LMFDB - Embedded newform 210.3.e.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(71,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("210.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.e (of order $2$, degree $1$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 $ x^16 - 8x^15 + 34x^14 - 80x^13 + 97x^12 - 80x^11 + 498x^10 - 3288x^9 + 11844x^8 - 29592x^7 + 40338x^6 - 58320x^5 + 636417x^4 - 4723920x^3 + 18068994x^2 - 38263752*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.3
Root			$1.86110 - 2.35293i$ of defining polynomial
Character	$\chi$	$=$	210.71
Dual form			210.3.e.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.86110 + 2.35293i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.32755 + 2.63200i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-2.07259 - 8.75810i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.86110 + 2.35293i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.32755 + 2.63200i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-2.07259 - 8.75810i) q^{9} -3.16228 q^{10} +19.0319i q^{11} +(3.72221 - 4.70587i) q^{12} -1.55479 q^{13} -3.74166i q^{14} +(5.26132 + 4.16155i) q^{15} +4.00000 q^{16} +28.9019i q^{17} +(-12.3858 + 2.93108i) q^{18} +23.3574 q^{19} +4.47214i q^{20} +(-4.92402 + 6.22527i) q^{21} +26.9152 q^{22} +23.7695i q^{23} +(-6.65510 - 5.26400i) q^{24} -5.00000 q^{25} +2.19880i q^{26} +(24.4645 + 11.4231i) q^{27} -5.29150 q^{28} +18.0074i q^{29} +(5.88533 - 7.44063i) q^{30} +7.88473 q^{31} -5.65685i q^{32} +(-44.7809 - 35.4204i) q^{33} +40.8735 q^{34} -5.91608i q^{35} +(4.14517 + 17.5162i) q^{36} -20.5218 q^{37} -33.0324i q^{38} +(2.89362 - 3.65831i) q^{39} +6.32456 q^{40} -50.8988i q^{41} +(8.80387 + 6.96361i) q^{42} -31.2503 q^{43} -38.0639i q^{44} +(-19.5837 + 4.63444i) q^{45} +33.6151 q^{46} -15.7642i q^{47} +(-7.44442 + 9.41173i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(-68.0043 - 53.7895i) q^{51} +3.10957 q^{52} +78.7951i q^{53} +(16.1547 - 34.5981i) q^{54} +42.5567 q^{55} +7.48331i q^{56} +(-43.4706 + 54.9585i) q^{57} +25.4663 q^{58} -89.1948i q^{59} +(-10.5226 - 8.32311i) q^{60} +56.4152 q^{61} -11.1507i q^{62} +(-5.48355 - 23.1718i) q^{63} -8.00000 q^{64} +3.47661i q^{65} +(-50.0920 + 63.3297i) q^{66} +56.2048 q^{67} -57.8038i q^{68} +(-55.9280 - 44.2375i) q^{69} -8.36660 q^{70} +28.4101i q^{71} +(24.7717 - 5.86216i) q^{72} -120.253 q^{73} +29.0222i q^{74} +(9.30552 - 11.7647i) q^{75} -46.7149 q^{76} +50.3538i q^{77} +(-5.17363 - 4.09220i) q^{78} -72.1123 q^{79} -8.94427i q^{80} +(-72.4088 + 36.3038i) q^{81} -71.9818 q^{82} +104.179i q^{83} +(9.84804 - 12.4505i) q^{84} +64.6267 q^{85} +44.1946i q^{86} +(-42.3702 - 33.5136i) q^{87} -53.8304 q^{88} -36.3947i q^{89} +(6.55409 + 27.6956i) q^{90} -4.11358 q^{91} -47.5389i q^{92} +(-14.6743 + 18.5522i) q^{93} -22.2940 q^{94} -52.2288i q^{95} +(13.3102 + 10.5280i) q^{96} -57.1642 q^{97} -9.89949i q^{98} +(166.684 - 39.4453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−1.86110	+	2.35293i	−0.620368	+	0.784311i
$3$	−1.86110	+	2.35293i	−0.620368	+	0.784311i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	3.32755	+	2.63200i	0.554592	+	0.438666i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			2.82843i			0.353553i
$9$	−2.07259	−	8.75810i	−0.230287	−	0.973123i
$10$	−3.16228			−0.316228
$11$			19.0319i			1.73018i	0.501620	+	0.865088i	$0.332737\pi$
$11$			19.0319i			1.73018i	−0.501620	+	0.865088i	$0.667263\pi$
$12$	3.72221	−	4.70587i	0.310184	−	0.392155i
$13$	−1.55479			−0.119599			−0.0597995	−	0.998210i	$-0.519046\pi$
$13$	−1.55479			−0.119599			−0.0597995	+	0.998210i	$0.519046\pi$
$14$		−	3.74166i		−	0.267261i
$15$	5.26132	+	4.16155i	0.350755	+	0.277437i
$16$	4.00000			0.250000
$17$			28.9019i			1.70011i	0.526692	+	0.850056i	$0.323432\pi$
$17$			28.9019i			1.70011i	−0.526692	+	0.850056i	$0.676568\pi$
$18$	−12.3858	+	2.93108i	−0.688102	+	0.162838i
$19$	23.3574			1.22934			0.614669	−	0.788785i	$-0.289289\pi$
$19$	23.3574			1.22934			0.614669	+	0.788785i	$0.289289\pi$
$20$			4.47214i			0.223607i
$21$	−4.92402	+	6.22527i	−0.234477	+	0.296442i
$22$	26.9152			1.22342
$23$			23.7695i			1.03346i	0.856150	+	0.516728i	$0.172850\pi$
$23$			23.7695i			1.03346i	−0.856150	+	0.516728i	$0.827150\pi$
$24$	−6.65510	−	5.26400i	−0.277296	−	0.219333i
$25$	−5.00000			−0.200000
$26$			2.19880i			0.0845693i
$27$	24.4645	+	11.4231i	0.906094	+	0.423077i
$28$	−5.29150			−0.188982
$29$			18.0074i			0.620945i	0.950582	+	0.310472i	$0.100487\pi$
$29$			18.0074i			0.620945i	−0.950582	+	0.310472i	$0.899513\pi$
$30$	5.88533	−	7.44063i	0.196178	−	0.248021i
$31$	7.88473			0.254346			0.127173	−	0.991881i	$-0.459410\pi$
$31$	7.88473			0.254346			0.127173	+	0.991881i	$0.459410\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−44.7809	−	35.4204i	−1.35700	−	1.07335i
$34$	40.8735			1.20216
$35$		−	5.91608i		−	0.169031i
$36$	4.14517	+	17.5162i	0.115144	+	0.486561i
$37$	−20.5218			−0.554642			−0.277321	−	0.960777i	$-0.589447\pi$
$37$	−20.5218			−0.554642			−0.277321	+	0.960777i	$0.589447\pi$
$38$		−	33.0324i		−	0.869274i
$39$	2.89362	−	3.65831i	0.0741954	−	0.0938028i
$40$	6.32456			0.158114
$41$		−	50.8988i		−	1.24143i	−0.784034	−	0.620717i	$-0.786841\pi$
$41$		−	50.8988i		−	1.24143i	0.784034	−	0.620717i	$-0.213159\pi$
$42$	8.80387	+	6.96361i	0.209616	+	0.165800i
$43$	−31.2503			−0.726752			−0.363376	−	0.931643i	$-0.618376\pi$
$43$	−31.2503			−0.726752			−0.363376	+	0.931643i	$0.618376\pi$
$44$		−	38.0639i		−	0.865088i
$45$	−19.5837	+	4.63444i	−0.435194	+	0.102988i
$46$	33.6151			0.730763
$47$		−	15.7642i		−	0.335409i	−0.985837	−	0.167704i	$-0.946365\pi$
$47$		−	15.7642i		−	0.335409i	0.985837	−	0.167704i	$-0.0536354\pi$
$48$	−7.44442	+	9.41173i	−0.155092	+	0.196078i
$49$	7.00000			0.142857
$50$			7.07107i			0.141421i
$51$	−68.0043	−	53.7895i	−1.33342	−	1.05470i
$52$	3.10957			0.0597995
$53$			78.7951i			1.48670i	0.668903	+	0.743350i	$0.266764\pi$
$53$			78.7951i			1.48670i	−0.668903	+	0.743350i	$0.733236\pi$
$54$	16.1547	−	34.5981i	0.299161	−	0.640705i
$55$	42.5567			0.773758
$56$			7.48331i			0.133631i
$57$	−43.4706	+	54.9585i	−0.762642	+	0.964184i
$58$	25.4663			0.439074
$59$		−	89.1948i		−	1.51178i	−0.654700	−	0.755889i	$-0.727205\pi$
$59$		−	89.1948i		−	1.51178i	0.654700	−	0.755889i	$-0.272795\pi$
$60$	−10.5226	−	8.32311i	−0.175377	−	0.138718i
$61$	56.4152			0.924840			0.462420	−	0.886661i	$-0.346981\pi$
$61$	56.4152			0.924840			0.462420	+	0.886661i	$0.346981\pi$
$62$		−	11.1507i		−	0.179850i
$63$	−5.48355	−	23.1718i	−0.0870404	−	0.367806i
$64$	−8.00000			−0.125000
$65$			3.47661i			0.0534863i
$66$	−50.0920	+	63.3297i	−0.758970	+	0.959541i
$67$	56.2048			0.838878			0.419439	−	0.907784i	$-0.362227\pi$
$67$	56.2048			0.838878			0.419439	+	0.907784i	$0.362227\pi$
$68$		−	57.8038i		−	0.850056i
$69$	−55.9280	−	44.2375i	−0.810550	−	0.641123i
$70$	−8.36660			−0.119523
$71$			28.4101i			0.400143i	0.979781	+	0.200071i	$0.0641174\pi$
$71$			28.4101i			0.400143i	−0.979781	+	0.200071i	$0.935883\pi$
$72$	24.7717	−	5.86216i	0.344051	−	0.0814188i
$73$	−120.253			−1.64730			−0.823648	−	0.567102i	$-0.808065\pi$
$73$	−120.253			−1.64730			−0.823648	+	0.567102i	$0.808065\pi$
$74$			29.0222i			0.392191i
$75$	9.30552	−	11.7647i	0.124074	−	0.156862i
$76$	−46.7149			−0.614669
$77$			50.3538i			0.653945i
$78$	−5.17363	−	4.09220i	−0.0663286	−	0.0524641i
$79$	−72.1123			−0.912814			−0.456407	−	0.889771i	$-0.650864\pi$
$79$	−72.1123			−0.912814			−0.456407	+	0.889771i	$0.650864\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−72.4088	+	36.3038i	−0.893936	+	0.448196i
$82$	−71.9818			−0.877827
$83$			104.179i			1.25517i	0.778547	+	0.627587i	$0.215957\pi$
$83$			104.179i			1.25517i	−0.778547	+	0.627587i	$0.784043\pi$
$84$	9.84804	−	12.4505i	0.117239	−	0.148221i
$85$	64.6267			0.760314
$86$			44.1946i			0.513891i
$87$	−42.3702	−	33.5136i	−0.487014	−	0.385214i
$88$	−53.8304			−0.611709
$89$		−	36.3947i		−	0.408929i	−0.978874	−	0.204465i	$-0.934455\pi$
$89$		−	36.3947i		−	0.408929i	0.978874	−	0.204465i	$-0.0655453\pi$
$90$	6.55409	+	27.6956i	0.0728232	+	0.307728i
$91$	−4.11358			−0.0452042
$92$		−	47.5389i		−	0.516728i
$93$	−14.6743	+	18.5522i	−0.157788	+	0.199486i
$94$	−22.2940			−0.237170
$95$		−	52.2288i		−	0.549777i
$96$	13.3102	+	10.5280i	0.138648	+	0.109667i
$97$	−57.1642			−0.589321			−0.294661	−	0.955602i	$-0.595207\pi$
$97$	−57.1642			−0.589321			−0.294661	+	0.955602i	$0.595207\pi$
$98$		−	9.89949i		−	0.101015i
$99$	166.684	−	39.4453i	1.68367	−	0.398437i
$100$	10.0000			0.100000
$101$		−	144.925i		−	1.43490i	−0.696610	−	0.717450i	$-0.745309\pi$
$101$		−	144.925i		−	1.43490i	0.696610	−	0.717450i	$-0.254691\pi$
$102$	−76.0698	+	96.1726i	−0.745782	+	0.942868i
$103$	173.742			1.68681			0.843407	−	0.537276i	$-0.180547\pi$
$103$	173.742			1.68681			0.843407	+	0.537276i	$0.180547\pi$
$104$		−	4.39760i		−	0.0422846i
$105$	13.9201	+	11.0104i	0.132573	+	0.104861i
$106$	111.433			1.05126
$107$		−	93.7622i		−	0.876282i	−0.898906	−	0.438141i	$-0.855637\pi$
$107$		−	93.7622i		−	0.876282i	0.898906	−	0.438141i	$-0.144363\pi$
$108$	−48.9291	−	22.8462i	−0.453047	−	0.211539i
$109$	196.881			1.80625			0.903125	−	0.429378i	$-0.141267\pi$
$109$	196.881			1.80625			0.903125	+	0.429378i	$0.141267\pi$
$110$		−	60.1843i		−	0.547130i
$111$	38.1931	−	48.2863i	0.344082	−	0.435012i
$112$	10.5830			0.0944911
$113$			114.317i			1.01166i	0.862634	+	0.505829i	$0.168813\pi$
$113$			114.317i			1.01166i	−0.862634	+	0.505829i	$0.831187\pi$
$114$	77.7230	+	61.4767i	0.681781	+	0.539270i
$115$	53.1502			0.462175
$116$		−	36.0148i		−	0.310472i
$117$	3.22243	+	13.6170i	0.0275421	+	0.116384i
$118$	−126.141			−1.06899
$119$			76.4673i			0.642582i
$120$	−11.7707	+	14.8813i	−0.0980888	+	0.124010i
$121$	−241.214			−1.99351
$122$		−	79.7832i		−	0.653960i
$123$	119.762	+	94.7280i	0.973671	+	0.770146i
$124$	−15.7695			−0.127173
$125$			11.1803i			0.0894427i
$126$	−32.7698	+	7.75490i	−0.260078	+	0.0615469i
$127$	14.2601			0.112284			0.0561422	−	0.998423i	$-0.482120\pi$
$127$	14.2601			0.112284			0.0561422	+	0.998423i	$0.482120\pi$
$128$			11.3137i			0.0883883i
$129$	58.1601	−	73.5299i	0.450853	−	0.569999i
$130$	4.91667			0.0378205
$131$			86.1081i			0.657313i	0.944449	+	0.328657i	$0.106596\pi$
$131$			86.1081i			0.657313i	−0.944449	+	0.328657i	$0.893404\pi$
$132$	89.5617	+	70.8408i	0.678498	+	0.536673i
$133$	61.7980			0.464646
$134$		−	79.4856i		−	0.593176i
$135$	25.5428	−	54.7043i	0.189206	−	0.405217i
$136$	−81.7470			−0.601081
$137$		−	87.4123i		−	0.638046i	−0.947747	−	0.319023i	$-0.896645\pi$
$137$		−	87.4123i		−	0.638046i	0.947747	−	0.319023i	$-0.103355\pi$
$138$	−62.5612	+	79.0941i	−0.453342	+	0.573146i
$139$	188.559			1.35654			0.678269	−	0.734814i	$-0.262730\pi$
$139$	188.559			1.35654			0.678269	+	0.734814i	$0.262730\pi$
$140$			11.8322i			0.0845154i
$141$	37.0921	+	29.3388i	0.263065	+	0.208077i
$142$	40.1780			0.282944
$143$		−	29.5906i		−	0.206927i
$144$	−8.29034	−	35.0324i	−0.0575718	−	0.243281i
$145$	40.2658			0.277695
$146$			170.063i			1.16481i
$147$	−13.0277	+	16.4705i	−0.0886240	+	0.112044i
$148$	41.0435			0.277321
$149$			120.358i			0.807775i	0.914809	+	0.403888i	$0.132341\pi$
$149$			120.358i			0.807775i	−0.914809	+	0.403888i	$0.867659\pi$
$150$	−16.6377	−	13.1600i	−0.110918	−	0.0877333i
$151$	−41.6199			−0.275628			−0.137814	−	0.990458i	$-0.544008\pi$
$151$	−41.6199			−0.275628			−0.137814	+	0.990458i	$0.544008\pi$
$152$			66.0648i			0.434637i
$153$	253.126	−	59.9017i	1.65442	−	0.391514i
$154$	71.2110			0.462409
$155$		−	17.6308i		−	0.113747i
$156$	−5.78724	+	7.31662i	−0.0370977	+	0.0469014i
$157$	−58.4437			−0.372253			−0.186126	−	0.982526i	$-0.559593\pi$
$157$	−58.4437			−0.372253			−0.186126	+	0.982526i	$0.559593\pi$
$158$			101.982i			0.645457i
$159$	−185.400	−	146.646i	−1.16604	−	0.922301i
$160$	−12.6491			−0.0790569
$161$			62.8881i			0.390609i
$162$	51.3414	+	102.401i	0.316922	+	0.632108i
$163$	−79.4862			−0.487646			−0.243823	−	0.969820i	$-0.578402\pi$
$163$	−79.4862			−0.487646			−0.243823	+	0.969820i	$0.578402\pi$
$164$			101.798i			0.620717i
$165$	−79.2024	+	100.133i	−0.480015	+	0.606867i
$166$	147.332			0.887542
$167$		−	72.1686i		−	0.432147i	−0.976377	−	0.216074i	$-0.930675\pi$
$167$		−	72.1686i		−	0.432147i	0.976377	−	0.216074i	$-0.0693251\pi$
$168$	−17.6077	−	13.9272i	−0.104808	−	0.0829002i
$169$	−166.583			−0.985696
$170$		−	91.3959i		−	0.537623i
$171$	−48.4103	−	204.567i	−0.283101	−	1.19630i
$172$	62.5006			0.363376
$173$			235.654i			1.36216i	0.732209	+	0.681080i	$0.238489\pi$
$173$			235.654i			1.36216i	−0.732209	+	0.681080i	$0.761511\pi$
$174$	−47.3955	+	59.9205i	−0.272388	+	0.344371i
$175$	−13.2288			−0.0755929
$176$			76.1277i			0.432544i
$177$	209.869	+	166.001i	1.18570	+	0.937858i
$178$	−51.4699			−0.289157
$179$		−	132.607i		−	0.740823i	−0.928868	−	0.370411i	$-0.879217\pi$
$179$		−	132.607i		−	0.740823i	0.928868	−	0.370411i	$-0.120783\pi$
$180$	39.1674	−	9.26888i	0.217597	−	0.0514938i
$181$	47.9269			0.264790			0.132395	−	0.991197i	$-0.457733\pi$
$181$	47.9269			0.264790			0.132395	+	0.991197i	$0.457733\pi$
$182$			5.81748i			0.0319642i
$183$	−104.995	+	132.741i	−0.573741	+	0.725362i
$184$	−67.2302			−0.365382
$185$			45.8881i			0.248044i
$186$	26.2368	+	20.7526i	0.141058	+	0.111573i
$187$	−550.059			−2.94149
$188$			31.5284i			0.167704i
$189$	64.7271	+	30.2226i	0.342471	+	0.159908i
$190$	−73.8627			−0.388751
$191$			183.885i			0.962750i	0.876515	+	0.481375i	$0.159863\pi$
$191$			183.885i			0.962750i	−0.876515	+	0.481375i	$0.840137\pi$
$192$	14.8888	−	18.8235i	0.0775460	−	0.0980389i
$193$	107.757			0.558325			0.279162	−	0.960244i	$-0.409943\pi$
$193$	107.757			0.558325			0.279162	+	0.960244i	$0.409943\pi$
$194$			80.8423i			0.416713i
$195$	−8.18023	−	6.47033i	−0.0419499	−	0.0331812i
$196$	−14.0000			−0.0714286
$197$		−	297.246i		−	1.50886i	−0.656378	−	0.754432i	$-0.727912\pi$
$197$		−	297.246i		−	1.50886i	0.656378	−	0.754432i	$-0.272088\pi$
$198$	−55.7841	−	235.726i	−0.281738	−	1.19054i
$199$	246.886			1.24064			0.620318	−	0.784351i	$-0.287004\pi$
$199$	246.886			1.24064			0.620318	+	0.784351i	$0.287004\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	−104.603	+	132.246i	−0.520413	+	0.657941i
$202$	−204.955			−1.01463
$203$			47.6431i			0.234695i
$204$	136.009	+	107.579i	0.666709	+	0.527348i
$205$	−113.813			−0.555187
$206$		−	245.708i		−	1.19276i
$207$	208.176	−	49.2643i	1.00568	−	0.237992i
$208$	−6.21915			−0.0298997
$209$			444.537i			2.12697i
$210$	15.5711	−	19.6860i	0.0741482	−	0.0937431i
$211$	292.191			1.38479			0.692396	−	0.721517i	$-0.256555\pi$
$211$	292.191			1.38479			0.692396	+	0.721517i	$0.256555\pi$
$212$		−	157.590i		−	0.743350i
$213$	−66.8471	−	52.8742i	−0.313836	−	0.248236i
$214$	−132.600			−0.619625
$215$			69.8778i			0.325013i
$216$	−32.3094	+	69.1961i	−0.149580	+	0.320352i
$217$	20.8610			0.0961338
$218$		−	278.432i		−	1.27721i
$219$	223.802	−	282.946i	1.02193	−	1.29199i
$220$	−85.1134			−0.386879
$221$		−	44.9363i		−	0.203332i
$222$	−68.2872	−	54.0133i	−0.307600	−	0.243303i
$223$	−226.770			−1.01691			−0.508453	−	0.861090i	$-0.669782\pi$
$223$	−226.770			−1.01691			−0.508453	+	0.861090i	$0.669782\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	10.3629	+	43.7905i	0.0460575	+	0.194625i
$226$	161.669			0.715350
$227$		−	293.354i		−	1.29231i	−0.763206	−	0.646155i	$-0.776376\pi$
$227$		−	293.354i		−	1.29231i	0.763206	−	0.646155i	$-0.223624\pi$
$228$	86.9412	−	109.917i	0.381321	−	0.482092i
$229$	−183.861			−0.802889			−0.401444	−	0.915883i	$-0.631492\pi$
$229$	−183.861			−0.802889			−0.401444	+	0.915883i	$0.631492\pi$
$230$		−	75.1657i		−	0.326807i
$231$	−118.479	−	93.7136i	−0.512896	−	0.405686i
$232$	−50.9326			−0.219537
$233$		−	338.163i		−	1.45134i	−0.688042	−	0.725671i	$-0.741530\pi$
$233$		−	338.163i		−	1.45134i	0.688042	−	0.725671i	$-0.258470\pi$
$234$	19.2573	−	4.55720i	0.0822963	−	0.0194752i
$235$	−35.2499			−0.149999
$236$			178.390i			0.755889i
$237$	134.208	−	169.675i	0.566280	−	0.715930i
$238$	108.141			0.454374
$239$			295.300i			1.23557i	0.786349	+	0.617783i	$0.211969\pi$
$239$			295.300i			1.23557i	−0.786349	+	0.617783i	$0.788031\pi$
$240$	21.0453	+	16.6462i	0.0876886	+	0.0693592i
$241$	−224.922			−0.933286			−0.466643	−	0.884446i	$-0.654537\pi$
$241$	−224.922			−0.933286			−0.466643	+	0.884446i	$0.654537\pi$
$242$			341.129i			1.40962i
$243$	49.3398	−	237.938i	0.203044	−	0.979170i
$244$	−112.830			−0.462420
$245$		−	15.6525i		−	0.0638877i
$246$	133.966	−	169.368i	0.544576	−	0.688489i
$247$	−36.3158			−0.147028
$248$			22.3014i			0.0899250i
$249$	−245.127	−	193.889i	−0.984446	−	0.778670i
$250$	15.8114			0.0632456
$251$		−	26.3337i		−	0.104915i	−0.998623	−	0.0524575i	$-0.983295\pi$
$251$		−	26.3337i		−	0.104915i	0.998623	−	0.0524575i	$-0.0167054\pi$
$252$	10.9671	+	46.3435i	0.0435202	+	0.183903i
$253$	−452.379			−1.78806
$254$		−	20.1668i		−	0.0793970i
$255$	−120.277	+	152.062i	−0.471674	+	0.596322i
$256$	16.0000			0.0625000
$257$		−	129.147i		−	0.502518i	−0.967920	−	0.251259i	$-0.919155\pi$
$257$		−	129.147i		−	0.502518i	0.967920	−	0.251259i	$-0.0808447\pi$
$258$	−103.987	−	82.2508i	−0.403050	−	0.318801i
$259$	−54.2955			−0.209635
$260$		−	6.95322i		−	0.0267431i
$261$	157.711	−	37.3219i	0.604256	−	0.142996i
$262$	121.775			0.464791
$263$			234.149i			0.890301i	0.895456	+	0.445150i	$0.146850\pi$
$263$			234.149i			0.890301i	−0.895456	+	0.445150i	$0.853150\pi$
$264$	100.184	−	126.659i	0.379485	−	0.479770i
$265$	176.191			0.664873
$266$		−	87.3955i		−	0.328555i
$267$	85.6343	+	67.7343i	0.320728	+	0.253686i
$268$	−112.410			−0.419439
$269$			109.020i			0.405280i	0.979253	+	0.202640i	$0.0649522\pi$
$269$			109.020i			0.405280i	−0.979253	+	0.202640i	$0.935048\pi$
$270$	−77.3636	−	36.1230i	−0.286532	−	0.133789i
$271$	204.213			0.753554			0.376777	−	0.926304i	$-0.377032\pi$
$271$	204.213			0.753554			0.376777	+	0.926304i	$0.377032\pi$
$272$			115.608i			0.425028i
$273$	7.65580	−	9.67898i	0.0280432	−	0.0354541i
$274$	−123.620			−0.451167
$275$		−	95.1597i		−	0.346035i
$276$	111.856	+	88.4749i	0.405275	+	0.320561i
$277$	343.561			1.24029			0.620146	−	0.784486i	$-0.287073\pi$
$277$	343.561			1.24029			0.620146	+	0.784486i	$0.287073\pi$
$278$		−	266.662i		−	0.959217i
$279$	−16.3418	−	69.0553i	−0.0585727	−	0.247510i
$280$	16.7332			0.0597614
$281$		−	402.006i		−	1.43063i	−0.698804	−	0.715313i	$-0.746284\pi$
$281$		−	402.006i		−	1.43063i	0.698804	−	0.715313i	$-0.253716\pi$
$282$	41.4914	−	52.4562i	0.147133	−	0.186015i
$283$	290.257			1.02564			0.512821	−	0.858496i	$-0.328601\pi$
$283$	290.257			1.02564			0.512821	+	0.858496i	$0.328601\pi$
$284$		−	56.8203i		−	0.200071i
$285$	122.891	+	97.2032i	0.431196	+	0.341064i
$286$	−41.8474			−0.146320
$287$		−	134.666i		−	0.469218i
$288$	−49.5433	+	11.7243i	−0.172025	+	0.0407094i
$289$	−546.321			−1.89038
$290$		−	56.9444i		−	0.196360i
$291$	106.388	−	134.503i	0.365596	−	0.462211i
$292$	240.505			0.823648
$293$		−	443.480i		−	1.51358i	−0.653655	−	0.756792i	$-0.726765\pi$
$293$		−	443.480i		−	1.51358i	0.653655	−	0.756792i	$-0.273235\pi$
$294$	23.2928	+	18.4240i	0.0792274	+	0.0626666i
$295$	−199.446			−0.676087
$296$		−	58.0443i		−	0.196096i
$297$	−217.403	+	465.607i	−0.731998	+	1.56770i
$298$	170.213			0.571183
$299$		−	36.9565i		−	0.123600i
$300$	−18.6110	+	23.5293i	−0.0620368	+	0.0784311i
$301$	−82.6806			−0.274686
$302$			58.8594i			0.194899i
$303$	340.999	+	269.720i	1.12541	+	0.890166i
$304$	93.4297			0.307335
$305$		−	126.148i		−	0.413601i
$306$	−84.7138	−	357.974i	−0.276842	−	1.16985i
$307$	37.5506			0.122315			0.0611574	−	0.998128i	$-0.480521\pi$
$307$	37.5506			0.122315			0.0611574	+	0.998128i	$0.480521\pi$
$308$		−	100.708i		−	0.326972i
$309$	−323.351	+	408.803i	−1.04644	+	1.32299i
$310$	−24.9337			−0.0804313
$311$			133.398i			0.428933i	0.976731	+	0.214467i	$0.0688013\pi$
$311$			133.398i			0.428933i	−0.976731	+	0.214467i	$0.931199\pi$
$312$	10.3473	+	8.18439i	0.0331643	+	0.0262320i
$313$	220.130			0.703290			0.351645	−	0.936133i	$-0.385622\pi$
$313$	220.130			0.703290			0.351645	+	0.936133i	$0.385622\pi$
$314$			82.6518i			0.263222i
$315$	−51.8136	+	12.2616i	−0.164488	+	0.0389257i
$316$	144.225			0.456407
$317$			328.688i			1.03687i	0.855117	+	0.518435i	$0.173485\pi$
$317$			328.688i			1.03687i	−0.855117	+	0.518435i	$0.826515\pi$
$318$	−207.389	+	262.195i	−0.652165	+	0.824511i
$319$	−342.716			−1.07434
$320$			17.8885i			0.0559017i
$321$	220.616	+	174.501i	0.687278	+	0.543617i
$322$	88.9372			0.276203
$323$			675.075i			2.09001i
$324$	144.818	−	72.6077i	0.446968	−	0.224098i
$325$	7.77393			0.0239198
$326$			112.411i			0.344817i
$327$	−366.416	+	463.248i	−1.12054	+	1.41666i
$328$	143.964			0.438914
$329$		−	41.7082i		−	0.126773i
$330$	141.610	+	112.009i	0.429120	+	0.339422i
$331$	−440.198			−1.32990			−0.664952	−	0.746886i	$-0.731548\pi$
$331$	−440.198			−1.32990			−0.664952	+	0.746886i	$0.731548\pi$
$332$		−	208.359i		−	0.627587i
$333$	42.5331	+	179.732i	0.127727	+	0.539735i
$334$	−102.062			−0.305574
$335$		−	125.678i		−	0.375158i
$336$	−19.6961	+	24.9011i	−0.0586193	+	0.0741104i
$337$	−136.800			−0.405934			−0.202967	−	0.979186i	$-0.565058\pi$
$337$	−136.800			−0.405934			−0.202967	+	0.979186i	$0.565058\pi$
$338$			235.583i			0.696992i
$339$	−268.981	−	212.756i	−0.793454	−	0.627600i
$340$	−129.253			−0.380157
$341$			150.062i			0.440064i
$342$	−289.301	+	68.4625i	−0.845910	+	0.200183i
$343$	18.5203			0.0539949
$344$		−	88.3892i		−	0.256945i
$345$	−98.9180	+	125.059i	−0.286719	+	0.362489i
$346$	333.265			0.963192
$347$		−	101.080i		−	0.291296i	−0.989336	−	0.145648i	$-0.953473\pi$
$347$		−	101.080i		−	0.291296i	0.989336	−	0.145648i	$-0.0465266\pi$
$348$	84.7404	+	67.0273i	0.243507	+	0.192607i
$349$	66.6889			0.191086			0.0955428	−	0.995425i	$-0.469541\pi$
$349$	66.6889			0.191086			0.0955428	+	0.995425i	$0.469541\pi$
$350$			18.7083i			0.0534522i
$351$	−38.0371	−	17.7605i	−0.108368	−	0.0505996i
$352$	107.661			0.305855
$353$		−	163.078i		−	0.461976i	−0.972957	−	0.230988i	$-0.925804\pi$
$353$		−	163.078i		−	0.461976i	0.972957	−	0.230988i	$-0.0741958\pi$
$354$	234.761	−	296.800i	0.663166	−	0.838419i
$355$	63.5270			0.178949
$356$			72.7894i			0.204465i
$357$	−179.922	−	142.314i	−0.503984	−	0.398637i
$358$	−187.535			−0.523841
$359$			316.890i			0.882702i	0.897334	+	0.441351i	$0.145501\pi$
$359$			316.890i			0.882702i	−0.897334	+	0.441351i	$0.854499\pi$
$360$	−13.1082	−	55.3911i	−0.0364116	−	0.153864i
$361$	184.570			0.511273
$362$		−	67.7789i		−	0.187235i
$363$	448.925	−	567.561i	1.23671	−	1.56353i
$364$	8.22716			0.0226021
$365$			268.893i			0.736693i
$366$	187.724	+	148.485i	0.512908	+	0.405696i
$367$	492.889			1.34302			0.671511	−	0.740994i	$-0.265646\pi$
$367$	492.889			1.34302			0.671511	+	0.740994i	$0.265646\pi$
$368$			95.0779i			0.258364i
$369$	−445.777	+	105.492i	−1.20807	+	0.285887i
$370$	64.8955			0.175393
$371$			208.472i			0.561920i
$372$	29.3486	−	37.1045i	0.0788941	−	0.0997432i
$373$	614.112			1.64641			0.823207	−	0.567742i	$-0.192183\pi$
$373$	614.112			1.64641			0.823207	+	0.567742i	$0.192183\pi$
$374$			777.901i			2.07995i
$375$	−26.3066	−	20.8078i	−0.0701509	−	0.0554874i
$376$	44.5879			0.118585
$377$		−	27.9977i		−	0.0742644i
$378$	42.7413	−	91.5379i	0.113072	−	0.242164i
$379$	492.230			1.29876			0.649380	−	0.760464i	$-0.275028\pi$
$379$	492.230			1.29876			0.649380	+	0.760464i	$0.275028\pi$
$380$			104.458i			0.274888i
$381$	−26.5395	+	33.5531i	−0.0696576	+	0.0880658i
$382$	260.053			0.680767
$383$		−	292.505i		−	0.763722i	−0.924220	−	0.381861i	$-0.875283\pi$
$383$		−	292.505i		−	0.763722i	0.924220	−	0.381861i	$-0.124717\pi$
$384$	−26.6204	−	21.0560i	−0.0693239	−	0.0548333i
$385$	112.594			0.292453
$386$		−	152.391i		−	0.394795i
$387$	64.7689	+	273.694i	0.167362	+	0.707218i
$388$	114.328			0.294661
$389$		−	447.326i		−	1.14994i	−0.818175	−	0.574969i	$-0.805014\pi$
$389$		−	447.326i		−	1.14994i	0.818175	−	0.574969i	$-0.194986\pi$
$390$	−9.15043	+	11.5686i	−0.0234626	+	0.0296630i
$391$	−686.983			−1.75699
$392$			19.7990i			0.0505076i
$393$	−202.606	−	160.256i	−0.515538	−	0.407776i
$394$	−420.370			−1.06693
$395$			161.248i			0.408223i
$396$	−333.367	+	78.8906i	−0.841837	+	0.199219i
$397$	293.499			0.739293			0.369646	−	0.929172i	$-0.379479\pi$
$397$	293.499			0.739293			0.369646	+	0.929172i	$0.379479\pi$
$398$		−	349.150i		−	0.877262i
$399$	−115.012	+	145.406i	−0.288252	+	0.364427i
$400$	−20.0000			−0.0500000
$401$		−	450.848i		−	1.12431i	−0.827032	−	0.562155i	$-0.809972\pi$
$401$		−	450.848i		−	1.12431i	0.827032	−	0.562155i	$-0.190028\pi$
$402$	187.024	+	147.931i	0.465235	+	0.367988i
$403$	−12.2591			−0.0304195
$404$			289.850i			0.717450i
$405$	81.1778	+	161.911i	0.200439	+	0.399780i
$406$	67.3775			0.165955
$407$		−	390.569i		−	0.959629i
$408$	152.140	−	192.345i	0.372891	−	0.471434i
$409$	304.167			0.743686			0.371843	−	0.928296i	$-0.378726\pi$
$409$	304.167			0.743686			0.371843	+	0.928296i	$0.378726\pi$
$410$			160.956i			0.392576i
$411$	205.675	+	162.683i	0.500427	+	0.395823i
$412$	−347.484			−0.843407
$413$		−	235.987i		−	0.571398i
$414$	−69.6702	−	294.405i	−0.168285	−	0.711122i
$415$	232.952			0.561331
$416$			8.79520i			0.0211423i
$417$	−350.928	+	443.666i	−0.841553	+	1.06395i
$418$	628.670			1.50400
$419$			151.970i			0.362698i	0.983419	+	0.181349i	$0.0580463\pi$
$419$			151.970i			0.362698i	−0.983419	+	0.181349i	$0.941954\pi$
$420$	−27.8403	−	22.0209i	−0.0662864	−	0.0524307i
$421$	165.499			0.393109			0.196554	−	0.980493i	$-0.437025\pi$
$421$	165.499			0.393109			0.196554	+	0.980493i	$0.437025\pi$
$422$		−	413.221i		−	0.979196i
$423$	−138.065	+	32.6727i	−0.326394	+	0.0772404i
$424$	−222.866			−0.525628
$425$		−	144.510i		−	0.340023i
$426$	−74.7754	+	94.5361i	−0.175529	+	0.221916i
$427$	149.261			0.349556
$428$			187.524i			0.438141i
$429$	69.6247	+	55.0712i	0.162295	+	0.128371i
$430$	98.8222			0.229819
$431$		−	240.737i		−	0.558555i	−0.960210	−	0.279277i	$-0.909905\pi$
$431$		−	240.737i		−	0.558555i	0.960210	−	0.279277i	$-0.0900949\pi$
$432$	97.8581	+	45.6923i	0.226523	+	0.105769i
$433$	551.714			1.27417			0.637083	−	0.770795i	$-0.280141\pi$
$433$	551.714			1.27417			0.637083	+	0.770795i	$0.280141\pi$
$434$		−	29.5020i		−	0.0679769i
$435$	−74.9388	+	94.7427i	−0.172273	+	0.217799i
$436$	−393.762			−0.903125
$437$			555.194i			1.27047i
$438$	−400.146	−	316.504i	−0.913576	−	0.722613i
$439$	85.9944			0.195887			0.0979435	−	0.995192i	$-0.468774\pi$
$439$	85.9944			0.195887			0.0979435	+	0.995192i	$0.468774\pi$
$440$			120.369i			0.273565i
$441$	−14.5081	−	61.3067i	−0.0328982	−	0.139018i
$442$	−63.5496			−0.143777
$443$			407.274i			0.919354i	0.888086	+	0.459677i	$0.152035\pi$
$443$			407.274i			0.919354i	−0.888086	+	0.459677i	$0.847965\pi$
$444$	−76.3863	+	96.5727i	−0.172041	+	0.217506i
$445$	−81.3810			−0.182879
$446$			320.701i			0.719061i
$447$	−283.195	−	224.000i	−0.633547	−	0.501118i
$448$	−21.1660			−0.0472456
$449$		−	373.874i		−	0.832682i	−0.909209	−	0.416341i	$-0.863312\pi$
$449$		−	373.874i		−	0.832682i	0.909209	−	0.416341i	$-0.136688\pi$
$450$	61.9291	−	14.6554i	0.137620	−	0.0325675i
$451$	968.703			2.14790
$452$		−	228.635i		−	0.505829i
$453$	77.4589	−	97.9287i	0.170991	−	0.216178i
$454$	−414.866			−0.913801
$455$			9.19824i			0.0202159i
$456$	−155.446	−	122.953i	−0.340890	−	0.269635i
$457$	29.2307			0.0639623			0.0319811	−	0.999488i	$-0.489818\pi$
$457$	29.2307			0.0639623			0.0319811	+	0.999488i	$0.489818\pi$
$458$			260.019i			0.567728i
$459$	−330.149	+	707.072i	−0.719279	+	1.54046i
$460$	−106.300			−0.231088
$461$		−	354.370i		−	0.768699i	−0.923188	−	0.384350i	$-0.874426\pi$
$461$		−	354.370i		−	0.768699i	0.923188	−	0.384350i	$-0.125574\pi$
$462$	−132.531	+	167.555i	−0.286864	+	0.362672i
$463$	−488.004			−1.05400			−0.527002	−	0.849864i	$-0.676684\pi$
$463$	−488.004			−1.05400			−0.527002	+	0.849864i	$0.676684\pi$
$464$			72.0296i			0.155236i
$465$	41.4841	+	32.8127i	0.0892131	+	0.0705650i
$466$	−478.234			−1.02625
$467$		−	400.445i		−	0.857484i	−0.903427	−	0.428742i	$-0.858957\pi$
$467$		−	400.445i		−	0.857484i	0.903427	−	0.428742i	$-0.141043\pi$
$468$	−6.44486	−	27.2340i	−0.0137711	−	0.0581922i
$469$	148.704			0.317066
$470$			49.8508i			0.106066i
$471$	108.770	−	137.514i	0.230934	−	0.291962i
$472$	252.281			0.534494
$473$		−	594.754i		−	1.25741i
$474$	−239.957	−	189.799i	−0.506239	−	0.400421i
$475$	−116.787			−0.245868
$476$		−	152.935i		−	0.321291i
$477$	690.096	−	163.310i	1.44674	−	0.342368i
$478$	417.617			0.873677
$479$			724.371i			1.51226i	0.654424	+	0.756128i	$0.272911\pi$
$479$			724.371i			1.51226i	−0.654424	+	0.756128i	$0.727089\pi$
$480$	23.5413	−	29.7625i	0.0490444	−	0.0620052i
$481$	31.9070			0.0663347
$482$			318.088i			0.659933i
$483$	−147.972	−	117.041i	−0.306359	−	0.242322i
$484$	482.429			0.996754
$485$			127.823i			0.263552i
$486$	−336.495	−	69.7770i	−0.692377	−	0.143574i
$487$	−497.194			−1.02093			−0.510466	−	0.859898i	$-0.670527\pi$
$487$	−497.194			−1.02093			−0.510466	+	0.859898i	$0.670527\pi$
$488$			159.566i			0.326980i
$489$	147.932	−	187.026i	0.302520	−	0.382466i
$490$	−22.1359			−0.0451754
$491$		−	520.399i		−	1.05988i	−0.848036	−	0.529938i	$-0.822215\pi$
$491$		−	520.399i		−	1.05988i	0.848036	−	0.529938i	$-0.177785\pi$
$492$	−239.523	−	189.456i	−0.486835	−	0.385073i
$493$	−520.449			−1.05568
$494$			51.3583i			0.103964i
$495$	−88.2024	−	372.716i	−0.178187	−	0.752962i
$496$	31.5389			0.0635865
$497$			75.1662i			0.151240i
$498$	−274.200	+	346.662i	−0.550603	+	0.696109i
$499$	645.961			1.29451			0.647256	−	0.762273i	$-0.275916\pi$
$499$	645.961			1.29451			0.647256	+	0.762273i	$0.275916\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	169.808	+	134.313i	0.338938	+	0.268090i
$502$	−37.2414			−0.0741861
$503$			21.7943i			0.0433287i	0.999765	+	0.0216644i	$0.00689652\pi$
$503$			21.7943i			0.0433287i	−0.999765	+	0.0216644i	$0.993103\pi$
$504$	65.5397	−	15.5098i	0.130039	−	0.0307734i
$505$	−324.062			−0.641707
$506$			639.761i			1.26435i
$507$	310.028	−	391.958i	0.611494	−	0.773092i
$508$	−28.5202			−0.0561422
$509$		−	466.441i		−	0.916386i	−0.888853	−	0.458193i	$-0.848497\pi$
$509$		−	466.441i		−	0.916386i	0.888853	−	0.458193i	$-0.151503\pi$
$510$	215.048	+	170.097i	0.421664	+	0.333524i
$511$	−318.158			−0.622619
$512$		−	22.6274i		−	0.0441942i
$513$	571.429	+	266.814i	1.11390	+	0.520105i
$514$	−182.642			−0.355334
$515$		−	388.498i		−	0.754366i
$516$	−116.320	+	147.060i	−0.225427	+	0.285000i
$517$	300.023			0.580316
$518$			76.7854i			0.148234i
$519$	−554.477	−	438.576i	−1.06836	−	0.845040i
$520$	−9.83334			−0.0189103
$521$			234.319i			0.449749i	0.974388	+	0.224875i	$0.0721973\pi$
$521$			234.319i			0.449749i	−0.974388	+	0.224875i	$0.927803\pi$
$522$	−52.7811	−	223.037i	−0.101113	−	0.427273i
$523$	569.920			1.08971			0.544856	−	0.838529i	$-0.316584\pi$
$523$	569.920			1.08971			0.544856	+	0.838529i	$0.316584\pi$
$524$		−	172.216i		−	0.328657i
$525$	24.6201	−	31.1264i	0.0468954	−	0.0592883i
$526$	331.137			0.629538
$527$			227.884i			0.432417i
$528$	−179.123	−	141.682i	−0.339249	−	0.268336i
$529$	−35.9879			−0.0680300
$530$		−	249.172i		−	0.470136i
$531$	−781.178	+	184.864i	−1.47114	+	0.348143i
$532$	−123.596			−0.232323
$533$			79.1368i			0.148474i
$534$	95.7908	−	121.105i	0.179383	−	0.226789i
$535$	−209.659			−0.391885
$536$			158.971i			0.296588i
$537$	312.016	+	246.796i	0.581035	+	0.459583i
$538$	154.178			0.286576
$539$			133.224i			0.247168i
$540$	−51.0856	+	109.409i	−0.0946030	+	0.202609i
$541$	−891.572			−1.64801			−0.824003	−	0.566585i	$-0.808264\pi$
$541$	−891.572			−1.64801			−0.824003	+	0.566585i	$0.808264\pi$
$542$		−	288.801i		−	0.532843i
$543$	−89.1970	+	112.769i	−0.164267	+	0.207677i
$544$	163.494			0.300540
$545$		−	440.240i		−	0.807779i
$546$	−13.6881	−	10.8269i	−0.0250699	−	0.0198295i
$547$	−196.251			−0.358777			−0.179389	−	0.983778i	$-0.557412\pi$
$547$	−196.251			−0.358777			−0.179389	+	0.983778i	$0.557412\pi$
$548$			174.825i			0.319023i
$549$	−116.925	−	494.090i	−0.212979	−	0.899982i
$550$	−134.576			−0.244684
$551$			420.607i			0.763352i
$552$	125.122	−	158.188i	0.226671	−	0.286573i
$553$	−190.791			−0.345011
$554$		−	485.869i		−	0.877019i
$555$	−107.972	−	85.4025i	−0.194543	−	0.153878i
$556$	−377.118			−0.678269
$557$		−	1016.07i		−	1.82418i	−0.409992	−	0.912089i	$-0.634468\pi$
$557$		−	1016.07i		−	1.82418i	0.409992	−	0.912089i	$-0.365532\pi$
$558$	−97.6589	+	23.1108i	−0.175016	+	0.0414171i
$559$	48.5876			0.0869187
$560$		−	23.6643i		−	0.0422577i
$561$	1023.72	−	1294.25i	1.82481	−	2.30705i
$562$	−568.522			−1.01161
$563$		−	104.346i		−	0.185340i	−0.995697	−	0.0926698i	$-0.970460\pi$
$563$		−	104.346i		−	0.185340i	0.995697	−	0.0926698i	$-0.0295401\pi$
$564$	−74.1843	−	58.6777i	−0.131532	−	0.104038i
$565$	255.621			0.452427
$566$		−	410.485i		−	0.725238i
$567$	−191.576	+	96.0509i	−0.337876	+	0.169402i
$568$	−80.3560			−0.141472
$569$			12.9324i			0.0227284i	0.999935	+	0.0113642i	$0.00361741\pi$
$569$			12.9324i			0.0227284i	−0.999935	+	0.0113642i	$0.996383\pi$
$570$	137.466	−	173.794i	0.241169	−	0.304902i
$571$	986.261			1.72725			0.863626	−	0.504133i	$-0.168188\pi$
$571$	986.261			1.72725			0.863626	+	0.504133i	$0.168188\pi$
$572$			59.1812i			0.103464i
$573$	−432.670	−	342.230i	−0.755096	−	0.597259i
$574$	−190.446			−0.331787
$575$		−	118.847i		−	0.206691i
$576$	16.5807	+	70.0648i	0.0287859	+	0.121640i
$577$	305.085			0.528744			0.264372	−	0.964421i	$-0.414835\pi$
$577$	305.085			0.528744			0.264372	+	0.964421i	$0.414835\pi$
$578$			772.615i			1.33670i
$579$	−200.546	+	253.544i	−0.346367	+	0.437900i
$580$	−80.5316			−0.138848
$581$			275.633i			0.474411i
$582$	−190.217	−	150.456i	−0.326833	−	0.258515i
$583$	−1499.62			−2.57225
$584$		−	340.126i		−	0.582407i
$585$	30.4485	−	7.20557i	0.0520487	−	0.0123172i
$586$	−627.176			−1.07027
$587$			469.411i			0.799679i	0.916585	+	0.399839i	$0.130934\pi$
$587$			469.411i			0.799679i	−0.916585	+	0.399839i	$0.869066\pi$
$588$	26.0555	−	32.9411i	0.0443120	−	0.0560222i
$589$	184.167			0.312678
$590$			282.059i			0.478066i
$591$	699.401	+	553.206i	1.18342	+	0.936051i
$592$	−82.0871			−0.138661
$593$			280.787i			0.473502i	0.971570	+	0.236751i	$0.0760826\pi$
$593$			280.787i			0.473502i	−0.971570	+	0.236751i	$0.923917\pi$
$594$	658.468	+	307.455i	1.10853	+	0.517601i
$595$	170.986			0.287372
$596$		−	240.717i		−	0.403888i
$597$	−459.481	+	580.907i	−0.769650	+	0.973044i
$598$	−52.2643			−0.0873985
$599$			257.993i			0.430706i	0.976536	+	0.215353i	$0.0690902\pi$
$599$			257.993i			0.430706i	−0.976536	+	0.215353i	$0.930910\pi$
$600$	33.2755	+	26.3200i	0.0554592	+	0.0438666i
$601$	−373.606			−0.621641			−0.310820	−	0.950469i	$-0.600604\pi$
$601$	−373.606			−0.621641			−0.310820	+	0.950469i	$0.600604\pi$
$602$			116.928i			0.194233i
$603$	−116.489	−	492.248i	−0.193183	−	0.816331i
$604$	83.2397			0.137814
$605$			539.372i			0.891524i
$606$	381.442	−	482.245i	0.629443	−	0.795784i
$607$	−227.281			−0.374434			−0.187217	−	0.982319i	$-0.559947\pi$
$607$	−227.281			−0.374434			−0.187217	+	0.982319i	$0.559947\pi$
$608$		−	132.130i		−	0.217318i
$609$	−112.101	−	88.6688i	−0.184074	−	0.145597i
$610$	−178.401			−0.292460
$611$			24.5100i			0.0401146i
$612$	−506.252	+	119.803i	−0.827209	+	0.195757i
$613$	−731.598			−1.19347			−0.596736	−	0.802438i	$-0.703536\pi$
$613$	−731.598			−1.19347			−0.596736	+	0.802438i	$0.703536\pi$
$614$		−	53.1046i		−	0.0864896i
$615$	211.818	−	267.795i	0.344420	−	0.435439i
$616$	−142.422			−0.231204
$617$		−	488.323i		−	0.791447i	−0.918370	−	0.395724i	$-0.870494\pi$
$617$		−	488.323i		−	0.791447i	0.918370	−	0.395724i	$-0.129506\pi$
$618$	578.134	+	457.288i	0.935492	+	0.739948i
$619$	304.696			0.492240			0.246120	−	0.969239i	$-0.420844\pi$
$619$	304.696			0.492240			0.246120	+	0.969239i	$0.420844\pi$
$620$			35.2616i			0.0568735i
$621$	−271.521	+	581.509i	−0.437232	+	0.936407i
$622$	188.654			0.303302
$623$		−	96.2913i		−	0.154561i
$624$	11.5745	−	14.6332i	0.0185488	−	0.0234507i
$625$	25.0000			0.0400000
$626$		−	311.311i		−	0.497301i
$627$	−1045.97	−	827.330i	−1.66821	−	1.31951i
$628$	116.887			0.186126
$629$		−	593.118i		−	0.942955i
$630$	17.3405	+	73.2756i	0.0275246	+	0.116310i
$631$	−568.874			−0.901544			−0.450772	−	0.892639i	$-0.648851\pi$
$631$	−568.874			−0.901544			−0.450772	+	0.892639i	$0.648851\pi$
$632$		−	203.964i		−	0.322728i
$633$	−543.798	+	687.506i	−0.859081	+	1.08611i
$634$	464.835			0.733177
$635$		−	31.8866i		−	0.0502151i
$636$	370.799	+	293.292i	0.583018	+	0.461151i
$637$	−10.8835			−0.0170856
$638$			484.673i			0.759676i
$639$	248.819	−	58.8824i	0.389388	−	0.0921478i
$640$	25.2982			0.0395285
$641$			565.547i			0.882289i	0.897436	+	0.441144i	$0.145427\pi$
$641$			565.547i			0.882289i	−0.897436	+	0.441144i	$0.854573\pi$
$642$	246.782	−	311.998i	0.384396	−	0.485979i
$643$	−47.4562			−0.0738043			−0.0369022	−	0.999319i	$-0.511749\pi$
$643$	−47.4562			−0.0738043			−0.0369022	+	0.999319i	$0.511749\pi$
$644$		−	125.776i		−	0.195305i
$645$	−164.418	−	130.050i	−0.254911	−	0.201628i
$646$	954.700			1.47786
$647$			427.152i			0.660204i	0.943945	+	0.330102i	$0.107083\pi$
$647$			427.152i			0.660204i	−0.943945	+	0.330102i	$0.892917\pi$
$648$	−102.683	−	204.803i	−0.158461	−	0.316054i
$649$	1697.55			2.61564
$650$		−	10.9940i		−	0.0169139i
$651$	−38.8246	+	49.0846i	−0.0596383	+	0.0753988i
$652$	158.972			0.243823
$653$		−	1157.00i		−	1.77182i	−0.463856	−	0.885910i	$-0.653535\pi$
$653$		−	1157.00i		−	1.77182i	0.463856	−	0.885910i	$-0.346465\pi$
$654$	655.132	+	518.191i	1.00173	+	0.792341i
$655$	192.543			0.293960
$656$		−	203.595i		−	0.310359i
$657$	249.234	+	1053.18i	0.379351	+	1.60302i
$658$	−58.9843			−0.0896418
$659$			522.811i			0.793340i	0.917961	+	0.396670i	$0.129834\pi$
$659$			522.811i			0.793340i	−0.917961	+	0.396670i	$0.870166\pi$
$660$	158.405	−	200.266i	0.240007	−	0.303433i
$661$	885.681			1.33991			0.669956	−	0.742401i	$-0.266313\pi$
$661$	885.681			1.33991			0.669956	+	0.742401i	$0.266313\pi$
$662$			622.534i			0.940384i
$663$	105.732	+	83.6312i	0.159475	+	0.126141i
$664$	−294.664			−0.443771
$665$		−	138.184i		−	0.207796i
$666$	254.179	−	60.1509i	0.381650	−	0.0903167i
$667$	−428.026			−0.641719
$668$			144.337i			0.216074i
$669$	422.042	−	533.575i	0.630856	−	0.797570i
$670$	−177.735			−0.265276
$671$			1073.69i			1.60013i
$672$	35.2155	+	27.8545i	0.0524040	+	0.0414501i
$673$	−969.877			−1.44112			−0.720562	−	0.693390i	$-0.756116\pi$
$673$	−969.877			−1.44112			−0.720562	+	0.693390i	$0.756116\pi$
$674$			193.464i			0.287039i
$675$	−122.323	−	57.1154i	−0.181219	−	0.0846155i
$676$	333.165			0.492848
$677$			497.683i			0.735130i	0.929998	+	0.367565i	$0.119809\pi$
$677$			497.683i			0.735130i	−0.929998	+	0.367565i	$0.880191\pi$
$678$	−300.883	+	380.397i	−0.443780	+	0.561057i
$679$	−151.242			−0.222743
$680$			182.792i			0.268811i
$681$	690.243	+	545.963i	1.01357	+	0.801708i
$682$	212.219			0.311172
$683$			1188.03i			1.73943i	0.493553	+	0.869716i	$0.335698\pi$
$683$			1188.03i			1.73943i	−0.493553	+	0.869716i	$0.664302\pi$
$684$	96.8205	+	409.134i	0.141551	+	0.598149i
$685$	−195.460			−0.285343
$686$		−	26.1916i		−	0.0381802i
$687$	342.185	−	432.614i	0.498086	−	0.629714i
$688$	−125.001			−0.181688
$689$		−	122.510i		−	0.177808i
$690$	176.860	+	139.891i	0.256319	+	0.202741i
$691$	−1194.03			−1.72797			−0.863985	−	0.503517i	$-0.832039\pi$
$691$	−1194.03			−1.72797			−0.863985	+	0.503517i	$0.832039\pi$
$692$		−	471.307i		−	0.681080i
$693$	441.003	−	104.362i	0.636369	−	0.150595i
$694$	−142.948			−0.205977
$695$		−	421.630i		−	0.606662i
$696$	94.7909	−	119.841i	0.136194	−	0.172185i
$697$	1471.07			2.11058
$698$		−	94.3123i		−	0.135118i
$699$	795.674	+	629.356i	1.13830	+	0.900366i
$700$	26.4575			0.0377964
$701$			724.767i			1.03390i	0.856014	+	0.516952i	$0.172933\pi$
$701$			724.767i			1.03390i	−0.856014	+	0.516952i	$0.827067\pi$
$702$	−25.1171	+	53.7926i	−0.0357793	+	0.0766277i
$703$	−479.336			−0.681843
$704$		−	152.255i		−	0.216272i
$705$	65.6036	−	82.9405i	0.0930548	−	0.117646i
$706$	−230.627			−0.326666
$707$		−	383.435i		−	0.542341i
$708$	−419.739	−	332.002i	−0.592852	−	0.468929i
$709$	336.704			0.474900			0.237450	−	0.971400i	$-0.423688\pi$
$709$	336.704			0.474900			0.237450	+	0.971400i	$0.423688\pi$
$710$		−	89.8407i		−	0.126536i
$711$	149.459	+	631.567i	0.210209	+	0.888280i
$712$	102.940			0.144578
$713$			187.416i			0.262855i
$714$	−201.262	+	254.449i	−0.281879	+	0.356371i
$715$	−66.1666			−0.0925407
$716$			265.215i			0.370411i
$717$	−694.821	−	549.584i	−0.969068	−	0.766505i
$718$	448.150			0.624165
$719$			819.998i			1.14047i	0.821482	+	0.570235i	$0.193148\pi$
$719$			819.998i			1.14047i	−0.821482	+	0.570235i	$0.806852\pi$
$720$	−78.3349	+	18.5378i	−0.108798	+	0.0257469i
$721$	459.678			0.637555
$722$		−	261.021i		−	0.361525i
$723$	418.603	−	529.226i	0.578981	−	0.731987i
$724$	−95.8538			−0.132395
$725$		−	90.0370i		−	0.124189i
$726$	−802.653	−	634.876i	−1.10558	−	0.874485i
$727$	−1265.71			−1.74100			−0.870500	−	0.492168i	$-0.836204\pi$
$727$	−1265.71			−1.74100			−0.870500	+	0.492168i	$0.836204\pi$
$728$		−	11.6350i		−	0.0159821i
$729$	468.026	+	558.921i	0.642011	+	0.766695i
$730$	380.272			0.520920
$731$		−	903.194i		−	1.23556i
$732$	209.989	−	265.482i	0.286870	−	0.362681i
$733$	−244.877			−0.334075			−0.167038	−	0.985951i	$-0.553420\pi$
$733$	−244.877			−0.334075			−0.167038	+	0.985951i	$0.553420\pi$
$734$		−	697.051i		−	0.949660i
$735$	36.8292	+	29.1309i	0.0501078	+	0.0396339i
$736$	134.460			0.182691
$737$			1069.69i			1.45141i
$738$	149.188	+	630.424i	0.202152	+	0.854233i
$739$	−887.684			−1.20120			−0.600598	−	0.799551i	$-0.705071\pi$
$739$	−887.684			−1.20120			−0.600598	+	0.799551i	$0.705071\pi$
$740$		−	91.7761i		−	0.124022i
$741$	67.5875	−	85.4487i	0.0912112	−	0.115315i
$742$	294.824			0.397337
$743$			1200.69i			1.61600i	0.589183	+	0.807999i	$0.299450\pi$
$743$			1200.69i			1.61600i	−0.589183	+	0.807999i	$0.700550\pi$
$744$	−52.4737	−	41.5052i	−0.0705291	−	0.0557866i
$745$	269.130			0.361248
$746$		−	868.486i		−	1.16419i
$747$	912.414	−	215.921i	1.22144	−	0.289051i
$748$	1100.12			1.47075
$749$		−	248.071i		−	0.331204i
$750$	−29.4266	+	37.2031i	−0.0392355	+	0.0496042i
$751$	423.204			0.563521			0.281760	−	0.959485i	$-0.409082\pi$
$751$	423.204			0.563521			0.281760	+	0.959485i	$0.409082\pi$
$752$		−	63.0569i		−	0.0838522i
$753$	61.9614	+	49.0097i	0.0822860	+	0.0650859i
$754$	−39.5947			−0.0525128
$755$			93.0648i			0.123265i
$756$	−129.454	−	60.4453i	−0.171236	−	0.0799541i
$757$	1039.54			1.37323			0.686617	−	0.727020i	$-0.259095\pi$
$757$	1039.54			1.37323			0.686617	+	0.727020i	$0.259095\pi$
$758$		−	696.119i		−	0.918362i
$759$	841.924	−	1064.42i	1.10925	−	1.40239i
$760$	147.725			0.194376
$761$		−	653.459i		−	0.858684i	−0.903142	−	0.429342i	$-0.858746\pi$
$761$		−	653.459i		−	0.858684i	0.903142	−	0.429342i	$-0.141254\pi$
$762$	47.4512	+	37.5326i	0.0622719	+	0.0492554i
$763$	520.899			0.682698
$764$		−	367.771i		−	0.481375i
$765$	−133.944	−	566.007i	−0.175091	−	0.739878i
$766$	−413.665			−0.540033
$767$			138.679i			0.180807i
$768$	−29.7777	+	37.6469i	−0.0387730	+	0.0490194i
$769$	−631.211			−0.820820			−0.410410	−	0.911901i	$-0.634614\pi$
$769$	−631.211			−0.820820			−0.410410	+	0.911901i	$0.634614\pi$
$770$		−	159.233i		−	0.206796i
$771$	303.875	+	240.356i	0.394131	+	0.311746i
$772$	−215.513			−0.279162
$773$			525.003i			0.679176i	0.940574	+	0.339588i	$0.110288\pi$
$773$			525.003i			0.679176i	−0.940574	+	0.339588i	$0.889712\pi$
$774$	387.061	−	91.5971i	0.500079	−	0.118343i
$775$	−39.4237			−0.0508692
$776$		−	161.685i		−	0.208357i
$777$	101.050	−	127.754i	0.130051	−	0.164419i
$778$	−632.615			−0.813130
$779$		−	1188.87i		−	1.52614i
$780$	16.3605	+	12.9407i	0.0209749	+	0.0165906i
$781$	−540.700			−0.692317
$782$			971.541i			1.24238i
$783$	−205.700	+	440.543i	−0.262708	+	0.562634i
$784$	28.0000			0.0357143
$785$			130.684i			0.166476i
$786$	−226.636	+	286.529i	−0.288341	+	0.364541i
$787$	−406.916			−0.517047			−0.258524	−	0.966005i	$-0.583236\pi$
$787$	−406.916			−0.517047			−0.258524	+	0.966005i	$0.583236\pi$
$788$			594.493i			0.754432i
$789$	−550.937	−	435.776i	−0.698273	−	0.552314i
$790$	228.039			0.288657
$791$			302.455i			0.382371i
$792$	111.568	+	471.453i	0.140869	+	0.595268i
$793$	−87.7136			−0.110610
$794$		−	415.071i		−	0.522759i
$795$	−327.910	+	414.566i	−0.412466	+	0.521467i
$796$	−493.773			−0.620318
$797$			599.391i			0.752059i	0.926608	+	0.376030i	$0.122711\pi$
$797$			599.391i			0.752059i	−0.926608	+	0.376030i	$0.877289\pi$
$798$	205.636	+	162.652i	0.257689	+	0.203825i
$799$	455.616			0.570233
$800$			28.2843i			0.0353553i
$801$	−318.748	+	75.4311i	−0.397938	+	0.0941712i
$802$	−637.596			−0.795007
$803$		−	2288.64i		−	2.85011i
$804$	209.206	−	264.492i	0.260206	−	0.328971i
$805$	140.622			0.174686
$806$			17.3370i			0.0215099i
$807$	−256.518	−	202.898i	−0.317866	−	0.251423i
$808$	409.910			0.507314
$809$		−	528.965i		−	0.653851i	−0.945050	−	0.326925i	$-0.893987\pi$
$809$		−	528.965i		−	0.653851i	0.945050	−	0.326925i	$-0.106013\pi$
$810$	228.977	−	114.803i	0.282687	−	0.141732i
$811$	−462.281			−0.570013			−0.285007	−	0.958526i	$-0.591996\pi$
$811$	−462.281			−0.570013			−0.285007	+	0.958526i	$0.591996\pi$
$812$		−	95.2862i		−	0.117348i
$813$	−380.062	+	480.500i	−0.467481	+	0.591021i
$814$	−552.348			−0.678560
$815$			177.737i			0.218082i
$816$	−272.017	−	215.158i	−0.333354	−	0.263674i
$817$	−729.927			−0.893424
$818$		−	430.158i		−	0.525865i
$819$	8.52574	+	36.0272i	0.0104099	+	0.0439892i
$820$	227.626			0.277593
$821$			955.594i			1.16394i	0.813210	+	0.581970i	$0.197718\pi$
$821$			955.594i			1.16394i	−0.813210	+	0.581970i	$0.802282\pi$
$822$	230.069	−	290.869i	0.279889	−	0.353855i
$823$	−339.294			−0.412265			−0.206132	−	0.978524i	$-0.566088\pi$
$823$	−339.294			−0.412265			−0.206132	+	0.978524i	$0.566088\pi$
$824$			491.416i			0.596379i
$825$	223.904	+	177.102i	0.271399	+	0.214669i
$826$	−333.737			−0.404039
$827$			1124.72i			1.36000i	0.733211	+	0.680001i	$0.238021\pi$
$827$			1124.72i			1.36000i	−0.733211	+	0.680001i	$0.761979\pi$
$828$	−416.351	+	98.5285i	−0.502839	+	0.118996i
$829$	−918.780			−1.10830			−0.554149	−	0.832417i	$-0.686956\pi$
$829$	−918.780			−1.10830			−0.554149	+	0.832417i	$0.686956\pi$
$830$		−	329.444i		−	0.396921i
$831$	−639.403	+	808.376i	−0.769438	+	0.972775i
$832$	12.4383			0.0149499
$833$			202.313i			0.242873i
$834$	627.439	+	496.286i	0.752325	+	0.595068i
$835$	−161.374			−0.193262
$836$		−	889.074i		−	1.06349i
$837$	192.896	+	90.0680i	0.230461	+	0.107608i
$838$	214.919			0.256466
$839$			477.085i			0.568635i	0.958730	+	0.284317i	$0.0917670\pi$
$839$			477.085i			0.568635i	−0.958730	+	0.284317i	$0.908233\pi$
$840$	−31.1422	+	39.3721i	−0.0370741	+	0.0468715i
$841$	516.733			0.614427
$842$		−	234.051i		−	0.277970i
$843$	945.893	+	748.175i	1.12206	+	0.887515i
$844$	−584.383			−0.692396
$845$			372.490i			0.440817i
$846$	46.2061	+	195.253i	0.0546172	+	0.230795i
$847$	−638.193			−0.753475
$848$			315.180i			0.371675i
$849$	−540.198	+	682.954i	−0.636275	+	0.804422i
$850$	−204.367			−0.240432
$851$		−	487.792i		−	0.573198i
$852$	133.694	+	105.748i	0.156918	+	0.124118i
$853$	−203.019			−0.238006			−0.119003	−	0.992894i	$-0.537970\pi$
$853$	−203.019			−0.238006			−0.119003	+	0.992894i	$0.537970\pi$
$854$		−	211.086i		−	0.247174i
$855$	−457.425	+	108.249i	−0.535000	+	0.126607i
$856$	265.200			0.309813
$857$		−	209.889i		−	0.244912i	−0.992474	−	0.122456i	$-0.960923\pi$
$857$		−	209.889i		−	0.244912i	0.992474	−	0.122456i	$-0.0390770\pi$
$858$	77.8824	−	98.4642i	0.0907720	−	0.114760i
$859$	708.676			0.825001			0.412501	−	0.910957i	$-0.364655\pi$
$859$	708.676			0.825001			0.412501	+	0.910957i	$0.364655\pi$
$860$		−	139.756i		−	0.162507i
$861$	316.859	+	250.627i	0.368013	+	0.291088i
$862$	−340.454			−0.394958
$863$		−	996.198i		−	1.15434i	−0.816623	−	0.577171i	$-0.804156\pi$
$863$		−	996.198i		−	1.15434i	0.816623	−	0.577171i	$-0.195844\pi$
$864$	64.6187	−	138.392i	0.0747902	−	0.160176i
$865$	526.938			0.609176
$866$		−	780.242i		−	0.900972i
$867$	1016.76	−	1285.46i	1.17273	−	1.48265i
$868$	−41.7221			−0.0480669
$869$		−	1372.44i		−	1.57933i
$870$	133.986	+	105.979i	0.154007	+	0.121815i
$871$	−87.3865			−0.100329
$872$			556.864i			0.638606i
$873$	118.478	+	500.650i	0.135713	+	0.573482i
$874$	785.163			0.898356
$875$			29.5804i			0.0338062i
$876$	−447.605	+	565.892i	−0.510965	+	0.645996i
$877$	510.287			0.581855			0.290927	−	0.956745i	$-0.406036\pi$
$877$	510.287			0.581855			0.290927	+	0.956745i	$0.406036\pi$
$878$		−	121.614i		−	0.138513i
$879$	1043.48	+	825.363i	1.18712	+	0.938979i
$880$	170.227			0.193440
$881$		−	469.010i		−	0.532361i	−0.963923	−	0.266181i	$-0.914238\pi$
$881$		−	469.010i		−	0.532361i	0.963923	−	0.266181i	$-0.0857617\pi$
$882$	−86.7008	+	20.5175i	−0.0983002	+	0.0232625i
$883$	−978.480			−1.10813			−0.554065	−	0.832473i	$-0.686924\pi$
$883$	−978.480			−1.10813			−0.554065	+	0.832473i	$0.686924\pi$
$884$			89.8726i			0.101666i
$885$	371.189	−	469.282i	0.419423	−	0.530263i
$886$	575.972			0.650082
$887$		−	162.637i		−	0.183356i	−0.995789	−	0.0916778i	$-0.970777\pi$
$887$		−	162.637i		−	0.183356i	0.995789	−	0.0916778i	$-0.0292230\pi$
$888$	136.574	+	108.027i	0.153800	+	0.121651i
$889$	37.7287			0.0424395
$890$			115.090i			0.129315i
$891$	−690.932	−	1378.08i	−0.775457	−	1.54667i
$892$	453.540			0.508453
$893$		−	368.212i		−	0.412331i
$894$	−316.783	+	400.499i	−0.354344	+	0.447985i
$895$	−296.519			−0.331306
$896$			29.9333i			0.0334077i
$897$	86.9561	+	68.7798i	0.0969410	+	0.0766776i
$898$	−528.738			−0.588795
$899$			141.984i			0.157935i
$900$	−20.7259	−	87.5810i	−0.0230287	−	0.0973123i
$901$	−2277.33			−2.52756
$902$		−	1369.95i		−	1.51879i
$903$	153.877	−	194.542i	0.170407	−	0.215439i
$904$	−323.338			−0.357675
$905$		−	107.168i		−	0.118418i
$906$	−138.492	−	109.543i	−0.152861	−	0.120909i
$907$	−446.893			−0.492716			−0.246358	−	0.969179i	$-0.579234\pi$
$907$	−446.893			−0.492716			−0.246358	+	0.969179i	$0.579234\pi$
$908$			586.709i			0.646155i
$909$	−1269.27	+	300.369i	−1.39633	+	0.330439i
$910$	13.0083			0.0142948
$911$			1085.65i			1.19171i	0.803092	+	0.595855i	$0.203187\pi$
$911$			1085.65i			1.19171i	−0.803092	+	0.595855i	$0.796813\pi$
$912$	−173.882	+	219.834i	−0.190661	+	0.241046i
$913$	−1982.74			−2.17167
$914$		−	41.3385i		−	0.0452281i
$915$	296.818	+	234.775i	0.324392	+	0.256585i
$916$	367.723			0.401444
$917$			227.821i			0.248441i
$918$	999.951	+	466.901i	1.08927	+	0.508607i
$919$	601.801			0.654843			0.327422	−	0.944878i	$-0.393820\pi$
$919$	601.801			0.654843			0.327422	+	0.944878i	$0.393820\pi$
$920$			150.331i			0.163404i
$921$	−69.8856	+	88.3541i	−0.0758801	+	0.0959328i
$922$	−501.155			−0.543553
$923$		−	44.1717i		−	0.0478567i
$924$	236.958	+	187.427i	0.256448	+	0.202843i
$925$	102.609			0.110928
$926$			690.142i			0.745293i
$927$	−360.095	−	1521.65i	−0.388452	−	1.64148i
$928$	101.865			0.109769
$929$		−	1434.34i		−	1.54397i	−0.635643	−	0.771983i	$-0.719265\pi$
$929$		−	1434.34i		−	1.54397i	0.635643	−	0.771983i	$-0.280735\pi$
$930$	46.4042	−	58.6673i	0.0498970	−	0.0630832i
$931$	163.502			0.175620
$932$			676.325i			0.725671i
$933$	−313.877	−	248.268i	−0.336417	−	0.266096i
$934$	−566.315			−0.606333
$935$			1229.97i			1.31548i
$936$	−38.5146	+	9.11440i	−0.0411481	+	0.00973761i
$937$	49.4833			0.0528104			0.0264052	−	0.999651i	$-0.491594\pi$
$937$	49.4833			0.0528104			0.0264052	+	0.999651i	$0.491594\pi$
$938$		−	210.299i		−	0.224200i
$939$	−409.685	+	517.951i	−0.436299	+	0.551598i
$940$	70.4997			0.0749997
$941$			1178.58i			1.25248i	0.779631	+	0.626239i	$0.215406\pi$
$941$			1178.58i			1.25248i	−0.779631	+	0.626239i	$0.784594\pi$
$942$	−194.474	−	153.824i	−0.206448	−	0.163295i
$943$	1209.84			1.28297
$944$		−	356.779i		−	0.377944i
$945$	67.5799	−	144.734i	0.0715131	−	0.153158i
$946$	−841.109			−0.889122
$947$		−	640.256i		−	0.676089i	−0.941130	−	0.338044i	$-0.890235\pi$
$947$		−	640.256i		−	0.676089i	0.941130	−	0.338044i	$-0.109765\pi$
$948$	−268.417	+	339.351i	−0.283140	+	0.357965i
$949$	186.967			0.197015
$950$			165.162i			0.173855i
$951$	−773.380	−	611.722i	−0.813228	−	0.643241i
$952$	−216.282			−0.227187
$953$			1270.84i			1.33352i	0.745273	+	0.666759i	$0.232319\pi$
$953$			1270.84i			1.33352i	−0.745273	+	0.666759i	$0.767681\pi$
$954$	−230.955	−	975.943i	−0.242091	−	1.02300i
$955$	411.180			0.430555
$956$		−	590.600i		−	0.617783i
$957$	637.829	−	806.387i	0.666488	−	0.842620i
$958$	1024.41			1.06933
$959$		−	231.271i		−	0.241159i
$960$	−42.0905	−	33.2924i	−0.0438443	−	0.0346796i
$961$	−898.831			−0.935308
$962$		−	45.1233i		−	0.0469057i
$963$	−821.179	+	194.330i	−0.852730	+	0.201797i
$964$	449.844			0.466643
$965$		−	240.951i		−	0.249690i
$966$	−165.521	+	209.263i	−0.171347	+	0.216629i
$967$	201.964			0.208856			0.104428	−	0.994532i	$-0.466699\pi$
$967$	201.964			0.208856			0.104428	+	0.994532i	$0.466699\pi$
$968$		−	682.258i		−	0.704811i
$969$	−1588.41	−	1256.38i	−1.63922	−	1.29658i
$970$	180.769			0.186360
$971$			900.525i			0.927420i	0.885987	+	0.463710i	$0.153482\pi$
$971$			900.525i			0.927420i	−0.885987	+	0.463710i	$0.846518\pi$
$972$	−98.6795	+	475.876i	−0.101522	+	0.489585i
$973$	498.880			0.512723
$974$			703.138i			0.721908i
$975$	−14.4681	+	18.2915i	−0.0148391	+	0.0187606i
$976$	225.661			0.231210
$977$			820.874i			0.840199i	0.907478	+	0.420099i	$0.138005\pi$
$977$			820.874i			0.840199i	−0.907478	+	0.420099i	$0.861995\pi$
$978$	−264.494	−	209.208i	−0.270444	−	0.213914i
$979$	692.661			0.707519
$980$			31.3050i			0.0319438i
$981$	−408.053	−	1724.31i	−0.415956	−	1.75770i
$982$	−735.956			−0.749446
$983$		−	1354.26i		−	1.37768i	−0.724914	−	0.688840i	$-0.758120\pi$
$983$		−	1354.26i		−	1.37768i	0.724914	−	0.688840i	$-0.241880\pi$
$984$	−267.931	+	338.737i	−0.272288	+	0.344245i
$985$	−664.663			−0.674785
$986$			736.025i			0.746476i
$987$	98.1366	+	77.6233i	0.0994291	+	0.0786457i
$988$	72.6317			0.0735138
$989$		−	742.804i		−	0.751065i
$990$	−527.100	+	124.737i	−0.532424	+	0.125997i
$991$	1289.97			1.30168			0.650841	−	0.759214i	$-0.274416\pi$
$991$	1289.97			1.30168			0.650841	+	0.759214i	$0.274416\pi$
$992$		−	44.6028i		−	0.0449625i
$993$	819.254	−	1035.76i	0.825030	−	1.04306i
$994$	106.301			0.106943
$995$		−	552.055i		−	0.554829i
$996$	490.254	+	387.777i	0.492223	+	0.389335i
$997$	−757.496			−0.759775			−0.379888	−	0.925033i	$-0.624037\pi$
$997$	−757.496			−0.759775			−0.379888	+	0.925033i	$0.624037\pi$
$998$		−	913.528i		−	0.915358i
$999$	−502.055	−	234.422i	−0.502558	−	0.234657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.e.a.71.3	✓	16
3.2	odd	2	inner	210.3.e.a.71.11	yes	16
4.3	odd	2		1680.3.l.c.1121.11		16
5.2	odd	4		1050.3.c.c.449.28		32
5.3	odd	4		1050.3.c.c.449.5		32
5.4	even	2		1050.3.e.d.701.14		16
12.11	even	2		1680.3.l.c.1121.12		16
15.2	even	4		1050.3.c.c.449.6		32
15.8	even	4		1050.3.c.c.449.27		32
15.14	odd	2		1050.3.e.d.701.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.3	✓	16	1.1	even	1	trivial
210.3.e.a.71.11	yes	16	3.2	odd	2	inner
1050.3.c.c.449.5		32	5.3	odd	4
1050.3.c.c.449.6		32	15.2	even	4
1050.3.c.c.449.27		32	15.8	even	4
1050.3.c.c.449.28		32	5.2	odd	4
1050.3.e.d.701.6		16	15.14	odd	2
1050.3.e.d.701.14		16	5.4	even	2
1680.3.l.c.1121.11		16	4.3	odd	2
1680.3.l.c.1121.12		16	12.11	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.86110 + 2.35293i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.32755 + 2.63200i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-2.07259 - 8.75810i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.86110 + 2.35293i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.32755 + 2.63200i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-2.07259 - 8.75810i) q^{9} -3.16228 q^{10} +19.0319i q^{11} +(3.72221 - 4.70587i) q^{12} -1.55479 q^{13} -3.74166i q^{14} +(5.26132 + 4.16155i) q^{15} +4.00000 q^{16} +28.9019i q^{17} +(-12.3858 + 2.93108i) q^{18} +23.3574 q^{19} +4.47214i q^{20} +(-4.92402 + 6.22527i) q^{21} +26.9152 q^{22} +23.7695i q^{23} +(-6.65510 - 5.26400i) q^{24} -5.00000 q^{25} +2.19880i q^{26} +(24.4645 + 11.4231i) q^{27} -5.29150 q^{28} +18.0074i q^{29} +(5.88533 - 7.44063i) q^{30} +7.88473 q^{31} -5.65685i q^{32} +(-44.7809 - 35.4204i) q^{33} +40.8735 q^{34} -5.91608i q^{35} +(4.14517 + 17.5162i) q^{36} -20.5218 q^{37} -33.0324i q^{38} +(2.89362 - 3.65831i) q^{39} +6.32456 q^{40} -50.8988i q^{41} +(8.80387 + 6.96361i) q^{42} -31.2503 q^{43} -38.0639i q^{44} +(-19.5837 + 4.63444i) q^{45} +33.6151 q^{46} -15.7642i q^{47} +(-7.44442 + 9.41173i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(-68.0043 - 53.7895i) q^{51} +3.10957 q^{52} +78.7951i q^{53} +(16.1547 - 34.5981i) q^{54} +42.5567 q^{55} +7.48331i q^{56} +(-43.4706 + 54.9585i) q^{57} +25.4663 q^{58} -89.1948i q^{59} +(-10.5226 - 8.32311i) q^{60} +56.4152 q^{61} -11.1507i q^{62} +(-5.48355 - 23.1718i) q^{63} -8.00000 q^{64} +3.47661i q^{65} +(-50.0920 + 63.3297i) q^{66} +56.2048 q^{67} -57.8038i q^{68} +(-55.9280 - 44.2375i) q^{69} -8.36660 q^{70} +28.4101i q^{71} +(24.7717 - 5.86216i) q^{72} -120.253 q^{73} +29.0222i q^{74} +(9.30552 - 11.7647i) q^{75} -46.7149 q^{76} +50.3538i q^{77} +(-5.17363 - 4.09220i) q^{78} -72.1123 q^{79} -8.94427i q^{80} +(-72.4088 + 36.3038i) q^{81} -71.9818 q^{82} +104.179i q^{83} +(9.84804 - 12.4505i) q^{84} +64.6267 q^{85} +44.1946i q^{86} +(-42.3702 - 33.5136i) q^{87} -53.8304 q^{88} -36.3947i q^{89} +(6.55409 + 27.6956i) q^{90} -4.11358 q^{91} -47.5389i q^{92} +(-14.6743 + 18.5522i) q^{93} -22.2940 q^{94} -52.2288i q^{95} +(13.3102 + 10.5280i) q^{96} -57.1642 q^{97} -9.89949i q^{98} +(166.684 - 39.4453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more