LMFDB - Embedded newform 1870.2.c.e.441.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1870,2,Mod(441,1870)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1870, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1870.441");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1870.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:	$14.9320251780$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 39 x^{16} + 629 x^{14} + 5475 x^{12} + 28167 x^{10} + 87917 x^{8} + 163243 x^{6} + 166385 x^{4} + \cdots + 4096 $ x^18 + 39x^16 + 629x^14 + 5475x^12 + 28167x^10 + 87917x^8 + 163243x^6 + 166385x^4 + 74176x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			441.5
Root			$-1.77959i$ of defining polynomial
Character	$\chi$	$=$	1870.441
Dual form			1870.2.c.e.441.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.77959i q^{3} +1.00000 q^{4} -1.00000i q^{5} +1.77959i q^{6} +3.32458i q^{7} -1.00000 q^{8} -0.166944 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.77959i q^{3} +1.00000 q^{4} -1.00000i q^{5} +1.77959i q^{6} +3.32458i q^{7} -1.00000 q^{8} -0.166944 q^{9} +1.00000i q^{10} +1.00000i q^{11} -1.77959i q^{12} +5.47357 q^{13} -3.32458i q^{14} -1.77959 q^{15} +1.00000 q^{16} +(-1.81817 + 3.70057i) q^{17} +0.166944 q^{18} -7.50818 q^{19} -1.00000i q^{20} +5.91640 q^{21} -1.00000i q^{22} -0.835896i q^{23} +1.77959i q^{24} -1.00000 q^{25} -5.47357 q^{26} -5.04168i q^{27} +3.32458i q^{28} +10.7644i q^{29} +1.77959 q^{30} +4.18551i q^{31} -1.00000 q^{32} +1.77959 q^{33} +(1.81817 - 3.70057i) q^{34} +3.32458 q^{35} -0.166944 q^{36} +4.64051i q^{37} +7.50818 q^{38} -9.74071i q^{39} +1.00000i q^{40} -1.40761i q^{41} -5.91640 q^{42} -9.47161 q^{43} +1.00000i q^{44} +0.166944i q^{45} +0.835896i q^{46} -10.6872 q^{47} -1.77959i q^{48} -4.05286 q^{49} +1.00000 q^{50} +(6.58551 + 3.23561i) q^{51} +5.47357 q^{52} -5.74202 q^{53} +5.04168i q^{54} +1.00000 q^{55} -3.32458i q^{56} +13.3615i q^{57} -10.7644i q^{58} -12.2005 q^{59} -1.77959 q^{60} +15.1557i q^{61} -4.18551i q^{62} -0.555020i q^{63} +1.00000 q^{64} -5.47357i q^{65} -1.77959 q^{66} +14.2478 q^{67} +(-1.81817 + 3.70057i) q^{68} -1.48755 q^{69} -3.32458 q^{70} +7.30504i q^{71} +0.166944 q^{72} +8.61281i q^{73} -4.64051i q^{74} +1.77959i q^{75} -7.50818 q^{76} -3.32458 q^{77} +9.74071i q^{78} -8.22977i q^{79} -1.00000i q^{80} -9.47296 q^{81} +1.40761i q^{82} +4.64828 q^{83} +5.91640 q^{84} +(3.70057 + 1.81817i) q^{85} +9.47161 q^{86} +19.1563 q^{87} -1.00000i q^{88} -9.63322 q^{89} -0.166944i q^{90} +18.1973i q^{91} -0.835896i q^{92} +7.44849 q^{93} +10.6872 q^{94} +7.50818i q^{95} +1.77959i q^{96} -11.0058i q^{97} +4.05286 q^{98} -0.166944i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} - 18 q^{8} - 24 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 18 * q^4 - 18 * q^8 - 24 * q^9	$ 18 q - 18 q^{2} + 18 q^{4} - 18 q^{8} - 24 q^{9} + 10 q^{13} - 2 q^{15} + 18 q^{16} + 2 q^{17} + 24 q^{18} - 26 q^{19} + 24 q^{21} - 18 q^{25} - 10 q^{26} + 2 q^{30} - 18 q^{32} + 2 q^{33} - 2 q^{34} - 24 q^{36} + 26 q^{38} - 24 q^{42} - 4 q^{43} - 2 q^{47} - 30 q^{49} + 18 q^{50} + 14 q^{51} + 10 q^{52} - 42 q^{53} + 18 q^{55} - 26 q^{59} - 2 q^{60} + 18 q^{64} - 2 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} + 24 q^{72} - 26 q^{76} - 14 q^{81} - 4 q^{83} + 24 q^{84} + 6 q^{85} + 4 q^{86} - 78 q^{87} + 50 q^{89} - 58 q^{93} + 2 q^{94} + 30 q^{98}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 - 18 * q^8 - 24 * q^9 + 10 * q^13 - 2 * q^15 + 18 * q^16 + 2 * q^17 + 24 * q^18 - 26 * q^19 + 24 * q^21 - 18 * q^25 - 10 * q^26 + 2 * q^30 - 18 * q^32 + 2 * q^33 - 2 * q^34 - 24 * q^36 + 26 * q^38 - 24 * q^42 - 4 * q^43 - 2 * q^47 - 30 * q^49 + 18 * q^50 + 14 * q^51 + 10 * q^52 - 42 * q^53 + 18 * q^55 - 26 * q^59 - 2 * q^60 + 18 * q^64 - 2 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 + 24 * q^72 - 26 * q^76 - 14 * q^81 - 4 * q^83 + 24 * q^84 + 6 * q^85 + 4 * q^86 - 78 * q^87 + 50 * q^89 - 58 * q^93 + 2 * q^94 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1870\mathbb{Z}\right)^\times$.

$n$	$1431$	$1497$	$1531$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.77959i		−	1.02745i	−0.857956	−	0.513724i	$-0.828266\pi$
$3$		−	1.77959i		−	1.02745i	0.857956	−	0.513724i	$-0.171734\pi$
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$			1.77959i			0.726515i
$7$			3.32458i			1.25657i	0.777981	+	0.628287i	$0.216244\pi$
$7$			3.32458i			1.25657i	−0.777981	+	0.628287i	$0.783756\pi$
$8$	−1.00000			−0.353553
$9$	−0.166944			−0.0556480
$10$			1.00000i			0.316228i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$		−	1.77959i		−	0.513724i
$13$	5.47357			1.51809			0.759047	−	0.651035i	$-0.225665\pi$
$13$	5.47357			1.51809			0.759047	+	0.651035i	$0.225665\pi$
$14$		−	3.32458i		−	0.888532i
$15$	−1.77959			−0.459488
$16$	1.00000			0.250000
$17$	−1.81817	+	3.70057i	−0.440972	+	0.897521i
$17$	−1.81817	+	3.70057i	−0.440972	+	0.897521i
$18$	0.166944			0.0393491
$19$	−7.50818			−1.72250			−0.861248	−	0.508185i	$-0.830316\pi$
$19$	−7.50818			−1.72250			−0.861248	+	0.508185i	$0.830316\pi$
$20$		−	1.00000i		−	0.223607i
$21$	5.91640			1.29106
$22$		−	1.00000i		−	0.213201i
$23$		−	0.835896i		−	0.174296i	−0.996195	−	0.0871482i	$-0.972225\pi$
$23$		−	0.835896i		−	0.174296i	0.996195	−	0.0871482i	$-0.0277754\pi$
$24$			1.77959i			0.363257i
$25$	−1.00000			−0.200000
$26$	−5.47357			−1.07346
$27$		−	5.04168i		−	0.970272i
$28$			3.32458i			0.628287i
$29$			10.7644i			1.99890i	0.0331346	+	0.999451i	$0.489451\pi$
$29$			10.7644i			1.99890i	−0.0331346	+	0.999451i	$0.510549\pi$
$30$	1.77959			0.324907
$31$			4.18551i			0.751739i	0.926673	+	0.375869i	$0.122656\pi$
$31$			4.18551i			0.751739i	−0.926673	+	0.375869i	$0.877344\pi$
$32$	−1.00000			−0.176777
$33$	1.77959			0.309787
$34$	1.81817	−	3.70057i	0.311814	−	0.634643i
$35$	3.32458			0.561957
$36$	−0.166944			−0.0278240
$37$			4.64051i			0.762896i	0.924390	+	0.381448i	$0.124574\pi$
$37$			4.64051i			0.762896i	−0.924390	+	0.381448i	$0.875426\pi$
$38$	7.50818			1.21799
$39$		−	9.74071i		−	1.55976i
$40$			1.00000i			0.158114i
$41$		−	1.40761i		−	0.219832i	−0.993941	−	0.109916i	$-0.964942\pi$
$41$		−	1.40761i		−	0.219832i	0.993941	−	0.109916i	$-0.0350581\pi$
$42$	−5.91640			−0.912920
$43$	−9.47161			−1.44441			−0.722203	−	0.691681i	$-0.756870\pi$
$43$	−9.47161			−1.44441			−0.722203	+	0.691681i	$0.756870\pi$
$44$			1.00000i			0.150756i
$45$			0.166944i			0.0248866i
$46$			0.835896i			0.123246i
$47$	−10.6872			−1.55890			−0.779448	−	0.626467i	$-0.784500\pi$
$47$	−10.6872			−1.55890			−0.779448	+	0.626467i	$0.784500\pi$
$48$		−	1.77959i		−	0.256862i
$49$	−4.05286			−0.578980
$50$	1.00000			0.141421
$51$	6.58551	+	3.23561i	0.922155	+	0.453076i
$52$	5.47357			0.759047
$53$	−5.74202			−0.788727			−0.394363	−	0.918955i	$-0.629035\pi$
$53$	−5.74202			−0.788727			−0.394363	+	0.918955i	$0.629035\pi$
$54$			5.04168i			0.686086i
$55$	1.00000			0.134840
$56$		−	3.32458i		−	0.444266i
$57$			13.3615i			1.76977i
$58$		−	10.7644i		−	1.41344i
$59$	−12.2005			−1.58837			−0.794183	−	0.607679i	$-0.792101\pi$
$59$	−12.2005			−1.58837			−0.794183	+	0.607679i	$0.792101\pi$
$60$	−1.77959			−0.229744
$61$			15.1557i			1.94048i	0.242139	+	0.970241i	$0.422151\pi$
$61$			15.1557i			1.94048i	−0.242139	+	0.970241i	$0.577849\pi$
$62$		−	4.18551i		−	0.531560i
$63$		−	0.555020i		−	0.0699259i
$64$	1.00000			0.125000
$65$		−	5.47357i		−	0.678913i
$66$	−1.77959			−0.219053
$67$	14.2478			1.74065			0.870324	−	0.492480i	$-0.163909\pi$
$67$	14.2478			1.74065			0.870324	+	0.492480i	$0.163909\pi$
$68$	−1.81817	+	3.70057i	−0.220486	+	0.448760i
$69$	−1.48755			−0.179080
$70$	−3.32458			−0.397364
$71$			7.30504i			0.866948i	0.901166	+	0.433474i	$0.142712\pi$
$71$			7.30504i			0.866948i	−0.901166	+	0.433474i	$0.857288\pi$
$72$	0.166944			0.0196746
$73$			8.61281i			1.00805i	0.863688	+	0.504027i	$0.168149\pi$
$73$			8.61281i			1.00805i	−0.863688	+	0.504027i	$0.831851\pi$
$74$		−	4.64051i		−	0.539449i
$75$			1.77959i			0.205489i
$76$	−7.50818			−0.861248
$77$	−3.32458			−0.378872
$78$			9.74071i			1.10292i
$79$		−	8.22977i		−	0.925922i	−0.886379	−	0.462961i	$-0.846787\pi$
$79$		−	8.22977i		−	0.925922i	0.886379	−	0.462961i	$-0.153213\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−9.47296			−1.05255
$82$			1.40761i			0.155445i
$83$	4.64828			0.510215			0.255107	−	0.966913i	$-0.417889\pi$
$83$	4.64828			0.510215			0.255107	+	0.966913i	$0.417889\pi$
$84$	5.91640			0.645532
$85$	3.70057	+	1.81817i	0.401383	+	0.197209i
$86$	9.47161			1.02135
$87$	19.1563			2.05377
$88$		−	1.00000i		−	0.106600i
$89$	−9.63322			−1.02112			−0.510560	−	0.859842i	$-0.670562\pi$
$89$	−9.63322			−1.02112			−0.510560	+	0.859842i	$0.670562\pi$
$90$		−	0.166944i		−	0.0175975i
$91$			18.1973i			1.90760i
$92$		−	0.835896i		−	0.0871482i
$93$	7.44849			0.772372
$94$	10.6872			1.10231
$95$			7.50818i			0.770323i
$96$			1.77959i			0.181629i
$97$		−	11.0058i		−	1.11747i	−0.829348	−	0.558733i	$-0.811288\pi$
$97$		−	11.0058i		−	1.11747i	0.829348	−	0.558733i	$-0.188712\pi$
$98$	4.05286			0.409401
$99$		−	0.166944i		−	0.0167785i
$100$	−1.00000			−0.100000
$101$	1.18421			0.117833			0.0589164	−	0.998263i	$-0.481235\pi$
$101$	1.18421			0.117833			0.0589164	+	0.998263i	$0.481235\pi$
$102$	−6.58551	−	3.23561i	−0.652062	−	0.320373i
$103$	17.6949			1.74353			0.871763	−	0.489927i	$-0.162977\pi$
$103$	17.6949			1.74353			0.871763	+	0.489927i	$0.162977\pi$
$104$	−5.47357			−0.536728
$105$		−	5.91640i		−	0.577381i
$106$	5.74202			0.557714
$107$		−	10.3553i		−	1.00109i	−0.865711	−	0.500543i	$-0.833134\pi$
$107$		−	10.3553i		−	1.00109i	0.865711	−	0.500543i	$-0.166866\pi$
$108$		−	5.04168i		−	0.485136i
$109$			6.91977i			0.662794i	0.943491	+	0.331397i	$0.107520\pi$
$109$			6.91977i			0.662794i	−0.943491	+	0.331397i	$0.892480\pi$
$110$	−1.00000			−0.0953463
$111$	8.25821			0.783835
$112$			3.32458i			0.314144i
$113$		−	8.75281i		−	0.823396i	−0.911320	−	0.411698i	$-0.864936\pi$
$113$		−	8.75281i		−	0.823396i	0.911320	−	0.411698i	$-0.135064\pi$
$114$		−	13.3615i		−	1.25142i
$115$	−0.835896			−0.0779477
$116$			10.7644i			0.999451i
$117$	−0.913780			−0.0844790
$118$	12.2005			1.12314
$119$	−12.3029	−	6.04468i	−1.12780	−	0.554114i
$120$	1.77959			0.162454
$121$	−1.00000			−0.0909091
$122$		−	15.1557i		−	1.37213i
$123$	−2.50497			−0.225866
$124$			4.18551i			0.375869i
$125$			1.00000i			0.0894427i
$126$			0.555020i			0.0494451i
$127$	4.05185			0.359544			0.179772	−	0.983708i	$-0.442464\pi$
$127$	4.05185			0.359544			0.179772	+	0.983708i	$0.442464\pi$
$128$	−1.00000			−0.0883883
$129$			16.8556i			1.48405i
$130$			5.47357i			0.480064i
$131$		−	16.6451i		−	1.45429i	−0.686482	−	0.727146i	$-0.740846\pi$
$131$		−	16.6451i		−	1.45429i	0.686482	−	0.727146i	$-0.259154\pi$
$132$	1.77959			0.154894
$133$		−	24.9616i		−	2.16444i
$134$	−14.2478			−1.23082
$135$	−5.04168			−0.433919
$136$	1.81817	−	3.70057i	0.155907	−	0.317322i
$137$	10.0477			0.858436			0.429218	−	0.903201i	$-0.358789\pi$
$137$	10.0477			0.858436			0.429218	+	0.903201i	$0.358789\pi$
$138$	1.48755			0.126629
$139$			12.7318i			1.07990i	0.841698	+	0.539948i	$0.181556\pi$
$139$			12.7318i			1.07990i	−0.841698	+	0.539948i	$0.818444\pi$
$140$	3.32458			0.280979
$141$			19.0189i			1.60168i
$142$		−	7.30504i		−	0.613025i
$143$			5.47357i			0.457723i
$144$	−0.166944			−0.0139120
$145$	10.7644			0.893936
$146$		−	8.61281i		−	0.712801i
$147$			7.21243i			0.594871i
$148$			4.64051i			0.381448i
$149$	4.39110			0.359733			0.179867	−	0.983691i	$-0.442433\pi$
$149$	4.39110			0.359733			0.179867	+	0.983691i	$0.442433\pi$
$150$		−	1.77959i		−	0.145303i
$151$	3.97889			0.323798			0.161899	−	0.986807i	$-0.448238\pi$
$151$	3.97889			0.323798			0.161899	+	0.986807i	$0.448238\pi$
$152$	7.50818			0.608994
$153$	0.303534	−	0.617789i	0.0245392	−	0.0499453i
$154$	3.32458			0.267903
$155$	4.18551			0.336188
$156$		−	9.74071i		−	0.779881i
$157$	8.32426			0.664348			0.332174	−	0.943218i	$-0.392218\pi$
$157$	8.32426			0.664348			0.332174	+	0.943218i	$0.392218\pi$
$158$			8.22977i			0.654726i
$159$			10.2184i			0.810375i
$160$			1.00000i			0.0790569i
$161$	2.77901			0.219016
$162$	9.47296			0.744266
$163$		−	3.07901i		−	0.241167i	−0.992703	−	0.120583i	$-0.961523\pi$
$163$		−	3.07901i		−	0.241167i	0.992703	−	0.120583i	$-0.0384765\pi$
$164$		−	1.40761i		−	0.109916i
$165$		−	1.77959i		−	0.138541i
$166$	−4.64828			−0.360776
$167$		−	5.64428i		−	0.436767i	−0.975863	−	0.218384i	$-0.929922\pi$
$167$		−	5.64428i		−	0.436767i	0.975863	−	0.218384i	$-0.0700784\pi$
$168$	−5.91640			−0.456460
$169$	16.9599			1.30461
$170$	−3.70057	−	1.81817i	−0.283821	−	0.139448i
$171$	1.25345			0.0958535
$172$	−9.47161			−0.722203
$173$			10.1825i			0.774164i	0.922045	+	0.387082i	$0.126517\pi$
$173$			10.1825i			0.774164i	−0.922045	+	0.387082i	$0.873483\pi$
$174$	−19.1563			−1.45223
$175$		−	3.32458i		−	0.251315i
$176$			1.00000i			0.0753778i
$177$			21.7118i			1.63196i
$178$	9.63322			0.722040
$179$	13.1745			0.984706			0.492353	−	0.870396i	$-0.336137\pi$
$179$	13.1745			0.984706			0.492353	+	0.870396i	$0.336137\pi$
$180$			0.166944i			0.0124433i
$181$			10.8731i			0.808190i	0.914717	+	0.404095i	$0.132414\pi$
$181$			10.8731i			0.808190i	−0.914717	+	0.404095i	$0.867586\pi$
$182$		−	18.1973i		−	1.34888i
$183$	26.9709			1.99374
$184$			0.835896i			0.0616231i
$185$	4.64051			0.341177
$186$	−7.44849			−0.546150
$187$	−3.70057	−	1.81817i	−0.270613	−	0.132958i
$188$	−10.6872			−0.779448
$189$	16.7615			1.21922
$190$		−	7.50818i		−	0.544701i
$191$	12.7424			0.922009			0.461005	−	0.887398i	$-0.347489\pi$
$191$	12.7424			0.922009			0.461005	+	0.887398i	$0.347489\pi$
$192$		−	1.77959i		−	0.128431i
$193$		−	5.46753i		−	0.393562i	−0.980448	−	0.196781i	$-0.936951\pi$
$193$		−	5.46753i		−	0.393562i	0.980448	−	0.196781i	$-0.0630487\pi$
$194$			11.0058i			0.790168i
$195$	−9.74071			−0.697547
$196$	−4.05286			−0.289490
$197$		−	2.81411i		−	0.200497i	−0.994962	−	0.100249i	$-0.968036\pi$
$197$		−	2.81411i		−	0.200497i	0.994962	−	0.100249i	$-0.0319638\pi$
$198$			0.166944i			0.0118642i
$199$			7.32390i			0.519178i	0.965719	+	0.259589i	$0.0835870\pi$
$199$			7.32390i			0.519178i	−0.965719	+	0.259589i	$0.916413\pi$
$200$	1.00000			0.0707107
$201$		−	25.3553i		−	1.78842i
$202$	−1.18421			−0.0833204
$203$	−35.7872			−2.51177
$204$	6.58551	+	3.23561i	0.461078	+	0.226538i
$205$	−1.40761			−0.0983117
$206$	−17.6949			−1.23286
$207$			0.139548i			0.00969925i
$208$	5.47357			0.379524
$209$		−	7.50818i		−	0.519352i
$210$			5.91640i			0.408270i
$211$			22.1967i			1.52809i	0.645165	+	0.764043i	$0.276788\pi$
$211$			22.1967i			1.52809i	−0.645165	+	0.764043i	$0.723212\pi$
$212$	−5.74202			−0.394363
$213$	13.0000			0.890744
$214$			10.3553i			0.707875i
$215$			9.47161i			0.645958i
$216$			5.04168i			0.343043i
$217$	−13.9151			−0.944616
$218$		−	6.91977i		−	0.468666i
$219$	15.3273			1.03572
$220$	1.00000			0.0674200
$221$	−9.95190	+	20.2553i	−0.669438	+	1.36252i
$222$	−8.25821			−0.554255
$223$	20.3393			1.36202			0.681010	−	0.732275i	$-0.261541\pi$
$223$	20.3393			1.36202			0.681010	+	0.732275i	$0.261541\pi$
$224$		−	3.32458i		−	0.222133i
$225$	0.166944			0.0111296
$226$			8.75281i			0.582229i
$227$			7.45363i			0.494715i	0.968924	+	0.247357i	$0.0795622\pi$
$227$			7.45363i			0.494715i	−0.968924	+	0.247357i	$0.920438\pi$
$228$			13.3615i			0.884887i
$229$	−21.2141			−1.40186			−0.700932	−	0.713228i	$-0.747232\pi$
$229$	−21.2141			−1.40186			−0.700932	+	0.713228i	$0.747232\pi$
$230$	0.835896			0.0551174
$231$			5.91640i			0.389271i
$232$		−	10.7644i		−	0.706719i
$233$		−	0.998709i		−	0.0654276i	−0.999465	−	0.0327138i	$-0.989585\pi$
$233$		−	0.998709i		−	0.0654276i	0.999465	−	0.0327138i	$-0.0104150\pi$
$234$	0.913780			0.0597357
$235$			10.6872i			0.697159i
$236$	−12.2005			−0.794183
$237$	−14.6456			−0.951336
$238$	12.3029	+	6.04468i	0.797476	+	0.391818i
$239$	2.09382			0.135438			0.0677190	−	0.997704i	$-0.478428\pi$
$239$	2.09382			0.135438			0.0677190	+	0.997704i	$0.478428\pi$
$240$	−1.77959			−0.114872
$241$			9.44404i			0.608344i	0.952617	+	0.304172i	$0.0983797\pi$
$241$			9.44404i			0.608344i	−0.952617	+	0.304172i	$0.901620\pi$
$242$	1.00000			0.0642824
$243$			1.73296i			0.111169i
$244$			15.1557i			0.970241i
$245$			4.05286i			0.258928i
$246$	2.50497			0.159711
$247$	−41.0966			−2.61491
$248$		−	4.18551i		−	0.265780i
$249$		−	8.27203i		−	0.524219i
$250$		−	1.00000i		−	0.0632456i
$251$	−14.4312			−0.910887			−0.455444	−	0.890265i	$-0.650519\pi$
$251$	−14.4312			−0.910887			−0.455444	+	0.890265i	$0.650519\pi$
$252$		−	0.555020i		−	0.0349630i
$253$	0.835896			0.0525523
$254$	−4.05185			−0.254236
$255$	3.23561	−	6.58551i	0.202622	−	0.412400i
$256$	1.00000			0.0625000
$257$	−14.8694			−0.927528			−0.463764	−	0.885959i	$-0.653501\pi$
$257$	−14.8694			−0.927528			−0.463764	+	0.885959i	$0.653501\pi$
$258$		−	16.8556i		−	1.04938i
$259$	−15.4278			−0.958635
$260$		−	5.47357i		−	0.339456i
$261$		−	1.79706i		−	0.111235i
$262$			16.6451i			1.02834i
$263$	16.2563			1.00241			0.501204	−	0.865329i	$-0.332891\pi$
$263$	16.2563			1.00241			0.501204	+	0.865329i	$0.332891\pi$
$264$	−1.77959			−0.109526
$265$			5.74202i			0.352729i
$266$			24.9616i			1.53049i
$267$			17.1432i			1.04915i
$268$	14.2478			0.870324
$269$			25.7418i			1.56951i	0.619809	+	0.784753i	$0.287210\pi$
$269$			25.7418i			1.56951i	−0.619809	+	0.784753i	$0.712790\pi$
$270$	5.04168			0.306827
$271$	−3.50039			−0.212633			−0.106317	−	0.994332i	$-0.533906\pi$
$271$	−3.50039			−0.212633			−0.106317	+	0.994332i	$0.533906\pi$
$272$	−1.81817	+	3.70057i	−0.110243	+	0.224380i
$273$	32.3838			1.95996
$274$	−10.0477			−0.607006
$275$		−	1.00000i		−	0.0603023i
$276$	−1.48755			−0.0895402
$277$		−	3.99236i		−	0.239878i	−0.992781	−	0.119939i	$-0.961730\pi$
$277$		−	3.99236i		−	0.239878i	0.992781	−	0.119939i	$-0.0382698\pi$
$278$		−	12.7318i		−	0.763602i
$279$		−	0.698746i		−	0.0418328i
$280$	−3.32458			−0.198682
$281$	20.3786			1.21569			0.607843	−	0.794057i	$-0.292035\pi$
$281$	20.3786			1.21569			0.607843	+	0.794057i	$0.292035\pi$
$282$		−	19.0189i		−	1.13256i
$283$		−	10.9563i		−	0.651284i	−0.945493	−	0.325642i	$-0.894420\pi$
$283$		−	10.9563i		−	0.651284i	0.945493	−	0.325642i	$-0.105580\pi$
$284$			7.30504i			0.433474i
$285$	13.3615			0.791467
$286$		−	5.47357i		−	0.323659i
$287$	4.67972			0.276235
$288$	0.166944			0.00983728
$289$	−10.3885	−	13.4566i	−0.611087	−	0.791563i
$290$	−10.7644			−0.632108
$291$	−19.5858			−1.14814
$292$			8.61281i			0.504027i
$293$	2.40762			0.140655			0.0703274	−	0.997524i	$-0.477596\pi$
$293$	2.40762			0.140655			0.0703274	+	0.997524i	$0.477596\pi$
$294$		−	7.21243i		−	0.420638i
$295$			12.2005i			0.710339i
$296$		−	4.64051i		−	0.269724i
$297$	5.04168			0.292548
$298$	−4.39110			−0.254370
$299$		−	4.57533i		−	0.264598i
$300$			1.77959i			0.102745i
$301$		−	31.4892i		−	1.81500i
$302$	−3.97889			−0.228960
$303$		−	2.10740i		−	0.121067i
$304$	−7.50818			−0.430624
$305$	15.1557			0.867810
$306$	−0.303534	+	0.617789i	−0.0173519	+	0.0353166i
$307$	−16.1702			−0.922882			−0.461441	−	0.887171i	$-0.652667\pi$
$307$	−16.1702			−0.922882			−0.461441	+	0.887171i	$0.652667\pi$
$308$	−3.32458			−0.189436
$309$		−	31.4896i		−	1.79138i
$310$	−4.18551			−0.237721
$311$		−	21.3833i		−	1.21253i	−0.795261	−	0.606267i	$-0.792666\pi$
$311$		−	21.3833i		−	1.21253i	0.795261	−	0.606267i	$-0.207334\pi$
$312$			9.74071i			0.551459i
$313$		−	8.61203i		−	0.486781i	−0.969928	−	0.243390i	$-0.921740\pi$
$313$		−	8.61203i		−	0.486781i	0.969928	−	0.243390i	$-0.0782596\pi$
$314$	−8.32426			−0.469765
$315$	−0.555020			−0.0312718
$316$		−	8.22977i		−	0.462961i
$317$			12.2816i			0.689804i	0.938639	+	0.344902i	$0.112088\pi$
$317$			12.2816i			0.689804i	−0.938639	+	0.344902i	$0.887912\pi$
$318$		−	10.2184i		−	0.573022i
$319$	−10.7644			−0.602692
$320$		−	1.00000i		−	0.0559017i
$321$	−18.4282			−1.02856
$322$	−2.77901			−0.154868
$323$	13.6512	−	27.7846i	0.759573	−	1.54598i
$324$	−9.47296			−0.526276
$325$	−5.47357			−0.303619
$326$			3.07901i			0.170531i
$327$	12.3144			0.680986
$328$			1.40761i			0.0777223i
$329$		−	35.5307i		−	1.95887i
$330$			1.77959i			0.0979633i
$331$	−21.8693			−1.20205			−0.601024	−	0.799231i	$-0.705240\pi$
$331$	−21.8693			−1.20205			−0.601024	+	0.799231i	$0.705240\pi$
$332$	4.64828			0.255107
$333$		−	0.774706i		−	0.0424536i
$334$			5.64428i			0.308841i
$335$		−	14.2478i		−	0.778441i
$336$	5.91640			0.322766
$337$		−	24.1584i		−	1.31599i	−0.753021	−	0.657996i	$-0.771404\pi$
$337$		−	24.1584i		−	1.31599i	0.753021	−	0.657996i	$-0.228596\pi$
$338$	−16.9599			−0.922500
$339$	−15.5764			−0.845996
$340$	3.70057	+	1.81817i	0.200692	+	0.0986044i
$341$	−4.18551			−0.226658
$342$	−1.25345			−0.0677787
$343$			9.79802i			0.529043i
$344$	9.47161			0.510675
$345$			1.48755i			0.0800872i
$346$		−	10.1825i		−	0.547417i
$347$		−	28.9128i		−	1.55212i	−0.630660	−	0.776059i	$-0.717216\pi$
$347$		−	28.9128i		−	1.55212i	0.630660	−	0.776059i	$-0.282784\pi$
$348$	19.1563			1.02688
$349$	14.3251			0.766807			0.383403	−	0.923581i	$-0.374752\pi$
$349$	14.3251			0.766807			0.383403	+	0.923581i	$0.374752\pi$
$350$			3.32458i			0.177706i
$351$		−	27.5960i		−	1.47296i
$352$		−	1.00000i		−	0.0533002i
$353$	9.08538			0.483566			0.241783	−	0.970330i	$-0.422268\pi$
$353$	9.08538			0.483566			0.241783	+	0.970330i	$0.422268\pi$
$354$		−	21.7118i		−	1.15397i
$355$	7.30504			0.387711
$356$	−9.63322			−0.510560
$357$	−10.7571	+	21.8941i	−0.569323	+	1.15876i
$358$	−13.1745			−0.696292
$359$	−31.8408			−1.68049			−0.840247	−	0.542203i	$-0.817590\pi$
$359$	−31.8408			−1.68049			−0.840247	+	0.542203i	$0.817590\pi$
$360$		−	0.166944i		−	0.00879873i
$361$	37.3728			1.96699
$362$		−	10.8731i		−	0.571477i
$363$			1.77959i			0.0934043i
$364$			18.1973i			0.953800i
$365$	8.61281			0.450815
$366$	−26.9709			−1.40979
$367$			2.14823i			0.112137i	0.998427	+	0.0560685i	$0.0178565\pi$
$367$			2.14823i			0.112137i	−0.998427	+	0.0560685i	$0.982143\pi$
$368$		−	0.835896i		−	0.0435741i
$369$			0.234992i			0.0122332i
$370$	−4.64051			−0.241249
$371$		−	19.0898i		−	0.991094i
$372$	7.44849			0.386186
$373$	15.9012			0.823332			0.411666	−	0.911335i	$-0.364947\pi$
$373$	15.9012			0.823332			0.411666	+	0.911335i	$0.364947\pi$
$374$	3.70057	+	1.81817i	0.191352	+	0.0940156i
$375$	1.77959			0.0918977
$376$	10.6872			0.551153
$377$			58.9198i			3.03452i
$378$	−16.7615			−0.862118
$379$			20.7035i			1.06347i	0.846912	+	0.531734i	$0.178459\pi$
$379$			20.7035i			1.06347i	−0.846912	+	0.531734i	$0.821541\pi$
$380$			7.50818i			0.385162i
$381$		−	7.21064i		−	0.369413i
$382$	−12.7424			−0.651959
$383$	5.25406			0.268470			0.134235	−	0.990950i	$-0.457142\pi$
$383$	5.25406			0.268470			0.134235	+	0.990950i	$0.457142\pi$
$384$			1.77959i			0.0908144i
$385$			3.32458i			0.169436i
$386$			5.46753i			0.278290i
$387$	1.58123			0.0803784
$388$		−	11.0058i		−	0.558733i
$389$	11.6382			0.590079			0.295040	−	0.955485i	$-0.404667\pi$
$389$	11.6382			0.590079			0.295040	+	0.955485i	$0.404667\pi$
$390$	9.74071			0.493240
$391$	3.09329	+	1.51981i	0.156435	+	0.0768599i
$392$	4.05286			0.204700
$393$	−29.6215			−1.49421
$394$			2.81411i			0.141773i
$395$	−8.22977			−0.414085
$396$		−	0.166944i		−	0.00838926i
$397$			25.9488i			1.30233i	0.758936	+	0.651166i	$0.225720\pi$
$397$			25.9488i			1.30233i	−0.758936	+	0.651166i	$0.774280\pi$
$398$		−	7.32390i		−	0.367114i
$399$	−44.4214			−2.22385
$400$	−1.00000			−0.0500000
$401$		−	0.218956i		−	0.0109342i	−0.999985	−	0.00546708i	$-0.998260\pi$
$401$		−	0.218956i		−	0.0109342i	0.999985	−	0.00546708i	$-0.00174024\pi$
$402$			25.3553i			1.26461i
$403$			22.9096i			1.14121i
$404$	1.18421			0.0589164
$405$			9.47296i			0.470715i
$406$	35.7872			1.77609
$407$	−4.64051			−0.230022
$408$	−6.58551	−	3.23561i	−0.326031	−	0.160186i
$409$	−11.1599			−0.551819			−0.275910	−	0.961184i	$-0.588979\pi$
$409$	−11.1599			−0.551819			−0.275910	+	0.961184i	$0.588979\pi$
$410$	1.40761			0.0695169
$411$		−	17.8809i		−	0.881998i
$412$	17.6949			0.871763
$413$		−	40.5615i		−	1.99590i
$414$		−	0.139548i		−	0.00685841i
$415$		−	4.64828i		−	0.228175i
$416$	−5.47357			−0.268364
$417$	22.6574			1.10954
$418$			7.50818i			0.367237i
$419$		−	12.0487i		−	0.588617i	−0.955710	−	0.294309i	$-0.904911\pi$
$419$		−	12.0487i		−	0.588617i	0.955710	−	0.294309i	$-0.0950893\pi$
$420$		−	5.91640i		−	0.288691i
$421$	−17.5463			−0.855155			−0.427578	−	0.903979i	$-0.640633\pi$
$421$	−17.5463			−0.855155			−0.427578	+	0.903979i	$0.640633\pi$
$422$		−	22.1967i		−	1.08052i
$423$	1.78417			0.0867495
$424$	5.74202			0.278857
$425$	1.81817	−	3.70057i	0.0881944	−	0.179504i
$426$	−13.0000			−0.629851
$427$	−50.3863			−2.43836
$428$		−	10.3553i		−	0.500543i
$429$	9.74071			0.470286
$430$		−	9.47161i		−	0.456761i
$431$		−	9.15092i		−	0.440784i	−0.975411	−	0.220392i	$-0.929266\pi$
$431$		−	9.15092i		−	0.440784i	0.975411	−	0.220392i	$-0.0707337\pi$
$432$		−	5.04168i		−	0.242568i
$433$	27.9304			1.34225			0.671124	−	0.741345i	$-0.265812\pi$
$433$	27.9304			1.34225			0.671124	+	0.741345i	$0.265812\pi$
$434$	13.9151			0.667944
$435$		−	19.1563i		−	0.918472i
$436$			6.91977i			0.331397i
$437$			6.27606i			0.300225i
$438$	−15.3273			−0.732366
$439$		−	3.57929i		−	0.170830i	−0.996345	−	0.0854151i	$-0.972778\pi$
$439$		−	3.57929i		−	0.170830i	0.996345	−	0.0854151i	$-0.0272217\pi$
$440$	−1.00000			−0.0476731
$441$	0.676601			0.0322191
$442$	9.95190	−	20.2553i	0.473364	−	0.963448i
$443$	−35.7230			−1.69725			−0.848626	−	0.528994i	$-0.822570\pi$
$443$	−35.7230			−1.69725			−0.848626	+	0.528994i	$0.822570\pi$
$444$	8.25821			0.391917
$445$			9.63322i			0.456658i
$446$	−20.3393			−0.963093
$447$		−	7.81437i		−	0.369607i
$448$			3.32458i			0.157072i
$449$		−	20.5509i		−	0.969857i	−0.874554	−	0.484928i	$-0.838846\pi$
$449$		−	20.5509i		−	0.969857i	0.874554	−	0.484928i	$-0.161154\pi$
$450$	−0.166944			−0.00786982
$451$	1.40761			0.0662818
$452$		−	8.75281i		−	0.411698i
$453$		−	7.08080i		−	0.332685i
$454$		−	7.45363i		−	0.349816i
$455$	18.1973			0.853104
$456$		−	13.3615i		−	0.625709i
$457$	−4.94779			−0.231448			−0.115724	−	0.993281i	$-0.536919\pi$
$457$	−4.94779			−0.231448			−0.115724	+	0.993281i	$0.536919\pi$
$458$	21.2141			0.991268
$459$	18.6571	+	9.16666i	0.870839	+	0.427863i
$460$	−0.835896			−0.0389739
$461$	26.6952			1.24332			0.621660	−	0.783288i	$-0.286459\pi$
$461$	26.6952			1.24332			0.621660	+	0.783288i	$0.286459\pi$
$462$		−	5.91640i		−	0.275256i
$463$	18.8198			0.874629			0.437314	−	0.899309i	$-0.355930\pi$
$463$	18.8198			0.874629			0.437314	+	0.899309i	$0.355930\pi$
$464$			10.7644i			0.499725i
$465$		−	7.44849i		−	0.345415i
$466$			0.998709i			0.0462643i
$467$	−14.7818			−0.684021			−0.342011	−	0.939696i	$-0.611108\pi$
$467$	−14.7818			−0.684021			−0.342011	+	0.939696i	$0.611108\pi$
$468$	−0.913780			−0.0422395
$469$			47.3681i			2.18725i
$470$		−	10.6872i		−	0.492966i
$471$		−	14.8138i		−	0.682583i
$472$	12.2005			0.561572
$473$		−	9.47161i		−	0.435505i
$474$	14.6456			0.672696
$475$	7.50818			0.344499
$476$	−12.3029	−	6.04468i	−0.563901	−	0.277057i
$477$	0.958596			0.0438911
$478$	−2.09382			−0.0957691
$479$			0.103077i			0.00470973i	0.999997	+	0.00235486i	$0.000749577\pi$
$479$			0.103077i			0.00470973i	−0.999997	+	0.00235486i	$0.999250\pi$
$480$	1.77959			0.0812268
$481$			25.4002i			1.15815i
$482$		−	9.44404i		−	0.430164i
$483$		−	4.94550i		−	0.225028i
$484$	−1.00000			−0.0454545
$485$	−11.0058			−0.499746
$486$		−	1.73296i		−	0.0786085i
$487$		−	32.9639i		−	1.49374i	−0.664971	−	0.746869i	$-0.731556\pi$
$487$		−	32.9639i		−	1.49374i	0.664971	−	0.746869i	$-0.268444\pi$
$488$		−	15.1557i		−	0.686064i
$489$	−5.47938			−0.247786
$490$		−	4.05286i		−	0.183089i
$491$	28.7913			1.29933			0.649666	−	0.760220i	$-0.274909\pi$
$491$	28.7913			1.29933			0.649666	+	0.760220i	$0.274909\pi$
$492$	−2.50497			−0.112933
$493$	−39.8345	−	19.5716i	−1.79406	−	0.881460i
$494$	41.0966			1.84902
$495$	−0.166944			−0.00750358
$496$			4.18551i			0.187935i
$497$	−24.2862			−1.08939
$498$			8.27203i			0.370678i
$499$			10.7662i			0.481960i	0.970530	+	0.240980i	$0.0774689\pi$
$499$			10.7662i			0.481960i	−0.970530	+	0.240980i	$0.922531\pi$
$500$			1.00000i			0.0447214i
$501$	−10.0445			−0.448755
$502$	14.4312			0.644095
$503$			6.02982i			0.268856i	0.990923	+	0.134428i	$0.0429197\pi$
$503$			6.02982i			0.268856i	−0.990923	+	0.134428i	$0.957080\pi$
$504$			0.555020i			0.0247225i
$505$		−	1.18421i		−	0.0526965i
$506$	−0.835896			−0.0371601
$507$		−	30.1818i		−	1.34042i
$508$	4.05185			0.179772
$509$	−22.5438			−0.999236			−0.499618	−	0.866246i	$-0.666526\pi$
$509$	−22.5438			−0.999236			−0.499618	+	0.866246i	$0.666526\pi$
$510$	−3.23561	+	6.58551i	−0.143275	+	0.291611i
$511$	−28.6340			−1.26669
$512$	−1.00000			−0.0441942
$513$			37.8539i			1.67129i
$514$	14.8694			0.655861
$515$		−	17.6949i		−	0.779729i
$516$			16.8556i			0.742026i
$517$		−	10.6872i		−	0.470025i
$518$	15.4278			0.677857
$519$	18.1208			0.795413
$520$			5.47357i			0.240032i
$521$			36.1702i			1.58465i	0.610101	+	0.792324i	$0.291129\pi$
$521$			36.1702i			1.58465i	−0.610101	+	0.792324i	$0.708871\pi$
$522$			1.79706i			0.0786550i
$523$	9.06328			0.396310			0.198155	−	0.980171i	$-0.436505\pi$
$523$	9.06328			0.396310			0.198155	+	0.980171i	$0.436505\pi$
$524$		−	16.6451i		−	0.727146i
$525$	−5.91640			−0.258213
$526$	−16.2563			−0.708809
$527$	−15.4888	−	7.60998i	−0.674701	−	0.331496i
$528$	1.77959			0.0774468
$529$	22.3013			0.969621
$530$		−	5.74202i		−	0.249417i
$531$	2.03680			0.0883894
$532$		−	24.9616i		−	1.08222i
$533$		−	7.70465i		−	0.333725i
$534$		−	17.1432i		−	0.741859i
$535$	−10.3553			−0.447700
$536$	−14.2478			−0.615412
$537$		−	23.4452i		−	1.01173i
$538$		−	25.7418i		−	1.10981i
$539$		−	4.05286i		−	0.174569i
$540$	−5.04168			−0.216959
$541$		−	30.9190i		−	1.32931i	−0.747150	−	0.664655i	$-0.768578\pi$
$541$		−	30.9190i		−	1.32931i	0.747150	−	0.664655i	$-0.231422\pi$
$542$	3.50039			0.150355
$543$	19.3497			0.830373
$544$	1.81817	−	3.70057i	0.0779536	−	0.158661i
$545$	6.91977			0.296410
$546$	−32.3838			−1.38590
$547$			44.0250i			1.88237i	0.337890	+	0.941186i	$0.390287\pi$
$547$			44.0250i			1.88237i	−0.337890	+	0.941186i	$0.609713\pi$
$548$	10.0477			0.429218
$549$		−	2.53015i		−	0.107984i
$550$			1.00000i			0.0426401i
$551$		−	80.8212i		−	3.44310i
$552$	1.48755			0.0633145
$553$	27.3606			1.16349
$554$			3.99236i			0.169619i
$555$		−	8.25821i		−	0.350542i
$556$			12.7318i			0.539948i
$557$	−21.0873			−0.893498			−0.446749	−	0.894659i	$-0.647418\pi$
$557$	−21.0873			−0.893498			−0.446749	+	0.894659i	$0.647418\pi$
$558$			0.698746i			0.0295803i
$559$	−51.8435			−2.19275
$560$	3.32458			0.140489
$561$	−3.23561	+	6.58551i	−0.136607	+	0.278040i
$562$	−20.3786			−0.859620
$563$	−35.4483			−1.49397			−0.746985	−	0.664841i	$-0.768499\pi$
$563$	−35.4483			−1.49397			−0.746985	+	0.664841i	$0.768499\pi$
$564$			19.0189i			0.800841i
$565$	−8.75281			−0.368234
$566$			10.9563i			0.460528i
$567$		−	31.4937i		−	1.32261i
$568$		−	7.30504i		−	0.306513i
$569$	33.2461			1.39375			0.696876	−	0.717192i	$-0.254573\pi$
$569$	33.2461			1.39375			0.696876	+	0.717192i	$0.254573\pi$
$570$	−13.3615			−0.559651
$571$		−	12.5548i		−	0.525403i	−0.964877	−	0.262702i	$-0.915387\pi$
$571$		−	12.5548i		−	0.525403i	0.964877	−	0.262702i	$-0.0846134\pi$
$572$			5.47357i			0.228861i
$573$		−	22.6763i		−	0.947316i
$574$	−4.67972			−0.195328
$575$			0.835896i			0.0348593i
$576$	−0.166944			−0.00695601
$577$	28.1155			1.17046			0.585231	−	0.810867i	$-0.301004\pi$
$577$	28.1155			1.17046			0.585231	+	0.810867i	$0.301004\pi$
$578$	10.3885	+	13.4566i	0.432104	+	0.559720i
$579$	−9.72997			−0.404364
$580$	10.7644			0.446968
$581$			15.4536i			0.641123i
$582$	19.5858			0.811856
$583$		−	5.74202i		−	0.237810i
$584$		−	8.61281i		−	0.356401i
$585$			0.913780i			0.0377802i
$586$	−2.40762			−0.0994580
$587$	32.1719			1.32788			0.663938	−	0.747788i	$-0.268884\pi$
$587$	32.1719			1.32788			0.663938	+	0.747788i	$0.268884\pi$
$588$			7.21243i			0.297436i
$589$		−	31.4255i		−	1.29487i
$590$		−	12.2005i		−	0.502285i
$591$	−5.00797			−0.206000
$592$			4.64051i			0.190724i
$593$	−7.08261			−0.290848			−0.145424	−	0.989369i	$-0.546455\pi$
$593$	−7.08261			−0.290848			−0.145424	+	0.989369i	$0.546455\pi$
$594$	−5.04168			−0.206863
$595$	−6.04468	+	12.3029i	−0.247808	+	0.504368i
$596$	4.39110			0.179867
$597$	13.0335			0.533428
$598$			4.57533i			0.187099i
$599$	31.7101			1.29564			0.647819	−	0.761794i	$-0.275681\pi$
$599$	31.7101			1.29564			0.647819	+	0.761794i	$0.275681\pi$
$600$		−	1.77959i		−	0.0726515i
$601$		−	30.2937i		−	1.23571i	−0.786293	−	0.617854i	$-0.788002\pi$
$601$		−	30.2937i		−	1.23571i	0.786293	−	0.617854i	$-0.211998\pi$
$602$			31.4892i			1.28340i
$603$	−2.37859			−0.0968636
$604$	3.97889			0.161899
$605$			1.00000i			0.0406558i
$606$			2.10740i			0.0856074i
$607$			18.4791i			0.750044i	0.927016	+	0.375022i	$0.122365\pi$
$607$			18.4791i			0.750044i	−0.927016	+	0.375022i	$0.877635\pi$
$608$	7.50818			0.304497
$609$			63.6866i			2.58071i
$610$	−15.1557			−0.613635
$611$	−58.4974			−2.36655
$612$	0.303534	−	0.617789i	0.0122696	−	0.0249726i
$613$	−10.1130			−0.408460			−0.204230	−	0.978923i	$-0.565469\pi$
$613$	−10.1130			−0.408460			−0.204230	+	0.978923i	$0.565469\pi$
$614$	16.1702			0.652576
$615$			2.50497i			0.101010i
$616$	3.32458			0.133951
$617$			14.8518i			0.597911i	0.954267	+	0.298956i	$0.0966382\pi$
$617$			14.8518i			0.597911i	−0.954267	+	0.298956i	$0.903362\pi$
$618$			31.4896i			1.26670i
$619$			4.33759i			0.174342i	0.996193	+	0.0871712i	$0.0277827\pi$
$619$			4.33759i			0.174342i	−0.996193	+	0.0871712i	$0.972217\pi$
$620$	4.18551			0.168094
$621$	−4.21432			−0.169115
$622$			21.3833i			0.857391i
$623$		−	32.0265i		−	1.28311i
$624$		−	9.74071i		−	0.389941i
$625$	1.00000			0.0400000
$626$			8.61203i			0.344206i
$627$	−13.3615			−0.533607
$628$	8.32426			0.332174
$629$	−17.1726	−	8.43726i	−0.684715	−	0.336416i
$630$	0.555020			0.0221125
$631$	−43.6698			−1.73847			−0.869233	−	0.494403i	$-0.835387\pi$
$631$	−43.6698			−1.73847			−0.869233	+	0.494403i	$0.835387\pi$
$632$			8.22977i			0.327363i
$633$	39.5011			1.57003
$634$		−	12.2816i		−	0.487765i
$635$		−	4.05185i		−	0.160793i
$636$			10.2184i			0.405188i
$637$	−22.1836			−0.878946
$638$	10.7644			0.426167
$639$		−	1.21953i		−	0.0482440i
$640$			1.00000i			0.0395285i
$641$			10.4379i			0.412274i	0.978523	+	0.206137i	$0.0660892\pi$
$641$			10.4379i			0.412274i	−0.978523	+	0.206137i	$0.933911\pi$
$642$	18.4282			0.727304
$643$			33.2027i			1.30939i	0.755894	+	0.654694i	$0.227203\pi$
$643$			33.2027i			1.30939i	−0.755894	+	0.654694i	$0.772797\pi$
$644$	2.77901			0.109508
$645$	16.8556			0.663688
$646$	−13.6512	+	27.7846i	−0.537099	+	1.09317i
$647$	6.50458			0.255721			0.127861	−	0.991792i	$-0.459189\pi$
$647$	6.50458			0.255721			0.127861	+	0.991792i	$0.459189\pi$
$648$	9.47296			0.372133
$649$		−	12.2005i		−	0.478910i
$650$	5.47357			0.214691
$651$			24.7631i			0.970543i
$652$		−	3.07901i		−	0.120583i
$653$		−	17.7642i		−	0.695167i	−0.937649	−	0.347584i	$-0.887002\pi$
$653$		−	17.7642i		−	0.695167i	0.937649	−	0.347584i	$-0.112998\pi$
$654$	−12.3144			−0.481529
$655$	−16.6451			−0.650379
$656$		−	1.40761i		−	0.0549579i
$657$		−	1.43786i		−	0.0560962i
$658$			35.5307i			1.38513i
$659$	−10.5590			−0.411321			−0.205661	−	0.978623i	$-0.565934\pi$
$659$	−10.5590			−0.411321			−0.205661	+	0.978623i	$0.565934\pi$
$660$		−	1.77959i		−	0.0692705i
$661$	28.4203			1.10542			0.552710	−	0.833374i	$-0.313594\pi$
$661$	28.4203			1.10542			0.552710	+	0.833374i	$0.313594\pi$
$662$	21.8693			0.849976
$663$	36.0462	+	17.7103i	1.39992	+	0.687812i
$664$	−4.64828			−0.180388
$665$	−24.9616			−0.967969
$666$			0.774706i			0.0300193i
$667$	8.99793			0.348401
$668$		−	5.64428i		−	0.218384i
$669$		−	36.1956i		−	1.39940i
$670$			14.2478i			0.550441i
$671$	−15.1557			−0.585078
$672$	−5.91640			−0.228230
$673$		−	13.6160i		−	0.524860i	−0.964951	−	0.262430i	$-0.915476\pi$
$673$		−	13.6160i		−	0.524860i	0.964951	−	0.262430i	$-0.0845239\pi$
$674$			24.1584i			0.930547i
$675$			5.04168i			0.194054i
$676$	16.9599			0.652306
$677$			7.50798i			0.288555i	0.989537	+	0.144278i	$0.0460858\pi$
$677$			7.50798i			0.288555i	−0.989537	+	0.144278i	$0.953914\pi$
$678$	15.5764			0.598209
$679$	36.5896			1.40418
$680$	−3.70057	−	1.81817i	−0.141910	−	0.0697238i
$681$	13.2644			0.508293
$682$	4.18551			0.160271
$683$			35.2104i			1.34729i	0.739056	+	0.673644i	$0.235272\pi$
$683$			35.2104i			1.34729i	−0.739056	+	0.673644i	$0.764728\pi$
$684$	1.25345			0.0479268
$685$		−	10.0477i		−	0.383904i
$686$		−	9.79802i		−	0.374090i
$687$			37.7523i			1.44034i
$688$	−9.47161			−0.361102
$689$	−31.4293			−1.19736
$690$		−	1.48755i		−	0.0566302i
$691$		−	32.3520i		−	1.23073i	−0.788243	−	0.615364i	$-0.789009\pi$
$691$		−	32.3520i		−	1.23073i	0.788243	−	0.615364i	$-0.210991\pi$
$692$			10.1825i			0.387082i
$693$	0.555020			0.0210835
$694$			28.9128i			1.09751i
$695$	12.7318			0.482944
$696$	−19.1563			−0.726116
$697$	5.20896	+	2.55928i	0.197304	+	0.0969397i
$698$	−14.3251			−0.542214
$699$	−1.77729			−0.0672234
$700$		−	3.32458i		−	0.125657i
$701$	−31.7748			−1.20012			−0.600059	−	0.799955i	$-0.704856\pi$
$701$	−31.7748			−1.20012			−0.600059	+	0.799955i	$0.704856\pi$
$702$			27.5960i			1.04154i
$703$		−	34.8418i		−	1.31408i
$704$			1.00000i			0.0376889i
$705$	19.0189			0.716294
$706$	−9.08538			−0.341933
$707$			3.93699i			0.148066i
$708$			21.7118i			0.815981i
$709$		−	35.8621i		−	1.34683i	−0.739265	−	0.673415i	$-0.764827\pi$
$709$		−	35.8621i		−	1.34683i	0.739265	−	0.673415i	$-0.235173\pi$
$710$	−7.30504			−0.274153
$711$			1.37391i			0.0515257i
$712$	9.63322			0.361020
$713$	3.49865			0.131025
$714$	10.7571	−	21.8941i	0.402572	−	0.819365i
$715$	5.47357			0.204700
$716$	13.1745			0.492353
$717$		−	3.72614i		−	0.139155i
$718$	31.8408			1.18829
$719$			4.90770i			0.183026i	0.995804	+	0.0915131i	$0.0291703\pi$
$719$			4.90770i			0.183026i	−0.995804	+	0.0915131i	$0.970830\pi$
$720$			0.166944i			0.00622164i
$721$			58.8281i			2.19087i
$722$	−37.3728			−1.39087
$723$	16.8065			0.625041
$724$			10.8731i			0.404095i
$725$		−	10.7644i		−	0.399780i
$726$		−	1.77959i		−	0.0660468i
$727$	−37.7730			−1.40092			−0.700461	−	0.713691i	$-0.747022\pi$
$727$	−37.7730			−1.40092			−0.700461	+	0.713691i	$0.747022\pi$
$728$		−	18.1973i		−	0.674438i
$729$	−25.3349			−0.938331
$730$	−8.61281			−0.318774
$731$	17.2210	−	35.0504i	0.636943	−	1.29638i
$732$	26.9709			0.996872
$733$	−33.6289			−1.24211			−0.621056	−	0.783766i	$-0.713296\pi$
$733$	−33.6289			−1.24211			−0.621056	+	0.783766i	$0.713296\pi$
$734$		−	2.14823i		−	0.0792928i
$735$	7.21243			0.266035
$736$			0.835896i			0.0308115i
$737$			14.2478i			0.524825i
$738$		−	0.234992i		−	0.00865018i
$739$	38.7291			1.42467			0.712336	−	0.701838i	$-0.247637\pi$
$739$	38.7291			1.42467			0.712336	+	0.701838i	$0.247637\pi$
$740$	4.64051			0.170589
$741$			73.1351i			2.68668i
$742$			19.0898i			0.700809i
$743$		−	27.0802i		−	0.993475i	−0.867901	−	0.496738i	$-0.834531\pi$
$743$		−	27.0802i		−	0.993475i	0.867901	−	0.496738i	$-0.165469\pi$
$744$	−7.44849			−0.273075
$745$		−	4.39110i		−	0.160878i
$746$	−15.9012			−0.582184
$747$	−0.776002			−0.0283924
$748$	−3.70057	−	1.81817i	−0.135306	−	0.0664791i
$749$	34.4271			1.25794
$750$	−1.77959			−0.0649815
$751$			7.96156i			0.290522i	0.989393	+	0.145261i	$0.0464021\pi$
$751$			7.96156i			0.290522i	−0.989393	+	0.145261i	$0.953598\pi$
$752$	−10.6872			−0.389724
$753$			25.6816i			0.935889i
$754$		−	58.9198i		−	2.14573i
$755$		−	3.97889i		−	0.144807i
$756$	16.7615			0.609610
$757$	13.7219			0.498731			0.249365	−	0.968409i	$-0.419778\pi$
$757$	13.7219			0.498731			0.249365	+	0.968409i	$0.419778\pi$
$758$		−	20.7035i		−	0.751985i
$759$		−	1.48755i		−	0.0539948i
$760$		−	7.50818i		−	0.272350i
$761$	13.7601			0.498802			0.249401	−	0.968400i	$-0.419766\pi$
$761$	13.7601			0.498802			0.249401	+	0.968400i	$0.419766\pi$
$762$			7.21064i			0.261214i
$763$	−23.0054			−0.832850
$764$	12.7424			0.461005
$765$	−0.617789	−	0.303534i	−0.0223362	−	0.0109743i
$766$	−5.25406			−0.189837
$767$	−66.7801			−2.41129
$768$		−	1.77959i		−	0.0642155i
$769$	−11.5922			−0.418026			−0.209013	−	0.977913i	$-0.567025\pi$
$769$	−11.5922			−0.418026			−0.209013	+	0.977913i	$0.567025\pi$
$770$		−	3.32458i		−	0.119810i
$771$			26.4615i			0.952986i
$772$		−	5.46753i		−	0.196781i
$773$	−23.8514			−0.857874			−0.428937	−	0.903335i	$-0.641112\pi$
$773$	−23.8514			−0.857874			−0.428937	+	0.903335i	$0.641112\pi$
$774$	−1.58123			−0.0568361
$775$		−	4.18551i		−	0.150348i
$776$			11.0058i			0.395084i
$777$			27.4551i			0.984947i
$778$	−11.6382			−0.417249
$779$			10.5686i			0.378659i
$780$	−9.74071			−0.348773
$781$	−7.30504			−0.261395
$782$	−3.09329	−	1.51981i	−0.110616	−	0.0543481i
$783$	54.2707			1.93948
$784$	−4.05286			−0.144745
$785$		−	8.32426i		−	0.297106i
$786$	29.6215			1.05657
$787$			0.561057i			0.0199995i	0.999950	+	0.00999975i	$0.00318307\pi$
$787$			0.561057i			0.0199995i	−0.999950	+	0.00999975i	$0.996817\pi$
$788$		−	2.81411i		−	0.100249i
$789$		−	28.9296i		−	1.02992i
$790$	8.22977			0.292802
$791$	29.0995			1.03466
$792$			0.166944i			0.00593210i
$793$			82.9555i			2.94584i
$794$		−	25.9488i		−	0.920887i
$795$	10.2184			0.362411
$796$			7.32390i			0.259589i
$797$	−3.02106			−0.107011			−0.0535057	−	0.998568i	$-0.517040\pi$
$797$	−3.02106			−0.107011			−0.0535057	+	0.998568i	$0.517040\pi$
$798$	44.4214			1.57250
$799$	19.4313	−	39.5489i	0.687429	−	1.39914i
$800$	1.00000			0.0353553
$801$	1.60821			0.0568233
$802$			0.218956i			0.00773162i
$803$	−8.61281			−0.303940
$804$		−	25.3553i		−	0.894212i
$805$		−	2.77901i		−	0.0979471i
$806$		−	22.9096i		−	0.806958i
$807$	45.8099			1.61258
$808$	−1.18421			−0.0416602
$809$		−	26.3385i		−	0.926012i	−0.886355	−	0.463006i	$-0.846771\pi$
$809$		−	26.3385i		−	0.926012i	0.886355	−	0.463006i	$-0.153229\pi$
$810$		−	9.47296i		−	0.332846i
$811$			48.2149i			1.69305i	0.532345	+	0.846527i	$0.321311\pi$
$811$			48.2149i			1.69305i	−0.532345	+	0.846527i	$0.678689\pi$
$812$	−35.7872			−1.25588
$813$			6.22926i			0.218470i
$814$	4.64051			0.162650
$815$	−3.07901			−0.107853
$816$	6.58551	+	3.23561i	0.230539	+	0.113269i
$817$	71.1146			2.48798
$818$	11.1599			0.390195
$819$		−	3.03794i		−	0.106154i
$820$	−1.40761			−0.0491559
$821$		−	37.0932i		−	1.29456i	−0.762252	−	0.647281i	$-0.775906\pi$
$821$		−	37.0932i		−	1.29456i	0.762252	−	0.647281i	$-0.224094\pi$
$822$			17.8809i			0.623666i
$823$			44.0741i			1.53633i	0.640255	+	0.768163i	$0.278829\pi$
$823$			44.0741i			1.53633i	−0.640255	+	0.768163i	$0.721171\pi$
$824$	−17.6949			−0.616430
$825$	−1.77959			−0.0619574
$826$			40.5615i			1.41131i
$827$		−	7.89837i		−	0.274653i	−0.990526	−	0.137327i	$-0.956149\pi$
$827$		−	7.89837i		−	0.274653i	0.990526	−	0.137327i	$-0.0438510\pi$
$828$			0.139548i			0.00484963i
$829$	0.548786			0.0190601			0.00953006	−	0.999955i	$-0.496966\pi$
$829$	0.548786			0.0190601			0.00953006	+	0.999955i	$0.496966\pi$
$830$			4.64828i			0.161344i
$831$	−7.10477			−0.246462
$832$	5.47357			0.189762
$833$	7.36881	−	14.9979i	0.255314	−	0.519646i
$834$	−22.6574			−0.784560
$835$	−5.64428			−0.195328
$836$		−	7.50818i		−	0.259676i
$837$	21.1020			0.729391
$838$			12.0487i			0.416215i
$839$			29.6601i			1.02398i	0.858992	+	0.511989i	$0.171091\pi$
$839$			29.6601i			1.02398i	−0.858992	+	0.511989i	$0.828909\pi$
$840$			5.91640i			0.204135i
$841$	−86.8726			−2.99561
$842$	17.5463			0.604686
$843$		−	36.2656i		−	1.24905i
$844$			22.1967i			0.764043i
$845$		−	16.9599i		−	0.583440i
$846$	−1.78417			−0.0613411
$847$		−	3.32458i		−	0.114234i
$848$	−5.74202			−0.197182
$849$	−19.4977			−0.669160
$850$	−1.81817	+	3.70057i	−0.0623629	+	0.126929i
$851$	3.87899			0.132970
$852$	13.0000			0.445372
$853$			28.1443i			0.963644i	0.876269	+	0.481822i	$0.160025\pi$
$853$			28.1443i			0.963644i	−0.876269	+	0.481822i	$0.839975\pi$
$854$	50.3863			1.72418
$855$		−	1.25345i		−	0.0428670i
$856$			10.3553i			0.353938i
$857$			24.0642i			0.822016i	0.911632	+	0.411008i	$0.134823\pi$
$857$			24.0642i			0.822016i	−0.911632	+	0.411008i	$0.865177\pi$
$858$	−9.74071			−0.332542
$859$	55.6810			1.89981			0.949905	−	0.312538i	$-0.101179\pi$
$859$	55.6810			1.89981			0.949905	+	0.312538i	$0.101179\pi$
$860$			9.47161i			0.322979i
$861$		−	8.32798i		−	0.283817i
$862$			9.15092i			0.311682i
$863$	25.3940			0.864423			0.432212	−	0.901772i	$-0.357733\pi$
$863$	25.3940			0.864423			0.432212	+	0.901772i	$0.357733\pi$
$864$			5.04168i			0.171521i
$865$	10.1825			0.346217
$866$	−27.9304			−0.949113
$867$	−23.9472	+	18.4872i	−0.813290	+	0.627860i
$868$	−13.9151			−0.472308
$869$	8.22977			0.279176
$870$			19.1563i			0.649458i
$871$	77.9864			2.64247
$872$		−	6.91977i		−	0.234333i
$873$			1.83735i			0.0621848i
$874$		−	6.27606i		−	0.212291i
$875$	−3.32458			−0.112391
$876$	15.3273			0.517861
$877$			1.66687i			0.0562863i	0.999604	+	0.0281431i	$0.00895942\pi$
$877$			1.66687i			0.0562863i	−0.999604	+	0.0281431i	$0.991041\pi$
$878$			3.57929i			0.120795i
$879$		−	4.28458i		−	0.144515i
$880$	1.00000			0.0337100
$881$		−	34.5706i		−	1.16471i	−0.812933	−	0.582357i	$-0.802130\pi$
$881$		−	34.5706i		−	1.16471i	0.812933	−	0.582357i	$-0.197870\pi$
$882$	−0.676601			−0.0227823
$883$	38.1652			1.28436			0.642180	−	0.766554i	$-0.278030\pi$
$883$	38.1652			1.28436			0.642180	+	0.766554i	$0.278030\pi$
$884$	−9.95190	+	20.2553i	−0.334719	+	0.681261i
$885$	21.7118			0.729835
$886$	35.7230			1.20014
$887$			15.8103i			0.530857i	0.964131	+	0.265429i	$0.0855135\pi$
$887$			15.8103i			0.530857i	−0.964131	+	0.265429i	$0.914487\pi$
$888$	−8.25821			−0.277128
$889$			13.4707i			0.451794i
$890$		−	9.63322i		−	0.322906i
$891$		−	9.47296i		−	0.317356i
$892$	20.3393			0.681010
$893$	80.2418			2.68519
$894$			7.81437i			0.261352i
$895$		−	13.1745i		−	0.440374i
$896$		−	3.32458i		−	0.111067i
$897$	−8.14222			−0.271861
$898$			20.5509i			0.685792i
$899$	−45.0545			−1.50265
$900$	0.166944			0.00556480
$901$	10.4400	−	21.2488i	0.347807	−	0.707899i
$902$	−1.40761			−0.0468683
$903$	−56.0378			−1.86482
$904$			8.75281i			0.291114i
$905$	10.8731			0.361434
$906$			7.08080i			0.235244i
$907$			0.900785i			0.0299101i	0.999888	+	0.0149550i	$0.00476052\pi$
$907$			0.900785i			0.0299101i	−0.999888	+	0.0149550i	$0.995239\pi$
$908$			7.45363i			0.247357i
$909$	−0.197696			−0.00655717
$910$	−18.1973			−0.603236
$911$			6.08221i			0.201513i	0.994911	+	0.100756i	$0.0321263\pi$
$911$			6.08221i			0.201513i	−0.994911	+	0.100756i	$0.967874\pi$
$912$			13.3615i			0.442443i
$913$			4.64828i			0.153835i
$914$	4.94779			0.163658
$915$		−	26.9709i		−	0.891629i
$916$	−21.2141			−0.700932
$917$	55.3382			1.82743
$918$	−18.6571	−	9.16666i	−0.615776	−	0.302545i
$919$	19.0602			0.628738			0.314369	−	0.949301i	$-0.398207\pi$
$919$	19.0602			0.628738			0.314369	+	0.949301i	$0.398207\pi$
$920$	0.835896			0.0275587
$921$			28.7763i			0.948212i
$922$	−26.6952			−0.879159
$923$			39.9846i			1.31611i
$924$			5.91640i			0.194635i
$925$		−	4.64051i		−	0.152579i
$926$	−18.8198			−0.618456
$927$	−2.95405			−0.0970239
$928$		−	10.7644i		−	0.353359i
$929$			57.9724i			1.90201i	0.309171	+	0.951007i	$0.399949\pi$
$929$			57.9724i			1.90201i	−0.309171	+	0.951007i	$0.600051\pi$
$930$			7.44849i			0.244246i
$931$	30.4296			0.997290
$932$		−	0.998709i		−	0.0327138i
$933$	−38.0535			−1.24581
$934$	14.7818			0.483676
$935$	−1.81817	+	3.70057i	−0.0594607	+	0.121022i
$936$	0.913780			0.0298678
$937$	−50.6233			−1.65379			−0.826896	−	0.562355i	$-0.809895\pi$
$937$	−50.6233			−1.65379			−0.826896	+	0.562355i	$0.809895\pi$
$938$		−	47.3681i		−	1.54662i
$939$	−15.3259			−0.500141
$940$			10.6872i			0.348580i
$941$		−	21.5749i		−	0.703323i	−0.936127	−	0.351661i	$-0.885617\pi$
$941$		−	21.5749i		−	0.703323i	0.936127	−	0.351661i	$-0.114383\pi$
$942$			14.8138i			0.482659i
$943$	−1.17662			−0.0383159
$944$	−12.2005			−0.397091
$945$		−	16.7615i		−	0.545251i
$946$			9.47161i			0.307949i
$947$		−	18.6071i		−	0.604650i	−0.953205	−	0.302325i	$-0.902237\pi$
$947$		−	18.6071i		−	0.604650i	0.953205	−	0.302325i	$-0.0977628\pi$
$948$	−14.6456			−0.475668
$949$			47.1428i			1.53032i
$950$	−7.50818			−0.243598
$951$	21.8562			0.708737
$952$	12.3029	+	6.04468i	0.398738	+	0.195909i
$953$	−34.5867			−1.12037			−0.560186	−	0.828367i	$-0.689270\pi$
$953$	−34.5867			−1.12037			−0.560186	+	0.828367i	$0.689270\pi$
$954$	−0.958596			−0.0310357
$955$		−	12.7424i		−	0.412335i
$956$	2.09382			0.0677190
$957$			19.1563i			0.619234i
$958$		−	0.103077i		−	0.00333028i
$959$			33.4045i			1.07869i
$960$	−1.77959			−0.0574361
$961$	13.4815			0.434889
$962$		−	25.4002i		−	0.818934i
$963$			1.72876i			0.0557085i
$964$			9.44404i			0.304172i
$965$	−5.46753			−0.176006
$966$			4.94550i			0.159119i
$967$	19.6039			0.630418			0.315209	−	0.949022i	$-0.397925\pi$
$967$	19.6039			0.630418			0.315209	+	0.949022i	$0.397925\pi$
$968$	1.00000			0.0321412
$969$	−49.4452	−	24.2935i	−1.58841	−	0.780421i
$970$	11.0058			0.353374
$971$	−20.3753			−0.653876			−0.326938	−	0.945046i	$-0.606017\pi$
$971$	−20.3753			−0.653876			−0.326938	+	0.945046i	$0.606017\pi$
$972$			1.73296i			0.0555846i
$973$	−42.3279			−1.35697
$974$			32.9639i			1.05623i
$975$			9.74071i			0.311952i
$976$			15.1557i			0.485121i
$977$	35.9953			1.15159			0.575796	−	0.817594i	$-0.304692\pi$
$977$	35.9953			1.15159			0.575796	+	0.817594i	$0.304692\pi$
$978$	5.47938			0.175211
$979$		−	9.63322i		−	0.307879i
$980$			4.05286i			0.129464i
$981$		−	1.15521i		−	0.0368832i
$982$	−28.7913			−0.918766
$983$			29.5053i			0.941073i	0.882381	+	0.470536i	$0.155940\pi$
$983$			29.5053i			0.941073i	−0.882381	+	0.470536i	$0.844060\pi$
$984$	2.50497			0.0798555
$985$	−2.81411			−0.0896651
$986$	39.8345	+	19.5716i	1.26859	+	0.623286i
$987$	−63.2300			−2.01263
$988$	−41.0966			−1.30746
$989$			7.91728i			0.251755i
$990$	0.166944			0.00530583
$991$		−	25.4730i		−	0.809177i	−0.914499	−	0.404588i	$-0.867415\pi$
$991$		−	25.4730i		−	0.809177i	0.914499	−	0.404588i	$-0.132585\pi$
$992$		−	4.18551i		−	0.132890i
$993$			38.9185i			1.23504i
$994$	24.2862			0.770312
$995$	7.32390			0.232183
$996$		−	8.27203i		−	0.262109i
$997$			9.11967i			0.288823i	0.989518	+	0.144412i	$0.0461289\pi$
$997$			9.11967i			0.288823i	−0.989518	+	0.144412i	$0.953871\pi$
$998$		−	10.7662i		−	0.340797i
$999$	23.3960			0.740216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.2.c.e.441.5	✓	18
17.16	even	2	inner	1870.2.c.e.441.14	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.2.c.e.441.5	✓	18	1.1	even	1	trivial
1870.2.c.e.441.14	yes	18	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1870.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.77959i q^{3} +1.00000 q^{4} -1.00000i q^{5} +1.77959i q^{6} +3.32458i q^{7} -1.00000 q^{8} -0.166944 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.77959i q^{3} +1.00000 q^{4} -1.00000i q^{5} +1.77959i q^{6} +3.32458i q^{7} -1.00000 q^{8} -0.166944 q^{9} +1.00000i q^{10} +1.00000i q^{11} -1.77959i q^{12} +5.47357 q^{13} -3.32458i q^{14} -1.77959 q^{15} +1.00000 q^{16} +(-1.81817 + 3.70057i) q^{17} +0.166944 q^{18} -7.50818 q^{19} -1.00000i q^{20} +5.91640 q^{21} -1.00000i q^{22} -0.835896i q^{23} +1.77959i q^{24} -1.00000 q^{25} -5.47357 q^{26} -5.04168i q^{27} +3.32458i q^{28} +10.7644i q^{29} +1.77959 q^{30} +4.18551i q^{31} -1.00000 q^{32} +1.77959 q^{33} +(1.81817 - 3.70057i) q^{34} +3.32458 q^{35} -0.166944 q^{36} +4.64051i q^{37} +7.50818 q^{38} -9.74071i q^{39} +1.00000i q^{40} -1.40761i q^{41} -5.91640 q^{42} -9.47161 q^{43} +1.00000i q^{44} +0.166944i q^{45} +0.835896i q^{46} -10.6872 q^{47} -1.77959i q^{48} -4.05286 q^{49} +1.00000 q^{50} +(6.58551 + 3.23561i) q^{51} +5.47357 q^{52} -5.74202 q^{53} +5.04168i q^{54} +1.00000 q^{55} -3.32458i q^{56} +13.3615i q^{57} -10.7644i q^{58} -12.2005 q^{59} -1.77959 q^{60} +15.1557i q^{61} -4.18551i q^{62} -0.555020i q^{63} +1.00000 q^{64} -5.47357i q^{65} -1.77959 q^{66} +14.2478 q^{67} +(-1.81817 + 3.70057i) q^{68} -1.48755 q^{69} -3.32458 q^{70} +7.30504i q^{71} +0.166944 q^{72} +8.61281i q^{73} -4.64051i q^{74} +1.77959i q^{75} -7.50818 q^{76} -3.32458 q^{77} +9.74071i q^{78} -8.22977i q^{79} -1.00000i q^{80} -9.47296 q^{81} +1.40761i q^{82} +4.64828 q^{83} +5.91640 q^{84} +(3.70057 + 1.81817i) q^{85} +9.47161 q^{86} +19.1563 q^{87} -1.00000i q^{88} -9.63322 q^{89} -0.166944i q^{90} +18.1973i q^{91} -0.835896i q^{92} +7.44849 q^{93} +10.6872 q^{94} +7.50818i q^{95} +1.77959i q^{96} -11.0058i q^{97} +4.05286 q^{98} -0.166944i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} - 18 q^{8} - 24 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 18 * q^4 - 18 * q^8 - 24 * q^9	\( 18 q - 18 q^{2} + 18 q^{4} - 18 q^{8} - 24 q^{9} + 10 q^{13} - 2 q^{15} + 18 q^{16} + 2 q^{17} + 24 q^{18} - 26 q^{19} + 24 q^{21} - 18 q^{25} - 10 q^{26} + 2 q^{30} - 18 q^{32} + 2 q^{33} - 2 q^{34} - 24 q^{36} + 26 q^{38} - 24 q^{42} - 4 q^{43} - 2 q^{47} - 30 q^{49} + 18 q^{50} + 14 q^{51} + 10 q^{52} - 42 q^{53} + 18 q^{55} - 26 q^{59} - 2 q^{60} + 18 q^{64} - 2 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} + 24 q^{72} - 26 q^{76} - 14 q^{81} - 4 q^{83} + 24 q^{84} + 6 q^{85} + 4 q^{86} - 78 q^{87} + 50 q^{89} - 58 q^{93} + 2 q^{94} + 30 q^{98}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 - 18 * q^8 - 24 * q^9 + 10 * q^13 - 2 * q^15 + 18 * q^16 + 2 * q^17 + 24 * q^18 - 26 * q^19 + 24 * q^21 - 18 * q^25 - 10 * q^26 + 2 * q^30 - 18 * q^32 + 2 * q^33 - 2 * q^34 - 24 * q^36 + 26 * q^38 - 24 * q^42 - 4 * q^43 - 2 * q^47 - 30 * q^49 + 18 * q^50 + 14 * q^51 + 10 * q^52 - 42 * q^53 + 18 * q^55 - 26 * q^59 - 2 * q^60 + 18 * q^64 - 2 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 + 24 * q^72 - 26 * q^76 - 14 * q^81 - 4 * q^83 + 24 * q^84 + 6 * q^85 + 4 * q^86 - 78 * q^87 + 50 * q^89 - 58 * q^93 + 2 * q^94 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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