LMFDB - Embedded newform 197.3.c.a.14.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,3,Mod(14,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			14.10
Character	$\chi$	$=$	197.14
Dual form			197.3.c.a.183.10

$q$-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} -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} + 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}+ \cdots - 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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	−0.928387	−	0.371614i	$-0.878805\pi$
$2$	−1.11355	+	1.11355i	−0.556774	+	0.556774i	0.371614	+	0.928387i	$0.378805\pi$
$3$	2.19442	−	2.19442i	0.731472	−	0.731472i	−0.239440	−	0.970911i	$-0.576964\pi$
$3$	2.19442	−	2.19442i	0.731472	−	0.731472i	0.970911	+	0.239440i	$0.0769637\pi$
$4$			1.52002i			0.380006i
$5$	−1.87378	+	1.87378i	−0.374757	+	0.374757i	−0.869206	−	0.494449i	$-0.835370\pi$
$5$	−1.87378	+	1.87378i	−0.374757	+	0.374757i	0.494449	+	0.869206i	$0.335370\pi$
$6$			4.88717i			0.814529i
$7$			5.07096i			0.724422i	0.932096	+	0.362211i	$0.117978\pi$
$7$			5.07096i			0.724422i	−0.932096	+	0.362211i	$0.882022\pi$
$8$	−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	−0.988932	−	0.148370i	$-0.952597\pi$
$11$	−9.24618	+	9.24618i	−0.840562	+	0.840562i	0.148370	+	0.988932i	$0.452597\pi$
$12$	3.33556	+	3.33556i	0.277963	+	0.277963i
$13$	2.79068	−	2.79068i	0.214668	−	0.214668i	−0.591579	−	0.806247i	$-0.701495\pi$
$13$	2.79068	−	2.79068i	0.214668	−	0.214668i	0.806247	+	0.591579i	$0.201495\pi$
$14$	−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	0.235132	−	0.971964i	$-0.424448\pi$
$17$	−12.5261	−	12.5261i	−0.736832	−	0.736832i	−0.971964	+	0.235132i	$0.924448\pi$
$18$	0.702555	+	0.702555i	0.0390308	+	0.0390308i
$19$			33.2908i			1.75215i	0.482176	+	0.876075i	$0.339847\pi$
$19$			33.2908i			1.75215i	−0.482176	+	0.876075i	$0.660153\pi$
$20$	−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	−0.785468	−	0.618902i	$-0.787578\pi$
$31$	−5.16354	+	5.16354i	−0.166566	+	0.166566i	0.618902	+	0.785468i	$0.287578\pi$
$32$	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	$0.000894125\pi$
$41$			0.230336i			0.00561795i	−0.999996	+	0.00280897i	$0.999106\pi$
$42$	−24.7826			−0.590063
$43$		−	70.5045i		−	1.63964i	−0.572622	−	0.819819i	$-0.694074\pi$
$43$		−	70.5045i		−	1.63964i	0.572622	−	0.819819i	$-0.305926\pi$
$44$	−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	$0.199277\pi$
$47$			55.0790i			1.17189i	−0.810350	+	0.585947i	$0.800723\pi$
$48$	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	−0.817751	−	0.575572i	$-0.804779\pi$
$67$	−16.2260	+	16.2260i	−0.242179	+	0.242179i	0.575572	+	0.817751i	$0.304779\pi$
$68$	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	0.0690518	−	0.997613i	$-0.478003\pi$
$71$	−65.9279	−	65.9279i	−0.928561	−	0.928561i	−0.997613	+	0.0690518i	$0.978003\pi$
$72$	−3.87812	+	3.87812i	−0.0538627	+	0.0538627i
$73$	53.0731	−	53.0731i	0.727029	−	0.727029i	−0.242998	−	0.970027i	$-0.578131\pi$
$73$	53.0731	−	53.0731i	0.727029	−	0.727029i	0.970027	+	0.242998i	$0.0781309\pi$
$74$	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	0.912827	−	0.408346i	$-0.133894\pi$
$79$	39.8540	+	39.8540i	0.504481	+	0.504481i	−0.408346	+	0.912827i	$0.633894\pi$
$80$	−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	$-0.738722\pi$
$83$		−	121.464i		−	1.46342i	0.681616	−	0.731710i	$-0.261278\pi$
$84$	−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	0.0841065	−	0.996457i	$-0.473196\pi$
$89$	−81.1992	−	81.1992i	−0.912350	−	0.912350i	−0.996457	+	0.0841065i	$0.973196\pi$
$90$	−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	$0.334309\pi$
$97$			168.306i			1.73511i	−0.497342	+	0.867554i	$0.665691\pi$
$98$	−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	−0.655303	−	0.755366i	$-0.727459\pi$
$103$	10.3065	−	10.3065i	0.100063	−	0.100063i	0.755366	+	0.655303i	$0.227459\pi$
$104$	−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	$-0.923815\pi$
$107$		−	50.7316i		−	0.474127i	0.971494	−	0.237064i	$-0.0761850\pi$
$108$	−27.9156	+	27.9156i	−0.258478	+	0.258478i
$109$			158.400i			1.45322i	0.687053	+	0.726608i	$0.258904\pi$
$109$			158.400i			1.45322i	−0.687053	+	0.726608i	$0.741096\pi$
$110$	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	0.713647	−	0.700506i	$-0.247042\pi$
$113$	1.48490	+	1.48490i	0.0131407	+	0.0131407i	−0.700506	+	0.713647i	$0.747042\pi$
$114$	−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	$-0.839316\pi$
$127$		−	122.844i		−	0.967273i	0.875269	−	0.483636i	$-0.160684\pi$
$128$	−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	−0.811187	−	0.584786i	$-0.801178\pi$
$131$	−29.6586	+	29.6586i	−0.226401	+	0.226401i	0.584786	+	0.811187i	$0.301178\pi$
$132$	−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	$0.0677685\pi$
$137$			57.8952i			0.422593i	−0.977422	+	0.211296i	$0.932231\pi$
$138$			148.461i			1.07581i
$139$	47.3212	+	47.3212i	0.340440	+	0.340440i	0.856533	−	0.516093i	$-0.172614\pi$
$139$	47.3212	+	47.3212i	0.340440	+	0.340440i	−0.516093	+	0.856533i	$0.672614\pi$
$140$	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	0.589451	−	0.807804i	$-0.299344\pi$
$149$	−32.5345	−	32.5345i	−0.218352	−	0.218352i	−0.807804	+	0.589451i	$0.799344\pi$
$150$	−87.8609			−0.585739
$151$	109.726	+	109.726i	0.726659	+	0.726659i	0.969953	−	0.243293i	$-0.0782277\pi$
$151$	109.726	+	109.726i	0.726659	+	0.726659i	−0.243293	+	0.969953i	$0.578228\pi$
$152$	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	$0.106628\pi$
$157$			103.228i			0.657505i	−0.944416	+	0.328752i	$0.893372\pi$
$158$	−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	$-0.766075\pi$
$163$		−	218.586i		−	1.34102i	0.741900	−	0.670511i	$-0.233925\pi$
$164$	−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	−0.139380	+	0.990239i	$0.544511\pi$
$167$	−188.646	+	188.646i	−1.12962	+	1.12962i	−0.990239	+	0.139380i	$0.955489\pi$
$168$		−	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	$0.278831\pi$
$173$			265.786i			1.53633i	−0.640250	+	0.768167i	$0.721169\pi$
$174$		−	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	−0.936777	−	0.349928i	$-0.886206\pi$
$179$	−105.046	+	105.046i	−0.586849	+	0.586849i	0.349928	+	0.936777i	$0.386206\pi$
$180$	−1.79697	+	1.79697i	−0.00998317	+	0.00998317i
$181$			40.7615i			0.225202i	0.993640	+	0.112601i	$0.0359182\pi$
$181$			40.7615i			0.225202i	−0.993640	+	0.112601i	$0.964082\pi$
$182$	−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	−0.534903	−	0.844914i	$-0.679652\pi$
$199$	61.6921	−	61.6921i	0.310011	−	0.310011i	0.844914	+	0.534903i	$0.179652\pi$
$200$	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	0.299904	−	0.953969i	$-0.403045\pi$
$211$	−138.008	−	138.008i	−0.654065	−	0.654065i	−0.953969	+	0.299904i	$0.903045\pi$
$212$			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	$0.0295641\pi$
$223$			41.3642i			0.185490i	−0.995690	+	0.0927448i	$0.970436\pi$
$224$	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	0.719135	−	0.694871i	$-0.244538\pi$
$227$	5.50797	+	5.50797i	0.0242642	+	0.0242642i	−0.694871	+	0.719135i	$0.744538\pi$
$228$	−111.044	+	111.044i	−0.487033	+	0.487033i
$229$	−215.133	+	215.133i	−0.939445	+	0.939445i	−0.998268	−	0.0588238i	$-0.981265\pi$
$229$	−215.133	+	215.133i	−0.939445	+	0.939445i	0.0588238	+	0.998268i	$0.481265\pi$
$230$		−	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	0.165079	−	0.986280i	$-0.447212\pi$
$241$	−197.909	−	197.909i	−0.821201	−	0.821201i	−0.986280	+	0.165079i	$0.947212\pi$
$242$	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	0.999960	+	0.00888848i	$0.00282933\pi$
$263$	265.327	+	265.327i	1.00885	+	1.00885i	0.00888848	+	0.999960i	$0.497171\pi$
$264$	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	−0.659238	−	0.751934i	$-0.729121\pi$
$269$	24.9352	−	24.9352i	0.0926961	−	0.0926961i	0.751934	+	0.659238i	$0.229121\pi$
$270$	76.6400	−	76.6400i	0.283852	−	0.283852i
$271$	337.196	−	337.196i	1.24427	−	1.24427i	0.286052	−	0.958214i	$-0.407657\pi$
$271$	337.196	−	337.196i	1.24427	−	1.24427i	0.958214	−	0.286052i	$-0.0923431\pi$
$272$	−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	−0.597290	−	0.802025i	$-0.703756\pi$
$277$	56.7117	−	56.7117i	0.204735	−	0.204735i	0.802025	+	0.597290i	$0.203756\pi$
$278$	−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	0.360057	−	0.932930i	$-0.382757\pi$
$281$	363.329	−	363.329i	1.29299	−	1.29299i	0.932930	−	0.360057i	$-0.117243\pi$
$282$	−269.181			−0.954541
$283$	−124.123	−	124.123i	−0.438596	−	0.438596i	0.452944	−	0.891539i	$-0.350374\pi$
$283$	−124.123	−	124.123i	−0.438596	−	0.438596i	−0.891539	+	0.452944i	$0.850374\pi$
$284$	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	$0.192597\pi$
$293$			333.324i			1.13763i	−0.822467	+	0.568813i	$0.807403\pi$
$294$			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	0.725357	−	0.688373i	$-0.241675\pi$
$307$	11.3542	+	11.3542i	0.0369844	+	0.0369844i	−0.688373	+	0.725357i	$0.741675\pi$
$308$	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	$-0.914057\pi$
$313$		−	166.973i		−	0.533460i	0.963771	−	0.266730i	$-0.0859432\pi$
$314$	−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	−0.851796	−	0.523874i	$-0.824486\pi$
$317$	−103.951	+	103.951i	−0.327923	+	0.327923i	0.523874	+	0.851796i	$0.324486\pi$
$318$			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	$0.0159910\pi$
$331$			33.2430i			0.100432i	−0.998738	+	0.0502161i	$0.984009\pi$
$332$	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	−0.948737	−	0.316068i	$-0.897637\pi$
$337$	−213.210	+	213.210i	−0.632669	+	0.632669i	0.316068	+	0.948737i	$0.397637\pi$
$338$	−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	−0.484083	−	0.875022i	$-0.660847\pi$
$349$	136.438	−	136.438i	0.390939	−	0.390939i	0.875022	+	0.484083i	$0.160847\pi$
$350$	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	−0.851158	−	0.524910i	$-0.824099\pi$
$359$	−117.123	+	117.123i	−0.326247	+	0.326247i	0.524910	+	0.851158i	$0.324099\pi$
$360$		−	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	−0.494048	−	0.869435i	$-0.664483\pi$
$367$	137.767	−	137.767i	0.375387	−	0.375387i	0.869435	+	0.494048i	$0.164483\pi$
$368$	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	−0.475976	−	0.879458i	$-0.657905\pi$
$373$	150.499	−	150.499i	0.403482	−	0.403482i	0.879458	+	0.475976i	$0.157905\pi$
$374$	−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	0.869117	−	0.494606i	$-0.164688\pi$
$383$	143.438	+	143.438i	0.374511	+	0.374511i	−0.494606	+	0.869117i	$0.664688\pi$
$384$	−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	0.694227	−	0.719756i	$-0.255746\pi$
$389$	−9.93096	−	9.93096i	−0.0255295	−	0.0255295i	−0.719756	+	0.694227i	$0.755746\pi$
$390$	−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	−0.495706	−	0.868490i	$-0.665091\pi$
$397$	147.995	−	147.995i	0.372784	−	0.372784i	0.868490	+	0.495706i	$0.165091\pi$
$398$			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	$0.203479\pi$
$401$			478.467i			1.19318i	−0.802545	+	0.596592i	$0.796521\pi$
$402$	−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	$-0.765178\pi$
$409$		−	550.186i		−	1.34520i	0.740007	−	0.672599i	$-0.234822\pi$
$410$	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	$-0.896067\pi$
$419$		−	268.783i		−	0.641486i	0.947166	−	0.320743i	$-0.103933\pi$
$420$		−	63.3882i		−	0.150924i
$421$	−210.501	−	210.501i	−0.500002	−	0.500002i	0.411436	−	0.911439i	$-0.365027\pi$
$421$	−210.501	−	210.501i	−0.500002	−	0.500002i	−0.911439	+	0.411436i	$0.865027\pi$
$422$	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	$0.141216\pi$
$433$			371.716i			0.858467i	−0.903194	+	0.429233i	$0.858784\pi$
$434$	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	−0.973537	−	0.228530i	$-0.926608\pi$
$439$	−527.707	−	527.707i	−1.20207	−	1.20207i	−0.228530	−	0.973537i	$-0.573392\pi$
$440$	−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	$-0.719224\pi$
$449$		−	693.314i		−	1.54413i	0.635544	−	0.772065i	$-0.280776\pi$
$450$	−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	−0.845253	−	0.534367i	$-0.820550\pi$
$461$	−143.318	+	143.318i	−0.310886	+	0.310886i	0.534367	+	0.845253i	$0.320550\pi$
$462$	229.145	−	229.145i	0.495985	−	0.495985i
$463$	85.4692	−	85.4692i	0.184599	−	0.184599i	−0.608758	−	0.793356i	$-0.708332\pi$
$463$	85.4692	−	85.4692i	0.184599	−	0.184599i	0.793356	+	0.608758i	$0.208332\pi$
$464$	−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	−0.376534	−	0.926403i	$-0.622884\pi$
$467$	256.789	−	256.789i	0.549869	−	0.549869i	0.926403	+	0.376534i	$0.122884\pi$
$468$	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	$-0.760918\pi$
$487$		−	664.697i		−	1.36488i	0.730941	−	0.682441i	$-0.239082\pi$
$488$	−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	$-0.805148\pi$
$491$		−	564.280i		−	1.14925i	0.818418	−	0.574624i	$-0.194852\pi$
$492$	−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	$0.207568\pi$
$503$			610.493i			1.21370i	−0.794815	+	0.606852i	$0.792432\pi$
$504$	−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	−0.996626	−	0.0820715i	$-0.973846\pi$
$509$	−465.508	+	465.508i	−0.914555	+	0.914555i	0.0820715	+	0.996626i	$0.473846\pi$
$510$			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	$0.00543661\pi$
$521$			17.7961i			0.0341576i	−0.999854	+	0.0170788i	$0.994563\pi$
$522$	−25.6072	−	25.6072i	−0.0490560	−	0.0490560i
$523$	−649.537	−	649.537i	−1.24194	−	1.24194i	−0.959193	−	0.282752i	$-0.908753\pi$
$523$	−649.537	−	649.537i	−1.24194	−	1.24194i	−0.282752	−	0.959193i	$-0.591247\pi$
$524$	−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	−0.394086	−	0.919073i	$-0.628939\pi$
$541$	284.018	−	284.018i	0.524987	−	0.524987i	0.919073	+	0.394086i	$0.128939\pi$
$542$			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	0.344491	−	0.938790i	$-0.388051\pi$
$547$	701.955	−	701.955i	1.28328	−	1.28328i	0.938790	−	0.344491i	$-0.111949\pi$
$548$	−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	$-0.832244\pi$
$557$		−	560.297i		−	1.00592i	0.864310	−	0.502960i	$-0.167756\pi$
$558$	−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	$-0.935207\pi$
$563$		−	227.622i		−	0.404302i	0.979354	−	0.202151i	$-0.0647931\pi$
$564$	−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	−0.994295	−	0.106666i	$-0.965983\pi$
$571$	−506.836	+	506.836i	−0.887629	+	0.887629i	0.106666	+	0.994295i	$0.465983\pi$
$572$	−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	−0.904734	−	0.425977i	$-0.859930\pi$
$577$	−276.243	+	276.243i	−0.478757	+	0.478757i	0.425977	+	0.904734i	$0.359930\pi$
$578$	−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	0.376346	−	0.926479i	$-0.377180\pi$
$593$	772.575	−	772.575i	1.30283	−	1.30283i	0.926479	−	0.376346i	$-0.122820\pi$
$594$	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	0.842159	−	0.539230i	$-0.181285\pi$
$599$	181.454	+	181.454i	0.302929	+	0.302929i	−0.539230	+	0.842159i	$0.681285\pi$
$600$		−	484.994i		−	0.808324i
$601$		−	683.225i		−	1.13681i	−0.822747	−	0.568407i	$-0.807560\pi$
$601$		−	683.225i		−	1.13681i	0.822747	−	0.568407i	$-0.192440\pi$
$602$	−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	$0.0863957\pi$
$613$			328.690i			0.536199i	−0.963391	+	0.268100i	$0.913604\pi$
$614$	−25.2869			−0.0411839
$615$	−1.89422			−0.00308003
$616$			576.411i			0.935732i
$617$			561.376i			0.909847i	0.890531	+	0.454924i	$0.150333\pi$
$617$			561.376i			0.909847i	−0.890531	+	0.454924i	$0.849667\pi$
$618$	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	0.583127	−	0.812381i	$-0.301829\pi$
$641$	−146.951	−	146.951i	−0.229253	−	0.229253i	−0.812381	+	0.583127i	$0.801829\pi$
$642$	247.934			0.386190
$643$	377.506	+	377.506i	0.587100	+	0.587100i	0.936845	−	0.349745i	$-0.113732\pi$
$643$	377.506	+	377.506i	0.587100	+	0.587100i	−0.349745	+	0.936845i	$0.613732\pi$
$644$	−234.151			−0.363588
$645$	579.809			0.898929
$646$			928.711i			1.43763i
$647$	644.180	−	644.180i	0.995642	−	0.995642i	−0.00434900	−	0.999991i	$-0.501384\pi$
$647$	644.180	−	644.180i	0.995642	−	0.995642i	0.999991	+	0.00434900i	$0.00138433\pi$
$648$	−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	$0.0458228\pi$
$653$			187.359i			0.286920i	−0.989656	+	0.143460i	$0.954177\pi$
$654$	−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	−0.0919724	+	0.995762i	$0.529317\pi$
$659$	−716.817	+	716.817i	−1.08773	+	1.08773i	−0.995762	+	0.0919724i	$0.970683\pi$
$660$	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	0.990214	−	0.139556i	$-0.0445676\pi$
$673$	572.493	+	572.493i	0.850658	+	0.850658i	−0.139556	+	0.990214i	$0.544568\pi$
$674$		−	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	−0.945025	−	0.326998i	$-0.893963\pi$
$677$	−861.160	−	861.160i	−1.27202	−	1.27202i	−0.326998	−	0.945025i	$-0.606037\pi$
$678$	−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	$0.221295\pi$
$683$			874.996i			1.28111i	−0.767914	+	0.640553i	$0.778705\pi$
$684$			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	0.646164	−	0.763199i	$-0.276372\pi$
$701$	−82.0413	−	82.0413i	−0.117035	−	0.117035i	−0.763199	+	0.646164i	$0.776372\pi$
$702$	−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	−0.0705643	+	0.997507i	$0.522480\pi$
$709$	−757.263	+	757.263i	−1.06807	+	1.06807i	−0.997507	+	0.0705643i	$0.977520\pi$
$710$	−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	0.831873	+	0.554966i	$0.187269\pi$
$719$	997.137	+	997.137i	1.38684	+	1.38684i	0.554966	+	0.831873i	$0.312731\pi$
$720$	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	$-0.887617\pi$
$727$		−	502.751i		−	0.691542i	0.938319	−	0.345771i	$-0.112383\pi$
$728$		−	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	$-0.834103\pi$
$739$		−	735.904i		−	0.995811i	0.867231	−	0.497905i	$-0.165897\pi$
$740$	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	−0.898707	−	0.438549i	$-0.855493\pi$
$743$	−341.898	+	341.898i	−0.460159	+	0.460159i	0.438549	+	0.898707i	$0.355493\pi$
$744$	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	$-0.885301\pi$
$751$		−	529.592i		−	0.705182i	0.935778	−	0.352591i	$-0.114699\pi$
$752$			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	0.982026	−	0.188744i	$-0.0604415\pi$
$757$	600.515	+	600.515i	0.793283	+	0.793283i	−0.188744	+	0.982026i	$0.560441\pi$
$758$	−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	−0.846171	−	0.532912i	$-0.821098\pi$
$761$	−238.390	+	238.390i	−0.313259	+	0.313259i	0.532912	+	0.846171i	$0.321098\pi$
$762$	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
$775$	−92.8293	−	92.8293i	−0.119780	−	0.119780i
$776$	1034.54	−	1034.54i	1.33317	−	1.33317i
$777$	−478.129	−	478.129i	−0.615352	−	0.615352i
$778$	22.1172			0.0284283
$779$	−7.66807			−0.00984348
$780$	−34.8843	+	34.8843i	−0.0447234	+	0.0447234i
$781$	1219.16			1.56103
$782$	847.445			1.08369
$783$	−669.390	−	669.390i	−0.854905	−	0.854905i
$784$	177.189			0.226006
$785$	−193.428	−	193.428i	−0.246405	−	0.246405i
$786$	−144.947	−	144.947i	−0.184410	−	0.184410i
$787$		−	908.205i		−	1.15401i	−0.816741	−	0.577005i	$-0.804221\pi$
$787$		−	908.205i		−	1.15401i	0.816741	−	0.577005i	$-0.195779\pi$
$788$	−299.302	−	9.22304i	−0.379825	−	0.0117044i
$789$	1164.48			1.47589
$790$	166.315	−	166.315i	0.210525	−	0.210525i
$791$	−7.52989	+	7.52989i	−0.00951945	+	0.00951945i
$792$		−	71.7156i		−	0.0905500i
$793$	233.446	−	233.446i	0.294384	−	0.294384i
$794$			329.600i			0.415113i
$795$			613.101i			0.771196i
$796$	93.7734	+	93.7734i	0.117806	+	0.117806i
$797$		−	567.038i		−	0.711466i	−0.934588	−	0.355733i	$-0.884231\pi$
$797$		−	567.038i		−	0.711466i	0.934588	−	0.355733i	$-0.115769\pi$
$798$		−	825.035i		−	1.03388i
$799$	689.927	−	689.927i	0.863488	−	0.863488i
$800$	289.691	+	289.691i	0.362114	+	0.362114i
$801$	−51.2298	+	51.2298i	−0.0639573	+	0.0639573i
$802$	−532.795	−	532.795i	−0.664334	−	0.664334i
$803$			981.447i			1.22223i
$804$	−108.245			−0.134634
$805$	−288.646	−	288.646i	−0.358566	−	0.358566i
$806$	−32.0920	−	32.0920i	−0.0398164	−	0.0398164i
$807$		−	109.437i		−	0.135609i
$808$	−40.0955	−	40.0955i	−0.0496231	−	0.0496231i
$809$	334.456	+	334.456i	0.413420	+	0.413420i	0.882928	−	0.469508i	$-0.155569\pi$
$809$	334.456	+	334.456i	0.413420	+	0.413420i	−0.469508	+	0.882928i	$0.655569\pi$
$810$		−	360.056i		−	0.444513i
$811$	719.666			0.887381			0.443691	−	0.896180i	$-0.353669\pi$
$811$	719.666			0.887381			0.443691	+	0.896180i	$0.353669\pi$
$812$	280.946			0.345993
$813$		−	1479.90i		−	1.82029i
$814$			884.784i			1.08696i
$815$	409.584	+	409.584i	0.502557	+	0.502557i
$816$	−418.330			−0.512659
$817$	2347.15			2.87289
$818$	612.659	+	612.659i	0.748971	+	0.748971i
$819$	8.92836	−	8.92836i	0.0109015	−	0.0109015i
$820$	0.656042	−	0.656042i	0.000800051	−	0.000800051i
$821$			924.934i			1.12659i	0.826254	+	0.563297i	$0.190467\pi$
$821$			924.934i			1.12659i	−0.826254	+	0.563297i	$0.809533\pi$
$822$	−282.944			−0.344214
$823$	622.657	+	622.657i	0.756570	+	0.756570i	0.975696	−	0.219127i	$-0.0703208\pi$
$823$	622.657	+	622.657i	0.756570	+	0.756570i	−0.219127	+	0.975696i	$0.570321\pi$
$824$	−126.704			−0.153767
$825$	−729.540			−0.884291
$826$	−427.751	−	427.751i	−0.517858	−	0.517858i
$827$		−	658.812i		−	0.796629i	−0.917249	−	0.398315i	$-0.869595\pi$
$827$		−	658.812i		−	0.796629i	0.917249	−	0.398315i	$-0.130405\pi$
$828$	29.1324			0.0351841
$829$			386.367i			0.466063i	0.972469	+	0.233032i	$0.0748646\pi$
$829$			386.367i			0.466063i	−0.972469	+	0.233032i	$0.925135\pi$
$830$	−506.881			−0.610700
$831$		−	248.898i		−	0.299516i
$832$	185.091	+	185.091i	0.222465	+	0.222465i
$833$	−291.676	−	291.676i	−0.350151	−	0.350151i
$834$	−231.267	+	231.267i	−0.277298	+	0.277298i
$835$		−	706.966i		−	0.846666i
$836$	467.883	−	467.883i	0.559669	−	0.559669i
$837$	−189.659			−0.226594
$838$	299.302	+	299.302i	0.357163	+	0.357163i
$839$	1009.98			1.20379			0.601897	−	0.798574i	$-0.294412\pi$
$839$	1009.98			1.20379			0.601897	+	0.798574i	$0.294412\pi$
$840$	256.335	+	256.335i	0.305161	+	0.305161i
$841$	487.512			0.579681
$842$	468.806			0.556776
$843$		−	1594.59i		−	1.89157i
$844$	209.775	−	209.775i	0.248548	−	0.248548i
$845$	−287.484	−	287.484i	−0.340218	−	0.340218i
$846$	−38.6960	+	38.6960i	−0.0457400	+	0.0457400i
$847$	253.466			0.299252
$848$	567.304			0.668991
$849$	−544.753			−0.641640
$850$			501.527i			0.590031i
$851$	−1305.24			−1.53378
$852$		−	439.813i		−	0.516212i
$853$		−	509.223i		−	0.596979i	−0.954413	−	0.298490i	$-0.903517\pi$
$853$		−	509.223i		−	0.596979i	0.954413	−	0.298490i	$-0.0964828\pi$
$854$	−472.362	−	472.362i	−0.553117	−	0.553117i
$855$	−39.3564	+	39.3564i	−0.0460309	+	0.0460309i
$856$	−311.837	+	311.837i	−0.364296	+	0.364296i
$857$	1058.82	−	1058.82i	1.23550	−	1.23550i	0.273674	−	0.961822i	$-0.411761\pi$
$857$	1058.82	−	1058.82i	1.23550	−	1.23550i	0.961822	−	0.273674i	$-0.0882390\pi$
$858$	−252.209			−0.293950
$859$	−223.494	−	223.494i	−0.260180	−	0.260180i	0.564947	−	0.825127i	$-0.308896\pi$
$859$	−223.494	−	223.494i	−0.260180	−	0.260180i	−0.825127	+	0.564947i	$0.808896\pi$
$860$	−200.811	+	200.811i	−0.233501	+	0.233501i
$861$	−2.56313	+	2.56313i	−0.00297692	+	0.00297692i
$862$	168.867	−	168.867i	0.195902	−	0.195902i
$863$	−294.944	−	294.944i	−0.341766	−	0.341766i	0.515265	−	0.857031i	$-0.327693\pi$
$863$	−294.944	−	294.944i	−0.341766	−	0.341766i	−0.857031	+	0.515265i	$0.827693\pi$
$864$	591.866			0.685031
$865$	−498.025	−	498.025i	−0.575752	−	0.575752i
$866$	−413.924	−	413.924i	−0.477972	−	0.477972i
$867$	54.4398	+	54.4398i	0.0627910	+	0.0627910i
$868$	39.8004	−	39.8004i	0.0458530	−	0.0458530i
$869$	−736.995			−0.848096
$870$	333.780	+	333.780i	0.383655	+	0.383655i
$871$			90.5631i			0.103976i
$872$	973.657	−	973.657i	1.11658	−	1.11658i
$873$	106.187			0.121634
$874$	−1126.13	−	1126.13i	−1.28848	−	1.28848i
$875$	408.371	−	408.371i	0.466709	−	0.466709i
$876$	354.057			0.404175
$877$	−439.490	−	439.490i	−0.501129	−	0.501129i	0.410659	−	0.911789i	$-0.365299\pi$
$877$	−439.490	−	439.490i	−0.501129	−	0.501129i	−0.911789	+	0.410659i	$0.865299\pi$
$878$	1175.25			1.33856
$879$	731.452	+	731.452i	0.832141	+	0.832141i
$880$		−	263.673i		−	0.299628i
$881$			423.372i			0.480558i	0.970704	+	0.240279i	$0.0772390\pi$
$881$			423.372i			0.480558i	−0.970704	+	0.240279i	$0.922761\pi$
$882$	16.3593	+	16.3593i	0.0185479	+	0.0185479i
$883$	−70.8268	−	70.8268i	−0.0802115	−	0.0802115i	0.665863	−	0.746074i	$-0.268064\pi$
$883$	−70.8268	−	70.8268i	−0.0802115	−	0.0802115i	−0.746074	+	0.665863i	$0.768064\pi$
$884$		−	106.269i		−	0.120214i
$885$			622.960i			0.703910i
$886$	−334.662	+	334.662i	−0.377723	+	0.377723i
$887$	−32.2743	−	32.2743i	−0.0363859	−	0.0363859i	0.688680	−	0.725066i	$-0.258191\pi$
$887$	−32.2743	−	32.2743i	−0.0363859	−	0.0363859i	−0.725066	+	0.688680i	$0.758191\pi$
$888$	1159.14			1.30533
$889$	622.935			0.700714
$890$	−338.852	+	338.852i	−0.380733	+	0.380733i
$891$	−797.763	+	797.763i	−0.895356	+	0.895356i
$892$	−62.8745			−0.0704871
$893$	−1833.63			−2.05333
$894$	159.002	−	159.002i	0.177854	−	0.177854i
$895$		−	393.667i		−	0.439851i
$896$	47.6700	−	47.6700i	0.0532032	−	0.0532032i
$897$		−	372.062i		−	0.414784i
$898$	772.038	+	772.038i	0.859731	+	0.859731i
$899$	188.204	−	188.204i	0.209349	−	0.209349i
$900$			17.2409i			0.0191565i
$901$	−933.857	−	933.857i	−1.03647	−	1.03647i
$902$	4.74311			0.00525843
$903$	784.558	−	784.558i	0.868835	−	0.868835i
$904$		−	18.2549i		−	0.0201934i
$905$	−76.3783	−	76.3783i	−0.0843960	−	0.0843960i
$906$	−536.248	+	536.248i	−0.591885	+	0.591885i
$907$	−184.683	+	184.683i	−0.203620	+	0.203620i	−0.801549	−	0.597929i	$-0.795990\pi$
$907$	−184.683	+	184.683i	−0.203620	+	0.203620i	0.597929	+	0.801549i	$0.295990\pi$
$908$	−8.37224	+	8.37224i	−0.00922052	+	0.00922052i
$909$		−	4.11545i		−	0.00452744i
$910$	59.0553	−	59.0553i	0.0648960	−	0.0648960i
$911$	611.053	+	611.053i	0.670749	+	0.670749i	0.957889	−	0.287139i	$-0.0927043\pi$
$911$	611.053	+	611.053i	0.670749	+	0.670749i	−0.287139	+	0.957889i	$0.592704\pi$
$912$	555.899	+	555.899i	0.609539	+	0.609539i
$913$	1123.08	+	1123.08i	1.23010	+	1.23010i
$914$	−538.198	+	538.198i	−0.588838	+	0.588838i
$915$			687.931i			0.751837i
$916$	−327.007	−	327.007i	−0.356994	−	0.356994i
$917$	−150.397	−	150.397i	−0.164010	−	0.164010i
$918$	512.334	+	512.334i	0.558098	+	0.558098i
$919$	−876.742	+	876.742i	−0.954018	+	0.954018i	−0.998988	−	0.0449707i	$-0.985681\pi$
$919$	−876.742	+	876.742i	−0.954018	+	0.954018i	0.0449707	+	0.998988i	$0.485681\pi$
$920$	699.769			0.760619
$921$	49.8317			0.0541061
$922$		−	319.183i		−	0.346186i
$923$	−367.968			−0.398665
$924$		−	312.789i		−	0.338516i
$925$		−	772.456i		−	0.835088i
$926$			190.348i			0.205560i
$927$	−6.50251	−	6.50251i	−0.00701457	−	0.00701457i
$928$	−587.327	+	587.327i	−0.632895	+	0.632895i
$929$	789.446	+	789.446i	0.849780	+	0.849780i	0.990105	−	0.140326i	$-0.0448149\pi$
$929$	789.446	+	789.446i	0.849780	+	0.849780i	−0.140326	+	0.990105i	$0.544815\pi$
$930$	94.5703			0.101688
$931$			775.190i			0.832643i
$932$			182.445i			0.195756i
$933$	35.4463	−	35.4463i	0.0379917	−	0.0379917i
$934$			571.893i			0.612305i
$935$	−434.040	+	434.040i	−0.464214	+	0.464214i
$936$			21.6452i			0.0231252i
$937$	−673.462	−	673.462i	−0.718742	−	0.718742i	0.249605	−	0.968348i	$-0.419699\pi$
$937$	−673.462	−	673.462i	−0.718742	−	0.718742i	−0.968348	+	0.249605i	$0.919699\pi$
$938$	183.248			0.195360
$939$	−366.408	−	366.408i	−0.390211	−	0.390211i
$940$	156.876	−	156.876i	0.166889	−	0.166889i
$941$	178.035	−	178.035i	0.189198	−	0.189198i	−0.606152	−	0.795349i	$-0.707287\pi$
$941$	178.035	−	178.035i	0.189198	−	0.189198i	0.795349	+	0.606152i	$0.207287\pi$
$942$	−504.494			−0.535557
$943$			6.99708i			0.00742002i
$944$	576.427			0.610622
$945$		−	349.009i		−	0.369321i
$946$	−1451.84			−1.53471
$947$	507.508	−	507.508i	0.535911	−	0.535911i	−0.386414	−	0.922325i	$-0.626286\pi$
$947$	507.508	−	507.508i	0.535911	−	0.535911i	0.922325	+	0.386414i	$0.126286\pi$
$948$			265.871i			0.280455i
$949$		−	296.220i		−	0.312140i
$950$	666.456	−	666.456i	0.701533	−	0.701533i
$951$			456.225i			0.479732i
$952$	−780.885			−0.820257
$953$	−859.033	−	859.033i	−0.901399	−	0.901399i	0.0941584	−	0.995557i	$-0.469984\pi$
$953$	−859.033	−	859.033i	−0.901399	−	0.901399i	−0.995557	+	0.0941584i	$0.969984\pi$
$954$	52.3773	+	52.3773i	0.0549029	+	0.0549029i
$955$	−454.975	+	454.975i	−0.476414	+	0.476414i
$956$			267.025i			0.279315i
$957$		−	1479.09i		−	1.54555i
$958$	146.913	−	146.913i	0.153353	−	0.153353i
$959$	−293.584			−0.306136
$960$	−545.436			−0.568162
$961$			907.676i			0.944512i
$962$		−	267.046i		−	0.277594i
$963$	−32.0074			−0.0332371
$964$	300.827	−	300.827i	0.312061	−	0.312061i
$965$	−295.159	+	295.159i	−0.305864	+	0.305864i
$966$	−752.840			−0.779338
$967$	−543.137	+	543.137i	−0.561672	+	0.561672i	−0.929782	−	0.368110i	$-0.880005\pi$
$967$	−543.137	+	543.137i	−0.561672	+	0.561672i	0.368110	+	0.929782i	$0.380005\pi$
$968$	−307.241	+	307.241i	−0.317398	+	0.317398i
$969$		−	1830.17i		−	1.88872i
$970$	702.356			0.724078
$971$	804.709	−	804.709i	0.828742	−	0.828742i	−0.158601	−	0.987343i	$-0.550698\pi$
$971$	804.709	−	804.709i	0.828742	−	0.828742i	0.987343	+	0.158601i	$0.0506982\pi$
$972$	36.5525	+	36.5525i	0.0376055	+	0.0376055i
$973$	−239.964	+	239.964i	−0.246622	+	0.246622i
$974$	740.172	+	740.172i	0.759931	+	0.759931i
$975$	220.190			0.225836
$976$	636.545			0.652197
$977$	−935.588	+	935.588i	−0.957613	+	0.957613i	−0.999137	−	0.0415248i	$-0.986778\pi$
$977$	−935.588	+	935.588i	−0.957613	+	0.957613i	0.0415248	+	0.999137i	$0.486778\pi$
$978$	1068.27			1.09230
$979$	1501.57			1.53377
$980$	−66.3214	−	66.3214i	−0.0676749	−	0.0676749i
$981$	99.9373			0.101873
$982$	628.353	+	628.353i	0.639871	+	0.639871i
$983$	−91.3371	−	91.3371i	−0.0929167	−	0.0929167i	0.659121	−	0.752037i	$-0.270929\pi$
$983$	−91.3371	−	91.3371i	−0.0929167	−	0.0929167i	−0.752037	+	0.659121i	$0.770929\pi$
$984$		−	6.21384i		−	0.00631488i
$985$	−357.591	−	380.330i	−0.363036	−	0.386122i
$986$	−1016.81			−1.03125
$987$	−612.907	+	612.907i	−0.620980	+	0.620980i
$988$	−141.217	+	141.217i	−0.142932	+	0.142932i
$989$		−	2141.77i		−	2.16559i
$990$	24.3440	−	24.3440i	0.0245899	−	0.0245899i
$991$			566.300i			0.571443i	0.958313	+	0.285722i	$0.0922332\pi$
$991$			566.300i			0.571443i	−0.958313	+	0.285722i	$0.907767\pi$
$992$			166.408i			0.167750i
$993$	72.9491	+	72.9491i	0.0734633	+	0.0734633i
$994$			744.556i			0.749051i
$995$			231.195i			0.232357i
$996$	405.150	−	405.150i	0.406778	−	0.406778i
$997$	691.752	+	691.752i	0.693834	+	0.693834i	0.963073	−	0.269240i	$-0.0867723\pi$
$997$	691.752	+	691.752i	0.693834	+	0.693834i	−0.269240	+	0.963073i	$0.586772\pi$
$998$	−947.300	+	947.300i	−0.949199	+	0.949199i
$999$	−789.101	−	789.101i	−0.789891	−	0.789891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.c.a.14.10	✓	64
197.183	odd	4	inner	197.3.c.a.183.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.c.a.14.10	✓	64	1.1	even	1	trivial
197.3.c.a.183.10	yes	64	197.183	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) \) 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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Representations

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Database

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