LMFDB - Embedded newform 675.2.e.e.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(226,675)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			226.2
Root			$-0.236627 - 0.409850i$ of defining polynomial
Character	$\chi$	$=$	675.226
Dual form			675.2.e.e.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.220178\pi$
$2$	−0.236627	−	0.409850i	−0.167321	−	0.289808i	−0.937477	+	0.348047i	$0.886845\pi$
$3$		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	$-0.00571495\pi$
$7$	1.28153	+	2.21967i	0.484372	+	0.838956i	−0.515467	+	0.856909i	$0.672382\pi$
$8$	−1.78702			−0.631808
$9$		0			0
$10$		0			0
$11$	−3.08430	−	5.34217i	−0.929952	−	1.61072i	−0.783397	−	0.621522i	$-0.786515\pi$
$11$	−3.08430	−	5.34217i	−0.929952	−	1.61072i	−0.146555	−	0.989202i	$-0.546819\pi$
$12$		0			0
$13$	1.06615	−	1.84662i	0.295696	−	0.512161i	−0.679450	−	0.733722i	$-0.737782\pi$
$13$	1.06615	−	1.84662i	0.295696	−	0.512161i	0.975147	+	0.221560i	$0.0711150\pi$
$14$	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	$-0.374460\pi$
$17$	3.16860			0.768500			0.384250	+	0.923229i	$0.374460\pi$
$18$		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	$-0.688584\pi$
$23$	2.10649	−	3.64854i	0.439233	−	0.760774i	0.997631	+	0.0687995i	$0.0219169\pi$
$24$		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	0.933627	−	0.358247i	$-0.116625\pi$
$29$	0.843116	+	1.46032i	0.156563	+	0.271174i	−0.777064	+	0.629421i	$0.783292\pi$
$30$		0			0
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	−0.210128	−	0.977674i	$-0.567388\pi$
$31$	4.12920	−	7.15199i	0.741627	−	1.28453i	0.951754	−	0.306861i	$-0.0992787\pi$
$32$	−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	$-0.596523\pi$
$37$	−3.63274			−0.597219			−0.298609	+	0.954375i	$0.596523\pi$
$38$	−0.0843024	−	0.146016i	−0.0136757	−	0.0236869i
$39$		0			0
$40$		0			0
$41$	−1.36677	+	2.36731i	−0.213453	+	0.369711i	−0.952793	−	0.303621i	$-0.901804\pi$
$41$	−1.36677	+	2.36731i	−0.213453	+	0.369711i	0.739340	+	0.673332i	$0.235138\pi$
$42$		0			0
$43$	−3.83908	−	6.64949i	−0.585455	−	1.01404i	−0.994819	−	0.101666i	$-0.967583\pi$
$43$	−3.83908	−	6.64949i	−0.585455	−	1.01404i	0.409364	−	0.912371i	$-0.365751\pi$
$44$	−10.9556			−1.65162
$45$		0			0
$46$	−1.99381			−0.293971
$47$	5.71444	+	9.89770i	0.833537	+	1.44373i	0.895216	+	0.445632i	$0.147021\pi$
$47$	5.71444	+	9.89770i	0.833537	+	1.44373i	−0.0616792	+	0.998096i	$0.519646\pi$
$48$		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	$-0.724396\pi$
$53$	−9.43507			−1.29601			−0.648003	+	0.761637i	$0.724396\pi$
$54$		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	−0.314287	−	0.949328i	$-0.601765\pi$
$59$	5.10795	−	8.84723i	0.664999	−	1.15181i	0.979286	−	0.202484i	$-0.0649013\pi$
$60$		0			0
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	0.866377	−	0.499390i	$-0.166443\pi$
$61$	0.00549659	+	0.00952038i	0.000703767	+	0.00121896i	−0.865673	+	0.500609i	$0.833109\pi$
$62$	−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	$-0.814212\pi$
$67$	0.491409	−	0.851145i	0.0600351	−	0.103984i	0.894481	+	0.447106i	$0.147545\pi$
$68$	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	$-0.626521\pi$
$73$	−6.61467			−0.774189			−0.387094	+	0.922040i	$0.626521\pi$
$74$	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	0.999266	+	0.0383057i	$0.0121961\pi$
$79$	4.73569	+	8.20246i	0.532807	+	0.922848i	−0.466459	+	0.884543i	$0.654471\pi$
$80$		0			0
$81$		0			0
$82$	1.29366			0.142860
$83$	5.20988	+	9.02378i	0.571859	+	0.990489i	0.996375	+	0.0850682i	$0.0271108\pi$
$83$	5.20988	+	9.02378i	0.571859	+	0.990489i	−0.424516	+	0.905420i	$0.639556\pi$
$84$		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	$-0.0474384\pi$
$97$	3.60339	+	6.24126i	0.365869	+	0.633704i	−0.623046	+	0.782185i	$0.714105\pi$
$98$	−0.203858			−0.0205927
$99$		0			0
$100$		0			0
$101$	3.48547	+	6.03701i	0.346817	+	0.600705i	0.985682	−	0.168614i	$-0.0539291\pi$
$101$	3.48547	+	6.03701i	0.346817	+	0.600705i	−0.638865	+	0.769319i	$0.720596\pi$
$102$		0			0
$103$	−3.05756	+	5.29584i	−0.301270	+	0.521815i	−0.976424	−	0.215862i	$-0.930744\pi$
$103$	−3.05756	+	5.29584i	−0.301270	+	0.521815i	0.675154	+	0.737677i	$0.264077\pi$
$104$	−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	$-0.747964\pi$
$107$	−14.5349			−1.40514			−0.702570	+	0.711615i	$0.747964\pi$
$108$		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	$-0.733184\pi$
$113$	3.28962	−	5.69780i	0.309462	−	0.536004i	0.978245	+	0.207454i	$0.0665178\pi$
$114$		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	$-0.365258\pi$
$127$	9.25840			0.821550			0.410775	+	0.911737i	$0.365258\pi$
$128$	5.59196	+	9.68555i	0.494264	+	0.856090i
$129$		0			0
$130$		0			0
$131$	0.134698	−	0.233305i	0.0117687	−	0.0203839i	−0.860081	−	0.510157i	$-0.829587\pi$
$131$	0.134698	−	0.233305i	0.0117687	−	0.0203839i	0.871850	+	0.489773i	$0.162920\pi$
$132$		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	$-0.214110\pi$
$137$	−1.73809	−	3.01046i	−0.148495	−	0.257201i	−0.930671	+	0.365856i	$0.880776\pi$
$138$		0			0
$139$	−7.37393	+	12.7720i	−0.625448	+	1.08331i	0.363006	+	0.931787i	$0.381751\pi$
$139$	−7.37393	+	12.7720i	−0.625448	+	1.08331i	−0.988454	+	0.151521i	$0.951583\pi$
$140$		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	−0.995522	−	0.0945305i	$-0.969865\pi$
$149$	−5.07665	+	8.79301i	−0.415895	+	0.720352i	0.579627	+	0.814882i	$0.303198\pi$
$150$		0			0
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	0.995915	−	0.0902940i	$-0.0287807\pi$
$151$	5.15811	+	8.93410i	0.419761	+	0.727047i	−0.576155	+	0.817341i	$0.695447\pi$
$152$	−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	$-0.819832\pi$
$157$	0.531305	−	0.920247i	0.0424028	−	0.0734437i	0.886448	+	0.462828i	$0.153165\pi$
$158$	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	$-0.265780\pi$
$163$	17.1386			1.34240			0.671198	+	0.741278i	$0.265780\pi$
$164$	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	$-0.779210\pi$
$167$	2.18672	−	3.78752i	0.169214	−	0.293087i	0.938144	+	0.346246i	$0.112544\pi$
$168$		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	0.997721	+	0.0674723i	$0.0214934\pi$
$173$	7.33005	+	12.6960i	0.557293	+	0.965260i	−0.440428	+	0.897788i	$0.645173\pi$
$174$		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	0.999993	−	0.00366109i	$-0.00116536\pi$
$191$	6.86627	+	11.8927i	0.496826	+	0.860528i	−0.503167	+	0.864189i	$0.667832\pi$
$192$		0			0
$193$	−0.241187	+	0.417748i	−0.0173610	+	0.0300701i	−0.874575	−	0.484890i	$-0.838860\pi$
$193$	−0.241187	+	0.417748i	−0.0173610	+	0.0300701i	0.857214	+	0.514960i	$0.172193\pi$
$194$	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	$-0.436824\pi$
$197$	5.53488			0.394344			0.197172	+	0.980369i	$0.436824\pi$
$198$		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	−0.836482	−	0.547994i	$-0.815392\pi$
$211$	0.818328	−	1.41739i	0.0563360	−	0.0975769i	0.892818	+	0.450417i	$0.148725\pi$
$212$	−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	$-0.0831362\pi$
$223$	3.87393	+	6.70984i	0.259417	+	0.449324i	−0.706669	+	0.707545i	$0.749803\pi$
$224$	−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	$-0.0447606\pi$
$227$	5.63014	+	9.75169i	0.373685	+	0.647242i	−0.616444	+	0.787399i	$0.711427\pi$
$228$		0			0
$229$	5.23879	−	9.07384i	0.346189	−	0.599616i	−0.639380	−	0.768891i	$-0.720809\pi$
$229$	5.23879	−	9.07384i	0.346189	−	0.599616i	0.985569	+	0.169274i	$0.0541424\pi$
$230$		0			0
$231$		0			0
$232$	−1.50667	−	2.60962i	−0.0989176	−	0.171330i
$233$	−2.90214			−0.190125			−0.0950627	−	0.995471i	$-0.530305\pi$
$233$	−2.90214			−0.190125			−0.0950627	+	0.995471i	$0.530305\pi$
$234$		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	−0.470489	−	0.882406i	$-0.655923\pi$
$239$	8.17723	−	14.1634i	0.528941	−	0.916153i	0.999430	−	0.0337471i	$-0.0107441\pi$
$240$		0			0
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	−0.997105	−	0.0760416i	$-0.975772\pi$
$241$	−8.76194	−	15.1761i	−0.564406	−	0.977580i	0.432698	−	0.901539i	$-0.357562\pi$
$242$	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	$-0.804777\pi$
$257$	1.43625	−	2.48766i	0.0895910	−	0.155176i	0.907338	+	0.420401i	$0.138111\pi$
$258$		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	−0.925955	−	0.377633i	$-0.876738\pi$
$263$	−12.8119	−	22.1909i	−0.790017	−	1.36835i	0.135938	−	0.990717i	$-0.456595\pi$
$264$		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	0.958962	+	0.283533i	$0.0915067\pi$
$277$	12.0669	+	20.9004i	0.725028	+	1.25579i	−0.233934	+	0.972252i	$0.575160\pi$
$278$	6.97949			0.418602
$279$		0			0
$280$		0			0
$281$	1.68363	+	2.91613i	0.100437	+	0.173962i	0.911865	−	0.410491i	$-0.134643\pi$
$281$	1.68363	+	2.91613i	0.100437	+	0.173962i	−0.811428	+	0.584453i	$0.801309\pi$
$282$		0			0
$283$	10.9249	−	18.9224i	0.649415	−	1.12482i	−0.333848	−	0.942627i	$-0.608347\pi$
$283$	10.9249	−	18.9224i	0.649415	−	1.12482i	0.983263	−	0.182193i	$-0.0583195\pi$
$284$	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	$-0.964935\pi$
$293$	−6.87702	+	11.9114i	−0.401760	+	0.695869i	0.592179	+	0.805807i	$0.298268\pi$
$294$		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	$-0.930815\pi$
$307$	−34.2183			−1.95294			−0.976472	+	0.215644i	$0.930815\pi$
$308$	−14.0399	−	24.3179i	−0.799999	−	1.38564i
$309$		0			0
$310$		0			0
$311$	11.5199	−	19.9530i	0.653232	−	1.13143i	−0.329102	−	0.944294i	$-0.606746\pi$
$311$	11.5199	−	19.9530i	0.653232	−	1.13143i	0.982334	−	0.187136i	$-0.0599206\pi$
$312$		0			0
$313$	−1.79565	−	3.11016i	−0.101496	−	0.175796i	0.810805	−	0.585316i	$-0.199030\pi$
$313$	−1.79565	−	3.11016i	−0.101496	−	0.175796i	−0.912301	+	0.409520i	$0.865696\pi$
$314$	−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	$-0.287360\pi$
$317$	−6.59033	−	11.4148i	−0.370150	−	0.641118i	−0.989588	+	0.143927i	$0.954027\pi$
$318$		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	0.849319	−	0.527881i	$-0.177013\pi$
$331$	−0.591264	−	1.02410i	−0.0324988	−	0.0562896i	−0.881817	+	0.471591i	$0.843680\pi$
$332$	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	0.300879	+	0.953662i	$0.402720\pi$
$337$	−12.3997	+	21.4770i	−0.675457	+	1.16993i	−0.976335	+	0.216263i	$0.930613\pi$
$338$	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	0.398488	+	0.917174i	$0.369535\pi$
$347$	−11.0846	+	19.1991i	−0.595052	+	1.03066i	−0.993540	+	0.113486i	$0.963798\pi$
$348$		0			0
$349$	−7.45925	−	12.9198i	−0.399285	−	0.691581i	0.594353	−	0.804204i	$-0.297408\pi$
$349$	−7.45925	−	12.9198i	−0.399285	−	0.691581i	−0.993638	+	0.112623i	$0.964075\pi$
$350$		0			0
$351$		0			0
$352$	29.9476			1.59621
$353$	−8.45726	−	14.6484i	−0.450134	−	0.779656i	0.548260	−	0.836308i	$-0.315291\pi$
$353$	−8.45726	−	14.6484i	−0.450134	−	0.779656i	−0.998394	+	0.0566525i	$0.981957\pi$
$354$		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	0.999591	+	0.0285858i	$0.00910039\pi$
$367$	10.0490	+	17.4053i	0.524552	+	0.908550i	−0.475040	+	0.879964i	$0.657566\pi$
$368$	−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	0.491415	+	0.870925i	$0.336480\pi$
$373$	−9.82146	+	17.0113i	−0.508536	+	0.880810i	−0.999951	+	0.00988448i	$0.996854\pi$
$374$	−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	−0.124830	−	0.992178i	$-0.539839\pi$
$383$	15.5944	−	27.0103i	0.796836	−	1.38016i	0.921667	−	0.387983i	$-0.126828\pi$
$384$		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	−0.921385	−	0.388650i	$-0.872941\pi$
$389$	−15.7247	−	27.2360i	−0.797274	−	1.38092i	0.124111	−	0.992268i	$-0.460392\pi$
$390$		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	$-0.646656\pi$
$397$	−17.7174			−0.889211			−0.444606	+	0.895726i	$0.646656\pi$
$398$	−4.13128	−	7.15558i	−0.207082	−	0.358677i
$399$		0			0
$400$		0			0
$401$	−3.57124	+	6.18556i	−0.178339	+	0.308892i	−0.941312	−	0.337538i	$-0.890406\pi$
$401$	−3.57124	+	6.18556i	−0.178339	+	0.308892i	0.762973	+	0.646431i	$0.223739\pi$
$402$		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	0.378964	+	0.925412i	$0.376281\pi$
$409$	−12.3759	+	21.4357i	−0.611948	+	1.05993i	−0.990912	+	0.134514i	$0.957053\pi$
$410$		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	−0.966339	−	0.257272i	$-0.917176\pi$
$419$	−5.32956	+	9.23106i	−0.260366	+	0.450967i	0.705973	+	0.708238i	$0.250510\pi$
$420$		0			0
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	0.948302	−	0.317370i	$-0.102800\pi$
$421$	4.08931	+	7.08288i	0.199301	+	0.345199i	−0.749001	+	0.662569i	$0.769466\pi$
$422$	−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	$-0.423075\pi$
$433$	9.95994			0.478644			0.239322	+	0.970940i	$0.423075\pi$
$434$	−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	0.671615	−	0.740901i	$-0.265601\pi$
$439$	−6.40788	−	11.0988i	−0.305832	−	0.529716i	−0.977446	+	0.211185i	$0.932268\pi$
$440$		0			0
$441$		0			0
$442$	−3.19750			−0.152090
$443$	3.87702	+	6.71520i	0.184203	+	0.319049i	0.943308	−	0.331920i	$-0.107696\pi$
$443$	3.87702	+	6.71520i	0.184203	+	0.319049i	−0.759105	+	0.650968i	$0.774363\pi$
$444$		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	−0.835148	−	0.550026i	$-0.814618\pi$
$457$	−19.1096	−	33.0988i	−0.893910	−	1.54830i	−0.0587626	−	0.998272i	$-0.518715\pi$
$458$	−4.95856			−0.231698
$459$		0			0
$460$		0			0
$461$	15.6517	+	27.1095i	0.728971	+	1.26261i	0.957319	+	0.289035i	$0.0933343\pi$
$461$	15.6517	+	27.1095i	0.728971	+	1.26261i	−0.228348	+	0.973580i	$0.573332\pi$
$462$		0			0
$463$	6.04258	−	10.4661i	0.280823	−	0.486399i	−0.690765	−	0.723079i	$-0.742726\pi$
$463$	6.04258	−	10.4661i	0.280823	−	0.486399i	0.971588	+	0.236680i	$0.0760594\pi$
$464$	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	$-0.556300\pi$
$467$	−7.60466			−0.351902			−0.175951	+	0.984399i	$0.556300\pi$
$468$		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	−0.951537	−	0.307534i	$-0.900496\pi$
$479$	−16.2417	−	28.1314i	−0.742101	−	1.28536i	0.209437	−	0.977822i	$-0.432837\pi$
$480$		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	$-0.467771\pi$
$487$	4.46121			0.202157			0.101078	+	0.994878i	$0.467771\pi$
$488$	−0.00982254	−	0.0170131i	−0.000444645	−	0.000770148i
$489$		0			0
$490$		0			0
$491$	16.4210	−	28.4420i	0.741070	−	1.28357i	−0.210938	−	0.977499i	$-0.567652\pi$
$491$	16.4210	−	28.4420i	0.741070	−	1.28357i	0.952008	−	0.306072i	$-0.0990148\pi$
$492$		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	−0.174410	−	0.984673i	$-0.555802\pi$
$499$	17.1010	−	29.6198i	0.765547	−	1.32597i	0.939957	−	0.341293i	$-0.110865\pi$
$500$		0			0
$501$		0			0
$502$	2.00423	+	3.47143i	0.0894532	+	0.154938i
$503$	22.1773			0.988837			0.494419	−	0.869224i	$-0.335381\pi$
$503$	22.1773			0.988837			0.494419	+	0.869224i	$0.335381\pi$
$504$		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	−0.999679	−	0.0253489i	$-0.991930\pi$
$509$	−10.7816	+	18.6743i	−0.477887	+	0.827724i	0.521792	+	0.853073i	$0.325264\pi$
$510$		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	$-0.744820\pi$
$523$	−31.8114			−1.39101			−0.695507	+	0.718520i	$0.744820\pi$
$524$	−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	$-0.194517\pi$
$547$	−2.04372	−	3.53982i	−0.0873831	−	0.151352i	−0.906404	+	0.422411i	$0.861184\pi$
$548$	−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	$-0.589815\pi$
$557$	−13.1425			−0.556864			−0.278432	+	0.960456i	$0.589815\pi$
$558$		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	−0.483069	−	0.875582i	$-0.660478\pi$
$563$	12.2611	−	21.2368i	0.516742	−	0.895023i	0.999811	−	0.0194410i	$-0.00618864\pi$
$564$		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	0.999636	−	0.0269915i	$-0.00859271\pi$
$569$	11.3649	+	19.6846i	0.476442	+	0.825223i	−0.523193	+	0.852214i	$0.675259\pi$
$570$		0			0
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	−0.860809	−	0.508928i	$-0.830042\pi$
$571$	0.247093	−	0.427977i	0.0103405	−	0.0179103i	0.871149	+	0.491018i	$0.163375\pi$
$572$	−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	$-0.437234\pi$
$577$	9.41187			0.391821			0.195911	+	0.980622i	$0.437234\pi$
$578$	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	$-0.232653\pi$
$587$	−4.98661	−	8.63705i	−0.205819	−	0.356489i	−0.950393	+	0.311050i	$0.899319\pi$
$588$		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	$-0.211499\pi$
$593$	38.3421			1.57452			0.787260	+	0.616621i	$0.211499\pi$
$594$		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	−0.950903	−	0.309489i	$-0.899842\pi$
$599$	−5.07665	+	8.79301i	−0.207426	+	0.359273i	0.743477	+	0.668762i	$0.233175\pi$
$600$		0			0
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	0.997205	−	0.0747146i	$-0.0238046\pi$
$601$	10.6371	+	18.4241i	0.433898	+	0.751533i	−0.563307	+	0.826248i	$0.690471\pi$
$602$	−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	0.173993	+	0.984747i	$0.444333\pi$
$607$	−18.8678	+	32.6799i	−0.765819	+	1.32644i	−0.939812	+	0.341691i	$0.889000\pi$
$608$	−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	$-0.274119\pi$
$613$	32.2633			1.30310			0.651551	+	0.758605i	$0.274119\pi$
$614$	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	−0.475900	−	0.879499i	$-0.657878\pi$
$617$	13.0089	−	22.5321i	0.523719	−	0.907108i	0.999619	−	0.0276084i	$-0.00878914\pi$
$618$		0			0
$619$	5.94077	+	10.2897i	0.238780	+	0.413578i	0.960364	−	0.278748i	$-0.0899193\pi$
$619$	5.94077	+	10.2897i	0.238780	+	0.413578i	−0.721585	+	0.692326i	$0.756586\pi$
$620$		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	0.845665	+	0.533713i	$0.179204\pi$
$641$	22.4075	+	38.8109i	0.885042	+	1.53294i	0.0393765	+	0.999224i	$0.487463\pi$
$642$		0			0
$643$	−7.46275	+	12.9259i	−0.294302	+	0.509747i	−0.974822	−	0.222983i	$-0.928421\pi$
$643$	−7.46275	+	12.9259i	−0.294302	+	0.509747i	0.680520	+	0.732729i	$0.261754\pi$
$644$	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	$-0.801193\pi$
$647$	−41.2684			−1.62243			−0.811214	+	0.584749i	$0.801193\pi$
$648$		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	0.458345	+	0.888774i	$0.348442\pi$
$653$	−13.8126	+	23.9241i	−0.540528	+	0.936223i	−0.998874	+	0.0474484i	$0.984891\pi$
$654$		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	0.932215	+	0.361905i	$0.117874\pi$
$659$	20.0112	+	34.6605i	0.779527	+	1.35018i	−0.152688	+	0.988274i	$0.548793\pi$
$660$		0			0
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	−0.999872	−	0.0160270i	$-0.994898\pi$
$661$	−12.4965	+	21.6445i	−0.486056	+	0.841874i	0.513816	+	0.857901i	$0.328232\pi$
$662$	−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	−0.928126	−	0.372265i	$-0.878581\pi$
$673$	−20.4024	−	35.3380i	−0.786454	−	1.36218i	0.141672	−	0.989914i	$-0.454752\pi$
$674$	11.7365			0.452072
$675$		0			0
$676$	15.0133			0.577436
$677$	−20.5947	−	35.6710i	−0.791518	−	1.37095i	−0.925027	−	0.379901i	$-0.875958\pi$
$677$	−20.5947	−	35.6710i	−0.791518	−	1.37095i	0.133509	−	0.991048i	$-0.457375\pi$
$678$		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	$-0.491850\pi$
$683$	1.33820			0.0512047			0.0256023	+	0.999672i	$0.491850\pi$
$684$		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	0.999759	−	0.0219459i	$-0.00698617\pi$
$691$	12.6407	+	21.8943i	0.480874	+	0.832898i	−0.518885	+	0.854844i	$0.673653\pi$
$692$	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	−0.928818	−	0.370537i	$-0.879174\pi$
$709$	−20.9103	−	36.2177i	−0.785304	−	1.36019i	0.143514	−	0.989648i	$-0.454160\pi$
$710$		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	−0.911291	−	0.411764i	$-0.864913\pi$
$727$	−21.9005	−	37.9327i	−0.812243	−	1.40685i	0.0990474	−	0.995083i	$-0.468420\pi$
$728$	−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	$-0.873334\pi$
$733$	−3.39332	+	5.87740i	−0.125335	+	0.217087i	0.796529	+	0.604601i	$0.206667\pi$
$734$	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	−0.418891	−	0.908036i	$-0.637581\pi$
$743$	15.7262	−	27.2385i	0.576937	−	0.999284i	0.995828	−	0.0912477i	$-0.0290855\pi$
$744$		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	−0.948478	−	0.316844i	$-0.897377\pi$
$751$	−5.47659	+	9.48574i	−0.199844	+	0.346139i	0.748634	+	0.662984i	$0.230710\pi$
$752$	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	$-0.187075\pi$
$757$	45.7942			1.66442			0.832210	+	0.554461i	$0.187075\pi$
$758$	1.87934	+	3.25511i	0.0682607	+	0.118231i
$759$		0			0
$760$		0			0
$761$	−16.9569	+	29.3702i	−0.614687	+	1.06467i	0.375753	+	0.926720i	$0.377384\pi$
$761$	−16.9569	+	29.3702i	−0.614687	+	1.06467i	−0.990439	+	0.137948i	$0.955949\pi$
$762$		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	−0.923325	−	0.384018i	$-0.874540\pi$
$769$	−3.57986	+	6.20050i	−0.129093	+	0.223596i	0.794232	+	0.607614i	$0.207873\pi$
$770$		0			0
$771$		0			0
$772$	0.428355	+	0.741933i	0.0154168	+	0.0267027i
$773$	−14.5998			−0.525117			−0.262558	−	0.964916i	$-0.584566\pi$
$773$	−14.5998			−0.525117			−0.262558	+	0.964916i	$0.584566\pi$
$774$		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	$-0.726540\pi$
$787$	9.23638	−	15.9979i	0.329242	−	0.570263i	0.982362	+	0.186991i	$0.0598736\pi$
$788$	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	0.231414	+	0.972855i	$0.425665\pi$
$797$	−20.5187	+	35.5395i	−0.726810	+	1.25887i	−0.958225	+	0.286017i	$0.907669\pi$
$798$		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	0.860133	−	0.510069i	$-0.170380\pi$
$821$	−0.334280	−	0.578990i	−0.0116665	−	0.0202069i	−0.871800	+	0.489863i	$0.837047\pi$
$822$		0			0
$823$	−0.710165	+	1.23004i	−0.0247548	+	0.0428766i	−0.878137	−	0.478408i	$-0.841214\pi$
$823$	−0.710165	+	1.23004i	−0.0247548	+	0.0428766i	0.853383	+	0.521285i	$0.174547\pi$
$824$	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	$-0.166586\pi$
$827$	49.8169			1.73230			0.866152	+	0.499782i	$0.166586\pi$
$828$		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	0.638900	−	0.769290i	$-0.279390\pi$
$839$	−10.0445	−	17.3976i	−0.346774	−	0.600631i	−0.985674	+	0.168659i	$0.946056\pi$
$840$		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	$-0.0142784\pi$
$853$	13.4542	+	23.3034i	0.460663	+	0.797892i	−0.538331	+	0.842733i	$0.680945\pi$
$854$	0.0133345			0.000456296
$855$		0			0
$856$	25.9742			0.887779
$857$	24.4204	+	42.2973i	0.834184	+	1.44485i	0.894693	+	0.446682i	$0.147394\pi$
$857$	24.4204	+	42.2973i	0.834184	+	1.44485i	−0.0605088	+	0.998168i	$0.519272\pi$
$858$		0			0
$859$	20.7047	−	35.8616i	0.706435	−	1.22358i	−0.259736	−	0.965680i	$-0.583635\pi$
$859$	20.7047	−	35.8616i	0.706435	−	1.22358i	0.966171	−	0.257902i	$-0.0830312\pi$
$860$		0			0
$861$		0			0
$862$	0.395754	+	0.685465i	0.0134794	+	0.0233470i
$863$	−50.8101			−1.72960			−0.864799	−	0.502119i	$-0.832554\pi$
$863$	−50.8101			−1.72960			−0.864799	+	0.502119i	$0.832554\pi$
$864$		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	$-0.835535\pi$
$877$	−0.204795	+	0.354715i	−0.00691542	+	0.0119779i	0.862547	+	0.505977i	$0.168868\pi$
$878$	−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	$-0.423167\pi$
$883$	14.2064			0.478083			0.239042	+	0.971009i	$0.423167\pi$
$884$	−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	$-0.794591\pi$
$887$	3.61597	−	6.26304i	0.121412	−	0.210292i	0.920325	+	0.391155i	$0.127924\pi$
$888$		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	0.984455	+	0.175639i	$0.0561990\pi$
$907$	19.4051	+	33.6106i	0.644335	+	1.11602i	−0.340120	+	0.940382i	$0.610468\pi$
$908$	19.9986			0.663677
$909$		0			0
$910$		0			0
$911$	−20.1390	−	34.8819i	−0.667236	−	1.15569i	−0.978674	−	0.205421i	$-0.934144\pi$
$911$	−20.1390	−	34.8819i	−0.667236	−	1.15569i	0.311437	−	0.950267i	$-0.399190\pi$
$912$		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	0.868425	−	0.495820i	$-0.165132\pi$
$929$	0.146912	+	0.254460i	0.00482004	+	0.00834855i	−0.863605	+	0.504168i	$0.831799\pi$
$930$		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	$-0.410898\pi$
$937$	16.9141			0.552559			0.276280	+	0.961077i	$0.410898\pi$
$938$	−0.596067	−	1.03242i	−0.0194623	−	0.0337097i
$939$		0			0
$940$		0			0
$941$	28.6046	−	49.5447i	0.932485	−	1.61511i	0.153426	−	0.988160i	$-0.450969\pi$
$941$	28.6046	−	49.5447i	0.932485	−	1.61511i	0.779059	−	0.626951i	$-0.215697\pi$
$942$		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	0.987219	+	0.159369i	$0.0509460\pi$
$947$	19.4373	+	33.6664i	0.631627	+	1.09401i	−0.355592	+	0.934641i	$0.615721\pi$
$948$		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	$-0.843756\pi$
$953$	−54.4516			−1.76386			−0.881930	+	0.471381i	$0.843756\pi$
$954$		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	$-0.935226\pi$
$967$	−9.78507	+	16.9482i	−0.314666	+	0.545018i	0.664700	+	0.747110i	$0.268559\pi$
$968$	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	$-0.871199\pi$
$977$	−3.70955	+	6.42514i	−0.118679	+	0.205558i	0.800565	+	0.599245i	$0.204533\pi$
$978$		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	$-0.110626\pi$
$983$	5.49137	+	9.51134i	0.175148	+	0.303365i	−0.765065	+	0.643953i	$0.777293\pi$
$984$		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	$-0.327310\pi$
$997$	−15.2674	−	26.4439i	−0.483524	−	0.837487i	−0.999821	+	0.0189220i	$0.993977\pi$
$998$	−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.e.226.2		8
3.2	odd	2		225.2.e.c.76.3	✓	8
5.2	odd	4		675.2.k.c.199.5		16
5.3	odd	4		675.2.k.c.199.4		16
5.4	even	2		675.2.e.c.226.3		8
9.2	odd	6		225.2.e.c.151.3	yes	8
9.4	even	3		2025.2.a.p.1.3		4
9.5	odd	6		2025.2.a.y.1.2		4
9.7	even	3	inner	675.2.e.e.451.2		8
15.2	even	4		225.2.k.c.49.4		16
15.8	even	4		225.2.k.c.49.5		16
15.14	odd	2		225.2.e.e.76.2	yes	8
45.2	even	12		225.2.k.c.124.5		16
45.4	even	6		2025.2.a.z.1.2		4
45.7	odd	12		675.2.k.c.424.4		16
45.13	odd	12		2025.2.b.o.649.4		8
45.14	odd	6		2025.2.a.q.1.3		4
45.22	odd	12		2025.2.b.o.649.5		8
45.23	even	12		2025.2.b.n.649.5		8
45.29	odd	6		225.2.e.e.151.2	yes	8
45.32	even	12		2025.2.b.n.649.4		8
45.34	even	6		675.2.e.c.451.3		8
45.38	even	12		225.2.k.c.124.4		16
45.43	odd	12		675.2.k.c.424.5		16

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

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

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