LMFDB - Embedded newform 108.6.i.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	108.25
Dual form			108.6.i.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.9624 - 8.65895i) q^{3} +(-29.6003 + 24.8376i) q^{5} +(188.011 - 68.4304i) q^{7} +(93.0451 + 224.481i) q^{9} +O(q^{10})$	\(q+(-12.9624 - 8.65895i) q^{3} +(-29.6003 + 24.8376i) q^{5} +(188.011 - 68.4304i) q^{7} +(93.0451 + 224.481i) q^{9} +(-71.8529 - 60.2917i) q^{11} +(93.0043 + 527.454i) q^{13} +(598.758 - 65.6462i) q^{15} +(-1072.95 - 1858.41i) q^{17} +(954.907 - 1653.95i) q^{19} +(-3029.60 - 740.959i) q^{21} +(-1988.35 - 723.699i) q^{23} +(-283.379 + 1607.12i) q^{25} +(737.685 - 3715.47i) q^{27} +(-17.9172 + 101.614i) q^{29} +(-7458.30 - 2714.60i) q^{31} +(409.319 + 1403.69i) q^{33} +(-3865.54 + 6695.31i) q^{35} +(-6188.31 - 10718.5i) q^{37} +(3361.64 - 7642.36i) q^{39} +(-2895.53 - 16421.4i) q^{41} +(7948.95 + 6669.96i) q^{43} +(-8329.74 - 4333.69i) q^{45} +(19238.6 - 7002.28i) q^{47} +(17790.5 - 14928.0i) q^{49} +(-2183.88 + 33380.0i) q^{51} -13735.8 q^{53} +3624.37 q^{55} +(-26699.3 + 13170.6i) q^{57} +(-23318.8 + 19566.8i) q^{59} +(26179.1 - 9528.41i) q^{61} +(32854.8 + 35837.7i) q^{63} +(-15853.7 - 13302.8i) q^{65} +(3001.69 + 17023.4i) q^{67} +(19507.2 + 26597.9i) q^{69} +(-29940.8 - 51858.9i) q^{71} +(16837.6 - 29163.5i) q^{73} +(17589.2 - 18378.3i) q^{75} +(-17634.9 - 6418.58i) q^{77} +(1001.10 - 5677.53i) q^{79} +(-41734.2 + 41773.7i) q^{81} +(-11078.6 + 62829.7i) q^{83} +(77918.1 + 28359.9i) q^{85} +(1112.12 - 1162.01i) q^{87} +(9255.67 - 16031.3i) q^{89} +(53579.7 + 92802.8i) q^{91} +(73171.5 + 99768.6i) q^{93} +(12814.6 + 72675.0i) q^{95} +(-22186.6 - 18616.8i) q^{97} +(6848.77 - 21739.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) $ 90 * q - 87 * q^5 + 330 * q^9	$ 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) $ 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−12.9624	−	8.65895i	−0.831535	−	0.555472i
$3$	−12.9624	−	8.65895i	−0.831535	−	0.555472i
$4$		0			0
$5$	−29.6003	+	24.8376i	−0.529507	+	0.444309i	−0.867931	−	0.496685i	$-0.834551\pi$
$5$	−29.6003	+	24.8376i	−0.529507	+	0.444309i	0.338424	+	0.940994i	$0.390106\pi$
$6$		0			0
$7$	188.011	−	68.4304i	1.45023	−	0.527842i	0.507577	−	0.861606i	$-0.330541\pi$
$7$	188.011	−	68.4304i	1.45023	−	0.527842i	0.942657	+	0.333764i	$0.108319\pi$
$8$		0			0
$9$	93.0451	+	224.481i	0.382902	+	0.923789i
$10$		0			0
$11$	−71.8529	−	60.2917i	−0.179045	−	0.150237i	0.548861	−	0.835914i	$-0.315062\pi$
$11$	−71.8529	−	60.2917i	−0.179045	−	0.150237i	−0.727906	+	0.685677i	$0.759506\pi$
$12$		0			0
$13$	93.0043	+	527.454i	0.152632	+	0.865618i	0.960919	+	0.276829i	$0.0892837\pi$
$13$	93.0043	+	527.454i	0.152632	+	0.865618i	−0.808287	+	0.588788i	$0.799605\pi$
$14$		0			0
$15$	598.758	−	65.6462i	0.687105	−	0.0753324i
$16$		0			0
$17$	−1072.95	−	1858.41i	−0.900446	−	1.55962i	−0.826916	−	0.562326i	$-0.809907\pi$
$17$	−1072.95	−	1858.41i	−0.900446	−	1.55962i	−0.0735306	−	0.997293i	$-0.523427\pi$
$18$		0			0
$19$	954.907	−	1653.95i	0.606844	−	1.05108i	−0.384913	−	0.922953i	$-0.625769\pi$
$19$	954.907	−	1653.95i	0.606844	−	1.05108i	0.991757	−	0.128132i	$-0.0408980\pi$
$20$		0			0
$21$	−3029.60	−	740.959i	−1.49912	−	0.366645i
$22$		0			0
$23$	−1988.35	−	723.699i	−0.783741	−	0.285258i	−0.0810095	−	0.996713i	$-0.525814\pi$
$23$	−1988.35	−	723.699i	−0.783741	−	0.285258i	−0.702732	+	0.711455i	$0.748037\pi$
$24$		0			0
$25$	−283.379	+	1607.12i	−0.0906812	+	0.514278i
$26$		0			0
$27$	737.685	−	3715.47i	0.194743	−	0.980854i
$28$		0			0
$29$	−17.9172	+	101.614i	−0.00395618	+	0.0224366i	−0.986722	−	0.162419i	$-0.948071\pi$
$29$	−17.9172	+	101.614i	−0.00395618	+	0.0224366i	0.982766	+	0.184855i	$0.0591816\pi$
$30$		0			0
$31$	−7458.30	−	2714.60i	−1.39391	−	0.507343i	−0.467547	−	0.883968i	$-0.654862\pi$
$31$	−7458.30	−	2714.60i	−1.39391	−	0.507343i	−0.926366	+	0.376625i	$0.877084\pi$
$32$		0			0
$33$	409.319	+	1403.69i	0.0654300	+	0.224382i
$34$		0			0
$35$	−3865.54	+	6695.31i	−0.533384	+	0.923848i
$36$		0			0
$37$	−6188.31	−	10718.5i	−0.743135	−	1.28715i	−0.951061	−	0.309003i	$-0.900005\pi$
$37$	−6188.31	−	10718.5i	−0.743135	−	1.28715i	0.207926	−	0.978144i	$-0.433329\pi$
$38$		0			0
$39$	3361.64	−	7642.36i	0.353908	−	0.804574i
$40$		0			0
$41$	−2895.53	−	16421.4i	−0.269010	−	1.52563i	−0.757367	−	0.652989i	$-0.773515\pi$
$41$	−2895.53	−	16421.4i	−0.269010	−	1.52563i	0.488357	−	0.872644i	$-0.337596\pi$
$42$		0			0
$43$	7948.95	+	6669.96i	0.655600	+	0.550113i	0.908764	−	0.417310i	$-0.137027\pi$
$43$	7948.95	+	6669.96i	0.655600	+	0.550113i	−0.253165	+	0.967423i	$0.581471\pi$
$44$		0			0
$45$	−8329.74	−	4333.69i	−0.613197	−	0.319026i
$46$		0			0
$47$	19238.6	−	7002.28i	1.27037	−	0.462375i	0.383131	−	0.923694i	$-0.374846\pi$
$47$	19238.6	−	7002.28i	1.27037	−	0.462375i	0.887234	+	0.461319i	$0.152624\pi$
$48$		0			0
$49$	17790.5	−	14928.0i	1.05852	−	0.888201i
$50$		0			0
$51$	−2183.88	+	33380.0i	−0.117572	+	1.79705i
$52$		0			0
$53$	−13735.8			−0.671683			−0.335842	−	0.941918i	$-0.609021\pi$
$53$	−13735.8			−0.671683			−0.335842	+	0.941918i	$0.609021\pi$
$54$		0			0
$55$	3624.37			0.161557
$56$		0			0
$57$	−26699.3	+	13170.6i	−1.08846	+	0.536929i
$58$		0			0
$59$	−23318.8	+	19566.8i	−0.872119	+	0.731794i	−0.964543	−	0.263925i	$-0.914983\pi$
$59$	−23318.8	+	19566.8i	−0.872119	+	0.731794i	0.0924244	+	0.995720i	$0.470538\pi$
$60$		0			0
$61$	26179.1	−	9528.41i	0.900804	−	0.327866i	0.150229	−	0.988651i	$-0.451999\pi$
$61$	26179.1	−	9528.41i	0.900804	−	0.327866i	0.750575	+	0.660785i	$0.229777\pi$
$62$		0			0
$63$	32854.8	+	35837.7i	1.04291	+	1.13760i
$64$		0			0
$65$	−15853.7	−	13302.8i	−0.465421	−	0.390535i
$66$		0			0
$67$	3001.69	+	17023.4i	0.0816918	+	0.463297i	0.998022	+	0.0628727i	$0.0200262\pi$
$67$	3001.69	+	17023.4i	0.0816918	+	0.463297i	−0.916330	+	0.400424i	$0.868863\pi$
$68$		0			0
$69$	19507.2	+	26597.9i	0.493255	+	0.672549i
$70$		0			0
$71$	−29940.8	−	51858.9i	−0.704883	−	1.22089i	−0.966734	−	0.255785i	$-0.917666\pi$
$71$	−29940.8	−	51858.9i	−0.704883	−	1.22089i	0.261851	−	0.965108i	$-0.415667\pi$
$72$		0			0
$73$	16837.6	−	29163.5i	0.369804	−	0.640520i	−0.619731	−	0.784815i	$-0.712758\pi$
$73$	16837.6	−	29163.5i	0.369804	−	0.640520i	0.989535	+	0.144295i	$0.0460914\pi$
$74$		0			0
$75$	17589.2	−	18378.3i	0.361072	−	0.377270i
$76$		0			0
$77$	−17634.9	−	6418.58i	−0.338958	−	0.123371i
$78$		0			0
$79$	1001.10	−	5677.53i	0.0180472	−	0.102351i	−0.974454	−	0.224589i	$-0.927896\pi$
$79$	1001.10	−	5677.53i	0.0180472	−	0.102351i	0.992501	+	0.122238i	$0.0390071\pi$
$80$		0			0
$81$	−41734.2	+	41773.7i	−0.706773	+	0.707441i
$82$		0			0
$83$	−11078.6	+	62829.7i	−0.176518	+	1.00108i	0.759859	+	0.650087i	$0.225268\pi$
$83$	−11078.6	+	62829.7i	−0.176518	+	1.00108i	−0.936377	+	0.350995i	$0.885843\pi$
$84$		0			0
$85$	77918.1	+	28359.9i	1.16975	+	0.425752i
$86$		0			0
$87$	1112.12	−	1162.01i	0.0157526	−	0.0164593i
$88$		0			0
$89$	9255.67	−	16031.3i	0.123860	−	0.214533i	−0.797426	−	0.603416i	$-0.793806\pi$
$89$	9255.67	−	16031.3i	0.123860	−	0.214533i	0.921287	+	0.388883i	$0.127139\pi$
$90$		0			0
$91$	53579.7	+	92802.8i	0.678261	+	1.17478i
$92$		0			0
$93$	73171.5	+	99768.6i	0.877273	+	1.19615i
$94$		0			0
$95$	12814.6	+	72675.0i	0.145678	+	0.826183i
$96$		0			0
$97$	−22186.6	−	18616.8i	−0.239421	−	0.200898i	0.515180	−	0.857082i	$-0.327725\pi$
$97$	−22186.6	−	18616.8i	−0.239421	−	0.200898i	−0.754601	+	0.656184i	$0.772169\pi$
$98$		0			0
$99$	6848.77	−	21739.4i	0.0702303	−	0.222926i
$100$		0			0
$101$	−52046.8	+	18943.5i	−0.507680	+	0.184781i	−0.583145	−	0.812368i	$-0.698178\pi$
$101$	−52046.8	+	18943.5i	−0.507680	+	0.184781i	0.0754649	+	0.997148i	$0.475956\pi$
$102$		0			0
$103$	110866.	−	93027.7i	1.02969	−	0.864010i	0.0388739	−	0.999244i	$-0.487623\pi$
$103$	110866.	−	93027.7i	1.02969	−	0.864010i	0.990814	+	0.135234i	$0.0431785\pi$
$104$		0			0
$105$	108081.	−	53315.4i	0.956699	−	0.471932i
$106$		0			0
$107$	−25143.9			−0.212311			−0.106156	−	0.994350i	$-0.533854\pi$
$107$	−25143.9			−0.212311			−0.106156	+	0.994350i	$0.533854\pi$
$108$		0			0
$109$	−57420.7			−0.462916			−0.231458	−	0.972845i	$-0.574350\pi$
$109$	−57420.7			−0.462916			−0.231458	+	0.972845i	$0.574350\pi$
$110$		0			0
$111$	−12595.6	+	192521.i	−0.0970315	+	1.48310i
$112$		0			0
$113$	122051.	−	102413.i	0.899177	−	0.754499i	−0.0708522	−	0.997487i	$-0.522572\pi$
$113$	122051.	−	102413.i	0.899177	−	0.754499i	0.970029	+	0.242988i	$0.0781274\pi$
$114$		0			0
$115$	76830.7	−	27964.1i	0.541739	−	0.197177i
$116$		0			0
$117$	−109750.	+	69954.7i	−0.741205	+	0.472446i
$118$		0			0
$119$	−328898.	−	275978.i	−2.12909	−	1.78652i
$120$		0			0
$121$	−26438.5	−	149940.i	−0.164162	−	0.931009i
$122$		0			0
$123$	−104659.	+	237932.i	−0.623755	+	1.41805i
$124$		0			0
$125$	−91904.7	−	159184.i	−0.526093	−	0.911220i
$126$		0			0
$127$	25202.3	−	43651.6i	0.138653	−	0.240154i	−0.788334	−	0.615248i	$-0.789056\pi$
$127$	25202.3	−	43651.6i	0.138653	−	0.240154i	0.926987	+	0.375093i	$0.122389\pi$
$128$		0			0
$129$	−45282.2	−	155288.i	−0.239582	−	0.821606i
$130$		0			0
$131$	−94711.1	−	34472.0i	−0.482195	−	0.175505i	0.0894738	−	0.995989i	$-0.471481\pi$
$131$	−94711.1	−	34472.0i	−0.482195	−	0.175505i	−0.571669	+	0.820485i	$0.693704\pi$
$132$		0			0
$133$	66352.7	−	376305.i	0.325259	−	1.84464i
$134$		0			0
$135$	70447.8	+	128302.i	0.332685	+	0.605895i
$136$		0			0
$137$	−59219.1	+	335848.i	−0.269563	+	1.52877i	0.486155	+	0.873872i	$0.338399\pi$
$137$	−59219.1	+	335848.i	−0.269563	+	1.52877i	−0.755719	+	0.654896i	$0.772712\pi$
$138$		0			0
$139$	295307.	+	107483.i	1.29639	+	0.471849i	0.895821	−	0.444416i	$-0.146589\pi$
$139$	295307.	+	107483.i	1.29639	+	0.471849i	0.400573	+	0.916265i	$0.368811\pi$
$140$		0			0
$141$	−310010.	−	75820.1i	−1.31319	−	0.321171i
$142$		0			0
$143$	25118.5	−	43506.5i	0.102720	−	0.177915i
$144$		0			0
$145$	−1993.49	−	3452.82i	−0.00787396	−	0.0136381i
$146$		0			0
$147$	−359867.	+	39454.9i	−1.37356	+	0.150594i
$148$		0			0
$149$	−56192.3	−	318682.i	−0.207353	−	1.17596i	−0.893693	−	0.448678i	$-0.851895\pi$
$149$	−56192.3	−	318682.i	−0.207353	−	1.17596i	0.686340	−	0.727281i	$-0.259216\pi$
$150$		0			0
$151$	−239084.	−	200615.i	−0.853311	−	0.716013i	0.107205	−	0.994237i	$-0.465810\pi$
$151$	−239084.	−	200615.i	−0.853311	−	0.716013i	−0.960516	+	0.278224i	$0.910254\pi$
$152$		0			0
$153$	317344.	−	413773.i	1.09598	−	1.42900i
$154$		0			0
$155$	288192.	−	104893.i	0.963503	−	0.350687i
$156$		0			0
$157$	−341911.	+	286897.i	−1.10704	+	0.928918i	−0.997878	−	0.0651060i	$-0.979261\pi$
$157$	−341911.	+	286897.i	−1.10704	+	0.928918i	−0.109163	+	0.994024i	$0.534817\pi$
$158$		0			0
$159$	178048.	+	118938.i	0.558528	+	0.373101i
$160$		0			0
$161$	−423354.			−1.28718
$162$		0			0
$163$	−63707.1			−0.187810			−0.0939051	−	0.995581i	$-0.529935\pi$
$163$	−63707.1			−0.187810			−0.0939051	+	0.995581i	$0.529935\pi$
$164$		0			0
$165$	−46980.4	−	31383.3i	−0.134340	−	0.0897404i
$166$		0			0
$167$	54737.1	−	45929.9i	0.151876	−	0.127439i	−0.563683	−	0.825991i	$-0.690616\pi$
$167$	54737.1	−	45929.9i	0.151876	−	0.127439i	0.715560	+	0.698552i	$0.246172\pi$
$168$		0			0
$169$	79343.5	−	28878.7i	0.213695	−	0.0777787i
$170$		0			0
$171$	460129.	+	60466.5i	1.20334	+	0.158134i
$172$		0			0
$173$	236607.	+	198536.i	0.601051	+	0.504342i	0.891783	−	0.452463i	$-0.149454\pi$
$173$	236607.	+	198536.i	0.601051	+	0.504342i	−0.290732	+	0.956804i	$0.593899\pi$
$174$		0			0
$175$	56697.6	+	321548.i	0.139949	+	0.793689i
$176$		0			0
$177$	471694.	−	51715.3i	1.13169	−	0.124075i
$178$		0			0
$179$	174555.	+	302338.i	0.407193	+	0.705278i	0.994574	−	0.104032i	$-0.0331744\pi$
$179$	174555.	+	302338.i	0.407193	+	0.705278i	−0.587381	+	0.809310i	$0.699841\pi$
$180$		0			0
$181$	−13307.4	+	23049.1i	−0.0301924	+	0.0522948i	−0.880727	−	0.473625i	$-0.842945\pi$
$181$	−13307.4	+	23049.1i	−0.0301924	+	0.0522948i	0.850534	+	0.525919i	$0.176279\pi$
$182$		0			0
$183$	−421849.	−	103173.i	−0.931170	−	0.227739i
$184$		0			0
$185$	449397.	+	163567.i	0.965386	+	0.351372i
$186$		0			0
$187$	−34951.9	+	198222.i	−0.0730914	+	0.414522i
$188$		0			0
$189$	−115558.	−	749029.i	−0.235314	−	1.52526i
$190$		0			0
$191$	−83086.4	+	471206.i	−0.164796	+	0.934604i	0.784479	+	0.620156i	$0.212931\pi$
$191$	−83086.4	+	471206.i	−0.164796	+	0.934604i	−0.949275	+	0.314448i	$0.898180\pi$
$192$		0			0
$193$	−399603.	−	145443.i	−0.772209	−	0.281061i	−0.0742891	−	0.997237i	$-0.523669\pi$
$193$	−399603.	−	145443.i	−0.772209	−	0.281061i	−0.697920	+	0.716176i	$0.745891\pi$
$194$		0			0
$195$	90312.4	+	309712.i	0.170083	+	0.583272i
$196$		0			0
$197$	−10673.0	+	18486.2i	−0.0195939	+	0.0339377i	−0.875656	−	0.482935i	$-0.839571\pi$
$197$	−10673.0	+	18486.2i	−0.0195939	+	0.0339377i	0.856062	+	0.516873i	$0.172904\pi$
$198$		0			0
$199$	225742.	+	390997.i	0.404092	+	0.699908i	0.994215	−	0.107405i	$-0.0342541\pi$
$199$	225742.	+	390997.i	0.404092	+	0.699908i	−0.590123	+	0.807313i	$0.700921\pi$
$200$		0			0
$201$	108496.	−	246655.i	0.189419	−	0.430625i
$202$		0			0
$203$	3584.83	+	20330.6i	0.00610560	+	0.0346266i
$204$		0			0
$205$	493577.	+	414160.i	0.820295	+	0.688310i
$206$		0			0
$207$	−22549.4	−	513682.i	−0.0365772	−	0.833238i
$208$		0			0
$209$	−168332.	+	61267.9i	−0.266564	+	0.0970213i
$210$		0			0
$211$	643208.	−	539716.i	0.994593	−	0.834562i	0.00836651	−	0.999965i	$-0.497337\pi$
$211$	643208.	−	539716.i	0.994593	−	0.834562i	0.986226	+	0.165403i	$0.0528924\pi$
$212$		0			0
$213$	−60941.2	+	931469.i	−0.0920369	+	1.40676i
$214$		0			0
$215$	−400958.			−0.591565
$216$		0			0
$217$	−1.58800e6			−2.28930
$218$		0			0
$219$	−470780.	+	232232.i	−0.663296	+	0.327199i
$220$		0			0
$221$	880435.	−	738772.i	1.21260	−	1.01749i
$222$		0			0
$223$	−256756.	+	93451.5i	−0.345747	+	0.125842i	−0.509056	−	0.860733i	$-0.670005\pi$
$223$	−256756.	+	93451.5i	−0.345747	+	0.125842i	0.163309	+	0.986575i	$0.447783\pi$
$224$		0			0
$225$	−387135.	+	85921.6i	−0.509807	+	0.113148i
$226$		0			0
$227$	855842.	+	718137.i	1.10237	+	0.925001i	0.997582	−	0.0694929i	$-0.0221381\pi$
$227$	855842.	+	718137.i	1.10237	+	0.925001i	0.104791	+	0.994494i	$0.466583\pi$
$228$		0			0
$229$	228440.	+	1.29555e6i	0.287861	+	1.63254i	0.694883	+	0.719122i	$0.255456\pi$
$229$	228440.	+	1.29555e6i	0.287861	+	1.63254i	−0.407022	+	0.913418i	$0.633433\pi$
$230$		0			0
$231$	173012.	+	235900.i	0.213327	+	0.290869i
$232$		0			0
$233$	−314061.	−	543969.i	−0.378987	−	0.656424i	0.611928	−	0.790913i	$-0.290394\pi$
$233$	−314061.	−	543969.i	−0.378987	−	0.656424i	−0.990915	+	0.134489i	$0.957061\pi$
$234$		0			0
$235$	−395549.	+	685111.i	−0.467230	+	0.809266i
$236$		0			0
$237$	−62138.1	+	64925.7i	−0.0718600	+	0.0750837i
$238$		0			0
$239$	1.34737e6	+	490401.i	1.52578	+	0.555337i	0.962583	−	0.270987i	$-0.0873502\pi$
$239$	1.34737e6	+	490401.i	1.52578	+	0.555337i	0.563194	+	0.826325i	$0.309572\pi$
$240$		0			0
$241$	130095.	−	737807.i	0.144284	−	0.818277i	−0.823655	−	0.567092i	$-0.808069\pi$
$241$	130095.	−	737807.i	0.144284	−	0.818277i	0.967939	−	0.251185i	$-0.0808204\pi$
$242$		0			0
$243$	902690.	−	180110.i	0.980670	−	0.195670i
$244$		0			0
$245$	−155828.	+	883747.i	−0.165856	+	0.940617i
$246$		0			0
$247$	961191.	+	349845.i	1.00246	+	0.364866i
$248$		0			0
$249$	687644.	−	718492.i	0.702854	−	0.734385i
$250$		0			0
$251$	400595.	−	693851.i	0.401348	−	0.695155i	−0.592541	−	0.805540i	$-0.701875\pi$
$251$	400595.	−	693851.i	0.401348	−	0.695155i	0.993889	+	0.110385i	$0.0352085\pi$
$252$		0			0
$253$	99235.4	+	171881.i	0.0974687	+	0.168821i
$254$		0			0
$255$	−764435.	−	1.04230e6i	−0.736191	−	1.00379i
$256$		0			0
$257$	338943.	+	1.92224e6i	0.320106	+	1.81541i	0.542044	+	0.840350i	$0.317651\pi$
$257$	338943.	+	1.92224e6i	0.320106	+	1.81541i	−0.221938	+	0.975061i	$0.571238\pi$
$258$		0			0
$259$	−1.89694e6	−	1.59172e6i	−1.75713	−	1.47441i
$260$		0			0
$261$	−24477.4	+	5432.58i	−0.0222415	+	0.00493634i
$262$		0			0
$263$	−885623.	+	322341.i	−0.789514	+	0.287360i	−0.705134	−	0.709074i	$-0.749113\pi$
$263$	−885623.	+	322341.i	−0.789514	+	0.287360i	−0.0843799	+	0.996434i	$0.526891\pi$
$264$		0			0
$265$	406584.	−	341165.i	0.355661	−	0.298435i
$266$		0			0
$267$	−258789.	+	127659.i	−0.222161	+	0.109590i
$268$		0			0
$269$	1.84654e6			1.55589			0.777944	−	0.628333i	$-0.216263\pi$
$269$	1.84654e6			1.55589			0.777944	+	0.628333i	$0.216263\pi$
$270$		0			0
$271$	−1.56625e6			−1.29550			−0.647751	−	0.761852i	$-0.724290\pi$
$271$	−1.56625e6			−1.29550			−0.647751	+	0.761852i	$0.724290\pi$
$272$		0			0
$273$	109056.	−	1.66689e6i	0.0885609	−	1.35363i
$274$		0			0
$275$	117258.	−	98390.8i	0.0934995	−	0.0784554i
$276$		0			0
$277$	−1.24738e6	+	454010.i	−0.976788	+	0.355522i	−0.780591	−	0.625043i	$-0.785082\pi$
$277$	−1.24738e6	+	454010.i	−0.976788	+	0.355522i	−0.196197	+	0.980564i	$0.562859\pi$
$278$		0			0
$279$	−84583.1	−	1.92682e6i	−0.0650538	−	1.48194i
$280$		0			0
$281$	1.57724e6	+	1.32347e6i	1.19161	+	0.999878i	0.999830	+	0.0184391i	$0.00586968\pi$
$281$	1.57724e6	+	1.32347e6i	1.19161	+	0.999878i	0.191778	+	0.981438i	$0.438575\pi$
$282$		0			0
$283$	−18214.3	−	103298.i	−0.0135191	−	0.0766704i	0.977302	−	0.211852i	$-0.0679494\pi$
$283$	−18214.3	−	103298.i	−0.0135191	−	0.0766704i	−0.990821	+	0.135181i	$0.956838\pi$
$284$		0			0
$285$	463182.	−	1.05300e6i	0.337785	−	0.767920i
$286$		0			0
$287$	−1.66811e6	−	2.88926e6i	−1.19542	−	2.07053i
$288$		0			0
$289$	−1.59252e6	+	2.75833e6i	−1.12161	+	1.94268i
$290$		0			0
$291$	126389.	+	433430.i	0.0874936	+	0.300045i
$292$		0			0
$293$	−30281.7	−	11021.6i	−0.0206068	−	0.00750027i	0.331696	−	0.943386i	$-0.392379\pi$
$293$	−30281.7	−	11021.6i	−0.0206068	−	0.00750027i	−0.352303	+	0.935886i	$0.614601\pi$
$294$		0			0
$295$	204251.	−	1.15837e6i	0.136650	−	0.774980i
$296$		0			0
$297$	−277017.	+	222491.i	−0.182228	+	0.146360i
$298$		0			0
$299$	196793.	−	1.11607e6i	0.127301	−	0.721960i
$300$		0			0
$301$	1.95092e6	+	710076.i	1.24115	+	0.451740i
$302$		0			0
$303$	838679.	+	205118.i	0.524794	+	0.128351i
$304$		0			0
$305$	−538247.	+	932271.i	−0.331308	+	0.573842i
$306$		0			0
$307$	143144.	+	247932.i	0.0866815	+	0.150137i	0.906107	−	0.423050i	$-0.139040\pi$
$307$	143144.	+	247932.i	0.0866815	+	0.150137i	−0.819425	+	0.573186i	$0.805707\pi$
$308$		0			0
$309$	−2.24261e6	+	245873.i	−1.33616	+	0.146493i
$310$		0			0
$311$	−165904.	−	940886.i	−0.0972646	−	0.551615i	−0.994030	−	0.109108i	$-0.965200\pi$
$311$	−165904.	−	940886.i	−0.0972646	−	0.551615i	0.896765	−	0.442507i	$-0.145911\pi$
$312$		0			0
$313$	−1.20905e6	−	1.01452e6i	−0.697565	−	0.585327i	0.223514	−	0.974701i	$-0.428247\pi$
$313$	−1.20905e6	−	1.01452e6i	−0.697565	−	0.585327i	−0.921080	+	0.389374i	$0.872691\pi$
$314$		0			0
$315$	−1.86264e6	−	244773.i	−1.05767	−	0.138991i
$316$		0			0
$317$	−2.55210e6	+	928887.i	−1.42643	+	0.519176i	−0.935905	−	0.352253i	$-0.885416\pi$
$317$	−2.55210e6	+	928887.i	−1.42643	+	0.519176i	−0.490520	+	0.871430i	$0.663193\pi$
$318$		0			0
$319$	7413.87	−	6220.97i	0.00407914	−	0.00342280i
$320$		0			0
$321$	325924.	+	217720.i	0.176544	+	0.117933i
$322$		0			0
$323$	−4.09828e6			−2.18572
$324$		0			0
$325$	−874037.			−0.459009
$326$		0			0
$327$	744308.	+	497203.i	0.384931	+	0.257137i
$328$		0			0
$329$	3.13790e6	−	2.63301e6i	1.59827	−	1.34110i
$330$		0			0
$331$	2.67628e6	−	974086.i	1.34265	−	0.488683i	0.432001	−	0.901873i	$-0.357808\pi$
$331$	2.67628e6	−	974086.i	1.34265	−	0.488683i	0.910645	+	0.413190i	$0.135585\pi$
$332$		0			0
$333$	1.83030e6	−	2.38646e6i	0.904505	−	1.17935i
$334$		0			0
$335$	−511672.	−	429344.i	−0.249103	−	0.209023i
$336$		0			0
$337$	−341830.	−	1.93862e6i	−0.163959	−	0.929859i	−0.950131	−	0.311851i	$-0.899051\pi$
$337$	−341830.	−	1.93862e6i	−0.163959	−	0.929859i	0.786172	−	0.618008i	$-0.212060\pi$
$338$		0			0
$339$	−2.46886e6	+	270679.i	−1.16680	+	0.127925i
$340$		0			0
$341$	372232.	+	644725.i	0.173352	+	0.300254i
$342$		0			0
$343$	641931.	−	1.11186e6i	0.294614	−	0.510286i
$344$		0			0
$345$	−1.23805e6	−	302793.i	−0.560002	−	0.136961i
$346$		0			0
$347$	−439965.	−	160134.i	−0.196153	−	0.0713938i	0.242076	−	0.970257i	$-0.422172\pi$
$347$	−439965.	−	160134.i	−0.196153	−	0.0713938i	−0.438229	+	0.898864i	$0.644394\pi$
$348$		0			0
$349$	185066.	−	1.04956e6i	0.0813322	−	0.461258i	−0.916756	−	0.399448i	$-0.869202\pi$
$349$	185066.	−	1.04956e6i	0.0813322	−	0.461258i	0.998088	−	0.0618095i	$-0.0196871\pi$
$350$		0			0
$351$	2.02835e6	+	43539.6i	0.878769	+	0.0188632i
$352$		0			0
$353$	−292110.	+	1.65664e6i	−0.124770	+	0.707606i	0.856674	+	0.515858i	$0.172527\pi$
$353$	−292110.	+	1.65664e6i	−0.124770	+	0.707606i	−0.981444	+	0.191748i	$0.938584\pi$
$354$		0			0
$355$	2.17431e6	+	791384.i	0.915694	+	0.333285i
$356$		0			0
$357$	1.87361e6	+	6.42524e6i	0.778052	+	2.66820i
$358$		0			0
$359$	1.44684e6	−	2.50600e6i	0.592494	−	1.02623i	−0.401401	−	0.915902i	$-0.631477\pi$
$359$	1.44684e6	−	2.50600e6i	0.592494	−	1.02623i	0.993895	−	0.110328i	$-0.0351900\pi$
$360$		0			0
$361$	−585644.	−	1.01437e6i	−0.236519	−	0.409663i
$362$		0			0
$363$	−955619.	+	2.17250e6i	−0.380643	+	0.865355i
$364$		0			0
$365$	225955.	+	1.28145e6i	0.0887748	+	0.503467i
$366$		0			0
$367$	2.28487e6	+	1.91723e6i	0.885515	+	0.743035i	0.967305	−	0.253614i	$-0.0816194\pi$
$367$	2.28487e6	+	1.91723e6i	0.885515	+	0.743035i	−0.0817905	+	0.996650i	$0.526064\pi$
$368$		0			0
$369$	3.41687e6	−	2.17792e6i	1.30636	−	0.832676i
$370$		0			0
$371$	−2.58248e6	+	939947.i	−0.974098	+	0.354543i
$372$		0			0
$373$	−2.21976e6	+	1.86260e6i	−0.826103	+	0.693183i	−0.954393	−	0.298554i	$-0.903496\pi$
$373$	−2.21976e6	+	1.86260e6i	−0.826103	+	0.693183i	0.128290	+	0.991737i	$0.459051\pi$
$374$		0			0
$375$	−187062.	+	2.85919e6i	−0.0686923	+	1.04994i
$376$		0			0
$377$	−55262.9			−0.0200254
$378$		0			0
$379$	3.22272e6			1.15246			0.576228	−	0.817289i	$-0.304524\pi$
$379$	3.22272e6			1.15246			0.576228	+	0.817289i	$0.304524\pi$
$380$		0			0
$381$	−704657.	+	347602.i	−0.248694	+	0.122679i
$382$		0			0
$383$	2.76210e6	−	2.31768e6i	0.962150	−	0.807340i	−0.0191516	−	0.999817i	$-0.506097\pi$
$383$	2.76210e6	−	2.31768e6i	0.962150	−	0.807340i	0.981301	+	0.192477i	$0.0616521\pi$
$384$		0			0
$385$	681422.	−	248017.i	0.234296	−	0.0852766i
$386$		0			0
$387$	−757667.	+	2.40499e6i	−0.257159	+	0.816275i
$388$		0			0
$389$	3.19599e6	+	2.68176e6i	1.07086	+	0.898557i	0.995130	−	0.0985718i	$-0.0314274\pi$
$389$	3.19599e6	+	2.68176e6i	1.07086	+	0.898557i	0.0757283	+	0.997128i	$0.475872\pi$
$390$		0			0
$391$	788473.	+	4.47165e6i	0.260822	+	1.47920i
$392$		0			0
$393$	929187.	+	1.26694e6i	0.303474	+	0.413784i
$394$		0			0
$395$	111384.	+	192922.i	0.0359193	+	0.0622141i
$396$		0			0
$397$	−886435.	+	1.53535e6i	−0.282274	+	0.488913i	−0.971944	−	0.235210i	$-0.924422\pi$
$397$	−886435.	+	1.53535e6i	−0.282274	+	0.488913i	0.689670	+	0.724123i	$0.257755\pi$
$398$		0			0
$399$	−4.11849e6	+	4.30325e6i	−1.29511	+	1.35321i
$400$		0			0
$401$	−780728.	−	284162.i	−0.242459	−	0.0882479i	0.217932	−	0.975964i	$-0.430069\pi$
$401$	−780728.	−	284162.i	−0.242459	−	0.0882479i	−0.460392	+	0.887716i	$0.652291\pi$
$402$		0			0
$403$	738172.	−	4.18638e6i	0.226410	−	1.28403i
$404$		0			0
$405$	197788.	−	2.27309e6i	0.0599186	−	0.688620i
$406$		0			0
$407$	−201587.	+	1.14326e6i	−0.0603221	+	0.342103i
$408$		0			0
$409$	−829829.	−	302033.i	−0.245290	−	0.0892783i	0.216449	−	0.976294i	$-0.430552\pi$
$409$	−829829.	−	302033.i	−0.245290	−	0.0892783i	−0.461740	+	0.887016i	$0.652775\pi$
$410$		0			0
$411$	3.67571e6	−	3.84061e6i	1.07334	−	1.12149i
$412$		0			0
$413$	−3.04522e6	+	5.27448e6i	−0.878504	+	1.52161i
$414$		0			0
$415$	−1.23261e6	−	2.13495e6i	−0.351323	−	0.608508i
$416$		0			0
$417$	−2.89718e6	−	3.95028e6i	−0.815898	−	1.11247i
$418$		0			0
$419$	−555752.	−	3.15183e6i	−0.154649	−	0.877056i	−0.959106	−	0.283046i	$-0.908655\pi$
$419$	−555752.	−	3.15183e6i	−0.154649	−	0.877056i	0.804458	−	0.594010i	$-0.202456\pi$
$420$		0			0
$421$	−3.40255e6	−	2.85508e6i	−0.935620	−	0.785079i	0.0411974	−	0.999151i	$-0.486883\pi$
$421$	−3.40255e6	−	2.85508e6i	−0.935620	−	0.785079i	−0.976818	+	0.214072i	$0.931327\pi$
$422$		0			0
$423$	3.36193e6	+	3.66717e6i	0.913562	+	0.996506i
$424$		0			0
$425$	3.29073e6	−	1.19773e6i	0.883732	−	0.321652i
$426$		0			0
$427$	4.26993e6	−	3.58289e6i	1.13331	−	0.950964i
$428$		0			0
$429$	−702315.	+	346446.i	−0.184242	+	0.0908851i
$430$		0			0
$431$	−4.35575e6			−1.12946			−0.564729	−	0.825276i	$-0.691019\pi$
$431$	−4.35575e6			−1.12946			−0.564729	+	0.825276i	$0.691019\pi$
$432$		0			0
$433$	4.24953e6			1.08923			0.544616	−	0.838685i	$-0.316675\pi$
$433$	4.24953e6			1.08923			0.544616	+	0.838685i	$0.316675\pi$
$434$		0			0
$435$	−4057.53	+	62018.2i	−0.00102811	+	0.0157143i
$436$		0			0
$437$	−3.09565e6	+	2.59756e6i	−0.775439	+	0.650671i
$438$		0			0
$439$	2.86650e6	−	1.04332e6i	0.709890	−	0.258379i	0.0382627	−	0.999268i	$-0.487818\pi$
$439$	2.86650e6	−	1.04332e6i	0.709890	−	0.258379i	0.671628	+	0.740889i	$0.265595\pi$
$440$		0			0
$441$	5.00637e6	+	2.60465e6i	1.22582	+	0.637753i
$442$		0			0
$443$	−2.72460e6	−	2.28621e6i	−0.659619	−	0.553486i	0.250353	−	0.968155i	$-0.419453\pi$
$443$	−2.72460e6	−	2.28621e6i	−0.659619	−	0.553486i	−0.909973	+	0.414668i	$0.863898\pi$
$444$		0			0
$445$	124208.	+	704420.i	0.0297338	+	0.168629i
$446$		0			0
$447$	−2.03107e6	+	4.61744e6i	−0.480791	+	1.09303i
$448$		0			0
$449$	−2.28344e6	−	3.95504e6i	−0.534533	−	0.925839i	−0.999186	−	0.0403455i	$-0.987154\pi$
$449$	−2.28344e6	−	3.95504e6i	−0.534533	−	0.925839i	0.464653	−	0.885493i	$-0.346179\pi$
$450$		0			0
$451$	−782021.	+	1.35450e6i	−0.181041	+	0.313572i
$452$		0			0
$453$	1.36197e6	+	4.67066e6i	0.311833	+	1.06938i
$454$		0			0
$455$	−3.89098e6	−	1.41620e6i	−0.881110	−	0.320698i
$456$		0			0
$457$	−551682.	+	3.12874e6i	−0.123566	+	0.700776i	0.858584	+	0.512674i	$0.171345\pi$
$457$	−551682.	+	3.12874e6i	−0.123566	+	0.700776i	−0.982149	+	0.188103i	$0.939766\pi$
$458$		0			0
$459$	−7.69636e6	+	2.61560e6i	−1.70511	+	0.579482i
$460$		0			0
$461$	190975.	−	1.08307e6i	0.0418528	−	0.237359i	−0.956704	−	0.291062i	$-0.905991\pi$
$461$	190975.	−	1.08307e6i	0.0418528	−	0.237359i	0.998557	+	0.0537031i	$0.0171025\pi$
$462$		0			0
$463$	2.73571e6	+	995719.i	0.593087	+	0.215866i	0.621087	−	0.783742i	$-0.286692\pi$
$463$	2.73571e6	+	995719.i	0.593087	+	0.215866i	−0.0279997	+	0.999608i	$0.508914\pi$
$464$		0			0
$465$	−4.64392e6	−	1.13578e6i	−0.995984	−	0.243591i
$466$		0			0
$467$	2.45229e6	−	4.24750e6i	0.520332	−	0.901241i	−0.479389	−	0.877603i	$-0.659142\pi$
$467$	2.45229e6	−	4.24750e6i	0.520332	−	0.901241i	0.999721	−	0.0236386i	$-0.00752509\pi$
$468$		0			0
$469$	1.72927e6	+	2.99518e6i	0.363020	+	0.628769i
$470$		0			0
$471$	6.91620e6	−	758274.i	1.43653	−	0.157498i
$472$		0			0
$473$	−169011.	−	958512.i	−0.0347347	−	0.196990i
$474$		0			0
$475$	2.38749e6	+	2.00334e6i	0.485521	+	0.407400i
$476$		0			0
$477$	−1.27805e6	−	3.08342e6i	−0.257189	−	0.620494i
$478$		0			0
$479$	−5.75088e6	+	2.09315e6i	−1.14524	+	0.416832i	−0.843802	−	0.536654i	$-0.819688\pi$
$479$	−5.75088e6	+	2.09315e6i	−1.14524	+	0.416832i	−0.301435	+	0.953487i	$0.597466\pi$
$480$		0			0
$481$	5.07796e6	−	4.26091e6i	1.00075	−	0.839730i
$482$		0			0
$483$	5.48767e6	+	3.66580e6i	1.07034	+	0.714992i
$484$		0			0
$485$	1.11913e6			0.216036
$486$		0			0
$487$	−3.84197e6			−0.734059			−0.367030	−	0.930209i	$-0.619625\pi$
$487$	−3.84197e6			−0.734059			−0.367030	+	0.930209i	$0.619625\pi$
$488$		0			0
$489$	825794.	+	551637.i	0.156171	+	0.104323i
$490$		0			0
$491$	4.68500e6	−	3.93118e6i	0.877013	−	0.735901i	−0.0885499	−	0.996072i	$-0.528223\pi$
$491$	4.68500e6	−	3.93118e6i	0.877013	−	0.735901i	0.965563	+	0.260171i	$0.0837788\pi$
$492$		0			0
$493$	208064.	−	75729.1i	0.0385549	−	0.0140328i
$494$		0			0
$495$	337230.	+	813602.i	0.0618605	+	0.149245i
$496$		0			0
$497$	−9.17792e6	−	7.70119e6i	−1.66668	−	1.39851i
$498$		0			0
$499$	−491965.	−	2.79007e6i	−0.0884470	−	0.501608i	−0.996559	−	0.0828815i	$-0.973588\pi$
$499$	−491965.	−	2.79007e6i	−0.0884470	−	0.501608i	0.908112	−	0.418727i	$-0.137523\pi$
$500$		0			0
$501$	−1.10723e6	+	121393.i	−0.197080	+	0.0216073i
$502$		0			0
$503$	587836.	+	1.01816e6i	0.103594	+	0.179431i	0.913163	−	0.407594i	$-0.133632\pi$
$503$	587836.	+	1.01816e6i	0.103594	+	0.179431i	−0.809569	+	0.587025i	$0.800299\pi$
$504$		0			0
$505$	1.07009e6	−	1.85345e6i	0.186721	−	0.323409i
$506$		0			0
$507$	−1.27854e6	−	312696.i	−0.220899	−	0.0540260i
$508$		0			0
$509$	−495632.	−	180395.i	−0.0847940	−	0.0308625i	0.299275	−	0.954167i	$-0.403255\pi$
$509$	−495632.	−	180395.i	−0.0847940	−	0.0308625i	−0.384069	+	0.923304i	$0.625477\pi$
$510$		0			0
$511$	1.16997e6	−	6.63526e6i	0.198209	−	1.12410i
$512$		0			0
$513$	−5.44077e6	−	4.76802e6i	−0.912782	−	0.799917i
$514$		0			0
$515$	−971085.	+	5.50730e6i	−0.161339	+	0.914999i
$516$		0			0
$517$	−1.80453e6	−	656794.i	−0.296918	−	0.108069i
$518$		0			0
$519$	−1.34786e6	−	4.62226e6i	−0.219647	−	0.753245i
$520$		0			0
$521$	3.39837e6	−	5.88615e6i	0.548500	−	0.950030i	−0.449878	−	0.893090i	$-0.648532\pi$
$521$	3.39837e6	−	5.88615e6i	0.548500	−	0.950030i	0.998378	−	0.0569395i	$-0.0181342\pi$
$522$		0			0
$523$	−626369.	−	1.08490e6i	−0.100133	−	0.173435i	0.811606	−	0.584205i	$-0.198593\pi$
$523$	−626369.	−	1.08490e6i	−0.100133	−	0.173435i	−0.911739	+	0.410770i	$0.865260\pi$
$524$		0			0
$525$	2.04933e6	−	4.65896e6i	0.324500	−	0.737718i
$526$		0			0
$527$	2.95757e6	+	1.67732e7i	0.463882	+	2.63081i
$528$		0			0
$529$	−1.50074e6	−	1.25927e6i	−0.233166	−	0.195650i
$530$		0			0
$531$	−6.56206e6	−	3.41402e6i	−1.00996	−	0.525448i
$532$		0			0
$533$	8.39223e6	−	3.05452e6i	1.27956	−	0.465720i
$534$		0			0
$535$	744267.	−	624514.i	0.112420	−	0.0943317i
$536$		0			0
$537$	355288.	−	5.43048e6i	0.0531674	−	0.812648i
$538$		0			0
$539$	−2.17833e6			−0.322963
$540$		0			0
$541$	−6.93423e6			−1.01860			−0.509302	−	0.860588i	$-0.670096\pi$
$541$	−6.93423e6			−1.01860			−0.509302	+	0.860588i	$0.670096\pi$
$542$		0			0
$543$	372077.	−	183543.i	0.0541543	−	0.0267139i
$544$		0			0
$545$	1.69967e6	−	1.42619e6i	0.245117	−	0.205678i
$546$		0			0
$547$	−9.73428e6	+	3.54299e6i	−1.39103	+	0.506292i	−0.925502	−	0.378743i	$-0.876357\pi$
$547$	−9.73428e6	+	3.54299e6i	−1.39103	+	0.506292i	−0.465525	+	0.885035i	$0.654134\pi$
$548$		0			0
$549$	4.57478e6	+	4.99013e6i	0.647798	+	0.706612i
$550$		0			0
$551$	150954.	+	126666.i	0.0211820	+	0.0177738i
$552$		0			0
$553$	−200298.	−	1.13594e6i	−0.0278524	−	0.157959i
$554$		0			0
$555$	−4.40892e6	−	6.01152e6i	−0.607575	−	0.828423i
$556$		0			0
$557$	−1.07302e6	−	1.85852e6i	−0.146544	−	0.253822i	0.783404	−	0.621513i	$-0.213482\pi$
$557$	−1.07302e6	−	1.85852e6i	−0.146544	−	0.253822i	−0.929948	+	0.367691i	$0.880148\pi$
$558$		0			0
$559$	−2.77881e6	+	4.81304e6i	−0.376123	+	0.651463i
$560$		0			0
$561$	2.16945e6	−	2.26678e6i	0.291034	−	0.304089i
$562$		0			0
$563$	−8.53904e6	−	3.10796e6i	−1.13537	−	0.413241i	−0.295132	−	0.955457i	$-0.595364\pi$
$563$	−8.53904e6	−	3.10796e6i	−1.13537	−	0.413241i	−0.840240	+	0.542215i	$0.817586\pi$
$564$		0			0
$565$	−1.06906e6	+	6.06292e6i	−0.140890	+	0.799025i
$566$		0			0
$567$	−4.98790e6	+	1.07098e7i	−0.651569	+	1.39902i
$568$		0			0
$569$	−618973.	+	3.51037e6i	−0.0801477	+	0.454540i	0.918151	+	0.396231i	$0.129682\pi$
$569$	−618973.	+	3.51037e6i	−0.0801477	+	0.454540i	−0.998299	+	0.0583091i	$0.981429\pi$
$570$		0			0
$571$	−7.43529e6	−	2.70622e6i	−0.954350	−	0.347355i	−0.182533	−	0.983200i	$-0.558430\pi$
$571$	−7.43529e6	−	2.70622e6i	−0.954350	−	0.347355i	−0.771817	+	0.635845i	$0.780652\pi$
$572$		0			0
$573$	5.15715e6	−	5.38850e6i	0.656180	−	0.685617i
$574$		0			0
$575$	1.72653e6	−	2.99043e6i	0.217773	−	0.377194i
$576$		0			0
$577$	−6.45262e6	−	1.11763e7i	−0.806857	−	1.39752i	−0.915030	−	0.403386i	$-0.867833\pi$
$577$	−6.45262e6	−	1.11763e7i	−0.806857	−	1.39752i	0.108172	−	0.994132i	$-0.465500\pi$
$578$		0			0
$579$	3.92040e6	+	5.34543e6i	0.485998	+	0.662653i
$580$		0			0
$581$	2.21657e6	+	1.25708e7i	0.272421	+	1.54498i
$582$		0			0
$583$	986957.	+	828155.i	0.120262	+	0.100911i
$584$		0			0
$585$	1.51112e6	−	4.79660e6i	0.182561	−	0.579488i
$586$		0			0
$587$	1.46209e7	−	5.32157e6i	1.75137	−	0.637448i	0.751620	−	0.659597i	$-0.229273\pi$
$587$	1.46209e7	−	5.32157e6i	1.75137	−	0.637448i	0.999755	+	0.0221485i	$0.00705065\pi$
$588$		0			0
$589$	−1.16118e7	+	9.74344e6i	−1.37915	+	1.15724i
$590$		0			0
$591$	298418.	−	147208.i	0.0351445	−	0.0173365i
$592$		0			0
$593$	1.18624e7			1.38528			0.692639	−	0.721284i	$-0.256448\pi$
$593$	1.18624e7			1.38528			0.692639	+	0.721284i	$0.256448\pi$
$594$		0			0
$595$	1.65901e7			1.92113
$596$		0			0
$597$	459475.	−	7.02294e6i	0.0527625	−	0.806460i
$598$		0			0
$599$	3.57373e6	−	2.99872e6i	0.406963	−	0.341482i	−0.416215	−	0.909266i	$-0.636644\pi$
$599$	3.57373e6	−	2.99872e6i	0.406963	−	0.341482i	0.823178	+	0.567784i	$0.192199\pi$
$600$		0			0
$601$	−407429.	+	148292.i	−0.0460115	+	0.0167468i	−0.364923	−	0.931038i	$-0.618905\pi$
$601$	−407429.	+	148292.i	−0.0460115	+	0.0167468i	0.318912	+	0.947784i	$0.396683\pi$
$602$		0			0
$603$	−3.54214e6	+	2.25777e6i	−0.396709	+	0.252863i
$604$		0			0
$605$	4.50674e6	+	3.78161e6i	0.500581	+	0.420037i
$606$		0			0
$607$	−598631.	−	3.39500e6i	−0.0659458	−	0.373997i	−0.999864	−	0.0165098i	$-0.994745\pi$
$607$	−598631.	−	3.39500e6i	−0.0659458	−	0.373997i	0.933918	−	0.357488i	$-0.116367\pi$
$608$		0			0
$609$	129574.	−	294573.i	0.0141571	−	0.0321847i
$610$		0			0
$611$	5.48265e6	+	9.49623e6i	0.594138	+	1.02908i
$612$		0			0
$613$	3.46113e6	−	5.99485e6i	0.372020	−	0.644358i	−0.617856	−	0.786291i	$-0.711999\pi$
$613$	3.46113e6	−	5.99485e6i	0.372020	−	0.644358i	0.989876	+	0.141933i	$0.0453319\pi$
$614$		0			0
$615$	−2.81172e6	−	9.64235e6i	−0.299768	−	1.02800i
$616$		0			0
$617$	−1.58712e7	−	5.77663e6i	−1.67840	−	0.610888i	−0.685312	−	0.728249i	$-0.740334\pi$
$617$	−1.58712e7	−	5.77663e6i	−1.67840	−	0.610888i	−0.993089	+	0.117361i	$0.962557\pi$
$618$		0			0
$619$	−3.09224e6	+	1.75370e7i	−0.324374	+	1.83962i	0.189662	+	0.981849i	$0.439261\pi$
$619$	−3.09224e6	+	1.75370e7i	−0.324374	+	1.83962i	−0.514036	+	0.857768i	$0.671850\pi$
$620$		0			0
$621$	−4.15566e6	+	6.85379e6i	−0.432425	+	0.713184i
$622$		0			0
$623$	643140.	−	3.64743e6i	0.0663873	−	0.376501i
$624$		0			0
$625$	1.88198e6	+	684984.i	0.192715	+	0.0701424i
$626$		0			0
$627$	2.71250e6	+	663404.i	0.275550	+	0.0673921i
$628$		0			0
$629$	−1.32795e7	+	2.30008e7i	−1.33831	+	2.31801i
$630$		0			0
$631$	8.54803e6	+	1.48056e7i	0.854659	+	1.48031i	0.876961	+	0.480561i	$0.159567\pi$
$631$	8.54803e6	+	1.48056e7i	0.854659	+	1.48031i	−0.0223021	+	0.999751i	$0.507100\pi$
$632$		0			0
$633$	−1.30109e7	+	1.42648e6i	−1.29061	+	0.141500i
$634$		0			0
$635$	338207.	+	1.91807e6i	0.0332849	+	0.188768i
$636$		0			0
$637$	9.52842e6	+	7.99529e6i	0.930406	+	0.780703i
$638$		0			0
$639$	8.85549e6	−	1.15463e7i	0.857947	−	1.11865i
$640$		0			0
$641$	1.09220e7	−	3.97527e6i	1.04992	−	0.382139i	0.241287	−	0.970454i	$-0.422431\pi$
$641$	1.09220e7	−	3.97527e6i	1.04992	−	0.382139i	0.808632	+	0.588315i	$0.200208\pi$
$642$		0			0
$643$	−1.74369e6	+	1.46313e6i	−0.166319	+	0.139558i	−0.722149	−	0.691738i	$-0.756845\pi$
$643$	−1.74369e6	+	1.46313e6i	−0.166319	+	0.139558i	0.555829	+	0.831296i	$0.312401\pi$
$644$		0			0
$645$	5.19735e6	+	3.47187e6i	0.491907	+	0.328598i
$646$		0			0
$647$	1.50309e7			1.41164			0.705821	−	0.708390i	$-0.250578\pi$
$647$	1.50309e7			1.41164			0.705821	+	0.708390i	$0.250578\pi$
$648$		0			0
$649$	2.85523e6			0.266091
$650$		0			0
$651$	2.05843e7	+	1.37504e7i	1.90363	+	1.27164i
$652$		0			0
$653$	6.99870e6	−	5.87261e6i	0.642295	−	0.538950i	−0.262427	−	0.964952i	$-0.584523\pi$
$653$	6.99870e6	−	5.87261e6i	0.642295	−	0.538950i	0.904722	+	0.426002i	$0.140078\pi$
$654$		0			0
$655$	3.65968e6	−	1.33202e6i	0.333304	−	0.121313i
$656$		0			0
$657$	8.11330e6	+	1.06619e6i	0.733304	+	0.0963650i
$658$		0			0
$659$	−3.46130e6	−	2.90438e6i	−0.310475	−	0.260519i	0.474213	−	0.880410i	$-0.342732\pi$
$659$	−3.46130e6	−	2.90438e6i	−0.310475	−	0.260519i	−0.784688	+	0.619891i	$0.787177\pi$
$660$		0			0
$661$	−546443.	−	3.09903e6i	−0.0486454	−	0.275882i	0.950777	−	0.309877i	$-0.100288\pi$
$661$	−546443.	−	3.09903e6i	−0.0486454	−	0.275882i	−0.999422	+	0.0339956i	$0.989177\pi$
$662$		0			0
$663$	−1.78095e7	+	1.95259e6i	−1.57350	+	0.172515i
$664$		0			0
$665$	7.38246e6	+	1.27868e7i	0.647361	+	1.12126i
$666$		0			0
$667$	109163.	−	189077.i	0.00950086	−	0.0164560i
$668$		0			0
$669$	4.13735e6	+	1.01189e6i	0.357402	+	0.0874111i
$670$		0			0
$671$	−2.45553e6	−	893739.i	−0.210542	−	0.0766310i
$672$		0			0
$673$	−1.97139e6	+	1.11803e7i	−0.167778	+	0.951517i	0.778376	+	0.627799i	$0.216044\pi$
$673$	−1.97139e6	+	1.11803e7i	−0.167778	+	0.951517i	−0.946154	+	0.323718i	$0.895067\pi$
$674$		0			0
$675$	5.76216e6	+	2.23843e6i	0.486773	+	0.189097i
$676$		0			0
$677$	1.30948e6	−	7.42642e6i	0.109806	−	0.622742i	−0.879385	−	0.476111i	$-0.842046\pi$
$677$	1.30948e6	−	7.42642e6i	0.109806	−	0.622742i	0.989191	−	0.146631i	$-0.0468428\pi$
$678$		0			0
$679$	−5.44528e6	−	1.98192e6i	−0.453258	−	0.164972i
$680$		0			0
$681$	−4.87541e6	−	1.67194e7i	−0.402850	−	1.38151i
$682$		0			0
$683$	−2.29131e6	+	3.96866e6i	−0.187945	+	0.325531i	−0.944565	−	0.328324i	$-0.893516\pi$
$683$	−2.29131e6	+	3.96866e6i	−0.187945	+	0.325531i	0.756620	+	0.653855i	$0.226849\pi$
$684$		0			0
$685$	−6.58877e6	−	1.14121e7i	−0.536510	−	0.929263i
$686$		0			0
$687$	8.25695e6	−	1.87714e7i	0.667464	−	1.51741i
$688$		0			0
$689$	−1.27749e6	−	7.24500e6i	−0.102520	−	0.581421i
$690$		0			0
$691$	2.91574e6	+	2.44660e6i	0.232302	+	0.194925i	0.751507	−	0.659725i	$-0.229327\pi$
$691$	2.91574e6	+	2.44660e6i	0.232302	+	0.194925i	−0.519205	+	0.854650i	$0.673772\pi$
$692$		0			0
$693$	−199994.	−	4.55592e6i	−0.0158192	−	0.360365i
$694$		0			0
$695$	−1.14108e7	+	4.15320e6i	−0.896096	+	0.326152i
$696$		0			0
$697$	−2.74108e7	+	2.30004e7i	−2.13718	+	1.79330i
$698$		0			0
$699$	−639237.	+	9.77056e6i	−0.0494845	+	0.756356i
$700$		0			0
$701$	3.18954e6			0.245151			0.122575	−	0.992459i	$-0.460885\pi$
$701$	3.18954e6			0.245151			0.122575	+	0.992459i	$0.460885\pi$
$702$		0			0
$703$	−2.36370e7			−1.80387
$704$		0			0
$705$	1.10596e7	−	5.45561e6i	0.838042	−	0.413400i
$706$		0			0
$707$	−8.48905e6	+	7.12316e6i	−0.638720	+	0.535950i
$708$		0			0
$709$	−6.31316e6	+	2.29780e6i	−0.471662	+	0.171671i	−0.566905	−	0.823783i	$-0.691859\pi$
$709$	−6.31316e6	+	2.29780e6i	−0.471662	+	0.171671i	0.0952429	+	0.995454i	$0.469637\pi$
$710$		0			0
$711$	1.36764e6	−	303539.i	0.101461	−	0.0225185i
$712$		0			0
$713$	1.28651e7	+	1.07951e7i	0.947743	+	0.795251i
$714$		0			0
$715$	337082.	+	1.91169e6i	0.0246587	+	0.139847i
$716$		0			0
$717$	−1.32187e7	−	1.80235e7i	−0.960263	−	1.30931i
$718$		0			0
$719$	8.82374e6	+	1.52832e7i	0.636547	+	1.10253i	0.986185	+	0.165647i	$0.0529713\pi$
$719$	8.82374e6	+	1.52832e7i	0.636547	+	1.10253i	−0.349638	+	0.936885i	$0.613695\pi$
$720$		0			0
$721$	1.44781e7	−	2.50768e7i	1.03723	−	1.79653i
$722$		0			0
$723$	−8.07498e6	+	8.43723e6i	−0.574507	+	0.600280i
$724$		0			0
$725$	−158228.	−	57590.3i	−0.0111799	−	0.00406916i
$726$		0			0
$727$	901251.	−	5.11125e6i	0.0632426	−	0.358667i	−0.936721	−	0.350078i	$-0.886155\pi$
$727$	901251.	−	5.11125e6i	0.0632426	−	0.358667i	0.999963	−	0.00858847i	$-0.00273383\pi$
$728$		0			0
$729$	−1.32605e7	−	5.48169e6i	−0.924151	−	0.382029i
$730$		0			0
$731$	3.86666e6	−	2.19289e7i	0.267635	−	1.51783i
$732$		0			0
$733$	−2.57487e7	−	9.37176e6i	−1.77009	−	0.644260i	−0.999980	−	0.00634869i	$-0.997979\pi$
$733$	−2.57487e7	−	9.37176e6i	−1.77009	−	0.644260i	−0.770110	−	0.637911i	$-0.779799\pi$
$734$		0			0
$735$	9.67223e6	−	1.01061e7i	0.660402	−	0.690028i
$736$		0			0
$737$	810691.	−	1.40416e6i	0.0549777	−	0.0952242i
$738$		0			0
$739$	9.92631e6	+	1.71929e7i	0.668616	+	1.15808i	0.978291	+	0.207234i	$0.0664463\pi$
$739$	9.92631e6	+	1.71929e7i	0.668616	+	1.15808i	−0.309675	+	0.950842i	$0.600220\pi$
$740$		0			0
$741$	−9.43001e6	−	1.28577e7i	−0.630909	−	0.860238i
$742$		0			0
$743$	4.13933e6	+	2.34753e7i	0.275079	+	1.56005i	0.738709	+	0.674024i	$0.235436\pi$
$743$	4.13933e6	+	2.34753e7i	0.275079	+	1.56005i	−0.463630	+	0.886029i	$0.653453\pi$
$744$		0			0
$745$	9.57862e6	+	8.03742e6i	0.632284	+	0.530550i
$746$		0			0
$747$	−1.51349e7	+	3.35907e6i	−0.992378	+	0.220251i
$748$		0			0
$749$	−4.72732e6	+	1.72060e6i	−0.307901	+	0.112067i
$750$		0			0
$751$	9.74151e6	−	8.17410e6i	0.630270	−	0.528859i	−0.270743	−	0.962652i	$-0.587269\pi$
$751$	9.74151e6	−	8.17410e6i	0.630270	−	0.528859i	0.901013	+	0.433792i	$0.142825\pi$
$752$		0			0
$753$	−1.12007e7	+	5.52520e6i	−0.719874	+	0.355108i
$754$		0			0
$755$	1.20598e7			0.769965
$756$		0			0
$757$	1.56635e7			0.993456			0.496728	−	0.867906i	$-0.334535\pi$
$757$	1.56635e7			0.993456			0.496728	+	0.867906i	$0.334535\pi$
$758$		0			0
$759$	201983.	−	3.08725e6i	0.0127265	−	0.194522i
$760$		0			0
$761$	1.30728e7	−	1.09694e7i	0.818288	−	0.686625i	−0.134282	−	0.990943i	$-0.542873\pi$
$761$	1.30728e7	−	1.09694e7i	0.818288	−	0.686625i	0.952571	+	0.304318i	$0.0984285\pi$
$762$		0			0
$763$	−1.07957e7	+	3.92932e6i	−0.671337	+	0.244347i
$764$		0			0
$765$	883654.	+	2.01299e7i	0.0545919	+	1.24362i
$766$		0			0
$767$	−1.24893e7	−	1.04798e7i	−0.766567	−	0.643226i
$768$		0			0
$769$	−3.75332e6	−	2.12862e7i	−0.228876	−	1.29802i	−0.855135	−	0.518405i	$-0.826526\pi$
$769$	−3.75332e6	−	2.12862e7i	−0.228876	−	1.29802i	0.626259	−	0.779615i	$-0.284585\pi$
$770$		0			0
$771$	1.22511e7	−	2.78517e7i	0.742231	−	1.68739i
$772$		0			0
$773$	−5.10706e6	−	8.84569e6i	−0.307413	−	0.532455i	0.670383	−	0.742016i	$-0.266130\pi$
$773$	−5.10706e6	−	8.84569e6i	−0.307413	−	0.532455i	−0.977796	+	0.209561i	$0.932797\pi$
$774$		0			0
$775$	6.47621e6	−	1.12171e7i	0.387317	−	0.670853i
$776$		0			0
$777$	1.08062e7	+	3.70579e7i	0.642123	+	2.20206i
$778$		0			0
$779$	−2.99251e7	−	1.08918e7i	−1.76682	−	0.643069i
$780$		0			0
$781$	−975334.	+	5.53139e6i	−0.0572171	+	0.324494i
$782$		0			0
$783$	364326.	+	141530.i	0.0212366	+	0.00824980i
$784$		0			0
$785$	2.99483e6	−	1.69845e7i	0.173459	−	0.983737i
$786$		0			0
$787$	−1.61128e7	−	5.86456e6i	−0.927327	−	0.337520i	−0.166178	−	0.986096i	$-0.553143\pi$
$787$	−1.61128e7	−	5.86456e6i	−0.927327	−	0.337520i	−0.761150	+	0.648576i	$0.775365\pi$
$788$		0			0
$789$	1.42709e7	+	3.49028e6i	0.816129	+	0.199603i
$790$		0			0
$791$	1.59388e7	−	2.76068e7i	0.905761	−	1.56882i
$792$		0			0
$793$	7.46057e6	+	1.29221e7i	0.421298	+	0.729709i
$794$		0			0
$795$	−8.22442e6	+	901704.i	−0.461517	+	0.0505995i
$796$		0			0
$797$	2.74809e6	+	1.55852e7i	0.153245	+	0.869094i	0.960373	+	0.278718i	$0.0899094\pi$
$797$	2.74809e6	+	1.55852e7i	0.153245	+	0.869094i	−0.807128	+	0.590376i	$0.798979\pi$
$798$		0			0
$799$	−3.36552e7	−	2.82400e7i	−1.86503	−	1.56494i
$800$		0			0
$801$	4.45991e6	+	586086.i	0.245609	+	0.0322761i
$802$		0			0
$803$	−2.96814e6	+	1.08032e6i	−0.162441	+	0.0591237i
$804$		0			0
$805$	1.25314e7	−	1.05151e7i	0.681570	−	0.571905i
$806$		0			0
$807$	−2.39355e7	−	1.59891e7i	−1.29378	−	0.864253i
$808$		0			0
$809$	−2.41671e7			−1.29824			−0.649119	−	0.760687i	$-0.724862\pi$
$809$	−2.41671e7			−1.29824			−0.649119	+	0.760687i	$0.724862\pi$
$810$		0			0
$811$	2.67029e7			1.42563			0.712813	−	0.701354i	$-0.247421\pi$
$811$	2.67029e7			1.42563			0.712813	+	0.701354i	$0.247421\pi$
$812$		0			0
$813$	2.03023e7	+	1.35621e7i	1.07726	+	0.719615i
$814$		0			0
$815$	1.88575e6	−	1.58233e6i	0.0994467	−	0.0834457i
$816$		0			0
$817$	1.86223e7	−	6.77795e6i	0.976062	−	0.355258i
$818$		0			0
$819$	−1.58471e7	+	2.06625e7i	−0.825544	+	1.07640i
$820$		0			0
$821$	3.51964e6	+	2.95333e6i	0.182238	+	0.152916i	0.729343	−	0.684148i	$-0.239826\pi$
$821$	3.51964e6	+	2.95333e6i	0.182238	+	0.152916i	−0.547105	+	0.837064i	$0.684270\pi$
$822$		0			0
$823$	3.00668e6	+	1.70517e7i	0.154735	+	0.877544i	0.959028	+	0.283311i	$0.0914330\pi$
$823$	3.00668e6	+	1.70517e7i	0.154735	+	0.877544i	−0.804293	+	0.594233i	$0.797456\pi$
$824$		0			0
$825$	−2.37190e6	+	260048.i	−0.121328	+	0.0133021i
$826$		0			0
$827$	2.15081e6	+	3.72532e6i	0.109355	+	0.189409i	0.915509	−	0.402297i	$-0.131788\pi$
$827$	2.15081e6	+	3.72532e6i	0.109355	+	0.189409i	−0.806154	+	0.591706i	$0.798455\pi$
$828$		0			0
$829$	6.57073e6	−	1.13808e7i	0.332068	−	0.575159i	−0.650849	−	0.759207i	$-0.725587\pi$
$829$	6.57073e6	−	1.13808e7i	0.332068	−	0.575159i	0.982917	+	0.184048i	$0.0589202\pi$
$830$		0			0
$831$	2.01003e7	+	4.91599e6i	1.00972	+	0.246950i
$832$		0			0
$833$	−4.68306e7	−	1.70450e7i	−2.33839	−	0.851105i
$834$		0			0
$835$	−479447.	+	2.71908e6i	−0.0237971	+	0.134960i
$836$		0			0
$837$	−1.55879e7	+	2.57086e7i	−0.769084	+	1.26842i
$838$		0			0
$839$	1.12980e6	−	6.40739e6i	0.0554109	−	0.314251i	−0.944487	−	0.328549i	$-0.893440\pi$
$839$	1.12980e6	−	6.40739e6i	0.0554109	−	0.314251i	0.999898	+	0.0142983i	$0.00455144\pi$
$840$		0			0
$841$	1.92642e7	+	7.01158e6i	0.939205	+	0.341843i
$842$		0			0
$843$	−8.98498e6	−	3.08125e7i	−0.435460	−	1.49334i
$844$		0			0
$845$	−1.63132e6	+	2.82552e6i	−0.0785953	+	0.136131i
$846$		0			0
$847$	−1.52312e7	−	2.63812e7i	−0.729499	−	1.26353i
$848$		0			0
$849$	−658356.	+	1.49671e6i	−0.0313467	+	0.0712636i
$850$		0			0
$851$	4.54756e6	+	2.57905e7i	0.215256	+	1.22078i
$852$		0			0
$853$	3.06489e7	+	2.57175e7i	1.44225	+	1.21019i	0.937998	+	0.346641i	$0.112678\pi$
$853$	3.06489e7	+	2.57175e7i	1.44225	+	1.21019i	0.504256	+	0.863554i	$0.331767\pi$
$854$		0			0
$855$	−1.51218e7	+	9.63868e6i	−0.707438	+	0.450923i
$856$		0			0
$857$	−2.28549e7	+	8.31852e6i	−1.06299	+	0.386896i	−0.813550	−	0.581495i	$-0.802468\pi$
$857$	−2.28549e7	+	8.31852e6i	−1.06299	+	0.386896i	−0.249438	+	0.968391i	$0.580246\pi$
$858$		0			0
$859$	3.17077e7	−	2.66059e7i	1.46616	−	1.23025i	0.546548	−	0.837428i	$-0.315942\pi$
$859$	3.17077e7	−	2.66059e7i	1.46616	−	1.23025i	0.919613	−	0.392827i	$-0.128503\pi$
$860$		0			0
$861$	−3.39527e6	+	5.18957e7i	−0.156087	+	2.38574i
$862$		0			0
$863$	1.40747e7			0.643296			0.321648	−	0.946859i	$-0.395763\pi$
$863$	1.40747e7			0.643296			0.321648	+	0.946859i	$0.395763\pi$
$864$		0			0
$865$	−1.19348e7			−0.542344
$866$		0			0
$867$	4.45271e7	−	2.19649e7i	2.01176	−	0.992386i
$868$		0			0
$869$	−414240.	+	347589.i	−0.0186081	+	0.0156141i
$870$		0			0
$871$	−8.69989e6	+	3.16650e6i	−0.388569	+	0.141428i
$872$		0			0
$873$	2.11475e6	−	6.71267e6i	0.0939126	−	0.298098i
$874$		0			0
$875$	−2.81721e7	−	2.36392e7i	−1.24394	−	1.04379i
$876$		0			0
$877$	3.13139e6	+	1.77590e7i	0.137480	+	0.779685i	0.973101	+	0.230379i	$0.0739967\pi$
$877$	3.13139e6	+	1.77590e7i	0.137480	+	0.779685i	−0.835621	+	0.549306i	$0.814892\pi$
$878$		0			0
$879$	297086.	+	405074.i	0.0129691	+	0.0176833i
$880$		0			0
$881$	7.51888e6	+	1.30231e7i	0.326372	+	0.565293i	0.981789	−	0.189974i	$-0.0608404\pi$
$881$	7.51888e6	+	1.30231e7i	0.326372	+	0.565293i	−0.655417	+	0.755267i	$0.727507\pi$
$882$		0			0
$883$	−1.35581e7	+	2.34834e7i	−0.585191	+	1.01358i	0.409661	+	0.912238i	$0.365647\pi$
$883$	−1.35581e7	+	2.34834e7i	−0.585191	+	1.01358i	−0.994852	+	0.101343i	$0.967686\pi$
$884$		0			0
$885$	−1.26778e7	+	1.32465e7i	−0.544109	+	0.568518i
$886$		0			0
$887$	−565241.	−	205731.i	−0.0241226	−	0.00877991i	0.329931	−	0.944005i	$-0.392975\pi$
$887$	−565241.	−	205731.i	−0.0241226	−	0.00877991i	−0.354053	+	0.935225i	$0.615197\pi$
$888$		0			0
$889$	1.75120e6	−	9.93157e6i	0.0743160	−	0.421467i
$890$		0			0
$891$	5.51733e6	−	485331.i	0.232828	−	0.0204806i
$892$		0			0
$893$	6.78967e6	−	3.85061e7i	0.284918	−	1.61585i
$894$		0			0
$895$	−1.26763e7	−	4.61378e6i	−0.528973	−	0.192530i
$896$		0			0
$897$	−1.22149e7	+	1.27629e7i	−0.506884	+	0.529623i
$898$		0			0
$899$	409473.	−	709227.i	0.0168976	−	0.0292675i
$900$		0			0
$901$	1.47379e7	+	2.55267e7i	0.604815	+	1.04757i
$902$		0			0
$903$	−1.91400e7	−	2.60972e7i	−0.781127	−	1.06506i
$904$		0			0
$905$	−178582.	−	1.01279e6i	−0.00724795	−	0.0411052i
$906$		0			0
$907$	5.78393e6	+	4.85329e6i	0.233456	+	0.195893i	0.752009	−	0.659152i	$-0.229085\pi$
$907$	5.78393e6	+	4.85329e6i	0.233456	+	0.195893i	−0.518553	+	0.855045i	$0.673529\pi$
$908$		0			0
$909$	−9.09514e6	−	9.92090e6i	−0.365090	−	0.398237i
$910$		0			0
$911$	−1.24841e7	+	4.54385e6i	−0.498382	+	0.181396i	−0.578966	−	0.815352i	$-0.696544\pi$
$911$	−1.24841e7	+	4.54385e6i	−0.498382	+	0.181396i	0.0805842	+	0.996748i	$0.474321\pi$
$912$		0			0
$913$	4.58414e6	−	3.84655e6i	0.182004	−	0.152719i
$914$		0			0
$915$	1.50494e7	−	7.42377e6i	0.594248	−	0.293138i
$916$		0			0
$917$	−2.01656e7			−0.791934
$918$		0			0
$919$	−2.42641e7			−0.947710			−0.473855	−	0.880603i	$-0.657138\pi$
$919$	−2.42641e7			−0.947710			−0.473855	+	0.880603i	$0.657138\pi$
$920$		0			0
$921$	291354.	−	4.45326e6i	0.0113181	−	0.172993i
$922$		0			0
$923$	2.45686e7	−	2.06155e7i	0.949239	−	0.796506i
$924$		0			0
$925$	1.89795e7	−	6.90797e6i	0.729340	−	0.265458i
$926$		0			0
$927$	3.11985e7	+	1.62315e7i	1.19243	+	0.620383i
$928$		0			0
$929$	3.03530e7	+	2.54692e7i	1.15388	+	0.968223i	0.999803	−	0.0198355i	$-0.00631425\pi$
$929$	3.03530e7	+	2.54692e7i	1.15388	+	0.968223i	0.154080	+	0.988058i	$0.450759\pi$
$930$		0			0
$931$	−7.70185e6	−	4.36794e7i	−0.291220	−	1.65159i
$932$		0			0
$933$	−5.99659e6	+	1.36326e7i	−0.225528	+	0.512715i
$934$		0			0
$935$	−3.88878e6	−	6.73556e6i	−0.145473	−	0.251967i
$936$		0			0
$937$	7.16426e6	−	1.24089e7i	0.266577	−	0.461724i	−0.701399	−	0.712769i	$-0.747441\pi$
$937$	7.16426e6	−	1.24089e7i	0.266577	−	0.461724i	0.967975	+	0.251045i	$0.0807741\pi$
$938$		0			0
$939$	6.88753e6	+	2.36197e7i	0.254918	+	0.874198i
$940$		0			0
$941$	−4.03815e7	−	1.46977e7i	−1.48665	−	0.541096i	−0.534085	−	0.845431i	$-0.679344\pi$
$941$	−4.03815e7	−	1.46977e7i	−1.48665	−	0.541096i	−0.952565	+	0.304335i	$0.901566\pi$
$942$		0			0
$943$	−6.12682e6	+	3.47469e7i	−0.224365	+	1.27244i
$944$		0			0
$945$	2.20247e7	+	1.93013e7i	0.802288	+	0.703085i
$946$		0			0
$947$	−4.27306e6	+	2.42337e7i	−0.154833	+	0.878103i	0.804105	+	0.594488i	$0.202645\pi$
$947$	−4.27306e6	+	2.42337e7i	−0.154833	+	0.878103i	−0.958938	+	0.283616i	$0.908466\pi$
$948$		0			0
$949$	1.69484e7	+	6.16870e6i	0.610889	+	0.222345i
$950$		0			0
$951$	4.11244e7	+	1.00579e7i	1.47451	+	0.360626i
$952$		0			0
$953$	−9.99428e6	+	1.73106e7i	−0.356467	+	0.617419i	−0.987368	−	0.158444i	$-0.949352\pi$
$953$	−9.99428e6	+	1.73106e7i	−0.356467	+	0.617419i	0.630901	+	0.775863i	$0.282685\pi$
$954$		0			0
$955$	−9.24426e6	−	1.60115e7i	−0.327992	−	0.568100i
$956$		0			0
$957$	−149968.	+	16442.1i	−0.00529322	+	0.000580334i
$958$		0			0
$959$	1.18484e7	+	6.71956e7i	0.416019	+	2.35936i
$960$		0			0
$961$	2.63260e7	+	2.20901e7i	0.919552	+	0.771596i
$962$		0			0
$963$	−2.33951e6	−	5.64431e6i	−0.0812943	−	0.196131i
$964$		0			0
$965$	1.54408e7	−	5.62001e6i	0.533768	−	0.194276i
$966$		0			0
$967$	−2.81977e7	+	2.36607e7i	−0.969724	+	0.813695i	−0.982507	−	0.186223i	$-0.940375\pi$
$967$	−2.81977e7	+	2.36607e7i	−0.969724	+	0.813695i	0.0127836	+	0.999918i	$0.495931\pi$
$968$		0			0
$969$	5.31233e7	+	3.54868e7i	1.81750	+	1.21411i
$970$		0			0
$971$	−4.91285e6			−0.167219			−0.0836094	−	0.996499i	$-0.526645\pi$
$971$	−4.91285e6			−0.167219			−0.0836094	+	0.996499i	$0.526645\pi$
$972$		0			0
$973$	6.28761e7			2.12914
$974$		0			0
$975$	1.13296e7	+	7.56825e6i	0.381682	+	0.254967i
$976$		0			0
$977$	2.39085e6	−	2.00616e6i	0.0801340	−	0.0672404i	−0.601841	−	0.798616i	$-0.705566\pi$
$977$	2.39085e6	−	2.00616e6i	0.0801340	−	0.0672404i	0.681975	+	0.731376i	$0.261121\pi$
$978$		0			0
$979$	−1.63160e6	+	593854.i	−0.0544073	+	0.0198026i
$980$		0			0
$981$	−5.34272e6	−	1.28899e7i	−0.177251	−	0.427637i
$982$		0			0
$983$	3.85498e7	+	3.23471e7i	1.27244	+	1.06771i	0.994239	+	0.107184i	$0.0341833\pi$
$983$	3.85498e7	+	3.23471e7i	1.27244	+	1.06771i	0.278203	+	0.960522i	$0.410261\pi$
$984$		0			0
$985$	−143229.	−	812290.i	−0.00470370	−	0.0266760i
$986$		0			0
$987$	−6.34736e7	+	6.95908e6i	−2.07396	+	0.227384i
$988$		0			0
$989$	−1.09782e7	−	1.90149e7i	−0.356896	−	0.618162i
$990$		0			0
$991$	2.09749e7	−	3.63296e7i	0.678447	−	1.17511i	−0.297001	−	0.954877i	$-0.595986\pi$
$991$	2.09749e7	−	3.63296e7i	0.678447	−	1.17511i	0.975448	−	0.220228i	$-0.0706802\pi$
$992$		0			0
$993$	−4.31254e7	−	1.05473e7i	−1.38791	−	0.339445i
$994$		0			0
$995$	−1.63935e7	−	5.96675e6i	−0.524945	−	0.191064i
$996$		0			0
$997$	3.00044e6	−	1.70164e7i	0.0955978	−	0.542162i	−0.898965	−	0.438021i	$-0.855680\pi$
$997$	3.00044e6	−	1.70164e7i	0.0955978	−	0.542162i	0.994563	−	0.104141i	$-0.0332093\pi$
$998$		0			0
$999$	−4.43892e7	+	1.50856e7i	−1.40722	+	0.478244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.25.4	yes	90
3.2	odd	2		324.6.i.a.73.11		90
27.13	even	9	inner	108.6.i.a.13.4	✓	90
27.14	odd	18		324.6.i.a.253.11		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.4	✓	90	27.13	even	9	inner
108.6.i.a.25.4	yes	90	1.1	even	1	trivial
324.6.i.a.73.11		90	3.2	odd	2
324.6.i.a.253.11		90	27.14	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.9624 - 8.65895i) q^{3} +(-29.6003 + 24.8376i) q^{5} +(188.011 - 68.4304i) q^{7} +(93.0451 + 224.481i) q^{9} +O(q^{10})\)	\(q+(-12.9624 - 8.65895i) q^{3} +(-29.6003 + 24.8376i) q^{5} +(188.011 - 68.4304i) q^{7} +(93.0451 + 224.481i) q^{9} +(-71.8529 - 60.2917i) q^{11} +(93.0043 + 527.454i) q^{13} +(598.758 - 65.6462i) q^{15} +(-1072.95 - 1858.41i) q^{17} +(954.907 - 1653.95i) q^{19} +(-3029.60 - 740.959i) q^{21} +(-1988.35 - 723.699i) q^{23} +(-283.379 + 1607.12i) q^{25} +(737.685 - 3715.47i) q^{27} +(-17.9172 + 101.614i) q^{29} +(-7458.30 - 2714.60i) q^{31} +(409.319 + 1403.69i) q^{33} +(-3865.54 + 6695.31i) q^{35} +(-6188.31 - 10718.5i) q^{37} +(3361.64 - 7642.36i) q^{39} +(-2895.53 - 16421.4i) q^{41} +(7948.95 + 6669.96i) q^{43} +(-8329.74 - 4333.69i) q^{45} +(19238.6 - 7002.28i) q^{47} +(17790.5 - 14928.0i) q^{49} +(-2183.88 + 33380.0i) q^{51} -13735.8 q^{53} +3624.37 q^{55} +(-26699.3 + 13170.6i) q^{57} +(-23318.8 + 19566.8i) q^{59} +(26179.1 - 9528.41i) q^{61} +(32854.8 + 35837.7i) q^{63} +(-15853.7 - 13302.8i) q^{65} +(3001.69 + 17023.4i) q^{67} +(19507.2 + 26597.9i) q^{69} +(-29940.8 - 51858.9i) q^{71} +(16837.6 - 29163.5i) q^{73} +(17589.2 - 18378.3i) q^{75} +(-17634.9 - 6418.58i) q^{77} +(1001.10 - 5677.53i) q^{79} +(-41734.2 + 41773.7i) q^{81} +(-11078.6 + 62829.7i) q^{83} +(77918.1 + 28359.9i) q^{85} +(1112.12 - 1162.01i) q^{87} +(9255.67 - 16031.3i) q^{89} +(53579.7 + 92802.8i) q^{91} +(73171.5 + 99768.6i) q^{93} +(12814.6 + 72675.0i) q^{95} +(-22186.6 - 18616.8i) q^{97} +(6848.77 - 21739.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 90 * q - 87 * q^5 + 330 * q^9	\( 90 q - 87 q^{5} + 330 q^{9} - 1257 q^{11} + 531 q^{15} - 3468 q^{17} + 12894 q^{21} + 8106 q^{23} + 4959 q^{25} - 17415 q^{27} + 3468 q^{29} - 6651 q^{31} + 33624 q^{33} - 8229 q^{35} - 10545 q^{39} + 68673 q^{41} + 9459 q^{43} - 53469 q^{45} - 57087 q^{47} - 5490 q^{49} + 42831 q^{51} - 4146 q^{53} + 24624 q^{57} + 5388 q^{59} + 70110 q^{61} - 98115 q^{63} - 172425 q^{65} - 15039 q^{67} + 251037 q^{69} + 67812 q^{71} - 27009 q^{73} - 75273 q^{75} + 23991 q^{77} - 216180 q^{79} + 177822 q^{81} - 76725 q^{83} - 53100 q^{85} - 201483 q^{87} - 98814 q^{89} - 90999 q^{91} + 21765 q^{93} - 143490 q^{95} - 71739 q^{97} + 13635 q^{99}+O(q^{100}) \) 90 * q - 87 * q^5 + 330 * q^9 - 1257 * q^11 + 531 * q^15 - 3468 * q^17 + 12894 * q^21 + 8106 * q^23 + 4959 * q^25 - 17415 * q^27 + 3468 * q^29 - 6651 * q^31 + 33624 * q^33 - 8229 * q^35 - 10545 * q^39 + 68673 * q^41 + 9459 * q^43 - 53469 * q^45 - 57087 * q^47 - 5490 * q^49 + 42831 * q^51 - 4146 * q^53 + 24624 * q^57 + 5388 * q^59 + 70110 * q^61 - 98115 * q^63 - 172425 * q^65 - 15039 * q^67 + 251037 * q^69 + 67812 * q^71 - 27009 * q^73 - 75273 * q^75 + 23991 * q^77 - 216180 * q^79 + 177822 * q^81 - 76725 * q^83 - 53100 * q^85 - 201483 * q^87 - 98814 * q^89 - 90999 * q^91 + 21765 * q^93 - 143490 * q^95 - 71739 * q^97 + 13635 * q^99

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