LMFDB - Embedded newform 3325.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3325,2,Mod(1,3325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3325, 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("3325.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3325 = 5^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3325.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:	$26.5502586721$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -1.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -1.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} -1.61803 q^{11} +4.23607 q^{12} +1.00000 q^{13} -0.618034 q^{14} +1.85410 q^{16} +2.85410 q^{17} +2.38197 q^{18} -1.00000 q^{19} +2.61803 q^{21} -1.00000 q^{22} -3.47214 q^{23} +5.85410 q^{24} +0.618034 q^{26} -2.23607 q^{27} +1.61803 q^{28} +3.61803 q^{29} -10.5623 q^{31} +5.61803 q^{32} +4.23607 q^{33} +1.76393 q^{34} -6.23607 q^{36} +11.4721 q^{37} -0.618034 q^{38} -2.61803 q^{39} +10.0902 q^{41} +1.61803 q^{42} +0.472136 q^{43} +2.61803 q^{44} -2.14590 q^{46} +1.47214 q^{47} -4.85410 q^{48} +1.00000 q^{49} -7.47214 q^{51} -1.61803 q^{52} +1.85410 q^{53} -1.38197 q^{54} +2.23607 q^{56} +2.61803 q^{57} +2.23607 q^{58} +12.2361 q^{59} +5.94427 q^{61} -6.52786 q^{62} -3.85410 q^{63} -0.236068 q^{64} +2.61803 q^{66} -13.3262 q^{67} -4.61803 q^{68} +9.09017 q^{69} -4.70820 q^{71} -8.61803 q^{72} -4.32624 q^{73} +7.09017 q^{74} +1.61803 q^{76} +1.61803 q^{77} -1.61803 q^{78} +4.47214 q^{79} -5.70820 q^{81} +6.23607 q^{82} -9.85410 q^{83} -4.23607 q^{84} +0.291796 q^{86} -9.47214 q^{87} +3.61803 q^{88} +7.23607 q^{89} -1.00000 q^{91} +5.61803 q^{92} +27.6525 q^{93} +0.909830 q^{94} -14.7082 q^{96} +1.47214 q^{97} +0.618034 q^{98} -6.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 2 q^{7} + q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 2 * q^7 + q^9	$ 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 2 q^{7} + q^{9} - q^{11} + 4 q^{12} + 2 q^{13} + q^{14} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{21} - 2 q^{22} + 2 q^{23} + 5 q^{24} - q^{26} + q^{28} + 5 q^{29} - q^{31} + 9 q^{32} + 4 q^{33} + 8 q^{34} - 8 q^{36} + 14 q^{37} + q^{38} - 3 q^{39} + 9 q^{41} + q^{42} - 8 q^{43} + 3 q^{44} - 11 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} - 6 q^{51} - q^{52} - 3 q^{53} - 5 q^{54} + 3 q^{57} + 20 q^{59} - 6 q^{61} - 22 q^{62} - q^{63} + 4 q^{64} + 3 q^{66} - 11 q^{67} - 7 q^{68} + 7 q^{69} + 4 q^{71} - 15 q^{72} + 7 q^{73} + 3 q^{74} + q^{76} + q^{77} - q^{78} + 2 q^{81} + 8 q^{82} - 13 q^{83} - 4 q^{84} + 14 q^{86} - 10 q^{87} + 5 q^{88} + 10 q^{89} - 2 q^{91} + 9 q^{92} + 24 q^{93} + 13 q^{94} - 16 q^{96} - 6 q^{97} - q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 2 * q^7 + q^9 - q^11 + 4 * q^12 + 2 * q^13 + q^14 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^21 - 2 * q^22 + 2 * q^23 + 5 * q^24 - q^26 + q^28 + 5 * q^29 - q^31 + 9 * q^32 + 4 * q^33 + 8 * q^34 - 8 * q^36 + 14 * q^37 + q^38 - 3 * q^39 + 9 * q^41 + q^42 - 8 * q^43 + 3 * q^44 - 11 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 - 6 * q^51 - q^52 - 3 * q^53 - 5 * q^54 + 3 * q^57 + 20 * q^59 - 6 * q^61 - 22 * q^62 - q^63 + 4 * q^64 + 3 * q^66 - 11 * q^67 - 7 * q^68 + 7 * q^69 + 4 * q^71 - 15 * q^72 + 7 * q^73 + 3 * q^74 + q^76 + q^77 - q^78 + 2 * q^81 + 8 * q^82 - 13 * q^83 - 4 * q^84 + 14 * q^86 - 10 * q^87 + 5 * q^88 + 10 * q^89 - 2 * q^91 + 9 * q^92 + 24 * q^93 + 13 * q^94 - 16 * q^96 - 6 * q^97 - q^98 - 8 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	−1.61803	−0.809017
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.23607	−0.790569
$9$	3.85410	1.28470
$10$	0	0
$11$	−1.61803	−0.487856	−0.243928	−	0.969793i	$-0.578436\pi$
$11$	−1.61803	−0.487856	−0.243928	+	0.969793i	$0.578436\pi$
$12$	4.23607	1.22285
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	−0.618034	−0.165177
$15$	0	0
$16$	1.85410	0.463525
$17$	2.85410	0.692221	0.346111	−	0.938194i	$-0.387502\pi$
$17$	2.85410	0.692221	0.346111	+	0.938194i	$0.387502\pi$
$18$	2.38197	0.561435
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	2.61803	0.571302
$22$	−1.00000	−0.213201
$23$	−3.47214	−0.723990	−0.361995	−	0.932180i	$-0.617904\pi$
$23$	−3.47214	−0.723990	−0.361995	+	0.932180i	$0.617904\pi$
$24$	5.85410	1.19496
$25$	0	0
$26$	0.618034	0.121206
$27$	−2.23607	−0.430331
$28$	1.61803	0.305780
$29$	3.61803	0.671852	0.335926	−	0.941888i	$-0.390951\pi$
$29$	3.61803	0.671852	0.335926	+	0.941888i	$0.390951\pi$
$30$	0	0
$31$	−10.5623	−1.89705	−0.948523	−	0.316708i	$-0.897422\pi$
$31$	−10.5623	−1.89705	−0.948523	+	0.316708i	$0.897422\pi$
$32$	5.61803	0.993137
$33$	4.23607	0.737405
$34$	1.76393	0.302512
$35$	0	0
$36$	−6.23607	−1.03934
$37$	11.4721	1.88601	0.943004	−	0.332782i	$-0.107987\pi$
$37$	11.4721	1.88601	0.943004	+	0.332782i	$0.107987\pi$
$38$	−0.618034	−0.100258
$39$	−2.61803	−0.419221
$40$	0	0
$41$	10.0902	1.57582	0.787910	−	0.615791i	$-0.211163\pi$
$41$	10.0902	1.57582	0.787910	+	0.615791i	$0.211163\pi$
$42$	1.61803	0.249668
$43$	0.472136	0.0720001	0.0360000	−	0.999352i	$-0.488538\pi$
$43$	0.472136	0.0720001	0.0360000	+	0.999352i	$0.488538\pi$
$44$	2.61803	0.394683
$45$	0	0
$46$	−2.14590	−0.316395
$47$	1.47214	0.214733	0.107367	−	0.994220i	$-0.465758\pi$
$47$	1.47214	0.214733	0.107367	+	0.994220i	$0.465758\pi$
$48$	−4.85410	−0.700629
$49$	1.00000	0.142857
$50$	0	0
$51$	−7.47214	−1.04631
$52$	−1.61803	−0.224381
$53$	1.85410	0.254680	0.127340	−	0.991859i	$-0.459356\pi$
$53$	1.85410	0.254680	0.127340	+	0.991859i	$0.459356\pi$
$54$	−1.38197	−0.188062
$55$	0	0
$56$	2.23607	0.298807
$57$	2.61803	0.346767
$58$	2.23607	0.293610
$59$	12.2361	1.59300	0.796500	−	0.604638i	$-0.206682\pi$
$59$	12.2361	1.59300	0.796500	+	0.604638i	$0.206682\pi$
$60$	0	0
$61$	5.94427	0.761086	0.380543	−	0.924763i	$-0.375737\pi$
$61$	5.94427	0.761086	0.380543	+	0.924763i	$0.375737\pi$
$62$	−6.52786	−0.829040
$63$	−3.85410	−0.485571
$64$	−0.236068	−0.0295085
$65$	0	0
$66$	2.61803	0.322258
$67$	−13.3262	−1.62806	−0.814030	−	0.580823i	$-0.802731\pi$
$67$	−13.3262	−1.62806	−0.814030	+	0.580823i	$0.802731\pi$
$68$	−4.61803	−0.560019
$69$	9.09017	1.09433
$70$	0	0
$71$	−4.70820	−0.558761	−0.279381	−	0.960180i	$-0.590129\pi$
$71$	−4.70820	−0.558761	−0.279381	+	0.960180i	$0.590129\pi$
$72$	−8.61803	−1.01565
$73$	−4.32624	−0.506348	−0.253174	−	0.967421i	$-0.581474\pi$
$73$	−4.32624	−0.506348	−0.253174	+	0.967421i	$0.581474\pi$
$74$	7.09017	0.824216
$75$	0	0
$76$	1.61803	0.185601
$77$	1.61803	0.184392
$78$	−1.61803	−0.183206
$79$	4.47214	0.503155	0.251577	−	0.967837i	$-0.419051\pi$
$79$	4.47214	0.503155	0.251577	+	0.967837i	$0.419051\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	6.23607	0.688659
$83$	−9.85410	−1.08163	−0.540814	−	0.841142i	$-0.681884\pi$
$83$	−9.85410	−1.08163	−0.540814	+	0.841142i	$0.681884\pi$
$84$	−4.23607	−0.462193
$85$	0	0
$86$	0.291796	0.0314652
$87$	−9.47214	−1.01552
$88$	3.61803	0.385684
$89$	7.23607	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$89$	7.23607	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	5.61803	0.585721
$93$	27.6525	2.86743
$94$	0.909830	0.0938418
$95$	0	0
$96$	−14.7082	−1.50115
$97$	1.47214	0.149473	0.0747364	−	0.997203i	$-0.476188\pi$
$97$	1.47214	0.149473	0.0747364	+	0.997203i	$0.476188\pi$
$98$	0.618034	0.0624309
$99$	−6.23607	−0.626748
$100$	0	0
$101$	−19.1803	−1.90852	−0.954258	−	0.298986i	$-0.903352\pi$
$101$	−19.1803	−1.90852	−0.954258	+	0.298986i	$0.903352\pi$
$102$	−4.61803	−0.457254
$103$	−0.708204	−0.0697814	−0.0348907	−	0.999391i	$-0.511108\pi$
$103$	−0.708204	−0.0697814	−0.0348907	+	0.999391i	$0.511108\pi$
$104$	−2.23607	−0.219265
$105$	0	0
$106$	1.14590	0.111299
$107$	−10.2361	−0.989558	−0.494779	−	0.869019i	$-0.664751\pi$
$107$	−10.2361	−0.989558	−0.494779	+	0.869019i	$0.664751\pi$
$108$	3.61803	0.348145
$109$	−7.76393	−0.743650	−0.371825	−	0.928303i	$-0.621268\pi$
$109$	−7.76393	−0.743650	−0.371825	+	0.928303i	$0.621268\pi$
$110$	0	0
$111$	−30.0344	−2.85074
$112$	−1.85410	−0.175196
$113$	−13.2705	−1.24838	−0.624192	−	0.781271i	$-0.714572\pi$
$113$	−13.2705	−1.24838	−0.624192	+	0.781271i	$0.714572\pi$
$114$	1.61803	0.151543
$115$	0	0
$116$	−5.85410	−0.543540
$117$	3.85410	0.356312
$118$	7.56231	0.696167
$119$	−2.85410	−0.261635
$120$	0	0
$121$	−8.38197	−0.761997
$122$	3.67376	0.332607
$123$	−26.4164	−2.38189
$124$	17.0902	1.53474
$125$	0	0
$126$	−2.38197	−0.212202
$127$	−9.70820	−0.861464	−0.430732	−	0.902480i	$-0.641745\pi$
$127$	−9.70820	−0.861464	−0.430732	+	0.902480i	$0.641745\pi$
$128$	−11.3820	−1.00603
$129$	−1.23607	−0.108830
$130$	0	0
$131$	14.5623	1.27231	0.636157	−	0.771559i	$-0.280523\pi$
$131$	14.5623	1.27231	0.636157	+	0.771559i	$0.280523\pi$
$132$	−6.85410	−0.596573
$133$	1.00000	0.0867110
$134$	−8.23607	−0.711488
$135$	0	0
$136$	−6.38197	−0.547249
$137$	10.9443	0.935032	0.467516	−	0.883985i	$-0.345149\pi$
$137$	10.9443	0.935032	0.467516	+	0.883985i	$0.345149\pi$
$138$	5.61803	0.478239
$139$	−0.527864	−0.0447728	−0.0223864	−	0.999749i	$-0.507126\pi$
$139$	−0.527864	−0.0447728	−0.0223864	+	0.999749i	$0.507126\pi$
$140$	0	0
$141$	−3.85410	−0.324574
$142$	−2.90983	−0.244188
$143$	−1.61803	−0.135307
$144$	7.14590	0.595492
$145$	0	0
$146$	−2.67376	−0.221282
$147$	−2.61803	−0.215932
$148$	−18.5623	−1.52581
$149$	−19.4721	−1.59522	−0.797610	−	0.603174i	$-0.793903\pi$
$149$	−19.4721	−1.59522	−0.797610	+	0.603174i	$0.793903\pi$
$150$	0	0
$151$	19.0344	1.54900	0.774500	−	0.632573i	$-0.218001\pi$
$151$	19.0344	1.54900	0.774500	+	0.632573i	$0.218001\pi$
$152$	2.23607	0.181369
$153$	11.0000	0.889297
$154$	1.00000	0.0805823
$155$	0	0
$156$	4.23607	0.339157
$157$	−3.32624	−0.265463	−0.132731	−	0.991152i	$-0.542375\pi$
$157$	−3.32624	−0.265463	−0.132731	+	0.991152i	$0.542375\pi$
$158$	2.76393	0.219887
$159$	−4.85410	−0.384955
$160$	0	0
$161$	3.47214	0.273643
$162$	−3.52786	−0.277175
$163$	20.7984	1.62905	0.814527	−	0.580125i	$-0.196996\pi$
$163$	20.7984	1.62905	0.814527	+	0.580125i	$0.196996\pi$
$164$	−16.3262	−1.27486
$165$	0	0
$166$	−6.09017	−0.472689
$167$	1.47214	0.113917	0.0569587	−	0.998377i	$-0.481860\pi$
$167$	1.47214	0.113917	0.0569587	+	0.998377i	$0.481860\pi$
$168$	−5.85410	−0.451654
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−3.85410	−0.294731
$172$	−0.763932	−0.0582493
$173$	−16.7639	−1.27454	−0.637269	−	0.770641i	$-0.719936\pi$
$173$	−16.7639	−1.27454	−0.637269	+	0.770641i	$0.719936\pi$
$174$	−5.85410	−0.443798
$175$	0	0
$176$	−3.00000	−0.226134
$177$	−32.0344	−2.40786
$178$	4.47214	0.335201
$179$	−18.7426	−1.40089	−0.700446	−	0.713706i	$-0.747015\pi$
$179$	−18.7426	−1.40089	−0.700446	+	0.713706i	$0.747015\pi$
$180$	0	0
$181$	−16.0902	−1.19597	−0.597986	−	0.801506i	$-0.704032\pi$
$181$	−16.0902	−1.19597	−0.597986	+	0.801506i	$0.704032\pi$
$182$	−0.618034	−0.0458117
$183$	−15.5623	−1.15040
$184$	7.76393	0.572365
$185$	0	0
$186$	17.0902	1.25311
$187$	−4.61803	−0.337704
$188$	−2.38197	−0.173723
$189$	2.23607	0.162650
$190$	0	0
$191$	14.0344	1.01550	0.507748	−	0.861505i	$-0.330478\pi$
$191$	14.0344	1.01550	0.507748	+	0.861505i	$0.330478\pi$
$192$	0.618034	0.0446028
$193$	−5.90983	−0.425399	−0.212699	−	0.977118i	$-0.568226\pi$
$193$	−5.90983	−0.425399	−0.212699	+	0.977118i	$0.568226\pi$
$194$	0.909830	0.0653220
$195$	0	0
$196$	−1.61803	−0.115574
$197$	19.5623	1.39376	0.696878	−	0.717189i	$-0.254572\pi$
$197$	19.5623	1.39376	0.696878	+	0.717189i	$0.254572\pi$
$198$	−3.85410	−0.273899
$199$	10.5279	0.746300	0.373150	−	0.927771i	$-0.378278\pi$
$199$	10.5279	0.746300	0.373150	+	0.927771i	$0.378278\pi$
$200$	0	0
$201$	34.8885	2.46085
$202$	−11.8541	−0.834052
$203$	−3.61803	−0.253936
$204$	12.0902	0.846481
$205$	0	0
$206$	−0.437694	−0.0304956
$207$	−13.3820	−0.930111
$208$	1.85410	0.128559
$209$	1.61803	0.111922
$210$	0	0
$211$	1.67376	0.115227	0.0576133	−	0.998339i	$-0.481651\pi$
$211$	1.67376	0.115227	0.0576133	+	0.998339i	$0.481651\pi$
$212$	−3.00000	−0.206041
$213$	12.3262	0.844580
$214$	−6.32624	−0.432453
$215$	0	0
$216$	5.00000	0.340207
$217$	10.5623	0.717016
$218$	−4.79837	−0.324987
$219$	11.3262	0.765356
$220$	0	0
$221$	2.85410	0.191988
$222$	−18.5623	−1.24582
$223$	−2.41641	−0.161815	−0.0809073	−	0.996722i	$-0.525782\pi$
$223$	−2.41641	−0.161815	−0.0809073	+	0.996722i	$0.525782\pi$
$224$	−5.61803	−0.375371
$225$	0	0
$226$	−8.20163	−0.545564
$227$	−5.43769	−0.360912	−0.180456	−	0.983583i	$-0.557757\pi$
$227$	−5.43769	−0.360912	−0.180456	+	0.983583i	$0.557757\pi$
$228$	−4.23607	−0.280540
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−4.23607	−0.278713
$232$	−8.09017	−0.531146
$233$	−6.56231	−0.429911	−0.214955	−	0.976624i	$-0.568961\pi$
$233$	−6.56231	−0.429911	−0.214955	+	0.976624i	$0.568961\pi$
$234$	2.38197	0.155714
$235$	0	0
$236$	−19.7984	−1.28876
$237$	−11.7082	−0.760530
$238$	−1.76393	−0.114339
$239$	−25.0000	−1.61712	−0.808558	−	0.588417i	$-0.799751\pi$
$239$	−25.0000	−1.61712	−0.808558	+	0.588417i	$0.799751\pi$
$240$	0	0
$241$	−8.65248	−0.557355	−0.278677	−	0.960385i	$-0.589896\pi$
$241$	−8.65248	−0.557355	−0.278677	+	0.960385i	$0.589896\pi$
$242$	−5.18034	−0.333005
$243$	21.6525	1.38901
$244$	−9.61803	−0.615732
$245$	0	0
$246$	−16.3262	−1.04092
$247$	−1.00000	−0.0636285
$248$	23.6180	1.49975
$249$	25.7984	1.63491
$250$	0	0
$251$	26.2705	1.65818	0.829090	−	0.559115i	$-0.188859\pi$
$251$	26.2705	1.65818	0.829090	+	0.559115i	$0.188859\pi$
$252$	6.23607	0.392835
$253$	5.61803	0.353203
$254$	−6.00000	−0.376473
$255$	0	0
$256$	−6.56231	−0.410144
$257$	2.32624	0.145107	0.0725534	−	0.997365i	$-0.476885\pi$
$257$	2.32624	0.145107	0.0725534	+	0.997365i	$0.476885\pi$
$258$	−0.763932	−0.0475603
$259$	−11.4721	−0.712844
$260$	0	0
$261$	13.9443	0.863129
$262$	9.00000	0.556022
$263$	3.56231	0.219661	0.109831	−	0.993950i	$-0.464969\pi$
$263$	3.56231	0.219661	0.109831	+	0.993950i	$0.464969\pi$
$264$	−9.47214	−0.582970
$265$	0	0
$266$	0.618034	0.0378941
$267$	−18.9443	−1.15937
$268$	21.5623	1.31713
$269$	20.9787	1.27909	0.639547	−	0.768752i	$-0.279122\pi$
$269$	20.9787	1.27909	0.639547	+	0.768752i	$0.279122\pi$
$270$	0	0
$271$	−5.43769	−0.330316	−0.165158	−	0.986267i	$-0.552813\pi$
$271$	−5.43769	−0.330316	−0.165158	+	0.986267i	$0.552813\pi$
$272$	5.29180	0.320862
$273$	2.61803	0.158451
$274$	6.76393	0.408624
$275$	0	0
$276$	−14.7082	−0.885330
$277$	−23.1246	−1.38942	−0.694712	−	0.719288i	$-0.744468\pi$
$277$	−23.1246	−1.38942	−0.694712	+	0.719288i	$0.744468\pi$
$278$	−0.326238	−0.0195665
$279$	−40.7082	−2.43714
$280$	0	0
$281$	−24.7082	−1.47397	−0.736984	−	0.675910i	$-0.763751\pi$
$281$	−24.7082	−1.47397	−0.736984	+	0.675910i	$0.763751\pi$
$282$	−2.38197	−0.141844
$283$	−27.0902	−1.61034	−0.805172	−	0.593042i	$-0.797927\pi$
$283$	−27.0902	−1.61034	−0.805172	+	0.593042i	$0.797927\pi$
$284$	7.61803	0.452047
$285$	0	0
$286$	−1.00000	−0.0591312
$287$	−10.0902	−0.595604
$288$	21.6525	1.27588
$289$	−8.85410	−0.520830
$290$	0	0
$291$	−3.85410	−0.225931
$292$	7.00000	0.409644
$293$	−21.7639	−1.27146	−0.635731	−	0.771910i	$-0.719301\pi$
$293$	−21.7639	−1.27146	−0.635731	+	0.771910i	$0.719301\pi$
$294$	−1.61803	−0.0943657
$295$	0	0
$296$	−25.6525	−1.49102
$297$	3.61803	0.209940
$298$	−12.0344	−0.697136
$299$	−3.47214	−0.200799
$300$	0	0
$301$	−0.472136	−0.0272135
$302$	11.7639	0.676938
$303$	50.2148	2.88476
$304$	−1.85410	−0.106340
$305$	0	0
$306$	6.79837	0.388637
$307$	10.7426	0.613115	0.306558	−	0.951852i	$-0.400823\pi$
$307$	10.7426	0.613115	0.306558	+	0.951852i	$0.400823\pi$
$308$	−2.61803	−0.149176
$309$	1.85410	0.105476
$310$	0	0
$311$	22.4508	1.27307	0.636535	−	0.771247i	$-0.280367\pi$
$311$	22.4508	1.27307	0.636535	+	0.771247i	$0.280367\pi$
$312$	5.85410	0.331423
$313$	25.5967	1.44681	0.723407	−	0.690422i	$-0.242575\pi$
$313$	25.5967	1.44681	0.723407	+	0.690422i	$0.242575\pi$
$314$	−2.05573	−0.116011
$315$	0	0
$316$	−7.23607	−0.407061
$317$	5.41641	0.304216	0.152108	−	0.988364i	$-0.451394\pi$
$317$	5.41641	0.304216	0.152108	+	0.988364i	$0.451394\pi$
$318$	−3.00000	−0.168232
$319$	−5.85410	−0.327767
$320$	0	0
$321$	26.7984	1.49574
$322$	2.14590	0.119586
$323$	−2.85410	−0.158806
$324$	9.23607	0.513115
$325$	0	0
$326$	12.8541	0.711923
$327$	20.3262	1.12404
$328$	−22.5623	−1.24579
$329$	−1.47214	−0.0811615
$330$	0	0
$331$	7.85410	0.431700	0.215850	−	0.976426i	$-0.430748\pi$
$331$	7.85410	0.431700	0.215850	+	0.976426i	$0.430748\pi$
$332$	15.9443	0.875056
$333$	44.2148	2.42296
$334$	0.909830	0.0497837
$335$	0	0
$336$	4.85410	0.264813
$337$	−17.7984	−0.969539	−0.484770	−	0.874642i	$-0.661097\pi$
$337$	−17.7984	−0.969539	−0.484770	+	0.874642i	$0.661097\pi$
$338$	−7.41641	−0.403399
$339$	34.7426	1.88696
$340$	0	0
$341$	17.0902	0.925485
$342$	−2.38197	−0.128802
$343$	−1.00000	−0.0539949
$344$	−1.05573	−0.0569210
$345$	0	0
$346$	−10.3607	−0.556994
$347$	−22.7984	−1.22388	−0.611940	−	0.790904i	$-0.709611\pi$
$347$	−22.7984	−1.22388	−0.611940	+	0.790904i	$0.709611\pi$
$348$	15.3262	0.821573
$349$	−10.9787	−0.587677	−0.293839	−	0.955855i	$-0.594933\pi$
$349$	−10.9787	−0.587677	−0.293839	+	0.955855i	$0.594933\pi$
$350$	0	0
$351$	−2.23607	−0.119352
$352$	−9.09017	−0.484508
$353$	20.2705	1.07889	0.539445	−	0.842021i	$-0.318634\pi$
$353$	20.2705	1.07889	0.539445	+	0.842021i	$0.318634\pi$
$354$	−19.7984	−1.05227
$355$	0	0
$356$	−11.7082	−0.620534
$357$	7.47214	0.395467
$358$	−11.5836	−0.612212
$359$	−22.5623	−1.19079	−0.595396	−	0.803432i	$-0.703005\pi$
$359$	−22.5623	−1.19079	−0.595396	+	0.803432i	$0.703005\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−9.94427	−0.522659
$363$	21.9443	1.15178
$364$	1.61803	0.0848080
$365$	0	0
$366$	−9.61803	−0.502743
$367$	14.2361	0.743117	0.371558	−	0.928410i	$-0.378824\pi$
$367$	14.2361	0.743117	0.371558	+	0.928410i	$0.378824\pi$
$368$	−6.43769	−0.335588
$369$	38.8885	2.02446
$370$	0	0
$371$	−1.85410	−0.0962602
$372$	−44.7426	−2.31980
$373$	−15.3820	−0.796448	−0.398224	−	0.917288i	$-0.630373\pi$
$373$	−15.3820	−0.796448	−0.398224	+	0.917288i	$0.630373\pi$
$374$	−2.85410	−0.147582
$375$	0	0
$376$	−3.29180	−0.169761
$377$	3.61803	0.186338
$378$	1.38197	0.0710807
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	0	0
$381$	25.4164	1.30212
$382$	8.67376	0.443788
$383$	12.7082	0.649359	0.324679	−	0.945824i	$-0.394744\pi$
$383$	12.7082	0.649359	0.324679	+	0.945824i	$0.394744\pi$
$384$	29.7984	1.52064
$385$	0	0
$386$	−3.65248	−0.185906
$387$	1.81966	0.0924985
$388$	−2.38197	−0.120926
$389$	−17.4377	−0.884126	−0.442063	−	0.896984i	$-0.645753\pi$
$389$	−17.4377	−0.884126	−0.442063	+	0.896984i	$0.645753\pi$
$390$	0	0
$391$	−9.90983	−0.501162
$392$	−2.23607	−0.112938
$393$	−38.1246	−1.92313
$394$	12.0902	0.609094
$395$	0	0
$396$	10.0902	0.507050
$397$	4.76393	0.239095	0.119547	−	0.992828i	$-0.461856\pi$
$397$	4.76393	0.239095	0.119547	+	0.992828i	$0.461856\pi$
$398$	6.50658	0.326145
$399$	−2.61803	−0.131066
$400$	0	0
$401$	−23.9787	−1.19744	−0.598720	−	0.800958i	$-0.704324\pi$
$401$	−23.9787	−1.19744	−0.598720	+	0.800958i	$0.704324\pi$
$402$	21.5623	1.07543
$403$	−10.5623	−0.526146
$404$	31.0344	1.54402
$405$	0	0
$406$	−2.23607	−0.110974
$407$	−18.5623	−0.920099
$408$	16.7082	0.827179
$409$	28.2148	1.39513	0.697566	−	0.716521i	$-0.254267\pi$
$409$	28.2148	1.39513	0.697566	+	0.716521i	$0.254267\pi$
$410$	0	0
$411$	−28.6525	−1.41332
$412$	1.14590	0.0564543
$413$	−12.2361	−0.602098
$414$	−8.27051	−0.406473
$415$	0	0
$416$	5.61803	0.275447
$417$	1.38197	0.0676752
$418$	1.00000	0.0489116
$419$	0.527864	0.0257878	0.0128939	−	0.999917i	$-0.495896\pi$
$419$	0.527864	0.0257878	0.0128939	+	0.999917i	$0.495896\pi$
$420$	0	0
$421$	30.4164	1.48241	0.741203	−	0.671281i	$-0.234256\pi$
$421$	30.4164	1.48241	0.741203	+	0.671281i	$0.234256\pi$
$422$	1.03444	0.0503558
$423$	5.67376	0.275868
$424$	−4.14590	−0.201343
$425$	0	0
$426$	7.61803	0.369095
$427$	−5.94427	−0.287663
$428$	16.5623	0.800569
$429$	4.23607	0.204519
$430$	0	0
$431$	−23.5279	−1.13330	−0.566649	−	0.823960i	$-0.691760\pi$
$431$	−23.5279	−1.13330	−0.566649	+	0.823960i	$0.691760\pi$
$432$	−4.14590	−0.199470
$433$	−24.1246	−1.15935	−0.579677	−	0.814846i	$-0.696821\pi$
$433$	−24.1246	−1.15935	−0.579677	+	0.814846i	$0.696821\pi$
$434$	6.52786	0.313348
$435$	0	0
$436$	12.5623	0.601625
$437$	3.47214	0.166095
$438$	7.00000	0.334473
$439$	−23.4164	−1.11760	−0.558802	−	0.829301i	$-0.688739\pi$
$439$	−23.4164	−1.11760	−0.558802	+	0.829301i	$0.688739\pi$
$440$	0	0
$441$	3.85410	0.183529
$442$	1.76393	0.0839017
$443$	−10.9098	−0.518342	−0.259171	−	0.965831i	$-0.583449\pi$
$443$	−10.9098	−0.518342	−0.259171	+	0.965831i	$0.583449\pi$
$444$	48.5967	2.30630
$445$	0	0
$446$	−1.49342	−0.0707156
$447$	50.9787	2.41121
$448$	0.236068	0.0111532
$449$	−11.3820	−0.537148	−0.268574	−	0.963259i	$-0.586552\pi$
$449$	−11.3820	−0.537148	−0.268574	+	0.963259i	$0.586552\pi$
$450$	0	0
$451$	−16.3262	−0.768773
$452$	21.4721	1.00996
$453$	−49.8328	−2.34135
$454$	−3.36068	−0.157725
$455$	0	0
$456$	−5.85410	−0.274143
$457$	−14.9098	−0.697452	−0.348726	−	0.937225i	$-0.613386\pi$
$457$	−14.9098	−0.697452	−0.348726	+	0.937225i	$0.613386\pi$
$458$	6.18034	0.288788
$459$	−6.38197	−0.297885
$460$	0	0
$461$	26.1459	1.21774	0.608868	−	0.793272i	$-0.291624\pi$
$461$	26.1459	1.21774	0.608868	+	0.793272i	$0.291624\pi$
$462$	−2.61803	−0.121802
$463$	35.0689	1.62979	0.814895	−	0.579609i	$-0.196795\pi$
$463$	35.0689	1.62979	0.814895	+	0.579609i	$0.196795\pi$
$464$	6.70820	0.311421
$465$	0	0
$466$	−4.05573	−0.187878
$467$	8.90983	0.412298	0.206149	−	0.978521i	$-0.433907\pi$
$467$	8.90983	0.412298	0.206149	+	0.978521i	$0.433907\pi$
$468$	−6.23607	−0.288262
$469$	13.3262	0.615348
$470$	0	0
$471$	8.70820	0.401253
$472$	−27.3607	−1.25938
$473$	−0.763932	−0.0351256
$474$	−7.23607	−0.332364
$475$	0	0
$476$	4.61803	0.211667
$477$	7.14590	0.327188
$478$	−15.4508	−0.706705
$479$	9.79837	0.447699	0.223850	−	0.974624i	$-0.428138\pi$
$479$	9.79837	0.447699	0.223850	+	0.974624i	$0.428138\pi$
$480$	0	0
$481$	11.4721	0.523084
$482$	−5.34752	−0.243573
$483$	−9.09017	−0.413617
$484$	13.5623	0.616468
$485$	0	0
$486$	13.3820	0.607018
$487$	14.2361	0.645098	0.322549	−	0.946553i	$-0.395460\pi$
$487$	14.2361	0.645098	0.322549	+	0.946553i	$0.395460\pi$
$488$	−13.2918	−0.601691
$489$	−54.4508	−2.46235
$490$	0	0
$491$	17.5279	0.791021	0.395511	−	0.918461i	$-0.370568\pi$
$491$	17.5279	0.791021	0.395511	+	0.918461i	$0.370568\pi$
$492$	42.7426	1.92699
$493$	10.3262	0.465070
$494$	−0.618034	−0.0278067
$495$	0	0
$496$	−19.5836	−0.879329
$497$	4.70820	0.211192
$498$	15.9443	0.714480
$499$	−28.6180	−1.28112	−0.640560	−	0.767908i	$-0.721298\pi$
$499$	−28.6180	−1.28112	−0.640560	+	0.767908i	$0.721298\pi$
$500$	0	0
$501$	−3.85410	−0.172189
$502$	16.2361	0.724651
$503$	4.94427	0.220454	0.110227	−	0.993906i	$-0.464842\pi$
$503$	4.94427	0.220454	0.110227	+	0.993906i	$0.464842\pi$
$504$	8.61803	0.383878
$505$	0	0
$506$	3.47214	0.154355
$507$	31.4164	1.39525
$508$	15.7082	0.696939
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	4.32624	0.191381
$512$	18.7082	0.826794
$513$	2.23607	0.0987248
$514$	1.43769	0.0634140
$515$	0	0
$516$	2.00000	0.0880451
$517$	−2.38197	−0.104759
$518$	−7.09017	−0.311524
$519$	43.8885	1.92649
$520$	0	0
$521$	−9.18034	−0.402198	−0.201099	−	0.979571i	$-0.564451\pi$
$521$	−9.18034	−0.402198	−0.201099	+	0.979571i	$0.564451\pi$
$522$	8.61803	0.377201
$523$	3.11146	0.136054	0.0680272	−	0.997683i	$-0.478330\pi$
$523$	3.11146	0.136054	0.0680272	+	0.997683i	$0.478330\pi$
$524$	−23.5623	−1.02932
$525$	0	0
$526$	2.20163	0.0959955
$527$	−30.1459	−1.31318
$528$	7.85410	0.341806
$529$	−10.9443	−0.475838
$530$	0	0
$531$	47.1591	2.04653
$532$	−1.61803	−0.0701507
$533$	10.0902	0.437054
$534$	−11.7082	−0.506664
$535$	0	0
$536$	29.7984	1.28709
$537$	49.0689	2.11748
$538$	12.9656	0.558985
$539$	−1.61803	−0.0696937
$540$	0	0
$541$	−35.8885	−1.54297	−0.771485	−	0.636248i	$-0.780485\pi$
$541$	−35.8885	−1.54297	−0.771485	+	0.636248i	$0.780485\pi$
$542$	−3.36068	−0.144354
$543$	42.1246	1.80774
$544$	16.0344	0.687471
$545$	0	0
$546$	1.61803	0.0692455
$547$	13.3820	0.572172	0.286086	−	0.958204i	$-0.407646\pi$
$547$	13.3820	0.572172	0.286086	+	0.958204i	$0.407646\pi$
$548$	−17.7082	−0.756457
$549$	22.9098	0.977768
$550$	0	0
$551$	−3.61803	−0.154133
$552$	−20.3262	−0.865142
$553$	−4.47214	−0.190175
$554$	−14.2918	−0.607200
$555$	0	0
$556$	0.854102	0.0362220
$557$	12.2016	0.516999	0.258500	−	0.966011i	$-0.416772\pi$
$557$	12.2016	0.516999	0.258500	+	0.966011i	$0.416772\pi$
$558$	−25.1591	−1.06507
$559$	0.472136	0.0199692
$560$	0	0
$561$	12.0902	0.510447
$562$	−15.2705	−0.644148
$563$	−11.7639	−0.495791	−0.247895	−	0.968787i	$-0.579739\pi$
$563$	−11.7639	−0.495791	−0.247895	+	0.968787i	$0.579739\pi$
$564$	6.23607	0.262586
$565$	0	0
$566$	−16.7426	−0.703746
$567$	5.70820	0.239722
$568$	10.5279	0.441739
$569$	8.41641	0.352834	0.176417	−	0.984316i	$-0.443549\pi$
$569$	8.41641	0.352834	0.176417	+	0.984316i	$0.443549\pi$
$570$	0	0
$571$	−3.65248	−0.152851	−0.0764257	−	0.997075i	$-0.524351\pi$
$571$	−3.65248	−0.152851	−0.0764257	+	0.997075i	$0.524351\pi$
$572$	2.61803	0.109466
$573$	−36.7426	−1.53495
$574$	−6.23607	−0.260288
$575$	0	0
$576$	−0.909830	−0.0379096
$577$	12.7295	0.529936	0.264968	−	0.964257i	$-0.414639\pi$
$577$	12.7295	0.529936	0.264968	+	0.964257i	$0.414639\pi$
$578$	−5.47214	−0.227611
$579$	15.4721	0.643000
$580$	0	0
$581$	9.85410	0.408817
$582$	−2.38197	−0.0987357
$583$	−3.00000	−0.124247
$584$	9.67376	0.400303
$585$	0	0
$586$	−13.4508	−0.555649
$587$	−38.0000	−1.56843	−0.784214	−	0.620491i	$-0.786934\pi$
$587$	−38.0000	−1.56843	−0.784214	+	0.620491i	$0.786934\pi$
$588$	4.23607	0.174692
$589$	10.5623	0.435212
$590$	0	0
$591$	−51.2148	−2.10669
$592$	21.2705	0.874213
$593$	17.1803	0.705512	0.352756	−	0.935715i	$-0.385245\pi$
$593$	17.1803	0.705512	0.352756	+	0.935715i	$0.385245\pi$
$594$	2.23607	0.0917470
$595$	0	0
$596$	31.5066	1.29056
$597$	−27.5623	−1.12805
$598$	−2.14590	−0.0877523
$599$	10.9787	0.448578	0.224289	−	0.974523i	$-0.427994\pi$
$599$	10.9787	0.448578	0.224289	+	0.974523i	$0.427994\pi$
$600$	0	0
$601$	14.4377	0.588926	0.294463	−	0.955663i	$-0.404859\pi$
$601$	14.4377	0.588926	0.294463	+	0.955663i	$0.404859\pi$
$602$	−0.291796	−0.0118927
$603$	−51.3607	−2.09157
$604$	−30.7984	−1.25317
$605$	0	0
$606$	31.0344	1.26069
$607$	14.2361	0.577824	0.288912	−	0.957356i	$-0.406706\pi$
$607$	14.2361	0.577824	0.288912	+	0.957356i	$0.406706\pi$
$608$	−5.61803	−0.227841
$609$	9.47214	0.383830
$610$	0	0
$611$	1.47214	0.0595562
$612$	−17.7984	−0.719457
$613$	0.798374	0.0322460	0.0161230	−	0.999870i	$-0.494868\pi$
$613$	0.798374	0.0322460	0.0161230	+	0.999870i	$0.494868\pi$
$614$	6.63932	0.267941
$615$	0	0
$616$	−3.61803	−0.145775
$617$	42.8541	1.72524	0.862621	−	0.505851i	$-0.168822\pi$
$617$	42.8541	1.72524	0.862621	+	0.505851i	$0.168822\pi$
$618$	1.14590	0.0460948
$619$	1.38197	0.0555459	0.0277730	−	0.999614i	$-0.491158\pi$
$619$	1.38197	0.0555459	0.0277730	+	0.999614i	$0.491158\pi$
$620$	0	0
$621$	7.76393	0.311556
$622$	13.8754	0.556352
$623$	−7.23607	−0.289907
$624$	−4.85410	−0.194320
$625$	0	0
$626$	15.8197	0.632281
$627$	−4.23607	−0.169172
$628$	5.38197	0.214764
$629$	32.7426	1.30553
$630$	0	0
$631$	23.1803	0.922795	0.461397	−	0.887194i	$-0.347348\pi$
$631$	23.1803	0.922795	0.461397	+	0.887194i	$0.347348\pi$
$632$	−10.0000	−0.397779
$633$	−4.38197	−0.174168
$634$	3.34752	0.132947
$635$	0	0
$636$	7.85410	0.311435
$637$	1.00000	0.0396214
$638$	−3.61803	−0.143239
$639$	−18.1459	−0.717841
$640$	0	0
$641$	12.2016	0.481935	0.240968	−	0.970533i	$-0.422535\pi$
$641$	12.2016	0.481935	0.240968	+	0.970533i	$0.422535\pi$
$642$	16.5623	0.653662
$643$	−19.6525	−0.775018	−0.387509	−	0.921866i	$-0.626664\pi$
$643$	−19.6525	−0.775018	−0.387509	+	0.921866i	$0.626664\pi$
$644$	−5.61803	−0.221382
$645$	0	0
$646$	−1.76393	−0.0694010
$647$	10.4164	0.409511	0.204756	−	0.978813i	$-0.434360\pi$
$647$	10.4164	0.409511	0.204756	+	0.978813i	$0.434360\pi$
$648$	12.7639	0.501415
$649$	−19.7984	−0.777154
$650$	0	0
$651$	−27.6525	−1.08379
$652$	−33.6525	−1.31793
$653$	−13.0689	−0.511425	−0.255712	−	0.966753i	$-0.582310\pi$
$653$	−13.0689	−0.511425	−0.255712	+	0.966753i	$0.582310\pi$
$654$	12.5623	0.491225
$655$	0	0
$656$	18.7082	0.730433
$657$	−16.6738	−0.650505
$658$	−0.909830	−0.0354689
$659$	−5.32624	−0.207481	−0.103740	−	0.994604i	$-0.533081\pi$
$659$	−5.32624	−0.207481	−0.103740	+	0.994604i	$0.533081\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	4.85410	0.188660
$663$	−7.47214	−0.290194
$664$	22.0344	0.855102
$665$	0	0
$666$	27.3262	1.05887
$667$	−12.5623	−0.486414
$668$	−2.38197	−0.0921610
$669$	6.32624	0.244586
$670$	0	0
$671$	−9.61803	−0.371300
$672$	14.7082	0.567381
$673$	22.5066	0.867565	0.433782	−	0.901018i	$-0.357179\pi$
$673$	22.5066	0.867565	0.433782	+	0.901018i	$0.357179\pi$
$674$	−11.0000	−0.423704
$675$	0	0
$676$	19.4164	0.746785
$677$	39.1591	1.50500	0.752502	−	0.658590i	$-0.228847\pi$
$677$	39.1591	1.50500	0.752502	+	0.658590i	$0.228847\pi$
$678$	21.4721	0.824632
$679$	−1.47214	−0.0564954
$680$	0	0
$681$	14.2361	0.545527
$682$	10.5623	0.404452
$683$	−50.7082	−1.94030	−0.970148	−	0.242515i	$-0.922028\pi$
$683$	−50.7082	−1.94030	−0.970148	+	0.242515i	$0.922028\pi$
$684$	6.23607	0.238442
$685$	0	0
$686$	−0.618034	−0.0235966
$687$	−26.1803	−0.998842
$688$	0.875388	0.0333739
$689$	1.85410	0.0706357
$690$	0	0
$691$	−46.5410	−1.77050	−0.885252	−	0.465112i	$-0.846014\pi$
$691$	−46.5410	−1.77050	−0.885252	+	0.465112i	$0.846014\pi$
$692$	27.1246	1.03112
$693$	6.23607	0.236889
$694$	−14.0902	−0.534856
$695$	0	0
$696$	21.1803	0.802839
$697$	28.7984	1.09082
$698$	−6.78522	−0.256824
$699$	17.1803	0.649820
$700$	0	0
$701$	−16.9443	−0.639976	−0.319988	−	0.947422i	$-0.603679\pi$
$701$	−16.9443	−0.639976	−0.319988	+	0.947422i	$0.603679\pi$
$702$	−1.38197	−0.0521589
$703$	−11.4721	−0.432680
$704$	0.381966	0.0143959
$705$	0	0
$706$	12.5279	0.471492
$707$	19.1803	0.721351
$708$	51.8328	1.94800
$709$	9.87539	0.370878	0.185439	−	0.982656i	$-0.440629\pi$
$709$	9.87539	0.370878	0.185439	+	0.982656i	$0.440629\pi$
$710$	0	0
$711$	17.2361	0.646403
$712$	−16.1803	−0.606384
$713$	36.6738	1.37344
$714$	4.61803	0.172826
$715$	0	0
$716$	30.3262	1.13334
$717$	65.4508	2.44431
$718$	−13.9443	−0.520396
$719$	−2.11146	−0.0787440	−0.0393720	−	0.999225i	$-0.512536\pi$
$719$	−2.11146	−0.0787440	−0.0393720	+	0.999225i	$0.512536\pi$
$720$	0	0
$721$	0.708204	0.0263749
$722$	0.618034	0.0230008
$723$	22.6525	0.842455
$724$	26.0344	0.967562
$725$	0	0
$726$	13.5623	0.503344
$727$	26.5967	0.986419	0.493209	−	0.869911i	$-0.335824\pi$
$727$	26.5967	0.986419	0.493209	+	0.869911i	$0.335824\pi$
$728$	2.23607	0.0828742
$729$	−39.5623	−1.46527
$730$	0	0
$731$	1.34752	0.0498400
$732$	25.1803	0.930692
$733$	−0.583592	−0.0215555	−0.0107777	−	0.999942i	$-0.503431\pi$
$733$	−0.583592	−0.0215555	−0.0107777	+	0.999942i	$0.503431\pi$
$734$	8.79837	0.324754
$735$	0	0
$736$	−19.5066	−0.719022
$737$	21.5623	0.794258
$738$	24.0344	0.884720
$739$	29.4721	1.08415	0.542075	−	0.840330i	$-0.317639\pi$
$739$	29.4721	1.08415	0.542075	+	0.840330i	$0.317639\pi$
$740$	0	0
$741$	2.61803	0.0961759
$742$	−1.14590	−0.0420672
$743$	−39.6525	−1.45471	−0.727354	−	0.686262i	$-0.759250\pi$
$743$	−39.6525	−1.45471	−0.727354	+	0.686262i	$0.759250\pi$
$744$	−61.8328	−2.26690
$745$	0	0
$746$	−9.50658	−0.348061
$747$	−37.9787	−1.38957
$748$	7.47214	0.273208
$749$	10.2361	0.374018
$750$	0	0
$751$	19.5623	0.713839	0.356919	−	0.934135i	$-0.383827\pi$
$751$	19.5623	0.713839	0.356919	+	0.934135i	$0.383827\pi$
$752$	2.72949	0.0995343
$753$	−68.7771	−2.50638
$754$	2.23607	0.0814328
$755$	0	0
$756$	−3.61803	−0.131587
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−9.27051	−0.336720
$759$	−14.7082	−0.533874
$760$	0	0
$761$	22.5279	0.816634	0.408317	−	0.912840i	$-0.366116\pi$
$761$	22.5279	0.816634	0.408317	+	0.912840i	$0.366116\pi$
$762$	15.7082	0.569048
$763$	7.76393	0.281073
$764$	−22.7082	−0.821554
$765$	0	0
$766$	7.85410	0.283780
$767$	12.2361	0.441819
$768$	17.1803	0.619942
$769$	3.41641	0.123199	0.0615994	−	0.998101i	$-0.480380\pi$
$769$	3.41641	0.123199	0.0615994	+	0.998101i	$0.480380\pi$
$770$	0	0
$771$	−6.09017	−0.219332
$772$	9.56231	0.344155
$773$	−42.5410	−1.53009	−0.765047	−	0.643974i	$-0.777284\pi$
$773$	−42.5410	−1.53009	−0.765047	+	0.643974i	$0.777284\pi$
$774$	1.12461	0.0404233
$775$	0	0
$776$	−3.29180	−0.118169
$777$	30.0344	1.07748
$778$	−10.7771	−0.386377
$779$	−10.0902	−0.361518
$780$	0	0
$781$	7.61803	0.272595
$782$	−6.12461	−0.219016
$783$	−8.09017	−0.289119
$784$	1.85410	0.0662179
$785$	0	0
$786$	−23.5623	−0.840440
$787$	−23.7771	−0.847562	−0.423781	−	0.905765i	$-0.639297\pi$
$787$	−23.7771	−0.847562	−0.423781	+	0.905765i	$0.639297\pi$
$788$	−31.6525	−1.12757
$789$	−9.32624	−0.332023
$790$	0	0
$791$	13.2705	0.471845
$792$	13.9443	0.495488
$793$	5.94427	0.211087
$794$	2.94427	0.104488
$795$	0	0
$796$	−17.0344	−0.603770
$797$	−38.8541	−1.37628	−0.688141	−	0.725577i	$-0.741573\pi$
$797$	−38.8541	−1.37628	−0.688141	+	0.725577i	$0.741573\pi$
$798$	−1.61803	−0.0572778
$799$	4.20163	0.148643
$800$	0	0
$801$	27.8885	0.985393
$802$	−14.8197	−0.523300
$803$	7.00000	0.247025
$804$	−56.4508	−1.99087
$805$	0	0
$806$	−6.52786	−0.229934
$807$	−54.9230	−1.93338
$808$	42.8885	1.50881
$809$	−12.2361	−0.430197	−0.215099	−	0.976592i	$-0.569007\pi$
$809$	−12.2361	−0.430197	−0.215099	+	0.976592i	$0.569007\pi$
$810$	0	0
$811$	−38.0000	−1.33436	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000	−1.33436	−0.667180	+	0.744896i	$0.732499\pi$
$812$	5.85410	0.205439
$813$	14.2361	0.499281
$814$	−11.4721	−0.402098
$815$	0	0
$816$	−13.8541	−0.484991
$817$	−0.472136	−0.0165179
$818$	17.4377	0.609695
$819$	−3.85410	−0.134673
$820$	0	0
$821$	29.8885	1.04312	0.521559	−	0.853215i	$-0.325351\pi$
$821$	29.8885	1.04312	0.521559	+	0.853215i	$0.325351\pi$
$822$	−17.7082	−0.617645
$823$	11.1246	0.387780	0.193890	−	0.981023i	$-0.437890\pi$
$823$	11.1246	0.387780	0.193890	+	0.981023i	$0.437890\pi$
$824$	1.58359	0.0551670
$825$	0	0
$826$	−7.56231	−0.263126
$827$	−40.2361	−1.39915	−0.699573	−	0.714562i	$-0.746626\pi$
$827$	−40.2361	−1.39915	−0.699573	+	0.714562i	$0.746626\pi$
$828$	21.6525	0.752476
$829$	−8.94427	−0.310647	−0.155324	−	0.987864i	$-0.549642\pi$
$829$	−8.94427	−0.310647	−0.155324	+	0.987864i	$0.549642\pi$
$830$	0	0
$831$	60.5410	2.10014
$832$	−0.236068	−0.00818418
$833$	2.85410	0.0988888
$834$	0.854102	0.0295751
$835$	0	0
$836$	−2.61803	−0.0905466
$837$	23.6180	0.816359
$838$	0.326238	0.0112697
$839$	−52.3607	−1.80769	−0.903846	−	0.427859i	$-0.859268\pi$
$839$	−52.3607	−1.80769	−0.903846	+	0.427859i	$0.859268\pi$
$840$	0	0
$841$	−15.9098	−0.548615
$842$	18.7984	0.647835
$843$	64.6869	2.22794
$844$	−2.70820	−0.0932202
$845$	0	0
$846$	3.50658	0.120559
$847$	8.38197	0.288008
$848$	3.43769	0.118051
$849$	70.9230	2.43407
$850$	0	0
$851$	−39.8328	−1.36545
$852$	−19.9443	−0.683279
$853$	−41.5623	−1.42307	−0.711533	−	0.702653i	$-0.751999\pi$
$853$	−41.5623	−1.42307	−0.711533	+	0.702653i	$0.751999\pi$
$854$	−3.67376	−0.125714
$855$	0	0
$856$	22.8885	0.782314
$857$	7.72949	0.264034	0.132017	−	0.991247i	$-0.457855\pi$
$857$	7.72949	0.264034	0.132017	+	0.991247i	$0.457855\pi$
$858$	2.61803	0.0893782
$859$	−9.79837	−0.334316	−0.167158	−	0.985930i	$-0.553459\pi$
$859$	−9.79837	−0.334316	−0.167158	+	0.985930i	$0.553459\pi$
$860$	0	0
$861$	26.4164	0.900269
$862$	−14.5410	−0.495269
$863$	−20.5066	−0.698052	−0.349026	−	0.937113i	$-0.613488\pi$
$863$	−20.5066	−0.698052	−0.349026	+	0.937113i	$0.613488\pi$
$864$	−12.5623	−0.427378
$865$	0	0
$866$	−14.9098	−0.506657
$867$	23.1803	0.787246
$868$	−17.0902	−0.580078
$869$	−7.23607	−0.245467
$870$	0	0
$871$	−13.3262	−0.451542
$872$	17.3607	0.587907
$873$	5.67376	0.192028
$874$	2.14590	0.0725861
$875$	0	0
$876$	−18.3262	−0.619186
$877$	35.0132	1.18231	0.591155	−	0.806558i	$-0.298672\pi$
$877$	35.0132	1.18231	0.591155	+	0.806558i	$0.298672\pi$
$878$	−14.4721	−0.488411
$879$	56.9787	1.92184
$880$	0	0
$881$	−1.09017	−0.0367288	−0.0183644	−	0.999831i	$-0.505846\pi$
$881$	−1.09017	−0.0367288	−0.0183644	+	0.999831i	$0.505846\pi$
$882$	2.38197	0.0802050
$883$	−4.52786	−0.152375	−0.0761874	−	0.997094i	$-0.524275\pi$
$883$	−4.52786	−0.152375	−0.0761874	+	0.997094i	$0.524275\pi$
$884$	−4.61803	−0.155321
$885$	0	0
$886$	−6.74265	−0.226524
$887$	15.9443	0.535356	0.267678	−	0.963508i	$-0.413744\pi$
$887$	15.9443	0.535356	0.267678	+	0.963508i	$0.413744\pi$
$888$	67.1591	2.25371
$889$	9.70820	0.325603
$890$	0	0
$891$	9.23607	0.309420
$892$	3.90983	0.130911
$893$	−1.47214	−0.0492632
$894$	31.5066	1.05374
$895$	0	0
$896$	11.3820	0.380245
$897$	9.09017	0.303512
$898$	−7.03444	−0.234742
$899$	−38.2148	−1.27453
$900$	0	0
$901$	5.29180	0.176295
$902$	−10.0902	−0.335966
$903$	1.23607	0.0411338
$904$	29.6738	0.986935
$905$	0	0
$906$	−30.7984	−1.02321
$907$	−7.47214	−0.248108	−0.124054	−	0.992275i	$-0.539590\pi$
$907$	−7.47214	−0.248108	−0.124054	+	0.992275i	$0.539590\pi$
$908$	8.79837	0.291984
$909$	−73.9230	−2.45187
$910$	0	0
$911$	22.0000	0.728893	0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000	0.728893	0.364446	+	0.931224i	$0.381258\pi$
$912$	4.85410	0.160735
$913$	15.9443	0.527678
$914$	−9.21478	−0.304798
$915$	0	0
$916$	−16.1803	−0.534613
$917$	−14.5623	−0.480890
$918$	−3.94427	−0.130180
$919$	−39.0689	−1.28876	−0.644382	−	0.764704i	$-0.722885\pi$
$919$	−39.0689	−1.28876	−0.644382	+	0.764704i	$0.722885\pi$
$920$	0	0
$921$	−28.1246	−0.926737
$922$	16.1591	0.532170
$923$	−4.70820	−0.154972
$924$	6.85410	0.225483
$925$	0	0
$926$	21.6738	0.712244
$927$	−2.72949	−0.0896482
$928$	20.3262	0.667241
$929$	−47.5623	−1.56047	−0.780234	−	0.625487i	$-0.784900\pi$
$929$	−47.5623	−1.56047	−0.780234	+	0.625487i	$0.784900\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	10.6180	0.347805
$933$	−58.7771	−1.92428
$934$	5.50658	0.180181
$935$	0	0
$936$	−8.61803	−0.281689
$937$	−12.9230	−0.422176	−0.211088	−	0.977467i	$-0.567701\pi$
$937$	−12.9230	−0.422176	−0.211088	+	0.977467i	$0.567701\pi$
$938$	8.23607	0.268917
$939$	−67.0132	−2.18689
$940$	0	0
$941$	−39.3050	−1.28130	−0.640652	−	0.767831i	$-0.721336\pi$
$941$	−39.3050	−1.28130	−0.640652	+	0.767831i	$0.721336\pi$
$942$	5.38197	0.175354
$943$	−35.0344	−1.14088
$944$	22.6869	0.738396
$945$	0	0
$946$	−0.472136	−0.0153505
$947$	−36.6180	−1.18993	−0.594963	−	0.803753i	$-0.702833\pi$
$947$	−36.6180	−1.18993	−0.594963	+	0.803753i	$0.702833\pi$
$948$	18.9443	0.615281
$949$	−4.32624	−0.140436
$950$	0	0
$951$	−14.1803	−0.459829
$952$	6.38197	0.206841
$953$	24.7426	0.801493	0.400746	−	0.916189i	$-0.368751\pi$
$953$	24.7426	0.801493	0.400746	+	0.916189i	$0.368751\pi$
$954$	4.41641	0.142986
$955$	0	0
$956$	40.4508	1.30827
$957$	15.3262	0.495427
$958$	6.05573	0.195652
$959$	−10.9443	−0.353409
$960$	0	0
$961$	80.5623	2.59878
$962$	7.09017	0.228596
$963$	−39.4508	−1.27129
$964$	14.0000	0.450910
$965$	0	0
$966$	−5.61803	−0.180757
$967$	−18.4508	−0.593339	−0.296670	−	0.954980i	$-0.595876\pi$
$967$	−18.4508	−0.593339	−0.296670	+	0.954980i	$0.595876\pi$
$968$	18.7426	0.602411
$969$	7.47214	0.240040
$970$	0	0
$971$	23.1803	0.743893	0.371946	−	0.928254i	$-0.378691\pi$
$971$	23.1803	0.743893	0.371946	+	0.928254i	$0.378691\pi$
$972$	−35.0344	−1.12373
$973$	0.527864	0.0169225
$974$	8.79837	0.281918
$975$	0	0
$976$	11.0213	0.352783
$977$	−37.5967	−1.20283	−0.601413	−	0.798938i	$-0.705395\pi$
$977$	−37.5967	−1.20283	−0.601413	+	0.798938i	$0.705395\pi$
$978$	−33.6525	−1.07609
$979$	−11.7082	−0.374196
$980$	0	0
$981$	−29.9230	−0.955367
$982$	10.8328	0.345689
$983$	−47.5410	−1.51632	−0.758162	−	0.652067i	$-0.773902\pi$
$983$	−47.5410	−1.51632	−0.758162	+	0.652067i	$0.773902\pi$
$984$	59.0689	1.88305
$985$	0	0
$986$	6.38197	0.203243
$987$	3.85410	0.122677
$988$	1.61803	0.0514765
$989$	−1.63932	−0.0521274
$990$	0	0
$991$	5.81966	0.184868	0.0924338	−	0.995719i	$-0.470535\pi$
$991$	5.81966	0.184868	0.0924338	+	0.995719i	$0.470535\pi$
$992$	−59.3394	−1.88403
$993$	−20.5623	−0.652525
$994$	2.90983	0.0922942
$995$	0	0
$996$	−41.7426	−1.32267
$997$	−23.4508	−0.742696	−0.371348	−	0.928494i	$-0.621104\pi$
$997$	−23.4508	−0.742696	−0.371348	+	0.928494i	$0.621104\pi$
$998$	−17.6869	−0.559870
$999$	−25.6525	−0.811608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3325.2.a.m.1.2		2
5.4	even	2		133.2.a.c.1.1	✓	2
15.14	odd	2		1197.2.a.g.1.2		2
20.19	odd	2		2128.2.a.c.1.1		2
35.4	even	6		931.2.f.d.324.2		4
35.9	even	6		931.2.f.d.704.2		4
35.19	odd	6		931.2.f.e.704.2		4
35.24	odd	6		931.2.f.e.324.2		4
35.34	odd	2		931.2.a.j.1.1		2
40.19	odd	2		8512.2.a.bb.1.2		2
40.29	even	2		8512.2.a.f.1.1		2
95.94	odd	2		2527.2.a.a.1.2		2
105.104	even	2		8379.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.c.1.1	✓	2	5.4	even	2
931.2.a.j.1.1		2	35.34	odd	2
931.2.f.d.324.2		4	35.4	even	6
931.2.f.d.704.2		4	35.9	even	6
931.2.f.e.324.2		4	35.24	odd	6
931.2.f.e.704.2		4	35.19	odd	6
1197.2.a.g.1.2		2	15.14	odd	2
2128.2.a.c.1.1		2	20.19	odd	2
2527.2.a.a.1.2		2	95.94	odd	2
3325.2.a.m.1.2		2	1.1	even	1	trivial
8379.2.a.w.1.2		2	105.104	even	2
8512.2.a.f.1.1		2	40.29	even	2
8512.2.a.bb.1.2		2	40.19	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3325 = 5^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3325.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -1.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} -2.61803 q^{3} -1.61803 q^{4} -1.61803 q^{6} -1.00000 q^{7} -2.23607 q^{8} +3.85410 q^{9} -1.61803 q^{11} +4.23607 q^{12} +1.00000 q^{13} -0.618034 q^{14} +1.85410 q^{16} +2.85410 q^{17} +2.38197 q^{18} -1.00000 q^{19} +2.61803 q^{21} -1.00000 q^{22} -3.47214 q^{23} +5.85410 q^{24} +0.618034 q^{26} -2.23607 q^{27} +1.61803 q^{28} +3.61803 q^{29} -10.5623 q^{31} +5.61803 q^{32} +4.23607 q^{33} +1.76393 q^{34} -6.23607 q^{36} +11.4721 q^{37} -0.618034 q^{38} -2.61803 q^{39} +10.0902 q^{41} +1.61803 q^{42} +0.472136 q^{43} +2.61803 q^{44} -2.14590 q^{46} +1.47214 q^{47} -4.85410 q^{48} +1.00000 q^{49} -7.47214 q^{51} -1.61803 q^{52} +1.85410 q^{53} -1.38197 q^{54} +2.23607 q^{56} +2.61803 q^{57} +2.23607 q^{58} +12.2361 q^{59} +5.94427 q^{61} -6.52786 q^{62} -3.85410 q^{63} -0.236068 q^{64} +2.61803 q^{66} -13.3262 q^{67} -4.61803 q^{68} +9.09017 q^{69} -4.70820 q^{71} -8.61803 q^{72} -4.32624 q^{73} +7.09017 q^{74} +1.61803 q^{76} +1.61803 q^{77} -1.61803 q^{78} +4.47214 q^{79} -5.70820 q^{81} +6.23607 q^{82} -9.85410 q^{83} -4.23607 q^{84} +0.291796 q^{86} -9.47214 q^{87} +3.61803 q^{88} +7.23607 q^{89} -1.00000 q^{91} +5.61803 q^{92} +27.6525 q^{93} +0.909830 q^{94} -14.7082 q^{96} +1.47214 q^{97} +0.618034 q^{98} -6.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 2 q^{7} + q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 2 * q^7 + q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} - q^{6} - 2 q^{7} + q^{9} - q^{11} + 4 q^{12} + 2 q^{13} + q^{14} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{21} - 2 q^{22} + 2 q^{23} + 5 q^{24} - q^{26} + q^{28} + 5 q^{29} - q^{31} + 9 q^{32} + 4 q^{33} + 8 q^{34} - 8 q^{36} + 14 q^{37} + q^{38} - 3 q^{39} + 9 q^{41} + q^{42} - 8 q^{43} + 3 q^{44} - 11 q^{46} - 6 q^{47} - 3 q^{48} + 2 q^{49} - 6 q^{51} - q^{52} - 3 q^{53} - 5 q^{54} + 3 q^{57} + 20 q^{59} - 6 q^{61} - 22 q^{62} - q^{63} + 4 q^{64} + 3 q^{66} - 11 q^{67} - 7 q^{68} + 7 q^{69} + 4 q^{71} - 15 q^{72} + 7 q^{73} + 3 q^{74} + q^{76} + q^{77} - q^{78} + 2 q^{81} + 8 q^{82} - 13 q^{83} - 4 q^{84} + 14 q^{86} - 10 q^{87} + 5 q^{88} + 10 q^{89} - 2 q^{91} + 9 q^{92} + 24 q^{93} + 13 q^{94} - 16 q^{96} - 6 q^{97} - q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - q^6 - 2 * q^7 + q^9 - q^11 + 4 * q^12 + 2 * q^13 + q^14 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^21 - 2 * q^22 + 2 * q^23 + 5 * q^24 - q^26 + q^28 + 5 * q^29 - q^31 + 9 * q^32 + 4 * q^33 + 8 * q^34 - 8 * q^36 + 14 * q^37 + q^38 - 3 * q^39 + 9 * q^41 + q^42 - 8 * q^43 + 3 * q^44 - 11 * q^46 - 6 * q^47 - 3 * q^48 + 2 * q^49 - 6 * q^51 - q^52 - 3 * q^53 - 5 * q^54 + 3 * q^57 + 20 * q^59 - 6 * q^61 - 22 * q^62 - q^63 + 4 * q^64 + 3 * q^66 - 11 * q^67 - 7 * q^68 + 7 * q^69 + 4 * q^71 - 15 * q^72 + 7 * q^73 + 3 * q^74 + q^76 + q^77 - q^78 + 2 * q^81 + 8 * q^82 - 13 * q^83 - 4 * q^84 + 14 * q^86 - 10 * q^87 + 5 * q^88 + 10 * q^89 - 2 * q^91 + 9 * q^92 + 24 * q^93 + 13 * q^94 - 16 * q^96 - 6 * q^97 - q^98 - 8 * q^99

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