LMFDB - Embedded newform 1295.2.j.a.186.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			186.14
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.801447 + 1.38815i) q^{2} +(-1.11974 + 1.93944i) q^{3} +(-0.284634 + 0.493001i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.58964 q^{6} +(-0.281235 + 2.63076i) q^{7} +2.29331 q^{8} +(-1.00763 - 1.74526i) q^{9} +(0.801447 - 1.38815i) q^{10} +(-1.42953 + 2.47603i) q^{11} +(-0.637432 - 1.10407i) q^{12} -3.48980 q^{13} +(-3.87728 + 1.71802i) q^{14} +2.23948 q^{15} +(2.40724 + 4.16945i) q^{16} +(1.01938 - 1.76561i) q^{17} +(1.61512 - 2.79747i) q^{18} +(3.18953 + 5.52443i) q^{19} +0.569269 q^{20} +(-4.78731 - 3.49120i) q^{21} -4.58279 q^{22} +(-1.80672 - 3.12934i) q^{23} +(-2.56791 + 4.44775i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.79689 - 4.84436i) q^{26} -2.20531 q^{27} +(-1.21692 - 0.887454i) q^{28} -3.33608 q^{29} +(1.79482 + 3.10872i) q^{30} +(-1.86554 + 3.23121i) q^{31} +(-1.56523 + 2.71106i) q^{32} +(-3.20141 - 5.54501i) q^{33} +3.26791 q^{34} +(2.41892 - 1.07182i) q^{35} +1.14722 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-5.11248 + 8.85508i) q^{38} +(3.90767 - 6.76828i) q^{39} +(-1.14666 - 1.98606i) q^{40} -4.95006 q^{41} +(1.00953 - 9.44350i) q^{42} -0.192899 q^{43} +(-0.813790 - 1.40953i) q^{44} +(-1.00763 + 1.74526i) q^{45} +(2.89599 - 5.01600i) q^{46} +(-2.34249 - 4.05732i) q^{47} -10.7819 q^{48} +(-6.84181 - 1.47972i) q^{49} -1.60289 q^{50} +(2.28287 + 3.95405i) q^{51} +(0.993318 - 1.72048i) q^{52} +(6.90724 - 11.9637i) q^{53} +(-1.76744 - 3.06129i) q^{54} +2.85907 q^{55} +(-0.644959 + 6.03315i) q^{56} -14.2858 q^{57} +(-2.67369 - 4.63097i) q^{58} +(-4.21887 + 7.30730i) q^{59} +(-0.637432 + 1.10407i) q^{60} +(-2.20147 - 3.81305i) q^{61} -5.98052 q^{62} +(4.87476 - 2.16000i) q^{63} +4.61114 q^{64} +(1.74490 + 3.02226i) q^{65} +(5.13152 - 8.88806i) q^{66} +(0.193415 - 0.335005i) q^{67} +(0.580300 + 1.00511i) q^{68} +8.09223 q^{69} +(3.42649 + 2.49881i) q^{70} +9.77799 q^{71} +(-2.31081 - 4.00243i) q^{72} +(-4.03067 + 6.98132i) q^{73} +(0.801447 - 1.38815i) q^{74} +(-1.11974 - 1.93944i) q^{75} -3.63140 q^{76} +(-6.11180 - 4.45711i) q^{77} +12.5272 q^{78} +(5.96105 + 10.3248i) q^{79} +(2.40724 - 4.16945i) q^{80} +(5.49225 - 9.51286i) q^{81} +(-3.96721 - 6.87141i) q^{82} -5.18099 q^{83} +(3.08380 - 1.36643i) q^{84} -2.03875 q^{85} +(-0.154599 - 0.267773i) q^{86} +(3.73554 - 6.47014i) q^{87} +(-3.27837 + 5.67830i) q^{88} +(7.65258 + 13.2547i) q^{89} -3.23025 q^{90} +(0.981454 - 9.18084i) q^{91} +2.05702 q^{92} +(-4.17783 - 7.23621i) q^{93} +(3.75477 - 6.50345i) q^{94} +(3.18953 - 5.52443i) q^{95} +(-3.50530 - 6.07136i) q^{96} -4.92715 q^{97} +(-3.42928 - 10.6834i) q^{98} +5.76176 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.801447	+	1.38815i	0.566709	+	0.981568i	0.996888	+	0.0788249i	$0.0251168\pi$
$2$	0.801447	+	1.38815i	0.566709	+	0.981568i	−0.430180	+	0.902743i	$0.641550\pi$
$3$	−1.11974	+	1.93944i	−0.646481	+	1.11974i	0.337476	+	0.941334i	$0.390427\pi$
$3$	−1.11974	+	1.93944i	−0.646481	+	1.11974i	−0.983957	+	0.178404i	$0.942906\pi$
$4$	−0.284634	+	0.493001i	−0.142317	+	0.246501i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.58964			−1.46547
$7$	−0.281235	+	2.63076i	−0.106297	+	0.994334i
$7$	−0.281235	+	2.63076i	−0.106297	+	0.994334i
$8$	2.29331			0.810808
$9$	−1.00763	−	1.74526i	−0.335876	−	0.581755i
$10$	0.801447	−	1.38815i	0.253440	−	0.438971i
$11$	−1.42953	+	2.47603i	−0.431021	+	0.746550i	−0.996962	−	0.0778958i	$-0.975180\pi$
$11$	−1.42953	+	2.47603i	−0.431021	+	0.746550i	0.565941	+	0.824446i	$0.308513\pi$
$12$	−0.637432	−	1.10407i	−0.184011	−	0.318716i
$13$	−3.48980			−0.967897			−0.483949	−	0.875096i	$-0.660798\pi$
$13$	−3.48980			−0.967897			−0.483949	+	0.875096i	$0.660798\pi$
$14$	−3.87728	+	1.71802i	−1.03625	+	0.459160i
$15$	2.23948			0.578231
$16$	2.40724	+	4.16945i	0.601809	+	1.04236i
$17$	1.01938	−	1.76561i	0.247235	−	0.428224i	−0.715522	−	0.698590i	$-0.753811\pi$
$17$	1.01938	−	1.76561i	0.247235	−	0.428224i	0.962758	+	0.270366i	$0.0871446\pi$
$18$	1.61512	−	2.79747i	0.380688	−	0.659371i
$19$	3.18953	+	5.52443i	0.731729	+	1.26739i	0.956144	+	0.292898i	$0.0946195\pi$
$19$	3.18953	+	5.52443i	0.731729	+	1.26739i	−0.224415	+	0.974494i	$0.572047\pi$
$20$	0.569269			0.127292
$21$	−4.78731	−	3.49120i	−1.04468	−	0.761843i
$22$	−4.58279			−0.977053
$23$	−1.80672	−	3.12934i	−0.376728	−	0.652512i	0.613856	−	0.789418i	$-0.289618\pi$
$23$	−1.80672	−	3.12934i	−0.376728	−	0.652512i	−0.990584	+	0.136906i	$0.956284\pi$
$24$	−2.56791	+	4.44775i	−0.524172	+	0.907893i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.79689	−	4.84436i	−0.548516	−	0.950057i
$27$	−2.20531			−0.424411
$28$	−1.21692	−	0.887454i	−0.229976	−	0.167713i
$29$	−3.33608			−0.619495			−0.309747	−	0.950819i	$-0.600244\pi$
$29$	−3.33608			−0.619495			−0.309747	+	0.950819i	$0.600244\pi$
$30$	1.79482	+	3.10872i	0.327688	+	0.567573i
$31$	−1.86554	+	3.23121i	−0.335061	+	0.580342i	−0.983496	−	0.180927i	$-0.942090\pi$
$31$	−1.86554	+	3.23121i	−0.335061	+	0.580342i	0.648436	+	0.761269i	$0.275423\pi$
$32$	−1.56523	+	2.71106i	−0.276697	+	0.479253i
$33$	−3.20141	−	5.54501i	−0.557294	−	0.965262i
$34$	3.26791			0.560441
$35$	2.41892	−	1.07182i	0.408873	−	0.181171i
$36$	1.14722			0.191204
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	−5.11248	+	8.85508i	−0.829354	+	1.43648i
$39$	3.90767	−	6.76828i	0.625728	−	1.08379i
$40$	−1.14666	−	1.98606i	−0.181302	−	0.314024i
$41$	−4.95006			−0.773070			−0.386535	−	0.922275i	$-0.626328\pi$
$41$	−4.95006			−0.773070			−0.386535	+	0.922275i	$0.626328\pi$
$42$	1.00953	−	9.44350i	0.155774	−	1.45716i
$43$	−0.192899			−0.0294169			−0.0147084	−	0.999892i	$-0.504682\pi$
$43$	−0.192899			−0.0294169			−0.0147084	+	0.999892i	$0.504682\pi$
$44$	−0.813790	−	1.40953i	−0.122683	−	0.212494i
$45$	−1.00763	+	1.74526i	−0.150208	+	0.260169i
$46$	2.89599	−	5.01600i	0.426990	−	0.739568i
$47$	−2.34249	−	4.05732i	−0.341688	−	0.591820i	0.643059	−	0.765817i	$-0.277665\pi$
$47$	−2.34249	−	4.05732i	−0.341688	−	0.591820i	−0.984746	+	0.173997i	$0.944332\pi$
$48$	−10.7819			−1.55623
$49$	−6.84181	−	1.47972i	−0.977402	−	0.211389i
$50$	−1.60289			−0.226683
$51$	2.28287	+	3.95405i	0.319666	+	0.553678i
$52$	0.993318	−	1.72048i	0.137748	−	0.238587i
$53$	6.90724	−	11.9637i	0.948782	−	1.64334i	0.200788	−	0.979635i	$-0.435650\pi$
$53$	6.90724	−	11.9637i	0.948782	−	1.64334i	0.747995	−	0.663705i	$-0.231017\pi$
$54$	−1.76744	−	3.06129i	−0.240518	−	0.416589i
$55$	2.85907			0.385517
$56$	−0.644959	+	6.03315i	−0.0861862	+	0.806214i
$57$	−14.2858			−1.89220
$58$	−2.67369	−	4.63097i	−0.351073	−	0.608076i
$59$	−4.21887	+	7.30730i	−0.549250	+	0.951330i	0.449076	+	0.893494i	$0.351753\pi$
$59$	−4.21887	+	7.30730i	−0.549250	+	0.951330i	−0.998326	+	0.0578360i	$0.981580\pi$
$60$	−0.637432	+	1.10407i	−0.0822922	+	0.142534i
$61$	−2.20147	−	3.81305i	−0.281869	−	0.488211i	0.689976	−	0.723832i	$-0.257621\pi$
$61$	−2.20147	−	3.81305i	−0.281869	−	0.488211i	−0.971845	+	0.235621i	$0.924288\pi$
$62$	−5.98052			−0.759527
$63$	4.87476	−	2.16000i	0.614162	−	0.272135i
$64$	4.61114			0.576392
$65$	1.74490	+	3.02226i	0.216428	+	0.374865i
$66$	5.13152	−	8.88806i	0.631647	−	1.09404i
$67$	0.193415	−	0.335005i	0.0236295	−	0.0409274i	−0.853969	−	0.520324i	$-0.825811\pi$
$67$	0.193415	−	0.335005i	0.0236295	−	0.0409274i	0.877598	+	0.479397i	$0.159144\pi$
$68$	0.580300	+	1.00511i	0.0703717	+	0.121887i
$69$	8.09223			0.974191
$70$	3.42649	+	2.49881i	0.409544	+	0.298665i
$71$	9.77799			1.16043			0.580217	−	0.814462i	$-0.302968\pi$
$71$	9.77799			1.16043			0.580217	+	0.814462i	$0.302968\pi$
$72$	−2.31081	−	4.00243i	−0.272331	−	0.471691i
$73$	−4.03067	+	6.98132i	−0.471754	+	0.817102i	−0.999478	−	0.0323140i	$-0.989712\pi$
$73$	−4.03067	+	6.98132i	−0.471754	+	0.817102i	0.527724	+	0.849416i	$0.323046\pi$
$74$	0.801447	−	1.38815i	0.0931663	−	0.161369i
$75$	−1.11974	−	1.93944i	−0.129296	−	0.223948i
$76$	−3.63140			−0.416550
$77$	−6.11180	−	4.45711i	−0.696504	−	0.507935i
$78$	12.5272			1.41842
$79$	5.96105	+	10.3248i	0.670670	+	1.16164i	0.977714	+	0.209940i	$0.0673268\pi$
$79$	5.96105	+	10.3248i	0.670670	+	1.16164i	−0.307044	+	0.951695i	$0.599340\pi$
$80$	2.40724	−	4.16945i	0.269137	−	0.466159i
$81$	5.49225	−	9.51286i	0.610250	−	1.05698i
$82$	−3.96721	−	6.87141i	−0.438105	−	0.758820i
$83$	−5.18099			−0.568688			−0.284344	−	0.958722i	$-0.591776\pi$
$83$	−5.18099			−0.568688			−0.284344	+	0.958722i	$0.591776\pi$
$84$	3.08380	−	1.36643i	0.336470	−	0.149090i
$85$	−2.03875			−0.221134
$86$	−0.154599	−	0.267773i	−0.0166708	−	0.0288747i
$87$	3.73554	−	6.47014i	0.400492	−	0.693672i
$88$	−3.27837	+	5.67830i	−0.349475	+	0.605309i
$89$	7.65258	+	13.2547i	0.811172	+	1.40499i	0.912044	+	0.410092i	$0.134504\pi$
$89$	7.65258	+	13.2547i	0.811172	+	1.40499i	−0.100872	+	0.994899i	$0.532163\pi$
$90$	−3.23025			−0.340498
$91$	0.981454	−	9.18084i	0.102884	−	0.962414i
$92$	2.05702			0.214460
$93$	−4.17783	−	7.23621i	−0.433221	−	0.750360i
$94$	3.75477	−	6.50345i	0.387275	−	0.670779i
$95$	3.18953	−	5.52443i	0.327239	−	0.566795i
$96$	−3.50530	−	6.07136i	−0.357758	−	0.619656i
$97$	−4.92715			−0.500277			−0.250138	−	0.968210i	$-0.580476\pi$
$97$	−4.92715			−0.500277			−0.250138	+	0.968210i	$0.580476\pi$
$98$	−3.42928	−	10.6834i	−0.346409	−	1.07918i
$99$	5.76176			0.579079
$100$	−0.284634	−	0.493001i	−0.0284634	−	0.0493001i
$101$	0.888321	−	1.53862i	0.0883913	−	0.153098i	−0.818440	−	0.574592i	$-0.805161\pi$
$101$	0.888321	−	1.53862i	0.0883913	−	0.153098i	0.906831	+	0.421494i	$0.138494\pi$
$102$	−3.65920	+	6.33792i	−0.362315	+	0.627548i
$103$	−8.98865	−	15.5688i	−0.885678	−	1.53404i	−0.844935	−	0.534870i	$-0.820361\pi$
$103$	−8.98865	−	15.5688i	−0.885678	−	1.53404i	−0.0407435	−	0.999170i	$-0.512973\pi$
$104$	−8.00320			−0.784779
$105$	−0.629819	+	5.89153i	−0.0614640	+	0.574955i
$106$	22.1431			2.15073
$107$	8.78712	+	15.2197i	0.849483	+	1.47135i	0.881670	+	0.471866i	$0.156419\pi$
$107$	8.78712	+	15.2197i	0.849483	+	1.47135i	−0.0321870	+	0.999482i	$0.510247\pi$
$108$	0.627706	−	1.08722i	0.0604011	−	0.104618i
$109$	−0.593461	+	1.02791i	−0.0568433	+	0.0984555i	−0.893047	−	0.449964i	$-0.851437\pi$
$109$	−0.593461	+	1.02791i	−0.0568433	+	0.0984555i	0.836203	+	0.548419i	$0.184770\pi$
$110$	2.29139	+	3.96881i	0.218476	+	0.378411i
$111$	2.23948			0.212562
$112$	−11.6458	+	5.16027i	−1.10043	+	0.487599i
$113$	−8.36114			−0.786550			−0.393275	−	0.919421i	$-0.628658\pi$
$113$	−8.36114			−0.786550			−0.393275	+	0.919421i	$0.628658\pi$
$114$	−11.4493	−	19.8307i	−1.07232	−	1.85732i
$115$	−1.80672	+	3.12934i	−0.168478	+	0.291812i
$116$	0.949563	−	1.64469i	0.0881647	−	0.152706i
$117$	3.51643	+	6.09063i	0.325094	+	0.563079i
$118$	−13.5248			−1.24506
$119$	4.35822	+	3.17829i	0.399518	+	0.291353i
$120$	5.13582			0.468834
$121$	1.41286	+	2.44715i	0.128442	+	0.222468i
$122$	3.52872	−	6.11192i	0.319475	−	0.553347i
$123$	5.54277	−	9.60037i	0.499775	−	0.865636i
$124$	−1.06199	−	1.83943i	−0.0953698	−	0.165185i
$125$	1.00000			0.0894427
$126$	6.90526	+	5.03575i	0.615169	+	0.448620i
$127$	3.60437			0.319836			0.159918	−	0.987130i	$-0.448877\pi$
$127$	3.60437			0.319836			0.159918	+	0.987130i	$0.448877\pi$
$128$	6.82605	+	11.8231i	0.603343	+	1.04502i
$129$	0.215997	−	0.374117i	0.0190175	−	0.0329392i
$130$	−2.79689	+	4.84436i	−0.245304	+	0.424878i
$131$	3.32452	+	5.75824i	0.290465	+	0.503100i	0.973920	−	0.226893i	$-0.0728568\pi$
$131$	3.32452	+	5.75824i	0.290465	+	0.503100i	−0.683455	+	0.729993i	$0.739523\pi$
$132$	3.64493			0.317250
$133$	−15.4305	+	6.83723i	−1.33799	+	0.592863i
$134$	0.620049			0.0535641
$135$	1.10265	+	1.90985i	0.0949013	+	0.164374i
$136$	2.33775	−	4.04910i	0.200460	−	0.347207i
$137$	5.98775	−	10.3711i	0.511568	−	0.886061i	−0.488342	−	0.872652i	$-0.662398\pi$
$137$	5.98775	−	10.3711i	0.511568	−	0.886061i	0.999910	−	0.0134093i	$-0.00426844\pi$
$138$	6.48550	+	11.2332i	0.552082	+	0.956234i
$139$	−5.73090			−0.486088			−0.243044	−	0.970015i	$-0.578146\pi$
$139$	−5.73090			−0.486088			−0.243044	+	0.970015i	$0.578146\pi$
$140$	−0.160098	+	1.49761i	−0.0135308	+	0.126571i
$141$	10.4919			0.883579
$142$	7.83654	+	13.5733i	0.657628	+	1.13904i
$143$	4.98880	−	8.64085i	0.417184	−	0.722584i
$144$	4.85120	−	8.40253i	0.404267	−	0.700211i
$145$	1.66804	+	2.88913i	0.138523	+	0.239929i
$146$	−12.9215			−1.06939
$147$	10.5309	−	11.6124i	0.868573	−	0.957776i
$148$	0.569269			0.0467936
$149$	7.87742	+	13.6441i	0.645343	+	1.11777i	0.984222	+	0.176938i	$0.0566191\pi$
$149$	7.87742	+	13.6441i	0.645343	+	1.11777i	−0.338879	+	0.940830i	$0.610048\pi$
$150$	1.79482	−	3.10872i	0.146547	−	0.253826i
$151$	2.42056	−	4.19253i	0.196982	−	0.341183i	−0.750566	−	0.660795i	$-0.770219\pi$
$151$	2.42056	−	4.19253i	0.196982	−	0.341183i	0.947549	+	0.319612i	$0.103552\pi$
$152$	7.31458	+	12.6692i	0.593291	+	1.02761i
$153$	−4.10862			−0.332162
$154$	1.28884	−	12.0562i	0.103858	−	0.971518i
$155$	3.73108			0.299687
$156$	2.22451	+	3.85297i	0.178104	+	0.308485i
$157$	−1.68044	+	2.91061i	−0.134114	+	0.232292i	−0.925259	−	0.379337i	$-0.876152\pi$
$157$	−1.68044	+	2.91061i	−0.134114	+	0.232292i	0.791145	+	0.611629i	$0.209486\pi$
$158$	−9.55493	+	16.5496i	−0.760149	+	1.31662i
$159$	15.4686	+	26.7924i	1.22674	+	2.12478i
$160$	3.13047			0.247485
$161$	8.74066	−	3.87298i	0.688860	−	0.305234i
$162$	17.6070			1.38334
$163$	10.8086	+	18.7210i	0.846595	+	1.46635i	0.884229	+	0.467054i	$0.154685\pi$
$163$	10.8086	+	18.7210i	0.846595	+	1.46635i	−0.0376340	+	0.999292i	$0.511982\pi$
$164$	1.40896	−	2.44039i	0.110021	−	0.190562i
$165$	−3.20141	+	5.54501i	−0.249229	+	0.431678i
$166$	−4.15229	−	7.19197i	−0.322280	−	0.558205i
$167$	12.5724			0.972883			0.486442	−	0.873713i	$-0.338295\pi$
$167$	12.5724			0.972883			0.486442	+	0.873713i	$0.338295\pi$
$168$	−10.9788	−	8.00642i	−0.847031	−	0.617708i
$169$	−0.821270			−0.0631746
$170$	−1.63395	−	2.83009i	−0.125318	−	0.217058i
$171$	6.42773	−	11.1332i	0.491541	−	0.851373i
$172$	0.0549058	−	0.0950996i	0.00418653	−	0.00725128i
$173$	4.98079	+	8.62698i	0.378682	+	0.655897i	0.990871	−	0.134815i	$-0.0430439\pi$
$173$	4.98079	+	8.62698i	0.378682	+	0.655897i	−0.612188	+	0.790712i	$0.709711\pi$
$174$	11.9753			0.907848
$175$	−2.13769	−	1.55894i	−0.161594	−	0.117845i
$176$	−13.7649			−1.03757
$177$	−9.44807	−	16.3645i	−0.710160	−	1.23003i
$178$	−12.2663	+	21.2458i	−0.919397	+	1.59244i
$179$	−9.48315	+	16.4253i	−0.708804	+	1.22768i	0.256497	+	0.966545i	$0.417432\pi$
$179$	−9.48315	+	16.4253i	−0.708804	+	1.22768i	−0.965301	+	0.261140i	$0.915902\pi$
$180$	−0.573612	−	0.993525i	−0.0427545	−	0.0740530i
$181$	−7.20783			−0.535754			−0.267877	−	0.963453i	$-0.586322\pi$
$181$	−7.20783			−0.535754			−0.267877	+	0.963453i	$0.586322\pi$
$182$	13.5309	−	5.99555i	1.00298	−	0.444420i
$183$	9.86027			0.728892
$184$	−4.14338	−	7.17654i	−0.305454	−	0.529062i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	6.69662	−	11.5989i	0.491020	−	0.850471i
$187$	2.91447	+	5.04801i	0.213127	+	0.369147i
$188$	2.66702			0.194512
$189$	0.620209	−	5.80164i	0.0451136	−	0.422007i
$190$	10.2250			0.741797
$191$	−6.65915	−	11.5340i	−0.481839	−	0.834569i	0.517944	−	0.855415i	$-0.326698\pi$
$191$	−6.65915	−	11.5340i	−0.481839	−	0.834569i	−0.999783	+	0.0208452i	$0.993364\pi$
$192$	−5.16327	+	8.94304i	−0.372627	+	0.645409i
$193$	1.17789	−	2.04017i	0.0847864	−	0.146854i	−0.820514	−	0.571627i	$-0.806313\pi$
$193$	1.17789	−	2.04017i	0.0847864	−	0.146854i	0.905300	+	0.424772i	$0.139646\pi$
$194$	−3.94885	−	6.83961i	−0.283511	−	0.491056i
$195$	−7.81534			−0.559668
$196$	2.67692	−	2.95184i	0.191209	−	0.210846i
$197$	−6.23870			−0.444489			−0.222244	−	0.974991i	$-0.571338\pi$
$197$	−6.23870			−0.444489			−0.222244	+	0.974991i	$0.571338\pi$
$198$	4.61775	+	7.99817i	0.328169	+	0.568406i
$199$	0.421013	−	0.729217i	0.0298449	−	0.0516928i	−0.850717	−	0.525624i	$-0.823832\pi$
$199$	0.421013	−	0.729217i	0.0298449	−	0.0516928i	0.880562	+	0.473931i	$0.157165\pi$
$200$	−1.14666	+	1.98606i	−0.0810808	+	0.140436i
$201$	0.433149	+	0.750237i	0.0305520	+	0.0529176i
$202$	2.84777			0.200368
$203$	0.938222	−	8.77643i	0.0658503	−	0.615985i
$204$	−2.59914			−0.181976
$205$	2.47503	+	4.28688i	0.172864	+	0.299409i
$206$	14.4079	−	24.9551i	1.00384	−	1.73871i
$207$	−3.64102	+	6.30642i	−0.253068	+	0.438327i
$208$	−8.40078	−	14.5506i	−0.582489	−	1.00890i
$209$	−18.2382			−1.26156
$210$	−8.68308	+	3.84747i	−0.599189	+	0.265501i
$211$	4.55754			0.313754			0.156877	−	0.987618i	$-0.449857\pi$
$211$	4.55754			0.313754			0.156877	+	0.987618i	$0.449857\pi$
$212$	3.93208	+	6.81056i	0.270056	+	0.467751i
$213$	−10.9488	+	18.9639i	−0.750199	+	1.29938i
$214$	−14.0848	+	24.3956i	−0.962819	+	1.66765i
$215$	0.0964497	+	0.167056i	0.00657781	+	0.0113931i
$216$	−5.05745			−0.344116
$217$	−7.97588	−	5.81651i	−0.541438	−	0.394851i
$218$	−1.90251			−0.128854
$219$	−9.02659	−	15.6345i	−0.609961	−	1.05648i
$220$	−0.813790	+	1.40953i	−0.0548657	+	0.0950302i
$221$	−3.55743	+	6.16164i	−0.239298	+	0.414477i
$222$	1.79482	+	3.10872i	0.120461	+	0.208644i
$223$	13.6964			0.917178			0.458589	−	0.888649i	$-0.348355\pi$
$223$	13.6964			0.917178			0.458589	+	0.888649i	$0.348355\pi$
$224$	−6.69196	−	4.88020i	−0.447125	−	0.326072i
$225$	2.01526			0.134351
$226$	−6.70101	−	11.6065i	−0.445744	−	0.772052i
$227$	7.96656	−	13.7985i	0.528759	−	0.915838i	−0.470678	−	0.882305i	$-0.655991\pi$
$227$	7.96656	−	13.7985i	0.528759	−	0.915838i	0.999438	−	0.0335331i	$-0.0106759\pi$
$228$	4.06622	−	7.04290i	0.269292	−	0.466427i
$229$	6.46342	+	11.1950i	0.427115	+	0.739785i	0.996615	−	0.0822062i	$-0.0261966\pi$
$229$	6.46342	+	11.1950i	0.427115	+	0.739785i	−0.569500	+	0.821991i	$0.692863\pi$
$230$	−5.79197			−0.381911
$231$	15.4879	−	6.86270i	1.01903	−	0.451533i
$232$	−7.65067			−0.502291
$233$	7.75623	+	13.4342i	0.508127	+	0.880102i	0.999956	+	0.00941025i	$0.00299542\pi$
$233$	7.75623	+	13.4342i	0.508127	+	0.880102i	−0.491828	+	0.870692i	$0.663671\pi$
$234$	−5.63646	+	9.76264i	−0.368467	+	0.638204i
$235$	−2.34249	+	4.05732i	−0.152807	+	0.264670i
$236$	−2.40167	−	4.15982i	−0.156336	−	0.270781i
$237$	−26.6993			−1.73430
$238$	−0.919049	+	8.59708i	−0.0595731	+	0.557266i
$239$	−20.4475			−1.32264			−0.661318	−	0.750106i	$-0.730003\pi$
$239$	−20.4475			−1.32264			−0.661318	+	0.750106i	$0.730003\pi$
$240$	5.39095	+	9.33740i	0.347984	+	0.602726i
$241$	6.52721	−	11.3055i	0.420454	−	0.728248i	−0.575530	−	0.817781i	$-0.695204\pi$
$241$	6.52721	−	11.3055i	0.420454	−	0.728248i	0.995984	+	0.0895327i	$0.0285374\pi$
$242$	−2.26466	+	3.92251i	−0.145578	+	0.252149i
$243$	8.99182	+	15.5743i	0.576825	+	0.999091i
$244$	2.50645			0.160459
$245$	2.13943	+	6.66505i	0.136683	+	0.425814i
$246$	17.7690			1.13291
$247$	−11.1308	−	19.2792i	−0.708238	−	1.22670i
$248$	−4.27826	+	7.41016i	−0.271670	+	0.470546i
$249$	5.80135	−	10.0482i	0.367646	−	0.636781i
$250$	0.801447	+	1.38815i	0.0506880	+	0.0877941i
$251$	8.50092			0.536573			0.268287	−	0.963339i	$-0.413543\pi$
$251$	8.50092			0.536573			0.268287	+	0.963339i	$0.413543\pi$
$252$	−0.322639	+	3.01807i	−0.0203244	+	0.190121i
$253$	10.3311			0.649511
$254$	2.88871	+	5.00339i	0.181254	+	0.313941i
$255$	2.28287	−	3.95405i	0.142959	−	0.247612i
$256$	−6.33029	+	10.9644i	−0.395643	+	0.685274i
$257$	−3.62244	−	6.27425i	−0.225962	−	0.391377i	0.730646	−	0.682757i	$-0.239219\pi$
$257$	−3.62244	−	6.27425i	−0.225962	−	0.391377i	−0.956608	+	0.291380i	$0.905886\pi$
$258$	0.692440			0.0431094
$259$	2.41892	−	1.07182i	0.150305	−	0.0665999i
$260$	−1.98664			−0.123206
$261$	3.36153	+	5.82234i	0.208074	+	0.360394i
$262$	−5.32886	+	9.22985i	−0.329218	+	0.570222i
$263$	−14.2056	+	24.6048i	−0.875955	+	1.51720i	−0.0202121	+	0.999796i	$0.506434\pi$
$263$	−14.2056	+	24.6048i	−0.875955	+	1.51720i	−0.855742	+	0.517402i	$0.826899\pi$
$264$	−7.34183	−	12.7164i	−0.451858	−	0.782642i
$265$	−13.8145			−0.848617
$266$	−21.8578	−	15.9401i	−1.34019	−	0.977349i
$267$	−34.2756			−2.09763
$268$	0.110105	+	0.190708i	0.00672576	+	0.0116494i
$269$	−11.5906	+	20.0755i	−0.706690	+	1.22402i	0.259388	+	0.965773i	$0.416479\pi$
$269$	−11.5906	+	20.0755i	−0.706690	+	1.22402i	−0.966078	+	0.258250i	$0.916854\pi$
$270$	−1.76744	+	3.06129i	−0.107563	+	0.186304i
$271$	6.21981	+	10.7730i	0.377826	+	0.654414i	0.990746	−	0.135731i	$-0.0433383\pi$
$271$	6.21981	+	10.7730i	0.377826	+	0.654414i	−0.612919	+	0.790145i	$0.710005\pi$
$272$	9.81552			0.595153
$273$	16.7068	+	12.1836i	1.01114	+	0.737386i
$274$	19.1954			1.15964
$275$	−1.42953	−	2.47603i	−0.0862042	−	0.149310i
$276$	−2.30333	+	3.98948i	−0.138644	+	0.240139i
$277$	−7.15677	+	12.3959i	−0.430009	+	0.744797i	−0.996874	−	0.0790141i	$-0.974823\pi$
$277$	−7.15677	+	12.3959i	−0.430009	+	0.744797i	0.566865	+	0.823811i	$0.308156\pi$
$278$	−4.59301	−	7.95532i	−0.275470	−	0.477129i
$279$	7.51908			0.450156
$280$	5.54734	−	2.45803i	0.331517	−	0.146895i
$281$	2.65928			0.158639			0.0793197	−	0.996849i	$-0.474725\pi$
$281$	2.65928			0.158639			0.0793197	+	0.996849i	$0.474725\pi$
$282$	8.40872	+	14.5643i	0.500732	+	0.867293i
$283$	−12.1229	+	20.9975i	−0.720632	+	1.24817i	0.240115	+	0.970745i	$0.422815\pi$
$283$	−12.1229	+	20.9975i	−0.720632	+	1.24817i	−0.960747	+	0.277427i	$0.910518\pi$
$284$	−2.78315	+	4.82056i	−0.165150	+	0.286048i
$285$	7.14288	+	12.3718i	0.423108	+	0.732844i
$286$	15.9930			0.945687
$287$	1.39213	−	13.0224i	0.0821748	−	0.768690i
$288$	6.30870			0.371743
$289$	6.42174	+	11.1228i	0.377749	+	0.654281i
$290$	−2.67369	+	4.63097i	−0.157005	+	0.271940i
$291$	5.51712	−	9.55594i	0.323420	−	0.560179i
$292$	−2.29453	−	3.97425i	−0.134277	−	0.232575i
$293$	7.56345			0.441861			0.220931	−	0.975290i	$-0.429091\pi$
$293$	7.56345			0.441861			0.220931	+	0.975290i	$0.429091\pi$
$294$	24.5597	+	5.31168i	1.43235	+	0.309784i
$295$	8.43775			0.491265
$296$	−1.14666	−	1.98606i	−0.0666480	−	0.115438i
$297$	3.15256	−	5.46040i	0.182930	−	0.316844i
$298$	−12.6267	+	21.8700i	−0.731443	+	1.26690i
$299$	6.30511	+	10.9208i	0.364634	+	0.631565i
$300$	1.27486			0.0736043
$301$	0.0542500	−	0.507472i	0.00312692	−	0.0292502i
$302$	7.75980			0.446526
$303$	1.98937	+	3.44570i	0.114287	+	0.197950i
$304$	−15.3559	+	26.5972i	−0.880721	+	1.52545i
$305$	−2.20147	+	3.81305i	−0.126056	+	0.218335i
$306$	−3.29284	−	5.70336i	−0.188239	−	0.326039i
$307$	1.32000			0.0753365			0.0376682	−	0.999290i	$-0.488007\pi$
$307$	1.32000			0.0753365			0.0376682	+	0.999290i	$0.488007\pi$
$308$	3.93699	−	1.74448i	0.224331	−	0.0994009i
$309$	40.2598			2.29030
$310$	2.99026	+	5.17928i	0.169835	+	0.294163i
$311$	−4.61587	+	7.99492i	−0.261742	+	0.453350i	−0.966705	−	0.255894i	$-0.917630\pi$
$311$	−4.61587	+	7.99492i	−0.261742	+	0.453350i	0.704963	+	0.709244i	$0.250964\pi$
$312$	8.96149	−	15.5218i	0.507345	−	0.878747i
$313$	−3.02040	−	5.23148i	−0.170723	−	0.295701i	0.767950	−	0.640510i	$-0.221277\pi$
$313$	−3.02040	−	5.23148i	−0.170723	−	0.295701i	−0.938673	+	0.344809i	$0.887944\pi$
$314$	−5.38715			−0.304014
$315$	−4.30800	−	3.14166i	−0.242728	−	0.177013i
$316$	−6.78688			−0.381792
$317$	15.3587	+	26.6021i	0.862633	+	1.49412i	0.869378	+	0.494147i	$0.164519\pi$
$317$	15.3587	+	26.6021i	0.862633	+	1.49412i	−0.00674551	+	0.999977i	$0.502147\pi$
$318$	−24.7945	+	42.9454i	−1.39041	+	2.40826i
$319$	4.76904	−	8.26023i	0.267015	−	0.462484i
$320$	−2.30557	−	3.99336i	−0.128885	−	0.223236i
$321$	−39.3571			−2.19670
$322$	12.3814	+	9.02932i	0.689991	+	0.503185i
$323$	13.0053			0.723636
$324$	3.12657	+	5.41538i	0.173698	+	0.300854i
$325$	1.74490	−	3.02226i	0.0967897	−	0.167645i
$326$	−17.3250	+	30.0078i	−0.959545	+	1.66198i
$327$	−1.32904	−	2.30197i	−0.0734963	−	0.127299i
$328$	−11.3520			−0.626811
$329$	11.3326	−	5.02148i	0.624788	−	0.276843i
$330$	−10.2630			−0.564962
$331$	−11.4798	−	19.8835i	−0.630985	−	1.09290i	−0.987351	−	0.158551i	$-0.949318\pi$
$331$	−11.4798	−	19.8835i	−0.630985	−	1.09290i	0.356366	−	0.934346i	$-0.384016\pi$
$332$	1.47469	−	2.55423i	0.0809340	−	0.140182i
$333$	−1.00763	+	1.74526i	−0.0552177	+	0.0956399i
$334$	10.0761	+	17.4524i	0.551341	+	0.954951i
$335$	−0.386831			−0.0211348
$336$	3.03225	−	28.3646i	0.165423	−	1.54742i
$337$	−11.7466			−0.639880			−0.319940	−	0.947438i	$-0.603663\pi$
$337$	−11.7466			−0.639880			−0.319940	+	0.947438i	$0.603663\pi$
$338$	−0.658205	−	1.14004i	−0.0358016	−	0.0620102i
$339$	9.36229	−	16.2160i	0.508490	−	0.880730i
$340$	0.580300	−	1.00511i	0.0314712	−	0.0545097i
$341$	−5.33370	−	9.23825i	−0.288836	−	0.500279i
$342$	20.6059			1.11424
$343$	5.81696	−	17.5830i	0.314086	−	0.949394i
$344$	−0.442378			−0.0238514
$345$	−4.04612	−	7.00808i	−0.217836	−	0.377302i
$346$	−7.98368	+	13.8281i	−0.429205	+	0.743405i
$347$	11.9329	−	20.6685i	0.640594	−	1.10954i	−0.344707	−	0.938710i	$-0.612022\pi$
$347$	11.9329	−	20.6685i	0.640594	−	1.10954i	0.985300	−	0.170830i	$-0.0546450\pi$
$348$	2.12653	+	3.68325i	0.113994	+	0.197443i
$349$	−7.11217			−0.380706			−0.190353	−	0.981716i	$-0.560963\pi$
$349$	−7.11217			−0.380706			−0.190353	+	0.981716i	$0.560963\pi$
$350$	0.450790	−	4.21683i	0.0240957	−	0.225399i
$351$	7.69609			0.410787
$352$	−4.47511	−	7.75112i	−0.238524	−	0.413136i
$353$	16.6449	−	28.8299i	0.885920	−	1.53446i	0.0412642	−	0.999148i	$-0.486861\pi$
$353$	16.6449	−	28.8299i	0.885920	−	1.53446i	0.844656	−	0.535310i	$-0.179805\pi$
$354$	15.1443	−	26.2306i	0.804908	−	1.39414i
$355$	−4.88899	−	8.46799i	−0.259481	−	0.449434i
$356$	−8.71276			−0.461775
$357$	−11.0442	+	4.89367i	−0.584520	+	0.259001i
$358$	−30.4010			−1.60674
$359$	−0.105424	−	0.182600i	−0.00556406	−	0.00963724i	0.863230	−	0.504811i	$-0.168438\pi$
$359$	−0.105424	−	0.182600i	−0.00556406	−	0.00963724i	−0.868794	+	0.495174i	$0.835104\pi$
$360$	−2.31081	+	4.00243i	−0.121790	+	0.210947i
$361$	−10.8462	+	18.7862i	−0.570854	+	0.988747i
$362$	−5.77669	−	10.0055i	−0.303616	−	0.525879i
$363$	−6.32814			−0.332141
$364$	4.24681	+	3.09704i	0.222593	+	0.162329i
$365$	8.06134			0.421950
$366$	7.90248	+	13.6875i	0.413069	+	0.715457i
$367$	12.9727	−	22.4693i	0.677168	−	1.17289i	−0.298662	−	0.954359i	$-0.596540\pi$
$367$	12.9727	−	22.4693i	0.677168	−	1.17289i	0.975830	−	0.218531i	$-0.0701264\pi$
$368$	8.69842	−	15.0661i	0.453436	−	0.785375i
$369$	4.98782	+	8.63917i	0.259656	+	0.449737i
$370$	−1.60289			−0.0833305
$371$	29.5311	+	21.5359i	1.53318	+	1.11809i
$372$	4.75662			0.246619
$373$	13.1008	+	22.6913i	0.678334	+	1.17491i	0.975482	+	0.220077i	$0.0706309\pi$
$373$	13.1008	+	22.6913i	0.678334	+	1.17491i	−0.297149	+	0.954831i	$0.596036\pi$
$374$	−4.67159	+	8.09142i	−0.241562	+	0.418398i
$375$	−1.11974	+	1.93944i	−0.0578231	+	0.100152i
$376$	−5.37206	−	9.30468i	−0.277043	−	0.479852i
$377$	11.6423			0.599607
$378$	8.55059	−	3.78876i	0.439795	−	0.194873i
$379$	−21.9297			−1.12645			−0.563227	−	0.826302i	$-0.690440\pi$
$379$	−21.9297			−1.12645			−0.563227	+	0.826302i	$0.690440\pi$
$380$	1.81570	+	3.14489i	0.0931435	+	0.161329i
$381$	−4.03595	+	6.99047i	−0.206768	+	0.358133i
$382$	10.6739	−	18.4877i	0.546124	−	0.945915i
$383$	11.0018	+	19.0557i	0.562167	+	0.973702i	0.997307	+	0.0733395i	$0.0233657\pi$
$383$	11.0018	+	19.0557i	0.562167	+	0.973702i	−0.435140	+	0.900363i	$0.643301\pi$
$384$	−30.5736			−1.56020
$385$	−0.804070	+	7.52153i	−0.0409792	+	0.383333i
$386$	3.77607			0.192197
$387$	0.194371	+	0.336660i	0.00988043	+	0.0171134i
$388$	1.40244	−	2.42909i	0.0711980	−	0.123319i
$389$	12.8927	−	22.3307i	0.653684	−	1.13221i	−0.328538	−	0.944491i	$-0.606556\pi$
$389$	12.8927	−	22.3307i	0.653684	−	1.13221i	0.982222	−	0.187723i	$-0.0601107\pi$
$390$	−6.26358	−	10.8488i	−0.317169	−	0.549352i
$391$	−7.36693			−0.372562
$392$	−15.6904	−	3.39347i	−0.792485	−	0.171396i
$393$	−14.8904			−0.751120
$394$	−4.99998	−	8.66023i	−0.251896	−	0.436296i
$395$	5.96105	−	10.3248i	0.299933	−	0.519499i
$396$	−1.64000	+	2.84056i	−0.0824129	+	0.142743i
$397$	7.73585	+	13.3989i	0.388251	+	0.672471i	0.992214	−	0.124541i	$-0.0397459\pi$
$397$	7.73585	+	13.3989i	0.388251	+	0.672471i	−0.603963	+	0.797012i	$0.706413\pi$
$398$	1.34968			0.0676533
$399$	4.01765	−	37.5824i	0.201134	−	1.88148i
$400$	−4.81447			−0.240724
$401$	−11.1276	−	19.2736i	−0.555688	−	0.962480i	−0.997850	−	0.0655444i	$-0.979122\pi$
$401$	−11.1276	−	19.2736i	−0.555688	−	0.962480i	0.442162	−	0.896935i	$-0.354212\pi$
$402$	−0.694293	+	1.20255i	−0.0346282	+	0.0599777i
$403$	6.51036	−	11.2763i	0.324304	−	0.561711i
$404$	0.505694	+	0.875887i	0.0251592	+	0.0435770i
$405$	−10.9845			−0.545825
$406$	12.9349	−	5.73146i	0.641949	−	0.284447i
$407$	2.85907			0.141719
$408$	5.23533	+	9.06786i	0.259188	+	0.448926i
$409$	−10.3632	+	17.9496i	−0.512427	+	0.887550i	0.487469	+	0.873140i	$0.337920\pi$
$409$	−10.3632	+	17.9496i	−0.512427	+	0.887550i	−0.999896	+	0.0144097i	$0.995413\pi$
$410$	−3.96721	+	6.87141i	−0.195927	+	0.339355i
$411$	13.4094	+	23.2258i	0.661438	+	1.14564i
$412$	10.2339			0.504189
$413$	−18.0373	−	13.1539i	−0.887556	−	0.647262i
$414$	−11.6723			−0.573663
$415$	2.59049	+	4.48687i	0.127162	+	0.220252i
$416$	5.46235	−	9.46108i	0.267814	−	0.463867i
$417$	6.41710	−	11.1148i	0.314247	−	0.544292i
$418$	−14.6169	−	25.3173i	−0.714938	−	1.23831i
$419$	20.6748			1.01003			0.505016	−	0.863110i	$-0.331487\pi$
$419$	20.6748			1.01003			0.505016	+	0.863110i	$0.331487\pi$
$420$	−2.72526	−	1.98743i	−0.132979	−	0.0969769i
$421$	4.43614			0.216204			0.108102	−	0.994140i	$-0.465523\pi$
$421$	4.43614			0.216204			0.108102	+	0.994140i	$0.465523\pi$
$422$	3.65263	+	6.32654i	0.177807	+	0.307971i
$423$	−4.72073	+	8.17654i	−0.229530	+	0.397557i
$424$	15.8404	−	27.4365i	0.769280	−	1.33243i
$425$	1.01938	+	1.76561i	0.0494470	+	0.0856448i
$426$	−35.0995			−1.70058
$427$	10.6504	−	4.71917i	0.515407	−	0.228377i
$428$	−10.0045			−0.483584
$429$	11.1723	+	19.3510i	0.539404	+	0.934274i
$430$	−0.154599	+	0.267773i	−0.00745541	+	0.0129131i
$431$	11.5884	−	20.0717i	0.558195	−	0.966822i	−0.439452	−	0.898266i	$-0.644827\pi$
$431$	11.5884	−	20.0717i	0.558195	−	0.966822i	0.997647	−	0.0685560i	$-0.0218392\pi$
$432$	−5.30869	−	9.19492i	−0.255415	−	0.442391i
$433$	14.2985			0.687144			0.343572	−	0.939126i	$-0.388363\pi$
$433$	14.2985			0.687144			0.343572	+	0.939126i	$0.388363\pi$
$434$	1.68193	−	15.7333i	0.0807352	−	0.755224i
$435$	−7.47108			−0.358211
$436$	−0.337839	−	0.585154i	−0.0161796	−	0.0280238i
$437$	11.5252	−	19.9622i	0.551325	−	0.954923i
$438$	14.4687	−	25.0605i	0.691340	−	1.19744i
$439$	8.76374	+	15.1793i	0.418271	+	0.724466i	0.995766	−	0.0919281i	$-0.0293030\pi$
$439$	8.76374	+	15.1793i	0.418271	+	0.724466i	−0.577495	+	0.816394i	$0.695970\pi$
$440$	6.55673			0.312580
$441$	4.31150	+	13.4318i	0.205310	+	0.639609i
$442$	−11.4044			−0.542450
$443$	−19.1257	−	33.1267i	−0.908689	−	1.57390i	−0.815887	−	0.578211i	$-0.803751\pi$
$443$	−19.1257	−	33.1267i	−0.908689	−	1.57390i	−0.0928022	−	0.995685i	$-0.529582\pi$
$444$	−0.637432	+	1.10407i	−0.0302512	+	0.0523966i
$445$	7.65258	−	13.2547i	0.362767	−	0.628331i
$446$	10.9769	+	19.0126i	0.519772	+	0.900272i
$447$	−35.2826			−1.66881
$448$	−1.29681	+	12.1308i	−0.0612686	+	0.573127i
$449$	32.4281			1.53038			0.765189	−	0.643805i	$-0.222645\pi$
$449$	32.4281			1.53038			0.765189	+	0.643805i	$0.222645\pi$
$450$	1.61512	+	2.79747i	0.0761376	+	0.131874i
$451$	7.07628	−	12.2565i	0.333209	−	0.577135i
$452$	2.37987	−	4.12205i	0.111940	−	0.193885i
$453$	5.42079	+	9.38908i	0.254691	+	0.441138i
$454$	25.5391			1.19861
$455$	−8.44157	+	3.74046i	−0.395747	+	0.175355i
$456$	−32.7617			−1.53421
$457$	−5.94037	−	10.2890i	−0.277879	−	0.481300i	0.692979	−	0.720958i	$-0.256298\pi$
$457$	−5.94037	−	10.2890i	−0.277879	−	0.481300i	−0.970857	+	0.239658i	$0.922965\pi$
$458$	−10.3602	+	17.9444i	−0.484099	+	0.838485i
$459$	−2.24804	+	3.89372i	−0.104929	+	0.181743i
$460$	−1.02851	−	1.78143i	−0.0479546	−	0.0830598i
$461$	34.9849			1.62941			0.814703	−	0.579878i	$-0.196900\pi$
$461$	34.9849			1.62941			0.814703	+	0.579878i	$0.196900\pi$
$462$	21.9392	+	15.9994i	1.02070	+	0.744361i
$463$	3.31346			0.153989			0.0769947	−	0.997032i	$-0.475468\pi$
$463$	3.31346			0.153989			0.0769947	+	0.997032i	$0.475468\pi$
$464$	−8.03073	−	13.9096i	−0.372817	−	0.645739i
$465$	−4.17783	+	7.23621i	−0.193742	+	0.335571i
$466$	−12.4324	+	21.5336i	−0.575920	+	0.997523i
$467$	10.0913	+	17.4786i	0.466970	+	0.808815i	0.999288	−	0.0377290i	$-0.0120124\pi$
$467$	10.0913	+	17.4786i	0.466970	+	0.808815i	−0.532318	+	0.846544i	$0.678679\pi$
$468$	−4.00359			−0.185066
$469$	0.826924	+	0.603045i	0.0381838	+	0.0278460i
$470$	−7.50953			−0.346389
$471$	−3.76332	−	6.51825i	−0.173404	−	0.300345i
$472$	−9.67518	+	16.7579i	−0.445336	+	0.771345i
$473$	0.275756	−	0.477624i	0.0126793	−	0.0219612i
$474$	−21.3980	−	37.0625i	−0.982845	−	1.70234i
$475$	−6.37906			−0.292691
$476$	−2.80740	+	1.24396i	−0.128677	+	0.0570167i
$477$	−27.8397			−1.27469
$478$	−16.3876	−	28.3841i	−0.749549	−	1.29826i
$479$	6.32737	−	10.9593i	0.289105	−	0.500744i	−0.684491	−	0.729021i	$-0.739976\pi$
$479$	6.32737	−	10.9593i	0.289105	−	0.500744i	0.973596	+	0.228276i	$0.0733090\pi$
$480$	−3.50530	+	6.07136i	−0.159994	+	0.277119i
$481$	1.74490	+	3.02226i	0.0795607	+	0.137803i
$482$	20.9248			0.953100
$483$	−2.27582	+	21.2887i	−0.103553	+	0.968671i
$484$	−1.60859			−0.0731179
$485$	2.46358	+	4.26704i	0.111865	+	0.193756i
$486$	−14.4129	+	24.9639i	−0.653784	+	1.13239i
$487$	15.0702	−	26.1023i	0.682895	−	1.18281i	−0.291198	−	0.956663i	$-0.594054\pi$
$487$	15.0702	−	26.1023i	0.682895	−	1.18281i	0.974093	−	0.226146i	$-0.0726127\pi$
$488$	−5.04865	−	8.74451i	−0.228541	−	0.395845i
$489$	−48.4112			−2.18923
$490$	−7.53742	+	8.31152i	−0.340506	+	0.375476i
$491$	31.4494			1.41929			0.709647	−	0.704558i	$-0.248855\pi$
$491$	31.4494			1.41929			0.709647	+	0.704558i	$0.248855\pi$
$492$	3.15533	+	5.46519i	0.142253	+	0.246390i
$493$	−3.40072	+	5.89023i	−0.153161	+	0.265282i
$494$	17.8416	−	30.9025i	0.802729	−	1.39037i
$495$	−2.88088	−	4.98983i	−0.129486	−	0.224276i
$496$	−17.9632			−0.806570
$497$	−2.74991	+	25.7236i	−0.123350	+	1.15386i
$498$	18.5979			0.833392
$499$	19.0287	+	32.9587i	0.851843	+	1.47544i	0.879543	+	0.475819i	$0.157848\pi$
$499$	19.0287	+	32.9587i	0.851843	+	1.47544i	−0.0276999	+	0.999616i	$0.508818\pi$
$500$	−0.284634	+	0.493001i	−0.0127292	+	0.0220477i
$501$	−14.0778	+	24.3835i	−0.628951	+	1.08938i
$502$	6.81303	+	11.8005i	0.304081	+	0.526683i
$503$	32.9900			1.47095			0.735476	−	0.677550i	$-0.236958\pi$
$503$	32.9900			1.47095			0.735476	+	0.677550i	$0.236958\pi$
$504$	11.1793	−	4.95356i	0.497967	−	0.220649i
$505$	−1.77664			−0.0790595
$506$	8.27983	+	14.3411i	0.368083	+	0.637539i
$507$	0.919608	−	1.59281i	0.0408412	−	0.0707391i
$508$	−1.02593	+	1.77696i	−0.0455182	+	0.0788398i
$509$	−0.0177382	−	0.0307234i	−0.000786231	−	0.00136179i	0.865632	−	0.500681i	$-0.166917\pi$
$509$	−0.0177382	−	0.0307234i	−0.000786231	−	0.00136179i	−0.866418	+	0.499319i	$0.833584\pi$
$510$	7.31840			0.324064
$511$	−17.2326	−	12.5671i	−0.762327	−	0.555937i
$512$	7.01062			0.309828
$513$	−7.03389	−	12.1831i	−0.310554	−	0.537895i
$514$	5.80639	−	10.0570i	0.256109	−	0.443593i
$515$	−8.98865	+	15.5688i	−0.396087	+	0.686043i
$516$	0.122960	+	0.212973i	0.00541302	+	0.00937563i
$517$	13.3947			0.589098
$518$	3.42649	+	2.49881i	0.150551	+	0.109791i
$519$	−22.3087			−0.979244
$520$	4.00160	+	6.93098i	0.175482	+	0.303943i
$521$	16.0131	−	27.7355i	0.701548	−	1.21512i	−0.266375	−	0.963869i	$-0.585826\pi$
$521$	16.0131	−	27.7355i	0.701548	−	1.21512i	0.967923	−	0.251247i	$-0.0808406\pi$
$522$	−5.38818	+	9.33260i	−0.235834	+	0.408477i
$523$	−20.8127	−	36.0487i	−0.910076	−	1.57630i	−0.813955	−	0.580928i	$-0.802690\pi$
$523$	−20.8127	−	36.0487i	−0.910076	−	1.57630i	−0.0961213	−	0.995370i	$-0.530644\pi$
$524$	−3.78509			−0.165353
$525$	5.41712	−	2.40033i	0.236423	−	0.104759i
$526$	−45.5401			−1.98564
$527$	3.80337	+	6.58763i	0.165678	+	0.286962i
$528$	15.4131	−	26.6963i	0.670769	−	1.16181i
$529$	4.97150	−	8.61089i	0.216152	−	0.374386i
$530$	−11.0716	−	19.1765i	−0.480918	−	0.832975i
$531$	17.0042			0.737921
$532$	1.02128	−	9.55335i	0.0442780	−	0.414190i
$533$	17.2747			0.748252
$534$	−27.4701	−	47.5795i	−1.18875	−	2.05897i
$535$	8.78712	−	15.2197i	0.379900	−	0.658007i
$536$	0.443562	−	0.768271i	0.0191589	−	0.0331843i
$537$	−21.2373	−	36.7841i	−0.916457	−	1.58735i
$538$	−37.1569			−1.60195
$539$	13.4444	−	14.8252i	0.579093	−	0.638567i
$540$	−1.25541			−0.0540243
$541$	−5.30027	−	9.18033i	−0.227876	−	0.394693i	0.729302	−	0.684192i	$-0.239845\pi$
$541$	−5.30027	−	9.18033i	−0.227876	−	0.394693i	−0.957178	+	0.289498i	$0.906512\pi$
$542$	−9.96969	+	17.2680i	−0.428235	+	0.741724i
$543$	8.07088	−	13.9792i	0.346355	−	0.599904i
$544$	3.19112	+	5.52719i	0.136818	+	0.236976i
$545$	1.18692			0.0508422
$546$	−3.52307	+	32.9560i	−0.150774	+	1.41038i
$547$	−42.8221			−1.83094			−0.915471	−	0.402385i	$-0.868181\pi$
$547$	−42.8221			−1.83094			−0.915471	+	0.402385i	$0.868181\pi$
$548$	3.40864	+	5.90393i	0.145610	+	0.252204i
$549$	−4.43652	+	7.68429i	−0.189346	+	0.327957i
$550$	2.29139	−	3.96881i	0.0977053	−	0.169231i
$551$	−10.6405	−	18.4299i	−0.453302	−	0.785142i
$552$	18.5580			0.789881
$553$	−28.8386	+	12.7784i	−1.22634	+	0.543393i
$554$	−22.9431			−0.974758
$555$	−1.11974	−	1.93944i	−0.0475303	−	0.0823248i
$556$	1.63121	−	2.82534i	0.0691787	−	0.119821i
$557$	5.20160	−	9.00943i	0.220399	−	0.381742i	−0.734530	−	0.678576i	$-0.762597\pi$
$557$	5.20160	−	9.00943i	0.220399	−	0.381742i	0.954929	+	0.296834i	$0.0959308\pi$
$558$	6.02615	+	10.4376i	0.255107	+	0.441858i
$559$	0.673181			0.0284725
$560$	10.2918	+	7.50546i	0.434910	+	0.317163i
$561$	−13.0538			−0.551131
$562$	2.13127	+	3.69147i	0.0899023	+	0.155715i
$563$	0.460926	−	0.798347i	0.0194257	−	0.0336463i	−0.856149	−	0.516729i	$-0.827150\pi$
$563$	0.460926	−	0.798347i	0.0194257	−	0.0336463i	0.875575	+	0.483083i	$0.160483\pi$
$564$	−2.98636	+	5.17253i	−0.125748	+	0.217803i
$565$	4.18057	+	7.24096i	0.175878	+	0.304629i
$566$	−38.8635			−1.63355
$567$	23.4815	+	17.1242i	0.986129	+	0.719147i
$568$	22.4240			0.940888
$569$	5.21276	+	9.02877i	0.218530	+	0.378506i	0.954359	−	0.298662i	$-0.0965404\pi$
$569$	5.21276	+	9.02877i	0.218530	+	0.378506i	−0.735829	+	0.677168i	$0.763207\pi$
$570$	−11.4493	+	19.8307i	−0.479558	+	0.830618i
$571$	−16.5301	+	28.6309i	−0.691761	+	1.19817i	0.279499	+	0.960146i	$0.409832\pi$
$571$	−16.5301	+	28.6309i	−0.691761	+	1.19817i	−0.971260	+	0.238020i	$0.923502\pi$
$572$	2.83997	+	4.91897i	0.118745	+	0.205672i
$573$	29.8260			1.24600
$574$	19.1928	−	8.50431i	0.801090	−	0.354963i
$575$	3.61345			0.150691
$576$	−4.64632	−	8.04766i	−0.193597	−	0.335319i
$577$	−18.8533	+	32.6549i	−0.784874	+	1.35944i	0.144201	+	0.989548i	$0.453939\pi$
$577$	−18.8533	+	32.6549i	−0.784874	+	1.35944i	−0.929075	+	0.369893i	$0.879395\pi$
$578$	−10.2934	+	17.8286i	−0.428148	+	0.741574i
$579$	2.63786	+	4.56891i	0.109626	+	0.189877i
$580$	−1.89913			−0.0788569
$581$	1.45707	−	13.6299i	0.0604496	−	0.565466i
$582$	17.6867			0.733139
$583$	19.7483	+	34.2050i	0.817890	+	1.41663i
$584$	−9.24357	+	16.0103i	−0.382502	+	0.662513i
$585$	3.51643	−	6.09063i	0.145386	−	0.251817i
$586$	6.06170	+	10.4992i	0.250407	+	0.433717i
$587$	43.2908			1.78680			0.893400	−	0.449261i	$-0.148313\pi$
$587$	43.2908			1.78680			0.893400	+	0.449261i	$0.148313\pi$
$588$	2.72748	+	8.49703i	0.112479	+	0.350412i
$589$	−23.8008			−0.980693
$590$	6.76241	+	11.7128i	0.278404	+	0.482210i
$591$	6.98571	−	12.0996i	0.287354	−	0.497711i
$592$	2.40724	−	4.16945i	0.0989368	−	0.171364i
$593$	2.12218	+	3.67572i	0.0871473	+	0.150944i	0.906304	−	0.422626i	$-0.138892\pi$
$593$	2.12218	+	3.67572i	0.0871473	+	0.150944i	−0.819157	+	0.573570i	$0.805558\pi$
$594$	10.1064			0.414673
$595$	0.573369	−	5.36348i	0.0235058	−	0.219881i
$596$	−8.96874			−0.367374
$597$	0.942850	+	1.63306i	0.0385883	+	0.0668369i
$598$	−10.1064	+	17.5048i	−0.413282	+	0.715826i
$599$	2.49966	−	4.32954i	0.102133	−	0.176900i	−0.810430	−	0.585835i	$-0.800766\pi$
$599$	2.49966	−	4.32954i	0.102133	−	0.176900i	0.912563	+	0.408935i	$0.134100\pi$
$600$	−2.56791	−	4.44775i	−0.104834	−	0.181579i
$601$	−16.8399			−0.686913			−0.343456	−	0.939169i	$-0.611598\pi$
$601$	−16.8399			−0.686913			−0.343456	+	0.939169i	$0.611598\pi$
$602$	0.747924	−	0.331405i	0.0304831	−	0.0135071i
$603$	−0.779564			−0.0317463
$604$	1.37795	+	2.38668i	0.0560680	+	0.0971126i
$605$	1.41286	−	2.44715i	0.0574409	−	0.0994906i
$606$	−3.18876	+	5.52309i	−0.129534	+	0.224360i
$607$	−8.11873	−	14.0621i	−0.329529	−	0.570761i	0.652889	−	0.757453i	$-0.273557\pi$
$607$	−8.11873	−	14.0621i	−0.329529	−	0.570761i	−0.982418	+	0.186692i	$0.940223\pi$
$608$	−19.9694			−0.809867
$609$	15.9708	+	11.6469i	0.647171	+	0.471958i
$610$	−7.05744			−0.285747
$611$	8.17484	+	14.1592i	0.330719	+	0.572821i
$612$	1.16945	−	2.02555i	0.0472724	−	0.0818781i
$613$	11.3223	−	19.6108i	0.457303	−	0.792071i	−0.541515	−	0.840691i	$-0.682149\pi$
$613$	11.3223	−	19.6108i	0.457303	−	0.792071i	0.998817	+	0.0486198i	$0.0154823\pi$
$614$	1.05791	+	1.83236i	0.0426938	+	0.0739479i
$615$	−11.0855			−0.447012
$616$	−14.0163	−	10.2215i	−0.564731	−	0.411837i
$617$	−1.88719			−0.0759756			−0.0379878	−	0.999278i	$-0.512095\pi$
$617$	−1.88719			−0.0759756			−0.0379878	+	0.999278i	$0.512095\pi$
$618$	32.2661	+	55.8865i	1.29793	+	2.24808i
$619$	−3.77745	+	6.54273i	−0.151828	+	0.262974i	−0.931900	−	0.362716i	$-0.881849\pi$
$619$	−3.77745	+	6.54273i	−0.151828	+	0.262974i	0.780071	+	0.625691i	$0.215183\pi$
$620$	−1.06199	+	1.83943i	−0.0426507	+	0.0738731i
$621$	3.98438	+	6.90115i	0.159888	+	0.276934i
$622$	−14.7975			−0.593326
$623$	−37.0220	+	16.4045i	−1.48326	+	0.657231i
$624$	37.6267			1.50627
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.84137	−	8.38551i	0.193500	−	0.335152i
$627$	20.4220	−	35.3719i	0.815576	−	1.41262i
$628$	−0.956624	−	1.65692i	−0.0381735	−	0.0661184i
$629$	−2.03875			−0.0812904
$630$	0.908457	−	8.49801i	0.0361938	−	0.338569i
$631$	−27.3098			−1.08718			−0.543592	−	0.839349i	$-0.682936\pi$
$631$	−27.3098			−1.08718			−0.543592	+	0.839349i	$0.682936\pi$
$632$	13.6705	+	23.6781i	0.543785	+	0.941863i
$633$	−5.10326	+	8.83910i	−0.202836	+	0.351323i
$634$	−24.6184	+	42.6404i	−0.977723	+	1.69347i
$635$	−1.80218	−	3.12148i	−0.0715175	−	0.123872i
$636$	−17.6116			−0.698345
$637$	23.8766	+	5.16394i	0.946025	+	0.204603i
$638$	15.2885			0.605279
$639$	−9.85259	−	17.0652i	−0.389762	−	0.675088i
$640$	6.82605	−	11.8231i	0.269823	−	0.467348i
$641$	4.75047	−	8.22806i	0.187632	−	0.324989i	−0.756828	−	0.653614i	$-0.773252\pi$
$641$	4.75047	−	8.22806i	0.187632	−	0.324989i	0.944460	+	0.328625i	$0.106585\pi$
$642$	−31.5426	−	54.6335i	−1.24489	−	2.15621i
$643$	23.4592			0.925142			0.462571	−	0.886582i	$-0.346927\pi$
$643$	23.4592			0.925142			0.462571	+	0.886582i	$0.346927\pi$
$644$	−0.578507	+	5.41154i	−0.0227964	+	0.213244i
$645$	−0.431994			−0.0170097
$646$	10.4231	+	18.0533i	0.410091	+	0.710298i
$647$	−13.1598	+	22.7934i	−0.517363	+	0.896099i	0.482433	+	0.875933i	$0.339753\pi$
$647$	−13.1598	+	22.7934i	−0.517363	+	0.896099i	−0.999797	+	0.0201668i	$0.993580\pi$
$648$	12.5954	−	21.8159i	0.494796	−	0.857011i
$649$	−12.0621	−	20.8921i	−0.473477	−	0.820086i
$650$	5.59379			0.219406
$651$	20.2117	−	8.95580i	0.792159	−	0.351005i
$652$	−12.3060			−0.481940
$653$	−16.0679	−	27.8303i	−0.628784	−	1.08909i	−0.987796	−	0.155753i	$-0.950220\pi$
$653$	−16.0679	−	27.8303i	−0.628784	−	1.08909i	0.359012	−	0.933333i	$-0.383114\pi$
$654$	2.13032	−	3.68981i	0.0833019	−	0.144283i
$655$	3.32452	−	5.75824i	0.129900	−	0.224993i
$656$	−11.9160	−	20.6390i	−0.465240	−	0.805819i
$657$	16.2457			0.633804
$658$	16.0530	+	11.7069i	0.625813	+	0.456382i
$659$	0.428155			0.0166785			0.00833927	−	0.999965i	$-0.497345\pi$
$659$	0.428155			0.0166785			0.00833927	+	0.999965i	$0.497345\pi$
$660$	−1.82246	−	3.15660i	−0.0709393	−	0.122870i
$661$	15.1160	−	26.1816i	0.587943	−	1.01835i	−0.406559	−	0.913625i	$-0.633271\pi$
$661$	15.1160	−	26.1816i	0.587943	−	1.01835i	0.994502	−	0.104722i	$-0.0333952\pi$
$662$	18.4008	−	31.8712i	0.715169	−	1.23871i
$663$	−7.96677	−	13.7989i	−0.309404	−	0.535903i
$664$	−11.8816			−0.461096
$665$	13.6365	+	9.94456i	0.528799	+	0.385633i
$666$	−3.23025			−0.125169
$667$	6.02738	+	10.4397i	0.233381	+	0.404228i
$668$	−3.57855	+	6.19822i	−0.138458	+	0.239816i
$669$	−15.3364	+	26.5634i	−0.592938	+	1.02700i
$670$	−0.310024	−	0.536978i	−0.0119773	−	0.0207453i
$671$	12.5883			0.485966
$672$	16.9581	−	7.51414i	0.654174	−	0.289864i
$673$	35.7646			1.37862			0.689311	−	0.724465i	$-0.257913\pi$
$673$	35.7646			1.37862			0.689311	+	0.724465i	$0.257913\pi$
$674$	−9.41431	−	16.3061i	−0.362626	−	0.628086i
$675$	1.10265	−	1.90985i	0.0424411	−	0.0735102i
$676$	0.233762	−	0.404887i	0.00899084	−	0.0155726i
$677$	15.8709	+	27.4892i	0.609969	+	1.05650i	0.991245	+	0.132036i	$0.0421515\pi$
$677$	15.8709	+	27.4892i	0.609969	+	1.05650i	−0.381276	+	0.924461i	$0.624515\pi$
$678$	30.0135			1.15266
$679$	1.38569	−	12.9622i	0.0531778	−	0.497442i
$680$	−4.67550			−0.179297
$681$	17.8409	+	30.9014i	0.683666	+	1.18414i
$682$	8.54936	−	14.8079i	0.327372	−	0.567025i
$683$	−16.3936	+	28.3946i	−0.627284	+	1.08649i	0.360810	+	0.932639i	$0.382500\pi$
$683$	−16.3936	+	28.3946i	−0.627284	+	1.08649i	−0.988094	+	0.153849i	$0.950833\pi$
$684$	3.65911	+	6.33776i	0.139909	+	0.242330i
$685$	−11.9755			−0.457560
$686$	29.0698	−	6.01708i	1.10989	−	0.229733i
$687$	−28.9494			−1.10449
$688$	−0.464354	−	0.804285i	−0.0177033	−	0.0306631i
$689$	−24.1049	+	41.7509i	−0.918324	+	1.59058i
$690$	6.48550	−	11.2332i	0.246899	−	0.427641i
$691$	−10.9242	−	18.9212i	−0.415576	−	0.719798i	0.579913	−	0.814678i	$-0.303087\pi$
$691$	−10.9242	−	18.9212i	−0.415576	−	0.719798i	−0.995489	+	0.0948803i	$0.969753\pi$
$692$	−5.67082			−0.215572
$693$	−1.62041	+	15.1578i	−0.0615542	+	0.575798i
$694$	38.2545			1.45212
$695$	2.86545	+	4.96310i	0.108693	+	0.188261i
$696$	8.56675	−	14.8380i	0.324722	−	0.562435i
$697$	−5.04598	+	8.73989i	−0.191130	+	0.331047i
$698$	−5.70003	−	9.87274i	−0.215749	−	0.373689i
$699$	−34.7398			−1.31398
$700$	1.37702	−	0.610156i	0.0520464	−	0.0230617i
$701$	−32.6578			−1.23347			−0.616734	−	0.787172i	$-0.711544\pi$
$701$	−32.6578			−1.23347			−0.616734	+	0.787172i	$0.711544\pi$
$702$	6.16801	+	10.6833i	0.232796	+	0.403215i
$703$	3.18953	−	5.52443i	0.120295	−	0.208358i
$704$	−6.59178	+	11.4173i	−0.248437	+	0.430306i
$705$	−5.24596	−	9.08627i	−0.197574	−	0.342209i
$706$	53.3601			2.00823
$707$	3.79791	+	2.76967i	0.142835	+	0.104164i
$708$	10.7570			0.404272
$709$	−13.7745	−	23.8581i	−0.517310	−	0.896008i	−0.999798	−	0.0201050i	$-0.993600\pi$
$709$	−13.7745	−	23.8581i	−0.517310	−	0.896008i	0.482487	−	0.875903i	$-0.339733\pi$
$710$	7.83654	−	13.5733i	0.294100	−	0.509396i
$711$	12.0131	−	20.8072i	0.450525	−	0.780332i
$712$	17.5498	+	30.3971i	0.657705	+	1.13918i
$713$	13.4820			0.504907
$714$	−15.6445	−	11.4089i	−0.585479	−	0.426968i
$715$	−9.97759			−0.373141
$716$	−5.39846	−	9.35041i	−0.201750	−	0.349441i
$717$	22.8958	−	39.6567i	0.855060	−	1.48101i
$718$	0.168983	−	0.292688i	0.00630641	−	0.0109230i
$719$	−14.0784	−	24.3846i	−0.525037	−	0.909391i	−0.999575	−	0.0291558i	$-0.990718\pi$
$719$	−14.0784	−	24.3846i	−0.525037	−	0.909391i	0.474538	−	0.880235i	$-0.342615\pi$
$720$	−9.70240			−0.361587
$721$	43.4857	−	19.2685i	1.61949	−	0.717597i
$722$	−34.7707			−1.29403
$723$	14.6175	+	25.3183i	0.543632	+	0.941598i
$724$	2.05160	−	3.55347i	0.0762470	−	0.132064i
$725$	1.66804	−	2.88913i	0.0619495	−	0.107300i
$726$	−5.07166	−	8.78438i	−0.188227	−	0.326019i
$727$	0.418224			0.0155111			0.00775553	−	0.999970i	$-0.497531\pi$
$727$	0.418224			0.0155111			0.00775553	+	0.999970i	$0.497531\pi$
$728$	2.25078	−	21.0545i	0.0834194	−	0.780332i
$729$	−7.32042			−0.271127
$730$	6.46074	+	11.1903i	0.239123	+	0.414172i
$731$	−0.196637	+	0.340585i	−0.00727289	+	0.0125970i
$732$	−2.80657	+	4.86113i	−0.103734	+	0.179672i
$733$	−4.31174	−	7.46814i	−0.159258	−	0.275842i	0.775344	−	0.631540i	$-0.217577\pi$
$733$	−4.31174	−	7.46814i	−0.159258	−	0.275842i	−0.934601	+	0.355697i	$0.884243\pi$
$734$	41.5876			1.53503
$735$	−15.3221	−	3.31381i	−0.565164	−	0.122232i
$736$	11.3118			0.416957
$737$	0.552988	+	0.957804i	0.0203696	+	0.0352811i
$738$	−7.99495	+	13.8477i	−0.294298	+	0.509740i
$739$	6.98266	−	12.0943i	0.256861	−	0.444897i	−0.708538	−	0.705673i	$-0.750645\pi$
$739$	6.98266	−	12.0943i	0.256861	−	0.444897i	0.965399	+	0.260776i	$0.0839783\pi$
$740$	−0.284634	−	0.493001i	−0.0104634	−	0.0181231i
$741$	49.8545			1.83145
$742$	−6.22742	+	58.2533i	−0.228616	+	2.13855i
$743$	−48.7950			−1.79012			−0.895058	−	0.445951i	$-0.852866\pi$
$743$	−48.7950			−1.79012			−0.895058	+	0.445951i	$0.852866\pi$
$744$	−9.58106	−	16.5949i	−0.351259	−	0.608398i
$745$	7.87742	−	13.6441i	0.288606	−	0.499881i
$746$	−20.9992	+	36.3717i	−0.768835	+	1.33166i
$747$	5.22052	+	9.04220i	0.191009	+	0.330837i
$748$	−3.31823			−0.121327
$749$	−42.5108	+	18.8365i	−1.55331	+	0.688271i
$750$	−3.58964			−0.131075
$751$	0.558946	+	0.968122i	0.0203962	+	0.0353273i	0.876043	−	0.482232i	$-0.160174\pi$
$751$	0.558946	+	0.968122i	0.0203962	+	0.0353273i	−0.855647	+	0.517560i	$0.826841\pi$
$752$	11.2779	−	19.5338i	0.411261	−	0.712325i
$753$	−9.51880	+	16.4871i	−0.346885	+	0.600822i
$754$	9.33066	+	16.1612i	0.339803	+	0.588555i
$755$	−4.84112			−0.176186
$756$	2.68368	+	1.95711i	0.0976045	+	0.0711794i
$757$	−33.7927			−1.22822			−0.614108	−	0.789222i	$-0.710484\pi$
$757$	−33.7927			−1.22822			−0.614108	+	0.789222i	$0.710484\pi$
$758$	−17.5755	−	30.4417i	−0.638372	−	1.10569i
$759$	−11.5681	+	20.0366i	−0.419897	+	0.727282i
$760$	7.31458	−	12.6692i	0.265328	−	0.459561i
$761$	25.3321	+	43.8766i	0.918289	+	1.59052i	0.802013	+	0.597307i	$0.203763\pi$
$761$	25.3321	+	43.8766i	0.918289	+	1.59052i	0.116277	+	0.993217i	$0.462904\pi$
$762$	−12.9384			−0.468709
$763$	−2.53727	−	1.85034i	−0.0918554	−	0.0669867i
$764$	7.58169			0.274296
$765$	2.05431	+	3.55817i	0.0742737	+	0.128646i
$766$	−17.6348	+	30.5443i	−0.637170	+	1.10361i
$767$	14.7230	−	25.5011i	0.531618	−	0.920790i
$768$	−14.1765	−	24.5545i	−0.511552	−	0.886034i
$769$	−12.1028			−0.436437			−0.218219	−	0.975900i	$-0.570025\pi$
$769$	−12.1028			−0.436437			−0.218219	+	0.975900i	$0.570025\pi$
$770$	−11.0854	+	4.91194i	−0.399490	+	0.177014i
$771$	16.2247			0.584320
$772$	0.670536	+	1.16140i	0.0241331	+	0.0417998i
$773$	14.4505	−	25.0289i	0.519747	−	0.900228i	−0.479989	−	0.877274i	$-0.659359\pi$
$773$	14.4505	−	25.0289i	0.519747	−	0.900228i	0.999737	−	0.0229541i	$-0.00730717\pi$
$774$	−0.311556	+	0.539631i	−0.0111987	+	0.0193966i
$775$	−1.86554	−	3.23121i	−0.0670121	−	0.116068i
$776$	−11.2995			−0.405628
$777$	−0.629819	+	5.89153i	−0.0225946	+	0.211357i
$778$	41.3311			1.48179
$779$	−15.7884	−	27.3463i	−0.565677	−	0.979781i
$780$	2.22451	−	3.85297i	0.0796504	−	0.137958i
$781$	−13.9780	+	24.2106i	−0.500171	+	0.866322i
$782$	−5.90420	−	10.2264i	−0.211134	−	0.365695i
$783$	7.35708			0.262921
$784$	−10.3002	−	32.0887i	−0.367865	−	1.14602i
$785$	3.36089			0.119955
$786$	−11.9338	−	20.6700i	−0.425666	−	0.737276i
$787$	−23.2949	+	40.3479i	−0.830373	+	1.43825i	0.0673705	+	0.997728i	$0.478539\pi$
$787$	−23.2949	+	40.3479i	−0.830373	+	1.43825i	−0.897743	+	0.440519i	$0.854794\pi$
$788$	1.77575	−	3.07568i	0.0632584	−	0.109567i
$789$	−31.8131	−	55.1019i	−1.13258	−	1.96168i
$790$	19.1099			0.679898
$791$	2.35144	−	21.9962i	0.0836077	−	0.782093i
$792$	13.2135			0.469522
$793$	7.68269	+	13.3068i	0.272820	+	0.472539i
$794$	−12.3998	+	21.4770i	−0.440051	+	0.762190i
$795$	15.4686	−	26.7924i	0.548615	−	0.950229i
$796$	0.239670	+	0.415120i	0.00849487	+	0.0147136i
$797$	−18.9933			−0.672777			−0.336389	−	0.941723i	$-0.609206\pi$
$797$	−18.9933			−0.672777			−0.336389	+	0.941723i	$0.609206\pi$
$798$	55.3899	−	24.5432i	1.96078	−	0.868821i
$799$	−9.55153			−0.337909
$800$	−1.56523	−	2.71106i	−0.0553393	−	0.0958505i
$801$	15.4219	−	26.7116i	0.544907	−	0.943807i
$802$	17.8364	−	30.8936i	0.629826	−	1.09089i
$803$	−11.5240	−	19.9601i	−0.406672	−	0.704376i
$804$	−0.493157			−0.0173923
$805$	−7.72443	−	5.63314i	−0.272250	−	0.198542i
$806$	20.8708			0.735144
$807$	−25.9568	−	44.9585i	−0.913724	−	1.58262i
$808$	2.03720	−	3.52853i	0.0716683	−	0.124133i
$809$	−0.279698	+	0.484451i	−0.00983366	+	0.0170324i	−0.870900	−	0.491460i	$-0.836464\pi$
$809$	−0.279698	+	0.484451i	−0.00983366	+	0.0170324i	0.861067	+	0.508492i	$0.169797\pi$
$810$	−8.80350	−	15.2481i	−0.309324	−	0.535764i
$811$	6.79271			0.238524			0.119262	−	0.992863i	$-0.461947\pi$
$811$	6.79271			0.238524			0.119262	+	0.992863i	$0.461947\pi$
$812$	4.05974	+	2.96062i	0.142469	+	0.103897i
$813$	−27.8582			−0.977031
$814$	2.29139	+	3.96881i	0.0803133	+	0.139107i
$815$	10.8086	−	18.7210i	0.378609	−	0.655770i
$816$	−10.9908	+	19.0367i	−0.384756	+	0.666416i
$817$	−0.615258	−	1.06566i	−0.0215252	−	0.0372827i
$818$	−33.2222			−1.16159
$819$	−17.0119	+	7.53799i	−0.594445	+	0.263399i
$820$	−2.81792			−0.0984059
$821$	3.27399	+	5.67072i	0.114263	+	0.197909i	0.917485	−	0.397771i	$-0.130216\pi$
$821$	3.27399	+	5.67072i	0.114263	+	0.197909i	−0.803222	+	0.595680i	$0.796883\pi$
$822$	−21.4939	+	37.2285i	−0.749685	+	1.29849i
$823$	−2.49020	+	4.31315i	−0.0868029	+	0.150347i	−0.906158	−	0.422939i	$-0.860998\pi$
$823$	−2.49020	+	4.31315i	−0.0868029	+	0.150347i	0.819355	+	0.573286i	$0.194332\pi$
$824$	−20.6138	−	35.7041i	−0.718114	−	1.24381i
$825$	6.40282			0.222918
$826$	3.80365	−	35.5806i	0.132346	−	1.23801i
$827$	10.5604			0.367223			0.183611	−	0.982999i	$-0.441221\pi$
$827$	10.5604			0.367223			0.183611	+	0.982999i	$0.441221\pi$
$828$	−2.07272	−	3.59005i	−0.0720319	−	0.124763i
$829$	−8.75467	+	15.1635i	−0.304062	+	0.526651i	−0.977052	−	0.213000i	$-0.931676\pi$
$829$	−8.75467	+	15.1635i	−0.304062	+	0.526651i	0.672990	+	0.739652i	$0.265010\pi$
$830$	−4.15229	+	7.19197i	−0.144128	+	0.249637i
$831$	−16.0274	−	27.7603i	−0.555985	−	0.962994i
$832$	−16.0920			−0.557889
$833$	−9.58701	+	10.5716i	−0.332170	+	0.366284i
$834$	20.5719			0.712346
$835$	−6.28621	−	10.8880i	−0.217543	−	0.376796i
$836$	5.19122	−	8.99145i	0.179542	−	0.310976i
$837$	4.11408	−	7.12580i	0.142204	−	0.246304i
$838$	16.5698	+	28.6997i	0.572393	+	0.991414i
$839$	13.8473			0.478061			0.239031	−	0.971012i	$-0.423170\pi$
$839$	13.8473			0.478061			0.239031	+	0.971012i	$0.423170\pi$
$840$	−1.44437	+	13.5111i	−0.0498355	+	0.466178i
$841$	−17.8706			−0.616226
$842$	3.55533	+	6.15801i	0.122525	+	0.212219i
$843$	−2.97770	+	5.15752i	−0.102557	+	0.177635i
$844$	−1.29723	+	2.24688i	−0.0446526	+	0.0773406i
$845$	0.410635	+	0.711241i	0.0141263	+	0.0244674i
$846$	−15.1337			−0.520306
$847$	−6.83520	+	3.02868i	−0.234860	+	0.104067i
$848$	66.5094			2.28394
$849$	−27.1490	−	47.0234i	−0.931750	−	1.61384i
$850$	−1.63395	+	2.83009i	−0.0560441	+	0.0970713i
$851$	−1.80672	+	3.12934i	−0.0619337	+	0.107272i
$852$	−6.23281	−	10.7955i	−0.213532	−	0.369849i
$853$	−47.1132			−1.61312			−0.806562	−	0.591149i	$-0.798675\pi$
$853$	−47.1132			−1.61312			−0.806562	+	0.591149i	$0.798675\pi$
$854$	15.0866	+	11.0021i	0.516253	+	0.376484i
$855$	−12.8555			−0.439647
$856$	20.1516	+	34.9036i	0.688767	+	1.19298i
$857$	12.3193	−	21.3377i	0.420820	−	0.728881i	−0.575200	−	0.818013i	$-0.695076\pi$
$857$	12.3193	−	21.3377i	0.420820	−	0.728881i	0.996020	+	0.0891315i	$0.0284091\pi$
$858$	−17.9080	+	31.0176i	−0.611369	+	1.05892i
$859$	−14.3307	−	24.8215i	−0.488958	−	0.846899i	0.510962	−	0.859603i	$-0.329289\pi$
$859$	−14.3307	−	24.8215i	−0.488958	−	0.846899i	−0.999919	+	0.0127042i	$0.995956\pi$
$860$	−0.109812			−0.00374454
$861$	23.6975	+	17.2817i	0.807607	+	0.588958i
$862$	37.1500			1.26534
$863$	−22.9116	−	39.6840i	−0.779919	−	1.35086i	−0.931988	−	0.362490i	$-0.881927\pi$
$863$	−22.9116	−	39.6840i	−0.779919	−	1.35086i	0.152069	−	0.988370i	$-0.451407\pi$
$864$	3.45182	−	5.97872i	0.117433	−	0.203400i
$865$	4.98079	−	8.62698i	0.169352	−	0.293326i
$866$	11.4595	+	19.8485i	0.389410	+	0.674479i
$867$	−28.7627			−0.976832
$868$	5.13776	−	2.27654i	0.174387	−	0.0772708i
$869$	−34.0861			−1.15629
$870$	−5.98767	−	10.3710i	−0.203001	−	0.351608i
$871$	−0.674982	+	1.16910i	−0.0228709	+	0.0396135i
$872$	−1.36099	+	2.35731i	−0.0460890	+	0.0798284i
$873$	4.96474	+	8.59919i	0.168031	+	0.291038i
$874$	36.9474			1.24976
$875$	−0.281235	+	2.63076i	−0.00950747	+	0.0889360i
$876$	10.2771			0.347232
$877$	5.07639	+	8.79256i	0.171417	+	0.296904i	0.938916	−	0.344147i	$-0.111832\pi$
$877$	5.07639	+	8.79256i	0.171417	+	0.296904i	−0.767498	+	0.641051i	$0.778499\pi$
$878$	−14.0474	+	24.3307i	−0.474075	+	0.821122i
$879$	−8.46909	+	14.6689i	−0.285655	+	0.494769i
$880$	6.88245	+	11.9208i	0.232007	+	0.401849i
$881$	−57.9134			−1.95115			−0.975576	−	0.219662i	$-0.929505\pi$
$881$	−57.9134			−1.95115			−0.975576	+	0.219662i	$0.929505\pi$
$882$	−15.1899	+	16.7499i	−0.511469	+	0.563997i
$883$	−21.7280			−0.731205			−0.365602	−	0.930771i	$-0.619137\pi$
$883$	−21.7280			−0.731205			−0.365602	+	0.930771i	$0.619137\pi$
$884$	−2.02513	−	3.50763i	−0.0681125	−	0.117974i
$885$	−9.44807	+	16.3645i	−0.317593	+	0.550088i
$886$	30.6565	−	53.0985i	1.02992	−	1.78388i
$887$	4.21084	+	7.29339i	0.141386	+	0.244888i	0.928019	−	0.372533i	$-0.121511\pi$
$887$	4.21084	+	7.29339i	0.141386	+	0.244888i	−0.786633	+	0.617421i	$0.788177\pi$
$888$	5.13582			0.172347
$889$	−1.01367	+	9.48224i	−0.0339975	+	0.318024i
$890$	24.5326			0.822333
$891$	15.7027	+	27.1979i	0.526062	+	0.911165i
$892$	−3.89846	+	6.75233i	−0.130530	+	0.226085i
$893$	14.9429	−	25.8819i	0.500045	−	0.866104i
$894$	−28.2771	−	48.9774i	−0.945729	−	1.63805i
$895$	18.9663			0.633974
$896$	−33.0234	+	14.6326i	−1.10323	+	0.488842i
$897$	−28.2403			−0.942916
$898$	25.9894	+	45.0150i	0.867279	+	1.50217i
$899$	6.22358	−	10.7796i	0.207568	−	0.359519i
$900$	−0.573612	+	0.993525i	−0.0191204	+	0.0331175i
$901$	−14.0822	−	24.3910i	−0.469145	−	0.812583i
$902$	22.6851			0.755330
$903$	0.923468	+	0.673451i	0.0307311	+	0.0224110i
$904$	−19.1747			−0.637740
$905$	3.60391	+	6.24216i	0.119798	+	0.207496i
$906$	−8.68895	+	15.0497i	−0.288671	+	0.499993i
$907$	−22.7344	+	39.3771i	−0.754883	+	1.30750i	0.190549	+	0.981678i	$0.438973\pi$
$907$	−22.7344	+	39.3771i	−0.754883	+	1.30750i	−0.945432	+	0.325818i	$0.894360\pi$
$908$	4.53512	+	7.85505i	0.150503	+	0.260679i
$909$	−3.58039			−0.118754
$910$	−11.9578	−	8.72036i	−0.396396	−	0.289077i
$911$	−14.8633			−0.492443			−0.246221	−	0.969214i	$-0.579189\pi$
$911$	−14.8633			−0.492443			−0.246221	+	0.969214i	$0.579189\pi$
$912$	−34.3892	−	59.5638i	−1.13874	−	1.97236i
$913$	7.40641	−	12.8283i	0.245116	−	0.424554i
$914$	9.52178	−	16.4922i	0.314953	−	0.545514i
$915$	−4.93014	−	8.53924i	−0.162985	−	0.282299i
$916$	−7.35885			−0.243143
$917$	−16.0835	+	7.12661i	−0.531125	+	0.235341i
$918$	−7.20674			−0.237858
$919$	20.5758	+	35.6384i	0.678734	+	1.17560i	0.975362	+	0.220609i	$0.0708045\pi$
$919$	20.5758	+	35.6384i	0.678734	+	1.17560i	−0.296628	+	0.954993i	$0.595862\pi$
$920$	−4.14338	+	7.17654i	−0.136603	+	0.236604i
$921$	−1.47806	+	2.56007i	−0.0487036	+	0.0843572i
$922$	28.0385	+	48.5641i	0.923399	+	1.59937i
$923$	−34.1233			−1.12318
$924$	−1.02508	+	9.58893i	−0.0337227	+	0.315453i
$925$	1.00000			0.0328798
$926$	2.65556	+	4.59957i	0.0872671	+	0.151151i
$927$	−18.1145	+	31.3752i	−0.594957	+	1.03050i
$928$	5.22174	−	9.04432i	0.171412	−	0.296894i
$929$	1.05095	+	1.82030i	0.0344805	+	0.0597219i	0.882751	−	0.469842i	$-0.155689\pi$
$929$	1.05095	+	1.82030i	0.0344805	+	0.0597219i	−0.848270	+	0.529564i	$0.822356\pi$
$930$	−13.3932			−0.439182
$931$	−13.6475	−	42.5167i	−0.447280	−	1.39343i
$932$	−8.83076			−0.289261
$933$	−10.3371	−	17.9044i	−0.338423	−	0.586165i
$934$	−16.1753	+	28.0164i	−0.529272	+	0.916725i
$935$	2.91447	−	5.04801i	0.0953134	−	0.165088i
$936$	8.06426	+	13.9677i	0.263589	+	0.456549i
$937$	−26.0598			−0.851335			−0.425668	−	0.904880i	$-0.639961\pi$
$937$	−26.0598			−0.851335			−0.425668	+	0.904880i	$0.639961\pi$
$938$	−0.174379	+	1.63120i	−0.00569369	+	0.0532606i
$939$	13.5282			0.441477
$940$	−1.33351	−	2.30970i	−0.0434942	−	0.0753342i
$941$	−1.53495	+	2.65861i	−0.0500380	+	0.0866683i	−0.889960	−	0.456040i	$-0.849268\pi$
$941$	−1.53495	+	2.65861i	−0.0500380	+	0.0866683i	0.839922	+	0.542708i	$0.182601\pi$
$942$	6.03220	−	10.4481i	0.196540	−	0.340416i
$943$	8.94339	+	15.4904i	0.291237	+	0.504437i
$944$	−40.6233			−1.32218
$945$	−5.33447	+	2.36370i	−0.173530	+	0.0768912i
$946$	0.884016			0.0287418
$947$	−24.3389	−	42.1562i	−0.790908	−	1.36989i	−0.925405	−	0.378979i	$-0.876275\pi$
$947$	−24.3389	−	42.1562i	−0.790908	−	1.36989i	0.134497	−	0.990914i	$-0.457058\pi$
$948$	7.59953	−	13.1628i	0.246821	−	0.427507i
$949$	14.0662	−	24.3634i	0.456610	−	0.790871i
$950$	−5.11248	−	8.85508i	−0.165871	−	0.287297i
$951$	−68.7911			−2.23070
$952$	9.99475	+	7.28880i	0.323932	+	0.236231i
$953$	2.61312			0.0846472			0.0423236	−	0.999104i	$-0.486524\pi$
$953$	2.61312			0.0846472			0.0423236	+	0.999104i	$0.486524\pi$
$954$	−22.3121	−	38.6457i	−0.722380	−	1.25120i
$955$	−6.65915	+	11.5340i	−0.215485	+	0.373231i
$956$	5.82005	−	10.0806i	0.188234	−	0.326031i
$957$	10.6802	+	18.4986i	0.345241	+	0.597974i
$958$	20.2842			0.655353
$959$	25.5999	+	18.6690i	0.826663	+	0.602855i
$960$	10.3265			0.333288
$961$	8.53954	+	14.7909i	0.275469	+	0.477126i
$962$	−2.79689	+	4.84436i	−0.0901754	+	0.156188i
$963$	17.7083	−	30.6717i	0.570643	−	0.988382i
$964$	3.71574	+	6.43584i	0.119676	+	0.207285i
$965$	−2.35578			−0.0758353
$966$	−31.3758	+	13.9026i	−1.00950	+	0.447310i
$967$	−30.5434			−0.982208			−0.491104	−	0.871101i	$-0.663407\pi$
$967$	−30.5434			−0.982208			−0.491104	+	0.871101i	$0.663407\pi$
$968$	3.24013	+	5.61206i	0.104142	+	0.180379i
$969$	−14.5626	+	25.2231i	−0.467817	+	0.810284i
$970$	−3.94885	+	6.83961i	−0.126790	+	0.219607i
$971$	18.3673	+	31.8131i	0.589434	+	1.02093i	0.994307	+	0.106557i	$0.0339826\pi$
$971$	18.3673	+	31.8131i	0.589434	+	1.02093i	−0.404872	+	0.914373i	$0.632684\pi$
$972$	−10.2375			−0.328369
$973$	1.61173	−	15.0766i	0.0516696	−	0.483334i
$974$	48.3118			1.54801
$975$	3.90767	+	6.76828i	0.125146	+	0.216758i
$976$	10.5989	−	18.3578i	0.339262	−	0.587620i
$977$	−2.76264	+	4.78503i	−0.0883847	+	0.153087i	−0.906828	−	0.421500i	$-0.861504\pi$
$977$	−2.76264	+	4.78503i	−0.0883847	+	0.153087i	0.818444	+	0.574587i	$0.194837\pi$
$978$	−38.7990	−	67.2019i	−1.24066	−	2.14888i
$979$	−43.7585			−1.39853
$980$	−3.89483	−	0.842361i	−0.124416	−	0.0269082i
$981$	2.39196			0.0763693
$982$	25.2051	+	43.6564i	0.804326	+	1.39313i
$983$	−24.5433	+	42.5103i	−0.782810	+	1.35587i	0.147488	+	0.989064i	$0.452881\pi$
$983$	−24.5433	+	42.5103i	−0.782810	+	1.35587i	−0.930299	+	0.366803i	$0.880452\pi$
$984$	12.7113	−	22.0166i	0.405221	−	0.701864i
$985$	3.11935	+	5.40287i	0.0993907	+	0.172150i
$986$	−10.9020			−0.347190
$987$	−2.95069	+	27.6017i	−0.0939216	+	0.878573i
$988$	12.6729			0.403178
$989$	0.348516	+	0.603647i	0.0110822	+	0.0191949i
$990$	4.61775	−	7.99817i	0.146762	−	0.254199i
$991$	22.1924	−	38.4383i	0.704963	−	1.22103i	−0.261741	−	0.965138i	$-0.584297\pi$
$991$	22.1924	−	38.4383i	0.704963	−	1.22103i	0.966705	−	0.255895i	$-0.0823700\pi$
$992$	−5.84000	−	10.1152i	−0.185420	−	0.321157i
$993$	51.4173			1.63168
$994$	−37.9120	+	16.7988i	−1.20250	+	0.532825i
$995$	−0.842027			−0.0266940
$996$	3.30253	+	5.72015i	0.104645	+	0.181250i
$997$	−11.0676	+	19.1696i	−0.350514	+	0.607108i	−0.986340	−	0.164724i	$-0.947327\pi$
$997$	−11.0676	+	19.1696i	−0.350514	+	0.607108i	0.635825	+	0.771833i	$0.280660\pi$
$998$	−30.5010	+	52.8294i	−0.965494	+	1.67228i
$999$	1.10265	+	1.90985i	0.0348864	+	0.0604250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.14	✓	38
7.2	even	3	inner	1295.2.j.a.926.14	yes	38
7.3	odd	6		9065.2.a.s.1.6		19
7.4	even	3		9065.2.a.r.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.14	✓	38	1.1	even	1	trivial
1295.2.j.a.926.14	yes	38	7.2	even	3	inner
9065.2.a.r.1.6		19	7.4	even	3
9065.2.a.s.1.6		19	7.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.801447 + 1.38815i) q^{2} +(-1.11974 + 1.93944i) q^{3} +(-0.284634 + 0.493001i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.58964 q^{6} +(-0.281235 + 2.63076i) q^{7} +2.29331 q^{8} +(-1.00763 - 1.74526i) q^{9} +(0.801447 - 1.38815i) q^{10} +(-1.42953 + 2.47603i) q^{11} +(-0.637432 - 1.10407i) q^{12} -3.48980 q^{13} +(-3.87728 + 1.71802i) q^{14} +2.23948 q^{15} +(2.40724 + 4.16945i) q^{16} +(1.01938 - 1.76561i) q^{17} +(1.61512 - 2.79747i) q^{18} +(3.18953 + 5.52443i) q^{19} +0.569269 q^{20} +(-4.78731 - 3.49120i) q^{21} -4.58279 q^{22} +(-1.80672 - 3.12934i) q^{23} +(-2.56791 + 4.44775i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.79689 - 4.84436i) q^{26} -2.20531 q^{27} +(-1.21692 - 0.887454i) q^{28} -3.33608 q^{29} +(1.79482 + 3.10872i) q^{30} +(-1.86554 + 3.23121i) q^{31} +(-1.56523 + 2.71106i) q^{32} +(-3.20141 - 5.54501i) q^{33} +3.26791 q^{34} +(2.41892 - 1.07182i) q^{35} +1.14722 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-5.11248 + 8.85508i) q^{38} +(3.90767 - 6.76828i) q^{39} +(-1.14666 - 1.98606i) q^{40} -4.95006 q^{41} +(1.00953 - 9.44350i) q^{42} -0.192899 q^{43} +(-0.813790 - 1.40953i) q^{44} +(-1.00763 + 1.74526i) q^{45} +(2.89599 - 5.01600i) q^{46} +(-2.34249 - 4.05732i) q^{47} -10.7819 q^{48} +(-6.84181 - 1.47972i) q^{49} -1.60289 q^{50} +(2.28287 + 3.95405i) q^{51} +(0.993318 - 1.72048i) q^{52} +(6.90724 - 11.9637i) q^{53} +(-1.76744 - 3.06129i) q^{54} +2.85907 q^{55} +(-0.644959 + 6.03315i) q^{56} -14.2858 q^{57} +(-2.67369 - 4.63097i) q^{58} +(-4.21887 + 7.30730i) q^{59} +(-0.637432 + 1.10407i) q^{60} +(-2.20147 - 3.81305i) q^{61} -5.98052 q^{62} +(4.87476 - 2.16000i) q^{63} +4.61114 q^{64} +(1.74490 + 3.02226i) q^{65} +(5.13152 - 8.88806i) q^{66} +(0.193415 - 0.335005i) q^{67} +(0.580300 + 1.00511i) q^{68} +8.09223 q^{69} +(3.42649 + 2.49881i) q^{70} +9.77799 q^{71} +(-2.31081 - 4.00243i) q^{72} +(-4.03067 + 6.98132i) q^{73} +(0.801447 - 1.38815i) q^{74} +(-1.11974 - 1.93944i) q^{75} -3.63140 q^{76} +(-6.11180 - 4.45711i) q^{77} +12.5272 q^{78} +(5.96105 + 10.3248i) q^{79} +(2.40724 - 4.16945i) q^{80} +(5.49225 - 9.51286i) q^{81} +(-3.96721 - 6.87141i) q^{82} -5.18099 q^{83} +(3.08380 - 1.36643i) q^{84} -2.03875 q^{85} +(-0.154599 - 0.267773i) q^{86} +(3.73554 - 6.47014i) q^{87} +(-3.27837 + 5.67830i) q^{88} +(7.65258 + 13.2547i) q^{89} -3.23025 q^{90} +(0.981454 - 9.18084i) q^{91} +2.05702 q^{92} +(-4.17783 - 7.23621i) q^{93} +(3.75477 - 6.50345i) q^{94} +(3.18953 - 5.52443i) q^{95} +(-3.50530 - 6.07136i) q^{96} -4.92715 q^{97} +(-3.42928 - 10.6834i) q^{98} +5.76176 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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