LMFDB - Embedded newform 209.2.k.c.18.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(18,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("209.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.k (of order $10$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			18.14
Character	$\chi$	$=$	209.18
Dual form			209.2.k.c.151.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04958 + 1.48911i) q^{2} +(-2.98595 - 0.970193i) q^{3} +(1.36531 + 4.20198i) q^{4} +(-2.80019 + 2.03445i) q^{5} +(-4.67522 - 6.43489i) q^{6} +(0.130591 - 0.0424315i) q^{7} +(-1.89316 + 5.82655i) q^{8} +(5.54755 + 4.03053i) q^{9} -8.76873 q^{10} +(-2.93767 + 1.53952i) q^{11} -13.8715i q^{12} +(-0.209673 - 0.152336i) q^{13} +(0.330841 + 0.107497i) q^{14} +(10.3350 - 3.35805i) q^{15} +(-5.40770 + 3.92892i) q^{16} +(2.40685 + 3.31275i) q^{17} +(5.36826 + 16.5218i) q^{18} +(3.11953 - 3.04442i) q^{19} +(-12.3719 - 8.98868i) q^{20} -0.431104 q^{21} +(-8.31350 - 1.21914i) q^{22} +3.85070 q^{23} +(11.3057 - 15.5610i) q^{24} +(2.15695 - 6.63842i) q^{25} +(-0.202897 - 0.624451i) q^{26} +(-7.11806 - 9.79717i) q^{27} +(0.356593 + 0.490808i) q^{28} +(2.04657 + 6.29870i) q^{29} +(26.1830 + 8.50736i) q^{30} +(-3.73581 + 5.14190i) q^{31} -4.68133 q^{32} +(10.2653 - 1.74681i) q^{33} +10.3738i q^{34} +(-0.279353 + 0.384497i) q^{35} +(-9.36213 + 28.8137i) q^{36} +(-0.615510 + 0.199991i) q^{37} +(10.9272 - 1.59447i) q^{38} +(0.478277 + 0.658291i) q^{39} +(-6.55264 - 20.1670i) q^{40} +(-0.326912 + 1.00613i) q^{41} +(-0.883582 - 0.641960i) q^{42} -4.91923i q^{43} +(-10.4798 - 10.2421i) q^{44} -23.7341 q^{45} +(7.89232 + 5.73410i) q^{46} +(1.74188 - 5.36096i) q^{47} +(19.9589 - 6.48505i) q^{48} +(-5.64787 + 4.10341i) q^{49} +(14.3062 - 10.3940i) q^{50} +(-3.97273 - 12.2268i) q^{51} +(0.353847 - 1.08903i) q^{52} +(-1.08801 + 1.49752i) q^{53} -30.6797i q^{54} +(5.09394 - 10.2875i) q^{55} +0.841222i q^{56} +(-12.2684 + 6.06394i) q^{57} +(-5.18483 + 15.9573i) q^{58} +(-3.78753 + 1.23064i) q^{59} +(28.2210 + 38.8428i) q^{60} +(-1.44173 - 1.98437i) q^{61} +(-15.3137 + 4.97572i) q^{62} +(0.895481 + 0.290959i) q^{63} +(1.22064 + 0.886845i) q^{64} +0.897044 q^{65} +(23.6409 + 11.7060i) q^{66} -3.19367i q^{67} +(-10.6340 + 14.6365i) q^{68} +(-11.4980 - 3.73592i) q^{69} +(-1.14512 + 0.372070i) q^{70} +(-2.80305 - 3.85807i) q^{71} +(-33.9865 + 24.6926i) q^{72} +(6.35844 - 2.06598i) q^{73} +(-1.55935 - 0.506663i) q^{74} +(-12.8811 + 17.7293i) q^{75} +(17.0517 + 8.95166i) q^{76} +(-0.318308 + 0.325696i) q^{77} +2.06143i q^{78} +(8.16513 + 5.93231i) q^{79} +(7.14935 - 22.0034i) q^{80} +(5.39207 + 16.5951i) q^{81} +(-2.16827 + 1.57534i) q^{82} +(7.13976 + 9.82703i) q^{83} +(-0.588589 - 1.81149i) q^{84} +(-13.4793 - 4.37968i) q^{85} +(7.32527 - 10.0824i) q^{86} -20.7932i q^{87} +(-3.40859 - 20.0310i) q^{88} +16.2720i q^{89} +(-48.6450 - 35.3427i) q^{90} +(-0.0338452 - 0.0109970i) q^{91} +(5.25738 + 16.1806i) q^{92} +(16.1436 - 11.7290i) q^{93} +(11.5532 - 8.39387i) q^{94} +(-2.54153 + 14.8715i) q^{95} +(13.9782 + 4.54179i) q^{96} +(7.26679 - 10.0019i) q^{97} -17.6862 q^{98} +(-22.5019 - 3.29982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 32 q^{4} - 10 q^{5} - 20 q^{6} + 20 q^{7} + 32 q^{9} - 28 q^{11} + 20 q^{16} + 10 q^{17} - 10 q^{19} - 52 q^{20} - 20 q^{23} + 40 q^{24} + 12 q^{25} + 16 q^{26} + 10 q^{28} + 20 q^{30} + 60 q^{35}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 32 * q^4 - 10 * q^5 - 20 * q^6 + 20 * q^7 + 32 * q^9 - 28 * q^11 + 20 * q^16 + 10 * q^17 - 10 * q^19 - 52 * q^20 - 20 * q^23 + 40 * q^24 + 12 * q^25 + 16 * q^26 + 10 * q^28 + 20 * q^30 + 60 * q^35 - 32 * q^36 - 10 * q^38 - 40 * q^39 - 48 * q^42 - 38 * q^44 - 60 * q^45 + 6 * q^47 - 46 * q^49 - 12 * q^55 - 10 * q^57 + 74 * q^58 + 20 * q^61 - 30 * q^62 - 90 * q^63 + 48 * q^64 + 74 * q^66 - 170 * q^68 - 30 * q^73 - 20 * q^74 + 24 * q^77 + 18 * q^80 + 82 * q^81 - 12 * q^82 + 110 * q^83 + 30 * q^85 + 20 * q^92 + 82 * q^93 - 100 * q^95 + 20 * q^96 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	2.04958	+	1.48911i	1.44927	+	1.05296i	0.986000	+	0.166743i	$0.0533249\pi$
$2$	2.04958	+	1.48911i	1.44927	+	1.05296i	0.463273	+	0.886216i	$0.346675\pi$
$3$	−2.98595	−	0.970193i	−1.72394	−	0.560141i	−0.731386	−	0.681964i	$-0.761126\pi$
$3$	−2.98595	−	0.970193i	−1.72394	−	0.560141i	−0.992552	+	0.121823i	$0.961126\pi$
$4$	1.36531	+	4.20198i	0.682654	+	2.10099i
$5$	−2.80019	+	2.03445i	−1.25228	+	0.909836i	−0.998352	−	0.0573872i	$-0.981723\pi$
$5$	−2.80019	+	2.03445i	−1.25228	+	0.909836i	−0.253929	+	0.967223i	$0.581723\pi$
$6$	−4.67522	−	6.43489i	−1.90865	−	2.62703i
$7$	0.130591	−	0.0424315i	0.0493587	−	0.0160376i	−0.284234	−	0.958755i	$-0.591739\pi$
$7$	0.130591	−	0.0424315i	0.0493587	−	0.0160376i	0.333592	+	0.942717i	$0.391739\pi$
$8$	−1.89316	+	5.82655i	−0.669333	+	2.06000i
$9$	5.54755	+	4.03053i	1.84918	+	1.34351i
$10$	−8.76873			−2.77292
$11$	−2.93767	+	1.53952i	−0.885740	+	0.464181i
$11$	−2.93767	+	1.53952i	−0.885740	+	0.464181i
$12$		−	13.8715i		−	4.00436i
$13$	−0.209673	−	0.152336i	−0.0581528	−	0.0422505i	0.558329	−	0.829620i	$-0.311443\pi$
$13$	−0.209673	−	0.152336i	−0.0581528	−	0.0422505i	−0.616482	+	0.787369i	$0.711443\pi$
$14$	0.330841	+	0.107497i	0.0884211	+	0.0287298i
$15$	10.3350	−	3.35805i	2.66849	−	0.867045i
$16$	−5.40770	+	3.92892i	−1.35192	+	0.982231i
$17$	2.40685	+	3.31275i	0.583748	+	0.803460i	0.994100	−	0.108467i	$-0.0345942\pi$
$17$	2.40685	+	3.31275i	0.583748	+	0.803460i	−0.410352	+	0.911927i	$0.634594\pi$
$18$	5.36826	+	16.5218i	1.26531	+	3.89423i
$19$	3.11953	−	3.04442i	0.715670	−	0.698439i
$19$	3.11953	−	3.04442i	0.715670	−	0.698439i
$20$	−12.3719	−	8.98868i	−2.76643	−	2.00993i
$21$	−0.431104			−0.0940745
$22$	−8.31350	−	1.21914i	−1.77244	−	0.259922i
$23$	3.85070			0.802926			0.401463	−	0.915875i	$-0.368502\pi$
$23$	3.85070			0.802926			0.401463	+	0.915875i	$0.368502\pi$
$24$	11.3057	−	15.5610i	2.30778	−	3.17638i
$25$	2.15695	−	6.63842i	0.431391	−	1.32768i
$26$	−0.202897	−	0.624451i	−0.0397913	−	0.122465i
$27$	−7.11806	−	9.79717i	−1.36987	−	1.88547i
$28$	0.356593	+	0.490808i	0.0673897	+	0.0927540i
$29$	2.04657	+	6.29870i	0.380039	+	1.16964i	0.940016	+	0.341131i	$0.110810\pi$
$29$	2.04657	+	6.29870i	0.380039	+	1.16964i	−0.559977	+	0.828508i	$0.689190\pi$
$30$	26.1830	+	8.50736i	4.78033	+	1.55322i
$31$	−3.73581	+	5.14190i	−0.670971	+	0.923512i	−0.999782	−	0.0208836i	$-0.993352\pi$
$31$	−3.73581	+	5.14190i	−0.670971	+	0.923512i	0.328811	+	0.944396i	$0.393352\pi$
$32$	−4.68133			−0.827549
$33$	10.2653	−	1.74681i	1.78697	−	0.304080i
$34$			10.3738i			1.77910i
$35$	−0.279353	+	0.384497i	−0.0472193	+	0.0649918i
$36$	−9.36213	+	28.8137i	−1.56035	+	4.80228i
$37$	−0.615510	+	0.199991i	−0.101189	+	0.0328784i	−0.359174	−	0.933271i	$-0.616942\pi$
$37$	−0.615510	+	0.199991i	−0.101189	+	0.0328784i	0.257985	+	0.966149i	$0.416942\pi$
$38$	10.9272	−	1.59447i	1.77263	−	0.258658i
$39$	0.478277	+	0.658291i	0.0765856	+	0.105411i
$40$	−6.55264	−	20.1670i	−1.03606	−	3.18868i
$41$	−0.326912	+	1.00613i	−0.0510552	+	0.157132i	−0.973333	−	0.229395i	$-0.926325\pi$
$41$	−0.326912	+	1.00613i	−0.0510552	+	0.157132i	0.922278	+	0.386527i	$0.126325\pi$
$42$	−0.883582	−	0.641960i	−0.136340	−	0.0990566i
$43$		−	4.91923i		−	0.750176i	−0.926989	−	0.375088i	$-0.877612\pi$
$43$		−	4.91923i		−	0.750176i	0.926989	−	0.375088i	$-0.122388\pi$
$44$	−10.4798	−	10.2421i	−1.57990	−	1.54406i
$45$	−23.7341			−3.53807
$46$	7.89232	+	5.73410i	1.16366	+	0.845447i
$47$	1.74188	−	5.36096i	0.254079	−	0.781976i	−0.739930	−	0.672684i	$-0.765142\pi$
$47$	1.74188	−	5.36096i	0.254079	−	0.781976i	0.994010	−	0.109292i	$-0.0348585\pi$
$48$	19.9589	−	6.48505i	2.88082	−	0.936036i
$49$	−5.64787	+	4.10341i	−0.806838	+	0.586202i
$50$	14.3062	−	10.3940i	2.02320	−	1.46994i
$51$	−3.97273	−	12.2268i	−0.556294	−	1.71210i
$52$	0.353847	−	1.08903i	0.0490697	−	0.151021i
$53$	−1.08801	+	1.49752i	−0.149450	+	0.205700i	−0.877178	−	0.480166i	$-0.840576\pi$
$53$	−1.08801	+	1.49752i	−0.149450	+	0.205700i	0.727728	+	0.685866i	$0.240576\pi$
$54$		−	30.6797i		−	4.17497i
$55$	5.09394	−	10.2875i	0.686867	−	1.38716i
$56$			0.841222i			0.112413i
$57$	−12.2684	+	6.06394i	−1.62499	+	0.803188i
$58$	−5.18483	+	15.9573i	−0.680802	+	2.09529i
$59$	−3.78753	+	1.23064i	−0.493095	+	0.160216i	−0.545000	−	0.838436i	$-0.683470\pi$
$59$	−3.78753	+	1.23064i	−0.493095	+	0.160216i	0.0519057	+	0.998652i	$0.483470\pi$
$60$	28.2210	+	38.8428i	3.64331	+	5.01459i
$61$	−1.44173	−	1.98437i	−0.184595	−	0.254073i	0.706683	−	0.707530i	$-0.250191\pi$
$61$	−1.44173	−	1.98437i	−0.184595	−	0.254073i	−0.891278	+	0.453457i	$0.850191\pi$
$62$	−15.3137	+	4.97572i	−1.94484	+	0.631917i
$63$	0.895481	+	0.290959i	0.112820	+	0.0366574i
$64$	1.22064	+	0.886845i	0.152580	+	0.110856i
$65$	0.897044			0.111265
$66$	23.6409	+	11.7060i	2.90999	+	1.44091i
$67$		−	3.19367i		−	0.390169i	−0.980786	−	0.195084i	$-0.937502\pi$
$67$		−	3.19367i		−	0.390169i	0.980786	−	0.195084i	$-0.0624981\pi$
$68$	−10.6340	+	14.6365i	−1.28957	+	1.77494i
$69$	−11.4980	−	3.73592i	−1.38419	−	0.449752i
$70$	−1.14512	+	0.372070i	−0.136867	+	0.0444709i
$71$	−2.80305	−	3.85807i	−0.332661	−	0.457869i	0.609619	−	0.792695i	$-0.291323\pi$
$71$	−2.80305	−	3.85807i	−0.332661	−	0.457869i	−0.942280	+	0.334826i	$0.891323\pi$
$72$	−33.9865	+	24.6926i	−4.00535	+	2.91006i
$73$	6.35844	−	2.06598i	0.744199	−	0.241805i	0.0877159	−	0.996146i	$-0.472043\pi$
$73$	6.35844	−	2.06598i	0.744199	−	0.241805i	0.656483	+	0.754341i	$0.272043\pi$
$74$	−1.55935	−	0.506663i	−0.181270	−	0.0588983i
$75$	−12.8811	+	17.7293i	−1.48738	+	2.04720i
$76$	17.0517	+	8.95166i	1.95597	+	1.02683i
$77$	−0.318308	+	0.325696i	−0.0362746	+	0.0371165i
$78$			2.06143i			0.233411i
$79$	8.16513	+	5.93231i	0.918649	+	0.667437i	0.943187	−	0.332262i	$-0.107812\pi$
$79$	8.16513	+	5.93231i	0.918649	+	0.667437i	−0.0245386	+	0.999699i	$0.507812\pi$
$80$	7.14935	−	22.0034i	0.799321	−	2.46006i
$81$	5.39207	+	16.5951i	0.599119	+	1.84390i
$82$	−2.16827	+	1.57534i	−0.239446	+	0.173968i
$83$	7.13976	+	9.82703i	0.783690	+	1.07866i	0.994865	+	0.101209i	$0.0322711\pi$
$83$	7.13976	+	9.82703i	0.783690	+	1.07866i	−0.211175	+	0.977448i	$0.567729\pi$
$84$	−0.588589	−	1.81149i	−0.0642203	−	0.197650i
$85$	−13.4793	−	4.37968i	−1.46203	−	0.475043i
$86$	7.32527	−	10.0824i	0.789904	−	1.08721i
$87$		−	20.7932i		−	2.22926i
$88$	−3.40859	−	20.0310i	−0.363357	−	2.13531i
$89$			16.2720i			1.72483i	0.506204	+	0.862414i	$0.331048\pi$
$89$			16.2720i			1.72483i	−0.506204	+	0.862414i	$0.668952\pi$
$90$	−48.6450	−	35.3427i	−5.12764	−	3.72545i
$91$	−0.0338452	−	0.0109970i	−0.00354794	−	0.00115280i
$92$	5.25738	+	16.1806i	0.548120	+	1.68694i
$93$	16.1436	−	11.7290i	1.67401	−	1.21624i
$94$	11.5532	−	8.39387i	1.19162	−	0.865762i
$95$	−2.54153	+	14.8715i	−0.260756	+	1.52578i
$96$	13.9782	+	4.54179i	1.42664	+	0.463545i
$97$	7.26679	−	10.0019i	0.737831	−	1.01554i	−0.260910	−	0.965363i	$-0.584023\pi$
$97$	7.26679	−	10.0019i	0.737831	−	1.01554i	0.998741	−	0.0501736i	$-0.0159775\pi$
$98$	−17.6862			−1.78657
$99$	−22.5019	−	3.29982i	−2.26153	−	0.331645i
$100$	30.8394			3.08394
$101$	4.83489	−	6.65465i	0.481089	−	0.662162i	−0.497625	−	0.867393i	$-0.665794\pi$
$101$	4.83489	−	6.65465i	0.481089	−	0.662162i	0.978714	+	0.205230i	$0.0657943\pi$
$102$	10.0646	−	30.9757i	0.996545	−	3.06705i
$103$	4.80354	−	1.56076i	0.473307	−	0.153787i	−0.0626439	−	0.998036i	$-0.519953\pi$
$103$	4.80354	−	1.56076i	0.473307	−	0.153787i	0.535951	+	0.844249i	$0.319953\pi$
$104$	1.28454	−	0.933272i	0.125959	−	0.0915148i
$105$	1.20717	−	0.877061i	0.117808	−	0.0855924i
$106$	−4.45993	+	1.44912i	−0.433187	+	0.140751i
$107$	2.33626	−	7.19026i	0.225855	−	0.695109i	−0.772349	−	0.635198i	$-0.780918\pi$
$107$	2.33626	−	7.19026i	0.225855	−	0.695109i	0.998204	−	0.0599106i	$-0.0190816\pi$
$108$	31.4492	−	43.2861i	3.02620	−	4.16521i
$109$	−1.97613			−0.189279			−0.0946397	−	0.995512i	$-0.530170\pi$
$109$	−1.97613			−0.189279			−0.0946397	+	0.995512i	$0.530170\pi$
$110$	25.7596	−	13.4996i	2.45608	−	1.28714i
$111$	2.03191			0.192861
$112$	−0.539485	+	0.742538i	−0.0509766	+	0.0701632i
$113$	−8.12560	−	2.64017i	−0.764392	−	0.248366i	−0.0992293	−	0.995065i	$-0.531638\pi$
$113$	−8.12560	−	2.64017i	−0.764392	−	0.248366i	−0.665162	+	0.746699i	$0.731638\pi$
$114$	−34.1750	−	5.84050i	−3.20078	−	0.547013i
$115$	−10.7827	+	7.83406i	−1.00549	+	0.730530i
$116$	−23.6728	+	17.1993i	−2.19797	+	1.59692i
$117$	−0.549175	−	1.69019i	−0.0507713	−	0.156258i
$118$	−9.59542	−	3.11774i	−0.883330	−	0.287011i
$119$	0.454878	+	0.330488i	0.0416986	+	0.0302958i
$120$			66.5748i			6.07742i
$121$	6.25978	−	9.04517i	0.569071	−	0.822288i
$122$		−	6.21402i		−	0.562591i
$123$	1.95229	−	2.68709i	0.176032	−	0.242287i
$124$	−26.7067	−	8.67753i	−2.39833	−	0.779266i
$125$	2.11781	+	6.51794i	0.189423	+	0.582983i
$126$	1.40209	+	1.92981i	0.124908	+	0.171921i
$127$	2.59613	−	1.88620i	0.230369	−	0.167373i	−0.466613	−	0.884462i	$-0.654526\pi$
$127$	2.59613	−	1.88620i	0.230369	−	0.167373i	0.696982	+	0.717089i	$0.254526\pi$
$128$	4.07441	+	12.5397i	0.360130	+	1.10837i
$129$	−4.77261	+	14.6886i	−0.420204	+	1.29326i
$130$	1.83857	+	1.33580i	0.161253	+	0.117157i
$131$			5.53155i			0.483294i	0.970364	+	0.241647i	$0.0776875\pi$
$131$			5.53155i			0.483294i	−0.970364	+	0.241647i	$0.922312\pi$
$132$	21.3554	+	40.7499i	1.85875	+	3.54682i
$133$	0.278203	−	0.529940i	0.0241232	−	0.0459516i
$134$	4.75572	−	6.54569i	0.410832	−	0.565461i
$135$	39.8638	+	12.9525i	3.43093	+	1.11478i
$136$	−23.8585	+	7.75208i	−2.04585	+	0.664736i
$137$	11.0885	−	8.05627i	0.947354	−	0.688293i	−0.00282525	−	0.999996i	$-0.500899\pi$
$137$	11.0885	−	8.05627i	0.947354	−	0.688293i	0.950180	+	0.311703i	$0.100899\pi$
$138$	−18.0028	−	24.7788i	−1.53250	−	2.10931i
$139$	17.9454	−	5.83081i	1.52211	−	0.494563i	0.575734	−	0.817637i	$-0.304716\pi$
$139$	17.9454	−	5.83081i	1.52211	−	0.494563i	0.946374	+	0.323075i	$0.104716\pi$
$140$	−1.99705	−	0.648882i	−0.168782	−	0.0548405i
$141$	−10.4023	+	14.3176i	−0.876034	+	1.20576i
$142$		−	12.0815i		−	1.01386i
$143$	0.850473	+	0.124719i	0.0711202	+	0.0104295i
$144$	−45.8352			−3.81960
$145$	−18.5452	−	13.4739i	−1.54009	−	1.11894i
$146$	16.1086	+	5.23401i	1.33316	+	0.433169i
$147$	20.8453	−	6.77306i	1.71929	−	0.558632i
$148$	−1.68072	−	2.31331i	−0.138154	−	0.190153i
$149$	3.60881	+	4.96711i	0.295646	+	0.406921i	0.930838	−	0.365433i	$-0.119079\pi$
$149$	3.60881	+	4.96711i	0.295646	+	0.406921i	−0.635192	+	0.772354i	$0.719079\pi$
$150$	−52.8017	+	17.1563i	−4.31124	+	1.40081i
$151$	0.366675	−	1.12851i	0.0298396	−	0.0918369i	−0.935028	−	0.354575i	$-0.884626\pi$
$151$	0.366675	−	1.12851i	0.0298396	−	0.0918369i	0.964867	+	0.262738i	$0.0846255\pi$
$152$	11.8327	+	23.9397i	0.959759	+	1.94176i
$153$			28.0786i			2.27002i
$154$	−1.13740	+	0.193545i	−0.0916539	+	0.0155963i
$155$		−	21.9986i		−	1.76697i
$156$	−2.11314	+	2.90848i	−0.169186	+	0.232865i
$157$	−6.30677	+	19.4102i	−0.503335	+	1.54911i	0.300216	+	0.953871i	$0.402941\pi$
$157$	−6.30677	+	19.4102i	−0.503335	+	1.54911i	−0.803552	+	0.595235i	$0.797059\pi$
$158$	7.90124	+	24.3175i	0.628589	+	1.93460i
$159$	4.70162	−	3.41593i	0.372863	−	0.270901i
$160$	13.1086	−	9.52394i	1.03632	−	0.752934i
$161$	0.502865	−	0.163391i	0.0396313	−	0.0128770i
$162$	−13.6604	+	42.0424i	−1.07326	+	3.30316i
$163$	−17.1594	−	12.4671i	−1.34403	−	0.976495i	−0.999285	−	0.0377991i	$-0.987965\pi$
$163$	−17.1594	−	12.4671i	−1.34403	−	0.976495i	−0.344745	−	0.938696i	$-0.612035\pi$
$164$	−4.67409			−0.364985
$165$	−25.1911	+	25.7758i	−1.96112	+	2.00664i
$166$			30.7732i			2.38846i
$167$	3.81181	+	2.76944i	0.294967	+	0.214306i	0.725419	−	0.688308i	$-0.241646\pi$
$167$	3.81181	+	2.76944i	0.294967	+	0.214306i	−0.430453	+	0.902613i	$0.641646\pi$
$168$	0.816148	−	2.51185i	0.0629672	−	0.193793i
$169$	−3.99646	−	12.2999i	−0.307420	−	0.946143i
$170$	−21.1051	−	29.0486i	−1.61868	−	2.22793i
$171$	29.5764	−	4.31572i	2.26177	−	0.330031i
$172$	20.6705	−	6.71627i	1.57611	−	0.512110i
$173$	6.90606	−	21.2547i	0.525058	−	1.61596i	−0.239143	−	0.970984i	$-0.576867\pi$
$173$	6.90606	−	21.2547i	0.525058	−	1.61596i	0.764201	−	0.644978i	$-0.223133\pi$
$174$	30.9633	−	42.6173i	2.34732	−	3.23081i
$175$		−	0.958438i		−	0.0724511i
$176$	9.83738	−	19.8671i	0.741521	−	1.49754i
$177$	12.5033			0.939808
$178$	−24.2308	+	33.3508i	−1.81617	+	2.49975i
$179$	−7.47523	−	2.42885i	−0.558725	−	0.181541i	0.0160223	−	0.999872i	$-0.494900\pi$
$179$	−7.47523	−	2.42885i	−0.558725	−	0.181541i	−0.574748	+	0.818331i	$0.694900\pi$
$180$	−32.4044	−	99.7304i	−2.41528	−	7.43347i
$181$	10.6500	+	14.6584i	0.791605	+	1.08955i	0.993906	+	0.110228i	$0.0351580\pi$
$181$	10.6500	+	14.6584i	0.791605	+	1.08955i	−0.202301	+	0.979323i	$0.564842\pi$
$182$	−0.0529928	−	0.0729383i	−0.00392809	−	0.00540655i
$183$	2.37971	+	7.32398i	0.175913	+	0.541404i
$184$	−7.28998	+	22.4363i	−0.537425	+	1.65402i
$185$	1.31667	−	1.81224i	0.0968035	−	0.133239i
$186$	50.5533			3.70674
$187$	−12.1706	−	6.02637i	−0.890000	−	0.440692i
$188$	24.9049			1.81637
$189$	−1.34526	−	0.977389i	−0.0978533	−	0.0710946i
$190$	−27.3543	+	26.6957i	−1.98449	+	1.93671i
$191$	−1.25378	−	3.85874i	−0.0907203	−	0.279208i	0.895394	−	0.445274i	$-0.146894\pi$
$191$	−1.25378	−	3.85874i	−0.0907203	−	0.279208i	−0.986115	+	0.166065i	$0.946894\pi$
$192$	−2.78435	−	3.83232i	−0.200943	−	0.276574i
$193$	−2.58040	+	1.87477i	−0.185741	+	0.134949i	−0.676770	−	0.736194i	$-0.736621\pi$
$193$	−2.58040	+	1.87477i	−0.185741	+	0.134949i	0.491029	+	0.871143i	$0.336621\pi$
$194$	29.7878	−	9.67863i	2.13864	−	0.694885i
$195$	−2.67853	−	0.870306i	−0.191813	−	0.0623239i
$196$	−24.9536	−	18.1298i	−1.78240	−	1.29499i
$197$			13.4581i			0.958847i	0.877584	+	0.479423i	$0.159154\pi$
$197$			13.4581i			0.958847i	−0.877584	+	0.479423i	$0.840846\pi$
$198$	−41.2058	−	40.2711i	−2.92837	−	2.86194i
$199$	0.583285			0.0413480			0.0206740	−	0.999786i	$-0.493419\pi$
$199$	0.583285			0.0413480			0.0206740	+	0.999786i	$0.493419\pi$
$200$	34.5956	+	25.1352i	2.44628	+	1.77732i
$201$	−3.09848	+	9.53613i	−0.218550	+	0.672627i
$202$	19.8190	−	6.43958i	1.39446	−	0.453087i
$203$	0.534527	+	0.735713i	0.0375164	+	0.0516369i
$204$	45.9529	−	33.3867i	3.21735	−	2.33754i
$205$	−1.13152	−	3.48245i	−0.0790285	−	0.243225i
$206$	12.1694	+	3.95408i	0.847882	+	0.275494i
$207$	21.3619	+	15.5204i	1.48476	+	1.07874i
$208$	1.73237			0.120118
$209$	−4.47721	+	13.7461i	−0.309695	+	0.950836i
$210$	3.78023			0.260861
$211$	13.7731	+	10.0067i	0.948177	+	0.688891i	0.950375	−	0.311107i	$-0.100700\pi$
$211$	13.7731	+	10.0067i	0.948177	+	0.688891i	−0.00219837	+	0.999998i	$0.500700\pi$
$212$	−7.77802	−	2.52723i	−0.534196	−	0.173571i
$213$	4.62670	+	14.2395i	0.317016	+	0.975675i
$214$	15.4954	−	11.2581i	1.05925	−	0.769587i
$215$	10.0080	+	13.7748i	0.682537	+	0.939431i
$216$	70.5593	−	22.9261i	4.80095	−	1.55992i
$217$	−0.269683	+	0.830000i	−0.0183073	+	0.0563441i
$218$	−4.05025	−	2.94268i	−0.274317	−	0.199303i
$219$	−20.9904			−1.41840
$220$	50.1826	+	7.35909i	3.38331	+	0.496150i
$221$		−	1.06125i		−	0.0713871i
$222$	4.16457	+	3.02574i	0.279508	+	0.203074i
$223$	−18.6029	−	6.04446i	−1.24574	−	0.404767i	−0.389350	−	0.921090i	$-0.627300\pi$
$223$	−18.6029	−	6.04446i	−1.24574	−	0.404767i	−0.856394	+	0.516323i	$0.827300\pi$
$224$	−0.611338	+	0.198636i	−0.0408467	+	0.0132719i
$225$	38.7222	−	28.1333i	2.58148	−	1.87555i
$226$	−12.7226	−	17.5111i	−0.846293	−	1.16482i
$227$	2.23626	+	6.88251i	0.148426	+	0.456809i	0.997436	−	0.0715689i	$-0.0228006\pi$
$227$	2.23626	+	6.88251i	0.148426	+	0.456809i	−0.849010	+	0.528377i	$0.822801\pi$
$228$	−42.2308	−	43.2727i	−2.79680	−	2.86580i
$229$	20.7371	+	15.0664i	1.37035	+	0.995615i	0.997710	+	0.0676368i	$0.0215459\pi$
$229$	20.7371	+	15.0664i	1.37035	+	0.995615i	0.372636	+	0.927978i	$0.378454\pi$
$230$	−33.7657			−2.22645
$231$	1.26644	−	0.663691i	0.0833256	−	0.0436677i
$232$	−40.5741			−2.66382
$233$	6.44904	−	8.87635i	0.422491	−	0.581509i	−0.543718	−	0.839268i	$-0.682984\pi$
$233$	6.44904	−	8.87635i	0.422491	−	0.581509i	0.966209	+	0.257759i	$0.0829840\pi$
$234$	1.39129	−	4.28196i	0.0909517	−	0.279920i
$235$	6.02903	+	18.5555i	0.393291	+	1.21042i
$236$	−10.3423	−	14.2349i	−0.673226	−	0.926616i
$237$	−18.6252	−	25.6353i	−1.20983	−	1.66519i
$238$	0.440177	+	1.35472i	0.0285324	+	0.0878138i
$239$	−12.5889	−	4.09037i	−0.814306	−	0.264584i	−0.127885	−	0.991789i	$-0.540819\pi$
$239$	−12.5889	−	4.09037i	−0.814306	−	0.264584i	−0.686420	+	0.727205i	$0.740819\pi$
$240$	−42.6952	+	58.7648i	−2.75596	+	3.79325i
$241$	−29.5672			−1.90459			−0.952297	−	0.305173i	$-0.901286\pi$
$241$	−29.5672			−1.90459			−0.952297	+	0.305173i	$0.901286\pi$
$242$	26.2992	−	9.21733i	1.69057	−	0.592512i
$243$		−	18.4535i		−	1.18379i
$244$	6.36989	−	8.76740i	0.407791	−	0.561276i
$245$	7.46686	−	22.9806i	0.477040	−	1.46818i
$246$	8.00274	−	2.60025i	0.510236	−	0.165786i
$247$	−1.11786	+	0.163115i	−0.0711276	+	0.0103788i
$248$	−22.8870	−	31.5013i	−1.45333	−	2.00033i
$249$	−11.7848	−	36.2700i	−0.746833	−	2.29851i
$250$	−5.36530	+	16.5127i	−0.339332	+	1.04436i
$251$	−11.2645	−	8.18410i	−0.711006	−	0.516576i	0.172492	−	0.985011i	$-0.444818\pi$
$251$	−11.2645	−	8.18410i	−0.711006	−	0.516576i	−0.883498	+	0.468435i	$0.844818\pi$
$252$			4.16005i			0.262058i
$253$	−11.3121	+	5.92821i	−0.711183	+	0.372703i
$254$	8.12972			0.510104
$255$	35.9993	+	26.1550i	2.25436	+	1.63789i
$256$	−9.38971	+	28.8985i	−0.586857	+	1.80616i
$257$	−1.11705	+	0.362951i	−0.0696796	+	0.0226403i	−0.343649	−	0.939098i	$-0.611663\pi$
$257$	−1.11705	+	0.362951i	−0.0696796	+	0.0226403i	0.273970	+	0.961738i	$0.411663\pi$
$258$	−31.6547	+	22.9985i	−1.97074	+	1.43182i
$259$	−0.0718940	+	0.0522340i	−0.00446728	+	0.00324567i
$260$	1.22474	+	3.76937i	0.0759552	+	0.233766i
$261$	−14.0337	+	43.1912i	−0.868662	+	2.67347i
$262$	−8.23707	+	11.3374i	−0.508888	+	0.700424i
$263$			21.0000i			1.29492i	0.762101	+	0.647459i	$0.224168\pi$
$263$			21.0000i			1.29492i	−0.762101	+	0.647459i	$0.775832\pi$
$264$	−9.25608	+	63.1185i	−0.569672	+	3.88468i
$265$		−	6.40684i		−	0.393569i
$266$	1.35934	−	0.671881i	0.0833463	−	0.0411957i
$267$	15.7870	−	48.5873i	0.966147	−	2.97350i
$268$	13.4198	−	4.36034i	0.819742	−	0.266350i
$269$	−0.530513	−	0.730189i	−0.0323460	−	0.0445204i	0.792538	−	0.609823i	$-0.208759\pi$
$269$	−0.530513	−	0.730189i	−0.0323460	−	0.0445204i	−0.824884	+	0.565303i	$0.808759\pi$
$270$	62.4163	+	85.9087i	3.79854	+	5.22824i
$271$	−18.7748	+	6.10030i	−1.14049	+	0.370567i	−0.817552	−	0.575855i	$-0.804669\pi$
$271$	−18.7748	+	6.10030i	−1.14049	+	0.370567i	−0.322935	+	0.946421i	$0.604669\pi$
$272$	−26.0311	−	8.45801i	−1.57837	−	0.512842i
$273$	0.0903908	+	0.0656727i	0.00547070	+	0.00397470i
$274$	34.7234			2.09772
$275$	3.88354	+	22.8221i	0.234186	+	1.37623i
$276$		−	53.4150i		−	3.21520i
$277$	2.49124	−	3.42890i	0.149684	−	0.206023i	−0.727590	−	0.686012i	$-0.759360\pi$
$277$	2.49124	−	3.42890i	0.149684	−	0.206023i	0.877274	+	0.479990i	$0.159360\pi$
$278$	45.4632	+	14.7719i	2.72670	+	0.885960i
$279$	−41.4492	+	13.4677i	−2.48150	+	0.806288i
$280$	−1.71143	−	2.35558i	−0.102277	−	0.140773i
$281$	5.32765	−	3.87076i	0.317821	−	0.230910i	−0.417424	−	0.908712i	$-0.637067\pi$
$281$	5.32765	−	3.87076i	0.317821	−	0.230910i	0.735245	+	0.677801i	$0.237067\pi$
$282$	−42.6408	+	13.8548i	−2.53922	+	0.825044i
$283$	−20.6965	−	6.72471i	−1.23028	−	0.399743i	−0.379465	−	0.925206i	$-0.623892\pi$
$283$	−20.6965	−	6.72471i	−1.23028	−	0.399743i	−0.850816	+	0.525463i	$0.823892\pi$
$284$	12.3845	−	17.0458i	0.734887	−	1.01148i
$285$	22.0171	−	41.9397i	1.30418	−	2.48430i
$286$	1.55740	+	1.52207i	0.0920907	+	0.0900018i
$287$			0.145263i			0.00857461i
$288$	−25.9699	−	18.8682i	−1.53029	−	1.11182i
$289$	0.0719172	−	0.221339i	0.00423043	−	0.0130199i
$290$	−17.9458	−	55.2316i	−1.05382	−	3.24331i
$291$	−31.4020	+	22.8149i	−1.84082	+	1.33743i
$292$	17.3625	+	23.8974i	1.01606	+	1.39849i
$293$	3.58892	+	11.0456i	0.209667	+	0.645289i	0.999489	+	0.0319529i	$0.0101727\pi$
$293$	3.58892	+	11.0456i	0.209667	+	0.645289i	−0.789822	+	0.613336i	$0.789827\pi$
$294$	52.8100	+	17.1590i	3.07994	+	1.00073i
$295$	8.10210	−	11.1516i	0.471723	−	0.649271i
$296$		−	3.96491i		−	0.230456i
$297$	35.9934	+	17.8225i	2.08855	+	1.03416i
$298$			15.5544i			0.901042i
$299$	−0.807387	−	0.586601i	−0.0466924	−	0.0339240i
$300$	−92.0849	−	29.9202i	−5.31652	−	1.72744i
$301$	−0.208730	−	0.642406i	−0.0120310	−	0.0370277i
$302$	2.43201	−	1.76696i	0.139946	−	0.101677i
$303$	−20.8930	+	15.1797i	−1.20027	+	0.872049i
$304$	−4.90819	+	28.7197i	−0.281504	+	1.64719i
$305$	8.07422	+	2.62347i	0.462329	+	0.150220i
$306$	−41.8120	+	57.5493i	−2.39024	+	3.28988i
$307$	17.3462			0.989999			0.494999	−	0.868893i	$-0.335168\pi$
$307$	17.3462			0.989999			0.494999	+	0.868893i	$0.335168\pi$
$308$	−1.80316	−	0.892851i	−0.102745	−	0.0508749i
$309$	−15.8574			−0.902094
$310$	32.7583	−	45.0879i	1.86055	−	2.56082i
$311$	2.26863	−	6.98212i	0.128642	−	0.395920i	−0.865905	−	0.500209i	$-0.833257\pi$
$311$	2.26863	−	6.98212i	0.128642	−	0.395920i	0.994547	+	0.104289i	$0.0332566\pi$
$312$	−4.74102	+	1.54045i	−0.268407	+	0.0872108i
$313$	20.4512	−	14.8587i	1.15597	−	0.839861i	0.166707	−	0.986007i	$-0.446687\pi$
$313$	20.4512	−	14.8587i	1.15597	−	0.839861i	0.989263	+	0.146145i	$0.0466867\pi$
$314$	−41.8302	+	30.3914i	−2.36061	+	1.71509i
$315$	−3.09946	+	1.00707i	−0.174635	+	0.0567422i
$316$	−13.7796	+	42.4092i	−0.775162	+	2.38570i
$317$	15.5122	−	21.3507i	0.871253	−	1.19918i	−0.107515	−	0.994203i	$-0.534289\pi$
$317$	15.5122	−	21.3507i	0.871253	−	1.19918i	0.978768	−	0.204973i	$-0.0657106\pi$
$318$	14.7230			0.825628
$319$	−15.7091	−	15.3528i	−0.879540	−	0.859589i
$320$	−5.22225			−0.291933
$321$	−13.9519	+	19.2031i	−0.778718	+	1.07181i
$322$	1.27397	+	0.413938i	0.0709956	+	0.0230679i
$323$	17.5937	+	3.00675i	0.978939	+	0.167300i
$324$	−62.3705	+	45.3148i	−3.46503	+	2.51749i
$325$	−1.46353	+	1.06331i	−0.0811818	+	0.0589821i
$326$	−16.6049	−	51.1045i	−0.919658	−	2.83042i
$327$	5.90063	+	1.91723i	0.326306	+	0.106023i
$328$	−5.24338	−	3.80954i	−0.289517	−	0.210347i
$329$		−	0.774002i		−	0.0426721i
$330$	−90.0141	+	15.3173i	−4.95511	+	0.843189i
$331$		−	6.11365i		−	0.336037i	−0.985784	−	0.168018i	$-0.946263\pi$
$331$		−	6.11365i		−	0.336037i	0.985784	−	0.168018i	$-0.0537368\pi$
$332$	−31.5451	+	43.4181i	−1.73126	+	2.38288i
$333$	−4.22065	−	1.37137i	−0.231290	−	0.0751507i
$334$	3.68861	+	11.3524i	0.201832	+	0.621175i
$335$	6.49738	+	8.94287i	0.354990	+	0.488601i
$336$	2.33128	−	1.69377i	0.127182	−	0.0924029i
$337$	−6.80589	−	20.9464i	−0.370740	−	1.14102i	−0.946308	−	0.323267i	$-0.895219\pi$
$337$	−6.80589	−	20.9464i	−0.370740	−	1.14102i	0.575568	−	0.817754i	$-0.304781\pi$
$338$	10.1247	−	31.1607i	0.550713	−	1.69492i
$339$	21.7011	+	15.7668i	1.17864	+	0.856335i
$340$		−	62.6193i		−	3.39601i
$341$	3.05853	−	20.8565i	0.165629	−	1.12944i
$342$	67.0459	+	35.1971i	3.62543	+	1.90324i
$343$	−1.12841	+	1.55312i	−0.0609285	+	0.0838609i
$344$	28.6621	+	9.31289i	1.54536	+	0.502118i
$345$	39.7970	−	12.9308i	2.14260	−	0.696173i
$346$	45.8050	−	33.2793i	2.46249	−	1.78911i
$347$	−3.95178	−	5.43916i	−0.212143	−	0.291989i	0.689664	−	0.724130i	$-0.257758\pi$
$347$	−3.95178	−	5.43916i	−0.212143	−	0.291989i	−0.901806	+	0.432141i	$0.857758\pi$
$348$	87.3725	−	28.3890i	4.68366	−	1.52181i
$349$	0.0799057	+	0.0259629i	0.00427725	+	0.00138976i	0.311155	−	0.950359i	$-0.399284\pi$
$349$	0.0799057	+	0.0259629i	0.00427725	+	0.00138976i	−0.306878	+	0.951749i	$0.599284\pi$
$350$	1.42722	−	1.96440i	0.0762880	−	0.105001i
$351$			3.13854i			0.167523i
$352$	13.7522	−	7.20698i	0.732994	−	0.384133i
$353$	15.7503			0.838301			0.419151	−	0.907917i	$-0.362328\pi$
$353$	15.7503			0.838301			0.419151	+	0.907917i	$0.362328\pi$
$354$	25.6266	+	18.6188i	1.36204	+	0.989579i
$355$	15.6981	+	5.10064i	0.833171	+	0.270714i
$356$	−68.3747	+	22.2163i	−3.62385	+	1.17746i
$357$	−1.03760	−	1.42814i	−0.0549158	−	0.0755852i
$358$	−11.7043	−	16.1096i	−0.618590	−	0.851417i
$359$	−32.0198	+	10.4039i	−1.68994	+	0.549095i	−0.986798	−	0.161954i	$-0.948221\pi$
$359$	−32.0198	+	10.4039i	−1.68994	+	0.549095i	−0.703143	+	0.711049i	$0.748221\pi$
$360$	44.9325	−	138.288i	2.36815	−	7.28841i
$361$	0.462972	−	18.9944i	0.0243670	−	0.999703i
$362$			45.9025i			2.41258i
$363$	−27.4669	+	20.9352i	−1.44164	+	1.09881i
$364$		−	0.157231i		−	0.00824116i
$365$	−13.6017	+	18.7211i	−0.711944	+	0.979907i
$366$	−6.02880	+	18.5547i	−0.315130	+	0.969872i
$367$	−5.88525	−	18.1129i	−0.307207	−	0.945487i	−0.978844	−	0.204607i	$-0.934408\pi$
$367$	−5.88525	−	18.1129i	−0.307207	−	0.945487i	0.671637	−	0.740880i	$-0.265592\pi$
$368$	−20.8234	+	15.1291i	−1.08549	+	0.788658i
$369$	−5.86882	+	4.26395i	−0.305519	+	0.221972i
$370$	5.39724	−	1.75367i	0.280589	−	0.0911690i
$371$	−0.0785421	+	0.241728i	−0.00407770	+	0.0125499i
$372$	71.3259	+	51.8213i	3.69808	+	2.68681i
$373$	−11.2690			−0.583487			−0.291744	−	0.956497i	$-0.594235\pi$
$373$	−11.2690			−0.583487			−0.291744	+	0.956497i	$0.594235\pi$
$374$	−15.9707	−	30.4748i	−0.825823	−	1.57582i
$375$		−	21.5169i		−	1.11113i
$376$	27.9382	+	20.2983i	1.44080	+	1.04680i
$377$	0.530410	−	1.63243i	0.0273175	−	0.0840746i
$378$	−1.30178	−	4.00648i	−0.0669565	−	0.206071i
$379$	10.5585	+	14.5325i	0.542353	+	0.746484i	0.988950	−	0.148251i	$-0.0473643\pi$
$379$	10.5585	+	14.5325i	0.542353	+	0.746484i	−0.446597	+	0.894735i	$0.647364\pi$
$380$	−65.9598	+	9.62469i	−3.38367	+	0.493736i
$381$	−9.58187	+	3.11334i	−0.490894	+	0.159501i
$382$	3.17635	−	9.77581i	0.162516	−	0.500174i
$383$	−19.5048	+	26.8461i	−0.996649	+	1.37177i	−0.0692905	+	0.997597i	$0.522074\pi$
$383$	−19.5048	+	26.8461i	−0.996649	+	1.37177i	−0.927359	+	0.374173i	$0.877926\pi$
$384$		−	41.3959i		−	2.11248i
$385$	0.228708	−	1.55959i	0.0116561	−	0.0794842i
$386$	−8.08048			−0.411286
$387$	19.8271	−	27.2897i	1.00787	−	1.38721i
$388$	51.9491	+	16.8793i	2.63732	+	0.856916i
$389$	0.646913	+	1.99099i	0.0327998	+	0.100947i	0.966116	−	0.258108i	$-0.0830990\pi$
$389$	0.646913	+	1.99099i	0.0327998	+	0.100947i	−0.933316	+	0.359055i	$0.883099\pi$
$390$	−4.19388	−	5.77238i	−0.212365	−	0.292296i
$391$	9.26807	+	12.7564i	0.468706	+	0.645119i
$392$	−13.2164	−	40.6760i	−0.667530	−	2.05445i
$393$	5.36667	−	16.5169i	0.270713	−	0.833168i
$394$	−20.0405	+	27.5834i	−1.00963	+	1.38963i
$395$	−34.9329			−1.75766
$396$	−16.8563	−	99.0581i	−0.847060	−	4.97786i
$397$	11.2696			0.565604			0.282802	−	0.959178i	$-0.408736\pi$
$397$	11.2696			0.565604			0.282802	+	0.959178i	$0.408736\pi$
$398$	1.19549	+	0.868575i	0.0599245	+	0.0435377i
$399$	−1.34484	+	1.31246i	−0.0673263	+	0.0657053i
$400$	14.4177	+	44.3731i	0.720884	+	2.21865i
$401$	14.8992	+	20.5070i	0.744032	+	1.02407i	0.998377	+	0.0569586i	$0.0181403\pi$
$401$	14.8992	+	20.5070i	0.744032	+	1.02407i	−0.254344	+	0.967114i	$0.581860\pi$
$402$	−20.5509	+	14.9311i	−1.02499	+	0.744696i
$403$	1.56660	−	0.509018i	0.0780377	−	0.0253560i
$404$	34.5638	+	11.2305i	1.71962	+	0.558737i
$405$	−48.8607	−	35.4994i	−2.42791	−	1.76398i
$406$			2.30387i			0.114339i
$407$	1.50027	−	1.53510i	0.0743659	−	0.0760919i
$408$	78.7611			3.89926
$409$	−16.3659	−	11.8905i	−0.809243	−	0.587949i	0.104368	−	0.994539i	$-0.466718\pi$
$409$	−16.3659	−	11.8905i	−0.809243	−	0.587949i	−0.913611	+	0.406589i	$0.866718\pi$
$410$	2.86661	−	8.82251i	0.141572	−	0.435713i
$411$	−40.9258	+	13.2976i	−2.01872	+	0.655922i
$412$	13.1166	+	18.0535i	0.646209	+	0.889431i
$413$	−0.442398	+	0.321421i	−0.0217690	+	0.0158161i
$414$	20.6716	+	63.6205i	1.01595	+	3.12678i
$415$	−39.9853	−	12.9920i	−1.96280	−	0.637753i
$416$	0.981547	+	0.713136i	0.0481243	+	0.0349644i
$417$	−59.2410			−2.90104
$418$	−29.6458	+	21.5066i	−1.45002	+	1.05192i
$419$	−29.7251			−1.45217			−0.726084	−	0.687606i	$-0.758661\pi$
$419$	−29.7251			−1.45217			−0.726084	+	0.687606i	$0.758661\pi$
$420$	5.33356	+	3.87505i	0.260251	+	0.189083i
$421$	21.0100	+	6.82655i	1.02396	+	0.332706i	0.772401	−	0.635136i	$-0.219056\pi$
$421$	21.0100	+	6.82655i	1.02396	+	0.332706i	0.251562	+	0.967841i	$0.419056\pi$
$422$	13.3279	+	41.0192i	0.648793	+	1.99678i
$423$	31.2707	−	22.7195i	1.52043	−	1.10466i
$424$	−6.66558	−	9.17438i	−0.323709	−	0.445547i
$425$	27.1829	−	8.83226i	1.31856	−	0.428427i
$426$	−11.7214	+	36.0747i	−0.567902	+	1.74782i
$427$	−0.272476	−	0.197966i	−0.0131861	−	0.00958023i
$428$	33.4031			1.61460
$429$	−2.41847	−	1.19753i	−0.116765	−	0.0578171i
$430$			43.1354i			2.08018i
$431$	−8.96290	−	6.51192i	−0.431727	−	0.313668i	0.350612	−	0.936521i	$-0.385974\pi$
$431$	−8.96290	−	6.51192i	−0.431727	−	0.313668i	−0.782339	+	0.622853i	$0.785974\pi$
$432$	76.9846	+	25.0138i	3.70392	+	1.20348i
$433$	6.60592	−	2.14639i	0.317460	−	0.103149i	−0.145953	−	0.989292i	$-0.546625\pi$
$433$	6.60592	−	2.14639i	0.317460	−	0.103149i	0.463413	+	0.886142i	$0.346625\pi$
$434$	−1.78870	+	1.29957i	−0.0858603	+	0.0623811i
$435$	42.3027	+	58.2247i	2.02826	+	2.79166i
$436$	−2.69803	−	8.30369i	−0.129212	−	0.397674i
$437$	12.0124	−	11.7231i	0.574630	−	0.560794i
$438$	−43.0215	−	31.2569i	−2.05565	−	1.49351i
$439$	10.1663			0.485210			0.242605	−	0.970125i	$-0.421998\pi$
$439$	10.1663			0.485210			0.242605	+	0.970125i	$0.421998\pi$
$440$	50.2968	+	49.1559i	2.39781	+	2.34342i
$441$	−47.8708			−2.27956
$442$	1.58031	−	2.17511i	0.0751677	−	0.103459i
$443$	−3.11987	+	9.60196i	−0.148229	+	0.456203i	−0.997412	−	0.0718960i	$-0.977095\pi$
$443$	−3.11987	+	9.60196i	−0.148229	+	0.456203i	0.849183	+	0.528099i	$0.177095\pi$
$444$	2.77418	+	8.53806i	0.131657	+	0.405198i
$445$	−33.1046	−	45.5646i	−1.56931	−	2.15997i
$446$	−29.1274	−	40.0904i	−1.37922	−	1.89833i
$447$	−5.95668	−	18.3328i	−0.281741	−	0.867110i
$448$	0.197034	+	0.0640202i	0.00930898	+	0.00302467i
$449$	8.18624	−	11.2674i	0.386333	−	0.531741i	−0.570916	−	0.821009i	$-0.693412\pi$
$449$	8.18624	−	11.2674i	0.386333	−	0.531741i	0.957248	+	0.289268i	$0.0934117\pi$
$450$	121.258			5.71615
$451$	−0.588598	−	3.45897i	−0.0277160	−	0.162877i
$452$		−	37.7483i		−	1.77553i
$453$	−2.18975	+	3.01393i	−0.102883	+	0.141607i
$454$	−5.66540	+	17.4363i	−0.265891	+	0.818327i
$455$	0.117146	−	0.0380629i	0.00549187	−	0.00178442i
$456$	−12.1057	−	82.9626i	−0.566901	−	3.88508i
$457$	−1.41642	−	1.94953i	−0.0662572	−	0.0911952i	0.774602	−	0.632449i	$-0.217950\pi$
$457$	−1.41642	−	1.94953i	−0.0662572	−	0.0911952i	−0.840860	+	0.541253i	$0.817950\pi$
$458$	20.0669	+	61.7596i	0.937664	+	2.88583i
$459$	15.3234	−	47.1607i	0.715237	−	2.20127i
$460$	−47.6403	−	34.6127i	−2.22124	−	1.61382i
$461$		−	11.1812i		−	0.520763i	−0.965506	−	0.260381i	$-0.916152\pi$
$461$		−	11.1812i		−	0.520763i	0.965506	−	0.260381i	$-0.0838483\pi$
$462$	3.58398	+	0.525576i	0.166742	+	0.0244520i
$463$	26.0577			1.21100			0.605501	−	0.795845i	$-0.292973\pi$
$463$	26.0577			1.21100			0.605501	+	0.795845i	$0.292973\pi$
$464$	−35.8144	−	26.0206i	−1.66264	−	1.20798i
$465$	−21.3429	+	65.6867i	−0.989753	+	3.04615i
$466$	26.4357	−	8.58947i	1.22461	−	0.397900i
$467$	−12.4728	+	9.06203i	−0.577173	+	0.419341i	−0.837704	−	0.546125i	$-0.816102\pi$
$467$	−12.4728	+	9.06203i	−0.577173	+	0.419341i	0.260531	+	0.965466i	$0.416102\pi$
$468$	6.35235	−	4.61525i	0.293637	−	0.213340i
$469$	−0.135512	−	0.417064i	−0.00625737	−	0.0192582i
$470$	−15.2741	+	47.0088i	−0.704541	+	2.16835i
$471$	37.6634	−	51.8392i	1.73544	−	2.38862i
$472$		−	24.3980i		−	1.12301i
$473$	7.57324	+	14.4511i	0.348218	+	0.664461i
$474$		−	80.2765i		−	3.68722i
$475$	−13.4815	−	27.2754i	−0.618572	−	1.25148i
$476$	−0.767658	+	2.36261i	−0.0351855	+	0.108290i
$477$	−12.0716	+	3.92230i	−0.552720	+	0.179590i
$478$	−19.7109	−	27.1297i	−0.901555	−	1.24088i
$479$	−16.3369	−	22.4859i	−0.746454	−	1.02741i	−0.998221	−	0.0596179i	$-0.981012\pi$
$479$	−16.3369	−	22.4859i	−0.746454	−	1.02741i	0.251767	−	0.967788i	$-0.418988\pi$
$480$	−48.3816	+	15.7201i	−2.20831	+	0.717523i
$481$	0.159522	+	0.0518318i	0.00727357	+	0.00236333i
$482$	−60.6005	−	44.0288i	−2.76028	−	2.00546i
$483$	−1.66005			−0.0755349
$484$	46.5542	+	13.9541i	2.11610	+	0.634276i
$485$			42.7911i			1.94304i
$486$	27.4793	−	37.8220i	1.24649	−	1.71564i
$487$	35.2338	+	11.4482i	1.59660	+	0.518766i	0.966263	−	0.257559i	$-0.0829181\pi$
$487$	35.2338	+	11.4482i	1.59660	+	0.518766i	0.630334	+	0.776324i	$0.282918\pi$
$488$	14.2915	−	4.64357i	0.646944	−	0.210205i
$489$	39.1417	+	53.8739i	1.77005	+	2.43626i
$490$	49.5246	−	35.9817i	2.23729	−	1.62549i
$491$	−9.91341	+	3.22106i	−0.447386	+	0.145364i	−0.524041	−	0.851693i	$-0.675576\pi$
$491$	−9.91341	+	3.22106i	−0.447386	+	0.145364i	0.0766549	+	0.997058i	$0.475576\pi$
$492$	13.9566	+	4.53477i	0.629212	+	0.204443i
$493$	−15.9402	+	21.9398i	−0.717912	+	0.988121i
$494$	−2.53404	−	1.33029i	−0.114012	−	0.0598527i
$495$	69.7230	−	36.5391i	3.13381	−	1.64231i
$496$		−	42.4835i		−	1.90757i
$497$	−0.529757	−	0.384891i	−0.0237628	−	0.0172647i
$498$	29.8559	−	91.8871i	1.33788	−	4.11756i
$499$	0.191324	+	0.588835i	0.00856485	+	0.0263599i	0.955248	−	0.295807i	$-0.0955887\pi$
$499$	0.191324	+	0.588835i	0.00856485	+	0.0263599i	−0.946683	+	0.322167i	$0.895589\pi$
$500$	−24.4968	+	17.7980i	−1.09553	+	0.795951i
$501$	−8.69496	−	11.9676i	−0.388462	−	0.534673i
$502$	−10.9004	−	33.5480i	−0.486509	−	1.49732i
$503$	21.5933	+	7.01609i	0.962798	+	0.312832i	0.747905	−	0.663805i	$-0.231060\pi$
$503$	21.5933	+	7.01609i	0.962798	+	0.312832i	0.214893	+	0.976638i	$0.431060\pi$
$504$	−3.39058	+	4.66673i	−0.151028	+	0.207873i
$505$			28.4706i			1.26693i
$506$	−32.0127	−	4.69454i	−1.42314	−	0.208698i
$507$			40.6041i			1.80329i
$508$	11.4703	+	8.33364i	0.508911	+	0.369746i
$509$	35.0040	+	11.3735i	1.55152	+	0.504121i	0.954527	−	0.298123i	$-0.0963607\pi$
$509$	35.0040	+	11.3735i	1.55152	+	0.504121i	0.596996	+	0.802244i	$0.296361\pi$
$510$	34.8358	+	107.214i	1.54256	+	4.74750i
$511$	0.742691	−	0.539596i	0.0328547	−	0.0238703i
$512$	−40.9442	+	29.7477i	−1.80949	+	1.31467i
$513$	−52.0317	−	8.89220i	−2.29726	−	0.392600i
$514$	−2.82996	−	0.919509i	−0.124824	−	0.0405578i
$515$	−10.2755	+	14.1430i	−0.452793	+	0.623216i
$516$	−68.2372			−3.00398
$517$	3.13621	+	18.4304i	0.137930	+	0.810566i
$518$	−0.225135			−0.00989185
$519$	−41.2423	+	56.7651i	−1.81033	+	2.49171i
$520$	−1.69825	+	5.22667i	−0.0744731	+	0.229205i
$521$	16.4113	−	5.33234i	0.718990	−	0.233614i	0.0734048	−	0.997302i	$-0.476614\pi$
$521$	16.4113	−	5.33234i	0.718990	−	0.233614i	0.645585	+	0.763688i	$0.276614\pi$
$522$	−93.0794	+	67.6262i	−4.07398	+	2.95992i
$523$	22.0043	−	15.9871i	0.962181	−	0.699066i	0.00852486	−	0.999964i	$-0.497286\pi$
$523$	22.0043	−	15.9871i	0.962181	−	0.699066i	0.953656	+	0.300898i	$0.0972864\pi$
$524$	−23.2435	+	7.55226i	−1.01540	+	0.329922i
$525$	−0.929870	+	2.86185i	−0.0405829	+	0.124901i
$526$	−31.2713	+	43.0413i	−1.36349	+	1.87669i
$527$	−26.0254			−1.13368
$528$	−48.6488	+	49.7780i	−2.11717	+	2.16631i
$529$	−8.17214			−0.355311
$530$	9.54047	−	13.1313i	0.414412	−	0.570389i
$531$	−25.9717	−	8.43871i	−1.12708	−	0.366209i
$532$	2.60663	+	0.445472i	0.113012	+	0.0193137i
$533$	0.221815	−	0.161158i	0.00960789	−	0.00698054i
$534$	104.708	−	76.0751i	4.53118	−	3.29209i
$535$	8.08630	+	24.8871i	0.349601	+	1.07596i
$536$	18.6081	+	6.04613i	0.803746	+	0.261153i
$537$	19.9642	+	14.5048i	0.861519	+	0.625930i
$538$		−	2.28657i		−	0.0985812i
$539$	10.2743	−	20.7494i	0.442545	−	0.893742i
$540$			185.191i			7.96936i
$541$	18.6297	−	25.6416i	0.800955	−	1.10242i	−0.191701	−	0.981453i	$-0.561400\pi$
$541$	18.6297	−	25.6416i	0.800955	−	1.10242i	0.992657	−	0.120967i	$-0.0385995\pi$
$542$	−47.5644	−	15.4546i	−2.04307	−	0.663833i
$543$	−17.5787	−	54.1018i	−0.754375	−	2.32173i
$544$	−11.2673	−	15.5081i	−0.483080	−	0.664903i
$545$	5.53354	−	4.02035i	0.237031	−	0.172213i
$546$	0.0874695	+	0.269203i	0.00374335	+	0.0115208i
$547$	−4.84953	+	14.9253i	−0.207351	+	0.638161i	0.792258	+	0.610187i	$0.208906\pi$
$547$	−4.84953	+	14.9253i	−0.207351	+	0.638161i	−0.999609	+	0.0279742i	$0.991094\pi$
$548$	48.9915	+	35.5944i	2.09281	+	1.52052i
$549$		−	16.8193i		−	0.717832i
$550$	−26.0250	+	52.5588i	−1.10971	+	2.24112i
$551$	25.5603	+	13.4184i	1.08890	+	0.571642i
$552$	43.5350	−	59.9208i	1.85297	−	2.55040i
$553$	1.31801	+	0.428246i	0.0560474	+	0.0182109i
$554$	10.2120	−	3.31808i	0.433866	−	0.140972i
$555$	−5.68973	+	4.13383i	−0.241516	+	0.175471i
$556$	49.0019	+	67.4454i	2.07814	+	2.86032i
$557$	6.98636	−	2.27001i	0.296022	−	0.0961832i	−0.157241	−	0.987560i	$-0.550260\pi$
$557$	6.98636	−	2.27001i	0.296022	−	0.0961832i	0.453263	+	0.891377i	$0.350260\pi$
$558$	−105.008	−	34.1193i	−4.44536	−	1.44438i
$559$	−0.749378	+	1.03143i	−0.0316953	+	0.0436248i
$560$		−	3.17680i		−	0.134244i
$561$	30.4939	+	29.8022i	1.28746	+	1.25825i
$562$	16.6834			0.703748
$563$	−31.7751	−	23.0860i	−1.33916	−	0.972958i	−0.999474	−	0.0324192i	$-0.989679\pi$
$563$	−31.7751	−	23.0860i	−1.33916	−	0.972958i	−0.339687	−	0.940539i	$-0.610321\pi$
$564$	−74.3646	−	24.1625i	−3.13131	−	1.01743i
$565$	28.1245	−	9.13820i	1.18321	−	0.384447i
$566$	−32.4054	−	44.6022i	−1.36210	−	1.87477i
$567$	1.40831	+	1.93837i	0.0591434	+	0.0814039i
$568$	27.7859	−	9.02818i	1.16587	−	0.378814i
$569$	−8.53104	+	26.2558i	−0.357640	+	1.10070i	0.596823	+	0.802373i	$0.296429\pi$
$569$	−8.53104	+	26.2558i	−0.357640	+	1.10070i	−0.954463	+	0.298329i	$0.903571\pi$
$570$	107.579	−	53.1730i	4.50597	−	2.22717i
$571$		−	6.08304i		−	0.254567i	−0.991866	−	0.127284i	$-0.959374\pi$
$571$		−	6.08304i		−	0.254567i	0.991866	−	0.127284i	$-0.0406259\pi$
$572$	0.637092	+	3.74396i	0.0266382	+	0.156543i
$573$			12.7384i			0.532154i
$574$	−0.216312	+	0.297728i	−0.00902870	+	0.0124269i
$575$	8.30577	−	25.5625i	0.346374	−	1.06603i
$576$	3.19709	+	9.83964i	0.133212	+	0.409985i
$577$	−2.84735	+	2.06872i	−0.118537	+	0.0861220i	−0.645474	−	0.763782i	$-0.723340\pi$
$577$	−2.84735	+	2.06872i	−0.118537	+	0.0861220i	0.526937	+	0.849904i	$0.323340\pi$
$578$	0.476997	−	0.346559i	0.0198405	−	0.0144149i
$579$	9.52384	−	3.09448i	0.395797	−	0.128602i
$580$	31.2971	−	96.3226i	1.29954	−	3.99958i
$581$	1.34936	+	0.980369i	0.0559810	+	0.0406726i
$582$	−98.3348			−4.07611
$583$	0.890760	−	6.07422i	0.0368915	−	0.251568i
$584$			40.9590i			1.69489i
$585$	4.97640	+	3.61557i	0.205749	+	0.149485i
$586$	−9.09225	+	27.9831i	−0.375597	+	1.15597i
$587$	−6.37398	−	19.6171i	−0.263082	−	0.809684i	−0.992129	−	0.125220i	$-0.960036\pi$
$587$	−6.37398	−	19.6171i	−0.263082	−	0.809684i	0.729047	−	0.684464i	$-0.239964\pi$
$588$	56.9206	+	78.3445i	2.34737	+	3.23087i
$589$	4.00014	+	27.4137i	0.164823	+	1.12956i
$590$	33.2118	−	10.7912i	1.36731	−	0.444266i
$591$	13.0569	−	40.1850i	0.537090	−	1.65299i
$592$	2.54274	−	3.49979i	0.104506	−	0.143840i
$593$		−	42.5234i		−	1.74623i	−0.487517	−	0.873114i	$-0.662097\pi$
$593$		−	42.5234i		−	1.74623i	0.487517	−	0.873114i	$-0.337903\pi$
$594$	47.2318	+	90.1266i	1.93794	+	3.69794i
$595$	−1.94611			−0.0797826
$596$	−15.9446	+	21.9458i	−0.653115	+	0.898935i
$597$	−1.74166	−	0.565899i	−0.0712814	−	0.0231607i
$598$	−0.781293	−	2.40457i	−0.0319494	−	0.0983303i
$599$	−5.50390	−	7.57546i	−0.224883	−	0.309525i	0.681635	−	0.731693i	$-0.261269\pi$
$599$	−5.50390	−	7.57546i	−0.224883	−	0.309525i	−0.906518	+	0.422168i	$0.861269\pi$
$600$	−78.9146	−	108.617i	−3.22168	−	4.43426i
$601$	6.21285	+	19.1212i	0.253427	+	0.779969i	0.994135	+	0.108142i	$0.0344902\pi$
$601$	6.21285	+	19.1212i	0.253427	+	0.779969i	−0.740708	+	0.671827i	$0.765510\pi$
$602$	0.528802	−	1.62749i	0.0215524	−	0.0663314i
$603$	12.8722	−	17.7171i	0.524196	−	0.721494i
$604$	5.24261			0.213319
$605$	0.873434	+	38.0634i	0.0355102	+	1.54750i
$606$	−65.4261			−2.65775
$607$	30.6422	+	22.2629i	1.24373	+	0.903623i	0.997841	−	0.0656753i	$-0.0209201\pi$
$607$	30.6422	+	22.2629i	1.24373	+	0.903623i	0.245889	+	0.969298i	$0.420920\pi$
$608$	−14.6036	+	14.2519i	−0.592252	+	0.577993i
$609$	−0.882285	−	2.71539i	−0.0357520	−	0.110033i
$610$	12.6421	+	17.4004i	0.511865	+	0.704522i
$611$	−1.18189	+	0.858696i	−0.0478143	+	0.0347391i
$612$	−117.986	+	38.3359i	−4.76929	+	1.54964i
$613$	16.6908	+	5.42318i	0.674136	+	0.219040i	0.626026	−	0.779802i	$-0.284680\pi$
$613$	16.6908	+	5.42318i	0.674136	+	0.219040i	0.0481096	+	0.998842i	$0.484680\pi$
$614$	35.5524	+	25.8303i	1.43478	+	1.04243i
$615$			11.4962i			0.463571i
$616$	−1.29508	−	2.47123i	−0.0521801	−	0.0995688i
$617$	−18.2578			−0.735031			−0.367516	−	0.930017i	$-0.619792\pi$
$617$	−18.2578			−0.735031			−0.367516	+	0.930017i	$0.619792\pi$
$618$	−32.5010	−	23.6133i	−1.30738	−	0.949867i
$619$	8.26220	−	25.4284i	0.332086	−	1.02205i	−0.636054	−	0.771644i	$-0.719435\pi$
$619$	8.26220	−	25.4284i	0.332086	−	1.02205i	0.968140	−	0.250410i	$-0.0805655\pi$
$620$	92.4378	−	30.0349i	3.71239	−	1.20623i
$621$	−27.4095	−	37.7259i	−1.09990	−	1.51389i
$622$	15.0469	−	10.9322i	0.603325	−	0.438341i
$623$	0.690445	+	2.12497i	0.0276621	+	0.0851352i
$624$	−5.17275	−	1.68073i	−0.207076	−	0.0672830i
$625$	9.04416	+	6.57097i	0.361766	+	0.262839i
$626$	64.0426			2.55966
$627$	26.7051	−	36.7013i	1.06650	−	1.46571i
$628$	−90.1722			−3.59826
$629$	−2.14397	−	1.55768i	−0.0854855	−	0.0621089i
$630$	−7.85223	−	2.55134i	−0.312840	−	0.101648i
$631$	10.5000	+	32.3156i	0.417998	+	1.28646i	0.909542	+	0.415612i	$0.136433\pi$
$631$	10.5000	+	32.3156i	0.417998	+	1.28646i	−0.491545	+	0.870852i	$0.663567\pi$
$632$	−50.0228	+	36.3437i	−1.98980	+	1.44567i
$633$	−31.4172	−	43.2420i	−1.24872	−	1.71872i
$634$	63.5871	−	20.6607i	2.52537	−	0.820541i
$635$	−3.43226	+	10.5634i	−0.136205	+	0.419196i
$636$	20.7728	+	15.0924i	0.823697	+	0.598451i
$637$	1.80930			0.0716872
$638$	−9.33516	−	54.8593i	−0.369582	−	2.17190i
$639$		−	32.7007i		−	1.29362i
$640$	−36.9206	−	26.8244i	−1.45942	−	1.06033i
$641$	−12.3438	−	4.01074i	−0.487551	−	0.158415i	0.0549178	−	0.998491i	$-0.482510\pi$
$641$	−12.3438	−	4.01074i	−0.487551	−	0.158415i	−0.542469	+	0.840076i	$0.682510\pi$
$642$	−57.1910	+	18.5825i	−2.25715	+	0.733393i
$643$	−12.6778	+	9.21093i	−0.499962	+	0.363244i	−0.809002	−	0.587805i	$-0.799992\pi$
$643$	−12.6778	+	9.21093i	−0.499962	+	0.363244i	0.309041	+	0.951049i	$0.399992\pi$
$644$	1.37313	+	1.88995i	0.0541089	+	0.0744746i
$645$	−16.5190	−	50.8404i	−0.650437	−	2.00184i
$646$	31.5823	+	32.3615i	1.24259	+	1.27325i
$647$	−27.6676	−	20.1017i	−1.08772	−	0.790278i	−0.108711	−	0.994073i	$-0.534672\pi$
$647$	−27.6676	−	20.1017i	−1.08772	−	0.790278i	−0.979014	+	0.203795i	$0.934672\pi$
$648$	−106.900			−4.19943
$649$	9.23191	−	9.44619i	0.362384	−	0.370795i
$650$	−4.58301			−0.179760
$651$	1.61052	−	2.21669i	0.0631213	−	0.0868790i
$652$	28.9585	−	89.1250i	1.13410	−	3.49041i
$653$	1.08802	+	3.34859i	0.0425777	+	0.131041i	0.970086	−	0.242763i	$-0.0780536\pi$
$653$	1.08802	+	3.34859i	0.0425777	+	0.131041i	−0.927508	+	0.373803i	$0.878054\pi$
$654$	9.23886	+	12.7162i	0.361268	+	0.497243i
$655$	−11.2537	−	15.4894i	−0.439718	−	0.605219i
$656$	−2.18518	−	6.72528i	−0.0853168	−	0.262578i
$657$	43.6008	+	14.1668i	1.70103	+	0.552698i
$658$	1.15257	−	1.58638i	0.0449320	−	0.0618435i
$659$	26.8668			1.04658			0.523292	−	0.852154i	$-0.324704\pi$
$659$	26.8668			1.04658			0.523292	+	0.852154i	$0.324704\pi$
$660$	−142.703	−	70.6607i	−5.55470	−	2.75046i
$661$		−	27.2289i		−	1.05908i	−0.848285	−	0.529541i	$-0.822364\pi$
$661$		−	27.2289i		−	1.05908i	0.848285	−	0.529541i	$-0.177636\pi$
$662$	9.10389	−	12.5304i	0.353833	−	0.487009i
$663$	−1.02961	+	3.16882i	−0.0399869	+	0.123067i
$664$	−70.7744	+	22.9960i	−2.74658	+	0.892417i
$665$	0.299119	+	2.04992i	0.0115994	+	0.0794925i
$666$	−6.60844	−	9.09574i	−0.256072	−	0.352453i
$667$	7.88072	+	24.2544i	0.305143	+	0.939133i
$668$	−6.43286	+	19.7983i	−0.248895	+	0.766019i
$669$	49.6831	+	36.0969i	1.92086	+	1.39559i
$670$			28.0044i			1.08191i
$671$	7.29029	+	3.60986i	0.281439	+	0.139357i
$672$	2.01814			0.0778513
$673$	−30.2702	−	21.9926i	−1.16683	−	0.847753i	−0.176205	−	0.984353i	$-0.556382\pi$
$673$	−30.2702	−	21.9926i	−1.16683	−	0.847753i	−0.990626	+	0.136601i	$0.956382\pi$
$674$	17.2422	−	53.0660i	0.664144	−	2.04403i
$675$	−80.3910	+	26.1206i	−3.09425	+	1.00538i
$676$	46.2274	−	33.5862i	1.77798	−	1.29178i
$677$	4.75616	−	3.45555i	0.182794	−	0.132808i	−0.492625	−	0.870242i	$-0.663963\pi$
$677$	4.75616	−	3.45555i	0.182794	−	0.132808i	0.675419	+	0.737434i	$0.263963\pi$
$678$	20.9998	+	64.6307i	0.806491	+	2.48213i
$679$	0.524581	−	1.61449i	0.0201316	−	0.0619586i
$680$	51.0369	−	70.2462i	1.95717	−	2.69382i
$681$		−	22.7204i		−	0.870649i
$682$	37.3263	−	38.1927i	1.42930	−	1.46247i
$683$		−	5.27417i		−	0.201811i	−0.994896	−	0.100905i	$-0.967826\pi$
$683$		−	5.27417i		−	0.201811i	0.994896	−	0.100905i	$-0.0321739\pi$
$684$	58.5155	+	118.387i	2.23740	+	4.52666i
$685$	−14.6598	+	45.1181i	−0.560120	+	1.72387i
$686$	−4.62554	+	1.50293i	−0.176604	+	0.0573821i
$687$	−47.3026	−	65.1064i	−1.80471	−	2.48396i
$688$	19.3273	+	26.6017i	0.736846	+	1.01418i
$689$	0.456253	−	0.148245i	0.0173818	−	0.00564770i
$690$	100.823	+	32.7593i	3.83825	+	1.24712i
$691$	8.60656	+	6.25303i	0.327409	+	0.237877i	0.739330	−	0.673343i	$-0.235142\pi$
$691$	8.60656	+	6.25303i	0.327409	+	0.237877i	−0.411921	+	0.911219i	$0.635142\pi$
$692$	98.7407			3.75356
$693$	−3.07856	+	0.523865i	−0.116945	+	0.0199000i
$694$		−	17.0326i		−	0.646550i
$695$	−38.3879	+	52.8364i	−1.45614	+	2.00420i
$696$	121.152	+	39.3648i	4.59226	+	1.49212i
$697$	−4.11990	+	1.33864i	−0.156052	+	0.0507045i
$698$	0.125112	+	0.172201i	0.00473554	+	0.00651792i
$699$	−27.8683	+	20.2475i	−1.05407	+	0.765830i
$700$	4.02734	−	1.30856i	0.152219	−	0.0494590i
$701$	−5.27208	−	1.71300i	−0.199124	−	0.0646992i	0.207757	−	0.978180i	$-0.433384\pi$
$701$	−5.27208	−	1.71300i	−0.199124	−	0.0646992i	−0.406881	+	0.913481i	$0.633384\pi$
$702$	−4.67362	+	6.43269i	−0.176395	+	0.242786i
$703$	−1.31125	+	2.49775i	−0.0494546	+	0.0942046i
$704$	−4.95114	−	0.726065i	−0.186603	−	0.0273646i
$705$		−	61.2549i		−	2.30699i
$706$	32.2814	+	23.4538i	1.21493	+	0.882697i
$707$	0.349025	−	1.07419i	0.0131264	−	0.0403990i
$708$	17.0709	+	52.5388i	0.641563	+	1.97453i
$709$	−19.1339	+	13.9016i	−0.718588	+	0.522085i	−0.885933	−	0.463814i	$-0.846481\pi$
$709$	−19.1339	+	13.9016i	−0.718588	+	0.522085i	0.167345	+	0.985898i	$0.446481\pi$
$710$	24.5792	+	33.8304i	0.922442	+	1.26963i
$711$	21.3861	+	65.8197i	0.802042	+	2.46843i
$712$	−94.8095	−	30.8055i	−3.55314	−	1.15448i
$713$	−14.3855	+	19.7999i	−0.538740	+	0.741512i
$714$		−	4.47219i		−	0.167368i
$715$	−2.63522	+	1.38101i	−0.0985516	+	0.0516470i
$716$		−	34.7269i		−	1.29781i
$717$	33.6212	+	24.4273i	1.25561	+	0.912252i
$718$	−81.1197	−	26.3574i	−3.02736	−	0.983649i
$719$	4.03760	+	12.4264i	0.150577	+	0.463428i	0.997686	−	0.0679910i	$-0.0216589\pi$
$719$	4.03760	+	12.4264i	0.150577	+	0.463428i	−0.847109	+	0.531419i	$0.821659\pi$
$720$	128.347	−	93.2495i	4.78321	−	3.47521i
$721$	0.561072	−	0.407643i	0.0208954	−	0.0151814i
$722$	29.2336	−	38.2411i	1.08796	−	1.42319i
$723$	88.2862	+	28.6859i	3.28340	+	1.06684i
$724$	−47.0539	+	64.7642i	−1.74875	+	2.40694i
$725$	46.2278			1.71686
$726$	−87.4705	+	2.00717i	−3.24634	+	0.0744931i
$727$	−8.42725			−0.312549			−0.156275	−	0.987714i	$-0.549948\pi$
$727$	−8.42725			−0.312549			−0.156275	+	0.987714i	$0.549948\pi$
$728$	0.128149	−	0.176382i	0.00474951	−	0.00653714i
$729$	−1.72725	+	5.31594i	−0.0639724	+	0.196887i
$730$	−55.7555	+	18.1160i	−2.06360	+	0.670505i
$731$	16.2962	−	11.8399i	0.602737	−	0.437914i
$732$	−27.5262	+	19.9990i	−1.01740	+	0.739184i
$733$	−37.3482	+	12.1352i	−1.37949	+	0.448223i	−0.902501	−	0.430687i	$-0.858271\pi$
$733$	−37.3482	+	12.1352i	−1.37949	+	0.448223i	−0.476987	+	0.878910i	$0.658271\pi$
$734$	14.9098	−	45.8877i	0.550331	−	1.69375i
$735$	−44.5913	+	61.3747i	−1.64478	+	2.26384i
$736$	−18.0264			−0.664461
$737$	4.91671	+	9.38194i	0.181109	+	0.345588i
$738$	−18.3781			−0.676507
$739$	−16.6620	+	22.9333i	−0.612923	+	0.843616i	−0.996814	−	0.0797621i	$-0.974584\pi$
$739$	−16.6620	+	22.9333i	−0.612923	+	0.843616i	0.383891	+	0.923379i	$0.374584\pi$
$740$	9.41267	+	3.05836i	0.346017	+	0.112428i
$741$	3.49612	+	0.597485i	0.128433	+	0.0219492i
$742$	−0.520937	+	0.378483i	−0.0191242	+	0.0138946i
$743$	0.392061	−	0.284849i	0.0143833	−	0.0104501i	−0.580570	−	0.814210i	$-0.697170\pi$
$743$	0.392061	−	0.284849i	0.0143833	−	0.0104501i	0.594954	+	0.803760i	$0.297170\pi$
$744$	37.7771	+	116.266i	1.38498	+	4.26252i
$745$	−20.2107	−	6.56685i	−0.740463	−	0.240591i
$746$	−23.0968	−	16.7808i	−0.845632	−	0.614388i
$747$			83.2931i			3.04753i
$748$	8.70614	−	59.3684i	0.318328	−	2.17072i
$749$		−	1.03811i		−	0.0379318i
$750$	32.0410	−	44.1007i	1.16997	−	1.61033i
$751$	39.4869	+	12.8301i	1.44090	+	0.468176i	0.922177	−	0.386767i	$-0.126408\pi$
$751$	39.4869	+	12.8301i	1.44090	+	0.468176i	0.518721	+	0.854943i	$0.326408\pi$
$752$	11.6432	+	35.8342i	0.424585	+	1.30674i
$753$	25.6949	+	35.3660i	0.936374	+	1.28881i
$754$	3.51799	−	2.55597i	0.128118	−	0.0930829i
$755$	1.26914	+	3.90602i	0.0461889	+	0.142155i
$756$	2.27028	−	6.98720i	0.0825693	−	0.254122i
$757$	3.19621	+	2.32219i	0.116168	+	0.0844012i	0.644353	−	0.764729i	$-0.277127\pi$
$757$	3.19621	+	2.32219i	0.116168	+	0.0844012i	−0.528184	+	0.849130i	$0.677127\pi$
$758$			45.5083i			1.65293i
$759$	39.5287	−	6.72643i	1.43480	−	0.244154i
$760$	−81.8379	−	42.9625i	−2.96857	−	1.55841i
$761$	24.7924	−	34.1239i	0.898725	−	1.23699i	−0.0721481	−	0.997394i	$-0.522985\pi$
$761$	24.7924	−	34.1239i	0.898725	−	1.23699i	0.970873	−	0.239595i	$-0.0770146\pi$
$762$	−24.2749	−	7.88740i	−0.879388	−	0.285730i
$763$	−0.258065	+	0.0838503i	−0.00934257	+	0.00303559i
$764$	14.5026	−	10.5367i	0.524684	−	0.381205i
$765$	−57.1246	−	78.6252i	−2.06534	−	2.84270i
$766$	−79.9534	+	25.9784i	−2.88883	+	0.938639i
$767$	0.981614	+	0.318946i	0.0354440	+	0.0115165i
$768$	56.0743	−	77.1797i	2.02341	−	2.78498i
$769$			30.7971i			1.11057i	0.831659	+	0.555287i	$0.187391\pi$
$769$			30.7971i			1.11057i	−0.831659	+	0.555287i	$0.812609\pi$
$770$	2.79116	−	2.85594i	0.100586	−	0.102921i
$771$	3.68758			0.132805
$772$	−11.4008	−	8.28317i	−0.410324	−	0.298118i
$773$	−24.9333	−	8.10132i	−0.896789	−	0.291384i	−0.175878	−	0.984412i	$-0.556276\pi$
$773$	−24.9333	−	8.10132i	−0.896789	−	0.291384i	−0.720911	+	0.693028i	$0.756276\pi$
$774$	81.2747	−	26.4077i	2.92136	−	0.949207i
$775$	26.0761	+	35.8907i	0.936681	+	1.28923i
$776$	44.5192	+	61.2754i	1.59815	+	2.19966i
$777$	0.265349	−	0.0862170i	0.00951933	−	0.00309302i
$778$	−1.63890	+	5.04402i	−0.0587575	+	0.180837i
$779$	2.04328	+	4.13393i	0.0732081	+	0.148113i
$780$		−	12.4434i		−	0.445544i
$781$	14.1740	+	7.01839i	0.507186	+	0.251138i
$782$			39.9464i			1.42848i
$783$	47.1418	−	64.8851i	1.68471	−	2.31880i
$784$	14.4200	−	44.3801i	0.514998	−	1.58500i
$785$	−21.8291	−	67.1831i	−0.779115	−	2.39787i
$786$	35.5949	−	25.8612i	1.26963	−	0.922438i
$787$	−31.4446	+	22.8459i	−1.12088	+	0.814367i	−0.984342	−	0.176268i	$-0.943598\pi$
$787$	−31.4446	+	22.8459i	−1.12088	+	0.814367i	−0.136538	+	0.990635i	$0.543598\pi$
$788$	−56.5505	+	18.3744i	−2.01453	+	0.654560i
$789$	20.3741	−	62.7050i	0.725337	−	2.23236i
$790$	−71.5978	−	52.0189i	−2.54734	−	1.85075i
$791$	−1.17315			−0.0417125
$792$	61.8263	−	124.862i	2.19690	−	4.43676i
$793$			0.635697i			0.0225743i
$794$	23.0979	+	16.7816i	0.819715	+	0.595558i
$795$	−6.21587	+	19.1305i	−0.220454	+	0.678488i
$796$	0.796364	+	2.45096i	0.0282264	+	0.0868718i
$797$	7.86781	+	10.8291i	0.278692	+	0.383587i	0.925300	−	0.379236i	$-0.123813\pi$
$797$	7.86781	+	10.8291i	0.278692	+	0.383587i	−0.646608	+	0.762823i	$0.723813\pi$
$798$	−4.71076	+	0.687383i	−0.166759	+	0.0243331i
$799$	21.9520	−	7.13263i	0.776605	−	0.252334i
$800$	−10.0974	+	31.0766i	−0.356997	+	1.09872i
$801$	−65.5848	+	90.2698i	−2.31733	+	3.18953i
$802$			64.2174i			2.26760i
$803$	−15.4984	+	15.8581i	−0.546926	+	0.559620i
$804$	−44.3010			−1.56238
$805$	−1.07570	+	1.48058i	−0.0379136	+	0.0521836i
$806$	3.96885	+	1.28956i	0.139797	+	0.0454227i
$807$	0.875660	+	2.69501i	0.0308247	+	0.0948687i
$808$	29.6204	+	40.7690i	1.04204	+	1.43425i
$809$	−10.3151	−	14.1975i	−0.362659	−	0.499157i	0.588228	−	0.808695i	$-0.299826\pi$
$809$	−10.3151	−	14.1975i	−0.362659	−	0.499157i	−0.950887	+	0.309538i	$0.899826\pi$
$810$	−47.2816	−	145.518i	−1.66131	−	5.11298i
$811$	12.0206	−	36.9956i	0.422100	−	1.29909i	−0.483644	−	0.875265i	$-0.660687\pi$
$811$	12.0206	−	36.9956i	0.422100	−	1.29909i	0.905744	−	0.423825i	$-0.139313\pi$
$812$	−2.36166	+	3.25055i	−0.0828780	+	0.114072i
$813$	61.9790			2.17370
$814$	5.36086	−	0.912234i	0.187898	−	0.0319738i
$815$	73.4133			2.57155
$816$	69.5216	+	50.5104i	2.43374	+	1.76822i
$817$	−14.9762	−	15.3457i	−0.523952	−	0.536878i
$818$	−15.8370	−	48.7413i	−0.553728	−	1.70420i
$819$	−0.143434	−	0.197421i	−0.00501200	−	0.00689843i
$820$	13.0883	−	9.50923i	0.457064	−	0.332077i
$821$	10.9656	−	3.56295i	0.382703	−	0.124348i	−0.111346	−	0.993782i	$-0.535516\pi$
$821$	10.9656	−	3.56295i	0.382703	−	0.124348i	0.494049	+	0.869434i	$0.335516\pi$
$822$	−103.682	−	33.6884i	−3.61634	−	1.17502i
$823$	14.1268	+	10.2637i	0.492428	+	0.357770i	0.806117	−	0.591756i	$-0.201565\pi$
$823$	14.1268	+	10.2637i	0.492428	+	0.357770i	−0.313690	+	0.949526i	$0.601565\pi$
$824$			30.9428i			1.07794i
$825$	10.5458	−	71.9134i	0.367158	−	2.50370i
$826$	−1.38536			−0.0482029
$827$	−31.3633	−	22.7868i	−1.09061	−	0.792374i	−0.111108	−	0.993808i	$-0.535440\pi$
$827$	−31.3633	−	22.7868i	−1.09061	−	0.792374i	−0.979502	+	0.201434i	$0.935440\pi$
$828$	−36.0507	+	110.953i	−1.25285	+	3.85587i
$829$	43.8503	−	14.2478i	1.52298	−	0.494847i	0.576362	−	0.817195i	$-0.304472\pi$
$829$	43.8503	−	14.2478i	1.52298	−	0.494847i	0.946621	+	0.322347i	$0.104472\pi$
$830$	−62.6066	−	86.1706i	−2.17311	−	2.99103i
$831$	−10.7654	+	7.82153i	−0.373448	+	0.271326i
$832$	−0.120836	−	0.371895i	−0.00418923	−	0.0128931i
$833$	−27.1872	−	8.83365i	−0.941980	−	0.306068i
$834$	−121.419	−	88.2162i	−4.20440	−	3.05468i
$835$	−16.3081			−0.564364
$836$	−63.8736	−	0.0455604i	−2.20911	−	0.00157574i
$837$	76.9677			2.66039
$838$	−60.9241	−	44.2639i	−2.10459	−	1.52907i
$839$	−17.8202	−	5.79013i	−0.615221	−	0.199897i	−0.0152036	−	0.999884i	$-0.504840\pi$
$839$	−17.8202	−	5.79013i	−0.615221	−	0.199897i	−0.600017	+	0.799987i	$0.704840\pi$
$840$	2.82487	+	8.69405i	0.0974672	+	0.299973i
$841$	−12.0237	+	8.73571i	−0.414609	+	0.301231i
$842$	32.8961	+	45.2777i	1.13368	+	1.56037i
$843$	−19.6635	+	6.38905i	−0.677246	+	0.220050i
$844$	−23.2436	+	71.5364i	−0.800077	+	2.46239i
$845$	36.2143	+	26.3113i	1.24581	+	0.905135i
$846$	97.9236			3.36668
$847$	0.433669	−	1.44683i	0.0149011	−	0.0497136i
$848$		−	12.3728i		−	0.424885i
$849$	55.2745	+	40.1593i	1.89702	+	1.37826i
$850$	68.8658	+	22.3758i	2.36208	+	0.767485i
$851$	−2.37014	+	0.770106i	−0.0812475	+	0.0263989i
$852$	−53.5173	+	38.8826i	−1.83347	+	1.33210i
$853$	23.2900	+	32.0560i	0.797436	+	1.09758i	0.993142	+	0.116913i	$0.0373000\pi$
$853$	23.2900	+	32.0560i	0.797436	+	1.09758i	−0.195706	+	0.980663i	$0.562700\pi$
$854$	−0.263670	−	0.811494i	−0.00902261	−	0.0277687i
$855$	−74.0394	+	72.2567i	−2.53209	+	2.47113i
$856$	37.4715	+	27.2246i	1.28075	+	0.930518i
$857$	−4.56025			−0.155775			−0.0778876	−	0.996962i	$-0.524818\pi$
$857$	−4.56025			−0.155775			−0.0778876	+	0.996962i	$0.524818\pi$
$858$	−3.17360	−	6.05579i	−0.108345	−	0.206741i
$859$	31.5235			1.07557			0.537783	−	0.843083i	$-0.319262\pi$
$859$	31.5235			1.07557			0.537783	+	0.843083i	$0.319262\pi$
$860$	−44.2174	+	60.8601i	−1.50780	+	2.07531i
$861$	0.140933	−	0.433748i	0.00480299	−	0.0147821i
$862$	−8.67323	−	26.6934i	−0.295411	−	0.909182i
$863$	27.0347	+	37.2101i	0.920271	+	1.26665i	0.963535	+	0.267581i	$0.0862244\pi$
$863$	27.0347	+	37.2101i	0.920271	+	1.26665i	−0.0432638	+	0.999064i	$0.513776\pi$
$864$	33.3220	+	45.8637i	1.13364	+	1.56032i
$865$	23.9034	+	73.5671i	0.812740	+	2.50136i
$866$	16.7356	+	5.43772i	0.568699	+	0.184781i
$867$	−0.429482	+	0.591132i	−0.0145860	+	0.0200759i
$868$	−3.85585			−0.130876
$869$	−33.1193	−	4.85682i	−1.12350	−	0.164756i
$870$			182.330i			6.18155i
$871$	−0.486512	+	0.669626i	−0.0164848	+	0.0226894i
$872$	3.74114	−	11.5140i	0.126691	−	0.389915i
$873$	80.6258	−	26.1969i	2.72877	−	0.886631i
$874$	42.0774	−	6.13983i	1.42329	−	0.207683i
$875$	0.553132	+	0.761321i	0.0186993	+	0.0257374i
$876$	−28.6583	−	88.2012i	−0.968275	−	2.98004i
$877$	−3.49736	+	10.7638i	−0.118098	+	0.363467i	−0.992580	−	0.121589i	$-0.961201\pi$
$877$	−3.49736	+	10.7638i	−0.118098	+	0.363467i	0.874483	+	0.485056i	$0.161201\pi$
$878$	20.8366	+	15.1387i	0.703201	+	0.510906i
$879$		−	36.4634i		−	1.22988i
$880$	12.8722	+	75.6453i	0.433923	+	2.55000i
$881$	−9.45151			−0.318429			−0.159215	−	0.987244i	$-0.550896\pi$
$881$	−9.45151			−0.318429			−0.159215	+	0.987244i	$0.550896\pi$
$882$	−98.1151	−	71.2848i	−3.30371	−	2.40028i
$883$	−6.19647	+	19.0708i	−0.208528	+	0.641782i	0.791022	+	0.611787i	$0.209549\pi$
$883$	−6.19647	+	19.0708i	−0.208528	+	0.641782i	−0.999550	+	0.0299951i	$0.990451\pi$
$884$	4.45934	−	1.44893i	0.149984	−	0.0487327i
$885$	−35.0116	+	25.4375i	−1.17690	+	0.855071i
$886$	−20.6928	+	15.0342i	−0.695188	+	0.505084i
$887$	8.99781	+	27.6924i	0.302117	+	0.929820i	0.980737	+	0.195331i	$0.0625781\pi$
$887$	8.99781	+	27.6924i	0.302117	+	0.929820i	−0.678621	+	0.734489i	$0.737422\pi$
$888$	−3.84673	+	11.8390i	−0.129088	+	0.397292i
$889$	0.258996	−	0.356477i	0.00868644	−	0.0119559i
$890$		−	142.685i		−	4.78280i
$891$	−41.3885	−	40.4497i	−1.38657	−	1.35511i
$892$		−	86.4218i		−	2.89361i
$893$	−10.8872	−	22.0267i	−0.364325	−	0.737096i
$894$	15.0908	−	46.4446i	0.504711	−	1.55334i
$895$	25.8734	−	8.40679i	0.864853	−	0.281008i
$896$	1.06416	+	1.46469i	0.0355511	+	0.0489318i
$897$	1.84170	+	2.53488i	0.0614925	+	0.0846372i
$898$	33.5567	−	10.9032i	1.11980	−	0.363846i
$899$	−40.0329	−	13.0075i	−1.33517	−	0.433823i
$900$	171.083	+	124.299i	5.70278	+	4.14331i
$901$	−7.57959			−0.252513
$902$	3.94440	−	7.96593i	0.131334	−	0.265236i
$903$			2.12070i			0.0705725i
$904$	30.7661	−	42.3459i	1.02327	−	1.40840i
$905$	−59.6437	−	19.3794i	−1.98262	−	0.644194i
$906$	−8.97613	+	2.91652i	−0.298212	+	0.0968949i
$907$	−10.0527	−	13.8363i	−0.333793	−	0.459427i	0.608823	−	0.793306i	$-0.291642\pi$
$907$	−10.0527	−	13.8363i	−0.333793	−	0.459427i	−0.942616	+	0.333879i	$0.891642\pi$
$908$	−25.8670	+	18.7935i	−0.858428	+	0.623684i
$909$	53.6436	−	17.4299i	1.77925	−	0.578112i
$910$	0.296779	+	0.0964295i	0.00983814	+	0.00319661i
$911$	18.4106	−	25.3400i	0.609969	−	0.839551i	−0.386606	−	0.922245i	$-0.626352\pi$
$911$	18.4106	−	25.3400i	0.609969	−	0.839551i	0.996575	+	0.0826943i	$0.0263525\pi$
$912$	42.5193	−	80.9937i	1.40795	−	2.68197i
$913$	−36.1031	−	17.8768i	−1.19484	−	0.591635i
$914$		−	6.10492i		−	0.201933i
$915$	−21.5639	−	15.6671i	−0.712882	−	0.517939i
$916$	−34.9962	+	107.707i	−1.15631	+	3.55875i
$917$	0.234712	+	0.722369i	0.00775087	+	0.0238547i
$918$	101.634	−	73.8415i	3.35442	−	2.43713i
$919$	−19.0570	−	26.2297i	−0.628633	−	0.865238i	0.369313	−	0.929305i	$-0.379593\pi$
$919$	−19.0570	−	26.2297i	−0.628633	−	0.865238i	−0.997946	+	0.0640666i	$0.979593\pi$
$920$	−25.2322	−	77.6568i	−0.831882	−	2.56027i
$921$	−51.7948	−	16.8291i	−1.70670	−	0.554539i
$922$	16.6501	−	22.9169i	0.548341	−	0.754727i
$923$			1.23594i			0.0406815i
$924$	4.51790	+	4.41542i	0.148628	+	0.145257i
$925$			4.51739i			0.148531i
$926$	53.4073	+	38.8027i	1.75507	+	1.27513i
$927$	32.9386	+	10.7024i	1.08185	+	0.351513i
$928$	−9.58067	−	29.4863i	−0.314501	−	0.967934i
$929$	−0.452127	+	0.328489i	−0.0148338	+	0.0107774i	−0.595177	−	0.803594i	$-0.702918\pi$
$929$	−0.452127	+	0.328489i	−0.0148338	+	0.0107774i	0.580344	+	0.814372i	$0.302918\pi$
$930$	−141.559	+	102.848i	−4.64189	+	3.37253i
$931$	−5.12617	+	29.9952i	−0.168003	+	0.983054i
$932$	46.1032	+	14.9798i	1.51016	+	0.490681i
$933$	−13.5480	+	18.6472i	−0.443542	+	0.610483i
$934$	−39.0584			−1.27803
$935$	46.3402	−	7.88551i	1.51549	−	0.257884i
$936$	10.8876			0.355873
$937$	28.4281	−	39.1279i	0.928705	−	1.27825i	−0.0316579	−	0.999499i	$-0.510079\pi$
$937$	28.4281	−	39.1279i	0.928705	−	1.27825i	0.960363	−	0.278754i	$-0.0899213\pi$
$938$	0.343310	−	1.05660i	0.0112095	−	0.0344992i
$939$	−75.4820	+	24.5256i	−2.46326	+	0.800362i
$940$	−69.7382	+	50.6678i	−2.27461	+	1.65260i
$941$	−20.2360	+	14.7023i	−0.659676	+	0.479283i	−0.866554	−	0.499084i	$-0.833670\pi$
$941$	−20.2360	+	14.7023i	−0.659676	+	0.479283i	0.206877	+	0.978367i	$0.433670\pi$
$942$	154.388	−	50.1638i	5.03024	−	1.63442i
$943$	−1.25884	+	3.87431i	−0.0409935	+	0.126165i
$944$	15.6467	−	21.5359i	0.509258	−	0.700933i
$945$	5.75543			0.187224
$946$	−5.99724	+	40.8960i	−0.194987	+	1.32964i
$947$	3.70294			0.120329			0.0601646	−	0.998188i	$-0.480837\pi$
$947$	3.70294			0.120329			0.0601646	+	0.998188i	$0.480837\pi$
$948$	82.2902	−	113.263i	2.67266	−	3.67860i
$949$	−1.64792	−	0.535441i	−0.0534937	−	0.0173811i
$950$	12.9847	−	75.9786i	0.421280	−	2.46507i
$951$	−67.0330	+	48.7023i	−2.17369	+	1.57928i
$952$	−2.78676	+	2.02470i	−0.0903194	+	0.0656209i
$953$	−10.3856	−	31.9635i	−0.336422	−	1.03540i	−0.966018	−	0.258477i	$-0.916780\pi$
$953$	−10.3856	−	31.9635i	−0.336422	−	1.03540i	0.629596	−	0.776923i	$-0.283220\pi$
$954$	−30.5824	−	9.93684i	−0.990143	−	0.321717i
$955$	11.3612	+	8.25443i	0.367641	+	0.267107i
$956$		−	58.4828i		−	1.89147i
$957$	32.0114	+	61.0834i	1.03478	+	1.97455i
$958$		−	70.4141i		−	2.27498i
$959$	1.10622	−	1.52258i	0.0357216	−	0.0491665i
$960$	15.5934	+	5.06659i	0.503274	+	0.163524i
$961$	−2.90333	−	8.93553i	−0.0936558	−	0.288243i
$962$	0.249770	+	0.343779i	0.00805290	+	0.0110839i
$963$	41.9411	−	30.4720i	1.35153	−	0.981947i
$964$	−40.3684	−	124.241i	−1.30018	−	4.00154i
$965$	3.41147	−	10.4994i	0.109819	−	0.337988i
$966$	−3.40241	−	2.47199i	−0.109471	−	0.0795351i
$967$		−	26.5241i		−	0.852957i	−0.904498	−	0.426478i	$-0.859754\pi$
$967$		−	26.5241i		−	0.852957i	0.904498	−	0.426478i	$-0.140246\pi$
$968$	40.8513	+	53.5969i	1.31301	+	1.72267i
$969$	−49.6167	−	26.0473i	−1.59392	−	0.836759i
$970$	−63.7205	+	87.7038i	−2.04594	+	2.81600i
$971$	36.1932	+	11.7599i	1.16150	+	0.377393i	0.825462	−	0.564457i	$-0.190915\pi$
$971$	36.1932	+	11.7599i	1.16150	+	0.377393i	0.336033	+	0.941850i	$0.390915\pi$
$972$	77.5414	−	25.1947i	2.48714	−	0.808121i
$973$	2.09609	−	1.52290i	0.0671976	−	0.0488219i
$974$	55.1670	+	75.9309i	1.76767	+	2.43298i
$975$	5.40163	−	1.75510i	0.172991	−	0.0562081i
$976$	15.5929	+	5.06644i	0.499116	+	0.162173i
$977$	−11.3853	+	15.6706i	−0.364249	+	0.501346i	−0.951327	−	0.308185i	$-0.900278\pi$
$977$	−11.3853	+	15.6706i	−0.364249	+	0.501346i	0.587077	+	0.809531i	$0.300278\pi$
$978$			168.705i			5.39460i
$979$	−25.0510	−	47.8017i	−0.800633	−	1.52775i
$980$	106.759			3.41029
$981$	−10.9627	−	7.96488i	−0.350013	−	0.254299i
$982$	−25.1148	−	8.16031i	−0.801447	−	0.260406i
$983$	−38.7904	+	12.6038i	−1.23722	+	0.401998i	−0.853325	−	0.521379i	$-0.825418\pi$
$983$	−38.7904	+	12.6038i	−1.23722	+	0.401998i	−0.383896	+	0.923376i	$0.625418\pi$
$984$	11.9605	+	16.4622i	0.381286	+	0.524795i
$985$	−27.3798	−	37.6851i	−0.872393	−	1.20075i
$986$	−65.3416	+	21.2308i	−2.08090	+	0.676125i
$987$	−0.750931	+	2.31113i	−0.0239024	+	0.0735640i
$988$	−2.21163	−	4.47452i	−0.0703612	−	0.142353i
$989$		−	18.9425i		−	0.602335i
$990$	197.314	+	28.9353i	6.27104	+	0.919623i
$991$		−	57.0814i		−	1.81325i	−0.421939	−	0.906624i	$-0.638650\pi$
$991$		−	57.0814i		−	1.81325i	0.421939	−	0.906624i	$-0.361350\pi$
$992$	17.4885	−	24.0709i	0.555262	−	0.764252i
$993$	−5.93142	+	18.2550i	−0.188228	+	0.579306i
$994$	−0.512636	−	1.57773i	−0.0162598	−	0.0500426i
$995$	−1.63331	+	1.18667i	−0.0517793	+	0.0376199i
$996$	136.316	−	99.0393i	4.31933	−	3.13818i
$997$	56.4382	−	18.3379i	1.78742	−	0.580767i	0.788025	−	0.615643i	$-0.211104\pi$
$997$	56.4382	−	18.3379i	1.78742	−	0.580767i	0.999392	+	0.0348757i	$0.0111035\pi$
$998$	−0.484705	+	1.49177i	−0.0153431	+	0.0472211i
$999$	6.34059	+	4.60671i	0.200607	+	0.145750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.k.c.18.14	yes	56
11.8	odd	10	inner	209.2.k.c.151.1	yes	56
19.18	odd	2	inner	209.2.k.c.18.1	✓	56
209.151	even	10	inner	209.2.k.c.151.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.k.c.18.1	✓	56	19.18	odd	2	inner
209.2.k.c.18.14	yes	56	1.1	even	1	trivial
209.2.k.c.151.1	yes	56	11.8	odd	10	inner
209.2.k.c.151.14	yes	56	209.151	even	10	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04958 + 1.48911i) q^{2} +(-2.98595 - 0.970193i) q^{3} +(1.36531 + 4.20198i) q^{4} +(-2.80019 + 2.03445i) q^{5} +(-4.67522 - 6.43489i) q^{6} +(0.130591 - 0.0424315i) q^{7} +(-1.89316 + 5.82655i) q^{8} +(5.54755 + 4.03053i) q^{9} -8.76873 q^{10} +(-2.93767 + 1.53952i) q^{11} -13.8715i q^{12} +(-0.209673 - 0.152336i) q^{13} +(0.330841 + 0.107497i) q^{14} +(10.3350 - 3.35805i) q^{15} +(-5.40770 + 3.92892i) q^{16} +(2.40685 + 3.31275i) q^{17} +(5.36826 + 16.5218i) q^{18} +(3.11953 - 3.04442i) q^{19} +(-12.3719 - 8.98868i) q^{20} -0.431104 q^{21} +(-8.31350 - 1.21914i) q^{22} +3.85070 q^{23} +(11.3057 - 15.5610i) q^{24} +(2.15695 - 6.63842i) q^{25} +(-0.202897 - 0.624451i) q^{26} +(-7.11806 - 9.79717i) q^{27} +(0.356593 + 0.490808i) q^{28} +(2.04657 + 6.29870i) q^{29} +(26.1830 + 8.50736i) q^{30} +(-3.73581 + 5.14190i) q^{31} -4.68133 q^{32} +(10.2653 - 1.74681i) q^{33} +10.3738i q^{34} +(-0.279353 + 0.384497i) q^{35} +(-9.36213 + 28.8137i) q^{36} +(-0.615510 + 0.199991i) q^{37} +(10.9272 - 1.59447i) q^{38} +(0.478277 + 0.658291i) q^{39} +(-6.55264 - 20.1670i) q^{40} +(-0.326912 + 1.00613i) q^{41} +(-0.883582 - 0.641960i) q^{42} -4.91923i q^{43} +(-10.4798 - 10.2421i) q^{44} -23.7341 q^{45} +(7.89232 + 5.73410i) q^{46} +(1.74188 - 5.36096i) q^{47} +(19.9589 - 6.48505i) q^{48} +(-5.64787 + 4.10341i) q^{49} +(14.3062 - 10.3940i) q^{50} +(-3.97273 - 12.2268i) q^{51} +(0.353847 - 1.08903i) q^{52} +(-1.08801 + 1.49752i) q^{53} -30.6797i q^{54} +(5.09394 - 10.2875i) q^{55} +0.841222i q^{56} +(-12.2684 + 6.06394i) q^{57} +(-5.18483 + 15.9573i) q^{58} +(-3.78753 + 1.23064i) q^{59} +(28.2210 + 38.8428i) q^{60} +(-1.44173 - 1.98437i) q^{61} +(-15.3137 + 4.97572i) q^{62} +(0.895481 + 0.290959i) q^{63} +(1.22064 + 0.886845i) q^{64} +0.897044 q^{65} +(23.6409 + 11.7060i) q^{66} -3.19367i q^{67} +(-10.6340 + 14.6365i) q^{68} +(-11.4980 - 3.73592i) q^{69} +(-1.14512 + 0.372070i) q^{70} +(-2.80305 - 3.85807i) q^{71} +(-33.9865 + 24.6926i) q^{72} +(6.35844 - 2.06598i) q^{73} +(-1.55935 - 0.506663i) q^{74} +(-12.8811 + 17.7293i) q^{75} +(17.0517 + 8.95166i) q^{76} +(-0.318308 + 0.325696i) q^{77} +2.06143i q^{78} +(8.16513 + 5.93231i) q^{79} +(7.14935 - 22.0034i) q^{80} +(5.39207 + 16.5951i) q^{81} +(-2.16827 + 1.57534i) q^{82} +(7.13976 + 9.82703i) q^{83} +(-0.588589 - 1.81149i) q^{84} +(-13.4793 - 4.37968i) q^{85} +(7.32527 - 10.0824i) q^{86} -20.7932i q^{87} +(-3.40859 - 20.0310i) q^{88} +16.2720i q^{89} +(-48.6450 - 35.3427i) q^{90} +(-0.0338452 - 0.0109970i) q^{91} +(5.25738 + 16.1806i) q^{92} +(16.1436 - 11.7290i) q^{93} +(11.5532 - 8.39387i) q^{94} +(-2.54153 + 14.8715i) q^{95} +(13.9782 + 4.54179i) q^{96} +(7.26679 - 10.0019i) q^{97} -17.6862 q^{98} +(-22.5019 - 3.29982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 32 q^{4} - 10 q^{5} - 20 q^{6} + 20 q^{7} + 32 q^{9} - 28 q^{11} + 20 q^{16} + 10 q^{17} - 10 q^{19} - 52 q^{20} - 20 q^{23} + 40 q^{24} + 12 q^{25} + 16 q^{26} + 10 q^{28} + 20 q^{30} + 60 q^{35}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 32 * q^4 - 10 * q^5 - 20 * q^6 + 20 * q^7 + 32 * q^9 - 28 * q^11 + 20 * q^16 + 10 * q^17 - 10 * q^19 - 52 * q^20 - 20 * q^23 + 40 * q^24 + 12 * q^25 + 16 * q^26 + 10 * q^28 + 20 * q^30 + 60 * q^35 - 32 * q^36 - 10 * q^38 - 40 * q^39 - 48 * q^42 - 38 * q^44 - 60 * q^45 + 6 * q^47 - 46 * q^49 - 12 * q^55 - 10 * q^57 + 74 * q^58 + 20 * q^61 - 30 * q^62 - 90 * q^63 + 48 * q^64 + 74 * q^66 - 170 * q^68 - 30 * q^73 - 20 * q^74 + 24 * q^77 + 18 * q^80 + 82 * q^81 - 12 * q^82 + 110 * q^83 + 30 * q^85 + 20 * q^92 + 82 * q^93 - 100 * q^95 + 20 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more