LMFDB - Embedded newform 804.2.y.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	804.121
Dual form			804.2.y.b.505.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.0929229 + 1.95069i) q^{11} +(6.57525 - 0.627860i) q^{13} +(-0.407377 + 2.83337i) q^{15} +(-0.498266 - 2.05388i) q^{17} +(6.01505 - 2.40806i) q^{19} +(-2.12161 + 1.09376i) q^{21} +(5.97032 + 1.15068i) q^{23} +(1.32681 - 2.90531i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(3.14109 - 5.44053i) q^{29} +(6.99582 + 0.668020i) q^{31} +(1.53509 + 1.20720i) q^{33} +(6.70919 - 1.29309i) q^{35} +(0.506614 + 0.877481i) q^{37} +(3.83137 - 5.38040i) q^{39} +(-2.25239 + 2.14765i) q^{41} +(-4.07902 - 1.19771i) q^{43} +(1.87454 + 2.16334i) q^{45} +(2.70871 + 7.82632i) q^{47} +(-0.942638 - 0.898803i) q^{49} +(-1.87852 - 0.968442i) q^{51} +(-5.19321 + 1.52486i) q^{53} +(-3.24263 - 4.55364i) q^{55} +(2.11913 - 6.12282i) q^{57} +(-0.533864 - 1.16900i) q^{59} +(-0.212043 + 4.45133i) q^{61} +(-0.562745 + 2.31967i) q^{63} +(-14.8621 + 11.6877i) q^{65} +(2.37673 - 7.83270i) q^{67} +(4.77936 - 3.75853i) q^{69} +(-1.57953 + 6.51090i) q^{71} +(-0.0356447 + 0.748274i) q^{73} +(-1.32681 - 2.90531i) q^{75} +(1.52462 - 4.40511i) q^{77} +(-3.92414 - 5.51069i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(9.09130 + 4.68689i) q^{83} +(4.37843 + 4.17483i) q^{85} +(-2.05470 - 5.93667i) q^{87} +(-9.03106 - 10.4224i) q^{89} +(-15.1275 - 4.44185i) q^{91} +(5.08615 - 4.84963i) q^{93} +(-10.7581 + 15.1077i) q^{95} +(-5.11159 - 8.85353i) q^{97} +(1.91761 - 0.369589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{26}{33}\right)$	$1$

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
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$		0			0
$5$	−2.40809	+	1.54759i	−1.07693	+	0.692102i	−0.953847	−	0.300294i	$-0.902915\pi$
$5$	−2.40809	+	1.54759i	−1.07693	+	0.692102i	−0.123085	+	0.992396i	$0.539279\pi$
$6$		0			0
$7$	−2.21597	−	0.887140i	−0.837557	−	0.335307i	−0.0870783	−	0.996201i	$-0.527753\pi$
$7$	−2.21597	−	0.887140i	−0.837557	−	0.335307i	−0.750479	+	0.660894i	$0.770177\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	0.0929229	+	1.95069i	0.0280173	+	0.588155i	0.968605	+	0.248605i	$0.0799720\pi$
$11$	0.0929229	+	1.95069i	0.0280173	+	0.588155i	−0.940588	+	0.339551i	$0.889725\pi$
$12$		0			0
$13$	6.57525	−	0.627860i	1.82365	−	0.174137i	0.873682	−	0.486498i	$-0.161726\pi$
$13$	6.57525	−	0.627860i	1.82365	−	0.174137i	0.949963	+	0.312361i	$0.101120\pi$
$14$		0			0
$15$	−0.407377	+	2.83337i	−0.105184	+	0.731573i
$16$		0			0
$17$	−0.498266	−	2.05388i	−0.120847	−	0.498140i	−0.999776	−	0.0211855i	$-0.993256\pi$
$17$	−0.498266	−	2.05388i	−0.120847	−	0.498140i	0.878928	−	0.476954i	$-0.158259\pi$
$18$		0			0
$19$	6.01505	−	2.40806i	1.37995	−	0.552448i	0.441310	−	0.897354i	$-0.354514\pi$
$19$	6.01505	−	2.40806i	1.37995	−	0.552448i	0.938637	+	0.344907i	$0.112090\pi$
$20$		0			0
$21$	−2.12161	+	1.09376i	−0.462973	+	0.238679i
$22$		0			0
$23$	5.97032	+	1.15068i	1.24490	+	0.239934i	0.768818	−	0.639468i	$-0.220845\pi$
$23$	5.97032	+	1.15068i	1.24490	+	0.239934i	0.476080	+	0.879402i	$0.342057\pi$
$24$		0			0
$25$	1.32681	−	2.90531i	0.265362	−	0.581062i
$26$		0			0
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$		0			0
$29$	3.14109	−	5.44053i	0.583286	−	1.01028i	−0.411800	−	0.911274i	$-0.635100\pi$
$29$	3.14109	−	5.44053i	0.583286	−	1.01028i	0.995087	−	0.0990074i	$-0.0315667\pi$
$30$		0			0
$31$	6.99582	+	0.668020i	1.25649	+	0.119980i	0.701978	−	0.712198i	$-0.252300\pi$
$31$	6.99582	+	0.668020i	1.25649	+	0.119980i	0.554508	+	0.832178i	$0.312906\pi$
$32$		0			0
$33$	1.53509	+	1.20720i	0.267224	+	0.210147i
$34$		0			0
$35$	6.70919	−	1.29309i	1.13406	−	0.218572i
$36$		0			0
$37$	0.506614	+	0.877481i	0.0832868	+	0.144257i	0.904660	−	0.426134i	$-0.140125\pi$
$37$	0.506614	+	0.877481i	0.0832868	+	0.144257i	−0.821373	+	0.570391i	$0.806792\pi$
$38$		0			0
$39$	3.83137	−	5.38040i	0.613509	−	0.861553i
$40$		0			0
$41$	−2.25239	+	2.14765i	−0.351764	+	0.335407i	−0.845273	−	0.534334i	$-0.820562\pi$
$41$	−2.25239	+	2.14765i	−0.351764	+	0.335407i	0.493509	+	0.869741i	$0.335714\pi$
$42$		0			0
$43$	−4.07902	−	1.19771i	−0.622044	−	0.182649i	−0.0445017	−	0.999009i	$-0.514170\pi$
$43$	−4.07902	−	1.19771i	−0.622044	−	0.182649i	−0.577542	+	0.816361i	$0.695988\pi$
$44$		0			0
$45$	1.87454	+	2.16334i	0.279440	+	0.322491i
$46$		0			0
$47$	2.70871	+	7.82632i	0.395107	+	1.14159i	0.950695	+	0.310128i	$0.100372\pi$
$47$	2.70871	+	7.82632i	0.395107	+	1.14159i	−0.555588	+	0.831458i	$0.687507\pi$
$48$		0			0
$49$	−0.942638	−	0.898803i	−0.134663	−	0.128400i
$50$		0			0
$51$	−1.87852	−	0.968442i	−0.263045	−	0.135609i
$52$		0			0
$53$	−5.19321	+	1.52486i	−0.713343	+	0.209456i	−0.618215	−	0.786009i	$-0.712144\pi$
$53$	−5.19321	+	1.52486i	−0.713343	+	0.209456i	−0.0951274	+	0.995465i	$0.530326\pi$
$54$		0			0
$55$	−3.24263	−	4.55364i	−0.437236	−	0.614013i
$56$		0			0
$57$	2.11913	−	6.12282i	0.280685	−	0.810987i
$58$		0			0
$59$	−0.533864	−	1.16900i	−0.0695031	−	0.152191i	0.871692	−	0.490054i	$-0.163023\pi$
$59$	−0.533864	−	1.16900i	−0.0695031	−	0.152191i	−0.941195	+	0.337864i	$0.890296\pi$
$60$		0			0
$61$	−0.212043	+	4.45133i	−0.0271493	+	0.569934i	0.943781	+	0.330572i	$0.107241\pi$
$61$	−0.212043	+	4.45133i	−0.0271493	+	0.569934i	−0.970930	+	0.239363i	$0.923062\pi$
$62$		0			0
$63$	−0.562745	+	2.31967i	−0.0708992	+	0.292251i
$64$		0			0
$65$	−14.8621	+	11.6877i	−1.84342	+	1.44968i
$66$		0			0
$67$	2.37673	−	7.83270i	0.290363	−	0.956916i
$67$	2.37673	−	7.83270i	0.290363	−	0.956916i
$68$		0			0
$69$	4.77936	−	3.75853i	0.575367	−	0.452474i
$70$		0			0
$71$	−1.57953	+	6.51090i	−0.187455	+	0.772702i	0.797984	+	0.602678i	$0.205900\pi$
$71$	−1.57953	+	6.51090i	−0.187455	+	0.772702i	−0.985440	+	0.170024i	$0.945615\pi$
$72$		0			0
$73$	−0.0356447	+	0.748274i	−0.00417189	+	0.0875788i	−0.999993	−	0.00374676i	$-0.998807\pi$
$73$	−0.0356447	+	0.748274i	−0.00417189	+	0.0875788i	0.995821	+	0.0913256i	$0.0291104\pi$
$74$		0			0
$75$	−1.32681	−	2.90531i	−0.153207	−	0.335476i
$76$		0			0
$77$	1.52462	−	4.40511i	0.173747	−	0.502008i
$78$		0			0
$79$	−3.92414	−	5.51069i	−0.441501	−	0.620001i	0.532532	−	0.846410i	$-0.321241\pi$
$79$	−3.92414	−	5.51069i	−0.441501	−	0.620001i	−0.974032	+	0.226409i	$0.927301\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	9.09130	+	4.68689i	0.997900	+	0.514453i	0.878168	−	0.478353i	$-0.158766\pi$
$83$	9.09130	+	4.68689i	0.997900	+	0.514453i	0.119733	+	0.992806i	$0.461796\pi$
$84$		0			0
$85$	4.37843	+	4.17483i	0.474908	+	0.452824i
$86$		0			0
$87$	−2.05470	−	5.93667i	−0.220287	−	0.636478i
$88$		0			0
$89$	−9.03106	−	10.4224i	−0.957290	−	1.10477i	−0.994423	−	0.105461i	$-0.966368\pi$
$89$	−9.03106	−	10.4224i	−0.957290	−	1.10477i	0.0371333	−	0.999310i	$-0.488177\pi$
$90$		0			0
$91$	−15.1275	−	4.44185i	−1.58580	−	0.465632i
$92$		0			0
$93$	5.08615	−	4.84963i	0.527409	−	0.502883i
$94$		0			0
$95$	−10.7581	+	15.1077i	−1.10376	+	1.55001i
$96$		0			0
$97$	−5.11159	−	8.85353i	−0.519003	−	0.898940i	−0.999756	−	0.0220839i	$-0.992970\pi$
$97$	−5.11159	−	8.85353i	−0.519003	−	0.898940i	0.480753	−	0.876856i	$-0.340363\pi$
$98$		0			0
$99$	1.91761	−	0.369589i	0.192727	−	0.0371451i
$100$		0			0
$101$	8.97811	+	7.06046i	0.893355	+	0.702542i	0.955332	−	0.295535i	$-0.0954980\pi$
$101$	8.97811	+	7.06046i	0.893355	+	0.702542i	−0.0619765	+	0.998078i	$0.519740\pi$
$102$		0			0
$103$	16.6613	+	1.59096i	1.64168	+	0.156762i	0.874620	−	0.484808i	$-0.161111\pi$
$103$	16.6613	+	1.59096i	1.64168	+	0.156762i	0.767064	+	0.641570i	$0.221717\pi$
$104$		0			0
$105$	3.41633	−	5.91726i	0.333400	−	0.577465i
$106$		0			0
$107$	4.50997	+	2.89838i	0.435996	+	0.280197i	0.740171	−	0.672419i	$-0.234745\pi$
$107$	4.50997	+	2.89838i	0.435996	+	0.280197i	−0.304175	+	0.952616i	$0.598381\pi$
$108$		0			0
$109$	3.15774	−	6.91448i	0.302457	−	0.662287i	−0.695987	−	0.718054i	$-0.745033\pi$
$109$	3.15774	−	6.91448i	0.302457	−	0.662287i	0.998444	+	0.0557667i	$0.0177603\pi$
$110$		0			0
$111$	0.994917	+	0.191755i	0.0944334	+	0.0182005i
$112$		0			0
$113$	−3.26500	+	1.68323i	−0.307146	+	0.158345i	−0.604908	−	0.796296i	$-0.706790\pi$
$113$	−3.26500	+	1.68323i	−0.307146	+	0.158345i	0.297762	+	0.954640i	$0.403760\pi$
$114$		0			0
$115$	−16.1579	+	6.46864i	−1.50673	+	0.603204i
$116$		0			0
$117$	−1.55722	−	6.41897i	−0.143965	−	0.593434i
$118$		0			0
$119$	−0.717938	+	4.99337i	−0.0658133	+	0.457742i
$120$		0			0
$121$	7.15363	−	0.683089i	0.650330	−	0.0620990i
$122$		0			0
$123$	0.148083	+	3.10865i	0.0133522	+	0.280298i
$124$		0			0
$125$	−0.735747	−	5.11723i	−0.0658072	−	0.457699i
$126$		0			0
$127$	12.0322	+	4.81697i	1.06769	+	0.427437i	0.837911	−	0.545807i	$-0.183777\pi$
$127$	12.0322	+	4.81697i	1.06769	+	0.427437i	0.229775	+	0.973244i	$0.426201\pi$
$128$		0			0
$129$	−3.57635	+	2.29838i	−0.314880	+	0.202361i
$130$		0			0
$131$	−6.78088	+	7.82555i	−0.592448	+	0.683721i	−0.970233	−	0.242172i	$-0.922140\pi$
$131$	−6.78088	+	7.82555i	−0.592448	+	0.683721i	0.377785	+	0.925893i	$0.376686\pi$
$132$		0			0
$133$	−15.4655			−1.34103
$134$		0			0
$135$	2.86251			0.246365
$136$		0			0
$137$	10.4044	−	12.0073i	0.888908	−	1.02585i	−0.110580	−	0.993867i	$-0.535271\pi$
$137$	10.4044	−	12.0073i	0.888908	−	1.02585i	0.999488	−	0.0319875i	$-0.0101837\pi$
$138$		0			0
$139$	−12.6415	+	8.12420i	−1.07224	+	0.689085i	−0.952752	−	0.303750i	$-0.901761\pi$
$139$	−12.6415	+	8.12420i	−1.07224	+	0.689085i	−0.119486	+	0.992836i	$0.538125\pi$
$140$		0			0
$141$	7.68857	+	3.07804i	0.647494	+	0.259218i
$142$		0			0
$143$	1.83575	+	12.7679i	0.153513	+	1.06771i
$144$		0			0
$145$	0.855656	+	17.9624i	0.0710583	+	1.49170i
$146$		0			0
$147$	−1.29657	+	0.123807i	−0.106939	+	0.0102114i
$148$		0			0
$149$	0.444328	−	3.09037i	0.0364008	−	0.253173i	−0.963493	−	0.267733i	$-0.913726\pi$
$149$	0.444328	−	3.09037i	0.0364008	−	0.253173i	0.999894	+	0.0145597i	$0.00463466\pi$
$150$		0			0
$151$	3.04315	+	12.5440i	0.247648	+	1.02082i	0.950807	+	0.309785i	$0.100257\pi$
$151$	3.04315	+	12.5440i	0.247648	+	1.02082i	−0.703159	+	0.711033i	$0.748228\pi$
$152$		0			0
$153$	−1.96207	+	0.785493i	−0.158624	+	0.0635033i
$154$		0			0
$155$	−17.8804	+	9.21799i	−1.43619	+	0.740407i
$156$		0			0
$157$	−5.69161	−	1.09697i	−0.454240	−	0.0875475i	−0.0430006	−	0.999075i	$-0.513692\pi$
$157$	−5.69161	−	1.09697i	−0.454240	−	0.0875475i	−0.411239	+	0.911528i	$0.634904\pi$
$158$		0			0
$159$	−2.24842	+	4.92334i	−0.178311	+	0.390446i
$160$		0			0
$161$	−12.2092	−	7.84639i	−0.962222	−	0.618382i
$162$		0			0
$163$	−3.07027	+	5.31786i	−0.240482	+	0.416527i	−0.960852	−	0.277064i	$-0.910639\pi$
$163$	−3.07027	+	5.31786i	−0.240482	+	0.416527i	0.720370	+	0.693590i	$0.243972\pi$
$164$		0			0
$165$	−5.56488	−	0.531382i	−0.433226	−	0.0413680i
$166$		0			0
$167$	8.39815	+	6.60438i	0.649868	+	0.511062i	0.887806	−	0.460218i	$-0.152229\pi$
$167$	8.39815	+	6.60438i	0.649868	+	0.511062i	−0.237937	+	0.971280i	$0.576471\pi$
$168$		0			0
$169$	30.0746	−	5.79640i	2.31343	−	0.445877i
$170$		0			0
$171$	−3.23958	−	5.61112i	−0.247737	−	0.429093i
$172$		0			0
$173$	10.4968	−	14.7407i	0.798059	−	1.12072i	−0.192184	−	0.981359i	$-0.561557\pi$
$173$	10.4968	−	14.7407i	0.798059	−	1.12072i	0.990242	−	0.139357i	$-0.0445037\pi$
$174$		0			0
$175$	−5.51759	+	5.26101i	−0.417091	+	0.397695i
$176$		0			0
$177$	−1.23308	−	0.362064i	−0.0926837	−	0.0272144i
$178$		0			0
$179$	−10.8678	−	12.5421i	−0.812298	−	0.937442i	0.186690	−	0.982419i	$-0.440224\pi$
$179$	−10.8678	−	12.5421i	−0.812298	−	0.937442i	−0.998988	+	0.0449766i	$0.985679\pi$
$180$		0			0
$181$	−7.12164	−	20.5766i	−0.529347	−	1.52945i	−0.819852	−	0.572575i	$-0.805944\pi$
$181$	−7.12164	−	20.5766i	−0.529347	−	1.52945i	0.290505	−	0.956874i	$-0.406177\pi$
$182$		0			0
$183$	3.22523	+	3.07525i	0.238416	+	0.227329i
$184$		0			0
$185$	−2.57795	−	1.32903i	−0.189535	−	0.0977120i
$186$		0			0
$187$	3.96019	−	1.16282i	0.289598	−	0.0850336i
$188$		0			0
$189$	1.38457	+	1.94435i	0.100712	+	0.141431i
$190$		0			0
$191$	2.24376	−	6.48292i	0.162353	−	0.469088i	−0.834256	−	0.551378i	$-0.814102\pi$
$191$	2.24376	−	6.48292i	0.162353	−	0.469088i	0.996608	+	0.0822903i	$0.0262235\pi$
$192$		0			0
$193$	−0.948658	−	2.07727i	−0.0682859	−	0.149525i	0.872411	−	0.488772i	$-0.162555\pi$
$193$	−0.948658	−	2.07727i	−0.0682859	−	0.149525i	−0.940697	+	0.339247i	$0.889828\pi$
$194$		0			0
$195$	−0.899645	+	18.8859i	−0.0644249	+	1.35245i
$196$		0			0
$197$	−5.74338	+	23.6746i	−0.409199	+	1.68674i	0.278249	+	0.960509i	$0.410246\pi$
$197$	−5.74338	+	23.6746i	−0.409199	+	1.68674i	−0.687448	+	0.726233i	$0.741269\pi$
$198$		0			0
$199$	−15.4771	+	12.1713i	−1.09714	+	0.862804i	−0.991306	−	0.131580i	$-0.957995\pi$
$199$	−15.4771	+	12.1713i	−1.09714	+	0.862804i	−0.105838	+	0.994383i	$0.533753\pi$
$200$		0			0
$201$	−4.36313	−	6.92554i	−0.307752	−	0.488490i
$202$		0			0
$203$	−11.7871	+	9.26946i	−0.827291	+	0.650589i
$204$		0			0
$205$	2.10029	−	8.65751i	0.146691	−	0.604667i
$206$		0			0
$207$	0.289307	−	6.07331i	0.0201083	−	0.422124i
$208$		0			0
$209$	5.25632	+	11.5097i	0.363587	+	0.796145i
$210$		0			0
$211$	4.64631	−	13.4246i	0.319865	−	0.924190i	−0.664382	−	0.747393i	$-0.731305\pi$
$211$	4.64631	−	13.4246i	0.319865	−	0.924190i	0.984247	−	0.176797i	$-0.0565735\pi$
$212$		0			0
$213$	3.88624	+	5.45746i	0.266281	+	0.373939i
$214$		0			0
$215$	11.6762	−	3.42844i	0.796311	−	0.233818i
$216$		0			0
$217$	−14.9099	−	7.68659i	−1.01215	−	0.521799i
$218$		0			0
$219$	0.542165	+	0.516954i	0.0366361	+	0.0349325i
$220$		0			0
$221$	−4.56577	−	13.1919i	−0.307127	−	0.887386i
$222$		0			0
$223$	−2.96708	−	3.42419i	−0.198690	−	0.229301i	0.647657	−	0.761932i	$-0.275749\pi$
$223$	−2.96708	−	3.42419i	−0.198690	−	0.229301i	−0.846348	+	0.532631i	$0.821203\pi$
$224$		0			0
$225$	−3.06456	−	0.899837i	−0.204304	−	0.0599892i
$226$		0			0
$227$	−9.77092	+	9.31655i	−0.648518	+	0.618361i	−0.941200	−	0.337849i	$-0.890301\pi$
$227$	−9.77092	+	9.31655i	−0.648518	+	0.618361i	0.292682	+	0.956210i	$0.405452\pi$
$228$		0			0
$229$	−15.5608	+	21.8520i	−1.02828	+	1.44402i	−0.137003	+	0.990571i	$0.543747\pi$
$229$	−15.5608	+	21.8520i	−1.02828	+	1.44402i	−0.891281	+	0.453452i	$0.850193\pi$
$230$		0			0
$231$	−2.33074	−	4.03696i	−0.153352	−	0.265613i
$232$		0			0
$233$	−24.9584	+	4.81034i	−1.63508	+	0.315136i	−0.922366	−	0.386318i	$-0.873747\pi$
$233$	−24.9584	+	4.81034i	−1.63508	+	0.315136i	−0.712715	+	0.701454i	$0.752535\pi$
$234$		0			0
$235$	−18.6348	−	14.6545i	−1.21560	−	0.955956i
$236$		0			0
$237$	−6.73447	−	0.643064i	−0.437451	−	0.0417715i
$238$		0			0
$239$	−0.911474	+	1.57872i	−0.0589584	+	0.102119i	−0.893998	−	0.448071i	$-0.852111\pi$
$239$	−0.911474	+	1.57872i	−0.0589584	+	0.102119i	0.835040	+	0.550190i	$0.185445\pi$
$240$		0			0
$241$	−10.2632	−	6.59576i	−0.661111	−	0.424870i	0.166600	−	0.986025i	$-0.446721\pi$
$241$	−10.2632	−	6.59576i	−0.661111	−	0.424870i	−0.827711	+	0.561154i	$0.810357\pi$
$242$		0			0
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$		0			0
$245$	3.66094	+	0.705588i	0.233889	+	0.0450784i
$246$		0			0
$247$	38.0385	−	19.6102i	2.42033	−	1.24777i
$248$		0			0
$249$	9.49566	−	3.80149i	0.601763	−	0.240909i
$250$		0			0
$251$	−4.02486	−	16.5907i	−0.254047	−	1.04720i	−0.945719	−	0.324985i	$-0.894641\pi$
$251$	−4.02486	−	16.5907i	−0.254047	−	1.04720i	0.691672	−	0.722212i	$-0.256874\pi$
$252$		0			0
$253$	−1.68985	+	11.7532i	−0.106240	+	0.738916i
$254$		0			0
$255$	6.02239	−	0.575069i	0.377137	−	0.0360122i
$256$		0			0
$257$	0.105536	+	2.21548i	0.00658318	+	0.138198i	0.999766	+	0.0216311i	$0.00688592\pi$
$257$	0.105536	+	2.21548i	0.00658318	+	0.138198i	−0.993183	+	0.116567i	$0.962811\pi$
$258$		0			0
$259$	−0.344192	−	2.39391i	−0.0213870	−	0.148750i
$260$		0			0
$261$	−5.83218	−	2.33485i	−0.361003	−	0.144524i
$262$		0			0
$263$	−18.8984	+	12.1453i	−1.16533	+	0.748909i	−0.972632	−	0.232350i	$-0.925359\pi$
$263$	−18.8984	+	12.1453i	−1.16533	+	0.748909i	−0.192693	+	0.981259i	$0.561722\pi$
$264$		0			0
$265$	10.1459	−	11.7090i	0.623256	−	0.719276i
$266$		0			0
$267$	−13.7908			−0.843984
$268$		0			0
$269$	−27.7856			−1.69412			−0.847058	−	0.531500i	$-0.821629\pi$
$269$	−27.7856			−1.69412			−0.847058	+	0.531500i	$0.821629\pi$
$270$		0			0
$271$	7.59717	−	8.76760i	0.461495	−	0.532594i	−0.476531	−	0.879157i	$-0.658106\pi$
$271$	7.59717	−	8.76760i	0.461495	−	0.532594i	0.938026	+	0.346564i	$0.112652\pi$
$272$		0			0
$273$	−13.2634	+	8.52384i	−0.802735	+	0.515886i
$274$		0			0
$275$	5.79066	+	2.31823i	0.349190	+	0.139794i
$276$		0			0
$277$	−1.11722	−	7.77043i	−0.0671272	−	0.466880i	−0.995464	−	0.0951394i	$-0.969670\pi$
$277$	−1.11722	−	7.77043i	−0.0671272	−	0.466880i	0.928337	−	0.371740i	$-0.121239\pi$
$278$		0			0
$279$	−0.334389	−	7.01968i	−0.0200193	−	0.420257i
$280$		0			0
$281$	11.4831	−	1.09651i	0.685026	−	0.0654120i	0.253261	−	0.967398i	$-0.418497\pi$
$281$	11.4831	−	1.09651i	0.685026	−	0.0654120i	0.431765	+	0.901986i	$0.357891\pi$
$282$		0			0
$283$	−1.37935	+	9.59356i	−0.0819936	+	0.570278i	0.906865	+	0.421421i	$0.138469\pi$
$283$	−1.37935	+	9.59356i	−0.0819936	+	0.570278i	−0.988859	+	0.148857i	$0.952441\pi$
$284$		0			0
$285$	4.37254	+	18.0239i	0.259007	+	1.06764i
$286$		0			0
$287$	6.89649	−	2.76094i	0.407087	−	0.162973i
$288$		0			0
$289$	11.1400	−	5.74309i	0.655296	−	0.337829i
$290$		0			0
$291$	−10.0384	−	1.93475i	−0.588463	−	0.113417i
$292$		0			0
$293$	2.44506	−	5.35394i	0.142842	−	0.312780i	−0.824666	−	0.565620i	$-0.808637\pi$
$293$	2.44506	−	5.35394i	0.142842	−	0.312780i	0.967508	+	0.252839i	$0.0813643\pi$
$294$		0			0
$295$	3.09472	+	1.98886i	0.180182	+	0.115796i
$296$		0			0
$297$	0.976451	−	1.69126i	0.0566595	−	0.0981371i
$298$		0			0
$299$	39.9788	+	3.81751i	2.31203	+	0.220772i
$300$		0			0
$301$	7.97644	+	6.27274i	0.459754	+	0.361555i
$302$		0			0
$303$	11.2154	−	2.16158i	0.644305	−	0.124180i
$304$		0			0
$305$	−6.37820	−	11.0474i	−0.365215	−	0.632570i
$306$		0			0
$307$	−8.92660	+	12.5357i	−0.509468	+	0.715448i	−0.986559	−	0.163406i	$-0.947752\pi$
$307$	−8.92660	+	12.5357i	−0.509468	+	0.715448i	0.477091	+	0.878854i	$0.341691\pi$
$308$		0			0
$309$	12.1132	−	11.5499i	0.689095	−	0.657051i
$310$		0			0
$311$	1.21115	+	0.355625i	0.0686779	+	0.0201657i	0.315891	−	0.948795i	$-0.397697\pi$
$311$	1.21115	+	0.355625i	0.0686779	+	0.0201657i	−0.247213	+	0.968961i	$0.579515\pi$
$312$		0			0
$313$	14.0570	+	16.2227i	0.794551	+	0.916961i	0.998069	−	0.0621101i	$-0.0197830\pi$
$313$	14.0570	+	16.2227i	0.794551	+	0.916961i	−0.203518	+	0.979071i	$0.565238\pi$
$314$		0			0
$315$	−2.23474	−	6.45687i	−0.125914	−	0.363803i
$316$		0			0
$317$	21.4339	+	20.4372i	1.20385	+	1.14787i	0.985082	+	0.172088i	$0.0550514\pi$
$317$	21.4339	+	20.4372i	1.20385	+	1.14787i	0.218765	+	0.975777i	$0.429797\pi$
$318$		0			0
$319$	10.9047	+	5.62175i	0.610545	+	0.314758i
$320$		0			0
$321$	5.14386	−	1.51037i	0.287102	−	0.0843008i
$322$		0			0
$323$	−7.94298	−	11.1543i	−0.441959	−	0.620645i
$324$		0			0
$325$	6.89998	−	19.9362i	0.382742	−	1.10586i
$326$		0			0
$327$	−3.15774	−	6.91448i	−0.174623	−	0.382372i
$328$		0			0
$329$	0.940612	−	19.7459i	0.0518576	−	1.08863i
$330$		0			0
$331$	−7.47518	+	30.8131i	−0.410873	+	1.69364i	0.271335	+	0.962485i	$0.412535\pi$
$331$	−7.47518	+	30.8131i	−0.410873	+	1.69364i	−0.682208	+	0.731158i	$0.738980\pi$
$332$		0			0
$333$	0.796451	−	0.626336i	0.0436452	−	0.0343230i
$334$		0			0
$335$	6.39841	+	22.5401i	0.349582	+	1.23150i
$336$		0			0
$337$	6.36798	−	5.00784i	0.346886	−	0.272794i	−0.429480	−	0.903076i	$-0.641303\pi$
$337$	6.36798	−	5.00784i	0.346886	−	0.272794i	0.776366	+	0.630282i	$0.217061\pi$
$338$		0			0
$339$	−0.866025	+	3.56980i	−0.0470360	+	0.193885i
$340$		0			0
$341$	−0.653029	+	13.7088i	−0.0353635	+	0.742371i
$342$		0			0
$343$	8.23252	+	18.0267i	0.444514	+	0.973350i
$344$		0			0
$345$	−5.69249	+	16.4474i	−0.306473	+	0.885496i
$346$		0			0
$347$	−13.0088	−	18.2682i	−0.698347	−	0.980691i	−0.999631	−	0.0271563i	$-0.991355\pi$
$347$	−13.0088	−	18.2682i	−0.698347	−	0.980691i	0.301285	−	0.953534i	$-0.402585\pi$
$348$		0			0
$349$	15.9919	−	4.69564i	0.856025	−	0.251352i	0.175864	−	0.984414i	$-0.443728\pi$
$349$	15.9919	−	4.69564i	0.856025	−	0.251352i	0.680161	+	0.733063i	$0.261910\pi$
$350$		0			0
$351$	−5.87090	−	3.02666i	−0.313365	−	0.161551i
$352$		0			0
$353$	−7.55064	−	7.19952i	−0.401880	−	0.383192i	0.462008	−	0.886876i	$-0.347129\pi$
$353$	−7.55064	−	7.19952i	−0.401880	−	0.383192i	−0.863888	+	0.503684i	$0.831978\pi$
$354$		0			0
$355$	−6.27254	−	18.1233i	−0.332912	−	0.961886i
$356$		0			0
$357$	3.30359	+	3.81254i	0.174844	+	0.201781i
$358$		0			0
$359$	31.8007	+	9.33751i	1.67837	+	0.492815i	0.975776	−	0.218772i	$-0.0702050\pi$
$359$	31.8007	+	9.33751i	1.67837	+	0.492815i	0.702598	+	0.711587i	$0.252023\pi$
$360$		0			0
$361$	16.6311	−	15.8577i	0.875322	−	0.834618i
$362$		0			0
$363$	4.16839	−	5.85368i	0.218784	−	0.307239i
$364$		0			0
$365$	−1.07218	−	1.85708i	−0.0561207	−	0.0972038i
$366$		0			0
$367$	−1.82089	+	0.350947i	−0.0950495	+	0.0183193i	−0.236554	−	0.971618i	$-0.576018\pi$
$367$	−1.82089	+	0.350947i	−0.0950495	+	0.0183193i	0.141505	+	0.989938i	$0.454806\pi$
$368$		0			0
$369$	2.44634	+	1.92382i	0.127351	+	0.100150i
$370$		0			0
$371$	12.8608	+	1.22805i	0.667698	+	0.0637574i
$372$		0			0
$373$	−10.1961	+	17.6601i	−0.527932	+	0.914404i	0.471538	+	0.881846i	$0.343699\pi$
$373$	−10.1961	+	17.6601i	−0.527932	+	0.914404i	−0.999470	+	0.0325588i	$0.989634\pi$
$374$		0			0
$375$	−4.34916	−	2.79503i	−0.224590	−	0.144335i
$376$		0			0
$377$	17.2376	−	37.7450i	0.887780	−	1.94397i
$378$		0			0
$379$	−9.89327	−	1.90677i	−0.508183	−	0.0979443i	−0.0712863	−	0.997456i	$-0.522710\pi$
$379$	−9.89327	−	1.90677i	−0.508183	−	0.0979443i	−0.436897	+	0.899512i	$0.643923\pi$
$380$		0			0
$381$	11.5198	−	5.93889i	0.590179	−	0.304259i
$382$		0			0
$383$	5.80952	−	2.32578i	0.296852	−	0.118842i	−0.218455	−	0.975847i	$-0.570102\pi$
$383$	5.80952	−	2.32578i	0.296852	−	0.118842i	0.515308	+	0.857005i	$0.327678\pi$
$384$		0			0
$385$	3.14586	+	12.9674i	0.160328	+	0.660880i
$386$		0			0
$387$	−0.605012	+	4.20795i	−0.0307545	+	0.213902i
$388$		0			0
$389$	−28.7904	+	2.74915i	−1.45973	+	0.139388i	−0.794507	−	0.607255i	$-0.792271\pi$
$389$	−28.7904	+	2.74915i	−1.45973	+	0.139388i	−0.665226	+	0.746642i	$0.731665\pi$
$390$		0			0
$391$	−0.611439	−	12.8357i	−0.0309218	−	0.649128i
$392$		0			0
$393$	1.47363	+	10.2493i	0.0743346	+	0.517008i
$394$		0			0
$395$	17.9780	+	7.19729i	0.904570	+	0.362135i
$396$		0			0
$397$	−23.7386	+	15.2559i	−1.19141	+	0.765671i	−0.977449	−	0.211172i	$-0.932272\pi$
$397$	−23.7386	+	15.2559i	−1.19141	+	0.765671i	−0.213958	+	0.976843i	$0.568636\pi$
$398$		0			0
$399$	−10.1277	+	11.6880i	−0.507020	+	0.585132i
$400$		0			0
$401$	28.3871			1.41758			0.708792	−	0.705418i	$-0.249241\pi$
$401$	28.3871			1.41758			0.708792	+	0.705418i	$0.249241\pi$
$402$		0			0
$403$	46.4187			2.31228
$404$		0			0
$405$	1.87454	−	2.16334i	0.0931468	−	0.107497i
$406$		0			0
$407$	−1.66462	+	1.06979i	−0.0825121	+	0.0530273i
$408$		0			0
$409$	−23.7005	−	9.48825i	−1.17191	−	0.469164i	−0.297679	−	0.954666i	$-0.596212\pi$
$409$	−23.7005	−	9.48825i	−1.17191	−	0.469164i	−0.874235	+	0.485502i	$0.838637\pi$
$410$		0			0
$411$	−2.26109	−	15.7262i	−0.111531	−	0.775719i
$412$		0			0
$413$	0.145960	+	3.06408i	0.00718222	+	0.150773i
$414$		0			0
$415$	−29.1461	+	2.78311i	−1.43073	+	0.136618i
$416$		0			0
$417$	−2.13856	+	14.8740i	−0.104726	+	0.728384i
$418$		0			0
$419$	−5.02151	−	20.6990i	−0.245317	−	1.01121i	−0.952587	−	0.304267i	$-0.901589\pi$
$419$	−5.02151	−	20.6990i	−0.245317	−	1.01121i	0.707270	−	0.706944i	$-0.249927\pi$
$420$		0			0
$421$	−8.87376	+	3.55252i	−0.432481	+	0.173139i	−0.577680	−	0.816263i	$-0.696042\pi$
$421$	−8.87376	+	3.55252i	−0.432481	+	0.173139i	0.145199	+	0.989402i	$0.453618\pi$
$422$		0			0
$423$	7.36117	−	3.79495i	0.357912	−	0.184517i
$424$		0			0
$425$	−6.62827	−	1.27749i	−0.321518	−	0.0619676i
$426$		0			0
$427$	4.41883	−	9.67589i	0.213842	−	0.468249i
$428$		0			0
$429$	10.8515	+	6.97385i	0.523916	+	0.336701i
$430$		0			0
$431$	14.0446	−	24.3260i	0.676506	−	1.17174i	−0.299520	−	0.954090i	$-0.596827\pi$
$431$	14.0446	−	24.3260i	0.676506	−	1.17174i	0.976026	−	0.217653i	$-0.0698402\pi$
$432$		0			0
$433$	−13.0116	−	1.24245i	−0.625296	−	0.0597086i	−0.222402	−	0.974955i	$-0.571390\pi$
$433$	−13.0116	−	1.24245i	−0.625296	−	0.0597086i	−0.402894	+	0.915246i	$0.631996\pi$
$434$		0			0
$435$	14.1354	+	11.1162i	0.677742	+	0.532982i
$436$		0			0
$437$	38.6827	−	7.45548i	1.85044	−	0.356644i
$438$		0			0
$439$	−3.87835	−	6.71750i	−0.185103	−	0.320609i	0.758508	−	0.651664i	$-0.225929\pi$
$439$	−3.87835	−	6.71750i	−0.185103	−	0.320609i	−0.943611	+	0.331055i	$0.892595\pi$
$440$		0			0
$441$	−0.755504	+	1.06096i	−0.0359764	+	0.0505217i
$442$		0			0
$443$	19.1488	−	18.2584i	0.909788	−	0.867481i	−0.0818355	−	0.996646i	$-0.526078\pi$
$443$	19.1488	−	18.2584i	0.909788	−	0.867481i	0.991623	+	0.129165i	$0.0412297\pi$
$444$		0			0
$445$	37.8772	+	11.1217i	1.79555	+	0.527221i
$446$		0			0
$447$	−2.04457	−	2.35956i	−0.0967050	−	0.111604i
$448$		0			0
$449$	5.05216	+	14.5973i	0.238426	+	0.688888i	0.999205	+	0.0398758i	$0.0126962\pi$
$449$	5.05216	+	14.5973i	0.238426	+	0.688888i	−0.760778	+	0.649012i	$0.775183\pi$
$450$		0			0
$451$	−4.39870	−	4.19415i	−0.207127	−	0.197495i
$452$		0			0
$453$	11.4730	+	5.91473i	0.539047	+	0.277898i
$454$		0			0
$455$	43.3027	−	12.7148i	2.03006	−	0.596080i
$456$		0			0
$457$	22.5687	+	31.6933i	1.05572	+	1.48255i	0.865565	+	0.500797i	$0.166960\pi$
$457$	22.5687	+	31.6933i	1.05572	+	1.48255i	0.190156	+	0.981754i	$0.439101\pi$
$458$		0			0
$459$	−0.691244	+	1.99722i	−0.0322645	+	0.0932222i
$460$		0			0
$461$	−12.7244	−	27.8626i	−0.592635	−	1.29769i	−0.933837	−	0.357699i	$-0.883561\pi$
$461$	−12.7244	−	27.8626i	−0.592635	−	1.29769i	0.341202	−	0.939990i	$-0.389166\pi$
$462$		0			0
$463$	−0.865967	+	18.1789i	−0.0402449	+	0.844845i	0.885027	+	0.465540i	$0.154140\pi$
$463$	−0.865967	+	18.1789i	−0.0402449	+	0.844845i	−0.925272	+	0.379305i	$0.876163\pi$
$464$		0			0
$465$	−4.74269	+	19.5496i	−0.219937	+	0.906592i
$466$		0			0
$467$	−4.12624	+	3.24491i	−0.190940	+	0.150156i	−0.709053	−	0.705156i	$-0.750877\pi$
$467$	−4.12624	+	3.24491i	−0.190940	+	0.150156i	0.518113	+	0.855312i	$0.326635\pi$
$468$		0			0
$469$	−12.2155	+	15.2485i	−0.564057	+	0.704112i
$470$		0			0
$471$	−4.55624	+	3.58307i	−0.209941	+	0.165099i
$472$		0			0
$473$	1.95732	−	8.06819i	0.0899978	−	0.370976i
$474$		0			0
$475$	0.984664	−	20.6706i	0.0451795	−	0.948434i
$476$		0			0
$477$	2.24842	+	4.92334i	0.102948	+	0.225424i
$478$		0			0
$479$	14.1475	−	40.8764i	0.646414	−	1.86769i	0.178438	−	0.983951i	$-0.442896\pi$
$479$	14.1475	−	40.8764i	0.646414	−	1.86769i	0.467977	−	0.883741i	$-0.344983\pi$
$480$		0			0
$481$	3.88205	+	5.45157i	0.177006	+	0.248570i
$482$		0			0
$483$	−13.9252	+	4.08882i	−0.633621	+	0.186048i
$484$		0			0
$485$	26.0108	+	13.4095i	1.18109	+	0.608894i
$486$		0			0
$487$	−18.6220	−	17.7561i	−0.843844	−	0.804604i	0.138758	−	0.990326i	$-0.455689\pi$
$487$	−18.6220	−	17.7561i	−0.843844	−	0.804604i	−0.982602	+	0.185723i	$0.940537\pi$
$488$		0			0
$489$	2.00837	+	5.80281i	0.0908217	+	0.262412i
$490$		0			0
$491$	−4.62424	−	5.33666i	−0.208689	−	0.240840i	0.641750	−	0.766914i	$-0.278209\pi$
$491$	−4.62424	−	5.33666i	−0.208689	−	0.240840i	−0.850439	+	0.526074i	$0.823663\pi$
$492$		0			0
$493$	−12.7393	−	3.74060i	−0.573750	−	0.168468i
$494$		0			0
$495$	−4.04582	+	3.85768i	−0.181846	+	0.173390i
$496$		0			0
$497$	9.27627	−	13.0267i	0.416098	−	0.584327i
$498$		0			0
$499$	21.1000	+	36.5463i	0.944567	+	1.63604i	0.756617	+	0.653859i	$0.226851\pi$
$499$	21.1000	+	36.5463i	0.944567	+	1.63604i	0.187950	+	0.982179i	$0.439816\pi$
$500$		0			0
$501$	10.4909	−	2.02195i	0.468698	−	0.0903341i
$502$		0			0
$503$	−16.4388	−	12.9276i	−0.732970	−	0.576414i	0.180376	−	0.983598i	$-0.442269\pi$
$503$	−16.4388	−	12.9276i	−0.732970	−	0.576414i	−0.913346	+	0.407183i	$0.866511\pi$
$504$		0			0
$505$	−32.5468	−	3.10784i	−1.44831	−	0.138297i
$506$		0			0
$507$	15.3140	−	26.5247i	0.680120	−	1.17800i
$508$		0			0
$509$	−33.8115	−	21.7293i	−1.49867	−	0.963136i	−0.995068	−	0.0991989i	$-0.968372\pi$
$509$	−33.8115	−	21.7293i	−1.49867	−	0.963136i	−0.503601	−	0.863937i	$-0.667992\pi$
$510$		0			0
$511$	0.742811	−	1.62653i	0.0328600	−	0.0719534i
$512$		0			0
$513$	−6.36208	−	1.22619i	−0.280893	−	0.0541376i
$514$		0			0
$515$	−42.5841	+	21.9536i	−1.87648	+	0.967392i
$516$		0			0
$517$	−15.0150	+	6.01111i	−0.660360	+	0.264368i
$518$		0			0
$519$	−4.26634	−	17.5861i	−0.187271	−	0.771944i
$520$		0			0
$521$	−1.22689	+	8.53320i	−0.0537510	+	0.373846i	0.945136	+	0.326677i	$0.105929\pi$
$521$	−1.22689	+	8.53320i	−0.0537510	+	0.373846i	−0.998887	+	0.0471690i	$0.984980\pi$
$522$		0			0
$523$	−8.40422	+	0.802505i	−0.367491	+	0.0350911i	−0.277168	−	0.960821i	$-0.589396\pi$
$523$	−8.40422	+	0.802505i	−0.367491	+	0.0350911i	−0.0903226	+	0.995913i	$0.528790\pi$
$524$		0			0
$525$	0.362754	+	7.61515i	0.0158319	+	0.332352i
$526$		0			0
$527$	−2.11375	−	14.7014i	−0.0920763	−	0.640405i
$528$		0			0
$529$	12.9682	+	5.19168i	0.563834	+	0.225725i
$530$		0			0
$531$	−1.08112	+	0.694796i	−0.0469167	+	0.0301516i
$532$		0			0
$533$	−13.4616	+	15.5355i	−0.583086	+	0.672918i
$534$		0			0
$535$	−15.3459			−0.663463
$536$		0			0
$537$	−16.5956			−0.716153
$538$		0			0
$539$	1.66570	−	1.92231i	0.0717466	−	0.0828000i
$540$		0			0
$541$	−9.92851	+	6.38067i	−0.426860	+	0.274326i	−0.736382	−	0.676566i	$-0.763467\pi$
$541$	−9.92851	+	6.38067i	−0.426860	+	0.274326i	0.309522	+	0.950892i	$0.399831\pi$
$542$		0			0
$543$	−20.2145	−	8.09265i	−0.867486	−	0.347289i
$544$		0			0
$545$	3.09664	+	21.5376i	0.132645	+	0.922569i
$546$		0			0
$547$	0.654749	+	13.7449i	0.0279950	+	0.587688i	0.968666	+	0.248368i	$0.0798941\pi$
$547$	0.654749	+	13.7449i	0.0279950	+	0.587688i	−0.940671	+	0.339320i	$0.889803\pi$
$548$		0			0
$549$	4.43620	−	0.423605i	0.189332	−	0.0180790i
$550$		0			0
$551$	5.79269	−	40.2890i	0.246777	−	1.71637i
$552$		0			0
$553$	3.80703	+	15.6928i	0.161891	+	0.667325i
$554$		0			0
$555$	−2.69261	+	1.07796i	−0.114295	+	0.0457568i
$556$		0			0
$557$	−5.98962	+	3.08786i	−0.253788	+	0.130837i	−0.580427	−	0.814312i	$-0.697114\pi$
$557$	−5.98962	+	3.08786i	−0.253788	+	0.130837i	0.326639	+	0.945149i	$0.394084\pi$
$558$		0			0
$559$	−27.5725	−	5.31417i	−1.16619	−	0.224765i
$560$		0			0
$561$	1.71457	−	3.75439i	0.0723894	−	0.158511i
$562$		0			0
$563$	16.2055	+	10.4147i	0.682982	+	0.438926i	0.835585	−	0.549362i	$-0.185129\pi$
$563$	16.2055	+	10.4147i	0.682982	+	0.438926i	−0.152603	+	0.988288i	$0.548765\pi$
$564$		0			0
$565$	5.25749	−	9.10624i	0.221184	−	0.383103i
$566$		0			0
$567$	2.37614	+	0.226894i	0.0997886	+	0.00952866i
$568$		0			0
$569$	−25.3526	−	19.9375i	−1.06284	−	0.835824i	−0.0759291	−	0.997113i	$-0.524192\pi$
$569$	−25.3526	−	19.9375i	−1.06284	−	0.835824i	−0.986907	+	0.161290i	$0.948435\pi$
$570$		0			0
$571$	−24.5983	+	4.74094i	−1.02941	+	0.198402i	−0.675872	−	0.737019i	$-0.736233\pi$
$571$	−24.5983	+	4.74094i	−1.02941	+	0.198402i	−0.353536	+	0.935421i	$0.615021\pi$
$572$		0			0
$573$	−3.43011	−	5.94113i	−0.143295	−	0.248194i
$574$		0			0
$575$	11.2646	−	15.8189i	0.469766	−	0.659694i
$576$		0			0
$577$	3.80338	−	3.62652i	0.158337	−	0.150974i	−0.606769	−	0.794878i	$-0.707535\pi$
$577$	3.80338	−	3.62652i	0.158337	−	0.150974i	0.765106	+	0.643904i	$0.222686\pi$
$578$		0			0
$579$	−2.19114	−	0.643376i	−0.0910605	−	0.0267378i
$580$		0			0
$581$	−15.9881	−	18.4513i	−0.663299	−	0.765488i
$582$		0			0
$583$	−3.45711	−	9.98866i	−0.143179	−	0.413688i
$584$		0			0
$585$	13.6839	+	13.0475i	0.565758	+	0.539449i
$586$		0			0
$587$	15.4859	+	7.98356i	0.639173	+	0.329517i	0.747168	−	0.664635i	$-0.231413\pi$
$587$	15.4859	+	7.98356i	0.639173	+	0.329517i	−0.107995	+	0.994151i	$0.534443\pi$
$588$		0			0
$589$	43.6889	−	12.8282i	1.80017	−	0.528577i
$590$		0			0
$591$	14.1309	+	19.8441i	0.581268	+	0.816277i
$592$		0			0
$593$	11.2522	−	32.5111i	0.462072	−	1.33507i	−0.437861	−	0.899043i	$-0.644264\pi$
$593$	11.2522	−	32.5111i	0.462072	−	1.33507i	0.899933	−	0.436027i	$-0.143615\pi$
$594$		0			0
$595$	−5.99882	−	13.1356i	−0.245928	−	0.538506i
$596$		0			0
$597$	−0.936872	+	19.6674i	−0.0383436	+	0.804932i
$598$		0			0
$599$	−7.49485	+	30.8942i	−0.306231	+	1.26230i	0.585847	+	0.810422i	$0.300762\pi$
$599$	−7.49485	+	30.8942i	−0.306231	+	1.26230i	−0.892078	+	0.451881i	$0.850753\pi$
$600$		0			0
$601$	3.47810	−	2.73521i	0.141875	−	0.111571i	−0.544699	−	0.838631i	$-0.683356\pi$
$601$	3.47810	−	2.73521i	0.141875	−	0.111571i	0.686574	+	0.727060i	$0.259114\pi$
$602$		0			0
$603$	−8.09122	−	1.23783i	−0.329500	−	0.0504082i
$604$		0			0
$605$	−16.1695	+	12.7158i	−0.657382	+	0.516971i
$606$		0			0
$607$	−2.80429	+	11.5594i	−0.113823	+	0.469183i	0.886161	+	0.463378i	$0.153363\pi$
$607$	−2.80429	+	11.5594i	−0.113823	+	0.469183i	−0.999983	+	0.00580484i	$0.998152\pi$
$608$		0			0
$609$	−0.713504	+	14.9783i	−0.0289126	+	0.606951i
$610$		0			0
$611$	22.7243	+	49.7593i	0.919327	+	2.01304i
$612$		0			0
$613$	14.0522	−	40.6011i	0.567562	−	1.63986i	−0.186048	−	0.982541i	$-0.559568\pi$
$613$	14.0522	−	40.6011i	0.567562	−	1.63986i	0.753610	−	0.657322i	$-0.228311\pi$
$614$		0			0
$615$	−5.16751	−	7.25676i	−0.208374	−	0.292621i
$616$		0			0
$617$	20.7253	−	6.08549i	0.834369	−	0.244993i	0.163476	−	0.986547i	$-0.447729\pi$
$617$	20.7253	−	6.08549i	0.834369	−	0.244993i	0.670893	+	0.741555i	$0.265911\pi$
$618$		0			0
$619$	41.8553	+	21.5779i	1.68231	+	0.867289i	0.989221	+	0.146434i	$0.0467795\pi$
$619$	41.8553	+	21.5779i	1.68231	+	0.867289i	0.693085	+	0.720855i	$0.256251\pi$
$620$		0			0
$621$	−4.40045	−	4.19582i	−0.176584	−	0.168372i
$622$		0			0
$623$	10.7664	+	31.1075i	0.431347	+	1.24630i
$624$		0			0
$625$	20.1490	+	23.2532i	0.805962	+	0.930130i
$626$		0			0
$627$	12.1406	+	3.56481i	0.484851	+	0.142365i
$628$		0			0
$629$	1.54981	−	1.47774i	0.0617951	−	0.0589215i
$630$		0			0
$631$	−3.05237	+	4.28645i	−0.121513	+	0.170641i	−0.870852	−	0.491546i	$-0.836432\pi$
$631$	−3.05237	+	4.28645i	−0.121513	+	0.170641i	0.749339	+	0.662187i	$0.230371\pi$
$632$		0			0
$633$	−7.10297	−	12.3027i	−0.282318	−	0.488989i
$634$		0			0
$635$	−36.4294	+	7.02118i	−1.44565	+	0.278627i
$636$		0			0
$637$	−6.76240	−	5.31801i	−0.267936	−	0.210707i
$638$		0			0
$639$	6.66942	+	0.636853i	0.263838	+	0.0251935i
$640$		0			0
$641$	−12.1023	+	20.9617i	−0.478010	+	0.827938i	−0.999682	−	0.0252079i	$-0.991975\pi$
$641$	−12.1023	+	20.9617i	−0.478010	+	0.827938i	0.521672	+	0.853146i	$0.325309\pi$
$642$		0			0
$643$	−7.55952	−	4.85821i	−0.298118	−	0.191589i	0.383027	−	0.923737i	$-0.374882\pi$
$643$	−7.55952	−	4.85821i	−0.298118	−	0.191589i	−0.681146	+	0.732148i	$0.738518\pi$
$644$		0			0
$645$	5.05524	−	11.0694i	0.199050	−	0.435859i
$646$		0			0
$647$	−10.5459	−	2.03256i	−0.414603	−	0.0799081i	−0.0223157	−	0.999751i	$-0.507104\pi$
$647$	−10.5459	−	2.03256i	−0.414603	−	0.0799081i	−0.392287	+	0.919843i	$0.628316\pi$
$648$		0			0
$649$	2.23075	−	1.15003i	0.0875645	−	0.0451426i
$650$		0			0
$651$	−15.5730	+	6.23450i	−0.610356	+	0.244350i
$652$		0			0
$653$	9.24076	+	38.0909i	0.361619	+	1.49061i	0.804457	+	0.594011i	$0.202456\pi$
$653$	9.24076	+	38.0909i	0.361619	+	1.49061i	−0.442838	+	0.896602i	$0.646028\pi$
$654$		0			0
$655$	4.21826	−	29.3387i	0.164821	−	1.14636i
$656$		0			0
$657$	0.745730	−	0.0712086i	0.0290937	−	0.00277811i
$658$		0			0
$659$	−2.02839	−	42.5811i	−0.0790148	−	1.65872i	−0.596189	−	0.802844i	$-0.703319\pi$
$659$	−2.02839	−	42.5811i	−0.0790148	−	1.65872i	0.517174	−	0.855880i	$-0.326984\pi$
$660$		0			0
$661$	−1.30506	−	9.07690i	−0.0507610	−	0.353051i	−0.999334	−	0.0364920i	$-0.988382\pi$
$661$	−1.30506	−	9.07690i	−0.0507610	−	0.353051i	0.948573	−	0.316559i	$-0.102527\pi$
$662$		0			0
$663$	−12.9597	−	5.18830i	−0.503315	−	0.201497i
$664$		0			0
$665$	37.2423	−	23.9341i	1.44419	−	0.928126i
$666$		0			0
$667$	25.0137	−	28.8673i	0.968533	−	1.11775i
$668$		0			0
$669$	−4.53085			−0.175173
$670$		0			0
$671$	−8.70287			−0.335971
$672$		0			0
$673$	−32.5600	+	37.5763i	−1.25510	+	1.44846i	−0.411563	+	0.911381i	$0.635017\pi$
$673$	−32.5600	+	37.5763i	−1.25510	+	1.44846i	−0.843533	+	0.537077i	$0.819528\pi$
$674$		0			0
$675$	−2.68691	+	1.72678i	−0.103419	+	0.0664636i
$676$		0			0
$677$	−41.5445	−	16.6319i	−1.59669	−	0.639216i	−0.608649	−	0.793440i	$-0.708288\pi$
$677$	−41.5445	−	16.6319i	−1.59669	−	0.639216i	−0.988036	+	0.154223i	$0.950712\pi$
$678$		0			0
$679$	3.47280	+	24.1538i	0.133274	+	0.926940i
$680$		0			0
$681$	0.642389	+	13.4854i	0.0246164	+	0.516762i
$682$		0			0
$683$	−1.10169	+	0.105199i	−0.0421551	+	0.00402533i	−0.116112	−	0.993236i	$-0.537043\pi$
$683$	−1.10169	+	0.105199i	−0.0421551	+	0.00402533i	0.0739572	+	0.997261i	$0.476437\pi$
$684$		0			0
$685$	−6.47239	+	45.0165i	−0.247297	+	1.71999i
$686$		0			0
$687$	6.32453	+	26.0701i	0.241296	+	0.994635i
$688$		0			0
$689$	−33.1892	+	13.2870i	−1.26441	+	0.506193i
$690$		0			0
$691$	12.4814	−	6.43462i	0.474816	−	0.244785i	−0.204171	−	0.978935i	$-0.565450\pi$
$691$	12.4814	−	6.43462i	0.474816	−	0.244785i	0.678987	+	0.734151i	$0.262419\pi$
$692$		0			0
$693$	−4.57724	−	0.882192i	−0.173875	−	0.0335117i
$694$		0			0
$695$	17.8690	−	39.1277i	0.677810	−	1.48420i
$696$		0			0
$697$	5.53331	+	3.55604i	0.209589	+	0.134695i
$698$		0			0
$699$	−12.7089	+	22.0124i	−0.480694	+	0.832586i
$700$		0			0
$701$	−7.66802	−	0.732208i	−0.289617	−	0.0276551i	−0.0507637	−	0.998711i	$-0.516166\pi$
$701$	−7.66802	−	0.732208i	−0.289617	−	0.0276551i	−0.238854	+	0.971056i	$0.576772\pi$
$702$		0			0
$703$	5.16034	+	4.05813i	0.194626	+	0.153055i
$704$		0			0
$705$	−23.2783	+	4.48653i	−0.876712	+	0.168972i
$706$		0			0
$707$	−13.6316	−	23.6106i	−0.512669	−	0.887968i
$708$		0			0
$709$	11.3239	−	15.9022i	0.425277	−	0.597218i	−0.545231	−	0.838286i	$-0.683558\pi$
$709$	11.3239	−	15.9022i	0.425277	−	0.597218i	0.970508	+	0.241068i	$0.0774975\pi$
$710$		0			0
$711$	−4.89613	+	4.66845i	−0.183619	+	0.175081i
$712$		0			0
$713$	40.9986	+	12.0383i	1.53541	+	0.450837i
$714$		0			0
$715$	−24.1802	−	27.9054i	−0.904286	−	1.04360i
$716$		0			0
$717$	0.596228	+	1.72269i	0.0222665	+	0.0643349i
$718$		0			0
$719$	12.0022	+	11.4441i	0.447608	+	0.426793i	0.880059	−	0.474864i	$-0.157503\pi$
$719$	12.0022	+	11.4441i	0.447608	+	0.426793i	−0.432451	+	0.901657i	$0.642351\pi$
$720$		0			0
$721$	−35.5095	−	18.3064i	−1.32244	−	0.681766i
$722$		0			0
$723$	−11.7057	+	3.43711i	−0.435340	+	0.127827i
$724$		0			0
$725$	−11.6388	−	16.3444i	−0.432254	−	0.607016i
$726$		0			0
$727$	−4.87250	+	14.0782i	−0.180711	+	0.522130i	−0.998580	−	0.0532744i	$-0.983034\pi$
$727$	−4.87250	+	14.0782i	−0.180711	+	0.522130i	0.817869	+	0.575405i	$0.195155\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−0.427513	+	8.97459i	−0.0158121	+	0.331937i
$732$		0			0
$733$	−2.09207	+	8.62362i	−0.0772723	+	0.318521i	−0.997309	−	0.0733112i	$-0.976643\pi$
$733$	−2.09207	+	8.62362i	−0.0772723	+	0.318521i	0.920037	+	0.391832i	$0.128159\pi$
$734$		0			0
$735$	2.93065	−	2.30469i	0.108099	−	0.0850098i
$736$		0			0
$737$	15.5000	+	3.90842i	0.570951	+	0.143969i
$738$		0			0
$739$	−31.5348	+	24.7993i	−1.16003	+	0.912256i	−0.997228	−	0.0744034i	$-0.976295\pi$
$739$	−31.5348	+	24.7993i	−1.16003	+	0.912256i	−0.162799	+	0.986659i	$0.552052\pi$
$740$		0			0
$741$	10.0895	−	41.5896i	0.370648	−	1.52783i
$742$		0			0
$743$	−1.45325	+	30.5075i	−0.0533147	+	1.11921i	0.800734	+	0.599020i	$0.204443\pi$
$743$	−1.45325	+	30.5075i	−0.0533147	+	1.11921i	−0.854049	+	0.520193i	$0.825860\pi$
$744$		0			0
$745$	3.71264	+	8.12954i	0.136020	+	0.297843i
$746$		0			0
$747$	3.34536	−	9.66578i	0.122400	−	0.353652i
$748$		0			0
$749$	−7.42269	−	10.4237i	−0.271219	−	0.380874i
$750$		0			0
$751$	9.34219	−	2.74311i	0.340901	−	0.100098i	−0.106801	−	0.994280i	$-0.534061\pi$
$751$	9.34219	−	2.74311i	0.340901	−	0.100098i	0.447702	+	0.894183i	$0.352243\pi$
$752$		0			0
$753$	−15.1742	−	7.82282i	−0.552977	−	0.285079i
$754$		0			0
$755$	−26.7411	−	25.4976i	−0.973210	−	0.927954i
$756$		0			0
$757$	−5.78932	−	16.7271i	−0.210416	−	0.607958i	0.789567	−	0.613664i	$-0.210305\pi$
$757$	−5.78932	−	16.7271i	−0.210416	−	0.607958i	−0.999984	+	0.00570587i	$0.998184\pi$
$758$		0			0
$759$	7.77584	+	8.97380i	0.282245	+	0.325728i
$760$		0			0
$761$	12.5219	+	3.67675i	0.453918	+	0.133282i	0.500696	−	0.865623i	$-0.333077\pi$
$761$	12.5219	+	3.67675i	0.453918	+	0.133282i	−0.0467786	+	0.998905i	$0.514896\pi$
$762$		0			0
$763$	−13.1316	+	12.5209i	−0.475395	+	0.453288i
$764$		0			0
$765$	3.50922	−	4.92801i	0.126876	−	0.178173i
$766$		0			0
$767$	−4.24425	−	7.35126i	−0.153251	−	0.265439i
$768$		0			0
$769$	−3.69433	+	0.712024i	−0.133221	+	0.0256762i	−0.255426	−	0.966829i	$-0.582216\pi$
$769$	−3.69433	+	0.712024i	−0.133221	+	0.0256762i	0.122205	+	0.992505i	$0.461004\pi$
$770$		0			0
$771$	1.74346	+	1.37107i	0.0627892	+	0.0493780i
$772$		0			0
$773$	−46.3869	−	4.42941i	−1.66842	−	0.159315i	−0.782342	−	0.622849i	$-0.785975\pi$
$773$	−46.3869	−	4.42941i	−1.66842	−	0.159315i	−0.886079	+	0.463534i	$0.846581\pi$
$774$		0			0
$775$	11.2229	−	19.4387i	0.403140	−	0.698259i
$776$		0			0
$777$	−2.03459	−	1.30755i	−0.0729906	−	0.0469082i
$778$		0			0
$779$	−8.37657	+	18.3421i	−0.300122	+	0.657175i
$780$		0			0
$781$	−12.8475	−	2.47616i	−0.459721	−	0.0886040i
$782$		0			0
$783$	−5.58383	+	2.87866i	−0.199550	+	0.102875i
$784$		0			0
$785$	15.4036	−	6.16666i	0.549777	−	0.220098i
$786$		0			0
$787$	−1.17270	−	4.83394i	−0.0418023	−	0.172311i	0.947084	−	0.320986i	$-0.104014\pi$
$787$	−1.17270	−	4.83394i	−0.0418023	−	0.172311i	−0.988886	+	0.148675i	$0.952499\pi$
$788$		0			0
$789$	−3.19704	+	22.2359i	−0.113818	+	0.791620i
$790$		0			0
$791$	8.72840	−	0.833461i	0.310346	−	0.0296345i
$792$		0			0
$793$	1.40058	+	29.4017i	0.0497359	+	1.04409i
$794$		0			0
$795$	−2.20491	−	15.3355i	−0.0782001	−	0.543894i
$796$		0			0
$797$	−13.1631	−	5.26970i	−0.466260	−	0.186662i	0.126623	−	0.991951i	$-0.459586\pi$
$797$	−13.1631	−	5.26970i	−0.466260	−	0.186662i	−0.592883	+	0.805289i	$0.702010\pi$
$798$		0			0
$799$	14.7247	−	9.46297i	0.520921	−	0.334776i
$800$		0			0
$801$	−9.03106	+	10.4224i	−0.319097	+	0.368257i
$802$		0			0
$803$	−1.46296			−0.0516268
$804$		0			0
$805$	41.5439			1.46423
$806$		0			0
$807$	−18.1957	+	20.9989i	−0.640518	+	0.739198i
$808$		0			0
$809$	−13.9968	+	8.99521i	−0.492102	+	0.316255i	−0.763050	−	0.646339i	$-0.776299\pi$
$809$	−13.9968	+	8.99521i	−0.492102	+	0.316255i	0.270948	+	0.962594i	$0.412663\pi$
$810$		0			0
$811$	−35.4550	−	14.1941i	−1.24499	−	0.498421i	−0.346767	−	0.937951i	$-0.612721\pi$
$811$	−35.4550	−	14.1941i	−1.24499	−	0.498421i	−0.898228	+	0.439530i	$0.855145\pi$
$812$		0			0
$813$	−1.65102	−	11.4831i	−0.0579039	−	0.402730i
$814$		0			0
$815$	−0.836362	−	17.5574i	−0.0292965	−	0.615009i
$816$		0			0
$817$	−27.4196	+	2.61826i	−0.959292	+	0.0916013i
$818$		0			0
$819$	−2.24376	+	15.6057i	−0.0784034	+	0.545307i
$820$		0			0
$821$	3.04469	+	12.5504i	0.106260	+	0.438011i	0.999943	−	0.0106889i	$-0.00340244\pi$
$821$	3.04469	+	12.5504i	0.106260	+	0.438011i	−0.893683	+	0.448700i	$0.851887\pi$
$822$		0			0
$823$	27.2827	−	10.9224i	0.951017	−	0.380730i	0.156300	−	0.987710i	$-0.450043\pi$
$823$	27.2827	−	10.9224i	0.951017	−	0.380730i	0.794717	+	0.606980i	$0.207619\pi$
$824$		0			0
$825$	5.54407	−	2.85817i	0.193020	−	0.0995087i
$826$		0			0
$827$	11.1998	+	2.15858i	0.389454	+	0.0750610i	0.380219	−	0.924896i	$-0.375848\pi$
$827$	11.1998	+	2.15858i	0.389454	+	0.0750610i	0.00923427	+	0.999957i	$0.497061\pi$
$828$		0			0
$829$	−2.30390	+	5.04485i	−0.0800179	+	0.175215i	−0.945412	−	0.325877i	$-0.894341\pi$
$829$	−2.30390	+	5.04485i	−0.0800179	+	0.175215i	0.865394	+	0.501091i	$0.167068\pi$
$830$		0			0
$831$	−6.60412	−	4.24421i	−0.229094	−	0.147230i
$832$		0			0
$833$	−1.37635	+	2.38391i	−0.0476878	+	0.0825976i
$834$		0			0
$835$	−30.4444	−	2.90709i	−1.05357	−	0.100604i
$836$		0			0
$837$	−5.52410	−	4.34420i	−0.190941	−	0.150158i
$838$		0			0
$839$	−10.6823	+	2.05885i	−0.368796	+	0.0710795i	−0.370282	−	0.928919i	$-0.620739\pi$
$839$	−10.6823	+	2.05885i	−0.368796	+	0.0710795i	0.00148642	+	0.999999i	$0.499527\pi$
$840$		0			0
$841$	−5.23292	−	9.06369i	−0.180446	−	0.312541i
$842$		0			0
$843$	6.69116	−	9.39642i	0.230456	−	0.323630i
$844$		0			0
$845$	−63.4519	+	60.5013i	−2.18281	+	2.08131i
$846$		0			0
$847$	−16.4582	−	4.83257i	−0.565511	−	0.166049i
$848$		0			0
$849$	6.34705	+	7.32489i	0.217830	+	0.251389i
$850$		0			0
$851$	2.01494	+	5.82179i	0.0690713	+	0.199569i
$852$		0			0
$853$	−2.21173	−	2.10888i	−0.0757283	−	0.0722068i	0.651270	−	0.758846i	$-0.274237\pi$
$853$	−2.21173	−	2.10888i	−0.0757283	−	0.0722068i	−0.726998	+	0.686639i	$0.759085\pi$
$854$		0			0
$855$	16.4849	+	8.49857i	0.563773	+	0.290645i
$856$		0			0
$857$	−34.2747	+	10.0640i	−1.17080	+	0.343778i	−0.808621	−	0.588330i	$-0.799786\pi$
$857$	−34.2747	+	10.0640i	−1.17080	+	0.343778i	−0.362180	+	0.932108i	$0.617967\pi$
$858$		0			0
$859$	6.31684	+	8.87076i	0.215528	+	0.302666i	0.908159	−	0.418626i	$-0.137488\pi$
$859$	6.31684	+	8.87076i	0.215528	+	0.302666i	−0.692631	+	0.721292i	$0.743549\pi$
$860$		0			0
$861$	2.42966	−	7.02005i	0.0828027	−	0.239243i
$862$		0			0
$863$	20.1078	+	44.0299i	0.684476	+	1.49879i	0.857830	+	0.513934i	$0.171812\pi$
$863$	20.1078	+	44.0299i	0.684476	+	1.49879i	−0.173354	+	0.984860i	$0.555460\pi$
$864$		0			0
$865$	−2.46477	+	51.7418i	−0.0838045	+	1.75927i
$866$		0			0
$867$	2.95484	−	12.1800i	0.100352	−	0.413655i
$868$		0			0
$869$	10.3850	−	8.16686i	0.352287	−	0.277042i
$870$		0			0
$871$	10.7097	−	52.9942i	0.362885	−	1.79564i
$872$		0			0
$873$	−8.03596	+	6.31955i	−0.271976	+	0.213884i
$874$		0			0
$875$	−2.90931	+	11.9923i	−0.0983526	+	0.405415i
$876$		0			0
$877$	−1.00908	+	21.1831i	−0.0340741	+	0.715303i	0.915605	+	0.402078i	$0.131712\pi$
$877$	−1.00908	+	21.1831i	−0.0340741	+	0.715303i	−0.949679	+	0.313224i	$0.898591\pi$
$878$		0			0
$879$	−2.44506	−	5.35394i	−0.0824699	−	0.180584i
$880$		0			0
$881$	−4.95963	+	14.3299i	−0.167094	+	0.482787i	−0.997197	−	0.0748236i	$-0.976161\pi$
$881$	−4.95963	+	14.3299i	−0.167094	+	0.482787i	0.830102	+	0.557611i	$0.188282\pi$
$882$		0			0
$883$	−23.4831	−	32.9774i	−0.790269	−	1.10978i	−0.991484	−	0.130230i	$-0.958428\pi$
$883$	−23.4831	−	32.9774i	−0.790269	−	1.10978i	0.201215	−	0.979547i	$-0.435511\pi$
$884$		0			0
$885$	3.52969	−	1.03641i	0.118649	−	0.0348385i
$886$		0			0
$887$	15.9225	+	8.20862i	0.534625	+	0.275618i	0.704325	−	0.709877i	$-0.251250\pi$
$887$	15.9225	+	8.20862i	0.534625	+	0.275618i	−0.169700	+	0.985496i	$0.554280\pi$
$888$		0			0
$889$	−22.3897	−	21.3485i	−0.750925	−	0.716006i
$890$		0			0
$891$	−0.638732	−	1.84549i	−0.0213983	−	0.0618264i
$892$		0			0
$893$	35.1393	+	40.5529i	1.17589	+	1.35705i
$894$		0			0
$895$	45.5807	+	13.3837i	1.52360	+	0.447368i
$896$		0			0
$897$	29.0656	−	27.7140i	0.970473	−	0.925344i
$898$		0			0
$899$	25.6089	−	35.9627i	0.854105	−	1.19942i
$900$		0			0
$901$	5.71950	+	9.90646i	0.190544	+	0.330032i
$902$		0			0
$903$	9.96408	−	1.92042i	0.331584	−	0.0639075i
$904$		0			0
$905$	48.9937	+	38.5291i	1.62861	+	1.28075i
$906$		0			0
$907$	−24.1706	−	2.30801i	−0.802572	−	0.0766363i	−0.314295	−	0.949325i	$-0.601768\pi$
$907$	−24.1706	−	2.30801i	−0.802572	−	0.0766363i	−0.488276	+	0.872689i	$0.662374\pi$
$908$		0			0
$909$	5.71088	−	9.89153i	0.189418	−	0.328081i
$910$		0			0
$911$	−39.7534	−	25.5480i	−1.31709	−	0.846442i	−0.322128	−	0.946696i	$-0.604398\pi$
$911$	−39.7534	−	25.5480i	−1.31709	−	0.846442i	−0.994962	+	0.100254i	$0.968034\pi$
$912$		0			0
$913$	−8.29789	+	18.1698i	−0.274620	+	0.601334i
$914$		0			0
$915$	−12.5259	−	2.41417i	−0.414093	−	0.0798098i
$916$		0			0
$917$	21.9686	−	11.3256i	0.725466	−	0.374004i
$918$		0			0
$919$	8.67117	−	3.47141i	0.286035	−	0.114511i	−0.224208	−	0.974541i	$-0.571980\pi$
$919$	8.67117	−	3.47141i	0.286035	−	0.114511i	0.510244	+	0.860030i	$0.329555\pi$
$920$		0			0
$921$	3.62814	+	14.9554i	0.119551	+	0.492797i
$922$		0			0
$923$	−6.29785	+	43.8025i	−0.207296	+	1.44178i
$924$		0			0
$925$	3.22154	−	0.307619i	0.105923	−	0.0101145i
$926$		0			0
$927$	−0.796382	−	16.7181i	−0.0261566	−	0.549095i
$928$		0			0
$929$	−7.14599	−	49.7014i	−0.234452	−	1.63065i	−0.678467	−	0.734631i	$-0.737355\pi$
$929$	−7.14599	−	49.7014i	−0.234452	−	1.63065i	0.444014	−	0.896020i	$-0.353554\pi$
$930$		0			0
$931$	−7.83439	−	3.13642i	−0.256762	−	0.102792i
$932$		0			0
$933$	1.06190	−	0.682440i	0.0347650	−	0.0223421i
$934$		0			0
$935$	−7.73694	+	8.92891i	−0.253025	+	0.292007i
$936$		0			0
$937$	33.1645			1.08344			0.541719	−	0.840560i	$-0.317774\pi$
$937$	33.1645			1.08344			0.541719	+	0.840560i	$0.317774\pi$
$938$		0			0
$939$	21.4657			0.700507
$940$		0			0
$941$	−12.4944	+	14.4193i	−0.407305	+	0.470055i	−0.921928	−	0.387361i	$-0.873387\pi$
$941$	−12.4944	+	14.4193i	−0.407305	+	0.470055i	0.514623	+	0.857417i	$0.327932\pi$
$942$		0			0
$943$	−15.9188	+	10.2304i	−0.518386	+	0.333146i
$944$		0			0
$945$	−6.34322	−	2.53944i	−0.206345	−	0.0826081i
$946$		0			0
$947$	−4.95586	−	34.4688i	−0.161044	−	1.12009i	−0.896671	−	0.442698i	$-0.854021\pi$
$947$	−4.95586	−	34.4688i	−0.161044	−	1.12009i	0.735627	−	0.677387i	$-0.236888\pi$
$948$		0			0
$949$	0.235439	+	4.94246i	0.00764266	+	0.160439i
$950$		0			0
$951$	29.4816	−	2.81515i	0.956006	−	0.0912875i
$952$		0			0
$953$	−3.72714	+	25.9228i	−0.120734	+	0.839723i	0.835994	+	0.548739i	$0.184892\pi$
$953$	−3.72714	+	25.9228i	−0.120734	+	0.839723i	−0.956728	+	0.290984i	$0.906017\pi$
$954$		0			0
$955$	4.62970	+	19.0839i	0.149814	+	0.617540i
$956$		0			0
$957$	11.3897	−	4.55974i	0.368176	−	0.147395i
$958$		0			0
$959$	−33.7080	+	17.3777i	−1.08849	+	0.561155i
$960$		0			0
$961$	18.0555	+	3.47991i	0.582435	+	0.112255i
$962$		0			0
$963$	2.22705	−	4.87655i	0.0717656	−	0.157145i
$964$		0			0
$965$	5.49922	+	3.53413i	0.177026	+	0.113768i
$966$		0			0
$967$	−22.2133	+	38.4746i	−0.714332	+	1.23726i	0.248885	+	0.968533i	$0.419936\pi$
$967$	−22.2133	+	38.4746i	−0.714332	+	1.23726i	−0.963217	+	0.268726i	$0.913397\pi$
$968$		0			0
$969$	−13.6314	−	1.30164i	−0.437905	−	0.0418148i
$970$		0			0
$971$	−13.2130	−	10.3908i	−0.424024	−	0.333456i	0.383238	−	0.923650i	$-0.374809\pi$
$971$	−13.2130	−	10.3908i	−0.424024	−	0.333456i	−0.807262	+	0.590193i	$0.799051\pi$
$972$		0			0
$973$	35.2205	−	6.78819i	1.12912	−	0.217619i
$974$		0			0
$975$	−10.5482	−	18.2701i	−0.337814	−	0.585111i
$976$		0			0
$977$	11.6082	−	16.3015i	0.371380	−	0.521531i	−0.586019	−	0.810297i	$-0.699306\pi$
$977$	11.6082	−	16.3015i	0.371380	−	0.521531i	0.957400	+	0.288767i	$0.0932451\pi$
$978$		0			0
$979$	19.4917	−	18.5853i	0.622957	−	0.593988i
$980$		0			0
$981$	−7.29350	−	2.14156i	−0.232863	−	0.0683749i
$982$		0			0
$983$	−12.1334	−	14.0027i	−0.386995	−	0.446616i	0.528507	−	0.848929i	$-0.322752\pi$
$983$	−12.1334	−	14.0027i	−0.386995	−	0.446616i	−0.915502	+	0.402313i	$0.868206\pi$
$984$		0			0
$985$	−22.8078	−	65.8989i	−0.726718	−	2.09971i
$986$		0			0
$987$	−14.3070	−	13.6417i	−0.455396	−	0.434219i
$988$		0			0
$989$	−22.9748	−	11.8444i	−0.730558	−	0.376629i
$990$		0			0
$991$	47.3053	−	13.8901i	1.50270	−	0.441233i	0.576132	−	0.817356i	$-0.304561\pi$
$991$	47.3053	−	13.8901i	1.50270	−	0.441233i	0.926570	+	0.376123i	$0.122743\pi$
$992$		0			0
$993$	18.3918	+	25.8277i	0.583646	+	0.819617i
$994$		0			0
$995$	18.4341	−	53.2619i	0.584401	−	1.68852i
$996$		0			0
$997$	−0.728228	−	1.59460i	−0.0230632	−	0.0505014i	0.897750	−	0.440506i	$-0.145201\pi$
$997$	−0.728228	−	1.59460i	−0.0230632	−	0.0505014i	−0.920813	+	0.390004i	$0.872474\pi$
$998$		0			0
$999$	0.0482113	−	1.01208i	0.00152534	−	0.0320208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.121.1	✓	120
67.36	even	33	inner	804.2.y.b.505.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.1	✓	120	1.1	even	1	trivial
804.2.y.b.505.1	yes	120	67.36	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{3} +(-2.40809 + 1.54759i) q^{5} +(-2.21597 - 0.887140i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.0929229 + 1.95069i) q^{11} +(6.57525 - 0.627860i) q^{13} +(-0.407377 + 2.83337i) q^{15} +(-0.498266 - 2.05388i) q^{17} +(6.01505 - 2.40806i) q^{19} +(-2.12161 + 1.09376i) q^{21} +(5.97032 + 1.15068i) q^{23} +(1.32681 - 2.90531i) q^{25} +(-0.841254 - 0.540641i) q^{27} +(3.14109 - 5.44053i) q^{29} +(6.99582 + 0.668020i) q^{31} +(1.53509 + 1.20720i) q^{33} +(6.70919 - 1.29309i) q^{35} +(0.506614 + 0.877481i) q^{37} +(3.83137 - 5.38040i) q^{39} +(-2.25239 + 2.14765i) q^{41} +(-4.07902 - 1.19771i) q^{43} +(1.87454 + 2.16334i) q^{45} +(2.70871 + 7.82632i) q^{47} +(-0.942638 - 0.898803i) q^{49} +(-1.87852 - 0.968442i) q^{51} +(-5.19321 + 1.52486i) q^{53} +(-3.24263 - 4.55364i) q^{55} +(2.11913 - 6.12282i) q^{57} +(-0.533864 - 1.16900i) q^{59} +(-0.212043 + 4.45133i) q^{61} +(-0.562745 + 2.31967i) q^{63} +(-14.8621 + 11.6877i) q^{65} +(2.37673 - 7.83270i) q^{67} +(4.77936 - 3.75853i) q^{69} +(-1.57953 + 6.51090i) q^{71} +(-0.0356447 + 0.748274i) q^{73} +(-1.32681 - 2.90531i) q^{75} +(1.52462 - 4.40511i) q^{77} +(-3.92414 - 5.51069i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(9.09130 + 4.68689i) q^{83} +(4.37843 + 4.17483i) q^{85} +(-2.05470 - 5.93667i) q^{87} +(-9.03106 - 10.4224i) q^{89} +(-15.1275 - 4.44185i) q^{91} +(5.08615 - 4.84963i) q^{93} +(-10.7581 + 15.1077i) q^{95} +(-5.11159 - 8.85353i) q^{97} +(1.91761 - 0.369589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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