LMFDB - Embedded newform 216.2.q.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	216.25
Dual form			216.2.q.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36303 + 1.06872i) q^{3} +(2.18080 - 1.82991i) q^{5} +(0.145059 - 0.0527971i) q^{7} +(0.715688 - 2.91338i) q^{9} +O(q^{10})$	\(q+(-1.36303 + 1.06872i) q^{3} +(2.18080 - 1.82991i) q^{5} +(0.145059 - 0.0527971i) q^{7} +(0.715688 - 2.91338i) q^{9} +(4.10127 + 3.44137i) q^{11} +(0.00459855 + 0.0260797i) q^{13} +(-1.01684 + 4.82488i) q^{15} +(2.88012 + 4.98852i) q^{17} +(3.10159 - 5.37211i) q^{19} +(-0.141294 + 0.226991i) q^{21} +(-3.35846 - 1.22238i) q^{23} +(0.539084 - 3.05730i) q^{25} +(2.13808 + 4.73589i) q^{27} +(0.0327963 - 0.185997i) q^{29} +(-2.56293 - 0.932831i) q^{31} +(-9.26799 - 0.307591i) q^{33} +(0.219731 - 0.380584i) q^{35} +(-4.11754 - 7.13179i) q^{37} +(-0.0341397 - 0.0306327i) q^{39} +(-0.00921569 - 0.0522648i) q^{41} +(-6.21877 - 5.21817i) q^{43} +(-3.77045 - 7.66315i) q^{45} +(-11.8622 + 4.31750i) q^{47} +(-5.34406 + 4.48420i) q^{49} +(-9.25700 - 3.72145i) q^{51} +13.8601 q^{53} +15.2414 q^{55} +(1.51371 + 10.6371i) q^{57} +(3.24676 - 2.72435i) q^{59} +(-4.47554 + 1.62897i) q^{61} +(-0.0500012 - 0.460398i) q^{63} +(0.0577519 + 0.0484596i) q^{65} +(1.03748 + 5.88386i) q^{67} +(5.88406 - 1.92311i) q^{69} +(-1.35870 - 2.35333i) q^{71} +(-7.37683 + 12.7770i) q^{73} +(2.53260 + 4.74331i) q^{75} +(0.776619 + 0.282666i) q^{77} +(0.880151 - 4.99159i) q^{79} +(-7.97558 - 4.17015i) q^{81} +(-0.538876 + 3.05612i) q^{83} +(15.4095 + 5.60860i) q^{85} +(0.154076 + 0.288569i) q^{87} +(2.11862 - 3.66956i) q^{89} +(0.00204399 + 0.00354029i) q^{91} +(4.49028 - 1.46757i) q^{93} +(-3.06653 - 17.3911i) q^{95} +(-9.25397 - 7.76500i) q^{97} +(12.9613 - 9.48561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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
$3$	−1.36303	+	1.06872i	−0.786944	+	0.617024i
$3$	−1.36303	+	1.06872i	−0.786944	+	0.617024i
$4$		0			0
$5$	2.18080	−	1.82991i	0.975284	−	0.818360i	−0.00808726	−	0.999967i	$-0.502574\pi$
$5$	2.18080	−	1.82991i	0.975284	−	0.818360i	0.983371	+	0.181607i	$0.0581298\pi$
$6$		0			0
$7$	0.145059	−	0.0527971i	0.0548271	−	0.0199554i	−0.314461	−	0.949270i	$-0.601824\pi$
$7$	0.145059	−	0.0527971i	0.0548271	−	0.0199554i	0.369288	+	0.929315i	$0.379602\pi$
$8$		0			0
$9$	0.715688	−	2.91338i	0.238563	−	0.971127i
$10$		0			0
$11$	4.10127	+	3.44137i	1.23658	+	1.03761i	0.997784	+	0.0665427i	$0.0211969\pi$
$11$	4.10127	+	3.44137i	1.23658	+	1.03761i	0.238795	+	0.971070i	$0.423248\pi$
$12$		0			0
$13$	0.00459855	+	0.0260797i	0.00127541	+	0.00723320i	0.985439	−	0.170030i	$-0.0543866\pi$
$13$	0.00459855	+	0.0260797i	0.00127541	+	0.00723320i	−0.984163	+	0.177264i	$0.943275\pi$
$14$		0			0
$15$	−1.01684	+	4.82488i	−0.262546	+	1.24578i
$16$		0			0
$17$	2.88012	+	4.98852i	0.698532	+	1.20989i	0.968975	+	0.247157i	$0.0794965\pi$
$17$	2.88012	+	4.98852i	0.698532	+	1.20989i	−0.270443	+	0.962736i	$0.587170\pi$
$18$		0			0
$19$	3.10159	−	5.37211i	0.711553	−	1.23245i	−0.252720	−	0.967539i	$-0.581325\pi$
$19$	3.10159	−	5.37211i	0.711553	−	1.23245i	0.964274	−	0.264907i	$-0.0853414\pi$
$20$		0			0
$21$	−0.141294	+	0.226991i	−0.0308329	+	0.0495334i
$22$		0			0
$23$	−3.35846	−	1.22238i	−0.700288	−	0.254884i	−0.0327542	−	0.999463i	$-0.510428\pi$
$23$	−3.35846	−	1.22238i	−0.700288	−	0.254884i	−0.667534	+	0.744579i	$0.732650\pi$
$24$		0			0
$25$	0.539084	−	3.05730i	0.107817	−	0.611460i
$26$		0			0
$27$	2.13808	+	4.73589i	0.411473	+	0.911422i
$28$		0			0
$29$	0.0327963	−	0.185997i	0.00609012	−	0.0345388i	−0.981611	−	0.190891i	$-0.938862\pi$
$29$	0.0327963	−	0.185997i	0.00609012	−	0.0345388i	0.987701	+	0.156352i	$0.0499735\pi$
$30$		0			0
$31$	−2.56293	−	0.932831i	−0.460316	−	0.167541i	0.101444	−	0.994841i	$-0.467654\pi$
$31$	−2.56293	−	0.932831i	−0.460316	−	0.167541i	−0.561761	+	0.827300i	$0.689876\pi$
$32$		0			0
$33$	−9.26799	−	0.307591i	−1.61335	−	0.0535447i
$34$		0			0
$35$	0.219731	−	0.380584i	0.0371412	−	0.0643305i
$36$		0			0
$37$	−4.11754	−	7.13179i	−0.676920	−	1.17246i	−0.975904	−	0.218201i	$-0.929981\pi$
$37$	−4.11754	−	7.13179i	−0.676920	−	1.17246i	0.298984	−	0.954258i	$-0.403352\pi$
$38$		0			0
$39$	−0.0341397	−	0.0306327i	−0.00546673	−	0.00490517i
$40$		0			0
$41$	−0.00921569	−	0.0522648i	−0.00143925	−	0.00816239i	0.984080	−	0.177728i	$-0.0568747\pi$
$41$	−0.00921569	−	0.0522648i	−0.00143925	−	0.00816239i	−0.985519	+	0.169565i	$0.945764\pi$
$42$		0			0
$43$	−6.21877	−	5.21817i	−0.948354	−	0.795763i	0.0306658	−	0.999530i	$-0.490237\pi$
$43$	−6.21877	−	5.21817i	−0.948354	−	0.795763i	−0.979020	+	0.203766i	$0.934682\pi$
$44$		0			0
$45$	−3.77045	−	7.66315i	−0.562066	−	1.14235i
$46$		0			0
$47$	−11.8622	+	4.31750i	−1.73028	+	0.629772i	−0.998651	−	0.0519270i	$-0.983464\pi$
$47$	−11.8622	+	4.31750i	−1.73028	+	0.629772i	−0.731633	+	0.681699i	$0.761241\pi$
$48$		0			0
$49$	−5.34406	+	4.48420i	−0.763437	+	0.640599i
$50$		0			0
$51$	−9.25700	−	3.72145i	−1.29624	−	0.521108i
$52$		0			0
$53$	13.8601			1.90384			0.951919	−	0.306350i	$-0.0991078\pi$
$53$	13.8601			1.90384			0.951919	+	0.306350i	$0.0991078\pi$
$54$		0			0
$55$	15.2414			2.05516
$56$		0			0
$57$	1.51371	+	10.6371i	0.200496	+	1.40891i
$58$		0			0
$59$	3.24676	−	2.72435i	0.422692	−	0.354680i	−0.406494	−	0.913653i	$-0.633249\pi$
$59$	3.24676	−	2.72435i	0.422692	−	0.354680i	0.829186	+	0.558973i	$0.188804\pi$
$60$		0			0
$61$	−4.47554	+	1.62897i	−0.573035	+	0.208568i	−0.612251	−	0.790663i	$-0.709736\pi$
$61$	−4.47554	+	1.62897i	−0.573035	+	0.208568i	0.0392166	+	0.999231i	$0.487514\pi$
$62$		0			0
$63$	−0.0500012	−	0.460398i	−0.00629956	−	0.0580047i
$64$		0			0
$65$	0.0577519	+	0.0484596i	0.00716325	+	0.00601068i
$66$		0			0
$67$	1.03748	+	5.88386i	0.126749	+	0.718827i	0.980254	+	0.197743i	$0.0633612\pi$
$67$	1.03748	+	5.88386i	0.126749	+	0.718827i	−0.853505	+	0.521084i	$0.825528\pi$
$68$		0			0
$69$	5.88406	−	1.92311i	0.708357	−	0.231515i
$70$		0			0
$71$	−1.35870	−	2.35333i	−0.161248	−	0.279289i	0.774069	−	0.633101i	$-0.218218\pi$
$71$	−1.35870	−	2.35333i	−0.161248	−	0.279289i	−0.935316	+	0.353812i	$0.884885\pi$
$72$		0			0
$73$	−7.37683	+	12.7770i	−0.863392	+	1.49544i	0.00524205	+	0.999986i	$0.498331\pi$
$73$	−7.37683	+	12.7770i	−0.863392	+	1.49544i	−0.868635	+	0.495453i	$0.835002\pi$
$74$		0			0
$75$	2.53260	+	4.74331i	0.292439	+	0.547710i
$76$		0			0
$77$	0.776619	+	0.282666i	0.0885040	+	0.0322128i
$78$		0			0
$79$	0.880151	−	4.99159i	0.0990247	−	0.561597i	−0.894415	−	0.447238i	$-0.852408\pi$
$79$	0.880151	−	4.99159i	0.0990247	−	0.561597i	0.993440	−	0.114359i	$-0.0364813\pi$
$80$		0			0
$81$	−7.97558	−	4.17015i	−0.886176	−	0.463349i
$82$		0			0
$83$	−0.538876	+	3.05612i	−0.0591494	+	0.335453i	−0.999994	−	0.00338482i	$-0.998923\pi$
$83$	−0.538876	+	3.05612i	−0.0591494	+	0.335453i	0.940845	+	0.338837i	$0.110034\pi$
$84$		0			0
$85$	15.4095	+	5.60860i	1.67140	+	0.608338i
$86$		0			0
$87$	0.154076	+	0.288569i	0.0165187	+	0.0309379i
$88$		0			0
$89$	2.11862	−	3.66956i	0.224574	−	0.388973i	−0.731618	−	0.681715i	$-0.761234\pi$
$89$	2.11862	−	3.66956i	0.224574	−	0.388973i	0.956191	+	0.292742i	$0.0945677\pi$
$90$		0			0
$91$	0.00204399	+	0.00354029i	0.000214268	+	0.000371124i
$92$		0			0
$93$	4.49028	−	1.46757i	0.465620	−	0.152180i
$94$		0			0
$95$	−3.06653	−	17.3911i	−0.314619	−	1.78429i
$96$		0			0
$97$	−9.25397	−	7.76500i	−0.939598	−	0.788416i	0.0379173	−	0.999281i	$-0.487928\pi$
$97$	−9.25397	−	7.76500i	−0.939598	−	0.788416i	−0.977515	+	0.210865i	$0.932372\pi$
$98$		0			0
$99$	12.9613	−	9.48561i	1.30266	−	0.953339i
$100$		0			0
$101$	−8.84886	+	3.22072i	−0.880495	+	0.320474i	−0.742409	−	0.669947i	$-0.766317\pi$
$101$	−8.84886	+	3.22072i	−0.880495	+	0.320474i	−0.138085	+	0.990420i	$0.544095\pi$
$102$		0			0
$103$	6.66917	−	5.59610i	0.657133	−	0.551400i	−0.252093	−	0.967703i	$-0.581119\pi$
$103$	6.66917	−	5.59610i	0.657133	−	0.551400i	0.909226	+	0.416303i	$0.136675\pi$
$104$		0			0
$105$	0.107238	+	0.753577i	0.0104654	+	0.0735416i
$106$		0			0
$107$	−0.149779			−0.0144797			−0.00723986	−	0.999974i	$-0.502305\pi$
$107$	−0.149779			−0.0144797			−0.00723986	+	0.999974i	$0.502305\pi$
$108$		0			0
$109$	10.0150			0.959265			0.479633	−	0.877469i	$-0.340770\pi$
$109$	10.0150			0.959265			0.479633	+	0.877469i	$0.340770\pi$
$110$		0			0
$111$	13.2342	+	5.32034i	1.25613	+	0.504985i
$112$		0			0
$113$	−10.6838	+	8.96477i	−1.00505	+	0.843334i	−0.987676	−	0.156515i	$-0.949974\pi$
$113$	−10.6838	+	8.96477i	−1.00505	+	0.843334i	−0.0173710	+	0.999849i	$0.505530\pi$
$114$		0			0
$115$	−9.56099	+	3.47991i	−0.891567	+	0.324504i
$116$		0			0
$117$	0.0792711	+	0.00526758i	0.00732862	+	0.000486988i
$118$		0			0
$119$	0.681166	+	0.571567i	0.0624424	+	0.0523954i
$120$		0			0
$121$	3.06722	+	17.3951i	0.278838	+	1.58137i
$122$		0			0
$123$	0.0684175	+	0.0613894i	0.00616900	+	0.00553529i
$124$		0			0
$125$	2.69814	+	4.67332i	0.241329	+	0.417994i
$126$		0			0
$127$	−1.33887	+	2.31899i	−0.118806	+	0.205777i	−0.919295	−	0.393570i	$-0.871240\pi$
$127$	−1.33887	+	2.31899i	−0.118806	+	0.205777i	0.800489	+	0.599347i	$0.204573\pi$
$128$		0			0
$129$	14.0531	+	0.466402i	1.23731	+	0.0410644i
$130$		0			0
$131$	3.77812	+	1.37512i	0.330096	+	0.120145i	0.501751	−	0.865012i	$-0.332689\pi$
$131$	3.77812	+	1.37512i	0.330096	+	0.120145i	−0.171655	+	0.985157i	$0.554912\pi$
$132$		0			0
$133$	0.166281	−	0.943027i	0.0144184	−	0.0817708i
$134$		0			0
$135$	13.3290	+	6.41554i	1.14717	+	0.552162i
$136$		0			0
$137$	−0.177470	+	1.00648i	−0.0151623	+	0.0859894i	−0.991450	−	0.130488i	$-0.958346\pi$
$137$	−0.177470	+	1.00648i	−0.0151623	+	0.0859894i	0.976288	+	0.216477i	$0.0694567\pi$
$138$		0			0
$139$	−12.3098	−	4.48042i	−1.04411	−	0.380024i	−0.237672	−	0.971346i	$-0.576384\pi$
$139$	−12.3098	−	4.48042i	−1.04411	−	0.380024i	−0.806436	+	0.591322i	$0.798606\pi$
$140$		0			0
$141$	11.5544	−	18.5622i	0.973053	−	1.56322i
$142$		0			0
$143$	−0.0708899	+	0.122785i	−0.00592811	+	0.0102678i
$144$		0			0
$145$	−0.268836	−	0.465637i	−0.0223256	−	0.0386690i
$146$		0			0
$147$	2.49176	−	11.8234i	0.205517	−	0.975175i
$148$		0			0
$149$	−1.34138	−	7.60735i	−0.109890	−	0.623219i	−0.989154	−	0.146883i	$-0.953076\pi$
$149$	−1.34138	−	7.60735i	−0.109890	−	0.623219i	0.879264	−	0.476336i	$-0.158035\pi$
$150$		0			0
$151$	11.4824	+	9.63488i	0.934425	+	0.784076i	0.976607	−	0.215034i	$-0.0689863\pi$
$151$	11.4824	+	9.63488i	0.934425	+	0.784076i	−0.0421814	+	0.999110i	$0.513431\pi$
$152$		0			0
$153$	16.5947	−	4.82067i	1.34160	−	0.389728i
$154$		0			0
$155$	−7.29624	+	2.65562i	−0.586048	+	0.213304i
$156$		0			0
$157$	−18.5483	+	15.5638i	−1.48031	+	1.24213i	−0.574462	+	0.818532i	$0.694789\pi$
$157$	−18.5483	+	15.5638i	−1.48031	+	1.24213i	−0.905850	+	0.423598i	$0.860767\pi$
$158$		0			0
$159$	−18.8918	+	14.8126i	−1.49821	+	1.17471i
$160$		0			0
$161$	−0.551713			−0.0434811
$162$		0			0
$163$	13.3534			1.04592			0.522961	−	0.852357i	$-0.324827\pi$
$163$	13.3534			1.04592			0.522961	+	0.852357i	$0.324827\pi$
$164$		0			0
$165$	−20.7745	+	16.2888i	−1.61729	+	1.26808i
$166$		0			0
$167$	7.07789	−	5.93906i	0.547704	−	0.459578i	−0.326459	−	0.945211i	$-0.605855\pi$
$167$	7.07789	−	5.93906i	0.547704	−	0.459578i	0.874163	+	0.485633i	$0.161411\pi$
$168$		0			0
$169$	12.2153	−	4.44602i	0.939642	−	0.342002i
$170$		0			0
$171$	−13.4312	−	12.8809i	−1.02711	−	0.985025i
$172$		0			0
$173$	−19.7459	−	16.5688i	−1.50126	−	1.25970i	−0.878937	−	0.476939i	$-0.841746\pi$
$173$	−19.7459	−	16.5688i	−1.50126	−	1.25970i	−0.622319	−	0.782764i	$-0.713809\pi$
$174$		0			0
$175$	−0.0832176	−	0.471950i	−0.00629066	−	0.0356761i
$176$		0			0
$177$	−1.51386	+	7.18323i	−0.113788	+	0.539925i
$178$		0			0
$179$	0.113553	+	0.196679i	0.00848732	+	0.0147005i	0.870238	−	0.492632i	$-0.163965\pi$
$179$	0.113553	+	0.196679i	0.00848732	+	0.0147005i	−0.861751	+	0.507332i	$0.830632\pi$
$180$		0			0
$181$	3.80048	−	6.58262i	0.282487	−	0.489282i	−0.689510	−	0.724277i	$-0.742174\pi$
$181$	3.80048	−	6.58262i	0.282487	−	0.489282i	0.971997	+	0.234995i	$0.0755072\pi$
$182$		0			0
$183$	4.35939	−	7.00341i	0.322255	−	0.517707i
$184$		0			0
$185$	−22.0301	−	8.01829i	−1.61968	−	0.589517i
$186$		0			0
$187$	−5.35520	+	30.3708i	−0.391611	+	2.22093i
$188$		0			0
$189$	0.560188	+	0.574098i	0.0407477	+	0.0417595i
$190$		0			0
$191$	−0.726932	+	4.12264i	−0.0525989	+	0.298303i	−0.999747	−	0.0224933i	$-0.992840\pi$
$191$	−0.726932	+	4.12264i	−0.0525989	+	0.298303i	0.947148	+	0.320797i	$0.103951\pi$
$192$		0			0
$193$	−0.376522	−	0.137043i	−0.0271027	−	0.00986456i	0.328433	−	0.944527i	$-0.393479\pi$
$193$	−0.376522	−	0.137043i	−0.0271027	−	0.00986456i	−0.355536	+	0.934663i	$0.615702\pi$
$194$		0			0
$195$	−0.130507	−	0.00433134i	−0.00934581	−	0.000310173i
$196$		0			0
$197$	3.55429	−	6.15621i	0.253233	−	0.438612i	−0.711181	−	0.703009i	$-0.751840\pi$
$197$	3.55429	−	6.15621i	0.253233	−	0.438612i	0.964414	+	0.264397i	$0.0851729\pi$
$198$		0			0
$199$	−10.9253	−	18.9232i	−0.774474	−	1.34143i	−0.935090	−	0.354411i	$-0.884681\pi$
$199$	−10.9253	−	18.9232i	−0.774474	−	1.34143i	0.160616	−	0.987017i	$-0.448652\pi$
$200$		0			0
$201$	−7.70229	−	6.91108i	−0.543278	−	0.487470i
$202$		0			0
$203$	−0.00506271	−	0.0287121i	−0.000355333	−	0.00201519i
$204$		0			0
$205$	−0.115737	−	0.0971152i	−0.00808345	−	0.00678282i
$206$		0			0
$207$	−5.96487	+	8.90964i	−0.414587	+	0.619263i
$208$		0			0
$209$	31.2079	−	11.3587i	2.15869	−	0.785700i
$210$		0			0
$211$	−7.19890	+	6.04060i	−0.495593	+	0.415852i	−0.856026	−	0.516933i	$-0.827073\pi$
$211$	−7.19890	+	6.04060i	−0.495593	+	0.415852i	0.360433	+	0.932785i	$0.382629\pi$
$212$		0			0
$213$	4.36699	+	1.75559i	0.299221	+	0.120291i
$214$		0			0
$215$	−23.1107			−1.57614
$216$		0			0
$217$	−0.421027			−0.0285812
$218$		0			0
$219$	−3.60022	−	25.2992i	−0.243280	−	1.70956i
$220$		0			0
$221$	−0.116854	+	0.0980526i	−0.00786048	+	0.00659573i
$222$		0			0
$223$	−13.0978	+	4.76722i	−0.877095	+	0.319237i	−0.741037	−	0.671464i	$-0.765666\pi$
$223$	−13.0978	+	4.76722i	−0.877095	+	0.319237i	−0.136058	+	0.990701i	$0.543443\pi$
$224$		0			0
$225$	−8.52126	−	3.75863i	−0.568084	−	0.250575i
$226$		0			0
$227$	13.2560	+	11.1231i	0.879831	+	0.738266i	0.966144	−	0.258002i	$-0.0830641\pi$
$227$	13.2560	+	11.1231i	0.879831	+	0.738266i	−0.0863130	+	0.996268i	$0.527509\pi$
$228$		0			0
$229$	−1.99437	−	11.3106i	−0.131792	−	0.747427i	−0.977040	−	0.213054i	$-0.931659\pi$
$229$	−1.99437	−	11.3106i	−0.131792	−	0.747427i	0.845249	−	0.534373i	$-0.179452\pi$
$230$		0			0
$231$	−1.36064	+	0.444704i	−0.0895238	+	0.0292594i
$232$		0			0
$233$	−0.552886	−	0.957626i	−0.0362208	−	0.0627362i	0.847347	−	0.531040i	$-0.178199\pi$
$233$	−0.552886	−	0.957626i	−0.0362208	−	0.0627362i	−0.883568	+	0.468304i	$0.844865\pi$
$234$		0			0
$235$	−17.9685	+	31.1224i	−1.17214	+	2.03020i
$236$		0			0
$237$	4.13492	+	7.74430i	0.268592	+	0.503046i
$238$		0			0
$239$	1.17137	+	0.426344i	0.0757696	+	0.0275779i	0.379627	−	0.925140i	$-0.376052\pi$
$239$	1.17137	+	0.426344i	0.0757696	+	0.0275779i	−0.303857	+	0.952718i	$0.598275\pi$
$240$		0			0
$241$	4.62907	−	26.2528i	0.298185	−	1.69109i	−0.355784	−	0.934568i	$-0.615786\pi$
$241$	4.62907	−	26.2528i	0.298185	−	1.69109i	0.653969	−	0.756522i	$-0.273103\pi$
$242$		0			0
$243$	15.3276	−	2.83962i	0.983269	−	0.182161i
$244$		0			0
$245$	−3.44865	+	19.5583i	−0.220326	+	1.24953i
$246$		0			0
$247$	0.154366	+	0.0561845i	0.00982205	+	0.00357493i
$248$		0			0
$249$	−2.53162	−	4.74148i	−0.160435	−	0.300479i
$250$		0			0
$251$	−8.75536	+	15.1647i	−0.552633	+	0.957189i	0.445450	+	0.895307i	$0.353044\pi$
$251$	−8.75536	+	15.1647i	−0.552633	+	0.957189i	−0.998083	+	0.0618822i	$0.980290\pi$
$252$		0			0
$253$	−9.56729	−	16.5710i	−0.601490	−	1.04181i
$254$		0			0
$255$	−26.9976	+	8.82373i	−1.69066	+	0.552563i
$256$		0			0
$257$	1.97148	+	11.1808i	0.122978	+	0.697440i	0.982489	+	0.186323i	$0.0596571\pi$
$257$	1.97148	+	11.1808i	0.122978	+	0.697440i	−0.859511	+	0.511117i	$0.829232\pi$
$258$		0			0
$259$	−0.973824	−	0.817135i	−0.0605105	−	0.0507743i
$260$		0			0
$261$	−0.518408	−	0.228664i	−0.0320887	−	0.0141539i
$262$		0			0
$263$	12.3794	−	4.50573i	0.763346	−	0.277835i	0.0691353	−	0.997607i	$-0.477976\pi$
$263$	12.3794	−	4.50573i	0.763346	−	0.277835i	0.694210	+	0.719772i	$0.255754\pi$
$264$		0			0
$265$	30.2262	−	25.3628i	1.85678	−	1.55803i
$266$		0			0
$267$	1.03398	+	7.26592i	0.0632787	+	0.444667i
$268$		0			0
$269$	−1.50575			−0.0918074			−0.0459037	−	0.998946i	$-0.514617\pi$
$269$	−1.50575			−0.0918074			−0.0459037	+	0.998946i	$0.514617\pi$
$270$		0			0
$271$	25.7002			1.56117			0.780587	−	0.625047i	$-0.214920\pi$
$271$	25.7002			1.56117			0.780587	+	0.625047i	$0.214920\pi$
$272$		0			0
$273$	−0.00656959	−	0.00264107i	−0.000397610	−	0.000159845i
$274$		0			0
$275$	12.7322	−	10.6836i	0.767782	−	0.644246i
$276$		0			0
$277$	7.61518	−	2.77170i	0.457552	−	0.166535i	−0.102953	−	0.994686i	$-0.532829\pi$
$277$	7.61518	−	2.77170i	0.457552	−	0.166535i	0.560505	+	0.828151i	$0.310607\pi$
$278$		0			0
$279$	−4.55195	+	6.79918i	−0.272518	+	0.407056i
$280$		0			0
$281$	−12.0856	−	10.1410i	−0.720968	−	0.604964i	0.206685	−	0.978408i	$-0.433733\pi$
$281$	−12.0856	−	10.1410i	−0.720968	−	0.604964i	−0.927653	+	0.373443i	$0.878177\pi$
$282$		0			0
$283$	−2.79183	−	15.8333i	−0.165957	−	0.941190i	−0.948072	−	0.318056i	$-0.896970\pi$
$283$	−2.79183	−	15.8333i	−0.165957	−	0.941190i	0.782115	−	0.623134i	$-0.214141\pi$
$284$		0			0
$285$	22.7660	+	20.4273i	1.34854	+	1.21001i
$286$		0			0
$287$	−0.00409625	−	0.00709491i	−0.000241794	−	0.000418799i
$288$		0			0
$289$	−8.09021	+	14.0127i	−0.475895	+	0.824274i
$290$		0			0
$291$	20.9120	+	0.694038i	1.22588	+	0.0406852i
$292$		0			0
$293$	11.8571	+	4.31565i	0.692701	+	0.252123i	0.664291	−	0.747474i	$-0.268733\pi$
$293$	11.8571	+	4.31565i	0.692701	+	0.252123i	0.0284099	+	0.999596i	$0.490956\pi$
$294$		0			0
$295$	2.09521	−	11.8825i	0.121988	−	0.691828i
$296$		0			0
$297$	−7.52912	+	26.7811i	−0.436884	+	1.55399i
$298$		0			0
$299$	0.0164352	−	0.0932088i	0.000950473	−	0.00539040i
$300$		0			0
$301$	−1.17759	−	0.428608i	−0.0678753	−	0.0247046i
$302$		0			0
$303$	8.61920	−	13.8469i	0.495160	−	0.795481i
$304$		0			0
$305$	−6.77941	+	11.7423i	−0.388188	+	0.672362i
$306$		0			0
$307$	−4.60942	−	7.98375i	−0.263074	−	0.455657i	0.703984	−	0.710216i	$-0.251403\pi$
$307$	−4.60942	−	7.98375i	−0.263074	−	0.455657i	−0.967057	+	0.254560i	$0.918070\pi$
$308$		0			0
$309$	−3.10962	+	14.7551i	−0.176900	+	0.839388i
$310$		0			0
$311$	5.17642	+	29.3569i	0.293528	+	1.66468i	0.673126	+	0.739528i	$0.264951\pi$
$311$	5.17642	+	29.3569i	0.293528	+	1.66468i	−0.379598	+	0.925152i	$0.623938\pi$
$312$		0			0
$313$	5.64949	+	4.74048i	0.319328	+	0.267948i	0.788335	−	0.615247i	$-0.210944\pi$
$313$	5.64949	+	4.74048i	0.319328	+	0.267948i	−0.469007	+	0.883195i	$0.655388\pi$
$314$		0			0
$315$	−0.951529	−	0.912539i	−0.0536126	−	0.0514157i
$316$		0			0
$317$	9.63254	−	3.50596i	0.541017	−	0.196914i	−0.0570337	−	0.998372i	$-0.518164\pi$
$317$	9.63254	−	3.50596i	0.541017	−	0.196914i	0.598051	+	0.801458i	$0.295942\pi$
$318$		0			0
$319$	0.774591	−	0.649959i	0.0433688	−	0.0363907i
$320$		0			0
$321$	0.204153	−	0.160072i	0.0113947	−	0.00893434i
$322$		0			0
$323$	35.7318			1.98817
$324$		0			0
$325$	0.0822123			0.00456032
$326$		0			0
$327$	−13.6508	+	10.7032i	−0.754888	+	0.591890i
$328$		0			0
$329$	−1.49277	+	1.25258i	−0.0822990	+	0.0690571i
$330$		0			0
$331$	23.6982	−	8.62542i	1.30257	−	0.474096i	0.404736	−	0.914433i	$-0.367363\pi$
$331$	23.6982	−	8.62542i	1.30257	−	0.474096i	0.897832	+	0.440337i	$0.145141\pi$
$332$		0			0
$333$	−23.7245	+	6.89183i	−1.30010	+	0.377670i
$334$		0			0
$335$	13.0295	+	10.9330i	0.711876	+	0.597335i
$336$		0			0
$337$	−0.600815	−	3.40739i	−0.0327285	−	0.185612i	0.964061	−	0.265682i	$-0.0855970\pi$
$337$	−0.600815	−	3.40739i	−0.0327285	−	0.185612i	−0.996789	+	0.0800692i	$0.974486\pi$
$338$		0			0
$339$	4.98151	−	23.6372i	0.270558	−	1.28379i
$340$		0			0
$341$	−7.30105	−	12.6458i	−0.395374	−	0.684808i
$342$		0			0
$343$	−1.07874	+	1.86843i	−0.0582465	+	0.100886i
$344$		0			0
$345$	9.31284	−	14.9612i	0.501387	−	0.805484i
$346$		0			0
$347$	21.9683	+	7.99579i	1.17932	+	0.429237i	0.855961	−	0.517040i	$-0.172966\pi$
$347$	21.9683	+	7.99579i	1.17932	+	0.429237i	0.323357	+	0.946277i	$0.395189\pi$
$348$		0			0
$349$	−2.94303	+	16.6908i	−0.157537	+	0.893437i	0.798893	+	0.601474i	$0.205420\pi$
$349$	−2.94303	+	16.6908i	−0.157537	+	0.893437i	−0.956430	+	0.291963i	$0.905692\pi$
$350$		0			0
$351$	−0.113678	+	0.0775385i	−0.00606770	+	0.00413870i
$352$		0			0
$353$	1.66836	−	9.46173i	0.0887977	−	0.503597i	−0.907675	−	0.419675i	$-0.862144\pi$
$353$	1.66836	−	9.46173i	0.0887977	−	0.503597i	0.996472	−	0.0839222i	$-0.0267447\pi$
$354$		0			0
$355$	−7.26943	−	2.64586i	−0.385821	−	0.140427i
$356$		0			0
$357$	−1.53929	−	0.0510868i	−0.0814679	−	0.00270380i
$358$		0			0
$359$	13.3015	−	23.0388i	0.702024	−	1.21594i	−0.265730	−	0.964047i	$-0.585613\pi$
$359$	13.3015	−	23.0388i	0.702024	−	1.21594i	0.967755	−	0.251895i	$-0.0810536\pi$
$360$		0			0
$361$	−9.73971	−	16.8697i	−0.512616	−	0.887878i
$362$		0			0
$363$	−22.7711	−	20.4320i	−1.19517	−	1.07240i
$364$		0			0
$365$	7.29343	+	41.3631i	0.381756	+	2.16504i
$366$		0			0
$367$	−4.05209	−	3.40011i	−0.211518	−	0.177484i	0.530874	−	0.847451i	$-0.321864\pi$
$367$	−4.05209	−	3.40011i	−0.211518	−	0.177484i	−0.742391	+	0.669967i	$0.766308\pi$
$368$		0			0
$369$	−0.158863	−	0.0105565i	−0.00827007	−	0.000549548i
$370$		0			0
$371$	2.01054	−	0.731776i	0.104382	−	0.0379919i
$372$		0			0
$373$	16.0823	−	13.4947i	0.832711	−	0.698728i	−0.123201	−	0.992382i	$-0.539316\pi$
$373$	16.0823	−	13.4947i	0.832711	−	0.698728i	0.955912	+	0.293654i	$0.0948714\pi$
$374$		0			0
$375$	−8.67209	−	3.48631i	−0.447825	−	0.180032i
$376$		0			0
$377$	0.00500156			0.000257593
$378$		0			0
$379$	−16.5959			−0.852476			−0.426238	−	0.904611i	$-0.640161\pi$
$379$	−16.5959			−0.852476			−0.426238	+	0.904611i	$0.640161\pi$
$380$		0			0
$381$	−0.653428	−	4.59172i	−0.0334761	−	0.235241i
$382$		0			0
$383$	−9.90918	+	8.31479i	−0.506335	+	0.424866i	−0.859837	−	0.510568i	$-0.829435\pi$
$383$	−9.90918	+	8.31479i	−0.506335	+	0.424866i	0.353502	+	0.935434i	$0.384991\pi$
$384$		0			0
$385$	2.21091	−	0.804704i	0.112678	−	0.0410115i
$386$		0			0
$387$	−19.6532	+	14.3831i	−0.999029	+	0.731133i
$388$		0			0
$389$	−19.1992	−	16.1100i	−0.973438	−	0.816812i	0.00964819	−	0.999953i	$-0.496929\pi$
$389$	−19.1992	−	16.1100i	−0.973438	−	0.816812i	−0.983087	+	0.183142i	$0.941373\pi$
$390$		0			0
$391$	−3.57492	−	20.2744i	−0.180791	−	1.02532i
$392$		0			0
$393$	−6.61930	+	2.16341i	−0.333899	+	0.109130i
$394$		0			0
$395$	−7.21471	−	12.4963i	−0.363012	−	0.628755i
$396$		0			0
$397$	−11.8226	+	20.4773i	−0.593359	+	1.02773i	0.400418	+	0.916333i	$0.368865\pi$
$397$	−11.8226	+	20.4773i	−0.593359	+	1.02773i	−0.993776	+	0.111395i	$0.964468\pi$
$398$		0			0
$399$	0.781183	+	1.46308i	0.0391081	+	0.0732456i
$400$		0			0
$401$	11.0226	+	4.01190i	0.550443	+	0.200345i	0.602243	−	0.798313i	$-0.294274\pi$
$401$	11.0226	+	4.01190i	0.550443	+	0.200345i	−0.0518003	+	0.998657i	$0.516496\pi$
$402$		0			0
$403$	0.0125422	−	0.0711301i	0.000624769	−	0.00354324i
$404$		0			0
$405$	−25.0241	+	5.50033i	−1.24346	+	0.273314i
$406$		0			0
$407$	7.65601	−	43.4194i	0.379494	−	2.15222i
$408$		0			0
$409$	10.3690	+	3.77401i	0.512715	+	0.186613i	0.585404	−	0.810742i	$-0.300936\pi$
$409$	10.3690	+	3.77401i	0.512715	+	0.186613i	−0.0726893	+	0.997355i	$0.523158\pi$
$410$		0			0
$411$	−0.833747	−	1.56153i	−0.0411257	−	0.0770244i
$412$		0			0
$413$	0.327133	−	0.566611i	0.0160972	−	0.0278811i
$414$		0			0
$415$	4.41724	+	7.65088i	0.216834	+	0.375567i
$416$		0			0
$417$	21.5670	−	7.04881i	1.05614	−	0.345182i
$418$		0			0
$419$	0.622392	+	3.52976i	0.0304058	+	0.172440i	0.996229	−	0.0867614i	$-0.0276518\pi$
$419$	0.622392	+	3.52976i	0.0304058	+	0.172440i	−0.965823	+	0.259201i	$0.916541\pi$
$420$		0			0
$421$	26.6737	+	22.3819i	1.30000	+	1.09083i	0.990145	+	0.140043i	$0.0447241\pi$
$421$	26.6737	+	22.3819i	1.30000	+	1.09083i	0.309853	+	0.950785i	$0.399720\pi$
$422$		0			0
$423$	4.08886	+	37.6492i	0.198807	+	1.83057i
$424$		0			0
$425$	16.8040	−	6.11616i	0.815115	−	0.296677i
$426$		0			0
$427$	−0.563213	+	0.472592i	−0.0272558	+	0.0228703i
$428$		0			0
$429$	−0.0345974	−	0.243121i	−0.00167038	−	0.0117380i
$430$		0			0
$431$	−28.6872			−1.38182			−0.690908	−	0.722943i	$-0.742789\pi$
$431$	−28.6872			−1.38182			−0.690908	+	0.722943i	$0.742789\pi$
$432$		0			0
$433$	−14.7618			−0.709407			−0.354703	−	0.934979i	$-0.615418\pi$
$433$	−14.7618			−0.709407			−0.354703	+	0.934979i	$0.615418\pi$
$434$		0			0
$435$	0.864064	+	0.347367i	0.0414287	+	0.0166550i
$436$		0			0
$437$	−16.9833	+	14.2507i	−0.812423	+	0.681704i
$438$		0			0
$439$	−6.35308	+	2.31233i	−0.303216	+	0.110362i	−0.489147	−	0.872201i	$-0.662692\pi$
$439$	−6.35308	+	2.31233i	−0.303216	+	0.110362i	0.185932	+	0.982563i	$0.440470\pi$
$440$		0			0
$441$	9.23949	+	18.7786i	0.439976	+	0.894217i
$442$		0			0
$443$	21.7900	+	18.2840i	1.03528	+	0.868700i	0.991469	−	0.130340i	$-0.0416070\pi$
$443$	21.7900	+	18.2840i	1.03528	+	0.868700i	0.0438065	+	0.999040i	$0.486051\pi$
$444$		0			0
$445$	−2.09467	−	11.8795i	−0.0992970	−	0.563141i
$446$		0			0
$447$	9.95845	+	8.93547i	0.471018	+	0.422633i
$448$		0			0
$449$	10.1001	+	17.4939i	0.476654	+	0.825589i	0.999642	−	0.0267507i	$-0.00851603\pi$
$449$	10.1001	+	17.4939i	0.476654	+	0.825589i	−0.522988	+	0.852340i	$0.675183\pi$
$450$		0			0
$451$	0.142067	−	0.246067i	0.00668965	−	0.0115868i
$452$		0			0
$453$	−25.9478	−	0.861169i	−1.21913	−	0.0404612i
$454$		0			0
$455$	0.0109360	+	0.00398036i	0.000512686	+	0.000186602i
$456$		0			0
$457$	1.40361	−	7.96027i	0.0656582	−	0.372366i	−0.934219	−	0.356700i	$-0.883902\pi$
$457$	1.40361	−	7.96027i	0.0656582	−	0.372366i	0.999877	−	0.0156663i	$-0.00498693\pi$
$458$		0			0
$459$	−17.4671	+	24.3058i	−0.815296	+	1.13450i
$460$		0			0
$461$	−3.45167	+	19.5754i	−0.160760	+	0.911717i	0.792568	+	0.609783i	$0.208743\pi$
$461$	−3.45167	+	19.5754i	−0.160760	+	0.911717i	−0.953329	+	0.301934i	$0.902368\pi$
$462$		0			0
$463$	18.0828	+	6.58158i	0.840377	+	0.305872i	0.726110	−	0.687578i	$-0.241326\pi$
$463$	18.0828	+	6.58158i	0.840377	+	0.305872i	0.114266	+	0.993450i	$0.463548\pi$
$464$		0			0
$465$	7.10688	−	11.4173i	0.329574	−	0.529464i
$466$		0			0
$467$	−1.04526	+	1.81045i	−0.0483690	+	0.0837776i	−0.889196	−	0.457526i	$-0.848736\pi$
$467$	−1.04526	+	1.81045i	−0.0483690	+	0.0837776i	0.840827	+	0.541304i	$0.182069\pi$
$468$		0			0
$469$	0.461147	+	0.798729i	0.0212938	+	0.0368819i
$470$		0			0
$471$	8.64845	−	41.0368i	0.398500	−	1.89087i
$472$		0			0
$473$	−7.54718	−	42.8022i	−0.347020	−	1.96805i
$474$		0			0
$475$	−14.7521	−	12.3785i	−0.676874	−	0.567965i
$476$		0			0
$477$	9.91955	−	40.3799i	0.454185	−	1.84887i
$478$		0			0
$479$	−25.9253	+	9.43604i	−1.18456	+	0.431143i	−0.857809	−	0.513968i	$-0.828175\pi$
$479$	−25.9253	+	9.43604i	−1.18456	+	0.431143i	−0.326748	+	0.945112i	$0.605953\pi$
$480$		0			0
$481$	0.167060	−	0.140180i	0.00761728	−	0.00639166i
$482$		0			0
$483$	0.752000	−	0.589625i	0.0342172	−	0.0268289i
$484$		0			0
$485$	−34.3903			−1.56158
$486$		0			0
$487$	−16.2691			−0.737223			−0.368612	−	0.929583i	$-0.620167\pi$
$487$	−16.2691			−0.737223			−0.368612	+	0.929583i	$0.620167\pi$
$488$		0			0
$489$	−18.2011	+	14.2710i	−0.823082	+	0.645359i
$490$		0			0
$491$	−23.5401	+	19.7525i	−1.06235	+	0.891418i	−0.994338	−	0.106266i	$-0.966110\pi$
$491$	−23.5401	+	19.7525i	−1.06235	+	0.891418i	−0.0680129	+	0.997684i	$0.521666\pi$
$492$		0			0
$493$	1.02231	−	0.372089i	0.0460424	−	0.0167581i
$494$		0			0
$495$	10.9081	−	44.4041i	0.490284	−	1.99582i
$496$		0			0
$497$	−0.321340	−	0.269636i	−0.0144141	−	0.0120948i
$498$		0			0
$499$	−0.645667	−	3.66176i	−0.0289040	−	0.163923i	0.966939	−	0.255007i	$-0.0820778\pi$
$499$	−0.645667	−	3.66176i	−0.0289040	−	0.163923i	−0.995843	+	0.0910844i	$0.970967\pi$
$500$		0			0
$501$	−3.30019	+	15.6594i	−0.147442	+	0.699609i
$502$		0			0
$503$	−3.24639	−	5.62291i	−0.144749	−	0.250713i	0.784530	−	0.620091i	$-0.212904\pi$
$503$	−3.24639	−	5.62291i	−0.144749	−	0.250713i	−0.929279	+	0.369378i	$0.879571\pi$
$504$		0			0
$505$	−13.4040	+	23.2164i	−0.596469	+	1.03311i
$506$		0			0
$507$	−11.8983	+	19.1148i	−0.528423	+	0.848918i
$508$		0			0
$509$	20.6356	+	7.51076i	0.914659	+	0.332909i	0.756112	−	0.654443i	$-0.227097\pi$
$509$	20.6356	+	7.51076i	0.914659	+	0.332909i	0.158547	+	0.987351i	$0.449319\pi$
$510$		0			0
$511$	−0.395483	+	2.24290i	−0.0174952	+	0.0992200i
$512$		0			0
$513$	32.0731	+	3.20279i	1.41606	+	0.141407i
$514$		0			0
$515$	4.30378	−	24.4079i	0.189647	−	1.07554i
$516$		0			0
$517$	−63.5083	−	23.1151i	−2.79309	−	1.01660i
$518$		0			0
$519$	44.6216	+	1.48092i	1.95867	+	0.0650054i
$520$		0			0
$521$	−13.6606	+	23.6608i	−0.598480	+	1.03660i	0.394566	+	0.918868i	$0.370895\pi$
$521$	−13.6606	+	23.6608i	−0.598480	+	1.03660i	−0.993046	+	0.117730i	$0.962438\pi$
$522$		0			0
$523$	−6.80343	−	11.7839i	−0.297493	−	0.515274i	0.678069	−	0.734999i	$-0.262817\pi$
$523$	−6.80343	−	11.7839i	−0.297493	−	0.515274i	−0.975562	+	0.219725i	$0.929484\pi$
$524$		0			0
$525$	0.617809	+	0.554345i	0.0269634	+	0.0241936i
$526$		0			0
$527$	−2.72811	−	15.4719i	−0.118839	−	0.673967i
$528$		0			0
$529$	−7.83396	−	6.57347i	−0.340607	−	0.285803i
$530$		0			0
$531$	−5.61341	−	11.4088i	−0.243601	−	0.495101i
$532$		0			0
$533$	0.00132067		0.000480684i	5.72045e−5		2.08207e-5i
$534$		0			0
$535$	−0.326639	+	0.274083i	−0.0141218	+	0.0118496i
$536$		0			0
$537$	−0.364970	−	0.146723i	−0.0157496	−	0.00633157i
$538$		0			0
$539$	−37.3492			−1.60874
$540$		0			0
$541$	19.3887			0.833584			0.416792	−	0.909002i	$-0.363154\pi$
$541$	19.3887			0.833584			0.416792	+	0.909002i	$0.363154\pi$
$542$		0			0
$543$	1.85480	+	13.0339i	0.0795971	+	0.559339i
$544$		0			0
$545$	21.8408	−	18.3266i	0.935556	−	0.785025i
$546$		0			0
$547$	9.85277	−	3.58612i	0.421274	−	0.153331i	−0.122680	−	0.992446i	$-0.539149\pi$
$547$	9.85277	−	3.58612i	0.421274	−	0.153331i	0.543954	+	0.839115i	$0.316927\pi$
$548$		0			0
$549$	1.54270	+	14.2048i	0.0658409	+	0.606246i
$550$		0			0
$551$	−0.897476	−	0.753072i	−0.0382338	−	0.0320819i
$552$		0			0
$553$	−0.135868	−	0.770543i	−0.00577767	−	0.0327668i
$554$		0			0
$555$	38.5969	−	12.6148i	1.63835	−	0.535467i
$556$		0			0
$557$	−14.3245	−	24.8107i	−0.606947	−	1.05126i	−0.991741	−	0.128260i	$-0.959061\pi$
$557$	−14.3245	−	24.8107i	−0.606947	−	1.05126i	0.384794	−	0.923003i	$-0.374273\pi$
$558$		0			0
$559$	0.107491	−	0.186179i	0.00454637	−	0.00787455i
$560$		0			0
$561$	−25.1585	−	47.1195i	−1.06219	−	1.98938i
$562$		0			0
$563$	−17.4077	−	6.33587i	−0.733646	−	0.267025i	−0.0519385	−	0.998650i	$-0.516540\pi$
$563$	−17.4077	−	6.33587i	−0.733646	−	0.267025i	−0.681707	+	0.731625i	$0.738762\pi$
$564$		0			0
$565$	−6.89452	+	39.1007i	−0.290054	+	1.64498i
$566$		0			0
$567$	−1.37710	−	0.183829i	−0.0578328	−	0.00772009i
$568$		0			0
$569$	2.20855	−	12.5253i	0.0925873	−	0.525088i	−0.902873	−	0.429908i	$-0.858546\pi$
$569$	2.20855	−	12.5253i	0.0925873	−	0.525088i	0.995460	−	0.0951806i	$-0.0303429\pi$
$570$		0			0
$571$	22.7338	+	8.27441i	0.951378	+	0.346273i	0.770649	−	0.637260i	$-0.219932\pi$
$571$	22.7338	+	8.27441i	0.951378	+	0.346273i	0.180729	+	0.983533i	$0.442154\pi$
$572$		0			0
$573$	−3.41510	−	6.39615i	−0.142668	−	0.267203i
$574$		0			0
$575$	−5.54768	+	9.60886i	−0.231354	+	0.400717i
$576$		0			0
$577$	4.40688	+	7.63294i	0.183461	+	0.317764i	0.943057	−	0.332632i	$-0.107937\pi$
$577$	4.40688	+	7.63294i	0.183461	+	0.317764i	−0.759596	+	0.650395i	$0.774603\pi$
$578$		0			0
$579$	0.659670	−	0.215602i	0.0274150	−	0.00896013i
$580$		0			0
$581$	0.0831855	+	0.471768i	0.00345111	+	0.0195722i
$582$		0			0
$583$	56.8442	+	47.6979i	2.35425	+	1.97545i
$584$		0			0
$585$	0.182514	−	0.133571i	0.00754601	−	0.00552250i
$586$		0			0
$587$	8.17717	−	2.97625i	0.337508	−	0.122843i	−0.167706	−	0.985837i	$-0.553636\pi$
$587$	8.17717	−	2.97625i	0.337508	−	0.122843i	0.505214	+	0.862994i	$0.331414\pi$
$588$		0			0
$589$	−12.9604	+	10.8751i	−0.534025	+	0.448101i
$590$		0			0
$591$	1.73465	+	12.1896i	0.0713540	+	0.501414i
$592$		0			0
$593$	4.83668			0.198619			0.0993094	−	0.995057i	$-0.468337\pi$
$593$	4.83668			0.198619			0.0993094	+	0.995057i	$0.468337\pi$
$594$		0			0
$595$	2.53140			0.103777
$596$		0			0
$597$	35.1150	+	14.1168i	1.43716	+	0.577760i
$598$		0			0
$599$	−11.0154	+	9.24301i	−0.450077	+	0.377659i	−0.839464	−	0.543415i	$-0.817131\pi$
$599$	−11.0154	+	9.24301i	−0.450077	+	0.377659i	0.389388	+	0.921074i	$0.372687\pi$
$600$		0			0
$601$	−14.2323	+	5.18014i	−0.580548	+	0.211302i	−0.615567	−	0.788084i	$-0.711073\pi$
$601$	−14.2323	+	5.18014i	−0.580548	+	0.211302i	0.0350189	+	0.999387i	$0.488851\pi$
$602$		0			0
$603$	17.8844	+	1.18842i	0.728310	+	0.0483964i
$604$		0			0
$605$	38.5204	+	32.3225i	1.56608	+	1.31410i
$606$		0			0
$607$	1.95372	+	11.0801i	0.0792991	+	0.449728i	0.998442	+	0.0558030i	$0.0177719\pi$
$607$	1.95372	+	11.0801i	0.0792991	+	0.449728i	−0.919143	+	0.393925i	$0.871117\pi$
$608$		0			0
$609$	0.0375857	+	0.0337247i	0.00152305	+	0.00136659i
$610$		0			0
$611$	−0.167148	−	0.289509i	−0.00676208	−	0.0117123i
$612$		0			0
$613$	9.66863	−	16.7466i	0.390512	−	0.676387i	−0.602005	−	0.798492i	$-0.705631\pi$
$613$	9.66863	−	16.7466i	0.390512	−	0.676387i	0.992517	+	0.122105i	$0.0389646\pi$
$614$		0			0
$615$	0.261542	+	0.00868019i	0.0105464	+	0.000350019i
$616$		0			0
$617$	−8.79610	−	3.20152i	−0.354118	−	0.128888i	0.158835	−	0.987305i	$-0.449226\pi$
$617$	−8.79610	−	3.20152i	−0.354118	−	0.128888i	−0.512953	+	0.858417i	$0.671448\pi$
$618$		0			0
$619$	−1.37563	+	7.80157i	−0.0552911	+	0.313571i	−0.999893	−	0.0146477i	$-0.995337\pi$
$619$	−1.37563	+	7.80157i	−0.0552911	+	0.313571i	0.944602	+	0.328219i	$0.106448\pi$
$620$		0			0
$621$	−1.39160	−	18.5188i	−0.0558429	−	0.743136i
$622$		0			0
$623$	0.113583	−	0.644160i	0.00455060	−	0.0258077i
$624$		0			0
$625$	29.0221	+	10.5632i	1.16088	+	0.422527i
$626$		0			0
$627$	−30.3979	+	48.8347i	−1.21398	+	1.95027i
$628$		0			0
$629$	23.7181	−	41.0809i	0.945701	−	1.63800i
$630$		0			0
$631$	11.8744	+	20.5670i	0.472711	+	0.818759i	0.999512	−	0.0312291i	$-0.00994216\pi$
$631$	11.8744	+	20.5670i	0.472711	+	0.818759i	−0.526801	+	0.849988i	$0.676609\pi$
$632$		0			0
$633$	3.35661	−	15.9271i	0.133413	−	0.633045i
$634$		0			0
$635$	1.32373	+	7.50727i	0.0525308	+	0.297917i
$636$		0			0
$637$	−0.141521	−	0.118750i	−0.00560727	−	0.00470506i
$638$		0			0
$639$	−7.82855	+	2.27415i	−0.309693	+	0.0899639i
$640$		0			0
$641$	3.44069	−	1.25231i	0.135899	−	0.0494633i	−0.273175	−	0.961964i	$-0.588074\pi$
$641$	3.44069	−	1.25231i	0.135899	−	0.0494633i	0.409074	+	0.912501i	$0.365852\pi$
$642$		0			0
$643$	−8.40157	+	7.04976i	−0.331326	+	0.278015i	−0.793240	−	0.608909i	$-0.791607\pi$
$643$	−8.40157	+	7.04976i	−0.331326	+	0.278015i	0.461914	+	0.886925i	$0.347163\pi$
$644$		0			0
$645$	31.5005	−	24.6988i	1.24033	−	0.972513i
$646$		0			0
$647$	23.9785			0.942691			0.471346	−	0.881949i	$-0.343768\pi$
$647$	23.9785			0.942691			0.471346	+	0.881949i	$0.343768\pi$
$648$		0			0
$649$	22.6913			0.890712
$650$		0			0
$651$	0.573871	−	0.449958i	0.0224918	−	0.0176353i
$652$		0			0
$653$	20.8792	−	17.5197i	0.817066	−	0.685600i	−0.135217	−	0.990816i	$-0.543173\pi$
$653$	20.8792	−	17.5197i	0.817066	−	0.685600i	0.952283	+	0.305216i	$0.0987287\pi$
$654$		0			0
$655$	10.7557	−	3.91475i	0.420259	−	0.152962i
$656$		0			0
$657$	31.9449	+	30.6359i	1.24629	+	1.19522i
$658$		0			0
$659$	−24.4799	−	20.5411i	−0.953602	−	0.800167i	0.0262987	−	0.999654i	$-0.491628\pi$
$659$	−24.4799	−	20.5411i	−0.953602	−	0.800167i	−0.979900	+	0.199487i	$0.936072\pi$
$660$		0			0
$661$	5.11913	+	29.0320i	0.199111	+	1.12922i	0.906441	+	0.422332i	$0.138788\pi$
$661$	5.11913	+	29.0320i	0.199111	+	1.12922i	−0.707330	+	0.706884i	$0.750100\pi$
$662$		0			0
$663$	0.0544855	−	0.258533i	0.00211604	−	0.0100406i
$664$		0			0
$665$	−1.36303	−	2.36083i	−0.0528560	−	0.0915492i
$666$		0			0
$667$	−0.337504	+	0.584575i	−0.0130682	+	0.0226348i
$668$		0			0
$669$	12.7579	−	20.4957i	0.493249	−	0.792410i
$670$		0			0
$671$	−23.9613	−	8.72119i	−0.925015	−	0.336678i
$672$		0			0
$673$	−4.96715	+	28.1701i	−0.191470	+	1.08588i	0.725887	+	0.687814i	$0.241429\pi$
$673$	−4.96715	+	28.1701i	−0.191470	+	1.08588i	−0.917357	+	0.398065i	$0.869682\pi$
$674$		0			0
$675$	15.6316	−	3.98370i	0.601662	−	0.153333i
$676$		0			0
$677$	3.84630	−	21.8134i	0.147825	−	0.838358i	−0.817230	−	0.576312i	$-0.804491\pi$
$677$	3.84630	−	21.8134i	0.147825	−	0.838358i	0.965055	−	0.262047i	$-0.0843974\pi$
$678$		0			0
$679$	−1.75234	−	0.637799i	−0.0672486	−	0.0244765i
$680$		0			0
$681$	−29.9557	−	0.994186i	−1.14791	−	0.0380973i
$682$		0			0
$683$	−7.20724	+	12.4833i	−0.275777	+	0.477660i	−0.970331	−	0.241781i	$-0.922269\pi$
$683$	−7.20724	+	12.4833i	−0.275777	+	0.477660i	0.694554	+	0.719441i	$0.255602\pi$
$684$		0			0
$685$	1.45474	+	2.51969i	0.0555828	+	0.0962723i
$686$		0			0
$687$	14.8062	+	13.2853i	0.564893	+	0.506865i
$688$		0			0
$689$	0.0637366	+	0.361468i	0.00242817	+	0.0137708i
$690$		0			0
$691$	2.16578	+	1.81731i	0.0823903	+	0.0691337i	0.683053	−	0.730369i	$-0.260652\pi$
$691$	2.16578	+	1.81731i	0.0823903	+	0.0691337i	−0.600662	+	0.799503i	$0.705096\pi$
$692$		0			0
$693$	1.37933	−	2.06029i	0.0523965	−	0.0782639i
$694$		0			0
$695$	−35.0441	+	12.7550i	−1.32930	+	0.483825i
$696$		0			0
$697$	0.234182	−	0.196502i	0.00887026	−	0.00744303i
$698$		0			0
$699$	1.77703	+	0.714393i	0.0672135	+	0.0270208i
$700$		0			0
$701$	−0.0227913			−0.000860816			−0.000430408	−	1.00000i	$-0.500137\pi$
$701$	−0.0227913			−0.000860816			−0.000430408		1.00000i	$0.500137\pi$
$702$		0			0
$703$	−51.0837			−1.92666
$704$		0			0
$705$	−8.76944	−	61.6240i	−0.330276	−	2.32089i
$706$		0			0
$707$	−1.11356	+	0.934388i	−0.0418798	+	0.0351413i
$708$		0			0
$709$	7.89357	−	2.87303i	0.296449	−	0.107899i	−0.189514	−	0.981878i	$-0.560691\pi$
$709$	7.89357	−	2.87303i	0.296449	−	0.107899i	0.485963	+	0.873979i	$0.338469\pi$
$710$		0			0
$711$	−13.9125	−	6.13663i	−0.521759	−	0.230142i
$712$		0			0
$713$	7.46724	+	6.26576i	0.279650	+	0.234654i
$714$		0			0
$715$	0.0700885	+	0.397492i	0.00262116	+	0.0148653i
$716$		0			0
$717$	−2.05225	+	0.670745i	−0.0766427	+	0.0250494i
$718$		0			0
$719$	18.8705	+	32.6847i	0.703753	+	1.21894i	0.967140	+	0.254245i	$0.0818269\pi$
$719$	18.8705	+	32.6847i	0.703753	+	1.21894i	−0.263387	+	0.964690i	$0.584840\pi$
$720$		0			0
$721$	0.671964	−	1.16388i	0.0250253	−	0.0433450i
$722$		0			0
$723$	21.7472	+	40.7304i	0.808788	+	1.51478i
$724$		0			0
$725$	−0.550969	−	0.200536i	−0.0204625	−	0.00744773i
$726$		0			0
$727$	7.62408	−	43.2383i	0.282761	−	1.60362i	−0.430413	−	0.902632i	$-0.641632\pi$
$727$	7.62408	−	43.2383i	0.282761	−	1.60362i	0.713174	−	0.700987i	$-0.247257\pi$
$728$		0			0
$729$	−17.8573	+	20.2514i	−0.661380	+	0.750051i
$730$		0			0
$731$	8.12011	−	46.0514i	0.300333	−	1.70327i
$732$		0			0
$733$	−41.1023	−	14.9600i	−1.51815	−	0.552560i	−0.557462	−	0.830203i	$-0.688225\pi$
$733$	−41.1023	−	14.9600i	−1.51815	−	0.552560i	−0.960684	+	0.277642i	$0.910447\pi$
$734$		0			0
$735$	−16.2017	−	30.3441i	−0.597607	−	1.11926i
$736$		0			0
$737$	−15.9935	+	27.7016i	−0.589130	+	1.02040i
$738$		0			0
$739$	−5.73565	−	9.93444i	−0.210989	−	0.365444i	0.741035	−	0.671466i	$-0.234335\pi$
$739$	−5.73565	−	9.93444i	−0.210989	−	0.365444i	−0.952024	+	0.306022i	$0.901002\pi$
$740$		0			0
$741$	−0.270450	+	0.0883921i	−0.00993523	+	0.00324717i
$742$		0			0
$743$	−1.09070	−	6.18567i	−0.0400139	−	0.226930i	0.958242	−	0.285957i	$-0.0923114\pi$
$743$	−1.09070	−	6.18567i	−0.0400139	−	0.226930i	−0.998256	+	0.0590266i	$0.981200\pi$
$744$		0			0
$745$	−16.8461	−	14.1355i	−0.617192	−	0.517885i
$746$		0			0
$747$	8.51797	+	3.75718i	0.311656	+	0.137468i
$748$		0			0
$749$	−0.0217268	+	0.00790792i	−0.000793881	+	0.000288949i
$750$		0			0
$751$	−6.91154	+	5.79947i	−0.252206	+	0.211626i	−0.760121	−	0.649781i	$-0.774861\pi$
$751$	−6.91154	+	5.79947i	−0.252206	+	0.211626i	0.507916	+	0.861407i	$0.330416\pi$
$752$		0			0
$753$	−4.27300	−	30.0269i	−0.155717	−	1.09424i
$754$		0			0
$755$	42.6718			1.55299
$756$		0			0
$757$	37.3499			1.35751			0.678753	−	0.734367i	$-0.262521\pi$
$757$	37.3499			1.35751			0.678753	+	0.734367i	$0.262521\pi$
$758$		0			0
$759$	30.7502	+	12.3620i	1.11616	+	0.448714i
$760$		0			0
$761$	−18.8028	+	15.7774i	−0.681601	+	0.571931i	−0.916474	−	0.400095i	$-0.868977\pi$
$761$	−18.8028	+	15.7774i	−0.681601	+	0.571931i	0.234872	+	0.972026i	$0.424533\pi$
$762$		0			0
$763$	1.45277	−	0.528764i	0.0525937	−	0.0191425i
$764$		0			0
$765$	27.3684	−	40.8798i	0.989507	−	1.47801i
$766$		0			0
$767$	0.0859805	+	0.0721462i	0.00310458	+	0.00260505i
$768$		0			0
$769$	2.87291	+	16.2931i	0.103600	+	0.587543i	0.991770	+	0.128030i	$0.0408652\pi$
$769$	2.87291	+	16.2931i	0.103600	+	0.587543i	−0.888171	+	0.459514i	$0.848024\pi$
$770$		0			0
$771$	−14.6363	−	13.1328i	−0.527114	−	0.472967i
$772$		0			0
$773$	−9.29539	−	16.1001i	−0.334332	−	0.579080i	0.649024	−	0.760768i	$-0.275177\pi$
$773$	−9.29539	−	16.1001i	−0.334332	−	0.579080i	−0.983356	+	0.181688i	$0.941844\pi$
$774$		0			0
$775$	−4.23358	+	7.33278i	−0.152075	+	0.263401i
$776$		0			0
$777$	2.20064	+	0.0730358i	0.0789474	+	0.00262014i
$778$		0			0
$779$	−0.309356	−	0.112596i	−0.0110838	−	0.00403418i
$780$		0			0
$781$	2.52631	−	14.3274i	0.0903985	−	0.512675i
$782$		0			0
$783$	0.950982	−	0.242356i	0.0339853	−	0.00866111i
$784$		0			0
$785$	−11.9697	+	67.8833i	−0.427215	+	2.42286i
$786$		0			0
$787$	21.2388	+	7.73030i	0.757082	+	0.275555i	0.691583	−	0.722297i	$-0.256914\pi$
$787$	21.2388	+	7.73030i	0.757082	+	0.275555i	0.0654995	+	0.997853i	$0.479136\pi$
$788$		0			0
$789$	−12.0581	+	19.3715i	−0.429280	+	0.689643i
$790$		0			0
$791$	−1.07646	+	1.86449i	−0.0382747	+	0.0662937i
$792$		0			0
$793$	−0.0630639	−	0.109230i	−0.00223946	−	0.00387886i
$794$		0			0
$795$	−14.0935	+	66.8735i	−0.499845	+	2.37176i
$796$		0			0
$797$	2.87762	+	16.3198i	0.101930	+	0.578076i	0.992402	+	0.123037i	$0.0392635\pi$
$797$	2.87762	+	16.3198i	0.101930	+	0.578076i	−0.890472	+	0.455039i	$0.849625\pi$
$798$		0			0
$799$	−55.7026	−	46.7400i	−1.97062	−	1.65354i
$800$		0			0
$801$	−9.17456	−	8.79862i	−0.324167	−	0.310884i
$802$		0			0
$803$	−74.2249	+	27.0157i	−2.61934	+	0.953362i
$804$		0			0
$805$	−1.20318	+	1.00958i	−0.0424064	+	0.0355832i
$806$		0			0
$807$	2.05238	−	1.60922i	0.0722473	−	0.0566474i
$808$		0			0
$809$	9.21641			0.324032			0.162016	−	0.986788i	$-0.448200\pi$
$809$	9.21641			0.324032			0.162016	+	0.986788i	$0.448200\pi$
$810$		0			0
$811$	33.0857			1.16180			0.580898	−	0.813976i	$-0.302701\pi$
$811$	33.0857			1.16180			0.580898	+	0.813976i	$0.302701\pi$
$812$		0			0
$813$	−35.0301	+	27.4662i	−1.22856	+	0.963282i
$814$		0			0
$815$	29.1212	−	24.4356i	1.02007	−	0.855941i
$816$		0			0
$817$	−47.3207	+	17.2233i	−1.65554	+	0.602567i
$818$		0			0
$819$	0.0117771	−	0.00342118i	0.000411525	−	0.000119546i
$820$		0			0
$821$	−21.7195	−	18.2249i	−0.758017	−	0.636052i	0.179593	−	0.983741i	$-0.442522\pi$
$821$	−21.7195	−	18.2249i	−0.758017	−	0.636052i	−0.937610	+	0.347689i	$0.886966\pi$
$822$		0			0
$823$	−0.223793	−	1.26919i	−0.00780092	−	0.0442412i	0.980659	−	0.195725i	$-0.0627060\pi$
$823$	−0.223793	−	1.26919i	−0.00780092	−	0.0442412i	−0.988460	+	0.151484i	$0.951595\pi$
$824$		0			0
$825$	−5.93663	+	28.1692i	−0.206687	+	0.980726i
$826$		0			0
$827$	−21.3919	−	37.0519i	−0.743870	−	1.28842i	−0.950721	−	0.310049i	$-0.899655\pi$
$827$	−21.3919	−	37.0519i	−0.743870	−	1.28842i	0.206850	−	0.978373i	$-0.433679\pi$
$828$		0			0
$829$	14.1816	−	24.5632i	0.492547	−	0.853116i	−0.507417	−	0.861701i	$-0.669399\pi$
$829$	14.1816	−	24.5632i	0.492547	−	0.853116i	0.999963	+	0.00858516i	$0.00273277\pi$
$830$		0			0
$831$	−7.41754	+	11.9164i	−0.257312	+	0.413375i
$832$		0			0
$833$	−37.7610	−	13.7439i	−1.30834	−	0.476198i
$834$		0			0
$835$	4.56754	−	25.9038i	0.158066	−	0.896438i
$836$		0			0
$837$	−1.06196	−	14.1322i	−0.0367069	−	0.488481i
$838$		0			0
$839$	0.381436	−	2.16323i	0.0131686	−	0.0746830i	−0.977515	−	0.210865i	$-0.932372\pi$
$839$	0.381436	−	2.16323i	0.0131686	−	0.0746830i	0.990684	+	0.136182i	$0.0434831\pi$
$840$		0			0
$841$	27.2176	+	9.90638i	0.938537	+	0.341599i
$842$		0			0
$843$	27.3110	+	0.906410i	0.940639	+	0.0312184i
$844$		0			0
$845$	18.5034	−	32.0489i	0.636537	−	1.10251i
$846$		0			0
$847$	1.36334	+	2.36137i	0.0468448	+	0.0811376i
$848$		0			0
$849$	20.7266	+	18.5975i	0.711336	+	0.638264i
$850$		0			0
$851$	5.11085	+	28.9851i	0.175198	+	0.993595i
$852$		0			0
$853$	−3.50247	−	2.93892i	−0.119922	−	0.100627i	0.580854	−	0.814008i	$-0.302719\pi$
$853$	−3.50247	−	2.93892i	−0.119922	−	0.100627i	−0.700777	+	0.713381i	$0.747163\pi$
$854$		0			0
$855$	−52.8617	−	3.51267i	−1.80783	−	0.120131i
$856$		0			0
$857$	21.1746	−	7.70694i	0.723312	−	0.263264i	0.0459809	−	0.998942i	$-0.485359\pi$
$857$	21.1746	−	7.70694i	0.723312	−	0.263264i	0.677331	+	0.735678i	$0.263136\pi$
$858$		0			0
$859$	35.7935	−	30.0343i	1.22126	−	1.02476i	0.222501	−	0.974933i	$-0.428578\pi$
$859$	35.7935	−	30.0343i	1.22126	−	1.02476i	0.998758	−	0.0498252i	$-0.0158664\pi$
$860$		0			0
$861$	0.0131657	+	0.00529283i	0.000448687	+	0.000180379i
$862$		0			0
$863$	7.31841			0.249122			0.124561	−	0.992212i	$-0.460248\pi$
$863$	7.31841			0.249122			0.124561	+	0.992212i	$0.460248\pi$
$864$		0			0
$865$	−73.3814			−2.49504
$866$		0			0
$867$	−3.94838	−	27.7458i	−0.134094	−	0.942296i
$868$		0			0
$869$	20.7876	−	17.4429i	0.705172	−	0.591710i
$870$		0			0
$871$	−0.148678	+	0.0541144i	−0.00503776	+	0.00183360i
$872$		0			0
$873$	−29.2454	+	21.4030i	−0.989805	+	0.724382i
$874$		0			0
$875$	0.638127	+	0.535452i	0.0215726	+	0.0181016i
$876$		0			0
$877$	−6.19410	−	35.1285i	−0.209160	−	1.18621i	−0.890758	−	0.454478i	$-0.849826\pi$
$877$	−6.19410	−	35.1285i	−0.209160	−	1.18621i	0.681598	−	0.731727i	$-0.261285\pi$
$878$		0			0
$879$	−20.7738	+	6.78958i	−0.700683	+	0.229007i
$880$		0			0
$881$	4.44794	+	7.70406i	0.149855	+	0.259556i	0.931174	−	0.364576i	$-0.118786\pi$
$881$	4.44794	+	7.70406i	0.149855	+	0.259556i	−0.781319	+	0.624132i	$0.785453\pi$
$882$		0			0
$883$	20.3831	−	35.3046i	0.685947	−	1.18809i	−0.287192	−	0.957873i	$-0.592722\pi$
$883$	20.3831	−	35.3046i	0.685947	−	1.18809i	0.973138	−	0.230221i	$-0.0739451\pi$
$884$		0			0
$885$	9.84324	+	18.4354i	0.330877	+	0.619700i
$886$		0			0
$887$	17.3762	+	6.32442i	0.583436	+	0.212353i	0.616840	−	0.787089i	$-0.288413\pi$
$887$	17.3762	+	6.32442i	0.583436	+	0.212353i	−0.0334041	+	0.999442i	$0.510635\pi$
$888$		0			0
$889$	−0.0717789	+	0.407079i	−0.00240739	+	0.0136530i
$890$		0			0
$891$	−18.3590	−	44.5498i	−0.615049	−	1.49248i
$892$		0			0
$893$	−13.5977	+	77.1163i	−0.455029	+	2.58060i
$894$		0			0
$895$	0.607540	+	0.221127i	0.0203078	+	0.00739145i
$896$		0			0
$897$	0.0772121	+	0.144611i	0.00257804	+	0.00482841i
$898$		0			0
$899$	−0.257559	+	0.446104i	−0.00859006	+	0.0148784i
$900$		0			0
$901$	39.9189	+	69.1416i	1.32989	+	2.30344i
$902$		0			0
$903$	2.06315	−	0.674307i	0.0686574	−	0.0224395i
$904$		0			0
$905$	−3.75751	−	21.3099i	−0.124904	−	0.708365i
$906$		0			0
$907$	−21.3031	−	17.8754i	−0.707357	−	0.593543i	0.216499	−	0.976283i	$-0.430536\pi$
$907$	−21.3031	−	17.8754i	−0.707357	−	0.593543i	−0.923856	+	0.382740i	$0.874981\pi$
$908$		0			0
$909$	3.05017	+	28.0851i	0.101168	+	0.931525i
$910$		0			0
$911$	27.4572	−	9.99359i	0.909696	−	0.331102i	0.155565	−	0.987826i	$-0.450280\pi$
$911$	27.4572	−	9.99359i	0.909696	−	0.331102i	0.754132	+	0.656723i	$0.228058\pi$
$912$		0			0
$913$	−12.7273	+	10.6795i	−0.421213	+	0.353439i
$914$		0			0
$915$	−3.30866	−	23.2503i	−0.109381	−	0.768633i
$916$		0			0
$917$	0.620652			0.0204957
$918$		0			0
$919$	−34.4464			−1.13628			−0.568140	−	0.822932i	$-0.692337\pi$
$919$	−34.4464			−1.13628			−0.568140	+	0.822932i	$0.692337\pi$
$920$		0			0
$921$	14.8151	+	5.95591i	0.488175	+	0.196254i
$922$		0			0
$923$	0.0551260	−	0.0462562i	0.00181450	−	0.00152254i
$924$		0			0
$925$	−24.0237	+	8.74392i	−0.789895	+	0.287498i
$926$		0			0
$927$	−11.5305	−	23.4349i	−0.378712	−	0.769703i
$928$		0			0
$929$	7.95774	+	6.67733i	0.261085	+	0.219076i	0.763928	−	0.645301i	$-0.223268\pi$
$929$	7.95774	+	6.67733i	0.261085	+	0.219076i	−0.502843	+	0.864378i	$0.667713\pi$
$930$		0			0
$931$	7.51453	+	42.6170i	0.246279	+	1.39672i
$932$		0			0
$933$	−38.4299	−	34.4822i	−1.25814	−	1.12890i
$934$		0			0
$935$	43.8972	+	76.0322i	1.43559	+	2.48652i
$936$		0			0
$937$	24.9638	−	43.2386i	0.815533	−	1.41254i	−0.0934120	−	0.995628i	$-0.529777\pi$
$937$	24.9638	−	43.2386i	0.815533	−	1.41254i	0.908945	−	0.416917i	$-0.136889\pi$
$938$		0			0
$939$	−12.7666	−	0.423706i	−0.416624	−	0.0138271i
$940$		0			0
$941$	40.0988	+	14.5948i	1.30718	+	0.475776i	0.899329	−	0.437272i	$-0.144055\pi$
$941$	40.0988	+	14.5948i	1.30718	+	0.475776i	0.407853	+	0.913047i	$0.366277\pi$
$942$		0			0
$943$	−0.0329369	+	0.186794i	−0.00107257	+	0.00608286i
$944$		0			0
$945$	2.27221	+	0.226900i	0.0739149	+	0.00738106i
$946$		0			0
$947$	0.101817	−	0.577431i	0.00330860	−	0.0187640i	−0.983109	−	0.183022i	$-0.941412\pi$
$947$	0.101817	−	0.577431i	0.00330860	−	0.0187640i	0.986417	+	0.164258i	$0.0525231\pi$
$948$		0			0
$949$	−0.367144	−	0.133629i	−0.0119180	−	0.00433779i
$950$		0			0
$951$	−9.38254	+	15.0732i	−0.304250	+	0.488781i
$952$		0			0
$953$	1.20182	−	2.08161i	0.0389307	−	0.0674299i	−0.845904	−	0.533336i	$-0.820938\pi$
$953$	1.20182	−	2.08161i	0.0389307	−	0.0674299i	0.884834	+	0.465906i	$0.154272\pi$
$954$		0			0
$955$	5.95876	+	10.3209i	0.192821	+	0.333975i
$956$		0			0
$957$	−0.361167	+	1.71373i	−0.0116749	+	0.0553971i
$958$		0			0
$959$	0.0273957	+	0.155369i	0.000884653	+	0.00501712i
$960$		0			0
$961$	−18.0489	−	15.1449i	−0.582224	−	0.488544i
$962$		0			0
$963$	−0.107195	+	0.436365i	−0.00345432	+	0.0140617i
$964$		0			0
$965$	−1.07190	+	0.390138i	−0.0345056	+	0.0125590i
$966$		0			0
$967$	−14.5185	+	12.1825i	−0.466885	+	0.391763i	−0.845657	−	0.533727i	$-0.820791\pi$
$967$	−14.5185	+	12.1825i	−0.466885	+	0.391763i	0.378772	+	0.925490i	$0.376346\pi$
$968$		0			0
$969$	−48.7035	+	38.1872i	−1.56458	+	1.22675i
$970$		0			0
$971$	41.3490			1.32695			0.663476	−	0.748197i	$-0.269080\pi$
$971$	41.3490			1.32695			0.663476	+	0.748197i	$0.269080\pi$
$972$		0			0
$973$	−2.02220			−0.0648289
$974$		0			0
$975$	−0.112058	+	0.0878617i	−0.00358872	+	0.00281383i
$976$		0			0
$977$	27.1804	−	22.8070i	0.869577	−	0.729662i	−0.0944318	−	0.995531i	$-0.530103\pi$
$977$	27.1804	−	22.8070i	0.869577	−	0.729662i	0.964009	+	0.265869i	$0.0856590\pi$
$978$		0			0
$979$	21.3174	−	7.75889i	0.681306	−	0.247975i
$980$		0			0
$981$	7.16763	−	29.1776i	0.228845	−	0.931569i
$982$		0			0
$983$	2.64290	+	2.21765i	0.0842954	+	0.0707322i	0.683962	−	0.729518i	$-0.260256\pi$
$983$	2.64290	+	2.21765i	0.0842954	+	0.0707322i	−0.599666	+	0.800250i	$0.704700\pi$
$984$		0			0
$985$	−3.51411	−	19.9295i	−0.111969	−	0.635006i
$986$		0			0
$987$	0.696030	−	3.30265i	0.0221549	−	0.105125i
$988$		0			0
$989$	14.5069	+	25.1267i	0.461293	+	0.798984i
$990$		0			0
$991$	11.1010	−	19.2275i	0.352636	−	0.610783i	−0.634075	−	0.773272i	$-0.718619\pi$
$991$	11.1010	−	19.2275i	0.352636	−	0.610783i	0.986710	+	0.162489i	$0.0519522\pi$
$992$		0			0
$993$	−23.0831	+	37.0833i	−0.732520	+	1.17680i
$994$		0			0
$995$	−58.4536	−	21.2754i	−1.85310	−	0.674475i
$996$		0			0
$997$	7.06268	−	40.0545i	0.223677	−	1.26854i	−0.641520	−	0.767106i	$-0.721696\pi$
$997$	7.06268	−	40.0545i	0.223677	−	1.26854i	0.865197	−	0.501431i	$-0.167193\pi$
$998$		0			0
$999$	24.9717	−	34.7485i	0.790071	−	1.09940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.25.1	✓	30
3.2	odd	2		648.2.q.b.73.1		30
4.3	odd	2		432.2.u.f.241.5		30
27.11	odd	18		5832.2.a.l.1.4		15
27.13	even	9	inner	216.2.q.b.121.1	yes	30
27.14	odd	18		648.2.q.b.577.1		30
27.16	even	9		5832.2.a.k.1.12		15
108.67	odd	18		432.2.u.f.337.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.1	✓	30	1.1	even	1	trivial
216.2.q.b.121.1	yes	30	27.13	even	9	inner
432.2.u.f.241.5		30	4.3	odd	2
432.2.u.f.337.5		30	108.67	odd	18
648.2.q.b.73.1		30	3.2	odd	2
648.2.q.b.577.1		30	27.14	odd	18
5832.2.a.k.1.12		15	27.16	even	9
5832.2.a.l.1.4		15	27.11	odd	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36303 + 1.06872i) q^{3} +(2.18080 - 1.82991i) q^{5} +(0.145059 - 0.0527971i) q^{7} +(0.715688 - 2.91338i) q^{9} +O(q^{10})\)	\(q+(-1.36303 + 1.06872i) q^{3} +(2.18080 - 1.82991i) q^{5} +(0.145059 - 0.0527971i) q^{7} +(0.715688 - 2.91338i) q^{9} +(4.10127 + 3.44137i) q^{11} +(0.00459855 + 0.0260797i) q^{13} +(-1.01684 + 4.82488i) q^{15} +(2.88012 + 4.98852i) q^{17} +(3.10159 - 5.37211i) q^{19} +(-0.141294 + 0.226991i) q^{21} +(-3.35846 - 1.22238i) q^{23} +(0.539084 - 3.05730i) q^{25} +(2.13808 + 4.73589i) q^{27} +(0.0327963 - 0.185997i) q^{29} +(-2.56293 - 0.932831i) q^{31} +(-9.26799 - 0.307591i) q^{33} +(0.219731 - 0.380584i) q^{35} +(-4.11754 - 7.13179i) q^{37} +(-0.0341397 - 0.0306327i) q^{39} +(-0.00921569 - 0.0522648i) q^{41} +(-6.21877 - 5.21817i) q^{43} +(-3.77045 - 7.66315i) q^{45} +(-11.8622 + 4.31750i) q^{47} +(-5.34406 + 4.48420i) q^{49} +(-9.25700 - 3.72145i) q^{51} +13.8601 q^{53} +15.2414 q^{55} +(1.51371 + 10.6371i) q^{57} +(3.24676 - 2.72435i) q^{59} +(-4.47554 + 1.62897i) q^{61} +(-0.0500012 - 0.460398i) q^{63} +(0.0577519 + 0.0484596i) q^{65} +(1.03748 + 5.88386i) q^{67} +(5.88406 - 1.92311i) q^{69} +(-1.35870 - 2.35333i) q^{71} +(-7.37683 + 12.7770i) q^{73} +(2.53260 + 4.74331i) q^{75} +(0.776619 + 0.282666i) q^{77} +(0.880151 - 4.99159i) q^{79} +(-7.97558 - 4.17015i) q^{81} +(-0.538876 + 3.05612i) q^{83} +(15.4095 + 5.60860i) q^{85} +(0.154076 + 0.288569i) q^{87} +(2.11862 - 3.66956i) q^{89} +(0.00204399 + 0.00354029i) q^{91} +(4.49028 - 1.46757i) q^{93} +(-3.06653 - 17.3911i) q^{95} +(-9.25397 - 7.76500i) q^{97} +(12.9613 - 9.48561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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