LMFDB - Embedded newform 912.2.bn.n.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Root			$1.66415 + 0.480229i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.n.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.416182 + 1.68131i) q^{3} +(-2.52758 - 1.45930i) q^{5} -0.106684 q^{7} +(-2.65359 + 1.39946i) q^{9} +O(q^{10})$	\(q+(0.416182 + 1.68131i) q^{3} +(-2.52758 - 1.45930i) q^{5} -0.106684 q^{7} +(-2.65359 + 1.39946i) q^{9} +0.387102i q^{11} +(-0.750981 + 0.433579i) q^{13} +(1.40160 - 4.85698i) q^{15} +(-2.03600 - 1.17548i) q^{17} +(1.50709 - 4.09007i) q^{19} +(-0.0443998 - 0.179368i) q^{21} +(4.19115 - 2.41976i) q^{23} +(1.75912 + 3.04689i) q^{25} +(-3.45729 - 3.87906i) q^{27} +(-4.23115 - 7.32856i) q^{29} -7.85306i q^{31} +(-0.650837 + 0.161105i) q^{33} +(0.269652 + 0.155684i) q^{35} +0.670104i q^{37} +(-1.04152 - 1.08218i) q^{39} +(0.717537 - 1.24281i) q^{41} +(-3.67525 + 6.36573i) q^{43} +(8.74939 + 0.335132i) q^{45} +(3.41859 - 1.97372i) q^{47} -6.98862 q^{49} +(1.12900 - 3.91235i) q^{51} +(-3.76741 - 6.52534i) q^{53} +(0.564898 - 0.978432i) q^{55} +(7.50389 + 0.831661i) q^{57} +(-3.53312 + 6.11954i) q^{59} +(-5.65069 - 9.78729i) q^{61} +(0.283095 - 0.149300i) q^{63} +2.53089 q^{65} +(-6.42436 + 3.70911i) q^{67} +(5.81264 + 6.03955i) q^{69} +(3.47097 - 6.01190i) q^{71} +(3.57752 - 6.19644i) q^{73} +(-4.39064 + 4.22569i) q^{75} -0.0412975i q^{77} +(13.2195 + 7.63230i) q^{79} +(5.08303 - 7.42717i) q^{81} +6.15558i q^{83} +(3.43077 + 5.94226i) q^{85} +(10.5606 - 10.1639i) q^{87} +(8.09570 + 14.0222i) q^{89} +(0.0801175 - 0.0462558i) q^{91} +(13.2034 - 3.26830i) q^{93} +(-9.77794 + 8.13871i) q^{95} +(-3.56089 - 2.05588i) q^{97} +(-0.541733 - 1.02721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9	$ 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) $ 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$	0.416182	+	1.68131i	0.240283	+	0.970703i
$3$	0.416182	+	1.68131i	0.240283	+	0.970703i
$4$		0			0
$5$	−2.52758	−	1.45930i	−1.13037	−	0.652620i	−0.186342	−	0.982485i	$-0.559663\pi$
$5$	−2.52758	−	1.45930i	−1.13037	−	0.652620i	−0.944028	+	0.329865i	$0.892997\pi$
$6$		0			0
$7$	−0.106684			−0.0403227			−0.0201613	−	0.999797i	$-0.506418\pi$
$7$	−0.106684			−0.0403227			−0.0201613	+	0.999797i	$0.506418\pi$
$8$		0			0
$9$	−2.65359	+	1.39946i	−0.884528	+	0.466486i
$10$		0			0
$11$			0.387102i			0.116716i	0.998296	+	0.0583578i	$0.0185864\pi$
$11$			0.387102i			0.116716i	−0.998296	+	0.0583578i	$0.981414\pi$
$12$		0			0
$13$	−0.750981	+	0.433579i	−0.208285	+	0.120253i	−0.600514	−	0.799614i	$-0.705037\pi$
$13$	−0.750981	+	0.433579i	−0.208285	+	0.120253i	0.392229	+	0.919867i	$0.371704\pi$
$14$		0			0
$15$	1.40160	−	4.85698i	0.361891	−	1.25407i
$16$		0			0
$17$	−2.03600	−	1.17548i	−0.493801	−	0.285096i	0.232349	−	0.972633i	$-0.425359\pi$
$17$	−2.03600	−	1.17548i	−0.493801	−	0.285096i	−0.726150	+	0.687536i	$0.758692\pi$
$18$		0			0
$19$	1.50709	−	4.09007i	0.345749	−	0.938327i
$19$	1.50709	−	4.09007i	0.345749	−	0.938327i
$20$		0			0
$21$	−0.0443998	−	0.179368i	−0.00968884	−	0.0391413i
$22$		0			0
$23$	4.19115	−	2.41976i	0.873915	−	0.504555i	0.00526762	−	0.999986i	$-0.498323\pi$
$23$	4.19115	−	2.41976i	0.873915	−	0.504555i	0.868647	+	0.495431i	$0.164990\pi$
$24$		0			0
$25$	1.75912	+	3.04689i	0.351825	+	0.609378i
$26$		0			0
$27$	−3.45729	−	3.87906i	−0.665356	−	0.746526i
$28$		0			0
$29$	−4.23115	−	7.32856i	−0.785705	−	1.36088i	−0.928577	−	0.371139i	$-0.878967\pi$
$29$	−4.23115	−	7.32856i	−0.785705	−	1.36088i	0.142873	−	0.989741i	$-0.454366\pi$
$30$		0			0
$31$		−	7.85306i		−	1.41045i	−0.708983	−	0.705226i	$-0.750846\pi$
$31$		−	7.85306i		−	1.41045i	0.708983	−	0.705226i	$-0.249154\pi$
$32$		0			0
$33$	−0.650837	+	0.161105i	−0.113296	+	0.0280447i
$34$		0			0
$35$	0.269652	+	0.155684i	0.0455796	+	0.0263154i
$36$		0			0
$37$			0.670104i			0.110164i	0.998482	+	0.0550822i	$0.0175421\pi$
$37$			0.670104i			0.110164i	−0.998482	+	0.0550822i	$0.982458\pi$
$38$		0			0
$39$	−1.04152	−	1.08218i	−0.166777	−	0.173288i
$40$		0			0
$41$	0.717537	−	1.24281i	0.112061	−	0.194095i	−0.804540	−	0.593898i	$-0.797588\pi$
$41$	0.717537	−	1.24281i	0.112061	−	0.194095i	0.916601	+	0.399803i	$0.130922\pi$
$42$		0			0
$43$	−3.67525	+	6.36573i	−0.560471	+	0.970764i	0.436984	+	0.899469i	$0.356047\pi$
$43$	−3.67525	+	6.36573i	−0.560471	+	0.970764i	−0.997455	+	0.0712952i	$0.977287\pi$
$44$		0			0
$45$	8.74939	+	0.335132i	1.30428	+	0.0499585i
$46$		0			0
$47$	3.41859	−	1.97372i	0.498652	−	0.287897i	−0.229505	−	0.973308i	$-0.573711\pi$
$47$	3.41859	−	1.97372i	0.498652	−	0.287897i	0.728157	+	0.685411i	$0.240377\pi$
$48$		0			0
$49$	−6.98862			−0.998374
$50$		0			0
$51$	1.12900	−	3.91235i	0.158092	−	0.547838i
$52$		0			0
$53$	−3.76741	−	6.52534i	−0.517493	−	0.896324i	−0.999794	−	0.0203184i	$-0.993532\pi$
$53$	−3.76741	−	6.52534i	−0.517493	−	0.896324i	0.482301	−	0.876006i	$-0.339801\pi$
$54$		0			0
$55$	0.564898	−	0.978432i	0.0761708	−	0.131932i
$56$		0			0
$57$	7.50389	+	0.831661i	0.993914	+	0.110156i
$58$		0			0
$59$	−3.53312	+	6.11954i	−0.459973	+	0.796696i	−0.998959	−	0.0456183i	$-0.985474\pi$
$59$	−3.53312	+	6.11954i	−0.459973	+	0.796696i	0.538986	+	0.842315i	$0.318808\pi$
$60$		0			0
$61$	−5.65069	−	9.78729i	−0.723497	−	1.25313i	−0.959590	−	0.281403i	$-0.909200\pi$
$61$	−5.65069	−	9.78729i	−0.723497	−	1.25313i	0.236092	−	0.971731i	$-0.424133\pi$
$62$		0			0
$63$	0.283095	−	0.149300i	0.0356666	−	0.0188100i
$64$		0			0
$65$	2.53089			0.313918
$66$		0			0
$67$	−6.42436	+	3.70911i	−0.784861	+	0.453139i	−0.838150	−	0.545440i	$-0.816363\pi$
$67$	−6.42436	+	3.70911i	−0.784861	+	0.453139i	0.0532895	+	0.998579i	$0.483029\pi$
$68$		0			0
$69$	5.81264	+	6.03955i	0.699760	+	0.727076i
$70$		0			0
$71$	3.47097	−	6.01190i	0.411928	−	0.713481i	−0.583172	−	0.812349i	$-0.698189\pi$
$71$	3.47097	−	6.01190i	0.411928	−	0.713481i	0.995101	+	0.0988677i	$0.0315221\pi$
$72$		0			0
$73$	3.57752	−	6.19644i	0.418717	−	0.725239i	−0.577094	−	0.816678i	$-0.695813\pi$
$73$	3.57752	−	6.19644i	0.418717	−	0.725239i	0.995811	+	0.0914389i	$0.0291466\pi$
$74$		0			0
$75$	−4.39064	+	4.22569i	−0.506988	+	0.487940i
$76$		0			0
$77$		−	0.0412975i		−	0.00470628i
$78$		0			0
$79$	13.2195	+	7.63230i	1.48731	+	0.858701i	0.999895	−	0.0144674i	$-0.00460526\pi$
$79$	13.2195	+	7.63230i	1.48731	+	0.858701i	0.487419	+	0.873168i	$0.337939\pi$
$80$		0			0
$81$	5.08303	−	7.42717i	0.564781	−	0.825241i
$82$		0			0
$83$			6.15558i			0.675663i	0.941207	+	0.337831i	$0.109693\pi$
$83$			6.15558i			0.675663i	−0.941207	+	0.337831i	$0.890307\pi$
$84$		0			0
$85$	3.43077	+	5.94226i	0.372119	+	0.644529i
$86$		0			0
$87$	10.5606	−	10.1639i	1.13222	−	1.08968i
$88$		0			0
$89$	8.09570	+	14.0222i	0.858142	+	1.48635i	0.873699	+	0.486467i	$0.161715\pi$
$89$	8.09570	+	14.0222i	0.858142	+	1.48635i	−0.0155569	+	0.999879i	$0.504952\pi$
$90$		0			0
$91$	0.0801175	−	0.0462558i	0.00839859	−	0.00484893i
$92$		0			0
$93$	13.2034	−	3.26830i	1.36913	−	0.338907i
$94$		0			0
$95$	−9.77794	+	8.13871i	−1.00320	+	0.835014i
$96$		0			0
$97$	−3.56089	−	2.05588i	−0.361554	−	0.208743i	0.308208	−	0.951319i	$-0.400271\pi$
$97$	−3.56089	−	2.05588i	−0.361554	−	0.208743i	−0.669762	+	0.742576i	$0.733604\pi$
$98$		0			0
$99$	−0.541733	−	1.02721i	−0.0544462	−	0.103238i
$100$		0			0
$101$	−0.676205	+	0.390407i	−0.0672849	+	0.0388470i	−0.533265	−	0.845948i	$-0.679035\pi$
$101$	−0.676205	+	0.390407i	−0.0672849	+	0.0388470i	0.465980	+	0.884795i	$0.345702\pi$
$102$		0			0
$103$			3.97989i			0.392151i	0.980589	+	0.196075i	$0.0628197\pi$
$103$			3.97989i			0.392151i	−0.980589	+	0.196075i	$0.937180\pi$
$104$		0			0
$105$	−0.149528	+	0.518161i	−0.0145924	+	0.0505673i
$106$		0			0
$107$	2.25561			0.218058			0.109029	−	0.994039i	$-0.465226\pi$
$107$	2.25561			0.218058			0.109029	+	0.994039i	$0.465226\pi$
$108$		0			0
$109$	−10.0591	−	5.80760i	−0.963483	−	0.556267i	−0.0662396	−	0.997804i	$-0.521100\pi$
$109$	−10.0591	−	5.80760i	−0.963483	−	0.556267i	−0.897243	+	0.441537i	$0.854433\pi$
$110$		0			0
$111$	−1.12665	+	0.278885i	−0.106937	+	0.0264706i
$112$		0			0
$113$	−9.76446			−0.918564			−0.459282	−	0.888291i	$-0.651893\pi$
$113$	−9.76446			−0.918564			−0.459282	+	0.888291i	$0.651893\pi$
$114$		0			0
$115$	−14.1246			−1.31713
$116$		0			0
$117$	1.38602	−	2.20150i	0.128137	−	0.203529i
$118$		0			0
$119$	0.217208	+	0.125405i	0.0199114	+	0.0114958i
$120$		0			0
$121$	10.8502			0.986377
$122$		0			0
$123$	2.38817	+	0.689165i	0.215334	+	0.0621399i
$124$		0			0
$125$			4.32465i			0.386809i
$126$		0			0
$127$	−14.5273	+	8.38732i	−1.28909	+	0.744254i	−0.978491	−	0.206288i	$-0.933862\pi$
$127$	−14.5273	+	8.38732i	−1.28909	+	0.744254i	−0.310595	+	0.950542i	$0.600528\pi$
$128$		0			0
$129$	−12.2323	−	3.52993i	−1.07700	−	0.310793i
$130$		0			0
$131$	−1.39311	−	0.804315i	−0.121717	−	0.0702733i	0.437905	−	0.899021i	$-0.355720\pi$
$131$	−1.39311	−	0.804315i	−0.121717	−	0.0702733i	−0.559622	+	0.828748i	$0.689054\pi$
$132$		0			0
$133$	−0.160782	+	0.436344i	−0.0139415	+	0.0378359i
$134$		0			0
$135$	3.07788	+	14.8499i	0.264902	+	1.27808i
$136$		0			0
$137$	11.2480	−	6.49401i	0.960977	−	0.554820i	0.0645036	−	0.997917i	$-0.479454\pi$
$137$	11.2480	−	6.49401i	0.960977	−	0.554820i	0.896474	+	0.443097i	$0.146120\pi$
$138$		0			0
$139$	−10.4726	−	18.1391i	−0.888273	−	1.53853i	−0.841915	−	0.539610i	$-0.818572\pi$
$139$	−10.4726	−	18.1391i	−0.888273	−	1.53853i	−0.0463581	−	0.998925i	$-0.514762\pi$
$140$		0			0
$141$	4.74119	+	4.92627i	0.399280	+	0.414866i
$142$		0			0
$143$	−0.167839	−	0.290706i	−0.0140354	−	0.0243100i
$144$		0			0
$145$			24.6981i			2.05106i
$146$		0			0
$147$	−2.90854	−	11.7500i	−0.239892	−	0.969125i
$148$		0			0
$149$	−8.83346	−	5.10000i	−0.723665	−	0.417808i	0.0924352	−	0.995719i	$-0.470535\pi$
$149$	−8.83346	−	5.10000i	−0.723665	−	0.417808i	−0.816100	+	0.577911i	$0.803868\pi$
$150$		0			0
$151$			15.7703i			1.28337i	0.766970	+	0.641683i	$0.221763\pi$
$151$			15.7703i			1.28337i	−0.766970	+	0.641683i	$0.778237\pi$
$152$		0			0
$153$	7.04773	+	0.269952i	0.569775	+	0.0218243i
$154$		0			0
$155$	−11.4600	+	19.8493i	−0.920488	+	1.59433i
$156$		0			0
$157$	2.39885	−	4.15493i	0.191449	−	0.331600i	−0.754282	−	0.656551i	$-0.772015\pi$
$157$	2.39885	−	4.15493i	0.191449	−	0.331600i	0.945731	+	0.324951i	$0.105348\pi$
$158$		0			0
$159$	9.40317	−	9.04989i	0.745720	−	0.717703i
$160$		0			0
$161$	−0.447128	+	0.258149i	−0.0352386	+	0.0203450i
$162$		0			0
$163$	−4.99186			−0.390993			−0.195496	−	0.980704i	$-0.562632\pi$
$163$	−4.99186			−0.390993			−0.195496	+	0.980704i	$0.562632\pi$
$164$		0			0
$165$	1.88014	+	0.542561i	0.146369	+	0.0422383i
$166$		0			0
$167$	−10.3652	−	17.9530i	−0.802082	−	1.38925i	−0.918244	−	0.396016i	$-0.870392\pi$
$167$	−10.3652	−	17.9530i	−0.802082	−	1.38925i	0.116162	−	0.993230i	$-0.462941\pi$
$168$		0			0
$169$	−6.12402	+	10.6071i	−0.471078	+	0.815932i
$170$		0			0
$171$	1.72470	+	12.9625i	0.131891	+	0.991264i
$172$		0			0
$173$	−5.76280	+	9.98147i	−0.438138	+	0.758877i	−0.997546	−	0.0700154i	$-0.977695\pi$
$173$	−5.76280	+	9.98147i	−0.438138	+	0.758877i	0.559408	+	0.828892i	$0.311029\pi$
$174$		0			0
$175$	−0.187670	−	0.325054i	−0.0141865	−	0.0245718i
$176$		0			0
$177$	−11.7592	−	3.39342i	−0.883879	−	0.255065i
$178$		0			0
$179$	14.9966			1.12090			0.560451	−	0.828188i	$-0.310628\pi$
$179$	14.9966			1.12090			0.560451	+	0.828188i	$0.310628\pi$
$180$		0			0
$181$	−12.8911	+	7.44267i	−0.958186	+	0.553209i	−0.895614	−	0.444831i	$-0.853264\pi$
$181$	−12.8911	+	7.44267i	−0.958186	+	0.553209i	−0.0625720	+	0.998040i	$0.519930\pi$
$182$		0			0
$183$	14.1037	−	13.5738i	1.04258	−	1.00341i
$184$		0			0
$185$	0.977884	−	1.69374i	0.0718955	−	0.124527i
$186$		0			0
$187$	0.455031	−	0.788137i	0.0332752	−	0.0576343i
$188$		0			0
$189$	0.368837	+	0.413833i	0.0268290	+	0.0301019i
$190$		0			0
$191$		−	4.56899i		−	0.330601i	−0.986243	−	0.165300i	$-0.947141\pi$
$191$		−	4.56899i		−	0.330601i	0.986243	−	0.165300i	$-0.0528594\pi$
$192$		0			0
$193$	−17.6162	−	10.1707i	−1.26804	−	0.732104i	−0.293424	−	0.955982i	$-0.594795\pi$
$193$	−17.6162	−	10.1707i	−1.26804	−	0.732104i	−0.974617	+	0.223879i	$0.928128\pi$
$194$		0			0
$195$	1.05331	+	4.25520i	0.0754291	+	0.304721i
$196$		0			0
$197$			10.5261i			0.749951i	0.927035	+	0.374976i	$0.122349\pi$
$197$			10.5261i			0.749951i	−0.927035	+	0.374976i	$0.877651\pi$
$198$		0			0
$199$	−4.67525	−	8.09778i	−0.331420	−	0.574036i	0.651371	−	0.758760i	$-0.274194\pi$
$199$	−4.67525	−	8.09778i	−0.331420	−	0.574036i	−0.982791	+	0.184724i	$0.940861\pi$
$200$		0			0
$201$	−8.90985	−	9.25766i	−0.628452	−	0.652985i
$202$		0			0
$203$	0.451395	+	0.781839i	0.0316817	+	0.0548743i
$204$		0			0
$205$	−3.62727	+	2.09421i	−0.253340	+	0.146266i
$206$		0			0
$207$	−7.73522	+	12.2864i	−0.537635	+	0.853962i
$208$		0			0
$209$	1.58327	+	0.583396i	0.109517	+	0.0403543i
$210$		0			0
$211$	2.64602	+	1.52768i	0.182160	+	0.105170i	0.588307	−	0.808638i	$-0.299795\pi$
$211$	2.64602	+	1.52768i	0.182160	+	0.105170i	−0.406147	+	0.913808i	$0.633128\pi$
$212$		0			0
$213$	11.5524	+	3.33372i	0.791557	+	0.228423i
$214$		0			0
$215$	18.5790	−	10.7266i	1.26708	−	0.731549i
$216$		0			0
$217$			0.837794i			0.0568732i
$218$		0			0
$219$	11.9070	+	3.43606i	0.804602	+	0.232187i
$220$		0			0
$221$	2.03866			0.137135
$222$		0			0
$223$	10.9921	+	6.34631i	0.736087	+	0.424980i	0.820645	−	0.571438i	$-0.193614\pi$
$223$	10.9921	+	6.34631i	0.736087	+	0.424980i	−0.0845577	+	0.996419i	$0.526948\pi$
$224$		0			0
$225$	−8.93198	−	5.62336i	−0.595465	−	0.374891i
$226$		0			0
$227$	5.95297			0.395112			0.197556	−	0.980292i	$-0.436699\pi$
$227$	5.95297			0.395112			0.197556	+	0.980292i	$0.436699\pi$
$228$		0			0
$229$	−24.2354			−1.60152			−0.800762	−	0.598983i	$-0.795572\pi$
$229$	−24.2354			−1.60152			−0.800762	+	0.598983i	$0.795572\pi$
$230$		0			0
$231$	0.0694337	−	0.0171873i	0.00456840	−	0.00113084i
$232$		0			0
$233$	20.3911	+	11.7728i	1.33586	+	0.771262i	0.986191	−	0.165610i	$-0.0529594\pi$
$233$	20.3911	+	11.7728i	1.33586	+	0.771262i	0.349673	+	0.936872i	$0.386293\pi$
$234$		0			0
$235$	−11.5210			−0.751549
$236$		0			0
$237$	−7.33051	+	25.4025i	−0.476168	+	1.65007i
$238$		0			0
$239$			20.7972i			1.34526i	0.739980	+	0.672629i	$0.234835\pi$
$239$			20.7972i			1.34526i	−0.739980	+	0.672629i	$0.765165\pi$
$240$		0			0
$241$	17.5774	−	10.1483i	1.13226	−	0.653710i	0.187757	−	0.982216i	$-0.439878\pi$
$241$	17.5774	−	10.1483i	1.13226	−	0.653710i	0.944502	+	0.328506i	$0.106545\pi$
$242$		0			0
$243$	14.6028	+	5.45508i	0.936771	+	0.349944i
$244$		0			0
$245$	17.6643	+	10.1985i	1.12853	+	0.651558i
$246$		0			0
$247$	0.641576	+	3.72501i	0.0408225	+	0.237016i
$248$		0			0
$249$	−10.3494	+	2.56184i	−0.655868	+	0.162350i
$250$		0			0
$251$	12.1969	−	7.04190i	0.769863	−	0.444481i	−0.0629627	−	0.998016i	$-0.520055\pi$
$251$	12.1969	−	7.04190i	0.769863	−	0.444481i	0.832826	+	0.553535i	$0.186722\pi$
$252$		0			0
$253$	0.936693	+	1.62240i	0.0588894	+	0.101999i
$254$		0			0
$255$	−8.56294	+	8.24123i	−0.536232	+	0.516086i
$256$		0			0
$257$	−9.66816	−	16.7457i	−0.603083	−	1.04457i	−0.992351	−	0.123446i	$-0.960605\pi$
$257$	−9.66816	−	16.7457i	−0.603083	−	1.04457i	0.389268	−	0.921125i	$-0.372728\pi$
$258$		0			0
$259$		−	0.0714892i		−	0.00444212i
$260$		0			0
$261$	21.4837	+	13.5257i	1.32981	+	0.837217i
$262$		0			0
$263$	4.74307	+	2.73841i	0.292470	+	0.168858i	0.639055	−	0.769161i	$-0.279325\pi$
$263$	4.74307	+	2.73841i	0.292470	+	0.168858i	−0.346585	+	0.938019i	$0.612659\pi$
$264$		0			0
$265$			21.9911i			1.35090i
$266$		0			0
$267$	−20.2063	+	19.4471i	−1.23660	+	1.19014i
$268$		0			0
$269$	0.374165	−	0.648073i	0.0228133	−	0.0395137i	−0.854393	−	0.519627i	$-0.826071\pi$
$269$	0.374165	−	0.648073i	0.0228133	−	0.0395137i	0.877207	+	0.480113i	$0.159404\pi$
$270$		0			0
$271$	4.17033	−	7.22323i	0.253330	−	0.438780i	−0.711111	−	0.703080i	$-0.751808\pi$
$271$	4.17033	−	7.22323i	0.253330	−	0.438780i	0.964440	+	0.264300i	$0.0851410\pi$
$272$		0			0
$273$	0.111114	+	0.115451i	0.00672491	+	0.00698742i
$274$		0			0
$275$	−1.17946	+	0.680959i	−0.0711239	+	0.0410634i
$276$		0			0
$277$	6.81427			0.409430			0.204715	−	0.978822i	$-0.434373\pi$
$277$	6.81427			0.409430			0.204715	+	0.978822i	$0.434373\pi$
$278$		0			0
$279$	10.9900	+	20.8388i	0.657956	+	1.24758i
$280$		0			0
$281$	−15.1503	−	26.2410i	−0.903789	−	1.56541i	−0.822534	−	0.568715i	$-0.807441\pi$
$281$	−15.1503	−	26.2410i	−0.903789	−	1.56541i	−0.0812546	−	0.996693i	$-0.525893\pi$
$282$		0			0
$283$	1.00087	−	1.73356i	0.0594957	−	0.103050i	−0.834743	−	0.550639i	$-0.814384\pi$
$283$	1.00087	−	1.73356i	0.0594957	−	0.103050i	0.894239	+	0.447590i	$0.147717\pi$
$284$		0			0
$285$	−17.7531	−	13.0525i	−1.05160	−	0.773165i
$286$		0			0
$287$	−0.0765496	+	0.132588i	−0.00451858	+	0.00782641i
$288$		0			0
$289$	−5.73648	−	9.93588i	−0.337440	−	0.584463i
$290$		0			0
$291$	1.97459	−	6.84257i	0.115752	−	0.401119i
$292$		0			0
$293$	24.2058			1.41412			0.707059	−	0.707155i	$-0.250022\pi$
$293$	24.2058			1.41412			0.707059	+	0.707155i	$0.250022\pi$
$294$		0			0
$295$	17.8605	−	10.3118i	1.03988	−	0.600375i
$296$		0			0
$297$	1.50159	−	1.33832i	0.0871312	−	0.0776574i
$298$		0			0
$299$	−2.09831	+	3.63439i	−0.121349	+	0.210182i
$300$		0			0
$301$	0.392090	−	0.679120i	0.0225997	−	0.0391438i
$302$		0			0
$303$	−0.937818	−	0.974428i	−0.0538762	−	0.0559794i
$304$		0			0
$305$			32.9843i			1.88867i
$306$		0			0
$307$	14.6812	+	8.47620i	0.837901	+	0.483763i	0.856550	−	0.516064i	$-0.172603\pi$
$307$	14.6812	+	8.47620i	0.837901	+	0.483763i	−0.0186490	+	0.999826i	$0.505937\pi$
$308$		0			0
$309$	−6.69142	+	1.65636i	−0.380662	+	0.0942270i
$310$		0			0
$311$		−	25.2586i		−	1.43229i	−0.697953	−	0.716143i	$-0.745906\pi$
$311$		−	25.2586i		−	1.43229i	0.697953	−	0.716143i	$-0.254094\pi$
$312$		0			0
$313$	13.9789	+	24.2122i	0.790136	+	1.36855i	0.925883	+	0.377811i	$0.123323\pi$
$313$	13.9789	+	24.2122i	0.790136	+	1.36855i	−0.135747	+	0.990744i	$0.543343\pi$
$314$		0			0
$315$	−0.933419	−	0.0357531i	−0.0525922	−	0.00201446i
$316$		0			0
$317$	13.4261	+	23.2547i	0.754085	+	1.30611i	0.945828	+	0.324668i	$0.105253\pi$
$317$	13.4261	+	23.2547i	0.754085	+	1.30611i	−0.191743	+	0.981445i	$0.561414\pi$
$318$		0			0
$319$	2.83690	−	1.63788i	0.158836	−	0.0917039i
$320$		0			0
$321$	0.938743	+	3.79237i	0.0523955	+	0.211669i
$322$		0			0
$323$	−7.87623	+	6.55581i	−0.438245	+	0.364775i
$324$		0			0
$325$	−2.64213	−	1.52544i	−0.146559	−	0.0846160i
$326$		0			0
$327$	5.57796	−	19.3294i	0.308462	−	1.06892i
$328$		0			0
$329$	−0.364708	+	0.210564i	−0.0201070	+	0.0116088i
$330$		0			0
$331$			8.21719i			0.451658i	0.974167	+	0.225829i	$0.0725090\pi$
$331$			8.21719i			0.451658i	−0.974167	+	0.225829i	$0.927491\pi$
$332$		0			0
$333$	−0.937783	−	1.77818i	−0.0513902	−	0.0974436i
$334$		0			0
$335$	21.6508			1.18291
$336$		0			0
$337$	18.6278	+	10.7548i	1.01472	+	0.585851i	0.912571	−	0.408918i	$-0.134094\pi$
$337$	18.6278	+	10.7548i	1.01472	+	0.585851i	0.102152	+	0.994769i	$0.467427\pi$
$338$		0			0
$339$	−4.06379	−	16.4171i	−0.220715	−	0.891652i
$340$		0			0
$341$	3.03993			0.164622
$342$		0			0
$343$	1.49236			0.0805798
$344$		0			0
$345$	−5.87842	−	23.7479i	−0.316483	−	1.27854i
$346$		0			0
$347$	−28.2077	−	16.2857i	−1.51427	−	0.874264i	−0.999860	−	0.0167203i	$-0.994678\pi$
$347$	−28.2077	−	16.2857i	−1.51427	−	0.874264i	−0.514410	−	0.857544i	$-0.671989\pi$
$348$		0			0
$349$	0.712328			0.0381301			0.0190650	−	0.999818i	$-0.493931\pi$
$349$	0.712328			0.0381301			0.0190650	+	0.999818i	$0.493931\pi$
$350$		0			0
$351$	4.27824	+	1.41409i	0.228356	+	0.0754786i
$352$		0			0
$353$		−	25.0058i		−	1.33092i	−0.746432	−	0.665462i	$-0.768235\pi$
$353$		−	25.0058i		−	1.33092i	0.746432	−	0.665462i	$-0.231765\pi$
$354$		0			0
$355$	−17.5463	+	10.1304i	−0.931263	+	0.537665i
$356$		0			0
$357$	−0.120446	+	0.417384i	−0.00637469	+	0.0220903i
$358$		0			0
$359$	−17.0182	−	9.82549i	−0.898188	−	0.518569i	−0.0215764	−	0.999767i	$-0.506869\pi$
$359$	−17.0182	−	9.82549i	−0.898188	−	0.518569i	−0.876612	+	0.481198i	$0.840202\pi$
$360$		0			0
$361$	−14.4574	−	12.3282i	−0.760915	−	0.648852i
$362$		0			0
$363$	4.51564	+	18.2424i	0.237009	+	0.957480i
$364$		0			0
$365$	−18.0850	+	10.4414i	−0.946610	+	0.546526i
$366$		0			0
$367$	−13.2279	−	22.9113i	−0.690489	−	1.19596i	−0.971678	−	0.236310i	$-0.924062\pi$
$367$	−13.2279	−	22.9113i	−0.690489	−	1.19596i	0.281189	−	0.959653i	$-0.409271\pi$
$368$		0			0
$369$	−0.164784	+	4.30207i	−0.00857831	+	0.223957i
$370$		0			0
$371$	0.401921	+	0.696148i	0.0208667	+	0.0361422i
$372$		0			0
$373$		−	15.2365i		−	0.788915i	−0.918914	−	0.394457i	$-0.870933\pi$
$373$		−	15.2365i		−	0.788915i	0.918914	−	0.394457i	$-0.129067\pi$
$374$		0			0
$375$	−7.27107	+	1.79984i	−0.375476	+	0.0929434i
$376$		0			0
$377$	6.35502	+	3.66907i	0.327300	+	0.188967i
$378$		0			0
$379$		−	2.47569i		−	0.127167i	−0.997977	−	0.0635837i	$-0.979747\pi$
$379$		−	2.47569i		−	0.127167i	0.997977	−	0.0635837i	$-0.0202530\pi$
$380$		0			0
$381$	−20.1476	−	20.9341i	−1.03219	−	1.07249i
$382$		0			0
$383$	−4.39842	+	7.61828i	−0.224749	+	0.389276i	−0.956244	−	0.292570i	$-0.905489\pi$
$383$	−4.39842	+	7.61828i	−0.224749	+	0.389276i	0.731495	+	0.681846i	$0.238823\pi$
$384$		0			0
$385$	−0.0602655	+	0.104383i	−0.00307141	+	0.00531984i
$386$		0			0
$387$	0.844030	−	22.0354i	0.0429045	−	1.12012i
$388$		0			0
$389$	25.4820	−	14.7120i	1.29199	−	0.745930i	0.312983	−	0.949759i	$-0.398672\pi$
$389$	25.4820	−	14.7120i	1.29199	−	0.745930i	0.979007	+	0.203829i	$0.0653385\pi$
$390$		0			0
$391$	−11.3775			−0.575387
$392$		0			0
$393$	0.772512	−	2.67699i	0.0389681	−	0.135037i
$394$		0			0
$395$	−22.2757	−	38.5826i	−1.12081	−	1.94130i
$396$		0			0
$397$	16.6922	−	28.9118i	0.837758	−	1.45104i	−0.0540061	−	0.998541i	$-0.517199\pi$
$397$	16.6922	−	28.9118i	0.837758	−	1.45104i	0.891765	−	0.452500i	$-0.149468\pi$
$398$		0			0
$399$	−0.800543	−	0.0887248i	−0.0400773	−	0.00444179i
$400$		0			0
$401$	−4.84634	+	8.39410i	−0.242015	+	0.419181i	−0.961288	−	0.275546i	$-0.911142\pi$
$401$	−4.84634	+	8.39410i	−0.242015	+	0.419181i	0.719273	+	0.694727i	$0.244475\pi$
$402$		0			0
$403$	3.40492	+	5.89750i	0.169611	+	0.293775i
$404$		0			0
$405$	−23.6863	+	11.3551i	−1.17698	+	0.564240i
$406$		0			0
$407$	−0.259398			−0.0128579
$408$		0			0
$409$	−1.22080	+	0.704832i	−0.0603649	+	0.0348517i	−0.529879	−	0.848073i	$-0.677763\pi$
$409$	−1.22080	+	0.704832i	−0.0603649	+	0.0348517i	0.469514	+	0.882925i	$0.344429\pi$
$410$		0			0
$411$	15.5996	+	16.2086i	0.769472	+	0.799510i
$412$		0			0
$413$	0.376927	−	0.652856i	0.0185473	−	0.0321249i
$414$		0			0
$415$	8.98285	−	15.5588i	0.440951	−	0.763749i
$416$		0			0
$417$	26.1388	−	25.1568i	1.28002	−	1.23193i
$418$		0			0
$419$			25.8333i			1.26204i	0.775767	+	0.631019i	$0.217363\pi$
$419$			25.8333i			1.26204i	−0.775767	+	0.631019i	$0.782637\pi$
$420$		0			0
$421$	−3.63922	−	2.10111i	−0.177365	−	0.102402i	0.408689	−	0.912674i	$-0.365986\pi$
$421$	−3.63922	−	2.10111i	−0.177365	−	0.102402i	−0.586054	+	0.810272i	$0.699319\pi$
$422$		0			0
$423$	−6.30937	+	10.0216i	−0.306772	+	0.487267i
$424$		0			0
$425$		−	8.27127i		−	0.401216i
$426$		0			0
$427$	0.602837	+	1.04415i	0.0291733	+	0.0505297i
$428$		0			0
$429$	0.418914	−	0.403175i	0.0202254	−	0.0194655i
$430$		0			0
$431$	−12.3407	−	21.3747i	−0.594431	−	1.02958i	−0.993627	−	0.112719i	$-0.964044\pi$
$431$	−12.3407	−	21.3747i	−0.594431	−	1.02958i	0.399196	−	0.916866i	$-0.369289\pi$
$432$		0			0
$433$	31.6773	−	18.2889i	1.52232	−	0.878909i	0.522663	−	0.852539i	$-0.324939\pi$
$433$	31.6773	−	18.2889i	1.52232	−	0.878909i	0.999652	−	0.0263696i	$-0.00839466\pi$
$434$		0			0
$435$	−41.5251	+	10.2789i	−1.99097	+	0.492835i
$436$		0			0
$437$	−3.58057	−	20.7889i	−0.171282	−	0.994467i
$438$		0			0
$439$	4.60729	+	2.66002i	0.219894	+	0.126956i	0.605901	−	0.795540i	$-0.292813\pi$
$439$	4.60729	+	2.66002i	0.219894	+	0.126956i	−0.386007	+	0.922496i	$0.626146\pi$
$440$		0			0
$441$	18.5449	−	9.78028i	0.883090	−	0.465728i
$442$		0			0
$443$	−11.1717	+	6.45001i	−0.530786	+	0.306449i	−0.741336	−	0.671134i	$-0.765808\pi$
$443$	−11.1717	+	6.45001i	−0.530786	+	0.306449i	0.210551	+	0.977583i	$0.432474\pi$
$444$		0			0
$445$		−	47.2563i		−	2.24016i
$446$		0			0
$447$	4.89834	−	16.9743i	0.231683	−	0.802856i
$448$		0			0
$449$	−37.0505			−1.74852			−0.874261	−	0.485456i	$-0.838654\pi$
$449$	−37.0505			−1.74852			−0.874261	+	0.485456i	$0.838654\pi$
$450$		0			0
$451$	0.481094	+	0.277760i	0.0226538	+	0.0130792i
$452$		0			0
$453$	−26.5147	+	6.56330i	−1.24577	+	0.308371i
$454$		0			0
$455$	−0.270005			−0.0126580
$456$		0			0
$457$	32.2933			1.51062			0.755310	−	0.655368i	$-0.227487\pi$
$457$	32.2933			1.51062			0.755310	+	0.655368i	$0.227487\pi$
$458$		0			0
$459$	2.47926	+	11.9617i	0.115722	+	0.558326i
$460$		0			0
$461$	−0.308037	−	0.177845i	−0.0143467	−	0.00828307i	0.492810	−	0.870137i	$-0.335970\pi$
$461$	−0.308037	−	0.177845i	−0.0143467	−	0.00828307i	−0.507156	+	0.861854i	$0.669303\pi$
$462$		0			0
$463$	8.93393			0.415195			0.207598	−	0.978214i	$-0.433436\pi$
$463$	8.93393			0.415195			0.207598	+	0.978214i	$0.433436\pi$
$464$		0			0
$465$	−38.1422	−	11.0068i	−1.76880	−	0.510430i
$466$		0			0
$467$			0.356546i			0.0164990i	0.999966	+	0.00824949i	$0.00262592\pi$
$467$			0.356546i			0.0164990i	−0.999966	+	0.00824949i	$0.997374\pi$
$468$		0			0
$469$	0.685375	−	0.395702i	0.0316477	−	0.0182718i
$470$		0			0
$471$	7.98407	+	2.30400i	0.367887	+	0.106163i
$472$		0			0
$473$	−2.46418	−	1.42270i	−0.113303	−	0.0654157i
$474$		0			0
$475$	15.1132	−	2.60301i	0.693439	−	0.119434i
$476$		0			0
$477$	19.1291	+	12.0432i	0.875860	+	0.551421i
$478$		0			0
$479$	−22.7389	+	13.1283i	−1.03896	+	0.599846i	−0.919540	−	0.392997i	$-0.871438\pi$
$479$	−22.7389	+	13.1283i	−1.03896	+	0.599846i	−0.119425	+	0.992843i	$0.538105\pi$
$480$		0			0
$481$	−0.290543	−	0.503235i	−0.0132476	−	0.0229455i
$482$		0			0
$483$	−0.620114	−	0.644322i	−0.0282162	−	0.0293176i
$484$		0			0
$485$	6.00030	+	10.3928i	0.272460	+	0.471914i
$486$		0			0
$487$			39.3795i			1.78445i	0.451587	+	0.892227i	$0.350858\pi$
$487$			39.3795i			1.78445i	−0.451587	+	0.892227i	$0.649142\pi$
$488$		0			0
$489$	−2.07752	−	8.39285i	−0.0939488	−	0.379538i
$490$		0			0
$491$	−14.5540	−	8.40273i	−0.656811	−	0.379210i	0.134250	−	0.990947i	$-0.457137\pi$
$491$	−14.5540	−	8.40273i	−0.656811	−	0.379210i	−0.791061	+	0.611738i	$0.790471\pi$
$492$		0			0
$493$			19.8946i			0.896006i
$494$		0			0
$495$	−0.129730	+	3.38690i	−0.00583093	+	0.152230i
$496$		0			0
$497$	−0.370296	+	0.641372i	−0.0166101	+	0.0287695i
$498$		0			0
$499$	−5.30439	+	9.18748i	−0.237457	+	0.411288i	−0.959984	−	0.280055i	$-0.909647\pi$
$499$	−5.30439	+	9.18748i	−0.237457	+	0.411288i	0.722527	+	0.691343i	$0.242981\pi$
$500$		0			0
$501$	25.8707	−	24.8988i	1.15582	−	1.11240i
$502$		0			0
$503$	9.93910	−	5.73834i	0.443162	−	0.255860i	−0.261776	−	0.965129i	$-0.584308\pi$
$503$	9.93910	−	5.73834i	0.443162	−	0.255860i	0.704938	+	0.709269i	$0.250975\pi$
$504$		0			0
$505$	2.27889			0.101409
$506$		0			0
$507$	−20.3825	−	5.88187i	−0.905219	−	0.261223i
$508$		0			0
$509$	−12.9738	−	22.4713i	−0.575053	−	0.996021i	−0.996036	−	0.0889524i	$-0.971648\pi$
$509$	−12.9738	−	22.4713i	−0.575053	−	0.996021i	0.420983	−	0.907069i	$-0.361685\pi$
$510$		0			0
$511$	−0.381663	+	0.661060i	−0.0168838	+	0.0292436i
$512$		0			0
$513$	−21.0761	+	8.29450i	−0.930532	+	0.366211i
$514$		0			0
$515$	5.80787	−	10.0595i	0.255925	−	0.443275i
$516$		0			0
$517$	0.764031	+	1.32334i	0.0336020	+	0.0582004i
$518$		0			0
$519$	−19.1803	−	5.53494i	−0.841921	−	0.242957i
$520$		0			0
$521$	−8.02933			−0.351771			−0.175886	−	0.984411i	$-0.556279\pi$
$521$	−8.02933			−0.351771			−0.175886	+	0.984411i	$0.556279\pi$
$522$		0			0
$523$	29.1226	−	16.8139i	1.27344	−	0.735222i	0.297808	−	0.954626i	$-0.403745\pi$
$523$	29.1226	−	16.8139i	1.27344	−	0.735222i	0.975634	+	0.219404i	$0.0704113\pi$
$524$		0			0
$525$	0.468410	−	0.450812i	0.0204431	−	0.0196751i
$526$		0			0
$527$	−9.23113	+	15.9888i	−0.402114	+	0.696483i
$528$		0			0
$529$	0.210482	−	0.364566i	0.00915141	−	0.0158507i
$530$		0			0
$531$	0.811388	−	21.1832i	0.0352113	−	0.919272i
$532$		0			0
$533$			1.24444i			0.0539025i
$534$		0			0
$535$	−5.70124	−	3.29161i	−0.246486	−	0.142309i
$536$		0			0
$537$	6.24133	+	25.2140i	0.269333	+	1.08806i
$538$		0			0
$539$		−	2.70531i		−	0.116526i
$540$		0			0
$541$	3.13328	+	5.42700i	0.134710	+	0.233325i	0.925487	−	0.378780i	$-0.123656\pi$
$541$	3.13328	+	5.42700i	0.134710	+	0.233325i	−0.790776	+	0.612105i	$0.790323\pi$
$542$		0			0
$543$	−17.8784	−	18.5764i	−0.767237	−	0.797188i
$544$		0			0
$545$	16.9501	+	29.3584i	0.726061	+	1.25758i
$546$		0			0
$547$	36.5689	−	21.1131i	1.56357	−	0.902730i	0.566684	−	0.823935i	$-0.308226\pi$
$547$	36.5689	−	21.1131i	1.56357	−	0.902730i	0.996891	−	0.0787950i	$-0.0251073\pi$
$548$		0			0
$549$	28.6915	+	18.0635i	1.22452	+	0.770931i
$550$		0			0
$551$	−36.3511	+	6.26092i	−1.54861	+	0.266724i
$552$		0			0
$553$	−1.41031	−	0.814243i	−0.0599725	−	0.0346251i
$554$		0			0
$555$	3.25468	+	0.939217i	0.138154	+	0.0398676i
$556$		0			0
$557$	−29.4094	+	16.9795i	−1.24612	+	0.719445i	−0.970332	−	0.241775i	$-0.922270\pi$
$557$	−29.4094	+	16.9795i	−1.24612	+	0.719445i	−0.275783	+	0.961220i	$0.588937\pi$
$558$		0			0
$559$		−	6.37405i		−	0.269594i
$560$		0			0
$561$	1.51448	+	0.437039i	0.0639412	+	0.0184518i
$562$		0			0
$563$	12.5490			0.528878			0.264439	−	0.964402i	$-0.414813\pi$
$563$	12.5490			0.528878			0.264439	+	0.964402i	$0.414813\pi$
$564$		0			0
$565$	24.6805	+	14.2493i	1.03832	+	0.599473i
$566$		0			0
$567$	−0.542277	+	0.792358i	−0.0227735	+	0.0332759i
$568$		0			0
$569$	−12.0746			−0.506195			−0.253097	−	0.967441i	$-0.581449\pi$
$569$	−12.0746			−0.506195			−0.253097	+	0.967441i	$0.581449\pi$
$570$		0			0
$571$	39.3367			1.64619			0.823095	−	0.567904i	$-0.192245\pi$
$571$	39.3367			1.64619			0.823095	+	0.567904i	$0.192245\pi$
$572$		0			0
$573$	7.68188	−	1.90153i	0.320915	−	0.0794376i
$574$		0			0
$575$	14.7455	+	8.51331i	0.614929	+	0.355030i
$576$		0			0
$577$	8.80975			0.366755			0.183377	−	0.983043i	$-0.441297\pi$
$577$	8.80975			0.366755			0.183377	+	0.983043i	$0.441297\pi$
$578$		0			0
$579$	9.76855	−	33.8511i	0.405967	−	1.40680i
$580$		0			0
$581$		−	0.656701i		−	0.0272445i
$582$		0			0
$583$	2.52597	−	1.45837i	0.104615	−	0.0603995i
$584$		0			0
$585$	−6.71593	+	3.54187i	−0.277670	+	0.146439i
$586$		0			0
$587$	18.5588	+	10.7149i	0.766004	+	0.442253i	0.831447	−	0.555604i	$-0.187513\pi$
$587$	18.5588	+	10.7149i	0.766004	+	0.442253i	−0.0654432	+	0.997856i	$0.520846\pi$
$588$		0			0
$589$	−32.1196	−	11.8352i	−1.32346	−	0.487663i
$590$		0			0
$591$	−17.6975	+	4.38076i	−0.727980	+	0.180200i
$592$		0			0
$593$	−15.0288	+	8.67687i	−0.617158	+	0.356316i	−0.775762	−	0.631026i	$-0.782634\pi$
$593$	−15.0288	+	8.67687i	−0.617158	+	0.356316i	0.158604	+	0.987342i	$0.449301\pi$
$594$		0			0
$595$	−0.366007	−	0.633943i	−0.0150048	−	0.0259891i
$596$		0			0
$597$	11.6691	−	11.2307i	0.477584	−	0.459641i
$598$		0			0
$599$	20.3433	+	35.2356i	0.831204	+	1.43969i	0.897084	+	0.441860i	$0.145681\pi$
$599$	20.3433	+	35.2356i	0.831204	+	1.43969i	−0.0658795	+	0.997828i	$0.520985\pi$
$600$		0			0
$601$			45.8601i			1.87067i	0.353760	+	0.935336i	$0.384903\pi$
$601$			45.8601i			1.87067i	−0.353760	+	0.935336i	$0.615097\pi$
$602$		0			0
$603$	11.8568	−	18.8331i	0.482848	−	0.766941i
$604$		0			0
$605$	−27.4247	−	15.8336i	−1.11497	−	0.643729i
$606$		0			0
$607$		−	8.77862i		−	0.356313i	−0.984002	−	0.178157i	$-0.942987\pi$
$607$		−	8.77862i		−	0.356313i	0.984002	−	0.178157i	$-0.0570134\pi$
$608$		0			0
$609$	−1.12665	+	1.08432i	−0.0456541	+	0.0439389i
$610$		0			0
$611$	−1.71153	+	2.96445i	−0.0692410	+	0.119929i
$612$		0			0
$613$	−4.67702	+	8.10083i	−0.188903	+	0.327190i	−0.944885	−	0.327403i	$-0.893827\pi$
$613$	−4.67702	+	8.10083i	−0.188903	+	0.327190i	0.755982	+	0.654593i	$0.227160\pi$
$614$		0			0
$615$	−5.03061	−	5.22699i	−0.202854	−	0.210773i
$616$		0			0
$617$	12.2210	−	7.05582i	0.492001	−	0.284057i	−0.233403	−	0.972380i	$-0.574986\pi$
$617$	12.2210	−	7.05582i	0.492001	−	0.284057i	0.725404	+	0.688323i	$0.241653\pi$
$618$		0			0
$619$	4.51688			0.181549			0.0907743	−	0.995871i	$-0.471066\pi$
$619$	4.51688			0.181549			0.0907743	+	0.995871i	$0.471066\pi$
$620$		0			0
$621$	−23.8764	−	7.89190i	−0.958128	−	0.316691i
$622$		0			0
$623$	−0.863680	−	1.49594i	−0.0346026	−	0.0599334i
$624$		0			0
$625$	15.1066	−	26.1654i	0.604264	−	1.04662i
$626$		0			0
$627$	−0.321937	+	2.90477i	−0.0128569	+	0.116005i
$628$		0			0
$629$	0.787695	−	1.36433i	0.0314075	−	0.0543993i
$630$		0			0
$631$	−10.8479	−	18.7891i	−0.431847	−	0.747981i	0.565186	−	0.824964i	$-0.308805\pi$
$631$	−10.8479	−	18.7891i	−0.431847	−	0.747981i	−0.997032	+	0.0769832i	$0.975471\pi$
$632$		0			0
$633$	−1.46727	+	5.08456i	−0.0583189	+	0.202093i
$634$		0			0
$635$	48.9585			1.94286
$636$		0			0
$637$	5.24832	−	3.03012i	0.207946	−	0.120058i
$638$		0			0
$639$	−0.797116	+	20.8106i	−0.0315334	+	0.823253i
$640$		0			0
$641$	9.69832	−	16.7980i	0.383061	−	0.663481i	−0.608437	−	0.793602i	$-0.708203\pi$
$641$	9.69832	−	16.7980i	0.383061	−	0.663481i	0.991498	+	0.130121i	$0.0415367\pi$
$642$		0			0
$643$	16.9742	−	29.4001i	0.669396	−	1.15943i	−0.308677	−	0.951167i	$-0.599886\pi$
$643$	16.9742	−	29.4001i	0.669396	−	1.15943i	0.978073	−	0.208261i	$-0.0667803\pi$
$644$		0			0
$645$	25.7670	+	26.7728i	1.01457	+	1.05418i
$646$		0			0
$647$		−	17.9566i		−	0.705949i	−0.935633	−	0.352974i	$-0.885170\pi$
$647$		−	17.9566i		−	0.705949i	0.935633	−	0.352974i	$-0.114830\pi$
$648$		0			0
$649$	−2.36888	−	1.36768i	−0.0929869	−	0.0536860i
$650$		0			0
$651$	−1.40859	+	0.348675i	−0.0552070	+	0.0136656i
$652$		0			0
$653$		−	31.8655i		−	1.24699i	−0.781826	−	0.623497i	$-0.785712\pi$
$653$		−	31.8655i		−	1.24699i	0.781826	−	0.623497i	$-0.214288\pi$
$654$		0			0
$655$	2.34748	+	4.06595i	0.0917235	+	0.158870i
$656$		0			0
$657$	−0.821585	+	21.4494i	−0.0320531	+	0.836820i
$658$		0			0
$659$	−4.26994	−	7.39575i	−0.166333	−	0.288098i	0.770795	−	0.637084i	$-0.219859\pi$
$659$	−4.26994	−	7.39575i	−0.166333	−	0.288098i	−0.937128	+	0.348986i	$0.886526\pi$
$660$		0			0
$661$	36.1357	−	20.8630i	1.40552	−	0.811475i	0.410564	−	0.911832i	$-0.365332\pi$
$661$	36.1357	−	20.8630i	1.40552	−	0.811475i	0.994952	+	0.100357i	$0.0319984\pi$
$662$		0			0
$663$	0.848452	+	3.42761i	0.0329511	+	0.133117i
$664$		0			0
$665$	1.04315	−	0.868268i	0.0404515	−	0.0336700i
$666$		0			0
$667$	−35.4667	−	20.4767i	−1.37328	−	0.792862i
$668$		0			0
$669$	−6.09537	+	21.1224i	−0.235661	+	0.816638i
$670$		0			0
$671$	3.78868	−	2.18739i	0.146260	−	0.0844434i
$672$		0			0
$673$			14.0465i			0.541454i	0.962656	+	0.270727i	$0.0872641\pi$
$673$			14.0465i			0.541454i	−0.962656	+	0.270727i	$0.912736\pi$
$674$		0			0
$675$	5.73727	−	17.3577i	0.220828	−	0.668100i
$676$		0			0
$677$	20.7216			0.796395			0.398198	−	0.917300i	$-0.369636\pi$
$677$	20.7216			0.796395			0.398198	+	0.917300i	$0.369636\pi$
$678$		0			0
$679$	0.379889	+	0.219329i	0.0145788	+	0.00841708i
$680$		0			0
$681$	2.47752	+	10.0088i	0.0949387	+	0.383537i
$682$		0			0
$683$	42.2802			1.61781			0.808904	−	0.587941i	$-0.200061\pi$
$683$	42.2802			1.61781			0.808904	+	0.587941i	$0.200061\pi$
$684$		0			0
$685$	−37.9069			−1.44835
$686$		0			0
$687$	−10.0864	−	40.7472i	−0.384818	−	1.55460i
$688$		0			0
$689$	5.65850	+	3.26694i	0.215572	+	0.124460i
$690$		0			0
$691$	6.92037			0.263263			0.131632	−	0.991299i	$-0.457978\pi$
$691$	6.92037			0.263263			0.131632	+	0.991299i	$0.457978\pi$
$692$		0			0
$693$	0.0577941	+	0.109586i	0.00219542	+	0.00416284i
$694$		0			0
$695$			61.1307i			2.31882i
$696$		0			0
$697$	−2.92181	+	1.68691i	−0.110671	+	0.0638961i
$698$		0			0
$699$	−11.3073	+	39.1833i	−0.427681	+	1.48205i
$700$		0			0
$701$	−7.99657	−	4.61682i	−0.302026	−	0.174375i	0.341327	−	0.939945i	$-0.389124\pi$
$701$	−7.99657	−	4.61682i	−0.302026	−	0.174375i	−0.643353	+	0.765570i	$0.722457\pi$
$702$		0			0
$703$	2.74077	+	1.00990i	0.103370	+	0.0380893i
$704$		0			0
$705$	−4.79484	−	19.3704i	−0.180584	−	0.729531i
$706$		0			0
$707$	0.0721401	−	0.0416501i	0.00271311	−	0.00156641i
$708$		0			0
$709$	−0.887288	−	1.53683i	−0.0333228	−	0.0577168i	0.848883	−	0.528581i	$-0.177276\pi$
$709$	−0.887288	−	1.53683i	−0.0333228	−	0.0577168i	−0.882206	+	0.470864i	$0.843942\pi$
$710$		0			0
$711$	−45.7603	−	1.75277i	−1.71614	−	0.0657342i
$712$		0			0
$713$	−19.0025	−	32.9133i	−0.711650	−	1.23261i
$714$		0			0
$715$			0.979711i			0.0366391i
$716$		0			0
$717$	−34.9665	+	8.65541i	−1.30585	+	0.323242i
$718$		0			0
$719$	34.4451	+	19.8869i	1.28459	+	0.741656i	0.977683	−	0.210086i	$-0.0673743\pi$
$719$	34.4451	+	19.8869i	1.28459	+	0.741656i	0.306902	+	0.951741i	$0.400708\pi$
$720$		0			0
$721$		−	0.424590i		−	0.0158126i
$722$		0			0
$723$	24.3778	+	25.3294i	0.906620	+	0.942012i
$724$		0			0
$725$	14.8862	−	25.7837i	0.552860	−	0.957582i
$726$		0			0
$727$	−20.0091	+	34.6568i	−0.742096	+	1.28535i	0.209443	+	0.977821i	$0.432835\pi$
$727$	−20.0091	+	34.6568i	−0.742096	+	1.28535i	−0.951539	+	0.307528i	$0.900498\pi$
$728$		0			0
$729$	−3.09425	+	26.8221i	−0.114602	+	0.993412i
$730$		0			0
$731$	14.9656	−	8.64039i	0.553523	−	0.319577i
$732$		0			0
$733$	−32.2123			−1.18979			−0.594895	−	0.803803i	$-0.702806\pi$
$733$	−32.2123			−1.18979			−0.594895	+	0.803803i	$0.702806\pi$
$734$		0			0
$735$	−9.79524	+	33.9436i	−0.361303	+	1.25203i
$736$		0			0
$737$	−1.43580	−	2.48688i	−0.0528884	−	0.0916054i
$738$		0			0
$739$	−11.0805	+	19.1921i	−0.407604	+	0.705991i	−0.994621	−	0.103584i	$-0.966969\pi$
$739$	−11.0805	+	19.1921i	−0.407604	+	0.705991i	0.587016	+	0.809575i	$0.300302\pi$
$740$		0			0
$741$	−5.99587	+	2.62897i	−0.220264	+	0.0965775i
$742$		0			0
$743$	−0.232079	+	0.401972i	−0.00851414	+	0.0147469i	−0.870251	−	0.492608i	$-0.836044\pi$
$743$	−0.232079	+	0.401972i	−0.00851414	+	0.0147469i	0.861737	+	0.507355i	$0.169377\pi$
$744$		0			0
$745$	14.8849	+	25.7814i	0.545340	+	0.944556i
$746$		0			0
$747$	−8.61448	−	16.3344i	−0.315187	−	0.597643i
$748$		0			0
$749$	−0.240637			−0.00879267
$750$		0			0
$751$	−6.14406	+	3.54727i	−0.224200	+	0.129442i	−0.607893	−	0.794019i	$-0.707985\pi$
$751$	−6.14406	+	3.54727i	−0.224200	+	0.129442i	0.383694	+	0.923460i	$0.374652\pi$
$752$		0			0
$753$	16.9157	+	17.5761i	0.616443	+	0.640507i
$754$		0			0
$755$	23.0136	−	39.8607i	0.837550	−	1.45068i
$756$		0			0
$757$	−10.4852	+	18.1609i	−0.381091	+	0.660068i	−0.991218	−	0.132235i	$-0.957785\pi$
$757$	−10.4852	+	18.1609i	−0.381091	+	0.660068i	0.610128	+	0.792303i	$0.291118\pi$
$758$		0			0
$759$	−2.33792	+	2.25008i	−0.0848611	+	0.0816728i
$760$		0			0
$761$			42.8591i			1.55364i	0.629722	+	0.776821i	$0.283169\pi$
$761$			42.8591i			1.55364i	−0.629722	+	0.776821i	$0.716831\pi$
$762$		0			0
$763$	1.07314	+	0.619577i	0.0388502	+	0.0224302i
$764$		0			0
$765$	−17.4198	−	10.9671i	−0.629814	−	0.396516i
$766$		0			0
$767$		−	6.12754i		−	0.221253i
$768$		0			0
$769$	−14.5242	−	25.1567i	−0.523758	−	0.907175i	−0.999618	−	0.0276538i	$-0.991196\pi$
$769$	−14.5242	−	25.1567i	−0.523758	−	0.907175i	0.475860	−	0.879521i	$-0.342137\pi$
$770$		0			0
$771$	24.1310	−	23.2244i	0.869058	−	0.836407i
$772$		0			0
$773$	4.83150	+	8.36840i	0.173777	+	0.300990i	0.939737	−	0.341897i	$-0.111070\pi$
$773$	4.83150	+	8.36840i	0.173777	+	0.300990i	−0.765960	+	0.642888i	$0.777736\pi$
$774$		0			0
$775$	23.9274	−	13.8145i	0.859498	−	0.496231i
$776$		0			0
$777$	0.120195	−	0.0297525i	0.00431198	−	0.00106737i
$778$		0			0
$779$	−4.00180	−	4.80780i	−0.143379	−	0.172257i
$780$		0			0
$781$	2.32721	+	1.34362i	0.0832743	+	0.0480784i
$782$		0			0
$783$	−13.7996	+	41.7499i	−0.493159	+	1.49202i
$784$		0			0
$785$	−12.1266	+	7.00129i	−0.432817	+	0.249887i
$786$		0			0
$787$			8.05092i			0.286984i	0.989651	+	0.143492i	$0.0458332\pi$
$787$			8.05092i			0.286984i	−0.989651	+	0.143492i	$0.954167\pi$
$788$		0			0
$789$	−2.63013	+	9.11424i	−0.0936353	+	0.324475i
$790$		0			0
$791$	1.04171			0.0370389
$792$		0			0
$793$	8.48712	+	4.90004i	0.301387	+	0.174006i
$794$		0			0
$795$	−36.9738	+	9.15231i	−1.31133	+	0.324599i
$796$		0			0
$797$	−4.15847			−0.147301			−0.0736503	−	0.997284i	$-0.523465\pi$
$797$	−4.15847			−0.147301			−0.0736503	+	0.997284i	$0.523465\pi$
$798$		0			0
$799$	−9.28030			−0.328313
$800$		0			0
$801$	−41.1061	−	25.8794i	−1.45241	−	0.914404i
$802$		0			0
$803$	2.39865	+	1.38486i	0.0846467	+	0.0488708i
$804$		0			0
$805$	1.50687			0.0531102
$806$		0			0
$807$	1.24533	+	0.359370i	0.0438377	+	0.0126504i
$808$		0			0
$809$			14.7272i			0.517782i	0.965907	+	0.258891i	$0.0833570\pi$
$809$			14.7272i			0.517782i	−0.965907	+	0.258891i	$0.916643\pi$
$810$		0			0
$811$	6.94177	−	4.00783i	0.243759	−	0.140734i	−0.373144	−	0.927773i	$-0.621720\pi$
$811$	6.94177	−	4.00783i	0.243759	−	0.140734i	0.616903	+	0.787039i	$0.288387\pi$
$812$		0			0
$813$	13.8801	+	4.00543i	0.486796	+	0.140477i
$814$		0			0
$815$	12.6174	+	7.28463i	0.441967	+	0.255170i
$816$		0			0
$817$	20.4974	+	24.6258i	0.717112	+	0.861546i
$818$		0			0
$819$	−0.147865	+	0.234865i	−0.00516683	+	0.00820684i
$820$		0			0
$821$	−28.5802	+	16.5008i	−0.997455	+	0.575881i	−0.907494	−	0.420064i	$-0.862007\pi$
$821$	−28.5802	+	16.5008i	−0.997455	+	0.575881i	−0.0899608	+	0.995945i	$0.528674\pi$
$822$		0			0
$823$	−7.02410	−	12.1661i	−0.244845	−	0.424083i	0.717243	−	0.696823i	$-0.245404\pi$
$823$	−7.02410	−	12.1661i	−0.244845	−	0.424083i	−0.962088	+	0.272739i	$0.912070\pi$
$824$		0			0
$825$	−1.63577	−	1.69962i	−0.0569502	−	0.0591733i
$826$		0			0
$827$	−1.08426	−	1.87799i	−0.0377033	−	0.0653040i	0.846558	−	0.532296i	$-0.178671\pi$
$827$	−1.08426	−	1.87799i	−0.0377033	−	0.0653040i	−0.884261	+	0.466992i	$0.845338\pi$
$828$		0			0
$829$		−	11.4747i		−	0.398531i	−0.979945	−	0.199266i	$-0.936144\pi$
$829$		−	11.4747i		−	0.398531i	0.979945	−	0.199266i	$-0.0638557\pi$
$830$		0			0
$831$	2.83598	+	11.4569i	0.0983789	+	0.397435i
$832$		0			0
$833$	14.2288	+	8.21500i	0.492998	+	0.284633i
$834$		0			0
$835$			60.5037i			2.09382i
$836$		0			0
$837$	−30.4625	+	27.1503i	−1.05294	+	0.938453i
$838$		0			0
$839$	−9.24428	+	16.0116i	−0.319148	+	0.552780i	−0.980310	−	0.197462i	$-0.936730\pi$
$839$	−9.24428	+	16.0116i	−0.319148	+	0.552780i	0.661163	+	0.750243i	$0.270063\pi$
$840$		0			0
$841$	−21.3052	+	36.9017i	−0.734663	+	1.27247i
$842$		0			0
$843$	37.8140	−	36.3933i	1.30238	−	1.25345i
$844$		0			0
$845$	30.9580	−	17.8736i	1.06499	−	0.614870i
$846$		0			0
$847$	−1.15754			−0.0397734
$848$		0			0
$849$	3.33119	+	0.961297i	0.114326	+	0.0329916i
$850$		0			0
$851$	1.62149	+	2.80851i	0.0555840	+	0.0962743i
$852$		0			0
$853$	13.3464	−	23.1166i	0.456970	−	0.791496i	−0.541829	−	0.840489i	$-0.682268\pi$
$853$	13.3464	−	23.1166i	0.456970	−	0.791496i	0.998799	+	0.0489929i	$0.0156012\pi$
$854$		0			0
$855$	14.5568	−	35.2806i	0.497832	−	1.20657i
$856$		0			0
$857$	15.8697	−	27.4871i	0.542097	−	0.938940i	−0.456686	−	0.889628i	$-0.650964\pi$
$857$	15.8697	−	27.4871i	0.542097	−	0.938940i	0.998783	−	0.0493120i	$-0.0157029\pi$
$858$		0			0
$859$	−24.5215	−	42.4725i	−0.836662	−	1.44914i	−0.892670	−	0.450711i	$-0.851170\pi$
$859$	−24.5215	−	42.4725i	−0.836662	−	1.44914i	0.0560076	−	0.998430i	$-0.482163\pi$
$860$		0			0
$861$	−0.254779	−	0.0735228i	−0.00868286	−	0.00250565i
$862$		0			0
$863$	−30.0248			−1.02206			−0.511028	−	0.859564i	$-0.670735\pi$
$863$	−30.0248			−1.02206			−0.511028	+	0.859564i	$0.670735\pi$
$864$		0			0
$865$	29.1320	−	16.8193i	0.990516	−	0.571875i
$866$		0			0
$867$	14.3178	−	13.7799i	0.486259	−	0.467991i
$868$		0			0
$869$	−2.95448	+	5.11730i	−0.100224	+	0.173593i
$870$		0			0
$871$	3.21638	−	5.57093i	0.108983	−	0.188764i
$872$		0			0
$873$	12.3262	+	0.472138i	0.417180	+	0.0159794i
$874$		0			0
$875$		−	0.461370i		−	0.0155972i
$876$		0			0
$877$	24.0858	+	13.9059i	0.813320	+	0.469571i	0.848107	−	0.529824i	$-0.177742\pi$
$877$	24.0858	+	13.9059i	0.813320	+	0.469571i	−0.0347875	+	0.999395i	$0.511075\pi$
$878$		0			0
$879$	10.0740	+	40.6974i	0.339788	+	1.37269i
$880$		0			0
$881$			7.77018i			0.261784i	0.991397	+	0.130892i	$0.0417841\pi$
$881$			7.77018i			0.261784i	−0.991397	+	0.130892i	$0.958216\pi$
$882$		0			0
$883$	10.4728	+	18.1393i	0.352436	+	0.610438i	0.986676	−	0.162699i	$-0.0520200\pi$
$883$	10.4728	+	18.1393i	0.352436	+	0.610438i	−0.634239	+	0.773137i	$0.718687\pi$
$884$		0			0
$885$	24.7705	+	25.7374i	0.832650	+	0.865154i
$886$		0			0
$887$	7.91269	+	13.7052i	0.265682	+	0.460175i	0.967742	−	0.251943i	$-0.0810695\pi$
$887$	7.91269	+	13.7052i	0.265682	+	0.460175i	−0.702060	+	0.712118i	$0.747736\pi$
$888$		0			0
$889$	1.54982	−	0.894791i	0.0519794	−	0.0300103i
$890$		0			0
$891$	2.87507	+	1.96765i	0.0963184	+	0.0659187i
$892$		0			0
$893$	−2.92056	−	16.9568i	−0.0977328	−	0.567439i
$894$		0			0
$895$	−37.9053	−	21.8846i	−1.26703	−	0.731523i
$896$		0			0
$897$	−6.98380	−	2.01534i	−0.233182	−	0.0672904i
$898$		0			0
$899$	−57.5516	+	33.2275i	−1.91945	+	1.10820i
$900$		0			0
$901$			17.7141i			0.590141i
$902$		0			0
$903$	1.30499	+	0.376586i	0.0434273	+	0.0125320i
$904$		0			0
$905$	43.4444			1.44414
$906$		0			0
$907$	36.3957	+	21.0130i	1.20850	+	0.697727i	0.962431	−	0.271526i	$-0.0875283\pi$
$907$	36.3957	+	21.0130i	1.20850	+	0.697727i	0.246067	+	0.969253i	$0.420862\pi$
$908$		0			0
$909$	1.24801	−	1.98230i	0.0413938	−	0.0657487i
$910$		0			0
$911$	38.2739			1.26807			0.634035	−	0.773304i	$-0.281397\pi$
$911$	38.2739			1.26807			0.634035	+	0.773304i	$0.281397\pi$
$912$		0			0
$913$	−2.38284			−0.0788603
$914$		0			0
$915$	−55.4567	+	13.7275i	−1.83334	+	0.453816i
$916$		0			0
$917$	0.148623	+	0.0858074i	0.00490796	+	0.00283361i
$918$		0			0
$919$	−18.9229			−0.624210			−0.312105	−	0.950048i	$-0.601034\pi$
$919$	−18.9229			−0.624210			−0.312105	+	0.950048i	$0.601034\pi$
$920$		0			0
$921$	−8.14105	+	28.2113i	−0.268257	+	0.929593i
$922$		0			0
$923$			6.01976i			0.198143i
$924$		0			0
$925$	−2.04173	+	1.17880i	−0.0671318	+	0.0387586i
$926$		0			0
$927$	−5.56970	−	10.5610i	−0.182933	−	0.346868i
$928$		0			0
$929$	−34.9229	−	20.1628i	−1.14578	−	0.661519i	−0.197928	−	0.980217i	$-0.563421\pi$
$929$	−34.9229	−	20.1628i	−1.14578	−	0.661519i	−0.947856	+	0.318698i	$0.896754\pi$
$930$		0			0
$931$	−10.5325	+	28.5840i	−0.345187	+	0.936801i
$932$		0			0
$933$	42.4675	−	10.5122i	1.39032	−	0.344154i
$934$		0			0
$935$	−2.30026	+	1.32806i	−0.0752265	+	0.0434321i
$936$		0			0
$937$	−4.87230	−	8.43907i	−0.159171	−	0.275693i	0.775399	−	0.631472i	$-0.217549\pi$
$937$	−4.87230	−	8.43907i	−0.159171	−	0.275693i	−0.934570	+	0.355779i	$0.884216\pi$
$938$		0			0
$939$	−34.8904	+	33.5795i	−1.13860	+	1.09583i
$940$		0			0
$941$	−7.85189	−	13.5999i	−0.255964	−	0.443343i	0.709193	−	0.705015i	$-0.249060\pi$
$941$	−7.85189	−	13.5999i	−0.255964	−	0.443343i	−0.965157	+	0.261672i	$0.915726\pi$
$942$		0			0
$943$		−	6.94508i		−	0.226163i
$944$		0			0
$945$	−0.328360	−	1.58424i	−0.0106815	−	0.0515354i
$946$		0			0
$947$	−20.3779	−	11.7652i	−0.662192	−	0.382317i	0.130919	−	0.991393i	$-0.458207\pi$
$947$	−20.3779	−	11.7652i	−0.662192	−	0.382317i	−0.793112	+	0.609076i	$0.791540\pi$
$948$		0			0
$949$			6.20455i			0.201408i
$950$		0			0
$951$	−33.5106	+	32.2516i	−1.08665	+	1.04583i
$952$		0			0
$953$	−1.48374	+	2.56990i	−0.0480629	+	0.0832474i	−0.889056	−	0.457798i	$-0.848638\pi$
$953$	−1.48374	+	2.56990i	−0.0480629	+	0.0832474i	0.840993	+	0.541046i	$0.181971\pi$
$954$		0			0
$955$	−6.66754	+	11.5485i	−0.215757	+	0.373701i
$956$		0			0
$957$	3.93445	+	4.08804i	0.127183	+	0.132148i
$958$		0			0
$959$	−1.19997	+	0.692805i	−0.0387492	+	0.0223718i
$960$		0			0
$961$	−30.6705			−0.989372
$962$		0			0
$963$	−5.98545	+	3.15663i	−0.192878	+	0.101721i
$964$		0			0
$965$	29.6843	+	51.4147i	0.955570	+	1.65510i
$966$		0			0
$967$	−10.8493	+	18.7916i	−0.348890	+	0.604296i	−0.986053	−	0.166434i	$-0.946775\pi$
$967$	−10.8493	+	18.7916i	−0.348890	+	0.604296i	0.637162	+	0.770730i	$0.280108\pi$
$968$		0			0
$969$	−14.3003	−	10.5139i	−0.459391	−	0.337757i
$970$		0			0
$971$	28.6166	−	49.5654i	0.918351	−	1.59063i	0.116432	−	0.993199i	$-0.462854\pi$
$971$	28.6166	−	49.5654i	0.918351	−	1.59063i	0.801920	−	0.597432i	$-0.203812\pi$
$972$		0			0
$973$	1.11726	+	1.93514i	0.0358176	+	0.0620378i
$974$		0			0
$975$	1.46512	−	5.07710i	0.0469214	−	0.162597i
$976$		0			0
$977$	−11.1449			−0.356558			−0.178279	−	0.983980i	$-0.557053\pi$
$977$	−11.1449			−0.356558			−0.178279	+	0.983980i	$0.557053\pi$
$978$		0			0
$979$	−5.42800	+	3.13386i	−0.173480	+	0.100159i
$980$		0			0
$981$	34.8201	+	1.33373i	1.11172	+	0.0425826i
$982$		0			0
$983$	1.44007	−	2.49428i	0.0459312	−	0.0795551i	−0.842146	−	0.539250i	$-0.818708\pi$
$983$	1.44007	−	2.49428i	0.0459312	−	0.0795551i	0.888077	+	0.459695i	$0.152041\pi$
$984$		0			0
$985$	15.3607	−	26.6055i	0.489433	−	0.847722i
$986$		0			0
$987$	−0.505808	−	0.525553i	−0.0161000	−	0.0167285i
$988$		0			0
$989$			35.5729i			1.13115i
$990$		0			0
$991$	−4.47628	−	2.58438i	−0.142194	−	0.0820955i	0.427215	−	0.904150i	$-0.359495\pi$
$991$	−4.47628	−	2.58438i	−0.142194	−	0.0820955i	−0.569409	+	0.822054i	$0.692828\pi$
$992$		0			0
$993$	−13.8156	+	3.41985i	−0.438425	+	0.108526i
$994$		0			0
$995$			27.2904i			0.865165i
$996$		0			0
$997$	0.222009	+	0.384531i	0.00703110	+	0.0121782i	0.869520	−	0.493899i	$-0.164429\pi$
$997$	0.222009	+	0.384531i	0.00703110	+	0.0121782i	−0.862488	+	0.506077i	$0.831095\pi$
$998$		0			0
$999$	2.59938	−	2.31675i	0.0822406	−	0.0732986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.n.65.5		16
3.2	odd	2		912.2.bn.o.65.7		16
4.3	odd	2		456.2.bf.d.65.4	yes	16
12.11	even	2		456.2.bf.c.65.2	✓	16
19.12	odd	6		912.2.bn.o.449.7		16
57.50	even	6	inner	912.2.bn.n.449.5		16
76.31	even	6		456.2.bf.c.449.2	yes	16
228.107	odd	6		456.2.bf.d.449.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.2	✓	16	12.11	even	2
456.2.bf.c.449.2	yes	16	76.31	even	6
456.2.bf.d.65.4	yes	16	4.3	odd	2
456.2.bf.d.449.4	yes	16	228.107	odd	6
912.2.bn.n.65.5		16	1.1	even	1	trivial
912.2.bn.n.449.5		16	57.50	even	6	inner
912.2.bn.o.65.7		16	3.2	odd	2
912.2.bn.o.449.7		16	19.12	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.416182 + 1.68131i) q^{3} +(-2.52758 - 1.45930i) q^{5} -0.106684 q^{7} +(-2.65359 + 1.39946i) q^{9} +O(q^{10})\)	\(q+(0.416182 + 1.68131i) q^{3} +(-2.52758 - 1.45930i) q^{5} -0.106684 q^{7} +(-2.65359 + 1.39946i) q^{9} +0.387102i q^{11} +(-0.750981 + 0.433579i) q^{13} +(1.40160 - 4.85698i) q^{15} +(-2.03600 - 1.17548i) q^{17} +(1.50709 - 4.09007i) q^{19} +(-0.0443998 - 0.179368i) q^{21} +(4.19115 - 2.41976i) q^{23} +(1.75912 + 3.04689i) q^{25} +(-3.45729 - 3.87906i) q^{27} +(-4.23115 - 7.32856i) q^{29} -7.85306i q^{31} +(-0.650837 + 0.161105i) q^{33} +(0.269652 + 0.155684i) q^{35} +0.670104i q^{37} +(-1.04152 - 1.08218i) q^{39} +(0.717537 - 1.24281i) q^{41} +(-3.67525 + 6.36573i) q^{43} +(8.74939 + 0.335132i) q^{45} +(3.41859 - 1.97372i) q^{47} -6.98862 q^{49} +(1.12900 - 3.91235i) q^{51} +(-3.76741 - 6.52534i) q^{53} +(0.564898 - 0.978432i) q^{55} +(7.50389 + 0.831661i) q^{57} +(-3.53312 + 6.11954i) q^{59} +(-5.65069 - 9.78729i) q^{61} +(0.283095 - 0.149300i) q^{63} +2.53089 q^{65} +(-6.42436 + 3.70911i) q^{67} +(5.81264 + 6.03955i) q^{69} +(3.47097 - 6.01190i) q^{71} +(3.57752 - 6.19644i) q^{73} +(-4.39064 + 4.22569i) q^{75} -0.0412975i q^{77} +(13.2195 + 7.63230i) q^{79} +(5.08303 - 7.42717i) q^{81} +6.15558i q^{83} +(3.43077 + 5.94226i) q^{85} +(10.5606 - 10.1639i) q^{87} +(8.09570 + 14.0222i) q^{89} +(0.0801175 - 0.0462558i) q^{91} +(13.2034 - 3.26830i) q^{93} +(-9.77794 + 8.13871i) q^{95} +(-3.56089 - 2.05588i) q^{97} +(-0.541733 - 1.02721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9}+O(q^{10}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9	\( 16 q - q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} - 12 q^{15} - 3 q^{17} - 11 q^{19} - 12 q^{21} + 3 q^{23} + 11 q^{25} - 4 q^{27} + 5 q^{29} + 14 q^{33} - 24 q^{35} + 9 q^{39} + 6 q^{41} - 13 q^{43} + 33 q^{45} - 27 q^{47} + 8 q^{49} + 18 q^{51} - 7 q^{53} + 12 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} + 26 q^{63} - 30 q^{65} + 24 q^{67} - 41 q^{69} - 27 q^{71} + 2 q^{73} - 21 q^{75} + 21 q^{79} - 13 q^{81} - 5 q^{85} + 23 q^{87} + 25 q^{89} + 78 q^{91} + 22 q^{93} - 13 q^{95} - 60 q^{97} + 20 q^{99}+O(q^{100}) \) 16 * q - q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 - 12 * q^15 - 3 * q^17 - 11 * q^19 - 12 * q^21 + 3 * q^23 + 11 * q^25 - 4 * q^27 + 5 * q^29 + 14 * q^33 - 24 * q^35 + 9 * q^39 + 6 * q^41 - 13 * q^43 + 33 * q^45 - 27 * q^47 + 8 * q^49 + 18 * q^51 - 7 * q^53 + 12 * q^55 - 36 * q^57 + 10 * q^59 - q^61 + 26 * q^63 - 30 * q^65 + 24 * q^67 - 41 * q^69 - 27 * q^71 + 2 * q^73 - 21 * q^75 + 21 * q^79 - 13 * q^81 - 5 * q^85 + 23 * q^87 + 25 * q^89 + 78 * q^91 + 22 * q^93 - 13 * q^95 - 60 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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