LMFDB - Embedded newform 756.2.bj.b.451.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(451,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 1]))

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

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

chi := DirichletCharacter("756.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.13
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.771545 - 1.18521i) q^{2} +(-0.809438 + 1.82888i) q^{4} +(0.917924 + 0.529964i) q^{5} +(-2.44585 + 1.00887i) q^{7} +(2.79212 - 0.451713i) q^{8} +O(q^{10})$	\(q+(-0.771545 - 1.18521i) q^{2} +(-0.809438 + 1.82888i) q^{4} +(0.917924 + 0.529964i) q^{5} +(-2.44585 + 1.00887i) q^{7} +(2.79212 - 0.451713i) q^{8} +(-0.0801021 - 1.49682i) q^{10} +(-2.33794 + 1.34981i) q^{11} +(2.33504 - 1.34814i) q^{13} +(3.08280 + 2.12046i) q^{14} +(-2.68962 - 2.96073i) q^{16} +(-7.01250 - 4.04867i) q^{17} +(3.48409 + 6.03463i) q^{19} +(-1.71224 + 1.24980i) q^{20} +(3.40363 + 1.72951i) q^{22} +(-2.82716 - 1.63226i) q^{23} +(-1.93828 - 3.35719i) q^{25} +(-3.39941 - 1.72736i) q^{26} +(0.134667 - 5.28979i) q^{28} +(-0.511543 + 0.886019i) q^{29} -8.50952 q^{31} +(-1.43392 + 5.47210i) q^{32} +(0.611942 + 11.4350i) q^{34} +(-2.77977 - 0.370150i) q^{35} +(0.487561 + 0.844481i) q^{37} +(4.46416 - 8.78536i) q^{38} +(2.80235 + 1.06509i) q^{40} +(-3.77646 + 2.18034i) q^{41} +(-5.77718 - 3.33546i) q^{43} +(-0.576227 - 5.36840i) q^{44} +(0.246710 + 4.61014i) q^{46} -4.75272 q^{47} +(4.96438 - 4.93507i) q^{49} +(-2.48351 + 4.88749i) q^{50} +(0.575514 + 5.36175i) q^{52} +(-1.93958 + 3.35945i) q^{53} -2.86140 q^{55} +(-6.37340 + 3.92170i) q^{56} +(1.44480 - 0.0773179i) q^{58} -2.39121 q^{59} +3.70331i q^{61} +(6.56548 + 10.0856i) q^{62} +(7.59191 - 2.52247i) q^{64} +2.85786 q^{65} +1.95585i q^{67} +(13.0807 - 9.54790i) q^{68} +(1.70601 + 3.58019i) q^{70} +12.7952i q^{71} +(2.43771 + 1.40741i) q^{73} +(0.624710 - 1.22942i) q^{74} +(-13.8568 + 1.48734i) q^{76} +(4.35647 - 5.66010i) q^{77} -7.59123i q^{79} +(-0.899789 - 4.14313i) q^{80} +(5.49786 + 2.79366i) q^{82} +(-1.06909 + 1.85171i) q^{83} +(-4.29130 - 7.43275i) q^{85} +(0.504142 + 9.42062i) q^{86} +(-5.91809 + 4.82491i) q^{88} +(-3.80947 + 2.19940i) q^{89} +(-4.35108 + 5.65309i) q^{91} +(5.27362 - 3.84933i) q^{92} +(3.66694 + 5.63296i) q^{94} +7.38578i q^{95} +(4.91146 + 2.83563i) q^{97} +(-9.67933 - 2.07620i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.771545	−	1.18521i	−0.545565	−	0.838069i
$2$	−0.771545	−	1.18521i	−0.545565	−	0.838069i
$3$		0			0
$3$		0			0
$4$	−0.809438	+	1.82888i	−0.404719	+	0.914441i
$5$	0.917924	+	0.529964i	0.410508	+	0.237007i	0.691008	−	0.722847i	$-0.257167\pi$
$5$	0.917924	+	0.529964i	0.410508	+	0.237007i	−0.280500	+	0.959854i	$0.590500\pi$
$6$		0			0
$7$	−2.44585	+	1.00887i	−0.924445	+	0.381315i
$7$	−2.44585	+	1.00887i	−0.924445	+	0.381315i
$8$	2.79212	−	0.451713i	0.987165	−	0.159704i
$9$		0			0
$10$	−0.0801021	−	1.49682i	−0.0253305	−	0.473337i
$11$	−2.33794	+	1.34981i	−0.704915	+	0.406983i	−0.809175	−	0.587567i	$-0.800086\pi$
$11$	−2.33794	+	1.34981i	−0.704915	+	0.406983i	0.104261	+	0.994550i	$0.466752\pi$
$12$		0			0
$13$	2.33504	−	1.34814i	0.647624	−	0.373906i	−0.139921	−	0.990163i	$-0.544685\pi$
$13$	2.33504	−	1.34814i	0.647624	−	0.373906i	0.787545	+	0.616257i	$0.211352\pi$
$14$	3.08280	+	2.12046i	0.823913	+	0.566716i
$15$		0			0
$16$	−2.68962	−	2.96073i	−0.672405	−	0.740183i
$17$	−7.01250	−	4.04867i	−1.70078	−	0.981947i	−0.944970	−	0.327158i	$-0.893909\pi$
$17$	−7.01250	−	4.04867i	−1.70078	−	0.981947i	−0.755812	−	0.654789i	$-0.772757\pi$
$18$		0			0
$19$	3.48409	+	6.03463i	0.799306	+	1.38444i	0.920069	+	0.391757i	$0.128133\pi$
$19$	3.48409	+	6.03463i	0.799306	+	1.38444i	−0.120763	+	0.992681i	$0.538534\pi$
$20$	−1.71224	+	1.24980i	−0.382869	+	0.279465i
$21$		0			0
$22$	3.40363	+	1.72951i	0.725656	+	0.368732i
$23$	−2.82716	−	1.63226i	−0.589503	−	0.340350i	0.175398	−	0.984498i	$-0.443879\pi$
$23$	−2.82716	−	1.63226i	−0.589503	−	0.340350i	−0.764901	+	0.644148i	$0.777212\pi$
$24$		0			0
$25$	−1.93828	−	3.35719i	−0.387655	−	0.671439i
$26$	−3.39941	−	1.72736i	−0.666680	−	0.338764i
$27$		0			0
$28$	0.134667	−	5.28979i	0.0254497	−	0.999676i
$29$	−0.511543	+	0.886019i	−0.0949912	+	0.164530i	−0.909605	−	0.415474i	$-0.863616\pi$
$29$	−0.511543	+	0.886019i	−0.0949912	+	0.164530i	0.814614	+	0.580004i	$0.196949\pi$
$30$		0			0
$31$	−8.50952			−1.52836			−0.764178	−	0.645006i	$-0.776855\pi$
$31$	−8.50952			−1.52836			−0.764178	+	0.645006i	$0.776855\pi$
$32$	−1.43392	+	5.47210i	−0.253484	+	0.967340i
$33$		0			0
$34$	0.611942	+	11.4350i	0.104947	+	1.96109i
$35$	−2.77977	−	0.370150i	−0.469867	−	0.0625669i
$36$		0			0
$37$	0.487561	+	0.844481i	0.0801546	+	0.138832i	0.903316	−	0.428975i	$-0.141125\pi$
$37$	0.487561	+	0.844481i	0.0801546	+	0.138832i	−0.823162	+	0.567807i	$0.807792\pi$
$38$	4.46416	−	8.78536i	0.724182	−	1.42517i
$39$		0			0
$40$	2.80235	+	1.06509i	0.443090	+	0.168405i
$41$	−3.77646	+	2.18034i	−0.589784	+	0.340512i	−0.765012	−	0.644016i	$-0.777267\pi$
$41$	−3.77646	+	2.18034i	−0.589784	+	0.340512i	0.175228	+	0.984528i	$0.443934\pi$
$42$		0			0
$43$	−5.77718	−	3.33546i	−0.881012	−	0.508652i	−0.0100199	−	0.999950i	$-0.503189\pi$
$43$	−5.77718	−	3.33546i	−0.881012	−	0.508652i	−0.870992	+	0.491297i	$0.836523\pi$
$44$	−0.576227	−	5.36840i	−0.0868696	−	0.809317i
$45$		0			0
$46$	0.246710	+	4.61014i	0.0363754	+	0.679727i
$47$	−4.75272			−0.693255			−0.346628	−	0.938003i	$-0.612673\pi$
$47$	−4.75272			−0.693255			−0.346628	+	0.938003i	$0.612673\pi$
$48$		0			0
$49$	4.96438	−	4.93507i	0.709197	−	0.705010i
$50$	−2.48351	+	4.88749i	−0.351221	+	0.691195i
$51$		0			0
$52$	0.575514	+	5.36175i	0.0798094	+	0.743541i
$53$	−1.93958	+	3.35945i	−0.266422	+	0.461456i	−0.967935	−	0.251200i	$-0.919175\pi$
$53$	−1.93958	+	3.35945i	−0.266422	+	0.461456i	0.701513	+	0.712656i	$0.252508\pi$
$54$		0			0
$55$	−2.86140			−0.385831
$56$	−6.37340	+	3.92170i	−0.851682	+	0.524059i
$57$		0			0
$58$	1.44480	−	0.0773179i	0.189711	−	0.0101523i
$59$	−2.39121			−0.311308			−0.155654	−	0.987812i	$-0.549749\pi$
$59$	−2.39121			−0.311308			−0.155654	+	0.987812i	$0.549749\pi$
$60$		0			0
$61$			3.70331i			0.474160i	0.971490	+	0.237080i	$0.0761904\pi$
$61$			3.70331i			0.474160i	−0.971490	+	0.237080i	$0.923810\pi$
$62$	6.56548	+	10.0856i	0.833817	+	1.28087i
$63$		0			0
$64$	7.59191	−	2.52247i	0.948989	−	0.315309i
$65$	2.85786			0.354474
$66$		0			0
$67$			1.95585i			0.238945i	0.992838	+	0.119472i	$0.0381203\pi$
$67$			1.95585i			0.238945i	−0.992838	+	0.119472i	$0.961880\pi$
$68$	13.0807	−	9.54790i	1.58627	−	1.15785i
$69$		0			0
$70$	1.70601	+	3.58019i	0.203907	+	0.427915i
$71$			12.7952i			1.51851i	0.650793	+	0.759255i	$0.274436\pi$
$71$			12.7952i			1.51851i	−0.650793	+	0.759255i	$0.725564\pi$
$72$		0			0
$73$	2.43771	+	1.40741i	0.285312	+	0.164725i	0.635826	−	0.771833i	$-0.280660\pi$
$73$	2.43771	+	1.40741i	0.285312	+	0.164725i	−0.350514	+	0.936558i	$0.613993\pi$
$74$	0.624710	−	1.22942i	0.0726211	−	0.142917i
$75$		0			0
$76$	−13.8568	+	1.48734i	−1.58948	+	0.170610i
$77$	4.35647	−	5.66010i	0.496466	−	0.645028i
$78$		0			0
$79$		−	7.59123i		−	0.854080i	−0.904233	−	0.427040i	$-0.859556\pi$
$79$		−	7.59123i		−	0.854080i	0.904233	−	0.427040i	$-0.140444\pi$
$80$	−0.899789	−	4.14313i	−0.100599	−	0.463216i
$81$		0			0
$82$	5.49786	+	2.79366i	0.607137	+	0.308508i
$83$	−1.06909	+	1.85171i	−0.117348	+	0.203252i	−0.918716	−	0.394919i	$-0.870772\pi$
$83$	−1.06909	+	1.85171i	−0.117348	+	0.203252i	0.801368	+	0.598171i	$0.204106\pi$
$84$		0			0
$85$	−4.29130	−	7.43275i	−0.465457	−	0.806195i
$86$	0.504142	+	9.42062i	0.0543630	+	1.01585i
$87$		0			0
$88$	−5.91809	+	4.82491i	−0.630870	+	0.514337i
$89$	−3.80947	+	2.19940i	−0.403803	+	0.233136i	−0.688124	−	0.725593i	$-0.741565\pi$
$89$	−3.80947	+	2.19940i	−0.403803	+	0.233136i	0.284321	+	0.958729i	$0.408232\pi$
$90$		0			0
$91$	−4.35108	+	5.65309i	−0.456117	+	0.592605i
$92$	5.27362	−	3.84933i	0.549813	−	0.401320i
$93$		0			0
$94$	3.66694	+	5.63296i	0.378215	+	0.580996i
$95$			7.38578i			0.757765i
$96$		0			0
$97$	4.91146	+	2.83563i	0.498683	+	0.287915i	0.728170	−	0.685397i	$-0.240371\pi$
$97$	4.91146	+	2.83563i	0.498683	+	0.287915i	−0.229486	+	0.973312i	$0.573705\pi$
$98$	−9.67933	−	2.07620i	−0.977760	−	0.209727i
$99$		0			0
$100$	7.70883	−	0.827442i	0.770883	−	0.0827442i
$101$	7.30585	−	4.21803i	0.726959	−	0.419710i	−0.0903498	−	0.995910i	$-0.528799\pi$
$101$	7.30585	−	4.21803i	0.726959	−	0.419710i	0.817309	+	0.576200i	$0.195465\pi$
$102$		0			0
$103$	3.93260	−	6.81146i	0.387490	−	0.671153i	−0.604621	−	0.796513i	$-0.706675\pi$
$103$	3.93260	−	6.81146i	0.387490	−	0.671153i	0.992111	+	0.125360i	$0.0400087\pi$
$104$	5.91076	−	4.81893i	0.579597	−	0.472535i
$105$		0			0
$106$	5.47813	−	0.293161i	0.532083	−	0.0284743i
$107$	−4.00395	+	2.31168i	−0.387076	+	0.223479i	−0.680893	−	0.732383i	$-0.738408\pi$
$107$	−4.00395	+	2.31168i	−0.387076	+	0.223479i	0.293816	+	0.955862i	$0.405075\pi$
$108$		0			0
$109$	−8.80372	+	15.2485i	−0.843244	+	1.46054i	0.0438939	+	0.999036i	$0.486024\pi$
$109$	−8.80372	+	15.2485i	−0.843244	+	1.46054i	−0.887138	+	0.461505i	$0.847310\pi$
$110$	2.20770	+	3.39136i	0.210496	+	0.323353i
$111$		0			0
$112$	9.56540	+	4.52804i	0.903845	+	0.427860i
$113$	8.00328	+	13.8621i	0.752886	+	1.30404i	0.946419	+	0.322942i	$0.104672\pi$
$113$	8.00328	+	13.8621i	0.752886	+	1.30404i	−0.193533	+	0.981094i	$0.561995\pi$
$114$		0			0
$115$	−1.73008	−	2.99658i	−0.161331	−	0.279433i
$116$	−1.20636	−	1.65273i	−0.112008	−	0.153452i
$117$		0			0
$118$	1.84492	+	2.83408i	0.169839	+	0.260898i
$119$	21.2361	+	2.82777i	1.94671	+	0.259221i
$120$		0			0
$121$	−1.85603	+	3.21474i	−0.168730	+	0.292249i
$122$	4.38920	−	2.85727i	0.397379	−	0.258685i
$123$		0			0
$124$	6.88793	−	15.5629i	0.618554	−	1.39759i
$125$		−	9.40851i		−	0.841522i
$126$		0			0
$127$		−	14.4863i		−	1.28545i	−0.766098	−	0.642724i	$-0.777804\pi$
$127$		−	14.4863i		−	1.28545i	0.766098	−	0.642724i	$-0.222196\pi$
$128$	−8.84716	−	7.05179i	−0.781986	−	0.623296i
$129$		0			0
$130$	−2.20496	−	3.38716i	−0.193388	−	0.297073i
$131$	5.42989	−	9.40485i	0.474412	−	0.821706i	−0.525159	−	0.851004i	$-0.675994\pi$
$131$	5.42989	−	9.40485i	0.474412	−	0.821706i	0.999571	+	0.0292985i	$0.00932735\pi$
$132$		0			0
$133$	−14.6097	−	11.2448i	−1.26682	−	0.975049i
$134$	2.31809	−	1.50902i	0.200252	−	0.130360i
$135$		0			0
$136$	−21.4086	−	8.13675i	−1.83577	−	0.697721i
$137$	−4.86818	−	8.43194i	−0.415917	−	0.720389i	0.579607	−	0.814896i	$-0.303206\pi$
$137$	−4.86818	−	8.43194i	−0.415917	−	0.720389i	−0.995524	+	0.0945069i	$0.969873\pi$
$138$		0			0
$139$	2.46836	+	4.27533i	0.209364	+	0.362628i	0.951514	−	0.307605i	$-0.0995274\pi$
$139$	2.46836	+	4.27533i	0.209364	+	0.362628i	−0.742151	+	0.670233i	$0.766194\pi$
$140$	2.92701	−	4.78426i	0.247378	−	0.404344i
$141$		0			0
$142$	15.1650	−	9.87206i	1.27262	−	0.828445i
$143$	−3.63946	+	6.30372i	−0.304347	+	0.527144i
$144$		0			0
$145$	−0.939116	+	0.542199i	−0.0779894	+	0.0450272i
$146$	−0.212725	−	3.97507i	−0.0176053	−	0.328979i
$147$		0			0
$148$	−1.93911	+	0.208138i	−0.159394	+	0.0171088i
$149$	4.53287	−	7.85116i	0.371347	−	0.643192i	−0.618426	−	0.785843i	$-0.712229\pi$
$149$	4.53287	−	7.85116i	0.371347	−	0.643192i	0.989773	+	0.142651i	$0.0455627\pi$
$150$		0			0
$151$	1.81910	−	1.05026i	0.148036	−	0.0854689i	−0.424152	−	0.905591i	$-0.639428\pi$
$151$	1.81910	−	1.05026i	0.148036	−	0.0854689i	0.572189	+	0.820122i	$0.306095\pi$
$152$	12.4539	+	15.2756i	1.01015	+	1.23902i
$153$		0			0
$154$	−10.0696	−	0.796309i	−0.811432	−	0.0641684i
$155$	−7.81110	−	4.50974i	−0.627403	−	0.362231i
$156$		0			0
$157$		−	18.4059i		−	1.46895i	−0.678635	−	0.734476i	$-0.737428\pi$
$157$		−	18.4059i		−	1.46895i	0.678635	−	0.734476i	$-0.262572\pi$
$158$	−8.99719	+	5.85698i	−0.715778	+	0.465956i
$159$		0			0
$160$	−4.21625	+	4.26305i	−0.333324	+	0.337024i
$161$	8.56154	+	1.14004i	0.674744	+	0.0898481i
$162$		0			0
$163$	−13.8740	+	8.01017i	−1.08670	+	0.627405i	−0.932695	−	0.360665i	$-0.882550\pi$
$163$	−13.8740	+	8.01017i	−1.08670	+	0.627405i	−0.154002	+	0.988070i	$0.549216\pi$
$164$	−0.930777	−	8.67155i	−0.0726815	−	0.677134i
$165$		0			0
$166$	3.01952	−	0.161589i	0.234360	−	0.0125417i
$167$	−0.0138224	−	0.0239411i	−0.00106961	−	0.00185262i	0.865490	−	0.500926i	$-0.167007\pi$
$167$	−0.0138224	−	0.0239411i	−0.00106961	−	0.00185262i	−0.866560	+	0.499073i	$0.833674\pi$
$168$		0			0
$169$	−2.86505	+	4.96241i	−0.220389	+	0.381724i
$170$	−5.49842	+	10.8208i	−0.421710	+	0.829916i
$171$		0			0
$172$	10.7764	−	7.86594i	0.821695	−	0.599772i
$173$		−	4.75427i		−	0.361461i	−0.983533	−	0.180730i	$-0.942154\pi$
$173$		−	4.75427i		−	0.361461i	0.983533	−	0.180730i	$-0.0578461\pi$
$174$		0			0
$175$	8.12769	+	6.25574i	0.614396	+	0.472889i
$176$	10.2846	+	3.29153i	0.775230	+	0.248109i
$177$		0			0
$178$	5.54592	+	2.81808i	0.415684	+	0.211224i
$179$	3.17006	+	1.83024i	0.236941	+	0.136798i	0.613770	−	0.789485i	$-0.289652\pi$
$179$	3.17006	+	1.83024i	0.236941	+	0.136798i	−0.376829	+	0.926283i	$0.622985\pi$
$180$		0			0
$181$		−	12.2768i		−	0.912526i	−0.889845	−	0.456263i	$-0.849188\pi$
$181$		−	12.2768i		−	0.912526i	0.889845	−	0.456263i	$-0.150812\pi$
$182$	10.0571	+	0.795323i	0.745485	+	0.0589532i
$183$		0			0
$184$	−8.63109	−	3.28041i	−0.636293	−	0.241835i
$185$			1.03356i			0.0759888i
$186$		0			0
$187$	21.8597			1.59854
$188$	3.84703	−	8.69216i	0.280573	−	0.633941i
$189$		0			0
$190$	8.75368	−	5.69846i	0.635059	−	0.413409i
$191$		−	17.3274i		−	1.25377i	−0.779113	−	0.626883i	$-0.784330\pi$
$191$		−	17.3274i		−	1.25377i	0.779113	−	0.626883i	$-0.215670\pi$
$192$		0			0
$193$	−2.14314			−0.154267			−0.0771334	−	0.997021i	$-0.524577\pi$
$193$	−2.14314			−0.154267			−0.0771334	+	0.997021i	$0.524577\pi$
$194$	−0.428596	−	8.00892i	−0.0307714	−	0.575007i
$195$		0			0
$196$	5.00731	+	13.0739i	0.357665	+	0.933850i
$197$	−15.3799			−1.09577			−0.547886	−	0.836553i	$-0.684567\pi$
$197$	−15.3799			−1.09577			−0.547886	+	0.836553i	$0.684567\pi$
$198$		0			0
$199$	−2.79870	+	4.84750i	−0.198395	+	0.343630i	−0.948008	−	0.318246i	$-0.896906\pi$
$199$	−2.79870	+	4.84750i	−0.198395	+	0.343630i	0.749613	+	0.661876i	$0.230239\pi$
$200$	−6.92839	−	8.49816i	−0.489911	−	0.600910i
$201$		0			0
$202$	−10.6360	−	5.40455i	−0.748349	−	0.380263i
$203$	0.357285	−	2.68315i	0.0250765	−	0.188320i
$204$		0			0
$205$	−4.62200			−0.322815
$206$	−11.1072	+	0.594398i	−0.773874	+	0.0414137i
$207$		0			0
$208$	−10.2719	−	3.28746i	−0.712225	−	0.227944i
$209$	−16.2912	−	9.40572i	−1.12689	−	0.650607i
$210$		0			0
$211$	5.47775	−	3.16258i	0.377104	−	0.217721i	−0.299454	−	0.954111i	$-0.596804\pi$
$211$	5.47775	−	3.16258i	0.377104	−	0.217721i	0.676557	+	0.736390i	$0.263471\pi$
$212$	−4.57408	−	6.26653i	−0.314149	−	0.430387i
$213$		0			0
$214$	5.82905	+	2.96195i	0.398466	+	0.202475i
$215$	−3.53534	−	6.12339i	−0.241108	−	0.417612i
$216$		0			0
$217$	20.8130	−	8.58497i	1.41288	−	0.582786i
$218$	24.8651	−	1.33065i	1.68408	−	0.0901230i
$219$		0			0
$220$	2.31613	−	5.23317i	0.156153	−	0.352820i
$221$	−21.8327			−1.46862
$222$		0			0
$223$	6.11784	−	10.5964i	0.409681	−	0.709588i	−0.585173	−	0.810909i	$-0.698973\pi$
$223$	6.11784	−	10.5964i	0.409681	−	0.709588i	0.994854	+	0.101320i	$0.0323067\pi$
$224$	−2.01346	−	14.8306i	−0.134530	−	0.990910i
$225$		0			0
$226$	10.2546	−	20.1808i	0.682124	−	1.34241i
$227$	4.52996	+	7.84613i	0.300664	+	0.520766i	0.976287	−	0.216482i	$-0.0694583\pi$
$227$	4.52996	+	7.84613i	0.300664	+	0.520766i	−0.675622	+	0.737248i	$0.736125\pi$
$228$		0			0
$229$	11.9882	+	6.92138i	0.792202	+	0.457378i	0.840737	−	0.541444i	$-0.182122\pi$
$229$	11.9882	+	6.92138i	0.792202	+	0.457378i	−0.0485353	+	0.998821i	$0.515455\pi$
$230$	−2.21674	+	4.36250i	−0.146168	+	0.287655i
$231$		0			0
$232$	−1.02807	+	2.70495i	−0.0674959	+	0.177588i
$233$	9.76646	+	16.9160i	0.639822	+	1.10820i	0.985472	+	0.169841i	$0.0543253\pi$
$233$	9.76646	+	16.9160i	0.639822	+	1.10820i	−0.345649	+	0.938364i	$0.612341\pi$
$234$		0			0
$235$	−4.36264	−	2.51877i	−0.284587	−	0.164306i
$236$	1.93553	−	4.37323i	0.125992	−	0.284673i
$237$		0			0
$238$	−13.0331	−	27.3510i	−0.844811	−	1.77290i
$239$	7.53604	−	4.35094i	0.487466	−	0.281439i	−0.236057	−	0.971739i	$-0.575855\pi$
$239$	7.53604	−	4.35094i	0.487466	−	0.281439i	0.723523	+	0.690301i	$0.242522\pi$
$240$		0			0
$241$	−12.7248	+	7.34665i	−0.819675	+	0.473240i	−0.850304	−	0.526291i	$-0.823582\pi$
$241$	−12.7248	+	7.34665i	−0.819675	+	0.473240i	0.0306294	+	0.999531i	$0.490249\pi$
$242$	5.24215	−	0.280532i	0.336978	−	0.0180333i
$243$		0			0
$244$	−6.77292	−	2.99760i	−0.433592	−	0.191902i
$245$	7.17234	−	1.89908i	0.458224	−	0.121328i
$246$		0			0
$247$	16.2710	+	9.39407i	1.03530	+	0.597731i
$248$	−23.7596	+	3.84386i	−1.50874	+	0.244085i
$249$		0			0
$250$	−11.1510	+	7.25908i	−0.705254	+	0.459105i
$251$	24.9521			1.57496			0.787481	−	0.616339i	$-0.211385\pi$
$251$	24.9521			1.57496			0.787481	+	0.616339i	$0.211385\pi$
$252$		0			0
$253$	8.81296			0.554066
$254$	−17.1692	+	11.1768i	−1.07729	+	0.701295i
$255$		0			0
$256$	−1.53187	+	15.9265i	−0.0957418	+	0.995406i
$257$	7.23287	+	4.17590i	0.451174	+	0.260485i	0.708326	−	0.705886i	$-0.249451\pi$
$257$	7.23287	+	4.17590i	0.451174	+	0.260485i	−0.257152	+	0.966371i	$0.582784\pi$
$258$		0			0
$259$	−2.04447	−	1.57359i	−0.127037	−	0.0977782i
$260$	−2.31326	+	5.22668i	−0.143462	+	0.324145i
$261$		0			0
$262$	−15.3361	+	0.820709i	−0.947468	+	0.0507035i
$263$	−11.8111	+	6.81912i	−0.728301	+	0.420485i	−0.817800	−	0.575502i	$-0.804807\pi$
$263$	−11.8111	+	6.81912i	−0.728301	+	0.420485i	0.0894990	+	0.995987i	$0.471473\pi$
$264$		0			0
$265$	−3.56078	+	2.05582i	−0.218737	+	0.126288i
$266$	−2.05541	+	25.9914i	−0.126025	+	1.59364i
$267$		0			0
$268$	−3.57702	−	1.58314i	−0.218501	−	0.0967054i
$269$	−1.96107	−	1.13222i	−0.119568	−	0.0690329i	0.439023	−	0.898476i	$-0.355325\pi$
$269$	−1.96107	−	1.13222i	−0.119568	−	0.0690329i	−0.558591	+	0.829443i	$0.688658\pi$
$270$		0			0
$271$	−9.35385	−	16.2013i	−0.568206	−	0.984162i	−0.996743	−	0.0806376i	$-0.974304\pi$
$271$	−9.35385	−	16.2013i	−0.568206	−	0.984162i	0.428538	−	0.903524i	$-0.359029\pi$
$272$	6.87395	+	31.6515i	0.416795	+	1.91916i
$273$		0			0
$274$	−6.23758	+	12.2754i	−0.376826	+	0.741585i
$275$	9.06314	+	5.23261i	0.546528	+	0.315538i
$276$		0			0
$277$	5.07500	+	8.79015i	0.304927	+	0.528149i	0.977245	−	0.212113i	$-0.0680346\pi$
$277$	5.07500	+	8.79015i	0.304927	+	0.528149i	−0.672318	+	0.740262i	$0.734701\pi$
$278$	3.16270	−	6.22413i	0.189686	−	0.373298i
$279$		0			0
$280$	−7.92866	+	0.222151i	−0.473828	+	0.0132760i
$281$	−16.5394	+	28.6470i	−0.986656	+	1.70894i	−0.352321	+	0.935879i	$0.614607\pi$
$281$	−16.5394	+	28.6470i	−0.986656	+	1.70894i	−0.634335	+	0.773059i	$0.718726\pi$
$282$		0			0
$283$	3.33841			0.198448			0.0992240	−	0.995065i	$-0.468364\pi$
$283$	3.33841			0.198448			0.0992240	+	0.995065i	$0.468364\pi$
$284$	−23.4009	−	10.3569i	−1.38859	−	0.614569i
$285$		0			0
$286$	10.2792	−	0.550090i	0.607823	−	0.0325275i
$287$	7.03699	−	9.14273i	0.415380	−	0.539678i
$288$		0			0
$289$	24.2835	+	42.0602i	1.42844	+	2.47413i
$290$	1.36719	+	0.694718i	0.0802841	+	0.0407952i
$291$		0			0
$292$	−4.54716	+	3.31907i	−0.266103	+	0.194234i
$293$	−2.78361	+	1.60712i	−0.162620	+	0.0938888i	−0.579101	−	0.815256i	$-0.696596\pi$
$293$	−2.78361	+	1.60712i	−0.162620	+	0.0938888i	0.416481	+	0.909144i	$0.363263\pi$
$294$		0			0
$295$	−2.19495	−	1.26725i	−0.127795	−	0.0737823i
$296$	1.74279	+	2.13766i	0.101298	+	0.124249i
$297$		0			0
$298$	−12.8026	+	0.685126i	−0.741633	+	0.0396883i
$299$	−8.80205			−0.509036
$300$		0			0
$301$	17.4952	+	2.32963i	1.00840	+	0.134278i
$302$	−2.64829	−	1.34569i	−0.152392	−	0.0774359i
$303$		0			0
$304$	8.49602	−	26.5463i	0.487280	−	1.52254i
$305$	−1.96262	+	3.39936i	−0.112379	+	0.194647i
$306$		0			0
$307$	24.8754			1.41971			0.709857	−	0.704345i	$-0.248759\pi$
$307$	24.8754			1.41971			0.709857	+	0.704345i	$0.248759\pi$
$308$	6.82536	+	12.5490i	0.388911	+	0.715044i
$309$		0			0
$310$	0.681631	+	12.7372i	0.0387140	+	0.723427i
$311$	2.45139			0.139006			0.0695028	−	0.997582i	$-0.477859\pi$
$311$	2.45139			0.139006			0.0695028	+	0.997582i	$0.477859\pi$
$312$		0			0
$313$		−	14.7692i		−	0.834803i	−0.908722	−	0.417402i	$-0.862941\pi$
$313$		−	14.7692i		−	0.834803i	0.908722	−	0.417402i	$-0.137059\pi$
$314$	−21.8148	+	14.2010i	−1.23108	+	0.801408i
$315$		0			0
$316$	13.8835	+	6.14463i	0.781006	+	0.345662i
$317$	26.0431			1.46272			0.731362	−	0.681989i	$-0.238885\pi$
$317$	26.0431			1.46272			0.731362	+	0.681989i	$0.238885\pi$
$318$		0			0
$319$		−	2.76194i		−	0.154639i
$320$	8.30562	+	1.70800i	0.464298	+	0.0954800i
$321$		0			0
$322$	−5.25442	−	11.0268i	−0.292818	−	0.614500i
$323$		−	56.4238i		−	3.13950i
$324$		0			0
$325$	−9.05192	−	5.22613i	−0.502110	−	0.289893i
$326$	20.1982	+	10.2634i	1.11867	+	0.568438i
$327$		0			0
$328$	−9.55945	+	7.79365i	−0.527832	+	0.430332i
$329$	11.6244	−	4.79486i	0.640876	−	0.264349i
$330$		0			0
$331$			19.1448i			1.05229i	0.850394	+	0.526146i	$0.176363\pi$
$331$			19.1448i			1.05229i	−0.850394	+	0.526146i	$0.823637\pi$
$332$	−2.52121	−	3.45408i	−0.138369	−	0.189567i
$333$		0			0
$334$	−0.0177106	+	0.0348541i	−0.000969081	+	0.00190713i
$335$	−1.03653	+	1.79532i	−0.0566316	+	0.0980888i
$336$		0			0
$337$	−0.842812	−	1.45979i	−0.0459109	−	0.0795200i	0.842157	−	0.539233i	$-0.181286\pi$
$337$	−0.842812	−	1.45979i	−0.0459109	−	0.0795200i	−0.888068	+	0.459713i	$0.847952\pi$
$338$	8.09201	−	0.433042i	0.440147	−	0.0235544i
$339$		0			0
$340$	17.0672	−	1.83194i	0.925597	−	0.0993507i
$341$	19.8947	−	11.4862i	1.07736	−	0.622014i
$342$		0			0
$343$	−7.16331	+	17.0788i	−0.386782	+	0.922171i
$344$	−17.6373	−	6.70338i	−0.950938	−	0.361422i
$345$		0			0
$346$	−5.63481	+	3.66814i	−0.302929	+	0.197200i
$347$			10.0361i			0.538764i	0.963033	+	0.269382i	$0.0868195\pi$
$347$			10.0361i			0.538764i	−0.963033	+	0.269382i	$0.913181\pi$
$348$		0			0
$349$	−14.3598	−	8.29062i	−0.768661	−	0.443787i	0.0637355	−	0.997967i	$-0.479699\pi$
$349$	−14.3598	−	8.29062i	−0.768661	−	0.443787i	−0.832397	+	0.554180i	$0.813032\pi$
$350$	1.14347	−	14.4596i	0.0611211	−	0.772898i
$351$		0			0
$352$	−4.03387	−	14.7289i	−0.215006	−	0.785056i
$353$	18.8996	−	10.9117i	1.00592	−	0.580770i	0.0959274	−	0.995388i	$-0.469418\pi$
$353$	18.8996	−	10.9117i	1.00592	−	0.580770i	0.909995	+	0.414619i	$0.136085\pi$
$354$		0			0
$355$	−6.78099	+	11.7450i	−0.359898	+	0.623361i
$356$	−0.938913	−	8.74735i	−0.0497623	−	0.463609i
$357$		0			0
$358$	−0.276633	−	5.16929i	−0.0146205	−	0.273206i
$359$	−16.2283	+	9.36941i	−0.856497	+	0.494499i	−0.862838	−	0.505481i	$-0.831315\pi$
$359$	−16.2283	+	9.36941i	−0.856497	+	0.494499i	0.00634068	+	0.999980i	$0.497982\pi$
$360$		0			0
$361$	−14.7778	+	25.5959i	−0.777780	+	1.34715i
$362$	−14.5505	+	9.47209i	−0.764760	+	0.497842i
$363$		0			0
$364$	−6.81691	−	12.5334i	−0.357303	−	0.656930i
$365$	1.49176	+	2.58380i	0.0780820	+	0.135242i
$366$		0			0
$367$	3.92233	+	6.79367i	0.204744	+	0.354627i	0.950051	−	0.312095i	$-0.101031\pi$
$367$	3.92233	+	6.79367i	0.204744	+	0.354627i	−0.745307	+	0.666721i	$0.767697\pi$
$368$	2.77130	+	12.7606i	0.144464	+	0.665194i
$369$		0			0
$370$	1.22498	−	0.797437i	0.0636838	−	0.0414568i
$371$	1.35469	−	10.1735i	0.0703320	−	0.528182i
$372$		0			0
$373$	−5.62096	+	9.73578i	−0.291042	+	0.504100i	−0.974056	−	0.226305i	$-0.927335\pi$
$373$	−5.62096	+	9.73578i	−0.291042	+	0.504100i	0.683014	+	0.730405i	$0.260669\pi$
$374$	−16.8658	−	25.9083i	−0.872107	−	1.33969i
$375$		0			0
$376$	−13.2702	+	2.14686i	−0.684357	+	0.110716i
$377$			2.75852i			0.142071i
$378$		0			0
$379$			3.63286i			0.186608i	0.995638	+	0.0933039i	$0.0297428\pi$
$379$			3.63286i			0.186608i	−0.995638	+	0.0933039i	$0.970257\pi$
$380$	−13.5077	−	5.97832i	−0.692931	−	0.306682i
$381$		0			0
$382$	−20.5366	+	13.3689i	−1.05074	+	0.684011i
$383$	−7.68495	+	13.3107i	−0.392683	+	0.680147i	−0.992802	−	0.119764i	$-0.961786\pi$
$383$	−7.68495	+	13.3107i	−0.392683	+	0.680147i	0.600120	+	0.799910i	$0.295120\pi$
$384$		0			0
$385$	6.99856	−	2.88677i	0.356680	−	0.147123i
$386$	1.65353	+	2.54007i	0.0841624	+	0.129286i
$387$		0			0
$388$	−9.16156	+	6.68722i	−0.465108	+	0.339492i
$389$	13.5557	+	23.4791i	0.687300	+	1.19044i	0.972708	+	0.232033i	$0.0745377\pi$
$389$	13.5557	+	23.4791i	0.687300	+	1.19044i	−0.285408	+	0.958406i	$0.592129\pi$
$390$		0			0
$391$	13.2170	+	22.8925i	0.668411	+	1.15772i
$392$	11.6319	−	16.0218i	0.587501	−	0.809223i
$393$		0			0
$394$	11.8663	+	18.2284i	0.597814	+	0.918332i
$395$	4.02308	−	6.96818i	0.202423	−	0.350607i
$396$		0			0
$397$	−16.9366	+	9.77834i	−0.850023	+	0.490761i	−0.860658	−	0.509183i	$-0.829948\pi$
$397$	−16.9366	+	9.77834i	−0.850023	+	0.490761i	0.0106358	+	0.999943i	$0.496614\pi$
$398$	7.90462	−	0.423014i	0.396223	−	0.0212038i
$399$		0			0
$400$	−4.72652	+	14.7683i	−0.236326	+	0.738415i
$401$	−12.4935	+	21.6394i	−0.623897	+	1.08062i	0.364856	+	0.931064i	$0.381118\pi$
$401$	−12.4935	+	21.6394i	−0.623897	+	1.08062i	−0.988753	+	0.149558i	$0.952215\pi$
$402$		0			0
$403$	−19.8701	+	11.4720i	−0.989800	+	0.571461i
$404$	1.80066	+	16.7758i	0.0895861	+	0.834625i
$405$		0			0
$406$	−3.45575	+	1.64671i	−0.171506	+	0.0817250i
$407$	−2.27978	−	1.31623i	−0.113004	−	0.0652430i
$408$		0			0
$409$			12.4141i			0.613839i	0.951735	+	0.306920i	$0.0992983\pi$
$409$			12.4141i			0.613839i	−0.951735	+	0.306920i	$0.900702\pi$
$410$	3.56608	+	5.47804i	0.176116	+	0.270541i
$411$		0			0
$412$	9.27417	+	12.7057i	0.456905	+	0.625966i
$413$	5.84853	−	2.41241i	0.287787	−	0.118707i
$414$		0			0
$415$	−1.96268	+	1.13316i	−0.0963443	+	0.0556244i
$416$	4.02888	+	14.7107i	0.197532	+	0.721252i
$417$		0			0
$418$	1.42164	+	26.5654i	0.0695347	+	1.29936i
$419$	−15.0148	−	26.0064i	−0.733521	−	1.27050i	−0.955369	−	0.295415i	$-0.904542\pi$
$419$	−15.0148	−	26.0064i	−0.733521	−	1.27050i	0.221848	−	0.975081i	$-0.428791\pi$
$420$		0			0
$421$	−17.0435	+	29.5202i	−0.830649	+	1.43873i	0.0668755	+	0.997761i	$0.478697\pi$
$421$	−17.0435	+	29.5202i	−0.830649	+	1.43873i	−0.897524	+	0.440965i	$0.854636\pi$
$422$	−7.97465	−	4.05220i	−0.388200	−	0.197258i
$423$		0			0
$424$	−3.89804	+	10.2561i	−0.189306	+	0.498082i
$425$			31.3898i			1.52263i
$426$		0			0
$427$	−3.73614	−	9.05775i	−0.180805	−	0.438335i
$428$	−0.986846	−	9.19391i	−0.0477010	−	0.444405i
$429$		0			0
$430$	−4.52982	+	8.91459i	−0.218447	+	0.429900i
$431$	−8.99967	−	5.19596i	−0.433499	−	0.250281i	0.267337	−	0.963603i	$-0.413856\pi$
$431$	−8.99967	−	5.19596i	−0.433499	−	0.250281i	−0.700836	+	0.713322i	$0.747190\pi$
$432$		0			0
$433$		−	37.3442i		−	1.79465i	−0.441371	−	0.897325i	$-0.645508\pi$
$433$		−	37.3442i		−	1.79465i	0.441371	−	0.897325i	$-0.354492\pi$
$434$	−26.2332	−	18.0441i	−1.25923	−	0.866144i
$435$		0			0
$436$	−20.7616	−	28.4437i	−0.994302	−	1.36221i
$437$		−	22.7478i		−	1.08817i
$438$		0			0
$439$	−18.9820			−0.905961			−0.452981	−	0.891520i	$-0.649639\pi$
$439$	−18.9820			−0.905961			−0.452981	+	0.891520i	$0.649639\pi$
$440$	−7.98939	+	1.29253i	−0.380879	+	0.0616190i
$441$		0			0
$442$	16.8449	+	25.8762i	0.801229	+	1.23081i
$443$			16.3567i			0.777133i	0.921421	+	0.388566i	$0.127030\pi$
$443$			16.3567i			0.777133i	−0.921421	+	0.388566i	$0.872970\pi$
$444$		0			0
$445$	−4.66241			−0.221019
$446$	−17.2791	+	0.924689i	−0.818191	+	0.0437853i
$447$		0			0
$448$	−16.0239	+	13.8288i	−0.757056	+	0.653350i
$449$	16.7544			0.790690			0.395345	−	0.918533i	$-0.370625\pi$
$449$	16.7544			0.790690			0.395345	+	0.918533i	$0.370625\pi$
$450$		0			0
$451$	5.88608	−	10.1950i	0.277165	−	0.480064i
$452$	−31.8303	+	3.41657i	−1.49717	+	0.160702i
$453$		0			0
$454$	5.80422	−	11.4226i	0.272406	−	0.536089i
$455$	−6.98989	+	2.88319i	−0.327691	+	0.135166i
$456$		0			0
$457$	4.37349			0.204583			0.102292	−	0.994754i	$-0.467383\pi$
$457$	4.37349			0.204583			0.102292	+	0.994754i	$0.467383\pi$
$458$	−1.04614	−	19.5487i	−0.0488830	−	0.913449i
$459$		0			0
$460$	6.88079	−	0.738563i	0.320819	−	0.0344357i
$461$	−26.4257	−	15.2569i	−1.23077	−	0.710584i	−0.263578	−	0.964638i	$-0.584902\pi$
$461$	−26.4257	−	15.2569i	−1.23077	−	0.710584i	−0.967190	+	0.254054i	$0.918236\pi$
$462$		0			0
$463$	20.1336	−	11.6242i	0.935689	−	0.540221i	0.0470829	−	0.998891i	$-0.485007\pi$
$463$	20.1336	−	11.6242i	0.935689	−	0.540221i	0.888606	+	0.458670i	$0.151674\pi$
$464$	3.99912	−	0.868513i	0.185655	−	0.0403197i
$465$		0			0
$466$	12.5137	−	24.6267i	0.579687	−	1.14081i
$467$	9.93664	+	17.2108i	0.459813	+	0.796419i	0.998951	−	0.0457981i	$-0.0145831\pi$
$467$	9.93664	+	17.2108i	0.459813	+	0.796419i	−0.539138	+	0.842218i	$0.681250\pi$
$468$		0			0
$469$	−1.97319	−	4.78371i	−0.0911133	−	0.220891i
$470$	0.380703	+	7.11398i	0.0175605	+	0.328143i
$471$		0			0
$472$	−6.67654	+	1.08014i	−0.307313	+	0.0497173i
$473$	18.0089			0.828051
$474$		0			0
$475$	13.5063	−	23.3936i	0.619710	−	1.07337i
$476$	−22.3610	+	36.5494i	−1.02491	+	1.67524i
$477$		0			0
$478$	−10.9712	−	5.57484i	−0.501809	−	0.254987i
$479$	−2.33757	−	4.04879i	−0.106806	−	0.184994i	0.807668	−	0.589637i	$-0.200729\pi$
$479$	−2.33757	−	4.04879i	−0.106806	−	0.184994i	−0.914475	+	0.404643i	$0.867396\pi$
$480$		0			0
$481$	2.27695	+	1.31460i	0.103820	+	0.0599405i
$482$	18.5251	+	9.41324i	0.843793	+	0.428761i
$483$		0			0
$484$	−4.37704	−	5.99659i	−0.198956	−	0.272572i
$485$	3.00557	+	5.20580i	0.136476	+	0.236383i
$486$		0			0
$487$	26.7465	+	15.4421i	1.21200	+	0.699750i	0.963195	−	0.268804i	$-0.0866282\pi$
$487$	26.7465	+	15.4421i	1.21200	+	0.699750i	0.248807	+	0.968553i	$0.419962\pi$
$488$	1.67283	+	10.3401i	0.0757256	+	0.468075i
$489$		0			0
$490$	−7.78458	−	7.03549i	−0.351672	−	0.317831i
$491$	−17.7038	+	10.2213i	−0.798962	+	0.461281i	−0.843108	−	0.537744i	$-0.819277\pi$
$491$	−17.7038	+	10.2213i	−0.798962	+	0.461281i	0.0441461	+	0.999025i	$0.485943\pi$
$492$		0			0
$493$	7.17440	−	4.14214i	0.323119	−	0.186553i
$494$	−1.41988	−	26.5325i	−0.0638834	−	1.19375i
$495$		0			0
$496$	22.8874	+	25.1944i	1.02767	+	1.13126i
$497$	−12.9086	−	31.2951i	−0.579031	−	1.40378i
$498$		0			0
$499$	−13.4024	−	7.73788i	−0.599974	−	0.346395i	0.169057	−	0.985606i	$-0.445928\pi$
$499$	−13.4024	−	7.73788i	−0.599974	−	0.346395i	−0.769031	+	0.639211i	$0.779261\pi$
$500$	17.2071	+	7.61560i	0.769523	+	0.340580i
$501$		0			0
$502$	−19.2516	−	29.5734i	−0.859243	−	1.31993i
$503$	−2.70437			−0.120582			−0.0602909	−	0.998181i	$-0.519203\pi$
$503$	−2.70437			−0.120582			−0.0602909	+	0.998181i	$0.519203\pi$
$504$		0			0
$505$	8.94162			0.397897
$506$	−6.79960	−	10.4452i	−0.302279	−	0.464346i
$507$		0			0
$508$	26.4937	+	11.7257i	1.17547	+	0.520245i
$509$	−30.5539	−	17.6403i	−1.35428	−	0.781893i	−0.365432	−	0.930838i	$-0.619079\pi$
$509$	−30.5539	−	17.6403i	−1.35428	−	0.781893i	−0.988845	+	0.148945i	$0.952412\pi$
$510$		0			0
$511$	−7.38216	−	0.982999i	−0.326568	−	0.0434853i
$512$	20.0581	−	10.4724i	0.886452	−	0.462820i
$513$		0			0
$514$	−0.631172	−	11.7943i	−0.0278398	−	0.520226i
$515$	7.21966	−	4.16827i	0.318136	−	0.183676i
$516$		0			0
$517$	11.1116	−	6.41526i	0.488686	−	0.282143i
$518$	−0.287633	+	3.63722i	−0.0126379	+	0.159810i
$519$		0			0
$520$	7.97949	−	1.29093i	0.349924	−	0.0566110i
$521$	23.4381	+	13.5320i	1.02684	+	0.592847i	0.916078	−	0.401000i	$-0.131337\pi$
$521$	23.4381	+	13.5320i	1.02684	+	0.592847i	0.110763	+	0.993847i	$0.464671\pi$
$522$		0			0
$523$	−16.0435	−	27.7882i	−0.701534	−	1.21509i	−0.967928	−	0.251228i	$-0.919166\pi$
$523$	−16.0435	−	27.7882i	−0.701534	−	1.21509i	0.266394	−	0.963864i	$-0.414168\pi$
$524$	12.8052	+	17.5433i	0.559398	+	0.766382i
$525$		0			0
$526$	17.1948	+	8.73731i	0.749731	+	0.380965i
$527$	59.6730	+	34.4523i	2.59940	+	1.50076i
$528$		0			0
$529$	−6.17145	−	10.6893i	−0.268324	−	0.464750i
$530$	5.18387	+	2.63411i	0.225173	+	0.114418i
$531$		0			0
$532$	32.3911	−	17.6175i	1.40433	−	0.763814i
$533$	−5.87879	+	10.1824i	−0.254639	+	0.441047i
$534$		0			0
$535$	−4.90043			−0.211864
$536$	0.883481	+	5.46097i	0.0381606	+	0.235878i
$537$		0			0
$538$	0.171131	+	3.19783i	0.00737800	+	0.137868i
$539$	−4.94501	+	18.2389i	−0.212996	+	0.785603i
$540$		0			0
$541$	−20.6581	−	35.7809i	−0.888161	−	1.53834i	−0.842047	−	0.539404i	$-0.818650\pi$
$541$	−20.6581	−	35.7809i	−0.888161	−	1.53834i	−0.0461139	−	0.998936i	$-0.514684\pi$
$542$	−11.9851	+	23.5863i	−0.514802	+	1.01312i
$543$		0			0
$544$	32.2101	−	32.5676i	1.38100	−	1.39633i
$545$	−16.1623	+	9.33131i	−0.692317	+	0.399710i
$546$		0			0
$547$	−2.51810	−	1.45383i	−0.107666	−	0.0621612i	0.445200	−	0.895431i	$-0.353133\pi$
$547$	−2.51810	−	1.45383i	−0.107666	−	0.0621612i	−0.552866	+	0.833270i	$0.686466\pi$
$548$	19.3615	−	2.07820i	0.827083	−	0.0887765i
$549$		0			0
$550$	−0.790889	−	14.7789i	−0.0337236	−	0.630174i
$551$	−7.12906			−0.303708
$552$		0			0
$553$	7.65854	+	18.5670i	0.325674	+	0.789550i
$554$	6.50257	−	12.7969i	0.276268	−	0.543689i
$555$		0			0
$556$	−9.81705	+	1.05373i	−0.416336	+	0.0446882i
$557$	3.49428	−	6.05228i	0.148058	−	0.256443i	−0.782452	−	0.622711i	$-0.786031\pi$
$557$	3.49428	−	6.05228i	0.148058	−	0.256443i	0.930510	+	0.366268i	$0.119365\pi$
$558$		0			0
$559$	−17.9866			−0.760753
$560$	6.38061	+	9.22572i	0.269630	+	0.389858i
$561$		0			0
$562$	46.7135	−	2.49986i	1.97049	−	0.105450i
$563$	−23.3656			−0.984744			−0.492372	−	0.870385i	$-0.663870\pi$
$563$	−23.3656			−0.984744			−0.492372	+	0.870385i	$0.663870\pi$
$564$		0			0
$565$			16.9658i			0.713757i
$566$	−2.57573	−	3.95671i	−0.108266	−	0.166313i
$567$		0			0
$568$	5.77975	+	35.7258i	0.242513	+	1.49902i
$569$	−34.9022			−1.46318			−0.731589	−	0.681746i	$-0.761221\pi$
$569$	−34.9022			−1.46318			−0.731589	+	0.681746i	$0.761221\pi$
$570$		0			0
$571$		−	31.3674i		−	1.31269i	−0.754463	−	0.656343i	$-0.772103\pi$
$571$		−	31.3674i		−	1.31269i	0.754463	−	0.656343i	$-0.227897\pi$
$572$	−8.58286	−	11.7586i	−0.358867	−	0.491652i
$573$		0			0
$574$	−16.2654	−	1.28627i	−0.678904	−	0.0536880i
$575$			12.6551i			0.527754i
$576$		0			0
$577$	22.7304	+	13.1234i	0.946278	+	0.546334i	0.891923	−	0.452188i	$-0.149356\pi$
$577$	22.7304	+	13.1234i	0.946278	+	0.546334i	0.0543554	+	0.998522i	$0.482690\pi$
$578$	31.1143	−	61.2323i	1.29418	−	2.54693i
$579$		0			0
$580$	−0.231462	−	2.15641i	−0.00961095	−	0.0895400i
$581$	0.746698	−	5.60758i	0.0309783	−	0.232642i
$582$		0			0
$583$		−	10.4723i		−	0.433717i
$584$	7.44213	+	2.82852i	0.307958	+	0.117045i
$585$		0			0
$586$	4.05245	+	2.05919i	0.167405	+	0.0850645i
$587$	5.56925	−	9.64623i	0.229868	−	0.398143i	−0.727901	−	0.685682i	$-0.759504\pi$
$587$	5.56925	−	9.64623i	0.229868	−	0.398143i	0.957769	+	0.287540i	$0.0928373\pi$
$588$		0			0
$589$	−29.6480	−	51.3518i	−1.22162	−	2.11591i
$590$	0.191541	+	3.57921i	0.00788560	+	0.147354i
$591$		0			0
$592$	1.18893	−	3.71487i	0.0488646	−	0.152680i
$593$	−2.12516	+	1.22696i	−0.0872700	+	0.0503854i	−0.543000	−	0.839733i	$-0.682712\pi$
$593$	−2.12516	+	1.22696i	−0.0872700	+	0.0503854i	0.455730	+	0.890118i	$0.349378\pi$
$594$		0			0
$595$	17.9945	+	13.8500i	0.737703	+	0.567797i
$596$	10.6898	+	14.6451i	0.437870	+	0.599887i
$597$		0			0
$598$	6.79117	+	10.4323i	0.277712	+	0.426607i
$599$		−	36.8045i		−	1.50379i	−0.659281	−	0.751896i	$-0.729139\pi$
$599$		−	36.8045i		−	1.50379i	0.659281	−	0.751896i	$-0.270861\pi$
$600$		0			0
$601$	21.1705	+	12.2228i	0.863561	+	0.498577i	0.865203	−	0.501421i	$-0.167189\pi$
$601$	21.1705	+	12.2228i	0.863561	+	0.498577i	−0.00164203	+	0.999999i	$0.500523\pi$
$602$	−10.7372	−	22.5328i	−0.437615	−	0.918369i
$603$		0			0
$604$	0.448351	+	4.17704i	0.0182431	+	0.169961i
$605$	−3.40739	+	1.96726i	−0.138530	+	0.0799804i
$606$		0			0
$607$	−6.15267	+	10.6567i	−0.249729	+	0.432544i	−0.963451	−	0.267886i	$-0.913675\pi$
$607$	−6.15267	+	10.6567i	−0.249729	+	0.432544i	0.713721	+	0.700430i	$0.247008\pi$
$608$	−38.0180	+	10.4121i	−1.54183	+	0.422268i
$609$		0			0
$610$	5.54320	−	0.296643i	0.224438	−	0.0120107i
$611$	−11.0978	+	6.40732i	−0.448969	+	0.259212i
$612$		0			0
$613$	2.07499	−	3.59399i	0.0838080	−	0.145160i	−0.821075	−	0.570821i	$-0.806625\pi$
$613$	2.07499	−	3.59399i	0.0838080	−	0.145160i	0.904883	+	0.425661i	$0.139958\pi$
$614$	−19.1925	−	29.4825i	−0.774546	−	1.18982i
$615$		0			0
$616$	9.60707	−	17.7716i	0.387080	−	0.716037i
$617$	−2.21526	−	3.83693i	−0.0891828	−	0.154469i	0.817983	−	0.575242i	$-0.195092\pi$
$617$	−2.21526	−	3.83693i	−0.0891828	−	0.154469i	−0.907166	+	0.420773i	$0.861759\pi$
$618$		0			0
$619$	19.7382	+	34.1876i	0.793345	+	1.37411i	0.923885	+	0.382671i	$0.124996\pi$
$619$	19.7382	+	34.1876i	0.793345	+	1.37411i	−0.130539	+	0.991443i	$0.541671\pi$
$620$	14.5704	−	10.6352i	0.585161	−	0.427121i
$621$		0			0
$622$	−1.89136	−	2.90541i	−0.0758366	−	0.116496i
$623$	7.09850	−	9.22265i	0.284395	−	0.369498i
$624$		0			0
$625$	−4.70521	+	8.14967i	−0.188209	+	0.325987i
$626$	−17.5046	+	11.3951i	−0.699623	+	0.455439i
$627$		0			0
$628$	33.6623	+	14.8984i	1.34327	+	0.594512i
$629$		−	7.89590i		−	0.314830i
$630$		0			0
$631$		−	6.09451i		−	0.242618i	−0.992615	−	0.121309i	$-0.961291\pi$
$631$		−	6.09451i		−	0.242618i	0.992615	−	0.121309i	$-0.0387093\pi$
$632$	−3.42905	−	21.1957i	−0.136400	−	0.843118i
$633$		0			0
$634$	−20.0934	−	30.8665i	−0.798011	−	1.22586i
$635$	7.67720	−	13.2973i	0.304660	−	0.527687i
$636$		0			0
$637$	4.93888	−	18.2163i	0.195686	−	0.721755i
$638$	−3.27348	+	2.13096i	−0.129598	+	0.0843656i
$639$		0			0
$640$	−4.38383	−	11.1617i	−0.173286	−	0.441205i
$641$	7.19194	+	12.4568i	0.284064	+	0.492014i	0.972382	−	0.233396i	$-0.0749837\pi$
$641$	7.19194	+	12.4568i	0.284064	+	0.492014i	−0.688317	+	0.725410i	$0.741650\pi$
$642$		0			0
$643$	2.34451	+	4.06080i	0.0924583	+	0.160142i	0.908545	−	0.417787i	$-0.137194\pi$
$643$	2.34451	+	4.06080i	0.0924583	+	0.160142i	−0.816087	+	0.577930i	$0.803861\pi$
$644$	−9.01504	+	14.7353i	−0.355242	+	0.580651i
$645$		0			0
$646$	−66.8739	+	43.5335i	−2.63112	+	1.71280i
$647$	12.5308	−	21.7040i	0.492638	−	0.853274i	−0.507326	−	0.861754i	$-0.669366\pi$
$647$	12.5308	−	21.7040i	0.492638	−	0.853274i	0.999964	+	0.00848030i	$0.00269940\pi$
$648$		0			0
$649$	5.59049	−	3.22767i	0.219446	−	0.126697i
$650$	0.789910	+	14.7606i	0.0309828	+	0.578958i
$651$		0			0
$652$	−3.41951	−	31.8577i	−0.133918	−	1.24764i
$653$	24.1215	−	41.7796i	0.943946	−	1.63496i	0.186098	−	0.982531i	$-0.440416\pi$
$653$	24.1215	−	41.7796i	0.943946	−	1.63496i	0.757848	−	0.652431i	$-0.226251\pi$
$654$		0			0
$655$	9.96847	−	5.75530i	0.389500	−	0.224878i
$656$	16.6126	+	5.31679i	0.648615	+	0.207586i
$657$		0			0
$658$	−14.6517	−	10.0779i	−0.571182	−	0.392879i
$659$	20.2388	+	11.6849i	0.788392	+	0.455179i	0.839396	−	0.543520i	$-0.182909\pi$
$659$	20.2388	+	11.6849i	0.788392	+	0.455179i	−0.0510039	+	0.998698i	$0.516242\pi$
$660$		0			0
$661$			2.82634i			0.109932i	0.998488	+	0.0549660i	$0.0175050\pi$
$661$			2.82634i			0.109932i	−0.998488	+	0.0549660i	$0.982495\pi$
$662$	22.6905	−	14.7710i	0.881893	−	0.574093i
$663$		0			0
$664$	−2.14858	+	5.65313i	−0.0833812	+	0.219384i
$665$	−7.45126	−	18.0645i	−0.288947	−	0.700512i
$666$		0			0
$667$	2.89243	−	1.66994i	0.111995	−	0.0646605i
$668$	0.0549738	−	0.00590072i	0.00212700	−	0.000228306i
$669$		0			0
$670$	2.92756	−	0.156668i	0.113101	−	0.00605259i
$671$	−4.99876	−	8.65811i	−0.192975	−	0.334243i
$672$		0			0
$673$	3.06361	−	5.30633i	0.118094	−	0.204544i	−0.800919	−	0.598773i	$-0.795655\pi$
$673$	3.06361	−	5.30633i	0.118094	−	0.204544i	0.919012	+	0.394229i	$0.128988\pi$
$674$	−1.07989	+	2.12520i	−0.0415959	+	0.0818598i
$675$		0			0
$676$	−6.75659	−	9.25661i	−0.259869	−	0.356023i
$677$			3.69011i			0.141822i	0.997483	+	0.0709112i	$0.0225907\pi$
$677$			3.69011i			0.141822i	−0.997483	+	0.0709112i	$0.977409\pi$
$678$		0			0
$679$	−14.8735	−	1.98053i	−0.570792	−	0.0760059i
$680$	−15.3393	−	18.8147i	−0.588235	−	0.721511i
$681$		0			0
$682$	−28.9633	−	14.7173i	−1.10906	−	0.563553i
$683$	2.48721	+	1.43599i	0.0951704	+	0.0549466i	0.546830	−	0.837244i	$-0.315834\pi$
$683$	2.48721	+	1.43599i	0.0951704	+	0.0549466i	−0.451659	+	0.892190i	$0.649168\pi$
$684$		0			0
$685$		−	10.3198i		−	0.394301i
$686$	25.7688	−	4.68708i	0.983858	−	0.178954i
$687$		0			0
$688$	5.66304	+	26.0758i	0.215901	+	0.994131i
$689$			10.4593i			0.398467i
$690$		0			0
$691$	−25.3811			−0.965542			−0.482771	−	0.875747i	$-0.660370\pi$
$691$	−25.3811			−0.965542			−0.482771	+	0.875747i	$0.660370\pi$
$692$	8.69501	+	3.84829i	0.330535	+	0.146290i
$693$		0			0
$694$	11.8948	−	7.74327i	0.451522	−	0.293931i
$695$			5.23257i			0.198483i
$696$		0			0
$697$	35.3099			1.33746
$698$	1.25310	+	23.4159i	0.0474304	+	0.886305i
$699$		0			0
$700$	−18.0199	+	9.80097i	−0.681087	+	0.370442i
$701$	−23.9938			−0.906233			−0.453117	−	0.891451i	$-0.649688\pi$
$701$	−23.9938			−0.906233			−0.453117	+	0.891451i	$0.649688\pi$
$702$		0			0
$703$	−3.39742	+	5.88450i	−0.128136	+	0.221938i
$704$	−14.3446	+	16.1450i	−0.540631	+	0.608488i
$705$		0			0
$706$	−27.5145	−	13.9811i	−1.03552	−	0.526185i
$707$	−13.6136	+	17.6873i	−0.511992	+	0.665199i
$708$		0			0
$709$	35.0244			1.31537			0.657684	−	0.753294i	$-0.271536\pi$
$709$	35.0244			1.31537			0.657684	+	0.753294i	$0.271536\pi$
$710$	19.1521	−	1.02492i	0.718767	−	0.0384646i
$711$		0			0
$712$	−9.64302	+	7.86178i	−0.361387	+	0.294633i
$713$	24.0578	+	13.8898i	0.900971	+	0.520176i
$714$		0			0
$715$	−6.68149	+	3.85756i	−0.249874	+	0.144265i
$716$	−5.91325	+	4.31621i	−0.220989	+	0.161304i
$717$		0			0
$718$	23.6256	+	12.0050i	0.881698	+	0.448022i
$719$	19.7380	+	34.1872i	0.736102	+	1.27497i	0.954238	+	0.299048i	$0.0966690\pi$
$719$	19.7380	+	34.1872i	0.736102	+	1.27497i	−0.218136	+	0.975918i	$0.569998\pi$
$720$		0			0
$721$	−2.74670	+	20.6273i	−0.102293	+	0.768200i
$722$	41.7383	−	2.23361i	1.55334	−	0.0831265i
$723$		0			0
$724$	22.4528	+	9.93729i	0.834451	+	0.369316i
$725$	3.96605			0.147295
$726$		0			0
$727$	−9.31052	+	16.1263i	−0.345308	+	0.598091i	−0.985410	−	0.170199i	$-0.945559\pi$
$727$	−9.31052	+	16.1263i	−0.345308	+	0.598091i	0.640102	+	0.768290i	$0.278892\pi$
$728$	−9.59518	+	17.7496i	−0.355621	+	0.657842i
$729$		0			0
$730$	1.91138	−	3.76155i	0.0707434	−	0.139221i
$731$	27.0083	+	46.7798i	0.998939	+	1.73021i
$732$		0			0
$733$	−38.3675	−	22.1515i	−1.41714	−	0.818184i	−0.421090	−	0.907019i	$-0.638352\pi$
$733$	−38.3675	−	22.1515i	−1.41714	−	0.818184i	−0.996046	+	0.0888346i	$0.971686\pi$
$734$	5.02566	−	9.89039i	0.185501	−	0.365061i
$735$		0			0
$736$	12.9858	−	13.1300i	0.478664	−	0.483977i
$737$	−2.64002	−	4.57265i	−0.0972464	−	0.168436i
$738$		0			0
$739$	7.61365	+	4.39574i	0.280072	+	0.161700i	0.633456	−	0.773779i	$-0.281636\pi$
$739$	7.61365	+	4.39574i	0.280072	+	0.161700i	−0.353384	+	0.935478i	$0.614969\pi$
$740$	−1.89026	−	0.836602i	−0.0694873	−	0.0307541i
$741$		0			0
$742$	−13.1029	+	6.24372i	−0.481023	+	0.229214i
$743$	−18.7141	+	10.8046i	−0.686553	+	0.396382i	−0.802319	−	0.596895i	$-0.796401\pi$
$743$	−18.7141	+	10.8046i	−0.686553	+	0.396382i	0.115766	+	0.993276i	$0.463068\pi$
$744$		0			0
$745$	8.32166	−	4.80451i	0.304882	−	0.176024i
$746$	15.8758	−	0.849587i	0.581253	−	0.0311056i
$747$		0			0
$748$	−17.6941	+	39.9789i	−0.646960	+	1.46177i
$749$	7.46089	−	9.69348i	0.272615	−	0.354192i
$750$		0			0
$751$	−42.8324	−	24.7293i	−1.56298	−	0.902385i	−0.996954	−	0.0779961i	$-0.975148\pi$
$751$	−42.8324	−	24.7293i	−1.56298	−	0.902385i	−0.566023	−	0.824389i	$-0.691519\pi$
$752$	12.7830	+	14.0715i	0.466149	+	0.513136i
$753$		0			0
$754$	3.26942	−	2.12832i	0.119065	−	0.0775090i
$755$	2.22640			0.0810269
$756$		0			0
$757$	−48.1032			−1.74834			−0.874170	−	0.485620i	$-0.838594\pi$
$757$	−48.1032			−1.74834			−0.874170	+	0.485620i	$0.838594\pi$
$758$	4.30570	−	2.80292i	0.156390	−	0.101807i
$759$		0			0
$760$	3.33625	+	20.6220i	0.121018	+	0.748039i
$761$	2.79853	+	1.61573i	0.101447	+	0.0585702i	0.549865	−	0.835254i	$-0.314679\pi$
$761$	2.79853	+	1.61573i	0.101447	+	0.0585702i	−0.448418	+	0.893824i	$0.648013\pi$
$762$		0			0
$763$	6.14891	−	46.1773i	0.222606	−	1.67173i
$764$	31.6898	+	14.0254i	1.14650	+	0.507423i
$765$		0			0
$766$	21.7053	−	1.16155i	0.784243	−	0.0419686i
$767$	−5.58357	+	3.22367i	−0.201611	+	0.116400i
$768$		0			0
$769$	−34.6628	+	20.0126i	−1.24997	+	0.721672i	−0.971104	−	0.238657i	$-0.923293\pi$
$769$	−34.6628	+	20.0126i	−1.24997	+	0.721672i	−0.278869	+	0.960329i	$0.589960\pi$
$770$	−8.82113	−	6.06748i	−0.317891	−	0.218657i
$771$		0			0
$772$	1.73474	−	3.91955i	0.0624346	−	0.141068i
$773$	−27.1598	−	15.6807i	−0.976869	−	0.563995i	−0.0755453	−	0.997142i	$-0.524070\pi$
$773$	−27.1598	−	15.6807i	−0.976869	−	0.563995i	−0.901323	+	0.433147i	$0.857403\pi$
$774$		0			0
$775$	16.4938	+	28.5681i	0.592475	+	1.02620i
$776$	14.9943	+	5.69887i	0.538264	+	0.204578i
$777$		0			0
$778$	17.3688	−	34.1815i	0.622703	−	1.22547i
$779$	−26.3151	−	15.1930i	−0.942835	−	0.544346i
$780$		0			0
$781$	−17.2711	−	29.9144i	−0.618007	−	1.07042i
$782$	16.9349	−	33.3274i	0.605589	−	1.19179i
$783$		0			0
$784$	−27.9637	−	1.42472i	−0.998705	−	0.0508828i
$785$	9.75447	−	16.8952i	0.348152	−	0.603017i
$786$		0			0
$787$	−32.1984			−1.14775			−0.573875	−	0.818943i	$-0.694560\pi$
$787$	−32.1984			−1.14775			−0.573875	+	0.818943i	$0.694560\pi$
$788$	12.4491	−	28.1280i	0.443479	−	1.00202i
$789$		0			0
$790$	−11.3627	+	0.608074i	−0.404268	+	0.0216343i
$791$	−33.5598	−	25.8304i	−1.19325	−	0.918423i
$792$		0			0
$793$	4.99257	+	8.64739i	0.177291	+	0.307078i
$794$	24.6567	+	12.5290i	0.875034	+	0.444636i
$795$		0			0
$796$	−6.60013	−	9.04224i	−0.233935	−	0.320494i
$797$	16.7898	−	9.69358i	0.594724	−	0.343364i	−0.172239	−	0.985055i	$-0.555100\pi$
$797$	16.7898	−	9.69358i	0.594724	−	0.343364i	0.766963	+	0.641691i	$0.221767\pi$
$798$		0			0
$799$	33.3284	+	19.2422i	1.17908	+	0.680740i
$800$	21.1502	−	5.79249i	0.747774	−	0.204796i
$801$		0			0
$802$	35.2866	−	1.88835i	1.24601	−	0.0666800i
$803$	−7.59895			−0.268161
$804$		0			0
$805$	7.25467	+	5.58378i	0.255693	+	0.196803i
$806$	28.9274	+	14.6990i	1.01892	+	0.517752i
$807$		0			0
$808$	18.4935	−	15.0774i	0.650599	−	0.530421i
$809$	−16.7748	+	29.0549i	−0.589772	+	1.02152i	0.404490	+	0.914543i	$0.367449\pi$
$809$	−16.7748	+	29.0549i	−0.589772	+	1.02152i	−0.994262	+	0.106973i	$0.965884\pi$
$810$		0			0
$811$	−12.0196			−0.422064			−0.211032	−	0.977479i	$-0.567682\pi$
$811$	−12.0196			−0.422064			−0.211032	+	0.977479i	$0.567682\pi$
$812$	4.61797	+	2.82527i	0.162059	+	0.0991477i
$813$		0			0
$814$	0.198943	+	3.71754i	0.00697295	+	0.130300i
$815$	−16.9804			−0.594798
$816$		0			0
$817$		−	46.4842i		−	1.62628i
$818$	14.7133	−	9.57806i	0.514440	−	0.334889i
$819$		0			0
$820$	3.74122	−	8.45310i	0.130649	−	0.295195i
$821$	11.5825			0.404233			0.202117	−	0.979361i	$-0.435218\pi$
$821$	11.5825			0.404233			0.202117	+	0.979361i	$0.435218\pi$
$822$		0			0
$823$		−	42.1768i		−	1.47019i	−0.677963	−	0.735096i	$-0.737137\pi$
$823$		−	42.1768i		−	1.47019i	0.677963	−	0.735096i	$-0.262863\pi$
$824$	7.90348	−	20.7948i	0.275331	−	0.724423i
$825$		0			0
$826$	−7.37161	−	5.07045i	−0.256491	−	0.176424i
$827$			27.0948i			0.942178i	0.882086	+	0.471089i	$0.156139\pi$
$827$			27.0948i			0.942178i	−0.882086	+	0.471089i	$0.843861\pi$
$828$		0			0
$829$	−3.83015	−	2.21134i	−0.133027	−	0.0768029i	0.432010	−	0.901869i	$-0.357805\pi$
$829$	−3.83015	−	2.21134i	−0.133027	−	0.0768029i	−0.565036	+	0.825066i	$0.691138\pi$
$830$	2.85732	+	1.45191i	0.0991791	+	0.0503965i
$831$		0			0
$832$	14.3268	−	16.1250i	0.496692	−	0.559035i
$833$	−54.7932	+	14.5081i	−1.89847	+	0.502675i
$834$		0			0
$835$		−	0.0293015i		−	0.00101402i
$836$	30.3887	−	22.1813i	1.05101	−	0.767157i
$837$		0			0
$838$	−19.2384	+	37.8608i	−0.664580	+	1.30788i
$839$	25.3280	−	43.8694i	0.874420	−	1.51454i	0.0170407	−	0.999855i	$-0.494576\pi$
$839$	25.3280	−	43.8694i	0.874420	−	1.51454i	0.857379	−	0.514685i	$-0.172091\pi$
$840$		0			0
$841$	13.9766	+	24.2083i	0.481953	+	0.834768i
$842$	48.1374	−	2.57606i	1.65892	−	0.0887769i
$843$		0			0
$844$	1.35009	+	12.5781i	0.0464721	+	0.432955i
$845$	−5.25980	+	3.03675i	−0.180943	+	0.104467i
$846$		0			0
$847$	1.29633	−	9.73526i	0.0445426	−	0.334508i
$848$	15.1632	−	3.29308i	0.520706	−	0.113085i
$849$		0			0
$850$	37.2034	−	24.2186i	1.27607	−	0.830691i
$851$		−	3.18331i		−	0.109122i
$852$		0			0
$853$	23.5900	+	13.6197i	0.807705	+	0.466329i	0.846158	−	0.532931i	$-0.178910\pi$
$853$	23.5900	+	13.6197i	0.807705	+	0.466329i	−0.0384530	+	0.999260i	$0.512243\pi$
$854$	−7.85272	+	11.4166i	−0.268715	+	0.390667i
$855$		0			0
$856$	−10.1353	+	8.26314i	−0.346418	+	0.282428i
$857$	−15.0167	+	8.66992i	−0.512962	+	0.296159i	−0.734050	−	0.679095i	$-0.762372\pi$
$857$	−15.0167	+	8.66992i	−0.512962	+	0.296159i	0.221088	+	0.975254i	$0.429039\pi$
$858$		0			0
$859$	−2.16490	+	3.74971i	−0.0738654	+	0.127939i	−0.900592	−	0.434665i	$-0.856867\pi$
$859$	−2.16490	+	3.74971i	−0.0738654	+	0.127939i	0.826727	+	0.562603i	$0.190200\pi$
$860$	14.0606	−	1.50922i	0.479463	−	0.0514641i
$861$		0			0
$862$	0.785350	+	14.6754i	0.0267491	+	0.499846i
$863$	−33.6005	+	19.3992i	−1.14377	+	0.660358i	−0.947362	−	0.320164i	$-0.896262\pi$
$863$	−33.6005	+	19.3992i	−1.14377	+	0.660358i	−0.196411	+	0.980522i	$0.562929\pi$
$864$		0			0
$865$	2.51959	−	4.36407i	0.0856688	−	0.148383i
$866$	−44.2607	+	28.8128i	−1.50404	+	0.979097i
$867$		0			0
$868$	−1.14595	+	45.0136i	−0.0388961	+	1.52786i
$869$	10.2467	+	17.7478i	0.347596	+	0.602054i
$870$		0			0
$871$	2.63675	+	4.56699i	0.0893429	+	0.154746i
$872$	−17.6932	+	46.5524i	−0.599166	+	1.57646i
$873$		0			0
$874$	−26.9609	+	17.5509i	−0.911966	+	0.593670i
$875$	9.49192	+	23.0118i	0.320885	+	0.777941i
$876$		0			0
$877$	−14.1706	+	24.5441i	−0.478506	+	0.828797i	−0.999696	−	0.0246436i	$-0.992155\pi$
$877$	−14.1706	+	24.5441i	−0.478506	+	0.828797i	0.521190	+	0.853441i	$0.325488\pi$
$878$	14.6455	+	22.4976i	0.494260	+	0.759258i
$879$		0			0
$880$	7.69609	+	8.47184i	0.259435	+	0.285586i
$881$		−	47.2247i		−	1.59104i	−0.605927	−	0.795520i	$-0.707198\pi$
$881$		−	47.2247i		−	1.59104i	0.605927	−	0.795520i	$-0.292802\pi$
$882$		0			0
$883$		−	31.8848i		−	1.07301i	−0.843897	−	0.536505i	$-0.819744\pi$
$883$		−	31.8848i		−	1.07301i	0.843897	−	0.536505i	$-0.180256\pi$
$884$	17.6722	−	39.9294i	0.594379	−	1.34297i
$885$		0			0
$886$	19.3862	−	12.6200i	0.651291	−	0.423976i
$887$	15.8297	−	27.4178i	0.531508	−	0.920599i	−0.467815	−	0.883826i	$-0.654959\pi$
$887$	15.8297	−	27.4178i	0.531508	−	0.920599i	0.999324	−	0.0367730i	$-0.0117079\pi$
$888$		0			0
$889$	14.6147	+	35.4313i	0.490161	+	1.18833i
$890$	3.59726	+	5.52592i	0.120580	+	0.185229i
$891$		0			0
$892$	14.4276	+	19.7659i	0.483071	+	0.661813i
$893$	−16.5589	−	28.6809i	−0.554123	−	0.959769i
$894$		0			0
$895$	1.93992	+	3.36004i	0.0648443	+	0.112314i
$896$	28.7531	+	8.32205i	0.960575	+	0.278020i
$897$		0			0
$898$	−12.9268	−	19.8575i	−0.431372	−	0.662653i
$899$	4.35299	−	7.53960i	0.145180	−	0.251460i
$900$		0			0
$901$	27.2026	−	15.7054i	0.906251	−	0.523224i
$902$	−16.6246	+	0.889660i	−0.553538	+	0.0296224i
$903$		0			0
$904$	28.6078	+	35.0895i	0.951483	+	1.16706i
$905$	6.50625	−	11.2692i	0.216275	−	0.374600i
$906$		0			0
$907$	−43.3260	+	25.0143i	−1.43862	+	0.830586i	−0.997754	−	0.0669886i	$-0.978661\pi$
$907$	−43.3260	+	25.0143i	−1.43862	+	0.830586i	−0.440863	+	0.897574i	$0.645328\pi$
$908$	−18.0164	+	1.93382i	−0.597894	+	0.0641761i
$909$		0			0
$910$	8.81020	+	6.05997i	0.292055	+	0.200886i
$911$	−25.2297	−	14.5664i	−0.835897	−	0.482605i	0.0199707	−	0.999801i	$-0.493643\pi$
$911$	−25.2297	−	14.5664i	−0.835897	−	0.482605i	−0.855867	+	0.517195i	$0.826976\pi$
$912$		0			0
$913$		−	5.77226i		−	0.191034i
$914$	−3.37434	−	5.18350i	−0.111613	−	0.171455i
$915$		0			0
$916$	−22.3621	+	16.3226i	−0.738864	+	0.539313i
$917$	−3.79248	+	28.4809i	−0.125239	+	0.940522i
$918$		0			0
$919$	−19.2593	+	11.1193i	−0.635304	+	0.366793i	−0.782803	−	0.622269i	$-0.786211\pi$
$919$	−19.2593	+	11.1193i	−0.635304	+	0.366793i	0.147499	+	0.989062i	$0.452878\pi$
$920$	−6.18419	−	7.58534i	−0.203887	−	0.250081i
$921$		0			0
$922$	2.30602	+	43.0913i	0.0759448	+	1.41914i
$923$	17.2497	+	29.8773i	0.567780	+	0.983424i
$924$		0			0
$925$	1.89006	−	3.27367i	0.0621447	−	0.107638i
$926$	−29.3111	−	14.8940i	−0.963221	−	0.489447i
$927$		0			0
$928$	−4.11487	−	4.06970i	−0.135077	−	0.133594i
$929$			41.6625i			1.36690i	0.729996	+	0.683451i	$0.239522\pi$
$929$			41.6625i			1.36690i	−0.729996	+	0.683451i	$0.760478\pi$
$930$		0			0
$931$	47.0777	+	12.7639i	1.54291	+	0.418321i
$932$	−38.8427	+	4.16926i	−1.27234	+	0.136569i
$933$		0			0
$934$	12.7318	−	25.0559i	0.416597	−	0.819853i
$935$	20.0656	+	11.5849i	0.656215	+	0.378866i
$936$		0			0
$937$		−	38.4609i		−	1.25646i	−0.778026	−	0.628232i	$-0.783779\pi$
$937$		−	38.4609i		−	1.25646i	0.778026	−	0.628232i	$-0.216221\pi$
$938$	−4.14729	+	6.02949i	−0.135414	+	0.196870i
$939$		0			0
$940$	8.13782	−	5.93996i	0.265426	−	0.193740i
$941$			3.15365i			0.102806i	0.998678	+	0.0514030i	$0.0163693\pi$
$941$			3.15365i			0.102806i	−0.998678	+	0.0514030i	$0.983631\pi$
$942$		0			0
$943$	14.2355			0.463573
$944$	6.43144	+	7.07972i	0.209325	+	0.230425i
$945$		0			0
$946$	−13.8947	−	21.3443i	−0.451755	−	0.693964i
$947$			20.0690i			0.652155i	0.945343	+	0.326077i	$0.105727\pi$
$947$			20.0690i			0.652155i	−0.945343	+	0.326077i	$0.894273\pi$
$948$		0			0
$949$	7.58954			0.246367
$950$	−38.1469	+	2.04142i	−1.23765	+	0.0662325i
$951$		0			0
$952$	60.5712	−	1.69712i	1.96312	−	0.0550041i
$953$	−29.2121			−0.946273			−0.473136	−	0.880989i	$-0.656878\pi$
$953$	−29.2121			−0.946273			−0.473136	+	0.880989i	$0.656878\pi$
$954$		0			0
$955$	9.18290	−	15.9052i	0.297152	−	0.514682i
$956$	1.85739	+	17.3043i	0.0600724	+	0.559662i
$957$		0			0
$958$	−2.99512	+	5.89433i	−0.0967680	+	0.190437i
$959$	20.4135	+	15.7119i	0.659188	+	0.507364i
$960$		0			0
$961$	41.4120			1.33587
$962$	−0.198697	−	3.71293i	−0.00640624	−	0.119710i
$963$		0			0
$964$	−3.13625	−	29.2188i	−0.101012	−	0.941074i
$965$	−1.96724	−	1.13579i	−0.0633278	−	0.0365623i
$966$		0			0
$967$	−40.7844	+	23.5469i	−1.31154	+	0.757217i	−0.982351	−	0.187047i	$-0.940108\pi$
$967$	−40.7844	+	23.5469i	−1.31154	+	0.757217i	−0.329188	+	0.944265i	$0.606775\pi$
$968$	−3.73013	+	9.81434i	−0.119891	+	0.315445i
$969$		0			0
$970$	3.85102	−	7.57873i	0.123649	−	0.243338i
$971$	−1.53241	−	2.65421i	−0.0491774	−	0.0851777i	0.840389	−	0.541984i	$-0.182327\pi$
$971$	−1.53241	−	2.65421i	−0.0491774	−	0.0851777i	−0.889566	+	0.456806i	$0.848993\pi$
$972$		0			0
$973$	−10.3505	−	7.96657i	−0.331821	−	0.255396i
$974$	−2.33402	−	43.6145i	−0.0747869	−	1.39750i
$975$		0			0
$976$	10.9645	−	9.96051i	0.350966	−	0.318828i
$977$	24.8947			0.796451			0.398226	−	0.917287i	$-0.369626\pi$
$977$	24.8947			0.796451			0.398226	+	0.917287i	$0.369626\pi$
$978$		0			0
$979$	5.93754	−	10.2841i	0.189764	−	0.328682i
$980$	−2.33236	+	14.6545i	−0.0745045	+	0.468122i
$981$		0			0
$982$	25.7737	+	13.0965i	0.822470	+	0.417927i
$983$	−19.1008	−	33.0836i	−0.609222	−	1.05520i	−0.991369	−	0.131101i	$-0.958149\pi$
$983$	−19.1008	−	33.0836i	−0.609222	−	1.05520i	0.382147	−	0.924101i	$-0.375185\pi$
$984$		0			0
$985$	−14.1176	−	8.15078i	−0.449823	−	0.259706i
$986$	−10.4447	−	5.30731i	−0.332626	−	0.169019i
$987$		0			0
$988$	−30.3510	+	22.1539i	−0.965595	+	0.704808i
$989$	10.8887	+	18.8597i	0.346240	+	0.599705i
$990$		0			0
$991$	16.6116	+	9.59071i	0.527685	+	0.304659i	0.740073	−	0.672526i	$-0.234791\pi$
$991$	16.6116	+	9.59071i	0.527685	+	0.304659i	−0.212388	+	0.977185i	$0.568124\pi$
$992$	12.2020	−	46.5650i	0.387413	−	1.47844i
$993$		0			0
$994$	−27.1317	+	39.4450i	−0.860564	+	1.25112i
$995$	−5.13800	+	2.96642i	−0.162885	+	0.0940420i
$996$		0			0
$997$	−14.5346	+	8.39153i	−0.460314	+	0.265762i	−0.712176	−	0.702001i	$-0.752290\pi$
$997$	−14.5346	+	8.39153i	−0.460314	+	0.265762i	0.251862	+	0.967763i	$0.418957\pi$
$998$	1.16955	+	21.8548i	0.0370215	+	0.691800i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.13		84
3.2	odd	2		252.2.bj.b.115.30	yes	84
4.3	odd	2	inner	756.2.bj.b.451.14		84
7.5	odd	6		756.2.n.b.19.16		84
9.4	even	3		756.2.n.b.199.41		84
9.5	odd	6		252.2.n.b.31.2	✓	84
12.11	even	2		252.2.bj.b.115.29	yes	84
21.5	even	6		252.2.n.b.187.27	yes	84
28.19	even	6		756.2.n.b.19.41		84
36.23	even	6		252.2.n.b.31.27	yes	84
36.31	odd	6		756.2.n.b.199.16		84
63.5	even	6		252.2.bj.b.103.30	yes	84
63.40	odd	6	inner	756.2.bj.b.523.13		84
84.47	odd	6		252.2.n.b.187.2	yes	84
252.103	even	6	inner	756.2.bj.b.523.14		84
252.131	odd	6		252.2.bj.b.103.29	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.2	✓	84	9.5	odd	6
252.2.n.b.31.27	yes	84	36.23	even	6
252.2.n.b.187.2	yes	84	84.47	odd	6
252.2.n.b.187.27	yes	84	21.5	even	6
252.2.bj.b.103.29	yes	84	252.131	odd	6
252.2.bj.b.103.30	yes	84	63.5	even	6
252.2.bj.b.115.29	yes	84	12.11	even	2
252.2.bj.b.115.30	yes	84	3.2	odd	2
756.2.n.b.19.16		84	7.5	odd	6
756.2.n.b.19.41		84	28.19	even	6
756.2.n.b.199.16		84	36.31	odd	6
756.2.n.b.199.41		84	9.4	even	3
756.2.bj.b.451.13		84	1.1	even	1	trivial
756.2.bj.b.451.14		84	4.3	odd	2	inner
756.2.bj.b.523.13		84	63.40	odd	6	inner
756.2.bj.b.523.14		84	252.103	even	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.771545 - 1.18521i) q^{2} +(-0.809438 + 1.82888i) q^{4} +(0.917924 + 0.529964i) q^{5} +(-2.44585 + 1.00887i) q^{7} +(2.79212 - 0.451713i) q^{8} +O(q^{10})\)	\(q+(-0.771545 - 1.18521i) q^{2} +(-0.809438 + 1.82888i) q^{4} +(0.917924 + 0.529964i) q^{5} +(-2.44585 + 1.00887i) q^{7} +(2.79212 - 0.451713i) q^{8} +(-0.0801021 - 1.49682i) q^{10} +(-2.33794 + 1.34981i) q^{11} +(2.33504 - 1.34814i) q^{13} +(3.08280 + 2.12046i) q^{14} +(-2.68962 - 2.96073i) q^{16} +(-7.01250 - 4.04867i) q^{17} +(3.48409 + 6.03463i) q^{19} +(-1.71224 + 1.24980i) q^{20} +(3.40363 + 1.72951i) q^{22} +(-2.82716 - 1.63226i) q^{23} +(-1.93828 - 3.35719i) q^{25} +(-3.39941 - 1.72736i) q^{26} +(0.134667 - 5.28979i) q^{28} +(-0.511543 + 0.886019i) q^{29} -8.50952 q^{31} +(-1.43392 + 5.47210i) q^{32} +(0.611942 + 11.4350i) q^{34} +(-2.77977 - 0.370150i) q^{35} +(0.487561 + 0.844481i) q^{37} +(4.46416 - 8.78536i) q^{38} +(2.80235 + 1.06509i) q^{40} +(-3.77646 + 2.18034i) q^{41} +(-5.77718 - 3.33546i) q^{43} +(-0.576227 - 5.36840i) q^{44} +(0.246710 + 4.61014i) q^{46} -4.75272 q^{47} +(4.96438 - 4.93507i) q^{49} +(-2.48351 + 4.88749i) q^{50} +(0.575514 + 5.36175i) q^{52} +(-1.93958 + 3.35945i) q^{53} -2.86140 q^{55} +(-6.37340 + 3.92170i) q^{56} +(1.44480 - 0.0773179i) q^{58} -2.39121 q^{59} +3.70331i q^{61} +(6.56548 + 10.0856i) q^{62} +(7.59191 - 2.52247i) q^{64} +2.85786 q^{65} +1.95585i q^{67} +(13.0807 - 9.54790i) q^{68} +(1.70601 + 3.58019i) q^{70} +12.7952i q^{71} +(2.43771 + 1.40741i) q^{73} +(0.624710 - 1.22942i) q^{74} +(-13.8568 + 1.48734i) q^{76} +(4.35647 - 5.66010i) q^{77} -7.59123i q^{79} +(-0.899789 - 4.14313i) q^{80} +(5.49786 + 2.79366i) q^{82} +(-1.06909 + 1.85171i) q^{83} +(-4.29130 - 7.43275i) q^{85} +(0.504142 + 9.42062i) q^{86} +(-5.91809 + 4.82491i) q^{88} +(-3.80947 + 2.19940i) q^{89} +(-4.35108 + 5.65309i) q^{91} +(5.27362 - 3.84933i) q^{92} +(3.66694 + 5.63296i) q^{94} +7.38578i q^{95} +(4.91146 + 2.83563i) q^{97} +(-9.67933 - 2.07620i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more