LMFDB - Embedded newform 108.6.i.a.13.9

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			13.9
Character	$\chi$	$=$	108.13
Dual form			108.6.i.a.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.571582 - 15.5780i) q^{3} +(-56.0600 - 47.0399i) q^{5} +(-23.6165 - 8.59570i) q^{7} +(-242.347 - 17.8082i) q^{9} +O(q^{10})$	\(q+(0.571582 - 15.5780i) q^{3} +(-56.0600 - 47.0399i) q^{5} +(-23.6165 - 8.59570i) q^{7} +(-242.347 - 17.8082i) q^{9} +(-12.2234 + 10.2566i) q^{11} +(-33.1302 + 187.890i) q^{13} +(-764.830 + 846.414i) q^{15} +(234.417 - 406.023i) q^{17} +(1017.21 + 1761.86i) q^{19} +(-147.402 + 362.984i) q^{21} +(-399.076 + 145.252i) q^{23} +(387.319 + 2196.59i) q^{25} +(-415.936 + 3765.09i) q^{27} +(-169.077 - 958.884i) q^{29} +(-249.258 + 90.7225i) q^{31} +(152.791 + 196.278i) q^{33} +(919.600 + 1592.79i) q^{35} +(-2928.19 + 5071.78i) q^{37} +(2908.02 + 623.495i) q^{39} +(-2442.94 + 13854.6i) q^{41} +(-13132.5 + 11019.5i) q^{43} +(12748.3 + 12398.3i) q^{45} +(-17085.1 - 6218.46i) q^{47} +(-12391.1 - 10397.3i) q^{49} +(-6191.02 - 3883.82i) q^{51} +14646.0 q^{53} +1167.71 q^{55} +(28027.6 - 14839.0i) q^{57} +(-19227.3 - 16133.6i) q^{59} +(-22753.1 - 8281.46i) q^{61} +(5570.30 + 2503.71i) q^{63} +(10695.6 - 8974.70i) q^{65} +(2234.83 - 12674.4i) q^{67} +(2034.63 + 6299.83i) q^{69} +(35082.2 - 60764.2i) q^{71} +(31308.7 + 54228.2i) q^{73} +(34439.8 - 4778.11i) q^{75} +(376.836 - 137.157i) q^{77} +(4175.78 + 23682.0i) q^{79} +(58414.7 + 8631.50i) q^{81} +(-19446.3 - 110285. i) q^{83} +(-32240.7 + 11734.7i) q^{85} +(-15034.1 + 2085.80i) q^{87} +(-21770.1 - 37707.0i) q^{89} +(2397.47 - 4152.54i) q^{91} +(1270.80 + 3934.79i) q^{93} +(25852.9 - 146619. i) q^{95} +(-36251.4 + 30418.6i) q^{97} +(3144.94 - 2267.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.571582	−	15.5780i	0.0366670	−	0.999328i
$3$	0.571582	−	15.5780i	0.0366670	−	0.999328i
$4$		0			0
$5$	−56.0600	−	47.0399i	−1.00283	−	0.841476i	−0.0154575	−	0.999881i	$-0.504920\pi$
$5$	−56.0600	−	47.0399i	−1.00283	−	0.841476i	−0.987374	+	0.158405i	$0.949365\pi$
$6$		0			0
$7$	−23.6165	−	8.59570i	−0.182167	−	0.0663035i	0.249326	−	0.968420i	$-0.419791\pi$
$7$	−23.6165	−	8.59570i	−0.182167	−	0.0663035i	−0.431493	+	0.902116i	$0.642013\pi$
$8$		0			0
$9$	−242.347	−	17.8082i	−0.997311	−	0.0732847i
$10$		0			0
$11$	−12.2234	+	10.2566i	−0.0304585	+	0.0255577i	−0.657890	−	0.753114i	$-0.728551\pi$
$11$	−12.2234	+	10.2566i	−0.0304585	+	0.0255577i	0.627431	+	0.778672i	$0.284106\pi$
$12$		0			0
$13$	−33.1302	+	187.890i	−0.0543707	+	0.308352i	−0.999850	−	0.0173311i	$-0.994483\pi$
$13$	−33.1302	+	187.890i	−0.0543707	+	0.308352i	0.945479	+	0.325683i	$0.105594\pi$
$14$		0			0
$15$	−764.830	+	846.414i	−0.877681	+	0.971303i
$16$		0			0
$17$	234.417	−	406.023i	0.196729	−	0.340744i	−0.750737	−	0.660601i	$-0.770302\pi$
$17$	234.417	−	406.023i	0.196729	−	0.340744i	0.947466	+	0.319857i	$0.103635\pi$
$18$		0			0
$19$	1017.21	+	1761.86i	0.646436	+	1.11966i	0.983968	+	0.178346i	$0.0570747\pi$
$19$	1017.21	+	1761.86i	0.646436	+	1.11966i	−0.337532	+	0.941314i	$0.609592\pi$
$20$		0			0
$21$	−147.402	+	362.984i	−0.0729384	+	0.179614i
$22$		0			0
$23$	−399.076	+	145.252i	−0.157303	+	0.0572535i	−0.419471	−	0.907769i	$-0.637785\pi$
$23$	−399.076	+	145.252i	−0.157303	+	0.0572535i	0.262169	+	0.965022i	$0.415562\pi$
$24$		0			0
$25$	387.319	+	2196.59i	0.123942	+	0.702910i
$26$		0			0
$27$	−415.936	+	3765.09i	−0.109804	+	0.993953i
$28$		0			0
$29$	−169.077	−	958.884i	−0.0373328	−	0.211725i	0.960435	−	0.278504i	$-0.0898386\pi$
$29$	−169.077	−	958.884i	−0.0373328	−	0.211725i	−0.997768	+	0.0667797i	$0.978728\pi$
$30$		0			0
$31$	−249.258	+	90.7225i	−0.0465849	+	0.0169555i	−0.365207	−	0.930926i	$-0.619002\pi$
$31$	−249.258	+	90.7225i	−0.0465849	+	0.0169555i	0.318623	+	0.947882i	$0.396780\pi$
$32$		0			0
$33$	152.791	+	196.278i	0.0244237	+	0.0313751i
$34$		0			0
$35$	919.600	+	1592.79i	0.126890	+	0.219781i
$36$		0			0
$37$	−2928.19	+	5071.78i	−0.351638	+	0.609054i	−0.986537	−	0.163541i	$-0.947708\pi$
$37$	−2928.19	+	5071.78i	−0.351638	+	0.609054i	0.634899	+	0.772595i	$0.281042\pi$
$38$		0			0
$39$	2908.02	+	623.495i	0.306151	+	0.0656405i
$40$		0			0
$41$	−2442.94	+	13854.6i	−0.226962	+	1.28717i	0.631936	+	0.775020i	$0.282260\pi$
$41$	−2442.94	+	13854.6i	−0.226962	+	1.28717i	−0.858898	+	0.512146i	$0.828851\pi$
$42$		0			0
$43$	−13132.5	+	11019.5i	−1.08312	+	0.908845i	−0.996176	−	0.0873687i	$-0.972154\pi$
$43$	−13132.5	+	11019.5i	−1.08312	+	0.908845i	−0.0869428	+	0.996213i	$0.527710\pi$
$44$		0			0
$45$	12748.3	+	12398.3i	0.938468	+	0.912705i
$46$		0			0
$47$	−17085.1	−	6218.46i	−1.12816	−	0.410618i	−0.290539	−	0.956863i	$-0.593835\pi$
$47$	−17085.1	−	6218.46i	−1.12816	−	0.410618i	−0.837626	+	0.546245i	$0.816057\pi$
$48$		0			0
$49$	−12391.1	−	10397.3i	−0.737256	−	0.618631i
$50$		0			0
$51$	−6191.02	−	3883.82i	−0.333301	−	0.209090i
$52$		0			0
$53$	14646.0			0.716193			0.358097	−	0.933685i	$-0.383426\pi$
$53$	14646.0			0.716193			0.358097	+	0.933685i	$0.383426\pi$
$54$		0			0
$55$	1167.71			0.0520510
$56$		0			0
$57$	28027.6	−	14839.0i	1.14261	−	0.604947i
$58$		0			0
$59$	−19227.3	−	16133.6i	−0.719100	−	0.603396i	0.208036	−	0.978121i	$-0.433293\pi$
$59$	−19227.3	−	16133.6i	−0.719100	−	0.603396i	−0.927136	+	0.374725i	$0.877737\pi$
$60$		0			0
$61$	−22753.1	−	8281.46i	−0.782918	−	0.284959i	−0.0805293	−	0.996752i	$-0.525661\pi$
$61$	−22753.1	−	8281.46i	−0.782918	−	0.284959i	−0.702389	+	0.711793i	$0.747883\pi$
$62$		0			0
$63$	5570.30	+	2503.71i	0.176818	+	0.0794753i
$64$		0			0
$65$	10695.6	−	8974.70i	0.313995	−	0.263473i
$66$		0			0
$67$	2234.83	−	12674.4i	0.0608216	−	0.344936i	−0.939177	−	0.343433i	$-0.888410\pi$
$67$	2234.83	−	12674.4i	0.0608216	−	0.344936i	0.999999	−	0.00150371i	$-0.000478645\pi$
$68$		0			0
$69$	2034.63	+	6299.83i	0.0514472	+	0.159296i
$70$		0			0
$71$	35082.2	−	60764.2i	0.825926	−	1.43055i	−0.0752842	−	0.997162i	$-0.523986\pi$
$71$	35082.2	−	60764.2i	0.825926	−	1.43055i	0.901210	−	0.433383i	$-0.142680\pi$
$72$		0			0
$73$	31308.7	+	54228.2i	0.687634	+	1.19102i	0.972601	+	0.232480i	$0.0746841\pi$
$73$	31308.7	+	54228.2i	0.687634	+	1.19102i	−0.284967	+	0.958537i	$0.591983\pi$
$74$		0			0
$75$	34439.8	−	4778.11i	0.706981	−	0.0980850i
$76$		0			0
$77$	376.836	−	137.157i	0.00724311	−	0.00263628i
$78$		0			0
$79$	4175.78	+	23682.0i	0.0752783	+	0.426925i	0.999034	+	0.0439425i	$0.0139918\pi$
$79$	4175.78	+	23682.0i	0.0752783	+	0.426925i	−0.923756	+	0.382982i	$0.874897\pi$
$80$		0			0
$81$	58414.7	+	8631.50i	0.989259	+	0.146175i
$82$		0			0
$83$	−19446.3	−	110285.i	−0.309842	−	1.75720i	−0.599787	−	0.800160i	$-0.704748\pi$
$83$	−19446.3	−	110285.i	−0.309842	−	1.75720i	0.289944	−	0.957044i	$-0.406363\pi$
$84$		0			0
$85$	−32240.7	+	11734.7i	−0.484013	+	0.176166i
$86$		0			0
$87$	−15034.1	+	2085.80i	−0.212951	+	0.0295443i
$88$		0			0
$89$	−21770.1	−	37707.0i	−0.291331	−	0.504599i	0.682794	−	0.730611i	$-0.260765\pi$
$89$	−21770.1	−	37707.0i	−0.291331	−	0.504599i	−0.974125	+	0.226011i	$0.927431\pi$
$90$		0			0
$91$	2397.47	−	4152.54i	0.0303494	−	0.0525666i
$92$		0			0
$93$	1270.80	+	3934.79i	0.0152360	+	0.0471752i
$94$		0			0
$95$	25852.9	−	146619.i	0.293900	−	1.66679i
$96$		0			0
$97$	−36251.4	+	30418.6i	−0.391197	+	0.328253i	−0.817079	−	0.576525i	$-0.804408\pi$
$97$	−36251.4	+	30418.6i	−0.391197	+	0.328253i	0.425882	+	0.904779i	$0.359964\pi$
$98$		0			0
$99$	3144.94	−	2267.98i	0.0322496	−	0.0232569i
$100$		0			0
$101$	−54110.2	−	19694.5i	−0.527808	−	0.192106i	0.0643515	−	0.997927i	$-0.479502\pi$
$101$	−54110.2	−	19694.5i	−0.527808	−	0.192106i	−0.592159	+	0.805821i	$0.701724\pi$
$102$		0			0
$103$	−31784.4	−	26670.3i	−0.295203	−	0.247705i	0.483141	−	0.875543i	$-0.339496\pi$
$103$	−31784.4	−	26670.3i	−0.295203	−	0.247705i	−0.778344	+	0.627837i	$0.783940\pi$
$104$		0			0
$105$	25338.1	−	13415.1i	0.224286	−	0.118746i
$106$		0			0
$107$	−5985.27			−0.0505387			−0.0252694	−	0.999681i	$-0.508044\pi$
$107$	−5985.27			−0.0505387			−0.0252694	+	0.999681i	$0.508044\pi$
$108$		0			0
$109$	−225825.			−1.82056			−0.910280	−	0.413993i	$-0.864134\pi$
$109$	−225825.			−1.82056			−0.910280	+	0.413993i	$0.864134\pi$
$110$		0			0
$111$	77334.4	+	48514.3i	0.595751	+	0.373733i
$112$		0			0
$113$	−15859.0	−	13307.3i	−0.116837	−	0.0980379i	0.582497	−	0.812833i	$-0.302076\pi$
$113$	−15859.0	−	13307.3i	−0.116837	−	0.0980379i	−0.699334	+	0.714795i	$0.746520\pi$
$114$		0			0
$115$	29204.9	+	10629.7i	0.205926	+	0.0749508i
$116$		0			0
$117$	11375.0	−	44944.6i	0.0768220	−	0.303538i
$118$		0			0
$119$	−9026.17	+	7573.86i	−0.0584300	+	0.0490286i
$120$		0			0
$121$	−27922.0	+	158354.i	−0.173374	+	0.983251i
$122$		0			0
$123$	214430.	+	45975.1i	1.27798	+	0.274006i
$124$		0			0
$125$	−32731.1	+	56691.8i	−0.187363	+	0.324523i
$126$		0			0
$127$	75920.9	+	131499.i	0.417688	+	0.723457i	0.995706	−	0.0925670i	$-0.0295072\pi$
$127$	75920.9	+	131499.i	0.417688	+	0.723457i	−0.578019	+	0.816024i	$0.696174\pi$
$128$		0			0
$129$	164155.	+	210876.i	0.868519	+	1.11572i
$130$		0			0
$131$	−50104.5	+	18236.5i	−0.255093	+	0.0928462i	−0.466401	−	0.884573i	$-0.654450\pi$
$131$	−50104.5	+	18236.5i	−0.255093	+	0.0928462i	0.211309	+	0.977419i	$0.432228\pi$
$132$		0			0
$133$	−8878.50	−	50352.5i	−0.0435222	−	0.246826i
$134$		0			0
$135$	200427.	−	191505.i	0.946502	−	0.904371i
$136$		0			0
$137$	71622.6	+	406192.i	0.326023	+	1.84897i	0.502385	+	0.864644i	$0.332456\pi$
$137$	71622.6	+	406192.i	0.326023	+	1.84897i	−0.176362	+	0.984325i	$0.556433\pi$
$138$		0			0
$139$	−351060.	+	127775.i	−1.54115	+	0.560931i	−0.966320	−	0.257344i	$-0.917153\pi$
$139$	−351060.	+	127775.i	−1.54115	+	0.560931i	−0.574826	+	0.818276i	$0.694930\pi$
$140$		0			0
$141$	−106637.	+	262597.i	−0.451709	+	1.11235i
$142$		0			0
$143$	−1522.16	−	2636.45i	−0.00622471	−	0.0107815i
$144$		0			0
$145$	−35627.4	+	61708.4i	−0.140723	+	0.243739i
$146$		0			0
$147$	−169052.	+	187085.i	−0.645248	+	0.714077i
$148$		0			0
$149$	54512.1	−	309154.i	0.201153	−	1.14080i	−0.702225	−	0.711955i	$-0.747810\pi$
$149$	54512.1	−	309154.i	0.201153	−	1.14080i	0.903379	−	0.428843i	$-0.141079\pi$
$150$		0			0
$151$	193417.	−	162296.i	0.690324	−	0.579250i	−0.228679	−	0.973502i	$-0.573441\pi$
$151$	193417.	−	162296.i	0.690324	−	0.579250i	0.919003	+	0.394252i	$0.128996\pi$
$152$		0			0
$153$	−64040.8	+	94223.7i	−0.221171	+	0.325410i
$154$		0			0
$155$	18241.0	+	6639.17i	0.0609844	+	0.0221965i
$156$		0			0
$157$	50500.1	+	42374.6i	0.163510	+	0.137201i	0.720871	−	0.693069i	$-0.243742\pi$
$157$	50500.1	+	42374.6i	0.163510	+	0.137201i	−0.557362	+	0.830270i	$0.688186\pi$
$158$		0			0
$159$	8371.40	−	228155.i	0.0262606	−	0.715711i
$160$		0			0
$161$	10673.3			0.0324515
$162$		0			0
$163$	−458666.			−1.35216			−0.676079	−	0.736830i	$-0.736322\pi$
$163$	−458666.			−1.35216			−0.676079	+	0.736830i	$0.736322\pi$
$164$		0			0
$165$	667.443	−	18190.6i	0.00190855	−	0.0520160i
$166$		0			0
$167$	−344029.	−	288674.i	−0.954561	−	0.800972i	0.0254987	−	0.999675i	$-0.491883\pi$
$167$	−344029.	−	288674.i	−0.954561	−	0.800972i	−0.980060	+	0.198703i	$0.936327\pi$
$168$		0			0
$169$	314696.	+	114540.i	0.847568	+	0.308490i
$170$		0			0
$171$	−215141.	−	445094.i	−0.562644	−	1.16402i
$172$		0			0
$173$	−203724.	+	170944.i	−0.517519	+	0.434250i	−0.863766	−	0.503894i	$-0.831900\pi$
$173$	−203724.	+	170944.i	−0.517519	+	0.434250i	0.346247	+	0.938143i	$0.387456\pi$
$174$		0			0
$175$	9734.15	−	55205.1i	0.0240272	−	0.136265i
$176$		0			0
$177$	−262320.	+	290301.i	−0.629358	+	0.696491i
$178$		0			0
$179$	23662.5	−	40984.7i	0.0551986	−	0.0956068i	−0.837106	−	0.547041i	$-0.815754\pi$
$179$	23662.5	−	40984.7i	0.0551986	−	0.0956068i	0.892304	+	0.451434i	$0.149087\pi$
$180$		0			0
$181$	329351.	+	570453.i	0.747245	+	1.29427i	0.949139	+	0.314858i	$0.101957\pi$
$181$	329351.	+	570453.i	0.747245	+	1.29427i	−0.201894	+	0.979407i	$0.564710\pi$
$182$		0			0
$183$	−142014.	+	349714.i	−0.313475	+	0.771943i
$184$		0			0
$185$	402731.	−	146582.i	0.865138	−	0.314885i
$186$		0			0
$187$	1299.05	+	7367.29i	0.00271658	+	0.0154065i
$188$		0			0
$189$	42186.6	−	85343.0i	0.0859052	−	0.173785i
$190$		0			0
$191$	−14183.9	−	80440.7i	−0.0281327	−	0.159548i	0.967505	−	0.252852i	$-0.0813685\pi$
$191$	−14183.9	−	80440.7i	−0.0281327	−	0.159548i	−0.995638	+	0.0933033i	$0.970257\pi$
$192$		0			0
$193$	395594.	−	143985.i	0.764464	−	0.278242i	0.0697848	−	0.997562i	$-0.477769\pi$
$193$	395594.	−	143985.i	0.764464	−	0.278242i	0.694679	+	0.719320i	$0.255547\pi$
$194$		0			0
$195$	−133694.	−	171746.i	−0.251783	−	0.323445i
$196$		0			0
$197$	168853.	+	292461.i	0.309986	+	0.536912i	0.978359	−	0.206915i	$-0.0663422\pi$
$197$	168853.	+	292461.i	0.309986	+	0.536912i	−0.668373	+	0.743826i	$0.733009\pi$
$198$		0			0
$199$	316570.	−	548315.i	0.566678	−	0.981516i	−0.430213	−	0.902727i	$-0.641562\pi$
$199$	316570.	−	548315.i	0.566678	−	0.981516i	0.996891	−	0.0787883i	$-0.0251051\pi$
$200$		0			0
$201$	−196164.	−	42058.6i	−0.342474	−	0.0734285i
$202$		0			0
$203$	−4249.27	+	24098.8i	−0.00723727	+	0.0410446i
$204$		0			0
$205$	788671.	−	661774.i	1.31072	−	1.09983i
$206$		0			0
$207$	99301.5	−	28094.5i	0.161076	−	0.0455717i
$208$		0			0
$209$	−30504.3	−	11102.7i	−0.0483054	−	0.0175817i
$210$		0			0
$211$	−859138.	−	720903.i	−1.32849	−	1.11473i	−0.984429	−	0.175783i	$-0.943754\pi$
$211$	−859138.	−	720903.i	−1.32849	−	1.11473i	−0.344057	−	0.938949i	$-0.611801\pi$
$212$		0			0
$213$	−926530.	−	581241.i	−1.39930	−	0.877824i
$214$		0			0
$215$	1.25456e6			1.85096
$216$		0			0
$217$	6666.42			0.00961045
$218$		0			0
$219$	862661.	−	456730.i	1.21543	−	0.643501i
$220$		0			0
$221$	68521.5	+	57496.4i	0.0943727	+	0.0791881i
$222$		0			0
$223$	376995.	+	137215.i	0.507660	+	0.184773i	0.583136	−	0.812374i	$-0.301825\pi$
$223$	376995.	+	137215.i	0.507660	+	0.184773i	−0.0754760	+	0.997148i	$0.524048\pi$
$224$		0			0
$225$	−54748.0	−	539234.i	−0.0720962	−	0.710103i
$226$		0			0
$227$	−694991.	+	583167.i	−0.895189	+	0.751153i	−0.969244	−	0.246101i	$-0.920850\pi$
$227$	−694991.	+	583167.i	−0.895189	+	0.751153i	0.0740551	+	0.997254i	$0.476406\pi$
$228$		0			0
$229$	235922.	−	1.33798e6i	0.297289	−	1.68601i	−0.360462	−	0.932774i	$-0.617381\pi$
$229$	235922.	−	1.33798e6i	0.297289	−	1.68601i	0.657751	−	0.753236i	$-0.271508\pi$
$230$		0			0
$231$	−1921.23	−	5948.73i	−0.00236892	−	0.00733490i
$232$		0			0
$233$	90377.6	−	156539.i	0.109061	−	0.188900i	−0.806329	−	0.591467i	$-0.798549\pi$
$233$	90377.6	−	156539.i	0.109061	−	0.188900i	0.915390	+	0.402568i	$0.131882\pi$
$234$		0			0
$235$	665274.	+	1.15229e6i	0.785834	+	1.36110i
$236$		0			0
$237$	371305.	−	51514.0i	0.429398	−	0.0595737i
$238$		0			0
$239$	−1.03426e6	+	376439.i	−1.17121	+	0.426285i	−0.853089	−	0.521765i	$-0.825274\pi$
$239$	−1.03426e6	+	376439.i	−1.17121	+	0.426285i	−0.318120	+	0.948050i	$0.603052\pi$
$240$		0			0
$241$	−236445.	−	1.34095e6i	−0.262233	−	1.48720i	−0.776800	−	0.629747i	$-0.783158\pi$
$241$	−236445.	−	1.34095e6i	−0.262233	−	1.48720i	0.514567	−	0.857450i	$-0.327953\pi$
$242$		0			0
$243$	167850.	−	905050.i	0.182350	−	0.983234i
$244$		0			0
$245$	205553.	+	1.16575e6i	0.218780	+	1.24077i
$246$		0			0
$247$	−364736.	+	132753.i	−0.380396	+	0.138453i
$248$		0			0
$249$	−1.72914e6	+	239896.i	−1.76738	+	0.245203i
$250$		0			0
$251$	818374.	+	1.41747e6i	0.819912	+	1.42013i	0.905746	+	0.423820i	$0.139311\pi$
$251$	818374.	+	1.41747e6i	0.819912	+	1.42013i	−0.0858338	+	0.996309i	$0.527355\pi$
$252$		0			0
$253$	3388.26	−	5868.64i	0.00332794	−	0.00576416i
$254$		0			0
$255$	164374.	+	508952.i	0.158301	+	0.490147i
$256$		0			0
$257$	−17660.7	+	100159.i	−0.0166792	+	0.0945922i	−0.992011	−	0.126152i	$-0.959737\pi$
$257$	−17660.7	+	100159.i	−0.0166792	+	0.0945922i	0.975332	+	0.220744i	$0.0708485\pi$
$258$		0			0
$259$	112749.	−	94607.8i	0.104439	−	0.0876350i
$260$		0			0
$261$	23899.3	+	235393.i	0.0217162	+	0.213891i
$262$		0			0
$263$	−771617.	−	280846.i	−0.687880	−	0.250368i	−0.0256528	−	0.999671i	$-0.508166\pi$
$263$	−771617.	−	280846.i	−0.687880	−	0.250368i	−0.662227	+	0.749303i	$0.730389\pi$
$264$		0			0
$265$	−821056.	−	688948.i	−0.718221	−	0.602659i
$266$		0			0
$267$	−599842.	+	317582.i	−0.514942	+	0.272633i
$268$		0			0
$269$	1.13503e6			0.956369			0.478185	−	0.878259i	$-0.341295\pi$
$269$	1.13503e6			0.956369			0.478185	+	0.878259i	$0.341295\pi$
$270$		0			0
$271$	1.09529e6			0.905952			0.452976	−	0.891523i	$-0.350362\pi$
$271$	1.09529e6			0.905952			0.452976	+	0.891523i	$0.350362\pi$
$272$		0			0
$273$	−63317.8	−	39721.2i	−0.0514185	−	0.0322564i
$274$		0			0
$275$	−27263.9	−	22877.1i	−0.0217399	−	0.0182419i
$276$		0			0
$277$	143364.	+	52180.1i	0.112264	+	0.0408606i	0.397541	−	0.917584i	$-0.369864\pi$
$277$	143364.	+	52180.1i	0.112264	+	0.0408606i	−0.285278	+	0.958445i	$0.592086\pi$
$278$		0			0
$279$	62022.4	−	17547.5i	0.0477022	−	0.0134960i
$280$		0			0
$281$	−1.40444e6	+	1.17846e6i	−1.06105	+	0.890330i	−0.994212	−	0.107434i	$-0.965737\pi$
$281$	−1.40444e6	+	1.17846e6i	−1.06105	+	0.890330i	−0.0668414	+	0.997764i	$0.521292\pi$
$282$		0			0
$283$	90201.3	−	511557.i	0.0669494	−	0.379689i	−0.932861	−	0.360236i	$-0.882696\pi$
$283$	90201.3	−	511557.i	0.0669494	−	0.379689i	0.999811	−	0.0194533i	$-0.00619257\pi$
$284$		0			0
$285$	−2.26925e6	−	486540.i	−1.65489	−	0.354819i
$286$		0			0
$287$	176784.	−	306199.i	0.126689	−	0.219431i
$288$		0			0
$289$	600026.	+	1.03927e6i	0.422596	+	0.731957i
$290$		0			0
$291$	453139.	+	582110.i	0.313689	+	0.402970i
$292$		0			0
$293$	−293674.	+	106888.i	−0.199846	+	0.0727381i	−0.440004	−	0.897996i	$-0.645023\pi$
$293$	−293674.	+	106888.i	−0.199846	+	0.0727381i	0.240158	+	0.970734i	$0.422801\pi$
$294$		0			0
$295$	318959.	+	1.80890e6i	0.213393	+	1.21021i
$296$		0			0
$297$	−33532.9	−	50288.1i	−0.0220587	−	0.0330807i
$298$		0			0
$299$	−14070.0	−	79794.9i	−0.00910156	−	0.0516175i
$300$		0			0
$301$	404864.	−	147358.i	0.257568	−	0.0937472i
$302$		0			0
$303$	−337729.	+	831670.i	−0.211330	+	0.520409i
$304$		0			0
$305$	885981.	+	1.53456e6i	0.545349	+	0.944573i
$306$		0			0
$307$	−1.20497e6	+	2.08706e6i	−0.729675	+	1.26383i	0.227346	+	0.973814i	$0.426995\pi$
$307$	−1.20497e6	+	2.08706e6i	−0.729675	+	1.26383i	−0.957021	+	0.290020i	$0.906338\pi$
$308$		0			0
$309$	−433637.	+	479893.i	−0.258363	+	0.285922i
$310$		0			0
$311$	432980.	−	2.45555e6i	0.253844	−	1.43962i	−0.545178	−	0.838320i	$-0.683538\pi$
$311$	432980.	−	2.45555e6i	0.253844	−	1.43962i	0.799022	−	0.601302i	$-0.205351\pi$
$312$		0			0
$313$	1.55679e6	−	1.30631e6i	0.898195	−	0.753675i	−0.0716418	−	0.997430i	$-0.522824\pi$
$313$	1.55679e6	−	1.30631e6i	0.898195	−	0.753675i	0.969837	+	0.243755i	$0.0783794\pi$
$314$		0			0
$315$	−194497.	−	402384.i	−0.110443	−	0.228489i
$316$		0			0
$317$	125027.	+	45506.2i	0.0698806	+	0.0254345i	0.376724	−	0.926326i	$-0.377051\pi$
$317$	125027.	+	45506.2i	0.0698806	+	0.0254345i	−0.306843	+	0.951760i	$0.599273\pi$
$318$		0			0
$319$	11901.6	+	9986.62i	0.00654830	+	0.00549467i
$320$		0			0
$321$	−3421.07	+	93238.4i	−0.00185310	+	0.0505047i
$322$		0			0
$323$	953805.			0.508690
$324$		0			0
$325$	−425551.			−0.223482
$326$		0			0
$327$	−129077.	+	3.51789e6i	−0.0667545	+	1.81934i
$328$		0			0
$329$	350038.	+	293717.i	0.178289	+	0.149602i
$330$		0			0
$331$	2.37630e6	+	864901.i	1.19215	+	0.433907i	0.860478	−	0.509488i	$-0.170165\pi$
$331$	2.37630e6	+	864901.i	1.19215	+	0.433907i	0.331671	+	0.943395i	$0.392388\pi$
$332$		0			0
$333$	799957.	−	1.17698e6i	0.395327	−	0.581647i
$334$		0			0
$335$	−721486.	+	605398.i	−0.351250	+	0.294733i
$336$		0			0
$337$	−95796.8	+	543290.i	−0.0459490	+	0.260590i	−0.999125	−	0.0418268i	$-0.986682\pi$
$337$	−95796.8	+	543290.i	−0.0459490	+	0.260590i	0.953176	+	0.302417i	$0.0977933\pi$
$338$		0			0
$339$	−216366.	+	239445.i	−0.102256	+	0.113164i
$340$		0			0
$341$	2116.26	−	3665.47i	0.000985561	−	0.00170704i
$342$		0			0
$343$	414459.	+	717864.i	0.190216	+	0.329463i
$344$		0			0
$345$	182282.	−	448877.i	0.0824511	−	0.203039i
$346$		0			0
$347$	−1.64626e6	+	599188.i	−0.733962	+	0.267140i	−0.681841	−	0.731500i	$-0.738820\pi$
$347$	−1.64626e6	+	599188.i	−0.733962	+	0.267140i	−0.0521210	+	0.998641i	$0.516598\pi$
$348$		0			0
$349$	−532115.	−	3.01777e6i	−0.233852	−	1.32624i	−0.845017	−	0.534739i	$-0.820410\pi$
$349$	−532115.	−	3.01777e6i	−0.233852	−	1.32624i	0.611165	−	0.791503i	$-0.290701\pi$
$350$		0			0
$351$	−693644.	−	202888.i	−0.300517	−	0.0879001i
$352$		0			0
$353$	420287.	+	2.38357e6i	0.179519	+	1.01810i	0.932798	+	0.360400i	$0.117360\pi$
$353$	420287.	+	2.38357e6i	0.179519	+	1.01810i	−0.753279	+	0.657701i	$0.771529\pi$
$354$		0			0
$355$	−4.82505e6	+	1.75617e6i	−2.03203	+	0.739600i
$356$		0			0
$357$	112826.	+	144939.i	0.0468532	+	0.0601885i
$358$		0			0
$359$	−1.08001e6	−	1.87062e6i	−0.442272	−	0.766038i	0.555585	−	0.831460i	$-0.312494\pi$
$359$	−1.08001e6	−	1.87062e6i	−0.442272	−	0.766038i	−0.997858	+	0.0654213i	$0.979161\pi$
$360$		0			0
$361$	−831374.	+	1.43998e6i	−0.335759	+	0.581552i
$362$		0			0
$363$	2.45087e6	+	525480.i	0.976233	+	0.209310i
$364$		0			0
$365$	795727.	−	4.51279e6i	0.312631	−	1.77302i
$366$		0			0
$367$	1.18726e6	−	996229.i	0.460130	−	0.386095i	−0.383049	−	0.923728i	$-0.625126\pi$
$367$	1.18726e6	−	996229.i	0.460130	−	0.386095i	0.843179	+	0.537633i	$0.180681\pi$
$368$		0			0
$369$	838764.	−	3.31411e6i	0.320681	−	1.26707i
$370$		0			0
$371$	−345888.	−	125893.i	−0.130467	−	0.0474861i
$372$		0			0
$373$	−2.32252e6	−	1.94882e6i	−0.864345	−	0.725271i	0.0985547	−	0.995132i	$-0.468578\pi$
$373$	−2.32252e6	−	1.94882e6i	−0.864345	−	0.725271i	−0.962900	+	0.269860i	$0.913023\pi$
$374$		0			0
$375$	864436.	+	542288.i	0.317435	+	0.199137i
$376$		0			0
$377$	185767.			0.0673154
$378$		0			0
$379$	−1.48676e6			−0.531671			−0.265836	−	0.964018i	$-0.585648\pi$
$379$	−1.48676e6			−0.531671			−0.265836	+	0.964018i	$0.585648\pi$
$380$		0			0
$381$	2.09188e6	−	1.10753e6i	0.738286	−	0.390880i
$382$		0			0
$383$	−3.08852e6	−	2.59158e6i	−1.07585	−	0.902749i	−0.0802842	−	0.996772i	$-0.525583\pi$
$383$	−3.08852e6	−	2.59158e6i	−1.07585	−	0.902749i	−0.995570	+	0.0940232i	$0.970027\pi$
$384$		0			0
$385$	−27577.3	−	10037.3i	−0.00948198	−	0.00345116i
$386$		0			0
$387$	3.37885e6	−	2.43667e6i	1.14681	−	0.827025i
$388$		0			0
$389$	−726639.	+	609722.i	−0.243469	+	0.204295i	−0.756354	−	0.654162i	$-0.773021\pi$
$389$	−726639.	+	609722.i	−0.243469	+	0.204295i	0.512885	+	0.858458i	$0.328577\pi$
$390$		0			0
$391$	−34574.8	+	196084.i	−0.0114372	+	0.0648634i
$392$		0			0
$393$	255449.	+	790950.i	0.0834303	+	0.258326i
$394$		0			0
$395$	879907.	−	1.52404e6i	0.283755	−	0.491479i
$396$		0			0
$397$	−2.79905e6	−	4.84810e6i	−0.891322	−	1.54381i	−0.838292	−	0.545222i	$-0.816446\pi$
$397$	−2.79905e6	−	4.84810e6i	−0.891322	−	1.54381i	−0.0530297	−	0.998593i	$-0.516888\pi$
$398$		0			0
$399$	−789464.	+	109528.i	−0.248256	+	0.0344425i
$400$		0			0
$401$	2.58695e6	−	941572.i	0.803391	−	0.292410i	0.0925001	−	0.995713i	$-0.470514\pi$
$401$	2.58695e6	−	941572.i	0.803391	−	0.292410i	0.710891	+	0.703302i	$0.248292\pi$
$402$		0			0
$403$	−8787.93	−	49838.8i	−0.00269540	−	0.0152864i
$404$		0			0
$405$	−2.86871e6	−	3.23171e6i	−0.869057	−	0.979026i
$406$		0			0
$407$	−16226.9	−	92027.5i	−0.00485568	−	0.0275379i
$408$		0			0
$409$	1.00991e6	−	367577.i	0.298521	−	0.108653i	−0.188418	−	0.982089i	$-0.560336\pi$
$409$	1.00991e6	−	367577.i	0.298521	−	0.108653i	0.486938	+	0.873436i	$0.338114\pi$
$410$		0			0
$411$	6.36858e6	−	883563.i	1.85968	−	0.258008i
$412$		0			0
$413$	315402.	+	546293.i	0.0909892	+	0.157598i
$414$		0			0
$415$	−4.09765e6	+	7.09734e6i	−1.16792	+	2.02290i
$416$		0			0
$417$	1.78982e6	+	5.54183e6i	0.504045	+	1.56068i
$418$		0			0
$419$	900353.	−	5.10615e6i	0.250540	−	1.42088i	−0.556725	−	0.830697i	$-0.687942\pi$
$419$	900353.	−	5.10615e6i	0.250540	−	1.42088i	0.807266	−	0.590188i	$-0.200947\pi$
$420$		0			0
$421$	1.47988e6	−	1.24176e6i	0.406931	−	0.341456i	−0.416234	−	0.909257i	$-0.636650\pi$
$421$	1.47988e6	−	1.24176e6i	0.406931	−	0.341456i	0.823165	+	0.567802i	$0.192206\pi$
$422$		0			0
$423$	4.02977e6	+	1.81128e6i	1.09504	+	0.492191i
$424$		0			0
$425$	982661.	+	357659.i	0.263895	+	0.0960500i
$426$		0			0
$427$	466164.	+	391158.i	0.123728	+	0.103820i
$428$		0			0
$429$	−41940.6	+	22205.2i	−0.0110025	+	0.00582520i
$430$		0			0
$431$	−591712.			−0.153433			−0.0767163	−	0.997053i	$-0.524444\pi$
$431$	−591712.			−0.153433			−0.0767163	+	0.997053i	$0.524444\pi$
$432$		0			0
$433$	4.60562e6			1.18051			0.590253	−	0.807219i	$-0.299028\pi$
$433$	4.60562e6			1.18051			0.590253	+	0.807219i	$0.299028\pi$
$434$		0			0
$435$	940928.	+	590274.i	0.238415	+	0.149565i
$436$		0			0
$437$	−661857.	−	555364.i	−0.165791	−	0.139115i
$438$		0			0
$439$	57408.8	+	20895.1i	0.0142173	+	0.00517468i	0.349119	−	0.937078i	$-0.386481\pi$
$439$	57408.8	+	20895.1i	0.0142173	+	0.00517468i	−0.334902	+	0.942253i	$0.608703\pi$
$440$		0			0
$441$	2.81777e6	+	2.74042e6i	0.689937	+	0.670997i
$442$		0			0
$443$	1.07756e6	−	904178.i	0.260874	−	0.218899i	−0.502964	−	0.864308i	$-0.667757\pi$
$443$	1.07756e6	−	904178.i	0.260874	−	0.218899i	0.763838	+	0.645408i	$0.223313\pi$
$444$		0			0
$445$	−553300.	+	3.13792e6i	−0.132453	+	0.751176i
$446$		0			0
$447$	−4.78483e6	−	1.02590e6i	−1.13266	−	0.242848i
$448$		0			0
$449$	343567.	−	595075.i	0.0804258	−	0.139302i	−0.823007	−	0.568031i	$-0.807705\pi$
$449$	343567.	−	595075.i	0.0804258	−	0.139302i	0.903433	+	0.428730i	$0.141039\pi$
$450$		0			0
$451$	−112240.	−	194406.i	−0.0259841	−	0.0450058i
$452$		0			0
$453$	−2.41769e6	−	3.10581e6i	−0.553549	−	0.711099i
$454$		0			0
$455$	−329737.	+	120015.i	−0.0746688	+	0.0271772i
$456$		0			0
$457$	699753.	+	3.96850e6i	0.156731	+	0.888865i	0.957186	+	0.289473i	$0.0934799\pi$
$457$	699753.	+	3.96850e6i	0.156731	+	0.888865i	−0.800455	+	0.599392i	$0.795409\pi$
$458$		0			0
$459$	1.43121e6	+	1.05148e6i	0.317082	+	0.232954i
$460$		0			0
$461$	−1.00123e6	−	5.67824e6i	−0.219422	−	1.24441i	−0.873066	−	0.487603i	$-0.837872\pi$
$461$	−1.00123e6	−	5.67824e6i	−0.219422	−	1.24441i	0.653644	−	0.756803i	$-0.273240\pi$
$462$		0			0
$463$	−2.13653e6	+	777632.i	−0.463186	+	0.168586i	−0.563063	−	0.826414i	$-0.690377\pi$
$463$	−2.13653e6	+	777632.i	−0.463186	+	0.168586i	0.0998770	+	0.995000i	$0.468155\pi$
$464$		0			0
$465$	113851.	−	280363.i	0.0244177	−	0.0601295i
$466$		0			0
$467$	−2.72626e6	−	4.72202e6i	−0.578462	−	1.00193i	−0.995656	−	0.0931078i	$-0.970320\pi$
$467$	−2.72626e6	−	4.72202e6i	−0.578462	−	1.00193i	0.417194	−	0.908817i	$-0.363013\pi$
$468$		0			0
$469$	−161724.	+	280114.i	−0.0339502	+	0.0588035i
$470$		0			0
$471$	688976.	−	762469.i	0.143104	−	0.158369i
$472$		0			0
$473$	47500.7	−	269390.i	0.00976218	−	0.0553641i
$474$		0			0
$475$	−3.47609e6	+	2.91679e6i	−0.706899	+	0.593159i
$476$		0			0
$477$	−3.54941e6	−	260819.i	−0.714267	−	0.0524860i
$478$		0			0
$479$	−3.25902e6	−	1.18619e6i	−0.649005	−	0.236218i	−0.00352265	−	0.999994i	$-0.501121\pi$
$479$	−3.25902e6	−	1.18619e6i	−0.649005	−	0.236218i	−0.645482	+	0.763775i	$0.723344\pi$
$480$		0			0
$481$	−855928.	−	718208.i	−0.168684	−	0.141543i
$482$		0			0
$483$	6100.68	−	166269.i	0.00118990	−	0.0324297i
$484$		0			0
$485$	3.46314e6			0.668522
$486$		0			0
$487$	−1.52300e6			−0.290989			−0.145494	−	0.989359i	$-0.546477\pi$
$487$	−1.52300e6			−0.290989			−0.145494	+	0.989359i	$0.546477\pi$
$488$		0			0
$489$	−262165.	+	7.14508e6i	−0.0495795	+	1.35125i
$490$		0			0
$491$	1.98722e6	+	1.66747e6i	0.371999	+	0.312144i	0.809552	−	0.587048i	$-0.199710\pi$
$491$	1.98722e6	+	1.66747e6i	0.371999	+	0.312144i	−0.437553	+	0.899193i	$0.644155\pi$
$492$		0			0
$493$	−428964.	−	156130.i	−0.0794883	−	0.0289314i
$494$		0			0
$495$	−282991.	−	20794.8i	−0.0519110	−	0.00381454i
$496$		0			0
$497$	−1.35083e6	+	1.13348e6i	−0.245307	+	0.205837i
$498$		0			0
$499$	166430.	−	943874.i	0.0299214	−	0.169692i	−0.966185	−	0.257849i	$-0.916986\pi$
$499$	166430.	−	943874.i	0.0299214	−	0.169692i	0.996107	+	0.0881563i	$0.0280975\pi$
$500$		0			0
$501$	−4.69360e6	+	5.19427e6i	−0.835434	+	0.924550i
$502$		0			0
$503$	815376.	−	1.41227e6i	0.143694	−	0.248885i	−0.785191	−	0.619254i	$-0.787435\pi$
$503$	815376.	−	1.41227e6i	0.143694	−	0.248885i	0.928885	+	0.370369i	$0.120769\pi$
$504$		0			0
$505$	2.10699e6	+	3.64941e6i	0.367650	+	0.636788i
$506$		0			0
$507$	1.96418e6	−	4.83686e6i	0.339360	−	0.835687i
$508$		0			0
$509$	−9.60387e6	+	3.49552e6i	−1.64305	+	0.598023i	−0.987569	−	0.157185i	$-0.949758\pi$
$509$	−9.60387e6	+	3.49552e6i	−1.64305	+	0.598023i	−0.655485	+	0.755208i	$0.727536\pi$
$510$		0			0
$511$	−273272.	−	1.54980e6i	−0.0462959	−	0.262557i
$512$		0			0
$513$	−7.05664e6	+	3.09706e6i	−1.18387	+	0.519584i
$514$		0			0
$515$	527266.	+	2.99027e6i	0.0876015	+	0.496813i
$516$		0			0
$517$	272617.	−	99224.6i	0.0448567	−	0.0163265i
$518$		0			0
$519$	2.54652e6	+	3.27131e6i	0.414982	+	0.533093i
$520$		0			0
$521$	3.68245e6	+	6.37819e6i	0.594350	+	1.02945i	0.993638	+	0.112620i	$0.0359241\pi$
$521$	3.68245e6	+	6.37819e6i	0.594350	+	1.02945i	−0.399288	+	0.916826i	$0.630743\pi$
$522$		0			0
$523$	−1.46927e6	+	2.54484e6i	−0.234880	+	0.406824i	−0.959238	−	0.282600i	$-0.908803\pi$
$523$	−1.46927e6	+	2.54484e6i	−0.234880	+	0.406824i	0.724358	+	0.689424i	$0.242136\pi$
$524$		0			0
$525$	−854420.	−	183193.i	−0.135292	−	0.0290075i
$526$		0			0
$527$	−21595.0	+	122471.i	−0.00338709	+	0.0192091i
$528$		0			0
$529$	−4.79236e6	+	4.02127e6i	−0.744578	+	0.624775i
$530$		0			0
$531$	4.37237e6	+	4.25234e6i	0.672946	+	0.654473i
$532$		0			0
$533$	−2.52221e6	−	918011.i	−0.384560	−	0.139968i
$534$		0			0
$535$	335534.	+	281547.i	0.0506818	+	0.0425271i
$536$		0			0
$537$	−624933.	−	392040.i	−0.0935186	−	0.0586671i
$538$		0			0
$539$	258102.			0.0382665
$540$		0			0
$541$	8.28213e6			1.21660			0.608302	−	0.793706i	$-0.291851\pi$
$541$	8.28213e6			1.21660			0.608302	+	0.793706i	$0.291851\pi$
$542$		0			0
$543$	9.07475e6	−	4.80456e6i	1.32079	−	0.699285i
$544$		0			0
$545$	1.26597e7	+	1.06228e7i	1.82572	+	1.53196i
$546$		0			0
$547$	−5.27806e6	−	1.92106e6i	−0.754234	−	0.274519i	−0.0638475	−	0.997960i	$-0.520337\pi$
$547$	−5.27806e6	−	1.92106e6i	−0.754234	−	0.274519i	−0.690386	+	0.723441i	$0.742559\pi$
$548$		0			0
$549$	5.36666e6	+	2.41218e6i	0.759930	+	0.341569i
$550$		0			0
$551$	1.51743e6	−	1.27327e6i	0.212926	−	0.178666i
$552$		0			0
$553$	104946.	−	595181.i	0.0145933	−	0.0827629i
$554$		0			0
$555$	−2.05326e6	−	6.35751e6i	−0.282951	−	0.876102i
$556$		0			0
$557$	−3.19733e6	+	5.53794e6i	−0.436666	+	0.756328i	−0.997430	−	0.0716475i	$-0.977174\pi$
$557$	−3.19733e6	+	5.53794e6i	−0.436666	+	0.756328i	0.560764	+	0.827976i	$0.310508\pi$
$558$		0			0
$559$	−1.63537e6	−	2.83255e6i	−0.221354	−	0.383396i
$560$		0			0
$561$	115510.	−	16025.6i	0.0154957	−	0.00214984i
$562$		0			0
$563$	−9.15086e6	+	3.33064e6i	−1.21672	+	0.442850i	−0.869030	−	0.494759i	$-0.835256\pi$
$563$	−9.15086e6	+	3.33064e6i	−1.21672	+	0.442850i	−0.347691	+	0.937609i	$0.613034\pi$
$564$		0			0
$565$	263082.	+	1.49201e6i	0.0346713	+	0.196631i
$566$		0			0
$567$	−1.30536e6	−	705962.i	−0.170519	−	0.0922196i
$568$		0			0
$569$	−52999.7	−	300576.i	−0.00686267	−	0.0389201i	0.981184	−	0.193074i	$-0.0618459\pi$
$569$	−52999.7	−	300576.i	−0.00686267	−	0.0389201i	−0.988047	+	0.154154i	$0.950735\pi$
$570$		0			0
$571$	5.86690e6	−	2.13538e6i	0.753040	−	0.274084i	0.0631558	−	0.998004i	$-0.479883\pi$
$571$	5.86690e6	−	2.13538e6i	0.753040	−	0.274084i	0.689885	+	0.723919i	$0.257661\pi$
$572$		0			0
$573$	−1.26121e6	+	174977.i	−0.160473	+	0.0222636i
$574$		0			0
$575$	−473629.	−	820350.i	−0.0597405	−	0.103474i
$576$		0			0
$577$	4.29816e6	−	7.44464e6i	0.537457	−	0.930902i	−0.461583	−	0.887097i	$-0.652718\pi$
$577$	4.29816e6	−	7.44464e6i	0.537457	−	0.930902i	0.999040	−	0.0438055i	$-0.0139482\pi$
$578$		0			0
$579$	−2.01687e6	−	6.24486e6i	−0.250024	−	0.774152i
$580$		0			0
$581$	−488726.	+	2.77170e6i	−0.0600655	+	0.340649i
$582$		0			0
$583$	−179023.	+	150219.i	−0.0218142	+	0.0183043i
$584$		0			0
$585$	−2.75187e6	+	1.98452e6i	−0.332459	+	0.239754i
$586$		0			0
$587$	636744.	+	231756.i	0.0762728	+	0.0277610i	0.379875	−	0.925038i	$-0.375967\pi$
$587$	636744.	+	231756.i	0.0762728	+	0.0277610i	−0.303602	+	0.952799i	$0.598189\pi$
$588$		0			0
$589$	−413387.	−	346873.i	−0.0490985	−	0.0411986i
$590$		0			0
$591$	4.65247e6	−	2.46322e6i	0.547917	−	0.290091i
$592$		0			0
$593$	−4.32841e6			−0.505466			−0.252733	−	0.967536i	$-0.581329\pi$
$593$	−4.32841e6			−0.505466			−0.252733	+	0.967536i	$0.581329\pi$
$594$		0			0
$595$	862281.			0.0998519
$596$		0			0
$597$	−8.36069e6	−	5.24492e6i	−0.960077	−	0.602287i
$598$		0			0
$599$	1.12668e7	+	9.45400e6i	1.28302	+	1.07659i	0.992820	+	0.119621i	$0.0381679\pi$
$599$	1.12668e7	+	9.45400e6i	1.28302	+	1.07659i	0.290205	+	0.956965i	$0.406277\pi$
$600$		0			0
$601$	−2.45535e6	−	893675.i	−0.277286	−	0.100924i	0.199634	−	0.979870i	$-0.436025\pi$
$601$	−2.45535e6	−	893675.i	−0.277286	−	0.100924i	−0.476920	+	0.878947i	$0.658247\pi$
$602$		0			0
$603$	−767311.	+	3.03179e6i	−0.0859366	+	0.339552i
$604$		0			0
$605$	9.01425e6	−	7.56385e6i	1.00125	−	0.840145i
$606$		0			0
$607$	2.60398e6	−	1.47679e7i	0.286858	−	1.62685i	−0.411716	−	0.911312i	$-0.635070\pi$
$607$	2.60398e6	−	1.47679e7i	0.286858	−	1.62685i	0.698573	−	0.715538i	$-0.253819\pi$
$608$		0			0
$609$	372982.	+	79969.5i	0.0407516	+	0.00873738i
$610$		0			0
$611$	1.73442e6	−	3.00411e6i	0.187954	−	0.325546i
$612$		0			0
$613$	−5.10359e6	−	8.83968e6i	−0.548561	−	0.950135i	−0.998373	−	0.0570119i	$-0.981843\pi$
$613$	−5.10359e6	−	8.83968e6i	−0.548561	−	0.950135i	0.449813	−	0.893123i	$-0.351491\pi$
$614$		0			0
$615$	−9.85830e6	−	1.26642e7i	−1.05103	−	1.35017i
$616$		0			0
$617$	−7.69971e6	+	2.80247e6i	−0.814257	+	0.296365i	−0.715381	−	0.698734i	$-0.753747\pi$
$617$	−7.69971e6	+	2.80247e6i	−0.814257	+	0.296365i	−0.0988761	+	0.995100i	$0.531525\pi$
$618$		0			0
$619$	−203861.	−	1.15616e6i	−0.0213850	−	0.121280i	0.972247	−	0.233959i	$-0.0751681\pi$
$619$	−203861.	−	1.15616e6i	−0.0213850	−	0.121280i	−0.993631	+	0.112679i	$0.964057\pi$
$620$		0			0
$621$	−380896.	−	1.56297e6i	−0.0396349	−	0.162638i
$622$		0			0
$623$	190016.	+	1.07764e6i	0.0196142	+	0.111238i
$624$		0			0
$625$	1.10516e7	−	4.02244e6i	1.13168	−	0.411898i
$626$		0			0
$627$	−190393.	+	468850.i	−0.0193411	+	0.0476283i
$628$		0			0
$629$	1.37284e6	+	2.37783e6i	0.138354	+	0.239637i
$630$		0			0
$631$	4.54789e6	−	7.87718e6i	0.454712	−	0.787585i	−0.543959	−	0.839112i	$-0.683075\pi$
$631$	4.54789e6	−	7.87718e6i	0.454712	−	0.787585i	0.998672	+	0.0515269i	$0.0164088\pi$
$632$		0			0
$633$	−1.17213e7	+	1.29716e7i	−1.16269	+	1.28672i
$634$		0			0
$635$	1.92957e6	−	1.09431e7i	0.189901	−	1.07698i
$636$		0			0
$637$	2.36408e6	−	1.98370e6i	0.230841	−	0.193699i
$638$		0			0
$639$	−9.58415e6	+	1.41012e7i	−0.928542	+	1.36617i
$640$		0			0
$641$	2.17585e6	+	791946.i	0.209163	+	0.0761290i	0.444477	−	0.895790i	$-0.353390\pi$
$641$	2.17585e6	+	791946.i	0.209163	+	0.0761290i	−0.235314	+	0.971919i	$0.575612\pi$
$642$		0			0
$643$	1.35369e7	+	1.13588e7i	1.29120	+	1.08344i	0.991595	+	0.129381i	$0.0412989\pi$
$643$	1.35369e7	+	1.13588e7i	1.29120	+	1.08344i	0.299604	+	0.954064i	$0.403146\pi$
$644$		0			0
$645$	717085.	−	1.95435e7i	0.0678690	−	1.84971i
$646$		0			0
$647$	−1.12054e7			−1.05237			−0.526185	−	0.850370i	$-0.676378\pi$
$647$	−1.12054e7			−1.05237			−0.526185	+	0.850370i	$0.676378\pi$
$648$		0			0
$649$	400499.			0.0373241
$650$		0			0
$651$	3810.41	−	103849.i	0.000352386	−	0.00960398i
$652$		0			0
$653$	8.88814e6	+	7.45804e6i	0.815696	+	0.684450i	0.951960	−	0.306223i	$-0.0990652\pi$
$653$	8.88814e6	+	7.45804e6i	0.815696	+	0.684450i	−0.136264	+	0.990673i	$0.543510\pi$
$654$		0			0
$655$	3.66670e6	+	1.33457e6i	0.333943	+	0.121545i
$656$		0			0
$657$	−6.62185e6	−	1.36996e7i	−0.598502	−	1.23821i
$658$		0			0
$659$	−79436.9	+	66655.5i	−0.00712539	+	0.00597892i	−0.646343	−	0.763047i	$-0.723703\pi$
$659$	−79436.9	+	66655.5i	−0.00712539	+	0.00597892i	0.639218	+	0.769026i	$0.279258\pi$
$660$		0			0
$661$	−2.50760e6	+	1.42213e7i	−0.223231	+	1.26601i	0.642806	+	0.766029i	$0.277770\pi$
$661$	−2.50760e6	+	1.42213e7i	−0.223231	+	1.26601i	−0.866037	+	0.499979i	$0.833341\pi$
$662$		0			0
$663$	934843.	−	1.03456e6i	0.0825952	−	0.0914056i
$664$		0			0
$665$	−1.87085e6	+	3.24040e6i	−0.164053	+	0.284148i
$666$		0			0
$667$	206755.	+	358109.i	0.0179945	+	0.0311674i
$668$		0			0
$669$	2.35301e6	−	5.79438e6i	0.203263	−	0.500544i
$670$		0			0
$671$	363059.	−	132143.i	0.0311294	−	0.0113302i
$672$		0			0
$673$	207134.	+	1.17472e6i	0.0176284	+	0.0999758i	0.992352	−	0.123436i	$-0.0393915\pi$
$673$	207134.	+	1.17472e6i	0.0176284	+	0.0999758i	−0.974724	+	0.223412i	$0.928280\pi$
$674$		0			0
$675$	−8.43147e6	+	544647.i	−0.712269	+	0.0460103i
$676$		0			0
$677$	−1.18366e6	−	6.71284e6i	−0.0992553	−	0.562905i	−0.993360	−	0.115047i	$-0.963298\pi$
$677$	−1.18366e6	−	6.71284e6i	−0.0992553	−	0.562905i	0.894105	−	0.447858i	$-0.147813\pi$
$678$		0			0
$679$	1.11760e6	−	406773.i	0.0930277	−	0.0338593i
$680$		0			0
$681$	8.68732e6	+	1.11599e7i	0.717824	+	0.922130i
$682$		0			0
$683$	−7.32907e6	−	1.26943e7i	−0.601170	−	1.04126i	−0.992644	−	0.121068i	$-0.961368\pi$
$683$	−7.32907e6	−	1.26943e7i	−0.601170	−	1.04126i	0.391474	−	0.920189i	$-0.371965\pi$
$684$		0			0
$685$	1.50921e7	−	2.61402e7i	1.22892	−	2.12855i
$686$		0			0
$687$	−2.07081e7	−	4.43994e6i	−1.67398	−	0.358910i
$688$		0			0
$689$	−485225.	+	2.75185e6i	−0.0389399	+	0.220839i
$690$		0			0
$691$	7.52354e6	−	6.31300e6i	0.599414	−	0.502968i	−0.291843	−	0.956466i	$-0.594269\pi$
$691$	7.52354e6	−	6.31300e6i	0.599414	−	0.502968i	0.891257	+	0.453498i	$0.149824\pi$
$692$		0			0
$693$	−93767.3	+	26528.8i	−0.00741683	+	0.00209838i
$694$		0			0
$695$	2.56909e7	+	9.35073e6i	2.01752	+	0.734317i
$696$		0			0
$697$	5.05262e6	+	4.23965e6i	0.393944	+	0.330558i
$698$		0			0
$699$	−2.38690e6	−	1.49738e6i	−0.184774	−	0.115914i
$700$		0			0
$701$	−3.18359e6			−0.244693			−0.122347	−	0.992487i	$-0.539042\pi$
$701$	−3.18359e6			−0.244693			−0.122347	+	0.992487i	$0.539042\pi$
$702$		0			0
$703$	−1.19143e7			−0.909245
$704$		0			0
$705$	1.83306e7	−	9.70499e6i	1.38900	−	0.735398i
$706$		0			0
$707$	1.10861e6	+	930231.i	0.0834120	+	0.0699910i
$708$		0			0
$709$	−868616.	−	316150.i	−0.0648951	−	0.0236199i	0.309369	−	0.950942i	$-0.399882\pi$
$709$	−868616.	−	316150.i	−0.0648951	−	0.0236199i	−0.374264	+	0.927322i	$0.622105\pi$
$710$		0			0
$711$	−590253.	−	5.81362e6i	−0.0437889	−	0.431294i
$712$		0			0
$713$	86295.3	−	72410.4i	0.00635717	−	0.00533430i
$714$		0			0
$715$	−38686.5	+	219402.i	−0.00283005	+	0.0160500i
$716$		0			0
$717$	5.27300e6	+	1.63268e7i	0.383054	+	1.18605i
$718$		0			0
$719$	−2.83625e6	+	4.91253e6i	−0.204608	+	0.354391i	−0.950008	−	0.312227i	$-0.898925\pi$
$719$	−2.83625e6	+	4.91253e6i	−0.204608	+	0.354391i	0.745400	+	0.666618i	$0.232259\pi$
$720$		0			0
$721$	521387.	+	903069.i	0.0373527	+	0.0646968i
$722$		0			0
$723$	−2.10244e7	+	2.91687e6i	−1.49581	+	0.207526i
$724$		0			0
$725$	2.04079e6	−	742787.i	0.144196	−	0.0524831i
$726$		0			0
$727$	−1.20185e6	−	6.81604e6i	−0.0843364	−	0.478295i	−0.997498	−	0.0706972i	$-0.977478\pi$
$727$	−1.20185e6	−	6.81604e6i	−0.0843364	−	0.478295i	0.913161	−	0.407598i	$-0.133634\pi$
$728$		0			0
$729$	−1.40029e7	−	3.13207e6i	−0.975886	−	0.218280i
$730$		0			0
$731$	1.39567e6	+	7.91525e6i	0.0966028	+	0.547862i
$732$		0			0
$733$	6.60066e6	−	2.40245e6i	0.453762	−	0.165156i	−0.105021	−	0.994470i	$-0.533491\pi$
$733$	6.60066e6	−	2.40245e6i	0.453762	−	0.165156i	0.558782	+	0.829314i	$0.311269\pi$
$734$		0			0
$735$	1.82775e7	−	2.53578e6i	1.24795	−	0.173138i
$736$		0			0
$737$	102679.	+	177845.i	0.00696325	+	0.0120607i
$738$		0			0
$739$	3.89884e6	−	6.75299e6i	0.262618	−	0.454867i	−0.704319	−	0.709884i	$-0.748747\pi$
$739$	3.89884e6	−	6.75299e6i	0.262618	−	0.454867i	0.966937	+	0.255016i	$0.0820808\pi$
$740$		0			0
$741$	1.85955e6	+	5.75773e6i	0.124412	+	0.385217i
$742$		0			0
$743$	−1.73621e6	+	9.84652e6i	−0.115380	+	0.654351i	0.871182	+	0.490961i	$0.163354\pi$
$743$	−1.73621e6	+	9.84652e6i	−0.115380	+	0.654351i	−0.986562	+	0.163390i	$0.947757\pi$
$744$		0			0
$745$	−1.75985e7	+	1.47669e7i	−1.16168	+	0.974763i
$746$		0			0
$747$	2.74876e6	+	2.70735e7i	0.180233	+	1.77519i
$748$		0			0
$749$	141351.	+	51447.6i	0.00920650	+	0.00335089i
$750$		0			0
$751$	1.09778e7	+	9.21146e6i	0.710257	+	0.595976i	0.924671	−	0.380767i	$-0.124340\pi$
$751$	1.09778e7	+	9.21146e6i	0.710257	+	0.595976i	−0.214414	+	0.976743i	$0.568784\pi$
$752$		0			0
$753$	2.25490e7	−	1.19384e7i	1.44924	−	0.767289i
$754$		0			0
$755$	−1.84774e7			−1.17970
$756$		0			0
$757$	−2.76566e7			−1.75412			−0.877061	−	0.480380i	$-0.840499\pi$
$757$	−2.76566e7			−1.75412			−0.877061	+	0.480380i	$0.840499\pi$
$758$		0			0
$759$	−89484.8	−	56136.6i	−0.00563826	−	0.00353705i
$760$		0			0
$761$	2.19308e7	+	1.84021e7i	1.37275	+	1.15188i	0.971807	+	0.235776i	$0.0757632\pi$
$761$	2.19308e7	+	1.84021e7i	1.37275	+	1.15188i	0.400947	+	0.916101i	$0.368681\pi$
$762$		0			0
$763$	5.33319e6	+	1.94112e6i	0.331646	+	0.120709i
$764$		0			0
$765$	8.02240e6	−	2.26971e6i	0.495622	−	0.140222i
$766$		0			0
$767$	3.66836e6	−	3.07812e6i	0.225156	−	0.188928i
$768$		0			0
$769$	−3.80373e6	+	2.15720e7i	−0.231950	+	1.31545i	0.616994	+	0.786968i	$0.288350\pi$
$769$	−3.80373e6	+	2.15720e7i	−0.231950	+	1.31545i	−0.848943	+	0.528484i	$0.822761\pi$
$770$		0			0
$771$	1.55017e6	+	332366.i	0.0939170	+	0.0201364i
$772$		0			0
$773$	−1.59183e7	+	2.75712e7i	−0.958179	+	1.65961i	−0.231260	+	0.972892i	$0.574285\pi$
$773$	−1.59183e7	+	2.75712e7i	−0.958179	+	1.65961i	−0.726919	+	0.686723i	$0.759049\pi$
$774$		0			0
$775$	−295822.	−	512380.i	−0.0176920	−	0.0306434i
$776$		0			0
$777$	−1.40935e6	−	1.81048e6i	−0.0837466	−	0.107582i
$778$		0			0
$779$	−2.68948e7	+	9.78891e6i	−1.58791	+	0.577950i
$780$		0			0
$781$	194412.	+	1.10257e6i	0.0114050	+	0.0646810i
$782$		0			0
$783$	3.68061e6	−	237756.i	0.214544	−	0.0138589i
$784$		0			0
$785$	−837737.	−	4.75105e6i	−0.0485215	−	0.275179i
$786$		0			0
$787$	−1.17155e7	+	4.26410e6i	−0.674255	+	0.245409i	−0.656379	−	0.754431i	$-0.727913\pi$
$787$	−1.17155e7	+	4.26410e6i	−0.674255	+	0.245409i	−0.0178764	+	0.999840i	$0.505691\pi$
$788$		0			0
$789$	−4.81605e6	+	1.18597e7i	−0.275422	+	0.678237i
$790$		0			0
$791$	260149.	+	450591.i	0.0147836	+	0.0256060i
$792$		0			0
$793$	2.30982e6	−	4.00073e6i	0.130435	−	0.225921i
$794$		0			0
$795$	−1.12017e7	+	1.23966e7i	−0.628589	+	0.695640i
$796$		0			0
$797$	4.78336e6	−	2.71278e7i	0.266739	−	1.51275i	−0.497297	−	0.867581i	$-0.665674\pi$
$797$	4.78336e6	−	2.71278e7i	0.266739	−	1.51275i	0.764036	−	0.645174i	$-0.223215\pi$
$798$		0			0
$799$	−6.52988e6	+	5.47922e6i	−0.361858	+	0.303635i
$800$		0			0
$801$	4.60443e6	+	9.52585e6i	0.253568	+	0.524593i
$802$		0			0
$803$	−938895.	−	341730.i	−0.0513840	−	0.0187022i
$804$		0			0
$805$	−598347.	−	502073.i	−0.0325434	−	0.0273072i
$806$		0			0
$807$	648761.	−	1.76814e7i	0.0350672	−	0.955726i
$808$		0			0
$809$	−2.91992e7			−1.56855			−0.784277	−	0.620411i	$-0.786966\pi$
$809$	−2.91992e7			−1.56855			−0.784277	+	0.620411i	$0.786966\pi$
$810$		0			0
$811$	−8.05513e6			−0.430051			−0.215026	−	0.976608i	$-0.568984\pi$
$811$	−8.05513e6			−0.430051			−0.215026	+	0.976608i	$0.568984\pi$
$812$		0			0
$813$	626047.	−	1.70624e7i	0.0332185	−	0.905343i
$814$		0			0
$815$	2.57128e7	+	2.15756e7i	1.35599	+	1.13781i
$816$		0			0
$817$	−3.27732e7	−	1.19285e7i	−1.71776	−	0.625215i
$818$		0			0
$819$	−654968.	+	963659.i	−0.0341201	+	0.0502011i
$820$		0			0
$821$	1.97442e7	−	1.65674e7i	1.02231	−	0.857819i	0.0323929	−	0.999475i	$-0.489687\pi$
$821$	1.97442e7	−	1.65674e7i	1.02231	−	0.857819i	0.989916	+	0.141656i	$0.0452428\pi$
$822$		0			0
$823$	2.28705e6	−	1.29705e7i	0.117700	−	0.667510i	−0.867678	−	0.497127i	$-0.834388\pi$
$823$	2.28705e6	−	1.29705e7i	0.117700	−	0.667510i	0.985378	−	0.170383i	$-0.0545006\pi$
$824$		0			0
$825$	−371963.	+	411640.i	−0.0190268	+	0.0210564i
$826$		0			0
$827$	6.92826e6	−	1.20001e7i	0.352258	−	0.610128i	−0.634387	−	0.773016i	$-0.718747\pi$
$827$	6.92826e6	−	1.20001e7i	0.352258	−	0.610128i	0.986645	+	0.162887i	$0.0520807\pi$
$828$		0			0
$829$	−5.06848e6	−	8.77886e6i	−0.256148	−	0.443661i	0.709059	−	0.705150i	$-0.249120\pi$
$829$	−5.06848e6	−	8.77886e6i	−0.256148	−	0.443661i	−0.965207	+	0.261488i	$0.915787\pi$
$830$		0			0
$831$	894803.	−	2.20349e6i	0.0449495	−	0.110690i
$832$		0			0
$833$	−7.12623e6	+	2.59374e6i	−0.355834	+	0.129513i
$834$		0			0
$835$	5.70703e6	+	3.23662e7i	0.283266	+	1.60648i
$836$		0			0
$837$	−237903.	−	976213.i	−0.0117378	−	0.0481649i
$838$		0			0
$839$	−1.44120e6	−	8.17348e6i	−0.0706839	−	0.400868i	−0.999537	−	0.0304206i	$-0.990315\pi$
$839$	−1.44120e6	−	8.17348e6i	−0.0706839	−	0.400868i	0.928853	−	0.370448i	$-0.120796\pi$
$840$		0			0
$841$	1.83833e7	−	6.69098e6i	0.896259	−	0.326212i
$842$		0			0
$843$	1.75553e7	+	2.25519e7i	0.850825	+	1.09299i
$844$		0			0
$845$	−1.22539e7	−	2.12244e7i	−0.590382	−	1.02257i
$846$		0			0
$847$	2.02058e6	−	3.49975e6i	0.0967760	−	0.167621i
$848$		0			0
$849$	−7.91746e6	−	1.69755e6i	−0.376979	−	0.0808264i
$850$		0			0
$851$	431887.	−	2.44935e6i	0.0204431	−	0.115938i
$852$		0			0
$853$	−1.73903e7	+	1.45922e7i	−0.818340	+	0.686669i	−0.952583	−	0.304279i	$-0.901584\pi$
$853$	−1.73903e7	+	1.45922e7i	−0.818340	+	0.686669i	0.134242	+	0.990949i	$0.457140\pi$
$854$		0			0
$855$	−8.87638e6	+	3.50722e7i	−0.415260	+	1.64077i
$856$		0			0
$857$	−3.52078e7	−	1.28146e7i	−1.63752	−	0.596009i	−0.650918	−	0.759148i	$-0.725616\pi$
$857$	−3.52078e7	−	1.28146e7i	−1.63752	−	0.596009i	−0.986603	+	0.163139i	$0.947838\pi$
$858$		0			0
$859$	4.57370e6	+	3.83779e6i	0.211487	+	0.177459i	0.742378	−	0.669982i	$-0.233698\pi$
$859$	4.57370e6	+	3.83779e6i	0.211487	+	0.177459i	−0.530890	+	0.847440i	$0.678142\pi$
$860$		0			0
$861$	−4.66891e6	−	2.92895e6i	−0.214638	−	0.134649i
$862$		0			0
$863$	3.64995e7			1.66825			0.834123	−	0.551578i	$-0.185974\pi$
$863$	3.64995e7			1.66825			0.834123	+	0.551578i	$0.185974\pi$
$864$		0			0
$865$	1.94620e7			0.884395
$866$		0			0
$867$	1.65328e7	−	8.75315e6i	0.746960	−	0.395473i
$868$		0			0
$869$	−293939.	−	246644.i	−0.0132041	−	0.0110795i
$870$		0			0
$871$	2.30735e6	+	839807.i	0.103055	+	0.0375089i
$872$		0			0
$873$	9.32711e6	−	6.72626e6i	0.414201	−	0.298702i
$874$		0			0
$875$	1.26030e6	−	1.05752e6i	0.0556485	−	0.0466946i
$876$		0			0
$877$	−6.59763e6	+	3.74170e7i	−0.289660	+	1.64274i	0.398487	+	0.917174i	$0.369535\pi$
$877$	−6.59763e6	+	3.74170e7i	−0.289660	+	1.64274i	−0.688148	+	0.725571i	$0.741576\pi$
$878$		0			0
$879$	1.49725e6	+	4.63594e6i	0.0653614	+	0.202379i
$880$		0			0
$881$	1.92127e7	−	3.32773e7i	0.833965	−	1.44447i	−0.0609051	−	0.998144i	$-0.519399\pi$
$881$	1.92127e7	−	3.32773e7i	0.833965	−	1.44447i	0.894870	−	0.446326i	$-0.147268\pi$
$882$		0			0
$883$	1.31016e7	+	2.26926e7i	0.565486	+	0.979451i	0.997004	+	0.0773465i	$0.0246448\pi$
$883$	1.31016e7	+	2.26926e7i	0.565486	+	0.979451i	−0.431518	+	0.902104i	$0.642022\pi$
$884$		0			0
$885$	2.83614e7	−	3.93479e6i	1.21722	−	0.168874i
$886$		0			0
$887$	−2.68252e7	+	9.76357e6i	−1.14481	+	0.416677i	−0.843649	−	0.536896i	$-0.819597\pi$
$887$	−2.68252e7	+	9.76357e6i	−1.14481	+	0.416677i	−0.301162	+	0.953573i	$0.597375\pi$
$888$		0			0
$889$	−662661.	−	3.75813e6i	−0.0281214	−	0.159484i
$890$		0			0
$891$	−802554.	+	493631.i	−0.0338672	+	0.0208309i
$892$		0			0
$893$	−6.42305e6	−	3.64269e7i	−0.269533	−	1.52860i
$894$		0			0
$895$	−3.25444e6	+	1.18452e6i	−0.135806	+	0.0494293i
$896$		0			0
$897$	−1.25108e6	+	173573.i	−0.0519165	+	0.00720278i
$898$		0			0
$899$	129136.	+	223670.i	0.00532904	+	0.00923016i
$900$		0			0
$901$	3.43328e6	−	5.94662e6i	0.140896	−	0.244038i
$902$		0			0
$903$	−2.06413e6	−	6.39118e6i	−0.0842399	−	0.260833i
$904$		0			0
$905$	8.37064e6	−	4.74722e7i	0.339733	−	1.92672i
$906$		0			0
$907$	−2.69407e6	+	2.26060e6i	−0.108741	+	0.0912441i	−0.695537	−	0.718490i	$-0.744833\pi$
$907$	−2.69407e6	+	2.26060e6i	−0.108741	+	0.0912441i	0.586796	+	0.809735i	$0.300389\pi$
$908$		0			0
$909$	1.27627e7	+	5.73650e6i	0.512310	+	0.230270i
$910$		0			0
$911$	3.29019e7	+	1.19753e7i	1.31348	+	0.478069i	0.901364	−	0.433061i	$-0.142567\pi$
$911$	3.29019e7	+	1.19753e7i	1.31348	+	0.478069i	0.412119	+	0.911130i	$0.364789\pi$
$912$		0			0
$913$	1.36885e6	+	1.14860e6i	0.0543474	+	0.0456029i
$914$		0			0
$915$	2.44118e7	−	1.29247e7i	0.963934	−	0.510348i
$916$		0			0
$917$	1.34005e6			0.0526256
$918$		0			0
$919$	−8.14629e6			−0.318179			−0.159089	−	0.987264i	$-0.550856\pi$
$919$	−8.14629e6			−0.318179			−0.159089	+	0.987264i	$0.550856\pi$
$920$		0			0
$921$	3.18235e7	+	1.99639e7i	1.23623	+	0.775525i
$922$		0			0
$923$	1.02547e7	+	8.60474e6i	0.396205	+	0.332455i
$924$		0			0
$925$	−1.22748e7	−	4.46765e6i	−0.471693	−	0.171682i
$926$		0			0
$927$	7.22790e6	+	7.02948e6i	0.276257	+	0.268673i
$928$		0			0
$929$	1.18959e7	−	9.98183e6i	0.452228	−	0.379464i	−0.388034	−	0.921645i	$-0.626846\pi$
$929$	1.18959e7	−	9.98183e6i	0.452228	−	0.379464i	0.840262	+	0.542181i	$0.182401\pi$
$930$		0			0
$931$	5.71432e6	−	3.24075e7i	0.216068	−	1.22538i
$932$		0			0
$933$	−3.80051e7	−	8.14851e6i	−1.42935	−	0.306460i
$934$		0			0
$935$	273732.	−	474117.i	0.0102399	−	0.0177360i
$936$		0			0
$937$	8.97785e6	+	1.55501e7i	0.334059	+	0.578608i	0.983304	−	0.181972i	$-0.0582481\pi$
$937$	8.97785e6	+	1.55501e7i	0.334059	+	0.578608i	−0.649244	+	0.760580i	$0.724915\pi$
$938$		0			0
$939$	−1.94598e7	−	2.49984e7i	−0.720234	−	0.925226i
$940$		0			0
$941$	−2.65685e7	+	9.67016e6i	−0.978123	+	0.356008i	−0.781110	−	0.624393i	$-0.785346\pi$
$941$	−2.65685e7	+	9.67016e6i	−0.978123	+	0.356008i	−0.197013	+	0.980401i	$0.563124\pi$
$942$		0			0
$943$	−1.03749e6	−	5.88389e6i	−0.0379930	−	0.215469i
$944$		0			0
$945$	−6.37951e6	+	2.79988e6i	−0.232385	+	0.101990i
$946$		0			0
$947$	−6.34551e6	−	3.59872e7i	−0.229928	−	1.30399i	−0.853037	−	0.521851i	$-0.825242\pi$
$947$	−6.34551e6	−	3.59872e7i	−0.229928	−	1.30399i	0.623109	−	0.782135i	$-0.285869\pi$
$948$		0			0
$949$	−1.12262e7	+	4.08601e6i	−0.404639	+	0.147277i
$950$		0			0
$951$	780358.	−	1.92166e6i	0.0279797	−	0.0689010i
$952$		0			0
$953$	−1.89374e7	−	3.28005e7i	−0.675442	−	1.16990i	−0.976340	−	0.216243i	$-0.930620\pi$
$953$	−1.89374e7	−	3.28005e7i	−0.675442	−	1.16990i	0.300898	−	0.953656i	$-0.402714\pi$
$954$		0			0
$955$	−2.98878e6	+	5.17671e6i	−0.106044	+	0.183673i
$956$		0			0
$957$	162374.	−	179695.i	0.00573108	−	0.00634242i
$958$		0			0
$959$	1.80003e6	−	1.02085e7i	0.0632023	−	0.358438i
$960$		0			0
$961$	−2.18773e7	+	1.83572e7i	−0.764162	+	0.641208i
$962$		0			0
$963$	1.45051e6	+	106587.i	0.0504028	+	0.00370371i
$964$		0			0
$965$	−2.89500e7	−	1.05370e7i	−1.00076	−	0.364248i
$966$		0			0
$967$	−3.54347e7	−	2.97333e7i	−1.21861	−	1.02253i	−0.998896	−	0.0469659i	$-0.985045\pi$
$967$	−3.54347e7	−	2.97333e7i	−1.21861	−	1.02253i	−0.219709	−	0.975565i	$-0.570511\pi$
$968$		0			0
$969$	545177.	−	1.48583e7i	0.0186521	−	0.508348i
$970$		0			0
$971$	1.57071e7			0.534624			0.267312	−	0.963610i	$-0.413865\pi$
$971$	1.57071e7			0.534624			0.267312	+	0.963610i	$0.413865\pi$
$972$		0			0
$973$	9.38911e6			0.317938
$974$		0			0
$975$	−243237.	+	6.62922e6i	−0.00819442	+	0.223332i
$976$		0			0
$977$	3.09223e7	+	2.59469e7i	1.03642	+	0.869660i	0.991601	−	0.129335i	$-0.0412844\pi$
$977$	3.09223e7	+	2.59469e7i	1.03642	+	0.869660i	0.0448192	+	0.998995i	$0.485729\pi$
$978$		0			0
$979$	652850.	+	237618.i	0.0217699	+	0.00792360i
$980$		0			0
$981$	5.47278e7	+	4.02152e6i	1.81566	+	0.133419i
$982$		0			0
$983$	−1.83981e7	+	1.54378e7i	−0.607280	+	0.509568i	−0.893776	−	0.448513i	$-0.851954\pi$
$983$	−1.83981e7	+	1.54378e7i	−0.607280	+	0.509568i	0.286496	+	0.958081i	$0.407509\pi$
$984$		0			0
$985$	4.29148e6	−	2.43382e7i	0.140934	−	0.799278i
$986$		0			0
$987$	4.77558e6	−	5.28500e6i	0.156039	−	0.172684i
$988$		0			0
$989$	3.64027e6	−	6.30513e6i	0.118343	−	0.204976i
$990$		0			0
$991$	−1.94066e7	−	3.36132e7i	−0.627718	−	1.08724i	−0.988008	−	0.154400i	$-0.950656\pi$
$991$	−1.94066e7	−	3.36132e7i	−0.627718	−	1.08724i	0.360290	−	0.932840i	$-0.382678\pi$
$992$		0			0
$993$	1.48317e7	−	3.65235e7i	0.477327	−	1.17544i
$994$		0			0
$995$	−4.35396e7	+	1.58471e7i	−1.39420	+	0.507449i
$996$		0			0
$997$	−2.45504e6	−	1.39232e7i	−0.0782205	−	0.443610i	−0.998615	−	0.0526187i	$-0.983243\pi$
$997$	−2.45504e6	−	1.39232e7i	−0.0782205	−	0.443610i	0.920394	−	0.390992i	$-0.127868\pi$
$998$		0			0
$999$	−1.78778e7	−	1.31345e7i	−0.566761	−	0.416388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.i.a.13.9	✓	90
3.2	odd	2		324.6.i.a.253.12		90
27.2	odd	18		324.6.i.a.73.12		90
27.25	even	9	inner	108.6.i.a.25.9	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.i.a.13.9	✓	90	1.1	even	1	trivial
108.6.i.a.25.9	yes	90	27.25	even	9	inner
324.6.i.a.73.12		90	27.2	odd	18
324.6.i.a.253.12		90	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.571582 - 15.5780i) q^{3} +(-56.0600 - 47.0399i) q^{5} +(-23.6165 - 8.59570i) q^{7} +(-242.347 - 17.8082i) q^{9} +O(q^{10})\)	\(q+(0.571582 - 15.5780i) q^{3} +(-56.0600 - 47.0399i) q^{5} +(-23.6165 - 8.59570i) q^{7} +(-242.347 - 17.8082i) q^{9} +(-12.2234 + 10.2566i) q^{11} +(-33.1302 + 187.890i) q^{13} +(-764.830 + 846.414i) q^{15} +(234.417 - 406.023i) q^{17} +(1017.21 + 1761.86i) q^{19} +(-147.402 + 362.984i) q^{21} +(-399.076 + 145.252i) q^{23} +(387.319 + 2196.59i) q^{25} +(-415.936 + 3765.09i) q^{27} +(-169.077 - 958.884i) q^{29} +(-249.258 + 90.7225i) q^{31} +(152.791 + 196.278i) q^{33} +(919.600 + 1592.79i) q^{35} +(-2928.19 + 5071.78i) q^{37} +(2908.02 + 623.495i) q^{39} +(-2442.94 + 13854.6i) q^{41} +(-13132.5 + 11019.5i) q^{43} +(12748.3 + 12398.3i) q^{45} +(-17085.1 - 6218.46i) q^{47} +(-12391.1 - 10397.3i) q^{49} +(-6191.02 - 3883.82i) q^{51} +14646.0 q^{53} +1167.71 q^{55} +(28027.6 - 14839.0i) q^{57} +(-19227.3 - 16133.6i) q^{59} +(-22753.1 - 8281.46i) q^{61} +(5570.30 + 2503.71i) q^{63} +(10695.6 - 8974.70i) q^{65} +(2234.83 - 12674.4i) q^{67} +(2034.63 + 6299.83i) q^{69} +(35082.2 - 60764.2i) q^{71} +(31308.7 + 54228.2i) q^{73} +(34439.8 - 4778.11i) q^{75} +(376.836 - 137.157i) q^{77} +(4175.78 + 23682.0i) q^{79} +(58414.7 + 8631.50i) q^{81} +(-19446.3 - 110285. i) q^{83} +(-32240.7 + 11734.7i) q^{85} +(-15034.1 + 2085.80i) q^{87} +(-21770.1 - 37707.0i) q^{89} +(2397.47 - 4152.54i) q^{91} +(1270.80 + 3934.79i) q^{93} +(25852.9 - 146619. i) q^{95} +(-36251.4 + 30418.6i) q^{97} +(3144.94 - 2267.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 87 q^{5} + 330 q^{9}+O(q^{10}) \) 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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