LMFDB - Embedded newform 675.2.e.c.451.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(226,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.226"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1223810289.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 $ x^8 - 2x^7 + 8x^6 - 2x^5 + 23x^4 - 8x^3 + 37x^2 + 15*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.3
Root			$-0.236627 + 0.409850i$ of defining polynomial
Character	$\chi$	$=$	675.451
Dual form			675.2.e.c.226.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.236627 - 0.409850i) q^{2} +(0.888015 + 1.53809i) q^{4} +(-1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-3.08430 + 5.34217i) q^{11} +(-1.06615 - 1.84662i) q^{13} +(0.606488 + 1.05047i) q^{14} +(-1.35317 + 2.34376i) q^{16} -3.16860 q^{17} +0.356267 q^{19} +(1.45966 + 2.52821i) q^{22} +(-2.10649 - 3.64854i) q^{23} -1.00912 q^{26} -4.55206 q^{28} +(0.843116 - 1.46032i) q^{29} +(4.12920 + 7.15199i) q^{31} +(2.42742 + 4.20441i) q^{32} +(-0.749778 + 1.29865i) q^{34} +3.63274 q^{37} +(0.0843024 - 0.146016i) q^{38} +(-1.36677 - 2.36731i) q^{41} +(3.83908 - 6.64949i) q^{43} -10.9556 q^{44} -1.99381 q^{46} +(-5.71444 + 9.89770i) q^{47} +(0.215378 + 0.373046i) q^{49} +(1.89351 - 3.27966i) q^{52} +9.43507 q^{53} +(-2.29012 + 3.96660i) q^{56} +(-0.399008 - 0.691103i) q^{58} +(5.10795 + 8.84723i) q^{59} +(0.00549659 - 0.00952038i) q^{61} +3.90833 q^{62} -3.11511 q^{64} +(-0.491409 - 0.851145i) q^{67} +(-2.81377 - 4.87359i) q^{68} +6.43507 q^{71} +6.61467 q^{73} +(0.859605 - 1.48888i) q^{74} +(0.316370 + 0.547969i) q^{76} +(-7.90523 - 13.6923i) q^{77} +(4.73569 - 8.20246i) q^{79} -1.29366 q^{82} +(-5.20988 + 9.02378i) q^{83} +(-1.81686 - 3.14690i) q^{86} +(-5.51172 + 9.54658i) q^{88} +6.26940 q^{89} +5.46519 q^{91} +(3.74119 - 6.47993i) q^{92} +(2.70439 + 4.68413i) q^{94} +(-3.60339 + 6.24126i) q^{97} +0.203858 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{4} - q^{7} + 18 q^{8} - q^{11} + 2 q^{13} + 3 q^{14} - 4 q^{16} + 22 q^{17} + 4 q^{19} + 3 q^{22} - 15 q^{23} + 20 q^{26} + 8 q^{28} + q^{29} + 4 q^{31} - 10 q^{32} - 9 q^{34} + 2 q^{37}+ \cdots + 26 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^4 - q^7 + 18 * q^8 - q^11 + 2 * q^13 + 3 * q^14 - 4 * q^16 + 22 * q^17 + 4 * q^19 + 3 * q^22 - 15 * q^23 + 20 * q^26 + 8 * q^28 + q^29 + 4 * q^31 - 10 * q^32 - 9 * q^34 + 2 * q^37 - 23 * q^38 - 5 * q^41 - 10 * q^43 - 44 * q^44 - 20 * q^47 + 3 * q^49 + 17 * q^52 + 40 * q^53 - 30 * q^56 - 18 * q^58 + 17 * q^59 + 13 * q^61 - 12 * q^62 + 38 * q^64 + 17 * q^67 - 34 * q^68 + 16 * q^71 - 4 * q^73 + 40 * q^74 - 11 * q^76 - 12 * q^77 + 7 * q^79 - 24 * q^82 - 30 * q^83 - 34 * q^86 + 9 * q^88 + 18 * q^89 - 34 * q^91 + 12 * q^92 - 3 * q^94 - 19 * q^97 + 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.236627	−	0.409850i	0.167321	−	0.289808i	−0.770156	−	0.637855i	$-0.779822\pi$
$2$	0.236627	−	0.409850i	0.167321	−	0.289808i	0.937477	+	0.348047i	$0.113155\pi$
$3$		0			0
$3$		0			0
$4$	0.888015	+	1.53809i	0.444008	+	0.769044i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.28153	+	2.21967i	−0.484372	+	0.838956i	−0.999839	−	0.0179531i	$-0.994285\pi$
$7$	−1.28153	+	2.21967i	−0.484372	+	0.838956i	0.515467	+	0.856909i	$0.327618\pi$
$8$	1.78702			0.631808
$9$		0			0
$10$		0			0
$11$	−3.08430	+	5.34217i	−0.929952	+	1.61072i	−0.146555	+	0.989202i	$0.546819\pi$
$11$	−3.08430	+	5.34217i	−0.929952	+	1.61072i	−0.783397	+	0.621522i	$0.786515\pi$
$12$		0			0
$13$	−1.06615	−	1.84662i	−0.295696	−	0.512161i	0.679450	−	0.733722i	$-0.262218\pi$
$13$	−1.06615	−	1.84662i	−0.295696	−	0.512161i	−0.975147	+	0.221560i	$0.928885\pi$
$14$	0.606488	+	1.05047i	0.162091	+	0.280750i
$15$		0			0
$16$	−1.35317	+	2.34376i	−0.338293	+	0.585941i
$17$	−3.16860			−0.768500			−0.384250	−	0.923229i	$-0.625540\pi$
$17$	−3.16860			−0.768500			−0.384250	+	0.923229i	$0.625540\pi$
$18$		0			0
$19$	0.356267			0.0817332			0.0408666	−	0.999165i	$-0.486988\pi$
$19$	0.356267			0.0817332			0.0408666	+	0.999165i	$0.486988\pi$
$20$		0			0
$21$		0			0
$22$	1.45966	+	2.52821i	0.311201	+	0.539015i
$23$	−2.10649	−	3.64854i	−0.439233	−	0.760774i	0.558397	−	0.829574i	$-0.311416\pi$
$23$	−2.10649	−	3.64854i	−0.439233	−	0.760774i	−0.997631	+	0.0687995i	$0.978083\pi$
$24$		0			0
$25$		0			0
$26$	−1.00912			−0.197905
$27$		0			0
$28$	−4.55206			−0.860259
$29$	0.843116	−	1.46032i	0.156563	−	0.271174i	−0.777064	−	0.629421i	$-0.783292\pi$
$29$	0.843116	−	1.46032i	0.156563	−	0.271174i	0.933627	+	0.358247i	$0.116625\pi$
$30$		0			0
$31$	4.12920	+	7.15199i	0.741627	+	1.28453i	0.951754	+	0.306861i	$0.0992787\pi$
$31$	4.12920	+	7.15199i	0.741627	+	1.28453i	−0.210128	+	0.977674i	$0.567388\pi$
$32$	2.42742	+	4.20441i	0.429111	+	0.743242i
$33$		0			0
$34$	−0.749778	+	1.29865i	−0.128586	+	0.222717i
$35$		0			0
$36$		0			0
$37$	3.63274			0.597219			0.298609	−	0.954375i	$-0.403477\pi$
$37$	3.63274			0.597219			0.298609	+	0.954375i	$0.403477\pi$
$38$	0.0843024	−	0.146016i	0.0136757	−	0.0236869i
$39$		0			0
$40$		0			0
$41$	−1.36677	−	2.36731i	−0.213453	−	0.369711i	0.739340	−	0.673332i	$-0.235138\pi$
$41$	−1.36677	−	2.36731i	−0.213453	−	0.369711i	−0.952793	+	0.303621i	$0.901804\pi$
$42$		0			0
$43$	3.83908	−	6.64949i	0.585455	−	1.01404i	−0.409364	−	0.912371i	$-0.634249\pi$
$43$	3.83908	−	6.64949i	0.585455	−	1.01404i	0.994819	−	0.101666i	$-0.0324174\pi$
$44$	−10.9556			−1.65162
$45$		0			0
$46$	−1.99381			−0.293971
$47$	−5.71444	+	9.89770i	−0.833537	+	1.44373i	0.0616792	+	0.998096i	$0.480354\pi$
$47$	−5.71444	+	9.89770i	−0.833537	+	1.44373i	−0.895216	+	0.445632i	$0.852979\pi$
$48$		0			0
$49$	0.215378	+	0.373046i	0.0307683	+	0.0532923i
$50$		0			0
$51$		0			0
$52$	1.89351	−	3.27966i	0.262583	−	0.454807i
$53$	9.43507			1.29601			0.648003	−	0.761637i	$-0.275604\pi$
$53$	9.43507			1.29601			0.648003	+	0.761637i	$0.275604\pi$
$54$		0			0
$55$		0			0
$56$	−2.29012	+	3.96660i	−0.306030	+	0.530059i
$57$		0			0
$58$	−0.399008	−	0.691103i	−0.0523924	−	0.0907462i
$59$	5.10795	+	8.84723i	0.664999	+	1.15181i	0.979286	+	0.202484i	$0.0649013\pi$
$59$	5.10795	+	8.84723i	0.664999	+	1.15181i	−0.314287	+	0.949328i	$0.601765\pi$
$60$		0			0
$61$	0.00549659	−	0.00952038i	0.000703767	−	0.00121896i	−0.865673	−	0.500609i	$-0.833109\pi$
$61$	0.00549659	−	0.00952038i	0.000703767	−	0.00121896i	0.866377	+	0.499390i	$0.166443\pi$
$62$	3.90833			0.496358
$63$		0			0
$64$	−3.11511			−0.389389
$65$		0			0
$66$		0			0
$67$	−0.491409	−	0.851145i	−0.0600351	−	0.103984i	0.834446	−	0.551090i	$-0.185788\pi$
$67$	−0.491409	−	0.851145i	−0.0600351	−	0.103984i	−0.894481	+	0.447106i	$0.852455\pi$
$68$	−2.81377	−	4.87359i	−0.341220	−	0.591010i
$69$		0			0
$70$		0			0
$71$	6.43507			0.763703			0.381851	−	0.924224i	$-0.375287\pi$
$71$	6.43507			0.763703			0.381851	+	0.924224i	$0.375287\pi$
$72$		0			0
$73$	6.61467			0.774189			0.387094	−	0.922040i	$-0.373479\pi$
$73$	6.61467			0.774189			0.387094	+	0.922040i	$0.373479\pi$
$74$	0.859605	−	1.48888i	0.0999271	−	0.173079i
$75$		0			0
$76$	0.316370	+	0.547969i	0.0362901	+	0.0628564i
$77$	−7.90523	−	13.6923i	−0.900885	−	1.56038i
$78$		0			0
$79$	4.73569	−	8.20246i	0.532807	−	0.922848i	−0.466459	−	0.884543i	$-0.654471\pi$
$79$	4.73569	−	8.20246i	0.532807	−	0.922848i	0.999266	−	0.0383057i	$-0.0121961\pi$
$80$		0			0
$81$		0			0
$82$	−1.29366			−0.142860
$83$	−5.20988	+	9.02378i	−0.571859	+	0.990489i	0.424516	+	0.905420i	$0.360444\pi$
$83$	−5.20988	+	9.02378i	−0.571859	+	0.990489i	−0.996375	+	0.0850682i	$0.972889\pi$
$84$		0			0
$85$		0			0
$86$	−1.81686	−	3.14690i	−0.195917	−	0.339339i
$87$		0			0
$88$	−5.51172	+	9.54658i	−0.587551	+	1.01767i
$89$	6.26940			0.664555			0.332277	−	0.943182i	$-0.392183\pi$
$89$	6.26940			0.664555			0.332277	+	0.943182i	$0.392183\pi$
$90$		0			0
$91$	5.46519			0.572908
$92$	3.74119	−	6.47993i	0.390046	−	0.675579i
$93$		0			0
$94$	2.70439	+	4.68413i	0.278936	+	0.483131i
$95$		0			0
$96$		0			0
$97$	−3.60339	+	6.24126i	−0.365869	+	0.633704i	−0.988915	−	0.148481i	$-0.952562\pi$
$97$	−3.60339	+	6.24126i	−0.365869	+	0.633704i	0.623046	+	0.782185i	$0.285895\pi$
$98$	0.203858			0.0205927
$99$		0			0
$100$		0			0
$101$	3.48547	−	6.03701i	0.346817	−	0.600705i	−0.638865	−	0.769319i	$-0.720596\pi$
$101$	3.48547	−	6.03701i	0.346817	−	0.600705i	0.985682	+	0.168614i	$0.0539291\pi$
$102$		0			0
$103$	3.05756	+	5.29584i	0.301270	+	0.521815i	0.976424	−	0.215862i	$-0.0692561\pi$
$103$	3.05756	+	5.29584i	0.301270	+	0.521815i	−0.675154	+	0.737677i	$0.735923\pi$
$104$	−1.90523	−	3.29996i	−0.186823	−	0.323588i
$105$		0			0
$106$	2.23260	−	3.86697i	0.216849	−	0.375593i
$107$	14.5349			1.40514			0.702570	−	0.711615i	$-0.252036\pi$
$107$	14.5349			1.40514			0.702570	+	0.711615i	$0.252036\pi$
$108$		0			0
$109$	1.90214			0.182192			0.0910958	−	0.995842i	$-0.470963\pi$
$109$	1.90214			0.182192			0.0910958	+	0.995842i	$0.470963\pi$
$110$		0			0
$111$		0			0
$112$	−3.46825	−	6.00719i	−0.327719	−	0.567626i
$113$	−3.28962	−	5.69780i	−0.309462	−	0.536004i	0.668783	−	0.743458i	$-0.266816\pi$
$113$	−3.28962	−	5.69780i	−0.309462	−	0.536004i	−0.978245	+	0.207454i	$0.933482\pi$
$114$		0			0
$115$		0			0
$116$	2.99480			0.278060
$117$		0			0
$118$	4.83472			0.445072
$119$	4.06065	−	7.03326i	0.372239	−	0.644737i
$120$		0			0
$121$	−13.5258	−	23.4274i	−1.22962	−	2.12977i
$122$	−0.00260129	−	0.00450556i	−0.000235509	−	0.000407914i
$123$		0			0
$124$	−7.33359	+	12.7021i	−0.658576	+	1.14069i
$125$		0			0
$126$		0			0
$127$	−9.25840			−0.821550			−0.410775	−	0.911737i	$-0.634742\pi$
$127$	−9.25840			−0.821550			−0.410775	+	0.911737i	$0.634742\pi$
$128$	−5.59196	+	9.68555i	−0.494264	+	0.856090i
$129$		0			0
$130$		0			0
$131$	0.134698	+	0.233305i	0.0117687	+	0.0203839i	0.871850	−	0.489773i	$-0.162920\pi$
$131$	0.134698	+	0.233305i	0.0117687	+	0.0203839i	−0.860081	+	0.510157i	$0.829587\pi$
$132$		0			0
$133$	−0.456565	+	0.790794i	−0.0395892	+	0.0685705i
$134$	−0.465123			−0.0401805
$135$		0			0
$136$	−5.66237			−0.485544
$137$	1.73809	−	3.01046i	0.148495	−	0.257201i	−0.782176	−	0.623057i	$-0.785890\pi$
$137$	1.73809	−	3.01046i	0.148495	−	0.257201i	0.930671	+	0.365856i	$0.119224\pi$
$138$		0			0
$139$	−7.37393	−	12.7720i	−0.625448	−	1.08331i	−0.988454	−	0.151521i	$-0.951583\pi$
$139$	−7.37393	−	12.7720i	−0.625448	−	1.08331i	0.363006	−	0.931787i	$-0.381751\pi$
$140$		0			0
$141$		0			0
$142$	1.52271	−	2.63742i	0.127783	−	0.221327i
$143$	13.1533			1.09993
$144$		0			0
$145$		0			0
$146$	1.56521	−	2.71103i	0.129538	−	0.224366i
$147$		0			0
$148$	3.22593	+	5.58747i	0.265170	+	0.459287i
$149$	−5.07665	−	8.79301i	−0.415895	−	0.720352i	0.579627	−	0.814882i	$-0.303198\pi$
$149$	−5.07665	−	8.79301i	−0.415895	−	0.720352i	−0.995522	+	0.0945305i	$0.969865\pi$
$150$		0			0
$151$	5.15811	−	8.93410i	0.419761	−	0.727047i	−0.576155	−	0.817341i	$-0.695447\pi$
$151$	5.15811	−	8.93410i	0.419761	−	0.727047i	0.995915	+	0.0902940i	$0.0287807\pi$
$152$	0.636657			0.0516397
$153$		0			0
$154$	−7.48237			−0.602947
$155$		0			0
$156$		0			0
$157$	−0.531305	−	0.920247i	−0.0424028	−	0.0734437i	0.844045	−	0.536272i	$-0.180168\pi$
$157$	−0.531305	−	0.920247i	−0.0424028	−	0.0734437i	−0.886448	+	0.462828i	$0.846835\pi$
$158$	−2.24119	−	3.88185i	−0.178299	−	0.308823i
$159$		0			0
$160$		0			0
$161$	10.7981			0.851008
$162$		0			0
$163$	−17.1386			−1.34240			−0.671198	−	0.741278i	$-0.734220\pi$
$163$	−17.1386			−1.34240			−0.671198	+	0.741278i	$0.734220\pi$
$164$	2.42742	−	4.20441i	0.189549	−	0.328309i
$165$		0			0
$166$	2.46560	+	4.27054i	0.191368	+	0.331459i
$167$	−2.18672	−	3.78752i	−0.169214	−	0.293087i	0.768930	−	0.639333i	$-0.220790\pi$
$167$	−2.18672	−	3.78752i	−0.169214	−	0.293087i	−0.938144	+	0.346246i	$0.887456\pi$
$168$		0			0
$169$	4.22666	−	7.32078i	0.325127	−	0.563137i
$170$		0			0
$171$		0			0
$172$	13.6367			1.03979
$173$	−7.33005	+	12.6960i	−0.557293	+	0.965260i	0.440428	+	0.897788i	$0.354827\pi$
$173$	−7.33005	+	12.6960i	−0.557293	+	0.965260i	−0.997721	+	0.0674723i	$0.978507\pi$
$174$		0			0
$175$		0			0
$176$	−8.34718	−	14.4577i	−0.629192	−	1.08979i
$177$		0			0
$178$	1.48351	−	2.56952i	0.111194	−	0.192593i
$179$	6.87014			0.513499			0.256749	−	0.966478i	$-0.417349\pi$
$179$	6.87014			0.513499			0.256749	+	0.966478i	$0.417349\pi$
$180$		0			0
$181$	−10.9709			−0.815463			−0.407732	−	0.913102i	$-0.633680\pi$
$181$	−10.9709			−0.815463			−0.407732	+	0.913102i	$0.633680\pi$
$182$	1.29321	−	2.23991i	0.0958593	−	0.166033i
$183$		0			0
$184$	−3.76434	−	6.52003i	−0.277511	−	0.480663i
$185$		0			0
$186$		0			0
$187$	9.77294	−	16.9272i	0.714668	−	1.23784i
$188$	−20.2980			−1.48039
$189$		0			0
$190$		0			0
$191$	6.86627	−	11.8927i	0.496826	−	0.860528i	−0.503167	−	0.864189i	$-0.667832\pi$
$191$	6.86627	−	11.8927i	0.496826	−	0.860528i	0.999993	+	0.00366109i	$0.00116536\pi$
$192$		0			0
$193$	0.241187	+	0.417748i	0.0173610	+	0.0300701i	0.874575	−	0.484890i	$-0.161140\pi$
$193$	0.241187	+	0.417748i	0.0173610	+	0.0300701i	−0.857214	+	0.514960i	$0.827807\pi$
$194$	1.70532	+	2.95370i	0.122435	+	0.212064i
$195$		0			0
$196$	−0.382518	+	0.662541i	−0.0273227	+	0.0473244i
$197$	−5.53488			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$197$	−5.53488			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$198$		0			0
$199$	17.4590			1.23764			0.618818	−	0.785534i	$-0.287612\pi$
$199$	17.4590			1.23764			0.618818	+	0.785534i	$0.287612\pi$
$200$		0			0
$201$		0			0
$202$	−1.64951	−	2.85704i	−0.116059	−	0.201021i
$203$	2.16095	+	3.74288i	0.151669	+	0.262698i
$204$		0			0
$205$		0			0
$206$	2.89401			0.201635
$207$		0			0
$208$	5.77073			0.400128
$209$	−1.09883	+	1.90324i	−0.0760079	+	0.131650i
$210$		0			0
$211$	0.818328	+	1.41739i	0.0563360	+	0.0975769i	0.892818	−	0.450417i	$-0.148725\pi$
$211$	0.818328	+	1.41739i	0.0563360	+	0.0975769i	−0.836482	+	0.547994i	$0.815392\pi$
$212$	8.37849	+	14.5120i	0.575437	+	0.996686i
$213$		0			0
$214$	3.43935	−	5.95713i	0.235109	−	0.407221i
$215$		0			0
$216$		0			0
$217$	−21.1667			−1.43689
$218$	0.450098	−	0.779592i	0.0304844	−	0.0528006i
$219$		0			0
$220$		0			0
$221$	3.37820	+	5.85122i	0.227243	+	0.393596i
$222$		0			0
$223$	−3.87393	+	6.70984i	−0.259417	+	0.449324i	−0.966086	−	0.258221i	$-0.916864\pi$
$223$	−3.87393	+	6.70984i	−0.259417	+	0.449324i	0.706669	+	0.707545i	$0.250197\pi$
$224$	−12.4432			−0.831397
$225$		0			0
$226$	−3.11366			−0.207118
$227$	−5.63014	+	9.75169i	−0.373685	+	0.647242i	−0.990129	−	0.140157i	$-0.955239\pi$
$227$	−5.63014	+	9.75169i	−0.373685	+	0.647242i	0.616444	+	0.787399i	$0.288573\pi$
$228$		0			0
$229$	5.23879	+	9.07384i	0.346189	+	0.599616i	0.985569	−	0.169274i	$-0.0541424\pi$
$229$	5.23879	+	9.07384i	0.346189	+	0.599616i	−0.639380	+	0.768891i	$0.720809\pi$
$230$		0			0
$231$		0			0
$232$	1.50667	−	2.60962i	0.0989176	−	0.171330i
$233$	2.90214			0.190125			0.0950627	−	0.995471i	$-0.469695\pi$
$233$	2.90214			0.190125			0.0950627	+	0.995471i	$0.469695\pi$
$234$		0			0
$235$		0			0
$236$	−9.07188	+	15.7130i	−0.590529	+	1.02283i
$237$		0			0
$238$	−1.92172	−	3.32852i	−0.124567	−	0.215756i
$239$	8.17723	+	14.1634i	0.528941	+	0.916153i	0.999430	+	0.0337471i	$0.0107441\pi$
$239$	8.17723	+	14.1634i	0.528941	+	0.916153i	−0.470489	+	0.882406i	$0.655923\pi$
$240$		0			0
$241$	−8.76194	+	15.1761i	−0.564406	+	0.977580i	0.432698	+	0.901539i	$0.357562\pi$
$241$	−8.76194	+	15.1761i	−0.564406	+	0.977580i	−0.997105	+	0.0760416i	$0.975772\pi$
$242$	−12.8023			−0.822965
$243$		0			0
$244$	0.0195242			0.00124991
$245$		0			0
$246$		0			0
$247$	−0.379833	−	0.657890i	−0.0241682	−	0.0418605i
$248$	7.37898	+	12.7808i	0.468566	+	0.811580i
$249$		0			0
$250$		0			0
$251$	−8.46999			−0.534621			−0.267311	−	0.963610i	$-0.586135\pi$
$251$	−8.46999			−0.534621			−0.267311	+	0.963610i	$0.586135\pi$
$252$		0			0
$253$	25.9882			1.63386
$254$	−2.19079	+	3.79456i	−0.137462	+	0.238092i
$255$		0			0
$256$	−0.468695	−	0.811804i	−0.0292934	−	0.0507377i
$257$	−1.43625	−	2.48766i	−0.0895910	−	0.155176i	0.817747	−	0.575577i	$-0.195223\pi$
$257$	−1.43625	−	2.48766i	−0.0895910	−	0.155176i	−0.907338	+	0.420401i	$0.861889\pi$
$258$		0			0
$259$	−4.65545	+	8.06348i	−0.289276	+	0.501040i
$260$		0			0
$261$		0			0
$262$	0.127493			0.00787656
$263$	12.8119	−	22.1909i	0.790017	−	1.36835i	−0.135938	−	0.990717i	$-0.543405\pi$
$263$	12.8119	−	22.1909i	0.790017	−	1.36835i	0.925955	−	0.377633i	$-0.123262\pi$
$264$		0			0
$265$		0			0
$266$	0.216072	+	0.374247i	0.0132482	+	0.0229465i
$267$		0			0
$268$	0.872756	−	1.51166i	0.0533121	−	0.0923392i
$269$	−0.337210			−0.0205600			−0.0102800	−	0.999947i	$-0.503272\pi$
$269$	−0.337210			−0.0205600			−0.0102800	+	0.999947i	$0.503272\pi$
$270$		0			0
$271$	21.5927			1.31166			0.655831	−	0.754908i	$-0.272318\pi$
$271$	21.5927			1.31166			0.655831	+	0.754908i	$0.272318\pi$
$272$	4.28767	−	7.42646i	0.259978	−	0.450295i
$273$		0			0
$274$	−0.822560	−	1.42472i	−0.0496927	−	0.0860702i
$275$		0			0
$276$		0			0
$277$	−12.0669	+	20.9004i	−0.725028	+	1.25579i	0.233934	+	0.972252i	$0.424840\pi$
$277$	−12.0669	+	20.9004i	−0.725028	+	1.25579i	−0.958962	+	0.283533i	$0.908493\pi$
$278$	−6.97949			−0.418602
$279$		0			0
$280$		0			0
$281$	1.68363	−	2.91613i	0.100437	−	0.173962i	−0.811428	−	0.584453i	$-0.801309\pi$
$281$	1.68363	−	2.91613i	0.100437	−	0.173962i	0.911865	+	0.410491i	$0.134643\pi$
$282$		0			0
$283$	−10.9249	−	18.9224i	−0.649415	−	1.12482i	−0.983263	−	0.182193i	$-0.941681\pi$
$283$	−10.9249	−	18.9224i	−0.649415	−	1.12482i	0.333848	−	0.942627i	$-0.391653\pi$
$284$	5.71444	+	9.89770i	0.339090	+	0.587321i
$285$		0			0
$286$	3.11243	−	5.39088i	0.184042	−	0.318770i
$287$	7.00619			0.413562
$288$		0			0
$289$	−6.95994			−0.409408
$290$		0			0
$291$		0			0
$292$	5.87393	+	10.1739i	0.343746	+	0.595385i
$293$	6.87702	+	11.9114i	0.401760	+	0.695869i	0.993938	−	0.109938i	$-0.0350653\pi$
$293$	6.87702	+	11.9114i	0.401760	+	0.695869i	−0.592179	+	0.805807i	$0.701732\pi$
$294$		0			0
$295$		0			0
$296$	6.49179			0.377328
$297$		0			0
$298$	−4.80509			−0.278352
$299$	−4.49166	+	7.77978i	−0.259759	+	0.449916i
$300$		0			0
$301$	9.83978	+	17.0430i	0.567155	+	0.982342i
$302$	−2.44110	−	4.22810i	−0.140469	−	0.243300i
$303$		0			0
$304$	−0.482090	+	0.835004i	−0.0276498	+	0.0478908i
$305$		0			0
$306$		0			0
$307$	34.2183			1.95294			0.976472	−	0.215644i	$-0.0691850\pi$
$307$	34.2183			1.95294			0.976472	+	0.215644i	$0.0691850\pi$
$308$	14.0399	−	24.3179i	0.799999	−	1.38564i
$309$		0			0
$310$		0			0
$311$	11.5199	+	19.9530i	0.653232	+	1.13143i	0.982334	+	0.187136i	$0.0599206\pi$
$311$	11.5199	+	19.9530i	0.653232	+	1.13143i	−0.329102	+	0.944294i	$0.606746\pi$
$312$		0			0
$313$	1.79565	−	3.11016i	0.101496	−	0.175796i	−0.810805	−	0.585316i	$-0.800970\pi$
$313$	1.79565	−	3.11016i	0.101496	−	0.175796i	0.912301	+	0.409520i	$0.134304\pi$
$314$	−0.502885			−0.0283794
$315$		0			0
$316$	16.8215			0.946281
$317$	6.59033	−	11.4148i	0.370150	−	0.641118i	−0.619439	−	0.785045i	$-0.712640\pi$
$317$	6.59033	−	11.4148i	0.370150	−	0.641118i	0.989588	+	0.143927i	$0.0459731\pi$
$318$		0			0
$319$	5.20085	+	9.00813i	0.291192	+	0.504359i
$320$		0			0
$321$		0			0
$322$	2.55512	−	4.42560i	0.142391	−	0.246629i
$323$	−1.12887			−0.0628119
$324$		0			0
$325$		0			0
$326$	−4.05545	+	7.02424i	−0.224611	+	0.389037i
$327$		0			0
$328$	−2.44244	−	4.23044i	−0.134861	−	0.233587i
$329$	−14.6464	−	25.3683i	−0.807483	−	1.39860i
$330$		0			0
$331$	−0.591264	+	1.02410i	−0.0324988	+	0.0562896i	−0.881817	−	0.471591i	$-0.843680\pi$
$331$	−0.591264	+	1.02410i	−0.0324988	+	0.0562896i	0.849319	+	0.527881i	$0.177013\pi$
$332$	−18.5058			−1.01564
$333$		0			0
$334$	−2.06975			−0.113252
$335$		0			0
$336$		0			0
$337$	12.3997	+	21.4770i	0.675457	+	1.16993i	0.976335	+	0.216263i	$0.0693868\pi$
$337$	12.3997	+	21.4770i	0.675457	+	1.16993i	−0.300879	+	0.953662i	$0.597280\pi$
$338$	−2.00028	−	3.46459i	−0.108801	−	0.188449i
$339$		0			0
$340$		0			0
$341$	−50.9428			−2.75871
$342$		0			0
$343$	−19.0454			−1.02836
$344$	6.86053	−	11.8828i	0.369895	−	0.640677i
$345$		0			0
$346$	3.46898	+	6.00845i	0.186493	+	0.323016i
$347$	11.0846	+	19.1991i	0.595052	+	1.03066i	0.993540	+	0.113486i	$0.0362018\pi$
$347$	11.0846	+	19.1991i	0.595052	+	1.03066i	−0.398488	+	0.917174i	$0.630465\pi$
$348$		0			0
$349$	−7.45925	+	12.9198i	−0.399285	+	0.691581i	−0.993638	−	0.112623i	$-0.964075\pi$
$349$	−7.45925	+	12.9198i	−0.399285	+	0.691581i	0.594353	+	0.804204i	$0.297408\pi$
$350$		0			0
$351$		0			0
$352$	−29.9476			−1.59621
$353$	8.45726	−	14.6484i	0.450134	−	0.779656i	−0.548260	−	0.836308i	$-0.684709\pi$
$353$	8.45726	−	14.6484i	0.450134	−	0.779656i	0.998394	+	0.0566525i	$0.0180427\pi$
$354$		0			0
$355$		0			0
$356$	5.56732	+	9.64288i	0.295067	+	0.511072i
$357$		0			0
$358$	1.62566	−	2.81573i	0.0859190	−	0.148816i
$359$	−0.636657			−0.0336015			−0.0168007	−	0.999859i	$-0.505348\pi$
$359$	−0.636657			−0.0336015			−0.0168007	+	0.999859i	$0.505348\pi$
$360$		0			0
$361$	−18.8731			−0.993320
$362$	−2.59602	+	4.49644i	−0.136444	+	0.236328i
$363$		0			0
$364$	4.85317	+	8.40594i	0.254375	+	0.440591i
$365$		0			0
$366$		0			0
$367$	−10.0490	+	17.4053i	−0.524552	+	0.908550i	0.475040	+	0.879964i	$0.342434\pi$
$367$	−10.0490	+	17.4053i	−0.524552	+	0.908550i	−0.999591	+	0.0285858i	$0.990900\pi$
$368$	11.4018			0.594358
$369$		0			0
$370$		0			0
$371$	−12.0913	+	20.9427i	−0.627749	+	1.08729i
$372$		0			0
$373$	9.82146	+	17.0113i	0.508536	+	0.880810i	0.999951	+	0.00988448i	$0.00314638\pi$
$373$	9.82146	+	17.0113i	0.508536	+	0.880810i	−0.491415	+	0.870925i	$0.663520\pi$
$374$	−4.62509	−	8.01088i	−0.239157	−	0.414233i
$375$		0			0
$376$	−10.2118	+	17.6874i	−0.526635	+	0.912159i
$377$	−3.59555			−0.185180
$378$		0			0
$379$	−7.94219			−0.407963			−0.203982	−	0.978975i	$-0.565388\pi$
$379$	−7.94219			−0.407963			−0.203982	+	0.978975i	$0.565388\pi$
$380$		0			0
$381$		0			0
$382$	−3.24949	−	5.62829i	−0.166259	−	0.287968i
$383$	−15.5944	−	27.0103i	−0.796836	−	1.38016i	−0.921667	−	0.387983i	$-0.873172\pi$
$383$	−15.5944	−	27.0103i	−0.796836	−	1.38016i	0.124830	−	0.992178i	$-0.460161\pi$
$384$		0			0
$385$		0			0
$386$	0.228285			0.0116194
$387$		0			0
$388$	−12.7995			−0.649795
$389$	−15.7247	+	27.2360i	−0.797274	+	1.38092i	0.124111	+	0.992268i	$0.460392\pi$
$389$	−15.7247	+	27.2360i	−0.797274	+	1.38092i	−0.921385	+	0.388650i	$0.872941\pi$
$390$		0			0
$391$	6.67463	+	11.5608i	0.337550	+	0.584655i
$392$	0.384886	+	0.666642i	0.0194397	+	0.0336705i
$393$		0			0
$394$	−1.30970	+	2.26847i	−0.0659819	+	0.114284i
$395$		0			0
$396$		0			0
$397$	17.7174			0.889211			0.444606	−	0.895726i	$-0.353344\pi$
$397$	17.7174			0.889211			0.444606	+	0.895726i	$0.353344\pi$
$398$	4.13128	−	7.15558i	0.207082	−	0.358677i
$399$		0			0
$400$		0			0
$401$	−3.57124	−	6.18556i	−0.178339	−	0.308892i	0.762973	−	0.646431i	$-0.223739\pi$
$401$	−3.57124	−	6.18556i	−0.178339	−	0.308892i	−0.941312	+	0.337538i	$0.890406\pi$
$402$		0			0
$403$	8.80468	−	15.2502i	0.438593	−	0.759665i
$404$	12.3806			0.615958
$405$		0			0
$406$	2.04536			0.101509
$407$	−11.2045	+	19.4067i	−0.555385	+	0.961955i
$408$		0			0
$409$	−12.3759	−	21.4357i	−0.611948	−	1.05993i	−0.990912	−	0.134514i	$-0.957053\pi$
$409$	−12.3759	−	21.4357i	−0.611948	−	1.05993i	0.378964	−	0.925412i	$-0.376281\pi$
$410$		0			0
$411$		0			0
$412$	−5.43031	+	9.40558i	−0.267532	+	0.463380i
$413$	−26.1839			−1.28843
$414$		0			0
$415$		0			0
$416$	5.17598	−	8.96505i	0.253773	−	0.439548i
$417$		0			0
$418$	0.520028	+	0.900715i	0.0254354	+	0.0440554i
$419$	−5.32956	−	9.23106i	−0.260366	−	0.450967i	0.705973	−	0.708238i	$-0.250510\pi$
$419$	−5.32956	−	9.23106i	−0.260366	−	0.450967i	−0.966339	+	0.257272i	$0.917176\pi$
$420$		0			0
$421$	4.08931	−	7.08288i	0.199301	−	0.345199i	−0.749001	−	0.662569i	$-0.769466\pi$
$421$	4.08931	−	7.08288i	0.199301	−	0.345199i	0.948302	+	0.317370i	$0.102800\pi$
$422$	0.774555			0.0377048
$423$		0			0
$424$	16.8607			0.818828
$425$		0			0
$426$		0			0
$427$	0.0140881	+	0.0244012i	0.000681769	+	0.00118086i
$428$	12.9072	+	22.3559i	0.623893	+	1.08061i
$429$		0			0
$430$		0			0
$431$	−1.67248			−0.0805604			−0.0402802	−	0.999188i	$-0.512825\pi$
$431$	−1.67248			−0.0805604			−0.0402802	+	0.999188i	$0.512825\pi$
$432$		0			0
$433$	−9.95994			−0.478644			−0.239322	−	0.970940i	$-0.576925\pi$
$433$	−9.95994			−0.478644			−0.239322	+	0.970940i	$0.576925\pi$
$434$	−5.00863	+	8.67519i	−0.240422	+	0.416423i
$435$		0			0
$436$	1.68913	+	2.92565i	0.0808945	+	0.140113i
$437$	−0.750471	−	1.29985i	−0.0358999	−	0.0621805i
$438$		0			0
$439$	−6.40788	+	11.0988i	−0.305832	+	0.529716i	−0.977446	−	0.211185i	$-0.932268\pi$
$439$	−6.40788	+	11.0988i	−0.305832	+	0.529716i	0.671615	+	0.740901i	$0.265601\pi$
$440$		0			0
$441$		0			0
$442$	3.19750			0.152090
$443$	−3.87702	+	6.71520i	−0.184203	+	0.319049i	−0.943308	−	0.331920i	$-0.892304\pi$
$443$	−3.87702	+	6.71520i	−0.184203	+	0.319049i	0.759105	+	0.650968i	$0.225637\pi$
$444$		0			0
$445$		0			0
$446$	1.83335	+	3.17546i	0.0868118	+	0.150362i
$447$		0			0
$448$	3.99210	−	6.91452i	0.188609	−	0.326681i
$449$	33.3401			1.57342			0.786709	−	0.617324i	$-0.211783\pi$
$449$	33.3401			1.57342			0.786709	+	0.617324i	$0.211783\pi$
$450$		0			0
$451$	16.8621			0.794004
$452$	5.84247	−	10.1195i	0.274807	−	0.475979i
$453$		0			0
$454$	2.66449	+	4.61503i	0.125051	+	0.216594i
$455$		0			0
$456$		0			0
$457$	19.1096	−	33.0988i	0.893910	−	1.54830i	0.0587626	−	0.998272i	$-0.481285\pi$
$457$	19.1096	−	33.0988i	0.893910	−	1.54830i	0.835148	−	0.550026i	$-0.185382\pi$
$458$	4.95856			0.231698
$459$		0			0
$460$		0			0
$461$	15.6517	−	27.1095i	0.728971	−	1.26261i	−0.228348	−	0.973580i	$-0.573332\pi$
$461$	15.6517	−	27.1095i	0.728971	−	1.26261i	0.957319	−	0.289035i	$-0.0933343\pi$
$462$		0			0
$463$	−6.04258	−	10.4661i	−0.280823	−	0.486399i	0.690765	−	0.723079i	$-0.257274\pi$
$463$	−6.04258	−	10.4661i	−0.280823	−	0.486399i	−0.971588	+	0.236680i	$0.923941\pi$
$464$	2.28176	+	3.95212i	0.105928	+	0.183473i
$465$		0			0
$466$	0.686725	−	1.18944i	0.0318119	−	0.0550998i
$467$	7.60466			0.351902			0.175951	−	0.984399i	$-0.443700\pi$
$467$	7.60466			0.351902			0.175951	+	0.984399i	$0.443700\pi$
$468$		0			0
$469$	2.51901			0.116317
$470$		0			0
$471$		0			0
$472$	9.12803	+	15.8102i	0.420152	+	0.727724i
$473$	23.6818	+	41.0181i	1.08889	+	1.88601i
$474$		0			0
$475$		0			0
$476$	14.4237			0.661108
$477$		0			0
$478$	7.73982			0.354011
$479$	−16.2417	+	28.1314i	−0.742101	+	1.28536i	0.209437	+	0.977822i	$0.432837\pi$
$479$	−16.2417	+	28.1314i	−0.742101	+	1.28536i	−0.951537	+	0.307534i	$0.900496\pi$
$480$		0			0
$481$	−3.87304	−	6.70830i	−0.176595	−	0.305872i
$482$	4.14663	+	7.18217i	0.188874	+	0.327139i
$483$		0			0
$484$	24.0223	−	41.6079i	1.09192	−	1.89127i
$485$		0			0
$486$		0			0
$487$	−4.46121			−0.202157			−0.101078	−	0.994878i	$-0.532229\pi$
$487$	−4.46121			−0.202157			−0.101078	+	0.994878i	$0.532229\pi$
$488$	0.00982254	−	0.0170131i	0.000444645	−	0.000770148i
$489$		0			0
$490$		0			0
$491$	16.4210	+	28.4420i	0.741070	+	1.28357i	0.952008	+	0.306072i	$0.0990148\pi$
$491$	16.4210	+	28.4420i	0.741070	+	1.28357i	−0.210938	+	0.977499i	$0.567652\pi$
$492$		0			0
$493$	−2.67150	+	4.62717i	−0.120318	+	0.208397i
$494$	−0.359515			−0.0161754
$495$		0			0
$496$	−22.3501			−1.00355
$497$	−8.24672	+	14.2837i	−0.369916	+	0.640713i
$498$		0			0
$499$	17.1010	+	29.6198i	0.765547	+	1.32597i	0.939957	+	0.341293i	$0.110865\pi$
$499$	17.1010	+	29.6198i	0.765547	+	1.32597i	−0.174410	+	0.984673i	$0.555802\pi$
$500$		0			0
$501$		0			0
$502$	−2.00423	+	3.47143i	−0.0894532	+	0.154938i
$503$	−22.1773			−0.988837			−0.494419	−	0.869224i	$-0.664619\pi$
$503$	−22.1773			−0.988837			−0.494419	+	0.869224i	$0.664619\pi$
$504$		0			0
$505$		0			0
$506$	6.14951	−	10.6513i	0.273379	−	0.473507i
$507$		0			0
$508$	−8.22160	−	14.2402i	−0.364775	−	0.631808i
$509$	−10.7816	−	18.6743i	−0.477887	−	0.827724i	0.521792	−	0.853073i	$-0.325264\pi$
$509$	−10.7816	−	18.6743i	−0.477887	−	0.827724i	−0.999679	+	0.0253489i	$0.991930\pi$
$510$		0			0
$511$	−8.47688	+	14.6824i	−0.374995	+	0.649510i
$512$	−22.8115			−1.00813
$513$		0			0
$514$	−1.35943			−0.0599617
$515$		0			0
$516$		0			0
$517$	−35.2501	−	61.0550i	−1.55030	−	2.68520i
$518$	2.20321	+	3.81608i	0.0968037	+	0.167669i
$519$		0			0
$520$		0			0
$521$	−20.2626			−0.887718			−0.443859	−	0.896097i	$-0.646391\pi$
$521$	−20.2626			−0.887718			−0.443859	+	0.896097i	$0.646391\pi$
$522$		0			0
$523$	31.8114			1.39101			0.695507	−	0.718520i	$-0.255180\pi$
$523$	31.8114			1.39101			0.695507	+	0.718520i	$0.255180\pi$
$524$	−0.239229	+	0.414356i	−0.0104507	+	0.0181012i
$525$		0			0
$526$	−6.06330	−	10.5019i	−0.264373	−	0.457907i
$527$	−13.0838	−	22.6618i	−0.569940	−	0.987164i
$528$		0			0
$529$	2.62541	−	4.54735i	0.114148	−	0.197711i
$530$		0			0
$531$		0			0
$532$	−1.62175			−0.0703117
$533$	−2.91435	+	5.04780i	−0.126235	+	0.218645i
$534$		0			0
$535$		0			0
$536$	−0.878159	−	1.52102i	−0.0379307	−	0.0656978i
$537$		0			0
$538$	−0.0797930	+	0.138205i	−0.00344012	+	0.00595846i
$539$	−2.65717			−0.114452
$540$		0			0
$541$	−15.1315			−0.650553			−0.325277	−	0.945619i	$-0.605457\pi$
$541$	−15.1315			−0.650553			−0.325277	+	0.945619i	$0.605457\pi$
$542$	5.10942	−	8.84977i	0.219468	−	0.380130i
$543$		0			0
$544$	−7.69153	−	13.3221i	−0.329772	−	0.571181i
$545$		0			0
$546$		0			0
$547$	2.04372	−	3.53982i	0.0873831	−	0.151352i	−0.819021	−	0.573763i	$-0.805483\pi$
$547$	2.04372	−	3.53982i	0.0873831	−	0.151352i	0.906404	+	0.422411i	$0.138816\pi$
$548$	6.17381			0.263732
$549$		0			0
$550$		0			0
$551$	0.300374	−	0.520263i	0.0127964	−	0.0221639i
$552$		0			0
$553$	12.1378	+	21.0233i	0.516153	+	0.894003i
$554$	5.71070	+	9.89123i	0.242625	+	0.420238i
$555$		0			0
$556$	13.0963	−	22.6835i	0.555408	−	0.961994i
$557$	13.1425			0.556864			0.278432	−	0.960456i	$-0.410185\pi$
$557$	13.1425			0.556864			0.278432	+	0.960456i	$0.410185\pi$
$558$		0			0
$559$	−16.3721			−0.692467
$560$		0			0
$561$		0			0
$562$	−0.796785	−	1.38007i	−0.0336104	−	0.0582149i
$563$	−12.2611	−	21.2368i	−0.516742	−	0.895023i	−0.999811	−	0.0194410i	$-0.993811\pi$
$563$	−12.2611	−	21.2368i	−0.516742	−	0.895023i	0.483069	−	0.875582i	$-0.339522\pi$
$564$		0			0
$565$		0			0
$566$	−10.3405			−0.434642
$567$		0			0
$568$	11.4996			0.482514
$569$	11.3649	−	19.6846i	0.476442	−	0.825223i	−0.523193	−	0.852214i	$-0.675259\pi$
$569$	11.3649	−	19.6846i	0.476442	−	0.825223i	0.999636	+	0.0269915i	$0.00859271\pi$
$570$		0			0
$571$	0.247093	+	0.427977i	0.0103405	+	0.0179103i	0.871149	−	0.491018i	$-0.163375\pi$
$571$	0.247093	+	0.427977i	0.0103405	+	0.0179103i	−0.860809	+	0.508928i	$0.830042\pi$
$572$	11.6803	+	20.2309i	0.488379	+	0.845897i
$573$		0			0
$574$	1.65786	−	2.87149i	0.0691976	−	0.119854i
$575$		0			0
$576$		0			0
$577$	−9.41187			−0.391821			−0.195911	−	0.980622i	$-0.562766\pi$
$577$	−9.41187			−0.391821			−0.195911	+	0.980622i	$0.562766\pi$
$578$	−1.64691	+	2.85254i	−0.0685025	+	0.118650i
$579$		0			0
$580$		0			0
$581$	−13.3532	−	23.1284i	−0.553984	−	0.959529i
$582$		0			0
$583$	−29.1006	+	50.4037i	−1.20522	+	2.08751i
$584$	11.8206			0.489139
$585$		0			0
$586$	6.50916			0.268891
$587$	4.98661	−	8.63705i	0.205819	−	0.356489i	−0.744574	−	0.667540i	$-0.767347\pi$
$587$	4.98661	−	8.63705i	0.205819	−	0.356489i	0.950393	+	0.311050i	$0.100681\pi$
$588$		0			0
$589$	1.47110	+	2.54801i	0.0606155	+	0.104989i
$590$		0			0
$591$		0			0
$592$	−4.91572	+	8.51428i	−0.202035	+	0.349935i
$593$	−38.3421			−1.57452			−0.787260	−	0.616621i	$-0.788501\pi$
$593$	−38.3421			−1.57452			−0.787260	+	0.616621i	$0.788501\pi$
$594$		0			0
$595$		0			0
$596$	9.01628	−	15.6167i	0.369321	−	0.639683i
$597$		0			0
$598$	2.12570	+	3.68182i	0.0869262	+	0.150561i
$599$	−5.07665	−	8.79301i	−0.207426	−	0.359273i	0.743477	−	0.668762i	$-0.233175\pi$
$599$	−5.07665	−	8.79301i	−0.207426	−	0.359273i	−0.950903	+	0.309489i	$0.899842\pi$
$600$		0			0
$601$	10.6371	−	18.4241i	0.433898	−	0.751533i	−0.563307	−	0.826248i	$-0.690471\pi$
$601$	10.6371	−	18.4241i	0.433898	−	0.751533i	0.997205	+	0.0747146i	$0.0238046\pi$
$602$	9.31344			0.379587
$603$		0			0
$604$	18.3219			0.745508
$605$		0			0
$606$		0			0
$607$	18.8678	+	32.6799i	0.765819	+	1.32644i	0.939812	+	0.341691i	$0.111000\pi$
$607$	18.8678	+	32.6799i	0.765819	+	1.32644i	−0.173993	+	0.984747i	$0.555667\pi$
$608$	0.864808	+	1.49789i	0.0350726	+	0.0607475i
$609$		0			0
$610$		0			0
$611$	24.3698			0.985895
$612$		0			0
$613$	−32.2633			−1.30310			−0.651551	−	0.758605i	$-0.725881\pi$
$613$	−32.2633			−1.30310			−0.651551	+	0.758605i	$0.725881\pi$
$614$	8.09699	−	14.0244i	0.326768	−	0.565979i
$615$		0			0
$616$	−14.1268	−	24.4684i	−0.569186	−	0.985860i
$617$	−13.0089	−	22.5321i	−0.523719	−	0.907108i	−0.999619	−	0.0276084i	$-0.991211\pi$
$617$	−13.0089	−	22.5321i	−0.523719	−	0.907108i	0.475900	−	0.879499i	$-0.342122\pi$
$618$		0			0
$619$	5.94077	−	10.2897i	0.238780	−	0.413578i	−0.721585	−	0.692326i	$-0.756586\pi$
$619$	5.94077	−	10.2897i	0.238780	−	0.413578i	0.960364	+	0.278748i	$0.0899193\pi$
$620$		0			0
$621$		0			0
$622$	10.9037			0.437197
$623$	−8.03440	+	13.9160i	−0.321891	+	0.557532i
$624$		0			0
$625$		0			0
$626$	−0.849799	−	1.47189i	−0.0339648	−	0.0588288i
$627$		0			0
$628$	0.943614	−	1.63439i	0.0376543	−	0.0652191i
$629$	−11.5107			−0.458962
$630$		0			0
$631$	−13.2726			−0.528372			−0.264186	−	0.964472i	$-0.585103\pi$
$631$	−13.2726			−0.528372			−0.264186	+	0.964472i	$0.585103\pi$
$632$	8.46279	−	14.6580i	0.336632	−	0.583063i
$633$		0			0
$634$	−3.11890	−	5.40210i	−0.123867	−	0.214545i
$635$		0			0
$636$		0			0
$637$	0.459251	−	0.795445i	0.0181962	−	0.0315167i
$638$	4.92265			0.194890
$639$		0			0
$640$		0			0
$641$	22.4075	−	38.8109i	0.885042	−	1.53294i	0.0393765	−	0.999224i	$-0.487463\pi$
$641$	22.4075	−	38.8109i	0.885042	−	1.53294i	0.845665	−	0.533713i	$-0.179204\pi$
$642$		0			0
$643$	7.46275	+	12.9259i	0.294302	+	0.509747i	0.974822	−	0.222983i	$-0.0715794\pi$
$643$	7.46275	+	12.9259i	0.294302	+	0.509747i	−0.680520	+	0.732729i	$0.738246\pi$
$644$	9.58886	+	16.6084i	0.377854	+	0.654462i
$645$		0			0
$646$	−0.267121	+	0.462667i	−0.0105097	+	0.0182034i
$647$	41.2684			1.62243			0.811214	−	0.584749i	$-0.198807\pi$
$647$	41.2684			1.62243			0.811214	+	0.584749i	$0.198807\pi$
$648$		0			0
$649$	−63.0179			−2.47367
$650$		0			0
$651$		0			0
$652$	−15.2193	−	26.3606i	−0.596034	−	1.03236i
$653$	13.8126	+	23.9241i	0.540528	+	0.936223i	0.998874	+	0.0474484i	$0.0151090\pi$
$653$	13.8126	+	23.9241i	0.540528	+	0.936223i	−0.458345	+	0.888774i	$0.651558\pi$
$654$		0			0
$655$		0			0
$656$	7.39788			0.288839
$657$		0			0
$658$	−13.8630			−0.540435
$659$	20.0112	−	34.6605i	0.779527	−	1.35018i	−0.152688	−	0.988274i	$-0.548793\pi$
$659$	20.0112	−	34.6605i	0.779527	−	1.35018i	0.932215	−	0.361905i	$-0.117874\pi$
$660$		0			0
$661$	−12.4965	−	21.6445i	−0.486056	−	0.841874i	0.513816	−	0.857901i	$-0.328232\pi$
$661$	−12.4965	−	21.6445i	−0.486056	−	0.841874i	−0.999872	+	0.0160270i	$0.994898\pi$
$662$	0.279818	+	0.484659i	0.0108754	+	0.0188368i
$663$		0			0
$664$	−9.31018	+	16.1257i	−0.361305	+	0.625799i
$665$		0			0
$666$		0			0
$667$	−7.10405			−0.275070
$668$	3.88369	−	6.72675i	0.150264	−	0.260266i
$669$		0			0
$670$		0			0
$671$	0.0339063	+	0.0587274i	0.00130894	+	0.00226715i
$672$		0			0
$673$	20.4024	−	35.3380i	0.786454	−	1.36218i	−0.141672	−	0.989914i	$-0.545248\pi$
$673$	20.4024	−	35.3380i	0.786454	−	1.36218i	0.928126	−	0.372265i	$-0.121419\pi$
$674$	11.7365			0.452072
$675$		0			0
$676$	15.0133			0.577436
$677$	20.5947	−	35.6710i	0.791518	−	1.37095i	−0.133509	−	0.991048i	$-0.542625\pi$
$677$	20.5947	−	35.6710i	0.791518	−	1.37095i	0.925027	−	0.379901i	$-0.124042\pi$
$678$		0			0
$679$	−9.23569	−	15.9967i	−0.354433	−	0.613896i
$680$		0			0
$681$		0			0
$682$	−12.0545	+	20.8789i	−0.461589	+	0.799496i
$683$	−1.33820			−0.0512047			−0.0256023	−	0.999672i	$-0.508150\pi$
$683$	−1.33820			−0.0512047			−0.0256023	+	0.999672i	$0.508150\pi$
$684$		0			0
$685$		0			0
$686$	−4.50667	+	7.80578i	−0.172065	+	0.298026i
$687$		0			0
$688$	10.3899	+	17.9958i	0.396110	+	0.686083i
$689$	−10.0592	−	17.4230i	−0.383225	−	0.663764i
$690$		0			0
$691$	12.6407	−	21.8943i	0.480874	−	0.832898i	−0.518885	−	0.854844i	$-0.673653\pi$
$691$	12.6407	−	21.8943i	0.480874	−	0.832898i	0.999759	+	0.0219459i	$0.00698617\pi$
$692$	−26.0368			−0.989770
$693$		0			0
$694$	10.4917			0.398258
$695$		0			0
$696$		0			0
$697$	4.33074	+	7.50106i	0.164039	+	0.284123i
$698$	3.53012	+	6.11435i	0.133617	+	0.231432i
$699$		0			0
$700$		0			0
$701$	18.2064			0.687645			0.343822	−	0.939035i	$-0.388278\pi$
$701$	18.2064			0.687645			0.343822	+	0.939035i	$0.388278\pi$
$702$		0			0
$703$	1.29422			0.0488126
$704$	9.60795	−	16.6415i	0.362113	−	0.627199i
$705$		0			0
$706$	−4.00244	−	6.93242i	−0.150634	−	0.260905i
$707$	8.93344	+	15.4732i	0.335977	+	0.581929i
$708$		0			0
$709$	−20.9103	+	36.2177i	−0.785304	+	1.36019i	0.143514	+	0.989648i	$0.454160\pi$
$709$	−20.9103	+	36.2177i	−0.785304	+	1.36019i	−0.928818	+	0.370537i	$0.879174\pi$
$710$		0			0
$711$		0			0
$712$	11.2036			0.419871
$713$	17.3962	−	30.1312i	0.651494	−	1.12842i
$714$		0			0
$715$		0			0
$716$	6.10079	+	10.5669i	0.227997	+	0.394903i
$717$		0			0
$718$	−0.150650	+	0.260934i	−0.00562222	+	0.00973797i
$719$	−48.9786			−1.82660			−0.913298	−	0.407293i	$-0.866473\pi$
$719$	−48.9786			−1.82660			−0.913298	+	0.407293i	$0.866473\pi$
$720$		0			0
$721$	−15.6734			−0.583707
$722$	−4.46588	+	7.73514i	−0.166203	+	0.287872i
$723$		0			0
$724$	−9.74236	−	16.8743i	−0.362072	−	0.627127i
$725$		0			0
$726$		0			0
$727$	21.9005	−	37.9327i	0.812243	−	1.40685i	−0.0990474	−	0.995083i	$-0.531580\pi$
$727$	21.9005	−	37.9327i	0.812243	−	1.40685i	0.911291	−	0.411764i	$-0.135087\pi$
$728$	9.76642			0.361968
$729$		0			0
$730$		0			0
$731$	−12.1645	+	21.0696i	−0.449922	+	0.779287i
$732$		0			0
$733$	3.39332	+	5.87740i	0.125335	+	0.217087i	0.921864	−	0.387514i	$-0.126666\pi$
$733$	3.39332	+	5.87740i	0.125335	+	0.217087i	−0.796529	+	0.604601i	$0.793333\pi$
$734$	4.75572	+	8.23715i	0.175537	+	0.304039i
$735$		0			0
$736$	10.2267	−	17.7131i	0.376960	−	0.652913i
$737$	6.06261			0.223319
$738$		0			0
$739$	28.7245			1.05665			0.528324	−	0.849043i	$-0.322821\pi$
$739$	28.7245			1.05665			0.528324	+	0.849043i	$0.322821\pi$
$740$		0			0
$741$		0			0
$742$	5.72226	+	9.91125i	0.210071	+	0.363853i
$743$	−15.7262	−	27.2385i	−0.576937	−	0.999284i	−0.995828	−	0.0912477i	$-0.970915\pi$
$743$	−15.7262	−	27.2385i	−0.576937	−	0.999284i	0.418891	−	0.908036i	$-0.362419\pi$
$744$		0			0
$745$		0			0
$746$	9.29610			0.340354
$747$		0			0
$748$	34.7141			1.26927
$749$	−18.6268	+	32.2626i	−0.680610	+	1.17885i
$750$		0			0
$751$	−5.47659	−	9.48574i	−0.199844	−	0.346139i	0.748634	−	0.662984i	$-0.230710\pi$
$751$	−5.47659	−	9.48574i	−0.199844	−	0.346139i	−0.948478	+	0.316844i	$0.897377\pi$
$752$	−15.4652	−	26.7866i	−0.563959	−	0.976806i
$753$		0			0
$754$	−0.850804	+	1.47364i	−0.0309845	+	0.0536667i
$755$		0			0
$756$		0			0
$757$	−45.7942			−1.66442			−0.832210	−	0.554461i	$-0.812925\pi$
$757$	−45.7942			−1.66442			−0.832210	+	0.554461i	$0.812925\pi$
$758$	−1.87934	+	3.25511i	−0.0682607	+	0.118231i
$759$		0			0
$760$		0			0
$761$	−16.9569	−	29.3702i	−0.614687	−	1.06467i	−0.990439	−	0.137948i	$-0.955949\pi$
$761$	−16.9569	−	29.3702i	−0.614687	−	1.06467i	0.375753	−	0.926720i	$-0.377384\pi$
$762$		0			0
$763$	−2.43764	+	4.22212i	−0.0882485	+	0.152851i
$764$	24.3894			0.882378
$765$		0			0
$766$	−14.7602			−0.533309
$767$	10.8917	−	18.8649i	0.393275	−	0.681173i
$768$		0			0
$769$	−3.57986	−	6.20050i	−0.129093	−	0.223596i	0.794232	−	0.607614i	$-0.207873\pi$
$769$	−3.57986	−	6.20050i	−0.129093	−	0.223596i	−0.923325	+	0.384018i	$0.874540\pi$
$770$		0			0
$771$		0			0
$772$	−0.428355	+	0.741933i	−0.0154168	+	0.0267027i
$773$	14.5998			0.525117			0.262558	−	0.964916i	$-0.415434\pi$
$773$	14.5998			0.525117			0.262558	+	0.964916i	$0.415434\pi$
$774$		0			0
$775$		0			0
$776$	−6.43935	+	11.1533i	−0.231159	+	0.400379i
$777$		0			0
$778$	7.44178	+	12.8895i	0.266801	+	0.462113i
$779$	−0.486933	−	0.843393i	−0.0174462	−	0.0302177i
$780$		0			0
$781$	−19.8477	+	34.3772i	−0.710207	+	1.23011i
$782$	6.31760			0.225917
$783$		0			0
$784$	−1.16578			−0.0416348
$785$		0			0
$786$		0			0
$787$	−9.23638	−	15.9979i	−0.329242	−	0.570263i	0.653120	−	0.757254i	$-0.273460\pi$
$787$	−9.23638	−	15.9979i	−0.329242	−	0.570263i	−0.982362	+	0.186991i	$0.940126\pi$
$788$	−4.91505	−	8.51312i	−0.175092	−	0.303267i
$789$		0			0
$790$		0			0
$791$	16.8630			0.599578
$792$		0			0
$793$	−0.0234407			−0.000832405
$794$	4.19242	−	7.26149i	0.148783	−	0.257700i
$795$		0			0
$796$	15.5039	+	26.8535i	0.549520	+	0.951796i
$797$	20.5187	+	35.5395i	0.726810	+	1.25887i	0.958225	+	0.286017i	$0.0923314\pi$
$797$	20.5187	+	35.5395i	0.726810	+	1.25887i	−0.231414	+	0.972855i	$0.574335\pi$
$798$		0			0
$799$	18.1068	−	31.3619i	0.640573	−	1.10950i
$800$		0			0
$801$		0			0
$802$	−3.38021			−0.119359
$803$	−20.4016	+	35.3367i	−0.719958	+	1.24700i
$804$		0			0
$805$		0			0
$806$	−4.16686	−	7.21721i	−0.146771	−	0.254215i
$807$		0			0
$808$	6.22861	−	10.7883i	0.219122	−	0.379530i
$809$	−7.19375			−0.252919			−0.126459	−	0.991972i	$-0.540361\pi$
$809$	−7.19375			−0.252919			−0.126459	+	0.991972i	$0.540361\pi$
$810$		0			0
$811$	38.2183			1.34203			0.671014	−	0.741445i	$-0.265859\pi$
$811$	38.2183			1.34203			0.671014	+	0.741445i	$0.265859\pi$
$812$	−3.83791	+	6.64746i	−0.134684	+	0.233280i
$813$		0			0
$814$	5.30257	+	9.18431i	0.185855	+	0.321910i
$815$		0			0
$816$		0			0
$817$	1.36774	−	2.36899i	0.0478511	−	0.0828805i
$818$	−11.7139			−0.409566
$819$		0			0
$820$		0			0
$821$	−0.334280	+	0.578990i	−0.0116665	+	0.0202069i	−0.871800	−	0.489863i	$-0.837047\pi$
$821$	−0.334280	+	0.578990i	−0.0116665	+	0.0202069i	0.860133	+	0.510069i	$0.170380\pi$
$822$		0			0
$823$	0.710165	+	1.23004i	0.0247548	+	0.0428766i	0.878137	−	0.478408i	$-0.158786\pi$
$823$	0.710165	+	1.23004i	0.0247548	+	0.0428766i	−0.853383	+	0.521285i	$0.825453\pi$
$824$	5.46393	+	9.46380i	0.190345	+	0.329687i
$825$		0			0
$826$	−6.19583	+	10.7315i	−0.215580	+	0.373396i
$827$	−49.8169			−1.73230			−0.866152	−	0.499782i	$-0.833414\pi$
$827$	−49.8169			−1.73230			−0.866152	+	0.499782i	$0.833414\pi$
$828$		0			0
$829$	36.4150			1.26475			0.632373	−	0.774664i	$-0.282081\pi$
$829$	36.4150			1.26475			0.632373	+	0.774664i	$0.282081\pi$
$830$		0			0
$831$		0			0
$832$	3.32117	+	5.75244i	0.115141	+	0.199430i
$833$	−0.682449	−	1.18204i	−0.0236455	−	0.0409551i
$834$		0			0
$835$		0			0
$836$	−3.90312			−0.134992
$837$		0			0
$838$	−5.04447			−0.174258
$839$	−10.0445	+	17.3976i	−0.346774	+	0.600631i	−0.985674	−	0.168659i	$-0.946056\pi$
$839$	−10.0445	+	17.3976i	−0.346774	+	0.600631i	0.638900	+	0.769290i	$0.279390\pi$
$840$		0			0
$841$	13.0783	+	22.6523i	0.450976	+	0.781114i
$842$	−1.93528	−	3.35201i	−0.0666942	−	0.115518i
$843$		0			0
$844$	−1.45338	+	2.51732i	−0.0500273	+	0.0866498i
$845$		0			0
$846$		0			0
$847$	69.3349			2.38238
$848$	−12.7673	+	22.1136i	−0.438430	+	0.759383i
$849$		0			0
$850$		0			0
$851$	−7.65232	−	13.2542i	−0.262318	−	0.454349i
$852$		0			0
$853$	−13.4542	+	23.3034i	−0.460663	+	0.797892i	−0.998994	−	0.0448418i	$-0.985722\pi$
$853$	−13.4542	+	23.3034i	−0.460663	+	0.797892i	0.538331	+	0.842733i	$0.319055\pi$
$854$	0.0133345			0.000456296
$855$		0			0
$856$	25.9742			0.887779
$857$	−24.4204	+	42.2973i	−0.834184	+	1.44485i	0.0605088	+	0.998168i	$0.480728\pi$
$857$	−24.4204	+	42.2973i	−0.834184	+	1.44485i	−0.894693	+	0.446682i	$0.852606\pi$
$858$		0			0
$859$	20.7047	+	35.8616i	0.706435	+	1.22358i	0.966171	+	0.257902i	$0.0830312\pi$
$859$	20.7047	+	35.8616i	0.706435	+	1.22358i	−0.259736	+	0.965680i	$0.583635\pi$
$860$		0			0
$861$		0			0
$862$	−0.395754	+	0.685465i	−0.0134794	+	0.0233470i
$863$	50.8101			1.72960			0.864799	−	0.502119i	$-0.167446\pi$
$863$	50.8101			1.72960			0.864799	+	0.502119i	$0.167446\pi$
$864$		0			0
$865$		0			0
$866$	−2.35679	+	4.08209i	−0.0800871	+	0.138715i
$867$		0			0
$868$	−18.7964	−	32.5563i	−0.637991	−	1.10503i
$869$	29.2126	+	50.5977i	0.990970	+	1.71641i
$870$		0			0
$871$	−1.04783	+	1.81489i	−0.0355043	+	0.0614953i
$872$	3.39916			0.115110
$873$		0			0
$874$	−0.710328			−0.0240272
$875$		0			0
$876$		0			0
$877$	0.204795	+	0.354715i	0.00691542	+	0.0119779i	0.869462	−	0.493999i	$-0.164465\pi$
$877$	0.204795	+	0.354715i	0.00691542	+	0.0119779i	−0.862547	+	0.505977i	$0.831132\pi$
$878$	3.03256	+	5.25255i	0.102344	+	0.177265i
$879$		0			0
$880$		0			0
$881$	5.32851			0.179522			0.0897610	−	0.995963i	$-0.471390\pi$
$881$	5.32851			0.179522			0.0897610	+	0.995963i	$0.471390\pi$
$882$		0			0
$883$	−14.2064			−0.478083			−0.239042	−	0.971009i	$-0.576833\pi$
$883$	−14.2064			−0.478083			−0.239042	+	0.971009i	$0.576833\pi$
$884$	−5.99979	+	10.3919i	−0.201795	+	0.349519i
$885$		0			0
$886$	1.83482	+	3.17800i	0.0616419	+	0.106767i
$887$	−3.61597	−	6.26304i	−0.121412	−	0.210292i	0.798913	−	0.601447i	$-0.205409\pi$
$887$	−3.61597	−	6.26304i	−0.121412	−	0.210292i	−0.920325	+	0.391155i	$0.872076\pi$
$888$		0			0
$889$	11.8649	−	20.5506i	0.397936	−	0.689245i
$890$		0			0
$891$		0			0
$892$	−13.7604			−0.460733
$893$	−2.03586	+	3.52622i	−0.0681276	+	0.118000i
$894$		0			0
$895$		0			0
$896$	−14.3325	−	24.8246i	−0.478815	−	0.829331i
$897$		0			0
$898$	7.88919	−	13.6645i	0.263266	−	0.455989i
$899$	13.9256			0.464444
$900$		0			0
$901$	−29.8960			−0.995981
$902$	3.99003	−	6.91093i	0.132853	−	0.230109i
$903$		0			0
$904$	−5.87864	−	10.1821i	−0.195521	−	0.338651i
$905$		0			0
$906$		0			0
$907$	−19.4051	+	33.6106i	−0.644335	+	1.11602i	0.340120	+	0.940382i	$0.389532\pi$
$907$	−19.4051	+	33.6106i	−0.644335	+	1.11602i	−0.984455	+	0.175639i	$0.943801\pi$
$908$	−19.9986			−0.663677
$909$		0			0
$910$		0			0
$911$	−20.1390	+	34.8819i	−0.667236	+	1.15569i	0.311437	+	0.950267i	$0.399190\pi$
$911$	−20.1390	+	34.8819i	−0.667236	+	1.15569i	−0.978674	+	0.205421i	$0.934144\pi$
$912$		0			0
$913$	−32.1377	−	55.6641i	−1.06360	−	1.84221i
$914$	−9.04371	−	15.6642i	−0.299139	−	0.518125i
$915$		0			0
$916$	−9.30424	+	16.1154i	−0.307421	+	0.532468i
$917$	−0.690479			−0.0228016
$918$		0			0
$919$	−13.0468			−0.430375			−0.215187	−	0.976573i	$-0.569036\pi$
$919$	−13.0468			−0.430375			−0.215187	+	0.976573i	$0.569036\pi$
$920$		0			0
$921$		0			0
$922$	−7.40722	−	12.8297i	−0.243944	−	0.422523i
$923$	−6.86074	−	11.8832i	−0.225824	−	0.391139i
$924$		0			0
$925$		0			0
$926$	−5.71936			−0.187950
$927$		0			0
$928$	8.18638			0.268731
$929$	0.146912	−	0.254460i	0.00482004	−	0.00834855i	−0.863605	−	0.504168i	$-0.831799\pi$
$929$	0.146912	−	0.254460i	0.00482004	−	0.00834855i	0.868425	+	0.495820i	$0.165132\pi$
$930$		0			0
$931$	0.0767321	+	0.132904i	0.00251479	+	0.00435575i
$932$	2.57714	+	4.46374i	0.0844171	+	0.146215i
$933$		0			0
$934$	1.79947	−	3.11678i	0.0588805	−	0.101984i
$935$		0			0
$936$		0			0
$937$	−16.9141			−0.552559			−0.276280	−	0.961077i	$-0.589102\pi$
$937$	−16.9141			−0.552559			−0.276280	+	0.961077i	$0.589102\pi$
$938$	0.596067	−	1.03242i	0.0194623	−	0.0337097i
$939$		0			0
$940$		0			0
$941$	28.6046	+	49.5447i	0.932485	+	1.61511i	0.779059	+	0.626951i	$0.215697\pi$
$941$	28.6046	+	49.5447i	0.932485	+	1.61511i	0.153426	+	0.988160i	$0.450969\pi$
$942$		0			0
$943$	−5.75815	+	9.97342i	−0.187511	+	0.324779i
$944$	−27.6478			−0.899858
$945$		0			0
$946$	22.4150			0.728775
$947$	−19.4373	+	33.6664i	−0.631627	+	1.09401i	0.355592	+	0.934641i	$0.384279\pi$
$947$	−19.4373	+	33.6664i	−0.631627	+	1.09401i	−0.987219	+	0.159369i	$0.949054\pi$
$948$		0			0
$949$	−7.05222	−	12.2148i	−0.228925	−	0.396509i
$950$		0			0
$951$		0			0
$952$	7.25648	−	12.5686i	0.235184	−	0.407350i
$953$	54.4516			1.76386			0.881930	−	0.471381i	$-0.156244\pi$
$953$	54.4516			1.76386			0.881930	+	0.471381i	$0.156244\pi$
$954$		0			0
$955$		0			0
$956$	−14.5230	+	25.1546i	−0.469708	+	0.813557i
$957$		0			0
$958$	7.68644	+	13.3133i	0.248338	+	0.430133i
$959$	4.45482	+	7.71598i	0.143854	+	0.249162i
$960$		0			0
$961$	−18.6006	+	32.2172i	−0.600020	+	1.03926i
$962$	−3.66587			−0.118192
$963$		0			0
$964$	−31.1229			−1.00240
$965$		0			0
$966$		0			0
$967$	9.78507	+	16.9482i	0.314666	+	0.545018i	0.979367	−	0.202092i	$-0.0647740\pi$
$967$	9.78507	+	16.9482i	0.314666	+	0.545018i	−0.664700	+	0.747110i	$0.731441\pi$
$968$	−24.1710	−	41.8654i	−0.776885	−	1.34560i
$969$		0			0
$970$		0			0
$971$	−6.31009			−0.202500			−0.101250	−	0.994861i	$-0.532284\pi$
$971$	−6.31009			−0.202500			−0.101250	+	0.994861i	$0.532284\pi$
$972$		0			0
$973$	37.7995			1.21180
$974$	−1.05564	+	1.82843i	−0.0338250	+	0.0585866i
$975$		0			0
$976$	0.0148757	+	0.0257654i	0.000476158	+	0.000824731i
$977$	3.70955	+	6.42514i	0.118679	+	0.205558i	0.919244	−	0.393687i	$-0.128801\pi$
$977$	3.70955	+	6.42514i	0.118679	+	0.205558i	−0.800565	+	0.599245i	$0.795467\pi$
$978$		0			0
$979$	−19.3367	+	33.4922i	−0.618004	+	1.07041i
$980$		0			0
$981$		0			0
$982$	15.5426			0.495986
$983$	−5.49137	+	9.51134i	−0.175148	+	0.303365i	−0.940212	−	0.340589i	$-0.889374\pi$
$983$	−5.49137	+	9.51134i	−0.175148	+	0.303365i	0.765065	+	0.643953i	$0.222707\pi$
$984$		0			0
$985$		0			0
$986$	1.26430	+	2.18983i	0.0402635	+	0.0697384i
$987$		0			0
$988$	0.674595	−	1.16843i	0.0214617	−	0.0371728i
$989$	−32.3479			−1.02860
$990$		0			0
$991$	−21.3721			−0.678908			−0.339454	−	0.940623i	$-0.610242\pi$
$991$	−21.3721			−0.678908			−0.339454	+	0.940623i	$0.610242\pi$
$992$	−20.0466	+	34.7217i	−0.636480	+	1.10242i
$993$		0			0
$994$	3.90280	+	6.75984i	0.123789	+	0.214409i
$995$		0			0
$996$		0			0
$997$	15.2674	−	26.4439i	0.483524	−	0.837487i	−0.516297	−	0.856409i	$-0.672690\pi$
$997$	15.2674	−	26.4439i	0.483524	−	0.837487i	0.999821	+	0.0189220i	$0.00602342\pi$
$998$	16.1863			0.512368
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.e.c.451.3		8
3.2	odd	2		225.2.e.e.151.2	yes	8
5.2	odd	4		675.2.k.c.424.5		16
5.3	odd	4		675.2.k.c.424.4		16
5.4	even	2		675.2.e.e.451.2		8
9.2	odd	6		2025.2.a.q.1.3		4
9.4	even	3	inner	675.2.e.c.226.3		8
9.5	odd	6		225.2.e.e.76.2	yes	8
9.7	even	3		2025.2.a.z.1.2		4
15.2	even	4		225.2.k.c.124.4		16
15.8	even	4		225.2.k.c.124.5		16
15.14	odd	2		225.2.e.c.151.3	yes	8
45.2	even	12		2025.2.b.n.649.5		8
45.4	even	6		675.2.e.e.226.2		8
45.7	odd	12		2025.2.b.o.649.4		8
45.13	odd	12		675.2.k.c.199.5		16
45.14	odd	6		225.2.e.c.76.3	✓	8
45.22	odd	12		675.2.k.c.199.4		16
45.23	even	12		225.2.k.c.49.4		16
45.29	odd	6		2025.2.a.y.1.2		4
45.32	even	12		225.2.k.c.49.5		16
45.34	even	6		2025.2.a.p.1.3		4
45.38	even	12		2025.2.b.n.649.4		8
45.43	odd	12		2025.2.b.o.649.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.3	✓	8	45.14	odd	6
225.2.e.c.151.3	yes	8	15.14	odd	2
225.2.e.e.76.2	yes	8	9.5	odd	6
225.2.e.e.151.2	yes	8	3.2	odd	2
225.2.k.c.49.4		16	45.23	even	12
225.2.k.c.49.5		16	45.32	even	12
225.2.k.c.124.4		16	15.2	even	4
225.2.k.c.124.5		16	15.8	even	4
675.2.e.c.226.3		8	9.4	even	3	inner
675.2.e.c.451.3		8	1.1	even	1	trivial
675.2.e.e.226.2		8	45.4	even	6
675.2.e.e.451.2		8	5.4	even	2
675.2.k.c.199.4		16	45.22	odd	12
675.2.k.c.199.5		16	45.13	odd	12
675.2.k.c.424.4		16	5.3	odd	4
675.2.k.c.424.5		16	5.2	odd	4
2025.2.a.p.1.3		4	45.34	even	6
2025.2.a.q.1.3		4	9.2	odd	6
2025.2.a.y.1.2		4	45.29	odd	6
2025.2.a.z.1.2		4	9.7	even	3
2025.2.b.n.649.4		8	45.38	even	12
2025.2.b.n.649.5		8	45.2	even	12
2025.2.b.o.649.4		8	45.7	odd	12
2025.2.b.o.649.5		8	45.43	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.236627 - 0.409850i) q^{2} +(0.888015 + 1.53809i) q^{4} +(-1.28153 + 2.21967i) q^{7} +1.78702 q^{8} +(-3.08430 + 5.34217i) q^{11} +(-1.06615 - 1.84662i) q^{13} +(0.606488 + 1.05047i) q^{14} +(-1.35317 + 2.34376i) q^{16} -3.16860 q^{17} +0.356267 q^{19} +(1.45966 + 2.52821i) q^{22} +(-2.10649 - 3.64854i) q^{23} -1.00912 q^{26} -4.55206 q^{28} +(0.843116 - 1.46032i) q^{29} +(4.12920 + 7.15199i) q^{31} +(2.42742 + 4.20441i) q^{32} +(-0.749778 + 1.29865i) q^{34} +3.63274 q^{37} +(0.0843024 - 0.146016i) q^{38} +(-1.36677 - 2.36731i) q^{41} +(3.83908 - 6.64949i) q^{43} -10.9556 q^{44} -1.99381 q^{46} +(-5.71444 + 9.89770i) q^{47} +(0.215378 + 0.373046i) q^{49} +(1.89351 - 3.27966i) q^{52} +9.43507 q^{53} +(-2.29012 + 3.96660i) q^{56} +(-0.399008 - 0.691103i) q^{58} +(5.10795 + 8.84723i) q^{59} +(0.00549659 - 0.00952038i) q^{61} +3.90833 q^{62} -3.11511 q^{64} +(-0.491409 - 0.851145i) q^{67} +(-2.81377 - 4.87359i) q^{68} +6.43507 q^{71} +6.61467 q^{73} +(0.859605 - 1.48888i) q^{74} +(0.316370 + 0.547969i) q^{76} +(-7.90523 - 13.6923i) q^{77} +(4.73569 - 8.20246i) q^{79} -1.29366 q^{82} +(-5.20988 + 9.02378i) q^{83} +(-1.81686 - 3.14690i) q^{86} +(-5.51172 + 9.54658i) q^{88} +6.26940 q^{89} +5.46519 q^{91} +(3.74119 - 6.47993i) q^{92} +(2.70439 + 4.68413i) q^{94} +(-3.60339 + 6.24126i) q^{97} +0.203858 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{4} - q^{7} + 18 q^{8} - q^{11} + 2 q^{13} + 3 q^{14} - 4 q^{16} + 22 q^{17} + 4 q^{19} + 3 q^{22} - 15 q^{23} + 20 q^{26} + 8 q^{28} + q^{29} + 4 q^{31} - 10 q^{32} - 9 q^{34} + 2 q^{37}+ \cdots + 26 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^4 - q^7 + 18 * q^8 - q^11 + 2 * q^13 + 3 * q^14 - 4 * q^16 + 22 * q^17 + 4 * q^19 + 3 * q^22 - 15 * q^23 + 20 * q^26 + 8 * q^28 + q^29 + 4 * q^31 - 10 * q^32 - 9 * q^34 + 2 * q^37 - 23 * q^38 - 5 * q^41 - 10 * q^43 - 44 * q^44 - 20 * q^47 + 3 * q^49 + 17 * q^52 + 40 * q^53 - 30 * q^56 - 18 * q^58 + 17 * q^59 + 13 * q^61 - 12 * q^62 + 38 * q^64 + 17 * q^67 - 34 * q^68 + 16 * q^71 - 4 * q^73 + 40 * q^74 - 11 * q^76 - 12 * q^77 + 7 * q^79 - 24 * q^82 - 30 * q^83 - 34 * q^86 + 9 * q^88 + 18 * q^89 - 34 * q^91 + 12 * q^92 - 3 * q^94 - 19 * q^97 + 26 * q^98

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