LMFDB - Embedded newform 63.6.e.c.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$-3.69493 + 2.71062i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.6.e.c.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.19493 - 5.53379i) q^{2} +(-4.41520 - 7.64735i) q^{4} +(19.3645 - 33.5404i) q^{5} +(-87.5000 - 95.6596i) q^{7} +148.051 q^{8} +(-123.737 - 214.318i) q^{10} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +(-808.916 + 178.580i) q^{14} +(614.298 - 1064.00i) q^{16} +(-664.850 - 1151.55i) q^{17} +(-471.237 + 816.206i) q^{19} -341.993 q^{20} -3683.05 q^{22} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +(1250.79 - 2166.43i) q^{26} +(-345.212 + 1091.50i) q^{28} +1463.54 q^{29} +(1956.21 + 3388.25i) q^{31} +(-1556.47 - 2695.89i) q^{32} -8496.61 q^{34} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(3011.14 + 5215.45i) q^{38} +(2866.93 - 4965.67i) q^{40} +13103.8 q^{41} +14733.5 q^{43} +(-2544.88 + 4407.86i) q^{44} +(5214.38 + 9031.58i) q^{46} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +10383.9 q^{50} +(-1728.51 - 2993.87i) q^{52} +(-1005.67 - 1741.87i) q^{53} -22323.0 q^{55} +(-12954.4 - 14162.5i) q^{56} +(4675.93 - 8098.94i) q^{58} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +24999.8 q^{62} +19423.8 q^{64} +(7581.04 - 13130.8i) q^{65} +(-25289.1 - 43802.0i) q^{67} +(-5870.89 + 10168.7i) q^{68} +(-9674.63 + 30589.5i) q^{70} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(-52078.5 - 90202.6i) q^{74} +8322.42 q^{76} +(-22533.2 + 71245.8i) q^{77} +(31575.7 - 54690.7i) q^{79} +(-23791.2 - 41207.6i) q^{80} +(41865.9 - 72513.8i) q^{82} -45572.4 q^{83} -51498.1 q^{85} +(47072.5 - 81532.0i) q^{86} +(-42667.5 - 73902.2i) q^{88} +(7843.34 - 13585.1i) q^{89} +(-34255.5 - 37449.9i) q^{91} +14411.9 q^{92} +(21771.9 + 37710.1i) q^{94} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +(87863.1 + 61754.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25}+ \cdots + 462021 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 - 65 * q^4 - 33 * q^5 - 350 * q^7 + 750 * q^8 - 921 * q^10 - 1137 * q^11 + 1850 * q^13 - 2352 * q^14 + 895 * q^16 - 324 * q^17 - 2311 * q^19 + 7374 * q^20 + 3162 * q^22 + 1596 * q^23 - 395 * q^25 - 2508 * q^26 + 13531 * q^28 + 4434 * q^29 - 4294 * q^31 + 1017 * q^32 - 35880 * q^34 - 15414 * q^35 + 19109 * q^37 - 6828 * q^38 - 10545 * q^40 + 25716 * q^41 - 5542 * q^43 - 36579 * q^44 + 40740 * q^46 - 23160 * q^47 - 5978 * q^49 + 58704 * q^50 - 33424 * q^52 - 31653 * q^53 + 35778 * q^55 - 65625 * q^56 + 2277 * q^58 + 41097 * q^59 - 42052 * q^61 + 204114 * q^62 - 60062 * q^64 - 23106 * q^65 - 30763 * q^67 + 44748 * q^68 + 151179 * q^70 - 204192 * q^71 + 28577 * q^73 - 77784 * q^74 + 170384 * q^76 + 96873 * q^77 + 18464 * q^79 - 71511 * q^80 + 86040 * q^82 - 122358 * q^83 - 247272 * q^85 + 258510 * q^86 - 212565 * q^88 + 29322 * q^89 - 161875 * q^91 - 333816 * q^92 - 109938 * q^94 - 61662 * q^95 - 19582 * q^97 + 462021 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	3.19493	−	5.53379i	0.564790	−	0.978245i	−0.432279	−	0.901740i	$-0.642291\pi$
$2$	3.19493	−	5.53379i	0.564790	−	0.978245i	0.997069	−	0.0765049i	$-0.0243761\pi$
$3$		0			0
$3$		0			0
$4$	−4.41520	−	7.64735i	−0.137975	−	0.238980i
$5$	19.3645	−	33.5404i	0.346403	−	0.599988i	−0.639204	−	0.769037i	$-0.720736\pi$
$5$	19.3645	−	33.5404i	0.346403	−	0.599988i	0.985608	+	0.169049i	$0.0540695\pi$
$6$		0			0
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$8$	148.051			0.817872
$9$		0			0
$10$	−123.737	−	214.318i	−0.391290	−	0.677734i
$11$	−288.195	−	499.168i	−0.718133	−	1.24384i	−0.961739	−	0.273968i	$-0.911664\pi$
$11$	−288.195	−	499.168i	−0.718133	−	1.24384i	0.243606	−	0.969874i	$-0.421670\pi$
$12$		0			0
$13$	391.491			0.642486			0.321243	−	0.946997i	$-0.395899\pi$
$13$	391.491			0.642486			0.321243	+	0.946997i	$0.395899\pi$
$14$	−808.916	+	178.580i	−1.10302	+	0.243508i
$15$		0			0
$16$	614.298	−	1064.00i	0.599901	−	1.03906i
$17$	−664.850	−	1151.55i	−0.557958	−	0.966412i	−0.997667	−	0.0682711i	$-0.978252\pi$
$17$	−664.850	−	1151.55i	−0.557958	−	0.966412i	0.439709	−	0.898140i	$-0.355082\pi$
$18$		0			0
$19$	−471.237	+	816.206i	−0.299471	+	0.518699i	−0.976015	−	0.217703i	$-0.930144\pi$
$19$	−471.237	+	816.206i	−0.299471	+	0.518699i	0.676544	+	0.736402i	$0.263477\pi$
$20$	−341.993			−0.191180
$21$		0			0
$22$	−3683.05			−1.62238
$23$	−816.040	+	1413.42i	−0.321656	+	0.557124i	−0.980830	−	0.194866i	$-0.937573\pi$
$23$	−816.040	+	1413.42i	−0.321656	+	0.557124i	0.659174	+	0.751991i	$0.270906\pi$
$24$		0			0
$25$	812.530	+	1407.34i	0.260009	+	0.450350i
$26$	1250.79	−	2166.43i	0.362869	−	0.628508i
$27$		0			0
$28$	−345.212	+	1091.50i	−0.0832130	+	0.263105i
$29$	1463.54			0.323155			0.161577	−	0.986860i	$-0.448342\pi$
$29$	1463.54			0.323155			0.161577	+	0.986860i	$0.448342\pi$
$30$		0			0
$31$	1956.21	+	3388.25i	0.365604	+	0.633245i	0.988873	−	0.148763i	$-0.0475291\pi$
$31$	1956.21	+	3388.25i	0.365604	+	0.633245i	−0.623269	+	0.782008i	$0.714196\pi$
$32$	−1556.47	−	2695.89i	−0.268700	−	0.465401i
$33$		0			0
$34$	−8496.61			−1.26052
$35$	−4902.85	+	1082.38i	−0.676517	+	0.149351i
$36$		0			0
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.311691	−	0.950184i	$-0.399105\pi$
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.667038	−	0.745024i	$-0.267562\pi$
$38$	3011.14	+	5215.45i	0.338277	+	0.585912i
$39$		0			0
$40$	2866.93	−	4965.67i	0.283314	−	0.490714i
$41$	13103.8			1.21741			0.608707	−	0.793395i	$-0.291688\pi$
$41$	13103.8			1.21741			0.608707	+	0.793395i	$0.291688\pi$
$42$		0			0
$43$	14733.5			1.21516			0.607582	−	0.794257i	$-0.292140\pi$
$43$	14733.5			1.21516			0.607582	+	0.794257i	$0.292140\pi$
$44$	−2544.88	+	4407.86i	−0.198169	+	0.343238i
$45$		0			0
$46$	5214.38	+	9031.58i	0.363336	+	0.629316i
$47$	−3407.26	+	5901.55i	−0.224989	+	0.389692i	−0.956316	−	0.292335i	$-0.905568\pi$
$47$	−3407.26	+	5901.55i	−0.224989	+	0.389692i	0.731327	+	0.682027i	$0.238901\pi$
$48$		0			0
$49$	−1494.50	+	16740.4i	−0.0889213	+	0.996039i
$50$	10383.9			0.587403
$51$		0			0
$52$	−1728.51	−	2993.87i	−0.0886470	−	0.153541i
$53$	−1005.67	−	1741.87i	−0.0491775	−	0.0851779i	0.840389	−	0.541984i	$-0.182327\pi$
$53$	−1005.67	−	1741.87i	−0.0491775	−	0.0851779i	−0.889566	+	0.456806i	$0.848993\pi$
$54$		0			0
$55$	−22323.0			−0.995054
$56$	−12954.4	−	14162.5i	−0.552012	−	0.603488i
$57$		0			0
$58$	4675.93	−	8098.94i	0.182515	−	0.316125i
$59$	25726.6	+	44559.7i	0.962170	+	1.66653i	0.717035	+	0.697037i	$0.245499\pi$
$59$	25726.6	+	44559.7i	0.962170	+	1.66653i	0.245135	+	0.969489i	$0.421168\pi$
$60$		0			0
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	0.258865	+	0.965913i	$0.416651\pi$
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	−0.965938	+	0.258773i	$0.916682\pi$
$62$	24999.8			0.825958
$63$		0			0
$64$	19423.8			0.592766
$65$	7581.04	−	13130.8i	0.222559	−	0.385484i
$66$		0			0
$67$	−25289.1	−	43802.0i	−0.688250	−	1.19208i	−0.972404	−	0.233305i	$-0.925046\pi$
$67$	−25289.1	−	43802.0i	−0.688250	−	1.19208i	0.284153	−	0.958779i	$-0.408288\pi$
$68$	−5870.89	+	10168.7i	−0.153968	+	0.266681i
$69$		0			0
$70$	−9674.63	+	30589.5i	−0.235988	+	0.746151i
$71$	−39970.6			−0.941012			−0.470506	−	0.882397i	$-0.655929\pi$
$71$	−39970.6			−0.941012			−0.470506	+	0.882397i	$0.655929\pi$
$72$		0			0
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	0.990984	+	0.133983i	$0.0427767\pi$
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	−0.379459	+	0.925208i	$0.623890\pi$
$74$	−52078.5	−	90202.6i	−1.10555	−	1.91487i
$75$		0			0
$76$	8322.42			0.165278
$77$	−22533.2	+	71245.8i	−0.433107	+	1.36941i
$78$		0			0
$79$	31575.7	−	54690.7i	0.569226	−	0.985929i	−0.427416	−	0.904055i	$-0.640576\pi$
$79$	31575.7	−	54690.7i	0.569226	−	0.985929i	0.996643	−	0.0818739i	$-0.0260905\pi$
$80$	−23791.2	−	41207.6i	−0.415615	−	0.719867i
$81$		0			0
$82$	41865.9	−	72513.8i	0.687583	−	1.19093i
$83$	−45572.4			−0.726116			−0.363058	−	0.931766i	$-0.618267\pi$
$83$	−45572.4			−0.726116			−0.363058	+	0.931766i	$0.618267\pi$
$84$		0			0
$85$	−51498.1			−0.773114
$86$	47072.5	−	81532.0i	0.686312	−	1.18873i
$87$		0			0
$88$	−42667.5	−	73902.2i	−0.587341	−	1.01730i
$89$	7843.34	−	13585.1i	0.104961	−	0.181797i	−0.808762	−	0.588137i	$-0.799862\pi$
$89$	7843.34	−	13585.1i	0.104961	−	0.181797i	0.913722	+	0.406340i	$0.133195\pi$
$90$		0			0
$91$	−34255.5	−	37449.9i	−0.433637	−	0.474075i
$92$	14411.9			0.177522
$93$		0			0
$94$	21771.9	+	37710.1i	0.254143	+	0.440188i
$95$	18250.6	+	31610.9i	0.207476	+	0.359358i
$96$		0			0
$97$	3128.49			0.0337603			0.0168801	−	0.999858i	$-0.494627\pi$
$97$	3128.49			0.0337603			0.0168801	+	0.999858i	$0.494627\pi$
$98$	87863.1	+	61754.8i	0.924148	+	0.649539i
$99$		0			0
$100$	7174.96	−	12427.4i	0.0717496	−	0.124274i
$101$	−84505.5	−	146368.i	−0.824292	−	1.42772i	−0.902459	−	0.430776i	$-0.858240\pi$
$101$	−84505.5	−	146368.i	−0.824292	−	1.42772i	0.0781663	−	0.996940i	$-0.475093\pi$
$102$		0			0
$103$	−56410.1	+	97705.1i	−0.523918	+	0.907453i	0.475694	+	0.879611i	$0.342197\pi$
$103$	−56410.1	+	97705.1i	−0.523918	+	0.907453i	−0.999612	+	0.0278422i	$0.991136\pi$
$104$	57960.5			0.525471
$105$		0			0
$106$	−12852.2			−0.111100
$107$	−11154.7	+	19320.6i	−0.0941890	+	0.163140i	−0.909270	−	0.416207i	$-0.863359\pi$
$107$	−11154.7	+	19320.6i	−0.0941890	+	0.163140i	0.815081	+	0.579347i	$0.196692\pi$
$108$		0			0
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	0.984032	−	0.177993i	$-0.0569604\pi$
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	−0.646162	+	0.763200i	$0.723627\pi$
$110$	−71320.6	+	123531.i	−0.561996	+	0.973406i
$111$		0			0
$112$	−155532.	+	34336.1i	−1.17159	+	0.258646i
$113$	40928.4			0.301529			0.150764	−	0.988570i	$-0.451826\pi$
$113$	40928.4			0.301529			0.150764	+	0.988570i	$0.451826\pi$
$114$		0			0
$115$	31604.4	+	54740.5i	0.222845	+	0.385980i
$116$	−6461.84	−	11192.2i	−0.0445873	−	0.0772275i
$117$		0			0
$118$	328779.			2.17369
$119$	−51982.8	+	164360.i	−0.336505	+	1.06397i
$120$		0			0
$121$	−85587.1	+	148241.i	−0.531429	+	0.920462i
$122$	131305.	+	227427.i	0.798695	+	1.38338i
$123$		0			0
$124$	17274.1	−	29919.6i	0.100888	−	0.174744i
$125$	183965.			1.05308
$126$		0			0
$127$	83270.1			0.458120			0.229060	−	0.973412i	$-0.426435\pi$
$127$	83270.1			0.458120			0.229060	+	0.973412i	$0.426435\pi$
$128$	111865.	−	193756.i	0.603488	−	1.04527i
$129$		0			0
$130$	−48441.9	−	83903.8i	−0.251398	−	0.435435i
$131$	−83437.4	+	144518.i	−0.424798	+	0.735772i	−0.996402	−	0.0847580i	$-0.972988\pi$
$131$	−83437.4	+	144518.i	−0.424798	+	0.735772i	0.571603	+	0.820530i	$0.306322\pi$
$132$		0			0
$133$	119311.	−	26339.7i	0.584860	−	0.129117i
$134$	−323188.			−1.55487
$135$		0			0
$136$	−98431.5	−	170488.i	−0.456338	−	0.790401i
$137$	19111.9	+	33102.9i	0.0869969	+	0.150683i	0.906240	−	0.422763i	$-0.138940\pi$
$137$	19111.9	+	33102.9i	0.0869969	+	0.150683i	−0.819244	+	0.573446i	$0.805606\pi$
$138$		0			0
$139$	106263.			0.466492			0.233246	−	0.972418i	$-0.425065\pi$
$139$	106263.			0.466492			0.233246	+	0.972418i	$0.425065\pi$
$140$	29924.4	+	32714.9i	0.129034	+	0.141067i
$141$		0			0
$142$	−127703.	+	221189.i	−0.531474	+	0.920540i
$143$	−112826.	−	195420.i	−0.461390	−	0.799151i
$144$		0			0
$145$	28340.8	−	49087.8i	0.111942	−	0.193889i
$146$	355830.			1.38153
$147$		0			0
$148$	−143938.			−0.540160
$149$	96277.8	−	166758.i	0.355271	−	0.615348i	−0.631893	−	0.775056i	$-0.717722\pi$
$149$	96277.8	−	166758.i	0.355271	−	0.615348i	0.987164	+	0.159708i	$0.0510551\pi$
$150$		0			0
$151$	−70849.3	−	122715.i	−0.252868	−	0.437980i	0.711447	−	0.702740i	$-0.248040\pi$
$151$	−70849.3	−	122715.i	−0.252868	−	0.437980i	−0.964314	+	0.264761i	$0.914707\pi$
$152$	−69766.9	+	120840.i	−0.244929	+	0.424230i
$153$		0			0
$154$	322267.	+	352319.i	1.09500	+	1.19711i
$155$	151524.			0.506586
$156$		0			0
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.805536	−	0.592546i	$-0.798123\pi$
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.110392	−	0.993888i	$-0.535211\pi$
$158$	−201764.	−	349466.i	−0.642986	−	1.11368i
$159$		0			0
$160$	−120562.			−0.372314
$161$	206611.	−	45612.4i	0.628186	−	0.138682i
$162$		0			0
$163$	215101.	−	372565.i	0.634121	−	1.09833i	−0.352579	−	0.935782i	$-0.614695\pi$
$163$	215101.	−	372565.i	0.634121	−	1.09833i	0.986701	−	0.162549i	$-0.0519714\pi$
$164$	−57856.0	−	100210.i	−0.167973	−	0.290937i
$165$		0			0
$166$	−145601.	+	252188.i	−0.410103	+	0.710319i
$167$	240265.			0.666653			0.333327	−	0.942811i	$-0.391829\pi$
$167$	240265.			0.666653			0.333327	+	0.942811i	$0.391829\pi$
$168$		0			0
$169$	−218028.			−0.587212
$170$	−164533.	+	284979.i	−0.436647	+	0.756295i
$171$		0			0
$172$	−65051.3	−	112672.i	−0.167662	−	0.290399i
$173$	−89650.1	+	155279.i	−0.227738	+	0.394454i	−0.957137	−	0.289634i	$-0.906466\pi$
$173$	−89650.1	+	155279.i	−0.227738	+	0.394454i	0.729399	+	0.684088i	$0.239800\pi$
$174$		0			0
$175$	63529.4	−	200869.i	0.156812	−	0.495812i
$176$	−708151.			−1.72323
$177$		0			0
$178$	−50117.9	−	86806.8i	−0.118561	−	0.205354i
$179$	−287780.	−	498449.i	−0.671317	−	1.16275i	−0.977531	−	0.210792i	$-0.932396\pi$
$179$	−287780.	−	498449.i	−0.671317	−	1.16275i	0.306214	−	0.951963i	$-0.400938\pi$
$180$		0			0
$181$	581006.			1.31821			0.659105	−	0.752051i	$-0.270935\pi$
$181$	581006.			1.31821			0.659105	+	0.752051i	$0.270935\pi$
$182$	−316684.	+	69912.7i	−0.708675	+	0.156451i
$183$		0			0
$184$	−120815.	+	209258.i	−0.263073	+	0.455657i
$185$	−315648.	−	546719.i	−0.678070	−	1.17445i
$186$		0			0
$187$	−383213.	+	663744.i	−0.801376	+	1.38802i
$188$	60174.9			0.124171
$189$		0			0
$190$	233237.			0.468721
$191$	−330280.	+	572062.i	−0.655087	+	1.13464i	0.326785	+	0.945099i	$0.394035\pi$
$191$	−330280.	+	572062.i	−0.655087	+	1.13464i	−0.981872	+	0.189545i	$0.939299\pi$
$192$		0			0
$193$	278655.	+	482645.i	0.538485	+	0.932684i	0.998986	+	0.0450243i	$0.0143365\pi$
$193$	278655.	+	482645.i	0.538485	+	0.932684i	−0.460501	+	0.887659i	$0.652330\pi$
$194$	9995.33	−	17312.4i	0.0190675	−	0.0330258i
$195$		0			0
$196$	134618.	−	62483.3i	0.250302	−	0.116178i
$197$	761400.			1.39781			0.698904	−	0.715216i	$-0.253672\pi$
$197$	761400.			1.39781			0.698904	+	0.715216i	$0.253672\pi$
$198$		0			0
$199$	67929.9	+	117658.i	0.121598	+	0.210615i	0.920398	−	0.390982i	$-0.127865\pi$
$199$	67929.9	+	117658.i	0.121598	+	0.210615i	−0.798800	+	0.601597i	$0.794531\pi$
$200$	120296.	+	208358.i	0.212655	+	0.368328i
$201$		0			0
$202$	−1.07996e6			−1.86221
$203$	−128060.	−	140002.i	−0.218109	−	0.238448i
$204$		0			0
$205$	253750.	−	439507.i	0.421716	−	0.730434i
$206$	360453.	+	624323.i	0.591807	+	1.02504i
$207$		0			0
$208$	240492.	−	416545.i	0.385428	−	0.667581i
$209$	543232.			0.860240
$210$		0			0
$211$	−991157.			−1.53263			−0.766313	−	0.642467i	$-0.777911\pi$
$211$	−991157.			−1.53263			−0.766313	+	0.642467i	$0.777911\pi$
$212$	−8880.48	+	15381.4i	−0.0135705	+	0.0235048i
$213$		0			0
$214$	71277.3	+	123456.i	0.106394	+	0.184280i
$215$	285307.	−	494167.i	0.420937	−	0.729084i
$216$		0			0
$217$	152951.	−	483602.i	0.220496	−	0.697170i
$218$	535596.			0.763301
$219$		0			0
$220$	98560.7	+	170712.i	0.137293	+	0.237798i
$221$	−260283.	−	450823.i	−0.358480	−	0.620906i
$222$		0			0
$223$	543344.			0.731666			0.365833	−	0.930681i	$-0.380784\pi$
$223$	543344.			0.731666			0.365833	+	0.930681i	$0.380784\pi$
$224$	−121696.	+	384782.i	−0.162053	+	0.512383i
$225$		0			0
$226$	130764.	−	226489.i	0.170300	−	0.294969i
$227$	8.16704	+	14.1457i	1.05196e−5	+	1.82205e-5i	0.866031	−	0.499991i	$-0.166663\pi$
$227$	8.16704	+	14.1457i	1.05196e−5	+	1.82205e-5i	−0.866020	+	0.500009i	$0.833330\pi$
$228$		0			0
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	−0.840619	−	0.541627i	$-0.817808\pi$
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	0.889372	+	0.457184i	$0.151142\pi$
$230$	403896.			0.503443
$231$		0			0
$232$	216679.			0.264299
$233$	−51828.6	+	89769.9i	−0.0625432	+	0.108328i	−0.895602	−	0.444857i	$-0.853254\pi$
$233$	−51828.6	+	89769.9i	−0.0625432	+	0.108328i	0.833058	+	0.553185i	$0.186588\pi$
$234$		0			0
$235$	131960.	+	228561.i	0.155874	+	0.269981i
$236$	227176.	−	393480.i	0.265511	−	0.459878i
$237$		0			0
$238$	743453.	+	812782.i	0.850768	+	0.930104i
$239$	−689109.			−0.780356			−0.390178	−	0.920739i	$-0.627587\pi$
$239$	−689109.			−0.780356			−0.390178	+	0.920739i	$0.627587\pi$
$240$		0			0
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	0.798458	−	0.602050i	$-0.205649\pi$
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	−0.920620	+	0.390460i	$0.872316\pi$
$242$	546890.	+	947242.i	0.600291	+	1.03973i
$243$		0			0
$244$	362910.			0.390234
$245$	532539.	+	374297.i	0.566809	+	0.398383i
$246$		0			0
$247$	−184485.	+	319537.i	−0.192406	+	0.333257i
$248$	289618.	+	501633.i	0.299017	+	0.517913i
$249$		0			0
$250$	587757.	−	1.01803e6i	0.594768	−	1.03017i
$251$	−1.43641e6			−1.43912			−0.719558	−	0.694433i	$-0.755655\pi$
$251$	−1.43641e6			−1.43912			−0.719558	+	0.694433i	$0.755655\pi$
$252$		0			0
$253$	940714.			0.923966
$254$	266042.	−	460799.i	0.258742	−	0.448154i
$255$		0			0
$256$	−404021.	−	699785.i	−0.385305	−	0.667367i
$257$	−454598.	+	787388.i	−0.429334	+	0.743628i	−0.996814	−	0.0797589i	$-0.974585\pi$
$257$	−454598.	+	787388.i	−0.429334	+	0.743628i	0.567480	+	0.823387i	$0.307918\pi$
$258$		0			0
$259$	−2.06352e6	+	455553.i	−1.91143	+	0.421977i
$260$	−133887.			−0.122830
$261$		0			0
$262$	533154.	+	923450.i	0.479843	+	0.831113i
$263$	374528.	+	648702.i	0.333884	+	0.578304i	0.983270	−	0.182155i	$-0.0583073\pi$
$263$	374528.	+	648702.i	0.333884	+	0.578304i	−0.649386	+	0.760459i	$0.724974\pi$
$264$		0			0
$265$	−77897.4			−0.0681410
$266$	235433.	−	744396.i	0.204015	−	0.645060i
$267$		0			0
$268$	−223313.	+	386789.i	−0.189923	+	0.328956i
$269$	334972.	+	580189.i	0.282246	+	0.488865i	0.971938	−	0.235238i	$-0.0755871\pi$
$269$	334972.	+	580189.i	0.282246	+	0.488865i	−0.689691	+	0.724104i	$0.742254\pi$
$270$		0			0
$271$	−270330.	+	468225.i	−0.223599	+	0.387285i	−0.955898	−	0.293698i	$-0.905114\pi$
$271$	−270330.	+	468225.i	−0.223599	+	0.387285i	0.732299	+	0.680983i	$0.238447\pi$
$272$	−1.63367e6			−1.33888
$273$		0			0
$274$	244246.			0.196540
$275$	468334.	−	811178.i	0.373443	−	0.646821i
$276$		0			0
$277$	200955.	+	348064.i	0.157362	+	0.272558i	0.933916	−	0.357491i	$-0.116368\pi$
$277$	200955.	+	348064.i	0.157362	+	0.272558i	−0.776555	+	0.630050i	$0.783035\pi$
$278$	339502.	−	588035.i	0.263470	−	0.456343i
$279$		0			0
$280$	−725871.	+	160247.i	−0.553304	+	0.122150i
$281$	429139.			0.324214			0.162107	−	0.986773i	$-0.448171\pi$
$281$	429139.			0.324214			0.162107	+	0.986773i	$0.448171\pi$
$282$		0			0
$283$	170463.	+	295251.i	0.126522	+	0.219142i	0.922327	−	0.386411i	$-0.126285\pi$
$283$	170463.	+	295251.i	0.126522	+	0.219142i	−0.795805	+	0.605553i	$0.792952\pi$
$284$	176478.	+	305669.i	0.129836	+	0.224883i
$285$		0			0
$286$	−1.44188e6			−1.04235
$287$	−1.14658e6	−	1.25351e6i	−0.821678	−	0.898301i
$288$		0			0
$289$	−174123.	+	301590.i	−0.122634	+	0.212409i
$290$	−181094.	−	313664.i	−0.126447	−	0.219013i
$291$		0			0
$292$	245868.	−	425855.i	0.168750	−	0.292284i
$293$	388847.			0.264612			0.132306	−	0.991209i	$-0.457762\pi$
$293$	388847.			0.264612			0.132306	+	0.991209i	$0.457762\pi$
$294$		0			0
$295$	1.99273e6			1.33319
$296$	1.20664e6	−	2.08996e6i	0.800475	−	1.38646i
$297$		0			0
$298$	−615202.	−	1.06556e6i	−0.401307	−	0.695085i
$299$	−319472.	+	553342.i	−0.206659	+	0.357945i
$300$		0			0
$301$	−1.28918e6	−	1.40940e6i	−0.820158	−	0.896640i
$302$	−905435.			−0.571268
$303$		0			0
$304$	578960.	+	1.00279e6i	0.359306	+	0.622336i
$305$	795840.	+	1.37844e6i	0.489865	+	0.848471i
$306$		0			0
$307$	−2.35747e6			−1.42758			−0.713789	−	0.700361i	$-0.753022\pi$
$307$	−2.35747e6			−1.42758			−0.713789	+	0.700361i	$0.753022\pi$
$308$	644330.	−	142246.i	0.387018	−	0.0854402i
$309$		0			0
$310$	484110.	−	838503.i	0.286114	−	0.495565i
$311$	−718314.	−	1.24416e6i	−0.421127	−	0.729414i	0.574923	−	0.818208i	$-0.305032\pi$
$311$	−718314.	−	1.24416e6i	−0.421127	−	0.729414i	−0.996050	+	0.0887939i	$0.971699\pi$
$312$		0			0
$313$	411400.	−	712566.i	0.237358	−	0.411116i	−0.722598	−	0.691269i	$-0.757052\pi$
$313$	411400.	−	712566.i	0.237358	−	0.411116i	0.959955	+	0.280153i	$0.0903853\pi$
$314$	−3.61520e6			−2.06923
$315$		0			0
$316$	−557652.			−0.314156
$317$	−883467.	+	1.53021e6i	−0.493790	+	0.855269i	−0.999974	−	0.00715584i	$-0.997722\pi$
$317$	−883467.	+	1.53021e6i	−0.493790	+	0.855269i	0.506184	+	0.862425i	$0.331056\pi$
$318$		0			0
$319$	−421786.	−	730555.i	−0.232068	−	0.401954i
$320$	376132.	−	651480.i	0.205336	−	0.355653i
$321$		0			0
$322$	407698.	−	1.28907e6i	0.219129	−	0.692845i
$323$	1.25321e6			0.668370
$324$		0			0
$325$	318098.	+	550962.i	0.167052	+	0.289343i
$326$	−1.37446e6	−	2.38064e6i	−0.716291	−	1.24065i
$327$		0			0
$328$	1.94003e6			0.995689
$329$	862675.	−	190448.i	0.439397	−	0.0970036i
$330$		0			0
$331$	1526.14	−	2643.35i	0.000765638	−	0.00132612i	−0.865642	−	0.500663i	$-0.833090\pi$
$331$	1526.14	−	2643.35i	0.000765638	−	0.00132612i	0.866408	+	0.499337i	$0.166423\pi$
$332$	201211.	+	348508.i	0.100186	+	0.173527i
$333$		0			0
$334$	767632.	−	1.32958e6i	0.376519	−	0.652150i
$335$	−1.95885e6			−0.953649
$336$		0			0
$337$	2.02939e6			0.973398			0.486699	−	0.873570i	$-0.338201\pi$
$337$	2.02939e6			0.973398			0.486699	+	0.873570i	$0.338201\pi$
$338$	−696584.	+	1.20652e6i	−0.331651	+	0.574437i
$339$		0			0
$340$	227374.	+	393824.i	0.106670	+	0.184759i
$341$	1.12754e6	−	1.95295e6i	0.525104	−	0.909507i
$342$		0			0
$343$	1.73215e6	−	1.32182e6i	0.794969	−	0.606650i
$344$	2.18130e6			0.993848
$345$		0			0
$346$	572852.	+	992209.i	0.257248	+	0.445567i
$347$	1.89109e6	+	3.27547e6i	0.843119	+	1.46033i	0.887245	+	0.461299i	$0.152617\pi$
$347$	1.89109e6	+	3.27547e6i	0.843119	+	1.46033i	−0.0441252	+	0.999026i	$0.514050\pi$
$348$		0			0
$349$	291147.			0.127953			0.0639763	−	0.997951i	$-0.479622\pi$
$349$	291147.			0.127953			0.0639763	+	0.997951i	$0.479622\pi$
$350$	−908592.	−	993320.i	−0.396460	−	0.433430i
$351$		0			0
$352$	−897136.	+	1.55389e6i	−0.385924	+	0.668440i
$353$	192538.	+	333486.i	0.0822394	+	0.142443i	0.904212	−	0.427085i	$-0.140459\pi$
$353$	192538.	+	333486.i	0.0822394	+	0.142443i	−0.821972	+	0.569528i	$0.807126\pi$
$354$		0			0
$355$	−774013.	+	1.34063e6i	−0.325970	+	0.564596i
$356$	−138520.			−0.0579277
$357$		0			0
$358$	−3.67775e6			−1.51661
$359$	−1.61507e6	+	2.79738e6i	−0.661385	+	1.14555i	0.318866	+	0.947800i	$0.396698\pi$
$359$	−1.61507e6	+	2.79738e6i	−0.661385	+	1.14555i	−0.980252	+	0.197753i	$0.936635\pi$
$360$		0			0
$361$	793921.	+	1.37511e6i	0.320634	+	0.555354i
$362$	1.85628e6	−	3.21517e6i	0.744511	−	1.28953i
$363$		0			0
$364$	−135148.	+	427312.i	−0.0534632	+	0.169041i
$365$	2.15669e6			0.847336
$366$		0			0
$367$	239779.	+	415310.i	0.0929280	+	0.160956i	0.908742	−	0.417358i	$-0.137044\pi$
$367$	239779.	+	415310.i	0.0929280	+	0.160956i	−0.815814	+	0.578314i	$0.803711\pi$
$368$	1.00258e6	+	1.73653e6i	0.385923	+	0.668439i
$369$		0			0
$370$	−4.03390e6			−1.53187
$371$	−78630.6	+	248616.i	−0.0296590	+	0.0937766i
$372$		0			0
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	−0.935724	−	0.352734i	$-0.885252\pi$
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	0.773339	+	0.633993i	$0.218585\pi$
$374$	2.44868e6	+	4.24124e6i	0.905217	+	1.56788i
$375$		0			0
$376$	−504447.	+	873728.i	−0.184012	+	0.318718i
$377$	572965.			0.207622
$378$		0			0
$379$	−2.43493e6			−0.870742			−0.435371	−	0.900251i	$-0.643383\pi$
$379$	−2.43493e6			−0.870742			−0.435371	+	0.900251i	$0.643383\pi$
$380$	161160.	−	279137.i	0.0572529	−	0.0991650i
$381$		0			0
$382$	2.11044e6	+	3.65540e6i	0.739973	+	1.28167i
$383$	−1.80584e6	+	3.12781e6i	−0.629047	+	1.08954i	0.358696	+	0.933454i	$0.383222\pi$
$383$	−1.80584e6	+	3.12781e6i	−0.629047	+	1.08954i	−0.987743	+	0.156087i	$0.950112\pi$
$384$		0			0
$385$	1.95327e6	+	2.13541e6i	0.671598	+	0.734226i
$386$	3.56114e6			1.21652
$387$		0			0
$388$	−13812.9	−	23924.7i	−0.00465807	−	0.00806802i
$389$	−87616.2	−	151756.i	−0.0293569	−	0.0508477i	0.850974	−	0.525208i	$-0.176013\pi$
$389$	−87616.2	−	151756.i	−0.0293569	−	0.0508477i	−0.880331	+	0.474361i	$0.842679\pi$
$390$		0			0
$391$	2.17018e6			0.717882
$392$	−221262.	+	2.47843e6i	−0.0727262	+	0.814632i
$393$		0			0
$394$	2.43262e6	−	4.21343e6i	0.789467	−	1.36740i
$395$	−1.22290e6	−	2.11812e6i	−0.394364	−	0.683058i
$396$		0			0
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	−0.976170	−	0.217007i	$-0.930371\pi$
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	0.676019	+	0.736885i	$0.263704\pi$
$398$	868126.			0.274710
$399$		0			0
$400$	1.99654e6			0.623920
$401$	669915.	−	1.16033e6i	0.208046	−	0.360346i	−0.743053	−	0.669232i	$-0.766623\pi$
$401$	669915.	−	1.16033e6i	0.208046	−	0.360346i	0.951099	+	0.308887i	$0.0999564\pi$
$402$		0			0
$403$	765839.	+	1.32647e6i	0.234895	+	0.406851i
$404$	−746217.	+	1.29249e6i	−0.227463	+	0.393978i
$405$		0			0
$406$	−1.18388e6	+	261360.i	−0.356446	+	0.0786909i
$407$	−9.39535e6			−2.81143
$408$		0			0
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.685043	−	0.728503i	$-0.740217\pi$
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.288381	−	0.957516i	$-0.593117\pi$
$410$	−1.62143e6	−	2.80839e6i	−0.476362	−	0.825084i
$411$		0			0
$412$	996247.			0.289150
$413$	2.01149e6	−	6.35996e6i	0.580286	−	1.83476i
$414$		0			0
$415$	−882487.	+	1.52851e6i	−0.251529	+	0.435661i
$416$	−609346.	−	1.05542e6i	−0.172636	−	0.299014i
$417$		0			0
$418$	1.73559e6	−	3.00613e6i	0.485855	−	0.841525i
$419$	6.96869e6			1.93917			0.969585	−	0.244754i	$-0.0787071\pi$
$419$	6.96869e6			1.93917			0.969585	+	0.244754i	$0.0787071\pi$
$420$		0			0
$421$	3.84041e6			1.05602			0.528010	−	0.849238i	$-0.322938\pi$
$421$	3.84041e6			1.05602			0.528010	+	0.849238i	$0.322938\pi$
$422$	−3.16668e6	+	5.48485e6i	−0.865612	+	1.49928i
$423$		0			0
$424$	−148890.	−	257886.i	−0.0402209	−	0.0696647i
$425$	1.08042e6	−	1.87134e6i	0.290149	−	0.502552i
$426$		0			0
$427$	5.20272e6	−	1.14858e6i	1.38090	−	0.304854i
$428$	197002.			0.0519829
$429$		0			0
$430$	−1.82308e6	−	3.15766e6i	−0.475481	−	0.823558i
$431$	1.51818e6	+	2.62957e6i	0.393668	+	0.681854i	0.992930	−	0.118699i	$-0.0378725\pi$
$431$	1.51818e6	+	2.62957e6i	0.393668	+	0.681854i	−0.599262	+	0.800553i	$0.704539\pi$
$432$		0			0
$433$	−941529.			−0.241332			−0.120666	−	0.992693i	$-0.538503\pi$
$433$	−941529.			−0.241332			−0.120666	+	0.992693i	$0.538503\pi$
$434$	−2.18749e6	−	2.39147e6i	−0.557469	−	0.609454i
$435$		0			0
$436$	370080.	−	640997.i	0.0932351	−	0.161488i
$437$	−769096.	−	1.33211e6i	−0.192653	−	0.333686i
$438$		0			0
$439$	−670546.	+	1.16142e6i	−0.166061	+	0.287626i	−0.937031	−	0.349245i	$-0.886438\pi$
$439$	−670546.	+	1.16142e6i	−0.166061	+	0.287626i	0.770971	+	0.636871i	$0.219771\pi$
$440$	−3.30494e6			−0.813827
$441$		0			0
$442$	−3.32635e6			−0.809864
$443$	−386171.	+	668867.i	−0.0934910	+	0.161931i	−0.908978	−	0.416844i	$-0.863136\pi$
$443$	−386171.	+	668867.i	−0.0934910	+	0.161931i	0.815487	+	0.578776i	$0.196469\pi$
$444$		0			0
$445$	−303765.	−	526137.i	−0.0727174	−	0.125950i
$446$	1.73595e6	−	3.00675e6i	0.413238	−	0.715748i
$447$		0			0
$448$	−1.69958e6	−	1.85807e6i	−0.400080	−	0.437388i
$449$	−2.25684e6			−0.528304			−0.264152	−	0.964481i	$-0.585092\pi$
$449$	−2.25684e6			−0.528304			−0.264152	+	0.964481i	$0.585092\pi$
$450$		0			0
$451$	−3.77646e6	−	6.54101e6i	−0.874265	−	1.51427i
$452$	−180707.	−	312994.i	−0.0416034	−	0.0720593i
$453$		0			0
$454$	104.373			2.37655e−5
$455$	−1.91942e6	+	423742.i	−0.434653	+	0.0959561i
$456$		0			0
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	−0.999733	−	0.0231196i	$-0.992640\pi$
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	0.519889	+	0.854234i	$0.325973\pi$
$458$	−247221.	−	428199.i	−0.0550708	−	0.0953854i
$459$		0			0
$460$	279080.	−	483381.i	0.0614942	−	0.106511i
$461$	3.10462e6			0.680387			0.340193	−	0.940355i	$-0.389507\pi$
$461$	3.10462e6			0.680387			0.340193	+	0.940355i	$0.389507\pi$
$462$		0			0
$463$	−3.53386e6			−0.766121			−0.383060	−	0.923723i	$-0.625130\pi$
$463$	−3.53386e6			−0.766121			−0.383060	+	0.923723i	$0.625130\pi$
$464$	899053.	−	1.55721e6i	0.193861	−	0.335777i
$465$		0			0
$466$	331178.	+	573617.i	0.0706475	+	0.122365i
$467$	1.36230e6	−	2.35957e6i	0.289054	−	0.500657i	−0.684530	−	0.728985i	$-0.739993\pi$
$467$	1.36230e6	−	2.35957e6i	0.289054	−	0.500657i	0.973584	+	0.228328i	$0.0733258\pi$
$468$		0			0
$469$	−1.97728e6	+	6.25182e6i	−0.415085	+	1.31242i
$470$	1.68641e6			0.352143
$471$		0			0
$472$	3.80883e6	+	6.59709e6i	0.786932	+	1.36301i
$473$	−4.24612e6	−	7.35449e6i	−0.872649	−	1.51147i
$474$		0			0
$475$	−1.53158e6			−0.311461
$476$	1.48643e6	−	328153.i	0.300697	−	0.0663833i
$477$		0			0
$478$	−2.20166e6	+	3.81338e6i	−0.440737	+	0.763379i
$479$	489342.	+	847566.i	0.0974482	+	0.168785i	0.910628	−	0.413228i	$-0.135599\pi$
$479$	489342.	+	847566.i	0.0974482	+	0.168785i	−0.813180	+	0.582013i	$0.802265\pi$
$480$		0			0
$481$	3.19072e6	−	5.52649e6i	0.628819	−	1.08915i
$482$	−1.40766e6			−0.275982
$483$		0			0
$484$	1.51154e6			0.293296
$485$	60581.8	−	104931.i	0.0116947	−	0.0202558i
$486$		0			0
$487$	−1.96372e6	−	3.40126e6i	−0.375195	−	0.649857i	0.615161	−	0.788401i	$-0.289091\pi$
$487$	−1.96372e6	−	3.40126e6i	−0.375195	−	0.649857i	−0.990356	+	0.138544i	$0.955758\pi$
$488$	−3.04228e6	+	5.26938e6i	−0.578295	+	1.00164i
$489$		0			0
$490$	3.77271e6	−	1.75111e6i	0.709844	−	0.329475i
$491$	−2.63241e6			−0.492777			−0.246388	−	0.969171i	$-0.579244\pi$
$491$	−2.63241e6			−0.492777			−0.246388	+	0.969171i	$0.579244\pi$
$492$		0			0
$493$	−973037.	−	1.68535e6i	−0.180307	−	0.312301i
$494$	1.17883e6	+	2.04180e6i	0.217338	+	0.376440i
$495$		0			0
$496$	4.80678e6			0.877305
$497$	3.49743e6	+	3.82357e6i	0.635123	+	0.694350i
$498$		0			0
$499$	−1.06272e6	+	1.84069e6i	−0.191059	+	0.330924i	−0.945601	−	0.325327i	$-0.894526\pi$
$499$	−1.06272e6	+	1.84069e6i	−0.191059	+	0.330924i	0.754542	+	0.656251i	$0.227859\pi$
$500$	−812244.	−	1.40685e6i	−0.145299	−	0.251665i
$501$		0			0
$502$	−4.58925e6	+	7.94881e6i	−0.812798	+	1.40781i
$503$	−2.60929e6			−0.459835			−0.229917	−	0.973210i	$-0.573846\pi$
$503$	−2.60929e6			−0.459835			−0.229917	+	0.973210i	$0.573846\pi$
$504$		0			0
$505$	−6.54564e6			−1.14215
$506$	3.00552e6	−	5.20571e6i	0.521847	−	0.903865i
$507$		0			0
$508$	−367654.	−	636795.i	−0.0632092	−	0.109481i
$509$	−5.00911e6	+	8.67603e6i	−0.856970	+	1.48432i	0.0178348	+	0.999841i	$0.494323\pi$
$509$	−5.00911e6	+	8.67603e6i	−0.856970	+	1.48432i	−0.874805	+	0.484475i	$0.839011\pi$
$510$		0			0
$511$	2.17699e6	−	6.88326e6i	0.368811	−	1.16612i
$512$	1.99607e6			0.336512
$513$		0			0
$514$	2.90482e6	+	5.03130e6i	0.484967	+	0.839987i
$515$	2.18471e6	+	3.78403e6i	0.362974	+	0.628689i
$516$		0			0
$517$	3.92782e6			0.646287
$518$	−4.07187e6	+	1.28745e7i	−0.666760	+	2.10818i
$519$		0			0
$520$	1.12238e6	−	1.94402e6i	0.182025	−	0.315277i
$521$	−2.08970e6	−	3.61947e6i	−0.337280	−	0.584186i	0.646640	−	0.762795i	$-0.276174\pi$
$521$	−2.08970e6	−	3.61947e6i	−0.337280	−	0.584186i	−0.983920	+	0.178609i	$0.942840\pi$
$522$		0			0
$523$	−1.80263e6	+	3.12224e6i	−0.288172	+	0.499128i	−0.973373	−	0.229225i	$-0.926381\pi$
$523$	−1.80263e6	+	3.12224e6i	−0.288172	+	0.499128i	0.685202	+	0.728353i	$0.259714\pi$
$524$	1.47357e6			0.234446
$525$		0			0
$526$	4.78637e6			0.754297
$527$	2.60117e6	−	4.50536e6i	0.407983	−	0.706648i
$528$		0			0
$529$	1.88633e6	+	3.26722e6i	0.293075	+	0.507621i
$530$	−248877.	+	431068.i	−0.0384853	+	0.0666586i
$531$		0			0
$532$	−728212.	−	796119.i	−0.111552	−	0.121955i
$533$	5.13003e6			0.782172
$534$		0			0
$535$	432013.	+	748268.i	0.0652547	+	0.113025i
$536$	−3.74407e6	−	6.48492e6i	−0.562901	−	0.974972i
$537$		0			0
$538$	4.28086e6			0.637640
$539$	8.78699e6	−	4.07850e6i	1.30277	−	0.604684i
$540$		0			0
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	−0.509193	−	0.860653i	$-0.670056\pi$
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	0.999943	+	0.0106475i	$0.00338926\pi$
$542$	1.72737e6	+	2.99189e6i	0.252573	+	0.437470i
$543$		0			0
$544$	−2.06964e6	+	3.58473e6i	−0.299846	+	0.519349i
$545$	3.24625e6			0.468156
$546$		0			0
$547$	8.69076e6			1.24191			0.620954	−	0.783847i	$-0.286745\pi$
$547$	8.69076e6			1.24191			0.620954	+	0.783847i	$0.286745\pi$
$548$	168766.	−	292312.i	0.0240068	−	0.0415810i
$549$		0			0
$550$	−2.99259e6	−	5.18332e6i	−0.421833	−	0.730636i
$551$	−689676.	+	1.19455e6i	−0.0967756	+	0.167620i
$552$		0			0
$553$	−7.99456e6	+	1.76492e6i	−1.11168	+	0.245421i
$554$	2.56815e6			0.355505
$555$		0			0
$556$	−469171.	−	812628.i	−0.0643642	−	0.111482i
$557$	3.12371e6	+	5.41042e6i	0.426612	+	0.738913i	0.996569	−	0.0827611i	$-0.0263738\pi$
$557$	3.12371e6	+	5.41042e6i	0.426612	+	0.738913i	−0.569958	+	0.821674i	$0.693040\pi$
$558$		0			0
$559$	5.76803e6			0.780725
$560$	−1.86017e6	+	5.88152e6i	−0.250658	+	0.792537i
$561$		0			0
$562$	1.37107e6	−	2.37476e6i	0.183113	−	0.317161i
$563$	−5.95223e6	−	1.03096e7i	−0.791423	−	1.37078i	−0.925086	−	0.379758i	$-0.876007\pi$
$563$	−5.95223e6	−	1.03096e7i	−0.791423	−	1.37078i	0.133663	−	0.991027i	$-0.457326\pi$
$564$		0			0
$565$	792560.	−	1.37275e6i	0.104451	−	0.180914i
$566$	2.17848e6			0.285833
$567$		0			0
$568$	−5.91768e6			−0.769627
$569$	10707.2	−	18545.4i	0.00138642	−	0.00240135i	−0.865331	−	0.501200i	$-0.832892\pi$
$569$	10707.2	−	18545.4i	0.00138642	−	0.00240135i	0.866718	+	0.498799i	$0.166225\pi$
$570$		0			0
$571$	−3.55823e6	−	6.16304e6i	−0.456714	−	0.791051i	0.542071	−	0.840333i	$-0.317640\pi$
$571$	−3.55823e6	−	6.16304e6i	−0.456714	−	0.791051i	−0.998785	+	0.0492811i	$0.984307\pi$
$572$	−996297.	+	1.72564e6i	−0.127321	+	0.220526i
$573$		0			0
$574$	−1.05999e7	+	2.34009e6i	−1.34283	+	0.296451i
$575$	−2.65223e6			−0.334534
$576$		0			0
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	0.978793	+	0.204854i	$0.0656719\pi$
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	−0.311988	+	0.950086i	$0.600995\pi$
$578$	1.11262e6	+	1.92712e6i	0.138525	+	0.239932i
$579$		0			0
$580$	−500522.			−0.0617808
$581$	3.98758e6	+	4.35943e6i	0.490083	+	0.535784i
$582$		0			0
$583$	−579659.	+	1.00400e6i	−0.0706319	+	0.122338i
$584$	4.12222e6	+	7.13990e6i	0.500149	+	0.866283i
$585$		0			0
$586$	1.24234e6	−	2.15180e6i	0.149450	−	0.258856i
$587$	1.30101e7			1.55843			0.779213	−	0.626759i	$-0.215619\pi$
$587$	1.30101e7			1.55843			0.779213	+	0.626759i	$0.215619\pi$
$588$		0			0
$589$	−3.68735e6			−0.437952
$590$	6.36664e6	−	1.10273e7i	0.752975	−	1.30419i
$591$		0			0
$592$	−1.00133e7	−	1.73435e7i	−1.17428	−	2.03391i
$593$	2.13043e6	−	3.69002e6i	0.248789	−	0.430915i	−0.714401	−	0.699736i	$-0.753301\pi$
$593$	2.13043e6	−	3.69002e6i	0.248789	−	0.430915i	0.963190	+	0.268821i	$0.0866342\pi$
$594$		0			0
$595$	4.50608e6	+	4.92628e6i	0.521803	+	0.570462i
$596$	−1.70034e6			−0.196074
$597$		0			0
$598$	2.04139e6	+	3.53578e6i	0.233438	+	0.404327i
$599$	−6.89790e6	−	1.19475e7i	−0.785507	−	1.36054i	−0.928696	−	0.370842i	$-0.879069\pi$
$599$	−6.89790e6	−	1.19475e7i	−0.785507	−	1.36054i	0.143189	−	0.989695i	$-0.454264\pi$
$600$		0			0
$601$	4.99695e6			0.564311			0.282155	−	0.959369i	$-0.408951\pi$
$601$	4.99695e6			0.564311			0.282155	+	0.959369i	$0.408951\pi$
$602$	−1.19182e7	+	2.63111e6i	−1.34035	+	0.295902i
$603$		0			0
$604$	−625628.	+	1.08362e6i	−0.0697788	+	0.120860i
$605$	3.31471e6	+	5.74125e6i	0.368177	+	0.637702i
$606$		0			0
$607$	1.52473e6	−	2.64091e6i	0.167966	−	0.290926i	−0.769739	−	0.638359i	$-0.779613\pi$
$607$	1.52473e6	−	2.64091e6i	0.167966	−	0.290926i	0.937705	+	0.347434i	$0.112947\pi$
$608$	2.93387e6			0.321871
$609$		0			0
$610$	1.01706e7			1.10668
$611$	−1.33391e6	+	2.31040e6i	−0.144552	+	0.250372i
$612$		0			0
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	0.990793	−	0.135388i	$-0.0432282\pi$
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$614$	−7.53195e6	+	1.30457e7i	−0.806281	+	1.39652i
$615$		0			0
$616$	−3.33605e6	+	1.05480e7i	−0.354226	+	1.12000i
$617$	−1.00066e7			−1.05822			−0.529108	−	0.848554i	$-0.677473\pi$
$617$	−1.00066e7			−1.05822			−0.529108	+	0.848554i	$0.677473\pi$
$618$		0			0
$619$	3.27533e6	+	5.67304e6i	0.343581	+	0.595099i	0.985095	−	0.172012i	$-0.0550268\pi$
$619$	3.27533e6	+	5.67304e6i	0.343581	+	0.595099i	−0.641514	+	0.767111i	$0.721693\pi$
$620$	−669010.	−	1.15876e6i	−0.0698962	−	0.121064i
$621$		0			0
$622$	−9.17986e6			−0.951393
$623$	−1.98583e6	+	438403.i	−0.204985	+	0.0452536i
$624$		0			0
$625$	1.02325e6	−	1.77232e6i	0.104781	−	0.181485i
$626$	−2.62879e6	−	4.55320e6i	−0.268114	−	0.464388i
$627$		0			0
$628$	−2.49799e6	+	4.32665e6i	−0.252750	+	0.437777i
$629$	−2.16746e7			−2.18436
$630$		0			0
$631$	2.22672e6			0.222635			0.111317	−	0.993785i	$-0.464493\pi$
$631$	2.22672e6			0.222635			0.111317	+	0.993785i	$0.464493\pi$
$632$	4.67480e6	−	8.09699e6i	0.465554	−	0.806364i
$633$		0			0
$634$	5.64524e6	+	9.77784e6i	0.557775	+	0.966095i
$635$	1.61249e6	−	2.79291e6i	0.158694	−	0.274867i
$636$		0			0
$637$	−585084.	+	6.55373e6i	−0.0571307	+	0.639941i
$638$	−5.39031e6			−0.524279
$639$		0			0
$640$	−4.33242e6	−	7.50397e6i	−0.418101	−	0.724171i
$641$	−7.96698e6	−	1.37992e7i	−0.765859	−	1.32651i	−0.939791	−	0.341749i	$-0.888981\pi$
$641$	−7.96698e6	−	1.37992e7i	−0.765859	−	1.32651i	0.173932	−	0.984758i	$-0.444353\pi$
$642$		0			0
$643$	−1.49933e7			−1.43011			−0.715056	−	0.699067i	$-0.753599\pi$
$643$	−1.49933e7			−1.43011			−0.715056	+	0.699067i	$0.753599\pi$
$644$	−1.26104e6	−	1.37864e6i	−0.119816	−	0.130989i
$645$		0			0
$646$	4.00391e6	−	6.93498e6i	0.377488	−	0.653829i
$647$	6.49027e6	+	1.12415e7i	0.609540	+	1.05575i	0.991316	+	0.131500i	$0.0419792\pi$
$647$	6.49027e6	+	1.12415e7i	0.609540	+	1.05575i	−0.381776	+	0.924255i	$0.624687\pi$
$648$		0			0
$649$	1.48285e7	−	2.56838e7i	1.38193	−	2.39357i
$650$	4.06521e6			0.377398
$651$		0			0
$652$	−3.79885e6			−0.349972
$653$	−8.27460e6	+	1.43320e7i	−0.759389	+	1.31530i	0.183774	+	0.982969i	$0.441169\pi$
$653$	−8.27460e6	+	1.43320e7i	−0.759389	+	1.31530i	−0.943163	+	0.332332i	$0.892165\pi$
$654$		0			0
$655$	3.23145e6	+	5.59704e6i	0.294303	+	0.509748i
$656$	8.04966e6	−	1.39424e7i	0.730328	−	1.26497i
$657$		0			0
$658$	1.70229e6	−	5.38233e6i	0.153274	−	0.484625i
$659$	−5.86879e6			−0.526423			−0.263212	−	0.964738i	$-0.584782\pi$
$659$	−5.86879e6			−0.526423			−0.263212	+	0.964738i	$0.584782\pi$
$660$		0			0
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	0.657389	−	0.753551i	$-0.271661\pi$
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	−0.981289	+	0.192540i	$0.938327\pi$
$662$	−9751.81	−	16890.6i	−0.000864849	−	0.00149796i
$663$		0			0
$664$	−6.74702e6			−0.593870
$665$	1.42696e6	−	4.51179e6i	0.125129	−	0.395635i
$666$		0			0
$667$	−1.19431e6	+	2.06861e6i	−0.103945	+	0.180038i
$668$	−1.06082e6	−	1.83739e6i	−0.0919815	−	0.159317i
$669$		0			0
$670$	−6.25838e6	+	1.08398e7i	−0.538611	+	0.932902i
$671$	2.36884e7			2.03109
$672$		0			0
$673$	−1.82417e7			−1.55248			−0.776241	−	0.630437i	$-0.782876\pi$
$673$	−1.82417e7			−1.55248			−0.776241	+	0.630437i	$0.782876\pi$
$674$	6.48376e6	−	1.12302e7i	0.549765	−	0.952222i
$675$		0			0
$676$	962636.	+	1.66733e6i	0.0810205	+	0.140332i
$677$	−3.88203e6	+	6.72387e6i	−0.325527	+	0.563829i	−0.981619	−	0.190852i	$-0.938875\pi$
$677$	−3.88203e6	+	6.72387e6i	−0.325527	+	0.563829i	0.656092	+	0.754681i	$0.272208\pi$
$678$		0			0
$679$	−273743.	−	299270.i	−0.0227860	−	0.0249109i
$680$	−7.62432e6			−0.632308
$681$		0			0
$682$	−7.20482e6	−	1.24791e7i	−0.593147	−	1.02736i
$683$	4.28162e6	+	7.41598e6i	0.351201	+	0.608299i	0.986460	−	0.164001i	$-0.0524399\pi$
$683$	4.28162e6	+	7.41598e6i	0.351201	+	0.608299i	−0.635259	+	0.772299i	$0.719107\pi$
$684$		0			0
$685$	1.48038e6			0.120544
$686$	−1.78059e6	−	1.38085e7i	−0.144462	−	1.12030i
$687$		0			0
$688$	9.05076e6	−	1.56764e7i	0.728978	−	1.26263i
$689$	−393712.	−	681928.i	−0.0315959	−	0.0547256i
$690$		0			0
$691$	−8.22547e6	+	1.42469e7i	−0.655338	+	1.13508i	0.326471	+	0.945207i	$0.394140\pi$
$691$	−8.22547e6	+	1.42469e7i	−0.655338	+	1.13508i	−0.981809	+	0.189872i	$0.939193\pi$
$692$	1.58329e6			0.125689
$693$		0			0
$694$	2.41677e7			1.90474
$695$	2.05773e6	−	3.56409e6i	0.161594	−	0.279890i
$696$		0			0
$697$	−8.71208e6	−	1.50898e7i	−0.679266	−	1.17652i
$698$	930197.	−	1.61115e6i	0.0722664	−	0.125169i
$699$		0			0
$700$	−1.81661e6	+	401044.i	−0.140125	+	0.0309347i
$701$	1.66928e7			1.28302			0.641512	−	0.767113i	$-0.278307\pi$
$701$	1.66928e7			1.28302			0.641512	+	0.767113i	$0.278307\pi$
$702$		0			0
$703$	7.68132e6	+	1.33044e7i	0.586202	+	1.01533i
$704$	−5.59783e6	−	9.69573e6i	−0.425685	−	0.737308i
$705$		0			0
$706$	2.46059e6			0.185792
$707$	−6.60725e6	+	2.08909e7i	−0.497132	+	1.57184i
$708$		0			0
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	−0.951669	−	0.307126i	$-0.900633\pi$
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	0.741813	+	0.670606i	$0.233966\pi$
$710$	4.94584e6	+	8.56644e6i	0.368209	+	0.637756i
$711$		0			0
$712$	1.16121e6	−	2.01128e6i	0.0858443	−	0.148687i
$713$	−6.38537e6			−0.470395
$714$		0			0
$715$	−8.73927e6			−0.639308
$716$	−2.54121e6	+	4.40150e6i	−0.185250	+	0.320862i
$717$		0			0
$718$	1.03201e7	+	1.78749e7i	0.747087	+	1.29399i
$719$	5.18592e6	−	8.98227e6i	0.374113	−	0.647983i	−0.616081	−	0.787683i	$-0.711280\pi$
$719$	5.18592e6	−	8.98227e6i	0.374113	−	0.647983i	0.990194	+	0.139700i	$0.0446138\pi$
$720$		0			0
$721$	1.42823e7	−	3.15303e6i	1.02320	−	0.225887i
$722$	1.01461e7			0.724363
$723$		0			0
$724$	−2.56526e6	−	4.44316e6i	−0.181880	−	0.315025i
$725$	1.18917e6	+	2.05971e6i	0.0840233	+	0.145533i
$726$		0			0
$727$	1.15369e7			0.809565			0.404783	−	0.914413i	$-0.367347\pi$
$727$	1.15369e7			0.809565			0.404783	+	0.914413i	$0.367347\pi$
$728$	−5.07155e6	−	5.54448e6i	−0.354660	−	0.387733i
$729$		0			0
$730$	6.89049e6	−	1.19347e7i	0.478567	−	0.828902i
$731$	−9.79557e6	−	1.69664e7i	−0.678010	−	1.17435i
$732$		0			0
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	0.486109	+	0.873898i	$0.338416\pi$
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	−0.999873	+	0.0159667i	$0.994917\pi$
$734$	3.06432e6			0.209939
$735$		0			0
$736$	5.08058e6			0.345715
$737$	−1.45764e7	+	2.52470e7i	−0.988510	+	1.71215i
$738$		0			0
$739$	−4.50682e6	−	7.80604e6i	−0.303570	−	0.525799i	0.673372	−	0.739304i	$-0.264845\pi$
$739$	−4.50682e6	−	7.80604e6i	−0.303570	−	0.525799i	−0.976942	+	0.213505i	$0.931512\pi$
$740$	−2.78730e6	+	4.82775e6i	−0.187113	+	0.324090i
$741$		0			0
$742$	1.12457e6	+	1.22944e6i	0.0749853	+	0.0819779i
$743$	2.10239e7			1.39714			0.698571	−	0.715541i	$-0.253820\pi$
$743$	2.10239e7			1.39714			0.698571	+	0.715541i	$0.253820\pi$
$744$		0			0
$745$	−3.72875e6	−	6.45838e6i	−0.246134	−	0.426317i
$746$	2.78811e6	+	4.82915e6i	0.183427	+	0.317705i
$747$		0			0
$748$	6.76785e6			0.442279
$749$	2.82424e6	−	623493.i	0.183949	−	0.0406094i
$750$		0			0
$751$	−2.02110e6	+	3.50064e6i	−0.130764	+	0.226489i	−0.923971	−	0.382462i	$-0.875076\pi$
$751$	−2.02110e6	+	3.50064e6i	−0.130764	+	0.226489i	0.793207	+	0.608952i	$0.208410\pi$
$752$	4.18615e6	+	7.25062e6i	0.269942	+	0.467553i
$753$		0			0
$754$	1.83058e6	−	3.17066e6i	0.117263	−	0.203106i
$755$	−5.48786e6			−0.350377
$756$		0			0
$757$	−1.82059e7			−1.15471			−0.577353	−	0.816495i	$-0.695914\pi$
$757$	−1.82059e7			−1.15471			−0.577353	+	0.816495i	$0.695914\pi$
$758$	−7.77945e6	+	1.34744e7i	−0.491786	+	0.851798i
$759$		0			0
$760$	2.70201e6	+	4.68001e6i	0.169689	+	0.293909i
$761$	−9.45999e6	+	1.63852e7i	−0.592146	+	1.02563i	0.401797	+	0.915729i	$0.368386\pi$
$761$	−9.45999e6	+	1.63852e7i	−0.592146	+	1.02563i	−0.993943	+	0.109898i	$0.964947\pi$
$762$		0			0
$763$	3.27681e6	−	1.03607e7i	0.203770	−	0.644283i
$764$	5.83301e6			0.361542
$765$		0			0
$766$	1.15391e7	+	1.99863e7i	0.710559	+	1.23072i
$767$	1.00717e7	+	1.74447e7i	0.618180	+	1.07072i
$768$		0			0
$769$	−1.12831e7			−0.688037			−0.344019	−	0.938963i	$-0.611788\pi$
$769$	−1.12831e7			−0.688037			−0.344019	+	0.938963i	$0.611788\pi$
$770$	1.80575e7	−	3.98646e6i	1.09756	−	0.242304i
$771$		0			0
$772$	2.46064e6	−	4.26195e6i	0.148595	−	0.257374i
$773$	−1.84282e6	−	3.19186e6i	−0.110926	−	0.192130i	0.805218	−	0.592979i	$-0.202048\pi$
$773$	−1.84282e6	−	3.19186e6i	−0.110926	−	0.192130i	−0.916144	+	0.400849i	$0.868715\pi$
$774$		0			0
$775$	−3.17896e6	+	5.50611e6i	−0.190121	+	0.329299i
$776$	463176.			0.0276116
$777$		0			0
$778$	−1.11971e6			−0.0663219
$779$	−6.17501e6	+	1.06954e7i	−0.364581	+	0.631472i
$780$		0			0
$781$	1.15193e7	+	1.99521e7i	0.675771	+	1.17047i
$782$	6.93357e6	−	1.20093e7i	0.405452	−	0.702264i
$783$		0			0
$784$	1.68937e7	+	1.18738e7i	0.981599	+	0.689919i
$785$	−2.19118e7			−1.26912
$786$		0			0
$787$	7.03741e6	+	1.21891e7i	0.405019	+	0.701514i	0.994324	−	0.106397i	$-0.0339314\pi$
$787$	7.03741e6	+	1.21891e7i	0.405019	+	0.701514i	−0.589304	+	0.807911i	$0.700598\pi$
$788$	−3.36173e6	−	5.82269e6i	−0.192862	−	0.334048i
$789$		0			0
$790$	−1.56283e7			−0.890930
$791$	−3.58124e6	−	3.91519e6i	−0.203513	−	0.222491i
$792$		0			0
$793$	−8.04472e6	+	1.39339e7i	−0.454284	+	0.786844i
$794$	6.02294e6	+	1.04320e7i	0.339045	+	0.587243i
$795$		0			0
$796$	599848.	−	1.03897e6i	0.0335551	−	0.0581191i
$797$	1.75191e7			0.976937			0.488469	−	0.872582i	$-0.337556\pi$
$797$	1.75191e7			0.976937			0.488469	+	0.872582i	$0.337556\pi$
$798$		0			0
$799$	9.06127e6			0.502137
$800$	2.52936e6	−	4.38099e6i	0.139729	−	0.242018i
$801$		0			0
$802$	−4.28067e6	−	7.41433e6i	−0.235004	−	0.407039i
$803$	1.60486e7	−	2.77970e7i	0.878311	−	1.52128i
$804$		0			0
$805$	2.47106e6	−	7.81306e6i	0.134398	−	0.424944i
$806$	9.78721e6			0.530666
$807$		0			0
$808$	−1.25111e7	−	2.16698e7i	−0.674166	−	1.16769i
$809$	407261.	+	705396.i	0.0218777	+	0.0378932i	0.876757	−	0.480934i	$-0.159702\pi$
$809$	407261.	+	705396.i	0.0218777	+	0.0378932i	−0.854879	+	0.518827i	$0.826369\pi$
$810$		0			0
$811$	1.26533e7			0.675540			0.337770	−	0.941229i	$-0.390327\pi$
$811$	1.26533e7			0.675540			0.337770	+	0.941229i	$0.390327\pi$
$812$	−505233.	+	1.59746e6i	−0.0268907	+	0.0850235i
$813$		0			0
$814$	−3.00175e7	+	5.19919e7i	−1.58787	+	2.75026i
$815$	−8.33064e6	−	1.44291e7i	−0.439324	−	0.760931i
$816$		0			0
$817$	−6.94297e6	+	1.20256e7i	−0.363907	+	0.630305i
$818$	−4.20854e7			−2.19912
$819$		0			0
$820$	−4.48142e6			−0.232745
$821$	2.13697e6	−	3.70133e6i	0.110647	−	0.191646i	−0.805384	−	0.592753i	$-0.798041\pi$
$821$	2.13697e6	−	3.70133e6i	0.110647	−	0.191646i	0.916031	+	0.401107i	$0.131374\pi$
$822$		0			0
$823$	−8.52317e6	−	1.47626e7i	−0.438633	−	0.759735i	0.558951	−	0.829201i	$-0.311204\pi$
$823$	−8.52317e6	−	1.47626e7i	−0.438633	−	0.759735i	−0.997584	+	0.0694656i	$0.977871\pi$
$824$	−8.35155e6	+	1.44653e7i	−0.428498	+	0.742180i
$825$		0			0
$826$	−2.87681e7	−	3.14508e7i	−1.46711	−	1.60392i
$827$	−2.60828e6			−0.132614			−0.0663071	−	0.997799i	$-0.521122\pi$
$827$	−2.60828e6			−0.132614			−0.0663071	+	0.997799i	$0.521122\pi$
$828$		0			0
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	−0.998880	−	0.0473066i	$-0.984936\pi$
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	0.458471	−	0.888709i	$-0.348397\pi$
$830$	5.63898e6	+	9.76700e6i	0.284122	+	0.492114i
$831$		0			0
$832$	7.60423e6			0.380844
$833$	2.02711e7	−	9.40887e6i	1.01220	−	0.469813i
$834$		0			0
$835$	4.65263e6	−	8.05859e6i	0.230931	−	0.399984i
$836$	−2.39848e6	−	4.15429e6i	−0.118692	−	0.205580i
$837$		0			0
$838$	2.22645e7	−	3.85632e7i	1.09522	−	1.89698i
$839$	−771393.			−0.0378330			−0.0189165	−	0.999821i	$-0.506022\pi$
$839$	−771393.			−0.0378330			−0.0189165	+	0.999821i	$0.506022\pi$
$840$		0			0
$841$	−1.83692e7			−0.895571
$842$	1.22699e7	−	2.12520e7i	0.596430	−	1.03305i
$843$		0			0
$844$	4.37616e6	+	7.57973e6i	0.211464	+	0.366267i
$845$	−4.22200e6	+	7.31272e6i	−0.203412	+	0.352320i
$846$		0			0
$847$	2.16696e7	−	4.78388e6i	1.03787	−	0.229125i
$848$	−2.47113e6			−0.118006
$849$		0			0
$850$	−6.90375e6	−	1.19576e7i	−0.327746	−	0.567673i
$851$	1.33017e7	+	2.30393e7i	0.629628	+	1.09055i
$852$		0			0
$853$	2.94032e7			1.38364			0.691818	−	0.722072i	$-0.256810\pi$
$853$	2.94032e7			1.38364			0.691818	+	0.722072i	$0.256810\pi$
$854$	1.02664e7	−	3.24604e7i	0.481694	−	1.52303i
$855$		0			0
$856$	−1.65147e6	+	2.86042e6i	−0.0770345	+	0.133428i
$857$	−1.32505e7	−	2.29505e7i	−0.616283	−	1.06743i	−0.990158	−	0.139954i	$-0.955304\pi$
$857$	−1.32505e7	−	2.29505e7i	−0.616283	−	1.06743i	0.373875	−	0.927479i	$-0.378029\pi$
$858$		0			0
$859$	1.83759e7	−	3.18281e7i	0.849702	−	1.47173i	−0.0317727	−	0.999495i	$-0.510115\pi$
$859$	1.83759e7	−	3.18281e7i	0.849702	−	1.47173i	0.881475	−	0.472232i	$-0.156551\pi$
$860$	−5.03876e6			−0.232315
$861$		0			0
$862$	1.94020e7			0.889360
$863$	5.90946e6	−	1.02355e7i	0.270098	−	0.467823i	−0.698789	−	0.715328i	$-0.746277\pi$
$863$	5.90946e6	−	1.02355e7i	0.270098	−	0.467823i	0.968887	+	0.247505i	$0.0796106\pi$
$864$		0			0
$865$	3.47207e6	+	6.01379e6i	0.157778	+	0.273280i
$866$	−3.00812e6	+	5.21022e6i	−0.136302	+	0.236081i
$867$		0			0
$868$	−4.37358e6	+	965534.i	−0.197033	+	0.0434979i
$869$	−3.63998e7			−1.63512
$870$		0			0
$871$	−9.90046e6	−	1.71481e7i	−0.442191	−	0.765897i
$872$	6.20477e6	+	1.07470e7i	0.276334	+	0.478625i
$873$		0			0
$874$	−9.82884e6			−0.435235
$875$	−1.60970e7	−	1.75980e7i	−0.710762	−	0.777042i
$876$		0			0
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	−0.939881	−	0.341503i	$-0.889064\pi$
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	0.765691	+	0.643209i	$0.222397\pi$
$878$	4.28470e6	+	7.42131e6i	0.187579	+	0.324896i
$879$		0			0
$880$	−1.37130e7	+	2.37516e7i	−0.596934	+	1.03392i
$881$	−4.20152e7			−1.82375			−0.911877	−	0.410464i	$-0.865367\pi$
$881$	−4.20152e7			−1.82375			−0.911877	+	0.410464i	$0.865367\pi$
$882$		0			0
$883$	2.12461e7			0.917016			0.458508	−	0.888690i	$-0.348384\pi$
$883$	2.12461e7			0.917016			0.458508	+	0.888690i	$0.348384\pi$
$884$	−2.29840e6	+	3.98095e6i	−0.0989226	+	0.171339i
$885$		0			0
$886$	2.46758e6	+	4.27397e6i	0.105606	+	0.182914i
$887$	9.42452e6	−	1.63238e7i	0.402208	−	0.696644i	−0.591784	−	0.806096i	$-0.701576\pi$
$887$	9.42452e6	−	1.63238e7i	0.402208	−	0.696644i	0.993992	+	0.109452i	$0.0349097\pi$
$888$		0			0
$889$	−7.28613e6	−	7.96558e6i	−0.309202	−	0.338036i
$890$	−3.88204e6			−0.164280
$891$		0			0
$892$	−2.39897e6	−	4.15514e6i	−0.100952	−	0.174853i
$893$	−3.21125e6	−	5.56205e6i	−0.134755	−	0.233403i
$894$		0			0
$895$	−2.22909e7			−0.930186
$896$	−2.83227e7	+	6.25267e6i	−1.17860	+	0.260193i
$897$		0			0
$898$	−7.21044e6	+	1.24889e7i	−0.298381	+	0.516811i
$899$	2.86300e6	+	4.95886e6i	0.118147	+	0.204636i
$900$		0			0
$901$	−1.33724e6	+	2.31617e6i	−0.0548780	+	0.0950514i
$902$	−4.82621e7			−1.97510
$903$		0			0
$904$	6.05948e6			0.246612
$905$	1.12509e7	−	1.94872e7i	0.456632	−	0.790910i
$906$		0			0
$907$	3.09723e6	+	5.36456e6i	0.125013	+	0.216529i	0.921738	−	0.387813i	$-0.126769\pi$
$907$	3.09723e6	+	5.36456e6i	0.125013	+	0.216529i	−0.796725	+	0.604342i	$0.793436\pi$
$908$	72.1183	−	124.912i	2.90289e−6	−	5.02795e-6i
$909$		0			0
$910$	−3.78753e6	+	1.19755e7i	−0.151619	+	0.479392i
$911$	2.50171e7			0.998712			0.499356	−	0.866397i	$-0.333570\pi$
$911$	2.50171e7			0.998712			0.499356	+	0.866397i	$0.333570\pi$
$912$		0			0
$913$	1.31337e7	+	2.27483e7i	0.521448	+	0.903174i
$914$	1.36893e7	+	2.37106e7i	0.542022	+	0.938810i
$915$		0			0
$916$	−683288.			−0.0269070
$917$	2.11253e7	−	4.66373e6i	0.829620	−	0.183151i
$918$		0			0
$919$	−7.74961e6	+	1.34227e7i	−0.302685	+	0.524266i	−0.976743	−	0.214412i	$-0.931216\pi$
$919$	−7.74961e6	+	1.34227e7i	−0.302685	+	0.524266i	0.674058	+	0.738678i	$0.264550\pi$
$920$	4.67906e6	+	8.10437e6i	0.182259	+	0.315682i
$921$		0			0
$922$	9.91905e6	−	1.71803e7i	0.384276	−	0.665585i
$923$	−1.56481e7			−0.604587
$924$		0			0
$925$	2.64890e7			1.01791
$926$	−1.12905e7	+	1.95556e7i	−0.432697	+	0.749453i
$927$		0			0
$928$	−2.27797e6	−	3.94556e6i	−0.0868316	−	0.150397i
$929$	1.87643e7	−	3.25007e7i	0.713333	−	1.23553i	−0.250266	−	0.968177i	$-0.580518\pi$
$929$	1.87643e7	−	3.25007e7i	0.713333	−	1.23553i	0.963599	−	0.267352i	$-0.0861485\pi$
$930$		0			0
$931$	−1.29594e7	−	9.10852e6i	−0.490015	−	0.344408i
$932$	915335.			0.0345176
$933$		0			0
$934$	−8.70489e6	−	1.50773e7i	−0.326510	−	0.565532i
$935$	1.48415e7	+	2.57062e7i	0.555198	+	0.961632i
$936$		0			0
$937$	−1.08298e7			−0.402969			−0.201485	−	0.979492i	$-0.564577\pi$
$937$	−1.08298e7			−0.402969			−0.201485	+	0.979492i	$0.564577\pi$
$938$	2.82789e7	+	3.09160e7i	1.04944	+	1.14730i
$939$		0			0
$940$	1.16526e6	−	2.01829e6i	0.0430133	−	0.0745013i
$941$	1.62295e7	+	2.81104e7i	0.597492	+	1.03489i	0.993190	+	0.116505i	$0.0371692\pi$
$941$	1.62295e7	+	2.81104e7i	0.597492	+	1.03489i	−0.395699	+	0.918380i	$0.629497\pi$
$942$		0			0
$943$	−1.06932e7	+	1.85212e7i	−0.391589	+	0.678251i
$944$	6.32151e7			2.30883
$945$		0			0
$946$	−5.42643e7			−1.97145
$947$	3.76939e6	−	6.52877e6i	0.136583	−	0.236568i	−0.789618	−	0.613598i	$-0.789721\pi$
$947$	3.76939e6	−	6.52877e6i	0.136583	−	0.236568i	0.926201	+	0.377030i	$0.123055\pi$
$948$		0			0
$949$	1.09004e7	+	1.88801e7i	0.392896	+	0.680516i
$950$	−4.89328e6	+	8.47541e6i	−0.175910	+	0.304686i
$951$		0			0
$952$	−7.69608e6	+	2.43336e7i	−0.275218	+	0.870191i
$953$	3.01356e7			1.07485			0.537424	−	0.843312i	$-0.319398\pi$
$953$	3.01356e7			1.07485			0.537424	+	0.843312i	$0.319398\pi$
$954$		0			0
$955$	1.27914e7	+	2.21554e7i	0.453848	+	0.786089i
$956$	3.04255e6	+	5.26986e6i	0.107670	+	0.186489i
$957$		0			0
$958$	6.25366e6			0.220151
$959$	1.49431e6	−	4.72474e6i	0.0524680	−	0.165894i
$960$		0			0
$961$	6.66107e6	−	1.15373e7i	0.232667	−	0.402992i
$962$	−2.03883e7	−	3.53135e7i	−0.710301	−	1.23028i
$963$		0			0
$964$	−972650.	+	1.68468e6i	−0.0337104	+	0.0583882i
$965$	2.15841e7			0.746132
$966$		0			0
$967$	2.88021e6			0.0990509			0.0495255	−	0.998773i	$-0.484229\pi$
$967$	2.88021e6			0.0990509			0.0495255	+	0.998773i	$0.484229\pi$
$968$	−1.26712e7	+	2.19472e7i	−0.434641	+	0.752820i
$969$		0			0
$970$	−387110.	−	670494.i	−0.0132101	−	0.0228805i
$971$	−1.37245e7	+	2.37715e7i	−0.467142	+	0.809113i	−0.999295	−	0.0375347i	$-0.988050\pi$
$971$	−1.37245e7	+	2.37715e7i	−0.467142	+	0.809113i	0.532154	+	0.846648i	$0.321383\pi$
$972$		0			0
$973$	−9.29799e6	−	1.01650e7i	−0.314852	−	0.344213i
$974$	−2.50958e7			−0.847626
$975$		0			0
$976$	2.52463e7	+	4.37279e7i	0.848347	+	1.46938i
$977$	−2.94262e7	−	5.09676e7i	−0.986274	−	1.70828i	−0.636133	−	0.771579i	$-0.719467\pi$
$977$	−2.94262e7	−	5.09676e7i	−0.986274	−	1.70828i	−0.350141	−	0.936697i	$-0.613866\pi$
$978$		0			0
$979$	−9.04164e6			−0.301502
$980$	511109.	−	5.72511e6i	0.0170000	−	0.190423i
$981$		0			0
$982$	−8.41039e6	+	1.45672e7i	−0.278315	+	0.482056i
$983$	9.30384e6	+	1.61147e7i	0.307099	+	0.531911i	0.977726	−	0.209883i	$-0.0673084\pi$
$983$	9.30384e6	+	1.61147e7i	0.307099	+	0.531911i	−0.670627	+	0.741794i	$0.733975\pi$
$984$		0			0
$985$	1.47442e7	−	2.55376e7i	0.484205	−	0.838668i
$986$	−1.24352e7			−0.407342
$987$		0			0
$988$	3.25815e6			0.106189
$989$	−1.20231e7	+	2.08246e7i	−0.390865	+	0.676997i
$990$		0			0
$991$	−1.23577e7	−	2.14041e7i	−0.399718	−	0.692331i	0.593973	−	0.804485i	$-0.297558\pi$
$991$	−1.23577e7	−	2.14041e7i	−0.399718	−	0.692331i	−0.993691	+	0.112154i	$0.964225\pi$
$992$	6.08958e6	−	1.05475e7i	0.196475	−	0.340305i
$993$		0			0
$994$	3.23329e7	−	7.13797e6i	1.03796	−	0.229144i
$995$	5.26172e6			0.168488
$996$		0			0
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	0.972871	−	0.231347i	$-0.0743131\pi$
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	−0.686788	+	0.726858i	$0.740980\pi$
$998$	6.79064e6	+	1.17617e7i	0.215816	+	0.373805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.c.37.2		4
3.2	odd	2		21.6.e.b.16.1	yes	4
7.2	even	3		441.6.a.t.1.1		2
7.4	even	3	inner	63.6.e.c.46.2		4
7.5	odd	6		441.6.a.s.1.1		2
12.11	even	2		336.6.q.e.289.1		4
21.2	odd	6		147.6.a.i.1.2		2
21.5	even	6		147.6.a.k.1.2		2
21.11	odd	6		21.6.e.b.4.1	✓	4
21.17	even	6		147.6.e.l.67.1		4
21.20	even	2		147.6.e.l.79.1		4
84.11	even	6		336.6.q.e.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.1	✓	4	21.11	odd	6
21.6.e.b.16.1	yes	4	3.2	odd	2
63.6.e.c.37.2		4	1.1	even	1	trivial
63.6.e.c.46.2		4	7.4	even	3	inner
147.6.a.i.1.2		2	21.2	odd	6
147.6.a.k.1.2		2	21.5	even	6
147.6.e.l.67.1		4	21.17	even	6
147.6.e.l.79.1		4	21.20	even	2
336.6.q.e.193.1		4	84.11	even	6
336.6.q.e.289.1		4	12.11	even	2
441.6.a.s.1.1		2	7.5	odd	6
441.6.a.t.1.1		2	7.2	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19493 - 5.53379i) q^{2} +(-4.41520 - 7.64735i) q^{4} +(19.3645 - 33.5404i) q^{5} +(-87.5000 - 95.6596i) q^{7} +148.051 q^{8} +(-123.737 - 214.318i) q^{10} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +(-808.916 + 178.580i) q^{14} +(614.298 - 1064.00i) q^{16} +(-664.850 - 1151.55i) q^{17} +(-471.237 + 816.206i) q^{19} -341.993 q^{20} -3683.05 q^{22} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +(1250.79 - 2166.43i) q^{26} +(-345.212 + 1091.50i) q^{28} +1463.54 q^{29} +(1956.21 + 3388.25i) q^{31} +(-1556.47 - 2695.89i) q^{32} -8496.61 q^{34} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(3011.14 + 5215.45i) q^{38} +(2866.93 - 4965.67i) q^{40} +13103.8 q^{41} +14733.5 q^{43} +(-2544.88 + 4407.86i) q^{44} +(5214.38 + 9031.58i) q^{46} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +10383.9 q^{50} +(-1728.51 - 2993.87i) q^{52} +(-1005.67 - 1741.87i) q^{53} -22323.0 q^{55} +(-12954.4 - 14162.5i) q^{56} +(4675.93 - 8098.94i) q^{58} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +24999.8 q^{62} +19423.8 q^{64} +(7581.04 - 13130.8i) q^{65} +(-25289.1 - 43802.0i) q^{67} +(-5870.89 + 10168.7i) q^{68} +(-9674.63 + 30589.5i) q^{70} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(-52078.5 - 90202.6i) q^{74} +8322.42 q^{76} +(-22533.2 + 71245.8i) q^{77} +(31575.7 - 54690.7i) q^{79} +(-23791.2 - 41207.6i) q^{80} +(41865.9 - 72513.8i) q^{82} -45572.4 q^{83} -51498.1 q^{85} +(47072.5 - 81532.0i) q^{86} +(-42667.5 - 73902.2i) q^{88} +(7843.34 - 13585.1i) q^{89} +(-34255.5 - 37449.9i) q^{91} +14411.9 q^{92} +(21771.9 + 37710.1i) q^{94} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +(87863.1 + 61754.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25}+ \cdots + 462021 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 - 65 * q^4 - 33 * q^5 - 350 * q^7 + 750 * q^8 - 921 * q^10 - 1137 * q^11 + 1850 * q^13 - 2352 * q^14 + 895 * q^16 - 324 * q^17 - 2311 * q^19 + 7374 * q^20 + 3162 * q^22 + 1596 * q^23 - 395 * q^25 - 2508 * q^26 + 13531 * q^28 + 4434 * q^29 - 4294 * q^31 + 1017 * q^32 - 35880 * q^34 - 15414 * q^35 + 19109 * q^37 - 6828 * q^38 - 10545 * q^40 + 25716 * q^41 - 5542 * q^43 - 36579 * q^44 + 40740 * q^46 - 23160 * q^47 - 5978 * q^49 + 58704 * q^50 - 33424 * q^52 - 31653 * q^53 + 35778 * q^55 - 65625 * q^56 + 2277 * q^58 + 41097 * q^59 - 42052 * q^61 + 204114 * q^62 - 60062 * q^64 - 23106 * q^65 - 30763 * q^67 + 44748 * q^68 + 151179 * q^70 - 204192 * q^71 + 28577 * q^73 - 77784 * q^74 + 170384 * q^76 + 96873 * q^77 + 18464 * q^79 - 71511 * q^80 + 86040 * q^82 - 122358 * q^83 - 247272 * q^85 + 258510 * q^86 - 212565 * q^88 + 29322 * q^89 - 161875 * q^91 - 333816 * q^92 - 109938 * q^94 - 61662 * q^95 - 19582 * q^97 + 462021 * q^98

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