LMFDB - Embedded newform 570.2.u.i.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$2.57727i$ of defining polynomial
Character	$\chi$	$=$	570.301
Dual form			570.2.u.i.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-2.15664 - 3.73541i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-2.15664 - 3.73541i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.766044 - 0.642788i) q^{10} +(0.216948 - 0.375764i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.62838 - 0.956652i) q^{13} +(0.748993 - 4.24775i) q^{14} +(0.173648 + 0.984808i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.74595 - 1.46503i) q^{17} +1.00000 q^{18} +(-2.30141 - 3.70183i) q^{19} +1.00000 q^{20} +(3.30416 + 2.77252i) q^{21} +(0.407728 - 0.148401i) q^{22} +(-0.913569 - 5.18111i) q^{23} +(0.173648 - 0.984808i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-1.39853 - 2.42233i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(3.30416 - 2.77252i) q^{28} +(3.57021 - 2.99576i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.37951 + 4.12143i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0753451 + 0.427303i) q^{33} +(-0.395775 - 2.24455i) q^{34} +(-4.05316 + 1.47523i) q^{35} +(0.766044 + 0.642788i) q^{36} +4.91365 q^{37} +(0.616507 - 4.31508i) q^{38} +2.79706 q^{39} +(0.766044 + 0.642788i) q^{40} +(5.92281 - 2.15573i) q^{41} +(0.748993 + 4.24775i) q^{42} +(0.0742738 - 0.421228i) q^{43} +(0.407728 + 0.148401i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(2.63052 - 4.55619i) q^{46} +(-3.72989 + 3.12975i) q^{47} +(0.766044 - 0.642788i) q^{48} +(-5.80219 + 10.0497i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.14173 + 0.779525i) q^{51} +(0.485705 - 2.75457i) q^{52} +(0.542261 + 3.07532i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(-0.332383 - 0.278903i) q^{55} +4.31328 q^{56} +(3.42872 + 2.69145i) q^{57} +4.66058 q^{58} +(-5.18079 - 4.34720i) q^{59} +(-0.939693 + 0.342020i) q^{60} +(1.85333 + 10.5107i) q^{61} +(-0.826395 + 4.68672i) q^{62} +(-4.05316 - 1.47523i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.39853 + 2.42233i) q^{65} +(-0.332383 + 0.278903i) q^{66} +(7.44632 - 6.24820i) q^{67} +(1.13959 - 1.97383i) q^{68} +(2.63052 + 4.55619i) q^{69} +(-4.05316 - 1.47523i) q^{70} +(1.79015 - 10.1525i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-8.26505 + 3.00823i) q^{73} +(3.76407 + 3.15843i) q^{74} +1.00000 q^{75} +(3.24595 - 2.90926i) q^{76} -1.87151 q^{77} +(2.14267 + 1.79792i) q^{78} +(-16.1859 + 5.89119i) q^{79} +(0.173648 + 0.984808i) q^{80} +(0.173648 - 0.984808i) q^{81} +(5.92281 + 2.15573i) q^{82} +(-7.18750 - 12.4491i) q^{83} +(-2.15664 + 3.73541i) q^{84} +(-1.74595 + 1.46503i) q^{85} +(0.327657 - 0.274937i) q^{86} +(-2.33029 + 4.03618i) q^{87} +(0.216948 + 0.375764i) q^{88} +(-5.32515 - 1.93820i) q^{89} +(0.173648 - 0.984808i) q^{90} +(2.09498 + 11.8812i) q^{91} +(4.94375 - 1.79938i) q^{92} +(-3.64562 - 3.05904i) q^{93} -4.86903 q^{94} +(-4.04522 + 1.62363i) q^{95} +1.00000 q^{96} +(-6.06719 - 5.09098i) q^{97} +(-10.9046 + 3.96893i) q^{98} +(-0.0753451 - 0.427303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	−0.939693	−	0.342020i	−0.383628	−	0.139629i
$7$	−2.15664	−	3.73541i	−0.815133	−	1.41185i	−0.909232	−	0.416290i	$-0.863330\pi$
$7$	−2.15664	−	3.73541i	−0.815133	−	1.41185i	0.0940987	−	0.995563i	$-0.470003\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	0.766044	−	0.642788i	0.242245	−	0.203267i
$11$	0.216948	−	0.375764i	0.0654122	−	0.113297i	−0.831465	−	0.555578i	$-0.812497\pi$
$11$	0.216948	−	0.375764i	0.0654122	−	0.113297i	0.896877	+	0.442281i	$0.145830\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.62838	−	0.956652i	−0.728981	−	0.265327i	−0.0492476	−	0.998787i	$-0.515682\pi$
$13$	−2.62838	−	0.956652i	−0.728981	−	0.265327i	−0.679733	+	0.733459i	$0.737905\pi$
$14$	0.748993	−	4.24775i	0.200177	−	1.13526i
$15$	0.173648	+	0.984808i	0.0448358	+	0.254276i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.74595	−	1.46503i	−0.423456	−	0.355321i	0.406020	−	0.913864i	$-0.366916\pi$
$17$	−1.74595	−	1.46503i	−0.423456	−	0.355321i	−0.829476	+	0.558543i	$0.811361\pi$
$18$	1.00000			0.235702
$19$	−2.30141	−	3.70183i	−0.527979	−	0.849257i
$19$	−2.30141	−	3.70183i	−0.527979	−	0.849257i
$20$	1.00000			0.223607
$21$	3.30416	+	2.77252i	0.721028	+	0.605014i
$22$	0.407728	−	0.148401i	0.0869279	−	0.0316392i
$23$	−0.913569	−	5.18111i	−0.190492	−	1.08034i	−0.918693	−	0.394972i	$-0.870754\pi$
$23$	−0.913569	−	5.18111i	−0.190492	−	1.08034i	0.728201	−	0.685364i	$-0.240357\pi$
$24$	0.173648	−	0.984808i	0.0354458	−	0.201023i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−1.39853	−	2.42233i	−0.274274	−	0.475057i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	3.30416	−	2.77252i	0.624428	−	0.523958i
$29$	3.57021	−	2.99576i	0.662971	−	0.556299i	−0.248005	−	0.968759i	$-0.579775\pi$
$29$	3.57021	−	2.99576i	0.662971	−	0.556299i	0.910976	+	0.412460i	$0.135330\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	2.37951	+	4.12143i	0.427373	+	0.740231i	0.996639	−	0.0819223i	$-0.0261059\pi$
$31$	2.37951	+	4.12143i	0.427373	+	0.740231i	−0.569266	+	0.822153i	$0.692773\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−0.0753451	+	0.427303i	−0.0131159	+	0.0743840i
$34$	−0.395775	−	2.24455i	−0.0678749	−	0.384938i
$35$	−4.05316	+	1.47523i	−0.685109	+	0.249359i
$36$	0.766044	+	0.642788i	0.127674	+	0.107131i
$37$	4.91365			0.807799			0.403900	−	0.914803i	$-0.367655\pi$
$37$	4.91365			0.807799			0.403900	+	0.914803i	$0.367655\pi$
$38$	0.616507	−	4.31508i	0.100011	−	0.699998i
$39$	2.79706			0.447888
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	5.92281	−	2.15573i	0.924987	−	0.336668i	0.164767	−	0.986333i	$-0.447313\pi$
$41$	5.92281	−	2.15573i	0.924987	−	0.336668i	0.760221	+	0.649665i	$0.225091\pi$
$42$	0.748993	+	4.24775i	0.115572	+	0.655442i
$43$	0.0742738	−	0.421228i	0.0113267	−	0.0642366i	−0.978621	−	0.205674i	$-0.934061\pi$
$43$	0.0742738	−	0.421228i	0.0113267	−	0.0642366i	0.989947	+	0.141437i	$0.0451724\pi$
$44$	0.407728	+	0.148401i	0.0614673	+	0.0223723i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	2.63052	−	4.55619i	0.387848	−	0.671773i
$47$	−3.72989	+	3.12975i	−0.544060	+	0.456521i	−0.872924	−	0.487857i	$-0.837779\pi$
$47$	−3.72989	+	3.12975i	−0.544060	+	0.456521i	0.328863	+	0.944378i	$0.393334\pi$
$48$	0.766044	−	0.642788i	0.110569	−	0.0927784i
$49$	−5.80219	+	10.0497i	−0.828885	+	1.43567i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	2.14173	+	0.779525i	0.299902	+	0.109155i
$52$	0.485705	−	2.75457i	0.0673551	−	0.381990i
$53$	0.542261	+	3.07532i	0.0744853	+	0.422427i	0.999134	+	0.0416061i	$0.0132475\pi$
$53$	0.542261	+	3.07532i	0.0744853	+	0.422427i	−0.924649	+	0.380821i	$0.875641\pi$
$54$	−0.939693	+	0.342020i	−0.127876	+	0.0465430i
$55$	−0.332383	−	0.278903i	−0.0448185	−	0.0376072i
$56$	4.31328			0.576386
$57$	3.42872	+	2.69145i	0.454145	+	0.356491i
$58$	4.66058			0.611964
$59$	−5.18079	−	4.34720i	−0.674482	−	0.565958i	0.239906	−	0.970796i	$-0.422883\pi$
$59$	−5.18079	−	4.34720i	−0.674482	−	0.565958i	−0.914388	+	0.404839i	$0.867328\pi$
$60$	−0.939693	+	0.342020i	−0.121314	+	0.0441546i
$61$	1.85333	+	10.5107i	0.237294	+	1.34576i	0.837728	+	0.546088i	$0.183884\pi$
$61$	1.85333	+	10.5107i	0.237294	+	1.34576i	−0.600433	+	0.799675i	$0.705005\pi$
$62$	−0.826395	+	4.68672i	−0.104952	+	0.595214i
$63$	−4.05316	−	1.47523i	−0.510650	−	0.185861i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.39853	+	2.42233i	−0.173466	+	0.300453i
$66$	−0.332383	+	0.278903i	−0.0409135	+	0.0343305i
$67$	7.44632	−	6.24820i	0.909713	−	0.763340i	−0.0623517	−	0.998054i	$-0.519860\pi$
$67$	7.44632	−	6.24820i	0.909713	−	0.763340i	0.972064	+	0.234715i	$0.0754156\pi$
$68$	1.13959	−	1.97383i	0.138195	−	0.239362i
$69$	2.63052	+	4.55619i	0.316677	+	0.548501i
$70$	−4.05316	−	1.47523i	−0.484445	−	0.176324i
$71$	1.79015	−	10.1525i	0.212452	−	1.20488i	−0.672821	−	0.739805i	$-0.734918\pi$
$71$	1.79015	−	10.1525i	0.212452	−	1.20488i	0.885273	−	0.465071i	$-0.153971\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	−8.26505	+	3.00823i	−0.967351	+	0.352087i	−0.776910	−	0.629612i	$-0.783214\pi$
$73$	−8.26505	+	3.00823i	−0.967351	+	0.352087i	−0.190441	+	0.981699i	$0.560992\pi$
$74$	3.76407	+	3.15843i	0.437565	+	0.367160i
$75$	1.00000			0.115470
$76$	3.24595	−	2.90926i	0.372336	−	0.333715i
$77$	−1.87151			−0.213279
$78$	2.14267	+	1.79792i	0.242610	+	0.203574i
$79$	−16.1859	+	5.89119i	−1.82106	+	0.662811i	−0.825982	+	0.563697i	$0.809379\pi$
$79$	−16.1859	+	5.89119i	−1.82106	+	0.662811i	−0.995076	+	0.0991144i	$0.968399\pi$
$80$	0.173648	+	0.984808i	0.0194145	+	0.110105i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	5.92281	+	2.15573i	0.654065	+	0.238060i
$83$	−7.18750	−	12.4491i	−0.788931	−	1.36647i	−0.926622	−	0.375993i	$-0.877302\pi$
$83$	−7.18750	−	12.4491i	−0.788931	−	1.36647i	0.137692	−	0.990475i	$-0.456032\pi$
$84$	−2.15664	+	3.73541i	−0.235309	+	0.407567i
$85$	−1.74595	+	1.46503i	−0.189375	+	0.158905i
$86$	0.327657	−	0.274937i	0.0353322	−	0.0296472i
$87$	−2.33029	+	4.03618i	−0.249833	+	0.432724i
$88$	0.216948	+	0.375764i	0.0231267	+	0.0400566i
$89$	−5.32515	−	1.93820i	−0.564465	−	0.205448i	0.0439967	−	0.999032i	$-0.485991\pi$
$89$	−5.32515	−	1.93820i	−0.564465	−	0.205448i	−0.608462	+	0.793583i	$0.708213\pi$
$90$	0.173648	−	0.984808i	0.0183041	−	0.103808i
$91$	2.09498	+	11.8812i	0.219614	+	1.24549i
$92$	4.94375	−	1.79938i	0.515422	−	0.187598i
$93$	−3.64562	−	3.05904i	−0.378033	−	0.317208i
$94$	−4.86903			−0.502202
$95$	−4.04522	+	1.62363i	−0.415031	+	0.166581i
$96$	1.00000			0.102062
$97$	−6.06719	−	5.09098i	−0.616030	−	0.516910i	0.280523	−	0.959847i	$-0.409492\pi$
$97$	−6.06719	−	5.09098i	−0.616030	−	0.516910i	−0.896553	+	0.442937i	$0.853937\pi$
$98$	−10.9046	+	3.96893i	−1.10153	+	0.400923i
$99$	−0.0753451	−	0.427303i	−0.00757247	−	0.0429456i
$100$	0.173648	−	0.984808i	0.0173648	−	0.0984808i
$101$	13.5218	+	4.92154i	1.34547	+	0.489711i	0.911531	−	0.411231i	$-0.134901\pi$
$101$	13.5218	+	4.92154i	1.34547	+	0.489711i	0.433939	+	0.900942i	$0.357123\pi$
$102$	1.13959	+	1.97383i	0.112836	+	0.195438i
$103$	−0.430083	+	0.744926i	−0.0423773	+	0.0733997i	−0.886436	−	0.462851i	$-0.846827\pi$
$103$	−0.430083	+	0.744926i	−0.0423773	+	0.0733997i	0.844059	+	0.536251i	$0.180160\pi$
$104$	2.14267	−	1.79792i	0.210106	−	0.176300i
$105$	3.30416	−	2.77252i	0.322453	−	0.270571i
$106$	−1.56138	+	2.70439i	−0.151655	+	0.262673i
$107$	0.197611	+	0.342273i	0.0191038	+	0.0330887i	0.875419	−	0.483364i	$-0.160585\pi$
$107$	0.197611	+	0.342273i	0.0191038	+	0.0330887i	−0.856315	+	0.516453i	$0.827252\pi$
$108$	−0.939693	−	0.342020i	−0.0904220	−	0.0329109i
$109$	−2.18034	+	12.3653i	−0.208839	+	1.18438i	0.682445	+	0.730937i	$0.260917\pi$
$109$	−2.18034	+	12.3653i	−0.208839	+	1.18438i	−0.891284	+	0.453446i	$0.850194\pi$
$110$	−0.0753451	−	0.427303i	−0.00718388	−	0.0407418i
$111$	−4.61732	+	1.68057i	−0.438257	+	0.159512i
$112$	3.30416	+	2.77252i	0.312214	+	0.261979i
$113$	16.8594			1.58600			0.793000	−	0.609222i	$-0.208518\pi$
$113$	16.8594			1.58600			0.793000	+	0.609222i	$0.208518\pi$
$114$	0.896518	+	4.26571i	0.0839666	+	0.399520i
$115$	−5.26103			−0.490594
$116$	3.57021	+	2.99576i	0.331486	+	0.278149i
$117$	−2.62838	+	0.956652i	−0.242994	+	0.0884425i
$118$	−1.17439	−	6.66030i	−0.108111	−	0.613130i
$119$	−1.70709	+	9.68138i	−0.156489	+	0.887491i
$120$	−0.939693	−	0.342020i	−0.0857818	−	0.0312220i
$121$	5.40587	+	9.36324i	0.491442	+	0.851203i
$122$	−5.33644	+	9.24299i	−0.483139	+	0.836821i
$123$	−4.82832	+	4.05144i	−0.435355	+	0.365306i
$124$	−3.64562	+	3.05904i	−0.327386	+	0.274710i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	−2.15664	−	3.73541i	−0.192129	−	0.332777i
$127$	5.87531	+	2.13844i	0.521350	+	0.189756i	0.589272	−	0.807935i	$-0.299415\pi$
$127$	5.87531	+	2.13844i	0.521350	+	0.189756i	−0.0679221	+	0.997691i	$0.521637\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.0742738	+	0.421228i	0.00653944	+	0.0370870i
$130$	−2.62838	+	0.956652i	−0.230524	+	0.0839039i
$131$	4.20151	+	3.52549i	0.367088	+	0.308023i	0.807608	−	0.589719i	$-0.200762\pi$
$131$	4.20151	+	3.52549i	0.367088	+	0.308023i	−0.440520	+	0.897743i	$0.645206\pi$
$132$	−0.433895			−0.0377657
$133$	−8.86453	+	16.5802i	−0.768652	+	1.43769i
$134$	9.72048			0.839721
$135$	0.766044	+	0.642788i	0.0659306	+	0.0553223i
$136$	2.14173	−	0.779525i	0.183652	−	0.0668437i
$137$	−2.69157	−	15.2647i	−0.229956	−	1.30415i	−0.852980	−	0.521944i	$-0.825207\pi$
$137$	−2.69157	−	15.2647i	−0.229956	−	1.30415i	0.623023	−	0.782203i	$-0.285904\pi$
$138$	−0.913569	+	5.18111i	−0.0777681	+	0.441045i
$139$	−2.18765	−	0.796239i	−0.185554	−	0.0675361i	0.247572	−	0.968869i	$-0.420367\pi$
$139$	−2.18765	−	0.796239i	−0.185554	−	0.0675361i	−0.433126	+	0.901333i	$0.642590\pi$
$140$	−2.15664	−	3.73541i	−0.182269	−	0.315700i
$141$	2.43451	−	4.21670i	0.205023	−	0.355110i
$142$	7.89722	−	6.62656i	0.662720	−	0.556088i
$143$	−0.929696	+	0.780108i	−0.0777451	+	0.0652359i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.33029	−	4.03618i	−0.193520	−	0.335186i
$146$	−8.26505	−	3.00823i	−0.684020	−	0.248963i
$147$	2.01508	−	11.4281i	0.166201	−	0.942573i
$148$	0.853246	+	4.83900i	0.0701364	+	0.397763i
$149$	12.7752	−	4.64979i	1.04658	−	0.380925i	0.239212	−	0.970967i	$-0.423111\pi$
$149$	12.7752	−	4.64979i	1.04658	−	0.380925i	0.807373	+	0.590042i	$0.200889\pi$
$150$	0.766044	+	0.642788i	0.0625473	+	0.0524834i
$151$	14.2731			1.16153			0.580765	−	0.814071i	$-0.302753\pi$
$151$	14.2731			1.16153			0.580765	+	0.814071i	$0.302753\pi$
$152$	4.35658	−	0.142165i	0.353365	−	0.0115311i
$153$	−2.27918			−0.184261
$154$	−1.43366	−	1.20298i	−0.115528	−	0.0969393i
$155$	4.47202	−	1.62768i	0.359201	−	0.130738i
$156$	0.485705	+	2.75457i	0.0388875	+	0.220542i
$157$	−2.98145	+	16.9087i	−0.237946	+	1.34946i	0.598374	+	0.801217i	$0.295814\pi$
$157$	−2.98145	+	16.9087i	−0.237946	+	1.34946i	−0.836320	+	0.548242i	$0.815297\pi$
$158$	−16.1859	−	5.89119i	−1.28768	−	0.468678i
$159$	−1.56138	−	2.70439i	−0.123825	−	0.214472i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−17.3833	+	14.5863i	−1.37000	+	1.14956i
$162$	0.766044	−	0.642788i	0.0601861	−	0.0505022i
$163$	7.44242	−	12.8907i	0.582936	−	1.00967i	−0.412194	−	0.911096i	$-0.635237\pi$
$163$	7.44242	−	12.8907i	0.582936	−	1.00967i	0.995129	−	0.0985780i	$-0.0314294\pi$
$164$	3.15146	+	5.45849i	0.246088	+	0.426236i
$165$	0.407728	+	0.148401i	0.0317416	+	0.0115530i
$166$	2.49619	−	14.1566i	0.193742	−	1.09877i
$167$	1.77785	+	10.0827i	0.137574	+	0.780222i	0.973032	+	0.230668i	$0.0740911\pi$
$167$	1.77785	+	10.0827i	0.137574	+	0.780222i	−0.835458	+	0.549554i	$0.814798\pi$
$168$	−4.05316	+	1.47523i	−0.312708	+	0.113816i
$169$	−3.96539	−	3.32735i	−0.305030	−	0.255950i
$170$	−2.27918			−0.174805
$171$	−4.14247	−	1.35645i	−0.316783	−	0.103730i
$172$	0.427726			0.0326138
$173$	−6.33615	−	5.31666i	−0.481729	−	0.404218i	0.369322	−	0.929301i	$-0.379590\pi$
$173$	−6.33615	−	5.31666i	−0.481729	−	0.404218i	−0.851051	+	0.525083i	$0.824034\pi$
$174$	−4.37951	+	1.59401i	−0.332010	+	0.120842i
$175$	0.748993	+	4.24775i	0.0566186	+	0.321100i
$176$	−0.0753451	+	0.427303i	−0.00567935	+	0.0322092i
$177$	6.35518	+	2.31310i	0.477685	+	0.173863i
$178$	−2.83345	−	4.90769i	−0.212376	−	0.367847i
$179$	9.06473	−	15.7006i	0.677530	−	1.17352i	−0.298192	−	0.954506i	$-0.596384\pi$
$179$	9.06473	−	15.7006i	0.677530	−	1.17352i	0.975722	−	0.219011i	$-0.0702829\pi$
$180$	0.766044	−	0.642788i	0.0570976	−	0.0479106i
$181$	8.49175	−	7.12542i	0.631187	−	0.529628i	−0.270111	−	0.962829i	$-0.587060\pi$
$181$	8.49175	−	7.12542i	0.631187	−	0.529628i	0.901297	+	0.433201i	$0.142616\pi$
$182$	−6.03226	+	10.4482i	−0.447141	+	0.774470i
$183$	−5.33644	−	9.24299i	−0.394481	−	0.683262i
$184$	4.94375	+	1.79938i	0.364458	+	0.132652i
$185$	0.853246	−	4.83900i	0.0627319	−	0.355770i
$186$	−0.826395	−	4.68672i	−0.0605942	−	0.343647i
$187$	−0.929285	+	0.338232i	−0.0679561	+	0.0247340i
$188$	−3.72989	−	3.12975i	−0.272030	−	0.228260i
$189$	4.31328			0.313745
$190$	−4.14247	−	1.35645i	−0.300526	−	0.0984070i
$191$	−5.79147			−0.419056			−0.209528	−	0.977803i	$-0.567193\pi$
$191$	−5.79147			−0.419056			−0.209528	+	0.977803i	$0.567193\pi$
$192$	0.766044	+	0.642788i	0.0552845	+	0.0463892i
$193$	10.7300	−	3.90540i	0.772363	−	0.281117i	0.0743784	−	0.997230i	$-0.476303\pi$
$193$	10.7300	−	3.90540i	0.772363	−	0.281117i	0.697984	+	0.716113i	$0.254081\pi$
$194$	−1.37532	−	7.79983i	−0.0987423	−	0.559995i
$195$	0.485705	−	2.75457i	0.0347820	−	0.197259i
$196$	−10.9046	−	3.96893i	−0.778897	−	0.283495i
$197$	−7.69720	−	13.3319i	−0.548403	−	0.949861i	−0.998384	−	0.0568234i	$-0.981903\pi$
$197$	−7.69720	−	13.3319i	−0.548403	−	0.949861i	0.449982	−	0.893038i	$-0.351431\pi$
$198$	0.216948	−	0.375764i	0.0154178	−	0.0267044i
$199$	14.5582	−	12.2158i	1.03200	−	0.865954i	0.0409154	−	0.999163i	$-0.486973\pi$
$199$	14.5582	−	12.2158i	1.03200	−	0.865954i	0.991088	+	0.133209i	$0.0425281\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−4.86024	+	8.41818i	−0.342815	+	0.593773i
$202$	7.19480	+	12.4618i	0.506225	+	0.876807i
$203$	−18.8901	−	6.87542i	−1.32582	−	0.482560i
$204$	−0.395775	+	2.24455i	−0.0277098	+	0.157150i
$205$	−1.09449	−	6.20717i	−0.0764426	−	0.433527i
$206$	−0.808292	+	0.294194i	−0.0563164	+	0.0204975i
$207$	−4.03018	−	3.38173i	−0.280117	−	0.235046i
$208$	2.79706			0.193941
$209$	−1.89030	+	0.0616848i	−0.130755	+	0.00426683i
$210$	4.31328			0.297645
$211$	7.32350	+	6.14514i	0.504170	+	0.423049i	0.859072	−	0.511854i	$-0.171041\pi$
$211$	7.32350	+	6.14514i	0.504170	+	0.423049i	−0.354902	+	0.934904i	$0.615486\pi$
$212$	−2.93443	+	1.06805i	−0.201538	+	0.0733537i
$213$	1.79015	+	10.1525i	0.122659	+	0.695636i
$214$	−0.0686296	+	0.389218i	−0.00469143	+	0.0266064i
$215$	−0.401931	−	0.146291i	−0.0274115	−	0.00997695i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	10.2635	−	17.7769i	0.696731	−	1.20677i
$218$	−9.61852	+	8.07089i	−0.651448	+	0.546630i
$219$	6.73773	−	5.65363i	0.455294	−	0.382037i
$220$	0.216948	−	0.375764i	0.0146266	−	0.0253340i
$221$	3.18750	+	5.52091i	0.214415	+	0.371377i
$222$	−4.61732	−	1.68057i	−0.309894	−	0.112792i
$223$	−1.77100	+	10.0438i	−0.118595	+	0.672585i	0.866312	+	0.499503i	$0.166484\pi$
$223$	−1.77100	+	10.0438i	−0.118595	+	0.672585i	−0.984907	+	0.173083i	$0.944627\pi$
$224$	0.748993	+	4.24775i	0.0500442	+	0.283815i
$225$	−0.939693	+	0.342020i	−0.0626462	+	0.0228013i
$226$	12.9151	+	10.8370i	0.859097	+	0.720868i
$227$	14.5939			0.968630			0.484315	−	0.874894i	$-0.339069\pi$
$227$	14.5939			0.968630			0.484315	+	0.874894i	$0.339069\pi$
$228$	−2.05517	+	3.84399i	−0.136107	+	0.254575i
$229$	10.1931			0.673577			0.336789	−	0.941580i	$-0.390659\pi$
$229$	10.1931			0.673577			0.336789	+	0.941580i	$0.390659\pi$
$230$	−4.03018	−	3.38173i	−0.265743	−	0.222984i
$231$	1.75865	−	0.640095i	0.115710	−	0.0421151i
$232$	0.809301	+	4.58977i	0.0531332	+	0.301333i
$233$	−3.53084	+	20.0244i	−0.231313	+	1.31184i	0.618928	+	0.785448i	$0.287567\pi$
$233$	−3.53084	+	20.0244i	−0.231313	+	1.31184i	−0.850241	+	0.526393i	$0.823544\pi$
$234$	−2.62838	−	0.956652i	−0.171822	−	0.0625383i
$235$	2.43451	+	4.21670i	0.158810	+	0.275067i
$236$	3.38152	−	5.85697i	0.220118	−	0.381256i
$237$	13.1949	−	11.0718i	0.857100	−	0.719192i
$238$	−7.53078	+	6.31907i	−0.488148	+	0.409605i
$239$	−4.59299	+	7.95529i	−0.297096	+	0.514585i	−0.975470	−	0.220131i	$-0.929351\pi$
$239$	−4.59299	+	7.95529i	−0.297096	+	0.514585i	0.678374	+	0.734716i	$0.262685\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−19.3821	−	7.05451i	−1.24851	−	0.454421i	−0.368613	−	0.929583i	$-0.620167\pi$
$241$	−19.3821	−	7.05451i	−1.24851	−	0.454421i	−0.879899	+	0.475162i	$0.842390\pi$
$242$	−1.87744	+	10.6475i	−0.120686	+	0.684446i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−10.0292	+	3.65034i	−0.642056	+	0.233689i
$245$	8.88948	+	7.45916i	0.567928	+	0.476548i
$246$	−6.30292			−0.401860
$247$	2.50762	+	11.9314i	0.159556	+	0.759180i
$248$	−4.75902			−0.302198
$249$	11.0119	+	9.24007i	0.697850	+	0.585566i
$250$	−0.939693	+	0.342020i	−0.0594314	+	0.0216313i
$251$	−4.25055	−	24.1061i	−0.268293	−	1.52156i	−0.759492	−	0.650516i	$-0.774553\pi$
$251$	−4.25055	−	24.1061i	−0.268293	−	1.52156i	0.491200	−	0.871047i	$-0.336559\pi$
$252$	0.748993	−	4.24775i	0.0471821	−	0.267583i
$253$	−2.14507	−	0.780742i	−0.134859	−	0.0490848i
$254$	3.12619	+	5.41472i	0.196155	+	0.339750i
$255$	1.13959	−	1.97383i	0.0713638	−	0.123606i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.418919	−	0.351514i	0.0261314	−	0.0219269i	−0.629628	−	0.776896i	$-0.716793\pi$
$257$	0.418919	−	0.351514i	0.0261314	−	0.0219269i	0.655760	+	0.754970i	$0.272348\pi$
$258$	−0.213863	+	0.370421i	−0.0133145	+	0.0230614i
$259$	−10.5970	−	18.3545i	−0.658464	−	1.14049i
$260$	−2.62838	−	0.956652i	−0.163005	−	0.0593290i
$261$	0.809301	−	4.58977i	0.0500945	−	0.284100i
$262$	0.952406	+	5.40136i	0.0588398	+	0.333697i
$263$	12.2426	−	4.45593i	0.754909	−	0.274764i	0.0642391	−	0.997935i	$-0.479538\pi$
$263$	12.2426	−	4.45593i	0.754909	−	0.274764i	0.690670	+	0.723170i	$0.257316\pi$
$264$	−0.332383	−	0.278903i	−0.0204568	−	0.0171653i
$265$	3.12276			0.191829
$266$	−17.4482	+	7.00317i	−1.06982	+	0.429392i
$267$	5.66691			0.346809
$268$	7.44632	+	6.24820i	0.454856	+	0.381670i
$269$	26.5754	−	9.67265i	1.62033	−	0.589752i	0.636885	−	0.770959i	$-0.280223\pi$
$269$	26.5754	−	9.67265i	1.62033	−	0.589752i	0.983445	+	0.181207i	$0.0580005\pi$
$270$	0.173648	+	0.984808i	0.0105679	+	0.0599335i
$271$	−2.07979	+	11.7951i	−0.126338	+	0.716499i	0.854166	+	0.520000i	$0.174068\pi$
$271$	−2.07979	+	11.7951i	−0.126338	+	0.716499i	−0.980504	+	0.196498i	$0.937043\pi$
$272$	2.14173	+	0.779525i	0.129861	+	0.0472656i
$273$	−6.03226	−	10.4482i	−0.365089	−	0.632352i
$274$	7.75007	−	13.4235i	0.468199	−	0.810944i
$275$	−0.332383	+	0.278903i	−0.0200435	+	0.0168185i
$276$	−4.03018	+	3.38173i	−0.242589	+	0.203556i
$277$	0.431547	−	0.747461i	0.0259291	−	0.0449105i	−0.852770	−	0.522287i	$-0.825079\pi$
$277$	0.431547	−	0.747461i	0.0259291	−	0.0449105i	0.878699	+	0.477377i	$0.158412\pi$
$278$	−1.16402	−	2.01615i	−0.0698135	−	0.120921i
$279$	4.47202	+	1.62768i	0.267733	+	0.0974467i
$280$	0.748993	−	4.24775i	0.0447609	−	0.253852i
$281$	1.48262	+	8.40836i	0.0884457	+	0.501600i	0.996560	+	0.0828775i	$0.0264110\pi$
$281$	1.48262	+	8.40836i	0.0884457	+	0.501600i	−0.908114	+	0.418723i	$0.862478\pi$
$282$	4.57539	−	1.66531i	0.272460	−	0.0991675i
$283$	−7.09099	−	5.95005i	−0.421516	−	0.353694i	0.407224	−	0.913329i	$-0.366497\pi$
$283$	−7.09099	−	5.95005i	−0.421516	−	0.353694i	−0.828739	+	0.559635i	$0.810941\pi$
$284$	10.3091			0.611732
$285$	3.24595	−	2.90926i	0.192274	−	0.172330i
$286$	−1.21363			−0.0717636
$287$	−20.8259	−	17.4750i	−1.22931	−	1.03152i
$288$	−0.939693	+	0.342020i	−0.0553719	+	0.0201537i
$289$	−2.04998	−	11.6260i	−0.120587	−	0.683882i
$290$	0.809301	−	4.58977i	0.0475238	−	0.269521i
$291$	7.44251	+	2.70885i	0.436288	+	0.158796i
$292$	−4.39774	−	7.61711i	−0.257358	−	0.445758i
$293$	5.93387	−	10.2778i	0.346661	−	0.600434i	−0.638993	−	0.769212i	$-0.720649\pi$
$293$	5.93387	−	10.2778i	0.346661	−	0.600434i	0.985654	+	0.168778i	$0.0539822\pi$
$294$	8.88948	−	7.45916i	0.518445	−	0.435027i
$295$	−5.18079	+	4.34720i	−0.301637	+	0.253104i
$296$	−2.45682	+	4.25535i	−0.142800	+	0.247337i
$297$	0.216948	+	0.375764i	0.0125886	+	0.0218041i
$298$	12.7752	+	4.64979i	0.740047	+	0.269355i
$299$	−2.55531	+	14.4919i	−0.147777	+	0.838087i
$300$	0.173648	+	0.984808i	0.0100256	+	0.0568579i
$301$	−1.73364	+	0.630994i	−0.0999254	+	0.0363699i
$302$	10.9338	+	9.17459i	0.629172	+	0.527938i
$303$	−14.3896			−0.826661
$304$	3.42872	+	2.69145i	0.196650	+	0.154365i
$305$	10.6729			0.611128
$306$	−1.74595	−	1.46503i	−0.0998094	−	0.0837500i
$307$	−29.4040	+	10.7022i	−1.67818	+	0.610806i	−0.993058	−	0.117626i	$-0.962471\pi$
$307$	−29.4040	+	10.7022i	−1.67818	+	0.610806i	−0.685118	+	0.728432i	$0.740249\pi$
$308$	−0.324985	−	1.84308i	−0.0185177	−	0.105019i
$309$	0.149366	−	0.847098i	0.00849715	−	0.0481897i
$310$	4.47202	+	1.62768i	0.253993	+	0.0924460i
$311$	4.53912	+	7.86199i	0.257390	+	0.445812i	0.965542	−	0.260248i	$-0.0838042\pi$
$311$	4.53912	+	7.86199i	0.257390	+	0.445812i	−0.708152	+	0.706060i	$0.750471\pi$
$312$	−1.39853	+	2.42233i	−0.0791762	+	0.137137i
$313$	24.0651	−	20.1930i	1.36024	−	1.14138i	0.384335	−	0.923194i	$-0.374431\pi$
$313$	24.0651	−	20.1930i	1.36024	−	1.14138i	0.975907	−	0.218185i	$-0.0700135\pi$
$314$	−13.1526	+	11.0363i	−0.742245	+	0.622817i
$315$	−2.15664	+	3.73541i	−0.121513	+	0.210467i
$316$	−8.61235	−	14.9170i	−0.484482	−	0.839148i
$317$	11.6060	+	4.22424i	0.651858	+	0.237257i	0.646717	−	0.762730i	$-0.276141\pi$
$317$	11.6060	+	4.22424i	0.651858	+	0.237257i	0.00514102	+	0.999987i	$0.498364\pi$
$318$	0.542261	−	3.07532i	0.0304085	−	0.172455i
$319$	−0.351152	−	1.99148i	−0.0196607	−	0.111501i
$320$	−0.939693	+	0.342020i	−0.0525304	+	0.0191195i
$321$	−0.302758	−	0.254044i	−0.0168983	−	0.0141794i
$322$	−22.6923			−1.26459
$323$	−1.40513	+	9.83484i	−0.0781835	+	0.547225i
$324$	1.00000			0.0555556
$325$	2.14267	+	1.79792i	0.118854	+	0.0997305i
$326$	13.9872	−	5.09092i	0.774678	−	0.281960i
$327$	−2.18034	−	12.3653i	−0.120573	−	0.683804i
$328$	−1.09449	+	6.20717i	−0.0604331	+	0.342733i
$329$	19.7349	+	7.18293i	1.08802	+	0.396008i
$330$	0.216948	+	0.375764i	0.0119426	+	0.0206851i
$331$	17.9391	−	31.0715i	0.986025	−	1.70784i	0.348733	−	0.937222i	$-0.386612\pi$
$331$	17.9391	−	31.0715i	0.986025	−	1.70784i	0.637292	−	0.770622i	$-0.280055\pi$
$332$	11.0119	−	9.24007i	0.604356	−	0.507115i
$333$	3.76407	−	3.15843i	0.206270	−	0.173081i
$334$	−5.11912	+	8.86657i	−0.280106	+	0.485157i
$335$	−4.86024	−	8.41818i	−0.265543	−	0.459934i
$336$	−4.05316	−	1.47523i	−0.221118	−	0.0804803i
$337$	−0.156116	+	0.885375i	−0.00850416	+	0.0482295i	−0.988765	−	0.149481i	$-0.952240\pi$
$337$	−0.156116	+	0.885375i	−0.00850416	+	0.0482295i	0.980260	+	0.197711i	$0.0633507\pi$
$338$	−0.898880	−	5.09780i	−0.0488926	−	0.277284i
$339$	−15.8427	+	5.76626i	−0.860455	+	0.313180i
$340$	−1.74595	−	1.46503i	−0.0946875	−	0.0794523i
$341$	2.06492			0.111821
$342$	−2.30141	−	3.70183i	−0.124446	−	0.200172i
$343$	19.8600			1.07234
$344$	0.327657	+	0.274937i	0.0176661	+	0.0148236i
$345$	4.94375	−	1.79938i	0.266163	−	0.0968753i
$346$	−1.43629	−	8.14560i	−0.0772154	−	0.437910i
$347$	−5.62993	+	31.9289i	−0.302230	+	1.71403i	0.334033	+	0.942561i	$0.391590\pi$
$347$	−5.62993	+	31.9289i	−0.302230	+	1.71403i	−0.636264	+	0.771472i	$0.719521\pi$
$348$	−4.37951	−	1.59401i	−0.234766	−	0.0854480i
$349$	−6.42823	−	11.1340i	−0.344095	−	0.595991i	0.641094	−	0.767463i	$-0.278481\pi$
$349$	−6.42823	−	11.1340i	−0.344095	−	0.595991i	−0.985189	+	0.171472i	$0.945148\pi$
$350$	−2.15664	+	3.73541i	−0.115277	+	0.199666i
$351$	2.14267	−	1.79792i	0.114367	−	0.0959657i
$352$	−0.332383	+	0.278903i	−0.0177161	+	0.0148656i
$353$	−4.95014	+	8.57390i	−0.263470	+	0.456343i	−0.967162	−	0.254163i	$-0.918200\pi$
$353$	−4.95014	+	8.57390i	−0.263470	+	0.456343i	0.703692	+	0.710505i	$0.251534\pi$
$354$	3.38152	+	5.85697i	0.179726	+	0.311294i
$355$	−9.68738	−	3.52592i	−0.514153	−	0.187136i
$356$	0.984048	−	5.58082i	0.0521545	−	0.295783i
$357$	−1.70709	−	9.68138i	−0.0903487	−	0.512393i
$358$	17.0361	−	6.20064i	0.900387	−	0.327714i
$359$	−13.2019	−	11.0777i	−0.696772	−	0.584661i	0.224081	−	0.974570i	$-0.428062\pi$
$359$	−13.2019	−	11.0777i	−0.696772	−	0.584661i	−0.920853	+	0.389909i	$0.872506\pi$
$360$	1.00000			0.0527046
$361$	−8.40704	+	17.0388i	−0.442476	+	0.896781i
$362$	11.0852			0.582624
$363$	−8.28227	−	6.94965i	−0.434706	−	0.364762i
$364$	−11.3369	+	4.12631i	−0.594217	+	0.216277i
$365$	1.52732	+	8.66186i	0.0799436	+	0.453382i
$366$	1.85333	−	10.5107i	0.0968750	−	0.549405i
$367$	0.700652	+	0.255017i	0.0365737	+	0.0133118i	0.360242	−	0.932859i	$-0.382694\pi$
$367$	0.700652	+	0.255017i	0.0365737	+	0.0133118i	−0.323669	+	0.946171i	$0.604916\pi$
$368$	2.63052	+	4.55619i	0.137125	+	0.237508i
$369$	3.15146	−	5.45849i	0.164059	−	0.284158i
$370$	3.76407	−	3.15843i	0.195685	−	0.164199i
$371$	10.3181	−	8.65792i	0.535689	−	0.449497i
$372$	2.37951	−	4.12143i	0.123372	−	0.213686i
$373$	−10.9441	−	18.9557i	−0.566664	−	0.981490i	−0.996893	−	0.0787704i	$-0.974901\pi$
$373$	−10.9441	−	18.9557i	−0.566664	−	0.981490i	0.430229	−	0.902720i	$-0.358433\pi$
$374$	−0.929285	−	0.338232i	−0.0480522	−	0.0174896i
$375$	0.173648	−	0.984808i	0.00896715	−	0.0508553i
$376$	−0.845498	−	4.79506i	−0.0436032	−	0.247286i
$377$	−12.2498	+	4.45855i	−0.630895	+	0.229627i
$378$	3.30416	+	2.77252i	0.169948	+	0.142603i
$379$	−26.9827			−1.38601			−0.693004	−	0.720934i	$-0.743713\pi$
$379$	−26.9827			−1.38601			−0.693004	+	0.720934i	$0.743713\pi$
$380$	−2.30141	−	3.70183i	−0.118060	−	0.189900i
$381$	−6.25238			−0.320319
$382$	−4.43653	−	3.72269i	−0.226992	−	0.190469i
$383$	−3.56262	+	1.29669i	−0.182041	+	0.0662576i	−0.431433	−	0.902145i	$-0.641992\pi$
$383$	−3.56262	+	1.29669i	−0.182041	+	0.0662576i	0.249391	+	0.968403i	$0.419769\pi$
$384$	0.173648	+	0.984808i	0.00886145	+	0.0502558i
$385$	−0.324985	+	1.84308i	−0.0165628	+	0.0939320i
$386$	10.7300	+	3.90540i	0.546143	+	0.198780i
$387$	−0.213863	−	0.370421i	−0.0108713	−	0.0188296i
$388$	3.96008	−	6.85906i	0.201042	−	0.348216i
$389$	11.7937	−	9.89608i	0.597964	−	0.501751i	−0.292827	−	0.956166i	$-0.594596\pi$
$389$	11.7937	−	9.89608i	0.597964	−	0.501751i	0.890790	+	0.454414i	$0.150151\pi$
$390$	2.14267	−	1.79792i	0.108499	−	0.0910411i
$391$	−5.99542	+	10.3844i	−0.303201	+	0.525160i
$392$	−5.80219	−	10.0497i	−0.293055	−	0.507586i
$393$	−5.15392	−	1.87587i	−0.259981	−	0.0946253i
$394$	2.67321	−	15.1605i	0.134674	−	0.763776i
$395$	2.99104	+	16.9630i	0.150495	+	0.853502i
$396$	0.407728	−	0.148401i	0.0204891	−	0.00745743i
$397$	−0.320834	−	0.269212i	−0.0161022	−	0.0135114i	0.634701	−	0.772758i	$-0.281123\pi$
$397$	−0.320834	−	0.269212i	−0.0161022	−	0.0135114i	−0.650803	+	0.759246i	$0.725568\pi$
$398$	19.0044			0.952603
$399$	2.65917	−	18.6122i	0.133125	−	0.931773i
$400$	1.00000			0.0500000
$401$	16.2933	+	13.6717i	0.813650	+	0.682733i	0.951476	−	0.307723i	$-0.0995671\pi$
$401$	16.2933	+	13.6717i	0.813650	+	0.682733i	−0.137826	+	0.990456i	$0.544012\pi$
$402$	−9.13426	+	3.32460i	−0.455576	+	0.165816i
$403$	−2.31148	−	13.1090i	−0.115143	−	0.653008i
$404$	−2.49873	+	14.1710i	−0.124316	+	0.705033i
$405$	−0.939693	−	0.342020i	−0.0466937	−	0.0169951i
$406$	−10.0512	−	17.4092i	−0.498832	−	0.864002i
$407$	1.06600	−	1.84637i	0.0528399	−	0.0915214i
$408$	−1.74595	+	1.46503i	−0.0864375	+	0.0725297i
$409$	−11.6621	+	9.78567i	−0.576654	+	0.483870i	−0.883846	−	0.467777i	$-0.845055\pi$
$409$	−11.6621	+	9.78567i	−0.576654	+	0.483870i	0.307192	+	0.951647i	$0.400610\pi$
$410$	3.15146	−	5.45849i	0.155640	−	0.269576i
$411$	7.75007	+	13.4235i	0.382283	+	0.662133i
$412$	−0.808292	−	0.294194i	−0.0398217	−	0.0144939i
$413$	−5.06548	+	28.7277i	−0.249256	+	1.41360i
$414$	−0.913569	−	5.18111i	−0.0448995	−	0.254637i
$415$	−13.5081	+	4.91654i	−0.663086	+	0.241343i
$416$	2.14267	+	1.79792i	0.105053	+	0.0881501i
$417$	2.32805			0.114005
$418$	−1.48770	−	1.16781i	−0.0727660	−	0.0571193i
$419$	20.0229			0.978184			0.489092	−	0.872232i	$-0.337328\pi$
$419$	20.0229			0.978184			0.489092	+	0.872232i	$0.337328\pi$
$420$	3.30416	+	2.77252i	0.161227	+	0.135285i
$421$	35.1556	−	12.7956i	1.71338	−	0.623619i	0.716147	−	0.697950i	$-0.245904\pi$
$421$	35.1556	−	12.7956i	1.71338	−	0.623619i	0.997234	+	0.0743304i	$0.0236819\pi$
$422$	1.66010	+	9.41491i	0.0808125	+	0.458310i
$423$	−0.845498	+	4.79506i	−0.0411095	+	0.233144i
$424$	−2.93443	−	1.06805i	−0.142509	−	0.0518689i
$425$	1.13959	+	1.97383i	0.0552782	+	0.0957446i
$426$	−5.15455	+	8.92793i	−0.249739	+	0.432560i
$427$	35.2650	−	29.5908i	1.70659	−	1.43200i
$428$	−0.302758	+	0.254044i	−0.0146344	+	0.0122797i
$429$	0.606816	−	1.05104i	0.0292974	−	0.0507445i
$430$	−0.213863	−	0.370421i	−0.0103134	−	0.0178633i
$431$	−27.2087	−	9.90315i	−1.31060	−	0.477018i	−0.410163	−	0.912012i	$-0.634528\pi$
$431$	−27.2087	−	9.90315i	−1.31060	−	0.477018i	−0.900433	+	0.434994i	$0.856750\pi$
$432$	0.173648	−	0.984808i	0.00835465	−	0.0473816i
$433$	−4.60754	−	26.1307i	−0.221424	−	1.25576i	−0.869404	−	0.494102i	$-0.835497\pi$
$433$	−4.60754	−	26.1307i	−0.221424	−	1.25576i	0.647980	−	0.761658i	$-0.275614\pi$
$434$	19.2891	−	7.02064i	0.925904	−	0.337002i
$435$	3.57021	+	2.99576i	0.171178	+	0.143636i
$436$	−12.5561			−0.601327
$437$	−17.0771	+	15.3057i	−0.816907	+	0.732172i
$438$	8.79548			0.420264
$439$	−3.28003	−	2.75227i	−0.156547	−	0.131359i	0.561150	−	0.827714i	$-0.310359\pi$
$439$	−3.28003	−	2.75227i	−0.156547	−	0.131359i	−0.717697	+	0.696356i	$0.754804\pi$
$440$	0.407728	−	0.148401i	0.0194377	−	0.00707474i
$441$	2.01508	+	11.4281i	0.0959562	+	0.544195i
$442$	−1.10701	+	6.27815i	−0.0526550	+	0.298621i
$443$	15.0348	+	5.47222i	0.714325	+	0.259993i	0.673515	−	0.739174i	$-0.264784\pi$
$443$	15.0348	+	5.47222i	0.714325	+	0.259993i	0.0408105	+	0.999167i	$0.487006\pi$
$444$	−2.45682	−	4.25535i	−0.116596	−	0.201950i
$445$	−2.83345	+	4.90769i	−0.134319	+	0.232647i
$446$	−7.81272	+	6.55565i	−0.369943	+	0.310419i
$447$	−10.4144	+	8.73874i	−0.492586	+	0.413328i
$448$	−2.15664	+	3.73541i	−0.101892	+	0.176482i
$449$	−6.49477	−	11.2493i	−0.306507	−	0.530886i	0.671089	−	0.741377i	$-0.265827\pi$
$449$	−6.49477	−	11.2493i	−0.306507	−	0.530886i	−0.977596	+	0.210491i	$0.932494\pi$
$450$	−0.939693	−	0.342020i	−0.0442975	−	0.0161230i
$451$	0.474894	−	2.69326i	0.0223619	−	0.126821i
$452$	2.92761	+	16.6033i	0.137703	+	0.780953i
$453$	−13.4124	+	4.88170i	−0.630167	+	0.229362i
$454$	11.1796	+	9.38076i	0.524683	+	0.440261i
$455$	12.0645			0.565593
$456$	−4.04522	+	1.62363i	−0.189435	+	0.0760334i
$457$	−19.4669			−0.910625			−0.455313	−	0.890332i	$-0.650473\pi$
$457$	−19.4669			−0.910625			−0.455313	+	0.890332i	$0.650473\pi$
$458$	7.80835	+	6.55198i	0.364860	+	0.306154i
$459$	2.14173	−	0.779525i	0.0999673	−	0.0363851i
$460$	−0.913569	−	5.18111i	−0.0425954	−	0.241570i
$461$	2.64815	−	15.0184i	0.123336	−	0.699476i	−0.858946	−	0.512067i	$-0.828880\pi$
$461$	2.64815	−	15.0184i	0.123336	−	0.699476i	0.982282	−	0.187409i	$-0.0600089\pi$
$462$	1.75865	+	0.640095i	0.0818196	+	0.0297799i
$463$	15.3925	+	26.6606i	0.715351	+	1.23902i	0.962824	+	0.270129i	$0.0870664\pi$
$463$	15.3925	+	26.6606i	0.715351	+	1.23902i	−0.247473	+	0.968895i	$0.579600\pi$
$464$	−2.33029	+	4.03618i	−0.108181	+	0.187375i
$465$	−3.64562	+	3.05904i	−0.169062	+	0.141860i
$466$	−15.5762	+	13.0700i	−0.721554	+	0.605456i
$467$	17.1875	−	29.7697i	0.795344	−	1.37758i	−0.127276	−	0.991867i	$-0.540623\pi$
$467$	17.1875	−	29.7697i	0.795344	−	1.37758i	0.922620	−	0.385709i	$-0.126043\pi$
$468$	−1.39853	−	2.42233i	−0.0646471	−	0.111972i
$469$	−39.3986	−	14.3399i	−1.81926	−	0.662156i
$470$	−0.845498	+	4.79506i	−0.0389999	+	0.221179i
$471$	−2.98145	−	16.9087i	−0.137378	−	0.779110i
$472$	6.35518	−	2.31310i	0.292521	−	0.106469i
$473$	−0.142169	−	0.119294i	−0.00653693	−	0.00548514i
$474$	17.2247			0.791156
$475$	0.896518	+	4.26571i	0.0411350	+	0.195724i
$476$	−9.83074			−0.450591
$477$	2.39217	+	2.00727i	0.109530	+	0.0919066i
$478$	−8.63200	+	3.14179i	−0.394818	+	0.143702i
$479$	4.40594	+	24.9874i	0.201313	+	1.14170i	0.903137	+	0.429352i	$0.141258\pi$
$479$	4.40594	+	24.9874i	0.201313	+	1.14170i	−0.701825	+	0.712350i	$0.747631\pi$
$480$	0.173648	−	0.984808i	0.00792592	−	0.0449501i
$481$	−12.9149	−	4.70065i	−0.588870	−	0.214331i
$482$	−10.3130	−	17.8627i	−0.469745	−	0.813622i
$483$	11.3462	−	19.6521i	0.516268	−	0.894202i
$484$	−8.28227	+	6.94965i	−0.376467	+	0.315893i
$485$	−6.06719	+	5.09098i	−0.275497	+	0.231169i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	1.08155	+	1.87330i	0.0490097	+	0.0848874i	0.889490	−	0.456955i	$-0.151060\pi$
$487$	1.08155	+	1.87330i	0.0490097	+	0.0848874i	−0.840480	+	0.541843i	$0.817727\pi$
$488$	−10.0292	−	3.65034i	−0.454002	−	0.165243i
$489$	−2.58473	+	14.6587i	−0.116885	+	0.662890i
$490$	2.01508	+	11.4281i	0.0910321	+	0.516269i
$491$	−28.2596	+	10.2857i	−1.27534	+	0.464186i	−0.888888	−	0.458124i	$-0.848521\pi$
$491$	−28.2596	+	10.2857i	−1.27534	+	0.464186i	−0.386451	+	0.922310i	$0.626299\pi$
$492$	−4.82832	−	4.05144i	−0.217677	−	0.182653i
$493$	−10.6223			−0.478404
$494$	−5.74844	+	10.7519i	−0.258635	+	0.483750i
$495$	−0.433895			−0.0195021
$496$	−3.64562	−	3.05904i	−0.163693	−	0.137355i
$497$	−41.7844	+	15.2083i	−1.87429	+	0.682184i
$498$	2.49619	+	14.1566i	0.111857	+	0.634373i
$499$	−4.73979	+	26.8807i	−0.212182	+	1.20335i	0.673547	+	0.739144i	$0.264770\pi$
$499$	−4.73979	+	26.8807i	−0.212182	+	1.20335i	−0.885730	+	0.464201i	$0.846341\pi$
$500$	−0.939693	−	0.342020i	−0.0420243	−	0.0152956i
$501$	−5.11912	−	8.86657i	−0.228705	−	0.396129i
$502$	12.2390	−	21.1985i	0.546253	−	0.946137i
$503$	−8.81987	+	7.40075i	−0.393259	+	0.329983i	−0.817881	−	0.575387i	$-0.804851\pi$
$503$	−8.81987	+	7.40075i	−0.393259	+	0.329983i	0.424622	+	0.905371i	$0.360407\pi$
$504$	3.30416	−	2.77252i	0.147179	−	0.123498i
$505$	7.19480	−	12.4618i	0.320165	−	0.554541i
$506$	−1.14137	−	1.97691i	−0.0507400	−	0.0878843i
$507$	4.86427	+	1.77045i	0.216030	+	0.0786284i
$508$	−1.08571	+	6.15739i	−0.0481708	+	0.273190i
$509$	−5.97732	−	33.8991i	−0.264940	−	1.50255i	−0.769205	−	0.639002i	$-0.779348\pi$
$509$	−5.97732	−	33.8991i	−0.264940	−	1.50255i	0.504265	−	0.863549i	$-0.331763\pi$
$510$	2.14173	−	0.779525i	0.0948373	−	0.0345179i
$511$	29.0617	+	24.3857i	1.28561	+	1.07876i
$512$	1.00000			0.0441942
$513$	4.35658	−	0.142165i	0.192348	−	0.00627675i
$514$	0.546859			0.0241209
$515$	0.658926	+	0.552904i	0.0290357	+	0.0243639i
$516$	−0.401931	+	0.146291i	−0.0176940	+	0.00644010i
$517$	0.366857	+	2.08055i	0.0161344	+	0.0915026i
$518$	3.68029	−	20.8720i	0.161703	−	0.917062i
$519$	7.77244	+	2.82894i	0.341172	+	0.124177i
$520$	−1.39853	−	2.42233i	−0.0613296	−	0.106226i
$521$	−14.3002	+	24.7687i	−0.626504	+	1.08514i	0.361744	+	0.932277i	$0.382181\pi$
$521$	−14.3002	+	24.7687i	−0.626504	+	1.08514i	−0.988248	+	0.152859i	$0.951152\pi$
$522$	3.57021	−	2.99576i	0.156264	−	0.131121i
$523$	0.223899	−	0.187874i	0.00979043	−	0.00821515i	−0.637879	−	0.770136i	$-0.720188\pi$
$523$	0.223899	−	0.187874i	0.00979043	−	0.00821515i	0.647670	+	0.761921i	$0.275744\pi$
$524$	−2.74234	+	4.74988i	−0.119800	+	0.207499i
$525$	−2.15664	−	3.73541i	−0.0941235	−	0.163027i
$526$	12.2426	+	4.45593i	0.533801	+	0.194288i
$527$	1.88350	−	10.6819i	0.0820466	−	0.465309i
$528$	−0.0753451	−	0.427303i	−0.00327898	−	0.0185960i
$529$	−4.39632	+	1.60013i	−0.191144	+	0.0695709i
$530$	2.39217	+	2.00727i	0.103909	+	0.0871902i
$531$	−6.76305			−0.293491
$532$	−17.8676	−	5.85073i	−0.774660	−	0.253661i
$533$	−17.6297			−0.763625
$534$	4.34110	+	3.64262i	0.187858	+	0.157632i
$535$	0.371388	−	0.135174i	0.0160565	−	0.00584408i
$536$	1.68794	+	9.57280i	0.0729081	+	0.413482i
$537$	−3.14815	+	17.8540i	−0.135853	+	0.770459i
$538$	26.5754	+	9.67265i	1.14575	+	0.417017i
$539$	2.51754	+	4.36052i	0.108438	+	0.187821i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−31.2923	+	26.2574i	−1.34536	+	1.12889i	−0.365148	+	0.930949i	$0.618982\pi$
$541$	−31.2923	+	26.2574i	−1.34536	+	1.12889i	−0.980214	+	0.197943i	$0.936574\pi$
$542$	−9.17493	+	7.69868i	−0.394097	+	0.330687i
$543$	−5.54259	+	9.60005i	−0.237855	+	0.411978i
$544$	1.13959	+	1.97383i	0.0488595	+	0.0846271i
$545$	11.7989	+	4.29443i	0.505408	+	0.183953i
$546$	2.09498	−	11.8812i	0.0896569	−	0.508470i
$547$	−0.558704	−	3.16857i	−0.0238885	−	0.135478i	0.970531	−	0.240976i	$-0.0774675\pi$
$547$	−0.558704	−	3.16857i	−0.0238885	−	0.135478i	−0.994420	+	0.105498i	$0.966356\pi$
$548$	14.5654	−	5.30136i	0.622202	−	0.226463i
$549$	8.17591	+	6.86040i	0.348939	+	0.292795i
$550$	−0.433895			−0.0185014
$551$	−19.3063	−	6.32182i	−0.822476	−	0.269319i
$552$	−5.26103			−0.223924
$553$	56.9132	+	47.7559i	2.42020	+	2.03079i
$554$	0.811042	−	0.295195i	0.0344579	−	0.0125416i
$555$	0.853246	+	4.83900i	0.0362183	+	0.205404i
$556$	0.404261	−	2.29268i	0.0171445	−	0.0972312i
$557$	20.5784	+	7.48991i	0.871933	+	0.317358i	0.738950	−	0.673761i	$-0.235322\pi$
$557$	20.5784	+	7.48991i	0.871933	+	0.317358i	0.132983	+	0.991118i	$0.457544\pi$
$558$	2.37951	+	4.12143i	0.100733	+	0.174474i
$559$	−0.598188	+	1.03609i	−0.0253007	+	0.0438220i
$560$	3.30416	−	2.77252i	0.139626	−	0.117160i
$561$	0.757560	−	0.635669i	0.0319842	−	0.0268379i
$562$	−4.26903	+	7.39418i	−0.180078	+	0.311905i
$563$	14.6178	+	25.3188i	0.616068	+	1.06706i	0.990196	+	0.139685i	$0.0446089\pi$
$563$	14.6178	+	25.3188i	0.616068	+	1.06706i	−0.374128	+	0.927377i	$0.622058\pi$
$564$	4.57539	+	1.66531i	0.192659	+	0.0701220i
$565$	2.92761	−	16.6033i	0.123165	−	0.698505i
$566$	−1.60740	−	9.11601i	−0.0675640	−	0.383174i
$567$	−4.05316	+	1.47523i	−0.170217	+	0.0619538i
$568$	7.89722	+	6.62656i	0.331360	+	0.278044i
$569$	29.9248			1.25451			0.627257	−	0.778812i	$-0.284177\pi$
$569$	29.9248			1.25451			0.627257	+	0.778812i	$0.284177\pi$
$570$	4.35658	−	0.142165i	0.182477	−	0.00595465i
$571$	38.9094			1.62831			0.814153	−	0.580650i	$-0.197202\pi$
$571$	38.9094			1.62831			0.814153	+	0.580650i	$0.197202\pi$
$572$	−0.929696	−	0.780108i	−0.0388725	−	0.0326179i
$573$	5.44221	−	1.98080i	0.227351	−	0.0827491i
$574$	−4.72085	−	26.7732i	−0.197044	−	1.11749i
$575$	−0.913569	+	5.18111i	−0.0380985	+	0.216067i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	8.79483	+	15.2331i	0.366134	+	0.634162i	0.988957	−	0.148200i	$-0.0473479\pi$
$577$	8.79483	+	15.2331i	0.366134	+	0.634162i	−0.622824	+	0.782362i	$0.714015\pi$
$578$	5.90267	−	10.2237i	0.245519	−	0.425251i
$579$	−8.74718	+	7.33976i	−0.363520	+	0.305030i
$580$	3.57021	−	2.99576i	0.148245	−	0.124392i
$581$	−31.0017	+	53.6965i	−1.28617	+	2.22771i
$582$	3.96008	+	6.85906i	0.164150	+	0.284317i
$583$	1.27324	+	0.463420i	0.0527321	+	0.0191929i
$584$	1.52732	−	8.66186i	0.0632009	−	0.358430i
$585$	0.485705	+	2.75457i	0.0200814	+	0.113887i
$586$	11.1520	−	4.05901i	0.460686	−	0.167676i
$587$	−22.3451	−	18.7498i	−0.922281	−	0.773886i	0.0521343	−	0.998640i	$-0.483398\pi$
$587$	−22.3451	−	18.7498i	−0.922281	−	0.773886i	−0.974415	+	0.224754i	$0.927842\pi$
$588$	11.6044			0.478557
$589$	9.78060	−	18.2936i	0.403003	−	0.753776i
$590$	−6.76305			−0.278430
$591$	11.7928	+	9.89533i	0.485091	+	0.407039i
$592$	−4.61732	+	1.68057i	−0.189771	+	0.0690709i
$593$	2.49967	+	14.1763i	0.102649	+	0.582152i	0.992133	+	0.125186i	$0.0399528\pi$
$593$	2.49967	+	14.1763i	0.102649	+	0.582152i	−0.889484	+	0.456966i	$0.848936\pi$
$594$	−0.0753451	+	0.427303i	−0.00309145	+	0.0175325i
$595$	9.23787	+	3.36231i	0.378716	+	0.137841i
$596$	6.79753	+	11.7737i	0.278438	+	0.482269i
$597$	−9.50219	+	16.4583i	−0.388899	+	0.673592i
$598$	−11.2727	+	9.45890i	−0.460974	+	0.386803i
$599$	−27.9542	+	23.4564i	−1.14218	+	0.958401i	−0.999508	−	0.0313688i	$-0.990013\pi$
$599$	−27.9542	+	23.4564i	−1.14218	+	0.958401i	−0.142670	+	0.989770i	$0.545569\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−22.1554	−	38.3743i	−0.903739	−	1.56532i	−0.822601	−	0.568620i	$-0.807478\pi$
$601$	−22.1554	−	38.3743i	−0.903739	−	1.56532i	−0.0811387	−	0.996703i	$-0.525856\pi$
$602$	−1.73364	−	0.630994i	−0.0706579	−	0.0257174i
$603$	1.68794	−	9.57280i	0.0687384	−	0.389835i
$604$	2.47850	+	14.0563i	0.100849	+	0.571942i
$605$	10.1597	−	3.69783i	0.413051	−	0.150338i
$606$	−11.0231	−	9.24946i	−0.447782	−	0.375734i
$607$	−8.64242			−0.350785			−0.175392	−	0.984499i	$-0.556119\pi$
$607$	−8.64242			−0.350785			−0.175392	+	0.984499i	$0.556119\pi$
$608$	0.896518	+	4.26571i	0.0363586	+	0.172997i
$609$	20.1024			0.814589
$610$	8.17591	+	6.86040i	0.331033	+	0.277769i
$611$	12.7976	−	4.65796i	0.517737	−	0.188441i
$612$	−0.395775	−	2.24455i	−0.0159983	−	0.0907307i
$613$	−4.67009	+	26.4854i	−0.188623	+	1.06974i	0.732588	+	0.680673i	$0.238312\pi$
$613$	−4.67009	+	26.4854i	−0.188623	+	1.06974i	−0.921211	+	0.389063i	$0.872799\pi$
$614$	−29.4040	−	10.7022i	−1.18665	−	0.431905i
$615$	3.15146	+	5.45849i	0.127079	+	0.220108i
$616$	0.935756	−	1.62078i	0.0377027	−	0.0653030i
$617$	−21.3015	+	17.8740i	−0.857565	+	0.719582i	−0.961442	−	0.275008i	$-0.911319\pi$
$617$	−21.3015	+	17.8740i	−0.857565	+	0.719582i	0.103877	+	0.994590i	$0.466875\pi$
$618$	0.658926	−	0.552904i	0.0265059	−	0.0222411i
$619$	−22.7591	+	39.4200i	−0.914767	+	1.58442i	−0.107524	+	0.994202i	$0.534292\pi$
$619$	−22.7591	+	39.4200i	−0.914767	+	1.58442i	−0.807243	+	0.590220i	$0.799041\pi$
$620$	2.37951	+	4.12143i	0.0955634	+	0.165521i
$621$	4.94375	+	1.79938i	0.198386	+	0.0722066i
$622$	−1.57642	+	8.94032i	−0.0632087	+	0.358474i
$623$	4.24448	+	24.0716i	0.170051	+	0.964409i
$624$	−2.62838	+	0.956652i	−0.105219	+	0.0382967i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	31.4148			1.25559
$627$	1.75520	−	0.704485i	0.0700961	−	0.0281344i
$628$	−17.1695			−0.685138
$629$	−8.57900	−	7.19863i	−0.342067	−	0.287028i
$630$	−4.05316	+	1.47523i	−0.161482	+	0.0587745i
$631$	2.22197	+	12.6014i	0.0884552	+	0.501654i	0.996557	+	0.0829057i	$0.0264200\pi$
$631$	2.22197	+	12.6014i	0.0884552	+	0.501654i	−0.908102	+	0.418749i	$0.862469\pi$
$632$	2.99104	−	16.9630i	0.118977	−	0.674752i
$633$	−8.98360	−	3.26976i	−0.357066	−	0.129961i
$634$	6.17543	+	10.6962i	0.245258	+	0.424799i
$635$	3.12619	−	5.41472i	0.124059	−	0.214877i
$636$	2.39217	−	2.00727i	0.0948557	−	0.0795934i
$637$	24.8644	−	20.8637i	0.985164	−	0.826651i
$638$	1.01110	−	1.75128i	0.0400299	−	0.0693338i
$639$	−5.15455	−	8.92793i	−0.203911	−	0.353184i
$640$	−0.939693	−	0.342020i	−0.0371446	−	0.0135195i
$641$	2.26223	−	12.8298i	0.0893528	−	0.506745i	−0.906979	−	0.421175i	$-0.861618\pi$
$641$	2.26223	−	12.8298i	0.0893528	−	0.506745i	0.996332	−	0.0855699i	$-0.0272711\pi$
$642$	−0.0686296	−	0.389218i	−0.00270860	−	0.0153612i
$643$	15.5574	−	5.66244i	0.613525	−	0.223305i	−0.0165199	−	0.999864i	$-0.505259\pi$
$643$	15.5574	−	5.66244i	0.613525	−	0.223305i	0.630045	+	0.776559i	$0.283036\pi$
$644$	−17.3833	−	14.5863i	−0.684999	−	0.574782i
$645$	0.427726			0.0168417
$646$	−7.39810	+	6.63072i	−0.291074	+	0.260882i
$647$	7.36007			0.289354			0.144677	−	0.989479i	$-0.453786\pi$
$647$	7.36007			0.289354			0.144677	+	0.989479i	$0.453786\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	−2.75748	+	1.00364i	−0.108241	+	0.0393964i
$650$	0.485705	+	2.75457i	0.0190509	+	0.108043i
$651$	−3.56447	+	20.2151i	−0.139703	+	0.792294i
$652$	13.9872	+	5.09092i	0.547780	+	0.199376i
$653$	−7.62359	−	13.2044i	−0.298334	−	0.516730i	0.677421	−	0.735596i	$-0.263098\pi$
$653$	−7.62359	−	13.2044i	−0.298334	−	0.516730i	−0.975755	+	0.218866i	$0.929764\pi$
$654$	6.27804	−	10.8739i	0.245491	−	0.425203i
$655$	4.20151	−	3.52549i	0.164167	−	0.137752i
$656$	−4.82832	+	4.05144i	−0.188514	+	0.158182i
$657$	−4.39774	+	7.61711i	−0.171572	+	0.297172i
$658$	10.5007	+	18.1878i	0.409361	+	0.709035i
$659$	31.0913	+	11.3163i	1.21115	+	0.440821i	0.867101	−	0.498132i	$-0.165981\pi$
$659$	31.0913	+	11.3163i	1.21115	+	0.440821i	0.344044	+	0.938953i	$0.388203\pi$
$660$	−0.0753451	+	0.427303i	−0.00293280	+	0.0166328i
$661$	−4.47525	−	25.3804i	−0.174067	−	0.987183i	−0.939215	−	0.343329i	$-0.888446\pi$
$661$	−4.47525	−	25.3804i	−0.174067	−	0.987183i	0.765148	−	0.643854i	$-0.222666\pi$
$662$	33.7146	−	12.2711i	1.31035	−	0.476930i
$663$	−4.88354	−	4.09777i	−0.189661	−	0.159144i
$664$	14.3750			0.557858
$665$	14.7890	+	11.6090i	0.573493	+	0.450177i
$666$	4.91365			0.190400
$667$	−18.7830	−	15.7608i	−0.727280	−	0.610261i
$668$	−9.62079	+	3.50168i	−0.372240	+	0.135484i
$669$	−1.77100	−	10.0438i	−0.0684708	−	0.388317i
$670$	1.68794	−	9.57280i	0.0652109	−	0.369830i
$671$	4.35164	+	1.58387i	0.167993	+	0.0611445i
$672$	−2.15664	−	3.73541i	−0.0831942	−	0.144097i
$673$	−16.4872	+	28.5566i	−0.635533	+	1.10078i	0.350869	+	0.936425i	$0.385886\pi$
$673$	−16.4872	+	28.5566i	−0.635533	+	1.10078i	−0.986402	+	0.164351i	$0.947447\pi$
$674$	−0.688700	+	0.577888i	−0.0265277	+	0.0222594i
$675$	0.766044	−	0.642788i	0.0294851	−	0.0247409i
$676$	2.58822	−	4.48293i	0.0995470	−	0.172420i
$677$	6.47079	+	11.2077i	0.248693	+	0.430748i	0.963163	−	0.268917i	$-0.0866658\pi$
$677$	6.47079	+	11.2077i	0.248693	+	0.430748i	−0.714471	+	0.699665i	$0.753332\pi$
$678$	−15.8427	−	5.76626i	−0.608434	−	0.221452i
$679$	−5.93214	+	33.6429i	−0.227655	+	1.29109i
$680$	−0.395775	−	2.24455i	−0.0151773	−	0.0860747i
$681$	−13.7138	+	4.99140i	−0.525512	+	0.191271i
$682$	1.58182	+	1.32730i	0.0605709	+	0.0508250i
$683$	37.2633			1.42584			0.712921	−	0.701244i	$-0.247372\pi$
$683$	37.2633			1.42584			0.712921	+	0.701244i	$0.247372\pi$
$684$	0.616507	−	4.31508i	0.0235727	−	0.164991i
$685$	−15.5001			−0.592230
$686$	15.2137	+	12.7658i	0.580860	+	0.487400i
$687$	−9.57836	+	3.48624i	−0.365437	+	0.133008i
$688$	0.0742738	+	0.421228i	0.00283166	+	0.0160592i
$689$	1.51674	−	8.60185i	0.0577831	−	0.327704i
$690$	4.94375	+	1.79938i	0.188205	+	0.0685012i
$691$	−19.9952	−	34.6327i	−0.760654	−	1.31749i	−0.942514	−	0.334166i	$-0.891545\pi$
$691$	−19.9952	−	34.6327i	−0.760654	−	1.31749i	0.181861	−	0.983324i	$-0.441788\pi$
$692$	4.13563	−	7.16312i	0.157213	−	0.272301i
$693$	−1.43366	+	1.20298i	−0.0544603	+	0.0456976i
$694$	−24.8363	+	20.8401i	−0.942772	+	0.791080i
$695$	−1.16402	+	2.01615i	−0.0441539	+	0.0764769i
$696$	−2.33029	−	4.03618i	−0.0883294	−	0.152991i
$697$	−13.4991	−	4.91328i	−0.511316	−	0.186104i
$698$	2.23250	−	12.6611i	0.0845014	−	0.479231i
$699$	−3.53084	−	20.0244i	−0.133549	−	0.757392i
$700$	−4.05316	+	1.47523i	−0.153195	+	0.0557584i
$701$	−35.1068	−	29.4581i	−1.32597	−	1.11262i	−0.985002	−	0.172542i	$-0.944802\pi$
$701$	−35.1068	−	29.4581i	−1.32597	−	1.11262i	−0.340964	−	0.940076i	$-0.610754\pi$
$702$	2.79706			0.105568
$703$	−11.3083	−	18.1895i	−0.426501	−	0.686029i
$704$	−0.433895			−0.0163530
$705$	−3.72989	−	3.12975i	−0.140476	−	0.117873i
$706$	−9.30323	+	3.38610i	−0.350132	+	0.127437i
$707$	−10.7777	−	61.1235i	−0.405338	−	2.29879i
$708$	−1.17439	+	6.66030i	−0.0441363	+	0.250309i
$709$	−17.7234	−	6.45080i	−0.665617	−	0.242265i	−0.0129576	−	0.999916i	$-0.504125\pi$
$709$	−17.7234	−	6.45080i	−0.665617	−	0.242265i	−0.652660	+	0.757651i	$0.726347\pi$
$710$	−5.15455	−	8.92793i	−0.193447	−	0.335059i
$711$	−8.61235	+	14.9170i	−0.322988	+	0.559432i
$712$	4.34110	−	3.64262i	0.162690	−	0.136513i
$713$	19.1797	−	16.0937i	0.718286	−	0.602714i
$714$	4.91537	−	8.51367i	0.183953	−	0.318616i
$715$	0.606816	+	1.05104i	0.0226936	+	0.0393065i
$716$	17.0361	+	6.20064i	0.636670	+	0.231729i
$717$	1.59513	−	9.04643i	0.0595712	−	0.337845i
$718$	−2.99264	−	16.9721i	−0.111684	−	0.633393i
$719$	−23.5294	+	8.56399i	−0.877498	+	0.319383i	−0.741199	−	0.671285i	$-0.765743\pi$
$719$	−23.5294	+	8.56399i	−0.877498	+	0.319383i	−0.136298	+	0.990668i	$0.543520\pi$
$720$	0.766044	+	0.642788i	0.0285488	+	0.0239553i
$721$	3.71014			0.138173
$722$	−17.3925	+	7.64856i	−0.647282	+	0.284650i
$723$	20.6260			0.767090
$724$	8.49175	+	7.12542i	0.315593	+	0.264814i
$725$	−4.37951	+	1.59401i	−0.162651	+	0.0592001i
$726$	−1.87744	−	10.6475i	−0.0696783	−	0.395165i
$727$	−3.80054	+	21.5539i	−0.140954	+	0.799391i	0.829573	+	0.558399i	$0.188584\pi$
$727$	−3.80054	+	21.5539i	−0.140954	+	0.799391i	−0.970527	+	0.240992i	$0.922527\pi$
$728$	−11.3369	−	4.12631i	−0.420175	−	0.152931i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−4.39774	+	7.61711i	−0.162768	+	0.281922i
$731$	−0.746789	+	0.626630i	−0.0276210	+	0.0231768i
$732$	8.17591	−	6.86040i	0.302190	−	0.253568i
$733$	3.18195	−	5.51130i	0.117528	−	0.203565i	−0.801259	−	0.598317i	$-0.795836\pi$
$733$	3.18195	−	5.51130i	0.117528	−	0.203565i	0.918787	+	0.394753i	$0.129170\pi$
$734$	0.372809	+	0.645725i	0.0137606	+	0.0238341i
$735$	−10.9046	−	3.96893i	−0.402221	−	0.146396i
$736$	−0.913569	+	5.18111i	−0.0336746	+	0.190978i
$737$	−0.732391	−	4.15359i	−0.0269780	−	0.153000i
$738$	5.92281	−	2.15573i	0.218022	−	0.0793534i
$739$	−12.1729	−	10.2143i	−0.447786	−	0.375737i	0.390827	−	0.920464i	$-0.372189\pi$
$739$	−12.1729	−	10.2143i	−0.447786	−	0.375737i	−0.838614	+	0.544727i	$0.816633\pi$
$740$	4.91365			0.180629
$741$	−6.43718	−	10.3542i	−0.236476	−	0.380372i
$742$	13.4693			0.494475
$743$	13.0236	+	10.9281i	0.477790	+	0.400914i	0.849627	−	0.527385i	$-0.176827\pi$
$743$	13.0236	+	10.9281i	0.477790	+	0.400914i	−0.371836	+	0.928298i	$0.621272\pi$
$744$	4.47202	−	1.62768i	0.163952	−	0.0596737i
$745$	−2.36076	−	13.3885i	−0.0864915	−	0.490518i
$746$	3.80084	−	21.5557i	0.139159	−	0.789208i
$747$	−13.5081	−	4.91654i	−0.494235	−	0.179887i
$748$	−0.494462	−	0.856434i	−0.0180793	−	0.0313143i
$749$	0.852353	−	1.47632i	0.0311443	−	0.0539435i
$750$	0.766044	−	0.642788i	0.0279720	−	0.0234713i
$751$	6.77043	−	5.68107i	0.247057	−	0.207305i	−0.510847	−	0.859672i	$-0.670668\pi$
$751$	6.77043	−	5.68107i	0.247057	−	0.207305i	0.757904	+	0.652367i	$0.226224\pi$
$752$	2.43451	−	4.21670i	0.0887776	−	0.153767i
$753$	12.2390	+	21.1985i	0.446013	+	0.772518i
$754$	−12.2498	−	4.45855i	−0.446110	−	0.162371i
$755$	2.47850	−	14.0563i	0.0902019	−	0.511561i
$756$	0.748993	+	4.24775i	0.0272406	+	0.154489i
$757$	−2.49791	+	0.909165i	−0.0907881	+	0.0330442i	−0.387015	−	0.922073i	$-0.626494\pi$
$757$	−2.49791	+	0.909165i	−0.0907881	+	0.0330442i	0.296227	+	0.955118i	$0.404272\pi$
$758$	−20.6699	−	17.3441i	−0.750766	−	0.629968i
$759$	2.28274			0.0828581
$760$	0.616507	−	4.31508i	0.0223630	−	0.156524i
$761$	−38.8040			−1.40664			−0.703321	−	0.710872i	$-0.748300\pi$
$761$	−38.8040			−1.40664			−0.703321	+	0.710872i	$0.748300\pi$
$762$	−4.78960	−	4.01895i	−0.173509	−	0.145591i
$763$	50.8918	−	18.5231i	1.84241	−	0.670581i
$764$	−1.00568	−	5.70349i	−0.0363842	−	0.206345i
$765$	−0.395775	+	2.24455i	−0.0143093	+	0.0811520i
$766$	−3.56262	−	1.29669i	−0.128723	−	0.0468512i
$767$	9.45833	+	16.3823i	0.341520	+	0.591531i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	15.0232	−	12.6060i	0.541752	−	0.454584i	−0.330385	−	0.943846i	$-0.607178\pi$
$769$	15.0232	−	12.6060i	0.541752	−	0.454584i	0.872137	+	0.489263i	$0.162734\pi$
$770$	−1.43366	+	1.20298i	−0.0516656	+	0.0433526i
$771$	−0.273430	+	0.473594i	−0.00984733	+	0.0170561i
$772$	5.70932	+	9.88883i	0.205483	+	0.355907i
$773$	3.31804	+	1.20767i	0.119342	+	0.0434368i	0.401001	−	0.916078i	$-0.368662\pi$
$773$	3.31804	+	1.20767i	0.119342	+	0.0434368i	−0.281659	+	0.959515i	$0.590885\pi$
$774$	0.0742738	−	0.421228i	0.00266972	−	0.0151407i
$775$	−0.826395	−	4.68672i	−0.0296850	−	0.168352i
$776$	7.44251	−	2.70885i	0.267171	−	0.0972421i
$777$	16.2355	+	13.6232i	0.582446	+	0.488730i
$778$	15.3956			0.551958
$779$	−21.6109	−	16.9640i	−0.774292	−	0.607799i
$780$	2.79706			0.100151
$781$	−3.42657	−	2.87523i	−0.122612	−	0.102884i
$782$	−11.2677	+	4.10111i	−0.402932	+	0.146655i
$783$	0.809301	+	4.58977i	0.0289220	+	0.164025i
$784$	2.01508	−	11.4281i	0.0719672	−	0.408146i
$785$	16.1341	+	5.87232i	0.575849	+	0.209592i
$786$	−2.74234	−	4.74988i	−0.0978162	−	0.169423i
$787$	−3.59410	+	6.22517i	−0.128116	+	0.221903i	−0.922947	−	0.384928i	$-0.874226\pi$
$787$	−3.59410	+	6.22517i	−0.128116	+	0.221903i	0.794831	+	0.606831i	$0.207560\pi$
$788$	11.7928	−	9.89533i	0.420101	−	0.352506i
$789$	−9.98023	+	8.37441i	−0.355306	+	0.298137i
$790$	−8.61235	+	14.9170i	−0.306414	+	0.530724i
$791$	−36.3597	−	62.9768i	−1.29280	−	2.23920i
$792$	0.407728	+	0.148401i	0.0144880	+	0.00527320i
$793$	5.18387	−	29.3992i	0.184085	−	1.04400i
$794$	−0.0727272	−	0.412457i	−0.00258099	−	0.0146375i
$795$	−2.93443	+	1.06805i	−0.104074	+	0.0378797i
$796$	14.5582	+	12.2158i	0.516002	+	0.432977i
$797$	26.8856			0.952335			0.476168	−	0.879355i	$-0.342026\pi$
$797$	26.8856			0.952335			0.476168	+	0.879355i	$0.342026\pi$
$798$	14.0007	−	12.5485i	0.495619	−	0.444211i
$799$	11.0974			0.392597
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−5.32515	+	1.93820i	−0.188155	+	0.0684828i
$802$	3.69340	+	20.9463i	0.130418	+	0.739639i
$803$	−0.662697	+	3.75834i	−0.0233861	+	0.132629i
$804$	−9.13426	−	3.32460i	−0.322141	−	0.117250i
$805$	11.3462	+	19.6521i	0.399899	+	0.692646i
$806$	6.65564	−	11.5279i	0.234435	−	0.406053i
$807$	−21.6645	+	18.1786i	−0.762625	+	0.639918i
$808$	−11.0231	+	9.24946i	−0.387791	+	0.325395i
$809$	0.116363	−	0.201547i	0.00409112	−	0.00708602i	−0.863973	−	0.503539i	$-0.832031\pi$
$809$	0.116363	−	0.201547i	0.00409112	−	0.00708602i	0.868064	+	0.496453i	$0.165364\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	11.6046	+	4.22372i	0.407492	+	0.148315i	0.537630	−	0.843181i	$-0.319320\pi$
$811$	11.6046	+	4.22372i	0.407492	+	0.148315i	−0.130138	+	0.991496i	$0.541542\pi$
$812$	3.49074	−	19.7970i	0.122501	−	0.694738i
$813$	−2.07979	−	11.7951i	−0.0729413	−	0.413671i
$814$	2.00343	−	0.729190i	0.0702203	−	0.0255581i
$815$	−11.4025	−	9.56780i	−0.399411	−	0.335145i
$816$	−2.27918			−0.0797872
$817$	−1.73025	+	0.694468i	−0.0605337	+	0.0242964i
$818$	−15.2238			−0.532287
$819$	9.24195	+	7.75492i	0.322940	+	0.270979i
$820$	5.92281	−	2.15573i	0.206833	−	0.0752812i
$821$	−5.65820	−	32.0893i	−0.197473	−	1.11992i	−0.908853	−	0.417116i	$-0.863041\pi$
$821$	−5.65820	−	32.0893i	−0.197473	−	1.11992i	0.711381	−	0.702807i	$-0.248070\pi$
$822$	−2.69157	+	15.2647i	−0.0938793	+	0.532416i
$823$	51.1209	+	18.6065i	1.78196	+	0.648582i	0.999670	+	0.0256711i	$0.00817226\pi$
$823$	51.1209	+	18.6065i	1.78196	+	0.648582i	0.782293	+	0.622911i	$0.214050\pi$
$824$	−0.430083	−	0.744926i	−0.0149827	−	0.0259507i
$825$	0.216948	−	0.375764i	0.00755315	−	0.0130824i
$826$	−22.3462	+	18.7507i	−0.777524	+	0.652420i
$827$	27.8955	−	23.4071i	0.970023	−	0.813946i	−0.0125315	−	0.999921i	$-0.503989\pi$
$827$	27.8955	−	23.4071i	0.970023	−	0.813946i	0.982554	+	0.185976i	$0.0595446\pi$
$828$	2.63052	−	4.55619i	0.0914168	−	0.158338i
$829$	−5.06525	−	8.77327i	−0.175923	−	0.304708i	0.764557	−	0.644556i	$-0.222958\pi$
$829$	−5.06525	−	8.77327i	−0.175923	−	0.304708i	−0.940480	+	0.339848i	$0.889624\pi$
$830$	−13.5081	−	4.91654i	−0.468872	−	0.170656i
$831$	−0.149875	+	0.849981i	−0.00519909	+	0.0294855i
$832$	0.485705	+	2.75457i	0.0168388	+	0.0954975i
$833$	24.8534	−	9.04591i	0.861120	−	0.313422i
$834$	1.78339	+	1.49644i	0.0617537	+	0.0518175i
$835$	10.2382			0.354309
$836$	−0.388995	−	1.85087i	−0.0134537	−	0.0640137i
$837$	−4.75902			−0.164496
$838$	15.3384	+	12.8705i	0.529858	+	0.444604i
$839$	−40.1975	+	14.6307i	−1.38777	+	0.505107i	−0.924525	−	0.381122i	$-0.875538\pi$
$839$	−40.1975	+	14.6307i	−1.38777	+	0.505107i	−0.463246	+	0.886230i	$0.653315\pi$
$840$	0.748993	+	4.24775i	0.0258427	+	0.146561i
$841$	−1.26399	+	7.16844i	−0.0435858	+	0.247188i
$842$	35.1556	+	12.7956i	1.21154	+	0.440966i
$843$	−4.26903	−	7.39418i	−0.147033	−	0.254669i
$844$	−4.78007	+	8.27933i	−0.164537	+	0.284986i
$845$	−3.96539	+	3.32735i	−0.136413	+	0.114464i
$846$	−3.72989	+	3.12975i	−0.128236	+	0.107603i
$847$	23.3170	−	40.3863i	0.801182	−	1.38769i
$848$	−1.56138	−	2.70439i	−0.0536180	−	0.0928690i
$849$	8.69839	+	3.16596i	0.298528	+	0.108655i
$850$	−0.395775	+	2.24455i	−0.0135750	+	0.0769875i
$851$	−4.48896	−	25.4581i	−0.153879	−	0.872694i
$852$	−9.68738	+	3.52592i	−0.331884	+	0.120796i
$853$	−20.4835	−	17.1877i	−0.701341	−	0.588495i	0.220814	−	0.975316i	$-0.429129\pi$
$853$	−20.4835	−	17.1877i	−0.701341	−	0.588495i	−0.922155	+	0.386821i	$0.873573\pi$
$854$	46.0352			1.57529
$855$	−2.05517	+	3.84399i	−0.0702854	+	0.131462i
$856$	−0.395222			−0.0135084
$857$	2.51593	+	2.11111i	0.0859425	+	0.0721143i	0.684747	−	0.728781i	$-0.259913\pi$
$857$	2.51593	+	2.11111i	0.0859425	+	0.0721143i	−0.598804	+	0.800895i	$0.704357\pi$
$858$	1.14044	−	0.415087i	0.0389340	−	0.0141708i
$859$	−0.794090	−	4.50351i	−0.0270940	−	0.153658i	0.968259	−	0.249948i	$-0.0804135\pi$
$859$	−0.794090	−	4.50351i	−0.0270940	−	0.153658i	−0.995353	+	0.0962901i	$0.969302\pi$
$860$	0.0742738	−	0.421228i	0.00253272	−	0.0143637i
$861$	25.5467	+	9.29825i	0.870630	+	0.316884i
$862$	−14.4774	−	25.0757i	−0.493104	−	0.854081i
$863$	23.3727	−	40.4827i	0.795617	−	1.37805i	−0.126830	−	0.991924i	$-0.540480\pi$
$863$	23.3727	−	40.4827i	0.795617	−	1.37805i	0.922447	−	0.386124i	$-0.126186\pi$
$864$	0.766044	−	0.642788i	0.0260614	−	0.0218681i
$865$	−6.33615	+	5.31666i	−0.215436	+	0.180772i
$866$	13.2669	−	22.9789i	0.450827	−	0.780855i
$867$	5.90267	+	10.2237i	0.200465	+	0.347216i
$868$	19.2891	+	7.02064i	0.654713	+	0.238296i
$869$	−1.29780	+	7.36017i	−0.0440247	+	0.249677i
$870$	0.809301	+	4.58977i	0.0274379	+	0.155608i
$871$	−25.5491	+	9.29911i	−0.865698	+	0.315088i
$872$	−9.61852	−	8.07089i	−0.325724	−	0.273315i
$873$	−7.92015			−0.268057
$874$	−22.9201	+	0.747936i	−0.775284	+	0.0252993i
$875$	4.31328			0.145815
$876$	6.73773	+	5.65363i	0.227647	+	0.191018i
$877$	−20.7920	+	7.56767i	−0.702096	+	0.255542i	−0.668305	−	0.743887i	$-0.732980\pi$
$877$	−20.7920	+	7.56767i	−0.702096	+	0.255542i	−0.0337904	+	0.999429i	$0.510758\pi$
$878$	−0.743521	−	4.21672i	−0.0250926	−	0.142307i
$879$	−2.06081	+	11.6874i	−0.0695095	+	0.394208i
$880$	0.407728	+	0.148401i	0.0137445	+	0.00500259i
$881$	−24.7362	−	42.8443i	−0.833383	−	1.44346i	−0.895340	−	0.445383i	$-0.853067\pi$
$881$	−24.7362	−	42.8443i	−0.833383	−	1.44346i	0.0619566	−	0.998079i	$-0.480266\pi$
$882$	−5.80219	+	10.0497i	−0.195370	+	0.338391i
$883$	38.4282	−	32.2451i	1.29321	−	1.08513i	0.301938	−	0.953328i	$-0.402366\pi$
$883$	38.4282	−	32.2451i	1.29321	−	1.08513i	0.991275	−	0.131807i	$-0.0420780\pi$
$884$	−4.88354	+	4.09777i	−0.164251	+	0.137823i
$885$	3.38152	−	5.85697i	0.113669	−	0.196880i
$886$	7.99985	+	13.8562i	0.268760	+	0.465507i
$887$	31.0178	+	11.2896i	1.04148	+	0.379067i	0.805440	−	0.592677i	$-0.201929\pi$
$887$	31.0178	+	11.2896i	1.04148	+	0.379067i	0.236037	+	0.971744i	$0.424151\pi$
$888$	0.853246	−	4.83900i	0.0286331	−	0.162386i
$889$	−4.68299	−	26.5586i	−0.157062	−	0.890745i
$890$	−5.32515	+	1.93820i	−0.178500	+	0.0649685i
$891$	−0.332383	−	0.278903i	−0.0111353	−	0.00934359i
$892$	−10.1988			−0.341480
$893$	20.1698	+	6.60457i	0.674956	+	0.221014i
$894$	−13.5951			−0.454687
$895$	−13.8880	−	11.6534i	−0.464224	−	0.389530i
$896$	−4.05316	+	1.47523i	−0.135407	+	0.0492839i
$897$	−2.55531	−	14.4919i	−0.0853193	−	0.483870i
$898$	2.25561	−	12.7922i	0.0752707	−	0.426881i
$899$	20.8422	+	7.58593i	0.695125	+	0.253005i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	3.55866	−	6.16378i	0.118556	−	0.205345i
$902$	2.09498	−	1.75790i	0.0697554	−	0.0585317i
$903$	1.41328	−	1.18588i	0.0470309	−	0.0394636i
$904$	−8.42971	+	14.6007i	−0.280368	+	0.485611i
$905$	−5.54259	−	9.60005i	−0.184242	−	0.319117i
$906$	−13.4124	−	4.88170i	−0.445595	−	0.162183i
$907$	−1.27170	+	7.21217i	−0.0422261	+	0.239476i	−0.998615	−	0.0526218i	$-0.983242\pi$
$907$	−1.27170	+	7.21217i	−0.0422261	+	0.239476i	0.956388	+	0.292098i	$0.0943533\pi$
$908$	2.53420	+	14.3722i	0.0841004	+	0.476957i
$909$	13.5218	−	4.92154i	0.448490	−	0.163237i
$910$	9.24195	+	7.75492i	0.306368	+	0.257073i
$911$	10.0929			0.334392			0.167196	−	0.985924i	$-0.446529\pi$
$911$	10.0929			0.334392			0.167196	+	0.985924i	$0.446529\pi$
$912$	−4.14247	−	1.35645i	−0.137171	−	0.0449164i
$913$	−6.23725			−0.206423
$914$	−14.9125	−	12.5131i	−0.493263	−	0.413897i
$915$	−10.0292	+	3.65034i	−0.331556	+	0.120677i
$916$	1.77001	+	10.0382i	0.0584827	+	0.331672i
$917$	4.10799	−	23.2976i	0.135658	−	0.769354i
$918$	2.14173	+	0.779525i	0.0706875	+	0.0257282i
$919$	19.9219	+	34.5057i	0.657162	+	1.13824i	0.981347	+	0.192245i	$0.0615768\pi$
$919$	19.9219	+	34.5057i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$920$	2.63052	−	4.55619i	0.0867256	−	0.150213i
$921$	23.9704	−	20.1135i	0.789851	−	0.662763i
$922$	11.6822	−	9.80255i	0.384734	−	0.322830i
$923$	−14.4176	+	24.9720i	−0.474561	+	0.821963i
$924$	0.935756	+	1.62078i	0.0307841	+	0.0533196i
$925$	−4.61732	−	1.68057i	−0.151817	−	0.0552567i
$926$	−5.34576	+	30.3173i	−0.175673	+	0.996289i
$927$	0.149366	+	0.847098i	0.00490583	+	0.0278224i
$928$	−4.37951	+	1.59401i	−0.143764	+	0.0523260i
$929$	−31.6354	−	26.5453i	−1.03792	−	0.870922i	−0.0461514	−	0.998934i	$-0.514696\pi$
$929$	−31.6354	−	26.5453i	−1.03792	−	0.870922i	−0.991773	+	0.128013i	$0.959140\pi$
$930$	−4.75902			−0.156054
$931$	50.5554	−	1.64974i	1.65689	−	0.0540681i
$932$	−20.3333			−0.666039
$933$	−6.95433	−	5.83538i	−0.227675	−	0.191042i
$934$	32.3020	−	11.7570i	1.05695	−	0.384700i
$935$	0.171725	+	0.973901i	0.00561601	+	0.0318500i
$936$	0.485705	−	2.75457i	0.0158758	−	0.0900359i
$937$	18.6034	+	6.77108i	0.607747	+	0.221202i	0.627517	−	0.778603i	$-0.284071\pi$
$937$	18.6034	+	6.77108i	0.607747	+	0.221202i	−0.0197703	+	0.999805i	$0.506294\pi$
$938$	−20.9636	−	36.3100i	−0.684485	−	1.18556i
$939$	−15.7074	+	27.2060i	−0.512592	+	0.887835i
$940$	−3.72989	+	3.12975i	−0.121656	+	0.102081i
$941$	25.5188	−	21.4128i	0.831889	−	0.698038i	−0.123834	−	0.992303i	$-0.539519\pi$
$941$	25.5188	−	21.4128i	0.831889	−	0.698038i	0.955724	+	0.294265i	$0.0950747\pi$
$942$	8.58476	−	14.8692i	0.279706	−	0.484466i
$943$	−16.5799	−	28.7173i	−0.539917	−	0.935164i
$944$	6.35518	+	2.31310i	0.206844	+	0.0752849i
$945$	0.748993	−	4.24775i	0.0243648	−	0.138179i
$946$	−0.0322271	−	0.182769i	−0.00104779	−	0.00594232i
$947$	−52.7415	+	19.1963i	−1.71387	+	0.623797i	−0.997281	−	0.0736982i	$-0.976520\pi$
$947$	−52.7415	+	19.1963i	−1.71387	+	0.623797i	−0.716589	+	0.697496i	$0.754298\pi$
$948$	13.1949	+	11.0718i	0.428550	+	0.359596i
$949$	24.6015			0.798599
$950$	−2.05517	+	3.84399i	−0.0666786	+	0.124716i
$951$	−12.3509			−0.400504
$952$	−7.53078	−	6.31907i	−0.244074	−	0.204802i
$953$	−6.71598	+	2.44442i	−0.217552	+	0.0791824i	−0.448497	−	0.893784i	$-0.648040\pi$
$953$	−6.71598	+	2.44442i	−0.217552	+	0.0791824i	0.230945	+	0.972967i	$0.425818\pi$
$954$	0.542261	+	3.07532i	0.0175564	+	0.0995670i
$955$	−1.00568	+	5.70349i	−0.0325430	+	0.184561i
$956$	−8.63200	−	3.14179i	−0.279179	−	0.101613i
$957$	1.01110	+	1.75128i	0.0326843	+	0.0566108i
$958$	−12.6864	+	21.9735i	−0.409879	+	0.709932i
$959$	−51.2150	+	42.9745i	−1.65382	+	1.38772i
$960$	0.766044	−	0.642788i	0.0247240	−	0.0207459i
$961$	4.17587	−	7.23281i	0.134705	−	0.233317i
$962$	−6.87189	−	11.9025i	−0.221559	−	0.383751i
$963$	0.371388	+	0.135174i	0.0119678	+	0.00435592i
$964$	3.58167	−	20.3127i	0.115358	−	0.654227i
$965$	−1.98282	−	11.2452i	−0.0638294	−	0.361994i
$966$	21.3238	−	7.76123i	0.686082	−	0.249713i
$967$	40.3697	+	33.8742i	1.29820	+	1.08932i	0.990453	+	0.137852i	$0.0440197\pi$
$967$	40.3697	+	33.8742i	1.29820	+	1.08932i	0.307748	+	0.951468i	$0.400425\pi$
$968$	−10.8117			−0.347502
$969$	−2.04332	−	9.72231i	−0.0656410	−	0.312325i
$970$	−7.92015			−0.254301
$971$	23.2414	+	19.5019i	0.745854	+	0.625845i	0.934403	−	0.356218i	$-0.115934\pi$
$971$	23.2414	+	19.5019i	0.745854	+	0.625845i	−0.188549	+	0.982064i	$0.560379\pi$
$972$	−0.939693	+	0.342020i	−0.0301407	+	0.0109703i
$973$	1.74369	+	9.88897i	0.0559002	+	0.317026i
$974$	−0.375619	+	2.13024i	−0.0120356	+	0.0682573i
$975$	−2.62838	−	0.956652i	−0.0841755	−	0.0306374i
$976$	−5.33644	−	9.24299i	−0.170815	−	0.295861i
$977$	3.10088	−	5.37088i	0.0992060	−	0.171830i	−0.812150	−	0.583448i	$-0.801703\pi$
$977$	3.10088	−	5.37088i	0.0992060	−	0.171830i	0.911356	+	0.411619i	$0.135036\pi$
$978$	−11.4025	+	9.56780i	−0.364610	+	0.305944i
$979$	−1.88358	+	1.58052i	−0.0601996	+	0.0505135i
$980$	−5.80219	+	10.0497i	−0.185344	+	0.321026i
$981$	6.27804	+	10.8739i	0.200442	+	0.347176i
$982$	−28.2596	−	10.2857i	−0.901801	−	0.328229i
$983$	−4.04992	+	22.9682i	−0.129172	+	0.732572i	0.849570	+	0.527476i	$0.176862\pi$
$983$	−4.04992	+	22.9682i	−0.129172	+	0.732572i	−0.978742	+	0.205096i	$0.934249\pi$
$984$	−1.09449	−	6.20717i	−0.0348911	−	0.197877i
$985$	−14.4660	+	5.26519i	−0.460925	+	0.167763i
$986$	−8.13714	−	6.82787i	−0.259139	−	0.217444i
$987$	−21.0015			−0.668484
$988$	−11.3147	+	4.54139i	−0.359970	+	0.144481i
$989$	−2.25028			−0.0715547
$990$	−0.332383	−	0.278903i	−0.0105638	−	0.00886410i
$991$	−44.0771	+	16.0428i	−1.40016	+	0.509615i	−0.928225	−	0.372020i	$-0.878665\pi$
$991$	−44.0771	+	16.0428i	−1.40016	+	0.509615i	−0.471932	+	0.881635i	$0.656443\pi$
$992$	−0.826395	−	4.68672i	−0.0262381	−	0.148803i
$993$	−6.23020	+	35.3332i	−0.197709	+	1.12127i
$994$	−41.7844	−	15.2083i	−1.32532	−	0.482377i
$995$	−9.50219	−	16.4583i	−0.301240	−	0.521762i
$996$	−7.18750	+	12.4491i	−0.227745	+	0.394465i
$997$	−27.2963	+	22.9043i	−0.864482	+	0.725386i	−0.962929	−	0.269756i	$-0.913057\pi$
$997$	−27.2963	+	22.9043i	−0.864482	+	0.725386i	0.0984470	+	0.995142i	$0.468613\pi$
$998$	−20.9095	+	17.5451i	−0.661878	+	0.555381i
$999$	−2.45682	+	4.25535i	−0.0777305	+	0.134633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.i.301.1	✓	12
19.6	even	9	inner	570.2.u.i.481.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.i.301.1	✓	12	1.1	even	1	trivial
570.2.u.i.481.1	yes	12	19.6	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-2.15664 - 3.73541i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-2.15664 - 3.73541i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.766044 - 0.642788i) q^{10} +(0.216948 - 0.375764i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.62838 - 0.956652i) q^{13} +(0.748993 - 4.24775i) q^{14} +(0.173648 + 0.984808i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.74595 - 1.46503i) q^{17} +1.00000 q^{18} +(-2.30141 - 3.70183i) q^{19} +1.00000 q^{20} +(3.30416 + 2.77252i) q^{21} +(0.407728 - 0.148401i) q^{22} +(-0.913569 - 5.18111i) q^{23} +(0.173648 - 0.984808i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-1.39853 - 2.42233i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(3.30416 - 2.77252i) q^{28} +(3.57021 - 2.99576i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.37951 + 4.12143i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-0.0753451 + 0.427303i) q^{33} +(-0.395775 - 2.24455i) q^{34} +(-4.05316 + 1.47523i) q^{35} +(0.766044 + 0.642788i) q^{36} +4.91365 q^{37} +(0.616507 - 4.31508i) q^{38} +2.79706 q^{39} +(0.766044 + 0.642788i) q^{40} +(5.92281 - 2.15573i) q^{41} +(0.748993 + 4.24775i) q^{42} +(0.0742738 - 0.421228i) q^{43} +(0.407728 + 0.148401i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(2.63052 - 4.55619i) q^{46} +(-3.72989 + 3.12975i) q^{47} +(0.766044 - 0.642788i) q^{48} +(-5.80219 + 10.0497i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.14173 + 0.779525i) q^{51} +(0.485705 - 2.75457i) q^{52} +(0.542261 + 3.07532i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(-0.332383 - 0.278903i) q^{55} +4.31328 q^{56} +(3.42872 + 2.69145i) q^{57} +4.66058 q^{58} +(-5.18079 - 4.34720i) q^{59} +(-0.939693 + 0.342020i) q^{60} +(1.85333 + 10.5107i) q^{61} +(-0.826395 + 4.68672i) q^{62} +(-4.05316 - 1.47523i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.39853 + 2.42233i) q^{65} +(-0.332383 + 0.278903i) q^{66} +(7.44632 - 6.24820i) q^{67} +(1.13959 - 1.97383i) q^{68} +(2.63052 + 4.55619i) q^{69} +(-4.05316 - 1.47523i) q^{70} +(1.79015 - 10.1525i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-8.26505 + 3.00823i) q^{73} +(3.76407 + 3.15843i) q^{74} +1.00000 q^{75} +(3.24595 - 2.90926i) q^{76} -1.87151 q^{77} +(2.14267 + 1.79792i) q^{78} +(-16.1859 + 5.89119i) q^{79} +(0.173648 + 0.984808i) q^{80} +(0.173648 - 0.984808i) q^{81} +(5.92281 + 2.15573i) q^{82} +(-7.18750 - 12.4491i) q^{83} +(-2.15664 + 3.73541i) q^{84} +(-1.74595 + 1.46503i) q^{85} +(0.327657 - 0.274937i) q^{86} +(-2.33029 + 4.03618i) q^{87} +(0.216948 + 0.375764i) q^{88} +(-5.32515 - 1.93820i) q^{89} +(0.173648 - 0.984808i) q^{90} +(2.09498 + 11.8812i) q^{91} +(4.94375 - 1.79938i) q^{92} +(-3.64562 - 3.05904i) q^{93} -4.86903 q^{94} +(-4.04522 + 1.62363i) q^{95} +1.00000 q^{96} +(-6.06719 - 5.09098i) q^{97} +(-10.9046 + 3.96893i) q^{98} +(-0.0753451 - 0.427303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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