LMFDB - Embedded newform 273.2.j.c.100.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.10
Root			$-1.35774 + 2.35168i$ of defining polynomial
Character	$\chi$	$=$	273.100
Dual form			273.2.j.c.172.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35774 + 2.35168i) q^{2} +1.00000 q^{3} +(-2.68694 + 4.65391i) q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(0.587055 + 2.57980i) q^{7} -9.16172 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.35774 + 2.35168i) q^{2} +1.00000 q^{3} +(-2.68694 + 4.65391i) q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(0.587055 + 2.57980i) q^{7} -9.16172 q^{8} +1.00000 q^{9} +10.5585 q^{10} -1.63165 q^{11} +(-2.68694 + 4.65391i) q^{12} +(-3.59984 - 0.202826i) q^{13} +(-5.26980 + 4.88327i) q^{14} +(1.94413 - 3.36734i) q^{15} +(-7.06539 - 12.2376i) q^{16} +(2.09582 - 3.63006i) q^{17} +(1.35774 + 2.35168i) q^{18} +1.69453 q^{19} +(10.4475 + 18.0956i) q^{20} +(0.587055 + 2.57980i) q^{21} +(-2.21536 - 3.83712i) q^{22} +(-0.395707 - 0.685385i) q^{23} -9.16172 q^{24} +(-5.05930 - 8.76296i) q^{25} +(-4.41068 - 8.74107i) q^{26} +1.00000 q^{27} +(-13.5835 - 4.19966i) q^{28} +(-0.242434 + 0.419908i) q^{29} +10.5585 q^{30} +(-0.915382 - 1.58549i) q^{31} +(10.0243 - 17.3625i) q^{32} -1.63165 q^{33} +11.3823 q^{34} +(9.82836 + 3.03866i) q^{35} +(-2.68694 + 4.65391i) q^{36} +(-0.344621 - 0.596901i) q^{37} +(2.30074 + 3.98500i) q^{38} +(-3.59984 - 0.202826i) q^{39} +(-17.8116 + 30.8506i) q^{40} +(2.96941 - 5.14316i) q^{41} +(-5.26980 + 4.88327i) q^{42} +(2.79224 + 4.83630i) q^{43} +(4.38414 - 7.59355i) q^{44} +(1.94413 - 3.36734i) q^{45} +(1.07454 - 1.86116i) q^{46} +(-0.292223 + 0.506146i) q^{47} +(-7.06539 - 12.2376i) q^{48} +(-6.31073 + 3.02897i) q^{49} +(13.7385 - 23.7957i) q^{50} +(2.09582 - 3.63006i) q^{51} +(10.6165 - 16.2084i) q^{52} +(3.04896 + 5.28096i) q^{53} +(1.35774 + 2.35168i) q^{54} +(-3.17214 + 5.49431i) q^{55} +(-5.37843 - 23.6354i) q^{56} +1.69453 q^{57} -1.31665 q^{58} +(-4.13854 + 7.16816i) q^{59} +(10.4475 + 18.0956i) q^{60} -9.08491 q^{61} +(2.48571 - 4.30537i) q^{62} +(0.587055 + 2.57980i) q^{63} +26.1800 q^{64} +(-7.68155 + 11.7276i) q^{65} +(-2.21536 - 3.83712i) q^{66} +1.00054 q^{67} +(11.2626 + 19.5075i) q^{68} +(-0.395707 - 0.685385i) q^{69} +(6.19844 + 27.2389i) q^{70} +(7.93720 + 13.7476i) q^{71} -9.16172 q^{72} +(-2.92626 - 5.06843i) q^{73} +(0.935814 - 1.62088i) q^{74} +(-5.05930 - 8.76296i) q^{75} +(-4.55310 + 7.88620i) q^{76} +(-0.957867 - 4.20933i) q^{77} +(-4.41068 - 8.74107i) q^{78} +(0.643065 - 1.11382i) q^{79} -54.9442 q^{80} +1.00000 q^{81} +16.1268 q^{82} -6.18202 q^{83} +(-13.5835 - 4.19966i) q^{84} +(-8.14908 - 14.1146i) q^{85} +(-7.58229 + 13.1329i) q^{86} +(-0.242434 + 0.419908i) q^{87} +14.9487 q^{88} +(2.20434 + 3.81803i) q^{89} +10.5585 q^{90} +(-1.59005 - 9.40594i) q^{91} +4.25296 q^{92} +(-0.915382 - 1.58549i) q^{93} -1.58706 q^{94} +(3.29439 - 5.70606i) q^{95} +(10.0243 - 17.3625i) q^{96} +(5.08782 + 8.81236i) q^{97} +(-15.6915 - 10.7283i) q^{98} -1.63165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.35774	+	2.35168i	0.960070	+	1.66289i	0.722314	+	0.691565i	$0.243078\pi$
$2$	1.35774	+	2.35168i	0.960070	+	1.66289i	0.237756	+	0.971325i	$0.423588\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.68694	+	4.65391i	−1.34347	+	2.32696i
$5$	1.94413	−	3.36734i	0.869442	−	1.50592i	0.00687463	−	0.999976i	$-0.497812\pi$
$5$	1.94413	−	3.36734i	0.869442	−	1.50592i	0.862568	−	0.505942i	$-0.168855\pi$
$6$	1.35774	+	2.35168i	0.554297	+	0.960070i
$7$	0.587055	+	2.57980i	0.221886	+	0.975073i
$7$	0.587055	+	2.57980i	0.221886	+	0.975073i
$8$	−9.16172			−3.23916
$9$	1.00000			0.333333
$10$	10.5585			3.33890
$11$	−1.63165			−0.491961			−0.245980	−	0.969275i	$-0.579110\pi$
$11$	−1.63165			−0.491961			−0.245980	+	0.969275i	$0.579110\pi$
$12$	−2.68694	+	4.65391i	−0.775652	+	1.34347i
$13$	−3.59984	−	0.202826i	−0.998417	−	0.0562537i
$13$	−3.59984	−	0.202826i	−0.998417	−	0.0562537i
$14$	−5.26980	+	4.88327i	−1.40841	+	1.30511i
$15$	1.94413	−	3.36734i	0.501973	−	0.869442i
$16$	−7.06539	−	12.2376i	−1.76635	−	3.05940i
$17$	2.09582	−	3.63006i	0.508310	−	0.880419i	−0.491644	−	0.870796i	$-0.663604\pi$
$17$	2.09582	−	3.63006i	0.508310	−	0.880419i	0.999954	−	0.00962217i	$-0.00306288\pi$
$18$	1.35774	+	2.35168i	0.320023	+	0.554297i
$19$	1.69453			0.388752			0.194376	−	0.980927i	$-0.437732\pi$
$19$	1.69453			0.388752			0.194376	+	0.980927i	$0.437732\pi$
$20$	10.4475	+	18.0956i	2.33614	+	4.04631i
$21$	0.587055	+	2.57980i	0.128106	+	0.562958i
$22$	−2.21536	−	3.83712i	−0.472317	−	0.818077i
$23$	−0.395707	−	0.685385i	−0.0825107	−	0.142913i	0.821817	−	0.569751i	$-0.192961\pi$
$23$	−0.395707	−	0.685385i	−0.0825107	−	0.142913i	−0.904328	+	0.426839i	$0.859627\pi$
$24$	−9.16172			−1.87013
$25$	−5.05930	−	8.76296i	−1.01186	−	1.75259i
$26$	−4.41068	−	8.74107i	−0.865006	−	1.71426i
$27$	1.00000			0.192450
$28$	−13.5835	−	4.19966i	−2.56705	−	0.793661i
$29$	−0.242434	+	0.419908i	−0.0450188	+	0.0779749i	−0.887657	−	0.460506i	$-0.847668\pi$
$29$	−0.242434	+	0.419908i	−0.0450188	+	0.0779749i	0.842638	+	0.538481i	$0.181001\pi$
$30$	10.5585			1.92772
$31$	−0.915382	−	1.58549i	−0.164407	−	0.284762i	0.772037	−	0.635577i	$-0.219238\pi$
$31$	−0.915382	−	1.58549i	−0.164407	−	0.284762i	−0.936445	+	0.350815i	$0.885905\pi$
$32$	10.0243	−	17.3625i	1.77206	−	3.06929i
$33$	−1.63165			−0.284034
$34$	11.3823			1.95205
$35$	9.82836	+	3.03866i	1.66130	+	0.513627i
$36$	−2.68694	+	4.65391i	−0.447823	+	0.775652i
$37$	−0.344621	−	0.596901i	−0.0566553	−	0.0981299i	0.836307	−	0.548262i	$-0.184710\pi$
$37$	−0.344621	−	0.596901i	−0.0566553	−	0.0981299i	−0.892962	+	0.450132i	$0.851377\pi$
$38$	2.30074	+	3.98500i	0.373229	+	0.646452i
$39$	−3.59984	−	0.202826i	−0.576436	−	0.0324781i
$40$	−17.8116	+	30.8506i	−2.81626	+	4.87790i
$41$	2.96941	−	5.14316i	0.463743	−	0.803227i	−0.535400	−	0.844598i	$-0.679839\pi$
$41$	2.96941	−	5.14316i	0.463743	−	0.803227i	0.999144	+	0.0413712i	$0.0131726\pi$
$42$	−5.26980	+	4.88327i	−0.813147	+	0.753505i
$43$	2.79224	+	4.83630i	0.425813	+	0.737529i	0.996496	−	0.0836411i	$-0.0266549\pi$
$43$	2.79224	+	4.83630i	0.425813	+	0.737529i	−0.570683	+	0.821170i	$0.693322\pi$
$44$	4.38414	−	7.59355i	0.660934	−	1.14477i
$45$	1.94413	−	3.36734i	0.289814	−	0.501973i
$46$	1.07454	−	1.86116i	0.158432	−	0.274412i
$47$	−0.292223	+	0.506146i	−0.0426252	+	0.0738289i	−0.886551	−	0.462631i	$-0.846905\pi$
$47$	−0.292223	+	0.506146i	−0.0426252	+	0.0738289i	0.843926	+	0.536460i	$0.180239\pi$
$48$	−7.06539	−	12.2376i	−1.01980	−	1.76635i
$49$	−6.31073	+	3.02897i	−0.901533	+	0.432710i
$50$	13.7385	−	23.7957i	1.94291	−	3.36522i
$51$	2.09582	−	3.63006i	0.293473	−	0.508310i
$52$	10.6165	−	16.2084i	1.47224	−	2.24770i
$53$	3.04896	+	5.28096i	0.418807	+	0.725396i	0.995820	−	0.0913397i	$-0.0291149\pi$
$53$	3.04896	+	5.28096i	0.418807	+	0.725396i	−0.577012	+	0.816735i	$0.695782\pi$
$54$	1.35774	+	2.35168i	0.184766	+	0.320023i
$55$	−3.17214	+	5.49431i	−0.427731	+	0.740853i
$56$	−5.37843	−	23.6354i	−0.718723	−	3.15841i
$57$	1.69453			0.224446
$58$	−1.31665			−0.172885
$59$	−4.13854	+	7.16816i	−0.538792	+	0.933215i	0.460178	+	0.887827i	$0.347786\pi$
$59$	−4.13854	+	7.16816i	−0.538792	+	0.933215i	−0.998969	+	0.0453878i	$0.985548\pi$
$60$	10.4475	+	18.0956i	1.34877	+	2.33614i
$61$	−9.08491			−1.16320			−0.581602	−	0.813473i	$-0.697574\pi$
$61$	−9.08491			−1.16320			−0.581602	+	0.813473i	$0.697574\pi$
$62$	2.48571	−	4.30537i	0.315685	−	0.546783i
$63$	0.587055	+	2.57980i	0.0739619	+	0.325024i
$64$	26.1800			3.27250
$65$	−7.68155	+	11.7276i	−0.952779	+	1.45462i
$66$	−2.21536	−	3.83712i	−0.272692	−	0.472317i
$67$	1.00054			0.122236			0.0611178	−	0.998131i	$-0.480533\pi$
$67$	1.00054			0.122236			0.0611178	+	0.998131i	$0.480533\pi$
$68$	11.2626	+	19.5075i	1.36580	+	2.36563i
$69$	−0.395707	−	0.685385i	−0.0476376	−	0.0825107i
$70$	6.19844	+	27.2389i	0.740855	+	3.25567i
$71$	7.93720	+	13.7476i	0.941972	+	1.63154i	0.761703	+	0.647927i	$0.224364\pi$
$71$	7.93720	+	13.7476i	0.941972	+	1.63154i	0.180270	+	0.983617i	$0.442303\pi$
$72$	−9.16172			−1.07972
$73$	−2.92626	−	5.06843i	−0.342492	−	0.593214i	0.642402	−	0.766367i	$-0.277938\pi$
$73$	−2.92626	−	5.06843i	−0.342492	−	0.593214i	−0.984895	+	0.173153i	$0.944604\pi$
$74$	0.935814	−	1.62088i	0.108786	−	0.188423i
$75$	−5.05930	−	8.76296i	−0.584197	−	1.01186i
$76$	−4.55310	+	7.88620i	−0.522276	+	0.904609i
$77$	−0.957867	−	4.20933i	−0.109159	−	0.479698i
$78$	−4.41068	−	8.74107i	−0.499411	−	0.989731i
$79$	0.643065	−	1.11382i	0.0723505	−	0.125315i	−0.827581	−	0.561347i	$-0.810283\pi$
$79$	0.643065	−	1.11382i	0.0723505	−	0.125315i	0.899931	+	0.436032i	$0.143617\pi$
$80$	−54.9442			−6.14295
$81$	1.00000			0.111111
$82$	16.1268			1.78090
$83$	−6.18202			−0.678565			−0.339283	−	0.940684i	$-0.610184\pi$
$83$	−6.18202			−0.678565			−0.339283	+	0.940684i	$0.610184\pi$
$84$	−13.5835	−	4.19966i	−1.48209	−	0.458220i
$85$	−8.14908	−	14.1146i	−0.883892	−	1.53095i
$86$	−7.58229	+	13.1329i	−0.817620	+	1.41616i
$87$	−0.242434	+	0.419908i	−0.0259916	+	0.0450188i
$88$	14.9487			1.59354
$89$	2.20434	+	3.81803i	0.233660	+	0.404711i	0.958882	−	0.283804i	$-0.0915964\pi$
$89$	2.20434	+	3.81803i	0.233660	+	0.404711i	−0.725222	+	0.688515i	$0.758263\pi$
$90$	10.5585			1.11297
$91$	−1.59005	−	9.40594i	−0.166683	−	0.986011i
$92$	4.25296			0.443402
$93$	−0.915382	−	1.58549i	−0.0949207	−	0.164407i
$94$	−1.58706			−0.163693
$95$	3.29439	−	5.70606i	0.337998	−	0.585429i
$96$	10.0243	−	17.3625i	1.02310	−	1.77206i
$97$	5.08782	+	8.81236i	0.516590	+	0.894759i	0.999814	+	0.0192631i	$0.00613202\pi$
$97$	5.08782	+	8.81236i	0.516590	+	0.894759i	−0.483225	+	0.875496i	$0.660535\pi$
$98$	−15.6915	−	10.7283i	−1.58508	−	1.08372i
$99$	−1.63165			−0.163987
$100$	54.3761			5.43761
$101$	14.1729			1.41025			0.705126	−	0.709082i	$-0.250890\pi$
$101$	14.1729			1.41025			0.705126	+	0.709082i	$0.250890\pi$
$102$	11.3823			1.12702
$103$	−0.891175	+	1.54356i	−0.0878101	+	0.152092i	−0.906585	−	0.422023i	$-0.861320\pi$
$103$	−0.891175	+	1.54356i	−0.0878101	+	0.152092i	0.818775	+	0.574114i	$0.194654\pi$
$104$	32.9807	+	1.85823i	3.23403	+	0.182214i
$105$	9.82836	+	3.03866i	0.959150	+	0.296543i
$106$	−8.27942	+	14.3404i	−0.804169	+	1.39286i
$107$	−9.60772	−	16.6411i	−0.928814	−	1.60875i	−0.785310	−	0.619103i	$-0.787496\pi$
$107$	−9.60772	−	16.6411i	−0.928814	−	1.60875i	−0.143504	−	0.989650i	$-0.545837\pi$
$108$	−2.68694	+	4.65391i	−0.258551	+	0.447823i
$109$	−5.34907	−	9.26486i	−0.512348	−	0.887413i	−0.999898	−	0.0143174i	$-0.995442\pi$
$109$	−5.34907	−	9.26486i	−0.512348	−	0.887413i	0.487550	−	0.873095i	$-0.337891\pi$
$110$	−17.2278			−1.64261
$111$	−0.344621	−	0.596901i	−0.0327100	−	0.0566553i
$112$	27.4228	−	25.4114i	2.59121	−	2.40116i
$113$	−3.82284	−	6.62135i	−0.359622	−	0.622884i	0.628275	−	0.777991i	$-0.283761\pi$
$113$	−3.82284	−	6.62135i	−0.359622	−	0.622884i	−0.987898	+	0.155107i	$0.950428\pi$
$114$	2.30074	+	3.98500i	0.215484	+	0.373229i
$115$	−3.07723			−0.286953
$116$	−1.30281	−	2.25653i	−0.120963	−	0.209514i
$117$	−3.59984	−	0.202826i	−0.332806	−	0.0187512i
$118$	−22.4763			−2.06911
$119$	10.5952	+	3.27574i	0.971259	+	0.300287i
$120$	−17.8116	+	30.8506i	−1.62597	+	2.81626i
$121$	−8.33772			−0.757975
$122$	−12.3350	−	21.3648i	−1.11676	−	1.93428i
$123$	2.96941	−	5.14316i	0.267742	−	0.463743i
$124$	9.83829			0.883505
$125$	−19.9025			−1.78013
$126$	−5.26980	+	4.88327i	−0.469471	+	0.435037i
$127$	1.88510	−	3.26510i	0.167276	−	0.289730i	−0.770185	−	0.637820i	$-0.779836\pi$
$127$	1.88510	−	3.26510i	0.167276	−	0.289730i	0.937461	+	0.348090i	$0.113170\pi$
$128$	15.4972	+	26.8419i	1.36977	+	2.37251i
$129$	2.79224	+	4.83630i	0.245843	+	0.425813i
$130$	−38.0091	−	2.14154i	−3.33361	−	0.187826i
$131$	9.00807	−	15.6024i	0.787039	−	1.36319i	−0.140735	−	0.990047i	$-0.544947\pi$
$131$	9.00807	−	15.6024i	0.787039	−	1.36319i	0.927774	−	0.373143i	$-0.121720\pi$
$132$	4.38414	−	7.59355i	0.381590	−	0.660934i
$133$	0.994783	+	4.37155i	0.0862586	+	0.379062i
$134$	1.35848	+	2.35296i	0.117355	+	0.203264i
$135$	1.94413	−	3.36734i	0.167324	−	0.289814i
$136$	−19.2013	+	33.2576i	−1.64649	+	2.85181i
$137$	−10.8986	+	18.8769i	−0.931128	+	1.61276i	−0.149731	+	0.988727i	$0.547841\pi$
$137$	−10.8986	+	18.8769i	−0.931128	+	1.61276i	−0.781397	+	0.624035i	$0.785492\pi$
$138$	1.07454	−	1.86116i	0.0914708	−	0.158432i
$139$	0.355981	+	0.616576i	0.0301939	+	0.0522973i	0.880727	−	0.473623i	$-0.157054\pi$
$139$	0.355981	+	0.616576i	0.0301939	+	0.0522973i	−0.850534	+	0.525921i	$0.823721\pi$
$140$	−40.5499	+	37.5756i	−3.42709	+	3.17572i
$141$	−0.292223	+	0.506146i	−0.0246096	+	0.0426252i
$142$	−21.5534	+	37.3315i	−1.80872	+	3.13279i
$143$	5.87368	+	0.330940i	0.491182	+	0.0276746i
$144$	−7.06539	−	12.2376i	−0.588782	−	1.01980i
$145$	0.942647	+	1.63271i	0.0782826	+	0.135589i
$146$	7.94622	−	13.7632i	0.657633	−	1.13905i
$147$	−6.31073	+	3.02897i	−0.520501	+	0.249825i
$148$	3.70390			0.304459
$149$	−5.59281			−0.458181			−0.229090	−	0.973405i	$-0.573575\pi$
$149$	−5.59281			−0.458181			−0.229090	+	0.973405i	$0.573575\pi$
$150$	13.7385	−	23.7957i	1.12174	−	1.94291i
$151$	4.99718	+	8.65536i	0.406664	+	0.704364i	0.994514	−	0.104607i	$-0.0333585\pi$
$151$	4.99718	+	8.65536i	0.406664	+	0.704364i	−0.587849	+	0.808971i	$0.700025\pi$
$152$	−15.5248			−1.25923
$153$	2.09582	−	3.63006i	0.169437	−	0.293473i
$154$	8.59846	−	7.96779i	0.692884	−	0.642063i
$155$	−7.11849			−0.571771
$156$	10.6165	−	16.2084i	0.849999	−	1.29771i
$157$	9.42039	+	16.3166i	0.751829	+	1.30221i	0.946935	+	0.321424i	$0.104162\pi$
$157$	9.42039	+	16.3166i	0.751829	+	1.30221i	−0.195106	+	0.980782i	$0.562505\pi$
$158$	3.49247			0.277846
$159$	3.04896	+	5.28096i	0.241799	+	0.418807i
$160$	−38.9770	−	67.5101i	−3.08140	−	5.33714i
$161$	1.53586	−	1.42320i	0.121042	−	0.112164i
$162$	1.35774	+	2.35168i	0.106674	+	0.184766i
$163$	−24.4471			−1.91485			−0.957423	−	0.288690i	$-0.906780\pi$
$163$	−24.4471			−1.91485			−0.957423	+	0.288690i	$0.906780\pi$
$164$	15.9572	+	27.6387i	1.24605	+	2.15822i
$165$	−3.17214	+	5.49431i	−0.246951	+	0.427731i
$166$	−8.39361	−	14.5382i	−0.651470	−	1.12838i
$167$	−4.28482	+	7.42152i	−0.331569	+	0.574295i	−0.982820	−	0.184568i	$-0.940911\pi$
$167$	−4.28482	+	7.42152i	−0.331569	+	0.574295i	0.651251	+	0.758863i	$0.274245\pi$
$168$	−5.37843	−	23.6354i	−0.414955	−	1.82351i
$169$	12.9177	+	1.46028i	0.993671	+	0.112329i
$170$	22.1287	−	38.3281i	1.69720	−	2.93963i
$171$	1.69453			0.129584
$172$	−30.0103			−2.28826
$173$	7.68079			0.583960			0.291980	−	0.956424i	$-0.405686\pi$
$173$	7.68079			0.583960			0.291980	+	0.956424i	$0.405686\pi$
$174$	−1.31665			−0.0998152
$175$	19.6366	−	18.1963i	1.48439	−	1.37551i
$176$	11.5282	+	19.9675i	0.868974	+	1.50511i
$177$	−4.13854	+	7.16816i	−0.311072	+	0.538792i
$178$	−5.98587	+	10.3678i	−0.448660	+	0.777101i
$179$	9.74388			0.728292			0.364146	−	0.931342i	$-0.381361\pi$
$179$	9.74388			0.728292			0.364146	+	0.931342i	$0.381361\pi$
$180$	10.4475	+	18.0956i	0.778712	+	1.34877i
$181$	−6.23699			−0.463592			−0.231796	−	0.972764i	$-0.574460\pi$
$181$	−6.23699			−0.463592			−0.231796	+	0.972764i	$0.574460\pi$
$182$	19.9609	−	16.5102i	1.47960	−	1.22381i
$183$	−9.08491			−0.671576
$184$	3.62536	+	6.27931i	0.267265	+	0.462917i
$185$	−2.67995			−0.197034
$186$	2.48571	−	4.30537i	0.182261	−	0.315685i
$187$	−3.41964	+	5.92298i	−0.250069	+	0.433131i
$188$	−1.57037	−	2.71996i	−0.114531	−	0.198374i
$189$	0.587055	+	2.57980i	0.0427019	+	0.187653i
$190$	17.8918			1.29801
$191$	3.04764			0.220520			0.110260	−	0.993903i	$-0.464832\pi$
$191$	3.04764			0.220520			0.110260	+	0.993903i	$0.464832\pi$
$192$	26.1800			1.88938
$193$	8.98343			0.646642			0.323321	−	0.946289i	$-0.395201\pi$
$193$	8.98343			0.646642			0.323321	+	0.946289i	$0.395201\pi$
$194$	−13.8159	+	23.9299i	−0.991924	+	1.71806i
$195$	−7.68155	+	11.7276i	−0.550087	+	0.839828i
$196$	2.86000	−	37.5082i	0.204286	−	2.67916i
$197$	−8.42977	+	14.6008i	−0.600596	+	1.04026i	0.392135	+	0.919908i	$0.371737\pi$
$197$	−8.42977	+	14.6008i	−0.600596	+	1.04026i	−0.992731	+	0.120355i	$0.961597\pi$
$198$	−2.21536	−	3.83712i	−0.157439	−	0.272692i
$199$	1.02262	−	1.77124i	0.0724919	−	0.125560i	−0.827501	−	0.561464i	$-0.810238\pi$
$199$	1.02262	−	1.77124i	0.0724919	−	0.125560i	0.899993	+	0.435905i	$0.143572\pi$
$200$	46.3519	+	80.2838i	3.27757	+	5.67692i
$201$	1.00054			0.0705728
$202$	19.2431	+	33.3300i	1.35394	+	2.34509i
$203$	−1.22560	−	0.378922i	−0.0860203	−	0.0265951i
$204$	11.2626	+	19.5075i	0.788543	+	1.36580i
$205$	−11.5458	−	19.9980i	−0.806396	−	1.39672i
$206$	−4.83995			−0.337215
$207$	−0.395707	−	0.685385i	−0.0275036	−	0.0476376i
$208$	22.9522	+	45.4865i	1.59145	+	3.15392i
$209$	−2.76488			−0.191251
$210$	6.19844	+	27.2389i	0.427733	+	1.87966i
$211$	12.3382	−	21.3705i	0.849400	−	1.47120i	−0.0323446	−	0.999477i	$-0.510297\pi$
$211$	12.3382	−	21.3705i	0.849400	−	1.47120i	0.881745	−	0.471727i	$-0.156369\pi$
$212$	−32.7695			−2.25062
$213$	7.93720	+	13.7476i	0.543848	+	0.941972i
$214$	26.0897	−	45.1886i	1.78345	−	3.08903i
$215$	21.7139			1.48088
$216$	−9.16172			−0.623376
$217$	3.55286	−	3.29227i	0.241184	−	0.223494i
$218$	14.5253	−	25.1586i	0.983780	−	1.70396i
$219$	−2.92626	−	5.06843i	−0.197738	−	0.342492i
$220$	−17.0467	−	29.5257i	−1.14929	−	1.99062i
$221$	−8.28087	+	12.6426i	−0.557032	+	0.850430i
$222$	0.935814	−	1.62088i	0.0628077	−	0.108786i
$223$	−8.99595	+	15.5814i	−0.602413	+	1.04341i	0.390041	+	0.920797i	$0.372461\pi$
$223$	−8.99595	+	15.5814i	−0.602413	+	1.04341i	−0.992455	+	0.122613i	$0.960873\pi$
$224$	50.6767	+	15.6678i	3.38598	+	1.04685i
$225$	−5.05930	−	8.76296i	−0.337287	−	0.584197i
$226$	10.3809	−	17.9802i	0.690525	−	1.19603i
$227$	4.17286	−	7.22761i	0.276963	−	0.479713i	−0.693666	−	0.720297i	$-0.744006\pi$
$227$	4.17286	−	7.22761i	0.276963	−	0.479713i	0.970628	+	0.240584i	$0.0773389\pi$
$228$	−4.55310	+	7.88620i	−0.301536	+	0.522276i
$229$	−11.1172	+	19.2556i	−0.734647	+	1.27245i	0.220232	+	0.975448i	$0.429319\pi$
$229$	−11.1172	+	19.2556i	−0.734647	+	1.27245i	−0.954878	+	0.296998i	$0.904015\pi$
$230$	−4.17809	−	7.23666i	−0.275495	−	0.477172i
$231$	−0.957867	−	4.20933i	−0.0630230	−	0.276953i
$232$	2.22111	−	3.84708i	0.145823	−	0.252573i
$233$	2.50918	−	4.34602i	0.164382	−	0.284717i	−0.772054	−	0.635557i	$-0.780771\pi$
$233$	2.50918	−	4.34602i	0.164382	−	0.284717i	0.936435	+	0.350840i	$0.114104\pi$
$234$	−4.41068	−	8.74107i	−0.288335	−	0.571421i
$235$	1.13624	+	1.96803i	0.0741202	+	0.128380i
$236$	−22.2400	−	38.5208i	−1.44770	−	2.50749i
$237$	0.643065	−	1.11382i	0.0417716	−	0.0723505i
$238$	6.68205	+	29.3641i	0.433133	+	1.90339i
$239$	9.28305			0.600470			0.300235	−	0.953865i	$-0.402935\pi$
$239$	9.28305			0.600470			0.300235	+	0.953865i	$0.402935\pi$
$240$	−54.9442			−3.54663
$241$	7.39469	−	12.8080i	0.476334	−	0.825035i	−0.523298	−	0.852150i	$-0.675299\pi$
$241$	7.39469	−	12.8080i	0.476334	−	0.825035i	0.999632	+	0.0271148i	$0.00863198\pi$
$242$	−11.3205	−	19.6077i	−0.727709	−	1.26043i
$243$	1.00000			0.0641500
$244$	24.4106	−	42.2804i	1.56273	−	2.70672i
$245$	−2.06935	+	27.1391i	−0.132206	+	1.73385i
$246$	16.1268			1.02821
$247$	−6.10005	−	0.343694i	−0.388137	−	0.0218687i
$248$	8.38647	+	14.5258i	0.532541	+	0.922388i
$249$	−6.18202			−0.391770
$250$	−27.0224	−	46.8042i	−1.70905	−	2.96016i
$251$	4.80626	+	8.32468i	0.303368	+	0.525449i	0.976897	−	0.213712i	$-0.0685555\pi$
$251$	4.80626	+	8.32468i	0.303368	+	0.525449i	−0.673529	+	0.739161i	$0.735222\pi$
$252$	−13.5835	−	4.19966i	−0.855683	−	0.264554i
$253$	0.645656	+	1.11831i	0.0405920	+	0.0703075i
$254$	10.2380			0.642386
$255$	−8.14908	−	14.1146i	−0.510315	−	0.883892i
$256$	−15.9024	+	27.5438i	−0.993902	+	1.72149i
$257$	−2.52788	−	4.37842i	−0.157685	−	0.273118i	0.776349	−	0.630304i	$-0.217070\pi$
$257$	−2.52788	−	4.37842i	−0.157685	−	0.273118i	−0.934033	+	0.357186i	$0.883736\pi$
$258$	−7.58229	+	13.1329i	−0.472053	+	0.817620i
$259$	1.33757	−	1.23947i	0.0831128	−	0.0770167i
$260$	−33.9392	−	67.2605i	−2.10482	−	4.17132i
$261$	−0.242434	+	0.419908i	−0.0150063	+	0.0259916i
$262$	48.9226			3.02245
$263$	23.3538			1.44005			0.720027	−	0.693946i	$-0.244129\pi$
$263$	23.3538			1.44005			0.720027	+	0.693946i	$0.244129\pi$
$264$	14.9487			0.920029
$265$	23.7104			1.45652
$266$	−8.92984	+	8.27486i	−0.547523	+	0.507364i
$267$	2.20434	+	3.81803i	0.134904	+	0.233660i
$268$	−2.68839	+	4.65644i	−0.164220	+	0.284437i
$269$	15.6957	−	27.1858i	0.956984	−	1.65754i	0.227223	−	0.973843i	$-0.427035\pi$
$269$	15.6957	−	27.1858i	0.956984	−	1.65754i	0.729761	−	0.683702i	$-0.239631\pi$
$270$	10.5585			0.642572
$271$	5.66515	+	9.81233i	0.344134	+	0.596057i	0.985196	−	0.171432i	$-0.0548394\pi$
$271$	5.66515	+	9.81233i	0.344134	+	0.596057i	−0.641062	+	0.767489i	$0.721506\pi$
$272$	−59.2310			−3.59141
$273$	−1.59005	−	9.40594i	−0.0962345	−	0.569273i
$274$	−59.1899			−3.57579
$275$	8.25500	+	14.2981i	0.497795	+	0.862207i
$276$	4.25296			0.255998
$277$	−8.96129	+	15.5214i	−0.538432	+	0.932592i	0.460557	+	0.887630i	$0.347650\pi$
$277$	−8.96129	+	15.5214i	−0.538432	+	0.932592i	−0.998989	+	0.0449613i	$0.985684\pi$
$278$	−0.966661	+	1.67431i	−0.0579765	+	0.100418i
$279$	−0.915382	−	1.58549i	−0.0548025	−	0.0949207i
$280$	−90.0447	−	27.8393i	−5.38120	−	1.66372i
$281$	−11.6172			−0.693021			−0.346511	−	0.938046i	$-0.612634\pi$
$281$	−11.6172			−0.693021			−0.346511	+	0.938046i	$0.612634\pi$
$282$	−1.58706			−0.0945079
$283$	−8.09192			−0.481015			−0.240507	−	0.970647i	$-0.577314\pi$
$283$	−8.09192			−0.481015			−0.240507	+	0.970647i	$0.577314\pi$
$284$	−85.3070			−5.06204
$285$	3.29439	−	5.70606i	0.195143	−	0.337998i
$286$	7.19669	+	14.2624i	0.425549	+	0.843351i
$287$	15.0115	+	4.64116i	0.886103	+	0.273959i
$288$	10.0243	−	17.3625i	0.590685	−	1.02310i
$289$	−0.284884	−	0.493434i	−0.0167579	−	0.0290255i
$290$	−2.55975	+	4.43361i	−0.150313	+	0.260351i
$291$	5.08782	+	8.81236i	0.298253	+	0.516590i
$292$	31.4507			1.84051
$293$	−8.90887	−	15.4306i	−0.520461	−	0.901466i	−0.999717	−	0.0237903i	$-0.992427\pi$
$293$	−8.90887	−	15.4306i	−0.520461	−	0.901466i	0.479255	−	0.877675i	$-0.340907\pi$
$294$	−15.6915	−	10.7283i	−0.915148	−	0.625686i
$295$	16.0917	+	27.8717i	0.936897	+	1.62275i
$296$	3.15732	+	5.46864i	0.183515	+	0.317858i
$297$	−1.63165			−0.0946779
$298$	−7.59360	−	13.1525i	−0.439885	−	0.761904i
$299$	1.28547	+	2.54754i	0.0743407	+	0.147328i
$300$	54.3761			3.13940
$301$	−10.8375	+	10.0426i	−0.624663	+	0.578845i
$302$	−13.5698	+	23.5035i	−0.780853	+	1.35248i
$303$	14.1729			0.814209
$304$	−11.9725	−	20.7370i	−0.686671	−	1.18935i
$305$	−17.6623	+	30.5920i	−1.01134	+	1.75169i
$306$	11.3823			0.650684
$307$	16.1633			0.922487			0.461244	−	0.887274i	$-0.347403\pi$
$307$	16.1633			0.922487			0.461244	+	0.887274i	$0.347403\pi$
$308$	22.1636	+	6.85237i	1.26289	+	0.390450i
$309$	−0.891175	+	1.54356i	−0.0506972	+	0.0878101i
$310$	−9.66509	−	16.7404i	−0.548940	−	0.950792i
$311$	9.06145	+	15.6949i	0.513827	+	0.889975i	0.999871	+	0.0160409i	$0.00510619\pi$
$311$	9.06145	+	15.6949i	0.513827	+	0.889975i	−0.486044	+	0.873934i	$0.661560\pi$
$312$	32.9807	+	1.85823i	1.86717	+	0.105202i
$313$	12.8068	−	22.1820i	0.723882	−	1.25380i	−0.235550	−	0.971862i	$-0.575689\pi$
$313$	12.8068	−	22.1820i	0.723882	−	1.25380i	0.959432	−	0.281939i	$-0.0909774\pi$
$314$	−25.5810	+	44.3075i	−1.44362	+	2.50042i
$315$	9.82836	+	3.03866i	0.553766	+	0.171209i
$316$	3.45575	+	5.98554i	0.194401	+	0.336713i
$317$	13.7304	−	23.7817i	0.771174	−	1.33571i	−0.165746	−	0.986168i	$-0.553003\pi$
$317$	13.7304	−	23.7817i	0.771174	−	1.33571i	0.936920	−	0.349544i	$-0.113663\pi$
$318$	−8.27942	+	14.3404i	−0.464287	+	0.804169i
$319$	0.395567	−	0.685142i	0.0221475	−	0.0383606i
$320$	50.8973	−	88.1568i	2.84525	−	4.92811i
$321$	−9.60772	−	16.6411i	−0.536251	−	0.928814i
$322$	5.43222	+	1.67949i	0.302726	+	0.0935946i
$323$	3.55143	−	6.15125i	0.197607	−	0.342265i
$324$	−2.68694	+	4.65391i	−0.149274	+	0.258551i
$325$	16.4353	+	32.5714i	0.911668	+	1.80674i
$326$	−33.1929	−	57.4918i	−1.83839	−	3.18418i
$327$	−5.34907	−	9.26486i	−0.295804	−	0.512348i
$328$	−27.2049	+	47.1202i	−1.50214	+	2.60178i
$329$	−1.47731	−	0.456742i	−0.0814465	−	0.0251810i
$330$	−17.2278			−0.948361
$331$	6.95125			0.382075			0.191038	−	0.981583i	$-0.438815\pi$
$331$	6.95125			0.382075			0.191038	+	0.981583i	$0.438815\pi$
$332$	16.6107	−	28.7706i	0.911631	−	1.57899i
$333$	−0.344621	−	0.596901i	−0.0188851	−	0.0327100i
$334$	−23.2707			−1.27332
$335$	1.94519	−	3.36916i	0.106277	−	0.184077i
$336$	27.4228	−	25.4114i	1.49604	−	1.38631i
$337$	29.0505			1.58248			0.791242	−	0.611503i	$-0.209435\pi$
$337$	29.0505			1.58248			0.791242	+	0.611503i	$0.209435\pi$
$338$	14.1048	+	32.3611i	0.767203	+	1.76021i
$339$	−3.82284	−	6.62135i	−0.207628	−	0.359622i
$340$	87.5843			4.74993
$341$	1.49358	+	2.58696i	0.0808820	+	0.140092i
$342$	2.30074	+	3.98500i	0.124410	+	0.215484i
$343$	−11.5189	−	14.5023i	−0.621961	−	0.783048i
$344$	−25.5817	−	44.3088i	−1.37927	−	2.38897i
$345$	−3.07723			−0.165672
$346$	10.4285	+	18.0628i	0.560642	+	0.971061i
$347$	−2.55423	+	4.42405i	−0.137118	+	0.237496i	−0.926405	−	0.376530i	$-0.877117\pi$
$347$	−2.55423	+	4.42405i	−0.137118	+	0.237496i	0.789286	+	0.614025i	$0.210451\pi$
$348$	−1.30281	−	2.25653i	−0.0698379	−	0.120963i
$349$	12.2420	−	21.2038i	0.655300	−	1.13501i	−0.326519	−	0.945191i	$-0.605876\pi$
$349$	12.2420	−	21.2038i	0.655300	−	1.13501i	0.981819	−	0.189822i	$-0.0607911\pi$
$350$	69.4534	+	21.4731i	3.71244	+	1.14779i
$351$	−3.59984	−	0.202826i	−0.192145	−	0.0108260i
$352$	−16.3561	+	28.3296i	−0.871782	+	1.50997i
$353$	4.14180			0.220446			0.110223	−	0.993907i	$-0.464844\pi$
$353$	4.14180			0.220446			0.110223	+	0.993907i	$0.464844\pi$
$354$	−22.4763			−1.19460
$355$	61.7239			3.27596
$356$	−23.6917			−1.25566
$357$	10.5952	+	3.27574i	0.560757	+	0.173371i
$358$	13.2297	+	22.9145i	0.699211	+	1.21107i
$359$	6.45007	−	11.1718i	0.340421	−	0.589627i	−0.644090	−	0.764950i	$-0.722764\pi$
$359$	6.45007	−	11.1718i	0.340421	−	0.589627i	0.984511	+	0.175323i	$0.0560969\pi$
$360$	−17.8116	+	30.8506i	−0.938753	+	1.62597i
$361$	−16.1286			−0.848872
$362$	−8.46824	−	14.6674i	−0.445081	−	0.770903i
$363$	−8.33772			−0.437617
$364$	48.0468	+	17.8732i	2.51834	+	0.936810i
$365$	−22.7561			−1.19111
$366$	−12.3350	−	21.3648i	−0.644760	−	1.11676i
$367$	7.36576			0.384490			0.192245	−	0.981347i	$-0.438423\pi$
$367$	7.36576			0.384490			0.192245	+	0.981347i	$0.438423\pi$
$368$	−5.59165	+	9.68503i	−0.291485	+	0.504867i
$369$	2.96941	−	5.14316i	0.154581	−	0.267742i
$370$	−3.63869	−	6.30240i	−0.189167	−	0.327646i
$371$	−11.8339	+	10.9659i	−0.614386	+	0.569323i
$372$	9.83829			0.510092
$373$	−23.6568			−1.22490			−0.612451	−	0.790509i	$-0.709816\pi$
$373$	−23.6568			−1.22490			−0.612451	+	0.790509i	$0.709816\pi$
$374$	−18.5720			−0.960333
$375$	−19.9025			−1.02776
$376$	2.67727	−	4.63716i	0.138070	−	0.239143i
$377$	0.957892	−	1.46243i	0.0493339	−	0.0753190i
$378$	−5.26980	+	4.88327i	−0.271049	+	0.251168i
$379$	−5.12668	+	8.87966i	−0.263340	+	0.456118i	−0.967127	−	0.254293i	$-0.918157\pi$
$379$	−5.12668	+	8.87966i	−0.263340	+	0.456118i	0.703788	+	0.710410i	$0.251491\pi$
$380$	17.7037	+	30.6636i	0.908178	+	1.57301i
$381$	1.88510	−	3.26510i	0.0965768	−	0.167276i
$382$	4.13792	+	7.16708i	0.211714	+	0.366700i
$383$	−19.3320			−0.987818			−0.493909	−	0.869514i	$-0.664432\pi$
$383$	−19.3320			−0.987818			−0.493909	+	0.869514i	$0.664432\pi$
$384$	15.4972	+	26.8419i	0.790837	+	1.36977i
$385$	−16.0364	−	4.95803i	−0.817293	−	0.252685i
$386$	12.1972	+	21.1262i	0.620821	+	1.07529i
$387$	2.79224	+	4.83630i	0.141938	+	0.245843i
$388$	−54.6826			−2.77609
$389$	−5.95876	−	10.3209i	−0.302121	−	0.523289i	0.674495	−	0.738279i	$-0.264361\pi$
$389$	−5.95876	−	10.3209i	−0.302121	−	0.523289i	−0.976616	+	0.214990i	$0.931028\pi$
$390$	−38.0091	−	2.14154i	−1.92466	−	0.108441i
$391$	−3.31732			−0.167764
$392$	57.8171	−	27.7505i	2.92021	−	1.40161i
$393$	9.00807	−	15.6024i	0.454397	−	0.787039i
$394$	−45.7819			−2.30646
$395$	−2.50041	−	4.33083i	−0.125809	−	0.217908i
$396$	4.38414	−	7.59355i	0.220311	−	0.381590i
$397$	0.967212			0.0485430			0.0242715	−	0.999705i	$-0.492273\pi$
$397$	0.967212			0.0485430			0.0242715	+	0.999705i	$0.492273\pi$
$398$	5.55385			0.278389
$399$	0.994783	+	4.37155i	0.0498014	+	0.218851i
$400$	−71.4918	+	123.827i	−3.57459	+	6.19137i
$401$	11.7373	+	20.3295i	0.586131	+	1.01521i	0.994733	+	0.102496i	$0.0326828\pi$
$401$	11.7373	+	20.3295i	0.586131	+	1.01521i	−0.408603	+	0.912712i	$0.633984\pi$
$402$	1.35848	+	2.35296i	0.0677548	+	0.117355i
$403$	2.97365	+	5.89317i	0.148128	+	0.293560i
$404$	−38.0816	+	65.9592i	−1.89463	+	3.28159i
$405$	1.94413	−	3.36734i	0.0966047	−	0.167324i
$406$	−0.772947	−	3.39670i	−0.0383607	−	0.168575i
$407$	0.562300	+	0.973933i	0.0278722	+	0.0482761i
$408$	−19.2013	+	33.2576i	−0.950604	+	1.64649i
$409$	9.51587	−	16.4820i	0.470529	−	0.814981i	−0.528903	−	0.848683i	$-0.677396\pi$
$409$	9.51587	−	16.4820i	0.470529	−	0.814981i	0.999432	+	0.0337019i	$0.0107297\pi$
$410$	31.3526	−	54.3043i	1.54839	−	2.68190i
$411$	−10.8986	+	18.8769i	−0.537587	+	0.931128i
$412$	−4.78907	−	8.29490i	−0.235940	−	0.408661i
$413$	−20.9220	−	6.46850i	−1.02950	−	0.318294i
$414$	1.07454	−	1.86116i	0.0528107	−	0.0914708i
$415$	−12.0187	+	20.8169i	−0.589973	+	1.02186i
$416$	−39.6073	+	60.4692i	−1.94191	+	2.96475i
$417$	0.355981	+	0.616576i	0.0174324	+	0.0301939i
$418$	−3.75400	−	6.50212i	−0.183614	−	0.318029i
$419$	16.1312	−	27.9400i	0.788060	−	1.36496i	−0.139093	−	0.990279i	$-0.544419\pi$
$419$	16.1312	−	27.9400i	0.788060	−	1.36496i	0.927154	−	0.374681i	$-0.122248\pi$
$420$	−40.5499	+	37.5756i	−1.97863	+	1.83350i
$421$	−34.4202			−1.67754			−0.838769	−	0.544488i	$-0.816724\pi$
$421$	−34.4202			−1.67754			−0.838769	+	0.544488i	$0.816724\pi$
$422$	67.0087			3.26193
$423$	−0.292223	+	0.506146i	−0.0142084	+	0.0246096i
$424$	−27.9337	−	48.3827i	−1.35658	−	2.34967i
$425$	−42.4134			−2.05735
$426$	−21.5534	+	37.3315i	−1.04426	+	1.80872i
$427$	−5.33334	−	23.4373i	−0.258099	−	1.13421i
$428$	103.261			4.99133
$429$	5.87368	+	0.330940i	0.283584	+	0.0159779i
$430$	29.4820	+	51.0643i	1.42175	+	2.46254i
$431$	1.99382			0.0960390			0.0480195	−	0.998846i	$-0.484709\pi$
$431$	1.99382			0.0960390			0.0480195	+	0.998846i	$0.484709\pi$
$432$	−7.06539	−	12.2376i	−0.339934	−	0.588782i
$433$	3.70848	+	6.42328i	0.178218	+	0.308683i	0.941270	−	0.337654i	$-0.109633\pi$
$433$	3.70848	+	6.42328i	0.178218	+	0.308683i	−0.763052	+	0.646337i	$0.776300\pi$
$434$	12.5662	+	3.88514i	0.603199	+	0.186493i
$435$	0.942647	+	1.63271i	0.0451965	+	0.0782826i
$436$	57.4905			2.75329
$437$	−0.670539	−	1.16141i	−0.0320762	−	0.0555576i
$438$	7.94622	−	13.7632i	0.379685	−	0.657633i
$439$	−10.3873	−	17.9914i	−0.495760	−	0.858681i	0.504228	−	0.863570i	$-0.331777\pi$
$439$	−10.3873	−	17.9914i	−0.495760	−	0.858681i	−0.999988	+	0.00488930i	$0.998444\pi$
$440$	29.0623	−	50.3373i	1.38549	−	2.39974i
$441$	−6.31073	+	3.02897i	−0.300511	+	0.144237i
$442$	−40.9746	−	2.30863i	−1.94896	−	0.109810i
$443$	−2.67178	+	4.62766i	−0.126940	+	0.219867i	−0.922490	−	0.386022i	$-0.873849\pi$
$443$	−2.67178	+	4.62766i	−0.126940	+	0.219867i	0.795550	+	0.605889i	$0.207182\pi$
$444$	3.70390			0.175779
$445$	17.1421			0.812615
$446$	−48.8568			−2.31344
$447$	−5.59281			−0.264531
$448$	15.3691	+	67.5391i	0.726121	+	3.19092i
$449$	−15.0969	−	26.1486i	−0.712468	−	1.23403i	−0.963928	−	0.266163i	$-0.914244\pi$
$449$	−15.0969	−	26.1486i	−0.712468	−	1.23403i	0.251460	−	0.967868i	$-0.419089\pi$
$450$	13.7385	−	23.7957i	0.647637	−	1.12174i
$451$	−4.84503	+	8.39184i	−0.228144	+	0.395156i
$452$	41.0869			1.93257
$453$	4.99718	+	8.65536i	0.234788	+	0.406664i
$454$	22.6627			1.06361
$455$	−34.7642	−	12.9321i	−1.62977	−	0.606268i
$456$	−15.5248			−0.727016
$457$	15.5102	+	26.8645i	0.725538	+	1.25667i	0.958752	+	0.284243i	$0.0917422\pi$
$457$	15.5102	+	26.8645i	0.725538	+	1.25667i	−0.233215	+	0.972425i	$0.574924\pi$
$458$	−60.3774			−2.82125
$459$	2.09582	−	3.63006i	0.0978243	−	0.169437i
$460$	8.26832	−	14.3212i	0.385513	−	0.667727i
$461$	−2.19226	−	3.79710i	−0.102104	−	0.176848i	0.810448	−	0.585811i	$-0.199224\pi$
$461$	−2.19226	−	3.79710i	−0.102104	−	0.176848i	−0.912551	+	0.408963i	$0.865891\pi$
$462$	8.59846	−	7.96779i	0.400037	−	0.370695i
$463$	4.93368			0.229288			0.114644	−	0.993407i	$-0.463427\pi$
$463$	4.93368			0.229288			0.114644	+	0.993407i	$0.463427\pi$
$464$	6.85156			0.318076
$465$	−7.11849			−0.330112
$466$	13.6273			0.631271
$467$	3.98764	−	6.90680i	0.184526	−	0.319609i	−0.758891	−	0.651218i	$-0.774258\pi$
$467$	3.98764	−	6.90680i	0.184526	−	0.319609i	0.943417	+	0.331610i	$0.107592\pi$
$468$	10.6165	−	16.2084i	0.490747	−	0.749232i
$469$	0.587373	+	2.58120i	0.0271224	+	0.119189i
$470$	−3.08545	+	5.34416i	−0.142321	+	0.246508i
$471$	9.42039	+	16.3166i	0.434069	+	0.751829i
$472$	37.9161	−	65.6726i	1.74523	−	3.02283i
$473$	−4.55596	−	7.89115i	−0.209483	−	0.362835i
$474$	3.49247			0.160415
$475$	−8.57314	−	14.8491i	−0.393363	−	0.681324i
$476$	−43.7136	+	40.5073i	−2.00361	+	1.85665i
$477$	3.04896	+	5.28096i	0.139602	+	0.241799i
$478$	12.6040	+	21.8308i	0.576494	+	0.998516i
$479$	−32.3454			−1.47790			−0.738949	−	0.673762i	$-0.764677\pi$
$479$	−32.3454			−1.47790			−0.738949	+	0.673762i	$0.764677\pi$
$480$	−38.9770	−	67.5101i	−1.77905	−	3.08140i
$481$	1.11951	+	2.21865i	0.0510454	+	0.101162i
$482$	40.1604			1.82926
$483$	1.53586	−	1.42320i	0.0698838	−	0.0647581i
$484$	22.4029	−	38.8030i	1.01832	−	1.76377i
$485$	39.5656			1.79658
$486$	1.35774	+	2.35168i	0.0615885	+	0.106674i
$487$	−16.5551	+	28.6742i	−0.750182	+	1.29935i	0.197553	+	0.980292i	$0.436701\pi$
$487$	−16.5551	+	28.6742i	−0.750182	+	1.29935i	−0.947734	+	0.319060i	$0.896633\pi$
$488$	83.2334			3.76780
$489$	−24.4471			−1.10554
$490$	−66.6321	+	31.9815i	−3.01013	+	1.44477i
$491$	5.01799	−	8.69141i	0.226459	−	0.392238i	−0.730297	−	0.683129i	$-0.760618\pi$
$491$	5.01799	−	8.69141i	0.226459	−	0.392238i	0.956756	+	0.290891i	$0.0939518\pi$
$492$	15.9572	+	27.6387i	0.719407	+	1.24605i
$493$	1.01619	+	1.76010i	0.0457670	+	0.0792708i
$494$	−7.47404	−	14.8120i	−0.336273	−	0.666424i
$495$	−3.17214	+	5.49431i	−0.142577	+	0.246951i
$496$	−12.9351	+	22.4042i	−0.580801	+	1.00598i
$497$	−30.8066	+	28.5470i	−1.38186	+	1.28051i
$498$	−8.39361	−	14.5382i	−0.376126	−	0.651470i
$499$	−10.4771	+	18.1469i	−0.469021	+	0.812369i	−0.999373	−	0.0354090i	$-0.988727\pi$
$499$	−10.4771	+	18.1469i	−0.469021	+	0.812369i	0.530352	+	0.847778i	$0.322060\pi$
$500$	53.4766	−	92.6243i	2.39155	−	4.14228i
$501$	−4.28482	+	7.42152i	−0.191432	+	0.331569i
$502$	−13.0513	+	22.6056i	−0.582509	+	1.00894i
$503$	18.5489	+	32.1277i	0.827056	+	1.43250i	0.900338	+	0.435192i	$0.143319\pi$
$503$	18.5489	+	32.1277i	0.827056	+	1.43250i	−0.0732818	+	0.997311i	$0.523347\pi$
$504$	−5.37843	−	23.6354i	−0.239574	−	1.05280i
$505$	27.5539	−	47.7248i	1.22613	−	2.12372i
$506$	−1.75327	+	3.03675i	−0.0779424	+	0.135000i
$507$	12.9177	+	1.46028i	0.573696	+	0.0648533i
$508$	10.1303	+	17.5462i	0.449460	+	0.778488i
$509$	−3.71031	−	6.42645i	−0.164457	−	0.284847i	0.772006	−	0.635616i	$-0.219254\pi$
$509$	−3.71031	−	6.42645i	−0.164457	−	0.284847i	−0.936462	+	0.350768i	$0.885920\pi$
$510$	22.1287	−	38.3281i	0.979877	−	1.69720i
$511$	11.3577	−	10.5246i	0.502433	−	0.465581i
$512$	−24.3770			−1.07732
$513$	1.69453			0.0748154
$514$	6.86443	−	11.8895i	0.302777	−	0.524425i
$515$	3.46513	+	6.00177i	0.152692	+	0.264470i
$516$	−30.0103			−1.32113
$517$	0.476806	−	0.825852i	0.0209699	−	0.0363209i
$518$	4.73091	+	1.46267i	0.207864	+	0.0642660i
$519$	7.68079			0.337149
$520$	70.3762	−	107.445i	3.08620	−	4.71175i
$521$	−4.32959	−	7.49907i	−0.189683	−	0.328540i	0.755462	−	0.655193i	$-0.227413\pi$
$521$	−4.32959	−	7.49907i	−0.189683	−	0.328540i	−0.945144	+	0.326653i	$0.894079\pi$
$522$	−1.31665			−0.0576283
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	0.999793	−	0.0203588i	$-0.00648085\pi$
$523$	11.0290	+	19.1028i	0.482265	+	0.835308i	−0.517528	+	0.855667i	$0.673148\pi$
$524$	48.4082	+	83.8455i	2.11472	+	3.66281i
$525$	19.6366	−	18.1963i	0.857012	−	0.794152i
$526$	31.7084	+	54.9206i	1.38255	+	2.39465i
$527$	−7.67388			−0.334280
$528$	11.5282	+	19.9675i	0.501702	+	0.868974i
$529$	11.1868	−	19.3762i	0.486384	−	0.842442i
$530$	32.1926	+	55.7592i	1.39836	+	2.42202i
$531$	−4.13854	+	7.16816i	−0.179597	+	0.311072i
$532$	−23.0177	−	7.11645i	−0.997945	−	0.308537i
$533$	−11.7326	+	17.9123i	−0.508194	+	0.775868i
$534$	−5.98587	+	10.3678i	−0.259034	+	0.448660i
$535$	−74.7147			−3.23020
$536$	−9.16668			−0.395940
$537$	9.74388			0.420480
$538$	85.2430			3.67509
$539$	10.2969	−	4.94221i	0.443519	−	0.212876i
$540$	10.4475	+	18.0956i	0.449590	+	0.778712i
$541$	1.78963	−	3.09972i	0.0769421	−	0.133268i	−0.824987	−	0.565152i	$-0.808818\pi$
$541$	1.78963	−	3.09972i	0.0769421	−	0.133268i	0.901929	+	0.431884i	$0.142151\pi$
$542$	−15.3837	+	26.6453i	−0.660785	+	1.14451i
$543$	−6.23699			−0.267655
$544$	−42.0180	−	72.7773i	−1.80151	−	3.12030i
$545$	−41.5972			−1.78183
$546$	19.9609	−	16.5102i	0.854247	−	0.706570i
$547$	−11.6996			−0.500238			−0.250119	−	0.968215i	$-0.580470\pi$
$547$	−11.6996			−0.500238			−0.250119	+	0.968215i	$0.580470\pi$
$548$	−58.5676	−	101.442i	−2.50188	−	4.33339i
$549$	−9.08491			−0.387735
$550$	−22.4164	+	38.8263i	−0.955837	+	1.65556i
$551$	−0.410812	+	0.711547i	−0.0175012	+	0.0303129i
$552$	3.62536	+	6.27931i	0.154306	+	0.267265i
$553$	3.25095	+	1.00511i	0.138245	+	0.0427414i
$554$	−48.6686			−2.06773
$555$	−2.67995			−0.113758
$556$	−3.82599			−0.162258
$557$	16.1738			0.685305			0.342653	−	0.939462i	$-0.388675\pi$
$557$	16.1738			0.685305			0.342653	+	0.939462i	$0.388675\pi$
$558$	2.48571	−	4.30537i	0.105228	−	0.182261i
$559$	−9.07070	−	17.9763i	−0.383650	−	0.760315i
$560$	−32.2553	−	141.745i	−1.36303	−	5.98982i
$561$	−3.41964	+	5.92298i	−0.144377	+	0.250069i
$562$	−15.7731	−	27.3198i	−0.665349	−	1.15242i
$563$	12.3858	−	21.4528i	0.521998	−	0.904127i	−0.477674	−	0.878537i	$-0.658520\pi$
$563$	12.3858	−	21.4528i	0.521998	−	0.904127i	0.999673	−	0.0255903i	$-0.00814655\pi$
$564$	−1.57037	−	2.71996i	−0.0661246	−	0.114531i
$565$	−29.7284			−1.25068
$566$	−10.9868	−	19.0296i	−0.461808	−	0.799875i
$567$	0.587055	+	2.57980i	0.0246540	+	0.108341i
$568$	−72.7184	−	125.952i	−3.05119	−	5.28482i
$569$	−16.7260	−	28.9702i	−0.701189	−	1.21450i	−0.968049	−	0.250760i	$-0.919319\pi$
$569$	−16.7260	−	28.9702i	−0.701189	−	1.21450i	0.266860	−	0.963735i	$-0.414014\pi$
$570$	17.8918			0.749404
$571$	−6.32788	−	10.9602i	−0.264814	−	0.458671i	0.702701	−	0.711485i	$-0.251977\pi$
$571$	−6.32788	−	10.9602i	−0.264814	−	0.458671i	−0.967515	+	0.252815i	$0.918644\pi$
$572$	−17.3224	+	26.4464i	−0.724285	+	1.10578i
$573$	3.04764			0.127317
$574$	9.46730	+	41.6039i	0.395157	+	1.73651i
$575$	−4.00400	+	6.93514i	−0.166979	+	0.289215i
$576$	26.1800			1.09083
$577$	10.9471	+	18.9609i	0.455733	+	0.789352i	0.998730	−	0.0503824i	$-0.0160440\pi$
$577$	10.9471	+	18.9609i	0.455733	+	0.789352i	−0.542997	+	0.839734i	$0.682711\pi$
$578$	0.773600	−	1.33991i	0.0321775	−	0.0557331i
$579$	8.98343			0.373339
$580$	−10.1313			−0.420681
$581$	−3.62919	−	15.9484i	−0.150564	−	0.661650i
$582$	−13.8159	+	23.9299i	−0.572688	+	0.991924i
$583$	−4.97484	−	8.61668i	−0.206037	−	0.356866i
$584$	26.8095	+	46.4355i	1.10939	+	1.92151i
$585$	−7.68155	+	11.7276i	−0.317593	+	0.484875i
$586$	24.1919	−	41.9016i	0.999359	−	1.73094i
$587$	20.0260	−	34.6860i	0.826561	−	1.43164i	−0.0741601	−	0.997246i	$-0.523628\pi$
$587$	20.0260	−	34.6860i	0.826561	−	1.43164i	0.900721	−	0.434399i	$-0.143039\pi$
$588$	2.86000	−	37.5082i	0.117944	−	1.54681i
$589$	−1.55114	−	2.68666i	−0.0639137	−	0.110702i
$590$	−43.6969	+	75.6852i	−1.79897	+	3.11591i
$591$	−8.42977	+	14.6008i	−0.346754	+	0.600596i
$592$	−4.86976	+	8.43467i	−0.200146	+	0.346663i
$593$	5.18181	−	8.97516i	0.212791	−	0.368566i	−0.739796	−	0.672832i	$-0.765078\pi$
$593$	5.18181	−	8.97516i	0.212791	−	0.368566i	0.952587	+	0.304266i	$0.0984112\pi$
$594$	−2.21536	−	3.83712i	−0.0908974	−	0.157439i
$595$	31.6290	−	29.3091i	1.29666	−	1.20155i
$596$	15.0275	−	26.0284i	0.615551	−	1.06617i
$597$	1.02262	−	1.77124i	0.0418532	−	0.0724919i
$598$	−4.24566	+	6.48192i	−0.173618	+	0.265066i
$599$	6.86263	+	11.8864i	0.280400	+	0.485666i	0.971483	−	0.237108i	$-0.0761997\pi$
$599$	6.86263	+	11.8864i	0.280400	+	0.485666i	−0.691084	+	0.722775i	$0.742866\pi$
$600$	46.3519	+	80.2838i	1.89231	+	3.27757i
$601$	−0.234944	+	0.406935i	−0.00958356	+	0.0165992i	−0.870777	−	0.491677i	$-0.836384\pi$
$601$	−0.234944	+	0.406935i	−0.00958356	+	0.0165992i	0.861194	+	0.508277i	$0.169717\pi$
$602$	−38.3315	−	11.8511i	−1.56228	−	0.483013i
$603$	1.00054			0.0407452
$604$	−53.7084			−2.18536
$605$	−16.2096	+	28.0759i	−0.659015	+	1.14145i
$606$	19.2431	+	33.3300i	0.781698	+	1.35394i
$607$	23.0517			0.935639			0.467819	−	0.883824i	$-0.345040\pi$
$607$	23.0517			0.935639			0.467819	+	0.883824i	$0.345040\pi$
$608$	16.9864	−	29.4214i	0.688891	−	1.19319i
$609$	−1.22560	−	0.378922i	−0.0496638	−	0.0153547i
$610$	−95.9234			−3.88382
$611$	1.15462	−	1.76277i	0.0467108	−	0.0713142i
$612$	11.2626	+	19.5075i	0.455266	+	0.788543i
$613$	34.8011			1.40560			0.702801	−	0.711386i	$-0.251932\pi$
$613$	34.8011			1.40560			0.702801	+	0.711386i	$0.251932\pi$
$614$	21.9456	+	38.0109i	0.885652	+	1.53399i
$615$	−11.5458	−	19.9980i	−0.465573	−	0.806396i
$616$	8.77571	+	38.5647i	0.353583	+	1.55381i
$617$	15.9481	+	27.6229i	0.642045	+	1.11205i	0.984976	+	0.172694i	$0.0552470\pi$
$617$	15.9481	+	27.6229i	0.642045	+	1.11205i	−0.342931	+	0.939361i	$0.611420\pi$
$618$	−4.83995			−0.194691
$619$	−11.1376	−	19.2910i	−0.447660	−	0.775369i	0.550574	−	0.834787i	$-0.314409\pi$
$619$	−11.1376	−	19.2910i	−0.447660	−	0.775369i	−0.998233	+	0.0594173i	$0.981076\pi$
$620$	19.1269	−	33.1288i	0.768156	−	1.33049i
$621$	−0.395707	−	0.685385i	−0.0158792	−	0.0275036i
$622$	−24.6062	+	42.6193i	−0.986621	+	1.70888i
$623$	−8.55569	+	7.92816i	−0.342777	+	0.317635i
$624$	22.9522	+	45.4865i	0.918823	+	1.82092i
$625$	−13.3965	+	23.2034i	−0.535860	+	0.928137i
$626$	69.5533			2.77991
$627$	−2.76488			−0.110419
$628$	−101.248			−4.04024
$629$	−2.88905			−0.115194
$630$	6.19844	+	27.2389i	0.246952	+	1.08522i
$631$	23.9160	+	41.4237i	0.952081	+	1.64905i	0.740910	+	0.671604i	$0.234394\pi$
$631$	23.9160	+	41.4237i	0.952081	+	1.64905i	0.211171	+	0.977449i	$0.432272\pi$
$632$	−5.89158	+	10.2045i	−0.234355	+	0.405914i
$633$	12.3382	−	21.3705i	0.490401	−	0.849400i
$634$	74.5692			2.96152
$635$	−7.32978	−	12.6956i	−0.290874	−	0.503808i
$636$	−32.7695			−1.29940
$637$	23.3320	−	9.62382i	0.924447	−	0.381310i
$638$	2.14832			0.0850526
$639$	7.93720	+	13.7476i	0.313991	+	0.543848i
$640$	120.514			4.76374
$641$	7.31139	−	12.6637i	0.288783	−	0.500186i	−0.684737	−	0.728790i	$-0.740083\pi$
$641$	7.31139	−	12.6637i	0.288783	−	0.500186i	0.973519	+	0.228604i	$0.0734162\pi$
$642$	26.0897	−	45.1886i	1.02968	−	1.78345i
$643$	−17.9675	−	31.1207i	−0.708570	−	1.22728i	−0.965388	−	0.260819i	$-0.916007\pi$
$643$	−17.9675	−	31.1207i	−0.708570	−	1.22728i	0.256818	−	0.966460i	$-0.417326\pi$
$644$	2.49672	+	10.9718i	0.0983847	+	0.432349i
$645$	21.7139			0.854985
$646$	19.2877			0.758865
$647$	−30.4464			−1.19697			−0.598487	−	0.801133i	$-0.704231\pi$
$647$	−30.4464			−1.19697			−0.598487	+	0.801133i	$0.704231\pi$
$648$	−9.16172			−0.359906
$649$	6.75264	−	11.6959i	0.265064	−	0.459105i
$650$	−54.2827	+	82.8743i	−2.12914	+	3.25060i
$651$	3.55286	−	3.29227i	0.139248	−	0.129034i
$652$	65.6879	−	113.775i	2.57253	−	4.45576i
$653$	−15.1716	−	26.2779i	−0.593709	−	1.02833i	−0.993728	−	0.111827i	$-0.964330\pi$
$653$	−15.1716	−	26.2779i	−0.593709	−	1.02833i	0.400019	−	0.916507i	$-0.369004\pi$
$654$	14.5253	−	25.1586i	0.567986	−	0.983780i
$655$	−35.0257	−	60.6664i	−1.36857	−	2.37043i
$656$	−83.9201			−3.27653
$657$	−2.92626	−	5.06843i	−0.114164	−	0.197738i
$658$	−0.931690	−	4.09429i	−0.0363210	−	0.159612i
$659$	−18.9462	−	32.8157i	−0.738038	−	1.27832i	−0.953377	−	0.301781i	$-0.902419\pi$
$659$	−18.9462	−	32.8157i	−0.738038	−	1.27832i	0.215339	−	0.976539i	$-0.430914\pi$
$660$	−17.0467	−	29.5257i	−0.663542	−	1.14929i
$661$	10.9586			0.426239			0.213119	−	0.977026i	$-0.431638\pi$
$661$	10.9586			0.426239			0.213119	+	0.977026i	$0.431638\pi$
$662$	9.43802	+	16.3471i	0.366819	+	0.635349i
$663$	−8.28087	+	12.6426i	−0.321602	+	0.490996i
$664$	56.6379			2.19798
$665$	16.6545	+	5.14911i	0.645833	+	0.199674i
$666$	0.935814	−	1.62088i	0.0362620	−	0.0628077i
$667$	0.383732			0.0148581
$668$	−23.0261	−	39.8823i	−0.890906	−	1.54309i
$669$	−8.99595	+	15.5814i	−0.347804	+	0.602413i
$670$	10.5643			0.408133
$671$	14.8234			0.572251
$672$	50.6767	+	15.6678i	1.95489	+	0.604400i
$673$	−11.7007	+	20.2661i	−0.451027	+	0.781202i	−0.998450	−	0.0556538i	$-0.982276\pi$
$673$	−11.7007	+	20.2661i	−0.451027	+	0.781202i	0.547423	+	0.836856i	$0.315609\pi$
$674$	39.4432	+	68.3176i	1.51930	+	2.63150i
$675$	−5.05930	−	8.76296i	−0.194732	−	0.337287i
$676$	−41.5051	+	56.1943i	−1.59635	+	2.16132i
$677$	−4.05218	+	7.01858i	−0.155738	+	0.269746i	−0.933327	−	0.359026i	$-0.883109\pi$
$677$	−4.05218	+	7.01858i	−0.155738	+	0.269746i	0.777590	+	0.628772i	$0.216442\pi$
$678$	10.3809	−	17.9802i	0.398675	−	0.690525i
$679$	−19.7473	+	18.2989i	−0.757832	+	0.702247i
$680$	74.6596	+	129.314i	2.86306	+	4.95897i
$681$	4.17286	−	7.22761i	0.159904	−	0.276963i
$682$	−4.05580	+	7.02486i	−0.155305	+	0.268996i
$683$	−0.340883	+	0.590426i	−0.0130435	+	0.0225920i	−0.872473	−	0.488661i	$-0.837485\pi$
$683$	−0.340883	+	0.590426i	−0.0130435	+	0.0225920i	0.859430	+	0.511253i	$0.170819\pi$
$684$	−4.55310	+	7.88620i	−0.174092	+	0.301536i
$685$	42.3765	+	73.3983i	1.61912	+	2.80441i
$686$	18.4650	−	46.7791i	0.704997	−	1.78603i
$687$	−11.1172	+	19.2556i	−0.424148	+	0.734647i
$688$	39.4565	−	68.3407i	1.50427	−	2.60547i
$689$	−9.90467	−	19.6290i	−0.377338	−	0.747806i
$690$	−4.17809	−	7.23666i	−0.159057	−	0.275495i
$691$	−20.9669	−	36.3158i	−0.797620	−	1.38152i	−0.921162	−	0.389179i	$-0.872759\pi$
$691$	−20.9669	−	36.3158i	−0.797620	−	1.38152i	0.123543	−	0.992339i	$-0.460574\pi$
$692$	−20.6378	+	35.7457i	−0.784532	+	1.35885i
$693$	−0.957867	−	4.20933i	−0.0363864	−	0.159899i
$694$	−13.8720			−0.526572
$695$	2.76829			0.105007
$696$	2.22111	−	3.84708i	0.0841910	−	0.145823i
$697$	−12.4467	−	21.5582i	−0.471451	−	0.816577i
$698$	66.4861			2.51654
$699$	2.50918	−	4.34602i	0.0949057	−	0.164382i
$700$	31.9217	+	140.279i	1.20653	+	5.30206i
$701$	5.85701			0.221216			0.110608	−	0.993864i	$-0.464720\pi$
$701$	5.85701			0.221216			0.110608	+	0.993864i	$0.464720\pi$
$702$	−4.41068	−	8.74107i	−0.166470	−	0.329910i
$703$	−0.583971	−	1.01147i	−0.0220249	−	0.0381482i
$704$	−42.7165			−1.60994
$705$	1.13624	+	1.96803i	0.0427933	+	0.0741202i
$706$	5.62350	+	9.74019i	0.211643	+	0.366577i
$707$	8.32024	+	36.5631i	0.312915	+	1.37510i
$708$	−22.2400	−	38.5208i	−0.835830	−	1.44770i
$709$	−14.6352			−0.549637			−0.274818	−	0.961496i	$-0.588618\pi$
$709$	−14.6352			−0.549637			−0.274818	+	0.961496i	$0.588618\pi$
$710$	83.8052	+	145.155i	3.14515	+	5.44756i
$711$	0.643065	−	1.11382i	0.0241168	−	0.0417716i
$712$	−20.1956	−	34.9797i	−0.756861	−	1.31092i
$713$	−0.724447	+	1.25478i	−0.0271307	+	0.0469918i
$714$	6.68205	+	29.3641i	0.250069	+	1.09892i
$715$	12.5336	−	19.1353i	0.468730	−	0.715618i
$716$	−26.1812	+	45.3472i	−0.978438	+	1.69470i
$717$	9.28305			0.346682
$718$	35.0302			1.30731
$719$	9.61130			0.358441			0.179220	−	0.983809i	$-0.442642\pi$
$719$	9.61130			0.358441			0.179220	+	0.983809i	$0.442642\pi$
$720$	−54.9442			−2.04765
$721$	−4.50525	−	1.39290i	−0.167784	−	0.0518743i
$722$	−21.8985	−	37.9292i	−0.814976	−	1.41158i
$723$	7.39469	−	12.8080i	0.275012	−	0.476334i
$724$	16.7584	−	29.0264i	0.622821	−	1.07876i
$725$	4.90618			0.182211
$726$	−11.3205	−	19.6077i	−0.420143	−	0.727709i
$727$	−42.7269			−1.58465			−0.792327	−	0.610097i	$-0.791131\pi$
$727$	−42.7269			−1.58465			−0.792327	+	0.610097i	$0.791131\pi$
$728$	14.5676	+	86.1746i	0.539912	+	3.19384i
$729$	1.00000			0.0370370
$730$	−30.8970	−	53.5151i	−1.14355	−	1.98068i
$731$	23.4081			0.865779
$732$	24.4106	−	42.2804i	0.902242	−	1.56273i
$733$	4.17505	−	7.23139i	0.154209	−	0.267098i	−0.778562	−	0.627568i	$-0.784050\pi$
$733$	4.17505	−	7.23139i	0.154209	−	0.267098i	0.932771	+	0.360470i	$0.117384\pi$
$734$	10.0008	+	17.3219i	0.369137	+	0.639364i
$735$	−2.06935	+	27.1391i	−0.0763291	+	1.00104i
$736$	−15.8667			−0.584854
$737$	−1.63253			−0.0601352
$738$	16.1268			0.593635
$739$	29.0362			1.06811			0.534056	−	0.845449i	$-0.320667\pi$
$739$	29.0362			1.06811			0.534056	+	0.845449i	$0.320667\pi$
$740$	7.20087	−	12.4723i	0.264709	−	0.458490i
$741$	−6.10005	−	0.343694i	−0.224091	−	0.0126259i
$742$	−41.8558	−	12.9407i	−1.53657	−	0.475067i
$743$	−12.5402	+	21.7202i	−0.460055	+	0.796838i	−0.998963	−	0.0455263i	$-0.985504\pi$
$743$	−12.5402	+	21.7202i	−0.460055	+	0.796838i	0.538909	+	0.842364i	$0.318837\pi$
$744$	8.38647	+	14.5258i	0.307463	+	0.532541i
$745$	−10.8732	+	18.8329i	−0.398362	+	0.689982i
$746$	−32.1199	−	55.6332i	−1.17599	−	2.03688i
$747$	−6.18202			−0.226188
$748$	−18.3767	−	31.8294i	−0.671918	−	1.16380i
$749$	37.2904	−	34.5552i	1.36256	−	1.26262i
$750$	−27.0224	−	46.8042i	−0.986720	−	1.70905i
$751$	−0.178694	−	0.309508i	−0.00652065	−	0.0112941i	0.862747	−	0.505636i	$-0.168742\pi$
$751$	−0.178694	−	0.309508i	−0.00652065	−	0.0112941i	−0.869267	+	0.494342i	$0.835409\pi$
$752$	8.25869			0.301163
$753$	4.80626	+	8.32468i	0.175150	+	0.303368i
$754$	4.73974	+	0.267051i	0.172611	+	0.00972542i
$755$	38.8607			1.41429
$756$	−13.5835	−	4.19966i	−0.494029	−	0.152740i
$757$	−25.0343	+	43.3607i	−0.909888	+	1.57597i	−0.0956688	+	0.995413i	$0.530499\pi$
$757$	−25.0343	+	43.3607i	−0.909888	+	1.57597i	−0.814219	+	0.580558i	$0.802834\pi$
$758$	−27.8428			−1.01130
$759$	0.645656	+	1.11831i	0.0234358	+	0.0405920i
$760$	−30.1823	+	52.2773i	−1.09483	+	1.89630i
$761$	−8.83779			−0.320370			−0.160185	−	0.987087i	$-0.551209\pi$
$761$	−8.83779			−0.320370			−0.160185	+	0.987087i	$0.551209\pi$
$762$	10.2380			0.370882
$763$	20.7613	−	19.2385i	0.751609	−	0.696481i
$764$	−8.18882	+	14.1835i	−0.296261	+	0.513139i
$765$	−8.14908	−	14.1146i	−0.294631	−	0.510315i
$766$	−26.2479	−	45.4626i	−0.948374	−	1.64263i
$767$	16.3520	−	24.9648i	0.590435	−	0.901428i
$768$	−15.9024	+	27.5438i	−0.573829	+	0.993902i
$769$	−13.9753	+	24.2059i	−0.503962	+	0.872887i	0.496028	+	0.868307i	$0.334791\pi$
$769$	−13.9753	+	24.2059i	−0.503962	+	0.872887i	−0.999990	+	0.00458075i	$0.998542\pi$
$770$	−10.1137	−	44.4443i	−0.364472	−	1.60166i
$771$	−2.52788	−	4.37842i	−0.0910394	−	0.157685i
$772$	−24.1379	+	41.8081i	−0.868743	+	1.50471i
$773$	15.3917	−	26.6592i	0.553600	−	0.958863i	−0.444411	−	0.895823i	$-0.646587\pi$
$773$	15.3917	−	26.6592i	0.553600	−	0.958863i	0.998011	−	0.0630403i	$-0.0200797\pi$
$774$	−7.58229	+	13.1329i	−0.272540	+	0.472053i
$775$	−9.26238	+	16.0429i	−0.332714	+	0.576278i
$776$	−46.6131	−	80.7363i	−1.67331	−	2.89827i
$777$	1.33757	−	1.23947i	0.0479852	−	0.0444656i
$778$	16.1809	−	28.0262i	0.580115	−	1.00479i
$779$	5.03175	−	8.71525i	0.180281	−	0.312256i
$780$	−33.9392	−	67.2605i	−1.21522	−	2.40831i
$781$	−12.9507	−	22.4313i	−0.463413	−	0.802656i
$782$	−4.50407	−	7.80128i	−0.161065	−	0.278973i
$783$	−0.242434	+	0.419908i	−0.00866388	+	0.0150063i
$784$	81.6551	+	55.8275i	2.91625	+	1.99384i
$785$	73.2579			2.61469
$786$	48.9226			1.74501
$787$	−22.1655	+	38.3918i	−0.790114	+	1.36852i	0.135781	+	0.990739i	$0.456646\pi$
$787$	−22.1655	+	38.3918i	−0.790114	+	1.36852i	−0.925896	+	0.377779i	$0.876688\pi$
$788$	−45.3005	−	78.4628i	−1.61376	−	2.79512i
$789$	23.3538			0.831416
$790$	6.78983	−	11.7603i	0.241571	−	0.418414i
$791$	14.8375	−	13.7493i	0.527562	−	0.488867i
$792$	14.9487			0.531179
$793$	32.7043	+	1.84265i	1.16136	+	0.0654345i
$794$	1.31323	+	2.27458i	0.0466047	+	0.0807217i
$795$	23.7104			0.840920
$796$	5.49545	+	9.51840i	0.194781	+	0.337371i
$797$	2.40661	+	4.16837i	0.0852464	+	0.147651i	0.905496	−	0.424354i	$-0.139499\pi$
$797$	2.40661	+	4.16837i	0.0852464	+	0.147651i	−0.820250	+	0.572005i	$0.806166\pi$
$798$	−8.92984	+	8.27486i	−0.316113	+	0.292927i
$799$	1.22489	+	2.12158i	0.0433336	+	0.0750560i
$800$	−202.863			−7.17229
$801$	2.20434	+	3.81803i	0.0778866	+	0.134904i
$802$	−31.8724	+	55.2046i	−1.12545	+	1.94934i
$803$	4.77463	+	8.26989i	0.168493	+	0.291838i
$804$	−2.68839	+	4.65644i	−0.0948124	+	0.164220i
$805$	−1.80650	−	7.93864i	−0.0636708	−	0.279800i
$806$	−9.82139	+	14.9945i	−0.345944	+	0.528159i
$807$	15.6957	−	27.1858i	0.552515	−	0.956984i
$808$	−129.848			−4.56803
$809$	7.97087			0.280241			0.140120	−	0.990134i	$-0.455251\pi$
$809$	7.97087			0.280241			0.140120	+	0.990134i	$0.455251\pi$
$810$	10.5585			0.370989
$811$	−41.5780			−1.46000			−0.730000	−	0.683447i	$-0.760480\pi$
$811$	−41.5780			−1.46000			−0.730000	+	0.683447i	$0.760480\pi$
$812$	5.05658	−	4.68569i	0.177451	−	0.164436i
$813$	5.66515	+	9.81233i	0.198686	+	0.344134i
$814$	−1.52692	+	2.64470i	−0.0535185	+	0.0926968i
$815$	−47.5284	+	82.3216i	−1.66485	+	2.88360i
$816$	−59.2310			−2.07350
$817$	4.73154	+	8.19527i	0.165536	+	0.286716i
$818$	51.6804			1.80696
$819$	−1.59005	−	9.40594i	−0.0555610	−	0.328670i
$820$	124.092			4.33347
$821$	5.28157	+	9.14795i	0.184328	+	0.319265i	0.943350	−	0.331800i	$-0.107656\pi$
$821$	5.28157	+	9.14795i	0.184328	+	0.319265i	−0.759022	+	0.651065i	$0.774322\pi$
$822$	−59.1899			−2.06448
$823$	−19.5203	+	33.8101i	−0.680433	+	1.17855i	0.294415	+	0.955678i	$0.404875\pi$
$823$	−19.5203	+	33.8101i	−0.680433	+	1.17855i	−0.974849	+	0.222868i	$0.928458\pi$
$824$	8.16470	−	14.1417i	0.284431	−	0.492648i
$825$	8.25500	+	14.2981i	0.287402	+	0.497795i
$826$	−13.1948	−	57.9843i	−0.459106	−	2.01753i
$827$	35.0709			1.21954			0.609768	−	0.792580i	$-0.291263\pi$
$827$	35.0709			1.21954			0.609768	+	0.792580i	$0.291263\pi$
$828$	4.25296			0.147801
$829$	9.11299			0.316507			0.158254	−	0.987399i	$-0.449414\pi$
$829$	9.11299			0.316507			0.158254	+	0.987399i	$0.449414\pi$
$830$	−65.2731			−2.26566
$831$	−8.96129	+	15.5214i	−0.310864	+	0.538432i
$832$	−94.2438	−	5.30997i	−3.26732	−	0.184090i
$833$	−2.23080	+	29.2565i	−0.0772928	+	1.01368i
$834$	−0.966661	+	1.67431i	−0.0334727	+	0.0579765i
$835$	16.6605	+	28.8568i	0.576560	+	0.998632i
$836$	7.42906	−	12.8675i	0.256939	−	0.445032i
$837$	−0.915382	−	1.58549i	−0.0316402	−	0.0548025i
$838$	87.6081			3.02637
$839$	−7.08223	−	12.2668i	−0.244506	−	0.423496i	0.717487	−	0.696572i	$-0.245292\pi$
$839$	−7.08223	−	12.2668i	−0.244506	−	0.423496i	−0.961993	+	0.273076i	$0.911959\pi$
$840$	−90.0447	−	27.8393i	−3.10684	−	0.960549i
$841$	14.3825	+	24.9111i	0.495947	+	0.859005i
$842$	−46.7338	−	80.9453i	−1.61055	−	2.78956i
$843$	−11.6172			−0.400116
$844$	66.3042	+	114.842i	2.28228	+	3.95303i
$845$	30.0310	−	40.6593i	1.03310	−	1.39872i
$846$	−1.58706			−0.0545642
$847$	−4.89470	−	21.5096i	−0.168184	−	0.739080i
$848$	43.0842	−	74.6241i	1.47952	−	2.56260i
$849$	−8.09192			−0.277714
$850$	−57.5866	−	99.7429i	−1.97520	−	3.42115i
$851$	−0.272738	+	0.472396i	−0.00934934	+	0.0161935i
$852$	−85.3070			−2.92257
$853$	0.914536			0.0313131			0.0156566	−	0.999877i	$-0.495016\pi$
$853$	0.914536			0.0313131			0.0156566	+	0.999877i	$0.495016\pi$
$854$	47.8757	−	44.3641i	1.63827	−	1.51811i
$855$	3.29439	−	5.70606i	0.112666	−	0.195143i
$856$	88.0232	+	152.461i	3.00857	+	5.21100i
$857$	−9.58886	−	16.6084i	−0.327549	−	0.567332i	0.654476	−	0.756083i	$-0.272889\pi$
$857$	−9.58886	−	16.6084i	−0.327549	−	0.567332i	−0.982025	+	0.188751i	$0.939556\pi$
$858$	7.19669	+	14.2624i	0.245691	+	0.486909i
$859$	−2.83001	+	4.90173i	−0.0965588	+	0.167245i	−0.910258	−	0.414041i	$-0.864117\pi$
$859$	−2.83001	+	4.90173i	−0.0965588	+	0.167245i	0.813699	+	0.581286i	$0.197450\pi$
$860$	−58.3440	+	101.055i	−1.98951	+	3.44594i
$861$	15.0115	+	4.64116i	0.511592	+	0.158170i
$862$	2.70710	+	4.68883i	0.0922042	+	0.159702i
$863$	−14.6246	+	25.3305i	−0.497826	+	0.862259i	−0.999997	−	0.00250891i	$-0.999201\pi$
$863$	−14.6246	+	25.3305i	−0.497826	+	0.862259i	0.502171	+	0.864768i	$0.332535\pi$
$864$	10.0243	−	17.3625i	0.341032	−	0.590685i
$865$	14.9325	−	25.8638i	0.507719	−	0.879396i
$866$	−10.0703	+	17.4423i	−0.342204	+	0.592714i
$867$	−0.284884	−	0.493434i	−0.00967518	−	0.0167579i
$868$	5.77562	+	25.3808i	0.196037	+	0.861481i
$869$	−1.04926	+	1.81737i	−0.0355936	+	0.0616499i
$870$	−2.55975	+	4.43361i	−0.0867835	+	0.150313i
$871$	−3.60179	−	0.202936i	−0.122042	−	0.00687621i
$872$	49.0067	+	84.8820i	1.65957	+	2.87447i
$873$	5.08782	+	8.81236i	0.172197	+	0.298253i
$874$	1.82084	−	3.15379i	0.0615908	−	0.106678i
$875$	−11.6838	−	51.3443i	−0.394986	−	1.73576i
$876$	31.4507			1.06262
$877$	−9.09361			−0.307070			−0.153535	−	0.988143i	$-0.549066\pi$
$877$	−9.09361			−0.307070			−0.153535	+	0.988143i	$0.549066\pi$
$878$	28.2066	−	48.8553i	0.951928	−	1.64879i
$879$	−8.90887	−	15.4306i	−0.300489	−	0.520461i
$880$	89.6497			3.02209
$881$	−4.38792	+	7.60010i	−0.147833	+	0.256054i	−0.930426	−	0.366479i	$-0.880563\pi$
$881$	−4.38792	+	7.60010i	−0.147833	+	0.256054i	0.782593	+	0.622533i	$0.213896\pi$
$882$	−15.6915	−	10.7283i	−0.528361	−	0.361240i
$883$	−53.6724			−1.80622			−0.903111	−	0.429408i	$-0.858722\pi$
$883$	−53.6724			−1.80622			−0.903111	+	0.429408i	$0.858722\pi$
$884$	−36.5871	−	72.5082i	−1.23056	−	2.43871i
$885$	16.0917	+	27.8717i	0.540917	+	0.936897i
$886$	−14.5104			−0.487486
$887$	14.9136	+	25.8311i	0.500749	+	0.867323i	1.00000		0.000865013i	$0.000275342\pi$
$887$	14.9136	+	25.8311i	0.500749	+	0.867323i	−0.499251	+	0.866458i	$0.666391\pi$
$888$	3.15732	+	5.46864i	0.105953	+	0.183515i
$889$	9.52995	+	2.94640i	0.319624	+	0.0988191i
$890$	23.2746	+	40.3128i	0.780167	+	1.35129i
$891$	−1.63165			−0.0546623
$892$	−48.3431	−	83.7327i	−1.61865	−	2.80358i
$893$	−0.495182	+	0.857680i	−0.0165706	+	0.0287012i
$894$	−7.59360	−	13.1525i	−0.253968	−	0.439885i
$895$	18.9434	−	32.8109i	0.633208	−	1.09675i
$896$	−60.1490	+	55.7373i	−2.00944	+	1.86205i
$897$	1.28547	+	2.54754i	0.0429206	+	0.0850598i
$898$	40.9955	−	71.0063i	1.36804	−	2.36951i
$899$	0.887678			0.0296057
$900$	54.3761			1.81254
$901$	25.5603			0.851536
$902$	−26.3132			−0.876135
$903$	−10.8375	+	10.0426i	−0.360649	+	0.334197i
$904$	35.0238	+	60.6629i	1.16487	+	2.01762i
$905$	−12.1255	+	21.0020i	−0.403067	+	0.698132i
$906$	−13.5698	+	23.5035i	−0.450826	+	0.780853i
$907$	16.4090			0.544851			0.272425	−	0.962177i	$-0.412174\pi$
$907$	16.4090			0.544851			0.272425	+	0.962177i	$0.412174\pi$
$908$	22.4244	+	38.8403i	0.744181	+	1.28896i
$909$	14.1729			0.470084
$910$	−16.7886	−	99.3129i	−0.556538	−	3.29219i
$911$	−30.3790			−1.00650			−0.503251	−	0.864140i	$-0.667863\pi$
$911$	−30.3790			−1.00650			−0.503251	+	0.864140i	$0.667863\pi$
$912$	−11.9725	−	20.7370i	−0.396450	−	0.686671i
$913$	10.0869			0.333828
$914$	−42.1178	+	72.9502i	−1.39313	+	2.41298i
$915$	−17.6623	+	30.5920i	−0.583897	+	1.01134i
$916$	−59.7426	−	103.477i	−1.97395	−	3.41898i
$917$	45.5394	+	14.0795i	1.50384	+	0.464947i
$918$	11.3823			0.375673
$919$	1.15929			0.0382414			0.0191207	−	0.999817i	$-0.493913\pi$
$919$	1.15929			0.0382414			0.0191207	+	0.999817i	$0.493913\pi$
$920$	28.1927			0.929486
$921$	16.1633			0.532598
$922$	5.95304	−	10.3110i	0.196053	−	0.339574i
$923$	−25.7843	−	51.0992i	−0.848700	−	1.68195i
$924$	22.1636	+	6.85237i	0.729128	+	0.225426i
$925$	−3.48708	+	6.03980i	−0.114654	+	0.198587i
$926$	6.69867	+	11.6024i	0.220132	+	0.381280i
$927$	−0.891175	+	1.54356i	−0.0292700	+	0.0506972i
$928$	4.86044	+	8.41853i	0.159552	+	0.276352i
$929$	23.1584			0.759802			0.379901	−	0.925027i	$-0.375958\pi$
$929$	23.1584			0.759802			0.379901	+	0.925027i	$0.375958\pi$
$930$	−9.66509	−	16.7404i	−0.316931	−	0.548940i
$931$	−10.6937	+	5.13268i	−0.350473	+	0.168217i
$932$	13.4840	+	23.3550i	0.441683	+	0.765017i
$933$	9.06145	+	15.6949i	0.296658	+	0.513827i
$934$	21.6568			0.708632
$935$	13.2964	+	23.0301i	0.434840	+	0.753165i
$936$	32.9807	+	1.85823i	1.07801	+	0.0607382i
$937$	40.2025			1.31336			0.656679	−	0.754170i	$-0.271961\pi$
$937$	40.2025			1.31336			0.656679	+	0.754170i	$0.271961\pi$
$938$	−5.27265	+	4.88592i	−0.172158	+	0.159531i
$939$	12.8068	−	22.1820i	0.417934	−	0.723882i
$940$	−12.2120			−0.398313
$941$	−0.479740	−	0.830934i	−0.0156391	−	0.0270877i	0.858100	−	0.513483i	$-0.171645\pi$
$941$	−0.479740	−	0.830934i	−0.0156391	−	0.0270877i	−0.873739	+	0.486395i	$0.838312\pi$
$942$	−25.5810	+	44.3075i	−0.833473	+	1.44362i
$943$	−4.70007			−0.153055
$944$	116.962			3.80677
$945$	9.82836	+	3.03866i	0.319717	+	0.0988477i
$946$	12.3716	−	21.4283i	0.402237	−	0.696695i
$947$	17.0281	+	29.4935i	0.553338	+	0.958409i	0.998031	+	0.0627260i	$0.0199794\pi$
$947$	17.0281	+	29.4935i	0.553338	+	0.958409i	−0.444693	+	0.895683i	$0.646687\pi$
$948$	3.45575	+	5.98554i	0.112238	+	0.194401i
$949$	9.50606	+	18.8391i	0.308580	+	0.611541i
$950$	23.2803	−	40.3226i	0.755311	−	1.30824i
$951$	13.7304	−	23.7817i	0.445237	−	0.771174i
$952$	−97.0701	−	30.0114i	−3.14606	−	0.972675i
$953$	−19.1908	−	33.2394i	−0.621651	−	1.07673i	−0.989178	−	0.146718i	$-0.953129\pi$
$953$	−19.1908	−	33.2394i	−0.621651	−	1.07673i	0.367528	−	0.930013i	$-0.380204\pi$
$954$	−8.27942	+	14.3404i	−0.268056	+	0.464287i
$955$	5.92502	−	10.2624i	0.191729	−	0.332084i
$956$	−24.9430	+	43.2025i	−0.806713	+	1.39727i
$957$	0.395567	−	0.685142i	0.0127869	−	0.0221475i
$958$	−43.9167	−	76.0660i	−1.41888	−	2.45758i
$959$	−55.0966	−	17.0344i	−1.77916	−	0.550069i
$960$	50.8973	−	88.1568i	1.64270	−	2.84525i
$961$	13.8242	−	23.9441i	0.445940	−	0.772391i
$962$	−3.69754	+	5.64509i	−0.119213	+	0.182005i
$963$	−9.60772	−	16.6411i	−0.309605	−	0.536251i
$964$	39.7382	+	68.8285i	1.27988	+	2.21682i
$965$	17.4650	−	30.2502i	0.562217	−	0.973789i
$966$	5.43222	+	1.67949i	0.174779	+	0.0540369i
$967$	−10.7031			−0.344188			−0.172094	−	0.985080i	$-0.555053\pi$
$967$	−10.7031			−0.344188			−0.172094	+	0.985080i	$0.555053\pi$
$968$	76.3878			2.45520
$969$	3.55143	−	6.15125i	0.114088	−	0.197607i
$970$	53.7199	+	93.0456i	1.72484	+	2.98751i
$971$	−19.9835			−0.641300			−0.320650	−	0.947198i	$-0.603901\pi$
$971$	−19.9835			−0.641300			−0.320650	+	0.947198i	$0.603901\pi$
$972$	−2.68694	+	4.65391i	−0.0861836	+	0.149274i
$973$	−1.38166	+	1.28032i	−0.0442941	+	0.0410453i
$974$	−89.9102			−2.88091
$975$	16.4353	+	32.5714i	0.526352	+	1.04312i
$976$	64.1885	+	111.178i	2.05462	+	3.55871i
$977$	−3.02854			−0.0968915			−0.0484457	−	0.998826i	$-0.515427\pi$
$977$	−3.02854			−0.0968915			−0.0484457	+	0.998826i	$0.515427\pi$
$978$	−33.1929	−	57.4918i	−1.06139	−	1.83839i
$979$	−3.59671	−	6.22969i	−0.114952	−	0.199102i
$980$	−120.743	−	82.5516i	−3.85698	−	2.63701i
$981$	−5.34907	−	9.26486i	−0.170783	−	0.295804i
$982$	27.2526			0.869665
$983$	−17.7590	−	30.7595i	−0.566425	−	0.981076i	−0.996916	−	0.0784815i	$-0.974993\pi$
$983$	−17.7590	−	30.7595i	−0.566425	−	0.981076i	0.430491	−	0.902595i	$-0.358340\pi$
$984$	−27.2049	+	47.1202i	−0.867259	+	1.50214i
$985$	32.7772	+	56.7717i	1.04437	+	1.80890i
$986$	−2.75946	+	4.77953i	−0.0878791	+	0.152211i
$987$	−1.47731	−	0.456742i	−0.0470232	−	0.0145383i
$988$	17.9900	−	27.4656i	0.572337	−	0.873797i
$989$	2.20982	−	3.82752i	0.0702682	−	0.121708i
$990$	−17.2278			−0.547536
$991$	−35.3019			−1.12140			−0.560701	−	0.828018i	$-0.689468\pi$
$991$	−35.3019			−1.12140			−0.560701	+	0.828018i	$0.689468\pi$
$992$	−36.7041			−1.16536
$993$	6.95125			0.220591
$994$	−108.961	−	33.6877i	−3.45603	−	1.06851i
$995$	−3.97623	−	6.88704i	−0.126055	−	0.218334i
$996$	16.6107	−	28.7706i	0.526331	−	0.911631i
$997$	7.72657	−	13.3828i	0.244703	−	0.423838i	−0.717345	−	0.696718i	$-0.754643\pi$
$997$	7.72657	−	13.3828i	0.244703	−	0.423838i	0.962048	+	0.272880i	$0.0879762\pi$
$998$	−56.9011			−1.80117
$999$	−0.344621	−	0.596901i	−0.0109033	−	0.0188851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.100.10	✓	20
3.2	odd	2		819.2.n.f.100.1		20
7.4	even	3		273.2.l.c.256.1	yes	20
13.3	even	3		273.2.l.c.16.1	yes	20
21.11	odd	6		819.2.s.f.802.10		20
39.29	odd	6		819.2.s.f.289.10		20
91.81	even	3	inner	273.2.j.c.172.10	yes	20
273.263	odd	6		819.2.n.f.172.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.10	✓	20	1.1	even	1	trivial
273.2.j.c.172.10	yes	20	91.81	even	3	inner
273.2.l.c.16.1	yes	20	13.3	even	3
273.2.l.c.256.1	yes	20	7.4	even	3
819.2.n.f.100.1		20	3.2	odd	2
819.2.n.f.172.1		20	273.263	odd	6
819.2.s.f.289.10		20	39.29	odd	6
819.2.s.f.802.10		20	21.11	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35774 + 2.35168i) q^{2} +1.00000 q^{3} +(-2.68694 + 4.65391i) q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(0.587055 + 2.57980i) q^{7} -9.16172 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.35774 + 2.35168i) q^{2} +1.00000 q^{3} +(-2.68694 + 4.65391i) q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 + 2.35168i) q^{6} +(0.587055 + 2.57980i) q^{7} -9.16172 q^{8} +1.00000 q^{9} +10.5585 q^{10} -1.63165 q^{11} +(-2.68694 + 4.65391i) q^{12} +(-3.59984 - 0.202826i) q^{13} +(-5.26980 + 4.88327i) q^{14} +(1.94413 - 3.36734i) q^{15} +(-7.06539 - 12.2376i) q^{16} +(2.09582 - 3.63006i) q^{17} +(1.35774 + 2.35168i) q^{18} +1.69453 q^{19} +(10.4475 + 18.0956i) q^{20} +(0.587055 + 2.57980i) q^{21} +(-2.21536 - 3.83712i) q^{22} +(-0.395707 - 0.685385i) q^{23} -9.16172 q^{24} +(-5.05930 - 8.76296i) q^{25} +(-4.41068 - 8.74107i) q^{26} +1.00000 q^{27} +(-13.5835 - 4.19966i) q^{28} +(-0.242434 + 0.419908i) q^{29} +10.5585 q^{30} +(-0.915382 - 1.58549i) q^{31} +(10.0243 - 17.3625i) q^{32} -1.63165 q^{33} +11.3823 q^{34} +(9.82836 + 3.03866i) q^{35} +(-2.68694 + 4.65391i) q^{36} +(-0.344621 - 0.596901i) q^{37} +(2.30074 + 3.98500i) q^{38} +(-3.59984 - 0.202826i) q^{39} +(-17.8116 + 30.8506i) q^{40} +(2.96941 - 5.14316i) q^{41} +(-5.26980 + 4.88327i) q^{42} +(2.79224 + 4.83630i) q^{43} +(4.38414 - 7.59355i) q^{44} +(1.94413 - 3.36734i) q^{45} +(1.07454 - 1.86116i) q^{46} +(-0.292223 + 0.506146i) q^{47} +(-7.06539 - 12.2376i) q^{48} +(-6.31073 + 3.02897i) q^{49} +(13.7385 - 23.7957i) q^{50} +(2.09582 - 3.63006i) q^{51} +(10.6165 - 16.2084i) q^{52} +(3.04896 + 5.28096i) q^{53} +(1.35774 + 2.35168i) q^{54} +(-3.17214 + 5.49431i) q^{55} +(-5.37843 - 23.6354i) q^{56} +1.69453 q^{57} -1.31665 q^{58} +(-4.13854 + 7.16816i) q^{59} +(10.4475 + 18.0956i) q^{60} -9.08491 q^{61} +(2.48571 - 4.30537i) q^{62} +(0.587055 + 2.57980i) q^{63} +26.1800 q^{64} +(-7.68155 + 11.7276i) q^{65} +(-2.21536 - 3.83712i) q^{66} +1.00054 q^{67} +(11.2626 + 19.5075i) q^{68} +(-0.395707 - 0.685385i) q^{69} +(6.19844 + 27.2389i) q^{70} +(7.93720 + 13.7476i) q^{71} -9.16172 q^{72} +(-2.92626 - 5.06843i) q^{73} +(0.935814 - 1.62088i) q^{74} +(-5.05930 - 8.76296i) q^{75} +(-4.55310 + 7.88620i) q^{76} +(-0.957867 - 4.20933i) q^{77} +(-4.41068 - 8.74107i) q^{78} +(0.643065 - 1.11382i) q^{79} -54.9442 q^{80} +1.00000 q^{81} +16.1268 q^{82} -6.18202 q^{83} +(-13.5835 - 4.19966i) q^{84} +(-8.14908 - 14.1146i) q^{85} +(-7.58229 + 13.1329i) q^{86} +(-0.242434 + 0.419908i) q^{87} +14.9487 q^{88} +(2.20434 + 3.81803i) q^{89} +10.5585 q^{90} +(-1.59005 - 9.40594i) q^{91} +4.25296 q^{92} +(-0.915382 - 1.58549i) q^{93} -1.58706 q^{94} +(3.29439 - 5.70606i) q^{95} +(10.0243 - 17.3625i) q^{96} +(5.08782 + 8.81236i) q^{97} +(-15.6915 - 10.7283i) q^{98} -1.63165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

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