LMFDB - Embedded newform 91.2.g.b.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(9,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.g (of order $3$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.3
Root			$-0.437442 + 0.757672i$ of defining polynomial
Character	$\chi$	$=$	91.9
Dual form			91.2.g.b.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.134063 + 0.232203i) q^{2} -1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +(-0.153235 - 0.265410i) q^{6} +(0.773854 + 2.53005i) q^{7} +1.05323 q^{8} -1.69353 q^{9} +O(q^{10})$	\(q+(0.134063 + 0.232203i) q^{2} -1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +(-0.153235 - 0.265410i) q^{6} +(0.773854 + 2.53005i) q^{7} +1.05323 q^{8} -1.69353 q^{9} +0.686871 q^{10} +3.94600 q^{11} +(-1.10192 + 1.90859i) q^{12} +(-3.15374 + 1.74755i) q^{13} +(-0.483741 + 0.518876i) q^{14} +(-1.46405 + 2.53582i) q^{15} +(-1.78691 - 3.09502i) q^{16} +(-0.392550 + 0.679916i) q^{17} +(-0.227039 - 0.393243i) q^{18} -7.49527 q^{19} +(-2.46967 - 4.27760i) q^{20} +(-0.884522 - 2.89187i) q^{21} +(0.529011 + 0.916274i) q^{22} +(3.97759 + 6.88938i) q^{23} -1.20385 q^{24} +(-0.781294 - 1.35324i) q^{25} +(-0.828585 - 0.498028i) q^{26} +5.36475 q^{27} +(4.97069 + 1.14693i) q^{28} +(-1.17586 + 2.03666i) q^{29} -0.785100 q^{30} +(1.27718 + 2.21215i) q^{31} +(1.53234 - 2.65409i) q^{32} -4.51032 q^{33} -0.210505 q^{34} +(6.60424 + 1.52385i) q^{35} +(-1.63266 + 2.82784i) q^{36} +(-3.37858 - 5.85187i) q^{37} +(-1.00484 - 1.74043i) q^{38} +(3.60475 - 1.99746i) q^{39} +(1.34905 - 2.33663i) q^{40} +(1.21874 - 2.11091i) q^{41} +(0.552920 - 0.593080i) q^{42} +(1.12473 + 1.94809i) q^{43} +(3.80416 - 6.58900i) q^{44} +(-2.16920 + 3.75717i) q^{45} +(-1.06649 + 1.84722i) q^{46} +(-0.658276 + 1.14017i) q^{47} +(2.04246 + 3.53764i) q^{48} +(-5.80230 + 3.91578i) q^{49} +(0.209485 - 0.362838i) q^{50} +(0.448688 - 0.777151i) q^{51} +(-0.122340 + 6.95082i) q^{52} +(-4.63977 - 8.03632i) q^{53} +(0.719212 + 1.24571i) q^{54} +(5.05434 - 8.75438i) q^{55} +(0.815042 + 2.66471i) q^{56} +8.56716 q^{57} -0.630558 q^{58} +(4.48335 - 7.76540i) q^{59} +(2.82286 + 4.88933i) q^{60} +9.44547 q^{61} +(-0.342445 + 0.593132i) q^{62} +(-1.31054 - 4.28472i) q^{63} -6.32592 q^{64} +(-0.162546 + 9.23511i) q^{65} +(-0.604665 - 1.04731i) q^{66} -1.35256 q^{67} +(0.756879 + 1.31095i) q^{68} +(-4.54642 - 7.87463i) q^{69} +(0.531538 + 1.73782i) q^{70} +(-6.15808 - 10.6661i) q^{71} -1.78367 q^{72} +(-0.384295 - 0.665619i) q^{73} +(0.905882 - 1.56903i) q^{74} +(0.893026 + 1.54677i) q^{75} +(-7.22585 + 12.5155i) q^{76} +(3.05363 + 9.98358i) q^{77} +(0.947080 + 0.569251i) q^{78} +(-3.09642 + 5.36316i) q^{79} -9.15525 q^{80} -1.05136 q^{81} +0.653548 q^{82} -1.07292 q^{83} +(-5.68155 - 1.31095i) q^{84} +(1.00562 + 1.74178i) q^{85} +(-0.301568 + 0.522332i) q^{86} +(1.34402 - 2.32792i) q^{87} +4.15603 q^{88} +(-3.83149 - 6.63634i) q^{89} -1.16324 q^{90} +(-6.86191 - 6.62678i) q^{91} +15.3384 q^{92} +(-1.45983 - 2.52850i) q^{93} -0.353001 q^{94} +(-9.60052 + 16.6286i) q^{95} +(-1.75148 + 3.03365i) q^{96} +(1.18601 + 2.05423i) q^{97} +(-1.68713 - 0.822354i) q^{98} -6.68267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.134063	+	0.232203i	0.0947966	+	0.164193i	0.909524	−	0.415652i	$-0.136447\pi$
$2$	0.134063	+	0.232203i	0.0947966	+	0.164193i	−0.814727	+	0.579845i	$0.803113\pi$
$3$	−1.14301			−0.659917			−0.329958	−	0.943996i	$-0.607035\pi$
$3$	−1.14301			−0.659917			−0.329958	+	0.943996i	$0.607035\pi$
$4$	0.964054	−	1.66979i	0.482027	−	0.834896i
$5$	1.28088	−	2.21854i	0.572826	−	0.992163i	−0.423448	−	0.905920i	$-0.639180\pi$
$5$	1.28088	−	2.21854i	0.572826	−	0.992163i	0.996274	−	0.0862431i	$-0.0274862\pi$
$6$	−0.153235	−	0.265410i	−0.0625578	−	0.108353i
$7$	0.773854	+	2.53005i	0.292489	+	0.956269i
$7$	0.773854	+	2.53005i	0.292489	+	0.956269i
$8$	1.05323			0.372371
$9$	−1.69353			−0.564510
$10$	0.686871			0.217208
$11$	3.94600			1.18976			0.594882	−	0.803813i	$-0.297199\pi$
$11$	3.94600			1.18976			0.594882	+	0.803813i	$0.297199\pi$
$12$	−1.10192	+	1.90859i	−0.318098	+	0.550961i
$13$	−3.15374	+	1.74755i	−0.874690	+	0.484682i
$13$	−3.15374	+	1.74755i	−0.874690	+	0.484682i
$14$	−0.483741	+	0.518876i	−0.129285	+	0.138676i
$15$	−1.46405	+	2.53582i	−0.378017	+	0.654745i
$16$	−1.78691	−	3.09502i	−0.446728	−	0.773755i
$17$	−0.392550	+	0.679916i	−0.0952073	+	0.164904i	−0.909695	−	0.415277i	$-0.863685\pi$
$17$	−0.392550	+	0.679916i	−0.0952073	+	0.164904i	0.814488	+	0.580181i	$0.197018\pi$
$18$	−0.227039	−	0.393243i	−0.0535136	−	0.0926883i
$19$	−7.49527			−1.71953			−0.859767	−	0.510687i	$-0.829391\pi$
$19$	−7.49527			−1.71953			−0.859767	+	0.510687i	$0.829391\pi$
$20$	−2.46967	−	4.27760i	−0.552235	−	0.956500i
$21$	−0.884522	−	2.89187i	−0.193018	−	0.631058i
$22$	0.529011	+	0.916274i	0.112786	+	0.195350i
$23$	3.97759	+	6.88938i	0.829384	+	1.43654i	0.898522	+	0.438929i	$0.144642\pi$
$23$	3.97759	+	6.88938i	0.829384	+	1.43654i	−0.0691375	+	0.997607i	$0.522025\pi$
$24$	−1.20385			−0.245734
$25$	−0.781294	−	1.35324i	−0.156259	−	0.270648i
$26$	−0.828585	−	0.498028i	−0.162499	−	0.0976714i
$27$	5.36475			1.03245
$28$	4.97069	+	1.14693i	0.939372	+	0.216750i
$29$	−1.17586	+	2.03666i	−0.218353	+	0.378198i	−0.954304	−	0.298836i	$-0.903402\pi$
$29$	−1.17586	+	2.03666i	−0.218353	+	0.378198i	0.735952	+	0.677034i	$0.236735\pi$
$30$	−0.785100			−0.143339
$31$	1.27718	+	2.21215i	0.229389	+	0.397313i	0.957627	−	0.288011i	$-0.0929939\pi$
$31$	1.27718	+	2.21215i	0.229389	+	0.397313i	−0.728238	+	0.685324i	$0.759661\pi$
$32$	1.53234	−	2.65409i	0.270882	−	0.469182i
$33$	−4.51032			−0.785145
$34$	−0.210505			−0.0361013
$35$	6.60424	+	1.52385i	1.11632	+	0.257578i
$36$	−1.63266	+	2.82784i	−0.272109	+	0.471307i
$37$	−3.37858	−	5.85187i	−0.555435	−	0.962041i	−0.997870	−	0.0652406i	$-0.979219\pi$
$37$	−3.37858	−	5.85187i	−0.555435	−	0.962041i	0.442435	−	0.896801i	$-0.354115\pi$
$38$	−1.00484	−	1.74043i	−0.163006	−	0.282334i
$39$	3.60475	−	1.99746i	0.577223	−	0.319850i
$40$	1.34905	−	2.33663i	0.213304	−	0.369453i
$41$	1.21874	−	2.11091i	0.190335	−	0.329669i	−0.755027	−	0.655694i	$-0.772376\pi$
$41$	1.21874	−	2.11091i	0.190335	−	0.329669i	0.945361	+	0.326025i	$0.105709\pi$
$42$	0.552920	−	0.593080i	0.0853174	−	0.0915143i
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	0.938951	−	0.344050i	$-0.111799\pi$
$43$	1.12473	+	1.94809i	0.171520	+	0.297081i	−0.767432	+	0.641131i	$0.778466\pi$
$44$	3.80416	−	6.58900i	0.573499	−	0.993329i
$45$	−2.16920	+	3.75717i	−0.323366	+	0.560086i
$46$	−1.06649	+	1.84722i	−0.157246	+	0.272357i
$47$	−0.658276	+	1.14017i	−0.0960195	+	0.166311i	−0.910034	−	0.414534i	$-0.863944\pi$
$47$	−0.658276	+	1.14017i	−0.0960195	+	0.166311i	0.814014	+	0.580845i	$0.197278\pi$
$48$	2.04246	+	3.53764i	0.294803	+	0.510614i
$49$	−5.80230	+	3.91578i	−0.828900	+	0.559397i
$50$	0.209485	−	0.362838i	0.0296256	−	0.0513130i
$51$	0.448688	−	0.777151i	0.0628289	−	0.108823i
$52$	−0.122340	+	6.95082i	−0.0169655	+	0.963905i
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	−0.986018	−	0.166637i	$-0.946709\pi$
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	0.348697	−	0.937236i	$-0.386624\pi$
$54$	0.719212	+	1.24571i	0.0978724	+	0.169520i
$55$	5.05434	−	8.75438i	0.681528	−	1.18044i
$56$	0.815042	+	2.66471i	0.108915	+	0.356087i
$57$	8.56716			1.13475
$58$	−0.630558			−0.0827963
$59$	4.48335	−	7.76540i	0.583683	−	1.01097i	−0.411355	−	0.911475i	$-0.634944\pi$
$59$	4.48335	−	7.76540i	0.583683	−	1.01097i	0.995038	−	0.0994935i	$-0.0317223\pi$
$60$	2.82286	+	4.88933i	0.364429	+	0.631210i
$61$	9.44547			1.20937			0.604684	−	0.796465i	$-0.293299\pi$
$61$	9.44547			1.20937			0.604684	+	0.796465i	$0.293299\pi$
$62$	−0.342445	+	0.593132i	−0.0434906	+	0.0753279i
$63$	−1.31054	−	4.28472i	−0.165113	−	0.539823i
$64$	−6.32592			−0.790741
$65$	−0.162546	+	9.23511i	−0.0201613	+	1.14547i
$66$	−0.604665	−	1.04731i	−0.0744291	−	0.128915i
$67$	−1.35256			−0.165242			−0.0826209	−	0.996581i	$-0.526329\pi$
$67$	−1.35256			−0.165242			−0.0826209	+	0.996581i	$0.526329\pi$
$68$	0.756879	+	1.31095i	0.0917851	+	0.158976i
$69$	−4.54642	−	7.87463i	−0.547324	−	0.947994i
$70$	0.531538	+	1.73782i	0.0635309	+	0.207709i
$71$	−6.15808	−	10.6661i	−0.730829	−	1.26583i	−0.956529	−	0.291637i	$-0.905800\pi$
$71$	−6.15808	−	10.6661i	−0.730829	−	1.26583i	0.225700	−	0.974197i	$-0.427533\pi$
$72$	−1.78367			−0.210207
$73$	−0.384295	−	0.665619i	−0.0449783	−	0.0779048i	0.842660	−	0.538446i	$-0.180989\pi$
$73$	−0.384295	−	0.665619i	−0.0449783	−	0.0779048i	−0.887638	+	0.460542i	$0.847655\pi$
$74$	0.905882	−	1.56903i	0.105307	−	0.182396i
$75$	0.893026	+	1.54677i	0.103118	+	0.178605i
$76$	−7.22585	+	12.5155i	−0.828862	+	1.43563i
$77$	3.05363	+	9.98358i	0.347993	+	1.13773i
$78$	0.947080	+	0.569251i	0.107236	+	0.0644550i
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	−0.985961	−	0.166976i	$-0.946600\pi$
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	0.637586	+	0.770379i	$0.279933\pi$
$80$	−9.15525			−1.02359
$81$	−1.05136			−0.116818
$82$	0.653548			0.0721723
$83$	−1.07292			−0.117768			−0.0588841	−	0.998265i	$-0.518754\pi$
$83$	−1.07292			−0.117768			−0.0588841	+	0.998265i	$0.518754\pi$
$84$	−5.68155	−	1.31095i	−0.619907	−	0.143037i
$85$	1.00562	+	1.74178i	0.109074	+	0.188922i
$86$	−0.301568	+	0.522332i	−0.0325190	+	0.0563245i
$87$	1.34402	−	2.32792i	0.144094	−	0.249579i
$88$	4.15603			0.443034
$89$	−3.83149	−	6.63634i	−0.406138	−	0.703451i	0.588316	−	0.808631i	$-0.299791\pi$
$89$	−3.83149	−	6.63634i	−0.406138	−	0.703451i	−0.994453	+	0.105180i	$0.966458\pi$
$90$	−1.16324			−0.122616
$91$	−6.86191	−	6.62678i	−0.719324	−	0.694675i
$92$	15.3384			1.59914
$93$	−1.45983	−	2.52850i	−0.151378	−	0.262194i
$94$	−0.353001			−0.0364093
$95$	−9.60052	+	16.6286i	−0.984993	+	1.70606i
$96$	−1.75148	+	3.03365i	−0.178760	+	0.309621i
$97$	1.18601	+	2.05423i	0.120421	+	0.208575i	0.919934	−	0.392074i	$-0.128242\pi$
$97$	1.18601	+	2.05423i	0.120421	+	0.208575i	−0.799513	+	0.600649i	$0.794909\pi$
$98$	−1.68713	−	0.822354i	−0.170426	−	0.0830703i
$99$	−6.68267			−0.671634
$100$	−3.01284			−0.301284
$101$	−0.797330			−0.0793373			−0.0396686	−	0.999213i	$-0.512630\pi$
$101$	−0.797330			−0.0793373			−0.0396686	+	0.999213i	$0.512630\pi$
$102$	0.240609			0.0238239
$103$	−1.08309	+	1.87597i	−0.106720	+	0.184844i	−0.914440	−	0.404722i	$-0.867368\pi$
$103$	−1.08309	+	1.87597i	−0.106720	+	0.184844i	0.807720	+	0.589567i	$0.200701\pi$
$104$	−3.32160	+	1.84056i	−0.325710	+	0.180482i
$105$	−7.54871	−	1.74178i	−0.736678	−	0.169980i
$106$	1.24404	−	2.15474i	0.120832	−	0.209287i
$107$	5.76311	+	9.98201i	0.557141	+	0.964997i	0.997733	+	0.0672896i	$0.0214351\pi$
$107$	5.76311	+	9.98201i	0.557141	+	0.964997i	−0.440592	+	0.897707i	$0.645232\pi$
$108$	5.17191	−	8.95801i	0.497667	−	0.861985i
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	0.605151	−	0.796111i	$-0.293113\pi$
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	−0.992028	+	0.126020i	$0.959780\pi$
$110$	2.71039			0.258426
$111$	3.86174	+	6.68874i	0.366541	+	0.634867i
$112$	6.44775	−	6.91607i	0.609255	−	0.653507i
$113$	−4.02067	−	6.96401i	−0.378233	−	0.655119i	0.612572	−	0.790415i	$-0.290135\pi$
$113$	−4.02067	−	6.96401i	−0.378233	−	0.655119i	−0.990805	+	0.135296i	$0.956802\pi$
$114$	1.14854	+	1.98932i	0.107570	+	0.186317i
$115$	20.3792			1.90037
$116$	2.26719	+	3.92690i	0.210504	+	0.364603i
$117$	5.34096	−	2.95952i	0.493772	−	0.273608i
$118$	2.40420			0.221325
$119$	−2.02400	−	0.467015i	−0.185540	−	0.0428112i
$120$	−1.54198	+	2.67079i	−0.140763	+	0.243808i
$121$	4.57093			0.415539
$122$	1.26628	+	2.19327i	0.114644	+	0.198569i
$123$	−1.39303	+	2.41279i	−0.125605	+	0.217554i
$124$	4.92510			0.442287
$125$	8.80581			0.787615
$126$	0.819230	−	0.878733i	0.0729828	−	0.0782838i
$127$	−0.894023	+	1.54849i	−0.0793317	+	0.137406i	−0.902962	−	0.429721i	$-0.858612\pi$
$127$	−0.894023	+	1.54849i	−0.0793317	+	0.137406i	0.823630	+	0.567127i	$0.191945\pi$
$128$	−3.91275	−	6.77709i	−0.345842	−	0.599015i
$129$	−1.28558	−	2.22668i	−0.113189	−	0.196049i
$130$	−2.16621	+	1.20034i	−0.189989	+	0.105277i
$131$	3.19545	−	5.53469i	0.279188	−	0.483568i	−0.691995	−	0.721902i	$-0.743268\pi$
$131$	3.19545	−	5.53469i	0.279188	−	0.483568i	0.971183	+	0.238334i	$0.0766014\pi$
$132$	−4.34819	+	7.53129i	−0.378461	+	0.655514i
$133$	−5.80024	−	18.9634i	−0.502945	−	1.64434i
$134$	−0.181328	−	0.314069i	−0.0156644	−	0.0271315i
$135$	6.87158	−	11.9019i	0.591412	−	1.02436i
$136$	−0.413443	+	0.716105i	−0.0354525	+	0.0614055i
$137$	−5.01827	+	8.69190i	−0.428740	+	0.742599i	−0.996762	−	0.0804144i	$-0.974376\pi$
$137$	−5.01827	+	8.69190i	−0.428740	+	0.742599i	0.568022	+	0.823014i	$0.307709\pi$
$138$	1.21901	−	2.11139i	0.103769	−	0.179733i
$139$	2.77278	+	4.80260i	0.235184	+	0.407351i	0.959326	−	0.282300i	$-0.0910972\pi$
$139$	2.77278	+	4.80260i	0.235184	+	0.407351i	−0.724142	+	0.689651i	$0.757764\pi$
$140$	8.91137	−	9.55862i	0.753148	−	0.807851i
$141$	0.752416	−	1.30322i	0.0633648	−	0.109751i
$142$	1.65114	−	2.85985i	0.138560	−	0.239993i
$143$	−12.4447	+	6.89582i	−1.04068	+	0.576658i
$144$	3.02619	+	5.24151i	0.252182	+	0.436793i
$145$	3.01228	+	5.21742i	0.250156	+	0.433283i
$146$	0.103039	−	0.178469i	0.00852759	−	0.0147702i
$147$	6.63208	−	4.47577i	0.547005	−	0.369155i
$148$	−13.0285			−1.07094
$149$	18.4651			1.51272			0.756359	−	0.654157i	$-0.226976\pi$
$149$	18.4651			1.51272			0.756359	+	0.654157i	$0.226976\pi$
$150$	−0.239443	+	0.414727i	−0.0195504	+	0.0338623i
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	0.831470	−	0.555570i	$-0.187500\pi$
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	−0.896872	+	0.442289i	$0.854166\pi$
$152$	−7.89421			−0.640305
$153$	0.664795	−	1.15146i	0.0537455	−	0.0930900i
$154$	−1.90884	+	2.04749i	−0.153819	+	0.164991i
$155$	6.54366			0.525600
$156$	0.139836	−	7.94485i	0.0111958	−	0.636097i
$157$	0.822967	+	1.42542i	0.0656799	+	0.113761i	0.896995	−	0.442040i	$-0.145745\pi$
$157$	0.822967	+	1.42542i	0.0656799	+	0.113761i	−0.831315	+	0.555801i	$0.812412\pi$
$158$	−1.66046			−0.132099
$159$	5.30330	+	9.18558i	0.420579	+	0.728464i
$160$	−3.92548	−	6.79913i	−0.310337	−	0.537519i
$161$	−14.3524	+	15.3949i	−1.13113	+	1.21329i
$162$	−0.140949	−	0.244130i	−0.0110740	−	0.0191807i
$163$	−6.54819			−0.512894			−0.256447	−	0.966558i	$-0.582552\pi$
$163$	−6.54819			−0.512894			−0.256447	+	0.966558i	$0.582552\pi$
$164$	−2.34986	−	4.07007i	−0.183493	−	0.317819i
$165$	−5.77716	+	10.0063i	−0.449751	+	0.778992i
$166$	−0.143838	−	0.249135i	−0.0111640	−	0.0193367i
$167$	−4.77440	+	8.26950i	−0.369454	+	0.639913i	−0.989480	−	0.144668i	$-0.953789\pi$
$167$	−4.77440	+	8.26950i	−0.369454	+	0.639913i	0.620026	+	0.784581i	$0.287122\pi$
$168$	−0.931600	−	3.04579i	−0.0718745	−	0.234988i
$169$	6.89216	−	11.0226i	0.530166	−	0.847894i
$170$	−0.269631	+	0.467015i	−0.0206798	+	0.0358184i
$171$	12.6935			0.970694
$172$	4.33720			0.330709
$173$	11.1316			0.846322			0.423161	−	0.906054i	$-0.360920\pi$
$173$	11.1316			0.846322			0.423161	+	0.906054i	$0.360920\pi$
$174$	0.720733			0.0546386
$175$	2.81916	−	3.02392i	0.213108	−	0.228587i
$176$	−7.05115	−	12.2130i	−0.531501	−	0.920586i
$177$	−5.12451	+	8.87592i	−0.385182	+	0.667155i
$178$	1.02732	−	1.77937i	0.0770009	−	0.133369i
$179$	−12.6435			−0.945017			−0.472508	−	0.881326i	$-0.656651\pi$
$179$	−12.6435			−0.945017			−0.472508	+	0.881326i	$0.656651\pi$
$180$	4.18246	+	7.24424i	0.311742	+	0.539954i
$181$	14.9158			1.10868			0.554341	−	0.832289i	$-0.312970\pi$
$181$	14.9158			1.10868			0.554341	+	0.832289i	$0.312970\pi$
$182$	0.618833	−	2.48176i	0.0458709	−	0.183960i
$183$	−10.7963			−0.798082
$184$	4.18930	+	7.25607i	0.308839	+	0.534925i
$185$	−17.3102			−1.27267
$186$	0.391418	−	0.677956i	0.0287001	−	0.0497101i
$187$	−1.54900	+	2.68295i	−0.113274	+	0.196197i
$188$	1.26923	+	2.19837i	0.0925680	+	0.160332i
$189$	4.15153	+	13.5731i	0.301979	+	0.987296i
$190$	−5.14829			−0.373496
$191$	−14.1306			−1.02245			−0.511226	−	0.859447i	$-0.670808\pi$
$191$	−14.1306			−1.02245			−0.511226	+	0.859447i	$0.670808\pi$
$192$	7.23059			0.521823
$193$	3.89454			0.280335			0.140167	−	0.990128i	$-0.455236\pi$
$193$	3.89454			0.280335			0.140167	+	0.990128i	$0.455236\pi$
$194$	−0.317999	+	0.550790i	−0.0228310	+	0.0395444i
$195$	0.185791	−	10.5558i	0.0133048	−	0.755917i
$196$	0.944795	+	13.4637i	0.0674853	+	0.961689i
$197$	5.85445	−	10.1402i	0.417112	−	0.722459i	−0.578536	−	0.815657i	$-0.696376\pi$
$197$	5.85445	−	10.1402i	0.417112	−	0.722459i	0.995648	+	0.0931979i	$0.0297089\pi$
$198$	−0.895897	−	1.55174i	−0.0636686	−	0.110277i
$199$	−1.74842	+	3.02835i	−0.123942	+	0.214674i	−0.921319	−	0.388808i	$-0.872887\pi$
$199$	−1.74842	+	3.02835i	−0.123942	+	0.214674i	0.797377	+	0.603482i	$0.206220\pi$
$200$	−0.822878	−	1.42527i	−0.0581863	−	0.100782i
$201$	1.54599			0.109046
$202$	−0.106892	−	0.185143i	−0.00752090	−	0.0130266i
$203$	−6.06279	−	1.39892i	−0.425524	−	0.0981850i
$204$	−0.865120	−	1.49843i	−0.0605705	−	0.104911i
$205$	−3.12210	−	5.40764i	−0.218057	−	0.377686i
$206$	−0.580807			−0.0404667
$207$	−6.73617	−	11.6674i	−0.468196	−	0.810939i
$208$	11.0441	+	6.63818i	0.765774	+	0.460275i
$209$	−29.5764			−2.04584
$210$	−0.607552	−	1.98634i	−0.0419251	−	0.137071i
$211$	−9.50258	+	16.4589i	−0.654184	+	1.13308i	0.327913	+	0.944708i	$0.393655\pi$
$211$	−9.50258	+	16.4589i	−0.654184	+	1.13308i	−0.982098	+	0.188373i	$0.939679\pi$
$212$	−17.8920			−1.22882
$213$	7.03874	+	12.1915i	0.482286	+	0.835345i
$214$	−1.54524	+	2.67643i	−0.105630	+	0.182957i
$215$	5.76256			0.393004
$216$	5.65029			0.384453
$217$	−4.60849	+	4.94321i	−0.312844	+	0.335567i
$218$	1.08299	−	1.87579i	0.0733492	−	0.127045i
$219$	0.439253	+	0.760808i	0.0296820	+	0.0514106i
$220$	−9.74533	−	16.8794i	−0.657030	−	1.13801i
$221$	0.0498153	−	2.83028i	0.00335094	−	0.190385i
$222$	−1.03543	+	1.79342i	−0.0694936	+	0.120366i
$223$	5.98311	−	10.3630i	0.400658	−	0.693961i	−0.593147	−	0.805094i	$-0.702115\pi$
$223$	5.98311	−	10.3630i	0.400658	−	0.693961i	0.993805	+	0.111133i	$0.0354481\pi$
$224$	7.90079	+	1.82302i	0.527894	+	0.121806i
$225$	1.32315	+	2.29175i	0.0882097	+	0.152784i
$226$	1.07804	−	1.86723i	0.0717104	−	0.124206i
$227$	−7.69209	+	13.3231i	−0.510542	+	0.884284i	0.489384	+	0.872069i	$0.337222\pi$
$227$	−7.69209	+	13.3231i	−0.510542	+	0.884284i	−0.999925	+	0.0122157i	$0.996112\pi$
$228$	8.25921	−	14.3054i	0.546980	−	0.947396i
$229$	−4.33084	+	7.50123i	−0.286190	+	0.495695i	−0.972897	−	0.231239i	$-0.925722\pi$
$229$	−4.33084	+	7.50123i	−0.286190	+	0.495695i	0.686707	+	0.726934i	$0.259055\pi$
$230$	2.73209	+	4.73212i	0.180149	+	0.312027i
$231$	−3.49032	−	11.4113i	−0.229646	−	0.750810i
$232$	−1.23845	+	2.14506i	−0.0813082	+	0.140830i
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	0.316402	+	0.948625i	$0.397525\pi$
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	−0.979734	+	0.200301i	$0.935808\pi$
$234$	1.40323	+	0.843426i	0.0917322	+	0.0551365i
$235$	1.68634	+	2.92083i	0.110005	+	0.190534i
$236$	−8.64440	−	14.9725i	−0.562702	−	0.974629i
$237$	3.53924	−	6.13014i	0.229898	−	0.398195i
$238$	−0.162900	−	0.532588i	−0.0105592	−	0.0345226i
$239$	16.5526			1.07070			0.535350	−	0.844630i	$-0.320180\pi$
$239$	16.5526			1.07070			0.535350	+	0.844630i	$0.320180\pi$
$240$	10.4645			0.675483
$241$	8.20038	−	14.2035i	0.528233	−	0.914926i	−0.471225	−	0.882013i	$-0.656188\pi$
$241$	8.20038	−	14.2035i	0.528233	−	0.914926i	0.999458	−	0.0329132i	$-0.0104785\pi$
$242$	0.612791	+	1.06138i	0.0393917	+	0.0682284i
$243$	−14.8925			−0.955356
$244$	9.10595	−	15.7720i	0.582949	−	1.00970i
$245$	1.25529	+	17.8883i	0.0801974	+	1.14284i
$246$	−0.747011			−0.0476277
$247$	23.6381	−	13.0983i	1.50406	−	0.833427i
$248$	1.34516	+	2.32989i	0.0854178	+	0.147948i
$249$	1.22636			0.0777172
$250$	1.18053	+	2.04474i	0.0746632	+	0.129321i
$251$	10.2154	+	17.6935i	0.644788	+	1.11681i	0.984350	+	0.176222i	$0.0563876\pi$
$251$	10.2154	+	17.6935i	0.644788	+	1.11681i	−0.339563	+	0.940583i	$0.610279\pi$
$252$	−8.41802	−	1.94236i	−0.530285	−	0.122357i
$253$	15.6956	+	27.1855i	0.986772	+	1.70914i
$254$	−0.479420			−0.0300815
$255$	−1.14943	−	1.99087i	−0.0719800	−	0.124673i
$256$	−5.27682	+	9.13972i	−0.329801	+	0.571232i
$257$	−6.88895	−	11.9320i	−0.429721	−	0.744299i	0.567127	−	0.823630i	$-0.308055\pi$
$257$	−6.88895	−	11.9320i	−0.429721	−	0.744299i	−0.996848	+	0.0793315i	$0.974721\pi$
$258$	0.344695	−	0.597030i	0.0214598	−	0.0371695i
$259$	12.1910	−	13.0765i	0.757511	−	0.812532i
$260$	15.2640	+	9.17456i	0.946633	+	0.568982i
$261$	1.99136	−	3.44914i	0.123262	−	0.213496i
$262$	1.71356			0.105864
$263$	25.9173			1.59813			0.799065	−	0.601244i	$-0.205328\pi$
$263$	25.9173			1.59813			0.799065	+	0.601244i	$0.205328\pi$
$264$	−4.75038			−0.292366
$265$	−23.7719			−1.46030
$266$	3.62577	−	3.88912i	0.222310	−	0.238457i
$267$	4.37943	+	7.58540i	0.268017	+	0.464219i
$268$	−1.30394	+	2.25850i	−0.0796510	+	0.137960i
$269$	15.0333	−	26.0384i	0.916596	−	1.58759i	0.112050	−	0.993703i	$-0.464258\pi$
$269$	15.0333	−	26.0384i	0.916596	−	1.58759i	0.804547	−	0.593889i	$-0.202408\pi$
$270$	3.68489			0.224255
$271$	−7.22527	−	12.5145i	−0.438904	−	0.760204i	0.558701	−	0.829369i	$-0.311300\pi$
$271$	−7.22527	−	12.5145i	−0.438904	−	0.760204i	−0.997605	+	0.0691651i	$0.977966\pi$
$272$	2.80581			0.170127
$273$	7.84323	+	7.57446i	0.474694	+	0.458427i
$274$	−2.69105			−0.162572
$275$	−3.08299	−	5.33989i	−0.185911	−	0.322008i
$276$	−17.5320			−1.05530
$277$	7.66274	−	13.2723i	0.460409	−	0.797452i	−0.538572	−	0.842580i	$-0.681036\pi$
$277$	7.66274	−	13.2723i	0.460409	−	0.797452i	0.998981	+	0.0451272i	$0.0143693\pi$
$278$	−0.743453	+	1.28770i	−0.0445894	+	0.0772310i
$279$	−2.16295	−	3.74634i	−0.129492	−	0.224287i
$280$	6.95575	+	1.60496i	0.415686	+	0.0959148i
$281$	5.29279			0.315741			0.157871	−	0.987460i	$-0.449537\pi$
$281$	5.29279			0.315741			0.157871	+	0.987460i	$0.449537\pi$
$282$	0.403483			0.0240271
$283$	−30.7845			−1.82995			−0.914975	−	0.403511i	$-0.867790\pi$
$283$	−30.7845			−1.82995			−0.914975	+	0.403511i	$0.867790\pi$
$284$	−23.7469			−1.40912
$285$	10.9735	−	19.0066i	0.650013	−	1.12586i
$286$	−3.26960	−	1.96522i	−0.193335	−	0.116206i
$287$	6.28384	+	1.44992i	0.370923	+	0.0855864i
$288$	−2.59507	+	4.49479i	−0.152916	+	0.264858i
$289$	8.19181	+	14.1886i	0.481871	+	0.834625i
$290$	−0.807667	+	1.39892i	−0.0474279	+	0.0821474i
$291$	−1.35562	−	2.34800i	−0.0794677	−	0.137642i
$292$	−1.48193			−0.0867231
$293$	8.75864	+	15.1704i	0.511685	+	0.886265i	0.999908	+	0.0135461i	$0.00431197\pi$
$293$	8.75864	+	15.1704i	0.511685	+	0.886265i	−0.488223	+	0.872719i	$0.662355\pi$
$294$	1.92840	+	0.939958i	0.112467	+	0.0548195i
$295$	−11.4853	−	19.8930i	−0.668697	−	1.15822i
$296$	−3.55840	−	6.16333i	−0.206828	−	0.358237i
$297$	21.1693			1.22837
$298$	2.47548	+	4.28765i	0.143400	+	0.248377i
$299$	−24.5838	−	14.7763i	−1.42172	−	0.854536i
$300$	3.44370			0.198822
$301$	−4.05839	+	4.35316i	−0.233921	+	0.250912i
$302$	0.215486	−	0.373233i	0.0123998	−	0.0214772i
$303$	0.911355			0.0523560
$304$	13.3934	+	23.1980i	0.768163	+	1.33050i
$305$	12.0985	−	20.9552i	0.692757	−	1.19989i
$306$	0.356497			0.0203796
$307$	−8.63573			−0.492867			−0.246434	−	0.969160i	$-0.579259\pi$
$307$	−8.63573			−0.492867			−0.246434	+	0.969160i	$0.579259\pi$
$308$	19.6144	+	4.52579i	1.11763	+	0.257881i
$309$	1.23798	−	2.14425i	0.0704262	−	0.121982i
$310$	0.877260	+	1.51946i	0.0498250	+	0.0862995i
$311$	8.21130	+	14.2224i	0.465620	+	0.806478i	0.999229	−	0.0392535i	$-0.0124980\pi$
$311$	8.21130	+	14.2224i	0.465620	+	0.806478i	−0.533609	+	0.845731i	$0.679165\pi$
$312$	3.79662	−	2.10378i	0.214941	−	0.119103i
$313$	−5.02308	+	8.70024i	−0.283921	+	0.491766i	−0.972347	−	0.233541i	$-0.924969\pi$
$313$	−5.02308	+	8.70024i	−0.283921	+	0.491766i	0.688426	+	0.725307i	$0.258302\pi$
$314$	−0.220658	+	0.382191i	−0.0124525	+	0.0215683i
$315$	−11.1845	−	2.58069i	−0.630174	−	0.145406i
$316$	5.97024	+	10.3408i	0.335852	+	0.581713i
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	−0.972585	−	0.232549i	$-0.925294\pi$
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	0.687685	+	0.726009i	$0.258627\pi$
$318$	−1.42195	+	2.46289i	−0.0797389	+	0.138112i
$319$	−4.63996	+	8.03665i	−0.259788	+	0.449966i
$320$	−8.10273	+	14.0343i	−0.452957	+	0.784544i
$321$	−6.58729	−	11.4095i	−0.367667	−	0.636817i
$322$	−5.49886	−	1.26880i	−0.306440	−	0.0707075i
$323$	2.94227	−	5.09616i	0.163712	−	0.283558i
$324$	−1.01357	+	1.75556i	−0.0563095	+	0.0975310i
$325$	4.82885	+	2.90242i	0.267856	+	0.160998i
$326$	−0.877867	−	1.52051i	−0.0486206	−	0.0842133i
$327$	4.61674	+	7.99644i	0.255307	+	0.442204i
$328$	1.28360	−	2.22327i	0.0708751	−	0.122759i
$329$	−3.39409	−	0.783149i	−0.187122	−	0.0431764i
$330$	−3.09801			−0.170540
$331$	2.31916			0.127473			0.0637363	−	0.997967i	$-0.479698\pi$
$331$	2.31916			0.127473			0.0637363	+	0.997967i	$0.479698\pi$
$332$	−1.03435	+	1.79155i	−0.0567675	+	0.0983242i
$333$	5.72172	+	9.91032i	0.313549	+	0.543082i
$334$	−2.56027			−0.140092
$335$	−1.73247	+	3.00072i	−0.0946547	+	0.163947i
$336$	−7.36983	+	7.90512i	−0.402057	+	0.431260i
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$	3.48347	+	0.122662i	0.189476	+	0.00667193i
$339$	4.59567	+	7.95993i	0.249602	+	0.432324i
$340$	3.87788			0.210307
$341$	5.03977	+	8.72913i	0.272919	+	0.472709i
$342$	1.70172	+	2.94747i	0.0920185	+	0.159381i
$343$	−14.3972	−	11.6499i	−0.777378	−	0.629034i
$344$	1.18459	+	2.05178i	0.0638690	+	0.110624i
$345$	−23.2936			−1.25409
$346$	1.49234	+	2.58480i	0.0802285	+	0.138960i
$347$	11.4104	−	19.7634i	0.612543	−	1.06096i	−0.378267	−	0.925696i	$-0.623480\pi$
$347$	11.4104	−	19.7634i	0.612543	−	1.06096i	0.990810	−	0.135259i	$-0.0431867\pi$
$348$	−2.59142	−	4.48848i	−0.138915	−	0.240608i
$349$	11.3511	−	19.6607i	0.607612	−	1.05241i	−0.384021	−	0.923324i	$-0.625461\pi$
$349$	11.3511	−	19.6607i	0.607612	−	1.05241i	0.991633	−	0.129090i	$-0.0412056\pi$
$350$	1.08011	+	0.249223i	0.0577342	+	0.0133215i
$351$	−16.9190	+	9.37515i	−0.903071	+	0.500408i
$352$	6.04662	−	10.4731i	0.322286	−	0.558216i
$353$	−27.2644			−1.45114			−0.725568	−	0.688150i	$-0.758423\pi$
$353$	−27.2644			−1.45114			−0.725568	+	0.688150i	$0.758423\pi$
$354$	−2.74802			−0.146056
$355$	−31.5510			−1.67455
$356$	−14.7751			−0.783077
$357$	2.31345	+	0.533802i	0.122441	+	0.0282518i
$358$	−1.69502	−	2.93585i	−0.0895844	−	0.155165i
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	−0.610469	−	0.792040i	$-0.709019\pi$
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	0.991161	+	0.132662i	$0.0423524\pi$
$360$	−2.28466	+	3.95715i	−0.120412	+	0.208560i
$361$	37.1791			1.95679
$362$	1.99965	+	3.46350i	0.105099	+	0.182037i
$363$	−5.22461			−0.274221
$364$	−17.6806	+	5.06939i	−0.926715	+	0.265708i
$365$	−1.96894			−0.103059
$366$	−1.44737	−	2.50693i	−0.0756555	−	0.131039i
$367$	−11.3917			−0.594643			−0.297322	−	0.954777i	$-0.596093\pi$
$367$	−11.3917			−0.594643			−0.297322	+	0.954777i	$0.596093\pi$
$368$	14.2152	−	24.6214i	0.741018	−	1.28348i
$369$	−2.06397	+	3.57489i	−0.107446	+	0.186102i
$370$	−2.32065	−	4.01948i	−0.120645	−	0.208963i
$371$	16.7418	−	17.9578i	0.869190	−	0.932321i
$372$	−5.62943			−0.291872
$373$	−30.9629			−1.60320			−0.801599	−	0.597862i	$-0.796017\pi$
$373$	−30.9629			−1.60320			−0.801599	+	0.597862i	$0.796017\pi$
$374$	−0.830653			−0.0429521
$375$	−10.0651			−0.519760
$376$	−0.693313	+	1.20085i	−0.0357549	+	0.0619293i
$377$	0.149219	−	8.47796i	0.00768518	−	0.436637i
$378$	−2.59515	+	2.78364i	−0.133480	+	0.143175i
$379$	−5.29330	+	9.16826i	−0.271898	+	0.470942i	−0.969348	−	0.245692i	$-0.920985\pi$
$379$	−5.29330	+	9.16826i	−0.271898	+	0.470942i	0.697450	+	0.716634i	$0.254318\pi$
$380$	18.5109	+	32.0617i	0.949587	+	1.64473i
$381$	1.02188	−	1.76994i	0.0523523	−	0.0906768i
$382$	−1.89438	−	3.28116i	−0.0969249	−	0.167879i
$383$	30.7517			1.57134			0.785668	−	0.618648i	$-0.212319\pi$
$383$	30.7517			1.57134			0.785668	+	0.618648i	$0.212319\pi$
$384$	4.47231	+	7.74627i	0.228227	+	0.395300i
$385$	26.0603	+	6.01313i	1.32816	+	0.306458i
$386$	0.522112	+	0.904324i	0.0265748	+	0.0460289i
$387$	−1.90476	−	3.29915i	−0.0968246	−	0.167705i
$388$	4.57351			0.232185
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	0.995453	−	0.0952492i	$-0.0303648\pi$
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	−0.580215	+	0.814463i	$0.697031\pi$
$390$	2.47600	−	1.37200i	0.125377	−	0.0694738i
$391$	−6.24561			−0.315854
$392$	−6.11113	+	4.12419i	−0.308659	+	0.208303i
$393$	−3.65243	+	6.32620i	−0.184241	+	0.319114i
$394$	3.13945			0.158163
$395$	7.93227	+	13.7391i	0.399116	+	0.691289i
$396$	−6.44246	+	11.1587i	−0.323746	+	0.560744i
$397$	−15.8827			−0.797127			−0.398564	−	0.917141i	$-0.630491\pi$
$397$	−15.8827			−0.797127			−0.398564	+	0.917141i	$0.630491\pi$
$398$	−0.937591			−0.0469972
$399$	6.62973	+	21.6753i	0.331902	+	1.08512i
$400$	−2.79221	+	4.83624i	−0.139610	+	0.241812i
$401$	−3.31787	−	5.74671i	−0.165686	−	0.286977i	0.771212	−	0.636578i	$-0.219651\pi$
$401$	−3.31787	−	5.74671i	−0.165686	−	0.286977i	−0.936899	+	0.349601i	$0.886317\pi$
$402$	0.207259	+	0.358984i	0.0103372	+	0.0179045i
$403$	−7.89373	−	4.74460i	−0.393215	−	0.236345i
$404$	−0.768670	+	1.33137i	−0.0382427	+	0.0662384i
$405$	−1.34667	+	2.33250i	−0.0669164	+	0.115903i
$406$	−0.487959	−	1.59534i	−0.0242170	−	0.0791755i
$407$	−13.3319	−	23.0915i	−0.660836	−	1.14460i
$408$	0.472570	−	0.818515i	0.0233957	−	0.0405225i
$409$	−2.93617	+	5.08560i	−0.145184	+	0.251467i	−0.929442	−	0.368969i	$-0.879711\pi$
$409$	−2.93617	+	5.08560i	−0.145184	+	0.251467i	0.784257	+	0.620436i	$0.213044\pi$
$410$	0.837115	−	1.44992i	0.0413421	−	0.0716067i
$411$	5.73593	−	9.93492i	0.282933	−	0.490053i
$412$	2.08831	+	3.61707i	0.102884	+	0.178200i
$413$	23.1163	+	5.33383i	1.13748	+	0.262460i
$414$	1.80614	−	3.12832i	0.0887667	−	0.153749i
$415$	−1.37428	+	2.38032i	−0.0674607	+	0.116845i
$416$	−0.194457	+	11.0482i	−0.00953403	+	0.541680i
$417$	−3.16932	−	5.48942i	−0.155202	−	0.268818i
$418$	−3.96508	−	6.86773i	−0.193939	−	0.335911i
$419$	15.0712	−	26.1040i	0.736274	−	1.27526i	−0.217888	−	0.975974i	$-0.569917\pi$
$419$	15.0712	−	26.1040i	0.736274	−	1.27526i	0.954162	−	0.299290i	$-0.0967499\pi$
$420$	−10.1858	+	10.9256i	−0.497015	+	0.533114i
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	−5.09576			−0.248058
$423$	1.11481	−	1.93091i	0.0542040	−	0.0938840i
$424$	−4.88672	−	8.46405i	−0.237320	−	0.411051i
$425$	1.22679			0.0595079
$426$	−1.88726	+	3.26884i	−0.0914382	+	0.158376i
$427$	7.30941	+	23.8975i	0.353727	+	1.15648i
$428$	22.2238			1.07423
$429$	14.2244	−	7.88199i	0.686759	−	0.380546i
$430$	0.772544	+	1.33809i	0.0372554	+	0.0645282i
$431$	−3.91587			−0.188621			−0.0943104	−	0.995543i	$-0.530065\pi$
$431$	−3.91587			−0.188621			−0.0943104	+	0.995543i	$0.530065\pi$
$432$	−9.58632	−	16.6040i	−0.461222	−	0.798860i
$433$	20.3963	+	35.3274i	0.980182	+	1.69772i	0.661650	+	0.749813i	$0.269856\pi$
$433$	20.3963	+	35.3274i	0.980182	+	1.69772i	0.318532	+	0.947912i	$0.396810\pi$
$434$	−1.76566	−	0.407405i	−0.0847542	−	0.0195561i
$435$	−3.44306	−	5.96355i	−0.165082	−	0.285930i
$436$	−15.5757			−0.745941
$437$	−29.8131	−	51.6378i	−1.42615	−	2.47017i
$438$	−0.117775	+	0.203992i	−0.00562750	+	0.00974711i
$439$	12.7811	+	22.1376i	0.610010	+	1.05657i	0.991238	+	0.132087i	$0.0421680\pi$
$439$	12.7811	+	22.1376i	0.610010	+	1.05657i	−0.381228	+	0.924481i	$0.624499\pi$
$440$	5.32336	−	9.22033i	0.253781	−	0.439562i
$441$	9.82637	−	6.63149i	0.467923	−	0.315785i
$442$	0.663878	−	0.367867i	0.0315775	−	0.0174977i
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	−0.330330	−	0.943866i	$-0.607160\pi$
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	0.982576	−	0.185859i	$-0.0595067\pi$
$444$	14.8917			0.706730
$445$	−19.6307			−0.930584
$446$	3.20844			0.151924
$447$	−21.1057			−0.998267
$448$	−4.89534	−	16.0049i	−0.231283	−	0.756161i
$449$	7.40181	+	12.8203i	0.349313	+	0.605028i	0.986128	−	0.165989i	$-0.0530816\pi$
$449$	7.40181	+	12.8203i	0.349313	+	0.605028i	−0.636815	+	0.771017i	$0.719748\pi$
$450$	−0.354769	+	0.614477i	−0.0167240	+	0.0289667i
$451$	4.80913	−	8.32966i	0.226453	−	0.392229i
$452$	−15.5046			−0.729275
$453$	0.918611	+	1.59108i	0.0431601	+	0.0747555i
$454$	−4.12489			−0.193590
$455$	−23.4911	+	6.73537i	−1.10128	+	0.315759i
$456$	9.02315			0.422548
$457$	0.325975	+	0.564606i	0.0152485	+	0.0264112i	0.873549	−	0.486736i	$-0.161813\pi$
$457$	0.325975	+	0.564606i	0.0152485	+	0.0264112i	−0.858300	+	0.513147i	$0.828479\pi$
$458$	−2.32241			−0.108519
$459$	−2.10593	+	3.64758i	−0.0982965	+	0.170254i
$460$	19.6467	−	34.0290i	0.916031	−	1.58661i
$461$	−6.24774	−	10.8214i	−0.290986	−	0.504003i	0.683057	−	0.730365i	$-0.260650\pi$
$461$	−6.24774	−	10.8214i	−0.290986	−	0.504003i	−0.974043	+	0.226362i	$0.927317\pi$
$462$	2.18182	−	2.34030i	0.101508	−	0.108880i
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	8.40466			0.390176
$465$	−7.47946			−0.346852
$466$	−5.42972			−0.251527
$467$	−12.2387	+	21.1980i	−0.566338	+	0.980926i	0.430586	+	0.902549i	$0.358307\pi$
$467$	−12.2387	+	21.1980i	−0.566338	+	0.980926i	−0.996924	+	0.0783762i	$0.975026\pi$
$468$	0.207187	−	11.7714i	0.00957722	−	0.544134i
$469$	−1.04668	−	3.42205i	−0.0483314	−	0.158016i
$470$	−0.452151	+	0.783149i	−0.0208562	+	0.0361240i
$471$	−0.940659	−	1.62927i	−0.0433433	−	0.0750727i
$472$	4.72198	−	8.17871i	0.217347	−	0.376456i
$473$	4.43818	+	7.68716i	0.204068	+	0.353456i
$474$	1.89792			0.0871742
$475$	5.85601	+	10.1429i	0.268692	+	0.465389i
$476$	−2.73106	+	2.92943i	−0.125178	+	0.134270i
$477$	7.85759	+	13.6097i	0.359774	+	0.623147i
$478$	2.21909	+	3.84357i	0.101499	+	0.175801i
$479$	8.13850			0.371858			0.185929	−	0.982563i	$-0.440471\pi$
$479$	8.13850			0.371858			0.185929	+	0.982563i	$0.440471\pi$
$480$	4.48686	+	7.77147i	0.204796	+	0.354718i
$481$	20.8816	+	12.5511i	0.952118	+	0.572279i
$482$	4.39746			0.200299
$483$	16.4049	−	17.5965i	0.746450	−	0.800667i
$484$	4.40662	−	7.63250i	0.200301	−	0.346932i
$485$	6.07653			0.275921
$486$	−1.99653	−	3.45809i	−0.0905645	−	0.156862i
$487$	−2.30480	+	3.99203i	−0.104440	+	0.180896i	−0.913509	−	0.406817i	$-0.866638\pi$
$487$	−2.30480	+	3.99203i	−0.104440	+	0.180896i	0.809069	+	0.587714i	$0.199972\pi$
$488$	9.94821			0.450334
$489$	7.48464			0.338467
$490$	−3.98543	+	2.68963i	−0.180044	+	0.121505i
$491$	−6.50947	+	11.2747i	−0.293768	+	0.508822i	−0.974698	−	0.223527i	$-0.928243\pi$
$491$	−6.50947	+	11.2747i	−0.293768	+	0.508822i	0.680929	+	0.732349i	$0.261576\pi$
$492$	2.68591	+	4.65213i	0.121090	+	0.209734i
$493$	−0.923171	−	1.59898i	−0.0415775	−	0.0720144i
$494$	6.21047	+	3.73286i	0.279422	+	0.167949i
$495$	−8.55969	+	14.8258i	−0.384729	+	0.666371i
$496$	4.56443	−	7.90582i	0.204949	−	0.354982i
$497$	22.2203	−	23.8342i	0.996718	−	1.06911i
$498$	0.164409	+	0.284764i	0.00736733	+	0.0127606i
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	−0.236178	−	0.971710i	$-0.575895\pi$
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	0.959614	−	0.281319i	$-0.0907717\pi$
$500$	8.48928	−	14.7039i	0.379652	−	0.657577i
$501$	5.45718	−	9.45211i	0.243809	−	0.422289i
$502$	−2.73900	+	4.74408i	−0.122247	+	0.211739i
$503$	15.9126	+	27.5615i	0.709509	+	1.22891i	0.965039	+	0.262105i	$0.0844165\pi$
$503$	15.9126	+	27.5615i	0.709509	+	1.22891i	−0.255531	+	0.966801i	$0.582250\pi$
$504$	−1.38030	−	4.51277i	−0.0614834	−	0.201015i
$505$	−1.02128	+	1.76891i	−0.0454465	+	0.0787156i
$506$	−4.20838	+	7.28912i	−0.187085	+	0.324041i
$507$	−7.87780	+	12.5990i	−0.349866	+	0.559539i
$508$	1.72377	+	2.98566i	0.0764801	+	0.132467i
$509$	−1.12788	−	1.95354i	−0.0499922	−	0.0865891i	0.839946	−	0.542669i	$-0.182586\pi$
$509$	−1.12788	−	1.95354i	−0.0499922	−	0.0865891i	−0.889939	+	0.456080i	$0.849253\pi$
$510$	0.308191	−	0.533802i	0.0136469	−	0.0236372i
$511$	1.38666	−	1.48738i	0.0613422	−	0.0657977i
$512$	−18.4807			−0.816739
$513$	−40.2102			−1.77533
$514$	1.84710	−	3.19927i	0.0814722	−	0.141114i
$515$	2.77461	+	4.80576i	0.122264	+	0.211767i
$516$	−4.95746			−0.218240
$517$	−2.59756	+	4.49911i	−0.114241	+	0.197870i
$518$	4.67075	+	1.07772i	0.205221	+	0.0473525i
$519$	−12.7236			−0.558502
$520$	−0.171197	+	9.72665i	−0.00750749	+	0.426542i
$521$	−5.38562	−	9.32817i	−0.235948	−	0.408675i	0.723600	−	0.690220i	$-0.242486\pi$
$521$	−5.38562	−	9.32817i	−0.235948	−	0.408675i	−0.959548	+	0.281546i	$0.909153\pi$
$522$	1.06787			0.0467393
$523$	−3.70397	−	6.41546i	−0.161963	−	0.280528i	0.773610	−	0.633663i	$-0.218449\pi$
$523$	−3.70397	−	6.41546i	−0.161963	−	0.280528i	−0.935573	+	0.353134i	$0.885116\pi$
$524$	−6.16118	−	10.6715i	−0.269152	−	0.466186i
$525$	−3.22232	+	3.45637i	−0.140634	+	0.150848i
$526$	3.47454	+	6.01809i	0.151497	+	0.262401i
$527$	−2.00543			−0.0873580
$528$	8.05953	+	13.9595i	0.350746	+	0.607510i
$529$	−20.1424	+	34.8877i	−0.875757	+	1.51686i
$530$	−3.18692	−	5.51991i	−0.138431	−	0.239770i
$531$	−7.59270	+	13.1509i	−0.329495	+	0.570702i
$532$	−37.2567	−	8.59656i	−1.61528	−	0.372708i
$533$	−0.154660	+	8.78707i	−0.00669906	+	0.380610i
$534$	−1.17424	+	2.03384i	−0.0508142	+	0.0880127i
$535$	29.5274			1.27658
$536$	−1.42455			−0.0615313
$537$	14.4516			0.623632
$538$	8.06161			0.347561
$539$	−22.8959	+	15.4517i	−0.986196	+	0.665550i
$540$	−13.2492	−	22.9482i	−0.570153	−	0.987534i
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	0.268902	+	0.963168i	$0.413339\pi$
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	−0.968579	+	0.248708i	$0.919994\pi$
$542$	1.93728	−	3.35546i	0.0832132	−	0.144129i
$543$	−17.0489			−0.731638
$544$	1.20304	+	2.08373i	0.0515799	+	0.0893391i
$545$	−20.6944			−0.886453
$546$	−0.707332	+	2.83668i	−0.0302710	+	0.121399i
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	9.67577	+	16.7589i	0.413329	+	0.715906i
$549$	−15.9962			−0.682701
$550$	0.826627	−	1.43176i	0.0352475	−	0.0610504i
$551$	8.81342	−	15.2653i	0.375464	−	0.650323i
$552$	−4.78840	−	8.29376i	−0.203808	−	0.353006i
$553$	−15.9652	−	3.68380i	−0.678911	−	0.156651i
$554$	4.10915			0.174581
$555$	19.7857			0.839856
$556$	10.6925			0.453461
$557$	−29.7703			−1.26141			−0.630703	−	0.776024i	$-0.717233\pi$
$557$	−29.7703			−1.26141			−0.630703	+	0.776024i	$0.717233\pi$
$558$	0.579941	−	1.00449i	0.0245509	−	0.0425233i
$559$	−6.95148	−	4.17825i	−0.294016	−	0.176721i
$560$	−7.08483	−	23.1632i	−0.299389	−	0.978826i
$561$	1.77052	−	3.06664i	0.0747516	−	0.129474i
$562$	0.709566	+	1.22900i	0.0299312	+	0.0518424i
$563$	−7.06629	+	12.2392i	−0.297809	+	0.515819i	−0.975634	−	0.219403i	$-0.929589\pi$
$563$	−7.06629	+	12.2392i	−0.297809	+	0.515819i	0.677826	+	0.735223i	$0.262922\pi$
$564$	−1.45074	−	2.51275i	−0.0610872	−	0.105806i
$565$	−20.6000			−0.866647
$566$	−4.12705	−	7.14826i	−0.173473	−	0.300464i
$567$	−0.813601	−	2.66000i	−0.0341680	−	0.111710i
$568$	−6.48584	−	11.2338i	−0.272140	−	0.471360i
$569$	12.1270	+	21.0046i	0.508391	+	0.880558i	0.999953	+	0.00971585i	$0.00309270\pi$
$569$	12.1270	+	21.0046i	0.508391	+	0.880558i	−0.491562	+	0.870842i	$0.663574\pi$
$570$	5.88454			0.246476
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	0.853107	−	0.521736i	$-0.174715\pi$
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	−0.878390	+	0.477944i	$0.841382\pi$
$572$	−0.482755	+	27.4279i	−0.0201850	+	1.14682i
$573$	16.1514			0.674732
$574$	0.505750	+	1.65351i	0.0211096	+	0.0690161i
$575$	6.21533	−	10.7653i	0.259197	−	0.448943i
$576$	10.7131			0.446381
$577$	7.30518	+	12.6529i	0.304119	+	0.526749i	0.977065	−	0.212943i	$-0.0683047\pi$
$577$	7.30518	+	12.6529i	0.304119	+	0.526749i	−0.672946	+	0.739692i	$0.734971\pi$
$578$	−2.19643	+	3.80433i	−0.0913595	+	0.158239i
$579$	−4.45149			−0.184998
$580$	11.6160			0.482328
$581$	−0.830283	−	2.71454i	−0.0344459	−	0.112618i
$582$	0.363475	−	0.629558i	0.0150665	−	0.0260960i
$583$	−18.3085	−	31.7113i	−0.758262	−	1.31335i
$584$	−0.404749	−	0.701046i	−0.0167486	−	0.0290095i
$585$	0.275276	−	15.6399i	0.0113813	−	0.646632i
$586$	−2.34841	+	4.06757i	−0.0970120	+	0.168030i
$587$	−10.7548	+	18.6278i	−0.443897	+	0.768852i	−0.997975	−	0.0636132i	$-0.979738\pi$
$587$	−10.7548	+	18.6278i	−0.443897	+	0.768852i	0.554078	+	0.832465i	$0.313071\pi$
$588$	−1.07991	−	15.3891i	−0.0445347	−	0.634635i
$589$	−9.57284	−	16.5806i	−0.394442	−	0.683193i
$590$	3.07949	−	5.33383i	0.126780	−	0.219590i
$591$	−6.69168	+	11.5903i	−0.275259	+	0.476763i
$592$	−12.0744	+	20.9135i	−0.496256	+	0.859541i
$593$	1.32429	−	2.29373i	0.0543820	−	0.0941923i	−0.837553	−	0.546356i	$-0.816014\pi$
$593$	1.32429	−	2.29373i	0.0543820	−	0.0941923i	0.891935	+	0.452164i	$0.149348\pi$
$594$	2.83801	+	4.91558i	0.116445	+	0.201689i
$595$	−3.62859	+	3.89214i	−0.148758	+	0.159562i
$596$	17.8013	−	30.8328i	0.729171	−	1.26296i
$597$	1.99846	−	3.46143i	0.0817915	−	0.141667i
$598$	0.135340	−	7.68939i	0.00553445	−	0.314443i
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	0.903975	+	0.427584i	$0.140635\pi$
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	−0.0816889	+	0.996658i	$0.526031\pi$
$600$	0.940558	+	1.62909i	0.0383981	+	0.0665075i
$601$	−19.1725	+	33.2077i	−0.782061	+	1.35457i	0.148679	+	0.988886i	$0.452498\pi$
$601$	−19.1725	+	33.2077i	−0.782061	+	1.35457i	−0.930739	+	0.365683i	$0.880835\pi$
$602$	−1.55490	−	0.358775i	−0.0633728	−	0.0146226i
$603$	2.29060			0.0932806
$604$	−3.09916			−0.126103
$605$	5.85480	−	10.1408i	0.238031	−	0.412283i
$606$	0.122179	+	0.211620i	0.00496317	+	0.00859646i
$607$	42.5547			1.72724			0.863620	−	0.504143i	$-0.168192\pi$
$607$	42.5547			1.72724			0.863620	+	0.504143i	$0.168192\pi$
$608$	−11.4853	+	19.8931i	−0.465791	+	0.806773i
$609$	6.92982	+	1.59898i	0.280811	+	0.0647939i
$610$	6.48782			0.262684
$611$	0.0835364	−	4.74616i	0.00337952	−	0.192009i
$612$	−1.28180	−	2.22014i	−0.0518136	−	0.0897438i
$613$	15.2652			0.616556			0.308278	−	0.951296i	$-0.400247\pi$
$613$	15.2652			0.616556			0.308278	+	0.951296i	$0.400247\pi$
$614$	−1.15773	−	2.00524i	−0.0467221	−	0.0809251i
$615$	3.56859	+	6.18098i	0.143899	+	0.249241i
$616$	3.21616	+	10.5150i	0.129583	+	0.423660i
$617$	−6.99061	−	12.1081i	−0.281431	−	0.487453i	0.690306	−	0.723517i	$-0.257476\pi$
$617$	−6.99061	−	12.1081i	−0.281431	−	0.487453i	−0.971737	+	0.236064i	$0.924142\pi$
$618$	0.663868			0.0267047
$619$	4.25792	+	7.37494i	0.171140	+	0.296424i	0.938819	−	0.344411i	$-0.111921\pi$
$619$	4.25792	+	7.37494i	0.171140	+	0.296424i	−0.767678	+	0.640835i	$0.778588\pi$
$620$	6.30845	−	10.9265i	0.253353	−	0.438821i
$621$	21.3388	+	36.9598i	0.856295	+	1.48315i
$622$	−2.20166	+	3.81338i	−0.0882784	+	0.152903i
$623$	13.8253	−	14.8294i	0.553897	−	0.594129i
$624$	−12.6236	−	7.58750i	−0.505347	−	0.303743i
$625$	15.1856	−	26.3023i	0.607425	−	1.05209i
$626$	−2.69363			−0.107659
$627$	33.8060			1.35008
$628$	3.17354			0.126638
$629$	5.30504			0.211526
$630$	−0.900175	−	2.94305i	−0.0358638	−	0.117254i
$631$	−18.4146	−	31.8950i	−0.733074	−	1.26972i	−0.955563	−	0.294786i	$-0.904752\pi$
$631$	−18.4146	−	31.8950i	−0.733074	−	1.26972i	0.222490	−	0.974935i	$-0.428582\pi$
$632$	−3.26123	+	5.64861i	−0.129725	+	0.224690i
$633$	10.8615	−	18.8127i	0.431707	−	0.747739i
$634$	−2.72013			−0.108030
$635$	2.29027	+	3.96686i	0.0908865	+	0.157420i
$636$	20.4507			0.810922
$637$	11.4560	−	22.4891i	0.453901	−	0.891052i
$638$	−2.48818			−0.0985081
$639$	10.4289	+	18.0634i	0.412561	+	0.714576i
$640$	−20.0470			−0.792428
$641$	−12.9374	+	22.4082i	−0.510996	+	0.885070i	0.488923	+	0.872327i	$0.337390\pi$
$641$	−12.9374	+	22.4082i	−0.510996	+	0.885070i	−0.999919	+	0.0127435i	$0.995944\pi$
$642$	1.76622	−	3.05918i	0.0697071	−	0.120736i
$643$	−20.2626	−	35.0958i	−0.799078	−	1.38404i	−0.920217	−	0.391408i	$-0.871988\pi$
$643$	−20.2626	−	35.0958i	−0.799078	−	1.38404i	0.121139	−	0.992636i	$-0.461345\pi$
$644$	11.8697	+	38.8070i	0.467732	+	1.52921i
$645$	−6.58666			−0.259350
$646$	1.57779			0.0620774
$647$	1.78400			0.0701364			0.0350682	−	0.999385i	$-0.488835\pi$
$647$	1.78400			0.0701364			0.0350682	+	0.999385i	$0.488835\pi$
$648$	−1.10732			−0.0434997
$649$	17.6913	−	30.6423i	0.694445	−	1.20281i
$650$	−0.0265840	+	1.51038i	−0.00104271	+	0.0592420i
$651$	5.26754	−	5.65014i	0.206451	−	0.221446i
$652$	−6.31281	+	10.9341i	−0.247229	+	0.428213i
$653$	−6.20210	−	10.7424i	−0.242707	−	0.420381i	0.718778	−	0.695240i	$-0.244702\pi$
$653$	−6.20210	−	10.7424i	−0.242707	−	0.420381i	−0.961484	+	0.274860i	$0.911369\pi$
$654$	−1.23787	+	2.14405i	−0.0484044	+	0.0838389i
$655$	−8.18597	−	14.1785i	−0.319852	−	0.554000i
$656$	−8.71109			−0.340111
$657$	0.650815	+	1.12725i	0.0253907	+	0.0439780i
$658$	−0.273171	−	0.893110i	−0.0106493	−	0.0348171i
$659$	0.564336	+	0.977458i	0.0219834	+	0.0380764i	0.876808	−	0.480841i	$-0.159669\pi$
$659$	0.564336	+	0.977458i	0.0219834	+	0.0380764i	−0.854824	+	0.518917i	$0.826335\pi$
$660$	11.1390	+	19.2933i	0.433585	+	0.750991i
$661$	−28.9254			−1.12507			−0.562534	−	0.826774i	$-0.690174\pi$
$661$	−28.9254			−1.12507			−0.562534	+	0.826774i	$0.690174\pi$
$662$	0.310913	+	0.538517i	0.0120840	+	0.0209301i
$663$	−0.0569393	+	3.23503i	−0.00221134	+	0.125638i
$664$	−1.13003			−0.0438535
$665$	−49.5006	−	11.4217i	−1.91955	−	0.442915i
$666$	−1.53414	+	2.65721i	−0.0594467	+	0.102965i
$667$	−18.7084			−0.724393
$668$	9.20556	+	15.9445i	0.356174	+	0.616911i
$669$	−6.83874	+	11.8451i	−0.264401	+	0.457956i
$670$	−0.929036			−0.0358918
$671$	37.2718			1.43886
$672$	−9.03068	−	2.08373i	−0.348366	−	0.0803815i
$673$	3.54980	−	6.14843i	0.136835	−	0.237005i	−0.789462	−	0.613799i	$-0.789640\pi$
$673$	3.54980	−	6.14843i	0.136835	−	0.237005i	0.926297	+	0.376795i	$0.122974\pi$
$674$	−2.14498	−	3.71521i	−0.0826214	−	0.143104i
$675$	−4.19145	−	7.25980i	−0.161329	−	0.279430i
$676$	−11.7610	−	22.1349i	−0.452348	−	0.851341i
$677$	25.2010	−	43.6494i	0.968552	−	1.67758i	0.268800	−	0.963196i	$-0.413373\pi$
$677$	25.2010	−	43.6494i	0.968552	−	1.67758i	0.699752	−	0.714386i	$-0.253294\pi$
$678$	−1.23221	+	2.13426i	−0.0473229	+	0.0819657i
$679$	−4.27950	+	4.59033i	−0.164232	+	0.176161i
$680$	1.05914	+	1.83449i	0.0406162	+	0.0703493i
$681$	8.79213	−	15.2284i	0.336915	−	0.583554i
$682$	−1.35129	+	2.34050i	−0.0517435	+	0.0896224i
$683$	−13.7641	+	23.8401i	−0.526669	+	0.912217i	0.472848	+	0.881144i	$0.343226\pi$
$683$	−13.7641	+	23.8401i	−0.526669	+	0.912217i	−0.999517	+	0.0310735i	$0.990107\pi$
$684$	12.2372	−	21.1954i	0.467901	−	0.810428i
$685$	12.8556	+	22.2665i	0.491186	+	0.850760i
$686$	0.775007	−	4.90490i	0.0295899	−	0.187270i
$687$	4.95019	−	8.57398i	0.188861	−	0.327118i
$688$	4.01958	−	6.96212i	0.153245	−	0.265428i
$689$	28.6765	+	17.2362i	1.09249	+	0.656649i
$690$	−3.12280	−	5.40885i	−0.118883	−	0.205912i
$691$	12.1669	+	21.0737i	0.462851	+	0.801682i	0.999102	−	0.0423772i	$-0.0134931\pi$
$691$	12.1669	+	21.0737i	0.462851	+	0.801682i	−0.536251	+	0.844059i	$0.680160\pi$
$692$	10.7315	−	18.5875i	0.407950	−	0.706591i
$693$	−5.17141	−	16.9075i	−0.196446	−	0.642263i
$694$	6.11884			0.232268
$695$	14.2064			0.538879
$696$	1.41556	−	2.45182i	0.0536566	−	0.0929360i
$697$	0.956829	+	1.65728i	0.0362425	+	0.0627738i
$698$	6.08704			0.230398
$699$	11.5733	−	20.0456i	0.437744	−	0.758195i
$700$	−2.33150	−	7.62263i	−0.0881223	−	0.288108i
$701$	−20.5588			−0.776495			−0.388248	−	0.921555i	$-0.626919\pi$
$701$	−20.5588			−0.776495			−0.388248	+	0.921555i	$0.626919\pi$
$702$	−4.44515	−	2.67180i	−0.167771	−	0.100840i
$703$	25.3234	+	43.8613i	0.955088	+	1.65426i
$704$	−24.9621			−0.940795
$705$	−1.92751	−	3.33854i	−0.0725940	−	0.125737i
$706$	−3.65513	−	6.33088i	−0.137563	−	0.238266i
$707$	−0.617017	−	2.01728i	−0.0232053	−	0.0758678i
$708$	9.88062	+	17.1137i	0.371336	+	0.643174i
$709$	40.9089			1.53637			0.768183	−	0.640230i	$-0.221161\pi$
$709$	40.9089			1.53637			0.768183	+	0.640230i	$0.221161\pi$
$710$	−4.22981	−	7.32624i	−0.158742	−	0.274949i
$711$	5.24388	−	9.08267i	0.196661	−	0.340627i
$712$	−4.03543	−	6.98956i	−0.151234	−	0.261945i
$713$	−10.1602	+	17.5980i	−0.380503	+	0.659051i
$714$	0.186196	+	0.608753i	0.00696822	+	0.0227820i
$715$	−0.641405	+	36.4418i	−0.0239872	+	1.36284i
$716$	−12.1890	+	21.1119i	−0.455524	+	0.788990i
$717$	−18.9198			−0.706572
$718$	3.86802			0.144353
$719$	−1.19947			−0.0447326			−0.0223663	−	0.999750i	$-0.507120\pi$
$719$	−1.19947			−0.0447326			−0.0223663	+	0.999750i	$0.507120\pi$
$720$	15.5047			0.577826
$721$	−5.58444	−	1.28855i	−0.207975	−	0.0479880i
$722$	4.98433	+	8.63311i	0.185497	+	0.321291i
$723$	−9.37311	+	16.2347i	−0.348590	+	0.603775i
$724$	14.3796	−	24.9063i	0.534415	−	0.925634i
$725$	3.67478			0.136478
$726$	−0.700425	−	1.21317i	−0.0259952	−	0.0450250i
$727$	−2.06230			−0.0764865			−0.0382433	−	0.999268i	$-0.512176\pi$
$727$	−2.06230			−0.0764865			−0.0382433	+	0.999268i	$0.512176\pi$
$728$	−7.22714	−	6.97949i	−0.267856	−	0.258677i
$729$	20.1764			0.747273
$730$	−0.263961	−	0.457194i	−0.00976964	−	0.0169215i
$731$	−1.76605			−0.0653197
$732$	−10.4082	+	18.0275i	−0.384697	+	0.666315i
$733$	−15.0310	+	26.0345i	−0.555184	+	0.961606i	0.442706	+	0.896667i	$0.354019\pi$
$733$	−15.0310	+	26.0345i	−0.555184	+	0.961606i	−0.997889	+	0.0649392i	$0.979315\pi$
$734$	−1.52720	−	2.64520i	−0.0563702	−	0.0976360i
$735$	−1.43481	−	20.4465i	−0.0529236	−	0.754180i
$736$	24.3801			0.898662
$737$	−5.33721			−0.196599
$738$	−1.10680			−0.0407420
$739$	44.2548			1.62794			0.813969	−	0.580908i	$-0.197303\pi$
$739$	44.2548			1.62794			0.813969	+	0.580908i	$0.197303\pi$
$740$	−16.6880	+	28.9044i	−0.613461	+	1.06255i
$741$	−27.0186	+	14.9715i	−0.992553	+	0.549992i
$742$	6.41430	+	1.48003i	0.235476	+	0.0543335i
$743$	4.31326	−	7.47078i	0.158238	−	0.274076i	−0.775995	−	0.630739i	$-0.782752\pi$
$743$	4.31326	−	7.47078i	0.158238	−	0.274076i	0.934233	+	0.356662i	$0.116085\pi$
$744$	−1.53753	−	2.66308i	−0.0563686	−	0.0976334i
$745$	23.6515	−	40.9656i	0.866524	−	1.50086i
$746$	−4.15097	−	7.18969i	−0.151978	−	0.263233i
$747$	1.81702			0.0664814
$748$	2.98665	+	5.17302i	0.109203	+	0.189144i
$749$	−20.7952	+	22.3056i	−0.759839	+	0.815028i
$750$	−1.34936	−	2.33715i	−0.0492715	−	0.0853408i
$751$	−2.86105	−	4.95549i	−0.104401	−	0.180828i	0.809092	−	0.587682i	$-0.199959\pi$
$751$	−2.86105	−	4.95549i	−0.104401	−	0.180828i	−0.913493	+	0.406853i	$0.866626\pi$
$752$	4.70512			0.171578
$753$	−11.6763	−	20.2239i	−0.425506	−	0.736998i
$754$	1.98862	−	1.10193i	0.0724211	−	0.0401299i
$755$	−4.11765			−0.149857
$756$	26.6665	+	6.15300i	0.969851	+	0.223782i
$757$	17.3611	−	30.0703i	0.631000	−	1.09292i	−0.356347	−	0.934354i	$-0.615978\pi$
$757$	17.3611	−	30.0703i	0.631000	−	1.09292i	0.987348	−	0.158571i	$-0.0506887\pi$
$758$	−2.83853			−0.103100
$759$	−17.9402	−	31.0733i	−0.651187	−	1.12789i
$760$	−10.1115	+	17.5137i	−0.366783	+	0.635287i
$761$	−53.1735			−1.92754			−0.963768	−	0.266741i	$-0.914053\pi$
$761$	−53.1735			−1.92754			−0.963768	+	0.266741i	$0.914053\pi$
$762$	0.547981			0.0198513
$763$	14.5744	−	15.6330i	0.527630	−	0.565953i
$764$	−13.6226	+	23.5951i	−0.492849	+	0.853640i
$765$	−1.70304	−	2.94976i	−0.0615736	−	0.106649i
$766$	4.12265	+	7.14063i	0.148957	+	0.258002i
$767$	−0.568946	+	32.3249i	−0.0205434	+	1.16719i
$768$	6.03145	−	10.4468i	0.217641	−	0.376966i
$769$	−2.45578	+	4.25354i	−0.0885578	+	0.153387i	−0.906902	−	0.421342i	$-0.861559\pi$
$769$	−2.45578	+	4.25354i	−0.0885578	+	0.153387i	0.818344	+	0.574729i	$0.194892\pi$
$770$	2.09745	+	6.85743i	0.0755868	+	0.247125i
$771$	7.87414	+	13.6384i	0.283580	+	0.491175i
$772$	3.75455	−	6.50306i	0.135129	−	0.234050i
$773$	11.4903	−	19.9018i	0.413279	−	0.715819i	−0.581967	−	0.813212i	$-0.697717\pi$
$773$	11.4903	−	19.9018i	0.413279	−	0.715819i	0.995246	+	0.0973926i	$0.0310502\pi$
$774$	0.510715	−	0.884585i	0.0183573	−	0.0317957i
$775$	1.99571	−	3.45667i	0.0716881	−	0.124167i
$776$	1.24913	+	2.16356i	0.0448413	+	0.0776674i
$777$	−13.9344	+	14.9465i	−0.499894	+	0.536203i
$778$	−2.19589	+	3.80339i	−0.0787264	+	0.136358i
$779$	−9.13476	+	15.8219i	−0.327287	+	0.566877i
$780$	−17.4469	−	10.4866i	−0.624699	−	0.375481i
$781$	−24.2998	−	42.0885i	−0.869515	−	1.50604i
$782$	−0.837302	−	1.45025i	−0.0299419	−	0.0518608i
$783$	−6.30821	+	10.9261i	−0.225437	+	0.390469i
$784$	22.4876	+	10.9611i	0.803129	+	0.391468i
$785$	4.21648			0.150493
$786$	−1.95862			−0.0698616
$787$	1.59387	−	2.76067i	0.0568154	−	0.0984071i	−0.836219	−	0.548396i	$-0.815239\pi$
$787$	1.59387	−	2.76067i	0.0568154	−	0.0984071i	0.893034	+	0.449989i	$0.148572\pi$
$788$	−11.2880	−	19.5514i	−0.402119	−	0.696490i
$789$	−29.6237			−1.05463
$790$	−2.12684	+	3.68380i	−0.0756696	+	0.131064i
$791$	14.5079	−	15.5616i	0.515841	−	0.553308i
$792$	−7.03836			−0.250097
$793$	−29.7886	+	16.5064i	−1.05782	+	0.586159i
$794$	−2.12927	−	3.68800i	−0.0755650	−	0.130882i
$795$	27.1715			0.963674
$796$	3.37114	+	5.83899i	0.119487	+	0.206958i
$797$	−27.3255	−	47.3291i	−0.967918	−	1.67648i	−0.701562	−	0.712608i	$-0.747514\pi$
$797$	−27.3255	−	47.3291i	−0.967918	−	1.67648i	−0.266355	−	0.963875i	$-0.585820\pi$
$798$	−4.14429	+	4.44530i	−0.146706	+	0.157362i
$799$	−0.516813	−	0.895146i	−0.0182835	−	0.0316680i
$800$	−4.78884			−0.169311
$801$	6.48875	+	11.2388i	0.229269	+	0.397105i
$802$	0.889604	−	1.54084i	0.0314130	−	0.0544089i
$803$	−1.51643	−	2.62653i	−0.0535136	−	0.0926883i
$804$	1.49042	−	2.58148i	0.0525630	−	0.0910418i
$805$	15.7705	+	51.5604i	0.555838	+	1.81727i
$806$	0.0434569	−	2.46902i	0.00153070	−	0.0869677i
$807$	−17.1832	+	29.7622i	−0.604877	+	1.04768i
$808$	−0.839768			−0.0295429
$809$	−20.2995			−0.713694			−0.356847	−	0.934163i	$-0.616148\pi$
$809$	−20.2995			−0.713694			−0.356847	+	0.934163i	$0.616148\pi$
$810$	−0.722151			−0.0253738
$811$	2.43587			0.0855350			0.0427675	−	0.999085i	$-0.486383\pi$
$811$	2.43587			0.0855350			0.0427675	+	0.999085i	$0.486383\pi$
$812$	−8.18076	+	8.77496i	−0.287089	+	0.307941i
$813$	8.25855	+	14.3042i	0.289640	+	0.501671i
$814$	3.57461	−	6.19141i	0.125290	−	0.217009i
$815$	−8.38742	+	14.5274i	−0.293799	+	0.508874i
$816$	−3.20706			−0.112270
$817$	−8.43015	−	14.6015i	−0.294934	−	0.510840i
$818$	−1.57452			−0.0550519
$819$	11.6209	+	11.2226i	0.406066	+	0.392151i
$820$	−12.0395			−0.420438
$821$	−22.6762	−	39.2763i	−0.791405	−	1.37075i	−0.925097	−	0.379731i	$-0.876017\pi$
$821$	−22.6762	−	39.2763i	−0.791405	−	1.37075i	0.133692	−	0.991023i	$-0.457317\pi$
$822$	3.07589			0.107284
$823$	1.37871	−	2.38800i	0.0480588	−	0.0832403i	−0.840995	−	0.541042i	$-0.818030\pi$
$823$	1.37871	−	2.38800i	0.0480588	−	0.0832403i	0.889054	+	0.457802i	$0.151363\pi$
$824$	−1.14074	+	1.97581i	−0.0397394	+	0.0688307i
$825$	3.52388	+	6.10354i	0.122686	+	0.212498i
$826$	1.86050	+	6.08275i	0.0647351	+	0.211646i
$827$	−8.64504			−0.300618			−0.150309	−	0.988639i	$-0.548027\pi$
$827$	−8.64504			−0.300618			−0.150309	+	0.988639i	$0.548027\pi$
$828$	−25.9761			−0.902733
$829$	−29.5741			−1.02715			−0.513576	−	0.858044i	$-0.671680\pi$
$829$	−29.5741			−1.02715			−0.513576	+	0.858044i	$0.671680\pi$
$830$	−0.736958			−0.0255802
$831$	−8.75858	+	15.1703i	−0.303832	+	0.526252i
$832$	19.9503	−	11.0548i	0.691653	−	0.383258i
$833$	−0.384708	−	5.48222i	−0.0133293	−	0.189948i
$834$	0.849774	−	1.47185i	0.0294253	−	0.0509660i
$835$	12.2308	+	21.1844i	0.423266	+	0.733117i
$836$	−28.5132	+	49.3863i	−0.986150	+	1.70806i
$837$	6.85177	+	11.8676i	0.236832	+	0.410204i
$838$	8.08191			0.279185
$839$	−12.6236	−	21.8648i	−0.435817	−	0.754857i	0.561545	−	0.827446i	$-0.310207\pi$
$839$	−12.6236	−	21.8648i	−0.435817	−	0.754857i	−0.997362	+	0.0725895i	$0.976874\pi$
$840$	−7.95049	−	1.83449i	−0.274318	−	0.0632958i
$841$	11.7347	+	20.3251i	0.404644	+	0.700865i
$842$	5.37028	+	9.30159i	0.185072	+	0.320554i
$843$	−6.04971			−0.208363
$844$	18.3220	+	31.7346i	0.630669	+	1.09235i
$845$	−15.6262	−	29.4092i	−0.537556	−	1.01171i
$846$	0.597818			0.0205534
$847$	3.53723	+	11.5647i	0.121541	+	0.397367i
$848$	−16.5817	+	28.7204i	−0.569418	+	0.986261i
$849$	35.1870			1.20761
$850$	0.164466	+	0.284864i	0.00564115	+	0.00977076i
$851$	26.8772	−	46.5526i	0.921338	−	1.59580i
$852$	27.1429			0.929901
$853$	−35.1368			−1.20306			−0.601531	−	0.798850i	$-0.705442\pi$
$853$	−35.1368			−1.20306			−0.601531	+	0.798850i	$0.705442\pi$
$854$	−4.56916	+	4.90103i	−0.156353	+	0.167710i
$855$	16.2588	−	28.1610i	0.556039	−	0.963087i
$856$	6.06986	+	10.5133i	0.207463	+	0.359337i
$857$	0.671345	+	1.16280i	0.0229327	+	0.0397206i	0.877264	−	0.480008i	$-0.159366\pi$
$857$	0.671345	+	1.16280i	0.0229327	+	0.0397206i	−0.854331	+	0.519729i	$0.826033\pi$
$858$	3.73718	+	2.24626i	0.127585	+	0.0766862i
$859$	−2.38386	+	4.12897i	−0.0813363	+	0.140879i	−0.903824	−	0.427904i	$-0.859252\pi$
$859$	−2.38386	+	4.12897i	−0.0813363	+	0.140879i	0.822488	+	0.568783i	$0.192585\pi$
$860$	5.55542	−	9.62228i	0.189438	−	0.328117i
$861$	−7.18248	−	1.65728i	−0.244778	−	0.0564799i
$862$	−0.524972	−	0.909278i	−0.0178806	−	0.0309701i
$863$	13.3052	−	23.0453i	0.452915	−	0.784472i	−0.545650	−	0.838013i	$-0.683717\pi$
$863$	13.3052	−	23.0453i	0.452915	−	0.784472i	0.998566	+	0.0535407i	$0.0170507\pi$
$864$	8.22062	−	14.2385i	0.279671	−	0.484405i
$865$	14.2583	−	24.6960i	0.484795	−	0.839690i
$866$	−5.46875	+	9.47216i	−0.185836	+	0.321877i
$867$	−9.36331	−	16.2177i	−0.317995	−	0.550783i
$868$	3.81130	+	12.4607i	0.129364	+	0.422945i
$869$	−12.2185	+	21.1630i	−0.414484	+	0.717907i
$870$	0.923171	−	1.59898i	0.0312984	−	0.0542105i
$871$	4.26563	−	2.36366i	0.144535	−	0.0800897i
$872$	−4.25410	−	7.36831i	−0.144062	−	0.249523i
$873$	−2.00854	−	3.47890i	−0.0679788	−	0.117743i
$874$	7.99364	−	13.8454i	0.270389	−	0.468328i
$875$	6.81441	+	22.2791i	0.230369	+	0.753172i
$876$	1.69385			0.0572300
$877$	8.03696			0.271389			0.135695	−	0.990751i	$-0.456673\pi$
$877$	8.03696			0.271389			0.135695	+	0.990751i	$0.456673\pi$
$878$	−3.42694	+	5.93564i	−0.115654	+	0.200318i
$879$	−10.0112	−	17.3399i	−0.337670	−	0.584861i
$880$	−36.1266			−1.21783
$881$	27.3349	−	47.3454i	0.920935	−	1.59511i	0.122964	−	0.992411i	$-0.460760\pi$
$881$	27.3349	−	47.3454i	0.920935	−	1.59511i	0.797971	−	0.602695i	$-0.205907\pi$
$882$	2.85720	+	1.39268i	0.0962070	+	0.0468940i
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	−4.67795	−	2.81172i	−0.157337	−	0.0945685i
$885$	13.1277	+	22.7379i	0.441284	+	0.764327i
$886$	7.36176			0.247323
$887$	5.17784	+	8.96829i	0.173855	+	0.301126i	0.939764	−	0.341823i	$-0.111044\pi$
$887$	5.17784	+	8.96829i	0.173855	+	0.301126i	−0.765909	+	0.642948i	$0.777711\pi$
$888$	4.06729	+	7.04475i	0.136489	+	0.236406i
$889$	−4.60961	−	1.06361i	−0.154601	−	0.0356725i
$890$	−2.63174	−	4.55831i	−0.0882162	−	0.152795i
$891$	−4.14868			−0.138986
$892$	−11.5361	−	19.9811i	−0.386256	−	0.669016i
$893$	4.93396	−	8.54587i	0.165109	−	0.285977i
$894$	−2.82949	−	4.90082i	−0.0946323	−	0.163908i
$895$	−16.1947	+	28.0501i	−0.541330	+	0.937611i
$896$	14.1185	−	15.1439i	0.471665	−	0.505923i
$897$	28.0995	+	16.8895i	0.938215	+	0.563923i
$898$	−1.98461	+	3.43745i	−0.0662274	+	0.114709i
$899$	−6.00718			−0.200351
$900$	5.10234			0.170078
$901$	7.28536			0.242711
$902$	2.57890			0.0858680
$903$	4.63877	−	4.97570i	0.154369	−	0.165581i
$904$	−4.23468	−	7.33467i	−0.140843	−	0.243948i
$905$	19.1053	−	33.0914i	0.635082	−	1.09999i
$906$	−0.246303	+	0.426609i	−0.00818287	+	0.0141731i
$907$	18.4804			0.613631			0.306815	−	0.951769i	$-0.400737\pi$
$907$	18.4804			0.613631			0.306815	+	0.951769i	$0.400737\pi$
$908$	14.8312	+	25.6884i	0.492190	+	0.852498i
$909$	1.35030			0.0447867
$910$	−4.71325	−	4.55174i	−0.156243	−	0.150889i
$911$	−26.6282			−0.882230			−0.441115	−	0.897451i	$-0.645417\pi$
$911$	−26.6282			−0.882230			−0.441115	+	0.897451i	$0.645417\pi$
$912$	−15.3088	−	26.5155i	−0.506924	−	0.878017i
$913$	−4.23374			−0.140116
$914$	−0.0874022	+	0.151385i	−0.00289101	+	0.00500737i
$915$	−13.8287	+	23.9520i	−0.457162	+	0.791828i
$916$	8.35033	+	14.4632i	0.275903	+	0.477877i
$917$	16.4758	+	3.80162i	0.544080	+	0.125540i
$918$	−1.12931			−0.0372727
$919$	−11.1493			−0.367783			−0.183891	−	0.982947i	$-0.558869\pi$
$919$	−11.1493			−0.367783			−0.183891	+	0.982947i	$0.558869\pi$
$920$	21.4639			0.707644
$921$	9.87072			0.325251
$922$	1.67518	−	2.90149i	0.0551690	−	0.0955555i
$923$	38.0605	+	22.8766i	1.25278	+	0.752993i
$924$	−22.4194	−	5.17302i	−0.737544	−	0.170180i
$925$	−5.27933	+	9.14406i	−0.173583	+	0.300655i
$926$	−0.0414927	−	0.0718675i	−0.00136354	−	0.00236171i
$927$	1.83424	−	3.17700i	0.0602445	−	0.104347i
$928$	3.60365	+	6.24170i	0.118296	+	0.204894i
$929$	7.74510			0.254108			0.127054	−	0.991896i	$-0.459448\pi$
$929$	7.74510			0.254108			0.127054	+	0.991896i	$0.459448\pi$
$930$	−1.00272	−	1.73676i	−0.0328804	−	0.0569505i
$931$	43.4898	−	29.3498i	1.42532	−	0.961901i
$932$	19.5227	+	33.8144i	0.639489	+	1.10763i
$933$	−9.38559	−	16.2563i	−0.307270	−	0.532208i
$934$	−6.56299			−0.214748
$935$	3.96817	+	6.87306i	0.129773	+	0.224773i
$936$	5.62523	−	3.11704i	0.183866	−	0.101884i
$937$	36.4239			1.18992			0.594959	−	0.803756i	$-0.297168\pi$
$937$	36.4239			1.18992			0.594959	+	0.803756i	$0.297168\pi$
$938$	0.654289	−	0.701812i	0.0213633	−	0.0229150i
$939$	5.74143	−	9.94445i	0.187364	−	0.324525i
$940$	6.50291			0.212101
$941$	9.89466	+	17.1381i	0.322557	+	0.558685i	0.981015	−	0.193933i	$-0.0621243\pi$
$941$	9.89466	+	17.1381i	0.322557	+	0.558685i	−0.658458	+	0.752617i	$0.728791\pi$
$942$	0.252214	−	0.436848i	0.00821759	−	0.0142333i
$943$	19.3905			0.631442
$944$	−32.0454			−1.04299
$945$	35.4301	+	8.17509i	1.15254	+	0.265936i
$946$	−1.18999	+	2.06112i	−0.0386899	+	0.0670129i
$947$	−4.97398	−	8.61519i	−0.161633	−	0.279956i	0.773822	−	0.633403i	$-0.218343\pi$
$947$	−4.97398	−	8.61519i	−0.161633	−	0.279956i	−0.935454	+	0.353448i	$0.885009\pi$
$948$	−6.82403	−	11.8196i	−0.221634	−	0.383882i
$949$	2.37517	+	1.42762i	0.0771012	+	0.0463424i
$950$	−1.57014	+	2.71957i	−0.0509422	+	0.0882345i
$951$	5.79790	−	10.0423i	0.188010	−	0.325643i
$952$	−2.13173	−	0.491872i	−0.0690896	−	0.0159417i
$953$	−0.0105567	−	0.0182847i	−0.000341965	−	0.000592300i	0.865854	−	0.500296i	$-0.166776\pi$
$953$	−0.0105567	−	0.0182847i	−0.000341965	−	0.000592300i	−0.866196	+	0.499704i	$0.833442\pi$
$954$	−2.10682	+	3.64912i	−0.0682108	+	0.118144i
$955$	−18.0995	+	31.3493i	−0.585686	+	1.01444i
$956$	15.9576	−	27.6394i	0.516106	−	0.893922i
$957$	5.30352	−	9.18596i	0.171438	−	0.296940i
$958$	1.09107	+	1.88979i	0.0352508	+	0.0610562i
$959$	−25.8743	−	5.97022i	−0.835526	−	0.192788i
$960$	9.26150	−	16.0414i	0.298914	−	0.517733i
$961$	12.2376	−	21.1962i	0.394761	−	0.683747i
$962$	−0.114958	+	6.53140i	−0.00370640	+	0.210581i
$963$	−9.76001	−	16.9048i	−0.314512	−	0.544751i
$964$	−15.8112	−	27.3858i	−0.509245	−	0.882039i
$965$	4.98842	−	8.64020i	0.160583	−	0.278138i
$966$	6.28525	+	1.45025i	0.202225	+	0.0466610i
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	4.81422			0.154735
$969$	−3.36304	+	5.82495i	−0.108036	+	0.187124i
$970$	0.814635	+	1.41099i	0.0261563	+	0.0453041i
$971$	−3.61774			−0.116099			−0.0580493	−	0.998314i	$-0.518488\pi$
$971$	−3.61774			−0.116099			−0.0580493	+	0.998314i	$0.518488\pi$
$972$	−14.3572	+	24.8674i	−0.460508	+	0.797622i
$973$	−10.0051	+	10.7318i	−0.320749	+	0.344045i
$974$	−1.23595			−0.0396024
$975$	−5.51942	−	3.31750i	−0.176763	−	0.106245i
$976$	−16.8782	−	29.2339i	−0.540258	−	0.935755i
$977$	2.16169			0.0691586			0.0345793	−	0.999402i	$-0.488991\pi$
$977$	2.16169			0.0691586			0.0345793	+	0.999402i	$0.488991\pi$
$978$	1.00341	+	1.73796i	0.0320855	+	0.0555737i
$979$	−15.1191	−	26.1870i	−0.483208	−	0.836941i
$980$	31.0799	+	15.1492i	0.992810	+	0.483924i
$981$	6.84036	+	11.8479i	0.218396	+	0.378273i
$982$	−3.49071			−0.111393
$983$	15.0545	+	26.0752i	0.480165	+	0.831671i	0.999741	−	0.0227535i	$-0.00724329\pi$
$983$	15.0545	+	26.0752i	0.480165	+	0.831671i	−0.519576	+	0.854424i	$0.673910\pi$
$984$	−1.46717	+	2.54121i	−0.0467717	+	0.0810109i
$985$	−14.9977	−	25.9767i	−0.477865	−	0.827687i
$986$	0.247525	−	0.428727i	0.00788281	−	0.0136534i
$987$	3.87948	+	0.895146i	0.123485	+	0.0284928i
$988$	0.916973	−	52.0983i	0.0291728	−	1.65747i
$989$	−8.94742	+	15.4974i	−0.284511	+	0.492788i
$990$	−4.59014			−0.145884
$991$	−27.1460			−0.862323			−0.431161	−	0.902275i	$-0.641896\pi$
$991$	−27.1460			−0.862323			−0.431161	+	0.902275i	$0.641896\pi$
$992$	7.82832			0.248549
$993$	−2.65082			−0.0841213
$994$	8.51330	+	1.96435i	0.270026	+	0.0623054i
$995$	4.47902	+	7.75790i	0.141995	+	0.245942i
$996$	1.18227	−	2.04776i	0.0374618	−	0.0648858i
$997$	−25.4005	+	43.9949i	−0.804441	+	1.39333i	0.112227	+	0.993683i	$0.464202\pi$
$997$	−25.4005	+	43.9949i	−0.804441	+	1.39333i	−0.916668	+	0.399650i	$0.869132\pi$
$998$	8.66599			0.274317
$999$	−18.1252	−	31.3938i	−0.573456	−	0.993256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.g.b.9.3	✓	12
3.2	odd	2		819.2.n.d.100.4		12
7.2	even	3		637.2.f.k.295.3		12
7.3	odd	6		637.2.h.l.165.4		12
7.4	even	3		91.2.h.b.74.4	yes	12
7.5	odd	6		637.2.f.j.295.3		12
7.6	odd	2		637.2.g.l.373.3		12
13.3	even	3		91.2.h.b.16.4	yes	12
13.4	even	6		1183.2.e.g.170.4		12
13.9	even	3		1183.2.e.h.170.3		12
21.11	odd	6		819.2.s.d.802.3		12
39.29	odd	6		819.2.s.d.289.3		12
91.3	odd	6		637.2.g.l.263.3		12
91.4	even	6		1183.2.e.g.508.4		12
91.9	even	3		8281.2.a.bz.1.4		6
91.16	even	3		637.2.f.k.393.3		12
91.30	even	6		8281.2.a.ce.1.3		6
91.55	odd	6		637.2.h.l.471.4		12
91.61	odd	6		8281.2.a.ca.1.4		6
91.68	odd	6		637.2.f.j.393.3		12
91.74	even	3		1183.2.e.h.508.3		12
91.81	even	3	inner	91.2.g.b.81.3	yes	12
91.82	odd	6		8281.2.a.cf.1.3		6
273.263	odd	6		819.2.n.d.172.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	1.1	even	1	trivial
91.2.g.b.81.3	yes	12	91.81	even	3	inner
91.2.h.b.16.4	yes	12	13.3	even	3
91.2.h.b.74.4	yes	12	7.4	even	3
637.2.f.j.295.3		12	7.5	odd	6
637.2.f.j.393.3		12	91.68	odd	6
637.2.f.k.295.3		12	7.2	even	3
637.2.f.k.393.3		12	91.16	even	3
637.2.g.l.263.3		12	91.3	odd	6
637.2.g.l.373.3		12	7.6	odd	2
637.2.h.l.165.4		12	7.3	odd	6
637.2.h.l.471.4		12	91.55	odd	6
819.2.n.d.100.4		12	3.2	odd	2
819.2.n.d.172.4		12	273.263	odd	6
819.2.s.d.289.3		12	39.29	odd	6
819.2.s.d.802.3		12	21.11	odd	6
1183.2.e.g.170.4		12	13.4	even	6
1183.2.e.g.508.4		12	91.4	even	6
1183.2.e.h.170.3		12	13.9	even	3
1183.2.e.h.508.3		12	91.74	even	3
8281.2.a.bz.1.4		6	91.9	even	3
8281.2.a.ca.1.4		6	91.61	odd	6
8281.2.a.ce.1.3		6	91.30	even	6
8281.2.a.cf.1.3		6	91.82	odd	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134063 + 0.232203i) q^{2} -1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +(-0.153235 - 0.265410i) q^{6} +(0.773854 + 2.53005i) q^{7} +1.05323 q^{8} -1.69353 q^{9} +O(q^{10})\)	\(q+(0.134063 + 0.232203i) q^{2} -1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +(-0.153235 - 0.265410i) q^{6} +(0.773854 + 2.53005i) q^{7} +1.05323 q^{8} -1.69353 q^{9} +0.686871 q^{10} +3.94600 q^{11} +(-1.10192 + 1.90859i) q^{12} +(-3.15374 + 1.74755i) q^{13} +(-0.483741 + 0.518876i) q^{14} +(-1.46405 + 2.53582i) q^{15} +(-1.78691 - 3.09502i) q^{16} +(-0.392550 + 0.679916i) q^{17} +(-0.227039 - 0.393243i) q^{18} -7.49527 q^{19} +(-2.46967 - 4.27760i) q^{20} +(-0.884522 - 2.89187i) q^{21} +(0.529011 + 0.916274i) q^{22} +(3.97759 + 6.88938i) q^{23} -1.20385 q^{24} +(-0.781294 - 1.35324i) q^{25} +(-0.828585 - 0.498028i) q^{26} +5.36475 q^{27} +(4.97069 + 1.14693i) q^{28} +(-1.17586 + 2.03666i) q^{29} -0.785100 q^{30} +(1.27718 + 2.21215i) q^{31} +(1.53234 - 2.65409i) q^{32} -4.51032 q^{33} -0.210505 q^{34} +(6.60424 + 1.52385i) q^{35} +(-1.63266 + 2.82784i) q^{36} +(-3.37858 - 5.85187i) q^{37} +(-1.00484 - 1.74043i) q^{38} +(3.60475 - 1.99746i) q^{39} +(1.34905 - 2.33663i) q^{40} +(1.21874 - 2.11091i) q^{41} +(0.552920 - 0.593080i) q^{42} +(1.12473 + 1.94809i) q^{43} +(3.80416 - 6.58900i) q^{44} +(-2.16920 + 3.75717i) q^{45} +(-1.06649 + 1.84722i) q^{46} +(-0.658276 + 1.14017i) q^{47} +(2.04246 + 3.53764i) q^{48} +(-5.80230 + 3.91578i) q^{49} +(0.209485 - 0.362838i) q^{50} +(0.448688 - 0.777151i) q^{51} +(-0.122340 + 6.95082i) q^{52} +(-4.63977 - 8.03632i) q^{53} +(0.719212 + 1.24571i) q^{54} +(5.05434 - 8.75438i) q^{55} +(0.815042 + 2.66471i) q^{56} +8.56716 q^{57} -0.630558 q^{58} +(4.48335 - 7.76540i) q^{59} +(2.82286 + 4.88933i) q^{60} +9.44547 q^{61} +(-0.342445 + 0.593132i) q^{62} +(-1.31054 - 4.28472i) q^{63} -6.32592 q^{64} +(-0.162546 + 9.23511i) q^{65} +(-0.604665 - 1.04731i) q^{66} -1.35256 q^{67} +(0.756879 + 1.31095i) q^{68} +(-4.54642 - 7.87463i) q^{69} +(0.531538 + 1.73782i) q^{70} +(-6.15808 - 10.6661i) q^{71} -1.78367 q^{72} +(-0.384295 - 0.665619i) q^{73} +(0.905882 - 1.56903i) q^{74} +(0.893026 + 1.54677i) q^{75} +(-7.22585 + 12.5155i) q^{76} +(3.05363 + 9.98358i) q^{77} +(0.947080 + 0.569251i) q^{78} +(-3.09642 + 5.36316i) q^{79} -9.15525 q^{80} -1.05136 q^{81} +0.653548 q^{82} -1.07292 q^{83} +(-5.68155 - 1.31095i) q^{84} +(1.00562 + 1.74178i) q^{85} +(-0.301568 + 0.522332i) q^{86} +(1.34402 - 2.32792i) q^{87} +4.15603 q^{88} +(-3.83149 - 6.63634i) q^{89} -1.16324 q^{90} +(-6.86191 - 6.62678i) q^{91} +15.3384 q^{92} +(-1.45983 - 2.52850i) q^{93} -0.353001 q^{94} +(-9.60052 + 16.6286i) q^{95} +(-1.75148 + 3.03365i) q^{96} +(1.18601 + 2.05423i) q^{97} +(-1.68713 - 0.822354i) q^{98} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

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