LMFDB - Embedded newform 950.2.h.e.381.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.8
Character	$\chi$	$=$	950.381
Dual form			950.2.h.e.571.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.685786 - 0.498253i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.20717 - 0.358335i) q^{5} +(-0.685786 - 0.498253i) q^{6} +3.58997 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.705004 + 2.16978i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.685786 - 0.498253i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.20717 - 0.358335i) q^{5} +(-0.685786 - 0.498253i) q^{6} +3.58997 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.705004 + 2.16978i) q^{9} +(-1.02285 - 1.98841i) q^{10} +(-1.78472 - 5.49282i) q^{11} +(-0.261947 + 0.806190i) q^{12} +(-0.563649 + 1.73473i) q^{13} +(-1.10936 - 3.41426i) q^{14} +(1.33510 - 1.34547i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.44623 + 3.95692i) q^{17} +2.28144 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.57501 + 1.58724i) q^{20} +(2.46195 - 1.78871i) q^{21} +(-4.67247 + 3.39475i) q^{22} +(-2.20174 - 6.77626i) q^{23} +0.847678 q^{24} +(4.74319 - 1.58181i) q^{25} +1.82400 q^{26} +(1.38346 + 4.25785i) q^{27} +(-2.90435 + 2.11013i) q^{28} +(2.16636 - 1.57396i) q^{29} +(-1.69219 - 0.853987i) q^{30} +(1.00042 + 0.726848i) q^{31} -1.00000 q^{32} +(-3.96075 - 2.87765i) q^{33} +(2.08028 - 6.40243i) q^{34} +(7.92367 - 1.28641i) q^{35} +(-0.705004 - 2.16978i) q^{36} +(-2.56064 + 7.88085i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(0.477793 + 1.47049i) q^{39} +(1.99626 + 1.00744i) q^{40} +(-1.62345 + 4.99647i) q^{41} +(-2.46195 - 1.78871i) q^{42} +0.882966 q^{43} +(4.67247 + 3.39475i) q^{44} +(-0.778555 + 5.04170i) q^{45} +(-5.76423 + 4.18796i) q^{46} +(0.839936 - 0.610249i) q^{47} +(-0.261947 - 0.806190i) q^{48} +5.88787 q^{49} +(-2.97012 - 4.02224i) q^{50} +5.70650 q^{51} +(-0.563649 - 1.73473i) q^{52} +(6.77928 - 4.92544i) q^{53} +(3.62194 - 2.63149i) q^{54} +(-5.90746 - 11.4840i) q^{55} +(2.90435 + 2.11013i) q^{56} -0.847678 q^{57} +(-2.16636 - 1.57396i) q^{58} +(-0.113424 + 0.349083i) q^{59} +(-0.289275 + 1.87326i) q^{60} +(-1.08477 - 3.33859i) q^{61} +(0.382127 - 1.17607i) q^{62} +(-2.53094 + 7.78944i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.622453 + 4.03082i) q^{65} +(-1.51287 + 4.65614i) q^{66} +(-6.26903 - 4.55472i) q^{67} -6.73191 q^{68} +(-4.88621 - 3.55004i) q^{69} +(-3.67200 - 7.13833i) q^{70} +(3.78957 - 2.75328i) q^{71} +(-1.84572 + 1.34100i) q^{72} +(-2.81194 - 8.65426i) q^{73} +8.28642 q^{74} +(2.46467 - 3.44809i) q^{75} +1.00000 q^{76} +(-6.40710 - 19.7190i) q^{77} +(1.25088 - 0.908816i) q^{78} +(-1.27191 + 0.924099i) q^{79} +(0.341256 - 2.20987i) q^{80} +(-2.46693 - 1.79233i) q^{81} +5.25360 q^{82} +(-11.5416 - 8.38547i) q^{83} +(-0.940382 + 2.89420i) q^{84} +(13.4387 + 6.78202i) q^{85} +(-0.272851 - 0.839750i) q^{86} +(0.701435 - 2.15879i) q^{87} +(1.78472 - 5.49282i) q^{88} +(0.970222 + 2.98604i) q^{89} +(5.03553 - 0.817520i) q^{90} +(-2.02348 + 6.22763i) q^{91} +(5.76423 + 4.18796i) q^{92} +1.04823 q^{93} +(-0.839936 - 0.610249i) q^{94} +(-1.99626 - 1.00744i) q^{95} +(-0.685786 + 0.498253i) q^{96} +(15.2164 - 11.0554i) q^{97} +(-1.81945 - 5.59970i) q^{98} +13.1764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.685786	−	0.498253i	0.395939	−	0.287666i	−0.371946	−	0.928254i	$-0.621309\pi$
$3$	0.685786	−	0.498253i	0.395939	−	0.287666i	0.767885	+	0.640588i	$0.221309\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.20717	−	0.358335i	0.987076	−	0.160252i
$5$	2.20717	−	0.358335i	0.987076	−	0.160252i
$6$	−0.685786	−	0.498253i	−0.279971	−	0.203411i
$7$	3.58997			1.35688			0.678440	−	0.734656i	$-0.262656\pi$
$7$	3.58997			1.35688			0.678440	+	0.734656i	$0.262656\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.705004	+	2.16978i	−0.235001	+	0.723260i
$10$	−1.02285	−	1.98841i	−0.323453	−	0.628791i
$11$	−1.78472	−	5.49282i	−0.538115	−	1.65615i	−0.736821	−	0.676088i	$-0.763674\pi$
$11$	−1.78472	−	5.49282i	−0.538115	−	1.65615i	0.198707	−	0.980059i	$-0.436326\pi$
$12$	−0.261947	+	0.806190i	−0.0756176	+	0.232727i
$13$	−0.563649	+	1.73473i	−0.156328	+	0.481128i	−0.998293	−	0.0584040i	$-0.981399\pi$
$13$	−0.563649	+	1.73473i	−0.156328	+	0.481128i	0.841965	+	0.539532i	$0.181399\pi$
$14$	−1.10936	−	3.41426i	−0.296489	−	0.912500i
$15$	1.33510	−	1.34547i	0.344723	−	0.347399i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	5.44623	+	3.95692i	1.32091	+	0.959694i	0.999920	+	0.0126097i	$0.00401389\pi$
$17$	5.44623	+	3.95692i	1.32091	+	0.959694i	0.320985	+	0.947084i	$0.395986\pi$
$18$	2.28144			0.537741
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	−1.57501	+	1.58724i	−0.352184	+	0.354918i
$21$	2.46195	−	1.78871i	0.537242	−	0.390329i
$22$	−4.67247	+	3.39475i	−0.996174	+	0.723763i
$23$	−2.20174	−	6.77626i	−0.459095	−	1.41295i	−0.866260	−	0.499594i	$-0.833483\pi$
$23$	−2.20174	−	6.77626i	−0.459095	−	1.41295i	0.407165	−	0.913355i	$-0.366517\pi$
$24$	0.847678			0.173032
$25$	4.74319	−	1.58181i	0.948638	−	0.316362i
$26$	1.82400			0.357717
$27$	1.38346	+	4.25785i	0.266247	+	0.819423i
$28$	−2.90435	+	2.11013i	−0.548870	+	0.398777i
$29$	2.16636	−	1.57396i	0.402284	−	0.292276i	−0.368187	−	0.929752i	$-0.620021\pi$
$29$	2.16636	−	1.57396i	0.402284	−	0.292276i	0.770471	+	0.637476i	$0.220021\pi$
$30$	−1.69219	−	0.853987i	−0.308950	−	0.155916i
$31$	1.00042	+	0.726848i	0.179681	+	0.130546i	0.673990	−	0.738740i	$-0.264579\pi$
$31$	1.00042	+	0.726848i	0.179681	+	0.130546i	−0.494309	+	0.869286i	$0.664579\pi$
$32$	−1.00000			−0.176777
$33$	−3.96075	−	2.87765i	−0.689478	−	0.500935i
$34$	2.08028	−	6.40243i	0.356764	−	1.09801i
$35$	7.92367	−	1.28641i	1.33934	−	0.217443i
$36$	−0.705004	−	2.16978i	−0.117501	−	0.361630i
$37$	−2.56064	+	7.88085i	−0.420967	+	1.29560i	0.485836	+	0.874050i	$0.338515\pi$
$37$	−2.56064	+	7.88085i	−0.420967	+	1.29560i	−0.906803	+	0.421554i	$0.861485\pi$
$38$	−0.309017	+	0.951057i	−0.0501292	+	0.154282i
$39$	0.477793	+	1.47049i	0.0765081	+	0.235468i
$40$	1.99626	+	1.00744i	0.315637	+	0.159291i
$41$	−1.62345	+	4.99647i	−0.253541	+	0.780318i	0.740573	+	0.671976i	$0.234554\pi$
$41$	−1.62345	+	4.99647i	−0.253541	+	0.780318i	−0.994114	+	0.108342i	$0.965446\pi$
$42$	−2.46195	−	1.78871i	−0.379887	−	0.276004i
$43$	0.882966			0.134651			0.0673255	−	0.997731i	$-0.478553\pi$
$43$	0.882966			0.134651			0.0673255	+	0.997731i	$0.478553\pi$
$44$	4.67247	+	3.39475i	0.704401	+	0.511777i
$45$	−0.778555	+	5.04170i	−0.116060	+	0.751572i
$46$	−5.76423	+	4.18796i	−0.849890	+	0.617481i
$47$	0.839936	−	0.610249i	0.122517	−	0.0890140i	−0.524839	−	0.851201i	$-0.675875\pi$
$47$	0.839936	−	0.610249i	0.122517	−	0.0890140i	0.647356	+	0.762187i	$0.275875\pi$
$48$	−0.261947	−	0.806190i	−0.0378088	−	0.116364i
$49$	5.88787			0.841125
$50$	−2.97012	−	4.02224i	−0.420038	−	0.568830i
$51$	5.70650			0.799070
$52$	−0.563649	−	1.73473i	−0.0781640	−	0.240564i
$53$	6.77928	−	4.92544i	0.931206	−	0.676561i	−0.0150820	−	0.999886i	$-0.504801\pi$
$53$	6.77928	−	4.92544i	0.931206	−	0.676561i	0.946288	+	0.323326i	$0.104801\pi$
$54$	3.62194	−	2.63149i	0.492884	−	0.358101i
$55$	−5.90746	−	11.4840i	−0.796561	−	1.54851i
$56$	2.90435	+	2.11013i	0.388109	+	0.281978i
$57$	−0.847678			−0.112278
$58$	−2.16636	−	1.57396i	−0.284458	−	0.206671i
$59$	−0.113424	+	0.349083i	−0.0147665	+	0.0454467i	−0.958168	−	0.286205i	$-0.907606\pi$
$59$	−0.113424	+	0.349083i	−0.0147665	+	0.0454467i	0.943402	+	0.331652i	$0.107606\pi$
$60$	−0.289275	+	1.87326i	−0.0373453	+	0.241837i
$61$	−1.08477	−	3.33859i	−0.138891	−	0.427463i	0.857284	−	0.514844i	$-0.172150\pi$
$61$	−1.08477	−	3.33859i	−0.138891	−	0.427463i	−0.996175	+	0.0873814i	$0.972150\pi$
$62$	0.382127	−	1.17607i	0.0485302	−	0.149360i
$63$	−2.53094	+	7.78944i	−0.318869	+	0.981377i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.622453	+	4.03082i	−0.0772057	+	0.499962i
$66$	−1.51287	+	4.65614i	−0.186222	+	0.573131i
$67$	−6.26903	−	4.55472i	−0.765884	−	0.556447i	0.134825	−	0.990869i	$-0.456953\pi$
$67$	−6.26903	−	4.55472i	−0.765884	−	0.556447i	−0.900709	+	0.434422i	$0.856953\pi$
$68$	−6.73191			−0.816364
$69$	−4.88621	−	3.55004i	−0.588231	−	0.427375i
$70$	−3.67200	−	7.13833i	−0.438888	−	0.853194i
$71$	3.78957	−	2.75328i	0.449739	−	0.326755i	−0.339754	−	0.940514i	$-0.610344\pi$
$71$	3.78957	−	2.75328i	0.449739	−	0.326755i	0.789493	+	0.613760i	$0.210344\pi$
$72$	−1.84572	+	1.34100i	−0.217521	+	0.158038i
$73$	−2.81194	−	8.65426i	−0.329113	−	1.01290i	−0.969550	−	0.244894i	$-0.921247\pi$
$73$	−2.81194	−	8.65426i	−0.329113	−	1.01290i	0.640437	−	0.768011i	$-0.278753\pi$
$74$	8.28642			0.963277
$75$	2.46467	−	3.44809i	0.284596	−	0.398152i
$76$	1.00000			0.114708
$77$	−6.40710	−	19.7190i	−0.730157	−	2.24719i
$78$	1.25088	−	0.908816i	0.141634	−	0.102903i
$79$	−1.27191	+	0.924099i	−0.143101	+	0.103969i	−0.657033	−	0.753862i	$-0.728189\pi$
$79$	−1.27191	+	0.924099i	−0.143101	+	0.103969i	0.513931	+	0.857831i	$0.328189\pi$
$80$	0.341256	−	2.20987i	0.0381536	−	0.247071i
$81$	−2.46693	−	1.79233i	−0.274104	−	0.199148i
$82$	5.25360			0.580164
$83$	−11.5416	−	8.38547i	−1.26686	−	0.920425i	−0.267783	−	0.963479i	$-0.586291\pi$
$83$	−11.5416	−	8.38547i	−1.26686	−	0.920425i	−0.999073	+	0.0430543i	$0.986291\pi$
$84$	−0.940382	+	2.89420i	−0.102604	+	0.315783i
$85$	13.4387	+	6.78202i	1.45763	+	0.735613i
$86$	−0.272851	−	0.839750i	−0.0294223	−	0.0905526i
$87$	0.701435	−	2.15879i	0.0752017	−	0.231447i
$88$	1.78472	−	5.49282i	0.190252	−	0.585536i
$89$	0.970222	+	2.98604i	0.102843	+	0.316519i	0.989218	−	0.146449i	$-0.0467844\pi$
$89$	0.970222	+	2.98604i	0.102843	+	0.316519i	−0.886375	+	0.462968i	$0.846784\pi$
$90$	5.03553	−	0.817520i	0.530791	−	0.0861742i
$91$	−2.02348	+	6.22763i	−0.212118	+	0.652833i
$92$	5.76423	+	4.18796i	0.600963	+	0.436625i
$93$	1.04823			0.108696
$94$	−0.839936	−	0.610249i	−0.0866327	−	0.0629424i
$95$	−1.99626	−	1.00744i	−0.204812	−	0.103361i
$96$	−0.685786	+	0.498253i	−0.0699928	+	0.0508527i
$97$	15.2164	−	11.0554i	1.54500	−	1.12251i	0.597893	−	0.801576i	$-0.296005\pi$
$97$	15.2164	−	11.0554i	1.54500	−	1.12251i	0.947103	−	0.320930i	$-0.103995\pi$
$98$	−1.81945	−	5.59970i	−0.183793	−	0.565655i
$99$	13.1764			1.32428
$100$	−2.90756	+	4.06769i	−0.290756	+	0.406769i
$101$	−14.9587			−1.48845			−0.744223	−	0.667931i	$-0.767180\pi$
$101$	−14.9587			−1.48845			−0.744223	+	0.667931i	$0.767180\pi$
$102$	−1.76340	−	5.42720i	−0.174603	−	0.537373i
$103$	−11.7457	+	8.53374i	−1.15734	+	0.840854i	−0.989439	−	0.144950i	$-0.953698\pi$
$103$	−11.7457	+	8.53374i	−1.15734	+	0.840854i	−0.167898	+	0.985804i	$0.553698\pi$
$104$	−1.47565	+	1.07212i	−0.144699	+	0.105130i
$105$	4.79298	−	4.83019i	0.467747	−	0.471379i
$106$	−6.77928	−	4.92544i	−0.658462	−	0.478401i
$107$	−4.93412			−0.476999			−0.238500	−	0.971143i	$-0.576656\pi$
$107$	−4.93412			−0.476999			−0.238500	+	0.971143i	$0.576656\pi$
$108$	−3.62194	−	2.63149i	−0.348521	−	0.253216i
$109$	−4.26962	+	13.1405i	−0.408955	+	1.25864i	0.508592	+	0.861008i	$0.330166\pi$
$109$	−4.26962	+	13.1405i	−0.408955	+	1.25864i	−0.917547	+	0.397627i	$0.869834\pi$
$110$	−9.09647	+	9.16709i	−0.867315	+	0.874048i
$111$	2.17060	+	6.68043i	0.206025	+	0.634078i
$112$	1.10936	−	3.41426i	0.104825	−	0.322618i
$113$	−1.78812	+	5.50326i	−0.168212	+	0.517703i	−0.999259	−	0.0384997i	$-0.987742\pi$
$113$	−1.78812	+	5.50326i	−0.168212	+	0.517703i	0.831047	+	0.556203i	$0.187742\pi$
$114$	0.261947	+	0.806190i	0.0245336	+	0.0755066i
$115$	−7.28779	−	14.1674i	−0.679590	−	1.32112i
$116$	−0.827478	+	2.54671i	−0.0768294	+	0.236457i
$117$	−3.36661	−	2.44599i	−0.311243	−	0.226132i
$118$	0.367047			0.0337894
$119$	19.5518	+	14.2052i	1.79231	+	1.30219i
$120$	1.87097	−	0.303753i	0.170795	−	0.0277287i
$121$	−18.0866	+	13.1407i	−1.64424	+	1.19461i
$122$	−2.83997	+	2.06336i	−0.257119	+	0.186808i
$123$	1.37617	+	4.23540i	0.124085	+	0.381893i
$124$	−1.23659			−0.111049
$125$	9.90221	−	5.19098i	0.885680	−	0.464295i
$126$	8.19030			0.729650
$127$	5.09195	+	15.6714i	0.451837	+	1.39061i	0.874808	+	0.484469i	$0.160987\pi$
$127$	5.09195	+	15.6714i	0.451837	+	1.39061i	−0.422971	+	0.906143i	$0.639013\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	0.605526	−	0.439940i	0.0533136	−	0.0387346i
$130$	4.02589	−	0.653605i	0.353094	−	0.0573249i
$131$	7.57169	+	5.50115i	0.661542	+	0.480638i	0.867183	−	0.497989i	$-0.165928\pi$
$131$	7.57169	+	5.50115i	0.661542	+	0.480638i	−0.205642	+	0.978627i	$0.565928\pi$
$132$	4.89576			0.426121
$133$	−2.90435	−	2.11013i	−0.251839	−	0.182972i
$134$	−2.39456	+	7.36969i	−0.206858	+	0.636644i
$135$	4.57926	+	8.90204i	0.394120	+	0.766166i
$136$	2.08028	+	6.40243i	0.178382	+	0.549004i
$137$	−0.724216	+	2.22891i	−0.0618740	+	0.190429i	−0.977215	−	0.212250i	$-0.931921\pi$
$137$	−0.724216	+	2.22891i	−0.0618740	+	0.190429i	0.915341	+	0.402679i	$0.131921\pi$
$138$	−1.86637	+	5.74409i	−0.158876	+	0.488969i
$139$	−3.33455	−	10.2627i	−0.282832	−	0.870469i	−0.987040	−	0.160475i	$-0.948698\pi$
$139$	−3.33455	−	10.2627i	−0.282832	−	0.870469i	0.704207	−	0.709994i	$-0.251302\pi$
$140$	−5.65425	+	5.69814i	−0.477871	+	0.481581i
$141$	0.271958	−	0.837001i	0.0229030	−	0.0704882i
$142$	−3.78957	−	2.75328i	−0.318014	−	0.231050i
$143$	10.5345			0.880941
$144$	1.84572	+	1.34100i	0.153810	+	0.111750i
$145$	4.21753	−	4.25027i	0.350247	−	0.352966i
$146$	−7.36175	+	5.34863i	−0.609263	+	0.442656i
$147$	4.03782	−	2.93365i	0.333034	−	0.241963i
$148$	−2.56064	−	7.88085i	−0.210484	−	0.647802i
$149$	5.97032			0.489108			0.244554	−	0.969636i	$-0.421359\pi$
$149$	5.97032			0.489108			0.244554	+	0.969636i	$0.421359\pi$
$150$	−4.04096	−	1.27852i	−0.329943	−	0.104391i
$151$	−11.6928			−0.951550			−0.475775	−	0.879567i	$-0.657832\pi$
$151$	−11.6928			−0.951550			−0.475775	+	0.879567i	$0.657832\pi$
$152$	−0.309017	−	0.951057i	−0.0250646	−	0.0771409i
$153$	−12.4253	+	9.02748i	−1.00452	+	0.729829i
$154$	−16.7740	+	12.1870i	−1.35169	+	0.982059i
$155$	2.46855	+	1.24579i	0.198279	+	0.100064i
$156$	−1.25088	−	0.908816i	−0.100150	−	0.0727635i
$157$	−20.9294			−1.67035			−0.835174	−	0.549986i	$-0.814633\pi$
$157$	−20.9294			−1.67035			−0.835174	+	0.549986i	$0.814633\pi$
$158$	1.27191	+	0.924099i	0.101188	+	0.0735174i
$159$	2.19502	−	6.75559i	0.174077	−	0.535753i
$160$	−2.20717	+	0.358335i	−0.174492	+	0.0283289i
$161$	−7.90418	−	24.3266i	−0.622937	−	1.91720i
$162$	−0.942285	+	2.90006i	−0.0740329	+	0.227850i
$163$	−4.03675	+	12.4238i	−0.316183	+	0.973110i	0.659082	+	0.752071i	$0.270945\pi$
$163$	−4.03675	+	12.4238i	−0.316183	+	0.973110i	−0.975265	+	0.221039i	$0.929055\pi$
$164$	−1.62345	−	4.99647i	−0.126770	−	0.390159i
$165$	−9.77321	−	4.93219i	−0.760844	−	0.383971i
$166$	−4.40850	+	13.5680i	−0.342166	+	1.05308i
$167$	12.0349	+	8.74385i	0.931287	+	0.676620i	0.946308	−	0.323268i	$-0.104781\pi$
$167$	12.0349	+	8.74385i	0.931287	+	0.676620i	−0.0150206	+	0.999887i	$0.504781\pi$
$168$	3.04314			0.234783
$169$	7.82563	+	5.68565i	0.601971	+	0.437358i
$170$	2.29731	−	14.8767i	0.176195	−	1.14099i
$171$	1.84572	−	1.34100i	0.141146	−	0.102549i
$172$	−0.714334	+	0.518994i	−0.0544675	+	0.0395729i
$173$	−5.76620	−	17.7465i	−0.438396	−	1.34924i	−0.889566	−	0.456806i	$-0.848993\pi$
$173$	−5.76620	−	17.7465i	−0.438396	−	1.34924i	0.451170	−	0.892438i	$-0.351007\pi$
$174$	−2.26989			−0.172080
$175$	17.0279	−	5.67866i	1.28719	−	0.429266i
$176$	−5.77549			−0.435344
$177$	0.0961469	+	0.295910i	0.00722685	+	0.0222419i
$178$	2.54007	−	1.84547i	0.190387	−	0.138324i
$179$	7.61301	−	5.53117i	0.569023	−	0.413419i	−0.265727	−	0.964048i	$-0.585612\pi$
$179$	7.61301	−	5.53117i	0.569023	−	0.413419i	0.834750	+	0.550629i	$0.185612\pi$
$180$	−2.33357	−	4.53644i	−0.173934	−	0.338127i
$181$	5.75645	+	4.18230i	0.427873	+	0.310868i	0.780798	−	0.624784i	$-0.214813\pi$
$181$	5.75645	+	4.18230i	0.427873	+	0.310868i	−0.352925	+	0.935652i	$0.614813\pi$
$182$	6.54812			0.485379
$183$	−2.40738	−	1.74907i	−0.177959	−	0.129295i
$184$	2.20174	−	6.77626i	0.162314	−	0.499553i
$185$	−2.82779	+	18.3119i	−0.207903	+	1.34632i
$186$	−0.323921	−	0.996925i	−0.0237510	−	0.0730981i
$187$	12.0146	−	36.9772i	0.878595	−	2.70404i
$188$	−0.320827	+	0.987403i	−0.0233987	+	0.0720138i
$189$	4.96657	+	15.2855i	0.361265	+	1.11186i
$190$	−0.341256	+	2.20987i	−0.0247573	+	0.160321i
$191$	−6.84547	+	21.0682i	−0.495321	+	1.52444i	0.321134	+	0.947034i	$0.395936\pi$
$191$	−6.84547	+	21.0682i	−0.495321	+	1.52444i	−0.816456	+	0.577408i	$0.804064\pi$
$192$	0.685786	+	0.498253i	0.0494924	+	0.0359583i
$193$	11.3475			0.816813			0.408406	−	0.912800i	$-0.366085\pi$
$193$	11.3475			0.816813			0.408406	+	0.912800i	$0.366085\pi$
$194$	−15.2164	−	11.0554i	−1.09248	−	0.793731i
$195$	1.58150	+	3.07442i	0.113253	+	0.220164i
$196$	−4.76339	+	3.46081i	−0.340242	+	0.247200i
$197$	−13.1995	+	9.59003i	−0.940428	+	0.683261i	−0.948524	−	0.316706i	$-0.897423\pi$
$197$	−13.1995	+	9.59003i	−0.940428	+	0.683261i	0.00809553	+	0.999967i	$0.497423\pi$
$198$	−4.07174	−	12.5315i	−0.289366	−	0.890578i
$199$	5.08183			0.360242			0.180121	−	0.983644i	$-0.442351\pi$
$199$	5.08183			0.360242			0.180121	+	0.983644i	$0.442351\pi$
$200$	4.76709	+	1.50827i	0.337084	+	0.106650i
$201$	−6.56862			−0.463314
$202$	4.62249	+	14.2266i	0.325237	+	1.00098i
$203$	7.77718	−	5.65045i	0.545851	−	0.396584i
$204$	−4.61665	+	3.35420i	−0.323230	+	0.234841i
$205$	−1.79282	+	11.6098i	−0.125216	+	0.810864i
$206$	11.7457	+	8.53374i	0.818361	+	0.594574i
$207$	16.2552			1.12982
$208$	1.47565	+	1.07212i	0.102318	+	0.0743384i
$209$	−1.78472	+	5.49282i	−0.123452	+	0.379946i
$210$	−6.07490	−	3.06579i	−0.419208	−	0.211559i
$211$	−1.34025	−	4.12485i	−0.0922663	−	0.283967i	0.894265	−	0.447537i	$-0.147699\pi$
$211$	−1.34025	−	4.12485i	−0.0922663	−	0.283967i	−0.986532	+	0.163571i	$0.947699\pi$
$212$	−2.58945	+	7.96952i	−0.177844	+	0.547349i
$213$	1.22700	−	3.77633i	0.0840729	−	0.258750i
$214$	1.52473	+	4.69263i	0.104228	+	0.320781i
$215$	1.94886	−	0.316398i	0.132911	−	0.0215781i
$216$	−1.38346	+	4.25785i	−0.0941324	+	0.289710i
$217$	3.59148	+	2.60936i	0.243806	+	0.177135i
$218$	13.8168			0.935790
$219$	−6.24040	−	4.53392i	−0.421687	−	0.306374i
$220$	11.5294	+	5.81847i	0.777311	+	0.392281i
$221$	−9.93396	+	7.21744i	−0.668230	+	0.485498i
$222$	5.68271	−	4.12873i	0.381399	−	0.277102i
$223$	1.37130	+	4.22042i	0.0918289	+	0.282620i	0.986414	−	0.164277i	$-0.0525290\pi$
$223$	1.37130	+	4.22042i	0.0918289	+	0.282620i	−0.894585	+	0.446897i	$0.852529\pi$
$224$	−3.58997			−0.239865
$225$	0.0882135	+	11.4069i	0.00588090	+	0.760458i
$226$	5.78647			0.384910
$227$	6.04650	+	18.6092i	0.401320	+	1.23514i	0.923929	+	0.382564i	$0.124959\pi$
$227$	6.04650	+	18.6092i	0.401320	+	1.23514i	−0.522608	+	0.852573i	$0.675041\pi$
$228$	0.685786	−	0.498253i	0.0454173	−	0.0329976i
$229$	−5.90183	+	4.28793i	−0.390004	+	0.283354i	−0.765457	−	0.643487i	$-0.777487\pi$
$229$	−5.90183	+	4.28793i	−0.390004	+	0.283354i	0.375453	+	0.926841i	$0.377487\pi$
$230$	−11.2219	+	11.3091i	−0.739953	+	0.745697i
$231$	−14.2190	−	10.3307i	−0.935540	−	0.679709i
$232$	2.67777			0.175804
$233$	9.61184	+	6.98341i	0.629692	+	0.457498i	0.856294	−	0.516489i	$-0.172761\pi$
$233$	9.61184	+	6.98341i	0.629692	+	0.457498i	−0.226601	+	0.973988i	$0.572761\pi$
$234$	−1.28593	+	3.95769i	−0.0840639	+	0.258722i
$235$	1.63521	−	1.64790i	0.106669	−	0.107497i
$236$	−0.113424	−	0.349083i	−0.00738326	−	0.0227233i
$237$	−0.411826	+	1.26747i	−0.0267509	+	0.0823309i
$238$	7.46812	−	22.9845i	0.484087	−	1.48987i
$239$	−1.01742	−	3.13130i	−0.0658116	−	0.202547i	0.912743	−	0.408534i	$-0.133960\pi$
$239$	−1.01742	−	3.13130i	−0.0658116	−	0.202547i	−0.978555	+	0.205986i	$0.933960\pi$
$240$	−0.867048	−	1.68553i	−0.0559677	−	0.108801i
$241$	−8.38376	+	25.8026i	−0.540046	+	1.66209i	0.192441	+	0.981309i	$0.438360\pi$
$241$	−8.38376	+	25.8026i	−0.540046	+	1.66209i	−0.732487	+	0.680781i	$0.761640\pi$
$242$	18.0866	+	13.1407i	1.16265	+	0.844716i
$243$	−16.0157			−1.02741
$244$	2.83997	+	2.06336i	0.181811	+	0.132093i
$245$	12.9955	−	2.10983i	0.830254	−	0.134792i
$246$	3.60285	−	2.61762i	0.229709	−	0.166894i
$247$	1.47565	−	1.07212i	0.0938934	−	0.0682176i
$248$	0.382127	+	1.17607i	0.0242651	+	0.0746802i
$249$	−12.0932			−0.766373
$250$	−7.99686	−	7.81346i	−0.505766	−	0.494167i
$251$	18.6364			1.17632			0.588161	−	0.808744i	$-0.299852\pi$
$251$	18.6364			1.17632			0.588161	+	0.808744i	$0.299852\pi$
$252$	−2.53094	−	7.78944i	−0.159434	−	0.490689i
$253$	−33.2913	+	24.1875i	−2.09300	+	1.52066i
$254$	13.3309	−	9.68546i	0.836454	−	0.607720i
$255$	12.5952	−	2.04484i	0.788742	−	0.128053i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−19.5225			−1.21778			−0.608890	−	0.793255i	$-0.708385\pi$
$257$	−19.5225			−1.21778			−0.608890	+	0.793255i	$0.708385\pi$
$258$	−0.605526	−	0.439940i	−0.0376984	−	0.0273895i
$259$	−9.19263	+	28.2920i	−0.571202	+	1.75798i
$260$	−1.86568	−	3.62687i	−0.115705	−	0.224929i
$261$	1.88784	+	5.81018i	0.116854	+	0.359641i
$262$	2.89213	−	8.90105i	0.178676	−	0.549909i
$263$	5.55633	−	17.1006i	0.342618	−	1.05447i	−0.620229	−	0.784421i	$-0.712960\pi$
$263$	5.55633	−	17.1006i	0.342618	−	1.05447i	0.962847	−	0.270048i	$-0.0870396\pi$
$264$	−1.51287	−	4.65614i	−0.0931109	−	0.286566i
$265$	13.1981	−	13.3005i	0.810751	−	0.817045i
$266$	−1.10936	+	3.41426i	−0.0680193	+	0.209342i
$267$	2.15317	+	1.56437i	0.131772	+	0.0957377i
$268$	7.74895			0.473342
$269$	11.0590	+	8.03485i	0.674281	+	0.489893i	0.871455	−	0.490475i	$-0.163177\pi$
$269$	11.0590	+	8.03485i	0.674281	+	0.489893i	−0.197175	+	0.980368i	$0.563177\pi$
$270$	7.05128	−	7.10602i	0.429127	−	0.432459i
$271$	−0.309280	+	0.224705i	−0.0187874	+	0.0136499i	−0.597139	−	0.802138i	$-0.703696\pi$
$271$	−0.309280	+	0.224705i	−0.0187874	+	0.0136499i	0.578352	+	0.815787i	$0.303696\pi$
$272$	5.44623	−	3.95692i	0.330226	−	0.239923i
$273$	1.71526	+	5.27903i	0.103812	+	0.319501i
$274$	2.34361			0.141583
$275$	−17.1539	−	23.2304i	−1.03442	−	1.40085i
$276$	6.03969			0.363547
$277$	−0.404032	−	1.24348i	−0.0242760	−	0.0747137i	0.938185	−	0.346135i	$-0.112506\pi$
$277$	−0.404032	−	1.24348i	−0.0242760	−	0.0747137i	−0.962461	+	0.271422i	$0.912506\pi$
$278$	−8.72995	+	6.34268i	−0.523588	+	0.380409i
$279$	−2.28240	+	1.65826i	−0.136644	+	0.0992775i
$280$	7.16652	+	3.61669i	0.428281	+	0.216138i
$281$	6.92441	+	5.03088i	0.413075	+	0.300117i	0.774846	−	0.632150i	$-0.217828\pi$
$281$	6.92441	+	5.03088i	0.413075	+	0.300117i	−0.361770	+	0.932267i	$0.617828\pi$
$282$	−0.880074			−0.0524077
$283$	−15.0312	−	10.9208i	−0.893511	−	0.649174i	0.0432801	−	0.999063i	$-0.486219\pi$
$283$	−15.0312	−	10.9208i	−0.893511	−	0.649174i	−0.936791	+	0.349889i	$0.886219\pi$
$284$	−1.44749	+	4.45491i	−0.0858925	+	0.264350i
$285$	−1.87097	+	0.303753i	−0.110827	+	0.0179928i
$286$	−3.25535	−	10.0189i	−0.192493	−	0.592431i
$287$	−5.82814	+	17.9372i	−0.344025	+	1.05880i
$288$	0.705004	−	2.16978i	0.0415428	−	0.127855i
$289$	8.75095	+	26.9326i	0.514762	+	1.58427i
$290$	−5.34554	−	2.69770i	−0.313901	−	0.158415i
$291$	4.92685	−	15.1633i	0.288817	−	0.888887i
$292$	7.36175	+	5.34863i	0.430814	+	0.313005i
$293$	18.0621			1.05520			0.527600	−	0.849493i	$-0.323092\pi$
$293$	18.0621			1.05520			0.527600	+	0.849493i	$0.323092\pi$
$294$	−4.03782	−	2.93365i	−0.235491	−	0.171094i
$295$	−0.125257	+	0.811128i	−0.00729275	+	0.0472257i
$296$	−6.70385	+	4.87064i	−0.389654	+	0.283100i
$297$	20.9185	−	15.1982i	1.21381	−	0.881887i
$298$	−1.84493	−	5.67811i	−0.106874	−	0.328924i
$299$	12.9960			0.751578
$300$	0.0327761	+	4.23827i	0.00189233	+	0.244696i
$301$	3.16982			0.182705
$302$	3.61329	+	11.1206i	0.207921	+	0.639916i
$303$	−10.2585	+	7.45321i	−0.589334	+	0.428176i
$304$	−0.809017	+	0.587785i	−0.0464003	+	0.0337118i
$305$	−3.59061	−	6.98012i	−0.205598	−	0.399680i
$306$	12.4253	+	9.02748i	0.710305	+	0.516067i
$307$	−34.3604			−1.96105			−0.980525	−	0.196393i	$-0.937077\pi$
$307$	−34.3604			−1.96105			−0.980525	+	0.196393i	$0.937077\pi$
$308$	16.7740	+	12.1870i	0.955788	+	0.694421i
$309$	−3.80307	+	11.7046i	−0.216349	+	0.665854i
$310$	0.421993	−	2.73270i	0.0239676	−	0.155207i
$311$	4.95372	+	15.2460i	0.280900	+	0.864520i	0.987598	+	0.157005i	$0.0501839\pi$
$311$	4.95372	+	15.2460i	0.280900	+	0.864520i	−0.706698	+	0.707515i	$0.749816\pi$
$312$	−0.477793	+	1.47049i	−0.0270497	+	0.0832504i
$313$	6.50352	−	20.0158i	0.367601	−	1.13136i	−0.580735	−	0.814092i	$-0.697235\pi$
$313$	6.50352	−	20.0158i	0.367601	−	1.13136i	0.948336	−	0.317267i	$-0.102765\pi$
$314$	6.46754	+	19.9050i	0.364984	+	1.12331i
$315$	−2.79499	+	18.0995i	−0.157480	+	1.01979i
$316$	0.485828	−	1.49522i	0.0273299	−	0.0841129i
$317$	−10.9436	−	7.95100i	−0.614655	−	0.446573i	0.236396	−	0.971657i	$-0.424034\pi$
$317$	−10.9436	−	7.95100i	−0.614655	−	0.446573i	−0.851050	+	0.525084i	$0.824034\pi$
$318$	−7.10325			−0.398330
$319$	−12.5118	−	9.09037i	−0.700527	−	0.508963i
$320$	1.02285	+	1.98841i	0.0571790	+	0.111156i
$321$	−3.38375	+	2.45844i	−0.188863	+	0.137217i
$322$	−20.6934	+	15.0346i	−1.15320	+	0.837848i
$323$	−2.08028	−	6.40243i	−0.115750	−	0.356241i
$324$	3.04930			0.169405
$325$	0.0705264	+	9.11975i	0.00391210	+	0.505873i
$326$	13.0632			0.723504
$327$	3.61926	+	11.1389i	0.200146	+	0.615985i
$328$	−4.25025	+	3.08799i	−0.234681	+	0.170506i
$329$	3.01534	−	2.19077i	0.166241	−	0.120781i
$330$	−1.67071	+	10.8190i	−0.0919694	+	0.595567i
$331$	−12.9982	−	9.44376i	−0.714447	−	0.519076i	0.170159	−	0.985417i	$-0.445572\pi$
$331$	−12.9982	−	9.44376i	−0.714447	−	0.519076i	−0.884605	+	0.466341i	$0.845572\pi$
$332$	14.2662			0.782960
$333$	−15.2945	−	11.1121i	−0.838131	−	0.608938i
$334$	4.59692	−	14.1478i	0.251532	−	0.774136i
$335$	−15.4689	−	7.80662i	−0.845158	−	0.426521i
$336$	−0.940382	−	2.89420i	−0.0513020	−	0.157891i
$337$	9.28171	−	28.5662i	0.505607	−	1.55610i	−0.294141	−	0.955762i	$-0.595034\pi$
$337$	9.28171	−	28.5662i	0.505607	−	1.55610i	0.799748	−	0.600336i	$-0.204966\pi$
$338$	2.98912	−	9.19958i	0.162587	−	0.500391i
$339$	1.51575	+	4.66499i	0.0823241	+	0.253368i
$340$	−14.8585	+	2.41228i	−0.805814	+	0.130824i
$341$	2.20697	−	6.79235i	0.119514	−	0.367827i
$342$	−1.84572	−	1.34100i	−0.0998054	−	0.0725128i
$343$	−3.99250			−0.215575
$344$	0.714334	+	0.518994i	0.0385143	+	0.0279823i
$345$	−12.0568	−	6.08464i	−0.649117	−	0.327586i
$346$	−15.0961	+	10.9680i	−0.811572	+	0.589641i
$347$	−10.7422	+	7.80470i	−0.576674	+	0.418978i	−0.837524	−	0.546401i	$-0.815997\pi$
$347$	−10.7422	+	7.80470i	−0.576674	+	0.418978i	0.260849	+	0.965379i	$0.415997\pi$
$348$	0.701435	+	2.15879i	0.0376009	+	0.115724i
$349$	−13.0351			−0.697755			−0.348877	−	0.937168i	$-0.613437\pi$
$349$	−13.0351			−0.697755			−0.348877	+	0.937168i	$0.613437\pi$
$350$	−10.6626	−	14.4397i	−0.569942	−	0.771835i
$351$	−8.16600			−0.435869
$352$	1.78472	+	5.49282i	0.0951261	+	0.292768i
$353$	−22.8714	+	16.6170i	−1.21732	+	0.884435i	−0.995875	−	0.0907378i	$-0.971077\pi$
$353$	−22.8714	+	16.6170i	−1.21732	+	0.884435i	−0.221445	+	0.975173i	$0.571077\pi$
$354$	0.251716	−	0.182882i	0.0133786	−	0.00972009i
$355$	7.37762	−	7.43490i	0.391564	−	0.394603i
$356$	−2.54007	−	1.84547i	−0.134624	−	0.0978098i
$357$	20.4861			1.08424
$358$	−7.61301	−	5.53117i	−0.402360	−	0.292332i
$359$	7.03880	−	21.6632i	0.371494	−	1.14334i	−0.574320	−	0.818631i	$-0.694734\pi$
$359$	7.03880	−	21.6632i	0.371494	−	1.14334i	0.945814	−	0.324709i	$-0.105266\pi$
$360$	−3.59330	+	3.62120i	−0.189384	+	0.190854i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	2.19877	−	6.76711i	0.115565	−	0.355671i
$363$	−5.85616	+	18.0234i	−0.307369	+	0.945984i
$364$	−2.02348	−	6.22763i	−0.106059	−	0.326417i
$365$	−9.30755	−	18.0938i	−0.487180	−	0.947073i
$366$	−0.919539	+	2.83005i	−0.0480651	+	0.147929i
$367$	−9.67030	−	7.02588i	−0.504786	−	0.366748i	0.306056	−	0.952013i	$-0.400990\pi$
$367$	−9.67030	−	7.02588i	−0.504786	−	0.366748i	−0.810842	+	0.585265i	$0.800990\pi$
$368$	−7.12498			−0.371415
$369$	−9.69671	−	7.04507i	−0.504790	−	0.366752i
$370$	18.2895	−	2.96931i	0.950827	−	0.154367i
$371$	24.3374	−	17.6822i	1.26353	−	0.918012i
$372$	−0.848035	+	0.616134i	−0.0439686	+	0.0319450i
$373$	6.69279	+	20.5983i	0.346540	+	1.06654i	0.960754	+	0.277400i	$0.0894728\pi$
$373$	6.69279	+	20.5983i	0.346540	+	1.06654i	−0.614215	+	0.789139i	$0.710527\pi$
$374$	−38.8801			−2.01044
$375$	4.20438	−	8.49371i	0.217113	−	0.438613i
$376$	1.03822			0.0535420
$377$	1.50932	+	4.64522i	0.0777341	+	0.239241i
$378$	13.0026	−	9.44698i	0.668784	−	0.485900i
$379$	−2.73153	+	1.98458i	−0.140309	+	0.101941i	−0.655726	−	0.754999i	$-0.727637\pi$
$379$	−2.73153	+	1.98458i	−0.140309	+	0.101941i	0.515416	+	0.856940i	$0.327637\pi$
$380$	2.20717	−	0.358335i	0.113225	−	0.0183822i
$381$	11.3003	+	8.21015i	0.578932	+	0.420619i
$382$	22.1524			1.13342
$383$	−0.230867	−	0.167734i	−0.0117967	−	0.00857083i	0.581871	−	0.813281i	$-0.302321\pi$
$383$	−0.230867	−	0.167734i	−0.0117967	−	0.00857083i	−0.593668	+	0.804710i	$0.702321\pi$
$384$	0.261947	−	0.806190i	0.0133674	−	0.0411407i
$385$	−21.2076	−	41.2274i	−1.08084	−	2.10114i
$386$	−3.50658	−	10.7921i	−0.178480	−	0.549305i
$387$	−0.622495	+	1.91584i	−0.0316432	+	0.0973877i
$388$	−5.81217	+	17.8880i	−0.295068	+	0.908126i
$389$	−1.58804	−	4.88747i	−0.0805166	−	0.247805i	0.902693	−	0.430286i	$-0.141587\pi$
$389$	−1.58804	−	4.88747i	−0.0805166	−	0.247805i	−0.983209	+	0.182481i	$0.941587\pi$
$390$	2.43524	−	2.45414i	0.123313	−	0.124270i
$391$	14.8219	−	45.6172i	0.749577	−	2.30696i
$392$	4.76339	+	3.46081i	0.240588	+	0.174797i
$393$	7.93353			0.400193
$394$	13.1995	+	9.59003i	0.664983	+	0.483139i
$395$	−2.47619	+	2.49541i	−0.124591	+	0.125558i
$396$	−10.6600	+	7.74492i	−0.535683	+	0.389197i
$397$	14.6269	−	10.6270i	0.734102	−	0.533356i	−0.156756	−	0.987637i	$-0.550104\pi$
$397$	14.6269	−	10.6270i	0.734102	−	0.533356i	0.890858	+	0.454281i	$0.150104\pi$
$398$	−1.57037	−	4.83311i	−0.0787157	−	0.242262i
$399$	−3.04314			−0.152347
$400$	−0.0386657	−	4.99985i	−0.00193329	−	0.249993i
$401$	−8.65028			−0.431975			−0.215987	−	0.976396i	$-0.569297\pi$
$401$	−8.65028			−0.431975			−0.215987	+	0.976396i	$0.569297\pi$
$402$	2.02981	+	6.24712i	0.101238	+	0.311578i
$403$	−1.82477	+	1.32578i	−0.0908984	+	0.0660416i
$404$	12.1018	−	8.79250i	0.602089	−	0.437443i
$405$	−6.08720	−	3.07199i	−0.302475	−	0.152649i
$406$	−7.77718	−	5.65045i	−0.385975	−	0.280427i
$407$	47.8581			2.37224
$408$	4.61665	+	3.35420i	0.228558	+	0.166057i
$409$	−5.87793	+	18.0904i	−0.290645	+	0.894512i	0.694005	+	0.719970i	$0.255845\pi$
$409$	−5.87793	+	18.0904i	−0.290645	+	0.894512i	−0.984650	+	0.174542i	$0.944155\pi$
$410$	11.5956	−	1.88255i	0.572666	−	0.0929725i
$411$	0.613903	+	1.88940i	0.0302816	+	0.0931971i
$412$	4.48645	−	13.8079i	0.221032	−	0.680265i
$413$	−0.407188	+	1.25320i	−0.0200364	+	0.0616657i
$414$	−5.02314	−	15.4596i	−0.246874	−	0.759800i
$415$	−28.4791	−	14.3724i	−1.39798	−	0.705513i
$416$	0.563649	−	1.73473i	0.0276351	−	0.0850522i
$417$	−7.40019	−	5.37656i	−0.362389	−	0.263291i
$418$	5.77549			0.282488
$419$	8.40133	+	6.10393i	0.410432	+	0.298196i	0.773777	−	0.633459i	$-0.218365\pi$
$419$	8.40133	+	6.10393i	0.410432	+	0.298196i	−0.363345	+	0.931655i	$0.618365\pi$
$420$	−1.03849	+	6.72495i	−0.0506731	+	0.328144i
$421$	−8.70527	+	6.32475i	−0.424269	+	0.308249i	−0.779353	−	0.626585i	$-0.784452\pi$
$421$	−8.70527	+	6.32475i	−0.424269	+	0.308249i	0.355084	+	0.934834i	$0.384452\pi$
$422$	−3.50881	+	2.54930i	−0.170806	+	0.124098i
$423$	0.731948	+	2.25270i	0.0355885	+	0.109530i
$424$	8.37965			0.406952
$425$	32.0916	+	10.1535i	1.55667	+	0.492518i
$426$	−3.97067			−0.192379
$427$	−3.89430	−	11.9854i	−0.188458	−	0.580016i
$428$	3.99179	−	2.90020i	0.192950	−	0.140187i
$429$	7.22443	−	5.24886i	0.348799	−	0.253417i
$430$	−0.903141	−	1.75570i	−0.0435533	−	0.0846673i
$431$	26.3233	+	19.1250i	1.26795	+	0.921219i	0.999119	−	0.0419686i	$-0.0133629\pi$
$431$	26.3233	+	19.1250i	1.26795	+	0.921219i	0.268830	+	0.963188i	$0.413363\pi$
$432$	4.47696			0.215398
$433$	−8.00772	−	5.81795i	−0.384827	−	0.279593i	0.378506	−	0.925599i	$-0.376438\pi$
$433$	−8.00772	−	5.81795i	−0.384827	−	0.279593i	−0.763332	+	0.646006i	$0.776438\pi$
$434$	1.37182	−	4.22204i	0.0658496	−	0.202664i
$435$	0.774614	−	5.01617i	0.0371399	−	0.240507i
$436$	−4.26962	−	13.1405i	−0.204478	−	0.629318i
$437$	−2.20174	+	6.77626i	−0.105324	+	0.324153i
$438$	−2.38362	+	7.33603i	−0.113894	+	0.350529i
$439$	−6.87274	−	21.1521i	−0.328018	−	1.00954i	−0.970060	−	0.242866i	$-0.921913\pi$
$439$	−6.87274	−	21.1521i	−0.328018	−	1.00954i	0.642042	−	0.766669i	$-0.278087\pi$
$440$	1.97092	−	12.7631i	0.0939599	−	0.608457i
$441$	−4.15098	+	12.7754i	−0.197665	+	0.608352i
$442$	9.93396	+	7.21744i	0.472510	+	0.343299i
$443$	−0.317284			−0.0150746			−0.00753732	−	0.999972i	$-0.502399\pi$
$443$	−0.317284			−0.0150746			−0.00753732	+	0.999972i	$0.502399\pi$
$444$	−5.68271	−	4.12873i	−0.269690	−	0.195941i
$445$	3.21144	+	6.24302i	0.152237	+	0.295948i
$446$	3.59010	−	2.60836i	0.169996	−	0.123510i
$447$	4.09436	−	2.97473i	0.193657	−	0.140700i
$448$	1.10936	+	3.41426i	0.0524124	+	0.161309i
$449$	−25.2486			−1.19155			−0.595776	−	0.803150i	$-0.703156\pi$
$449$	−25.2486			−1.19155			−0.595776	+	0.803150i	$0.703156\pi$
$450$	10.8213	−	3.60881i	0.510122	−	0.170121i
$451$	30.3421			1.42876
$452$	−1.78812	−	5.50326i	−0.0841059	−	0.258851i
$453$	−8.01879	+	5.82599i	−0.376756	+	0.273729i
$454$	15.8299	−	11.5011i	0.742936	−	0.539775i
$455$	−2.23459	+	14.4705i	−0.104759	+	0.678389i
$456$	−0.685786	−	0.498253i	−0.0321149	−	0.0233328i
$457$	−25.8353			−1.20853			−0.604263	−	0.796785i	$-0.706532\pi$
$457$	−25.8353			−1.20853			−0.604263	+	0.796785i	$0.706532\pi$
$458$	5.90183	+	4.28793i	0.275774	+	0.200362i
$459$	−9.31332	+	28.6634i	−0.434708	+	1.33790i
$460$	14.2233	+	7.17801i	0.663166	+	0.334676i
$461$	5.98974	+	18.4345i	0.278970	+	0.858581i	0.988142	+	0.153545i	$0.0490690\pi$
$461$	5.98974	+	18.4345i	0.278970	+	0.858581i	−0.709172	+	0.705036i	$0.750931\pi$
$462$	−5.43116	+	16.7154i	−0.252681	+	0.777671i
$463$	−6.80112	+	20.9317i	−0.316075	+	0.972778i	0.659235	+	0.751937i	$0.270880\pi$
$463$	−6.80112	+	20.9317i	−0.316075	+	0.972778i	−0.975310	+	0.220841i	$0.929120\pi$
$464$	−0.827478	−	2.54671i	−0.0384147	−	0.118228i
$465$	2.31362	−	0.375617i	0.107292	−	0.0174188i
$466$	3.67139	−	11.2994i	0.170074	−	0.523434i
$467$	−1.76357	−	1.28131i	−0.0816081	−	0.0592918i	0.546233	−	0.837633i	$-0.316061\pi$
$467$	−1.76357	−	1.28131i	−0.0816081	−	0.0592918i	−0.627841	+	0.778341i	$0.716061\pi$
$468$	4.16136			0.192359
$469$	−22.5056	−	16.3513i	−1.03921	−	0.755033i
$470$	−2.07255	−	1.04594i	−0.0955998	−	0.0482458i
$471$	−14.3531	+	10.4281i	−0.661356	+	0.480503i
$472$	−0.296947	+	0.215745i	−0.0136681	+	0.00993047i
$473$	−1.57585	−	4.84997i	−0.0724577	−	0.223002i
$474$	1.33270			0.0612127
$475$	−4.76709	−	1.50827i	−0.218729	−	0.0692040i
$476$	−24.1674			−1.10771
$477$	5.90769	+	18.1820i	0.270494	+	0.832496i
$478$	−2.66365	+	1.93525i	−0.121832	+	0.0885164i
$479$	5.07055	−	3.68397i	0.231679	−	0.168325i	−0.465889	−	0.884843i	$-0.654265\pi$
$479$	5.07055	−	3.68397i	0.231679	−	0.168325i	0.697568	+	0.716518i	$0.254265\pi$
$480$	−1.33510	+	1.34547i	−0.0609389	+	0.0614120i
$481$	−12.2279	−	8.88406i	−0.557543	−	0.405078i
$482$	27.1304			1.23576
$483$	−17.5414	−	12.7445i	−0.798159	−	0.579897i
$484$	6.90847	−	21.2621i	0.314021	−	0.966458i
$485$	29.6237	−	29.8537i	1.34514	−	1.35559i
$486$	4.94913	+	15.2319i	0.224497	+	0.690931i
$487$	11.5515	−	35.5517i	0.523447	−	1.61100i	−0.243920	−	0.969795i	$-0.578434\pi$
$487$	11.5515	−	35.5517i	0.523447	−	1.61100i	0.767367	−	0.641208i	$-0.221566\pi$
$488$	1.08477	−	3.33859i	0.0491054	−	0.151131i
$489$	3.42187	+	10.5314i	0.154742	+	0.476247i
$490$	−6.02241	−	11.7075i	−0.272065	−	0.528892i
$491$	0.452087	−	1.39138i	0.0204024	−	0.0627921i	−0.940337	−	0.340245i	$-0.889490\pi$
$491$	0.452087	−	1.39138i	0.0204024	−	0.0627921i	0.960739	+	0.277453i	$0.0894901\pi$
$492$	−3.60285	−	2.61762i	−0.162429	−	0.118012i
$493$	18.0265			0.811875
$494$	−1.47565	−	1.07212i	−0.0663927	−	0.0482371i
$495$	29.0826	−	4.72158i	1.30717	−	0.212219i
$496$	1.00042	−	0.726848i	0.0449202	−	0.0326365i
$497$	13.6044	−	9.88420i	0.610242	−	0.443367i
$498$	3.73699	+	11.5013i	0.167459	+	0.515385i
$499$	4.00102			0.179110			0.0895551	−	0.995982i	$-0.471455\pi$
$499$	4.00102			0.179110			0.0895551	+	0.995982i	$0.471455\pi$
$500$	−4.95987	+	10.0200i	−0.221812	+	0.448106i
$501$	12.6100			0.563373
$502$	−5.75898	−	17.7243i	−0.257036	−	0.791074i
$503$	14.8820	−	10.8124i	0.663555	−	0.482101i	−0.204306	−	0.978907i	$-0.565494\pi$
$503$	14.8820	−	10.8124i	0.663555	−	0.482101i	0.867862	+	0.496806i	$0.165494\pi$
$504$	−6.62609	+	4.81414i	−0.295150	+	0.214439i
$505$	−33.0164	+	5.36022i	−1.46921	+	0.238527i
$506$	33.2913	+	24.1875i	1.47998	+	1.07527i
$507$	8.19960			0.364157
$508$	−13.3309	−	9.68546i	−0.591463	−	0.429723i
$509$	10.2660	−	31.5954i	0.455031	−	1.40044i	−0.416068	−	0.909333i	$-0.636592\pi$
$509$	10.2660	−	31.5954i	0.455031	−	1.40044i	0.871099	−	0.491107i	$-0.163408\pi$
$510$	−5.83689	−	11.3469i	−0.258462	−	0.502448i
$511$	−10.0948	−	31.0685i	−0.446567	−	1.37439i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	1.38346	−	4.25785i	0.0610812	−	0.187988i
$514$	6.03279	+	18.5670i	0.266095	+	0.818956i
$515$	−22.8668	+	23.0443i	−1.00763	+	1.01545i
$516$	−0.231290	+	0.711838i	−0.0101820	+	0.0313369i
$517$	−4.85104	−	3.52449i	−0.213348	−	0.155007i
$518$	29.7480			1.30705
$519$	−12.7966	−	9.29731i	−0.561710	−	0.408106i
$520$	−2.87283	+	2.89513i	−0.125982	+	0.126960i
$521$	8.97895	−	6.52359i	0.393375	−	0.285804i	−0.373462	−	0.927645i	$-0.621829\pi$
$521$	8.97895	−	6.52359i	0.393375	−	0.285804i	0.766837	+	0.641842i	$0.221829\pi$
$522$	4.94243	−	3.59089i	0.216324	−	0.157169i
$523$	9.44920	+	29.0816i	0.413184	+	1.27165i	0.913865	+	0.406019i	$0.133083\pi$
$523$	9.44920	+	29.0816i	0.413184	+	1.27165i	−0.500680	+	0.865632i	$0.666917\pi$
$524$	−9.35912			−0.408855
$525$	8.84810	−	12.3785i	0.386163	−	0.540244i
$526$	−17.9806			−0.783993
$527$	2.57244	+	7.91717i	0.112057	+	0.344877i
$528$	−3.96075	+	2.87765i	−0.172370	+	0.125234i
$529$	−22.4627	+	16.3201i	−0.976637	+	0.709569i
$530$	−16.7280	−	8.44202i	−0.726617	−	0.366698i
$531$	−0.677468	−	0.492209i	−0.0293996	−	0.0213601i
$532$	3.58997			0.155645
$533$	−7.75249	−	5.63251i	−0.335797	−	0.243971i
$534$	0.822436	−	2.53120i	0.0355903	−	0.109536i
$535$	−10.8904	+	1.76807i	−0.470835	+	0.0764403i
$536$	−2.39456	−	7.36969i	−0.103429	−	0.318322i
$537$	2.46497	−	7.58640i	0.106371	−	0.327378i
$538$	4.22417	−	13.0007i	0.182117	−	0.560498i
$539$	−10.5082	−	32.3410i	−0.452622	−	1.39303i
$540$	−8.93719	−	4.51028i	−0.384595	−	0.194092i
$541$	6.07740	−	18.7043i	0.261288	−	0.804161i	−0.731238	−	0.682123i	$-0.761057\pi$
$541$	6.07740	−	18.7043i	0.261288	−	0.804161i	0.992525	−	0.122038i	$-0.0389431\pi$
$542$	0.309280	+	0.224705i	0.0132847	+	0.00965191i
$543$	6.03154			0.258838
$544$	−5.44623	−	3.95692i	−0.233505	−	0.169652i
$545$	−4.71506	+	30.5333i	−0.201971	+	1.30790i
$546$	4.49061	−	3.26262i	0.192180	−	0.139627i
$547$	−16.9039	+	12.2814i	−0.722758	+	0.525114i	−0.887264	−	0.461262i	$-0.847397\pi$
$547$	−16.9039	+	12.2814i	−0.722758	+	0.525114i	0.164506	+	0.986376i	$0.447397\pi$
$548$	−0.724216	−	2.22891i	−0.0309370	−	0.0952143i
$549$	8.00877			0.341806
$550$	−16.7926	+	23.4929i	−0.716037	+	1.00174i
$551$	−2.67777			−0.114077
$552$	−1.86637	−	5.74409i	−0.0794379	−	0.244485i
$553$	−4.56613	+	3.31749i	−0.194172	+	0.141074i
$554$	−1.05777	+	0.768515i	−0.0449404	+	0.0326511i
$555$	7.18472	+	13.9670i	0.304974	+	0.592868i
$556$	8.72995	+	6.34268i	0.370233	+	0.268990i
$557$	−2.70942			−0.114802			−0.0574009	−	0.998351i	$-0.518281\pi$
$557$	−2.70942			−0.114802			−0.0574009	+	0.998351i	$0.518281\pi$
$558$	2.28240	+	1.65826i	0.0966218	+	0.0701998i
$559$	−0.497682	+	1.53171i	−0.0210497	+	0.0647844i
$560$	1.22510	−	7.93338i	0.0517698	−	0.335246i
$561$	−10.1845	−	31.3447i	−0.429991	−	1.32338i
$562$	2.64489	−	8.14013i	0.111568	−	0.343371i
$563$	12.4934	−	38.4508i	0.526534	−	1.62051i	−0.234727	−	0.972061i	$-0.575420\pi$
$563$	12.4934	−	38.4508i	0.526534	−	1.62051i	0.761262	−	0.648445i	$-0.224580\pi$
$564$	0.271958	+	0.837001i	0.0114515	+	0.0352441i
$565$	−1.97467	+	12.7874i	−0.0830748	+	0.537968i
$566$	−5.74140	+	17.6702i	−0.241329	+	0.742734i
$567$	−8.85622	−	6.43442i	−0.371926	−	0.270220i
$568$	4.68417			0.196543
$569$	31.7506	+	23.0682i	1.33105	+	0.967068i	0.999723	+	0.0235537i	$0.00749807\pi$
$569$	31.7506	+	23.0682i	1.33105	+	0.967068i	0.331332	+	0.943514i	$0.392502\pi$
$570$	0.867048	+	1.68553i	0.0363166	+	0.0705992i
$571$	22.8639	−	16.6116i	0.956825	−	0.695174i	0.00441417	−	0.999990i	$-0.498595\pi$
$571$	22.8639	−	16.6116i	0.956825	−	0.695174i	0.952411	+	0.304816i	$0.0985949\pi$
$572$	−8.52261	+	6.19204i	−0.356348	+	0.258902i
$573$	5.80276	+	17.8591i	0.242414	+	0.746073i
$574$	18.8603			0.787213
$575$	−21.1621	−	28.6584i	−0.882519	−	1.19514i
$576$	−2.28144			−0.0950601
$577$	−10.5120	−	32.3525i	−0.437619	−	1.34685i	−0.890379	−	0.455220i	$-0.849561\pi$
$577$	−10.5120	−	32.3525i	−0.437619	−	1.34685i	0.452761	−	0.891632i	$-0.350439\pi$
$578$	22.9103	−	16.6453i	0.952942	−	0.692353i
$579$	7.78198	−	5.65394i	0.323408	−	0.234970i
$580$	−0.913806	+	5.91754i	−0.0379437	+	0.245713i
$581$	−41.4340	−	30.1036i	−1.71897	−	1.24891i
$582$	−15.9436			−0.660884
$583$	−39.1537	−	28.4468i	−1.62158	−	1.17815i
$584$	2.81194	−	8.65426i	0.116359	−	0.358116i
$585$	−8.30716	−	4.19233i	−0.343459	−	0.173332i
$586$	−5.58150	−	17.1781i	−0.230570	−	0.709620i
$587$	−0.315733	+	0.971726i	−0.0130317	+	0.0401074i	−0.957361	−	0.288895i	$-0.906712\pi$
$587$	−0.315733	+	0.971726i	−0.0130317	+	0.0401074i	0.944329	+	0.329002i	$0.106712\pi$
$588$	−1.54231	+	4.74675i	−0.0636038	+	0.195752i
$589$	−0.382127	−	1.17607i	−0.0157453	−	0.0484589i
$590$	0.810135	−	0.131526i	0.0333527	−	0.00541483i
$591$	−4.27380	+	13.1534i	−0.175801	+	0.541059i
$592$	6.70385	+	4.87064i	0.275527	+	0.200182i
$593$	5.85714			0.240524			0.120262	−	0.992742i	$-0.461627\pi$
$593$	5.85714			0.240524			0.120262	+	0.992742i	$0.461627\pi$
$594$	−20.9185	−	15.1982i	−0.858295	−	0.623588i
$595$	48.2444	+	24.3472i	1.97783	+	0.998139i
$596$	−4.83009	+	3.50927i	−0.197848	+	0.143745i
$597$	3.48505	−	2.53204i	0.142634	−	0.103629i
$598$	−4.01599	−	12.3599i	−0.164226	−	0.505435i
$599$	1.61343			0.0659231			0.0329616	−	0.999457i	$-0.489506\pi$
$599$	1.61343			0.0659231			0.0329616	+	0.999457i	$0.489506\pi$
$600$	4.02070	−	1.34087i	0.164144	−	0.0547407i
$601$	4.60798			0.187963			0.0939816	−	0.995574i	$-0.470040\pi$
$601$	4.60798			0.187963			0.0939816	+	0.995574i	$0.470040\pi$
$602$	−0.979528	−	3.01468i	−0.0399226	−	0.122869i
$603$	14.3024	−	10.3913i	0.582440	−	0.423167i
$604$	9.45971	−	6.87288i	0.384910	−	0.279654i
$605$	−35.2114	+	35.4848i	−1.43155	+	1.44266i
$606$	10.2585	+	7.45321i	0.416722	+	0.302766i
$607$	−4.76990			−0.193604			−0.0968021	−	0.995304i	$-0.530861\pi$
$607$	−4.76990			−0.193604			−0.0968021	+	0.995304i	$0.530861\pi$
$608$	0.809017	+	0.587785i	0.0328100	+	0.0238378i
$609$	2.51813	−	7.75001i	0.102040	−	0.314046i
$610$	−5.52893	+	5.57185i	−0.223860	+	0.225598i
$611$	0.585190	+	1.80103i	0.0236742	+	0.0728618i
$612$	4.74603	−	14.6068i	0.191847	−	0.590444i
$613$	4.48375	−	13.7996i	0.181097	−	0.557359i	−0.818762	−	0.574132i	$-0.805339\pi$
$613$	4.48375	−	13.7996i	0.181097	−	0.557359i	0.999859	+	0.0167735i	$0.00533943\pi$
$614$	10.6179	+	32.6787i	0.428505	+	1.31880i
$615$	4.55512	+	8.85512i	0.183680	+	0.357073i
$616$	6.40710	−	19.7190i	0.258150	−	0.794503i
$617$	14.0106	+	10.1793i	0.564047	+	0.409804i	0.832938	−	0.553366i	$-0.186657\pi$
$617$	14.0106	+	10.1793i	0.564047	+	0.409804i	−0.268891	+	0.963171i	$0.586657\pi$
$618$	12.3070			0.495060
$619$	22.1727	+	16.1094i	0.891198	+	0.647493i	0.936190	−	0.351494i	$-0.114326\pi$
$619$	22.1727	+	16.1094i	0.891198	+	0.647493i	−0.0449924	+	0.998987i	$0.514326\pi$
$620$	−2.72936	+	0.443113i	−0.109614	+	0.0177958i
$621$	25.8063	−	18.7493i	1.03557	−	0.752385i
$622$	12.9690	−	9.42254i	0.520010	−	0.377809i
$623$	3.48307	+	10.7198i	0.139546	+	0.429479i
$624$	1.54617			0.0618963
$625$	19.9957	−	15.0057i	0.799830	−	0.600227i
$626$	−21.0458			−0.841161
$627$	1.51287	+	4.65614i	0.0604183	+	0.185948i
$628$	16.9322	−	12.3020i	0.675670	−	0.490903i
$629$	−45.1298	+	32.7887i	−1.79944	+	1.30737i
$630$	18.0774	−	2.93487i	0.720220	−	0.116928i
$631$	−32.5398	−	23.6415i	−1.29539	−	0.941155i	−0.295489	−	0.955346i	$-0.595483\pi$
$631$	−32.5398	−	23.6415i	−1.29539	−	0.941155i	−0.999899	+	0.0141914i	$0.995483\pi$
$632$	−1.57217			−0.0625376
$633$	−2.97434	−	2.16099i	−0.118219	−	0.0858915i
$634$	−4.18009	+	12.8650i	−0.166013	+	0.510934i
$635$	16.8544	+	32.7648i	0.668847	+	1.30023i
$636$	2.19502	+	6.75559i	0.0870384	+	0.267877i
$637$	−3.31869	+	10.2139i	−0.131491	+	0.404689i
$638$	−4.77909	+	14.7085i	−0.189206	+	0.582316i
$639$	3.30236	+	10.1636i	0.130639	+	0.402066i
$640$	1.57501	−	1.58724i	0.0622579	−	0.0627412i
$641$	4.21185	−	12.9627i	0.166358	−	0.511998i	−0.832776	−	0.553611i	$-0.813250\pi$
$641$	4.21185	−	12.9627i	0.166358	−	0.511998i	0.999134	+	0.0416129i	$0.0132496\pi$
$642$	3.38375	+	2.45844i	0.133546	+	0.0970269i
$643$	0.962723			0.0379661			0.0189831	−	0.999820i	$-0.493957\pi$
$643$	0.962723			0.0379661			0.0189831	+	0.999820i	$0.493957\pi$
$644$	20.6934	+	15.0346i	0.815435	+	0.592448i
$645$	1.17885	−	1.18800i	0.0464173	−	0.0467776i
$646$	−5.44623	+	3.95692i	−0.214279	+	0.155683i
$647$	−7.95987	+	5.78319i	−0.312935	+	0.227360i	−0.733155	−	0.680062i	$-0.761953\pi$
$647$	−7.95987	+	5.78319i	−0.312935	+	0.227360i	0.420220	+	0.907422i	$0.361953\pi$
$648$	−0.942285	−	2.90006i	−0.0370165	−	0.113925i
$649$	2.11988			0.0832125
$650$	8.65161	−	2.88523i	0.339344	−	0.113168i
$651$	3.76311			0.147488
$652$	−4.03675	−	12.4238i	−0.158091	−	0.486555i
$653$	24.7365	−	17.9721i	0.968013	−	0.703302i	0.0130150	−	0.999915i	$-0.495857\pi$
$653$	24.7365	−	17.9721i	0.968013	−	0.703302i	0.954998	+	0.296613i	$0.0958571\pi$
$654$	9.47536	−	6.88425i	0.370516	−	0.269195i
$655$	18.6833	+	9.42878i	0.730015	+	0.368413i
$656$	4.25025	+	3.08799i	0.165945	+	0.120566i
$657$	20.7603			0.809935
$658$	−3.01534	−	2.19077i	−0.117550	−	0.0854053i
$659$	−13.7599	+	42.3486i	−0.536009	+	1.64967i	0.205449	+	0.978668i	$0.434135\pi$
$659$	−13.7599	+	42.3486i	−0.536009	+	1.64967i	−0.741458	+	0.670999i	$0.765865\pi$
$660$	10.8058	−	1.75432i	0.420614	−	0.0682869i
$661$	−15.8336	−	48.7307i	−0.615854	−	1.89541i	−0.387730	−	0.921773i	$-0.626741\pi$
$661$	−15.8336	−	48.7307i	−0.615854	−	1.89541i	−0.228125	−	0.973632i	$-0.573259\pi$
$662$	−4.96488	+	15.2803i	−0.192965	+	0.593886i
$663$	−3.21646	+	9.89924i	−0.124917	+	0.384455i
$664$	−4.40850	−	13.5680i	−0.171083	−	0.526540i
$665$	−7.16652	−	3.61669i	−0.277906	−	0.140249i
$666$	−5.84196	+	17.9797i	−0.226371	+	0.696699i
$667$	−15.4353	−	11.2144i	−0.597658	−	0.434224i
$668$	−14.8759			−0.575567
$669$	3.04325	+	2.21105i	0.117659	+	0.0854842i
$670$	−2.64437	+	17.1242i	−0.102161	+	0.661566i
$671$	−16.4022	+	11.9169i	−0.633201	+	0.460048i
$672$	−2.46195	+	1.78871i	−0.0949718	+	0.0690011i
$673$	13.8115	+	42.5076i	0.532396	+	1.63855i	0.749209	+	0.662334i	$0.230434\pi$
$673$	13.8115	+	42.5076i	0.532396	+	1.63855i	−0.216813	+	0.976213i	$0.569566\pi$
$674$	−30.0362			−1.15695
$675$	13.2971	+	18.0074i	0.511806	+	0.693105i
$676$	−9.67301			−0.372039
$677$	−9.76835	−	30.0639i	−0.375428	−	1.15545i	−0.943189	−	0.332256i	$-0.892190\pi$
$677$	−9.76835	−	30.0639i	−0.375428	−	1.15545i	0.567761	−	0.823193i	$-0.307810\pi$
$678$	3.96828	−	2.88312i	0.152401	−	0.110726i
$679$	54.6266	−	39.6885i	2.09638	−	1.52311i
$680$	6.88574	+	13.3858i	0.264056	+	0.513322i
$681$	13.4187	+	9.74926i	0.514206	+	0.373592i
$682$	−7.14190			−0.273478
$683$	−5.08957	−	3.69779i	−0.194747	−	0.141492i	0.486139	−	0.873882i	$-0.338405\pi$
$683$	−5.08957	−	3.69779i	−0.194747	−	0.141492i	−0.680886	+	0.732390i	$0.738405\pi$
$684$	−0.705004	+	2.16978i	−0.0269565	+	0.0829636i
$685$	−0.799772	+	5.17909i	−0.0305577	+	0.197883i
$686$	1.23375	+	3.79709i	0.0471048	+	0.144974i
$687$	−1.91092	+	5.88121i	−0.0729062	+	0.224382i
$688$	0.272851	−	0.839750i	0.0104024	−	0.0320152i
$689$	4.72318	+	14.5364i	0.179939	+	0.553795i
$690$	−2.06108	+	13.3470i	−0.0784640	+	0.508110i
$691$	8.57146	−	26.3802i	0.326074	−	1.00355i	−0.644880	−	0.764284i	$-0.723093\pi$
$691$	8.57146	−	26.3802i	0.326074	−	1.00355i	0.970954	−	0.239268i	$-0.0769073\pi$
$692$	15.0961	+	10.9680i	0.573868	+	0.416939i
$693$	47.3030			1.79689
$694$	10.7422	+	7.80470i	0.407770	+	0.296262i
$695$	−11.0374	−	21.4566i	−0.418672	−	0.813894i
$696$	1.83638	−	1.33421i	0.0696078	−	0.0505730i
$697$	−28.6123	+	20.7881i	−1.08377	+	0.787405i
$698$	4.02808	+	12.3972i	0.152465	+	0.469239i
$699$	10.0712			0.380927
$700$	−10.4380	+	14.6029i	−0.394521	+	0.551937i
$701$	4.64736			0.175528			0.0877642	−	0.996141i	$-0.472028\pi$
$701$	4.64736			0.175528			0.0877642	+	0.996141i	$0.472028\pi$
$702$	2.52343	+	7.76633i	0.0952409	+	0.293121i
$703$	6.70385	−	4.87064i	0.252841	−	0.183699i
$704$	4.67247	−	3.39475i	0.176100	−	0.127944i
$705$	0.300331	−	1.94485i	0.0113111	−	0.0732474i
$706$	22.8714	+	16.6170i	0.860775	+	0.625390i
$707$	−53.7012			−2.01964
$708$	−0.251716	−	0.182882i	−0.00946006	−	0.00687314i
$709$	−13.8323	+	42.5714i	−0.519483	+	1.59880i	0.255491	+	0.966811i	$0.417763\pi$
$709$	−13.8323	+	42.5714i	−0.519483	+	1.59880i	−0.774974	+	0.631993i	$0.782237\pi$
$710$	−9.35082	−	4.71903i	−0.350930	−	0.177102i
$711$	−1.10839	−	3.41126i	−0.0415678	−	0.127932i
$712$	−0.970222	+	2.98604i	−0.0363606	+	0.111906i
$713$	2.72265	−	8.37945i	0.101964	−	0.313813i
$714$	−6.33057	−	19.4835i	−0.236916	−	0.729151i
$715$	23.2515	−	3.77489i	0.869556	−	0.141173i
$716$	−2.90791	+	8.94963i	−0.108674	+	0.334463i
$717$	−2.25792	−	1.64047i	−0.0843234	−	0.0612645i
$718$	−22.7780			−0.850069
$719$	24.9675	+	18.1399i	0.931129	+	0.676505i	0.946269	−	0.323381i	$-0.104819\pi$
$719$	24.9675	+	18.1399i	0.931129	+	0.676505i	−0.0151400	+	0.999885i	$0.504819\pi$
$720$	4.55435	+	2.29842i	0.169731	+	0.0856571i
$721$	−42.1666	+	30.6359i	−1.57037	+	1.14094i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	7.10674	+	21.8723i	0.264302	+	0.813439i
$724$	−7.11536			−0.264440
$725$	7.78578	−	10.8924i	0.289157	−	0.404532i
$726$	18.9509			0.703335
$727$	10.8800	+	33.4853i	0.403518	+	1.24190i	0.922126	+	0.386889i	$0.126451\pi$
$727$	10.8800	+	33.4853i	0.403518	+	1.24190i	−0.518608	+	0.855012i	$0.673549\pi$
$728$	−5.29754	+	3.84889i	−0.196340	+	0.142649i
$729$	−3.58255	+	2.60288i	−0.132687	+	0.0964029i
$730$	−14.3320	+	14.4433i	−0.530453	+	0.534571i
$731$	4.80884	+	3.49382i	0.177861	+	0.129224i
$732$	2.97569			0.109985
$733$	−24.9058	−	18.0951i	−0.919916	−	0.668358i	0.0235871	−	0.999722i	$-0.492491\pi$
$733$	−24.9058	−	18.0951i	−0.919916	−	0.668358i	−0.943503	+	0.331364i	$0.892491\pi$
$734$	−3.69373	+	11.3681i	−0.136338	+	0.419605i
$735$	7.86093	−	7.92195i	0.289955	−	0.292206i
$736$	2.20174	+	6.77626i	0.0811572	+	0.249776i
$737$	−13.8297	+	42.5636i	−0.509425	+	1.56785i
$738$	−3.70381	+	11.3992i	−0.136339	+	0.419609i
$739$	−10.4470	−	32.1527i	−0.384300	−	1.18276i	−0.936986	−	0.349366i	$-0.886397\pi$
$739$	−10.4470	−	32.1527i	−0.384300	−	1.18276i	0.552686	−	0.833390i	$-0.313603\pi$
$740$	−8.47576	−	16.4768i	−0.311575	−	0.605700i
$741$	0.477793	−	1.47049i	0.0175522	−	0.0540200i
$742$	−24.3374	−	17.6822i	−0.893454	−	0.649132i
$743$	−18.8032			−0.689822			−0.344911	−	0.938635i	$-0.612091\pi$
$743$	−18.8032			−0.689822			−0.344911	+	0.938635i	$0.612091\pi$
$744$	0.848035	+	0.616134i	0.0310905	+	0.0225886i
$745$	13.1775	−	2.13937i	0.482786	−	0.0783806i
$746$	17.5220	−	12.7304i	0.641524	−	0.466095i
$747$	26.3315	−	19.1310i	0.963419	−	0.699965i
$748$	12.0146	+	36.9772i	0.439298	+	1.35202i
$749$	−17.7133			−0.647231
$750$	−9.37722	−	1.37390i	−0.342408	−	0.0501678i
$751$	43.8546			1.60028			0.800138	−	0.599815i	$-0.204759\pi$
$751$	43.8546			1.60028			0.800138	+	0.599815i	$0.204759\pi$
$752$	−0.320827	−	0.987403i	−0.0116994	−	0.0360069i
$753$	12.7806	−	9.28566i	0.465751	−	0.338388i
$754$	3.95146	−	2.87090i	0.143904	−	0.104552i
$755$	−25.8081	+	4.18996i	−0.939253	+	0.152488i
$756$	−13.0026	−	9.44698i	−0.472902	−	0.343583i
$757$	23.2900			0.846490			0.423245	−	0.906015i	$-0.360891\pi$
$757$	23.2900			0.846490			0.423245	+	0.906015i	$0.360891\pi$
$758$	2.73153	+	1.98458i	0.0992138	+	0.0720830i
$759$	−10.7792	+	33.1749i	−0.391260	+	1.20417i
$760$	−1.02285	−	1.98841i	−0.0371027	−	0.0721273i
$761$	−12.0241	−	37.0065i	−0.435875	−	1.34148i	−0.892187	−	0.451665i	$-0.850830\pi$
$761$	−12.0241	−	37.0065i	−0.435875	−	1.34148i	0.456313	−	0.889820i	$-0.349170\pi$
$762$	4.31633	−	13.2843i	0.156364	−	0.481240i
$763$	−15.3278	+	47.1741i	−0.554904	+	1.70782i
$764$	−6.84547	−	21.0682i	−0.247661	−	0.762221i
$765$	−24.1898	+	24.3776i	−0.874584	+	0.881373i
$766$	−0.0881832	+	0.271400i	−0.00318619	+	0.00980608i
$767$	−0.541634	−	0.393520i	−0.0195573	−	0.0142092i
$768$	−0.847678			−0.0305880
$769$	16.0790	+	11.6821i	0.579823	+	0.421266i	0.838660	−	0.544655i	$-0.183339\pi$
$769$	16.0790	+	11.6821i	0.579823	+	0.421266i	−0.258837	+	0.965921i	$0.583339\pi$
$770$	−32.6561	+	32.9096i	−1.17684	+	1.18598i
$771$	−13.3883	+	9.72714i	−0.482167	+	0.350315i
$772$	−9.18034	+	6.66991i	−0.330408	+	0.240055i
$773$	−10.9684	−	33.7574i	−0.394507	−	1.21417i	−0.929344	−	0.369214i	$-0.879627\pi$
$773$	−10.9684	−	33.7574i	−0.394507	−	1.21417i	0.534837	−	0.844955i	$-0.320373\pi$
$774$	2.01443			0.0724074
$775$	5.89493	+	1.86510i	0.211752	+	0.0669965i
$776$	18.8086			0.675188
$777$	7.79240	+	23.9825i	0.279551	+	0.860368i
$778$	−4.15753	+	3.02062i	−0.149055	+	0.108295i
$779$	4.25025	−	3.08799i	0.152281	−	0.110639i
$780$	−3.08656	−	1.55768i	−0.110517	−	0.0557738i
$781$	−21.8866	−	15.9016i	−0.783165	−	0.569003i
$782$	−47.9648			−1.71522
$783$	9.69874	+	7.04654i	0.346605	+	0.251823i
$784$	1.81945	−	5.59970i	0.0649805	−	0.199989i
$785$	−46.1947	+	7.49974i	−1.64876	+	0.267677i
$786$	−2.45159	−	7.54523i	−0.0874455	−	0.269129i
$787$	−10.1168	+	31.1362i	−0.360624	+	1.10989i	0.592052	+	0.805900i	$0.298318\pi$
$787$	−10.1168	+	31.1362i	−0.360624	+	1.10989i	−0.952676	+	0.303987i	$0.901682\pi$
$788$	5.04178	−	15.5170i	0.179606	−	0.552770i
$789$	−4.70998	−	14.4958i	−0.167680	−	0.516065i
$790$	3.13846	+	1.58387i	0.111662	+	0.0563516i
$791$	−6.41928	+	19.7565i	−0.228243	+	0.702461i
$792$	10.6600	+	7.74492i	0.378785	+	0.275204i
$793$	6.40299			0.227377
$794$	−14.6269	−	10.6270i	−0.519089	−	0.377140i
$795$	2.42403	−	15.6973i	0.0859713	−	0.556725i
$796$	−4.11129	+	2.98703i	−0.145721	+	0.105872i
$797$	−39.9750	+	29.0435i	−1.41599	+	1.02878i	−0.423570	+	0.905863i	$0.639223\pi$
$797$	−39.9750	+	29.0435i	−1.41599	+	1.02878i	−0.992418	+	0.122912i	$0.960777\pi$
$798$	0.940382	+	2.89420i	0.0332891	+	0.102453i
$799$	6.98919			0.247260
$800$	−4.74319	+	1.58181i	−0.167697	+	0.0559255i
$801$	−7.16305			−0.253094
$802$	2.67308	+	8.22691i	0.0943899	+	0.290502i
$803$	−42.5177	+	30.8909i	−1.50042	+	1.09012i
$804$	5.31412	−	3.86094i	0.187415	−	0.136165i
$805$	−26.1629	−	50.8605i	−0.922122	−	1.79260i
$806$	1.82477	+	1.32578i	0.0642749	+	0.0466984i
$807$	11.5875			0.407900
$808$	−12.1018	−	8.79250i	−0.425741	−	0.309319i
$809$	−4.57706	+	14.0868i	−0.160921	+	0.495264i	−0.998713	−	0.0507263i	$-0.983846\pi$
$809$	−4.57706	+	14.0868i	−0.160921	+	0.495264i	0.837792	+	0.545990i	$0.183846\pi$
$810$	−1.04059	+	6.73857i	−0.0365627	+	0.236769i
$811$	14.4280	+	44.4049i	0.506637	+	1.55927i	0.798001	+	0.602656i	$0.205891\pi$
$811$	14.4280	+	44.4049i	0.506637	+	1.55927i	−0.291364	+	0.956612i	$0.594109\pi$
$812$	−2.97062	+	9.14263i	−0.104248	+	0.320843i
$813$	−0.100140	+	0.308199i	−0.00351206	+	0.0108090i
$814$	−14.7890	−	45.5158i	−0.518353	−	1.59533i
$815$	−4.45789	+	28.8680i	−0.156153	+	1.01120i
$816$	1.76340	−	5.42720i	0.0617315	−	0.189990i
$817$	−0.714334	−	0.518994i	−0.0249914	−	0.0181573i
$818$	19.0214			0.665067
$819$	−12.0860	−	8.78101i	−0.422320	−	0.306833i
$820$	−5.37365	−	10.4463i	−0.187656	−	0.364801i
$821$	33.4695	−	24.3170i	1.16809	−	0.848669i	0.177314	−	0.984154i	$-0.443259\pi$
$821$	33.4695	−	24.3170i	1.16809	−	0.848669i	0.990779	+	0.135485i	$0.0432593\pi$
$822$	1.60722	−	1.16771i	0.0560582	−	0.0407286i
$823$	−6.14103	−	18.9002i	−0.214063	−	0.658818i	−0.999219	−	0.0395197i	$-0.987417\pi$
$823$	−6.14103	−	18.9002i	−0.214063	−	0.658818i	0.785156	−	0.619298i	$-0.212583\pi$
$824$	−14.5185			−0.505775
$825$	−23.3385	−	7.38410i	−0.812543	−	0.257081i
$826$	1.31769			0.0458482
$827$	−0.818660	−	2.51958i	−0.0284676	−	0.0876142i	0.935813	−	0.352496i	$-0.114667\pi$
$827$	−0.818660	−	2.51958i	−0.0284676	−	0.0876142i	−0.964281	+	0.264882i	$0.914667\pi$
$828$	−13.1508	+	9.55458i	−0.457020	+	0.332045i
$829$	44.4155	−	32.2698i	1.54262	−	1.12078i	0.593947	−	0.804504i	$-0.297569\pi$
$829$	44.4155	−	32.2698i	1.54262	−	1.12078i	0.948669	−	0.316271i	$-0.102431\pi$
$830$	−4.86843	+	31.5265i	−0.168986	+	1.09430i
$831$	−0.896649	−	0.651454i	−0.0311044	−	0.0225987i
$832$	−1.82400			−0.0632360
$833$	32.0667	+	23.2978i	1.11105	+	0.807222i
$834$	−2.82662	+	8.69945i	−0.0978779	+	0.301237i
$835$	29.6962	+	14.9866i	1.02768	+	0.518634i
$836$	−1.78472	−	5.49282i	−0.0617260	−	0.189973i
$837$	−1.71077	+	5.26520i	−0.0591328	+	0.181992i
$838$	3.20902	−	9.87636i	0.110854	−	0.341173i
$839$	−7.76002	−	23.8829i	−0.267905	−	0.824528i	−0.991010	−	0.133789i	$-0.957285\pi$
$839$	−7.76002	−	23.8829i	−0.267905	−	0.824528i	0.723104	−	0.690739i	$-0.242715\pi$
$840$	6.71672	−	1.09046i	0.231749	−	0.0376246i
$841$	−6.74569	+	20.7611i	−0.232610	+	0.715900i
$842$	8.70527	+	6.32475i	0.300003	+	0.217965i
$843$	7.25531			0.249886
$844$	3.50881	+	2.54930i	0.120778	+	0.0877505i
$845$	19.3098	+	9.74500i	0.664279	+	0.335238i
$846$	1.91626	−	1.39225i	0.0658825	−	0.0478664i
$847$	−64.9304	+	47.1747i	−2.23103	+	1.62094i
$848$	−2.58945	−	7.96952i	−0.0889222	−	0.273674i
$849$	−15.7495			−0.540521
$850$	−0.260294	−	33.6586i	−0.00892802	−	1.15448i
$851$	59.0406			2.02389
$852$	1.22700	+	3.77633i	0.0420364	+	0.129375i
$853$	−12.6394	+	9.18303i	−0.432763	+	0.314421i	−0.782753	−	0.622333i	$-0.786185\pi$
$853$	−12.6394	+	9.18303i	−0.432763	+	0.314421i	0.349990	+	0.936754i	$0.386185\pi$
$854$	−10.1954	+	7.40740i	−0.348880	+	0.253476i
$855$	3.59330	−	3.62120i	0.122888	−	0.123842i
$856$	−3.99179	−	2.90020i	−0.136436	−	0.0991269i
$857$	−11.0097			−0.376083			−0.188042	−	0.982161i	$-0.560214\pi$
$857$	−11.0097			−0.376083			−0.188042	+	0.982161i	$0.560214\pi$
$858$	−7.22443	−	5.24886i	−0.246638	−	0.179193i
$859$	2.67137	−	8.22162i	0.0911459	−	0.280518i	−0.895084	−	0.445897i	$-0.852885\pi$
$859$	2.67137	−	8.22162i	0.0911459	−	0.280518i	0.986230	+	0.165379i	$0.0528847\pi$
$860$	−1.39068	+	1.40148i	−0.0474219	+	0.0477900i
$861$	4.94039	+	15.2050i	0.168368	+	0.518184i
$862$	10.0546	−	30.9449i	0.342461	−	1.05399i
$863$	3.59106	−	11.0521i	0.122241	−	0.376219i	−0.871147	−	0.491022i	$-0.836624\pi$
$863$	3.59106	−	11.0521i	0.122241	−	0.376219i	0.993388	+	0.114802i	$0.0366235\pi$
$864$	−1.38346	−	4.25785i	−0.0470662	−	0.144855i
$865$	−19.0862	−	37.1034i	−0.648950	−	1.26155i
$866$	−3.05868	+	9.41364i	−0.103938	+	0.319889i
$867$	19.4205	+	14.1099i	0.659556	+	0.479196i
$868$	−4.43931			−0.150680
$869$	7.34592	+	5.33712i	0.249193	+	0.181050i
$870$	−5.01003	+	0.813382i	−0.169856	+	0.0275762i
$871$	11.4347	−	8.30783i	0.387452	−	0.281500i
$872$	−11.1780	+	8.12130i	−0.378535	+	0.275022i
$873$	13.2601	+	40.8104i	0.448787	+	1.38122i
$874$	7.12498			0.241006
$875$	35.5486	−	18.6354i	1.20176	−	0.629993i
$876$	7.71356			0.260617
$877$	9.50908	+	29.2659i	0.321099	+	0.988241i	0.973171	+	0.230084i	$0.0739000\pi$
$877$	9.50908	+	29.2659i	0.321099	+	0.988241i	−0.652072	+	0.758157i	$0.726100\pi$
$878$	−17.9931	+	13.0727i	−0.607236	+	0.441183i
$879$	12.3867	−	8.99949i	0.417794	−	0.303545i
$880$	−12.7475	+	2.06956i	−0.429718	+	0.0697649i
$881$	12.4610	+	9.05344i	0.419821	+	0.305018i	0.777566	−	0.628801i	$-0.216454\pi$
$881$	12.4610	+	9.05344i	0.419821	+	0.305018i	−0.357745	+	0.933820i	$0.616454\pi$
$882$	13.4328			0.452307
$883$	37.9872	+	27.5993i	1.27837	+	0.928790i	0.999502	−	0.0315397i	$-0.0100411\pi$
$883$	37.9872	+	27.5993i	1.27837	+	0.928790i	0.278867	+	0.960330i	$0.410041\pi$
$884$	3.79443	−	11.6781i	0.127621	−	0.392776i
$885$	0.318247	+	0.618670i	0.0106978	+	0.0207964i
$886$	0.0980463	+	0.301755i	0.00329393	+	0.0101377i
$887$	11.8107	−	36.3495i	0.396564	−	1.22050i	−0.531174	−	0.847263i	$-0.678249\pi$
$887$	11.8107	−	36.3495i	0.396564	−	1.22050i	0.927737	−	0.373234i	$-0.121751\pi$
$888$	−2.17060	+	6.68043i	−0.0728407	+	0.224181i
$889$	18.2799	+	56.2598i	0.613089	+	1.88689i
$890$	4.94508	−	4.98347i	0.165759	−	0.167046i
$891$	−5.44216	+	16.7492i	−0.182319	+	0.561121i
$892$	−3.59010	−	2.60836i	−0.120206	−	0.0873344i
$893$	−1.03822			−0.0347426
$894$	−4.09436	−	2.97473i	−0.136936	−	0.0994898i
$895$	14.8212	−	14.9362i	0.495417	−	0.499264i
$896$	2.90435	−	2.11013i	0.0970274	−	0.0704945i
$897$	8.91248	−	6.47530i	0.297579	−	0.216204i
$898$	7.80223	+	24.0128i	0.260364	+	0.801317i
$899$	3.31130			0.110438
$900$	−6.77615	−	9.17650i	−0.225872	−	0.305883i
$901$	56.4111			1.87933
$902$	−9.37624	−	28.8571i	−0.312194	−	0.960836i
$903$	2.17382	−	1.57937i	0.0723402	−	0.0525582i
$904$	−4.68135	+	3.40120i	−0.155699	+	0.113122i
$905$	14.2041	+	7.16832i	0.472161	+	0.238283i
$906$	8.01879	+	5.82599i	0.266407	+	0.193556i
$907$	−40.2962			−1.33801			−0.669006	−	0.743257i	$-0.733280\pi$
$907$	−40.2962			−1.33801			−0.669006	+	0.743257i	$0.733280\pi$
$908$	−15.8299	−	11.5011i	−0.525335	−	0.381678i
$909$	10.5459	−	32.4571i	0.349787	−	1.07653i
$910$	14.4528	−	2.34642i	0.479106	−	0.0777831i
$911$	−9.15730	−	28.1833i	−0.303395	−	0.933753i	−0.980271	−	0.197657i	$-0.936667\pi$
$911$	−9.15730	−	28.1833i	−0.303395	−	0.933753i	0.676876	−	0.736097i	$-0.263333\pi$
$912$	−0.261947	+	0.806190i	−0.00867393	+	0.0266956i
$913$	−25.4613	+	78.3617i	−0.842645	+	2.59339i
$914$	7.98355	+	24.5708i	0.264072	+	0.812731i
$915$	−5.94026	−	2.99784i	−0.196379	−	0.0991054i
$916$	2.25430	−	6.93802i	0.0744841	−	0.229239i
$917$	27.1821	+	19.7490i	0.897633	+	0.652168i
$918$	30.1385			0.994720
$919$	15.5060	+	11.2657i	0.511494	+	0.371622i	0.813390	−	0.581719i	$-0.197620\pi$
$919$	15.5060	+	11.2657i	0.511494	+	0.371622i	−0.301896	+	0.953341i	$0.597620\pi$
$920$	2.43144	−	15.7453i	0.0801623	−	0.519108i
$921$	−23.5639	+	17.1202i	−0.776456	+	0.564128i
$922$	15.6813	−	11.3932i	0.516437	−	0.375214i
$923$	2.64022	+	8.12577i	0.0869040	+	0.267463i
$924$	17.5756			0.578195
$925$	0.320400	+	41.4309i	0.0105347	+	1.36224i
$926$	22.0089			0.723257
$927$	−10.2356	−	31.5019i	−0.336181	−	1.03466i
$928$	−2.16636	+	1.57396i	−0.0711144	+	0.0516676i
$929$	−6.28045	+	4.56301i	−0.206055	+	0.149708i	−0.686027	−	0.727576i	$-0.740647\pi$
$929$	−6.28045	+	4.56301i	−0.206055	+	0.149708i	0.479972	+	0.877284i	$0.340647\pi$
$930$	−1.07218	−	2.08431i	−0.0351582	−	0.0683472i
$931$	−4.76339	−	3.46081i	−0.156114	−	0.113423i
$932$	−11.8809			−0.389171
$933$	10.9935	+	7.98728i	0.359913	+	0.261492i
$934$	−0.673622	+	2.07320i	−0.0220416	+	0.0678371i
$935$	13.2681	−	85.9201i	0.433912	−	2.80989i
$936$	−1.28593	−	3.95769i	−0.0420320	−	0.129361i
$937$	−11.6085	+	35.7273i	−0.379233	+	1.16716i	0.561345	+	0.827582i	$0.310284\pi$
$937$	−11.6085	+	35.7273i	−0.379233	+	1.16716i	−0.940578	+	0.339578i	$0.889716\pi$
$938$	−8.59638	+	26.4569i	−0.280682	+	0.863850i
$939$	−5.51290	−	16.9670i	−0.179907	−	0.553696i
$940$	−0.354298	+	2.29433i	−0.0115559	+	0.0748328i
$941$	10.2294	−	31.4829i	0.333469	−	1.02631i	−0.634002	−	0.773332i	$-0.718589\pi$
$941$	10.2294	−	31.4829i	0.333469	−	1.02631i	0.967471	−	0.252982i	$-0.0814112\pi$
$942$	14.3531	+	10.4281i	0.467649	+	0.339767i
$943$	37.4318			1.21895
$944$	0.296947	+	0.215745i	0.00966482	+	0.00702190i
$945$	16.4394	+	31.9581i	0.534774	+	1.03960i
$946$	−4.12563	+	2.99745i	−0.134136	+	0.0974554i
$947$	42.8367	−	31.1227i	1.39200	−	1.01135i	0.396363	−	0.918094i	$-0.370272\pi$
$947$	42.8367	−	31.1227i	1.39200	−	1.01135i	0.995642	−	0.0932567i	$-0.0297277\pi$
$948$	−0.411826	−	1.26747i	−0.0133755	−	0.0411655i
$949$	16.5978			0.538786
$950$	0.0386657	+	4.99985i	0.00125448	+	0.162217i
$951$	−11.4666			−0.371830
$952$	7.46812	+	22.9845i	0.242043	+	0.744933i
$953$	−10.5522	+	7.66662i	−0.341819	+	0.248346i	−0.745429	−	0.666585i	$-0.767755\pi$
$953$	−10.5522	+	7.66662i	−0.341819	+	0.248346i	0.403610	+	0.914931i	$0.367755\pi$
$954$	15.4665	−	11.2371i	0.500747	−	0.363814i
$955$	−7.55965	+	48.9541i	−0.244624	+	1.58412i
$956$	2.66365	+	1.93525i	0.0861485	+	0.0625905i
$957$	−13.1097			−0.423777
$958$	−5.07055	−	3.68397i	−0.163822	−	0.119024i
$959$	−2.59991	+	8.00171i	−0.0839556	+	0.258389i
$960$	1.69219	+	0.853987i	0.0546151	+	0.0275623i
$961$	−9.10699	−	28.0284i	−0.293774	−	0.904143i
$962$	−4.67063	+	14.3747i	−0.150587	+	0.463459i
$963$	3.47858	−	10.7060i	0.112096	−	0.344995i
$964$	−8.38376	−	25.8026i	−0.270023	−	0.831045i
$965$	25.0459	−	4.06622i	0.806256	−	0.130896i
$966$	−6.70020	+	20.6211i	−0.215575	+	0.663473i
$967$	−9.57213	−	6.95456i	−0.307819	−	0.223643i	0.423141	−	0.906064i	$-0.360927\pi$
$967$	−9.57213	−	6.95456i	−0.307819	−	0.223643i	−0.730960	+	0.682420i	$0.760927\pi$
$968$	−22.3563			−0.718558
$969$	−4.61665	−	3.35420i	−0.148308	−	0.107752i
$970$	−37.5468	−	18.9485i	−1.20556	−	0.608401i
$971$	−39.6491	+	28.8068i	−1.27240	+	0.924454i	−0.999296	−	0.0375300i	$-0.988051\pi$
$971$	−39.6491	+	28.8068i	−1.27240	+	0.924454i	−0.273106	+	0.961984i	$0.588051\pi$
$972$	12.9570	−	9.41380i	0.415596	−	0.301948i
$973$	−11.9709	−	36.8427i	−0.383770	−	1.18112i
$974$	−37.3813			−1.19777
$975$	4.59231	+	6.21906i	0.147072	+	0.199169i
$976$	−3.51040			−0.112365
$977$	−14.9449	−	45.9956i	−0.478129	−	1.47153i	−0.841691	−	0.539959i	$-0.818440\pi$
$977$	−14.9449	−	45.9956i	−0.478129	−	1.47153i	0.363562	−	0.931570i	$-0.381560\pi$
$978$	8.95856	−	6.50878i	0.286463	−	0.208128i
$979$	14.6702	−	10.6585i	0.468861	−	0.340647i
$980$	−9.27348	+	9.34547i	−0.296230	+	0.298530i
$981$	−25.5020	−	18.5283i	−0.814215	−	0.591562i
$982$	−1.46298			−0.0466857
$983$	−41.7878	−	30.3606i	−1.33282	−	0.968353i	−0.999675	−	0.0254784i	$-0.991889\pi$
$983$	−41.7878	−	30.3606i	−1.33282	−	0.968353i	−0.333148	−	0.942875i	$-0.608111\pi$
$984$	−1.37617	+	4.23540i	−0.0438706	+	0.135020i
$985$	−25.6972	+	25.8967i	−0.818780	+	0.825136i
$986$	−5.57051	−	17.1443i	−0.177401	−	0.545985i
$987$	0.976321	−	3.00481i	0.0310766	−	0.0956440i
$988$	−0.563649	+	1.73473i	−0.0179320	+	0.0551892i
$989$	−1.94406	−	5.98321i	−0.0618176	−	0.190255i
$990$	−13.4775	−	26.2002i	−0.428344	−	0.832696i
$991$	−4.61067	+	14.1902i	−0.146463	+	0.450766i	−0.997196	−	0.0748314i	$-0.976158\pi$
$991$	−4.61067	+	14.1902i	−0.146463	+	0.450766i	0.850733	+	0.525597i	$0.176158\pi$
$992$	−1.00042	−	0.726848i	−0.0317634	−	0.0230775i
$993$	−13.6194			−0.432198
$994$	−13.6044	−	9.88420i	−0.431507	−	0.313508i
$995$	11.2165	−	1.82100i	0.355586	−	0.0577296i
$996$	9.78357	−	7.10818i	0.310004	−	0.225231i
$997$	34.0115	−	24.7108i	1.07716	−	0.782599i	0.0999707	−	0.994990i	$-0.468125\pi$
$997$	34.0115	−	24.7108i	1.07716	−	0.782599i	0.977185	+	0.212391i	$0.0681251\pi$
$998$	−1.23638	−	3.80519i	−0.0391370	−	0.120451i
$999$	−37.0980			−1.17373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.381.8	✓	44
25.21	even	5	inner	950.2.h.e.571.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.381.8	✓	44	1.1	even	1	trivial
950.2.h.e.571.8	yes	44	25.21	even	5	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.685786 - 0.498253i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.20717 - 0.358335i) q^{5} +(-0.685786 - 0.498253i) q^{6} +3.58997 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.705004 + 2.16978i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.685786 - 0.498253i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.20717 - 0.358335i) q^{5} +(-0.685786 - 0.498253i) q^{6} +3.58997 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.705004 + 2.16978i) q^{9} +(-1.02285 - 1.98841i) q^{10} +(-1.78472 - 5.49282i) q^{11} +(-0.261947 + 0.806190i) q^{12} +(-0.563649 + 1.73473i) q^{13} +(-1.10936 - 3.41426i) q^{14} +(1.33510 - 1.34547i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.44623 + 3.95692i) q^{17} +2.28144 q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.57501 + 1.58724i) q^{20} +(2.46195 - 1.78871i) q^{21} +(-4.67247 + 3.39475i) q^{22} +(-2.20174 - 6.77626i) q^{23} +0.847678 q^{24} +(4.74319 - 1.58181i) q^{25} +1.82400 q^{26} +(1.38346 + 4.25785i) q^{27} +(-2.90435 + 2.11013i) q^{28} +(2.16636 - 1.57396i) q^{29} +(-1.69219 - 0.853987i) q^{30} +(1.00042 + 0.726848i) q^{31} -1.00000 q^{32} +(-3.96075 - 2.87765i) q^{33} +(2.08028 - 6.40243i) q^{34} +(7.92367 - 1.28641i) q^{35} +(-0.705004 - 2.16978i) q^{36} +(-2.56064 + 7.88085i) q^{37} +(-0.309017 + 0.951057i) q^{38} +(0.477793 + 1.47049i) q^{39} +(1.99626 + 1.00744i) q^{40} +(-1.62345 + 4.99647i) q^{41} +(-2.46195 - 1.78871i) q^{42} +0.882966 q^{43} +(4.67247 + 3.39475i) q^{44} +(-0.778555 + 5.04170i) q^{45} +(-5.76423 + 4.18796i) q^{46} +(0.839936 - 0.610249i) q^{47} +(-0.261947 - 0.806190i) q^{48} +5.88787 q^{49} +(-2.97012 - 4.02224i) q^{50} +5.70650 q^{51} +(-0.563649 - 1.73473i) q^{52} +(6.77928 - 4.92544i) q^{53} +(3.62194 - 2.63149i) q^{54} +(-5.90746 - 11.4840i) q^{55} +(2.90435 + 2.11013i) q^{56} -0.847678 q^{57} +(-2.16636 - 1.57396i) q^{58} +(-0.113424 + 0.349083i) q^{59} +(-0.289275 + 1.87326i) q^{60} +(-1.08477 - 3.33859i) q^{61} +(0.382127 - 1.17607i) q^{62} +(-2.53094 + 7.78944i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.622453 + 4.03082i) q^{65} +(-1.51287 + 4.65614i) q^{66} +(-6.26903 - 4.55472i) q^{67} -6.73191 q^{68} +(-4.88621 - 3.55004i) q^{69} +(-3.67200 - 7.13833i) q^{70} +(3.78957 - 2.75328i) q^{71} +(-1.84572 + 1.34100i) q^{72} +(-2.81194 - 8.65426i) q^{73} +8.28642 q^{74} +(2.46467 - 3.44809i) q^{75} +1.00000 q^{76} +(-6.40710 - 19.7190i) q^{77} +(1.25088 - 0.908816i) q^{78} +(-1.27191 + 0.924099i) q^{79} +(0.341256 - 2.20987i) q^{80} +(-2.46693 - 1.79233i) q^{81} +5.25360 q^{82} +(-11.5416 - 8.38547i) q^{83} +(-0.940382 + 2.89420i) q^{84} +(13.4387 + 6.78202i) q^{85} +(-0.272851 - 0.839750i) q^{86} +(0.701435 - 2.15879i) q^{87} +(1.78472 - 5.49282i) q^{88} +(0.970222 + 2.98604i) q^{89} +(5.03553 - 0.817520i) q^{90} +(-2.02348 + 6.22763i) q^{91} +(5.76423 + 4.18796i) q^{92} +1.04823 q^{93} +(-0.839936 - 0.610249i) q^{94} +(-1.99626 - 1.00744i) q^{95} +(-0.685786 + 0.498253i) q^{96} +(15.2164 - 11.0554i) q^{97} +(-1.81945 - 5.59970i) q^{98} +13.1764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Introduction

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