	+	0.989467i	$0.546241\pi$
$132$	−3.82843	−0.333222
$133$	0	0
$134$	13.6569	1.17977
$135$	1.00000	0.0860663
$136$	−5.17157	−0.443459
$137$	−13.3137	−1.13747	−0.568733	−	0.822522i	$-0.692566\pi$
$137$	−13.3137	−1.13747	−0.568733	+	0.822522i	$0.692566\pi$
$138$	9.65685	0.822046
$139$	−0.485281	−0.0411610	−0.0205805	−	0.999788i	$-0.506551\pi$
$139$	−0.485281	−0.0411610	−0.0205805	+	0.999788i	$0.506551\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−5.65685	−0.474713
$143$	−5.65685	−0.473050
$144$	3.00000	0.250000
$145$	−4.82843	−0.400979
$146$	27.3137	2.26050
$147$	0	0
$148$	44.6274	3.66835
$149$	1.51472	0.124091	0.0620453	−	0.998073i	$-0.480238\pi$
$149$	1.51472	0.124091	0.0620453	+	0.998073i	$0.480238\pi$
$150$	−2.41421	−0.197120
$151$	16.4853	1.34155	0.670777	−	0.741659i	$-0.265961\pi$
$151$	16.4853	1.34155	0.670777	+	0.741659i	$0.265961\pi$
$152$	−30.1421	−2.44485
$153$	1.17157	0.0947161
$154$	0	0
$155$	0	0
$156$	21.6569	1.73394
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−20.4853	−1.62972
$159$	9.31371	0.738625
$160$	1.58579	0.125367
$161$	0	0
$162$	−2.41421	−0.189679
$163$	−7.31371	−0.572854	−0.286427	−	0.958102i	$-0.592468\pi$
$163$	−7.31371	−0.572854	−0.286427	+	0.958102i	$0.592468\pi$
$164$	−18.4853	−1.44346
$165$	−1.00000	−0.0778499
$166$	−24.1421	−1.87379
$167$	13.3137	1.03025	0.515123	−	0.857116i	$-0.327746\pi$
$167$	13.3137	1.03025	0.515123	+	0.857116i	$0.327746\pi$
$168$	0	0
$169$	19.0000	1.46154
$170$	−2.82843	−0.216930
$171$	6.82843	0.522183
$172$	−33.7990	−2.57715
$173$	−2.82843	−0.215041	−0.107521	−	0.994203i	$-0.534291\pi$
$173$	−2.82843	−0.215041	−0.107521	+	0.994203i	$0.534291\pi$
$174$	11.6569	0.883704
$175$	0	0
$176$	−3.00000	−0.226134
$177$	4.00000	0.300658
$178$	8.82843	0.661719
$179$	−17.6569	−1.31974	−0.659868	−	0.751382i	$-0.729388\pi$
$179$	−17.6569	−1.31974	−0.659868	+	0.751382i	$0.729388\pi$
$180$	3.82843	0.285354
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	0	0
$183$	11.6569	0.861699
$184$	17.6569	1.30168
$185$	11.6569	0.857029
$186$	0	0
$187$	−1.17157	−0.0856739
$188$	15.3137	1.11687
$189$	0	0
$190$	−16.4853	−1.19597
$191$	5.65685	0.409316	0.204658	−	0.978834i	$-0.434392\pi$
$191$	5.65685	0.409316	0.204658	+	0.978834i	$0.434392\pi$
$192$	−9.82843	−0.709306
$193$	13.6569	0.983042	0.491521	−	0.870866i	$-0.336441\pi$
$193$	13.6569	0.983042	0.491521	+	0.870866i	$0.336441\pi$
$194$	28.1421	2.02049
$195$	5.65685	0.405096
$196$	0	0
$197$	−8.48528	−0.604551	−0.302276	−	0.953221i	$-0.597746\pi$
$197$	−8.48528	−0.604551	−0.302276	+	0.953221i	$0.597746\pi$
$198$	2.41421	0.171571
$199$	21.6569	1.53521	0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569	1.53521	0.767607	+	0.640921i	$0.221447\pi$
$200$	−4.41421	−0.312132
$201$	−5.65685	−0.399004
$202$	−2.00000	−0.140720
$203$	0	0
$204$	4.48528	0.314033
$205$	−4.82843	−0.337232
$206$	−8.00000	−0.557386
$207$	−4.00000	−0.278019
$208$	16.9706	1.17670
$209$	−6.82843	−0.472332
$210$	0	0
$211$	1.17157	0.0806544	0.0403272	−	0.999187i	$-0.487160\pi$
$211$	1.17157	0.0806544	0.0403272	+	0.999187i	$0.487160\pi$
$212$	35.6569	2.44892
$213$	2.34315	0.160550
$214$	−41.7990	−2.85732
$215$	−8.82843	−0.602094
$216$	−4.41421	−0.300349
$217$	0	0
$218$	−41.7990	−2.83098
$219$	−11.3137	−0.764510
$220$	−3.82843	−0.258113
$221$	6.62742	0.445808
$222$	−28.1421	−1.88878
$223$	6.34315	0.424768	0.212384	−	0.977186i	$-0.431877\pi$
$223$	6.34315	0.424768	0.212384	+	0.977186i	$0.431877\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	45.7990	3.04650
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	26.1421	1.73131
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	9.65685	0.636754
$231$	0	0
$232$	21.3137	1.39931
$233$	−18.8284	−1.23349	−0.616746	−	0.787163i	$-0.711549\pi$
$233$	−18.8284	−1.23349	−0.616746	+	0.787163i	$0.711549\pi$
$234$	−13.6569	−0.892776
$235$	4.00000	0.260931
$236$	15.3137	0.996838
$237$	8.48528	0.551178
$238$	0	0
$239$	17.6569	1.14213	0.571063	−	0.820906i	$-0.306531\pi$
$239$	17.6569	1.14213	0.571063	+	0.820906i	$0.306531\pi$
$240$	3.00000	0.193649
$241$	12.3431	0.795092	0.397546	−	0.917582i	$-0.369862\pi$
$241$	12.3431	0.795092	0.397546	+	0.917582i	$0.369862\pi$
$242$	−2.41421	−0.155192
$243$	1.00000	0.0641500
$244$	44.6274	2.85698
$245$	0	0
$246$	11.6569	0.743214
$247$	38.6274	2.45780
$248$	0	0
$249$	10.0000	0.633724
$250$	−2.41421	−0.152688
$251$	−20.9706	−1.32365	−0.661825	−	0.749658i	$-0.730218\pi$
$251$	−20.9706	−1.32365	−0.661825	+	0.749658i	$0.730218\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	34.9706	2.19425
$255$	1.17157	0.0733667
$256$	−29.9706	−1.87316
$257$	16.3431	1.01946	0.509729	−	0.860335i	$-0.329746\pi$
$257$	16.3431	1.01946	0.509729	+	0.860335i	$0.329746\pi$
$258$	21.3137	1.32693
$259$	0	0
$260$	21.6569	1.34310
$261$	−4.82843	−0.298872
$262$	8.00000	0.494242
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	4.41421	0.271676
$265$	9.31371	0.572137
$266$	0	0
$267$	−3.65685	−0.223796
$268$	−21.6569	−1.32290
$269$	−20.6274	−1.25768	−0.628838	−	0.777536i	$-0.716469\pi$
$269$	−20.6274	−1.25768	−0.628838	+	0.777536i	$0.716469\pi$
$270$	−2.41421	−0.146924
$271$	11.7990	0.716738	0.358369	−	0.933580i	$-0.383333\pi$
$271$	11.7990	0.716738	0.358369	+	0.933580i	$0.383333\pi$
$272$	3.51472	0.213111
$273$	0	0
$274$	32.1421	1.94178
$275$	−1.00000	−0.0603023
$276$	−15.3137	−0.921777
$277$	−2.34315	−0.140786	−0.0703930	−	0.997519i	$-0.522425\pi$
$277$	−2.34315	−0.140786	−0.0703930	+	0.997519i	$0.522425\pi$
$278$	1.17157	0.0702663
$279$	0	0
$280$	0	0
$281$	−11.1716	−0.666440	−0.333220	−	0.942849i	$-0.608135\pi$
$281$	−11.1716	−0.666440	−0.333220	+	0.942849i	$0.608135\pi$
$282$	−9.65685	−0.575057
$283$	8.82843	0.524796	0.262398	−	0.964960i	$-0.415487\pi$
$283$	8.82843	0.524796	0.262398	+	0.964960i	$0.415487\pi$
$284$	8.97056	0.532305
$285$	6.82843	0.404481
$286$	13.6569	0.807547
$287$	0	0
$288$	1.58579	0.0934434
$289$	−15.6274	−0.919260
$290$	11.6569	0.684514
$291$	−11.6569	−0.683337
$292$	−43.3137	−2.53474
$293$	6.82843	0.398921	0.199460	−	0.979906i	$-0.436081\pi$
$293$	6.82843	0.398921	0.199460	+	0.979906i	$0.436081\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	−51.4558	−2.99081
$297$	−1.00000	−0.0580259
$298$	−3.65685	−0.211836
$299$	−22.6274	−1.30858
$300$	3.82843	0.221034
$301$	0	0
$302$	−39.7990	−2.29017
$303$	0.828427	0.0475919
$304$	20.4853	1.17491
$305$	11.6569	0.667470
$306$	−2.82843	−0.161690
$307$	3.17157	0.181011	0.0905056	−	0.995896i	$-0.471152\pi$
$307$	3.17157	0.181011	0.0905056	+	0.995896i	$0.471152\pi$
$308$	0	0
$309$	3.31371	0.188510
$310$	0	0
$311$	3.31371	0.187903	0.0939516	−	0.995577i	$-0.470050\pi$
$311$	3.31371	0.187903	0.0939516	+	0.995577i	$0.470050\pi$
$312$	−24.9706	−1.41368
$313$	−15.6569	−0.884978	−0.442489	−	0.896774i	$-0.645904\pi$
$313$	−15.6569	−0.884978	−0.442489	+	0.896774i	$0.645904\pi$
$314$	43.4558	2.45236
$315$	0	0
$316$	32.4853	1.82744
$317$	−26.2843	−1.47627	−0.738136	−	0.674652i	$-0.764294\pi$
$317$	−26.2843	−1.47627	−0.738136	+	0.674652i	$0.764294\pi$
$318$	−22.4853	−1.26091
$319$	4.82843	0.270340
$320$	−9.82843	−0.549426
$321$	17.3137	0.966357
$322$	0	0
$323$	8.00000	0.445132
$324$	3.82843	0.212690
$325$	5.65685	0.313786
$326$	17.6569	0.977923
$327$	17.3137	0.957450
$328$	21.3137	1.17685
$329$	0	0
$330$	2.41421	0.132898
$331$	6.34315	0.348651	0.174325	−	0.984688i	$-0.444226\pi$
$331$	6.34315	0.348651	0.174325	+	0.984688i	$0.444226\pi$
$332$	38.2843	2.10112
$333$	11.6569	0.638792
$334$	−32.1421	−1.75874
$335$	−5.65685	−0.309067
$336$	0	0
$337$	3.31371	0.180509	0.0902546	−	0.995919i	$-0.471232\pi$
$337$	3.31371	0.180509	0.0902546	+	0.995919i	$0.471232\pi$
$338$	−45.8701	−2.49500
$339$	−18.9706	−1.03034
$340$	4.48528	0.243249
$341$	0	0
$342$	−16.4853	−0.891422
$343$	0	0
$344$	38.9706	2.10115
$345$	−4.00000	−0.215353
$346$	6.82843	0.367099
$347$	−29.3137	−1.57364	−0.786821	−	0.617181i	$-0.788275\pi$
$347$	−29.3137	−1.57364	−0.786821	+	0.617181i	$0.788275\pi$
$348$	−18.4853	−0.990915
$349$	−10.9706	−0.587241	−0.293620	−	0.955922i	$-0.594860\pi$
$349$	−10.9706	−0.587241	−0.293620	+	0.955922i	$0.594860\pi$
$350$	0	0
$351$	5.65685	0.301941
$352$	−1.58579	−0.0845227
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	−9.65685	−0.513256
$355$	2.34315	0.124361
$356$	−14.0000	−0.741999
$357$	0	0
$358$	42.6274	2.25293
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	−4.41421	−0.232649
$361$	27.6274	1.45407
$362$	−33.7990	−1.77644
$363$	1.00000	0.0524864
$364$	0	0
$365$	−11.3137	−0.592187
$366$	−28.1421	−1.47101
$367$	−9.65685	−0.504084	−0.252042	−	0.967716i	$-0.581102\pi$
$367$	−9.65685	−0.504084	−0.252042	+	0.967716i	$0.581102\pi$
$368$	−12.0000	−0.625543
$369$	−4.82843	−0.251358
$370$	−28.1421	−1.46304
$371$	0	0
$372$	0	0
$373$	10.6274	0.550267	0.275133	−	0.961406i	$-0.411278\pi$
$373$	10.6274	0.550267	0.275133	+	0.961406i	$0.411278\pi$
$374$	2.82843	0.146254
$375$	1.00000	0.0516398
$376$	−17.6569	−0.910583
$377$	−27.3137	−1.40673
$378$	0	0
$379$	−23.3137	−1.19754	−0.598772	−	0.800919i	$-0.704345\pi$
$379$	−23.3137	−1.19754	−0.598772	+	0.800919i	$0.704345\pi$
$380$	26.1421	1.34106
$381$	−14.4853	−0.742103
$382$	−13.6569	−0.698745
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	20.5563	1.04901
$385$	0	0
$386$	−32.9706	−1.67816
$387$	−8.82843	−0.448774
$388$	−44.6274	−2.26561
$389$	−23.6569	−1.19945	−0.599725	−	0.800206i	$-0.704723\pi$
$389$	−23.6569	−1.19945	−0.599725	+	0.800206i	$0.704723\pi$
$390$	−13.6569	−0.691542
$391$	−4.68629	−0.236996
$392$	0	0
$393$	−3.31371	−0.167154
$394$	20.4853	1.03203
$395$	8.48528	0.426941
$396$	−3.82843	−0.192386
$397$	14.9706	0.751351	0.375676	−	0.926751i	$-0.377411\pi$
$397$	14.9706	0.751351	0.375676	+	0.926751i	$0.377411\pi$
$398$	−52.2843	−2.62077
$399$	0	0
$400$	3.00000	0.150000
$401$	−6.68629	−0.333897	−0.166949	−	0.985966i	$-0.553391\pi$
$401$	−6.68629	−0.333897	−0.166949	+	0.985966i	$0.553391\pi$
$402$	13.6569	0.681142
$403$	0	0
$404$	3.17157	0.157792
$405$	1.00000	0.0496904
$406$	0	0
$407$	−11.6569	−0.577809
$408$	−5.17157	−0.256031
$409$	19.6569	0.971969	0.485984	−	0.873967i	$-0.338461\pi$
$409$	19.6569	0.971969	0.485984	+	0.873967i	$0.338461\pi$
$410$	11.6569	0.575691
$411$	−13.3137	−0.656717
$412$	12.6863	0.625009
$413$	0	0
$414$	9.65685	0.474608
$415$	10.0000	0.490881
$416$	8.97056	0.439818
$417$	−0.485281	−0.0237643
$418$	16.4853	0.806321
$419$	36.9706	1.80613	0.903065	−	0.429504i	$-0.141311\pi$
$419$	36.9706	1.80613	0.903065	+	0.429504i	$0.141311\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−2.82843	−0.137686
$423$	4.00000	0.194487
$424$	−41.1127	−1.99661
$425$	1.17157	0.0568296
$426$	−5.65685	−0.274075
$427$	0	0
$428$	66.2843	3.20397
$429$	−5.65685	−0.273115
$430$	21.3137	1.02784
$431$	21.6569	1.04317	0.521587	−	0.853198i	$-0.325340\pi$
$431$	21.6569	1.04317	0.521587	+	0.853198i	$0.325340\pi$
$432$	3.00000	0.144338
$433$	15.6569	0.752420	0.376210	−	0.926534i	$-0.377227\pi$
$433$	15.6569	0.752420	0.376210	+	0.926534i	$0.377227\pi$
$434$	0	0
$435$	−4.82843	−0.231505
$436$	66.2843	3.17444
$437$	−27.3137	−1.30659
$438$	27.3137	1.30510
$439$	20.4853	0.977709	0.488855	−	0.872365i	$-0.337415\pi$
$439$	20.4853	0.977709	0.488855	+	0.872365i	$0.337415\pi$
$440$	4.41421	0.210439
$441$	0	0
$442$	−16.0000	−0.761042
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	44.6274	2.11792
$445$	−3.65685	−0.173352
$446$	−15.3137	−0.725125
$447$	1.51472	0.0716437
$448$	0	0
$449$	30.9706	1.46159	0.730796	−	0.682596i	$-0.239149\pi$
$449$	30.9706	1.46159	0.730796	+	0.682596i	$0.239149\pi$
$450$	−2.41421	−0.113807
$451$	4.82843	0.227362
$452$	−72.6274	−3.41611
$453$	16.4853	0.774546
$454$	−33.7990	−1.58627
$455$	0	0
$456$	−30.1421	−1.41153
$457$	−23.3137	−1.09057	−0.545285	−	0.838251i	$-0.683578\pi$
$457$	−23.3137	−1.09057	−0.545285	+	0.838251i	$0.683578\pi$
$458$	−4.82843	−0.225618
$459$	1.17157	0.0546843
$460$	−15.3137	−0.714005
$461$	−0.142136	−0.00661992	−0.00330996	−	0.999995i	$-0.501054\pi$
$461$	−0.142136	−0.00661992	−0.00330996	+	0.999995i	$0.501054\pi$
$462$	0	0
$463$	4.97056	0.231002	0.115501	−	0.993307i	$-0.463153\pi$
$463$	4.97056	0.231002	0.115501	+	0.993307i	$0.463153\pi$
$464$	−14.4853	−0.672462
$465$	0	0
$466$	45.4558	2.10570
$467$	22.6274	1.04707	0.523536	−	0.852004i	$-0.324613\pi$
$467$	22.6274	1.04707	0.523536	+	0.852004i	$0.324613\pi$
$468$	21.6569	1.00109
$469$	0	0
$470$	−9.65685	−0.445437
$471$	−18.0000	−0.829396
$472$	−17.6569	−0.812723
$473$	8.82843	0.405932
$474$	−20.4853	−0.940920
$475$	6.82843	0.313310
$476$	0	0
$477$	9.31371	0.426445
$478$	−42.6274	−1.94973
$479$	−36.9706	−1.68923	−0.844614	−	0.535376i	$-0.820170\pi$
$479$	−36.9706	−1.68923	−0.844614	+	0.535376i	$0.820170\pi$
$480$	1.58579	0.0723809
$481$	65.9411	3.00666
$482$	−29.7990	−1.35731
$483$	0	0
$484$	3.82843	0.174019
$485$	−11.6569	−0.529310
$486$	−2.41421	−0.109511
$487$	−12.9706	−0.587752	−0.293876	−	0.955844i	$-0.594945\pi$
$487$	−12.9706	−0.587752	−0.293876	+	0.955844i	$0.594945\pi$
$488$	−51.4558	−2.32930
$489$	−7.31371	−0.330737
$490$	0	0
$491$	14.3431	0.647297	0.323649	−	0.946177i	$-0.395090\pi$
$491$	14.3431	0.647297	0.323649	+	0.946177i	$0.395090\pi$
$492$	−18.4853	−0.833381
$493$	−5.65685	−0.254772
$494$	−93.2548	−4.19573
$495$	−1.00000	−0.0449467
$496$	0	0
$497$	0	0
$498$	−24.1421	−1.08183
$499$	−22.3431	−1.00022	−0.500108	−	0.865963i	$-0.666706\pi$
$499$	−22.3431	−1.00022	−0.500108	+	0.865963i	$0.666706\pi$
$500$	3.82843	0.171212
$501$	13.3137	0.594813
$502$	50.6274	2.25961
$503$	−17.3137	−0.771980	−0.385990	−	0.922503i	$-0.626140\pi$
$503$	−17.3137	−0.771980	−0.385990	+	0.922503i	$0.626140\pi$
$504$	0	0
$505$	0.828427	0.0368645
$506$	−9.65685	−0.429300
$507$	19.0000	0.843820
$508$	−55.4558	−2.46046
$509$	−18.6863	−0.828255	−0.414128	−	0.910219i	$-0.635913\pi$
$509$	−18.6863	−0.828255	−0.414128	+	0.910219i	$0.635913\pi$
$510$	−2.82843	−0.125245
$511$	0	0
$512$	31.2426	1.38074
$513$	6.82843	0.301482
$514$	−39.4558	−1.74032
$515$	3.31371	0.146019
$516$	−33.7990	−1.48792
$517$	−4.00000	−0.175920
$518$	0	0
$519$	−2.82843	−0.124154
$520$	−24.9706	−1.09503
$521$	32.6274	1.42943	0.714717	−	0.699414i	$-0.246556\pi$
$521$	32.6274	1.42943	0.714717	+	0.699414i	$0.246556\pi$
$522$	11.6569	0.510207
$523$	9.51472	0.416050	0.208025	−	0.978124i	$-0.433297\pi$
$523$	9.51472	0.416050	0.208025	+	0.978124i	$0.433297\pi$
$524$	−12.6863	−0.554203
$525$	0	0
$526$	−43.4558	−1.89476
$527$	0	0
$528$	−3.00000	−0.130558
$529$	−7.00000	−0.304348
$530$	−22.4853	−0.976698
$531$	4.00000	0.173585
$532$	0	0
$533$	−27.3137	−1.18309
$534$	8.82843	0.382043
$535$	17.3137	0.748537
$536$	24.9706	1.07856
$537$	−17.6569	−0.761950
$538$	49.7990	2.14699
$539$	0	0
$540$	3.82843	0.164749
$541$	17.3137	0.744374	0.372187	−	0.928158i	$-0.378608\pi$
$541$	17.3137	0.744374	0.372187	+	0.928158i	$0.378608\pi$
$542$	−28.4853	−1.22355
$543$	14.0000	0.600798
$544$	1.85786	0.0796553
$545$	17.3137	0.741638
$546$	0	0
$547$	−8.14214	−0.348133	−0.174066	−	0.984734i	$-0.555691\pi$
$547$	−8.14214	−0.348133	−0.174066	+	0.984734i	$0.555691\pi$
$548$	−50.9706	−2.17735
$549$	11.6569	0.497502
$550$	2.41421	0.102942
$551$	−32.9706	−1.40459
$552$	17.6569	0.751526
$553$	0	0
$554$	5.65685	0.240337
$555$	11.6569	0.494806
$556$	−1.85786	−0.0787910
$557$	5.17157	0.219127	0.109563	−	0.993980i	$-0.465055\pi$
$557$	5.17157	0.219127	0.109563	+	0.993980i	$0.465055\pi$
$558$	0	0
$559$	−49.9411	−2.11228
$560$	0	0
$561$	−1.17157	−0.0494638
$562$	26.9706	1.13768
$563$	−31.6569	−1.33418	−0.667089	−	0.744978i	$-0.732460\pi$
$563$	−31.6569	−1.33418	−0.667089	+	0.744978i	$0.732460\pi$
$564$	15.3137	0.644823
$565$	−18.9706	−0.798098
$566$	−21.3137	−0.895882
$567$	0	0
$568$	−10.3431	−0.433989
$569$	−35.4558	−1.48639	−0.743193	−	0.669077i	$-0.766690\pi$
$569$	−35.4558	−1.48639	−0.743193	+	0.669077i	$0.766690\pi$
$570$	−16.4853	−0.690492
$571$	−16.4853	−0.689888	−0.344944	−	0.938623i	$-0.612102\pi$
$571$	−16.4853	−0.689888	−0.344944	+	0.938623i	$0.612102\pi$
$572$	−21.6569	−0.905519
$573$	5.65685	0.236318
$574$	0	0
$575$	−4.00000	−0.166812
$576$	−9.82843	−0.409518
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	37.7279	1.56927
$579$	13.6569	0.567559
$580$	−18.4853	−0.767560
$581$	0	0
$582$	28.1421	1.16653
$583$	−9.31371	−0.385734
$584$	49.9411	2.06658
$585$	5.65685	0.233882
$586$	−16.4853	−0.681001
$587$	−14.6274	−0.603738	−0.301869	−	0.953349i	$-0.597611\pi$
$587$	−14.6274	−0.603738	−0.301869	+	0.953349i	$0.597611\pi$
$588$	0	0
$589$	0	0
$590$	−9.65685	−0.397566
$591$	−8.48528	−0.349038
$592$	34.9706	1.43728
$593$	22.8284	0.937451	0.468726	−	0.883344i	$-0.344713\pi$
$593$	22.8284	0.937451	0.468726	+	0.883344i	$0.344713\pi$
$594$	2.41421	0.0990564
$595$	0	0
$596$	5.79899	0.237536
$597$	21.6569	0.886356
$598$	54.6274	2.23388
$599$	27.3137	1.11601	0.558004	−	0.829838i	$-0.311567\pi$
$599$	27.3137	1.11601	0.558004	+	0.829838i	$0.311567\pi$
$600$	−4.41421	−0.180210
$601$	5.31371	0.216751	0.108375	−	0.994110i	$-0.465435\pi$
$601$	5.31371	0.216751	0.108375	+	0.994110i	$0.465435\pi$
$602$	0	0
$603$	−5.65685	−0.230365
$604$	63.1127	2.56802
$605$	1.00000	0.0406558
$606$	−2.00000	−0.0812444
$607$	−1.51472	−0.0614805	−0.0307403	−	0.999527i	$-0.509786\pi$
$607$	−1.51472	−0.0614805	−0.0307403	+	0.999527i	$0.509786\pi$
$608$	10.8284	0.439151
$609$	0	0
$610$	−28.1421	−1.13944
$611$	22.6274	0.915407
$612$	4.48528	0.181307
$613$	−45.9411	−1.85554	−0.927772	−	0.373147i	$-0.878279\pi$
$613$	−45.9411	−1.85554	−0.927772	+	0.373147i	$0.878279\pi$
$614$	−7.65685	−0.309005
$615$	−4.82843	−0.194701
$616$	0	0
$617$	0.343146	0.0138145	0.00690726	−	0.999976i	$-0.497801\pi$
$617$	0.343146	0.0138145	0.00690726	+	0.999976i	$0.497801\pi$
$618$	−8.00000	−0.321807
$619$	14.3431	0.576500	0.288250	−	0.957555i	$-0.406927\pi$
$619$	14.3431	0.576500	0.288250	+	0.957555i	$0.406927\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	−8.00000	−0.320771
$623$	0	0
$624$	16.9706	0.679366
$625$	1.00000	0.0400000
$626$	37.7990	1.51075
$627$	−6.82843	−0.272701
$628$	−68.9117	−2.74988
$629$	13.6569	0.544534
$630$	0	0
$631$	45.6569	1.81757	0.908785	−	0.417264i	$-0.137011\pi$
$631$	45.6569	1.81757	0.908785	+	0.417264i	$0.137011\pi$
$632$	−37.4558	−1.48991
$633$	1.17157	0.0465658
$634$	63.4558	2.52015
$635$	−14.4853	−0.574831
$636$	35.6569	1.41389
$637$	0	0
$638$	−11.6569	−0.461499
$639$	2.34315	0.0926934
$640$	20.5563	0.812561
$641$	6.97056	0.275321	0.137660	−	0.990479i	$-0.456042\pi$
$641$	6.97056	0.275321	0.137660	+	0.990479i	$0.456042\pi$
$642$	−41.7990	−1.64967
$643$	−37.9411	−1.49625	−0.748126	−	0.663557i	$-0.769046\pi$
$643$	−37.9411	−1.49625	−0.748126	+	0.663557i	$0.769046\pi$
$644$	0	0
$645$	−8.82843	−0.347619
$646$	−19.3137	−0.759888
$647$	−4.68629	−0.184237	−0.0921186	−	0.995748i	$-0.529364\pi$
$647$	−4.68629	−0.184237	−0.0921186	+	0.995748i	$0.529364\pi$
$648$	−4.41421	−0.173407
$649$	−4.00000	−0.157014
$650$	−13.6569	−0.535666
$651$	0	0
$652$	−28.0000	−1.09656
$653$	6.97056	0.272779	0.136390	−	0.990655i	$-0.456450\pi$
$653$	6.97056	0.272779	0.136390	+	0.990655i	$0.456450\pi$
$654$	−41.7990	−1.63447
$655$	−3.31371	−0.129477
$656$	−14.4853	−0.565555
$657$	−11.3137	−0.441390
$658$	0	0
$659$	−15.3137	−0.596537	−0.298269	−	0.954482i	$-0.596409\pi$
$659$	−15.3137	−0.596537	−0.298269	+	0.954482i	$0.596409\pi$
$660$	−3.82843	−0.149021
$661$	−9.31371	−0.362261	−0.181131	−	0.983459i	$-0.557976\pi$
$661$	−9.31371	−0.362261	−0.181131	+	0.983459i	$0.557976\pi$
$662$	−15.3137	−0.595184
$663$	6.62742	0.257388
$664$	−44.1421	−1.71305
$665$	0	0
$666$	−28.1421	−1.09049
$667$	19.3137	0.747830
$668$	50.9706	1.97211
$669$	6.34315	0.245240
$670$	13.6569	0.527610
$671$	−11.6569	−0.450008
$672$	0	0
$673$	18.3431	0.707076	0.353538	−	0.935420i	$-0.384978\pi$
$673$	18.3431	0.707076	0.353538	+	0.935420i	$0.384978\pi$
$674$	−8.00000	−0.308148
$675$	1.00000	0.0384900
$676$	72.7401	2.79770
$677$	−29.4558	−1.13208	−0.566040	−	0.824378i	$-0.691525\pi$
$677$	−29.4558	−1.13208	−0.566040	+	0.824378i	$0.691525\pi$
$678$	45.7990	1.75890
$679$	0	0
$680$	−5.17157	−0.198321
$681$	14.0000	0.536481
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	26.1421	0.999570
$685$	−13.3137	−0.508691
$686$	0	0
$687$	2.00000	0.0763048
$688$	−26.4853	−1.00974
$689$	52.6863	2.00719
$690$	9.65685	0.367630
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−10.8284	−0.411635
$693$	0	0
$694$	70.7696	2.68638
$695$	−0.485281	−0.0184078
$696$	21.3137	0.807894
$697$	−5.65685	−0.214269
$698$	26.4853	1.00248
$699$	−18.8284	−0.712157
$700$	0	0
$701$	36.1421	1.36507	0.682535	−	0.730853i	$-0.260878\pi$
$701$	36.1421	1.36507	0.682535	+	0.730853i	$0.260878\pi$
$702$	−13.6569	−0.515445
$703$	79.5980	3.00209
$704$	9.82843	0.370423
$705$	4.00000	0.150649
$706$	62.7696	2.36236
$707$	0	0
$708$	15.3137	0.575524
$709$	6.68629	0.251109	0.125554	−	0.992087i	$-0.459929\pi$
$709$	6.68629	0.251109	0.125554	+	0.992087i	$0.459929\pi$
$710$	−5.65685	−0.212298
$711$	8.48528	0.318223
$712$	16.1421	0.604952
$713$	0	0
$714$	0	0
$715$	−5.65685	−0.211554
$716$	−67.5980	−2.52626
$717$	17.6569	0.659407
$718$	−28.9706	−1.08117
$719$	47.5980	1.77511	0.887553	−	0.460706i	$-0.152404\pi$
$719$	47.5980	1.77511	0.887553	+	0.460706i	$0.152404\pi$
$720$	3.00000	0.111803
$721$	0	0
$722$	−66.6985	−2.48226
$723$	12.3431	0.459047
$724$	53.5980	1.99195
$725$	−4.82843	−0.179323
$726$	−2.41421	−0.0895999
$727$	−33.9411	−1.25881	−0.629403	−	0.777079i	$-0.716701\pi$
$727$	−33.9411	−1.25881	−0.629403	+	0.777079i	$0.716701\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	27.3137	1.01093
$731$	−10.3431	−0.382555
$732$	44.6274	1.64948
$733$	6.34315	0.234289	0.117145	−	0.993115i	$-0.462626\pi$
$733$	6.34315	0.234289	0.117145	+	0.993115i	$0.462626\pi$
$734$	23.3137	0.860525
$735$	0	0
$736$	−6.34315	−0.233811
$737$	5.65685	0.208373
$738$	11.6569	0.429095
$739$	−15.1127	−0.555930	−0.277965	−	0.960591i	$-0.589660\pi$
$739$	−15.1127	−0.555930	−0.277965	+	0.960591i	$0.589660\pi$
$740$	44.6274	1.64054
$741$	38.6274	1.41901
$742$	0	0
$743$	36.3431	1.33330	0.666650	−	0.745371i	$-0.267727\pi$
$743$	36.3431	1.33330	0.666650	+	0.745371i	$0.267727\pi$
$744$	0	0
$745$	1.51472	0.0554950
$746$	−25.6569	−0.939364
$747$	10.0000	0.365881
$748$	−4.48528	−0.163998
$749$	0	0
$750$	−2.41421	−0.0881546
$751$	20.2843	0.740184	0.370092	−	0.928995i	$-0.379326\pi$
$751$	20.2843	0.740184	0.370092	+	0.928995i	$0.379326\pi$
$752$	12.0000	0.437595
$753$	−20.9706	−0.764210
$754$	65.9411	2.40143
$755$	16.4853	0.599961
$756$	0	0
$757$	−36.6274	−1.33125	−0.665623	−	0.746288i	$-0.731834\pi$
$757$	−36.6274	−1.33125	−0.665623	+	0.746288i	$0.731834\pi$
$758$	56.2843	2.04434
$759$	4.00000	0.145191
$760$	−30.1421	−1.09337
$761$	28.8284	1.04503	0.522515	−	0.852630i	$-0.324994\pi$
$761$	28.8284	1.04503	0.522515	+	0.852630i	$0.324994\pi$
$762$	34.9706	1.26685
$763$	0	0
$764$	21.6569	0.783517
$765$	1.17157	0.0423583
$766$	−19.3137	−0.697833
$767$	22.6274	0.817029
$768$	−29.9706	−1.08147
$769$	−10.6863	−0.385358	−0.192679	−	0.981262i	$-0.561718\pi$
$769$	−10.6863	−0.385358	−0.192679	+	0.981262i	$0.561718\pi$
$770$	0	0
$771$	16.3431	0.588584
$772$	52.2843	1.88175
$773$	−3.65685	−0.131528	−0.0657640	−	0.997835i	$-0.520948\pi$
$773$	−3.65685	−0.131528	−0.0657640	+	0.997835i	$0.520948\pi$
$774$	21.3137	0.766105
$775$	0	0
$776$	51.4558	1.84716
$777$	0	0
$778$	57.1127	2.04759
$779$	−32.9706	−1.18129
$780$	21.6569	0.775440
$781$	−2.34315	−0.0838443
$782$	11.3137	0.404577
$783$	−4.82843	−0.172554
$784$	0	0
$785$	−18.0000	−0.642448
$786$	8.00000	0.285351
$787$	20.1421	0.717990	0.358995	−	0.933340i	$-0.383120\pi$
$787$	20.1421	0.717990	0.358995	+	0.933340i	$0.383120\pi$
$788$	−32.4853	−1.15724
$789$	18.0000	0.640817
$790$	−20.4853	−0.728834
$791$	0	0
$792$	4.41421	0.156852
$793$	65.9411	2.34164
$794$	−36.1421	−1.28264
$795$	9.31371	0.330323
$796$	82.9117	2.93873
$797$	−34.9706	−1.23872	−0.619360	−	0.785107i	$-0.712608\pi$
$797$	−34.9706	−1.23872	−0.619360	+	0.785107i	$0.712608\pi$
$798$	0	0
$799$	4.68629	0.165789
$800$	1.58579	0.0560660
$801$	−3.65685	−0.129209
$802$	16.1421	0.569999
$803$	11.3137	0.399252
$804$	−21.6569	−0.763778
$805$	0	0
$806$	0	0
$807$	−20.6274	−0.726119
$808$	−3.65685	−0.128648
$809$	28.4264	0.999419	0.499710	−	0.866193i	$-0.333440\pi$
$809$	28.4264	0.999419	0.499710	+	0.866193i	$0.333440\pi$
$810$	−2.41421	−0.0848268
$811$	−0.485281	−0.0170405	−0.00852027	−	0.999964i	$-0.502712\pi$
$811$	−0.485281	−0.0170405	−0.00852027	+	0.999964i	$0.502712\pi$
$812$	0	0
$813$	11.7990	0.413809
$814$	28.1421	0.986381
$815$	−7.31371	−0.256188
$816$	3.51472	0.123040
$817$	−60.2843	−2.10908
$818$	−47.4558	−1.65925
$819$	0	0
$820$	−18.4853	−0.645534
$821$	−12.8284	−0.447715	−0.223858	−	0.974622i	$-0.571865\pi$
$821$	−12.8284	−0.447715	−0.223858	+	0.974622i	$0.571865\pi$
$822$	32.1421	1.12109
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	−14.6274	−0.509570
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	41.3137	1.43662	0.718309	−	0.695724i	$-0.244916\pi$
$827$	41.3137	1.43662	0.718309	+	0.695724i	$0.244916\pi$
$828$	−15.3137	−0.532188
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	−24.1421	−0.837986
$831$	−2.34315	−0.0812828
$832$	−55.5980	−1.92751
$833$	0	0
$834$	1.17157	0.0405683
$835$	13.3137	0.460740
$836$	−26.1421	−0.904145
$837$	0	0
$838$	−89.2548	−3.08326
$839$	22.6274	0.781185	0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274	0.781185	0.390593	+	0.920564i	$0.372270\pi$
$840$	0	0
$841$	−5.68629	−0.196079
$842$	14.4853	0.499196
$843$	−11.1716	−0.384769
$844$	4.48528	0.154390
$845$	19.0000	0.653620
$846$	−9.65685	−0.332009
$847$	0	0
$848$	27.9411	0.959502
$849$	8.82843	0.302991
$850$	−2.82843	−0.0970143
$851$	−46.6274	−1.59837
$852$	8.97056	0.307326
$853$	8.68629	0.297413	0.148706	−	0.988881i	$-0.452489\pi$
$853$	8.68629	0.297413	0.148706	+	0.988881i	$0.452489\pi$
$854$	0	0
$855$	6.82843	0.233527
$856$	−76.4264	−2.61220
$857$	28.4853	0.973039	0.486519	−	0.873670i	$-0.338266\pi$
$857$	28.4853	0.973039	0.486519	+	0.873670i	$0.338266\pi$
$858$	13.6569	0.466237
$859$	52.9706	1.80733	0.903666	−	0.428238i	$-0.140865\pi$
$859$	52.9706	1.80733	0.903666	+	0.428238i	$0.140865\pi$
$860$	−33.7990	−1.15254
$861$	0	0
$862$	−52.2843	−1.78081
$863$	−20.6863	−0.704170	−0.352085	−	0.935968i	$-0.614527\pi$
$863$	−20.6863	−0.704170	−0.352085	+	0.935968i	$0.614527\pi$
$864$	1.58579	0.0539496
$865$	−2.82843	−0.0961694
$866$	−37.7990	−1.28446
$867$	−15.6274	−0.530735
$868$	0	0
$869$	−8.48528	−0.287843
$870$	11.6569	0.395204
$871$	−32.0000	−1.08428
$872$	−76.4264	−2.58812
$873$	−11.6569	−0.394525
$874$	65.9411	2.23049
$875$	0	0
$876$	−43.3137	−1.46343
$877$	2.62742	0.0887216	0.0443608	−	0.999016i	$-0.485875\pi$
$877$	2.62742	0.0887216	0.0443608	+	0.999016i	$0.485875\pi$
$878$	−49.4558	−1.66905
$879$	6.82843	0.230317
$880$	−3.00000	−0.101130
$881$	46.9706	1.58248	0.791239	−	0.611507i	$-0.209436\pi$
$881$	46.9706	1.58248	0.791239	+	0.611507i	$0.209436\pi$
$882$	0	0
$883$	−5.37258	−0.180802	−0.0904009	−	0.995905i	$-0.528815\pi$
$883$	−5.37258	−0.180802	−0.0904009	+	0.995905i	$0.528815\pi$
$884$	25.3726	0.853372
$885$	4.00000	0.134459
$886$	−28.9706	−0.973285
$887$	15.6569	0.525706	0.262853	−	0.964836i	$-0.415337\pi$
$887$	15.6569	0.525706	0.262853	+	0.964836i	$0.415337\pi$
$888$	−51.4558	−1.72675
$889$	0	0
$890$	8.82843	0.295930
$891$	−1.00000	−0.0335013
$892$	24.2843	0.813098
$893$	27.3137	0.914018
$894$	−3.65685	−0.122304
$895$	−17.6569	−0.590204
$896$	0	0
$897$	−22.6274	−0.755507
$898$	−74.7696	−2.49509
$899$	0	0
$900$	3.82843	0.127614
$901$	10.9117	0.363521
$902$	−11.6569	−0.388131
$903$	0	0
$904$	83.7401	2.78515
$905$	14.0000	0.465376
$906$	−39.7990	−1.32223
$907$	40.9706	1.36041	0.680203	−	0.733024i	$-0.261892\pi$
$907$	40.9706	1.36041	0.680203	+	0.733024i	$0.261892\pi$
$908$	53.5980	1.77871
$909$	0.828427	0.0274772
$910$	0	0
$911$	−48.9706	−1.62247	−0.811234	−	0.584722i	$-0.801203\pi$
$911$	−48.9706	−1.62247	−0.811234	+	0.584722i	$0.801203\pi$
$912$	20.4853	0.678335
$913$	−10.0000	−0.330952
$914$	56.2843	1.86172
$915$	11.6569	0.385364
$916$	7.65685	0.252990
$917$	0	0
$918$	−2.82843	−0.0933520
$919$	11.5147	0.379836	0.189918	−	0.981800i	$-0.439178\pi$
$919$	11.5147	0.379836	0.189918	+	0.981800i	$0.439178\pi$
$920$	17.6569	0.582129
$921$	3.17157	0.104507
$922$	0.343146	0.0113009
$923$	13.2548	0.436288
$924$	0	0
$925$	11.6569	0.383275
$926$	−12.0000	−0.394344
$927$	3.31371	0.108836
$928$	−7.65685	−0.251349
$929$	45.5980	1.49602	0.748011	−	0.663687i	$-0.231009\pi$
$929$	45.5980	1.49602	0.748011	+	0.663687i	$0.231009\pi$
$930$	0	0
$931$	0	0
$932$	−72.0833	−2.36117
$933$	3.31371	0.108486
$934$	−54.6274	−1.78746
$935$	−1.17157	−0.0383145
$936$	−24.9706	−0.816188
$937$	−11.0294	−0.360316	−0.180158	−	0.983638i	$-0.557661\pi$
$937$	−11.0294	−0.360316	−0.180158	+	0.983638i	$0.557661\pi$
$938$	0	0
$939$	−15.6569	−0.510942
$940$	15.3137	0.499478
$941$	34.7696	1.13346	0.566728	−	0.823905i	$-0.308209\pi$
$941$	34.7696	1.13346	0.566728	+	0.823905i	$0.308209\pi$
$942$	43.4558	1.41587
$943$	19.3137	0.628941
$944$	12.0000	0.390567
$945$	0	0
$946$	−21.3137	−0.692968
$947$	6.62742	0.215362	0.107681	−	0.994185i	$-0.465657\pi$
$947$	6.62742	0.215362	0.107681	+	0.994185i	$0.465657\pi$
$948$	32.4853	1.05507
$949$	−64.0000	−2.07753
$950$	−16.4853	−0.534853
$951$	−26.2843	−0.852326
$952$	0	0
$953$	−11.7990	−0.382207	−0.191103	−	0.981570i	$-0.561207\pi$
$953$	−11.7990	−0.382207	−0.191103	+	0.981570i	$0.561207\pi$
$954$	−22.4853	−0.727988
$955$	5.65685	0.183052
$956$	67.5980	2.18627
$957$	4.82843	0.156081
$958$	89.2548	2.88369
$959$	0	0
$960$	−9.82843	−0.317211
$961$	−31.0000	−1.00000
$962$	−159.196	−5.13268
$963$	17.3137	0.557926
$964$	47.2548	1.52198
$965$	13.6569	0.439630
$966$	0	0
$967$	11.4558	0.368395	0.184198	−	0.982889i	$-0.441031\pi$
$967$	11.4558	0.368395	0.184198	+	0.982889i	$0.441031\pi$
$968$	−4.41421	−0.141878
$969$	8.00000	0.256997
$970$	28.1421	0.903590
$971$	34.6274	1.11125	0.555623	−	0.831434i	$-0.312480\pi$
$971$	34.6274	1.11125	0.555623	+	0.831434i	$0.312480\pi$
$972$	3.82843	0.122797
$973$	0	0
$974$	31.3137	1.00336
$975$	5.65685	0.181164
$976$	34.9706	1.11938
$977$	2.68629	0.0859421	0.0429710	−	0.999076i	$-0.486318\pi$
$977$	2.68629	0.0859421	0.0429710	+	0.999076i	$0.486318\pi$
$978$	17.6569	0.564604
$979$	3.65685	0.116874
$980$	0	0
$981$	17.3137	0.552784
$982$	−34.6274	−1.10501
$983$	30.6274	0.976863	0.488431	−	0.872602i	$-0.337569\pi$
$983$	30.6274	0.976863	0.488431	+	0.872602i	$0.337569\pi$
$984$	21.3137	0.679456
$985$	−8.48528	−0.270364
$986$	13.6569	0.434923
$987$	0	0
$988$	147.882	4.70476
$989$	35.3137	1.12291
$990$	2.41421	0.0767287
$991$	−30.6274	−0.972912	−0.486456	−	0.873705i	$-0.661711\pi$
$991$	−30.6274	−0.972912	−0.486456	+	0.873705i	$0.661711\pi$
$992$	0	0
$993$	6.34315	0.201294
$994$	0	0
$995$	21.6569	0.686568
$996$	38.2843	1.21308
$997$	39.3137	1.24508	0.622539	−	0.782589i	$-0.286101\pi$
$997$	39.3137	1.24508	0.622539	+	0.782589i	$0.286101\pi$
$998$	53.9411	1.70748
$999$	11.6569	0.368807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ba.1.1		2
7.6	odd	2		165.2.a.a.1.1	✓	2
21.20	even	2		495.2.a.d.1.2		2
28.27	even	2		2640.2.a.bb.1.1		2
35.13	even	4		825.2.c.e.199.4		4
35.27	even	4		825.2.c.e.199.1		4
35.34	odd	2		825.2.a.g.1.2		2
77.76	even	2		1815.2.a.k.1.2		2
84.83	odd	2		7920.2.a.cg.1.1		2
105.62	odd	4		2475.2.c.m.199.4		4
105.83	odd	4		2475.2.c.m.199.1		4
105.104	even	2		2475.2.a.m.1.1		2
231.230	odd	2		5445.2.a.m.1.1		2
385.384	even	2		9075.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.a.a.1.1	✓	2	7.6	odd	2
495.2.a.d.1.2		2	21.20	even	2
825.2.a.g.1.2		2	35.34	odd	2
825.2.c.e.199.1		4	35.27	even	4
825.2.c.e.199.4		4	35.13	even	4
1815.2.a.k.1.2		2	77.76	even	2
2475.2.a.m.1.1		2	105.104	even	2
2475.2.c.m.199.1		4	105.83	odd	4
2475.2.c.m.199.4		4	105.62	odd	4
2640.2.a.bb.1.1		2	28.27	even	2
5445.2.a.m.1.1		2	231.230	odd	2
7920.2.a.cg.1.1		2	84.83	odd	2
8085.2.a.ba.1.1		2	1.1	even	1	trivial
9075.2.a.v.1.1		2	385.384	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} +1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} -2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} +1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} -2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} -1.00000 q^{11} +3.82843 q^{12} +5.65685 q^{13} +1.00000 q^{15} +3.00000 q^{16} +1.17157 q^{17} -2.41421 q^{18} +6.82843 q^{19} +3.82843 q^{20} +2.41421 q^{22} -4.00000 q^{23} -4.41421 q^{24} +1.00000 q^{25} -13.6569 q^{26} +1.00000 q^{27} -4.82843 q^{29} -2.41421 q^{30} +1.58579 q^{32} -1.00000 q^{33} -2.82843 q^{34} +3.82843 q^{36} +11.6569 q^{37} -16.4853 q^{38} +5.65685 q^{39} -4.41421 q^{40} -4.82843 q^{41} -8.82843 q^{43} -3.82843 q^{44} +1.00000 q^{45} +9.65685 q^{46} +4.00000 q^{47} +3.00000 q^{48} -2.41421 q^{50} +1.17157 q^{51} +21.6569 q^{52} +9.31371 q^{53} -2.41421 q^{54} -1.00000 q^{55} +6.82843 q^{57} +11.6569 q^{58} +4.00000 q^{59} +3.82843 q^{60} +11.6569 q^{61} -9.82843 q^{64} +5.65685 q^{65} +2.41421 q^{66} -5.65685 q^{67} +4.48528 q^{68} -4.00000 q^{69} +2.34315 q^{71} -4.41421 q^{72} -11.3137 q^{73} -28.1421 q^{74} +1.00000 q^{75} +26.1421 q^{76} -13.6569 q^{78} +8.48528 q^{79} +3.00000 q^{80} +1.00000 q^{81} +11.6569 q^{82} +10.0000 q^{83} +1.17157 q^{85} +21.3137 q^{86} -4.82843 q^{87} +4.41421 q^{88} -3.65685 q^{89} -2.41421 q^{90} -15.3137 q^{92} -9.65685 q^{94} +6.82843 q^{95} +1.58579 q^{96} -11.6569 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} + 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} - 6 q^{24} + 2 q^{25} - 16 q^{26} + 2 q^{27} - 4 q^{29} - 2 q^{30} + 6 q^{32} - 2 q^{33} + 2 q^{36} + 12 q^{37} - 16 q^{38} - 6 q^{40} - 4 q^{41} - 12 q^{43} - 2 q^{44} + 2 q^{45} + 8 q^{46} + 8 q^{47} + 6 q^{48} - 2 q^{50} + 8 q^{51} + 32 q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} + 8 q^{57} + 12 q^{58} + 8 q^{59} + 2 q^{60} + 12 q^{61} - 14 q^{64} + 2 q^{66} - 8 q^{68} - 8 q^{69} + 16 q^{71} - 6 q^{72} - 28 q^{74} + 2 q^{75} + 24 q^{76} - 16 q^{78} + 6 q^{80} + 2 q^{81} + 12 q^{82} + 20 q^{83} + 8 q^{85} + 20 q^{86} - 4 q^{87} + 6 q^{88} + 4 q^{89} - 2 q^{90} - 8 q^{92} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 12 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 + 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 - 6 * q^24 + 2 * q^25 - 16 * q^26 + 2 * q^27 - 4 * q^29 - 2 * q^30 + 6 * q^32 - 2 * q^33 + 2 * q^36 + 12 * q^37 - 16 * q^38 - 6 * q^40 - 4 * q^41 - 12 * q^43 - 2 * q^44 + 2 * q^45 + 8 * q^46 + 8 * q^47 + 6 * q^48 - 2 * q^50 + 8 * q^51 + 32 * q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 + 8 * q^57 + 12 * q^58 + 8 * q^59 + 2 * q^60 + 12 * q^61 - 14 * q^64 + 2 * q^66 - 8 * q^68 - 8 * q^69 + 16 * q^71 - 6 * q^72 - 28 * q^74 + 2 * q^75 + 24 * q^76 - 16 * q^78 + 6 * q^80 + 2 * q^81 + 12 * q^82 + 20 * q^83 + 8 * q^85 + 20 * q^86 - 4 * q^87 + 6 * q^88 + 4 * q^89 - 2 * q^90 - 8 * q^92 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 12 * q^97 - 2 * q^99

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