LMFDB - Embedded newform 273.2.i.c.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	273.235
Dual form			273.2.i.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} +(-0.346011 - 0.599308i) q^{5} +0.801938 q^{6} +(2.20291 + 1.46533i) q^{7} -2.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} +(-0.346011 - 0.599308i) q^{5} +0.801938 q^{6} +(2.20291 + 1.46533i) q^{7} -2.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.277479 + 0.480608i) q^{10} +(2.82640 - 4.89546i) q^{11} +(0.678448 + 1.17511i) q^{12} +1.00000 q^{13} +(0.134375 - 2.11747i) q^{14} +0.692021 q^{15} +(-0.277479 - 0.480608i) q^{16} +(0.266594 - 0.461754i) q^{17} +(-0.400969 + 0.694498i) q^{18} +(0.698062 + 1.20908i) q^{19} -0.939001 q^{20} +(-2.37047 + 1.17511i) q^{21} -4.53319 q^{22} +(-1.67845 - 2.90716i) q^{23} +(1.34601 - 2.33136i) q^{24} +(2.26055 - 3.91539i) q^{25} +(-0.400969 - 0.694498i) q^{26} +1.00000 q^{27} +(3.21648 - 1.59450i) q^{28} +2.80194 q^{29} +(-0.277479 - 0.480608i) q^{30} +(2.59903 - 4.50165i) q^{31} +(-2.91454 + 5.04814i) q^{32} +(2.82640 + 4.89546i) q^{33} -0.427583 q^{34} +(0.115957 - 1.82724i) q^{35} -1.35690 q^{36} +(4.06853 + 7.04690i) q^{37} +(0.559802 - 0.969606i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.931468 + 1.61335i) q^{40} -8.80194 q^{41} +(1.76659 + 1.17511i) q^{42} -8.96077 q^{43} +(-3.83513 - 6.64263i) q^{44} +(-0.346011 + 0.599308i) q^{45} +(-1.34601 + 2.33136i) q^{46} +(5.98792 + 10.3714i) q^{47} +0.554958 q^{48} +(2.70560 + 6.45599i) q^{49} -3.62565 q^{50} +(0.266594 + 0.461754i) q^{51} +(0.678448 - 1.17511i) q^{52} +(-1.11260 + 1.92709i) q^{53} +(-0.400969 - 0.694498i) q^{54} -3.91185 q^{55} +(-5.93027 - 3.94471i) q^{56} -1.39612 q^{57} +(-1.12349 - 1.94594i) q^{58} +(-3.25786 + 5.64279i) q^{59} +(0.469501 - 0.813199i) q^{60} +(4.67241 + 8.09285i) q^{61} -4.16852 q^{62} +(0.167563 - 2.64044i) q^{63} +3.56465 q^{64} +(-0.346011 - 0.599308i) q^{65} +(2.26659 - 3.92586i) q^{66} +(-6.12229 + 10.6041i) q^{67} +(-0.361740 - 0.626552i) q^{68} +3.35690 q^{69} +(-1.31551 + 0.652135i) q^{70} -1.97823 q^{71} +(1.34601 + 2.33136i) q^{72} +(0.818864 - 1.41831i) q^{73} +(3.26271 - 5.65118i) q^{74} +(2.26055 + 3.91539i) q^{75} +1.89440 q^{76} +(13.3998 - 6.64263i) q^{77} +0.801938 q^{78} +(-4.20291 - 7.27965i) q^{79} +(-0.192021 + 0.332591i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.52930 + 6.11293i) q^{82} +1.44504 q^{83} +(-0.227365 + 3.58280i) q^{84} -0.368977 q^{85} +(3.59299 + 6.22324i) q^{86} +(-1.40097 + 2.42655i) q^{87} +(-7.60872 + 13.1787i) q^{88} +(7.49127 + 12.9753i) q^{89} +0.554958 q^{90} +(2.20291 + 1.46533i) q^{91} -4.55496 q^{92} +(2.59903 + 4.50165i) q^{93} +(4.80194 - 8.31720i) q^{94} +(0.483074 - 0.836709i) q^{95} +(-2.91454 - 5.04814i) q^{96} -0.0827692 q^{97} +(3.39881 - 4.46768i) q^{98} -5.65279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 6 q^{13} - 7 q^{14} - 6 q^{15} - 2 q^{16} + 5 q^{17} + 2 q^{18} + 13 q^{19} + 14 q^{20} - 34 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 2 q^{26} + 6 q^{27} + 8 q^{29} - 2 q^{30} + 20 q^{31} - 7 q^{32} - q^{33} + 30 q^{34} + 21 q^{35} + 19 q^{37} - 18 q^{38} - 3 q^{39} + 11 q^{40} - 44 q^{41} + 14 q^{42} - 28 q^{43} - 21 q^{44} + 3 q^{45} - 3 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{50} + 5 q^{51} - 5 q^{53} + 2 q^{54} - 16 q^{55} - 26 q^{57} - 2 q^{58} - 7 q^{59} - 7 q^{60} + 5 q^{61} + 36 q^{62} - 22 q^{64} + 3 q^{65} + 17 q^{66} + 9 q^{67} + 28 q^{68} + 12 q^{69} + 7 q^{70} - 18 q^{71} + 3 q^{72} + 12 q^{73} - 15 q^{74} - 2 q^{75} - 28 q^{76} + 35 q^{77} - 4 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 10 q^{82} + 8 q^{83} + 21 q^{84} - 32 q^{85} + 7 q^{86} - 4 q^{87} - 6 q^{88} + 29 q^{89} + 4 q^{90} - 28 q^{92} + 20 q^{93} + 20 q^{94} - 13 q^{95} - 7 q^{96} - 14 q^{97} + 35 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + 6 * q^13 - 7 * q^14 - 6 * q^15 - 2 * q^16 + 5 * q^17 + 2 * q^18 + 13 * q^19 + 14 * q^20 - 34 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 2 * q^26 + 6 * q^27 + 8 * q^29 - 2 * q^30 + 20 * q^31 - 7 * q^32 - q^33 + 30 * q^34 + 21 * q^35 + 19 * q^37 - 18 * q^38 - 3 * q^39 + 11 * q^40 - 44 * q^41 + 14 * q^42 - 28 * q^43 - 21 * q^44 + 3 * q^45 - 3 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^50 + 5 * q^51 - 5 * q^53 + 2 * q^54 - 16 * q^55 - 26 * q^57 - 2 * q^58 - 7 * q^59 - 7 * q^60 + 5 * q^61 + 36 * q^62 - 22 * q^64 + 3 * q^65 + 17 * q^66 + 9 * q^67 + 28 * q^68 + 12 * q^69 + 7 * q^70 - 18 * q^71 + 3 * q^72 + 12 * q^73 - 15 * q^74 - 2 * q^75 - 28 * q^76 + 35 * q^77 - 4 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 10 * q^82 + 8 * q^83 + 21 * q^84 - 32 * q^85 + 7 * q^86 - 4 * q^87 - 6 * q^88 + 29 * q^89 + 4 * q^90 - 28 * q^92 + 20 * q^93 + 20 * q^94 - 13 * q^95 - 7 * q^96 - 14 * q^97 + 35 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.400969	−	0.694498i	−0.283528	−	0.491085i	0.688723	−	0.725024i	$-0.258171\pi$
$2$	−0.400969	−	0.694498i	−0.283528	−	0.491085i	−0.972251	+	0.233940i	$0.924838\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.678448	−	1.17511i	0.339224	−	0.587553i
$5$	−0.346011	−	0.599308i	−0.154741	−	0.268019i	0.778224	−	0.627987i	$-0.216121\pi$
$5$	−0.346011	−	0.599308i	−0.154741	−	0.268019i	−0.932965	+	0.359968i	$0.882788\pi$
$6$	0.801938			0.327390
$7$	2.20291	+	1.46533i	0.832620	+	0.553844i
$7$	2.20291	+	1.46533i	0.832620	+	0.553844i
$8$	−2.69202			−0.951773
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.277479	+	0.480608i	−0.0877466	+	0.151982i
$11$	2.82640	−	4.89546i	0.852191	−	1.47604i	−0.0270365	−	0.999634i	$-0.508607\pi$
$11$	2.82640	−	4.89546i	0.852191	−	1.47604i	0.879227	−	0.476403i	$-0.158060\pi$
$12$	0.678448	+	1.17511i	0.195851	+	0.339224i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	0.134375	−	2.11747i	0.0359132	−	0.565917i
$15$	0.692021			0.178679
$16$	−0.277479	−	0.480608i	−0.0693698	−	0.120152i
$17$	0.266594	−	0.461754i	0.0646585	−	0.111992i	−0.831884	−	0.554950i	$-0.812738\pi$
$17$	0.266594	−	0.461754i	0.0646585	−	0.111992i	0.896542	+	0.442958i	$0.146071\pi$
$18$	−0.400969	+	0.694498i	−0.0945093	+	0.163695i
$19$	0.698062	+	1.20908i	0.160146	+	0.277382i	0.934921	−	0.354856i	$-0.115470\pi$
$19$	0.698062	+	1.20908i	0.160146	+	0.277382i	−0.774775	+	0.632238i	$0.782137\pi$
$20$	−0.939001			−0.209967
$21$	−2.37047	+	1.17511i	−0.517279	+	0.256429i
$22$	−4.53319			−0.966479
$23$	−1.67845	−	2.90716i	−0.349981	−	0.606184i	0.636265	−	0.771471i	$-0.280478\pi$
$23$	−1.67845	−	2.90716i	−0.349981	−	0.606184i	−0.986246	+	0.165286i	$0.947145\pi$
$24$	1.34601	−	2.33136i	0.274753	−	0.475887i
$25$	2.26055	−	3.91539i	0.452111	−	0.783079i
$26$	−0.400969	−	0.694498i	−0.0786365	−	0.136202i
$27$	1.00000			0.192450
$28$	3.21648	−	1.59450i	0.607858	−	0.301332i
$29$	2.80194			0.520307			0.260153	−	0.965567i	$-0.416227\pi$
$29$	2.80194			0.520307			0.260153	+	0.965567i	$0.416227\pi$
$30$	−0.277479	−	0.480608i	−0.0506605	−	0.0877466i
$31$	2.59903	−	4.50165i	0.466800	−	0.808521i	−0.532481	−	0.846442i	$-0.678740\pi$
$31$	2.59903	−	4.50165i	0.466800	−	0.808521i	0.999281	+	0.0379211i	$0.0120735\pi$
$32$	−2.91454	+	5.04814i	−0.515223	+	0.892393i
$33$	2.82640	+	4.89546i	0.492012	+	0.852191i
$34$	−0.427583			−0.0733300
$35$	0.115957	−	1.82724i	0.0196003	−	0.308860i
$36$	−1.35690			−0.226149
$37$	4.06853	+	7.04690i	0.668862	+	1.15850i	0.978223	+	0.207559i	$0.0665518\pi$
$37$	4.06853	+	7.04690i	0.668862	+	1.15850i	−0.309360	+	0.950945i	$0.600115\pi$
$38$	0.559802	−	0.969606i	0.0908120	−	0.157291i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$	0.931468	+	1.61335i	0.147278	+	0.255093i
$41$	−8.80194			−1.37463			−0.687316	−	0.726359i	$-0.741211\pi$
$41$	−8.80194			−1.37463			−0.687316	+	0.726359i	$0.741211\pi$
$42$	1.76659	+	1.17511i	0.272591	+	0.181323i
$43$	−8.96077			−1.36650			−0.683252	−	0.730182i	$-0.739435\pi$
$43$	−8.96077			−1.36650			−0.683252	+	0.730182i	$0.739435\pi$
$44$	−3.83513	−	6.64263i	−0.578167	−	1.00141i
$45$	−0.346011	+	0.599308i	−0.0515802	+	0.0893396i
$46$	−1.34601	+	2.33136i	−0.198458	+	0.343740i
$47$	5.98792	+	10.3714i	0.873428	+	1.51282i	0.858428	+	0.512934i	$0.171441\pi$
$47$	5.98792	+	10.3714i	0.873428	+	1.51282i	0.0149994	+	0.999888i	$0.495225\pi$
$48$	0.554958			0.0801013
$49$	2.70560	+	6.45599i	0.386514	+	0.922284i
$50$	−3.62565			−0.512744
$51$	0.266594	+	0.461754i	0.0373306	+	0.0646585i
$52$	0.678448	−	1.17511i	0.0940838	−	0.162958i
$53$	−1.11260	+	1.92709i	−0.152828	+	0.264706i	−0.932266	−	0.361773i	$-0.882171\pi$
$53$	−1.11260	+	1.92709i	−0.152828	+	0.264706i	0.779438	+	0.626479i	$0.215505\pi$
$54$	−0.400969	−	0.694498i	−0.0545650	−	0.0945093i
$55$	−3.91185			−0.527474
$56$	−5.93027	−	3.94471i	−0.792466	−	0.527134i
$57$	−1.39612			−0.184921
$58$	−1.12349	−	1.94594i	−0.147521	−	0.255515i
$59$	−3.25786	+	5.64279i	−0.424138	+	0.734628i	−0.996339	−	0.0854847i	$-0.972756\pi$
$59$	−3.25786	+	5.64279i	−0.424138	+	0.734628i	0.572202	+	0.820113i	$0.306089\pi$
$60$	0.469501	−	0.813199i	0.0606123	−	0.104984i
$61$	4.67241	+	8.09285i	0.598240	+	1.03618i	0.993081	+	0.117433i	$0.0374666\pi$
$61$	4.67241	+	8.09285i	0.598240	+	1.03618i	−0.394840	+	0.918750i	$0.629200\pi$
$62$	−4.16852			−0.529403
$63$	0.167563	−	2.64044i	0.0211109	−	0.332664i
$64$	3.56465			0.445581
$65$	−0.346011	−	0.599308i	−0.0429173	−	0.0743350i
$66$	2.26659	−	3.92586i	0.278998	−	0.483239i
$67$	−6.12229	+	10.6041i	−0.747957	+	1.29550i	0.200843	+	0.979623i	$0.435632\pi$
$67$	−6.12229	+	10.6041i	−0.747957	+	1.29550i	−0.948800	+	0.315876i	$0.897701\pi$
$68$	−0.361740	−	0.626552i	−0.0438674	−	0.0759806i
$69$	3.35690			0.404123
$70$	−1.31551	+	0.652135i	−0.157234	+	0.0779450i
$71$	−1.97823			−0.234773			−0.117386	−	0.993086i	$-0.537452\pi$
$71$	−1.97823			−0.234773			−0.117386	+	0.993086i	$0.537452\pi$
$72$	1.34601	+	2.33136i	0.158629	+	0.274753i
$73$	0.818864	−	1.41831i	0.0958407	−	0.166001i	−0.814118	−	0.580699i	$-0.802779\pi$
$73$	0.818864	−	1.41831i	0.0958407	−	0.166001i	0.909959	+	0.414698i	$0.136113\pi$
$74$	3.26271	−	5.65118i	0.379282	−	0.656936i
$75$	2.26055	+	3.91539i	0.261026	+	0.452111i
$76$	1.89440			0.217302
$77$	13.3998	−	6.64263i	1.52705	−	0.756998i
$78$	0.801938			0.0908016
$79$	−4.20291	−	7.27965i	−0.472864	−	0.819024i	0.526654	−	0.850080i	$-0.323446\pi$
$79$	−4.20291	−	7.27965i	−0.472864	−	0.819024i	−0.999518	+	0.0310555i	$0.990113\pi$
$80$	−0.192021	+	0.332591i	−0.0214687	+	0.0371848i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.52930	+	6.11293i	0.389746	+	0.675060i
$83$	1.44504			0.158614			0.0793070	−	0.996850i	$-0.474729\pi$
$83$	1.44504			0.158614			0.0793070	+	0.996850i	$0.474729\pi$
$84$	−0.227365	+	3.58280i	−0.0248076	+	0.390916i
$85$	−0.368977			−0.0400212
$86$	3.59299	+	6.22324i	0.387442	+	0.671069i
$87$	−1.40097	+	2.42655i	−0.150200	+	0.260153i
$88$	−7.60872	+	13.1787i	−0.811092	+	1.40485i
$89$	7.49127	+	12.9753i	0.794073	+	1.37537i	0.923426	+	0.383776i	$0.125377\pi$
$89$	7.49127	+	12.9753i	0.794073	+	1.37537i	−0.129353	+	0.991599i	$0.541290\pi$
$90$	0.554958			0.0584977
$91$	2.20291	+	1.46533i	0.230927	+	0.153609i
$92$	−4.55496			−0.474887
$93$	2.59903	+	4.50165i	0.269507	+	0.466800i
$94$	4.80194	−	8.31720i	0.495282	−	0.857854i
$95$	0.483074	−	0.836709i	0.0495624	−	0.0858445i
$96$	−2.91454	−	5.04814i	−0.297464	−	0.515223i
$97$	−0.0827692			−0.00840394			−0.00420197	−	0.999991i	$-0.501338\pi$
$97$	−0.0827692			−0.00840394			−0.00420197	+	0.999991i	$0.501338\pi$
$98$	3.39881	−	4.46768i	0.343332	−	0.451304i
$99$	−5.65279			−0.568127
$100$	−3.06734	−	5.31278i	−0.306734	−	0.531278i
$101$	−1.14795	+	1.98831i	−0.114225	+	0.197844i	−0.917470	−	0.397806i	$-0.869772\pi$
$101$	−1.14795	+	1.98831i	−0.114225	+	0.197844i	0.803245	+	0.595649i	$0.203105\pi$
$102$	0.213792	−	0.370298i	0.0211685	−	0.0366650i
$103$	−6.73490	−	11.6652i	−0.663609	−	1.14940i	−0.979660	−	0.200663i	$-0.935690\pi$
$103$	−6.73490	−	11.6652i	−0.663609	−	1.14940i	0.316051	−	0.948742i	$-0.397643\pi$
$104$	−2.69202			−0.263974
$105$	1.52446	+	1.01404i	0.148772	+	0.0989604i
$106$	1.78448			0.173324
$107$	−2.76659	−	4.79188i	−0.267457	−	0.463249i	0.700748	−	0.713409i	$-0.252850\pi$
$107$	−2.76659	−	4.79188i	−0.267457	−	0.463249i	−0.968204	+	0.250161i	$0.919517\pi$
$108$	0.678448	−	1.17511i	0.0652837	−	0.113075i
$109$	5.85354	−	10.1386i	0.560668	−	0.971105i	−0.436771	−	0.899573i	$-0.643878\pi$
$109$	5.85354	−	10.1386i	0.560668	−	0.971105i	0.997438	−	0.0715321i	$-0.0227888\pi$
$110$	1.56853	+	2.71678i	0.149554	+	0.259034i
$111$	−8.13706			−0.772336
$112$	0.0929903	−	1.46533i	0.00878676	−	0.138461i
$113$	15.0151			1.41250			0.706249	−	0.707963i	$-0.250386\pi$
$113$	15.0151			1.41250			0.706249	+	0.707963i	$0.250386\pi$
$114$	0.559802	+	0.969606i	0.0524303	+	0.0908120i
$115$	−1.16152	+	2.01182i	−0.108312	+	0.187603i
$116$	1.90097	−	3.29257i	0.176501	−	0.305708i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	5.22521			0.481020
$119$	1.26391	−	0.626552i	0.115862	−	0.0574360i
$120$	−1.86294			−0.170062
$121$	−10.4770	−	18.1468i	−0.952458	−	1.64970i
$122$	3.74698	−	6.48996i	0.339236	−	0.587573i
$123$	4.40097	−	7.62270i	0.396822	−	0.687316i
$124$	−3.52661	−	6.10828i	−0.316699	−	0.548539i
$125$	−6.58881			−0.589321
$126$	−1.90097	+	0.942362i	−0.169352	+	0.0839523i
$127$	−6.98254			−0.619600			−0.309800	−	0.950802i	$-0.600262\pi$
$127$	−6.98254			−0.619600			−0.309800	+	0.950802i	$0.600262\pi$
$128$	4.39977	+	7.62063i	0.388889	+	0.673575i
$129$	4.48039	−	7.76026i	0.394476	−	0.683252i
$130$	−0.277479	+	0.480608i	−0.0243365	+	0.0421521i
$131$	−5.89762	−	10.2150i	−0.515277	−	0.892486i	−0.999843	−	0.0177313i	$-0.994356\pi$
$131$	−5.89762	−	10.2150i	−0.515277	−	0.892486i	0.484566	−	0.874755i	$-0.338978\pi$
$132$	7.67025			0.667610
$133$	−0.233939	+	3.68638i	−0.0202850	+	0.319650i
$134$	9.81940			0.848267
$135$	−0.346011	−	0.599308i	−0.0297799	−	0.0515802i
$136$	−0.717677	+	1.24305i	−0.0615403	+	0.106591i
$137$	−0.898280	+	1.55587i	−0.0767453	+	0.132927i	−0.901844	−	0.432062i	$-0.857786\pi$
$137$	−0.898280	+	1.55587i	−0.0767453	+	0.132927i	0.825099	+	0.564989i	$0.191119\pi$
$138$	−1.34601	−	2.33136i	−0.114580	−	0.198458i
$139$	−4.36227			−0.370003			−0.185002	−	0.982738i	$-0.559229\pi$
$139$	−4.36227			−0.370003			−0.185002	+	0.982738i	$0.559229\pi$
$140$	−2.06853	−	1.37595i	−0.174823	−	0.116289i
$141$	−11.9758			−1.00855
$142$	0.793209	+	1.37388i	0.0665646	+	0.115293i
$143$	2.82640	−	4.89546i	0.236355	−	0.409379i
$144$	−0.277479	+	0.480608i	−0.0231233	+	0.0400507i
$145$	−0.969501	−	1.67922i	−0.0805126	−	0.139452i
$146$	−1.31336			−0.108694
$147$	−6.94385	−	0.884879i	−0.572719	−	0.0729836i
$148$	11.0411			0.907577
$149$	1.74094	+	3.01539i	0.142623	+	0.247031i	0.928484	−	0.371373i	$-0.121113\pi$
$149$	1.74094	+	3.01539i	0.142623	+	0.247031i	−0.785860	+	0.618404i	$0.787780\pi$
$150$	1.81282	−	3.13990i	0.148016	−	0.256372i
$151$	−9.48188	+	16.4231i	−0.771624	+	1.33649i	0.165048	+	0.986286i	$0.447222\pi$
$151$	−9.48188	+	16.4231i	−0.771624	+	1.33649i	−0.936672	+	0.350207i	$0.886111\pi$
$152$	−1.87920	−	3.25487i	−0.152423	−	0.264005i
$153$	−0.533188			−0.0431057
$154$	−9.98619	−	6.64263i	−0.804710	−	0.535279i
$155$	−3.59717			−0.288932
$156$	0.678448	+	1.17511i	0.0543193	+	0.0940838i
$157$	8.93780	−	15.4807i	0.713314	−	1.23550i	−0.250292	−	0.968171i	$-0.580526\pi$
$157$	8.93780	−	15.4807i	0.713314	−	1.23550i	0.963606	−	0.267326i	$-0.0861402\pi$
$158$	−3.37047	+	5.83782i	−0.268140	+	0.464432i
$159$	−1.11260	−	1.92709i	−0.0882353	−	0.152828i
$160$	4.03385			0.318904
$161$	0.562491	−	8.86368i	0.0443305	−	0.698556i
$162$	0.801938			0.0630062
$163$	9.28501	+	16.0821i	0.727258	+	1.25965i	0.958038	+	0.286642i	$0.0925391\pi$
$163$	9.28501	+	16.0821i	0.727258	+	1.25965i	−0.230779	+	0.973006i	$0.574128\pi$
$164$	−5.97166	+	10.3432i	−0.466308	+	0.807669i
$165$	1.95593	−	3.38776i	0.152269	−	0.263737i
$166$	−0.579417	−	1.00358i	−0.0449715	−	0.0778929i
$167$	−0.408206			−0.0315879			−0.0157940	−	0.999875i	$-0.505028\pi$
$167$	−0.408206			−0.0315879			−0.0157940	+	0.999875i	$0.505028\pi$
$168$	6.38135	−	3.16341i	0.492332	−	0.244062i
$169$	1.00000			0.0769231
$170$	0.147948	+	0.256254i	0.0113471	+	0.0196538i
$171$	0.698062	−	1.20908i	0.0533822	−	0.0924606i
$172$	−6.07942	+	10.5299i	−0.463551	+	0.802894i
$173$	10.0429	+	17.3948i	0.763546	+	1.32250i	0.941012	+	0.338373i	$0.109877\pi$
$173$	10.0429	+	17.3948i	0.763546	+	1.32250i	−0.177466	+	0.984127i	$0.556790\pi$
$174$	2.24698			0.170343
$175$	10.7171	−	5.31278i	0.810140	−	0.401608i
$176$	−3.13706			−0.236465
$177$	−3.25786	−	5.64279i	−0.244876	−	0.424138i
$178$	6.00753	−	10.4054i	0.450284	−	0.779914i
$179$	−4.77144	+	8.26437i	−0.356634	+	0.617708i	−0.987396	−	0.158268i	$-0.949409\pi$
$179$	−4.77144	+	8.26437i	−0.356634	+	0.617708i	0.630762	+	0.775976i	$0.282742\pi$
$180$	0.469501	+	0.813199i	0.0349945	+	0.0606123i
$181$	−13.9933			−1.04011			−0.520057	−	0.854132i	$-0.674089\pi$
$181$	−13.9933			−1.04011			−0.520057	+	0.854132i	$0.674089\pi$
$182$	0.134375	−	2.11747i	0.00996053	−	0.156957i
$183$	−9.34481			−0.690789
$184$	4.51842	+	7.82613i	0.333102	+	0.576950i
$185$	2.81551	−	4.87661i	0.207001	−	0.358535i
$186$	2.08426	−	3.61005i	0.152825	−	0.264701i
$187$	−1.50700	−	2.61020i	−0.110203	−	0.190877i
$188$	16.2500			1.18515
$189$	2.20291	+	1.46533i	0.160238	+	0.106587i
$190$	−0.774791			−0.0562092
$191$	−2.08695	−	3.61470i	−0.151006	−	0.261551i	0.780591	−	0.625042i	$-0.214918\pi$
$191$	−2.08695	−	3.61470i	−0.151006	−	0.261551i	−0.931598	+	0.363491i	$0.881585\pi$
$192$	−1.78232	+	3.08707i	−0.128628	+	0.222790i
$193$	13.1930	−	22.8509i	0.949652	−	1.64484i	0.203493	−	0.979076i	$-0.434771\pi$
$193$	13.1930	−	22.8509i	0.949652	−	1.64484i	0.746159	−	0.665768i	$-0.231896\pi$
$194$	0.0331879	+	0.0574831i	0.00238275	+	0.00412704i
$195$	0.692021			0.0495567
$196$	9.42208	+	1.20069i	0.673005	+	0.0857635i
$197$	14.8019			1.05459			0.527297	−	0.849681i	$-0.323205\pi$
$197$	14.8019			1.05459			0.527297	+	0.849681i	$0.323205\pi$
$198$	2.26659	+	3.92586i	0.161080	+	0.278998i
$199$	4.96950	−	8.60743i	0.352279	−	0.610164i	−0.634370	−	0.773030i	$-0.718740\pi$
$199$	4.96950	−	8.60743i	0.352279	−	0.610164i	0.986648	+	0.162865i	$0.0520736\pi$
$200$	−6.08546	+	10.5403i	−0.430307	+	0.745313i
$201$	−6.12229	−	10.6041i	−0.431833	−	0.747957i
$202$	1.84117			0.129544
$203$	6.17241	+	4.10577i	0.433218	+	0.288169i
$204$	0.723480			0.0506538
$205$	3.04556	+	5.27507i	0.212711	+	0.368427i
$206$	−5.40097	+	9.35475i	−0.376303	+	0.651776i
$207$	−1.67845	+	2.90716i	−0.116660	+	0.202061i
$208$	−0.277479	−	0.480608i	−0.0192397	−	0.0333242i
$209$	7.89200			0.545901
$210$	0.0929903	−	1.46533i	0.00641694	−	0.101118i
$211$	−7.19567			−0.495370			−0.247685	−	0.968841i	$-0.579670\pi$
$211$	−7.19567			−0.495370			−0.247685	+	0.968841i	$0.579670\pi$
$212$	1.50969	+	2.61486i	0.103686	+	0.179589i
$213$	0.989115	−	1.71320i	0.0677730	−	0.117386i
$214$	−2.21864	+	3.84279i	−0.151663	+	0.262688i
$215$	3.10052	+	5.37026i	0.211454	+	0.366249i
$216$	−2.69202			−0.183169
$217$	12.3218	−	6.10828i	0.836462	−	0.414657i
$218$	−9.38835			−0.635860
$219$	0.818864	+	1.41831i	0.0553337	+	0.0958407i
$220$	−2.65399	+	4.59684i	−0.178932	+	0.309919i
$221$	0.266594	−	0.461754i	0.0179330	−	0.0310610i
$222$	3.26271	+	5.65118i	0.218979	+	0.379282i
$223$	−2.35152			−0.157469			−0.0787347	−	0.996896i	$-0.525088\pi$
$223$	−2.35152			−0.157469			−0.0787347	+	0.996896i	$0.525088\pi$
$224$	−13.8177	+	6.84979i	−0.923232	+	0.457671i
$225$	−4.52111			−0.301407
$226$	−6.02057	−	10.4279i	−0.400483	−	0.693656i
$227$	−12.6528	+	21.9153i	−0.839795	+	1.45457i	0.0502702	+	0.998736i	$0.483992\pi$
$227$	−12.6528	+	21.9153i	−0.839795	+	1.45457i	−0.890066	+	0.455833i	$0.849342\pi$
$228$	−0.947198	+	1.64059i	−0.0627297	+	0.108651i
$229$	−2.59783	−	4.49958i	−0.171670	−	0.297341i	0.767334	−	0.641248i	$-0.221583\pi$
$229$	−2.59783	−	4.49958i	−0.171670	−	0.297341i	−0.939004	+	0.343907i	$0.888250\pi$
$230$	1.86294			0.122838
$231$	−0.947198	+	14.9259i	−0.0623210	+	0.982049i
$232$	−7.54288			−0.495214
$233$	−7.58426	−	13.1363i	−0.496861	−	0.860589i	0.503132	−	0.864210i	$-0.332181\pi$
$233$	−7.58426	−	13.1363i	−0.496861	−	0.860589i	−0.999993	+	0.00362028i	$0.998848\pi$
$234$	−0.400969	+	0.694498i	−0.0262122	+	0.0454008i
$235$	4.14377	−	7.17722i	0.270310	−	0.468190i
$236$	4.42058	+	7.65667i	0.287755	+	0.498407i
$237$	8.40581			0.546016
$238$	−0.941926	−	0.626552i	−0.0610560	−	0.0406134i
$239$	9.78448			0.632905			0.316453	−	0.948608i	$-0.397508\pi$
$239$	9.78448			0.632905			0.316453	+	0.948608i	$0.397508\pi$
$240$	−0.192021	−	0.332591i	−0.0123949	−	0.0214687i
$241$	−13.2555	+	22.9592i	−0.853860	+	1.47893i	0.0238386	+	0.999716i	$0.492411\pi$
$241$	−13.2555	+	22.9592i	−0.853860	+	1.47893i	−0.877699	+	0.479213i	$0.840922\pi$
$242$	−8.40193	+	14.5526i	−0.540096	+	0.935474i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	12.6799			0.811750
$245$	2.93296	−	3.85533i	0.187380	−	0.246308i
$246$	−7.05861			−0.450040
$247$	0.698062	+	1.20908i	0.0444166	+	0.0769319i
$248$	−6.99665	+	12.1185i	−0.444288	+	0.769529i
$249$	−0.722521	+	1.25144i	−0.0457879	+	0.0793070i
$250$	2.64191	+	4.57592i	0.167089	+	0.289406i
$251$	27.2597			1.72061			0.860307	−	0.509776i	$-0.170272\pi$
$251$	27.2597			1.72061			0.860307	+	0.509776i	$0.170272\pi$
$252$	−2.98911	−	1.98831i	−0.188297	−	0.125251i
$253$	−18.9758			−1.19300
$254$	2.79978	+	4.84936i	0.175674	+	0.304276i
$255$	0.184489	−	0.319544i	0.0115531	−	0.0200106i
$256$	7.09299	−	12.2854i	0.443312	−	0.767839i
$257$	2.27748	+	3.94471i	0.142065	+	0.246064i	0.928274	−	0.371897i	$-0.121292\pi$
$257$	2.27748	+	3.94471i	0.142065	+	0.246064i	−0.786209	+	0.617961i	$0.787959\pi$
$258$	−7.18598			−0.447380
$259$	−1.36347	+	21.4854i	−0.0847218	+	1.33504i
$260$	−0.939001			−0.0582344
$261$	−1.40097	−	2.42655i	−0.0867178	−	0.150200i
$262$	−4.72952	+	8.19177i	−0.292191	+	0.506089i
$263$	2.95324	−	5.11516i	0.182104	−	0.315414i	−0.760493	−	0.649347i	$-0.775042\pi$
$263$	2.95324	−	5.11516i	0.182104	−	0.315414i	0.942597	+	0.333932i	$0.108376\pi$
$264$	−7.60872	−	13.1787i	−0.468284	−	0.811092i
$265$	1.53989			0.0945949
$266$	2.65399	−	1.31565i	0.162727	−	0.0806680i
$267$	−14.9825			−0.916917
$268$	8.30731	+	14.3887i	0.507450	+	0.878929i
$269$	−8.84817	+	15.3255i	−0.539482	+	0.934411i	0.459450	+	0.888204i	$0.348047\pi$
$269$	−8.84817	+	15.3255i	−0.539482	+	0.934411i	−0.998932	+	0.0462068i	$0.985287\pi$
$270$	−0.277479	+	0.480608i	−0.0168868	+	0.0292489i
$271$	−15.4242	−	26.7156i	−0.936955	−	1.62285i	−0.771110	−	0.636703i	$-0.780298\pi$
$271$	−15.4242	−	26.7156i	−0.936955	−	1.62285i	−0.165846	−	0.986152i	$-0.553035\pi$
$272$	−0.295897			−0.0179414
$273$	−2.37047	+	1.17511i	−0.143467	+	0.0711207i
$274$	1.44073			0.0870377
$275$	−12.7784	−	22.1329i	−0.770569	−	1.33466i
$276$	2.27748	−	3.94471i	0.137088	−	0.237444i
$277$	−9.22132	+	15.9718i	−0.554056	+	0.959653i	0.443921	+	0.896066i	$0.353587\pi$
$277$	−9.22132	+	15.9718i	−0.554056	+	0.959653i	−0.997976	+	0.0635865i	$0.979746\pi$
$278$	1.74914	+	3.02959i	0.104906	+	0.181703i
$279$	−5.19806			−0.311200
$280$	−0.312159	+	4.91897i	−0.0186551	+	0.293965i
$281$	14.9172			0.889887			0.444944	−	0.895559i	$-0.353224\pi$
$281$	14.9172			0.889887			0.444944	+	0.895559i	$0.353224\pi$
$282$	4.80194	+	8.31720i	0.285951	+	0.495282i
$283$	−7.38135	+	12.7849i	−0.438776	+	0.759982i	−0.997595	−	0.0693071i	$-0.977921\pi$
$283$	−7.38135	+	12.7849i	−0.438776	+	0.759982i	0.558819	+	0.829289i	$0.311255\pi$
$284$	−1.34213	+	2.32463i	−0.0796405	+	0.137941i
$285$	0.483074	+	0.836709i	0.0286148	+	0.0495624i
$286$	−4.53319			−0.268053
$287$	−19.3898	−	12.8978i	−1.14455	−	0.761332i
$288$	5.82908			0.343482
$289$	8.35786	+	14.4762i	0.491639	+	0.851543i
$290$	−0.777479	+	1.34663i	−0.0456551	+	0.0790770i
$291$	0.0413846	−	0.0716802i	0.00242601	−	0.00420197i
$292$	−1.11111	−	1.92450i	−0.0650230	−	0.112623i
$293$	−26.8321			−1.56755			−0.783773	−	0.621047i	$-0.786707\pi$
$293$	−26.8321			−1.56755			−0.783773	+	0.621047i	$0.786707\pi$
$294$	2.16972	+	5.17730i	0.126541	+	0.301946i
$295$	4.50902			0.262526
$296$	−10.9526	−	18.9704i	−0.636605	−	1.10263i
$297$	2.82640	−	4.89546i	0.164004	−	0.284064i
$298$	1.39612	−	2.41816i	0.0808753	−	0.140080i
$299$	−1.67845	−	2.90716i	−0.0970672	−	0.168125i
$300$	6.13467			0.354185
$301$	−19.7397	−	13.1305i	−1.13778	−	0.756831i
$302$	15.2078			0.875108
$303$	−1.14795	−	1.98831i	−0.0659479	−	0.114225i
$304$	0.387395	−	0.670988i	0.0222186	−	0.0384838i
$305$	3.23341	−	5.60042i	0.185144	−	0.320679i
$306$	0.213792	+	0.370298i	0.0122217	+	0.0211685i
$307$	0.850855			0.0485609			0.0242804	−	0.999705i	$-0.492271\pi$
$307$	0.850855			0.0485609			0.0242804	+	0.999705i	$0.492271\pi$
$308$	1.28525	−	20.2528i	0.0732338	−	1.15401i
$309$	13.4698			0.766270
$310$	1.44235	+	2.49823i	0.0819202	+	0.141890i
$311$	4.67121	−	8.09077i	0.264880	−	0.458786i	−0.702652	−	0.711534i	$-0.748001\pi$
$311$	4.67121	−	8.09077i	0.264880	−	0.458786i	0.967532	+	0.252748i	$0.0813343\pi$
$312$	1.34601	−	2.33136i	0.0762029	−	0.131987i
$313$	8.14526	+	14.1080i	0.460397	+	0.797432i	0.998981	−	0.0451407i	$-0.0143736\pi$
$313$	8.14526	+	14.1080i	0.460397	+	0.797432i	−0.538583	+	0.842572i	$0.681040\pi$
$314$	−14.3351			−0.808978
$315$	−1.64042	+	0.813199i	−0.0924270	+	0.0458186i
$316$	−11.4058			−0.641627
$317$	−4.24914	−	7.35972i	−0.238655	−	0.413363i	0.721673	−	0.692234i	$-0.243373\pi$
$317$	−4.24914	−	7.35972i	−0.238655	−	0.413363i	−0.960329	+	0.278871i	$0.910040\pi$
$318$	−0.892240	+	1.54540i	−0.0500343	+	0.0866620i
$319$	7.91939	−	13.7168i	0.443401	−	0.767992i
$320$	−1.23341	−	2.13632i	−0.0689495	−	0.119424i
$321$	5.53319			0.308832
$322$	−6.38135	+	3.16341i	−0.355619	+	0.176290i
$323$	0.744397			0.0414193
$324$	0.678448	+	1.17511i	0.0376916	+	0.0652837i
$325$	2.26055	−	3.91539i	0.125393	−	0.217187i
$326$	7.44600	−	12.8969i	0.412396	−	0.714291i
$327$	5.85354	+	10.1386i	0.323702	+	0.560668i
$328$	23.6950			1.30834
$329$	−2.00670	+	31.6215i	−0.110633	+	1.74335i
$330$	−3.13706			−0.172690
$331$	1.77748	+	3.07868i	0.0976991	+	0.169220i	0.910732	−	0.412998i	$-0.135518\pi$
$331$	1.77748	+	3.07868i	0.0976991	+	0.169220i	−0.813033	+	0.582218i	$0.802185\pi$
$332$	0.980386	−	1.69808i	0.0538057	−	0.0931941i
$333$	4.06853	−	7.04690i	0.222954	−	0.386168i
$334$	0.163678	+	0.283499i	0.00895606	+	0.0155123i
$335$	8.47352			0.462958
$336$	1.22252	+	0.813199i	0.0666940	+	0.0443636i
$337$	11.0640			0.602694			0.301347	−	0.953515i	$-0.402564\pi$
$337$	11.0640			0.602694			0.301347	+	0.953515i	$0.402564\pi$
$338$	−0.400969	−	0.694498i	−0.0218098	−	0.0377757i
$339$	−7.50753	+	13.0034i	−0.407753	+	0.706249i
$340$	−0.250332	+	0.433588i	−0.0135762	+	0.0235146i
$341$	−14.6918	−	25.4469i	−0.795605	−	1.37803i
$342$	−1.11960			−0.0605413
$343$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$344$	24.1226			1.30060
$345$	−1.16152	−	2.01182i	−0.0625342	−	0.108312i
$346$	8.05376	−	13.9495i	0.432973	−	0.749931i
$347$	5.64579	−	9.77880i	0.303082	−	0.524953i	−0.673750	−	0.738959i	$-0.735318\pi$
$347$	5.64579	−	9.77880i	0.303082	−	0.524953i	0.976832	+	0.214006i	$0.0686511\pi$
$348$	1.90097	+	3.29257i	0.101903	+	0.176501i
$349$	−14.1903			−0.759589			−0.379794	−	0.925071i	$-0.624005\pi$
$349$	−14.1903			−0.759589			−0.379794	+	0.925071i	$0.624005\pi$
$350$	−7.98696	−	5.31278i	−0.426921	−	0.283980i
$351$	1.00000			0.0533761
$352$	16.4753	+	28.5361i	0.878137	+	1.52098i
$353$	1.52297	−	2.63786i	0.0810593	−	0.140399i	−0.822646	−	0.568554i	$-0.807503\pi$
$353$	1.52297	−	2.63786i	0.0810593	−	0.140399i	0.903705	+	0.428155i	$0.140836\pi$
$354$	−2.61260	+	4.52516i	−0.138858	+	0.240510i
$355$	0.684489	+	1.18557i	0.0363289	+	0.0629235i
$356$	20.3297			1.07747
$357$	−0.0893425	+	1.40785i	−0.00472850	+	0.0745114i
$358$	7.65279			0.404463
$359$	−1.75571	−	3.04098i	−0.0926628	−	0.160497i	0.815968	−	0.578097i	$-0.196205\pi$
$359$	−1.75571	−	3.04098i	−0.0926628	−	0.160497i	−0.908631	+	0.417600i	$0.862871\pi$
$360$	0.931468	−	1.61335i	0.0490927	−	0.0850310i
$361$	8.52542	−	14.7665i	0.448706	−	0.777182i
$362$	5.61088	+	9.71832i	0.294901	+	0.510784i
$363$	20.9541			1.09980
$364$	3.21648	−	1.59450i	0.168589	−	0.0835743i
$365$	−1.13334			−0.0593219
$366$	3.74698	+	6.48996i	0.195858	+	0.339236i
$367$	2.99880	−	5.19408i	0.156536	−	0.271129i	−0.777081	−	0.629400i	$-0.783301\pi$
$367$	2.99880	−	5.19408i	0.156536	−	0.271129i	0.933617	+	0.358272i	$0.116634\pi$
$368$	−0.931468	+	1.61335i	−0.0485561	+	0.0841017i
$369$	4.40097	+	7.62270i	0.229105	+	0.396822i
$370$	−4.51573			−0.234762
$371$	−5.27479	+	2.61486i	−0.273853	+	0.135757i
$372$	7.05323			0.365693
$373$	0.966812	+	1.67457i	0.0500596	+	0.0867058i	0.889969	−	0.456020i	$-0.150726\pi$
$373$	0.966812	+	1.67457i	0.0500596	+	0.0867058i	−0.839910	+	0.542726i	$0.817392\pi$
$374$	−1.20852	+	2.09322i	−0.0624911	+	0.108238i
$375$	3.29440	−	5.70608i	0.170122	−	0.294661i
$376$	−16.1196	−	27.9200i	−0.831305	−	1.43986i
$377$	2.80194			0.144307
$378$	0.134375	−	2.11747i	0.00691150	−	0.108911i
$379$	−4.55735			−0.234095			−0.117048	−	0.993126i	$-0.537343\pi$
$379$	−4.55735			−0.234095			−0.117048	+	0.993126i	$0.537343\pi$
$380$	−0.655481	−	1.13533i	−0.0336255	−	0.0582410i
$381$	3.49127	−	6.04706i	0.178863	−	0.309800i
$382$	−1.67360	+	2.89877i	−0.0856290	+	0.148314i
$383$	−15.8523	−	27.4571i	−0.810017	−	1.40299i	−0.912851	−	0.408292i	$-0.866124\pi$
$383$	−15.8523	−	27.4571i	−0.810017	−	1.40299i	0.102834	−	0.994699i	$-0.467209\pi$
$384$	−8.79954			−0.449050
$385$	−8.61745	−	5.73217i	−0.439186	−	0.292138i
$386$	−21.1599			−1.07701
$387$	4.48039	+	7.76026i	0.227751	+	0.394476i
$388$	−0.0561546	+	0.0972626i	−0.00285082	+	0.00493776i
$389$	−0.238250	+	0.412662i	−0.0120798	+	0.0209228i	−0.872002	−	0.489502i	$-0.837179\pi$
$389$	−0.238250	+	0.412662i	−0.0120798	+	0.0209228i	0.859922	+	0.510425i	$0.170512\pi$
$390$	−0.277479	−	0.480608i	−0.0140507	−	0.0243365i
$391$	−1.78986			−0.0905169
$392$	−7.28352	−	17.3797i	−0.367873	−	0.877805i
$393$	11.7952			0.594991
$394$	−5.93512	−	10.2799i	−0.299007	−	0.517895i
$395$	−2.90850	+	5.03767i	−0.146343	+	0.253473i
$396$	−3.83513	+	6.64263i	−0.192722	+	0.333805i
$397$	−4.41239	−	7.64248i	−0.221451	−	0.383565i	0.733798	−	0.679368i	$-0.237746\pi$
$397$	−4.41239	−	7.64248i	−0.221451	−	0.383565i	−0.955249	+	0.295803i	$0.904413\pi$
$398$	−7.97046			−0.399523
$399$	−3.07553	−	2.04579i	−0.153969	−	0.102418i
$400$	−2.50902			−0.125451
$401$	16.3509	+	28.3205i	0.816523	+	1.41426i	0.908229	+	0.418473i	$0.137434\pi$
$401$	16.3509	+	28.3205i	0.816523	+	1.41426i	−0.0917066	+	0.995786i	$0.529232\pi$
$402$	−4.90970	+	8.50385i	−0.244873	+	0.424133i
$403$	2.59903	−	4.50165i	0.129467	−	0.224243i
$404$	1.55765	+	2.69792i	0.0774958	+	0.134227i
$405$	0.692021			0.0343868
$406$	0.376510	−	5.93301i	0.0186859	−	0.294451i
$407$	45.9971			2.27999
$408$	−0.717677	−	1.24305i	−0.0355303	−	0.0615403i
$409$	9.99612	−	17.3138i	0.494276	−	0.856111i	−0.505702	−	0.862708i	$-0.668767\pi$
$409$	9.99612	−	17.3138i	0.494276	−	0.856111i	0.999978	+	0.00659685i	$0.00209986\pi$
$410$	2.44235	−	4.23028i	0.120619	−	0.208919i
$411$	−0.898280	−	1.55587i	−0.0443089	−	0.0767453i
$412$	−18.2771			−0.900449
$413$	−15.4453	+	7.65667i	−0.760015	+	0.376760i
$414$	2.69202			0.132306
$415$	−0.500000	−	0.866025i	−0.0245440	−	0.0425115i
$416$	−2.91454	+	5.04814i	−0.142897	+	0.247505i
$417$	2.18114	−	3.77784i	0.106811	−	0.185002i
$418$	−3.16445	−	5.48098i	−0.154778	−	0.268084i
$419$	−26.4819			−1.29372			−0.646862	−	0.762607i	$-0.723919\pi$
$419$	−26.4819			−1.29372			−0.646862	+	0.762607i	$0.723919\pi$
$420$	2.22587	−	1.10343i	0.108611	−	0.0538417i
$421$	31.9530			1.55729			0.778647	−	0.627462i	$-0.215906\pi$
$421$	31.9530			1.55729			0.778647	+	0.627462i	$0.215906\pi$
$422$	2.88524	+	4.99738i	0.140451	+	0.243269i
$423$	5.98792	−	10.3714i	0.291143	−	0.504274i
$424$	2.99516	−	5.18776i	0.145458	−	0.251940i
$425$	−1.20530	−	2.08764i	−0.0584656	−	0.101265i
$426$	−1.58642			−0.0768622
$427$	−1.56584	+	24.6744i	−0.0757765	+	1.19408i
$428$	−7.50796			−0.362911
$429$	2.82640	+	4.89546i	0.136460	+	0.236355i
$430$	2.48643	−	4.30662i	0.119906	−	0.207684i
$431$	15.5423	−	26.9201i	0.748648	−	1.29670i	−0.199822	−	0.979832i	$-0.564036\pi$
$431$	15.5423	−	26.9201i	0.748648	−	1.29670i	0.948471	−	0.316865i	$-0.102630\pi$
$432$	−0.277479	−	0.480608i	−0.0133502	−	0.0231233i
$433$	−9.28919			−0.446410			−0.223205	−	0.974772i	$-0.571652\pi$
$433$	−9.28919			−0.446410			−0.223205	+	0.974772i	$0.571652\pi$
$434$	−9.18287	−	6.10828i	−0.440792	−	0.293207i
$435$	1.93900			0.0929680
$436$	−7.94265	−	13.7571i	−0.380384	−	0.658844i
$437$	2.34332	−	4.05875i	0.112096	−	0.194157i
$438$	0.656678	−	1.13740i	0.0313773	−	0.0543470i
$439$	11.6102	+	20.1095i	0.554125	+	0.959773i	0.997971	+	0.0636698i	$0.0202804\pi$
$439$	11.6102	+	20.1095i	0.554125	+	0.959773i	−0.443846	+	0.896103i	$0.646386\pi$
$440$	10.5308			0.502036
$441$	4.23825	−	5.57111i	0.201821	−	0.265291i
$442$	−0.427583			−0.0203381
$443$	−19.7690	−	34.2410i	−0.939256	−	1.62684i	−0.766864	−	0.641810i	$-0.778184\pi$
$443$	−19.7690	−	34.2410i	−0.939256	−	1.62684i	−0.172392	−	0.985028i	$-0.555150\pi$
$444$	−5.52057	+	9.56191i	−0.261995	+	0.453788i
$445$	5.18412	−	8.97916i	0.245751	−	0.425653i
$446$	0.942886	+	1.63313i	0.0446469	+	0.0773308i
$447$	−3.48188			−0.164687
$448$	7.85258	+	5.22340i	0.371000	+	0.246782i
$449$	33.8799			1.59889			0.799446	−	0.600738i	$-0.205126\pi$
$449$	33.8799			1.59889			0.799446	+	0.600738i	$0.205126\pi$
$450$	1.81282	+	3.13990i	0.0854573	+	0.148016i
$451$	−24.8778	+	43.0896i	−1.17145	+	2.02901i
$452$	10.1869	−	17.6443i	0.479153	−	0.829918i
$453$	−9.48188	−	16.4231i	−0.445497	−	0.771624i
$454$	20.2935			0.952421
$455$	0.115957	−	1.82724i	0.00543615	−	0.0856624i
$456$	3.75840			0.176003
$457$	14.3068	+	24.7801i	0.669243	+	1.15916i	0.978116	+	0.208060i	$0.0667148\pi$
$457$	14.3068	+	24.7801i	0.669243	+	1.15916i	−0.308873	+	0.951103i	$0.599952\pi$
$458$	−2.08330	+	3.60838i	−0.0973463	+	0.168609i
$459$	0.266594	−	0.461754i	0.0124435	−	0.0215528i
$460$	1.57606	+	2.72982i	0.0734844	+	0.127279i
$461$	−28.6286			−1.33337			−0.666684	−	0.745340i	$-0.732287\pi$
$461$	−28.6286			−1.33337			−0.666684	+	0.745340i	$0.732287\pi$
$462$	10.7458	−	5.32698i	0.499939	−	0.247833i
$463$	2.44398			0.113581			0.0567906	−	0.998386i	$-0.481913\pi$
$463$	2.44398			0.113581			0.0567906	+	0.998386i	$0.481913\pi$
$464$	−0.777479	−	1.34663i	−0.0360936	−	0.0625159i
$465$	1.79859	−	3.11524i	0.0834074	−	0.144466i
$466$	−6.08211	+	10.5345i	−0.281748	+	0.488002i
$467$	4.09903	+	7.09973i	0.189681	+	0.328536i	0.945144	−	0.326655i	$-0.105921\pi$
$467$	4.09903	+	7.09973i	0.189681	+	0.328536i	−0.755463	+	0.655191i	$0.772588\pi$
$468$	−1.35690			−0.0627225
$469$	−29.0254	+	14.3887i	−1.34027	+	0.664408i
$470$	−6.64609			−0.306561
$471$	8.93780	+	15.4807i	0.411832	+	0.713314i
$472$	8.77024	−	15.1905i	0.403683	−	0.699200i
$473$	−25.3267	+	43.8671i	−1.16452	+	2.01701i
$474$	−3.37047	−	5.83782i	−0.154811	−	0.268140i
$475$	6.31203			0.289616
$476$	0.121228	−	1.91031i	0.00555649	−	0.0875588i
$477$	2.22521			0.101885
$478$	−3.92327	−	6.79531i	−0.179446	−	0.310810i
$479$	13.9562	−	24.1729i	0.637676	−	1.10449i	−0.348265	−	0.937396i	$-0.613229\pi$
$479$	13.9562	−	24.1729i	0.637676	−	1.10449i	0.985941	−	0.167091i	$-0.0534375\pi$
$480$	−2.01693	+	3.49342i	−0.0920597	+	0.159452i
$481$	4.06853	+	7.04690i	0.185509	+	0.321311i
$482$	21.2601			0.968372
$483$	7.39493	+	4.91897i	0.336481	+	0.223821i
$484$	−28.4325			−1.29239
$485$	0.0286390	+	0.0496043i	0.00130043	+	0.00225241i
$486$	−0.400969	+	0.694498i	−0.0181883	+	0.0315031i
$487$	11.1649	−	19.3381i	0.505929	−	0.876294i	−0.494048	−	0.869435i	$-0.664483\pi$
$487$	11.1649	−	19.3381i	0.505929	−	0.876294i	0.999976	−	0.00685952i	$-0.00218347\pi$
$488$	−12.5782	−	21.7861i	−0.569389	−	0.986211i
$489$	−18.5700			−0.839765
$490$	−3.85354	−	0.491071i	−0.174085	−	0.0221843i
$491$	−16.3739			−0.738943			−0.369471	−	0.929242i	$-0.620461\pi$
$491$	−16.3739			−0.738943			−0.369471	+	0.929242i	$0.620461\pi$
$492$	−5.97166	−	10.3432i	−0.269223	−	0.466308i
$493$	0.746980	−	1.29381i	0.0336423	−	0.0582701i
$494$	0.559802	−	0.969606i	0.0251867	−	0.0436247i
$495$	1.95593	+	3.38776i	0.0879124	+	0.152269i
$496$	−2.88471			−0.129527
$497$	−4.35786	−	2.89877i	−0.195477	−	0.130027i
$498$	1.15883			0.0519286
$499$	−10.5060	−	18.1970i	−0.470315	−	0.814609i	0.529109	−	0.848554i	$-0.322526\pi$
$499$	−10.5060	−	18.1970i	−0.470315	−	0.814609i	−0.999424	+	0.0339446i	$0.989193\pi$
$500$	−4.47016	+	7.74255i	−0.199912	+	0.346257i
$501$	0.204103	−	0.353517i	0.00911865	−	0.0157940i
$502$	−10.9303	−	18.9318i	−0.487842	−	0.844967i
$503$	−34.8702			−1.55479			−0.777393	−	0.629015i	$-0.783459\pi$
$503$	−34.8702			−1.55479			−0.777393	+	0.629015i	$0.783459\pi$
$504$	−0.451083	+	7.10812i	−0.0200928	+	0.316621i
$505$	1.58881			0.0707011
$506$	7.60872	+	13.1787i	0.338249	+	0.585864i
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$	−4.73729	+	8.20523i	−0.210183	+	0.364048i
$509$	0.543541	+	0.941440i	0.0240920	+	0.0417286i	0.877820	−	0.478991i	$-0.158997\pi$
$509$	0.543541	+	0.941440i	0.0240920	+	0.0417286i	−0.853728	+	0.520719i	$0.825664\pi$
$510$	−0.295897			−0.0131025
$511$	3.88218	−	1.92450i	0.171738	−	0.0851350i
$512$	6.22282			0.275012
$513$	0.698062	+	1.20908i	0.0308202	+	0.0533822i
$514$	1.82640	−	3.16341i	0.0805589	−	0.139532i
$515$	−4.66069	+	8.07256i	−0.205375	+	0.355719i
$516$	−6.07942	−	10.5299i	−0.267631	−	0.463551i
$517$	67.6969			2.97731
$518$	15.4683	−	7.66806i	0.679638	−	0.336915i
$519$	−20.0858			−0.881667
$520$	0.931468	+	1.61335i	0.0408476	+	0.0707501i
$521$	2.57995	−	4.46860i	0.113030	−	0.195773i	−0.803961	−	0.594682i	$-0.797278\pi$
$521$	2.57995	−	4.46860i	0.113030	−	0.195773i	0.916990	+	0.398909i	$0.130611\pi$
$522$	−1.12349	+	1.94594i	−0.0491738	+	0.0851715i
$523$	18.1836	+	31.4949i	0.795113	+	1.37718i	0.922768	+	0.385357i	$0.125922\pi$
$523$	18.1836	+	31.4949i	0.795113	+	1.37718i	−0.127655	+	0.991819i	$0.540745\pi$
$524$	−16.0049			−0.699177
$525$	−0.757569	+	11.9377i	−0.0330630	+	0.521004i
$526$	−4.73663			−0.206527
$527$	−1.38577	−	2.40023i	−0.0603652	−	0.104556i
$528$	1.56853	−	2.71678i	0.0682616	−	0.118233i
$529$	5.86563	−	10.1596i	0.255027	−	0.441720i
$530$	−0.617449	−	1.06945i	−0.0268203	−	0.0464541i
$531$	6.51573			0.282759
$532$	4.17318	+	2.77592i	0.180930	+	0.120351i
$533$	−8.80194			−0.381254
$534$	6.00753	+	10.4054i	0.259971	+	0.450284i
$535$	−1.91454	+	3.31608i	−0.0827729	+	0.143367i
$536$	16.4813	−	28.5465i	0.711886	−	1.23302i
$537$	−4.77144	−	8.26437i	−0.205903	−	0.356634i
$538$	14.1914			0.611833
$539$	39.2521	+	5.00204i	1.69071	+	0.215453i
$540$	−0.939001			−0.0404082
$541$	−7.07971	−	12.2624i	−0.304381	−	0.527203i	0.672743	−	0.739877i	$-0.265116\pi$
$541$	−7.07971	−	12.2624i	−0.304381	−	0.527203i	−0.977123	+	0.212674i	$0.931783\pi$
$542$	−12.3693	+	21.4242i	−0.531306	+	0.920249i
$543$	6.99665	−	12.1185i	0.300255	−	0.520057i
$544$	1.55400	+	2.69160i	0.0666271	+	0.115402i
$545$	−8.10156			−0.347033
$546$	1.76659	+	1.17511i	0.0756032	+	0.0502899i
$547$	3.58509			0.153287			0.0766437	−	0.997059i	$-0.475580\pi$
$547$	3.58509			0.153287			0.0766437	+	0.997059i	$0.475580\pi$
$548$	1.21887	+	2.11115i	0.0520677	+	0.0901839i
$549$	4.67241	−	8.09285i	0.199413	−	0.345394i
$550$	−10.2475	+	17.7492i	−0.436955	+	0.756829i
$551$	1.95593	+	3.38776i	0.0833253	+	0.144324i
$552$	−9.03684			−0.384633
$553$	1.40850	−	22.1950i	0.0598956	−	0.943829i
$554$	14.7899			0.628361
$555$	2.81551	+	4.87661i	0.119512	+	0.207001i
$556$	−2.95957	+	5.12613i	−0.125514	+	0.217397i
$557$	−11.1799	+	19.3642i	−0.473709	+	0.820488i	−0.999547	−	0.0300964i	$-0.990419\pi$
$557$	−11.1799	+	19.3642i	−0.473709	+	0.820488i	0.525838	+	0.850585i	$0.323752\pi$
$558$	2.08426	+	3.61005i	0.0882338	+	0.152825i
$559$	−8.96077			−0.379000
$560$	−0.910362	+	0.451291i	−0.0384698	+	0.0190705i
$561$	3.01400			0.127251
$562$	−5.98135	−	10.3600i	−0.252308	−	0.437010i
$563$	−9.15548	+	15.8578i	−0.385858	+	0.668325i	−0.991888	−	0.127117i	$-0.959428\pi$
$563$	−9.15548	+	15.8578i	−0.385858	+	0.668325i	0.606030	+	0.795442i	$0.292761\pi$
$564$	−8.12498	+	14.0729i	−0.342123	+	0.592575i
$565$	−5.19537	−	8.99865i	−0.218571	−	0.378576i
$566$	11.8388			0.497621
$567$	−2.37047	+	1.17511i	−0.0995504	+	0.0493498i
$568$	5.32544			0.223450
$569$	−15.0109	−	25.9996i	−0.629289	−	1.08996i	−0.987695	−	0.156395i	$-0.950013\pi$
$569$	−15.0109	−	25.9996i	−0.629289	−	1.08996i	0.358406	−	0.933566i	$-0.383320\pi$
$570$	0.387395	−	0.670988i	0.0162262	−	0.0281046i
$571$	0.455927	−	0.789689i	0.0190800	−	0.0330474i	−0.856328	−	0.516433i	$-0.827260\pi$
$571$	0.455927	−	0.789689i	0.0190800	−	0.0330474i	0.875408	+	0.483385i	$0.160593\pi$
$572$	−3.83513	−	6.64263i	−0.160355	−	0.277742i
$573$	4.17390			0.174367
$574$	−1.18276	+	18.6378i	−0.0493674	+	0.777928i
$575$	−15.1769			−0.632920
$576$	−1.78232	−	3.08707i	−0.0742635	−	0.128628i
$577$	−5.72013	+	9.90755i	−0.238132	+	0.412457i	−0.960178	−	0.279388i	$-0.909868\pi$
$577$	−5.72013	+	9.90755i	−0.238132	+	0.412457i	0.722046	+	0.691845i	$0.243202\pi$
$578$	6.70248	−	11.6090i	0.278786	−	0.482872i
$579$	13.1930	+	22.8509i	0.548282	+	0.949652i
$580$	−2.63102			−0.109247
$581$	3.18329	+	2.11747i	0.132065	+	0.0878474i
$582$	−0.0663757			−0.00275136
$583$	6.28932	+	10.8934i	0.260477	+	0.451160i
$584$	−2.20440	+	3.81813i	−0.0912187	+	0.157995i
$585$	−0.346011	+	0.599308i	−0.0143058	+	0.0247783i
$586$	10.7588	+	18.6348i	0.444443	+	0.769798i
$587$	−24.2747			−1.00192			−0.500962	−	0.865469i	$-0.667021\pi$
$587$	−24.2747			−1.00192			−0.500962	+	0.865469i	$0.667021\pi$
$588$	−5.75086	+	7.55941i	−0.237162	+	0.311745i
$589$	7.25714			0.299025
$590$	−1.80798	−	3.13151i	−0.0744333	−	0.128922i
$591$	−7.40097	+	12.8189i	−0.304435	+	0.527297i
$592$	2.25786	−	3.91074i	0.0927977	−	0.160730i
$593$	−3.56584	−	6.17622i	−0.146432	−	0.253627i	0.783475	−	0.621424i	$-0.213446\pi$
$593$	−3.56584	−	6.17622i	−0.146432	−	0.253627i	−0.929906	+	0.367797i	$0.880112\pi$
$594$	−4.53319			−0.185999
$595$	−0.812823	−	0.540675i	−0.0333225	−	0.0221655i
$596$	4.72455			0.193525
$597$	4.96950	+	8.60743i	0.203388	+	0.352279i
$598$	−1.34601	+	2.33136i	−0.0550425	+	0.0953364i
$599$	−5.63826	+	9.76575i	−0.230373	+	0.399018i	−0.957918	−	0.287042i	$-0.907328\pi$
$599$	−5.63826	+	9.76575i	−0.230373	+	0.399018i	0.727545	+	0.686060i	$0.240661\pi$
$600$	−6.08546	−	10.5403i	−0.248438	−	0.430307i
$601$	−18.7487			−0.764776			−0.382388	−	0.924002i	$-0.624898\pi$
$601$	−18.7487			−0.764776			−0.382388	+	0.924002i	$0.624898\pi$
$602$	−1.20410	+	18.9741i	−0.0490756	+	0.773329i
$603$	12.2446			0.498638
$604$	12.8659	+	22.2844i	0.523507	+	0.906741i
$605$	−7.25033	+	12.5579i	−0.294768	+	0.510553i
$606$	−0.920583	+	1.59450i	−0.0373961	+	0.0647720i
$607$	−1.16272	−	2.01389i	−0.0471933	−	0.0817412i	0.841464	−	0.540313i	$-0.181694\pi$
$607$	−1.16272	−	2.01389i	−0.0471933	−	0.0817412i	−0.888657	+	0.458572i	$0.848361\pi$
$608$	−8.13813			−0.330045
$609$	−6.64191	+	3.29257i	−0.269144	+	0.133422i
$610$	−5.18598			−0.209974
$611$	5.98792	+	10.3714i	0.242245	+	0.419581i
$612$	−0.361740	+	0.626552i	−0.0146225	+	0.0253269i
$613$	4.39224	−	7.60758i	0.177401	−	0.307267i	−0.763589	−	0.645703i	$-0.776564\pi$
$613$	4.39224	−	7.60758i	0.177401	−	0.307267i	0.940990	+	0.338436i	$0.109898\pi$
$614$	−0.341166	−	0.590918i	−0.0137684	−	0.0238475i
$615$	−6.09113			−0.245618
$616$	−36.0725	+	17.8821i	−1.45340	+	0.720491i
$617$	−19.6765			−0.792145			−0.396073	−	0.918219i	$-0.629627\pi$
$617$	−19.6765			−0.792145			−0.396073	+	0.918219i	$0.629627\pi$
$618$	−5.40097	−	9.35475i	−0.217259	−	0.376303i
$619$	1.81216	−	3.13875i	0.0728368	−	0.126157i	−0.827307	−	0.561750i	$-0.810128\pi$
$619$	1.81216	−	3.13875i	0.0728368	−	0.126157i	0.900144	+	0.435593i	$0.143461\pi$
$620$	−2.44049	+	4.22706i	−0.0980126	+	0.169763i
$621$	−1.67845	−	2.90716i	−0.0673538	−	0.116660i
$622$	−7.49204			−0.300403
$623$	−2.51052	+	39.5605i	−0.100582	+	1.58496i
$624$	0.554958			0.0222161
$625$	−9.02297	−	15.6282i	−0.360919	−	0.625129i
$626$	6.53199	−	11.3137i	0.261071	−	0.452188i
$627$	−3.94600	+	6.83467i	−0.157588	+	0.272951i
$628$	−12.1277	−	21.0057i	−0.483947	−	0.838220i
$629$	4.33858			0.172991
$630$	1.22252	+	0.813199i	0.0487064	+	0.0323986i
$631$	16.1491			0.642887			0.321444	−	0.946929i	$-0.395832\pi$
$631$	16.1491			0.642887			0.321444	+	0.946929i	$0.395832\pi$
$632$	11.3143	+	19.5970i	0.450059	+	0.779526i
$633$	3.59783	−	6.23163i	0.143001	−	0.247685i
$634$	−3.40754	+	5.90204i	−0.135331	+	0.234400i
$635$	2.41603	+	4.18469i	0.0958774	+	0.166065i
$636$	−3.01938			−0.119726
$637$	2.70560	+	6.45599i	0.107200	+	0.255795i
$638$	−12.7017			−0.502866
$639$	0.989115	+	1.71320i	0.0391288	+	0.0677730i
$640$	3.04474	−	5.27364i	0.120354	−	0.208459i
$641$	−19.8017	+	34.2976i	−0.782120	+	1.35467i	0.148584	+	0.988900i	$0.452528\pi$
$641$	−19.8017	+	34.2976i	−0.782120	+	1.35467i	−0.930704	+	0.365772i	$0.880805\pi$
$642$	−2.21864	−	3.84279i	−0.0875626	−	0.151663i
$643$	−38.2978			−1.51032			−0.755159	−	0.655541i	$-0.772440\pi$
$643$	−38.2978			−1.51032			−0.755159	+	0.655541i	$0.772440\pi$
$644$	−10.0341	−	6.67453i	−0.395401	−	0.263013i
$645$	−6.20105			−0.244166
$646$	−0.298480	−	0.516982i	−0.0117435	−	0.0203404i
$647$	24.9197	−	43.1622i	0.979694	−	1.69688i	0.316209	−	0.948689i	$-0.397590\pi$
$647$	24.9197	−	43.1622i	0.979694	−	1.69688i	0.663485	−	0.748190i	$-0.269077\pi$
$648$	1.34601	−	2.33136i	0.0528763	−	0.0915844i
$649$	18.4160	+	31.8975i	0.722893	+	1.25209i
$650$	−3.62565			−0.142210
$651$	−0.871002	+	13.7252i	−0.0341373	+	0.537932i
$652$	25.1976			0.986814
$653$	18.7826	+	32.5325i	0.735021	+	1.27309i	0.954714	+	0.297524i	$0.0961609\pi$
$653$	18.7826	+	32.5325i	0.735021	+	1.27309i	−0.219694	+	0.975569i	$0.570506\pi$
$654$	4.69418	−	8.13055i	0.183557	−	0.317930i
$655$	−4.08128	+	7.06898i	−0.159469	+	0.276208i
$656$	2.44235	+	4.23028i	0.0953579	+	0.165165i
$657$	−1.63773			−0.0638938
$658$	22.7657	−	11.2856i	0.887499	−	0.439957i
$659$	28.1909			1.09816			0.549080	−	0.835769i	$-0.314978\pi$
$659$	28.1909			1.09816			0.549080	+	0.835769i	$0.314978\pi$
$660$	−2.65399	−	4.59684i	−0.103306	−	0.178932i
$661$	1.53319	−	2.65556i	0.0596341	−	0.103289i	−0.834667	−	0.550755i	$-0.814340\pi$
$661$	1.53319	−	2.65556i	0.0596341	−	0.103289i	0.894301	+	0.447466i	$0.147673\pi$
$662$	1.42543	−	2.46891i	0.0554008	−	0.0959570i
$663$	0.266594	+	0.461754i	0.0103537	+	0.0179330i
$664$	−3.89008			−0.150965
$665$	2.29022	−	1.13533i	0.0888111	−	0.0440261i
$666$	−6.52542			−0.252855
$667$	−4.70291	−	8.14567i	−0.182097	−	0.315402i
$668$	−0.276947	+	0.479686i	−0.0107154	+	0.0185596i
$669$	1.17576	−	2.03648i	0.0454575	−	0.0787347i
$670$	−3.39762	−	5.88484i	−0.131261	−	0.227351i
$671$	52.8243			2.03926
$672$	0.976738	−	15.3913i	0.0376785	−	0.593734i
$673$	−14.5254			−0.559914			−0.279957	−	0.960013i	$-0.590320\pi$
$673$	−14.5254			−0.559914			−0.279957	+	0.960013i	$0.590320\pi$
$674$	−4.43631	−	7.68392i	−0.170880	−	0.295973i
$675$	2.26055	−	3.91539i	0.0870087	−	0.150704i
$676$	0.678448	−	1.17511i	0.0260942	−	0.0451964i
$677$	−14.1387	−	24.4889i	−0.543394	−	0.941186i	−0.998706	−	0.0508540i	$-0.983806\pi$
$677$	−14.1387	−	24.4889i	−0.543394	−	0.941186i	0.455312	−	0.890332i	$-0.349528\pi$
$678$	12.0411			0.462437
$679$	−0.182333	−	0.121284i	−0.00699729	−	0.00465447i
$680$	0.993295			0.0380911
$681$	−12.6528	−	21.9153i	−0.484856	−	0.839795i
$682$	−11.7819	+	20.4068i	−0.451152	+	0.781418i
$683$	−2.28405	+	3.95609i	−0.0873968	+	0.151376i	−0.906410	−	0.422399i	$-0.861188\pi$
$683$	−2.28405	+	3.95609i	−0.0873968	+	0.151376i	0.819013	+	0.573775i	$0.194521\pi$
$684$	−0.947198	−	1.64059i	−0.0362170	−	0.0627297i
$685$	1.24326			0.0475025
$686$	14.0339	−	4.86149i	0.535817	−	0.185613i
$687$	5.19567			0.198227
$688$	2.48643	+	4.30662i	0.0947941	+	0.164188i
$689$	−1.11260	+	1.92709i	−0.0423869	+	0.0734162i
$690$	−0.931468	+	1.61335i	−0.0354604	+	0.0614192i
$691$	1.82693	+	3.16433i	0.0694996	+	0.120377i	0.898681	−	0.438603i	$-0.144526\pi$
$691$	1.82693	+	3.16433i	0.0694996	+	0.120377i	−0.829182	+	0.558979i	$0.811193\pi$
$692$	27.2543			1.03605
$693$	−12.4526	−	8.28323i	−0.473034	−	0.314654i
$694$	−9.05515			−0.343729
$695$	1.50939	+	2.61435i	0.0572545	+	0.0991678i
$696$	3.77144	−	6.53232i	0.142956	−	0.247607i
$697$	−2.34654	+	4.06433i	−0.0888817	+	0.153948i
$698$	5.68987	+	9.85514i	0.215365	+	0.373022i
$699$	15.1685			0.573726
$700$	1.02794	−	16.1982i	0.0388526	−	0.612235i
$701$	22.3913			0.845709			0.422855	−	0.906198i	$-0.361028\pi$
$701$	22.3913			0.845709			0.422855	+	0.906198i	$0.361028\pi$
$702$	−0.400969	−	0.694498i	−0.0151336	−	0.0262122i
$703$	−5.68018	+	9.83835i	−0.214232	+	0.371061i
$704$	10.0751	−	17.4506i	0.379720	−	0.657694i
$705$	4.14377	+	7.17722i	0.156063	+	0.270310i
$706$	−2.44265			−0.0919303
$707$	−5.44235	+	2.69792i	−0.204681	+	0.101466i
$708$	−8.84117			−0.332271
$709$	−4.38889	−	7.60178i	−0.164828	−	0.285491i	0.771766	−	0.635906i	$-0.219374\pi$
$709$	−4.38889	−	7.60178i	−0.164828	−	0.285491i	−0.936594	+	0.350416i	$0.886040\pi$
$710$	0.548917	−	0.950753i	0.0206005	−	0.0356811i
$711$	−4.20291	+	7.27965i	−0.157621	+	0.273008i
$712$	−20.1667	−	34.9297i	−0.755778	−	1.30905i
$713$	−17.4494			−0.653483
$714$	1.01357	−	0.502456i	0.0379320	−	0.0188039i
$715$	−3.91185			−0.146295
$716$	6.47434	+	11.2139i	0.241958	+	0.419083i
$717$	−4.89224	+	8.47361i	−0.182704	+	0.316453i
$718$	−1.40797	+	2.43867i	−0.0525449	+	0.0910105i
$719$	7.96293	+	13.7922i	0.296967	+	0.514362i	0.975441	−	0.220263i	$-0.0706915\pi$
$719$	7.96293	+	13.7922i	0.296967	+	0.514362i	−0.678473	+	0.734625i	$0.737358\pi$
$720$	0.384043			0.0143124
$721$	2.25704	−	35.5662i	0.0840564	−	1.32455i
$722$	−13.6737			−0.508883
$723$	−13.2555	−	22.9592i	−0.492976	−	0.853860i
$724$	−9.49372	+	16.4436i	−0.352831	+	0.611122i
$725$	6.33393	−	10.9707i	0.235236	−	0.407441i
$726$	−8.40193	−	14.5526i	−0.311825	−	0.540096i
$727$	7.63043			0.282997			0.141499	−	0.989938i	$-0.454808\pi$
$727$	7.63043			0.282997			0.141499	+	0.989938i	$0.454808\pi$
$728$	−5.93027	−	3.94471i	−0.219790	−	0.146201i
$729$	1.00000			0.0370370
$730$	0.454435	+	0.787105i	0.0168194	+	0.0291320i
$731$	−2.38889	+	4.13767i	−0.0883562	+	0.153037i
$732$	−6.33997	+	10.9812i	−0.234332	+	0.405875i
$733$	24.3756	+	42.2198i	0.900334	+	1.55942i	0.827061	+	0.562112i	$0.190011\pi$
$733$	24.3756	+	42.2198i	0.900334	+	1.55942i	0.0732723	+	0.997312i	$0.476656\pi$
$734$	−4.80971			−0.177530
$735$	1.87233	+	4.46768i	0.0690619	+	0.164793i
$736$	19.5676			0.721272
$737$	34.6081	+	59.9429i	1.27480	+	2.20803i
$738$	3.52930	−	6.11293i	0.129915	−	0.225020i
$739$	19.8279	−	34.3429i	0.729381	−	1.26332i	−0.227765	−	0.973716i	$-0.573142\pi$
$739$	19.8279	−	34.3429i	0.729381	−	1.26332i	0.957145	−	0.289608i	$-0.0935250\pi$
$740$	−3.82036	−	6.61705i	−0.140439	−	0.243248i
$741$	−1.39612			−0.0512879
$742$	3.93104	+	2.61486i	0.144313	+	0.0959944i
$743$	−26.3569			−0.966941			−0.483470	−	0.875361i	$-0.660624\pi$
$743$	−26.3569			−0.966941			−0.483470	+	0.875361i	$0.660624\pi$
$744$	−6.99665	−	12.1185i	−0.256510	−	0.444288i
$745$	1.20477	−	2.08672i	0.0441392	−	0.0764514i
$746$	0.775323	−	1.34290i	0.0283866	−	0.0491670i
$747$	−0.722521	−	1.25144i	−0.0264357	−	0.0457879i
$748$	−4.08968			−0.149534
$749$	0.927156	−	14.6100i	0.0338776	−	0.533840i
$750$	−5.28382			−0.192938
$751$	−6.79590	−	11.7708i	−0.247986	−	0.429524i	0.714981	−	0.699144i	$-0.246435\pi$
$751$	−6.79590	−	11.7708i	−0.247986	−	0.429524i	−0.962967	+	0.269620i	$0.913102\pi$
$752$	3.32304	−	5.75568i	0.121179	−	0.209888i
$753$	−13.6298	+	23.6076i	−0.496698	+	0.860307i
$754$	−1.12349	−	1.94594i	−0.0409151	−	0.0708670i
$755$	13.1233			0.477607
$756$	3.21648	−	1.59450i	0.116982	−	0.0579913i
$757$	−11.6775			−0.424428			−0.212214	−	0.977223i	$-0.568067\pi$
$757$	−11.6775			−0.424428			−0.212214	+	0.977223i	$0.568067\pi$
$758$	1.82736	+	3.16507i	0.0663726	+	0.114961i
$759$	9.48792	−	16.4336i	0.344390	−	0.596500i
$760$	−1.30045	+	2.25244i	−0.0471721	+	0.0817045i
$761$	4.18382	+	7.24660i	0.151664	+	0.262689i	0.931839	−	0.362872i	$-0.118204\pi$
$761$	4.18382	+	7.24660i	0.151664	+	0.262689i	−0.780176	+	0.625561i	$0.784870\pi$
$762$	−5.59956			−0.202851
$763$	27.7513	−	13.7571i	1.00466	−	0.498039i
$764$	−5.66355			−0.204900
$765$	0.184489	+	0.319544i	0.00667020	+	0.0115531i
$766$	−12.7126	+	22.0189i	−0.459325	+	0.795574i
$767$	−3.25786	+	5.64279i	−0.117635	+	0.203749i
$768$	7.09299	+	12.2854i	0.255946	+	0.443312i
$769$	23.3461			0.841883			0.420942	−	0.907088i	$-0.361700\pi$
$769$	23.3461			0.841883			0.420942	+	0.907088i	$0.361700\pi$
$770$	−0.525655	+	8.28323i	−0.0189433	+	0.298507i
$771$	−4.55496			−0.164043
$772$	−17.9015	−	31.0063i	−0.644289	−	1.11594i
$773$	−9.39426	+	16.2713i	−0.337888	+	0.585240i	−0.984035	−	0.177973i	$-0.943046\pi$
$773$	−9.39426	+	16.2713i	−0.337888	+	0.585240i	0.646147	+	0.763213i	$0.276379\pi$
$774$	3.59299	−	6.22324i	0.129147	−	0.223690i
$775$	−11.7505	−	20.3525i	−0.422090	−	0.731082i
$776$	0.222816			0.00799864
$777$	−17.9252	−	11.9235i	−0.643063	−	0.427754i
$778$	0.382124			0.0136998
$779$	−6.14430	−	10.6422i	−0.220142	−	0.381298i
$780$	0.469501	−	0.813199i	0.0168108	−	0.0291172i
$781$	−5.59126	+	9.68435i	−0.200071	+	0.346533i
$782$	0.717677	+	1.24305i	0.0256641	+	0.0444515i
$783$	2.80194			0.100133
$784$	2.35205	−	3.09173i	0.0840018	−	0.110419i
$785$	−12.3703			−0.441515
$786$	−4.72952	−	8.19177i	−0.168696	−	0.292191i
$787$	10.3705	−	17.9622i	0.369667	−	0.640283i	−0.619846	−	0.784723i	$-0.712805\pi$
$787$	10.3705	−	17.9622i	0.369667	−	0.640283i	0.989513	+	0.144441i	$0.0461383\pi$
$788$	10.0423	−	17.3939i	0.357744	−	0.619630i
$789$	2.95324	+	5.11516i	0.105138	+	0.182104i
$790$	4.66487			0.165969
$791$	33.0768	+	22.0021i	1.17608	+	0.782304i
$792$	15.2174			0.540728
$793$	4.67241	+	8.09285i	0.165922	+	0.287385i
$794$	−3.53846	+	6.12879i	−0.125575	+	0.217503i
$795$	−0.769946	+	1.33359i	−0.0273072	+	0.0472974i
$796$	−6.74309	−	11.6794i	−0.239003	−	0.413965i
$797$	15.6805			0.555433			0.277716	−	0.960663i	$-0.410422\pi$
$797$	15.6805			0.555433			0.277716	+	0.960663i	$0.410422\pi$
$798$	−0.187604	+	2.95625i	−0.00664111	+	0.104650i
$799$	6.38537			0.225898
$800$	13.1770	+	22.8232i	0.465876	+	0.806920i
$801$	7.49127	−	12.9753i	0.264691	−	0.458458i
$802$	13.1124	−	22.7113i	0.463014	−	0.801963i
$803$	−4.62887	−	8.01743i	−0.163349	−	0.282929i
$804$	−16.6146			−0.585953
$805$	−5.50670	+	2.72982i	−0.194086	+	0.0962136i
$806$	−4.16852			−0.146830
$807$	−8.84817	−	15.3255i	−0.311470	−	0.539482i
$808$	3.09030	−	5.35256i	0.108716	−	0.188302i
$809$	−15.8218	+	27.4042i	−0.556267	+	0.963482i	0.441537	+	0.897243i	$0.354433\pi$
$809$	−15.8218	+	27.4042i	−0.556267	+	0.963482i	−0.997804	+	0.0662390i	$0.978900\pi$
$810$	−0.277479	−	0.480608i	−0.00974962	−	0.0168868i
$811$	11.3110			0.397182			0.198591	−	0.980082i	$-0.436364\pi$
$811$	11.3110			0.397182			0.198591	+	0.980082i	$0.436364\pi$
$812$	9.01238	−	4.46768i	0.316272	−	0.156785i
$813$	30.8485			1.08190
$814$	−18.4434	−	31.9449i	−0.646441	−	1.11967i
$815$	6.42543	−	11.1292i	0.225073	−	0.389838i
$816$	0.147948	−	0.256254i	0.00517923	−	0.00897069i
$817$	−6.25518	−	10.8343i	−0.218841	−	0.379044i
$818$	−16.0325			−0.560564
$819$	0.167563	−	2.64044i	0.00585512	−	0.0922644i
$820$	8.26503			0.288627
$821$	−23.6579	−	40.9767i	−0.825668	−	1.43010i	−0.901408	−	0.432971i	$-0.857465\pi$
$821$	−23.6579	−	40.9767i	−0.825668	−	1.43010i	0.0757405	−	0.997128i	$-0.475868\pi$
$822$	−0.720365	+	1.24771i	−0.0251256	+	0.0435188i
$823$	8.34266	−	14.4499i	0.290807	−	0.503692i	−0.683194	−	0.730237i	$-0.739410\pi$
$823$	8.34266	−	14.4499i	0.290807	−	0.503692i	0.974001	+	0.226545i	$0.0727430\pi$
$824$	18.1305	+	31.4029i	0.631606	+	1.09397i
$825$	25.5569			0.889776
$826$	11.5106	+	7.65667i	0.400507	+	0.266410i
$827$	10.1105			0.351577			0.175788	−	0.984428i	$-0.443753\pi$
$827$	10.1105			0.351577			0.175788	+	0.984428i	$0.443753\pi$
$828$	2.27748	+	3.94471i	0.0791479	+	0.137088i
$829$	18.8415	−	32.6344i	0.654391	−	1.13344i	−0.327655	−	0.944797i	$-0.606258\pi$
$829$	18.8415	−	32.6344i	0.654391	−	1.13344i	0.982046	−	0.188641i	$-0.0604083\pi$
$830$	−0.400969	+	0.694498i	−0.0139178	+	0.0241064i
$831$	−9.22132	−	15.9718i	−0.319884	−	0.554056i
$832$	3.56465			0.123582
$833$	3.70237	+	0.471807i	0.128280	+	0.0163471i
$834$	−3.49827			−0.121135
$835$	0.141244	+	0.244641i	0.00488794	+	0.00846616i
$836$	5.35431	−	9.27394i	0.185183	−	0.320746i
$837$	2.59903	−	4.50165i	0.0898357	−	0.155600i
$838$	10.6184	+	18.3916i	0.366807	+	0.635328i
$839$	28.2064			0.973794			0.486897	−	0.873459i	$-0.338129\pi$
$839$	28.2064			0.973794			0.486897	+	0.873459i	$0.338129\pi$
$840$	−4.10388	−	2.72982i	−0.141597	−	0.0941879i
$841$	−21.1491			−0.729281
$842$	−12.8122	−	22.1913i	−0.441536	−	0.764763i
$843$	−7.45862	+	12.9187i	−0.256888	+	0.444944i
$844$	−4.88189	+	8.45568i	−0.168041	+	0.291056i
$845$	−0.346011	−	0.599308i	−0.0119031	−	0.0206168i
$846$	−9.60388			−0.330188
$847$	3.51112	−	55.3280i	0.120644	−	1.90109i
$848$	1.23490			0.0424066
$849$	−7.38135	−	12.7849i	−0.253327	−	0.438776i
$850$	−0.966575	+	1.67416i	−0.0331533	+	0.0574231i
$851$	13.6576	−	23.6557i	0.468178	−	0.810908i
$852$	−1.34213	−	2.32463i	−0.0459805	−	0.0796405i
$853$	−22.1062			−0.756902			−0.378451	−	0.925621i	$-0.623543\pi$
$853$	−22.1062			−0.756902			−0.378451	+	0.925621i	$0.623543\pi$
$854$	17.7642	−	8.80620i	0.607878	−	0.301342i
$855$	−0.966148			−0.0330416
$856$	7.44773	+	12.8998i	0.254558	+	0.440908i
$857$	−3.52930	+	6.11293i	−0.120559	+	0.208814i	−0.919988	−	0.391946i	$-0.871802\pi$
$857$	−3.52930	+	6.11293i	−0.120559	+	0.208814i	0.799429	+	0.600760i	$0.205135\pi$
$858$	2.26659	−	3.92586i	0.0773802	−	0.134027i
$859$	−2.73825	−	4.74279i	−0.0934279	−	0.161822i	0.815524	−	0.578724i	$-0.196449\pi$
$859$	−2.73825	−	4.74279i	−0.0934279	−	0.161822i	−0.908951	+	0.416902i	$0.863116\pi$
$860$	8.41417			0.286921
$861$	20.8647	−	10.3432i	0.711068	−	0.352496i
$862$	−24.9280			−0.849051
$863$	−21.0864	−	36.5227i	−0.717790	−	1.24325i	−0.961874	−	0.273495i	$-0.911820\pi$
$863$	−21.0864	−	36.5227i	−0.717790	−	1.24325i	0.244084	−	0.969754i	$-0.421513\pi$
$864$	−2.91454	+	5.04814i	−0.0991547	+	0.171741i
$865$	6.94989	−	12.0376i	0.236303	−	0.409289i
$866$	3.72468	+	6.45133i	0.126570	+	0.219225i
$867$	−16.7157			−0.567695
$868$	1.18186	−	18.6236i	0.0401149	−	0.632127i
$869$	−47.5163			−1.61188
$870$	−0.777479	−	1.34663i	−0.0263590	−	0.0456551i
$871$	−6.12229	+	10.6041i	−0.207446	+	0.359307i
$872$	−15.7579	+	27.2934i	−0.533629	+	0.924272i
$873$	0.0413846	+	0.0716802i	0.00140066	+	0.00242601i
$874$	−3.75840			−0.127130
$875$	−14.5145	−	9.65480i	−0.490681	−	0.326392i
$876$	2.22223			0.0750820
$877$	15.4189	+	26.7062i	0.520658	+	0.901806i	0.999711	+	0.0240201i	$0.00764656\pi$
$877$	15.4189	+	26.7062i	0.520658	+	0.901806i	−0.479054	+	0.877786i	$0.659020\pi$
$878$	9.31067	−	16.1265i	0.314220	−	0.544245i
$879$	13.4160	−	23.2373i	0.452512	−	0.783773i
$880$	1.08546	+	1.88007i	0.0365908	+	0.0633771i
$881$	−9.08277			−0.306006			−0.153003	−	0.988226i	$-0.548894\pi$
$881$	−9.08277			−0.306006			−0.153003	+	0.988226i	$0.548894\pi$
$882$	−5.56853	−	0.709618i	−0.187502	−	0.0238941i
$883$	−56.0334			−1.88567			−0.942837	−	0.333255i	$-0.891853\pi$
$883$	−56.0334			−1.88567			−0.942837	+	0.333255i	$0.891853\pi$
$884$	−0.361740	−	0.626552i	−0.0121666	−	0.0210732i
$885$	−2.25451	+	3.90493i	−0.0757846	+	0.131263i
$886$	−15.8535	+	27.4591i	−0.532610	+	0.922508i
$887$	−14.9596	−	25.9107i	−0.502293	−	0.869998i	−0.999996	−	0.00265018i	$-0.999156\pi$
$887$	−14.9596	−	25.9107i	−0.502293	−	0.869998i	0.497703	−	0.867347i	$-0.334177\pi$
$888$	21.9051			0.735089
$889$	−15.3819	−	10.2318i	−0.515892	−	0.343162i
$890$	−8.31468			−0.278709
$891$	2.82640	+	4.89546i	0.0946878	+	0.164004i
$892$	−1.59538	+	2.76328i	−0.0534174	+	0.0925216i
$893$	−8.35988	+	14.4797i	−0.279753	+	0.484546i
$894$	1.39612	+	2.41816i	0.0466934	+	0.0808753i
$895$	6.60388			0.220743
$896$	−1.47448	+	23.2347i	−0.0492588	+	0.776216i
$897$	3.35690			0.112083
$898$	−13.5848	−	23.5296i	−0.453330	−	0.785191i
$899$	7.28232	−	12.6134i	0.242879	−	0.420679i
$900$	−3.06734	+	5.31278i	−0.102245	+	0.177093i
$901$	0.593227	+	1.02750i	0.0197633	+	0.0342310i
$902$	39.9008			1.32855
$903$	21.2412	−	10.5299i	0.706864	−	0.350412i
$904$	−40.4209			−1.34438
$905$	4.84183	+	8.38630i	0.160948	+	0.278770i
$906$	−7.60388	+	13.1703i	−0.252622	+	0.437554i
$907$	−14.5390	+	25.1823i	−0.482759	+	0.836164i	−0.999804	−	0.0197947i	$-0.993699\pi$
$907$	−14.5390	+	25.1823i	−0.482759	+	0.836164i	0.517045	+	0.855958i	$0.327032\pi$
$908$	17.1685	+	29.7368i	0.569757	+	0.986849i
$909$	2.29590			0.0761501
$910$	−1.31551	+	0.652135i	−0.0436088	+	0.0216181i
$911$	10.6679			0.353442			0.176721	−	0.984261i	$-0.443451\pi$
$911$	10.6679			0.353442			0.176721	+	0.984261i	$0.443451\pi$
$912$	0.387395	+	0.670988i	0.0128279	+	0.0222186i
$913$	4.08426	−	7.07415i	0.135169	−	0.234120i
$914$	11.4731	−	19.8721i	0.379498	−	0.657310i
$915$	3.23341	+	5.60042i	0.106893	+	0.185144i
$916$	−7.04998			−0.232938
$917$	1.97644	−	31.1446i	0.0652679	−	1.02849i
$918$	−0.427583			−0.0141124
$919$	11.8738	+	20.5661i	0.391681	+	0.678412i	0.992671	−	0.120845i	$-0.0385603\pi$
$919$	11.8738	+	20.5661i	0.391681	+	0.678412i	−0.600990	+	0.799256i	$0.705227\pi$
$920$	3.12684	−	5.41585i	0.103089	−	0.178555i
$921$	−0.425428	+	0.736862i	−0.0140183	+	0.0242804i
$922$	11.4792	+	19.8825i	0.378047	+	0.654797i
$923$	−1.97823			−0.0651142
$924$	16.8968	+	11.2395i	0.555865	+	0.369752i
$925$	36.7885			1.20960
$926$	−0.979959	−	1.69734i	−0.0322034	−	0.0557780i
$927$	−6.73490	+	11.6652i	−0.221203	+	0.383135i
$928$	−8.16637	+	14.1446i	−0.268074	+	0.464318i
$929$	5.28554	+	9.15483i	0.173413	+	0.300360i	0.939611	−	0.342244i	$-0.111187\pi$
$929$	5.28554	+	9.15483i	0.173413	+	0.300360i	−0.766198	+	0.642605i	$0.777854\pi$
$930$	−2.88471			−0.0945933
$931$	−5.91713	+	7.77796i	−0.193926	+	0.254912i
$932$	−20.5821			−0.674189
$933$	4.67121	+	8.09077i	0.152929	+	0.264880i
$934$	3.28717	−	5.69354i	0.107559	−	0.186298i
$935$	−1.04288	+	1.80632i	−0.0341057	+	0.0590728i
$936$	1.34601	+	2.33136i	0.0439957	+	0.0762029i
$937$	−59.2307			−1.93498			−0.967491	−	0.252904i	$-0.918614\pi$
$937$	−59.2307			−1.93498			−0.967491	+	0.252904i	$0.918614\pi$
$938$	21.6312	+	14.3887i	0.706284	+	0.469807i
$939$	−16.2905			−0.531621
$940$	−5.62266	−	9.73874i	−0.183391	−	0.317643i
$941$	6.43309	−	11.1424i	0.209713	−	0.363233i	−0.741911	−	0.670498i	$-0.766080\pi$
$941$	6.43309	−	11.1424i	0.209713	−	0.363233i	0.951624	+	0.307265i	$0.0994138\pi$
$942$	7.16756	−	12.4146i	0.233532	−	0.404489i
$943$	14.7736	+	25.5886i	0.481094	+	0.833280i
$944$	3.61596			0.117689
$945$	0.115957	−	1.82724i	0.00377208	−	0.0594402i
$946$	40.6209			1.32070
$947$	18.5097	+	32.0597i	0.601484	+	1.04180i	0.992597	+	0.121458i	$0.0387570\pi$
$947$	18.5097	+	32.0597i	0.601484	+	1.04180i	−0.391112	+	0.920343i	$0.627910\pi$
$948$	5.70291	−	9.87772i	0.185222	−	0.320814i
$949$	0.818864	−	1.41831i	0.0265814	−	0.0460404i
$950$	−2.53093	−	4.38369i	−0.0821141	−	0.142226i
$951$	8.49827			0.275575
$952$	−3.40246	+	1.68669i	−0.110274	+	0.0546660i
$953$	−42.6064			−1.38016			−0.690078	−	0.723735i	$-0.742424\pi$
$953$	−42.6064			−1.38016			−0.690078	+	0.723735i	$0.742424\pi$
$954$	−0.892240	−	1.54540i	−0.0288873	−	0.0500343i
$955$	−1.44421	+	2.50145i	−0.0467337	+	0.0809451i
$956$	6.63826	−	11.4978i	0.214697	−	0.371866i
$957$	7.91939	+	13.7168i	0.255997	+	0.443401i
$958$	−22.3840			−0.723196
$959$	−4.25869	+	2.11115i	−0.137520	+	0.0681726i
$960$	2.46681			0.0796160
$961$	1.99007	+	3.44691i	0.0641959	+	0.111191i
$962$	3.26271	−	5.65118i	0.105194	−	0.182201i
$963$	−2.76659	+	4.79188i	−0.0891522	+	0.154416i
$964$	17.9863	+	31.1532i	0.579300	+	1.00338i
$965$	−18.2597			−0.587799
$966$	0.451083	−	7.10812i	0.0145133	−	0.228700i
$967$	−32.1629			−1.03429			−0.517144	−	0.855898i	$-0.673005\pi$
$967$	−32.1629			−1.03429			−0.517144	+	0.855898i	$0.673005\pi$
$968$	28.2044	+	48.8515i	0.906524	+	1.57015i
$969$	−0.372198	+	0.644666i	−0.0119567	+	0.0207097i
$970$	0.0229667	−	0.0397795i	0.000737417	−	0.00127724i
$971$	11.6763	+	20.2239i	0.374710	+	0.649017i	0.990284	−	0.139063i	$-0.0444089\pi$
$971$	11.6763	+	20.2239i	0.374710	+	0.649017i	−0.615574	+	0.788079i	$0.711076\pi$
$972$	−1.35690			−0.0435225
$973$	−9.60968	−	6.39218i	−0.308072	−	0.204924i
$974$	−17.9071			−0.573779
$975$	2.26055	+	3.91539i	0.0723956	+	0.125393i
$976$	2.59299	−	4.49119i	0.0829996	−	0.143760i
$977$	4.51991	−	7.82871i	0.144605	−	0.250463i	−0.784621	−	0.619976i	$-0.787142\pi$
$977$	4.51991	−	7.82871i	0.144605	−	0.250463i	0.929225	+	0.369513i	$0.120476\pi$
$978$	7.44600	+	12.8969i	0.238097	+	0.412396i
$979$	84.6932			2.70681
$980$	−2.54056	−	6.06218i	−0.0811551	−	0.193649i
$981$	−11.7071			−0.373779
$982$	6.56542	+	11.3716i	0.209511	+	0.362883i
$983$	17.7089	−	30.6728i	0.564828	−	0.978310i	−0.432238	−	0.901760i	$-0.642276\pi$
$983$	17.7089	−	30.6728i	0.564828	−	0.978310i	0.997066	−	0.0765507i	$-0.0243907\pi$
$984$	−11.8475	+	20.5205i	−0.377685	+	0.654169i
$985$	−5.12163	−	8.87092i	−0.163189	−	0.282651i
$986$	−1.19806			−0.0381541
$987$	−26.3817	−	17.5486i	−0.839737	−	0.558578i
$988$	1.89440			0.0602688
$989$	15.0402	+	26.0504i	0.478250	+	0.828354i
$990$	1.56853	−	2.71678i	0.0498512	−	0.0863448i
$991$	6.87263	−	11.9037i	0.218316	−	0.378135i	−0.735977	−	0.677006i	$-0.763277\pi$
$991$	6.87263	−	11.9037i	0.218316	−	0.378135i	0.954293	+	0.298872i	$0.0966103\pi$
$992$	15.1500	+	26.2405i	0.481012	+	0.833137i
$993$	−3.55496			−0.112813
$994$	−0.265824	+	4.18884i	−0.00843144	+	0.132862i
$995$	−6.87800			−0.218047
$996$	0.980386	+	1.69808i	0.0310647	+	0.0538057i
$997$	−8.73676	+	15.1325i	−0.276696	+	0.479251i	−0.970562	−	0.240853i	$-0.922573\pi$
$997$	−8.73676	+	15.1325i	−0.276696	+	0.479251i	0.693866	+	0.720104i	$0.255906\pi$
$998$	−8.42519	+	14.5929i	−0.266695	+	0.461929i
$999$	4.06853	+	7.04690i	0.128723	+	0.222954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.c.235.1	yes	6
3.2	odd	2		819.2.j.d.235.3		6
7.2	even	3	inner	273.2.i.c.79.1	✓	6
7.3	odd	6		1911.2.a.l.1.3		3
7.4	even	3		1911.2.a.m.1.3		3
21.2	odd	6		819.2.j.d.352.3		6
21.11	odd	6		5733.2.a.bb.1.1		3
21.17	even	6		5733.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.c.79.1	✓	6	7.2	even	3	inner
273.2.i.c.235.1	yes	6	1.1	even	1	trivial
819.2.j.d.235.3		6	3.2	odd	2
819.2.j.d.352.3		6	21.2	odd	6
1911.2.a.l.1.3		3	7.3	odd	6
1911.2.a.m.1.3		3	7.4	even	3
5733.2.a.ba.1.1		3	21.17	even	6
5733.2.a.bb.1.1		3	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} +(-0.346011 - 0.599308i) q^{5} +0.801938 q^{6} +(2.20291 + 1.46533i) q^{7} -2.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.400969 - 0.694498i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.678448 - 1.17511i) q^{4} +(-0.346011 - 0.599308i) q^{5} +0.801938 q^{6} +(2.20291 + 1.46533i) q^{7} -2.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.277479 + 0.480608i) q^{10} +(2.82640 - 4.89546i) q^{11} +(0.678448 + 1.17511i) q^{12} +1.00000 q^{13} +(0.134375 - 2.11747i) q^{14} +0.692021 q^{15} +(-0.277479 - 0.480608i) q^{16} +(0.266594 - 0.461754i) q^{17} +(-0.400969 + 0.694498i) q^{18} +(0.698062 + 1.20908i) q^{19} -0.939001 q^{20} +(-2.37047 + 1.17511i) q^{21} -4.53319 q^{22} +(-1.67845 - 2.90716i) q^{23} +(1.34601 - 2.33136i) q^{24} +(2.26055 - 3.91539i) q^{25} +(-0.400969 - 0.694498i) q^{26} +1.00000 q^{27} +(3.21648 - 1.59450i) q^{28} +2.80194 q^{29} +(-0.277479 - 0.480608i) q^{30} +(2.59903 - 4.50165i) q^{31} +(-2.91454 + 5.04814i) q^{32} +(2.82640 + 4.89546i) q^{33} -0.427583 q^{34} +(0.115957 - 1.82724i) q^{35} -1.35690 q^{36} +(4.06853 + 7.04690i) q^{37} +(0.559802 - 0.969606i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.931468 + 1.61335i) q^{40} -8.80194 q^{41} +(1.76659 + 1.17511i) q^{42} -8.96077 q^{43} +(-3.83513 - 6.64263i) q^{44} +(-0.346011 + 0.599308i) q^{45} +(-1.34601 + 2.33136i) q^{46} +(5.98792 + 10.3714i) q^{47} +0.554958 q^{48} +(2.70560 + 6.45599i) q^{49} -3.62565 q^{50} +(0.266594 + 0.461754i) q^{51} +(0.678448 - 1.17511i) q^{52} +(-1.11260 + 1.92709i) q^{53} +(-0.400969 - 0.694498i) q^{54} -3.91185 q^{55} +(-5.93027 - 3.94471i) q^{56} -1.39612 q^{57} +(-1.12349 - 1.94594i) q^{58} +(-3.25786 + 5.64279i) q^{59} +(0.469501 - 0.813199i) q^{60} +(4.67241 + 8.09285i) q^{61} -4.16852 q^{62} +(0.167563 - 2.64044i) q^{63} +3.56465 q^{64} +(-0.346011 - 0.599308i) q^{65} +(2.26659 - 3.92586i) q^{66} +(-6.12229 + 10.6041i) q^{67} +(-0.361740 - 0.626552i) q^{68} +3.35690 q^{69} +(-1.31551 + 0.652135i) q^{70} -1.97823 q^{71} +(1.34601 + 2.33136i) q^{72} +(0.818864 - 1.41831i) q^{73} +(3.26271 - 5.65118i) q^{74} +(2.26055 + 3.91539i) q^{75} +1.89440 q^{76} +(13.3998 - 6.64263i) q^{77} +0.801938 q^{78} +(-4.20291 - 7.27965i) q^{79} +(-0.192021 + 0.332591i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.52930 + 6.11293i) q^{82} +1.44504 q^{83} +(-0.227365 + 3.58280i) q^{84} -0.368977 q^{85} +(3.59299 + 6.22324i) q^{86} +(-1.40097 + 2.42655i) q^{87} +(-7.60872 + 13.1787i) q^{88} +(7.49127 + 12.9753i) q^{89} +0.554958 q^{90} +(2.20291 + 1.46533i) q^{91} -4.55496 q^{92} +(2.59903 + 4.50165i) q^{93} +(4.80194 - 8.31720i) q^{94} +(0.483074 - 0.836709i) q^{95} +(-2.91454 - 5.04814i) q^{96} -0.0827692 q^{97} +(3.39881 - 4.46768i) q^{98} -5.65279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - 3 q^{3} + 3 q^{5} - 4 q^{6} - 6 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 6 q^{13} - 7 q^{14} - 6 q^{15} - 2 q^{16} + 5 q^{17} + 2 q^{18} + 13 q^{19} + 14 q^{20} - 34 q^{22} - 6 q^{23} + 3 q^{24} - 2 q^{25} + 2 q^{26} + 6 q^{27} + 8 q^{29} - 2 q^{30} + 20 q^{31} - 7 q^{32} - q^{33} + 30 q^{34} + 21 q^{35} + 19 q^{37} - 18 q^{38} - 3 q^{39} + 11 q^{40} - 44 q^{41} + 14 q^{42} - 28 q^{43} - 21 q^{44} + 3 q^{45} - 3 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{50} + 5 q^{51} - 5 q^{53} + 2 q^{54} - 16 q^{55} - 26 q^{57} - 2 q^{58} - 7 q^{59} - 7 q^{60} + 5 q^{61} + 36 q^{62} - 22 q^{64} + 3 q^{65} + 17 q^{66} + 9 q^{67} + 28 q^{68} + 12 q^{69} + 7 q^{70} - 18 q^{71} + 3 q^{72} + 12 q^{73} - 15 q^{74} - 2 q^{75} - 28 q^{76} + 35 q^{77} - 4 q^{78} - 12 q^{79} + 9 q^{80} - 3 q^{81} - 10 q^{82} + 8 q^{83} + 21 q^{84} - 32 q^{85} + 7 q^{86} - 4 q^{87} - 6 q^{88} + 29 q^{89} + 4 q^{90} - 28 q^{92} + 20 q^{93} + 20 q^{94} - 13 q^{95} - 7 q^{96} - 14 q^{97} + 35 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 3 * q^3 + 3 * q^5 - 4 * q^6 - 6 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + 6 * q^13 - 7 * q^14 - 6 * q^15 - 2 * q^16 + 5 * q^17 + 2 * q^18 + 13 * q^19 + 14 * q^20 - 34 * q^22 - 6 * q^23 + 3 * q^24 - 2 * q^25 + 2 * q^26 + 6 * q^27 + 8 * q^29 - 2 * q^30 + 20 * q^31 - 7 * q^32 - q^33 + 30 * q^34 + 21 * q^35 + 19 * q^37 - 18 * q^38 - 3 * q^39 + 11 * q^40 - 44 * q^41 + 14 * q^42 - 28 * q^43 - 21 * q^44 + 3 * q^45 - 3 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^50 + 5 * q^51 - 5 * q^53 + 2 * q^54 - 16 * q^55 - 26 * q^57 - 2 * q^58 - 7 * q^59 - 7 * q^60 + 5 * q^61 + 36 * q^62 - 22 * q^64 + 3 * q^65 + 17 * q^66 + 9 * q^67 + 28 * q^68 + 12 * q^69 + 7 * q^70 - 18 * q^71 + 3 * q^72 + 12 * q^73 - 15 * q^74 - 2 * q^75 - 28 * q^76 + 35 * q^77 - 4 * q^78 - 12 * q^79 + 9 * q^80 - 3 * q^81 - 10 * q^82 + 8 * q^83 + 21 * q^84 - 32 * q^85 + 7 * q^86 - 4 * q^87 - 6 * q^88 + 29 * q^89 + 4 * q^90 - 28 * q^92 + 20 * q^93 + 20 * q^94 - 13 * q^95 - 7 * q^96 - 14 * q^97 + 35 * q^98 + 2 * q^99

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