LMFDB - Embedded newform 4334.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
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} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.67591$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.67591 q^{3} +1.00000 q^{4} -3.90939 q^{5} +1.67591 q^{6} -0.186287 q^{7} -1.00000 q^{8} -0.191317 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.67591 q^{3} +1.00000 q^{4} -3.90939 q^{5} +1.67591 q^{6} -0.186287 q^{7} -1.00000 q^{8} -0.191317 q^{9} +3.90939 q^{10} +1.00000 q^{11} -1.67591 q^{12} -6.91563 q^{13} +0.186287 q^{14} +6.55180 q^{15} +1.00000 q^{16} -0.375922 q^{17} +0.191317 q^{18} +0.115664 q^{19} -3.90939 q^{20} +0.312200 q^{21} -1.00000 q^{22} +2.11998 q^{23} +1.67591 q^{24} +10.2834 q^{25} +6.91563 q^{26} +5.34837 q^{27} -0.186287 q^{28} +1.10627 q^{29} -6.55180 q^{30} -8.13360 q^{31} -1.00000 q^{32} -1.67591 q^{33} +0.375922 q^{34} +0.728268 q^{35} -0.191317 q^{36} +10.2588 q^{37} -0.115664 q^{38} +11.5900 q^{39} +3.90939 q^{40} +3.93374 q^{41} -0.312200 q^{42} +5.46223 q^{43} +1.00000 q^{44} +0.747935 q^{45} -2.11998 q^{46} -3.16576 q^{47} -1.67591 q^{48} -6.96530 q^{49} -10.2834 q^{50} +0.630013 q^{51} -6.91563 q^{52} +9.17102 q^{53} -5.34837 q^{54} -3.90939 q^{55} +0.186287 q^{56} -0.193842 q^{57} -1.10627 q^{58} -5.00551 q^{59} +6.55180 q^{60} +2.17956 q^{61} +8.13360 q^{62} +0.0356399 q^{63} +1.00000 q^{64} +27.0359 q^{65} +1.67591 q^{66} -1.99832 q^{67} -0.375922 q^{68} -3.55289 q^{69} -0.728268 q^{70} +3.16971 q^{71} +0.191317 q^{72} -3.04510 q^{73} -10.2588 q^{74} -17.2340 q^{75} +0.115664 q^{76} -0.186287 q^{77} -11.5900 q^{78} -2.40602 q^{79} -3.90939 q^{80} -8.38945 q^{81} -3.93374 q^{82} +8.81641 q^{83} +0.312200 q^{84} +1.46963 q^{85} -5.46223 q^{86} -1.85401 q^{87} -1.00000 q^{88} +1.79289 q^{89} -0.747935 q^{90} +1.28829 q^{91} +2.11998 q^{92} +13.6312 q^{93} +3.16576 q^{94} -0.452175 q^{95} +1.67591 q^{96} -15.3150 q^{97} +6.96530 q^{98} -0.191317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * 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
$3$	−1.67591	−0.967589	−0.483794	−	0.875182i	$-0.660742\pi$
$3$	−1.67591	−0.967589	−0.483794	+	0.875182i	$0.660742\pi$
$4$	1.00000	0.500000
$5$	−3.90939	−1.74833	−0.874167	−	0.485625i	$-0.838592\pi$
$5$	−3.90939	−1.74833	−0.874167	+	0.485625i	$0.838592\pi$
$6$	1.67591	0.684188
$7$	−0.186287	−0.0704098	−0.0352049	−	0.999380i	$-0.511208\pi$
$7$	−0.186287	−0.0704098	−0.0352049	+	0.999380i	$0.511208\pi$
$8$	−1.00000	−0.353553
$9$	−0.191317	−0.0637725
$10$	3.90939	1.23626
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.67591	−0.483794
$13$	−6.91563	−1.91805	−0.959025	−	0.283322i	$-0.908563\pi$
$13$	−6.91563	−1.91805	−0.959025	+	0.283322i	$0.908563\pi$
$14$	0.186287	0.0497872
$15$	6.55180	1.69167
$16$	1.00000	0.250000
$17$	−0.375922	−0.0911745	−0.0455873	−	0.998960i	$-0.514516\pi$
$17$	−0.375922	−0.0911745	−0.0455873	+	0.998960i	$0.514516\pi$
$18$	0.191317	0.0450939
$19$	0.115664	0.0265351	0.0132675	−	0.999912i	$-0.495777\pi$
$19$	0.115664	0.0265351	0.0132675	+	0.999912i	$0.495777\pi$
$20$	−3.90939	−0.874167
$21$	0.312200	0.0681277
$22$	−1.00000	−0.213201
$23$	2.11998	0.442045	0.221023	−	0.975269i	$-0.429061\pi$
$23$	2.11998	0.442045	0.221023	+	0.975269i	$0.429061\pi$
$24$	1.67591	0.342094
$25$	10.2834	2.05667
$26$	6.91563	1.35627
$27$	5.34837	1.02929
$28$	−0.186287	−0.0352049
$29$	1.10627	0.205429	0.102714	−	0.994711i	$-0.467247\pi$
$29$	1.10627	0.205429	0.102714	+	0.994711i	$0.467247\pi$
$30$	−6.55180	−1.19619
$31$	−8.13360	−1.46084	−0.730419	−	0.682999i	$-0.760675\pi$
$31$	−8.13360	−1.46084	−0.730419	+	0.682999i	$0.760675\pi$
$32$	−1.00000	−0.176777
$33$	−1.67591	−0.291739
$34$	0.375922	0.0644701
$35$	0.728268	0.123100
$36$	−0.191317	−0.0318862
$37$	10.2588	1.68654	0.843268	−	0.537494i	$-0.180629\pi$
$37$	10.2588	1.68654	0.843268	+	0.537494i	$0.180629\pi$
$38$	−0.115664	−0.0187631
$39$	11.5900	1.85588
$40$	3.90939	0.618130
$41$	3.93374	0.614347	0.307174	−	0.951654i	$-0.400617\pi$
$41$	3.93374	0.614347	0.307174	+	0.951654i	$0.400617\pi$
$42$	−0.312200	−0.0481735
$43$	5.46223	0.832982	0.416491	−	0.909140i	$-0.363260\pi$
$43$	5.46223	0.832982	0.416491	+	0.909140i	$0.363260\pi$
$44$	1.00000	0.150756
$45$	0.747935	0.111496
$46$	−2.11998	−0.312573
$47$	−3.16576	−0.461773	−0.230887	−	0.972981i	$-0.574163\pi$
$47$	−3.16576	−0.461773	−0.230887	+	0.972981i	$0.574163\pi$
$48$	−1.67591	−0.241897
$49$	−6.96530	−0.995042
$50$	−10.2834	−1.45429
$51$	0.630013	0.0882194
$52$	−6.91563	−0.959025
$53$	9.17102	1.25974	0.629868	−	0.776702i	$-0.283109\pi$
$53$	9.17102	1.25974	0.629868	+	0.776702i	$0.283109\pi$
$54$	−5.34837	−0.727821
$55$	−3.90939	−0.527143
$56$	0.186287	0.0248936
$57$	−0.193842	−0.0256750
$58$	−1.10627	−0.145260
$59$	−5.00551	−0.651662	−0.325831	−	0.945428i	$-0.605644\pi$
$59$	−5.00551	−0.651662	−0.325831	+	0.945428i	$0.605644\pi$
$60$	6.55180	0.845834
$61$	2.17956	0.279064	0.139532	−	0.990218i	$-0.455440\pi$
$61$	2.17956	0.279064	0.139532	+	0.990218i	$0.455440\pi$
$62$	8.13360	1.03297
$63$	0.0356399	0.00449020
$64$	1.00000	0.125000
$65$	27.0359	3.35339
$66$	1.67591	0.206291
$67$	−1.99832	−0.244134	−0.122067	−	0.992522i	$-0.538952\pi$
$67$	−1.99832	−0.244134	−0.122067	+	0.992522i	$0.538952\pi$
$68$	−0.375922	−0.0455873
$69$	−3.55289	−0.427718
$70$	−0.728268	−0.0870447
$71$	3.16971	0.376176	0.188088	−	0.982152i	$-0.439771\pi$
$71$	3.16971	0.376176	0.188088	+	0.982152i	$0.439771\pi$
$72$	0.191317	0.0225470
$73$	−3.04510	−0.356402	−0.178201	−	0.983994i	$-0.557028\pi$
$73$	−3.04510	−0.356402	−0.178201	+	0.983994i	$0.557028\pi$
$74$	−10.2588	−1.19256
$75$	−17.2340	−1.99001
$76$	0.115664	0.0132675
$77$	−0.186287	−0.0212293
$78$	−11.5900	−1.31231
$79$	−2.40602	−0.270698	−0.135349	−	0.990798i	$-0.543216\pi$
$79$	−2.40602	−0.270698	−0.135349	+	0.990798i	$0.543216\pi$
$80$	−3.90939	−0.437084
$81$	−8.38945	−0.932161
$82$	−3.93374	−0.434409
$83$	8.81641	0.967727	0.483863	−	0.875143i	$-0.339233\pi$
$83$	8.81641	0.967727	0.483863	+	0.875143i	$0.339233\pi$
$84$	0.312200	0.0340638
$85$	1.46963	0.159404
$86$	−5.46223	−0.589007
$87$	−1.85401	−0.198770
$88$	−1.00000	−0.106600
$89$	1.79289	0.190046	0.0950230	−	0.995475i	$-0.469708\pi$
$89$	1.79289	0.190046	0.0950230	+	0.995475i	$0.469708\pi$
$90$	−0.747935	−0.0788393
$91$	1.28829	0.135049
$92$	2.11998	0.221023
$93$	13.6312	1.41349
$94$	3.16576	0.326523
$95$	−0.452175	−0.0463922
$96$	1.67591	0.171047
$97$	−15.3150	−1.55500	−0.777502	−	0.628880i	$-0.783514\pi$
$97$	−15.3150	−1.55500	−0.777502	+	0.628880i	$0.783514\pi$
$98$	6.96530	0.703601
$99$	−0.191317	−0.0192281
$100$	10.2834	1.02834
$101$	14.7993	1.47258	0.736291	−	0.676665i	$-0.236576\pi$
$101$	14.7993	1.47258	0.736291	+	0.676665i	$0.236576\pi$
$102$	−0.630013	−0.0623806
$103$	15.1653	1.49428	0.747140	−	0.664667i	$-0.231426\pi$
$103$	15.1653	1.49428	0.747140	+	0.664667i	$0.231426\pi$
$104$	6.91563	0.678133
$105$	−1.22051	−0.119110
$106$	−9.17102	−0.890769
$107$	−3.94080	−0.380972	−0.190486	−	0.981690i	$-0.561006\pi$
$107$	−3.94080	−0.380972	−0.190486	+	0.981690i	$0.561006\pi$
$108$	5.34837	0.514647
$109$	15.1512	1.45122	0.725612	−	0.688104i	$-0.241557\pi$
$109$	15.1512	1.45122	0.725612	+	0.688104i	$0.241557\pi$
$110$	3.90939	0.372746
$111$	−17.1928	−1.63187
$112$	−0.186287	−0.0176024
$113$	2.79724	0.263142	0.131571	−	0.991307i	$-0.457998\pi$
$113$	2.79724	0.263142	0.131571	+	0.991307i	$0.457998\pi$
$114$	0.193842	0.0181550
$115$	−8.28782	−0.772843
$116$	1.10627	0.102714
$117$	1.32308	0.122319
$118$	5.00551	0.460794
$119$	0.0700293	0.00641958
$120$	−6.55180	−0.598095
$121$	1.00000	0.0909091
$122$	−2.17956	−0.197328
$123$	−6.59260	−0.594435
$124$	−8.13360	−0.730419
$125$	−20.6548	−1.84742
$126$	−0.0356399	−0.00317505
$127$	3.43310	0.304639	0.152319	−	0.988331i	$-0.451326\pi$
$127$	3.43310	0.304639	0.152319	+	0.988331i	$0.451326\pi$
$128$	−1.00000	−0.0883883
$129$	−9.15422	−0.805984
$130$	−27.0359	−2.37121
$131$	2.60122	0.227270	0.113635	−	0.993523i	$-0.463751\pi$
$131$	2.60122	0.227270	0.113635	+	0.993523i	$0.463751\pi$
$132$	−1.67591	−0.145869
$133$	−0.0215466	−0.00186833
$134$	1.99832	0.172628
$135$	−20.9089	−1.79955
$136$	0.375922	0.0322351
$137$	13.9251	1.18970	0.594849	−	0.803837i	$-0.297212\pi$
$137$	13.9251	1.18970	0.594849	+	0.803837i	$0.297212\pi$
$138$	3.55289	0.302442
$139$	−5.90655	−0.500987	−0.250493	−	0.968118i	$-0.580593\pi$
$139$	−5.90655	−0.500987	−0.250493	+	0.968118i	$0.580593\pi$
$140$	0.728268	0.0615499
$141$	5.30553	0.446806
$142$	−3.16971	−0.265996
$143$	−6.91563	−0.578314
$144$	−0.191317	−0.0159431
$145$	−4.32483	−0.359158
$146$	3.04510	0.252014
$147$	11.6732	0.962792
$148$	10.2588	0.843268
$149$	−4.69838	−0.384907	−0.192453	−	0.981306i	$-0.561644\pi$
$149$	−4.69838	−0.384907	−0.192453	+	0.981306i	$0.561644\pi$
$150$	17.2340	1.40715
$151$	−17.2650	−1.40501	−0.702504	−	0.711680i	$-0.747935\pi$
$151$	−17.2650	−1.40501	−0.702504	+	0.711680i	$0.747935\pi$
$152$	−0.115664	−0.00938156
$153$	0.0719205	0.00581442
$154$	0.186287	0.0150114
$155$	31.7975	2.55403
$156$	11.5900	0.927941
$157$	−12.3386	−0.984729	−0.492364	−	0.870389i	$-0.663867\pi$
$157$	−12.3386	−0.984729	−0.492364	+	0.870389i	$0.663867\pi$
$158$	2.40602	0.191413
$159$	−15.3698	−1.21891
$160$	3.90939	0.309065
$161$	−0.394923	−0.0311243
$162$	8.38945	0.659137
$163$	−4.50886	−0.353161	−0.176581	−	0.984286i	$-0.556504\pi$
$163$	−4.50886	−0.353161	−0.176581	+	0.984286i	$0.556504\pi$
$164$	3.93374	0.307174
$165$	6.55180	0.510057
$166$	−8.81641	−0.684286
$167$	16.5849	1.28338	0.641689	−	0.766965i	$-0.278234\pi$
$167$	16.5849	1.28338	0.641689	+	0.766965i	$0.278234\pi$
$168$	−0.312200	−0.0240868
$169$	34.8259	2.67891
$170$	−1.46963	−0.112715
$171$	−0.0221285	−0.00169221
$172$	5.46223	0.416491
$173$	11.7366	0.892317	0.446159	−	0.894954i	$-0.352792\pi$
$173$	11.7366	0.892317	0.446159	+	0.894954i	$0.352792\pi$
$174$	1.85401	0.140552
$175$	−1.91565	−0.144810
$176$	1.00000	0.0753778
$177$	8.38879	0.630540
$178$	−1.79289	−0.134383
$179$	−4.16924	−0.311624	−0.155812	−	0.987787i	$-0.549799\pi$
$179$	−4.16924	−0.311624	−0.155812	+	0.987787i	$0.549799\pi$
$180$	0.747935	0.0557478
$181$	−2.00532	−0.149054	−0.0745272	−	0.997219i	$-0.523745\pi$
$181$	−2.00532	−0.149054	−0.0745272	+	0.997219i	$0.523745\pi$
$182$	−1.28829	−0.0954944
$183$	−3.65275	−0.270019
$184$	−2.11998	−0.156287
$185$	−40.1057	−2.94863
$186$	−13.6312	−0.999489
$187$	−0.375922	−0.0274902
$188$	−3.16576	−0.230887
$189$	−0.996330	−0.0724723
$190$	0.452175	0.0328042
$191$	−13.6944	−0.990891	−0.495445	−	0.868639i	$-0.664995\pi$
$191$	−13.6944	−0.990891	−0.495445	+	0.868639i	$0.664995\pi$
$192$	−1.67591	−0.120949
$193$	−15.0608	−1.08410	−0.542050	−	0.840346i	$-0.682352\pi$
$193$	−15.0608	−1.08410	−0.542050	+	0.840346i	$0.682352\pi$
$194$	15.3150	1.09955
$195$	−45.3098	−3.24470
$196$	−6.96530	−0.497521
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	0.191317	0.0135963
$199$	−13.5967	−0.963845	−0.481922	−	0.876214i	$-0.660061\pi$
$199$	−13.5967	−0.963845	−0.481922	+	0.876214i	$0.660061\pi$
$200$	−10.2834	−0.727144
$201$	3.34901	0.236221
$202$	−14.7993	−1.04127
$203$	−0.206083	−0.0144642
$204$	0.630013	0.0441097
$205$	−15.3785	−1.07408
$206$	−15.1653	−1.05662
$207$	−0.405588	−0.0281903
$208$	−6.91563	−0.479512
$209$	0.115664	0.00800062
$210$	1.22051	0.0842235
$211$	−21.5575	−1.48408	−0.742038	−	0.670357i	$-0.766141\pi$
$211$	−21.5575	−1.48408	−0.742038	+	0.670357i	$0.766141\pi$
$212$	9.17102	0.629868
$213$	−5.31216	−0.363983
$214$	3.94080	0.269388
$215$	−21.3540	−1.45633
$216$	−5.34837	−0.363910
$217$	1.51518	0.102857
$218$	−15.1512	−1.02617
$219$	5.10332	0.344850
$220$	−3.90939	−0.263571
$221$	2.59974	0.174877
$222$	17.1928	1.15391
$223$	22.4994	1.50667	0.753336	−	0.657636i	$-0.228444\pi$
$223$	22.4994	1.50667	0.753336	+	0.657636i	$0.228444\pi$
$224$	0.186287	0.0124468
$225$	−1.96739	−0.131159
$226$	−2.79724	−0.186070
$227$	24.3244	1.61447	0.807233	−	0.590234i	$-0.200964\pi$
$227$	24.3244	1.61447	0.807233	+	0.590234i	$0.200964\pi$
$228$	−0.193842	−0.0128375
$229$	24.5542	1.62259	0.811294	−	0.584638i	$-0.198763\pi$
$229$	24.5542	1.62259	0.811294	+	0.584638i	$0.198763\pi$
$230$	8.28782	0.546483
$231$	0.312200	0.0205413
$232$	−1.10627	−0.0726300
$233$	−5.83047	−0.381967	−0.190983	−	0.981593i	$-0.561168\pi$
$233$	−5.83047	−0.381967	−0.190983	+	0.981593i	$0.561168\pi$
$234$	−1.32308	−0.0864924
$235$	12.3762	0.807334
$236$	−5.00551	−0.325831
$237$	4.03228	0.261925
$238$	−0.0700293	−0.00453933
$239$	−3.31189	−0.214228	−0.107114	−	0.994247i	$-0.534161\pi$
$239$	−3.31189	−0.214228	−0.107114	+	0.994247i	$0.534161\pi$
$240$	6.55180	0.422917
$241$	−27.3280	−1.76035	−0.880176	−	0.474647i	$-0.842576\pi$
$241$	−27.3280	−1.76035	−0.880176	+	0.474647i	$0.842576\pi$
$242$	−1.00000	−0.0642824
$243$	−1.98513	−0.127346
$244$	2.17956	0.139532
$245$	27.2301	1.73967
$246$	6.59260	0.420329
$247$	−0.799887	−0.0508956
$248$	8.13360	0.516484
$249$	−14.7755	−0.936362
$250$	20.6548	1.30632
$251$	−21.1374	−1.33418	−0.667091	−	0.744976i	$-0.732461\pi$
$251$	−21.1374	−1.33418	−0.667091	+	0.744976i	$0.732461\pi$
$252$	0.0356399	0.00224510
$253$	2.11998	0.133282
$254$	−3.43310	−0.215412
$255$	−2.46297	−0.154237
$256$	1.00000	0.0625000
$257$	−19.9480	−1.24432	−0.622160	−	0.782890i	$-0.713745\pi$
$257$	−19.9480	−1.24432	−0.622160	+	0.782890i	$0.713745\pi$
$258$	9.15422	0.569917
$259$	−1.91108	−0.118749
$260$	27.0359	1.67670
$261$	−0.211648	−0.0131007
$262$	−2.60122	−0.160704
$263$	11.2461	0.693461	0.346731	−	0.937965i	$-0.387292\pi$
$263$	11.2461	0.693461	0.346731	+	0.937965i	$0.387292\pi$
$264$	1.67591	0.103145
$265$	−35.8531	−2.20244
$266$	0.0215466	0.00132111
$267$	−3.00473	−0.183886
$268$	−1.99832	−0.122067
$269$	0.706125	0.0430532	0.0215266	−	0.999768i	$-0.493147\pi$
$269$	0.706125	0.0430532	0.0215266	+	0.999768i	$0.493147\pi$
$270$	20.9089	1.27247
$271$	−20.1652	−1.22495	−0.612475	−	0.790490i	$-0.709826\pi$
$271$	−20.1652	−1.22495	−0.612475	+	0.790490i	$0.709826\pi$
$272$	−0.375922	−0.0227936
$273$	−2.15906	−0.130672
$274$	−13.9251	−0.841243
$275$	10.2834	0.620110
$276$	−3.55289	−0.213859
$277$	9.68442	0.581880	0.290940	−	0.956741i	$-0.406032\pi$
$277$	9.68442	0.581880	0.290940	+	0.956741i	$0.406032\pi$
$278$	5.90655	0.354251
$279$	1.55610	0.0931612
$280$	−0.728268	−0.0435224
$281$	−13.8011	−0.823302	−0.411651	−	0.911341i	$-0.635048\pi$
$281$	−13.8011	−0.823302	−0.411651	+	0.911341i	$0.635048\pi$
$282$	−5.30553	−0.315940
$283$	−14.4517	−0.859065	−0.429533	−	0.903051i	$-0.641322\pi$
$283$	−14.4517	−0.859065	−0.429533	+	0.903051i	$0.641322\pi$
$284$	3.16971	0.188088
$285$	0.757805	0.0448885
$286$	6.91563	0.408930
$287$	−0.732804	−0.0432560
$288$	0.191317	0.0112735
$289$	−16.8587	−0.991687
$290$	4.32483	0.253963
$291$	25.6666	1.50460
$292$	−3.04510	−0.178201
$293$	−17.8150	−1.04077	−0.520383	−	0.853933i	$-0.674211\pi$
$293$	−17.8150	−1.04077	−0.520383	+	0.853933i	$0.674211\pi$
$294$	−11.6732	−0.680797
$295$	19.5685	1.13932
$296$	−10.2588	−0.596280
$297$	5.34837	0.310344
$298$	4.69838	0.272170
$299$	−14.6610	−0.847865
$300$	−17.2340	−0.995007
$301$	−1.01754	−0.0586501
$302$	17.2650	0.993490
$303$	−24.8023	−1.42485
$304$	0.115664	0.00663376
$305$	−8.52075	−0.487897
$306$	−0.0719205	−0.00411142
$307$	−14.3009	−0.816195	−0.408098	−	0.912938i	$-0.633808\pi$
$307$	−14.3009	−0.816195	−0.408098	+	0.912938i	$0.633808\pi$
$308$	−0.186287	−0.0106147
$309$	−25.4157	−1.44585
$310$	−31.7975	−1.80597
$311$	16.6604	0.944723	0.472361	−	0.881405i	$-0.343402\pi$
$311$	16.6604	0.944723	0.472361	+	0.881405i	$0.343402\pi$
$312$	−11.5900	−0.656154
$313$	−12.6430	−0.714622	−0.357311	−	0.933985i	$-0.616306\pi$
$313$	−12.6430	−0.714622	−0.357311	+	0.933985i	$0.616306\pi$
$314$	12.3386	0.696309
$315$	−0.139330	−0.00785038
$316$	−2.40602	−0.135349
$317$	6.35861	0.357135	0.178568	−	0.983928i	$-0.442854\pi$
$317$	6.35861	0.357135	0.178568	+	0.983928i	$0.442854\pi$
$318$	15.3698	0.861897
$319$	1.10627	0.0619390
$320$	−3.90939	−0.218542
$321$	6.60444	0.368624
$322$	0.394923	0.0220082
$323$	−0.0434805	−0.00241932
$324$	−8.38945	−0.466080
$325$	−71.1159	−3.94480
$326$	4.50886	0.249723
$327$	−25.3921	−1.40419
$328$	−3.93374	−0.217204
$329$	0.589738	0.0325133
$330$	−6.55180	−0.360665
$331$	−6.23320	−0.342607	−0.171304	−	0.985218i	$-0.554798\pi$
$331$	−6.23320	−0.342607	−0.171304	+	0.985218i	$0.554798\pi$
$332$	8.81641	0.483863
$333$	−1.96269	−0.107555
$334$	−16.5849	−0.907485
$335$	7.81222	0.426827
$336$	0.312200	0.0170319
$337$	35.4341	1.93022	0.965110	−	0.261844i	$-0.0843306\pi$
$337$	35.4341	1.93022	0.965110	+	0.261844i	$0.0843306\pi$
$338$	−34.8259	−1.89428
$339$	−4.68793	−0.254614
$340$	1.46963	0.0797018
$341$	−8.13360	−0.440459
$342$	0.0221285	0.00119657
$343$	2.60155	0.140470
$344$	−5.46223	−0.294504
$345$	13.8897	0.747794
$346$	−11.7366	−0.630964
$347$	−11.8480	−0.636034	−0.318017	−	0.948085i	$-0.603017\pi$
$347$	−11.8480	−0.636034	−0.318017	+	0.948085i	$0.603017\pi$
$348$	−1.85401	−0.0993851
$349$	16.1290	0.863364	0.431682	−	0.902026i	$-0.357920\pi$
$349$	16.1290	0.863364	0.431682	+	0.902026i	$0.357920\pi$
$350$	1.91565	0.102396
$351$	−36.9873	−1.97424
$352$	−1.00000	−0.0533002
$353$	−11.6988	−0.622663	−0.311331	−	0.950301i	$-0.600775\pi$
$353$	−11.6988	−0.622663	−0.311331	+	0.950301i	$0.600775\pi$
$354$	−8.38879	−0.445859
$355$	−12.3917	−0.657681
$356$	1.79289	0.0950230
$357$	−0.117363	−0.00621151
$358$	4.16924	0.220351
$359$	−21.0933	−1.11326	−0.556632	−	0.830759i	$-0.687907\pi$
$359$	−21.0933	−1.11326	−0.556632	+	0.830759i	$0.687907\pi$
$360$	−0.747935	−0.0394196
$361$	−18.9866	−0.999296
$362$	2.00532	0.105397
$363$	−1.67591	−0.0879626
$364$	1.28829	0.0675247
$365$	11.9045	0.623110
$366$	3.65275	0.190932
$367$	25.3523	1.32338	0.661689	−	0.749779i	$-0.269840\pi$
$367$	25.3523	1.32338	0.661689	+	0.749779i	$0.269840\pi$
$368$	2.11998	0.110511
$369$	−0.752593	−0.0391784
$370$	40.1057	2.08499
$371$	−1.70844	−0.0886978
$372$	13.6312	0.706745
$373$	11.3365	0.586981	0.293490	−	0.955962i	$-0.405183\pi$
$373$	11.3365	0.586981	0.293490	+	0.955962i	$0.405183\pi$
$374$	0.375922	0.0194385
$375$	34.6156	1.78754
$376$	3.16576	0.163261
$377$	−7.65053	−0.394022
$378$	0.996330	0.0512457
$379$	22.4310	1.15220	0.576102	−	0.817378i	$-0.304573\pi$
$379$	22.4310	1.15220	0.576102	+	0.817378i	$0.304573\pi$
$380$	−0.452175	−0.0231961
$381$	−5.75358	−0.294765
$382$	13.6944	0.700666
$383$	−8.55722	−0.437254	−0.218627	−	0.975809i	$-0.570158\pi$
$383$	−8.55722	−0.437254	−0.218627	+	0.975809i	$0.570158\pi$
$384$	1.67591	0.0855236
$385$	0.728268	0.0371160
$386$	15.0608	0.766574
$387$	−1.04502	−0.0531213
$388$	−15.3150	−0.777502
$389$	30.3391	1.53825	0.769127	−	0.639096i	$-0.220692\pi$
$389$	30.3391	1.53825	0.769127	+	0.639096i	$0.220692\pi$
$390$	45.3098	2.29435
$391$	−0.796946	−0.0403033
$392$	6.96530	0.351801
$393$	−4.35942	−0.219904
$394$	−1.00000	−0.0503793
$395$	9.40608	0.473271
$396$	−0.191317	−0.00961406
$397$	−26.9110	−1.35063	−0.675313	−	0.737531i	$-0.735992\pi$
$397$	−26.9110	−1.35063	−0.675313	+	0.737531i	$0.735992\pi$
$398$	13.5967	0.681541
$399$	0.0361102	0.00180777
$400$	10.2834	0.514168
$401$	−27.3761	−1.36710	−0.683549	−	0.729905i	$-0.739564\pi$
$401$	−27.3761	−1.36710	−0.683549	+	0.729905i	$0.739564\pi$
$402$	−3.34901	−0.167033
$403$	56.2490	2.80196
$404$	14.7993	0.736291
$405$	32.7977	1.62973
$406$	0.206083	0.0102277
$407$	10.2588	0.508510
$408$	−0.630013	−0.0311903
$409$	13.9726	0.690899	0.345450	−	0.938437i	$-0.387726\pi$
$409$	13.9726	0.690899	0.345450	+	0.938437i	$0.387726\pi$
$410$	15.3785	0.759492
$411$	−23.3372	−1.15114
$412$	15.1653	0.747140
$413$	0.932460	0.0458833
$414$	0.405588	0.0199336
$415$	−34.4668	−1.69191
$416$	6.91563	0.339066
$417$	9.89886	0.484749
$418$	−0.115664	−0.00565729
$419$	2.12115	0.103625	0.0518126	−	0.998657i	$-0.483500\pi$
$419$	2.12115	0.103625	0.0518126	+	0.998657i	$0.483500\pi$
$420$	−1.22051	−0.0595550
$421$	−8.19111	−0.399210	−0.199605	−	0.979876i	$-0.563966\pi$
$421$	−8.19111	−0.399210	−0.199605	+	0.979876i	$0.563966\pi$
$422$	21.5575	1.04940
$423$	0.605664	0.0294484
$424$	−9.17102	−0.445384
$425$	−3.86575	−0.187516
$426$	5.31216	0.257375
$427$	−0.406023	−0.0196488
$428$	−3.94080	−0.190486
$429$	11.5900	0.559570
$430$	21.3540	1.02978
$431$	3.75889	0.181059	0.0905296	−	0.995894i	$-0.471144\pi$
$431$	3.75889	0.181059	0.0905296	+	0.995894i	$0.471144\pi$
$432$	5.34837	0.257324
$433$	0.505075	0.0242724	0.0121362	−	0.999926i	$-0.496137\pi$
$433$	0.505075	0.0242724	0.0121362	+	0.999926i	$0.496137\pi$
$434$	−1.51518	−0.0727311
$435$	7.24804	0.347517
$436$	15.1512	0.725612
$437$	0.245204	0.0117297
$438$	−5.10332	−0.243846
$439$	−8.53428	−0.407319	−0.203660	−	0.979042i	$-0.565284\pi$
$439$	−8.53428	−0.407319	−0.203660	+	0.979042i	$0.565284\pi$
$440$	3.90939	0.186373
$441$	1.33258	0.0634563
$442$	−2.59974	−0.123657
$443$	40.0089	1.90088	0.950439	−	0.310911i	$-0.100634\pi$
$443$	40.0089	1.90088	0.950439	+	0.310911i	$0.100634\pi$
$444$	−17.1928	−0.815936
$445$	−7.00912	−0.332264
$446$	−22.4994	−1.06538
$447$	7.87408	0.372431
$448$	−0.186287	−0.00880122
$449$	18.2096	0.859365	0.429682	−	0.902980i	$-0.358626\pi$
$449$	18.2096	0.859365	0.429682	+	0.902980i	$0.358626\pi$
$450$	1.96739	0.0927435
$451$	3.93374	0.185233
$452$	2.79724	0.131571
$453$	28.9347	1.35947
$454$	−24.3244	−1.14160
$455$	−5.03643	−0.236112
$456$	0.193842	0.00907749
$457$	−41.9076	−1.96035	−0.980176	−	0.198127i	$-0.936514\pi$
$457$	−41.9076	−1.96035	−0.980176	+	0.198127i	$0.936514\pi$
$458$	−24.5542	−1.14734
$459$	−2.01057	−0.0938454
$460$	−8.28782	−0.386422
$461$	−10.3457	−0.481849	−0.240924	−	0.970544i	$-0.577451\pi$
$461$	−10.3457	−0.481849	−0.240924	+	0.970544i	$0.577451\pi$
$462$	−0.312200	−0.0145249
$463$	30.0975	1.39875	0.699376	−	0.714754i	$-0.253461\pi$
$463$	30.0975	1.39875	0.699376	+	0.714754i	$0.253461\pi$
$464$	1.10627	0.0513571
$465$	−53.2898	−2.47125
$466$	5.83047	0.270091
$467$	3.42983	0.158714	0.0793569	−	0.996846i	$-0.474713\pi$
$467$	3.42983	0.158714	0.0793569	+	0.996846i	$0.474713\pi$
$468$	1.32308	0.0611594
$469$	0.372260	0.0171894
$470$	−12.3762	−0.570871
$471$	20.6784	0.952812
$472$	5.00551	0.230397
$473$	5.46223	0.251154
$474$	−4.03228	−0.185209
$475$	1.18941	0.0545739
$476$	0.0700293	0.00320979
$477$	−1.75458	−0.0803365
$478$	3.31189	0.151482
$479$	−11.6583	−0.532683	−0.266342	−	0.963879i	$-0.585815\pi$
$479$	−11.6583	−0.532683	−0.266342	+	0.963879i	$0.585815\pi$
$480$	−6.55180	−0.299048
$481$	−70.9460	−3.23486
$482$	27.3280	1.24476
$483$	0.661857	0.0301155
$484$	1.00000	0.0454545
$485$	59.8724	2.71867
$486$	1.98513	0.0900473
$487$	8.38284	0.379863	0.189931	−	0.981797i	$-0.439173\pi$
$487$	8.38284	0.379863	0.189931	+	0.981797i	$0.439173\pi$
$488$	−2.17956	−0.0986640
$489$	7.55645	0.341715
$490$	−27.2301	−1.23013
$491$	38.7701	1.74967	0.874835	−	0.484422i	$-0.160970\pi$
$491$	38.7701	1.74967	0.874835	+	0.484422i	$0.160970\pi$
$492$	−6.59260	−0.297218
$493$	−0.415870	−0.0187299
$494$	0.799887	0.0359886
$495$	0.747935	0.0336172
$496$	−8.13360	−0.365210
$497$	−0.590475	−0.0264864
$498$	14.7755	0.662108
$499$	−36.9625	−1.65467	−0.827334	−	0.561711i	$-0.810143\pi$
$499$	−36.9625	−1.65467	−0.827334	+	0.561711i	$0.810143\pi$
$500$	−20.6548	−0.923709
$501$	−27.7948	−1.24178
$502$	21.1374	0.943409
$503$	36.0606	1.60786	0.803930	−	0.594723i	$-0.202738\pi$
$503$	36.0606	1.60786	0.803930	+	0.594723i	$0.202738\pi$
$504$	−0.0356399	−0.00158753
$505$	−57.8561	−2.57456
$506$	−2.11998	−0.0942444
$507$	−58.3651	−2.59209
$508$	3.43310	0.152319
$509$	−21.5326	−0.954414	−0.477207	−	0.878791i	$-0.658351\pi$
$509$	−21.5326	−0.954414	−0.477207	+	0.878791i	$0.658351\pi$
$510$	2.46297	0.109062
$511$	0.567262	0.0250942
$512$	−1.00000	−0.0441942
$513$	0.618612	0.0273124
$514$	19.9480	0.879867
$515$	−59.2871	−2.61250
$516$	−9.15422	−0.402992
$517$	−3.16576	−0.139230
$518$	1.91108	0.0839679
$519$	−19.6695	−0.863396
$520$	−27.0359	−1.18560
$521$	−0.602802	−0.0264092	−0.0132046	−	0.999913i	$-0.504203\pi$
$521$	−0.602802	−0.0264092	−0.0132046	+	0.999913i	$0.504203\pi$
$522$	0.211648	0.00926358
$523$	−32.8661	−1.43713	−0.718567	−	0.695458i	$-0.755202\pi$
$523$	−32.8661	−1.43713	−0.718567	+	0.695458i	$0.755202\pi$
$524$	2.60122	0.113635
$525$	3.21047	0.140116
$526$	−11.2461	−0.490351
$527$	3.05760	0.133191
$528$	−1.67591	−0.0729347
$529$	−18.5057	−0.804596
$530$	35.8531	1.55736
$531$	0.957641	0.0415581
$532$	−0.0215466	−0.000934164 0
$533$	−27.2043	−1.17835
$534$	3.00473	0.130027
$535$	15.4062	0.666066
$536$	1.99832	0.0863142
$537$	6.98728	0.301523
$538$	−0.706125	−0.0304432
$539$	−6.96530	−0.300017
$540$	−20.9089	−0.899775
$541$	24.8767	1.06953	0.534766	−	0.845000i	$-0.320400\pi$
$541$	24.8767	1.06953	0.534766	+	0.845000i	$0.320400\pi$
$542$	20.1652	0.866171
$543$	3.36074	0.144223
$544$	0.375922	0.0161175
$545$	−59.2321	−2.53723
$546$	2.15906	0.0923992
$547$	−37.2875	−1.59430	−0.797149	−	0.603783i	$-0.793659\pi$
$547$	−37.2875	−1.59430	−0.797149	+	0.603783i	$0.793659\pi$
$548$	13.9251	0.594849
$549$	−0.416987	−0.0177966
$550$	−10.2834	−0.438484
$551$	0.127955	0.00545106
$552$	3.55289	0.151221
$553$	0.448209	0.0190598
$554$	−9.68442	−0.411452
$555$	67.2136	2.85306
$556$	−5.90655	−0.250493
$557$	−16.2171	−0.687141	−0.343570	−	0.939127i	$-0.611636\pi$
$557$	−16.2171	−0.687141	−0.343570	+	0.939127i	$0.611636\pi$
$558$	−1.55610	−0.0658749
$559$	−37.7747	−1.59770
$560$	0.728268	0.0307750
$561$	0.630013	0.0265992
$562$	13.8011	0.582163
$563$	28.0403	1.18176	0.590878	−	0.806761i	$-0.298781\pi$
$563$	28.0403	1.18176	0.590878	+	0.806761i	$0.298781\pi$
$564$	5.30553	0.223403
$565$	−10.9355	−0.460061
$566$	14.4517	0.607451
$567$	1.56284	0.0656332
$568$	−3.16971	−0.132998
$569$	36.0770	1.51243	0.756213	−	0.654325i	$-0.227047\pi$
$569$	36.0770	1.51243	0.756213	+	0.654325i	$0.227047\pi$
$570$	−0.757805	−0.0317410
$571$	−10.5330	−0.440793	−0.220397	−	0.975410i	$-0.570735\pi$
$571$	−10.5330	−0.440793	−0.220397	+	0.975410i	$0.570735\pi$
$572$	−6.91563	−0.289157
$573$	22.9506	0.958775
$574$	0.732804	0.0305866
$575$	21.8005	0.909143
$576$	−0.191317	−0.00797156
$577$	−35.3170	−1.47027	−0.735133	−	0.677922i	$-0.762880\pi$
$577$	−35.3170	−1.47027	−0.735133	+	0.677922i	$0.762880\pi$
$578$	16.8587	0.701229
$579$	25.2406	1.04896
$580$	−4.32483	−0.179579
$581$	−1.64238	−0.0681374
$582$	−25.6666	−1.06392
$583$	9.17102	0.379825
$584$	3.04510	0.126007
$585$	−5.17244	−0.213854
$586$	17.8150	0.735932
$587$	25.9530	1.07120	0.535598	−	0.844473i	$-0.320086\pi$
$587$	25.9530	1.07120	0.535598	+	0.844473i	$0.320086\pi$
$588$	11.6732	0.481396
$589$	−0.940762	−0.0387634
$590$	−19.5685	−0.805623
$591$	−1.67591	−0.0689378
$592$	10.2588	0.421634
$593$	14.6024	0.599648	0.299824	−	0.953994i	$-0.403072\pi$
$593$	14.6024	0.599648	0.299824	+	0.953994i	$0.403072\pi$
$594$	−5.34837	−0.219446
$595$	−0.273772	−0.0112236
$596$	−4.69838	−0.192453
$597$	22.7869	0.932605
$598$	14.6610	0.599531
$599$	25.2757	1.03274	0.516369	−	0.856366i	$-0.327283\pi$
$599$	25.2757	1.03274	0.516369	+	0.856366i	$0.327283\pi$
$600$	17.2340	0.703576
$601$	−31.7861	−1.29658	−0.648291	−	0.761393i	$-0.724516\pi$
$601$	−31.7861	−1.29658	−0.648291	+	0.761393i	$0.724516\pi$
$602$	1.01754	0.0414719
$603$	0.382313	0.0155690
$604$	−17.2650	−0.702504
$605$	−3.90939	−0.158939
$606$	24.8023	1.00752
$607$	0.0382850	0.00155394	0.000776971	−	1.00000i	$-0.499753\pi$
$607$	0.0382850	0.00155394	0.000776971		1.00000i	$0.499753\pi$
$608$	−0.115664	−0.00469078
$609$	0.345377	0.0139954
$610$	8.52075	0.344995
$611$	21.8932	0.885704
$612$	0.0719205	0.00290721
$613$	34.1026	1.37739	0.688695	−	0.725051i	$-0.258184\pi$
$613$	34.1026	1.37739	0.688695	+	0.725051i	$0.258184\pi$
$614$	14.3009	0.577137
$615$	25.7731	1.03927
$616$	0.186287	0.00750571
$617$	−19.4385	−0.782564	−0.391282	−	0.920271i	$-0.627968\pi$
$617$	−19.4385	−0.782564	−0.391282	+	0.920271i	$0.627968\pi$
$618$	25.4157	1.02237
$619$	−0.298313	−0.0119902	−0.00599510	−	0.999982i	$-0.501908\pi$
$619$	−0.298313	−0.0119902	−0.00599510	+	0.999982i	$0.501908\pi$
$620$	31.7975	1.27702
$621$	11.3384	0.454995
$622$	−16.6604	−0.668020
$623$	−0.333992	−0.0133811
$624$	11.5900	0.463971
$625$	29.3308	1.17323
$626$	12.6430	0.505314
$627$	−0.193842	−0.00774131
$628$	−12.3386	−0.492364
$629$	−3.85651	−0.153769
$630$	0.139330	0.00555105
$631$	−7.82835	−0.311642	−0.155821	−	0.987785i	$-0.549802\pi$
$631$	−7.82835	−0.311642	−0.155821	+	0.987785i	$0.549802\pi$
$632$	2.40602	0.0957063
$633$	36.1284	1.43598
$634$	−6.35861	−0.252533
$635$	−13.4214	−0.532610
$636$	−15.3698	−0.609453
$637$	48.1694	1.90854
$638$	−1.10627	−0.0437975
$639$	−0.606421	−0.0239896
$640$	3.90939	0.154532
$641$	−20.1068	−0.794169	−0.397085	−	0.917782i	$-0.629978\pi$
$641$	−20.1068	−0.794169	−0.397085	+	0.917782i	$0.629978\pi$
$642$	−6.60444	−0.260657
$643$	11.1334	0.439057	0.219528	−	0.975606i	$-0.429548\pi$
$643$	11.1334	0.439057	0.219528	+	0.975606i	$0.429548\pi$
$644$	−0.394923	−0.0155622
$645$	35.7874	1.40913
$646$	0.0434805	0.00171072
$647$	26.5897	1.04535	0.522674	−	0.852532i	$-0.324934\pi$
$647$	26.5897	1.04535	0.522674	+	0.852532i	$0.324934\pi$
$648$	8.38945	0.329569
$649$	−5.00551	−0.196483
$650$	71.1159	2.78940
$651$	−2.53931	−0.0995235
$652$	−4.50886	−0.176581
$653$	−24.6029	−0.962787	−0.481393	−	0.876505i	$-0.659869\pi$
$653$	−24.6029	−0.962787	−0.481393	+	0.876505i	$0.659869\pi$
$654$	25.3921	0.992911
$655$	−10.1692	−0.397344
$656$	3.93374	0.153587
$657$	0.582581	0.0227286
$658$	−0.589738	−0.0229904
$659$	−0.0742645	−0.00289293	−0.00144647	−	0.999999i	$-0.500460\pi$
$659$	−0.0742645	−0.00289293	−0.00144647	+	0.999999i	$0.500460\pi$
$660$	6.55180	0.255029
$661$	27.7640	1.07989	0.539947	−	0.841699i	$-0.318444\pi$
$661$	27.7640	1.07989	0.539947	+	0.841699i	$0.318444\pi$
$662$	6.23320	0.242260
$663$	−4.35693	−0.169209
$664$	−8.81641	−0.342143
$665$	0.0842342	0.00326646
$666$	1.96269	0.0760525
$667$	2.34526	0.0908087
$668$	16.5849	0.641689
$669$	−37.7070	−1.45784
$670$	−7.81222	−0.301812
$671$	2.17956	0.0841409
$672$	−0.312200	−0.0120434
$673$	1.85246	0.0714071	0.0357035	−	0.999362i	$-0.488633\pi$
$673$	1.85246	0.0714071	0.0357035	+	0.999362i	$0.488633\pi$
$674$	−35.4341	−1.36487
$675$	54.9992	2.11692
$676$	34.8259	1.33946
$677$	9.85875	0.378902	0.189451	−	0.981890i	$-0.439329\pi$
$677$	9.85875	0.378902	0.189451	+	0.981890i	$0.439329\pi$
$678$	4.68793	0.180039
$679$	2.85298	0.109487
$680$	−1.46963	−0.0563577
$681$	−40.7655	−1.56214
$682$	8.13360	0.311452
$683$	−2.82679	−0.108164	−0.0540820	−	0.998536i	$-0.517223\pi$
$683$	−2.82679	−0.108164	−0.0540820	+	0.998536i	$0.517223\pi$
$684$	−0.0221285	−0.000846103 0
$685$	−54.4385	−2.07999
$686$	−2.60155	−0.0993276
$687$	−41.1507	−1.57000
$688$	5.46223	0.208246
$689$	−63.4234	−2.41624
$690$	−13.8897	−0.528770
$691$	−15.4385	−0.587310	−0.293655	−	0.955912i	$-0.594872\pi$
$691$	−15.4385	−0.587310	−0.293655	+	0.955912i	$0.594872\pi$
$692$	11.7366	0.446159
$693$	0.0356399	0.00135385
$694$	11.8480	0.449744
$695$	23.0910	0.875893
$696$	1.85401	0.0702759
$697$	−1.47878	−0.0560128
$698$	−16.1290	−0.610491
$699$	9.77135	0.369586
$700$	−1.91565	−0.0724049
$701$	8.88379	0.335536	0.167768	−	0.985826i	$-0.446344\pi$
$701$	8.88379	0.335536	0.167768	+	0.985826i	$0.446344\pi$
$702$	36.9873	1.39600
$703$	1.18657	0.0447523
$704$	1.00000	0.0376889
$705$	−20.7414	−0.781167
$706$	11.6988	0.440289
$707$	−2.75691	−0.103684
$708$	8.38879	0.315270
$709$	−7.81895	−0.293647	−0.146823	−	0.989163i	$-0.546905\pi$
$709$	−7.81895	−0.293647	−0.146823	+	0.989163i	$0.546905\pi$
$710$	12.3917	0.465050
$711$	0.460313	0.0172631
$712$	−1.79289	−0.0671914
$713$	−17.2430	−0.645757
$714$	0.117363	0.00439220
$715$	27.0359	1.01109
$716$	−4.16924	−0.155812
$717$	5.55043	0.207285
$718$	21.0933	0.787197
$719$	50.8058	1.89474	0.947369	−	0.320145i	$-0.103732\pi$
$719$	50.8058	1.89474	0.947369	+	0.320145i	$0.103732\pi$
$720$	0.747935	0.0278739
$721$	−2.82509	−0.105212
$722$	18.9866	0.706609
$723$	45.7994	1.70330
$724$	−2.00532	−0.0745272
$725$	11.3761	0.422499
$726$	1.67591	0.0621989
$727$	−27.0833	−1.00446	−0.502231	−	0.864733i	$-0.667487\pi$
$727$	−27.0833	−1.00446	−0.502231	+	0.864733i	$0.667487\pi$
$728$	−1.28829	−0.0477472
$729$	28.4952	1.05538
$730$	−11.9045	−0.440605
$731$	−2.05337	−0.0759468
$732$	−3.65275	−0.135010
$733$	−36.2968	−1.34065	−0.670326	−	0.742066i	$-0.733846\pi$
$733$	−36.2968	−1.34065	−0.670326	+	0.742066i	$0.733846\pi$
$734$	−25.3523	−0.935769
$735$	−45.6353	−1.68328
$736$	−2.11998	−0.0781433
$737$	−1.99832	−0.0736090
$738$	0.752593	0.0277033
$739$	29.7712	1.09515	0.547576	−	0.836756i	$-0.315551\pi$
$739$	29.7712	1.09515	0.547576	+	0.836756i	$0.315551\pi$
$740$	−40.1057	−1.47431
$741$	1.34054	0.0492460
$742$	1.70844	0.0627188
$743$	−24.6412	−0.903998	−0.451999	−	0.892018i	$-0.649289\pi$
$743$	−24.6412	−0.903998	−0.451999	+	0.892018i	$0.649289\pi$
$744$	−13.6312	−0.499744
$745$	18.3678	0.672945
$746$	−11.3365	−0.415058
$747$	−1.68673	−0.0617143
$748$	−0.375922	−0.0137451
$749$	0.734120	0.0268241
$750$	−34.6156	−1.26398
$751$	−2.19522	−0.0801049	−0.0400524	−	0.999198i	$-0.512752\pi$
$751$	−2.19522	−0.0801049	−0.0400524	+	0.999198i	$0.512752\pi$
$752$	−3.16576	−0.115443
$753$	35.4245	1.29094
$754$	7.65053	0.278616
$755$	67.4958	2.45642
$756$	−0.996330	−0.0362362
$757$	−4.25354	−0.154598	−0.0772988	−	0.997008i	$-0.524630\pi$
$757$	−4.25354	−0.154598	−0.0772988	+	0.997008i	$0.524630\pi$
$758$	−22.4310	−0.814731
$759$	−3.55289	−0.128962
$760$	0.452175	0.0164021
$761$	−10.5671	−0.383056	−0.191528	−	0.981487i	$-0.561344\pi$
$761$	−10.5671	−0.383056	−0.191528	+	0.981487i	$0.561344\pi$
$762$	5.75358	0.208430
$763$	−2.82247	−0.102180
$764$	−13.6944	−0.495445
$765$	−0.281165	−0.0101656
$766$	8.55722	0.309185
$767$	34.6162	1.24992
$768$	−1.67591	−0.0604743
$769$	−8.08777	−0.291653	−0.145826	−	0.989310i	$-0.546584\pi$
$769$	−8.08777	−0.291653	−0.145826	+	0.989310i	$0.546584\pi$
$770$	−0.728268	−0.0262450
$771$	33.4310	1.20399
$772$	−15.0608	−0.542050
$773$	−42.0068	−1.51088	−0.755440	−	0.655217i	$-0.772577\pi$
$773$	−42.0068	−1.51088	−0.755440	+	0.655217i	$0.772577\pi$
$774$	1.04502	0.0375624
$775$	−83.6408	−3.00447
$776$	15.3150	0.549777
$777$	3.20280	0.114900
$778$	−30.3391	−1.08771
$779$	0.454991	0.0163017
$780$	−45.3098	−1.62235
$781$	3.16971	0.113421
$782$	0.796946	0.0284987
$783$	5.91672	0.211446
$784$	−6.96530	−0.248761
$785$	48.2365	1.72164
$786$	4.35942	0.155496
$787$	1.90354	0.0678538	0.0339269	−	0.999424i	$-0.489199\pi$
$787$	1.90354	0.0678538	0.0339269	+	0.999424i	$0.489199\pi$
$788$	1.00000	0.0356235
$789$	−18.8474	−0.670985
$790$	−9.40608	−0.334653
$791$	−0.521089	−0.0185278
$792$	0.191317	0.00679817
$793$	−15.0730	−0.535258
$794$	26.9110	0.955037
$795$	60.0867	2.13106
$796$	−13.5967	−0.481922
$797$	−0.804885	−0.0285105	−0.0142552	−	0.999898i	$-0.504538\pi$
$797$	−0.804885	−0.0285105	−0.0142552	+	0.999898i	$0.504538\pi$
$798$	−0.0361102	−0.00127829
$799$	1.19008	0.0421020
$800$	−10.2834	−0.363572
$801$	−0.343011	−0.0121197
$802$	27.3761	0.966684
$803$	−3.04510	−0.107459
$804$	3.34901	0.118110
$805$	1.54391	0.0544157
$806$	−56.2490	−1.98129
$807$	−1.18340	−0.0416578
$808$	−14.7993	−0.520636
$809$	−1.65247	−0.0580979	−0.0290489	−	0.999578i	$-0.509248\pi$
$809$	−1.65247	−0.0580979	−0.0290489	+	0.999578i	$0.509248\pi$
$810$	−32.7977	−1.15239
$811$	35.3305	1.24062	0.620311	−	0.784356i	$-0.287007\pi$
$811$	35.3305	1.24062	0.620311	+	0.784356i	$0.287007\pi$
$812$	−0.206083	−0.00723209
$813$	33.7952	1.18525
$814$	−10.2588	−0.359571
$815$	17.6269	0.617444
$816$	0.630013	0.0220549
$817$	0.631781	0.0221032
$818$	−13.9726	−0.488539
$819$	−0.246472	−0.00861243
$820$	−15.3785	−0.537042
$821$	−32.0493	−1.11853	−0.559264	−	0.828990i	$-0.688916\pi$
$821$	−32.0493	−1.11853	−0.559264	+	0.828990i	$0.688916\pi$
$822$	23.3372	0.813978
$823$	10.0207	0.349298	0.174649	−	0.984631i	$-0.444121\pi$
$823$	10.0207	0.349298	0.174649	+	0.984631i	$0.444121\pi$
$824$	−15.1653	−0.528308
$825$	−17.2340	−0.600012
$826$	−0.932460	−0.0324444
$827$	−2.42462	−0.0843122	−0.0421561	−	0.999111i	$-0.513423\pi$
$827$	−2.42462	−0.0843122	−0.0421561	+	0.999111i	$0.513423\pi$
$828$	−0.405588	−0.0140952
$829$	32.8503	1.14094	0.570470	−	0.821319i	$-0.306761\pi$
$829$	32.8503	1.14094	0.570470	+	0.821319i	$0.306761\pi$
$830$	34.4668	1.19636
$831$	−16.2302	−0.563021
$832$	−6.91563	−0.239756
$833$	2.61841	0.0907225
$834$	−9.89886	−0.342769
$835$	−64.8369	−2.24377
$836$	0.115664	0.00400031
$837$	−43.5015	−1.50363
$838$	−2.12115	−0.0732741
$839$	−2.59846	−0.0897089	−0.0448545	−	0.998994i	$-0.514282\pi$
$839$	−2.59846	−0.0897089	−0.0448545	+	0.998994i	$0.514282\pi$
$840$	1.22051	0.0421117
$841$	−27.7762	−0.957799
$842$	8.19111	0.282284
$843$	23.1294	0.796618
$844$	−21.5575	−0.742038
$845$	−136.148	−4.68364
$846$	−0.605664	−0.0208232
$847$	−0.186287	−0.00640089
$848$	9.17102	0.314934
$849$	24.2198	0.831222
$850$	3.86575	0.132594
$851$	21.7484	0.745525
$852$	−5.31216	−0.181992
$853$	31.1353	1.06605	0.533025	−	0.846099i	$-0.321055\pi$
$853$	31.1353	1.06605	0.533025	+	0.846099i	$0.321055\pi$
$854$	0.406023	0.0138938
$855$	0.0865089	0.00295854
$856$	3.94080	0.134694
$857$	3.49682	0.119449	0.0597246	−	0.998215i	$-0.480978\pi$
$857$	3.49682	0.119449	0.0597246	+	0.998215i	$0.480978\pi$
$858$	−11.5900	−0.395676
$859$	13.5088	0.460914	0.230457	−	0.973082i	$-0.425978\pi$
$859$	13.5088	0.460914	0.230457	+	0.973082i	$0.425978\pi$
$860$	−21.3540	−0.728166
$861$	1.22811	0.0418540
$862$	−3.75889	−0.128028
$863$	31.2746	1.06460	0.532301	−	0.846555i	$-0.321328\pi$
$863$	31.2746	1.06460	0.532301	+	0.846555i	$0.321328\pi$
$864$	−5.34837	−0.181955
$865$	−45.8830	−1.56007
$866$	−0.505075	−0.0171631
$867$	28.2537	0.959545
$868$	1.51518	0.0514286
$869$	−2.40602	−0.0816186
$870$	−7.24804	−0.245732
$871$	13.8196	0.468260
$872$	−15.1512	−0.513085
$873$	2.93003	0.0991664
$874$	−0.245204	−0.00829415
$875$	3.84771	0.130076
$876$	5.10332	0.172425
$877$	30.2030	1.01988	0.509942	−	0.860209i	$-0.329667\pi$
$877$	30.2030	1.01988	0.509942	+	0.860209i	$0.329667\pi$
$878$	8.53428	0.288018
$879$	29.8564	1.00703
$880$	−3.90939	−0.131786
$881$	17.9701	0.605429	0.302714	−	0.953081i	$-0.402107\pi$
$881$	17.9701	0.605429	0.302714	+	0.953081i	$0.402107\pi$
$882$	−1.33258	−0.0448704
$883$	0.988212	0.0332560	0.0166280	−	0.999862i	$-0.494707\pi$
$883$	0.988212	0.0332560	0.0166280	+	0.999862i	$0.494707\pi$
$884$	2.59974	0.0874387
$885$	−32.7951	−1.10240
$886$	−40.0089	−1.34412
$887$	−19.9624	−0.670272	−0.335136	−	0.942170i	$-0.608782\pi$
$887$	−19.9624	−0.670272	−0.335136	+	0.942170i	$0.608782\pi$
$888$	17.1928	0.576954
$889$	−0.639542	−0.0214495
$890$	7.00912	0.234946
$891$	−8.38945	−0.281057
$892$	22.4994	0.753336
$893$	−0.366163	−0.0122532
$894$	−7.87408	−0.263349
$895$	16.2992	0.544822
$896$	0.186287	0.00622340
$897$	24.5705	0.820384
$898$	−18.2096	−0.607663
$899$	−8.99793	−0.300098
$900$	−1.96739	−0.0655795
$901$	−3.44759	−0.114856
$902$	−3.93374	−0.130979
$903$	1.70531	0.0567491
$904$	−2.79724	−0.0930349
$905$	7.83959	0.260597
$906$	−28.9347	−0.961290
$907$	27.7598	0.921749	0.460874	−	0.887465i	$-0.347536\pi$
$907$	27.7598	0.921749	0.460874	+	0.887465i	$0.347536\pi$
$908$	24.3244	0.807233
$909$	−2.83136	−0.0939101
$910$	5.03643	0.166956
$911$	−55.7120	−1.84582	−0.922910	−	0.385015i	$-0.874196\pi$
$911$	−55.7120	−1.84582	−0.922910	+	0.385015i	$0.874196\pi$
$912$	−0.193842	−0.00641875
$913$	8.81641	0.291781
$914$	41.9076	1.38618
$915$	14.2800	0.472084
$916$	24.5542	0.811294
$917$	−0.484573	−0.0160020
$918$	2.01057	0.0663587
$919$	16.0170	0.528351	0.264176	−	0.964475i	$-0.414900\pi$
$919$	16.0170	0.528351	0.264176	+	0.964475i	$0.414900\pi$
$920$	8.28782	0.273241
$921$	23.9670	0.789741
$922$	10.3457	0.340718
$923$	−21.9205	−0.721523
$924$	0.312200	0.0102706
$925$	105.495	3.46865
$926$	−30.0975	−0.989067
$927$	−2.90138	−0.0952939
$928$	−1.10627	−0.0363150
$929$	−32.2968	−1.05963	−0.529813	−	0.848115i	$-0.677738\pi$
$929$	−32.2968	−1.05963	−0.529813	+	0.848115i	$0.677738\pi$
$930$	53.2898	1.74744
$931$	−0.805632	−0.0264035
$932$	−5.83047	−0.190983
$933$	−27.9213	−0.914103
$934$	−3.42983	−0.112228
$935$	1.46963	0.0480620
$936$	−1.32308	−0.0432462
$937$	3.83194	0.125184	0.0625920	−	0.998039i	$-0.480063\pi$
$937$	3.83194	0.125184	0.0625920	+	0.998039i	$0.480063\pi$
$938$	−0.372260	−0.0121547
$939$	21.1885	0.691460
$940$	12.3762	0.403667
$941$	6.21455	0.202588	0.101294	−	0.994857i	$-0.467702\pi$
$941$	6.21455	0.202588	0.101294	+	0.994857i	$0.467702\pi$
$942$	−20.6784	−0.673740
$943$	8.33943	0.271569
$944$	−5.00551	−0.162915
$945$	3.89505	0.126706
$946$	−5.46223	−0.177592
$947$	−9.29858	−0.302163	−0.151082	−	0.988521i	$-0.548276\pi$
$947$	−9.29858	−0.302163	−0.151082	+	0.988521i	$0.548276\pi$
$948$	4.03228	0.130962
$949$	21.0588	0.683597
$950$	−1.18941	−0.0385896
$951$	−10.6565	−0.345560
$952$	−0.0700293	−0.00226966
$953$	5.78009	0.187235	0.0936177	−	0.995608i	$-0.470157\pi$
$953$	5.78009	0.187235	0.0936177	+	0.995608i	$0.470157\pi$
$954$	1.75458	0.0568065
$955$	53.5368	1.73241
$956$	−3.31189	−0.107114
$957$	−1.85401	−0.0599315
$958$	11.6583	0.376664
$959$	−2.59405	−0.0837663
$960$	6.55180	0.211459
$961$	35.1555	1.13405
$962$	70.9460	2.28739
$963$	0.753944	0.0242955
$964$	−27.3280	−0.880176
$965$	58.8786	1.89537
$966$	−0.661857	−0.0212949
$967$	−32.9708	−1.06027	−0.530134	−	0.847914i	$-0.677859\pi$
$967$	−32.9708	−1.06027	−0.530134	+	0.847914i	$0.677859\pi$
$968$	−1.00000	−0.0321412
$969$	0.0728696	0.00234091
$970$	−59.8724	−1.92239
$971$	1.50896	0.0484247	0.0242124	−	0.999707i	$-0.492292\pi$
$971$	1.50896	0.0484247	0.0242124	+	0.999707i	$0.492292\pi$
$972$	−1.98513	−0.0636730
$973$	1.10031	0.0352744
$974$	−8.38284	−0.268604
$975$	119.184	3.81694
$976$	2.17956	0.0697660
$977$	−46.0591	−1.47356	−0.736781	−	0.676132i	$-0.763655\pi$
$977$	−46.0591	−1.47356	−0.736781	+	0.676132i	$0.763655\pi$
$978$	−7.55645	−0.241629
$979$	1.79289	0.0573010
$980$	27.2301	0.869833
$981$	−2.89869	−0.0925482
$982$	−38.7701	−1.23720
$983$	59.3224	1.89209	0.946045	−	0.324036i	$-0.105040\pi$
$983$	59.3224	1.89209	0.946045	+	0.324036i	$0.105040\pi$
$984$	6.59260	0.210165
$985$	−3.90939	−0.124564
$986$	0.415870	0.0132440
$987$	−0.988350	−0.0314595
$988$	−0.799887	−0.0254478
$989$	11.5798	0.368216
$990$	−0.747935	−0.0237709
$991$	−40.2884	−1.27980	−0.639901	−	0.768457i	$-0.721025\pi$
$991$	−40.2884	−1.27980	−0.639901	+	0.768457i	$0.721025\pi$
$992$	8.13360	0.258242
$993$	10.4463	0.331503
$994$	0.590475	0.0187287
$995$	53.1549	1.68512
$996$	−14.7755	−0.468181
$997$	11.7352	0.371658	0.185829	−	0.982582i	$-0.440503\pi$
$997$	11.7352	0.371658	0.185829	+	0.982582i	$0.440503\pi$
$998$	36.9625	1.17003
$999$	54.8678	1.73594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.4	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.4	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.67591 q^{3} +1.00000 q^{4} -3.90939 q^{5} +1.67591 q^{6} -0.186287 q^{7} -1.00000 q^{8} -0.191317 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.67591 q^{3} +1.00000 q^{4} -3.90939 q^{5} +1.67591 q^{6} -0.186287 q^{7} -1.00000 q^{8} -0.191317 q^{9} +3.90939 q^{10} +1.00000 q^{11} -1.67591 q^{12} -6.91563 q^{13} +0.186287 q^{14} +6.55180 q^{15} +1.00000 q^{16} -0.375922 q^{17} +0.191317 q^{18} +0.115664 q^{19} -3.90939 q^{20} +0.312200 q^{21} -1.00000 q^{22} +2.11998 q^{23} +1.67591 q^{24} +10.2834 q^{25} +6.91563 q^{26} +5.34837 q^{27} -0.186287 q^{28} +1.10627 q^{29} -6.55180 q^{30} -8.13360 q^{31} -1.00000 q^{32} -1.67591 q^{33} +0.375922 q^{34} +0.728268 q^{35} -0.191317 q^{36} +10.2588 q^{37} -0.115664 q^{38} +11.5900 q^{39} +3.90939 q^{40} +3.93374 q^{41} -0.312200 q^{42} +5.46223 q^{43} +1.00000 q^{44} +0.747935 q^{45} -2.11998 q^{46} -3.16576 q^{47} -1.67591 q^{48} -6.96530 q^{49} -10.2834 q^{50} +0.630013 q^{51} -6.91563 q^{52} +9.17102 q^{53} -5.34837 q^{54} -3.90939 q^{55} +0.186287 q^{56} -0.193842 q^{57} -1.10627 q^{58} -5.00551 q^{59} +6.55180 q^{60} +2.17956 q^{61} +8.13360 q^{62} +0.0356399 q^{63} +1.00000 q^{64} +27.0359 q^{65} +1.67591 q^{66} -1.99832 q^{67} -0.375922 q^{68} -3.55289 q^{69} -0.728268 q^{70} +3.16971 q^{71} +0.191317 q^{72} -3.04510 q^{73} -10.2588 q^{74} -17.2340 q^{75} +0.115664 q^{76} -0.186287 q^{77} -11.5900 q^{78} -2.40602 q^{79} -3.90939 q^{80} -8.38945 q^{81} -3.93374 q^{82} +8.81641 q^{83} +0.312200 q^{84} +1.46963 q^{85} -5.46223 q^{86} -1.85401 q^{87} -1.00000 q^{88} +1.79289 q^{89} -0.747935 q^{90} +1.28829 q^{91} +2.11998 q^{92} +13.6312 q^{93} +3.16576 q^{94} -0.452175 q^{95} +1.67591 q^{96} -15.3150 q^{97} +6.96530 q^{98} -0.191317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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