LMFDB - Embedded newform 8034.2.a.u.1.5

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:	$1$
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} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.12575$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.539721 q^{5} -1.00000 q^{6} +0.708670 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.539721 q^{5} -1.00000 q^{6} +0.708670 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.539721 q^{10} -1.10147 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.708670 q^{14} +0.539721 q^{15} +1.00000 q^{16} -4.54976 q^{17} +1.00000 q^{18} +0.931175 q^{19} -0.539721 q^{20} -0.708670 q^{21} -1.10147 q^{22} +2.10547 q^{23} -1.00000 q^{24} -4.70870 q^{25} -1.00000 q^{26} -1.00000 q^{27} +0.708670 q^{28} +8.33493 q^{29} +0.539721 q^{30} +2.29970 q^{31} +1.00000 q^{32} +1.10147 q^{33} -4.54976 q^{34} -0.382485 q^{35} +1.00000 q^{36} -0.809455 q^{37} +0.931175 q^{38} +1.00000 q^{39} -0.539721 q^{40} +5.39691 q^{41} -0.708670 q^{42} -6.65786 q^{43} -1.10147 q^{44} -0.539721 q^{45} +2.10547 q^{46} -4.25716 q^{47} -1.00000 q^{48} -6.49779 q^{49} -4.70870 q^{50} +4.54976 q^{51} -1.00000 q^{52} -8.93249 q^{53} -1.00000 q^{54} +0.594486 q^{55} +0.708670 q^{56} -0.931175 q^{57} +8.33493 q^{58} +4.89092 q^{59} +0.539721 q^{60} -1.40771 q^{61} +2.29970 q^{62} +0.708670 q^{63} +1.00000 q^{64} +0.539721 q^{65} +1.10147 q^{66} +5.39027 q^{67} -4.54976 q^{68} -2.10547 q^{69} -0.382485 q^{70} -14.4479 q^{71} +1.00000 q^{72} +16.3009 q^{73} -0.809455 q^{74} +4.70870 q^{75} +0.931175 q^{76} -0.780579 q^{77} +1.00000 q^{78} -3.67867 q^{79} -0.539721 q^{80} +1.00000 q^{81} +5.39691 q^{82} -9.54181 q^{83} -0.708670 q^{84} +2.45560 q^{85} -6.65786 q^{86} -8.33493 q^{87} -1.10147 q^{88} -17.5318 q^{89} -0.539721 q^{90} -0.708670 q^{91} +2.10547 q^{92} -2.29970 q^{93} -4.25716 q^{94} -0.502575 q^{95} -1.00000 q^{96} -6.25897 q^{97} -6.49779 q^{98} -1.10147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.539721	−0.241371	−0.120685	−	0.992691i	$-0.538509\pi$
$5$	−0.539721	−0.241371	−0.120685	+	0.992691i	$0.538509\pi$
$6$	−1.00000	−0.408248
$7$	0.708670	0.267852	0.133926	−	0.990991i	$-0.457242\pi$
$7$	0.708670	0.267852	0.133926	+	0.990991i	$0.457242\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.539721	−0.170675
$11$	−1.10147	−0.332105	−0.166053	−	0.986117i	$-0.553102\pi$
$11$	−1.10147	−0.332105	−0.166053	+	0.986117i	$0.553102\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.708670	0.189400
$15$	0.539721	0.139355
$16$	1.00000	0.250000
$17$	−4.54976	−1.10348	−0.551739	−	0.834017i	$-0.686036\pi$
$17$	−4.54976	−1.10348	−0.551739	+	0.834017i	$0.686036\pi$
$18$	1.00000	0.235702
$19$	0.931175	0.213626	0.106813	−	0.994279i	$-0.465935\pi$
$19$	0.931175	0.213626	0.106813	+	0.994279i	$0.465935\pi$
$20$	−0.539721	−0.120685
$21$	−0.708670	−0.154645
$22$	−1.10147	−0.234834
$23$	2.10547	0.439020	0.219510	−	0.975610i	$-0.429554\pi$
$23$	2.10547	0.439020	0.219510	+	0.975610i	$0.429554\pi$
$24$	−1.00000	−0.204124
$25$	−4.70870	−0.941740
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0.708670	0.133926
$29$	8.33493	1.54776	0.773879	−	0.633334i	$-0.218314\pi$
$29$	8.33493	1.54776	0.773879	+	0.633334i	$0.218314\pi$
$30$	0.539721	0.0985392
$31$	2.29970	0.413038	0.206519	−	0.978443i	$-0.433786\pi$
$31$	2.29970	0.413038	0.206519	+	0.978443i	$0.433786\pi$
$32$	1.00000	0.176777
$33$	1.10147	0.191741
$34$	−4.54976	−0.780277
$35$	−0.382485	−0.0646517
$36$	1.00000	0.166667
$37$	−0.809455	−0.133074	−0.0665368	−	0.997784i	$-0.521195\pi$
$37$	−0.809455	−0.133074	−0.0665368	+	0.997784i	$0.521195\pi$
$38$	0.931175	0.151057
$39$	1.00000	0.160128
$40$	−0.539721	−0.0853374
$41$	5.39691	0.842855	0.421428	−	0.906862i	$-0.361529\pi$
$41$	5.39691	0.842855	0.421428	+	0.906862i	$0.361529\pi$
$42$	−0.708670	−0.109350
$43$	−6.65786	−1.01531	−0.507657	−	0.861559i	$-0.669488\pi$
$43$	−6.65786	−1.01531	−0.507657	+	0.861559i	$0.669488\pi$
$44$	−1.10147	−0.166053
$45$	−0.539721	−0.0804569
$46$	2.10547	0.310434
$47$	−4.25716	−0.620971	−0.310486	−	0.950578i	$-0.600492\pi$
$47$	−4.25716	−0.620971	−0.310486	+	0.950578i	$0.600492\pi$
$48$	−1.00000	−0.144338
$49$	−6.49779	−0.928255
$50$	−4.70870	−0.665911
$51$	4.54976	0.637094
$52$	−1.00000	−0.138675
$53$	−8.93249	−1.22697	−0.613486	−	0.789706i	$-0.710233\pi$
$53$	−8.93249	−1.22697	−0.613486	+	0.789706i	$0.710233\pi$
$54$	−1.00000	−0.136083
$55$	0.594486	0.0801605
$56$	0.708670	0.0947001
$57$	−0.931175	−0.123337
$58$	8.33493	1.09443
$59$	4.89092	0.636744	0.318372	−	0.947966i	$-0.396864\pi$
$59$	4.89092	0.636744	0.318372	+	0.947966i	$0.396864\pi$
$60$	0.539721	0.0696777
$61$	−1.40771	−0.180239	−0.0901193	−	0.995931i	$-0.528725\pi$
$61$	−1.40771	−0.180239	−0.0901193	+	0.995931i	$0.528725\pi$
$62$	2.29970	0.292062
$63$	0.708670	0.0892841
$64$	1.00000	0.125000
$65$	0.539721	0.0669442
$66$	1.10147	0.135581
$67$	5.39027	0.658526	0.329263	−	0.944238i	$-0.393200\pi$
$67$	5.39027	0.658526	0.329263	+	0.944238i	$0.393200\pi$
$68$	−4.54976	−0.551739
$69$	−2.10547	−0.253468
$70$	−0.382485	−0.0457157
$71$	−14.4479	−1.71465	−0.857324	−	0.514777i	$-0.827875\pi$
$71$	−14.4479	−1.71465	−0.857324	+	0.514777i	$0.827875\pi$
$72$	1.00000	0.117851
$73$	16.3009	1.90788	0.953939	−	0.299999i	$-0.0969864\pi$
$73$	16.3009	1.90788	0.953939	+	0.299999i	$0.0969864\pi$
$74$	−0.809455	−0.0940973
$75$	4.70870	0.543714
$76$	0.931175	0.106813
$77$	−0.780579	−0.0889552
$78$	1.00000	0.113228
$79$	−3.67867	−0.413883	−0.206941	−	0.978353i	$-0.566351\pi$
$79$	−3.67867	−0.413883	−0.206941	+	0.978353i	$0.566351\pi$
$80$	−0.539721	−0.0603427
$81$	1.00000	0.111111
$82$	5.39691	0.595988
$83$	−9.54181	−1.04735	−0.523675	−	0.851918i	$-0.675439\pi$
$83$	−9.54181	−1.04735	−0.523675	+	0.851918i	$0.675439\pi$
$84$	−0.708670	−0.0773223
$85$	2.45560	0.266347
$86$	−6.65786	−0.717935
$87$	−8.33493	−0.893598
$88$	−1.10147	−0.117417
$89$	−17.5318	−1.85837	−0.929186	−	0.369612i	$-0.879491\pi$
$89$	−17.5318	−1.85837	−0.929186	+	0.369612i	$0.879491\pi$
$90$	−0.539721	−0.0568916
$91$	−0.708670	−0.0742889
$92$	2.10547	0.219510
$93$	−2.29970	−0.238468
$94$	−4.25716	−0.439093
$95$	−0.502575	−0.0515631
$96$	−1.00000	−0.102062
$97$	−6.25897	−0.635502	−0.317751	−	0.948174i	$-0.602928\pi$
$97$	−6.25897	−0.635502	−0.317751	+	0.948174i	$0.602928\pi$
$98$	−6.49779	−0.656376
$99$	−1.10147	−0.110702
$100$	−4.70870	−0.470870
$101$	0.636449	0.0633291	0.0316645	−	0.999499i	$-0.489919\pi$
$101$	0.636449	0.0633291	0.0316645	+	0.999499i	$0.489919\pi$
$102$	4.54976	0.450493
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	0.382485	0.0373267
$106$	−8.93249	−0.867600
$107$	10.5194	1.01695	0.508473	−	0.861078i	$-0.330210\pi$
$107$	10.5194	1.01695	0.508473	+	0.861078i	$0.330210\pi$
$108$	−1.00000	−0.0962250
$109$	5.95205	0.570103	0.285052	−	0.958512i	$-0.407989\pi$
$109$	5.95205	0.570103	0.285052	+	0.958512i	$0.407989\pi$
$110$	0.594486	0.0566821
$111$	0.809455	0.0768301
$112$	0.708670	0.0669631
$113$	10.5535	0.992792	0.496396	−	0.868096i	$-0.334656\pi$
$113$	10.5535	0.992792	0.496396	+	0.868096i	$0.334656\pi$
$114$	−0.931175	−0.0872125
$115$	−1.13636	−0.105967
$116$	8.33493	0.773879
$117$	−1.00000	−0.0924500
$118$	4.89092	0.450246
$119$	−3.22428	−0.295569
$120$	0.539721	0.0492696
$121$	−9.78677	−0.889706
$122$	−1.40771	−0.127448
$123$	−5.39691	−0.486623
$124$	2.29970	0.206519
$125$	5.23999	0.468679
$126$	0.708670	0.0631334
$127$	−14.6892	−1.30345	−0.651726	−	0.758455i	$-0.725955\pi$
$127$	−14.6892	−1.30345	−0.651726	+	0.758455i	$0.725955\pi$
$128$	1.00000	0.0883883
$129$	6.65786	0.586192
$130$	0.539721	0.0473367
$131$	3.19757	0.279373	0.139686	−	0.990196i	$-0.455391\pi$
$131$	3.19757	0.279373	0.139686	+	0.990196i	$0.455391\pi$
$132$	1.10147	0.0958706
$133$	0.659896	0.0572203
$134$	5.39027	0.465648
$135$	0.539721	0.0464518
$136$	−4.54976	−0.390139
$137$	−7.01255	−0.599122	−0.299561	−	0.954077i	$-0.596840\pi$
$137$	−7.01255	−0.599122	−0.299561	+	0.954077i	$0.596840\pi$
$138$	−2.10547	−0.179229
$139$	−18.1955	−1.54332	−0.771660	−	0.636035i	$-0.780573\pi$
$139$	−18.1955	−1.54332	−0.771660	+	0.636035i	$0.780573\pi$
$140$	−0.382485	−0.0323258
$141$	4.25716	0.358518
$142$	−14.4479	−1.21244
$143$	1.10147	0.0921095
$144$	1.00000	0.0833333
$145$	−4.49854	−0.373583
$146$	16.3009	1.34907
$147$	6.49779	0.535928
$148$	−0.809455	−0.0665368
$149$	6.29462	0.515675	0.257838	−	0.966188i	$-0.416990\pi$
$149$	6.29462	0.515675	0.257838	+	0.966188i	$0.416990\pi$
$150$	4.70870	0.384464
$151$	−18.5954	−1.51327	−0.756634	−	0.653838i	$-0.773158\pi$
$151$	−18.5954	−1.51327	−0.756634	+	0.653838i	$0.773158\pi$
$152$	0.931175	0.0755283
$153$	−4.54976	−0.367826
$154$	−0.780579	−0.0629008
$155$	−1.24120	−0.0996953
$156$	1.00000	0.0800641
$157$	−9.61035	−0.766990	−0.383495	−	0.923543i	$-0.625280\pi$
$157$	−9.61035	−0.766990	−0.383495	+	0.923543i	$0.625280\pi$
$158$	−3.67867	−0.292659
$159$	8.93249	0.708393
$160$	−0.539721	−0.0426687
$161$	1.49208	0.117592
$162$	1.00000	0.0785674
$163$	−6.50347	−0.509391	−0.254695	−	0.967021i	$-0.581975\pi$
$163$	−6.50347	−0.509391	−0.254695	+	0.967021i	$0.581975\pi$
$164$	5.39691	0.421428
$165$	−0.594486	−0.0462807
$166$	−9.54181	−0.740588
$167$	9.69537	0.750251	0.375125	−	0.926974i	$-0.377600\pi$
$167$	9.69537	0.750251	0.375125	+	0.926974i	$0.377600\pi$
$168$	−0.708670	−0.0546751
$169$	1.00000	0.0769231
$170$	2.45560	0.188336
$171$	0.931175	0.0712087
$172$	−6.65786	−0.507657
$173$	8.72919	0.663668	0.331834	−	0.943338i	$-0.392333\pi$
$173$	8.72919	0.663668	0.331834	+	0.943338i	$0.392333\pi$
$174$	−8.33493	−0.631870
$175$	−3.33692	−0.252247
$176$	−1.10147	−0.0830264
$177$	−4.89092	−0.367624
$178$	−17.5318	−1.31407
$179$	−16.0011	−1.19598	−0.597988	−	0.801505i	$-0.704033\pi$
$179$	−16.0011	−1.19598	−0.597988	+	0.801505i	$0.704033\pi$
$180$	−0.539721	−0.0402285
$181$	−6.58006	−0.489092	−0.244546	−	0.969638i	$-0.578639\pi$
$181$	−6.58006	−0.489092	−0.244546	+	0.969638i	$0.578639\pi$
$182$	−0.708670	−0.0525302
$183$	1.40771	0.104061
$184$	2.10547	0.155217
$185$	0.436880	0.0321201
$186$	−2.29970	−0.168622
$187$	5.01142	0.366471
$188$	−4.25716	−0.310486
$189$	−0.708670	−0.0515482
$190$	−0.502575	−0.0364606
$191$	3.85740	0.279112	0.139556	−	0.990214i	$-0.455432\pi$
$191$	3.85740	0.279112	0.139556	+	0.990214i	$0.455432\pi$
$192$	−1.00000	−0.0721688
$193$	−0.327993	−0.0236095	−0.0118047	−	0.999930i	$-0.503758\pi$
$193$	−0.327993	−0.0236095	−0.0118047	+	0.999930i	$0.503758\pi$
$194$	−6.25897	−0.449368
$195$	−0.539721	−0.0386502
$196$	−6.49779	−0.464128
$197$	−11.1650	−0.795473	−0.397737	−	0.917500i	$-0.630204\pi$
$197$	−11.1650	−0.795473	−0.397737	+	0.917500i	$0.630204\pi$
$198$	−1.10147	−0.0782780
$199$	−22.1952	−1.57338	−0.786688	−	0.617350i	$-0.788206\pi$
$199$	−22.1952	−1.57338	−0.786688	+	0.617350i	$0.788206\pi$
$200$	−4.70870	−0.332955
$201$	−5.39027	−0.380200
$202$	0.636449	0.0447804
$203$	5.90672	0.414570
$204$	4.54976	0.318547
$205$	−2.91283	−0.203441
$206$	1.00000	0.0696733
$207$	2.10547	0.146340
$208$	−1.00000	−0.0693375
$209$	−1.02566	−0.0709464
$210$	0.382485	0.0263939
$211$	8.36529	0.575890	0.287945	−	0.957647i	$-0.407028\pi$
$211$	8.36529	0.575890	0.287945	+	0.957647i	$0.407028\pi$
$212$	−8.93249	−0.613486
$213$	14.4479	0.989953
$214$	10.5194	0.719089
$215$	3.59339	0.245067
$216$	−1.00000	−0.0680414
$217$	1.62973	0.110633
$218$	5.95205	0.403124
$219$	−16.3009	−1.10151
$220$	0.594486	0.0400803
$221$	4.54976	0.306050
$222$	0.809455	0.0543271
$223$	17.2527	1.15532	0.577662	−	0.816276i	$-0.303965\pi$
$223$	17.2527	1.15532	0.577662	+	0.816276i	$0.303965\pi$
$224$	0.708670	0.0473500
$225$	−4.70870	−0.313913
$226$	10.5535	0.702010
$227$	26.1340	1.73458	0.867288	−	0.497806i	$-0.165861\pi$
$227$	26.1340	1.73458	0.867288	+	0.497806i	$0.165861\pi$
$228$	−0.931175	−0.0616686
$229$	3.69647	0.244269	0.122135	−	0.992514i	$-0.461026\pi$
$229$	3.69647	0.244269	0.122135	+	0.992514i	$0.461026\pi$
$230$	−1.13636	−0.0749297
$231$	0.780579	0.0513583
$232$	8.33493	0.547215
$233$	−23.2932	−1.52599	−0.762996	−	0.646404i	$-0.776272\pi$
$233$	−23.2932	−1.52599	−0.762996	+	0.646404i	$0.776272\pi$
$234$	−1.00000	−0.0653720
$235$	2.29768	0.149884
$236$	4.89092	0.318372
$237$	3.67867	0.238955
$238$	−3.22428	−0.208999
$239$	15.2849	0.988695	0.494348	−	0.869264i	$-0.335407\pi$
$239$	15.2849	0.988695	0.494348	+	0.869264i	$0.335407\pi$
$240$	0.539721	0.0348389
$241$	−15.6401	−1.00747	−0.503735	−	0.863858i	$-0.668041\pi$
$241$	−15.6401	−1.00747	−0.503735	+	0.863858i	$0.668041\pi$
$242$	−9.78677	−0.629117
$243$	−1.00000	−0.0641500
$244$	−1.40771	−0.0901193
$245$	3.50699	0.224054
$246$	−5.39691	−0.344094
$247$	−0.931175	−0.0592493
$248$	2.29970	0.146031
$249$	9.54181	0.604688
$250$	5.23999	0.331406
$251$	−26.0731	−1.64572	−0.822860	−	0.568245i	$-0.807623\pi$
$251$	−26.0731	−1.64572	−0.822860	+	0.568245i	$0.807623\pi$
$252$	0.708670	0.0446420
$253$	−2.31911	−0.145801
$254$	−14.6892	−0.921679
$255$	−2.45560	−0.153776
$256$	1.00000	0.0625000
$257$	8.64083	0.539000	0.269500	−	0.963000i	$-0.413142\pi$
$257$	8.64083	0.539000	0.269500	+	0.963000i	$0.413142\pi$
$258$	6.65786	0.414500
$259$	−0.573637	−0.0356441
$260$	0.539721	0.0334721
$261$	8.33493	0.515919
$262$	3.19757	0.197546
$263$	−2.21714	−0.136715	−0.0683573	−	0.997661i	$-0.521776\pi$
$263$	−2.21714	−0.136715	−0.0683573	+	0.997661i	$0.521776\pi$
$264$	1.10147	0.0677907
$265$	4.82106	0.296155
$266$	0.659896	0.0404608
$267$	17.5318	1.07293
$268$	5.39027	0.329263
$269$	−1.98455	−0.121000	−0.0605002	−	0.998168i	$-0.519270\pi$
$269$	−1.98455	−0.121000	−0.0605002	+	0.998168i	$0.519270\pi$
$270$	0.539721	0.0328464
$271$	20.2639	1.23095	0.615473	−	0.788158i	$-0.288965\pi$
$271$	20.2639	1.23095	0.615473	+	0.788158i	$0.288965\pi$
$272$	−4.54976	−0.275870
$273$	0.708670	0.0428907
$274$	−7.01255	−0.423643
$275$	5.18649	0.312757
$276$	−2.10547	−0.126734
$277$	−8.71751	−0.523785	−0.261892	−	0.965097i	$-0.584347\pi$
$277$	−8.71751	−0.523785	−0.261892	+	0.965097i	$0.584347\pi$
$278$	−18.1955	−1.09129
$279$	2.29970	0.137679
$280$	−0.382485	−0.0228578
$281$	13.0568	0.778903	0.389452	−	0.921047i	$-0.372665\pi$
$281$	13.0568	0.778903	0.389452	+	0.921047i	$0.372665\pi$
$282$	4.25716	0.253510
$283$	−5.27042	−0.313294	−0.156647	−	0.987655i	$-0.550068\pi$
$283$	−5.27042	−0.313294	−0.156647	+	0.987655i	$0.550068\pi$
$284$	−14.4479	−0.857324
$285$	0.502575	0.0297700
$286$	1.10147	0.0651312
$287$	3.82463	0.225761
$288$	1.00000	0.0589256
$289$	3.70030	0.217665
$290$	−4.49854	−0.264163
$291$	6.25897	0.366907
$292$	16.3009	0.953939
$293$	2.50680	0.146449	0.0732245	−	0.997315i	$-0.476671\pi$
$293$	2.50680	0.146449	0.0732245	+	0.997315i	$0.476671\pi$
$294$	6.49779	0.378959
$295$	−2.63974	−0.153691
$296$	−0.809455	−0.0470486
$297$	1.10147	0.0639137
$298$	6.29462	0.364638
$299$	−2.10547	−0.121762
$300$	4.70870	0.271857
$301$	−4.71823	−0.271954
$302$	−18.5954	−1.07004
$303$	−0.636449	−0.0365631
$304$	0.931175	0.0534066
$305$	0.759770	0.0435043
$306$	−4.54976	−0.260092
$307$	−4.99635	−0.285157	−0.142579	−	0.989783i	$-0.545539\pi$
$307$	−4.99635	−0.285157	−0.142579	+	0.989783i	$0.545539\pi$
$308$	−0.780579	−0.0444776
$309$	−1.00000	−0.0568880
$310$	−1.24120	−0.0704952
$311$	4.07333	0.230977	0.115489	−	0.993309i	$-0.463157\pi$
$311$	4.07333	0.230977	0.115489	+	0.993309i	$0.463157\pi$
$312$	1.00000	0.0566139
$313$	24.5742	1.38901	0.694507	−	0.719486i	$-0.255623\pi$
$313$	24.5742	1.38901	0.694507	+	0.719486i	$0.255623\pi$
$314$	−9.61035	−0.542344
$315$	−0.382485	−0.0215506
$316$	−3.67867	−0.206941
$317$	−35.4866	−1.99313	−0.996564	−	0.0828267i	$-0.973605\pi$
$317$	−35.4866	−1.99313	−0.996564	+	0.0828267i	$0.973605\pi$
$318$	8.93249	0.500909
$319$	−9.18067	−0.514019
$320$	−0.539721	−0.0301713
$321$	−10.5194	−0.587134
$322$	1.49208	0.0831504
$323$	−4.23662	−0.235732
$324$	1.00000	0.0555556
$325$	4.70870	0.261192
$326$	−6.50347	−0.360194
$327$	−5.95205	−0.329149
$328$	5.39691	0.297994
$329$	−3.01693	−0.166329
$330$	−0.594486	−0.0327254
$331$	−33.8590	−1.86106	−0.930529	−	0.366219i	$-0.880652\pi$
$331$	−33.8590	−1.86106	−0.930529	+	0.366219i	$0.880652\pi$
$332$	−9.54181	−0.523675
$333$	−0.809455	−0.0443579
$334$	9.69537	0.530507
$335$	−2.90924	−0.158949
$336$	−0.708670	−0.0386611
$337$	−13.0622	−0.711542	−0.355771	−	0.934573i	$-0.615782\pi$
$337$	−13.0622	−0.711542	−0.355771	+	0.934573i	$0.615782\pi$
$338$	1.00000	0.0543928
$339$	−10.5535	−0.573188
$340$	2.45560	0.133174
$341$	−2.53305	−0.137172
$342$	0.931175	0.0503522
$343$	−9.56548	−0.516488
$344$	−6.65786	−0.358968
$345$	1.13636	0.0611798
$346$	8.72919	0.469284
$347$	30.6772	1.64684	0.823419	−	0.567434i	$-0.192064\pi$
$347$	30.6772	1.64684	0.823419	+	0.567434i	$0.192064\pi$
$348$	−8.33493	−0.446799
$349$	−26.7454	−1.43165	−0.715825	−	0.698280i	$-0.753949\pi$
$349$	−26.7454	−1.43165	−0.715825	+	0.698280i	$0.753949\pi$
$350$	−3.33692	−0.178366
$351$	1.00000	0.0533761
$352$	−1.10147	−0.0587085
$353$	−0.849340	−0.0452058	−0.0226029	−	0.999745i	$-0.507195\pi$
$353$	−0.849340	−0.0452058	−0.0226029	+	0.999745i	$0.507195\pi$
$354$	−4.89092	−0.259950
$355$	7.79783	0.413866
$356$	−17.5318	−0.929186
$357$	3.22428	0.170647
$358$	−16.0011	−0.845683
$359$	2.74359	0.144801	0.0724006	−	0.997376i	$-0.476934\pi$
$359$	2.74359	0.144801	0.0724006	+	0.997376i	$0.476934\pi$
$360$	−0.539721	−0.0284458
$361$	−18.1329	−0.954364
$362$	−6.58006	−0.345841
$363$	9.78677	0.513672
$364$	−0.708670	−0.0371444
$365$	−8.79796	−0.460506
$366$	1.40771	0.0735821
$367$	−0.938217	−0.0489745	−0.0244873	−	0.999700i	$-0.507795\pi$
$367$	−0.938217	−0.0489745	−0.0244873	+	0.999700i	$0.507795\pi$
$368$	2.10547	0.109755
$369$	5.39691	0.280952
$370$	0.436880	0.0227123
$371$	−6.33019	−0.328647
$372$	−2.29970	−0.119234
$373$	−4.14694	−0.214720	−0.107360	−	0.994220i	$-0.534240\pi$
$373$	−4.14694	−0.214720	−0.107360	+	0.994220i	$0.534240\pi$
$374$	5.01142	0.259134
$375$	−5.23999	−0.270592
$376$	−4.25716	−0.219547
$377$	−8.33493	−0.429271
$378$	−0.708670	−0.0364501
$379$	−2.20095	−0.113055	−0.0565276	−	0.998401i	$-0.518003\pi$
$379$	−2.20095	−0.113055	−0.0565276	+	0.998401i	$0.518003\pi$
$380$	−0.502575	−0.0257816
$381$	14.6892	0.752548
$382$	3.85740	0.197362
$383$	−17.1982	−0.878786	−0.439393	−	0.898295i	$-0.644806\pi$
$383$	−17.1982	−0.878786	−0.439393	+	0.898295i	$0.644806\pi$
$384$	−1.00000	−0.0510310
$385$	0.421295	0.0214712
$386$	−0.327993	−0.0166944
$387$	−6.65786	−0.338438
$388$	−6.25897	−0.317751
$389$	−14.5221	−0.736302	−0.368151	−	0.929766i	$-0.620009\pi$
$389$	−14.5221	−0.736302	−0.368151	+	0.929766i	$0.620009\pi$
$390$	−0.539721	−0.0273299
$391$	−9.57936	−0.484449
$392$	−6.49779	−0.328188
$393$	−3.19757	−0.161296
$394$	−11.1650	−0.562485
$395$	1.98546	0.0998992
$396$	−1.10147	−0.0553509
$397$	−23.2270	−1.16573	−0.582864	−	0.812570i	$-0.698068\pi$
$397$	−23.2270	−1.16573	−0.582864	+	0.812570i	$0.698068\pi$
$398$	−22.1952	−1.11255
$399$	−0.659896	−0.0330361
$400$	−4.70870	−0.235435
$401$	−12.4247	−0.620461	−0.310231	−	0.950661i	$-0.600406\pi$
$401$	−12.4247	−0.620461	−0.310231	+	0.950661i	$0.600406\pi$
$402$	−5.39027	−0.268842
$403$	−2.29970	−0.114556
$404$	0.636449	0.0316645
$405$	−0.539721	−0.0268190
$406$	5.90672	0.293146
$407$	0.891590	0.0441945
$408$	4.54976	0.225247
$409$	−5.42363	−0.268181	−0.134091	−	0.990969i	$-0.542811\pi$
$409$	−5.42363	−0.268181	−0.134091	+	0.990969i	$0.542811\pi$
$410$	−2.91283	−0.143854
$411$	7.01255	0.345903
$412$	1.00000	0.0492665
$413$	3.46605	0.170553
$414$	2.10547	0.103478
$415$	5.14992	0.252800
$416$	−1.00000	−0.0490290
$417$	18.1955	0.891036
$418$	−1.02566	−0.0501667
$419$	−30.2821	−1.47938	−0.739688	−	0.672950i	$-0.765027\pi$
$419$	−30.2821	−1.47938	−0.739688	+	0.672950i	$0.765027\pi$
$420$	0.382485	0.0186633
$421$	−5.44729	−0.265485	−0.132742	−	0.991151i	$-0.542378\pi$
$421$	−5.44729	−0.265485	−0.132742	+	0.991151i	$0.542378\pi$
$422$	8.36529	0.407216
$423$	−4.25716	−0.206990
$424$	−8.93249	−0.433800
$425$	21.4234	1.03919
$426$	14.4479	0.700002
$427$	−0.997602	−0.0482773
$428$	10.5194	0.508473
$429$	−1.10147	−0.0531794
$430$	3.59339	0.173289
$431$	37.5961	1.81094	0.905471	−	0.424409i	$-0.139518\pi$
$431$	37.5961	1.81094	0.905471	+	0.424409i	$0.139518\pi$
$432$	−1.00000	−0.0481125
$433$	36.4527	1.75180	0.875901	−	0.482490i	$-0.160268\pi$
$433$	36.4527	1.75180	0.875901	+	0.482490i	$0.160268\pi$
$434$	1.62973	0.0782294
$435$	4.49854	0.215689
$436$	5.95205	0.285052
$437$	1.96056	0.0937861
$438$	−16.3009	−0.778888
$439$	10.4691	0.499663	0.249831	−	0.968289i	$-0.419625\pi$
$439$	10.4691	0.499663	0.249831	+	0.968289i	$0.419625\pi$
$440$	0.594486	0.0283410
$441$	−6.49779	−0.309418
$442$	4.54976	0.216410
$443$	7.06705	0.335766	0.167883	−	0.985807i	$-0.446307\pi$
$443$	7.06705	0.335766	0.167883	+	0.985807i	$0.446307\pi$
$444$	0.809455	0.0384151
$445$	9.46231	0.448557
$446$	17.2527	0.816938
$447$	−6.29462	−0.297725
$448$	0.708670	0.0334815
$449$	10.6264	0.501491	0.250746	−	0.968053i	$-0.419324\pi$
$449$	10.6264	0.501491	0.250746	+	0.968053i	$0.419324\pi$
$450$	−4.70870	−0.221970
$451$	−5.94452	−0.279917
$452$	10.5535	0.496396
$453$	18.5954	0.873686
$454$	26.1340	1.22653
$455$	0.382485	0.0179312
$456$	−0.931175	−0.0436063
$457$	−2.61894	−0.122509	−0.0612544	−	0.998122i	$-0.519510\pi$
$457$	−2.61894	−0.122509	−0.0612544	+	0.998122i	$0.519510\pi$
$458$	3.69647	0.172725
$459$	4.54976	0.212365
$460$	−1.13636	−0.0529833
$461$	−12.8560	−0.598762	−0.299381	−	0.954134i	$-0.596780\pi$
$461$	−12.8560	−0.598762	−0.299381	+	0.954134i	$0.596780\pi$
$462$	0.780579	0.0363158
$463$	−26.0165	−1.20909	−0.604544	−	0.796571i	$-0.706645\pi$
$463$	−26.0165	−1.20909	−0.604544	+	0.796571i	$0.706645\pi$
$464$	8.33493	0.386939
$465$	1.24120	0.0575591
$466$	−23.2932	−1.07904
$467$	14.0895	0.651986	0.325993	−	0.945372i	$-0.394301\pi$
$467$	14.0895	0.651986	0.325993	+	0.945372i	$0.394301\pi$
$468$	−1.00000	−0.0462250
$469$	3.81993	0.176388
$470$	2.29768	0.105984
$471$	9.61035	0.442822
$472$	4.89092	0.225123
$473$	7.33342	0.337191
$474$	3.67867	0.168967
$475$	−4.38462	−0.201180
$476$	−3.22428	−0.147785
$477$	−8.93249	−0.408991
$478$	15.2849	0.699113
$479$	−2.86549	−0.130928	−0.0654638	−	0.997855i	$-0.520853\pi$
$479$	−2.86549	−0.130928	−0.0654638	+	0.997855i	$0.520853\pi$
$480$	0.539721	0.0246348
$481$	0.809455	0.0369080
$482$	−15.6401	−0.712388
$483$	−1.49208	−0.0678920
$484$	−9.78677	−0.444853
$485$	3.37810	0.153392
$486$	−1.00000	−0.0453609
$487$	35.4875	1.60809	0.804047	−	0.594566i	$-0.202676\pi$
$487$	35.4875	1.60809	0.804047	+	0.594566i	$0.202676\pi$
$488$	−1.40771	−0.0637240
$489$	6.50347	0.294097
$490$	3.50699	0.158430
$491$	−23.4161	−1.05675	−0.528377	−	0.849010i	$-0.677199\pi$
$491$	−23.4161	−1.05675	−0.528377	+	0.849010i	$0.677199\pi$
$492$	−5.39691	−0.243311
$493$	−37.9219	−1.70792
$494$	−0.931175	−0.0418955
$495$	0.594486	0.0267202
$496$	2.29970	0.103259
$497$	−10.2388	−0.459272
$498$	9.54181	0.427579
$499$	−35.3167	−1.58099	−0.790497	−	0.612466i	$-0.790178\pi$
$499$	−35.3167	−1.58099	−0.790497	+	0.612466i	$0.790178\pi$
$500$	5.23999	0.234340
$501$	−9.69537	−0.433157
$502$	−26.0731	−1.16370
$503$	−14.3136	−0.638212	−0.319106	−	0.947719i	$-0.603383\pi$
$503$	−14.3136	−0.638212	−0.319106	+	0.947719i	$0.603383\pi$
$504$	0.708670	0.0315667
$505$	−0.343505	−0.0152858
$506$	−2.31911	−0.103097
$507$	−1.00000	−0.0444116
$508$	−14.6892	−0.651726
$509$	−20.6756	−0.916429	−0.458215	−	0.888842i	$-0.651511\pi$
$509$	−20.6756	−0.916429	−0.458215	+	0.888842i	$0.651511\pi$
$510$	−2.45560	−0.108736
$511$	11.5520	0.511030
$512$	1.00000	0.0441942
$513$	−0.931175	−0.0411124
$514$	8.64083	0.381131
$515$	−0.539721	−0.0237830
$516$	6.65786	0.293096
$517$	4.68914	0.206228
$518$	−0.573637	−0.0252042
$519$	−8.72919	−0.383169
$520$	0.539721	0.0236683
$521$	−11.0642	−0.484730	−0.242365	−	0.970185i	$-0.577923\pi$
$521$	−11.0642	−0.484730	−0.242365	+	0.970185i	$0.577923\pi$
$522$	8.33493	0.364810
$523$	−3.78438	−0.165479	−0.0827397	−	0.996571i	$-0.526367\pi$
$523$	−3.78438	−0.165479	−0.0827397	+	0.996571i	$0.526367\pi$
$524$	3.19757	0.139686
$525$	3.33692	0.145635
$526$	−2.21714	−0.0966718
$527$	−10.4631	−0.455778
$528$	1.10147	0.0479353
$529$	−18.5670	−0.807262
$530$	4.82106	0.209413
$531$	4.89092	0.212248
$532$	0.659896	0.0286101
$533$	−5.39691	−0.233766
$534$	17.5318	0.758677
$535$	−5.67752	−0.245461
$536$	5.39027	0.232824
$537$	16.0011	0.690497
$538$	−1.98455	−0.0855602
$539$	7.15711	0.308279
$540$	0.539721	0.0232259
$541$	−0.819193	−0.0352199	−0.0176099	−	0.999845i	$-0.505606\pi$
$541$	−0.819193	−0.0352199	−0.0176099	+	0.999845i	$0.505606\pi$
$542$	20.2639	0.870411
$543$	6.58006	0.282378
$544$	−4.54976	−0.195069
$545$	−3.21245	−0.137606
$546$	0.708670	0.0303283
$547$	14.6752	0.627464	0.313732	−	0.949512i	$-0.398421\pi$
$547$	14.6752	0.627464	0.313732	+	0.949512i	$0.398421\pi$
$548$	−7.01255	−0.299561
$549$	−1.40771	−0.0600795
$550$	5.18649	0.221153
$551$	7.76128	0.330642
$552$	−2.10547	−0.0896146
$553$	−2.60696	−0.110859
$554$	−8.71751	−0.370372
$555$	−0.436880	−0.0185445
$556$	−18.1955	−0.771660
$557$	4.72433	0.200176	0.100088	−	0.994979i	$-0.468087\pi$
$557$	4.72433	0.200176	0.100088	+	0.994979i	$0.468087\pi$
$558$	2.29970	0.0973540
$559$	6.65786	0.281597
$560$	−0.382485	−0.0161629
$561$	−5.01142	−0.211582
$562$	13.0568	0.550768
$563$	43.9808	1.85357	0.926785	−	0.375592i	$-0.122560\pi$
$563$	43.9808	1.85357	0.926785	+	0.375592i	$0.122560\pi$
$564$	4.25716	0.179259
$565$	−5.69596	−0.239631
$566$	−5.27042	−0.221532
$567$	0.708670	0.0297614
$568$	−14.4479	−0.606220
$569$	−43.0814	−1.80607	−0.903033	−	0.429572i	$-0.858664\pi$
$569$	−43.0814	−1.80607	−0.903033	+	0.429572i	$0.858664\pi$
$570$	0.502575	0.0210506
$571$	−27.9191	−1.16838	−0.584190	−	0.811617i	$-0.698588\pi$
$571$	−27.9191	−1.16838	−0.584190	+	0.811617i	$0.698588\pi$
$572$	1.10147	0.0460547
$573$	−3.85740	−0.161145
$574$	3.82463	0.159637
$575$	−9.91401	−0.413443
$576$	1.00000	0.0416667
$577$	−4.89224	−0.203667	−0.101833	−	0.994801i	$-0.532471\pi$
$577$	−4.89224	−0.203667	−0.101833	+	0.994801i	$0.532471\pi$
$578$	3.70030	0.153912
$579$	0.327993	0.0136309
$580$	−4.49854	−0.186792
$581$	−6.76200	−0.280535
$582$	6.25897	0.259443
$583$	9.83886	0.407484
$584$	16.3009	0.674537
$585$	0.539721	0.0223147
$586$	2.50680	0.103555
$587$	1.84483	0.0761443	0.0380722	−	0.999275i	$-0.487878\pi$
$587$	1.84483	0.0761443	0.0380722	+	0.999275i	$0.487878\pi$
$588$	6.49779	0.267964
$589$	2.14142	0.0882357
$590$	−2.63974	−0.108676
$591$	11.1650	0.459267
$592$	−0.809455	−0.0332684
$593$	19.2327	0.789791	0.394895	−	0.918726i	$-0.370781\pi$
$593$	19.2327	0.789791	0.394895	+	0.918726i	$0.370781\pi$
$594$	1.10147	0.0451938
$595$	1.74021	0.0713417
$596$	6.29462	0.257838
$597$	22.1952	0.908389
$598$	−2.10547	−0.0860989
$599$	−27.7377	−1.13333	−0.566666	−	0.823948i	$-0.691767\pi$
$599$	−27.7377	−1.13333	−0.566666	+	0.823948i	$0.691767\pi$
$600$	4.70870	0.192232
$601$	−12.3774	−0.504885	−0.252442	−	0.967612i	$-0.581234\pi$
$601$	−12.3774	−0.504885	−0.252442	+	0.967612i	$0.581234\pi$
$602$	−4.71823	−0.192301
$603$	5.39027	0.219509
$604$	−18.5954	−0.756634
$605$	5.28213	0.214749
$606$	−0.636449	−0.0258540
$607$	−2.32133	−0.0942198	−0.0471099	−	0.998890i	$-0.515001\pi$
$607$	−2.32133	−0.0942198	−0.0471099	+	0.998890i	$0.515001\pi$
$608$	0.931175	0.0377641
$609$	−5.90672	−0.239352
$610$	0.759770	0.0307622
$611$	4.25716	0.172226
$612$	−4.54976	−0.183913
$613$	−31.5510	−1.27433	−0.637167	−	0.770726i	$-0.719894\pi$
$613$	−31.5510	−1.27433	−0.637167	+	0.770726i	$0.719894\pi$
$614$	−4.99635	−0.201636
$615$	2.91283	0.117456
$616$	−0.780579	−0.0314504
$617$	12.8471	0.517203	0.258601	−	0.965984i	$-0.416738\pi$
$617$	12.8471	0.517203	0.258601	+	0.965984i	$0.416738\pi$
$618$	−1.00000	−0.0402259
$619$	34.5508	1.38872	0.694358	−	0.719630i	$-0.255688\pi$
$619$	34.5508	1.38872	0.694358	+	0.719630i	$0.255688\pi$
$620$	−1.24120	−0.0498476
$621$	−2.10547	−0.0844894
$622$	4.07333	0.163326
$623$	−12.4243	−0.497769
$624$	1.00000	0.0400320
$625$	20.7154	0.828615
$626$	24.5742	0.982181
$627$	1.02566	0.0409609
$628$	−9.61035	−0.383495
$629$	3.68283	0.146844
$630$	−0.382485	−0.0152386
$631$	−27.8491	−1.10865	−0.554327	−	0.832299i	$-0.687024\pi$
$631$	−27.8491	−1.10865	−0.554327	+	0.832299i	$0.687024\pi$
$632$	−3.67867	−0.146330
$633$	−8.36529	−0.332490
$634$	−35.4866	−1.40935
$635$	7.92805	0.314615
$636$	8.93249	0.354196
$637$	6.49779	0.257452
$638$	−9.18067	−0.363466
$639$	−14.4479	−0.571549
$640$	−0.539721	−0.0213344
$641$	35.7002	1.41007	0.705037	−	0.709171i	$-0.250930\pi$
$641$	35.7002	1.41007	0.705037	+	0.709171i	$0.250930\pi$
$642$	−10.5194	−0.415166
$643$	7.39959	0.291811	0.145906	−	0.989298i	$-0.453390\pi$
$643$	7.39959	0.291811	0.145906	+	0.989298i	$0.453390\pi$
$644$	1.49208	0.0587962
$645$	−3.59339	−0.141489
$646$	−4.23662	−0.166688
$647$	6.93155	0.272507	0.136254	−	0.990674i	$-0.456494\pi$
$647$	6.93155	0.272507	0.136254	+	0.990674i	$0.456494\pi$
$648$	1.00000	0.0392837
$649$	−5.38720	−0.211466
$650$	4.70870	0.184690
$651$	−1.62973	−0.0638741
$652$	−6.50347	−0.254695
$653$	17.0877	0.668693	0.334346	−	0.942450i	$-0.391484\pi$
$653$	17.0877	0.668693	0.334346	+	0.942450i	$0.391484\pi$
$654$	−5.95205	−0.232744
$655$	−1.72580	−0.0674324
$656$	5.39691	0.210714
$657$	16.3009	0.635960
$658$	−3.01693	−0.117612
$659$	−13.9300	−0.542635	−0.271318	−	0.962490i	$-0.587459\pi$
$659$	−13.9300	−0.542635	−0.271318	+	0.962490i	$0.587459\pi$
$660$	−0.594486	−0.0231404
$661$	21.7214	0.844864	0.422432	−	0.906395i	$-0.361177\pi$
$661$	21.7214	0.844864	0.422432	+	0.906395i	$0.361177\pi$
$662$	−33.8590	−1.31597
$663$	−4.54976	−0.176698
$664$	−9.54181	−0.370294
$665$	−0.356160	−0.0138113
$666$	−0.809455	−0.0313658
$667$	17.5489	0.679496
$668$	9.69537	0.375125
$669$	−17.2527	−0.667027
$670$	−2.90924	−0.112394
$671$	1.55055	0.0598582
$672$	−0.708670	−0.0273376
$673$	30.2097	1.16450	0.582250	−	0.813010i	$-0.302173\pi$
$673$	30.2097	1.16450	0.582250	+	0.813010i	$0.302173\pi$
$674$	−13.0622	−0.503136
$675$	4.70870	0.181238
$676$	1.00000	0.0384615
$677$	−8.46865	−0.325476	−0.162738	−	0.986669i	$-0.552033\pi$
$677$	−8.46865	−0.325476	−0.162738	+	0.986669i	$0.552033\pi$
$678$	−10.5535	−0.405305
$679$	−4.43555	−0.170221
$680$	2.45560	0.0941680
$681$	−26.1340	−1.00146
$682$	−2.53305	−0.0969954
$683$	25.4534	0.973947	0.486973	−	0.873417i	$-0.338101\pi$
$683$	25.4534	0.973947	0.486973	+	0.873417i	$0.338101\pi$
$684$	0.931175	0.0356044
$685$	3.78482	0.144611
$686$	−9.56548	−0.365212
$687$	−3.69647	−0.141029
$688$	−6.65786	−0.253828
$689$	8.93249	0.340301
$690$	1.13636	0.0432607
$691$	23.1131	0.879265	0.439632	−	0.898178i	$-0.355109\pi$
$691$	23.1131	0.879265	0.439632	+	0.898178i	$0.355109\pi$
$692$	8.72919	0.331834
$693$	−0.780579	−0.0296517
$694$	30.6772	1.16449
$695$	9.82049	0.372512
$696$	−8.33493	−0.315935
$697$	−24.5546	−0.930072
$698$	−26.7454	−1.01233
$699$	23.2932	0.881031
$700$	−3.33692	−0.126124
$701$	−39.9624	−1.50936	−0.754680	−	0.656093i	$-0.772208\pi$
$701$	−39.9624	−1.50936	−0.754680	+	0.656093i	$0.772208\pi$
$702$	1.00000	0.0377426
$703$	−0.753745	−0.0284280
$704$	−1.10147	−0.0415132
$705$	−2.29768	−0.0865357
$706$	−0.849340	−0.0319653
$707$	0.451033	0.0169628
$708$	−4.89092	−0.183812
$709$	−9.69031	−0.363927	−0.181964	−	0.983305i	$-0.558245\pi$
$709$	−9.69031	−0.363927	−0.181964	+	0.983305i	$0.558245\pi$
$710$	7.79783	0.292647
$711$	−3.67867	−0.137961
$712$	−17.5318	−0.657034
$713$	4.84193	0.181332
$714$	3.22428	0.120666
$715$	−0.594486	−0.0222325
$716$	−16.0011	−0.597988
$717$	−15.2849	−0.570824
$718$	2.74359	0.102390
$719$	24.4712	0.912620	0.456310	−	0.889821i	$-0.349171\pi$
$719$	24.4712	0.912620	0.456310	+	0.889821i	$0.349171\pi$
$720$	−0.539721	−0.0201142
$721$	0.708670	0.0263923
$722$	−18.1329	−0.674837
$723$	15.6401	0.581663
$724$	−6.58006	−0.244546
$725$	−39.2467	−1.45759
$726$	9.78677	0.363221
$727$	45.4357	1.68512	0.842558	−	0.538606i	$-0.181049\pi$
$727$	45.4357	1.68512	0.842558	+	0.538606i	$0.181049\pi$
$728$	−0.708670	−0.0262651
$729$	1.00000	0.0370370
$730$	−8.79796	−0.325627
$731$	30.2916	1.12038
$732$	1.40771	0.0520304
$733$	−37.8066	−1.39642	−0.698209	−	0.715894i	$-0.746020\pi$
$733$	−37.8066	−1.39642	−0.698209	+	0.715894i	$0.746020\pi$
$734$	−0.938217	−0.0346302
$735$	−3.50699	−0.129357
$736$	2.10547	0.0776085
$737$	−5.93722	−0.218700
$738$	5.39691	0.198663
$739$	31.9130	1.17394	0.586969	−	0.809609i	$-0.300321\pi$
$739$	31.9130	1.17394	0.586969	+	0.809609i	$0.300321\pi$
$740$	0.436880	0.0160600
$741$	0.931175	0.0342076
$742$	−6.33019	−0.232389
$743$	8.58617	0.314996	0.157498	−	0.987519i	$-0.449657\pi$
$743$	8.58617	0.314996	0.157498	+	0.987519i	$0.449657\pi$
$744$	−2.29970	−0.0843110
$745$	−3.39734	−0.124469
$746$	−4.14694	−0.151830
$747$	−9.54181	−0.349117
$748$	5.01142	0.183236
$749$	7.45476	0.272391
$750$	−5.23999	−0.191337
$751$	−28.0920	−1.02509	−0.512546	−	0.858660i	$-0.671298\pi$
$751$	−28.0920	−1.02509	−0.512546	+	0.858660i	$0.671298\pi$
$752$	−4.25716	−0.155243
$753$	26.0731	0.950156
$754$	−8.33493	−0.303540
$755$	10.0363	0.365259
$756$	−0.708670	−0.0257741
$757$	−4.39733	−0.159824	−0.0799118	−	0.996802i	$-0.525464\pi$
$757$	−4.39733	−0.159824	−0.0799118	+	0.996802i	$0.525464\pi$
$758$	−2.20095	−0.0799421
$759$	2.31911	0.0841782
$760$	−0.502575	−0.0182303
$761$	41.3215	1.49790	0.748952	−	0.662625i	$-0.230558\pi$
$761$	41.3215	1.49790	0.748952	+	0.662625i	$0.230558\pi$
$762$	14.6892	0.532132
$763$	4.21805	0.152703
$764$	3.85740	0.139556
$765$	2.45560	0.0887825
$766$	−17.1982	−0.621396
$767$	−4.89092	−0.176601
$768$	−1.00000	−0.0360844
$769$	13.3570	0.481667	0.240833	−	0.970566i	$-0.422579\pi$
$769$	13.3570	0.481667	0.240833	+	0.970566i	$0.422579\pi$
$770$	0.421295	0.0151824
$771$	−8.64083	−0.311192
$772$	−0.327993	−0.0118047
$773$	−5.44941	−0.196002	−0.0980008	−	0.995186i	$-0.531245\pi$
$773$	−5.44941	−0.196002	−0.0980008	+	0.995186i	$0.531245\pi$
$774$	−6.65786	−0.239312
$775$	−10.8286	−0.388974
$776$	−6.25897	−0.224684
$777$	0.573637	0.0205791
$778$	−14.5221	−0.520644
$779$	5.02546	0.180056
$780$	−0.539721	−0.0193251
$781$	15.9139	0.569444
$782$	−9.57936	−0.342557
$783$	−8.33493	−0.297866
$784$	−6.49779	−0.232064
$785$	5.18691	0.185129
$786$	−3.19757	−0.114053
$787$	43.2576	1.54197	0.770983	−	0.636856i	$-0.219765\pi$
$787$	43.2576	1.54197	0.770983	+	0.636856i	$0.219765\pi$
$788$	−11.1650	−0.397737
$789$	2.21714	0.0789322
$790$	1.98546	0.0706394
$791$	7.47897	0.265921
$792$	−1.10147	−0.0391390
$793$	1.40771	0.0499892
$794$	−23.2270	−0.824294
$795$	−4.82106	−0.170985
$796$	−22.1952	−0.786688
$797$	43.2364	1.53151	0.765756	−	0.643131i	$-0.222365\pi$
$797$	43.2364	1.53151	0.765756	+	0.643131i	$0.222365\pi$
$798$	−0.659896	−0.0233601
$799$	19.3691	0.685228
$800$	−4.70870	−0.166478
$801$	−17.5318	−0.619457
$802$	−12.4247	−0.438732
$803$	−17.9550	−0.633617
$804$	−5.39027	−0.190100
$805$	−0.805308	−0.0283834
$806$	−2.29970	−0.0810034
$807$	1.98455	0.0698596
$808$	0.636449	0.0223902
$809$	−11.1553	−0.392199	−0.196100	−	0.980584i	$-0.562828\pi$
$809$	−11.1553	−0.392199	−0.196100	+	0.980584i	$0.562828\pi$
$810$	−0.539721	−0.0189639
$811$	−10.9739	−0.385347	−0.192674	−	0.981263i	$-0.561716\pi$
$811$	−10.9739	−0.385347	−0.192674	+	0.981263i	$0.561716\pi$
$812$	5.90672	0.207285
$813$	−20.2639	−0.710687
$814$	0.891590	0.0312502
$815$	3.51006	0.122952
$816$	4.54976	0.159273
$817$	−6.19963	−0.216898
$818$	−5.42363	−0.189633
$819$	−0.708670	−0.0247630
$820$	−2.91283	−0.101720
$821$	24.1611	0.843229	0.421615	−	0.906775i	$-0.361463\pi$
$821$	24.1611	0.843229	0.421615	+	0.906775i	$0.361463\pi$
$822$	7.01255	0.244591
$823$	54.2513	1.89108	0.945542	−	0.325501i	$-0.105533\pi$
$823$	54.2513	1.89108	0.945542	+	0.325501i	$0.105533\pi$
$824$	1.00000	0.0348367
$825$	−5.18649	−0.180570
$826$	3.46605	0.120599
$827$	46.1538	1.60492	0.802462	−	0.596703i	$-0.203523\pi$
$827$	46.1538	1.60492	0.802462	+	0.596703i	$0.203523\pi$
$828$	2.10547	0.0731700
$829$	−49.8573	−1.73162	−0.865808	−	0.500377i	$-0.833195\pi$
$829$	−49.8573	−1.73162	−0.865808	+	0.500377i	$0.833195\pi$
$830$	5.14992	0.178756
$831$	8.71751	0.302407
$832$	−1.00000	−0.0346688
$833$	29.5634	1.02431
$834$	18.1955	0.630058
$835$	−5.23280	−0.181089
$836$	−1.02566	−0.0354732
$837$	−2.29970	−0.0794892
$838$	−30.2821	−1.04608
$839$	−35.5586	−1.22762	−0.613810	−	0.789454i	$-0.710364\pi$
$839$	−35.5586	−1.22762	−0.613810	+	0.789454i	$0.710364\pi$
$840$	0.382485	0.0131970
$841$	40.4711	1.39555
$842$	−5.44729	−0.187726
$843$	−13.0568	−0.449700
$844$	8.36529	0.287945
$845$	−0.539721	−0.0185670
$846$	−4.25716	−0.146364
$847$	−6.93559	−0.238310
$848$	−8.93249	−0.306743
$849$	5.27042	0.180880
$850$	21.4234	0.734818
$851$	−1.70428	−0.0584220
$852$	14.4479	0.494976
$853$	−28.9649	−0.991739	−0.495869	−	0.868397i	$-0.665151\pi$
$853$	−28.9649	−0.991739	−0.495869	+	0.868397i	$0.665151\pi$
$854$	−0.997602	−0.0341372
$855$	−0.502575	−0.0171877
$856$	10.5194	0.359544
$857$	41.7470	1.42605	0.713025	−	0.701139i	$-0.247325\pi$
$857$	41.7470	1.42605	0.713025	+	0.701139i	$0.247325\pi$
$858$	−1.10147	−0.0376035
$859$	−48.6254	−1.65908	−0.829538	−	0.558450i	$-0.811396\pi$
$859$	−48.6254	−1.65908	−0.829538	+	0.558450i	$0.811396\pi$
$860$	3.59339	0.122533
$861$	−3.82463	−0.130343
$862$	37.5961	1.28053
$863$	33.3513	1.13529	0.567646	−	0.823273i	$-0.307854\pi$
$863$	33.3513	1.13529	0.567646	+	0.823273i	$0.307854\pi$
$864$	−1.00000	−0.0340207
$865$	−4.71133	−0.160190
$866$	36.4527	1.23871
$867$	−3.70030	−0.125669
$868$	1.62973	0.0553166
$869$	4.05194	0.137453
$870$	4.49854	0.152515
$871$	−5.39027	−0.182642
$872$	5.95205	0.201562
$873$	−6.25897	−0.211834
$874$	1.96056	0.0663168
$875$	3.71343	0.125537
$876$	−16.3009	−0.550757
$877$	−8.38434	−0.283119	−0.141560	−	0.989930i	$-0.545212\pi$
$877$	−8.38434	−0.283119	−0.141560	+	0.989930i	$0.545212\pi$
$878$	10.4691	0.353315
$879$	−2.50680	−0.0845523
$880$	0.594486	0.0200401
$881$	1.35001	0.0454829	0.0227415	−	0.999741i	$-0.492761\pi$
$881$	1.35001	0.0454829	0.0227415	+	0.999741i	$0.492761\pi$
$882$	−6.49779	−0.218792
$883$	−33.3934	−1.12378	−0.561889	−	0.827213i	$-0.689925\pi$
$883$	−33.3934	−1.12378	−0.561889	+	0.827213i	$0.689925\pi$
$884$	4.54976	0.153025
$885$	2.63974	0.0887338
$886$	7.06705	0.237422
$887$	−15.3796	−0.516397	−0.258199	−	0.966092i	$-0.583129\pi$
$887$	−15.3796	−0.516397	−0.258199	+	0.966092i	$0.583129\pi$
$888$	0.809455	0.0271635
$889$	−10.4098	−0.349132
$890$	9.46231	0.317177
$891$	−1.10147	−0.0369006
$892$	17.2527	0.577662
$893$	−3.96417	−0.132656
$894$	−6.29462	−0.210524
$895$	8.63612	0.288674
$896$	0.708670	0.0236750
$897$	2.10547	0.0702994
$898$	10.6264	0.354608
$899$	19.1678	0.639283
$900$	−4.70870	−0.156957
$901$	40.6407	1.35394
$902$	−5.94452	−0.197931
$903$	4.71823	0.157013
$904$	10.5535	0.351005
$905$	3.55140	0.118053
$906$	18.5954	0.617789
$907$	48.9116	1.62408	0.812042	−	0.583600i	$-0.198356\pi$
$907$	48.9116	1.62408	0.812042	+	0.583600i	$0.198356\pi$
$908$	26.1340	0.867288
$909$	0.636449	0.0211097
$910$	0.382485	0.0126792
$911$	34.3078	1.13667	0.568335	−	0.822798i	$-0.307588\pi$
$911$	34.3078	1.13667	0.568335	+	0.822798i	$0.307588\pi$
$912$	−0.931175	−0.0308343
$913$	10.5100	0.347831
$914$	−2.61894	−0.0866268
$915$	−0.759770	−0.0251172
$916$	3.69647	0.122135
$917$	2.26602	0.0748306
$918$	4.54976	0.150164
$919$	−7.64584	−0.252213	−0.126106	−	0.992017i	$-0.540248\pi$
$919$	−7.64584	−0.252213	−0.126106	+	0.992017i	$0.540248\pi$
$920$	−1.13636	−0.0374648
$921$	4.99635	0.164635
$922$	−12.8560	−0.423389
$923$	14.4479	0.475558
$924$	0.780579	0.0256792
$925$	3.81148	0.125321
$926$	−26.0165	−0.854955
$927$	1.00000	0.0328443
$928$	8.33493	0.273608
$929$	−18.6909	−0.613230	−0.306615	−	0.951834i	$-0.599196\pi$
$929$	−18.6909	−0.613230	−0.306615	+	0.951834i	$0.599196\pi$
$930$	1.24120	0.0407004
$931$	−6.05058	−0.198300
$932$	−23.2932	−0.762996
$933$	−4.07333	−0.133355
$934$	14.0895	0.461024
$935$	−2.70477	−0.0884554
$936$	−1.00000	−0.0326860
$937$	−6.83423	−0.223265	−0.111632	−	0.993750i	$-0.535608\pi$
$937$	−6.83423	−0.223265	−0.111632	+	0.993750i	$0.535608\pi$
$938$	3.81993	0.124725
$939$	−24.5742	−0.801948
$940$	2.29768	0.0749422
$941$	26.5529	0.865600	0.432800	−	0.901490i	$-0.357526\pi$
$941$	26.5529	0.865600	0.432800	+	0.901490i	$0.357526\pi$
$942$	9.61035	0.313122
$943$	11.3630	0.370030
$944$	4.89092	0.159186
$945$	0.382485	0.0124422
$946$	7.33342	0.238430
$947$	−51.8518	−1.68496	−0.842479	−	0.538729i	$-0.818905\pi$
$947$	−51.8518	−1.68496	−0.842479	+	0.538729i	$0.818905\pi$
$948$	3.67867	0.119478
$949$	−16.3009	−0.529150
$950$	−4.38462	−0.142256
$951$	35.4866	1.15073
$952$	−3.22428	−0.104499
$953$	30.2925	0.981270	0.490635	−	0.871365i	$-0.336765\pi$
$953$	30.2925	0.981270	0.490635	+	0.871365i	$0.336765\pi$
$954$	−8.93249	−0.289200
$955$	−2.08192	−0.0673694
$956$	15.2849	0.494348
$957$	9.18067	0.296769
$958$	−2.86549	−0.0925798
$959$	−4.96958	−0.160476
$960$	0.539721	0.0174194
$961$	−25.7114	−0.829400
$962$	0.809455	0.0260979
$963$	10.5194	0.338982
$964$	−15.6401	−0.503735
$965$	0.177025	0.00569864
$966$	−1.49208	−0.0480069
$967$	25.0304	0.804924	0.402462	−	0.915437i	$-0.368155\pi$
$967$	25.0304	0.804924	0.402462	+	0.915437i	$0.368155\pi$
$968$	−9.78677	−0.314559
$969$	4.23662	0.136100
$970$	3.37810	0.108464
$971$	38.9227	1.24909	0.624545	−	0.780989i	$-0.285284\pi$
$971$	38.9227	1.24909	0.624545	+	0.780989i	$0.285284\pi$
$972$	−1.00000	−0.0320750
$973$	−12.8946	−0.413382
$974$	35.4875	1.13709
$975$	−4.70870	−0.150799
$976$	−1.40771	−0.0450597
$977$	9.35201	0.299197	0.149599	−	0.988747i	$-0.452202\pi$
$977$	9.35201	0.299197	0.149599	+	0.988747i	$0.452202\pi$
$978$	6.50347	0.207958
$979$	19.3108	0.617175
$980$	3.50699	0.112027
$981$	5.95205	0.190034
$982$	−23.4161	−0.747238
$983$	−23.4496	−0.747925	−0.373963	−	0.927444i	$-0.622001\pi$
$983$	−23.4496	−0.747925	−0.373963	+	0.927444i	$0.622001\pi$
$984$	−5.39691	−0.172047
$985$	6.02599	0.192004
$986$	−37.9219	−1.20768
$987$	3.01693	0.0960298
$988$	−0.931175	−0.0296246
$989$	−14.0179	−0.445743
$990$	0.594486	0.0188940
$991$	−31.1811	−0.990501	−0.495251	−	0.868750i	$-0.664924\pi$
$991$	−31.1811	−0.990501	−0.495251	+	0.868750i	$0.664924\pi$
$992$	2.29970	0.0730155
$993$	33.8590	1.07448
$994$	−10.2388	−0.324755
$995$	11.9792	0.379767
$996$	9.54181	0.302344
$997$	9.71301	0.307614	0.153807	−	0.988101i	$-0.450847\pi$
$997$	9.71301	0.307614	0.153807	+	0.988101i	$0.450847\pi$
$998$	−35.3167	−1.11793
$999$	0.809455	0.0256100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.539721 q^{5} -1.00000 q^{6} +0.708670 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.539721 q^{5} -1.00000 q^{6} +0.708670 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.539721 q^{10} -1.10147 q^{11} -1.00000 q^{12} -1.00000 q^{13} +0.708670 q^{14} +0.539721 q^{15} +1.00000 q^{16} -4.54976 q^{17} +1.00000 q^{18} +0.931175 q^{19} -0.539721 q^{20} -0.708670 q^{21} -1.10147 q^{22} +2.10547 q^{23} -1.00000 q^{24} -4.70870 q^{25} -1.00000 q^{26} -1.00000 q^{27} +0.708670 q^{28} +8.33493 q^{29} +0.539721 q^{30} +2.29970 q^{31} +1.00000 q^{32} +1.10147 q^{33} -4.54976 q^{34} -0.382485 q^{35} +1.00000 q^{36} -0.809455 q^{37} +0.931175 q^{38} +1.00000 q^{39} -0.539721 q^{40} +5.39691 q^{41} -0.708670 q^{42} -6.65786 q^{43} -1.10147 q^{44} -0.539721 q^{45} +2.10547 q^{46} -4.25716 q^{47} -1.00000 q^{48} -6.49779 q^{49} -4.70870 q^{50} +4.54976 q^{51} -1.00000 q^{52} -8.93249 q^{53} -1.00000 q^{54} +0.594486 q^{55} +0.708670 q^{56} -0.931175 q^{57} +8.33493 q^{58} +4.89092 q^{59} +0.539721 q^{60} -1.40771 q^{61} +2.29970 q^{62} +0.708670 q^{63} +1.00000 q^{64} +0.539721 q^{65} +1.10147 q^{66} +5.39027 q^{67} -4.54976 q^{68} -2.10547 q^{69} -0.382485 q^{70} -14.4479 q^{71} +1.00000 q^{72} +16.3009 q^{73} -0.809455 q^{74} +4.70870 q^{75} +0.931175 q^{76} -0.780579 q^{77} +1.00000 q^{78} -3.67867 q^{79} -0.539721 q^{80} +1.00000 q^{81} +5.39691 q^{82} -9.54181 q^{83} -0.708670 q^{84} +2.45560 q^{85} -6.65786 q^{86} -8.33493 q^{87} -1.10147 q^{88} -17.5318 q^{89} -0.539721 q^{90} -0.708670 q^{91} +2.10547 q^{92} -2.29970 q^{93} -4.25716 q^{94} -0.502575 q^{95} -1.00000 q^{96} -6.25897 q^{97} -6.49779 q^{98} -1.10147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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