LMFDB - Embedded newform 315.2.i.f.211.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.i (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 10 x^{13} + 40 x^{12} - 45 x^{11} + 159 x^{10} - 180 x^{9} + 576 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 8x^14 - 10x^13 + 40x^12 - 45x^11 + 159x^10 - 180x^9 + 576x^8 - 540x^7 + 1431x^6 - 1215x^5 + 3240x^4 - 2430x^3 + 5832x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.6
Root			$0.803782 - 1.53425i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.f.106.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.627726 + 1.08725i) q^{2} +(1.73059 - 0.0710311i) q^{3} +(0.211920 - 0.367057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.16357 + 1.83701i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.04302 q^{8} +(2.98991 - 0.245852i) q^{9} +O(q^{10})$	\(q+(0.627726 + 1.08725i) q^{2} +(1.73059 - 0.0710311i) q^{3} +(0.211920 - 0.367057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.16357 + 1.83701i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.04302 q^{8} +(2.98991 - 0.245852i) q^{9} -1.25545 q^{10} +(-2.97073 - 5.14546i) q^{11} +(0.340676 - 0.650279i) q^{12} +(-1.86187 + 3.22486i) q^{13} +(-0.627726 + 1.08725i) q^{14} +(-0.803782 + 1.53425i) q^{15} +(1.48634 + 2.57441i) q^{16} -6.19375 q^{17} +(2.14415 + 3.09646i) q^{18} +5.61903 q^{19} +(0.211920 + 0.367057i) q^{20} +(0.926812 + 1.46322i) q^{21} +(3.72961 - 6.45988i) q^{22} +(-2.98418 + 5.16876i) q^{23} +(5.26622 - 0.216149i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.67498 q^{26} +(5.15685 - 0.637847i) q^{27} +0.423841 q^{28} +(-1.86010 - 3.22178i) q^{29} +(-2.17268 + 0.0891762i) q^{30} +(-1.11770 + 1.93592i) q^{31} +(1.17699 - 2.03860i) q^{32} +(-5.50662 - 8.69369i) q^{33} +(-3.88798 - 6.73417i) q^{34} -1.00000 q^{35} +(0.543381 - 1.14957i) q^{36} -3.36866 q^{37} +(3.52721 + 6.10930i) q^{38} +(-2.99308 + 5.71317i) q^{39} +(-1.52151 + 2.63533i) q^{40} +(-0.0273015 + 0.0472876i) q^{41} +(-1.00911 + 1.92618i) q^{42} +(-2.71288 - 4.69884i) q^{43} -2.51824 q^{44} +(-1.28204 + 2.71226i) q^{45} -7.49300 q^{46} +(1.73256 + 3.00088i) q^{47} +(2.75511 + 4.34969i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.627726 - 1.08725i) q^{50} +(-10.7189 + 0.439949i) q^{51} +(0.789137 + 1.36683i) q^{52} -1.74963 q^{53} +(3.93059 + 5.20641i) q^{54} +5.94147 q^{55} +(1.52151 + 2.63533i) q^{56} +(9.72425 - 0.399126i) q^{57} +(2.33526 - 4.04479i) q^{58} +(4.83356 - 8.37197i) q^{59} +(0.392821 + 0.620173i) q^{60} +(-3.41217 - 5.91005i) q^{61} -2.80645 q^{62} +(1.70787 + 2.46641i) q^{63} +8.90066 q^{64} +(-1.86187 - 3.22486i) q^{65} +(5.99559 - 11.4443i) q^{66} +(-0.411109 + 0.712062i) q^{67} +(-1.31258 + 2.27346i) q^{68} +(-4.79727 + 9.15699i) q^{69} +(-0.627726 - 1.08725i) q^{70} -13.2014 q^{71} +(9.09834 - 0.748131i) q^{72} +1.27550 q^{73} +(-2.11459 - 3.66258i) q^{74} +(-0.926812 - 1.46322i) q^{75} +(1.19079 - 2.06250i) q^{76} +(2.97073 - 5.14546i) q^{77} +(-8.09049 + 0.332069i) q^{78} +(-2.54186 - 4.40263i) q^{79} -2.97268 q^{80} +(8.87911 - 1.47015i) q^{81} -0.0685515 q^{82} +(3.88153 + 6.72301i) q^{83} +(0.733496 - 0.0301059i) q^{84} +(3.09687 - 5.36394i) q^{85} +(3.40589 - 5.89917i) q^{86} +(-3.44792 - 5.44347i) q^{87} +(-9.03999 - 15.6577i) q^{88} -4.88072 q^{89} +(-3.75369 + 0.308655i) q^{90} -3.72374 q^{91} +(1.26482 + 2.19073i) q^{92} +(-1.79678 + 3.42968i) q^{93} +(-2.17515 + 3.76746i) q^{94} +(-2.80951 + 4.86622i) q^{95} +(1.89208 - 3.61160i) q^{96} +(3.74711 + 6.49019i) q^{97} -1.25545 q^{98} +(-10.1472 - 14.6541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.627726	+	1.08725i	0.443869	+	0.768804i	0.997973	−	0.0636437i	$-0.0202721\pi$
$2$	0.627726	+	1.08725i	0.443869	+	0.768804i	−0.554103	+	0.832448i	$0.686939\pi$
$3$	1.73059	−	0.0710311i	0.999159	−	0.0410098i
$3$	1.73059	−	0.0710311i	0.999159	−	0.0410098i
$4$	0.211920	−	0.367057i	0.105960	−	0.183528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.16357	+	1.83701i	0.475024	+	0.749954i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	3.04302			1.07587
$9$	2.98991	−	0.245852i	0.996636	−	0.0819507i
$10$	−1.25545			−0.397009
$11$	−2.97073	−	5.14546i	−0.895710	−	1.55141i	−0.832924	−	0.553388i	$-0.813335\pi$
$11$	−2.97073	−	5.14546i	−0.895710	−	1.55141i	−0.0627861	−	0.998027i	$-0.519999\pi$
$12$	0.340676	−	0.650279i	0.0983446	−	0.187719i
$13$	−1.86187	+	3.22486i	−0.516390	+	0.894415i	0.483428	+	0.875384i	$0.339391\pi$
$13$	−1.86187	+	3.22486i	−0.516390	+	0.894415i	−0.999819	+	0.0190307i	$0.993942\pi$
$14$	−0.627726	+	1.08725i	−0.167767	+	0.290581i
$15$	−0.803782	+	1.53425i	−0.207536	+	0.396143i
$16$	1.48634	+	2.57441i	0.371585	+	0.643604i
$17$	−6.19375			−1.50220			−0.751102	−	0.660186i	$-0.770477\pi$
$17$	−6.19375			−1.50220			−0.751102	+	0.660186i	$0.770477\pi$
$18$	2.14415	+	3.09646i	0.505380	+	0.729843i
$19$	5.61903			1.28909			0.644546	−	0.764565i	$-0.277046\pi$
$19$	5.61903			1.28909			0.644546	+	0.764565i	$0.277046\pi$
$20$	0.211920	+	0.367057i	0.0473868	+	0.0820764i
$21$	0.926812	+	1.46322i	0.202247	+	0.319301i
$22$	3.72961	−	6.45988i	0.795156	−	1.37725i
$23$	−2.98418	+	5.16876i	−0.622245	+	1.07776i	0.366821	+	0.930291i	$0.380446\pi$
$23$	−2.98418	+	5.16876i	−0.622245	+	1.07776i	−0.989067	+	0.147469i	$0.952887\pi$
$24$	5.26622	−	0.216149i	1.07496	−	0.0441212i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.67498			−0.916839
$27$	5.15685	−	0.637847i	0.992437	−	0.122754i
$28$	0.423841			0.0800984
$29$	−1.86010	−	3.22178i	−0.345411	−	0.598270i	0.640017	−	0.768361i	$-0.278927\pi$
$29$	−1.86010	−	3.22178i	−0.345411	−	0.598270i	−0.985428	+	0.170091i	$0.945594\pi$
$30$	−2.17268	+	0.0891762i	−0.396675	+	0.0162813i
$31$	−1.11770	+	1.93592i	−0.200745	+	0.347701i	−0.948769	−	0.315971i	$-0.897670\pi$
$31$	−1.11770	+	1.93592i	−0.200745	+	0.347701i	0.748023	+	0.663672i	$0.231003\pi$
$32$	1.17699	−	2.03860i	0.208064	−	0.360378i
$33$	−5.50662	−	8.69369i	−0.958580	−	1.51338i
$34$	−3.88798	−	6.73417i	−0.666782	−	1.15490i
$35$	−1.00000			−0.169031
$36$	0.543381	−	1.14957i	0.0905635	−	0.191595i
$37$	−3.36866			−0.553804			−0.276902	−	0.960898i	$-0.589308\pi$
$37$	−3.36866			−0.553804			−0.276902	+	0.960898i	$0.589308\pi$
$38$	3.52721	+	6.10930i	0.572189	+	0.991060i
$39$	−2.99308	+	5.71317i	−0.479276	+	0.914839i
$40$	−1.52151	+	2.63533i	−0.240571	+	0.416682i
$41$	−0.0273015	+	0.0472876i	−0.00426378	+	0.00738508i	−0.868149	−	0.496303i	$-0.834691\pi$
$41$	−0.0273015	+	0.0472876i	−0.00426378	+	0.00738508i	0.863886	+	0.503688i	$0.168024\pi$
$42$	−1.00911	+	1.92618i	−0.155709	+	0.297216i
$43$	−2.71288	−	4.69884i	−0.413710	−	0.716566i	0.581582	−	0.813488i	$-0.302434\pi$
$43$	−2.71288	−	4.69884i	−0.413710	−	0.716566i	−0.995292	+	0.0969213i	$0.969100\pi$
$44$	−2.51824			−0.379638
$45$	−1.28204	+	2.71226i	−0.191115	+	0.404320i
$46$	−7.49300			−1.10478
$47$	1.73256	+	3.00088i	0.252720	+	0.437724i	0.964274	−	0.264908i	$-0.0853415\pi$
$47$	1.73256	+	3.00088i	0.252720	+	0.437724i	−0.711554	+	0.702632i	$0.752008\pi$
$48$	2.75511	+	4.34969i	0.397666	+	0.627823i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.627726	−	1.08725i	0.0887738	−	0.153761i
$51$	−10.7189	+	0.439949i	−1.50094	+	0.0616052i
$52$	0.789137	+	1.36683i	0.109434	+	0.189545i
$53$	−1.74963			−0.240330			−0.120165	−	0.992754i	$-0.538342\pi$
$53$	−1.74963			−0.240330			−0.120165	+	0.992754i	$0.538342\pi$
$54$	3.93059	+	5.20641i	0.534886	+	0.708503i
$55$	5.94147			0.801147
$56$	1.52151	+	2.63533i	0.203320	+	0.352161i
$57$	9.72425	−	0.399126i	1.28801	−	0.0528655i
$58$	2.33526	−	4.04479i	0.306635	−	0.531107i
$59$	4.83356	−	8.37197i	0.629276	−	1.08994i	−0.358421	−	0.933560i	$-0.616685\pi$
$59$	4.83356	−	8.37197i	0.629276	−	1.08994i	0.987697	−	0.156378i	$-0.0499819\pi$
$60$	0.392821	+	0.620173i	0.0507129	+	0.0800640i
$61$	−3.41217	−	5.91005i	−0.436883	−	0.756704i	0.560564	−	0.828111i	$-0.310584\pi$
$61$	−3.41217	−	5.91005i	−0.436883	−	0.756704i	−0.997447	+	0.0714072i	$0.977251\pi$
$62$	−2.80645			−0.356419
$63$	1.70787	+	2.46641i	0.215171	+	0.310739i
$64$	8.90066			1.11258
$65$	−1.86187	−	3.22486i	−0.230937	−	0.399994i
$66$	5.99559	−	11.4443i	0.738006	−	1.40870i
$67$	−0.411109	+	0.712062i	−0.0502250	+	0.0869922i	−0.890045	−	0.455873i	$-0.849327\pi$
$67$	−0.411109	+	0.712062i	−0.0502250	+	0.0869922i	0.839820	+	0.542865i	$0.182661\pi$
$68$	−1.31258	+	2.27346i	−0.159174	+	0.275697i
$69$	−4.79727	+	9.15699i	−0.577523	+	1.10237i
$70$	−0.627726	−	1.08725i	−0.0750276	−	0.129952i
$71$	−13.2014			−1.56671			−0.783357	−	0.621572i	$-0.786495\pi$
$71$	−13.2014			−1.56671			−0.783357	+	0.621572i	$0.786495\pi$
$72$	9.09834	−	0.748131i	1.07225	−	0.0881681i
$73$	1.27550			0.149286			0.0746428	−	0.997210i	$-0.476218\pi$
$73$	1.27550			0.149286			0.0746428	+	0.997210i	$0.476218\pi$
$74$	−2.11459	−	3.66258i	−0.245816	−	0.425766i
$75$	−0.926812	−	1.46322i	−0.107019	−	0.168958i
$76$	1.19079	−	2.06250i	0.136593	−	0.236585i
$77$	2.97073	−	5.14546i	0.338546	−	0.586380i
$78$	−8.09049	+	0.332069i	−0.916068	+	0.0375994i
$79$	−2.54186	−	4.40263i	−0.285981	−	0.495334i	0.686865	−	0.726785i	$-0.258986\pi$
$79$	−2.54186	−	4.40263i	−0.285981	−	0.495334i	−0.972847	+	0.231451i	$0.925653\pi$
$80$	−2.97268			−0.332355
$81$	8.87911	−	1.47015i	0.986568	−	0.163350i
$82$	−0.0685515			−0.00757024
$83$	3.88153	+	6.72301i	0.426053	+	0.737946i	0.996518	−	0.0833762i	$-0.0265703\pi$
$83$	3.88153	+	6.72301i	0.426053	+	0.737946i	−0.570465	+	0.821322i	$0.693237\pi$
$84$	0.733496	−	0.0301059i	0.0800310	−	0.00328482i
$85$	3.09687	−	5.36394i	0.335903	−	0.581801i
$86$	3.40589	−	5.89917i	0.367266	−	0.636123i
$87$	−3.44792	−	5.44347i	−0.369656	−	0.583601i
$88$	−9.03999	−	15.6577i	−0.963666	−	1.66912i
$89$	−4.88072			−0.517355			−0.258678	−	0.965964i	$-0.583287\pi$
$89$	−4.88072			−0.517355			−0.258678	+	0.965964i	$0.583287\pi$
$90$	−3.75369	+	0.308655i	−0.395673	+	0.0325351i
$91$	−3.72374			−0.390355
$92$	1.26482	+	2.19073i	0.131866	+	0.228399i
$93$	−1.79678	+	3.42968i	−0.186317	+	0.355641i
$94$	−2.17515	+	3.76746i	−0.224349	+	0.388584i
$95$	−2.80951	+	4.86622i	−0.288250	+	0.499263i
$96$	1.89208	−	3.61160i	0.193110	−	0.368607i
$97$	3.74711	+	6.49019i	0.380461	+	0.658979i	0.991128	−	0.132909i	$-0.0424318\pi$
$97$	3.74711	+	6.49019i	0.380461	+	0.658979i	−0.610667	+	0.791888i	$0.709099\pi$
$98$	−1.25545			−0.126820
$99$	−10.1472	−	14.6541i	−1.01984	−	1.47279i
$100$	−0.423841			−0.0423841
$101$	5.81894	+	10.0787i	0.579007	+	1.00287i	0.995594	+	0.0937730i	$0.0298928\pi$
$101$	5.81894	+	10.0787i	0.579007	+	1.00287i	−0.416587	+	0.909096i	$0.636774\pi$
$102$	−7.20684	−	11.3779i	−0.713584	−	1.12658i
$103$	1.66292	−	2.88027i	0.163853	−	0.283801i	−0.772395	−	0.635143i	$-0.780941\pi$
$103$	1.66292	−	2.88027i	0.163853	−	0.283801i	0.936247	+	0.351342i	$0.114275\pi$
$104$	−5.66571	+	9.81329i	−0.555568	+	0.962272i
$105$	−1.73059	+	0.0710311i	−0.168889	+	0.00693193i
$106$	−1.09829	−	1.90229i	−0.106675	−	0.184767i
$107$	14.9277			1.44312			0.721558	−	0.692354i	$-0.243426\pi$
$107$	14.9277			1.44312			0.721558	+	0.692354i	$0.243426\pi$
$108$	0.858717	−	2.02803i	0.0826301	−	0.195147i
$109$	15.1043			1.44673			0.723364	−	0.690467i	$-0.242595\pi$
$109$	15.1043			1.44673			0.723364	+	0.690467i	$0.242595\pi$
$110$	3.72961	+	6.45988i	0.355605	+	0.615925i
$111$	−5.82977	+	0.239279i	−0.553338	+	0.0227114i
$112$	−1.48634	+	2.57441i	−0.140446	+	0.243259i
$113$	6.95999	−	12.0551i	0.654741	−	1.13404i	−0.327218	−	0.944949i	$-0.606111\pi$
$113$	6.95999	−	12.0551i	0.654741	−	1.13404i	0.981959	−	0.189096i	$-0.0605557\pi$
$114$	6.53811	+	10.3222i	0.612350	+	0.966761i
$115$	−2.98418	−	5.16876i	−0.278277	−	0.481989i
$116$	−1.57677			−0.146399
$117$	−4.77399	+	10.0998i	−0.441356	+	0.933725i
$118$	12.1366			1.11727
$119$	−3.09687	−	5.36394i	−0.283890	−	0.491712i
$120$	−2.44592	+	4.66876i	−0.223281	+	0.426197i
$121$	−12.1505	+	21.0453i	−1.10459	+	1.91321i
$122$	4.28381	−	7.41978i	0.387838	−	0.671755i
$123$	−0.0438889	+	0.0837749i	−0.00395733	+	0.00755373i
$124$	0.473728	+	0.820521i	0.0425420	+	0.0736850i
$125$	1.00000			0.0894427
$126$	−1.60954	+	3.40512i	−0.143389	+	0.303352i
$127$	17.2711			1.53256			0.766281	−	0.642506i	$-0.222105\pi$
$127$	17.2711			1.53256			0.766281	+	0.642506i	$0.222105\pi$
$128$	3.23320	+	5.60006i	0.285777	+	0.494980i
$129$	−5.02865	−	7.93908i	−0.442748	−	0.698997i
$130$	2.33749	−	4.04865i	0.205012	−	0.355090i
$131$	−10.7335	+	18.5909i	−0.937788	+	1.62430i	−0.168203	+	0.985752i	$0.553796\pi$
$131$	−10.7335	+	18.5909i	−0.937788	+	1.62430i	−0.769585	+	0.638544i	$0.779537\pi$
$132$	−4.35804	+	0.178873i	−0.379319	+	0.0155689i
$133$	2.80951	+	4.86622i	0.243616	+	0.421955i
$134$	−1.03226			−0.0891733
$135$	−2.02604	+	4.78489i	−0.174373	+	0.411818i
$136$	−18.8477			−1.61617
$137$	−6.44311	−	11.1598i	−0.550472	−	0.953445i	−0.998240	−	0.0592956i	$-0.981115\pi$
$137$	−6.44311	−	11.1598i	−0.550472	−	0.953445i	0.447769	−	0.894149i	$-0.352219\pi$
$138$	−12.9673	+	0.532236i	−1.10385	+	0.0453069i
$139$	−0.324093	+	0.561346i	−0.0274892	+	0.0476128i	−0.879443	−	0.476005i	$-0.842085\pi$
$139$	−0.324093	+	0.561346i	−0.0274892	+	0.0476128i	0.851954	+	0.523617i	$0.175418\pi$
$140$	−0.211920	+	0.367057i	−0.0179105	+	0.0310220i
$141$	3.21152	+	5.07024i	0.270458	+	0.426992i
$142$	−8.28684	−	14.3532i	−0.695417	−	1.20450i
$143$	22.1245			1.85014
$144$	5.07694	+	7.33185i	0.423079	+	0.610987i
$145$	3.72019			0.308945
$146$	0.800663	+	1.38679i	0.0662633	+	0.114771i
$147$	−0.803782	+	1.53425i	−0.0662948	+	0.126543i
$148$	−0.713887	+	1.23649i	−0.0586811	+	0.101639i
$149$	−0.0909805	+	0.157583i	−0.00745341	+	0.0129097i	−0.869728	−	0.493531i	$-0.835706\pi$
$149$	−0.0909805	+	0.157583i	−0.00745341	+	0.0129097i	0.862275	+	0.506441i	$0.169039\pi$
$150$	1.00911	−	1.92618i	0.0823935	−	0.157272i
$151$	9.91481	+	17.1730i	0.806856	+	1.39751i	0.915031	+	0.403383i	$0.132166\pi$
$151$	9.91481	+	17.1730i	0.806856	+	1.39751i	−0.108176	+	0.994132i	$0.534501\pi$
$152$	17.0988			1.38689
$153$	−18.5187	+	1.52275i	−1.49715	+	0.123107i
$154$	7.45923			0.601081
$155$	−1.11770	−	1.93592i	−0.0897761	−	0.155497i
$156$	1.46276	+	2.30937i	0.117115	+	0.184897i
$157$	−0.594331	+	1.02941i	−0.0474328	+	0.0821560i	−0.888767	−	0.458359i	$-0.848437\pi$
$157$	−0.594331	+	1.02941i	−0.0474328	+	0.0821560i	0.841334	+	0.540515i	$0.181771\pi$
$158$	3.19118	−	5.52728i	0.253877	−	0.439727i
$159$	−3.02790	+	0.124278i	−0.240128	+	0.00985590i
$160$	1.17699	+	2.03860i	0.0930491	+	0.161166i
$161$	−5.96837			−0.470373
$162$	7.17208	+	8.73099i	0.563491	+	0.685972i
$163$	−13.4766			−1.05557			−0.527784	−	0.849379i	$-0.676977\pi$
$163$	−13.4766			−1.05557			−0.527784	+	0.849379i	$0.676977\pi$
$164$	0.0115715	+	0.0200424i	0.000903582	+	0.00156505i
$165$	10.2823	−	0.422029i	0.800473	−	0.0328549i
$166$	−4.87307	+	8.44041i	−0.378224	+	0.655103i
$167$	−9.26206	+	16.0424i	−0.716720	+	1.24139i	0.245573	+	0.969378i	$0.421024\pi$
$167$	−9.26206	+	16.0424i	−0.716720	+	1.24139i	−0.962293	+	0.272017i	$0.912309\pi$
$168$	2.82030	+	4.45261i	0.217591	+	0.343526i
$169$	−0.433137	−	0.750216i	−0.0333183	−	0.0577089i
$170$	7.77595			0.596388
$171$	16.8004	−	1.38145i	1.28476	−	0.105642i
$172$	−2.29965			−0.175347
$173$	8.10573	+	14.0395i	0.616267	+	1.06741i	0.990161	+	0.139934i	$0.0446892\pi$
$173$	8.10573	+	14.0395i	0.616267	+	1.06741i	−0.373894	+	0.927472i	$0.621977\pi$
$174$	3.75408	−	7.16577i	0.284596	−	0.543235i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	8.83103	−	15.2958i	0.665664	−	1.15296i
$177$	7.77026	−	14.8318i	0.584049	−	1.11483i
$178$	−3.06376	−	5.30658i	−0.229638	−	0.397745i
$179$	16.7891			1.25488			0.627440	−	0.778665i	$-0.284103\pi$
$179$	16.7891			1.25488			0.627440	+	0.778665i	$0.284103\pi$
$180$	0.723864	+	1.04537i	0.0539537	+	0.0779170i
$181$	14.2143			1.05654			0.528271	−	0.849076i	$-0.322841\pi$
$181$	14.2143			1.05654			0.528271	+	0.849076i	$0.322841\pi$
$182$	−2.33749	−	4.04865i	−0.173266	−	0.300106i
$183$	−6.32487	−	9.98552i	−0.467548	−	0.738151i
$184$	−9.08092	+	15.7286i	−0.669454	+	1.15953i
$185$	1.68433	−	2.91734i	0.123834	−	0.214487i
$186$	−4.85682	+	0.199345i	−0.356119	+	0.0146167i
$187$	18.4000	+	31.8697i	1.34554	+	2.33054i
$188$	1.46866			0.107113
$189$	3.13082	+	4.14704i	0.227734	+	0.301653i
$190$	−7.05442			−0.511781
$191$	−7.80383	−	13.5166i	−0.564665	−	0.978029i	−0.997081	−	0.0763545i	$-0.975672\pi$
$191$	−7.80383	−	13.5166i	−0.564665	−	0.978029i	0.432415	−	0.901674i	$-0.357661\pi$
$192$	15.4034	−	0.632224i	1.11165	−	0.0456268i
$193$	1.55665	−	2.69619i	0.112050	−	0.194076i	−0.804547	−	0.593889i	$-0.797592\pi$
$193$	1.55665	−	2.69619i	0.112050	−	0.194076i	0.916597	+	0.399813i	$0.130925\pi$
$194$	−4.70432	+	8.14812i	−0.337750	+	0.585001i
$195$	−3.45121	−	5.44867i	−0.247146	−	0.390187i
$196$	0.211920	+	0.367057i	0.0151372	+	0.0262183i
$197$	−14.4895			−1.03233			−0.516166	−	0.856489i	$-0.672641\pi$
$197$	−14.4895			−1.03233			−0.516166	+	0.856489i	$0.672641\pi$
$198$	9.56303	−	20.2314i	0.679615	−	1.43778i
$199$	−17.5095			−1.24122			−0.620609	−	0.784120i	$-0.713115\pi$
$199$	−17.5095			−1.24122			−0.620609	+	0.784120i	$0.713115\pi$
$200$	−1.52151	−	2.63533i	−0.107587	−	0.186346i
$201$	−0.660884	+	1.26149i	−0.0466152	+	0.0889787i
$202$	−7.30540	+	12.6533i	−0.514006	+	0.890285i
$203$	1.86010	−	3.22178i	0.130553	−	0.226125i
$204$	−2.11006	+	4.02767i	−0.147734	+	0.281993i
$205$	−0.0273015	−	0.0472876i	−0.00190682	−	0.00330271i
$206$	4.17544			0.290916
$207$	−7.65169	+	16.1878i	−0.531829	+	1.12513i
$208$	−11.0695			−0.767531
$209$	−16.6926	−	28.9125i	−1.15465	−	1.99992i
$210$	−1.16357	−	1.83701i	−0.0802938	−	0.126765i
$211$	−10.5408	+	18.2571i	−0.725656	+	1.25687i	0.233048	+	0.972465i	$0.425130\pi$
$211$	−10.5408	+	18.2571i	−0.725656	+	1.25687i	−0.958704	+	0.284407i	$0.908203\pi$
$212$	−0.370782	+	0.642214i	−0.0254654	+	0.0441074i
$213$	−22.8462	+	0.937708i	−1.56540	+	0.0642507i
$214$	9.37051	+	16.2302i	0.640555	+	1.10947i
$215$	5.42575			0.370033
$216$	15.6924	−	1.94098i	1.06773	−	0.132067i
$217$	−2.23541			−0.151749
$218$	9.48135	+	16.4222i	0.642158	+	1.11225i
$219$	2.20737	−	0.0906000i	0.149160	−	0.00612218i
$220$	1.25912	−	2.18086i	0.0848897	−	0.147033i
$221$	11.5320	−	19.9740i	0.775724	−	1.34359i
$222$	−3.91966	−	6.18824i	−0.263070	−	0.415327i
$223$	−9.14729	−	15.8436i	−0.612548	−	1.06096i	−0.990809	−	0.135265i	$-0.956811\pi$
$223$	−9.14729	−	15.8436i	−0.612548	−	1.06096i	0.378262	−	0.925699i	$-0.376522\pi$
$224$	2.35398			0.157282
$225$	−1.70787	−	2.46641i	−0.113858	−	0.164427i
$226$	17.4759			1.16248
$227$	5.14640	+	8.91382i	0.341578	+	0.591631i	0.984726	−	0.174111i	$-0.0557052\pi$
$227$	5.14640	+	8.91382i	0.341578	+	0.591631i	−0.643148	+	0.765742i	$0.722372\pi$
$228$	1.91426	−	3.65394i	0.126775	−	0.241988i
$229$	5.28867	−	9.16025i	0.349485	−	0.605326i	−0.636673	−	0.771134i	$-0.719690\pi$
$229$	5.28867	−	9.16025i	0.349485	−	0.605326i	0.986158	+	0.165808i	$0.0530231\pi$
$230$	3.74650	−	6.48913i	0.247037	−	0.427880i
$231$	4.77564	−	9.11572i	0.314214	−	0.599770i
$232$	−5.66030	−	9.80393i	−0.371617	−	0.643659i
$233$	10.3442			0.677674			0.338837	−	0.940845i	$-0.389966\pi$
$233$	10.3442			0.677674			0.338837	+	0.940845i	$0.389966\pi$
$234$	−13.9778	+	1.14935i	−0.913756	+	0.0751356i
$235$	−3.46512			−0.226040
$236$	−2.04866	−	3.54838i	−0.133356	−	0.230980i
$237$	−4.71165	−	7.43861i	−0.306054	−	0.483189i
$238$	3.88798	−	6.73417i	0.252020	−	0.436512i
$239$	0.521265	−	0.902858i	0.0337178	−	0.0584010i	−0.848674	−	0.528916i	$-0.822599\pi$
$239$	0.521265	−	0.902858i	0.0337178	−	0.0584010i	0.882392	+	0.470515i	$0.155932\pi$
$240$	−5.14450	+	0.211153i	−0.332076	+	0.0136298i
$241$	−6.01656	−	10.4210i	−0.387561	−	0.671275i	0.604560	−	0.796559i	$-0.293349\pi$
$241$	−6.01656	−	10.4210i	−0.387561	−	0.671275i	−0.992121	+	0.125285i	$0.960016\pi$
$242$	−30.5088			−1.96118
$243$	15.2617	−	3.17493i	0.979039	−	0.203672i
$244$	−2.89243			−0.185169
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	−0.118635	+	0.00486929i	−0.00756388	+	0.000310454i
$247$	−10.4619	+	18.1206i	−0.665675	+	1.15298i
$248$	−3.40119	+	5.89103i	−0.215976	+	0.374081i
$249$	7.19489	+	11.3591i	0.455958	+	0.719853i
$250$	0.627726	+	1.08725i	0.0397009	+	0.0687639i
$251$	6.22952			0.393204			0.196602	−	0.980483i	$-0.437009\pi$
$251$	6.22952			0.393204			0.196602	+	0.980483i	$0.437009\pi$
$252$	1.26725	−	0.104202i	0.0798290	−	0.00656412i
$253$	35.4609			2.22940
$254$	10.8415	+	18.7780i	0.680257	+	1.17824i
$255$	4.97842	−	9.50278i	0.311761	−	0.595087i
$256$	4.84154	−	8.38579i	0.302596	−	0.524112i
$257$	6.88825	−	11.9308i	0.429677	−	0.744223i	−0.567167	−	0.823603i	$-0.691961\pi$
$257$	6.88825	−	11.9308i	0.429677	−	0.744223i	0.996844	+	0.0793798i	$0.0252940\pi$
$258$	5.47518	−	10.4510i	0.340870	−	0.650650i
$259$	−1.68433	−	2.91734i	−0.104659	−	0.181275i
$260$	−1.57827			−0.0978804
$261$	−6.35360	−	9.17552i	−0.393278	−	0.567951i
$262$	−26.9507			−1.66502
$263$	10.0733	+	17.4475i	0.621149	+	1.07586i	0.989272	+	0.146084i	$0.0466670\pi$
$263$	10.0733	+	17.4475i	0.621149	+	1.07586i	−0.368124	+	0.929777i	$0.620000\pi$
$264$	−16.7567	−	26.4550i	−1.03131	−	1.62819i
$265$	0.874815	−	1.51522i	0.0537395	−	0.0930795i
$266$	−3.52721	+	6.10930i	−0.216267	+	0.374585i
$267$	−8.44655	+	0.346683i	−0.516920	+	0.0212167i
$268$	0.174245	+	0.301801i	0.0106437	+	0.0184354i
$269$	13.4990			0.823046			0.411523	−	0.911399i	$-0.364997\pi$
$269$	13.4990			0.823046			0.411523	+	0.911399i	$0.364997\pi$
$270$	−6.47418	+	0.800786i	−0.394006	+	0.0487343i
$271$	13.8321			0.840238			0.420119	−	0.907469i	$-0.361988\pi$
$271$	13.8321			0.840238			0.420119	+	0.907469i	$0.361988\pi$
$272$	−9.20601	−	15.9453i	−0.558196	−	0.966824i
$273$	−6.44429	+	0.264502i	−0.390026	+	0.0160084i
$274$	8.08901	−	14.0106i	0.488675	−	0.846410i
$275$	−2.97073	+	5.14546i	−0.179142	+	0.310283i
$276$	2.34450	+	3.70142i	0.141122	+	0.222799i
$277$	2.22404	+	3.85216i	0.133630	+	0.231454i	0.925073	−	0.379789i	$-0.124003\pi$
$277$	2.22404	+	3.85216i	0.133630	+	0.231454i	−0.791443	+	0.611242i	$0.790670\pi$
$278$	−0.813767			−0.0488065
$279$	−2.86588	+	6.06301i	−0.171576	+	0.362983i
$280$	−3.04302			−0.181855
$281$	−7.00863	−	12.1393i	−0.418100	−	0.724170i	0.577648	−	0.816286i	$-0.303970\pi$
$281$	−7.00863	−	12.1393i	−0.418100	−	0.724170i	−0.995748	+	0.0921154i	$0.970637\pi$
$282$	−3.49669	+	6.67445i	−0.208225	+	0.397458i
$283$	−12.2667	+	21.2465i	−0.729177	+	1.26297i	0.228055	+	0.973648i	$0.426763\pi$
$283$	−12.2667	+	21.2465i	−0.729177	+	1.26297i	−0.957232	+	0.289323i	$0.906570\pi$
$284$	−2.79764	+	4.84566i	−0.166009	+	0.287537i
$285$	−4.51647	+	8.62101i	−0.267533	+	0.510665i
$286$	13.8881	+	24.0549i	0.821222	+	1.42240i
$287$	−0.0546030			−0.00322311
$288$	3.01789	−	6.38461i	0.177831	−	0.376217i
$289$	21.3625			1.25662
$290$	2.33526	+	4.04479i	0.137131	+	0.237518i
$291$	6.94573	+	10.9657i	0.407166	+	0.642822i
$292$	0.270304	−	0.468180i	0.0158183	−	0.0273982i
$293$	5.99137	−	10.3774i	0.350020	−	0.606252i	−0.636233	−	0.771497i	$-0.719508\pi$
$293$	5.99137	−	10.3774i	0.350020	−	0.606252i	0.986253	+	0.165245i	$0.0528415\pi$
$294$	−2.17268	+	0.0891762i	−0.126713	+	0.00520086i
$295$	4.83356	+	8.37197i	0.281421	+	0.487435i
$296$	−10.2509			−0.595820
$297$	−18.6017	−	24.6395i	−1.07938	−	1.42973i
$298$	−0.228443			−0.0132334
$299$	−11.1123	−	19.2471i	−0.642643	−	1.11309i
$300$	−0.733496	+	0.0301059i	−0.0423484	+	0.00173816i
$301$	2.71288	−	4.69884i	0.156368	−	0.270837i
$302$	−12.4476	+	21.5598i	−0.716277	+	1.24063i
$303$	10.7861	+	17.0288i	0.619647	+	0.978280i
$304$	8.35177	+	14.4657i	0.479007	+	0.829665i
$305$	6.82433			0.390760
$306$	−13.2803	−	19.1787i	−0.759184	−	1.09637i
$307$	−28.6629			−1.63588			−0.817939	−	0.575304i	$-0.804884\pi$
$307$	−28.6629			−1.63588			−0.817939	+	0.575304i	$0.804884\pi$
$308$	−1.25912	−	2.18086i	−0.0717449	−	0.124266i
$309$	2.67325	−	5.10269i	0.152076	−	0.290282i
$310$	1.40322	−	2.43045i	0.0796977	−	0.138040i
$311$	6.03175	−	10.4473i	0.342029	−	0.592411i	−0.642780	−	0.766050i	$-0.722219\pi$
$311$	6.03175	−	10.4473i	0.342029	−	0.592411i	0.984809	+	0.173639i	$0.0555526\pi$
$312$	−9.10799	+	17.3853i	−0.515638	+	0.984247i
$313$	−13.0032	−	22.5222i	−0.734985	−	1.27303i	−0.954730	−	0.297473i	$-0.903856\pi$
$313$	−13.0032	−	22.5222i	−0.734985	−	1.27303i	0.219746	−	0.975557i	$-0.429477\pi$
$314$	−1.49231			−0.0842158
$315$	−2.98991	+	0.245852i	−0.168462	+	0.0138522i
$316$	−2.15469			−0.121211
$317$	−12.2621	−	21.2386i	−0.688708	−	1.19288i	−0.972256	−	0.233919i	$-0.924845\pi$
$317$	−12.2621	−	21.2386i	−0.688708	−	1.19288i	0.283548	−	0.958958i	$-0.408488\pi$
$318$	−2.03581	−	3.21408i	−0.114163	−	0.180237i
$319$	−11.0517	+	19.1421i	−0.618776	+	1.07175i
$320$	−4.45033	+	7.70820i	−0.248781	+	0.430901i
$321$	25.8338	−	1.06033i	1.44190	−	0.0591820i
$322$	−3.74650	−	6.48913i	−0.208784	−	0.361625i
$323$	−34.8028			−1.93648
$324$	1.34204	−	3.57069i	0.0745576	−	0.198372i
$325$	3.72374			0.206556
$326$	−8.45960	−	14.6525i	−0.468534	−	0.811525i
$327$	26.1394	−	1.07287i	1.44551	−	0.0593301i
$328$	−0.0830789	+	0.143897i	−0.00458727	+	0.00794538i
$329$	−1.73256	+	3.00088i	−0.0955192	+	0.165444i
$330$	6.91330	+	10.9145i	0.380564	+	0.600824i
$331$	−4.97577	−	8.61829i	−0.273493	−	0.473704i	0.696261	−	0.717789i	$-0.254846\pi$
$331$	−4.97577	−	8.61829i	−0.273493	−	0.473704i	−0.969754	+	0.244085i	$0.921512\pi$
$332$	3.29030			0.180579
$333$	−10.0720	+	0.828191i	−0.551941	+	0.0453846i
$334$	−23.2561			−1.27252
$335$	−0.411109	−	0.712062i	−0.0224613	−	0.0389041i
$336$	−2.38938	+	4.56084i	−0.130352	+	0.248814i
$337$	3.98469	−	6.90169i	0.217060	−	0.375959i	−0.736848	−	0.676059i	$-0.763687\pi$
$337$	3.98469	−	6.90169i	0.217060	−	0.375959i	0.953908	+	0.300100i	$0.0970199\pi$
$338$	0.543783	−	0.941860i	0.0295779	−	0.0512304i
$339$	11.1886	−	21.3568i	0.607683	−	1.15994i
$340$	−1.31258	−	2.27346i	−0.0711847	−	0.123296i
$341$	13.2816			0.719239
$342$	12.0480	+	17.3991i	0.651482	+	0.940835i
$343$	−1.00000			−0.0539949
$344$	−8.25532	−	14.2986i	−0.445097	−	0.770931i
$345$	−5.53155	−	8.73305i	−0.297809	−	0.470172i
$346$	−10.1764	+	17.6260i	−0.547084	+	0.947577i
$347$	9.99966	−	17.3199i	0.536810	−	0.929782i	−0.462263	−	0.886743i	$-0.652963\pi$
$347$	9.99966	−	17.3199i	0.536810	−	0.929782i	0.999073	−	0.0430395i	$-0.0137041\pi$
$348$	−2.72875	+	0.112000i	−0.146276	+	0.00600381i
$349$	−12.4008	−	21.4787i	−0.663797	−	1.14973i	−0.979610	−	0.200909i	$-0.935610\pi$
$349$	−12.4008	−	21.4787i	−0.663797	−	1.14973i	0.315812	−	0.948822i	$-0.397723\pi$
$350$	1.25545			0.0671067
$351$	−7.54444	+	17.8177i	−0.402692	+	0.951039i
$352$	−13.9861			−0.745460
$353$	−5.25198	−	9.09670i	−0.279535	−	0.484169i	0.691734	−	0.722152i	$-0.256847\pi$
$353$	−5.25198	−	9.09670i	−0.279535	−	0.484169i	−0.971269	+	0.237983i	$0.923514\pi$
$354$	21.0035	−	0.862077i	1.11633	−	0.0458189i
$355$	6.60069	−	11.4327i	0.350328	−	0.606786i
$356$	−1.03432	+	1.79150i	−0.0548191	+	0.0949494i
$357$	−5.74044	−	9.06283i	−0.303816	−	0.479656i
$358$	10.5390	+	18.2540i	0.557002	+	0.964756i
$359$	24.3090			1.28298			0.641491	−	0.767131i	$-0.278316\pi$
$359$	24.3090			1.28298			0.641491	+	0.767131i	$0.278316\pi$
$360$	−3.90127	+	8.25346i	−0.205615	+	0.434995i
$361$	12.5734			0.661760
$362$	8.92269	+	15.4546i	0.468966	+	0.812274i
$363$	−19.5327	+	37.2839i	−1.02520	+	1.95690i
$364$	−0.789137	+	1.36683i	−0.0413620	+	0.0716412i
$365$	−0.637749	+	1.10461i	−0.0333813	+	0.0578181i
$366$	6.88650	−	13.1449i	0.359963	−	0.687095i
$367$	0.0160537	+	0.0278059i	0.000837998	+	0.00145146i	0.866444	−	0.499274i	$-0.166400\pi$
$367$	0.0160537	+	0.0278059i	0.000837998	+	0.00145146i	−0.865606	+	0.500726i	$0.833067\pi$
$368$	−17.7420			−0.924867
$369$	−0.0700033	+	0.148098i	−0.00364423	+	0.00770966i
$370$	4.22918			0.219865
$371$	−0.874815	−	1.51522i	−0.0454181	−	0.0786665i
$372$	0.878114	+	1.38634i	0.0455281	+	0.0718784i
$373$	0.548671	−	0.950327i	0.0284091	−	0.0492060i	−0.851471	−	0.524401i	$-0.824289\pi$
$373$	0.548671	−	0.950327i	0.0284091	−	0.0492060i	0.879880	+	0.475195i	$0.157623\pi$
$374$	−23.1003	+	40.0109i	−1.19449	+	2.06891i
$375$	1.73059	−	0.0710311i	0.0893675	−	0.00366803i
$376$	5.27221	+	9.13173i	0.271893	+	0.470933i
$377$	13.8530			0.713468
$378$	−2.54359	+	6.00720i	−0.130828	+	0.308977i
$379$	−23.8702			−1.22613			−0.613064	−	0.790033i	$-0.710063\pi$
$379$	−23.8702			−1.22613			−0.613064	+	0.790033i	$0.710063\pi$
$380$	1.19079	+	2.06250i	0.0610860	+	0.105804i
$381$	29.8892	−	1.22678i	1.53127	−	0.0628501i
$382$	9.79733	−	16.9695i	0.501275	−	0.868234i
$383$	−4.26470	+	7.38668i	−0.217916	+	0.377442i	−0.954171	−	0.299263i	$-0.903259\pi$
$383$	−4.26470	+	7.38668i	−0.217916	+	0.377442i	0.736255	+	0.676705i	$0.236593\pi$
$384$	5.99313	+	9.46177i	0.305836	+	0.482844i
$385$	2.97073	+	5.14546i	0.151403	+	0.262237i
$386$	3.90859			0.198942
$387$	−9.26647	−	13.3821i	−0.471041	−	0.680252i
$388$	3.17636			0.161255
$389$	9.40968	+	16.2980i	0.477090	+	0.826344i	0.999655	−	0.0262553i	$-0.00835828\pi$
$389$	9.40968	+	16.2980i	0.477090	+	0.826344i	−0.522565	+	0.852599i	$0.675025\pi$
$390$	3.75767	−	7.17261i	0.190277	−	0.363199i
$391$	18.4833	−	32.0140i	0.934740	−	1.61902i
$392$	−1.52151	+	2.63533i	−0.0768477	+	0.133104i
$393$	−17.2548	+	32.9357i	−0.870387	+	1.66139i
$394$	−9.09541	−	15.7537i	−0.458220	−	0.793661i
$395$	5.08371			0.255789
$396$	−7.52930	+	0.619113i	−0.378361	+	0.0311116i
$397$	−4.46269			−0.223976			−0.111988	−	0.993710i	$-0.535722\pi$
$397$	−4.46269			−0.223976			−0.111988	+	0.993710i	$0.535722\pi$
$398$	−10.9912	−	19.0373i	−0.550938	−	0.954253i
$399$	5.20778	+	8.22188i	0.260715	+	0.411609i
$400$	1.48634	−	2.57441i	0.0743169	−	0.128721i
$401$	−10.7465	+	18.6135i	−0.536654	+	0.929513i	0.462427	+	0.886657i	$0.346979\pi$
$401$	−10.7465	+	18.6135i	−0.536654	+	0.929513i	−0.999081	+	0.0428552i	$0.986355\pi$
$402$	−1.78641	+	0.0733223i	−0.0890983	+	0.00365698i
$403$	−4.16204	−	7.20887i	−0.207326	−	0.359099i
$404$	4.93261			0.245407
$405$	−3.16637	+	8.42461i	−0.157338	+	0.418622i
$406$	4.67052			0.231794
$407$	10.0074	+	17.3333i	0.496047	+	0.859179i
$408$	−32.6177	+	1.33877i	−1.61481	+	0.0662790i
$409$	1.46252	−	2.53316i	0.0723169	−	0.125257i	−0.827599	−	0.561319i	$-0.810294\pi$
$409$	1.46252	−	2.53316i	0.0723169	−	0.125257i	0.899916	+	0.436063i	$0.143627\pi$
$410$	0.0342757	−	0.0593673i	0.00169276	−	0.00293194i
$411$	−11.9431	−	18.8554i	−0.589109	−	0.930068i
$412$	−0.704814	−	1.22077i	−0.0347237	−	0.0601432i
$413$	9.66712			0.475688
$414$	−22.4034	+	1.84217i	−1.10107	+	0.0905376i
$415$	−7.76306			−0.381074
$416$	4.38281	+	7.59124i	0.214885	+	0.372191i
$417$	−0.521001	+	0.994483i	−0.0255135	+	0.0487000i
$418$	20.9568	−	36.2982i	1.02503	−	1.77540i
$419$	0.0390937	−	0.0677123i	0.00190985	−	0.00330796i	−0.865069	−	0.501653i	$-0.832725\pi$
$419$	0.0390937	−	0.0677123i	0.00190985	−	0.00330796i	0.866979	+	0.498345i	$0.166059\pi$
$420$	−0.340676	+	0.650279i	−0.0166233	+	0.0317304i
$421$	−13.0678	−	22.6340i	−0.636883	−	1.10311i	−0.986113	−	0.166077i	$-0.946890\pi$
$421$	−13.0678	−	22.6340i	−0.636883	−	1.10311i	0.349230	−	0.937037i	$-0.386443\pi$
$422$	−26.4668			−1.28839
$423$	5.91797	+	8.54642i	0.287742	+	0.415541i
$424$	−5.32415			−0.258564
$425$	3.09687	+	5.36394i	0.150220	+	0.260189i
$426$	−15.3607	−	24.2510i	−0.744228	−	1.17496i
$427$	3.41217	−	5.91005i	0.165126	−	0.286007i
$428$	3.16349	−	5.47932i	0.152913	−	0.264853i
$429$	38.2885	−	1.57153i	1.84859	−	0.0758741i
$430$	3.40589	+	5.89917i	0.164246	+	0.284483i
$431$	11.7727			0.567069			0.283534	−	0.958962i	$-0.408493\pi$
$431$	11.7727			0.567069			0.283534	+	0.958962i	$0.408493\pi$
$432$	9.30691	+	12.3278i	0.447779	+	0.593123i
$433$	36.0207			1.73104			0.865522	−	0.500871i	$-0.166987\pi$
$433$	36.0207			1.73104			0.865522	+	0.500871i	$0.166987\pi$
$434$	−1.40322	−	2.43045i	−0.0673568	−	0.116665i
$435$	6.43814	−	0.264249i	0.308685	−	0.0126698i
$436$	3.20091	−	5.54413i	0.153296	−	0.265516i
$437$	−16.7682	+	29.0434i	−0.802132	+	1.38933i
$438$	1.48413	+	2.34310i	0.0709143	+	0.111957i
$439$	−11.8595	−	20.5412i	−0.566022	−	0.980379i	−0.996954	−	0.0779944i	$-0.975148\pi$
$439$	−11.8595	−	20.5412i	−0.566022	−	0.980379i	0.430932	−	0.902384i	$-0.358185\pi$
$440$	18.0800			0.861929
$441$	−1.28204	+	2.71226i	−0.0610495	+	0.129155i
$442$	28.9557			1.37728
$443$	10.9974	+	19.0480i	0.522500	+	0.904997i	0.999657	+	0.0261790i	$0.00833398\pi$
$443$	10.9974	+	19.0480i	0.522500	+	0.904997i	−0.477157	+	0.878818i	$0.658333\pi$
$444$	−1.14762	+	2.19057i	−0.0544636	+	0.103960i
$445$	2.44036	−	4.22683i	0.115684	−	0.200371i
$446$	11.4840	−	19.8908i	0.543782	−	0.941858i
$447$	−0.146257	+	0.279174i	−0.00691772	+	0.0132045i
$448$	4.45033	+	7.70820i	0.210258	+	0.364178i
$449$	−1.49118			−0.0703732			−0.0351866	−	0.999381i	$-0.511203\pi$
$449$	−1.49118			−0.0703732			−0.0351866	+	0.999381i	$0.511203\pi$
$450$	1.60954	−	3.40512i	0.0758744	−	0.160519i
$451$	0.324422			0.0152764
$452$	−2.94993	−	5.10943i	−0.138753	−	0.240327i
$453$	18.3783	+	29.0151i	0.863489	+	1.36325i
$454$	−6.46105	+	11.1909i	−0.303232	+	0.525214i
$455$	1.86187	−	3.22486i	0.0872859	−	0.151184i
$456$	29.5910	−	1.21455i	1.38573	−	0.0568763i
$457$	5.71863	+	9.90496i	0.267506	+	0.463334i	0.968217	−	0.250111i	$-0.0804671\pi$
$457$	5.71863	+	9.90496i	0.267506	+	0.463334i	−0.700711	+	0.713445i	$0.747134\pi$
$458$	13.2793			0.620503
$459$	−31.9403	+	3.95066i	−1.49084	+	0.184401i
$460$	−2.52964			−0.117945
$461$	4.56952	+	7.91465i	0.212824	+	0.368622i	0.952597	−	0.304234i	$-0.0984006\pi$
$461$	4.56952	+	7.91465i	0.212824	+	0.368622i	−0.739773	+	0.672856i	$0.765067\pi$
$462$	12.9089	−	0.529837i	0.600576	−	0.0246503i
$463$	11.2427	−	19.4730i	0.522493	−	0.904985i	−0.477164	−	0.878814i	$-0.658335\pi$
$463$	11.2427	−	19.4730i	0.522493	−	0.904985i	0.999657	−	0.0261709i	$-0.00833142\pi$
$464$	5.52947	−	9.57732i	0.256699	−	0.444616i
$465$	−2.07180	−	3.27090i	−0.0960775	−	0.151684i
$466$	6.49335	+	11.2468i	0.300799	+	0.520999i
$467$	−1.60517			−0.0742784			−0.0371392	−	0.999310i	$-0.511824\pi$
$467$	−1.60517			−0.0742784			−0.0371392	+	0.999310i	$0.511824\pi$
$468$	2.69549	+	3.89267i	0.124599	+	0.179939i
$469$	−0.822218			−0.0379665
$470$	−2.17515	−	3.76746i	−0.100332	−	0.173780i
$471$	−0.955425	+	1.82371i	−0.0440237	+	0.0840321i
$472$	14.7086	−	25.4760i	0.677018	−	1.17263i
$473$	−16.1185	+	27.9180i	−0.741128	+	1.28367i
$474$	5.13003	−	9.79216i	0.235630	−	0.449769i
$475$	−2.80951	−	4.86622i	−0.128909	−	0.223277i
$476$	−2.62516			−0.120324
$477$	−5.23124	+	0.430150i	−0.239522	+	0.0196952i
$478$	1.30885			0.0598652
$479$	18.3344	+	31.7562i	0.837721	+	1.45098i	0.891795	+	0.452439i	$0.149446\pi$
$479$	18.3344	+	31.7562i	0.837721	+	1.45098i	−0.0540740	+	0.998537i	$0.517221\pi$
$480$	2.18169	+	3.44439i	0.0995802	+	0.157214i
$481$	6.27201	−	10.8634i	0.285979	−	0.495330i
$482$	7.55350	−	13.0830i	0.344053	−	0.595916i
$483$	−10.3288	+	0.423940i	−0.469977	+	0.0192899i
$484$	5.14988	+	8.91986i	0.234086	+	0.405448i
$485$	−7.49422			−0.340295
$486$	13.0321	+	14.6004i	0.591149	+	0.662286i
$487$	4.29419			0.194588			0.0972942	−	0.995256i	$-0.468981\pi$
$487$	4.29419			0.194588			0.0972942	+	0.995256i	$0.468981\pi$
$488$	−10.3833	−	17.9844i	−0.470029	−	0.814114i
$489$	−23.3225	+	0.957257i	−1.05468	+	0.0432887i
$490$	0.627726	−	1.08725i	0.0283578	−	0.0491171i
$491$	3.17148	−	5.49316i	0.143127	−	0.247903i	−0.785546	−	0.618804i	$-0.787618\pi$
$491$	3.17148	−	5.49316i	0.143127	−	0.247903i	0.928672	+	0.370901i	$0.120951\pi$
$492$	0.0214492	+	0.0338633i	0.000967004	+	0.00152668i
$493$	11.5210	+	19.9549i	0.518878	+	0.898723i
$494$	−26.2688			−1.18189
$495$	17.7644	−	1.46072i	0.798452	−	0.0656546i
$496$	−6.64514			−0.298376
$497$	−6.60069	−	11.4327i	−0.296081	−	0.512828i
$498$	−7.83378	+	14.9531i	−0.351040	+	0.670063i
$499$	−5.89554	+	10.2114i	−0.263921	+	0.457124i	−0.967280	−	0.253710i	$-0.918349\pi$
$499$	−5.89554	+	10.2114i	−0.263921	+	0.457124i	0.703360	+	0.710834i	$0.251682\pi$
$500$	0.211920	−	0.367057i	0.00947737	−	0.0164153i
$501$	−14.8894	+	28.4207i	−0.665207	+	1.26974i
$502$	3.91043	+	6.77306i	0.174531	+	0.302296i
$503$	−20.1116			−0.896732			−0.448366	−	0.893850i	$-0.647994\pi$
$503$	−20.1116			−0.896732			−0.448366	+	0.893850i	$0.647994\pi$
$504$	5.19707	+	7.50533i	0.231496	+	0.334314i
$505$	−11.6379			−0.517879
$506$	22.2597	+	38.5549i	0.989564	+	1.71398i
$507$	−0.802873	−	1.26755i	−0.0356569	−	0.0562940i
$508$	3.66010	−	6.33947i	0.162390	−	0.281269i
$509$	4.35841	−	7.54899i	0.193183	−	0.334603i	−0.753120	−	0.657883i	$-0.771452\pi$
$509$	4.35841	−	7.54899i	0.193183	−	0.334603i	0.946303	+	0.323280i	$0.104786\pi$
$510$	13.4570	−	0.552335i	0.595887	−	0.0244578i
$511$	0.637749	+	1.10461i	0.0282123	+	0.0488652i
$512$	25.0894			1.10881
$513$	28.9765	−	3.58408i	1.27934	−	0.158241i
$514$	17.2957			0.762882
$515$	1.66292	+	2.88027i	0.0732771	+	0.126920i
$516$	−3.97977	+	0.163347i	−0.175200	+	0.00719095i
$517$	10.2940	−	17.8296i	0.452728	−	0.784147i
$518$	2.11459	−	3.66258i	0.0929099	−	0.160925i
$519$	15.0250	+	23.7210i	0.659523	+	1.04124i
$520$	−5.66571	−	9.81329i	−0.248458	−	0.430341i
$521$	−24.6502			−1.07995			−0.539973	−	0.841682i	$-0.681566\pi$
$521$	−24.6502			−1.07995			−0.539973	+	0.841682i	$0.681566\pi$
$522$	5.98780	−	12.6677i	0.262079	−	0.554450i
$523$	−31.7891			−1.39004			−0.695020	−	0.718990i	$-0.744605\pi$
$523$	−31.7891			−1.39004			−0.695020	+	0.718990i	$0.744605\pi$
$524$	4.54928	+	7.87959i	0.198736	+	0.344222i
$525$	0.803782	−	1.53425i	0.0350799	−	0.0669603i
$526$	−12.6466	+	21.9045i	−0.551418	+	0.955083i
$527$	6.92277	−	11.9906i	0.301561	−	0.522318i
$528$	14.1965	−	27.0981i	0.617821	−	1.17929i
$529$	−6.31070	−	10.9305i	−0.274378	−	0.475237i
$530$	2.19658			0.0954132
$531$	12.3936	−	26.2198i	0.537838	−	1.13784i
$532$	2.38157			0.103254
$533$	−0.101664	−	0.176087i	−0.00440355	−	0.00762717i
$534$	−5.67905	−	8.96591i	−0.245756	−	0.387993i
$535$	−7.46386	+	12.9278i	−0.322691	+	0.558917i
$536$	−1.25101	+	2.16682i	−0.0540355	+	0.0935922i
$537$	29.0552	−	1.19255i	1.25382	−	0.0514624i
$538$	8.47365	+	14.6768i	0.365325	+	0.632761i
$539$	5.94147			0.255917
$540$	1.32697	+	1.75769i	0.0571036	+	0.0756388i
$541$	3.56166			0.153128			0.0765639	−	0.997065i	$-0.475605\pi$
$541$	3.56166			0.153128			0.0765639	+	0.997065i	$0.475605\pi$
$542$	8.68274	+	15.0389i	0.372956	+	0.645978i
$543$	24.5992	−	1.00966i	1.05565	−	0.0433286i
$544$	−7.28997	+	12.6266i	−0.312555	+	0.541361i
$545$	−7.55214	+	13.0807i	−0.323498	+	0.560315i
$546$	−4.33283	−	6.84054i	−0.185428	−	0.292748i
$547$	19.8413	+	34.3661i	0.848352	+	1.46939i	0.882678	+	0.469979i	$0.155738\pi$
$547$	19.8413	+	34.3661i	0.848352	+	1.46939i	−0.0343253	+	0.999411i	$0.510928\pi$
$548$	−5.46170			−0.233312
$549$	−11.6551	−	16.8316i	−0.497426	−	0.718356i
$550$	−7.45923			−0.318062
$551$	−10.4519	−	18.1033i	−0.445267	−	0.771225i
$552$	−14.5982	+	27.8649i	−0.621339	+	1.18601i
$553$	2.54186	−	4.40263i	0.108091	−	0.187219i
$554$	−2.79218	+	4.83620i	−0.118628	+	0.205470i
$555$	2.70767	−	5.16837i	0.114934	−	0.219385i
$556$	0.137364	+	0.237921i	0.00582553	+	0.0100901i
$557$	−23.2510			−0.985176			−0.492588	−	0.870263i	$-0.663949\pi$
$557$	−23.2510			−0.985176			−0.492588	+	0.870263i	$0.663949\pi$
$558$	−8.39102	+	0.689970i	−0.355220	+	0.0292088i
$559$	20.2041			0.854543
$560$	−1.48634	−	2.57441i	−0.0628093	−	0.108789i
$561$	34.1066	+	53.8465i	1.43998	+	2.27340i
$562$	8.79900	−	15.2403i	0.371163	−	0.642874i
$563$	5.85910	−	10.1483i	0.246931	−	0.427698i	−0.715741	−	0.698365i	$-0.753911\pi$
$563$	5.85910	−	10.1483i	0.246931	−	0.427698i	0.962673	+	0.270668i	$0.0872444\pi$
$564$	2.54165	−	0.104321i	0.107023	−	0.00439269i
$565$	6.95999	+	12.0551i	0.292809	+	0.507160i
$566$	−30.8004			−1.29464
$567$	5.71274	+	6.95446i	0.239913	+	0.292060i
$568$	−40.1720			−1.68558
$569$	−6.98246	−	12.0940i	−0.292720	−	0.507006i	0.681732	−	0.731602i	$-0.261227\pi$
$569$	−6.98246	−	12.0940i	−0.292720	−	0.507006i	−0.974452	+	0.224596i	$0.927894\pi$
$570$	−12.2083	+	0.501083i	−0.511351	+	0.0209881i
$571$	16.4450	−	28.4836i	0.688202	−	1.19200i	−0.284217	−	0.958760i	$-0.591734\pi$
$571$	16.4450	−	28.4836i	0.688202	−	1.19200i	0.972419	−	0.233241i	$-0.0749329\pi$
$572$	4.68863	−	8.12095i	0.196042	−	0.339554i
$573$	−14.4654	−	22.8375i	−0.604299	−	0.954049i
$574$	−0.0342757	−	0.0593673i	−0.00143064	−	0.00247794i
$575$	5.96837			0.248898
$576$	26.6122	−	2.18825i	1.10884	−	0.0911769i
$577$	−30.5346			−1.27117			−0.635586	−	0.772030i	$-0.719242\pi$
$577$	−30.5346			−1.27117			−0.635586	+	0.772030i	$0.719242\pi$
$578$	13.4098	+	23.2265i	0.557774	+	0.966093i
$579$	2.50241	−	4.77659i	0.103997	−	0.198508i
$580$	0.788385	−	1.36552i	0.0327359	−	0.0567002i
$581$	−3.88153	+	6.72301i	−0.161033	+	0.278917i
$582$	−7.56249	+	14.4352i	−0.313475	+	0.598360i
$583$	5.19769	+	9.00266i	0.215266	+	0.372852i
$584$	3.88136			0.160612
$585$	−6.35967	−	9.18429i	−0.262940	−	0.379723i
$586$	15.0438			0.621452
$587$	1.79966	+	3.11711i	0.0742801	+	0.128657i	0.900773	−	0.434290i	$-0.143001\pi$
$587$	1.79966	+	3.11711i	0.0742801	+	0.128657i	−0.826493	+	0.562947i	$0.809667\pi$
$588$	0.392821	+	0.620173i	0.0161996	+	0.0255755i
$589$	−6.28040	+	10.8780i	−0.258779	+	0.448219i
$590$	−6.06830	+	10.5106i	−0.249828	+	0.432715i
$591$	−25.0754	+	1.02920i	−1.03146	+	0.0423358i
$592$	−5.00696	−	8.67231i	−0.205785	−	0.356430i
$593$	−23.6263			−0.970215			−0.485107	−	0.874455i	$-0.661219\pi$
$593$	−23.6263			−0.970215			−0.485107	+	0.874455i	$0.661219\pi$
$594$	15.1127	−	35.6916i	0.620080	−	1.46444i
$595$	6.19375			0.253919
$596$	0.0385612	+	0.0667900i	0.00157953	+	0.00273583i
$597$	−30.3019	+	1.24372i	−1.24017	+	0.0509021i
$598$	13.9510	−	24.1638i	0.570499	−	0.988133i
$599$	−8.62393	+	14.9371i	−0.352364	+	0.610313i	−0.986663	−	0.162775i	$-0.947955\pi$
$599$	−8.62393	+	14.9371i	−0.352364	+	0.610313i	0.634299	+	0.773088i	$0.281289\pi$
$600$	−2.82030	−	4.45261i	−0.115138	−	0.181777i
$601$	−17.2737	−	29.9189i	−0.704609	−	1.22042i	−0.966832	−	0.255412i	$-0.917789\pi$
$601$	−17.2737	−	29.9189i	−0.704609	−	1.22042i	0.262223	−	0.965007i	$-0.415544\pi$
$602$	6.81177			0.277627
$603$	−1.05412	+	2.23007i	−0.0429270	+	0.0908156i
$604$	8.40460			0.341978
$605$	−12.1505	−	21.0453i	−0.493989	−	0.855613i
$606$	−11.7439	+	22.4167i	−0.477064	+	0.910616i
$607$	−10.2721	+	17.7918i	−0.416932	+	0.722147i	−0.995629	−	0.0933954i	$-0.970228\pi$
$607$	−10.2721	+	17.7918i	−0.416932	+	0.722147i	0.578697	+	0.815542i	$0.303561\pi$
$608$	6.61353	−	11.4550i	0.268214	−	0.464560i
$609$	2.99022	−	5.70772i	0.121170	−	0.231288i
$610$	4.28381	+	7.41978i	0.173446	+	0.300418i
$611$	−12.9032			−0.522009
$612$	−3.36556	+	7.12013i	−0.136045	+	0.287814i
$613$	−9.84761			−0.397741			−0.198871	−	0.980026i	$-0.563727\pi$
$613$	−9.84761			−0.397741			−0.198871	+	0.980026i	$0.563727\pi$
$614$	−17.9925	−	31.1638i	−0.726116	−	1.25767i
$615$	−0.0506067	−	0.0798964i	−0.00204066	−	0.00322173i
$616$	9.03999	−	15.6577i	0.364231	−	0.630867i
$617$	−6.85844	+	11.8792i	−0.276110	+	0.478237i	−0.970415	−	0.241444i	$-0.922379\pi$
$617$	−6.85844	+	11.8792i	−0.276110	+	0.478237i	0.694304	+	0.719682i	$0.255712\pi$
$618$	7.22598	−	0.296586i	0.290672	−	0.0119304i
$619$	1.60782	+	2.78482i	0.0646237	+	0.111931i	0.896527	−	0.442989i	$-0.146082\pi$
$619$	1.60782	+	2.78482i	0.0646237	+	0.111931i	−0.831903	+	0.554921i	$0.812749\pi$
$620$	−0.947456			−0.0380508
$621$	−12.0921	+	28.5580i	−0.485240	+	1.14599i
$622$	15.1451			0.607264
$623$	−2.44036	−	4.22683i	−0.0977710	−	0.169344i
$624$	−19.1568	+	0.786278i	−0.766885	+	0.0314763i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	16.3249	−	28.2756i	0.652474	−	1.13012i
$627$	−30.9418	−	48.8501i	−1.23570	−	1.95088i
$628$	0.251902	+	0.436306i	0.0100520	+	0.0174105i
$629$	20.8646			0.831926
$630$	−2.14415	−	3.09646i	−0.0854249	−	0.123366i
$631$	−46.2438			−1.84094			−0.920468	−	0.390818i	$-0.872192\pi$
$631$	−46.2438			−1.84094			−0.920468	+	0.390818i	$0.872192\pi$
$632$	−7.73491	−	13.3973i	−0.307678	−	0.532914i
$633$	−16.9449	+	32.3444i	−0.673501	+	1.28557i
$634$	15.3945	−	26.6640i	0.611393	−	1.05896i
$635$	−8.63554	+	14.9572i	−0.342691	+	0.593558i
$636$	−0.596056	+	1.13775i	−0.0236352	+	0.0451147i
$637$	−1.86187	−	3.22486i	−0.0737701	−	0.127774i
$638$	−27.7498			−1.09862
$639$	−39.4709	+	3.24558i	−1.56145	+	0.128393i
$640$	−6.46639			−0.255607
$641$	−13.3366	−	23.0996i	−0.526763	−	0.912381i	−0.999514	−	0.0311842i	$-0.990072\pi$
$641$	−13.3366	−	23.0996i	−0.526763	−	0.912381i	0.472750	−	0.881196i	$-0.343261\pi$
$642$	17.3694	+	27.4223i	0.685515	+	1.08227i
$643$	−15.2748	+	26.4567i	−0.602378	+	1.04335i	0.390082	+	0.920780i	$0.372447\pi$
$643$	−15.2748	+	26.4567i	−0.602378	+	1.04335i	−0.992460	+	0.122570i	$0.960887\pi$
$644$	−1.26482	+	2.19073i	−0.0498408	+	0.0863269i
$645$	9.38977	−	0.385397i	0.369722	−	0.0151750i
$646$	−21.8466	−	37.8395i	−0.859544	−	1.48877i
$647$	−21.1788			−0.832626			−0.416313	−	0.909221i	$-0.636678\pi$
$647$	−21.1788			−0.832626			−0.416313	+	0.909221i	$0.636678\pi$
$648$	27.0193	−	4.47369i	1.06142	−	0.175743i
$649$	−57.4369			−2.25460
$650$	2.33749	+	4.04865i	0.0916839	+	0.158801i
$651$	−3.86858	+	0.158783i	−0.151622	+	0.00622321i
$652$	−2.85596	+	4.94667i	−0.111848	+	0.193727i
$653$	9.83930	−	17.0422i	0.385042	−	0.666911i	−0.606733	−	0.794905i	$-0.707520\pi$
$653$	9.83930	−	17.0422i	0.385042	−	0.666911i	0.991775	+	0.127994i	$0.0408538\pi$
$654$	17.5749	+	27.7467i	0.687231	+	1.08498i
$655$	−10.7335	−	18.5909i	−0.419392	−	0.726408i
$656$	−0.162317			−0.00633742
$657$	3.81362	−	0.313584i	0.148784	−	0.0122341i
$658$	−4.35029			−0.169592
$659$	17.3478	+	30.0473i	0.675775	+	1.17048i	0.976242	+	0.216684i	$0.0695241\pi$
$659$	17.3478	+	30.0473i	0.675775	+	1.17048i	−0.300467	+	0.953792i	$0.597143\pi$
$660$	2.02411	−	3.86361i	0.0787885	−	0.150391i
$661$	−7.56071	+	13.0955i	−0.294077	+	0.509357i	−0.974770	−	0.223212i	$-0.928346\pi$
$661$	−7.56071	+	13.0955i	−0.294077	+	0.509357i	0.680692	+	0.732569i	$0.261679\pi$
$662$	6.24685	−	10.8199i	0.242791	−	0.420526i
$663$	18.5384	−	35.3859i	0.719971	−	1.37428i
$664$	11.8116	+	20.4582i	0.458377	+	0.793932i
$665$	−5.61903			−0.217896
$666$	−7.22289	−	10.4309i	−0.279881	−	0.404190i
$667$	22.2035			0.859722
$668$	3.92564	+	6.79940i	0.151887	+	0.263077i
$669$	−16.9556	−	26.7690i	−0.655542	−	1.03495i
$670$	0.516128	−	0.893959i	0.0199398	−	0.0345367i
$671$	−20.2733	+	35.1143i	−0.782641	+	1.35557i
$672$	4.07378	−	0.167206i	0.157149	−	0.00645010i
$673$	−14.4164	−	24.9699i	−0.555710	−	0.962517i	−0.997848	−	0.0655703i	$-0.979113\pi$
$673$	−14.4164	−	24.9699i	−0.555710	−	0.962517i	0.442138	−	0.896947i	$-0.354220\pi$
$674$	10.0052			0.385385
$675$	−3.13082	−	4.14704i	−0.120505	−	0.159620i
$676$	−0.367162			−0.0141216
$677$	−10.5482	−	18.2700i	−0.405399	−	0.702172i	0.588968	−	0.808156i	$-0.299534\pi$
$677$	−10.5482	−	18.2700i	−0.405399	−	0.702172i	−0.994368	+	0.105984i	$0.966201\pi$
$678$	30.2436	−	1.24133i	1.16150	−	0.0476730i
$679$	−3.74711	+	6.49019i	−0.143801	+	0.249070i
$680$	9.42383	−	16.3226i	0.361388	−	0.625942i
$681$	9.53948	+	15.0606i	0.365554	+	0.577125i
$682$	8.33720	+	14.4405i	0.319248	+	0.552954i
$683$	4.88979			0.187103			0.0935514	−	0.995614i	$-0.470178\pi$
$683$	4.88979			0.187103			0.0935514	+	0.995614i	$0.470178\pi$
$684$	3.05327	−	6.45945i	0.116745	−	0.246983i
$685$	12.8862			0.492357
$686$	−0.627726	−	1.08725i	−0.0239667	−	0.0415115i
$687$	8.50188	−	16.2283i	0.324367	−	0.619149i
$688$	8.06451	−	13.9681i	0.307456	−	0.532530i
$689$	3.25759	−	5.64231i	0.124104	−	0.214955i
$690$	6.02274	−	11.4962i	0.229282	−	0.437651i
$691$	12.2985	+	21.3016i	0.467857	+	0.810352i	0.999325	−	0.0367263i	$-0.0116930\pi$
$691$	12.2985	+	21.3016i	0.467857	+	0.810352i	−0.531469	+	0.847078i	$0.678360\pi$
$692$	6.87108			0.261199
$693$	7.61720	−	16.1148i	0.289354	−	0.612151i
$694$	25.1082			0.953094
$695$	−0.324093	−	0.561346i	−0.0122936	−	0.0212931i
$696$	−10.4921	−	16.5646i	−0.397701	−	0.627878i
$697$	0.169099	−	0.292888i	0.00640507	−	0.0110939i
$698$	15.5686	−	26.9655i	0.589278	−	1.02066i
$699$	17.9017	−	0.734763i	0.677104	−	0.0277913i
$700$	−0.211920	−	0.367057i	−0.00800984	−	0.0138734i
$701$	−25.8016			−0.974514			−0.487257	−	0.873259i	$-0.662003\pi$
$701$	−25.8016			−0.974514			−0.487257	+	0.873259i	$0.662003\pi$
$702$	−24.1082	+	2.98192i	−0.909906	+	0.112545i
$703$	−18.9286			−0.713904
$704$	−26.4415	−	45.7980i	−0.996551	−	1.72608i
$705$	−5.99672	+	0.246131i	−0.225849	+	0.00926985i
$706$	6.59361	−	11.4205i	0.248154	−	0.429815i
$707$	−5.81894	+	10.0787i	−0.218844	+	0.379049i
$708$	−3.79744	−	5.99529i	−0.142717	−	0.225317i
$709$	−2.46156	−	4.26355i	−0.0924460	−	0.160121i	0.816094	−	0.577919i	$-0.196135\pi$
$709$	−2.46156	−	4.26355i	−0.0924460	−	0.160121i	−0.908540	+	0.417798i	$0.862802\pi$
$710$	16.5737			0.621999
$711$	−8.68232	−	12.5385i	−0.325612	−	0.470232i
$712$	−14.8521			−0.556606
$713$	−6.67086	−	11.5543i	−0.249826	−	0.432711i
$714$	6.25017	−	11.9303i	0.233907	−	0.446480i
$715$	−11.0623	+	19.1604i	−0.413705	+	0.716558i
$716$	3.55796	−	6.16257i	0.132967	−	0.230306i
$717$	0.837967	−	1.59951i	0.0312945	−	0.0597346i
$718$	15.2594	+	26.4301i	0.569476	+	0.986362i
$719$	14.8760			0.554782			0.277391	−	0.960757i	$-0.410530\pi$
$719$	14.8760			0.554782			0.277391	+	0.960757i	$0.410530\pi$
$720$	−8.88804	+	0.730839i	−0.331238	+	0.0272368i
$721$	3.32584			0.123861
$722$	7.89268	+	13.6705i	0.293735	+	0.508764i
$723$	−11.1524	−	17.6071i	−0.414763	−	0.654816i
$724$	3.01230	−	5.21746i	0.111951	−	0.193905i
$725$	−1.86010	+	3.22178i	−0.0690822	+	0.119654i
$726$	−52.7983	+	2.16707i	−1.95953	+	0.0804276i
$727$	−13.2911	−	23.0209i	−0.492941	−	0.853799i	0.507026	−	0.861931i	$-0.330745\pi$
$727$	−13.2911	−	23.0209i	−0.492941	−	0.853799i	−0.999967	+	0.00813159i	$0.997412\pi$
$728$	−11.3314			−0.419970
$729$	26.1863	−	6.57856i	0.969863	−	0.243651i
$730$	−1.60133			−0.0592677
$731$	16.8029	+	29.1034i	0.621477	+	1.07643i
$732$	−5.00562	+	0.205453i	−0.185013	+	0.00759375i
$733$	−24.0055	+	41.5787i	−0.886662	+	1.53574i	−0.0428658	+	0.999081i	$0.513649\pi$
$733$	−24.0055	+	41.5787i	−0.886662	+	1.53574i	−0.843796	+	0.536663i	$0.819685\pi$
$734$	−0.0201547	+	0.0349089i	−0.000743923	+	0.00128851i
$735$	−0.926812	−	1.46322i	−0.0341860	−	0.0539718i
$736$	7.02470	+	12.1671i	0.258934	+	0.448487i
$737$	4.88518			0.179948
$738$	−0.204963	+	0.0168535i	−0.00754478	+	0.000620387i
$739$	28.3935			1.04447			0.522236	−	0.852801i	$-0.325098\pi$
$739$	28.3935			1.04447			0.522236	+	0.852801i	$0.325098\pi$
$740$	−0.713887	−	1.23649i	−0.0262430	−	0.0454542i
$741$	−16.8182	+	32.1024i	−0.617832	+	1.17931i
$742$	1.09829	−	1.90229i	0.0403194	−	0.0698353i
$743$	23.9650	−	41.5086i	0.879190	−	1.52280i	0.0269580	−	0.999637i	$-0.491418\pi$
$743$	23.9650	−	41.5086i	0.879190	−	1.52280i	0.852232	−	0.523165i	$-0.175249\pi$
$744$	−5.46763	+	10.4366i	−0.200453	+	0.382623i
$745$	−0.0909805	−	0.157583i	−0.00333327	−	0.00577339i
$746$	1.37766			0.0504397
$747$	13.2583	+	19.1469i	0.485095	+	0.700548i
$748$	15.5973			0.570294
$749$	7.46386	+	12.9278i	0.272723	+	0.472371i
$750$	1.16357	+	1.83701i	0.0424875	+	0.0670780i
$751$	−0.610216	+	1.05693i	−0.0222671	+	0.0385678i	−0.876944	−	0.480592i	$-0.840422\pi$
$751$	−0.610216	+	1.05693i	−0.0222671	+	0.0385678i	0.854677	+	0.519160i	$0.173755\pi$
$752$	−5.15034	+	8.92066i	−0.187814	+	0.325303i
$753$	10.7808	−	0.442489i	0.392873	−	0.0161252i
$754$	8.69592	+	15.0618i	0.316687	+	0.548517i
$755$	−19.8296			−0.721674
$756$	2.18569	−	0.270345i	0.0794926	−	0.00983237i
$757$	35.0173			1.27272			0.636362	−	0.771390i	$-0.280438\pi$
$757$	35.0173			1.27272			0.636362	+	0.771390i	$0.280438\pi$
$758$	−14.9839	−	25.9529i	−0.544241	−	0.942652i
$759$	61.3683	−	2.51882i	2.22753	−	0.0914275i
$760$	−8.54939	+	14.8080i	−0.310119	+	0.537142i
$761$	−2.47813	+	4.29224i	−0.0898320	+	0.155594i	−0.907440	−	0.420182i	$-0.861966\pi$
$761$	−2.47813	+	4.29224i	−0.0898320	+	0.155594i	0.817608	+	0.575775i	$0.195300\pi$
$762$	20.0961	+	31.7271i	0.728004	+	1.14935i
$763$	7.55214	+	13.0807i	0.273406	+	0.473553i
$764$	−6.61516			−0.239328
$765$	7.94064	−	16.7991i	0.287094	−	0.607372i
$766$	−10.7083			−0.386905
$767$	17.9989	+	31.1751i	0.649904	+	1.12567i
$768$	7.78308	−	14.8563i	0.280848	−	0.536080i
$769$	−7.92872	+	13.7329i	−0.285917	+	0.495223i	−0.972831	−	0.231516i	$-0.925631\pi$
$769$	−7.92872	+	13.7329i	−0.285917	+	0.495223i	0.686914	+	0.726738i	$0.258965\pi$
$770$	−3.72961	+	6.45988i	−0.134406	+	0.232798i
$771$	11.0733	−	21.1367i	0.398795	−	0.761218i
$772$	−0.659771	−	1.14276i	−0.0237457	−	0.0411287i
$773$	−29.3137			−1.05434			−0.527171	−	0.849759i	$-0.676747\pi$
$773$	−29.3137			−1.05434			−0.527171	+	0.849759i	$0.676747\pi$
$774$	8.73296	−	18.4753i	0.313900	−	0.664081i
$775$	2.23541			0.0802982
$776$	11.4025	+	19.7497i	0.409326	+	0.708974i
$777$	−3.12211	−	4.92909i	−0.112005	−	0.176830i
$778$	−11.8134	+	20.4614i	−0.423531	+	0.733577i
$779$	−0.153408	+	0.265710i	−0.00549641	+	0.00952006i
$780$	−2.73135	+	0.112107i	−0.0977981	+	0.00401406i
$781$	39.2178	+	67.9272i	1.40332	+	2.43062i
$782$	46.4097			1.65961
$783$	−11.6472	−	15.4278i	−0.416239	−	0.551345i
$784$	−2.97268			−0.106167
$785$	−0.594331	−	1.02941i	−0.0212126	−	0.0367413i
$786$	−46.6408	+	1.91434i	−1.66362	+	0.0682822i
$787$	23.9854	−	41.5439i	0.854987	−	1.48088i	−0.0216693	−	0.999765i	$-0.506898\pi$
$787$	23.9854	−	41.5439i	0.854987	−	1.48088i	0.876657	−	0.481116i	$-0.159769\pi$
$788$	−3.07061	+	5.31846i	−0.109386	+	0.189462i
$789$	18.6722	+	29.4791i	0.664747	+	1.04948i
$790$	3.19118	+	5.52728i	0.113537	+	0.196652i
$791$	13.9200			0.494938
$792$	−30.8782	−	44.5927i	−1.09721	−	1.58453i
$793$	25.4121			0.902409
$794$	−2.80135	−	4.85208i	−0.0994162	−	0.172194i
$795$	1.40632	−	2.68438i	0.0498771	−	0.0952050i
$796$	−3.71063	+	6.42699i	−0.131520	+	0.227799i
$797$	20.8320	−	36.0821i	0.737909	−	1.27810i	−0.215527	−	0.976498i	$-0.569147\pi$
$797$	20.8320	−	36.0821i	0.737909	−	1.27810i	0.953435	−	0.301597i	$-0.0975198\pi$
$798$	−5.67021	+	10.8233i	−0.200723	+	0.383139i
$799$	−10.7310	−	18.5867i	−0.379637	−	0.657551i
$800$	−2.35398			−0.0832257
$801$	−14.5929	+	1.19994i	−0.515615	+	0.0423976i
$802$	−26.9834			−0.952817
$803$	−3.78916	−	6.56302i	−0.133717	−	0.231604i
$804$	0.322984	+	0.509918i	0.0113908	+	0.0179834i
$805$	2.98418	−	5.16876i	0.105179	−	0.182175i
$806$	5.22524	−	9.05039i	0.184051	−	0.318786i
$807$	23.3612	−	0.958846i	0.822354	−	0.0337530i
$808$	17.7071	+	30.6697i	0.622935	+	1.07895i
$809$	32.4179			1.13975			0.569876	−	0.821730i	$-0.306991\pi$
$809$	32.4179			1.13975			0.569876	+	0.821730i	$0.306991\pi$
$810$	−11.1473	+	1.84570i	−0.391676	+	0.0648514i
$811$	−55.6693			−1.95481			−0.977406	−	0.211370i	$-0.932207\pi$
$811$	−55.6693			−1.95481			−0.977406	+	0.211370i	$0.932207\pi$
$812$	−0.788385	−	1.36552i	−0.0276669	−	0.0479204i
$813$	23.9377	−	0.982507i	0.839531	−	0.0344580i
$814$	−12.5638	+	21.7611i	−0.440360	+	0.762726i
$815$	6.73829	−	11.6711i	0.236032	−	0.408820i
$816$	−17.0645	−	26.9409i	−0.597376	−	0.943119i
$817$	−15.2437	−	26.4029i	−0.533310	−	0.923720i
$818$	3.67225			0.128397
$819$	−11.1337	+	0.915490i	−0.389042	+	0.0319898i
$820$	−0.0231430			−0.000808188
$821$	20.1434	+	34.8894i	0.703009	+	1.21765i	0.967405	+	0.253233i	$0.0814940\pi$
$821$	20.1434	+	34.8894i	0.703009	+	1.21765i	−0.264396	+	0.964414i	$0.585173\pi$
$822$	13.0036	−	24.8212i	0.453553	−	0.865738i
$823$	6.13861	−	10.6324i	0.213978	−	0.370621i	−0.738978	−	0.673730i	$-0.764691\pi$
$823$	6.13861	−	10.6324i	0.213978	−	0.370621i	0.952956	+	0.303108i	$0.0980245\pi$
$824$	5.06030	−	8.76469i	0.176284	−	0.305332i
$825$	−4.77564	+	9.11572i	−0.166267	+	0.317369i
$826$	6.06830	+	10.5106i	0.211143	+	0.365711i
$827$	−24.3336			−0.846161			−0.423080	−	0.906092i	$-0.639051\pi$
$827$	−24.3336			−0.846161			−0.423080	+	0.906092i	$0.639051\pi$
$828$	4.32029	+	6.23913i	0.150140	+	0.216825i
$829$	−25.2906			−0.878378			−0.439189	−	0.898395i	$-0.644734\pi$
$829$	−25.2906			−0.878378			−0.439189	+	0.898395i	$0.644734\pi$
$830$	−4.87307	−	8.44041i	−0.169147	−	0.292971i
$831$	4.12254	+	6.50854i	0.143009	+	0.225779i
$832$	−16.5719	+	28.7034i	−0.574527	+	0.995110i
$833$	3.09687	−	5.36394i	0.107300	−	0.185850i
$834$	−1.40830	+	0.0578028i	−0.0487654	+	0.00200155i
$835$	−9.26206	−	16.0424i	−0.320527	−	0.555169i
$836$	−14.1500			−0.489389
$837$	−4.52901	+	10.6962i	−0.156546	+	0.369714i
$838$	0.0981605			0.00339090
$839$	2.78722	+	4.82761i	0.0962256	+	0.166668i	0.910119	−	0.414346i	$-0.135990\pi$
$839$	2.78722	+	4.82761i	0.0962256	+	0.166668i	−0.813894	+	0.581014i	$0.802656\pi$
$840$	−5.26622	+	0.216149i	−0.181702	+	0.00745784i
$841$	7.58008	−	13.1291i	0.261382	−	0.452727i
$842$	16.4059	−	28.4159i	0.565386	−	0.979277i
$843$	−12.9914	−	20.5104i	−0.447446	−	0.706415i
$844$	4.46760	+	7.73812i	0.153781	+	0.266357i
$845$	0.866275			0.0298008
$846$	−5.57725	+	11.7991i	−0.191750	+	0.405663i
$847$	−24.3010			−0.834993
$848$	−2.60054	−	4.50427i	−0.0893030	−	0.154677i
$849$	−19.7194	+	37.6403i	−0.676769	+	1.29181i
$850$	−3.88798	+	6.73417i	−0.133356	+	0.230980i
$851$	10.0527	−	17.4118i	0.344602	−	0.596868i
$852$	−4.49739	+	8.58458i	−0.154078	+	0.294103i
$853$	−7.28300	−	12.6145i	−0.249365	−	0.431913i	0.713985	−	0.700161i	$-0.246889\pi$
$853$	−7.28300	−	12.6145i	−0.249365	−	0.431913i	−0.963350	+	0.268248i	$0.913555\pi$
$854$	8.56762			0.293178
$855$	−7.20382	+	15.2403i	−0.246365	+	0.521206i
$856$	45.4253			1.55260
$857$	7.35564	+	12.7403i	0.251264	+	0.435202i	0.963874	−	0.266358i	$-0.0858205\pi$
$857$	7.35564	+	12.7403i	0.251264	+	0.435202i	−0.712610	+	0.701560i	$0.752487\pi$
$858$	25.7434	+	40.6428i	0.878864	+	1.38752i
$859$	20.3981	−	35.3306i	0.695976	−	1.20547i	−0.273875	−	0.961765i	$-0.588306\pi$
$859$	20.3981	−	35.3306i	0.695976	−	1.20547i	0.969851	−	0.243700i	$-0.0783612\pi$
$860$	1.14983	−	1.99156i	0.0392088	−	0.0679116i
$861$	−0.0944957	+	0.00387851i	−0.00322040	+	0.000132179i
$862$	7.39000	+	12.7999i	0.251704	+	0.435965i
$863$	−4.77517			−0.162549			−0.0812744	−	0.996692i	$-0.525899\pi$
$863$	−4.77517			−0.162549			−0.0812744	+	0.996692i	$0.525899\pi$
$864$	4.76924	−	11.2635i	0.162253	−	0.383193i
$865$	−16.2115			−0.551206
$866$	22.6111	+	39.1636i	0.768357	+	1.33083i
$867$	36.9698	−	1.51740i	1.25556	−	0.0515337i
$868$	−0.473728	+	0.820521i	−0.0160794	+	0.0278503i
$869$	−15.1024	+	26.1581i	−0.512313	+	0.887351i
$870$	4.32869	+	6.83401i	0.146756	+	0.231695i
$871$	−1.53087	−	2.65154i	−0.0518714	−	0.0898439i
$872$	45.9626			1.55649
$873$	12.7991	+	18.4838i	0.433185	+	0.625583i
$874$	−42.1033			−1.42417
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	0.434531	−	0.829429i	0.0146814	−	0.0280238i
$877$	−3.85918	+	6.68429i	−0.130315	+	0.225712i	−0.923798	−	0.382880i	$-0.874932\pi$
$877$	−3.85918	+	6.68429i	−0.130315	+	0.225712i	0.793483	+	0.608593i	$0.208266\pi$
$878$	14.8890	−	25.7885i	0.502480	−	0.870320i
$879$	9.63152	−	18.3846i	0.324863	−	0.620096i
$880$	8.83103	+	15.2958i	0.297694	+	0.515621i
$881$	13.1164			0.441903			0.220951	−	0.975285i	$-0.429084\pi$
$881$	13.1164			0.441903			0.220951	+	0.975285i	$0.429084\pi$
$882$	−3.75369	+	0.308655i	−0.126393	+	0.0103930i
$883$	36.7965			1.23830			0.619150	−	0.785273i	$-0.287477\pi$
$883$	36.7965			1.23830			0.619150	+	0.785273i	$0.287477\pi$
$884$	−4.88772	−	8.46578i	−0.164392	−	0.284735i
$885$	8.95960	+	14.1452i	0.301174	+	0.475484i
$886$	−13.8067	+	23.9138i	−0.463844	+	0.803401i
$887$	−13.2081	+	22.8771i	−0.443484	+	0.768137i	−0.997945	−	0.0640727i	$-0.979591\pi$
$887$	−13.2081	+	22.8771i	−0.443484	+	0.768137i	0.554461	+	0.832210i	$0.312924\pi$
$888$	−17.7401	+	0.728131i	−0.595318	+	0.0244345i
$889$	8.63554	+	14.9572i	0.289627	+	0.501648i
$890$	6.12751			0.205395
$891$	−33.9421	−	41.3197i	−1.13710	−	1.38426i
$892$	−7.75399			−0.259623
$893$	9.73530	+	16.8620i	0.325780	+	0.564267i
$894$	−0.395343	+	0.0162266i	−0.0132222	+	0.000542698i
$895$	−8.39457	+	14.5398i	−0.280600	+	0.486013i
$896$	−3.23320	+	5.60006i	−0.108014	+	0.187085i
$897$	−20.5981	−	32.5196i	−0.687750	−	1.08580i
$898$	−0.936053	−	1.62129i	−0.0312365	−	0.0541032i
$899$	8.31614			0.277359
$900$	−1.26725	+	0.104202i	−0.0422415	+	0.00347340i
$901$	10.8368			0.361025
$902$	0.203648	+	0.352729i	0.00678074	+	0.0117446i
$903$	4.36112	−	8.32448i	0.145129	−	0.277021i
$904$	21.1794	−	36.6837i	0.704415	−	1.22008i
$905$	−7.10716	+	12.3100i	−0.236250	+	0.409197i
$906$	−20.0103	+	38.1954i	−0.664796	+	1.26896i
$907$	15.1348	+	26.2143i	0.502544	+	0.870432i	0.999996	+	0.00294038i	$0.000935954\pi$
$907$	15.1348	+	26.2143i	0.502544	+	0.870432i	−0.497451	+	0.867492i	$0.665731\pi$
$908$	4.36250			0.144775
$909$	19.8760	+	28.7038i	0.659245	+	0.952046i
$910$	4.67498			0.154974
$911$	−17.3716	−	30.0885i	−0.575547	−	0.996876i	−0.995982	−	0.0895537i	$-0.971456\pi$
$911$	−17.3716	−	30.0885i	−0.575547	−	0.996876i	0.420435	−	0.907323i	$-0.361877\pi$
$912$	15.4810	+	24.4410i	0.512629	+	0.809323i
$913$	23.0620	−	39.9445i	0.763240	−	1.32197i
$914$	−7.17947	+	12.4352i	−0.237476	+	0.411320i
$915$	11.8101	−	0.484740i	0.390431	−	0.0160250i
$916$	−2.24156	−	3.88249i	−0.0740631	−	0.128281i
$917$	−21.4670			−0.708901
$918$	−24.3451	−	32.2472i	−0.803508	−	1.06432i
$919$	5.64364			0.186166			0.0930832	−	0.995658i	$-0.470328\pi$
$919$	5.64364			0.186166			0.0930832	+	0.995658i	$0.470328\pi$
$920$	−9.08092	−	15.7286i	−0.299389	−	0.518557i
$921$	−49.6039	+	2.03596i	−1.63450	+	0.0670871i
$922$	−5.73682	+	9.93646i	−0.188932	+	0.327240i
$923$	24.5793	−	42.5725i	0.809037	−	1.40129i
$924$	−2.33393	−	3.68474i	−0.0767807	−	0.121219i
$925$	1.68433	+	2.91734i	0.0553804	+	0.0959216i
$926$	28.2294			0.927675
$927$	4.26387	−	9.02056i	0.140044	−	0.296274i
$928$	−8.75725			−0.287471
$929$	−10.0348	−	17.3808i	−0.329231	−	0.570246i	0.653128	−	0.757247i	$-0.273456\pi$
$929$	−10.0348	−	17.3808i	−0.329231	−	0.570246i	−0.982360	+	0.187002i	$0.940123\pi$
$930$	2.25577	−	4.30580i	0.0739696	−	0.141193i
$931$	−2.80951	+	4.86622i	−0.0920781	+	0.159484i
$932$	2.19216	−	3.79693i	0.0718065	−	0.124372i
$933$	9.69642	−	18.5085i	0.317446	−	0.605940i
$934$	−1.00761	−	1.74523i	−0.0329699	−	0.0571055i
$935$	−36.7999			−1.20349
$936$	−14.5273	+	30.7338i	−0.474841	+	1.00456i
$937$	15.5996			0.509618			0.254809	−	0.966991i	$-0.417987\pi$
$937$	15.5996			0.509618			0.254809	+	0.966991i	$0.417987\pi$
$938$	−0.516128	−	0.893959i	−0.0168522	−	0.0291888i
$939$	−24.1030	−	38.0532i	−0.786573	−	1.24182i
$940$	−0.734330	+	1.27190i	−0.0239512	+	0.0414847i
$941$	2.07600	−	3.59573i	0.0676756	−	0.117217i	−0.830202	−	0.557462i	$-0.811775\pi$
$941$	2.07600	−	3.59573i	0.0676756	−	0.117217i	0.897878	+	0.440245i	$0.145108\pi$
$942$	−2.58258	+	0.106000i	−0.0841449	+	0.00345368i
$943$	−0.162945	−	0.282230i	−0.00530623	−	0.00919067i
$944$	28.7372			0.935317
$945$	−5.15685	+	0.637847i	−0.167753	+	0.0207492i
$946$	−40.4719			−1.31586
$947$	19.4194	+	33.6354i	0.631045	+	1.09300i	0.987338	+	0.158628i	$0.0507071\pi$
$947$	19.4194	+	33.6354i	0.631045	+	1.09300i	−0.356293	+	0.934374i	$0.615960\pi$
$948$	−3.72889	+	0.153050i	−0.121109	+	0.00497082i
$949$	−2.37481	+	4.11330i	−0.0770897	+	0.133523i
$950$	3.52721	−	6.10930i	0.114438	−	0.198212i
$951$	−22.7293	−	35.8844i	−0.737048	−	1.16363i
$952$	−9.42383	−	16.3226i	−0.305428	−	0.529017i
$953$	26.2820			0.851359			0.425679	−	0.904874i	$-0.360035\pi$
$953$	26.2820			0.851359			0.425679	+	0.904874i	$0.360035\pi$
$954$	−3.75146	−	5.41766i	−0.121458	−	0.175403i
$955$	15.6077			0.505052
$956$	−0.220933	−	0.382668i	−0.00714550	−	0.0123764i
$957$	−17.7663	+	33.9122i	−0.574303	+	1.09623i
$958$	−23.0180	+	39.8683i	−0.743677	+	1.28809i
$959$	6.44311	−	11.1598i	0.208059	−	0.360368i
$960$	−7.15419	+	13.6559i	−0.230901	+	0.440741i
$961$	13.0015	+	22.5192i	0.419403	+	0.726427i
$962$	15.7484			0.507749
$963$	44.6325	−	3.67001i	1.43826	−	0.118264i
$964$	−5.10013			−0.164264
$965$	1.55665	+	2.69619i	0.0501103	+	0.0867936i
$966$	−6.94460	−	10.9639i	−0.223439	−	0.352758i
$967$	−9.51284	+	16.4767i	−0.305912	+	0.529856i	−0.977464	−	0.211102i	$-0.932295\pi$
$967$	−9.51284	+	16.4767i	−0.305912	+	0.529856i	0.671552	+	0.740958i	$0.265628\pi$
$968$	−36.9742	+	64.0412i	−1.18840	+	2.05836i
$969$	−60.2295	+	2.47208i	−1.93485	+	0.0794148i
$970$	−4.70432	−	8.14812i	−0.151047	−	0.261620i
$971$	−6.71639			−0.215539			−0.107770	−	0.994176i	$-0.534371\pi$
$971$	−6.71639			−0.215539			−0.107770	+	0.994176i	$0.534371\pi$
$972$	2.06889	−	6.27475i	0.0663597	−	0.201263i
$973$	−0.648187			−0.0207799
$974$	2.69558	+	4.66888i	0.0863718	+	0.149600i
$975$	6.44429	−	0.264502i	0.206382	−	0.00847084i
$976$	10.1433	−	17.5687i	0.324678	−	0.562359i
$977$	−15.7994	+	27.3654i	−0.505468	+	0.875497i	0.494512	+	0.869171i	$0.335347\pi$
$977$	−15.7994	+	27.3654i	−0.505468	+	0.875497i	−0.999980	+	0.00632594i	$0.997986\pi$
$978$	−15.6809	−	24.7566i	−0.501420	−	0.791628i
$979$	14.4993	+	25.1136i	0.463400	+	0.802633i
$980$	−0.423841			−0.0135391
$981$	45.1604	−	3.71342i	1.44186	−	0.118560i
$982$	7.96327			0.254118
$983$	−2.50377	−	4.33666i	−0.0798578	−	0.138318i	0.823331	−	0.567562i	$-0.192113\pi$
$983$	−2.50377	−	4.33666i	−0.0798578	−	0.138318i	−0.903188	+	0.429244i	$0.858780\pi$
$984$	−0.133555	+	0.254928i	−0.00425757	+	0.00812682i
$985$	7.24473	−	12.5482i	0.230836	−	0.399820i
$986$	−14.4640	+	25.0524i	−0.460628	+	0.797831i
$987$	−2.78520	+	5.31638i	−0.0886540	+	0.169222i
$988$	4.43418	+	7.68023i	0.141070	+	0.244341i
$989$	32.3829			1.02972
$990$	12.7394	+	18.3975i	0.404884	+	0.584711i
$991$	−31.9930			−1.01629			−0.508146	−	0.861271i	$-0.669669\pi$
$991$	−31.9930			−1.01629			−0.508146	+	0.861271i	$0.669669\pi$
$992$	2.63105	+	4.55711i	0.0835359	+	0.144688i
$993$	−9.22321	−	14.5613i	−0.292690	−	0.462090i
$994$	8.28684	−	14.3532i	0.262843	−	0.455257i
$995$	8.75477	−	15.1637i	0.277545	−	0.480722i
$996$	5.69417	−	0.233714i	0.180427	−	0.00740550i
$997$	12.3381	+	21.3701i	0.390750	+	0.676799i	0.992549	−	0.121849i	$-0.0388823\pi$
$997$	12.3381	+	21.3701i	0.390750	+	0.676799i	−0.601798	+	0.798648i	$0.705549\pi$
$998$	−14.8031			−0.468585
$999$	−17.3717	+	2.14869i	−0.549615	+	0.0679814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.f.211.6	yes	16
3.2	odd	2		945.2.i.f.631.3		16
9.2	odd	6		945.2.i.f.316.3		16
9.4	even	3		2835.2.a.x.1.3		8
9.5	odd	6		2835.2.a.y.1.6		8
9.7	even	3	inner	315.2.i.f.106.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.f.106.6	✓	16	9.7	even	3	inner
315.2.i.f.211.6	yes	16	1.1	even	1	trivial
945.2.i.f.316.3		16	9.2	odd	6
945.2.i.f.631.3		16	3.2	odd	2
2835.2.a.x.1.3		8	9.4	even	3
2835.2.a.y.1.6		8	9.5	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627726 + 1.08725i) q^{2} +(1.73059 - 0.0710311i) q^{3} +(0.211920 - 0.367057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.16357 + 1.83701i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.04302 q^{8} +(2.98991 - 0.245852i) q^{9} +O(q^{10})\)	\(q+(0.627726 + 1.08725i) q^{2} +(1.73059 - 0.0710311i) q^{3} +(0.211920 - 0.367057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.16357 + 1.83701i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.04302 q^{8} +(2.98991 - 0.245852i) q^{9} -1.25545 q^{10} +(-2.97073 - 5.14546i) q^{11} +(0.340676 - 0.650279i) q^{12} +(-1.86187 + 3.22486i) q^{13} +(-0.627726 + 1.08725i) q^{14} +(-0.803782 + 1.53425i) q^{15} +(1.48634 + 2.57441i) q^{16} -6.19375 q^{17} +(2.14415 + 3.09646i) q^{18} +5.61903 q^{19} +(0.211920 + 0.367057i) q^{20} +(0.926812 + 1.46322i) q^{21} +(3.72961 - 6.45988i) q^{22} +(-2.98418 + 5.16876i) q^{23} +(5.26622 - 0.216149i) q^{24} +(-0.500000 - 0.866025i) q^{25} -4.67498 q^{26} +(5.15685 - 0.637847i) q^{27} +0.423841 q^{28} +(-1.86010 - 3.22178i) q^{29} +(-2.17268 + 0.0891762i) q^{30} +(-1.11770 + 1.93592i) q^{31} +(1.17699 - 2.03860i) q^{32} +(-5.50662 - 8.69369i) q^{33} +(-3.88798 - 6.73417i) q^{34} -1.00000 q^{35} +(0.543381 - 1.14957i) q^{36} -3.36866 q^{37} +(3.52721 + 6.10930i) q^{38} +(-2.99308 + 5.71317i) q^{39} +(-1.52151 + 2.63533i) q^{40} +(-0.0273015 + 0.0472876i) q^{41} +(-1.00911 + 1.92618i) q^{42} +(-2.71288 - 4.69884i) q^{43} -2.51824 q^{44} +(-1.28204 + 2.71226i) q^{45} -7.49300 q^{46} +(1.73256 + 3.00088i) q^{47} +(2.75511 + 4.34969i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.627726 - 1.08725i) q^{50} +(-10.7189 + 0.439949i) q^{51} +(0.789137 + 1.36683i) q^{52} -1.74963 q^{53} +(3.93059 + 5.20641i) q^{54} +5.94147 q^{55} +(1.52151 + 2.63533i) q^{56} +(9.72425 - 0.399126i) q^{57} +(2.33526 - 4.04479i) q^{58} +(4.83356 - 8.37197i) q^{59} +(0.392821 + 0.620173i) q^{60} +(-3.41217 - 5.91005i) q^{61} -2.80645 q^{62} +(1.70787 + 2.46641i) q^{63} +8.90066 q^{64} +(-1.86187 - 3.22486i) q^{65} +(5.99559 - 11.4443i) q^{66} +(-0.411109 + 0.712062i) q^{67} +(-1.31258 + 2.27346i) q^{68} +(-4.79727 + 9.15699i) q^{69} +(-0.627726 - 1.08725i) q^{70} -13.2014 q^{71} +(9.09834 - 0.748131i) q^{72} +1.27550 q^{73} +(-2.11459 - 3.66258i) q^{74} +(-0.926812 - 1.46322i) q^{75} +(1.19079 - 2.06250i) q^{76} +(2.97073 - 5.14546i) q^{77} +(-8.09049 + 0.332069i) q^{78} +(-2.54186 - 4.40263i) q^{79} -2.97268 q^{80} +(8.87911 - 1.47015i) q^{81} -0.0685515 q^{82} +(3.88153 + 6.72301i) q^{83} +(0.733496 - 0.0301059i) q^{84} +(3.09687 - 5.36394i) q^{85} +(3.40589 - 5.89917i) q^{86} +(-3.44792 - 5.44347i) q^{87} +(-9.03999 - 15.6577i) q^{88} -4.88072 q^{89} +(-3.75369 + 0.308655i) q^{90} -3.72374 q^{91} +(1.26482 + 2.19073i) q^{92} +(-1.79678 + 3.42968i) q^{93} +(-2.17515 + 3.76746i) q^{94} +(-2.80951 + 4.86622i) q^{95} +(1.89208 - 3.61160i) q^{96} +(3.74711 + 6.49019i) q^{97} -1.25545 q^{98} +(-10.1472 - 14.6541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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