LMFDB - Embedded newform 273.2.j.c.172.3

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			172.3
Root			$0.904928 + 1.56738i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.c.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.904928 + 1.56738i) q^{2} +1.00000 q^{3} +(-0.637789 - 1.10468i) q^{4} +(1.98776 + 3.44291i) q^{5} +(-0.904928 + 1.56738i) q^{6} +(-2.60384 - 0.469078i) q^{7} -1.31110 q^{8} +1.00000 q^{9} -7.19513 q^{10} -0.286654 q^{11} +(-0.637789 - 1.10468i) q^{12} +(3.60075 + 0.185985i) q^{13} +(3.09151 - 3.65672i) q^{14} +(1.98776 + 3.44291i) q^{15} +(2.46203 - 4.26436i) q^{16} +(2.30091 + 3.98530i) q^{17} +(-0.904928 + 1.56738i) q^{18} -6.96749 q^{19} +(2.53555 - 4.39170i) q^{20} +(-2.60384 - 0.469078i) q^{21} +(0.259402 - 0.449297i) q^{22} +(3.61929 - 6.26879i) q^{23} -1.31110 q^{24} +(-5.40240 + 9.35723i) q^{25} +(-3.54993 + 5.47545i) q^{26} +1.00000 q^{27} +(1.14252 + 3.17559i) q^{28} +(0.421754 + 0.730500i) q^{29} -7.19513 q^{30} +(-0.212854 + 0.368675i) q^{31} +(3.14482 + 5.44698i) q^{32} -0.286654 q^{33} -8.32864 q^{34} +(-3.56082 - 9.89718i) q^{35} +(-0.637789 - 1.10468i) q^{36} +(2.18208 - 3.77948i) q^{37} +(6.30507 - 10.9207i) q^{38} +(3.60075 + 0.185985i) q^{39} +(-2.60615 - 4.51399i) q^{40} +(-0.509885 - 0.883147i) q^{41} +(3.09151 - 3.65672i) q^{42} +(0.585291 - 1.01375i) q^{43} +(0.182825 + 0.316662i) q^{44} +(1.98776 + 3.44291i) q^{45} +(6.55039 + 11.3456i) q^{46} +(2.71264 + 4.69843i) q^{47} +(2.46203 - 4.26436i) q^{48} +(6.55993 + 2.44280i) q^{49} +(-9.77756 - 16.9352i) q^{50} +(2.30091 + 3.98530i) q^{51} +(-2.09107 - 4.09631i) q^{52} +(-0.574226 + 0.994589i) q^{53} +(-0.904928 + 1.56738i) q^{54} +(-0.569801 - 0.986924i) q^{55} +(3.41389 + 0.615007i) q^{56} -6.96749 q^{57} -1.52663 q^{58} +(2.42927 + 4.20762i) q^{59} +(2.53555 - 4.39170i) q^{60} +8.16848 q^{61} +(-0.385236 - 0.667248i) q^{62} +(-2.60384 - 0.469078i) q^{63} -1.53522 q^{64} +(6.51711 + 12.7667i) q^{65} +(0.259402 - 0.449297i) q^{66} +1.57387 q^{67} +(2.93499 - 5.08356i) q^{68} +(3.61929 - 6.26879i) q^{69} +(18.7349 + 3.37507i) q^{70} +(-3.22369 + 5.58359i) q^{71} -1.31110 q^{72} +(8.24845 - 14.2867i) q^{73} +(3.94925 + 6.84031i) q^{74} +(-5.40240 + 9.35723i) q^{75} +(4.44379 + 7.69686i) q^{76} +(0.746401 + 0.134463i) q^{77} +(-3.54993 + 5.47545i) q^{78} +(-3.84412 - 6.65821i) q^{79} +19.5757 q^{80} +1.00000 q^{81} +1.84564 q^{82} +13.3888 q^{83} +(1.14252 + 3.17559i) q^{84} +(-9.14733 + 15.8436i) q^{85} +(1.05929 + 1.83475i) q^{86} +(0.421754 + 0.730500i) q^{87} +0.375832 q^{88} +(1.10786 - 1.91886i) q^{89} -7.19513 q^{90} +(-9.28853 - 2.17331i) q^{91} -9.23336 q^{92} +(-0.212854 + 0.368675i) q^{93} -9.81898 q^{94} +(-13.8497 - 23.9884i) q^{95} +(3.14482 + 5.44698i) q^{96} +(9.52241 - 16.4933i) q^{97} +(-9.76507 + 8.07135i) q^{98} -0.286654 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} + 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}+ \cdots + 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

Character values

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

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

Coefficient data

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

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

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

$2$	−0.904928	+	1.56738i	−0.639881	+	1.10831i	0.345578	+	0.938390i	$0.387683\pi$
$2$	−0.904928	+	1.56738i	−0.639881	+	1.10831i	−0.985459	+	0.169916i	$0.945650\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.637789	−	1.10468i	−0.318895	−	0.552342i
$5$	1.98776	+	3.44291i	0.888954	+	1.53971i	0.841113	+	0.540859i	$0.181901\pi$
$5$	1.98776	+	3.44291i	0.888954	+	1.53971i	0.0478412	+	0.998855i	$0.484766\pi$
$6$	−0.904928	+	1.56738i	−0.369435	+	0.639881i
$7$	−2.60384	−	0.469078i	−0.984158	−	0.177295i
$7$	−2.60384	−	0.469078i	−0.984158	−	0.177295i
$8$	−1.31110			−0.463543
$9$	1.00000			0.333333
$10$	−7.19513			−2.27530
$11$	−0.286654			−0.0864295			−0.0432148	−	0.999066i	$-0.513760\pi$
$11$	−0.286654			−0.0864295			−0.0432148	+	0.999066i	$0.513760\pi$
$12$	−0.637789	−	1.10468i	−0.184114	−	0.318895i
$13$	3.60075	+	0.185985i	0.998669	+	0.0515830i
$13$	3.60075	+	0.185985i	0.998669	+	0.0515830i
$14$	3.09151	−	3.65672i	0.826240	−	0.977300i
$15$	1.98776	+	3.44291i	0.513238	+	0.888954i
$16$	2.46203	−	4.26436i	0.615507	−	1.06609i
$17$	2.30091	+	3.98530i	0.558053	+	0.966577i	0.997659	+	0.0683857i	$0.0217848\pi$
$17$	2.30091	+	3.98530i	0.558053	+	0.966577i	−0.439606	+	0.898191i	$0.644882\pi$
$18$	−0.904928	+	1.56738i	−0.213294	+	0.369435i
$19$	−6.96749			−1.59845			−0.799225	−	0.601031i	$-0.794757\pi$
$19$	−6.96749			−1.59845			−0.799225	+	0.601031i	$0.794757\pi$
$20$	2.53555	−	4.39170i	0.566965	−	0.982013i
$21$	−2.60384	−	0.469078i	−0.568204	−	0.102361i
$22$	0.259402	−	0.449297i	0.0553046	−	0.0957904i
$23$	3.61929	−	6.26879i	0.754673	−	1.30713i	−0.190863	−	0.981617i	$-0.561129\pi$
$23$	3.61929	−	6.26879i	0.754673	−	1.30713i	0.945537	−	0.325516i	$-0.105538\pi$
$24$	−1.31110			−0.267627
$25$	−5.40240	+	9.35723i	−1.08048	+	1.87145i
$26$	−3.54993	+	5.47545i	−0.696199	+	1.07382i
$27$	1.00000			0.192450
$28$	1.14252	+	3.17559i	0.215915	+	0.600130i
$29$	0.421754	+	0.730500i	0.0783178	+	0.135650i	0.902524	−	0.430639i	$-0.141712\pi$
$29$	0.421754	+	0.730500i	0.0783178	+	0.135650i	−0.824206	+	0.566289i	$0.808378\pi$
$30$	−7.19513			−1.31364
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	−0.884507	−	0.466527i	$-0.845505\pi$
$31$	−0.212854	+	0.368675i	−0.0382298	+	0.0662159i	0.846277	+	0.532742i	$0.178839\pi$
$32$	3.14482	+	5.44698i	0.555930	+	0.962900i
$33$	−0.286654			−0.0499001
$34$	−8.32864			−1.42835
$35$	−3.56082	−	9.89718i	−0.601888	−	1.67293i
$36$	−0.637789	−	1.10468i	−0.106298	−	0.184114i
$37$	2.18208	−	3.77948i	0.358732	−	0.621342i	−0.629017	−	0.777391i	$-0.716542\pi$
$37$	2.18208	−	3.77948i	0.358732	−	0.621342i	0.987749	+	0.156049i	$0.0498758\pi$
$38$	6.30507	−	10.9207i	1.02282	−	1.77157i
$39$	3.60075	+	0.185985i	0.576582	+	0.0297814i
$40$	−2.60615	−	4.51399i	−0.412069	−	0.713724i
$41$	−0.509885	−	0.883147i	−0.0796307	−	0.137924i	0.823460	−	0.567374i	$-0.192041\pi$
$41$	−0.509885	−	0.883147i	−0.0796307	−	0.137924i	−0.903091	+	0.429450i	$0.858707\pi$
$42$	3.09151	−	3.65672i	0.477030	−	0.564245i
$43$	0.585291	−	1.01375i	0.0892560	−	0.154596i	−0.817941	−	0.575302i	$-0.804884\pi$
$43$	0.585291	−	1.01375i	0.0892560	−	0.154596i	0.907197	+	0.420706i	$0.138218\pi$
$44$	0.182825	+	0.316662i	0.0275619	+	0.0477386i
$45$	1.98776	+	3.44291i	0.296318	+	0.513238i
$46$	6.55039	+	11.3456i	0.965802	+	1.67282i
$47$	2.71264	+	4.69843i	0.395680	+	0.685337i	0.993188	−	0.116526i	$-0.0371758\pi$
$47$	2.71264	+	4.69843i	0.395680	+	0.685337i	−0.597508	+	0.801863i	$0.703842\pi$
$48$	2.46203	−	4.26436i	0.355363	−	0.615507i
$49$	6.55993	+	2.44280i	0.937133	+	0.348972i
$50$	−9.77756	−	16.9352i	−1.38276	−	2.39500i
$51$	2.30091	+	3.98530i	0.322192	+	0.558053i
$52$	−2.09107	−	4.09631i	−0.289979	−	0.568056i
$53$	−0.574226	+	0.994589i	−0.0788760	+	0.136617i	−0.902765	−	0.430134i	$-0.858466\pi$
$53$	−0.574226	+	0.994589i	−0.0788760	+	0.136617i	0.823889	+	0.566751i	$0.191800\pi$
$54$	−0.904928	+	1.56738i	−0.123145	+	0.213294i
$55$	−0.569801	−	0.986924i	−0.0768319	−	0.133077i
$56$	3.41389	+	0.615007i	0.456200	+	0.0821838i
$57$	−6.96749			−0.922866
$58$	−1.52663			−0.200456
$59$	2.42927	+	4.20762i	0.316264	+	0.547785i	0.979705	−	0.200443i	$-0.0642381\pi$
$59$	2.42927	+	4.20762i	0.316264	+	0.547785i	−0.663441	+	0.748228i	$0.730905\pi$
$60$	2.53555	−	4.39170i	0.327338	−	0.566965i
$61$	8.16848			1.04587			0.522933	−	0.852374i	$-0.324838\pi$
$61$	8.16848			1.04587			0.522933	+	0.852374i	$0.324838\pi$
$62$	−0.385236	−	0.667248i	−0.0489250	−	0.0847406i
$63$	−2.60384	−	0.469078i	−0.328053	−	0.0590983i
$64$	−1.53522			−0.191902
$65$	6.51711	+	12.7667i	0.808348	+	1.58352i
$66$	0.259402	−	0.449297i	0.0319301	−	0.0553046i
$67$	1.57387			0.192279			0.0961397	−	0.995368i	$-0.469350\pi$
$67$	1.57387			0.192279			0.0961397	+	0.995368i	$0.469350\pi$
$68$	2.93499	−	5.08356i	0.355920	−	0.616472i
$69$	3.61929	−	6.26879i	0.435711	−	0.754673i
$70$	18.7349	+	3.37507i	2.23925	+	0.403399i
$71$	−3.22369	+	5.58359i	−0.382581	+	0.662650i	−0.991430	−	0.130636i	$-0.958298\pi$
$71$	−3.22369	+	5.58359i	−0.382581	+	0.662650i	0.608849	+	0.793286i	$0.291631\pi$
$72$	−1.31110			−0.154514
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.256893	−	0.966440i	$-0.417301\pi$
$73$	8.24845	−	14.2867i	0.965408	−	1.67214i	0.708515	−	0.705696i	$-0.249365\pi$
$74$	3.94925	+	6.84031i	0.459092	+	0.795170i
$75$	−5.40240	+	9.35723i	−0.623815	+	1.08048i
$76$	4.44379	+	7.69686i	0.509737	+	0.882891i
$77$	0.746401	+	0.134463i	0.0850603	+	0.0153235i
$78$	−3.54993	+	5.47545i	−0.401950	+	0.619972i
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	0.564590	−	0.825371i	$-0.309034\pi$
$79$	−3.84412	−	6.65821i	−0.432497	−	0.749107i	−0.997088	+	0.0762639i	$0.975701\pi$
$80$	19.5757			2.18863
$81$	1.00000			0.111111
$82$	1.84564			0.203817
$83$	13.3888			1.46961			0.734805	−	0.678279i	$-0.237274\pi$
$83$	13.3888			1.46961			0.734805	+	0.678279i	$0.237274\pi$
$84$	1.14252	+	3.17559i	0.124659	+	0.346485i
$85$	−9.14733	+	15.8436i	−0.992168	+	1.71848i
$86$	1.05929	+	1.83475i	0.114226	+	0.197846i
$87$	0.421754	+	0.730500i	0.0452168	+	0.0783178i
$88$	0.375832			0.0400639
$89$	1.10786	−	1.91886i	0.117433	−	0.203399i	−0.801317	−	0.598240i	$-0.795867\pi$
$89$	1.10786	−	1.91886i	0.117433	−	0.203399i	0.918750	+	0.394841i	$0.129200\pi$
$90$	−7.19513			−0.758433
$91$	−9.28853	−	2.17331i	−0.973702	−	0.227825i
$92$	−9.23336			−0.962645
$93$	−0.212854	+	0.368675i	−0.0220720	+	0.0382298i
$94$	−9.81898			−1.01275
$95$	−13.8497	−	23.9884i	−1.42095	−	2.46116i
$96$	3.14482	+	5.44698i	0.320967	+	0.555930i
$97$	9.52241	−	16.4933i	0.966854	−	1.67464i	0.262306	−	0.964985i	$-0.415517\pi$
$97$	9.52241	−	16.4933i	0.966854	−	1.67464i	0.704549	−	0.709656i	$-0.251150\pi$
$98$	−9.76507	+	8.07135i	−0.986421	+	0.815330i
$99$	−0.286654			−0.0288098
$100$	13.7824			1.37824
$101$	−9.08855			−0.904344			−0.452172	−	0.891931i	$-0.649351\pi$
$101$	−9.08855			−0.904344			−0.452172	+	0.891931i	$0.649351\pi$
$102$	−8.32864			−0.824658
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	0.958097	−	0.286443i	$-0.0924729\pi$
$103$	2.34421	+	4.06029i	0.230982	+	0.400072i	−0.727116	+	0.686515i	$0.759140\pi$
$104$	−4.72094	−	0.243845i	−0.462926	−	0.0239109i
$105$	−3.56082	−	9.89718i	−0.347500	−	0.965866i
$106$	−1.03927	−	1.80006i	−0.100943	−	0.174838i
$107$	−7.25279	+	12.5622i	−0.701154	+	1.21443i	0.266908	+	0.963722i	$0.413998\pi$
$107$	−7.25279	+	12.5622i	−0.701154	+	1.21443i	−0.968062	+	0.250712i	$0.919335\pi$
$108$	−0.637789	−	1.10468i	−0.0613713	−	0.106298i
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	−0.747952	−	0.663752i	$-0.768963\pi$
$109$	2.09694	−	3.63200i	0.200850	−	0.347883i	0.948803	+	0.315870i	$0.102296\pi$
$110$	2.06251			0.196653
$111$	2.18208	−	3.77948i	0.207114	−	0.358732i
$112$	−8.41104	+	9.94881i	−0.794768	+	0.940074i
$113$	4.12305	−	7.14133i	0.387864	−	0.671800i	−0.604298	−	0.796758i	$-0.706546\pi$
$113$	4.12305	−	7.14133i	0.387864	−	0.671800i	0.992162	+	0.124958i	$0.0398797\pi$
$114$	6.30507	−	10.9207i	0.590524	−	1.02282i
$115$	28.7771			2.68348
$116$	0.537981	−	0.931810i	0.0499503	−	0.0865164i
$117$	3.60075	+	0.185985i	0.332890	+	0.0171943i
$118$	−8.79326			−0.809485
$119$	−4.12179	−	11.4564i	−0.377843	−	1.05020i
$120$	−2.60615	−	4.51399i	−0.237908	−	0.412069i
$121$	−10.9178			−0.992530
$122$	−7.39189	+	12.8031i	−0.669230	+	1.15914i
$123$	−0.509885	−	0.883147i	−0.0459748	−	0.0796307i
$124$	0.543025			0.0487651
$125$	−23.0771			−2.06408
$126$	3.09151	−	3.65672i	0.275413	−	0.325767i
$127$	−3.92173	−	6.79263i	−0.347997	−	0.602748i	0.637897	−	0.770122i	$-0.279805\pi$
$127$	−3.92173	−	6.79263i	−0.347997	−	0.602748i	−0.985894	+	0.167374i	$0.946471\pi$
$128$	−4.90037	+	8.48769i	−0.433136	+	0.750213i
$129$	0.585291	−	1.01375i	0.0515320	−	0.0892560i
$130$	−25.9079	−	1.33819i	−2.27227	−	0.117367i
$131$	−4.04277	−	7.00228i	−0.353218	−	0.611792i	0.633593	−	0.773666i	$-0.281579\pi$
$131$	−4.04277	−	7.00228i	−0.353218	−	0.611792i	−0.986811	+	0.161874i	$0.948246\pi$
$132$	0.182825	+	0.316662i	0.0159129	+	0.0275619i
$133$	18.1422	+	3.26829i	1.57313	+	0.283397i
$134$	−1.42424	+	2.46686i	−0.123036	+	0.213104i
$135$	1.98776	+	3.44291i	0.171079	+	0.296318i
$136$	−3.01672	−	5.22512i	−0.258682	−	0.448050i
$137$	−0.754841	−	1.30742i	−0.0644904	−	0.111701i	0.831977	−	0.554809i	$-0.187209\pi$
$137$	−0.754841	−	1.30742i	−0.0644904	−	0.111701i	−0.896468	+	0.443109i	$0.853876\pi$
$138$	6.55039	+	11.3456i	0.557606	+	0.965802i
$139$	2.02132	−	3.50104i	0.171446	−	0.296954i	−0.767479	−	0.641074i	$-0.778489\pi$
$139$	2.02132	−	3.50104i	0.171446	−	0.296954i	0.938926	+	0.344120i	$0.111823\pi$
$140$	−8.66220	+	10.2459i	−0.732089	+	0.865936i
$141$	2.71264	+	4.69843i	0.228446	+	0.395680i
$142$	−5.83441	−	10.1055i	−0.489613	−	0.848034i
$143$	−1.03217	−	0.0533134i	−0.0863145	−	0.00445829i
$144$	2.46203	−	4.26436i	0.205169	−	0.355363i
$145$	−1.67670	+	2.90412i	−0.139242	+	0.241174i
$146$	14.9285	+	25.8569i	1.23549	+	2.13993i
$147$	6.55993	+	2.44280i	0.541054	+	0.201479i
$148$	−5.56683			−0.457591
$149$	−19.1947			−1.57249			−0.786247	−	0.617912i	$-0.787979\pi$
$149$	−19.1947			−1.57249			−0.786247	+	0.617912i	$0.787979\pi$
$150$	−9.77756	−	16.9352i	−0.798335	−	1.38276i
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	0.166125	+	0.986105i	$0.446874\pi$
$151$	−9.47334	+	16.4083i	−0.770929	+	1.33529i	−0.937054	+	0.349184i	$0.886459\pi$
$152$	9.13506			0.740951
$153$	2.30091	+	3.98530i	0.186018	+	0.322192i
$154$	−0.886194	+	1.04822i	−0.0714116	+	0.0844676i
$155$	−1.69242			−0.135938
$156$	−2.09107	−	4.09631i	−0.167419	−	0.327967i
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	0.207197	+	0.978299i	$0.433566\pi$
$157$	−9.31770	+	16.1387i	−0.743633	+	1.28801i	−0.950831	+	0.309711i	$0.899768\pi$
$158$	13.9146			1.10699
$159$	−0.574226	+	0.994589i	−0.0455391	+	0.0788760i
$160$	−12.5023	+	21.6546i	−0.988394	+	1.71195i
$161$	−12.3646	+	14.6252i	−0.974465	+	1.15262i
$162$	−0.904928	+	1.56738i	−0.0710979	+	0.123145i
$163$	10.7052			0.838500			0.419250	−	0.907871i	$-0.362293\pi$
$163$	10.7052			0.838500			0.419250	+	0.907871i	$0.362293\pi$
$164$	−0.650398	+	1.12652i	−0.0507876	+	0.0879667i
$165$	−0.569801	−	0.986924i	−0.0443589	−	0.0768319i
$166$	−12.1159	+	20.9853i	−0.940375	+	1.62878i
$167$	0.0240620	+	0.0416766i	0.00186197	+	0.00322503i	0.866955	−	0.498387i	$-0.166074\pi$
$167$	0.0240620	+	0.0416766i	0.00186197	+	0.00322503i	−0.865093	+	0.501612i	$0.832741\pi$
$168$	3.41389	+	0.615007i	0.263387	+	0.0474489i
$169$	12.9308	+	1.33937i	0.994678	+	0.103029i
$170$	−16.5554	−	28.6747i	−1.26974	−	2.19925i
$171$	−6.96749			−0.532817
$172$	−1.49317			−0.113853
$173$	−14.0297			−1.06666			−0.533330	−	0.845907i	$-0.679060\pi$
$173$	−14.0297			−1.06666			−0.533330	+	0.845907i	$0.679060\pi$
$174$	−1.52663			−0.115733
$175$	18.4562	−	21.8306i	1.39516	−	1.65023i
$176$	−0.705751	+	1.22240i	−0.0531980	+	0.0921416i
$177$	2.42927	+	4.20762i	0.182595	+	0.316264i
$178$	2.00506	+	3.47287i	0.150286	+	0.260302i
$179$	4.69863			0.351192			0.175596	−	0.984462i	$-0.443815\pi$
$179$	4.69863			0.351192			0.175596	+	0.984462i	$0.443815\pi$
$180$	2.53555	−	4.39170i	0.188988	−	0.327338i
$181$	−22.0382			−1.63809			−0.819044	−	0.573730i	$-0.805496\pi$
$181$	−22.0382			−1.63809			−0.819044	+	0.573730i	$0.805496\pi$
$182$	11.8118	−	12.5920i	0.875552	−	0.933379i
$183$	8.16848			0.603832
$184$	−4.74524	+	8.21900i	−0.349824	+	0.605913i
$185$	17.3498			1.27559
$186$	−0.385236	−	0.667248i	−0.0282469	−	0.0489250i
$187$	−0.659567	−	1.14240i	−0.0482323	−	0.0835408i
$188$	3.46019	−	5.99322i	0.252360	−	0.437101i
$189$	−2.60384	−	0.469078i	−0.189401	−	0.0341204i
$190$	50.1319			3.63695
$191$	11.0974			0.802982			0.401491	−	0.915863i	$-0.368492\pi$
$191$	11.0974			0.802982			0.401491	+	0.915863i	$0.368492\pi$
$192$	−1.53522			−0.110795
$193$	−0.486230			−0.0349996			−0.0174998	−	0.999847i	$-0.505571\pi$
$193$	−0.486230			−0.0349996			−0.0174998	+	0.999847i	$0.505571\pi$
$194$	17.2342	+	29.8505i	1.23734	+	2.14314i
$195$	6.51711	+	12.7667i	0.466700	+	0.914245i
$196$	−1.48533	−	8.80464i	−0.106095	−	0.628903i
$197$	−8.53814	−	14.7885i	−0.608317	−	1.05364i	−0.991518	−	0.129971i	$-0.958511\pi$
$197$	−8.53814	−	14.7885i	−0.608317	−	1.05364i	0.383200	−	0.923665i	$-0.374822\pi$
$198$	0.259402	−	0.449297i	0.0184349	−	0.0319301i
$199$	−11.5849	−	20.0656i	−0.821230	−	1.42241i	−0.904766	−	0.425908i	$-0.859955\pi$
$199$	−11.5849	−	20.0656i	−0.821230	−	1.42241i	0.0835360	−	0.996505i	$-0.473379\pi$
$200$	7.08308	−	12.2683i	0.500849	−	0.867497i
$201$	1.57387			0.111013
$202$	8.22448	−	14.2452i	0.578673	−	1.00229i
$203$	−0.755518	−	2.09994i	−0.0530270	−	0.147387i
$204$	2.93499	−	5.08356i	0.205491	−	0.355920i
$205$	2.02706	−	3.51097i	0.141576	−	0.245217i
$206$	−8.48536			−0.591203
$207$	3.61929	−	6.26879i	0.251558	−	0.435711i
$208$	9.65826	−	14.8970i	0.669680	−	1.03292i
$209$	1.99726			0.138153
$210$	18.7349	+	3.37507i	1.29283	+	0.232902i
$211$	1.40788	+	2.43852i	0.0969224	+	0.167874i	0.910409	−	0.413709i	$-0.135767\pi$
$211$	1.40788	+	2.43852i	0.0969224	+	0.167874i	−0.813487	+	0.581583i	$0.802433\pi$
$212$	1.46494			0.100613
$213$	−3.22369	+	5.58359i	−0.220883	+	0.382581i
$214$	−13.1265	−	22.7358i	−0.897310	−	1.55419i
$215$	4.65368			0.317378
$216$	−1.31110			−0.0892090
$217$	0.727175	−	0.860123i	0.0493639	−	0.0583890i
$218$	3.79515	+	6.57340i	0.257040	+	0.445207i
$219$	8.24845	−	14.2867i	0.557379	−	0.965408i
$220$	−0.726825	+	1.25890i	−0.0490026	+	0.0848749i
$221$	7.54381	+	14.7780i	0.507451	+	0.994076i
$222$	3.94925	+	6.84031i	0.265057	+	0.459092i
$223$	−8.16232	−	14.1375i	−0.546589	−	0.946720i	−0.998505	−	0.0546597i	$-0.982593\pi$
$223$	−8.16232	−	14.1375i	−0.546589	−	0.946720i	0.451916	−	0.892061i	$-0.350741\pi$
$224$	−5.63353	−	15.6582i	−0.376406	−	1.04621i
$225$	−5.40240	+	9.35723i	−0.360160	+	0.623815i
$226$	7.46213	+	12.9248i	0.496373	+	0.859744i
$227$	3.10289	+	5.37436i	0.205946	+	0.356709i	0.950434	−	0.310927i	$-0.100640\pi$
$227$	3.10289	+	5.37436i	0.205946	+	0.356709i	−0.744488	+	0.667636i	$0.767306\pi$
$228$	4.44379	+	7.69686i	0.294297	+	0.509737i
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	0.874535	−	0.484962i	$-0.161167\pi$
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	−0.857257	+	0.514889i	$0.827833\pi$
$230$	−26.0412	+	45.1047i	−1.71711	+	2.97412i
$231$	0.746401	+	0.134463i	0.0491096	+	0.00884703i
$232$	−0.552962	−	0.957758i	−0.0363037	−	0.0628799i
$233$	−6.48273	−	11.2284i	−0.424697	−	0.735598i	0.571695	−	0.820466i	$-0.306286\pi$
$233$	−6.48273	−	11.2284i	−0.424697	−	0.735598i	−0.996392	+	0.0848689i	$0.972953\pi$
$234$	−3.54993	+	5.47545i	−0.232066	+	0.357941i
$235$	−10.7842	+	18.6787i	−0.703482	+	1.21847i
$236$	3.09872	−	5.36715i	0.201710	−	0.349371i
$237$	−3.84412	−	6.65821i	−0.249702	−	0.432497i
$238$	21.6864	+	3.90678i	1.40572	+	0.253239i
$239$	−4.79605			−0.310231			−0.155116	−	0.987896i	$-0.549575\pi$
$239$	−4.79605			−0.310231			−0.155116	+	0.987896i	$0.549575\pi$
$240$	19.5757			1.26361
$241$	−5.20975	−	9.02355i	−0.335589	−	0.581258i	0.648008	−	0.761633i	$-0.275602\pi$
$241$	−5.20975	−	9.02355i	−0.335589	−	0.581258i	−0.983598	+	0.180375i	$0.942269\pi$
$242$	9.87985	−	17.1124i	0.635101	−	1.10003i
$243$	1.00000			0.0641500
$244$	−5.20977	−	9.02358i	−0.333521	−	0.577676i
$245$	4.62924	+	27.4409i	0.295751	+	1.75314i
$246$	1.84564			0.117674
$247$	−25.0882	−	1.29585i	−1.59632	−	0.0824529i
$248$	0.279073	−	0.483369i	0.0177212	−	0.0306940i
$249$	13.3888			0.848479
$250$	20.8831	−	36.1706i	1.32077	−	2.28763i
$251$	−5.10645	+	8.84463i	−0.322316	+	0.558268i	−0.980966	−	0.194182i	$-0.937795\pi$
$251$	−5.10645	+	8.84463i	−0.322316	+	0.558268i	0.658649	+	0.752450i	$0.271128\pi$
$252$	1.14252	+	3.17559i	0.0719718	+	0.200043i
$253$	−1.03748	+	1.79698i	−0.0652261	+	0.112975i
$254$	14.1955			0.890706
$255$	−9.14733	+	15.8436i	−0.572828	+	0.992168i
$256$	−10.4042	−	18.0206i	−0.650262	−	1.12629i
$257$	3.18140	−	5.51035i	0.198450	−	0.343726i	−0.749576	−	0.661919i	$-0.769742\pi$
$257$	3.18140	−	5.51035i	0.198450	−	0.343726i	0.948026	+	0.318192i	$0.103076\pi$
$258$	1.05929	+	1.83475i	0.0659486	+	0.114226i
$259$	−7.45466	+	8.81758i	−0.463210	+	0.547898i
$260$	9.94666	−	15.3418i	0.616866	−	0.951460i
$261$	0.421754	+	0.730500i	0.0261059	+	0.0452168i
$262$	14.6337			0.904070
$263$	−17.0135			−1.04910			−0.524550	−	0.851380i	$-0.675766\pi$
$263$	−17.0135			−1.04910			−0.524550	+	0.851380i	$0.675766\pi$
$264$	0.375832			0.0231309
$265$	−4.56570			−0.280469
$266$	−21.5400	+	25.4782i	−1.32070	+	1.56217i
$267$	1.10786	−	1.91886i	0.0677997	−	0.117433i
$268$	−1.00380	−	1.73863i	−0.0613168	−	0.106204i
$269$	4.53019	+	7.84653i	0.276211	+	0.478411i	0.970440	−	0.241343i	$-0.0775879\pi$
$269$	4.53019	+	7.84653i	0.276211	+	0.478411i	−0.694229	+	0.719754i	$0.744255\pi$
$270$	−7.19513			−0.437881
$271$	−1.11398	+	1.92947i	−0.0676696	+	0.117207i	−0.897875	−	0.440250i	$-0.854890\pi$
$271$	−1.11398	+	1.92947i	−0.0676696	+	0.117207i	0.830206	+	0.557457i	$0.188223\pi$
$272$	22.6596			1.37394
$273$	−9.28853	−	2.17331i	−0.562167	−	0.131535i
$274$	2.73231			0.165065
$275$	1.54862	−	2.68229i	0.0933854	−	0.161748i
$276$	−9.23336			−0.555783
$277$	3.90377	+	6.76153i	0.234555	+	0.406261i	0.959143	−	0.282921i	$-0.0913034\pi$
$277$	3.90377	+	6.76153i	0.234555	+	0.406261i	−0.724588	+	0.689182i	$0.757970\pi$
$278$	3.65830	+	6.33637i	0.219411	+	0.380030i
$279$	−0.212854	+	0.368675i	−0.0127433	+	0.0220720i
$280$	4.66858	+	12.9762i	0.279001	+	0.775475i
$281$	−12.7531			−0.760789			−0.380394	−	0.924824i	$-0.624212\pi$
$281$	−12.7531			−0.760789			−0.380394	+	0.924824i	$0.624212\pi$
$282$	−9.81898			−0.584712
$283$	16.3439			0.971542			0.485771	−	0.874086i	$-0.338539\pi$
$283$	16.3439			0.971542			0.485771	+	0.874086i	$0.338539\pi$
$284$	8.22413			0.488012
$285$	−13.8497	−	23.9884i	−0.820386	−	1.42095i
$286$	1.01760	−	1.56956i	0.0601721	−	0.0928101i
$287$	0.913393	+	2.53875i	0.0539159	+	0.149857i
$288$	3.14482	+	5.44698i	0.185310	+	0.320967i
$289$	−2.08840	+	3.61721i	−0.122847	+	0.212777i
$290$	−3.03458	−	5.25604i	−0.178196	−	0.308645i
$291$	9.52241	−	16.4933i	0.558214	−	0.966854i
$292$	−21.0431			−1.23145
$293$	11.8319	−	20.4935i	0.691227	−	1.19724i	−0.280209	−	0.959939i	$-0.590404\pi$
$293$	11.8319	−	20.4935i	0.691227	−	1.19724i	0.971436	−	0.237302i	$-0.0762630\pi$
$294$	−9.76507	+	8.07135i	−0.569511	+	0.470731i
$295$	−9.65762	+	16.7275i	−0.562288	+	0.973912i
$296$	−2.86093	+	4.95527i	−0.166288	+	0.288019i
$297$	−0.286654			−0.0166334
$298$	17.3699	−	30.0855i	1.00621	−	1.74280i
$299$	14.1980	−	21.8992i	0.821094	−	1.26646i
$300$	13.7824			0.795725
$301$	−1.99953	+	2.36510i	−0.115251	+	0.136322i
$302$	−17.1454	−	29.6967i	−0.986605	−	1.70885i
$303$	−9.08855			−0.522124
$304$	−17.1541	+	29.7119i	−0.983858	+	1.70409i
$305$	16.2370	+	28.1233i	0.929728	+	1.61034i
$306$	−8.32864			−0.476117
$307$	8.99691			0.513481			0.256740	−	0.966480i	$-0.417351\pi$
$307$	8.99691			0.513481			0.256740	+	0.966480i	$0.417351\pi$
$308$	−0.327507	−	0.910296i	−0.0186615	−	0.0518689i
$309$	2.34421	+	4.06029i	0.133357	+	0.230982i
$310$	1.53151	−	2.65266i	0.0869842	−	0.150661i
$311$	15.4498	−	26.7598i	0.876077	−	1.51741i	0.0204655	−	0.999791i	$-0.493485\pi$
$311$	15.4498	−	26.7598i	0.876077	−	1.51741i	0.855611	−	0.517619i	$-0.173181\pi$
$312$	−4.72094	−	0.243845i	−0.267271	−	0.0138050i
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	0.952254	−	0.305308i	$-0.0987595\pi$
$313$	3.74574	+	6.48782i	0.211722	+	0.366713i	−0.740532	+	0.672022i	$0.765426\pi$
$314$	−16.8637	−	29.2088i	−0.951673	−	1.64835i
$315$	−3.56082	−	9.89718i	−0.200629	−	0.557643i
$316$	−4.90348	+	8.49307i	−0.275842	+	0.477773i
$317$	8.11402	+	14.0539i	0.455729	+	0.789346i	0.998730	−	0.0503864i	$-0.0160453\pi$
$317$	8.11402	+	14.0539i	0.455729	+	0.789346i	−0.543001	+	0.839732i	$0.682712\pi$
$318$	−1.03927	−	1.80006i	−0.0582792	−	0.100943i
$319$	−0.120898	−	0.209401i	−0.00676897	−	0.0117242i
$320$	−3.05165	−	5.28562i	−0.170593	−	0.295475i
$321$	−7.25279	+	12.5622i	−0.404811	+	0.701154i
$322$	−11.7342	−	32.6147i	−0.653919	−	1.81755i
$323$	−16.0316	−	27.7675i	−0.892021	−	1.54503i
$324$	−0.637789	−	1.10468i	−0.0354327	−	0.0613713i
$325$	−21.1930	+	32.6883i	−1.17558	+	1.81322i
$326$	−9.68748	+	16.7792i	−0.536540	+	0.929314i
$327$	2.09694	−	3.63200i	0.115961	−	0.200850i
$328$	0.668510	+	1.15789i	0.0369123	+	0.0639340i
$329$	−4.85935	−	13.5064i	−0.267904	−	0.744632i
$330$	2.06251			0.113538
$331$	5.58434			0.306943			0.153472	−	0.988153i	$-0.450955\pi$
$331$	5.58434			0.306943			0.153472	+	0.988153i	$0.450955\pi$
$332$	−8.53922	−	14.7904i	−0.468650	−	0.811726i
$333$	2.18208	−	3.77948i	0.119577	−	0.207114i
$334$	−0.0870976			−0.00476577
$335$	3.12849	+	5.41870i	0.170928	+	0.296055i
$336$	−8.41104	+	9.94881i	−0.458860	+	0.542752i
$337$	−0.504097			−0.0274599			−0.0137299	−	0.999906i	$-0.504371\pi$
$337$	−0.504097			−0.0274599			−0.0137299	+	0.999906i	$0.504371\pi$
$338$	−13.8008	+	19.0555i	−0.750663	+	1.03648i
$339$	4.12305	−	7.14133i	0.223933	−	0.387864i
$340$	23.3363			1.26559
$341$	0.0610156	−	0.105682i	0.00330418	−	0.00572301i
$342$	6.30507	−	10.9207i	0.340939	−	0.590524i
$343$	−15.9351	−	9.43778i	−0.860416	−	0.509592i
$344$	−0.767374	+	1.32913i	−0.0413740	+	0.0716619i
$345$	28.7771			1.54931
$346$	12.6959	−	21.9899i	0.682535	−	1.18219i
$347$	6.06672	+	10.5079i	0.325678	+	0.564092i	0.981649	−	0.190694i	$-0.0610740\pi$
$347$	6.06672	+	10.5079i	0.325678	+	0.564092i	−0.655971	+	0.754786i	$0.727741\pi$
$348$	0.537981	−	0.931810i	0.0288388	−	0.0499503i
$349$	10.9086	+	18.8943i	0.583924	+	1.01139i	0.995009	+	0.0997893i	$0.0318169\pi$
$349$	10.9086	+	18.8943i	0.583924	+	1.01139i	−0.411084	+	0.911597i	$0.634850\pi$
$350$	17.5152	+	48.6830i	0.936229	+	2.60222i
$351$	3.60075	+	0.185985i	0.192194	+	0.00992715i
$352$	−0.901476	−	1.56140i	−0.0480488	−	0.0832230i
$353$	−12.0879			−0.643375			−0.321688	−	0.946846i	$-0.604250\pi$
$353$	−12.0879			−0.643375			−0.321688	+	0.946846i	$0.604250\pi$
$354$	−8.79326			−0.467356
$355$	−25.6317			−1.36039
$356$	−2.82631			−0.149794
$357$	−4.12179	−	11.4564i	−0.218148	−	0.606335i
$358$	−4.25192	+	7.36454i	−0.224721	+	0.389228i
$359$	−7.22027	−	12.5059i	−0.381071	−	0.660035i	0.610144	−	0.792290i	$-0.291111\pi$
$359$	−7.22027	−	12.5059i	−0.381071	−	0.660035i	−0.991216	+	0.132255i	$0.957778\pi$
$360$	−2.60615	−	4.51399i	−0.137356	−	0.237908i
$361$	29.5459			1.55505
$362$	19.9430	−	34.5423i	1.04818	−	1.81550i
$363$	−10.9178			−0.573037
$364$	3.52331	+	11.6470i	0.184671	+	0.610468i
$365$	65.5838			3.43281
$366$	−7.39189	+	12.8031i	−0.386380	+	0.669230i
$367$	24.3787			1.27256			0.636280	−	0.771459i	$-0.280472\pi$
$367$	24.3787			1.27256			0.636280	+	0.771459i	$0.280472\pi$
$368$	−17.8216	−	30.8679i	−0.929013	−	1.60910i
$369$	−0.509885	−	0.883147i	−0.0265436	−	0.0459748i
$370$	−15.7004	+	27.1938i	−0.816223	+	1.41374i
$371$	1.96173	−	2.32039i	0.101848	−	0.120469i
$372$	0.543025			0.0281545
$373$	−8.40033			−0.434953			−0.217476	−	0.976066i	$-0.569782\pi$
$373$	−8.40033			−0.434953			−0.217476	+	0.976066i	$0.569782\pi$
$374$	2.38744			0.123452
$375$	−23.0771			−1.19170
$376$	−3.55654	−	6.16011i	−0.183415	−	0.317684i
$377$	1.38277	+	2.70879i	0.0712163	+	0.139510i
$378$	3.09151	−	3.65672i	0.159010	−	0.188082i
$379$	−1.82895	−	3.16783i	−0.0939467	−	0.162720i	0.815222	−	0.579149i	$-0.196615\pi$
$379$	−1.82895	−	3.16783i	−0.0939467	−	0.162720i	−0.909169	+	0.416428i	$0.863282\pi$
$380$	−17.6664	+	30.5991i	−0.906266	+	1.56970i
$381$	−3.92173	−	6.79263i	−0.200916	−	0.347997i
$382$	−10.0424	+	17.3939i	−0.513812	+	0.889949i
$383$	−30.7052			−1.56896			−0.784481	−	0.620152i	$-0.787071\pi$
$383$	−30.7052			−1.56896			−0.784481	+	0.620152i	$0.787071\pi$
$384$	−4.90037	+	8.48769i	−0.250071	+	0.433136i
$385$	1.02072	+	2.83707i	0.0520209	+	0.144590i
$386$	0.440003	−	0.762108i	0.0223956	−	0.0387903i
$387$	0.585291	−	1.01375i	0.0297520	−	0.0515320i
$388$	−24.2932			−1.23330
$389$	−9.21889	+	15.9676i	−0.467416	+	0.809589i	−0.999307	−	0.0372241i	$-0.988148\pi$
$389$	−9.21889	+	15.9676i	−0.467416	+	0.809589i	0.531890	+	0.846813i	$0.321482\pi$
$390$	−25.9079	−	1.33819i	−1.31190	−	0.0677617i
$391$	33.3106			1.68459
$392$	−8.60072	−	3.20276i	−0.434402	−	0.161764i
$393$	−4.04277	−	7.00228i	−0.203931	−	0.353218i
$394$	30.9056			1.55700
$395$	15.2824	−	26.4699i	0.768941	−	1.33184i
$396$	0.182825	+	0.316662i	0.00918730	+	0.0159129i
$397$	−2.26064			−0.113458			−0.0567290	−	0.998390i	$-0.518067\pi$
$397$	−2.26064			−0.113458			−0.0567290	+	0.998390i	$0.518067\pi$
$398$	41.9339			2.10196
$399$	18.1422	+	3.26829i	0.908246	+	0.163619i
$400$	26.6017	+	46.0755i	1.33009	+	2.30378i
$401$	−14.2609	+	24.7005i	−0.712153	+	1.23349i	0.251894	+	0.967755i	$0.418947\pi$
$401$	−14.2609	+	24.7005i	−0.712153	+	1.23349i	−0.964047	+	0.265731i	$0.914387\pi$
$402$	−1.42424	+	2.46686i	−0.0710348	+	0.123036i
$403$	−0.835004	+	1.28792i	−0.0415945	+	0.0641558i
$404$	5.79658	+	10.0400i	0.288391	+	0.499507i
$405$	1.98776	+	3.44291i	0.0987727	+	0.171079i
$406$	3.97509	+	0.716108i	0.197281	+	0.0355398i
$407$	−0.625503	+	1.08340i	−0.0310051	+	0.0537023i
$408$	−3.01672	−	5.22512i	−0.149350	−	0.258682i
$409$	−5.42700	−	9.39983i	−0.268348	−	0.464792i	0.700088	−	0.714057i	$-0.253144\pi$
$409$	−5.42700	−	9.39983i	−0.268348	−	0.464792i	−0.968435	+	0.249265i	$0.919811\pi$
$410$	3.66869	+	6.35436i	0.181184	+	0.313819i
$411$	−0.754841	−	1.30742i	−0.0372335	−	0.0644904i
$412$	2.99022	−	5.17921i	0.147318	−	0.255162i
$413$	−4.35172	−	12.0955i	−0.214134	−	0.595179i
$414$	6.55039	+	11.3456i	0.321934	+	0.557606i
$415$	26.6137	+	46.0963i	1.30642	+	2.26278i
$416$	10.3106	+	20.1981i	0.505521	+	0.990294i
$417$	2.02132	−	3.50104i	0.0989846	−	0.171446i
$418$	−1.80738	+	3.13047i	−0.0884017	+	0.153116i
$419$	−7.68279	−	13.3070i	−0.375329	−	0.650089i	0.615047	−	0.788490i	$-0.289137\pi$
$419$	−7.68279	−	13.3070i	−0.375329	−	0.650089i	−0.990376	+	0.138401i	$0.955804\pi$
$420$	−8.66220	+	10.2459i	−0.422672	+	0.499948i
$421$	−3.33695			−0.162633			−0.0813166	−	0.996688i	$-0.525912\pi$
$421$	−3.33695			−0.162633			−0.0813166	+	0.996688i	$0.525912\pi$
$422$	−5.09612			−0.248075
$423$	2.71264	+	4.69843i	0.131893	+	0.228446i
$424$	0.752867	−	1.30400i	0.0365625	−	0.0633281i
$425$	−49.7218			−2.41186
$426$	−5.83441	−	10.1055i	−0.282678	−	0.489613i
$427$	−21.2694	−	3.83165i	−1.02930	−	0.185427i
$428$	18.5030			0.894377
$429$	−1.03217	−	0.0533134i	−0.0498337	−	0.00257400i
$430$	−4.21124	+	7.29408i	−0.203084	+	0.351752i
$431$	−4.26093			−0.205242			−0.102621	−	0.994721i	$-0.532723\pi$
$431$	−4.26093			−0.205242			−0.102621	+	0.994721i	$0.532723\pi$
$432$	2.46203	−	4.26436i	0.118454	−	0.205169i
$433$	−5.56416	+	9.63741i	−0.267396	+	0.463144i	−0.968189	−	0.250221i	$-0.919497\pi$
$433$	−5.56416	+	9.63741i	−0.267396	+	0.463144i	0.700792	+	0.713365i	$0.252830\pi$
$434$	0.690100	+	1.91811i	0.0331259	+	0.0920722i
$435$	−1.67670	+	2.90412i	−0.0803914	+	0.139242i
$436$	−5.34961			−0.256200
$437$	−25.2173	+	43.6777i	−1.20631	+	2.08939i
$438$	14.9285	+	25.8569i	0.713312	+	1.23549i
$439$	−20.5012	+	35.5092i	−0.978470	+	1.69476i	−0.310497	+	0.950574i	$0.600496\pi$
$439$	−20.5012	+	35.5092i	−0.978470	+	1.69476i	−0.667973	+	0.744186i	$0.732838\pi$
$440$	0.747065	+	1.29395i	0.0356149	+	0.0616869i
$441$	6.55993	+	2.44280i	0.312378	+	0.116324i
$442$	−29.9894	−	1.54900i	−1.42645	−	0.0736785i
$443$	−7.92693	−	13.7298i	−0.376620	−	0.652325i	0.613948	−	0.789346i	$-0.289580\pi$
$443$	−7.92693	−	13.7298i	−0.376620	−	0.652325i	−0.990568	+	0.137022i	$0.956247\pi$
$444$	−5.56683			−0.264190
$445$	8.80862			0.417569
$446$	29.5452			1.39901
$447$	−19.1947			−0.907880
$448$	3.99746	+	0.720137i	0.188862	+	0.0340233i
$449$	−7.54997	+	13.0769i	−0.356305	+	0.617139i	−0.987340	−	0.158616i	$-0.949297\pi$
$449$	−7.54997	+	13.0769i	−0.356305	+	0.617139i	0.631035	+	0.775754i	$0.282630\pi$
$450$	−9.77756	−	16.9352i	−0.460919	−	0.798335i
$451$	0.146161	+	0.253158i	0.00688244	+	0.0119207i
$452$	−10.5185			−0.494751
$453$	−9.47334	+	16.4083i	−0.445096	+	0.770929i
$454$	−11.2316			−0.527123
$455$	−10.9809	−	36.2995i	−0.514792	−	1.70175i
$456$	9.13506			0.427789
$457$	0.0139240	−	0.0241170i	0.000651335	−	0.00112815i	−0.865700	−	0.500564i	$-0.833126\pi$
$457$	0.0139240	−	0.0241170i	0.000651335	−	0.00112815i	0.866351	+	0.499436i	$0.166459\pi$
$458$	−0.946420			−0.0442233
$459$	2.30091	+	3.98530i	0.107397	+	0.186018i
$460$	−18.3537	−	31.7896i	−0.855747	−	1.48220i
$461$	14.0543	−	24.3428i	0.654575	−	1.13376i	−0.327425	−	0.944877i	$-0.606181\pi$
$461$	14.0543	−	24.3428i	0.654575	−	1.13376i	0.982000	−	0.188880i	$-0.0604859\pi$
$462$	−0.886194	+	1.04822i	−0.0412295	+	0.0487674i
$463$	−0.266538			−0.0123871			−0.00619354	−	0.999981i	$-0.501971\pi$
$463$	−0.266538			−0.0123871			−0.00619354	+	0.999981i	$0.501971\pi$
$464$	4.15349			0.192821
$465$	−1.69242			−0.0784839
$466$	23.4656			1.08702
$467$	−18.5400	−	32.1123i	−0.857931	−	1.48598i	−0.873899	−	0.486107i	$-0.838417\pi$
$467$	−18.5400	−	32.1123i	−0.857931	−	1.48598i	0.0159687	−	0.999872i	$-0.494917\pi$
$468$	−2.09107	−	4.09631i	−0.0966595	−	0.189352i
$469$	−4.09811	−	0.738270i	−0.189233	−	0.0340901i
$470$	−19.5178	−	33.8058i	−0.900289	−	1.55935i
$471$	−9.31770	+	16.1387i	−0.429337	+	0.743633i
$472$	−3.18501	−	5.51660i	−0.146602	−	0.253922i
$473$	−0.167776	+	0.290597i	−0.00771436	+	0.0133617i
$474$	13.9146			0.639119
$475$	37.6411	−	65.1964i	1.72709	−	2.99141i
$476$	−10.0268	+	11.8600i	−0.459579	+	0.543603i
$477$	−0.574226	+	0.994589i	−0.0262920	+	0.0455391i
$478$	4.34008	−	7.51725i	0.198511	−	0.343831i
$479$	28.7986			1.31584			0.657922	−	0.753086i	$-0.271436\pi$
$479$	28.7986			1.31584			0.657922	+	0.753086i	$0.271436\pi$
$480$	−12.5023	+	21.6546i	−0.570649	+	0.988394i
$481$	8.56006	−	13.2031i	0.390305	−	0.602011i
$482$	18.8578			0.858949
$483$	−12.3646	+	14.6252i	−0.562608	+	0.665468i
$484$	6.96327	+	12.0607i	0.316512	+	0.548216i
$485$	75.7132			3.43796
$486$	−0.904928	+	1.56738i	−0.0410484	+	0.0710979i
$487$	6.86516	+	11.8908i	0.311090	+	0.538824i	0.978599	−	0.205778i	$-0.0659725\pi$
$487$	6.86516	+	11.8908i	0.311090	+	0.538824i	−0.667508	+	0.744602i	$0.732639\pi$
$488$	−10.7097			−0.484805
$489$	10.7052			0.484108
$490$	−47.1995	−	17.5763i	−2.13226	−	0.794016i
$491$	13.7632	+	23.8386i	0.621126	+	1.07582i	0.989276	+	0.146056i	$0.0466579\pi$
$491$	13.7632	+	23.8386i	0.621126	+	1.07582i	−0.368150	+	0.929766i	$0.620009\pi$
$492$	−0.650398	+	1.12652i	−0.0293222	+	0.0507876i
$493$	−1.94084	+	3.36163i	−0.0874110	+	0.151400i
$494$	24.7341	−	38.1501i	1.11284	−	1.71645i
$495$	−0.569801	−	0.986924i	−0.0256106	−	0.0443589i
$496$	1.04811	+	1.81537i	0.0470614	+	0.0815127i
$497$	11.0131	−	13.0266i	0.494005	−	0.584323i
$498$	−12.1159	+	20.9853i	−0.542925	+	0.940375i
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	0.906284	−	0.422669i	$-0.138907\pi$
$499$	1.94567	+	3.37000i	0.0871001	+	0.150862i	−0.819184	+	0.573531i	$0.805573\pi$
$500$	14.7183	+	25.4929i	0.658224	+	1.14008i
$501$	0.0240620	+	0.0416766i	0.00107501	+	0.00186197i
$502$	−9.24194	−	16.0075i	−0.412488	−	0.714450i
$503$	−1.87991	+	3.25610i	−0.0838212	+	0.145183i	−0.904888	−	0.425649i	$-0.860046\pi$
$503$	−1.87991	+	3.25610i	−0.0838212	+	0.145183i	0.821067	+	0.570832i	$0.193379\pi$
$504$	3.41389	+	0.615007i	0.152067	+	0.0273946i
$505$	−18.0659	−	31.2910i	−0.803921	−	1.39243i
$506$	−1.87770	−	3.25227i	−0.0834738	−	0.144581i
$507$	12.9308	+	1.33937i	0.574278	+	0.0594836i
$508$	−5.00247	+	8.66453i	−0.221949	+	0.384426i
$509$	19.2740	−	33.3836i	0.854307	−	1.47970i	−0.0229793	−	0.999736i	$-0.507315\pi$
$509$	19.2740	−	33.3836i	0.854307	−	1.47970i	0.877286	−	0.479967i	$-0.159351\pi$
$510$	−16.5554	−	28.6747i	−0.733084	−	1.26974i
$511$	−28.1792	+	33.3312i	−1.24657	+	1.47448i
$512$	18.0587			0.798088
$513$	−6.96749			−0.307622
$514$	5.75788	+	9.97294i	0.253969	+	0.439888i
$515$	−9.31946	+	16.1418i	−0.410664	+	0.711291i
$516$	−1.49317			−0.0657331
$517$	−0.777591	−	1.34683i	−0.0341984	−	0.0592334i
$518$	−7.07458	−	19.6636i	−0.310839	−	0.863967i
$519$	−14.0297			−0.615837
$520$	−8.54457	−	16.7385i	−0.374704	−	0.734030i
$521$	−6.92277	+	11.9906i	−0.303292	+	0.525318i	−0.976880	−	0.213790i	$-0.931419\pi$
$521$	−6.92277	+	11.9906i	−0.303292	+	0.525318i	0.673587	+	0.739108i	$0.264753\pi$
$522$	−1.52663			−0.0668188
$523$	−10.0335	+	17.3786i	−0.438736	+	0.759913i	−0.997592	−	0.0693515i	$-0.977907\pi$
$523$	−10.0335	+	17.3786i	−0.438736	+	0.759913i	0.558856	+	0.829265i	$0.311240\pi$
$524$	−5.15687	+	8.93196i	−0.225279	+	0.390194i
$525$	18.4562	−	21.8306i	0.805496	−	0.952763i
$526$	15.3960	−	26.6667i	0.671299	−	1.16272i
$527$	−1.95904			−0.0853370
$528$	−0.705751	+	1.22240i	−0.0307139	+	0.0531980i
$529$	−14.6985	−	25.4585i	−0.639063	−	1.10689i
$530$	4.13163	−	7.15619i	0.179467	−	0.310845i
$531$	2.42927	+	4.20762i	0.105421	+	0.182595i
$532$	−7.96047	−	22.1259i	−0.345130	−	0.959278i
$533$	−1.67172	−	3.27482i	−0.0724101	−	0.141848i
$534$	2.00506	+	3.47287i	0.0867674	+	0.150286i
$535$	−57.6673			−2.49318
$536$	−2.06351			−0.0891298
$537$	4.69863			0.202761
$538$	−16.3980			−0.706968
$539$	−1.88043	−	0.700240i	−0.0809960	−	0.0301615i
$540$	2.53555	−	4.39170i	0.109113	−	0.188988i
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	−0.909788	−	0.415072i	$-0.863756\pi$
$541$	−18.9415	−	32.8076i	−0.814357	−	1.41051i	0.0954310	−	0.995436i	$-0.469577\pi$
$542$	−2.01615	−	3.49207i	−0.0866009	−	0.149997i
$543$	−22.0382			−0.945751
$544$	−14.4719	+	25.0661i	−0.620478	+	1.07470i
$545$	16.6728			0.714186
$546$	11.8118	−	12.5920i	0.505500	−	0.538887i
$547$	29.3783			1.25613			0.628063	−	0.778162i	$-0.283848\pi$
$547$	29.3783			1.25613			0.628063	+	0.778162i	$0.283848\pi$
$548$	−0.962858	+	1.66772i	−0.0411313	+	0.0712415i
$549$	8.16848			0.348622
$550$	2.80278	+	4.85456i	0.119511	+	0.206999i
$551$	−2.93857	−	5.08975i	−0.125187	−	0.216831i
$552$	−4.74524	+	8.21900i	−0.201971	+	0.349824i
$553$	6.88624	+	19.1401i	0.292833	+	0.813919i
$554$	−14.1305			−0.600349
$555$	17.3498			0.736460
$556$	−5.15671			−0.218693
$557$	1.02608			0.0434763			0.0217381	−	0.999764i	$-0.493080\pi$
$557$	1.02608			0.0434763			0.0217381	+	0.999764i	$0.493080\pi$
$558$	−0.385236	−	0.667248i	−0.0163083	−	0.0282469i
$559$	2.29603	−	3.54142i	0.0971117	−	0.149786i
$560$	−50.9720	−	9.18253i	−2.15396	−	0.388033i
$561$	−0.659567	−	1.14240i	−0.0278469	−	0.0482323i
$562$	11.5407	−	19.9890i	0.486814	−	0.843187i
$563$	18.1124	+	31.3716i	0.763348	+	1.32216i	0.941116	+	0.338085i	$0.109779\pi$
$563$	18.1124	+	31.3716i	0.763348	+	1.32216i	−0.177768	+	0.984072i	$0.556888\pi$
$564$	3.46019	−	5.99322i	0.145700	−	0.252360i
$565$	32.7826			1.37917
$566$	−14.7900	+	25.6171i	−0.621671	+	1.07677i
$567$	−2.60384	−	0.469078i	−0.109351	−	0.0196994i
$568$	4.22657	−	7.32064i	0.177343	−	0.307167i
$569$	−1.41835	+	2.45666i	−0.0594605	+	0.102989i	−0.894223	−	0.447621i	$-0.852271\pi$
$569$	−1.41835	+	2.45666i	−0.0594605	+	0.102989i	0.834763	+	0.550610i	$0.185605\pi$
$570$	50.1319			2.09980
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	−0.813921	−	0.580975i	$-0.802671\pi$
$571$	2.29825	−	3.98069i	0.0961789	−	0.166587i	0.910100	+	0.414389i	$0.136005\pi$
$572$	0.599413	+	1.17422i	0.0250627	+	0.0490968i
$573$	11.0974			0.463602
$574$	−4.80574	−	0.865748i	−0.200588	−	0.0361356i
$575$	39.1057	+	67.7330i	1.63082	+	2.82466i
$576$	−1.53522			−0.0639675
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	−0.624329	−	0.781161i	$-0.714628\pi$
$577$	8.75176	−	15.1585i	0.364341	−	0.631056i	0.988670	+	0.150105i	$0.0479611\pi$
$578$	−3.77970	−	6.54662i	−0.157215	−	0.272304i
$579$	−0.486230			−0.0202070
$580$	4.27751			0.177614
$581$	−34.8622	−	6.28038i	−1.44633	−	0.260554i
$582$	17.2342	+	29.8505i	0.714380	+	1.23734i
$583$	0.164604	−	0.285103i	0.00681722	−	0.0118078i
$584$	−10.8145	+	18.7313i	−0.447509	+	0.775108i
$585$	6.51711	+	12.7667i	0.269449	+	0.527840i
$586$	21.4140	+	37.0902i	0.884606	+	1.53218i
$587$	−0.671155	−	1.16247i	−0.0277015	−	0.0479805i	0.851842	−	0.523798i	$-0.175485\pi$
$587$	−0.671155	−	1.16247i	−0.0277015	−	0.0479805i	−0.879544	+	0.475818i	$0.842152\pi$
$588$	−1.48533	−	8.80464i	−0.0612539	−	0.363097i
$589$	1.48306	−	2.56874i	0.0611084	−	0.105843i
$590$	−17.4789	−	30.2743i	−0.719595	−	1.24638i
$591$	−8.53814	−	14.7885i	−0.351212	−	0.608317i
$592$	−10.7447	−	18.6104i	−0.441604	−	0.764881i
$593$	22.0843	+	38.2512i	0.906895	+	1.57079i	0.818353	+	0.574716i	$0.194888\pi$
$593$	22.0843	+	38.2512i	0.906895	+	1.57079i	0.0885427	+	0.996072i	$0.471779\pi$
$594$	0.259402	−	0.449297i	0.0106434	−	0.0184349i
$595$	31.2501	−	36.9635i	1.28113	−	1.51535i
$596$	12.2422	+	21.2041i	0.501460	+	0.868554i
$597$	−11.5849	−	20.0656i	−0.474138	−	0.821230i
$598$	21.4762	+	42.0710i	0.878227	+	1.72041i
$599$	8.46583	−	14.6632i	0.345904	−	0.599124i	−0.639613	−	0.768697i	$-0.720905\pi$
$599$	8.46583	−	14.6632i	0.345904	−	0.599124i	0.985518	+	0.169573i	$0.0542388\pi$
$600$	7.08308	−	12.2683i	0.289166	−	0.500849i
$601$	7.56311	+	13.0997i	0.308506	+	0.534348i	0.978036	−	0.208437i	$-0.0668378\pi$
$601$	7.56311	+	13.0997i	0.308506	+	0.534348i	−0.669530	+	0.742785i	$0.733504\pi$
$602$	−1.89758	−	5.27427i	−0.0773398	−	0.214963i
$603$	1.57387			0.0640931
$604$	24.1680			0.983381
$605$	−21.7021	−	37.5891i	−0.882314	−	1.52821i
$606$	8.22448	−	14.2452i	0.334097	−	0.578673i
$607$	47.7239			1.93705			0.968527	−	0.248910i	$-0.0800722\pi$
$607$	47.7239			1.93705			0.968527	+	0.248910i	$0.0800722\pi$
$608$	−21.9115	−	37.9518i	−0.888628	−	1.53915i
$609$	−0.755518	−	2.09994i	−0.0306151	−	0.0850938i
$610$	−58.7733			−2.37966
$611$	8.89371	+	17.4224i	0.359801	+	0.704835i
$612$	2.93499	−	5.08356i	0.118640	−	0.205491i
$613$	23.9708			0.968173			0.484086	−	0.875020i	$-0.339152\pi$
$613$	23.9708			0.968173			0.484086	+	0.875020i	$0.339152\pi$
$614$	−8.14155	+	14.1016i	−0.328566	+	0.569094i
$615$	2.02706	−	3.51097i	0.0817390	−	0.141576i
$616$	−0.978606	−	0.176295i	−0.0394292	−	0.00710311i
$617$	−1.41810	+	2.45623i	−0.0570907	+	0.0988839i	−0.893158	−	0.449743i	$-0.851516\pi$
$617$	−1.41810	+	2.45623i	−0.0570907	+	0.0988839i	0.836068	+	0.548626i	$0.184849\pi$
$618$	−8.48536			−0.341331
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	−0.852488	−	0.522746i	$-0.824908\pi$
$619$	0.658494	−	1.14055i	0.0264671	−	0.0458424i	0.878956	+	0.476904i	$0.158241\pi$
$620$	1.07940	+	1.86958i	0.0433499	+	0.0750843i
$621$	3.61929	−	6.26879i	0.145237	−	0.251558i
$622$	27.9619	+	48.4314i	1.12117	+	1.94192i
$623$	−3.78477	+	4.47674i	−0.151634	+	0.179357i
$624$	9.65826	−	14.8970i	0.386640	−	0.596357i
$625$	−18.8598	−	32.6662i	−0.754393	−	1.30665i
$626$	−13.5585			−0.541907
$627$	1.99726			0.0797629
$628$	23.7709			0.948562
$629$	20.0831			0.800766
$630$	18.7349	+	3.37507i	0.746418	+	0.134466i
$631$	−11.5676	+	20.0356i	−0.460497	+	0.797604i	−0.998986	−	0.0450286i	$-0.985662\pi$
$631$	−11.5676	+	20.0356i	−0.460497	+	0.797604i	0.538489	+	0.842633i	$0.318995\pi$
$632$	5.04002	+	8.72957i	0.200481	+	0.347244i
$633$	1.40788	+	2.43852i	0.0559582	+	0.0969224i
$634$	−29.3704			−1.16645
$635$	15.5909	−	27.0043i	0.618707	−	1.07163i
$636$	1.46494			0.0580887
$637$	23.1664	+	10.0160i	0.917885	+	0.396848i
$638$	0.437615			0.0173253
$639$	−3.22369	+	5.58359i	−0.127527	+	0.220883i
$640$	−38.9631			−1.54015
$641$	18.3262	+	31.7420i	0.723843	+	1.25373i	0.959448	+	0.281884i	$0.0909594\pi$
$641$	18.3262	+	31.7420i	0.723843	+	1.25373i	−0.235605	+	0.971849i	$0.575707\pi$
$642$	−13.1265	−	22.7358i	−0.518062	−	0.897310i
$643$	−1.86917	+	3.23749i	−0.0737127	+	0.127674i	−0.900526	−	0.434803i	$-0.856818\pi$
$643$	−1.86917	+	3.23749i	−0.0737127	+	0.127674i	0.826813	+	0.562477i	$0.190151\pi$
$644$	24.0422	+	4.33117i	0.947394	+	0.170672i
$645$	4.65368			0.183238
$646$	58.0297			2.28315
$647$	−1.52619			−0.0600006			−0.0300003	−	0.999550i	$-0.509551\pi$
$647$	−1.52619			−0.0600006			−0.0300003	+	0.999550i	$0.509551\pi$
$648$	−1.31110			−0.0515048
$649$	−0.696361	−	1.20613i	−0.0273345	−	0.0473448i
$650$	−32.0569	−	62.7981i	−1.25737	−	2.46314i
$651$	0.727175	−	0.860123i	0.0285002	−	0.0337109i
$652$	−6.82769	−	11.8259i	−0.267393	−	0.463138i
$653$	−4.47546	+	7.75172i	−0.175138	+	0.303348i	−0.940209	−	0.340598i	$-0.889371\pi$
$653$	−4.47546	+	7.75172i	−0.175138	+	0.303348i	0.765071	+	0.643946i	$0.222704\pi$
$654$	3.79515	+	6.57340i	0.148402	+	0.257040i
$655$	16.0721	−	27.8377i	0.627990	−	1.08771i
$656$	−5.02141			−0.196053
$657$	8.24845	−	14.2867i	0.321803	−	0.557379i
$658$	25.5670	+	4.60587i	0.996707	+	0.179555i
$659$	4.30599	−	7.45819i	0.167737	−	0.290530i	−0.769887	−	0.638181i	$-0.779687\pi$
$659$	4.30599	−	7.45819i	0.167737	−	0.290530i	0.937624	+	0.347651i	$0.113021\pi$
$660$	−0.726825	+	1.25890i	−0.0282916	+	0.0490026i
$661$	−40.0783			−1.55887			−0.779433	−	0.626486i	$-0.784493\pi$
$661$	−40.0783			−1.55887			−0.779433	+	0.626486i	$0.784493\pi$
$662$	−5.05343	+	8.75279i	−0.196407	+	0.340187i
$663$	7.54381	+	14.7780i	0.292977	+	0.573930i
$664$	−17.5540			−0.681228
$665$	24.8100	+	68.9585i	0.962089	+	2.67409i
$666$	3.94925	+	6.84031i	0.153031	+	0.265057i
$667$	6.10580			0.236417
$668$	0.0306930	−	0.0531618i	0.00118755	−	0.00205689i
$669$	−8.16232	−	14.1375i	−0.315573	−	0.546589i
$670$	−11.3242			−0.437493
$671$	−2.34153			−0.0903938
$672$	−5.63353	−	15.6582i	−0.217318	−	0.604029i
$673$	−22.0131	−	38.1277i	−0.848541	−	1.46972i	−0.882510	−	0.470294i	$-0.844148\pi$
$673$	−22.0131	−	38.1277i	−0.848541	−	1.46972i	0.0339689	−	0.999423i	$-0.489185\pi$
$674$	0.456171	−	0.790112i	0.0175711	−	0.0304340i
$675$	−5.40240	+	9.35723i	−0.207938	+	0.360160i
$676$	−6.76755	−	15.1387i	−0.260291	−	0.582258i
$677$	−12.0556	−	20.8809i	−0.463334	−	0.802518i	0.535791	−	0.844351i	$-0.320014\pi$
$677$	−12.0556	−	20.8809i	−0.463334	−	0.802518i	−0.999125	+	0.0418328i	$0.986680\pi$
$678$	7.46213	+	12.9248i	0.286581	+	0.496373i
$679$	−32.5314	+	38.4791i	−1.24844	+	1.47669i
$680$	11.9931	−	20.7726i	0.459913	−	0.796592i
$681$	3.10289	+	5.37436i	0.118903	+	0.205946i
$682$	0.110430	+	0.191270i	0.00422856	+	0.00732409i
$683$	9.29276	+	16.0955i	0.355578	+	0.615878i	0.987217	−	0.159384i	$-0.0509508\pi$
$683$	9.29276	+	16.0955i	0.355578	+	0.615878i	−0.631639	+	0.775263i	$0.717618\pi$
$684$	4.44379	+	7.69686i	0.169912	+	0.294297i
$685$	3.00089	−	5.19769i	0.114658	−	0.198594i
$686$	29.2127	−	16.4359i	1.11535	−	0.627526i
$687$	0.261463	+	0.452867i	0.00997543	+	0.0172779i
$688$	−2.88201	−	4.99178i	−0.109875	−	0.190310i
$689$	−2.25262	+	3.47447i	−0.0858182	+	0.132367i
$690$	−26.0412	+	45.1047i	−0.991372	+	1.71711i
$691$	11.3187	−	19.6045i	0.430583	−	0.745792i	−0.566340	−	0.824171i	$-0.691641\pi$
$691$	11.3187	−	19.6045i	0.430583	−	0.745792i	0.996924	+	0.0783796i	$0.0249746\pi$
$692$	8.94801	+	15.4984i	0.340152	+	0.589161i
$693$	0.746401	+	0.134463i	0.0283534	+	0.00510783i
$694$	−21.9598			−0.833581
$695$	16.0716			0.609632
$696$	−0.552962	−	0.957758i	−0.0209600	−	0.0363037i
$697$	2.34640	−	4.06409i	0.0888763	−	0.153938i
$698$	−39.4860			−1.49457
$699$	−6.48273	−	11.2284i	−0.245199	−	0.424697i
$700$	−35.8870	−	6.46500i	−1.35640	−	0.244354i
$701$	50.1432			1.89388			0.946941	−	0.321407i	$-0.104156\pi$
$701$	50.1432			1.89388			0.946941	+	0.321407i	$0.104156\pi$
$702$	−3.54993	+	5.47545i	−0.133983	+	0.206657i
$703$	−15.2036	+	26.3335i	−0.573416	+	0.993185i
$704$	0.440077			0.0165860
$705$	−10.7842	+	18.6787i	−0.406156	+	0.703482i
$706$	10.9387	−	18.9464i	0.411683	−	0.713056i
$707$	23.6651	+	4.26324i	0.890018	+	0.160336i
$708$	3.09872	−	5.36715i	0.116457	−	0.201710i
$709$	−29.7112			−1.11583			−0.557913	−	0.829899i	$-0.688398\pi$
$709$	−29.7112			−1.11583			−0.557913	+	0.829899i	$0.688398\pi$
$710$	23.1948	−	40.1746i	0.870487	−	1.50773i
$711$	−3.84412	−	6.65821i	−0.144166	−	0.249702i
$712$	−1.45251	+	2.51582i	−0.0544351	+	0.0942843i
$713$	1.54076	+	2.66868i	0.0577020	+	0.0999428i
$714$	21.6864	+	3.90678i	0.811594	+	0.146208i
$715$	−1.86816	−	3.65964i	−0.0698651	−	0.136863i
$716$	−2.99673	−	5.19049i	−0.111993	−	0.193978i
$717$	−4.79605			−0.179112
$718$	26.1353			0.975361
$719$	−29.8693			−1.11394			−0.556968	−	0.830534i	$-0.688035\pi$
$719$	−29.8693			−1.11394			−0.556968	+	0.830534i	$0.688035\pi$
$720$	19.5757			0.729544
$721$	−4.19934	−	11.6719i	−0.156392	−	0.434686i
$722$	−26.7369	+	46.3096i	−0.995044	+	1.72347i
$723$	−5.20975	−	9.02355i	−0.193753	−	0.335589i
$724$	14.0557	+	24.3453i	0.522378	+	0.904785i
$725$	−9.11394			−0.338483
$726$	9.87985	−	17.1124i	0.366676	−	0.635101i
$727$	36.0210			1.33594			0.667972	−	0.744186i	$-0.267163\pi$
$727$	36.0210			1.33594			0.667972	+	0.744186i	$0.267163\pi$
$728$	12.1782	+	2.84942i	0.451353	+	0.105607i
$729$	1.00000			0.0370370
$730$	−59.3486	+	102.795i	−2.19659	+	3.80461i
$731$	5.38681			0.199238
$732$	−5.20977	−	9.02358i	−0.192559	−	0.333521i
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	0.982816	−	0.184586i	$-0.0590945\pi$
$733$	8.97642	+	15.5476i	0.331552	+	0.574265i	−0.651265	+	0.758851i	$0.725761\pi$
$734$	−22.0610	+	38.2108i	−0.814286	+	1.41038i
$735$	4.62924	+	27.4409i	0.170752	+	1.01217i
$736$	45.5280			1.67818
$737$	−0.451158			−0.0166186
$738$	1.84564			0.0679388
$739$	44.4938			1.63673			0.818366	−	0.574698i	$-0.194880\pi$
$739$	44.4938			1.63673			0.818366	+	0.574698i	$0.194880\pi$
$740$	−11.0655	−	19.1661i	−0.406777	−	0.704559i
$741$	−25.0882	−	1.29585i	−0.921637	−	0.0476042i
$742$	1.86171	+	5.17457i	0.0683456	+	0.189964i
$743$	−10.7390	−	18.6004i	−0.393975	−	0.682384i	0.598995	−	0.800753i	$-0.295567\pi$
$743$	−10.7390	−	18.6004i	−0.393975	−	0.682384i	−0.992970	+	0.118368i	$0.962234\pi$
$744$	0.279073	−	0.483369i	0.0102313	−	0.0177212i
$745$	−38.1546	−	66.0857i	−1.39788	−	2.42119i
$746$	7.60169	−	13.1665i	0.278318	−	0.482061i
$747$	13.3888			0.489870
$748$	−0.841329	+	1.45722i	−0.0307620	+	0.0532814i
$749$	24.7777	−	29.3078i	0.905359	−	1.07088i
$750$	20.8831	−	36.1706i	0.762544	−	1.32077i
$751$	−1.60018	+	2.77159i	−0.0583913	+	0.101137i	−0.893743	−	0.448579i	$-0.851930\pi$
$751$	−1.60018	+	2.77159i	−0.0583913	+	0.101137i	0.835352	+	0.549715i	$0.185264\pi$
$752$	26.7144			0.974174
$753$	−5.10645	+	8.84463i	−0.186089	+	0.322316i
$754$	−5.49701	−	0.283930i	−0.200189	−	0.0103401i
$755$	−75.3230			−2.74128
$756$	1.14252	+	3.17559i	0.0415529	+	0.115495i
$757$	−12.8640	−	22.2811i	−0.467550	−	0.809821i	0.531762	−	0.846894i	$-0.321530\pi$
$757$	−12.8640	−	22.2811i	−0.467550	−	0.809821i	−0.999313	+	0.0370727i	$0.988197\pi$
$758$	6.62026			0.240459
$759$	−1.03748	+	1.79698i	−0.0376583	+	0.0652261i
$760$	18.1583	+	31.4512i	0.658672	+	1.14085i
$761$	28.7496			1.04217			0.521087	−	0.853504i	$-0.325527\pi$
$761$	28.7496			1.04217			0.521087	+	0.853504i	$0.325527\pi$
$762$	14.1955			0.514249
$763$	−7.16377	+	8.47351i	−0.259346	+	0.306762i
$764$	−7.07782	−	12.2591i	−0.256066	−	0.443520i
$765$	−9.14733	+	15.8436i	−0.330723	+	0.572828i
$766$	27.7860	−	48.1268i	1.00395	−	1.73889i
$767$	7.96464	+	15.6024i	0.287587	+	0.563370i
$768$	−10.4042	−	18.0206i	−0.375429	−	0.650262i
$769$	8.98213	+	15.5575i	0.323904	+	0.561018i	0.981290	−	0.192536i	$-0.0616712\pi$
$769$	8.98213	+	15.5575i	0.323904	+	0.561018i	−0.657386	+	0.753554i	$0.728338\pi$
$770$	−5.37045	−	0.967480i	−0.193538	−	0.0348656i
$771$	3.18140	−	5.51035i	0.114575	−	0.198450i
$772$	0.310112	+	0.537131i	0.0111612	+	0.0193318i
$773$	−19.8326	−	34.3511i	−0.713329	−	1.23552i	−0.963601	−	0.267346i	$-0.913853\pi$
$773$	−19.8326	−	34.3511i	−0.713329	−	1.23552i	0.250272	−	0.968176i	$-0.419480\pi$
$774$	1.05929	+	1.83475i	0.0380755	+	0.0659486i
$775$	−2.29985	−	3.98345i	−0.0826130	−	0.143090i
$776$	−12.4848	+	21.6243i	−0.448179	+	0.776269i
$777$	−7.45466	+	8.81758i	−0.267434	+	0.316329i
$778$	−16.6849	−	28.8990i	−0.598182	−	1.03608i
$779$	3.55262	+	6.15331i	0.127286	+	0.220465i
$780$	9.94666	−	15.3418i	0.356148	−	0.549326i
$781$	0.924084	−	1.60056i	0.0330663	−	0.0572725i
$782$	−30.1437	+	52.2105i	−1.07794	+	1.86704i
$783$	0.421754	+	0.730500i	0.0150723	+	0.0261059i
$784$	26.5677	−	21.9596i	0.948848	−	0.784273i
$785$	−74.0855			−2.64422
$786$	14.6337			0.521965
$787$	19.7833	+	34.2657i	0.705199	+	1.22144i	0.966620	+	0.256215i	$0.0824756\pi$
$787$	19.7833	+	34.2657i	0.705199	+	1.22144i	−0.261421	+	0.965225i	$0.584191\pi$
$788$	−10.8911	+	18.8639i	−0.387978	+	0.671998i
$789$	−17.0135			−0.605698
$790$	27.6589	+	47.9067i	0.984061	+	1.70444i
$791$	−14.0856	+	16.6608i	−0.500826	+	0.592391i
$792$	0.375832			0.0133546
$793$	29.4127	+	1.51922i	1.04447	+	0.0539489i
$794$	2.04571	−	3.54328i	0.0725996	−	0.125746i
$795$	−4.56570			−0.161929
$796$	−14.7774	+	25.5952i	−0.523772	+	0.907199i
$797$	−9.72309	+	16.8409i	−0.344409	+	0.596535i	−0.985246	−	0.171142i	$-0.945254\pi$
$797$	−9.72309	+	16.8409i	−0.344409	+	0.596535i	0.640837	+	0.767677i	$0.278588\pi$
$798$	−21.5400	+	25.4782i	−0.762509	+	0.901917i
$799$	−12.4831	+	21.6214i	−0.441621	+	0.764909i
$800$	−67.9582			−2.40269
$801$	1.10786	−	1.91886i	0.0391442	−	0.0677997i
$802$	−25.8101	−	44.7044i	−0.911386	−	1.57857i
$803$	−2.36445	+	4.09535i	−0.0834398	+	0.144522i
$804$	−1.00380	−	1.73863i	−0.0354013	−	0.0613168i
$805$	−74.9309	−	13.4987i	−2.64097	−	0.475767i
$806$	−1.26304	−	2.47424i	−0.0444887	−	0.0871515i
$807$	4.53019	+	7.84653i	0.159470	+	0.276211i
$808$	11.9160			0.419203
$809$	−17.3084			−0.608531			−0.304265	−	0.952587i	$-0.598411\pi$
$809$	−17.3084			−0.608531			−0.304265	+	0.952587i	$0.598411\pi$
$810$	−7.19513			−0.252811
$811$	−2.62646			−0.0922275			−0.0461138	−	0.998936i	$-0.514684\pi$
$811$	−2.62646			−0.0922275			−0.0461138	+	0.998936i	$0.514684\pi$
$812$	−1.83791	+	2.17393i	−0.0644978	+	0.0762899i
$813$	−1.11398	+	1.92947i	−0.0390690	+	0.0676696i
$814$	−1.13207	−	1.96080i	−0.0396791	−	0.0687262i
$815$	21.2795	+	36.8572i	0.745388	+	1.29105i
$816$	22.6596			0.793246
$817$	−4.07801	+	7.06331i	−0.142671	+	0.247114i
$818$	19.6442			0.686842
$819$	−9.28853	−	2.17331i	−0.324567	−	0.0759415i
$820$	−5.17135			−0.180591
$821$	16.1977	−	28.0553i	0.565305	−	0.979137i	−0.431716	−	0.902009i	$-0.642092\pi$
$821$	16.1977	−	28.0553i	0.565305	−	0.979137i	0.997021	−	0.0771274i	$-0.0245748\pi$
$822$	2.73231			0.0953001
$823$	20.5081	+	35.5210i	0.714866	+	1.23818i	0.963011	+	0.269461i	$0.0868457\pi$
$823$	20.5081	+	35.5210i	0.714866	+	1.23818i	−0.248145	+	0.968723i	$0.579821\pi$
$824$	−3.07349	−	5.32344i	−0.107070	−	0.185451i
$825$	1.54862	−	2.68229i	0.0539161	−	0.0933854i
$826$	22.8962	+	4.12472i	0.796661	+	0.143517i
$827$	−44.2260			−1.53789			−0.768944	−	0.639316i	$-0.779218\pi$
$827$	−44.2260			−1.53789			−0.768944	+	0.639316i	$0.779218\pi$
$828$	−9.23336			−0.320882
$829$	−5.49562			−0.190871			−0.0954354	−	0.995436i	$-0.530424\pi$
$829$	−5.49562			−0.190871			−0.0954354	+	0.995436i	$0.530424\pi$
$830$	−96.3339			−3.34380
$831$	3.90377	+	6.76153i	0.135420	+	0.234555i
$832$	−5.52794	−	0.285528i	−0.191647	−	0.00989890i
$833$	5.35853	+	31.7640i	0.185662	+	1.10056i
$834$	3.65830	+	6.33637i	0.126677	+	0.219411i
$835$	−0.0956591	+	0.165686i	−0.00331042	+	0.00573382i
$836$	−1.27383	−	2.20634i	−0.0440564	−	0.0763079i
$837$	−0.212854	+	0.368675i	−0.00735732	+	0.0127433i
$838$	27.8095			0.960663
$839$	−21.4269	+	37.1125i	−0.739739	+	1.28127i	0.212873	+	0.977080i	$0.431718\pi$
$839$	−21.4269	+	37.1125i	−0.739739	+	1.28127i	−0.952612	+	0.304186i	$0.901615\pi$
$840$	4.66858	+	12.9762i	0.161081	+	0.447721i
$841$	14.1442	−	24.4986i	0.487733	−	0.844778i
$842$	3.01970	−	5.23028i	0.104066	−	0.180247i
$843$	−12.7531			−0.439242
$844$	1.79586	−	3.11052i	0.0618160	−	0.107069i
$845$	21.0921	+	47.1819i	0.725589	+	1.62311i
$846$	−9.81898			−0.337584
$847$	28.4282	+	5.12131i	0.976806	+	0.175970i
$848$	2.82752	+	4.89741i	0.0970975	+	0.168178i
$849$	16.3439			0.560920
$850$	44.9946	−	77.9330i	1.54330	−	2.67308i
$851$	−15.7952	−	27.3580i	−0.541451	−	0.937821i
$852$	8.22413			0.281754
$853$	−46.0876			−1.57801			−0.789004	−	0.614388i	$-0.789403\pi$
$853$	−46.0876			−1.57801			−0.789004	+	0.614388i	$0.789403\pi$
$854$	25.2529	−	29.8699i	0.864137	−	1.02213i
$855$	−13.8497	−	23.9884i	−0.473650	−	0.820386i
$856$	9.50913	−	16.4703i	0.325015	−	0.562943i
$857$	3.33662	−	5.77919i	0.113977	−	0.197413i	−0.803394	−	0.595448i	$-0.796974\pi$
$857$	3.33662	−	5.77919i	0.113977	−	0.197413i	0.917370	+	0.398035i	$0.130308\pi$
$858$	1.01760	−	1.56956i	0.0347404	−	0.0535839i
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	0.971409	−	0.237411i	$-0.0762987\pi$
$859$	8.20940	+	14.2191i	0.280101	+	0.485149i	−0.691308	+	0.722560i	$0.742965\pi$
$860$	−2.96806	−	5.14084i	−0.101210	−	0.175301i
$861$	0.913393	+	2.53875i	0.0311284	+	0.0865203i
$862$	3.85584	−	6.67851i	0.131330	−	0.227471i
$863$	4.92500	+	8.53035i	0.167649	+	0.290377i	0.937593	−	0.347735i	$-0.113049\pi$
$863$	4.92500	+	8.53035i	0.167649	+	0.290377i	−0.769944	+	0.638112i	$0.779716\pi$
$864$	3.14482	+	5.44698i	0.106989	+	0.185310i
$865$	−27.8878	−	48.3030i	−0.948213	−	1.64235i
$866$	−10.0703	−	17.4423i	−0.342204	−	0.592714i
$867$	−2.08840	+	3.61721i	−0.0709256	+	0.122847i
$868$	−1.41395	−	0.254721i	−0.0479925	−	0.00864579i
$869$	1.10193	+	1.90861i	0.0373805	+	0.0647450i
$870$	−3.03458	−	5.25604i	−0.102882	−	0.178196i
$871$	5.66713	+	0.292717i	0.192023	+	0.00991834i
$872$	−2.74929	+	4.76191i	−0.0931027	+	0.161259i
$873$	9.52241	−	16.4933i	0.322285	−	0.558214i
$874$	−45.6397	−	79.0503i	−1.54379	−	2.67392i
$875$	60.0890	+	10.8250i	2.03138	+	0.365951i
$876$	−21.0431			−0.710980
$877$	6.04112			0.203994			0.101997	−	0.994785i	$-0.467477\pi$
$877$	6.04112			0.203994			0.101997	+	0.994785i	$0.467477\pi$
$878$	−37.1043	−	64.2665i	−1.25221	−	2.16889i
$879$	11.8319	−	20.4935i	0.399080	−	0.691227i
$880$	−5.61146			−0.189162
$881$	15.5861	+	26.9959i	0.525109	+	0.909516i	0.999572	+	0.0292404i	$0.00930885\pi$
$881$	15.5861	+	26.9959i	0.525109	+	0.909516i	−0.474463	+	0.880275i	$0.657358\pi$
$882$	−9.76507	+	8.07135i	−0.328807	+	0.271777i
$883$	−18.2205			−0.613169			−0.306584	−	0.951844i	$-0.599186\pi$
$883$	−18.2205			−0.613169			−0.306584	+	0.951844i	$0.599186\pi$
$884$	11.5136	−	17.7588i	0.387246	−	0.597292i
$885$	−9.65762	+	16.7275i	−0.324637	+	0.562288i
$886$	28.6932			0.963967
$887$	−3.70842	+	6.42317i	−0.124517	+	0.215669i	−0.921544	−	0.388274i	$-0.873071\pi$
$887$	−3.70842	+	6.42317i	−0.124517	+	0.215669i	0.797027	+	0.603943i	$0.206405\pi$
$888$	−2.86093	+	4.95527i	−0.0960064	+	0.166288i
$889$	7.02526	+	19.5265i	0.235620	+	0.654898i
$890$	−7.97117	+	13.8065i	−0.267194	+	0.462794i
$891$	−0.286654			−0.00960328
$892$	−10.4117	+	18.0336i	−0.348609	+	0.603808i
$893$	−18.9003	−	32.7363i	−0.632474	−	1.09548i
$894$	17.3699	−	30.0855i	0.580935	−	1.00621i
$895$	9.33975	+	16.1769i	0.312194	+	0.540735i
$896$	16.7412	−	19.8019i	0.559283	−	0.661535i
$897$	14.1980	−	21.8992i	0.474059	−	0.731193i
$898$	−13.6644	−	23.6674i	−0.455986	−	0.789790i
$899$	−0.359089			−0.0119763
$900$	13.7824			0.459412
$901$	−5.28498			−0.176068
$902$	−0.529060			−0.0176158
$903$	−1.99953	+	2.36510i	−0.0665402	+	0.0787056i
$904$	−5.40573	+	9.36299i	−0.179792	+	0.311409i
$905$	−43.8068	−	75.8756i	−1.45619	−	2.52219i
$906$	−17.1454	−	29.6967i	−0.569617	−	0.986605i
$907$	−17.4144			−0.578234			−0.289117	−	0.957294i	$-0.593362\pi$
$907$	−17.4144			−0.578234			−0.289117	+	0.957294i	$0.593362\pi$
$908$	3.95797	−	6.85541i	0.131350	−	0.227505i
$909$	−9.08855			−0.301448
$910$	66.8321	+	15.6372i	2.21546	+	0.518369i
$911$	−40.5753			−1.34432			−0.672159	−	0.740407i	$-0.734633\pi$
$911$	−40.5753			−1.34432			−0.672159	+	0.740407i	$0.734633\pi$
$912$	−17.1541	+	29.7119i	−0.568031	+	0.983858i
$913$	−3.83795			−0.127018
$914$	0.0252004	+	0.0436483i	0.000833554	+	0.00144376i
$915$	16.2370	+	28.1233i	0.536779	+	0.929728i
$916$	0.333516	−	0.577667i	0.0110197	−	0.0190867i
$917$	7.24209	+	20.1292i	0.239155	+	0.664724i
$918$	−8.32864			−0.274886
$919$	−48.5466			−1.60140			−0.800702	−	0.599062i	$-0.795540\pi$
$919$	−48.5466			−1.60140			−0.800702	+	0.599062i	$0.795540\pi$
$920$	−37.7297			−1.24391
$921$	8.99691			0.296458
$922$	25.4363	+	44.0570i	0.837700	+	1.45094i
$923$	−12.6462	+	19.5056i	−0.416253	+	0.642033i
$924$	−0.327507	−	0.910296i	−0.0107742	−	0.0299465i
$925$	23.5770	+	40.8365i	0.775206	+	1.34270i
$926$	0.241198	−	0.417767i	0.00792625	−	0.0137287i
$927$	2.34421	+	4.06029i	0.0769939	+	0.133357i
$928$	−2.65268	+	4.59458i	−0.0870785	+	0.150824i
$929$	−8.13928			−0.267041			−0.133521	−	0.991046i	$-0.542628\pi$
$929$	−8.13928			−0.267041			−0.133521	+	0.991046i	$0.542628\pi$
$930$	1.53151	−	2.65266i	0.0502203	−	0.0869842i
$931$	−45.7062	−	17.0202i	−1.49796	−	0.557815i
$932$	−8.26922	+	14.3227i	−0.270867	+	0.469156i
$933$	15.4498	−	26.7598i	0.505803	−	0.876077i
$934$	67.1096			2.19589
$935$	2.62212	−	4.54165i	0.0857526	−	0.148528i
$936$	−4.72094	−	0.243845i	−0.154309	−	0.00797032i
$937$	30.6536			1.00141			0.500705	−	0.865618i	$-0.333074\pi$
$937$	30.6536			1.00141			0.500705	+	0.865618i	$0.333074\pi$
$938$	4.86565	−	5.75522i	0.158869	−	0.187915i
$939$	3.74574	+	6.48782i	0.122238	+	0.211722i
$940$	27.5121			0.897347
$941$	4.34815	−	7.53122i	0.141746	−	0.245511i	−0.786408	−	0.617707i	$-0.788062\pi$
$941$	4.34815	−	7.53122i	0.141746	−	0.245511i	0.928154	+	0.372196i	$0.121395\pi$
$942$	−16.8637	−	29.2088i	−0.549449	−	0.951673i
$943$	−7.38168			−0.240381
$944$	23.9237			0.778651
$945$	−3.56082	−	9.89718i	−0.115833	−	0.321955i
$946$	−0.303651	−	0.525938i	−0.00987254	−	0.0170997i
$947$	5.73610	−	9.93522i	0.186398	−	0.322851i	−0.757649	−	0.652663i	$-0.773652\pi$
$947$	5.73610	−	9.93522i	0.186398	−	0.322851i	0.944047	+	0.329812i	$0.106985\pi$
$948$	−4.90348	+	8.49307i	−0.159258	+	0.275842i
$949$	32.3577	−	49.9089i	1.05038	−	1.62011i
$950$	68.1250	+	117.996i	2.21027	+	3.82830i
$951$	8.11402	+	14.0539i	0.263115	+	0.455729i
$952$	5.40407	+	15.0204i	0.175147	+	0.486815i
$953$	−23.1731	+	40.1370i	−0.750650	+	1.30016i	0.196859	+	0.980432i	$0.436926\pi$
$953$	−23.1731	+	40.1370i	−0.750650	+	1.30016i	−0.947508	+	0.319731i	$0.896407\pi$
$954$	−1.03927	−	1.80006i	−0.0336475	−	0.0582792i
$955$	22.0590	+	38.2074i	0.713814	+	1.23636i
$956$	3.05887	+	5.29812i	0.0989310	+	0.171353i
$957$	−0.120898	−	0.209401i	−0.00390807	−	0.00676897i
$958$	−26.0607	+	45.1384i	−0.841983	+	1.45836i
$959$	1.35220	+	3.75839i	0.0436648	+	0.121365i
$960$	−3.05165	−	5.28562i	−0.0984916	−	0.170593i
$961$	15.4094	+	26.6898i	0.497077	+	0.860963i
$962$	12.9481	+	25.3648i	0.417463	+	0.817793i
$963$	−7.25279	+	12.5622i	−0.233718	+	0.404811i
$964$	−6.64544	+	11.5102i	−0.214035	+	0.370720i
$965$	−0.966511	−	1.67405i	−0.0311131	−	0.0538894i
$966$	−11.7342	−	32.6147i	−0.377541	−	1.04936i
$967$	8.71419			0.280229			0.140115	−	0.990135i	$-0.455253\pi$
$967$	8.71419			0.280229			0.140115	+	0.990135i	$0.455253\pi$
$968$	14.3144			0.460081
$969$	−16.0316	−	27.7675i	−0.515008	−	0.892021i
$970$	−68.5149	+	118.671i	−2.19988	+	3.81031i
$971$	40.0563			1.28547			0.642733	−	0.766090i	$-0.277800\pi$
$971$	40.0563			1.28547			0.642733	+	0.766090i	$0.277800\pi$
$972$	−0.637789	−	1.10468i	−0.0204571	−	0.0354327i
$973$	−6.90545	+	8.16797i	−0.221379	+	0.261853i
$974$	−24.8499			−0.796243
$975$	−21.1930	+	32.6883i	−0.678719	+	1.04686i
$976$	20.1110	−	34.8333i	0.643738	−	1.11499i
$977$	−42.3067			−1.35351			−0.676755	−	0.736208i	$-0.736614\pi$
$977$	−42.3067			−1.35351			−0.676755	+	0.736208i	$0.736614\pi$
$978$	−9.68748	+	16.7792i	−0.309771	+	0.536540i
$979$	−0.317572	+	0.550050i	−0.0101496	+	0.0175797i
$980$	27.3611	−	22.6154i	0.874017	−	0.722422i
$981$	2.09694	−	3.63200i	0.0669500	−	0.115961i
$982$	−49.8189			−1.58979
$983$	2.44395	−	4.23305i	0.0779501	−	0.135013i	−0.824415	−	0.565985i	$-0.808496\pi$
$983$	2.44395	−	4.23305i	0.0779501	−	0.135013i	0.902365	+	0.430972i	$0.141829\pi$
$984$	0.668510	+	1.15789i	0.0213113	+	0.0369123i
$985$	33.9436	−	58.7920i	1.08153	−	1.87327i
$986$	−3.51264	−	6.08407i	−0.111865	−	0.193756i
$987$	−4.85935	−	13.5064i	−0.154675	−	0.429913i
$988$	14.5695	+	28.5410i	0.463517	+	0.908009i
$989$	−4.23667	−	7.33813i	−0.134718	−	0.233339i
$990$	2.06251			0.0655510
$991$	−18.5959			−0.590718			−0.295359	−	0.955386i	$-0.595439\pi$
$991$	−18.5959			−0.590718			−0.295359	+	0.955386i	$0.595439\pi$
$992$	−2.67755			−0.0850124
$993$	5.58434			0.177214
$994$	10.4516	+	29.0498i	0.331504	+	0.921405i
$995$	46.0560	−	79.7713i	1.46007	−	2.52892i
$996$	−8.53922	−	14.7904i	−0.270575	−	0.468650i
$997$	12.8181	+	22.2017i	0.405954	+	0.703133i	0.994432	−	0.105380i	$-0.0336059\pi$
$997$	12.8181	+	22.2017i	0.405954	+	0.703133i	−0.588478	+	0.808513i	$0.700273\pi$
$998$	−7.04276			−0.222935
$999$	2.18208	−	3.77948i	0.0690380	−	0.119577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.172.3	yes	20
3.2	odd	2		819.2.n.f.172.8		20
7.2	even	3		273.2.l.c.16.8	yes	20
13.9	even	3		273.2.l.c.256.8	yes	20
21.2	odd	6		819.2.s.f.289.3		20
39.35	odd	6		819.2.s.f.802.3		20
91.9	even	3	inner	273.2.j.c.100.3	✓	20
273.191	odd	6		819.2.n.f.100.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.3	✓	20	91.9	even	3	inner
273.2.j.c.172.3	yes	20	1.1	even	1	trivial
273.2.l.c.16.8	yes	20	7.2	even	3
273.2.l.c.256.8	yes	20	13.9	even	3
819.2.n.f.100.8		20	273.191	odd	6
819.2.n.f.172.8		20	3.2	odd	2
819.2.s.f.289.3		20	21.2	odd	6
819.2.s.f.802.3		20	39.35	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+(-0.904928 + 1.56738i) q^{2} +1.00000 q^{3} +(-0.637789 - 1.10468i) q^{4} +(1.98776 + 3.44291i) q^{5} +(-0.904928 + 1.56738i) q^{6} +(-2.60384 - 0.469078i) q^{7} -1.31110 q^{8} +1.00000 q^{9} -7.19513 q^{10} -0.286654 q^{11} +(-0.637789 - 1.10468i) q^{12} +(3.60075 + 0.185985i) q^{13} +(3.09151 - 3.65672i) q^{14} +(1.98776 + 3.44291i) q^{15} +(2.46203 - 4.26436i) q^{16} +(2.30091 + 3.98530i) q^{17} +(-0.904928 + 1.56738i) q^{18} -6.96749 q^{19} +(2.53555 - 4.39170i) q^{20} +(-2.60384 - 0.469078i) q^{21} +(0.259402 - 0.449297i) q^{22} +(3.61929 - 6.26879i) q^{23} -1.31110 q^{24} +(-5.40240 + 9.35723i) q^{25} +(-3.54993 + 5.47545i) q^{26} +1.00000 q^{27} +(1.14252 + 3.17559i) q^{28} +(0.421754 + 0.730500i) q^{29} -7.19513 q^{30} +(-0.212854 + 0.368675i) q^{31} +(3.14482 + 5.44698i) q^{32} -0.286654 q^{33} -8.32864 q^{34} +(-3.56082 - 9.89718i) q^{35} +(-0.637789 - 1.10468i) q^{36} +(2.18208 - 3.77948i) q^{37} +(6.30507 - 10.9207i) q^{38} +(3.60075 + 0.185985i) q^{39} +(-2.60615 - 4.51399i) q^{40} +(-0.509885 - 0.883147i) q^{41} +(3.09151 - 3.65672i) q^{42} +(0.585291 - 1.01375i) q^{43} +(0.182825 + 0.316662i) q^{44} +(1.98776 + 3.44291i) q^{45} +(6.55039 + 11.3456i) q^{46} +(2.71264 + 4.69843i) q^{47} +(2.46203 - 4.26436i) q^{48} +(6.55993 + 2.44280i) q^{49} +(-9.77756 - 16.9352i) q^{50} +(2.30091 + 3.98530i) q^{51} +(-2.09107 - 4.09631i) q^{52} +(-0.574226 + 0.994589i) q^{53} +(-0.904928 + 1.56738i) q^{54} +(-0.569801 - 0.986924i) q^{55} +(3.41389 + 0.615007i) q^{56} -6.96749 q^{57} -1.52663 q^{58} +(2.42927 + 4.20762i) q^{59} +(2.53555 - 4.39170i) q^{60} +8.16848 q^{61} +(-0.385236 - 0.667248i) q^{62} +(-2.60384 - 0.469078i) q^{63} -1.53522 q^{64} +(6.51711 + 12.7667i) q^{65} +(0.259402 - 0.449297i) q^{66} +1.57387 q^{67} +(2.93499 - 5.08356i) q^{68} +(3.61929 - 6.26879i) q^{69} +(18.7349 + 3.37507i) q^{70} +(-3.22369 + 5.58359i) q^{71} -1.31110 q^{72} +(8.24845 - 14.2867i) q^{73} +(3.94925 + 6.84031i) q^{74} +(-5.40240 + 9.35723i) q^{75} +(4.44379 + 7.69686i) q^{76} +(0.746401 + 0.134463i) q^{77} +(-3.54993 + 5.47545i) q^{78} +(-3.84412 - 6.65821i) q^{79} +19.5757 q^{80} +1.00000 q^{81} +1.84564 q^{82} +13.3888 q^{83} +(1.14252 + 3.17559i) q^{84} +(-9.14733 + 15.8436i) q^{85} +(1.05929 + 1.83475i) q^{86} +(0.421754 + 0.730500i) q^{87} +0.375832 q^{88} +(1.10786 - 1.91886i) q^{89} -7.19513 q^{90} +(-9.28853 - 2.17331i) q^{91} -9.23336 q^{92} +(-0.212854 + 0.368675i) q^{93} -9.81898 q^{94} +(-13.8497 - 23.9884i) q^{95} +(3.14482 + 5.44698i) q^{96} +(9.52241 - 16.4933i) q^{97} +(-9.76507 + 8.07135i) q^{98} -0.286654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more