LMFDB - Embedded newform 5290.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.1509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 4 $ x^3 - x^2 - 7*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.92542$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} -1.00000 q^{10} +0.925423 q^{11} -2.92542 q^{12} +2.55810 q^{13} -4.55810 q^{14} +2.92542 q^{15} +1.00000 q^{16} -6.92542 q^{17} +5.55810 q^{18} +3.29275 q^{19} -1.00000 q^{20} +13.3344 q^{21} +0.925423 q^{22} -2.92542 q^{24} +1.00000 q^{25} +2.55810 q^{26} -7.48352 q^{27} -4.55810 q^{28} -1.26535 q^{29} +2.92542 q^{30} +10.4089 q^{31} +1.00000 q^{32} -2.70725 q^{33} -6.92542 q^{34} +4.55810 q^{35} +5.55810 q^{36} -9.70169 q^{37} +3.29275 q^{38} -7.48352 q^{39} -1.00000 q^{40} -0.925423 q^{41} +13.3344 q^{42} +1.26535 q^{43} +0.925423 q^{44} -5.55810 q^{45} +10.9670 q^{47} -2.92542 q^{48} +13.7763 q^{49} +1.00000 q^{50} +20.2598 q^{51} +2.55810 q^{52} +3.11620 q^{53} -7.48352 q^{54} -0.925423 q^{55} -4.55810 q^{56} -9.63268 q^{57} -1.26535 q^{58} -7.26535 q^{59} +2.92542 q^{60} +11.8925 q^{61} +10.4089 q^{62} -25.3344 q^{63} +1.00000 q^{64} -2.55810 q^{65} -2.70725 q^{66} +7.85085 q^{67} -6.92542 q^{68} +4.55810 q^{70} -6.92542 q^{71} +5.55810 q^{72} -9.26535 q^{73} -9.70169 q^{74} -2.92542 q^{75} +3.29275 q^{76} -4.21817 q^{77} -7.48352 q^{78} +10.9670 q^{79} -1.00000 q^{80} +5.21817 q^{81} -0.925423 q^{82} -0.585493 q^{83} +13.3344 q^{84} +6.92542 q^{85} +1.26535 q^{86} +3.70169 q^{87} +0.925423 q^{88} -9.11620 q^{89} -5.55810 q^{90} -11.6601 q^{91} -30.4506 q^{93} +10.9670 q^{94} -3.29275 q^{95} -2.92542 q^{96} +3.22373 q^{97} +13.7763 q^{98} +5.14359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 3 q^{10} - 5 q^{11} - q^{12} - 3 q^{13} - 3 q^{14} + q^{15} + 3 q^{16} - 13 q^{17} + 6 q^{18} + 5 q^{19} - 3 q^{20} + 6 q^{21} - 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} - 3 q^{28} + 2 q^{29} + q^{30} + 5 q^{31} + 3 q^{32} - 13 q^{33} - 13 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} + 5 q^{38} - 4 q^{39} - 3 q^{40} + 5 q^{41} + 6 q^{42} - 2 q^{43} - 5 q^{44} - 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} + 19 q^{51} - 3 q^{52} - 12 q^{53} - 4 q^{54} + 5 q^{55} - 3 q^{56} - 26 q^{57} + 2 q^{58} - 16 q^{59} + q^{60} - 9 q^{61} + 5 q^{62} - 42 q^{63} + 3 q^{64} + 3 q^{65} - 13 q^{66} + 8 q^{67} - 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} + 2 q^{74} - q^{75} + 5 q^{76} - 4 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} + 5 q^{82} + 8 q^{83} + 6 q^{84} + 13 q^{85} - 2 q^{86} - 20 q^{87} - 5 q^{88} - 6 q^{89} - 6 q^{90} - 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} + 33 q^{97} + 18 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 3 * q^10 - 5 * q^11 - q^12 - 3 * q^13 - 3 * q^14 + q^15 + 3 * q^16 - 13 * q^17 + 6 * q^18 + 5 * q^19 - 3 * q^20 + 6 * q^21 - 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 - 3 * q^28 + 2 * q^29 + q^30 + 5 * q^31 + 3 * q^32 - 13 * q^33 - 13 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 + 5 * q^38 - 4 * q^39 - 3 * q^40 + 5 * q^41 + 6 * q^42 - 2 * q^43 - 5 * q^44 - 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 + 19 * q^51 - 3 * q^52 - 12 * q^53 - 4 * q^54 + 5 * q^55 - 3 * q^56 - 26 * q^57 + 2 * q^58 - 16 * q^59 + q^60 - 9 * q^61 + 5 * q^62 - 42 * q^63 + 3 * q^64 + 3 * q^65 - 13 * q^66 + 8 * q^67 - 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 + 2 * q^74 - q^75 + 5 * q^76 - 4 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 + 5 * q^82 + 8 * q^83 + 6 * q^84 + 13 * q^85 - 2 * q^86 - 20 * q^87 - 5 * q^88 - 6 * q^89 - 6 * q^90 - 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 + 33 * q^97 + 18 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.92542	−1.68899	−0.844497	−	0.535561i	$-0.820100\pi$
$3$	−2.92542	−1.68899	−0.844497	+	0.535561i	$0.820100\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.92542	−1.19430
$7$	−4.55810	−1.72280	−0.861400	−	0.507928i	$-0.830412\pi$
$7$	−4.55810	−1.72280	−0.861400	+	0.507928i	$0.830412\pi$
$8$	1.00000	0.353553
$9$	5.55810	1.85270
$10$	−1.00000	−0.316228
$11$	0.925423	0.279026	0.139513	−	0.990220i	$-0.455446\pi$
$11$	0.925423	0.279026	0.139513	+	0.990220i	$0.455446\pi$
$12$	−2.92542	−0.844497
$13$	2.55810	0.709489	0.354745	−	0.934963i	$-0.384568\pi$
$13$	2.55810	0.709489	0.354745	+	0.934963i	$0.384568\pi$
$14$	−4.55810	−1.21820
$15$	2.92542	0.755341
$16$	1.00000	0.250000
$17$	−6.92542	−1.67966	−0.839831	−	0.542848i	$-0.817346\pi$
$17$	−6.92542	−1.67966	−0.839831	+	0.542848i	$0.817346\pi$
$18$	5.55810	1.31006
$19$	3.29275	0.755408	0.377704	−	0.925926i	$-0.376714\pi$
$19$	3.29275	0.755408	0.377704	+	0.925926i	$0.376714\pi$
$20$	−1.00000	−0.223607
$21$	13.3344	2.90980
$22$	0.925423	0.197301
$23$	0	0
$23$	0	0
$24$	−2.92542	−0.597149
$25$	1.00000	0.200000
$26$	2.55810	0.501685
$27$	−7.48352	−1.44020
$28$	−4.55810	−0.861400
$29$	−1.26535	−0.234970	−0.117485	−	0.993075i	$-0.537483\pi$
$29$	−1.26535	−0.234970	−0.117485	+	0.993075i	$0.537483\pi$
$30$	2.92542	0.534107
$31$	10.4089	1.86950	0.934751	−	0.355304i	$-0.115623\pi$
$31$	10.4089	1.86950	0.934751	+	0.355304i	$0.115623\pi$
$32$	1.00000	0.176777
$33$	−2.70725	−0.471272
$34$	−6.92542	−1.18770
$35$	4.55810	0.770459
$36$	5.55810	0.926350
$37$	−9.70169	−1.59495	−0.797474	−	0.603353i	$-0.793831\pi$
$37$	−9.70169	−1.59495	−0.797474	+	0.603353i	$0.793831\pi$
$38$	3.29275	0.534154
$39$	−7.48352	−1.19832
$40$	−1.00000	−0.158114
$41$	−0.925423	−0.144527	−0.0722634	−	0.997386i	$-0.523022\pi$
$41$	−0.925423	−0.144527	−0.0722634	+	0.997386i	$0.523022\pi$
$42$	13.3344	2.05754
$43$	1.26535	0.192964	0.0964822	−	0.995335i	$-0.469241\pi$
$43$	1.26535	0.192964	0.0964822	+	0.995335i	$0.469241\pi$
$44$	0.925423	0.139513
$45$	−5.55810	−0.828553
$46$	0	0
$47$	10.9670	1.59971	0.799854	−	0.600195i	$-0.204910\pi$
$47$	10.9670	1.59971	0.799854	+	0.600195i	$0.204910\pi$
$48$	−2.92542	−0.422248
$49$	13.7763	1.96804
$50$	1.00000	0.141421
$51$	20.2598	2.83694
$52$	2.55810	0.354745
$53$	3.11620	0.428043	0.214021	−	0.976829i	$-0.431344\pi$
$53$	3.11620	0.428043	0.214021	+	0.976829i	$0.431344\pi$
$54$	−7.48352	−1.01838
$55$	−0.925423	−0.124784
$56$	−4.55810	−0.609102
$57$	−9.63268	−1.27588
$58$	−1.26535	−0.166149
$59$	−7.26535	−0.945868	−0.472934	−	0.881098i	$-0.656805\pi$
$59$	−7.26535	−0.945868	−0.472934	+	0.881098i	$0.656805\pi$
$60$	2.92542	0.377670
$61$	11.8925	1.52267	0.761337	−	0.648356i	$-0.224543\pi$
$61$	11.8925	1.52267	0.761337	+	0.648356i	$0.224543\pi$
$62$	10.4089	1.32194
$63$	−25.3344	−3.19183
$64$	1.00000	0.125000
$65$	−2.55810	−0.317293
$66$	−2.70725	−0.333240
$67$	7.85085	0.959133	0.479567	−	0.877505i	$-0.340794\pi$
$67$	7.85085	0.959133	0.479567	+	0.877505i	$0.340794\pi$
$68$	−6.92542	−0.839831
$69$	0	0
$70$	4.55810	0.544797
$71$	−6.92542	−0.821896	−0.410948	−	0.911659i	$-0.634802\pi$
$71$	−6.92542	−0.821896	−0.410948	+	0.911659i	$0.634802\pi$
$72$	5.55810	0.655028
$73$	−9.26535	−1.08443	−0.542214	−	0.840241i	$-0.682414\pi$
$73$	−9.26535	−1.08443	−0.542214	+	0.840241i	$0.682414\pi$
$74$	−9.70169	−1.12780
$75$	−2.92542	−0.337799
$76$	3.29275	0.377704
$77$	−4.21817	−0.480705
$78$	−7.48352	−0.847342
$79$	10.9670	1.23389	0.616944	−	0.787007i	$-0.288370\pi$
$79$	10.9670	1.23389	0.616944	+	0.787007i	$0.288370\pi$
$80$	−1.00000	−0.111803
$81$	5.21817	0.579797
$82$	−0.925423	−0.102196
$83$	−0.585493	−0.0642662	−0.0321331	−	0.999484i	$-0.510230\pi$
$83$	−0.585493	−0.0642662	−0.0321331	+	0.999484i	$0.510230\pi$
$84$	13.3344	1.45490
$85$	6.92542	0.751168
$86$	1.26535	0.136446
$87$	3.70169	0.396863
$88$	0.925423	0.0986504
$89$	−9.11620	−0.966315	−0.483158	−	0.875533i	$-0.660510\pi$
$89$	−9.11620	−0.966315	−0.483158	+	0.875533i	$0.660510\pi$
$90$	−5.55810	−0.585875
$91$	−11.6601	−1.22231
$92$	0	0
$93$	−30.4506	−3.15758
$94$	10.9670	1.13116
$95$	−3.29275	−0.337829
$96$	−2.92542	−0.298575
$97$	3.22373	0.327320	0.163660	−	0.986517i	$-0.447670\pi$
$97$	3.22373	0.327320	0.163660	+	0.986517i	$0.447670\pi$
$98$	13.7763	1.39161
$99$	5.14359	0.516950
$100$	1.00000	0.100000
$101$	9.70169	0.965354	0.482677	−	0.875798i	$-0.339664\pi$
$101$	9.70169	0.965354	0.482677	+	0.875798i	$0.339664\pi$
$102$	20.2598	2.00602
$103$	19.7433	1.94537	0.972683	−	0.232136i	$-0.0745716\pi$
$103$	19.7433	1.94537	0.972683	+	0.232136i	$0.0745716\pi$
$104$	2.55810	0.250842
$105$	−13.3344	−1.30130
$106$	3.11620	0.302672
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−7.48352	−0.720102
$109$	−15.2927	−1.46478	−0.732390	−	0.680886i	$-0.761595\pi$
$109$	−15.2927	−1.46478	−0.732390	+	0.680886i	$0.761595\pi$
$110$	−0.925423	−0.0882356
$111$	28.3816	2.69386
$112$	−4.55810	−0.430700
$113$	−7.26535	−0.683467	−0.341733	−	0.939797i	$-0.611014\pi$
$113$	−7.26535	−0.683467	−0.341733	+	0.939797i	$0.611014\pi$
$114$	−9.63268	−0.902183
$115$	0	0
$116$	−1.26535	−0.117485
$117$	14.2182	1.31447
$118$	−7.26535	−0.668830
$119$	31.5668	2.89372
$120$	2.92542	0.267053
$121$	−10.1436	−0.922145
$122$	11.8925	1.07669
$123$	2.70725	0.244105
$124$	10.4089	0.934751
$125$	−1.00000	−0.0894427
$126$	−25.3344	−2.25696
$127$	−18.2872	−1.62273	−0.811363	−	0.584543i	$-0.801274\pi$
$127$	−18.2872	−1.62273	−0.811363	+	0.584543i	$0.801274\pi$
$128$	1.00000	0.0883883
$129$	−3.70169	−0.325916
$130$	−2.55810	−0.224360
$131$	−15.7017	−1.37186	−0.685932	−	0.727666i	$-0.740605\pi$
$131$	−15.7017	−1.37186	−0.685932	+	0.727666i	$0.740605\pi$
$132$	−2.70725	−0.235636
$133$	−15.0087	−1.30142
$134$	7.85085	0.678210
$135$	7.48352	0.644079
$136$	−6.92542	−0.593850
$137$	−2.02739	−0.173212	−0.0866060	−	0.996243i	$-0.527602\pi$
$137$	−2.02739	−0.173212	−0.0866060	+	0.996243i	$0.527602\pi$
$138$	0	0
$139$	6.14915	0.521564	0.260782	−	0.965398i	$-0.416020\pi$
$139$	6.14915	0.521564	0.260782	+	0.965398i	$0.416020\pi$
$140$	4.55810	0.385230
$141$	−32.0832	−2.70190
$142$	−6.92542	−0.581169
$143$	2.36732	0.197966
$144$	5.55810	0.463175
$145$	1.26535	0.105082
$146$	−9.26535	−0.766806
$147$	−40.3014	−3.32400
$148$	−9.70169	−0.797474
$149$	−8.70725	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$149$	−8.70725	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$150$	−2.92542	−0.238860
$151$	13.0746	1.06399	0.531997	−	0.846746i	$-0.321442\pi$
$151$	13.0746	1.06399	0.531997	+	0.846746i	$0.321442\pi$
$152$	3.29275	0.267077
$153$	−38.4922	−3.11191
$154$	−4.21817	−0.339910
$155$	−10.4089	−0.836067
$156$	−7.48352	−0.599161
$157$	4.14915	0.331139	0.165569	−	0.986198i	$-0.447054\pi$
$157$	4.14915	0.331139	0.165569	+	0.986198i	$0.447054\pi$
$158$	10.9670	0.872491
$159$	−9.11620	−0.722962
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	5.21817	0.409978
$163$	−7.82345	−0.612780	−0.306390	−	0.951906i	$-0.599121\pi$
$163$	−7.82345	−0.612780	−0.306390	+	0.951906i	$0.599121\pi$
$164$	−0.925423	−0.0722634
$165$	2.70725	0.210759
$166$	−0.585493	−0.0454431
$167$	−6.58549	−0.509601	−0.254800	−	0.966994i	$-0.582010\pi$
$167$	−6.58549	−0.509601	−0.254800	+	0.966994i	$0.582010\pi$
$168$	13.3344	1.02877
$169$	−6.45613	−0.496625
$170$	6.92542	0.531156
$171$	18.3014	1.39954
$172$	1.26535	0.0964822
$173$	−0.925423	−0.0703586	−0.0351793	−	0.999381i	$-0.511200\pi$
$173$	−0.925423	−0.0703586	−0.0351793	+	0.999381i	$0.511200\pi$
$174$	3.70169	0.280625
$175$	−4.55810	−0.344560
$176$	0.925423	0.0697564
$177$	21.2542	1.59757
$178$	−9.11620	−0.683288
$179$	−2.88380	−0.215545	−0.107773	−	0.994176i	$-0.534372\pi$
$179$	−2.88380	−0.215545	−0.107773	+	0.994176i	$0.534372\pi$
$180$	−5.55810	−0.414276
$181$	−5.82345	−0.432854	−0.216427	−	0.976299i	$-0.569440\pi$
$181$	−5.82345	−0.432854	−0.216427	+	0.976299i	$0.569440\pi$
$182$	−11.6601	−0.864302
$183$	−34.7905	−2.57179
$184$	0	0
$185$	9.70169	0.713283
$186$	−30.4506	−2.23274
$187$	−6.40895	−0.468668
$188$	10.9670	0.799854
$189$	34.1106	2.48118
$190$	−3.29275	−0.238881
$191$	−21.1162	−1.52791	−0.763957	−	0.645267i	$-0.776746\pi$
$191$	−21.1162	−1.52791	−0.763957	+	0.645267i	$0.776746\pi$
$192$	−2.92542	−0.211124
$193$	3.85085	0.277190	0.138595	−	0.990349i	$-0.455741\pi$
$193$	3.85085	0.277190	0.138595	+	0.990349i	$0.455741\pi$
$194$	3.22373	0.231450
$195$	7.48352	0.535906
$196$	13.7763	0.984019
$197$	−14.7763	−1.05277	−0.526383	−	0.850248i	$-0.676452\pi$
$197$	−14.7763	−1.05277	−0.526383	+	0.850248i	$0.676452\pi$
$198$	5.14359	0.365539
$199$	−15.7017	−1.11306	−0.556532	−	0.830826i	$-0.687868\pi$
$199$	−15.7017	−1.11306	−0.556532	+	0.830826i	$0.687868\pi$
$200$	1.00000	0.0707107
$201$	−22.9670	−1.61997
$202$	9.70169	0.682609
$203$	5.76760	0.404806
$204$	20.2598	1.41847
$205$	0.925423	0.0646343
$206$	19.7433	1.37558
$207$	0	0
$208$	2.55810	0.177372
$209$	3.04718	0.210778
$210$	−13.3344	−0.920159
$211$	−8.81789	−0.607049	−0.303524	−	0.952824i	$-0.598163\pi$
$211$	−8.81789	−0.607049	−0.303524	+	0.952824i	$0.598163\pi$
$212$	3.11620	0.214021
$213$	20.2598	1.38818
$214$	−6.00000	−0.410152
$215$	−1.26535	−0.0862963
$216$	−7.48352	−0.509189
$217$	−47.4450	−3.22078
$218$	−15.2927	−1.03576
$219$	27.1051	1.83159
$220$	−0.925423	−0.0623920
$221$	−17.7159	−1.19170
$222$	28.3816	1.90484
$223$	12.3816	0.829130	0.414565	−	0.910020i	$-0.363934\pi$
$223$	12.3816	0.829130	0.414565	+	0.910020i	$0.363934\pi$
$224$	−4.55810	−0.304551
$225$	5.55810	0.370540
$226$	−7.26535	−0.483284
$227$	−6.81789	−0.452519	−0.226260	−	0.974067i	$-0.572650\pi$
$227$	−6.81789	−0.452519	−0.226260	+	0.974067i	$0.572650\pi$
$228$	−9.63268	−0.637940
$229$	−21.7017	−1.43409	−0.717044	−	0.697028i	$-0.754505\pi$
$229$	−21.7017	−1.43409	−0.717044	+	0.697028i	$0.754505\pi$
$230$	0	0
$231$	12.3399	0.811908
$232$	−1.26535	−0.0830745
$233$	7.85085	0.514326	0.257163	−	0.966368i	$-0.417212\pi$
$233$	7.85085	0.514326	0.257163	+	0.966368i	$0.417212\pi$
$234$	14.2182	0.929471
$235$	−10.9670	−0.715411
$236$	−7.26535	−0.472934
$237$	−32.0832	−2.08403
$238$	31.5668	2.04617
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	2.92542	0.188835
$241$	15.7017	1.01143	0.505717	−	0.862699i	$-0.331228\pi$
$241$	15.7017	1.01143	0.505717	+	0.862699i	$0.331228\pi$
$242$	−10.1436	−0.652055
$243$	7.18521	0.460932
$244$	11.8925	0.761337
$245$	−13.7763	−0.880134
$246$	2.70725	0.172608
$247$	8.42317	0.535954
$248$	10.4089	0.660969
$249$	1.71282	0.108545
$250$	−1.00000	−0.0632456
$251$	−0.762041	−0.0480996	−0.0240498	−	0.999711i	$-0.507656\pi$
$251$	−0.762041	−0.0480996	−0.0240498	+	0.999711i	$0.507656\pi$
$252$	−25.3344	−1.59592
$253$	0	0
$254$	−18.2872	−1.14744
$255$	−20.2598	−1.26872
$256$	1.00000	0.0625000
$257$	6.67986	0.416678	0.208339	−	0.978057i	$-0.433194\pi$
$257$	6.67986	0.416678	0.208339	+	0.978057i	$0.433194\pi$
$258$	−3.70169	−0.230457
$259$	44.2213	2.74778
$260$	−2.55810	−0.158647
$261$	−7.03296	−0.435329
$262$	−15.7017	−0.970054
$263$	−16.0416	−0.989169	−0.494584	−	0.869130i	$-0.664680\pi$
$263$	−16.0416	−0.989169	−0.494584	+	0.869130i	$0.664680\pi$
$264$	−2.70725	−0.166620
$265$	−3.11620	−0.191427
$266$	−15.0087	−0.920240
$267$	26.6687	1.63210
$268$	7.85085	0.479567
$269$	−23.5525	−1.43602	−0.718012	−	0.696031i	$-0.754948\pi$
$269$	−23.5525	−1.43602	−0.718012	+	0.696031i	$0.754948\pi$
$270$	7.48352	0.455433
$271$	−8.99444	−0.546373	−0.273187	−	0.961961i	$-0.588078\pi$
$271$	−8.99444	−0.546373	−0.273187	+	0.961961i	$0.588078\pi$
$272$	−6.92542	−0.419915
$273$	34.1106	2.06447
$274$	−2.02739	−0.122479
$275$	0.925423	0.0558051
$276$	0	0
$277$	11.1710	0.671200	0.335600	−	0.942005i	$-0.391061\pi$
$277$	11.1710	0.671200	0.335600	+	0.942005i	$0.391061\pi$
$278$	6.14915	0.368802
$279$	57.8539	3.46363
$280$	4.55810	0.272399
$281$	−26.6687	−1.59092	−0.795462	−	0.606004i	$-0.792772\pi$
$281$	−26.6687	−1.59092	−0.795462	+	0.606004i	$0.792772\pi$
$282$	−32.0832	−1.91053
$283$	1.26535	0.0752174	0.0376087	−	0.999293i	$-0.488026\pi$
$283$	1.26535	0.0752174	0.0376087	+	0.999293i	$0.488026\pi$
$284$	−6.92542	−0.410948
$285$	9.63268	0.570591
$286$	2.36732	0.139983
$287$	4.21817	0.248991
$288$	5.55810	0.327514
$289$	30.9615	1.82126
$290$	1.26535	0.0743041
$291$	−9.43078	−0.552842
$292$	−9.26535	−0.542214
$293$	25.4034	1.48408	0.742041	−	0.670355i	$-0.233858\pi$
$293$	25.4034	1.48408	0.742041	+	0.670355i	$0.233858\pi$
$294$	−40.3014	−2.35043
$295$	7.26535	0.423005
$296$	−9.70169	−0.563899
$297$	−6.92542	−0.401854
$298$	−8.70725	−0.504398
$299$	0	0
$300$	−2.92542	−0.168899
$301$	−5.76760	−0.332439
$302$	13.0746	0.752357
$303$	−28.3816	−1.63048
$304$	3.29275	0.188852
$305$	−11.8925	−0.680961
$306$	−38.4922	−2.20045
$307$	−20.4780	−1.16874	−0.584369	−	0.811488i	$-0.698658\pi$
$307$	−20.4780	−1.16874	−0.584369	+	0.811488i	$0.698658\pi$
$308$	−4.21817	−0.240353
$309$	−57.7575	−3.28571
$310$	−10.4089	−0.591188
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−7.48352	−0.423671
$313$	2.02739	0.114595	0.0572975	−	0.998357i	$-0.481752\pi$
$313$	2.02739	0.114595	0.0572975	+	0.998357i	$0.481752\pi$
$314$	4.14915	0.234150
$315$	25.3344	1.42743
$316$	10.9670	0.616944
$317$	2.25979	0.126923	0.0634613	−	0.997984i	$-0.479786\pi$
$317$	2.25979	0.126923	0.0634613	+	0.997984i	$0.479786\pi$
$318$	−9.11620	−0.511211
$319$	−1.17099	−0.0655626
$320$	−1.00000	−0.0559017
$321$	17.5525	0.979687
$322$	0	0
$323$	−22.8037	−1.26883
$324$	5.21817	0.289898
$325$	2.55810	0.141898
$326$	−7.82345	−0.433301
$327$	44.7378	2.47400
$328$	−0.925423	−0.0510979
$329$	−49.9889	−2.75598
$330$	2.70725	0.149029
$331$	−5.11620	−0.281212	−0.140606	−	0.990066i	$-0.544905\pi$
$331$	−5.11620	−0.281212	−0.140606	+	0.990066i	$0.544905\pi$
$332$	−0.585493	−0.0321331
$333$	−53.9230	−2.95496
$334$	−6.58549	−0.360342
$335$	−7.85085	−0.428938
$336$	13.3344	0.727449
$337$	−0.856408	−0.0466515	−0.0233257	−	0.999728i	$-0.507425\pi$
$337$	−0.856408	−0.0466515	−0.0233257	+	0.999728i	$0.507425\pi$
$338$	−6.45613	−0.351167
$339$	21.2542	1.15437
$340$	6.92542	0.375584
$341$	9.63268	0.521639
$342$	18.3014	0.989627
$343$	−30.8869	−1.66774
$344$	1.26535	0.0682232
$345$	0	0
$346$	−0.925423	−0.0497510
$347$	27.0087	1.44990	0.724951	−	0.688801i	$-0.241863\pi$
$347$	27.0087	1.44990	0.724951	+	0.688801i	$0.241863\pi$
$348$	3.70169	0.198432
$349$	−21.6469	−1.15873	−0.579366	−	0.815067i	$-0.696700\pi$
$349$	−21.6469	−1.15873	−0.579366	+	0.815067i	$0.696700\pi$
$350$	−4.55810	−0.243641
$351$	−19.1436	−1.02181
$352$	0.925423	0.0493252
$353$	−21.3486	−1.13627	−0.568136	−	0.822935i	$-0.692335\pi$
$353$	−21.3486	−1.13627	−0.568136	+	0.822935i	$0.692335\pi$
$354$	21.2542	1.12965
$355$	6.92542	0.367563
$356$	−9.11620	−0.483158
$357$	−92.3461	−4.88748
$358$	−2.88380	−0.152414
$359$	14.6687	0.774186	0.387093	−	0.922041i	$-0.373479\pi$
$359$	14.6687	0.774186	0.387093	+	0.922041i	$0.373479\pi$
$360$	−5.55810	−0.292938
$361$	−8.15782	−0.429359
$362$	−5.82345	−0.306074
$363$	29.6743	1.55750
$364$	−11.6601	−0.611154
$365$	9.26535	0.484971
$366$	−34.7905	−1.81853
$367$	1.17099	0.0611250	0.0305625	−	0.999533i	$-0.490270\pi$
$367$	1.17099	0.0611250	0.0305625	+	0.999533i	$0.490270\pi$
$368$	0	0
$369$	−5.14359	−0.267765
$370$	9.70169	0.504367
$371$	−14.2039	−0.737432
$372$	−30.4506	−1.57879
$373$	8.88380	0.459986	0.229993	−	0.973192i	$-0.426130\pi$
$373$	8.88380	0.459986	0.229993	+	0.973192i	$0.426130\pi$
$374$	−6.40895	−0.331399
$375$	2.92542	0.151068
$376$	10.9670	0.565582
$377$	−3.23690	−0.166709
$378$	34.1106	1.75446
$379$	23.0746	1.18526	0.592631	−	0.805474i	$-0.298089\pi$
$379$	23.0746	1.18526	0.592631	+	0.805474i	$0.298089\pi$
$380$	−3.29275	−0.168914
$381$	53.4977	2.74077
$382$	−21.1162	−1.08040
$383$	21.9341	1.12078	0.560390	−	0.828229i	$-0.310651\pi$
$383$	21.9341	1.12078	0.560390	+	0.828229i	$0.310651\pi$
$384$	−2.92542	−0.149287
$385$	4.21817	0.214978
$386$	3.85085	0.196003
$387$	7.03296	0.357505
$388$	3.22373	0.163660
$389$	1.74331	0.0883895	0.0441947	−	0.999023i	$-0.485928\pi$
$389$	1.74331	0.0883895	0.0441947	+	0.999023i	$0.485928\pi$
$390$	7.48352	0.378943
$391$	0	0
$392$	13.7763	0.695807
$393$	45.9341	2.31707
$394$	−14.7763	−0.744418
$395$	−10.9670	−0.551812
$396$	5.14359	0.258475
$397$	−13.0087	−0.652886	−0.326443	−	0.945217i	$-0.605850\pi$
$397$	−13.0087	−0.652886	−0.326443	+	0.945217i	$0.605850\pi$
$398$	−15.7017	−0.787055
$399$	43.9067	2.19808
$400$	1.00000	0.0500000
$401$	−37.9889	−1.89707	−0.948537	−	0.316666i	$-0.897436\pi$
$401$	−37.9889	−1.89707	−0.948537	+	0.316666i	$0.897436\pi$
$402$	−22.9670	−1.14549
$403$	26.6271	1.32639
$404$	9.70169	0.482677
$405$	−5.21817	−0.259293
$406$	5.76760	0.286241
$407$	−8.97817	−0.445031
$408$	20.2598	1.00301
$409$	10.2598	0.507314	0.253657	−	0.967294i	$-0.418367\pi$
$409$	10.2598	0.507314	0.253657	+	0.967294i	$0.418367\pi$
$410$	0.925423	0.0457034
$411$	5.93098	0.292554
$412$	19.7433	0.972683
$413$	33.1162	1.62954
$414$	0	0
$415$	0.585493	0.0287407
$416$	2.55810	0.125421
$417$	−17.9889	−0.880919
$418$	3.04718	0.149043
$419$	−16.9670	−0.828894	−0.414447	−	0.910073i	$-0.636025\pi$
$419$	−16.9670	−0.828894	−0.414447	+	0.910073i	$0.636025\pi$
$420$	−13.3344	−0.650651
$421$	−16.4637	−0.802393	−0.401197	−	0.915992i	$-0.631406\pi$
$421$	−16.4637	−0.802393	−0.401197	+	0.915992i	$0.631406\pi$
$422$	−8.81789	−0.429248
$423$	60.9559	2.96378
$424$	3.11620	0.151336
$425$	−6.92542	−0.335932
$426$	20.2598	0.981590
$427$	−54.2070	−2.62326
$428$	−6.00000	−0.290021
$429$	−6.92542	−0.334363
$430$	−1.26535	−0.0610207
$431$	−8.29831	−0.399715	−0.199858	−	0.979825i	$-0.564048\pi$
$431$	−8.29831	−0.399715	−0.199858	+	0.979825i	$0.564048\pi$
$432$	−7.48352	−0.360051
$433$	−20.2598	−0.973623	−0.486812	−	0.873507i	$-0.661840\pi$
$433$	−20.2598	−0.973623	−0.486812	+	0.873507i	$0.661840\pi$
$434$	−47.4450	−2.27743
$435$	−3.70169	−0.177483
$436$	−15.2927	−0.732390
$437$	0	0
$438$	27.1051	1.29513
$439$	−25.7575	−1.22934	−0.614670	−	0.788784i	$-0.710711\pi$
$439$	−25.7575	−1.22934	−0.614670	+	0.788784i	$0.710711\pi$
$440$	−0.925423	−0.0441178
$441$	76.5699	3.64618
$442$	−17.7159	−0.842660
$443$	−22.1106	−1.05051	−0.525254	−	0.850945i	$-0.676030\pi$
$443$	−22.1106	−1.05051	−0.525254	+	0.850945i	$0.676030\pi$
$444$	28.3816	1.34693
$445$	9.11620	0.432149
$446$	12.3816	0.586283
$447$	25.4724	1.20480
$448$	−4.55810	−0.215350
$449$	15.0777	0.711560	0.355780	−	0.934570i	$-0.384215\pi$
$449$	15.0777	0.711560	0.355780	+	0.934570i	$0.384215\pi$
$450$	5.55810	0.262011
$451$	−0.856408	−0.0403267
$452$	−7.26535	−0.341733
$453$	−38.2487	−1.79708
$454$	−6.81789	−0.319979
$455$	11.6601	0.546633
$456$	−9.63268	−0.451091
$457$	−22.9670	−1.07435	−0.537177	−	0.843470i	$-0.680509\pi$
$457$	−22.9670	−1.07435	−0.537177	+	0.843470i	$0.680509\pi$
$458$	−21.7017	−1.01405
$459$	51.8266	2.41906
$460$	0	0
$461$	27.1162	1.26293	0.631464	−	0.775405i	$-0.282455\pi$
$461$	27.1162	1.26293	0.631464	+	0.775405i	$0.282455\pi$
$462$	12.3399	0.574105
$463$	23.3486	1.08510	0.542551	−	0.840023i	$-0.317459\pi$
$463$	23.3486	1.08510	0.542551	+	0.840023i	$0.317459\pi$
$464$	−1.26535	−0.0587425
$465$	30.4506	1.41211
$466$	7.85085	0.363683
$467$	−0.585493	−0.0270934	−0.0135467	−	0.999908i	$-0.504312\pi$
$467$	−0.585493	−0.0270934	−0.0135467	+	0.999908i	$0.504312\pi$
$468$	14.2182	0.657235
$469$	−35.7849	−1.65239
$470$	−10.9670	−0.505872
$471$	−12.1380	−0.559291
$472$	−7.26535	−0.334415
$473$	1.17099	0.0538420
$474$	−32.0832	−1.47363
$475$	3.29275	0.151082
$476$	31.5668	1.44686
$477$	17.3201	0.793035
$478$	12.0000	0.548867
$479$	36.8179	1.68225	0.841126	−	0.540839i	$-0.181893\pi$
$479$	36.8179	1.68225	0.841126	+	0.540839i	$0.181893\pi$
$480$	2.92542	0.133527
$481$	−24.8179	−1.13160
$482$	15.7017	0.715192
$483$	0	0
$484$	−10.1436	−0.461072
$485$	−3.22373	−0.146382
$486$	7.18521	0.325928
$487$	−13.1162	−0.594352	−0.297176	−	0.954823i	$-0.596045\pi$
$487$	−13.1162	−0.594352	−0.297176	+	0.954823i	$0.596045\pi$
$488$	11.8925	0.538347
$489$	22.8869	1.03498
$490$	−13.7763	−0.622348
$491$	−21.1162	−0.952961	−0.476480	−	0.879185i	$-0.658088\pi$
$491$	−21.1162	−0.952961	−0.476480	+	0.879185i	$0.658088\pi$
$492$	2.70725	0.122052
$493$	8.76310	0.394670
$494$	8.42317	0.378976
$495$	−5.14359	−0.231187
$496$	10.4089	0.467375
$497$	31.5668	1.41596
$498$	1.71282	0.0767531
$499$	−4.43634	−0.198598	−0.0992989	−	0.995058i	$-0.531660\pi$
$499$	−4.43634	−0.198598	−0.0992989	+	0.995058i	$0.531660\pi$
$500$	−1.00000	−0.0447214
$501$	19.2654	0.860712
$502$	−0.762041	−0.0340116
$503$	−30.1939	−1.34628	−0.673139	−	0.739516i	$-0.735055\pi$
$503$	−30.1939	−1.34628	−0.673139	+	0.739516i	$0.735055\pi$
$504$	−25.3344	−1.12848
$505$	−9.70169	−0.431720
$506$	0	0
$507$	18.8869	0.838797
$508$	−18.2872	−0.811363
$509$	21.0218	0.931776	0.465888	−	0.884844i	$-0.345735\pi$
$509$	21.0218	0.931776	0.465888	+	0.884844i	$0.345735\pi$
$510$	−20.2598	−0.897119
$511$	42.2324	1.86825
$512$	1.00000	0.0441942
$513$	−24.6413	−1.08794
$514$	6.67986	0.294636
$515$	−19.7433	−0.869994
$516$	−3.70169	−0.162958
$517$	10.1492	0.446359
$518$	44.2213	1.94297
$519$	2.70725	0.118835
$520$	−2.55810	−0.112180
$521$	18.3704	0.804823	0.402412	−	0.915459i	$-0.368172\pi$
$521$	18.3704	0.804823	0.402412	+	0.915459i	$0.368172\pi$
$522$	−7.03296	−0.307824
$523$	3.11620	0.136262	0.0681309	−	0.997676i	$-0.478296\pi$
$523$	3.11620	0.136262	0.0681309	+	0.997676i	$0.478296\pi$
$524$	−15.7017	−0.685932
$525$	13.3344	0.581960
$526$	−16.0416	−0.699448
$527$	−72.0863	−3.14013
$528$	−2.70725	−0.117818
$529$	0	0
$530$	−3.11620	−0.135359
$531$	−40.3816	−1.75241
$532$	−15.0087	−0.650708
$533$	−2.36732	−0.102540
$534$	26.6687	1.15407
$535$	6.00000	0.259403
$536$	7.85085	0.339105
$537$	8.43634	0.364055
$538$	−23.5525	−1.01542
$539$	12.7489	0.549133
$540$	7.48352	0.322040
$541$	24.9670	1.07342	0.536709	−	0.843768i	$-0.319667\pi$
$541$	24.9670	1.07342	0.536709	+	0.843768i	$0.319667\pi$
$542$	−8.99444	−0.386344
$543$	17.0361	0.731087
$544$	−6.92542	−0.296925
$545$	15.2927	0.655069
$546$	34.1106	1.45980
$547$	−4.47486	−0.191331	−0.0956655	−	0.995414i	$-0.530498\pi$
$547$	−4.47486	−0.191331	−0.0956655	+	0.995414i	$0.530498\pi$
$548$	−2.02739	−0.0866060
$549$	66.0995	2.82106
$550$	0.925423	0.0394602
$551$	−4.16649	−0.177498
$552$	0	0
$553$	−49.9889	−2.12574
$554$	11.1710	0.474610
$555$	−28.3816	−1.20473
$556$	6.14915	0.260782
$557$	−34.8727	−1.47760	−0.738801	−	0.673923i	$-0.764608\pi$
$557$	−34.8727	−1.47760	−0.738801	+	0.673923i	$0.764608\pi$
$558$	57.8539	2.44915
$559$	3.23690	0.136906
$560$	4.55810	0.192615
$561$	18.7489	0.791578
$562$	−26.6687	−1.12495
$563$	41.1051	1.73237	0.866186	−	0.499721i	$-0.166564\pi$
$563$	41.1051	1.73237	0.866186	+	0.499721i	$0.166564\pi$
$564$	−32.0832	−1.35095
$565$	7.26535	0.305656
$566$	1.26535	0.0531867
$567$	−23.7849	−0.998873
$568$	−6.92542	−0.290584
$569$	12.6799	0.531567	0.265784	−	0.964033i	$-0.414369\pi$
$569$	12.6799	0.531567	0.265784	+	0.964033i	$0.414369\pi$
$570$	9.63268	0.403468
$571$	2.09641	0.0877320	0.0438660	−	0.999037i	$-0.486033\pi$
$571$	2.09641	0.0877320	0.0438660	+	0.999037i	$0.486033\pi$
$572$	2.36732	0.0989828
$573$	61.7738	2.58064
$574$	4.21817	0.176063
$575$	0	0
$576$	5.55810	0.231587
$577$	−10.8179	−0.450355	−0.225177	−	0.974318i	$-0.572296\pi$
$577$	−10.8179	−0.450355	−0.225177	+	0.974318i	$0.572296\pi$
$578$	30.9615	1.28783
$579$	−11.2654	−0.468172
$580$	1.26535	0.0525409
$581$	2.66874	0.110718
$582$	−9.43078	−0.390918
$583$	2.88380	0.119435
$584$	−9.26535	−0.383403
$585$	−14.2182	−0.587849
$586$	25.4034	1.04940
$587$	23.3070	0.961982	0.480991	−	0.876726i	$-0.340277\pi$
$587$	23.3070	0.961982	0.480991	+	0.876726i	$0.340277\pi$
$588$	−40.3014	−1.66200
$589$	34.2740	1.41224
$590$	7.26535	0.299110
$591$	43.2268	1.77811
$592$	−9.70169	−0.398737
$593$	20.5307	0.843095	0.421548	−	0.906806i	$-0.361487\pi$
$593$	20.5307	0.843095	0.421548	+	0.906806i	$0.361487\pi$
$594$	−6.92542	−0.284154
$595$	−31.5668	−1.29411
$596$	−8.70725	−0.356663
$597$	45.9341	1.87996
$598$	0	0
$599$	−1.37289	−0.0560946	−0.0280473	−	0.999607i	$-0.508929\pi$
$599$	−1.37289	−0.0560946	−0.0280473	+	0.999607i	$0.508929\pi$
$600$	−2.92542	−0.119430
$601$	−23.6743	−0.965695	−0.482847	−	0.875705i	$-0.660397\pi$
$601$	−23.6743	−0.965695	−0.482847	+	0.875705i	$0.660397\pi$
$602$	−5.76760	−0.235070
$603$	43.6358	1.77699
$604$	13.0746	0.531997
$605$	10.1436	0.412396
$606$	−28.3816	−1.15292
$607$	−21.4145	−0.869188	−0.434594	−	0.900626i	$-0.643108\pi$
$607$	−21.4145	−0.869188	−0.434594	+	0.900626i	$0.643108\pi$
$608$	3.29275	0.133539
$609$	−16.8727	−0.683715
$610$	−11.8925	−0.481512
$611$	28.0548	1.13498
$612$	−38.4922	−1.55595
$613$	1.26535	0.0511071	0.0255536	−	0.999673i	$-0.491865\pi$
$613$	1.26535	0.0511071	0.0255536	+	0.999673i	$0.491865\pi$
$614$	−20.4780	−0.826423
$615$	−2.70725	−0.109167
$616$	−4.21817	−0.169955
$617$	−9.45613	−0.380689	−0.190345	−	0.981717i	$-0.560961\pi$
$617$	−9.45613	−0.380689	−0.190345	+	0.981717i	$0.560961\pi$
$618$	−57.7575	−2.32335
$619$	17.0056	0.683511	0.341756	−	0.939789i	$-0.388978\pi$
$619$	17.0056	0.683511	0.341756	+	0.939789i	$0.388978\pi$
$620$	−10.4089	−0.418033
$621$	0	0
$622$	12.0000	0.481156
$623$	41.5525	1.66477
$624$	−7.48352	−0.299581
$625$	1.00000	0.0400000
$626$	2.02739	0.0810310
$627$	−8.91430	−0.356003
$628$	4.14915	0.165569
$629$	67.1883	2.67897
$630$	25.3344	1.00935
$631$	−4.38155	−0.174427	−0.0872134	−	0.996190i	$-0.527796\pi$
$631$	−4.38155	−0.174427	−0.0872134	+	0.996190i	$0.527796\pi$
$632$	10.9670	0.436246
$633$	25.7961	1.02530
$634$	2.25979	0.0897478
$635$	18.2872	0.725705
$636$	−9.11620	−0.361481
$637$	35.2411	1.39630
$638$	−1.17099	−0.0463598
$639$	−38.4922	−1.52273
$640$	−1.00000	−0.0395285
$641$	34.6139	1.36717	0.683584	−	0.729871i	$-0.260420\pi$
$641$	34.6139	1.36717	0.683584	+	0.729871i	$0.260420\pi$
$642$	17.5525	0.692743
$643$	32.3156	1.27440	0.637202	−	0.770697i	$-0.280092\pi$
$643$	32.3156	1.27440	0.637202	+	0.770697i	$0.280092\pi$
$644$	0	0
$645$	3.70169	0.145754
$646$	−22.8037	−0.897198
$647$	−26.3156	−1.03457	−0.517287	−	0.855812i	$-0.673058\pi$
$647$	−26.3156	−1.03457	−0.517287	+	0.855812i	$0.673058\pi$
$648$	5.21817	0.204989
$649$	−6.72352	−0.263921
$650$	2.55810	0.100337
$651$	138.797	5.43987
$652$	−7.82345	−0.306390
$653$	20.0274	0.783732	0.391866	−	0.920022i	$-0.371830\pi$
$653$	20.0274	0.783732	0.391866	+	0.920022i	$0.371830\pi$
$654$	44.7378	1.74938
$655$	15.7017	0.613516
$656$	−0.925423	−0.0361317
$657$	−51.4977	−2.00912
$658$	−49.9889	−1.94877
$659$	−22.0285	−0.858107	−0.429053	−	0.903279i	$-0.641153\pi$
$659$	−22.0285	−0.858107	−0.429053	+	0.903279i	$0.641153\pi$
$660$	2.70725	0.105380
$661$	3.12936	0.121718	0.0608591	−	0.998146i	$-0.480616\pi$
$661$	3.12936	0.121718	0.0608591	+	0.998146i	$0.480616\pi$
$662$	−5.11620	−0.198847
$663$	51.8266	2.01278
$664$	−0.585493	−0.0227215
$665$	15.0087	0.582011
$666$	−53.9230	−2.08947
$667$	0	0
$668$	−6.58549	−0.254800
$669$	−36.2213	−1.40040
$670$	−7.85085	−0.303305
$671$	11.0056	0.424865
$672$	13.3344	0.514384
$673$	−41.4866	−1.59919	−0.799596	−	0.600538i	$-0.794953\pi$
$673$	−41.4866	−1.59919	−0.799596	+	0.600538i	$0.794953\pi$
$674$	−0.856408	−0.0329876
$675$	−7.48352	−0.288041
$676$	−6.45613	−0.248313
$677$	38.9011	1.49509	0.747546	−	0.664210i	$-0.231232\pi$
$677$	38.9011	1.49509	0.747546	+	0.664210i	$0.231232\pi$
$678$	21.2542	0.816264
$679$	−14.6941	−0.563907
$680$	6.92542	0.265578
$681$	19.9452	0.764302
$682$	9.63268	0.368854
$683$	27.8782	1.06673	0.533366	−	0.845885i	$-0.320927\pi$
$683$	27.8782	1.06673	0.533366	+	0.845885i	$0.320927\pi$
$684$	18.3014	0.699772
$685$	2.02739	0.0774627
$686$	−30.8869	−1.17927
$687$	63.4866	2.42217
$688$	1.26535	0.0482411
$689$	7.97155	0.303692
$690$	0	0
$691$	−30.7520	−1.16986	−0.584930	−	0.811084i	$-0.698878\pi$
$691$	−30.7520	−1.16986	−0.584930	+	0.811084i	$0.698878\pi$
$692$	−0.925423	−0.0351793
$693$	−23.4450	−0.890602
$694$	27.0087	1.02523
$695$	−6.14915	−0.233251
$696$	3.70169	0.140312
$697$	6.40895	0.242756
$698$	−21.6469	−0.819347
$699$	−22.9670	−0.868693
$700$	−4.55810	−0.172280
$701$	−6.17655	−0.233285	−0.116643	−	0.993174i	$-0.537213\pi$
$701$	−6.17655	−0.233285	−0.116643	+	0.993174i	$0.537213\pi$
$702$	−19.1436	−0.722528
$703$	−31.9452	−1.20484
$704$	0.925423	0.0348782
$705$	32.0832	1.20832
$706$	−21.3486	−0.803465
$707$	−44.2213	−1.66311
$708$	21.2542	0.798783
$709$	−40.9539	−1.53806	−0.769028	−	0.639216i	$-0.779259\pi$
$709$	−40.9539	−1.53806	−0.769028	+	0.639216i	$0.779259\pi$
$710$	6.92542	0.259906
$711$	60.9559	2.28603
$712$	−9.11620	−0.341644
$713$	0	0
$714$	−92.3461	−3.45597
$715$	−2.36732	−0.0885329
$716$	−2.88380	−0.107773
$717$	−35.1051	−1.31102
$718$	14.6687	0.547432
$719$	7.22684	0.269515	0.134758	−	0.990879i	$-0.456974\pi$
$719$	7.22684	0.269515	0.134758	+	0.990879i	$0.456974\pi$
$720$	−5.55810	−0.207138
$721$	−89.9920	−3.35148
$722$	−8.15782	−0.303603
$723$	−45.9341	−1.70831
$724$	−5.82345	−0.216427
$725$	−1.26535	−0.0469940
$726$	29.6743	1.10132
$727$	−28.7215	−1.06522	−0.532610	−	0.846361i	$-0.678789\pi$
$727$	−28.7215	−1.06522	−0.532610	+	0.846361i	$0.678789\pi$
$728$	−11.6601	−0.432151
$729$	−36.6743	−1.35831
$730$	9.26535	0.342926
$731$	−8.76310	−0.324115
$732$	−34.7905	−1.28589
$733$	10.5196	0.388550	0.194275	−	0.980947i	$-0.437765\pi$
$733$	10.5196	0.388550	0.194275	+	0.980947i	$0.437765\pi$
$734$	1.17099	0.0432219
$735$	40.3014	1.48654
$736$	0	0
$737$	7.26535	0.267623
$738$	−5.14359	−0.189338
$739$	15.6184	0.574534	0.287267	−	0.957851i	$-0.407253\pi$
$739$	15.6184	0.574534	0.287267	+	0.957851i	$0.407253\pi$
$740$	9.70169	0.356641
$741$	−24.6413	−0.905222
$742$	−14.2039	−0.521443
$743$	−3.38711	−0.124261	−0.0621306	−	0.998068i	$-0.519790\pi$
$743$	−3.38711	−0.124261	−0.0621306	+	0.998068i	$0.519790\pi$
$744$	−30.4506	−1.11637
$745$	8.70725	0.319009
$746$	8.88380	0.325259
$747$	−3.25423	−0.119066
$748$	−6.40895	−0.234334
$749$	27.3486	0.999296
$750$	2.92542	0.106821
$751$	−5.41451	−0.197578	−0.0987891	−	0.995108i	$-0.531497\pi$
$751$	−5.41451	−0.197578	−0.0987891	+	0.995108i	$0.531497\pi$
$752$	10.9670	0.399927
$753$	2.22929	0.0812400
$754$	−3.23690	−0.117881
$755$	−13.0746	−0.475833
$756$	34.1106	1.24059
$757$	−3.11620	−0.113260	−0.0566301	−	0.998395i	$-0.518036\pi$
$757$	−3.11620	−0.113260	−0.0566301	+	0.998395i	$0.518036\pi$
$758$	23.0746	0.838106
$759$	0	0
$760$	−3.29275	−0.119440
$761$	5.96148	0.216104	0.108052	−	0.994145i	$-0.465539\pi$
$761$	5.96148	0.216104	0.108052	+	0.994145i	$0.465539\pi$
$762$	53.4977	1.93802
$763$	69.7059	2.52352
$764$	−21.1162	−0.763957
$765$	38.4922	1.39169
$766$	21.9341	0.792511
$767$	−18.5855	−0.671083
$768$	−2.92542	−0.105562
$769$	−15.7017	−0.566217	−0.283109	−	0.959088i	$-0.591366\pi$
$769$	−15.7017	−0.566217	−0.283109	+	0.959088i	$0.591366\pi$
$770$	4.21817	0.152012
$771$	−19.5414	−0.703767
$772$	3.85085	0.138595
$773$	−29.7849	−1.07129	−0.535645	−	0.844443i	$-0.679931\pi$
$773$	−29.7849	−1.07129	−0.535645	+	0.844443i	$0.679931\pi$
$774$	7.03296	0.252794
$775$	10.4089	0.373900
$776$	3.22373	0.115725
$777$	−129.366	−4.64098
$778$	1.74331	0.0625008
$779$	−3.04718	−0.109177
$780$	7.48352	0.267953
$781$	−6.40895	−0.229330
$782$	0	0
$783$	9.46929	0.338405
$784$	13.7763	0.492010
$785$	−4.14915	−0.148090
$786$	45.9341	1.63841
$787$	−20.3156	−0.724174	−0.362087	−	0.932144i	$-0.617936\pi$
$787$	−20.3156	−0.724174	−0.362087	+	0.932144i	$0.617936\pi$
$788$	−14.7763	−0.526383
$789$	46.9285	1.67070
$790$	−10.9670	−0.390190
$791$	33.1162	1.17748
$792$	5.14359	0.182770
$793$	30.4221	1.08032
$794$	−13.0087	−0.461660
$795$	9.11620	0.323318
$796$	−15.7017	−0.556532
$797$	−36.5855	−1.29592	−0.647962	−	0.761672i	$-0.724379\pi$
$797$	−36.5855	−1.29592	−0.647962	+	0.761672i	$0.724379\pi$
$798$	43.9067	1.55428
$799$	−75.9514	−2.68697
$800$	1.00000	0.0353553
$801$	−50.6687	−1.79029
$802$	−37.9889	−1.34143
$803$	−8.57437	−0.302583
$804$	−22.9670	−0.809985
$805$	0	0
$806$	26.6271	0.937900
$807$	68.9011	2.42543
$808$	9.70169	0.341304
$809$	−33.0087	−1.16052	−0.580261	−	0.814430i	$-0.697050\pi$
$809$	−33.0087	−1.16052	−0.580261	+	0.814430i	$0.697050\pi$
$810$	−5.21817	−0.183348
$811$	25.6073	0.899195	0.449597	−	0.893231i	$-0.351567\pi$
$811$	25.6073	0.899195	0.449597	+	0.893231i	$0.351567\pi$
$812$	5.76760	0.202403
$813$	26.3125	0.922821
$814$	−8.97817	−0.314685
$815$	7.82345	0.274044
$816$	20.2598	0.709235
$817$	4.16649	0.145767
$818$	10.2598	0.358725
$819$	−64.8078	−2.26457
$820$	0.925423	0.0323172
$821$	−5.78493	−0.201896	−0.100948	−	0.994892i	$-0.532188\pi$
$821$	−5.78493	−0.201896	−0.100948	+	0.994892i	$0.532188\pi$
$822$	5.93098	0.206867
$823$	−28.9011	−1.00743	−0.503715	−	0.863870i	$-0.668034\pi$
$823$	−28.9011	−1.00743	−0.503715	+	0.863870i	$0.668034\pi$
$824$	19.7433	0.687791
$825$	−2.70725	−0.0942545
$826$	33.1162	1.15226
$827$	−7.98888	−0.277800	−0.138900	−	0.990306i	$-0.544357\pi$
$827$	−7.98888	−0.277800	−0.138900	+	0.990306i	$0.544357\pi$
$828$	0	0
$829$	−6.76310	−0.234892	−0.117446	−	0.993079i	$-0.537471\pi$
$829$	−6.76310	−0.234892	−0.117446	+	0.993079i	$0.537471\pi$
$830$	0.585493	0.0203228
$831$	−32.6799	−1.13365
$832$	2.55810	0.0886861
$833$	−95.4065	−3.30564
$834$	−17.9889	−0.622904
$835$	6.58549	0.227900
$836$	3.04718	0.105389
$837$	−77.8956	−2.69246
$838$	−16.9670	−0.586117
$839$	−15.2106	−0.525127	−0.262564	−	0.964915i	$-0.584568\pi$
$839$	−15.2106	−0.525127	−0.262564	+	0.964915i	$0.584568\pi$
$840$	−13.3344	−0.460079
$841$	−27.3989	−0.944789
$842$	−16.4637	−0.567378
$843$	78.0173	2.68706
$844$	−8.81789	−0.303524
$845$	6.45613	0.222098
$846$	60.9559	2.09571
$847$	46.2355	1.58867
$848$	3.11620	0.107011
$849$	−3.70169	−0.127042
$850$	−6.92542	−0.237540
$851$	0	0
$852$	20.2598	0.694089
$853$	−5.08880	−0.174237	−0.0871187	−	0.996198i	$-0.527766\pi$
$853$	−5.08880	−0.174237	−0.0871187	+	0.996198i	$0.527766\pi$
$854$	−54.2070	−1.85493
$855$	−18.3014	−0.625895
$856$	−6.00000	−0.205076
$857$	9.56366	0.326688	0.163344	−	0.986569i	$-0.447772\pi$
$857$	9.56366	0.326688	0.163344	+	0.986569i	$0.447772\pi$
$858$	−6.92542	−0.236430
$859$	45.9889	1.56912	0.784560	−	0.620053i	$-0.212889\pi$
$859$	45.9889	1.56912	0.784560	+	0.620053i	$0.212889\pi$
$860$	−1.26535	−0.0431482
$861$	−12.3399	−0.420544
$862$	−8.29831	−0.282642
$863$	−55.4034	−1.88595	−0.942977	−	0.332859i	$-0.891987\pi$
$863$	−55.4034	−1.88595	−0.942977	+	0.332859i	$0.891987\pi$
$864$	−7.48352	−0.254595
$865$	0.925423	0.0314653
$866$	−20.2598	−0.688456
$867$	−90.5754	−3.07610
$868$	−47.4450	−1.61039
$869$	10.1492	0.344286
$870$	−3.70169	−0.125499
$871$	20.0832	0.680495
$872$	−15.2927	−0.517878
$873$	17.9178	0.606426
$874$	0	0
$875$	4.55810	0.154092
$876$	27.1051	0.915796
$877$	9.98683	0.337231	0.168616	−	0.985682i	$-0.446070\pi$
$877$	9.98683	0.337231	0.168616	+	0.985682i	$0.446070\pi$
$878$	−25.7575	−0.869275
$879$	−74.3156	−2.50660
$880$	−0.925423	−0.0311960
$881$	−32.7631	−1.10382	−0.551908	−	0.833905i	$-0.686100\pi$
$881$	−32.7631	−1.10382	−0.551908	+	0.833905i	$0.686100\pi$
$882$	76.5699	2.57824
$883$	28.2882	0.951975	0.475988	−	0.879452i	$-0.342091\pi$
$883$	28.2882	0.951975	0.475988	+	0.879452i	$0.342091\pi$
$884$	−17.7159	−0.595851
$885$	−21.2542	−0.714453
$886$	−22.1106	−0.742821
$887$	−48.1380	−1.61632	−0.808158	−	0.588965i	$-0.799536\pi$
$887$	−48.1380	−1.61632	−0.808158	+	0.588965i	$0.799536\pi$
$888$	28.3816	0.952422
$889$	83.3548	2.79563
$890$	9.11620	0.305576
$891$	4.82901	0.161778
$892$	12.3816	0.414565
$893$	36.1117	1.20843
$894$	25.4724	0.851924
$895$	2.88380	0.0963949
$896$	−4.55810	−0.152275
$897$	0	0
$898$	15.0777	0.503149
$899$	−13.1710	−0.439277
$900$	5.55810	0.185270
$901$	−21.5810	−0.718967
$902$	−0.856408	−0.0285153
$903$	16.8727	0.561488
$904$	−7.26535	−0.241642
$905$	5.82345	0.193578
$906$	−38.2487	−1.27073
$907$	0.938589	0.0311653	0.0155827	−	0.999879i	$-0.495040\pi$
$907$	0.938589	0.0311653	0.0155827	+	0.999879i	$0.495040\pi$
$908$	−6.81789	−0.226260
$909$	53.9230	1.78851
$910$	11.6601	0.386528
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	−9.63268	−0.318970
$913$	−0.541829	−0.0179319
$914$	−22.9670	−0.759682
$915$	34.7905	1.15014
$916$	−21.7017	−0.717044
$917$	71.5699	2.36345
$918$	51.8266	1.71053
$919$	−18.7235	−0.617632	−0.308816	−	0.951122i	$-0.599933\pi$
$919$	−18.7235	−0.617632	−0.308816	+	0.951122i	$0.599933\pi$
$920$	0	0
$921$	59.9067	1.97399
$922$	27.1162	0.893024
$923$	−17.7159	−0.583127
$924$	12.3399	0.405954
$925$	−9.70169	−0.318990
$926$	23.3486	0.767282
$927$	109.735	3.60418
$928$	−1.26535	−0.0415372
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	30.4506	0.998513
$931$	45.3618	1.48667
$932$	7.85085	0.257163
$933$	−35.1051	−1.14929
$934$	−0.585493	−0.0191579
$935$	6.40895	0.209595
$936$	14.2182	0.464735
$937$	55.9067	1.82639	0.913196	−	0.407521i	$-0.133607\pi$
$937$	55.9067	1.82639	0.913196	+	0.407521i	$0.133607\pi$
$938$	−35.7849	−1.16842
$939$	−5.93098	−0.193550
$940$	−10.9670	−0.357706
$941$	−16.2740	−0.530518	−0.265259	−	0.964177i	$-0.585457\pi$
$941$	−16.2740	−0.530518	−0.265259	+	0.964177i	$0.585457\pi$
$942$	−12.1380	−0.395478
$943$	0	0
$944$	−7.26535	−0.236467
$945$	−34.1106	−1.10962
$946$	1.17099	0.0380721
$947$	−1.53627	−0.0499220	−0.0249610	−	0.999688i	$-0.507946\pi$
$947$	−1.53627	−0.0499220	−0.0249610	+	0.999688i	$0.507946\pi$
$948$	−32.0832	−1.04202
$949$	−23.7017	−0.769389
$950$	3.29275	0.106831
$951$	−6.61084	−0.214371
$952$	31.5668	1.02308
$953$	38.3288	1.24159	0.620796	−	0.783972i	$-0.286810\pi$
$953$	38.3288	1.24159	0.620796	+	0.783972i	$0.286810\pi$
$954$	17.3201	0.560760
$955$	21.1162	0.683304
$956$	12.0000	0.388108
$957$	3.42563	0.110735
$958$	36.8179	1.18953
$959$	9.24106	0.298409
$960$	2.92542	0.0944176
$961$	77.3461	2.49504
$962$	−24.8179	−0.800161
$963$	−33.3486	−1.07464
$964$	15.7017	0.505717
$965$	−3.85085	−0.123963
$966$	0	0
$967$	−9.03296	−0.290480	−0.145240	−	0.989396i	$-0.546395\pi$
$967$	−9.03296	−0.290480	−0.145240	+	0.989396i	$0.546395\pi$
$968$	−10.1436	−0.326027
$969$	66.7104	2.14305
$970$	−3.22373	−0.103508
$971$	−51.4561	−1.65131	−0.825653	−	0.564178i	$-0.809193\pi$
$971$	−51.4561	−1.65131	−0.825653	+	0.564178i	$0.809193\pi$
$972$	7.18521	0.230466
$973$	−28.0285	−0.898551
$974$	−13.1162	−0.420270
$975$	−7.48352	−0.239665
$976$	11.8925	0.380669
$977$	42.1939	1.34990	0.674951	−	0.737863i	$-0.264165\pi$
$977$	42.1939	1.34990	0.674951	+	0.737863i	$0.264165\pi$
$978$	22.8869	0.731843
$979$	−8.43634	−0.269627
$980$	−13.7763	−0.440067
$981$	−84.9986	−2.71380
$982$	−21.1162	−0.673845
$983$	−19.9584	−0.636573	−0.318287	−	0.947994i	$-0.603107\pi$
$983$	−19.9584	−0.636573	−0.318287	+	0.947994i	$0.603107\pi$
$984$	2.70725	0.0863041
$985$	14.7763	0.470811
$986$	8.76310	0.279074
$987$	146.239	4.65483
$988$	8.42317	0.267977
$989$	0	0
$990$	−5.14359	−0.163474
$991$	−40.7763	−1.29530	−0.647650	−	0.761938i	$-0.724248\pi$
$991$	−40.7763	−1.29530	−0.647650	+	0.761938i	$0.724248\pi$
$992$	10.4089	0.330484
$993$	14.9670	0.474965
$994$	31.5668	1.00124
$995$	15.7017	0.497777
$996$	1.71282	0.0542726
$997$	21.4034	0.677852	0.338926	−	0.940813i	$-0.389936\pi$
$997$	21.4034	0.677852	0.338926	+	0.940813i	$0.389936\pi$
$998$	−4.43634	−0.140430
$999$	72.6028	2.29705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.p.1.1	✓	3
23.22	odd	2		5290.2.a.q.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.p.1.1	✓	3	1.1	even	1	trivial
5290.2.a.q.1.1	yes	3	23.22	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.92542 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.92542 q^{6} -4.55810 q^{7} +1.00000 q^{8} +5.55810 q^{9} -1.00000 q^{10} +0.925423 q^{11} -2.92542 q^{12} +2.55810 q^{13} -4.55810 q^{14} +2.92542 q^{15} +1.00000 q^{16} -6.92542 q^{17} +5.55810 q^{18} +3.29275 q^{19} -1.00000 q^{20} +13.3344 q^{21} +0.925423 q^{22} -2.92542 q^{24} +1.00000 q^{25} +2.55810 q^{26} -7.48352 q^{27} -4.55810 q^{28} -1.26535 q^{29} +2.92542 q^{30} +10.4089 q^{31} +1.00000 q^{32} -2.70725 q^{33} -6.92542 q^{34} +4.55810 q^{35} +5.55810 q^{36} -9.70169 q^{37} +3.29275 q^{38} -7.48352 q^{39} -1.00000 q^{40} -0.925423 q^{41} +13.3344 q^{42} +1.26535 q^{43} +0.925423 q^{44} -5.55810 q^{45} +10.9670 q^{47} -2.92542 q^{48} +13.7763 q^{49} +1.00000 q^{50} +20.2598 q^{51} +2.55810 q^{52} +3.11620 q^{53} -7.48352 q^{54} -0.925423 q^{55} -4.55810 q^{56} -9.63268 q^{57} -1.26535 q^{58} -7.26535 q^{59} +2.92542 q^{60} +11.8925 q^{61} +10.4089 q^{62} -25.3344 q^{63} +1.00000 q^{64} -2.55810 q^{65} -2.70725 q^{66} +7.85085 q^{67} -6.92542 q^{68} +4.55810 q^{70} -6.92542 q^{71} +5.55810 q^{72} -9.26535 q^{73} -9.70169 q^{74} -2.92542 q^{75} +3.29275 q^{76} -4.21817 q^{77} -7.48352 q^{78} +10.9670 q^{79} -1.00000 q^{80} +5.21817 q^{81} -0.925423 q^{82} -0.585493 q^{83} +13.3344 q^{84} +6.92542 q^{85} +1.26535 q^{86} +3.70169 q^{87} +0.925423 q^{88} -9.11620 q^{89} -5.55810 q^{90} -11.6601 q^{91} -30.4506 q^{93} +10.9670 q^{94} -3.29275 q^{95} -2.92542 q^{96} +3.22373 q^{97} +13.7763 q^{98} +5.14359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 3 q^{10} - 5 q^{11} - q^{12} - 3 q^{13} - 3 q^{14} + q^{15} + 3 q^{16} - 13 q^{17} + 6 q^{18} + 5 q^{19} - 3 q^{20} + 6 q^{21} - 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} - 3 q^{28} + 2 q^{29} + q^{30} + 5 q^{31} + 3 q^{32} - 13 q^{33} - 13 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} + 5 q^{38} - 4 q^{39} - 3 q^{40} + 5 q^{41} + 6 q^{42} - 2 q^{43} - 5 q^{44} - 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} + 19 q^{51} - 3 q^{52} - 12 q^{53} - 4 q^{54} + 5 q^{55} - 3 q^{56} - 26 q^{57} + 2 q^{58} - 16 q^{59} + q^{60} - 9 q^{61} + 5 q^{62} - 42 q^{63} + 3 q^{64} + 3 q^{65} - 13 q^{66} + 8 q^{67} - 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} + 2 q^{74} - q^{75} + 5 q^{76} - 4 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} + 5 q^{82} + 8 q^{83} + 6 q^{84} + 13 q^{85} - 2 q^{86} - 20 q^{87} - 5 q^{88} - 6 q^{89} - 6 q^{90} - 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} + 33 q^{97} + 18 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 3 * q^10 - 5 * q^11 - q^12 - 3 * q^13 - 3 * q^14 + q^15 + 3 * q^16 - 13 * q^17 + 6 * q^18 + 5 * q^19 - 3 * q^20 + 6 * q^21 - 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 - 3 * q^28 + 2 * q^29 + q^30 + 5 * q^31 + 3 * q^32 - 13 * q^33 - 13 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 + 5 * q^38 - 4 * q^39 - 3 * q^40 + 5 * q^41 + 6 * q^42 - 2 * q^43 - 5 * q^44 - 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 + 19 * q^51 - 3 * q^52 - 12 * q^53 - 4 * q^54 + 5 * q^55 - 3 * q^56 - 26 * q^57 + 2 * q^58 - 16 * q^59 + q^60 - 9 * q^61 + 5 * q^62 - 42 * q^63 + 3 * q^64 + 3 * q^65 - 13 * q^66 + 8 * q^67 - 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 + 2 * q^74 - q^75 + 5 * q^76 - 4 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 + 5 * q^82 + 8 * q^83 + 6 * q^84 + 13 * q^85 - 2 * q^86 - 20 * q^87 - 5 * q^88 - 6 * q^89 - 6 * q^90 - 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 + 33 * q^97 + 18 * q^98 - 5 * q^99

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