LMFDB - Embedded newform 4334.2.a.b.1.2

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} - 6 x^{14} - 8 x^{13} + 94 x^{12} - 13 x^{11} - 582 x^{10} + 295 x^{9} + 1814 x^{8} - 1056 x^{7} + \cdots - 45 $ x^15 - 6x^14 - 8x^13 + 94x^12 - 13x^11 - 582x^10 + 295x^9 + 1814x^8 - 1056x^7 - 2966x^6 + 1621x^5 + 2328x^4 - 1160x^3 - 589x^2 + 364x - 45
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			1.2
Root			$-1.92605$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.92605 q^{3} +1.00000 q^{4} +1.09129 q^{5} -2.92605 q^{6} +3.40685 q^{7} +1.00000 q^{8} +5.56174 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.92605 q^{3} +1.00000 q^{4} +1.09129 q^{5} -2.92605 q^{6} +3.40685 q^{7} +1.00000 q^{8} +5.56174 q^{9} +1.09129 q^{10} +1.00000 q^{11} -2.92605 q^{12} -3.81293 q^{13} +3.40685 q^{14} -3.19316 q^{15} +1.00000 q^{16} -3.33073 q^{17} +5.56174 q^{18} +1.90467 q^{19} +1.09129 q^{20} -9.96861 q^{21} +1.00000 q^{22} -3.59532 q^{23} -2.92605 q^{24} -3.80909 q^{25} -3.81293 q^{26} -7.49577 q^{27} +3.40685 q^{28} -6.74647 q^{29} -3.19316 q^{30} -5.13925 q^{31} +1.00000 q^{32} -2.92605 q^{33} -3.33073 q^{34} +3.71786 q^{35} +5.56174 q^{36} -8.51692 q^{37} +1.90467 q^{38} +11.1568 q^{39} +1.09129 q^{40} +3.42169 q^{41} -9.96861 q^{42} +2.38816 q^{43} +1.00000 q^{44} +6.06947 q^{45} -3.59532 q^{46} -8.43610 q^{47} -2.92605 q^{48} +4.60665 q^{49} -3.80909 q^{50} +9.74587 q^{51} -3.81293 q^{52} +7.61190 q^{53} -7.49577 q^{54} +1.09129 q^{55} +3.40685 q^{56} -5.57315 q^{57} -6.74647 q^{58} -11.9731 q^{59} -3.19316 q^{60} -6.83304 q^{61} -5.13925 q^{62} +18.9480 q^{63} +1.00000 q^{64} -4.16101 q^{65} -2.92605 q^{66} +1.98094 q^{67} -3.33073 q^{68} +10.5201 q^{69} +3.71786 q^{70} +9.55385 q^{71} +5.56174 q^{72} +3.01541 q^{73} -8.51692 q^{74} +11.1456 q^{75} +1.90467 q^{76} +3.40685 q^{77} +11.1568 q^{78} -14.8466 q^{79} +1.09129 q^{80} +5.24774 q^{81} +3.42169 q^{82} -15.4118 q^{83} -9.96861 q^{84} -3.63479 q^{85} +2.38816 q^{86} +19.7405 q^{87} +1.00000 q^{88} -3.85593 q^{89} +6.06947 q^{90} -12.9901 q^{91} -3.59532 q^{92} +15.0377 q^{93} -8.43610 q^{94} +2.07855 q^{95} -2.92605 q^{96} +13.8084 q^{97} +4.60665 q^{98} +5.56174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.92605	−1.68935	−0.844677	−	0.535277i	$-0.820207\pi$
$3$	−2.92605	−1.68935	−0.844677	+	0.535277i	$0.820207\pi$
$4$	1.00000	0.500000
$5$	1.09129	0.488039	0.244020	−	0.969770i	$-0.421534\pi$
$5$	1.09129	0.488039	0.244020	+	0.969770i	$0.421534\pi$
$6$	−2.92605	−1.19455
$7$	3.40685	1.28767	0.643835	−	0.765165i	$-0.277342\pi$
$7$	3.40685	1.28767	0.643835	+	0.765165i	$0.277342\pi$
$8$	1.00000	0.353553
$9$	5.56174	1.85391
$10$	1.09129	0.345096
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.92605	−0.844677
$13$	−3.81293	−1.05752	−0.528759	−	0.848772i	$-0.677342\pi$
$13$	−3.81293	−1.05752	−0.528759	+	0.848772i	$0.677342\pi$
$14$	3.40685	0.910520
$15$	−3.19316	−0.824471
$16$	1.00000	0.250000
$17$	−3.33073	−0.807821	−0.403910	−	0.914799i	$-0.632349\pi$
$17$	−3.33073	−0.807821	−0.403910	+	0.914799i	$0.632349\pi$
$18$	5.56174	1.31092
$19$	1.90467	0.436961	0.218481	−	0.975841i	$-0.429890\pi$
$19$	1.90467	0.436961	0.218481	+	0.975841i	$0.429890\pi$
$20$	1.09129	0.244020
$21$	−9.96861	−2.17533
$22$	1.00000	0.213201
$23$	−3.59532	−0.749677	−0.374839	−	0.927090i	$-0.622302\pi$
$23$	−3.59532	−0.749677	−0.374839	+	0.927090i	$0.622302\pi$
$24$	−2.92605	−0.597277
$25$	−3.80909	−0.761817
$26$	−3.81293	−0.747778
$27$	−7.49577	−1.44256
$28$	3.40685	0.643835
$29$	−6.74647	−1.25279	−0.626394	−	0.779507i	$-0.715470\pi$
$29$	−6.74647	−1.25279	−0.626394	+	0.779507i	$0.715470\pi$
$30$	−3.19316	−0.582989
$31$	−5.13925	−0.923037	−0.461519	−	0.887131i	$-0.652695\pi$
$31$	−5.13925	−0.923037	−0.461519	+	0.887131i	$0.652695\pi$
$32$	1.00000	0.176777
$33$	−2.92605	−0.509359
$34$	−3.33073	−0.571215
$35$	3.71786	0.628433
$36$	5.56174	0.926957
$37$	−8.51692	−1.40017	−0.700087	−	0.714058i	$-0.746855\pi$
$37$	−8.51692	−1.40017	−0.700087	+	0.714058i	$0.746855\pi$
$38$	1.90467	0.308978
$39$	11.1568	1.78652
$40$	1.09129	0.172548
$41$	3.42169	0.534378	0.267189	−	0.963644i	$-0.413905\pi$
$41$	3.42169	0.534378	0.267189	+	0.963644i	$0.413905\pi$
$42$	−9.96861	−1.53819
$43$	2.38816	0.364191	0.182096	−	0.983281i	$-0.441712\pi$
$43$	2.38816	0.364191	0.182096	+	0.983281i	$0.441712\pi$
$44$	1.00000	0.150756
$45$	6.06947	0.904783
$46$	−3.59532	−0.530102
$47$	−8.43610	−1.23053	−0.615266	−	0.788320i	$-0.710951\pi$
$47$	−8.43610	−1.23053	−0.615266	+	0.788320i	$0.710951\pi$
$48$	−2.92605	−0.422338
$49$	4.60665	0.658092
$50$	−3.80909	−0.538686
$51$	9.74587	1.36469
$52$	−3.81293	−0.528759
$53$	7.61190	1.04557	0.522787	−	0.852463i	$-0.324892\pi$
$53$	7.61190	1.04557	0.522787	+	0.852463i	$0.324892\pi$
$54$	−7.49577	−1.02005
$55$	1.09129	0.147149
$56$	3.40685	0.455260
$57$	−5.57315	−0.738182
$58$	−6.74647	−0.885855
$59$	−11.9731	−1.55876	−0.779381	−	0.626550i	$-0.784466\pi$
$59$	−11.9731	−1.55876	−0.779381	+	0.626550i	$0.784466\pi$
$60$	−3.19316	−0.412235
$61$	−6.83304	−0.874881	−0.437441	−	0.899247i	$-0.644115\pi$
$61$	−6.83304	−0.874881	−0.437441	+	0.899247i	$0.644115\pi$
$62$	−5.13925	−0.652686
$63$	18.9480	2.38723
$64$	1.00000	0.125000
$65$	−4.16101	−0.516110
$66$	−2.92605	−0.360171
$67$	1.98094	0.242010	0.121005	−	0.992652i	$-0.461388\pi$
$67$	1.98094	0.242010	0.121005	+	0.992652i	$0.461388\pi$
$68$	−3.33073	−0.403910
$69$	10.5201	1.26647
$70$	3.71786	0.444370
$71$	9.55385	1.13383	0.566917	−	0.823775i	$-0.308136\pi$
$71$	9.55385	1.13383	0.566917	+	0.823775i	$0.308136\pi$
$72$	5.56174	0.655458
$73$	3.01541	0.352927	0.176464	−	0.984307i	$-0.443534\pi$
$73$	3.01541	0.352927	0.176464	+	0.984307i	$0.443534\pi$
$74$	−8.51692	−0.990072
$75$	11.1456	1.28698
$76$	1.90467	0.218481
$77$	3.40685	0.388247
$78$	11.1568	1.26326
$79$	−14.8466	−1.67037	−0.835186	−	0.549968i	$-0.814640\pi$
$79$	−14.8466	−1.67037	−0.835186	+	0.549968i	$0.814640\pi$
$80$	1.09129	0.122010
$81$	5.24774	0.583083
$82$	3.42169	0.377862
$83$	−15.4118	−1.69166	−0.845831	−	0.533451i	$-0.820895\pi$
$83$	−15.4118	−1.69166	−0.845831	+	0.533451i	$0.820895\pi$
$84$	−9.96861	−1.08766
$85$	−3.63479	−0.394248
$86$	2.38816	0.257522
$87$	19.7405	2.11640
$88$	1.00000	0.106600
$89$	−3.85593	−0.408727	−0.204364	−	0.978895i	$-0.565512\pi$
$89$	−3.85593	−0.408727	−0.204364	+	0.978895i	$0.565512\pi$
$90$	6.06947	0.639778
$91$	−12.9901	−1.36173
$92$	−3.59532	−0.374839
$93$	15.0377	1.55934
$94$	−8.43610	−0.870117
$95$	2.07855	0.213254
$96$	−2.92605	−0.298638
$97$	13.8084	1.40203	0.701014	−	0.713148i	$-0.252731\pi$
$97$	13.8084	1.40203	0.701014	+	0.713148i	$0.252731\pi$
$98$	4.60665	0.465341
$99$	5.56174	0.558976
$100$	−3.80909	−0.380909
$101$	12.1551	1.20948	0.604739	−	0.796424i	$-0.293277\pi$
$101$	12.1551	1.20948	0.604739	+	0.796424i	$0.293277\pi$
$102$	9.74587	0.964985
$103$	12.9885	1.27979	0.639897	−	0.768460i	$-0.278977\pi$
$103$	12.9885	1.27979	0.639897	+	0.768460i	$0.278977\pi$
$104$	−3.81293	−0.373889
$105$	−10.8786	−1.06165
$106$	7.61190	0.739333
$107$	12.4501	1.20360	0.601798	−	0.798648i	$-0.294451\pi$
$107$	12.4501	1.20360	0.601798	+	0.798648i	$0.294451\pi$
$108$	−7.49577	−0.721281
$109$	10.2606	0.982783	0.491391	−	0.870939i	$-0.336489\pi$
$109$	10.2606	0.982783	0.491391	+	0.870939i	$0.336489\pi$
$110$	1.09129	0.104050
$111$	24.9209	2.36539
$112$	3.40685	0.321917
$113$	10.8934	1.02477	0.512383	−	0.858757i	$-0.328763\pi$
$113$	10.8934	1.02477	0.512383	+	0.858757i	$0.328763\pi$
$114$	−5.57315	−0.521973
$115$	−3.92354	−0.365872
$116$	−6.74647	−0.626394
$117$	−21.2066	−1.96055
$118$	−11.9731	−1.10221
$119$	−11.3473	−1.04021
$120$	−3.19316	−0.291495
$121$	1.00000	0.0909091
$122$	−6.83304	−0.618634
$123$	−10.0120	−0.902753
$124$	−5.13925	−0.461519
$125$	−9.61326	−0.859836
$126$	18.9480	1.68803
$127$	−8.46414	−0.751071	−0.375535	−	0.926808i	$-0.622541\pi$
$127$	−8.46414	−0.751071	−0.375535	+	0.926808i	$0.622541\pi$
$128$	1.00000	0.0883883
$129$	−6.98787	−0.615248
$130$	−4.16101	−0.364945
$131$	−5.91934	−0.517175	−0.258588	−	0.965988i	$-0.583257\pi$
$131$	−5.91934	−0.517175	−0.258588	+	0.965988i	$0.583257\pi$
$132$	−2.92605	−0.254680
$133$	6.48893	0.562662
$134$	1.98094	0.171127
$135$	−8.18006	−0.704027
$136$	−3.33073	−0.285608
$137$	19.4957	1.66563	0.832814	−	0.553553i	$-0.186728\pi$
$137$	19.4957	1.66563	0.832814	+	0.553553i	$0.186728\pi$
$138$	10.5201	0.895529
$139$	−14.1718	−1.20204	−0.601020	−	0.799234i	$-0.705239\pi$
$139$	−14.1718	−1.20204	−0.601020	+	0.799234i	$0.705239\pi$
$140$	3.71786	0.314217
$141$	24.6844	2.07880
$142$	9.55385	0.801741
$143$	−3.81293	−0.318854
$144$	5.56174	0.463478
$145$	−7.36235	−0.611410
$146$	3.01541	0.249557
$147$	−13.4793	−1.11175
$148$	−8.51692	−0.700087
$149$	−13.0701	−1.07075	−0.535374	−	0.844615i	$-0.679829\pi$
$149$	−13.0701	−1.07075	−0.535374	+	0.844615i	$0.679829\pi$
$150$	11.1456	0.910031
$151$	−8.33031	−0.677911	−0.338955	−	0.940802i	$-0.610074\pi$
$151$	−8.33031	−0.677911	−0.338955	+	0.940802i	$0.610074\pi$
$152$	1.90467	0.154489
$153$	−18.5247	−1.49763
$154$	3.40685	0.274532
$155$	−5.60841	−0.450479
$156$	11.1568	0.893260
$157$	−5.39025	−0.430188	−0.215094	−	0.976593i	$-0.569006\pi$
$157$	−5.39025	−0.430188	−0.215094	+	0.976593i	$0.569006\pi$
$158$	−14.8466	−1.18113
$159$	−22.2728	−1.76634
$160$	1.09129	0.0862740
$161$	−12.2487	−0.965336
$162$	5.24774	0.412302
$163$	−10.6505	−0.834211	−0.417105	−	0.908858i	$-0.636955\pi$
$163$	−10.6505	−0.834211	−0.417105	+	0.908858i	$0.636955\pi$
$164$	3.42169	0.267189
$165$	−3.19316	−0.248587
$166$	−15.4118	−1.19619
$167$	−0.182834	−0.0141481	−0.00707405	−	0.999975i	$-0.502252\pi$
$167$	−0.182834	−0.0141481	−0.00707405	+	0.999975i	$0.502252\pi$
$168$	−9.96861	−0.769095
$169$	1.53846	0.118343
$170$	−3.63479	−0.278776
$171$	10.5933	0.810089
$172$	2.38816	0.182096
$173$	−12.8389	−0.976121	−0.488060	−	0.872810i	$-0.662295\pi$
$173$	−12.8389	−0.976121	−0.488060	+	0.872810i	$0.662295\pi$
$174$	19.7405	1.49652
$175$	−12.9770	−0.980969
$176$	1.00000	0.0753778
$177$	35.0338	2.63330
$178$	−3.85593	−0.289014
$179$	−10.6853	−0.798658	−0.399329	−	0.916808i	$-0.630757\pi$
$179$	−10.6853	−0.798658	−0.399329	+	0.916808i	$0.630757\pi$
$180$	6.06947	0.452392
$181$	−19.0222	−1.41391	−0.706955	−	0.707259i	$-0.749932\pi$
$181$	−19.0222	−1.41391	−0.706955	+	0.707259i	$0.749932\pi$
$182$	−12.9901	−0.962891
$183$	19.9938	1.47798
$184$	−3.59532	−0.265051
$185$	−9.29442	−0.683340
$186$	15.0377	1.10262
$187$	−3.33073	−0.243567
$188$	−8.43610	−0.615266
$189$	−25.5370	−1.85754
$190$	2.07855	0.150794
$191$	−19.5588	−1.41523	−0.707614	−	0.706600i	$-0.750228\pi$
$191$	−19.5588	−1.41523	−0.707614	+	0.706600i	$0.750228\pi$
$192$	−2.92605	−0.211169
$193$	12.9607	0.932935	0.466467	−	0.884538i	$-0.345527\pi$
$193$	12.9607	0.932935	0.466467	+	0.884538i	$0.345527\pi$
$194$	13.8084	0.991383
$195$	12.1753	0.871893
$196$	4.60665	0.329046
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	5.56174	0.395256
$199$	−20.7796	−1.47303	−0.736514	−	0.676422i	$-0.763530\pi$
$199$	−20.7796	−1.47303	−0.736514	+	0.676422i	$0.763530\pi$
$200$	−3.80909	−0.269343
$201$	−5.79632	−0.408841
$202$	12.1551	0.855230
$203$	−22.9842	−1.61318
$204$	9.74587	0.682347
$205$	3.73405	0.260797
$206$	12.9885	0.904952
$207$	−19.9963	−1.38984
$208$	−3.81293	−0.264379
$209$	1.90467	0.131749
$210$	−10.8786	−0.750697
$211$	5.07378	0.349294	0.174647	−	0.984631i	$-0.444122\pi$
$211$	5.07378	0.349294	0.174647	+	0.984631i	$0.444122\pi$
$212$	7.61190	0.522787
$213$	−27.9550	−1.91545
$214$	12.4501	0.851071
$215$	2.60618	0.177740
$216$	−7.49577	−0.510023
$217$	−17.5087	−1.18857
$218$	10.2606	0.694932
$219$	−8.82324	−0.596219
$220$	1.09129	0.0735747
$221$	12.6999	0.854285
$222$	24.9209	1.67258
$223$	−9.58698	−0.641992	−0.320996	−	0.947081i	$-0.604018\pi$
$223$	−9.58698	−0.641992	−0.320996	+	0.947081i	$0.604018\pi$
$224$	3.40685	0.227630
$225$	−21.1852	−1.41234
$226$	10.8934	0.724619
$227$	15.0136	0.996489	0.498244	−	0.867037i	$-0.333978\pi$
$227$	15.0136	0.996489	0.498244	+	0.867037i	$0.333978\pi$
$228$	−5.57315	−0.369091
$229$	8.60810	0.568839	0.284420	−	0.958700i	$-0.408199\pi$
$229$	8.60810	0.568839	0.284420	+	0.958700i	$0.408199\pi$
$230$	−3.92354	−0.258711
$231$	−9.96861	−0.655886
$232$	−6.74647	−0.442928
$233$	7.55199	0.494747	0.247374	−	0.968920i	$-0.420432\pi$
$233$	7.55199	0.494747	0.247374	+	0.968920i	$0.420432\pi$
$234$	−21.2066	−1.38632
$235$	−9.20622	−0.600548
$236$	−11.9731	−0.779381
$237$	43.4418	2.82185
$238$	−11.3473	−0.735537
$239$	−6.31413	−0.408427	−0.204214	−	0.978926i	$-0.565464\pi$
$239$	−6.31413	−0.408427	−0.204214	+	0.978926i	$0.565464\pi$
$240$	−3.19316	−0.206118
$241$	15.2793	0.984223	0.492112	−	0.870532i	$-0.336225\pi$
$241$	15.2793	0.984223	0.492112	+	0.870532i	$0.336225\pi$
$242$	1.00000	0.0642824
$243$	7.13218	0.457529
$244$	−6.83304	−0.437441
$245$	5.02718	0.321175
$246$	−10.0120	−0.638343
$247$	−7.26238	−0.462094
$248$	−5.13925	−0.326343
$249$	45.0955	2.85781
$250$	−9.61326	−0.607996
$251$	17.3683	1.09628	0.548138	−	0.836388i	$-0.315337\pi$
$251$	17.3683	1.09628	0.548138	+	0.836388i	$0.315337\pi$
$252$	18.9480	1.19361
$253$	−3.59532	−0.226036
$254$	−8.46414	−0.531087
$255$	10.6356	0.666025
$256$	1.00000	0.0625000
$257$	7.82805	0.488300	0.244150	−	0.969737i	$-0.421491\pi$
$257$	7.82805	0.488300	0.244150	+	0.969737i	$0.421491\pi$
$258$	−6.98787	−0.435046
$259$	−29.0159	−1.80296
$260$	−4.16101	−0.258055
$261$	−37.5221	−2.32256
$262$	−5.91934	−0.365698
$263$	15.1482	0.934081	0.467040	−	0.884236i	$-0.345320\pi$
$263$	15.1482	0.934081	0.467040	+	0.884236i	$0.345320\pi$
$264$	−2.92605	−0.180086
$265$	8.30678	0.510282
$266$	6.48893	0.397862
$267$	11.2826	0.690485
$268$	1.98094	0.121005
$269$	−28.7223	−1.75123	−0.875616	−	0.483009i	$-0.839544\pi$
$269$	−28.7223	−1.75123	−0.875616	+	0.483009i	$0.839544\pi$
$270$	−8.18006	−0.497822
$271$	2.87354	0.174555	0.0872776	−	0.996184i	$-0.472183\pi$
$271$	2.87354	0.174555	0.0872776	+	0.996184i	$0.472183\pi$
$272$	−3.33073	−0.201955
$273$	38.0096	2.30045
$274$	19.4957	1.17778
$275$	−3.80909	−0.229697
$276$	10.5201	0.633235
$277$	−5.34306	−0.321033	−0.160517	−	0.987033i	$-0.551316\pi$
$277$	−5.34306	−0.321033	−0.160517	+	0.987033i	$0.551316\pi$
$278$	−14.1718	−0.849971
$279$	−28.5832	−1.71123
$280$	3.71786	0.222185
$281$	4.20392	0.250785	0.125393	−	0.992107i	$-0.459981\pi$
$281$	4.20392	0.250785	0.125393	+	0.992107i	$0.459981\pi$
$282$	24.6844	1.46993
$283$	−15.0099	−0.892248	−0.446124	−	0.894971i	$-0.647196\pi$
$283$	−15.0099	−0.892248	−0.446124	+	0.894971i	$0.647196\pi$
$284$	9.55385	0.566917
$285$	−6.08192	−0.360262
$286$	−3.81293	−0.225464
$287$	11.6572	0.688102
$288$	5.56174	0.327729
$289$	−5.90624	−0.347426
$290$	−7.36235	−0.432332
$291$	−40.4039	−2.36852
$292$	3.01541	0.176464
$293$	−21.8303	−1.27534	−0.637671	−	0.770309i	$-0.720102\pi$
$293$	−21.8303	−1.27534	−0.637671	+	0.770309i	$0.720102\pi$
$294$	−13.4793	−0.786126
$295$	−13.0661	−0.760737
$296$	−8.51692	−0.495036
$297$	−7.49577	−0.434949
$298$	−13.0701	−0.757133
$299$	13.7087	0.792797
$300$	11.1456	0.643489
$301$	8.13612	0.468958
$302$	−8.33031	−0.479355
$303$	−35.5664	−2.04323
$304$	1.90467	0.109240
$305$	−7.45682	−0.426977
$306$	−18.5247	−1.05898
$307$	3.87352	0.221073	0.110537	−	0.993872i	$-0.464743\pi$
$307$	3.87352	0.221073	0.110537	+	0.993872i	$0.464743\pi$
$308$	3.40685	0.194123
$309$	−38.0049	−2.16203
$310$	−5.60841	−0.318536
$311$	−28.5791	−1.62057	−0.810286	−	0.586035i	$-0.800688\pi$
$311$	−28.5791	−1.62057	−0.810286	+	0.586035i	$0.800688\pi$
$312$	11.1568	0.631630
$313$	15.8009	0.893117	0.446559	−	0.894754i	$-0.352649\pi$
$313$	15.8009	0.893117	0.446559	+	0.894754i	$0.352649\pi$
$314$	−5.39025	−0.304189
$315$	20.6778	1.16506
$316$	−14.8466	−0.835186
$317$	31.2948	1.75769	0.878846	−	0.477105i	$-0.158314\pi$
$317$	31.2948	1.75769	0.878846	+	0.477105i	$0.158314\pi$
$318$	−22.2728	−1.24899
$319$	−6.74647	−0.377730
$320$	1.09129	0.0610049
$321$	−36.4295	−2.03330
$322$	−12.2487	−0.682596
$323$	−6.34394	−0.352986
$324$	5.24774	0.291541
$325$	14.5238	0.805635
$326$	−10.6505	−0.589876
$327$	−30.0228	−1.66027
$328$	3.42169	0.188931
$329$	−28.7405	−1.58452
$330$	−3.19316	−0.175778
$331$	9.07500	0.498807	0.249403	−	0.968400i	$-0.419765\pi$
$331$	9.07500	0.498807	0.249403	+	0.968400i	$0.419765\pi$
$332$	−15.4118	−0.845831
$333$	−47.3689	−2.59580
$334$	−0.182834	−0.0100042
$335$	2.16178	0.118111
$336$	−9.96861	−0.543832
$337$	18.8308	1.02578	0.512890	−	0.858455i	$-0.328575\pi$
$337$	18.8308	1.02578	0.512890	+	0.858455i	$0.328575\pi$
$338$	1.53846	0.0836814
$339$	−31.8746	−1.73119
$340$	−3.63479	−0.197124
$341$	−5.13925	−0.278306
$342$	10.5933	0.572819
$343$	−8.15381	−0.440264
$344$	2.38816	0.128761
$345$	11.4805	0.618087
$346$	−12.8389	−0.690221
$347$	3.83527	0.205888	0.102944	−	0.994687i	$-0.467174\pi$
$347$	3.83527	0.205888	0.102944	+	0.994687i	$0.467174\pi$
$348$	19.7405	1.05820
$349$	22.8146	1.22124	0.610618	−	0.791925i	$-0.290921\pi$
$349$	22.8146	1.22124	0.610618	+	0.791925i	$0.290921\pi$
$350$	−12.9770	−0.693650
$351$	28.5809	1.52553
$352$	1.00000	0.0533002
$353$	19.9157	1.06000	0.530002	−	0.847996i	$-0.322191\pi$
$353$	19.9157	1.06000	0.530002	+	0.847996i	$0.322191\pi$
$354$	35.0338	1.86202
$355$	10.4260	0.553356
$356$	−3.85593	−0.204364
$357$	33.2027	1.75727
$358$	−10.6853	−0.564736
$359$	3.95962	0.208981	0.104490	−	0.994526i	$-0.466679\pi$
$359$	3.95962	0.208981	0.104490	+	0.994526i	$0.466679\pi$
$360$	6.06947	0.319889
$361$	−15.3722	−0.809065
$362$	−19.0222	−0.999785
$363$	−2.92605	−0.153578
$364$	−12.9901	−0.680866
$365$	3.29069	0.172242
$366$	19.9938	1.04509
$367$	−32.0595	−1.67349	−0.836746	−	0.547591i	$-0.815545\pi$
$367$	−32.0595	−1.67349	−0.836746	+	0.547591i	$0.815545\pi$
$368$	−3.59532	−0.187419
$369$	19.0305	0.990690
$370$	−9.29442	−0.483194
$371$	25.9326	1.34635
$372$	15.0377	0.779668
$373$	−11.9222	−0.617310	−0.308655	−	0.951174i	$-0.599879\pi$
$373$	−11.9222	−0.617310	−0.308655	+	0.951174i	$0.599879\pi$
$374$	−3.33073	−0.172228
$375$	28.1288	1.45257
$376$	−8.43610	−0.435059
$377$	25.7238	1.32485
$378$	−25.5370	−1.31348
$379$	−7.46839	−0.383625	−0.191813	−	0.981432i	$-0.561437\pi$
$379$	−7.46839	−0.383625	−0.191813	+	0.981432i	$0.561437\pi$
$380$	2.07855	0.106627
$381$	24.7665	1.26882
$382$	−19.5588	−1.00072
$383$	28.8972	1.47658	0.738288	−	0.674486i	$-0.235635\pi$
$383$	28.8972	1.47658	0.738288	+	0.674486i	$0.235635\pi$
$384$	−2.92605	−0.149319
$385$	3.71786	0.189480
$386$	12.9607	0.659684
$387$	13.2823	0.675179
$388$	13.8084	0.701014
$389$	17.2563	0.874930	0.437465	−	0.899235i	$-0.355876\pi$
$389$	17.2563	0.874930	0.437465	+	0.899235i	$0.355876\pi$
$390$	12.1753	0.616521
$391$	11.9751	0.605605
$392$	4.60665	0.232671
$393$	17.3203	0.873692
$394$	−1.00000	−0.0503793
$395$	−16.2019	−0.815207
$396$	5.56174	0.279488
$397$	5.19478	0.260718	0.130359	−	0.991467i	$-0.458387\pi$
$397$	5.19478	0.260718	0.130359	+	0.991467i	$0.458387\pi$
$398$	−20.7796	−1.04159
$399$	−18.9869	−0.950534
$400$	−3.80909	−0.190454
$401$	25.8128	1.28903	0.644515	−	0.764592i	$-0.277059\pi$
$401$	25.8128	1.28903	0.644515	+	0.764592i	$0.277059\pi$
$402$	−5.79632	−0.289094
$403$	19.5956	0.976128
$404$	12.1551	0.604739
$405$	5.72681	0.284567
$406$	−22.9842	−1.14069
$407$	−8.51692	−0.422168
$408$	9.74587	0.482492
$409$	14.3648	0.710294	0.355147	−	0.934811i	$-0.384431\pi$
$409$	14.3648	0.710294	0.355147	+	0.934811i	$0.384431\pi$
$410$	3.73405	0.184412
$411$	−57.0452	−2.81383
$412$	12.9885	0.639897
$413$	−40.7905	−2.00717
$414$	−19.9963	−0.982763
$415$	−16.8187	−0.825598
$416$	−3.81293	−0.186944
$417$	41.4675	2.03067
$418$	1.90467	0.0931605
$419$	13.6428	0.666495	0.333247	−	0.942839i	$-0.391856\pi$
$419$	13.6428	0.666495	0.333247	+	0.942839i	$0.391856\pi$
$420$	−10.8786	−0.530823
$421$	−22.2159	−1.08274	−0.541369	−	0.840785i	$-0.682094\pi$
$421$	−22.2159	−1.08274	−0.541369	+	0.840785i	$0.682094\pi$
$422$	5.07378	0.246988
$423$	−46.9194	−2.28130
$424$	7.61190	0.369666
$425$	12.6870	0.615412
$426$	−27.9550	−1.35442
$427$	−23.2792	−1.12656
$428$	12.4501	0.601798
$429$	11.1568	0.538656
$430$	2.60618	0.125681
$431$	−12.5862	−0.606256	−0.303128	−	0.952950i	$-0.598031\pi$
$431$	−12.5862	−0.606256	−0.303128	+	0.952950i	$0.598031\pi$
$432$	−7.49577	−0.360641
$433$	15.1588	0.728485	0.364242	−	0.931304i	$-0.381328\pi$
$433$	15.1588	0.728485	0.364242	+	0.931304i	$0.381328\pi$
$434$	−17.5087	−0.840443
$435$	21.5426	1.03289
$436$	10.2606	0.491391
$437$	−6.84791	−0.327580
$438$	−8.82324	−0.421590
$439$	13.9874	0.667583	0.333791	−	0.942647i	$-0.391672\pi$
$439$	13.9874	0.667583	0.333791	+	0.942647i	$0.391672\pi$
$440$	1.09129	0.0520252
$441$	25.6210	1.22005
$442$	12.6999	0.604070
$443$	−18.2935	−0.869149	−0.434574	−	0.900636i	$-0.643101\pi$
$443$	−18.2935	−0.869149	−0.434574	+	0.900636i	$0.643101\pi$
$444$	24.9209	1.18269
$445$	−4.20793	−0.199475
$446$	−9.58698	−0.453957
$447$	38.2438	1.80887
$448$	3.40685	0.160959
$449$	−35.2073	−1.66154	−0.830768	−	0.556618i	$-0.812099\pi$
$449$	−35.2073	−1.66154	−0.830768	+	0.556618i	$0.812099\pi$
$450$	−21.1852	−0.998678
$451$	3.42169	0.161121
$452$	10.8934	0.512383
$453$	24.3749	1.14523
$454$	15.0136	0.704624
$455$	−14.1760	−0.664579
$456$	−5.57315	−0.260987
$457$	−34.5517	−1.61626	−0.808130	−	0.589004i	$-0.799520\pi$
$457$	−34.5517	−1.61626	−0.808130	+	0.589004i	$0.799520\pi$
$458$	8.60810	0.402230
$459$	24.9664	1.16533
$460$	−3.92354	−0.182936
$461$	−38.9173	−1.81256	−0.906279	−	0.422681i	$-0.861089\pi$
$461$	−38.9173	−1.81256	−0.906279	+	0.422681i	$0.861089\pi$
$462$	−9.96861	−0.463782
$463$	8.89641	0.413451	0.206726	−	0.978399i	$-0.433719\pi$
$463$	8.89641	0.413451	0.206726	+	0.978399i	$0.433719\pi$
$464$	−6.74647	−0.313197
$465$	16.4105	0.761017
$466$	7.55199	0.349839
$467$	−3.34932	−0.154988	−0.0774940	−	0.996993i	$-0.524692\pi$
$467$	−3.34932	−0.154988	−0.0774940	+	0.996993i	$0.524692\pi$
$468$	−21.2066	−0.980273
$469$	6.74877	0.311629
$470$	−9.20622	−0.424651
$471$	15.7721	0.726740
$472$	−11.9731	−0.551106
$473$	2.38816	0.109808
$474$	43.4418	1.99535
$475$	−7.25506	−0.332885
$476$	−11.3473	−0.520103
$477$	42.3354	1.93841
$478$	−6.31413	−0.288802
$479$	0.887412	0.0405469	0.0202734	−	0.999794i	$-0.493546\pi$
$479$	0.887412	0.0405469	0.0202734	+	0.999794i	$0.493546\pi$
$480$	−3.19316	−0.145747
$481$	32.4745	1.48071
$482$	15.2793	0.695951
$483$	35.8404	1.63079
$484$	1.00000	0.0454545
$485$	15.0689	0.684245
$486$	7.13218	0.323522
$487$	28.7939	1.30478	0.652388	−	0.757885i	$-0.273767\pi$
$487$	28.7939	1.30478	0.652388	+	0.757885i	$0.273767\pi$
$488$	−6.83304	−0.309317
$489$	31.1638	1.40928
$490$	5.02718	0.227105
$491$	20.3846	0.919944	0.459972	−	0.887933i	$-0.347859\pi$
$491$	20.3846	0.919944	0.459972	+	0.887933i	$0.347859\pi$
$492$	−10.0120	−0.451376
$493$	22.4707	1.01203
$494$	−7.26238	−0.326750
$495$	6.06947	0.272802
$496$	−5.13925	−0.230759
$497$	32.5486	1.46000
$498$	45.0955	2.02078
$499$	13.8221	0.618763	0.309382	−	0.950938i	$-0.399878\pi$
$499$	13.8221	0.618763	0.309382	+	0.950938i	$0.399878\pi$
$500$	−9.61326	−0.429918
$501$	0.534980	0.0239011
$502$	17.3683	0.775184
$503$	−7.46168	−0.332700	−0.166350	−	0.986067i	$-0.553198\pi$
$503$	−7.46168	−0.332700	−0.166350	+	0.986067i	$0.553198\pi$
$504$	18.9480	0.844013
$505$	13.2647	0.590273
$506$	−3.59532	−0.159832
$507$	−4.50162	−0.199924
$508$	−8.46414	−0.375535
$509$	−0.661999	−0.0293426	−0.0146713	−	0.999892i	$-0.504670\pi$
$509$	−0.661999	−0.0293426	−0.0146713	+	0.999892i	$0.504670\pi$
$510$	10.6356	0.470951
$511$	10.2731	0.454454
$512$	1.00000	0.0441942
$513$	−14.2770	−0.630344
$514$	7.82805	0.345281
$515$	14.1742	0.624590
$516$	−6.98787	−0.307624
$517$	−8.43610	−0.371019
$518$	−29.0159	−1.27489
$519$	37.5671	1.64901
$520$	−4.16101	−0.182473
$521$	13.3616	0.585382	0.292691	−	0.956207i	$-0.405449\pi$
$521$	13.3616	0.585382	0.292691	+	0.956207i	$0.405449\pi$
$522$	−37.5221	−1.64230
$523$	17.9280	0.783936	0.391968	−	0.919979i	$-0.371794\pi$
$523$	17.9280	0.783936	0.391968	+	0.919979i	$0.371794\pi$
$524$	−5.91934	−0.258588
$525$	37.9713	1.65720
$526$	15.1482	0.660495
$527$	17.1175	0.745648
$528$	−2.92605	−0.127340
$529$	−10.0736	−0.437984
$530$	8.30678	0.360824
$531$	−66.5912	−2.88981
$532$	6.48893	0.281331
$533$	−13.0467	−0.565114
$534$	11.2826	0.488246
$535$	13.5867	0.587402
$536$	1.98094	0.0855636
$537$	31.2657	1.34922
$538$	−28.7223	−1.23831
$539$	4.60665	0.198422
$540$	−8.18006	−0.352014
$541$	17.3260	0.744902	0.372451	−	0.928052i	$-0.378518\pi$
$541$	17.3260	0.744902	0.372451	+	0.928052i	$0.378518\pi$
$542$	2.87354	0.123429
$543$	55.6599	2.38859
$544$	−3.33073	−0.142804
$545$	11.1972	0.479637
$546$	38.0096	1.62666
$547$	−5.81643	−0.248692	−0.124346	−	0.992239i	$-0.539683\pi$
$547$	−5.81643	−0.248692	−0.124346	+	0.992239i	$0.539683\pi$
$548$	19.4957	0.832814
$549$	−38.0036	−1.62195
$550$	−3.80909	−0.162420
$551$	−12.8498	−0.547420
$552$	10.5201	0.447764
$553$	−50.5801	−2.15089
$554$	−5.34306	−0.227005
$555$	27.1959	1.15440
$556$	−14.1718	−0.601020
$557$	−17.1247	−0.725597	−0.362799	−	0.931868i	$-0.618179\pi$
$557$	−17.1247	−0.725597	−0.362799	+	0.931868i	$0.618179\pi$
$558$	−28.5832	−1.21002
$559$	−9.10591	−0.385139
$560$	3.71786	0.157108
$561$	9.74587	0.411471
$562$	4.20392	0.177332
$563$	−35.7758	−1.50777	−0.753884	−	0.657007i	$-0.771822\pi$
$563$	−35.7758	−1.50777	−0.753884	+	0.657007i	$0.771822\pi$
$564$	24.6844	1.03940
$565$	11.8879	0.500126
$566$	−15.0099	−0.630915
$567$	17.8783	0.750818
$568$	9.55385	0.400871
$569$	43.8830	1.83967	0.919836	−	0.392303i	$-0.128322\pi$
$569$	43.8830	1.83967	0.919836	+	0.392303i	$0.128322\pi$
$570$	−6.08192	−0.254744
$571$	−14.4751	−0.605765	−0.302882	−	0.953028i	$-0.597949\pi$
$571$	−14.4751	−0.605765	−0.302882	+	0.953028i	$0.597949\pi$
$572$	−3.81293	−0.159427
$573$	57.2300	2.39082
$574$	11.6572	0.486561
$575$	13.6949	0.571117
$576$	5.56174	0.231739
$577$	−25.4546	−1.05969	−0.529844	−	0.848095i	$-0.677749\pi$
$577$	−25.4546	−1.05969	−0.529844	+	0.848095i	$0.677749\pi$
$578$	−5.90624	−0.245667
$579$	−37.9237	−1.57606
$580$	−7.36235	−0.305705
$581$	−52.5056	−2.17830
$582$	−40.4039	−1.67480
$583$	7.61190	0.315253
$584$	3.01541	0.124779
$585$	−23.1425	−0.956824
$586$	−21.8303	−0.901803
$587$	34.7443	1.43405	0.717025	−	0.697048i	$-0.245503\pi$
$587$	34.7443	1.43405	0.717025	+	0.697048i	$0.245503\pi$
$588$	−13.4793	−0.555875
$589$	−9.78858	−0.403332
$590$	−13.0661	−0.537923
$591$	2.92605	0.120361
$592$	−8.51692	−0.350043
$593$	−21.2055	−0.870804	−0.435402	−	0.900236i	$-0.643394\pi$
$593$	−21.2055	−0.870804	−0.435402	+	0.900236i	$0.643394\pi$
$594$	−7.49577	−0.307555
$595$	−12.3832	−0.507662
$596$	−13.0701	−0.535374
$597$	60.8021	2.48847
$598$	13.7087	0.560592
$599$	13.7811	0.563081	0.281540	−	0.959549i	$-0.409155\pi$
$599$	13.7811	0.563081	0.281540	+	0.959549i	$0.409155\pi$
$600$	11.1456	0.455016
$601$	22.5117	0.918273	0.459136	−	0.888366i	$-0.348159\pi$
$601$	22.5117	0.918273	0.459136	+	0.888366i	$0.348159\pi$
$602$	8.13612	0.331603
$603$	11.0175	0.448666
$604$	−8.33031	−0.338955
$605$	1.09129	0.0443672
$606$	−35.5664	−1.44479
$607$	−30.0318	−1.21895	−0.609476	−	0.792805i	$-0.708620\pi$
$607$	−30.0318	−1.21895	−0.609476	+	0.792805i	$0.708620\pi$
$608$	1.90467	0.0772446
$609$	67.2529	2.72523
$610$	−7.45682	−0.301918
$611$	32.1663	1.30131
$612$	−18.5247	−0.748815
$613$	−15.3327	−0.619282	−0.309641	−	0.950854i	$-0.600209\pi$
$613$	−15.3327	−0.619282	−0.309641	+	0.950854i	$0.600209\pi$
$614$	3.87352	0.156322
$615$	−10.9260	−0.440579
$616$	3.40685	0.137266
$617$	47.8125	1.92486	0.962430	−	0.271530i	$-0.0875295\pi$
$617$	47.8125	1.92486	0.962430	+	0.271530i	$0.0875295\pi$
$618$	−38.0049	−1.52878
$619$	−6.38997	−0.256835	−0.128417	−	0.991720i	$-0.540990\pi$
$619$	−6.38997	−0.256835	−0.128417	+	0.991720i	$0.540990\pi$
$620$	−5.60841	−0.225239
$621$	26.9497	1.08146
$622$	−28.5791	−1.14592
$623$	−13.1366	−0.526306
$624$	11.1568	0.446630
$625$	8.55458	0.342183
$626$	15.8009	0.631529
$627$	−5.57315	−0.222570
$628$	−5.39025	−0.215094
$629$	28.3676	1.13109
$630$	20.6778	0.823823
$631$	40.5895	1.61584	0.807921	−	0.589291i	$-0.200593\pi$
$631$	40.5895	1.61584	0.807921	+	0.589291i	$0.200593\pi$
$632$	−14.8466	−0.590566
$633$	−14.8461	−0.590080
$634$	31.2948	1.24288
$635$	−9.23682	−0.366552
$636$	−22.2728	−0.883172
$637$	−17.5648	−0.695944
$638$	−6.74647	−0.267095
$639$	53.1361	2.10203
$640$	1.09129	0.0431370
$641$	38.5806	1.52384	0.761921	−	0.647670i	$-0.224256\pi$
$641$	38.5806	1.52384	0.761921	+	0.647670i	$0.224256\pi$
$642$	−36.4295	−1.43776
$643$	−37.2816	−1.47024	−0.735122	−	0.677935i	$-0.762875\pi$
$643$	−37.2816	−1.47024	−0.735122	+	0.677935i	$0.762875\pi$
$644$	−12.2487	−0.482668
$645$	−7.62579	−0.300265
$646$	−6.34394	−0.249599
$647$	−44.3022	−1.74170	−0.870849	−	0.491551i	$-0.836430\pi$
$647$	−44.3022	−1.74170	−0.870849	+	0.491551i	$0.836430\pi$
$648$	5.24774	0.206151
$649$	−11.9731	−0.469984
$650$	14.5238	0.569670
$651$	51.2312	2.00791
$652$	−10.6505	−0.417105
$653$	21.9958	0.860763	0.430382	−	0.902647i	$-0.358379\pi$
$653$	21.9958	0.860763	0.430382	+	0.902647i	$0.358379\pi$
$654$	−30.0228	−1.17399
$655$	−6.45971	−0.252402
$656$	3.42169	0.133594
$657$	16.7709	0.654297
$658$	−28.7405	−1.12042
$659$	12.3050	0.479333	0.239667	−	0.970855i	$-0.422962\pi$
$659$	12.3050	0.479333	0.239667	+	0.970855i	$0.422962\pi$
$660$	−3.19316	−0.124294
$661$	8.04859	0.313054	0.156527	−	0.987674i	$-0.449970\pi$
$661$	8.04859	0.313054	0.156527	+	0.987674i	$0.449970\pi$
$662$	9.07500	0.352710
$663$	−37.1603	−1.44319
$664$	−15.4118	−0.598093
$665$	7.08130	0.274601
$666$	−47.3689	−1.83551
$667$	24.2558	0.939187
$668$	−0.182834	−0.00707405
$669$	28.0519	1.08455
$670$	2.16178	0.0835168
$671$	−6.83304	−0.263787
$672$	−9.96861	−0.384547
$673$	−23.0447	−0.888307	−0.444154	−	0.895951i	$-0.646496\pi$
$673$	−23.0447	−0.888307	−0.444154	+	0.895951i	$0.646496\pi$
$674$	18.8308	0.725335
$675$	28.5521	1.09897
$676$	1.53846	0.0591717
$677$	−8.57839	−0.329694	−0.164847	−	0.986319i	$-0.552713\pi$
$677$	−8.57839	−0.329694	−0.164847	+	0.986319i	$0.552713\pi$
$678$	−31.8746	−1.22414
$679$	47.0431	1.80535
$680$	−3.63479	−0.139388
$681$	−43.9305	−1.68342
$682$	−5.13925	−0.196792
$683$	−23.2532	−0.889758	−0.444879	−	0.895591i	$-0.646753\pi$
$683$	−23.2532	−0.889758	−0.444879	+	0.895591i	$0.646753\pi$
$684$	10.5933	0.405044
$685$	21.2754	0.812892
$686$	−8.15381	−0.311314
$687$	−25.1877	−0.960970
$688$	2.38816	0.0910478
$689$	−29.0237	−1.10571
$690$	11.4805	0.437053
$691$	−9.47549	−0.360464	−0.180232	−	0.983624i	$-0.557685\pi$
$691$	−9.47549	−0.360464	−0.180232	+	0.983624i	$0.557685\pi$
$692$	−12.8389	−0.488060
$693$	18.9480	0.719776
$694$	3.83527	0.145585
$695$	−15.4656	−0.586643
$696$	19.7405	0.748261
$697$	−11.3967	−0.431681
$698$	22.8146	0.863544
$699$	−22.0975	−0.835803
$700$	−12.9770	−0.490484
$701$	−34.4153	−1.29985	−0.649924	−	0.760000i	$-0.725199\pi$
$701$	−34.4153	−1.29985	−0.649924	+	0.760000i	$0.725199\pi$
$702$	28.5809	1.07872
$703$	−16.2219	−0.611821
$704$	1.00000	0.0376889
$705$	26.9378	1.01454
$706$	19.9157	0.749536
$707$	41.4106	1.55741
$708$	35.0338	1.31665
$709$	−11.1175	−0.417527	−0.208763	−	0.977966i	$-0.566944\pi$
$709$	−11.1175	−0.417527	−0.208763	+	0.977966i	$0.566944\pi$
$710$	10.4260	0.391281
$711$	−82.5729	−3.09673
$712$	−3.85593	−0.144507
$713$	18.4773	0.691980
$714$	33.2027	1.24258
$715$	−4.16101	−0.155613
$716$	−10.6853	−0.399329
$717$	18.4754	0.689977
$718$	3.95962	0.147772
$719$	43.7015	1.62979	0.814896	−	0.579607i	$-0.196794\pi$
$719$	43.7015	1.62979	0.814896	+	0.579607i	$0.196794\pi$
$720$	6.06947	0.226196
$721$	44.2499	1.64795
$722$	−15.3722	−0.572095
$723$	−44.7078	−1.66270
$724$	−19.0222	−0.706955
$725$	25.6979	0.954396
$726$	−2.92605	−0.108596
$727$	3.13666	0.116332	0.0581661	−	0.998307i	$-0.481475\pi$
$727$	3.13666	0.116332	0.0581661	+	0.998307i	$0.481475\pi$
$728$	−12.9901	−0.481445
$729$	−36.6123	−1.35601
$730$	3.29069	0.121794
$731$	−7.95432	−0.294201
$732$	19.9938	0.738992
$733$	18.3582	0.678077	0.339038	−	0.940773i	$-0.389898\pi$
$733$	18.3582	0.678077	0.339038	+	0.940773i	$0.389898\pi$
$734$	−32.0595	−1.18334
$735$	−14.7098	−0.542578
$736$	−3.59532	−0.132525
$737$	1.98094	0.0729688
$738$	19.0305	0.700524
$739$	−21.9964	−0.809150	−0.404575	−	0.914505i	$-0.632581\pi$
$739$	−21.9964	−0.809150	−0.404575	+	0.914505i	$0.632581\pi$
$740$	−9.29442	−0.341670
$741$	21.2501	0.780640
$742$	25.9326	0.952016
$743$	46.8012	1.71697	0.858484	−	0.512840i	$-0.171407\pi$
$743$	46.8012	1.71697	0.858484	+	0.512840i	$0.171407\pi$
$744$	15.0377	0.551308
$745$	−14.2633	−0.522567
$746$	−11.9222	−0.436504
$747$	−85.7163	−3.13620
$748$	−3.33073	−0.121784
$749$	42.4156	1.54983
$750$	28.1288	1.02712
$751$	−15.7389	−0.574321	−0.287160	−	0.957882i	$-0.592711\pi$
$751$	−15.7389	−0.574321	−0.287160	+	0.957882i	$0.592711\pi$
$752$	−8.43610	−0.307633
$753$	−50.8203	−1.85200
$754$	25.7238	0.936807
$755$	−9.09078	−0.330847
$756$	−25.5370	−0.928771
$757$	10.0184	0.364126	0.182063	−	0.983287i	$-0.441723\pi$
$757$	10.0184	0.364126	0.182063	+	0.983287i	$0.441723\pi$
$758$	−7.46839	−0.271264
$759$	10.5201	0.381855
$760$	2.07855	0.0753968
$761$	−21.0742	−0.763939	−0.381969	−	0.924175i	$-0.624754\pi$
$761$	−21.0742	−0.763939	−0.381969	+	0.924175i	$0.624754\pi$
$762$	24.7665	0.897194
$763$	34.9562	1.26550
$764$	−19.5588	−0.707614
$765$	−20.2158	−0.730903
$766$	28.8972	1.04410
$767$	45.6525	1.64842
$768$	−2.92605	−0.105585
$769$	−1.58836	−0.0572777	−0.0286388	−	0.999590i	$-0.509117\pi$
$769$	−1.58836	−0.0572777	−0.0286388	+	0.999590i	$0.509117\pi$
$770$	3.71786	0.133982
$771$	−22.9052	−0.824912
$772$	12.9607	0.466467
$773$	−42.4001	−1.52503	−0.762513	−	0.646973i	$-0.776035\pi$
$773$	−42.4001	−1.52503	−0.762513	+	0.646973i	$0.776035\pi$
$774$	13.2823	0.477424
$775$	19.5759	0.703186
$776$	13.8084	0.495692
$777$	84.9018	3.04584
$778$	17.2563	0.618669
$779$	6.51719	0.233502
$780$	12.1753	0.435946
$781$	9.55385	0.341864
$782$	11.9751	0.428227
$783$	50.5700	1.80722
$784$	4.60665	0.164523
$785$	−5.88232	−0.209949
$786$	17.3203	0.617793
$787$	−15.6432	−0.557621	−0.278810	−	0.960346i	$-0.589940\pi$
$787$	−15.6432	−0.557621	−0.278810	+	0.960346i	$0.589940\pi$
$788$	−1.00000	−0.0356235
$789$	−44.3245	−1.57799
$790$	−16.2019	−0.576439
$791$	37.1123	1.31956
$792$	5.56174	0.197628
$793$	26.0539	0.925202
$794$	5.19478	0.184356
$795$	−24.3060	−0.862046
$796$	−20.7796	−0.736514
$797$	−14.6949	−0.520522	−0.260261	−	0.965538i	$-0.583809\pi$
$797$	−14.6949	−0.520522	−0.260261	+	0.965538i	$0.583809\pi$
$798$	−18.9869	−0.672129
$799$	28.0984	0.994049
$800$	−3.80909	−0.134672
$801$	−21.4457	−0.757745
$802$	25.8128	0.911481
$803$	3.01541	0.106412
$804$	−5.79632	−0.204420
$805$	−13.3669	−0.471122
$806$	19.5956	0.690227
$807$	84.0428	2.95845
$808$	12.1551	0.427615
$809$	11.6877	0.410918	0.205459	−	0.978666i	$-0.434131\pi$
$809$	11.6877	0.410918	0.205459	+	0.978666i	$0.434131\pi$
$810$	5.72681	0.201220
$811$	−24.3194	−0.853970	−0.426985	−	0.904259i	$-0.640424\pi$
$811$	−24.3194	−0.853970	−0.426985	+	0.904259i	$0.640424\pi$
$812$	−22.9842	−0.806588
$813$	−8.40812	−0.294885
$814$	−8.51692	−0.298518
$815$	−11.6228	−0.407128
$816$	9.74587	0.341174
$817$	4.54866	0.159138
$818$	14.3648	0.502254
$819$	−72.2476	−2.52454
$820$	3.73405	0.130399
$821$	−30.2768	−1.05667	−0.528334	−	0.849037i	$-0.677183\pi$
$821$	−30.2768	−1.05667	−0.528334	+	0.849037i	$0.677183\pi$
$822$	−57.0452	−1.98968
$823$	−39.0942	−1.36274	−0.681369	−	0.731940i	$-0.738615\pi$
$823$	−39.0942	−1.36274	−0.681369	+	0.731940i	$0.738615\pi$
$824$	12.9885	0.452476
$825$	11.1456	0.388039
$826$	−40.7905	−1.41928
$827$	−8.02761	−0.279148	−0.139574	−	0.990212i	$-0.544573\pi$
$827$	−8.02761	−0.279148	−0.139574	+	0.990212i	$0.544573\pi$
$828$	−19.9963	−0.694918
$829$	−19.0935	−0.663144	−0.331572	−	0.943430i	$-0.607579\pi$
$829$	−19.0935	−0.663144	−0.331572	+	0.943430i	$0.607579\pi$
$830$	−16.8187	−0.583786
$831$	15.6340	0.542339
$832$	−3.81293	−0.132190
$833$	−15.3435	−0.531620
$834$	41.4675	1.43590
$835$	−0.199525	−0.00690483
$836$	1.90467	0.0658744
$837$	38.5227	1.33154
$838$	13.6428	0.471283
$839$	−46.2853	−1.59795	−0.798973	−	0.601367i	$-0.794623\pi$
$839$	−46.2853	−1.59795	−0.798973	+	0.601367i	$0.794623\pi$
$840$	−10.8786	−0.375349
$841$	16.5149	0.569478
$842$	−22.2159	−0.765611
$843$	−12.3009	−0.423664
$844$	5.07378	0.174647
$845$	1.67891	0.0577562
$846$	−46.9194	−1.61312
$847$	3.40685	0.117061
$848$	7.61190	0.261394
$849$	43.9198	1.50732
$850$	12.6870	0.435162
$851$	30.6211	1.04968
$852$	−27.9550	−0.957723
$853$	−56.8509	−1.94654	−0.973269	−	0.229669i	$-0.926236\pi$
$853$	−56.8509	−1.94654	−0.973269	+	0.229669i	$0.926236\pi$
$854$	−23.2792	−0.796597
$855$	11.5603	0.395355
$856$	12.4501	0.425535
$857$	14.1015	0.481698	0.240849	−	0.970563i	$-0.422574\pi$
$857$	14.1015	0.481698	0.240849	+	0.970563i	$0.422574\pi$
$858$	11.1568	0.380887
$859$	−45.8974	−1.56600	−0.783000	−	0.622022i	$-0.786311\pi$
$859$	−45.8974	−1.56600	−0.783000	+	0.622022i	$0.786311\pi$
$860$	2.60618	0.0888699
$861$	−34.1095	−1.16245
$862$	−12.5862	−0.428688
$863$	33.9194	1.15463	0.577316	−	0.816521i	$-0.304100\pi$
$863$	33.9194	1.15463	0.577316	+	0.816521i	$0.304100\pi$
$864$	−7.49577	−0.255011
$865$	−14.0109	−0.476385
$866$	15.1588	0.515117
$867$	17.2819	0.586925
$868$	−17.5087	−0.594283
$869$	−14.8466	−0.503636
$870$	21.5426	0.730362
$871$	−7.55319	−0.255930
$872$	10.2606	0.347466
$873$	76.7986	2.59924
$874$	−6.84791	−0.231634
$875$	−32.7510	−1.10719
$876$	−8.82324	−0.298109
$877$	34.9999	1.18186	0.590931	−	0.806722i	$-0.298761\pi$
$877$	34.9999	1.18186	0.590931	+	0.806722i	$0.298761\pi$
$878$	13.9874	0.472052
$879$	63.8766	2.15450
$880$	1.09129	0.0367874
$881$	26.6454	0.897706	0.448853	−	0.893606i	$-0.351833\pi$
$881$	26.6454	0.897706	0.448853	+	0.893606i	$0.351833\pi$
$882$	25.6210	0.862703
$883$	26.1825	0.881112	0.440556	−	0.897725i	$-0.354781\pi$
$883$	26.1825	0.881112	0.440556	+	0.897725i	$0.354781\pi$
$884$	12.6999	0.427142
$885$	38.2320	1.28515
$886$	−18.2935	−0.614581
$887$	17.3894	0.583878	0.291939	−	0.956437i	$-0.405700\pi$
$887$	17.3894	0.583878	0.291939	+	0.956437i	$0.405700\pi$
$888$	24.9209	0.836290
$889$	−28.8361	−0.967131
$890$	−4.20793	−0.141050
$891$	5.24774	0.175806
$892$	−9.58698	−0.320996
$893$	−16.0680	−0.537695
$894$	38.2438	1.27907
$895$	−11.6608	−0.389777
$896$	3.40685	0.113815
$897$	−40.1124	−1.33931
$898$	−35.2073	−1.17488
$899$	34.6718	1.15637
$900$	−21.1852	−0.706172
$901$	−25.3532	−0.844637
$902$	3.42169	0.113930
$903$	−23.8066	−0.792236
$904$	10.8934	0.362310
$905$	−20.7587	−0.690044
$906$	24.3749	0.809800
$907$	3.04219	0.101014	0.0505072	−	0.998724i	$-0.483916\pi$
$907$	3.04219	0.101014	0.0505072	+	0.998724i	$0.483916\pi$
$908$	15.0136	0.498244
$909$	67.6035	2.24227
$910$	−14.1760	−0.469929
$911$	17.9870	0.595936	0.297968	−	0.954576i	$-0.403691\pi$
$911$	17.9870	0.595936	0.297968	+	0.954576i	$0.403691\pi$
$912$	−5.57315	−0.184545
$913$	−15.4118	−0.510055
$914$	−34.5517	−1.14287
$915$	21.8190	0.721314
$916$	8.60810	0.284420
$917$	−20.1663	−0.665951
$918$	24.9664	0.824014
$919$	−27.6080	−0.910704	−0.455352	−	0.890312i	$-0.650487\pi$
$919$	−27.6080	−0.910704	−0.455352	+	0.890312i	$0.650487\pi$
$920$	−3.92354	−0.129355
$921$	−11.3341	−0.373471
$922$	−38.9173	−1.28167
$923$	−36.4282	−1.19905
$924$	−9.96861	−0.327943
$925$	32.4417	1.06668
$926$	8.89641	0.292354
$927$	72.2387	2.37263
$928$	−6.74647	−0.221464
$929$	27.1756	0.891604	0.445802	−	0.895132i	$-0.352919\pi$
$929$	27.1756	0.891604	0.445802	+	0.895132i	$0.352919\pi$
$930$	16.4105	0.538121
$931$	8.77414	0.287561
$932$	7.55199	0.247374
$933$	83.6237	2.73772
$934$	−3.34932	−0.109593
$935$	−3.63479	−0.118870
$936$	−21.2066	−0.693158
$937$	−11.8659	−0.387642	−0.193821	−	0.981037i	$-0.562088\pi$
$937$	−11.8659	−0.387642	−0.193821	+	0.981037i	$0.562088\pi$
$938$	6.74877	0.220355
$939$	−46.2340	−1.50879
$940$	−9.20622	−0.300274
$941$	−32.6287	−1.06366	−0.531832	−	0.846850i	$-0.678496\pi$
$941$	−32.6287	−1.06366	−0.531832	+	0.846850i	$0.678496\pi$
$942$	15.7721	0.513883
$943$	−12.3021	−0.400611
$944$	−11.9731	−0.389690
$945$	−27.8682	−0.906554
$946$	2.38816	0.0776459
$947$	21.5267	0.699524	0.349762	−	0.936839i	$-0.386263\pi$
$947$	21.5267	0.699524	0.349762	+	0.936839i	$0.386263\pi$
$948$	43.4418	1.41092
$949$	−11.4976	−0.373227
$950$	−7.25506	−0.235385
$951$	−91.5701	−2.96936
$952$	−11.3473	−0.367768
$953$	9.50415	0.307870	0.153935	−	0.988081i	$-0.450805\pi$
$953$	9.50415	0.307870	0.153935	+	0.988081i	$0.450805\pi$
$954$	42.3354	1.37066
$955$	−21.3443	−0.690687
$956$	−6.31413	−0.204214
$957$	19.7405	0.638119
$958$	0.887412	0.0286710
$959$	66.4189	2.14478
$960$	−3.19316	−0.103059
$961$	−4.58808	−0.148002
$962$	32.4745	1.04702
$963$	69.2442	2.23136
$964$	15.2793	0.492112
$965$	14.1439	0.455309
$966$	35.8404	1.15315
$967$	48.3667	1.55537	0.777684	−	0.628655i	$-0.216394\pi$
$967$	48.3667	1.55537	0.777684	+	0.628655i	$0.216394\pi$
$968$	1.00000	0.0321412
$969$	18.5627	0.596319
$970$	15.0689	0.483834
$971$	46.8873	1.50468	0.752342	−	0.658773i	$-0.228924\pi$
$971$	46.8873	1.50468	0.752342	+	0.658773i	$0.228924\pi$
$972$	7.13218	0.228765
$973$	−48.2814	−1.54783
$974$	28.7939	0.922616
$975$	−42.4973	−1.36100
$976$	−6.83304	−0.218720
$977$	−23.3877	−0.748240	−0.374120	−	0.927380i	$-0.622055\pi$
$977$	−23.3877	−0.748240	−0.374120	+	0.927380i	$0.622055\pi$
$978$	31.1638	0.996509
$979$	−3.85593	−0.123236
$980$	5.02718	0.160587
$981$	57.0665	1.82199
$982$	20.3846	0.650498
$983$	−30.3619	−0.968395	−0.484197	−	0.874959i	$-0.660888\pi$
$983$	−30.3619	−0.968395	−0.484197	+	0.874959i	$0.660888\pi$
$984$	−10.0120	−0.319171
$985$	−1.09129	−0.0347714
$986$	22.4707	0.715612
$987$	84.0961	2.67681
$988$	−7.26238	−0.231047
$989$	−8.58622	−0.273026
$990$	6.06947	0.192900
$991$	47.0889	1.49583	0.747914	−	0.663795i	$-0.231055\pi$
$991$	47.0889	1.49583	0.747914	+	0.663795i	$0.231055\pi$
$992$	−5.13925	−0.163171
$993$	−26.5539	−0.842661
$994$	32.5486	1.03238
$995$	−22.6766	−0.718896
$996$	45.0955	1.42891
$997$	−15.9992	−0.506699	−0.253349	−	0.967375i	$-0.581532\pi$
$997$	−15.9992	−0.506699	−0.253349	+	0.967375i	$0.581532\pi$
$998$	13.8221	0.437532
$999$	63.8409	2.01984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.b.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.92605 q^{3} +1.00000 q^{4} +1.09129 q^{5} -2.92605 q^{6} +3.40685 q^{7} +1.00000 q^{8} +5.56174 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.92605 q^{3} +1.00000 q^{4} +1.09129 q^{5} -2.92605 q^{6} +3.40685 q^{7} +1.00000 q^{8} +5.56174 q^{9} +1.09129 q^{10} +1.00000 q^{11} -2.92605 q^{12} -3.81293 q^{13} +3.40685 q^{14} -3.19316 q^{15} +1.00000 q^{16} -3.33073 q^{17} +5.56174 q^{18} +1.90467 q^{19} +1.09129 q^{20} -9.96861 q^{21} +1.00000 q^{22} -3.59532 q^{23} -2.92605 q^{24} -3.80909 q^{25} -3.81293 q^{26} -7.49577 q^{27} +3.40685 q^{28} -6.74647 q^{29} -3.19316 q^{30} -5.13925 q^{31} +1.00000 q^{32} -2.92605 q^{33} -3.33073 q^{34} +3.71786 q^{35} +5.56174 q^{36} -8.51692 q^{37} +1.90467 q^{38} +11.1568 q^{39} +1.09129 q^{40} +3.42169 q^{41} -9.96861 q^{42} +2.38816 q^{43} +1.00000 q^{44} +6.06947 q^{45} -3.59532 q^{46} -8.43610 q^{47} -2.92605 q^{48} +4.60665 q^{49} -3.80909 q^{50} +9.74587 q^{51} -3.81293 q^{52} +7.61190 q^{53} -7.49577 q^{54} +1.09129 q^{55} +3.40685 q^{56} -5.57315 q^{57} -6.74647 q^{58} -11.9731 q^{59} -3.19316 q^{60} -6.83304 q^{61} -5.13925 q^{62} +18.9480 q^{63} +1.00000 q^{64} -4.16101 q^{65} -2.92605 q^{66} +1.98094 q^{67} -3.33073 q^{68} +10.5201 q^{69} +3.71786 q^{70} +9.55385 q^{71} +5.56174 q^{72} +3.01541 q^{73} -8.51692 q^{74} +11.1456 q^{75} +1.90467 q^{76} +3.40685 q^{77} +11.1568 q^{78} -14.8466 q^{79} +1.09129 q^{80} +5.24774 q^{81} +3.42169 q^{82} -15.4118 q^{83} -9.96861 q^{84} -3.63479 q^{85} +2.38816 q^{86} +19.7405 q^{87} +1.00000 q^{88} -3.85593 q^{89} +6.06947 q^{90} -12.9901 q^{91} -3.59532 q^{92} +15.0377 q^{93} -8.43610 q^{94} +2.07855 q^{95} -2.92605 q^{96} +13.8084 q^{97} +4.60665 q^{98} +5.56174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

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