LMFDB - Embedded newform 1155.2.a.w.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.352076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 $ x^5 - x^4 - 8x^3 + 3x^2 + 8*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.20109$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66516 q^{2} +1.00000 q^{3} +5.10307 q^{4} -1.00000 q^{5} +2.66516 q^{6} +1.00000 q^{7} +8.27017 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.66516 q^{2} +1.00000 q^{3} +5.10307 q^{4} -1.00000 q^{5} +2.66516 q^{6} +1.00000 q^{7} +8.27017 q^{8} +1.00000 q^{9} -2.66516 q^{10} +1.00000 q^{11} +5.10307 q^{12} -3.60501 q^{13} +2.66516 q^{14} -1.00000 q^{15} +11.8352 q^{16} -2.62904 q^{17} +2.66516 q^{18} -2.10307 q^{19} -5.10307 q^{20} +1.00000 q^{21} +2.66516 q^{22} +1.22725 q^{23} +8.27017 q^{24} +1.00000 q^{25} -9.60793 q^{26} +1.00000 q^{27} +5.10307 q^{28} +5.23016 q^{29} -2.66516 q^{30} +2.27470 q^{31} +15.0023 q^{32} +1.00000 q^{33} -7.00680 q^{34} -1.00000 q^{35} +5.10307 q^{36} -10.3371 q^{37} -5.60501 q^{38} -3.60501 q^{39} -8.27017 q^{40} -4.20322 q^{41} +2.66516 q^{42} -4.70420 q^{43} +5.10307 q^{44} -1.00000 q^{45} +3.27081 q^{46} +4.13098 q^{47} +11.8352 q^{48} +1.00000 q^{49} +2.66516 q^{50} -2.62904 q^{51} -18.3966 q^{52} -10.8352 q^{53} +2.66516 q^{54} -1.00000 q^{55} +8.27017 q^{56} -2.10307 q^{57} +13.9392 q^{58} -8.30629 q^{59} -5.10307 q^{60} +11.9828 q^{61} +6.06242 q^{62} +1.00000 q^{63} +16.3131 q^{64} +3.60501 q^{65} +2.66516 q^{66} +14.0624 q^{67} -13.4162 q^{68} +1.22725 q^{69} -2.66516 q^{70} -11.7877 q^{71} +8.27017 q^{72} -10.1347 q^{73} -27.5501 q^{74} +1.00000 q^{75} -10.7321 q^{76} +1.00000 q^{77} -9.60793 q^{78} +13.6050 q^{79} -11.8352 q^{80} +1.00000 q^{81} -11.2023 q^{82} +9.31309 q^{83} +5.10307 q^{84} +2.62904 q^{85} -12.5374 q^{86} +5.23016 q^{87} +8.27017 q^{88} -7.25359 q^{89} -2.66516 q^{90} -3.60501 q^{91} +6.26273 q^{92} +2.27470 q^{93} +11.0097 q^{94} +2.10307 q^{95} +15.0023 q^{96} +10.9103 q^{97} +2.66516 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + 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 $

$2$	2.66516	1.88455	0.942276	−	0.334838i	$-0.108682\pi$
$2$	2.66516	1.88455	0.942276	+	0.334838i	$0.108682\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.10307	2.55153
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.66516	1.08805
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	8.27017	2.92395
$9$	1.00000	0.333333
$10$	−2.66516	−0.842797
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.10307	1.47313
$13$	−3.60501	−0.999851	−0.499925	−	0.866069i	$-0.666639\pi$
$13$	−3.60501	−0.999851	−0.499925	+	0.866069i	$0.666639\pi$
$14$	2.66516	0.712294
$15$	−1.00000	−0.258199
$16$	11.8352	2.95879
$17$	−2.62904	−0.637635	−0.318818	−	0.947816i	$-0.603286\pi$
$17$	−2.62904	−0.637635	−0.318818	+	0.947816i	$0.603286\pi$
$18$	2.66516	0.628184
$19$	−2.10307	−0.482477	−0.241239	−	0.970466i	$-0.577554\pi$
$19$	−2.10307	−0.482477	−0.241239	+	0.970466i	$0.577554\pi$
$20$	−5.10307	−1.14108
$21$	1.00000	0.218218
$22$	2.66516	0.568214
$23$	1.22725	0.255899	0.127949	−	0.991781i	$-0.459160\pi$
$23$	1.22725	0.255899	0.127949	+	0.991781i	$0.459160\pi$
$24$	8.27017	1.68814
$25$	1.00000	0.200000
$26$	−9.60793	−1.88427
$27$	1.00000	0.192450
$28$	5.10307	0.964389
$29$	5.23016	0.971217	0.485609	−	0.874176i	$-0.338598\pi$
$29$	5.23016	0.971217	0.485609	+	0.874176i	$0.338598\pi$
$30$	−2.66516	−0.486589
$31$	2.27470	0.408547	0.204274	−	0.978914i	$-0.434517\pi$
$31$	2.27470	0.408547	0.204274	+	0.978914i	$0.434517\pi$
$32$	15.0023	2.65205
$33$	1.00000	0.174078
$34$	−7.00680	−1.20166
$35$	−1.00000	−0.169031
$36$	5.10307	0.850512
$37$	−10.3371	−1.69941	−0.849706	−	0.527257i	$-0.823221\pi$
$37$	−10.3371	−1.69941	−0.849706	+	0.527257i	$0.823221\pi$
$38$	−5.60501	−0.909253
$39$	−3.60501	−0.577264
$40$	−8.27017	−1.30763
$41$	−4.20322	−0.656433	−0.328216	−	0.944603i	$-0.606448\pi$
$41$	−4.20322	−0.656433	−0.328216	+	0.944603i	$0.606448\pi$
$42$	2.66516	0.411243
$43$	−4.70420	−0.717383	−0.358692	−	0.933456i	$-0.616777\pi$
$43$	−4.70420	−0.717383	−0.358692	+	0.933456i	$0.616777\pi$
$44$	5.10307	0.769317
$45$	−1.00000	−0.149071
$46$	3.27081	0.482255
$47$	4.13098	0.602566	0.301283	−	0.953535i	$-0.402585\pi$
$47$	4.13098	0.602566	0.301283	+	0.953535i	$0.402585\pi$
$48$	11.8352	1.70826
$49$	1.00000	0.142857
$50$	2.66516	0.376910
$51$	−2.62904	−0.368139
$52$	−18.3966	−2.55115
$53$	−10.8352	−1.48833	−0.744163	−	0.667998i	$-0.767151\pi$
$53$	−10.8352	−1.48833	−0.744163	+	0.667998i	$0.767151\pi$
$54$	2.66516	0.362682
$55$	−1.00000	−0.134840
$56$	8.27017	1.10515
$57$	−2.10307	−0.278558
$58$	13.9392	1.83031
$59$	−8.30629	−1.08139	−0.540693	−	0.841220i	$-0.681838\pi$
$59$	−8.30629	−1.08139	−0.540693	+	0.841220i	$0.681838\pi$
$60$	−5.10307	−0.658803
$61$	11.9828	1.53424	0.767119	−	0.641505i	$-0.221690\pi$
$61$	11.9828	1.53424	0.767119	+	0.641505i	$0.221690\pi$
$62$	6.06242	0.769929
$63$	1.00000	0.125988
$64$	16.3131	2.03914
$65$	3.60501	0.447147
$66$	2.66516	0.328058
$67$	14.0624	1.71800	0.858999	−	0.511977i	$-0.171087\pi$
$67$	14.0624	1.71800	0.858999	+	0.511977i	$0.171087\pi$
$68$	−13.4162	−1.62695
$69$	1.22725	0.147743
$70$	−2.66516	−0.318547
$71$	−11.7877	−1.39895	−0.699473	−	0.714659i	$-0.746582\pi$
$71$	−11.7877	−1.39895	−0.699473	+	0.714659i	$0.746582\pi$
$72$	8.27017	0.974649
$73$	−10.1347	−1.18617	−0.593086	−	0.805139i	$-0.702091\pi$
$73$	−10.1347	−1.18617	−0.593086	+	0.805139i	$0.702091\pi$
$74$	−27.5501	−3.20263
$75$	1.00000	0.115470
$76$	−10.7321	−1.23106
$77$	1.00000	0.113961
$78$	−9.60793	−1.08788
$79$	13.6050	1.53068	0.765342	−	0.643624i	$-0.222570\pi$
$79$	13.6050	1.53068	0.765342	+	0.643624i	$0.222570\pi$
$80$	−11.8352	−1.32321
$81$	1.00000	0.111111
$82$	−11.2023	−1.23708
$83$	9.31309	1.02224	0.511122	−	0.859508i	$-0.329230\pi$
$83$	9.31309	1.02224	0.511122	+	0.859508i	$0.329230\pi$
$84$	5.10307	0.556790
$85$	2.62904	0.285159
$86$	−12.5374	−1.35195
$87$	5.23016	0.560732
$88$	8.27017	0.881603
$89$	−7.25359	−0.768879	−0.384439	−	0.923150i	$-0.625605\pi$
$89$	−7.25359	−0.768879	−0.384439	+	0.923150i	$0.625605\pi$
$90$	−2.66516	−0.280932
$91$	−3.60501	−0.377908
$92$	6.26273	0.652935
$93$	2.27470	0.235875
$94$	11.0097	1.13557
$95$	2.10307	0.215770
$96$	15.0023	1.53116
$97$	10.9103	1.10778	0.553888	−	0.832591i	$-0.313143\pi$
$97$	10.9103	1.10778	0.553888	+	0.832591i	$0.313143\pi$
$98$	2.66516	0.269222
$99$	1.00000	0.100504
$100$	5.10307	0.510307
$101$	3.42521	0.340821	0.170411	−	0.985373i	$-0.445491\pi$
$101$	3.42521	0.340821	0.170411	+	0.985373i	$0.445491\pi$
$102$	−7.00680	−0.693777
$103$	−7.70808	−0.759500	−0.379750	−	0.925089i	$-0.623990\pi$
$103$	−7.70808	−0.759500	−0.379750	+	0.925089i	$0.623990\pi$
$104$	−29.8141	−2.92351
$105$	−1.00000	−0.0975900
$106$	−28.8775	−2.80483
$107$	3.15052	0.304572	0.152286	−	0.988336i	$-0.451337\pi$
$107$	3.15052	0.304572	0.152286	+	0.988336i	$0.451337\pi$
$108$	5.10307	0.491043
$109$	12.0829	1.15733	0.578667	−	0.815564i	$-0.303573\pi$
$109$	12.0829	1.15733	0.578667	+	0.815564i	$0.303573\pi$
$110$	−2.66516	−0.254113
$111$	−10.3371	−0.981156
$112$	11.8352	1.11832
$113$	−13.8391	−1.30187	−0.650935	−	0.759134i	$-0.725623\pi$
$113$	−13.8391	−1.30187	−0.650935	+	0.759134i	$0.725623\pi$
$114$	−5.60501	−0.524957
$115$	−1.22725	−0.114441
$116$	26.6899	2.47809
$117$	−3.60501	−0.333284
$118$	−22.1376	−2.03793
$119$	−2.62904	−0.241004
$120$	−8.27017	−0.754960
$121$	1.00000	0.0909091
$122$	31.9360	2.89135
$123$	−4.20322	−0.378992
$124$	11.6079	1.04242
$125$	−1.00000	−0.0894427
$126$	2.66516	0.237431
$127$	−5.45389	−0.483955	−0.241977	−	0.970282i	$-0.577796\pi$
$127$	−5.45389	−0.483955	−0.241977	+	0.970282i	$0.577796\pi$
$128$	13.4724	1.19081
$129$	−4.70420	−0.414181
$130$	9.60793	0.842671
$131$	−3.58159	−0.312925	−0.156462	−	0.987684i	$-0.550009\pi$
$131$	−3.58159	−0.312925	−0.156462	+	0.987684i	$0.550009\pi$
$132$	5.10307	0.444165
$133$	−2.10307	−0.182359
$134$	37.4786	3.23766
$135$	−1.00000	−0.0860663
$136$	−21.7426	−1.86441
$137$	−9.00389	−0.769254	−0.384627	−	0.923072i	$-0.625670\pi$
$137$	−9.00389	−0.769254	−0.384627	+	0.923072i	$0.625670\pi$
$138$	3.27081	0.278430
$139$	8.13466	0.689973	0.344987	−	0.938608i	$-0.387883\pi$
$139$	8.13466	0.689973	0.344987	+	0.938608i	$0.387883\pi$
$140$	−5.10307	−0.431288
$141$	4.13098	0.347891
$142$	−31.4162	−2.63639
$143$	−3.60501	−0.301466
$144$	11.8352	0.986265
$145$	−5.23016	−0.434341
$146$	−27.0105	−2.23540
$147$	1.00000	0.0824786
$148$	−52.7510	−4.33611
$149$	−11.3927	−0.933330	−0.466665	−	0.884434i	$-0.654545\pi$
$149$	−11.3927	−0.933330	−0.466665	+	0.884434i	$0.654545\pi$
$150$	2.66516	0.217609
$151$	4.27178	0.347632	0.173816	−	0.984778i	$-0.444390\pi$
$151$	4.27178	0.347632	0.173816	+	0.984778i	$0.444390\pi$
$152$	−17.3927	−1.41074
$153$	−2.62904	−0.212545
$154$	2.66516	0.214765
$155$	−2.27470	−0.182708
$156$	−18.3966	−1.47291
$157$	−4.75225	−0.379271	−0.189635	−	0.981855i	$-0.560731\pi$
$157$	−4.75225	−0.379271	−0.189635	+	0.981855i	$0.560731\pi$
$158$	36.2595	2.88465
$159$	−10.8352	−0.859285
$160$	−15.0023	−1.18603
$161$	1.22725	0.0967207
$162$	2.66516	0.209395
$163$	18.6870	1.46368	0.731838	−	0.681478i	$-0.238663\pi$
$163$	18.6870	1.46368	0.731838	+	0.681478i	$0.238663\pi$
$164$	−21.4493	−1.67491
$165$	−1.00000	−0.0778499
$166$	24.8209	1.92647
$167$	−11.9902	−0.927828	−0.463914	−	0.885880i	$-0.653555\pi$
$167$	−11.9902	−0.927828	−0.463914	+	0.885880i	$0.653555\pi$
$168$	8.27017	0.638058
$169$	−0.00388633	−0.000298949 0
$170$	7.00680	0.537397
$171$	−2.10307	−0.160826
$172$	−24.0058	−1.83043
$173$	0.0480515	0.00365329	0.00182664	−	0.999998i	$-0.499419\pi$
$173$	0.0480515	0.00365329	0.00182664	+	0.999998i	$0.499419\pi$
$174$	13.9392	1.05673
$175$	1.00000	0.0755929
$176$	11.8352	0.892110
$177$	−8.30629	−0.624339
$178$	−19.3320	−1.44899
$179$	25.8013	1.92848	0.964241	−	0.265027i	$-0.0853807\pi$
$179$	25.8013	1.92848	0.964241	+	0.265027i	$0.0853807\pi$
$180$	−5.10307	−0.380360
$181$	−11.6087	−0.862868	−0.431434	−	0.902145i	$-0.641992\pi$
$181$	−11.6087	−0.862868	−0.431434	+	0.902145i	$0.641992\pi$
$182$	−9.60793	−0.712187
$183$	11.9828	0.885792
$184$	10.1495	0.748235
$185$	10.3371	0.760000
$186$	6.06242	0.444518
$187$	−2.62904	−0.192254
$188$	21.0807	1.53747
$189$	1.00000	0.0727393
$190$	5.60501	0.406630
$191$	−7.85705	−0.568516	−0.284258	−	0.958748i	$-0.591747\pi$
$191$	−7.85705	−0.568516	−0.284258	+	0.958748i	$0.591747\pi$
$192$	16.3131	1.17730
$193$	−1.12418	−0.0809201	−0.0404601	−	0.999181i	$-0.512882\pi$
$193$	−1.12418	−0.0809201	−0.0404601	+	0.999181i	$0.512882\pi$
$194$	29.0778	2.08766
$195$	3.60501	0.258160
$196$	5.10307	0.364505
$197$	26.2205	1.86813	0.934067	−	0.357098i	$-0.116234\pi$
$197$	26.2205	1.86813	0.934067	+	0.357098i	$0.116234\pi$
$198$	2.66516	0.189405
$199$	−1.85629	−0.131589	−0.0657943	−	0.997833i	$-0.520958\pi$
$199$	−1.85629	−0.131589	−0.0657943	+	0.997833i	$0.520958\pi$
$200$	8.27017	0.584789
$201$	14.0624	0.991887
$202$	9.12873	0.642295
$203$	5.23016	0.367086
$204$	−13.4162	−0.939319
$205$	4.20322	0.293566
$206$	−20.5433	−1.43132
$207$	1.22725	0.0852996
$208$	−42.6660	−2.95835
$209$	−2.10307	−0.145472
$210$	−2.66516	−0.183913
$211$	−12.6899	−0.873608	−0.436804	−	0.899557i	$-0.643890\pi$
$211$	−12.6899	−0.873608	−0.436804	+	0.899557i	$0.643890\pi$
$212$	−55.2927	−3.79752
$213$	−11.7877	−0.807682
$214$	8.39663	0.573982
$215$	4.70420	0.320823
$216$	8.27017	0.562714
$217$	2.27470	0.154416
$218$	32.2029	2.18106
$219$	−10.1347	−0.684837
$220$	−5.10307	−0.344049
$221$	9.47771	0.637540
$222$	−27.5501	−1.84904
$223$	24.6229	1.64887	0.824436	−	0.565955i	$-0.191493\pi$
$223$	24.6229	1.64887	0.824436	+	0.565955i	$0.191493\pi$
$224$	15.0023	1.00238
$225$	1.00000	0.0666667
$226$	−36.8833	−2.45344
$227$	−7.70440	−0.511359	−0.255679	−	0.966762i	$-0.582299\pi$
$227$	−7.70440	−0.511359	−0.255679	+	0.966762i	$0.582299\pi$
$228$	−10.7321	−0.710751
$229$	27.3964	1.81041	0.905203	−	0.424979i	$-0.139718\pi$
$229$	27.3964	1.81041	0.905203	+	0.424979i	$0.139718\pi$
$230$	−3.27081	−0.215671
$231$	1.00000	0.0657952
$232$	43.2543	2.83979
$233$	7.98727	0.523263	0.261632	−	0.965168i	$-0.415739\pi$
$233$	7.98727	0.523263	0.261632	+	0.965168i	$0.415739\pi$
$234$	−9.60793	−0.628090
$235$	−4.13098	−0.269476
$236$	−42.3876	−2.75920
$237$	13.6050	0.883741
$238$	−7.00680	−0.454184
$239$	23.3648	1.51135	0.755673	−	0.654950i	$-0.227310\pi$
$239$	23.3648	1.51135	0.755673	+	0.654950i	$0.227310\pi$
$240$	−11.8352	−0.763957
$241$	−25.0183	−1.61157	−0.805784	−	0.592210i	$-0.798256\pi$
$241$	−25.0183	−1.61157	−0.805784	+	0.592210i	$0.798256\pi$
$242$	2.66516	0.171323
$243$	1.00000	0.0641500
$244$	61.1489	3.91466
$245$	−1.00000	−0.0638877
$246$	−11.2023	−0.714229
$247$	7.58159	0.482405
$248$	18.8121	1.19457
$249$	9.31309	0.590193
$250$	−2.66516	−0.168559
$251$	−14.1437	−0.892743	−0.446372	−	0.894848i	$-0.647284\pi$
$251$	−14.1437	−0.892743	−0.446372	+	0.894848i	$0.647284\pi$
$252$	5.10307	0.321463
$253$	1.22725	0.0771564
$254$	−14.5355	−0.912037
$255$	2.62904	0.164637
$256$	3.27995	0.204997
$257$	11.0458	0.689018	0.344509	−	0.938783i	$-0.388045\pi$
$257$	11.0458	0.689018	0.344509	+	0.938783i	$0.388045\pi$
$258$	−12.5374	−0.780546
$259$	−10.3371	−0.642317
$260$	18.3966	1.14091
$261$	5.23016	0.323739
$262$	−9.54550	−0.589723
$263$	−6.73211	−0.415120	−0.207560	−	0.978222i	$-0.566552\pi$
$263$	−6.73211	−0.415120	−0.207560	+	0.978222i	$0.566552\pi$
$264$	8.27017	0.508994
$265$	10.8352	0.665600
$266$	−5.60501	−0.343665
$267$	−7.25359	−0.443912
$268$	71.7615	4.38353
$269$	17.1242	1.04408	0.522042	−	0.852920i	$-0.325170\pi$
$269$	17.1242	1.04408	0.522042	+	0.852920i	$0.325170\pi$
$270$	−2.66516	−0.162196
$271$	16.8195	1.02171	0.510857	−	0.859666i	$-0.329328\pi$
$271$	16.8195	1.02171	0.510857	+	0.859666i	$0.329328\pi$
$272$	−31.1151	−1.88663
$273$	−3.60501	−0.218185
$274$	−23.9968	−1.44970
$275$	1.00000	0.0603023
$276$	6.26273	0.376972
$277$	14.2451	0.855908	0.427954	−	0.903801i	$-0.359235\pi$
$277$	14.2451	0.855908	0.427954	+	0.903801i	$0.359235\pi$
$278$	21.6802	1.30029
$279$	2.27470	0.136182
$280$	−8.27017	−0.494237
$281$	−17.3447	−1.03470	−0.517349	−	0.855775i	$-0.673081\pi$
$281$	−17.3447	−1.03470	−0.517349	+	0.855775i	$0.673081\pi$
$282$	11.0097	0.655619
$283$	−28.4061	−1.68857	−0.844285	−	0.535894i	$-0.819974\pi$
$283$	−28.4061	−1.68857	−0.844285	+	0.535894i	$0.819974\pi$
$284$	−60.1536	−3.56946
$285$	2.10307	0.124575
$286$	−9.60793	−0.568129
$287$	−4.20322	−0.248108
$288$	15.0023	0.884018
$289$	−10.0882	−0.593421
$290$	−13.9392	−0.818539
$291$	10.9103	0.639575
$292$	−51.7179	−3.02656
$293$	15.6883	0.916523	0.458261	−	0.888817i	$-0.348472\pi$
$293$	15.6883	0.916523	0.458261	+	0.888817i	$0.348472\pi$
$294$	2.66516	0.155435
$295$	8.30629	0.483611
$296$	−85.4897	−4.96899
$297$	1.00000	0.0580259
$298$	−30.3635	−1.75891
$299$	−4.42424	−0.255861
$300$	5.10307	0.294626
$301$	−4.70420	−0.271145
$302$	11.3850	0.655131
$303$	3.42521	0.196773
$304$	−24.8902	−1.42755
$305$	−11.9828	−0.686132
$306$	−7.00680	−0.400552
$307$	33.5332	1.91384	0.956921	−	0.290347i	$-0.0937707\pi$
$307$	33.5332	1.91384	0.956921	+	0.290347i	$0.0937707\pi$
$308$	5.10307	0.290774
$309$	−7.70808	−0.438497
$310$	−6.06242	−0.344323
$311$	−10.6463	−0.603694	−0.301847	−	0.953356i	$-0.597603\pi$
$311$	−10.6463	−0.603694	−0.301847	+	0.953356i	$0.597603\pi$
$312$	−29.8141	−1.68789
$313$	3.45389	0.195226	0.0976128	−	0.995224i	$-0.468879\pi$
$313$	3.45389	0.195226	0.0976128	+	0.995224i	$0.468879\pi$
$314$	−12.6655	−0.714755
$315$	−1.00000	−0.0563436
$316$	69.4273	3.90559
$317$	−29.7758	−1.67237	−0.836187	−	0.548445i	$-0.815220\pi$
$317$	−29.7758	−1.67237	−0.836187	+	0.548445i	$0.815220\pi$
$318$	−28.8775	−1.61937
$319$	5.23016	0.292833
$320$	−16.3131	−0.911930
$321$	3.15052	0.175845
$322$	3.27081	0.182275
$323$	5.52905	0.307645
$324$	5.10307	0.283504
$325$	−3.60501	−0.199970
$326$	49.8037	2.75837
$327$	12.0829	0.668188
$328$	−34.7614	−1.91938
$329$	4.13098	0.227748
$330$	−2.66516	−0.146712
$331$	15.2338	0.837328	0.418664	−	0.908141i	$-0.362499\pi$
$331$	15.2338	0.837328	0.418664	+	0.908141i	$0.362499\pi$
$332$	47.5254	2.60829
$333$	−10.3371	−0.566471
$334$	−31.9557	−1.74854
$335$	−14.0624	−0.768312
$336$	11.8352	0.645662
$337$	29.1632	1.58862	0.794312	−	0.607511i	$-0.207832\pi$
$337$	29.1632	1.58862	0.794312	+	0.607511i	$0.207832\pi$
$338$	−0.0103577	−0.000563384 0
$339$	−13.8391	−0.751635
$340$	13.4162	0.727594
$341$	2.27470	0.123182
$342$	−5.60501	−0.303084
$343$	1.00000	0.0539949
$344$	−38.9045	−2.09759
$345$	−1.22725	−0.0660728
$346$	0.128065	0.00688481
$347$	−14.3330	−0.769437	−0.384719	−	0.923034i	$-0.625702\pi$
$347$	−14.3330	−0.769437	−0.384719	+	0.923034i	$0.625702\pi$
$348$	26.6899	1.43073
$349$	25.8879	1.38575	0.692873	−	0.721059i	$-0.256345\pi$
$349$	25.8879	1.38575	0.692873	+	0.721059i	$0.256345\pi$
$350$	2.66516	0.142459
$351$	−3.60501	−0.192421
$352$	15.0023	0.799624
$353$	23.0865	1.22877	0.614386	−	0.789006i	$-0.289404\pi$
$353$	23.0865	1.22877	0.614386	+	0.789006i	$0.289404\pi$
$354$	−22.1376	−1.17660
$355$	11.7877	0.625628
$356$	−37.0156	−1.96182
$357$	−2.62904	−0.139143
$358$	68.7646	3.63432
$359$	−4.05717	−0.214129	−0.107065	−	0.994252i	$-0.534145\pi$
$359$	−4.05717	−0.214129	−0.107065	+	0.994252i	$0.534145\pi$
$360$	−8.27017	−0.435876
$361$	−14.5771	−0.767216
$362$	−30.9390	−1.62612
$363$	1.00000	0.0524864
$364$	−18.3966	−0.964245
$365$	10.1347	0.530473
$366$	31.9360	1.66932
$367$	6.00912	0.313673	0.156837	−	0.987625i	$-0.449870\pi$
$367$	6.00912	0.313673	0.156837	+	0.987625i	$0.449870\pi$
$368$	14.5247	0.757152
$369$	−4.20322	−0.218811
$370$	27.5501	1.43226
$371$	−10.8352	−0.562534
$372$	11.6079	0.601843
$373$	−14.9272	−0.772899	−0.386449	−	0.922311i	$-0.626299\pi$
$373$	−14.9272	−0.772899	−0.386449	+	0.922311i	$0.626299\pi$
$374$	−7.00680	−0.362313
$375$	−1.00000	−0.0516398
$376$	34.1639	1.76187
$377$	−18.8548	−0.971072
$378$	2.66516	0.137081
$379$	−8.83518	−0.453833	−0.226916	−	0.973914i	$-0.572864\pi$
$379$	−8.83518	−0.453833	−0.226916	+	0.973914i	$0.572864\pi$
$380$	10.7321	0.550545
$381$	−5.45389	−0.279411
$382$	−20.9403	−1.07140
$383$	−7.68426	−0.392647	−0.196324	−	0.980539i	$-0.562900\pi$
$383$	−7.68426	−0.392647	−0.196324	+	0.980539i	$0.562900\pi$
$384$	13.4724	0.687512
$385$	−1.00000	−0.0509647
$386$	−2.99611	−0.152498
$387$	−4.70420	−0.239128
$388$	55.6762	2.82653
$389$	−10.9900	−0.557214	−0.278607	−	0.960405i	$-0.589873\pi$
$389$	−10.9900	−0.557214	−0.278607	+	0.960405i	$0.589873\pi$
$390$	9.60793	0.486516
$391$	−3.22648	−0.163170
$392$	8.27017	0.417707
$393$	−3.58159	−0.180667
$394$	69.8818	3.52059
$395$	−13.6050	−0.684542
$396$	5.10307	0.256439
$397$	16.3584	0.821004	0.410502	−	0.911860i	$-0.365353\pi$
$397$	16.3584	0.821004	0.410502	+	0.911860i	$0.365353\pi$
$398$	−4.94730	−0.247986
$399$	−2.10307	−0.105285
$400$	11.8352	0.591759
$401$	2.41841	0.120770	0.0603848	−	0.998175i	$-0.480767\pi$
$401$	2.41841	0.120770	0.0603848	+	0.998175i	$0.480767\pi$
$402$	37.4786	1.86926
$403$	−8.20031	−0.408486
$404$	17.4791	0.869618
$405$	−1.00000	−0.0496904
$406$	13.9392	0.691792
$407$	−10.3371	−0.512392
$408$	−21.7426	−1.07642
$409$	22.7699	1.12590	0.562950	−	0.826491i	$-0.309667\pi$
$409$	22.7699	1.12590	0.562950	+	0.826491i	$0.309667\pi$
$410$	11.2023	0.553240
$411$	−9.00389	−0.444129
$412$	−39.3349	−1.93789
$413$	−8.30629	−0.408726
$414$	3.27081	0.160752
$415$	−9.31309	−0.457162
$416$	−54.0834	−2.65166
$417$	8.13466	0.398356
$418$	−5.60501	−0.274150
$419$	20.2308	0.988341	0.494170	−	0.869365i	$-0.335472\pi$
$419$	20.2308	0.988341	0.494170	+	0.869365i	$0.335472\pi$
$420$	−5.10307	−0.249004
$421$	14.0738	0.685916	0.342958	−	0.939351i	$-0.388571\pi$
$421$	14.0738	0.685916	0.342958	+	0.939351i	$0.388571\pi$
$422$	−33.8206	−1.64636
$423$	4.13098	0.200855
$424$	−89.6088	−4.35179
$425$	−2.62904	−0.127527
$426$	−31.4162	−1.52212
$427$	11.9828	0.579887
$428$	16.0773	0.777126
$429$	−3.60501	−0.174052
$430$	12.5374	0.604608
$431$	3.59356	0.173096	0.0865478	−	0.996248i	$-0.472416\pi$
$431$	3.59356	0.173096	0.0865478	+	0.996248i	$0.472416\pi$
$432$	11.8352	0.569420
$433$	13.3545	0.641777	0.320888	−	0.947117i	$-0.396019\pi$
$433$	13.3545	0.641777	0.320888	+	0.947117i	$0.396019\pi$
$434$	6.06242	0.291006
$435$	−5.23016	−0.250767
$436$	61.6600	2.95298
$437$	−2.58099	−0.123465
$438$	−27.0105	−1.29061
$439$	40.6882	1.94194	0.970972	−	0.239193i	$-0.0768829\pi$
$439$	40.6882	1.94194	0.970972	+	0.239193i	$0.0768829\pi$
$440$	−8.27017	−0.394265
$441$	1.00000	0.0476190
$442$	25.2596	1.20148
$443$	−6.85240	−0.325567	−0.162784	−	0.986662i	$-0.552047\pi$
$443$	−6.85240	−0.325567	−0.162784	+	0.986662i	$0.552047\pi$
$444$	−52.7510	−2.50345
$445$	7.25359	0.343853
$446$	65.6239	3.10738
$447$	−11.3927	−0.538858
$448$	16.3131	0.770721
$449$	2.12515	0.100292	0.0501460	−	0.998742i	$-0.484031\pi$
$449$	2.12515	0.100292	0.0501460	+	0.998742i	$0.484031\pi$
$450$	2.66516	0.125637
$451$	−4.20322	−0.197922
$452$	−70.6217	−3.32177
$453$	4.27178	0.200706
$454$	−20.5334	−0.963682
$455$	3.60501	0.169006
$456$	−17.3927	−0.814490
$457$	16.7978	0.785769	0.392884	−	0.919588i	$-0.371477\pi$
$457$	16.7978	0.785769	0.392884	+	0.919588i	$0.371477\pi$
$458$	73.0158	3.41180
$459$	−2.62904	−0.122713
$460$	−6.26273	−0.292001
$461$	29.4388	1.37110	0.685551	−	0.728024i	$-0.259561\pi$
$461$	29.4388	1.37110	0.685551	+	0.728024i	$0.259561\pi$
$462$	2.66516	0.123994
$463$	−9.14760	−0.425125	−0.212563	−	0.977147i	$-0.568181\pi$
$463$	−9.14760	−0.425125	−0.212563	+	0.977147i	$0.568181\pi$
$464$	61.8999	2.87363
$465$	−2.27470	−0.105486
$466$	21.2873	0.986117
$467$	0.549391	0.0254228	0.0127114	−	0.999919i	$-0.495954\pi$
$467$	0.549391	0.0254228	0.0127114	+	0.999919i	$0.495954\pi$
$468$	−18.3966	−0.850384
$469$	14.0624	0.649342
$470$	−11.0097	−0.507840
$471$	−4.75225	−0.218972
$472$	−68.6944	−3.16192
$473$	−4.70420	−0.216299
$474$	36.2595	1.66545
$475$	−2.10307	−0.0964954
$476$	−13.4162	−0.614929
$477$	−10.8352	−0.496109
$478$	62.2710	2.84821
$479$	−18.5297	−0.846641	−0.423321	−	0.905980i	$-0.639136\pi$
$479$	−18.5297	−0.846641	−0.423321	+	0.905980i	$0.639136\pi$
$480$	−15.0023	−0.684757
$481$	37.2654	1.69916
$482$	−66.6776	−3.03708
$483$	1.22725	0.0558417
$484$	5.10307	0.231958
$485$	−10.9103	−0.495413
$486$	2.66516	0.120894
$487$	−29.8277	−1.35162	−0.675810	−	0.737075i	$-0.736206\pi$
$487$	−29.8277	−1.35162	−0.675810	+	0.737075i	$0.736206\pi$
$488$	99.0996	4.48603
$489$	18.6870	0.845054
$490$	−2.66516	−0.120400
$491$	27.2835	1.23129	0.615644	−	0.788024i	$-0.288896\pi$
$491$	27.2835	1.23129	0.615644	+	0.788024i	$0.288896\pi$
$492$	−21.4493	−0.967011
$493$	−13.7503	−0.619282
$494$	20.2061	0.909117
$495$	−1.00000	−0.0449467
$496$	26.9214	1.20881
$497$	−11.7877	−0.528752
$498$	24.8209	1.11225
$499$	−19.1994	−0.859483	−0.429742	−	0.902952i	$-0.641395\pi$
$499$	−19.1994	−0.859483	−0.429742	+	0.902952i	$0.641395\pi$
$500$	−5.10307	−0.228216
$501$	−11.9902	−0.535682
$502$	−37.6952	−1.68242
$503$	−7.88916	−0.351760	−0.175880	−	0.984412i	$-0.556277\pi$
$503$	−7.88916	−0.351760	−0.175880	+	0.984412i	$0.556277\pi$
$504$	8.27017	0.368383
$505$	−3.42521	−0.152420
$506$	3.27081	0.145405
$507$	−0.00388633	−0.000172598 0
$508$	−27.8316	−1.23483
$509$	40.0255	1.77410	0.887049	−	0.461676i	$-0.152752\pi$
$509$	40.0255	1.77410	0.887049	+	0.461676i	$0.152752\pi$
$510$	7.00680	0.310266
$511$	−10.1347	−0.448331
$512$	−18.2033	−0.804478
$513$	−2.10307	−0.0928528
$514$	29.4388	1.29849
$515$	7.70808	0.339659
$516$	−24.0058	−1.05680
$517$	4.13098	0.181680
$518$	−27.5501	−1.21048
$519$	0.0480515	0.00210923
$520$	29.8141	1.30743
$521$	−29.9142	−1.31057	−0.655283	−	0.755384i	$-0.727451\pi$
$521$	−29.9142	−1.31057	−0.655283	+	0.755384i	$0.727451\pi$
$522$	13.9392	0.610103
$523$	−31.8629	−1.39327	−0.696633	−	0.717427i	$-0.745320\pi$
$523$	−31.8629	−1.39327	−0.696633	+	0.717427i	$0.745320\pi$
$524$	−18.2771	−0.798439
$525$	1.00000	0.0436436
$526$	−17.9421	−0.782314
$527$	−5.98026	−0.260504
$528$	11.8352	0.515060
$529$	−21.4939	−0.934516
$530$	28.8775	1.25436
$531$	−8.30629	−0.360462
$532$	−10.7321	−0.465296
$533$	15.1527	0.656335
$534$	−19.3320	−0.836576
$535$	−3.15052	−0.136209
$536$	116.299	5.02334
$537$	25.8013	1.11341
$538$	45.6388	1.96763
$539$	1.00000	0.0430730
$540$	−5.10307	−0.219601
$541$	3.36768	0.144788	0.0723939	−	0.997376i	$-0.476936\pi$
$541$	3.36768	0.144788	0.0723939	+	0.997376i	$0.476936\pi$
$542$	44.8267	1.92547
$543$	−11.6087	−0.498177
$544$	−39.4416	−1.69104
$545$	−12.0829	−0.517576
$546$	−9.60793	−0.411181
$547$	18.9436	0.809969	0.404984	−	0.914324i	$-0.367277\pi$
$547$	18.9436	0.809969	0.404984	+	0.914324i	$0.367277\pi$
$548$	−45.9475	−1.96278
$549$	11.9828	0.511412
$550$	2.66516	0.113643
$551$	−10.9994	−0.468590
$552$	10.1495	0.431993
$553$	13.6050	0.578544
$554$	37.9656	1.61300
$555$	10.3371	0.438786
$556$	41.5118	1.76049
$557$	−8.81795	−0.373629	−0.186814	−	0.982395i	$-0.559816\pi$
$557$	−8.81795	−0.373629	−0.186814	+	0.982395i	$0.559816\pi$
$558$	6.06242	0.256643
$559$	16.9587	0.717276
$560$	−11.8352	−0.500127
$561$	−2.62904	−0.110998
$562$	−46.2263	−1.94994
$563$	−32.9987	−1.39073	−0.695365	−	0.718657i	$-0.744757\pi$
$563$	−32.9987	−1.39073	−0.695365	+	0.718657i	$0.744757\pi$
$564$	21.0807	0.887657
$565$	13.8391	0.582214
$566$	−75.7069	−3.18220
$567$	1.00000	0.0419961
$568$	−97.4865	−4.09044
$569$	26.3863	1.10617	0.553086	−	0.833124i	$-0.313450\pi$
$569$	26.3863	1.10617	0.553086	+	0.833124i	$0.313450\pi$
$570$	5.60501	0.234768
$571$	29.4679	1.23319	0.616597	−	0.787279i	$-0.288511\pi$
$571$	29.4679	1.23319	0.616597	+	0.787279i	$0.288511\pi$
$572$	−18.3966	−0.769202
$573$	−7.85705	−0.328233
$574$	−11.2023	−0.467573
$575$	1.22725	0.0511798
$576$	16.3131	0.679712
$577$	−29.1198	−1.21227	−0.606136	−	0.795361i	$-0.707281\pi$
$577$	−29.1198	−1.21227	−0.606136	+	0.795361i	$0.707281\pi$
$578$	−26.8865	−1.11833
$579$	−1.12418	−0.0467193
$580$	−26.6899	−1.10824
$581$	9.31309	0.386372
$582$	29.0778	1.20531
$583$	−10.8352	−0.448747
$584$	−83.8154	−3.46831
$585$	3.60501	0.149049
$586$	41.8119	1.72723
$587$	−14.9919	−0.618783	−0.309391	−	0.950935i	$-0.600125\pi$
$587$	−14.9919	−0.618783	−0.309391	+	0.950935i	$0.600125\pi$
$588$	5.10307	0.210447
$589$	−4.78384	−0.197115
$590$	22.1376	0.911390
$591$	26.2205	1.07857
$592$	−122.342	−5.02821
$593$	−39.7952	−1.63419	−0.817097	−	0.576501i	$-0.804418\pi$
$593$	−39.7952	−1.63419	−0.817097	+	0.576501i	$0.804418\pi$
$594$	2.66516	0.109353
$595$	2.62904	0.107780
$596$	−58.1379	−2.38142
$597$	−1.85629	−0.0759727
$598$	−11.7913	−0.482182
$599$	−32.5149	−1.32852	−0.664262	−	0.747500i	$-0.731254\pi$
$599$	−32.5149	−1.32852	−0.664262	+	0.747500i	$0.731254\pi$
$600$	8.27017	0.337628
$601$	−38.4087	−1.56672	−0.783361	−	0.621567i	$-0.786496\pi$
$601$	−38.4087	−1.56672	−0.783361	+	0.621567i	$0.786496\pi$
$602$	−12.5374	−0.510987
$603$	14.0624	0.572666
$604$	21.7992	0.886996
$605$	−1.00000	−0.0406558
$606$	9.12873	0.370829
$607$	42.5852	1.72848	0.864239	−	0.503081i	$-0.167800\pi$
$607$	42.5852	1.72848	0.864239	+	0.503081i	$0.167800\pi$
$608$	−31.5508	−1.27956
$609$	5.23016	0.211937
$610$	−31.9360	−1.29305
$611$	−14.8922	−0.602475
$612$	−13.4162	−0.542316
$613$	−11.1393	−0.449913	−0.224956	−	0.974369i	$-0.572224\pi$
$613$	−11.1393	−0.449913	−0.224956	+	0.974369i	$0.572224\pi$
$614$	89.3714	3.60674
$615$	4.20322	0.169490
$616$	8.27017	0.333215
$617$	−11.2581	−0.453233	−0.226617	−	0.973984i	$-0.572766\pi$
$617$	−11.2581	−0.453233	−0.226617	+	0.973984i	$0.572766\pi$
$618$	−20.5433	−0.826371
$619$	−25.1066	−1.00912	−0.504560	−	0.863377i	$-0.668345\pi$
$619$	−25.1066	−1.00912	−0.504560	+	0.863377i	$0.668345\pi$
$620$	−11.6079	−0.466186
$621$	1.22725	0.0492477
$622$	−28.3740	−1.13769
$623$	−7.25359	−0.290609
$624$	−42.6660	−1.70801
$625$	1.00000	0.0400000
$626$	9.20517	0.367913
$627$	−2.10307	−0.0839885
$628$	−24.2510	−0.967722
$629$	27.1767	1.08361
$630$	−2.66516	−0.106182
$631$	44.6562	1.77774	0.888869	−	0.458162i	$-0.151492\pi$
$631$	44.6562	1.77774	0.888869	+	0.458162i	$0.151492\pi$
$632$	112.516	4.47564
$633$	−12.6899	−0.504378
$634$	−79.3571	−3.15167
$635$	5.45389	0.216431
$636$	−55.2927	−2.19250
$637$	−3.60501	−0.142836
$638$	13.9392	0.551859
$639$	−11.7877	−0.466315
$640$	−13.4724	−0.532544
$641$	−8.92843	−0.352652	−0.176326	−	0.984332i	$-0.556421\pi$
$641$	−8.92843	−0.352652	−0.176326	+	0.984332i	$0.556421\pi$
$642$	8.39663	0.331388
$643$	−50.0255	−1.97281	−0.986406	−	0.164328i	$-0.947455\pi$
$643$	−50.0255	−1.97281	−0.986406	+	0.164328i	$0.947455\pi$
$644$	6.26273	0.246786
$645$	4.70420	0.185228
$646$	14.7358	0.579772
$647$	6.92260	0.272155	0.136078	−	0.990698i	$-0.456550\pi$
$647$	6.92260	0.272155	0.136078	+	0.990698i	$0.456550\pi$
$648$	8.27017	0.324883
$649$	−8.30629	−0.326050
$650$	−9.60793	−0.376854
$651$	2.27470	0.0891523
$652$	95.3609	3.73462
$653$	−32.4094	−1.26828	−0.634139	−	0.773219i	$-0.718645\pi$
$653$	−32.4094	−1.26828	−0.634139	+	0.773219i	$0.718645\pi$
$654$	32.2029	1.25923
$655$	3.58159	0.139944
$656$	−49.7459	−1.94225
$657$	−10.1347	−0.395391
$658$	11.0097	0.429204
$659$	−21.7693	−0.848013	−0.424006	−	0.905659i	$-0.639377\pi$
$659$	−21.7693	−0.848013	−0.424006	+	0.905659i	$0.639377\pi$
$660$	−5.10307	−0.198637
$661$	24.2078	0.941573	0.470787	−	0.882247i	$-0.343970\pi$
$661$	24.2078	0.941573	0.470787	+	0.882247i	$0.343970\pi$
$662$	40.6006	1.57799
$663$	9.47771	0.368084
$664$	77.0209	2.98899
$665$	2.10307	0.0815535
$666$	−27.5501	−1.06754
$667$	6.41871	0.248533
$668$	−61.1867	−2.36739
$669$	24.6229	0.951976
$670$	−37.4786	−1.44792
$671$	11.9828	0.462590
$672$	15.0023	0.578725
$673$	−22.0345	−0.849368	−0.424684	−	0.905342i	$-0.639615\pi$
$673$	−22.0345	−0.849368	−0.424684	+	0.905342i	$0.639615\pi$
$674$	77.7247	2.99384
$675$	1.00000	0.0384900
$676$	−0.0198322	−0.000762778 0
$677$	−22.1142	−0.849919	−0.424959	−	0.905212i	$-0.639712\pi$
$677$	−22.1142	−0.849919	−0.424959	+	0.905212i	$0.639712\pi$
$678$	−36.8833	−1.41649
$679$	10.9103	0.418700
$680$	21.7426	0.833790
$681$	−7.70440	−0.295233
$682$	6.06242	0.232142
$683$	15.3673	0.588015	0.294008	−	0.955803i	$-0.405011\pi$
$683$	15.3673	0.588015	0.294008	+	0.955803i	$0.405011\pi$
$684$	−10.7321	−0.410352
$685$	9.00389	0.344021
$686$	2.66516	0.101756
$687$	27.3964	1.04524
$688$	−55.6750	−2.12259
$689$	39.0609	1.48810
$690$	−3.27081	−0.124518
$691$	6.85977	0.260958	0.130479	−	0.991451i	$-0.458349\pi$
$691$	6.85977	0.260958	0.130479	+	0.991451i	$0.458349\pi$
$692$	0.245210	0.00932149
$693$	1.00000	0.0379869
$694$	−38.1998	−1.45004
$695$	−8.13466	−0.308565
$696$	43.2543	1.63955
$697$	11.0504	0.418565
$698$	68.9953	2.61151
$699$	7.98727	0.302106
$700$	5.10307	0.192878
$701$	49.4124	1.86628	0.933140	−	0.359514i	$-0.117057\pi$
$701$	49.4124	1.86628	0.933140	+	0.359514i	$0.117057\pi$
$702$	−9.60793	−0.362628
$703$	21.7397	0.819927
$704$	16.3131	0.614823
$705$	−4.13098	−0.155582
$706$	61.5292	2.31568
$707$	3.42521	0.128818
$708$	−42.3876	−1.59302
$709$	15.4822	0.581446	0.290723	−	0.956807i	$-0.406104\pi$
$709$	15.4822	0.581446	0.290723	+	0.956807i	$0.406104\pi$
$710$	31.4162	1.17903
$711$	13.6050	0.510228
$712$	−59.9884	−2.24816
$713$	2.79161	0.104547
$714$	−7.00680	−0.262223
$715$	3.60501	0.134820
$716$	131.666	4.92059
$717$	23.3648	0.872576
$718$	−10.8130	−0.403537
$719$	−10.6000	−0.395312	−0.197656	−	0.980271i	$-0.563333\pi$
$719$	−10.6000	−0.395312	−0.197656	+	0.980271i	$0.563333\pi$
$720$	−11.8352	−0.441071
$721$	−7.70808	−0.287064
$722$	−38.8503	−1.44586
$723$	−25.0183	−0.930439
$724$	−59.2400	−2.20164
$725$	5.23016	0.194243
$726$	2.66516	0.0989133
$727$	15.4058	0.571371	0.285685	−	0.958323i	$-0.407779\pi$
$727$	15.4058	0.571371	0.285685	+	0.958323i	$0.407779\pi$
$728$	−29.8141	−1.10498
$729$	1.00000	0.0370370
$730$	27.0105	0.999703
$731$	12.3675	0.457429
$732$	61.1489	2.26013
$733$	−23.2498	−0.858751	−0.429375	−	0.903126i	$-0.641266\pi$
$733$	−23.2498	−0.858751	−0.429375	+	0.903126i	$0.641266\pi$
$734$	16.0152	0.591133
$735$	−1.00000	−0.0368856
$736$	18.4115	0.678657
$737$	14.0624	0.517996
$738$	−11.2023	−0.412361
$739$	−22.1073	−0.813229	−0.406614	−	0.913600i	$-0.633291\pi$
$739$	−22.1073	−0.813229	−0.406614	+	0.913600i	$0.633291\pi$
$740$	52.7510	1.93917
$741$	7.58159	0.278517
$742$	−28.8775	−1.06012
$743$	−25.8395	−0.947958	−0.473979	−	0.880536i	$-0.657183\pi$
$743$	−25.8395	−0.947958	−0.473979	+	0.880536i	$0.657183\pi$
$744$	18.8121	0.689686
$745$	11.3927	0.417398
$746$	−39.7832	−1.45657
$747$	9.31309	0.340748
$748$	−13.4162	−0.490543
$749$	3.15052	0.115117
$750$	−2.66516	−0.0973178
$751$	8.14284	0.297136	0.148568	−	0.988902i	$-0.452534\pi$
$751$	8.14284	0.297136	0.148568	+	0.988902i	$0.452534\pi$
$752$	48.8909	1.78287
$753$	−14.1437	−0.515426
$754$	−50.2510	−1.83004
$755$	−4.27178	−0.155466
$756$	5.10307	0.185597
$757$	1.69119	0.0614675	0.0307337	−	0.999528i	$-0.490216\pi$
$757$	1.69119	0.0614675	0.0307337	+	0.999528i	$0.490216\pi$
$758$	−23.5471	−0.855271
$759$	1.22725	0.0445463
$760$	17.3927	0.630901
$761$	2.82314	0.102339	0.0511695	−	0.998690i	$-0.483705\pi$
$761$	2.82314	0.102339	0.0511695	+	0.998690i	$0.483705\pi$
$762$	−14.5355	−0.526565
$763$	12.0829	0.437431
$764$	−40.0951	−1.45059
$765$	2.62904	0.0950531
$766$	−20.4798	−0.739964
$767$	29.9443	1.08123
$768$	3.27995	0.118355
$769$	32.0401	1.15540	0.577698	−	0.816250i	$-0.303951\pi$
$769$	32.0401	1.15540	0.577698	+	0.816250i	$0.303951\pi$
$770$	−2.66516	−0.0960456
$771$	11.0458	0.397805
$772$	−5.73676	−0.206471
$773$	35.0865	1.26197	0.630987	−	0.775793i	$-0.282650\pi$
$773$	35.0865	1.26197	0.630987	+	0.775793i	$0.282650\pi$
$774$	−12.5374	−0.450648
$775$	2.27470	0.0817095
$776$	90.2303	3.23908
$777$	−10.3371	−0.370842
$778$	−29.2900	−1.05010
$779$	8.83967	0.316714
$780$	18.3966	0.658705
$781$	−11.7877	−0.421798
$782$	−8.59908	−0.307503
$783$	5.23016	0.186911
$784$	11.8352	0.422685
$785$	4.75225	0.169615
$786$	−9.54550	−0.340477
$787$	−7.05971	−0.251652	−0.125826	−	0.992052i	$-0.540158\pi$
$787$	−7.05971	−0.251652	−0.125826	+	0.992052i	$0.540158\pi$
$788$	133.805	4.76661
$789$	−6.73211	−0.239669
$790$	−36.2595	−1.29006
$791$	−13.8391	−0.492060
$792$	8.27017	0.293868
$793$	−43.1981	−1.53401
$794$	43.5977	1.54722
$795$	10.8352	0.384284
$796$	−9.47275	−0.335753
$797$	26.2620	0.930246	0.465123	−	0.885246i	$-0.346010\pi$
$797$	26.2620	0.930246	0.465123	+	0.885246i	$0.346010\pi$
$798$	−5.60501	−0.198415
$799$	−10.8605	−0.384217
$800$	15.0023	0.530411
$801$	−7.25359	−0.256293
$802$	6.44545	0.227597
$803$	−10.1347	−0.357645
$804$	71.7615	2.53083
$805$	−1.22725	−0.0432548
$806$	−21.8551	−0.769814
$807$	17.1242	0.602802
$808$	28.3271	0.996544
$809$	8.92190	0.313677	0.156839	−	0.987624i	$-0.449870\pi$
$809$	8.92190	0.313677	0.156839	+	0.987624i	$0.449870\pi$
$810$	−2.66516	−0.0936441
$811$	−20.6028	−0.723461	−0.361730	−	0.932283i	$-0.617814\pi$
$811$	−20.6028	−0.723461	−0.361730	+	0.932283i	$0.617814\pi$
$812$	26.6899	0.936631
$813$	16.8195	0.589887
$814$	−27.5501	−0.965629
$815$	−18.6870	−0.654576
$816$	−31.1151	−1.08925
$817$	9.89325	0.346121
$818$	60.6854	2.12182
$819$	−3.60501	−0.125969
$820$	21.4493	0.749043
$821$	24.8311	0.866611	0.433305	−	0.901247i	$-0.357347\pi$
$821$	24.8311	0.866611	0.433305	+	0.901247i	$0.357347\pi$
$822$	−23.9968	−0.836984
$823$	−21.7975	−0.759812	−0.379906	−	0.925025i	$-0.624044\pi$
$823$	−21.7975	−0.759812	−0.379906	+	0.925025i	$0.624044\pi$
$824$	−63.7471	−2.22074
$825$	1.00000	0.0348155
$826$	−22.1376	−0.770265
$827$	38.3134	1.33229	0.666144	−	0.745823i	$-0.267944\pi$
$827$	38.3134	1.33229	0.666144	+	0.745823i	$0.267944\pi$
$828$	6.26273	0.217645
$829$	−37.8916	−1.31603	−0.658015	−	0.753005i	$-0.728604\pi$
$829$	−37.8916	−1.31603	−0.658015	+	0.753005i	$0.728604\pi$
$830$	−24.8209	−0.861545
$831$	14.2451	0.494158
$832$	−58.8089	−2.03883
$833$	−2.62904	−0.0910908
$834$	21.6802	0.750723
$835$	11.9902	0.414937
$836$	−10.7321	−0.371178
$837$	2.27470	0.0786250
$838$	53.9184	1.86258
$839$	−35.5311	−1.22667	−0.613335	−	0.789823i	$-0.710173\pi$
$839$	−35.5311	−1.22667	−0.613335	+	0.789823i	$0.710173\pi$
$840$	−8.27017	−0.285348
$841$	−1.64538	−0.0567374
$842$	37.5089	1.29264
$843$	−17.3447	−0.597383
$844$	−64.7574	−2.22904
$845$	0.00388633	0.000133694 0
$846$	11.0097	0.378522
$847$	1.00000	0.0343604
$848$	−128.236	−4.40365
$849$	−28.4061	−0.974896
$850$	−7.00680	−0.240331
$851$	−12.6862	−0.434878
$852$	−60.1536	−2.06083
$853$	30.5753	1.04688	0.523438	−	0.852064i	$-0.324649\pi$
$853$	30.5753	1.04688	0.523438	+	0.852064i	$0.324649\pi$
$854$	31.9360	1.09283
$855$	2.10307	0.0719234
$856$	26.0553	0.890552
$857$	−30.9543	−1.05738	−0.528689	−	0.848815i	$-0.677316\pi$
$857$	−30.9543	−1.05738	−0.528689	+	0.848815i	$0.677316\pi$
$858$	−9.60793	−0.328009
$859$	46.4341	1.58431	0.792156	−	0.610319i	$-0.208959\pi$
$859$	46.4341	1.58431	0.792156	+	0.610319i	$0.208959\pi$
$860$	24.0058	0.818592
$861$	−4.20322	−0.143245
$862$	9.57740	0.326207
$863$	−41.5106	−1.41304	−0.706518	−	0.707695i	$-0.749735\pi$
$863$	−41.5106	−1.41304	−0.706518	+	0.707695i	$0.749735\pi$
$864$	15.0023	0.510388
$865$	−0.0480515	−0.00163380
$866$	35.5919	1.20946
$867$	−10.0882	−0.342612
$868$	11.6079	0.393999
$869$	13.6050	0.461518
$870$	−13.9392	−0.472584
$871$	−50.6952	−1.71774
$872$	99.9279	3.38399
$873$	10.9103	0.369259
$874$	−6.87874	−0.232677
$875$	−1.00000	−0.0338062
$876$	−51.7179	−1.74739
$877$	−29.7068	−1.00313	−0.501564	−	0.865121i	$-0.667242\pi$
$877$	−29.7068	−1.00313	−0.501564	+	0.865121i	$0.667242\pi$
$878$	108.441	3.65969
$879$	15.6883	0.529155
$880$	−11.8352	−0.398964
$881$	18.6484	0.628280	0.314140	−	0.949377i	$-0.398284\pi$
$881$	18.6484	0.628280	0.314140	+	0.949377i	$0.398284\pi$
$882$	2.66516	0.0897406
$883$	−26.5305	−0.892823	−0.446412	−	0.894828i	$-0.647298\pi$
$883$	−26.5305	−0.892823	−0.446412	+	0.894828i	$0.647298\pi$
$884$	48.3654	1.62671
$885$	8.30629	0.279213
$886$	−18.2627	−0.613548
$887$	−30.3782	−1.02000	−0.510001	−	0.860174i	$-0.670355\pi$
$887$	−30.3782	−1.02000	−0.510001	+	0.860174i	$0.670355\pi$
$888$	−85.4897	−2.86885
$889$	−5.45389	−0.182918
$890$	19.3320	0.648009
$891$	1.00000	0.0335013
$892$	125.652	4.20715
$893$	−8.68774	−0.290724
$894$	−30.3635	−1.01551
$895$	−25.8013	−0.862443
$896$	13.4724	0.450082
$897$	−4.42424	−0.147721
$898$	5.66386	0.189005
$899$	11.8970	0.396788
$900$	5.10307	0.170102
$901$	28.4861	0.949009
$902$	−11.2023	−0.372994
$903$	−4.70420	−0.156546
$904$	−114.451	−3.80660
$905$	11.6087	0.385886
$906$	11.3850	0.378240
$907$	−34.7084	−1.15247	−0.576236	−	0.817283i	$-0.695479\pi$
$907$	−34.7084	−1.15247	−0.576236	+	0.817283i	$0.695479\pi$
$908$	−39.3161	−1.30475
$909$	3.42521	0.113607
$910$	9.60793	0.318500
$911$	−36.9304	−1.22356	−0.611779	−	0.791029i	$-0.709546\pi$
$911$	−36.9304	−1.22356	−0.611779	+	0.791029i	$0.709546\pi$
$912$	−24.8902	−0.824197
$913$	9.31309	0.308218
$914$	44.7688	1.48082
$915$	−11.9828	−0.396138
$916$	139.806	4.61932
$917$	−3.58159	−0.118275
$918$	−7.00680	−0.231259
$919$	3.89991	0.128646	0.0643231	−	0.997929i	$-0.479511\pi$
$919$	3.89991	0.128646	0.0643231	+	0.997929i	$0.479511\pi$
$920$	−10.1495	−0.334621
$921$	33.5332	1.10496
$922$	78.4591	2.58391
$923$	42.4949	1.39874
$924$	5.10307	0.167879
$925$	−10.3371	−0.339882
$926$	−24.3798	−0.801170
$927$	−7.70808	−0.253167
$928$	78.4644	2.57572
$929$	49.1165	1.61146	0.805730	−	0.592284i	$-0.201774\pi$
$929$	49.1165	1.61146	0.805730	+	0.592284i	$0.201774\pi$
$930$	−6.06242	−0.198795
$931$	−2.10307	−0.0689253
$932$	40.7596	1.33512
$933$	−10.6463	−0.348543
$934$	1.46421	0.0479106
$935$	2.62904	0.0859787
$936$	−29.8141	−0.974503
$937$	38.7411	1.26562	0.632809	−	0.774308i	$-0.281902\pi$
$937$	38.7411	1.26562	0.632809	+	0.774308i	$0.281902\pi$
$938$	37.4786	1.22372
$939$	3.45389	0.112713
$940$	−21.0807	−0.687576
$941$	−39.0972	−1.27453	−0.637266	−	0.770644i	$-0.719935\pi$
$941$	−39.0972	−1.27453	−0.637266	+	0.770644i	$0.719935\pi$
$942$	−12.6655	−0.412664
$943$	−5.15839	−0.167980
$944$	−98.3064	−3.19960
$945$	−1.00000	−0.0325300
$946$	−12.5374	−0.407627
$947$	−33.0088	−1.07264	−0.536322	−	0.844014i	$-0.680187\pi$
$947$	−33.0088	−1.07264	−0.536322	+	0.844014i	$0.680187\pi$
$948$	69.4273	2.25489
$949$	36.5356	1.18600
$950$	−5.60501	−0.181851
$951$	−29.7758	−0.965545
$952$	−21.7426	−0.704681
$953$	−9.33860	−0.302507	−0.151253	−	0.988495i	$-0.548331\pi$
$953$	−9.33860	−0.302507	−0.151253	+	0.988495i	$0.548331\pi$
$954$	−28.8775	−0.934942
$955$	7.85705	0.254248
$956$	119.232	3.85625
$957$	5.23016	0.169067
$958$	−49.3845	−1.59554
$959$	−9.00389	−0.290751
$960$	−16.3131	−0.526503
$961$	−25.8258	−0.833089
$962$	99.3183	3.20215
$963$	3.15052	0.101524
$964$	−127.670	−4.11197
$965$	1.12418	0.0361886
$966$	3.27081	0.105237
$967$	−23.9201	−0.769217	−0.384609	−	0.923080i	$-0.625664\pi$
$967$	−23.9201	−0.769217	−0.384609	+	0.923080i	$0.625664\pi$
$968$	8.27017	0.265813
$969$	5.52905	0.177619
$970$	−29.0778	−0.933631
$971$	−49.2121	−1.57929	−0.789646	−	0.613562i	$-0.789736\pi$
$971$	−49.2121	−1.57929	−0.789646	+	0.613562i	$0.789736\pi$
$972$	5.10307	0.163681
$973$	8.13466	0.260785
$974$	−79.4955	−2.54720
$975$	−3.60501	−0.115453
$976$	141.818	4.53949
$977$	−9.23968	−0.295604	−0.147802	−	0.989017i	$-0.547220\pi$
$977$	−9.23968	−0.295604	−0.147802	+	0.989017i	$0.547220\pi$
$978$	49.8037	1.59255
$979$	−7.25359	−0.231826
$980$	−5.10307	−0.163012
$981$	12.0829	0.385778
$982$	72.7149	2.32043
$983$	−7.65675	−0.244212	−0.122106	−	0.992517i	$-0.538965\pi$
$983$	−7.65675	−0.244212	−0.122106	+	0.992517i	$0.538965\pi$
$984$	−34.7614	−1.10815
$985$	−26.2205	−0.835455
$986$	−36.6467	−1.16707
$987$	4.13098	0.131491
$988$	38.6894	1.23087
$989$	−5.77321	−0.183577
$990$	−2.66516	−0.0847043
$991$	−17.0577	−0.541854	−0.270927	−	0.962600i	$-0.587330\pi$
$991$	−17.0577	−0.541854	−0.270927	+	0.962600i	$0.587330\pi$
$992$	34.1256	1.08349
$993$	15.2338	0.483432
$994$	−31.4162	−0.996460
$995$	1.85629	0.0588482
$996$	47.5254	1.50590
$997$	16.4974	0.522476	0.261238	−	0.965274i	$-0.415869\pi$
$997$	16.4974	0.522476	0.261238	+	0.965274i	$0.415869\pi$
$998$	−51.1694	−1.61974
$999$	−10.3371	−0.327052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.w.1.5	✓	5
3.2	odd	2		3465.2.a.bm.1.1		5
5.4	even	2		5775.2.a.cg.1.1		5
7.6	odd	2		8085.2.a.bv.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.w.1.5	✓	5	1.1	even	1	trivial
3465.2.a.bm.1.1		5	3.2	odd	2
5775.2.a.cg.1.1		5	5.4	even	2
8085.2.a.bv.1.5		5	7.6	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+2.66516 q^{2} +1.00000 q^{3} +5.10307 q^{4} -1.00000 q^{5} +2.66516 q^{6} +1.00000 q^{7} +8.27017 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.66516 q^{2} +1.00000 q^{3} +5.10307 q^{4} -1.00000 q^{5} +2.66516 q^{6} +1.00000 q^{7} +8.27017 q^{8} +1.00000 q^{9} -2.66516 q^{10} +1.00000 q^{11} +5.10307 q^{12} -3.60501 q^{13} +2.66516 q^{14} -1.00000 q^{15} +11.8352 q^{16} -2.62904 q^{17} +2.66516 q^{18} -2.10307 q^{19} -5.10307 q^{20} +1.00000 q^{21} +2.66516 q^{22} +1.22725 q^{23} +8.27017 q^{24} +1.00000 q^{25} -9.60793 q^{26} +1.00000 q^{27} +5.10307 q^{28} +5.23016 q^{29} -2.66516 q^{30} +2.27470 q^{31} +15.0023 q^{32} +1.00000 q^{33} -7.00680 q^{34} -1.00000 q^{35} +5.10307 q^{36} -10.3371 q^{37} -5.60501 q^{38} -3.60501 q^{39} -8.27017 q^{40} -4.20322 q^{41} +2.66516 q^{42} -4.70420 q^{43} +5.10307 q^{44} -1.00000 q^{45} +3.27081 q^{46} +4.13098 q^{47} +11.8352 q^{48} +1.00000 q^{49} +2.66516 q^{50} -2.62904 q^{51} -18.3966 q^{52} -10.8352 q^{53} +2.66516 q^{54} -1.00000 q^{55} +8.27017 q^{56} -2.10307 q^{57} +13.9392 q^{58} -8.30629 q^{59} -5.10307 q^{60} +11.9828 q^{61} +6.06242 q^{62} +1.00000 q^{63} +16.3131 q^{64} +3.60501 q^{65} +2.66516 q^{66} +14.0624 q^{67} -13.4162 q^{68} +1.22725 q^{69} -2.66516 q^{70} -11.7877 q^{71} +8.27017 q^{72} -10.1347 q^{73} -27.5501 q^{74} +1.00000 q^{75} -10.7321 q^{76} +1.00000 q^{77} -9.60793 q^{78} +13.6050 q^{79} -11.8352 q^{80} +1.00000 q^{81} -11.2023 q^{82} +9.31309 q^{83} +5.10307 q^{84} +2.62904 q^{85} -12.5374 q^{86} +5.23016 q^{87} +8.27017 q^{88} -7.25359 q^{89} -2.66516 q^{90} -3.60501 q^{91} +6.26273 q^{92} +2.27470 q^{93} +11.0097 q^{94} +2.10307 q^{95} +15.0023 q^{96} +10.9103 q^{97} +2.66516 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * q^99

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