LMFDB - Embedded newform 1078.2.i.d.901.9

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			901.9
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.d.1011.9

$q$-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} +(-1.30225 + 3.05027i) 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} +(-0.734219 - 6.08418i) 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} +(-3.29274 + 0.397356i) 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} +(2.40624 - 5.63617i) 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} +(-3.05027 - 1.30225i) 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
$11$	−1.30225	+	3.05027i	−0.392642	+	0.919691i
$11$	−1.30225	+	3.05027i	−0.392642	+	0.919691i
$12$	−1.60021	−	0.923880i	−0.461940	−	0.266701i
$13$	1.96452			0.544859			0.272429	−	0.962176i	$-0.412173\pi$
$13$	1.96452			0.544859			0.272429	+	0.962176i	$0.412173\pi$
$14$		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	$-0.926411\pi$
$17$	−2.82487	−	4.89282i	−0.685131	−	1.18668i	0.288264	−	0.957551i	$-0.406922\pi$
$18$	0.358719	−	0.207107i	0.0845510	−	0.0488155i
$19$	−0.453489	+	0.785466i	−0.104038	+	0.180198i	−0.913345	−	0.407188i	$-0.866510\pi$
$19$	−0.453489	+	0.785466i	−0.104038	+	0.180198i	0.809307	+	0.587386i	$0.199843\pi$
$20$		−	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	$-0.754656\pi$
$29$		−	7.50358i		−	1.39338i	0.717373	−	0.696689i	$-0.245344\pi$
$30$	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
$33$	−0.734219	−	6.08418i	−0.127811	−	1.05912i
$34$		−	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	$-0.317921\pi$
$41$	6.93240			1.08266			0.541329	+	0.840811i	$0.317921\pi$
$42$		0			0
$43$		−	6.80940i		−	1.03842i	−0.854645	−	0.519212i	$-0.826225\pi$
$43$		−	6.80940i		−	1.03842i	0.854645	−	0.519212i	$-0.173775\pi$
$44$	−3.29274	+	0.397356i	−0.496399	+	0.0599037i
$45$	−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	$0.442369\pi$
$61$	−5.95014	+	10.3059i	−0.761838	+	1.31954i	−0.941902	+	0.335887i	$0.890964\pi$
$62$	−4.71925			−0.599346
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.20484	−	2.42766i	−0.521546	−	0.301115i
$66$	2.40624	−	5.63617i	0.296188	−	0.693764i
$67$	−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	$0.0525876\pi$
$73$	5.43072	+	9.40628i	0.635617	+	1.10092i	−0.350767	+	0.936463i	$0.614079\pi$
$74$	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	0.852745	−	0.522328i	$-0.174936\pi$
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	−0.0259772	+	0.999663i	$0.508270\pi$
$80$	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	$-0.414493\pi$
$83$	4.83601			0.530821			0.265411	+	0.964135i	$0.414493\pi$
$84$		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
$88$	−3.05027	−	1.30225i	−0.325160	−	0.138820i
$89$	−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	$-0.878022\pi$
$101$	−7.91466	−	13.7086i	−0.787538	−	1.36406i	0.139933	−	0.990161i	$-0.455311\pi$
$102$	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	0.993399	−	0.114708i	$-0.0365933\pi$
$107$	14.3861	+	8.30583i	1.39076	+	0.802955i	0.397359	+	0.917663i	$0.369927\pi$
$108$	4.13779	−	2.38896i	0.398159	−	0.229877i
$109$	−5.19615	+	3.00000i	−0.497701	+	0.287348i	−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−5.19615	+	3.00000i	−0.497701	+	0.287348i	0.230063	+	0.973176i	$0.426107\pi$
$110$	8.13804	−	0.982072i	0.775932	−	0.0936369i
$111$			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
$121$	−7.60831	−	7.94441i	−0.691664	−	0.722219i
$122$	−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	$0.309891\pi$
$127$			18.6371i			1.65378i	−0.562367	+	0.826888i	$0.690109\pi$
$128$	−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	$-0.495516\pi$
$131$	9.99173	−	17.3062i	0.872982	−	1.51205i	0.858897	−	0.512148i	$-0.171150\pi$
$132$	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	$-0.650090\pi$
$139$	−10.7109			−0.908484			−0.454242	+	0.890878i	$0.650090\pi$
$140$		0			0
$141$	7.39519			0.622787
$142$	−10.0013	−	5.77423i	−0.839288	−	0.484563i
$143$	−2.55828	+	5.99231i	−0.213935	+	0.501102i
$144$	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	−0.125503	−	0.992093i	$-0.540055\pi$
$149$	−12.7855	−	7.38174i	−1.04743	−	0.604736i	−0.921930	+	0.387358i	$0.873388\pi$
$150$	−1.02401	−	1.77364i	−0.0836104	−	0.144817i
$151$	9.09017	−	5.24821i	0.739748	−	0.427093i	−0.0822300	−	0.996613i	$-0.526204\pi$
$151$	9.09017	−	5.24821i	0.739748	−	0.427093i	0.821978	+	0.569520i	$0.192871\pi$
$152$	−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
$165$	−5.94705	+	13.9299i	−0.462978	+	1.08444i
$166$	4.18811	+	2.41800i	0.325060	+	0.187674i
$167$	−7.37045			−0.570342			−0.285171	−	0.958477i	$-0.592050\pi$
$167$	−7.37045			−0.570342			−0.285171	+	0.958477i	$0.592050\pi$
$168$		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	−0.996309	−	0.0858362i	$-0.972644\pi$
$173$	−5.57446	+	9.65525i	−0.423818	+	0.734075i	0.572491	+	0.819911i	$0.305977\pi$
$174$			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
$187$	18.6031	−	2.24496i	1.36039	−	0.164168i
$188$		−	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	−0.478207	−	0.878247i	$-0.658713\pi$
$193$	0.601170	−	0.347086i	0.0432731	−	0.0249838i	0.521481	+	0.853263i	$0.325380\pi$
$194$	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	$0.112853\pi$
$197$			9.74519i			0.694316i	−0.937807	+	0.347158i	$0.887147\pi$
$198$	0.164590	+	1.36390i	0.0116969	+	0.0969279i
$199$	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	$-0.688294\pi$
$211$		−	24.1152i		−	1.66016i	0.557643	−	0.830081i	$-0.311706\pi$
$212$	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
$220$	7.53879	+	3.21852i	0.508265	+	0.216993i
$221$	−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	0.520928	−	0.853601i	$-0.325586\pi$
$227$	−7.21349	−	12.4941i	−0.478776	−	0.829265i	−0.999704	+	0.0243362i	$0.992253\pi$
$228$	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	0.613376	−	0.789791i	$-0.289811\pi$
$233$	3.60367	+	2.08058i	0.236084	+	0.136303i	−0.377291	+	0.926095i	$0.623145\pi$
$234$	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	$0.222061\pi$
$239$			19.8625i			1.28480i	−0.766371	+	0.642399i	$0.777939\pi$
$240$	−2.28338	+	3.95493i	−0.147392	+	0.255290i
$241$	7.24467	+	12.5481i	0.466670	+	0.808297i	0.999275	−	0.0380673i	$-0.0121201\pi$
$241$	7.24467	+	12.5481i	0.466670	+	0.808297i	−0.532605	+	0.846364i	$0.678787\pi$
$242$	−2.61678	−	10.6842i	−0.168213	−	0.686807i
$243$	−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	−0.709150	−	0.705058i	$-0.750921\pi$
$263$	−7.34847	+	4.24264i	−0.453126	+	0.261612i	0.256023	+	0.966671i	$0.417588\pi$
$264$	6.08418	−	0.734219i	0.374456	−	0.0451881i
$265$			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	−0.993843	−	0.110794i	$-0.964661\pi$
$271$	−6.60081	+	11.4329i	−0.400971	+	0.694502i	0.592872	+	0.805296i	$0.297994\pi$
$272$	5.64974			0.342566
$273$		0			0
$274$		−	16.4394i		−	0.993138i
$275$	−3.64962	+	0.440424i	−0.220080	+	0.0265586i
$276$	−1.49909	+	0.865501i	−0.0902347	+	0.0520970i
$277$	3.45445	−	1.99443i	0.207558	−	0.119834i	−0.392618	−	0.919702i	$-0.628431\pi$
$277$	3.45445	−	1.99443i	0.207558	−	0.119834i	0.600176	+	0.799868i	$0.295097\pi$
$278$	−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	$-0.943276\pi$
$281$		−	5.94293i		−	0.354526i	0.984164	−	0.177263i	$-0.0567243\pi$
$282$	6.40442	+	3.69760i	0.381378	+	0.220189i
$283$	10.6331	+	18.4170i	0.632070	+	1.09478i	0.987128	+	0.159933i	$0.0511279\pi$
$283$	10.6331	+	18.4170i	0.632070	+	1.09478i	−0.355058	+	0.934844i	$0.615539\pi$
$284$	−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	$-0.801519\pi$
$293$	−27.7920			−1.62362			−0.811812	+	0.583919i	$0.801519\pi$
$294$		0			0
$295$	−2.38658			−0.138952
$296$	8.33978	+	4.81498i	0.484740	+	0.279865i
$297$	14.5739	+	6.22202i	0.845665	+	0.361038i
$298$	−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	$-0.346337\pi$
$307$	16.2674			0.928427			0.464214	+	0.885723i	$0.346337\pi$
$308$		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
$319$	22.8879	+	9.77151i	1.28148	+	0.547099i
$320$	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	$-0.930406\pi$
$337$		−	7.96341i		−	0.433795i	0.976194	−	0.216897i	$-0.0695937\pi$
$338$	−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
$341$	−1.87523	−	15.5393i	−0.101549	−	0.841498i
$342$			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	0.199174	−	0.979964i	$-0.436174\pi$
$347$	21.3743	−	12.3405i	1.14743	−	0.662472i	0.948261	+	0.317492i	$0.102841\pi$
$348$	−6.93240	+	12.0073i	−0.371616	+	0.643657i
$349$	11.1489			0.596788			0.298394	−	0.954443i	$-0.403549\pi$
$349$	11.1489			0.596788			0.298394	+	0.954443i	$0.403549\pi$
$350$		0			0
$351$		−	9.38628i		−	0.501003i
$352$	−0.397356	−	3.29274i	−0.0211792	−	0.175503i
$353$	−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	0.635856	−	0.771807i	$-0.280647\pi$
$359$	5.40718	+	3.12184i	0.285380	+	0.164764i	−0.350477	+	0.936572i	$0.613980\pi$
$360$	−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	0.196622	−	0.980479i	$-0.437003\pi$
$373$	−10.7031	−	6.17945i	−0.554187	−	0.319960i	−0.750809	+	0.660519i	$0.770336\pi$
$374$	17.2332	+	7.35736i	0.891109	+	0.380440i
$375$	−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
$396$	−0.539408	+	1.26346i	−0.0271063	+	0.0634914i
$397$	−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	0.959800	−	0.280685i	$-0.0905615\pi$
$409$	4.78939	+	8.29546i	0.236820	+	0.410184i	−0.722980	+	0.690869i	$0.757228\pi$
$410$	−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
$418$	−0.360394	−	2.98644i	−0.0176274	−	0.146072i
$419$			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
$429$	−1.44238	−	11.9525i	−0.0696390	−	0.577071i
$430$	−14.5748	+	8.41477i	−0.702860	+	0.405796i
$431$	14.7967	−	8.54290i	0.712734	−	0.411497i	−0.0993388	−	0.995054i	$-0.531673\pi$
$431$	14.7967	−	8.54290i	0.712734	−	0.411497i	0.812072	+	0.583557i	$0.198339\pi$
$432$	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	−0.714436	−	0.699701i	$-0.753317\pi$
$439$	5.21169	−	9.02692i	0.248741	−	0.430831i	0.963177	+	0.268869i	$0.0866500\pi$
$440$	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
$451$	−9.02770	+	21.1457i	−0.425098	+	0.995712i
$452$	−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	0.818990	−	0.573807i	$-0.194534\pi$
$457$	15.6388	+	9.02908i	0.731554	+	0.422363i	−0.0874367	+	0.996170i	$0.527868\pi$
$458$	−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	$-0.585914\pi$
$461$	−11.4500			−0.533281			−0.266641	+	0.963796i	$0.585914\pi$
$462$		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
$473$	20.7705	+	8.86753i	0.955030	+	0.407729i
$474$	−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	0.558773	−	0.829321i	$-0.311272\pi$
$479$	−9.60418	−	16.6349i	−0.438826	−	0.760069i	−0.997599	+	0.0692512i	$0.977939\pi$
$480$	−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	$0.00749741\pi$
$491$			1.04374i			0.0471033i	−0.999723	+	0.0235516i	$0.992503\pi$
$492$	−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
$495$	−0.406788	−	3.37089i	−0.0182837	−	0.151510i
$496$		−	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	$-0.195593\pi$
$503$	36.6503			1.63415			0.817077	+	0.576529i	$0.195593\pi$
$504$		0			0
$505$			39.1224i			1.74092i
$506$	0.372248	+	3.08467i	0.0165484	+	0.137130i
$507$	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	$-0.443368\pi$
$523$	21.5163	−	37.2674i	0.940844	−	1.62959i	0.763867	−	0.645374i	$-0.223298\pi$
$524$	19.9835			0.872982
$525$		0			0
$526$	−8.48528			−0.369976
$527$	23.0904	+	13.3313i	1.00584	+	0.580719i
$528$	5.63617	+	2.40624i	0.245283	+	0.104718i
$529$	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	0.818595	−	0.574370i	$-0.194753\pi$
$541$	16.9904	+	9.80940i	0.730474	+	0.421739i	−0.0881217	+	0.996110i	$0.528086\pi$
$542$	−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	$0.364146\pi$
$547$			42.5800i			1.82059i	−0.413959	+	0.910295i	$0.635854\pi$
$548$	8.21968	−	14.2369i	0.351127	−	0.608170i
$549$	2.46463	+	4.26886i	0.105188	+	0.182191i
$550$	−3.38087	−	1.44339i	−0.144161	−	0.0615464i
$551$	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	−0.653742	−	0.756717i	$-0.726802\pi$
$557$	−7.67681	+	4.43221i	−0.325277	+	0.187799i	0.328465	+	0.944516i	$0.393469\pi$
$558$	−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	0.642157	−	0.766573i	$-0.278040\pi$
$563$	−8.13368	−	14.0879i	−0.342794	−	0.593736i	−0.984950	+	0.172837i	$0.944707\pi$
$564$	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	$-0.974204\pi$
$569$	−37.3354	−	21.5556i	−1.56518	−	0.903659i	−0.568465	−	0.822708i	$-0.692462\pi$
$570$	−3.58704	+	2.07098i	−0.150244	+	0.0867437i
$571$	−4.15542	+	2.39913i	−0.173899	+	0.100400i	−0.584423	−	0.811449i	$-0.698679\pi$
$571$	−4.15542	+	2.39913i	−0.173899	+	0.100400i	0.410524	+	0.911850i	$0.365346\pi$
$572$	−6.46863	+	0.780613i	−0.270467	+	0.0326391i
$573$		−	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
$583$	21.6226	−	2.60935i	0.895517	−	0.108068i
$584$	−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	−0.685136	−	0.728415i	$-0.740257\pi$
$593$	7.01955	−	12.1582i	0.288258	−	0.499278i	0.973394	+	0.229137i	$0.0735905\pi$
$594$	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	$-0.622013\pi$
$601$	−18.3373			−0.747995			−0.373998	+	0.927430i	$0.622013\pi$
$602$		0			0
$603$	−2.78353			−0.113354
$604$	9.09017	+	5.24821i	0.369874	+	0.213547i
$605$	6.46741	+	26.4062i	0.262938	+	1.07356i
$606$	14.6244	+	25.3302i	0.594075	+	1.02897i
$607$	0.106462	−	0.184397i	0.00432114	−	0.00748444i	−0.863857	−	0.503738i	$-0.831958\pi$
$607$	0.106462	−	0.184397i	0.00432114	−	0.00748444i	0.868178	+	0.496253i	$0.165291\pi$
$608$		−	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	−0.765406	−	0.643548i	$-0.777462\pi$
$613$	−14.6270	+	8.44493i	−0.590781	+	0.341087i	0.174625	+	0.984635i	$0.444129\pi$
$614$	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
$627$	5.11188	+	2.18241i	0.204149	+	0.0871569i
$628$	−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
$649$	0.383701	+	3.17958i	0.0150616	+	0.124810i
$650$			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	$0.306663\pi$
$659$			42.1591i			1.64229i	−0.570723	+	0.821143i	$0.693337\pi$
$660$	−15.0371	+	1.81463i	−0.585320	+	0.0706345i
$661$	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	$-0.829880\pi$
$673$		−	26.4282i		−	1.01873i	0.860550	−	0.509366i	$-0.170120\pi$
$674$	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	−0.731250	−	0.682109i	$-0.761063\pi$
$677$	5.85689	−	10.1444i	0.225099	−	0.389882i	0.956349	+	0.292227i	$0.0943962\pi$
$678$	10.6509			0.409044
$679$		0			0
$680$	−13.9634			−0.535472
$681$	23.0861	+	13.3288i	0.884663	+	0.510760i
$682$	6.14563	−	14.3950i	0.235328	−	0.551213i
$683$	−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	$-0.730941\pi$
$701$		−	39.6167i		−	1.49630i	0.663527	−	0.748152i	$-0.269059\pi$
$702$	4.69314	−	8.12876i	0.177131	−	0.306800i
$703$	4.36708	+	7.56400i	0.164707	+	0.285282i
$704$	1.30225	−	3.05027i	0.0490803	−	0.114961i
$705$	−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
$726$	14.0583	+	14.6794i	0.521753	+	0.544802i
$727$			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	$0.475884\pi$
$733$	−22.3549	+	38.7197i	−0.825695	+	1.43015i	−0.901387	+	0.433015i	$0.857450\pi$
$734$	28.7533			1.06130
$735$		0			0
$736$			0.936812i			0.0345313i
$737$	22.1273	−	2.67025i	0.815070	−	0.0983600i
$738$	2.48679	−	1.43575i	0.0915399	−	0.0528506i
$739$	−18.7939	+	10.8507i	−0.691345	+	0.399148i	−0.804116	−	0.594473i	$-0.797361\pi$
$739$	−18.7939	+	10.8507i	−0.691345	+	0.399148i	0.112771	+	0.993621i	$0.464027\pi$
$740$	−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	$-0.951897\pi$
$743$		−	8.20708i		−	0.301089i	0.988603	−	0.150544i	$-0.0481026\pi$
$744$	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
$759$	−5.28003	−	2.25419i	−0.191653	−	0.0818220i
$760$	1.12080	+	1.94129i	0.0406559	+	0.0704180i
$761$	−1.91789	+	3.32189i	−0.0695235	+	0.120418i	−0.898692	−	0.438581i	$-0.855481\pi$
$761$	−1.91789	+	3.32189i	−0.0695235	+	0.120418i	0.829168	+	0.558999i	$0.188815\pi$
$762$		−	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	$-0.262662\pi$
$769$	37.6267			1.35685			0.678427	+	0.734667i	$0.262662\pi$
$770$		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
$781$	15.0390	−	35.2260i	0.538136	−	1.26048i
$782$	−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	0.580713	−	0.814108i	$-0.302774\pi$
$787$	−11.6333	−	20.1495i	−0.414682	−	0.718250i	−0.995395	+	0.0958579i	$0.969441\pi$
$788$	−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
$803$	−35.7638	+	4.31586i	−1.26208	+	0.152303i
$804$			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	−0.483351	−	0.875427i	$-0.660581\pi$
$809$	0.941891	−	0.543801i	0.0331151	−	0.0191190i	0.516466	+	0.856308i	$0.327247\pi$
$810$	12.4454	−	21.5561i	0.437287	−	0.757403i
$811$	−23.7806			−0.835051			−0.417525	−	0.908665i	$-0.637103\pi$
$811$	−23.7806			−0.835051			−0.417525	+	0.908665i	$0.637103\pi$
$812$		0			0
$813$		−	24.3934i		−	0.855515i
$814$	3.82652	+	31.7089i	0.134120	+	1.11140i
$815$	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	0.982332	−	0.187147i	$-0.0599241\pi$
$821$	37.5764	+	21.6947i	1.31142	+	0.757151i	0.329092	+	0.944298i	$0.393257\pi$
$822$	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	$-0.782509\pi$
$827$		−	36.3112i		−	1.26266i	0.775513	−	0.631332i	$-0.217491\pi$
$828$	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
$836$	1.18111	−	2.76653i	0.0408495	−	0.0956824i
$837$	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	$-0.449544\pi$
$853$	9.22034			0.315698			0.157849	+	0.987463i	$0.449544\pi$
$854$		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	0.931721	−	0.363174i	$-0.118307\pi$
$857$	4.43049	+	7.67383i	0.151343	+	0.262133i	−0.780379	+	0.625307i	$0.784974\pi$
$858$	4.72709	−	11.0723i	0.161380	−	0.378003i
$859$	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	0.269151	−	0.963098i	$-0.413257\pi$
$877$	−12.7442	−	7.35787i	−0.430341	−	0.248458i	−0.699492	+	0.714640i	$0.746590\pi$
$878$	9.02692	−	5.21169i	0.304644	−	0.175886i
$879$	44.4729	−	25.6764i	1.50003	−	0.866044i
$880$	0.982072	+	8.13804i	0.0331056	+	0.274333i
$881$			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	−0.968302	−	0.249783i	$-0.919641\pi$
$887$	−7.97672	+	13.8161i	−0.267832	+	0.463899i	0.700470	+	0.713682i	$0.252974\pi$
$888$	−17.7938			−0.597122
$889$		0			0
$890$			31.4724i			1.05496i
$891$	−33.1614	+	4.00180i	−1.11095	+	0.134065i
$892$	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
$913$	−6.29768	+	14.7511i	−0.208423	+	0.488191i
$914$	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	0.281810	−	0.959470i	$-0.409065\pi$
$919$	−12.3749	−	7.14467i	−0.408211	−	0.235681i	−0.690021	+	0.723789i	$0.742399\pi$
$920$	−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
$935$	−42.5922	−	18.1838i	−1.39291	−	0.594674i
$936$	0.704710	+	0.406865i	0.0230342	+	0.0132988i
$937$	50.6154			1.65353			0.826767	−	0.562544i	$-0.190177\pi$
$937$	50.6154			1.65353			0.826767	+	0.562544i	$0.190177\pi$
$938$		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	$-0.976021\pi$
$941$	−17.2937	−	29.9536i	−0.563759	−	0.976459i	0.433405	−	0.901199i	$-0.357312\pi$
$942$	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	$0.0528549\pi$
$953$			10.2050i			0.330573i	−0.986246	+	0.165287i	$0.947145\pi$
$954$	−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
$957$	−45.6531	+	5.50927i	−1.47576	+	0.178089i
$958$		−	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	$0.158683\pi$
$967$			29.7361i			0.956249i	−0.878292	+	0.478124i	$0.841317\pi$
$968$	7.94441	−	7.60831i	0.255343	−	0.244540i
$969$	−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
$990$	1.33316	−	3.12267i	0.0423705	−	0.0992449i
$991$	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	0.965012	−	0.262207i	$-0.0844503\pi$
$997$	8.06522	+	13.9694i	0.255428	+	0.442414i	−0.709584	+	0.704621i	$0.751117\pi$
$998$	−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.901.9		32
7.2	even	3		1078.2.c.c.1077.2	✓	16
7.3	odd	6	inner	1078.2.i.d.1011.5		32
7.4	even	3	inner	1078.2.i.d.1011.6		32
7.5	odd	6		1078.2.c.c.1077.7	yes	16
7.6	odd	2	inner	1078.2.i.d.901.10		32
11.10	odd	2	inner	1078.2.i.d.901.5		32
77.10	even	6	inner	1078.2.i.d.1011.9		32
77.32	odd	6	inner	1078.2.i.d.1011.10		32
77.54	even	6		1078.2.c.c.1077.15	yes	16
77.65	odd	6		1078.2.c.c.1077.10	yes	16
77.76	even	2	inner	1078.2.i.d.901.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.2	✓	16	7.2	even	3
1078.2.c.c.1077.7	yes	16	7.5	odd	6
1078.2.c.c.1077.10	yes	16	77.65	odd	6
1078.2.c.c.1077.15	yes	16	77.54	even	6
1078.2.i.d.901.5		32	11.10	odd	2	inner
1078.2.i.d.901.6		32	77.76	even	2	inner
1078.2.i.d.901.9		32	1.1	even	1	trivial
1078.2.i.d.901.10		32	7.6	odd	2	inner
1078.2.i.d.1011.5		32	7.3	odd	6	inner
1078.2.i.d.1011.6		32	7.4	even	3	inner
1078.2.i.d.1011.9		32	77.10	even	6	inner
1078.2.i.d.1011.10		32	77.32	odd	6	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} +(-1.30225 + 3.05027i) 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} +(-0.734219 - 6.08418i) 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} +(-3.29274 + 0.397356i) 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} +(2.40624 - 5.63617i) 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} +(-3.05027 - 1.30225i) 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

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Database

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