LMFDB - Embedded newform 197.3.c.a.183.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(14,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("197.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.c (of order $4$, 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:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			183.10
Character	$\chi$	$=$	197.183
Dual form			197.3.c.a.14.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11355 - 1.11355i) q^{2} +(2.19442 + 2.19442i) q^{3} -1.52002i q^{4} +(-1.87378 - 1.87378i) q^{5} -4.88717i q^{6} -5.07096i q^{7} +(-6.14681 + 6.14681i) q^{8} +0.630916i q^{9} +O(q^{10})$	\(q+(-1.11355 - 1.11355i) q^{2} +(2.19442 + 2.19442i) q^{3} -1.52002i q^{4} +(-1.87378 - 1.87378i) q^{5} -4.88717i q^{6} -5.07096i q^{7} +(-6.14681 + 6.14681i) q^{8} +0.630916i q^{9} +4.17310i q^{10} +(-9.24618 - 9.24618i) q^{11} +(3.33556 - 3.33556i) q^{12} +(2.79068 + 2.79068i) q^{13} +(-5.64675 + 5.64675i) q^{14} -8.22372i q^{15} +7.60944 q^{16} +(-12.5261 + 12.5261i) q^{17} +(0.702555 - 0.702555i) q^{18} -33.2908i q^{19} +(-2.84820 + 2.84820i) q^{20} +(11.1278 - 11.1278i) q^{21} +20.5921i q^{22} +30.3777 q^{23} -26.9773 q^{24} -17.9779i q^{25} -6.21512i q^{26} +(18.3652 - 18.3652i) q^{27} -7.70797 q^{28} -36.4488 q^{29} +(-9.15751 + 9.15751i) q^{30} +(-5.16354 - 5.16354i) q^{31} +(16.1138 + 16.1138i) q^{32} -40.5799i q^{33} +27.8969 q^{34} +(-9.50188 + 9.50188i) q^{35} +0.959006 q^{36} -42.9671 q^{37} +(-37.0709 + 37.0709i) q^{38} +12.2478i q^{39} +23.0356 q^{40} -0.230336i q^{41} -24.7826 q^{42} +70.5045i q^{43} +(-14.0544 + 14.0544i) q^{44} +(1.18220 - 1.18220i) q^{45} +(-33.8271 - 33.8271i) q^{46} -55.0790i q^{47} +(16.6983 + 16.6983i) q^{48} +23.2854 q^{49} +(-20.0192 + 20.0192i) q^{50} -54.9751 q^{51} +(4.24190 - 4.24190i) q^{52} +74.5527 q^{53} -40.9012 q^{54} +34.6507i q^{55} +(31.1702 + 31.1702i) q^{56} +(73.0539 - 73.0539i) q^{57} +(40.5874 + 40.5874i) q^{58} +75.7516 q^{59} -12.5002 q^{60} +83.6520 q^{61} +11.4997i q^{62} +3.19935 q^{63} -66.3246i q^{64} -10.4583i q^{65} +(-45.1877 + 45.1877i) q^{66} +(-16.2260 - 16.2260i) q^{67} +(19.0400 + 19.0400i) q^{68} +(66.6614 + 66.6614i) q^{69} +21.1616 q^{70} +(-65.9279 + 65.9279i) q^{71} +(-3.87812 - 3.87812i) q^{72} +(53.0731 + 53.0731i) q^{73} +(47.8459 + 47.8459i) q^{74} +(39.4509 - 39.4509i) q^{75} -50.6028 q^{76} +(-46.8870 + 46.8870i) q^{77} +(13.6386 - 13.6386i) q^{78} +(39.8540 - 39.8540i) q^{79} +(-14.2585 - 14.2585i) q^{80} +86.2802 q^{81} +(-0.256490 + 0.256490i) q^{82} +121.464i q^{83} +(-16.9145 - 16.9145i) q^{84} +46.9426 q^{85} +(78.5101 - 78.5101i) q^{86} +(-79.9837 - 79.9837i) q^{87} +113.669 q^{88} +(-81.1992 + 81.1992i) q^{89} -2.63287 q^{90} +(14.1514 - 14.1514i) q^{91} -46.1749i q^{92} -22.6619i q^{93} +(-61.3331 + 61.3331i) q^{94} +(-62.3799 + 62.3799i) q^{95} +70.7206i q^{96} -168.306i q^{97} +(-25.9294 - 25.9294i) q^{98} +(5.83356 - 5.83356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8}+O(q^{10}) $ 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8	$ 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28} + 56 q^{29} - 70 q^{30} - 64 q^{31} - 156 q^{32} - 52 q^{34} - 92 q^{35} - 36 q^{36} - 160 q^{37} + 40 q^{38} + 52 q^{40} + 80 q^{42} + 140 q^{44} + 324 q^{45} + 214 q^{46} + 216 q^{48} - 836 q^{49} + 126 q^{50} + 124 q^{51} - 10 q^{52} - 16 q^{53} + 400 q^{54} - 40 q^{56} + 68 q^{57} - 266 q^{58} - 364 q^{59} - 68 q^{60} - 168 q^{61} - 12 q^{63} + 238 q^{66} - 112 q^{67} - 148 q^{68} - 48 q^{69} + 48 q^{70} + 150 q^{71} - 474 q^{72} + 18 q^{73} + 236 q^{74} + 64 q^{75} - 260 q^{76} - 388 q^{77} - 782 q^{78} + 202 q^{79} + 796 q^{80} - 516 q^{81} + 72 q^{82} - 294 q^{84} - 696 q^{85} + 618 q^{86} + 464 q^{87} - 244 q^{88} - 536 q^{89} + 1484 q^{90} + 212 q^{91} + 132 q^{94} + 370 q^{95} - 530 q^{98} - 66 q^{99}+O(q^{100}) $ 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.11355	−	1.11355i	−0.556774	−	0.556774i	0.371614	−	0.928387i	$-0.378805\pi$
$2$	−1.11355	−	1.11355i	−0.556774	−	0.556774i	−0.928387	+	0.371614i	$0.878805\pi$
$3$	2.19442	+	2.19442i	0.731472	+	0.731472i	0.970911	−	0.239440i	$-0.0769637\pi$
$3$	2.19442	+	2.19442i	0.731472	+	0.731472i	−0.239440	+	0.970911i	$0.576964\pi$
$4$		−	1.52002i		−	0.380006i
$5$	−1.87378	−	1.87378i	−0.374757	−	0.374757i	0.494449	−	0.869206i	$-0.335370\pi$
$5$	−1.87378	−	1.87378i	−0.374757	−	0.374757i	−0.869206	+	0.494449i	$0.835370\pi$
$6$		−	4.88717i		−	0.814529i
$7$		−	5.07096i		−	0.724422i	−0.932096	−	0.362211i	$-0.882022\pi$
$7$		−	5.07096i		−	0.724422i	0.932096	−	0.362211i	$-0.117978\pi$
$8$	−6.14681	+	6.14681i	−0.768351	+	0.768351i
$9$			0.630916i			0.0701017i
$10$			4.17310i			0.417310i
$11$	−9.24618	−	9.24618i	−0.840562	−	0.840562i	0.148370	−	0.988932i	$-0.452597\pi$
$11$	−9.24618	−	9.24618i	−0.840562	−	0.840562i	−0.988932	+	0.148370i	$0.952597\pi$
$12$	3.33556	−	3.33556i	0.277963	−	0.277963i
$13$	2.79068	+	2.79068i	0.214668	+	0.214668i	0.806247	−	0.591579i	$-0.201495\pi$
$13$	2.79068	+	2.79068i	0.214668	+	0.214668i	−0.591579	+	0.806247i	$0.701495\pi$
$14$	−5.64675	+	5.64675i	−0.403339	+	0.403339i
$15$		−	8.22372i		−	0.548248i
$16$	7.60944			0.475590
$17$	−12.5261	+	12.5261i	−0.736832	+	0.736832i	−0.971964	−	0.235132i	$-0.924448\pi$
$17$	−12.5261	+	12.5261i	−0.736832	+	0.736832i	0.235132	+	0.971964i	$0.424448\pi$
$18$	0.702555	−	0.702555i	0.0390308	−	0.0390308i
$19$		−	33.2908i		−	1.75215i	−0.482176	−	0.876075i	$-0.660153\pi$
$19$		−	33.2908i		−	1.75215i	0.482176	−	0.876075i	$-0.339847\pi$
$20$	−2.84820	+	2.84820i	−0.142410	+	0.142410i
$21$	11.1278	−	11.1278i	0.529894	−	0.529894i
$22$			20.5921i			0.936006i
$23$	30.3777			1.32077			0.660386	−	0.750927i	$-0.270393\pi$
$23$	30.3777			1.32077			0.660386	+	0.750927i	$0.270393\pi$
$24$	−26.9773			−1.12405
$25$		−	17.9779i		−	0.719114i
$26$		−	6.21512i		−	0.239043i
$27$	18.3652	−	18.3652i	0.680194	−	0.680194i
$28$	−7.70797			−0.275285
$29$	−36.4488			−1.25685			−0.628427	−	0.777869i	$-0.716301\pi$
$29$	−36.4488			−1.25685			−0.628427	+	0.777869i	$0.716301\pi$
$30$	−9.15751	+	9.15751i	−0.305250	+	0.305250i
$31$	−5.16354	−	5.16354i	−0.166566	−	0.166566i	0.618902	−	0.785468i	$-0.287578\pi$
$31$	−5.16354	−	5.16354i	−0.166566	−	0.166566i	−0.785468	+	0.618902i	$0.787578\pi$
$32$	16.1138	+	16.1138i	0.503555	+	0.503555i
$33$		−	40.5799i		−	1.22970i
$34$	27.8969			0.820497
$35$	−9.50188	+	9.50188i	−0.271482	+	0.271482i
$36$	0.959006			0.0266391
$37$	−42.9671			−1.16127			−0.580636	−	0.814163i	$-0.697196\pi$
$37$	−42.9671			−1.16127			−0.580636	+	0.814163i	$0.697196\pi$
$38$	−37.0709	+	37.0709i	−0.975551	+	0.975551i
$39$			12.2478i			0.314047i
$40$	23.0356			0.575890
$41$		−	0.230336i		−	0.00561795i	−0.999996	−	0.00280897i	$-0.999106\pi$
$41$		−	0.230336i		−	0.00561795i	0.999996	−	0.00280897i	$-0.000894125\pi$
$42$	−24.7826			−0.590063
$43$			70.5045i			1.63964i	0.572622	+	0.819819i	$0.305926\pi$
$43$			70.5045i			1.63964i	−0.572622	+	0.819819i	$0.694074\pi$
$44$	−14.0544	+	14.0544i	−0.319418	+	0.319418i
$45$	1.18220	−	1.18220i	0.0262711	−	0.0262711i
$46$	−33.8271	−	33.8271i	−0.735371	−	0.735371i
$47$		−	55.0790i		−	1.17189i	−0.810350	−	0.585947i	$-0.800723\pi$
$47$		−	55.0790i		−	1.17189i	0.810350	−	0.585947i	$-0.199277\pi$
$48$	16.6983	+	16.6983i	0.347881	+	0.347881i
$49$	23.2854			0.475212
$50$	−20.0192	+	20.0192i	−0.400384	+	0.400384i
$51$	−54.9751			−1.07794
$52$	4.24190	−	4.24190i	0.0815751	−	0.0815751i
$53$	74.5527			1.40665			0.703327	−	0.710866i	$-0.251697\pi$
$53$	74.5527			1.40665			0.703327	+	0.710866i	$0.251697\pi$
$54$	−40.9012			−0.757429
$55$			34.6507i			0.630013i
$56$	31.1702	+	31.1702i	0.556611	+	0.556611i
$57$	73.0539	−	73.0539i	1.28165	−	1.28165i
$58$	40.5874	+	40.5874i	0.699783	+	0.699783i
$59$	75.7516			1.28393			0.641963	−	0.766736i	$-0.278120\pi$
$59$	75.7516			1.28393			0.641963	+	0.766736i	$0.278120\pi$
$60$	−12.5002			−0.208337
$61$	83.6520			1.37134			0.685672	−	0.727911i	$-0.259508\pi$
$61$	83.6520			1.37134			0.685672	+	0.727911i	$0.259508\pi$
$62$			11.4997i			0.185479i
$63$	3.19935			0.0507833
$64$		−	66.3246i		−	1.03632i
$65$		−	10.4583i		−	0.160897i
$66$	−45.1877	+	45.1877i	−0.684662	+	0.684662i
$67$	−16.2260	−	16.2260i	−0.242179	−	0.242179i	0.575572	−	0.817751i	$-0.304779\pi$
$67$	−16.2260	−	16.2260i	−0.242179	−	0.242179i	−0.817751	+	0.575572i	$0.804779\pi$
$68$	19.0400	+	19.0400i	0.280000	+	0.280000i
$69$	66.6614	+	66.6614i	0.966107	+	0.966107i
$70$	21.1616			0.302309
$71$	−65.9279	+	65.9279i	−0.928561	+	0.928561i	−0.997613	−	0.0690518i	$-0.978003\pi$
$71$	−65.9279	+	65.9279i	−0.928561	+	0.928561i	0.0690518	+	0.997613i	$0.478003\pi$
$72$	−3.87812	−	3.87812i	−0.0538627	−	0.0538627i
$73$	53.0731	+	53.0731i	0.727029	+	0.727029i	0.970027	−	0.242998i	$-0.0781309\pi$
$73$	53.0731	+	53.0731i	0.727029	+	0.727029i	−0.242998	+	0.970027i	$0.578131\pi$
$74$	47.8459	+	47.8459i	0.646566	+	0.646566i
$75$	39.4509	−	39.4509i	0.526012	−	0.526012i
$76$	−50.6028			−0.665827
$77$	−46.8870	+	46.8870i	−0.608922	+	0.608922i
$78$	13.6386	−	13.6386i	0.174853	−	0.174853i
$79$	39.8540	−	39.8540i	0.504481	−	0.504481i	−0.408346	−	0.912827i	$-0.633894\pi$
$79$	39.8540	−	39.8540i	0.504481	−	0.504481i	0.912827	+	0.408346i	$0.133894\pi$
$80$	−14.2585	−	14.2585i	−0.178231	−	0.178231i
$81$	86.2802			1.06519
$82$	−0.256490	+	0.256490i	−0.00312793	+	0.00312793i
$83$			121.464i			1.46342i	0.681616	+	0.731710i	$0.261278\pi$
$83$			121.464i			1.46342i	−0.681616	+	0.731710i	$0.738722\pi$
$84$	−16.9145	−	16.9145i	−0.201363	−	0.201363i
$85$	46.9426			0.552266
$86$	78.5101	−	78.5101i	0.912908	−	0.912908i
$87$	−79.9837	−	79.9837i	−0.919353	−	0.919353i
$88$	113.669			1.29169
$89$	−81.1992	+	81.1992i	−0.912350	+	0.912350i	−0.996457	−	0.0841065i	$-0.973196\pi$
$89$	−81.1992	+	81.1992i	−0.912350	+	0.912350i	0.0841065	+	0.996457i	$0.473196\pi$
$90$	−2.63287			−0.0292541
$91$	14.1514	−	14.1514i	0.155510	−	0.155510i
$92$		−	46.1749i		−	0.501901i
$93$		−	22.6619i		−	0.243676i
$94$	−61.3331	+	61.3331i	−0.652480	+	0.652480i
$95$	−62.3799	+	62.3799i	−0.656630	+	0.656630i
$96$			70.7206i			0.736673i
$97$		−	168.306i		−	1.73511i	−0.497342	−	0.867554i	$-0.665691\pi$
$97$		−	168.306i		−	1.73511i	0.497342	−	0.867554i	$-0.334309\pi$
$98$	−25.9294	−	25.9294i	−0.264586	−	0.264586i
$99$	5.83356	−	5.83356i	0.0589249	−	0.0589249i
$100$	−27.3268			−0.273268
$101$	6.52298			0.0645839			0.0322920	−	0.999478i	$-0.489719\pi$
$101$	6.52298			0.0645839			0.0322920	+	0.999478i	$0.489719\pi$
$102$	61.2174	+	61.2174i	0.600171	+	0.600171i
$103$	10.3065	+	10.3065i	0.100063	+	0.100063i	0.755366	−	0.655303i	$-0.227459\pi$
$103$	10.3065	+	10.3065i	0.100063	+	0.100063i	−0.655303	+	0.755366i	$0.727459\pi$
$104$	−34.3076			−0.329881
$105$	−41.7021			−0.397163
$106$	−83.0180	−	83.0180i	−0.783188	−	0.783188i
$107$			50.7316i			0.474127i	0.971494	+	0.237064i	$0.0761850\pi$
$107$			50.7316i			0.474127i	−0.971494	+	0.237064i	$0.923815\pi$
$108$	−27.9156	−	27.9156i	−0.258478	−	0.258478i
$109$		−	158.400i		−	1.45322i	−0.687053	−	0.726608i	$-0.741096\pi$
$109$		−	158.400i		−	1.45322i	0.687053	−	0.726608i	$-0.258904\pi$
$110$	38.5852	−	38.5852i	0.350775	−	0.350775i
$111$	−94.2876	−	94.2876i	−0.849438	−	0.849438i
$112$		−	38.5871i		−	0.344528i
$113$	1.48490	−	1.48490i	0.0131407	−	0.0131407i	−0.700506	−	0.713647i	$-0.747042\pi$
$113$	1.48490	−	1.48490i	0.0131407	−	0.0131407i	0.713647	+	0.700506i	$0.247042\pi$
$114$	−162.698			−1.42718
$115$	−56.9213	−	56.9213i	−0.494968	−	0.494968i
$116$			55.4030i			0.477612i
$117$	−1.76069	+	1.76069i	−0.0150486	+	0.0150486i
$118$	−84.3530	−	84.3530i	−0.714856	−	0.714856i
$119$	63.5195	+	63.5195i	0.533777	+	0.533777i
$120$	50.5497	+	50.5497i	0.421247	+	0.421247i
$121$			49.9839i			0.413090i
$122$	−93.1505	−	93.1505i	−0.763528	−	0.763528i
$123$	0.505452	−	0.505452i	0.00410937	−	0.00410937i
$124$	−7.84869	+	7.84869i	−0.0632959	+	0.0632959i
$125$	−80.5313	+	80.5313i	−0.644250	+	0.644250i
$126$	−3.56262	−	3.56262i	−0.0282748	−	0.0282748i
$127$			122.844i			0.967273i	0.875269	+	0.483636i	$0.160684\pi$
$127$			122.844i			0.967273i	−0.875269	+	0.483636i	$0.839316\pi$
$128$	−9.40060	+	9.40060i	−0.0734422	+	0.0734422i
$129$	−154.716	+	154.716i	−1.19935	+	1.19935i
$130$	−11.6458	+	11.6458i	−0.0895831	+	0.0895831i
$131$	−29.6586	−	29.6586i	−0.226401	−	0.226401i	0.584786	−	0.811187i	$-0.301178\pi$
$131$	−29.6586	−	29.6586i	−0.226401	−	0.226401i	−0.811187	+	0.584786i	$0.801178\pi$
$132$	−61.6824			−0.467291
$133$	−168.816			−1.26930
$134$			36.1368i			0.269677i
$135$	−68.8250			−0.509815
$136$		−	153.992i		−	1.13229i
$137$		−	57.8952i		−	0.422593i	−0.977422	−	0.211296i	$-0.932231\pi$
$137$		−	57.8952i		−	0.422593i	0.977422	−	0.211296i	$-0.0677685\pi$
$138$		−	148.461i		−	1.07581i
$139$	47.3212	−	47.3212i	0.340440	−	0.340440i	−0.516093	−	0.856533i	$-0.672614\pi$
$139$	47.3212	−	47.3212i	0.340440	−	0.340440i	0.856533	+	0.516093i	$0.172614\pi$
$140$	14.4431	+	14.4431i	0.103165	+	0.103165i
$141$	120.866	−	120.866i	0.857207	−	0.857207i
$142$	146.828			1.03400
$143$		−	51.6064i		−	0.360884i
$144$			4.80091i			0.0333397i
$145$	68.2971	+	68.2971i	0.471015	+	0.471015i
$146$		−	118.199i		−	0.809581i
$147$	51.0978	+	51.0978i	0.347604	+	0.347604i
$148$			65.3110i			0.441290i
$149$	−32.5345	+	32.5345i	−0.218352	+	0.218352i	−0.807804	−	0.589451i	$-0.799344\pi$
$149$	−32.5345	+	32.5345i	−0.218352	+	0.218352i	0.589451	+	0.807804i	$0.299344\pi$
$150$	−87.8609			−0.585739
$151$	109.726	−	109.726i	0.726659	−	0.726659i	−0.243293	−	0.969953i	$-0.578228\pi$
$151$	109.726	−	109.726i	0.726659	−	0.726659i	0.969953	+	0.243293i	$0.0782277\pi$
$152$	204.632	+	204.632i	1.34627	+	1.34627i
$153$	−7.90294	−	7.90294i	−0.0516532	−	0.0516532i
$154$	104.422			0.678064
$155$			19.3507i			0.124843i
$156$	18.6170			0.119340
$157$		−	103.228i		−	0.657505i	−0.944416	−	0.328752i	$-0.893372\pi$
$157$		−	103.228i		−	0.657505i	0.944416	−	0.328752i	$-0.106628\pi$
$158$	−88.7587			−0.561764
$159$	163.600	+	163.600i	1.02893	+	1.02893i
$160$		−	60.3875i		−	0.377422i
$161$		−	154.044i		−	0.956796i
$162$	−96.0771	−	96.0771i	−0.593069	−	0.593069i
$163$			218.586i			1.34102i	0.741900	+	0.670511i	$0.233925\pi$
$163$			218.586i			1.34102i	−0.741900	+	0.670511i	$0.766075\pi$
$164$	−0.350116			−0.00213485
$165$	−76.0381	+	76.0381i	−0.460837	+	0.460837i
$166$	135.256	−	135.256i	0.814795	−	0.814795i
$167$	−188.646	−	188.646i	−1.12962	−	1.12962i	−0.990239	−	0.139380i	$-0.955489\pi$
$167$	−188.646	−	188.646i	−1.12962	−	1.12962i	−0.139380	−	0.990239i	$-0.544511\pi$
$168$			136.801i			0.814290i
$169$		−	153.424i		−	0.907835i
$170$	−52.2728	−	52.2728i	−0.307487	−	0.307487i
$171$	21.0037			0.122829
$172$	107.168			0.623072
$173$		−	265.786i		−	1.53633i	−0.640250	−	0.768167i	$-0.721169\pi$
$173$		−	265.786i		−	1.53633i	0.640250	−	0.768167i	$-0.278831\pi$
$174$			178.131i			1.02374i
$175$	−91.1649			−0.520943
$176$	−70.3583	−	70.3583i	−0.399763	−	0.399763i
$177$	166.231	+	166.231i	0.939155	+	0.939155i
$178$	180.838			1.01595
$179$	−105.046	−	105.046i	−0.586849	−	0.586849i	0.349928	−	0.936777i	$-0.386206\pi$
$179$	−105.046	−	105.046i	−0.586849	−	0.586849i	−0.936777	+	0.349928i	$0.886206\pi$
$180$	−1.79697	−	1.79697i	−0.00998317	−	0.00998317i
$181$		−	40.7615i		−	0.225202i	−0.993640	−	0.112601i	$-0.964082\pi$
$181$		−	40.7615i		−	0.225202i	0.993640	−	0.112601i	$-0.0359182\pi$
$182$	−31.5166			−0.173168
$183$	183.567	+	183.567i	1.00310	+	1.00310i
$184$	−186.726	+	186.726i	−1.01482	+	1.01482i
$185$	80.5111	+	80.5111i	0.435195	+	0.435195i
$186$	−25.2351	+	25.2351i	−0.135673	+	0.135673i
$187$	231.638			1.23871
$188$	−83.7213			−0.445326
$189$	−93.1294	−	93.1294i	−0.492748	−	0.492748i
$190$	138.926			0.731189
$191$	242.811			1.27126			0.635630	−	0.771994i	$-0.280740\pi$
$191$	242.811			1.27126			0.635630	+	0.771994i	$0.280740\pi$
$192$	145.544	−	145.544i	0.758041	−	0.758041i
$193$	157.520			0.816166			0.408083	−	0.912945i	$-0.366197\pi$
$193$	157.520			0.816166			0.408083	+	0.912945i	$0.366197\pi$
$194$	−187.416	+	187.416i	−0.966063	+	0.966063i
$195$	22.9498	−	22.9498i	0.117691	−	0.117691i
$196$		−	35.3943i		−	0.180583i
$197$	−6.06770	−	196.907i	−0.0308005	−	0.999526i
$197$	−6.06770	−	196.907i	−0.0308005	−	0.999526i
$198$	−12.9919			−0.0656156
$199$	61.6921	+	61.6921i	0.310011	+	0.310011i	0.844914	−	0.534903i	$-0.179652\pi$
$199$	61.6921	+	61.6921i	0.310011	+	0.310011i	−0.534903	+	0.844914i	$0.679652\pi$
$200$	110.506	+	110.506i	0.552532	+	0.552532i
$201$		−	71.2130i		−	0.354294i
$202$	−7.26365	−	7.26365i	−0.0359586	−	0.0359586i
$203$			184.830i			0.910493i
$204$			83.5634i			0.409625i
$205$	−0.431600	+	0.431600i	−0.00210536	+	0.00210536i
$206$		−	22.9535i		−	0.111425i
$207$			19.1658i			0.0925883i
$208$	21.2355	+	21.2355i	0.102094	+	0.102094i
$209$	−307.813	+	307.813i	−1.47279	+	1.47279i
$210$	46.4373	+	46.4373i	0.221130	+	0.221130i
$211$	−138.008	+	138.008i	−0.654065	+	0.654065i	−0.953969	−	0.299904i	$-0.903045\pi$
$211$	−138.008	+	138.008i	−0.654065	+	0.654065i	0.299904	+	0.953969i	$0.403045\pi$
$212$		−	113.322i		−	0.534537i
$213$	−289.346			−1.35843
$214$	56.4921	−	56.4921i	0.263982	−	0.263982i
$215$	132.110	−	132.110i	0.614466	−	0.614466i
$216$			225.775i			1.04526i
$217$	−26.1841	+	26.1841i	−0.120664	+	0.120664i
$218$	−176.386	+	176.386i	−0.809112	+	0.809112i
$219$			232.929i			1.06360i
$220$	52.6699			0.239409
$221$	−69.9130			−0.316348
$222$			209.988i			0.945890i
$223$		−	41.3642i		−	0.185490i	−0.995690	−	0.0927448i	$-0.970436\pi$
$223$		−	41.3642i		−	0.185490i	0.995690	−	0.0927448i	$-0.0295641\pi$
$224$	81.7122	−	81.7122i	0.364787	−	0.364787i
$225$	11.3425			0.0504112
$226$	−3.30702			−0.0146329
$227$	5.50797	−	5.50797i	0.0242642	−	0.0242642i	−0.694871	−	0.719135i	$-0.744538\pi$
$227$	5.50797	−	5.50797i	0.0242642	−	0.0242642i	0.719135	+	0.694871i	$0.244538\pi$
$228$	−111.044	−	111.044i	−0.487033	−	0.487033i
$229$	−215.133	−	215.133i	−0.939445	−	0.939445i	0.0588238	−	0.998268i	$-0.481265\pi$
$229$	−215.133	−	215.133i	−0.939445	−	0.939445i	−0.998268	+	0.0588238i	$0.981265\pi$
$230$			126.769i			0.551171i
$231$	−205.779			−0.890819
$232$	224.044	−	224.044i	0.965705	−	0.965705i
$233$	120.028			0.515141			0.257570	−	0.966260i	$-0.417078\pi$
$233$	120.028			0.515141			0.257570	+	0.966260i	$0.417078\pi$
$234$	3.92122			0.0167573
$235$	−103.206	+	103.206i	−0.439175	+	0.439175i
$236$		−	115.144i		−	0.487899i
$237$	174.913			0.738027
$238$		−	141.464i		−	0.594387i
$239$	175.672			0.735029			0.367514	−	0.930018i	$-0.380209\pi$
$239$	175.672			0.735029			0.367514	+	0.930018i	$0.380209\pi$
$240$		−	62.5779i		−	0.260741i
$241$	−197.909	+	197.909i	−0.821201	+	0.821201i	−0.986280	−	0.165079i	$-0.947212\pi$
$241$	−197.909	+	197.909i	−0.821201	+	0.821201i	0.165079	+	0.986280i	$0.447212\pi$
$242$	55.6594	−	55.6594i	0.229998	−	0.229998i
$243$	24.0473	+	24.0473i	0.0989602	+	0.0989602i
$244$		−	127.153i		−	0.521119i
$245$	−43.6318	−	43.6318i	−0.178089	−	0.178089i
$246$	−1.12569			−0.00457598
$247$	92.9042	−	92.9042i	0.376130	−	0.376130i
$248$	63.4785			0.255962
$249$	−266.542	+	266.542i	−1.07045	+	1.07045i
$250$	179.351			0.717403
$251$	−186.861			−0.744466			−0.372233	−	0.928139i	$-0.621408\pi$
$251$	−186.861			−0.744466			−0.372233	+	0.928139i	$0.621408\pi$
$252$		−	4.86308i		−	0.0192979i
$253$	−280.878	−	280.878i	−1.11019	−	1.11019i
$254$	136.792	−	136.792i	0.538552	−	0.538552i
$255$	103.012	+	103.012i	0.403967	+	0.403967i
$256$	−244.363			−0.954541
$257$	68.8305			0.267823			0.133912	−	0.990993i	$-0.457246\pi$
$257$	68.8305			0.267823			0.133912	+	0.990993i	$0.457246\pi$
$258$	344.567			1.33553
$259$			217.884i			0.841252i
$260$	−15.8968			−0.0611417
$261$		−	22.9961i		−	0.0881076i
$262$			66.0525i			0.252109i
$263$	265.327	−	265.327i	1.00885	−	1.00885i	0.00888848	−	0.999960i	$-0.497171\pi$
$263$	265.327	−	265.327i	1.00885	−	1.00885i	0.999960	−	0.00888848i	$-0.00282933\pi$
$264$	249.437	+	249.437i	0.944838	+	0.944838i
$265$	−139.696	−	139.696i	−0.527154	−	0.527154i
$266$	187.985	+	187.985i	0.706711	+	0.706711i
$267$	−356.369			−1.33472
$268$	−24.6638	+	24.6638i	−0.0920292	+	0.0920292i
$269$	24.9352	+	24.9352i	0.0926961	+	0.0926961i	0.751934	−	0.659238i	$-0.229121\pi$
$269$	24.9352	+	24.9352i	0.0926961	+	0.0926961i	−0.659238	+	0.751934i	$0.729121\pi$
$270$	76.6400	+	76.6400i	0.283852	+	0.283852i
$271$	337.196	+	337.196i	1.24427	+	1.24427i	0.958214	+	0.286052i	$0.0923431\pi$
$271$	337.196	+	337.196i	1.24427	+	1.24427i	0.286052	+	0.958214i	$0.407657\pi$
$272$	−95.3169	+	95.3169i	−0.350430	+	0.350430i
$273$	62.1083			0.227503
$274$	−64.4691	+	64.4691i	−0.235289	+	0.235289i
$275$	−166.227	+	166.227i	−0.604460	+	0.604460i
$276$	101.327	−	101.327i	0.367126	−	0.367126i
$277$	56.7117	+	56.7117i	0.204735	+	0.204735i	0.802025	−	0.597290i	$-0.203756\pi$
$277$	56.7117	+	56.7117i	0.204735	+	0.204735i	−0.597290	+	0.802025i	$0.703756\pi$
$278$	−105.389			−0.379096
$279$	3.25776	−	3.25776i	0.0116765	−	0.0116765i
$280$		−	116.813i		−	0.417188i
$281$	363.329	+	363.329i	1.29299	+	1.29299i	0.932930	+	0.360057i	$0.117243\pi$
$281$	363.329	+	363.329i	1.29299	+	1.29299i	0.360057	+	0.932930i	$0.382757\pi$
$282$	−269.181			−0.954541
$283$	−124.123	+	124.123i	−0.438596	+	0.438596i	−0.891539	−	0.452944i	$-0.850374\pi$
$283$	−124.123	+	124.123i	−0.438596	+	0.438596i	0.452944	+	0.891539i	$0.350374\pi$
$284$	100.212	+	100.212i	0.352859	+	0.352859i
$285$	−273.775			−0.960613
$286$	−57.4662	+	57.4662i	−0.200931	+	0.200931i
$287$	−1.16802			−0.00406977
$288$	−10.1664	+	10.1664i	−0.0353001	+	0.0353001i
$289$		−	24.8083i		−	0.0858420i
$290$		−	152.104i		−	0.524497i
$291$	369.332	−	369.332i	1.26918	−	1.26918i
$292$	80.6723	−	80.6723i	0.276275	−	0.276275i
$293$		−	333.324i		−	1.13763i	−0.822467	−	0.568813i	$-0.807403\pi$
$293$		−	333.324i		−	1.13763i	0.822467	−	0.568813i	$-0.192597\pi$
$294$		−	113.800i		−	0.387074i
$295$	−141.942	−	141.942i	−0.481160	−	0.481160i
$296$	264.111	−	264.111i	0.892265	−	0.892265i
$297$	−339.617			−1.14349
$298$	72.4574			0.243146
$299$	84.7747	+	84.7747i	0.283527	+	0.283527i
$300$	−59.9663	−	59.9663i	−0.199888	−	0.199888i
$301$	357.525			1.18779
$302$	−244.369			−0.809170
$303$	14.3141	+	14.3141i	0.0472413	+	0.0472413i
$304$		−	253.325i		−	0.833304i
$305$	−156.746	−	156.746i	−0.513921	−	0.513921i
$306$			17.6006i			0.0575183i
$307$	11.3542	−	11.3542i	0.0369844	−	0.0369844i	−0.688373	−	0.725357i	$-0.741675\pi$
$307$	11.3542	−	11.3542i	0.0369844	−	0.0369844i	0.725357	+	0.688373i	$0.241675\pi$
$308$	71.2693	+	71.2693i	0.231394	+	0.231394i
$309$			45.2333i			0.146386i
$310$	21.5479	−	21.5479i	0.0695095	−	0.0695095i
$311$	16.1530			0.0519388			0.0259694	−	0.999663i	$-0.491733\pi$
$311$	16.1530			0.0519388			0.0259694	+	0.999663i	$0.491733\pi$
$312$	−75.2851	−	75.2851i	−0.241298	−	0.241298i
$313$			166.973i			0.533460i	0.963771	+	0.266730i	$0.0859432\pi$
$313$			166.973i			0.533460i	−0.963771	+	0.266730i	$0.914057\pi$
$314$	−114.950	+	114.950i	−0.366082	+	0.366082i
$315$	−5.99489	−	5.99489i	−0.0190314	−	0.0190314i
$316$	−60.5790	−	60.5790i	−0.191706	−	0.191706i
$317$	−103.951	−	103.951i	−0.327923	−	0.327923i	0.523874	−	0.851796i	$-0.324486\pi$
$317$	−103.951	−	103.951i	−0.327923	−	0.327923i	−0.851796	+	0.523874i	$0.824486\pi$
$318$		−	364.352i		−	1.14576i
$319$	337.012	+	337.012i	1.05646	+	1.05646i
$320$	−124.278	+	124.278i	−0.388369	+	0.388369i
$321$	−111.326	+	111.326i	−0.346811	+	0.346811i
$322$	−171.536	+	171.536i	−0.532719	+	0.532719i
$323$	417.006	+	417.006i	1.29104	+	1.29104i
$324$		−	131.148i		−	0.404777i
$325$	50.1705	−	50.1705i	0.154371	−	0.154371i
$326$	243.406	−	243.406i	0.746645	−	0.746645i
$327$	347.596	−	347.596i	1.06299	−	1.06299i
$328$	1.41583	+	1.41583i	0.00431656	+	0.00431656i
$329$	−279.303			−0.848946
$330$	169.344			0.513164
$331$		−	33.2430i		−	0.100432i	−0.998738	−	0.0502161i	$-0.984009\pi$
$331$		−	33.2430i		−	0.100432i	0.998738	−	0.0502161i	$-0.0159910\pi$
$332$	184.628			0.556108
$333$		−	27.1086i		−	0.0814072i
$334$			420.134i			1.25789i
$335$			60.8079i			0.181516i
$336$	84.6762	−	84.6762i	0.252012	−	0.252012i
$337$	−213.210	−	213.210i	−0.632669	−	0.632669i	0.316068	−	0.948737i	$-0.397637\pi$
$337$	−213.210	−	213.210i	−0.632669	−	0.632669i	−0.948737	+	0.316068i	$0.897637\pi$
$338$	−170.845	+	170.845i	−0.505459	+	0.505459i
$339$	6.51699			0.0192242
$340$		−	71.3538i		−	0.209864i
$341$			95.4860i			0.280018i
$342$	−23.3886	−	23.3886i	−0.0683878	−	0.0683878i
$343$		−	366.556i		−	1.06868i
$344$	−433.377	−	433.377i	−1.25982	−	1.25982i
$345$		−	249.818i		−	0.724110i
$346$	−295.965	+	295.965i	−0.855390	+	0.855390i
$347$	−624.394			−1.79941			−0.899703	−	0.436503i	$-0.856217\pi$
$347$	−624.394			−1.79941			−0.899703	+	0.436503i	$0.856217\pi$
$348$	−121.577	+	121.577i	−0.349359	+	0.349359i
$349$	136.438	+	136.438i	0.390939	+	0.390939i	0.875022	−	0.484083i	$-0.160847\pi$
$349$	136.438	+	136.438i	0.390939	+	0.390939i	−0.484083	+	0.875022i	$0.660847\pi$
$350$	101.517	+	101.517i	0.290047	+	0.290047i
$351$	102.503			0.292032
$352$		−	297.982i		−	0.846539i
$353$	−112.415			−0.318457			−0.159229	−	0.987242i	$-0.550901\pi$
$353$	−112.415			−0.318457			−0.159229	+	0.987242i	$0.550901\pi$
$354$		−	370.211i		−	1.04579i
$355$	247.069			0.695970
$356$	123.425	+	123.425i	0.346698	+	0.346698i
$357$			278.776i			0.780886i
$358$			233.947i			0.653484i
$359$	−117.123	−	117.123i	−0.326247	−	0.326247i	0.524910	−	0.851158i	$-0.324099\pi$
$359$	−117.123	−	117.123i	−0.326247	−	0.326247i	−0.851158	+	0.524910i	$0.824099\pi$
$360$			14.5335i			0.0403709i
$361$	−747.280			−2.07003
$362$	−45.3899	+	45.3899i	−0.125386	+	0.125386i
$363$	−109.685	+	109.685i	−0.302164	+	0.302164i
$364$	−21.5105	−	21.5105i	−0.0590948	−	0.0590948i
$365$		−	198.895i		−	0.544918i
$366$		−	408.822i		−	1.11700i
$367$	137.767	+	137.767i	0.375387	+	0.375387i	0.869435	−	0.494048i	$-0.164483\pi$
$367$	137.767	+	137.767i	0.375387	+	0.375387i	−0.494048	+	0.869435i	$0.664483\pi$
$368$	231.158			0.628145
$369$	0.145322			0.000393828
$370$		−	179.306i		−	0.484611i
$371$		−	378.053i		−	1.01901i
$372$	−34.4466			−0.0925983
$373$	150.499	+	150.499i	0.403482	+	0.403482i	0.879458	−	0.475976i	$-0.157905\pi$
$373$	150.499	+	150.499i	0.403482	+	0.403482i	−0.475976	+	0.879458i	$0.657905\pi$
$374$	−257.940	−	257.940i	−0.689679	−	0.689679i
$375$	−353.438			−0.942502
$376$	338.560	+	338.560i	0.900426	+	0.900426i
$377$	−101.717	−	101.717i	−0.269806	−	0.269806i
$378$			207.408i			0.548698i
$379$	422.210			1.11401			0.557005	−	0.830509i	$-0.311950\pi$
$379$	422.210			1.11401			0.557005	+	0.830509i	$0.311950\pi$
$380$	94.8188	+	94.8188i	0.249523	+	0.249523i
$381$	−269.570	+	269.570i	−0.707533	+	0.707533i
$382$	−270.381	−	270.381i	−0.707805	−	0.707805i
$383$	143.438	−	143.438i	0.374511	−	0.374511i	−0.494606	−	0.869117i	$-0.664688\pi$
$383$	143.438	−	143.438i	0.374511	−	0.374511i	0.869117	+	0.494606i	$0.164688\pi$
$384$	−41.2576			−0.107442
$385$	175.712			0.456396
$386$	−175.406	−	175.406i	−0.454420	−	0.454420i
$387$	−44.4824			−0.114941
$388$	−255.828			−0.659351
$389$	−9.93096	+	9.93096i	−0.0255295	+	0.0255295i	−0.719756	−	0.694227i	$-0.755746\pi$
$389$	−9.93096	+	9.93096i	−0.0255295	+	0.0255295i	0.694227	+	0.719756i	$0.255746\pi$
$390$	−51.1114			−0.131055
$391$	−380.516	+	380.516i	−0.973186	+	0.973186i
$392$	−143.131	+	143.131i	−0.365130	+	0.365130i
$393$		−	130.166i		−	0.331212i
$394$	−212.508	+	226.021i	−0.539361	+	0.573659i
$395$	−149.356			−0.378116
$396$	−8.86715	−	8.86715i	−0.0223918	−	0.0223918i
$397$	147.995	+	147.995i	0.372784	+	0.372784i	0.868490	−	0.495706i	$-0.165091\pi$
$397$	147.995	+	147.995i	0.372784	+	0.372784i	−0.495706	+	0.868490i	$0.665091\pi$
$398$		−	137.394i		−	0.345212i
$399$	−370.453	−	370.453i	−0.928454	−	0.928454i
$400$		−	136.801i		−	0.342004i
$401$		−	478.467i		−	1.19318i	−0.802545	−	0.596592i	$-0.796521\pi$
$401$		−	478.467i		−	1.19318i	0.802545	−	0.596592i	$-0.203479\pi$
$402$	−79.2991	+	79.2991i	−0.197261	+	0.197261i
$403$		−	28.8196i		−	0.0715127i
$404$		−	9.91507i		−	0.0245423i
$405$	−161.671	−	161.671i	−0.399186	−	0.399186i
$406$	205.817	−	205.817i	0.506939	−	0.506939i
$407$	397.282	+	397.282i	0.976122	+	0.976122i
$408$	337.921	−	337.921i	0.828239	−	0.828239i
$409$			550.186i			1.34520i	0.740007	+	0.672599i	$0.234822\pi$
$409$			550.186i			1.34520i	−0.740007	+	0.672599i	$0.765178\pi$
$410$	0.961214			0.00234442
$411$	127.046	−	127.046i	0.309115	−	0.309115i
$412$	15.6661	−	15.6661i	0.0380244	−	0.0380244i
$413$		−	384.133i		−	0.930105i
$414$	21.3420	−	21.3420i	0.0515508	−	0.0515508i
$415$	227.597	−	227.597i	0.548427	−	0.548427i
$416$			89.9369i			0.216194i
$417$	207.685			0.498045
$418$	685.529			1.64002
$419$			268.783i			0.641486i	0.947166	+	0.320743i	$0.103933\pi$
$419$			268.783i			0.641486i	−0.947166	+	0.320743i	$0.896067\pi$
$420$			63.3882i			0.150924i
$421$	−210.501	+	210.501i	−0.500002	+	0.500002i	−0.911439	−	0.411436i	$-0.865027\pi$
$421$	−210.501	+	210.501i	−0.500002	+	0.500002i	0.411436	+	0.911439i	$0.365027\pi$
$422$	307.356			0.728333
$423$	34.7502			0.0821518
$424$	−458.261	+	458.261i	−1.08080	+	1.08080i
$425$	225.193	+	225.193i	0.529866	+	0.529866i
$426$	322.201	+	322.201i	0.756340	+	0.756340i
$427$		−	424.196i		−	0.993432i
$428$	77.1132			0.180171
$429$	113.246	−	113.246i	0.263976	−	0.263976i
$430$	−294.222			−0.684237
$431$	−151.648			−0.351852			−0.175926	−	0.984403i	$-0.556292\pi$
$431$	−151.648			−0.351852			−0.175926	+	0.984403i	$0.556292\pi$
$432$	139.749	−	139.749i	0.323494	−	0.323494i
$433$		−	371.716i		−	0.858467i	−0.903194	−	0.429233i	$-0.858784\pi$
$433$		−	371.716i		−	0.858467i	0.903194	−	0.429233i	$-0.141216\pi$
$434$	58.3144			0.134365
$435$			299.745i			0.689068i
$436$	−240.772			−0.552230
$437$		−	1011.30i		−	2.31419i
$438$	259.377	−	259.377i	0.592186	−	0.592186i
$439$	−527.707	+	527.707i	−1.20207	+	1.20207i	−0.228530	+	0.973537i	$0.573392\pi$
$439$	−527.707	+	527.707i	−1.20207	+	1.20207i	−0.973537	+	0.228530i	$0.926608\pi$
$440$	−212.991	−	212.991i	−0.484071	−	0.484071i
$441$			14.6911i			0.0333132i
$442$	77.8515	+	77.8515i	0.176135	+	0.176135i
$443$	300.537			0.678413			0.339207	−	0.940712i	$-0.389841\pi$
$443$	300.537			0.678413			0.339207	+	0.940712i	$0.389841\pi$
$444$	−143.319	+	143.319i	−0.322791	+	0.322791i
$445$	304.300			0.683819
$446$	−46.0610	+	46.0610i	−0.103276	+	0.103276i
$447$	−142.788			−0.319437
$448$	−336.329			−0.750735
$449$			693.314i			1.54413i	0.635544	+	0.772065i	$0.280776\pi$
$449$			693.314i			1.54413i	−0.635544	+	0.772065i	$0.719224\pi$
$450$	−12.6304	−	12.6304i	−0.0280676	−	0.0280676i
$451$	−2.12973	+	2.12973i	−0.00472223	+	0.00472223i
$452$	−2.25709	−	2.25709i	−0.00499356	−	0.00499356i
$453$	481.567			1.06306
$454$	−12.2668			−0.0270193
$455$	−53.0335			−0.116557
$456$			898.097i			1.96951i
$457$	483.318			1.05759			0.528794	−	0.848750i	$-0.322644\pi$
$457$	483.318			1.05759			0.528794	+	0.848750i	$0.322644\pi$
$458$			479.121i			1.04612i
$459$			460.091i			1.00238i
$460$	−86.5218	+	86.5218i	−0.188091	+	0.188091i
$461$	−143.318	−	143.318i	−0.310886	−	0.310886i	0.534367	−	0.845253i	$-0.320550\pi$
$461$	−143.318	−	143.318i	−0.310886	−	0.310886i	−0.845253	+	0.534367i	$0.820550\pi$
$462$	229.145	+	229.145i	0.495985	+	0.495985i
$463$	85.4692	+	85.4692i	0.184599	+	0.184599i	0.793356	−	0.608758i	$-0.208332\pi$
$463$	85.4692	+	85.4692i	0.184599	+	0.184599i	−0.608758	+	0.793356i	$0.708332\pi$
$464$	−277.355			−0.597747
$465$	−42.4635	+	42.4635i	−0.0913194	+	0.0913194i
$466$	−133.657	−	133.657i	−0.286817	−	0.286817i
$467$	256.789	+	256.789i	0.549869	+	0.549869i	0.926403	−	0.376534i	$-0.122884\pi$
$467$	256.789	+	256.789i	0.549869	+	0.549869i	−0.376534	+	0.926403i	$0.622884\pi$
$468$	2.67628	+	2.67628i	0.00571855	+	0.00571855i
$469$	−82.2812	+	82.2812i	−0.175440	+	0.175440i
$470$	229.850			0.489043
$471$	226.526	−	226.526i	0.480946	−	0.480946i
$472$	−465.631	+	465.631i	−0.986506	+	0.986506i
$473$	651.897	−	651.897i	1.37822	−	1.37822i
$474$	−194.773	−	194.773i	−0.410914	−	0.410914i
$475$	−598.498			−1.26000
$476$	96.5511	−	96.5511i	0.202838	−	0.202838i
$477$			47.0364i			0.0986089i
$478$	−195.619	−	195.619i	−0.409245	−	0.409245i
$479$	−131.932			−0.275432			−0.137716	−	0.990472i	$-0.543976\pi$
$479$	−131.932			−0.275432			−0.137716	+	0.990472i	$0.543976\pi$
$480$	132.515	−	132.515i	0.276073	−	0.276073i
$481$	−119.908	−	119.908i	−0.249288	−	0.249288i
$482$	440.763			0.914446
$483$	338.037	−	338.037i	0.699869	−	0.699869i
$484$	75.9766			0.156977
$485$	−315.368	+	315.368i	−0.650244	+	0.650244i
$486$		−	53.5557i		−	0.110197i
$487$			664.697i			1.36488i	0.730941	+	0.682441i	$0.239082\pi$
$487$			664.697i			1.36488i	−0.730941	+	0.682441i	$0.760918\pi$
$488$	−514.193	+	514.193i	−1.05367	+	1.05367i
$489$	−479.669	+	479.669i	−0.980919	+	0.980919i
$490$			97.1722i			0.198311i
$491$			564.280i			1.14925i	0.818418	+	0.574624i	$0.194852\pi$
$491$			564.280i			1.14925i	−0.818418	+	0.574624i	$0.805148\pi$
$492$	−0.768299	−	0.768299i	−0.00156158	−	0.00156158i
$493$	456.562	−	456.562i	0.926090	−	0.926090i
$494$	−206.907			−0.418839
$495$	−21.8617			−0.0441650
$496$	−39.2916	−	39.2916i	−0.0792170	−	0.0792170i
$497$	334.317	+	334.317i	0.672671	+	0.672671i
$498$	593.615			1.19200
$499$	850.705			1.70482			0.852410	−	0.522875i	$-0.175140\pi$
$499$	850.705			1.70482			0.852410	+	0.522875i	$0.175140\pi$
$500$	122.409	+	122.409i	0.244819	+	0.244819i
$501$		−	827.937i		−	1.65257i
$502$	208.079	+	208.079i	0.414499	+	0.414499i
$503$		−	610.493i		−	1.21370i	−0.794815	−	0.606852i	$-0.792432\pi$
$503$		−	610.493i		−	1.21370i	0.794815	−	0.606852i	$-0.207568\pi$
$504$	−19.6658	+	19.6658i	−0.0390194	+	0.0390194i
$505$	−12.2227	−	12.2227i	−0.0242033	−	0.0242033i
$506$			625.542i			1.23625i
$507$	336.676	−	336.676i	0.664056	−	0.664056i
$508$	186.725			0.367569
$509$	−465.508	−	465.508i	−0.914555	−	0.914555i	0.0820715	−	0.996626i	$-0.473846\pi$
$509$	−465.508	−	465.508i	−0.914555	−	0.914555i	−0.996626	+	0.0820715i	$0.973846\pi$
$510$		−	229.416i		−	0.449836i
$511$	269.131	−	269.131i	0.526676	−	0.526676i
$512$	309.712	+	309.712i	0.604906	+	0.604906i
$513$	−611.394	−	611.394i	−1.19180	−	1.19180i
$514$	−76.6461	−	76.6461i	−0.149117	−	0.149117i
$515$		−	38.6242i		−	0.0749984i
$516$	235.172	+	235.172i	0.455760	+	0.455760i
$517$	−509.271	+	509.271i	−0.985050	+	0.985050i
$518$	242.625	−	242.625i	0.468387	−	0.468387i
$519$	583.244	−	583.244i	1.12378	−	1.12378i
$520$	64.2851	+	64.2851i	0.123625	+	0.123625i
$521$		−	17.7961i		−	0.0341576i	−0.999854	−	0.0170788i	$-0.994563\pi$
$521$		−	17.7961i		−	0.0341576i	0.999854	−	0.0170788i	$-0.00543661\pi$
$522$	−25.6072	+	25.6072i	−0.0490560	+	0.0490560i
$523$	−649.537	+	649.537i	−1.24194	+	1.24194i	−0.282752	+	0.959193i	$0.591247\pi$
$523$	−649.537	+	649.537i	−1.24194	+	1.24194i	−0.959193	+	0.282752i	$0.908753\pi$
$524$	−45.0817	+	45.0817i	−0.0860338	+	0.0860338i
$525$	−200.054	−	200.054i	−0.381055	−	0.381055i
$526$	−590.909			−1.12340
$527$	129.358			0.245462
$528$		−	308.791i		−	0.584831i
$529$	393.807			0.744436
$530$			311.116i			0.587011i
$531$			47.7929i			0.0900054i
$532$			256.605i			0.482340i
$533$	0.642794	−	0.642794i	0.00120599	−	0.00120599i
$534$	396.834	+	396.834i	0.743135	+	0.743135i
$535$	95.0601	−	95.0601i	0.177682	−	0.177682i
$536$	199.476			0.372156
$537$		−	461.029i		−	0.858527i
$538$		−	55.5332i		−	0.103221i
$539$	−215.301	−	215.301i	−0.399445	−	0.399445i
$540$			104.616i			0.193733i
$541$	284.018	+	284.018i	0.524987	+	0.524987i	0.919073	−	0.394086i	$-0.128939\pi$
$541$	284.018	+	284.018i	0.524987	+	0.524987i	−0.394086	+	0.919073i	$0.628939\pi$
$542$		−	750.968i		−	1.38555i
$543$	89.4477	−	89.4477i	0.164729	−	0.164729i
$544$	−403.686			−0.742071
$545$	−296.808	+	296.808i	−0.544603	+	0.544603i
$546$	−69.1605	−	69.1605i	−0.126668	−	0.126668i
$547$	701.955	+	701.955i	1.28328	+	1.28328i	0.938790	+	0.344491i	$0.111949\pi$
$547$	701.955	+	701.955i	1.28328	+	1.28328i	0.344491	+	0.938790i	$0.388051\pi$
$548$	−88.0020			−0.160588
$549$			52.7773i			0.0961336i
$550$	370.203			0.673096
$551$			1213.41i			2.20220i
$552$	−819.509			−1.48462
$553$	−202.098	−	202.098i	−0.365457	−	0.365457i
$554$		−	126.302i		−	0.227983i
$555$			353.350i			0.636666i
$556$	−71.9293	−	71.9293i	−0.129369	−	0.129369i
$557$			560.297i			1.00592i	0.864310	+	0.502960i	$0.167756\pi$
$557$			560.297i			1.00592i	−0.864310	+	0.502960i	$0.832244\pi$
$558$	−7.25533			−0.0130024
$559$	−196.756	+	196.756i	−0.351978	+	0.351978i
$560$	−72.3040	+	72.3040i	−0.129114	+	0.129114i
$561$	508.310	+	508.310i	0.906078	+	0.906078i
$562$		−	809.169i		−	1.43980i
$563$			227.622i			0.404302i	0.979354	+	0.202151i	$0.0647931\pi$
$563$			227.622i			0.404302i	−0.979354	+	0.202151i	$0.935207\pi$
$564$	−183.719	−	183.719i	−0.325744	−	0.325744i
$565$	−5.56478			−0.00984918
$566$	276.433			0.488397
$567$		−	437.523i		−	0.771646i
$568$		−	810.492i		−	1.42692i
$569$	798.239			1.40288			0.701441	−	0.712728i	$-0.252541\pi$
$569$	798.239			1.40288			0.701441	+	0.712728i	$0.252541\pi$
$570$	304.861	+	304.861i	0.534844	+	0.534844i
$571$	−506.836	−	506.836i	−0.887629	−	0.887629i	0.106666	−	0.994295i	$-0.465983\pi$
$571$	−506.836	−	506.836i	−0.887629	−	0.887629i	−0.994295	+	0.106666i	$0.965983\pi$
$572$	−78.4429			−0.137138
$573$	532.828	+	532.828i	0.929891	+	0.929891i
$574$	1.30065	+	1.30065i	0.00226594	+	0.00226594i
$575$		−	546.127i		−	0.949786i
$576$	41.8452			0.0726480
$577$	−276.243	−	276.243i	−0.478757	−	0.478757i	0.425977	−	0.904734i	$-0.359930\pi$
$577$	−276.243	−	276.243i	−0.478757	−	0.478757i	−0.904734	+	0.425977i	$0.859930\pi$
$578$	−27.6253	+	27.6253i	−0.0477946	+	0.0477946i
$579$	345.664	+	345.664i	0.597002	+	0.597002i
$580$	103.813	−	103.813i	0.178988	−	0.178988i
$581$	615.938			1.06013
$582$	−822.538			−1.41330
$583$	−689.328	−	689.328i	−1.18238	−	1.18238i
$584$	−652.460			−1.11723
$585$	6.59829			0.0112791
$586$	−371.173	+	371.173i	−0.633400	+	0.633400i
$587$	−93.0829			−0.158574			−0.0792870	−	0.996852i	$-0.525264\pi$
$587$	−93.0829			−0.158574			−0.0792870	+	0.996852i	$0.525264\pi$
$588$	77.6699	−	77.6699i	0.132092	−	0.132092i
$589$	−171.898	+	171.898i	−0.291848	+	0.291848i
$590$			316.119i			0.535795i
$591$	418.780	−	445.410i	0.708595	−	0.753654i
$592$	−326.955			−0.552290
$593$	772.575	+	772.575i	1.30283	+	1.30283i	0.926479	+	0.376346i	$0.122820\pi$
$593$	772.575	+	772.575i	1.30283	+	1.30283i	0.376346	+	0.926479i	$0.377180\pi$
$594$	378.180	+	378.180i	0.636666	+	0.636666i
$595$		−	238.044i		−	0.400074i
$596$	49.4532	+	49.4532i	0.0829751	+	0.0829751i
$597$			270.756i			0.453528i
$598$		−	188.801i		−	0.315721i
$599$	181.454	−	181.454i	0.302929	−	0.302929i	−0.539230	−	0.842159i	$-0.681285\pi$
$599$	181.454	−	181.454i	0.302929	−	0.302929i	0.842159	+	0.539230i	$0.181285\pi$
$600$			484.994i			0.808324i
$601$			683.225i			1.13681i	0.822747	+	0.568407i	$0.192440\pi$
$601$			683.225i			1.13681i	−0.822747	+	0.568407i	$0.807560\pi$
$602$	−398.121	−	398.121i	−0.661331	−	0.661331i
$603$	10.2372	−	10.2372i	0.0169771	−	0.0169771i
$604$	−166.785	−	166.785i	−0.276135	−	0.276135i
$605$	93.6590	−	93.6590i	0.154808	−	0.154808i
$606$		−	31.8789i		−	0.0526055i
$607$	56.7164			0.0934372			0.0467186	−	0.998908i	$-0.485124\pi$
$607$	56.7164			0.0934372			0.0467186	+	0.998908i	$0.485124\pi$
$608$	536.441	−	536.441i	0.882304	−	0.882304i
$609$	−405.594	+	405.594i	−0.666000	+	0.666000i
$610$			349.088i			0.572275i
$611$	153.708	−	153.708i	0.251568	−	0.251568i
$612$	−12.0126	+	12.0126i	−0.0196285	+	0.0196285i
$613$		−	328.690i		−	0.536199i	−0.963391	−	0.268100i	$-0.913604\pi$
$613$		−	328.690i		−	0.536199i	0.963391	−	0.268100i	$-0.0863957\pi$
$614$	−25.2869			−0.0411839
$615$	−1.89422			−0.00308003
$616$		−	576.411i		−	0.935732i
$617$		−	561.376i		−	0.909847i	−0.890531	−	0.454924i	$-0.849667\pi$
$617$		−	561.376i		−	0.909847i	0.890531	−	0.454924i	$-0.150333\pi$
$618$	50.3695	−	50.3695i	0.0815040	−	0.0815040i
$619$	−385.562			−0.622879			−0.311440	−	0.950266i	$-0.600811\pi$
$619$	−385.562			−0.622879			−0.311440	+	0.950266i	$0.600811\pi$
$620$	29.4135			0.0474412
$621$	557.895	−	557.895i	0.898381	−	0.898381i
$622$	−17.9871	−	17.9871i	−0.0289181	−	0.0289181i
$623$	411.757	+	411.757i	0.660927	+	0.660927i
$624$			93.1992i			0.149358i
$625$	−147.650			−0.236240
$626$	185.932	−	185.932i	0.297017	−	0.297017i
$627$	−1350.94			−2.15461
$628$	−156.909			−0.249856
$629$	538.212	−	538.212i	0.855663	−	0.855663i
$630$			13.3512i			0.0211924i
$631$	538.041			0.852680			0.426340	−	0.904563i	$-0.359803\pi$
$631$	538.041			0.852680			0.426340	+	0.904563i	$0.359803\pi$
$632$			489.950i			0.775237i
$633$	−605.693			−0.956860
$634$			231.510i			0.365157i
$635$	230.183	−	230.183i	0.362492	−	0.362492i
$636$	248.675	−	248.675i	0.390998	−	0.390998i
$637$	64.9822	+	64.9822i	0.102013	+	0.102013i
$638$		−	750.558i		−	1.17642i
$639$	−41.5949	−	41.5949i	−0.0650937	−	0.0650937i
$640$	35.2294			0.0550460
$641$	−146.951	+	146.951i	−0.229253	+	0.229253i	−0.812381	−	0.583127i	$-0.801829\pi$
$641$	−146.951	+	146.951i	−0.229253	+	0.229253i	0.583127	+	0.812381i	$0.301829\pi$
$642$	247.934			0.386190
$643$	377.506	−	377.506i	0.587100	−	0.587100i	−0.349745	−	0.936845i	$-0.613732\pi$
$643$	377.506	−	377.506i	0.587100	−	0.587100i	0.936845	+	0.349745i	$0.113732\pi$
$644$	−234.151			−0.363588
$645$	579.809			0.898929
$646$		−	928.711i		−	1.43763i
$647$	644.180	+	644.180i	0.995642	+	0.995642i	0.999991	−	0.00434900i	$-0.00138433\pi$
$647$	644.180	+	644.180i	0.995642	+	0.995642i	−0.00434900	+	0.999991i	$0.501384\pi$
$648$	−530.348	+	530.348i	−0.818438	+	0.818438i
$649$	−700.414	−	700.414i	−1.07922	−	1.07922i
$650$	−111.735			−0.171899
$651$	−114.917			−0.176524
$652$	332.256			0.509596
$653$		−	187.359i		−	0.286920i	−0.989656	−	0.143460i	$-0.954177\pi$
$653$		−	187.359i		−	0.286920i	0.989656	−	0.143460i	$-0.0458228\pi$
$654$	−774.130			−1.18369
$655$			111.148i			0.169691i
$656$		−	1.75273i		−	0.00267184i
$657$	−33.4846	+	33.4846i	−0.0509660	+	0.0509660i
$658$	311.017	+	311.017i	0.472671	+	0.472671i
$659$	−716.817	−	716.817i	−1.08773	−	1.08773i	−0.995762	−	0.0919724i	$-0.970683\pi$
$659$	−716.817	−	716.817i	−1.08773	−	1.08773i	−0.0919724	−	0.995762i	$-0.529317\pi$
$660$	115.580	+	115.580i	0.175121	+	0.175121i
$661$	−606.010			−0.916808			−0.458404	−	0.888744i	$-0.651579\pi$
$661$	−606.010			−0.916808			−0.458404	+	0.888744i	$0.651579\pi$
$662$	−37.0177	+	37.0177i	−0.0559180	+	0.0559180i
$663$	−153.418	−	153.418i	−0.231400	−	0.231400i
$664$	−746.616	−	746.616i	−1.12442	−	1.12442i
$665$	316.326	+	316.326i	0.475678	+	0.475678i
$666$	−30.1867	+	30.1867i	−0.0453254	+	0.0453254i
$667$	−1107.23			−1.66002
$668$	−286.747	+	286.747i	−0.429262	+	0.429262i
$669$	90.7702	−	90.7702i	0.135680	−	0.135680i
$670$	67.7125	−	67.7125i	0.101063	−	0.101063i
$671$	−773.462	−	773.462i	−1.15270	−	1.15270i
$672$	358.621			0.533662
$673$	572.493	−	572.493i	0.850658	−	0.850658i	−0.139556	−	0.990214i	$-0.544568\pi$
$673$	572.493	−	572.493i	0.850658	−	0.850658i	0.990214	+	0.139556i	$0.0445676\pi$
$674$			474.838i			0.704507i
$675$	−330.168	−	330.168i	−0.489137	−	0.489137i
$676$	−233.208			−0.344983
$677$	−861.160	+	861.160i	−1.27202	+	1.27202i	−0.326998	+	0.945025i	$0.606037\pi$
$677$	−861.160	+	861.160i	−1.27202	+	1.27202i	−0.945025	+	0.326998i	$0.893963\pi$
$678$	−7.25698	−	7.25698i	−0.0107035	−	0.0107035i
$679$	−853.470			−1.25695
$680$	−288.547	+	288.547i	−0.424334	+	0.424334i
$681$	24.1735			0.0354971
$682$	106.328	−	106.328i	0.155907	−	0.155907i
$683$		−	874.996i		−	1.28111i	−0.767914	−	0.640553i	$-0.778705\pi$
$683$		−	874.996i		−	1.28111i	0.767914	−	0.640553i	$-0.221295\pi$
$684$		−	31.9261i		−	0.0466756i
$685$	−108.483	+	108.483i	−0.158370	+	0.158370i
$686$	−408.178	+	408.178i	−0.595011	+	0.595011i
$687$		−	944.181i		−	1.37435i
$688$			536.499i			0.779796i
$689$	208.053	+	208.053i	0.301964	+	0.301964i
$690$	−278.184	+	278.184i	−0.403166	+	0.403166i
$691$	238.390			0.344993			0.172496	−	0.985010i	$-0.444817\pi$
$691$	238.390			0.344993			0.172496	+	0.985010i	$0.444817\pi$
$692$	−404.000			−0.583816
$693$	−29.5817	−	29.5817i	−0.0426865	−	0.0426865i
$694$	695.292	+	695.292i	1.00186	+	1.00186i
$695$	−177.339			−0.255165
$696$	983.289			1.41277
$697$	2.88522	+	2.88522i	0.00413948	+	0.00413948i
$698$		−	303.860i		−	0.435329i
$699$	263.391	+	263.391i	0.376811	+	0.376811i
$700$			138.573i			0.197961i
$701$	−82.0413	+	82.0413i	−0.117035	+	0.117035i	−0.763199	−	0.646164i	$-0.776372\pi$
$701$	−82.0413	+	82.0413i	−0.117035	+	0.117035i	0.646164	+	0.763199i	$0.276372\pi$
$702$	−114.142	−	114.142i	−0.162596	−	0.162596i
$703$			1430.41i			2.03472i
$704$	−613.250	+	613.250i	−0.871094	+	0.871094i
$705$	−452.954			−0.642489
$706$	125.180	+	125.180i	0.177309	+	0.177309i
$707$		−	33.0777i		−	0.0467860i
$708$	252.674	−	252.674i	0.356884	−	0.356884i
$709$	−757.263	−	757.263i	−1.06807	−	1.06807i	−0.997507	−	0.0705643i	$-0.977520\pi$
$709$	−757.263	−	757.263i	−1.06807	−	1.06807i	−0.0705643	−	0.997507i	$-0.522480\pi$
$710$	−275.123	−	275.123i	−0.387498	−	0.387498i
$711$	25.1445	+	25.1445i	0.0353650	+	0.0353650i
$712$		−	998.232i		−	1.40201i
$713$	−156.857	−	156.857i	−0.219995	−	0.219995i
$714$	310.431	−	310.431i	0.434777	−	0.434777i
$715$	−96.6992	+	96.6992i	−0.135244	+	0.135244i
$716$	−159.672	+	159.672i	−0.223006	+	0.223006i
$717$	385.497	+	385.497i	0.537653	+	0.537653i
$718$			260.844i			0.363292i
$719$	997.137	−	997.137i	1.38684	−	1.38684i	0.554966	−	0.831873i	$-0.312731\pi$
$719$	997.137	−	997.137i	1.38684	−	1.38684i	0.831873	−	0.554966i	$-0.187269\pi$
$720$	8.99588	−	8.99588i	0.0124943	−	0.0124943i
$721$	52.2636	−	52.2636i	0.0724877	−	0.0724877i
$722$	832.132	+	832.132i	1.15254	+	1.15254i
$723$	−868.591			−1.20137
$724$	−61.9585			−0.0855780
$725$			655.271i			0.903822i
$726$	244.280			0.336474
$727$			502.751i			0.691542i	0.938319	+	0.345771i	$0.112383\pi$
$727$			502.751i			0.691542i	−0.938319	+	0.345771i	$0.887617\pi$
$728$			173.972i			0.238973i
$729$		−	670.982i		−	0.920414i
$730$	−221.479	+	221.479i	−0.303396	+	0.303396i
$731$	−883.149	−	883.149i	−1.20814	−	1.20814i
$732$	279.026	−	279.026i	0.381183	−	0.381183i
$733$	667.873			0.911149			0.455575	−	0.890198i	$-0.349434\pi$
$733$	667.873			0.911149			0.455575	+	0.890198i	$0.349434\pi$
$734$		−	306.820i		−	0.418011i
$735$		−	191.493i		−	0.260534i
$736$	489.500	+	489.500i	0.665081	+	0.665081i
$737$			300.057i			0.407132i
$738$	−0.161823	−	0.161823i	−0.000219273	−	0.000219273i
$739$			735.904i			0.995811i	0.867231	+	0.497905i	$0.165897\pi$
$739$			735.904i			0.995811i	−0.867231	+	0.497905i	$0.834103\pi$
$740$	122.379	−	122.379i	0.165377	−	0.165377i
$741$	407.741			0.550258
$742$	−420.981	+	420.981i	−0.567359	+	0.567359i
$743$	−341.898	−	341.898i	−0.460159	−	0.460159i	0.438549	−	0.898707i	$-0.355493\pi$
$743$	−341.898	−	341.898i	−0.460159	−	0.460159i	−0.898707	+	0.438549i	$0.855493\pi$
$744$	139.298	+	139.298i	0.187229	+	0.187229i
$745$	121.925			0.163658
$746$		−	335.175i		−	0.449296i
$747$	−76.6335			−0.102588
$748$		−	352.095i		−	0.470715i
$749$	257.258			0.343468
$750$	393.570	+	393.570i	0.524760	+	0.524760i
$751$			529.592i			0.705182i	0.935778	+	0.352591i	$0.114699\pi$
$751$			529.592i			0.705182i	−0.935778	+	0.352591i	$0.885301\pi$
$752$		−	419.120i		−	0.557341i
$753$	−410.050	−	410.050i	−0.544556	−	0.544556i
$754$			226.533i			0.300442i
$755$	−411.204			−0.544641
$756$	−141.559	+	141.559i	−0.187247	+	0.187247i
$757$	600.515	−	600.515i	0.793283	−	0.793283i	−0.188744	−	0.982026i	$-0.560441\pi$
$757$	600.515	−	600.515i	0.793283	−	0.793283i	0.982026	+	0.188744i	$0.0604415\pi$
$758$	−470.151	−	470.151i	−0.620251	−	0.620251i
$759$		−	1232.73i		−	1.62415i
$760$		−	766.874i		−	1.00905i
$761$	−238.390	−	238.390i	−0.313259	−	0.313259i	0.532912	−	0.846171i	$-0.321098\pi$
$761$	−238.390	−	238.390i	−0.313259	−	0.313259i	−0.846171	+	0.532912i	$0.821098\pi$
$762$	600.358			0.787871
$763$	−803.242			−1.05274
$764$		−	369.078i		−	0.483086i
$765$			29.6168i			0.0387148i
$766$	−319.450			−0.417036
$767$	211.399	+	211.399i	0.275618	+	0.275618i
$768$	−536.233	−	536.233i	−0.698220	−	0.698220i
$769$	637.452			0.828937			0.414468	−	0.910064i	$-0.363968\pi$
$769$	637.452			0.828937			0.414468	+	0.910064i	$0.363968\pi$
$770$	−195.664	−	195.664i	−0.254109	−	0.254109i
$771$	151.043	+	151.043i	0.195905	+	0.195905i
$772$		−	239.434i		−	0.310148i
$773$	−457.236			−0.591508			−0.295754	−	0.955264i	$-0.595571\pi$
$773$	−457.236			−0.591508			−0.295754	+	0.955264i	$0.595571\pi$
$774$	49.5332	+	49.5332i	0.0639964	+	0.0639964i
$775$	&minus

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11355 - 1.11355i) q^{2} +(2.19442 + 2.19442i) q^{3} -1.52002i q^{4} +(-1.87378 - 1.87378i) q^{5} -4.88717i q^{6} -5.07096i q^{7} +(-6.14681 + 6.14681i) q^{8} +0.630916i q^{9} +O(q^{10})\)	\(q+(-1.11355 - 1.11355i) q^{2} +(2.19442 + 2.19442i) q^{3} -1.52002i q^{4} +(-1.87378 - 1.87378i) q^{5} -4.88717i q^{6} -5.07096i q^{7} +(-6.14681 + 6.14681i) q^{8} +0.630916i q^{9} +4.17310i q^{10} +(-9.24618 - 9.24618i) q^{11} +(3.33556 - 3.33556i) q^{12} +(2.79068 + 2.79068i) q^{13} +(-5.64675 + 5.64675i) q^{14} -8.22372i q^{15} +7.60944 q^{16} +(-12.5261 + 12.5261i) q^{17} +(0.702555 - 0.702555i) q^{18} -33.2908i q^{19} +(-2.84820 + 2.84820i) q^{20} +(11.1278 - 11.1278i) q^{21} +20.5921i q^{22} +30.3777 q^{23} -26.9773 q^{24} -17.9779i q^{25} -6.21512i q^{26} +(18.3652 - 18.3652i) q^{27} -7.70797 q^{28} -36.4488 q^{29} +(-9.15751 + 9.15751i) q^{30} +(-5.16354 - 5.16354i) q^{31} +(16.1138 + 16.1138i) q^{32} -40.5799i q^{33} +27.8969 q^{34} +(-9.50188 + 9.50188i) q^{35} +0.959006 q^{36} -42.9671 q^{37} +(-37.0709 + 37.0709i) q^{38} +12.2478i q^{39} +23.0356 q^{40} -0.230336i q^{41} -24.7826 q^{42} +70.5045i q^{43} +(-14.0544 + 14.0544i) q^{44} +(1.18220 - 1.18220i) q^{45} +(-33.8271 - 33.8271i) q^{46} -55.0790i q^{47} +(16.6983 + 16.6983i) q^{48} +23.2854 q^{49} +(-20.0192 + 20.0192i) q^{50} -54.9751 q^{51} +(4.24190 - 4.24190i) q^{52} +74.5527 q^{53} -40.9012 q^{54} +34.6507i q^{55} +(31.1702 + 31.1702i) q^{56} +(73.0539 - 73.0539i) q^{57} +(40.5874 + 40.5874i) q^{58} +75.7516 q^{59} -12.5002 q^{60} +83.6520 q^{61} +11.4997i q^{62} +3.19935 q^{63} -66.3246i q^{64} -10.4583i q^{65} +(-45.1877 + 45.1877i) q^{66} +(-16.2260 - 16.2260i) q^{67} +(19.0400 + 19.0400i) q^{68} +(66.6614 + 66.6614i) q^{69} +21.1616 q^{70} +(-65.9279 + 65.9279i) q^{71} +(-3.87812 - 3.87812i) q^{72} +(53.0731 + 53.0731i) q^{73} +(47.8459 + 47.8459i) q^{74} +(39.4509 - 39.4509i) q^{75} -50.6028 q^{76} +(-46.8870 + 46.8870i) q^{77} +(13.6386 - 13.6386i) q^{78} +(39.8540 - 39.8540i) q^{79} +(-14.2585 - 14.2585i) q^{80} +86.2802 q^{81} +(-0.256490 + 0.256490i) q^{82} +121.464i q^{83} +(-16.9145 - 16.9145i) q^{84} +46.9426 q^{85} +(78.5101 - 78.5101i) q^{86} +(-79.9837 - 79.9837i) q^{87} +113.669 q^{88} +(-81.1992 + 81.1992i) q^{89} -2.63287 q^{90} +(14.1514 - 14.1514i) q^{91} -46.1749i q^{92} -22.6619i q^{93} +(-61.3331 + 61.3331i) q^{94} +(-62.3799 + 62.3799i) q^{95} +70.7206i q^{96} -168.306i q^{97} +(-25.9294 - 25.9294i) q^{98} +(5.83356 - 5.83356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8}+O(q^{10}) \) 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28} + 56 q^{29} - 70 q^{30} - 64 q^{31} - 156 q^{32} - 52 q^{34} - 92 q^{35} - 36 q^{36} - 160 q^{37} + 40 q^{38} + 52 q^{40} + 80 q^{42} + 140 q^{44} + 324 q^{45} + 214 q^{46} + 216 q^{48} - 836 q^{49} + 126 q^{50} + 124 q^{51} - 10 q^{52} - 16 q^{53} + 400 q^{54} - 40 q^{56} + 68 q^{57} - 266 q^{58} - 364 q^{59} - 68 q^{60} - 168 q^{61} - 12 q^{63} + 238 q^{66} - 112 q^{67} - 148 q^{68} - 48 q^{69} + 48 q^{70} + 150 q^{71} - 474 q^{72} + 18 q^{73} + 236 q^{74} + 64 q^{75} - 260 q^{76} - 388 q^{77} - 782 q^{78} + 202 q^{79} + 796 q^{80} - 516 q^{81} + 72 q^{82} - 294 q^{84} - 696 q^{85} + 618 q^{86} + 464 q^{87} - 244 q^{88} - 536 q^{89} + 1484 q^{90} + 212 q^{91} + 132 q^{94} + 370 q^{95} - 530 q^{98} - 66 q^{99}+O(q^{100}) \) 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

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