LMFDB - Embedded newform 1045.2.b.d.419.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.10
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.790175i q^{2} +2.57534i q^{3} +1.37562 q^{4} +(1.76786 - 1.36919i) q^{5} +2.03497 q^{6} -0.0669205i q^{7} -2.66733i q^{8} -3.63236 q^{9} +O(q^{10})$	\(q-0.790175i q^{2} +2.57534i q^{3} +1.37562 q^{4} +(1.76786 - 1.36919i) q^{5} +2.03497 q^{6} -0.0669205i q^{7} -2.66733i q^{8} -3.63236 q^{9} +(-1.08190 - 1.39692i) q^{10} -1.00000 q^{11} +3.54270i q^{12} +4.14913i q^{13} -0.0528789 q^{14} +(3.52613 + 4.55283i) q^{15} +0.643589 q^{16} +6.61558i q^{17} +2.87020i q^{18} +1.00000 q^{19} +(2.43191 - 1.88349i) q^{20} +0.172343 q^{21} +0.790175i q^{22} +2.21109i q^{23} +6.86928 q^{24} +(1.25064 - 4.84106i) q^{25} +3.27854 q^{26} -1.62854i q^{27} -0.0920574i q^{28} -2.56775 q^{29} +(3.59753 - 2.78626i) q^{30} +8.77193 q^{31} -5.84321i q^{32} -2.57534i q^{33} +5.22747 q^{34} +(-0.0916269 - 0.118306i) q^{35} -4.99676 q^{36} -11.4277i q^{37} -0.790175i q^{38} -10.6854 q^{39} +(-3.65209 - 4.71546i) q^{40} +10.9830 q^{41} -0.136181i q^{42} +3.95978i q^{43} -1.37562 q^{44} +(-6.42149 + 4.97339i) q^{45} +1.74715 q^{46} +8.97459i q^{47} +1.65746i q^{48} +6.99552 q^{49} +(-3.82529 - 0.988221i) q^{50} -17.0374 q^{51} +5.70765i q^{52} -3.13641i q^{53} -1.28683 q^{54} +(-1.76786 + 1.36919i) q^{55} -0.178499 q^{56} +2.57534i q^{57} +2.02897i q^{58} -10.3362 q^{59} +(4.85062 + 6.26298i) q^{60} +2.76550 q^{61} -6.93135i q^{62} +0.243079i q^{63} -3.32998 q^{64} +(5.68095 + 7.33507i) q^{65} -2.03497 q^{66} -15.2686i q^{67} +9.10056i q^{68} -5.69431 q^{69} +(-0.0934823 + 0.0724013i) q^{70} -4.11096 q^{71} +9.68871i q^{72} +7.16167i q^{73} -9.02987 q^{74} +(12.4674 + 3.22081i) q^{75} +1.37562 q^{76} +0.0669205i q^{77} +8.44334i q^{78} -8.94984 q^{79} +(1.13777 - 0.881196i) q^{80} -6.70304 q^{81} -8.67846i q^{82} +3.78408i q^{83} +0.237079 q^{84} +(9.05799 + 11.6954i) q^{85} +3.12892 q^{86} -6.61283i q^{87} +2.66733i q^{88} -0.223450 q^{89} +(3.92985 + 5.07410i) q^{90} +0.277662 q^{91} +3.04163i q^{92} +22.5907i q^{93} +7.09149 q^{94} +(1.76786 - 1.36919i) q^{95} +15.0482 q^{96} -14.1106i q^{97} -5.52768i q^{98} +3.63236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

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 $

$2$		−	0.790175i		−	0.558738i	−0.960184	−	0.279369i	$-0.909875\pi$
$2$		−	0.790175i		−	0.558738i	0.960184	−	0.279369i	$-0.0901252\pi$
$3$			2.57534i			1.48687i	0.668807	+	0.743436i	$0.266805\pi$
$3$			2.57534i			1.48687i	−0.668807	+	0.743436i	$0.733195\pi$
$4$	1.37562			0.687812
$5$	1.76786	−	1.36919i	0.790610	−	0.612320i
$5$	1.76786	−	1.36919i	0.790610	−	0.612320i
$6$	2.03497			0.830771
$7$		−	0.0669205i		−	0.0252936i	−0.999920	−	0.0126468i	$-0.995974\pi$
$7$		−	0.0669205i		−	0.0252936i	0.999920	−	0.0126468i	$-0.00402570\pi$
$8$		−	2.66733i		−	0.943044i
$9$	−3.63236			−1.21079
$10$	−1.08190	−	1.39692i	−0.342127	−	0.441744i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			3.54270i			1.02269i
$13$			4.14913i			1.15076i	0.817885	+	0.575381i	$0.195146\pi$
$13$			4.14913i			1.15076i	−0.817885	+	0.575381i	$0.804854\pi$
$14$	−0.0528789			−0.0141325
$15$	3.52613	+	4.55283i	0.910442	+	1.17553i
$16$	0.643589			0.160897
$17$			6.61558i			1.60451i	0.596978	+	0.802257i	$0.296368\pi$
$17$			6.61558i			1.60451i	−0.596978	+	0.802257i	$0.703632\pi$
$18$			2.87020i			0.676512i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	2.43191	−	1.88349i	0.543791	−	0.421161i
$21$	0.172343			0.0376083
$22$			0.790175i			0.168466i
$23$			2.21109i			0.461045i	0.973067	+	0.230522i	$0.0740435\pi$
$23$			2.21109i			0.461045i	−0.973067	+	0.230522i	$0.925957\pi$
$24$	6.86928			1.40219
$25$	1.25064	−	4.84106i	0.250127	−	0.968213i
$26$	3.27854			0.642974
$27$		−	1.62854i		−	0.313413i
$28$		−	0.0920574i		−	0.0173972i
$29$	−2.56775			−0.476820			−0.238410	−	0.971165i	$-0.576626\pi$
$29$	−2.56775			−0.476820			−0.238410	+	0.971165i	$0.576626\pi$
$30$	3.59753	−	2.78626i	0.656816	−	0.508698i
$31$	8.77193			1.57548			0.787742	−	0.616005i	$-0.211250\pi$
$31$	8.77193			1.57548			0.787742	+	0.616005i	$0.211250\pi$
$32$		−	5.84321i		−	1.03294i
$33$		−	2.57534i		−	0.448309i
$34$	5.22747			0.896503
$35$	−0.0916269	−	0.118306i	−0.0154878	−	0.0199973i
$36$	−4.99676			−0.832794
$37$		−	11.4277i		−	1.87870i	−0.342960	−	0.939350i	$-0.611430\pi$
$37$		−	11.4277i		−	1.87870i	0.342960	−	0.939350i	$-0.388570\pi$
$38$		−	0.790175i		−	0.128183i
$39$	−10.6854			−1.71104
$40$	−3.65209	−	4.71546i	−0.577445	−	0.745580i
$41$	10.9830			1.71525			0.857626	−	0.514274i	$-0.171939\pi$
$41$	10.9830			1.71525			0.857626	+	0.514274i	$0.171939\pi$
$42$		−	0.136181i		−	0.0210132i
$43$			3.95978i			0.603861i	0.953330	+	0.301931i	$0.0976311\pi$
$43$			3.95978i			0.603861i	−0.953330	+	0.301931i	$0.902369\pi$
$44$	−1.37562			−0.207383
$45$	−6.42149	+	4.97339i	−0.957260	+	0.741390i
$46$	1.74715			0.257603
$47$			8.97459i			1.30908i	0.756028	+	0.654539i	$0.227137\pi$
$47$			8.97459i			1.30908i	−0.756028	+	0.654539i	$0.772863\pi$
$48$			1.65746i			0.239234i
$49$	6.99552			0.999360
$50$	−3.82529	−	0.988221i	−0.540977	−	0.139756i
$51$	−17.0374			−2.38571
$52$			5.70765i			0.791508i
$53$		−	3.13641i		−	0.430819i	−0.976524	−	0.215410i	$-0.930891\pi$
$53$		−	3.13641i		−	0.430819i	0.976524	−	0.215410i	$-0.0691087\pi$
$54$	−1.28683			−0.175116
$55$	−1.76786	+	1.36919i	−0.238378	+	0.184622i
$56$	−0.178499			−0.0238530
$57$			2.57534i			0.341112i
$58$			2.02897i			0.266417i
$59$	−10.3362			−1.34566			−0.672828	−	0.739799i	$-0.734921\pi$
$59$	−10.3362			−1.34566			−0.672828	+	0.739799i	$0.734921\pi$
$60$	4.85062	+	6.26298i	0.626213	+	0.808547i
$61$	2.76550			0.354086			0.177043	−	0.984203i	$-0.443347\pi$
$61$	2.76550			0.354086			0.177043	+	0.984203i	$0.443347\pi$
$62$		−	6.93135i		−	0.880283i
$63$			0.243079i			0.0306251i
$64$	−3.32998			−0.416248
$65$	5.68095	+	7.33507i	0.704635	+	0.909804i
$66$	−2.03497			−0.250487
$67$		−	15.2686i		−	1.86535i	−0.360713	−	0.932677i	$-0.617467\pi$
$67$		−	15.2686i		−	1.86535i	0.360713	−	0.932677i	$-0.382533\pi$
$68$			9.10056i			1.10360i
$69$	−5.69431			−0.685514
$70$	−0.0934823	+	0.0724013i	−0.0111733	+	0.00865360i
$71$	−4.11096			−0.487881			−0.243940	−	0.969790i	$-0.578440\pi$
$71$	−4.11096			−0.487881			−0.243940	+	0.969790i	$0.578440\pi$
$72$			9.68871i			1.14183i
$73$			7.16167i			0.838210i	0.907938	+	0.419105i	$0.137656\pi$
$73$			7.16167i			0.838210i	−0.907938	+	0.419105i	$0.862344\pi$
$74$	−9.02987			−1.04970
$75$	12.4674	+	3.22081i	1.43961	+	0.371907i
$76$	1.37562			0.157795
$77$			0.0669205i			0.00762630i
$78$			8.44334i			0.956020i
$79$	−8.94984			−1.00694			−0.503468	−	0.864014i	$-0.667943\pi$
$79$	−8.94984			−1.00694			−0.503468	+	0.864014i	$0.667943\pi$
$80$	1.13777	−	0.881196i	0.127207	−	0.0985207i
$81$	−6.70304			−0.744782
$82$		−	8.67846i		−	0.958376i
$83$			3.78408i			0.415357i	0.978197	+	0.207679i	$0.0665908\pi$
$83$			3.78408i			0.415357i	−0.978197	+	0.207679i	$0.933409\pi$
$84$	0.237079			0.0258674
$85$	9.05799	+	11.6954i	0.982477	+	1.26854i
$86$	3.12892			0.337400
$87$		−	6.61283i		−	0.708970i
$88$			2.66733i			0.284339i
$89$	−0.223450			−0.0236856			−0.0118428	−	0.999930i	$-0.503770\pi$
$89$	−0.223450			−0.0236856			−0.0118428	+	0.999930i	$0.503770\pi$
$90$	3.92985	+	5.07410i	0.414242	+	0.534857i
$91$	0.277662			0.0291069
$92$			3.04163i			0.317112i
$93$			22.5907i			2.34254i
$94$	7.09149			0.731431
$95$	1.76786	−	1.36919i	0.181378	−	0.140476i
$96$	15.0482			1.53585
$97$		−	14.1106i		−	1.43272i	−0.697732	−	0.716359i	$-0.745807\pi$
$97$		−	14.1106i		−	1.43272i	0.697732	−	0.716359i	$-0.254193\pi$
$98$		−	5.52768i		−	0.558380i
$99$	3.63236			0.365066
$100$	1.72041	−	6.65948i	0.172041	−	0.665948i
$101$	−11.6761			−1.16182			−0.580909	−	0.813968i	$-0.697303\pi$
$101$	−11.6761			−1.16182			−0.580909	+	0.813968i	$0.697303\pi$
$102$			13.4625i			1.33298i
$103$		−	11.6529i		−	1.14820i	−0.818786	−	0.574098i	$-0.805353\pi$
$103$		−	11.6529i		−	1.14820i	0.818786	−	0.574098i	$-0.194647\pi$
$104$	11.0671			1.08522
$105$	0.304677	−	0.235970i	0.0297335	−	0.0230283i
$106$	−2.47831			−0.240715
$107$		−	2.72445i		−	0.263382i	−0.991291	−	0.131691i	$-0.957959\pi$
$107$		−	2.72445i		−	0.263382i	0.991291	−	0.131691i	$-0.0420407\pi$
$108$		−	2.24026i		−	0.215569i
$109$	3.96882			0.380144			0.190072	−	0.981770i	$-0.439128\pi$
$109$	3.96882			0.380144			0.190072	+	0.981770i	$0.439128\pi$
$110$	1.08190	+	1.39692i	0.103155	+	0.133191i
$111$	29.4301			2.79339
$112$		−	0.0430693i		−	0.00406967i
$113$			2.81732i			0.265031i	0.991181	+	0.132516i	$0.0423055\pi$
$113$			2.81732i			0.265031i	−0.991181	+	0.132516i	$0.957695\pi$
$114$	2.03497			0.190592
$115$	3.02741	+	3.90890i	0.282307	+	0.364506i
$116$	−3.53226			−0.327962
$117$		−	15.0711i		−	1.39333i
$118$			8.16739i			0.751869i
$119$	0.442718			0.0405839
$120$	12.1439	−	9.40535i	1.10858	−	0.858587i
$121$	1.00000			0.0909091
$122$		−	2.18523i		−	0.197841i
$123$			28.2848i			2.55036i
$124$	12.0669			1.08364
$125$	−4.41739	−	10.2707i	−0.395104	−	0.918637i
$126$	0.192075			0.0171114
$127$			1.05561i			0.0936707i	0.998903	+	0.0468353i	$0.0149136\pi$
$127$			1.05561i			0.0936707i	−0.998903	+	0.0468353i	$0.985086\pi$
$128$		−	9.05516i		−	0.800371i
$129$	−10.1978			−0.897864
$130$	5.79599	−	4.48894i	0.508342	−	0.393706i
$131$	−18.2156			−1.59151			−0.795753	−	0.605621i	$-0.792925\pi$
$131$	−18.2156			−1.59151			−0.795753	+	0.605621i	$0.792925\pi$
$132$		−	3.54270i		−	0.308352i
$133$		−	0.0669205i		−	0.00580274i
$134$	−12.0648			−1.04224
$135$	−2.22978	−	2.87903i	−0.191909	−	0.247787i
$136$	17.6460			1.51313
$137$		−	7.14378i		−	0.610334i	−0.952299	−	0.305167i	$-0.901288\pi$
$137$		−	7.14378i		−	0.610334i	0.952299	−	0.305167i	$-0.0987123\pi$
$138$			4.49950i			0.383023i
$139$	−2.25667			−0.191408			−0.0957041	−	0.995410i	$-0.530510\pi$
$139$	−2.25667			−0.191408			−0.0957041	+	0.995410i	$0.530510\pi$
$140$	−0.126044	−	0.162744i	−0.0106527	−	0.0137544i
$141$	−23.1126			−1.94643
$142$			3.24837i			0.272598i
$143$		−	4.14913i		−	0.346968i
$144$	−2.33775			−0.194812
$145$	−4.53942	+	3.51574i	−0.376978	+	0.291967i
$146$	5.65897			0.468340
$147$			18.0158i			1.48592i
$148$		−	15.7202i		−	1.29219i
$149$	−5.60288			−0.459006			−0.229503	−	0.973308i	$-0.573710\pi$
$149$	−5.60288			−0.459006			−0.229503	+	0.973308i	$0.573710\pi$
$150$	2.54500	−	9.85140i	0.207799	−	0.804364i
$151$	−20.8631			−1.69782			−0.848908	−	0.528541i	$-0.822739\pi$
$151$	−20.8631			−1.69782			−0.848908	+	0.528541i	$0.822739\pi$
$152$		−	2.66733i		−	0.216349i
$153$		−	24.0302i		−	1.94273i
$154$	0.0528789			0.00426110
$155$	15.5075	−	12.0104i	1.24559	−	0.964701i
$156$	−14.6991			−1.17687
$157$			0.664796i			0.0530565i	0.999648	+	0.0265282i	$0.00844519\pi$
$157$			0.664796i			0.0530565i	−0.999648	+	0.0265282i	$0.991555\pi$
$158$			7.07194i			0.562613i
$159$	8.07732			0.640573
$160$	−8.00047	−	10.3300i	−0.632493	−	0.816655i
$161$	0.147967			0.0116615
$162$			5.29657i			0.416138i
$163$			0.357030i			0.0279647i	0.999902	+	0.0139824i	$0.00445087\pi$
$163$			0.357030i			0.0279647i	−0.999902	+	0.0139824i	$0.995549\pi$
$164$	15.1084			1.17977
$165$	−3.52613	−	4.55283i	−0.274509	−	0.354437i
$166$	2.99009			0.232076
$167$			12.2396i			0.947127i	0.880760	+	0.473563i	$0.157033\pi$
$167$			12.2396i			0.947127i	−0.880760	+	0.473563i	$0.842967\pi$
$168$		−	0.459696i		−	0.0354663i
$169$	−4.21530			−0.324253
$170$	9.24141	−	7.15740i	0.708784	−	0.548947i
$171$	−3.63236			−0.277774
$172$			5.44717i			0.415343i
$173$		−	14.4260i		−	1.09679i	−0.836220	−	0.548394i	$-0.815239\pi$
$173$		−	14.4260i		−	1.09679i	0.836220	−	0.548394i	$-0.184761\pi$
$174$	−5.22529			−0.396128
$175$	−0.323966	−	0.0836932i	−0.0244896	−	0.00632661i
$176$	−0.643589			−0.0485124
$177$		−	26.6191i		−	2.00082i
$178$			0.176564i			0.0132341i
$179$	−8.72275			−0.651969			−0.325984	−	0.945375i	$-0.605696\pi$
$179$	−8.72275			−0.651969			−0.325984	+	0.945375i	$0.605696\pi$
$180$	−8.83356	+	6.84152i	−0.658415	+	0.509937i
$181$	−13.9631			−1.03787			−0.518936	−	0.854813i	$-0.673672\pi$
$181$	−13.9631			−1.03787			−0.518936	+	0.854813i	$0.673672\pi$
$182$		−	0.219401i		−	0.0162631i
$183$			7.12209i			0.526480i
$184$	5.89772			0.434786
$185$	−15.6467	−	20.2025i	−1.15037	−	1.48532i
$186$	17.8506			1.30887
$187$		−	6.61558i		−	0.483779i
$188$			12.3457i			0.900400i
$189$	−0.108983			−0.00792733
$190$	−1.08190	−	1.39692i	−0.0784892	−	0.101343i
$191$	4.76262			0.344611			0.172306	−	0.985044i	$-0.444878\pi$
$191$	4.76262			0.344611			0.172306	+	0.985044i	$0.444878\pi$
$192$		−	8.57582i		−	0.618907i
$193$		−	5.69191i		−	0.409713i	−0.978792	−	0.204856i	$-0.934327\pi$
$193$		−	5.69191i		−	0.409713i	0.978792	−	0.204856i	$-0.0656727\pi$
$194$	−11.1499			−0.800514
$195$	−18.8903	+	14.6304i	−1.35276	+	1.04770i
$196$	9.62321			0.687372
$197$		−	19.1425i		−	1.36385i	−0.731424	−	0.681923i	$-0.761144\pi$
$197$		−	19.1425i		−	1.36385i	0.731424	−	0.681923i	$-0.238856\pi$
$198$		−	2.87020i		−	0.203976i
$199$	−21.1279			−1.49772			−0.748859	−	0.662730i	$-0.769398\pi$
$199$	−21.1279			−1.49772			−0.748859	+	0.662730i	$0.769398\pi$
$200$	−12.9127	−	3.33586i	−0.913068	−	0.235881i
$201$	39.3217			2.77354
$202$			9.22619i			0.649152i
$203$			0.171835i			0.0120605i
$204$	−23.4370			−1.64092
$205$	19.4163	−	15.0378i	1.35609	−	1.05028i
$206$	−9.20784			−0.641541
$207$		−	8.03149i		−	0.558227i
$208$			2.67034i			0.185155i
$209$	−1.00000			−0.0691714
$210$	−0.186458	−	0.240748i	−0.0128668	−	0.0166132i
$211$	21.9394			1.51037			0.755187	−	0.655510i	$-0.227546\pi$
$211$	21.9394			1.51037			0.755187	+	0.655510i	$0.227546\pi$
$212$		−	4.31452i		−	0.296323i
$213$		−	10.5871i		−	0.725416i
$214$	−2.15279			−0.147162
$215$	5.42169	+	7.00033i	0.369757	+	0.477418i
$216$	−4.34386			−0.295562
$217$		−	0.587022i		−	0.0398496i
$218$		−	3.13606i		−	0.212401i
$219$	−18.4437			−1.24631
$220$	−2.43191	+	1.88349i	−0.163959	+	0.126985i
$221$	−27.4489			−1.84641
$222$		−	23.2549i		−	1.56077i
$223$			23.0514i			1.54363i	0.635844	+	0.771817i	$0.280652\pi$
$223$			23.0514i			1.54363i	−0.635844	+	0.771817i	$0.719348\pi$
$224$	−0.391031			−0.0261268
$225$	−4.54276	+	17.5845i	−0.302851	+	1.17230i
$226$	2.22618			0.148083
$227$			12.1150i			0.804101i	0.915618	+	0.402050i	$0.131702\pi$
$227$			12.1150i			0.804101i	−0.915618	+	0.402050i	$0.868298\pi$
$228$			3.54270i			0.234621i
$229$	17.0184			1.12461			0.562303	−	0.826931i	$-0.309915\pi$
$229$	17.0184			1.12461			0.562303	+	0.826931i	$0.309915\pi$
$230$	3.08871	−	2.39218i	0.203664	−	0.157736i
$231$	−0.172343			−0.0113393
$232$			6.84905i			0.449662i
$233$		−	2.08834i		−	0.136812i	−0.997658	−	0.0684060i	$-0.978209\pi$
$233$		−	2.08834i		−	0.136812i	0.997658	−	0.0684060i	$-0.0217913\pi$
$234$	−11.9088			−0.778505
$235$	12.2879	+	15.8658i	0.801575	+	1.03497i
$236$	−14.2187			−0.925558
$237$		−	23.0488i		−	1.49718i
$238$		−	0.349825i		−	0.0226758i
$239$	16.8870			1.09233			0.546165	−	0.837677i	$-0.316087\pi$
$239$	16.8870			1.09233			0.546165	+	0.837677i	$0.316087\pi$
$240$	2.26938	+	2.93015i	0.146488	+	0.189140i
$241$	19.6461			1.26551			0.632757	−	0.774351i	$-0.281923\pi$
$241$	19.6461			1.26551			0.632757	+	0.774351i	$0.281923\pi$
$242$		−	0.790175i		−	0.0507944i
$243$		−	22.1482i		−	1.42081i
$244$	3.80429			0.243545
$245$	12.3671	−	9.57820i	0.790104	−	0.611929i
$246$	22.3500			1.42498
$247$			4.14913i			0.264003i
$248$		−	23.3976i		−	1.48575i
$249$	−9.74529			−0.617583
$250$	−8.11562	+	3.49051i	−0.513277	+	0.220759i
$251$	21.9810			1.38743			0.693714	−	0.720251i	$-0.255973\pi$
$251$	21.9810			1.38743			0.693714	+	0.720251i	$0.255973\pi$
$252$			0.334386i			0.0210643i
$253$		−	2.21109i		−	0.139010i
$254$	0.834120			0.0523374
$255$	−30.1196	+	23.3274i	−1.88616	+	1.46082i
$256$	−13.8151			−0.863445
$257$			27.5365i			1.71768i	0.512246	+	0.858839i	$0.328814\pi$
$257$			27.5365i			1.71768i	−0.512246	+	0.858839i	$0.671186\pi$
$258$			8.05802i			0.501671i
$259$	−0.764746			−0.0475190
$260$	7.81485	+	10.0903i	0.484657	+	0.625774i
$261$	9.32701			0.577327
$262$			14.3935i			0.889235i
$263$		−	21.4214i		−	1.32090i	−0.750871	−	0.660449i	$-0.770366\pi$
$263$		−	21.4214i		−	1.32090i	0.750871	−	0.660449i	$-0.229634\pi$
$264$	−6.86928			−0.422775
$265$	−4.29435	−	5.54473i	−0.263800	−	0.340610i
$266$	−0.0528789			−0.00324221
$267$		−	0.575459i		−	0.0352175i
$268$		−	21.0038i		−	1.28301i
$269$	−8.06510			−0.491738			−0.245869	−	0.969303i	$-0.579073\pi$
$269$	−8.06510			−0.491738			−0.245869	+	0.969303i	$0.579073\pi$
$270$	−2.27494	+	1.76192i	−0.138448	+	0.107227i
$271$	−14.7370			−0.895211			−0.447606	−	0.894231i	$-0.647723\pi$
$271$	−14.7370			−0.895211			−0.447606	+	0.894231i	$0.647723\pi$
$272$			4.25772i			0.258162i
$273$			0.715073i			0.0432782i
$274$	−5.64483			−0.341017
$275$	−1.25064	+	4.84106i	−0.0754162	+	0.291927i
$276$	−7.83323			−0.471505
$277$		−	32.5834i		−	1.95775i	−0.204470	−	0.978873i	$-0.565547\pi$
$277$		−	32.5834i		−	1.95775i	0.204470	−	0.978873i	$-0.434453\pi$
$278$			1.78316i			0.106947i
$279$	−31.8628			−1.90758
$280$	−0.315561	+	0.244399i	−0.0188584	+	0.0146057i
$281$	−16.8550			−1.00548			−0.502741	−	0.864437i	$-0.667675\pi$
$281$	−16.8550			−1.00548			−0.502741	+	0.864437i	$0.667675\pi$
$282$			18.2630i			1.08754i
$283$			6.26244i			0.372263i	0.982525	+	0.186132i	$0.0595951\pi$
$283$			6.26244i			0.372263i	−0.982525	+	0.186132i	$0.940405\pi$
$284$	−5.65513			−0.335570
$285$	3.52613	+	4.55283i	0.208870	+	0.269686i
$286$	−3.27854			−0.193864
$287$		−	0.734986i		−	0.0433848i
$288$			21.2247i			1.25067i
$289$	−26.7659			−1.57447
$290$	2.77805	+	3.58693i	0.163133	+	0.210632i
$291$	36.3396			2.13027
$292$			9.85177i			0.576531i
$293$		−	7.67080i		−	0.448133i	−0.974574	−	0.224067i	$-0.928067\pi$
$293$		−	7.67080i		−	0.448133i	0.974574	−	0.224067i	$-0.0719333\pi$
$294$	14.2356			0.830240
$295$	−18.2729	+	14.1522i	−1.06389	+	0.823973i
$296$	−30.4814			−1.77170
$297$			1.62854i			0.0944976i
$298$			4.42725i			0.256464i
$299$	−9.17411			−0.530553
$300$	17.1504	+	4.43062i	0.990180	+	0.255802i
$301$	0.264991			0.0152738
$302$			16.4855i			0.948634i
$303$		−	30.0700i		−	1.72748i
$304$	0.643589			0.0369124
$305$	4.88901	−	3.78649i	0.279944	−	0.216814i
$306$	−18.9880			−1.08547
$307$			0.00440478i			0.000251394i	1.00000		0.000125697i	$4.00106e-5\pi$
$307$			0.00440478i			0.000251394i	−1.00000		0.000125697i	$0.999960\pi$
$308$			0.0920574i			0.00524546i
$309$	30.0102			1.70722
$310$	−9.49034	−	12.2536i	−0.539015	−	0.695960i
$311$	12.0604			0.683883			0.341942	−	0.939721i	$-0.388915\pi$
$311$	12.0604			0.683883			0.341942	+	0.939721i	$0.388915\pi$
$312$			28.5015i			1.61358i
$313$			16.4882i			0.931967i	0.884793	+	0.465983i	$0.154299\pi$
$313$			16.4882i			0.931967i	−0.884793	+	0.465983i	$0.845701\pi$
$314$	0.525305			0.0296447
$315$	0.332822	+	0.429730i	0.0187524	+	0.0242125i
$316$	−12.3116			−0.692582
$317$		−	25.9591i		−	1.45801i	−0.684508	−	0.729005i	$-0.739983\pi$
$317$		−	25.9591i		−	1.45801i	0.684508	−	0.729005i	$-0.260017\pi$
$318$		−	6.38249i		−	0.357912i
$319$	2.56775			0.143767
$320$	−5.88693	+	4.55938i	−0.329089	+	0.254877i
$321$	7.01637			0.391616
$322$		−	0.116920i		−	0.00651570i
$323$			6.61558i			0.368101i
$324$	−9.22086			−0.512270
$325$	20.0862	+	5.18906i	1.11418	+	0.287837i
$326$	0.282116			0.0156249
$327$			10.2210i			0.565225i
$328$		−	29.2952i		−	1.61756i
$329$	0.600584			0.0331113
$330$	−3.59753	+	2.78626i	−0.198037	+	0.153378i
$331$	25.4456			1.39862			0.699310	−	0.714819i	$-0.253491\pi$
$331$	25.4456			1.39862			0.699310	+	0.714819i	$0.253491\pi$
$332$			5.20548i			0.285688i
$333$			41.5095i			2.27470i
$334$	9.67140			0.529196
$335$	−20.9056	−	26.9927i	−1.14219	−	1.47477i
$336$	0.110918			0.00605107
$337$			28.8344i			1.57071i	0.619046	+	0.785355i	$0.287520\pi$
$337$			28.8344i			1.57071i	−0.619046	+	0.785355i	$0.712480\pi$
$338$			3.33082i			0.181173i
$339$	−7.25555			−0.394067
$340$	12.4604	+	16.0885i	0.675760	+	0.872520i
$341$	−8.77193			−0.475026
$342$			2.87020i			0.155203i
$343$		−	0.936587i		−	0.0505710i
$344$	10.5621			0.569468
$345$	−10.0667	+	7.79659i	−0.541974	+	0.419754i
$346$	−11.3991			−0.612817
$347$			20.2741i			1.08837i	0.838965	+	0.544185i	$0.183161\pi$
$347$			20.2741i			1.08837i	−0.838965	+	0.544185i	$0.816839\pi$
$348$		−	9.09677i		−	0.487638i
$349$	−23.5879			−1.26263			−0.631316	−	0.775525i	$-0.717485\pi$
$349$	−23.5879			−1.26263			−0.631316	+	0.775525i	$0.717485\pi$
$350$	−0.0661323	+	0.255990i	−0.00353492	+	0.0136832i
$351$	6.75703			0.360664
$352$			5.84321i			0.311444i
$353$		−	26.1715i		−	1.39297i	−0.717573	−	0.696484i	$-0.754747\pi$
$353$		−	26.1715i		−	1.39297i	0.717573	−	0.696484i	$-0.245253\pi$
$354$	−21.0338			−1.11793
$355$	−7.26759	+	5.62868i	−0.385723	+	0.298739i
$356$	−0.307383			−0.0162913
$357$			1.14015i			0.0603431i
$358$			6.89249i			0.364280i
$359$	−32.5322			−1.71698			−0.858492	−	0.512828i	$-0.828598\pi$
$359$	−32.5322			−1.71698			−0.858492	+	0.512828i	$0.828598\pi$
$360$	13.2657	+	17.1283i	0.699163	+	0.902739i
$361$	1.00000			0.0526316
$362$			11.0333i			0.579898i
$363$			2.57534i			0.135170i
$364$	0.381958			0.0200201
$365$	9.80569	+	12.6608i	0.513253	+	0.662697i
$366$	5.62770			0.294164
$367$			9.12225i			0.476178i	0.971243	+	0.238089i	$0.0765210\pi$
$367$			9.12225i			0.476178i	−0.971243	+	0.238089i	$0.923479\pi$
$368$			1.42304i			0.0741808i
$369$	−39.8941			−2.07680
$370$	−15.9635	+	12.3636i	−0.829903	+	0.642753i
$371$	−0.209890			−0.0108970
$372$			31.0763i			1.61123i
$373$		−	32.3890i		−	1.67704i	−0.544872	−	0.838519i	$-0.683422\pi$
$373$		−	32.3890i		−	1.67704i	0.544872	−	0.838519i	$-0.316578\pi$
$374$	−5.22747			−0.270306
$375$	26.4504	−	11.3763i	1.36589	−	0.587468i
$376$	23.9382			1.23452
$377$		−	10.6539i		−	0.548706i
$378$			0.0861155i			0.00442930i
$379$	20.8497			1.07098			0.535489	−	0.844542i	$-0.320127\pi$
$379$	20.8497			1.07098			0.535489	+	0.844542i	$0.320127\pi$
$380$	2.43191	−	1.88349i	0.124754	−	0.0966210i
$381$	−2.71856			−0.139276
$382$		−	3.76330i		−	0.192547i
$383$		−	14.8606i		−	0.759342i	−0.925122	−	0.379671i	$-0.876037\pi$
$383$		−	14.8606i		−	0.759342i	0.925122	−	0.379671i	$-0.123963\pi$
$384$	23.3201			1.19005
$385$	0.0916269	+	0.118306i	0.00466974	+	0.00602943i
$386$	−4.49760			−0.228922
$387$		−	14.3834i		−	0.731147i
$388$		−	19.4109i		−	0.985441i
$389$	2.79047			0.141482			0.0707412	−	0.997495i	$-0.477464\pi$
$389$	2.79047			0.141482			0.0707412	+	0.997495i	$0.477464\pi$
$390$	11.5605	+	14.9266i	0.585391	+	0.755839i
$391$	−14.6277			−0.739753
$392$		−	18.6594i		−	0.942441i
$393$		−	46.9114i		−	2.36637i
$394$	−15.1259			−0.762032
$395$	−15.8220	+	12.2540i	−0.796093	+	0.616567i
$396$	4.99676			0.251097
$397$			9.55809i			0.479707i	0.970809	+	0.239853i	$0.0770994\pi$
$397$			9.55809i			0.479707i	−0.970809	+	0.239853i	$0.922901\pi$
$398$			16.6947i			0.836832i
$399$	0.172343			0.00862793
$400$	0.804896	−	3.11566i	0.0402448	−	0.155783i
$401$	−9.84081			−0.491427			−0.245713	−	0.969343i	$-0.579022\pi$
$401$	−9.84081			−0.491427			−0.245713	+	0.969343i	$0.579022\pi$
$402$		−	31.0710i		−	1.54968i
$403$			36.3959i			1.81301i
$404$	−16.0620			−0.799113
$405$	−11.8500	+	9.17773i	−0.588832	+	0.456045i
$406$	0.135780			0.00673864
$407$			11.4277i			0.566449i
$408$			45.4443i			2.24983i
$409$	−5.23929			−0.259066			−0.129533	−	0.991575i	$-0.541348\pi$
$409$	−5.23929			−0.259066			−0.129533	+	0.991575i	$0.541348\pi$
$410$	−11.8825	−	15.3423i	−0.586833	−	0.757701i
$411$	18.3976			0.907488
$412$		−	16.0300i		−	0.789743i
$413$			0.691702i			0.0340364i
$414$	−6.34628			−0.311902
$415$	5.18113	+	6.68972i	0.254332	+	0.328385i
$416$	24.2443			1.18867
$417$		−	5.81168i		−	0.284599i
$418$			0.790175i			0.0386487i
$419$	11.2351			0.548870			0.274435	−	0.961606i	$-0.411509\pi$
$419$	11.2351			0.548870			0.274435	+	0.961606i	$0.411509\pi$
$420$	0.419122	−	0.324606i	0.0204510	−	0.0158392i
$421$	34.2914			1.67126			0.835630	−	0.549292i	$-0.185103\pi$
$421$	34.2914			1.67126			0.835630	+	0.549292i	$0.185103\pi$
$422$		−	17.3360i		−	0.843903i
$423$		−	32.5989i		−	1.58501i
$424$	−8.36586			−0.406282
$425$	32.0265	+	8.27369i	1.55351	+	0.401333i
$426$	−8.36566			−0.405318
$427$		−	0.185069i		−	0.00895610i
$428$		−	3.74782i		−	0.181158i
$429$	10.6854			0.515897
$430$	5.53148	−	4.28409i	0.266752	−	0.206597i
$431$	24.2325			1.16724			0.583620	−	0.812027i	$-0.301636\pi$
$431$	24.2325			1.16724			0.583620	+	0.812027i	$0.301636\pi$
$432$		−	1.04811i		−	0.0504273i
$433$		−	11.5535i		−	0.555228i	−0.960693	−	0.277614i	$-0.910456\pi$
$433$		−	11.5535i		−	0.555228i	0.960693	−	0.277614i	$-0.0895436\pi$
$434$	−0.463850			−0.0222655
$435$	−9.05422	−	11.6905i	−0.434117	−	0.560518i
$436$	5.45960			0.261467
$437$			2.21109i			0.105771i
$438$			14.5738i			0.696361i
$439$	38.1975			1.82307			0.911534	−	0.411225i	$-0.134899\pi$
$439$	38.1975			1.82307			0.911534	+	0.411225i	$0.134899\pi$
$440$	3.65209	+	4.71546i	0.174106	+	0.224801i
$441$	−25.4103			−1.21001
$442$			21.6894i			1.03166i
$443$			19.8322i			0.942256i	0.882065	+	0.471128i	$0.156153\pi$
$443$			19.8322i			0.942256i	−0.882065	+	0.471128i	$0.843847\pi$
$444$	40.4848			1.92132
$445$	−0.395027	+	0.305945i	−0.0187261	+	0.0145032i
$446$	18.2146			0.862487
$447$		−	14.4293i		−	0.682483i
$448$			0.222844i			0.0105284i
$449$	−19.6541			−0.927532			−0.463766	−	0.885958i	$-0.653502\pi$
$449$	−19.6541			−0.927532			−0.463766	+	0.885958i	$0.653502\pi$
$450$	13.8948	+	3.58958i	0.655008	+	0.169214i
$451$	−10.9830			−0.517168
$452$			3.87557i			0.182292i
$453$		−	53.7295i		−	2.52443i
$454$	9.57296			0.449282
$455$	0.490867	−	0.380172i	0.0230122	−	0.0178227i
$456$	6.86928			0.321684
$457$		−	12.6434i		−	0.591432i	−0.955276	−	0.295716i	$-0.904442\pi$
$457$		−	12.6434i		−	0.591432i	0.955276	−	0.295716i	$-0.0955581\pi$
$458$		−	13.4475i		−	0.628360i
$459$	10.7738			0.502876
$460$	4.16457	+	5.37717i	0.194174	+	0.250712i
$461$	−2.24816			−0.104707			−0.0523536	−	0.998629i	$-0.516672\pi$
$461$	−2.24816			−0.104707			−0.0523536	+	0.998629i	$0.516672\pi$
$462$			0.136181i			0.00633571i
$463$			16.2839i			0.756778i	0.925647	+	0.378389i	$0.123522\pi$
$463$			16.2839i			0.756778i	−0.925647	+	0.378389i	$0.876478\pi$
$464$	−1.65258			−0.0767190
$465$	30.9309	+	39.9371i	1.43439	+	1.85204i
$466$	−1.65016			−0.0764420
$467$			2.08404i			0.0964378i	0.998837	+	0.0482189i	$0.0153545\pi$
$467$			2.08404i			0.0964378i	−0.998837	+	0.0482189i	$0.984645\pi$
$468$		−	20.7322i		−	0.958347i
$469$	−1.02178			−0.0471815
$470$	12.5367	−	9.70960i	0.578277	−	0.447870i
$471$	−1.71207			−0.0788881
$472$			27.5700i			1.26901i
$473$		−	3.95978i		−	0.182071i
$474$	−18.2126			−0.836533
$475$	1.25064	−	4.84106i	0.0573831	−	0.222123i
$476$	0.609014			0.0279141
$477$			11.3926i			0.521630i
$478$		−	13.3437i		−	0.610326i
$479$	−16.3963			−0.749164			−0.374582	−	0.927194i	$-0.622214\pi$
$479$	−16.3963			−0.749164			−0.374582	+	0.927194i	$0.622214\pi$
$480$	26.6031	−	20.6039i	1.21426	−	0.940435i
$481$	47.4150			2.16194
$482$		−	15.5238i		−	0.707090i
$483$			0.381066i			0.0173391i
$484$	1.37562			0.0625284
$485$	−19.3201	−	24.9456i	−0.877283	−	1.13272i
$486$	−17.5010			−0.793859
$487$			6.55183i			0.296892i	0.988921	+	0.148446i	$0.0474271\pi$
$487$			6.55183i			0.296892i	−0.988921	+	0.148446i	$0.952573\pi$
$488$		−	7.37651i		−	0.333919i
$489$	−0.919471			−0.0415799
$490$	−7.56845	−	9.77215i	−0.341908	−	0.441461i
$491$	29.7599			1.34305			0.671524	−	0.740983i	$-0.265640\pi$
$491$	29.7599			1.34305			0.671524	+	0.740983i	$0.265640\pi$
$492$			38.9093i			1.75417i
$493$		−	16.9872i		−	0.765064i
$494$	3.27854			0.147508
$495$	6.42149	−	4.97339i	0.288625	−	0.223537i
$496$	5.64552			0.253491
$497$			0.275107i			0.0123403i
$498$			7.70048i			0.345067i
$499$	25.0420			1.12104			0.560518	−	0.828142i	$-0.310602\pi$
$499$	25.0420			1.12104			0.560518	+	0.828142i	$0.310602\pi$
$500$	−6.07667	−	14.1286i	−0.271757	−	0.631849i
$501$	−31.5210			−1.40826
$502$		−	17.3688i		−	0.775208i
$503$		−	14.9942i		−	0.668560i	−0.942474	−	0.334280i	$-0.891507\pi$
$503$		−	14.9942i		−	0.668560i	0.942474	−	0.334280i	$-0.108493\pi$
$504$	0.648374			0.0288809
$505$	−20.6417	+	15.9868i	−0.918545	+	0.711405i
$506$	−1.74715			−0.0776703
$507$		−	10.8558i		−	0.482123i
$508$			1.45213i			0.0644278i
$509$	21.5572			0.955506			0.477753	−	0.878494i	$-0.341451\pi$
$509$	21.5572			0.955506			0.477753	+	0.878494i	$0.341451\pi$
$510$	18.4327	+	23.7998i	0.816214	+	1.05387i
$511$	0.479263			0.0212013
$512$		−	7.19396i		−	0.317931i
$513$		−	1.62854i		−	0.0719019i
$514$	21.7586			0.959731
$515$	−15.9551	−	20.6007i	−0.703064	−	0.907775i
$516$	−14.0283			−0.617562
$517$		−	8.97459i		−	0.394702i
$518$			0.604283i			0.0265507i
$519$	37.1518			1.63078
$520$	19.5651	−	15.1530i	0.857985	−	0.664502i
$521$	−34.7658			−1.52312			−0.761558	−	0.648097i	$-0.775565\pi$
$521$	−34.7658			−1.52312			−0.761558	+	0.648097i	$0.775565\pi$
$522$		−	7.36996i		−	0.322575i
$523$		−	26.7047i		−	1.16771i	−0.811856	−	0.583857i	$-0.801543\pi$
$523$		−	26.7047i		−	1.16771i	0.811856	−	0.583857i	$-0.198457\pi$
$524$	−25.0579			−1.09466
$525$	0.215538	−	0.834323i	0.00940686	−	0.0364128i
$526$	−16.9266			−0.738036
$527$			58.0314i			2.52789i
$528$		−	1.65746i		−	0.0721316i
$529$	18.1111			0.787438
$530$	−4.38130	+	3.39328i	−0.190312	+	0.147395i
$531$	37.5447			1.62930
$532$		−	0.0920574i		−	0.00399120i
$533$			45.5698i			1.97385i
$534$	−0.454713			−0.0196773
$535$	−3.73029	−	4.81644i	−0.161274	−	0.208233i
$536$	−40.7264			−1.75911
$537$		−	22.4640i		−	0.969394i
$538$			6.37284i			0.274753i
$539$	−6.99552			−0.301318
$540$	−3.06734	−	3.96046i	−0.131997	−	0.170431i
$541$	9.54398			0.410328			0.205164	−	0.978728i	$-0.434227\pi$
$541$	9.54398			0.410328			0.205164	+	0.978728i	$0.434227\pi$
$542$			11.6448i			0.500188i
$543$		−	35.9598i		−	1.54318i
$544$	38.6563			1.65737
$545$	7.01630	−	5.43407i	0.300545	−	0.232770i
$546$	0.565033			0.0241812
$547$			27.6080i			1.18043i	0.807245	+	0.590217i	$0.200958\pi$
$547$			27.6080i			1.18043i	−0.807245	+	0.590217i	$0.799042\pi$
$548$		−	9.82715i		−	0.419795i
$549$	−10.0453			−0.428723
$550$	3.82529	+	0.988221i	0.163111	+	0.0421379i
$551$	−2.56775			−0.109390
$552$			15.1886i			0.646470i
$553$			0.598928i			0.0254690i
$554$	−25.7466			−1.09387
$555$	52.0283	−	40.2955i	2.20848	−	1.71045i
$556$	−3.10433			−0.131653
$557$			14.9783i			0.634651i	0.948317	+	0.317325i	$0.102785\pi$
$557$			14.9783i			0.634651i	−0.948317	+	0.317325i	$0.897215\pi$
$558$			25.1772i			1.06583i
$559$	−16.4297			−0.694900
$560$	−0.0589701	−	0.0761404i	−0.00249194	−	0.00321752i
$561$	17.0374			0.719318
$562$			13.3184i			0.561801i
$563$		−	0.475683i		−	0.0200476i	−0.999950	−	0.0100238i	$-0.996809\pi$
$563$		−	0.475683i		−	0.0200476i	0.999950	−	0.0100238i	$-0.00319073\pi$
$564$	−31.7942			−1.33878
$565$	3.85745	+	4.98062i	0.162284	+	0.209536i
$566$	4.94842			0.207998
$567$			0.448571i			0.0188382i
$568$			10.9653i			0.460093i
$569$	9.06417			0.379990			0.189995	−	0.981785i	$-0.439153\pi$
$569$	9.06417			0.379990			0.189995	+	0.981785i	$0.439153\pi$
$570$	3.59753	−	2.78626i	0.150684	−	0.116703i
$571$	4.75692			0.199071			0.0995355	−	0.995034i	$-0.468264\pi$
$571$	4.75692			0.199071			0.0995355	+	0.995034i	$0.468264\pi$
$572$		−	5.70765i		−	0.238649i
$573$			12.2654i			0.512393i
$574$	−0.580767			−0.0242408
$575$	10.7040	+	2.76527i	0.446389	+	0.115320i
$576$	12.0957			0.503987
$577$			24.9499i			1.03868i	0.854569	+	0.519338i	$0.173822\pi$
$577$			24.9499i			1.03868i	−0.854569	+	0.519338i	$0.826178\pi$
$578$			21.1498i			0.879715i
$579$	14.6586			0.609190
$580$	−6.24454	+	4.83634i	−0.259290	+	0.200818i
$581$	0.253233			0.0105059
$582$		−	28.7147i		−	1.19026i
$583$			3.13641i			0.129897i
$584$	19.1026			0.790470
$585$	−20.6353	−	26.6436i	−0.853163	−	1.10158i
$586$	−6.06127			−0.250389
$587$			19.3052i			0.796810i	0.917210	+	0.398405i	$0.130436\pi$
$587$			19.3052i			0.796810i	−0.917210	+	0.398405i	$0.869564\pi$
$588$			24.7830i			1.02203i
$589$	8.77193			0.361441
$590$	11.1827	+	14.4388i	0.460385	+	0.594435i
$591$	49.2983			2.02786
$592$		−	7.35473i		−	0.302278i
$593$			6.49883i			0.266875i	0.991057	+	0.133437i	$0.0426015\pi$
$593$			6.49883i			0.266875i	−0.991057	+	0.133437i	$0.957398\pi$
$594$	1.28683			0.0527994
$595$	0.782662	−	0.606165i	0.0320860	−	0.0248504i
$596$	−7.70746			−0.315710
$597$		−	54.4115i		−	2.22691i
$598$			7.24915i			0.296440i
$599$	−8.10308			−0.331083			−0.165541	−	0.986203i	$-0.552937\pi$
$599$	−8.10308			−0.331083			−0.165541	+	0.986203i	$0.552937\pi$
$600$	8.59097	−	33.2546i	0.350725	−	1.35761i
$601$	−34.2650			−1.39770			−0.698848	−	0.715270i	$-0.746304\pi$
$601$	−34.2650			−1.39770			−0.698848	+	0.715270i	$0.746304\pi$
$602$		−	0.209389i		−	0.00853405i
$603$			55.4610i			2.25855i
$604$	−28.6998			−1.16778
$605$	1.76786	−	1.36919i	0.0718736	−	0.0556655i
$606$	−23.7605			−0.965206
$607$		−	16.9455i		−	0.687797i	−0.939007	−	0.343898i	$-0.888252\pi$
$607$		−	16.9455i		−	0.687797i	0.939007	−	0.343898i	$-0.111748\pi$
$608$		−	5.84321i		−	0.236974i
$609$	−0.442534			−0.0179324
$610$	−2.99199	−	3.86317i	−0.121142	−	0.156415i
$611$	−37.2367			−1.50644
$612$		−	33.0565i		−	1.33623i
$613$			1.47243i			0.0594709i	0.999558	+	0.0297354i	$0.00946648\pi$
$613$			1.47243i			0.0594709i	−0.999558	+	0.0297354i	$0.990534\pi$
$614$	0.00348055			0.000140464
$615$	38.7273	+	50.0036i	1.56164	+	2.01634i
$616$	0.178499			0.00719194
$617$		−	19.4675i		−	0.783731i	−0.920022	−	0.391866i	$-0.871830\pi$
$617$		−	19.4675i		−	0.783731i	0.920022	−	0.391866i	$-0.128170\pi$
$618$		−	23.7133i		−	0.953889i
$619$	−21.8377			−0.877732			−0.438866	−	0.898552i	$-0.644620\pi$
$619$	−21.8377			−0.877732			−0.438866	+	0.898552i	$0.644620\pi$
$620$	21.3325	−	16.5218i	0.856734	−	0.663533i
$621$	3.60086			0.144497
$622$		−	9.52983i		−	0.382112i
$623$			0.0149534i			0.000599094i
$624$	−6.87702			−0.275301
$625$	−21.8718	−	12.1088i	−0.874873	−	0.484353i
$626$	13.0285			0.520725
$627$		−	2.57534i		−	0.102849i
$628$			0.914509i			0.0364929i
$629$	75.6008			3.01440
$630$	0.339561	−	0.262987i	0.0135285	−	0.0104777i
$631$	0.393330			0.0156582			0.00782912	−	0.999969i	$-0.497508\pi$
$631$	0.393330			0.0156582			0.00782912	+	0.999969i	$0.497508\pi$
$632$			23.8722i			0.949585i
$633$			56.5015i			2.24573i
$634$	−20.5123			−0.814646
$635$	1.44534	+	1.86618i	0.0573565	+	0.0740569i
$636$	11.1114			0.440594
$637$			29.0253i			1.15003i
$638$		−	2.02897i		−	0.0803278i
$639$	14.9325			0.590720
$640$	−12.3982	−	16.0082i	−0.490083	−	0.632781i
$641$	2.08000			0.0821549			0.0410774	−	0.999156i	$-0.486921\pi$
$641$	2.08000			0.0821549			0.0410774	+	0.999156i	$0.486921\pi$
$642$		−	5.54416i		−	0.218811i
$643$		−	15.7787i		−	0.622250i	−0.950369	−	0.311125i	$-0.899294\pi$
$643$		−	15.7787i		−	0.622250i	0.950369	−	0.311125i	$-0.100706\pi$
$644$	0.203548			0.00802090
$645$	−18.0282	+	13.9627i	−0.709860	+	0.549780i
$646$	5.22747			0.205672
$647$			6.67760i			0.262524i	0.991348	+	0.131262i	$0.0419028\pi$
$647$			6.67760i			0.262524i	−0.991348	+	0.131262i	$0.958097\pi$
$648$			17.8792i			0.702363i
$649$	10.3362			0.405731
$650$	4.10026	−	15.8716i	0.160825	−	0.622536i
$651$	1.51178			0.0592513
$652$			0.491138i			0.0192345i
$653$		−	6.00890i		−	0.235147i	−0.993064	−	0.117573i	$-0.962488\pi$
$653$		−	6.00890i		−	0.235147i	0.993064	−	0.117573i	$-0.0375115\pi$
$654$	8.07641			0.315813
$655$	−32.2026	+	24.9407i	−1.25826	+	0.974512i
$656$	7.06852			0.275979
$657$		−	26.0138i		−	1.01489i
$658$		−	0.474566i		−	0.0185005i
$659$	−14.3389			−0.558566			−0.279283	−	0.960209i	$-0.590097\pi$
$659$	−14.3389			−0.558566			−0.279283	+	0.960209i	$0.590097\pi$
$660$	−4.85062	−	6.26298i	−0.188810	−	0.243786i
$661$	−4.17451			−0.162370			−0.0811849	−	0.996699i	$-0.525870\pi$
$661$	−4.17451			−0.162370			−0.0811849	+	0.996699i	$0.525870\pi$
$662$		−	20.1065i		−	0.781462i
$663$		−	70.6902i		−	2.74538i
$664$	10.0934			0.391700
$665$	−0.0916269	−	0.118306i	−0.00355314	−	0.00458770i
$666$	32.7997			1.27096
$667$		−	5.67754i		−	0.219835i
$668$			16.8371i			0.651445i
$669$	−59.3651			−2.29519
$670$	−21.3289	+	16.5191i	−0.824008	+	0.638187i
$671$	−2.76550			−0.106761
$672$		−	1.00704i		−	0.0388473i
$673$			1.71412i			0.0660745i	0.999454	+	0.0330373i	$0.0105180\pi$
$673$			1.71412i			0.0660745i	−0.999454	+	0.0330373i	$0.989482\pi$
$674$	22.7842			0.877615
$675$	−7.88387	−	2.03671i	−0.303450	−	0.0783931i
$676$	−5.79866			−0.223025
$677$			0.206434i			0.00793392i	0.999992	+	0.00396696i	$0.00126273\pi$
$677$			0.206434i			0.00793392i	−0.999992	+	0.00396696i	$0.998737\pi$
$678$			5.73315i			0.220180i
$679$	−0.944291			−0.0362386
$680$	31.1955	−	24.1607i	1.19629	−	0.926520i
$681$	−31.2002			−1.19559
$682$			6.93135i			0.265415i
$683$			29.3173i			1.12179i	0.827886	+	0.560897i	$0.189544\pi$
$683$			29.3173i			1.12179i	−0.827886	+	0.560897i	$0.810456\pi$
$684$	−4.99676			−0.191056
$685$	−9.78119	−	12.6292i	−0.373720	−	0.482536i
$686$	−0.740068			−0.0282559
$687$			43.8280i			1.67214i
$688$			2.54847i			0.0971596i
$689$	13.0134			0.495771
$690$	6.16067	+	7.95447i	0.234533	+	0.302821i
$691$	−44.8795			−1.70730			−0.853649	−	0.520849i	$-0.825615\pi$
$691$	−44.8795			−1.70730			−0.853649	+	0.520849i	$0.825615\pi$
$692$		−	19.8448i		−	0.754384i
$693$		−	0.243079i		−	0.00923382i
$694$	16.0201			0.608114
$695$	−3.98947	+	3.08981i	−0.151329	+	0.117203i
$696$	−17.6386			−0.668590
$697$			72.6587i			2.75215i
$698$			18.6386i			0.705481i
$699$	5.37819			0.203422
$700$	−0.445656	−	0.115130i	−0.0168442	−	0.00435152i
$701$	7.13370			0.269436			0.134718	−	0.990884i	$-0.456987\pi$
$701$	7.13370			0.269436			0.134718	+	0.990884i	$0.456987\pi$
$702$		−	5.33924i		−	0.201517i
$703$		−	11.4277i		−	0.431003i
$704$	3.32998			0.125503
$705$	−40.8597	+	31.6455i	−1.53887	+	1.19184i
$706$	−20.6800			−0.778304
$707$			0.781373i			0.0293865i
$708$		−	36.6179i		−	1.37619i
$709$	37.5143			1.40888			0.704440	−	0.709763i	$-0.251198\pi$
$709$	37.5143			1.40888			0.704440	+	0.709763i	$0.251198\pi$
$710$	4.44764	+	5.74266i	0.166917	+	0.215518i
$711$	32.5090			1.21918
$712$			0.596015i			0.0223366i
$713$			19.3955i			0.726369i
$714$	0.900916			0.0337160
$715$	−5.68095	−	7.33507i	−0.212456	−	0.274316i
$716$	−11.9992			−0.448432
$717$			43.4898i			1.62415i
$718$			25.7061i			0.959343i
$719$	9.92990			0.370323			0.185161	−	0.982708i	$-0.440719\pi$
$719$	9.92990			0.370323			0.185161	+	0.982708i	$0.440719\pi$
$720$	−4.13280	+	3.20082i	−0.154021	+	0.119288i
$721$	−0.779819			−0.0290420
$722$		−	0.790175i		−	0.0294073i
$723$			50.5952i			1.88166i
$724$	−19.2080			−0.713860
$725$	−3.21133	+	12.4307i	−0.119266	+	0.461663i
$726$	2.03497			0.0755247
$727$			16.4750i			0.611025i	0.952188	+	0.305513i	$0.0988278\pi$
$727$			16.4750i			0.611025i	−0.952188	+	0.305513i	$0.901172\pi$
$728$		−	0.740617i		−	0.0274491i
$729$	36.9300			1.36778
$730$	10.0043	−	7.74821i	0.370274	−	0.286774i
$731$	−26.1963			−0.968904
$732$			9.79732i			0.362119i
$733$			35.6615i			1.31719i	0.752498	+	0.658594i	$0.228849\pi$
$733$			35.6615i			1.31719i	−0.752498	+	0.658594i	$0.771151\pi$
$734$	7.20817			0.266059
$735$	24.6671	+	31.8494i	0.909859	+	1.17478i
$736$	12.9199			0.476233
$737$			15.2686i			0.562425i
$738$			31.5233i			1.16039i
$739$	−12.0150			−0.441977			−0.220989	−	0.975276i	$-0.570928\pi$
$739$	−12.0150			−0.441977			−0.220989	+	0.975276i	$0.570928\pi$
$740$	−21.5239	−	27.7911i	−0.791236	−	1.02162i
$741$	−10.6854			−0.392538
$742$			0.165850i			0.00608854i
$743$			6.68005i			0.245067i	0.992464	+	0.122534i	$0.0391019\pi$
$743$			6.68005i			0.245067i	−0.992464	+	0.122534i	$0.960898\pi$
$744$	60.2568			2.20912
$745$	−9.90509	+	7.67141i	−0.362894	+	0.281059i
$746$	−25.5930			−0.937025
$747$		−	13.7452i		−	0.502909i
$748$		−	9.10056i		−	0.332749i
$749$	−0.182321			−0.00666188
$750$	−8.98924	−	20.9005i	−0.328241	−	0.763177i
$751$	−6.22015			−0.226976			−0.113488	−	0.993539i	$-0.536202\pi$
$751$	−6.22015			−0.226976			−0.113488	+	0.993539i	$0.536202\pi$
$752$			5.77595i			0.210627i
$753$			56.6084i			2.06293i
$754$	−8.41848			−0.306583
$755$	−36.8830	+	28.5656i	−1.34231	+	1.03961i
$756$	−0.149919			−0.00545251
$757$			14.2550i			0.518105i	0.965863	+	0.259053i	$0.0834103\pi$
$757$			14.2550i			0.518105i	−0.965863	+	0.259053i	$0.916590\pi$
$758$		−	16.4749i		−	0.598396i
$759$	5.69431			0.206690
$760$	−3.65209	−	4.71546i	−0.132475	−	0.171048i
$761$	−3.46765			−0.125702			−0.0628512	−	0.998023i	$-0.520019\pi$
$761$	−3.46765			−0.125702			−0.0628512	+	0.998023i	$0.520019\pi$
$762$			2.14814i			0.0778189i
$763$		−	0.265595i		−	0.00961519i
$764$	6.55158			0.237028
$765$	−32.9019	−	42.4819i	−1.18957	−	1.53594i
$766$	−11.7425			−0.424273
$767$		−	42.8862i		−	1.54853i
$768$		−	35.5786i		−	1.28383i
$769$	38.6283			1.39297			0.696485	−	0.717571i	$-0.254746\pi$
$769$	38.6283			1.39297			0.696485	+	0.717571i	$0.254746\pi$
$770$	0.0934823	−	0.0724013i	0.00336887	−	0.00260916i
$771$	−70.9157			−2.55397
$772$		−	7.82993i		−	0.281805i
$773$			27.8564i			1.00193i	0.865469	+	0.500963i	$0.167021\pi$
$773$			27.8564i			1.00193i	−0.865469	+	0.500963i	$0.832979\pi$
$774$	−11.3654			−0.408520
$775$	10.9705	−	42.4655i	0.394072	−	1.52540i
$776$	−37.6378			−1.35112
$777$		−	1.96948i		−	0.0706547i
$778$		−	2.20496i		−	0.0790515i
$779$	10.9830			0.393506
$780$	−25.9859	+	20.1259i	−0.930445	+	0.720622i
$781$	4.11096			0.147102
$782$			11.5584i			0.413328i
$783$			4.18169i			0.149441i
$784$	4.50224			0.160794
$785$	0.910231	+	1.17526i	0.0324876	+	0.0419469i
$786$	−37.0682			−1.32218
$787$			9.77533i			0.348453i	0.984706	+	0.174226i	$0.0557425\pi$
$787$			9.77533i			0.348453i	−0.984706	+	0.174226i	$0.944258\pi$
$788$		−	26.3329i		−	0.938069i
$789$	55.1672			1.96401
$790$	9.68282	+	12.5022i	0.344499	+	0.444807i
$791$	0.188537			0.00670359
$792$		−	9.68871i		−	0.344273i
$793$			11.4744i			0.407469i
$794$	7.55256			0.268030
$795$	14.2795	−	11.0594i	0.506443	−	0.392236i
$796$	−29.0641			−1.03015
$797$		−	2.96470i		−	0.105015i	−0.998621	−	0.0525075i	$-0.983279\pi$
$797$		−	2.96470i		−	0.105015i	0.998621	−	0.0525075i	$-0.0167214\pi$
$798$		−	0.136181i		−	0.00482075i
$799$	−59.3721			−2.10043
$800$	−28.2874	−	7.30773i	−1.00011	−	0.258367i
$801$	0.811650			0.0286782
$802$			7.77596i			0.274579i
$803$		−	7.16167i		−	0.252730i
$804$	54.0919			1.90767
$805$	0.261585	−	0.202596i	0.00921967	−	0.00714055i
$806$	28.7591			1.01300
$807$		−	20.7704i		−	0.731151i
$808$			31.1441i			1.09565i
$809$	−36.2770			−1.27543			−0.637715	−	0.770272i	$-0.720120\pi$
$809$	−36.2770			−1.27543			−0.637715	+	0.770272i	$0.720120\pi$
$810$	7.25201	+	9.36358i	0.254810	+	0.329003i
$811$	28.4399			0.998661			0.499330	−	0.866412i	$-0.333579\pi$
$811$	28.4399			0.998661			0.499330	+	0.866412i	$0.333579\pi$
$812$			0.236381i			0.00829534i
$813$		−	37.9528i		−	1.33106i
$814$	9.02987			0.316497
$815$	0.488841	+	0.631177i	0.0171234	+	0.0221092i
$816$	−10.9651			−0.383854
$817$			3.95978i			0.138535i
$818$			4.13995i			0.144750i
$819$	−1.00857			−0.0352422
$820$	26.7096	−	20.6863i	0.932738	−	0.722398i
$821$	34.1352			1.19133			0.595663	−	0.803235i	$-0.296890\pi$
$821$	34.1352			1.19133			0.595663	+	0.803235i	$0.296890\pi$
$822$		−	14.5373i		−	0.507048i
$823$		−	21.6135i		−	0.753400i	−0.926335	−	0.376700i	$-0.877059\pi$
$823$		−	21.6135i		−	0.753400i	0.926335	−	0.376700i	$-0.122941\pi$
$824$	−31.0822			−1.08280
$825$	−12.4674	−	3.22081i	−0.434058	−	0.112134i
$826$	0.546566			0.0190175
$827$		−	3.22960i		−	0.112304i	−0.998422	−	0.0561522i	$-0.982117\pi$
$827$		−	3.22960i		−	0.112304i	0.998422	−	0.0561522i	$-0.0178832\pi$
$828$		−	11.0483i		−	0.383955i
$829$	−54.2752			−1.88506			−0.942528	−	0.334126i	$-0.891559\pi$
$829$	−54.2752			−1.88506			−0.942528	+	0.334126i	$0.891559\pi$
$830$	5.28605	−	4.09400i	0.183481	−	0.142105i
$831$	83.9132			2.91092
$832$		−	13.8165i		−	0.479002i
$833$			46.2795i			1.60349i
$834$	−4.59224			−0.159016
$835$	16.7583	+	21.6378i	0.579945	+	0.748808i
$836$	−1.37562			−0.0475769
$837$		−	14.2854i		−	0.493777i
$838$		−	8.87769i		−	0.306675i
$839$	−18.4633			−0.637422			−0.318711	−	0.947852i	$-0.603250\pi$
$839$	−18.4633			−0.637422			−0.318711	+	0.947852i	$0.603250\pi$
$840$	−0.629411	−	0.812676i	−0.0217167	−	0.0280400i
$841$	−22.4066			−0.772643
$842$		−	27.0962i		−	0.933797i
$843$		−	43.4072i		−	1.49502i
$844$	30.1804			1.03885
$845$	−7.45204	+	5.77154i	−0.256358	+	0.198547i
$846$	−25.7589			−0.885608
$847$		−	0.0669205i		−	0.00229942i
$848$		−	2.01856i		−	0.0693177i
$849$	−16.1279			−0.553508
$850$	6.53766	−	25.3065i	0.224240	−	0.868006i
$851$	25.2677			0.866164
$852$		−	14.5639i		−	0.498950i
$853$		−	39.7042i		−	1.35945i	−0.733469	−	0.679723i	$-0.762100\pi$
$853$		−	39.7042i		−	1.35945i	0.733469	−	0.679723i	$-0.237900\pi$
$854$	−0.146237			−0.00500411
$855$	−6.42149	+	4.97339i	−0.219610	+	0.170086i
$856$	−7.26701			−0.248381
$857$			52.0593i			1.77831i	0.457606	+	0.889155i	$0.348707\pi$
$857$			52.0593i			1.77831i	−0.457606	+	0.889155i	$0.651293\pi$
$858$		−	8.44334i		−	0.288251i
$859$	−14.9753			−0.510952			−0.255476	−	0.966815i	$-0.582232\pi$
$859$	−14.9753			−0.510952			−0.255476	+	0.966815i	$0.582232\pi$
$860$	7.45821	+	9.62982i	0.254323	+	0.328374i
$861$	1.89284			0.0645077
$862$		−	19.1479i		−	0.652182i
$863$			17.1586i			0.584086i	0.956405	+	0.292043i	$0.0943350\pi$
$863$			17.1586i			0.584086i	−0.956405	+	0.292043i	$0.905665\pi$
$864$	−9.51591			−0.323738
$865$	−19.7519	−	25.5031i	−0.671586	−	0.867132i
$866$	−9.12932			−0.310227
$867$		−	68.9313i		−	2.34103i
$868$		−	0.807521i		−	0.0274091i
$869$	8.94984			0.303602
$870$	−9.23757	+	7.15442i	−0.313183	+	0.242557i
$871$	63.3513			2.14658
$872$		−	10.5862i		−	0.358493i
$873$			51.2549i			1.73472i
$874$	1.74715			0.0590982
$875$	−0.687318	+	0.295614i	−0.0232356	+	0.00999358i
$876$	−25.3716			−0.857228
$877$		−	7.93413i		−	0.267917i	−0.990987	−	0.133958i	$-0.957231\pi$
$877$		−	7.93413i		−	0.267917i	0.990987	−	0.133958i	$-0.0427688\pi$
$878$		−	30.1827i		−	1.01862i
$879$	19.7549			0.666316
$880$	−1.13777	+	0.881196i	−0.0383543	+	0.0297051i
$881$	−15.2979			−0.515399			−0.257700	−	0.966225i	$-0.582964\pi$
$881$	−15.2979			−0.515399			−0.257700	+	0.966225i	$0.582964\pi$
$882$			20.0785i			0.676080i
$883$			0.534788i			0.0179971i	0.999960	+	0.00899853i	$0.00286436\pi$
$883$			0.534788i			0.0179971i	−0.999960	+	0.00899853i	$0.997136\pi$
$884$	−37.7594			−1.26999
$885$	−36.4467	−	47.0588i	−1.22514	−	1.58187i
$886$	15.6709			0.526474
$887$		−	9.87389i		−	0.331533i	−0.986165	−	0.165766i	$-0.946990\pi$
$887$		−	9.87389i		−	0.331533i	0.986165	−	0.165766i	$-0.0530098\pi$
$888$		−	78.5000i		−	2.63429i
$889$	0.0706423			0.00236927
$890$	0.241750	+	0.312141i	0.00810349	+	0.0104630i
$891$	6.70304			0.224560
$892$			31.7100i			1.06173i
$893$			8.97459i			0.300323i
$894$	−11.4017			−0.381329
$895$	−15.4206	+	11.9431i	−0.515453	+	0.399214i
$896$	−0.605976			−0.0202442
$897$		−	23.6264i		−	0.788864i
$898$			15.5301i			0.518247i
$899$	−22.5241			−0.751222
$900$	−6.24913	+	24.1896i	−0.208304	+	0.806322i
$901$	20.7492			0.691256
$902$			8.67846i			0.288961i
$903$			0.682440i			0.0227102i
$904$	7.51473			0.249936
$905$	−24.6848	+	19.1182i	−0.820551	+	0.635510i
$906$	−42.4557			−1.41050
$907$			32.3531i			1.07427i	0.843497	+	0.537133i	$0.180493\pi$
$907$			32.3531i			1.07427i	−0.843497	+	0.537133i	$0.819507\pi$
$908$			16.6657i			0.553070i
$909$	42.4119			1.40671
$910$	−0.300402	−	0.387870i	−0.00995824	−	0.0128578i
$911$	−58.8040			−1.94826			−0.974132	−	0.225978i	$-0.927442\pi$
$911$	−58.8040			−1.94826			−0.974132	+	0.225978i	$0.927442\pi$
$912$			1.65746i			0.0548840i
$913$		−	3.78408i		−	0.125235i
$914$	−9.99047			−0.330455
$915$	9.75150	+	12.5908i	0.322375	+	0.416240i
$916$	23.4109			0.773517
$917$			1.21900i			0.0402549i
$918$		−	8.51315i		−	0.280976i
$919$	22.2112			0.732679			0.366340	−	0.930481i	$-0.380611\pi$
$919$	22.2112			0.732679			0.366340	+	0.930481i	$0.380611\pi$
$920$	10.4263	−	8.07510i	0.343746	−	0.266228i
$921$	−0.0113438			−0.000373791
$922$			1.77644i			0.0585038i
$923$		−	17.0569i		−	0.561435i
$924$	−0.237079			−0.00779932
$925$	−55.3222	−	14.2919i	−1.81898	−	0.469914i
$926$	12.8672			0.422841
$927$			42.3276i			1.39022i
$928$			15.0039i			0.492528i
$929$	−8.60843			−0.282433			−0.141217	−	0.989979i	$-0.545101\pi$
$929$	−8.60843			−0.282433			−0.141217	+	0.989979i	$0.545101\pi$
$930$	31.5573	−	24.4408i	1.03480	−	0.801446i
$931$	6.99552			0.229269
$932$		−	2.87278i		−	0.0941009i
$933$			31.0596i			1.01685i
$934$	1.64675			0.0538835
$935$	−9.05799	−	11.6954i	−0.296228	−	0.382481i
$936$	−40.1998			−1.31397
$937$			25.1791i			0.822566i	0.911508	+	0.411283i	$0.134919\pi$
$937$			25.1791i			0.822566i	−0.911508	+	0.411283i	$0.865081\pi$
$938$			0.807385i			0.0263621i
$939$	−42.4626			−1.38571
$940$	16.9036	+	21.8254i	0.551333	+	0.711865i
$941$	25.5413			0.832622			0.416311	−	0.909222i	$-0.363323\pi$
$941$	25.5413			0.832622			0.416311	+	0.909222i	$0.363323\pi$
$942$			1.35284i			0.0440778i
$943$			24.2844i			0.790808i
$944$	−6.65225			−0.216512
$945$	−0.192666	+	0.149218i	−0.00626743	+	0.00485407i
$946$	−3.12892			−0.101730
$947$		−	21.1214i		−	0.686353i	−0.939271	−	0.343176i	$-0.888497\pi$
$947$		−	21.1214i		−	0.686353i	0.939271	−	0.343176i	$-0.111503\pi$
$948$		−	31.7065i		−	1.02978i
$949$	−29.7147			−0.964581
$950$	−3.82529	−	0.988221i	−0.124109	−	0.0320621i
$951$	66.8535			2.16787
$952$		−	1.18088i		−	0.0382724i
$953$		−	14.3865i		−	0.466025i	−0.972474	−	0.233012i	$-0.925142\pi$
$953$		−	14.3865i		−	0.466025i	0.972474	−	0.233012i	$-0.0748583\pi$
$954$	9.00213			0.291455
$955$	8.41963	−	6.52094i	0.272453	−	0.211013i
$956$	23.2302			0.751318
$957$			6.61283i			0.213762i
$958$			12.9559i			0.418587i
$959$	−0.478065			−0.0154375
$960$	−11.7419	−	15.1608i	−0.378969	−	0.489314i
$961$	45.9467			1.48215
$962$		−	37.4661i		−	1.20796i
$963$			9.89618i			0.318900i
$964$	27.0256			0.870436
$965$	−7.79331	−	10.0625i	−0.250875	−	0.323923i
$966$	0.301109			0.00968801
$967$			41.6857i			1.34052i	0.742125	+	0.670261i	$0.233818\pi$
$967$			41.6857i			1.34052i	−0.742125	+	0.670261i	$0.766182\pi$
$968$		−	2.66733i		−	0.0857313i
$969$	−17.0374			−0.547319
$970$	−19.7114	+	15.2663i	−0.632894	+	0.490171i
$971$	45.0663			1.44625			0.723123	−	0.690719i	$-0.242706\pi$
$971$	45.0663			1.44625			0.723123	+	0.690719i	$0.242706\pi$
$972$		−	30.4676i		−	0.977249i
$973$			0.151017i			0.00484139i
$974$	5.17709			0.165885
$975$	−13.3636	+	51.7288i	−0.427977	+	1.65665i
$976$	1.77985			0.0569715
$977$		−	9.51039i		−	0.304264i	−0.988360	−	0.152132i	$-0.951386\pi$
$977$		−	9.51039i		−	0.304264i	0.988360	−	0.152132i	$-0.0486140\pi$
$978$			0.726543i			0.0232323i
$979$	0.223450			0.00714149
$980$	17.0125	−	13.1760i	0.543443	−	0.420892i
$981$	−14.4162			−0.460273
$982$		−	23.5156i		−	0.750412i
$983$			38.9961i			1.24378i	0.783104	+	0.621891i	$0.213635\pi$
$983$			38.9961i			1.24378i	−0.783104	+	0.621891i	$0.786365\pi$
$984$	75.4451			2.40510
$985$	−26.2097	−	33.8412i	−0.835110	−	1.07827i
$986$	−13.4228			−0.427470
$987$			1.54671i			0.0492322i
$988$			5.70765i			0.181584i
$989$	−8.75544			−0.278407
$990$	−3.92985	−	5.07410i	−0.124899	−	0.161266i
$991$	61.4220			1.95113			0.975566	−	0.219705i	$-0.0705095\pi$
$991$	61.4220			1.95113			0.975566	+	0.219705i	$0.0705095\pi$
$992$		−	51.2562i		−	1.62739i
$993$			65.5311i			2.07957i
$994$	0.217383			0.00689497
$995$	−37.3511	+	28.9281i	−1.18411	+	0.917083i
$996$	−13.4059			−0.424781
$997$		−	8.89988i		−	0.281862i	−0.990019	−	0.140931i	$-0.954990\pi$
$997$		−	8.89988i		−	0.281862i	0.990019	−	0.140931i	$-0.0450096\pi$
$998$		−	19.7876i		−	0.626365i
$999$	−18.6105			−0.588809

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.10	✓	22
5.2	odd	4		5225.2.a.bb.1.13		22
5.3	odd	4		5225.2.a.bb.1.10		22
5.4	even	2	inner	1045.2.b.d.419.13	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.10	✓	22	1.1	even	1	trivial
1045.2.b.d.419.13	yes	22	5.4	even	2	inner
5225.2.a.bb.1.10		22	5.3	odd	4
5225.2.a.bb.1.13		22	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.790175i q^{2} +2.57534i q^{3} +1.37562 q^{4} +(1.76786 - 1.36919i) q^{5} +2.03497 q^{6} -0.0669205i q^{7} -2.66733i q^{8} -3.63236 q^{9} +O(q^{10})\)	\(q-0.790175i q^{2} +2.57534i q^{3} +1.37562 q^{4} +(1.76786 - 1.36919i) q^{5} +2.03497 q^{6} -0.0669205i q^{7} -2.66733i q^{8} -3.63236 q^{9} +(-1.08190 - 1.39692i) q^{10} -1.00000 q^{11} +3.54270i q^{12} +4.14913i q^{13} -0.0528789 q^{14} +(3.52613 + 4.55283i) q^{15} +0.643589 q^{16} +6.61558i q^{17} +2.87020i q^{18} +1.00000 q^{19} +(2.43191 - 1.88349i) q^{20} +0.172343 q^{21} +0.790175i q^{22} +2.21109i q^{23} +6.86928 q^{24} +(1.25064 - 4.84106i) q^{25} +3.27854 q^{26} -1.62854i q^{27} -0.0920574i q^{28} -2.56775 q^{29} +(3.59753 - 2.78626i) q^{30} +8.77193 q^{31} -5.84321i q^{32} -2.57534i q^{33} +5.22747 q^{34} +(-0.0916269 - 0.118306i) q^{35} -4.99676 q^{36} -11.4277i q^{37} -0.790175i q^{38} -10.6854 q^{39} +(-3.65209 - 4.71546i) q^{40} +10.9830 q^{41} -0.136181i q^{42} +3.95978i q^{43} -1.37562 q^{44} +(-6.42149 + 4.97339i) q^{45} +1.74715 q^{46} +8.97459i q^{47} +1.65746i q^{48} +6.99552 q^{49} +(-3.82529 - 0.988221i) q^{50} -17.0374 q^{51} +5.70765i q^{52} -3.13641i q^{53} -1.28683 q^{54} +(-1.76786 + 1.36919i) q^{55} -0.178499 q^{56} +2.57534i q^{57} +2.02897i q^{58} -10.3362 q^{59} +(4.85062 + 6.26298i) q^{60} +2.76550 q^{61} -6.93135i q^{62} +0.243079i q^{63} -3.32998 q^{64} +(5.68095 + 7.33507i) q^{65} -2.03497 q^{66} -15.2686i q^{67} +9.10056i q^{68} -5.69431 q^{69} +(-0.0934823 + 0.0724013i) q^{70} -4.11096 q^{71} +9.68871i q^{72} +7.16167i q^{73} -9.02987 q^{74} +(12.4674 + 3.22081i) q^{75} +1.37562 q^{76} +0.0669205i q^{77} +8.44334i q^{78} -8.94984 q^{79} +(1.13777 - 0.881196i) q^{80} -6.70304 q^{81} -8.67846i q^{82} +3.78408i q^{83} +0.237079 q^{84} +(9.05799 + 11.6954i) q^{85} +3.12892 q^{86} -6.61283i q^{87} +2.66733i q^{88} -0.223450 q^{89} +(3.92985 + 5.07410i) q^{90} +0.277662 q^{91} +3.04163i q^{92} +22.5907i q^{93} +7.09149 q^{94} +(1.76786 - 1.36919i) q^{95} +15.0482 q^{96} -14.1106i q^{97} -5.52768i q^{98} +3.63236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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