LMFDB - Embedded newform 76.2.i.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$2.26253 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	76.9
Dual form			76.2.i.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834130 + 0.699919i) q^{3} +(3.00735 + 1.09458i) q^{5} +(0.278396 - 0.482195i) q^{7} +(-0.315057 + 1.78678i) q^{9} +O(q^{10})$	\(q+(-0.834130 + 0.699919i) q^{3} +(3.00735 + 1.09458i) q^{5} +(0.278396 - 0.482195i) q^{7} +(-0.315057 + 1.78678i) q^{9} +(-1.96291 - 3.39985i) q^{11} +(-3.19334 - 2.67953i) q^{13} +(-3.27464 + 1.19187i) q^{15} +(-0.660076 - 3.74348i) q^{17} +(-1.84488 + 3.94923i) q^{19} +(0.105279 + 0.597068i) q^{21} +(4.67290 - 1.70080i) q^{23} +(4.01579 + 3.36965i) q^{25} +(-2.62112 - 4.53991i) q^{27} +(0.0201569 - 0.114315i) q^{29} +(-3.54372 + 6.13791i) q^{31} +(4.01694 + 1.46205i) q^{33} +(1.36503 - 1.14540i) q^{35} -5.67687 q^{37} +4.53912 q^{39} +(9.20379 - 7.72289i) q^{41} +(6.74642 + 2.45550i) q^{43} +(-2.90326 + 5.02860i) q^{45} +(-0.00419623 + 0.0237980i) q^{47} +(3.34499 + 5.79370i) q^{49} +(3.17072 + 2.66055i) q^{51} +(-8.18260 + 2.97822i) q^{53} +(-2.18171 - 12.3731i) q^{55} +(-1.22527 - 4.58544i) q^{57} +(1.88690 + 10.7011i) q^{59} +(-11.7981 + 4.29417i) q^{61} +(0.773865 + 0.649350i) q^{63} +(-6.67051 - 11.5537i) q^{65} +(2.27074 - 12.8780i) q^{67} +(-2.70739 + 4.68934i) q^{69} +(3.17872 + 1.15696i) q^{71} +(0.338853 - 0.284332i) q^{73} -5.70817 q^{75} -2.18586 q^{77} +(1.31335 - 1.10203i) q^{79} +(0.249157 + 0.0906859i) q^{81} +(-2.90300 + 5.02815i) q^{83} +(2.11247 - 11.9804i) q^{85} +(0.0631980 + 0.109462i) q^{87} +(1.83132 + 1.53666i) q^{89} +(-2.18107 + 0.793845i) q^{91} +(-1.34011 - 7.60013i) q^{93} +(-9.87095 + 9.85733i) q^{95} +(1.86728 + 10.5899i) q^{97} +(6.69320 - 2.43613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−0.834130	+	0.699919i	−0.481585	+	0.404098i	−0.850999	−	0.525167i	$-0.824003\pi$
$3$	−0.834130	+	0.699919i	−0.481585	+	0.404098i	0.369414	+	0.929265i	$0.379558\pi$
$4$		0			0
$5$	3.00735	+	1.09458i	1.34493	+	0.489513i	0.911360	−	0.411609i	$-0.135033\pi$
$5$	3.00735	+	1.09458i	1.34493	+	0.489513i	0.433565	+	0.901122i	$0.357255\pi$
$6$		0			0
$7$	0.278396	−	0.482195i	0.105224	−	0.182253i	−0.808606	−	0.588351i	$-0.799777\pi$
$7$	0.278396	−	0.482195i	0.105224	−	0.182253i	0.913830	+	0.406098i	$0.133111\pi$
$8$		0			0
$9$	−0.315057	+	1.78678i	−0.105019	+	0.595592i
$10$		0			0
$11$	−1.96291	−	3.39985i	−0.591838	−	1.02509i	−0.993985	−	0.109518i	$-0.965069\pi$
$11$	−1.96291	−	3.39985i	−0.591838	−	1.02509i	0.402147	−	0.915575i	$-0.368264\pi$
$12$		0			0
$13$	−3.19334	−	2.67953i	−0.885674	−	0.743169i	0.0816634	−	0.996660i	$-0.473977\pi$
$13$	−3.19334	−	2.67953i	−0.885674	−	0.743169i	−0.967338	+	0.253491i	$0.918421\pi$
$14$		0			0
$15$	−3.27464	+	1.19187i	−0.845508	+	0.307740i
$16$		0			0
$17$	−0.660076	−	3.74348i	−0.160092	−	0.907926i	−0.953982	−	0.299865i	$-0.903058\pi$
$17$	−0.660076	−	3.74348i	−0.160092	−	0.907926i	0.793890	−	0.608062i	$-0.208053\pi$
$18$		0			0
$19$	−1.84488	+	3.94923i	−0.423244	+	0.906016i
$19$	−1.84488	+	3.94923i	−0.423244	+	0.906016i
$20$		0			0
$21$	0.105279	+	0.597068i	0.0229738	+	0.130291i
$22$		0			0
$23$	4.67290	−	1.70080i	0.974368	−	0.354641i	0.194720	−	0.980859i	$-0.437620\pi$
$23$	4.67290	−	1.70080i	0.974368	−	0.354641i	0.779648	+	0.626218i	$0.215398\pi$
$24$		0			0
$25$	4.01579	+	3.36965i	0.803158	+	0.673929i
$26$		0			0
$27$	−2.62112	−	4.53991i	−0.504435	−	0.873706i
$28$		0			0
$29$	0.0201569	−	0.114315i	0.00374304	−	0.0212278i	−0.982879	−	0.184252i	$-0.941014\pi$
$29$	0.0201569	−	0.114315i	0.00374304	−	0.0212278i	0.986622	+	0.163024i	$0.0521249\pi$
$30$		0			0
$31$	−3.54372	+	6.13791i	−0.636472	+	1.10240i	0.349730	+	0.936851i	$0.386273\pi$
$31$	−3.54372	+	6.13791i	−0.636472	+	1.10240i	−0.986201	+	0.165550i	$0.947060\pi$
$32$		0			0
$33$	4.01694	+	1.46205i	0.699259	+	0.254510i
$34$		0			0
$35$	1.36503	−	1.14540i	0.230733	−	0.193608i
$36$		0			0
$37$	−5.67687			−0.933271			−0.466636	−	0.884450i	$-0.654534\pi$
$37$	−5.67687			−0.933271			−0.466636	+	0.884450i	$0.654534\pi$
$38$		0			0
$39$	4.53912			0.726841
$40$		0			0
$41$	9.20379	−	7.72289i	1.43739	−	1.20611i	0.496212	−	0.868201i	$-0.334724\pi$
$41$	9.20379	−	7.72289i	1.43739	−	1.20611i	0.941178	−	0.337912i	$-0.109721\pi$
$42$		0			0
$43$	6.74642	+	2.45550i	1.02882	+	0.374460i	0.800631	−	0.599157i	$-0.204498\pi$
$43$	6.74642	+	2.45550i	1.02882	+	0.374460i	0.228188	+	0.973617i	$0.426720\pi$
$44$		0			0
$45$	−2.90326	+	5.02860i	−0.432793	+	0.749619i
$46$		0			0
$47$	−0.00419623	+	0.0237980i	−0.000612084	+	0.00347130i	−0.985112	−	0.171912i	$-0.945005\pi$
$47$	−0.00419623	+	0.0237980i	−0.000612084	+	0.00347130i	0.984500	+	0.175384i	$0.0561166\pi$
$48$		0			0
$49$	3.34499	+	5.79370i	0.477856	+	0.827671i
$50$		0			0
$51$	3.17072	+	2.66055i	0.443989	+	0.372551i
$52$		0			0
$53$	−8.18260	+	2.97822i	−1.12397	+	0.409090i	−0.836098	−	0.548580i	$-0.815169\pi$
$53$	−8.18260	+	2.97822i	−1.12397	+	0.409090i	−0.287868	+	0.957670i	$0.592946\pi$
$54$		0			0
$55$	−2.18171	−	12.3731i	−0.294182	−	1.66839i
$56$		0			0
$57$	−1.22527	−	4.58544i	−0.162291	−	0.607356i
$58$		0			0
$59$	1.88690	+	10.7011i	0.245653	+	1.39317i	0.818972	+	0.573834i	$0.194545\pi$
$59$	1.88690	+	10.7011i	0.245653	+	1.39317i	−0.573319	+	0.819332i	$0.694344\pi$
$60$		0			0
$61$	−11.7981	+	4.29417i	−1.51060	+	0.549812i	−0.958779	−	0.284154i	$-0.908287\pi$
$61$	−11.7981	+	4.29417i	−1.51060	+	0.549812i	−0.551817	+	0.833966i	$0.686065\pi$
$62$		0			0
$63$	0.773865	+	0.649350i	0.0974978	+	0.0818104i
$64$		0			0
$65$	−6.67051	−	11.5537i	−0.827375	−	1.43306i
$66$		0			0
$67$	2.27074	−	12.8780i	0.277415	−	1.57330i	−0.453769	−	0.891119i	$-0.649921\pi$
$67$	2.27074	−	12.8780i	0.277415	−	1.57330i	0.731184	−	0.682180i	$-0.238968\pi$
$68$		0			0
$69$	−2.70739	+	4.68934i	−0.325932	+	0.564530i
$70$		0			0
$71$	3.17872	+	1.15696i	0.377244	+	0.137306i	0.523681	−	0.851914i	$-0.324558\pi$
$71$	3.17872	+	1.15696i	0.377244	+	0.137306i	−0.146437	+	0.989220i	$0.546781\pi$
$72$		0			0
$73$	0.338853	−	0.284332i	0.0396598	−	0.0332785i	−0.622742	−	0.782427i	$-0.713982\pi$
$73$	0.338853	−	0.284332i	0.0396598	−	0.0332785i	0.662402	+	0.749148i	$0.269537\pi$
$74$		0			0
$75$	−5.70817			−0.659123
$76$		0			0
$77$	−2.18586			−0.249101
$78$		0			0
$79$	1.31335	−	1.10203i	0.147764	−	0.123988i	−0.565909	−	0.824467i	$-0.691475\pi$
$79$	1.31335	−	1.10203i	0.147764	−	0.123988i	0.713673	+	0.700479i	$0.247030\pi$
$80$		0			0
$81$	0.249157	+	0.0906859i	0.0276842	+	0.0100762i
$82$		0			0
$83$	−2.90300	+	5.02815i	−0.318646	+	0.551911i	−0.980206	−	0.197981i	$-0.936561\pi$
$83$	−2.90300	+	5.02815i	−0.318646	+	0.551911i	0.661560	+	0.749892i	$0.269895\pi$
$84$		0			0
$85$	2.11247	−	11.9804i	0.229130	−	1.29946i
$86$		0			0
$87$	0.0631980	+	0.109462i	0.00677553	+	0.0117356i
$88$		0			0
$89$	1.83132	+	1.53666i	0.194120	+	0.162886i	0.734667	−	0.678428i	$-0.237338\pi$
$89$	1.83132	+	1.53666i	0.194120	+	0.162886i	−0.540547	+	0.841314i	$0.681783\pi$
$90$		0			0
$91$	−2.18107	+	0.793845i	−0.228638	+	0.0832176i
$92$		0			0
$93$	−1.34011	−	7.60013i	−0.138963	−	0.788097i
$94$		0			0
$95$	−9.87095	+	9.85733i	−1.01274	+	1.01134i
$96$		0			0
$97$	1.86728	+	10.5899i	0.189594	+	1.07524i	0.919909	+	0.392131i	$0.128262\pi$
$97$	1.86728	+	10.5899i	0.189594	+	1.07524i	−0.730315	+	0.683110i	$0.760627\pi$
$98$		0			0
$99$	6.69320	−	2.43613i	0.672692	−	0.244840i
$100$		0			0
$101$	5.12586	+	4.30110i	0.510042	+	0.427976i	0.861144	−	0.508361i	$-0.169749\pi$
$101$	5.12586	+	4.30110i	0.510042	+	0.427976i	−0.351102	+	0.936337i	$0.614193\pi$
$102$		0			0
$103$	6.52153	+	11.2956i	0.642586	+	1.11299i	0.984854	+	0.173388i	$0.0554716\pi$
$103$	6.52153	+	11.2956i	0.642586	+	1.11299i	−0.342268	+	0.939602i	$0.611195\pi$
$104$		0			0
$105$	−0.336930	+	1.91083i	−0.0328810	+	0.186478i
$106$		0			0
$107$	4.76100	−	8.24629i	0.460263	−	0.797199i	−0.538711	−	0.842491i	$-0.681088\pi$
$107$	4.76100	−	8.24629i	0.460263	−	0.797199i	0.998974	+	0.0452919i	$0.0144218\pi$
$108$		0			0
$109$	7.76788	+	2.82728i	0.744028	+	0.270804i	0.686090	−	0.727516i	$-0.259325\pi$
$109$	7.76788	+	2.82728i	0.744028	+	0.270804i	0.0579374	+	0.998320i	$0.481548\pi$
$110$		0			0
$111$	4.73525	−	3.97335i	0.449450	−	0.377133i
$112$		0			0
$113$	2.08270			0.195924			0.0979618	−	0.995190i	$-0.468768\pi$
$113$	2.08270			0.195924			0.0979618	+	0.995190i	$0.468768\pi$
$114$		0			0
$115$	15.9147			1.48405
$116$		0			0
$117$	5.79381	−	4.86159i	0.535638	−	0.449454i
$118$		0			0
$119$	−1.98885	−	0.723882i	−0.182317	−	0.0663581i
$120$		0			0
$121$	−2.20599	+	3.82089i	−0.200545	+	0.347354i
$122$		0			0
$123$	−2.27176	+	12.8838i	−0.204838	+	1.16169i
$124$		0			0
$125$	0.387625	+	0.671385i	0.0346702	+	0.0600505i
$126$		0			0
$127$	−12.9449	−	10.8621i	−1.14867	−	0.963853i	−0.148987	−	0.988839i	$-0.547601\pi$
$127$	−12.9449	−	10.8621i	−1.14867	−	0.963853i	−0.999688	+	0.0249866i	$0.992046\pi$
$128$		0			0
$129$	−7.34604	+	2.67374i	−0.646783	+	0.235410i
$130$		0			0
$131$	0.287814	+	1.63227i	0.0251464	+	0.142612i	0.994796	−	0.101886i	$-0.0324877\pi$
$131$	0.287814	+	1.63227i	0.0251464	+	0.142612i	−0.969650	+	0.244499i	$0.921377\pi$
$132$		0			0
$133$	1.39069	+	1.98904i	0.120589	+	0.172472i
$134$		0			0
$135$	−2.91330	−	16.5221i	−0.250737	−	1.42200i
$136$		0			0
$137$	3.84678	−	1.40012i	0.328653	−	0.119620i	−0.172423	−	0.985023i	$-0.555160\pi$
$137$	3.84678	−	1.40012i	0.328653	−	0.119620i	0.501076	+	0.865403i	$0.332938\pi$
$138$		0			0
$139$	−5.46307	−	4.58406i	−0.463372	−	0.388815i	0.380998	−	0.924576i	$-0.375580\pi$
$139$	−5.46307	−	4.58406i	−0.463372	−	0.388815i	−0.844370	+	0.535761i	$0.820025\pi$
$140$		0			0
$141$	−0.0131565	−	0.0227877i	−0.00110797	−	0.00191907i
$142$		0			0
$143$	−2.84179	+	16.1166i	−0.237642	+	1.34774i
$144$		0			0
$145$	0.185746	−	0.321722i	0.0154254	−	0.0267176i
$146$		0			0
$147$	−6.84527	−	2.49148i	−0.564589	−	0.205493i
$148$		0			0
$149$	4.50092	−	3.77672i	0.368729	−	0.309401i	−0.439529	−	0.898228i	$-0.644855\pi$
$149$	4.50092	−	3.77672i	0.368729	−	0.309401i	0.808259	+	0.588828i	$0.200410\pi$
$150$		0			0
$151$	6.47180			0.526667			0.263334	−	0.964705i	$-0.415178\pi$
$151$	6.47180			0.526667			0.263334	+	0.964705i	$0.415178\pi$
$152$		0			0
$153$	6.89672			0.557567
$154$		0			0
$155$	−17.3757	+	14.5799i	−1.39565	+	1.17109i
$156$		0			0
$157$	0.579693	+	0.210991i	0.0462646	+	0.0168389i	0.365049	−	0.930988i	$-0.381052\pi$
$157$	0.579693	+	0.210991i	0.0462646	+	0.0168389i	−0.318784	+	0.947827i	$0.603275\pi$
$158$		0			0
$159$	4.74084	−	8.21138i	0.375973	−	0.651204i
$160$		0			0
$161$	0.480799	−	2.72675i	0.0378923	−	0.214898i
$162$		0			0
$163$	−11.7455	−	20.3438i	−0.919979	−	1.59345i	−0.799443	−	0.600742i	$-0.794872\pi$
$163$	−11.7455	−	20.3438i	−0.919979	−	1.59345i	−0.120537	−	0.992709i	$-0.538462\pi$
$164$		0			0
$165$	10.4800	+	8.79375i	0.815866	+	0.684593i
$166$		0			0
$167$	−14.2110	+	5.17239i	−1.09968	+	0.400252i	−0.827199	−	0.561909i	$-0.810067\pi$
$167$	−14.2110	+	5.17239i	−1.09968	+	0.400252i	−0.272483	+	0.962160i	$0.587845\pi$
$168$		0			0
$169$	0.760119	+	4.31085i	0.0584707	+	0.331604i
$170$		0			0
$171$	−6.47515	−	4.54062i	−0.495167	−	0.347230i
$172$		0			0
$173$	0.583180	+	3.30738i	0.0443384	+	0.251455i	0.998918	−	0.0464995i	$-0.0148066\pi$
$173$	0.583180	+	3.30738i	0.0443384	+	0.251455i	−0.954580	+	0.297955i	$0.903695\pi$
$174$		0			0
$175$	2.74280	−	0.998299i	0.207337	−	0.0754643i
$176$		0			0
$177$	−9.06383	−	7.60545i	−0.681279	−	0.571661i
$178$		0			0
$179$	0.0510390	+	0.0884022i	0.00381484	+	0.00660749i	0.867927	−	0.496693i	$-0.165452\pi$
$179$	0.0510390	+	0.0884022i	0.00381484	+	0.00660749i	−0.864112	+	0.503300i	$0.832119\pi$
$180$		0			0
$181$	1.33951	−	7.59673i	0.0995649	−	0.564660i	−0.893688	−	0.448689i	$-0.851891\pi$
$181$	1.33951	−	7.59673i	0.0995649	−	0.564660i	0.993253	−	0.115971i	$-0.0369980\pi$
$182$		0			0
$183$	6.83561	−	11.8396i	0.505303	−	0.875210i
$184$		0			0
$185$	−17.0723	−	6.21381i	−1.25518	−	0.456848i
$186$		0			0
$187$	−11.4316	+	9.59225i	−0.835961	+	0.701455i
$188$		0			0
$189$	−2.91883			−0.212314
$190$		0			0
$191$	−15.0096			−1.08606			−0.543028	−	0.839715i	$-0.682722\pi$
$191$	−15.0096			−1.08606			−0.543028	+	0.839715i	$0.682722\pi$
$192$		0			0
$193$	−1.98477	+	1.66542i	−0.142867	+	0.119880i	−0.711420	−	0.702767i	$-0.751948\pi$
$193$	−1.98477	+	1.66542i	−0.142867	+	0.119880i	0.568553	+	0.822646i	$0.307503\pi$
$194$		0			0
$195$	13.6507	+	4.96845i	0.977547	+	0.355798i
$196$		0			0
$197$	3.21799	−	5.57372i	0.229272	−	0.397111i	−0.728320	−	0.685237i	$-0.759699\pi$
$197$	3.21799	−	5.57372i	0.229272	−	0.397111i	0.957593	+	0.288126i	$0.0930321\pi$
$198$		0			0
$199$	−0.957517	+	5.43035i	−0.0678765	+	0.384947i	0.931878	+	0.362773i	$0.118170\pi$
$199$	−0.957517	+	5.43035i	−0.0678765	+	0.384947i	−0.999754	+	0.0221741i	$0.992941\pi$
$200$		0			0
$201$	7.11946	+	12.3313i	0.502168	+	0.869781i
$202$		0			0
$203$	−0.0495107	−	0.0415444i	−0.00347497	−	0.00291585i
$204$		0			0
$205$	36.1323	−	13.1511i	2.52359	−	0.918512i
$206$		0			0
$207$	1.56672	+	8.88528i	0.108894	+	0.617570i
$208$		0			0
$209$	17.0481	−	1.47966i	1.17924	−	0.102350i
$210$		0			0
$211$	−1.30065	−	7.37636i	−0.0895405	−	0.507809i	−0.996284	−	0.0861271i	$-0.972551\pi$
$211$	−1.30065	−	7.37636i	−0.0895405	−	0.507809i	0.906744	−	0.421682i	$-0.138560\pi$
$212$		0			0
$213$	−3.46124	+	1.25979i	−0.237160	+	0.0863193i
$214$		0			0
$215$	17.6011	+	14.7690i	1.20038	+	1.00724i
$216$		0			0
$217$	1.97311	+	3.41753i	0.133944	+	0.231997i
$218$		0			0
$219$	−0.0836389	+	0.474340i	−0.00565179	+	0.0320529i
$220$		0			0
$221$	−7.92292	+	13.7229i	−0.532953	+	0.923102i
$222$		0			0
$223$	13.2194	+	4.81148i	0.885238	+	0.322200i	0.744322	−	0.667821i	$-0.232773\pi$
$223$	13.2194	+	4.81148i	0.885238	+	0.322200i	0.140916	+	0.990022i	$0.454995\pi$
$224$		0			0
$225$	−7.28601	+	6.11369i	−0.485734	+	0.407579i
$226$		0			0
$227$	25.3417			1.68199			0.840994	−	0.541044i	$-0.181971\pi$
$227$	25.3417			1.68199			0.840994	+	0.541044i	$0.181971\pi$
$228$		0			0
$229$	−19.8311			−1.31047			−0.655237	−	0.755423i	$-0.727431\pi$
$229$	−19.8311			−1.31047			−0.655237	+	0.755423i	$0.727431\pi$
$230$		0			0
$231$	1.82329	−	1.52992i	0.119964	−	0.100661i
$232$		0			0
$233$	−20.8061	−	7.57279i	−1.36305	−	0.496110i	−0.446055	−	0.895006i	$-0.647171\pi$
$233$	−20.8061	−	7.57279i	−1.36305	−	0.496110i	−0.916996	+	0.398895i	$0.869394\pi$
$234$		0			0
$235$	−0.0386685	+	0.0669757i	−0.00252245	+	0.00436901i
$236$		0			0
$237$	−0.324173	+	1.83848i	−0.0210573	+	0.119422i
$238$		0			0
$239$	−1.02364	−	1.77299i	−0.0662135	−	0.114685i	0.831018	−	0.556245i	$-0.187758\pi$
$239$	−1.02364	−	1.77299i	−0.0662135	−	0.114685i	−0.897232	+	0.441560i	$0.854425\pi$
$240$		0			0
$241$	0.941858	+	0.790313i	0.0606704	+	0.0509085i	0.672619	−	0.739989i	$-0.265169\pi$
$241$	0.941858	+	0.790313i	0.0606704	+	0.0509085i	−0.611948	+	0.790898i	$0.709614\pi$
$242$		0			0
$243$	14.5070	−	5.28011i	0.930623	−	0.338719i
$244$		0			0
$245$	3.71786	+	21.0850i	0.237525	+	1.34707i
$246$		0			0
$247$	16.4734	−	7.66784i	1.04818	−	0.487893i
$248$		0			0
$249$	−1.09781	−	6.22600i	−0.0695710	−	0.394557i
$250$		0			0
$251$	−6.52471	+	2.37480i	−0.411836	+	0.149896i	−0.539625	−	0.841905i	$-0.681434\pi$
$251$	−6.52471	+	2.37480i	−0.411836	+	0.149896i	0.127789	+	0.991801i	$0.459212\pi$
$252$		0			0
$253$	−14.9549	−	12.5487i	−0.940208	−	0.788928i
$254$		0			0
$255$	6.62325	+	11.4718i	0.414764	+	0.718392i
$256$		0			0
$257$	1.71799	−	9.74318i	0.107165	−	0.607763i	−0.883168	−	0.469056i	$-0.844594\pi$
$257$	1.71799	−	9.74318i	0.107165	−	0.607763i	0.990333	−	0.138707i	$-0.0442946\pi$
$258$		0			0
$259$	−1.58041	+	2.73736i	−0.0982022	+	0.170091i
$260$		0			0
$261$	0.197905	+	0.0720317i	0.0122500	+	0.00445865i
$262$		0			0
$263$	1.64566	−	1.38087i	0.101476	−	0.0851483i	−0.590638	−	0.806936i	$-0.701124\pi$
$263$	1.64566	−	1.38087i	0.101476	−	0.0851483i	0.692114	+	0.721788i	$0.256680\pi$
$264$		0			0
$265$	−27.8678			−1.71191
$266$		0			0
$267$	−2.60310			−0.159307
$268$		0			0
$269$	7.58263	−	6.36258i	0.462321	−	0.387933i	−0.381663	−	0.924301i	$-0.624649\pi$
$269$	7.58263	−	6.36258i	0.462321	−	0.387933i	0.843984	+	0.536368i	$0.180204\pi$
$270$		0			0
$271$	−17.4238	−	6.34176i	−1.05842	−	0.385234i	−0.246587	−	0.969121i	$-0.579309\pi$
$271$	−17.4238	−	6.34176i	−1.05842	−	0.385234i	−0.811836	+	0.583886i	$0.801531\pi$
$272$		0			0
$273$	1.26367	−	2.18874i	0.0764809	−	0.132469i
$274$		0			0
$275$	3.57369	−	20.2674i	0.215501	−	1.22217i
$276$		0			0
$277$	13.1235	+	22.7305i	0.788514	+	1.36575i	0.926877	+	0.375364i	$0.122482\pi$
$277$	13.1235	+	22.7305i	0.788514	+	1.36575i	−0.138364	+	0.990381i	$0.544184\pi$
$278$		0			0
$279$	−9.85060	−	8.26563i	−0.589740	−	0.494850i
$280$		0			0
$281$	20.0065	−	7.28179i	1.19349	−	0.434395i	0.332543	−	0.943088i	$-0.392093\pi$
$281$	20.0065	−	7.28179i	1.19349	−	0.434395i	0.860948	+	0.508693i	$0.169871\pi$
$282$		0			0
$283$	2.89350	+	16.4099i	0.172001	+	0.975465i	0.941549	+	0.336876i	$0.109370\pi$
$283$	2.89350	+	16.4099i	0.172001	+	0.975465i	−0.769548	+	0.638589i	$0.779518\pi$
$284$		0			0
$285$	1.33433	−	15.1312i	0.0790391	−	0.896292i
$286$		0			0
$287$	−1.16165	−	6.58804i	−0.0685700	−	0.388880i
$288$		0			0
$289$	2.39686	−	0.872386i	0.140992	−	0.0513168i
$290$		0			0
$291$	−8.96963	−	7.52641i	−0.525809	−	0.441206i
$292$		0			0
$293$	−10.8152	−	18.7324i	−0.631828	−	1.09436i	−0.987178	−	0.159625i	$-0.948971\pi$
$293$	−10.8152	−	18.7324i	−0.631828	−	1.09436i	0.355349	−	0.934734i	$-0.384362\pi$
$294$		0			0
$295$	−6.03873	+	34.2473i	−0.351588	+	1.99396i
$296$		0			0
$297$	−10.2900	+	17.8228i	−0.597087	+	1.03419i
$298$		0			0
$299$	−19.4795	−	7.08997i	−1.12653	−	0.410024i
$300$		0			0
$301$	3.06220	−	2.56949i	0.176502	−	0.148103i
$302$		0			0
$303$	−7.28606			−0.418573
$304$		0			0
$305$	−40.1814			−2.30078
$306$		0			0
$307$	−7.14077	+	5.99182i	−0.407545	+	0.341971i	−0.823401	−	0.567459i	$-0.807926\pi$
$307$	−7.14077	+	5.99182i	−0.407545	+	0.341971i	0.415856	+	0.909430i	$0.363482\pi$
$308$		0			0
$309$	−13.3458	−	4.85748i	−0.759217	−	0.276333i
$310$		0			0
$311$	16.5503	−	28.6659i	0.938481	−	1.62550i	0.170175	−	0.985414i	$-0.445567\pi$
$311$	16.5503	−	28.6659i	0.938481	−	1.62550i	0.768306	−	0.640083i	$-0.221100\pi$
$312$		0			0
$313$	−1.53367	+	8.69786i	−0.0866880	+	0.491632i	0.910292	+	0.413968i	$0.135857\pi$
$313$	−1.53367	+	8.69786i	−0.0866880	+	0.491632i	−0.996980	+	0.0776645i	$0.975254\pi$
$314$		0			0
$315$	1.61651	+	2.79988i	0.0910800	+	0.157755i
$316$		0			0
$317$	22.3790	+	18.7782i	1.25693	+	1.05469i	0.996002	+	0.0893315i	$0.0284730\pi$
$317$	22.3790	+	18.7782i	1.25693	+	1.05469i	0.260928	+	0.965358i	$0.415971\pi$
$318$		0			0
$319$	−0.428221	+	0.155860i	−0.0239758	+	0.00872647i
$320$		0			0
$321$	1.80044	+	10.2108i	0.100491	+	0.569911i
$322$		0			0
$323$	16.0016	+	4.29946i	0.890354	+	0.239229i
$324$		0			0
$325$	−3.79471	−	21.5209i	−0.210493	−	1.19376i
$326$		0			0
$327$	−8.45829	+	3.07856i	−0.467744	+	0.170245i
$328$		0			0
$329$	0.0103071	+	0.00864867i	0.000568248	+	0.000476816i
$330$		0			0
$331$	5.83418	+	10.1051i	0.320676	+	0.555426i	0.980628	−	0.195881i	$-0.0627567\pi$
$331$	5.83418	+	10.1051i	0.320676	+	0.555426i	−0.659952	+	0.751308i	$0.729423\pi$
$332$		0			0
$333$	1.78854	−	10.1433i	0.0980112	−	0.555849i
$334$		0			0
$335$	20.9250	−	36.2431i	1.14325	−	1.98017i
$336$		0			0
$337$	−2.01893	−	0.734831i	−0.109978	−	0.0400288i	0.286445	−	0.958097i	$-0.407526\pi$
$337$	−2.01893	−	0.734831i	−0.109978	−	0.0400288i	−0.396423	+	0.918068i	$0.629749\pi$
$338$		0			0
$339$	−1.73724	+	1.45772i	−0.0943539	+	0.0791723i
$340$		0			0
$341$	27.8240			1.50675
$342$		0			0
$343$	7.62246			0.411574
$344$		0			0
$345$	−13.2749	+	11.1390i	−0.714699	+	0.599703i
$346$		0			0
$347$	5.81918	+	2.11801i	0.312390	+	0.113701i	0.493457	−	0.869770i	$-0.335733\pi$
$347$	5.81918	+	2.11801i	0.312390	+	0.113701i	−0.181067	+	0.983471i	$0.557955\pi$
$348$		0			0
$349$	−5.71083	+	9.89145i	−0.305694	+	0.529477i	−0.977416	−	0.211326i	$-0.932222\pi$
$349$	−5.71083	+	9.89145i	−0.305694	+	0.529477i	0.671722	+	0.740803i	$0.265555\pi$
$350$		0			0
$351$	−3.79471	+	21.5209i	−0.202547	+	1.14870i
$352$		0			0
$353$	−1.61637	−	2.79963i	−0.0860305	−	0.149009i	0.819799	−	0.572651i	$-0.194085\pi$
$353$	−1.61637	−	2.79963i	−0.0860305	−	0.149009i	−0.905830	+	0.423642i	$0.860752\pi$
$354$		0			0
$355$	8.29311	+	6.95874i	0.440152	+	0.369332i
$356$		0			0
$357$	2.16562	−	0.788220i	0.114617	−	0.0417170i
$358$		0			0
$359$	0.981506	+	5.56640i	0.0518019	+	0.293783i	0.999692	−	0.0248140i	$-0.00789935\pi$
$359$	0.981506	+	5.56640i	0.0518019	+	0.293783i	−0.947890	+	0.318597i	$0.896788\pi$
$360$		0			0
$361$	−12.1929	−	14.5717i	−0.641729	−	0.766931i
$362$		0			0
$363$	−0.834227	−	4.73114i	−0.0437856	−	0.248320i
$364$		0			0
$365$	1.33027	−	0.484180i	0.0696298	−	0.0253432i
$366$		0			0
$367$	−0.742863	−	0.623336i	−0.0387771	−	0.0325379i	0.623193	−	0.782068i	$-0.285835\pi$
$367$	−0.742863	−	0.623336i	−0.0387771	−	0.0325379i	−0.661970	+	0.749530i	$0.730279\pi$
$368$		0			0
$369$	10.8994	+	18.8783i	0.567398	+	0.982763i
$370$		0			0
$371$	−0.841914	+	4.77473i	−0.0437100	+	0.247892i
$372$		0			0
$373$	8.27654	−	14.3354i	0.428543	−	0.742258i	−0.568201	−	0.822890i	$-0.692360\pi$
$373$	8.27654	−	14.3354i	0.428543	−	0.742258i	0.996744	+	0.0806318i	$0.0256938\pi$
$374$		0			0
$375$	−0.793245	−	0.288717i	−0.0409630	−	0.0149093i
$376$		0			0
$377$	−0.370680	+	0.311037i	−0.0190910	+	0.0160192i
$378$		0			0
$379$	22.9306			1.17787			0.588934	−	0.808181i	$-0.299548\pi$
$379$	22.9306			1.17787			0.588934	+	0.808181i	$0.299548\pi$
$380$		0			0
$381$	18.4003			0.942676
$382$		0			0
$383$	−12.8570	+	10.7883i	−0.656963	+	0.551257i	−0.909175	−	0.416415i	$-0.863286\pi$
$383$	−12.8570	+	10.7883i	−0.656963	+	0.551257i	0.252212	+	0.967672i	$0.418842\pi$
$384$		0			0
$385$	−6.57362	−	2.39260i	−0.335023	−	0.121938i
$386$		0			0
$387$	−6.51293	+	11.2807i	−0.331071	+	0.573431i
$388$		0			0
$389$	2.18972	−	12.4185i	0.111023	−	0.629643i	−0.877620	−	0.479358i	$-0.840870\pi$
$389$	2.18972	−	12.4185i	0.111023	−	0.629643i	0.988643	−	0.150285i	$-0.0480192\pi$
$390$		0			0
$391$	−9.45137	−	16.3703i	−0.477976	−	0.827879i
$392$		0			0
$393$	−1.38253	−	1.16008i	−0.0697396	−	0.0585185i
$394$		0			0
$395$	5.15597	−	1.87662i	0.259425	−	0.0944229i
$396$		0			0
$397$	3.86953	+	21.9452i	0.194206	+	1.10140i	0.913545	+	0.406738i	$0.133334\pi$
$397$	3.86953	+	21.9452i	0.194206	+	1.10140i	−0.719339	+	0.694659i	$0.755555\pi$
$398$		0			0
$399$	−2.55219	−	0.685746i	−0.127769	−	0.0343302i
$400$		0			0
$401$	5.54626	+	31.4544i	0.276967	+	1.57076i	0.732644	+	0.680612i	$0.238286\pi$
$401$	5.54626	+	31.4544i	0.276967	+	1.57076i	−0.455677	+	0.890145i	$0.650603\pi$
$402$		0			0
$403$	27.7631	−	10.1049i	1.38298	−	0.503362i
$404$		0			0
$405$	0.650039	+	0.545448i	0.0323007	+	0.0271035i
$406$		0			0
$407$	11.1432	+	19.3005i	0.552346	+	0.956691i
$408$		0			0
$409$	1.86728	−	10.5899i	0.0923313	−	0.523637i	−0.903201	−	0.429217i	$-0.858789\pi$
$409$	1.86728	−	10.5899i	0.0923313	−	0.523637i	0.995533	−	0.0944194i	$-0.0300995\pi$
$410$		0			0
$411$	−2.22875	+	3.86031i	−0.109936	+	0.190415i
$412$		0			0
$413$	5.68533	+	2.06929i	0.279757	+	0.101823i
$414$		0			0
$415$	−14.2341	+	11.9438i	−0.698723	+	0.586298i
$416$		0			0
$417$	7.76538			0.380272
$418$		0			0
$419$	5.43928			0.265726			0.132863	−	0.991134i	$-0.457583\pi$
$419$	5.43928			0.265726			0.132863	+	0.991134i	$0.457583\pi$
$420$		0			0
$421$	−1.90505	+	1.59852i	−0.0928463	+	0.0779073i	−0.688029	−	0.725683i	$-0.741524\pi$
$421$	−1.90505	+	1.59852i	−0.0928463	+	0.0779073i	0.595183	+	0.803590i	$0.297080\pi$
$422$		0			0
$423$	−0.0411997	−	0.0149955i	−0.00200320	−	0.000729104i
$424$		0			0
$425$	9.96347	−	17.2572i	0.483299	−	0.837099i
$426$		0			0
$427$	−1.21392	+	6.88448i	−0.0587457	+	0.333163i
$428$		0			0
$429$	−8.90986	−	15.4323i	−0.430172	−	0.745080i
$430$		0			0
$431$	−20.2174	−	16.9644i	−0.973840	−	0.817149i	0.00930869	−	0.999957i	$-0.497037\pi$
$431$	−20.2174	−	16.9644i	−0.973840	−	0.817149i	−0.983149	+	0.182808i	$0.941481\pi$
$432$		0			0
$433$	4.03750	−	1.46953i	0.194030	−	0.0706211i	−0.243178	−	0.969982i	$-0.578190\pi$
$433$	4.03750	−	1.46953i	0.194030	−	0.0706211i	0.437207	+	0.899361i	$0.355968\pi$
$434$		0			0
$435$	0.0702426	+	0.398366i	0.00336788	+	0.0191002i
$436$		0			0
$437$	−1.90409	+	21.5921i	−0.0910851	+	1.03289i
$438$		0			0
$439$	−5.68530	−	32.2429i	−0.271345	−	1.53887i	−0.750339	−	0.661054i	$-0.770110\pi$
$439$	−5.68530	−	32.2429i	−0.271345	−	1.53887i	0.478994	−	0.877818i	$-0.341002\pi$
$440$		0			0
$441$	−11.4059	+	4.15141i	−0.543138	+	0.197686i
$442$		0			0
$443$	−29.9985	−	25.1718i	−1.42527	−	1.19595i	−0.948441	−	0.316953i	$-0.897340\pi$
$443$	−29.9985	−	25.1718i	−1.42527	−	1.19595i	−0.476833	−	0.878994i	$-0.658215\pi$
$444$		0			0
$445$	3.82541	+	6.62580i	0.181342	+	0.314093i
$446$		0			0
$447$	−1.11096	+	6.30055i	−0.0525465	+	0.298006i
$448$		0			0
$449$	13.6553	−	23.6517i	0.644435	−	1.11619i	−0.339997	−	0.940427i	$-0.610426\pi$
$449$	13.6553	−	23.6517i	0.644435	−	1.11619i	0.984432	−	0.175768i	$-0.0562408\pi$
$450$		0			0
$451$	−44.3229	−	16.1322i	−2.08708	−	0.759636i
$452$		0			0
$453$	−5.39832	+	4.52973i	−0.253635	+	0.212825i
$454$		0			0
$455$	−7.42816			−0.348238
$456$		0			0
$457$	15.2138			0.711670			0.355835	−	0.934549i	$-0.384196\pi$
$457$	15.2138			0.711670			0.355835	+	0.934549i	$0.384196\pi$
$458$		0			0
$459$	−15.2649	+	12.8088i	−0.712505	+	0.597863i
$460$		0			0
$461$	−7.80157	−	2.83954i	−0.363356	−	0.132251i	0.153889	−	0.988088i	$-0.450820\pi$
$461$	−7.80157	−	2.83954i	−0.363356	−	0.132251i	−0.517245	+	0.855838i	$0.673042\pi$
$462$		0			0
$463$	−18.3022	+	31.7003i	−0.850574	+	1.47324i	0.0301179	+	0.999546i	$0.490412\pi$
$463$	−18.3022	+	31.7003i	−0.850574	+	1.47324i	−0.880691	+	0.473690i	$0.842922\pi$
$464$		0			0
$465$	4.28882	−	24.3231i	0.198889	−	1.12796i
$466$		0			0
$467$	−3.06233	−	5.30410i	−0.141708	−	0.245445i	0.786432	−	0.617677i	$-0.211926\pi$
$467$	−3.06233	−	5.30410i	−0.141708	−	0.245445i	−0.928140	+	0.372232i	$0.878593\pi$
$468$		0			0
$469$	−5.57755	−	4.68012i	−0.257547	−	0.216108i
$470$		0			0
$471$	−0.631217	+	0.229744i	−0.0290849	+	0.0105860i
$472$		0			0
$473$	−4.89426	−	27.7567i	−0.225038	−	1.27626i
$474$		0			0
$475$	−20.7161	+	9.64269i	−0.950522	+	0.442437i
$476$		0			0
$477$	−2.74343	−	15.5588i	−0.125613	−	0.712388i
$478$		0			0
$479$	−21.2232	+	7.72462i	−0.969713	+	0.352947i	−0.777833	−	0.628471i	$-0.783681\pi$
$479$	−21.2232	+	7.72462i	−0.969713	+	0.352947i	−0.191881	+	0.981418i	$0.561459\pi$
$480$		0			0
$481$	18.1282	+	15.2114i	0.826575	+	0.693578i
$482$		0			0
$483$	1.50745	+	2.61098i	0.0685914	+	0.118804i
$484$		0			0
$485$	−5.97597	+	33.8914i	−0.271355	+	1.53893i
$486$		0			0
$487$	2.27441	−	3.93940i	0.103063	−	0.178511i	−0.809882	−	0.586593i	$-0.800469\pi$
$487$	2.27441	−	3.93940i	0.103063	−	0.178511i	0.912945	+	0.408082i	$0.133802\pi$
$488$		0			0
$489$	24.0363	+	8.74850i	1.08696	+	0.395621i
$490$		0			0
$491$	31.2170	−	26.1941i	1.40880	−	1.18213i	0.451773	−	0.892133i	$-0.350792\pi$
$491$	31.2170	−	26.1941i	1.40880	−	1.18213i	0.957029	−	0.289993i	$-0.0936528\pi$
$492$		0			0
$493$	−0.441242			−0.0198725
$494$		0			0
$495$	22.7953			1.02457
$496$		0			0
$497$	1.44282	−	1.21067i	0.0647193	−	0.0543060i
$498$		0			0
$499$	−7.41383	−	2.69841i	−0.331889	−	0.120798i	0.170701	−	0.985323i	$-0.445397\pi$
$499$	−7.41383	−	2.69841i	−0.331889	−	0.120798i	−0.502589	+	0.864525i	$0.667619\pi$
$500$		0			0
$501$	8.23360	−	14.2610i	0.367850	−	0.637135i
$502$		0			0
$503$	2.85027	−	16.1647i	0.127087	−	0.720748i	−0.852959	−	0.521978i	$-0.825194\pi$
$503$	2.85027	−	16.1647i	0.127087	−	0.720748i	0.980046	−	0.198770i	$-0.0636946\pi$
$504$		0			0
$505$	10.7073	+	18.5456i	0.476469	+	0.825268i
$506$		0			0
$507$	−3.65128	−	3.06379i	−0.162159	−	0.136068i
$508$		0			0
$509$	−35.7499	+	13.0119i	−1.58459	+	0.576743i	−0.976195	−	0.216894i	$-0.930407\pi$
$509$	−35.7499	+	13.0119i	−1.58459	+	0.576743i	−0.608392	+	0.793637i	$0.708185\pi$
$510$		0			0
$511$	−0.0427682	−	0.242550i	−0.00189195	−	0.0107298i
$512$		0			0
$513$	22.7648	−	1.97582i	1.00509	−	0.0872347i
$514$		0			0
$515$	7.24848	+	41.1082i	0.319406	+	1.81144i
$516$		0			0
$517$	0.0891465	−	0.0324467i	0.00392066	−	0.00142700i
$518$		0			0
$519$	−2.80134	−	2.35061i	−0.122965	−	0.103180i
$520$		0			0
$521$	4.73838	+	8.20711i	0.207592	+	0.359560i	0.950955	−	0.309328i	$-0.100104\pi$
$521$	4.73838	+	8.20711i	0.207592	+	0.359560i	−0.743363	+	0.668888i	$0.766771\pi$
$522$		0			0
$523$	2.07903	−	11.7907i	0.0909095	−	0.515573i	−0.905015	−	0.425380i	$-0.860140\pi$
$523$	2.07903	−	11.7907i	0.0909095	−	0.515573i	0.995924	−	0.0901932i	$-0.0287484\pi$
$524$		0			0
$525$	−1.58913	+	2.75245i	−0.0693553	+	0.120127i
$526$		0			0
$527$	25.3162	+	9.21436i	1.10279	+	0.401384i
$528$		0			0
$529$	1.32430	−	1.11122i	0.0575783	−	0.0483139i
$530$		0			0
$531$	−19.7150			−0.855557
$532$		0			0
$533$	−50.0846			−2.16941
$534$		0			0
$535$	23.3442	−	19.5881i	1.00926	−	0.846868i
$536$		0			0
$537$	−0.104448	−	0.0380158i	−0.00450724	−	0.00164050i
$538$		0			0
$539$	13.1318	−	22.7450i	0.565627	−	0.979694i
$540$		0			0
$541$	−5.84939	+	33.1736i	−0.251485	+	1.42624i	0.553452	+	0.832881i	$0.313310\pi$
$541$	−5.84939	+	33.1736i	−0.251485	+	1.42624i	−0.804937	+	0.593361i	$0.797801\pi$
$542$		0			0
$543$	4.19977	+	7.27421i	0.180229	+	0.312166i
$544$		0			0
$545$	20.2660	+	17.0052i	0.868100	+	0.728422i
$546$		0			0
$547$	−14.2090	+	5.17166i	−0.607534	+	0.221124i	−0.627424	−	0.778678i	$-0.715891\pi$
$547$	−14.2090	+	5.17166i	−0.607534	+	0.221124i	0.0198899	+	0.999802i	$0.493668\pi$
$548$		0			0
$549$	−3.95564	−	22.4335i	−0.168822	−	0.957439i
$550$		0			0
$551$	0.414271	+	0.290502i	0.0176485	+	0.0123758i
$552$		0			0
$553$	−0.165764	−	0.940092i	−0.00704899	−	0.0399768i
$554$		0			0
$555$	18.5897	−	6.76609i	0.789088	−	0.287205i
$556$		0			0
$557$	14.7963	+	12.4155i	0.626937	+	0.526063i	0.899976	−	0.435940i	$-0.143584\pi$
$557$	14.7963	+	12.4155i	0.626937	+	0.526063i	−0.273038	+	0.962003i	$0.588029\pi$
$558$		0			0
$559$	−14.9641	−	25.9185i	−0.632912	−	1.09624i
$560$		0			0
$561$	2.82165	−	16.0024i	0.119130	−	0.675621i
$562$		0			0
$563$	−19.1965	+	33.2493i	−0.809037	+	1.40129i	0.104495	+	0.994525i	$0.466677\pi$
$563$	−19.1965	+	33.2493i	−0.809037	+	1.40129i	−0.913532	+	0.406767i	$0.866656\pi$
$564$		0			0
$565$	6.26338	+	2.27969i	0.263503	+	0.0959071i
$566$		0			0
$567$	0.113093	−	0.0948960i	0.00474944	−	0.00398526i
$568$		0			0
$569$	−4.84346			−0.203048			−0.101524	−	0.994833i	$-0.532372\pi$
$569$	−4.84346			−0.203048			−0.101524	+	0.994833i	$0.532372\pi$
$570$		0			0
$571$	37.5129			1.56987			0.784934	−	0.619580i	$-0.212697\pi$
$571$	37.5129			1.56987			0.784934	+	0.619580i	$0.212697\pi$
$572$		0			0
$573$	12.5200	−	10.5055i	0.523029	−	0.438873i
$574$		0			0
$575$	24.4965	+	8.91599i	1.02157	+	0.371822i
$576$		0			0
$577$	−1.22241	+	2.11728i	−0.0508896	+	0.0881433i	−0.890348	−	0.455280i	$-0.849539\pi$
$577$	−1.22241	+	2.11728i	−0.0508896	+	0.0881433i	0.839458	+	0.543424i	$0.182872\pi$
$578$		0			0
$579$	0.489900	−	2.77836i	0.0203596	−	0.115465i
$580$		0			0
$581$	1.61637	+	2.79963i	0.0670582	+	0.116148i
$582$		0			0
$583$	26.1872	+	21.9736i	1.08456	+	0.910055i
$584$		0			0
$585$	22.7454	−	8.27865i	0.940407	−	0.342280i
$586$		0			0
$587$	1.79011	+	10.1522i	0.0738856	+	0.419026i	0.999206	+	0.0398401i	$0.0126849\pi$
$587$	1.79011	+	10.1522i	0.0738856	+	0.419026i	−0.925320	+	0.379186i	$0.876204\pi$
$588$		0			0
$589$	−17.7023	−	25.3187i	−0.729410	−	1.04324i
$590$		0			0
$591$	1.21693	+	6.90154i	0.0500577	+	0.283891i
$592$		0			0
$593$	−9.02362	+	3.28433i	−0.370556	+	0.134871i	−0.520584	−	0.853810i	$-0.674286\pi$
$593$	−9.02362	+	3.28433i	−0.370556	+	0.134871i	0.150028	+	0.988682i	$0.452064\pi$
$594$		0			0
$595$	−5.18880	−	4.35392i	−0.212720	−	0.178493i
$596$		0			0
$597$	−3.00211	−	5.19980i	−0.122868	−	0.212814i
$598$		0			0
$599$	3.30188	−	18.7259i	0.134911	−	0.765118i	−0.840011	−	0.542570i	$-0.817451\pi$
$599$	3.30188	−	18.7259i	0.134911	−	0.765118i	0.974922	−	0.222548i	$-0.0714375\pi$
$600$		0			0
$601$	−7.65441	+	13.2578i	−0.312230	+	0.540798i	−0.978845	−	0.204604i	$-0.934409\pi$
$601$	−7.65441	+	13.2578i	−0.312230	+	0.540798i	0.666615	+	0.745402i	$0.267743\pi$
$602$		0			0
$603$	22.2947	+	8.11461i	0.907911	+	0.330452i
$604$		0			0
$605$	−10.8165	+	9.07610i	−0.439752	+	0.368996i
$606$		0			0
$607$	3.95975			0.160721			0.0803607	−	0.996766i	$-0.474393\pi$
$607$	3.95975			0.160721			0.0803607	+	0.996766i	$0.474393\pi$
$608$		0			0
$609$	0.0703761			0.00285178
$610$		0			0
$611$	0.0771676	−	0.0647513i	0.00312187	−	0.00261956i
$612$		0			0
$613$	10.0409	+	3.65457i	0.405547	+	0.147607i	0.536736	−	0.843751i	$-0.319657\pi$
$613$	10.0409	+	3.65457i	0.405547	+	0.147607i	−0.131189	+	0.991357i	$0.541879\pi$
$614$		0			0
$615$	−20.9344	+	36.2594i	−0.844156	+	1.46212i
$616$		0			0
$617$	0.954966	−	5.41588i	0.0384455	−	0.218035i	−0.959532	−	0.281599i	$-0.909135\pi$
$617$	0.954966	−	5.41588i	0.0384455	−	0.218035i	0.997978	+	0.0635633i	$0.0202465\pi$
$618$		0			0
$619$	13.8634	+	24.0122i	0.557219	+	0.965131i	0.997727	+	0.0673827i	$0.0214648\pi$
$619$	13.8634	+	24.0122i	0.557219	+	0.965131i	−0.440508	+	0.897748i	$0.645202\pi$
$620$		0			0
$621$	−19.9697	−	16.7566i	−0.801357	−	0.672418i
$622$		0			0
$623$	1.25080	−	0.455254i	0.0501123	−	0.0182394i
$624$		0			0
$625$	−4.12069	−	23.3696i	−0.164828	−	0.934784i
$626$		0			0
$627$	−13.1847	+	13.1665i	−0.526547	+	0.525820i
$628$		0			0
$629$	3.74716	+	21.2512i	0.149409	+	0.847342i
$630$		0			0
$631$	−0.0204469	+	0.00744206i	−0.000813978	+	0.000296264i	−0.342427	−	0.939544i	$-0.611249\pi$
$631$	−0.0204469	+	0.00744206i	−0.000813978	+	0.000296264i	0.341613	+	0.939841i	$0.389027\pi$
$632$		0			0
$633$	6.24776	+	5.24249i	0.248326	+	0.208370i
$634$		0			0
$635$	−27.0404	−	46.8353i	−1.07306	−	1.85860i
$636$		0			0
$637$	4.84269	−	27.4643i	0.191875	−	1.08817i
$638$		0			0
$639$	−3.06870	+	5.31515i	−0.121396	+	0.210264i
$640$		0			0
$641$	−27.9085	−	10.1579i	−1.10232	−	0.401211i	−0.274148	−	0.961687i	$-0.588396\pi$
$641$	−27.9085	−	10.1579i	−1.10232	−	0.401211i	−0.828170	+	0.560476i	$0.810618\pi$
$642$		0			0
$643$	12.1147	−	10.1655i	0.477758	−	0.400887i	−0.371857	−	0.928290i	$-0.621279\pi$
$643$	12.1147	−	10.1655i	0.477758	−	0.400887i	0.849615	+	0.527404i	$0.176834\pi$
$644$		0			0
$645$	−25.0187			−0.985111
$646$		0			0
$647$	−35.3133			−1.38831			−0.694154	−	0.719826i	$-0.744221\pi$
$647$	−35.3133			−1.38831			−0.694154	+	0.719826i	$0.744221\pi$
$648$		0			0
$649$	32.6784	−	27.4204i	1.28274	−	1.07635i
$650$		0			0
$651$	−4.03783	−	1.46965i	−0.158255	−	0.0576001i
$652$		0			0
$653$	−24.0337	+	41.6275i	−0.940510	+	1.62901i	−0.176010	+	0.984388i	$0.556319\pi$
$653$	−24.0337	+	41.6275i	−0.940510	+	1.62901i	−0.764500	+	0.644623i	$0.777014\pi$
$654$		0			0
$655$	−0.921106	+	5.22385i	−0.0359906	+	0.204113i
$656$		0			0
$657$	0.401279	+	0.695036i	0.0156554	+	0.0271159i
$658$		0			0
$659$	4.45303	+	3.73654i	0.173466	+	0.145555i	0.725387	−	0.688341i	$-0.241661\pi$
$659$	4.45303	+	3.73654i	0.173466	+	0.145555i	−0.551922	+	0.833896i	$0.686105\pi$
$660$		0			0
$661$	−26.1778	+	9.52794i	−1.01820	+	0.370594i	−0.796576	−	0.604539i	$-0.793357\pi$
$661$	−26.1778	+	9.52794i	−1.01820	+	0.370594i	−0.221623	+	0.975133i	$0.571135\pi$
$662$		0			0
$663$	−2.99616	−	16.9921i	−0.116361	−	0.659918i
$664$		0			0
$665$	2.00513	+	7.50396i	0.0777555	+	0.290991i
$666$		0			0
$667$	−0.100236	−	0.568468i	−0.00388116	−	0.0220112i
$668$		0			0
$669$	−14.3944	+	5.23912i	−0.556518	+	0.202556i
$670$		0			0
$671$	37.7581	+	31.6828i	1.45764	+	1.22310i
$672$		0			0
$673$	−22.5701	−	39.0926i	−0.870015	−	1.50691i	−0.861980	−	0.506943i	$-0.830775\pi$
$673$	−22.5701	−	39.0926i	−0.870015	−	1.50691i	−0.00803563	−	0.999968i	$-0.502558\pi$
$674$		0			0
$675$	4.77204	−	27.0636i	0.183676	−	1.04168i
$676$		0			0
$677$	−2.71076	+	4.69517i	−0.104183	+	0.180450i	−0.913404	−	0.407054i	$-0.866556\pi$
$677$	−2.71076	+	4.69517i	−0.104183	+	0.180450i	0.809221	+	0.587504i	$0.199889\pi$
$678$		0			0
$679$	5.62624	+	2.04778i	0.215915	+	0.0785868i
$680$		0			0
$681$	−21.1383	+	17.7371i	−0.810021	+	0.679689i
$682$		0			0
$683$	−33.9254			−1.29812			−0.649060	−	0.760738i	$-0.724837\pi$
$683$	−33.9254			−1.29812			−0.649060	+	0.760738i	$0.724837\pi$
$684$		0			0
$685$	13.1012			0.500569
$686$		0			0
$687$	16.5417	−	13.8801i	0.631105	−	0.529560i
$688$		0			0
$689$	34.1101	+	12.4151i	1.29949	+	0.472976i
$690$		0			0
$691$	14.2022	−	24.5990i	0.540278	−	0.935788i	−0.458610	−	0.888638i	$-0.651653\pi$
$691$	14.2022	−	24.5990i	0.540278	−	0.935788i	0.998888	−	0.0471508i	$-0.0150141\pi$
$692$		0			0
$693$	0.688669	−	3.90564i	0.0261604	−	0.148363i
$694$		0			0
$695$	−11.4117	−	19.7656i	−0.432870	−	0.749753i
$696$		0			0
$697$	−34.9857	−	29.3565i	−1.32518	−	1.11196i
$698$		0			0
$699$	22.6553	−	8.24586i	0.856903	−	0.311887i
$700$		0			0
$701$	−3.72496	−	21.1253i	−0.140690	−	0.797891i	−0.970727	−	0.240184i	$-0.922792\pi$
$701$	−3.72496	−	21.1253i	−0.140690	−	0.797891i	0.830038	−	0.557707i	$-0.188319\pi$
$702$		0			0
$703$	10.4731	−	22.4193i	0.395002	−	0.845559i
$704$		0			0
$705$	−0.0146230	−	0.0829313i	−0.000550735	−	0.00312337i
$706$		0			0
$707$	3.50099	−	1.27426i	0.131668	−	0.0479233i
$708$		0			0
$709$	4.40631	+	3.69734i	0.165483	+	0.138856i	0.721768	−	0.692135i	$-0.243330\pi$
$709$	4.40631	+	3.69734i	0.165483	+	0.138856i	−0.556286	+	0.830991i	$0.687774\pi$
$710$		0			0
$711$	1.55531	+	2.69387i	0.0583285	+	0.101028i
$712$		0			0
$713$	−6.12014	+	34.7090i	−0.229201	+	1.29986i
$714$		0			0
$715$	−26.1872	+	45.3575i	−0.979345	+	1.69627i
$716$		0			0
$717$	2.09479	+	0.762442i	0.0782315	+	0.0284739i
$718$		0			0
$719$	−9.67624	+	8.11933i	−0.360863	+	0.302800i	−0.805135	−	0.593092i	$-0.797907\pi$
$719$	−9.67624	+	8.11933i	−0.360863	+	0.302800i	0.444272	+	0.895892i	$0.353463\pi$
$720$		0			0
$721$	7.26226			0.270461
$722$		0			0
$723$	−1.33879			−0.0497900
$724$		0			0
$725$	0.466148	−	0.391145i	0.0173123	−	0.0145267i
$726$		0			0
$727$	19.6845	+	7.16458i	0.730058	+	0.265719i	0.680189	−	0.733036i	$-0.261897\pi$
$727$	19.6845	+	7.16458i	0.730058	+	0.265719i	0.0498687	+	0.998756i	$0.484120\pi$
$728$		0			0
$729$	−8.80279	+	15.2469i	−0.326029	+	0.564699i
$730$		0			0
$731$	4.73894	−	26.8759i	0.175276	−	0.994040i
$732$		0			0
$733$	−13.8459	−	23.9818i	−0.511410	−	0.885788i	−0.999913	−	0.0132253i	$-0.995790\pi$
$733$	−13.8459	−	23.9818i	−0.511410	−	0.885788i	0.488503	−	0.872562i	$-0.337543\pi$
$734$		0			0
$735$	−17.8590	−	14.9855i	−0.658738	−	0.552747i
$736$		0			0
$737$	−48.2406	+	17.5581i	−1.77696	+	0.646762i
$738$		0			0
$739$	1.13266	+	6.42366i	0.0416658	+	0.236298i	0.998528	−	0.0542449i	$-0.0172752\pi$
$739$	1.13266	+	6.42366i	0.0416658	+	0.236298i	−0.956862	+	0.290543i	$0.906164\pi$
$740$		0			0
$741$	−8.37412	+	17.9260i	−0.307631	+	0.658530i
$742$		0			0
$743$	8.37272	+	47.4840i	0.307165	+	1.74202i	0.613134	+	0.789979i	$0.289909\pi$
$743$	8.37272	+	47.4840i	0.307165	+	1.74202i	−0.305969	+	0.952042i	$0.598980\pi$
$744$		0			0
$745$	17.6697	−	6.43126i	0.647369	−	0.235623i
$746$		0			0
$747$	−8.06957	−	6.77117i	−0.295250	−	0.247744i
$748$		0			0
$749$	−2.65088	−	4.59146i	−0.0968611	−	0.167768i
$750$		0			0
$751$	−1.08778	+	6.16908i	−0.0396935	+	0.225113i	−0.998201	−	0.0599538i	$-0.980905\pi$
$751$	−1.08778	+	6.16908i	−0.0396935	+	0.225113i	0.958508	+	0.285067i	$0.0920158\pi$
$752$		0			0
$753$	3.78029	−	6.54766i	0.137762	−	0.238610i
$754$		0			0
$755$	19.4629	+	7.08392i	0.708328	+	0.257810i
$756$		0			0
$757$	24.5477	−	20.5979i	0.892200	−	0.748645i	−0.0764503	−	0.997073i	$-0.524359\pi$
$757$	24.5477	−	20.5979i	0.892200	−	0.748645i	0.968650	+	0.248429i	$0.0799142\pi$
$758$		0			0
$759$	21.2574			0.771595
$760$		0			0
$761$	43.1308			1.56349			0.781745	−	0.623598i	$-0.214330\pi$
$761$	43.1308			1.56349			0.781745	+	0.623598i	$0.214330\pi$
$762$		0			0
$763$	3.52584	−	2.95853i	0.127644	−	0.107106i
$764$		0			0
$765$	20.7408	+	7.54904i	0.749885	+	0.272936i
$766$		0			0
$767$	22.6485	−	39.2283i	0.817790	−	1.41645i
$768$		0			0
$769$	−5.88829	+	33.3942i	−0.212337	+	1.20422i	0.673131	+	0.739524i	$0.264949\pi$
$769$	−5.88829	+	33.3942i	−0.212337	+	1.20422i	−0.885468	+	0.464701i	$0.846162\pi$
$770$		0			0
$771$	5.38641	+	9.32954i	0.193987	+	0.335995i
$772$		0			0
$773$	14.2612	+	11.9666i	0.512939	+	0.430407i	0.862162	−	0.506633i	$-0.169110\pi$
$773$	14.2612	+	11.9666i	0.512939	+	0.430407i	−0.349223	+	0.937040i	$0.613554\pi$
$774$		0			0
$775$	−34.9134	+	12.7074i	−1.25413	+	0.456465i
$776$		0			0
$777$	−0.597656	−	3.38948i	−0.0214408	−	0.121597i
$778$		0			0
$779$	13.5196	+	50.5957i	0.484391	+	1.81278i
$780$		0			0
$781$	−2.30603	−	13.0782i	−0.0825163	−	0.467973i
$782$		0			0
$783$	−0.571815	+	0.208124i	−0.0204350	+	0.00743774i
$784$		0			0
$785$	1.51239	+	1.26905i	0.0539795	+	0.0452942i
$786$		0			0
$787$	7.59309	+	13.1516i	0.270664	+	0.468804i	0.969032	−	0.246935i	$-0.0794233\pi$
$787$	7.59309	+	13.1516i	0.270664	+	0.468804i	−0.698368	+	0.715739i	$0.746090\pi$
$788$		0			0
$789$	−0.406197	+	2.30366i	−0.0144610	+	0.0820123i
$790$		0			0
$791$	0.579813	−	1.00427i	0.0206158	−	0.0357076i
$792$		0			0
$793$	49.1818	+	17.9007i	1.74650	+	0.635673i
$794$		0			0
$795$	23.2454	−	19.5052i	0.824429	−	0.691778i
$796$		0			0
$797$	2.44693			0.0866746			0.0433373	−	0.999060i	$-0.486201\pi$
$797$	2.44693			0.0866746			0.0433373	+	0.999060i	$0.486201\pi$
$798$		0			0
$799$	0.0918572			0.00324967
$800$		0			0
$801$	−3.32264	+	2.78802i	−0.117400	+	0.0985100i
$802$		0			0
$803$	−1.63182	−	0.593935i	−0.0575858	−	0.0209595i
$804$		0			0
$805$	4.43058	−	7.67399i	0.156158	−	0.270473i
$806$		0			0
$807$	−1.87161	+	10.6144i	−0.0658839	+	0.373646i
$808$		0			0
$809$	−6.50615	−	11.2690i	−0.228744	−	0.396197i	0.728692	−	0.684842i	$-0.240129\pi$
$809$	−6.50615	−	11.2690i	−0.228744	−	0.396197i	−0.957436	+	0.288645i	$0.906795\pi$
$810$		0			0
$811$	9.08728	+	7.62513i	0.319098	+	0.267755i	0.788240	−	0.615368i	$-0.210993\pi$
$811$	9.08728	+	7.62513i	0.319098	+	0.267755i	−0.469143	+	0.883122i	$0.655437\pi$
$812$		0			0
$813$	18.9725	−	6.90542i	0.665394	−	0.242183i
$814$		0			0
$815$	−13.0548	−	74.0373i	−0.457289	−	2.59341i
$816$		0			0
$817$	−22.1436	+	22.1131i	−0.774708	+	0.773639i
$818$		0			0
$819$	−0.731262	−	4.14719i	−0.0255524	−	0.144915i
$820$		0			0
$821$	11.1000	−	4.04006i	0.387392	−	0.140999i	−0.140979	−	0.990013i	$-0.545025\pi$
$821$	11.1000	−	4.04006i	0.387392	−	0.140999i	0.528371	+	0.849013i	$0.322803\pi$
$822$		0			0
$823$	11.2113	+	9.40736i	0.390800	+	0.327920i	0.816925	−	0.576744i	$-0.195677\pi$
$823$	11.2113	+	9.40736i	0.390800	+	0.327920i	−0.426125	+	0.904664i	$0.640122\pi$
$824$		0			0
$825$	11.2046	+	19.4069i	0.390094	+	0.675662i
$826$		0			0
$827$	2.07253	−	11.7539i	0.0720691	−	0.408724i	−0.927336	−	0.374230i	$-0.877907\pi$
$827$	2.07253	−	11.7539i	0.0720691	−	0.408724i	0.999405	−	0.0344938i	$-0.0109819\pi$
$828$		0			0
$829$	−9.39076	+	16.2653i	−0.326154	+	0.564916i	−0.981745	−	0.190200i	$-0.939086\pi$
$829$	−9.39076	+	16.2653i	−0.326154	+	0.564916i	0.655591	+	0.755116i	$0.272420\pi$
$830$		0			0
$831$	−26.8562	−	9.77487i	−0.931632	−	0.339086i
$832$		0			0
$833$	19.4806	−	16.3462i	0.674963	−	0.566361i
$834$		0			0
$835$	−48.3991			−1.67492
$836$		0			0
$837$	37.1541			1.28423
$838$		0			0
$839$	−24.4639	+	20.5276i	−0.844587	+	0.708693i	−0.958591	−	0.284788i	$-0.908077\pi$
$839$	−24.4639	+	20.5276i	−0.844587	+	0.708693i	0.114004	+	0.993480i	$0.463632\pi$
$840$		0			0
$841$	27.2384	+	9.91398i	0.939256	+	0.341861i
$842$		0			0
$843$	−11.5914	+	20.0769i	−0.399229	+	0.691486i
$844$		0			0
$845$	−2.43265	+	13.7962i	−0.0836856	+	0.474605i
$846$		0			0
$847$	1.22828	+	2.12744i	0.0422041	+	0.0730997i
$848$		0			0
$849$	−13.8991	−	11.6628i	−0.477017	−	0.400265i
$850$		0			0
$851$	−26.5275	+	9.65521i	−0.909350	+	0.330976i
$852$		0			0
$853$	−3.31018	−	18.7730i	−0.113338	−	0.642775i	−0.987559	−	0.157246i	$-0.949738\pi$
$853$	−3.31018	−	18.7730i	−0.113338	−	0.642775i	0.874221	−	0.485528i	$-0.161373\pi$
$854$		0			0
$855$	−14.5029	−	20.7428i	−0.495990	−	0.709389i
$856$		0			0
$857$	−7.69018	−	43.6132i	−0.262691	−	1.48980i	−0.775529	−	0.631312i	$-0.782517\pi$
$857$	−7.69018	−	43.6132i	−0.262691	−	1.48980i	0.512838	−	0.858486i	$-0.328594\pi$
$858$		0			0
$859$	19.9800	−	7.27211i	0.681707	−	0.248121i	0.0221269	−	0.999755i	$-0.492956\pi$
$859$	19.9800	−	7.27211i	0.681707	−	0.248121i	0.659580	+	0.751634i	$0.270734\pi$
$860$		0			0
$861$	5.58006	+	4.68223i	0.190168	+	0.159570i
$862$		0			0
$863$	−8.32952	−	14.4272i	−0.283540	−	0.491106i	0.688714	−	0.725033i	$-0.258176\pi$
$863$	−8.32952	−	14.4272i	−0.283540	−	0.491106i	−0.972254	+	0.233927i	$0.924842\pi$
$864$		0			0
$865$	−1.86638	+	10.5848i	−0.0634588	+	0.359893i
$866$		0			0
$867$	−1.38869	+	2.40529i	−0.0471625	+	0.0816879i
$868$		0			0
$869$	−6.32473	−	2.30201i	−0.214552	−	0.0780904i
$870$		0			0
$871$	−41.7583	+	35.0394i	−1.41493	+	1.18726i
$872$		0			0
$873$	−19.5101			−0.660316
$874$		0			0
$875$	0.431652			0.0145925
$876$		0			0
$877$	−19.5025	+	16.3646i	−0.658554	+	0.552592i	−0.909653	−	0.415369i	$-0.863652\pi$
$877$	−19.5025	+	16.3646i	−0.658554	+	0.552592i	0.251099	+	0.967961i	$0.419208\pi$
$878$		0			0
$879$	22.1324	+	8.05554i	0.746508	+	0.271707i
$880$		0			0
$881$	13.5261	−	23.4279i	0.455707	−	0.789307i	−0.543022	−	0.839719i	$-0.682720\pi$
$881$	13.5261	−	23.4279i	0.455707	−	0.789307i	0.998729	+	0.0504114i	$0.0160532\pi$
$882$		0			0
$883$	−1.60183	+	9.08441i	−0.0539057	+	0.305715i	−0.999825	−	0.0186864i	$-0.994052\pi$
$883$	−1.60183	+	9.08441i	−0.0539057	+	0.305715i	0.945920	+	0.324401i	$0.105163\pi$
$884$		0			0
$885$	−18.9332	−	32.7933i	−0.636434	−	1.10234i
$886$		0			0
$887$	−12.8042	−	10.7440i	−0.429922	−	0.360748i	0.402000	−	0.915640i	$-0.368315\pi$
$887$	−12.8042	−	10.7440i	−0.429922	−	0.360748i	−0.831922	+	0.554892i	$0.812760\pi$
$888$		0			0
$889$	−8.84144	+	3.21802i	−0.296532	+	0.107929i
$890$		0			0
$891$	−0.180754	−	1.02511i	−0.00605548	−	0.0343423i
$892$		0			0
$893$	−0.0862423	−	0.0604763i	−0.00288599	−	0.00202376i
$894$		0			0
$895$	0.0567283	+	0.321722i	0.00189622	+	0.0107540i
$896$		0			0
$897$	21.2109	−	7.72013i	0.708211	−	0.257768i
$898$		0			0
$899$	0.630227	+	0.528823i	0.0210192	+	0.0176372i
$900$		0			0
$901$	16.5500	+	28.6655i	0.551362	+	0.954986i
$902$		0			0
$903$	−0.755840	+	4.28658i	−0.0251528	+	0.142649i
$904$		0			0
$905$	12.3436	−	21.3798i	0.410316	−	0.710688i
$906$		0			0
$907$	−6.49613	−	2.36440i	−0.215700	−	0.0785085i	0.231910	−	0.972737i	$-0.425503\pi$
$907$	−6.49613	−	2.36440i	−0.215700	−	0.0785085i	−0.447610	+	0.894229i	$0.647725\pi$
$908$		0			0
$909$	−9.30005	+	7.80367i	−0.308463	+	0.258831i
$910$		0			0
$911$	53.3065			1.76612			0.883062	−	0.469256i	$-0.155478\pi$
$911$	53.3065			1.76612			0.883062	+	0.469256i	$0.155478\pi$
$912$		0			0
$913$	22.7933			0.754348
$914$		0			0
$915$	33.5165	−	28.1237i	1.10802	−	0.929740i
$916$		0			0
$917$	0.867201	+	0.315635i	0.0286375	+	0.0104232i
$918$		0			0
$919$	−25.0547	+	43.3960i	−0.826477	+	1.43150i	0.0743077	+	0.997235i	$0.476325\pi$
$919$	−25.0547	+	43.3960i	−0.826477	+	1.43150i	−0.900785	+	0.434265i	$0.857008\pi$
$920$		0			0
$921$	1.76255	−	9.99592i	0.0580780	−	0.329377i
$922$		0			0
$923$	−7.05063	−	12.2120i	−0.232074	−	0.401964i
$924$		0			0
$925$	−22.7971	−	19.1290i	−0.749564	−	0.628959i
$926$		0			0
$927$	−22.2374	+	8.09375i	−0.730372	+	0.265834i
$928$		0			0
$929$	6.50614	+	36.8982i	0.213460	+	1.21059i	0.883559	+	0.468319i	$0.155140\pi$
$929$	6.50614	+	36.8982i	0.213460	+	1.21059i	−0.670100	+	0.742271i	$0.733749\pi$
$930$		0			0
$931$	−29.0517	+	2.52148i	−0.952132	+	0.0826383i
$932$		0			0
$933$	6.25872	+	35.4950i	0.204901	+	1.16205i
$934$		0			0
$935$	−44.8783	+	16.3344i	−1.46768	+	0.534191i
$936$		0			0
$937$	−26.3267	−	22.0907i	−0.860057	−	0.721673i	0.101924	−	0.994792i	$-0.467500\pi$
$937$	−26.3267	−	22.0907i	−0.860057	−	0.721673i	−0.961980	+	0.273119i	$0.911945\pi$
$938$		0			0
$939$	−4.80852	−	8.32860i	−0.156920	−	0.271793i
$940$		0			0
$941$	2.30597	−	13.0778i	0.0751724	−	0.426324i	−0.923875	−	0.382694i	$-0.874996\pi$
$941$	2.30597	−	13.0778i	0.0751724	−	0.426324i	0.999048	−	0.0436304i	$-0.0138924\pi$
$942$		0			0
$943$	29.8733	−	51.7421i	0.972810	−	1.68496i
$944$		0			0
$945$	−8.77793	−	3.19491i	−0.285546	−	0.103930i
$946$		0			0
$947$	10.1563	−	8.52215i	0.330035	−	0.276933i	−0.462679	−	0.886526i	$-0.653112\pi$
$947$	10.1563	−	8.52215i	0.330035	−	0.276933i	0.792714	+	0.609593i	$0.208667\pi$
$948$		0			0
$949$	−1.84395			−0.0598572
$950$		0			0
$951$	−31.8102			−1.03152
$952$		0			0
$953$	−23.3329	+	19.5786i	−0.755826	+	0.634213i	−0.937037	−	0.349231i	$-0.886443\pi$
$953$	−23.3329	+	19.5786i	−0.755826	+	0.634213i	0.181211	+	0.983444i	$0.441998\pi$
$954$		0			0
$955$	−45.1390	−	16.4293i	−1.46066	−	0.531638i
$956$		0			0
$957$	0.248103	−	0.429727i	0.00802004	−	0.0138911i
$958$		0			0
$959$	0.395799	−	2.24469i	0.0127810	−	0.0724847i
$960$		0			0
$961$	−9.61595	−	16.6553i	−0.310192	−	0.537268i
$962$		0			0
$963$	13.2343	+	11.1049i	0.426469	+	0.357850i
$964$		0			0
$965$	−7.79185	+	2.83600i	−0.250828	+	0.0912941i
$966$		0			0
$967$	−2.19804	−	12.4657i	−0.0706843	−	0.400871i	−0.999537	−	0.0304218i	$-0.990315\pi$
$967$	−2.19804	−	12.4657i	−0.0706843	−	0.400871i	0.928853	−	0.370449i	$-0.120796\pi$
$968$		0			0
$969$	−16.3567	+	7.61351i	−0.525453	+	0.244581i
$970$		0			0
$971$	0.716843	+	4.06542i	0.0230046	+	0.130465i	0.994147	−	0.108034i	$-0.0344556\pi$
$971$	0.716843	+	4.06542i	0.0230046	+	0.130465i	−0.971143	+	0.238500i	$0.923344\pi$
$972$		0			0
$973$	−3.73131	+	1.35808i	−0.119620	+	0.0435382i
$974$		0			0
$975$	18.2281	+	15.2952i	0.583768	+	0.489839i
$976$		0			0
$977$	−21.6929	−	37.5732i	−0.694017	−	1.20207i	−0.970511	−	0.241058i	$-0.922506\pi$
$977$	−21.6929	−	37.5732i	−0.694017	−	1.20207i	0.276493	−	0.961016i	$-0.410828\pi$
$978$		0			0
$979$	1.62971	−	9.24253i	0.0520857	−	0.295393i
$980$		0			0
$981$	−7.49904	+	12.9887i	−0.239426	+	0.414698i
$982$		0			0
$983$	15.4272	+	5.61506i	0.492053	+	0.179093i	0.576116	−	0.817368i	$-0.304568\pi$
$983$	15.4272	+	5.61506i	0.492053	+	0.179093i	−0.0840634	+	0.996460i	$0.526790\pi$
$984$		0			0
$985$	15.7785	−	13.2397i	0.502745	−	0.421853i
$986$		0			0
$987$	−0.0146508			−0.000466340
$988$		0			0
$989$	35.7017			1.13525
$990$		0			0
$991$	25.6095	−	21.4889i	0.813512	−	0.682618i	−0.137931	−	0.990442i	$-0.544045\pi$
$991$	25.6095	−	21.4889i	0.813512	−	0.682618i	0.951443	+	0.307824i	$0.0996009\pi$
$992$		0			0
$993$	−11.9392	−	4.34552i	−0.378880	−	0.137901i
$994$		0			0
$995$	−8.82355	+	15.2828i	−0.279725	+	0.484499i
$996$		0			0
$997$	9.22589	−	52.3226i	0.292187	−	1.65707i	−0.386235	−	0.922401i	$-0.626225\pi$
$997$	9.22589	−	52.3226i	0.292187	−	1.65707i	0.678421	−	0.734673i	$-0.262664\pi$
$998$		0			0
$999$	14.8798	+	25.7725i	0.470774	+	0.815405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.i.a.9.1	✓	12
3.2	odd	2		684.2.bo.c.541.1		12
4.3	odd	2		304.2.u.e.161.2		12
19.4	even	9		1444.2.e.g.429.5		12
19.6	even	9		1444.2.a.h.1.2		6
19.9	even	9		1444.2.e.g.653.5		12
19.10	odd	18		1444.2.e.h.653.2		12
19.13	odd	18		1444.2.a.g.1.5		6
19.15	odd	18		1444.2.e.h.429.2		12
19.17	even	9	inner	76.2.i.a.17.1	yes	12
57.17	odd	18		684.2.bo.c.397.1		12
76.51	even	18		5776.2.a.by.1.2		6
76.55	odd	18		304.2.u.e.17.2		12
76.63	odd	18		5776.2.a.bw.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.9.1	✓	12	1.1	even	1	trivial
76.2.i.a.17.1	yes	12	19.17	even	9	inner
304.2.u.e.17.2		12	76.55	odd	18
304.2.u.e.161.2		12	4.3	odd	2
684.2.bo.c.397.1		12	57.17	odd	18
684.2.bo.c.541.1		12	3.2	odd	2
1444.2.a.g.1.5		6	19.13	odd	18
1444.2.a.h.1.2		6	19.6	even	9
1444.2.e.g.429.5		12	19.4	even	9
1444.2.e.g.653.5		12	19.9	even	9
1444.2.e.h.429.2		12	19.15	odd	18
1444.2.e.h.653.2		12	19.10	odd	18
5776.2.a.bw.1.5		6	76.63	odd	18
5776.2.a.by.1.2		6	76.51	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834130 + 0.699919i) q^{3} +(3.00735 + 1.09458i) q^{5} +(0.278396 - 0.482195i) q^{7} +(-0.315057 + 1.78678i) q^{9} +O(q^{10})\)	\(q+(-0.834130 + 0.699919i) q^{3} +(3.00735 + 1.09458i) q^{5} +(0.278396 - 0.482195i) q^{7} +(-0.315057 + 1.78678i) q^{9} +(-1.96291 - 3.39985i) q^{11} +(-3.19334 - 2.67953i) q^{13} +(-3.27464 + 1.19187i) q^{15} +(-0.660076 - 3.74348i) q^{17} +(-1.84488 + 3.94923i) q^{19} +(0.105279 + 0.597068i) q^{21} +(4.67290 - 1.70080i) q^{23} +(4.01579 + 3.36965i) q^{25} +(-2.62112 - 4.53991i) q^{27} +(0.0201569 - 0.114315i) q^{29} +(-3.54372 + 6.13791i) q^{31} +(4.01694 + 1.46205i) q^{33} +(1.36503 - 1.14540i) q^{35} -5.67687 q^{37} +4.53912 q^{39} +(9.20379 - 7.72289i) q^{41} +(6.74642 + 2.45550i) q^{43} +(-2.90326 + 5.02860i) q^{45} +(-0.00419623 + 0.0237980i) q^{47} +(3.34499 + 5.79370i) q^{49} +(3.17072 + 2.66055i) q^{51} +(-8.18260 + 2.97822i) q^{53} +(-2.18171 - 12.3731i) q^{55} +(-1.22527 - 4.58544i) q^{57} +(1.88690 + 10.7011i) q^{59} +(-11.7981 + 4.29417i) q^{61} +(0.773865 + 0.649350i) q^{63} +(-6.67051 - 11.5537i) q^{65} +(2.27074 - 12.8780i) q^{67} +(-2.70739 + 4.68934i) q^{69} +(3.17872 + 1.15696i) q^{71} +(0.338853 - 0.284332i) q^{73} -5.70817 q^{75} -2.18586 q^{77} +(1.31335 - 1.10203i) q^{79} +(0.249157 + 0.0906859i) q^{81} +(-2.90300 + 5.02815i) q^{83} +(2.11247 - 11.9804i) q^{85} +(0.0631980 + 0.109462i) q^{87} +(1.83132 + 1.53666i) q^{89} +(-2.18107 + 0.793845i) q^{91} +(-1.34011 - 7.60013i) q^{93} +(-9.87095 + 9.85733i) q^{95} +(1.86728 + 10.5899i) q^{97} +(6.69320 - 2.43613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more