LMFDB - Embedded newform 435.2.c.e.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(349,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("435.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.c (of order $2$, degree $1$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.3899266318336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 6x^{7} + 19x^{6} - 12x^{5} + 4x^{4} + 2x^{3} + 9x^{2} - 6x + 2 $ x^10 - 2x^9 + 2x^8 + 6x^7 + 19x^6 - 12x^5 + 4x^4 + 2x^3 + 9x^2 - 6*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.4
Root			$0.313948 - 0.313948i$ of defining polynomial
Character	$\chi$	$=$	435.349
Dual form			435.2.c.e.349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.754474i q^{2} +1.00000i q^{3} +1.43077 q^{4} +(-2.23474 + 0.0770824i) q^{5} +0.754474 q^{6} -4.18524i q^{7} -2.58843i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.754474i q^{2} +1.00000i q^{3} +1.43077 q^{4} +(-2.23474 + 0.0770824i) q^{5} +0.754474 q^{6} -4.18524i q^{7} -2.58843i q^{8} -1.00000 q^{9} +(0.0581566 + 1.68605i) q^{10} +0.596817 q^{11} +1.43077i q^{12} -2.18524i q^{13} -3.15766 q^{14} +(-0.0770824 - 2.23474i) q^{15} +0.908639 q^{16} -2.81314i q^{17} +0.754474i q^{18} -0.528904 q^{19} +(-3.19740 + 0.110287i) q^{20} +4.18524 q^{21} -0.450283i q^{22} +0.590044i q^{23} +2.58843 q^{24} +(4.98812 - 0.344518i) q^{25} -1.64871 q^{26} -1.00000i q^{27} -5.98812i q^{28} -1.00000 q^{29} +(-1.68605 + 0.0581566i) q^{30} +8.02005 q^{31} -5.86240i q^{32} +0.596817i q^{33} -2.12244 q^{34} +(0.322608 + 9.35293i) q^{35} -1.43077 q^{36} +2.52465i q^{37} +0.399044i q^{38} +2.18524 q^{39} +(0.199522 + 5.78446i) q^{40} +1.57110 q^{41} -3.15766i q^{42} -6.98484i q^{43} +0.853908 q^{44} +(2.23474 - 0.0770824i) q^{45} +0.445173 q^{46} +2.57524i q^{47} +0.908639i q^{48} -10.5163 q^{49} +(-0.259930 - 3.76340i) q^{50} +2.81314 q^{51} -3.12658i q^{52} +10.3878i q^{53} -0.754474 q^{54} +(-1.33373 + 0.0460041i) q^{55} -10.8332 q^{56} -0.528904i q^{57} +0.754474i q^{58} -13.9168 q^{59} +(-0.110287 - 3.19740i) q^{60} -11.1942 q^{61} -6.05092i q^{62} +4.18524i q^{63} -2.60575 q^{64} +(0.168444 + 4.88345i) q^{65} +0.450283 q^{66} -0.614139i q^{67} -4.02495i q^{68} -0.590044 q^{69} +(7.05654 - 0.243400i) q^{70} +9.28010 q^{71} +2.58843i q^{72} +9.59116i q^{73} +1.90478 q^{74} +(0.344518 + 4.98812i) q^{75} -0.756739 q^{76} -2.49783i q^{77} -1.64871i q^{78} +10.3396 q^{79} +(-2.03057 + 0.0700400i) q^{80} +1.00000 q^{81} -1.18536i q^{82} +3.92531i q^{83} +5.98812 q^{84} +(0.216843 + 6.28663i) q^{85} -5.26988 q^{86} -1.00000i q^{87} -1.54482i q^{88} +12.3352 q^{89} +(-0.0581566 - 1.68605i) q^{90} -9.14577 q^{91} +0.844217i q^{92} +8.02005i q^{93} +1.94295 q^{94} +(1.18196 - 0.0407692i) q^{95} +5.86240 q^{96} -3.21794i q^{97} +7.93424i q^{98} -0.596817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9	$ 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9} + 4 q^{10} + 24 q^{11} - 12 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{19} + 8 q^{20} + 16 q^{21} - 18 q^{24} + 2 q^{25} - 10 q^{29} - 18 q^{30} + 4 q^{31} - 8 q^{34} + 2 q^{35} + 10 q^{36} - 4 q^{39} - 14 q^{40} - 28 q^{41} - 40 q^{44} - 12 q^{46} + 14 q^{49} - 12 q^{50} - 6 q^{54} + 2 q^{55} - 4 q^{56} - 8 q^{59} - 2 q^{60} - 24 q^{61} + 18 q^{64} + 6 q^{65} + 28 q^{66} - 16 q^{69} + 20 q^{70} + 60 q^{71} - 4 q^{74} + 12 q^{75} - 88 q^{76} + 36 q^{79} - 30 q^{80} + 10 q^{81} + 12 q^{84} - 14 q^{85} + 60 q^{86} + 44 q^{89} - 4 q^{90} - 24 q^{91} + 100 q^{94} - 36 q^{95} + 2 q^{96} - 24 q^{99}+O(q^{100}) $ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 + 4 * q^10 + 24 * q^11 - 12 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^19 + 8 * q^20 + 16 * q^21 - 18 * q^24 + 2 * q^25 - 10 * q^29 - 18 * q^30 + 4 * q^31 - 8 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^39 - 14 * q^40 - 28 * q^41 - 40 * q^44 - 12 * q^46 + 14 * q^49 - 12 * q^50 - 6 * q^54 + 2 * q^55 - 4 * q^56 - 8 * q^59 - 2 * q^60 - 24 * q^61 + 18 * q^64 + 6 * q^65 + 28 * q^66 - 16 * q^69 + 20 * q^70 + 60 * q^71 - 4 * q^74 + 12 * q^75 - 88 * q^76 + 36 * q^79 - 30 * q^80 + 10 * q^81 + 12 * q^84 - 14 * q^85 + 60 * q^86 + 44 * q^89 - 4 * q^90 - 24 * q^91 + 100 * q^94 - 36 * q^95 + 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	0.754474i		−	0.533494i	−0.963767	−	0.266747i	$-0.914051\pi$
$2$		−	0.754474i		−	0.533494i	0.963767	−	0.266747i	$-0.0859487\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.43077			0.715385
$5$	−2.23474	+	0.0770824i	−0.999406	+	0.0344723i
$5$	−2.23474	+	0.0770824i	−0.999406	+	0.0344723i
$6$	0.754474			0.308013
$7$		−	4.18524i		−	1.58187i	−0.611898	−	0.790937i	$-0.709594\pi$
$7$		−	4.18524i		−	1.58187i	0.611898	−	0.790937i	$-0.290406\pi$
$8$		−	2.58843i		−	0.915147i
$9$	−1.00000			−0.333333
$10$	0.0581566	+	1.68605i	0.0183907	+	0.533177i
$11$	0.596817			0.179947			0.0899736	−	0.995944i	$-0.471322\pi$
$11$	0.596817			0.179947			0.0899736	+	0.995944i	$0.471322\pi$
$12$			1.43077i			0.413027i
$13$		−	2.18524i		−	0.606077i	−0.952978	−	0.303039i	$-0.901999\pi$
$13$		−	2.18524i		−	0.606077i	0.952978	−	0.303039i	$-0.0980011\pi$
$14$	−3.15766			−0.843919
$15$	−0.0770824	−	2.23474i	−0.0199026	−	0.577007i
$16$	0.908639			0.227160
$17$		−	2.81314i		−	0.682286i	−0.940011	−	0.341143i	$-0.889186\pi$
$17$		−	2.81314i		−	0.682286i	0.940011	−	0.341143i	$-0.110814\pi$
$18$			0.754474i			0.177831i
$19$	−0.528904			−0.121339			−0.0606694	−	0.998158i	$-0.519324\pi$
$19$	−0.528904			−0.121339			−0.0606694	+	0.998158i	$0.519324\pi$
$20$	−3.19740	+	0.110287i	−0.714959	+	0.0246609i
$21$	4.18524			0.913295
$22$		−	0.450283i		−	0.0960007i
$23$			0.590044i			0.123033i	0.998106	+	0.0615163i	$0.0195936\pi$
$23$			0.590044i			0.123033i	−0.998106	+	0.0615163i	$0.980406\pi$
$24$	2.58843			0.528360
$25$	4.98812	−	0.344518i	0.997623	−	0.0689036i
$26$	−1.64871			−0.323338
$27$		−	1.00000i		−	0.192450i
$28$		−	5.98812i		−	1.13165i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−1.68605	+	0.0581566i	−0.307830	+	0.0106179i
$31$	8.02005			1.44044			0.720222	−	0.693744i	$-0.244040\pi$
$31$	8.02005			1.44044			0.720222	+	0.693744i	$0.244040\pi$
$32$		−	5.86240i		−	1.03633i
$33$			0.596817i			0.103893i
$34$	−2.12244			−0.363995
$35$	0.322608	+	9.35293i	0.0545308	+	1.58093i
$36$	−1.43077			−0.238462
$37$			2.52465i			0.415050i	0.978230	+	0.207525i	$0.0665408\pi$
$37$			2.52465i			0.415050i	−0.978230	+	0.207525i	$0.933459\pi$
$38$			0.399044i			0.0647335i
$39$	2.18524			0.349919
$40$	0.199522	+	5.78446i	0.0315472	+	0.914603i
$41$	1.57110			0.245365			0.122683	−	0.992446i	$-0.460850\pi$
$41$	1.57110			0.245365			0.122683	+	0.992446i	$0.460850\pi$
$42$		−	3.15766i		−	0.487237i
$43$		−	6.98484i		−	1.06518i	−0.846374	−	0.532589i	$-0.821219\pi$
$43$		−	6.98484i		−	1.06518i	0.846374	−	0.532589i	$-0.178781\pi$
$44$	0.853908			0.128731
$45$	2.23474	−	0.0770824i	0.333135	−	0.0114908i
$46$	0.445173			0.0656372
$47$			2.57524i			0.375638i	0.982204	+	0.187819i	$0.0601418\pi$
$47$			2.57524i			0.375638i	−0.982204	+	0.187819i	$0.939858\pi$
$48$			0.908639i			0.131151i
$49$	−10.5163			−1.50232
$50$	−0.259930	−	3.76340i	−0.0367596	−	0.532226i
$51$	2.81314			0.393918
$52$		−	3.12658i		−	0.433578i
$53$			10.3878i			1.42688i	0.700719	+	0.713438i	$0.252863\pi$
$53$			10.3878i			1.42688i	−0.700719	+	0.713438i	$0.747137\pi$
$54$	−0.754474			−0.102671
$55$	−1.33373	+	0.0460041i	−0.179840	+	0.00620319i
$56$	−10.8332			−1.44765
$57$		−	0.528904i		−	0.0700550i
$58$			0.754474i			0.0990673i
$59$	−13.9168			−1.81181			−0.905907	−	0.423477i	$-0.860810\pi$
$59$	−13.9168			−1.81181			−0.905907	+	0.423477i	$0.860810\pi$
$60$	−0.110287	−	3.19740i	−0.0142380	−	0.412782i
$61$	−11.1942			−1.43327			−0.716633	−	0.697450i	$-0.754318\pi$
$61$	−11.1942			−1.43327			−0.716633	+	0.697450i	$0.754318\pi$
$62$		−	6.05092i		−	0.768468i
$63$			4.18524i			0.527291i
$64$	−2.60575			−0.325718
$65$	0.168444	+	4.88345i	0.0208929	+	0.605717i
$66$	0.450283			0.0554260
$67$		−	0.614139i		−	0.0750290i	−0.999296	−	0.0375145i	$-0.988056\pi$
$67$		−	0.614139i		−	0.0750290i	0.999296	−	0.0375145i	$-0.0119440\pi$
$68$		−	4.02495i		−	0.488097i
$69$	−0.590044			−0.0710330
$70$	7.05654	−	0.243400i	0.843418	−	0.0290918i
$71$	9.28010			1.10134			0.550672	−	0.834721i	$-0.314371\pi$
$71$	9.28010			1.10134			0.550672	+	0.834721i	$0.314371\pi$
$72$			2.58843i			0.305049i
$73$			9.59116i			1.12256i	0.827626	+	0.561280i	$0.189691\pi$
$73$			9.59116i			1.12256i	−0.827626	+	0.561280i	$0.810309\pi$
$74$	1.90478			0.221427
$75$	0.344518	+	4.98812i	0.0397815	+	0.575978i
$76$	−0.756739			−0.0868039
$77$		−	2.49783i		−	0.284654i
$78$		−	1.64871i		−	0.186680i
$79$	10.3396			1.16330			0.581649	−	0.813440i	$-0.302408\pi$
$79$	10.3396			1.16330			0.581649	+	0.813440i	$0.302408\pi$
$80$	−2.03057	+	0.0700400i	−0.227025	+	0.00783071i
$81$	1.00000			0.111111
$82$		−	1.18536i		−	0.130901i
$83$			3.92531i			0.430859i	0.976519	+	0.215430i	$0.0691152\pi$
$83$			3.92531i			0.430859i	−0.976519	+	0.215430i	$0.930885\pi$
$84$	5.98812			0.653357
$85$	0.216843	+	6.28663i	0.0235200	+	0.681881i
$86$	−5.26988			−0.568265
$87$		−	1.00000i		−	0.107211i
$88$		−	1.54482i		−	0.164678i
$89$	12.3352			1.30752			0.653762	−	0.756700i	$-0.273190\pi$
$89$	12.3352			1.30752			0.653762	+	0.756700i	$0.273190\pi$
$90$	−0.0581566	−	1.68605i	−0.00613025	−	0.177726i
$91$	−9.14577			−0.958738
$92$			0.844217i			0.0880157i
$93$			8.02005i			0.831641i
$94$	1.94295			0.200400
$95$	1.18196	−	0.0407692i	0.121267	−	0.00418283i
$96$	5.86240			0.598328
$97$		−	3.21794i		−	0.326732i	−0.986566	−	0.163366i	$-0.947765\pi$
$97$		−	3.21794i		−	0.326732i	0.986566	−	0.163366i	$-0.0522352\pi$
$98$			7.93424i			0.801480i
$99$	−0.596817			−0.0599824
$100$	7.13684	−	0.492926i	0.713684	−	0.0492926i
$101$	9.31726			0.927102			0.463551	−	0.886070i	$-0.346575\pi$
$101$	9.31726			0.927102			0.463551	+	0.886070i	$0.346575\pi$
$102$		−	2.12244i		−	0.210153i
$103$			20.1574i			1.98617i	0.117393	+	0.993085i	$0.462546\pi$
$103$			20.1574i			1.98617i	−0.117393	+	0.993085i	$0.537454\pi$
$104$	−5.65634			−0.554650
$105$	−9.35293	+	0.322608i	−0.912752	+	0.0314834i
$106$	7.83733			0.761229
$107$		−	1.58569i		−	0.153295i	−0.997058	−	0.0766475i	$-0.975578\pi$
$107$		−	1.58569i		−	0.153295i	0.997058	−	0.0766475i	$-0.0244216\pi$
$108$		−	1.43077i		−	0.137676i
$109$	7.91051			0.757690			0.378845	−	0.925460i	$-0.376321\pi$
$109$	7.91051			0.757690			0.378845	+	0.925460i	$0.376321\pi$
$110$	0.0347089	+	1.00627i	0.00330936	+	0.0959436i
$111$	−2.52465			−0.239629
$112$		−	3.80287i		−	0.359338i
$113$		−	3.07328i		−	0.289110i	−0.989497	−	0.144555i	$-0.953825\pi$
$113$		−	3.07328i		−	0.289110i	0.989497	−	0.144555i	$-0.0461750\pi$
$114$	−0.399044			−0.0373739
$115$	−0.0454820	−	1.31859i	−0.00424122	−	0.122960i
$116$	−1.43077			−0.132844
$117$			2.18524i			0.202026i
$118$			10.4999i			0.966591i
$119$	−11.7737			−1.07929
$120$	−5.78446	+	0.199522i	−0.528046	+	0.0182138i
$121$	−10.6438			−0.967619
$122$			8.44571i			0.764639i
$123$			1.57110i			0.141662i
$124$	11.4748			1.03047
$125$	−11.1206	+	1.15440i	−0.994655	+	0.103253i
$126$	3.15766			0.281306
$127$			12.9254i			1.14694i	0.819225	+	0.573472i	$0.194404\pi$
$127$			12.9254i			1.14694i	−0.819225	+	0.573472i	$0.805596\pi$
$128$		−	9.75882i		−	0.862566i
$129$	6.98484			0.614980
$130$	3.68443	−	0.127086i	0.323146	−	0.0111462i
$131$	−5.69473			−0.497551			−0.248775	−	0.968561i	$-0.580028\pi$
$131$	−5.69473			−0.497551			−0.248775	+	0.968561i	$0.580028\pi$
$132$			0.853908i			0.0743231i
$133$			2.21359i			0.191943i
$134$	−0.463352			−0.0400275
$135$	0.0770824	+	2.23474i	0.00663419	+	0.192336i
$136$	−7.28160			−0.624392
$137$		−	18.7274i		−	1.59999i	−0.600005	−	0.799996i	$-0.704835\pi$
$137$		−	18.7274i		−	1.59999i	0.600005	−	0.799996i	$-0.295165\pi$
$138$			0.445173i			0.0378956i
$139$	−1.34376			−0.113976			−0.0569880	−	0.998375i	$-0.518150\pi$
$139$	−1.34376			−0.113976			−0.0569880	+	0.998375i	$0.518150\pi$
$140$	0.461578	+	13.3819i	0.0390105	+	1.13098i
$141$	−2.57524			−0.216875
$142$		−	7.00159i		−	0.587560i
$143$		−	1.30419i		−	0.109062i
$144$	−0.908639			−0.0757199
$145$	2.23474	−	0.0770824i	0.185585	−	0.00640134i
$146$	7.23628			0.598879
$147$		−	10.5163i		−	0.867366i
$148$			3.61219i			0.296920i
$149$	15.9925			1.31016			0.655079	−	0.755561i	$-0.272635\pi$
$149$	15.9925			1.31016			0.655079	+	0.755561i	$0.272635\pi$
$150$	3.76340	−	0.259930i	0.307281	−	0.0212232i
$151$	17.9595			1.46152			0.730760	−	0.682635i	$-0.239166\pi$
$151$	17.9595			1.46152			0.730760	+	0.682635i	$0.239166\pi$
$152$			1.36903i			0.111043i
$153$			2.81314i			0.227429i
$154$	−1.88454			−0.151861
$155$	−17.9227	+	0.618205i	−1.43959	+	0.0496554i
$156$	3.12658			0.250327
$157$		−	6.78158i		−	0.541229i	−0.962688	−	0.270615i	$-0.912773\pi$
$157$		−	6.78158i		−	0.541229i	0.962688	−	0.270615i	$-0.0872269\pi$
$158$		−	7.80097i		−	0.620612i
$159$	−10.3878			−0.823807
$160$	0.451887	+	13.1009i	0.0357248	+	1.03572i
$161$	2.46948			0.194622
$162$		−	0.754474i		−	0.0592771i
$163$			20.9951i			1.64447i	0.569151	+	0.822233i	$0.307272\pi$
$163$			20.9951i			1.64447i	−0.569151	+	0.822233i	$0.692728\pi$
$164$	2.24789			0.175531
$165$	−0.0460041	−	1.33373i	−0.00358141	−	0.103831i
$166$	2.96155			0.229861
$167$			14.9135i			1.15404i	0.816730	+	0.577020i	$0.195784\pi$
$167$			14.9135i			1.15404i	−0.816730	+	0.577020i	$0.804216\pi$
$168$		−	10.8332i		−	0.835799i
$169$	8.22471			0.632670
$170$	4.74310	−	0.163603i	0.363779	−	0.0125478i
$171$	0.528904			0.0404463
$172$		−	9.99369i		−	0.762011i
$173$		−	10.8685i		−	0.826318i	−0.910659	−	0.413159i	$-0.864425\pi$
$173$		−	10.8685i		−	0.826318i	0.910659	−	0.413159i	$-0.135575\pi$
$174$	−0.754474			−0.0571965
$175$	−1.44189	−	20.8765i	−0.108997	−	1.57811i
$176$	0.542291			0.0408767
$177$		−	13.9168i		−	1.04605i
$178$		−	9.30655i		−	0.697556i
$179$	−1.26613			−0.0946349			−0.0473175	−	0.998880i	$-0.515067\pi$
$179$	−1.26613			−0.0946349			−0.0473175	+	0.998880i	$0.515067\pi$
$180$	3.19740	−	0.110287i	0.238320	−	0.00822031i
$181$	−5.80673			−0.431611			−0.215805	−	0.976436i	$-0.569238\pi$
$181$	−5.80673			−0.431611			−0.215805	+	0.976436i	$0.569238\pi$
$182$			6.90025i			0.511480i
$183$		−	11.1942i		−	0.827497i
$184$	1.52729			0.112593
$185$	−0.194606	−	5.64194i	−0.0143077	−	0.414803i
$186$	6.05092			0.443675
$187$		−	1.67893i		−	0.122776i
$188$			3.68458i			0.268725i
$189$	−4.18524			−0.304432
$190$	−0.0307593	−	0.891759i	−0.00223151	−	0.0646950i
$191$	15.3358			1.10966			0.554830	−	0.831964i	$-0.312783\pi$
$191$	15.3358			1.10966			0.554830	+	0.831964i	$0.312783\pi$
$192$		−	2.60575i		−	0.188054i
$193$		−	16.4946i		−	1.18731i	−0.804721	−	0.593653i	$-0.797685\pi$
$193$		−	16.4946i		−	1.18731i	0.804721	−	0.593653i	$-0.202315\pi$
$194$	−2.42785			−0.174310
$195$	−4.88345	+	0.168444i	−0.349711	+	0.0120625i
$196$	−15.0463			−1.07474
$197$		−	24.2353i		−	1.72670i	−0.504609	−	0.863348i	$-0.668363\pi$
$197$		−	24.2353i		−	1.72670i	0.504609	−	0.863348i	$-0.331637\pi$
$198$			0.450283i			0.0320002i
$199$	−17.4875			−1.23965			−0.619826	−	0.784739i	$-0.712797\pi$
$199$	−17.4875			−1.23965			−0.619826	+	0.784739i	$0.712797\pi$
$200$	−0.891759	−	12.9114i	−0.0630569	−	0.912972i
$201$	0.614139			0.0433180
$202$		−	7.02963i		−	0.494603i
$203$			4.18524i			0.293746i
$204$	4.02495			0.281803
$205$	−3.51101	+	0.121104i	−0.245219	+	0.00845830i
$206$	15.2083			1.05961
$207$		−	0.590044i		−	0.0410109i
$208$		−	1.98560i		−	0.137676i
$209$	−0.315659			−0.0218346
$210$	0.243400	+	7.05654i	0.0167962	+	0.486947i
$211$	−26.0504			−1.79338			−0.896692	−	0.442655i	$-0.854037\pi$
$211$	−26.0504			−1.79338			−0.896692	+	0.442655i	$0.854037\pi$
$212$			14.8626i			1.02076i
$213$			9.28010i			0.635862i
$214$	−1.19637			−0.0817819
$215$	0.538408	+	15.6093i	0.0367191	+	1.06454i
$216$	−2.58843			−0.176120
$217$		−	33.5659i		−	2.27860i
$218$		−	5.96827i		−	0.404223i
$219$	−9.59116			−0.648110
$220$	−1.90826	+	0.0658212i	−0.128655	+	0.00443767i
$221$	−6.14739			−0.413518
$222$			1.90478i			0.127841i
$223$			10.7895i			0.722519i	0.932465	+	0.361259i	$0.117653\pi$
$223$			10.7895i			0.722519i	−0.932465	+	0.361259i	$0.882347\pi$
$224$	−24.5356			−1.63935
$225$	−4.98812	+	0.344518i	−0.332541	+	0.0229679i
$226$	−2.31871			−0.154238
$227$			6.99182i			0.464063i	0.972708	+	0.232032i	$0.0745373\pi$
$227$			6.99182i			0.464063i	−0.972708	+	0.232032i	$0.925463\pi$
$228$		−	0.756739i		−	0.0501163i
$229$	20.9503			1.38444			0.692218	−	0.721689i	$-0.256634\pi$
$229$	20.9503			1.38444			0.692218	+	0.721689i	$0.256634\pi$
$230$	−0.994845	+	0.0343150i	−0.0655981	+	0.00226266i
$231$	2.49783			0.164345
$232$			2.58843i			0.169938i
$233$		−	3.85567i		−	0.252593i	−0.991993	−	0.126297i	$-0.959691\pi$
$233$		−	3.85567i		−	0.252593i	0.991993	−	0.126297i	$-0.0403091\pi$
$234$	1.64871			0.107779
$235$	−0.198506	−	5.75500i	−0.0129491	−	0.375415i
$236$	−19.9117			−1.29614
$237$			10.3396i			0.671630i
$238$			8.88293i			0.575795i
$239$	25.3084			1.63706			0.818532	−	0.574461i	$-0.194788\pi$
$239$	25.3084			1.63706			0.818532	+	0.574461i	$0.194788\pi$
$240$	−0.0700400	−	2.03057i	−0.00452106	−	0.131073i
$241$	−22.8510			−1.47196			−0.735981	−	0.677002i	$-0.763279\pi$
$241$	−22.8510			−1.47196			−0.735981	+	0.677002i	$0.763279\pi$
$242$			8.03048i			0.516219i
$243$			1.00000i			0.0641500i
$244$	−16.0163			−1.02534
$245$	23.5011	−	0.810618i	1.50143	−	0.0517885i
$246$	1.18536			0.0755756
$247$			1.15578i			0.0735407i
$248$		−	20.7593i		−	1.31822i
$249$	−3.92531			−0.248757
$250$	0.870967	+	8.39019i	0.0550848	+	0.530642i
$251$	−7.37025			−0.465206			−0.232603	−	0.972572i	$-0.574724\pi$
$251$	−7.37025			−0.465206			−0.232603	+	0.972572i	$0.574724\pi$
$252$			5.98812i			0.377216i
$253$			0.352149i			0.0221394i
$254$	9.75188			0.611888
$255$	−6.28663	+	0.216843i	−0.393684	+	0.0135793i
$256$	−12.5743			−0.785892
$257$			3.21575i			0.200593i	0.994958	+	0.100296i	$0.0319791\pi$
$257$			3.21575i			0.200593i	−0.994958	+	0.100296i	$0.968021\pi$
$258$		−	5.26988i		−	0.328088i
$259$	10.5663			0.656557
$260$	0.241004	+	6.98709i	0.0149464	+	0.433321i
$261$	1.00000			0.0618984
$262$			4.29652i			0.265440i
$263$		−	16.0190i		−	0.987774i	−0.869526	−	0.493887i	$-0.835576\pi$
$263$		−	16.0190i		−	0.987774i	0.869526	−	0.493887i	$-0.164424\pi$
$264$	1.54482			0.0950769
$265$	−0.800717	−	23.2140i	−0.0491876	−	1.42603i
$266$	1.67010			0.102400
$267$			12.3352i			0.754899i
$268$		−	0.878691i		−	0.0536746i
$269$	19.9820			1.21832			0.609161	−	0.793047i	$-0.291506\pi$
$269$	19.9820			1.21832			0.609161	+	0.793047i	$0.291506\pi$
$270$	1.68605	−	0.0581566i	0.102610	−	0.00353930i
$271$	−8.72743			−0.530153			−0.265077	−	0.964227i	$-0.585397\pi$
$271$	−8.72743			−0.530153			−0.265077	+	0.964227i	$0.585397\pi$
$272$		−	2.55613i		−	0.154988i
$273$		−	9.14577i		−	0.553527i
$274$	−14.1294			−0.853585
$275$	2.97699	−	0.205614i	0.179520	−	0.0123990i
$276$	−0.844217			−0.0508159
$277$			30.5856i			1.83771i	0.394594	+	0.918856i	$0.370885\pi$
$277$			30.5856i			1.83771i	−0.394594	+	0.918856i	$0.629115\pi$
$278$			1.01383i			0.0608055i
$279$	−8.02005			−0.480148
$280$	24.2094	−	0.835048i	1.44679	−	0.0499037i
$281$	30.2570			1.80498			0.902490	−	0.430712i	$-0.141737\pi$
$281$	30.2570			1.80498			0.902490	+	0.430712i	$0.141737\pi$
$282$			1.94295i			0.115701i
$283$		−	9.35107i		−	0.555863i	−0.960601	−	0.277932i	$-0.910351\pi$
$283$		−	9.35107i		−	0.555863i	0.960601	−	0.277932i	$-0.0896489\pi$
$284$	13.2777			0.787885
$285$	0.0407692	+	1.18196i	0.00241496	+	0.0700134i
$286$	−0.983978			−0.0581838
$287$		−	6.57545i		−	0.388137i
$288$			5.86240i			0.345445i
$289$	9.08625			0.534485
$290$	−0.0581566	−	1.68605i	−0.00341508	−	0.0990084i
$291$	3.21794			0.188639
$292$			13.7227i			0.803062i
$293$		−	8.47749i		−	0.495260i	−0.968855	−	0.247630i	$-0.920348\pi$
$293$		−	8.47749i		−	0.495260i	0.968855	−	0.247630i	$-0.0796518\pi$
$294$	−7.93424			−0.462734
$295$	31.1004	−	1.07274i	1.81074	−	0.0624574i
$296$	6.53487			0.379832
$297$		−	0.596817i		−	0.0346309i
$298$		−	12.0659i		−	0.698961i
$299$	1.28939			0.0745673
$300$	0.492926	+	7.13684i	0.0284591	+	0.412046i
$301$	−29.2332			−1.68498
$302$		−	13.5499i		−	0.779711i
$303$			9.31726i			0.535263i
$304$	−0.480582			−0.0275633
$305$	25.0161	−	0.862873i	1.43242	−	0.0494080i
$306$	2.12244			0.121332
$307$		−	19.8740i		−	1.13427i	−0.823625	−	0.567135i	$-0.808052\pi$
$307$		−	19.8740i		−	1.13427i	0.823625	−	0.567135i	$-0.191948\pi$
$308$		−	3.57381i		−	0.203637i
$309$	−20.1574			−1.14672
$310$	0.466419	+	13.5222i	0.0264908	+	0.768011i
$311$	−12.5476			−0.711507			−0.355754	−	0.934580i	$-0.615776\pi$
$311$	−12.5476			−0.711507			−0.355754	+	0.934580i	$0.615776\pi$
$312$		−	5.65634i		−	0.320227i
$313$		−	2.82942i		−	0.159928i	−0.996798	−	0.0799640i	$-0.974519\pi$
$313$		−	2.82942i		−	0.159928i	0.996798	−	0.0799640i	$-0.0254805\pi$
$314$	−5.11653			−0.288742
$315$	−0.322608	−	9.35293i	−0.0181769	−	0.526978i
$316$	14.7936			0.832205
$317$		−	6.27390i		−	0.352377i	−0.984356	−	0.176189i	$-0.943623\pi$
$317$		−	6.27390i		−	0.352377i	0.984356	−	0.176189i	$-0.0563769\pi$
$318$			7.83733i			0.439496i
$319$	−0.596817			−0.0334154
$320$	5.82316	−	0.200857i	0.325525	−	0.0112283i
$321$	1.58569			0.0885049
$322$		−	1.86316i		−	0.103830i
$323$			1.48788i			0.0827878i
$324$	1.43077			0.0794872
$325$	−0.752856	−	10.9002i	−0.0417609	−	0.604637i
$326$	15.8403			0.877312
$327$			7.91051i			0.437452i
$328$		−	4.06669i		−	0.224545i
$329$	10.7780			0.594211
$330$	−1.00627	+	0.0347089i	−0.0553931	+	0.00191066i
$331$	−4.47271			−0.245843			−0.122921	−	0.992416i	$-0.539226\pi$
$331$	−4.47271			−0.245843			−0.122921	+	0.992416i	$0.539226\pi$
$332$			5.61622i			0.308230i
$333$		−	2.52465i		−	0.138350i
$334$	11.2518			0.615673
$335$	0.0473393	+	1.37244i	0.00258642	+	0.0749844i
$336$	3.80287			0.207464
$337$			3.62191i			0.197298i	0.995122	+	0.0986489i	$0.0314521\pi$
$337$			3.62191i			0.197298i	−0.995122	+	0.0986489i	$0.968548\pi$
$338$		−	6.20533i		−	0.337526i
$339$	3.07328			0.166918
$340$	0.310253	+	8.99472i	0.0168258	+	0.487807i
$341$	4.78651			0.259204
$342$		−	0.399044i		−	0.0215778i
$343$			14.7164i			0.794611i
$344$	−18.0797			−0.974794
$345$	1.31859	−	0.0454820i	0.0709907	−	0.00244867i
$346$	−8.20002			−0.440836
$347$			34.4636i			1.85010i	0.379844	+	0.925051i	$0.375978\pi$
$347$			34.4636i			1.85010i	−0.379844	+	0.925051i	$0.624022\pi$
$348$		−	1.43077i		−	0.0766973i
$349$	18.0401			0.965665			0.482832	−	0.875713i	$-0.339608\pi$
$349$	18.0401			0.965665			0.482832	+	0.875713i	$0.339608\pi$
$350$	−15.7508	+	1.08787i	−0.841914	+	0.0581491i
$351$	−2.18524			−0.116640
$352$		−	3.49878i		−	0.186486i
$353$			7.60470i			0.404757i	0.979307	+	0.202379i	$0.0648672\pi$
$353$			7.60470i			0.404757i	−0.979307	+	0.202379i	$0.935133\pi$
$354$	−10.4999			−0.558062
$355$	−20.7386	+	0.715332i	−1.10069	+	0.0379659i
$356$	17.6488			0.935382
$357$		−	11.7737i		−	0.623129i
$358$			0.955261i			0.0504871i
$359$	2.32286			0.122596			0.0612980	−	0.998120i	$-0.480476\pi$
$359$	2.32286			0.122596			0.0612980	+	0.998120i	$0.480476\pi$
$360$	−0.199522	−	5.78446i	−0.0105157	−	0.304868i
$361$	−18.7203			−0.985277
$362$			4.38103i			0.230262i
$363$		−	10.6438i		−	0.558655i
$364$	−13.0855			−0.685866
$365$	−0.739309	−	21.4337i	−0.0386972	−	1.12189i
$366$	−8.44571			−0.441464
$367$			6.38930i			0.333519i	0.985998	+	0.166759i	$0.0533303\pi$
$367$			6.38930i			0.333519i	−0.985998	+	0.166759i	$0.946670\pi$
$368$			0.536137i			0.0279481i
$369$	−1.57110			−0.0817884
$370$	−4.25669	+	0.146825i	−0.221295	+	0.00763308i
$371$	43.4755			2.25714
$372$			11.4748i			0.594943i
$373$		−	24.1627i		−	1.25110i	−0.780185	−	0.625549i	$-0.784875\pi$
$373$		−	24.1627i		−	1.25110i	0.780185	−	0.625549i	$-0.215125\pi$
$374$	−1.26671			−0.0654999
$375$	−1.15440	−	11.1206i	−0.0596131	−	0.574264i
$376$	6.66583			0.343764
$377$			2.18524i			0.112546i
$378$			3.15766i			0.162412i
$379$	29.2093			1.50038			0.750191	−	0.661222i	$-0.229962\pi$
$379$	29.2093			1.50038			0.750191	+	0.661222i	$0.229962\pi$
$380$	1.69111	−	0.0583312i	0.0867523	−	0.00299233i
$381$	−12.9254			−0.662189
$382$		−	11.5705i		−	0.591997i
$383$			31.7731i			1.62353i	0.583983	+	0.811766i	$0.301493\pi$
$383$			31.7731i			1.62353i	−0.583983	+	0.811766i	$0.698507\pi$
$384$	9.75882			0.498003
$385$	0.192538	+	5.58199i	0.00981266	+	0.284484i
$386$	−12.4447			−0.633420
$387$			6.98484i			0.355059i
$388$		−	4.60413i		−	0.233739i
$389$	−23.7158			−1.20244			−0.601220	−	0.799084i	$-0.705318\pi$
$389$	−23.7158			−1.20244			−0.601220	+	0.799084i	$0.705318\pi$
$390$	0.127086	+	3.68443i	0.00643527	+	0.186569i
$391$	1.65988			0.0839435
$392$			27.2206i			1.37485i
$393$		−	5.69473i		−	0.287261i
$394$	−18.2849			−0.921181
$395$	−23.1063	+	0.797002i	−1.16261	+	0.0401015i
$396$	−0.853908			−0.0429105
$397$			32.8280i			1.64759i	0.566889	+	0.823794i	$0.308147\pi$
$397$			32.8280i			1.64759i	−0.566889	+	0.823794i	$0.691853\pi$
$398$			13.1938i			0.661347i
$399$	−2.21359			−0.110818
$400$	4.53240	−	0.313042i	0.226620	−	0.0156521i
$401$	−8.21905			−0.410440			−0.205220	−	0.978716i	$-0.565791\pi$
$401$	−8.21905			−0.410440			−0.205220	+	0.978716i	$0.565791\pi$
$402$		−	0.463352i		−	0.0231099i
$403$		−	17.5258i		−	0.873020i
$404$	13.3308			0.663234
$405$	−2.23474	+	0.0770824i	−0.111045	+	0.00383025i
$406$	3.15766			0.156712
$407$			1.50676i			0.0746871i
$408$		−	7.28160i		−	0.360493i
$409$	−27.9114			−1.38013			−0.690065	−	0.723748i	$-0.742418\pi$
$409$	−27.9114			−1.38013			−0.690065	+	0.723748i	$0.742418\pi$
$410$	0.0913702	+	2.64896i	0.00451245	+	0.130823i
$411$	18.7274			0.923756
$412$			28.8406i			1.42088i
$413$			58.2452i			2.86606i
$414$	−0.445173			−0.0218791
$415$	−0.302572	−	8.77205i	−0.0148527	−	0.430603i
$416$	−12.8108			−0.628099
$417$		−	1.34376i		−	0.0658041i
$418$			0.238156i			0.0116486i
$419$	−27.0379			−1.32089			−0.660445	−	0.750874i	$-0.729632\pi$
$419$	−27.0379			−1.32089			−0.660445	+	0.750874i	$0.729632\pi$
$420$	−13.3819	+	0.461578i	−0.652969	+	0.0225227i
$421$	3.79559			0.184986			0.0924928	−	0.995713i	$-0.470516\pi$
$421$	3.79559			0.184986			0.0924928	+	0.995713i	$0.470516\pi$
$422$			19.6544i			0.956759i
$423$		−	2.57524i		−	0.125213i
$424$	26.8881			1.30580
$425$	−0.969177	−	14.0323i	−0.0470120	−	0.680665i
$426$	7.00159			0.339228
$427$			46.8503i			2.26725i
$428$		−	2.26876i		−	0.109665i
$429$	1.30419			0.0629669
$430$	11.7768	−	0.406215i	0.567928	−	0.0195894i
$431$	−0.405550			−0.0195347			−0.00976733	−	0.999952i	$-0.503109\pi$
$431$	−0.405550			−0.0195347			−0.00976733	+	0.999952i	$0.503109\pi$
$432$		−	0.908639i		−	0.0437169i
$433$		−	25.5978i		−	1.23015i	−0.788468	−	0.615075i	$-0.789126\pi$
$433$		−	25.5978i		−	1.23015i	0.788468	−	0.615075i	$-0.210874\pi$
$434$	−25.3246			−1.21562
$435$	0.0770824	+	2.23474i	0.00369582	+	0.107148i
$436$	11.3181			0.542039
$437$		−	0.312077i		−	0.0149286i
$438$			7.23628i			0.345763i
$439$	26.2378			1.25226			0.626132	−	0.779717i	$-0.284637\pi$
$439$	26.2378			1.25226			0.626132	+	0.779717i	$0.284637\pi$
$440$	0.119078	+	3.45226i	0.00567683	+	0.164580i
$441$	10.5163			0.500774
$442$			4.63805i			0.220609i
$443$			26.5050i			1.25929i	0.776883	+	0.629645i	$0.216800\pi$
$443$			26.5050i			1.25929i	−0.776883	+	0.629645i	$0.783200\pi$
$444$	−3.61219			−0.171427
$445$	−27.5659	+	0.950823i	−1.30675	+	0.0450733i
$446$	8.14040			0.385459
$447$			15.9925i			0.756420i
$448$			10.9057i			0.515245i
$449$	−5.57064			−0.262895			−0.131447	−	0.991323i	$-0.541962\pi$
$449$	−5.57064			−0.262895			−0.131447	+	0.991323i	$0.541962\pi$
$450$	0.259930	+	3.76340i	0.0122532	+	0.177409i
$451$	0.937662			0.0441528
$452$		−	4.39715i		−	0.206825i
$453$			17.9595i			0.843809i
$454$	5.27514			0.247575
$455$	20.4384	−	0.704978i	0.958168	−	0.0330499i
$456$	−1.36903			−0.0641106
$457$		−	25.3774i		−	1.18710i	−0.804796	−	0.593551i	$-0.797725\pi$
$457$		−	25.3774i		−	1.18710i	0.804796	−	0.593551i	$-0.202275\pi$
$458$		−	15.8065i		−	0.738587i
$459$	−2.81314			−0.131306
$460$	−0.0650742	−	1.88660i	−0.00303410	−	0.0879634i
$461$	2.20886			0.102877			0.0514384	−	0.998676i	$-0.483619\pi$
$461$	2.20886			0.102877			0.0514384	+	0.998676i	$0.483619\pi$
$462$		−	1.88454i		−	0.0876769i
$463$			7.56591i			0.351618i	0.984424	+	0.175809i	$0.0562541\pi$
$463$			7.56591i			0.351618i	−0.984424	+	0.175809i	$0.943746\pi$
$464$	−0.908639			−0.0421825
$465$	−0.618205	−	17.9227i	−0.0286686	−	0.831146i
$466$	−2.90900			−0.134757
$467$		−	19.9056i		−	0.921120i	−0.887629	−	0.460560i	$-0.847649\pi$
$467$		−	19.9056i		−	0.921120i	0.887629	−	0.460560i	$-0.152351\pi$
$468$			3.12658i			0.144526i
$469$	−2.57032			−0.118686
$470$	−4.34199	+	0.149767i	−0.200281	+	0.00690826i
$471$	6.78158			0.312479
$472$			36.0226i			1.65808i
$473$		−	4.16867i		−	0.191676i
$474$	7.80097			0.358311
$475$	−2.63823	+	0.182217i	−0.121050	+	0.00836068i
$476$	−16.8454			−0.772108
$477$		−	10.3878i		−	0.475625i
$478$		−	19.0945i		−	0.873363i
$479$	−10.3910			−0.474778			−0.237389	−	0.971415i	$-0.576292\pi$
$479$	−10.3910			−0.474778			−0.237389	+	0.971415i	$0.576292\pi$
$480$	−13.1009	+	0.451887i	−0.597973	+	0.0206257i
$481$	5.51698			0.251552
$482$			17.2405i			0.785282i
$483$			2.46948i			0.112365i
$484$	−15.2288			−0.692220
$485$	0.248046	+	7.19126i	0.0112632	+	0.326538i
$486$	0.754474			0.0342236
$487$		−	10.0574i		−	0.455744i	−0.973691	−	0.227872i	$-0.926823\pi$
$487$		−	10.0574i		−	0.455744i	0.973691	−	0.227872i	$-0.0731768\pi$
$488$			28.9753i			1.31165i
$489$	−20.9951			−0.949433
$490$	−0.611590	−	17.7310i	−0.0276288	−	0.801003i
$491$	−0.193599			−0.00873699			−0.00436849	−	0.999990i	$-0.501391\pi$
$491$	−0.193599			−0.00873699			−0.00436849	+	0.999990i	$0.501391\pi$
$492$			2.24789i			0.101343i
$493$			2.81314i			0.126697i
$494$	0.872008			0.0392335
$495$	1.33373	−	0.0460041i	0.0599467	−	0.00206773i
$496$	7.28733			0.327211
$497$		−	38.8395i		−	1.74219i
$498$			2.96155i			0.132710i
$499$	−13.6181			−0.609630			−0.304815	−	0.952412i	$-0.598595\pi$
$499$	−13.6181			−0.609630			−0.304815	+	0.952412i	$0.598595\pi$
$500$	−15.9110	+	1.65169i	−0.711561	+	0.0738656i
$501$	−14.9135			−0.666285
$502$			5.56066i			0.248185i
$503$		−	30.7553i		−	1.37131i	−0.727926	−	0.685655i	$-0.759516\pi$
$503$		−	30.7553i		−	1.37131i	0.727926	−	0.685655i	$-0.240484\pi$
$504$	10.8332			0.482549
$505$	−20.8216	+	0.718197i	−0.926551	+	0.0319593i
$506$	0.265687			0.0118112
$507$			8.22471i			0.365272i
$508$			18.4933i			0.820506i
$509$	1.01272			0.0448881			0.0224441	−	0.999748i	$-0.492855\pi$
$509$	1.01272			0.0448881			0.0224441	+	0.999748i	$0.492855\pi$
$510$	0.163603	+	4.74310i	0.00724445	+	0.210028i
$511$	40.1413			1.77575
$512$		−	10.0307i		−	0.443298i
$513$			0.528904i			0.0233517i
$514$	2.42620			0.107015
$515$	−1.55378	−	45.0466i	−0.0684679	−	1.98499i
$516$	9.99369			0.439948
$517$			1.53695i			0.0675950i
$518$		−	7.97198i		−	0.350269i
$519$	10.8685			0.477075
$520$	12.6404	−	0.436004i	0.554320	−	0.0191200i
$521$	6.02284			0.263865			0.131933	−	0.991259i	$-0.457882\pi$
$521$	6.02284			0.263865			0.131933	+	0.991259i	$0.457882\pi$
$522$		−	0.754474i		−	0.0330224i
$523$			20.3870i			0.891460i	0.895167	+	0.445730i	$0.147056\pi$
$523$			20.3870i			0.891460i	−0.895167	+	0.445730i	$0.852944\pi$
$524$	−8.14784			−0.355940
$525$	20.8765	−	1.44189i	0.911124	−	0.0629293i
$526$	−12.0859			−0.526971
$527$		−	22.5615i		−	0.982795i
$528$			0.542291i			0.0236002i
$529$	22.6518			0.984863
$530$	−17.5144	+	0.604120i	−0.760776	+	0.0262413i
$531$	13.9168			0.603938
$532$			3.16714i			0.137313i
$533$		−	3.43324i		−	0.148710i
$534$	9.30655			0.402734
$535$	0.122229	+	3.54361i	0.00528443	+	0.153204i
$536$	−1.58965			−0.0686625
$537$		−	1.26613i		−	0.0546375i
$538$		−	15.0759i		−	0.649967i
$539$	−6.27629			−0.270339
$540$	0.110287	+	3.19740i	0.00474600	+	0.137594i
$541$	−16.4420			−0.706895			−0.353448	−	0.935454i	$-0.614991\pi$
$541$	−16.4420			−0.706895			−0.353448	+	0.935454i	$0.614991\pi$
$542$			6.58461i			0.282833i
$543$		−	5.80673i		−	0.249191i
$544$	−16.4917			−0.707077
$545$	−17.6779	+	0.609761i	−0.757239	+	0.0261193i
$546$	−6.90025			−0.295303
$547$			28.2531i			1.20802i	0.796979	+	0.604008i	$0.206430\pi$
$547$			28.2531i			1.20802i	−0.796979	+	0.604008i	$0.793570\pi$
$548$		−	26.7946i		−	1.14461i
$549$	11.1942			0.477756
$550$	−0.155131	−	2.24606i	−0.00661479	−	0.0957725i
$551$	0.528904			0.0225321
$552$			1.52729i			0.0650056i
$553$		−	43.2738i		−	1.84019i
$554$	23.0760			0.980407
$555$	5.64194	−	0.194606i	0.239487	−	0.00826057i
$556$	−1.92261			−0.0815367
$557$		−	36.3662i		−	1.54089i	−0.637508	−	0.770443i	$-0.720035\pi$
$557$		−	36.3662i		−	1.54089i	0.637508	−	0.770443i	$-0.279965\pi$
$558$			6.05092i			0.256156i
$559$	−15.2636			−0.645580
$560$	0.293135	+	8.49843i	0.0123872	+	0.359124i
$561$	1.67893			0.0708845
$562$		−	22.8281i		−	0.962945i
$563$		−	5.24750i		−	0.221156i	−0.993867	−	0.110578i	$-0.964730\pi$
$563$		−	5.24750i		−	0.221156i	0.993867	−	0.110578i	$-0.0352701\pi$
$564$	−3.68458			−0.155149
$565$	0.236896	+	6.86798i	0.00996627	+	0.288938i
$566$	−7.05514			−0.296550
$567$		−	4.18524i		−	0.175764i
$568$		−	24.0208i		−	1.00789i
$569$	−17.3773			−0.728495			−0.364248	−	0.931302i	$-0.618674\pi$
$569$	−17.3773			−0.728495			−0.364248	+	0.931302i	$0.618674\pi$
$570$	0.891759	−	0.0307593i	0.0373517	−	0.00128836i
$571$	−22.2889			−0.932760			−0.466380	−	0.884584i	$-0.654442\pi$
$571$	−22.2889			−0.932760			−0.466380	+	0.884584i	$0.654442\pi$
$572$		−	1.86600i		−	0.0780212i
$573$			15.3358i			0.640663i
$574$	−4.96101			−0.207068
$575$	0.203281	+	2.94321i	0.00847740	+	0.122740i
$576$	2.60575			0.108573
$577$		−	26.1738i		−	1.08963i	−0.838556	−	0.544816i	$-0.816600\pi$
$577$		−	26.1738i		−	1.08963i	0.838556	−	0.544816i	$-0.183400\pi$
$578$		−	6.85534i		−	0.285145i
$579$	16.4946			0.685491
$580$	3.19740	−	0.110287i	0.132765	−	0.00457942i
$581$	16.4284			0.681564
$582$		−	2.42785i		−	0.100638i
$583$			6.19962i			0.256762i
$584$	24.8260			1.02731
$585$	−0.168444	−	4.88345i	−0.00696429	−	0.201906i
$586$	−6.39604			−0.264218
$587$			26.4002i			1.08965i	0.838549	+	0.544827i	$0.183405\pi$
$587$			26.4002i			1.08965i	−0.838549	+	0.544827i	$0.816595\pi$
$588$		−	15.0463i		−	0.620501i
$589$	−4.24184			−0.174782
$590$	−0.809355	−	23.4645i	−0.0333206	−	0.966017i
$591$	24.2353			0.996908
$592$			2.29400i			0.0942826i
$593$			19.4942i			0.800532i	0.916399	+	0.400266i	$0.131082\pi$
$593$			19.4942i			0.800532i	−0.916399	+	0.400266i	$0.868918\pi$
$594$	−0.450283			−0.0184753
$595$	26.3111	−	0.907542i	1.07865	−	0.0372056i
$596$	22.8816			0.937266
$597$		−	17.4875i		−	0.715714i
$598$		−	0.972811i		−	0.0397812i
$599$	−20.9453			−0.855800			−0.427900	−	0.903826i	$-0.640746\pi$
$599$	−20.9453			−0.855800			−0.427900	+	0.903826i	$0.640746\pi$
$600$	12.9114	−	0.891759i	0.527104	−	0.0364059i
$601$	14.3956			0.587208			0.293604	−	0.955927i	$-0.405145\pi$
$601$	14.3956			0.587208			0.293604	+	0.955927i	$0.405145\pi$
$602$			22.0557i			0.898924i
$603$			0.614139i			0.0250097i
$604$	25.6958			1.04555
$605$	23.7861	−	0.820450i	0.967044	−	0.0333560i
$606$	7.02963			0.285559
$607$			8.53979i			0.346620i	0.984867	+	0.173310i	$0.0554462\pi$
$607$			8.53979i			0.346620i	−0.984867	+	0.173310i	$0.944554\pi$
$608$			3.10064i			0.125748i
$609$	−4.18524			−0.169595
$610$	−0.651016	−	18.8740i	−0.0263588	−	0.764184i
$611$	5.62753			0.227666
$612$			4.02495i			0.162699i
$613$			36.7173i			1.48300i	0.670954	+	0.741499i	$0.265885\pi$
$613$			36.7173i			1.48300i	−0.670954	+	0.741499i	$0.734115\pi$
$614$	−14.9944			−0.605125
$615$	−0.121104	−	3.51101i	−0.00488340	−	0.141578i
$616$	−6.46544			−0.260500
$617$			45.1304i			1.81688i	0.418014	+	0.908441i	$0.362726\pi$
$617$			45.1304i			1.81688i	−0.418014	+	0.908441i	$0.637274\pi$
$618$			15.2083i			0.611766i
$619$	18.9737			0.762618			0.381309	−	0.924448i	$-0.375473\pi$
$619$	18.9737			0.762618			0.381309	+	0.924448i	$0.375473\pi$
$620$	−25.6433	+	0.884508i	−1.02986	+	0.0355227i
$621$	0.590044			0.0236777
$622$			9.46681i			0.379585i
$623$		−	51.6256i		−	2.06834i
$624$	1.98560			0.0794875
$625$	24.7626	−	3.43699i	0.990505	−	0.137480i
$626$	−2.13472			−0.0853206
$627$		−	0.315659i		−	0.0126062i
$628$		−	9.70288i		−	0.387187i
$629$	7.10219			0.283183
$630$	−7.05654	+	0.243400i	−0.281139	+	0.00969728i
$631$	−18.5514			−0.738518			−0.369259	−	0.929327i	$-0.620388\pi$
$631$	−18.5514			−0.738518			−0.369259	+	0.929327i	$0.620388\pi$
$632$		−	26.7633i		−	1.06459i
$633$		−	26.0504i		−	1.03541i
$634$	−4.73349			−0.187991
$635$	−0.996321	−	28.8849i	−0.0395378	−	1.14626i
$636$	−14.8626			−0.589339
$637$			22.9806i			0.910524i
$638$			0.450283i			0.0178269i
$639$	−9.28010			−0.367115
$640$	0.752233	+	21.8084i	0.0297346	+	0.862054i
$641$	−34.5735			−1.36557			−0.682785	−	0.730619i	$-0.739231\pi$
$641$	−34.5735			−1.36557			−0.682785	+	0.730619i	$0.739231\pi$
$642$		−	1.19637i		−	0.0472168i
$643$			6.58510i			0.259691i	0.991534	+	0.129846i	$0.0414482\pi$
$643$			6.58510i			0.259691i	−0.991534	+	0.129846i	$0.958552\pi$
$644$	3.53325			0.139230
$645$	−15.6093	+	0.538408i	−0.614615	+	0.0211998i
$646$	1.12257			0.0441668
$647$		−	10.0375i		−	0.394614i	−0.980342	−	0.197307i	$-0.936780\pi$
$647$		−	10.0375i		−	0.394614i	0.980342	−	0.197307i	$-0.0632196\pi$
$648$		−	2.58843i		−	0.101683i
$649$	−8.30579			−0.326031
$650$	−8.22395	+	0.568010i	−0.322570	+	0.0222792i
$651$	33.5659			1.31555
$652$			30.0392i			1.17643i
$653$			3.25188i			0.127256i	0.997974	+	0.0636280i	$0.0202671\pi$
$653$			3.25188i			0.127256i	−0.997974	+	0.0636280i	$0.979733\pi$
$654$	5.96827			0.233378
$655$	12.7262	−	0.438963i	0.497255	−	0.0171517i
$656$	1.42757			0.0557371
$657$		−	9.59116i		−	0.374187i
$658$		−	8.13173i		−	0.317008i
$659$	9.93148			0.386875			0.193438	−	0.981113i	$-0.438036\pi$
$659$	9.93148			0.386875			0.193438	+	0.981113i	$0.438036\pi$
$660$	−0.0658212	−	1.90826i	−0.00256209	−	0.0742790i
$661$	−9.44925			−0.367533			−0.183767	−	0.982970i	$-0.558829\pi$
$661$	−9.44925			−0.367533			−0.183767	+	0.982970i	$0.558829\pi$
$662$			3.37455i			0.131155i
$663$		−	6.14739i		−	0.238745i
$664$	10.1604			0.394299
$665$	−0.170629	−	4.94680i	−0.00661670	−	0.191829i
$666$	−1.90478			−0.0738088
$667$		−	0.590044i		−	0.0228466i
$668$			21.3377i			0.825582i
$669$	−10.7895			−0.417146
$670$	1.03547	−	0.0357162i	0.0400037	−	0.00137984i
$671$	−6.68088			−0.257912
$672$		−	24.5356i		−	0.946479i
$673$			11.1154i			0.428468i	0.976782	+	0.214234i	$0.0687254\pi$
$673$			11.1154i			0.428468i	−0.976782	+	0.214234i	$0.931275\pi$
$674$	2.73263			0.105257
$675$	−0.344518	−	4.98812i	−0.0132605	−	0.191993i
$676$	11.7677			0.452603
$677$			44.6045i			1.71429i	0.515075	+	0.857145i	$0.327764\pi$
$677$			44.6045i			1.71429i	−0.515075	+	0.857145i	$0.672236\pi$
$678$		−	2.31871i		−	0.0890495i
$679$	−13.4679			−0.516849
$680$	16.2725	−	0.561283i	0.624021	−	0.0215242i
$681$	−6.99182			−0.267927
$682$		−	3.61129i		−	0.138284i
$683$			0.490486i			0.0187679i	0.999956	+	0.00938396i	$0.00298705\pi$
$683$			0.490486i			0.0187679i	−0.999956	+	0.00938396i	$0.997013\pi$
$684$	0.756739			0.0289346
$685$	1.44355	+	41.8509i	0.0551554	+	1.59904i
$686$	11.1031			0.423920
$687$			20.9503i			0.799304i
$688$		−	6.34669i		−	0.241965i
$689$	22.6999			0.864797
$690$	−0.0343150	−	0.994845i	−0.00130635	−	0.0378731i
$691$	−6.72252			−0.255737			−0.127868	−	0.991791i	$-0.540814\pi$
$691$	−6.72252			−0.255737			−0.127868	+	0.991791i	$0.540814\pi$
$692$		−	15.5503i		−	0.591135i
$693$			2.49783i			0.0948845i
$694$	26.0019			0.987017
$695$	3.00295	−	0.103580i	0.113908	−	0.00392901i
$696$	−2.58843			−0.0981140
$697$		−	4.41973i		−	0.167409i
$698$		−	13.6108i		−	0.515176i
$699$	3.85567			0.145835
$700$	−2.06301	−	29.8694i	−0.0779746	−	1.12896i
$701$	−32.2913			−1.21963			−0.609813	−	0.792546i	$-0.708755\pi$
$701$	−32.2913			−1.21963			−0.609813	+	0.792546i	$0.708755\pi$
$702$			1.64871i			0.0622265i
$703$		−	1.33530i		−	0.0503617i
$704$	−1.55515			−0.0586121
$705$	5.75500	−	0.198506i	0.216746	−	0.00747616i
$706$	5.73755			0.215936
$707$		−	38.9950i		−	1.46656i
$708$		−	19.9117i		−	0.748329i
$709$	−9.75887			−0.366502			−0.183251	−	0.983066i	$-0.558662\pi$
$709$	−9.75887			−0.366502			−0.183251	+	0.983066i	$0.558662\pi$
$710$	0.539699	+	15.6467i	0.0202546	+	0.587211i
$711$	−10.3396			−0.387766
$712$		−	31.9286i		−	1.19658i
$713$			4.73218i			0.177222i
$714$	−8.88293			−0.332435
$715$	0.100530	+	2.91453i	0.00375961	+	0.108997i
$716$	−1.81154			−0.0677004
$717$			25.3084i			0.945159i
$718$		−	1.75254i		−	0.0654042i
$719$	−44.2063			−1.64862			−0.824308	−	0.566142i	$-0.808435\pi$
$719$	−44.2063			−1.64862			−0.824308	+	0.566142i	$0.808435\pi$
$720$	2.03057	−	0.0700400i	0.0756749	−	0.00261024i
$721$	84.3638			3.14187
$722$			14.1239i			0.525639i
$723$		−	22.8510i		−	0.849837i
$724$	−8.30809			−0.308768
$725$	−4.98812	+	0.344518i	−0.185254	+	0.0127951i
$726$	−8.03048			−0.298039
$727$		−	44.9849i		−	1.66840i	−0.551463	−	0.834199i	$-0.685930\pi$
$727$		−	44.9849i		−	1.66840i	0.551463	−	0.834199i	$-0.314070\pi$
$728$			23.6732i			0.877385i
$729$	−1.00000			−0.0370370
$730$	−16.1712	+	0.557789i	−0.598523	+	0.0206447i
$731$	−19.6493			−0.726756
$732$		−	16.0163i		−	0.591979i
$733$			1.59233i			0.0588142i	0.999568	+	0.0294071i	$0.00936191\pi$
$733$			1.59233i			0.0588142i	−0.999568	+	0.0294071i	$0.990638\pi$
$734$	4.82056			0.177930
$735$	0.810618	+	23.5011i	0.0299001	+	0.866851i
$736$	3.45907			0.127503
$737$		−	0.366529i		−	0.0135013i
$738$			1.18536i			0.0436336i
$739$	37.2457			1.37011			0.685053	−	0.728493i	$-0.259779\pi$
$739$	37.2457			1.37011			0.685053	+	0.728493i	$0.259779\pi$
$740$	−0.278436	−	8.07231i	−0.0102355	−	0.296744i
$741$	−1.15578			−0.0424588
$742$		−	32.8011i		−	1.20417i
$743$			41.1086i			1.50813i	0.656800	+	0.754065i	$0.271909\pi$
$743$			41.1086i			1.50813i	−0.656800	+	0.754065i	$0.728091\pi$
$744$	20.7593			0.761073
$745$	−35.7391	+	1.23274i	−1.30938	+	0.0451641i
$746$	−18.2301			−0.667452
$747$		−	3.92531i		−	0.143620i
$748$		−	2.40216i		−	0.0878317i
$749$	−6.63652			−0.242493
$750$	−8.39019	+	0.870967i	−0.306366	+	0.0318032i
$751$	−44.6707			−1.63006			−0.815029	−	0.579420i	$-0.803279\pi$
$751$	−44.6707			−1.63006			−0.815029	+	0.579420i	$0.803279\pi$
$752$			2.33997i			0.0853298i
$753$		−	7.37025i		−	0.268587i
$754$	1.64871			0.0600424
$755$	−40.1347	+	1.38436i	−1.46065	+	0.0503819i
$756$	−5.98812			−0.217786
$757$		−	13.8828i		−	0.504577i	−0.967652	−	0.252289i	$-0.918817\pi$
$757$		−	13.8828i		−	0.504577i	0.967652	−	0.252289i	$-0.0811833\pi$
$758$		−	22.0377i		−	0.800444i
$759$	−0.352149			−0.0127822
$760$	−0.105528	−	3.05942i	−0.00382790	−	0.110977i
$761$	−30.9137			−1.12062			−0.560310	−	0.828283i	$-0.689318\pi$
$761$	−30.9137			−1.12062			−0.560310	+	0.828283i	$0.689318\pi$
$762$			9.75188i			0.353273i
$763$		−	33.1074i		−	1.19857i
$764$	21.9420			0.793834
$765$	−0.216843	−	6.28663i	−0.00783999	−	0.227294i
$766$	23.9720			0.866144
$767$			30.4116i			1.09810i
$768$		−	12.5743i		−	0.453735i
$769$	−31.1489			−1.12326			−0.561630	−	0.827389i	$-0.689825\pi$
$769$	−31.1489			−1.12326			−0.561630	+	0.827389i	$0.689825\pi$
$770$	4.21146	−	0.145265i	0.151771	−	0.00523499i
$771$	−3.21575			−0.115812
$772$		−	23.5999i		−	0.849380i
$773$		−	25.7705i		−	0.926902i	−0.886123	−	0.463451i	$-0.846611\pi$
$773$		−	25.7705i		−	0.926902i	0.886123	−	0.463451i	$-0.153389\pi$
$774$	5.26988			0.189422
$775$	40.0050	−	2.76305i	1.43702	−	0.0992518i
$776$	−8.32940			−0.299008
$777$			10.5663i			0.379063i
$778$			17.8930i			0.641494i
$779$	−0.830963			−0.0297723
$780$	−6.98709	+	0.241004i	−0.250178	+	0.00862933i
$781$	5.53852			0.198184
$782$		−	1.25233i		−	0.0447833i
$783$			1.00000i			0.0357371i
$784$	−9.55548			−0.341267
$785$	0.522741	+	15.1551i	0.0186574	+	0.540908i
$786$	−4.29652			−0.153252
$787$		−	26.2806i		−	0.936802i	−0.883516	−	0.468401i	$-0.844830\pi$
$787$		−	26.2806i		−	0.936802i	0.883516	−	0.468401i	$-0.155170\pi$
$788$		−	34.6752i		−	1.23525i
$789$	16.0190			0.570292
$790$	0.601317	+	17.4331i	0.0213939	+	0.620243i
$791$	−12.8624			−0.457335
$792$			1.54482i			0.0548927i
$793$			24.4620i			0.868671i
$794$	24.7678			0.878978
$795$	23.2140	−	0.800717i	0.823317	−	0.0283985i
$796$	−25.0205			−0.886828
$797$		−	53.7239i		−	1.90300i	−0.307650	−	0.951500i	$-0.599543\pi$
$797$		−	53.7239i		−	1.90300i	0.307650	−	0.951500i	$-0.400457\pi$
$798$			1.67010i			0.0591208i
$799$	7.24452			0.256293
$800$	−2.01970	−	29.2423i	−0.0714072	−	1.03387i
$801$	−12.3352			−0.435841
$802$			6.20106i			0.218967i
$803$			5.72417i			0.202002i
$804$	0.878691			0.0309890
$805$	−5.51864	+	0.190353i	−0.194506	+	0.00670907i
$806$	−13.2227			−0.465751
$807$			19.9820i			0.703398i
$808$		−	24.1170i		−	0.848434i
$809$	6.02488			0.211824			0.105912	−	0.994376i	$-0.466224\pi$
$809$	6.02488			0.211824			0.105912	+	0.994376i	$0.466224\pi$
$810$	0.0581566	+	1.68605i	0.00204342	+	0.0592418i
$811$	−7.70554			−0.270578			−0.135289	−	0.990806i	$-0.543196\pi$
$811$	−7.70554			−0.270578			−0.135289	+	0.990806i	$0.543196\pi$
$812$			5.98812i			0.210142i
$813$		−	8.72743i		−	0.306084i
$814$	1.13681			0.0398451
$815$	−1.61836	−	46.9187i	−0.0566885	−	1.64349i
$816$	2.55613			0.0894823
$817$			3.69431i			0.129247i
$818$			21.0584i			0.736290i
$819$	9.14577			0.319579
$820$	−5.02344	+	0.173273i	−0.175426	+	0.00605094i
$821$	16.4338			0.573543			0.286772	−	0.957999i	$-0.407418\pi$
$821$	16.4338			0.573543			0.286772	+	0.957999i	$0.407418\pi$
$822$		−	14.1294i		−	0.492818i
$823$			45.4920i			1.58575i	0.609383	+	0.792876i	$0.291417\pi$
$823$			45.4920i			1.58575i	−0.609383	+	0.792876i	$0.708583\pi$
$824$	52.1760			1.81764
$825$	0.205614	+	2.97699i	0.00715857	+	0.103646i
$826$	43.9445			1.52902
$827$			33.1498i			1.15273i	0.817191	+	0.576367i	$0.195530\pi$
$827$			33.1498i			1.15273i	−0.817191	+	0.576367i	$0.804470\pi$
$828$		−	0.844217i		−	0.0293386i
$829$	−27.9403			−0.970407			−0.485203	−	0.874401i	$-0.661254\pi$
$829$	−27.9403			−0.970407			−0.485203	+	0.874401i	$0.661254\pi$
$830$	−6.61828	+	0.228283i	−0.229724	+	0.00792382i
$831$	−30.5856			−1.06100
$832$			5.69419i			0.197411i
$833$			29.5837i			1.02501i
$834$	−1.01383			−0.0351060
$835$	−1.14957	−	33.3277i	−0.0397824	−	1.15335i
$836$	−0.451635			−0.0156201
$837$		−	8.02005i		−	0.277214i
$838$			20.3994i			0.704686i
$839$	−27.5639			−0.951610			−0.475805	−	0.879551i	$-0.657843\pi$
$839$	−27.5639			−0.951610			−0.475805	+	0.879551i	$0.657843\pi$
$840$	0.835048	+	24.2094i	0.0288119	+	0.835302i
$841$	1.00000			0.0344828
$842$		−	2.86367i		−	0.0986886i
$843$			30.2570i			1.04211i
$844$	−37.2721			−1.28296
$845$	−18.3801	+	0.633980i	−0.632294	+	0.0218096i
$846$	−1.94295			−0.0668001
$847$			44.5469i			1.53065i
$848$			9.43876i			0.324128i
$849$	9.35107			0.320928
$850$	−10.5870	+	0.731219i	−0.363130	+	0.0250806i
$851$	−1.48966			−0.0510647
$852$			13.2777i			0.454886i
$853$		−	14.4467i		−	0.494645i	−0.968933	−	0.247323i	$-0.920449\pi$
$853$		−	14.4467i		−	0.494645i	0.968933	−	0.247323i	$-0.0795508\pi$
$854$	35.3474			1.20956
$855$	−1.18196	+	0.0407692i	−0.0404222	+	0.00139428i
$856$	−4.10445			−0.140287
$857$			20.6065i			0.703904i	0.936018	+	0.351952i	$0.114482\pi$
$857$			20.6065i			0.703904i	−0.936018	+	0.351952i	$0.885518\pi$
$858$		−	0.983978i		−	0.0335925i
$859$	22.6473			0.772717			0.386358	−	0.922349i	$-0.373733\pi$
$859$	22.6473			0.772717			0.386358	+	0.922349i	$0.373733\pi$
$860$	0.770337	+	22.3333i	0.0262683	+	0.761559i
$861$	6.57545			0.224091
$862$			0.305977i			0.0104216i
$863$		−	18.3880i		−	0.625935i	−0.949764	−	0.312967i	$-0.898677\pi$
$863$		−	18.3880i		−	0.625935i	0.949764	−	0.312967i	$-0.101323\pi$
$864$	−5.86240			−0.199443
$865$	0.837772	+	24.2883i	0.0284851	+	0.825827i
$866$	−19.3129			−0.656278
$867$			9.08625i			0.308585i
$868$		−	48.0250i		−	1.63007i
$869$	6.17086			0.209332
$870$	1.68605	−	0.0581566i	0.0571625	−	0.00197169i
$871$	−1.34204			−0.0454734
$872$		−	20.4758i		−	0.693397i
$873$			3.21794i			0.108911i
$874$	−0.235454			−0.00796434
$875$	4.83146	+	46.5423i	0.163333	+	1.57342i
$876$	−13.7227			−0.463648
$877$			20.7681i			0.701289i	0.936509	+	0.350645i	$0.114038\pi$
$877$			20.7681i			0.701289i	−0.936509	+	0.350645i	$0.885962\pi$
$878$		−	19.7958i		−	0.668075i
$879$	8.47749			0.285939
$880$	−1.21188	+	0.0418011i	−0.0408524	+	0.00140911i
$881$	25.7085			0.866140			0.433070	−	0.901360i	$-0.357430\pi$
$881$	25.7085			0.866140			0.433070	+	0.901360i	$0.357430\pi$
$882$		−	7.93424i		−	0.267160i
$883$			48.3574i			1.62736i	0.581315	+	0.813679i	$0.302539\pi$
$883$			48.3574i			1.62736i	−0.581315	+	0.813679i	$0.697461\pi$
$884$	−8.79550			−0.295825
$885$	1.07274	+	31.1004i	0.0360598	+	1.04543i
$886$	19.9973			0.671824
$887$			48.7809i			1.63790i	0.573864	+	0.818951i	$0.305444\pi$
$887$			48.7809i			1.63790i	−0.573864	+	0.818951i	$0.694556\pi$
$888$			6.53487i			0.219296i
$889$	54.0960			1.81432
$890$	0.717371	+	20.7977i	0.0240463	+	0.697141i
$891$	0.596817			0.0199941
$892$			15.4373i			0.516879i
$893$		−	1.36206i		−	0.0455795i
$894$	12.0659			0.403545
$895$	2.82947	−	0.0975962i	0.0945787	−	0.00326228i
$896$	−40.8430			−1.36447
$897$			1.28939i			0.0430515i
$898$			4.20291i			0.140253i
$899$	−8.02005			−0.267484
$900$	−7.13684	+	0.492926i	−0.237895	+	0.0164309i
$901$	29.2223			0.973537
$902$		−	0.707442i		−	0.0235552i
$903$		−	29.2332i		−	0.972821i
$904$	−7.95495			−0.264578
$905$	12.9765	−	0.447596i	0.431354	−	0.0148786i
$906$	13.5499			0.450166
$907$		−	10.8048i		−	0.358767i	−0.983779	−	0.179383i	$-0.942590\pi$
$907$		−	10.8048i		−	0.358767i	0.983779	−	0.179383i	$-0.0574103\pi$
$908$			10.0037i			0.331984i
$909$	−9.31726			−0.309034
$910$	−0.531887	−	15.4203i	−0.0176319	−	0.511176i
$911$	22.2530			0.737274			0.368637	−	0.929573i	$-0.379825\pi$
$911$	22.2530			0.737274			0.368637	+	0.929573i	$0.379825\pi$
$912$		−	0.480582i		−	0.0159137i
$913$			2.34269i			0.0775319i
$914$	−19.1466			−0.633312
$915$	0.862873	+	25.0161i	0.0285257	+	0.827005i
$916$	29.9751			0.990404
$917$			23.8338i			0.787062i
$918$			2.12244i			0.0700509i
$919$	−47.1476			−1.55526			−0.777628	−	0.628724i	$-0.783577\pi$
$919$	−47.1476			−1.55526			−0.777628	+	0.628724i	$0.783577\pi$
$920$	−3.41308	+	0.117727i	−0.112526	+	0.00388134i
$921$	19.8740			0.654871
$922$		−	1.66653i		−	0.0548841i
$923$		−	20.2793i		−	0.667500i
$924$	3.57381			0.117570
$925$	0.869788	+	12.5933i	0.0285984	+	0.414064i
$926$	5.70828			0.187586
$927$		−	20.1574i		−	0.662057i
$928$			5.86240i			0.192443i
$929$	−13.0115			−0.426893			−0.213446	−	0.976955i	$-0.568469\pi$
$929$	−13.0115			−0.426893			−0.213446	+	0.976955i	$0.568469\pi$
$930$	−13.5222	+	0.466419i	−0.443411	+	0.0152945i
$931$	5.56209			0.182290
$932$		−	5.51657i		−	0.180701i
$933$		−	12.5476i		−	0.410789i
$934$	−15.0182			−0.491412
$935$	0.129416	+	3.75197i	0.00423235	+	0.122703i
$936$	5.65634			0.184883
$937$		−	19.4077i		−	0.634021i	−0.948422	−	0.317011i	$-0.897321\pi$
$937$		−	19.4077i		−	0.634021i	0.948422	−	0.317011i	$-0.102679\pi$
$938$			1.93924i			0.0633184i
$939$	2.82942			0.0923345
$940$	−0.284016	−	8.23407i	−0.00926358	−	0.268566i
$941$	16.3192			0.531990			0.265995	−	0.963974i	$-0.414299\pi$
$941$	16.3192			0.531990			0.265995	+	0.963974i	$0.414299\pi$
$942$		−	5.11653i		−	0.166705i
$943$			0.927021i			0.0301880i
$944$	−12.6453			−0.411571
$945$	9.35293	−	0.322608i	0.304251	−	0.0104945i
$946$	−3.14515			−0.102258
$947$		−	20.0894i		−	0.652819i	−0.945229	−	0.326409i	$-0.894161\pi$
$947$		−	20.0894i		−	0.652819i	0.945229	−	0.326409i	$-0.105839\pi$
$948$			14.7936i			0.480474i
$949$	20.9590			0.680358
$950$	0.137478	+	1.99048i	0.00446037	+	0.0645796i
$951$	6.27390			0.203445
$952$			30.4753i			0.987709i
$953$			23.6518i			0.766158i	0.923716	+	0.383079i	$0.125136\pi$
$953$			23.6518i			0.766158i	−0.923716	+	0.383079i	$0.874864\pi$
$954$	−7.83733			−0.253743
$955$	−34.2715	+	1.18212i	−1.10900	+	0.0382525i
$956$	36.2105			1.17113
$957$		−	0.596817i		−	0.0192924i
$958$			7.83975i			0.253291i
$959$	−78.3788			−2.53098
$960$	0.200857	+	5.82316i	0.00648264	+	0.187942i
$961$	33.3212			1.07488
$962$		−	4.16241i		−	0.134202i
$963$			1.58569i			0.0510983i
$964$	−32.6945			−1.05302
$965$	1.27144	+	36.8611i	0.0409291	+	1.18660i
$966$	1.86316			0.0599461
$967$			5.19177i			0.166956i	0.996510	+	0.0834780i	$0.0266028\pi$
$967$			5.19177i			0.166956i	−0.996510	+	0.0834780i	$0.973397\pi$
$968$			27.5507i			0.885513i
$969$	−1.48788			−0.0477976
$970$	5.42561	−	0.187145i	0.174206	−	0.00600885i
$971$	−31.0165			−0.995366			−0.497683	−	0.867359i	$-0.665816\pi$
$971$	−31.0165			−0.995366			−0.497683	+	0.867359i	$0.665816\pi$
$972$			1.43077i			0.0458919i
$973$			5.62395i			0.180296i
$974$	−7.58804			−0.243137
$975$	10.9002	−	0.752856i	0.349087	−	0.0241107i
$976$	−10.1715			−0.325580
$977$		−	35.0578i		−	1.12160i	−0.827952	−	0.560798i	$-0.810494\pi$
$977$		−	35.0578i		−	1.12160i	0.827952	−	0.560798i	$-0.189506\pi$
$978$			15.8403i			0.506517i
$979$	7.36183			0.235285
$980$	33.6246	−	1.15981i	1.07410	−	0.0370487i
$981$	−7.91051			−0.252563
$982$			0.146065i			0.00466113i
$983$		−	11.3717i		−	0.362702i	−0.983418	−	0.181351i	$-0.941953\pi$
$983$		−	11.3717i		−	0.362702i	0.983418	−	0.181351i	$-0.0580471\pi$
$984$	4.06669			0.129641
$985$	1.86812	+	54.1596i	0.0595232	+	1.72567i
$986$	2.12244			0.0675922
$987$			10.7780i			0.343068i
$988$			1.65366i			0.0526099i
$989$	4.12136			0.131052
$990$	−0.0347089	−	1.00627i	−0.00110312	−	0.0319812i
$991$	−20.5008			−0.651230			−0.325615	−	0.945503i	$-0.605571\pi$
$991$	−20.5008			−0.651230			−0.325615	+	0.945503i	$0.605571\pi$
$992$		−	47.0167i		−	1.49278i
$993$		−	4.47271i		−	0.141937i
$994$	−29.3034			−0.929446
$995$	39.0799	−	1.34797i	1.23892	−	0.0427337i
$996$	−5.61622			−0.177957
$997$		−	8.50559i		−	0.269375i	−0.990888	−	0.134687i	$-0.956997\pi$
$997$		−	8.50559i		−	0.269375i	0.990888	−	0.134687i	$-0.0430030\pi$
$998$			10.2745i			0.325234i
$999$	2.52465			0.0798764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.c.e.349.4	✓	10
3.2	odd	2		1305.2.c.j.784.7		10
5.2	odd	4		2175.2.a.z.1.3		5
5.3	odd	4		2175.2.a.w.1.3		5
5.4	even	2	inner	435.2.c.e.349.7	yes	10
15.2	even	4		6525.2.a.bl.1.3		5
15.8	even	4		6525.2.a.bs.1.3		5
15.14	odd	2		1305.2.c.j.784.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.c.e.349.4	✓	10	1.1	even	1	trivial
435.2.c.e.349.7	yes	10	5.4	even	2	inner
1305.2.c.j.784.4		10	15.14	odd	2
1305.2.c.j.784.7		10	3.2	odd	2
2175.2.a.w.1.3		5	5.3	odd	4
2175.2.a.z.1.3		5	5.2	odd	4
6525.2.a.bl.1.3		5	15.2	even	4
6525.2.a.bs.1.3		5	15.8	even	4

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.754474i q^{2} +1.00000i q^{3} +1.43077 q^{4} +(-2.23474 + 0.0770824i) q^{5} +0.754474 q^{6} -4.18524i q^{7} -2.58843i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.754474i q^{2} +1.00000i q^{3} +1.43077 q^{4} +(-2.23474 + 0.0770824i) q^{5} +0.754474 q^{6} -4.18524i q^{7} -2.58843i q^{8} -1.00000 q^{9} +(0.0581566 + 1.68605i) q^{10} +0.596817 q^{11} +1.43077i q^{12} -2.18524i q^{13} -3.15766 q^{14} +(-0.0770824 - 2.23474i) q^{15} +0.908639 q^{16} -2.81314i q^{17} +0.754474i q^{18} -0.528904 q^{19} +(-3.19740 + 0.110287i) q^{20} +4.18524 q^{21} -0.450283i q^{22} +0.590044i q^{23} +2.58843 q^{24} +(4.98812 - 0.344518i) q^{25} -1.64871 q^{26} -1.00000i q^{27} -5.98812i q^{28} -1.00000 q^{29} +(-1.68605 + 0.0581566i) q^{30} +8.02005 q^{31} -5.86240i q^{32} +0.596817i q^{33} -2.12244 q^{34} +(0.322608 + 9.35293i) q^{35} -1.43077 q^{36} +2.52465i q^{37} +0.399044i q^{38} +2.18524 q^{39} +(0.199522 + 5.78446i) q^{40} +1.57110 q^{41} -3.15766i q^{42} -6.98484i q^{43} +0.853908 q^{44} +(2.23474 - 0.0770824i) q^{45} +0.445173 q^{46} +2.57524i q^{47} +0.908639i q^{48} -10.5163 q^{49} +(-0.259930 - 3.76340i) q^{50} +2.81314 q^{51} -3.12658i q^{52} +10.3878i q^{53} -0.754474 q^{54} +(-1.33373 + 0.0460041i) q^{55} -10.8332 q^{56} -0.528904i q^{57} +0.754474i q^{58} -13.9168 q^{59} +(-0.110287 - 3.19740i) q^{60} -11.1942 q^{61} -6.05092i q^{62} +4.18524i q^{63} -2.60575 q^{64} +(0.168444 + 4.88345i) q^{65} +0.450283 q^{66} -0.614139i q^{67} -4.02495i q^{68} -0.590044 q^{69} +(7.05654 - 0.243400i) q^{70} +9.28010 q^{71} +2.58843i q^{72} +9.59116i q^{73} +1.90478 q^{74} +(0.344518 + 4.98812i) q^{75} -0.756739 q^{76} -2.49783i q^{77} -1.64871i q^{78} +10.3396 q^{79} +(-2.03057 + 0.0700400i) q^{80} +1.00000 q^{81} -1.18536i q^{82} +3.92531i q^{83} +5.98812 q^{84} +(0.216843 + 6.28663i) q^{85} -5.26988 q^{86} -1.00000i q^{87} -1.54482i q^{88} +12.3352 q^{89} +(-0.0581566 - 1.68605i) q^{90} -9.14577 q^{91} +0.844217i q^{92} +8.02005i q^{93} +1.94295 q^{94} +(1.18196 - 0.0407692i) q^{95} +5.86240 q^{96} -3.21794i q^{97} +7.93424i q^{98} -0.596817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9	\( 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9} + 4 q^{10} + 24 q^{11} - 12 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{19} + 8 q^{20} + 16 q^{21} - 18 q^{24} + 2 q^{25} - 10 q^{29} - 18 q^{30} + 4 q^{31} - 8 q^{34} + 2 q^{35} + 10 q^{36} - 4 q^{39} - 14 q^{40} - 28 q^{41} - 40 q^{44} - 12 q^{46} + 14 q^{49} - 12 q^{50} - 6 q^{54} + 2 q^{55} - 4 q^{56} - 8 q^{59} - 2 q^{60} - 24 q^{61} + 18 q^{64} + 6 q^{65} + 28 q^{66} - 16 q^{69} + 20 q^{70} + 60 q^{71} - 4 q^{74} + 12 q^{75} - 88 q^{76} + 36 q^{79} - 30 q^{80} + 10 q^{81} + 12 q^{84} - 14 q^{85} + 60 q^{86} + 44 q^{89} - 4 q^{90} - 24 q^{91} + 100 q^{94} - 36 q^{95} + 2 q^{96} - 24 q^{99}+O(q^{100}) \) 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 + 4 * q^10 + 24 * q^11 - 12 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^19 + 8 * q^20 + 16 * q^21 - 18 * q^24 + 2 * q^25 - 10 * q^29 - 18 * q^30 + 4 * q^31 - 8 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^39 - 14 * q^40 - 28 * q^41 - 40 * q^44 - 12 * q^46 + 14 * q^49 - 12 * q^50 - 6 * q^54 + 2 * q^55 - 4 * q^56 - 8 * q^59 - 2 * q^60 - 24 * q^61 + 18 * q^64 + 6 * q^65 + 28 * q^66 - 16 * q^69 + 20 * q^70 + 60 * q^71 - 4 * q^74 + 12 * q^75 - 88 * q^76 + 36 * q^79 - 30 * q^80 + 10 * q^81 + 12 * q^84 - 14 * q^85 + 60 * q^86 + 44 * q^89 - 4 * q^90 - 24 * q^91 + 100 * q^94 - 36 * q^95 + 2 * q^96 - 24 * q^99

Introduction

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