LMFDB - Embedded newform 1045.2.f.a.626.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.7
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.a.626.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04337 q^{2} -0.838315i q^{3} +2.17535 q^{4} -1.00000 q^{5} +1.71299i q^{6} -4.78057i q^{7} -0.358306 q^{8} +2.29723 q^{9} +O(q^{10})$	\(q-2.04337 q^{2} -0.838315i q^{3} +2.17535 q^{4} -1.00000 q^{5} +1.71299i q^{6} -4.78057i q^{7} -0.358306 q^{8} +2.29723 q^{9} +2.04337 q^{10} +(-2.69484 - 1.93335i) q^{11} -1.82363i q^{12} -4.24020 q^{13} +9.76845i q^{14} +0.838315i q^{15} -3.61855 q^{16} -3.99629i q^{17} -4.69408 q^{18} +(-4.34129 + 0.391440i) q^{19} -2.17535 q^{20} -4.00762 q^{21} +(5.50654 + 3.95055i) q^{22} +5.80780 q^{23} +0.300373i q^{24} +1.00000 q^{25} +8.66428 q^{26} -4.44075i q^{27} -10.3994i q^{28} +0.280948 q^{29} -1.71299i q^{30} +1.69878i q^{31} +8.11064 q^{32} +(-1.62076 + 2.25912i) q^{33} +8.16589i q^{34} +4.78057i q^{35} +4.99727 q^{36} -2.87696i q^{37} +(8.87084 - 0.799856i) q^{38} +3.55462i q^{39} +0.358306 q^{40} +5.74842 q^{41} +8.18905 q^{42} +5.09337i q^{43} +(-5.86222 - 4.20572i) q^{44} -2.29723 q^{45} -11.8675 q^{46} -1.73791 q^{47} +3.03349i q^{48} -15.8538 q^{49} -2.04337 q^{50} -3.35015 q^{51} -9.22392 q^{52} -10.5567i q^{53} +9.07408i q^{54} +(2.69484 + 1.93335i) q^{55} +1.71290i q^{56} +(0.328151 + 3.63937i) q^{57} -0.574080 q^{58} -1.61310i q^{59} +1.82363i q^{60} -1.50074i q^{61} -3.47123i q^{62} -10.9820i q^{63} -9.33592 q^{64} +4.24020 q^{65} +(3.31181 - 4.61622i) q^{66} +12.0842i q^{67} -8.69333i q^{68} -4.86877i q^{69} -9.76845i q^{70} +12.3578i q^{71} -0.823109 q^{72} -0.489478i q^{73} +5.87868i q^{74} -0.838315i q^{75} +(-9.44382 + 0.851520i) q^{76} +(-9.24252 + 12.8828i) q^{77} -7.26340i q^{78} -6.76671 q^{79} +3.61855 q^{80} +3.16893 q^{81} -11.7461 q^{82} +14.7552i q^{83} -8.71798 q^{84} +3.99629i q^{85} -10.4076i q^{86} -0.235523i q^{87} +(0.965575 + 0.692731i) q^{88} +4.01878i q^{89} +4.69408 q^{90} +20.2706i q^{91} +12.6340 q^{92} +1.42411 q^{93} +3.55118 q^{94} +(4.34129 - 0.391440i) q^{95} -6.79928i q^{96} -11.2670i q^{97} +32.3952 q^{98} +(-6.19065 - 4.44135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.04337			−1.44488			−0.722439	−	0.691434i	$-0.756979\pi$
$2$	−2.04337			−1.44488			−0.722439	+	0.691434i	$0.756979\pi$
$3$		−	0.838315i		−	0.484002i	−0.970276	−	0.242001i	$-0.922196\pi$
$3$		−	0.838315i		−	0.484002i	0.970276	−	0.242001i	$-0.0778037\pi$
$4$	2.17535			1.08768
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$			1.71299i			0.699324i
$7$		−	4.78057i		−	1.80688i	−0.428710	−	0.903442i	$-0.641032\pi$
$7$		−	4.78057i		−	1.80688i	0.428710	−	0.903442i	$-0.358968\pi$
$8$	−0.358306			−0.126680
$9$	2.29723			0.765742
$10$	2.04337			0.646170
$11$	−2.69484	−	1.93335i	−0.812524	−	0.582928i
$11$	−2.69484	−	1.93335i	−0.812524	−	0.582928i
$12$		−	1.82363i		−	0.526437i
$13$	−4.24020			−1.17602			−0.588010	−	0.808854i	$-0.700088\pi$
$13$	−4.24020			−1.17602			−0.588010	+	0.808854i	$0.700088\pi$
$14$			9.76845i			2.61073i
$15$			0.838315i			0.216452i
$16$	−3.61855			−0.904638
$17$		−	3.99629i		−	0.969243i	−0.874724	−	0.484621i	$-0.838957\pi$
$17$		−	3.99629i		−	0.969243i	0.874724	−	0.484621i	$-0.161043\pi$
$18$	−4.69408			−1.10641
$19$	−4.34129	+	0.391440i	−0.995960	+	0.0898026i
$19$	−4.34129	+	0.391440i	−0.995960	+	0.0898026i
$20$	−2.17535			−0.486423
$21$	−4.00762			−0.874535
$22$	5.50654	+	3.95055i	1.17400	+	0.842260i
$23$	5.80780			1.21101			0.605505	−	0.795841i	$-0.292971\pi$
$23$	5.80780			1.21101			0.605505	+	0.795841i	$0.292971\pi$
$24$			0.300373i			0.0613134i
$25$	1.00000			0.200000
$26$	8.66428			1.69921
$27$		−	4.44075i		−	0.854622i
$28$		−	10.3994i		−	1.96530i
$29$	0.280948			0.0521707			0.0260854	−	0.999660i	$-0.491696\pi$
$29$	0.280948			0.0521707			0.0260854	+	0.999660i	$0.491696\pi$
$30$		−	1.71299i		−	0.312747i
$31$			1.69878i			0.305110i	0.988295	+	0.152555i	$0.0487501\pi$
$31$			1.69878i			0.305110i	−0.988295	+	0.152555i	$0.951250\pi$
$32$	8.11064			1.43377
$33$	−1.62076	+	2.25912i	−0.282138	+	0.393263i
$34$			8.16589i			1.40044i
$35$			4.78057i			0.808063i
$36$	4.99727			0.832879
$37$		−	2.87696i		−	0.472969i	−0.971635	−	0.236484i	$-0.924005\pi$
$37$		−	2.87696i		−	0.472969i	0.971635	−	0.236484i	$-0.0759952\pi$
$38$	8.87084	−	0.799856i	1.43904	−	0.129754i
$39$			3.55462i			0.569195i
$40$	0.358306			0.0566531
$41$	5.74842			0.897752			0.448876	−	0.893594i	$-0.351824\pi$
$41$	5.74842			0.897752			0.448876	+	0.893594i	$0.351824\pi$
$42$	8.18905			1.26360
$43$			5.09337i			0.776731i	0.921505	+	0.388365i	$0.126960\pi$
$43$			5.09337i			0.776731i	−0.921505	+	0.388365i	$0.873040\pi$
$44$	−5.86222	−	4.20572i	−0.883762	−	0.634036i
$45$	−2.29723			−0.342450
$46$	−11.8675			−1.74976
$47$	−1.73791			−0.253500			−0.126750	−	0.991935i	$-0.540455\pi$
$47$	−1.73791			−0.253500			−0.126750	+	0.991935i	$0.540455\pi$
$48$			3.03349i			0.437846i
$49$	−15.8538			−2.26483
$50$	−2.04337			−0.288976
$51$	−3.35015			−0.469115
$52$	−9.22392			−1.27913
$53$		−	10.5567i		−	1.45008i	−0.688708	−	0.725039i	$-0.741822\pi$
$53$		−	10.5567i		−	1.45008i	0.688708	−	0.725039i	$-0.258178\pi$
$54$			9.07408i			1.23483i
$55$	2.69484	+	1.93335i	0.363372	+	0.260693i
$56$			1.71290i			0.228896i
$57$	0.328151	+	3.63937i	0.0434646	+	0.482046i
$58$	−0.574080			−0.0753803
$59$		−	1.61310i		−	0.210007i	−0.994472	−	0.105004i	$-0.966515\pi$
$59$		−	1.61310i		−	0.210007i	0.994472	−	0.105004i	$-0.0334854\pi$
$60$			1.82363i			0.235430i
$61$		−	1.50074i		−	0.192150i	−0.995374	−	0.0960748i	$-0.969371\pi$
$61$		−	1.50074i		−	0.192150i	0.995374	−	0.0960748i	$-0.0306288\pi$
$62$		−	3.47123i		−	0.440847i
$63$		−	10.9820i		−	1.38361i
$64$	−9.33592			−1.16699
$65$	4.24020			0.525932
$66$	3.31181	−	4.61622i	0.407655	−	0.568217i
$67$			12.0842i			1.47632i	0.674624	+	0.738161i	$0.264306\pi$
$67$			12.0842i			1.47632i	−0.674624	+	0.738161i	$0.735694\pi$
$68$		−	8.69333i		−	1.05422i
$69$		−	4.86877i		−	0.586131i
$70$		−	9.76845i		−	1.16755i
$71$			12.3578i			1.46660i	0.679904	+	0.733302i	$0.262022\pi$
$71$			12.3578i			1.46660i	−0.679904	+	0.733302i	$0.737978\pi$
$72$	−0.823109			−0.0970043
$73$		−	0.489478i		−	0.0572891i	−0.999590	−	0.0286445i	$-0.990881\pi$
$73$		−	0.489478i		−	0.0572891i	0.999590	−	0.0286445i	$-0.00911909\pi$
$74$			5.87868i			0.683383i
$75$		−	0.838315i		−	0.0968003i
$76$	−9.44382	+	0.851520i	−1.08328	+	0.0976760i
$77$	−9.24252	+	12.8828i	−1.05328	+	1.46814i
$78$		−	7.26340i		−	0.822418i
$79$	−6.76671			−0.761315			−0.380657	−	0.924716i	$-0.624302\pi$
$79$	−6.76671			−0.761315			−0.380657	+	0.924716i	$0.624302\pi$
$80$	3.61855			0.404566
$81$	3.16893			0.352104
$82$	−11.7461			−1.29714
$83$			14.7552i			1.61960i	0.586708	+	0.809799i	$0.300424\pi$
$83$			14.7552i			1.61960i	−0.586708	+	0.809799i	$0.699576\pi$
$84$	−8.71798			−0.951210
$85$			3.99629i			0.433459i
$86$		−	10.4076i		−	1.12228i
$87$		−	0.235523i		−	0.0252507i
$88$	0.965575	+	0.692731i	0.102931	+	0.0738454i
$89$			4.01878i			0.425990i	0.977053	+	0.212995i	$0.0683218\pi$
$89$			4.01878i			0.425990i	−0.977053	+	0.212995i	$0.931678\pi$
$90$	4.69408			0.494799
$91$			20.2706i			2.12493i
$92$	12.6340			1.31719
$93$	1.42411			0.147674
$94$	3.55118			0.366276
$95$	4.34129	−	0.391440i	0.445407	−	0.0401609i
$96$		−	6.79928i		−	0.693948i
$97$		−	11.2670i		−	1.14399i	−0.820257	−	0.571996i	$-0.806169\pi$
$97$		−	11.2670i		−	1.14399i	0.820257	−	0.571996i	$-0.193831\pi$
$98$	32.3952			3.27241
$99$	−6.19065	−	4.44135i	−0.622184	−	0.446372i
$100$	2.17535			0.217535
$101$		−	7.47740i		−	0.744029i	−0.928227	−	0.372015i	$-0.878667\pi$
$101$		−	7.47740i		−	0.744029i	0.928227	−	0.372015i	$-0.121333\pi$
$102$	6.84559			0.677815
$103$			2.84871i			0.280691i	0.990103	+	0.140346i	$0.0448214\pi$
$103$			2.84871i			0.280691i	−0.990103	+	0.140346i	$0.955179\pi$
$104$	1.51929			0.148978
$105$	4.00762			0.391104
$106$			21.5713i			2.09519i
$107$	−5.91167			−0.571503			−0.285751	−	0.958304i	$-0.592243\pi$
$107$	−5.91167			−0.571503			−0.285751	+	0.958304i	$0.592243\pi$
$108$		−	9.66018i		−	0.929551i
$109$	−17.3818			−1.66488			−0.832439	−	0.554117i	$-0.813056\pi$
$109$	−17.3818			−1.66488			−0.832439	+	0.554117i	$0.813056\pi$
$110$	−5.50654	−	3.95055i	−0.525028	−	0.376670i
$111$	−2.41180			−0.228918
$112$			17.2987i			1.63458i
$113$		−	12.2517i		−	1.15254i	−0.817260	−	0.576270i	$-0.804508\pi$
$113$		−	12.2517i		−	1.15254i	0.817260	−	0.576270i	$-0.195492\pi$
$114$	−0.670532	−	7.43657i	−0.0628011	−	0.696498i
$115$	−5.80780			−0.541580
$116$	0.611160			0.0567448
$117$	−9.74070			−0.900528
$118$			3.29615i			0.303435i
$119$	−19.1045			−1.75131
$120$		−	0.300373i		−	0.0274202i
$121$	3.52430	+	10.4201i	0.320391	+	0.947286i
$122$			3.06655i			0.277633i
$123$		−	4.81899i		−	0.434514i
$124$			3.69544i			0.331860i
$125$	−1.00000			−0.0894427
$126$			22.4404i			1.99915i
$127$	1.70223			0.151049			0.0755243	−	0.997144i	$-0.475937\pi$
$127$	1.70223			0.151049			0.0755243	+	0.997144i	$0.475937\pi$
$128$	2.85543			0.252386
$129$	4.26985			0.375939
$130$	−8.66428			−0.759908
$131$		−	6.07917i		−	0.531140i	−0.964092	−	0.265570i	$-0.914440\pi$
$131$		−	6.07917i		−	0.531140i	0.964092	−	0.265570i	$-0.0855601\pi$
$132$	−3.52572	+	4.91439i	−0.306875	+	0.427742i
$133$	1.87131	+	20.7538i	0.162263	+	1.79958i
$134$		−	24.6925i		−	2.13311i
$135$			4.44075i			0.382199i
$136$			1.43189i			0.122784i
$137$	−19.5811			−1.67293			−0.836465	−	0.548020i	$-0.815382\pi$
$137$	−19.5811			−1.67293			−0.836465	+	0.548020i	$0.815382\pi$
$138$			9.94868i			0.846888i
$139$			14.8952i			1.26339i	0.775216	+	0.631696i	$0.217641\pi$
$139$			14.8952i			1.26339i	−0.775216	+	0.631696i	$0.782359\pi$
$140$			10.3994i			0.878910i
$141$			1.45691i			0.122694i
$142$		−	25.2516i		−	2.11906i
$143$	11.4266	+	8.19780i	0.955544	+	0.685534i
$144$	−8.31263			−0.692720
$145$	−0.280948			−0.0233314
$146$			1.00018i			0.0827758i
$147$			13.2905i			1.09618i
$148$		−	6.25839i		−	0.514436i
$149$			23.1713i			1.89826i	0.314878	+	0.949132i	$0.398036\pi$
$149$			23.1713i			1.89826i	−0.314878	+	0.949132i	$0.601964\pi$
$150$			1.71299i			0.139865i
$151$	−2.62018			−0.213227			−0.106614	−	0.994301i	$-0.534001\pi$
$151$	−2.62018			−0.213227			−0.106614	+	0.994301i	$0.534001\pi$
$152$	1.55551	−	0.140255i	0.126168	−	0.0113762i
$153$		−	9.18039i		−	0.742190i
$154$	18.8859	−	26.3244i	1.52187	−	2.12128i
$155$		−	1.69878i		−	0.136449i
$156$			7.73255i			0.619100i
$157$	−0.859743			−0.0686150			−0.0343075	−	0.999411i	$-0.510923\pi$
$157$	−0.859743			−0.0686150			−0.0343075	+	0.999411i	$0.510923\pi$
$158$	13.8269			1.10001
$159$	−8.84987			−0.701840
$160$	−8.11064			−0.641202
$161$		−	27.7646i		−	2.18816i
$162$	−6.47530			−0.508747
$163$	−4.37921			−0.343006			−0.171503	−	0.985184i	$-0.554862\pi$
$163$	−4.37921			−0.343006			−0.171503	+	0.985184i	$0.554862\pi$
$164$	12.5048			0.976463
$165$	1.62076	−	2.25912i	0.126176	−	0.175873i
$166$		−	30.1504i		−	2.34012i
$167$	9.39022			0.726637			0.363319	−	0.931665i	$-0.381644\pi$
$167$	9.39022			0.726637			0.363319	+	0.931665i	$0.381644\pi$
$168$	1.43595			0.110786
$169$	4.97928			0.383022
$170$		−	8.16589i		−	0.626295i
$171$	−9.97292	+	0.899227i	−0.762648	+	0.0687656i
$172$			11.0799i			0.844831i
$173$	12.6812			0.964136			0.482068	−	0.876134i	$-0.339886\pi$
$173$	12.6812			0.964136			0.482068	+	0.876134i	$0.339886\pi$
$174$			0.481260i			0.0364842i
$175$		−	4.78057i		−	0.361377i
$176$	9.75141	+	6.99593i	0.735040	+	0.527338i
$177$	−1.35228			−0.101644
$178$		−	8.21185i		−	0.615504i
$179$		−	0.803768i		−	0.0600764i	−0.999549	−	0.0300382i	$-0.990437\pi$
$179$		−	0.803768i		−	0.0600764i	0.999549	−	0.0300382i	$-0.00956290\pi$
$180$	−4.99727			−0.372475
$181$		−	24.2956i		−	1.80588i	−0.429770	−	0.902939i	$-0.641405\pi$
$181$		−	24.2956i		−	1.80588i	0.429770	−	0.902939i	$-0.358595\pi$
$182$		−	41.4202i		−	3.07027i
$183$	−1.25809			−0.0930007
$184$	−2.08097			−0.153411
$185$			2.87696i			0.211518i
$186$	−2.90999			−0.213371
$187$	−7.72624	+	10.7694i	−0.564999	+	0.787533i
$188$	−3.78055			−0.275725
$189$	−21.2293			−1.54420
$190$	−8.87084	+	0.799856i	−0.643559	+	0.0580277i
$191$	3.48103			0.251879			0.125939	−	0.992038i	$-0.459806\pi$
$191$	3.48103			0.251879			0.125939	+	0.992038i	$0.459806\pi$
$192$			7.82644i			0.564825i
$193$	−12.9504			−0.932187			−0.466094	−	0.884735i	$-0.654339\pi$
$193$	−12.9504			−0.932187			−0.466094	+	0.884735i	$0.654339\pi$
$194$			23.0226i			1.65293i
$195$		−	3.55462i		−	0.254552i
$196$	−34.4876			−2.46340
$197$		−	10.8525i		−	0.773210i	−0.922245	−	0.386605i	$-0.873648\pi$
$197$		−	10.8525i		−	0.773210i	0.922245	−	0.386605i	$-0.126352\pi$
$198$	12.6498	+	9.07531i	0.898981	+	0.644954i
$199$	21.8885			1.55163			0.775816	−	0.630959i	$-0.217338\pi$
$199$	21.8885			1.55163			0.775816	+	0.630959i	$0.217338\pi$
$200$	−0.358306			−0.0253360
$201$	10.1304			0.714543
$202$			15.2791i			1.07503i
$203$		−	1.34309i		−	0.0942664i
$204$	−7.28776			−0.510245
$205$	−5.74842			−0.401487
$206$		−	5.82096i		−	0.405565i
$207$	13.3418			0.927322
$208$	15.3434			1.06387
$209$	12.4559	+	7.33837i	0.861590	+	0.507606i
$210$	−8.18905			−0.565098
$211$	−13.9828			−0.962618			−0.481309	−	0.876551i	$-0.659839\pi$
$211$	−13.9828			−0.962618			−0.481309	+	0.876551i	$0.659839\pi$
$212$		−	22.9646i		−	1.57721i
$213$	10.3598			0.709838
$214$	12.0797			0.825753
$215$		−	5.09337i		−	0.347365i
$216$			1.59114i			0.108264i
$217$	8.12113			0.551298
$218$	35.5175			2.40555
$219$	−0.410337			−0.0277280
$220$	5.86222	+	4.20572i	0.395231	+	0.283550i
$221$			16.9451i			1.13985i
$222$	4.92819			0.330758
$223$		−	3.15124i		−	0.211022i	−0.994418	−	0.105511i	$-0.966352\pi$
$223$		−	3.15124i		−	0.211022i	0.994418	−	0.105511i	$-0.0336479\pi$
$224$		−	38.7735i		−	2.59066i
$225$	2.29723			0.153148
$226$			25.0346i			1.66528i
$227$	−7.54188			−0.500572			−0.250286	−	0.968172i	$-0.580525\pi$
$227$	−7.54188			−0.500572			−0.250286	+	0.968172i	$0.580525\pi$
$228$	0.713842	+	7.91690i	0.0472754	+	0.524310i
$229$	−12.1719			−0.804341			−0.402170	−	0.915565i	$-0.631744\pi$
$229$	−12.1719			−0.804341			−0.402170	+	0.915565i	$0.631744\pi$
$230$	11.8675			0.782518
$231$	10.7999	+	7.74815i	0.710581	+	0.509791i
$232$	−0.100665			−0.00660899
$233$		−	9.79180i		−	0.641482i	−0.947167	−	0.320741i	$-0.896068\pi$
$233$		−	9.79180i		−	0.641482i	0.947167	−	0.320741i	$-0.103932\pi$
$234$	19.9038			1.30115
$235$	1.73791			0.113368
$236$		−	3.50905i		−	0.228420i
$237$			5.67264i			0.368478i
$238$	39.0376			2.53043
$239$			21.3790i			1.38289i	0.722428	+	0.691446i	$0.243026\pi$
$239$			21.3790i			1.38289i	−0.722428	+	0.691446i	$0.756974\pi$
$240$		−	3.03349i		−	0.195811i
$241$	23.5429			1.51653			0.758266	−	0.651945i	$-0.226047\pi$
$241$	23.5429			1.51653			0.758266	+	0.651945i	$0.226047\pi$
$242$	−7.20143	−	21.2922i	−0.462926	−	1.36871i
$243$		−	15.9788i		−	1.02504i
$244$		−	3.26463i		−	0.208996i
$245$	15.8538			1.01286
$246$			9.84696i			0.627819i
$247$	18.4079	−	1.65978i	1.17127	−	0.105610i
$248$		−	0.608682i		−	0.0386513i
$249$	12.3695			0.783888
$250$	2.04337			0.129234
$251$	5.60396			0.353719			0.176860	−	0.984236i	$-0.443406\pi$
$251$	5.60396			0.353719			0.176860	+	0.984236i	$0.443406\pi$
$252$		−	23.8898i		−	1.50492i
$253$	−15.6511	−	11.2285i	−0.983975	−	0.705931i
$254$	−3.47829			−0.218247
$255$	3.35015			0.209795
$256$	12.8371			0.802322
$257$		−	17.9270i		−	1.11826i	−0.829081	−	0.559128i	$-0.811136\pi$
$257$		−	17.9270i		−	1.11826i	0.829081	−	0.559128i	$-0.188864\pi$
$258$	−8.72487			−0.543186
$259$	−13.7535			−0.854600
$260$	9.22392			0.572043
$261$	0.645401			0.0399493
$262$			12.4220i			0.767433i
$263$			4.35904i			0.268790i	0.990928	+	0.134395i	$0.0429090\pi$
$263$			4.35904i			0.268790i	−0.990928	+	0.134395i	$0.957091\pi$
$264$	0.580727	−	0.809457i	0.0357413	−	0.0498186i
$265$			10.5567i			0.648495i
$266$	−3.82377	−	42.4077i	−0.234450	−	2.60018i
$267$	3.36901			0.206180
$268$			26.2874i			1.60576i
$269$		−	21.1595i		−	1.29012i	−0.764133	−	0.645059i	$-0.776833\pi$
$269$		−	21.1595i		−	1.29012i	0.764133	−	0.645059i	$-0.223167\pi$
$270$		−	9.07408i		−	0.552231i
$271$		−	0.512638i		−	0.0311405i	−0.999879	−	0.0155703i	$-0.995044\pi$
$271$		−	0.512638i		−	0.0311405i	0.999879	−	0.0155703i	$-0.00495637\pi$
$272$			14.4608i			0.876814i
$273$	16.9931			1.02847
$274$	40.0115			2.41718
$275$	−2.69484	−	1.93335i	−0.162505	−	0.116586i
$276$		−	10.5913i		−	0.637520i
$277$			2.99976i			0.180238i	0.995931	+	0.0901191i	$0.0287248\pi$
$277$			2.99976i			0.180238i	−0.995931	+	0.0901191i	$0.971275\pi$
$278$		−	30.4363i		−	1.82545i
$279$			3.90248i			0.233636i
$280$		−	1.71290i		−	0.102366i
$281$	−18.2144			−1.08658			−0.543291	−	0.839544i	$-0.682822\pi$
$281$	−18.2144			−1.08658			−0.543291	+	0.839544i	$0.682822\pi$
$282$		−	2.97701i		−	0.177278i
$283$		−	31.9641i		−	1.90007i	−0.312148	−	0.950034i	$-0.601048\pi$
$283$		−	31.9641i		−	1.90007i	0.312148	−	0.950034i	$-0.398952\pi$
$284$			26.8826i			1.59519i
$285$	−0.328151	−	3.63937i	−0.0194380	−	0.215578i
$286$	−23.3488	−	16.7511i	−1.38065	−	0.990514i
$287$		−	27.4807i		−	1.62213i
$288$	18.6320			1.09790
$289$	1.02966			0.0605682
$290$	0.574080			0.0337111
$291$	−9.44531			−0.553694
$292$		−	1.06479i		−	0.0623119i
$293$	27.4990			1.60651			0.803253	−	0.595638i	$-0.203101\pi$
$293$	27.4990			1.60651			0.803253	+	0.595638i	$0.203101\pi$
$294$		−	27.1574i		−	1.58385i
$295$			1.61310i			0.0939181i
$296$			1.03083i			0.0599157i
$297$	−8.58553	+	11.9671i	−0.498183	+	0.694401i
$298$		−	47.3474i		−	2.74276i
$299$	−24.6262			−1.42417
$300$		−	1.82363i		−	0.105287i
$301$	24.3492			1.40346
$302$	5.35399			0.308087
$303$	−6.26842			−0.360111
$304$	15.7092	−	1.41645i	0.900983	−	0.0812388i
$305$			1.50074i			0.0859319i
$306$			18.7589i			1.07238i
$307$	12.2286			0.697924			0.348962	−	0.937137i	$-0.386534\pi$
$307$	12.2286			0.697924			0.348962	+	0.937137i	$0.386534\pi$
$308$	−20.1057	+	28.0247i	−1.14563	+	1.59686i
$309$	2.38812			0.135855
$310$			3.47123i			0.197153i
$311$	21.3158			1.20871			0.604355	−	0.796715i	$-0.293431\pi$
$311$	21.3158			1.20871			0.604355	+	0.796715i	$0.293431\pi$
$312$		−	1.27364i		−	0.0721057i
$313$	−6.70861			−0.379193			−0.189596	−	0.981862i	$-0.560718\pi$
$313$	−6.70861			−0.379193			−0.189596	+	0.981862i	$0.560718\pi$
$314$	1.75677			0.0991404
$315$			10.9820i			0.618768i
$316$	−14.7200			−0.828063
$317$			23.0700i			1.29574i	0.761750	+	0.647871i	$0.224340\pi$
$317$			23.0700i			1.29574i	−0.761750	+	0.647871i	$0.775660\pi$
$318$	18.0835			1.01407
$319$	−0.757109	−	0.543171i	−0.0423899	−	0.0304117i
$320$	9.33592			0.521894
$321$			4.95585i			0.276608i
$322$			56.7332i			3.16162i
$323$	1.56431	+	17.3490i	0.0870405	+	0.965327i
$324$	6.89354			0.382975
$325$	−4.24020			−0.235204
$326$	8.94833			0.495602
$327$			14.5715i			0.805804i
$328$	−2.05969			−0.113727
$329$			8.30817i			0.458044i
$330$	−3.31181	+	4.61622i	−0.182309	+	0.254115i
$331$			8.86321i			0.487166i	0.969880	+	0.243583i	$0.0783228\pi$
$331$			8.86321i			0.487166i	−0.969880	+	0.243583i	$0.921677\pi$
$332$			32.0978i			1.76160i
$333$		−	6.60902i		−	0.362172i
$334$	−19.1877			−1.04990
$335$		−	12.0842i		−	0.660232i
$336$	14.5018			0.791137
$337$	−26.1314			−1.42347			−0.711733	−	0.702450i	$-0.752090\pi$
$337$	−26.1314			−1.42347			−0.711733	+	0.702450i	$0.752090\pi$
$338$	−10.1745			−0.553420
$339$	−10.2708			−0.557831
$340$			8.69333i			0.471462i
$341$	3.28434	−	4.57793i	0.177857	−	0.247909i
$342$	20.3783	−	1.83745i	1.10193	−	0.0993580i
$343$			42.3263i			2.28540i
$344$		−	1.82498i		−	0.0983964i
$345$			4.86877i			0.262126i
$346$	−25.9124			−1.39306
$347$		−	6.17525i		−	0.331505i	−0.986167	−	0.165752i	$-0.946995\pi$
$347$		−	6.17525i		−	0.331505i	0.986167	−	0.165752i	$-0.0530052\pi$
$348$		−	0.512345i		−	0.0274646i
$349$		−	24.6872i		−	1.32147i	−0.750617	−	0.660737i	$-0.770244\pi$
$349$		−	24.6872i		−	1.32147i	0.750617	−	0.660737i	$-0.229756\pi$
$350$			9.76845i			0.522146i
$351$			18.8297i			1.00505i
$352$	−21.8569	−	15.6807i	−1.16497	−	0.835786i
$353$	−14.3112			−0.761711			−0.380855	−	0.924635i	$-0.624370\pi$
$353$	−14.3112			−0.761711			−0.380855	+	0.924635i	$0.624370\pi$
$354$	2.76321			0.146863
$355$		−	12.3578i		−	0.655885i
$356$			8.74226i			0.463339i
$357$			16.0156i			0.847637i
$358$			1.64239i			0.0868032i
$359$		−	33.9044i		−	1.78941i	−0.446662	−	0.894703i	$-0.647387\pi$
$359$		−	33.9044i		−	1.78941i	0.446662	−	0.894703i	$-0.352613\pi$
$360$	0.823109			0.0433817
$361$	18.6935	−	3.39871i	0.983871	−	0.178879i
$362$			49.6448i			2.60927i
$363$	8.73537	−	2.95447i	0.458488	−	0.155070i
$364$			44.0956i			2.31124i
$365$			0.489478i			0.0256205i
$366$	2.57074			0.134375
$367$	12.2487			0.639375			0.319687	−	0.947523i	$-0.396422\pi$
$367$	12.2487			0.639375			0.319687	+	0.947523i	$0.396422\pi$
$368$	−21.0158			−1.09553
$369$	13.2054			0.687447
$370$		−	5.87868i		−	0.305618i
$371$	−50.4672			−2.62012
$372$	3.09795			0.160621
$373$	−35.2303			−1.82416			−0.912078	−	0.410016i	$-0.865523\pi$
$373$	−35.2303			−1.82416			−0.912078	+	0.410016i	$0.865523\pi$
$374$	15.7875	−	22.0057i	0.816354	−	1.13789i
$375$			0.838315i			0.0432904i
$376$	0.622701			0.0321133
$377$	−1.19127			−0.0613538
$378$	43.3792			2.23119
$379$			22.4583i			1.15360i	0.816884	+	0.576802i	$0.195700\pi$
$379$			22.4583i			1.15360i	−0.816884	+	0.576802i	$0.804300\pi$
$380$	9.44382	−	0.851520i	0.484458	−	0.0436821i
$381$		−	1.42701i		−	0.0731078i
$382$	−7.11302			−0.363934
$383$		−	25.4026i		−	1.29801i	−0.760783	−	0.649006i	$-0.775185\pi$
$383$		−	25.4026i		−	1.29801i	0.760783	−	0.649006i	$-0.224815\pi$
$384$		−	2.39375i		−	0.122155i
$385$	9.24252	−	12.8828i	0.471042	−	0.656571i
$386$	26.4623			1.34690
$387$			11.7006i			0.594776i
$388$		−	24.5097i		−	1.24429i
$389$	16.7386			0.848679			0.424339	−	0.905503i	$-0.360506\pi$
$389$	16.7386			0.848679			0.424339	+	0.905503i	$0.360506\pi$
$390$			7.26340i			0.367797i
$391$		−	23.2097i		−	1.17376i
$392$	5.68051			0.286909
$393$	−5.09626			−0.257073
$394$			22.1757i			1.11720i
$395$	6.76671			0.340470
$396$	−13.4668	−	9.66149i	−0.676734	−	0.485508i
$397$	−29.2161			−1.46632			−0.733158	−	0.680058i	$-0.761955\pi$
$397$	−29.2161			−1.46632			−0.733158	+	0.680058i	$0.761955\pi$
$398$	−44.7262			−2.24192
$399$	17.3982	−	1.56875i	0.871002	−	0.0785355i
$400$	−3.61855			−0.180928
$401$		−	4.43897i		−	0.221671i	−0.993839	−	0.110836i	$-0.964647\pi$
$401$		−	4.43897i		−	0.221671i	0.993839	−	0.110836i	$-0.0353527\pi$
$402$	−20.7001			−1.03243
$403$		−	7.20316i		−	0.358815i
$404$		−	16.2660i		−	0.809262i
$405$	−3.16893			−0.157466
$406$			2.74443i			0.136204i
$407$	−5.56217	+	7.75293i	−0.275707	+	0.384299i
$408$	1.20038			0.0594276
$409$	18.3611			0.907897			0.453949	−	0.891028i	$-0.350015\pi$
$409$	18.3611			0.907897			0.453949	+	0.891028i	$0.350015\pi$
$410$	11.7461			0.580100
$411$			16.4152i			0.809701i
$412$			6.19694i			0.305301i
$413$	−7.71151			−0.379459
$414$	−27.2623			−1.33987
$415$		−	14.7552i		−	0.724306i
$416$	−34.3907			−1.68614
$417$	12.4869			0.611484
$418$	−25.4519	−	14.9950i	−1.24489	−	0.733429i
$419$	14.5981			0.713162			0.356581	−	0.934264i	$-0.383942\pi$
$419$	14.5981			0.713162			0.356581	+	0.934264i	$0.383942\pi$
$420$	8.71798			0.425394
$421$		−	32.5038i		−	1.58414i	−0.610430	−	0.792070i	$-0.709003\pi$
$421$		−	32.5038i		−	1.58414i	0.610430	−	0.792070i	$-0.290997\pi$
$422$	28.5721			1.39087
$423$	−3.99236			−0.194115
$424$			3.78253i			0.183696i
$425$		−	3.99629i		−	0.193849i
$426$	−21.1688			−1.02563
$427$	−7.17437			−0.347192
$428$	−12.8600			−0.621610
$429$	6.87234	−	9.57913i	0.331800	−	0.462485i
$430$			10.4076i			0.501900i
$431$	38.6568			1.86203			0.931016	−	0.364979i	$-0.118924\pi$
$431$	38.6568			1.86203			0.931016	+	0.364979i	$0.118924\pi$
$432$			16.0691i			0.773124i
$433$		−	4.08511i		−	0.196318i	−0.995171	−	0.0981590i	$-0.968705\pi$
$433$		−	4.08511i		−	0.196318i	0.995171	−	0.0981590i	$-0.0312954\pi$
$434$	−16.5945			−0.796559
$435$			0.235523i			0.0112925i
$436$	−37.8116			−1.81085
$437$	−25.2133	+	2.27341i	−1.20612	+	0.108752i
$438$	0.838469			0.0400636
$439$	−17.0748			−0.814937			−0.407468	−	0.913219i	$-0.633588\pi$
$439$	−17.0748			−0.814937			−0.407468	+	0.913219i	$0.633588\pi$
$440$	−0.965575	−	0.692731i	−0.0460320	−	0.0330246i
$441$	−36.4198			−1.73428
$442$		−	34.6250i		−	1.64694i
$443$	1.35565			0.0644090			0.0322045	−	0.999481i	$-0.489747\pi$
$443$	1.35565			0.0644090			0.0322045	+	0.999481i	$0.489747\pi$
$444$	−5.24650			−0.248988
$445$		−	4.01878i		−	0.190509i
$446$			6.43913i			0.304902i
$447$	19.4248			0.918763
$448$			44.6310i			2.10862i
$449$			32.3293i			1.52571i	0.646568	+	0.762857i	$0.276204\pi$
$449$			32.3293i			1.52571i	−0.646568	+	0.762857i	$0.723796\pi$
$450$	−4.69408			−0.221281
$451$	−15.4911	−	11.1137i	−0.729445	−	0.523325i
$452$		−	26.6517i		−	1.25359i
$453$			2.19654i			0.103202i
$454$	15.4108			0.723266
$455$		−	20.2706i		−	0.950298i
$456$	−0.117578	−	1.30401i	−0.00550610	−	0.0610657i
$457$			8.90740i			0.416671i	0.978057	+	0.208335i	$0.0668045\pi$
$457$			8.90740i			0.416671i	−0.978057	+	0.208335i	$0.933195\pi$
$458$	24.8716			1.16218
$459$	−17.7465			−0.828337
$460$	−12.6340			−0.589063
$461$			24.1691i			1.12567i	0.826570	+	0.562833i	$0.190289\pi$
$461$			24.1691i			1.12567i	−0.826570	+	0.562833i	$0.809711\pi$
$462$	−22.0681	−	15.8323i	−1.02670	−	0.736586i
$463$	−35.5508			−1.65218			−0.826092	−	0.563536i	$-0.809441\pi$
$463$	−35.5508			−1.65218			−0.826092	+	0.563536i	$0.809441\pi$
$464$	−1.01662			−0.0471956
$465$	−1.42411			−0.0660417
$466$			20.0082i			0.926864i
$467$	−26.5304			−1.22768			−0.613840	−	0.789430i	$-0.710376\pi$
$467$	−26.5304			−1.22768			−0.613840	+	0.789430i	$0.710376\pi$
$468$	−21.1894			−0.979482
$469$	57.7694			2.66754
$470$	−3.55118			−0.163804
$471$			0.720736i			0.0332098i
$472$			0.577981i			0.0266037i
$473$	9.84727	−	13.7258i	0.452778	−	0.631113i
$474$		−	11.5913i		−	0.532406i
$475$	−4.34129	+	0.391440i	−0.199192	+	0.0179605i
$476$	−41.5591			−1.90486
$477$		−	24.2512i		−	1.11039i
$478$		−	43.6851i		−	1.99811i
$479$		−	17.7512i		−	0.811073i	−0.914079	−	0.405536i	$-0.867085\pi$
$479$		−	17.7512i		−	0.811073i	0.914079	−	0.405536i	$-0.132915\pi$
$480$			6.79928i			0.310343i
$481$			12.1989i			0.556221i
$482$	−48.1068			−2.19120
$483$	−23.2755			−1.05907
$484$	7.66658	+	22.6675i	0.348481	+	1.03034i
$485$			11.2670i			0.511608i
$486$			32.6506i			1.48106i
$487$		−	16.5288i		−	0.748989i	−0.927229	−	0.374495i	$-0.877816\pi$
$487$		−	16.5288i		−	0.748989i	0.927229	−	0.374495i	$-0.122184\pi$
$488$			0.537722i			0.0243415i
$489$			3.67116i			0.166015i
$490$	−32.3952			−1.46346
$491$		−	2.95440i		−	0.133330i	−0.997775	−	0.0666651i	$-0.978764\pi$
$491$		−	2.95440i		−	0.133330i	0.997775	−	0.0666651i	$-0.0212359\pi$
$492$		−	10.4830i		−	0.472610i
$493$		−	1.12275i		−	0.0505661i
$494$	−37.6141	+	3.39155i	−1.69234	+	0.152593i
$495$	6.19065	+	4.44135i	0.278249	+	0.199624i
$496$		−	6.14712i		−	0.276014i
$497$	59.0774			2.64998
$498$	−25.2755			−1.13262
$499$	−5.61842			−0.251515			−0.125757	−	0.992061i	$-0.540136\pi$
$499$	−5.61842			−0.251515			−0.125757	+	0.992061i	$0.540136\pi$
$500$	−2.17535			−0.0972846
$501$		−	7.87197i		−	0.351694i
$502$	−11.4510			−0.511081
$503$			6.36857i			0.283960i	0.989870	+	0.141980i	$0.0453469\pi$
$503$			6.36857i			0.283960i	−0.989870	+	0.141980i	$0.954653\pi$
$504$			3.93493i			0.175276i
$505$			7.47740i			0.332740i
$506$	31.9809	+	22.9440i	1.42172	+	1.01999i
$507$		−	4.17421i		−	0.185383i
$508$	3.70295			0.164292
$509$			37.1203i			1.64533i	0.568527	+	0.822665i	$0.307514\pi$
$509$			37.1203i			1.64533i	−0.568527	+	0.822665i	$0.692486\pi$
$510$	−6.84559			−0.303128
$511$	−2.33998			−0.103515
$512$	−31.9419			−1.41164
$513$	1.73829	+	19.2786i	0.0767473	+	0.851169i
$514$			36.6315i			1.61574i
$515$		−	2.84871i		−	0.125529i
$516$	9.28841			0.408900
$517$	4.68337	+	3.35998i	0.205974	+	0.147772i
$518$	28.1034			1.23479
$519$		−	10.6309i		−	0.466644i
$520$	−1.51929			−0.0666251
$521$			28.8890i			1.26565i	0.774294	+	0.632826i	$0.218105\pi$
$521$			28.8890i			1.26565i	−0.774294	+	0.632826i	$0.781895\pi$
$522$	−1.31879			−0.0577219
$523$	9.81873			0.429343			0.214671	−	0.976686i	$-0.431132\pi$
$523$	9.81873			0.429343			0.214671	+	0.976686i	$0.431132\pi$
$524$		−	13.2243i		−	0.577708i
$525$	−4.00762			−0.174907
$526$		−	8.90711i		−	0.388369i
$527$	6.78882			0.295726
$528$	5.86480	−	8.17476i	0.255233	−	0.355761i
$529$	10.7305			0.466546
$530$		−	21.5713i		−	0.936996i
$531$		−	3.70565i		−	0.160811i
$532$	4.07075	+	45.1468i	0.176489	+	1.95736i
$533$	−24.3744			−1.05577
$534$	−6.88412			−0.297905
$535$	5.91167			0.255584
$536$		−	4.32984i		−	0.187021i
$537$	−0.673811			−0.0290771
$538$			43.2367i			1.86406i
$539$	42.7235	+	30.6510i	1.84023	+	1.32023i
$540$			9.66018i			0.415708i
$541$		−	23.4115i		−	1.00654i	−0.864129	−	0.503270i	$-0.832130\pi$
$541$		−	23.4115i		−	1.00654i	0.864129	−	0.503270i	$-0.167870\pi$
$542$			1.04751i			0.0449943i
$543$	−20.3674			−0.874048
$544$		−	32.4125i		−	1.38967i
$545$	17.3818			0.744556
$546$	−34.7232			−1.48602
$547$	−9.02603			−0.385925			−0.192963	−	0.981206i	$-0.561810\pi$
$547$	−9.02603			−0.385925			−0.192963	+	0.981206i	$0.561810\pi$
$548$	−42.5959			−1.81961
$549$		−	3.44753i		−	0.147137i
$550$	5.50654	+	3.95055i	0.234800	+	0.168452i
$551$	−1.21968	+	0.109974i	−0.0519599	+	0.00468506i
$552$			1.74451i			0.0742511i
$553$			32.3487i			1.37561i
$554$		−	6.12961i		−	0.260422i
$555$	2.41180			0.102375
$556$			32.4022i			1.37416i
$557$			4.62806i			0.196097i	0.995182	+	0.0980485i	$0.0312600\pi$
$557$			4.62806i			0.196097i	−0.995182	+	0.0980485i	$0.968740\pi$
$558$		−	7.97421i		−	0.337575i
$559$		−	21.5969i		−	0.913451i
$560$		−	17.2987i		−	0.731005i
$561$	9.02812	+	6.47703i	0.381167	+	0.273460i
$562$	37.2188			1.56998
$563$	6.88954			0.290359			0.145180	−	0.989405i	$-0.453624\pi$
$563$	6.88954			0.290359			0.145180	+	0.989405i	$0.453624\pi$
$564$			3.16930i			0.133451i
$565$			12.2517i			0.515431i
$566$			65.3144i			2.74537i
$567$		−	15.1493i		−	0.636211i
$568$		−	4.42787i		−	0.185789i
$569$	9.45500			0.396374			0.198187	−	0.980164i	$-0.436495\pi$
$569$	9.45500			0.396374			0.198187	+	0.980164i	$0.436495\pi$
$570$	0.670532	+	7.43657i	0.0280855	+	0.311484i
$571$		−	38.5665i		−	1.61396i	−0.590581	−	0.806979i	$-0.701101\pi$
$571$		−	38.5665i		−	1.61396i	0.590581	−	0.806979i	$-0.298899\pi$
$572$	24.8570	+	17.8331i	1.03932	+	0.745639i
$573$		−	2.91820i		−	0.121910i
$574$			56.1532i			2.34379i
$575$	5.80780			0.242202
$576$	−21.4467			−0.893613
$577$	−17.0872			−0.711349			−0.355674	−	0.934610i	$-0.615749\pi$
$577$	−17.0872			−0.711349			−0.355674	+	0.934610i	$0.615749\pi$
$578$	−2.10397			−0.0875138
$579$			10.8565i			0.451180i
$580$	−0.611160			−0.0253770
$581$	70.5384			2.92643
$582$	19.3002			0.800020
$583$	−20.4099	+	28.4487i	−0.845291	+	1.17822i
$584$			0.175383i			0.00725739i
$585$	9.74070			0.402728
$586$	−56.1905			−2.32121
$587$	4.62095			0.190727			0.0953636	−	0.995443i	$-0.469599\pi$
$587$	4.62095			0.190727			0.0953636	+	0.995443i	$0.469599\pi$
$588$			28.9115i			1.19229i
$589$	−0.664971	−	7.37489i	−0.0273996	−	0.303877i
$590$		−	3.29615i		−	0.135700i
$591$	−9.09784			−0.374235
$592$			10.4104i			0.427865i
$593$		−	24.1621i		−	0.992216i	−0.868261	−	0.496108i	$-0.834762\pi$
$593$		−	24.1621i		−	0.992216i	0.868261	−	0.496108i	$-0.165238\pi$
$594$	17.5434	−	24.4532i	0.719814	−	1.00333i
$595$	19.1045			0.783210
$596$			50.4056i			2.06469i
$597$		−	18.3494i		−	0.750993i
$598$	50.3204			2.05776
$599$		−	18.4185i		−	0.752559i	−0.926506	−	0.376280i	$-0.877203\pi$
$599$		−	18.4185i		−	0.752559i	0.926506	−	0.376280i	$-0.122797\pi$
$600$			0.300373i			0.0122627i
$601$	21.9532			0.895489			0.447744	−	0.894162i	$-0.352227\pi$
$601$	21.9532			0.895489			0.447744	+	0.894162i	$0.352227\pi$
$602$	−49.7543			−2.02783
$603$			27.7602i			1.13048i
$604$	−5.69981			−0.231922
$605$	−3.52430	−	10.4201i	−0.143283	−	0.423639i
$606$	12.8087			0.520318
$607$	−8.55737			−0.347333			−0.173666	−	0.984805i	$-0.555561\pi$
$607$	−8.55737			−0.347333			−0.173666	+	0.984805i	$0.555561\pi$
$608$	−35.2106	+	3.17483i	−1.42798	+	0.128756i
$609$	−1.12593			−0.0456251
$610$		−	3.06655i		−	0.124161i
$611$	7.36906			0.298120
$612$		−	19.9706i		−	0.807262i
$613$		−	2.23422i		−	0.0902395i	−0.998982	−	0.0451197i	$-0.985633\pi$
$613$		−	2.23422i		−	0.0902395i	0.998982	−	0.0451197i	$-0.0143669\pi$
$614$	−24.9876			−1.00842
$615$			4.81899i			0.194320i
$616$	3.31165	−	4.61600i	0.133430	−	0.185984i
$617$	6.18327			0.248929			0.124464	−	0.992224i	$-0.460279\pi$
$617$	6.18327			0.248929			0.124464	+	0.992224i	$0.460279\pi$
$618$	−4.87980			−0.196294
$619$	30.0279			1.20692			0.603462	−	0.797392i	$-0.293788\pi$
$619$	30.0279			1.20692			0.603462	+	0.797392i	$0.293788\pi$
$620$		−	3.69544i		−	0.148412i
$621$		−	25.7910i		−	1.03496i
$622$	−43.5560			−1.74644
$623$	19.2121			0.769715
$624$		−	12.8626i		−	0.514916i
$625$	1.00000			0.0400000
$626$	13.7082			0.547888
$627$	6.15187	−	10.4419i	0.245682	−	0.417011i
$628$	−1.87024			−0.0746308
$629$	−11.4972			−0.458422
$630$		−	22.4404i		−	0.894045i
$631$	−35.1837			−1.40064			−0.700320	−	0.713829i	$-0.746959\pi$
$631$	−35.1837			−1.40064			−0.700320	+	0.713829i	$0.746959\pi$
$632$	2.42455			0.0964435
$633$			11.7220i			0.465909i
$634$		−	47.1405i		−	1.87219i
$635$	−1.70223			−0.0675510
$636$	−19.2516			−0.763374
$637$	67.2233			2.66349
$638$	1.54705	+	1.10990i	0.0612483	+	0.0439413i
$639$			28.3887i			1.12304i
$640$	−2.85543			−0.112871
$641$			18.9080i			0.746821i	0.927666	+	0.373411i	$0.121812\pi$
$641$			18.9080i			0.746821i	−0.927666	+	0.373411i	$0.878188\pi$
$642$		−	10.1266i		−	0.399666i
$643$	11.4234			0.450495			0.225248	−	0.974302i	$-0.427681\pi$
$643$	11.4234			0.450495			0.225248	+	0.974302i	$0.427681\pi$
$644$		−	60.3977i		−	2.38000i
$645$	−4.26985			−0.168125
$646$	−3.19646	−	35.4505i	−0.125763	−	1.39478i
$647$	−6.93587			−0.272677			−0.136339	−	0.990662i	$-0.543534\pi$
$647$	−6.93587			−0.272677			−0.136339	+	0.990662i	$0.543534\pi$
$648$	−1.13545			−0.0446046
$649$	−3.11868	+	4.34703i	−0.122419	+	0.170636i
$650$	8.66428			0.339841
$651$		−	6.80807i		−	0.266829i
$652$	−9.52631			−0.373079
$653$	−10.1523			−0.397289			−0.198645	−	0.980072i	$-0.563654\pi$
$653$	−10.1523			−0.397289			−0.198645	+	0.980072i	$0.563654\pi$
$654$		−	29.7748i		−	1.16429i
$655$			6.07917i			0.237533i
$656$	−20.8009			−0.812141
$657$		−	1.12444i		−	0.0438687i
$658$		−	16.9766i		−	0.661819i
$659$	−37.0084			−1.44164			−0.720822	−	0.693121i	$-0.756235\pi$
$659$	−37.0084			−1.44164			−0.720822	+	0.693121i	$0.756235\pi$
$660$	3.52572	−	4.91439i	0.137238	−	0.191292i
$661$		−	29.2224i		−	1.13662i	−0.822815	−	0.568309i	$-0.807598\pi$
$661$		−	29.2224i		−	1.13662i	0.822815	−	0.568309i	$-0.192402\pi$
$662$		−	18.1108i		−	0.703896i
$663$	14.2053			0.551689
$664$		−	5.28688i		−	0.205171i
$665$	−1.87131	−	20.7538i	−0.0725662	−	0.804798i
$666$			13.5047i			0.523295i
$667$	1.63169			0.0631792
$668$	20.4270			0.790345
$669$	−2.64173			−0.102135
$670$			24.6925i			0.953955i
$671$	−2.90145	+	4.04424i	−0.112009	+	0.156126i
$672$	−32.5044			−1.25388
$673$	−32.3665			−1.24764			−0.623818	−	0.781570i	$-0.714419\pi$
$673$	−32.3665			−1.24764			−0.623818	+	0.781570i	$0.714419\pi$
$674$	53.3960			2.05674
$675$		−	4.44075i		−	0.170924i
$676$	10.8317			0.416603
$677$	36.1224			1.38830			0.694148	−	0.719832i	$-0.255781\pi$
$677$	36.1224			1.38830			0.694148	+	0.719832i	$0.255781\pi$
$678$	20.9869			0.805998
$679$	−53.8627			−2.06706
$680$		−	1.43189i		−	0.0549106i
$681$			6.32247i			0.242278i
$682$	−6.71111	+	9.35440i	−0.256982	+	0.358199i
$683$		−	7.52944i		−	0.288106i	−0.989570	−	0.144053i	$-0.953986\pi$
$683$		−	7.52944i		−	0.288106i	0.989570	−	0.144053i	$-0.0460136\pi$
$684$	−21.6946	+	1.95613i	−0.829514	+	0.0747947i
$685$	19.5811			0.748157
$686$		−	86.4881i		−	3.30213i
$687$			10.2039i			0.389302i
$688$		−	18.4306i		−	0.702660i
$689$			44.7626i			1.70532i
$690$		−	9.94868i		−	0.378740i
$691$	31.3023			1.19080			0.595398	−	0.803431i	$-0.296995\pi$
$691$	31.3023			1.19080			0.595398	+	0.803431i	$0.296995\pi$
$692$	27.5861			1.04867
$693$	−21.2322	+	29.5948i	−0.806543	+	1.12421i
$694$			12.6183i			0.478984i
$695$		−	14.8952i		−	0.565006i
$696$			0.0843892i			0.00319876i
$697$		−	22.9724i		−	0.870140i
$698$			50.4450i			1.90937i
$699$	−8.20862			−0.310478
$700$		−	10.3994i		−	0.393061i
$701$			3.29429i			0.124424i	0.998063	+	0.0622118i	$0.0198154\pi$
$701$			3.29429i			0.124424i	−0.998063	+	0.0622118i	$0.980185\pi$
$702$		−	38.4759i		−	1.45218i
$703$	1.12616	+	12.4897i	0.0424738	+	0.471058i
$704$	25.1588	+	18.0496i	0.948207	+	0.680271i
$705$		−	1.45691i		−	0.0548705i
$706$	29.2431			1.10058
$707$	−35.7462			−1.34438
$708$	−2.94169			−0.110555
$709$	−13.3297			−0.500607			−0.250303	−	0.968167i	$-0.580530\pi$
$709$	−13.3297			−0.500607			−0.250303	+	0.968167i	$0.580530\pi$
$710$			25.2516i			0.947674i
$711$	−15.5447			−0.582971
$712$		−	1.43995i		−	0.0539645i
$713$			9.86617i			0.369491i
$714$		−	32.7258i		−	1.22473i
$715$	−11.4266	−	8.19780i	−0.427332	−	0.306580i
$716$		−	1.74848i		−	0.0653437i
$717$	17.9223			0.669322
$718$			69.2791i			2.58547i
$719$	−18.2514			−0.680662			−0.340331	−	0.940306i	$-0.610539\pi$
$719$	−18.2514			−0.680662			−0.340331	+	0.940306i	$0.610539\pi$
$720$	8.31263			0.309794
$721$	13.6184			0.507177
$722$	−38.1978	+	6.94481i	−1.42157	+	0.258459i
$723$		−	19.7364i		−	0.734004i
$724$		−	52.8514i		−	1.96421i
$725$	0.280948			0.0104341
$726$	−17.8496	+	6.03707i	−0.662459	+	0.224057i
$727$	−5.73117			−0.212557			−0.106279	−	0.994336i	$-0.533894\pi$
$727$	−5.73117			−0.212557			−0.106279	+	0.994336i	$0.533894\pi$
$728$		−	7.26305i		−	0.269187i
$729$	−3.88848			−0.144018
$730$		−	1.00018i		−	0.0370185i
$731$	20.3546			0.752841
$732$	−2.73679			−0.101155
$733$			42.2696i			1.56126i	0.624991	+	0.780632i	$0.285103\pi$
$733$			42.2696i			1.56126i	−0.624991	+	0.780632i	$0.714897\pi$
$734$	−25.0285			−0.923819
$735$		−	13.2905i		−	0.490228i
$736$	47.1050			1.73631
$737$	23.3631	−	32.5650i	0.860590	−	1.19955i
$738$	−26.9835			−0.993277
$739$		−	46.6279i		−	1.71524i	−0.514287	−	0.857618i	$-0.671943\pi$
$739$		−	46.6279i		−	1.71524i	0.514287	−	0.857618i	$-0.328057\pi$
$740$			6.25839i			0.230063i
$741$	−1.39142	−	15.4316i	−0.0511152	−	0.566896i
$742$	103.123			3.78576
$743$	2.67695			0.0982077			0.0491038	−	0.998794i	$-0.484363\pi$
$743$	2.67695			0.0982077			0.0491038	+	0.998794i	$0.484363\pi$
$744$	−0.510268			−0.0187073
$745$		−	23.1713i		−	0.848930i
$746$	71.9885			2.63569
$747$			33.8961i			1.24019i
$748$	−16.8073	+	23.4271i	−0.614535	+	0.856580i
$749$			28.2611i			1.03264i
$750$		−	1.71299i		−	0.0625494i
$751$			29.4294i			1.07389i	0.843616	+	0.536946i	$0.180422\pi$
$751$			29.4294i			1.07389i	−0.843616	+	0.536946i	$0.819578\pi$
$752$	6.28870			0.229325
$753$		−	4.69789i		−	0.171201i
$754$	2.43421			0.0886488
$755$	2.62018			0.0953580
$756$	−46.1811			−1.67959
$757$	41.2088			1.49776			0.748879	−	0.662707i	$-0.230592\pi$
$757$	41.2088			1.49776			0.748879	+	0.662707i	$0.230592\pi$
$758$		−	45.8905i		−	1.66682i
$759$	−9.41305	+	13.1205i	−0.341672	+	0.476245i
$760$	−1.55551	+	0.140255i	−0.0564242	+	0.00508759i
$761$		−	21.4284i		−	0.776778i	−0.921496	−	0.388389i	$-0.873032\pi$
$761$		−	21.4284i		−	0.776778i	0.921496	−	0.388389i	$-0.126968\pi$
$762$			2.91590i			0.105632i
$763$			83.0950i			3.00824i
$764$	7.57246			0.273962
$765$			9.18039i			0.331918i
$766$			51.9069i			1.87547i
$767$			6.83985i			0.246973i
$768$		−	10.7616i		−	0.388325i
$769$		−	40.2910i		−	1.45293i	−0.687203	−	0.726466i	$-0.741162\pi$
$769$		−	40.2910i		−	1.45293i	0.687203	−	0.726466i	$-0.258838\pi$
$770$	−18.8859	+	26.3244i	−0.680599	+	0.948665i
$771$	−15.0285			−0.541238
$772$	−28.1716			−1.01392
$773$		−	45.7752i		−	1.64642i	−0.567738	−	0.823209i	$-0.692181\pi$
$773$		−	45.7752i		−	1.64642i	0.567738	−	0.823209i	$-0.307819\pi$
$774$		−	23.9087i		−	0.859379i
$775$			1.69878i			0.0610220i
$776$			4.03703i			0.144921i
$777$			11.5298i			0.413628i
$778$	−34.2030			−1.22624
$779$	−24.9555	+	2.25016i	−0.894125	+	0.0806205i
$780$		−	7.73255i		−	0.276870i
$781$	23.8920	−	33.3023i	0.854924	−	1.19165i
$782$			47.4259i			1.69595i
$783$		−	1.24762i		−	0.0445862i
$784$	57.3679			2.04885
$785$	0.859743			0.0306856
$786$	10.4135			0.371439
$787$	−26.4863			−0.944135			−0.472068	−	0.881562i	$-0.656492\pi$
$787$	−26.4863			−0.944135			−0.472068	+	0.881562i	$0.656492\pi$
$788$		−	23.6080i		−	0.841002i
$789$	3.65425			0.130095
$790$	−13.8269			−0.491938
$791$	−58.5699			−2.08251
$792$	2.21815	+	1.59136i	0.0788184	+	0.0565465i
$793$			6.36342i			0.225972i
$794$	59.6993			2.11865
$795$	8.84987			0.313873
$796$	47.6151			1.68767
$797$		−	25.5522i		−	0.905107i	−0.891737	−	0.452553i	$-0.850513\pi$
$797$		−	25.5522i		−	0.905107i	0.891737	−	0.452553i	$-0.149487\pi$
$798$	−35.5510	+	3.20552i	−1.25849	+	0.113474i
$799$			6.94517i			0.245703i
$800$	8.11064			0.286754
$801$			9.23206i			0.326199i
$802$			9.07044i			0.320288i
$803$	−0.946334	+	1.31906i	−0.0333954	+	0.0465488i
$804$	22.0372			0.777190
$805$			27.7646i			0.978573i
$806$			14.7187i			0.518444i
$807$	−17.7383			−0.624419
$808$			2.67919i			0.0942537i
$809$		−	16.4494i		−	0.578329i	−0.957279	−	0.289165i	$-0.906623\pi$
$809$		−	16.4494i		−	0.578329i	0.957279	−	0.289165i	$-0.0933775\pi$
$810$	6.47530			0.227519
$811$	10.1198			0.355353			0.177676	−	0.984089i	$-0.443142\pi$
$811$	10.1198			0.355353			0.177676	+	0.984089i	$0.443142\pi$
$812$		−	2.92169i		−	0.102531i
$813$	−0.429752			−0.0150721
$814$	11.3656	−	15.8421i	0.398363	−	0.555265i
$815$	4.37921			0.153397
$816$	12.1227			0.424379
$817$	−1.99375	−	22.1118i	−0.0697524	−	0.773593i
$818$	−37.5185			−1.31180
$819$			46.5661i			1.62715i
$820$	−12.5048			−0.436687
$821$		−	15.5106i		−	0.541324i	−0.962674	−	0.270662i	$-0.912757\pi$
$821$		−	15.5106i		−	0.541324i	0.962674	−	0.270662i	$-0.0872425\pi$
$822$		−	33.5422i		−	1.16992i
$823$	39.7706			1.38632			0.693158	−	0.720786i	$-0.256219\pi$
$823$	39.7706			1.38632			0.693158	+	0.720786i	$0.256219\pi$
$824$		−	1.02071i		−	0.0355580i
$825$	−1.62076	+	2.25912i	−0.0564276	+	0.0786526i
$826$	15.7575			0.548272
$827$	22.2810			0.774785			0.387393	−	0.921915i	$-0.373376\pi$
$827$	22.2810			0.774785			0.387393	+	0.921915i	$0.373376\pi$
$828$	29.0232			1.00862
$829$		−	27.9389i		−	0.970358i	−0.874415	−	0.485179i	$-0.838754\pi$
$829$		−	27.9389i		−	0.970358i	0.874415	−	0.485179i	$-0.161246\pi$
$830$			30.1504i			1.04653i
$831$	2.51475			0.0872356
$832$	39.5861			1.37240
$833$			63.3565i			2.19517i
$834$	−25.5152			−0.883520
$835$	−9.39022			−0.324962
$836$	27.0959	+	15.9635i	0.937130	+	0.552110i
$837$	7.54385			0.260754
$838$	−29.8292			−1.03043
$839$		−	38.1453i		−	1.31692i	−0.752616	−	0.658460i	$-0.771208\pi$
$839$		−	38.1453i		−	1.31692i	0.752616	−	0.658460i	$-0.228792\pi$
$840$	−1.43595			−0.0495451
$841$	−28.9211			−0.997278
$842$			66.4173i			2.28889i
$843$			15.2695i			0.525908i
$844$	−30.4176			−1.04702
$845$	−4.97928			−0.171293
$846$	8.15786			0.280473
$847$	49.8142	−	16.8481i	1.71164	−	0.578909i
$848$			38.2001i			1.31180i
$849$	−26.7960			−0.919636
$850$			8.16589i			0.280088i
$851$		−	16.7088i		−	0.572770i
$852$	22.5361			0.772074
$853$		−	18.2159i		−	0.623700i	−0.950131	−	0.311850i	$-0.899051\pi$
$853$		−	18.2159i		−	0.623700i	0.950131	−	0.311850i	$-0.100949\pi$
$854$	14.6599			0.501650
$855$	9.97292	−	0.899227i	0.341067	−	0.0307529i
$856$	2.11818			0.0723981
$857$	7.16167			0.244638			0.122319	−	0.992491i	$-0.460967\pi$
$857$	7.16167			0.244638			0.122319	+	0.992491i	$0.460967\pi$
$858$	−14.0427	+	19.5737i	−0.479411	+	0.668235i
$859$	−28.9464			−0.987638			−0.493819	−	0.869565i	$-0.664400\pi$
$859$	−28.9464			−0.987638			−0.493819	+	0.869565i	$0.664400\pi$
$860$		−	11.0799i		−	0.377820i
$861$	−23.0375			−0.785116
$862$	−78.9900			−2.69041
$863$			25.5181i			0.868646i	0.900757	+	0.434323i	$0.143012\pi$
$863$			25.5181i			0.868646i	−0.900757	+	0.434323i	$0.856988\pi$
$864$		−	36.0173i		−	1.22533i
$865$	−12.6812			−0.431175
$866$			8.34739i			0.283656i
$867$		−	0.863180i		−	0.0293151i
$868$	17.6663			0.599633
$869$	18.2352	+	13.0824i	0.618587	+	0.443791i
$870$		−	0.481260i		−	0.0163162i
$871$		−	51.2395i		−	1.73618i
$872$	6.22801			0.210907
$873$		−	25.8829i		−	0.876003i
$874$	51.5201	−	4.64541i	1.74269	−	0.157133i
$875$			4.78057i			0.161613i
$876$	−0.892627			−0.0301591
$877$	14.0400			0.474098			0.237049	−	0.971498i	$-0.423820\pi$
$877$	14.0400			0.474098			0.237049	+	0.971498i	$0.423820\pi$
$878$	34.8901			1.17748
$879$		−	23.0528i		−	0.777552i
$880$	−9.75141	−	6.99593i	−0.328720	−	0.235833i
$881$	−20.6744			−0.696537			−0.348269	−	0.937395i	$-0.613230\pi$
$881$	−20.6744			−0.696537			−0.348269	+	0.937395i	$0.613230\pi$
$882$	74.4191			2.50582
$883$	−32.0849			−1.07974			−0.539871	−	0.841748i	$-0.681527\pi$
$883$	−32.0849			−1.07974			−0.539871	+	0.841748i	$0.681527\pi$
$884$			36.8615i			1.23979i
$885$	1.35228			0.0454565
$886$	−2.77010			−0.0930632
$887$	14.4663			0.485730			0.242865	−	0.970060i	$-0.421913\pi$
$887$	14.4663			0.485730			0.242865	+	0.970060i	$0.421913\pi$
$888$	0.864160			0.0289993
$889$		−	8.13763i		−	0.272928i
$890$			8.21185i			0.275262i
$891$	−8.53976	−	6.12667i	−0.286093	−	0.205251i
$892$		−	6.85504i		−	0.229524i
$893$	7.54474	−	0.680286i	0.252475	−	0.0227649i
$894$	−39.6921			−1.32750
$895$			0.803768i			0.0268670i
$896$		−	13.6506i		−	0.456033i
$897$			20.6445i			0.689301i
$898$		−	66.0606i		−	2.20447i
$899$			0.477268i			0.0159178i
$900$	4.99727			0.166576
$901$	−42.1878			−1.40548
$902$	31.6539	+	22.7094i	1.05396	+	0.756141i
$903$		−	20.4123i		−	0.679278i
$904$			4.38984i			0.146004i
$905$			24.2956i			0.807613i
$906$		−	4.48833i		−	0.149115i
$907$			39.0709i			1.29733i	0.761074	+	0.648665i	$0.224672\pi$
$907$			39.0709i			1.29733i	−0.761074	+	0.648665i	$0.775328\pi$
$908$	−16.4062			−0.544460
$909$		−	17.1773i		−	0.569735i
$910$			41.4202i			1.37307i
$911$		−	18.7047i		−	0.619715i	−0.950783	−	0.309857i	$-0.899719\pi$
$911$		−	18.7047i		−	0.619715i	0.950783	−	0.309857i	$-0.100281\pi$
$912$	−1.18743	−	13.1692i	−0.0393197	−	0.436077i
$913$	28.5271	−	39.7630i	0.944108	−	1.31596i
$914$		−	18.2011i		−	0.602039i
$915$	1.25809			0.0415912
$916$	−26.4781			−0.874862
$917$	−29.0619			−0.959708
$918$	36.2627			1.19685
$919$		−	25.1876i		−	0.830863i	−0.909624	−	0.415432i	$-0.863631\pi$
$919$		−	25.1876i		−	0.830863i	0.909624	−	0.415432i	$-0.136369\pi$
$920$	2.08097			0.0686074
$921$		−	10.2514i		−	0.337796i
$922$		−	49.3863i		−	1.62645i
$923$		−	52.3996i		−	1.72475i
$924$	23.4936	+	16.8549i	0.772881	+	0.554487i
$925$		−	2.87696i		−	0.0945938i
$926$	72.6433			2.38721
$927$			6.54413i			0.214937i
$928$	2.27867			0.0748009
$929$	−58.4083			−1.91631			−0.958156	−	0.286245i	$-0.907593\pi$
$929$	−58.4083			−1.91631			−0.958156	+	0.286245i	$0.907593\pi$
$930$	2.90999			0.0954222
$931$	68.8260	−	6.20582i	2.25568	−	0.203388i
$932$		−	21.3006i		−	0.697724i
$933$		−	17.8694i		−	0.585017i
$934$	54.2114			1.77385
$935$	7.72624	−	10.7694i	0.252675	−	0.352196i
$936$	3.49015			0.114079
$937$		−	41.7955i		−	1.36540i	−0.730700	−	0.682699i	$-0.760806\pi$
$937$		−	41.7955i		−	1.36540i	0.730700	−	0.682699i	$-0.239194\pi$
$938$	−118.044			−3.85428
$939$			5.62393i			0.183530i
$940$	3.78055			0.123308
$941$	28.4760			0.928292			0.464146	−	0.885759i	$-0.346361\pi$
$941$	28.4760			0.928292			0.464146	+	0.885759i	$0.346361\pi$
$942$		−	1.47273i		−	0.0479841i
$943$	33.3857			1.08719
$944$			5.83707i			0.189980i
$945$	21.2293			0.690589
$946$	−20.1216	+	28.0468i	−0.654209	+	0.911881i
$947$	−32.9022			−1.06918			−0.534589	−	0.845112i	$-0.679534\pi$
$947$	−32.9022			−1.06918			−0.534589	+	0.845112i	$0.679534\pi$
$948$			12.3400i			0.400784i
$949$			2.07548i			0.0673731i
$950$	8.87084	−	0.799856i	0.287808	−	0.0259508i
$951$	19.3400			0.627141
$952$	6.84526			0.221856
$953$	−3.54330			−0.114779			−0.0573894	−	0.998352i	$-0.518278\pi$
$953$	−3.54330			−0.114779			−0.0573894	+	0.998352i	$0.518278\pi$
$954$			49.5541i			1.60437i
$955$	−3.48103			−0.112644
$956$			46.5068i			1.50414i
$957$	−0.455349	+	0.634696i	−0.0147193	+	0.0205168i
$958$			36.2722i			1.17190i
$959$			93.6090i			3.02279i
$960$		−	7.82644i		−	0.252597i
$961$	28.1141			0.906908
$962$		−	24.9268i		−	0.803671i
$963$	−13.5805			−0.437624
$964$	51.2141			1.64949
$965$	12.9504			0.416887
$966$	47.5604			1.53023
$967$			17.8620i			0.574402i	0.957870	+	0.287201i	$0.0927248\pi$
$967$			17.8620i			0.574402i	−0.957870	+	0.287201i	$0.907275\pi$
$968$	−1.26277	−	3.73359i	−0.0405871	−	0.120002i
$969$	14.5440	−	1.31138i	0.467220	−	0.0421278i
$970$		−	23.0226i		−	0.739212i
$971$			47.0160i			1.50882i	0.656406	+	0.754408i	$0.272076\pi$
$971$			47.0160i			1.50882i	−0.656406	+	0.754408i	$0.727924\pi$
$972$		−	34.7595i		−	1.11491i
$973$	71.2073			2.28280
$974$			33.7743i			1.08220i
$975$			3.55462i			0.113839i
$976$			5.43049i			0.173826i
$977$		−	60.2471i		−	1.92747i	−0.266852	−	0.963737i	$-0.585984\pi$
$977$		−	60.2471i		−	1.92747i	0.266852	−	0.963737i	$-0.414016\pi$
$978$		−	7.50152i		−	0.239872i
$979$	7.76972	−	10.8300i	0.248321	−	0.346127i
$980$	34.4876			1.10167
$981$	−39.9300			−1.27487
$982$			6.03692i			0.192646i
$983$		−	52.9616i		−	1.68921i	−0.535388	−	0.844607i	$-0.679834\pi$
$983$		−	52.9616i		−	1.68921i	0.535388	−	0.844607i	$-0.320166\pi$
$984$			1.72667i			0.0550442i
$985$			10.8525i			0.345790i
$986$			2.29419i			0.0730619i
$987$	6.96487			0.221694
$988$	40.0437	−	3.61061i	1.27396	−	0.114869i
$989$			29.5813i			0.940629i
$990$	−12.6498	−	9.07531i	−0.402036	−	0.288432i
$991$		−	13.9302i		−	0.442508i	−0.975216	−	0.221254i	$-0.928985\pi$
$991$		−	13.9302i		−	0.442508i	0.975216	−	0.221254i	$-0.0710150\pi$
$992$			13.7782i			0.437458i
$993$	7.43017			0.235789
$994$	−120.717			−3.82890
$995$	−21.8885			−0.693911
$996$	26.9081			0.852616
$997$		−	44.1823i		−	1.39927i	−0.714501	−	0.699634i	$-0.753346\pi$
$997$		−	44.1823i		−	1.39927i	0.714501	−	0.699634i	$-0.246654\pi$
$998$	11.4805			0.363409
$999$	−12.7758			−0.404210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.a.626.7	✓	40
11.10	odd	2	inner	1045.2.f.a.626.33	yes	40
19.18	odd	2	inner	1045.2.f.a.626.34	yes	40
209.208	even	2	inner	1045.2.f.a.626.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.a.626.7	✓	40	1.1	even	1	trivial
1045.2.f.a.626.8	yes	40	209.208	even	2	inner
1045.2.f.a.626.33	yes	40	11.10	odd	2	inner
1045.2.f.a.626.34	yes	40	19.18	odd	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.04337 q^{2} -0.838315i q^{3} +2.17535 q^{4} -1.00000 q^{5} +1.71299i q^{6} -4.78057i q^{7} -0.358306 q^{8} +2.29723 q^{9} +O(q^{10})\)	\(q-2.04337 q^{2} -0.838315i q^{3} +2.17535 q^{4} -1.00000 q^{5} +1.71299i q^{6} -4.78057i q^{7} -0.358306 q^{8} +2.29723 q^{9} +2.04337 q^{10} +(-2.69484 - 1.93335i) q^{11} -1.82363i q^{12} -4.24020 q^{13} +9.76845i q^{14} +0.838315i q^{15} -3.61855 q^{16} -3.99629i q^{17} -4.69408 q^{18} +(-4.34129 + 0.391440i) q^{19} -2.17535 q^{20} -4.00762 q^{21} +(5.50654 + 3.95055i) q^{22} +5.80780 q^{23} +0.300373i q^{24} +1.00000 q^{25} +8.66428 q^{26} -4.44075i q^{27} -10.3994i q^{28} +0.280948 q^{29} -1.71299i q^{30} +1.69878i q^{31} +8.11064 q^{32} +(-1.62076 + 2.25912i) q^{33} +8.16589i q^{34} +4.78057i q^{35} +4.99727 q^{36} -2.87696i q^{37} +(8.87084 - 0.799856i) q^{38} +3.55462i q^{39} +0.358306 q^{40} +5.74842 q^{41} +8.18905 q^{42} +5.09337i q^{43} +(-5.86222 - 4.20572i) q^{44} -2.29723 q^{45} -11.8675 q^{46} -1.73791 q^{47} +3.03349i q^{48} -15.8538 q^{49} -2.04337 q^{50} -3.35015 q^{51} -9.22392 q^{52} -10.5567i q^{53} +9.07408i q^{54} +(2.69484 + 1.93335i) q^{55} +1.71290i q^{56} +(0.328151 + 3.63937i) q^{57} -0.574080 q^{58} -1.61310i q^{59} +1.82363i q^{60} -1.50074i q^{61} -3.47123i q^{62} -10.9820i q^{63} -9.33592 q^{64} +4.24020 q^{65} +(3.31181 - 4.61622i) q^{66} +12.0842i q^{67} -8.69333i q^{68} -4.86877i q^{69} -9.76845i q^{70} +12.3578i q^{71} -0.823109 q^{72} -0.489478i q^{73} +5.87868i q^{74} -0.838315i q^{75} +(-9.44382 + 0.851520i) q^{76} +(-9.24252 + 12.8828i) q^{77} -7.26340i q^{78} -6.76671 q^{79} +3.61855 q^{80} +3.16893 q^{81} -11.7461 q^{82} +14.7552i q^{83} -8.71798 q^{84} +3.99629i q^{85} -10.4076i q^{86} -0.235523i q^{87} +(0.965575 + 0.692731i) q^{88} +4.01878i q^{89} +4.69408 q^{90} +20.2706i q^{91} +12.6340 q^{92} +1.42411 q^{93} +3.55118 q^{94} +(4.34129 - 0.391440i) q^{95} -6.79928i q^{96} -11.2670i q^{97} +32.3952 q^{98} +(-6.19065 - 4.44135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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