LMFDB - Embedded newform 5290.2.a.q.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:	$0$
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	$-0.169588\pi$
$7$	4.55810	1.72280	0.861400	+	0.507928i	$0.169588\pi$
$8$	1.00000	0.353553
$9$	5.55810	1.85270
$10$	1.00000	0.316228
$11$	−0.925423	−0.279026	−0.139513	−	0.990220i	$-0.544554\pi$
$11$	−0.925423	−0.279026	−0.139513	+	0.990220i	$0.544554\pi$
$12$	−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	$-0.182654\pi$
$17$	6.92542	1.67966	0.839831	+	0.542848i	$0.182654\pi$
$18$	5.55810	1.31006
$19$	−3.29275	−0.755408	−0.377704	−	0.925926i	$-0.623286\pi$
$19$	−3.29275	−0.755408	−0.377704	+	0.925926i	$0.623286\pi$
$20$	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	$-0.206169\pi$
$37$	9.70169	1.59495	0.797474	+	0.603353i	$0.206169\pi$
$38$	−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	$-0.530759\pi$
$43$	−1.26535	−0.192964	−0.0964822	+	0.995335i	$0.530759\pi$
$44$	−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	$-0.568656\pi$
$53$	−3.11620	−0.428043	−0.214021	+	0.976829i	$0.568656\pi$
$54$	−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	$-0.775457\pi$
$61$	−11.8925	−1.52267	−0.761337	+	0.648356i	$0.775457\pi$
$62$	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	$-0.659206\pi$
$67$	−7.85085	−0.959133	−0.479567	+	0.877505i	$0.659206\pi$
$68$	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	$-0.711630\pi$
$79$	−10.9670	−1.23389	−0.616944	+	0.787007i	$0.711630\pi$
$80$	1.00000	0.111803
$81$	5.21817	0.579797
$82$	−0.925423	−0.102196
$83$	0.585493	0.0642662	0.0321331	−	0.999484i	$-0.489770\pi$
$83$	0.585493	0.0642662	0.0321331	+	0.999484i	$0.489770\pi$
$84$	−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	$-0.339490\pi$
$89$	9.11620	0.966315	0.483158	+	0.875533i	$0.339490\pi$
$90$	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	$-0.552330\pi$
$97$	−3.22373	−0.327320	−0.163660	+	0.986517i	$0.552330\pi$
$98$	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	$-0.925428\pi$
$103$	−19.7433	−1.94537	−0.972683	+	0.232136i	$0.925428\pi$
$104$	2.55810	0.250842
$105$	−13.3344	−1.30130
$106$	−3.11620	−0.302672
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−7.48352	−0.720102
$109$	15.2927	1.46478	0.732390	−	0.680886i	$-0.238405\pi$
$109$	15.2927	1.46478	0.732390	+	0.680886i	$0.238405\pi$
$110$	−0.925423	−0.0882356
$111$	−28.3816	−2.69386
$112$	4.55810	0.430700
$113$	7.26535	0.683467	0.341733	−	0.939797i	$-0.388986\pi$
$113$	7.26535	0.683467	0.341733	+	0.939797i	$0.388986\pi$
$114$	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	$-0.472398\pi$
$137$	2.02739	0.173212	0.0866060	+	0.996243i	$0.472398\pi$
$138$	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	$-0.383914\pi$
$149$	8.70725	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$150$	−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	$-0.552946\pi$
$157$	−4.14915	−0.331139	−0.165569	+	0.986198i	$0.552946\pi$
$158$	−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	$-0.430560\pi$
$181$	5.82345	0.432854	0.216427	+	0.976299i	$0.430560\pi$
$182$	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	$-0.223254\pi$
$191$	21.1162	1.52791	0.763957	+	0.645267i	$0.223254\pi$
$192$	−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	$-0.312132\pi$
$199$	15.7017	1.11306	0.556532	+	0.830826i	$0.312132\pi$
$200$	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	$-0.427350\pi$
$227$	6.81789	0.452519	0.226260	+	0.974067i	$0.427350\pi$
$228$	9.63268	0.637940
$229$	21.7017	1.43409	0.717044	−	0.697028i	$-0.245495\pi$
$229$	21.7017	1.43409	0.717044	+	0.697028i	$0.245495\pi$
$230$	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	$-0.668772\pi$
$241$	−15.7017	−1.01143	−0.505717	+	0.862699i	$0.668772\pi$
$242$	−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	$-0.492344\pi$
$251$	0.762041	0.0480996	0.0240498	+	0.999711i	$0.492344\pi$
$252$	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	$-0.335320\pi$
$263$	16.0416	0.989169	0.494584	+	0.869130i	$0.335320\pi$
$264$	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	$-0.207228\pi$
$281$	26.6687	1.59092	0.795462	+	0.606004i	$0.207228\pi$
$282$	−32.0832	−1.91053
$283$	−1.26535	−0.0752174	−0.0376087	−	0.999293i	$-0.511974\pi$
$283$	−1.26535	−0.0752174	−0.0376087	+	0.999293i	$0.511974\pi$
$284$	−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	$-0.766142\pi$
$293$	−25.4034	−1.48408	−0.742041	+	0.670355i	$0.766142\pi$
$294$	−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	$-0.518248\pi$
$313$	−2.02739	−0.114595	−0.0572975	+	0.998357i	$0.518248\pi$
$314$	−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	$-0.492575\pi$
$337$	0.856408	0.0466515	0.0233257	+	0.999728i	$0.492575\pi$
$338$	−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	$-0.626521\pi$
$359$	−14.6687	−0.774186	−0.387093	+	0.922041i	$0.626521\pi$
$360$	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	$-0.509730\pi$
$367$	−1.17099	−0.0611250	−0.0305625	+	0.999533i	$0.509730\pi$
$368$	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	$-0.573870\pi$
$373$	−8.88380	−0.459986	−0.229993	+	0.973192i	$0.573870\pi$
$374$	−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	$-0.701911\pi$
$379$	−23.0746	−1.18526	−0.592631	+	0.805474i	$0.701911\pi$
$380$	−3.29275	−0.168914
$381$	53.4977	2.74077
$382$	21.1162	1.08040
$383$	−21.9341	−1.12078	−0.560390	−	0.828229i	$-0.689349\pi$
$383$	−21.9341	−1.12078	−0.560390	+	0.828229i	$0.689349\pi$
$384$	−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	$-0.514072\pi$
$389$	−1.74331	−0.0883895	−0.0441947	+	0.999023i	$0.514072\pi$
$390$	−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	$-0.102564\pi$
$401$	37.9889	1.89707	0.948537	+	0.316666i	$0.102564\pi$
$402$	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	$-0.363975\pi$
$419$	16.9670	0.828894	0.414447	+	0.910073i	$0.363975\pi$
$420$	−13.3344	−0.650651
$421$	16.4637	0.802393	0.401197	−	0.915992i	$-0.368594\pi$
$421$	16.4637	0.802393	0.401197	+	0.915992i	$0.368594\pi$
$422$	−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	$-0.435952\pi$
$431$	8.29831	0.399715	0.199858	+	0.979825i	$0.435952\pi$
$432$	−7.48352	−0.360051
$433$	20.2598	0.973623	0.486812	−	0.873507i	$-0.338160\pi$
$433$	20.2598	0.973623	0.486812	+	0.873507i	$0.338160\pi$
$434$	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	$-0.319491\pi$
$457$	22.9670	1.07435	0.537177	+	0.843470i	$0.319491\pi$
$458$	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	$-0.495688\pi$
$467$	0.585493	0.0270934	0.0135467	+	0.999908i	$0.495688\pi$
$468$	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	$-0.818107\pi$
$479$	−36.8179	−1.68225	−0.841126	+	0.540839i	$0.818107\pi$
$480$	−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	$-0.264945\pi$
$503$	30.1939	1.34628	0.673139	+	0.739516i	$0.264945\pi$
$504$	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	$-0.631828\pi$
$521$	−18.3704	−0.804823	−0.402412	+	0.915459i	$0.631828\pi$
$522$	−7.03296	−0.307824
$523$	−3.11620	−0.136262	−0.0681309	−	0.997676i	$-0.521704\pi$
$523$	−3.11620	−0.136262	−0.0681309	+	0.997676i	$0.521704\pi$
$524$	−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	$-0.235392\pi$
$557$	34.8727	1.47760	0.738801	+	0.673923i	$0.235392\pi$
$558$	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	$-0.833436\pi$
$563$	−41.1051	−1.73237	−0.866186	+	0.499721i	$0.833436\pi$
$564$	−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	$-0.585631\pi$
$569$	−12.6799	−0.531567	−0.265784	+	0.964033i	$0.585631\pi$
$570$	9.63268	0.403468
$571$	−2.09641	−0.0877320	−0.0438660	−	0.999037i	$-0.513967\pi$
$571$	−2.09641	−0.0877320	−0.0438660	+	0.999037i	$0.513967\pi$
$572$	−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	$-0.508135\pi$
$613$	−1.26535	−0.0511071	−0.0255536	+	0.999673i	$0.508135\pi$
$614$	−20.4780	−0.826423
$615$	2.70725	0.109167
$616$	−4.21817	−0.169955
$617$	9.45613	0.380689	0.190345	−	0.981717i	$-0.439039\pi$
$617$	9.45613	0.380689	0.190345	+	0.981717i	$0.439039\pi$
$618$	57.7575	2.32335
$619$	−17.0056	−0.683511	−0.341756	−	0.939789i	$-0.611022\pi$
$619$	−17.0056	−0.683511	−0.341756	+	0.939789i	$0.611022\pi$
$620$	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	$-0.472204\pi$
$631$	4.38155	0.174427	0.0872134	+	0.996190i	$0.472204\pi$
$632$	−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	$-0.739580\pi$
$641$	−34.6139	−1.36717	−0.683584	+	0.729871i	$0.739580\pi$
$642$	−17.5525	−0.692743
$643$	−32.3156	−1.27440	−0.637202	−	0.770697i	$-0.719908\pi$
$643$	−32.3156	−1.27440	−0.637202	+	0.770697i	$0.719908\pi$
$644$	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	$-0.358847\pi$
$659$	22.0285	0.858107	0.429053	+	0.903279i	$0.358847\pi$
$660$	2.70725	0.105380
$661$	−3.12936	−0.121718	−0.0608591	−	0.998146i	$-0.519384\pi$
$661$	−3.12936	−0.121718	−0.0608591	+	0.998146i	$0.519384\pi$
$662$	−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	$-0.768768\pi$
$677$	−38.9011	−1.49509	−0.747546	+	0.664210i	$0.768768\pi$
$678$	−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	$-0.462787\pi$
$701$	6.17655	0.233285	0.116643	+	0.993174i	$0.462787\pi$
$702$	−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	$-0.220741\pi$
$709$	40.9539	1.53806	0.769028	+	0.639216i	$0.220741\pi$
$710$	−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	$-0.321211\pi$
$727$	28.7215	1.06522	0.532610	+	0.846361i	$0.321211\pi$
$728$	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	$-0.562235\pi$
$733$	−10.5196	−0.388550	−0.194275	+	0.980947i	$0.562235\pi$
$734$	−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	$-0.480210\pi$
$743$	3.38711	0.124261	0.0621306	+	0.998068i	$0.480210\pi$
$744$	−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	$-0.468503\pi$
$751$	5.41451	0.197578	0.0987891	+	0.995108i	$0.468503\pi$
$752$	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	$-0.481964\pi$
$757$	3.11620	0.113260	0.0566301	+	0.998395i	$0.481964\pi$
$758$	−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	$-0.408634\pi$
$769$	15.7017	0.566217	0.283109	+	0.959088i	$0.408634\pi$
$770$	−4.21817	−0.152012
$771$	−19.5414	−0.703767
$772$	3.85085	0.138595
$773$	29.7849	1.07129	0.535645	−	0.844443i	$-0.320069\pi$
$773$	29.7849	1.07129	0.535645	+	0.844443i	$0.320069\pi$
$774$	−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	$-0.382064\pi$
$787$	20.3156	0.724174	0.362087	+	0.932144i	$0.382064\pi$
$788$	−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	$-0.275621\pi$
$797$	36.5855	1.29592	0.647962	+	0.761672i	$0.275621\pi$
$798$	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	$-0.455643\pi$
$827$	7.98888	0.277800	0.138900	+	0.990306i	$0.455643\pi$
$828$	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	$-0.415432\pi$
$839$	15.2106	0.525127	0.262564	+	0.964915i	$0.415432\pi$
$840$	−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	$-0.313900\pi$
$881$	32.7631	1.10382	0.551908	+	0.833905i	$0.313900\pi$
$882$	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	$-0.504960\pi$
$907$	−0.938589	−0.0311653	−0.0155827	+	0.999879i	$0.504960\pi$
$908$	6.81789	0.226260
$909$	53.9230	1.78851
$910$	11.6601	0.386528
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	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	$-0.400067\pi$
$919$	18.7235	0.617632	0.308816	+	0.951122i	$0.400067\pi$
$920$	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	$-0.866393\pi$
$937$	−55.9067	−1.82639	−0.913196	+	0.407521i	$0.866393\pi$
$938$	−35.7849	−1.16842
$939$	5.93098	0.193550
$940$	10.9670	0.357706
$941$	16.2740	0.530518	0.265259	−	0.964177i	$-0.414543\pi$
$941$	16.2740	0.530518	0.265259	+	0.964177i	$0.414543\pi$
$942$	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	$-0.713190\pi$
$953$	−38.3288	−1.24159	−0.620796	+	0.783972i	$0.713190\pi$
$954$	−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	$-0.190807\pi$
$971$	51.4561	1.65131	0.825653	+	0.564178i	$0.190807\pi$
$972$	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	$-0.735835\pi$
$977$	−42.1939	−1.34990	−0.674951	+	0.737863i	$0.735835\pi$
$978$	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	$-0.396893\pi$
$983$	19.9584	0.636573	0.318287	+	0.947994i	$0.396893\pi$
$984$	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.q.1.1	yes	3
23.22	odd	2		5290.2.a.p.1.1	✓	3

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

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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