LMFDB - Embedded newform 5290.2.a.bk.1.13

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.78829$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.78829 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78829 q^{6} +0.104808 q^{7} +1.00000 q^{8} +4.77457 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.78829 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78829 q^{6} +0.104808 q^{7} +1.00000 q^{8} +4.77457 q^{9} -1.00000 q^{10} -1.61337 q^{11} +2.78829 q^{12} -0.820624 q^{13} +0.104808 q^{14} -2.78829 q^{15} +1.00000 q^{16} -2.39546 q^{17} +4.77457 q^{18} +5.04341 q^{19} -1.00000 q^{20} +0.292235 q^{21} -1.61337 q^{22} +2.78829 q^{24} +1.00000 q^{25} -0.820624 q^{26} +4.94803 q^{27} +0.104808 q^{28} +9.29479 q^{29} -2.78829 q^{30} +6.93969 q^{31} +1.00000 q^{32} -4.49855 q^{33} -2.39546 q^{34} -0.104808 q^{35} +4.77457 q^{36} +3.78260 q^{37} +5.04341 q^{38} -2.28814 q^{39} -1.00000 q^{40} +10.1328 q^{41} +0.292235 q^{42} +1.06696 q^{43} -1.61337 q^{44} -4.77457 q^{45} -8.70310 q^{47} +2.78829 q^{48} -6.98902 q^{49} +1.00000 q^{50} -6.67923 q^{51} -0.820624 q^{52} +10.1839 q^{53} +4.94803 q^{54} +1.61337 q^{55} +0.104808 q^{56} +14.0625 q^{57} +9.29479 q^{58} -1.88759 q^{59} -2.78829 q^{60} -0.718868 q^{61} +6.93969 q^{62} +0.500413 q^{63} +1.00000 q^{64} +0.820624 q^{65} -4.49855 q^{66} +3.50684 q^{67} -2.39546 q^{68} -0.104808 q^{70} -1.31155 q^{71} +4.77457 q^{72} +11.3521 q^{73} +3.78260 q^{74} +2.78829 q^{75} +5.04341 q^{76} -0.169094 q^{77} -2.28814 q^{78} -13.5089 q^{79} -1.00000 q^{80} -0.527159 q^{81} +10.1328 q^{82} +12.0038 q^{83} +0.292235 q^{84} +2.39546 q^{85} +1.06696 q^{86} +25.9166 q^{87} -1.61337 q^{88} -12.3656 q^{89} -4.77457 q^{90} -0.0860079 q^{91} +19.3499 q^{93} -8.70310 q^{94} -5.04341 q^{95} +2.78829 q^{96} -18.1600 q^{97} -6.98902 q^{98} -7.70316 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * 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
$3$	2.78829	1.60982	0.804911	−	0.593396i	$-0.202213\pi$
$3$	2.78829	1.60982	0.804911	+	0.593396i	$0.202213\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.78829	1.13832
$7$	0.104808	0.0396136	0.0198068	−	0.999804i	$-0.493695\pi$
$7$	0.104808	0.0396136	0.0198068	+	0.999804i	$0.493695\pi$
$8$	1.00000	0.353553
$9$	4.77457	1.59152
$10$	−1.00000	−0.316228
$11$	−1.61337	−0.486450	−0.243225	−	0.969970i	$-0.578205\pi$
$11$	−1.61337	−0.486450	−0.243225	+	0.969970i	$0.578205\pi$
$12$	2.78829	0.804911
$13$	−0.820624	−0.227600	−0.113800	−	0.993504i	$-0.536302\pi$
$13$	−0.820624	−0.227600	−0.113800	+	0.993504i	$0.536302\pi$
$14$	0.104808	0.0280111
$15$	−2.78829	−0.719934
$16$	1.00000	0.250000
$17$	−2.39546	−0.580984	−0.290492	−	0.956877i	$-0.593819\pi$
$17$	−2.39546	−0.580984	−0.290492	+	0.956877i	$0.593819\pi$
$18$	4.77457	1.12538
$19$	5.04341	1.15704	0.578518	−	0.815669i	$-0.303631\pi$
$19$	5.04341	1.15704	0.578518	+	0.815669i	$0.303631\pi$
$20$	−1.00000	−0.223607
$21$	0.292235	0.0637709
$22$	−1.61337	−0.343972
$23$	0	0
$23$	0	0
$24$	2.78829	0.569158
$25$	1.00000	0.200000
$26$	−0.820624	−0.160938
$27$	4.94803	0.952250
$28$	0.104808	0.0198068
$29$	9.29479	1.72600	0.863000	−	0.505204i	$-0.168583\pi$
$29$	9.29479	1.72600	0.863000	+	0.505204i	$0.168583\pi$
$30$	−2.78829	−0.509070
$31$	6.93969	1.24641	0.623203	−	0.782060i	$-0.285831\pi$
$31$	6.93969	1.24641	0.623203	+	0.782060i	$0.285831\pi$
$32$	1.00000	0.176777
$33$	−4.49855	−0.783097
$34$	−2.39546	−0.410817
$35$	−0.104808	−0.0177158
$36$	4.77457	0.795762
$37$	3.78260	0.621856	0.310928	−	0.950433i	$-0.399360\pi$
$37$	3.78260	0.621856	0.310928	+	0.950433i	$0.399360\pi$
$38$	5.04341	0.818149
$39$	−2.28814	−0.366396
$40$	−1.00000	−0.158114
$41$	10.1328	1.58248	0.791240	−	0.611505i	$-0.209436\pi$
$41$	10.1328	1.58248	0.791240	+	0.611505i	$0.209436\pi$
$42$	0.292235	0.0450928
$43$	1.06696	0.162709	0.0813547	−	0.996685i	$-0.474075\pi$
$43$	1.06696	0.162709	0.0813547	+	0.996685i	$0.474075\pi$
$44$	−1.61337	−0.243225
$45$	−4.77457	−0.711752
$46$	0	0
$47$	−8.70310	−1.26948	−0.634739	−	0.772727i	$-0.718892\pi$
$47$	−8.70310	−1.26948	−0.634739	+	0.772727i	$0.718892\pi$
$48$	2.78829	0.402455
$49$	−6.98902	−0.998431
$50$	1.00000	0.141421
$51$	−6.67923	−0.935280
$52$	−0.820624	−0.113800
$53$	10.1839	1.39887	0.699436	−	0.714696i	$-0.253435\pi$
$53$	10.1839	1.39887	0.699436	+	0.714696i	$0.253435\pi$
$54$	4.94803	0.673342
$55$	1.61337	0.217547
$56$	0.104808	0.0140055
$57$	14.0625	1.86262
$58$	9.29479	1.22047
$59$	−1.88759	−0.245744	−0.122872	−	0.992423i	$-0.539210\pi$
$59$	−1.88759	−0.245744	−0.122872	+	0.992423i	$0.539210\pi$
$60$	−2.78829	−0.359967
$61$	−0.718868	−0.0920417	−0.0460208	−	0.998940i	$-0.514654\pi$
$61$	−0.718868	−0.0920417	−0.0460208	+	0.998940i	$0.514654\pi$
$62$	6.93969	0.881342
$63$	0.500413	0.0630461
$64$	1.00000	0.125000
$65$	0.820624	0.101786
$66$	−4.49855	−0.553733
$67$	3.50684	0.428429	0.214215	−	0.976787i	$-0.431281\pi$
$67$	3.50684	0.428429	0.214215	+	0.976787i	$0.431281\pi$
$68$	−2.39546	−0.290492
$69$	0	0
$70$	−0.104808	−0.0125269
$71$	−1.31155	−0.155652	−0.0778259	−	0.996967i	$-0.524798\pi$
$71$	−1.31155	−0.155652	−0.0778259	+	0.996967i	$0.524798\pi$
$72$	4.77457	0.562689
$73$	11.3521	1.32867	0.664333	−	0.747437i	$-0.268716\pi$
$73$	11.3521	1.32867	0.664333	+	0.747437i	$0.268716\pi$
$74$	3.78260	0.439719
$75$	2.78829	0.321964
$76$	5.04341	0.578518
$77$	−0.169094	−0.0192700
$78$	−2.28814	−0.259081
$79$	−13.5089	−1.51987	−0.759933	−	0.650002i	$-0.774768\pi$
$79$	−13.5089	−1.51987	−0.759933	+	0.650002i	$0.774768\pi$
$80$	−1.00000	−0.111803
$81$	−0.527159	−0.0585732
$82$	10.1328	1.11898
$83$	12.0038	1.31759	0.658794	−	0.752324i	$-0.271067\pi$
$83$	12.0038	1.31759	0.658794	+	0.752324i	$0.271067\pi$
$84$	0.292235	0.0318854
$85$	2.39546	0.259824
$86$	1.06696	0.115053
$87$	25.9166	2.77855
$88$	−1.61337	−0.171986
$89$	−12.3656	−1.31075	−0.655373	−	0.755305i	$-0.727489\pi$
$89$	−12.3656	−1.31075	−0.655373	+	0.755305i	$0.727489\pi$
$90$	−4.77457	−0.503284
$91$	−0.0860079	−0.00901607
$92$	0	0
$93$	19.3499	2.00649
$94$	−8.70310	−0.897656
$95$	−5.04341	−0.517443
$96$	2.78829	0.284579
$97$	−18.1600	−1.84387	−0.921936	−	0.387341i	$-0.873394\pi$
$97$	−18.1600	−1.84387	−0.921936	+	0.387341i	$0.873394\pi$
$98$	−6.98902	−0.705997
$99$	−7.70316	−0.774197
$100$	1.00000	0.100000
$101$	10.7972	1.07437	0.537183	−	0.843466i	$-0.319488\pi$
$101$	10.7972	1.07437	0.537183	+	0.843466i	$0.319488\pi$
$102$	−6.67923	−0.661343
$103$	3.49218	0.344094	0.172047	−	0.985089i	$-0.444962\pi$
$103$	3.49218	0.344094	0.172047	+	0.985089i	$0.444962\pi$
$104$	−0.820624	−0.0804688
$105$	−0.292235	−0.0285192
$106$	10.1839	0.989151
$107$	8.04757	0.777988	0.388994	−	0.921240i	$-0.372823\pi$
$107$	8.04757	0.777988	0.388994	+	0.921240i	$0.372823\pi$
$108$	4.94803	0.476125
$109$	4.75271	0.455227	0.227614	−	0.973752i	$-0.426908\pi$
$109$	4.75271	0.455227	0.227614	+	0.973752i	$0.426908\pi$
$110$	1.61337	0.153829
$111$	10.5470	1.00108
$112$	0.104808	0.00990341
$113$	12.0649	1.13497	0.567487	−	0.823383i	$-0.307916\pi$
$113$	12.0649	1.13497	0.567487	+	0.823383i	$0.307916\pi$
$114$	14.0625	1.31707
$115$	0	0
$116$	9.29479	0.863000
$117$	−3.91813	−0.362232
$118$	−1.88759	−0.173767
$119$	−0.251063	−0.0230149
$120$	−2.78829	−0.254535
$121$	−8.39703	−0.763367
$122$	−0.718868	−0.0650833
$123$	28.2533	2.54751
$124$	6.93969	0.623203
$125$	−1.00000	−0.0894427
$126$	0.500413	0.0445803
$127$	−7.72617	−0.685587	−0.342793	−	0.939411i	$-0.611373\pi$
$127$	−7.72617	−0.685587	−0.342793	+	0.939411i	$0.611373\pi$
$128$	1.00000	0.0883883
$129$	2.97499	0.261933
$130$	0.820624	0.0719735
$131$	−15.9385	−1.39255	−0.696276	−	0.717774i	$-0.745161\pi$
$131$	−15.9385	−1.39255	−0.696276	+	0.717774i	$0.745161\pi$
$132$	−4.49855	−0.391548
$133$	0.528588	0.0458344
$134$	3.50684	0.302945
$135$	−4.94803	−0.425859
$136$	−2.39546	−0.205409
$137$	−1.42400	−0.121661	−0.0608305	−	0.998148i	$-0.519375\pi$
$137$	−1.42400	−0.121661	−0.0608305	+	0.998148i	$0.519375\pi$
$138$	0	0
$139$	7.21002	0.611546	0.305773	−	0.952104i	$-0.401085\pi$
$139$	7.21002	0.611546	0.305773	+	0.952104i	$0.401085\pi$
$140$	−0.104808	−0.00885788
$141$	−24.2668	−2.04363
$142$	−1.31155	−0.110062
$143$	1.32397	0.110716
$144$	4.77457	0.397881
$145$	−9.29479	−0.771890
$146$	11.3521	0.939509
$147$	−19.4874	−1.60730
$148$	3.78260	0.310928
$149$	18.4817	1.51408	0.757038	−	0.653371i	$-0.226646\pi$
$149$	18.4817	1.51408	0.757038	+	0.653371i	$0.226646\pi$
$150$	2.78829	0.227663
$151$	7.08884	0.576881	0.288441	−	0.957498i	$-0.406863\pi$
$151$	7.08884	0.576881	0.288441	+	0.957498i	$0.406863\pi$
$152$	5.04341	0.409074
$153$	−11.4373	−0.924650
$154$	−0.169094	−0.0136260
$155$	−6.93969	−0.557410
$156$	−2.28814	−0.183198
$157$	−7.01390	−0.559770	−0.279885	−	0.960034i	$-0.590296\pi$
$157$	−7.01390	−0.559770	−0.279885	+	0.960034i	$0.590296\pi$
$158$	−13.5089	−1.07471
$159$	28.3958	2.25193
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−0.527159	−0.0414175
$163$	−12.3924	−0.970649	−0.485325	−	0.874334i	$-0.661299\pi$
$163$	−12.3924	−0.970649	−0.485325	+	0.874334i	$0.661299\pi$
$164$	10.1328	0.791240
$165$	4.49855	0.350212
$166$	12.0038	0.931675
$167$	−8.43589	−0.652789	−0.326395	−	0.945234i	$-0.605834\pi$
$167$	−8.43589	−0.652789	−0.326395	+	0.945234i	$0.605834\pi$
$168$	0.292235	0.0225464
$169$	−12.3266	−0.948198
$170$	2.39546	0.183723
$171$	24.0801	1.84145
$172$	1.06696	0.0813547
$173$	−20.9993	−1.59655	−0.798273	−	0.602295i	$-0.794253\pi$
$173$	−20.9993	−1.59655	−0.798273	+	0.602295i	$0.794253\pi$
$174$	25.9166	1.96473
$175$	0.104808	0.00792273
$176$	−1.61337	−0.121612
$177$	−5.26316	−0.395604
$178$	−12.3656	−0.926838
$179$	−14.6536	−1.09526	−0.547629	−	0.836721i	$-0.684470\pi$
$179$	−14.6536	−1.09526	−0.547629	+	0.836721i	$0.684470\pi$
$180$	−4.77457	−0.355876
$181$	−16.3855	−1.21793	−0.608964	−	0.793198i	$-0.708415\pi$
$181$	−16.3855	−1.21793	−0.608964	+	0.793198i	$0.708415\pi$
$182$	−0.0860079	−0.00637533
$183$	−2.00442	−0.148171
$184$	0	0
$185$	−3.78260	−0.278102
$186$	19.3499	1.41880
$187$	3.86476	0.282619
$188$	−8.70310	−0.634739
$189$	0.518593	0.0377221
$190$	−5.04341	−0.365887
$191$	−19.0662	−1.37959	−0.689793	−	0.724007i	$-0.742298\pi$
$191$	−19.0662	−1.37959	−0.689793	+	0.724007i	$0.742298\pi$
$192$	2.78829	0.201228
$193$	−3.51113	−0.252737	−0.126368	−	0.991983i	$-0.540332\pi$
$193$	−3.51113	−0.252737	−0.126368	+	0.991983i	$0.540332\pi$
$194$	−18.1600	−1.30382
$195$	2.28814	0.163857
$196$	−6.98902	−0.499215
$197$	16.3731	1.16654	0.583268	−	0.812280i	$-0.301774\pi$
$197$	16.3731	1.16654	0.583268	+	0.812280i	$0.301774\pi$
$198$	−7.70316	−0.547440
$199$	−24.3835	−1.72850	−0.864252	−	0.503059i	$-0.832208\pi$
$199$	−24.3835	−1.72850	−0.864252	+	0.503059i	$0.832208\pi$
$200$	1.00000	0.0707107
$201$	9.77811	0.689695
$202$	10.7972	0.759692
$203$	0.974167	0.0683731
$204$	−6.67923	−0.467640
$205$	−10.1328	−0.707707
$206$	3.49218	0.243311
$207$	0	0
$208$	−0.820624	−0.0569001
$209$	−8.13689	−0.562840
$210$	−0.292235	−0.0201661
$211$	−3.50940	−0.241597	−0.120799	−	0.992677i	$-0.538546\pi$
$211$	−3.50940	−0.241597	−0.120799	+	0.992677i	$0.538546\pi$
$212$	10.1839	0.699436
$213$	−3.65697	−0.250572
$214$	8.04757	0.550120
$215$	−1.06696	−0.0727659
$216$	4.94803	0.336671
$217$	0.727334	0.0493747
$218$	4.75271	0.321894
$219$	31.6530	2.13891
$220$	1.61337	0.108773
$221$	1.96577	0.132232
$222$	10.5470	0.707868
$223$	0.760922	0.0509551	0.0254776	−	0.999675i	$-0.491889\pi$
$223$	0.760922	0.0509551	0.0254776	+	0.999675i	$0.491889\pi$
$224$	0.104808	0.00700277
$225$	4.77457	0.318305
$226$	12.0649	0.802547
$227$	22.1110	1.46756	0.733780	−	0.679388i	$-0.237754\pi$
$227$	22.1110	1.46756	0.733780	+	0.679388i	$0.237754\pi$
$228$	14.0625	0.931311
$229$	18.3056	1.20967	0.604833	−	0.796352i	$-0.293240\pi$
$229$	18.3056	1.20967	0.604833	+	0.796352i	$0.293240\pi$
$230$	0	0
$231$	−0.471483	−0.0310213
$232$	9.29479	0.610233
$233$	−8.93455	−0.585322	−0.292661	−	0.956216i	$-0.594541\pi$
$233$	−8.93455	−0.585322	−0.292661	+	0.956216i	$0.594541\pi$
$234$	−3.91813	−0.256136
$235$	8.70310	0.567727
$236$	−1.88759	−0.122872
$237$	−37.6667	−2.44671
$238$	−0.251063	−0.0162740
$239$	−15.4332	−0.998289	−0.499145	−	0.866519i	$-0.666352\pi$
$239$	−15.4332	−0.998289	−0.499145	+	0.866519i	$0.666352\pi$
$240$	−2.78829	−0.179984
$241$	−24.2931	−1.56486	−0.782429	−	0.622740i	$-0.786019\pi$
$241$	−24.2931	−1.56486	−0.782429	+	0.622740i	$0.786019\pi$
$242$	−8.39703	−0.539782
$243$	−16.3140	−1.04654
$244$	−0.718868	−0.0460208
$245$	6.98902	0.446512
$246$	28.2533	1.80136
$247$	−4.13874	−0.263342
$248$	6.93969	0.440671
$249$	33.4701	2.12108
$250$	−1.00000	−0.0632456
$251$	−5.22097	−0.329545	−0.164772	−	0.986332i	$-0.552689\pi$
$251$	−5.22097	−0.329545	−0.164772	+	0.986332i	$0.552689\pi$
$252$	0.500413	0.0315230
$253$	0	0
$254$	−7.72617	−0.484783
$255$	6.67923	0.418270
$256$	1.00000	0.0625000
$257$	25.4108	1.58508	0.792542	−	0.609817i	$-0.208757\pi$
$257$	25.4108	1.58508	0.792542	+	0.609817i	$0.208757\pi$
$258$	2.97499	0.185215
$259$	0.396446	0.0246340
$260$	0.820624	0.0508930
$261$	44.3787	2.74697
$262$	−15.9385	−0.984682
$263$	13.4327	0.828296	0.414148	−	0.910210i	$-0.364080\pi$
$263$	13.4327	0.828296	0.414148	+	0.910210i	$0.364080\pi$
$264$	−4.49855	−0.276867
$265$	−10.1839	−0.625594
$266$	0.528588	0.0324098
$267$	−34.4788	−2.11007
$268$	3.50684	0.214215
$269$	7.33351	0.447132	0.223566	−	0.974689i	$-0.428230\pi$
$269$	7.33351	0.447132	0.223566	+	0.974689i	$0.428230\pi$
$270$	−4.94803	−0.301128
$271$	−3.57309	−0.217050	−0.108525	−	0.994094i	$-0.534613\pi$
$271$	−3.57309	−0.217050	−0.108525	+	0.994094i	$0.534613\pi$
$272$	−2.39546	−0.145246
$273$	−0.239815	−0.0145143
$274$	−1.42400	−0.0860273
$275$	−1.61337	−0.0972899
$276$	0	0
$277$	−14.3045	−0.859474	−0.429737	−	0.902954i	$-0.641394\pi$
$277$	−14.3045	−0.859474	−0.429737	+	0.902954i	$0.641394\pi$
$278$	7.21002	0.432428
$279$	33.1341	1.98369
$280$	−0.104808	−0.00626347
$281$	−20.0779	−1.19775	−0.598873	−	0.800844i	$-0.704385\pi$
$281$	−20.0779	−1.19775	−0.598873	+	0.800844i	$0.704385\pi$
$282$	−24.2668	−1.44507
$283$	12.5198	0.744225	0.372112	−	0.928188i	$-0.378634\pi$
$283$	12.5198	0.744225	0.372112	+	0.928188i	$0.378634\pi$
$284$	−1.31155	−0.0778259
$285$	−14.0625	−0.832990
$286$	1.32397	0.0782881
$287$	1.06200	0.0626878
$288$	4.77457	0.281345
$289$	−11.2618	−0.662458
$290$	−9.29479	−0.545809
$291$	−50.6355	−2.96831
$292$	11.3521	0.664333
$293$	4.15264	0.242600	0.121300	−	0.992616i	$-0.461294\pi$
$293$	4.15264	0.242600	0.121300	+	0.992616i	$0.461294\pi$
$294$	−19.4874	−1.13653
$295$	1.88759	0.109900
$296$	3.78260	0.219859
$297$	−7.98301	−0.463221
$298$	18.4817	1.07061
$299$	0	0
$300$	2.78829	0.160982
$301$	0.111825	0.00644551
$302$	7.08884	0.407917
$303$	30.1059	1.72954
$304$	5.04341	0.289259
$305$	0.718868	0.0411623
$306$	−11.4373	−0.653826
$307$	−16.8331	−0.960718	−0.480359	−	0.877072i	$-0.659494\pi$
$307$	−16.8331	−0.960718	−0.480359	+	0.877072i	$0.659494\pi$
$308$	−0.169094	−0.00963502
$309$	9.73721	0.553930
$310$	−6.93969	−0.394148
$311$	3.68661	0.209048	0.104524	−	0.994522i	$-0.466668\pi$
$311$	3.68661	0.209048	0.104524	+	0.994522i	$0.466668\pi$
$312$	−2.28814	−0.129540
$313$	−5.63837	−0.318700	−0.159350	−	0.987222i	$-0.550940\pi$
$313$	−5.63837	−0.318700	−0.159350	+	0.987222i	$0.550940\pi$
$314$	−7.01390	−0.395817
$315$	−0.500413	−0.0281951
$316$	−13.5089	−0.759933
$317$	20.4608	1.14919	0.574595	−	0.818438i	$-0.305159\pi$
$317$	20.4608	1.14919	0.574595	+	0.818438i	$0.305159\pi$
$318$	28.3958	1.59236
$319$	−14.9959	−0.839612
$320$	−1.00000	−0.0559017
$321$	22.4390	1.25242
$322$	0	0
$323$	−12.0813	−0.672219
$324$	−0.527159	−0.0292866
$325$	−0.820624	−0.0455201
$326$	−12.3924	−0.686353
$327$	13.2520	0.732835
$328$	10.1328	0.559491
$329$	−0.912153	−0.0502886
$330$	4.49855	0.247637
$331$	−8.99155	−0.494220	−0.247110	−	0.968987i	$-0.579481\pi$
$331$	−8.99155	−0.494220	−0.247110	+	0.968987i	$0.579481\pi$
$332$	12.0038	0.658794
$333$	18.0603	0.989699
$334$	−8.43589	−0.461592
$335$	−3.50684	−0.191599
$336$	0.292235	0.0159427
$337$	17.6675	0.962409	0.481204	−	0.876608i	$-0.340199\pi$
$337$	17.6675	0.962409	0.481204	+	0.876608i	$0.340199\pi$
$338$	−12.3266	−0.670477
$339$	33.6406	1.82710
$340$	2.39546	0.129912
$341$	−11.1963	−0.606314
$342$	24.0801	1.30210
$343$	−1.46616	−0.0791651
$344$	1.06696	0.0575265
$345$	0	0
$346$	−20.9993	−1.12893
$347$	0.101431	0.00544510	0.00272255	−	0.999996i	$-0.499133\pi$
$347$	0.101431	0.00544510	0.00272255	+	0.999996i	$0.499133\pi$
$348$	25.9166	1.38928
$349$	−15.8436	−0.848087	−0.424043	−	0.905642i	$-0.639390\pi$
$349$	−15.8436	−0.848087	−0.424043	+	0.905642i	$0.639390\pi$
$350$	0.104808	0.00560221
$351$	−4.06048	−0.216732
$352$	−1.61337	−0.0859930
$353$	−11.0240	−0.586748	−0.293374	−	0.955998i	$-0.594778\pi$
$353$	−11.0240	−0.586748	−0.293374	+	0.955998i	$0.594778\pi$
$354$	−5.26316	−0.279734
$355$	1.31155	0.0696096
$356$	−12.3656	−0.655373
$357$	−0.700036	−0.0370498
$358$	−14.6536	−0.774465
$359$	35.3001	1.86307	0.931534	−	0.363655i	$-0.118471\pi$
$359$	35.3001	1.86307	0.931534	+	0.363655i	$0.118471\pi$
$360$	−4.77457	−0.251642
$361$	6.43595	0.338734
$362$	−16.3855	−0.861205
$363$	−23.4134	−1.22888
$364$	−0.0860079	−0.00450804
$365$	−11.3521	−0.594197
$366$	−2.00442	−0.104772
$367$	24.1075	1.25840	0.629202	−	0.777242i	$-0.283382\pi$
$367$	24.1075	1.25840	0.629202	+	0.777242i	$0.283382\pi$
$368$	0	0
$369$	48.3799	2.51856
$370$	−3.78260	−0.196648
$371$	1.06736	0.0554144
$372$	19.3499	1.00325
$373$	2.20688	0.114268	0.0571341	−	0.998367i	$-0.481804\pi$
$373$	2.20688	0.114268	0.0571341	+	0.998367i	$0.481804\pi$
$374$	3.86476	0.199842
$375$	−2.78829	−0.143987
$376$	−8.70310	−0.448828
$377$	−7.62753	−0.392838
$378$	0.518593	0.0266735
$379$	−32.3416	−1.66128	−0.830639	−	0.556811i	$-0.812025\pi$
$379$	−32.3416	−1.66128	−0.830639	+	0.556811i	$0.812025\pi$
$380$	−5.04341	−0.258721
$381$	−21.5428	−1.10367
$382$	−19.0662	−0.975514
$383$	−35.7304	−1.82574	−0.912869	−	0.408254i	$-0.866138\pi$
$383$	−35.7304	−1.82574	−0.912869	+	0.408254i	$0.866138\pi$
$384$	2.78829	0.142289
$385$	0.169094	0.00861782
$386$	−3.51113	−0.178712
$387$	5.09427	0.258956
$388$	−18.1600	−0.921936
$389$	27.9098	1.41508	0.707542	−	0.706671i	$-0.249804\pi$
$389$	27.9098	1.41508	0.707542	+	0.706671i	$0.249804\pi$
$390$	2.28814	0.115865
$391$	0	0
$392$	−6.98902	−0.352999
$393$	−44.4411	−2.24176
$394$	16.3731	0.824865
$395$	13.5089	0.679704
$396$	−7.70316	−0.387098
$397$	−28.5928	−1.43503	−0.717515	−	0.696544i	$-0.754720\pi$
$397$	−28.5928	−1.43503	−0.717515	+	0.696544i	$0.754720\pi$
$398$	−24.3835	−1.22224
$399$	1.47386	0.0737853
$400$	1.00000	0.0500000
$401$	14.0942	0.703830	0.351915	−	0.936032i	$-0.385531\pi$
$401$	14.0942	0.703830	0.351915	+	0.936032i	$0.385531\pi$
$402$	9.77811	0.487688
$403$	−5.69488	−0.283682
$404$	10.7972	0.537183
$405$	0.527159	0.0261947
$406$	0.974167	0.0483471
$407$	−6.10274	−0.302502
$408$	−6.67923	−0.330671
$409$	3.26948	0.161665	0.0808327	−	0.996728i	$-0.474242\pi$
$409$	3.26948	0.161665	0.0808327	+	0.996728i	$0.474242\pi$
$410$	−10.1328	−0.500424
$411$	−3.97054	−0.195852
$412$	3.49218	0.172047
$413$	−0.197835	−0.00973481
$414$	0	0
$415$	−12.0038	−0.589243
$416$	−0.820624	−0.0402344
$417$	20.1037	0.984480
$418$	−8.13689	−0.397988
$419$	19.2547	0.940654	0.470327	−	0.882492i	$-0.344136\pi$
$419$	19.2547	0.940654	0.470327	+	0.882492i	$0.344136\pi$
$420$	−0.292235	−0.0142596
$421$	35.2902	1.71994	0.859970	−	0.510344i	$-0.170482\pi$
$421$	35.2902	1.71994	0.859970	+	0.510344i	$0.170482\pi$
$422$	−3.50940	−0.170835
$423$	−41.5536	−2.02040
$424$	10.1839	0.494576
$425$	−2.39546	−0.116197
$426$	−3.65697	−0.177181
$427$	−0.0753430	−0.00364611
$428$	8.04757	0.388994
$429$	3.69162	0.178233
$430$	−1.06696	−0.0514532
$431$	−32.6180	−1.57116	−0.785578	−	0.618763i	$-0.787634\pi$
$431$	−32.6180	−1.57116	−0.785578	+	0.618763i	$0.787634\pi$
$432$	4.94803	0.238062
$433$	−4.24030	−0.203776	−0.101888	−	0.994796i	$-0.532488\pi$
$433$	−4.24030	−0.203776	−0.101888	+	0.994796i	$0.532488\pi$
$434$	0.727334	0.0349132
$435$	−25.9166	−1.24261
$436$	4.75271	0.227614
$437$	0	0
$438$	31.6530	1.51244
$439$	17.7359	0.846487	0.423244	−	0.906016i	$-0.360891\pi$
$439$	17.7359	0.846487	0.423244	+	0.906016i	$0.360891\pi$
$440$	1.61337	0.0769144
$441$	−33.3696	−1.58903
$442$	1.96577	0.0935022
$443$	33.2025	1.57750	0.788750	−	0.614714i	$-0.210728\pi$
$443$	33.2025	1.57750	0.788750	+	0.614714i	$0.210728\pi$
$444$	10.5470	0.500538
$445$	12.3656	0.586184
$446$	0.760922	0.0360307
$447$	51.5323	2.43739
$448$	0.104808	0.00495170
$449$	−15.8541	−0.748201	−0.374101	−	0.927388i	$-0.622049\pi$
$449$	−15.8541	−0.748201	−0.374101	+	0.927388i	$0.622049\pi$
$450$	4.77457	0.225076
$451$	−16.3480	−0.769797
$452$	12.0649	0.567487
$453$	19.7658	0.928676
$454$	22.1110	1.03772
$455$	0.0860079	0.00403211
$456$	14.0625	0.658537
$457$	−23.3208	−1.09090	−0.545451	−	0.838143i	$-0.683642\pi$
$457$	−23.3208	−1.09090	−0.545451	+	0.838143i	$0.683642\pi$
$458$	18.3056	0.855363
$459$	−11.8528	−0.553241
$460$	0	0
$461$	35.0520	1.63254	0.816268	−	0.577673i	$-0.196039\pi$
$461$	35.0520	1.63254	0.816268	+	0.577673i	$0.196039\pi$
$462$	−0.471483	−0.0219354
$463$	21.7943	1.01287	0.506434	−	0.862279i	$-0.330963\pi$
$463$	21.7943	1.01287	0.506434	+	0.862279i	$0.330963\pi$
$464$	9.29479	0.431500
$465$	−19.3499	−0.897330
$466$	−8.93455	−0.413885
$467$	4.79248	0.221770	0.110885	−	0.993833i	$-0.464632\pi$
$467$	4.79248	0.221770	0.110885	+	0.993833i	$0.464632\pi$
$468$	−3.91813	−0.181116
$469$	0.367545	0.0169716
$470$	8.70310	0.401444
$471$	−19.5568	−0.901130
$472$	−1.88759	−0.0868836
$473$	−1.72140	−0.0791499
$474$	−37.6667	−1.73009
$475$	5.04341	0.231407
$476$	−0.251063	−0.0115074
$477$	48.6240	2.22634
$478$	−15.4332	−0.705897
$479$	18.4300	0.842088	0.421044	−	0.907040i	$-0.361664\pi$
$479$	18.4300	0.842088	0.421044	+	0.907040i	$0.361664\pi$
$480$	−2.78829	−0.127268
$481$	−3.10410	−0.141535
$482$	−24.2931	−1.10652
$483$	0	0
$484$	−8.39703	−0.381683
$485$	18.1600	0.824605
$486$	−16.3140	−0.740017
$487$	18.5292	0.839640	0.419820	−	0.907607i	$-0.362093\pi$
$487$	18.5292	0.839640	0.419820	+	0.907607i	$0.362093\pi$
$488$	−0.718868	−0.0325416
$489$	−34.5537	−1.56257
$490$	6.98902	0.315732
$491$	−42.7858	−1.93090	−0.965448	−	0.260594i	$-0.916082\pi$
$491$	−42.7858	−1.93090	−0.965448	+	0.260594i	$0.916082\pi$
$492$	28.2533	1.27376
$493$	−22.2653	−1.00278
$494$	−4.13874	−0.186211
$495$	7.70316	0.346231
$496$	6.93969	0.311601
$497$	−0.137460	−0.00616593
$498$	33.4701	1.49983
$499$	−3.23317	−0.144737	−0.0723684	−	0.997378i	$-0.523056\pi$
$499$	−3.23317	−0.144737	−0.0723684	+	0.997378i	$0.523056\pi$
$500$	−1.00000	−0.0447214
$501$	−23.5217	−1.05087
$502$	−5.22097	−0.233023
$503$	−33.8588	−1.50969	−0.754846	−	0.655902i	$-0.772288\pi$
$503$	−33.8588	−1.50969	−0.754846	+	0.655902i	$0.772288\pi$
$504$	0.500413	0.0222902
$505$	−10.7972	−0.480471
$506$	0	0
$507$	−34.3701	−1.52643
$508$	−7.72617	−0.342793
$509$	−10.1320	−0.449093	−0.224547	−	0.974463i	$-0.572090\pi$
$509$	−10.1320	−0.449093	−0.224547	+	0.974463i	$0.572090\pi$
$510$	6.67923	0.295761
$511$	1.18979	0.0526333
$512$	1.00000	0.0441942
$513$	24.9549	1.10179
$514$	25.4108	1.12082
$515$	−3.49218	−0.153884
$516$	2.97499	0.130967
$517$	14.0413	0.617537
$518$	0.396446	0.0174188
$519$	−58.5522	−2.57016
$520$	0.820624	0.0359868
$521$	−3.51501	−0.153995	−0.0769976	−	0.997031i	$-0.524533\pi$
$521$	−3.51501	−0.153995	−0.0769976	+	0.997031i	$0.524533\pi$
$522$	44.3787	1.94240
$523$	17.6643	0.772407	0.386204	−	0.922414i	$-0.373786\pi$
$523$	17.6643	0.772407	0.386204	+	0.922414i	$0.373786\pi$
$524$	−15.9385	−0.696276
$525$	0.292235	0.0127542
$526$	13.4327	0.585694
$527$	−16.6237	−0.724141
$528$	−4.49855	−0.195774
$529$	0	0
$530$	−10.1839	−0.442362
$531$	−9.01246	−0.391107
$532$	0.528588	0.0229172
$533$	−8.31524	−0.360173
$534$	−34.4788	−1.49204
$535$	−8.04757	−0.347927
$536$	3.50684	0.151473
$537$	−40.8584	−1.76317
$538$	7.33351	0.316170
$539$	11.2759	0.485686
$540$	−4.94803	−0.212929
$541$	4.93503	0.212174	0.106087	−	0.994357i	$-0.466168\pi$
$541$	4.93503	0.212174	0.106087	+	0.994357i	$0.466168\pi$
$542$	−3.57309	−0.153477
$543$	−45.6877	−1.96065
$544$	−2.39546	−0.102704
$545$	−4.75271	−0.203584
$546$	−0.239815	−0.0102631
$547$	44.2402	1.89158	0.945788	−	0.324786i	$-0.105292\pi$
$547$	44.2402	1.89158	0.945788	+	0.324786i	$0.105292\pi$
$548$	−1.42400	−0.0608305
$549$	−3.43229	−0.146487
$550$	−1.61337	−0.0687944
$551$	46.8774	1.99704
$552$	0	0
$553$	−1.41583	−0.0602074
$554$	−14.3045	−0.607740
$555$	−10.5470	−0.447695
$556$	7.21002	0.305773
$557$	−20.9490	−0.887637	−0.443818	−	0.896117i	$-0.646376\pi$
$557$	−20.9490	−0.887637	−0.443818	+	0.896117i	$0.646376\pi$
$558$	33.1341	1.40268
$559$	−0.875571	−0.0370327
$560$	−0.104808	−0.00442894
$561$	10.7761	0.454966
$562$	−20.0779	−0.846934
$563$	−14.4921	−0.610767	−0.305384	−	0.952229i	$-0.598785\pi$
$563$	−14.4921	−0.610767	−0.305384	+	0.952229i	$0.598785\pi$
$564$	−24.2668	−1.02182
$565$	−12.0649	−0.507575
$566$	12.5198	0.526246
$567$	−0.0552504	−0.00232030
$568$	−1.31155	−0.0550312
$569$	−17.0313	−0.713987	−0.356994	−	0.934107i	$-0.616198\pi$
$569$	−17.0313	−0.713987	−0.356994	+	0.934107i	$0.616198\pi$
$570$	−14.0625	−0.589013
$571$	−16.6349	−0.696150	−0.348075	−	0.937467i	$-0.613164\pi$
$571$	−16.6349	−0.696150	−0.348075	+	0.937467i	$0.613164\pi$
$572$	1.32397	0.0553580
$573$	−53.1623	−2.22089
$574$	1.06200	0.0443270
$575$	0	0
$576$	4.77457	0.198941
$577$	−13.1663	−0.548119	−0.274059	−	0.961713i	$-0.588367\pi$
$577$	−13.1663	−0.548119	−0.274059	+	0.961713i	$0.588367\pi$
$578$	−11.2618	−0.468429
$579$	−9.79006	−0.406861
$580$	−9.29479	−0.385945
$581$	1.25809	0.0521944
$582$	−50.6355	−2.09891
$583$	−16.4305	−0.680480
$584$	11.3521	0.469754
$585$	3.91813	0.161995
$586$	4.15264	0.171544
$587$	−42.1135	−1.73821	−0.869104	−	0.494629i	$-0.835304\pi$
$587$	−42.1135	−1.73821	−0.869104	+	0.494629i	$0.835304\pi$
$588$	−19.4874	−0.803648
$589$	34.9997	1.44214
$590$	1.88759	0.0777110
$591$	45.6530	1.87791
$592$	3.78260	0.155464
$593$	4.53513	0.186236	0.0931178	−	0.995655i	$-0.470317\pi$
$593$	4.53513	0.186236	0.0931178	+	0.995655i	$0.470317\pi$
$594$	−7.98301	−0.327547
$595$	0.251063	0.0102926
$596$	18.4817	0.757038
$597$	−67.9885	−2.78258
$598$	0	0
$599$	30.2169	1.23463	0.617314	−	0.786717i	$-0.288221\pi$
$599$	30.2169	1.23463	0.617314	+	0.786717i	$0.288221\pi$
$600$	2.78829	0.113832
$601$	−30.8107	−1.25679	−0.628397	−	0.777893i	$-0.716289\pi$
$601$	−30.8107	−1.25679	−0.628397	+	0.777893i	$0.716289\pi$
$602$	0.111825	0.00455766
$603$	16.7437	0.681856
$604$	7.08884	0.288441
$605$	8.39703	0.341388
$606$	30.1059	1.22297
$607$	−9.83550	−0.399211	−0.199605	−	0.979876i	$-0.563966\pi$
$607$	−9.83550	−0.399211	−0.199605	+	0.979876i	$0.563966\pi$
$608$	5.04341	0.204537
$609$	2.71626	0.110068
$610$	0.718868	0.0291061
$611$	7.14197	0.288933
$612$	−11.4373	−0.462325
$613$	17.5242	0.707794	0.353897	−	0.935284i	$-0.384856\pi$
$613$	17.5242	0.707794	0.353897	+	0.935284i	$0.384856\pi$
$614$	−16.8331	−0.679330
$615$	−28.2533	−1.13928
$616$	−0.169094	−0.00681299
$617$	−13.1614	−0.529859	−0.264930	−	0.964268i	$-0.585349\pi$
$617$	−13.1614	−0.529859	−0.264930	+	0.964268i	$0.585349\pi$
$618$	9.73721	0.391688
$619$	11.3157	0.454818	0.227409	−	0.973799i	$-0.426975\pi$
$619$	11.3157	0.454818	0.227409	+	0.973799i	$0.426975\pi$
$620$	−6.93969	−0.278705
$621$	0	0
$622$	3.68661	0.147820
$623$	−1.29601	−0.0519234
$624$	−2.28814	−0.0915989
$625$	1.00000	0.0400000
$626$	−5.63837	−0.225355
$627$	−22.6880	−0.906072
$628$	−7.01390	−0.279885
$629$	−9.06106	−0.361288
$630$	−0.500413	−0.0199369
$631$	−7.97357	−0.317423	−0.158711	−	0.987325i	$-0.550734\pi$
$631$	−7.97357	−0.317423	−0.158711	+	0.987325i	$0.550734\pi$
$632$	−13.5089	−0.537354
$633$	−9.78523	−0.388928
$634$	20.4608	0.812601
$635$	7.72617	0.306604
$636$	28.3958	1.12597
$637$	5.73536	0.227243
$638$	−14.9959	−0.593695
$639$	−6.26207	−0.247724
$640$	−1.00000	−0.0395285
$641$	−16.7615	−0.662041	−0.331020	−	0.943624i	$-0.607393\pi$
$641$	−16.7615	−0.662041	−0.331020	+	0.943624i	$0.607393\pi$
$642$	22.4390	0.885595
$643$	38.3427	1.51209	0.756044	−	0.654521i	$-0.227130\pi$
$643$	38.3427	1.51209	0.756044	+	0.654521i	$0.227130\pi$
$644$	0	0
$645$	−2.97499	−0.117140
$646$	−12.0813	−0.475331
$647$	24.4928	0.962913	0.481456	−	0.876470i	$-0.340108\pi$
$647$	24.4928	0.962913	0.481456	+	0.876470i	$0.340108\pi$
$648$	−0.527159	−0.0207088
$649$	3.04539	0.119542
$650$	−0.820624	−0.0321875
$651$	2.02802	0.0794844
$652$	−12.3924	−0.485325
$653$	20.8273	0.815037	0.407519	−	0.913197i	$-0.366394\pi$
$653$	20.8273	0.815037	0.407519	+	0.913197i	$0.366394\pi$
$654$	13.2520	0.518192
$655$	15.9385	0.622768
$656$	10.1328	0.395620
$657$	54.2016	2.11460
$658$	−0.912153	−0.0355594
$659$	33.2234	1.29420	0.647100	−	0.762405i	$-0.275981\pi$
$659$	33.2234	1.29420	0.647100	+	0.762405i	$0.275981\pi$
$660$	4.49855	0.175106
$661$	−7.64158	−0.297223	−0.148612	−	0.988896i	$-0.547480\pi$
$661$	−7.64158	−0.297223	−0.148612	+	0.988896i	$0.547480\pi$
$662$	−8.99155	−0.349466
$663$	5.48114	0.212870
$664$	12.0038	0.465837
$665$	−0.528588	−0.0204978
$666$	18.0603	0.699823
$667$	0	0
$668$	−8.43589	−0.326395
$669$	2.12167	0.0820286
$670$	−3.50684	−0.135481
$671$	1.15980	0.0447736
$672$	0.292235	0.0112732
$673$	−2.98332	−0.114999	−0.0574993	−	0.998346i	$-0.518313\pi$
$673$	−2.98332	−0.114999	−0.0574993	+	0.998346i	$0.518313\pi$
$674$	17.6675	0.680526
$675$	4.94803	0.190450
$676$	−12.3266	−0.474099
$677$	−17.0692	−0.656023	−0.328012	−	0.944674i	$-0.606379\pi$
$677$	−17.0692	−0.656023	−0.328012	+	0.944674i	$0.606379\pi$
$678$	33.6406	1.29196
$679$	−1.90331	−0.0730425
$680$	2.39546	0.0918616
$681$	61.6520	2.36251
$682$	−11.1963	−0.428728
$683$	−11.1574	−0.426927	−0.213464	−	0.976951i	$-0.568474\pi$
$683$	−11.1574	−0.426927	−0.213464	+	0.976951i	$0.568474\pi$
$684$	24.0801	0.920727
$685$	1.42400	0.0544084
$686$	−1.46616	−0.0559782
$687$	51.0413	1.94735
$688$	1.06696	0.0406774
$689$	−8.35719	−0.318383
$690$	0	0
$691$	−30.1266	−1.14607	−0.573036	−	0.819530i	$-0.694234\pi$
$691$	−30.1266	−1.14607	−0.573036	+	0.819530i	$0.694234\pi$
$692$	−20.9993	−0.798273
$693$	−0.807351	−0.0306687
$694$	0.101431	0.00385026
$695$	−7.21002	−0.273492
$696$	25.9166	0.982366
$697$	−24.2727	−0.919395
$698$	−15.8436	−0.599688
$699$	−24.9121	−0.942263
$700$	0.104808	0.00396136
$701$	−14.6121	−0.551892	−0.275946	−	0.961173i	$-0.588991\pi$
$701$	−14.6121	−0.551892	−0.275946	+	0.961173i	$0.588991\pi$
$702$	−4.06048	−0.153253
$703$	19.0772	0.719510
$704$	−1.61337	−0.0608062
$705$	24.2668	0.913940
$706$	−11.0240	−0.414894
$707$	1.13164	0.0425596
$708$	−5.26316	−0.197802
$709$	9.76279	0.366649	0.183325	−	0.983052i	$-0.441314\pi$
$709$	9.76279	0.366649	0.183325	+	0.983052i	$0.441314\pi$
$710$	1.31155	0.0492214
$711$	−64.4991	−2.41890
$712$	−12.3656	−0.463419
$713$	0	0
$714$	−0.700036	−0.0261982
$715$	−1.32397	−0.0495137
$716$	−14.6536	−0.547629
$717$	−43.0322	−1.60707
$718$	35.3001	1.31739
$719$	14.8218	0.552761	0.276381	−	0.961048i	$-0.410865\pi$
$719$	14.8218	0.552761	0.276381	+	0.961048i	$0.410865\pi$
$720$	−4.77457	−0.177938
$721$	0.366007	0.0136308
$722$	6.43595	0.239521
$723$	−67.7363	−2.51914
$724$	−16.3855	−0.608964
$725$	9.29479	0.345200
$726$	−23.4134	−0.868952
$727$	29.0598	1.07777	0.538885	−	0.842379i	$-0.318846\pi$
$727$	29.0598	1.07777	0.538885	+	0.842379i	$0.318846\pi$
$728$	−0.0860079	−0.00318766
$729$	−43.9067	−1.62617
$730$	−11.3521	−0.420161
$731$	−2.55585	−0.0945315
$732$	−2.00442	−0.0740853
$733$	−8.23520	−0.304174	−0.152087	−	0.988367i	$-0.548599\pi$
$733$	−8.23520	−0.304174	−0.152087	+	0.988367i	$0.548599\pi$
$734$	24.1075	0.889826
$735$	19.4874	0.718804
$736$	0	0
$737$	−5.65784	−0.208409
$738$	48.3799	1.78089
$739$	3.77121	0.138726	0.0693631	−	0.997591i	$-0.477903\pi$
$739$	3.77121	0.138726	0.0693631	+	0.997591i	$0.477903\pi$
$740$	−3.78260	−0.139051
$741$	−11.5400	−0.423933
$742$	1.06736	0.0391839
$743$	−1.77452	−0.0651007	−0.0325503	−	0.999470i	$-0.510363\pi$
$743$	−1.77452	−0.0651007	−0.0325503	+	0.999470i	$0.510363\pi$
$744$	19.3499	0.709402
$745$	−18.4817	−0.677115
$746$	2.20688	0.0807998
$747$	57.3130	2.09697
$748$	3.86476	0.141310
$749$	0.843448	0.0308189
$750$	−2.78829	−0.101814
$751$	−0.476437	−0.0173854	−0.00869272	−	0.999962i	$-0.502767\pi$
$751$	−0.476437	−0.0173854	−0.00869272	+	0.999962i	$0.502767\pi$
$752$	−8.70310	−0.317369
$753$	−14.5576	−0.530508
$754$	−7.62753	−0.277778
$755$	−7.08884	−0.257989
$756$	0.518593	0.0188610
$757$	−49.6224	−1.80356	−0.901779	−	0.432198i	$-0.857738\pi$
$757$	−49.6224	−1.80356	−0.901779	+	0.432198i	$0.857738\pi$
$758$	−32.3416	−1.17470
$759$	0	0
$760$	−5.04341	−0.182944
$761$	3.12436	0.113258	0.0566291	−	0.998395i	$-0.481965\pi$
$761$	3.12436	0.113258	0.0566291	+	0.998395i	$0.481965\pi$
$762$	−21.5428	−0.780414
$763$	0.498122	0.0180332
$764$	−19.0662	−0.689793
$765$	11.4373	0.413516
$766$	−35.7304	−1.29099
$767$	1.54901	0.0559314
$768$	2.78829	0.100614
$769$	−33.8619	−1.22109	−0.610545	−	0.791982i	$-0.709050\pi$
$769$	−33.8619	−1.22109	−0.610545	+	0.791982i	$0.709050\pi$
$770$	0.169094	0.00609372
$771$	70.8528	2.55170
$772$	−3.51113	−0.126368
$773$	−0.401860	−0.0144539	−0.00722695	−	0.999974i	$-0.502300\pi$
$773$	−0.401860	−0.0144539	−0.00722695	+	0.999974i	$0.502300\pi$
$774$	5.09427	0.183110
$775$	6.93969	0.249281
$776$	−18.1600	−0.651908
$777$	1.10541	0.0396563
$778$	27.9098	1.00062
$779$	51.1039	1.83099
$780$	2.28814	0.0819286
$781$	2.11601	0.0757168
$782$	0	0
$783$	45.9909	1.64358
$784$	−6.98902	−0.249608
$785$	7.01390	0.250337
$786$	−44.4411	−1.58516
$787$	25.0932	0.894477	0.447238	−	0.894415i	$-0.352408\pi$
$787$	25.0932	0.894477	0.447238	+	0.894415i	$0.352408\pi$
$788$	16.3731	0.583268
$789$	37.4543	1.33341
$790$	13.5089	0.480624
$791$	1.26450	0.0449604
$792$	−7.70316	−0.273720
$793$	0.589921	0.0209487
$794$	−28.5928	−1.01472
$795$	−28.3958	−1.00710
$796$	−24.3835	−0.864252
$797$	−6.68778	−0.236893	−0.118447	−	0.992960i	$-0.537791\pi$
$797$	−6.68778	−0.236893	−0.118447	+	0.992960i	$0.537791\pi$
$798$	1.47386	0.0521741
$799$	20.8479	0.737545
$800$	1.00000	0.0353553
$801$	−59.0403	−2.08609
$802$	14.0942	0.497683
$803$	−18.3152	−0.646329
$804$	9.77811	0.344847
$805$	0	0
$806$	−5.69488	−0.200594
$807$	20.4480	0.719803
$808$	10.7972	0.379846
$809$	−4.38696	−0.154237	−0.0771187	−	0.997022i	$-0.524572\pi$
$809$	−4.38696	−0.154237	−0.0771187	+	0.997022i	$0.524572\pi$
$810$	0.527159	0.0185225
$811$	27.1184	0.952257	0.476129	−	0.879376i	$-0.342040\pi$
$811$	27.1184	0.952257	0.476129	+	0.879376i	$0.342040\pi$
$812$	0.974167	0.0341866
$813$	−9.96281	−0.349411
$814$	−6.10274	−0.213901
$815$	12.3924	0.434088
$816$	−6.67923	−0.233820
$817$	5.38110	0.188261
$818$	3.26948	0.114315
$819$	−0.410651	−0.0143493
$820$	−10.1328	−0.353853
$821$	−24.6081	−0.858827	−0.429414	−	0.903108i	$-0.641280\pi$
$821$	−24.6081	−0.858827	−0.429414	+	0.903108i	$0.641280\pi$
$822$	−3.97054	−0.138489
$823$	10.2736	0.358116	0.179058	−	0.983838i	$-0.442695\pi$
$823$	10.2736	0.358116	0.179058	+	0.983838i	$0.442695\pi$
$824$	3.49218	0.121656
$825$	−4.49855	−0.156619
$826$	−0.197835	−0.00688355
$827$	−21.4151	−0.744675	−0.372337	−	0.928097i	$-0.621444\pi$
$827$	−21.4151	−0.744675	−0.372337	+	0.928097i	$0.621444\pi$
$828$	0	0
$829$	18.6204	0.646712	0.323356	−	0.946277i	$-0.395189\pi$
$829$	18.6204	0.646712	0.323356	+	0.946277i	$0.395189\pi$
$830$	−12.0038	−0.416658
$831$	−39.8851	−1.38360
$832$	−0.820624	−0.0284500
$833$	16.7419	0.580072
$834$	20.1037	0.696133
$835$	8.43589	0.291936
$836$	−8.13689	−0.281420
$837$	34.3378	1.18689
$838$	19.2547	0.665143
$839$	−16.1518	−0.557621	−0.278811	−	0.960346i	$-0.589940\pi$
$839$	−16.1518	−0.557621	−0.278811	+	0.960346i	$0.589940\pi$
$840$	−0.292235	−0.0100831
$841$	57.3931	1.97907
$842$	35.2902	1.21618
$843$	−55.9830	−1.92816
$844$	−3.50940	−0.120799
$845$	12.3266	0.424047
$846$	−41.5536	−1.42864
$847$	−0.880075	−0.0302397
$848$	10.1839	0.349718
$849$	34.9089	1.19807
$850$	−2.39546	−0.0821635
$851$	0	0
$852$	−3.65697	−0.125286
$853$	−40.8774	−1.39961	−0.699807	−	0.714332i	$-0.746731\pi$
$853$	−40.8774	−1.39961	−0.699807	+	0.714332i	$0.746731\pi$
$854$	−0.0753430	−0.00257819
$855$	−24.0801	−0.823523
$856$	8.04757	0.275060
$857$	38.1768	1.30409	0.652047	−	0.758179i	$-0.273911\pi$
$857$	38.1768	1.30409	0.652047	+	0.758179i	$0.273911\pi$
$858$	3.69162	0.126030
$859$	−54.2939	−1.85248	−0.926241	−	0.376931i	$-0.876979\pi$
$859$	−54.2939	−1.85248	−0.926241	+	0.376931i	$0.876979\pi$
$860$	−1.06696	−0.0363829
$861$	2.96116	0.100916
$862$	−32.6180	−1.11097
$863$	38.0704	1.29593	0.647966	−	0.761669i	$-0.275620\pi$
$863$	38.0704	1.29593	0.647966	+	0.761669i	$0.275620\pi$
$864$	4.94803	0.168336
$865$	20.9993	0.713997
$866$	−4.24030	−0.144091
$867$	−31.4012	−1.06644
$868$	0.727334	0.0246873
$869$	21.7948	0.739338
$870$	−25.9166	−0.878655
$871$	−2.87780	−0.0975106
$872$	4.75271	0.160947
$873$	−86.7065	−2.93457
$874$	0	0
$875$	−0.104808	−0.00354315
$876$	31.6530	1.06946
$877$	−10.6650	−0.360131	−0.180066	−	0.983655i	$-0.557631\pi$
$877$	−10.6650	−0.360131	−0.180066	+	0.983655i	$0.557631\pi$
$878$	17.7359	0.598557
$879$	11.5788	0.390542
$880$	1.61337	0.0543867
$881$	29.7448	1.00213	0.501064	−	0.865411i	$-0.332942\pi$
$881$	29.7448	1.00213	0.501064	+	0.865411i	$0.332942\pi$
$882$	−33.3696	−1.12361
$883$	33.4709	1.12639	0.563193	−	0.826326i	$-0.309573\pi$
$883$	33.4709	1.12639	0.563193	+	0.826326i	$0.309573\pi$
$884$	1.96577	0.0661160
$885$	5.26316	0.176919
$886$	33.2025	1.11546
$887$	0.763899	0.0256492	0.0128246	−	0.999918i	$-0.495918\pi$
$887$	0.763899	0.0256492	0.0128246	+	0.999918i	$0.495918\pi$
$888$	10.5470	0.353934
$889$	−0.809763	−0.0271586
$890$	12.3656	0.414495
$891$	0.850503	0.0284929
$892$	0.760922	0.0254776
$893$	−43.8933	−1.46883
$894$	51.5323	1.72350
$895$	14.6536	0.489814
$896$	0.104808	0.00350138
$897$	0	0
$898$	−15.8541	−0.529058
$899$	64.5030	2.15130
$900$	4.77457	0.159152
$901$	−24.3952	−0.812721
$902$	−16.3480	−0.544329
$903$	0.311802	0.0103761
$904$	12.0649	0.401274
$905$	16.3855	0.544674
$906$	19.7658	0.656673
$907$	18.7122	0.621329	0.310664	−	0.950520i	$-0.399449\pi$
$907$	18.7122	0.621329	0.310664	+	0.950520i	$0.399449\pi$
$908$	22.1110	0.733780
$909$	51.5523	1.70988
$910$	0.0860079	0.00285113
$911$	39.5665	1.31090	0.655448	−	0.755241i	$-0.272480\pi$
$911$	39.5665	1.31090	0.655448	+	0.755241i	$0.272480\pi$
$912$	14.0625	0.465656
$913$	−19.3666	−0.640940
$914$	−23.3208	−0.771385
$915$	2.00442	0.0662639
$916$	18.3056	0.604833
$917$	−1.67048	−0.0551640
$918$	−11.8528	−0.391201
$919$	−39.1397	−1.29110	−0.645549	−	0.763719i	$-0.723371\pi$
$919$	−39.1397	−1.29110	−0.645549	+	0.763719i	$0.723371\pi$
$920$	0	0
$921$	−46.9357	−1.54659
$922$	35.0520	1.15438
$923$	1.07629	0.0354264
$924$	−0.471483	−0.0155107
$925$	3.78260	0.124371
$926$	21.7943	0.716206
$927$	16.6737	0.547635
$928$	9.29479	0.305116
$929$	34.4775	1.13117	0.565584	−	0.824690i	$-0.308651\pi$
$929$	34.4775	1.13117	0.565584	+	0.824690i	$0.308651\pi$
$930$	−19.3499	−0.634508
$931$	−35.2484	−1.15522
$932$	−8.93455	−0.292661
$933$	10.2793	0.336531
$934$	4.79248	0.156815
$935$	−3.86476	−0.126391
$936$	−3.91813	−0.128068
$937$	46.1403	1.50734	0.753670	−	0.657253i	$-0.228282\pi$
$937$	46.1403	1.50734	0.753670	+	0.657253i	$0.228282\pi$
$938$	0.367545	0.0120008
$939$	−15.7214	−0.513050
$940$	8.70310	0.283864
$941$	0.749900	0.0244460	0.0122230	−	0.999925i	$-0.496109\pi$
$941$	0.749900	0.0244460	0.0122230	+	0.999925i	$0.496109\pi$
$942$	−19.5568	−0.637195
$943$	0	0
$944$	−1.88759	−0.0614360
$945$	−0.518593	−0.0168698
$946$	−1.72140	−0.0559674
$947$	−4.32198	−0.140446	−0.0702228	−	0.997531i	$-0.522371\pi$
$947$	−4.32198	−0.140446	−0.0702228	+	0.997531i	$0.522371\pi$
$948$	−37.6667	−1.22336
$949$	−9.31583	−0.302405
$950$	5.04341	0.163630
$951$	57.0506	1.84999
$952$	−0.251063	−0.00813699
$953$	18.8602	0.610942	0.305471	−	0.952201i	$-0.401186\pi$
$953$	18.8602	0.610942	0.305471	+	0.952201i	$0.401186\pi$
$954$	48.6240	1.57426
$955$	19.0662	0.616969
$956$	−15.4332	−0.499145
$957$	−41.8131	−1.35162
$958$	18.4300	0.595446
$959$	−0.149247	−0.00481943
$960$	−2.78829	−0.0899918
$961$	17.1593	0.553527
$962$	−3.10410	−0.100080
$963$	38.4237	1.23819
$964$	−24.2931	−0.782429
$965$	3.51113	0.113027
$966$	0	0
$967$	25.7430	0.827840	0.413920	−	0.910313i	$-0.364159\pi$
$967$	25.7430	0.827840	0.413920	+	0.910313i	$0.364159\pi$
$968$	−8.39703	−0.269891
$969$	−33.6861	−1.08215
$970$	18.1600	0.583084
$971$	−22.0733	−0.708365	−0.354182	−	0.935176i	$-0.615241\pi$
$971$	−22.0733	−0.708365	−0.354182	+	0.935176i	$0.615241\pi$
$972$	−16.3140	−0.523271
$973$	0.755667	0.0242256
$974$	18.5292	0.593715
$975$	−2.28814	−0.0732792
$976$	−0.718868	−0.0230104
$977$	−4.11932	−0.131789	−0.0658944	−	0.997827i	$-0.520990\pi$
$977$	−4.11932	−0.131789	−0.0658944	+	0.997827i	$0.520990\pi$
$978$	−34.5537	−1.10491
$979$	19.9502	0.637612
$980$	6.98902	0.223256
$981$	22.6922	0.724506
$982$	−42.7858	−1.36535
$983$	12.9570	0.413263	0.206631	−	0.978419i	$-0.433750\pi$
$983$	12.9570	0.413263	0.206631	+	0.978419i	$0.433750\pi$
$984$	28.2533	0.900681
$985$	−16.3731	−0.521691
$986$	−22.2653	−0.709071
$987$	−2.54335	−0.0809557
$988$	−4.13874	−0.131671
$989$	0	0
$990$	7.70316	0.244822
$991$	9.28169	0.294842	0.147421	−	0.989074i	$-0.452903\pi$
$991$	9.28169	0.294842	0.147421	+	0.989074i	$0.452903\pi$
$992$	6.93969	0.220335
$993$	−25.0711	−0.795606
$994$	−0.137460	−0.00435997
$995$	24.3835	0.773010
$996$	33.4701	1.06054
$997$	−12.6283	−0.399941	−0.199971	−	0.979802i	$-0.564085\pi$
$997$	−12.6283	−0.399941	−0.199971	+	0.979802i	$0.564085\pi$
$998$	−3.23317	−0.102344
$999$	18.7164	0.592162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.13		15
23.4	even	11		230.2.g.d.131.3	✓	30
23.6	even	11		230.2.g.d.151.3	yes	30
23.22	odd	2		5290.2.a.bl.1.13		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.131.3	✓	30	23.4	even	11
230.2.g.d.151.3	yes	30	23.6	even	11
5290.2.a.bk.1.13		15	1.1	even	1	trivial
5290.2.a.bl.1.13		15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.78829 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78829 q^{6} +0.104808 q^{7} +1.00000 q^{8} +4.77457 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.78829 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78829 q^{6} +0.104808 q^{7} +1.00000 q^{8} +4.77457 q^{9} -1.00000 q^{10} -1.61337 q^{11} +2.78829 q^{12} -0.820624 q^{13} +0.104808 q^{14} -2.78829 q^{15} +1.00000 q^{16} -2.39546 q^{17} +4.77457 q^{18} +5.04341 q^{19} -1.00000 q^{20} +0.292235 q^{21} -1.61337 q^{22} +2.78829 q^{24} +1.00000 q^{25} -0.820624 q^{26} +4.94803 q^{27} +0.104808 q^{28} +9.29479 q^{29} -2.78829 q^{30} +6.93969 q^{31} +1.00000 q^{32} -4.49855 q^{33} -2.39546 q^{34} -0.104808 q^{35} +4.77457 q^{36} +3.78260 q^{37} +5.04341 q^{38} -2.28814 q^{39} -1.00000 q^{40} +10.1328 q^{41} +0.292235 q^{42} +1.06696 q^{43} -1.61337 q^{44} -4.77457 q^{45} -8.70310 q^{47} +2.78829 q^{48} -6.98902 q^{49} +1.00000 q^{50} -6.67923 q^{51} -0.820624 q^{52} +10.1839 q^{53} +4.94803 q^{54} +1.61337 q^{55} +0.104808 q^{56} +14.0625 q^{57} +9.29479 q^{58} -1.88759 q^{59} -2.78829 q^{60} -0.718868 q^{61} +6.93969 q^{62} +0.500413 q^{63} +1.00000 q^{64} +0.820624 q^{65} -4.49855 q^{66} +3.50684 q^{67} -2.39546 q^{68} -0.104808 q^{70} -1.31155 q^{71} +4.77457 q^{72} +11.3521 q^{73} +3.78260 q^{74} +2.78829 q^{75} +5.04341 q^{76} -0.169094 q^{77} -2.28814 q^{78} -13.5089 q^{79} -1.00000 q^{80} -0.527159 q^{81} +10.1328 q^{82} +12.0038 q^{83} +0.292235 q^{84} +2.39546 q^{85} +1.06696 q^{86} +25.9166 q^{87} -1.61337 q^{88} -12.3656 q^{89} -4.77457 q^{90} -0.0860079 q^{91} +19.3499 q^{93} -8.70310 q^{94} -5.04341 q^{95} +2.78829 q^{96} -18.1600 q^{97} -6.98902 q^{98} -7.70316 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * q^99

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