LMFDB - Embedded newform 8034.2.a.v.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 $ x^11 - 5x^10 - 31x^9 + 168x^8 + 300x^7 - 1928x^6 - 736x^5 + 8532x^4 - 2065x^3 - 10494x^2 + 4024x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.14620$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.14620 q^{5} +1.00000 q^{6} +1.95604 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.14620 q^{5} +1.00000 q^{6} +1.95604 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.14620 q^{10} +4.29438 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.95604 q^{14} +3.14620 q^{15} +1.00000 q^{16} +1.01228 q^{17} +1.00000 q^{18} +0.956039 q^{19} +3.14620 q^{20} +1.95604 q^{21} +4.29438 q^{22} +4.90169 q^{23} +1.00000 q^{24} +4.89857 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.95604 q^{28} -7.40639 q^{29} +3.14620 q^{30} -0.956039 q^{31} +1.00000 q^{32} +4.29438 q^{33} +1.01228 q^{34} +6.15409 q^{35} +1.00000 q^{36} +0.238604 q^{37} +0.956039 q^{38} +1.00000 q^{39} +3.14620 q^{40} -7.48071 q^{41} +1.95604 q^{42} -6.52182 q^{43} +4.29438 q^{44} +3.14620 q^{45} +4.90169 q^{46} +6.09973 q^{47} +1.00000 q^{48} -3.17391 q^{49} +4.89857 q^{50} +1.01228 q^{51} +1.00000 q^{52} -2.16434 q^{53} +1.00000 q^{54} +13.5110 q^{55} +1.95604 q^{56} +0.956039 q^{57} -7.40639 q^{58} -14.3481 q^{59} +3.14620 q^{60} +7.32293 q^{61} -0.956039 q^{62} +1.95604 q^{63} +1.00000 q^{64} +3.14620 q^{65} +4.29438 q^{66} -0.0784225 q^{67} +1.01228 q^{68} +4.90169 q^{69} +6.15409 q^{70} +16.2104 q^{71} +1.00000 q^{72} -15.2429 q^{73} +0.238604 q^{74} +4.89857 q^{75} +0.956039 q^{76} +8.39997 q^{77} +1.00000 q^{78} -3.19294 q^{79} +3.14620 q^{80} +1.00000 q^{81} -7.48071 q^{82} -15.3915 q^{83} +1.95604 q^{84} +3.18484 q^{85} -6.52182 q^{86} -7.40639 q^{87} +4.29438 q^{88} -12.6337 q^{89} +3.14620 q^{90} +1.95604 q^{91} +4.90169 q^{92} -0.956039 q^{93} +6.09973 q^{94} +3.00789 q^{95} +1.00000 q^{96} -8.34288 q^{97} -3.17391 q^{98} +4.29438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.14620	1.40702	0.703511	−	0.710684i	$-0.251614\pi$
$5$	3.14620	1.40702	0.703511	+	0.710684i	$0.251614\pi$
$6$	1.00000	0.408248
$7$	1.95604	0.739313	0.369657	−	0.929168i	$-0.379475\pi$
$7$	1.95604	0.739313	0.369657	+	0.929168i	$0.379475\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.14620	0.994915
$11$	4.29438	1.29480	0.647402	−	0.762149i	$-0.275856\pi$
$11$	4.29438	1.29480	0.647402	+	0.762149i	$0.275856\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.95604	0.522773
$15$	3.14620	0.812345
$16$	1.00000	0.250000
$17$	1.01228	0.245514	0.122757	−	0.992437i	$-0.460826\pi$
$17$	1.01228	0.245514	0.122757	+	0.992437i	$0.460826\pi$
$18$	1.00000	0.235702
$19$	0.956039	0.219330	0.109665	−	0.993969i	$-0.465022\pi$
$19$	0.956039	0.219330	0.109665	+	0.993969i	$0.465022\pi$
$20$	3.14620	0.703511
$21$	1.95604	0.426843
$22$	4.29438	0.915564
$23$	4.90169	1.02207	0.511036	−	0.859559i	$-0.329262\pi$
$23$	4.90169	1.02207	0.511036	+	0.859559i	$0.329262\pi$
$24$	1.00000	0.204124
$25$	4.89857	0.979714
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	1.95604	0.369657
$29$	−7.40639	−1.37533	−0.687666	−	0.726027i	$-0.741365\pi$
$29$	−7.40639	−1.37533	−0.687666	+	0.726027i	$0.741365\pi$
$30$	3.14620	0.574415
$31$	−0.956039	−0.171710	−0.0858548	−	0.996308i	$-0.527362\pi$
$31$	−0.956039	−0.171710	−0.0858548	+	0.996308i	$0.527362\pi$
$32$	1.00000	0.176777
$33$	4.29438	0.747555
$34$	1.01228	0.173605
$35$	6.15409	1.04023
$36$	1.00000	0.166667
$37$	0.238604	0.0392263	0.0196131	−	0.999808i	$-0.493757\pi$
$37$	0.238604	0.0392263	0.0196131	+	0.999808i	$0.493757\pi$
$38$	0.956039	0.155090
$39$	1.00000	0.160128
$40$	3.14620	0.497458
$41$	−7.48071	−1.16829	−0.584146	−	0.811649i	$-0.698570\pi$
$41$	−7.48071	−1.16829	−0.584146	+	0.811649i	$0.698570\pi$
$42$	1.95604	0.301823
$43$	−6.52182	−0.994569	−0.497284	−	0.867588i	$-0.665669\pi$
$43$	−6.52182	−0.994569	−0.497284	+	0.867588i	$0.665669\pi$
$44$	4.29438	0.647402
$45$	3.14620	0.469008
$46$	4.90169	0.722714
$47$	6.09973	0.889738	0.444869	−	0.895596i	$-0.353250\pi$
$47$	6.09973	0.889738	0.444869	+	0.895596i	$0.353250\pi$
$48$	1.00000	0.144338
$49$	−3.17391	−0.453416
$50$	4.89857	0.692762
$51$	1.01228	0.141748
$52$	1.00000	0.138675
$53$	−2.16434	−0.297295	−0.148647	−	0.988890i	$-0.547492\pi$
$53$	−2.16434	−0.297295	−0.148647	+	0.988890i	$0.547492\pi$
$54$	1.00000	0.136083
$55$	13.5110	1.82182
$56$	1.95604	0.261387
$57$	0.956039	0.126630
$58$	−7.40639	−0.972507
$59$	−14.3481	−1.86797	−0.933983	−	0.357318i	$-0.883691\pi$
$59$	−14.3481	−1.86797	−0.933983	+	0.357318i	$0.883691\pi$
$60$	3.14620	0.406173
$61$	7.32293	0.937606	0.468803	−	0.883303i	$-0.344685\pi$
$61$	7.32293	0.937606	0.468803	+	0.883303i	$0.344685\pi$
$62$	−0.956039	−0.121417
$63$	1.95604	0.246438
$64$	1.00000	0.125000
$65$	3.14620	0.390238
$66$	4.29438	0.528601
$67$	−0.0784225	−0.00958084	−0.00479042	−	0.999989i	$-0.501525\pi$
$67$	−0.0784225	−0.00958084	−0.00479042	+	0.999989i	$0.501525\pi$
$68$	1.01228	0.122757
$69$	4.90169	0.590094
$70$	6.15409	0.735554
$71$	16.2104	1.92382	0.961909	−	0.273370i	$-0.0881384\pi$
$71$	16.2104	1.92382	0.961909	+	0.273370i	$0.0881384\pi$
$72$	1.00000	0.117851
$73$	−15.2429	−1.78404	−0.892021	−	0.451994i	$-0.850713\pi$
$73$	−15.2429	−1.78404	−0.892021	+	0.451994i	$0.850713\pi$
$74$	0.238604	0.0277372
$75$	4.89857	0.565638
$76$	0.956039	0.109665
$77$	8.39997	0.957265
$78$	1.00000	0.113228
$79$	−3.19294	−0.359234	−0.179617	−	0.983737i	$-0.557486\pi$
$79$	−3.19294	−0.359234	−0.179617	+	0.983737i	$0.557486\pi$
$80$	3.14620	0.351756
$81$	1.00000	0.111111
$82$	−7.48071	−0.826107
$83$	−15.3915	−1.68944	−0.844719	−	0.535210i	$-0.820233\pi$
$83$	−15.3915	−1.68944	−0.844719	+	0.535210i	$0.820233\pi$
$84$	1.95604	0.213421
$85$	3.18484	0.345444
$86$	−6.52182	−0.703266
$87$	−7.40639	−0.794048
$88$	4.29438	0.457782
$89$	−12.6337	−1.33917	−0.669583	−	0.742737i	$-0.733527\pi$
$89$	−12.6337	−1.33917	−0.669583	+	0.742737i	$0.733527\pi$
$90$	3.14620	0.331638
$91$	1.95604	0.205049
$92$	4.90169	0.511036
$93$	−0.956039	−0.0991366
$94$	6.09973	0.629139
$95$	3.00789	0.308603
$96$	1.00000	0.102062
$97$	−8.34288	−0.847091	−0.423546	−	0.905875i	$-0.639215\pi$
$97$	−8.34288	−0.847091	−0.423546	+	0.905875i	$0.639215\pi$
$98$	−3.17391	−0.320614
$99$	4.29438	0.431601
$100$	4.89857	0.489857
$101$	1.77842	0.176959	0.0884796	−	0.996078i	$-0.471799\pi$
$101$	1.77842	0.176959	0.0884796	+	0.996078i	$0.471799\pi$
$102$	1.01228	0.100231
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	6.15409	0.600577
$106$	−2.16434	−0.210219
$107$	−1.01223	−0.0978560	−0.0489280	−	0.998802i	$-0.515580\pi$
$107$	−1.01223	−0.0978560	−0.0489280	+	0.998802i	$0.515580\pi$
$108$	1.00000	0.0962250
$109$	8.63138	0.826736	0.413368	−	0.910564i	$-0.364352\pi$
$109$	8.63138	0.826736	0.413368	+	0.910564i	$0.364352\pi$
$110$	13.5110	1.28822
$111$	0.238604	0.0226473
$112$	1.95604	0.184828
$113$	−5.27694	−0.496413	−0.248207	−	0.968707i	$-0.579841\pi$
$113$	−5.27694	−0.496413	−0.248207	+	0.968707i	$0.579841\pi$
$114$	0.956039	0.0895412
$115$	15.4217	1.43808
$116$	−7.40639	−0.687666
$117$	1.00000	0.0924500
$118$	−14.3481	−1.32085
$119$	1.98006	0.181512
$120$	3.14620	0.287207
$121$	7.44167	0.676515
$122$	7.32293	0.662987
$123$	−7.48071	−0.674513
$124$	−0.956039	−0.0858548
$125$	−0.319125	−0.0285434
$126$	1.95604	0.174258
$127$	−8.89405	−0.789220	−0.394610	−	0.918849i	$-0.629120\pi$
$127$	−8.89405	−0.789220	−0.394610	+	0.918849i	$0.629120\pi$
$128$	1.00000	0.0883883
$129$	−6.52182	−0.574215
$130$	3.14620	0.275940
$131$	−10.0670	−0.879554	−0.439777	−	0.898107i	$-0.644943\pi$
$131$	−10.0670	−0.879554	−0.439777	+	0.898107i	$0.644943\pi$
$132$	4.29438	0.373777
$133$	1.87005	0.162154
$134$	−0.0784225	−0.00677467
$135$	3.14620	0.270782
$136$	1.01228	0.0868024
$137$	−9.77328	−0.834988	−0.417494	−	0.908680i	$-0.637091\pi$
$137$	−9.77328	−0.834988	−0.417494	+	0.908680i	$0.637091\pi$
$138$	4.90169	0.417259
$139$	−14.6247	−1.24045	−0.620224	−	0.784424i	$-0.712958\pi$
$139$	−14.6247	−1.24045	−0.620224	+	0.784424i	$0.712958\pi$
$140$	6.15409	0.520115
$141$	6.09973	0.513690
$142$	16.2104	1.36034
$143$	4.29438	0.359114
$144$	1.00000	0.0833333
$145$	−23.3020	−1.93512
$146$	−15.2429	−1.26151
$147$	−3.17391	−0.261780
$148$	0.238604	0.0196131
$149$	−6.70964	−0.549675	−0.274837	−	0.961491i	$-0.588624\pi$
$149$	−6.70964	−0.549675	−0.274837	+	0.961491i	$0.588624\pi$
$150$	4.89857	0.399966
$151$	20.0596	1.63243	0.816214	−	0.577750i	$-0.196069\pi$
$151$	20.0596	1.63243	0.816214	+	0.577750i	$0.196069\pi$
$152$	0.956039	0.0775450
$153$	1.01228	0.0818380
$154$	8.39997	0.676889
$155$	−3.00789	−0.241599
$156$	1.00000	0.0800641
$157$	−11.4648	−0.914987	−0.457494	−	0.889213i	$-0.651253\pi$
$157$	−11.4648	−0.914987	−0.457494	+	0.889213i	$0.651253\pi$
$158$	−3.19294	−0.254017
$159$	−2.16434	−0.171643
$160$	3.14620	0.248729
$161$	9.58789	0.755631
$162$	1.00000	0.0785674
$163$	2.39010	0.187207	0.0936035	−	0.995610i	$-0.470161\pi$
$163$	2.39010	0.187207	0.0936035	+	0.995610i	$0.470161\pi$
$164$	−7.48071	−0.584146
$165$	13.5110	1.05183
$166$	−15.3915	−1.19461
$167$	−4.92491	−0.381101	−0.190550	−	0.981677i	$-0.561027\pi$
$167$	−4.92491	−0.381101	−0.190550	+	0.981677i	$0.561027\pi$
$168$	1.95604	0.150912
$169$	1.00000	0.0769231
$170$	3.18484	0.244266
$171$	0.956039	0.0731101
$172$	−6.52182	−0.497284
$173$	17.4627	1.32766	0.663831	−	0.747883i	$-0.268929\pi$
$173$	17.4627	1.32766	0.663831	+	0.747883i	$0.268929\pi$
$174$	−7.40639	−0.561477
$175$	9.58179	0.724315
$176$	4.29438	0.323701
$177$	−14.3481	−1.07847
$178$	−12.6337	−0.946933
$179$	2.55721	0.191135	0.0955675	−	0.995423i	$-0.469533\pi$
$179$	2.55721	0.191135	0.0955675	+	0.995423i	$0.469533\pi$
$180$	3.14620	0.234504
$181$	6.11866	0.454797	0.227398	−	0.973802i	$-0.426978\pi$
$181$	6.11866	0.454797	0.227398	+	0.973802i	$0.426978\pi$
$182$	1.95604	0.144991
$183$	7.32293	0.541327
$184$	4.90169	0.361357
$185$	0.750696	0.0551923
$186$	−0.956039	−0.0701002
$187$	4.34711	0.317892
$188$	6.09973	0.444869
$189$	1.95604	0.142281
$190$	3.00789	0.218215
$191$	4.58071	0.331449	0.165724	−	0.986172i	$-0.447004\pi$
$191$	4.58071	0.331449	0.165724	+	0.986172i	$0.447004\pi$
$192$	1.00000	0.0721688
$193$	−2.95689	−0.212842	−0.106421	−	0.994321i	$-0.533939\pi$
$193$	−2.95689	−0.212842	−0.106421	+	0.994321i	$0.533939\pi$
$194$	−8.34288	−0.598984
$195$	3.14620	0.225304
$196$	−3.17391	−0.226708
$197$	16.8665	1.20169	0.600843	−	0.799367i	$-0.294832\pi$
$197$	16.8665	1.20169	0.600843	+	0.799367i	$0.294832\pi$
$198$	4.29438	0.305188
$199$	9.11100	0.645861	0.322931	−	0.946423i	$-0.395332\pi$
$199$	9.11100	0.645861	0.322931	+	0.946423i	$0.395332\pi$
$200$	4.89857	0.346381
$201$	−0.0784225	−0.00553150
$202$	1.77842	0.125129
$203$	−14.4872	−1.01680
$204$	1.01228	0.0708738
$205$	−23.5358	−1.64381
$206$	−1.00000	−0.0696733
$207$	4.90169	0.340691
$208$	1.00000	0.0693375
$209$	4.10559	0.283990
$210$	6.15409	0.424672
$211$	28.1166	1.93563	0.967814	−	0.251665i	$-0.0809782\pi$
$211$	28.1166	1.93563	0.967814	+	0.251665i	$0.0809782\pi$
$212$	−2.16434	−0.148647
$213$	16.2104	1.11072
$214$	−1.01223	−0.0691946
$215$	−20.5190	−1.39938
$216$	1.00000	0.0680414
$217$	−1.87005	−0.126947
$218$	8.63138	0.584591
$219$	−15.2429	−1.03002
$220$	13.5110	0.910909
$221$	1.01228	0.0680934
$222$	0.238604	0.0160141
$223$	15.0627	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$223$	15.0627	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$224$	1.95604	0.130693
$225$	4.89857	0.326571
$226$	−5.27694	−0.351017
$227$	−2.19074	−0.145405	−0.0727023	−	0.997354i	$-0.523162\pi$
$227$	−2.19074	−0.145405	−0.0727023	+	0.997354i	$0.523162\pi$
$228$	0.956039	0.0633152
$229$	−8.43982	−0.557719	−0.278860	−	0.960332i	$-0.589956\pi$
$229$	−8.43982	−0.557719	−0.278860	+	0.960332i	$0.589956\pi$
$230$	15.4217	1.01688
$231$	8.39997	0.552677
$232$	−7.40639	−0.486253
$233$	−5.04935	−0.330794	−0.165397	−	0.986227i	$-0.552890\pi$
$233$	−5.04935	−0.330794	−0.165397	+	0.986227i	$0.552890\pi$
$234$	1.00000	0.0653720
$235$	19.1910	1.25188
$236$	−14.3481	−0.933983
$237$	−3.19294	−0.207404
$238$	1.98006	0.128348
$239$	−16.5841	−1.07274	−0.536369	−	0.843983i	$-0.680205\pi$
$239$	−16.5841	−1.07274	−0.536369	+	0.843983i	$0.680205\pi$
$240$	3.14620	0.203086
$241$	9.10199	0.586311	0.293155	−	0.956065i	$-0.405295\pi$
$241$	9.10199	0.586311	0.293155	+	0.956065i	$0.405295\pi$
$242$	7.44167	0.478369
$243$	1.00000	0.0641500
$244$	7.32293	0.468803
$245$	−9.98576	−0.637967
$246$	−7.48071	−0.476953
$247$	0.956039	0.0608313
$248$	−0.956039	−0.0607085
$249$	−15.3915	−0.975398
$250$	−0.319125	−0.0201833
$251$	−16.6456	−1.05066	−0.525332	−	0.850897i	$-0.676059\pi$
$251$	−16.6456	−1.05066	−0.525332	+	0.850897i	$0.676059\pi$
$252$	1.95604	0.123219
$253$	21.0497	1.32338
$254$	−8.89405	−0.558063
$255$	3.18484	0.199442
$256$	1.00000	0.0625000
$257$	−13.6042	−0.848606	−0.424303	−	0.905520i	$-0.639481\pi$
$257$	−13.6042	−0.848606	−0.424303	+	0.905520i	$0.639481\pi$
$258$	−6.52182	−0.406031
$259$	0.466719	0.0290005
$260$	3.14620	0.195119
$261$	−7.40639	−0.458444
$262$	−10.0670	−0.621939
$263$	3.14651	0.194022	0.0970109	−	0.995283i	$-0.469072\pi$
$263$	3.14651	0.194022	0.0970109	+	0.995283i	$0.469072\pi$
$264$	4.29438	0.264301
$265$	−6.80944	−0.418301
$266$	1.87005	0.114660
$267$	−12.6337	−0.773168
$268$	−0.0784225	−0.00479042
$269$	−0.183494	−0.0111879	−0.00559393	−	0.999984i	$-0.501781\pi$
$269$	−0.183494	−0.0111879	−0.00559393	+	0.999984i	$0.501781\pi$
$270$	3.14620	0.191472
$271$	26.9702	1.63832	0.819162	−	0.573563i	$-0.194439\pi$
$271$	26.9702	1.63832	0.819162	+	0.573563i	$0.194439\pi$
$272$	1.01228	0.0613785
$273$	1.95604	0.118385
$274$	−9.77328	−0.590425
$275$	21.0363	1.26854
$276$	4.90169	0.295047
$277$	−10.1812	−0.611728	−0.305864	−	0.952075i	$-0.598945\pi$
$277$	−10.1812	−0.611728	−0.305864	+	0.952075i	$0.598945\pi$
$278$	−14.6247	−0.877130
$279$	−0.956039	−0.0572365
$280$	6.15409	0.367777
$281$	24.3900	1.45499	0.727494	−	0.686114i	$-0.240685\pi$
$281$	24.3900	1.45499	0.727494	+	0.686114i	$0.240685\pi$
$282$	6.09973	0.363234
$283$	−20.8406	−1.23885	−0.619423	−	0.785057i	$-0.712633\pi$
$283$	−20.8406	−1.23885	−0.619423	+	0.785057i	$0.712633\pi$
$284$	16.2104	0.961909
$285$	3.00789	0.178172
$286$	4.29438	0.253932
$287$	−14.6326	−0.863733
$288$	1.00000	0.0589256
$289$	−15.9753	−0.939723
$290$	−23.3020	−1.36834
$291$	−8.34288	−0.489068
$292$	−15.2429	−0.892021
$293$	28.4002	1.65915	0.829577	−	0.558392i	$-0.188581\pi$
$293$	28.4002	1.65915	0.829577	+	0.558392i	$0.188581\pi$
$294$	−3.17391	−0.185106
$295$	−45.1420	−2.62827
$296$	0.238604	0.0138686
$297$	4.29438	0.249185
$298$	−6.70964	−0.388679
$299$	4.90169	0.283472
$300$	4.89857	0.282819
$301$	−12.7569	−0.735298
$302$	20.0596	1.15430
$303$	1.77842	0.102167
$304$	0.956039	0.0548326
$305$	23.0394	1.31923
$306$	1.01228	0.0578682
$307$	9.32368	0.532130	0.266065	−	0.963955i	$-0.414276\pi$
$307$	9.32368	0.532130	0.266065	+	0.963955i	$0.414276\pi$
$308$	8.39997	0.478632
$309$	−1.00000	−0.0568880
$310$	−3.00789	−0.170837
$311$	−16.7133	−0.947725	−0.473863	−	0.880599i	$-0.657141\pi$
$311$	−16.7133	−0.947725	−0.473863	+	0.880599i	$0.657141\pi$
$312$	1.00000	0.0566139
$313$	−5.19761	−0.293786	−0.146893	−	0.989152i	$-0.546927\pi$
$313$	−5.19761	−0.293786	−0.146893	+	0.989152i	$0.546927\pi$
$314$	−11.4648	−0.646994
$315$	6.15409	0.346743
$316$	−3.19294	−0.179617
$317$	21.5003	1.20758	0.603788	−	0.797145i	$-0.293657\pi$
$317$	21.5003	1.20758	0.603788	+	0.797145i	$0.293657\pi$
$318$	−2.16434	−0.121370
$319$	−31.8058	−1.78078
$320$	3.14620	0.175878
$321$	−1.01223	−0.0564972
$322$	9.58789	0.534312
$323$	0.967779	0.0538487
$324$	1.00000	0.0555556
$325$	4.89857	0.271724
$326$	2.39010	0.132375
$327$	8.63138	0.477316
$328$	−7.48071	−0.413053
$329$	11.9313	0.657795
$330$	13.5110	0.743754
$331$	−21.1947	−1.16497	−0.582483	−	0.812843i	$-0.697919\pi$
$331$	−21.1947	−1.16497	−0.582483	+	0.812843i	$0.697919\pi$
$332$	−15.3915	−0.844719
$333$	0.238604	0.0130754
$334$	−4.92491	−0.269479
$335$	−0.246733	−0.0134805
$336$	1.95604	0.106711
$337$	29.0683	1.58345	0.791725	−	0.610877i	$-0.209183\pi$
$337$	29.0683	1.58345	0.791725	+	0.610877i	$0.209183\pi$
$338$	1.00000	0.0543928
$339$	−5.27694	−0.286604
$340$	3.18484	0.172722
$341$	−4.10559	−0.222330
$342$	0.956039	0.0516966
$343$	−19.9006	−1.07453
$344$	−6.52182	−0.351633
$345$	15.4217	0.830275
$346$	17.4627	0.938799
$347$	23.7617	1.27560	0.637798	−	0.770204i	$-0.279846\pi$
$347$	23.7617	1.27560	0.637798	+	0.770204i	$0.279846\pi$
$348$	−7.40639	−0.397024
$349$	2.62317	0.140415	0.0702074	−	0.997532i	$-0.477634\pi$
$349$	2.62317	0.140415	0.0702074	+	0.997532i	$0.477634\pi$
$350$	9.58179	0.512168
$351$	1.00000	0.0533761
$352$	4.29438	0.228891
$353$	−2.78959	−0.148475	−0.0742373	−	0.997241i	$-0.523652\pi$
$353$	−2.78959	−0.148475	−0.0742373	+	0.997241i	$0.523652\pi$
$354$	−14.3481	−0.762594
$355$	51.0011	2.70686
$356$	−12.6337	−0.669583
$357$	1.98006	0.104796
$358$	2.55721	0.135153
$359$	−5.31370	−0.280447	−0.140223	−	0.990120i	$-0.544782\pi$
$359$	−5.31370	−0.280447	−0.140223	+	0.990120i	$0.544782\pi$
$360$	3.14620	0.165819
$361$	−18.0860	−0.951894
$362$	6.11866	0.321590
$363$	7.44167	0.390586
$364$	1.95604	0.102524
$365$	−47.9571	−2.51019
$366$	7.32293	0.382776
$367$	−11.8363	−0.617852	−0.308926	−	0.951086i	$-0.599970\pi$
$367$	−11.8363	−0.617852	−0.308926	+	0.951086i	$0.599970\pi$
$368$	4.90169	0.255518
$369$	−7.48071	−0.389430
$370$	0.750696	0.0390268
$371$	−4.23353	−0.219794
$372$	−0.956039	−0.0495683
$373$	−6.48364	−0.335710	−0.167855	−	0.985812i	$-0.553684\pi$
$373$	−6.48364	−0.335710	−0.167855	+	0.985812i	$0.553684\pi$
$374$	4.34711	0.224784
$375$	−0.319125	−0.0164796
$376$	6.09973	0.314570
$377$	−7.40639	−0.381449
$378$	1.95604	0.100608
$379$	27.4563	1.41034	0.705168	−	0.709040i	$-0.250871\pi$
$379$	27.4563	1.41034	0.705168	+	0.709040i	$0.250871\pi$
$380$	3.00789	0.154301
$381$	−8.89405	−0.455656
$382$	4.58071	0.234370
$383$	5.61596	0.286962	0.143481	−	0.989653i	$-0.454170\pi$
$383$	5.61596	0.286962	0.143481	+	0.989653i	$0.454170\pi$
$384$	1.00000	0.0510310
$385$	26.4280	1.34689
$386$	−2.95689	−0.150502
$387$	−6.52182	−0.331523
$388$	−8.34288	−0.423546
$389$	8.32097	0.421890	0.210945	−	0.977498i	$-0.432346\pi$
$389$	8.32097	0.421890	0.210945	+	0.977498i	$0.432346\pi$
$390$	3.14620	0.159314
$391$	4.96188	0.250933
$392$	−3.17391	−0.160307
$393$	−10.0670	−0.507811
$394$	16.8665	0.849720
$395$	−10.0456	−0.505451
$396$	4.29438	0.215801
$397$	25.9242	1.30110	0.650549	−	0.759464i	$-0.274539\pi$
$397$	25.9242	1.30110	0.650549	+	0.759464i	$0.274539\pi$
$398$	9.11100	0.456693
$399$	1.87005	0.0936195
$400$	4.89857	0.244928
$401$	14.1642	0.707326	0.353663	−	0.935373i	$-0.384936\pi$
$401$	14.1642	0.707326	0.353663	+	0.935373i	$0.384936\pi$
$402$	−0.0784225	−0.00391136
$403$	−0.956039	−0.0476237
$404$	1.77842	0.0884796
$405$	3.14620	0.156336
$406$	−14.4872	−0.718987
$407$	1.02466	0.0507903
$408$	1.01228	0.0501154
$409$	32.2650	1.59540	0.797701	−	0.603053i	$-0.206049\pi$
$409$	32.2650	1.59540	0.797701	+	0.603053i	$0.206049\pi$
$410$	−23.5358	−1.16235
$411$	−9.77328	−0.482080
$412$	−1.00000	−0.0492665
$413$	−28.0655	−1.38101
$414$	4.90169	0.240905
$415$	−48.4248	−2.37708
$416$	1.00000	0.0490290
$417$	−14.6247	−0.716173
$418$	4.10559	0.200811
$419$	−15.9023	−0.776879	−0.388439	−	0.921474i	$-0.626986\pi$
$419$	−15.9023	−0.776879	−0.388439	+	0.921474i	$0.626986\pi$
$420$	6.15409	0.300289
$421$	−4.92155	−0.239862	−0.119931	−	0.992782i	$-0.538267\pi$
$421$	−4.92155	−0.239862	−0.119931	+	0.992782i	$0.538267\pi$
$422$	28.1166	1.36870
$423$	6.09973	0.296579
$424$	−2.16434	−0.105110
$425$	4.95873	0.240534
$426$	16.2104	0.785395
$427$	14.3239	0.693184
$428$	−1.01223	−0.0489280
$429$	4.29438	0.207334
$430$	−20.5190	−0.989512
$431$	−29.9317	−1.44176	−0.720880	−	0.693060i	$-0.756262\pi$
$431$	−29.9317	−1.44176	−0.720880	+	0.693060i	$0.756262\pi$
$432$	1.00000	0.0481125
$433$	−27.8805	−1.33985	−0.669925	−	0.742428i	$-0.733674\pi$
$433$	−27.8805	−1.33985	−0.669925	+	0.742428i	$0.733674\pi$
$434$	−1.87005	−0.0897652
$435$	−23.3020	−1.11724
$436$	8.63138	0.413368
$437$	4.68620	0.224171
$438$	−15.2429	−0.728332
$439$	20.8404	0.994656	0.497328	−	0.867563i	$-0.334315\pi$
$439$	20.8404	0.994656	0.497328	+	0.867563i	$0.334315\pi$
$440$	13.5110	0.644110
$441$	−3.17391	−0.151139
$442$	1.01228	0.0481493
$443$	31.9711	1.51899	0.759497	−	0.650511i	$-0.225445\pi$
$443$	31.9711	1.51899	0.759497	+	0.650511i	$0.225445\pi$
$444$	0.238604	0.0113236
$445$	−39.7480	−1.88424
$446$	15.0627	0.713238
$447$	−6.70964	−0.317355
$448$	1.95604	0.0924141
$449$	−3.18433	−0.150278	−0.0751390	−	0.997173i	$-0.523940\pi$
$449$	−3.18433	−0.150278	−0.0751390	+	0.997173i	$0.523940\pi$
$450$	4.89857	0.230921
$451$	−32.1250	−1.51271
$452$	−5.27694	−0.248207
$453$	20.0596	0.942482
$454$	−2.19074	−0.102817
$455$	6.15409	0.288508
$456$	0.956039	0.0447706
$457$	−0.631426	−0.0295369	−0.0147684	−	0.999891i	$-0.504701\pi$
$457$	−0.631426	−0.0295369	−0.0147684	+	0.999891i	$0.504701\pi$
$458$	−8.43982	−0.394367
$459$	1.01228	0.0472492
$460$	15.4217	0.719039
$461$	−14.0312	−0.653496	−0.326748	−	0.945111i	$-0.605953\pi$
$461$	−14.0312	−0.653496	−0.326748	+	0.945111i	$0.605953\pi$
$462$	8.39997	0.390802
$463$	28.2431	1.31257	0.656284	−	0.754514i	$-0.272127\pi$
$463$	28.2431	1.31257	0.656284	+	0.754514i	$0.272127\pi$
$464$	−7.40639	−0.343833
$465$	−3.00789	−0.139487
$466$	−5.04935	−0.233906
$467$	11.7598	0.544177	0.272089	−	0.962272i	$-0.412286\pi$
$467$	11.7598	0.544177	0.272089	+	0.962272i	$0.412286\pi$
$468$	1.00000	0.0462250
$469$	−0.153397	−0.00708324
$470$	19.1910	0.885214
$471$	−11.4648	−0.528268
$472$	−14.3481	−0.660425
$473$	−28.0072	−1.28777
$474$	−3.19294	−0.146657
$475$	4.68322	0.214881
$476$	1.98006	0.0907559
$477$	−2.16434	−0.0990983
$478$	−16.5841	−0.758541
$479$	2.60992	0.119250	0.0596252	−	0.998221i	$-0.481009\pi$
$479$	2.60992	0.119250	0.0596252	+	0.998221i	$0.481009\pi$
$480$	3.14620	0.143604
$481$	0.238604	0.0108794
$482$	9.10199	0.414584
$483$	9.58789	0.436264
$484$	7.44167	0.338258
$485$	−26.2484	−1.19188
$486$	1.00000	0.0453609
$487$	−7.74287	−0.350863	−0.175431	−	0.984492i	$-0.556132\pi$
$487$	−7.74287	−0.350863	−0.175431	+	0.984492i	$0.556132\pi$
$488$	7.32293	0.331494
$489$	2.39010	0.108084
$490$	−9.98576	−0.451111
$491$	20.6306	0.931047	0.465524	−	0.885035i	$-0.345866\pi$
$491$	20.6306	0.931047	0.465524	+	0.885035i	$0.345866\pi$
$492$	−7.48071	−0.337257
$493$	−7.49735	−0.337664
$494$	0.956039	0.0430142
$495$	13.5110	0.607273
$496$	−0.956039	−0.0429274
$497$	31.7081	1.42230
$498$	−15.3915	−0.689710
$499$	−16.2111	−0.725706	−0.362853	−	0.931846i	$-0.618197\pi$
$499$	−16.2111	−0.725706	−0.362853	+	0.931846i	$0.618197\pi$
$500$	−0.319125	−0.0142717
$501$	−4.92491	−0.220029
$502$	−16.6456	−0.742932
$503$	10.0027	0.445999	0.222999	−	0.974819i	$-0.428415\pi$
$503$	10.0027	0.445999	0.222999	+	0.974819i	$0.428415\pi$
$504$	1.95604	0.0871289
$505$	5.59525	0.248986
$506$	21.0497	0.935773
$507$	1.00000	0.0444116
$508$	−8.89405	−0.394610
$509$	37.3519	1.65559	0.827796	−	0.561029i	$-0.189594\pi$
$509$	37.3519	1.65559	0.827796	+	0.561029i	$0.189594\pi$
$510$	3.18484	0.141027
$511$	−29.8156	−1.31897
$512$	1.00000	0.0441942
$513$	0.956039	0.0422101
$514$	−13.6042	−0.600055
$515$	−3.14620	−0.138638
$516$	−6.52182	−0.287107
$517$	26.1946	1.15204
$518$	0.466719	0.0205064
$519$	17.4627	0.766526
$520$	3.14620	0.137970
$521$	−5.55986	−0.243582	−0.121791	−	0.992556i	$-0.538864\pi$
$521$	−5.55986	−0.243582	−0.121791	+	0.992556i	$0.538864\pi$
$522$	−7.40639	−0.324169
$523$	37.9558	1.65969	0.829845	−	0.557994i	$-0.188429\pi$
$523$	37.9558	1.65969	0.829845	+	0.557994i	$0.188429\pi$
$524$	−10.0670	−0.439777
$525$	9.58179	0.418184
$526$	3.14651	0.137194
$527$	−0.967779	−0.0421571
$528$	4.29438	0.186889
$529$	1.02652	0.0446314
$530$	−6.80944	−0.295783
$531$	−14.3481	−0.622655
$532$	1.87005	0.0810769
$533$	−7.48071	−0.324026
$534$	−12.6337	−0.546712
$535$	−3.18468	−0.137686
$536$	−0.0784225	−0.00338734
$537$	2.55721	0.110352
$538$	−0.183494	−0.00791101
$539$	−13.6300	−0.587085
$540$	3.14620	0.135391
$541$	17.1922	0.739151	0.369576	−	0.929201i	$-0.379503\pi$
$541$	17.1922	0.739151	0.369576	+	0.929201i	$0.379503\pi$
$542$	26.9702	1.15847
$543$	6.11866	0.262577
$544$	1.01228	0.0434012
$545$	27.1560	1.16324
$546$	1.95604	0.0837107
$547$	31.3992	1.34253	0.671267	−	0.741216i	$-0.265750\pi$
$547$	31.3992	1.34253	0.671267	+	0.741216i	$0.265750\pi$
$548$	−9.77328	−0.417494
$549$	7.32293	0.312535
$550$	21.0363	0.896991
$551$	−7.08080	−0.301652
$552$	4.90169	0.208630
$553$	−6.24552	−0.265587
$554$	−10.1812	−0.432557
$555$	0.750696	0.0318653
$556$	−14.6247	−0.620224
$557$	26.6192	1.12789	0.563947	−	0.825811i	$-0.309282\pi$
$557$	26.6192	1.12789	0.563947	+	0.825811i	$0.309282\pi$
$558$	−0.956039	−0.0404723
$559$	−6.52182	−0.275844
$560$	6.15409	0.260058
$561$	4.34711	0.183535
$562$	24.3900	1.02883
$563$	24.8397	1.04687	0.523435	−	0.852066i	$-0.324650\pi$
$563$	24.8397	1.04687	0.523435	+	0.852066i	$0.324650\pi$
$564$	6.09973	0.256845
$565$	−16.6023	−0.698465
$566$	−20.8406	−0.875997
$567$	1.95604	0.0821459
$568$	16.2104	0.680172
$569$	29.6752	1.24405	0.622025	−	0.782997i	$-0.286310\pi$
$569$	29.6752	1.24405	0.622025	+	0.782997i	$0.286310\pi$
$570$	3.00789	0.125987
$571$	−46.4595	−1.94427	−0.972135	−	0.234422i	$-0.924680\pi$
$571$	−46.4595	−1.94427	−0.972135	+	0.234422i	$0.924680\pi$
$572$	4.29438	0.179557
$573$	4.58071	0.191362
$574$	−14.6326	−0.610751
$575$	24.0112	1.00134
$576$	1.00000	0.0416667
$577$	33.6815	1.40218	0.701090	−	0.713073i	$-0.252697\pi$
$577$	33.6815	1.40218	0.701090	+	0.713073i	$0.252697\pi$
$578$	−15.9753	−0.664484
$579$	−2.95689	−0.122884
$580$	−23.3020	−0.967562
$581$	−30.1064	−1.24902
$582$	−8.34288	−0.345824
$583$	−9.29448	−0.384938
$584$	−15.2429	−0.630754
$585$	3.14620	0.130079
$586$	28.4002	1.17320
$587$	−8.82958	−0.364436	−0.182218	−	0.983258i	$-0.558328\pi$
$587$	−8.82958	−0.364436	−0.182218	+	0.983258i	$0.558328\pi$
$588$	−3.17391	−0.130890
$589$	−0.914010	−0.0376611
$590$	−45.1420	−1.85847
$591$	16.8665	0.693793
$592$	0.238604	0.00980657
$593$	12.9054	0.529962	0.264981	−	0.964254i	$-0.414634\pi$
$593$	12.9054	0.529962	0.264981	+	0.964254i	$0.414634\pi$
$594$	4.29438	0.176200
$595$	6.22966	0.255391
$596$	−6.70964	−0.274837
$597$	9.11100	0.372888
$598$	4.90169	0.200445
$599$	−7.90036	−0.322800	−0.161400	−	0.986889i	$-0.551601\pi$
$599$	−7.90036	−0.322800	−0.161400	+	0.986889i	$0.551601\pi$
$600$	4.89857	0.199983
$601$	27.4404	1.11932	0.559658	−	0.828724i	$-0.310933\pi$
$601$	27.4404	1.11932	0.559658	+	0.828724i	$0.310933\pi$
$602$	−12.7569	−0.519934
$603$	−0.0784225	−0.00319361
$604$	20.0596	0.816214
$605$	23.4130	0.951873
$606$	1.77842	0.0722433
$607$	−21.2335	−0.861841	−0.430920	−	0.902390i	$-0.641811\pi$
$607$	−21.2335	−0.861841	−0.430920	+	0.902390i	$0.641811\pi$
$608$	0.956039	0.0387725
$609$	−14.4872	−0.587050
$610$	23.0394	0.932838
$611$	6.09973	0.246769
$612$	1.01228	0.0409190
$613$	20.6364	0.833497	0.416749	−	0.909022i	$-0.363170\pi$
$613$	20.6364	0.833497	0.416749	+	0.909022i	$0.363170\pi$
$614$	9.32368	0.376273
$615$	−23.5358	−0.949056
$616$	8.39997	0.338444
$617$	−11.0859	−0.446303	−0.223151	−	0.974784i	$-0.571634\pi$
$617$	−11.0859	−0.446303	−0.223151	+	0.974784i	$0.571634\pi$
$618$	−1.00000	−0.0402259
$619$	−27.5613	−1.10778	−0.553891	−	0.832589i	$-0.686858\pi$
$619$	−27.5613	−1.10778	−0.553891	+	0.832589i	$0.686858\pi$
$620$	−3.00789	−0.120800
$621$	4.90169	0.196698
$622$	−16.7133	−0.670143
$623$	−24.7119	−0.990063
$624$	1.00000	0.0400320
$625$	−25.4969	−1.01987
$626$	−5.19761	−0.207738
$627$	4.10559	0.163961
$628$	−11.4648	−0.457494
$629$	0.241534	0.00963060
$630$	6.15409	0.245185
$631$	19.5543	0.778444	0.389222	−	0.921144i	$-0.372744\pi$
$631$	19.5543	0.778444	0.389222	+	0.921144i	$0.372744\pi$
$632$	−3.19294	−0.127009
$633$	28.1166	1.11754
$634$	21.5003	0.853885
$635$	−27.9825	−1.11045
$636$	−2.16434	−0.0858216
$637$	−3.17391	−0.125755
$638$	−31.8058	−1.25920
$639$	16.2104	0.641273
$640$	3.14620	0.124364
$641$	−14.6152	−0.577266	−0.288633	−	0.957440i	$-0.593201\pi$
$641$	−14.6152	−0.577266	−0.288633	+	0.957440i	$0.593201\pi$
$642$	−1.01223	−0.0399495
$643$	34.6003	1.36450	0.682251	−	0.731118i	$-0.261001\pi$
$643$	34.6003	1.36450	0.682251	+	0.731118i	$0.261001\pi$
$644$	9.58789	0.377816
$645$	−20.5190	−0.807933
$646$	0.967779	0.0380768
$647$	5.61392	0.220706	0.110353	−	0.993892i	$-0.464802\pi$
$647$	5.61392	0.220706	0.110353	+	0.993892i	$0.464802\pi$
$648$	1.00000	0.0392837
$649$	−61.6162	−2.41865
$650$	4.89857	0.192138
$651$	−1.87005	−0.0732930
$652$	2.39010	0.0936035
$653$	26.0773	1.02048	0.510242	−	0.860031i	$-0.329556\pi$
$653$	26.0773	1.02048	0.510242	+	0.860031i	$0.329556\pi$
$654$	8.63138	0.337514
$655$	−31.6727	−1.23755
$656$	−7.48071	−0.292073
$657$	−15.2429	−0.594681
$658$	11.9313	0.465131
$659$	41.2870	1.60831	0.804156	−	0.594419i	$-0.202618\pi$
$659$	41.2870	1.60831	0.804156	+	0.594419i	$0.202618\pi$
$660$	13.5110	0.525914
$661$	−27.0930	−1.05380	−0.526898	−	0.849929i	$-0.676645\pi$
$661$	−27.0930	−1.05380	−0.526898	+	0.849929i	$0.676645\pi$
$662$	−21.1947	−0.823755
$663$	1.01228	0.0393137
$664$	−15.3915	−0.597307
$665$	5.88354	0.228154
$666$	0.238604	0.00924572
$667$	−36.3038	−1.40569
$668$	−4.92491	−0.190550
$669$	15.0627	0.582356
$670$	−0.246733	−0.00953212
$671$	31.4474	1.21401
$672$	1.95604	0.0754558
$673$	13.4673	0.519125	0.259563	−	0.965726i	$-0.416422\pi$
$673$	13.4673	0.519125	0.259563	+	0.965726i	$0.416422\pi$
$674$	29.0683	1.11967
$675$	4.89857	0.188546
$676$	1.00000	0.0384615
$677$	20.9118	0.803706	0.401853	−	0.915704i	$-0.368366\pi$
$677$	20.9118	0.803706	0.401853	+	0.915704i	$0.368366\pi$
$678$	−5.27694	−0.202660
$679$	−16.3190	−0.626266
$680$	3.18484	0.122133
$681$	−2.19074	−0.0839494
$682$	−4.10559	−0.157211
$683$	−46.6728	−1.78589	−0.892943	−	0.450171i	$-0.851363\pi$
$683$	−46.6728	−1.78589	−0.892943	+	0.450171i	$0.851363\pi$
$684$	0.956039	0.0365550
$685$	−30.7487	−1.17485
$686$	−19.9006	−0.759807
$687$	−8.43982	−0.321999
$688$	−6.52182	−0.248642
$689$	−2.16434	−0.0824547
$690$	15.4217	0.587093
$691$	−2.56407	−0.0975417	−0.0487708	−	0.998810i	$-0.515530\pi$
$691$	−2.56407	−0.0975417	−0.0487708	+	0.998810i	$0.515530\pi$
$692$	17.4627	0.663831
$693$	8.39997	0.319088
$694$	23.7617	0.901982
$695$	−46.0121	−1.74534
$696$	−7.40639	−0.280739
$697$	−7.57258	−0.286832
$698$	2.62317	0.0992883
$699$	−5.04935	−0.190984
$700$	9.58179	0.362158
$701$	−21.5028	−0.812151	−0.406075	−	0.913840i	$-0.633103\pi$
$701$	−21.5028	−0.812151	−0.406075	+	0.913840i	$0.633103\pi$
$702$	1.00000	0.0377426
$703$	0.228115	0.00860351
$704$	4.29438	0.161850
$705$	19.1910	0.722774
$706$	−2.78959	−0.104987
$707$	3.47865	0.130828
$708$	−14.3481	−0.539235
$709$	−7.41367	−0.278426	−0.139213	−	0.990262i	$-0.544457\pi$
$709$	−7.41367	−0.278426	−0.139213	+	0.990262i	$0.544457\pi$
$710$	51.0011	1.91404
$711$	−3.19294	−0.119745
$712$	−12.6337	−0.473466
$713$	−4.68620	−0.175500
$714$	1.98006	0.0741019
$715$	13.5110	0.505281
$716$	2.55721	0.0955675
$717$	−16.5841	−0.619346
$718$	−5.31370	−0.198306
$719$	−8.07775	−0.301249	−0.150625	−	0.988591i	$-0.548128\pi$
$719$	−8.07775	−0.301249	−0.150625	+	0.988591i	$0.548128\pi$
$720$	3.14620	0.117252
$721$	−1.95604	−0.0728467
$722$	−18.0860	−0.673091
$723$	9.10199	0.338507
$724$	6.11866	0.227398
$725$	−36.2807	−1.34743
$726$	7.44167	0.276186
$727$	−20.4793	−0.759535	−0.379768	−	0.925082i	$-0.623996\pi$
$727$	−20.4793	−0.759535	−0.379768	+	0.925082i	$0.623996\pi$
$728$	1.95604	0.0724956
$729$	1.00000	0.0370370
$730$	−47.9571	−1.77497
$731$	−6.60192	−0.244181
$732$	7.32293	0.270663
$733$	−27.7231	−1.02397	−0.511987	−	0.858993i	$-0.671091\pi$
$733$	−27.7231	−1.02397	−0.511987	+	0.858993i	$0.671091\pi$
$734$	−11.8363	−0.436887
$735$	−9.98576	−0.368330
$736$	4.90169	0.180679
$737$	−0.336776	−0.0124053
$738$	−7.48071	−0.275369
$739$	−21.9937	−0.809052	−0.404526	−	0.914526i	$-0.632564\pi$
$739$	−21.9937	−0.809052	−0.404526	+	0.914526i	$0.632564\pi$
$740$	0.750696	0.0275961
$741$	0.956039	0.0351210
$742$	−4.23353	−0.155418
$743$	36.8982	1.35366	0.676832	−	0.736137i	$-0.263352\pi$
$743$	36.8982	1.35366	0.676832	+	0.736137i	$0.263352\pi$
$744$	−0.956039	−0.0350501
$745$	−21.1099	−0.773405
$746$	−6.48364	−0.237383
$747$	−15.3915	−0.563146
$748$	4.34711	0.158946
$749$	−1.97996	−0.0723462
$750$	−0.319125	−0.0116528
$751$	22.0589	0.804942	0.402471	−	0.915433i	$-0.368151\pi$
$751$	22.0589	0.804942	0.402471	+	0.915433i	$0.368151\pi$
$752$	6.09973	0.222434
$753$	−16.6456	−0.606601
$754$	−7.40639	−0.269725
$755$	63.1115	2.29686
$756$	1.95604	0.0711404
$757$	−17.9440	−0.652187	−0.326094	−	0.945337i	$-0.605732\pi$
$757$	−17.9440	−0.652187	−0.326094	+	0.945337i	$0.605732\pi$
$758$	27.4563	0.997259
$759$	21.0497	0.764055
$760$	3.00789	0.109108
$761$	−7.56315	−0.274164	−0.137082	−	0.990560i	$-0.543772\pi$
$761$	−7.56315	−0.274164	−0.137082	+	0.990560i	$0.543772\pi$
$762$	−8.89405	−0.322198
$763$	16.8833	0.611217
$764$	4.58071	0.165724
$765$	3.18484	0.115148
$766$	5.61596	0.202913
$767$	−14.3481	−0.518080
$768$	1.00000	0.0360844
$769$	−4.66260	−0.168138	−0.0840688	−	0.996460i	$-0.526792\pi$
$769$	−4.66260	−0.168138	−0.0840688	+	0.996460i	$0.526792\pi$
$770$	26.4280	0.952398
$771$	−13.6042	−0.489943
$772$	−2.95689	−0.106421
$773$	17.1126	0.615498	0.307749	−	0.951468i	$-0.400424\pi$
$773$	17.1126	0.615498	0.307749	+	0.951468i	$0.400424\pi$
$774$	−6.52182	−0.234422
$775$	−4.68322	−0.168226
$776$	−8.34288	−0.299492
$777$	0.466719	0.0167434
$778$	8.32097	0.298321
$779$	−7.15185	−0.256242
$780$	3.14620	0.112652
$781$	69.6135	2.49097
$782$	4.96188	0.177437
$783$	−7.40639	−0.264683
$784$	−3.17391	−0.113354
$785$	−36.0704	−1.28741
$786$	−10.0670	−0.359077
$787$	51.8482	1.84819	0.924094	−	0.382166i	$-0.124822\pi$
$787$	51.8482	1.84819	0.924094	+	0.382166i	$0.124822\pi$
$788$	16.8665	0.600843
$789$	3.14651	0.112019
$790$	−10.0456	−0.357408
$791$	−10.3219	−0.367005
$792$	4.29438	0.152594
$793$	7.32293	0.260045
$794$	25.9242	0.920016
$795$	−6.80944	−0.241506
$796$	9.11100	0.322931
$797$	−8.62435	−0.305490	−0.152745	−	0.988266i	$-0.548811\pi$
$797$	−8.62435	−0.305490	−0.152745	+	0.988266i	$0.548811\pi$
$798$	1.87005	0.0661990
$799$	6.17464	0.218443
$800$	4.89857	0.173191
$801$	−12.6337	−0.446388
$802$	14.1642	0.500155
$803$	−65.4586	−2.30998
$804$	−0.0784225	−0.00276575
$805$	30.1654	1.06319
$806$	−0.956039	−0.0336750
$807$	−0.183494	−0.00645931
$808$	1.77842	0.0625645
$809$	53.9744	1.89764	0.948820	−	0.315817i	$-0.102279\pi$
$809$	53.9744	1.89764	0.948820	+	0.315817i	$0.102279\pi$
$810$	3.14620	0.110546
$811$	−12.1886	−0.428000	−0.214000	−	0.976834i	$-0.568649\pi$
$811$	−12.1886	−0.428000	−0.214000	+	0.976834i	$0.568649\pi$
$812$	−14.4872	−0.508401
$813$	26.9702	0.945886
$814$	1.02466	0.0359142
$815$	7.51973	0.263404
$816$	1.01228	0.0354369
$817$	−6.23512	−0.218139
$818$	32.2650	1.12812
$819$	1.95604	0.0683495
$820$	−23.5358	−0.821906
$821$	30.4886	1.06406	0.532030	−	0.846726i	$-0.321429\pi$
$821$	30.4886	1.06406	0.532030	+	0.846726i	$0.321429\pi$
$822$	−9.77328	−0.340882
$823$	−28.0677	−0.978379	−0.489189	−	0.872178i	$-0.662707\pi$
$823$	−28.0677	−0.978379	−0.489189	+	0.872178i	$0.662707\pi$
$824$	−1.00000	−0.0348367
$825$	21.0363	0.732390
$826$	−28.0655	−0.976522
$827$	13.0731	0.454596	0.227298	−	0.973825i	$-0.427011\pi$
$827$	13.0731	0.454596	0.227298	+	0.973825i	$0.427011\pi$
$828$	4.90169	0.170345
$829$	14.9322	0.518618	0.259309	−	0.965794i	$-0.416505\pi$
$829$	14.9322	0.518618	0.259309	+	0.965794i	$0.416505\pi$
$830$	−48.4248	−1.68085
$831$	−10.1812	−0.353181
$832$	1.00000	0.0346688
$833$	−3.21289	−0.111320
$834$	−14.6247	−0.506411
$835$	−15.4947	−0.536217
$836$	4.10559	0.141995
$837$	−0.956039	−0.0330455
$838$	−15.9023	−0.549336
$839$	−45.7258	−1.57863	−0.789315	−	0.613989i	$-0.789564\pi$
$839$	−45.7258	−1.57863	−0.789315	+	0.613989i	$0.789564\pi$
$840$	6.15409	0.212336
$841$	25.8546	0.891539
$842$	−4.92155	−0.169608
$843$	24.3900	0.840038
$844$	28.1166	0.967814
$845$	3.14620	0.108233
$846$	6.09973	0.209713
$847$	14.5562	0.500157
$848$	−2.16434	−0.0743237
$849$	−20.8406	−0.715248
$850$	4.95873	0.170083
$851$	1.16956	0.0400921
$852$	16.2104	0.555358
$853$	−3.92947	−0.134543	−0.0672713	−	0.997735i	$-0.521429\pi$
$853$	−3.92947	−0.134543	−0.0672713	+	0.997735i	$0.521429\pi$
$854$	14.3239	0.490155
$855$	3.00789	0.102868
$856$	−1.01223	−0.0345973
$857$	−16.6481	−0.568688	−0.284344	−	0.958722i	$-0.591776\pi$
$857$	−16.6481	−0.568688	−0.284344	+	0.958722i	$0.591776\pi$
$858$	4.29438	0.146608
$859$	−7.06681	−0.241117	−0.120558	−	0.992706i	$-0.538468\pi$
$859$	−7.06681	−0.241117	−0.120558	+	0.992706i	$0.538468\pi$
$860$	−20.5190	−0.699691
$861$	−14.6326	−0.498676
$862$	−29.9317	−1.01948
$863$	−0.468547	−0.0159495	−0.00797476	−	0.999968i	$-0.502538\pi$
$863$	−0.468547	−0.0159495	−0.00797476	+	0.999968i	$0.502538\pi$
$864$	1.00000	0.0340207
$865$	54.9410	1.86805
$866$	−27.8805	−0.947418
$867$	−15.9753	−0.542549
$868$	−1.87005	−0.0634736
$869$	−13.7117	−0.465138
$870$	−23.3020	−0.790011
$871$	−0.0784225	−0.00265725
$872$	8.63138	0.292295
$873$	−8.34288	−0.282364
$874$	4.68620	0.158513
$875$	−0.624221	−0.0211025
$876$	−15.2429	−0.515008
$877$	−21.8701	−0.738500	−0.369250	−	0.929330i	$-0.620385\pi$
$877$	−21.8701	−0.738500	−0.369250	+	0.929330i	$0.620385\pi$
$878$	20.8404	0.703328
$879$	28.4002	0.957913
$880$	13.5110	0.455454
$881$	41.3258	1.39230	0.696150	−	0.717896i	$-0.254895\pi$
$881$	41.3258	1.39230	0.696150	+	0.717896i	$0.254895\pi$
$882$	−3.17391	−0.106871
$883$	12.1199	0.407868	0.203934	−	0.978985i	$-0.434627\pi$
$883$	12.1199	0.407868	0.203934	+	0.978985i	$0.434627\pi$
$884$	1.01228	0.0340467
$885$	−45.1420	−1.51743
$886$	31.9711	1.07409
$887$	−14.3236	−0.480939	−0.240469	−	0.970657i	$-0.577301\pi$
$887$	−14.3236	−0.480939	−0.240469	+	0.970657i	$0.577301\pi$
$888$	0.238604	0.00800703
$889$	−17.3971	−0.583480
$890$	−39.7480	−1.33236
$891$	4.29438	0.143867
$892$	15.0627	0.504335
$893$	5.83158	0.195146
$894$	−6.70964	−0.224404
$895$	8.04550	0.268931
$896$	1.95604	0.0653467
$897$	4.90169	0.163663
$898$	−3.18433	−0.106263
$899$	7.08080	0.236158
$900$	4.89857	0.163286
$901$	−2.19092	−0.0729901
$902$	−32.1250	−1.06965
$903$	−12.7569	−0.424524
$904$	−5.27694	−0.175509
$905$	19.2505	0.639909
$906$	20.0596	0.666436
$907$	8.86983	0.294518	0.147259	−	0.989098i	$-0.452955\pi$
$907$	8.86983	0.294518	0.147259	+	0.989098i	$0.452955\pi$
$908$	−2.19074	−0.0727023
$909$	1.77842	0.0589864
$910$	6.15409	0.204006
$911$	−25.8730	−0.857211	−0.428606	−	0.903492i	$-0.640995\pi$
$911$	−25.8730	−0.857211	−0.428606	+	0.903492i	$0.640995\pi$
$912$	0.956039	0.0316576
$913$	−66.0970	−2.18749
$914$	−0.631426	−0.0208857
$915$	23.0394	0.761659
$916$	−8.43982	−0.278860
$917$	−19.6914	−0.650266
$918$	1.01228	0.0334102
$919$	51.2605	1.69093	0.845464	−	0.534032i	$-0.179324\pi$
$919$	51.2605	1.69093	0.845464	+	0.534032i	$0.179324\pi$
$920$	15.4217	0.508438
$921$	9.32368	0.307226
$922$	−14.0312	−0.462092
$923$	16.2104	0.533571
$924$	8.39997	0.276339
$925$	1.16882	0.0384305
$926$	28.2431	0.928126
$927$	−1.00000	−0.0328443
$928$	−7.40639	−0.243127
$929$	18.6584	0.612164	0.306082	−	0.952005i	$-0.400982\pi$
$929$	18.6584	0.612164	0.306082	+	0.952005i	$0.400982\pi$
$930$	−3.00789	−0.0986325
$931$	−3.03438	−0.0994479
$932$	−5.04935	−0.165397
$933$	−16.7133	−0.547169
$934$	11.7598	0.384791
$935$	13.6769	0.447282
$936$	1.00000	0.0326860
$937$	35.1664	1.14883	0.574417	−	0.818563i	$-0.305229\pi$
$937$	35.1664	1.14883	0.574417	+	0.818563i	$0.305229\pi$
$938$	−0.153397	−0.00500861
$939$	−5.19761	−0.169617
$940$	19.1910	0.625941
$941$	8.16117	0.266047	0.133023	−	0.991113i	$-0.457531\pi$
$941$	8.16117	0.266047	0.133023	+	0.991113i	$0.457531\pi$
$942$	−11.4648	−0.373542
$943$	−36.6681	−1.19408
$944$	−14.3481	−0.466991
$945$	6.15409	0.200192
$946$	−28.0072	−0.910592
$947$	−9.78374	−0.317929	−0.158964	−	0.987284i	$-0.550816\pi$
$947$	−9.78374	−0.317929	−0.158964	+	0.987284i	$0.550816\pi$
$948$	−3.19294	−0.103702
$949$	−15.2429	−0.494804
$950$	4.68322	0.151944
$951$	21.5003	0.697194
$952$	1.98006	0.0641741
$953$	12.6936	0.411187	0.205593	−	0.978638i	$-0.434088\pi$
$953$	12.6936	0.411187	0.205593	+	0.978638i	$0.434088\pi$
$954$	−2.16434	−0.0700730
$955$	14.4118	0.466356
$956$	−16.5841	−0.536369
$957$	−31.8058	−1.02814
$958$	2.60992	0.0843228
$959$	−19.1169	−0.617317
$960$	3.14620	0.101543
$961$	−30.0860	−0.970516
$962$	0.238604	0.00769291
$963$	−1.01223	−0.0326187
$964$	9.10199	0.293155
$965$	−9.30296	−0.299473
$966$	9.58789	0.308485
$967$	9.19756	0.295773	0.147887	−	0.989004i	$-0.452753\pi$
$967$	9.19756	0.295773	0.147887	+	0.989004i	$0.452753\pi$
$968$	7.44167	0.239184
$969$	0.967779	0.0310896
$970$	−26.2484	−0.842784
$971$	−17.0628	−0.547571	−0.273785	−	0.961791i	$-0.588276\pi$
$971$	−17.0628	−0.547571	−0.273785	+	0.961791i	$0.588276\pi$
$972$	1.00000	0.0320750
$973$	−28.6064	−0.917080
$974$	−7.74287	−0.248097
$975$	4.89857	0.156880
$976$	7.32293	0.234401
$977$	36.4649	1.16661	0.583307	−	0.812252i	$-0.301758\pi$
$977$	36.4649	1.16661	0.583307	+	0.812252i	$0.301758\pi$
$978$	2.39010	0.0764269
$979$	−54.2537	−1.73396
$980$	−9.98576	−0.318983
$981$	8.63138	0.275579
$982$	20.6306	0.658350
$983$	22.5265	0.718483	0.359241	−	0.933245i	$-0.383035\pi$
$983$	22.5265	0.718483	0.359241	+	0.933245i	$0.383035\pi$
$984$	−7.48071	−0.238476
$985$	53.0652	1.69080
$986$	−7.49735	−0.238764
$987$	11.9313	0.379778
$988$	0.956039	0.0304156
$989$	−31.9679	−1.01652
$990$	13.5110	0.429407
$991$	28.9963	0.921099	0.460550	−	0.887634i	$-0.347652\pi$
$991$	28.9963	0.921099	0.460550	+	0.887634i	$0.347652\pi$
$992$	−0.956039	−0.0303543
$993$	−21.1947	−0.672593
$994$	31.7081	1.00572
$995$	28.6650	0.908742
$996$	−15.3915	−0.487699
$997$	43.3612	1.37326	0.686631	−	0.727006i	$-0.259089\pi$
$997$	43.3612	1.37326	0.686631	+	0.727006i	$0.259089\pi$
$998$	−16.2111	−0.513152
$999$	0.238604	0.00754910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.v.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.v.1.9	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.14620 q^{5} +1.00000 q^{6} +1.95604 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.14620 q^{5} +1.00000 q^{6} +1.95604 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.14620 q^{10} +4.29438 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.95604 q^{14} +3.14620 q^{15} +1.00000 q^{16} +1.01228 q^{17} +1.00000 q^{18} +0.956039 q^{19} +3.14620 q^{20} +1.95604 q^{21} +4.29438 q^{22} +4.90169 q^{23} +1.00000 q^{24} +4.89857 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.95604 q^{28} -7.40639 q^{29} +3.14620 q^{30} -0.956039 q^{31} +1.00000 q^{32} +4.29438 q^{33} +1.01228 q^{34} +6.15409 q^{35} +1.00000 q^{36} +0.238604 q^{37} +0.956039 q^{38} +1.00000 q^{39} +3.14620 q^{40} -7.48071 q^{41} +1.95604 q^{42} -6.52182 q^{43} +4.29438 q^{44} +3.14620 q^{45} +4.90169 q^{46} +6.09973 q^{47} +1.00000 q^{48} -3.17391 q^{49} +4.89857 q^{50} +1.01228 q^{51} +1.00000 q^{52} -2.16434 q^{53} +1.00000 q^{54} +13.5110 q^{55} +1.95604 q^{56} +0.956039 q^{57} -7.40639 q^{58} -14.3481 q^{59} +3.14620 q^{60} +7.32293 q^{61} -0.956039 q^{62} +1.95604 q^{63} +1.00000 q^{64} +3.14620 q^{65} +4.29438 q^{66} -0.0784225 q^{67} +1.01228 q^{68} +4.90169 q^{69} +6.15409 q^{70} +16.2104 q^{71} +1.00000 q^{72} -15.2429 q^{73} +0.238604 q^{74} +4.89857 q^{75} +0.956039 q^{76} +8.39997 q^{77} +1.00000 q^{78} -3.19294 q^{79} +3.14620 q^{80} +1.00000 q^{81} -7.48071 q^{82} -15.3915 q^{83} +1.95604 q^{84} +3.18484 q^{85} -6.52182 q^{86} -7.40639 q^{87} +4.29438 q^{88} -12.6337 q^{89} +3.14620 q^{90} +1.95604 q^{91} +4.90169 q^{92} -0.956039 q^{93} +6.09973 q^{94} +3.00789 q^{95} +1.00000 q^{96} -8.34288 q^{97} -3.17391 q^{98} +4.29438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * q^99

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