LMFDB - Embedded newform 2415.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 87x^{6} - 143x^{5} - 196x^{4} + 244x^{3} + 160x^{2} - 89x - 12 $ x^10 - 2x^9 - 16x^8 + 30x^7 + 87x^6 - 143x^5 - 196x^4 + 244x^3 + 160x^2 - 89*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.78717$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78717 q^{2} +1.00000 q^{3} +1.19399 q^{4} +1.00000 q^{5} -1.78717 q^{6} +1.00000 q^{7} +1.44048 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.78717 q^{2} +1.00000 q^{3} +1.19399 q^{4} +1.00000 q^{5} -1.78717 q^{6} +1.00000 q^{7} +1.44048 q^{8} +1.00000 q^{9} -1.78717 q^{10} -5.76695 q^{11} +1.19399 q^{12} +4.94069 q^{13} -1.78717 q^{14} +1.00000 q^{15} -4.96237 q^{16} -1.91492 q^{17} -1.78717 q^{18} +5.05003 q^{19} +1.19399 q^{20} +1.00000 q^{21} +10.3066 q^{22} -1.00000 q^{23} +1.44048 q^{24} +1.00000 q^{25} -8.82988 q^{26} +1.00000 q^{27} +1.19399 q^{28} +5.57387 q^{29} -1.78717 q^{30} -9.61929 q^{31} +5.98766 q^{32} -5.76695 q^{33} +3.42229 q^{34} +1.00000 q^{35} +1.19399 q^{36} +2.49363 q^{37} -9.02529 q^{38} +4.94069 q^{39} +1.44048 q^{40} +4.66157 q^{41} -1.78717 q^{42} +6.84362 q^{43} -6.88570 q^{44} +1.00000 q^{45} +1.78717 q^{46} +2.41954 q^{47} -4.96237 q^{48} +1.00000 q^{49} -1.78717 q^{50} -1.91492 q^{51} +5.89915 q^{52} +5.06154 q^{53} -1.78717 q^{54} -5.76695 q^{55} +1.44048 q^{56} +5.05003 q^{57} -9.96147 q^{58} -4.43104 q^{59} +1.19399 q^{60} +9.83388 q^{61} +17.1913 q^{62} +1.00000 q^{63} -0.776261 q^{64} +4.94069 q^{65} +10.3066 q^{66} +3.52693 q^{67} -2.28639 q^{68} -1.00000 q^{69} -1.78717 q^{70} -8.09959 q^{71} +1.44048 q^{72} +7.86940 q^{73} -4.45655 q^{74} +1.00000 q^{75} +6.02970 q^{76} -5.76695 q^{77} -8.82988 q^{78} -4.46714 q^{79} -4.96237 q^{80} +1.00000 q^{81} -8.33104 q^{82} -2.52906 q^{83} +1.19399 q^{84} -1.91492 q^{85} -12.2307 q^{86} +5.57387 q^{87} -8.30716 q^{88} +0.000952551 q^{89} -1.78717 q^{90} +4.94069 q^{91} -1.19399 q^{92} -9.61929 q^{93} -4.32414 q^{94} +5.05003 q^{95} +5.98766 q^{96} -4.66488 q^{97} -1.78717 q^{98} -5.76695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 9 q^{11} + 16 q^{12} + 14 q^{13} + 2 q^{14} + 10 q^{15} + 20 q^{16} + 8 q^{17} + 2 q^{18} + 13 q^{19} + 16 q^{20} + 10 q^{21} - 10 q^{23} + 6 q^{24} + 10 q^{25} - 11 q^{26} + 10 q^{27} + 16 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{31} - 11 q^{32} + 9 q^{33} - 5 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 10 q^{38} + 14 q^{39} + 6 q^{40} - 5 q^{41} + 2 q^{42} + 4 q^{43} + 3 q^{44} + 10 q^{45} - 2 q^{46} + q^{47} + 20 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 14 q^{52} + 9 q^{53} + 2 q^{54} + 9 q^{55} + 6 q^{56} + 13 q^{57} - 28 q^{58} - 17 q^{59} + 16 q^{60} + 19 q^{61} - 28 q^{62} + 10 q^{63} + 24 q^{64} + 14 q^{65} + 8 q^{68} - 10 q^{69} + 2 q^{70} + 6 q^{72} + 6 q^{73} + 3 q^{74} + 10 q^{75} + 15 q^{76} + 9 q^{77} - 11 q^{78} + 32 q^{79} + 20 q^{80} + 10 q^{81} + 14 q^{82} - 2 q^{83} + 16 q^{84} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 3 q^{88} + 10 q^{89} + 2 q^{90} + 14 q^{91} - 16 q^{92} + 8 q^{93} - 10 q^{94} + 13 q^{95} - 11 q^{96} + 18 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 9 * q^11 + 16 * q^12 + 14 * q^13 + 2 * q^14 + 10 * q^15 + 20 * q^16 + 8 * q^17 + 2 * q^18 + 13 * q^19 + 16 * q^20 + 10 * q^21 - 10 * q^23 + 6 * q^24 + 10 * q^25 - 11 * q^26 + 10 * q^27 + 16 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^31 - 11 * q^32 + 9 * q^33 - 5 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 10 * q^38 + 14 * q^39 + 6 * q^40 - 5 * q^41 + 2 * q^42 + 4 * q^43 + 3 * q^44 + 10 * q^45 - 2 * q^46 + q^47 + 20 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 14 * q^52 + 9 * q^53 + 2 * q^54 + 9 * q^55 + 6 * q^56 + 13 * q^57 - 28 * q^58 - 17 * q^59 + 16 * q^60 + 19 * q^61 - 28 * q^62 + 10 * q^63 + 24 * q^64 + 14 * q^65 + 8 * q^68 - 10 * q^69 + 2 * q^70 + 6 * q^72 + 6 * q^73 + 3 * q^74 + 10 * q^75 + 15 * q^76 + 9 * q^77 - 11 * q^78 + 32 * q^79 + 20 * q^80 + 10 * q^81 + 14 * q^82 - 2 * q^83 + 16 * q^84 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 3 * q^88 + 10 * q^89 + 2 * q^90 + 14 * q^91 - 16 * q^92 + 8 * q^93 - 10 * q^94 + 13 * q^95 - 11 * q^96 + 18 * q^97 + 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.78717	−1.26372	−0.631862	−	0.775081i	$-0.717709\pi$
$2$	−1.78717	−1.26372	−0.631862	+	0.775081i	$0.717709\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.19399	0.596996
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.78717	−0.729611
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.44048	0.509285
$9$	1.00000	0.333333
$10$	−1.78717	−0.565154
$11$	−5.76695	−1.73880	−0.869401	−	0.494107i	$-0.835495\pi$
$11$	−5.76695	−1.73880	−0.869401	+	0.494107i	$0.835495\pi$
$12$	1.19399	0.344676
$13$	4.94069	1.37030	0.685151	−	0.728401i	$-0.259736\pi$
$13$	4.94069	1.37030	0.685151	+	0.728401i	$0.259736\pi$
$14$	−1.78717	−0.477642
$15$	1.00000	0.258199
$16$	−4.96237	−1.24059
$17$	−1.91492	−0.464435	−0.232218	−	0.972664i	$-0.574598\pi$
$17$	−1.91492	−0.464435	−0.232218	+	0.972664i	$0.574598\pi$
$18$	−1.78717	−0.421241
$19$	5.05003	1.15856	0.579279	−	0.815130i	$-0.303334\pi$
$19$	5.05003	1.15856	0.579279	+	0.815130i	$0.303334\pi$
$20$	1.19399	0.266985
$21$	1.00000	0.218218
$22$	10.3066	2.19736
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.44048	0.294036
$25$	1.00000	0.200000
$26$	−8.82988	−1.73168
$27$	1.00000	0.192450
$28$	1.19399	0.225643
$29$	5.57387	1.03504	0.517521	−	0.855671i	$-0.326855\pi$
$29$	5.57387	1.03504	0.517521	+	0.855671i	$0.326855\pi$
$30$	−1.78717	−0.326292
$31$	−9.61929	−1.72768	−0.863838	−	0.503771i	$-0.831946\pi$
$31$	−9.61929	−1.72768	−0.863838	+	0.503771i	$0.831946\pi$
$32$	5.98766	1.05848
$33$	−5.76695	−1.00390
$34$	3.42229	0.586918
$35$	1.00000	0.169031
$36$	1.19399	0.198999
$37$	2.49363	0.409950	0.204975	−	0.978767i	$-0.434289\pi$
$37$	2.49363	0.409950	0.204975	+	0.978767i	$0.434289\pi$
$38$	−9.02529	−1.46410
$39$	4.94069	0.791144
$40$	1.44048	0.227759
$41$	4.66157	0.728015	0.364007	−	0.931396i	$-0.381408\pi$
$41$	4.66157	0.728015	0.364007	+	0.931396i	$0.381408\pi$
$42$	−1.78717	−0.275767
$43$	6.84362	1.04364	0.521821	−	0.853055i	$-0.325253\pi$
$43$	6.84362	1.04364	0.521821	+	0.853055i	$0.325253\pi$
$44$	−6.88570	−1.03806
$45$	1.00000	0.149071
$46$	1.78717	0.263504
$47$	2.41954	0.352926	0.176463	−	0.984307i	$-0.443534\pi$
$47$	2.41954	0.352926	0.176463	+	0.984307i	$0.443534\pi$
$48$	−4.96237	−0.716256
$49$	1.00000	0.142857
$50$	−1.78717	−0.252745
$51$	−1.91492	−0.268142
$52$	5.89915	0.818065
$53$	5.06154	0.695256	0.347628	−	0.937633i	$-0.386987\pi$
$53$	5.06154	0.695256	0.347628	+	0.937633i	$0.386987\pi$
$54$	−1.78717	−0.243204
$55$	−5.76695	−0.777616
$56$	1.44048	0.192492
$57$	5.05003	0.668893
$58$	−9.96147	−1.30801
$59$	−4.43104	−0.576873	−0.288436	−	0.957499i	$-0.593135\pi$
$59$	−4.43104	−0.576873	−0.288436	+	0.957499i	$0.593135\pi$
$60$	1.19399	0.154144
$61$	9.83388	1.25910	0.629550	−	0.776960i	$-0.283239\pi$
$61$	9.83388	1.25910	0.629550	+	0.776960i	$0.283239\pi$
$62$	17.1913	2.18330
$63$	1.00000	0.125988
$64$	−0.776261	−0.0970326
$65$	4.94069	0.612818
$66$	10.3066	1.26865
$67$	3.52693	0.430883	0.215442	−	0.976517i	$-0.430881\pi$
$67$	3.52693	0.430883	0.215442	+	0.976517i	$0.430881\pi$
$68$	−2.28639	−0.277266
$69$	−1.00000	−0.120386
$70$	−1.78717	−0.213608
$71$	−8.09959	−0.961244	−0.480622	−	0.876928i	$-0.659589\pi$
$71$	−8.09959	−0.961244	−0.480622	+	0.876928i	$0.659589\pi$
$72$	1.44048	0.169762
$73$	7.86940	0.921044	0.460522	−	0.887648i	$-0.347662\pi$
$73$	7.86940	0.921044	0.460522	+	0.887648i	$0.347662\pi$
$74$	−4.45655	−0.518063
$75$	1.00000	0.115470
$76$	6.02970	0.691654
$77$	−5.76695	−0.657205
$78$	−8.82988	−0.999787
$79$	−4.46714	−0.502593	−0.251296	−	0.967910i	$-0.580857\pi$
$79$	−4.46714	−0.502593	−0.251296	+	0.967910i	$0.580857\pi$
$80$	−4.96237	−0.554810
$81$	1.00000	0.111111
$82$	−8.33104	−0.920009
$83$	−2.52906	−0.277600	−0.138800	−	0.990320i	$-0.544325\pi$
$83$	−2.52906	−0.277600	−0.138800	+	0.990320i	$0.544325\pi$
$84$	1.19399	0.130275
$85$	−1.91492	−0.207702
$86$	−12.2307	−1.31888
$87$	5.57387	0.597581
$88$	−8.30716	−0.885547
$89$	0.000952551 0	0.000100970 0	5.04851e−5	−	1.00000i	$-0.499984\pi$
$89$	0.000952551 0	0.000100970 0	5.04851e−5		1.00000i	$0.499984\pi$
$90$	−1.78717	−0.188385
$91$	4.94069	0.517925
$92$	−1.19399	−0.124482
$93$	−9.61929	−0.997474
$94$	−4.32414	−0.446001
$95$	5.05003	0.518123
$96$	5.98766	0.611113
$97$	−4.66488	−0.473647	−0.236823	−	0.971553i	$-0.576106\pi$
$97$	−4.66488	−0.473647	−0.236823	+	0.971553i	$0.576106\pi$
$98$	−1.78717	−0.180532
$99$	−5.76695	−0.579601
$100$	1.19399	0.119399
$101$	7.30587	0.726961	0.363481	−	0.931602i	$-0.381588\pi$
$101$	7.30587	0.726961	0.363481	+	0.931602i	$0.381588\pi$
$102$	3.42229	0.338857
$103$	15.5664	1.53380	0.766902	−	0.641764i	$-0.221797\pi$
$103$	15.5664	1.53380	0.766902	+	0.641764i	$0.221797\pi$
$104$	7.11695	0.697875
$105$	1.00000	0.0975900
$106$	−9.04585	−0.878611
$107$	−2.54596	−0.246127	−0.123063	−	0.992399i	$-0.539272\pi$
$107$	−2.54596	−0.246127	−0.123063	+	0.992399i	$0.539272\pi$
$108$	1.19399	0.114892
$109$	−7.03401	−0.673736	−0.336868	−	0.941552i	$-0.609368\pi$
$109$	−7.03401	−0.673736	−0.336868	+	0.941552i	$0.609368\pi$
$110$	10.3066	0.982691
$111$	2.49363	0.236685
$112$	−4.96237	−0.468900
$113$	−10.9575	−1.03079	−0.515397	−	0.856952i	$-0.672356\pi$
$113$	−10.9575	−1.03079	−0.515397	+	0.856952i	$0.672356\pi$
$114$	−9.02529	−0.845296
$115$	−1.00000	−0.0932505
$116$	6.65515	0.617916
$117$	4.94069	0.456767
$118$	7.91905	0.729008
$119$	−1.91492	−0.175540
$120$	1.44048	0.131497
$121$	22.2578	2.02343
$122$	−17.5749	−1.59115
$123$	4.66157	0.420320
$124$	−11.4854	−1.03142
$125$	1.00000	0.0894427
$126$	−1.78717	−0.159214
$127$	−3.29967	−0.292798	−0.146399	−	0.989226i	$-0.546768\pi$
$127$	−3.29967	−0.292798	−0.146399	+	0.989226i	$0.546768\pi$
$128$	−10.5880	−0.935857
$129$	6.84362	0.602547
$130$	−8.82988	−0.774432
$131$	21.8368	1.90789	0.953943	−	0.299988i	$-0.0969825\pi$
$131$	21.8368	1.90789	0.953943	+	0.299988i	$0.0969825\pi$
$132$	−6.88570	−0.599323
$133$	5.05003	0.437894
$134$	−6.30324	−0.544517
$135$	1.00000	0.0860663
$136$	−2.75839	−0.236530
$137$	−14.4643	−1.23577	−0.617884	−	0.786270i	$-0.712010\pi$
$137$	−14.4643	−1.23577	−0.617884	+	0.786270i	$0.712010\pi$
$138$	1.78717	0.152134
$139$	−0.321407	−0.0272614	−0.0136307	−	0.999907i	$-0.504339\pi$
$139$	−0.321407	−0.0272614	−0.0136307	+	0.999907i	$0.504339\pi$
$140$	1.19399	0.100911
$141$	2.41954	0.203762
$142$	14.4754	1.21475
$143$	−28.4927	−2.38268
$144$	−4.96237	−0.413531
$145$	5.57387	0.462885
$146$	−14.0640	−1.16394
$147$	1.00000	0.0824786
$148$	2.97737	0.244738
$149$	14.7093	1.20503	0.602516	−	0.798107i	$-0.294165\pi$
$149$	14.7093	1.20503	0.602516	+	0.798107i	$0.294165\pi$
$150$	−1.78717	−0.145922
$151$	3.01776	0.245582	0.122791	−	0.992433i	$-0.460815\pi$
$151$	3.01776	0.245582	0.122791	+	0.992433i	$0.460815\pi$
$152$	7.27446	0.590036
$153$	−1.91492	−0.154812
$154$	10.3066	0.830526
$155$	−9.61929	−0.772640
$156$	5.89915	0.472310
$157$	16.9272	1.35093	0.675467	−	0.737390i	$-0.263942\pi$
$157$	16.9272	1.35093	0.675467	+	0.737390i	$0.263942\pi$
$158$	7.98356	0.635138
$159$	5.06154	0.401406
$160$	5.98766	0.473366
$161$	−1.00000	−0.0788110
$162$	−1.78717	−0.140414
$163$	−22.5392	−1.76541	−0.882703	−	0.469931i	$-0.844279\pi$
$163$	−22.5392	−1.76541	−0.882703	+	0.469931i	$0.844279\pi$
$164$	5.56588	0.434622
$165$	−5.76695	−0.448957
$166$	4.51987	0.350810
$167$	0.590948	0.0457290	0.0228645	−	0.999739i	$-0.492721\pi$
$167$	0.590948	0.0457290	0.0228645	+	0.999739i	$0.492721\pi$
$168$	1.44048	0.111135
$169$	11.4104	0.877727
$170$	3.42229	0.262478
$171$	5.05003	0.386186
$172$	8.17123	0.623051
$173$	−9.23360	−0.702017	−0.351009	−	0.936372i	$-0.614161\pi$
$173$	−9.23360	−0.702017	−0.351009	+	0.936372i	$0.614161\pi$
$174$	−9.96147	−0.755177
$175$	1.00000	0.0755929
$176$	28.6177	2.15714
$177$	−4.43104	−0.333058
$178$	−0.00170237	−0.000127598 0
$179$	10.2776	0.768184	0.384092	−	0.923295i	$-0.374514\pi$
$179$	10.2776	0.768184	0.384092	+	0.923295i	$0.374514\pi$
$180$	1.19399	0.0889949
$181$	24.9286	1.85293	0.926463	−	0.376387i	$-0.122834\pi$
$181$	24.9286	1.85293	0.926463	+	0.376387i	$0.122834\pi$
$182$	−8.82988	−0.654514
$183$	9.83388	0.726942
$184$	−1.44048	−0.106193
$185$	2.49363	0.183335
$186$	17.1913	1.26053
$187$	11.0432	0.807561
$188$	2.88891	0.210696
$189$	1.00000	0.0727393
$190$	−9.02529	−0.654764
$191$	−10.3252	−0.747105	−0.373552	−	0.927609i	$-0.621860\pi$
$191$	−10.3252	−0.747105	−0.373552	+	0.927609i	$0.621860\pi$
$192$	−0.776261	−0.0560218
$193$	12.0562	0.867826	0.433913	−	0.900955i	$-0.357133\pi$
$193$	12.0562	0.867826	0.433913	+	0.900955i	$0.357133\pi$
$194$	8.33696	0.598559
$195$	4.94069	0.353810
$196$	1.19399	0.0852851
$197$	−7.99771	−0.569813	−0.284907	−	0.958555i	$-0.591963\pi$
$197$	−7.99771	−0.569813	−0.284907	+	0.958555i	$0.591963\pi$
$198$	10.3066	0.732455
$199$	17.3059	1.22678	0.613392	−	0.789779i	$-0.289805\pi$
$199$	17.3059	1.22678	0.613392	+	0.789779i	$0.289805\pi$
$200$	1.44048	0.101857
$201$	3.52693	0.248771
$202$	−13.0569	−0.918678
$203$	5.57387	0.391209
$204$	−2.28639	−0.160080
$205$	4.66157	0.325578
$206$	−27.8199	−1.93830
$207$	−1.00000	−0.0695048
$208$	−24.5175	−1.69998
$209$	−29.1233	−2.01450
$210$	−1.78717	−0.123327
$211$	2.35893	0.162396	0.0811978	−	0.996698i	$-0.474125\pi$
$211$	2.35893	0.162396	0.0811978	+	0.996698i	$0.474125\pi$
$212$	6.04344	0.415065
$213$	−8.09959	−0.554975
$214$	4.55007	0.311036
$215$	6.84362	0.466731
$216$	1.44048	0.0980120
$217$	−9.61929	−0.653000
$218$	12.5710	0.851416
$219$	7.86940	0.531765
$220$	−6.88570	−0.464234
$221$	−9.46101	−0.636416
$222$	−4.45655	−0.299104
$223$	−27.7755	−1.85998	−0.929992	−	0.367580i	$-0.880186\pi$
$223$	−27.7755	−1.85998	−0.929992	+	0.367580i	$0.880186\pi$
$224$	5.98766	0.400067
$225$	1.00000	0.0666667
$226$	19.5829	1.30264
$227$	5.02844	0.333749	0.166875	−	0.985978i	$-0.446632\pi$
$227$	5.02844	0.333749	0.166875	+	0.985978i	$0.446632\pi$
$228$	6.02970	0.399327
$229$	28.4382	1.87925	0.939624	−	0.342208i	$-0.111175\pi$
$229$	28.4382	1.87925	0.939624	+	0.342208i	$0.111175\pi$
$230$	1.78717	0.117843
$231$	−5.76695	−0.379438
$232$	8.02903	0.527131
$233$	−17.1117	−1.12103	−0.560513	−	0.828146i	$-0.689396\pi$
$233$	−17.1117	−1.12103	−0.560513	+	0.828146i	$0.689396\pi$
$234$	−8.82988	−0.577227
$235$	2.41954	0.157833
$236$	−5.29063	−0.344391
$237$	−4.46714	−0.290172
$238$	3.42229	0.221834
$239$	17.3184	1.12023	0.560116	−	0.828414i	$-0.310756\pi$
$239$	17.3184	1.12023	0.560116	+	0.828414i	$0.310756\pi$
$240$	−4.96237	−0.320319
$241$	5.81472	0.374559	0.187280	−	0.982307i	$-0.440033\pi$
$241$	5.81472	0.374559	0.187280	+	0.982307i	$0.440033\pi$
$242$	−39.7785	−2.55706
$243$	1.00000	0.0641500
$244$	11.7416	0.751678
$245$	1.00000	0.0638877
$246$	−8.33104	−0.531168
$247$	24.9507	1.58757
$248$	−13.8564	−0.879880
$249$	−2.52906	−0.160273
$250$	−1.78717	−0.113031
$251$	−26.4843	−1.67167	−0.835837	−	0.548977i	$-0.815017\pi$
$251$	−26.4843	−1.67167	−0.835837	+	0.548977i	$0.815017\pi$
$252$	1.19399	0.0752144
$253$	5.76695	0.362565
$254$	5.89708	0.370016
$255$	−1.91492	−0.119917
$256$	20.4751	1.27970
$257$	15.0921	0.941422	0.470711	−	0.882287i	$-0.343997\pi$
$257$	15.0921	0.941422	0.470711	+	0.882287i	$0.343997\pi$
$258$	−12.2307	−0.761453
$259$	2.49363	0.154946
$260$	5.89915	0.365850
$261$	5.57387	0.345014
$262$	−39.0261	−2.41104
$263$	11.7189	0.722620	0.361310	−	0.932446i	$-0.382330\pi$
$263$	11.7189	0.722620	0.361310	+	0.932446i	$0.382330\pi$
$264$	−8.30716	−0.511271
$265$	5.06154	0.310928
$266$	−9.02529	−0.553376
$267$	0.000952551 0	5.82952e−5 0
$268$	4.21113	0.257236
$269$	−5.71714	−0.348580	−0.174290	−	0.984694i	$-0.555763\pi$
$269$	−5.71714	−0.348580	−0.174290	+	0.984694i	$0.555763\pi$
$270$	−1.78717	−0.108764
$271$	23.7785	1.44444	0.722220	−	0.691664i	$-0.243122\pi$
$271$	23.7785	1.44444	0.722220	+	0.691664i	$0.243122\pi$
$272$	9.50251	0.576175
$273$	4.94069	0.299024
$274$	25.8502	1.56167
$275$	−5.76695	−0.347760
$276$	−1.19399	−0.0718699
$277$	−17.4415	−1.04796	−0.523980	−	0.851730i	$-0.675553\pi$
$277$	−17.4415	−1.04796	−0.523980	+	0.851730i	$0.675553\pi$
$278$	0.574411	0.0344509
$279$	−9.61929	−0.575892
$280$	1.44048	0.0860849
$281$	22.6653	1.35210	0.676051	−	0.736855i	$-0.263690\pi$
$281$	22.6653	1.35210	0.676051	+	0.736855i	$0.263690\pi$
$282$	−4.32414	−0.257499
$283$	31.7559	1.88769	0.943846	−	0.330385i	$-0.107179\pi$
$283$	31.7559	1.88769	0.943846	+	0.330385i	$0.107179\pi$
$284$	−9.67084	−0.573859
$285$	5.05003	0.299138
$286$	50.9215	3.01105
$287$	4.66157	0.275164
$288$	5.98766	0.352826
$289$	−13.3331	−0.784300
$290$	−9.96147	−0.584958
$291$	−4.66488	−0.273460
$292$	9.39600	0.549859
$293$	22.9821	1.34263	0.671314	−	0.741173i	$-0.265730\pi$
$293$	22.9821	1.34263	0.671314	+	0.741173i	$0.265730\pi$
$294$	−1.78717	−0.104230
$295$	−4.43104	−0.257985
$296$	3.59201	0.208781
$297$	−5.76695	−0.334633
$298$	−26.2881	−1.52283
$299$	−4.94069	−0.285728
$300$	1.19399	0.0689352
$301$	6.84362	0.394460
$302$	−5.39327	−0.310348
$303$	7.30587	0.419711
$304$	−25.0601	−1.43730
$305$	9.83388	0.563087
$306$	3.42229	0.195639
$307$	14.3476	0.818858	0.409429	−	0.912342i	$-0.365728\pi$
$307$	14.3476	0.818858	0.409429	+	0.912342i	$0.365728\pi$
$308$	−6.88570	−0.392349
$309$	15.5664	0.885543
$310$	17.1913	0.976403
$311$	−31.2661	−1.77294	−0.886469	−	0.462789i	$-0.846849\pi$
$311$	−31.2661	−1.77294	−0.886469	+	0.462789i	$0.846849\pi$
$312$	7.11695	0.402918
$313$	−12.4626	−0.704429	−0.352215	−	0.935919i	$-0.614571\pi$
$313$	−12.4626	−0.704429	−0.352215	+	0.935919i	$0.614571\pi$
$314$	−30.2518	−1.70721
$315$	1.00000	0.0563436
$316$	−5.33373	−0.300046
$317$	33.0448	1.85598	0.927992	−	0.372601i	$-0.121534\pi$
$317$	33.0448	1.85598	0.927992	+	0.372601i	$0.121534\pi$
$318$	−9.04585	−0.507266
$319$	−32.1442	−1.79973
$320$	−0.776261	−0.0433943
$321$	−2.54596	−0.142101
$322$	1.78717	0.0995953
$323$	−9.67039	−0.538075
$324$	1.19399	0.0663329
$325$	4.94069	0.274060
$326$	40.2815	2.23099
$327$	−7.03401	−0.388982
$328$	6.71488	0.370767
$329$	2.41954	0.133394
$330$	10.3066	0.567357
$331$	12.1192	0.666130	0.333065	−	0.942904i	$-0.391917\pi$
$331$	12.1192	0.666130	0.333065	+	0.942904i	$0.391917\pi$
$332$	−3.01968	−0.165726
$333$	2.49363	0.136650
$334$	−1.05613	−0.0577887
$335$	3.52693	0.192697
$336$	−4.96237	−0.270719
$337$	7.17203	0.390686	0.195343	−	0.980735i	$-0.437418\pi$
$337$	7.17203	0.390686	0.195343	+	0.980735i	$0.437418\pi$
$338$	−20.3925	−1.10920
$339$	−10.9575	−0.595129
$340$	−2.28639	−0.123997
$341$	55.4740	3.00408
$342$	−9.02529	−0.488032
$343$	1.00000	0.0539949
$344$	9.85808	0.531512
$345$	−1.00000	−0.0538382
$346$	16.5020	0.887155
$347$	10.0503	0.539530	0.269765	−	0.962926i	$-0.413054\pi$
$347$	10.0503	0.539530	0.269765	+	0.962926i	$0.413054\pi$
$348$	6.65515	0.356754
$349$	−1.66481	−0.0891152	−0.0445576	−	0.999007i	$-0.514188\pi$
$349$	−1.66481	−0.0891152	−0.0445576	+	0.999007i	$0.514188\pi$
$350$	−1.78717	−0.0955285
$351$	4.94069	0.263715
$352$	−34.5306	−1.84049
$353$	4.57542	0.243525	0.121763	−	0.992559i	$-0.461145\pi$
$353$	4.57542	0.243525	0.121763	+	0.992559i	$0.461145\pi$
$354$	7.91905	0.420893
$355$	−8.09959	−0.429882
$356$	0.00113734	6.02788e−5 0
$357$	−1.91492	−0.101348
$358$	−18.3679	−0.970772
$359$	27.0943	1.42998	0.714992	−	0.699133i	$-0.246431\pi$
$359$	27.0943	1.42998	0.714992	+	0.699133i	$0.246431\pi$
$360$	1.44048	0.0759198
$361$	6.50285	0.342255
$362$	−44.5517	−2.34158
$363$	22.2578	1.16823
$364$	5.89915	0.309199
$365$	7.86940	0.411903
$366$	−17.5749	−0.918653
$367$	−11.2992	−0.589811	−0.294906	−	0.955526i	$-0.595288\pi$
$367$	−11.2992	−0.589811	−0.294906	+	0.955526i	$0.595288\pi$
$368$	4.96237	0.258681
$369$	4.66157	0.242672
$370$	−4.45655	−0.231685
$371$	5.06154	0.262782
$372$	−11.4854	−0.595488
$373$	−12.1176	−0.627424	−0.313712	−	0.949518i	$-0.601573\pi$
$373$	−12.1176	−0.627424	−0.313712	+	0.949518i	$0.601573\pi$
$374$	−19.7362	−1.02053
$375$	1.00000	0.0516398
$376$	3.48529	0.179740
$377$	27.5388	1.41832
$378$	−1.78717	−0.0919223
$379$	1.84435	0.0947381	0.0473690	−	0.998877i	$-0.484916\pi$
$379$	1.84435	0.0947381	0.0473690	+	0.998877i	$0.484916\pi$
$380$	6.02970	0.309317
$381$	−3.29967	−0.169047
$382$	18.4529	0.944133
$383$	4.33144	0.221326	0.110663	−	0.993858i	$-0.464703\pi$
$383$	4.33144	0.221326	0.110663	+	0.993858i	$0.464703\pi$
$384$	−10.5880	−0.540317
$385$	−5.76695	−0.293911
$386$	−21.5466	−1.09669
$387$	6.84362	0.347881
$388$	−5.56983	−0.282765
$389$	−0.930716	−0.0471892	−0.0235946	−	0.999722i	$-0.507511\pi$
$389$	−0.930716	−0.0471892	−0.0235946	+	0.999722i	$0.507511\pi$
$390$	−8.82988	−0.447118
$391$	1.91492	0.0968415
$392$	1.44048	0.0727551
$393$	21.8368	1.10152
$394$	14.2933	0.720086
$395$	−4.46714	−0.224766
$396$	−6.88570	−0.346019
$397$	−6.38273	−0.320340	−0.160170	−	0.987089i	$-0.551204\pi$
$397$	−6.38273	−0.320340	−0.160170	+	0.987089i	$0.551204\pi$
$398$	−30.9287	−1.55031
$399$	5.05003	0.252818
$400$	−4.96237	−0.248118
$401$	2.12336	0.106036	0.0530178	−	0.998594i	$-0.483116\pi$
$401$	2.12336	0.106036	0.0530178	+	0.998594i	$0.483116\pi$
$402$	−6.30324	−0.314377
$403$	−47.5259	−2.36744
$404$	8.72315	0.433993
$405$	1.00000	0.0496904
$406$	−9.96147	−0.494380
$407$	−14.3806	−0.712821
$408$	−2.75839	−0.136561
$409$	−14.1723	−0.700773	−0.350386	−	0.936605i	$-0.613950\pi$
$409$	−14.1723	−0.700773	−0.350386	+	0.936605i	$0.613950\pi$
$410$	−8.33104	−0.411441
$411$	−14.4643	−0.713471
$412$	18.5862	0.915675
$413$	−4.43104	−0.218037
$414$	1.78717	0.0878348
$415$	−2.52906	−0.124147
$416$	29.5832	1.45044
$417$	−0.321407	−0.0157394
$418$	52.0484	2.54577
$419$	−14.1577	−0.691649	−0.345825	−	0.938299i	$-0.612401\pi$
$419$	−14.1577	−0.691649	−0.345825	+	0.938299i	$0.612401\pi$
$420$	1.19399	0.0582608
$421$	21.7007	1.05763	0.528813	−	0.848738i	$-0.322637\pi$
$421$	21.7007	1.05763	0.528813	+	0.848738i	$0.322637\pi$
$422$	−4.21582	−0.205223
$423$	2.41954	0.117642
$424$	7.29103	0.354084
$425$	−1.91492	−0.0928871
$426$	14.4754	0.701334
$427$	9.83388	0.475895
$428$	−3.03985	−0.146937
$429$	−28.4927	−1.37564
$430$	−12.2307	−0.589819
$431$	−23.7748	−1.14519	−0.572597	−	0.819837i	$-0.694064\pi$
$431$	−23.7748	−1.14519	−0.572597	+	0.819837i	$0.694064\pi$
$432$	−4.96237	−0.238752
$433$	8.76012	0.420985	0.210492	−	0.977596i	$-0.432493\pi$
$433$	8.76012	0.420985	0.210492	+	0.977596i	$0.432493\pi$
$434$	17.1913	0.825211
$435$	5.57387	0.267247
$436$	−8.39855	−0.402218
$437$	−5.05003	−0.241576
$438$	−14.0640	−0.672003
$439$	−26.3016	−1.25531	−0.627654	−	0.778492i	$-0.715985\pi$
$439$	−26.3016	−1.25531	−0.627654	+	0.778492i	$0.715985\pi$
$440$	−8.30716	−0.396028
$441$	1.00000	0.0476190
$442$	16.9085	0.804254
$443$	−23.6660	−1.12441	−0.562203	−	0.826999i	$-0.690046\pi$
$443$	−23.6660	−1.12441	−0.562203	+	0.826999i	$0.690046\pi$
$444$	2.97737	0.141300
$445$	0.000952551 0	4.51552e−5 0
$446$	49.6396	2.35050
$447$	14.7093	0.695725
$448$	−0.776261	−0.0366749
$449$	−33.5290	−1.58233	−0.791166	−	0.611602i	$-0.790526\pi$
$449$	−33.5290	−1.58233	−0.791166	+	0.611602i	$0.790526\pi$
$450$	−1.78717	−0.0842482
$451$	−26.8831	−1.26587
$452$	−13.0832	−0.615380
$453$	3.01776	0.141787
$454$	−8.98670	−0.421767
$455$	4.94069	0.231623
$456$	7.27446	0.340658
$457$	−39.6400	−1.85428	−0.927140	−	0.374716i	$-0.877740\pi$
$457$	−39.6400	−1.85428	−0.927140	+	0.374716i	$0.877740\pi$
$458$	−50.8240	−2.37485
$459$	−1.91492	−0.0893806
$460$	−1.19399	−0.0556702
$461$	12.0439	0.560940	0.280470	−	0.959863i	$-0.409510\pi$
$461$	12.0439	0.560940	0.280470	+	0.959863i	$0.409510\pi$
$462$	10.3066	0.479504
$463$	−26.9415	−1.25208	−0.626038	−	0.779792i	$-0.715325\pi$
$463$	−26.9415	−1.25208	−0.626038	+	0.779792i	$0.715325\pi$
$464$	−27.6596	−1.28406
$465$	−9.61929	−0.446084
$466$	30.5816	1.41667
$467$	−1.68825	−0.0781230	−0.0390615	−	0.999237i	$-0.512437\pi$
$467$	−1.68825	−0.0781230	−0.0390615	+	0.999237i	$0.512437\pi$
$468$	5.89915	0.272688
$469$	3.52693	0.162859
$470$	−4.32414	−0.199458
$471$	16.9272	0.779962
$472$	−6.38282	−0.293793
$473$	−39.4669	−1.81469
$474$	7.98356	0.366697
$475$	5.05003	0.231711
$476$	−2.28639	−0.104797
$477$	5.06154	0.231752
$478$	−30.9510	−1.41566
$479$	33.6192	1.53610	0.768051	−	0.640388i	$-0.221227\pi$
$479$	33.6192	1.53610	0.768051	+	0.640388i	$0.221227\pi$
$480$	5.98766	0.273298
$481$	12.3202	0.561755
$482$	−10.3919	−0.473339
$483$	−1.00000	−0.0455016
$484$	26.5756	1.20798
$485$	−4.66488	−0.211821
$486$	−1.78717	−0.0810679
$487$	−6.91562	−0.313377	−0.156688	−	0.987648i	$-0.550082\pi$
$487$	−6.91562	−0.313377	−0.156688	+	0.987648i	$0.550082\pi$
$488$	14.1655	0.641241
$489$	−22.5392	−1.01926
$490$	−1.78717	−0.0807363
$491$	15.2501	0.688227	0.344114	−	0.938928i	$-0.388179\pi$
$491$	15.2501	0.688227	0.344114	+	0.938928i	$0.388179\pi$
$492$	5.56588	0.250929
$493$	−10.6735	−0.480710
$494$	−44.5912	−2.00625
$495$	−5.76695	−0.259205
$496$	47.7344	2.14334
$497$	−8.09959	−0.363316
$498$	4.51987	0.202540
$499$	−19.4633	−0.871295	−0.435647	−	0.900117i	$-0.643481\pi$
$499$	−19.4633	−0.871295	−0.435647	+	0.900117i	$0.643481\pi$
$500$	1.19399	0.0533969
$501$	0.590948	0.0264016
$502$	47.3321	2.11253
$503$	−10.9238	−0.487069	−0.243534	−	0.969892i	$-0.578307\pi$
$503$	−10.9238	−0.487069	−0.243534	+	0.969892i	$0.578307\pi$
$504$	1.44048	0.0641639
$505$	7.30587	0.325107
$506$	−10.3066	−0.458182
$507$	11.4104	0.506756
$508$	−3.93978	−0.174799
$509$	−1.04529	−0.0463317	−0.0231658	−	0.999732i	$-0.507375\pi$
$509$	−1.04529	−0.0463317	−0.0231658	+	0.999732i	$0.507375\pi$
$510$	3.42229	0.151541
$511$	7.86940	0.348122
$512$	−15.4166	−0.681325
$513$	5.05003	0.222964
$514$	−26.9723	−1.18970
$515$	15.5664	0.685938
$516$	8.17123	0.359718
$517$	−13.9534	−0.613669
$518$	−4.45655	−0.195809
$519$	−9.23360	−0.405310
$520$	7.11695	0.312099
$521$	−38.1598	−1.67181	−0.835906	−	0.548873i	$-0.815057\pi$
$521$	−38.1598	−1.67181	−0.835906	+	0.548873i	$0.815057\pi$
$522$	−9.96147	−0.436002
$523$	37.1955	1.62645	0.813223	−	0.581953i	$-0.197711\pi$
$523$	37.1955	1.62645	0.813223	+	0.581953i	$0.197711\pi$
$524$	26.0729	1.13900
$525$	1.00000	0.0436436
$526$	−20.9438	−0.913192
$527$	18.4201	0.802393
$528$	28.6177	1.24543
$529$	1.00000	0.0434783
$530$	−9.04585	−0.392927
$531$	−4.43104	−0.192291
$532$	6.02970	0.261421
$533$	23.0314	0.997600
$534$	−0.00170237	−7.36689e−5 0
$535$	−2.54596	−0.110071
$536$	5.08046	0.219443
$537$	10.2776	0.443511
$538$	10.2175	0.440508
$539$	−5.76695	−0.248400
$540$	1.19399	0.0513812
$541$	−29.7889	−1.28073	−0.640363	−	0.768072i	$-0.721216\pi$
$541$	−29.7889	−1.28073	−0.640363	+	0.768072i	$0.721216\pi$
$542$	−42.4963	−1.82537
$543$	24.9286	1.06979
$544$	−11.4659	−0.491595
$545$	−7.03401	−0.301304
$546$	−8.82988	−0.377884
$547$	−29.0335	−1.24138	−0.620691	−	0.784055i	$-0.713148\pi$
$547$	−29.0335	−1.24138	−0.620691	+	0.784055i	$0.713148\pi$
$548$	−17.2702	−0.737748
$549$	9.83388	0.419700
$550$	10.3066	0.439473
$551$	28.1482	1.19915
$552$	−1.44048	−0.0613108
$553$	−4.46714	−0.189962
$554$	31.1711	1.32433
$555$	2.49363	0.105849
$556$	−0.383758	−0.0162750
$557$	34.1718	1.44791	0.723953	−	0.689850i	$-0.242323\pi$
$557$	34.1718	1.44791	0.723953	+	0.689850i	$0.242323\pi$
$558$	17.1913	0.727768
$559$	33.8122	1.43011
$560$	−4.96237	−0.209698
$561$	11.0432	0.466246
$562$	−40.5069	−1.70868
$563$	18.4099	0.775887	0.387943	−	0.921683i	$-0.373186\pi$
$563$	18.4099	0.775887	0.387943	+	0.921683i	$0.373186\pi$
$564$	2.88891	0.121645
$565$	−10.9575	−0.460985
$566$	−56.7533	−2.38552
$567$	1.00000	0.0419961
$568$	−11.6673	−0.489548
$569$	−30.9396	−1.29705	−0.648527	−	0.761192i	$-0.724615\pi$
$569$	−30.9396	−1.29705	−0.648527	+	0.761192i	$0.724615\pi$
$570$	−9.02529	−0.378028
$571$	−5.88560	−0.246305	−0.123152	−	0.992388i	$-0.539300\pi$
$571$	−5.88560	−0.246305	−0.123152	+	0.992388i	$0.539300\pi$
$572$	−34.0201	−1.42245
$573$	−10.3252	−0.431341
$574$	−8.33104	−0.347731
$575$	−1.00000	−0.0417029
$576$	−0.776261	−0.0323442
$577$	23.3157	0.970646	0.485323	−	0.874335i	$-0.338702\pi$
$577$	23.3157	0.970646	0.485323	+	0.874335i	$0.338702\pi$
$578$	23.8286	0.991138
$579$	12.0562	0.501040
$580$	6.65515	0.276340
$581$	−2.52906	−0.104923
$582$	8.33696	0.345578
$583$	−29.1897	−1.20891
$584$	11.3357	0.469074
$585$	4.94069	0.204273
$586$	−41.0730	−1.69671
$587$	26.6706	1.10082	0.550408	−	0.834896i	$-0.314472\pi$
$587$	26.6706	1.10082	0.550408	+	0.834896i	$0.314472\pi$
$588$	1.19399	0.0492394
$589$	−48.5777	−2.00161
$590$	7.91905	0.326022
$591$	−7.99771	−0.328982
$592$	−12.3743	−0.508580
$593$	−48.4665	−1.99028	−0.995141	−	0.0984620i	$-0.968608\pi$
$593$	−48.4665	−1.99028	−0.995141	+	0.0984620i	$0.968608\pi$
$594$	10.3066	0.422883
$595$	−1.91492	−0.0785039
$596$	17.5628	0.719399
$597$	17.3059	0.708284
$598$	8.82988	0.361081
$599$	41.4387	1.69314	0.846571	−	0.532276i	$-0.178663\pi$
$599$	41.4387	1.69314	0.846571	+	0.532276i	$0.178663\pi$
$600$	1.44048	0.0588072
$601$	−35.4264	−1.44507	−0.722537	−	0.691332i	$-0.757024\pi$
$601$	−35.4264	−1.44507	−0.722537	+	0.691332i	$0.757024\pi$
$602$	−12.2307	−0.498488
$603$	3.52693	0.143628
$604$	3.60319	0.146612
$605$	22.2578	0.904907
$606$	−13.0569	−0.530399
$607$	−43.9254	−1.78288	−0.891438	−	0.453143i	$-0.850303\pi$
$607$	−43.9254	−1.78288	−0.891438	+	0.453143i	$0.850303\pi$
$608$	30.2379	1.22631
$609$	5.57387	0.225865
$610$	−17.5749	−0.711585
$611$	11.9542	0.483615
$612$	−2.28639	−0.0924220
$613$	−35.8777	−1.44909	−0.724544	−	0.689228i	$-0.757950\pi$
$613$	−35.8777	−1.44909	−0.724544	+	0.689228i	$0.757950\pi$
$614$	−25.6416	−1.03481
$615$	4.66157	0.187973
$616$	−8.30716	−0.334705
$617$	16.3149	0.656811	0.328406	−	0.944537i	$-0.393489\pi$
$617$	16.3149	0.656811	0.328406	+	0.944537i	$0.393489\pi$
$618$	−27.8199	−1.11908
$619$	−36.8025	−1.47922	−0.739610	−	0.673036i	$-0.764990\pi$
$619$	−36.8025	−1.47922	−0.739610	+	0.673036i	$0.764990\pi$
$620$	−11.4854	−0.461263
$621$	−1.00000	−0.0401286
$622$	55.8779	2.24050
$623$	0.000952551 0	3.81631e−5 0
$624$	−24.5175	−0.981487
$625$	1.00000	0.0400000
$626$	22.2729	0.890203
$627$	−29.1233	−1.16307
$628$	20.2109	0.806502
$629$	−4.77508	−0.190395
$630$	−1.78717	−0.0712027
$631$	−27.8981	−1.11061	−0.555303	−	0.831648i	$-0.687398\pi$
$631$	−27.8981	−1.11061	−0.555303	+	0.831648i	$0.687398\pi$
$632$	−6.43482	−0.255963
$633$	2.35893	0.0937591
$634$	−59.0569	−2.34545
$635$	−3.29967	−0.130943
$636$	6.04344	0.239638
$637$	4.94069	0.195757
$638$	57.4474	2.27436
$639$	−8.09959	−0.320415
$640$	−10.5880	−0.418528
$641$	−33.9862	−1.34237	−0.671187	−	0.741288i	$-0.734215\pi$
$641$	−33.9862	−1.34237	−0.671187	+	0.741288i	$0.734215\pi$
$642$	4.55007	0.179577
$643$	−19.7573	−0.779153	−0.389576	−	0.920994i	$-0.627379\pi$
$643$	−19.7573	−0.779153	−0.389576	+	0.920994i	$0.627379\pi$
$644$	−1.19399	−0.0470499
$645$	6.84362	0.269467
$646$	17.2827	0.679978
$647$	7.95723	0.312831	0.156416	−	0.987691i	$-0.450006\pi$
$647$	7.95723	0.312831	0.156416	+	0.987691i	$0.450006\pi$
$648$	1.44048	0.0565873
$649$	25.5536	1.00307
$650$	−8.82988	−0.346336
$651$	−9.61929	−0.377010
$652$	−26.9116	−1.05394
$653$	−21.0436	−0.823498	−0.411749	−	0.911297i	$-0.635082\pi$
$653$	−21.0436	−0.823498	−0.411749	+	0.911297i	$0.635082\pi$
$654$	12.5710	0.491565
$655$	21.8368	0.853233
$656$	−23.1324	−0.903169
$657$	7.86940	0.307015
$658$	−4.32414	−0.168573
$659$	38.8732	1.51428	0.757142	−	0.653250i	$-0.226595\pi$
$659$	38.8732	1.51428	0.757142	+	0.653250i	$0.226595\pi$
$660$	−6.88570	−0.268025
$661$	−11.4815	−0.446578	−0.223289	−	0.974752i	$-0.571679\pi$
$661$	−11.4815	−0.446578	−0.223289	+	0.974752i	$0.571679\pi$
$662$	−21.6591	−0.841804
$663$	−9.46101	−0.367435
$664$	−3.64305	−0.141378
$665$	5.05003	0.195832
$666$	−4.45655	−0.172688
$667$	−5.57387	−0.215821
$668$	0.705588	0.0273000
$669$	−27.7755	−1.07386
$670$	−6.30324	−0.243515
$671$	−56.7116	−2.18933
$672$	5.98766	0.230979
$673$	28.9694	1.11669	0.558345	−	0.829609i	$-0.311437\pi$
$673$	28.9694	1.11669	0.558345	+	0.829609i	$0.311437\pi$
$674$	−12.8177	−0.493718
$675$	1.00000	0.0384900
$676$	13.6240	0.523999
$677$	−45.0231	−1.73038	−0.865189	−	0.501445i	$-0.832802\pi$
$677$	−45.0231	−1.73038	−0.865189	+	0.501445i	$0.832802\pi$
$678$	19.5829	0.752078
$679$	−4.66488	−0.179022
$680$	−2.75839	−0.105779
$681$	5.02844	0.192690
$682$	−99.1417	−3.79633
$683$	−17.6839	−0.676657	−0.338329	−	0.941028i	$-0.609862\pi$
$683$	−17.6839	−0.676657	−0.338329	+	0.941028i	$0.609862\pi$
$684$	6.02970	0.230551
$685$	−14.4643	−0.552652
$686$	−1.78717	−0.0682346
$687$	28.4382	1.08498
$688$	−33.9606	−1.29473
$689$	25.0075	0.952710
$690$	1.78717	0.0680366
$691$	−4.13911	−0.157459	−0.0787296	−	0.996896i	$-0.525086\pi$
$691$	−4.13911	−0.157459	−0.0787296	+	0.996896i	$0.525086\pi$
$692$	−11.0248	−0.419102
$693$	−5.76695	−0.219068
$694$	−17.9617	−0.681816
$695$	−0.321407	−0.0121917
$696$	8.02903	0.304339
$697$	−8.92651	−0.338116
$698$	2.97530	0.112617
$699$	−17.1117	−0.647224
$700$	1.19399	0.0451287
$701$	10.1301	0.382607	0.191304	−	0.981531i	$-0.438729\pi$
$701$	10.1301	0.382607	0.191304	+	0.981531i	$0.438729\pi$
$702$	−8.82988	−0.333262
$703$	12.5929	0.474950
$704$	4.47666	0.168721
$705$	2.41954	0.0911252
$706$	−8.17707	−0.307748
$707$	7.30587	0.274766
$708$	−5.29063	−0.198834
$709$	−32.2470	−1.21106	−0.605531	−	0.795822i	$-0.707039\pi$
$709$	−32.2470	−1.21106	−0.605531	+	0.795822i	$0.707039\pi$
$710$	14.4754	0.543251
$711$	−4.46714	−0.167531
$712$	0.00137213	5.14226e−5 0
$713$	9.61929	0.360245
$714$	3.42229	0.128076
$715$	−28.4927	−1.06557
$716$	12.2714	0.458603
$717$	17.3184	0.646767
$718$	−48.4223	−1.80710
$719$	−45.6042	−1.70075	−0.850374	−	0.526178i	$-0.823625\pi$
$719$	−45.6042	−1.70075	−0.850374	+	0.526178i	$0.823625\pi$
$720$	−4.96237	−0.184937
$721$	15.5664	0.579724
$722$	−11.6217	−0.432516
$723$	5.81472	0.216252
$724$	29.7645	1.10619
$725$	5.57387	0.207008
$726$	−39.7785	−1.47632
$727$	34.1485	1.26650	0.633248	−	0.773949i	$-0.281721\pi$
$727$	34.1485	1.26650	0.633248	+	0.773949i	$0.281721\pi$
$728$	7.11695	0.263772
$729$	1.00000	0.0370370
$730$	−14.0640	−0.520532
$731$	−13.1050	−0.484705
$732$	11.7416	0.433981
$733$	−38.7771	−1.43226	−0.716132	−	0.697965i	$-0.754089\pi$
$733$	−38.7771	−1.43226	−0.716132	+	0.697965i	$0.754089\pi$
$734$	20.1936	0.745358
$735$	1.00000	0.0368856
$736$	−5.98766	−0.220708
$737$	−20.3397	−0.749221
$738$	−8.33104	−0.306670
$739$	−16.9026	−0.621773	−0.310887	−	0.950447i	$-0.600626\pi$
$739$	−16.9026	−0.621773	−0.310887	+	0.950447i	$0.600626\pi$
$740$	2.97737	0.109450
$741$	24.9507	0.916586
$742$	−9.04585	−0.332084
$743$	5.83512	0.214070	0.107035	−	0.994255i	$-0.465864\pi$
$743$	5.83512	0.214070	0.107035	+	0.994255i	$0.465864\pi$
$744$	−13.8564	−0.507999
$745$	14.7093	0.538906
$746$	21.6562	0.792890
$747$	−2.52906	−0.0925334
$748$	13.1855	0.482111
$749$	−2.54596	−0.0930272
$750$	−1.78717	−0.0652584
$751$	30.2412	1.10352	0.551759	−	0.834003i	$-0.313957\pi$
$751$	30.2412	1.10352	0.551759	+	0.834003i	$0.313957\pi$
$752$	−12.0066	−0.437837
$753$	−26.4843	−0.965142
$754$	−49.2166	−1.79236
$755$	3.01776	0.109828
$756$	1.19399	0.0434251
$757$	−48.5862	−1.76589	−0.882947	−	0.469473i	$-0.844444\pi$
$757$	−48.5862	−1.76589	−0.882947	+	0.469473i	$0.844444\pi$
$758$	−3.29618	−0.119723
$759$	5.76695	0.209327
$760$	7.27446	0.263872
$761$	−40.0065	−1.45024	−0.725118	−	0.688625i	$-0.758215\pi$
$761$	−40.0065	−1.45024	−0.725118	+	0.688625i	$0.758215\pi$
$762$	5.89708	0.213629
$763$	−7.03401	−0.254648
$764$	−12.3282	−0.446018
$765$	−1.91492	−0.0692339
$766$	−7.74103	−0.279695
$767$	−21.8924	−0.790490
$768$	20.4751	0.738833
$769$	−30.6407	−1.10493	−0.552466	−	0.833535i	$-0.686313\pi$
$769$	−30.6407	−1.10493	−0.552466	+	0.833535i	$0.686313\pi$
$770$	10.3066	0.371422
$771$	15.0921	0.543530
$772$	14.3950	0.518089
$773$	10.5381	0.379030	0.189515	−	0.981878i	$-0.439308\pi$
$773$	10.5381	0.379030	0.189515	+	0.981878i	$0.439308\pi$
$774$	−12.2307	−0.439625
$775$	−9.61929	−0.345535
$776$	−6.71965	−0.241221
$777$	2.49363	0.0894584
$778$	1.66335	0.0596340
$779$	23.5411	0.843447
$780$	5.89915	0.211223
$781$	46.7100	1.67141
$782$	−3.42229	−0.122381
$783$	5.57387	0.199194
$784$	−4.96237	−0.177227
$785$	16.9272	0.604156
$786$	−39.0261	−1.39201
$787$	−23.7561	−0.846814	−0.423407	−	0.905940i	$-0.639166\pi$
$787$	−23.7561	−0.846814	−0.423407	+	0.905940i	$0.639166\pi$
$788$	−9.54920	−0.340176
$789$	11.7189	0.417205
$790$	7.98356	0.284042
$791$	−10.9575	−0.389603
$792$	−8.30716	−0.295182
$793$	48.5862	1.72535
$794$	11.4071	0.404821
$795$	5.06154	0.179514
$796$	20.6631	0.732385
$797$	49.5197	1.75408	0.877039	−	0.480419i	$-0.159515\pi$
$797$	49.5197	1.75408	0.877039	+	0.480419i	$0.159515\pi$
$798$	−9.02529	−0.319492
$799$	−4.63322	−0.163911
$800$	5.98766	0.211696
$801$	0.000952551 0	3.36567e−5 0
$802$	−3.79481	−0.134000
$803$	−45.3825	−1.60151
$804$	4.21113	0.148515
$805$	−1.00000	−0.0352454
$806$	84.9371	2.99178
$807$	−5.71714	−0.201253
$808$	10.5239	0.370231
$809$	−4.98889	−0.175400	−0.0877000	−	0.996147i	$-0.527952\pi$
$809$	−4.98889	−0.175400	−0.0877000	+	0.996147i	$0.527952\pi$
$810$	−1.78717	−0.0627949
$811$	2.61994	0.0919986	0.0459993	−	0.998941i	$-0.485353\pi$
$811$	2.61994	0.0919986	0.0459993	+	0.998941i	$0.485353\pi$
$812$	6.65515	0.233550
$813$	23.7785	0.833947
$814$	25.7007	0.900809
$815$	−22.5392	−0.789514
$816$	9.50251	0.332655
$817$	34.5605	1.20912
$818$	25.3283	0.885583
$819$	4.94069	0.172642
$820$	5.56588	0.194369
$821$	−14.0592	−0.490670	−0.245335	−	0.969438i	$-0.578898\pi$
$821$	−14.0592	−0.490670	−0.245335	+	0.969438i	$0.578898\pi$
$822$	25.8502	0.901629
$823$	46.9108	1.63521	0.817603	−	0.575782i	$-0.195302\pi$
$823$	46.9108	1.63521	0.817603	+	0.575782i	$0.195302\pi$
$824$	22.4231	0.781144
$825$	−5.76695	−0.200780
$826$	7.91905	0.275539
$827$	9.97661	0.346921	0.173460	−	0.984841i	$-0.444505\pi$
$827$	9.97661	0.346921	0.173460	+	0.984841i	$0.444505\pi$
$828$	−1.19399	−0.0414941
$829$	27.6546	0.960485	0.480242	−	0.877136i	$-0.340549\pi$
$829$	27.6546	0.960485	0.480242	+	0.877136i	$0.340549\pi$
$830$	4.51987	0.156887
$831$	−17.4415	−0.605040
$832$	−3.83527	−0.132964
$833$	−1.91492	−0.0663479
$834$	0.574411	0.0198902
$835$	0.590948	0.0204506
$836$	−34.7730	−1.20265
$837$	−9.61929	−0.332491
$838$	25.3023	0.874053
$839$	8.92508	0.308128	0.154064	−	0.988061i	$-0.450764\pi$
$839$	8.92508	0.308128	0.154064	+	0.988061i	$0.450764\pi$
$840$	1.44048	0.0497012
$841$	2.06800	0.0713104
$842$	−38.7829	−1.33655
$843$	22.6653	0.780636
$844$	2.81655	0.0969495
$845$	11.4104	0.392531
$846$	−4.32414	−0.148667
$847$	22.2578	0.764786
$848$	−25.1172	−0.862529
$849$	31.7559	1.08986
$850$	3.42229	0.117384
$851$	−2.49363	−0.0854804
$852$	−9.67084	−0.331318
$853$	−8.56231	−0.293168	−0.146584	−	0.989198i	$-0.546828\pi$
$853$	−8.56231	−0.293168	−0.146584	+	0.989198i	$0.546828\pi$
$854$	−17.5749	−0.601399
$855$	5.05003	0.172708
$856$	−3.66739	−0.125349
$857$	7.46128	0.254872	0.127436	−	0.991847i	$-0.459325\pi$
$857$	7.46128	0.254872	0.127436	+	0.991847i	$0.459325\pi$
$858$	50.9215	1.73843
$859$	28.9288	0.987038	0.493519	−	0.869735i	$-0.335710\pi$
$859$	28.9288	0.987038	0.493519	+	0.869735i	$0.335710\pi$
$860$	8.17123	0.278637
$861$	4.66157	0.158866
$862$	42.4898	1.44721
$863$	23.3137	0.793609	0.396804	−	0.917903i	$-0.370119\pi$
$863$	23.3137	0.793609	0.396804	+	0.917903i	$0.370119\pi$
$864$	5.98766	0.203704
$865$	−9.23360	−0.313952
$866$	−15.6559	−0.532008
$867$	−13.3331	−0.452816
$868$	−11.4854	−0.389838
$869$	25.7618	0.873910
$870$	−9.96147	−0.337726
$871$	17.4255	0.590440
$872$	−10.1323	−0.343124
$873$	−4.66488	−0.157882
$874$	9.02529	0.305285
$875$	1.00000	0.0338062
$876$	9.39600	0.317461
$877$	4.79479	0.161908	0.0809542	−	0.996718i	$-0.474203\pi$
$877$	4.79479	0.161908	0.0809542	+	0.996718i	$0.474203\pi$
$878$	47.0056	1.58636
$879$	22.9821	0.775167
$880$	28.6177	0.964704
$881$	12.2290	0.412005	0.206003	−	0.978551i	$-0.433954\pi$
$881$	12.2290	0.412005	0.206003	+	0.978551i	$0.433954\pi$
$882$	−1.78717	−0.0601773
$883$	−1.28633	−0.0432885	−0.0216442	−	0.999766i	$-0.506890\pi$
$883$	−1.28633	−0.0432885	−0.0216442	+	0.999766i	$0.506890\pi$
$884$	−11.2964	−0.379938
$885$	−4.43104	−0.148948
$886$	42.2953	1.42094
$887$	−14.1304	−0.474453	−0.237227	−	0.971454i	$-0.576238\pi$
$887$	−14.1304	−0.474453	−0.237227	+	0.971454i	$0.576238\pi$
$888$	3.59201	0.120540
$889$	−3.29967	−0.110667
$890$	−0.00170237	−5.70637e−5 0
$891$	−5.76695	−0.193200
$892$	−33.1637	−1.11040
$893$	12.2188	0.408885
$894$	−26.2881	−0.879204
$895$	10.2776	0.343542
$896$	−10.5880	−0.353721
$897$	−4.94069	−0.164965
$898$	59.9222	1.99963
$899$	−53.6166	−1.78821
$900$	1.19399	0.0397997
$901$	−9.69242	−0.322901
$902$	48.0447	1.59971
$903$	6.84362	0.227742
$904$	−15.7840	−0.524968
$905$	24.9286	0.828653
$906$	−5.39327	−0.179179
$907$	18.6996	0.620910	0.310455	−	0.950588i	$-0.399519\pi$
$907$	18.6996	0.620910	0.310455	+	0.950588i	$0.399519\pi$
$908$	6.00392	0.199247
$909$	7.30587	0.242320
$910$	−8.82988	−0.292708
$911$	31.4339	1.04145	0.520726	−	0.853724i	$-0.325661\pi$
$911$	31.4339	1.04145	0.520726	+	0.853724i	$0.325661\pi$
$912$	−25.0601	−0.829824
$913$	14.5850	0.482692
$914$	70.8435	2.34330
$915$	9.83388	0.325098
$916$	33.9550	1.12190
$917$	21.8368	0.721113
$918$	3.42229	0.112952
$919$	−3.19367	−0.105349	−0.0526747	−	0.998612i	$-0.516775\pi$
$919$	−3.19367	−0.105349	−0.0526747	+	0.998612i	$0.516775\pi$
$920$	−1.44048	−0.0474911
$921$	14.3476	0.472768
$922$	−21.5245	−0.708873
$923$	−40.0176	−1.31719
$924$	−6.88570	−0.226523
$925$	2.49363	0.0819899
$926$	48.1491	1.58228
$927$	15.5664	0.511268
$928$	33.3744	1.09557
$929$	31.0697	1.01936	0.509682	−	0.860363i	$-0.329763\pi$
$929$	31.0697	1.01936	0.509682	+	0.860363i	$0.329763\pi$
$930$	17.1913	0.563726
$931$	5.05003	0.165508
$932$	−20.4313	−0.669248
$933$	−31.2661	−1.02361
$934$	3.01720	0.0987258
$935$	11.0432	0.361152
$936$	7.11695	0.232625
$937$	−21.1432	−0.690717	−0.345358	−	0.938471i	$-0.612243\pi$
$937$	−21.1432	−0.690717	−0.345358	+	0.938471i	$0.612243\pi$
$938$	−6.30324	−0.205808
$939$	−12.4626	−0.406702
$940$	2.88891	0.0942259
$941$	−19.8996	−0.648708	−0.324354	−	0.945936i	$-0.605147\pi$
$941$	−19.8996	−0.648708	−0.324354	+	0.945936i	$0.605147\pi$
$942$	−30.2518	−0.985656
$943$	−4.66157	−0.151802
$944$	21.9885	0.715664
$945$	1.00000	0.0325300
$946$	70.5342	2.29326
$947$	−18.5243	−0.601959	−0.300979	−	0.953631i	$-0.597314\pi$
$947$	−18.5243	−0.601959	−0.300979	+	0.953631i	$0.597314\pi$
$948$	−5.33373	−0.173232
$949$	38.8803	1.26211
$950$	−9.02529	−0.292819
$951$	33.0448	1.07155
$952$	−2.75839	−0.0894000
$953$	−5.04401	−0.163391	−0.0816957	−	0.996657i	$-0.526034\pi$
$953$	−5.04401	−0.163391	−0.0816957	+	0.996657i	$0.526034\pi$
$954$	−9.04585	−0.292870
$955$	−10.3252	−0.334115
$956$	20.6780	0.668774
$957$	−32.1442	−1.03908
$958$	−60.0835	−1.94121
$959$	−14.4643	−0.467076
$960$	−0.776261	−0.0250537
$961$	61.5307	1.98486
$962$	−22.0184	−0.709902
$963$	−2.54596	−0.0820423
$964$	6.94273	0.223610
$965$	12.0562	0.388104
$966$	1.78717	0.0575014
$967$	−46.3809	−1.49151	−0.745755	−	0.666220i	$-0.767911\pi$
$967$	−46.3809	−1.49151	−0.745755	+	0.666220i	$0.767911\pi$
$968$	32.0618	1.03050
$969$	−9.67039	−0.310658
$970$	8.33696	0.267684
$971$	−33.4656	−1.07396	−0.536981	−	0.843594i	$-0.680435\pi$
$971$	−33.4656	−1.07396	−0.536981	+	0.843594i	$0.680435\pi$
$972$	1.19399	0.0382973
$973$	−0.321407	−0.0103038
$974$	12.3594	0.396021
$975$	4.94069	0.158229
$976$	−48.7993	−1.56203
$977$	−56.3976	−1.80432	−0.902160	−	0.431401i	$-0.858019\pi$
$977$	−56.3976	−1.80432	−0.902160	+	0.431401i	$0.858019\pi$
$978$	40.2815	1.28806
$979$	−0.00549332	−0.000175567 0
$980$	1.19399	0.0381407
$981$	−7.03401	−0.224579
$982$	−27.2546	−0.869729
$983$	−37.0224	−1.18083	−0.590416	−	0.807099i	$-0.701036\pi$
$983$	−37.0224	−1.18083	−0.590416	+	0.807099i	$0.701036\pi$
$984$	6.71488	0.214063
$985$	−7.99771	−0.254828
$986$	19.0754	0.607484
$987$	2.41954	0.0770148
$988$	29.7909	0.947775
$989$	−6.84362	−0.217615
$990$	10.3066	0.327564
$991$	11.4366	0.363294	0.181647	−	0.983364i	$-0.441857\pi$
$991$	11.4366	0.363294	0.181647	+	0.983364i	$0.441857\pi$
$992$	−57.5970	−1.82871
$993$	12.1192	0.384591
$994$	14.4754	0.459131
$995$	17.3059	0.548634
$996$	−3.01968	−0.0956821
$997$	−29.7278	−0.941490	−0.470745	−	0.882269i	$-0.656015\pi$
$997$	−29.7278	−0.941490	−0.470745	+	0.882269i	$0.656015\pi$
$998$	34.7842	1.10108
$999$	2.49363	0.0788949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.w.1.3	✓	10
3.2	odd	2		7245.2.a.bv.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.w.1.3	✓	10	1.1	even	1	trivial
7245.2.a.bv.1.8		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q-1.78717 q^{2} +1.00000 q^{3} +1.19399 q^{4} +1.00000 q^{5} -1.78717 q^{6} +1.00000 q^{7} +1.44048 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.78717 q^{2} +1.00000 q^{3} +1.19399 q^{4} +1.00000 q^{5} -1.78717 q^{6} +1.00000 q^{7} +1.44048 q^{8} +1.00000 q^{9} -1.78717 q^{10} -5.76695 q^{11} +1.19399 q^{12} +4.94069 q^{13} -1.78717 q^{14} +1.00000 q^{15} -4.96237 q^{16} -1.91492 q^{17} -1.78717 q^{18} +5.05003 q^{19} +1.19399 q^{20} +1.00000 q^{21} +10.3066 q^{22} -1.00000 q^{23} +1.44048 q^{24} +1.00000 q^{25} -8.82988 q^{26} +1.00000 q^{27} +1.19399 q^{28} +5.57387 q^{29} -1.78717 q^{30} -9.61929 q^{31} +5.98766 q^{32} -5.76695 q^{33} +3.42229 q^{34} +1.00000 q^{35} +1.19399 q^{36} +2.49363 q^{37} -9.02529 q^{38} +4.94069 q^{39} +1.44048 q^{40} +4.66157 q^{41} -1.78717 q^{42} +6.84362 q^{43} -6.88570 q^{44} +1.00000 q^{45} +1.78717 q^{46} +2.41954 q^{47} -4.96237 q^{48} +1.00000 q^{49} -1.78717 q^{50} -1.91492 q^{51} +5.89915 q^{52} +5.06154 q^{53} -1.78717 q^{54} -5.76695 q^{55} +1.44048 q^{56} +5.05003 q^{57} -9.96147 q^{58} -4.43104 q^{59} +1.19399 q^{60} +9.83388 q^{61} +17.1913 q^{62} +1.00000 q^{63} -0.776261 q^{64} +4.94069 q^{65} +10.3066 q^{66} +3.52693 q^{67} -2.28639 q^{68} -1.00000 q^{69} -1.78717 q^{70} -8.09959 q^{71} +1.44048 q^{72} +7.86940 q^{73} -4.45655 q^{74} +1.00000 q^{75} +6.02970 q^{76} -5.76695 q^{77} -8.82988 q^{78} -4.46714 q^{79} -4.96237 q^{80} +1.00000 q^{81} -8.33104 q^{82} -2.52906 q^{83} +1.19399 q^{84} -1.91492 q^{85} -12.2307 q^{86} +5.57387 q^{87} -8.30716 q^{88} +0.000952551 q^{89} -1.78717 q^{90} +4.94069 q^{91} -1.19399 q^{92} -9.61929 q^{93} -4.32414 q^{94} +5.05003 q^{95} +5.98766 q^{96} -4.66488 q^{97} -1.78717 q^{98} -5.76695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} + 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 9 q^{11} + 16 q^{12} + 14 q^{13} + 2 q^{14} + 10 q^{15} + 20 q^{16} + 8 q^{17} + 2 q^{18} + 13 q^{19} + 16 q^{20} + 10 q^{21} - 10 q^{23} + 6 q^{24} + 10 q^{25} - 11 q^{26} + 10 q^{27} + 16 q^{28} + 10 q^{29} + 2 q^{30} + 8 q^{31} - 11 q^{32} + 9 q^{33} - 5 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 10 q^{38} + 14 q^{39} + 6 q^{40} - 5 q^{41} + 2 q^{42} + 4 q^{43} + 3 q^{44} + 10 q^{45} - 2 q^{46} + q^{47} + 20 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 14 q^{52} + 9 q^{53} + 2 q^{54} + 9 q^{55} + 6 q^{56} + 13 q^{57} - 28 q^{58} - 17 q^{59} + 16 q^{60} + 19 q^{61} - 28 q^{62} + 10 q^{63} + 24 q^{64} + 14 q^{65} + 8 q^{68} - 10 q^{69} + 2 q^{70} + 6 q^{72} + 6 q^{73} + 3 q^{74} + 10 q^{75} + 15 q^{76} + 9 q^{77} - 11 q^{78} + 32 q^{79} + 20 q^{80} + 10 q^{81} + 14 q^{82} - 2 q^{83} + 16 q^{84} + 8 q^{85} + 2 q^{86} + 10 q^{87} - 3 q^{88} + 10 q^{89} + 2 q^{90} + 14 q^{91} - 16 q^{92} + 8 q^{93} - 10 q^{94} + 13 q^{95} - 11 q^{96} + 18 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 + 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 9 * q^11 + 16 * q^12 + 14 * q^13 + 2 * q^14 + 10 * q^15 + 20 * q^16 + 8 * q^17 + 2 * q^18 + 13 * q^19 + 16 * q^20 + 10 * q^21 - 10 * q^23 + 6 * q^24 + 10 * q^25 - 11 * q^26 + 10 * q^27 + 16 * q^28 + 10 * q^29 + 2 * q^30 + 8 * q^31 - 11 * q^32 + 9 * q^33 - 5 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 10 * q^38 + 14 * q^39 + 6 * q^40 - 5 * q^41 + 2 * q^42 + 4 * q^43 + 3 * q^44 + 10 * q^45 - 2 * q^46 + q^47 + 20 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 14 * q^52 + 9 * q^53 + 2 * q^54 + 9 * q^55 + 6 * q^56 + 13 * q^57 - 28 * q^58 - 17 * q^59 + 16 * q^60 + 19 * q^61 - 28 * q^62 + 10 * q^63 + 24 * q^64 + 14 * q^65 + 8 * q^68 - 10 * q^69 + 2 * q^70 + 6 * q^72 + 6 * q^73 + 3 * q^74 + 10 * q^75 + 15 * q^76 + 9 * q^77 - 11 * q^78 + 32 * q^79 + 20 * q^80 + 10 * q^81 + 14 * q^82 - 2 * q^83 + 16 * q^84 + 8 * q^85 + 2 * q^86 + 10 * q^87 - 3 * q^88 + 10 * q^89 + 2 * q^90 + 14 * q^91 - 16 * q^92 + 8 * q^93 - 10 * q^94 + 13 * q^95 - 11 * q^96 + 18 * q^97 + 2 * q^98 + 9 * q^99

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