LMFDB - Embedded newform 891.2.k.a.161.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("891.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.5
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46797 - 1.06654i) q^{2} +(0.399387 + 1.22919i) q^{4} +(0.706314 + 0.972158i) q^{5} +(-4.60425 + 1.49601i) q^{7} +(-0.396737 + 1.22103i) q^{8} -2.18041i q^{10} +(3.30067 - 0.324896i) q^{11} +(-1.79861 + 2.47557i) q^{13} +(8.35446 + 2.71453i) q^{14} +(3.97590 - 2.88866i) q^{16} +(1.80866 - 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(-0.912871 + 1.25646i) q^{20} +(-5.19180 - 3.04337i) q^{22} -1.98738i q^{23} +(1.09887 - 3.38198i) q^{25} +(5.28060 - 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(-0.524067 - 1.61291i) q^{29} +(-4.29749 - 3.12231i) q^{31} -6.34963 q^{32} -4.05656 q^{34} +(-4.70641 - 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(4.87179 + 6.70545i) q^{38} +(-1.46726 + 0.476740i) q^{40} +(3.28550 - 10.1117i) q^{41} -3.79055i q^{43} +(1.71760 + 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(3.10538 + 1.00900i) q^{47} +(13.2980 - 9.66153i) q^{49} +(-5.22014 + 3.79265i) q^{50} +(-3.76128 - 1.22211i) q^{52} +(-0.749954 + 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} -6.21546i q^{56} +(-0.950924 + 2.92664i) q^{58} +(0.0300536 - 0.00976502i) q^{59} +(-0.697881 - 0.960551i) q^{61} +(2.97851 + 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} -3.67703 q^{65} -2.10554 q^{67} +(2.33759 + 1.69836i) q^{68} +(3.26192 + 10.0392i) q^{70} +(-2.26013 - 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(0.625746 - 1.92585i) q^{74} -5.90368i q^{76} +(-14.7111 + 6.43375i) q^{77} +(-2.24604 + 3.09141i) q^{79} +(5.61646 + 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(-5.88095 + 4.27276i) q^{83} +(2.55496 + 0.830157i) q^{85} +(-4.04278 + 5.56441i) q^{86} +(-0.912791 + 4.15912i) q^{88} -10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(2.44286 - 0.793733i) q^{92} +(-3.48246 - 4.79320i) q^{94} +(-1.69618 - 5.22031i) q^{95} +(-11.7345 - 8.52561i) q^{97} -29.8254 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−1.46797	−	1.06654i	−1.03801	−	0.754159i	−0.0681144	−	0.997678i	$-0.521698\pi$
$2$	−1.46797	−	1.06654i	−1.03801	−	0.754159i	−0.969896	+	0.243519i	$0.921698\pi$
$3$		0			0
$3$		0			0
$4$	0.399387	+	1.22919i	0.199693	+	0.614593i
$5$	0.706314	+	0.972158i	0.315873	+	0.434762i	0.937202	−	0.348788i	$-0.113407\pi$
$5$	0.706314	+	0.972158i	0.315873	+	0.434762i	−0.621328	+	0.783550i	$0.713407\pi$
$6$		0			0
$7$	−4.60425	+	1.49601i	−1.74024	+	0.565439i	−0.994866	−	0.101203i	$-0.967731\pi$
$7$	−4.60425	+	1.49601i	−1.74024	+	0.565439i	−0.745378	+	0.666643i	$0.767731\pi$
$8$	−0.396737	+	1.22103i	−0.140268	+	0.431700i
$9$		0			0
$10$		−	2.18041i		−	0.689506i
$11$	3.30067	−	0.324896i	0.995190	−	0.0979599i
$11$	3.30067	−	0.324896i	0.995190	−	0.0979599i
$12$		0			0
$13$	−1.79861	+	2.47557i	−0.498844	+	0.686599i	−0.981988	−	0.188941i	$-0.939494\pi$
$13$	−1.79861	+	2.47557i	−0.498844	+	0.686599i	0.483145	+	0.875541i	$0.339494\pi$
$14$	8.35446	+	2.71453i	2.23282	+	0.725488i
$15$		0			0
$16$	3.97590	−	2.88866i	0.993974	−	0.722164i
$17$	1.80866	−	1.31407i	0.438664	−	0.318708i	−0.346440	−	0.938072i	$-0.612610\pi$
$17$	1.80866	−	1.31407i	0.438664	−	0.318708i	0.785104	+	0.619364i	$0.212610\pi$
$18$		0			0
$19$	−4.34428	−	1.41154i	−0.996645	−	0.323830i	−0.235121	−	0.971966i	$-0.575549\pi$
$19$	−4.34428	−	1.41154i	−0.996645	−	0.323830i	−0.761524	+	0.648136i	$0.775549\pi$
$20$	−0.912871	+	1.25646i	−0.204124	+	0.280953i
$21$		0			0
$22$	−5.19180	−	3.04337i	−1.10690	−	0.648848i
$23$		−	1.98738i		−	0.414397i	−0.978299	−	0.207199i	$-0.933565\pi$
$23$		−	1.98738i		−	0.414397i	0.978299	−	0.207199i	$-0.0664346\pi$
$24$		0			0
$25$	1.09887	−	3.38198i	0.219775	−	0.676397i
$26$	5.28060	−	1.71577i	1.03561	−	0.336490i
$27$		0			0
$28$	−3.67776	−	5.06200i	−0.695030	−	0.956627i
$29$	−0.524067	−	1.61291i	−0.0973167	−	0.299510i	0.890534	−	0.454917i	$-0.150331\pi$
$29$	−0.524067	−	1.61291i	−0.0973167	−	0.299510i	−0.987851	+	0.155407i	$0.950331\pi$
$30$		0			0
$31$	−4.29749	−	3.12231i	−0.771852	−	0.560783i	0.130671	−	0.991426i	$-0.458287\pi$
$31$	−4.29749	−	3.12231i	−0.771852	−	0.560783i	−0.902523	+	0.430643i	$0.858287\pi$
$32$	−6.34963			−1.12247
$33$		0			0
$34$	−4.05656			−0.695694
$35$	−4.70641	−	3.41941i	−0.795528	−	0.577985i
$36$		0			0
$37$	0.344857	+	1.06136i	0.0566941	+	0.174486i	0.975394	−	0.220471i	$-0.0707594\pi$
$37$	0.344857	+	1.06136i	0.0566941	+	0.174486i	−0.918699	+	0.394957i	$0.870759\pi$
$38$	4.87179	+	6.70545i	0.790309	+	1.08777i
$39$		0			0
$40$	−1.46726	+	0.476740i	−0.231994	+	0.0753793i
$41$	3.28550	−	10.1117i	0.513109	−	1.57919i	−0.273587	−	0.961847i	$-0.588210\pi$
$41$	3.28550	−	10.1117i	0.513109	−	1.57919i	0.786696	−	0.617341i	$-0.211790\pi$
$42$		0			0
$43$		−	3.79055i		−	0.578054i	−0.957321	−	0.289027i	$-0.906668\pi$
$43$		−	3.79055i		−	0.578054i	0.957321	−	0.289027i	$-0.0933317\pi$
$44$	1.71760	+	3.92738i	0.258938	+	0.592075i
$45$		0			0
$46$	−2.11962	+	2.91741i	−0.312521	+	0.430149i
$47$	3.10538	+	1.00900i	0.452967	+	0.147178i	0.526610	−	0.850107i	$-0.323463\pi$
$47$	3.10538	+	1.00900i	0.452967	+	0.147178i	−0.0736436	+	0.997285i	$0.523463\pi$
$48$		0			0
$49$	13.2980	−	9.66153i	1.89971	−	1.38022i
$50$	−5.22014	+	3.79265i	−0.738239	+	0.536362i
$51$		0			0
$52$	−3.76128	−	1.22211i	−0.521595	−	0.169477i
$53$	−0.749954	+	1.03222i	−0.103014	+	0.141787i	−0.857412	−	0.514631i	$-0.827929\pi$
$53$	−0.749954	+	1.03222i	−0.103014	+	0.141787i	0.754398	+	0.656417i	$0.227929\pi$
$54$		0			0
$55$	2.64716	+	2.97930i	0.356943	+	0.401728i
$56$		−	6.21546i		−	0.830575i
$57$		0			0
$58$	−0.950924	+	2.92664i	−0.124862	+	0.384287i
$59$	0.0300536	−	0.00976502i	0.00391265	−	0.00127130i	−0.307060	−	0.951690i	$-0.599345\pi$
$59$	0.0300536	−	0.00976502i	0.00391265	−	0.00127130i	0.310973	+	0.950419i	$0.399345\pi$
$60$		0			0
$61$	−0.697881	−	0.960551i	−0.0893545	−	0.122986i	0.761999	−	0.647578i	$-0.224218\pi$
$61$	−0.697881	−	0.960551i	−0.0893545	−	0.122986i	−0.851354	+	0.524592i	$0.824218\pi$
$62$	2.97851	+	9.16690i	0.378271	+	1.16420i
$63$		0			0
$64$	1.36926	+	0.994827i	0.171158	+	0.124353i
$65$	−3.67703			−0.456079
$66$		0			0
$67$	−2.10554			−0.257233			−0.128617	−	0.991694i	$-0.541054\pi$
$67$	−2.10554			−0.257233			−0.128617	+	0.991694i	$0.541054\pi$
$68$	2.33759	+	1.69836i	0.283474	+	0.205956i
$69$		0			0
$70$	3.26192	+	10.0392i	0.389874	+	1.19991i
$71$	−2.26013	−	3.11080i	−0.268228	−	0.369184i	0.653563	−	0.756873i	$-0.273274\pi$
$71$	−2.26013	−	3.11080i	−0.268228	−	0.369184i	−0.921790	+	0.387688i	$0.873274\pi$
$72$		0			0
$73$	6.69980	−	2.17690i	0.784152	−	0.254786i	0.110540	−	0.993872i	$-0.464742\pi$
$73$	6.69980	−	2.17690i	0.784152	−	0.254786i	0.673612	+	0.739085i	$0.264742\pi$
$74$	0.625746	−	1.92585i	0.0727414	−	0.223875i
$75$		0			0
$76$		−	5.90368i		−	0.677198i
$77$	−14.7111	+	6.43375i	−1.67648	+	0.733194i
$78$		0			0
$79$	−2.24604	+	3.09141i	−0.252700	+	0.347811i	−0.916454	−	0.400139i	$-0.868962\pi$
$79$	−2.24604	+	3.09141i	−0.252700	+	0.347811i	0.663755	+	0.747950i	$0.268962\pi$
$80$	5.61646	+	1.82490i	0.627940	+	0.204030i
$81$		0			0
$82$	−15.6076	+	11.3396i	−1.72357	+	1.25225i
$83$	−5.88095	+	4.27276i	−0.645518	+	0.468996i	−0.861742	−	0.507348i	$-0.830626\pi$
$83$	−5.88095	+	4.27276i	−0.645518	+	0.468996i	0.216223	+	0.976344i	$0.430626\pi$
$84$		0			0
$85$	2.55496	+	0.830157i	0.277124	+	0.0900431i
$86$	−4.04278	+	5.56441i	−0.435945	+	0.600026i
$87$		0			0
$88$	−0.912791	+	4.15912i	−0.0973039	+	0.443364i
$89$		−	10.2875i		−	1.09048i	−0.838281	−	0.545238i	$-0.816439\pi$
$89$		−	10.2875i		−	1.09048i	0.838281	−	0.545238i	$-0.183561\pi$
$90$		0			0
$91$	4.57775	−	14.0889i	0.479879	−	1.47692i
$92$	2.44286	−	0.793733i	0.254686	−	0.0827524i
$93$		0			0
$94$	−3.48246	−	4.79320i	−0.359189	−	0.494381i
$95$	−1.69618	−	5.22031i	−0.174025	−	0.535593i
$96$		0			0
$97$	−11.7345	−	8.52561i	−1.19146	−	0.865644i	−0.198040	−	0.980194i	$-0.563458\pi$
$97$	−11.7345	−	8.52561i	−1.19146	−	0.865644i	−0.993418	+	0.114549i	$0.963458\pi$
$98$	−29.8254			−3.01282
$99$		0			0
$100$	4.59597			0.459597
$101$	−13.0136	−	9.45494i	−1.29490	−	0.940802i	−0.295011	−	0.955494i	$-0.595323\pi$
$101$	−13.0136	−	9.45494i	−1.29490	−	0.940802i	−0.999892	+	0.0146921i	$0.995323\pi$
$102$		0			0
$103$	−0.643116	−	1.97931i	−0.0633681	−	0.195027i	0.914360	−	0.404902i	$-0.132694\pi$
$103$	−0.643116	−	1.97931i	−0.0633681	−	0.195027i	−0.977728	+	0.209875i	$0.932694\pi$
$104$	−2.30917	−	3.17830i	−0.226433	−	0.311658i
$105$		0			0
$106$	2.20182	−	0.715414i	0.213859	−	0.0694871i
$107$	0.129361	−	0.398133i	0.0125058	−	0.0384889i	−0.944609	−	0.328198i	$-0.893559\pi$
$107$	0.129361	−	0.398133i	0.0125058	−	0.0384889i	0.957115	+	0.289709i	$0.0935586\pi$
$108$		0			0
$109$			14.6788i			1.40597i	0.711205	+	0.702985i	$0.248150\pi$
$109$			14.6788i			1.40597i	−0.711205	+	0.702985i	$0.751850\pi$
$110$	−0.708407	−	7.19682i	−0.0675440	−	0.686190i
$111$		0			0
$112$	−13.9846	+	19.2481i	−1.32142	+	1.81877i
$113$	−3.04019	−	0.987818i	−0.285997	−	0.0929261i	0.162505	−	0.986708i	$-0.448043\pi$
$113$	−3.04019	−	0.987818i	−0.285997	−	0.0929261i	−0.448503	+	0.893782i	$0.648043\pi$
$114$		0			0
$115$	1.93205	−	1.40371i	0.180164	−	0.130897i
$116$	1.77326	−	1.28835i	0.164643	−	0.119620i
$117$		0			0
$118$	−0.0545326	−	0.0177187i	−0.00502013	−	0.00163114i
$119$	−6.36165	+	8.75606i	−0.583172	+	0.802667i
$120$		0			0
$121$	10.7889	−	2.14475i	0.980808	−	0.194977i
$122$			2.15438i			0.195048i
$123$		0			0
$124$	2.12154	−	6.52943i	0.190520	−	0.586360i
$125$	9.77817	−	3.17712i	0.874587	−	0.284170i
$126$		0			0
$127$	−13.1088	−	18.0428i	−1.16322	−	1.60104i	−0.698567	−	0.715545i	$-0.746179\pi$
$127$	−13.1088	−	18.0428i	−1.16322	−	1.60104i	−0.464654	−	0.885492i	$-0.653821\pi$
$128$	2.97528	+	9.15696i	0.262980	+	0.809368i
$129$		0			0
$130$	5.39776	+	3.92170i	0.473415	+	0.343956i
$131$	15.4992			1.35417			0.677086	−	0.735904i	$-0.263243\pi$
$131$	15.4992			1.35417			0.677086	+	0.735904i	$0.263243\pi$
$132$		0			0
$133$	22.1138			1.91751
$134$	3.09087	+	2.24565i	0.267011	+	0.193995i
$135$		0			0
$136$	0.886955	+	2.72977i	0.0760557	+	0.234075i
$137$	10.0751	+	13.8672i	0.860773	+	1.18475i	0.981385	+	0.192053i	$0.0615144\pi$
$137$	10.0751	+	13.8672i	0.860773	+	1.18475i	−0.120612	+	0.992700i	$0.538486\pi$
$138$		0			0
$139$	−9.86040	+	3.20384i	−0.836348	+	0.271746i	−0.695717	−	0.718316i	$-0.744913\pi$
$139$	−9.86040	+	3.20384i	−0.836348	+	0.271746i	−0.140631	+	0.990062i	$0.544913\pi$
$140$	2.32341	−	7.15072i	0.196364	−	0.604346i
$141$		0			0
$142$			6.97708i			0.585503i
$143$	−5.13231	+	8.75541i	−0.429185	+	0.732164i
$144$		0			0
$145$	1.19785	−	1.64870i	0.0994759	−	0.136917i
$146$	−12.1568	−	3.95000i	−1.00611	−	0.326904i
$147$		0			0
$148$	−1.16688	+	0.847786i	−0.0959168	+	0.0696876i
$149$	−0.0327310	+	0.0237805i	−0.00268143	+	0.00194817i	−0.589125	−	0.808042i	$-0.700528\pi$
$149$	−0.0327310	+	0.0237805i	−0.00268143	+	0.00194817i	0.586444	+	0.809990i	$0.300528\pi$
$150$		0			0
$151$	2.61695	+	0.850299i	0.212964	+	0.0691964i	0.413556	−	0.910479i	$-0.364286\pi$
$151$	2.61695	+	0.850299i	0.212964	+	0.0691964i	−0.200592	+	0.979675i	$0.564286\pi$
$152$	3.44707	−	4.74449i	0.279594	−	0.384829i
$153$		0			0
$154$	28.4573	+	6.24544i	2.29315	+	0.503272i
$155$		−	6.38317i		−	0.512709i
$156$		0			0
$157$	0.651985	−	2.00660i	0.0520341	−	0.160145i	−0.921663	−	0.387992i	$-0.873169\pi$
$157$	0.651985	−	2.00660i	0.0520341	−	0.160145i	0.973697	+	0.227848i	$0.0731688\pi$
$158$	6.59424	−	2.14260i	0.524610	−	0.170456i
$159$		0			0
$160$	−4.48483	−	6.17284i	−0.354557	−	0.488006i
$161$	2.97314	+	9.15039i	0.234316	+	0.721152i
$162$		0			0
$163$	−11.8085	−	8.57941i	−0.924917	−	0.671991i	0.0198264	−	0.999803i	$-0.493689\pi$
$163$	−11.8085	−	8.57941i	−0.924917	−	0.671991i	−0.944743	+	0.327812i	$0.893689\pi$
$164$	13.7414			1.07302
$165$		0			0
$166$	13.1901			1.02375
$167$	−0.721863	−	0.524464i	−0.0558594	−	0.0405843i	0.559505	−	0.828827i	$-0.310991\pi$
$167$	−0.721863	−	0.524464i	−0.0558594	−	0.0405843i	−0.615365	+	0.788243i	$0.710991\pi$
$168$		0			0
$169$	1.12376	+	3.45858i	0.0864432	+	0.266045i
$170$	−2.86520	−	3.94362i	−0.219751	−	0.302461i
$171$		0			0
$172$	4.65930	−	1.51390i	0.355268	−	0.115434i
$173$	4.09368	−	12.5991i	0.311237	−	0.957889i	−0.666039	−	0.745917i	$-0.732011\pi$
$173$	4.09368	−	12.5991i	0.311237	−	0.957889i	0.977276	−	0.211972i	$-0.0679885\pi$
$174$		0			0
$175$			17.2154i			1.30136i
$176$	12.1846	−	10.8263i	0.918450	−	0.816060i
$177$		0			0
$178$	−10.9721	+	15.1018i	−0.822392	+	1.13193i
$179$	−19.1587	−	6.22502i	−1.43199	−	0.465280i	−0.512596	−	0.858630i	$-0.671316\pi$
$179$	−19.1587	−	6.22502i	−1.43199	−	0.465280i	−0.919389	+	0.393350i	$0.871316\pi$
$180$		0			0
$181$	3.63758	−	2.64286i	0.270379	−	0.196442i	−0.444331	−	0.895863i	$-0.646559\pi$
$181$	3.63758	−	2.64286i	0.270379	−	0.196442i	0.714710	+	0.699421i	$0.246559\pi$
$182$	−21.7464	+	15.7997i	−1.61195	+	1.17115i
$183$		0			0
$184$	2.42665	+	0.788467i	0.178895	+	0.0581265i
$185$	−0.788232	+	1.08491i	−0.0579520	+	0.0797641i
$186$		0			0
$187$	5.54285	−	4.92493i	0.405333	−	0.360146i
$188$			4.22008i			0.307781i
$189$		0			0
$190$	−3.07774	+	9.47231i	−0.223283	+	0.687193i
$191$	16.9040	−	5.49245i	1.22313	−	0.397420i	0.374910	−	0.927061i	$-0.377673\pi$
$191$	16.9040	−	5.49245i	1.22313	−	0.397420i	0.848222	+	0.529641i	$0.177673\pi$
$192$		0			0
$193$	3.62015	+	4.98270i	0.260584	+	0.358663i	0.919183	−	0.393831i	$-0.128851\pi$
$193$	3.62015	+	4.98270i	0.260584	+	0.358663i	−0.658599	+	0.752494i	$0.728851\pi$
$194$	8.13295	+	25.0307i	0.583912	+	1.79710i
$195$		0			0
$196$	17.1869	+	12.4870i	1.22763	+	0.891927i
$197$	22.5100			1.60377			0.801886	−	0.597477i	$-0.203830\pi$
$197$	22.5100			1.60377			0.801886	+	0.597477i	$0.203830\pi$
$198$		0			0
$199$	9.30680			0.659742			0.329871	−	0.944026i	$-0.392995\pi$
$199$	9.30680			0.659742			0.329871	+	0.944026i	$0.392995\pi$
$200$	3.69355	+	2.68352i	0.261173	+	0.189753i
$201$		0			0
$202$	9.01948	+	27.7591i	0.634609	+	1.95312i
$203$	4.82587	+	6.64224i	0.338710	+	0.466194i
$204$		0			0
$205$	12.1508	−	3.94804i	0.848649	−	0.275743i
$206$	−1.16694	+	3.59147i	−0.0813046	+	0.250230i
$207$		0			0
$208$			15.0382i			1.04271i
$209$	−14.7976	−	3.24760i	−1.02357	−	0.224641i
$210$		0			0
$211$	8.23554	−	11.3352i	0.566958	−	0.780351i	−0.425232	−	0.905084i	$-0.639808\pi$
$211$	8.23554	−	11.3352i	0.566958	−	0.780351i	0.992190	+	0.124734i	$0.0398076\pi$
$212$	−1.56832	−	0.509577i	−0.107712	−	0.0349979i
$213$		0			0
$214$	−0.614523	+	0.446477i	−0.0420079	+	0.0305206i
$215$	3.68502	−	2.67732i	0.251316	−	0.182592i
$216$		0			0
$217$	24.4577	+	7.94680i	1.66030	+	0.539464i
$218$	15.6555	−	21.5480i	1.06032	−	1.45941i
$219$		0			0
$220$	−2.60487	+	4.44375i	−0.175620	+	0.299597i
$221$			6.84094i			0.460172i
$222$		0			0
$223$	−4.98529	+	15.3432i	−0.333840	+	1.02745i	0.633451	+	0.773783i	$0.281638\pi$
$223$	−4.98529	+	15.3432i	−0.333840	+	1.02745i	−0.967291	+	0.253671i	$0.918362\pi$
$224$	29.2353	−	9.49912i	1.95336	−	0.634686i
$225$		0			0
$226$	3.40936	+	4.69258i	0.226787	+	0.312146i
$227$	−4.54715	−	13.9947i	−0.301805	−	0.928861i	−0.980850	−	0.194764i	$-0.937606\pi$
$227$	−4.54715	−	13.9947i	−0.301805	−	0.928861i	0.679045	−	0.734097i	$-0.262394\pi$
$228$		0			0
$229$	−17.9594	−	13.0482i	−1.18679	−	0.862252i	−0.193867	−	0.981028i	$-0.562103\pi$
$229$	−17.9594	−	13.0482i	−1.18679	−	0.862252i	−0.992921	+	0.118775i	$0.962103\pi$
$230$	−4.33330			−0.285729
$231$		0			0
$232$	2.17733			0.142949
$233$	4.18134	+	3.03792i	0.273929	+	0.199021i	0.716265	−	0.697828i	$-0.245850\pi$
$233$	4.18134	+	3.03792i	0.273929	+	0.199021i	−0.442336	+	0.896849i	$0.645850\pi$
$234$		0			0
$235$	1.21247	+	3.73159i	0.0790927	+	0.243422i
$236$	0.0240061	+	0.0330415i	0.00156266	+	0.00215082i
$237$		0			0
$238$	18.6774	−	6.06866i	1.21068	−	0.393373i
$239$	−4.22278	+	12.9964i	−0.273149	+	0.840665i	0.716555	+	0.697531i	$0.245718\pi$
$239$	−4.22278	+	12.9964i	−0.273149	+	0.840665i	−0.989703	+	0.143134i	$0.954282\pi$
$240$		0			0
$241$		−	7.05251i		−	0.454292i	−0.973861	−	0.227146i	$-0.927061\pi$
$241$		−	7.05251i		−	0.454292i	0.973861	−	0.227146i	$-0.0729395\pi$
$242$	−18.1252	−	8.35837i	−1.16513	−	0.537296i
$243$		0			0
$244$	0.901971	−	1.24146i	0.0577428	−	0.0794761i
$245$	18.7851	+	6.10364i	1.20013	+	0.389947i
$246$		0			0
$247$	11.3080	−	8.21575i	0.719512	−	0.522756i
$248$	5.51741	−	4.00863i	0.350356	−	0.254548i
$249$		0			0
$250$	−17.7426	−	5.76492i	−1.12214	−	0.364605i
$251$	3.95496	−	5.44354i	0.249635	−	0.343593i	−0.665748	−	0.746176i	$-0.731888\pi$
$251$	3.95496	−	5.44354i	0.249635	−	0.343593i	0.915383	+	0.402583i	$0.131888\pi$
$252$		0			0
$253$	−0.645692	−	6.55969i	−0.0405943	−	0.412404i
$254$			40.4673i			2.53915i
$255$		0			0
$256$	6.44469	−	19.8347i	0.402793	−	1.23967i
$257$	13.4589	−	4.37306i	0.839543	−	0.272784i	0.142483	−	0.989797i	$-0.454491\pi$
$257$	13.4589	−	4.37306i	0.839543	−	0.272784i	0.697060	+	0.717013i	$0.254491\pi$
$258$		0			0
$259$	−3.17561	−	4.37086i	−0.197323	−	0.271592i
$260$	−1.46856	−	4.51975i	−0.0910760	−	0.280303i
$261$		0			0
$262$	−22.7523	−	16.5305i	−1.40564	−	1.02126i
$263$	6.94583			0.428298			0.214149	−	0.976801i	$-0.431302\pi$
$263$	6.94583			0.428298			0.214149	+	0.976801i	$0.431302\pi$
$264$		0			0
$265$	−1.53319			−0.0941829
$266$	−32.4624	−	23.5853i	−1.99040	−	1.44611i
$267$		0			0
$268$	−0.840926	−	2.58811i	−0.0513678	−	0.158094i
$269$	−4.05850	−	5.58605i	−0.247451	−	0.340587i	0.667165	−	0.744910i	$-0.267507\pi$
$269$	−4.05850	−	5.58605i	−0.247451	−	0.340587i	−0.914617	+	0.404322i	$0.867507\pi$
$270$		0			0
$271$	−12.9581	+	4.21033i	−0.787146	+	0.255759i	−0.674888	−	0.737920i	$-0.735808\pi$
$271$	−12.9581	+	4.21033i	−0.787146	+	0.255759i	−0.112258	+	0.993679i	$0.535808\pi$
$272$	3.39514	−	10.4492i	0.205861	−	0.633575i
$273$		0			0
$274$		−	31.1021i		−	1.87895i
$275$	2.52823	−	11.5198i	0.152458	−	0.694673i
$276$		0			0
$277$	−6.85079	+	9.42931i	−0.411624	+	0.566552i	−0.963614	−	0.267299i	$-0.913869\pi$
$277$	−6.85079	+	9.42931i	−0.411624	+	0.566552i	0.551989	+	0.833851i	$0.313869\pi$
$278$	17.8918	+	5.81339i	1.07308	+	0.348664i
$279$		0			0
$280$	6.04241	−	4.39007i	0.361103	−	0.262357i
$281$	17.6693	−	12.8375i	1.05406	−	0.765823i	0.0810832	−	0.996707i	$-0.474162\pi$
$281$	17.6693	−	12.8375i	1.05406	−	0.765823i	0.972981	+	0.230885i	$0.0741621\pi$
$282$		0			0
$283$	−22.3258	−	7.25408i	−1.32713	−	0.431210i	−0.442191	−	0.896921i	$-0.645799\pi$
$283$	−22.3258	−	7.25408i	−1.32713	−	0.431210i	−0.884937	+	0.465711i	$0.845799\pi$
$284$	2.92109	−	4.02053i	0.173335	−	0.238575i
$285$		0			0
$286$	16.8721	−	7.37884i	0.997667	−	0.436320i
$287$			51.4721i			3.03830i
$288$		0			0
$289$	−3.70882	+	11.4146i	−0.218166	+	0.671445i
$290$	−3.51681	+	1.14268i	−0.206514	+	0.0671005i
$291$		0			0
$292$	5.35162	+	7.36588i	0.313180	+	0.431055i
$293$	−0.524298	−	1.61362i	−0.0306298	−	0.0942689i	0.934573	−	0.355772i	$-0.115782\pi$
$293$	−0.524298	−	1.61362i	−0.0306298	−	0.0942689i	−0.965203	+	0.261503i	$0.915782\pi$
$294$		0			0
$295$	0.0307205	+	0.0223197i	0.00178861	+	0.00129950i
$296$	−1.43277			−0.0832781
$297$		0			0
$298$	0.0734110			0.00425258
$299$	4.91989	+	3.57451i	0.284525	+	0.206719i
$300$		0			0
$301$	5.67071	+	17.4527i	0.326855	+	1.00595i
$302$	−2.93472	−	4.03930i	−0.168874	−	0.232436i
$303$		0			0
$304$	−21.3498	+	6.93699i	−1.22450	+	0.397863i
$305$	0.440884	−	1.35690i	0.0252449	−	0.0776959i
$306$		0			0
$307$		−	2.35281i		−	0.134282i	−0.997743	−	0.0671410i	$-0.978612\pi$
$307$		−	2.35281i		−	0.134282i	0.997743	−	0.0671410i	$-0.0213877\pi$
$308$	−13.7837	−	15.5131i	−0.785399	−	0.883941i
$309$		0			0
$310$	−6.80792	+	9.37029i	−0.386664	+	0.532197i
$311$	−10.0872	−	3.27754i	−0.571995	−	0.185852i	0.00871654	−	0.999962i	$-0.497225\pi$
$311$	−10.0872	−	3.27754i	−0.571995	−	0.185852i	−0.580711	+	0.814110i	$0.697225\pi$
$312$		0			0
$313$	20.4957	−	14.8910i	1.15849	−	0.841691i	0.168902	−	0.985633i	$-0.445978\pi$
$313$	20.4957	−	14.8910i	1.15849	−	0.841691i	0.989586	+	0.143942i	$0.0459779\pi$
$314$	−3.09722	+	2.25026i	−0.174786	+	0.126990i
$315$		0			0
$316$	−4.69696	−	1.52614i	−0.264225	−	0.0858518i
$317$	−15.7600	+	21.6917i	−0.885168	+	1.21833i	0.0897951	+	0.995960i	$0.471379\pi$
$317$	−15.7600	+	21.6917i	−0.885168	+	1.21833i	−0.974963	+	0.222368i	$0.928621\pi$
$318$		0			0
$319$	−2.25380	−	5.15343i	−0.126189	−	0.288536i
$320$			2.03380i			0.113693i
$321$		0			0
$322$	5.39479	−	16.6035i	0.300640	−	0.925275i
$323$	−9.71216	+	3.15567i	−0.540399	+	0.175586i
$324$		0			0
$325$	6.39590	+	8.80320i	0.354781	+	0.488314i
$326$	8.18427	+	25.1886i	0.453285	+	1.39507i
$327$		0			0
$328$	11.0433	+	8.02340i	0.609762	+	0.443018i
$329$	−15.8074			−0.871492
$330$		0			0
$331$	−17.3237			−0.952198			−0.476099	−	0.879392i	$-0.657950\pi$
$331$	−17.3237			−0.952198			−0.476099	+	0.879392i	$0.657950\pi$
$332$	−7.60079	−	5.52230i	−0.417148	−	0.303076i
$333$		0			0
$334$	0.500309	+	1.53979i	0.0273757	+	0.0842538i
$335$	−1.48717	−	2.04692i	−0.0812530	−	0.111835i
$336$		0			0
$337$	−12.3674	+	4.01842i	−0.673696	+	0.218897i	−0.625833	−	0.779957i	$-0.715241\pi$
$337$	−12.3674	+	4.01842i	−0.673696	+	0.218897i	−0.0478628	+	0.998854i	$0.515241\pi$
$338$	2.03908	−	6.27563i	0.110911	−	0.341349i
$339$		0			0
$340$			3.47208i			0.188300i
$341$	−15.1990	−	8.90948i	−0.823074	−	0.482476i
$342$		0			0
$343$	−26.8543	+	36.9618i	−1.45000	+	1.99575i
$344$	4.62838	+	1.50385i	0.249546	+	0.0810823i
$345$		0			0
$346$	−19.4468	+	14.1289i	−1.04547	+	0.759577i
$347$	−17.1967	+	12.4941i	−0.923168	+	0.670721i	−0.944310	−	0.329056i	$-0.893270\pi$
$347$	−17.1967	+	12.4941i	−0.923168	+	0.670721i	0.0211427	+	0.999776i	$0.493270\pi$
$348$		0			0
$349$	8.87430	+	2.88343i	0.475030	+	0.154347i	0.536740	−	0.843747i	$-0.319655\pi$
$349$	8.87430	+	2.88343i	0.475030	+	0.154347i	−0.0617102	+	0.998094i	$0.519655\pi$
$350$	18.3610	−	25.2717i	0.981436	−	1.35083i
$351$		0			0
$352$	−20.9580	+	2.06297i	−1.11707	+	0.109957i
$353$			9.12141i			0.485483i	0.970091	+	0.242742i	$0.0780468\pi$
$353$			9.12141i			0.485483i	−0.970091	+	0.242742i	$0.921953\pi$
$354$		0			0
$355$	1.42783	−	4.39440i	0.0757813	−	0.233231i
$356$	12.6453	−	4.10870i	0.670199	−	0.217761i
$357$		0			0
$358$	21.4851	+	29.5716i	1.13552	+	1.56291i
$359$	2.41692	+	7.43851i	0.127560	+	0.392589i	0.994359	−	0.106069i	$-0.0338263\pi$
$359$	2.41692	+	7.43851i	0.127560	+	0.392589i	−0.866799	+	0.498658i	$0.833826\pi$
$360$		0			0
$361$	1.50897	+	1.09633i	0.0794193	+	0.0577015i
$362$	−8.15857			−0.428805
$363$		0			0
$364$	19.1462			1.00353
$365$	6.84845	+	4.97569i	0.358464	+	0.260439i
$366$		0			0
$367$	7.57224	+	23.3050i	0.395268	+	1.21651i	0.928753	+	0.370700i	$0.120882\pi$
$367$	7.57224	+	23.3050i	0.395268	+	1.21651i	−0.533485	+	0.845810i	$0.679118\pi$
$368$	−5.74086	−	7.90161i	−0.299263	−	0.411900i
$369$		0			0
$370$	2.31420	−	0.751929i	0.120310	−	0.0390909i
$371$	1.90876	−	5.87455i	0.0990978	−	0.304992i
$372$		0			0
$373$		−	2.86129i		−	0.148152i	−0.997253	−	0.0740760i	$-0.976399\pi$
$373$		−	2.86129i		−	0.148152i	0.997253	−	0.0740760i	$-0.0236007\pi$
$374$	−13.3894	+	1.31796i	−0.692348	+	0.0681501i
$375$		0			0
$376$	−2.46404	+	3.39146i	−0.127073	+	0.174901i
$377$	4.93546	+	1.60363i	0.254189	+	0.0825911i
$378$		0			0
$379$	23.6747	−	17.2007i	1.21609	−	0.883540i	0.220320	−	0.975428i	$-0.429290\pi$
$379$	23.6747	−	17.2007i	1.21609	−	0.883540i	0.995769	+	0.0918872i	$0.0292899\pi$
$380$	5.73931	−	4.16985i	0.294420	−	0.213909i
$381$		0			0
$382$	−30.6725	−	9.96610i	−1.56934	−	0.509910i
$383$	16.7280	−	23.0242i	0.854762	−	1.17648i	−0.128031	−	0.991770i	$-0.540866\pi$
$383$	16.7280	−	23.0242i	0.854762	−	1.17648i	0.982793	−	0.184709i	$-0.0591343\pi$
$384$		0			0
$385$	−16.6453	−	9.75724i	−0.848321	−	0.497275i
$386$		−	11.1755i		−	0.568818i
$387$		0			0
$388$	5.79296	−	17.8289i	0.294093	−	0.905125i
$389$	−13.5825	+	4.41321i	−0.688658	+	0.223759i	−0.632382	−	0.774657i	$-0.717923\pi$
$389$	−13.5825	+	4.41321i	−0.688658	+	0.223759i	−0.0562761	+	0.998415i	$0.517923\pi$
$390$		0			0
$391$	−2.61155	−	3.59449i	−0.132072	−	0.181781i
$392$	6.52124	+	20.0703i	0.329372	+	1.01370i
$393$		0			0
$394$	−33.0440	−	24.0079i	−1.66473	−	1.20950i
$395$	−4.59175			−0.231036
$396$		0			0
$397$	2.20687			0.110760			0.0553798	−	0.998465i	$-0.482363\pi$
$397$	2.20687			0.110760			0.0553798	+	0.998465i	$0.482363\pi$
$398$	−13.6621	−	9.92609i	−0.684819	−	0.497550i
$399$		0			0
$400$	−5.40039	−	16.6207i	−0.270019	−	0.831034i
$401$	18.5405	+	25.5188i	0.925869	+	1.27435i	0.961449	+	0.274983i	$0.0886721\pi$
$401$	18.5405	+	25.5188i	0.925869	+	1.27435i	−0.0355802	+	0.999367i	$0.511328\pi$
$402$		0			0
$403$	15.4590	−	5.02293i	0.770067	−	0.250210i
$404$	6.42442	−	19.7723i	0.319627	−	0.983710i
$405$		0			0
$406$		−	14.8976i		−	0.739355i
$407$	1.48309	+	3.39116i	0.0735141	+	0.168093i
$408$		0			0
$409$	−3.98413	+	5.48368i	−0.197002	+	0.271150i	−0.896077	−	0.443898i	$-0.853595\pi$
$409$	−3.98413	+	5.48368i	−0.197002	+	0.271150i	0.699075	+	0.715048i	$0.253595\pi$
$410$	−22.0477	−	7.16375i	−1.08886	−	0.353792i
$411$		0			0
$412$	2.17609	−	1.58102i	0.107208	−	0.0778913i
$413$	−0.123766	+	0.0899212i	−0.00609012	+	0.00442473i
$414$		0			0
$415$	−8.30760	−	2.69930i	−0.407804	−	0.132504i
$416$	11.4205	−	15.7189i	0.559935	−	0.770685i
$417$		0			0
$418$	18.2588	+	20.5497i	0.893066	+	1.00512i
$419$			28.6088i			1.39763i	0.715302	+	0.698815i	$0.246289\pi$
$419$			28.6088i			1.39763i	−0.715302	+	0.698815i	$0.753711\pi$
$420$		0			0
$421$	−1.72842	+	5.31954i	−0.0842381	+	0.259258i	−0.984300	−	0.176504i	$-0.943521\pi$
$421$	−1.72842	+	5.31954i	−0.0842381	+	0.259258i	0.900062	+	0.435762i	$0.143521\pi$
$422$	−24.1790	+	7.85624i	−1.17702	+	0.382436i
$423$		0			0
$424$	−0.962842	−	1.32524i	−0.0467597	−	0.0643592i
$425$	−2.45667	−	7.56084i	−0.119166	−	0.366755i
$426$		0			0
$427$	4.65021	+	3.37858i	0.225040	+	0.163501i
$428$	0.541044			0.0261524
$429$		0			0
$430$	−8.26497			−0.398572
$431$	−15.7825	−	11.4667i	−0.760216	−	0.552329i	0.138760	−	0.990326i	$-0.455688\pi$
$431$	−15.7825	−	11.4667i	−0.760216	−	0.552329i	−0.898977	+	0.437997i	$0.855688\pi$
$432$		0			0
$433$	−6.96921	−	21.4490i	−0.334919	−	1.03077i	−0.966762	−	0.255678i	$-0.917701\pi$
$433$	−6.96921	−	21.4490i	−0.334919	−	1.03077i	0.631843	−	0.775096i	$-0.282299\pi$
$434$	−27.4276	−	37.7508i	−1.31657	−	1.81210i
$435$		0			0
$436$	−18.0429	+	5.86250i	−0.864099	+	0.280763i
$437$	−2.80527	+	8.63372i	−0.134194	+	0.413007i
$438$		0			0
$439$		−	29.9870i		−	1.43120i	−0.698509	−	0.715601i	$-0.746153\pi$
$439$		−	29.9870i		−	1.43120i	0.698509	−	0.715601i	$-0.253847\pi$
$440$	−4.68804	+	2.05027i	−0.223494	+	0.0977428i
$441$		0			0
$442$	7.29615	−	10.0423i	0.347043	−	0.477663i
$443$	−30.0035	−	9.74873i	−1.42551	−	0.463176i	−0.508161	−	0.861262i	$-0.669675\pi$
$443$	−30.0035	−	9.74873i	−1.42551	−	0.463176i	−0.917348	+	0.398086i	$0.869675\pi$
$444$		0			0
$445$	10.0011	−	7.26623i	0.474098	−	0.344452i
$446$	23.6824	−	17.2063i	1.12139	−	0.814740i
$447$		0			0
$448$	−7.79270	−	2.53200i	−0.368171	−	0.119626i
$449$	−22.3362	+	30.7432i	−1.05411	+	1.45086i	−0.168921	+	0.985630i	$0.554028\pi$
$449$	−22.3362	+	30.7432i	−1.05411	+	1.45086i	−0.885190	+	0.465229i	$0.845972\pi$
$450$		0			0
$451$	7.55911	−	34.4430i	0.355944	−	1.62186i
$452$		−	4.13148i		−	0.194329i
$453$		0			0
$454$	−8.25085	+	25.3935i	−0.387232	+	1.19178i
$455$	16.9300	−	5.50087i	0.793688	−	0.257885i
$456$		0			0
$457$	−23.0565	−	31.7345i	−1.07854	−	1.48448i	−0.861123	−	0.508397i	$-0.830238\pi$
$457$	−23.0565	−	31.7345i	−1.07854	−	1.48448i	−0.217413	−	0.976080i	$-0.569762\pi$
$458$	12.4473	+	38.3088i	0.581624	+	1.79005i
$459$		0			0
$460$	2.49706	+	1.81422i	0.116426	+	0.0845885i
$461$	−17.5521			−0.817482			−0.408741	−	0.912650i	$-0.634032\pi$
$461$	−17.5521			−0.817482			−0.408741	+	0.912650i	$0.634032\pi$
$462$		0			0
$463$	5.07239			0.235734			0.117867	−	0.993029i	$-0.462394\pi$
$463$	5.07239			0.235734			0.117867	+	0.993029i	$0.462394\pi$
$464$	−6.74278	−	4.89892i	−0.313026	−	0.227427i
$465$		0			0
$466$	−2.89801	−	8.91915i	−0.134248	−	0.413172i
$467$	9.96792	+	13.7197i	0.461260	+	0.634870i	0.974770	−	0.223214i	$-0.0716548\pi$
$467$	9.96792	+	13.7197i	0.461260	+	0.634870i	−0.513509	+	0.858084i	$0.671655\pi$
$468$		0			0
$469$	9.69445	−	3.14992i	0.447648	−	0.145450i
$470$	2.20004	−	6.77101i	0.101480	−	0.312324i
$471$		0			0
$472$			0.0405706i			0.00186741i
$473$	−1.23154	−	12.5114i	−0.0566261	−	0.575274i
$474$		0			0
$475$	−9.54762	+	13.1412i	−0.438075	+	0.602958i
$476$	−13.3036	−	4.32260i	−0.609769	−	0.198126i
$477$		0			0
$478$	20.0601	−	14.5745i	0.917526	−	0.666622i
$479$	−14.6267	+	10.6269i	−0.668310	+	0.485556i	−0.869459	−	0.494005i	$-0.835532\pi$
$479$	−14.6267	+	10.6269i	−0.668310	+	0.485556i	0.201149	+	0.979561i	$0.435532\pi$
$480$		0			0
$481$	−3.24773	−	1.05525i	−0.148084	−	0.0481153i
$482$	−7.52180	+	10.3529i	−0.342608	+	0.471560i
$483$		0			0
$484$	6.94524	+	12.4050i	0.315693	+	0.563862i
$485$		−	17.4295i		−	0.791435i
$486$		0			0
$487$	−8.03498	+	24.7291i	−0.364100	+	1.12058i	0.586443	+	0.809991i	$0.300528\pi$
$487$	−8.03498	+	24.7291i	−0.364100	+	1.12058i	−0.950543	+	0.310594i	$0.899472\pi$
$488$	1.44974	−	0.471048i	0.0656265	−	0.0213234i
$489$		0			0
$490$	−21.0661	−	28.9950i	−0.951670	−	1.30986i
$491$	−2.26569	−	6.97309i	−0.102249	−	0.314691i	0.886826	−	0.462104i	$-0.152905\pi$
$491$	−2.26569	−	6.97309i	−0.102249	−	0.314691i	−0.989075	+	0.147413i	$0.952905\pi$
$492$		0			0
$493$	−3.06733	−	2.22854i	−0.138146	−	0.100369i
$494$	−25.3622			−1.14110
$495$		0			0
$496$	−26.1057			−1.17218
$497$	15.0600	+	10.9417i	0.675533	+	0.490804i
$498$		0			0
$499$	−2.91064	−	8.95804i	−0.130298	−	0.401017i	0.864531	−	0.502580i	$-0.167616\pi$
$499$	−2.91064	−	8.95804i	−0.130298	−	0.401017i	−0.994829	+	0.101563i	$0.967616\pi$
$500$	7.81055	+	10.7503i	0.349298	+	0.480768i
$501$		0			0
$502$	−11.6115	+	3.77281i	−0.518247	+	0.168389i
$503$	10.3211	−	31.7652i	0.460196	−	1.41634i	−0.404728	−	0.914437i	$-0.632634\pi$
$503$	10.3211	−	31.7652i	0.460196	−	1.41634i	0.864925	−	0.501902i	$-0.167366\pi$
$504$		0			0
$505$		−	19.3294i		−	0.860149i
$506$	−6.04832	+	10.3181i	−0.268881	+	0.458694i
$507$		0			0
$508$	16.9424	−	23.3193i	0.751699	−	1.03462i
$509$	−19.5002	−	6.33601i	−0.864332	−	0.280839i	−0.156895	−	0.987615i	$-0.550149\pi$
$509$	−19.5002	−	6.33601i	−0.864332	−	0.280839i	−0.707437	+	0.706777i	$0.750149\pi$
$510$		0			0
$511$	−27.5909	+	20.0459i	−1.22055	+	0.886781i
$512$	−15.0364	+	10.9246i	−0.664521	+	0.482803i
$513$		0			0
$514$	−24.4213	−	7.93496i	−1.07718	−	0.349996i
$515$	1.46996	−	2.02322i	0.0647741	−	0.0891539i
$516$		0			0
$517$	10.5777	+	2.32145i	0.465206	+	0.102097i
$518$			9.80320i			0.430728i
$519$		0			0
$520$	1.45881	−	4.48976i	0.0639732	−	0.196889i
$521$	12.4115	−	4.03273i	0.543757	−	0.176677i	−0.0242430	−	0.999706i	$-0.507718\pi$
$521$	12.4115	−	4.03273i	0.543757	−	0.176677i	0.568000	+	0.823029i	$0.307718\pi$
$522$		0			0
$523$	−4.85832	−	6.68690i	−0.212439	−	0.292398i	0.689478	−	0.724307i	$-0.257840\pi$
$523$	−4.85832	−	6.68690i	−0.212439	−	0.292398i	−0.901917	+	0.431909i	$0.857840\pi$
$524$	6.19018	+	19.0514i	0.270419	+	0.832265i
$525$		0			0
$526$	−10.1963	−	7.40802i	−0.444578	−	0.323005i
$527$	−11.8756			−0.517310
$528$		0			0
$529$	19.0503			0.828275
$530$	2.25067	+	1.63521i	0.0977628	+	0.0710289i
$531$		0			0
$532$	8.83197	+	27.1820i	0.382915	+	1.17849i
$533$	19.1230	+	26.3205i	0.828308	+	1.14007i
$534$		0			0
$535$	0.478417	−	0.155447i	0.0206838	−	0.00672057i
$536$	0.835347	−	2.57093i	0.0360815	−	0.111047i
$537$		0			0
$538$			12.5287i			0.540151i
$539$	40.7532	−	36.2100i	1.75537	−	1.55968i
$540$		0			0
$541$	5.73469	−	7.89312i	0.246554	−	0.339352i	−0.667747	−	0.744388i	$-0.732741\pi$
$541$	5.73469	−	7.89312i	0.246554	−	0.339352i	0.914301	+	0.405036i	$0.132741\pi$
$542$	23.5125	+	7.63968i	1.00995	+	0.328152i
$543$		0			0
$544$	−11.4843	+	8.34383i	−0.492385	+	0.357739i
$545$	−14.2701	+	10.3678i	−0.611263	+	0.444108i
$546$		0			0
$547$	7.40406	+	2.40572i	0.316575	+	0.102861i	0.462994	−	0.886361i	$-0.346775\pi$
$547$	7.40406	+	2.40572i	0.316575	+	0.102861i	−0.146420	+	0.989223i	$0.546775\pi$
$548$	−13.0215	+	17.9225i	−0.556250	+	0.765613i
$549$		0			0
$550$	−15.9978	+	14.2143i	−0.682147	+	0.606100i
$551$			7.74667i			0.330019i
$552$		0			0
$553$	5.71655	−	17.5937i	0.243093	−	0.748162i
$554$	20.1135	−	6.53527i	0.854541	−	0.277657i
$555$		0			0
$556$	−7.87623	−	10.8407i	−0.334026	−	0.459748i
$557$	−1.09093	−	3.35755i	−0.0462244	−	0.142264i	0.925281	−	0.379283i	$-0.123829\pi$
$557$	−1.09093	−	3.35755i	−0.0462244	−	0.142264i	−0.971505	+	0.237019i	$0.923829\pi$
$558$		0			0
$559$	9.38378	+	6.81772i	0.396892	+	0.288359i
$560$	−28.5897			−1.20813
$561$		0			0
$562$	−39.6298			−1.67168
$563$	1.21567	+	0.883235i	0.0512343	+	0.0372239i	0.613108	−	0.789999i	$-0.289919\pi$
$563$	1.21567	+	0.883235i	0.0512343	+	0.0372239i	−0.561873	+	0.827223i	$0.689919\pi$
$564$		0			0
$565$	−1.18702	−	3.65326i	−0.0499381	−	0.153694i
$566$	25.0367	+	34.4601i	1.05237	+	1.44847i
$567$		0			0
$568$	4.69506	−	1.52552i	0.197000	−	0.0640093i
$569$	4.58518	−	14.1117i	0.192221	−	0.591595i	−0.807777	−	0.589488i	$-0.799329\pi$
$569$	4.58518	−	14.1117i	0.192221	−	0.591595i	0.999998	−	0.00210682i	$-0.000670621\pi$
$570$		0			0
$571$			29.8598i			1.24960i	0.780787	+	0.624798i	$0.214819\pi$
$571$			29.8598i			1.24960i	−0.780787	+	0.624798i	$0.785181\pi$
$572$	−12.8118	−	2.81177i	−0.535688	−	0.117566i
$573$		0			0
$574$	54.8972	−	75.5595i	2.29136	−	3.15379i
$575$	−6.72128	−	2.18388i	−0.280297	−	0.0910740i
$576$		0			0
$577$	−20.6394	+	14.9954i	−0.859228	+	0.624266i	−0.927675	−	0.373389i	$-0.878196\pi$
$577$	−20.6394	+	14.9954i	−0.859228	+	0.624266i	0.0684465	+	0.997655i	$0.478196\pi$
$578$	17.6185	−	12.8006i	0.732835	−	0.532436i
$579$		0			0
$580$	2.50496	+	0.813911i	0.104013	+	0.0337958i
$581$	20.6853	−	28.4708i	0.858170	−	1.18117i
$582$		0			0
$583$	−2.13999	+	3.65069i	−0.0886292	+	0.151196i
$584$			9.04432i			0.374256i
$585$		0			0
$586$	−0.951344	+	2.92793i	−0.0392996	+	0.120952i
$587$	22.4713	−	7.30137i	0.927491	−	0.301360i	0.193955	−	0.981011i	$-0.437869\pi$
$587$	22.4713	−	7.30137i	0.927491	−	0.301360i	0.733536	+	0.679651i	$0.237869\pi$
$588$		0			0
$589$	14.2622	+	19.6303i	0.587664	+	0.808851i
$590$	−0.0212918	−	0.0655293i	−0.000876568	−	0.00269780i
$591$		0			0
$592$	4.43702	+	3.22368i	0.182360	+	0.132493i
$593$	10.1681			0.417553			0.208777	−	0.977963i	$-0.433052\pi$
$593$	10.1681			0.417553			0.208777	+	0.977963i	$0.433052\pi$
$594$		0			0
$595$	−13.0056			−0.533178
$596$	−0.0423030	−	0.0307349i	−0.00173280	−	0.00125895i
$597$		0			0
$598$	−3.40988	−	10.4945i	−0.139441	−	0.429154i
$599$	−3.58279	−	4.93129i	−0.146389	−	0.201487i	0.729525	−	0.683954i	$-0.239741\pi$
$599$	−3.58279	−	4.93129i	−0.146389	−	0.201487i	−0.875914	+	0.482467i	$0.839741\pi$
$600$		0			0
$601$	13.3376	−	4.33365i	0.544053	−	0.176773i	−0.0240806	−	0.999710i	$-0.507666\pi$
$601$	13.3376	−	4.33365i	0.544053	−	0.176773i	0.568133	+	0.822937i	$0.307666\pi$
$602$	10.2896	−	31.6680i	0.419371	−	1.29069i
$603$		0			0
$604$			3.55632i			0.144705i
$605$	9.70538	+	8.97363i	0.394580	+	0.364830i
$606$		0			0
$607$	−0.497560	+	0.684833i	−0.0201953	+	0.0277965i	−0.818995	−	0.573800i	$-0.805469\pi$
$607$	−0.497560	+	0.684833i	−0.0201953	+	0.0277965i	0.798800	+	0.601597i	$0.205469\pi$
$608$	27.5845	+	8.96276i	1.11870	+	0.363488i
$609$		0			0
$610$	−2.09439	+	1.52167i	−0.0847996	+	0.0616105i
$611$	−8.08321	+	5.87280i	−0.327012	+	0.237588i
$612$		0			0
$613$	−24.1513	−	7.84724i	−0.975462	−	0.316947i	−0.222443	−	0.974946i	$-0.571403\pi$
$613$	−24.1513	−	7.84724i	−0.975462	−	0.316947i	−0.753019	+	0.657999i	$0.771403\pi$
$614$	−2.50937	+	3.45385i	−0.101270	+	0.139386i
$615$		0			0
$616$	−2.01938	−	20.5152i	−0.0813631	−	0.826581i
$617$		−	10.0839i		−	0.405962i	−0.979183	−	0.202981i	$-0.934937\pi$
$617$		−	10.0839i		−	0.405962i	0.979183	−	0.202981i	$-0.0650630\pi$
$618$		0			0
$619$	−8.05024	+	24.7761i	−0.323566	+	0.995835i	0.648517	+	0.761200i	$0.275389\pi$
$619$	−8.05024	+	24.7761i	−0.323566	+	0.995835i	−0.972084	+	0.234635i	$0.924611\pi$
$620$	7.84611	−	2.54935i	0.315107	−	0.102385i
$621$		0			0
$622$	11.3121	+	15.5698i	0.453574	+	0.624291i
$623$	15.3903	+	47.3664i	0.616598	+	1.89769i
$624$		0			0
$625$	−4.38931	−	3.18902i	−0.175573	−	0.127561i
$626$	−45.9690			−1.83729
$627$		0			0
$628$	2.72689			0.108815
$629$	2.01842	+	1.46647i	0.0804798	+	0.0584720i
$630$		0			0
$631$	3.44605	+	10.6058i	0.137185	+	0.422212i	0.995923	−	0.0902022i	$-0.0287513\pi$
$631$	3.44605	+	10.6058i	0.137185	+	0.422212i	−0.858739	+	0.512414i	$0.828751\pi$
$632$	−2.88362	−	3.96897i	−0.114704	−	0.157877i
$633$		0			0
$634$	46.2703	−	15.0341i	1.83763	−	0.597081i
$635$	8.28146	−	25.4877i	0.328640	−	1.01145i
$636$		0			0
$637$			50.2973i			1.99285i
$638$	−2.18783	+	9.96884i	−0.0866172	+	0.394670i
$639$		0			0
$640$	−6.80053	+	9.36013i	−0.268815	+	0.369991i
$641$	−10.4988	−	3.41127i	−0.414679	−	0.134737i	0.0942448	−	0.995549i	$-0.469956\pi$
$641$	−10.4988	−	3.41127i	−0.414679	−	0.134737i	−0.508923	+	0.860812i	$0.669956\pi$
$642$		0			0
$643$	−29.7234	+	21.5953i	−1.17218	+	0.851637i	−0.991268	−	0.131863i	$-0.957904\pi$
$643$	−29.7234	+	21.5953i	−1.17218	+	0.851637i	−0.180909	+	0.983500i	$0.557904\pi$
$644$	−10.0601	+	7.30909i	−0.396424	+	0.288019i
$645$		0			0
$646$	17.6228	+	5.72600i	0.693360	+	0.225286i
$647$	−1.59821	+	2.19975i	−0.0628321	+	0.0864810i	−0.839277	−	0.543705i	$-0.817021\pi$
$647$	−1.59821	+	2.19975i	−0.0628321	+	0.0864810i	0.776445	+	0.630186i	$0.217021\pi$
$648$		0			0
$649$	0.0960246	−	0.0419955i	0.00376930	−	0.00164847i
$650$		−	19.7443i		−	0.774436i
$651$		0			0
$652$	5.82952	−	17.9414i	0.228301	−	0.702640i
$653$	−42.0798	+	13.6726i	−1.64671	+	0.535048i	−0.978023	−	0.208496i	$-0.933143\pi$
$653$	−42.0798	+	13.6726i	−1.64671	+	0.535048i	−0.668686	+	0.743545i	$0.733143\pi$
$654$		0			0
$655$	10.9473	+	15.0677i	0.427747	+	0.588743i
$656$	−16.1465	−	49.6939i	−0.630416	−	1.94022i
$657$		0			0
$658$	23.2048	+	16.8593i	0.904618	+	0.657244i
$659$	9.17428			0.357379			0.178690	−	0.983905i	$-0.442814\pi$
$659$	9.17428			0.357379			0.178690	+	0.983905i	$0.442814\pi$
$660$		0			0
$661$	−9.89631			−0.384922			−0.192461	−	0.981305i	$-0.561647\pi$
$661$	−9.89631			−0.384922			−0.192461	+	0.981305i	$0.561647\pi$
$662$	25.4307	+	18.4765i	0.988391	+	0.718108i
$663$		0			0
$664$	−2.88398	−	8.87599i	−0.111920	−	0.344455i
$665$	15.6193	+	21.4981i	0.605691	+	0.833662i
$666$		0			0
$667$	−3.20547	+	1.04152i	−0.124116	+	0.0403278i
$668$	0.356362	−	1.09677i	0.0137880	−	0.0424352i
$669$		0			0
$670$			4.59095i			0.177364i
$671$	−2.61556	−	2.94372i	−0.100972	−	0.113641i
$672$		0			0
$673$	−10.3937	+	14.3057i	−0.400649	+	0.551446i	−0.960907	−	0.276872i	$-0.910702\pi$
$673$	−10.3937	+	14.3057i	−0.400649	+	0.551446i	0.560258	+	0.828318i	$0.310702\pi$
$674$	22.4408	+	7.29146i	0.864387	+	0.280856i
$675$		0			0
$676$	−3.80243	+	2.76263i	−0.146247	+	0.106255i
$677$	9.62387	−	6.99215i	0.369875	−	0.268730i	−0.387284	−	0.921961i	$-0.626587\pi$
$677$	9.62387	−	6.99215i	0.369875	−	0.268730i	0.757159	+	0.653230i	$0.226587\pi$
$678$		0			0
$679$	66.7830	+	21.6991i	2.56290	+	0.832735i
$680$	−2.02729	+	2.79033i	−0.0777432	+	0.107004i
$681$		0			0
$682$	12.8094	+	29.2892i	0.490496	+	1.12154i
$683$			18.2564i			0.698561i	0.937018	+	0.349280i	$0.113574\pi$
$683$			18.2564i			0.698561i	−0.937018	+	0.349280i	$0.886426\pi$
$684$		0			0
$685$	−6.36490	+	19.5892i	−0.243190	+	0.748463i
$686$	78.8425	−	25.6175i	3.01022	−	0.978080i
$687$		0			0
$688$	−10.9496	−	15.0708i	−0.417450	−	0.574571i
$689$	−1.20647	−	3.71312i	−0.0459627	−	0.141459i
$690$		0			0
$691$	−14.5818	−	10.5943i	−0.554719	−	0.403027i	0.274804	−	0.961500i	$-0.411387\pi$
$691$	−14.5818	−	10.5943i	−0.554719	−	0.403027i	−0.829522	+	0.558474i	$0.811387\pi$
$692$	17.1216			0.650864
$693$		0			0
$694$	38.5698			1.46409
$695$	−10.0792	−	7.32295i	−0.382325	−	0.277775i
$696$		0			0
$697$	−7.34515	−	22.6060i	−0.278217	−	0.856265i
$698$	−9.95189	−	13.6976i	−0.376684	−	0.518462i
$699$		0			0
$700$	−21.1610	+	6.87562i	−0.799810	+	0.259874i
$701$	2.60431	−	8.01524i	0.0983635	−	0.302732i	−0.889752	−	0.456444i	$-0.849123\pi$
$701$	2.60431	−	8.01524i	0.0983635	−	0.302732i	0.988116	+	0.153712i	$0.0491229\pi$
$702$		0			0
$703$		−	5.09762i		−	0.192260i
$704$	4.84270	+	2.83873i	0.182516	+	0.106989i
$705$		0			0
$706$	9.72836	−	13.3899i	0.366132	−	0.503937i
$707$	74.0626	+	24.0644i	2.78541	+	0.905035i
$708$		0			0
$709$	−16.7573	+	12.1749i	−0.629333	+	0.457237i	−0.856169	−	0.516696i	$-0.827162\pi$
$709$	−16.7573	+	12.1749i	−0.629333	+	0.457237i	0.226836	+	0.973933i	$0.427162\pi$
$710$	−6.78282	+	4.92801i	−0.254555	+	0.184945i
$711$		0			0
$712$	12.5614	+	4.08144i	0.470758	+	0.152959i
$713$	−6.20521	+	8.54074i	−0.232387	+	0.319853i
$714$		0			0
$715$	−12.1367	+	1.19465i	−0.453885	+	0.0446774i
$716$		−	26.0358i		−	0.973002i
$717$		0			0
$718$	4.38552	−	13.4972i	0.163666	−	0.503712i
$719$	34.3009	−	11.1450i	1.27921	−	0.415640i	0.410906	−	0.911678i	$-0.365212\pi$
$719$	34.3009	−	11.1450i	1.27921	−	0.415640i	0.868301	+	0.496038i	$0.165212\pi$
$720$		0			0
$721$	5.92214	+	8.15112i	0.220552	+	0.303564i
$722$	−1.04584	−	3.21875i	−0.0389220	−	0.119790i
$723$		0			0
$724$	4.70137	+	3.41574i	0.174725	+	0.126945i
$725$	−6.03072			−0.223975
$726$		0			0
$727$	−20.9857			−0.778316			−0.389158	−	0.921171i	$-0.627234\pi$
$727$	−20.9857			−0.778316			−0.389158	+	0.921171i	$0.627234\pi$
$728$	15.3868	+	11.1792i	0.570273	+	0.414327i
$729$		0			0
$730$	−4.74653	−	14.6083i	−0.175677	−	0.540678i
$731$	−4.98104	−	6.85581i	−0.184230	−	0.253571i
$732$		0			0
$733$	38.6350	−	12.5533i	1.42701	−	0.463665i	0.509191	−	0.860653i	$-0.329945\pi$
$733$	38.6350	−	12.5533i	1.42701	−	0.463665i	0.917824	+	0.396988i	$0.129945\pi$
$734$	13.7399	−	42.2871i	0.507149	−	1.56084i
$735$		0			0
$736$			12.6191i			0.465147i
$737$	−6.94971	+	0.684083i	−0.255996	+	0.0251985i
$738$		0			0
$739$	−0.159730	+	0.219850i	−0.00587578	+	0.00808731i	−0.811945	−	0.583734i	$-0.801591\pi$
$739$	−0.159730	+	0.219850i	−0.00587578	+	0.00808731i	0.806069	+	0.591822i	$0.201591\pi$
$740$	−1.64836	−	0.535586i	−0.0605951	−	0.0196885i
$741$		0			0
$742$	−9.06745	+	6.58789i	−0.332877	+	0.241849i
$743$	−16.6356	+	12.0864i	−0.610300	+	0.443409i	−0.849520	−	0.527557i	$-0.823108\pi$
$743$	−16.6356	+	12.0864i	−0.610300	+	0.443409i	0.239220	+	0.970965i	$0.423108\pi$
$744$		0			0
$745$	−0.0462368	−	0.0150232i	−0.00169398	−	0.000550409i
$746$	−3.05169	+	4.20029i	−0.111730	+	0.153783i
$747$		0			0
$748$	8.26740	+	4.84624i	0.302286	+	0.177196i
$749$			2.02663i			0.0740514i
$750$		0			0
$751$	−16.1057	+	49.5682i	−0.587705	+	1.80877i	0.000422486		1.00000i	$0.499866\pi$
$751$	−16.1057	+	49.5682i	−0.587705	+	1.80877i	−0.588127	+	0.808769i	$0.700134\pi$
$752$	15.2613	−	4.95871i	0.556524	−	0.180825i
$753$		0			0
$754$	−5.53477	−	7.61795i	−0.201564	−	0.277430i
$755$	1.02176	+	3.14467i	0.0371858	+	0.114446i
$756$		0			0
$757$	30.2153	+	21.9527i	1.09819	+	0.797884i	0.980764	−	0.195197i	$-0.0625347\pi$
$757$	30.2153	+	21.9527i	1.09819	+	0.797884i	0.117429	+	0.993081i	$0.462535\pi$
$758$	−53.0990			−1.92864
$759$		0			0
$760$	7.04711			0.255625
$761$	36.1152	+	26.2392i	1.30918	+	0.951171i	1.00000		0.000166228i	$5.29120e-5\pi$
$761$	36.1152	+	26.2392i	1.30918	+	0.951171i	0.309175	+	0.951005i	$0.399947\pi$
$762$		0			0
$763$	−21.9596	−	67.5847i	−0.794991	−	2.44673i
$764$	13.5025	+	18.5846i	0.488503	+	0.672367i
$765$		0			0
$766$	−49.1124	+	15.9576i	−1.77450	+	0.576571i
$767$	−0.0298807	+	0.0919633i	−0.00107893	+	0.00332060i
$768$		0			0
$769$			22.3246i			0.805047i	0.915410	+	0.402524i	$0.131867\pi$
$769$			22.3246i			0.805047i	−0.915410	+	0.402524i	$0.868133\pi$
$770$	14.0282	+	32.0762i	0.505542	+	1.15595i
$771$		0			0
$772$	−4.67883	+	6.43986i	−0.168395	+	0.231776i
$773$	−19.1268	−	6.21468i	−0.687944	−	0.223526i	−0.0558738	−	0.998438i	$-0.517794\pi$
$773$	−19.1268	−	6.21468i	−0.687944	−	0.223526i	−0.632070	+	0.774911i	$0.717794\pi$
$774$		0			0
$775$	−15.2820	+	11.1030i	−0.548946	+	0.398832i
$776$	15.0655	−	10.9458i	0.540822	−	0.392930i
$777$		0			0
$778$	24.6455	+	8.00781i	0.883584	+	0.287094i
$779$	−28.5463	+	39.2906i	−1.02278	+	1.40773i
$780$		0			0
$781$	−8.47063	−	9.53343i	−0.303103	−	0.341133i
$782$			8.06192i			0.288294i
$783$		0			0
$784$	24.9624	−	76.8265i	0.891516	−	2.74380i
$785$	2.41124	−	0.783461i	0.0860610	−	0.0279629i
$786$		0			0
$787$	−20.4658	−	28.1688i	−0.729527	−	1.00411i	−0.999153	−	0.0411431i	$-0.986900\pi$
$787$	−20.4658	−	28.1688i	−0.729527	−	1.00411i	0.269626	−	0.962965i	$-0.413100\pi$
$788$	8.99021	+	27.6690i	0.320263	+	0.985668i
$789$		0			0
$790$	6.74055	+	4.89730i	0.239818	+	0.174238i
$791$	15.4756			0.550249
$792$		0			0
$793$	3.63312			0.129016
$794$	−3.23961	−	2.35372i	−0.114970	−	0.0835303i
$795$		0			0
$796$	3.71701	+	11.4398i	0.131746	+	0.405473i
$797$	−0.462428	−	0.636478i	−0.0163800	−	0.0225452i	0.800748	−	0.599001i	$-0.204435\pi$
$797$	−0.462428	−	0.636478i	−0.0163800	−	0.0225452i	−0.817128	+	0.576456i	$0.804435\pi$
$798$		0			0
$799$	6.94247	−	2.25574i	0.245607	−	0.0798025i
$800$	−6.97744	+	21.4743i	−0.246690	+	0.759233i
$801$		0			0
$802$		−	57.2351i		−	2.02104i
$803$	21.4066	−	9.36196i	0.755421	−	0.330376i
$804$		0			0
$805$	−6.79565	+	9.35341i	−0.239515	+	0.329665i
$806$	−28.0505	−	9.11415i	−0.988036	−	0.321032i
$807$		0			0
$808$	16.7078	−	12.1389i	0.587777	−	0.427045i
$809$	−24.9035	+	18.0934i	−0.875560	+	0.636131i	−0.932073	−	0.362270i	$-0.882002\pi$
$809$	−24.9035	+	18.0934i	−0.875560	+	0.636131i	0.0565132	+	0.998402i	$0.482002\pi$
$810$		0			0
$811$	41.4535	+	13.4691i	1.45563	+	0.472963i	0.926732	−	0.375723i	$-0.122606\pi$
$811$	41.4535	+	13.4691i	1.45563	+	0.472963i	0.528898	+	0.848686i	$0.322606\pi$
$812$	−6.23716	+	8.58472i	−0.218881	+	0.301264i
$813$		0			0
$814$	1.43968	−	6.55989i	0.0504608	−	0.229924i
$815$		−	17.5395i		−	0.614383i
$816$		0			0
$817$	−5.35052	+	16.4672i	−0.187191	+	0.576115i
$818$	11.6971	−	3.80063i	0.408981	−	0.132886i
$819$		0			0
$820$	9.70574	+	13.3588i	0.338939	+	0.466510i
$821$	−12.0394	−	37.0534i	−0.420178	−	1.29317i	−0.907537	−	0.419972i	$-0.862040\pi$
$821$	−12.0394	−	37.0534i	−0.420178	−	1.29317i	0.487359	−	0.873202i	$-0.337960\pi$
$822$		0			0
$823$	−30.4030	−	22.0890i	−1.05978	−	0.769975i	−0.0857325	−	0.996318i	$-0.527323\pi$
$823$	−30.4030	−	22.0890i	−1.05978	−	0.769975i	−0.974048	+	0.226343i	$0.927323\pi$
$824$	2.67195			0.0930816
$825$		0			0
$826$	0.277589			0.00965857
$827$	−36.8905	−	26.8025i	−1.28281	−	0.932015i	−0.283175	−	0.959068i	$-0.591388\pi$
$827$	−36.8905	−	26.8025i	−1.28281	−	0.932015i	−0.999634	+	0.0270532i	$0.991388\pi$
$828$		0			0
$829$	8.83146	+	27.1804i	0.306729	+	0.944016i	0.979026	+	0.203734i	$0.0653078\pi$
$829$	8.83146	+	27.1804i	0.306729	+	0.944016i	−0.672297	+	0.740282i	$0.734692\pi$
$830$	9.31637	+	12.8229i	0.323376	+	0.445089i
$831$		0			0
$832$	−4.92553	+	1.60040i	−0.170762	+	0.0554839i
$833$	11.3556	−	34.9488i	0.393447	−	1.21090i
$834$		0			0
$835$		−	1.07220i		−	0.0371051i
$836$	−1.91808	−	19.4861i	−0.0663382	−	0.673941i
$837$		0			0
$838$	30.5125	−	41.9968i	1.05404	−	1.45076i
$839$	5.41296	+	1.75878i	0.186876	+	0.0607197i	0.400960	−	0.916096i	$-0.368677\pi$
$839$	5.41296	+	1.75878i	0.186876	+	0.0607197i	−0.214084	+	0.976815i	$0.568677\pi$
$840$		0			0
$841$	21.1347	−	15.3552i	0.728781	−	0.529491i
$842$	8.21078	−	5.96548i	0.282962	−	0.205584i
$843$		0			0
$844$	17.2223	+	5.59587i	0.592816	+	0.192618i
$845$	−2.56856	+	3.53532i	−0.0883612	+	0.121619i
$846$		0			0
$847$	−46.4662	+	26.0153i	−1.59660	+	0.893895i
$848$			6.27037i			0.215325i
$849$		0			0
$850$	−4.45764	+	13.7192i	−0.152896	+	0.470565i
$851$	2.10932	−	0.685361i	0.0723067	−	0.0234939i
$852$		0			0
$853$	14.7319	+	20.2767i	0.504410	+	0.694261i	0.982964	−	0.183797i	$-0.0588390\pi$
$853$	14.7319	+	20.2767i	0.504410	+	0.694261i	−0.478554	+	0.878058i	$0.658839\pi$
$854$	−3.22297	−	9.91929i	−0.110288	−	0.339431i
$855$		0			0
$856$	0.434810	+	0.315908i	0.0148615	+	0.0107975i
$857$	−35.9164			−1.22688			−0.613440	−	0.789741i	$-0.710215\pi$
$857$	−35.9164			−1.22688			−0.613440	+	0.789741i	$0.710215\pi$
$858$		0			0
$859$	−15.7324			−0.536783			−0.268391	−	0.963310i	$-0.586492\pi$
$859$	−15.7324			−0.536783			−0.268391	+	0.963310i	$0.586492\pi$
$860$	4.76268	+	3.46029i	0.162406	+	0.117995i
$861$		0			0
$862$	10.9385	+	33.6654i	0.372568	+	1.14665i
$863$	−16.0883	−	22.1436i	−0.547652	−	0.753778i	0.442039	−	0.896996i	$-0.354255\pi$
$863$	−16.0883	−	22.1436i	−0.547652	−	0.753778i	−0.989691	+	0.143217i	$0.954255\pi$
$864$		0			0
$865$	15.1397	−	4.91919i	0.514765	−	0.167257i
$866$	−12.6457	+	38.9194i	−0.429718	+	1.32254i
$867$		0			0
$868$			33.2370i			1.12814i
$869$	−6.40906	+	10.9335i	−0.217413	+	0.370893i
$870$		0			0
$871$	3.78704	−	5.21242i	0.128319	−	0.176616i
$872$	−17.9232	−	5.82361i	−0.606957	−	0.197212i
$873$		0			0
$874$	13.3263	−	9.68210i	0.450768	−	0.327502i
$875$	−40.2682	+	29.2565i	−1.36131	+	0.989051i
$876$		0			0
$877$	49.4957	+	16.0821i	1.67135	+	0.543055i	0.983203	−	0.182516i	$-0.0584242\pi$
$877$	49.4957	+	16.0821i	1.67135	+	0.543055i	0.688147	+	0.725571i	$0.258424\pi$
$878$	−31.9824	+	44.0200i	−1.07935	+	1.48560i
$879$		0			0
$880$	19.1310	+	4.19863i	0.644906	+	0.141536i
$881$		−	39.9758i		−	1.34682i	−0.739270	−	0.673409i	$-0.764829\pi$
$881$		−	39.9758i		−	1.34682i	0.739270	−	0.673409i	$-0.235171\pi$
$882$		0			0
$883$	−5.74452	+	17.6798i	−0.193318	+	0.594973i	0.806674	+	0.590997i	$0.201266\pi$
$883$	−5.74452	+	17.6798i	−0.193318	+	0.594973i	−0.999992	+	0.00397571i	$0.998734\pi$
$884$	−8.40880	+	2.73218i	−0.282818	+	0.0918933i
$885$		0			0
$886$	33.6468	+	46.3108i	1.13039	+	1.55584i
$887$	−16.8498	−	51.8583i	−0.565760	−	1.74123i	−0.665681	−	0.746236i	$-0.731859\pi$
$887$	−16.8498	−	51.8583i	−0.565760	−	1.74123i	0.0999207	−	0.994995i	$-0.468141\pi$
$888$		0			0
$889$	87.3486	+	63.4625i	2.92958	+	2.12846i
$890$	−22.4310			−0.751890
$891$		0			0
$892$	−20.8507			−0.698132
$893$	−12.0664	−	8.76675i	−0.403787	−	0.293368i
$894$		0			0
$895$	−7.48032	−	23.0221i	−0.250040	−	0.769543i
$896$	−27.3978	−	37.7099i	−0.915297	−	1.25980i
$897$		0			0
$898$	65.5777	−	21.3075i	2.18836	−	0.711040i
$899$	−2.78384	+	8.56777i	−0.0928461	+	0.285751i
$900$		0			0
$901$			2.85243i			0.0950281i
$902$	−47.8314	+	42.4991i	−1.59261	+	1.41507i
$903$		0			0
$904$	2.41231	−	3.32027i	0.0802324	−	0.110430i
$905$	5.13855	+	1.66962i	0.170811	+	0.0554999i
$906$		0			0
$907$	10.0586	−	7.30800i	0.333990	−	0.242658i	−0.408132	−	0.912923i	$-0.633820\pi$
$907$	10.0586	−	7.30800i	0.333990	−	0.242658i	0.742122	+	0.670265i	$0.233820\pi$
$908$	15.3860	−	11.1786i	0.510603	−	0.370975i
$909$		0			0
$910$	−30.7195	−	9.98139i	−1.01834	−	0.330880i
$911$	26.4433	−	36.3961i	0.876106	−	1.20586i	−0.101379	−	0.994848i	$-0.532325\pi$
$911$	26.4433	−	36.3961i	0.876106	−	1.20586i	0.977484	−	0.211008i	$-0.0676747\pi$
$912$		0			0
$913$	−18.0229	+	16.0137i	−0.596471	+	0.529976i
$914$			71.1759i			2.35429i
$915$		0			0
$916$	8.86599	−	27.2867i	0.292941	−	0.901578i
$917$	−71.3622	+	23.1870i	−2.35659	+	0.765702i
$918$		0			0
$919$	13.6185	+	18.7442i	0.449232	+	0.618315i	0.972232	−	0.234017i	$-0.0751872\pi$
$919$	13.6185	+	18.7442i	0.449232	+	0.618315i	−0.523000	+	0.852333i	$0.675187\pi$
$920$	0.947464	+	2.91599i	0.0312370	+	0.0961375i
$921$		0			0
$922$	25.7659	+	18.7200i	0.848555	+	0.616512i
$923$	11.7661			0.387285
$924$		0			0
$925$	3.96846			0.130482
$926$	−7.44610	−	5.40991i	−0.244694	−	0.177781i
$927$		0			0
$928$	3.32763	+	10.2414i	0.109235	+	0.336190i
$929$	−6.79920	−	9.35830i	−0.223075	−	0.307036i	0.682781	−	0.730624i	$-0.260771\pi$
$929$	−6.79920	−	9.35830i	−0.223075	−	0.307036i	−0.905855	+	0.423588i	$0.860771\pi$
$930$		0			0
$931$	−71.4077	+	23.2018i	−2.34029	+	0.760407i
$932$	−2.06420	+	6.35296i	−0.0676151	+	0.208098i
$933$		0			0
$934$		−	30.7712i		−	1.00687i
$935$	8.70280	+	1.90998i	0.284612	+	0.0624630i
$936$		0			0
$937$	15.1544	−	20.8582i	0.495071	−	0.681407i	−0.486242	−	0.873824i	$-0.661633\pi$
$937$	15.1544	−	20.8582i	0.495071	−	0.681407i	0.981313	+	0.192417i	$0.0616326\pi$
$938$	−17.5907	−	5.71555i	−0.574356	−	0.186619i
$939$		0			0
$940$	−4.10258	+	2.98070i	−0.133811	+	0.0972197i
$941$	47.8599	−	34.7722i	1.56019	−	1.13354i	0.624331	−	0.781160i	$-0.285372\pi$
$941$	47.8599	−	34.7722i	1.56019	−	1.13354i	0.935856	−	0.352383i	$-0.114628\pi$
$942$		0			0
$943$	−20.0959	−	6.52954i	−0.654411	−	0.212631i
$944$	0.0912824	−	0.125639i	0.00297099	−	0.00408921i
$945$		0			0
$946$	−11.5361	+	19.6798i	−0.375069	+	0.639845i
$947$			0.120799i			0.00392545i	0.999998	+	0.00196272i	$0.000624755\pi$
$947$			0.120799i			0.00392545i	−0.999998	+	0.00196272i	$0.999375\pi$
$948$		0			0
$949$	−6.66124	+	20.5012i	−0.216233	+	0.665497i
$950$	28.0312	−	9.10789i	0.909453	−	0.295499i
$951$		0			0
$952$	−8.16752	−	11.2416i	−0.264711	−	0.364343i
$953$	2.50261	+	7.70223i	0.0810674	+	0.249500i	0.983373	−	0.181597i	$-0.0581267\pi$
$953$	2.50261	+	7.70223i	0.0810674	+	0.249500i	−0.902306	+	0.431097i	$0.858127\pi$
$954$		0			0
$955$	17.2791	+	12.5540i	0.559138	+	0.406237i
$956$	−17.6615			−0.571213
$957$		0			0
$958$	32.8055			1.05990
$959$	−67.1337	−	48.7755i	−2.16786	−	1.57504i
$960$		0			0
$961$	−0.859922	−	2.64657i	−0.0277394	−	0.0853732i
$962$	3.64210	+	5.01292i	0.117426	+	0.161623i
$963$		0			0
$964$	8.66885	−	2.81668i	0.279205	−	0.0907192i
$965$	−2.28702	+	7.03871i	−0.0736216	+	0.226584i
$966$		0			0
$967$		−	9.94567i		−	0.319831i	−0.987131	−	0.159916i	$-0.948878\pi$
$967$		−	9.94567i		−	0.319831i	0.987131	−	0.159916i	$-0.0511222\pi$
$968$	−1.66154	+	14.0245i	−0.0534040	+	0.450763i
$969$		0			0
$970$	−18.5893	+	25.5860i	−0.596867	+	0.821518i
$971$	36.6171	+	11.8976i	1.17510	+	0.381813i	0.830544	−	0.556953i	$-0.188030\pi$
$971$	36.6171	+	11.8976i	1.17510	+	0.381813i	0.344555	+	0.938766i	$0.388030\pi$
$972$		0			0
$973$	40.6068	−	29.5025i	1.30179	−	0.945808i
$974$	38.1698	−	27.7320i	1.22304	−	0.888589i
$975$		0			0
$976$	−5.54940	−	1.80311i	−0.177632	−	0.0577161i
$977$	−11.9388	+	16.4324i	−0.381956	+	0.525718i	−0.956101	−	0.293036i	$-0.905334\pi$
$977$	−11.9388	+	16.4324i	−0.381956	+	0.525718i	0.574145	+	0.818753i	$0.305334\pi$
$978$		0			0
$979$	−3.34238	−	33.9558i	−0.106823	−	1.08523i
$980$			25.5281i			0.815464i
$981$		0			0
$982$	−4.11112	+	12.6527i	−0.131191	+	0.403765i
$983$	9.24723	−	3.00461i	0.294941	−	0.0958321i	−0.157809	−	0.987470i	$-0.550443\pi$
$983$	9.24723	−	3.00461i	0.294941	−	0.0958321i	0.452750	+	0.891638i	$0.350443\pi$
$984$		0			0
$985$	15.8991	+	21.8833i	0.506589	+	0.697260i
$986$	2.12591	+	6.54287i	0.0677027	+	0.208367i
$987$		0			0
$988$	14.6150	+	10.6184i	0.464964	+	0.337816i
$989$	−7.53327			−0.239544
$990$		0			0
$991$	−22.9196			−0.728065			−0.364032	−	0.931386i	$-0.618600\pi$
$991$	−22.9196			−0.728065			−0.364032	+	0.931386i	$0.618600\pi$
$992$	27.2875	+	19.8255i	0.866378	+	0.629460i
$993$		0			0
$994$	−10.4378	−	32.1242i	−0.331067	−	1.01892i
$995$	6.57352	+	9.04768i	0.208395	+	0.286831i
$996$		0			0
$997$	−20.4494	+	6.64441i	−0.647639	+	0.210431i	−0.614373	−	0.789016i	$-0.710591\pi$
$997$	−20.4494	+	6.64441i	−0.647639	+	0.210431i	−0.0332659	+	0.999447i	$0.510591\pi$
$998$	−5.28139	+	16.2544i	−0.167179	+	0.514525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.5		80
3.2	odd	2	inner	891.2.k.a.161.16		80
9.2	odd	6		297.2.t.a.260.8		80
9.4	even	3		297.2.t.a.62.8		80
9.5	odd	6		99.2.p.a.29.3	✓	80
9.7	even	3		99.2.p.a.95.3	yes	80
11.8	odd	10	inner	891.2.k.a.404.16		80
33.8	even	10	inner	891.2.k.a.404.5		80
99.41	even	30		99.2.p.a.74.3	yes	80
99.52	odd	30		99.2.p.a.41.3	yes	80
99.74	even	30		297.2.t.a.206.8		80
99.85	odd	30		297.2.t.a.8.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.3	✓	80	9.5	odd	6
99.2.p.a.41.3	yes	80	99.52	odd	30
99.2.p.a.74.3	yes	80	99.41	even	30
99.2.p.a.95.3	yes	80	9.7	even	3
297.2.t.a.8.8		80	99.85	odd	30
297.2.t.a.62.8		80	9.4	even	3
297.2.t.a.206.8		80	99.74	even	30
297.2.t.a.260.8		80	9.2	odd	6
891.2.k.a.161.5		80	1.1	even	1	trivial
891.2.k.a.161.16		80	3.2	odd	2	inner
891.2.k.a.404.5		80	33.8	even	10	inner
891.2.k.a.404.16		80	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46797 - 1.06654i) q^{2} +(0.399387 + 1.22919i) q^{4} +(0.706314 + 0.972158i) q^{5} +(-4.60425 + 1.49601i) q^{7} +(-0.396737 + 1.22103i) q^{8} -2.18041i q^{10} +(3.30067 - 0.324896i) q^{11} +(-1.79861 + 2.47557i) q^{13} +(8.35446 + 2.71453i) q^{14} +(3.97590 - 2.88866i) q^{16} +(1.80866 - 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(-0.912871 + 1.25646i) q^{20} +(-5.19180 - 3.04337i) q^{22} -1.98738i q^{23} +(1.09887 - 3.38198i) q^{25} +(5.28060 - 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(-0.524067 - 1.61291i) q^{29} +(-4.29749 - 3.12231i) q^{31} -6.34963 q^{32} -4.05656 q^{34} +(-4.70641 - 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(4.87179 + 6.70545i) q^{38} +(-1.46726 + 0.476740i) q^{40} +(3.28550 - 10.1117i) q^{41} -3.79055i q^{43} +(1.71760 + 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(3.10538 + 1.00900i) q^{47} +(13.2980 - 9.66153i) q^{49} +(-5.22014 + 3.79265i) q^{50} +(-3.76128 - 1.22211i) q^{52} +(-0.749954 + 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} -6.21546i q^{56} +(-0.950924 + 2.92664i) q^{58} +(0.0300536 - 0.00976502i) q^{59} +(-0.697881 - 0.960551i) q^{61} +(2.97851 + 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} -3.67703 q^{65} -2.10554 q^{67} +(2.33759 + 1.69836i) q^{68} +(3.26192 + 10.0392i) q^{70} +(-2.26013 - 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(0.625746 - 1.92585i) q^{74} -5.90368i q^{76} +(-14.7111 + 6.43375i) q^{77} +(-2.24604 + 3.09141i) q^{79} +(5.61646 + 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(-5.88095 + 4.27276i) q^{83} +(2.55496 + 0.830157i) q^{85} +(-4.04278 + 5.56441i) q^{86} +(-0.912791 + 4.15912i) q^{88} -10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(2.44286 - 0.793733i) q^{92} +(-3.48246 - 4.79320i) q^{94} +(-1.69618 - 5.22031i) q^{95} +(-11.7345 - 8.52561i) q^{97} -29.8254 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more