LMFDB - Embedded newform 1078.2.c.a.1077.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1077,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("1078.1077");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1077.3
Root			$0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.a.1077.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.08239i q^{3} -1.00000 q^{4} -1.08239i q^{5} +1.08239 q^{6} +1.00000i q^{8} +1.82843 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.08239i q^{3} -1.00000 q^{4} -1.08239i q^{5} +1.08239 q^{6} +1.00000i q^{8} +1.82843 q^{9} -1.08239 q^{10} +(-1.41421 + 3.00000i) q^{11} -1.08239i q^{12} +2.29610 q^{13} +1.17157 q^{15} +1.00000 q^{16} -1.82843i q^{18} -5.54328 q^{19} +1.08239i q^{20} +(3.00000 + 1.41421i) q^{22} +6.24264 q^{23} -1.08239 q^{24} +3.82843 q^{25} -2.29610i q^{26} +5.22625i q^{27} +1.75736i q^{29} -1.17157i q^{30} +1.39942i q^{31} -1.00000i q^{32} +(-3.24718 - 1.53073i) q^{33} -1.82843 q^{36} +6.00000 q^{37} +5.54328i q^{38} +2.48528i q^{39} +1.08239 q^{40} +4.59220 q^{41} +4.24264i q^{43} +(1.41421 - 3.00000i) q^{44} -1.97908i q^{45} -6.24264i q^{46} -4.90923i q^{47} +1.08239i q^{48} -3.82843i q^{50} -2.29610 q^{52} +4.48528 q^{53} +5.22625 q^{54} +(3.24718 + 1.53073i) q^{55} -6.00000i q^{57} +1.75736 q^{58} +7.20533i q^{59} -1.17157 q^{60} -5.54328 q^{61} +1.39942 q^{62} -1.00000 q^{64} -2.48528i q^{65} +(-1.53073 + 3.24718i) q^{66} +11.6569 q^{67} +6.75699i q^{69} +2.00000 q^{71} +1.82843i q^{72} +15.6788 q^{73} -6.00000i q^{74} +4.14386i q^{75} +5.54328 q^{76} +2.48528 q^{78} -8.48528i q^{79} -1.08239i q^{80} -0.171573 q^{81} -4.59220i q^{82} -13.3827 q^{83} +4.24264 q^{86} -1.90215 q^{87} +(-3.00000 - 1.41421i) q^{88} +3.56420i q^{89} -1.97908 q^{90} -6.24264 q^{92} -1.51472 q^{93} -4.90923 q^{94} +6.00000i q^{95} +1.08239 q^{96} +8.60474i q^{97} +(-2.58579 + 5.48528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 8 * q^9	$ 8 q - 8 q^{4} - 8 q^{9} + 32 q^{15} + 8 q^{16} + 24 q^{22} + 16 q^{23} + 8 q^{25} + 8 q^{36} + 48 q^{37} - 32 q^{53} + 48 q^{58} - 32 q^{60} - 8 q^{64} + 48 q^{67} + 16 q^{71} - 48 q^{78} - 24 q^{81} - 24 q^{88} - 16 q^{92} - 80 q^{93} - 32 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^9 + 32 * q^15 + 8 * q^16 + 24 * q^22 + 16 * q^23 + 8 * q^25 + 8 * q^36 + 48 * q^37 - 32 * q^53 + 48 * q^58 - 32 * q^60 - 8 * q^64 + 48 * q^67 + 16 * q^71 - 48 * q^78 - 24 * q^81 - 24 * q^88 - 16 * q^92 - 80 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.08239i			0.624919i	0.949931	+	0.312460i	$0.101153\pi$
$3$			1.08239i			0.624919i	−0.949931	+	0.312460i	$0.898847\pi$
$4$	−1.00000			−0.500000
$5$		−	1.08239i		−	0.484061i	−0.970269	−	0.242030i	$-0.922187\pi$
$5$		−	1.08239i		−	0.484061i	0.970269	−	0.242030i	$-0.0778133\pi$
$6$	1.08239			0.441885
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.82843			0.609476
$10$	−1.08239			−0.342282
$11$	−1.41421	+	3.00000i	−0.426401	+	0.904534i
$11$	−1.41421	+	3.00000i	−0.426401	+	0.904534i
$12$		−	1.08239i		−	0.312460i
$13$	2.29610			0.636824			0.318412	−	0.947952i	$-0.396851\pi$
$13$	2.29610			0.636824			0.318412	+	0.947952i	$0.396851\pi$
$14$		0			0
$15$	1.17157			0.302499
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		−	1.82843i		−	0.430964i
$19$	−5.54328			−1.27172			−0.635858	−	0.771806i	$-0.719353\pi$
$19$	−5.54328			−1.27172			−0.635858	+	0.771806i	$0.719353\pi$
$20$			1.08239i			0.242030i
$21$		0			0
$22$	3.00000	+	1.41421i	0.639602	+	0.301511i
$23$	6.24264			1.30168			0.650840	−	0.759215i	$-0.274417\pi$
$23$	6.24264			1.30168			0.650840	+	0.759215i	$0.274417\pi$
$24$	−1.08239			−0.220942
$25$	3.82843			0.765685
$26$		−	2.29610i		−	0.450302i
$27$			5.22625i			1.00579i
$28$		0			0
$29$			1.75736i			0.326333i	0.986599	+	0.163167i	$0.0521708\pi$
$29$			1.75736i			0.326333i	−0.986599	+	0.163167i	$0.947829\pi$
$30$		−	1.17157i		−	0.213899i
$31$			1.39942i			0.251343i	0.992072	+	0.125671i	$0.0401085\pi$
$31$			1.39942i			0.251343i	−0.992072	+	0.125671i	$0.959891\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.24718	−	1.53073i	−0.565261	−	0.266467i
$34$		0			0
$35$		0			0
$36$	−1.82843			−0.304738
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$			5.54328i			0.899238i
$39$			2.48528i			0.397964i
$40$	1.08239			0.171141
$41$	4.59220			0.717181			0.358591	−	0.933495i	$-0.383257\pi$
$41$	4.59220			0.717181			0.358591	+	0.933495i	$0.383257\pi$
$42$		0			0
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$	1.41421	−	3.00000i	0.213201	−	0.452267i
$45$		−	1.97908i		−	0.295023i
$46$		−	6.24264i		−	0.920427i
$47$		−	4.90923i		−	0.716084i	−0.933705	−	0.358042i	$-0.883444\pi$
$47$		−	4.90923i		−	0.716084i	0.933705	−	0.358042i	$-0.116556\pi$
$48$			1.08239i			0.156230i
$49$		0			0
$50$		−	3.82843i		−	0.541421i
$51$		0			0
$52$	−2.29610			−0.318412
$53$	4.48528			0.616101			0.308050	−	0.951370i	$-0.400323\pi$
$53$	4.48528			0.616101			0.308050	+	0.951370i	$0.400323\pi$
$54$	5.22625			0.711203
$55$	3.24718	+	1.53073i	0.437849	+	0.206404i
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	1.75736			0.230753
$59$			7.20533i			0.938054i	0.883184	+	0.469027i	$0.155395\pi$
$59$			7.20533i			0.938054i	−0.883184	+	0.469027i	$0.844605\pi$
$60$	−1.17157			−0.151249
$61$	−5.54328			−0.709744			−0.354872	−	0.934915i	$-0.615476\pi$
$61$	−5.54328			−0.709744			−0.354872	+	0.934915i	$0.615476\pi$
$62$	1.39942			0.177726
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	2.48528i		−	0.308261i
$66$	−1.53073	+	3.24718i	−0.188420	+	0.399700i
$67$	11.6569			1.42411			0.712056	−	0.702123i	$-0.247764\pi$
$67$	11.6569			1.42411			0.712056	+	0.702123i	$0.247764\pi$
$68$		0			0
$69$			6.75699i			0.813445i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			1.82843i			0.215482i
$73$	15.6788			1.83506			0.917530	−	0.397667i	$-0.130180\pi$
$73$	15.6788			1.83506			0.917530	+	0.397667i	$0.130180\pi$
$74$		−	6.00000i		−	0.697486i
$75$			4.14386i			0.478492i
$76$	5.54328			0.635858
$77$		0			0
$78$	2.48528			0.281403
$79$		−	8.48528i		−	0.954669i	−0.878722	−	0.477334i	$-0.841603\pi$
$79$		−	8.48528i		−	0.954669i	0.878722	−	0.477334i	$-0.158397\pi$
$80$		−	1.08239i		−	0.121015i
$81$	−0.171573			−0.0190637
$82$		−	4.59220i		−	0.507124i
$83$	−13.3827			−1.46894			−0.734469	−	0.678643i	$-0.762569\pi$
$83$	−13.3827			−1.46894			−0.734469	+	0.678643i	$0.762569\pi$
$84$		0			0
$85$		0			0
$86$	4.24264			0.457496
$87$	−1.90215			−0.203932
$88$	−3.00000	−	1.41421i	−0.319801	−	0.150756i
$89$			3.56420i			0.377805i	0.981996	+	0.188902i	$0.0604930\pi$
$89$			3.56420i			0.377805i	−0.981996	+	0.188902i	$0.939507\pi$
$90$	−1.97908			−0.208613
$91$		0			0
$92$	−6.24264			−0.650840
$93$	−1.51472			−0.157069
$94$	−4.90923			−0.506348
$95$			6.00000i			0.615587i
$96$	1.08239			0.110471
$97$			8.60474i			0.873679i	0.899539	+	0.436840i	$0.143902\pi$
$97$			8.60474i			0.873679i	−0.899539	+	0.436840i	$0.856098\pi$
$98$		0			0
$99$	−2.58579	+	5.48528i	−0.259881	+	0.551292i
$100$	−3.82843			−0.382843
$101$	16.6298			1.65473			0.827365	−	0.561665i	$-0.189839\pi$
$101$	16.6298			1.65473			0.827365	+	0.561665i	$0.189839\pi$
$102$		0			0
$103$		−	6.43996i		−	0.634548i	−0.948334	−	0.317274i	$-0.897232\pi$
$103$		−	6.43996i		−	0.634548i	0.948334	−	0.317274i	$-0.102768\pi$
$104$			2.29610i			0.225151i
$105$		0			0
$106$		−	4.48528i		−	0.435649i
$107$			12.7279i			1.23045i	0.788350	+	0.615227i	$0.210936\pi$
$107$			12.7279i			1.23045i	−0.788350	+	0.615227i	$0.789064\pi$
$108$		−	5.22625i		−	0.502896i
$109$			3.51472i			0.336649i	0.985732	+	0.168324i	$0.0538356\pi$
$109$			3.51472i			0.336649i	−0.985732	+	0.168324i	$0.946164\pi$
$110$	1.53073	−	3.24718i	0.145950	−	0.309606i
$111$			6.49435i			0.616417i
$112$		0			0
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$	−6.00000			−0.561951
$115$		−	6.75699i		−	0.630092i
$116$		−	1.75736i		−	0.163167i
$117$	4.19825			0.388129
$118$	7.20533			0.663304
$119$		0			0
$120$			1.17157i			0.106949i
$121$	−7.00000	−	8.48528i	−0.636364	−	0.771389i
$122$			5.54328i			0.501865i
$123$			4.97056i			0.448181i
$124$		−	1.39942i		−	0.125671i
$125$		−	9.55582i		−	0.854699i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$			1.00000i			0.0883883i
$129$	−4.59220			−0.404321
$130$	−2.48528			−0.217974
$131$	6.88830			0.601834			0.300917	−	0.953650i	$-0.402707\pi$
$131$	6.88830			0.601834			0.300917	+	0.953650i	$0.402707\pi$
$132$	3.24718	+	1.53073i	0.282630	+	0.133233i
$133$		0			0
$134$		−	11.6569i		−	1.00700i
$135$	5.65685			0.486864
$136$		0			0
$137$	−16.9706			−1.44989			−0.724947	−	0.688805i	$-0.758136\pi$
$137$	−16.9706			−1.44989			−0.724947	+	0.688805i	$0.758136\pi$
$138$	6.75699			0.575193
$139$	−13.3827			−1.13510			−0.567551	−	0.823338i	$-0.692109\pi$
$139$	−13.3827			−1.13510			−0.567551	+	0.823338i	$0.692109\pi$
$140$		0			0
$141$	5.31371			0.447495
$142$		−	2.00000i		−	0.167836i
$143$	−3.24718	+	6.88830i	−0.271543	+	0.576029i
$144$	1.82843			0.152369
$145$	1.90215			0.157965
$146$		−	15.6788i		−	1.29758i
$147$		0			0
$148$	−6.00000			−0.493197
$149$			6.72792i			0.551173i	0.961276	+	0.275586i	$0.0888720\pi$
$149$			6.72792i			0.551173i	−0.961276	+	0.275586i	$0.911128\pi$
$150$	4.14386			0.338345
$151$		−	6.00000i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$151$		−	6.00000i		−	0.488273i	0.969741	−	0.244137i	$-0.0785045\pi$
$152$		−	5.54328i		−	0.449619i
$153$		0			0
$154$		0			0
$155$	1.51472			0.121665
$156$		−	2.48528i		−	0.198982i
$157$		−	11.5349i		−	0.920585i	−0.887767	−	0.460292i	$-0.847745\pi$
$157$		−	11.5349i		−	0.920585i	0.887767	−	0.460292i	$-0.152255\pi$
$158$	−8.48528			−0.675053
$159$			4.85483i			0.385013i
$160$	−1.08239			−0.0855706
$161$		0			0
$162$			0.171573i			0.0134800i
$163$	−8.14214			−0.637741			−0.318871	−	0.947798i	$-0.603304\pi$
$163$	−8.14214			−0.637741			−0.318871	+	0.947798i	$0.603304\pi$
$164$	−4.59220			−0.358591
$165$	−1.65685	+	3.51472i	−0.128986	+	0.273620i
$166$			13.3827i			1.03870i
$167$	−20.2710			−1.56861			−0.784307	−	0.620373i	$-0.786981\pi$
$167$	−20.2710			−1.56861			−0.784307	+	0.620373i	$0.786981\pi$
$168$		0			0
$169$	−7.72792			−0.594456
$170$		0			0
$171$	−10.1355			−0.775079
$172$		−	4.24264i		−	0.323498i
$173$	−25.8142			−1.96262			−0.981310	−	0.192434i	$-0.938362\pi$
$173$	−25.8142			−1.96262			−0.981310	+	0.192434i	$0.938362\pi$
$174$			1.90215i			0.144202i
$175$		0			0
$176$	−1.41421	+	3.00000i	−0.106600	+	0.226134i
$177$	−7.79899			−0.586208
$178$	3.56420			0.267148
$179$	−5.65685			−0.422813			−0.211407	−	0.977398i	$-0.567804\pi$
$179$	−5.65685			−0.422813			−0.211407	+	0.977398i	$0.567804\pi$
$180$			1.97908i			0.147512i
$181$		−	20.4567i		−	1.52053i	−0.649612	−	0.760266i	$-0.725069\pi$
$181$		−	20.4567i		−	1.52053i	0.649612	−	0.760266i	$-0.274931\pi$
$182$		0			0
$183$		−	6.00000i		−	0.443533i
$184$			6.24264i			0.460214i
$185$		−	6.49435i		−	0.477474i
$186$			1.51472i			0.111065i
$187$		0			0
$188$			4.90923i			0.358042i
$189$		0			0
$190$	6.00000			0.435286
$191$	−1.75736			−0.127158			−0.0635790	−	0.997977i	$-0.520251\pi$
$191$	−1.75736			−0.127158			−0.0635790	+	0.997977i	$0.520251\pi$
$192$		−	1.08239i		−	0.0781149i
$193$			2.48528i			0.178894i	0.995992	+	0.0894472i	$0.0285100\pi$
$193$			2.48528i			0.178894i	−0.995992	+	0.0894472i	$0.971490\pi$
$194$	8.60474			0.617785
$195$	2.69005			0.192638
$196$		0			0
$197$			20.4853i			1.45952i	0.683706	+	0.729758i	$0.260367\pi$
$197$			20.4853i			1.45952i	−0.683706	+	0.729758i	$0.739633\pi$
$198$	5.48528	+	2.58579i	0.389822	+	0.183764i
$199$		−	24.6549i		−	1.74774i	−0.486159	−	0.873870i	$-0.661602\pi$
$199$		−	24.6549i		−	1.74774i	0.486159	−	0.873870i	$-0.338398\pi$
$200$			3.82843i			0.270711i
$201$			12.6173i			0.889955i
$202$		−	16.6298i		−	1.17007i
$203$		0			0
$204$		0			0
$205$		−	4.97056i		−	0.347159i
$206$	−6.43996			−0.448693
$207$	11.4142			0.793343
$208$	2.29610			0.159206
$209$	7.83938	−	16.6298i	0.542261	−	1.15031i
$210$		0			0
$211$		−	24.7279i		−	1.70234i	−0.524890	−	0.851170i	$-0.675893\pi$
$211$		−	24.7279i		−	1.70234i	0.524890	−	0.851170i	$-0.324107\pi$
$212$	−4.48528			−0.308050
$213$			2.16478i			0.148329i
$214$	12.7279			0.870063
$215$	4.59220			0.313186
$216$	−5.22625			−0.355601
$217$		0			0
$218$	3.51472			0.238047
$219$			16.9706i			1.14676i
$220$	−3.24718	−	1.53073i	−0.218925	−	0.103202i
$221$		0			0
$222$	6.49435			0.435872
$223$			7.89377i			0.528606i	0.964440	+	0.264303i	$0.0851419\pi$
$223$			7.89377i			0.528606i	−0.964440	+	0.264303i	$0.914858\pi$
$224$		0			0
$225$	7.00000			0.466667
$226$			1.41421i			0.0940721i
$227$	−0.951076			−0.0631251			−0.0315626	−	0.999502i	$-0.510048\pi$
$227$	−0.951076			−0.0631251			−0.0315626	+	0.999502i	$0.510048\pi$
$228$			6.00000i			0.397360i
$229$			28.4818i			1.88213i	0.338230	+	0.941064i	$0.390172\pi$
$229$			28.4818i			1.88213i	−0.338230	+	0.941064i	$0.609828\pi$
$230$	−6.75699			−0.445542
$231$		0			0
$232$	−1.75736			−0.115376
$233$		−	8.48528i		−	0.555889i	−0.960597	−	0.277945i	$-0.910347\pi$
$233$		−	8.48528i		−	0.555889i	0.960597	−	0.277945i	$-0.0896532\pi$
$234$		−	4.19825i		−	0.274448i
$235$	−5.31371			−0.346628
$236$		−	7.20533i		−	0.469027i
$237$	9.18440			0.596591
$238$		0			0
$239$			26.4853i			1.71319i	0.515989	+	0.856595i	$0.327425\pi$
$239$			26.4853i			1.71319i	−0.515989	+	0.856595i	$0.672575\pi$
$240$	1.17157			0.0756247
$241$	−4.59220			−0.295810			−0.147905	−	0.989002i	$-0.547253\pi$
$241$	−4.59220			−0.295810			−0.147905	+	0.989002i	$0.547253\pi$
$242$	−8.48528	+	7.00000i	−0.545455	+	0.449977i
$243$			15.4930i			0.993879i
$244$	5.54328			0.354872
$245$		0			0
$246$	4.97056			0.316912
$247$	−12.7279			−0.809858
$248$	−1.39942			−0.0888631
$249$		−	14.4853i		−	0.917967i
$250$	−9.55582			−0.604363
$251$		−	12.1689i		−	0.768097i	−0.923313	−	0.384049i	$-0.874530\pi$
$251$		−	12.1689i		−	0.768097i	0.923313	−	0.384049i	$-0.125470\pi$
$252$		0			0
$253$	−8.82843	+	18.7279i	−0.555038	+	1.17741i
$254$	−6.00000			−0.376473
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	22.0418i		−	1.37493i	−0.726218	−	0.687465i	$-0.758724\pi$
$257$		−	22.0418i		−	1.37493i	0.726218	−	0.687465i	$-0.241276\pi$
$258$			4.59220i			0.285898i
$259$		0			0
$260$			2.48528i			0.154131i
$261$			3.21320i			0.198892i
$262$		−	6.88830i		−	0.425561i
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$	1.53073	−	3.24718i	0.0942101	−	0.199850i
$265$		−	4.85483i		−	0.298230i
$266$		0			0
$267$	−3.85786			−0.236097
$268$	−11.6569			−0.712056
$269$			3.50981i			0.213997i	0.994259	+	0.106998i	$0.0341240\pi$
$269$			3.50981i			0.213997i	−0.994259	+	0.106998i	$0.965876\pi$
$270$		−	5.65685i		−	0.344265i
$271$	26.7653			1.62588			0.812938	−	0.582350i	$-0.197867\pi$
$271$	26.7653			1.62588			0.812938	+	0.582350i	$0.197867\pi$
$272$		0			0
$273$		0			0
$274$			16.9706i			1.02523i
$275$	−5.41421	+	11.4853i	−0.326489	+	0.692589i
$276$		−	6.75699i		−	0.406723i
$277$		−	18.7279i		−	1.12525i	−0.826712	−	0.562626i	$-0.809791\pi$
$277$		−	18.7279i		−	1.12525i	0.826712	−	0.562626i	$-0.190209\pi$
$278$			13.3827i			0.802638i
$279$			2.55873i			0.153187i
$280$		0			0
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$		−	5.31371i		−	0.316427i
$283$	−22.5671			−1.34147			−0.670736	−	0.741696i	$-0.734022\pi$
$283$	−22.5671			−1.34147			−0.670736	+	0.741696i	$0.734022\pi$
$284$	−2.00000			−0.118678
$285$	−6.49435			−0.384692
$286$	6.88830	+	3.24718i	0.407314	+	0.192010i
$287$		0			0
$288$		−	1.82843i		−	0.107741i
$289$	−17.0000			−1.00000
$290$		−	1.90215i		−	0.111698i
$291$	−9.31371			−0.545979
$292$	−15.6788			−0.917530
$293$	0.951076			0.0555625			0.0277812	−	0.999614i	$-0.491156\pi$
$293$	0.951076			0.0555625			0.0277812	+	0.999614i	$0.491156\pi$
$294$		0			0
$295$	7.79899			0.454075
$296$			6.00000i			0.348743i
$297$	−15.6788	−	7.39104i	−0.909774	−	0.428871i
$298$	6.72792			0.389738
$299$	14.3337			0.828941
$300$		−	4.14386i		−	0.239246i
$301$		0			0
$302$	−6.00000			−0.345261
$303$			18.0000i			1.03407i
$304$	−5.54328			−0.317929
$305$			6.00000i			0.343559i
$306$		0			0
$307$	7.44543			0.424933			0.212467	−	0.977168i	$-0.431850\pi$
$307$	7.44543			0.424933			0.212467	+	0.977168i	$0.431850\pi$
$308$		0			0
$309$	6.97056			0.396541
$310$		−	1.51472i		−	0.0860302i
$311$			33.3910i			1.89343i	0.322074	+	0.946714i	$0.395620\pi$
$311$			33.3910i			1.89343i	−0.322074	+	0.946714i	$0.604380\pi$
$312$	−2.48528			−0.140701
$313$			10.3212i			0.583388i	0.956512	+	0.291694i	$0.0942189\pi$
$313$			10.3212i			0.583388i	−0.956512	+	0.291694i	$0.905781\pi$
$314$	−11.5349			−0.650952
$315$		0			0
$316$			8.48528i			0.477334i
$317$	−22.9706			−1.29016			−0.645078	−	0.764117i	$-0.723175\pi$
$317$	−22.9706			−1.29016			−0.645078	+	0.764117i	$0.723175\pi$
$318$	4.85483			0.272246
$319$	−5.27208	−	2.48528i	−0.295180	−	0.139149i
$320$			1.08239i			0.0605076i
$321$	−13.7766			−0.768935
$322$		0			0
$323$		0			0
$324$	0.171573			0.00953183
$325$	8.79045			0.487607
$326$			8.14214i			0.450951i
$327$	−3.80430			−0.210378
$328$			4.59220i			0.253562i
$329$		0			0
$330$	3.51472	+	1.65685i	0.193479	+	0.0912068i
$331$	20.4853			1.12597			0.562986	−	0.826466i	$-0.309652\pi$
$331$	20.4853			1.12597			0.562986	+	0.826466i	$0.309652\pi$
$332$	13.3827			0.734469
$333$	10.9706			0.601183
$334$			20.2710i			1.10918i
$335$		−	12.6173i		−	0.689356i
$336$		0			0
$337$		−	26.4853i		−	1.44275i	−0.692547	−	0.721373i	$-0.743512\pi$
$337$		−	26.4853i		−	1.44275i	0.692547	−	0.721373i	$-0.256488\pi$
$338$			7.72792i			0.420344i
$339$		−	1.53073i		−	0.0831380i
$340$		0			0
$341$	−4.19825	−	1.97908i	−0.227348	−	0.107173i
$342$			10.1355i			0.548064i
$343$		0			0
$344$	−4.24264			−0.228748
$345$	7.31371			0.393757
$346$			25.8142i			1.38778i
$347$		−	7.75736i		−	0.416437i	−0.978082	−	0.208218i	$-0.933234\pi$
$347$		−	7.75736i		−	0.416437i	0.978082	−	0.208218i	$-0.0667665\pi$
$348$	1.90215			0.101966
$349$	29.0614			1.55562			0.777811	−	0.628498i	$-0.216330\pi$
$349$	29.0614			1.55562			0.777811	+	0.628498i	$0.216330\pi$
$350$		0			0
$351$			12.0000i			0.640513i
$352$	3.00000	+	1.41421i	0.159901	+	0.0753778i
$353$		−	1.21371i		−	0.0645992i	−0.999478	−	0.0322996i	$-0.989717\pi$
$353$		−	1.21371i		−	0.0645992i	0.999478	−	0.0322996i	$-0.0102831\pi$
$354$			7.79899i			0.414512i
$355$		−	2.16478i		−	0.114895i
$356$		−	3.56420i		−	0.188902i
$357$		0			0
$358$			5.65685i			0.298974i
$359$		−	2.48528i		−	0.131168i	−0.997847	−	0.0655841i	$-0.979109\pi$
$359$		−	2.48528i		−	0.131168i	0.997847	−	0.0655841i	$-0.0208911\pi$
$360$	1.97908			0.104306
$361$	11.7279			0.617259
$362$	−20.4567			−1.07518
$363$	9.18440	−	7.57675i	0.482056	−	0.397676i
$364$		0			0
$365$		−	16.9706i		−	0.888280i
$366$	−6.00000			−0.313625
$367$			11.1409i			0.581553i	0.956791	+	0.290776i	$0.0939136\pi$
$367$			11.1409i			0.581553i	−0.956791	+	0.290776i	$0.906086\pi$
$368$	6.24264			0.325420
$369$	8.39651			0.437105
$370$	−6.49435			−0.337625
$371$		0			0
$372$	1.51472			0.0785345
$373$		−	20.4853i		−	1.06069i	−0.847783	−	0.530344i	$-0.822063\pi$
$373$		−	20.4853i		−	1.06069i	0.847783	−	0.530344i	$-0.177937\pi$
$374$		0			0
$375$	10.3431			0.534118
$376$	4.90923			0.253174
$377$			4.03507i			0.207817i
$378$		0			0
$379$	−11.6569			−0.598772			−0.299386	−	0.954132i	$-0.596782\pi$
$379$	−11.6569			−0.598772			−0.299386	+	0.954132i	$0.596782\pi$
$380$		−	6.00000i		−	0.307794i
$381$	6.49435			0.332716
$382$			1.75736i			0.0899143i
$383$		−	14.4650i		−	0.739129i	−0.929205	−	0.369565i	$-0.879507\pi$
$383$		−	14.4650i		−	0.739129i	0.929205	−	0.369565i	$-0.120493\pi$
$384$	−1.08239			−0.0552356
$385$		0			0
$386$	2.48528			0.126497
$387$			7.75736i			0.394329i
$388$		−	8.60474i		−	0.436840i
$389$	−32.0000			−1.62246			−0.811232	−	0.584724i	$-0.801203\pi$
$389$	−32.0000			−1.62246			−0.811232	+	0.584724i	$0.801203\pi$
$390$		−	2.69005i		−	0.136216i
$391$		0			0
$392$		0			0
$393$			7.45584i			0.376098i
$394$	20.4853			1.03203
$395$	−9.18440			−0.462117
$396$	2.58579	−	5.48528i	0.129941	−	0.275646i
$397$		−	1.71644i		−	0.0861458i	−0.999072	−	0.0430729i	$-0.986285\pi$
$397$		−	1.71644i		−	0.0861458i	0.999072	−	0.0430729i	$-0.0137148\pi$
$398$	−24.6549			−1.23584
$399$		0			0
$400$	3.82843			0.191421
$401$	0.485281			0.0242338			0.0121169	−	0.999927i	$-0.496143\pi$
$401$	0.485281			0.0242338			0.0121169	+	0.999927i	$0.496143\pi$
$402$	12.6173			0.629293
$403$			3.21320i			0.160061i
$404$	−16.6298			−0.827365
$405$			0.185709i			0.00922796i
$406$		0			0
$407$	−8.48528	+	18.0000i	−0.420600	+	0.892227i
$408$		0			0
$409$	37.8519			1.87165			0.935827	−	0.352459i	$-0.114655\pi$
$409$	37.8519			1.87165			0.935827	+	0.352459i	$0.114655\pi$
$410$	−4.97056			−0.245479
$411$		−	18.3688i		−	0.906066i
$412$			6.43996i			0.317274i
$413$		0			0
$414$		−	11.4142i		−	0.560978i
$415$			14.4853i			0.711054i
$416$		−	2.29610i		−	0.112576i
$417$		−	14.4853i		−	0.709347i
$418$	−16.6298	−	7.83938i	−0.813392	−	0.383437i
$419$			8.47343i			0.413954i	0.978346	+	0.206977i	$0.0663625\pi$
$419$			8.47343i			0.413954i	−0.978346	+	0.206977i	$0.933637\pi$
$420$		0			0
$421$	17.6569			0.860542			0.430271	−	0.902700i	$-0.358418\pi$
$421$	17.6569			0.860542			0.430271	+	0.902700i	$0.358418\pi$
$422$	−24.7279			−1.20374
$423$		−	8.97616i		−	0.436436i
$424$			4.48528i			0.217825i
$425$		0			0
$426$	2.16478			0.104884
$427$		0			0
$428$		−	12.7279i		−	0.615227i
$429$	−7.45584	−	3.51472i	−0.359972	−	0.169692i
$430$		−	4.59220i		−	0.221456i
$431$		−	2.48528i		−	0.119712i	−0.998207	−	0.0598559i	$-0.980936\pi$
$431$		−	2.48528i		−	0.119712i	0.998207	−	0.0598559i	$-0.0190641\pi$
$432$			5.22625i			0.251448i
$433$			22.6758i			1.08973i	0.838523	+	0.544866i	$0.183419\pi$
$433$			22.6758i			1.08973i	−0.838523	+	0.544866i	$0.816581\pi$
$434$		0			0
$435$			2.05887i			0.0987155i
$436$		−	3.51472i		−	0.168324i
$437$	−34.6047			−1.65537
$438$	16.9706			0.810885
$439$	6.49435			0.309959			0.154979	−	0.987918i	$-0.450469\pi$
$439$	6.49435			0.309959			0.154979	+	0.987918i	$0.450469\pi$
$440$	−1.53073	+	3.24718i	−0.0729749	+	0.154803i
$441$		0			0
$442$		0			0
$443$	22.6274			1.07506			0.537531	−	0.843244i	$-0.319357\pi$
$443$	22.6274			1.07506			0.537531	+	0.843244i	$0.319357\pi$
$444$		−	6.49435i		−	0.308208i
$445$	3.85786			0.182880
$446$	7.89377			0.373781
$447$	−7.28225			−0.344439
$448$		0			0
$449$	−40.7279			−1.92207			−0.961035	−	0.276428i	$-0.910849\pi$
$449$	−40.7279			−1.92207			−0.961035	+	0.276428i	$0.910849\pi$
$450$		−	7.00000i		−	0.329983i
$451$	−6.49435	+	13.7766i	−0.305807	+	0.648715i
$452$	1.41421			0.0665190
$453$	6.49435			0.305131
$454$			0.951076i			0.0446362i
$455$		0			0
$456$	6.00000			0.280976
$457$		−	31.4558i		−	1.47144i	−0.677285	−	0.735721i	$-0.736843\pi$
$457$		−	31.4558i		−	1.47144i	0.677285	−	0.735721i	$-0.263157\pi$
$458$	28.4818			1.33086
$459$		0			0
$460$			6.75699i			0.315046i
$461$	29.0614			1.35352			0.676762	−	0.736201i	$-0.263382\pi$
$461$	29.0614			1.35352			0.676762	+	0.736201i	$0.263382\pi$
$462$		0			0
$463$	−5.31371			−0.246949			−0.123474	−	0.992348i	$-0.539404\pi$
$463$	−5.31371			−0.246949			−0.123474	+	0.992348i	$0.539404\pi$
$464$			1.75736i			0.0815834i
$465$			1.63952i			0.0760309i
$466$	−8.48528			−0.393073
$467$		−	32.1773i		−	1.48899i	−0.667630	−	0.744493i	$-0.732691\pi$
$467$		−	32.1773i		−	1.48899i	0.667630	−	0.744493i	$-0.267309\pi$
$468$	−4.19825			−0.194064
$469$		0			0
$470$			5.31371i			0.245103i
$471$	12.4853			0.575291
$472$	−7.20533			−0.331652
$473$	−12.7279	−	6.00000i	−0.585230	−	0.275880i
$474$		−	9.18440i		−	0.421854i
$475$	−21.2220			−0.973734
$476$		0			0
$477$	8.20101			0.375498
$478$	26.4853			1.21141
$479$	9.18440			0.419646			0.209823	−	0.977739i	$-0.432711\pi$
$479$	9.18440			0.419646			0.209823	+	0.977739i	$0.432711\pi$
$480$		−	1.17157i		−	0.0534747i
$481$	13.7766			0.628159
$482$			4.59220i			0.209169i
$483$		0			0
$484$	7.00000	+	8.48528i	0.318182	+	0.385695i
$485$	9.31371			0.422914
$486$	15.4930			0.702779
$487$	−2.44365			−0.110732			−0.0553662	−	0.998466i	$-0.517633\pi$
$487$	−2.44365			−0.110732			−0.0553662	+	0.998466i	$0.517633\pi$
$488$		−	5.54328i		−	0.250932i
$489$		−	8.81298i		−	0.398537i
$490$		0			0
$491$		−	39.9411i		−	1.80252i	−0.433281	−	0.901259i	$-0.642644\pi$
$491$		−	39.9411i		−	1.80252i	0.433281	−	0.901259i	$-0.357356\pi$
$492$		−	4.97056i		−	0.224090i
$493$		0			0
$494$			12.7279i			0.572656i
$495$	5.93723	+	2.79884i	0.266858	+	0.125798i
$496$			1.39942i			0.0628357i
$497$		0			0
$498$	−14.4853			−0.649101
$499$	28.6274			1.28154			0.640770	−	0.767733i	$-0.278615\pi$
$499$	28.6274			1.28154			0.640770	+	0.767733i	$0.278615\pi$
$500$			9.55582i			0.427349i
$501$		−	21.9411i		−	0.980257i
$502$	−12.1689			−0.543127
$503$	6.49435			0.289569			0.144784	−	0.989463i	$-0.453751\pi$
$503$	6.49435			0.289569			0.144784	+	0.989463i	$0.453751\pi$
$504$		0			0
$505$		−	18.0000i		−	0.800989i
$506$	18.7279	+	8.82843i	0.832558	+	0.392471i
$507$		−	8.36464i		−	0.371487i
$508$			6.00000i			0.266207i
$509$		−	32.4399i		−	1.43787i	−0.695076	−	0.718937i	$-0.744629\pi$
$509$		−	32.4399i		−	1.43787i	0.695076	−	0.718937i	$-0.255371\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	28.9706i		−	1.27908i
$514$	−22.0418			−0.972222
$515$	−6.97056			−0.307160
$516$	4.59220			0.202160
$517$	14.7277	+	6.94269i	0.647723	+	0.305339i
$518$		0			0
$519$		−	27.9411i		−	1.22648i
$520$	2.48528			0.108987
$521$			28.3504i			1.24206i	0.783789	+	0.621028i	$0.213285\pi$
$521$			28.3504i			1.24206i	−0.783789	+	0.621028i	$0.786715\pi$
$522$	3.21320			0.140638
$523$	0.951076			0.0415877			0.0207938	−	0.999784i	$-0.493381\pi$
$523$	0.951076			0.0415877			0.0207938	+	0.999784i	$0.493381\pi$
$524$	−6.88830			−0.300917
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	−3.24718	−	1.53073i	−0.141315	−	0.0666166i
$529$	15.9706			0.694372
$530$	−4.85483			−0.210880
$531$			13.1744i			0.571721i
$532$		0			0
$533$	10.5442			0.456718
$534$			3.85786i			0.166946i
$535$	13.7766			0.595615
$536$			11.6569i			0.503499i
$537$		−	6.12293i		−	0.264224i
$538$	3.50981			0.151319
$539$		0			0
$540$	−5.65685			−0.243432
$541$		−	10.9706i		−	0.471661i	−0.971794	−	0.235831i	$-0.924219\pi$
$541$		−	10.9706i		−	0.471661i	0.971794	−	0.235831i	$-0.0757811\pi$
$542$		−	26.7653i		−	1.14967i
$543$	22.1421			0.950210
$544$		0			0
$545$	3.80430			0.162958
$546$		0			0
$547$			24.0000i			1.02617i	0.858339	+	0.513083i	$0.171497\pi$
$547$			24.0000i			1.02617i	−0.858339	+	0.513083i	$0.828503\pi$
$548$	16.9706			0.724947
$549$	−10.1355			−0.432572
$550$	11.4853	+	5.41421i	0.489734	+	0.230863i
$551$		−	9.74153i		−	0.415003i
$552$	−6.75699			−0.287596
$553$		0			0
$554$	−18.7279			−0.795673
$555$	7.02944			0.298383
$556$	13.3827			0.567551
$557$		−	6.00000i		−	0.254228i	−0.991888	−	0.127114i	$-0.959429\pi$
$557$		−	6.00000i		−	0.254228i	0.991888	−	0.127114i	$-0.0405714\pi$
$558$	2.55873			0.108320
$559$			9.74153i			0.412023i
$560$		0			0
$561$		0			0
$562$	−12.0000			−0.506189
$563$	27.1593			1.14463			0.572313	−	0.820035i	$-0.306046\pi$
$563$	27.1593			1.14463			0.572313	+	0.820035i	$0.306046\pi$
$564$	−5.31371			−0.223747
$565$			1.53073i			0.0643985i
$566$			22.5671i			0.948564i
$567$		0			0
$568$			2.00000i			0.0839181i
$569$		−	30.0000i		−	1.25767i	−0.777541	−	0.628833i	$-0.783533\pi$
$569$		−	30.0000i		−	1.25767i	0.777541	−	0.628833i	$-0.216467\pi$
$570$			6.49435i			0.272019i
$571$		−	36.0000i		−	1.50655i	−0.657704	−	0.753277i	$-0.728472\pi$
$571$		−	36.0000i		−	1.50655i	0.657704	−	0.753277i	$-0.271528\pi$
$572$	3.24718	−	6.88830i	0.135771	−	0.288014i
$573$		−	1.90215i		−	0.0794635i
$574$		0			0
$575$	23.8995			0.996678
$576$	−1.82843			−0.0761845
$577$		−	33.2053i		−	1.38235i	−0.722686	−	0.691177i	$-0.757093\pi$
$577$		−	33.2053i		−	1.38235i	0.722686	−	0.691177i	$-0.242907\pi$
$578$			17.0000i			0.707107i
$579$	−2.69005			−0.111795
$580$	−1.90215			−0.0789826
$581$		0			0
$582$			9.31371i			0.386066i
$583$	−6.34315	+	13.4558i	−0.262706	+	0.557284i
$584$			15.6788i			0.648792i
$585$		−	4.54416i		−	0.187878i
$586$		−	0.951076i		−	0.0392886i
$587$			37.0321i			1.52848i	0.644933	+	0.764239i	$0.276885\pi$
$587$			37.0321i			1.52848i	−0.644933	+	0.764239i	$0.723115\pi$
$588$		0			0
$589$		−	7.75736i		−	0.319636i
$590$		−	7.79899i		−	0.321079i
$591$	−22.1731			−0.912080
$592$	6.00000			0.246598
$593$	−28.6675			−1.17723			−0.588616	−	0.808413i	$-0.700327\pi$
$593$	−28.6675			−1.17723			−0.588616	+	0.808413i	$0.700327\pi$
$594$	−7.39104	+	15.6788i	−0.303258	+	0.643307i
$595$		0			0
$596$		−	6.72792i		−	0.275586i
$597$	26.6863			1.09220
$598$		−	14.3337i		−	0.586150i
$599$	−26.0000			−1.06233			−0.531166	−	0.847268i	$-0.678246\pi$
$599$	−26.0000			−1.06233			−0.531166	+	0.847268i	$0.678246\pi$
$600$	−4.14386			−0.169172
$601$	−35.9497			−1.46642			−0.733210	−	0.680003i	$-0.761979\pi$
$601$	−35.9497			−1.46642			−0.733210	+	0.680003i	$0.761979\pi$
$602$		0			0
$603$	21.3137			0.867961
$604$			6.00000i			0.244137i
$605$	−9.18440	+	7.57675i	−0.373399	+	0.308039i
$606$	18.0000			0.731200
$607$	46.2484			1.87716			0.938582	−	0.345057i	$-0.112140\pi$
$607$	46.2484			1.87716			0.938582	+	0.345057i	$0.112140\pi$
$608$			5.54328i			0.224810i
$609$		0			0
$610$	6.00000			0.242933
$611$		−	11.2721i		−	0.456019i
$612$		0			0
$613$			13.7574i			0.555655i	0.960631	+	0.277827i	$0.0896143\pi$
$613$			13.7574i			0.555655i	−0.960631	+	0.277827i	$0.910386\pi$
$614$		−	7.44543i		−	0.300473i
$615$	5.38010			0.216947
$616$		0			0
$617$	1.41421			0.0569341			0.0284670	−	0.999595i	$-0.490937\pi$
$617$	1.41421			0.0569341			0.0284670	+	0.999595i	$0.490937\pi$
$618$		−	6.97056i		−	0.280397i
$619$			1.71644i			0.0689897i	0.999405	+	0.0344948i	$0.0109822\pi$
$619$			1.71644i			0.0689897i	−0.999405	+	0.0344948i	$0.989018\pi$
$620$	−1.51472			−0.0608326
$621$			32.6256i			1.30922i
$622$	33.3910			1.33886
$623$		0			0
$624$			2.48528i			0.0994909i
$625$	8.79899			0.351960
$626$	10.3212			0.412518
$627$	18.0000	+	8.48528i	0.718851	+	0.338869i
$628$			11.5349i			0.460292i
$629$		0			0
$630$		0			0
$631$	15.2132			0.605628			0.302814	−	0.953050i	$-0.402074\pi$
$631$	15.2132			0.605628			0.302814	+	0.953050i	$0.402074\pi$
$632$	8.48528			0.337526
$633$	26.7653			1.06383
$634$			22.9706i			0.912278i
$635$	−6.49435			−0.257721
$636$		−	4.85483i		−	0.192507i
$637$		0			0
$638$	−2.48528	+	5.27208i	−0.0983932	+	0.208724i
$639$	3.65685			0.144663
$640$	1.08239			0.0427853
$641$	2.78680			0.110072			0.0550359	−	0.998484i	$-0.482473\pi$
$641$	2.78680			0.110072			0.0550359	+	0.998484i	$0.482473\pi$
$642$			13.7766i			0.543719i
$643$			5.04054i			0.198780i	0.995049	+	0.0993898i	$0.0316891\pi$
$643$			5.04054i			0.198780i	−0.995049	+	0.0993898i	$0.968311\pi$
$644$		0			0
$645$			4.97056i			0.195716i
$646$		0			0
$647$		−	3.56420i		−	0.140123i	−0.997543	−	0.0700616i	$-0.977680\pi$
$647$		−	3.56420i		−	0.140123i	0.997543	−	0.0700616i	$-0.0223196\pi$
$648$		−	0.171573i		−	0.00674002i
$649$	−21.6160	−	10.1899i	−0.848501	−	0.399987i
$650$		−	8.79045i		−	0.344790i
$651$		0			0
$652$	8.14214			0.318871
$653$	21.4558			0.839632			0.419816	−	0.907609i	$-0.362095\pi$
$653$	21.4558			0.839632			0.419816	+	0.907609i	$0.362095\pi$
$654$			3.80430i			0.148760i
$655$		−	7.45584i		−	0.291324i
$656$	4.59220			0.179295
$657$	28.6675			1.11842
$658$		0			0
$659$			9.21320i			0.358895i	0.983768	+	0.179448i	$0.0574311\pi$
$659$			9.21320i			0.358895i	−0.983768	+	0.179448i	$0.942569\pi$
$660$	1.65685	−	3.51472i	0.0644930	−	0.136810i
$661$			33.4454i			1.30087i	0.759560	+	0.650437i	$0.225414\pi$
$661$			33.4454i			1.30087i	−0.759560	+	0.650437i	$0.774586\pi$
$662$		−	20.4853i		−	0.796183i
$663$		0			0
$664$		−	13.3827i		−	0.519348i
$665$		0			0
$666$		−	10.9706i		−	0.425101i
$667$			10.9706i			0.424782i
$668$	20.2710			0.784307
$669$	−8.54416			−0.330336
$670$	−12.6173			−0.487448
$671$	7.83938	−	16.6298i	0.302636	−	0.641988i
$672$		0			0
$673$		−	45.9411i		−	1.77090i	−0.464734	−	0.885450i	$-0.653850\pi$
$673$		−	45.9411i		−	1.77090i	0.464734	−	0.885450i	$-0.346150\pi$
$674$	−26.4853			−1.02017
$675$			20.0083i			0.770121i
$676$	7.72792			0.297228
$677$	−19.8770			−0.763935			−0.381968	−	0.924176i	$-0.624753\pi$
$677$	−19.8770			−0.763935			−0.381968	+	0.924176i	$0.624753\pi$
$678$	−1.53073			−0.0587875
$679$		0			0
$680$		0			0
$681$		−	1.02944i		−	0.0394481i
$682$	−1.97908	+	4.19825i	−0.0757827	+	0.160759i
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$	10.1355			0.387540
$685$			18.3688i			0.701836i
$686$		0			0
$687$	−30.8284			−1.17618
$688$			4.24264i			0.161749i
$689$	10.2987			0.392348
$690$		−	7.31371i		−	0.278428i
$691$			4.25265i			0.161778i	0.996723	+	0.0808891i	$0.0257760\pi$
$691$			4.25265i			0.161778i	−0.996723	+	0.0808891i	$0.974224\pi$
$692$	25.8142			0.981310
$693$		0			0
$694$	−7.75736			−0.294465
$695$			14.4853i			0.549458i
$696$		−	1.90215i		−	0.0721009i
$697$		0			0
$698$		−	29.0614i		−	1.09999i
$699$	9.18440			0.347386
$700$		0			0
$701$			39.9411i			1.50856i	0.656555	+	0.754278i	$0.272013\pi$
$701$			39.9411i			1.50856i	−0.656555	+	0.754278i	$0.727987\pi$
$702$	12.0000			0.452911
$703$	−33.2597			−1.25441
$704$	1.41421	−	3.00000i	0.0533002	−	0.113067i
$705$		−	5.75152i		−	0.216615i
$706$	−1.21371			−0.0456785
$707$		0			0
$708$	7.79899			0.293104
$709$	−23.3137			−0.875565			−0.437782	−	0.899081i	$-0.644236\pi$
$709$	−23.3137			−0.875565			−0.437782	+	0.899081i	$0.644236\pi$
$710$	−2.16478			−0.0812429
$711$		−	15.5147i		−	0.581847i
$712$	−3.56420			−0.133574
$713$			8.73606i			0.327168i
$714$		0			0
$715$	7.45584	+	3.51472i	0.278833	+	0.131443i
$716$	5.65685			0.211407
$717$	−28.6675			−1.07061
$718$	−2.48528			−0.0927499
$719$		−	23.2011i		−	0.865255i	−0.901573	−	0.432628i	$-0.857586\pi$
$719$		−	23.2011i		−	0.865255i	0.901573	−	0.432628i	$-0.142414\pi$
$720$		−	1.97908i		−	0.0737558i
$721$		0			0
$722$		−	11.7279i		−	0.436468i
$723$		−	4.97056i		−	0.184857i
$724$			20.4567i			0.760266i
$725$			6.72792i			0.249869i
$726$	−7.57675	−	9.18440i	−0.281199	−	0.340865i
$727$			25.9999i			0.964285i	0.876093	+	0.482142i	$0.160141\pi$
$727$			25.9999i			0.964285i	−0.876093	+	0.482142i	$0.839859\pi$
$728$		0			0
$729$	−17.2843			−0.640158
$730$	−16.9706			−0.628109
$731$		0			0
$732$			6.00000i			0.221766i
$733$	−0.951076			−0.0351288			−0.0175644	−	0.999846i	$-0.505591\pi$
$733$	−0.951076			−0.0351288			−0.0175644	+	0.999846i	$0.505591\pi$
$734$	11.1409			0.411220
$735$		0			0
$736$		−	6.24264i		−	0.230107i
$737$	−16.4853	+	34.9706i	−0.607243	+	1.28816i
$738$		−	8.39651i		−	0.309080i
$739$		−	24.0000i		−	0.882854i	−0.897297	−	0.441427i	$-0.854472\pi$
$739$		−	24.0000i		−	0.882854i	0.897297	−	0.441427i	$-0.145528\pi$
$740$			6.49435i			0.238737i
$741$		−	13.7766i		−	0.506096i
$742$		0			0
$743$			36.4264i			1.33636i	0.744002	+	0.668178i	$0.232925\pi$
$743$			36.4264i			1.33636i	−0.744002	+	0.668178i	$0.767075\pi$
$744$		−	1.51472i		−	0.0555323i
$745$	7.28225			0.266801
$746$	−20.4853			−0.750019
$747$	−24.4692			−0.895282
$748$		0			0
$749$		0			0
$750$		−	10.3431i		−	0.377678i
$751$	19.4142			0.708435			0.354217	−	0.935163i	$-0.384747\pi$
$751$	19.4142			0.708435			0.354217	+	0.935163i	$0.384747\pi$
$752$		−	4.90923i		−	0.179021i
$753$	13.1716			0.479999
$754$	4.03507			0.146949
$755$	−6.49435			−0.236354
$756$		0			0
$757$	−38.1421			−1.38630			−0.693150	−	0.720794i	$-0.743778\pi$
$757$	−38.1421			−1.38630			−0.693150	+	0.720794i	$0.743778\pi$
$758$			11.6569i			0.423396i
$759$	−20.2710	−	9.55582i	−0.735789	−	0.346854i
$760$	−6.00000			−0.217643
$761$	28.6675			1.03919			0.519597	−	0.854411i	$-0.326082\pi$
$761$	28.6675			1.03919			0.519597	+	0.854411i	$0.326082\pi$
$762$		−	6.49435i		−	0.235266i
$763$		0			0
$764$	1.75736			0.0635790
$765$		0			0
$766$	−14.4650			−0.522643
$767$			16.5442i			0.597375i
$768$			1.08239i			0.0390575i
$769$	−6.49435			−0.234192			−0.117096	−	0.993121i	$-0.537359\pi$
$769$	−6.49435			−0.234192			−0.117096	+	0.993121i	$0.537359\pi$
$770$		0			0
$771$	23.8579			0.859220
$772$		−	2.48528i		−	0.0894472i
$773$			25.6829i			0.923750i	0.886945	+	0.461875i	$0.152823\pi$
$773$			25.6829i			0.923750i	−0.886945	+	0.461875i	$0.847177\pi$
$774$	7.75736			0.278833
$775$			5.35757i			0.192450i
$776$	−8.60474			−0.308892
$777$		0			0
$778$			32.0000i			1.14726i
$779$	−25.4558			−0.912050
$780$	−2.69005			−0.0963192
$781$	−2.82843	+	6.00000i	−0.101209	+	0.214697i
$782$		0			0
$783$	−9.18440			−0.328224
$784$		0			0
$785$	−12.4853			−0.445619
$786$	7.45584			0.265941
$787$	8.79045			0.313346			0.156673	−	0.987651i	$-0.449923\pi$
$787$	8.79045			0.313346			0.156673	+	0.987651i	$0.449923\pi$
$788$		−	20.4853i		−	0.729758i
$789$	−25.9774			−0.924820
$790$			9.18440i			0.326766i
$791$		0			0
$792$	−5.48528	−	2.58579i	−0.194911	−	0.0918819i
$793$	−12.7279			−0.451982
$794$	−1.71644			−0.0609143
$795$	5.25483			0.186370
$796$			24.6549i			0.873870i
$797$		−	26.0543i		−	0.922892i	−0.887168	−	0.461446i	$-0.847331\pi$
$797$		−	26.0543i		−	0.922892i	0.887168	−	0.461446i	$-0.152669\pi$
$798$		0			0
$799$		0			0
$800$		−	3.82843i		−	0.135355i
$801$			6.51688i			0.230263i
$802$		−	0.485281i		−	0.0171359i
$803$	−22.1731	+	47.0363i	−0.782472	+	1.65987i
$804$		−	12.6173i		−	0.444977i
$805$		0			0
$806$	3.21320			0.113180
$807$	−3.79899			−0.133731
$808$			16.6298i			0.585035i
$809$			14.4853i			0.509275i	0.967037	+	0.254638i	$0.0819562\pi$
$809$			14.4853i			0.509275i	−0.967037	+	0.254638i	$0.918044\pi$
$810$	0.185709			0.00652515
$811$	−6.88830			−0.241881			−0.120940	−	0.992660i	$-0.538591\pi$
$811$	−6.88830			−0.241881			−0.120940	+	0.992660i	$0.538591\pi$
$812$		0			0
$813$			28.9706i			1.01604i
$814$	18.0000	+	8.48528i	0.630900	+	0.297409i
$815$			8.81298i			0.308705i
$816$		0			0
$817$		−	23.5181i		−	0.822795i
$818$		−	37.8519i		−	1.32346i
$819$		0			0
$820$			4.97056i			0.173580i
$821$		−	13.7574i		−	0.480135i	−0.970756	−	0.240068i	$-0.922830\pi$
$821$		−	13.7574i		−	0.480135i	0.970756	−	0.240068i	$-0.0771696\pi$
$822$	−18.3688			−0.640686
$823$	8.78680			0.306288			0.153144	−	0.988204i	$-0.451060\pi$
$823$	8.78680			0.306288			0.153144	+	0.988204i	$0.451060\pi$
$824$	6.43996			0.224347
$825$	−12.4316	−	5.86030i	−0.432812	−	0.204030i
$826$		0			0
$827$			16.9706i			0.590124i	0.955478	+	0.295062i	$0.0953404\pi$
$827$			16.9706i			0.590124i	−0.955478	+	0.295062i	$0.904660\pi$
$828$	−11.4142			−0.396671
$829$		−	21.9874i		−	0.763654i	−0.924234	−	0.381827i	$-0.875295\pi$
$829$		−	21.9874i		−	0.763654i	0.924234	−	0.381827i	$-0.124705\pi$
$830$	14.4853			0.502791
$831$	20.2710			0.703192
$832$	−2.29610			−0.0796030
$833$		0			0
$834$	−14.4853			−0.501584
$835$			21.9411i			0.759304i
$836$	−7.83938	+	16.6298i	−0.271131	+	0.575155i
$837$	−7.31371			−0.252799
$838$	8.47343			0.292710
$839$		−	27.0823i		−	0.934986i	−0.883997	−	0.467493i	$-0.845157\pi$
$839$		−	27.0823i		−	0.934986i	0.883997	−	0.467493i	$-0.154843\pi$
$840$		0			0
$841$	25.9117			0.893506
$842$		−	17.6569i		−	0.608495i
$843$	12.9887			0.447355
$844$			24.7279i			0.851170i
$845$			8.36464i			0.287752i
$846$	−8.97616			−0.308607
$847$		0			0
$848$	4.48528			0.154025
$849$		−	24.4264i		−	0.838312i
$850$		0			0
$851$	37.4558			1.28397
$852$		−	2.16478i		−	0.0741643i
$853$	5.54328			0.189798			0.0948991	−	0.995487i	$-0.469747\pi$
$853$	5.54328			0.189798			0.0948991	+	0.995487i	$0.469747\pi$
$854$		0			0
$855$			10.9706i			0.375185i
$856$	−12.7279			−0.435031
$857$	1.90215			0.0649763			0.0324881	−	0.999472i	$-0.489657\pi$
$857$	1.90215			0.0649763			0.0324881	+	0.999472i	$0.489657\pi$
$858$	−3.51472	+	7.45584i	−0.119991	+	0.254538i
$859$		−	11.5349i		−	0.393566i	−0.980447	−	0.196783i	$-0.936951\pi$
$859$		−	11.5349i		−	0.393566i	0.980447	−	0.196783i	$-0.0630494\pi$
$860$	−4.59220			−0.156593
$861$		0			0
$862$	−2.48528			−0.0846490
$863$	−30.7279			−1.04599			−0.522995	−	0.852336i	$-0.675185\pi$
$863$	−30.7279			−1.04599			−0.522995	+	0.852336i	$0.675185\pi$
$864$	5.22625			0.177801
$865$			27.9411i			0.950027i
$866$	22.6758			0.770557
$867$		−	18.4007i		−	0.624919i
$868$		0			0
$869$	25.4558	+	12.0000i	0.863530	+	0.407072i
$870$	2.05887			0.0698024
$871$	26.7653			0.906908
$872$	−3.51472			−0.119023
$873$			15.7331i			0.532486i
$874$			34.6047i			1.17052i
$875$		0			0
$876$		−	16.9706i		−	0.573382i
$877$			54.0000i			1.82345i	0.410801	+	0.911725i	$0.365249\pi$
$877$			54.0000i			1.82345i	−0.410801	+	0.911725i	$0.634751\pi$
$878$		−	6.49435i		−	0.219174i
$879$			1.02944i			0.0347221i
$880$	3.24718	+	1.53073i	0.109462	+	0.0516010i
$881$		−	31.4888i		−	1.06089i	−0.847721	−	0.530443i	$-0.822026\pi$
$881$		−	31.4888i		−	1.06089i	0.847721	−	0.530443i	$-0.177974\pi$
$882$		0			0
$883$	−42.4264			−1.42776			−0.713881	−	0.700267i	$-0.753064\pi$
$883$	−42.4264			−1.42776			−0.713881	+	0.700267i	$0.753064\pi$
$884$		0			0
$885$			8.44157i			0.283760i
$886$		−	22.6274i		−	0.760183i
$887$	−9.18440			−0.308382			−0.154191	−	0.988041i	$-0.549277\pi$
$887$	−9.18440			−0.308382			−0.154191	+	0.988041i	$0.549277\pi$
$888$	−6.49435			−0.217936
$889$		0			0
$890$		−	3.85786i		−	0.129316i
$891$	0.242641	−	0.514719i	0.00812877	−	0.0172437i
$892$		−	7.89377i		−	0.264303i
$893$			27.2132i			0.910655i
$894$			7.28225i			0.243555i
$895$			6.12293i			0.204667i
$896$		0			0
$897$			15.5147i			0.518021i
$898$			40.7279i			1.35911i
$899$	−2.45928			−0.0820216
$900$	−7.00000			−0.233333
$901$		0			0
$902$	13.7766	+	6.49435i	0.458711	+	0.216238i
$903$		0			0
$904$		−	1.41421i		−	0.0470360i
$905$	−22.1421			−0.736029
$906$		−	6.49435i		−	0.215760i
$907$	−1.79899			−0.0597345			−0.0298672	−	0.999554i	$-0.509508\pi$
$907$	−1.79899			−0.0597345			−0.0298672	+	0.999554i	$0.509508\pi$
$908$	0.951076			0.0315626
$909$	30.4064			1.00852
$910$		0			0
$911$	38.2426			1.26704			0.633518	−	0.773728i	$-0.281610\pi$
$911$	38.2426			1.26704			0.633518	+	0.773728i	$0.281610\pi$
$912$		−	6.00000i		−	0.198680i
$913$	18.9259	−	40.1480i	0.626357	−	1.32870i
$914$	−31.4558			−1.04047
$915$	−6.49435			−0.214697
$916$		−	28.4818i		−	0.941064i
$917$		0			0
$918$		0			0
$919$		−	30.4264i		−	1.00367i	−0.864962	−	0.501837i	$-0.832658\pi$
$919$		−	30.4264i		−	1.00367i	0.864962	−	0.501837i	$-0.167342\pi$
$920$	6.75699			0.222771
$921$			8.05887i			0.265549i
$922$		−	29.0614i		−	0.957087i
$923$	4.59220			0.151154
$924$		0			0
$925$	22.9706			0.755267
$926$			5.31371i			0.174619i
$927$		−	11.7750i		−	0.386742i
$928$	1.75736			0.0576881
$929$			42.2040i			1.38467i	0.721578	+	0.692334i	$0.243417\pi$
$929$			42.2040i			1.38467i	−0.721578	+	0.692334i	$0.756583\pi$
$930$	1.63952			0.0537620
$931$		0			0
$932$			8.48528i			0.277945i
$933$	−36.1421			−1.18324
$934$	−32.1773			−1.05287
$935$		0			0
$936$			4.19825i			0.137224i
$937$	−35.9497			−1.17443			−0.587213	−	0.809432i	$-0.699775\pi$
$937$	−35.9497			−1.17443			−0.587213	+	0.809432i	$0.699775\pi$
$938$		0			0
$939$	−11.1716			−0.364571
$940$	5.31371			0.173314
$941$	−40.1480			−1.30879			−0.654393	−	0.756155i	$-0.727076\pi$
$941$	−40.1480			−1.30879			−0.654393	+	0.756155i	$0.727076\pi$
$942$		−	12.4853i		−	0.406792i
$943$	28.6675			0.933541
$944$			7.20533i			0.234513i
$945$		0			0
$946$	−6.00000	+	12.7279i	−0.195077	+	0.413820i
$947$	−3.51472			−0.114213			−0.0571065	−	0.998368i	$-0.518187\pi$
$947$	−3.51472			−0.114213			−0.0571065	+	0.998368i	$0.518187\pi$
$948$	−9.18440			−0.298296
$949$	36.0000			1.16861
$950$			21.2220i			0.688534i
$951$		−	24.8632i		−	0.806243i
$952$		0			0
$953$		−	45.9411i		−	1.48818i	−0.668080	−	0.744090i	$-0.732884\pi$
$953$		−	45.9411i		−	1.48818i	0.668080	−	0.744090i	$-0.267116\pi$
$954$		−	8.20101i		−	0.265518i
$955$			1.90215i			0.0615522i
$956$		−	26.4853i		−	0.856595i
$957$	2.69005	−	5.70646i	0.0869569	−	0.184464i
$958$		−	9.18440i		−	0.296735i
$959$		0			0
$960$	−1.17157			−0.0378124
$961$	29.0416			0.936827
$962$		−	13.7766i		−	0.444176i
$963$			23.2721i			0.749932i
$964$	4.59220			0.147905
$965$	2.69005			0.0865957
$966$		0			0
$967$		−	19.4558i		−	0.625658i	−0.949810	−	0.312829i	$-0.898723\pi$
$967$		−	19.4558i		−	0.625658i	0.949810	−	0.312829i	$-0.101277\pi$
$968$	8.48528	−	7.00000i	0.272727	−	0.224989i
$969$		0			0
$970$		−	9.31371i		−	0.299045i
$971$			36.2442i			1.16313i	0.813499	+	0.581566i	$0.197560\pi$
$971$			36.2442i			1.16313i	−0.813499	+	0.581566i	$0.802440\pi$
$972$		−	15.4930i		−	0.496940i
$973$		0			0
$974$			2.44365i			0.0782996i
$975$			9.51472i			0.304715i
$976$	−5.54328			−0.177436
$977$	−44.2426			−1.41545			−0.707724	−	0.706489i	$-0.750278\pi$
$977$	−44.2426			−1.41545			−0.707724	+	0.706489i	$0.750278\pi$
$978$	−8.81298			−0.281808
$979$	−10.6926	−	5.04054i	−0.341737	−	0.161096i
$980$		0			0
$981$			6.42641i			0.205179i
$982$	−39.9411			−1.27457
$983$		−	45.0028i		−	1.43537i	−0.696370	−	0.717683i	$-0.745203\pi$
$983$		−	45.0028i		−	1.43537i	0.696370	−	0.717683i	$-0.254797\pi$
$984$	−4.97056			−0.158456
$985$	22.1731			0.706494
$986$		0			0
$987$		0			0
$988$	12.7279			0.404929
$989$			26.4853i			0.842183i
$990$	2.79884	−	5.93723i	0.0889528	−	0.188697i
$991$	−57.5980			−1.82966			−0.914830	−	0.403839i	$-0.867676\pi$
$991$	−57.5980			−1.82966			−0.914830	+	0.403839i	$0.867676\pi$
$992$	1.39942			0.0444316
$993$			22.1731i			0.703642i
$994$		0			0
$995$	−26.6863			−0.846012
$996$			14.4853i			0.458984i
$997$	−6.10040			−0.193202			−0.0966009	−	0.995323i	$-0.530797\pi$
$997$	−6.10040			−0.193202			−0.0966009	+	0.995323i	$0.530797\pi$
$998$		−	28.6274i		−	0.906185i
$999$			31.3575i			0.992108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.a.1077.3	yes	8
7.2	even	3		1078.2.i.a.1011.2		16
7.3	odd	6		1078.2.i.a.901.6		16
7.4	even	3		1078.2.i.a.901.7		16
7.5	odd	6		1078.2.i.a.1011.3		16
7.6	odd	2	inner	1078.2.c.a.1077.2	✓	8
11.10	odd	2	inner	1078.2.c.a.1077.7	yes	8
77.10	even	6		1078.2.i.a.901.2		16
77.32	odd	6		1078.2.i.a.901.3		16
77.54	even	6		1078.2.i.a.1011.7		16
77.65	odd	6		1078.2.i.a.1011.6		16
77.76	even	2	inner	1078.2.c.a.1077.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.a.1077.2	✓	8	7.6	odd	2	inner
1078.2.c.a.1077.3	yes	8	1.1	even	1	trivial
1078.2.c.a.1077.6	yes	8	77.76	even	2	inner
1078.2.c.a.1077.7	yes	8	11.10	odd	2	inner
1078.2.i.a.901.2		16	77.10	even	6
1078.2.i.a.901.3		16	77.32	odd	6
1078.2.i.a.901.6		16	7.3	odd	6
1078.2.i.a.901.7		16	7.4	even	3
1078.2.i.a.1011.2		16	7.2	even	3
1078.2.i.a.1011.3		16	7.5	odd	6
1078.2.i.a.1011.6		16	77.65	odd	6
1078.2.i.a.1011.7		16	77.54	even	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.08239i q^{3} -1.00000 q^{4} -1.08239i q^{5} +1.08239 q^{6} +1.00000i q^{8} +1.82843 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.08239i q^{3} -1.00000 q^{4} -1.08239i q^{5} +1.08239 q^{6} +1.00000i q^{8} +1.82843 q^{9} -1.08239 q^{10} +(-1.41421 + 3.00000i) q^{11} -1.08239i q^{12} +2.29610 q^{13} +1.17157 q^{15} +1.00000 q^{16} -1.82843i q^{18} -5.54328 q^{19} +1.08239i q^{20} +(3.00000 + 1.41421i) q^{22} +6.24264 q^{23} -1.08239 q^{24} +3.82843 q^{25} -2.29610i q^{26} +5.22625i q^{27} +1.75736i q^{29} -1.17157i q^{30} +1.39942i q^{31} -1.00000i q^{32} +(-3.24718 - 1.53073i) q^{33} -1.82843 q^{36} +6.00000 q^{37} +5.54328i q^{38} +2.48528i q^{39} +1.08239 q^{40} +4.59220 q^{41} +4.24264i q^{43} +(1.41421 - 3.00000i) q^{44} -1.97908i q^{45} -6.24264i q^{46} -4.90923i q^{47} +1.08239i q^{48} -3.82843i q^{50} -2.29610 q^{52} +4.48528 q^{53} +5.22625 q^{54} +(3.24718 + 1.53073i) q^{55} -6.00000i q^{57} +1.75736 q^{58} +7.20533i q^{59} -1.17157 q^{60} -5.54328 q^{61} +1.39942 q^{62} -1.00000 q^{64} -2.48528i q^{65} +(-1.53073 + 3.24718i) q^{66} +11.6569 q^{67} +6.75699i q^{69} +2.00000 q^{71} +1.82843i q^{72} +15.6788 q^{73} -6.00000i q^{74} +4.14386i q^{75} +5.54328 q^{76} +2.48528 q^{78} -8.48528i q^{79} -1.08239i q^{80} -0.171573 q^{81} -4.59220i q^{82} -13.3827 q^{83} +4.24264 q^{86} -1.90215 q^{87} +(-3.00000 - 1.41421i) q^{88} +3.56420i q^{89} -1.97908 q^{90} -6.24264 q^{92} -1.51472 q^{93} -4.90923 q^{94} +6.00000i q^{95} +1.08239 q^{96} +8.60474i q^{97} +(-2.58579 + 5.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 8 * q^9	\( 8 q - 8 q^{4} - 8 q^{9} + 32 q^{15} + 8 q^{16} + 24 q^{22} + 16 q^{23} + 8 q^{25} + 8 q^{36} + 48 q^{37} - 32 q^{53} + 48 q^{58} - 32 q^{60} - 8 q^{64} + 48 q^{67} + 16 q^{71} - 48 q^{78} - 24 q^{81} - 24 q^{88} - 16 q^{92} - 80 q^{93} - 32 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^9 + 32 * q^15 + 8 * q^16 + 24 * q^22 + 16 * q^23 + 8 * q^25 + 8 * q^36 + 48 * q^37 - 32 * q^53 + 48 * q^58 - 32 * q^60 - 8 * q^64 + 48 * q^67 + 16 * q^71 - 48 * q^78 - 24 * q^81 - 24 * q^88 - 16 * q^92 - 80 * q^93 - 32 * q^99

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