LMFDB - Embedded newform 1078.2.i.d.901.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.5
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.d.1011.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} +1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} +1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(1.23576 + 2.14039i) q^{10} +(3.29274 + 0.397356i) q^{11} +(-1.60021 - 0.923880i) q^{12} -1.96452 q^{13} +4.56676 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82487 + 4.89282i) q^{17} +(-0.358719 + 0.207107i) q^{18} +(0.453489 - 0.785466i) q^{19} -2.47151i q^{20} +(-2.65291 - 1.99049i) q^{22} +(0.468406 - 0.811303i) q^{23} +(0.923880 + 1.60021i) q^{24} +(0.554192 + 0.959889i) q^{25} +(1.70132 + 0.982258i) q^{26} -4.77791i q^{27} +7.50358i q^{29} +(-3.95493 - 2.28338i) q^{30} +(-4.08699 + 2.35963i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.63617 + 2.40624i) q^{33} -5.64974i q^{34} +0.414214 q^{36} +(4.81498 - 8.33978i) q^{37} +(-0.785466 + 0.453489i) q^{38} +(3.14363 - 1.81498i) q^{39} +(-1.23576 + 2.14039i) q^{40} -6.93240 q^{41} +6.80940i q^{43} +(1.30225 + 3.05027i) q^{44} +(-0.886580 + 0.511867i) q^{45} +(-0.811303 + 0.468406i) q^{46} +(-3.46605 - 2.00112i) q^{47} -1.84776i q^{48} -1.10838i q^{50} +(-9.04075 - 5.21968i) q^{51} +(-0.982258 - 1.70132i) q^{52} +(-3.28338 - 5.68698i) q^{53} +(-2.38896 + 4.13779i) q^{54} +(-6.55672 - 4.91952i) q^{55} +1.67588i q^{57} +(3.75179 - 6.49829i) q^{58} +(0.836265 - 0.482818i) q^{59} +(2.28338 + 3.95493i) q^{60} +(5.95014 - 10.3059i) q^{61} +4.71925 q^{62} -1.00000 q^{64} +(4.20484 + 2.42766i) q^{65} +(6.08418 + 0.734219i) q^{66} +(-3.36002 - 5.81973i) q^{67} +(-2.82487 + 4.89282i) q^{68} +1.73100i q^{69} -11.5485 q^{71} +(-0.358719 - 0.207107i) q^{72} +(-5.43072 - 9.40628i) q^{73} +(-8.33978 + 4.81498i) q^{74} +(-1.77364 - 1.02401i) q^{75} +0.906978 q^{76} -3.62995 q^{78} +(-7.34847 - 4.24264i) q^{79} +(2.14039 - 1.23576i) q^{80} +(5.03553 + 8.72180i) q^{81} +(6.00363 + 3.46620i) q^{82} -4.83601 q^{83} -13.9634i q^{85} +(3.40470 - 5.89712i) q^{86} +(-6.93240 - 12.0073i) q^{87} +(0.397356 - 3.29274i) q^{88} +(-11.0280 - 6.36702i) q^{89} +1.02373 q^{90} +0.936812 q^{92} +(4.36002 - 7.55178i) q^{93} +(2.00112 + 3.46605i) q^{94} +(-1.94129 + 1.12080i) q^{95} +(-0.923880 + 1.60021i) q^{96} -3.82683i q^{97} +(0.824487 - 1.09887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^9	$ 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.884871	−	0.465837i	$-0.845753\pi$
$3$	−1.60021	+	0.923880i	−0.923880	+	0.533402i	−0.0390089	+	0.999239i	$0.512420\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.14039	−	1.23576i	−0.957214	−	0.552647i	−0.0618992	−	0.998082i	$-0.519716\pi$
$5$	−2.14039	−	1.23576i	−0.957214	−	0.552647i	−0.895314	+	0.445435i	$0.853049\pi$
$6$	1.84776			0.754344
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.207107	−	0.358719i	0.0690356	−	0.119573i
$10$	1.23576	+	2.14039i	0.390781	+	0.676852i
$11$	3.29274	+	0.397356i	0.992797	+	0.119807i
$11$	3.29274	+	0.397356i	0.992797	+	0.119807i
$12$	−1.60021	−	0.923880i	−0.461940	−	0.266701i
$13$	−1.96452			−0.544859			−0.272429	−	0.962176i	$-0.587827\pi$
$13$	−1.96452			−0.544859			−0.272429	+	0.962176i	$0.587827\pi$
$14$		0			0
$15$	4.56676			1.17913
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.82487	+	4.89282i	0.685131	+	1.18668i	0.973395	+	0.229132i	$0.0735886\pi$
$17$	2.82487	+	4.89282i	0.685131	+	1.18668i	−0.288264	+	0.957551i	$0.593078\pi$
$18$	−0.358719	+	0.207107i	−0.0845510	+	0.0488155i
$19$	0.453489	−	0.785466i	0.104038	−	0.180198i	−0.809307	−	0.587386i	$-0.800157\pi$
$19$	0.453489	−	0.785466i	0.104038	−	0.180198i	0.913345	+	0.407188i	$0.133490\pi$
$20$		−	2.47151i		−	0.552647i
$21$		0			0
$22$	−2.65291	−	1.99049i	−0.565603	−	0.424374i
$23$	0.468406	−	0.811303i	0.0976694	−	0.169168i	−0.813050	−	0.582194i	$-0.802195\pi$
$23$	0.468406	−	0.811303i	0.0976694	−	0.169168i	0.910720	+	0.413025i	$0.135528\pi$
$24$	0.923880	+	1.60021i	0.188586	+	0.326641i
$25$	0.554192	+	0.959889i	0.110838	+	0.191978i
$26$	1.70132	+	0.982258i	0.333656	+	0.192637i
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$			7.50358i			1.39338i	0.717373	+	0.696689i	$0.245344\pi$
$29$			7.50358i			1.39338i	−0.717373	+	0.696689i	$0.754656\pi$
$30$	−3.95493	−	2.28338i	−0.722069	−	0.416887i
$31$	−4.08699	+	2.35963i	−0.734046	+	0.423801i	−0.819900	−	0.572506i	$-0.805971\pi$
$31$	−4.08699	+	2.35963i	−0.734046	+	0.423801i	0.0858548	+	0.996308i	$0.472638\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.63617	+	2.40624i	−0.981131	+	0.418872i
$34$		−	5.64974i		−	0.968922i
$35$		0			0
$36$	0.414214			0.0690356
$37$	4.81498	−	8.33978i	0.791577	−	1.37105i	−0.133413	−	0.991061i	$-0.542594\pi$
$37$	4.81498	−	8.33978i	0.791577	−	1.37105i	0.924990	−	0.379991i	$-0.124073\pi$
$38$	−0.785466	+	0.453489i	−0.127419	+	0.0735656i
$39$	3.14363	−	1.81498i	0.503384	−	0.290629i
$40$	−1.23576	+	2.14039i	−0.195390	+	0.338426i
$41$	−6.93240			−1.08266			−0.541329	−	0.840811i	$-0.682079\pi$
$41$	−6.93240			−1.08266			−0.541329	+	0.840811i	$0.682079\pi$
$42$		0			0
$43$			6.80940i			1.03842i	0.854645	+	0.519212i	$0.173775\pi$
$43$			6.80940i			1.03842i	−0.854645	+	0.519212i	$0.826225\pi$
$44$	1.30225	+	3.05027i	0.196321	+	0.459846i
$45$	−0.886580	+	0.511867i	−0.132164	+	0.0763047i
$46$	−0.811303	+	0.468406i	−0.119620	+	0.0690627i
$47$	−3.46605	−	2.00112i	−0.505575	−	0.291894i	0.225438	−	0.974258i	$-0.427619\pi$
$47$	−3.46605	−	2.00112i	−0.505575	−	0.291894i	−0.731013	+	0.682364i	$0.760952\pi$
$48$		−	1.84776i		−	0.266701i
$49$		0			0
$50$		−	1.10838i		−	0.156749i
$51$	−9.04075	−	5.21968i	−1.26596	−	0.730901i
$52$	−0.982258	−	1.70132i	−0.136215	−	0.235931i
$53$	−3.28338	−	5.68698i	−0.451007	−	0.781167i	0.547442	−	0.836844i	$-0.315602\pi$
$53$	−3.28338	−	5.68698i	−0.451007	−	0.781167i	−0.998449	+	0.0556765i	$0.982268\pi$
$54$	−2.38896	+	4.13779i	−0.325096	+	0.563082i
$55$	−6.55672	−	4.91952i	−0.884108	−	0.663348i
$56$		0			0
$57$			1.67588i			0.221975i
$58$	3.75179	−	6.49829i	0.492634	−	0.853267i
$59$	0.836265	−	0.482818i	0.108872	−	0.0628575i	−0.444575	−	0.895742i	$-0.646645\pi$
$59$	0.836265	−	0.482818i	0.108872	−	0.0628575i	0.553447	+	0.832884i	$0.313312\pi$
$60$	2.28338	+	3.95493i	0.294783	+	0.510580i
$61$	5.95014	−	10.3059i	0.761838	−	1.31954i	−0.180065	−	0.983655i	$-0.557631\pi$
$61$	5.95014	−	10.3059i	0.761838	−	1.31954i	0.941902	−	0.335887i	$-0.109036\pi$
$62$	4.71925			0.599346
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.20484	+	2.42766i	0.521546	+	0.301115i
$66$	6.08418	+	0.734219i	0.748911	+	0.0903761i
$67$	−3.36002	−	5.81973i	−0.410492	−	0.710993i	0.584452	−	0.811429i	$-0.301310\pi$
$67$	−3.36002	−	5.81973i	−0.410492	−	0.710993i	−0.994944	+	0.100436i	$0.967976\pi$
$68$	−2.82487	+	4.89282i	−0.342566	+	0.593341i
$69$			1.73100i			0.208388i
$70$		0			0
$71$	−11.5485			−1.37055			−0.685276	−	0.728284i	$-0.740318\pi$
$71$	−11.5485			−1.37055			−0.685276	+	0.728284i	$0.740318\pi$
$72$	−0.358719	−	0.207107i	−0.0422755	−	0.0244078i
$73$	−5.43072	−	9.40628i	−0.635617	−	1.10092i	−0.986384	−	0.164458i	$-0.947412\pi$
$73$	−5.43072	−	9.40628i	−0.635617	−	1.10092i	0.350767	−	0.936463i	$-0.385921\pi$
$74$	−8.33978	+	4.81498i	−0.969480	+	0.559730i
$75$	−1.77364	−	1.02401i	−0.204803	−	0.118243i
$76$	0.906978			0.104038
$77$		0			0
$78$	−3.62995			−0.411011
$79$	−7.34847	−	4.24264i	−0.826767	−	0.477334i	0.0259772	−	0.999663i	$-0.491730\pi$
$79$	−7.34847	−	4.24264i	−0.826767	−	0.477334i	−0.852745	+	0.522328i	$0.825064\pi$
$80$	2.14039	−	1.23576i	0.239303	−	0.138162i
$81$	5.03553	+	8.72180i	0.559504	+	0.969089i
$82$	6.00363	+	3.46620i	0.662990	+	0.382778i
$83$	−4.83601			−0.530821			−0.265411	−	0.964135i	$-0.585507\pi$
$83$	−4.83601			−0.530821			−0.265411	+	0.964135i	$0.585507\pi$
$84$		0			0
$85$		−	13.9634i		−	1.51454i
$86$	3.40470	−	5.89712i	0.367138	−	0.635902i
$87$	−6.93240	−	12.0073i	−0.743231	−	1.28731i
$88$	0.397356	−	3.29274i	0.0423583	−	0.351007i
$89$	−11.0280	−	6.36702i	−1.16897	−	0.674903i	−0.215530	−	0.976497i	$-0.569148\pi$
$89$	−11.0280	−	6.36702i	−1.16897	−	0.674903i	−0.953436	+	0.301594i	$0.902481\pi$
$90$	1.02373			0.107911
$91$		0			0
$92$	0.936812			0.0976694
$93$	4.36002	−	7.55178i	0.452113	−	0.783083i
$94$	2.00112	+	3.46605i	0.206400	+	0.357496i
$95$	−1.94129	+	1.12080i	−0.199172	+	0.114992i
$96$	−0.923880	+	1.60021i	−0.0942931	+	0.163320i
$97$		−	3.82683i		−	0.388556i	−0.980946	−	0.194278i	$-0.937764\pi$
$97$		−	3.82683i		−	0.388556i	0.980946	−	0.194278i	$-0.0622364\pi$
$98$		0			0
$99$	0.824487	−	1.09887i	0.0828641	−	0.110441i
$100$	−0.554192	+	0.959889i	−0.0554192	+	0.0959889i
$101$	7.91466	+	13.7086i	0.787538	+	1.36406i	0.927471	+	0.373895i	$0.121978\pi$
$101$	7.91466	+	13.7086i	0.787538	+	1.36406i	−0.139933	+	0.990161i	$0.544689\pi$
$102$	5.21968	+	9.04075i	0.516825	+	0.895167i
$103$	0.684352	+	0.395111i	0.0674312	+	0.0389314i	0.533337	−	0.845903i	$-0.320938\pi$
$103$	0.684352	+	0.395111i	0.0674312	+	0.0389314i	−0.465905	+	0.884835i	$0.654271\pi$
$104$			1.96452i			0.192637i
$105$		0			0
$106$			6.56676i			0.637820i
$107$	−14.3861	−	8.30583i	−1.39076	−	0.802955i	−0.397359	−	0.917663i	$-0.630073\pi$
$107$	−14.3861	−	8.30583i	−1.39076	−	0.802955i	−0.993399	+	0.114708i	$0.963407\pi$
$108$	4.13779	−	2.38896i	0.398159	−	0.229877i
$109$	5.19615	−	3.00000i	0.497701	−	0.287348i	−0.230063	−	0.973176i	$-0.573893\pi$
$109$	5.19615	−	3.00000i	0.497701	−	0.287348i	0.727764	+	0.685828i	$0.240560\pi$
$110$	3.21852	+	7.53879i	0.306874	+	0.718795i
$111$			17.7938i			1.68892i
$112$		0			0
$113$	−5.76421			−0.542251			−0.271126	−	0.962544i	$-0.587396\pi$
$113$	−5.76421			−0.542251			−0.271126	+	0.962544i	$0.587396\pi$
$114$	0.837939	−	1.45135i	0.0784801	−	0.135932i
$115$	−2.00515	+	1.15767i	−0.186981	+	0.107953i
$116$	−6.49829	+	3.75179i	−0.603351	+	0.348345i
$117$	−0.406865	+	0.704710i	−0.0376146	+	0.0651505i
$118$	−0.965635			−0.0888940
$119$		0			0
$120$		−	4.56676i		−	0.416887i
$121$	10.6842	+	2.61678i	0.971292	+	0.237889i
$122$	−10.3059	+	5.95014i	−0.933057	+	0.538701i
$123$	11.0933	−	6.40470i	1.00025	−	0.577493i
$124$	−4.08699	−	2.35963i	−0.367023	−	0.211901i
$125$			9.61818i			0.860277i
$126$		0			0
$127$		−	18.6371i		−	1.65378i	−0.562367	−	0.826888i	$-0.690109\pi$
$127$		−	18.6371i		−	1.65378i	0.562367	−	0.826888i	$-0.309891\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.29107	−	10.8965i	−0.553898	−	0.959379i
$130$	−2.42766	−	4.20484i	−0.212920	−	0.368789i
$131$	−9.99173	+	17.3062i	−0.872982	+	1.51205i	−0.0140849	+	0.999901i	$0.504484\pi$
$131$	−9.99173	+	17.3062i	−0.872982	+	1.51205i	−0.858897	+	0.512148i	$0.828850\pi$
$132$	−4.90195	−	3.67794i	−0.426660	−	0.320124i
$133$		0			0
$134$			6.72004i			0.580523i
$135$	−5.90434	+	10.2266i	−0.508164	+	0.880167i
$136$	4.89282	−	2.82487i	0.419556	−	0.242231i
$137$	−8.21968	−	14.2369i	−0.702254	−	1.21634i	−0.967673	−	0.252207i	$-0.918844\pi$
$137$	−8.21968	−	14.2369i	−0.702254	−	1.21634i	0.265419	−	0.964133i	$-0.414490\pi$
$138$	0.865501	−	1.49909i	0.0736764	−	0.127611i
$139$	10.7109			0.908484			0.454242	−	0.890878i	$-0.349910\pi$
$139$	10.7109			0.908484			0.454242	+	0.890878i	$0.349910\pi$
$140$		0			0
$141$	7.39519			0.622787
$142$	10.0013	+	5.77423i	0.839288	+	0.484563i
$143$	−6.46863	−	0.780613i	−0.540934	−	0.0652781i
$144$	0.207107	+	0.358719i	0.0172589	+	0.0298933i
$145$	9.27260	−	16.0606i	0.770047	−	1.33376i
$146$			10.8614i			0.898898i
$147$		0			0
$148$	9.62995			0.791577
$149$	12.7855	+	7.38174i	1.04743	+	0.604736i	0.921930	−	0.387358i	$-0.126612\pi$
$149$	12.7855	+	7.38174i	1.04743	+	0.604736i	0.125503	+	0.992093i	$0.459945\pi$
$150$	1.02401	+	1.77364i	0.0836104	+	0.144817i
$151$	−9.09017	+	5.24821i	−0.739748	+	0.427093i	−0.821978	−	0.569520i	$-0.807129\pi$
$151$	−9.09017	+	5.24821i	−0.739748	+	0.427093i	0.0822300	+	0.996613i	$0.473796\pi$
$152$	−0.785466	−	0.453489i	−0.0637097	−	0.0367828i
$153$	2.34020			0.189194
$154$		0			0
$155$	11.6637			0.936851
$156$	3.14363	+	1.81498i	0.251692	+	0.145314i
$157$	−3.99732	+	2.30785i	−0.319021	+	0.184187i	−0.650956	−	0.759115i	$-0.725632\pi$
$157$	−3.99732	+	2.30785i	−0.319021	+	0.184187i	0.331935	+	0.943302i	$0.392298\pi$
$158$	4.24264	+	7.34847i	0.337526	+	0.584613i
$159$	10.5082	+	6.06690i	0.833353	+	0.481136i
$160$	−2.47151			−0.195390
$161$		0			0
$162$		−	10.0711i		−	0.791258i
$163$	−7.28732	+	12.6220i	−0.570787	+	0.988632i	0.425698	+	0.904865i	$0.360028\pi$
$163$	−7.28732	+	12.6220i	−0.570787	+	0.988632i	−0.996485	+	0.0837671i	$0.973305\pi$
$164$	−3.46620	−	6.00363i	−0.270665	−	0.468805i
$165$	15.0371	+	1.81463i	1.17064	+	0.141269i
$166$	4.18811	+	2.41800i	0.325060	+	0.187674i
$167$	7.37045			0.570342			0.285171	−	0.958477i	$-0.407950\pi$
$167$	7.37045			0.570342			0.285171	+	0.958477i	$0.407950\pi$
$168$		0			0
$169$	−9.14068			−0.703129
$170$	−6.98171	+	12.0927i	−0.535472	+	0.927465i
$171$	−0.187841	−	0.325351i	−0.0143646	−	0.0248802i
$172$	−5.89712	+	3.40470i	−0.449651	+	0.259606i
$173$	5.57446	−	9.65525i	0.423818	−	0.734075i	−0.572491	−	0.819911i	$-0.694023\pi$
$173$	5.57446	−	9.65525i	0.423818	−	0.734075i	0.996309	+	0.0858362i	$0.0273562\pi$
$174$			13.8648i			1.05109i
$175$		0			0
$176$	−1.99049	+	2.65291i	−0.150039	+	0.199971i
$177$	−0.892131	+	1.54522i	−0.0670567	+	0.116146i
$178$	6.36702	+	11.0280i	0.477229	+	0.826584i
$179$	−7.90434	−	13.6907i	−0.590798	−	1.02329i	−0.994125	−	0.108236i	$-0.965480\pi$
$179$	−7.90434	−	13.6907i	−0.590798	−	1.02329i	0.403327	−	0.915056i	$-0.367854\pi$
$180$	−0.886580	−	0.511867i	−0.0660818	−	0.0381523i
$181$		−	16.6528i		−	1.23779i	−0.785473	−	0.618896i	$-0.787580\pi$
$181$		−	16.6528i		−	1.23779i	0.785473	−	0.618896i	$-0.212420\pi$
$182$		0			0
$183$			21.9889i			1.62546i
$184$	−0.811303	−	0.468406i	−0.0598100	−	0.0345313i
$185$	−20.6119	+	11.9003i	−1.51542	+	0.874926i
$186$	−7.55178	+	4.36002i	−0.553723	+	0.319692i
$187$	7.35736	+	17.2332i	0.538023	+	1.26022i
$188$		−	4.00225i		−	0.291894i
$189$		0			0
$190$	2.24161			0.162623
$191$	−13.1784	+	22.8257i	−0.953557	+	1.65161i	−0.215921	+	0.976411i	$0.569275\pi$
$191$	−13.1784	+	22.8257i	−0.953557	+	1.65161i	−0.737636	+	0.675199i	$0.764058\pi$
$192$	1.60021	−	0.923880i	0.115485	−	0.0666753i
$193$	−0.601170	+	0.347086i	−0.0432731	+	0.0249838i	−0.521481	−	0.853263i	$-0.674620\pi$
$193$	−0.601170	+	0.347086i	−0.0432731	+	0.0249838i	0.478207	+	0.878247i	$0.341287\pi$
$194$	−1.91342	+	3.31414i	−0.137375	+	0.237941i
$195$	−8.97148			−0.642461
$196$		0			0
$197$		−	9.74519i		−	0.694316i	−0.937807	−	0.347158i	$-0.887147\pi$
$197$		−	9.74519i		−	0.694316i	0.937807	−	0.347158i	$-0.112853\pi$
$198$	−1.26346	+	0.539408i	−0.0897904	+	0.0383341i
$199$	6.09214	−	3.51730i	0.431860	−	0.249335i	−0.268279	−	0.963341i	$-0.586455\pi$
$199$	6.09214	−	3.51730i	0.431860	−	0.249335i	0.700139	+	0.714007i	$0.253121\pi$
$200$	0.959889	−	0.554192i	0.0678744	−	0.0391873i
$201$	10.7535	+	6.20851i	0.758490	+	0.437915i
$202$		−	15.8293i		−	1.11375i
$203$		0			0
$204$		−	10.4394i		−	0.730901i
$205$	14.8381	+	8.56676i	1.03634	+	0.598329i
$206$	−0.395111	−	0.684352i	−0.0275287	−	0.0476811i
$207$	−0.194020	−	0.336053i	−0.0134853	−	0.0233573i
$208$	0.982258	−	1.70132i	0.0681073	−	0.117965i
$209$	1.80533	−	2.40614i	0.124877	−	0.166436i
$210$		0			0
$211$			24.1152i			1.66016i	0.557643	+	0.830081i	$0.311706\pi$
$211$			24.1152i			1.66016i	−0.557643	+	0.830081i	$0.688294\pi$
$212$	3.28338	−	5.68698i	0.225504	−	0.390584i
$213$	18.4799	−	10.6694i	1.26622	−	0.731055i
$214$	8.30583	+	14.3861i	0.567775	+	0.983415i
$215$	8.41477	−	14.5748i	0.573883	−	0.993994i
$216$	−4.77791			−0.325096
$217$		0			0
$218$	−6.00000			−0.406371
$219$	17.3805	+	10.0347i	1.17447	+	0.678079i
$220$	0.982072	−	8.13804i	0.0662113	−	0.548667i
$221$	−5.54950	−	9.61202i	−0.373300	−	0.646574i
$222$	8.89692	−	15.4099i	0.597122	−	1.03425i
$223$		−	2.90530i		−	0.194553i	−0.995257	−	0.0972765i	$-0.968987\pi$
$223$		−	2.90530i		−	0.194553i	0.995257	−	0.0972765i	$-0.0310131\pi$
$224$		0			0
$225$	0.459108			0.0306072
$226$	4.99195	+	2.88210i	0.332060	+	0.191715i
$227$	7.21349	+	12.4941i	0.478776	+	0.829265i	0.999704	−	0.0243362i	$-0.00774722\pi$
$227$	7.21349	+	12.4941i	0.478776	+	0.829265i	−0.520928	+	0.853601i	$0.674414\pi$
$228$	−1.45135	+	0.837939i	−0.0961181	+	0.0554938i
$229$	−6.14615	−	3.54848i	−0.406149	−	0.234490i	0.282985	−	0.959124i	$-0.408675\pi$
$229$	−6.14615	−	3.54848i	−0.406149	−	0.234490i	−0.689134	+	0.724634i	$0.742009\pi$
$230$	2.31534			0.152669
$231$		0			0
$232$	7.50358			0.492634
$233$	−3.60367	−	2.08058i	−0.236084	−	0.136303i	0.377291	−	0.926095i	$-0.376855\pi$
$233$	−3.60367	−	2.08058i	−0.236084	−	0.136303i	−0.613376	+	0.789791i	$0.710189\pi$
$234$	0.704710	−	0.406865i	0.0460683	−	0.0265976i
$235$	4.94581	+	8.56639i	0.322629	+	0.558810i
$236$	0.836265	+	0.482818i	0.0544362	+	0.0314288i
$237$	15.6788			1.01844
$238$		0			0
$239$		−	19.8625i		−	1.28480i	−0.766371	−	0.642399i	$-0.777939\pi$
$239$		−	19.8625i		−	1.28480i	0.766371	−	0.642399i	$-0.222061\pi$
$240$	−2.28338	+	3.95493i	−0.147392	+	0.255290i
$241$	−7.24467	−	12.5481i	−0.466670	−	0.808297i	0.532605	−	0.846364i	$-0.321213\pi$
$241$	−7.24467	−	12.5481i	−0.466670	−	0.808297i	−0.999275	+	0.0380673i	$0.987880\pi$
$242$	−7.94441	−	7.60831i	−0.510686	−	0.489080i
$243$	−3.70241	−	2.13759i	−0.237510	−	0.137126i
$244$	11.9003			0.761838
$245$		0			0
$246$	−12.8094			−0.816698
$247$	−0.890886	+	1.54306i	−0.0566857	+	0.0981826i
$248$	2.35963	+	4.08699i	0.149836	+	0.259524i
$249$	7.73861	−	4.46789i	0.490415	−	0.283141i
$250$	4.80909	−	8.32959i	0.304154	−	0.526810i
$251$			14.6156i			0.922529i	0.887263	+	0.461264i	$0.152604\pi$
$251$			14.6156i			0.922529i	−0.887263	+	0.461264i	$0.847396\pi$
$252$		0			0
$253$	1.86471	−	2.48528i	0.117234	−	0.156248i
$254$	−9.31855	+	16.1402i	−0.584698	+	1.01273i
$255$	12.9005	+	22.3443i	0.807861	+	1.39926i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	20.0209	+	11.5591i	1.24887	+	0.721035i	0.970884	−	0.239550i	$-0.0769998\pi$
$257$	20.0209	+	11.5591i	1.24887	+	0.721035i	0.277986	+	0.960585i	$0.410333\pi$
$258$			12.5821i			0.783330i
$259$		0			0
$260$			4.85533i			0.301115i
$261$	2.69168	+	1.55404i	0.166611	+	0.0961927i
$262$	17.3062	−	9.99173i	1.06918	−	0.617291i
$263$	7.34847	−	4.24264i	0.453126	−	0.261612i	−0.256023	−	0.966671i	$-0.582412\pi$
$263$	7.34847	−	4.24264i	0.453126	−	0.261612i	0.709150	+	0.705058i	$0.249079\pi$
$264$	2.40624	+	5.63617i	0.148094	+	0.346882i
$265$			16.2299i			0.996992i
$266$		0			0
$267$	23.5294			1.43998
$268$	3.36002	−	5.81973i	0.205246	−	0.355496i
$269$	26.5008	−	15.3003i	1.61578	−	0.932874i	0.627791	−	0.778382i	$-0.283959\pi$
$269$	26.5008	−	15.3003i	1.61578	−	0.932874i	0.987994	−	0.154492i	$-0.0493739\pi$
$270$	10.2266	−	5.90434i	0.622372	−	0.359327i
$271$	6.60081	−	11.4329i	0.400971	−	0.694502i	−0.592872	−	0.805296i	$-0.702006\pi$
$271$	6.60081	−	11.4329i	0.400971	−	0.694502i	0.993843	+	0.110794i	$0.0353395\pi$
$272$	−5.64974			−0.342566
$273$		0			0
$274$			16.4394i			0.993138i
$275$	1.44339	+	3.38087i	0.0870397	+	0.203874i
$276$	−1.49909	+	0.865501i	−0.0902347	+	0.0520970i
$277$	−3.45445	+	1.99443i	−0.207558	+	0.119834i	−0.600176	−	0.799868i	$-0.704903\pi$
$277$	−3.45445	+	1.99443i	−0.207558	+	0.119834i	0.392618	+	0.919702i	$0.371569\pi$
$278$	−9.27589	−	5.35544i	−0.556331	−	0.321198i
$279$			1.95478i			0.117030i
$280$		0			0
$281$			5.94293i			0.354526i	0.984164	+	0.177263i	$0.0567243\pi$
$281$			5.94293i			0.354526i	−0.984164	+	0.177263i	$0.943276\pi$
$282$	−6.40442	−	3.69760i	−0.381378	−	0.220189i
$283$	−10.6331	−	18.4170i	−0.632070	−	1.09478i	−0.987128	−	0.159933i	$-0.948872\pi$
$283$	−10.6331	−	18.4170i	−0.632070	−	1.09478i	0.355058	−	0.934844i	$-0.384461\pi$
$284$	−5.77423	−	10.0013i	−0.342638	−	0.593466i
$285$	2.07098	−	3.58704i	0.122674	−	0.212478i
$286$	5.21169	+	3.91035i	0.308174	+	0.231224i
$287$		0			0
$288$		−	0.414214i		−	0.0244078i
$289$	−7.45977	+	12.9207i	−0.438810	+	0.760042i
$290$	−16.0606	+	9.27260i	−0.943112	+	0.544506i
$291$	3.53553	+	6.12372i	0.207257	+	0.358979i
$292$	5.43072	−	9.40628i	0.317809	−	0.550461i
$293$	27.7920			1.62362			0.811812	−	0.583919i	$-0.198481\pi$
$293$	27.7920			1.62362			0.811812	+	0.583919i	$0.198481\pi$
$294$		0			0
$295$	−2.38658			−0.138952
$296$	−8.33978	−	4.81498i	−0.484740	−	0.279865i
$297$	1.89853	−	15.7324i	0.110164	−	0.912886i
$298$	−7.38174	−	12.7855i	−0.427613	−	0.740647i
$299$	−0.920191	+	1.59382i	−0.0532160	+	0.0921728i
$300$		−	2.04803i		−	0.118243i
$301$		0			0
$302$	10.4964			0.604001
$303$	−25.3302	−	14.6244i	−1.45518	−	0.840149i
$304$	0.453489	+	0.785466i	0.0260094	+	0.0450496i
$305$	−25.4713	+	14.7059i	−1.45848	+	0.842055i
$306$	−2.02667	−	1.17010i	−0.115857	−	0.0668901i
$307$	−16.2674			−0.928427			−0.464214	−	0.885723i	$-0.653663\pi$
$307$	−16.2674			−0.928427			−0.464214	+	0.885723i	$0.653663\pi$
$308$		0			0
$309$	−1.46014			−0.0830644
$310$	−10.1011	−	5.83185i	−0.573702	−	0.331227i
$311$	9.34656	−	5.39624i	0.529995	−	0.305993i	−0.211020	−	0.977482i	$-0.567678\pi$
$311$	9.34656	−	5.39624i	0.529995	−	0.305993i	0.741014	+	0.671489i	$0.234345\pi$
$312$	−1.81498	−	3.14363i	−0.102753	−	0.177973i
$313$	−15.8579	−	9.15556i	−0.896341	−	0.517503i	−0.0203300	−	0.999793i	$-0.506472\pi$
$313$	−15.8579	−	9.15556i	−0.896341	−	0.517503i	−0.876011	+	0.482290i	$0.839805\pi$
$314$	4.61571			0.260480
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	0.179452	−	0.310821i	0.0100791	−	0.0174574i	−0.860942	−	0.508703i	$-0.830125\pi$
$317$	0.179452	−	0.310821i	0.0100791	−	0.0174574i	0.871021	+	0.491246i	$0.163458\pi$
$318$	−6.06690	−	10.5082i	−0.340215	−	0.589269i
$319$	−2.98159	+	24.7073i	−0.166937	+	1.38334i
$320$	2.14039	+	1.23576i	0.119652	+	0.0690809i
$321$	30.6943			1.71319
$322$		0			0
$323$	5.12419			0.285118
$324$	−5.03553	+	8.72180i	−0.279752	+	0.484544i
$325$	−1.08872	−	1.88572i	−0.0603913	−	0.104601i
$326$	12.6220	−	7.28732i	0.699069	−	0.403607i
$327$	−5.54328	+	9.60124i	−0.306544	+	0.530950i
$328$			6.93240i			0.382778i
$329$		0			0
$330$	−12.1152	−	9.09009i	−0.666922	−	0.500393i
$331$	14.4567	−	25.0398i	0.794615	−	1.37631i	−0.128469	−	0.991714i	$-0.541006\pi$
$331$	14.4567	−	25.0398i	0.794615	−	1.37631i	0.923084	−	0.384599i	$-0.125660\pi$
$332$	−2.41800	−	4.18811i	−0.132705	−	0.229852i
$333$	−1.99443	−	3.45445i	−0.109294	−	0.189303i
$334$	−6.38299	−	3.68522i	−0.349262	−	0.201646i
$335$			16.6087i			0.907429i
$336$		0			0
$337$			7.96341i			0.433795i	0.976194	+	0.216897i	$0.0695937\pi$
$337$			7.96341i			0.433795i	−0.976194	+	0.216897i	$0.930406\pi$
$338$	7.91606	+	4.57034i	0.430577	+	0.248594i
$339$	9.22392	−	5.32543i	0.500975	−	0.289238i
$340$	12.0927	−	6.98171i	0.655817	−	0.378636i
$341$	−14.3950	+	6.14563i	−0.779533	+	0.332805i
$342$			0.375683i			0.0203146i
$343$		0			0
$344$	6.80940			0.367138
$345$	2.13910	−	3.70503i	0.115165	−	0.199472i
$346$	−9.65525	+	5.57446i	−0.519069	+	0.299685i
$347$	−21.3743	+	12.3405i	−1.14743	+	0.662472i	−0.948261	−	0.317492i	$-0.897159\pi$
$347$	−21.3743	+	12.3405i	−1.14743	+	0.662472i	−0.199174	+	0.979964i	$0.563826\pi$
$348$	6.93240	−	12.0073i	0.371616	−	0.643657i
$349$	−11.1489			−0.596788			−0.298394	−	0.954443i	$-0.596451\pi$
$349$	−11.1489			−0.596788			−0.298394	+	0.954443i	$0.596451\pi$
$350$		0			0
$351$			9.38628i			0.501003i
$352$	3.05027	−	1.30225i	0.162580	−	0.0694100i
$353$	−18.5202	+	10.6926i	−0.985729	+	0.569111i	−0.903995	−	0.427543i	$-0.859379\pi$
$353$	−18.5202	+	10.6926i	−0.985729	+	0.569111i	−0.0817341	+	0.996654i	$0.526046\pi$
$354$	1.54522	−	0.892131i	0.0821273	−	0.0474162i
$355$	24.7183	+	14.2711i	1.31191	+	0.757432i
$356$		−	12.7340i		−	0.674903i
$357$		0			0
$358$			15.8087i			0.835514i
$359$	−5.40718	−	3.12184i	−0.285380	−	0.164764i	0.350477	−	0.936572i	$-0.386020\pi$
$359$	−5.40718	−	3.12184i	−0.285380	−	0.164764i	−0.635856	+	0.771807i	$0.719353\pi$
$360$	0.511867	+	0.886580i	0.0269778	+	0.0467269i
$361$	9.08870	+	15.7421i	0.478352	+	0.828531i
$362$	−8.32639	+	14.4217i	−0.437625	+	0.757989i
$363$	−19.5145	+	5.68354i	−1.02425	+	0.298309i
$364$		0			0
$365$			26.8442i			1.40509i
$366$	10.9944	−	19.0429i	0.574688	−	0.995389i
$367$	24.9011	−	14.3767i	1.29983	−	0.750456i	0.319454	−	0.947602i	$-0.396501\pi$
$367$	24.9011	−	14.3767i	1.29983	−	0.750456i	0.980374	+	0.197146i	$0.0631673\pi$
$368$	0.468406	+	0.811303i	0.0244173	+	0.0422921i
$369$	−1.43575	+	2.48679i	−0.0747420	+	0.129457i
$370$	23.8006			1.23733
$371$		0			0
$372$	8.72004			0.452113
$373$	10.7031	+	6.17945i	0.554187	+	0.319960i	0.750809	−	0.660519i	$-0.229664\pi$
$373$	10.7031	+	6.17945i	0.554187	+	0.319960i	−0.196622	+	0.980479i	$0.562997\pi$
$374$	2.24496	−	18.6031i	0.116084	−	0.961943i
$375$	−8.88604	−	15.3911i	−0.458873	−	0.794792i
$376$	−2.00112	+	3.46605i	−0.103200	+	0.178748i
$377$		−	14.7409i		−	0.759195i
$378$		0			0
$379$	−23.7822			−1.22161			−0.610805	−	0.791781i	$-0.709154\pi$
$379$	−23.7822			−1.22161			−0.610805	+	0.791781i	$0.709154\pi$
$380$	−1.94129	−	1.12080i	−0.0995861	−	0.0574961i
$381$	17.2184	+	29.8232i	0.882127	+	1.52789i
$382$	22.8257	−	13.1784i	1.16786	−	0.674267i
$383$	−27.5955	−	15.9323i	−1.41006	−	0.814100i	−0.414669	−	0.909972i	$-0.636103\pi$
$383$	−27.5955	−	15.9323i	−1.41006	−	0.814100i	−0.995394	+	0.0958720i	$0.969436\pi$
$384$	−1.84776			−0.0942931
$385$		0			0
$386$	0.694171			0.0353324
$387$	2.44267	+	1.41027i	0.124168	+	0.0716882i
$388$	3.31414	−	1.91342i	0.168250	−	0.0971390i
$389$	−10.5077	−	18.1999i	−0.532763	−	0.922773i	−0.999268	−	0.0382540i	$-0.987820\pi$
$389$	−10.5077	−	18.1999i	−0.532763	−	0.922773i	0.466505	−	0.884519i	$-0.345513\pi$
$390$	7.76953	+	4.48574i	0.393425	+	0.227144i
$391$	5.29274			0.267665
$392$		0			0
$393$		−	36.9246i		−	1.86260i
$394$	−4.87259	+	8.43958i	−0.245478	+	0.425180i
$395$	10.4857	+	18.1618i	0.527595	+	0.913822i
$396$	1.36390	+	0.164590i	0.0685383	+	0.00827098i
$397$	−7.20364	−	4.15902i	−0.361540	−	0.208735i	0.308216	−	0.951316i	$-0.400268\pi$
$397$	−7.20364	−	4.15902i	−0.361540	−	0.208735i	−0.669756	+	0.742581i	$0.733601\pi$
$398$	−7.03460			−0.352612
$399$		0			0
$400$	−1.10838			−0.0554192
$401$	15.3410	−	26.5714i	0.766093	−	1.32691i	−0.173574	−	0.984821i	$-0.555532\pi$
$401$	15.3410	−	26.5714i	0.766093	−	1.32691i	0.939667	−	0.342091i	$-0.111135\pi$
$402$	−6.20851	−	10.7535i	−0.309652	−	0.536334i
$403$	8.02896	−	4.63552i	0.399951	−	0.230912i
$404$	−7.91466	+	13.7086i	−0.393769	+	0.682028i
$405$		−	24.8908i		−	1.23683i
$406$		0			0
$407$	19.1683	−	25.5474i	0.950138	−	1.26634i
$408$	−5.21968	+	9.04075i	−0.258413	+	0.447584i
$409$	−4.78939	−	8.29546i	−0.236820	−	0.410184i	0.722980	−	0.690869i	$-0.242772\pi$
$409$	−4.78939	−	8.29546i	−0.236820	−	0.410184i	−0.959800	+	0.280685i	$0.909438\pi$
$410$	−8.56676	−	14.8381i	−0.423082	−	0.732800i
$411$	26.3064	+	15.1880i	1.29760	+	0.749168i
$412$			0.790221i			0.0389314i
$413$		0			0
$414$			0.388040i			0.0190711i
$415$	10.3510	+	5.97613i	0.508109	+	0.293357i
$416$	−1.70132	+	0.982258i	−0.0834141	+	0.0481592i
$417$	−17.1396	+	9.89556i	−0.839330	+	0.484587i
$418$	−2.76653	+	1.18111i	−0.135315	+	0.0577700i
$419$			10.3074i			0.503550i	0.967786	+	0.251775i	$0.0810143\pi$
$419$			10.3074i			0.503550i	−0.967786	+	0.251775i	$0.918986\pi$
$420$		0			0
$421$	−25.8805			−1.26134			−0.630669	−	0.776052i	$-0.717219\pi$
$421$	−25.8805			−1.26134			−0.630669	+	0.776052i	$0.717219\pi$
$422$	12.0576	−	20.8844i	0.586956	−	1.01664i
$423$	−1.43568	+	0.828893i	−0.0698054	+	0.0403021i
$424$	−5.68698	+	3.28338i	−0.276184	+	0.159455i
$425$	−3.13104	+	5.42312i	−0.151878	+	0.263060i
$426$	−21.3388			−1.03387
$427$		0			0
$428$		−	16.6117i		−	0.802955i
$429$	11.0723	−	4.72709i	0.534577	−	0.228226i
$430$	−14.5748	+	8.41477i	−0.702860	+	0.405796i
$431$	−14.7967	+	8.54290i	−0.712734	+	0.411497i	−0.812072	−	0.583557i	$-0.801661\pi$
$431$	−14.7967	+	8.54290i	−0.712734	+	0.411497i	0.0993388	+	0.995054i	$0.468327\pi$
$432$	4.13779	+	2.38896i	0.199080	+	0.114939i
$433$			1.92881i			0.0926926i	0.998925	+	0.0463463i	$0.0147578\pi$
$433$			1.92881i			0.0926926i	−0.998925	+	0.0463463i	$0.985242\pi$
$434$		0			0
$435$			34.2671i			1.64298i
$436$	5.19615	+	3.00000i	0.248851	+	0.143674i
$437$	−0.424834	−	0.735834i	−0.0203226	−	0.0351997i
$438$	−10.0347	−	17.3805i	−0.479474	−	0.830474i
$439$	−5.21169	+	9.02692i	−0.248741	+	0.430831i	−0.963177	−	0.268869i	$-0.913350\pi$
$439$	−5.21169	+	9.02692i	−0.248741	+	0.430831i	0.714436	+	0.699701i	$0.246683\pi$
$440$	−4.91952	+	6.55672i	−0.234529	+	0.312579i
$441$		0			0
$442$			11.0990i			0.527926i
$443$	−7.96268	+	13.7918i	−0.378318	+	0.655267i	−0.990818	−	0.135204i	$-0.956831\pi$
$443$	−7.96268	+	13.7918i	−0.378318	+	0.655267i	0.612499	+	0.790471i	$0.290164\pi$
$444$	−15.4099	+	8.89692i	−0.731322	+	0.422229i
$445$	15.7362	+	27.2559i	0.745967	+	1.29205i
$446$	−1.45265	+	2.51606i	−0.0687849	+	0.119139i
$447$	−27.2794			−1.29027
$448$		0			0
$449$	10.4404			0.492712			0.246356	−	0.969179i	$-0.420767\pi$
$449$	10.4404			0.492712			0.246356	+	0.969179i	$0.420767\pi$
$450$	−0.397599	−	0.229554i	−0.0187430	−	0.0108213i
$451$	−22.8266	−	2.75463i	−1.07486	−	0.129711i
$452$	−2.88210	−	4.99195i	−0.135563	−	0.234802i
$453$	9.69743	−	16.7964i	0.455625	−	0.789166i
$454$		−	14.4270i		−	0.677092i
$455$		0			0
$456$	1.67588			0.0784801
$457$	−15.6388	−	9.02908i	−0.731554	−	0.422363i	0.0874367	−	0.996170i	$-0.472132\pi$
$457$	−15.6388	−	9.02908i	−0.731554	−	0.422363i	−0.818990	+	0.573807i	$0.805466\pi$
$458$	3.54848	+	6.14615i	0.165810	+	0.287191i
$459$	23.3774	−	13.4970i	1.09117	−	0.629985i
$460$	−2.00515	−	1.15767i	−0.0934904	−	0.0539767i
$461$	11.4500			0.533281			0.266641	−	0.963796i	$-0.414086\pi$
$461$	11.4500			0.533281			0.266641	+	0.963796i	$0.414086\pi$
$462$		0			0
$463$	−26.6805			−1.23995			−0.619975	−	0.784622i	$-0.712857\pi$
$463$	−26.6805			−1.23995			−0.619975	+	0.784622i	$0.712857\pi$
$464$	−6.49829	−	3.75179i	−0.301675	−	0.174172i
$465$	−18.6643	+	10.7759i	−0.865538	+	0.499718i
$466$	2.08058	+	3.60367i	0.0963810	+	0.166937i
$467$	−8.41452	−	4.85813i	−0.389378	−	0.224807i	0.292513	−	0.956262i	$-0.405509\pi$
$467$	−8.41452	−	4.85813i	−0.389378	−	0.224807i	−0.681890	+	0.731454i	$0.738842\pi$
$468$	−0.813729			−0.0376146
$469$		0			0
$470$		−	9.89162i		−	0.456266i
$471$	4.26436	−	7.38609i	0.196491	−	0.340333i
$472$	−0.482818	−	0.836265i	−0.0222235	−	0.0384922i
$473$	−2.70576	+	22.4216i	−0.124411	+	1.03094i
$474$	−13.5782	−	7.83938i	−0.623667	−	0.360075i
$475$	1.00528			0.0461254
$476$		0			0
$477$	−2.72004			−0.124542
$478$	−9.93124	+	17.2014i	−0.454244	+	0.786774i
$479$	9.60418	+	16.6349i	0.438826	+	0.760069i	0.997599	−	0.0692512i	$-0.0220610\pi$
$479$	9.60418	+	16.6349i	0.438826	+	0.760069i	−0.558773	+	0.829321i	$0.688728\pi$
$480$	3.95493	−	2.28338i	0.180517	−	0.104222i
$481$	−9.45910	+	16.3836i	−0.431298	+	0.747029i
$482$			14.4893i			0.659972i
$483$		0			0
$484$	3.07591	+	10.5612i	0.139814	+	0.480054i
$485$	−4.72904	+	8.19093i	−0.214735	+	0.371931i
$486$	2.13759	+	3.70241i	0.0969630	+	0.167945i
$487$	−0.181298	−	0.314017i	−0.00821539	−	0.0142295i	0.861888	−	0.507098i	$-0.169282\pi$
$487$	−0.181298	−	0.314017i	−0.00821539	−	0.0142295i	−0.870104	+	0.492868i	$0.835948\pi$
$488$	−10.3059	−	5.95014i	−0.466528	−	0.269350i
$489$		−	26.9304i		−	1.21784i
$490$		0			0
$491$		−	1.04374i		−	0.0471033i	−0.999723	−	0.0235516i	$-0.992503\pi$
$491$		−	1.04374i		−	0.0471033i	0.999723	−	0.0235516i	$-0.00749741\pi$
$492$	11.0933	+	6.40470i	0.500123	+	0.288746i
$493$	−36.7136	+	21.1966i	−1.65350	+	0.954648i
$494$	1.54306	−	0.890886i	0.0694256	−	0.0400829i
$495$	−3.12267	+	1.33316i	−0.140354	+	0.0599209i
$496$		−	4.71925i		−	0.211901i
$497$		0			0
$498$	−8.93578			−0.400422
$499$	−9.80041	+	16.9748i	−0.438727	+	0.759897i	−0.997592	−	0.0693620i	$-0.977904\pi$
$499$	−9.80041	+	16.9748i	−0.438727	+	0.759897i	0.558865	+	0.829259i	$0.311237\pi$
$500$	−8.32959	+	4.80909i	−0.372511	+	0.215069i
$501$	−11.7942	+	6.80940i	−0.526928	+	0.304222i
$502$	7.30780	−	12.6575i	0.326163	−	0.564931i
$503$	−36.6503			−1.63415			−0.817077	−	0.576529i	$-0.804407\pi$
$503$	−36.6503			−1.63415			−0.817077	+	0.576529i	$0.804407\pi$
$504$		0			0
$505$		−	39.1224i		−	1.74092i
$506$	−2.85753	+	1.21996i	−0.127033	+	0.0542339i
$507$	14.6270	−	8.44489i	0.649607	−	0.375051i
$508$	16.1402	−	9.31855i	0.716106	−	0.413444i
$509$	−32.1251	−	18.5474i	−1.42392	−	0.822101i	−0.427290	−	0.904115i	$-0.640531\pi$
$509$	−32.1251	−	18.5474i	−1.42392	−	0.822101i	−0.996631	+	0.0820139i	$0.973865\pi$
$510$		−	25.8010i		−	1.14249i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−3.75289	−	2.16673i	−0.165694	−	0.0956635i
$514$	−11.5591	−	20.0209i	−0.509849	−	0.883084i
$515$	−0.976522	−	1.69139i	−0.0430307	−	0.0745314i
$516$	6.29107	−	10.8965i	0.276949	−	0.479690i
$517$	−10.6176	−	7.96643i	−0.466963	−	0.350363i
$518$		0			0
$519$			20.6005i			0.904262i
$520$	2.42766	−	4.20484i	0.106460	−	0.184394i
$521$	−16.8745	+	9.74250i	−0.739285	+	0.426827i	−0.821809	−	0.569762i	$-0.807035\pi$
$521$	−16.8745	+	9.74250i	−0.739285	+	0.426827i	0.0825240	+	0.996589i	$0.473702\pi$
$522$	−1.55404	−	2.69168i	−0.0680185	−	0.117812i
$523$	−21.5163	+	37.2674i	−0.940844	+	1.62959i	−0.176977	+	0.984215i	$0.556632\pi$
$523$	−21.5163	+	37.2674i	−0.940844	+	1.62959i	−0.763867	+	0.645374i	$0.776702\pi$
$524$	−19.9835			−0.872982
$525$		0			0
$526$	−8.48528			−0.369976
$527$	−23.0904	−	13.3313i	−1.00584	−	0.580719i
$528$	0.734219	−	6.08418i	0.0319528	−	0.264780i
$529$	11.0612	+	19.1585i	0.480921	+	0.832980i
$530$	8.11493	−	14.0555i	0.352490	−	0.610530i
$531$		−	0.399979i		−	0.0173576i
$532$		0			0
$533$	13.6188			0.589896
$534$	−20.3771	−	11.7647i	−0.881803	−	0.509109i
$535$	20.5280	+	35.5555i	0.887502	+	1.53720i
$536$	−5.81973	+	3.36002i	−0.251374	+	0.145131i
$537$	25.2971	+	14.6053i	1.09165	+	0.630266i
$538$	−30.6005			−1.31928
$539$		0			0
$540$	−11.8087			−0.508164
$541$	−16.9904	−	9.80940i	−0.730474	−	0.421739i	0.0881217	−	0.996110i	$-0.471914\pi$
$541$	−16.9904	−	9.80940i	−0.730474	−	0.421739i	−0.818595	+	0.574370i	$0.805247\pi$
$542$	−11.4329	+	6.60081i	−0.491087	+	0.283529i
$543$	15.3852	+	26.6479i	0.660241	+	1.14357i
$544$	4.89282	+	2.82487i	0.209778	+	0.121115i
$545$	−14.8291			−0.635208
$546$		0			0
$547$		−	42.5800i		−	1.82059i	−0.413959	−	0.910295i	$-0.635854\pi$
$547$		−	42.5800i		−	1.82059i	0.413959	−	0.910295i	$-0.364146\pi$
$548$	8.21968	−	14.2369i	0.351127	−	0.608170i
$549$	−2.46463	−	4.26886i	−0.105188	−	0.182191i
$550$	0.440424	−	3.64962i	0.0187797	−	0.155620i
$551$	5.89380	+	3.40279i	0.251085	+	0.144964i
$552$	1.73100			0.0736764
$553$		0			0
$554$	3.98886			0.169470
$555$	21.9889	−	38.0858i	0.933375	−	1.61665i
$556$	5.35544	+	9.27589i	0.227121	+	0.393385i
$557$	7.67681	−	4.43221i	0.325277	−	0.187799i	−0.328465	−	0.944516i	$-0.606531\pi$
$557$	7.67681	−	4.43221i	0.325277	−	0.187799i	0.653742	+	0.756717i	$0.273198\pi$
$558$	0.977389	−	1.69289i	0.0413762	−	0.0716657i
$559$		−	13.3772i		−	0.565795i
$560$		0			0
$561$	−27.6947	−	20.7794i	−1.16927	−	0.877308i
$562$	2.97147	−	5.14673i	0.125344	−	0.217102i
$563$	8.13368	+	14.0879i	0.342794	+	0.593736i	0.984950	−	0.172837i	$-0.0552935\pi$
$563$	8.13368	+	14.0879i	0.342794	+	0.593736i	−0.642157	+	0.766573i	$0.721960\pi$
$564$	3.69760	+	6.40442i	0.155697	+	0.269675i
$565$	12.3377	+	7.12316i	0.519050	+	0.299674i
$566$			21.2661i			0.893882i
$567$		0			0
$568$			11.5485i			0.484563i
$569$	37.3354	+	21.5556i	1.56518	+	0.903659i	0.996718	+	0.0809508i	$0.0257957\pi$
$569$	37.3354	+	21.5556i	1.56518	+	0.903659i	0.568465	+	0.822708i	$0.307538\pi$
$570$	−3.58704	+	2.07098i	−0.150244	+	0.0867437i
$571$	4.15542	−	2.39913i	0.173899	−	0.100400i	−0.410524	−	0.911850i	$-0.634654\pi$
$571$	4.15542	−	2.39913i	0.173899	−	0.100400i	0.584423	+	0.811449i	$0.301321\pi$
$572$	−2.55828	−	5.99231i	−0.106967	−	0.250551i
$573$		−	48.7011i		−	2.03452i
$574$		0			0
$575$	1.03835			0.0433021
$576$	−0.207107	+	0.358719i	−0.00862945	+	0.0149466i
$577$	1.65586	−	0.956014i	0.0689345	−	0.0397994i	−0.465137	−	0.885239i	$-0.653995\pi$
$577$	1.65586	−	0.956014i	0.0689345	−	0.0397994i	0.534071	+	0.845440i	$0.320661\pi$
$578$	12.9207	−	7.45977i	0.537431	−	0.310286i
$579$	0.641330	−	1.11082i	0.0266528	−	0.0461640i
$580$	18.5452			0.770047
$581$		0			0
$582$		−	7.07107i		−	0.293105i
$583$	−8.55155	−	20.0304i	−0.354169	−	0.829575i
$584$	−9.40628	+	5.43072i	−0.389234	+	0.224725i
$585$	1.74170	−	1.00557i	0.0720105	−	0.0415753i
$586$	−24.0685	−	13.8960i	−0.994262	−	0.574038i
$587$		−	1.71510i		−	0.0707896i	−0.999373	−	0.0353948i	$-0.988731\pi$
$587$		−	1.71510i		−	0.0707896i	0.999373	−	0.0353948i	$-0.0112689\pi$
$588$		0			0
$589$			4.28026i			0.176365i
$590$	2.06684	+	1.19329i	0.0850905	+	0.0491270i
$591$	9.00338	+	15.5943i	0.370349	+	0.641464i
$592$	4.81498	+	8.33978i	0.197894	+	0.342763i
$593$	−7.01955	+	12.1582i	−0.288258	+	0.499278i	−0.973394	−	0.229137i	$-0.926410\pi$
$593$	−7.01955	+	12.1582i	−0.288258	+	0.499278i	0.685136	+	0.728415i	$0.259743\pi$
$594$	−9.51038	+	12.6754i	−0.390215	+	0.520077i
$595$		0			0
$596$			14.7635i			0.604736i
$597$	−6.49912	+	11.2568i	−0.265991	+	0.460710i
$598$	1.59382	−	0.920191i	0.0651760	−	0.0376294i
$599$	−3.03517	−	5.25707i	−0.124014	−	0.214798i	0.797333	−	0.603539i	$-0.206243\pi$
$599$	−3.03517	−	5.25707i	−0.124014	−	0.214798i	−0.921347	+	0.388741i	$0.872910\pi$
$600$	−1.02401	+	1.77364i	−0.0418052	+	0.0724087i
$601$	18.3373			0.747995			0.373998	−	0.927430i	$-0.377987\pi$
$601$	18.3373			0.747995			0.373998	+	0.927430i	$0.377987\pi$
$602$		0			0
$603$	−2.78353			−0.113354
$604$	−9.09017	−	5.24821i	−0.369874	−	0.213547i
$605$	−19.6347	−	18.8040i	−0.798265	−	0.764493i
$606$	14.6244	+	25.3302i	0.594075	+	1.02897i
$607$	−0.106462	+	0.184397i	−0.00432114	+	0.00748444i	−0.868178	−	0.496253i	$-0.834709\pi$
$607$	−0.106462	+	0.184397i	−0.00432114	+	0.00748444i	0.863857	+	0.503738i	$0.168042\pi$
$608$		−	0.906978i		−	0.0367828i
$609$		0			0
$610$	29.4117			1.19085
$611$	6.80911	+	3.93124i	0.275467	+	0.159041i
$612$	1.17010	+	2.02667i	0.0472985	+	0.0819233i
$613$	14.6270	−	8.44493i	0.590781	−	0.341087i	−0.174625	−	0.984635i	$-0.555871\pi$
$613$	14.6270	−	8.44493i	0.590781	−	0.341087i	0.765406	+	0.643548i	$0.222538\pi$
$614$	14.0879	+	8.13368i	0.568543	+	0.328249i
$615$	−31.6586			−1.27660
$616$		0			0
$617$	33.0864			1.33201			0.666004	−	0.745948i	$-0.268003\pi$
$617$	33.0864			1.33201			0.666004	+	0.745948i	$0.268003\pi$
$618$	1.26452	+	0.730069i	0.0508663	+	0.0293677i
$619$	12.3404	−	7.12472i	0.496001	−	0.286366i	−0.231059	−	0.972940i	$-0.574219\pi$
$619$	12.3404	−	7.12472i	0.496001	−	0.286366i	0.727061	+	0.686573i	$0.240886\pi$
$620$	5.83185	+	10.1011i	0.234213	+	0.405668i
$621$	−3.87633	−	2.23800i	−0.155552	−	0.0898079i
$622$	−10.7925			−0.432739
$623$		0			0
$624$			3.62995i			0.145314i
$625$	14.6567	−	25.3862i	0.586268	−	1.01545i
$626$	9.15556	+	15.8579i	0.365930	+	0.633809i
$627$	−0.665921	+	5.51822i	−0.0265943	+	0.220376i
$628$	−3.99732	−	2.30785i	−0.159510	−	0.0920934i
$629$	54.4067			2.16934
$630$		0			0
$631$	−19.3751			−0.771312			−0.385656	−	0.922643i	$-0.626025\pi$
$631$	−19.3751			−0.771312			−0.385656	+	0.922643i	$0.626025\pi$
$632$	−4.24264	+	7.34847i	−0.168763	+	0.292306i
$633$	−22.2796	−	38.5893i	−0.885533	−	1.53379i
$634$	−0.310821	+	0.179452i	−0.0123443	+	0.00712697i
$635$	−23.0309	+	39.8908i	−0.913955	+	1.58302i
$636$			12.1338i			0.481136i
$637$		0			0
$638$	14.9358	−	19.9063i	0.591313	−	0.788100i
$639$	−2.39177	+	4.14266i	−0.0946168	+	0.163881i
$640$	−1.23576	−	2.14039i	−0.0488476	−	0.0846065i
$641$	18.2543	+	31.6174i	0.721003	+	1.24881i	0.960598	+	0.277941i	$0.0896518\pi$
$641$	18.2543	+	31.6174i	0.721003	+	1.24881i	−0.239595	+	0.970873i	$0.577015\pi$
$642$	−26.5821	−	15.3472i	−1.04911	−	0.605705i
$643$			2.49558i			0.0984161i	0.998789	+	0.0492080i	$0.0156697\pi$
$643$			2.49558i			0.0984161i	−0.998789	+	0.0492080i	$0.984330\pi$
$644$		0			0
$645$			31.0969i			1.22444i
$646$	−4.43768	−	2.56209i	−0.174598	−	0.100804i
$647$	3.65045	−	2.10759i	0.143514	−	0.0828577i	−0.426524	−	0.904476i	$-0.640262\pi$
$647$	3.65045	−	2.10759i	0.143514	−	0.0828577i	0.570038	+	0.821619i	$0.306929\pi$
$648$	8.72180	−	5.03553i	0.342625	−	0.197814i
$649$	2.94545	−	1.25750i	0.115619	−	0.0493610i
$650$			2.17744i			0.0854062i
$651$		0			0
$652$	−14.5746			−0.570787
$653$	5.39862	−	9.35068i	0.211264	−	0.365920i	−0.740846	−	0.671675i	$-0.765575\pi$
$653$	5.39862	−	9.35068i	0.211264	−	0.365920i	0.952110	+	0.305754i	$0.0989086\pi$
$654$	9.60124	−	5.54328i	0.375438	−	0.216759i
$655$	42.7725	−	24.6947i	1.67126	−	0.964903i
$656$	3.46620	−	6.00363i	0.135332	−	0.234403i
$657$	−4.49895			−0.175521
$658$		0			0
$659$		−	42.1591i		−	1.64229i	−0.570723	−	0.821143i	$-0.693337\pi$
$659$		−	42.1591i		−	1.64229i	0.570723	−	0.821143i	$-0.306663\pi$
$660$	5.94705	+	13.9299i	0.231489	+	0.542219i
$661$	7.77796	−	4.49061i	0.302528	−	0.174664i	−0.341050	−	0.940045i	$-0.610783\pi$
$661$	7.77796	−	4.49061i	0.302528	−	0.174664i	0.643578	+	0.765381i	$0.277449\pi$
$662$	−25.0398	+	14.4567i	−0.973200	+	0.561877i
$663$	17.7607	+	10.2541i	0.689768	+	0.398238i
$664$			4.83601i			0.187674i
$665$		0			0
$666$			3.98886i			0.154565i
$667$	6.08767	+	3.51472i	0.235716	+	0.136090i
$668$	3.68522	+	6.38299i	0.142586	+	0.246965i
$669$	2.68414	+	4.64907i	0.103775	+	0.179744i
$670$	8.30434	−	14.3835i	0.320825	−	0.555685i
$671$	23.6874	−	31.5704i	0.914441	−	1.21876i
$672$		0			0
$673$			26.4282i			1.01873i	0.860550	+	0.509366i	$0.170120\pi$
$673$			26.4282i			1.01873i	−0.860550	+	0.509366i	$0.829880\pi$
$674$	3.98171	−	6.89652i	0.153370	−	0.265644i
$675$	4.58626	−	2.64788i	0.176525	−	0.101917i
$676$	−4.57034	−	7.91606i	−0.175782	−	0.304464i
$677$	−5.85689	+	10.1444i	−0.225099	+	0.389882i	−0.956349	−	0.292227i	$-0.905604\pi$
$677$	−5.85689	+	10.1444i	−0.225099	+	0.389882i	0.731250	+	0.682109i	$0.238937\pi$
$678$	−10.6509			−0.409044
$679$		0			0
$680$	−13.9634			−0.535472
$681$	−23.0861	−	13.3288i	−0.884663	−	0.510760i
$682$	15.5393	+	1.87523i	0.595029	+	0.0718061i
$683$	−17.9934	−	31.1655i	−0.688498	−	1.19251i	−0.972324	−	0.233638i	$-0.924937\pi$
$683$	−17.9934	−	31.1655i	−0.688498	−	1.19251i	0.283825	−	0.958876i	$-0.408396\pi$
$684$	0.187841	−	0.325351i	0.00718229	−	0.0124401i
$685$			40.6301i			1.55240i
$686$		0			0
$687$	13.1135			0.500310
$688$	−5.89712	−	3.40470i	−0.224825	−	0.129803i
$689$	6.45026	+	11.1722i	0.245735	+	0.425626i
$690$	−3.70503	+	2.13910i	−0.141048	+	0.0814341i
$691$	−5.11870	−	2.95528i	−0.194725	−	0.112424i	0.399468	−	0.916747i	$-0.369195\pi$
$691$	−5.11870	−	2.95528i	−0.194725	−	0.112424i	−0.594192	+	0.804323i	$0.702528\pi$
$692$	11.1489			0.423818
$693$		0			0
$694$	24.6810			0.936877
$695$	−22.9255	−	13.2360i	−0.869613	−	0.502072i
$696$	−12.0073	+	6.93240i	−0.455134	+	0.262772i
$697$	−19.5831	−	33.9190i	−0.741764	−	1.28477i
$698$	9.65525	+	5.57446i	0.365456	+	0.210996i
$699$	7.68882			0.290818
$700$		0			0
$701$			39.6167i			1.49630i	0.663527	+	0.748152i	$0.269059\pi$
$701$			39.6167i			1.49630i	−0.663527	+	0.748152i	$0.730941\pi$
$702$	4.69314	−	8.12876i	0.177131	−	0.306800i
$703$	−4.36708	−	7.56400i	−0.164707	−	0.285282i
$704$	−3.29274	−	0.397356i	−0.124100	−	0.0149759i
$705$	−15.8286	−	9.13866i	−0.596141	−	0.344182i
$706$	21.3852			0.804844
$707$		0			0
$708$	−1.78426			−0.0670567
$709$	10.2012	−	17.6689i	0.383113	−	0.663571i	−0.608392	−	0.793636i	$-0.708185\pi$
$709$	10.2012	−	17.6689i	0.383113	−	0.663571i	0.991505	+	0.130065i	$0.0415186\pi$
$710$	−14.2711	−	24.7183i	−0.535585	−	0.927661i
$711$	−3.04384	+	1.75736i	−0.114153	+	0.0659061i
$712$	−6.36702	+	11.0280i	−0.238614	+	0.413292i
$713$			4.42105i			0.165570i
$714$		0			0
$715$	12.8808	+	9.66448i	0.481714	+	0.361431i
$716$	7.90434	−	13.6907i	0.295399	−	0.511646i
$717$	18.3505	+	31.7841i	0.685313	+	1.18700i
$718$	3.12184	+	5.40718i	0.116506	+	0.201794i
$719$	−24.8714	−	14.3595i	−0.927545	−	0.535518i	−0.0415109	−	0.999138i	$-0.513217\pi$
$719$	−24.8714	−	14.3595i	−0.927545	−	0.535518i	−0.886034	+	0.463620i	$0.846550\pi$
$720$		−	1.02373i		−	0.0381523i
$721$		0			0
$722$		−	18.1774i		−	0.676492i
$723$	23.1859	+	13.3864i	0.862294	+	0.497846i
$724$	14.4217	−	8.32639i	0.535979	−	0.309448i
$725$	−7.20260	+	4.15842i	−0.267498	+	0.154440i
$726$	19.7419	+	4.83518i	0.732689	+	0.179450i
$727$			9.15820i			0.339659i	0.985473	+	0.169829i	$0.0543217\pi$
$727$			9.15820i			0.339659i	−0.985473	+	0.169829i	$0.945678\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	13.4221	−	23.2477i	0.496774	−	0.860438i
$731$	−33.3172	+	19.2357i	−1.23228	+	0.711457i
$732$	−19.0429	+	10.9944i	−0.703846	+	0.406366i
$733$	22.3549	−	38.7197i	0.825695	−	1.43015i	−0.0756916	−	0.997131i	$-0.524116\pi$
$733$	22.3549	−	38.7197i	0.825695	−	1.43015i	0.901387	−	0.433015i	$-0.142550\pi$
$734$	−28.7533			−1.06130
$735$		0			0
$736$		−	0.936812i		−	0.0345313i
$737$	−8.75116	−	20.4980i	−0.322353	−	0.755052i
$738$	2.48679	−	1.43575i	0.0915399	−	0.0528506i
$739$	18.7939	−	10.8507i	0.691345	−	0.399148i	−0.112771	−	0.993621i	$-0.535973\pi$
$739$	18.7939	−	10.8507i	0.691345	−	0.399148i	0.804116	+	0.594473i	$0.202639\pi$
$740$	−20.6119	−	11.9003i	−0.757708	−	0.437463i
$741$		−	3.29229i		−	0.120945i
$742$		0			0
$743$			8.20708i			0.301089i	0.988603	+	0.150544i	$0.0481026\pi$
$743$			8.20708i			0.301089i	−0.988603	+	0.150544i	$0.951897\pi$
$744$	−7.55178	−	4.36002i	−0.276862	−	0.159846i
$745$	−18.2441	−	31.5997i	−0.668411	−	1.15772i
$746$	−6.17945	−	10.7031i	−0.226246	−	0.391869i
$747$	−1.00157	+	1.73477i	−0.0366455	+	0.0634719i
$748$	−11.2457	+	14.9883i	−0.411185	+	0.548026i
$749$		0			0
$750$			17.7721i			0.648945i
$751$	9.71032	−	16.8188i	0.354335	−	0.613725i	−0.632669	−	0.774422i	$-0.718041\pi$
$751$	9.71032	−	16.8188i	0.354335	−	0.613725i	0.987004	+	0.160697i	$0.0513741\pi$
$752$	3.46605	−	2.00112i	0.126394	−	0.0729735i
$753$	−13.5031	−	23.3880i	−0.492079	−	0.852306i
$754$	−7.37045	+	12.7660i	−0.268416	+	0.464910i
$755$	25.9421			0.944128
$756$		0			0
$757$	44.7958			1.62813			0.814065	−	0.580774i	$-0.197250\pi$
$757$	44.7958			1.62813			0.814065	+	0.580774i	$0.197250\pi$
$758$	20.5960	+	11.8911i	0.748080	+	0.431904i
$759$	−0.687825	+	5.69973i	−0.0249665	+	0.206887i
$760$	1.12080	+	1.94129i	0.0406559	+	0.0704180i
$761$	1.91789	−	3.32189i	0.0695235	−	0.120418i	−0.829168	−	0.558999i	$-0.811185\pi$
$761$	1.91789	−	3.32189i	0.0695235	−	0.120418i	0.898692	+	0.438581i	$0.144519\pi$
$762$		−	34.4369i		−	1.24752i
$763$		0			0
$764$	−26.3568			−0.953557
$765$	−5.00895	−	2.89192i	−0.181099	−	0.104557i
$766$	15.9323	+	27.5955i	0.575656	+	0.997065i
$767$	−1.64286	+	0.948503i	−0.0593201	+	0.0342485i
$768$	1.60021	+	0.923880i	0.0577425	+	0.0333376i
$769$	−37.6267			−1.35685			−0.678427	−	0.734667i	$-0.737338\pi$
$769$	−37.6267			−1.35685			−0.678427	+	0.734667i	$0.737338\pi$
$770$		0			0
$771$	−42.7168			−1.53841
$772$	−0.601170	−	0.347086i	−0.0216366	−	0.0124919i
$773$	24.7455	−	14.2868i	0.890034	−	0.513861i	0.0160805	−	0.999871i	$-0.494881\pi$
$773$	24.7455	−	14.2868i	0.890034	−	0.513861i	0.873954	+	0.486009i	$0.161548\pi$
$774$	−1.41027	−	2.44267i	−0.0506912	−	0.0877998i
$775$	−4.52996	−	2.61537i	−0.162721	−	0.0939470i
$776$	−3.82683			−0.137375
$777$		0			0
$778$			21.0155i			0.753441i
$779$	−3.14377	+	5.44517i	−0.112637	+	0.195093i
$780$	−4.48574	−	7.76953i	−0.160615	−	0.278194i
$781$	−38.0261	−	4.58886i	−1.36068	−	0.164202i
$782$	−4.58365	−	2.64637i	−0.163911	−	0.0946340i
$783$	35.8514			1.28122
$784$		0			0
$785$	11.4078			0.407162
$786$	−18.4623	+	31.9777i	−0.658529	+	1.14061i
$787$	11.6333	+	20.1495i	0.414682	+	0.718250i	0.995395	−	0.0958579i	$-0.0305595\pi$
$787$	11.6333	+	20.1495i	0.414682	+	0.718250i	−0.580713	+	0.814108i	$0.697226\pi$
$788$	8.43958	−	4.87259i	0.300648	−	0.173579i
$789$	−7.83938	+	13.5782i	−0.279089	+	0.483397i
$790$		−	20.9715i		−	0.746132i
$791$		0			0
$792$	−1.09887	−	0.824487i	−0.0390468	−	0.0292969i
$793$	−11.6891	+	20.2462i	−0.415094	+	0.718964i
$794$	4.15902	+	7.20364i	0.147598	+	0.255648i
$795$	−14.9944	−	25.9711i	−0.531798	−	0.921100i
$796$	6.09214	+	3.51730i	0.215930	+	0.124667i
$797$		−	26.8026i		−	0.949396i	−0.880149	−	0.474698i	$-0.842557\pi$
$797$		−	26.8026i		−	0.949396i	0.880149	−	0.474698i	$-0.157443\pi$
$798$		0			0
$799$		−	22.6117i		−	0.799943i
$800$	0.959889	+	0.554192i	0.0339372	+	0.0195937i
$801$	−4.56795	+	2.63731i	−0.161401	+	0.0931847i
$802$	−26.5714	+	15.3410i	−0.938268	+	0.541709i
$803$	−14.1443	−	33.1303i	−0.499140	−	1.16914i
$804$			12.4170i			0.437915i
$805$		0			0
$806$	−9.27105			−0.326559
$807$	−28.2712	+	48.9672i	−0.995194	+	1.72373i
$808$	13.7086	−	7.91466i	0.482266	−	0.278437i
$809$	−0.941891	+	0.543801i	−0.0331151	+	0.0191190i	−0.516466	−	0.856308i	$-0.672753\pi$
$809$	−0.941891	+	0.543801i	−0.0331151	+	0.0191190i	0.483351	+	0.875427i	$0.339419\pi$
$810$	−12.4454	+	21.5561i	−0.437287	+	0.757403i
$811$	23.7806			0.835051			0.417525	−	0.908665i	$-0.362897\pi$
$811$	23.7806			0.835051			0.417525	+	0.908665i	$0.362897\pi$
$812$		0			0
$813$			24.3934i			0.855515i
$814$	−29.3740	+	12.5406i	−1.02956	+	0.439547i
$815$	31.1955	−	18.0107i	1.09273	−	0.630888i
$816$	9.04075	−	5.21968i	0.316489	−	0.182725i
$817$	5.34856	+	3.08799i	0.187122	+	0.108035i
$818$			9.57877i			0.334914i
$819$		0			0
$820$			17.1335i			0.598329i
$821$	−37.5764	−	21.6947i	−1.31142	−	0.757151i	−0.329092	−	0.944298i	$-0.606743\pi$
$821$	−37.5764	−	21.6947i	−1.31142	−	0.757151i	−0.982332	+	0.187147i	$0.940076\pi$
$822$	−15.1880	−	26.3064i	−0.529742	−	0.917540i
$823$	−3.40003	−	5.88903i	−0.118518	−	0.205279i	0.800663	−	0.599115i	$-0.204481\pi$
$823$	−3.40003	−	5.88903i	−0.118518	−	0.205279i	−0.919180	+	0.393837i	$0.871148\pi$
$824$	0.395111	−	0.684352i	0.0137643	−	0.0238405i
$825$	−5.43324	−	4.07658i	−0.189161	−	0.141928i
$826$		0			0
$827$			36.3112i			1.26266i	0.775513	+	0.631332i	$0.217491\pi$
$827$			36.3112i			1.26266i	−0.775513	+	0.631332i	$0.782509\pi$
$828$	0.194020	−	0.336053i	0.00674266	−	0.0116786i
$829$	29.6472	−	17.1168i	1.02969	−	0.594493i	0.112795	−	0.993618i	$-0.464020\pi$
$829$	29.6472	−	17.1168i	1.02969	−	0.594493i	0.916896	+	0.399126i	$0.130686\pi$
$830$	−5.97613	−	10.3510i	−0.207435	−	0.359287i
$831$	3.68522	−	6.38299i	0.127839	−	0.221424i
$832$	1.96452			0.0681073
$833$		0			0
$834$	19.7911			0.685310
$835$	−15.7757	−	9.10808i	−0.545939	−	0.315198i
$836$	2.98644	+	0.360394i	0.103288	+	0.0124645i
$837$	11.2741	+	19.5273i	0.389689	+	0.674962i
$838$	5.15371	−	8.92649i	0.178032	−	0.308360i
$839$			17.3286i			0.598250i	0.954214	+	0.299125i	$0.0966947\pi$
$839$			17.3286i			0.598250i	−0.954214	+	0.299125i	$0.903305\pi$
$840$		0			0
$841$	−27.3036			−0.941505
$842$	22.4131	+	12.9402i	0.772408	+	0.445950i
$843$	−5.49055	−	9.50992i	−0.189105	−	0.327539i
$844$	−20.8844	+	12.0576i	−0.718871	+	0.415040i
$845$	19.5647	+	11.2957i	0.673045	+	0.388582i
$846$	1.65779			0.0569958
$847$		0			0
$848$	6.56676			0.225504
$849$	34.0302	+	19.6473i	1.16791	+	0.674295i
$850$	5.42312	−	3.13104i	0.186012	−	0.107394i
$851$	−4.51073	−	7.81281i	−0.154626	−	0.267820i
$852$	18.4799	+	10.6694i	0.633112	+	0.365527i
$853$	−9.22034			−0.315698			−0.157849	−	0.987463i	$-0.550456\pi$
$853$	−9.22034			−0.315698			−0.157849	+	0.987463i	$0.550456\pi$
$854$		0			0
$855$			0.928505i			0.0317542i
$856$	−8.30583	+	14.3861i	−0.283887	+	0.491707i
$857$	−4.43049	−	7.67383i	−0.151343	−	0.262133i	0.780379	−	0.625307i	$-0.215026\pi$
$857$	−4.43049	−	7.67383i	−0.151343	−	0.262133i	−0.931721	+	0.363174i	$0.881693\pi$
$858$	−11.9525	−	1.44238i	−0.408051	−	0.0492422i
$859$	38.3919	+	22.1656i	1.30991	+	0.756279i	0.982081	−	0.188457i	$-0.0603487\pi$
$859$	38.3919	+	22.1656i	1.30991	+	0.756279i	0.327832	+	0.944736i	$0.393682\pi$
$860$	16.8295			0.573883
$861$		0			0
$862$	17.0858			0.581945
$863$	−2.45153	+	4.24618i	−0.0834511	+	0.144541i	−0.904730	−	0.425985i	$-0.859928\pi$
$863$	−2.45153	+	4.24618i	−0.0834511	+	0.144541i	0.821279	+	0.570527i	$0.193261\pi$
$864$	−2.38896	−	4.13779i	−0.0812739	−	0.140771i
$865$	−23.8631	+	13.7774i	−0.811369	+	0.468444i
$866$	0.964404	−	1.67040i	0.0327718	−	0.0567624i
$867$		−	27.5677i		−	0.936249i
$868$		0			0
$869$	−22.5107	−	16.8899i	−0.763624	−	0.572949i
$870$	17.1335	−	29.6761i	0.580881	−	1.00612i
$871$	6.60081	+	11.4329i	0.223660	+	0.387391i
$872$	−3.00000	−	5.19615i	−0.101593	−	0.175964i
$873$	−1.37276	−	0.792563i	−0.0464609	−	0.0268242i
$874$			0.849668i			0.0287404i
$875$		0			0
$876$			20.0693i			0.678079i
$877$	12.7442	+	7.35787i	0.430341	+	0.248458i	0.699492	−	0.714640i	$-0.253410\pi$
$877$	12.7442	+	7.35787i	0.430341	+	0.248458i	−0.269151	+	0.963098i	$0.586743\pi$
$878$	9.02692	−	5.21169i	0.304644	−	0.175886i
$879$	−44.4729	+	25.6764i	−1.50003	+	0.866044i
$880$	7.53879	−	3.21852i	0.254133	−	0.108496i
$881$			33.3550i			1.12376i	0.827219	+	0.561880i	$0.189922\pi$
$881$			33.3550i			1.12376i	−0.827219	+	0.561880i	$0.810078\pi$
$882$		0			0
$883$	45.3385			1.52576			0.762882	−	0.646538i	$-0.223784\pi$
$883$	45.3385			1.52576			0.762882	+	0.646538i	$0.223784\pi$
$884$	5.54950	−	9.61202i	0.186650	−	0.323287i
$885$	3.81902	−	2.20491i	0.128375	−	0.0741174i
$886$	13.7918	−	7.96268i	0.463344	−	0.267512i
$887$	7.97672	−	13.8161i	0.267832	−	0.463899i	−0.700470	−	0.713682i	$-0.747026\pi$
$887$	7.97672	−	13.8161i	0.267832	−	0.463899i	0.968302	+	0.249783i	$0.0803594\pi$
$888$	17.7938			0.597122
$889$		0			0
$890$		−	31.4724i		−	1.05496i
$891$	13.1150	+	30.7195i	0.439370	+	1.02914i
$892$	2.51606	−	1.45265i	0.0842439	−	0.0486383i
$893$	−3.14363	+	1.81498i	−0.105198	+	0.0607359i
$894$	23.6246	+	13.6397i	0.790125	+	0.456179i
$895$			39.0714i			1.30601i
$896$		0			0
$897$		−	3.40058i		−	0.113542i
$898$	−9.04164	−	5.22019i	−0.301723	−	0.174200i
$899$	−17.7056	−	30.6671i	−0.590516	−	1.02280i
$900$	0.229554	+	0.397599i	0.00765180	+	0.0132533i
$901$	18.5502	−	32.1300i	0.617998	−	1.07040i
$902$	18.3911	+	13.7989i	0.612355	+	0.459452i
$903$		0			0
$904$			5.76421i			0.191715i
$905$	−20.5788	+	35.6435i	−0.684062	+	1.18483i
$906$	−16.7964	+	9.69743i	−0.558025	+	0.322176i
$907$	8.09206	+	14.0159i	0.268692	+	0.465389i	0.968524	−	0.248919i	$-0.0800752\pi$
$907$	8.09206	+	14.0159i	0.268692	+	0.465389i	−0.699832	+	0.714307i	$0.746742\pi$
$908$	−7.21349	+	12.4941i	−0.239388	+	0.414632i
$909$	6.55672			0.217473
$910$		0			0
$911$	−39.2957			−1.30193			−0.650963	−	0.759110i	$-0.725635\pi$
$911$	−39.2957			−1.30193			−0.650963	+	0.759110i	$0.725635\pi$
$912$	−1.45135	−	0.837939i	−0.0480591	−	0.0277469i
$913$	−15.9237	−	1.92162i	−0.526998	−	0.0635963i
$914$	9.02908	+	15.6388i	0.298655	+	0.517286i
$915$	27.1729	−	47.0648i	0.898308	−	1.55592i
$916$		−	7.09696i		−	0.234490i
$917$		0			0
$918$	−26.9939			−0.890933
$919$	12.3749	+	7.14467i	0.408211	+	0.235681i	0.690021	−	0.723789i	$-0.257601\pi$
$919$	12.3749	+	7.14467i	0.408211	+	0.235681i	−0.281810	+	0.959470i	$0.590935\pi$
$920$	1.15767	+	2.00515i	0.0381673	+	0.0661077i
$921$	26.0311	−	15.0291i	0.857755	−	0.495225i
$922$	−9.91602	−	5.72502i	−0.326567	−	0.188543i
$923$	22.6872			0.746757
$924$		0			0
$925$	10.6737			0.350949
$926$	23.1060	+	13.3403i	0.759311	+	0.438388i
$927$	0.283468	−	0.163660i	0.00931030	−	0.00537531i
$928$	3.75179	+	6.49829i	0.123158	+	0.213317i
$929$	−18.3698	−	10.6058i	−0.602693	−	0.347965i	0.167407	−	0.985888i	$-0.446461\pi$
$929$	−18.3698	−	10.6058i	−0.602693	−	0.347965i	−0.770100	+	0.637923i	$0.779794\pi$
$930$	21.5517			0.706709
$931$		0			0
$932$		−	4.16116i		−	0.136303i
$933$	−9.97095	+	17.2702i	−0.326434	+	0.565401i
$934$	4.85813	+	8.41452i	0.158963	+	0.275332i
$935$	5.54845	−	45.9778i	0.181454	−	1.50364i
$936$	0.704710	+	0.406865i	0.0230342	+	0.0132988i
$937$	−50.6154			−1.65353			−0.826767	−	0.562544i	$-0.809823\pi$
$937$	−50.6154			−1.65353			−0.826767	+	0.562544i	$0.809823\pi$
$938$		0			0
$939$	33.8345			1.10415
$940$	−4.94581	+	8.56639i	−0.161314	+	0.279405i
$941$	17.2937	+	29.9536i	0.563759	+	0.976459i	0.997164	+	0.0752600i	$0.0239787\pi$
$941$	17.2937	+	29.9536i	0.563759	+	0.976459i	−0.433405	+	0.901199i	$0.642688\pi$
$942$	−7.38609	+	4.26436i	−0.240652	+	0.138940i
$943$	−3.24718	+	5.62427i	−0.105743	+	0.183152i
$944$			0.965635i			0.0314288i
$945$		0			0
$946$	13.5540	−	18.0648i	0.440680	−	0.587336i
$947$	−0.851692	+	1.47517i	−0.0276763	+	0.0479367i	−0.879532	−	0.475840i	$-0.842144\pi$
$947$	−0.851692	+	1.47517i	−0.0276763	+	0.0479367i	0.851856	+	0.523777i	$0.175477\pi$
$948$	7.83938	+	13.5782i	0.254611	+	0.440999i
$949$	10.6687	+	18.4788i	0.346322	+	0.599846i
$950$	−0.870599	−	0.502640i	−0.0282459	−	0.0163078i
$951$			0.663170i			0.0215047i
$952$		0			0
$953$		−	10.2050i		−	0.330573i	−0.986246	−	0.165287i	$-0.947145\pi$
$953$		−	10.2050i		−	0.330573i	0.986246	−	0.165287i	$-0.0528549\pi$
$954$	2.35563	+	1.36002i	0.0762662	+	0.0440323i
$955$	56.4140	−	32.5707i	1.82552	−	1.05396i
$956$	17.2014	−	9.93124i	0.556333	−	0.321199i
$957$	−18.0554	−	42.2914i	−0.583648	−	1.36709i
$958$		−	19.2084i		−	0.620594i
$959$		0			0
$960$	−4.56676			−0.147392
$961$	−4.36433	+	7.55923i	−0.140785	+	0.243846i
$962$	16.3836	−	9.45910i	0.528230	−	0.304974i
$963$	−5.95893	+	3.44039i	−0.192024	+	0.110865i
$964$	7.24467	−	12.5481i	0.233335	−	0.404148i
$965$	1.71565			0.0552289
$966$		0			0
$967$		−	29.7361i		−	0.956249i	−0.878292	−	0.478124i	$-0.841317\pi$
$967$		−	29.7361i		−	0.956249i	0.878292	−	0.478124i	$-0.158683\pi$
$968$	2.61678	−	10.6842i	0.0841065	−	0.343404i
$969$	−8.19976	+	4.73413i	−0.263414	+	0.152082i
$970$	8.19093	−	4.72904i	0.262995	−	0.151840i
$971$	30.8572	+	17.8154i	0.990253	+	0.571723i	0.905350	−	0.424666i	$-0.139608\pi$
$971$	30.8572	+	17.8154i	0.990253	+	0.571723i	0.0849034	+	0.996389i	$0.472942\pi$
$972$		−	4.27518i		−	0.137126i
$973$		0			0
$974$			0.362596i			0.0116183i
$975$	3.48435	+	2.01169i	0.111589	+	0.0644257i
$976$	5.95014	+	10.3059i	0.190459	+	0.329885i
$977$	13.8216	+	23.9397i	0.442193	+	0.765900i	0.997852	−	0.0655101i	$-0.0208675\pi$
$977$	13.8216	+	23.9397i	0.442193	+	0.765900i	−0.555659	+	0.831410i	$0.687534\pi$
$978$	−13.4652	+	23.3224i	−0.430570	+	0.745769i
$979$	−33.7823	−	25.3470i	−1.07969	−	0.810093i
$980$		0			0
$981$		−	2.48528i		−	0.0793489i
$982$	−0.521869	+	0.903904i	−0.0166535	+	0.0288447i
$983$	−37.4804	+	21.6393i	−1.19544	+	0.690187i	−0.959535	−	0.281590i	$-0.909138\pi$
$983$	−37.4804	+	21.6393i	−1.19544	+	0.690187i	−0.235903	+	0.971777i	$0.575805\pi$
$984$	−6.40470	−	11.0933i	−0.204174	−	0.353641i
$985$	−12.0427	+	20.8585i	−0.383712	+	0.664608i
$986$	42.3932			1.35008
$987$		0			0
$988$	−1.78177			−0.0566857
$989$	5.52449	+	3.18956i	0.175669	+	0.101422i
$990$	3.37089	+	0.406788i	0.107134	+	0.0129286i
$991$	1.74836	+	3.02825i	0.0555386	+	0.0961957i	0.892458	−	0.451130i	$-0.148979\pi$
$991$	1.74836	+	3.02825i	0.0555386	+	0.0961957i	−0.836919	+	0.547326i	$0.815646\pi$
$992$	−2.35963	+	4.08699i	−0.0749182	+	0.129762i
$993$			53.4252i			1.69540i
$994$		0			0
$995$	−17.3861			−0.551177
$996$	7.73861	+	4.46789i	0.245207	+	0.141571i
$997$	−8.06522	−	13.9694i	−0.255428	−	0.442414i	0.709584	−	0.704621i	$-0.248883\pi$
$997$	−8.06522	−	13.9694i	−0.255428	−	0.442414i	−0.965012	+	0.262207i	$0.915550\pi$
$998$	16.9748	−	9.80041i	0.537328	−	0.310227i
$999$	−39.8467	−	23.0055i	−1.26069	−	0.727863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.d.901.5		32
7.2	even	3		1078.2.c.c.1077.10	yes	16
7.3	odd	6	inner	1078.2.i.d.1011.9		32
7.4	even	3	inner	1078.2.i.d.1011.10		32
7.5	odd	6		1078.2.c.c.1077.15	yes	16
7.6	odd	2	inner	1078.2.i.d.901.6		32
11.10	odd	2	inner	1078.2.i.d.901.9		32
77.10	even	6	inner	1078.2.i.d.1011.5		32
77.32	odd	6	inner	1078.2.i.d.1011.6		32
77.54	even	6		1078.2.c.c.1077.7	yes	16
77.65	odd	6		1078.2.c.c.1077.2	✓	16
77.76	even	2	inner	1078.2.i.d.901.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.2	✓	16	77.65	odd	6
1078.2.c.c.1077.7	yes	16	77.54	even	6
1078.2.c.c.1077.10	yes	16	7.2	even	3
1078.2.c.c.1077.15	yes	16	7.5	odd	6
1078.2.i.d.901.5		32	1.1	even	1	trivial
1078.2.i.d.901.6		32	7.6	odd	2	inner
1078.2.i.d.901.9		32	11.10	odd	2	inner
1078.2.i.d.901.10		32	77.76	even	2	inner
1078.2.i.d.1011.5		32	77.10	even	6	inner
1078.2.i.d.1011.6		32	77.32	odd	6	inner
1078.2.i.d.1011.9		32	7.3	odd	6	inner
1078.2.i.d.1011.10		32	7.4	even	3	inner

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} +1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.60021 + 0.923880i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.14039 - 1.23576i) q^{5} +1.84776 q^{6} -1.00000i q^{8} +(0.207107 - 0.358719i) q^{9} +(1.23576 + 2.14039i) q^{10} +(3.29274 + 0.397356i) q^{11} +(-1.60021 - 0.923880i) q^{12} -1.96452 q^{13} +4.56676 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82487 + 4.89282i) q^{17} +(-0.358719 + 0.207107i) q^{18} +(0.453489 - 0.785466i) q^{19} -2.47151i q^{20} +(-2.65291 - 1.99049i) q^{22} +(0.468406 - 0.811303i) q^{23} +(0.923880 + 1.60021i) q^{24} +(0.554192 + 0.959889i) q^{25} +(1.70132 + 0.982258i) q^{26} -4.77791i q^{27} +7.50358i q^{29} +(-3.95493 - 2.28338i) q^{30} +(-4.08699 + 2.35963i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.63617 + 2.40624i) q^{33} -5.64974i q^{34} +0.414214 q^{36} +(4.81498 - 8.33978i) q^{37} +(-0.785466 + 0.453489i) q^{38} +(3.14363 - 1.81498i) q^{39} +(-1.23576 + 2.14039i) q^{40} -6.93240 q^{41} +6.80940i q^{43} +(1.30225 + 3.05027i) q^{44} +(-0.886580 + 0.511867i) q^{45} +(-0.811303 + 0.468406i) q^{46} +(-3.46605 - 2.00112i) q^{47} -1.84776i q^{48} -1.10838i q^{50} +(-9.04075 - 5.21968i) q^{51} +(-0.982258 - 1.70132i) q^{52} +(-3.28338 - 5.68698i) q^{53} +(-2.38896 + 4.13779i) q^{54} +(-6.55672 - 4.91952i) q^{55} +1.67588i q^{57} +(3.75179 - 6.49829i) q^{58} +(0.836265 - 0.482818i) q^{59} +(2.28338 + 3.95493i) q^{60} +(5.95014 - 10.3059i) q^{61} +4.71925 q^{62} -1.00000 q^{64} +(4.20484 + 2.42766i) q^{65} +(6.08418 + 0.734219i) q^{66} +(-3.36002 - 5.81973i) q^{67} +(-2.82487 + 4.89282i) q^{68} +1.73100i q^{69} -11.5485 q^{71} +(-0.358719 - 0.207107i) q^{72} +(-5.43072 - 9.40628i) q^{73} +(-8.33978 + 4.81498i) q^{74} +(-1.77364 - 1.02401i) q^{75} +0.906978 q^{76} -3.62995 q^{78} +(-7.34847 - 4.24264i) q^{79} +(2.14039 - 1.23576i) q^{80} +(5.03553 + 8.72180i) q^{81} +(6.00363 + 3.46620i) q^{82} -4.83601 q^{83} -13.9634i q^{85} +(3.40470 - 5.89712i) q^{86} +(-6.93240 - 12.0073i) q^{87} +(0.397356 - 3.29274i) q^{88} +(-11.0280 - 6.36702i) q^{89} +1.02373 q^{90} +0.936812 q^{92} +(4.36002 - 7.55178i) q^{93} +(2.00112 + 3.46605i) q^{94} +(-1.94129 + 1.12080i) q^{95} +(-0.923880 + 1.60021i) q^{96} -3.82683i q^{97} +(0.824487 - 1.09887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^9	\( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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