LMFDB - Embedded newform 42.9.c.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(13,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("42.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.c (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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7731 x^{10} + 218714 x^{9} + 46944238 x^{8} + 954612102 x^{7} + \cdots + 37\!\cdots\!84 $ x^12 - 2x^11 + 7731x^10 + 218714x^9 + 46944238x^8 + 954612102x^7 + 95335059229x^6 + 576178351086x^5 + 122405480888457x^4 + 247993465027288x^3 + 91263792176643256x^2 - 730882789543557696*x + 37671313072244229184
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{18}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.12
Root			$-18.3977 + 31.8658i$ of defining polynomial
Character	$\chi$	$=$	42.13
Dual form			42.9.c.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} +640.234i q^{5} +529.090i q^{6} +(2336.76 - 551.670i) q^{7} +1448.15 q^{8} -2187.00 q^{9} +O(q^{10})$	\(q+11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} +640.234i q^{5} +529.090i q^{6} +(2336.76 - 551.670i) q^{7} +1448.15 q^{8} -2187.00 q^{9} +7243.42i q^{10} -14618.3 q^{11} +5985.97i q^{12} +37230.1i q^{13} +(26437.5 - 6241.43i) q^{14} -29940.8 q^{15} +16384.0 q^{16} -1648.52i q^{17} -24743.1 q^{18} +142434. i q^{19} +81950.0i q^{20} +(25799.0 + 109280. i) q^{21} -165387. q^{22} -235174. q^{23} +67723.5i q^{24} -19275.0 q^{25} +421210. i q^{26} -102276. i q^{27} +(299106. - 70613.8i) q^{28} +711112. q^{29} -338741. q^{30} +543645. i q^{31} +185364. q^{32} -683631. i q^{33} -18650.8i q^{34} +(353198. + 1.49608e6i) q^{35} -279936. q^{36} -983911. q^{37} +1.61146e6i q^{38} -1.74108e6 q^{39} +927158. i q^{40} -365296. i q^{41} +(291883. + 1.23636e6i) q^{42} +742986. q^{43} -1.87115e6 q^{44} -1.40019e6i q^{45} -2.66069e6 q^{46} -5.81979e6i q^{47} +766204. i q^{48} +(5.15612e6 - 2.57824e6i) q^{49} -218072. q^{50} +77093.4 q^{51} +4.76545e6i q^{52} +1.07574e7 q^{53} -1.15712e6i q^{54} -9.35915e6i q^{55} +(3.38399e6 - 798903. i) q^{56} -6.66100e6 q^{57} +8.04531e6 q^{58} -2.28132e7i q^{59} -3.83242e6 q^{60} -1.24172e7i q^{61} +6.15064e6i q^{62} +(-5.11050e6 + 1.20650e6i) q^{63} +2.09715e6 q^{64} -2.38360e7 q^{65} -7.73440e6i q^{66} +3.94063e7 q^{67} -211010. i q^{68} -1.09980e7i q^{69} +(3.99598e6 + 1.69262e7i) q^{70} -2.81047e7 q^{71} -3.16711e6 q^{72} +1.58939e7i q^{73} -1.11317e7 q^{74} -901402. i q^{75} +1.82316e7i q^{76} +(-3.41596e7 + 8.06449e6i) q^{77} -1.96980e7 q^{78} +7.20665e7 q^{79} +1.04896e7i q^{80} +4.78297e6 q^{81} -4.13285e6i q^{82} +5.08181e7i q^{83} +(3.30228e6 + 1.39878e7i) q^{84} +1.05544e6 q^{85} +8.40592e6 q^{86} +3.32554e7i q^{87} -2.11696e7 q^{88} +3.33891e7i q^{89} -1.58414e7i q^{90} +(2.05387e7 + 8.69978e7i) q^{91} -3.01023e7 q^{92} -2.54238e7 q^{93} -6.58434e7i q^{94} -9.11914e7 q^{95} +8.66861e6i q^{96} +1.62855e8i q^{97} +(5.83349e7 - 2.91695e7i) q^{98} +3.19703e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9}+O(q^{10}) $ 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9	$ 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + 4344 q^{11} - 12288 q^{14} + 59616 q^{15} + 196608 q^{16} - 224856 q^{21} - 508416 q^{22} + 499800 q^{23} - 3001476 q^{25} + 821760 q^{28} - 1278408 q^{29} + 705024 q^{30} + 2028912 q^{35} - 3359232 q^{36} + 7068648 q^{37} - 5473008 q^{39} + 1513728 q^{42} - 11388024 q^{43} + 556032 q^{44} + 8171520 q^{46} - 12346788 q^{49} + 30019584 q^{50} + 16727472 q^{51} + 19714968 q^{53} - 1572864 q^{56} - 10386144 q^{57} - 17696256 q^{58} + 7630848 q^{60} - 14040540 q^{63} + 25165824 q^{64} - 93770592 q^{65} - 9394008 q^{67} + 11218944 q^{70} + 5393208 q^{71} + 58512384 q^{74} + 24982968 q^{77} + 32638464 q^{78} + 134560968 q^{79} + 57395628 q^{81} - 28781568 q^{84} - 102074640 q^{85} - 282934272 q^{86} - 65077248 q^{88} - 96105408 q^{91} + 63974400 q^{92} + 202339296 q^{93} - 378351840 q^{95} + 387747840 q^{98} - 9500328 q^{99}+O(q^{100}) $ 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9 + 4344 * q^11 - 12288 * q^14 + 59616 * q^15 + 196608 * q^16 - 224856 * q^21 - 508416 * q^22 + 499800 * q^23 - 3001476 * q^25 + 821760 * q^28 - 1278408 * q^29 + 705024 * q^30 + 2028912 * q^35 - 3359232 * q^36 + 7068648 * q^37 - 5473008 * q^39 + 1513728 * q^42 - 11388024 * q^43 + 556032 * q^44 + 8171520 * q^46 - 12346788 * q^49 + 30019584 * q^50 + 16727472 * q^51 + 19714968 * q^53 - 1572864 * q^56 - 10386144 * q^57 - 17696256 * q^58 + 7630848 * q^60 - 14040540 * q^63 + 25165824 * q^64 - 93770592 * q^65 - 9394008 * q^67 + 11218944 * q^70 + 5393208 * q^71 + 58512384 * q^74 + 24982968 * q^77 + 32638464 * q^78 + 134560968 * q^79 + 57395628 * q^81 - 28781568 * q^84 - 102074640 * q^85 - 282934272 * q^86 - 65077248 * q^88 - 96105408 * q^91 + 63974400 * q^92 + 202339296 * q^93 - 378351840 * q^95 + 387747840 * q^98 - 9500328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$-1$

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 $

$2$	11.3137			0.707107
$2$	11.3137			0.707107
$3$			46.7654i			0.577350i
$3$			46.7654i			0.577350i
$4$	128.000			0.500000
$5$			640.234i			1.02437i	0.858874	+	0.512187i	$0.171165\pi$
$5$			640.234i			1.02437i	−0.858874	+	0.512187i	$0.828835\pi$
$6$			529.090i			0.408248i
$7$	2336.76	−	551.670i	0.973246	−	0.229767i
$7$	2336.76	−	551.670i	0.973246	−	0.229767i
$8$	1448.15			0.353553
$9$	−2187.00			−0.333333
$10$			7243.42i			0.724342i
$11$	−14618.3			−0.998451			−0.499225	−	0.866472i	$-0.666382\pi$
$11$	−14618.3			−0.998451			−0.499225	+	0.866472i	$0.666382\pi$
$12$			5985.97i			0.288675i
$13$			37230.1i			1.30353i	0.758422	+	0.651764i	$0.225971\pi$
$13$			37230.1i			1.30353i	−0.758422	+	0.651764i	$0.774029\pi$
$14$	26437.5	−	6241.43i	0.688189	−	0.162470i
$15$	−29940.8			−0.591423
$16$	16384.0			0.250000
$17$		−	1648.52i		−	0.0197377i	−0.999951	−	0.00986887i	$-0.996859\pi$
$17$		−	1648.52i		−	0.0197377i	0.999951	−	0.00986887i	$-0.00314141\pi$
$18$	−24743.1			−0.235702
$19$			142434.i			1.09295i	0.837475	+	0.546475i	$0.184031\pi$
$19$			142434.i			1.09295i	−0.837475	+	0.546475i	$0.815969\pi$
$20$			81950.0i			0.512187i
$21$	25799.0	+	109280.i	0.132656	+	0.561904i
$22$	−165387.			−0.706011
$23$	−235174.			−0.840384			−0.420192	−	0.907435i	$-0.638037\pi$
$23$	−235174.			−0.840384			−0.420192	+	0.907435i	$0.638037\pi$
$24$			67723.5i			0.204124i
$25$	−19275.0			−0.0493440
$26$			421210.i			0.921734i
$27$		−	102276.i		−	0.192450i
$28$	299106.	−	70613.8i	0.486623	−	0.114883i
$29$	711112.			1.00542			0.502708	−	0.864456i	$-0.332337\pi$
$29$	711112.			1.00542			0.502708	+	0.864456i	$0.332337\pi$
$30$	−338741.			−0.418199
$31$			543645.i			0.588665i	0.955703	+	0.294333i	$0.0950974\pi$
$31$			543645.i			0.588665i	−0.955703	+	0.294333i	$0.904903\pi$
$32$	185364.			0.176777
$33$		−	683631.i		−	0.576456i
$34$		−	18650.8i		−	0.0139567i
$35$	353198.	+	1.49608e6i	0.235367	+	0.996969i
$36$	−279936.			−0.166667
$37$	−983911.			−0.524988			−0.262494	−	0.964934i	$-0.584545\pi$
$37$	−983911.			−0.524988			−0.262494	+	0.964934i	$0.584545\pi$
$38$			1.61146e6i			0.772833i
$39$	−1.74108e6			−0.752592
$40$			927158.i			0.362171i
$41$		−	365296.i		−	0.129273i	−0.997909	−	0.0646367i	$-0.979411\pi$
$41$		−	365296.i		−	0.129273i	0.997909	−	0.0646367i	$-0.0205888\pi$
$42$	291883.	+	1.23636e6i	0.0938019	+	0.397326i
$43$	742986.			0.217323			0.108662	−	0.994079i	$-0.465343\pi$
$43$	742986.			0.217323			0.108662	+	0.994079i	$0.465343\pi$
$44$	−1.87115e6			−0.499225
$45$		−	1.40019e6i		−	0.341458i
$46$	−2.66069e6			−0.594241
$47$		−	5.81979e6i		−	1.19266i	−0.802741	−	0.596328i	$-0.796626\pi$
$47$		−	5.81979e6i		−	1.19266i	0.802741	−	0.596328i	$-0.203374\pi$
$48$			766204.i			0.144338i
$49$	5.15612e6	−	2.57824e6i	0.894414	−	0.447239i
$50$	−218072.			−0.0348915
$51$	77093.4			0.0113956
$52$			4.76545e6i			0.651764i
$53$	1.07574e7			1.36334			0.681669	−	0.731661i	$-0.261254\pi$
$53$	1.07574e7			1.36334			0.681669	+	0.731661i	$0.261254\pi$
$54$		−	1.15712e6i		−	0.136083i
$55$		−	9.35915e6i		−	1.02279i
$56$	3.38399e6	−	798903.i	0.344094	−	0.0812348i
$57$	−6.66100e6			−0.631015
$58$	8.04531e6			0.710937
$59$		−	2.28132e7i		−	1.88269i	−0.337446	−	0.941345i	$-0.609563\pi$
$59$		−	2.28132e7i		−	1.88269i	0.337446	−	0.941345i	$-0.390437\pi$
$60$	−3.83242e6			−0.295712
$61$		−	1.24172e7i		−	0.896819i	−0.893828	−	0.448409i	$-0.851991\pi$
$61$		−	1.24172e7i		−	0.896819i	0.893828	−	0.448409i	$-0.148009\pi$
$62$			6.15064e6i			0.416249i
$63$	−5.11050e6	+	1.20650e6i	−0.324415	+	0.0765889i
$64$	2.09715e6			0.125000
$65$	−2.38360e7			−1.33530
$66$		−	7.73440e6i		−	0.407616i
$67$	3.94063e7			1.95554			0.977768	−	0.209687i	$-0.0672446\pi$
$67$	3.94063e7			1.95554			0.977768	+	0.209687i	$0.0672446\pi$
$68$		−	211010.i		−	0.00986887i
$69$		−	1.09980e7i		−	0.485196i
$70$	3.99598e6	+	1.69262e7i	0.166430	+	0.704963i
$71$	−2.81047e7			−1.10598			−0.552989	−	0.833189i	$-0.686513\pi$
$71$	−2.81047e7			−1.10598			−0.552989	+	0.833189i	$0.686513\pi$
$72$	−3.16711e6			−0.117851
$73$			1.58939e7i			0.559680i	0.960047	+	0.279840i	$0.0902814\pi$
$73$			1.58939e7i			0.559680i	−0.960047	+	0.279840i	$0.909719\pi$
$74$	−1.11317e7			−0.371222
$75$		−	901402.i		−	0.0284888i
$76$			1.82316e7i			0.546475i
$77$	−3.41596e7	+	8.06449e6i	−0.971738	+	0.229411i
$78$	−1.96980e7			−0.532163
$79$	7.20665e7			1.85023			0.925113	−	0.379692i	$-0.123970\pi$
$79$	7.20665e7			1.85023			0.925113	+	0.379692i	$0.123970\pi$
$80$			1.04896e7i			0.256094i
$81$	4.78297e6			0.111111
$82$		−	4.13285e6i		−	0.0914101i
$83$			5.08181e7i			1.07079i	0.844600	+	0.535397i	$0.179838\pi$
$83$			5.08181e7i			1.07079i	−0.844600	+	0.535397i	$0.820162\pi$
$84$	3.30228e6	+	1.39878e7i	0.0663279	+	0.280952i
$85$	1.05544e6			0.0202188
$86$	8.40592e6			0.153671
$87$			3.32554e7i			0.580477i
$88$	−2.11696e7			−0.353006
$89$			3.33891e7i			0.532163i	0.963950	+	0.266082i	$0.0857291\pi$
$89$			3.33891e7i			0.532163i	−0.963950	+	0.266082i	$0.914271\pi$
$90$		−	1.58414e7i		−	0.241447i
$91$	2.05387e7	+	8.69978e7i	0.299507	+	1.26865i
$92$	−3.01023e7			−0.420192
$93$	−2.54238e7			−0.339866
$94$		−	6.58434e7i		−	0.843336i
$95$	−9.11914e7			−1.11959
$96$			8.66861e6i			0.102062i
$97$			1.62855e8i			1.83956i	0.392434	+	0.919780i	$0.371633\pi$
$97$			1.62855e8i			1.83956i	−0.392434	+	0.919780i	$0.628367\pi$
$98$	5.83349e7	−	2.91695e7i	0.632447	−	0.316246i
$99$	3.19703e7			0.332817
$100$	−2.46720e6			−0.0246720
$101$		−	1.62872e8i		−	1.56516i	−0.622547	−	0.782582i	$-0.713902\pi$
$101$		−	1.62872e8i		−	1.56516i	0.622547	−	0.782582i	$-0.286098\pi$
$102$	872212.			0.00805789
$103$		−	5.42536e7i		−	0.482036i	−0.970521	−	0.241018i	$-0.922519\pi$
$103$		−	5.42536e7i		−	0.482036i	0.970521	−	0.241018i	$-0.0774813\pi$
$104$			5.39149e7i			0.460867i
$105$	−6.99645e7	+	1.65174e7i	−0.575600	+	0.135889i
$106$	1.21706e8			0.964026
$107$	−4.35489e7			−0.332233			−0.166116	−	0.986106i	$-0.553123\pi$
$107$	−4.35489e7			−0.332233			−0.166116	+	0.986106i	$0.553123\pi$
$108$		−	1.30913e7i		−	0.0962250i
$109$	6.83323e7			0.484083			0.242042	−	0.970266i	$-0.422183\pi$
$109$	6.83323e7			0.484083			0.242042	+	0.970266i	$0.422183\pi$
$110$		−	1.05887e8i		−	0.723220i
$111$		−	4.60130e7i		−	0.303102i
$112$	3.82855e7	−	9.03856e6i	0.243311	−	0.0574417i
$113$	−3.20202e7			−0.196386			−0.0981931	−	0.995167i	$-0.531306\pi$
$113$	−3.20202e7			−0.196386			−0.0981931	+	0.995167i	$0.531306\pi$
$114$	−7.53606e7			−0.446195
$115$		−	1.50566e8i		−	0.860868i
$116$	9.10223e7			0.502708
$117$		−	8.14222e7i		−	0.434509i
$118$		−	2.58102e8i		−	1.33126i
$119$	−909436.	−	3.85219e6i	−0.00453507	−	0.0192097i
$120$	−4.33589e7			−0.209100
$121$	−663575.			−0.00309563
$122$		−	1.40485e8i		−	0.634146i
$123$	1.70832e7			0.0746360
$124$			6.95865e7i			0.294333i
$125$			2.37751e8i			0.973828i
$126$	−5.78187e7	+	1.36500e7i	−0.229396	+	0.0541565i
$127$	6.42711e7			0.247059			0.123530	−	0.992341i	$-0.460579\pi$
$127$	6.42711e7			0.247059			0.123530	+	0.992341i	$0.460579\pi$
$128$	2.37266e7			0.0883883
$129$			3.47460e7i			0.125472i
$130$	−2.69673e8			−0.944201
$131$			1.56054e8i			0.529895i	0.964263	+	0.264948i	$0.0853547\pi$
$131$			1.56054e8i			0.529895i	−0.964263	+	0.264948i	$0.914645\pi$
$132$		−	8.75048e7i		−	0.288228i
$133$	7.85768e7	+	3.32836e8i	0.251124	+	1.06371i
$134$	4.45831e8			1.38277
$135$	6.54805e7			0.197141
$136$		−	2.38730e6i		−	0.00697834i
$137$	3.08925e7			0.0876943			0.0438472	−	0.999038i	$-0.486039\pi$
$137$	3.08925e7			0.0876943			0.0438472	+	0.999038i	$0.486039\pi$
$138$		−	1.24428e8i		−	0.343085i
$139$		−	6.96661e8i		−	1.86622i	−0.359594	−	0.933109i	$-0.617085\pi$
$139$		−	6.96661e8i		−	1.86622i	0.359594	−	0.933109i	$-0.382915\pi$
$140$	4.52093e7	+	1.91498e8i	0.117684	+	0.498484i
$141$	2.72164e8			0.688581
$142$	−3.17969e8			−0.782044
$143$		−	5.44241e8i		−	1.30151i
$144$	−3.58318e7			−0.0833333
$145$			4.55278e8i			1.02992i
$146$			1.79819e8i			0.395753i
$147$	1.20573e8	+	2.41128e8i	0.258214	+	0.516390i
$148$	−1.25941e8			−0.262494
$149$	2.45137e8			0.497351			0.248676	−	0.968587i	$-0.420005\pi$
$149$	2.45137e8			0.497351			0.248676	+	0.968587i	$0.420005\pi$
$150$		−	1.01982e7i		−	0.0201446i
$151$	−9.06787e8			−1.74420			−0.872102	−	0.489323i	$-0.837244\pi$
$151$	−9.06787e8			−1.74420			−0.872102	+	0.489323i	$0.837244\pi$
$152$			2.06267e8i			0.386416i
$153$			3.60530e6i			0.00657924i
$154$	−3.86471e8	+	9.12393e7i	−0.687123	+	0.162218i
$155$	−3.48060e8			−0.603014
$156$	−2.22858e8			−0.376296
$157$		−	5.76188e8i		−	0.948344i	−0.880432	−	0.474172i	$-0.842748\pi$
$157$		−	5.76188e8i		−	0.948344i	0.880432	−	0.474172i	$-0.157252\pi$
$158$	8.15339e8			1.30831
$159$			5.03074e8i			0.787124i
$160$			1.18676e8i			0.181086i
$161$	−5.49546e8	+	1.29738e8i	−0.817900	+	0.193092i
$162$	5.41131e7			0.0785674
$163$	4.69591e8			0.665226			0.332613	−	0.943063i	$-0.392070\pi$
$163$	4.69591e8			0.665226			0.332613	+	0.943063i	$0.392070\pi$
$164$		−	4.67578e7i		−	0.0646367i
$165$	4.37684e8			0.590507
$166$			5.74941e8i			0.757166i
$167$		−	7.14396e8i		−	0.918487i	−0.888310	−	0.459244i	$-0.848120\pi$
$167$		−	7.14396e8i		−	0.918487i	0.888310	−	0.459244i	$-0.151880\pi$
$168$	3.73610e7	+	1.58254e8i	0.0469009	+	0.198663i
$169$	−5.70347e8			−0.699186
$170$	1.19409e7			0.0142969
$171$		−	3.11504e8i		−	0.364317i
$172$	9.51021e7			0.108662
$173$			1.24178e9i			1.38631i	0.720786	+	0.693157i	$0.243781\pi$
$173$			1.24178e9i			1.38631i	−0.720786	+	0.693157i	$0.756219\pi$
$174$			3.76242e8i			0.410459i
$175$	−4.50411e7	+	1.06334e7i	−0.0480238	+	0.0113376i
$176$	−2.39507e8			−0.249613
$177$	1.06687e9			1.08697
$178$			3.77755e8i			0.376296i
$179$	7.60463e8			0.740740			0.370370	−	0.928884i	$-0.379231\pi$
$179$	7.60463e8			0.740740			0.370370	+	0.928884i	$0.379231\pi$
$180$		−	1.79225e8i		−	0.170729i
$181$			1.00497e9i			0.936352i	0.883635	+	0.468176i	$0.155089\pi$
$181$			1.00497e9i			0.936352i	−0.883635	+	0.468176i	$0.844911\pi$
$182$	2.32369e8	+	9.84268e8i	0.211784	+	0.897073i
$183$	5.80695e8			0.517778
$184$	−3.40568e8			−0.297121
$185$		−	6.29934e8i		−	0.537784i
$186$	−2.87637e8			−0.240322
$187$			2.40985e7i			0.0197072i
$188$		−	7.44933e8i		−	0.596328i
$189$	−5.64225e7	−	2.38994e8i	−0.0442186	−	0.187301i
$190$	−1.03171e9			−0.791671
$191$	−1.06993e9			−0.803935			−0.401968	−	0.915654i	$-0.631674\pi$
$191$	−1.06993e9			−0.803935			−0.401968	+	0.915654i	$0.631674\pi$
$192$			9.80741e7i			0.0721688i
$193$	−7.89358e8			−0.568912			−0.284456	−	0.958689i	$-0.591813\pi$
$193$	−7.89358e8			−0.568912			−0.284456	+	0.958689i	$0.591813\pi$
$194$			1.84249e9i			1.30077i
$195$		−	1.11470e9i		−	0.770937i
$196$	6.59984e8	−	3.30015e8i	0.447207	−	0.223619i
$197$	−2.62997e9			−1.74617			−0.873084	−	0.487570i	$-0.837883\pi$
$197$	−2.62997e9			−1.74617			−0.873084	+	0.487570i	$0.837883\pi$
$198$	3.61702e8			0.235337
$199$		−	2.91421e9i		−	1.85827i	−0.369744	−	0.929133i	$-0.620555\pi$
$199$		−	2.91421e9i		−	1.85827i	0.369744	−	0.929133i	$-0.379445\pi$
$200$	−2.79132e7			−0.0174457
$201$			1.84285e9i			1.12903i
$202$		−	1.84268e9i		−	1.10674i
$203$	1.66170e9	−	3.92299e8i	0.978517	−	0.231011i
$204$	9.86796e6			0.00569779
$205$	2.33875e8			0.132424
$206$		−	6.13810e8i		−	0.340851i
$207$	5.14325e8			0.280128
$208$			6.09977e8i			0.325882i
$209$		−	2.08215e9i		−	1.09126i
$210$	−7.91558e8	+	1.86873e8i	−0.407011	+	0.0960883i
$211$	2.58893e9			1.30614			0.653070	−	0.757297i	$-0.273481\pi$
$211$	2.58893e9			1.30614			0.653070	+	0.757297i	$0.273481\pi$
$212$	1.37695e9			0.681669
$213$		−	1.31433e9i		−	0.638536i
$214$	−4.92700e8			−0.234924
$215$			4.75685e8i			0.222621i
$216$		−	1.48111e8i		−	0.0680414i
$217$	2.99913e8	+	1.27037e9i	0.135256	+	0.572916i
$218$	7.73092e8			0.342298
$219$	−7.43285e8			−0.323131
$220$		−	1.19797e9i		−	0.511394i
$221$	6.13743e7			0.0257287
$222$		−	5.20577e8i		−	0.214325i
$223$			7.97208e8i			0.322368i	0.986924	+	0.161184i	$0.0515313\pi$
$223$			7.97208e8i			0.322368i	−0.986924	+	0.161184i	$0.948469\pi$
$224$	4.33151e8	−	1.02260e8i	0.172047	−	0.0406174i
$225$	4.21544e7			0.0164480
$226$	−3.62268e8			−0.138866
$227$		−	3.27153e9i		−	1.23210i	−0.787705	−	0.616052i	$-0.788731\pi$
$227$		−	3.27153e9i		−	1.23210i	0.787705	−	0.616052i	$-0.211269\pi$
$228$	−8.52608e8			−0.315508
$229$			2.49053e9i			0.905629i	0.891605	+	0.452815i	$0.149580\pi$
$229$			2.49053e9i			0.905629i	−0.891605	+	0.452815i	$0.850420\pi$
$230$		−	1.70346e9i		−	0.608726i
$231$	−3.77139e8	−	1.59748e9i	−0.132450	−	0.561033i
$232$	1.02980e9			0.355468
$233$	−2.20845e9			−0.749314			−0.374657	−	0.927164i	$-0.622239\pi$
$233$	−2.20845e9			−0.749314			−0.374657	+	0.927164i	$0.622239\pi$
$234$		−	9.21187e8i		−	0.307245i
$235$	3.72603e9			1.22173
$236$		−	2.92009e9i		−	0.941345i
$237$			3.37021e9i			1.06823i
$238$	−1.02891e7	−	4.35825e7i	−0.00320678	−	0.0135833i
$239$	1.24118e8			0.0380401			0.0190201	−	0.999819i	$-0.493945\pi$
$239$	1.24118e8			0.0380401			0.0190201	+	0.999819i	$0.493945\pi$
$240$	−4.90550e8			−0.147856
$241$		−	2.72019e9i		−	0.806365i	−0.915120	−	0.403183i	$-0.867904\pi$
$241$		−	2.72019e9i		−	0.806365i	0.915120	−	0.403183i	$-0.132096\pi$
$242$	−7.50750e6			−0.00218894
$243$			2.23677e8i			0.0641500i
$244$		−	1.58940e9i		−	0.448409i
$245$	1.65068e9	+	3.30113e9i	0.458140	+	0.916216i
$246$	1.93274e8			0.0527756
$247$	−5.30284e9			−1.42469
$248$			7.87282e8i			0.208125i
$249$	−2.37653e9			−0.618224
$250$			2.68985e9i			0.688601i
$251$			1.93821e9i			0.488322i	0.969735	+	0.244161i	$0.0785126\pi$
$251$			1.93821e9i			0.488322i	−0.969735	+	0.244161i	$0.921487\pi$
$252$	−6.54144e8	+	1.54432e8i	−0.162208	+	0.0382945i
$253$	3.43785e9			0.839082
$254$	7.27144e8			0.174697
$255$			4.93579e7i			0.0116734i
$256$	2.68435e8			0.0625000
$257$			7.45259e9i			1.70834i	0.519992	+	0.854171i	$0.325935\pi$
$257$			7.45259e9i			1.70834i	−0.519992	+	0.854171i	$0.674065\pi$
$258$			3.93106e8i			0.0887219i
$259$	−2.29917e9	+	5.42794e8i	−0.510942	+	0.120625i
$260$	−3.05100e9			−0.667651
$261$	−1.55520e9			−0.335139
$262$			1.76555e9i			0.374693i
$263$	9.66117e8			0.201933			0.100966	−	0.994890i	$-0.467807\pi$
$263$	9.66117e8			0.201933			0.100966	+	0.994890i	$0.467807\pi$
$264$		−	9.90004e8i		−	0.203808i
$265$			6.88725e9i			1.39657i
$266$	8.88995e8	+	3.76560e9i	0.177571	+	0.752156i
$267$	−1.56145e9			−0.307245
$268$	5.04400e9			0.977768
$269$			5.98056e9i			1.14218i	0.820889	+	0.571088i	$0.193478\pi$
$269$			5.98056e9i			1.14218i	−0.820889	+	0.571088i	$0.806522\pi$
$270$	7.40828e8			0.139400
$271$			2.31607e9i			0.429411i	0.976679	+	0.214706i	$0.0688792\pi$
$271$			2.31607e9i			0.429411i	−0.976679	+	0.214706i	$0.931121\pi$
$272$		−	2.70093e7i		−	0.00493443i
$273$	−4.06849e9	+	9.60500e8i	−0.732457	+	0.172921i
$274$	3.49509e8			0.0620092
$275$	2.81768e8			0.0492676
$276$		−	1.40774e9i		−	0.242598i
$277$	−1.17734e9			−0.199978			−0.0999892	−	0.994989i	$-0.531881\pi$
$277$	−1.17734e9			−0.199978			−0.0999892	+	0.994989i	$0.531881\pi$
$278$		−	7.88182e9i		−	1.31962i
$279$		−	1.18895e9i		−	0.196222i
$280$	5.11485e8	+	2.16655e9i	0.0832149	+	0.352482i
$281$	−6.76552e9			−1.08512			−0.542558	−	0.840019i	$-0.682544\pi$
$281$	−6.76552e9			−1.08512			−0.542558	+	0.840019i	$0.682544\pi$
$282$	3.07919e9			0.486900
$283$		−	1.18087e9i		−	0.184101i	−0.995754	−	0.0920505i	$-0.970658\pi$
$283$		−	1.18087e9i		−	0.184101i	0.995754	−	0.0920505i	$-0.0293421\pi$
$284$	−3.59741e9			−0.552989
$285$		−	4.26460e9i		−	0.646396i
$286$		−	6.15739e9i		−	0.920306i
$287$	−2.01523e8	−	8.53609e8i	−0.0297027	−	0.125815i
$288$	−4.05391e8			−0.0589256
$289$	6.97304e9			0.999610
$290$			5.15088e9i			0.728266i
$291$	−7.61597e9			−1.06207
$292$			2.03442e9i			0.279840i
$293$		−	2.46405e9i		−	0.334333i	−0.985929	−	0.167166i	$-0.946538\pi$
$293$		−	2.46405e9i		−	0.334333i	0.985929	−	0.167166i	$-0.0534617\pi$
$294$	1.36412e9	+	2.72805e9i	0.182585	+	0.365143i
$295$	1.46058e10			1.92858
$296$	−1.42486e9			−0.185611
$297$			1.49510e9i			0.192152i
$298$	2.77341e9			0.351681
$299$		−	8.75554e9i		−	1.09546i
$300$		−	1.15380e8i		−	0.0142444i
$301$	1.73618e9	−	4.09883e8i	0.211509	−	0.0499337i
$302$	−1.02591e10			−1.23334
$303$	7.61675e9			0.903648
$304$			2.33365e9i			0.273238i
$305$	7.94992e9			0.918678
$306$			4.07893e7i			0.00465223i
$307$			3.92016e9i			0.441316i	0.975351	+	0.220658i	$0.0708205\pi$
$307$			3.92016e9i			0.441316i	−0.975351	+	0.220658i	$0.929179\pi$
$308$	−4.37242e9	+	1.03225e9i	−0.485869	+	0.114705i
$309$	2.53719e9			0.278304
$310$	−3.93785e9			−0.426395
$311$		−	1.77976e10i		−	1.90248i	−0.308447	−	0.951241i	$-0.599809\pi$
$311$		−	1.77976e10i		−	1.90248i	0.308447	−	0.951241i	$-0.400191\pi$
$312$	−2.52135e9			−0.266082
$313$		−	1.84881e10i		−	1.92626i	−0.269029	−	0.963132i	$-0.586703\pi$
$313$		−	1.84881e10i		−	1.92626i	0.269029	−	0.963132i	$-0.413297\pi$
$314$		−	6.51883e9i		−	0.670580i
$315$	−7.72444e8	−	3.27192e9i	−0.0784558	−	0.332323i
$316$	9.22451e9			0.925113
$317$	1.10262e10			1.09191			0.545957	−	0.837813i	$-0.316166\pi$
$317$	1.10262e10			1.09191			0.545957	+	0.837813i	$0.316166\pi$
$318$			5.69163e9i			0.556581i
$319$	−1.03953e10			−1.00386
$320$			1.34267e9i			0.128047i
$321$		−	2.03658e9i		−	0.191815i
$322$	−6.21740e9	+	1.46782e9i	−0.578343	+	0.136537i
$323$	2.34805e8			0.0215724
$324$	6.12220e8			0.0555556
$325$		−	7.17609e8i		−	0.0643213i
$326$	5.31282e9			0.470386
$327$			3.19558e9i			0.279486i
$328$		−	5.29005e8i		−	0.0457050i
$329$	−3.21060e9	−	1.35995e10i	−0.274033	−	1.16075i
$330$	4.95183e9			0.417552
$331$	−2.24455e10			−1.86989			−0.934947	−	0.354787i	$-0.884553\pi$
$331$	−2.24455e10			−1.86989			−0.934947	+	0.354787i	$0.884553\pi$
$332$			6.50472e9i			0.535397i
$333$	2.15181e9			0.174996
$334$		−	8.08247e9i		−	0.649469i
$335$			2.52292e10i			2.00320i
$336$	4.22692e8	+	1.79044e9i	0.0331640	+	0.140476i
$337$	−1.51679e10			−1.17599			−0.587997	−	0.808863i	$-0.700083\pi$
$337$	−1.51679e10			−1.17599			−0.587997	+	0.808863i	$0.700083\pi$
$338$	−6.45274e9			−0.494399
$339$		−	1.49744e9i		−	0.113384i
$340$	1.35096e8			0.0101094
$341$		−	7.94718e9i		−	0.587754i
$342$		−	3.52427e9i		−	0.257611i
$343$	1.06263e10	−	8.86922e9i	0.767724	−	0.640780i
$344$	1.07596e9			0.0768354
$345$	7.04129e9			0.497022
$346$			1.40492e10i			0.980273i
$347$	4.79033e9			0.330406			0.165203	−	0.986260i	$-0.447172\pi$
$347$	4.79033e9			0.330406			0.165203	+	0.986260i	$0.447172\pi$
$348$			4.25669e9i			0.290239i
$349$			9.07018e9i			0.611384i	0.952130	+	0.305692i	$0.0988878\pi$
$349$			9.07018e9i			0.611384i	−0.952130	+	0.305692i	$0.901112\pi$
$350$	−5.09582e8	+	1.20304e8i	−0.0339580	+	0.00801690i
$351$	3.80774e9			0.250864
$352$	−2.70971e9			−0.176503
$353$			2.73289e9i			0.176005i	0.996120	+	0.0880023i	$0.0280483\pi$
$353$			2.73289e9i			0.176005i	−0.996120	+	0.0880023i	$0.971952\pi$
$354$	1.20702e10			0.768605
$355$		−	1.79936e10i		−	1.13294i
$356$			4.27381e9i			0.266082i
$357$	1.80149e8	−	4.25301e7i	0.0110907	−	0.00261833i
$358$	8.60365e9			0.523782
$359$	1.17204e10			0.705607			0.352804	−	0.935697i	$-0.385228\pi$
$359$	1.17204e10			0.705607			0.352804	+	0.935697i	$0.385228\pi$
$360$		−	2.02770e9i		−	0.120724i
$361$	−3.30400e9			−0.194541
$362$			1.13699e10i			0.662101i
$363$		−	3.10323e7i		−	0.00178726i
$364$	2.62895e9	+	1.11357e10i	0.149754	+	0.634327i
$365$	−1.01758e10			−0.573322
$366$	6.56982e9			0.366125
$367$			1.55147e10i			0.855224i	0.903962	+	0.427612i	$0.140645\pi$
$367$			1.55147e10i			0.855224i	−0.903962	+	0.427612i	$0.859355\pi$
$368$	−3.85309e9			−0.210096
$369$			7.98902e8i			0.0430911i
$370$		−	7.12689e9i		−	0.380271i
$371$	2.51375e10	−	5.93453e9i	1.32686	−	0.313250i
$372$	−3.25424e9			−0.169933
$373$	−1.86488e10			−0.963419			−0.481710	−	0.876331i	$-0.659984\pi$
$373$	−1.86488e10			−0.963419			−0.481710	+	0.876331i	$0.659984\pi$
$374$			2.72644e8i			0.0139351i
$375$	−1.11185e10			−0.562240
$376$		−	8.42795e9i		−	0.421668i
$377$			2.64747e10i			1.31059i
$378$	−6.38348e8	−	2.70391e9i	−0.0312673	−	0.132442i
$379$	−6.80023e9			−0.329584			−0.164792	−	0.986328i	$-0.552695\pi$
$379$	−6.80023e9			−0.329584			−0.164792	+	0.986328i	$0.552695\pi$
$380$	−1.16725e10			−0.559796
$381$			3.00566e9i			0.142640i
$382$	−1.21049e10			−0.568468
$383$			6.63942e9i			0.308557i	0.988027	+	0.154278i	$0.0493052\pi$
$383$			6.63942e9i			0.308557i	−0.988027	+	0.154278i	$0.950695\pi$
$384$			1.10958e9i			0.0510310i
$385$	−5.16316e9	−	2.18701e10i	−0.235003	−	0.995424i
$386$	−8.93057e9			−0.402281
$387$	−1.62491e9			−0.0724411
$388$			2.08454e10i			0.919780i
$389$	2.85316e10			1.24603			0.623013	−	0.782211i	$-0.285908\pi$
$389$	2.85316e10			1.24603			0.623013	+	0.782211i	$0.285908\pi$
$390$		−	1.26114e10i		−	0.545135i
$391$			3.87688e8i			0.0165873i
$392$	7.46686e9	−	3.73370e9i	0.316223	−	0.158123i
$393$	−7.29793e9			−0.305935
$394$	−2.97547e10			−1.23473
$395$			4.61394e10i			1.89533i
$396$	4.09219e9			0.166408
$397$			2.82635e10i			1.13779i	0.822409	+	0.568897i	$0.192630\pi$
$397$			2.82635e10i			1.13779i	−0.822409	+	0.568897i	$0.807370\pi$
$398$		−	3.29705e10i		−	1.31399i
$399$	−1.55652e10	+	3.67467e9i	−0.614133	+	0.144986i
$400$	−3.15802e8			−0.0123360
$401$	7.00764e9			0.271016			0.135508	−	0.990776i	$-0.456733\pi$
$401$	7.00764e9			0.271016			0.135508	+	0.990776i	$0.456733\pi$
$402$			2.08495e10i			0.798345i
$403$	−2.02399e10			−0.767342
$404$		−	2.08476e10i		−	0.782582i
$405$			3.06222e9i			0.113819i
$406$	1.88000e10	−	4.43836e9i	0.691916	−	0.163350i
$407$	1.43831e10			0.524174
$408$	1.11643e8			0.00402895
$409$			5.37459e9i			0.192067i	0.995378	+	0.0960334i	$0.0306156\pi$
$409$			5.37459e9i			0.192067i	−0.995378	+	0.0960334i	$0.969384\pi$
$410$	2.64599e9			0.0936382
$411$			1.44470e9i			0.0506303i
$412$		−	6.94446e9i		−	0.241018i
$413$	−1.25854e10	−	5.33091e10i	−0.432579	−	1.83232i
$414$	5.81893e9			0.198080
$415$	−3.25355e10			−1.09690
$416$			6.90111e9i			0.230433i
$417$	3.25796e10			1.07746
$418$		−	2.35569e10i		−	0.771636i
$419$			4.50132e10i			1.46044i	0.683212	+	0.730220i	$0.260582\pi$
$419$			4.50132e10i			1.46044i	−0.683212	+	0.730220i	$0.739418\pi$
$420$	−8.95546e9	+	2.11423e9i	−0.287800	+	0.0679447i
$421$	3.17143e10			1.00955			0.504773	−	0.863252i	$-0.331576\pi$
$421$	3.17143e10			1.00955			0.504773	+	0.863252i	$0.331576\pi$
$422$	2.92904e10			0.923581
$423$			1.27279e10i			0.397552i
$424$	1.55784e10			0.482013
$425$			3.17751e7i			0.000973938i
$426$		−	1.48699e10i		−	0.451513i
$427$	−6.85020e9	−	2.90161e10i	−0.206059	−	0.872825i
$428$	−5.57426e9			−0.166116
$429$	2.54516e10			0.751427
$430$			5.38176e9i			0.157417i
$431$	−7.16638e9			−0.207678			−0.103839	−	0.994594i	$-0.533113\pi$
$431$	−7.16638e9			−0.207678			−0.103839	+	0.994594i	$0.533113\pi$
$432$		−	1.67569e9i		−	0.0481125i
$433$		−	3.00426e9i		−	0.0854645i	−0.999087	−	0.0427323i	$-0.986394\pi$
$433$		−	3.00426e9i		−	0.0854645i	0.999087	−	0.0427323i	$-0.0136062\pi$
$434$	3.39312e9	+	1.43726e10i	0.0956402	+	0.405113i
$435$	−2.12913e10			−0.594626
$436$	8.74653e9			0.242042
$437$		−	3.34969e10i		−	0.918498i
$438$	−8.40931e9			−0.228488
$439$			6.23952e10i			1.67994i	0.542635	+	0.839968i	$0.317427\pi$
$439$			6.23952e10i			1.67994i	−0.542635	+	0.839968i	$0.682573\pi$
$440$		−	1.35535e10i		−	0.361610i
$441$	−1.12764e10	+	5.63862e9i	−0.298138	+	0.149080i
$442$	6.94371e8			0.0181929
$443$	4.92490e10			1.27874			0.639370	−	0.768899i	$-0.279195\pi$
$443$	4.92490e10			1.27874			0.639370	+	0.768899i	$0.279195\pi$
$444$		−	5.88966e9i		−	0.151551i
$445$	−2.13769e10			−0.545135
$446$			9.01937e9i			0.227949i
$447$			1.14639e10i			0.287146i
$448$	4.90055e9	−	1.15694e9i	0.121656	−	0.0287208i
$449$	−7.68396e10			−1.89060			−0.945300	−	0.326201i	$-0.894231\pi$
$449$	−7.68396e10			−1.89060			−0.945300	+	0.326201i	$0.894231\pi$
$450$	4.76923e8			0.0116305
$451$			5.34001e9i			0.129073i
$452$	−4.09859e9			−0.0981931
$453$		−	4.24062e10i		−	1.00702i
$454$		−	3.70132e10i		−	0.871230i
$455$	−5.56990e10	+	1.31496e10i	−1.29958	+	0.306808i
$456$	−9.64616e9			−0.223098
$457$	3.59810e10			0.824914			0.412457	−	0.910977i	$-0.364671\pi$
$457$	3.59810e10			0.824914			0.412457	+	0.910977i	$0.364671\pi$
$458$			2.81772e10i			0.640377i
$459$	−1.68603e8			−0.00379853
$460$		−	1.92725e10i		−	0.430434i
$461$		−	5.47301e10i		−	1.21178i	−0.795550	−	0.605888i	$-0.792818\pi$
$461$		−	5.47301e10i		−	1.21178i	0.795550	−	0.605888i	$-0.207182\pi$
$462$	−4.26684e9	−	1.80735e10i	−0.0936566	−	0.396710i
$463$	3.44204e10			0.749016			0.374508	−	0.927224i	$-0.377812\pi$
$463$	3.44204e10			0.749016			0.374508	+	0.927224i	$0.377812\pi$
$464$	1.16509e10			0.251354
$465$		−	1.62772e10i		−	0.348150i
$466$	−2.49857e10			−0.529845
$467$		−	4.05751e10i		−	0.853084i	−0.904468	−	0.426542i	$-0.859732\pi$
$467$		−	4.05751e10i		−	0.853084i	0.904468	−	0.426542i	$-0.140268\pi$
$468$		−	1.04220e10i		−	0.217255i
$469$	9.20831e10	−	2.17392e10i	1.90322	−	0.449317i
$470$	4.21552e10			0.863892
$471$	2.69457e10			0.547526
$472$		−	3.30371e10i		−	0.665631i
$473$	−1.08612e10			−0.216987
$474$			3.81296e10i			0.755352i
$475$		−	2.74542e9i		−	0.0539306i
$476$	−1.16408e8	−	4.93080e8i	−0.00226754	−	0.00960483i
$477$	−2.35264e10			−0.454446
$478$	1.40423e9			0.0268984
$479$			4.53236e10i			0.860959i	0.902600	+	0.430480i	$0.141656\pi$
$479$			4.53236e10i			0.860959i	−0.902600	+	0.430480i	$0.858344\pi$
$480$	−5.54994e9			−0.104550
$481$		−	3.66311e10i		−	0.684336i
$482$		−	3.07755e10i		−	0.570186i
$483$	−6.06726e9	−	2.56997e10i	−0.111482	−	0.472215i
$484$	−8.49376e7			−0.00154781
$485$	−1.04265e11			−1.88440
$486$			2.53062e9i			0.0453609i
$487$	4.32952e10			0.769705			0.384852	−	0.922978i	$-0.374252\pi$
$487$	4.32952e10			0.769705			0.384852	+	0.922978i	$0.374252\pi$
$488$		−	1.79820e10i		−	0.317073i
$489$			2.19606e10i			0.384069i
$490$	1.86753e10	+	3.73480e10i	0.323954	+	0.647862i
$491$	3.05896e10			0.526318			0.263159	−	0.964753i	$-0.415236\pi$
$491$	3.05896e10			0.526318			0.263159	+	0.964753i	$0.415236\pi$
$492$	2.18665e9			0.0373180
$493$		−	1.17228e9i		−	0.0198446i
$494$	−5.99948e10			−1.00741
$495$			2.04685e10i			0.340929i
$496$			8.90708e9i			0.147166i
$497$	−6.56741e10	+	1.55045e10i	−1.07639	+	0.254117i
$498$	−2.68873e10			−0.437150
$499$	−2.52720e10			−0.407604			−0.203802	−	0.979012i	$-0.565330\pi$
$499$	−2.52720e10			−0.407604			−0.203802	+	0.979012i	$0.565330\pi$
$500$			3.04321e10i			0.486914i
$501$	3.34090e10			0.530289
$502$			2.19284e10i			0.345296i
$503$		−	4.45581e10i		−	0.696073i	−0.937481	−	0.348037i	$-0.886848\pi$
$503$		−	4.45581e10i		−	0.696073i	0.937481	−	0.348037i	$-0.113152\pi$
$504$	−7.40080e9	+	1.74720e9i	−0.114698	+	0.0270783i
$505$	1.04276e11			1.60332
$506$	3.88948e10			0.593321
$507$		−	2.66725e10i		−	0.403675i
$508$	8.22670e9			0.123530
$509$			5.20245e9i			0.0775063i	0.999249	+	0.0387531i	$0.0123386\pi$
$509$			5.20245e9i			0.0775063i	−0.999249	+	0.0387531i	$0.987661\pi$
$510$			5.58420e8i			0.00825431i
$511$	8.76820e9	+	3.71403e10i	0.128596	+	0.544706i
$512$	3.03700e9			0.0441942
$513$	1.45676e10			0.210338
$514$			8.43165e10i			1.20798i
$515$	3.47350e10			0.493786
$516$			4.44749e9i			0.0627359i
$517$			8.50755e10i			1.19081i
$518$	−2.60121e10	+	6.14102e9i	−0.361290	+	0.0852945i
$519$	−5.80725e10			−0.800389
$520$	−3.45182e10			−0.472100
$521$		−	5.84028e10i		−	0.792652i	−0.918110	−	0.396326i	$-0.870285\pi$
$521$		−	5.84028e10i		−	0.792652i	0.918110	−	0.396326i	$-0.129715\pi$
$522$	−1.75951e10			−0.236979
$523$			1.59136e10i			0.212697i	0.994329	+	0.106349i	$0.0339159\pi$
$523$			1.59136e10i			0.212697i	−0.994329	+	0.106349i	$0.966084\pi$
$524$			1.99749e10i			0.264948i
$525$	−4.97277e8	−	2.10636e9i	−0.00654577	−	0.0277266i
$526$	1.09304e10			0.142788
$527$	8.96207e8			0.0116189
$528$		−	1.12006e10i		−	0.144114i
$529$	−2.30042e10			−0.293755
$530$			7.79204e10i			0.987524i
$531$			4.98925e10i			0.627563i
$532$	1.00578e10	+	4.26029e10i	0.125562	+	0.531855i
$533$	1.36000e10			0.168511
$534$	−1.76658e10			−0.217255
$535$		−	2.78815e10i		−	0.340331i
$536$	5.70664e10			0.691387
$537$			3.55633e10i			0.427666i
$538$			6.76623e10i			0.807640i
$539$	−7.53738e10	+	3.76896e10i	−0.893029	+	0.446546i
$540$	8.38151e9			0.0985705
$541$	−1.36800e11			−1.59697			−0.798483	−	0.602018i	$-0.794364\pi$
$541$	−1.36800e11			−1.59697			−0.798483	+	0.602018i	$0.794364\pi$
$542$			2.62033e10i			0.303640i
$543$	−4.69978e10			−0.540603
$544$		−	3.05575e8i		−	0.00348917i
$545$			4.37487e10i			0.495883i
$546$	−4.60297e10	+	1.08668e10i	−0.517926	+	0.122273i
$547$	1.41181e11			1.57698			0.788492	−	0.615045i	$-0.210862\pi$
$547$	1.41181e11			1.57698			0.788492	+	0.615045i	$0.210862\pi$
$548$	3.95425e9			0.0438472
$549$			2.71564e10i			0.298940i
$550$	3.18784e9			0.0348374
$551$			1.01287e11i			1.09887i
$552$		−	1.59268e10i		−	0.171543i
$553$	1.68402e11	−	3.97569e10i	1.80072	−	0.425120i
$554$	−1.33201e10			−0.141406
$555$	2.94591e10			0.310490
$556$		−	8.91726e10i		−	0.933109i
$557$	−1.20405e11			−1.25090			−0.625451	−	0.780263i	$-0.715085\pi$
$557$	−1.20405e11			−1.25090			−0.625451	+	0.780263i	$0.715085\pi$
$558$		−	1.34514e10i		−	0.138750i
$559$			2.76614e10i			0.283287i
$560$	5.78680e9	+	2.45117e10i	0.0588418	+	0.249242i
$561$	−1.12698e9			−0.0113779
$562$	−7.65431e10			−0.767292
$563$		−	1.74523e11i		−	1.73708i	−0.495618	−	0.868541i	$-0.665058\pi$
$563$		−	1.74523e11i		−	1.73708i	0.495618	−	0.868541i	$-0.334942\pi$
$564$	3.48370e10			0.344290
$565$		−	2.05005e10i		−	0.201173i
$566$		−	1.33600e10i		−	0.130179i
$567$	1.11767e10	−	2.63862e9i	0.108138	−	0.0255296i
$568$	−4.07000e10			−0.391022
$569$	1.24224e11			1.18510			0.592552	−	0.805532i	$-0.298120\pi$
$569$	1.24224e11			1.18510			0.592552	+	0.805532i	$0.298120\pi$
$570$		−	4.82484e10i		−	0.457071i
$571$	−8.39644e10			−0.789861			−0.394931	−	0.918711i	$-0.629231\pi$
$571$	−8.39644e10			−0.789861			−0.394931	+	0.918711i	$0.629231\pi$
$572$		−	6.96629e10i		−	0.650755i
$573$		−	5.00356e10i		−	0.464152i
$574$	−2.27997e9	−	9.65749e9i	−0.0210030	−	0.0889645i
$575$	4.53298e9			0.0414679
$576$	−4.58647e9			−0.0416667
$577$		−	1.66418e11i		−	1.50140i	−0.660642	−	0.750701i	$-0.729716\pi$
$577$		−	1.66418e11i		−	1.50140i	0.660642	−	0.750701i	$-0.270284\pi$
$578$	7.88909e10			0.706831
$579$		−	3.69146e10i		−	0.328461i
$580$			5.82756e10i			0.514962i
$581$	2.80348e10	+	1.18750e11i	0.246033	+	1.04215i
$582$	−8.61649e10			−0.750997
$583$	−1.57255e11			−1.36123
$584$			2.30169e10i			0.197877i
$585$	5.21293e10			0.445101
$586$		−	2.78776e10i		−	0.236409i
$587$		−	5.29885e10i		−	0.446302i	−0.974784	−	0.223151i	$-0.928366\pi$
$587$		−	5.29885e10i		−	0.446302i	0.974784	−	0.223151i	$-0.0716343\pi$
$588$	1.54333e10	+	3.08644e10i	0.129107	+	0.258195i
$589$	−7.74337e10			−0.643382
$590$	1.65246e11			1.36371
$591$		−	1.22992e11i		−	1.00815i
$592$	−1.61204e10			−0.131247
$593$		−	1.21844e11i		−	0.985339i	−0.870216	−	0.492670i	$-0.836021\pi$
$593$		−	1.21844e11i		−	0.985339i	0.870216	−	0.492670i	$-0.163979\pi$
$594$			1.69151e10i			0.135872i
$595$	2.46630e9	−	5.82252e8i	0.0196779	−	0.00464562i
$596$	3.13775e10			0.248676
$597$	1.36284e11			1.07287
$598$		−	9.90576e10i		−	0.774610i
$599$	−2.04022e10			−0.158479			−0.0792393	−	0.996856i	$-0.525249\pi$
$599$	−2.04022e10			−0.158479			−0.0792393	+	0.996856i	$0.525249\pi$
$600$		−	1.30537e9i		−	0.0100723i
$601$		−	8.86501e10i		−	0.679487i	−0.940518	−	0.339744i	$-0.889660\pi$
$601$		−	8.86501e10i		−	0.679487i	0.940518	−	0.339744i	$-0.110340\pi$
$602$	1.96426e10	−	4.63729e9i	0.149560	−	0.0353085i
$603$	−8.61815e10			−0.651846
$604$	−1.16069e11			−0.872102
$605$		−	4.24844e8i		−	0.00317108i
$606$	8.61737e10			0.638976
$607$			3.07317e10i			0.226377i	0.993574	+	0.113188i	$0.0361063\pi$
$607$			3.07317e10i			0.226377i	−0.993574	+	0.113188i	$0.963894\pi$
$608$			2.64022e10i			0.193208i
$609$	1.83460e10	+	7.77100e10i	0.133374	+	0.564947i
$610$	8.99431e10			0.649604
$611$	2.16671e11			1.55466
$612$			4.61479e8i			0.00328962i
$613$	9.65763e10			0.683957			0.341978	−	0.939708i	$-0.388903\pi$
$613$	9.65763e10			0.683957			0.341978	+	0.939708i	$0.388903\pi$
$614$			4.43515e10i			0.312058i
$615$			1.09372e10i			0.0764553i
$616$	−4.94683e10	+	1.16786e10i	−0.343561	+	0.0811090i
$617$	−3.19383e10			−0.220380			−0.110190	−	0.993911i	$-0.535146\pi$
$617$	−3.19383e10			−0.220380			−0.110190	+	0.993911i	$0.535146\pi$
$618$	2.87050e10			0.196791
$619$		−	4.77821e10i		−	0.325464i	−0.986670	−	0.162732i	$-0.947969\pi$
$619$		−	4.77821e10i		−	0.325464i	0.986670	−	0.162732i	$-0.0520306\pi$
$620$	−4.45517e10			−0.301507
$621$			2.40526e10i			0.161732i
$622$		−	2.01357e11i		−	1.34526i
$623$	1.84198e10	+	7.80225e10i	0.122273	+	0.517926i
$624$	−2.85258e10			−0.188148
$625$	−1.59746e11			−1.04691
$626$		−	2.09169e11i		−	1.36207i
$627$	9.73726e10			0.630038
$628$		−	7.37521e10i		−	0.474172i
$629$			1.62199e9i			0.0103621i
$630$	−8.73921e9	−	3.70175e10i	−0.0554766	−	0.234988i
$631$	−2.71219e11			−1.71082			−0.855408	−	0.517955i	$-0.826693\pi$
$631$	−2.71219e11			−1.71082			−0.855408	+	0.517955i	$0.826693\pi$
$632$	1.04363e11			0.654154
$633$			1.21072e11i			0.754100i
$634$	1.24747e11			0.772100
$635$			4.11485e10i			0.253081i
$636$			6.43934e10i			0.393562i
$637$	9.59882e10	+	1.91963e11i	0.582989	+	1.16589i
$638$	−1.17609e11			−0.709835
$639$	6.14651e10			0.368659
$640$			1.51906e10i			0.0905428i
$641$	4.13854e10			0.245140			0.122570	−	0.992460i	$-0.460886\pi$
$641$	4.13854e10			0.245140			0.122570	+	0.992460i	$0.460886\pi$
$642$		−	2.30413e10i		−	0.135633i
$643$		−	1.54368e11i		−	0.903052i	−0.892258	−	0.451526i	$-0.850880\pi$
$643$		−	1.54368e11i		−	0.903052i	0.892258	−	0.451526i	$-0.149120\pi$
$644$	−7.03418e10	+	1.66065e10i	−0.408950	+	0.0965461i
$645$	−2.22456e10			−0.128530
$646$	2.65652e9			0.0152540
$647$		−	1.45867e11i		−	0.832417i	−0.909269	−	0.416209i	$-0.863359\pi$
$647$		−	1.45867e11i		−	0.832417i	0.909269	−	0.416209i	$-0.136641\pi$
$648$	6.92648e9			0.0392837
$649$			3.33491e11i			1.87977i
$650$		−	8.11882e9i		−	0.0454820i
$651$	−5.94093e10	+	1.40255e10i	−0.330773	+	0.0780899i
$652$	6.01077e10			0.332613
$653$	−1.71740e11			−0.944535			−0.472267	−	0.881455i	$-0.656564\pi$
$653$	−1.71740e11			−0.944535			−0.472267	+	0.881455i	$0.656564\pi$
$654$			3.61539e10i			0.197626i
$655$	−9.99112e10			−0.542811
$656$		−	5.98500e9i		−	0.0323183i
$657$		−	3.47600e10i		−	0.186560i
$658$	−3.63238e10	−	1.53860e11i	−0.193771	−	0.820773i
$659$	2.10110e11			1.11405			0.557027	−	0.830495i	$-0.311942\pi$
$659$	2.10110e11			1.11405			0.557027	+	0.830495i	$0.311942\pi$
$660$	5.60236e10			0.295254
$661$			1.21944e11i			0.638787i	0.947622	+	0.319394i	$0.103479\pi$
$661$			1.21944e11i			0.638787i	−0.947622	+	0.319394i	$0.896521\pi$
$662$	−2.53942e11			−1.32221
$663$			2.87019e9i			0.0148545i
$664$			7.35925e10i			0.378583i
$665$	−2.13093e11	+	5.03076e10i	−1.08964	+	0.257245i
$666$	2.43450e10			0.123741
$667$	−1.67235e11			−0.844936
$668$		−	9.14427e10i		−	0.459244i
$669$	−3.72817e10			−0.186119
$670$			2.85436e11i			1.41648i
$671$			1.81519e11i			0.895429i
$672$	4.78221e9	+	2.02565e10i	0.0234505	+	0.0993315i
$673$	9.78746e10			0.477100			0.238550	−	0.971130i	$-0.423328\pi$
$673$	9.78746e10			0.477100			0.238550	+	0.971130i	$0.423328\pi$
$674$	−1.71605e11			−0.831554
$675$			1.97137e9i			0.00949626i
$676$	−7.30045e10			−0.349593
$677$			1.38167e11i			0.657734i	0.944376	+	0.328867i	$0.106667\pi$
$677$			1.38167e11i			0.657734i	−0.944376	+	0.328867i	$0.893333\pi$
$678$		−	1.69416e10i		−	0.0801743i
$679$	8.98422e10	+	3.80553e11i	0.422670	+	1.79034i
$680$	1.52843e9			0.00714844
$681$	1.52994e11			0.711356
$682$		−	8.99120e10i		−	0.415605i
$683$	1.74952e11			0.803965			0.401982	−	0.915647i	$-0.368321\pi$
$683$	1.74952e11			0.803965			0.401982	+	0.915647i	$0.368321\pi$
$684$		−	3.98725e10i		−	0.182158i
$685$			1.97785e10i			0.0898318i
$686$	1.20223e11	−	1.00344e11i	0.542863	−	0.453100i
$687$	−1.16471e11			−0.522865
$688$	1.21731e10			0.0543309
$689$			4.00499e11i			1.77715i
$690$	7.96631e10			0.351448
$691$		−	3.41380e11i		−	1.49736i	−0.662933	−	0.748678i	$-0.730689\pi$
$691$		−	3.41380e11i		−	1.49736i	0.662933	−	0.748678i	$-0.269311\pi$
$692$			1.58948e11i			0.693157i
$693$	7.47069e10	−	1.76370e10i	0.323913	−	0.0764703i
$694$	5.41964e10			0.233632
$695$	4.46026e11			1.91171
$696$			4.81590e10i			0.205230i
$697$	−6.02195e8			−0.00255156
$698$			1.02617e11i			0.432314i
$699$		−	1.03279e11i		−	0.432616i
$700$	−5.76526e9	+	1.36108e9i	−0.0240119	+	0.00566880i
$701$	−2.34774e11			−0.972250			−0.486125	−	0.873889i	$-0.661590\pi$
$701$	−2.34774e11			−0.972250			−0.486125	+	0.873889i	$0.661590\pi$
$702$	4.30796e10			0.177388
$703$		−	1.40143e11i		−	0.573785i
$704$	−3.06568e10			−0.124806
$705$			1.74249e11i			0.705365i
$706$			3.09192e10i			0.124454i
$707$	−8.98514e10	−	3.80592e11i	−0.359623	−	1.52329i
$708$	1.36559e11			0.543486
$709$	−3.63742e11			−1.43949			−0.719744	−	0.694240i	$-0.755741\pi$
$709$	−3.63742e11			−1.43949			−0.719744	+	0.694240i	$0.755741\pi$
$710$		−	2.03575e11i		−	0.801106i
$711$	−1.57609e11			−0.616742
$712$			4.83526e10i			0.188148i
$713$		−	1.27851e11i		−	0.494705i
$714$	2.03815e9	−	4.81173e8i	0.00784231	−	0.00185144i
$715$	3.48442e11			1.33323
$716$	9.73392e10			0.370370
$717$			5.80441e9i			0.0219625i
$718$	1.32601e11			0.498940
$719$			4.55541e11i			1.70456i	0.523087	+	0.852279i	$0.324780\pi$
$719$			4.55541e11i			1.70456i	−0.523087	+	0.852279i	$0.675220\pi$
$720$		−	2.29408e10i		−	0.0853646i
$721$	−2.99301e10	−	1.26778e11i	−0.110756	−	0.469140i
$722$	−3.73805e10			−0.137561
$723$	1.27211e11			0.465555
$724$			1.28636e11i			0.468176i
$725$	−1.37067e10			−0.0496112
$726$		−	3.51091e8i		−	0.00126378i
$727$		−	3.85016e11i		−	1.37829i	−0.724622	−	0.689147i	$-0.757986\pi$
$727$		−	3.85016e11i		−	1.37829i	0.724622	−	0.689147i	$-0.242014\pi$
$728$	2.97432e10	+	1.25986e11i	0.105892	+	0.448537i
$729$	−1.04604e10			−0.0370370
$730$	−1.15126e11			−0.405400
$731$		−	1.22482e9i		−	0.00428947i
$732$	7.43290e10			0.258889
$733$		−	2.70326e11i		−	0.936421i	−0.883617	−	0.468211i	$-0.844899\pi$
$733$		−	2.70326e11i		−	0.936421i	0.883617	−	0.468211i	$-0.155101\pi$
$734$			1.75529e11i			0.604735i
$735$	−1.54378e11	+	7.71947e10i	−0.528977	+	0.264507i
$736$	−4.35927e10			−0.148560
$737$	−5.76053e11			−1.95251
$738$			9.03854e9i			0.0304700i
$739$	−3.50148e11			−1.17402			−0.587009	−	0.809581i	$-0.699694\pi$
$739$	−3.50148e11			−1.17402			−0.587009	+	0.809581i	$0.699694\pi$
$740$		−	8.06315e10i		−	0.268892i
$741$		−	2.47989e11i		−	0.822546i
$742$	2.84398e11	−	6.71416e10i	0.938234	−	0.221501i
$743$	3.25691e11			1.06869			0.534344	−	0.845267i	$-0.320559\pi$
$743$	3.25691e11			1.06869			0.534344	+	0.845267i	$0.320559\pi$
$744$	−3.68175e10			−0.120161
$745$			1.56945e11i			0.509474i
$746$	−2.10987e11			−0.681240
$747$		−	1.11139e11i		−	0.356932i
$748$			3.08461e9i			0.00985358i
$749$	−1.01763e11	+	2.40246e10i	−0.323344	+	0.0763360i
$750$	−1.25792e11			−0.397564
$751$	4.07082e10			0.127974			0.0639871	−	0.997951i	$-0.479618\pi$
$751$	4.07082e10			0.127974			0.0639871	+	0.997951i	$0.479618\pi$
$752$		−	9.53514e10i		−	0.298164i
$753$	−9.06413e10			−0.281933
$754$			2.99527e11i			0.926726i
$755$		−	5.80556e11i		−	1.78672i
$756$	−7.22208e9	−	3.05913e10i	−0.0221093	−	0.0936506i
$757$	3.44467e11			1.04897			0.524487	−	0.851419i	$-0.324257\pi$
$757$	3.44467e11			1.04897			0.524487	+	0.851419i	$0.324257\pi$
$758$	−7.69358e10			−0.233051
$759$			1.60772e11i			0.484444i
$760$	−1.32059e11			−0.395835
$761$		−	2.77178e11i		−	0.826457i	−0.910627	−	0.413228i	$-0.864401\pi$
$761$		−	2.77178e11i		−	0.826457i	0.910627	−	0.413228i	$-0.135599\pi$
$762$			3.40052e10i			0.100861i
$763$	1.59676e11	−	3.76969e10i	0.471132	−	0.111226i
$764$	−1.36951e11			−0.401968
$765$	−2.30824e9			−0.00673961
$766$			7.51164e10i			0.218183i
$767$	8.49338e11			2.45414
$768$			1.25535e10i			0.0360844i
$769$			4.36810e11i			1.24907i	0.780996	+	0.624536i	$0.214712\pi$
$769$			4.36810e11i			1.24907i	−0.780996	+	0.624536i	$0.785288\pi$
$770$	−5.84145e10	−	2.47432e11i	−0.166172	−	0.703871i
$771$	−3.48523e11			−0.986312
$772$	−1.01038e11			−0.284456
$773$		−	1.32984e11i		−	0.372460i	−0.982506	−	0.186230i	$-0.940373\pi$
$773$		−	1.32984e11i		−	0.372460i	0.982506	−	0.186230i	$-0.0596270\pi$
$774$	−1.83838e10			−0.0512236
$775$		−	1.04788e10i		−	0.0290471i
$776$			2.35839e11i			0.650383i
$777$	−2.53840e10	−	1.07521e11i	−0.0696427	−	0.294992i
$778$	3.22798e11			0.881074
$779$	5.20307e10			0.141289
$780$		−	1.42681e11i		−	0.385468i
$781$	4.10844e11			1.10426
$782$			4.38619e9i			0.0117290i
$783$		−	7.27296e10i		−	0.193492i
$784$	8.44779e10	−	4.22419e10i	0.223604	−	0.111810i
$785$	3.68895e11			0.971460
$786$	−8.25666e10			−0.216329
$787$			4.44990e9i			0.0115998i	0.999983	+	0.00579991i	$0.00184618\pi$
$787$			4.44990e9i			0.0115998i	−0.999983	+	0.00579991i	$0.998154\pi$
$788$	−3.36636e11			−0.873084
$789$			4.51808e10i			0.116586i
$790$			5.22008e11i			1.34020i
$791$	−7.48237e10	+	1.76646e10i	−0.191132	+	0.0451230i
$792$	4.62979e10			0.117669
$793$	4.62293e11			1.16903
$794$			3.19765e11i			0.804542i
$795$	−3.22085e11			−0.806310
$796$		−	3.73019e11i		−	0.929133i
$797$		−	3.69213e11i		−	0.915049i	−0.889197	−	0.457524i	$-0.848736\pi$
$797$		−	3.69213e11i		−	0.915049i	0.889197	−	0.457524i	$-0.151264\pi$
$798$	−1.76100e11	+	4.15742e10i	−0.434258	+	0.102521i
$799$	−9.59400e9			−0.0235403
$800$	−3.57289e9			−0.00872287
$801$		−	7.30220e10i		−	0.177388i
$802$	7.92824e10			0.191637
$803$		−	2.32342e11i		−	0.558813i
$804$			2.35885e11i			0.564515i
$805$	−8.30629e10	−	3.51838e11i	−0.197799	−	0.837836i
$806$	−2.28989e11			−0.542593
$807$	−2.79683e11			−0.659435
$808$		−	2.35863e11i		−	0.553369i
$809$	−1.66834e11			−0.389485			−0.194743	−	0.980854i	$-0.562387\pi$
$809$	−1.66834e11			−0.389485			−0.194743	+	0.980854i	$0.562387\pi$
$810$			3.46451e10i			0.0804825i
$811$		−	6.64583e11i		−	1.53626i	−0.640292	−	0.768131i	$-0.721187\pi$
$811$		−	6.64583e11i		−	1.53626i	0.640292	−	0.768131i	$-0.278813\pi$
$812$	2.12698e11	−	5.02143e10i	0.489258	−	0.115506i
$813$	−1.08312e11			−0.247921
$814$	1.62727e11			0.370647
$815$			3.00648e11i			0.681441i
$816$	1.26310e9			0.00284890
$817$			1.05827e11i			0.237524i
$818$			6.08066e10i			0.135812i
$819$	−4.49182e10	−	1.90264e11i	−0.0998358	−	0.422884i
$820$	2.99360e10			0.0662122
$821$	7.87297e11			1.73287			0.866435	−	0.499290i	$-0.166406\pi$
$821$	7.87297e11			1.73287			0.866435	+	0.499290i	$0.166406\pi$
$822$			1.63449e10i			0.0358010i
$823$	−3.72056e11			−0.810977			−0.405489	−	0.914100i	$-0.632899\pi$
$823$	−3.72056e11			−0.810977			−0.405489	+	0.914100i	$0.632899\pi$
$824$		−	7.85676e10i		−	0.170426i
$825$			1.31770e10i			0.0284446i
$826$	−1.42387e11	−	6.03124e11i	−0.305880	−	1.29565i
$827$	−8.85822e11			−1.89376			−0.946878	−	0.321592i	$-0.895782\pi$
$827$	−8.85822e11			−1.89376			−0.946878	+	0.321592i	$0.895782\pi$
$828$	6.58336e10			0.140064
$829$			7.37225e11i			1.56092i	0.625203	+	0.780462i	$0.285016\pi$
$829$			7.37225e11i			1.56092i	−0.625203	+	0.780462i	$0.714984\pi$
$830$	−3.68097e11			−0.775622
$831$		−	5.50587e10i		−	0.115458i
$832$			7.80771e10i			0.162941i
$833$	−4.25027e9	−	8.49994e9i	−0.00882748	−	0.0176537i
$834$	3.68596e11			0.761880
$835$	4.57381e11			0.940875
$836$		−	2.66515e11i		−	0.545629i
$837$	5.56018e10			0.113289
$838$			5.09266e11i			1.03269i
$839$			7.97375e11i			1.60922i	0.593806	+	0.804609i	$0.297625\pi$
$839$			7.97375e11i			1.60922i	−0.593806	+	0.804609i	$0.702375\pi$
$840$	−1.01319e11	+	2.39198e10i	−0.203505	+	0.0480441i
$841$	5.43348e9			0.0108616
$842$	3.58806e11			0.713857
$843$		−	3.16392e11i		−	0.626492i
$844$	3.31382e11			0.653070
$845$		−	3.65156e11i		−	0.716228i
$846$			1.43999e11i			0.281112i
$847$	−1.55062e9	+	3.66074e8i	−0.00301281	+	0.000711272i
$848$	1.76249e11			0.340835
$849$	5.52238e10			0.106291
$850$			3.59494e8i			0.000688678i
$851$	2.31390e11			0.441191
$852$		−	1.68234e11i		−	0.319268i
$853$			3.38116e11i			0.638659i	0.947644	+	0.319330i	$0.103458\pi$
$853$			3.38116e11i			0.638659i	−0.947644	+	0.319330i	$0.896542\pi$
$854$	−7.75012e10	−	3.28279e11i	−0.145706	−	0.617180i
$855$	1.99436e11			0.373197
$856$	−6.30656e10			−0.117462
$857$			6.84827e11i			1.26957i	0.772688	+	0.634787i	$0.218912\pi$
$857$			6.84827e11i			1.26957i	−0.772688	+	0.634787i	$0.781088\pi$
$858$	2.87952e11			0.531339
$859$		−	6.79608e11i		−	1.24820i	−0.781342	−	0.624102i	$-0.785465\pi$
$859$		−	6.79608e11i		−	1.24820i	0.781342	−	0.624102i	$-0.214535\pi$
$860$			6.08877e10i			0.111310i
$861$	3.99194e10	−	9.42428e9i	0.0726392	−	0.0171489i
$862$	−8.10783e10			−0.146851
$863$	−7.44746e11			−1.34266			−0.671329	−	0.741160i	$-0.734276\pi$
$863$	−7.44746e11			−1.34266			−0.671329	+	0.741160i	$0.734276\pi$
$864$		−	1.89582e10i		−	0.0340207i
$865$	−7.95033e11			−1.42011
$866$		−	3.39893e10i		−	0.0604325i
$867$			3.26097e11i			0.577125i
$868$	3.83888e10	+	1.62607e11i	0.0676279	+	0.286458i
$869$	−1.05349e12			−1.84736
$870$	−2.40883e11			−0.420464
$871$			1.46710e12i			2.54910i
$872$	9.89557e10			0.171149
$873$		−	3.56164e11i		−	0.613187i
$874$		−	3.78974e11i		−	0.649476i
$875$	1.31160e11	+	5.55568e11i	0.223753	+	0.947774i
$876$	−9.51405e10			−0.161566
$877$	2.98320e11			0.504294			0.252147	−	0.967689i	$-0.418863\pi$
$877$	2.98320e11			0.504294			0.252147	+	0.967689i	$0.418863\pi$
$878$			7.05921e11i			1.18789i
$879$	1.15232e11			0.193027
$880$		−	1.53340e11i		−	0.255697i
$881$		−	3.78529e10i		−	0.0628342i	−0.999506	−	0.0314171i	$-0.989998\pi$
$881$		−	3.78529e10i		−	0.0628342i	0.999506	−	0.0314171i	$-0.0100020\pi$
$882$	−1.27578e11	+	6.37937e10i	−0.210816	+	0.105415i
$883$	−2.76215e11			−0.454365			−0.227183	−	0.973852i	$-0.572951\pi$
$883$	−2.76215e11			−0.454365			−0.227183	+	0.973852i	$0.572951\pi$
$884$	7.85591e9			0.0128643
$885$			6.83046e11i			1.11347i
$886$	5.57189e11			0.904206
$887$		−	9.17551e10i		−	0.148230i	−0.997250	−	0.0741149i	$-0.976387\pi$
$887$		−	9.17551e10i		−	0.148230i	0.997250	−	0.0741149i	$-0.0236132\pi$
$888$		−	6.66339e10i		−	0.107163i
$889$	1.50186e11	−	3.54564e10i	0.240449	−	0.0567659i
$890$	−2.41852e11			−0.385469
$891$	−6.99190e10			−0.110939
$892$			1.02043e11i			0.161184i
$893$	8.28938e11			1.30352
$894$			1.29699e11i			0.203043i
$895$			4.86874e11i			0.758796i
$896$	5.54434e10	−	1.30892e10i	0.0860236	−	0.0203087i
$897$	4.09456e11			0.632466
$898$	−8.69341e11			−1.33686
$899$			3.86592e11i			0.591854i
$900$	5.39577e9			0.00822400
$901$		−	1.77337e10i		−	0.0269092i
$902$			6.04153e10i			0.0912685i
$903$	1.91683e10	+	8.11932e10i	0.0288292	+	0.122115i
$904$	−4.63703e10			−0.0694330
$905$	−6.43416e11			−0.959175
$906$		−	4.79772e11i		−	0.712069i
$907$	1.97113e11			0.291264			0.145632	−	0.989339i	$-0.453478\pi$
$907$	1.97113e11			0.291264			0.145632	+	0.989339i	$0.453478\pi$
$908$		−	4.18756e11i		−	0.616052i
$909$			3.56200e11i			0.521721i
$910$	−6.30162e11	+	1.48771e11i	−0.918939	+	0.216946i
$911$	3.07128e11			0.445909			0.222954	−	0.974829i	$-0.428430\pi$
$911$	3.07128e11			0.445909			0.222954	+	0.974829i	$0.428430\pi$
$912$	−1.09134e11			−0.157754
$913$		−	7.42875e11i		−	1.06914i
$914$	4.07079e11			0.583303
$915$			3.71781e11i			0.530399i
$916$			3.18788e11i			0.452815i
$917$	8.60904e10	+	3.64661e11i	0.121752	+	0.515718i
$918$	−1.90753e9			−0.00268596
$919$	−4.03896e11			−0.566249			−0.283125	−	0.959083i	$-0.591371\pi$
$919$	−4.03896e11			−0.566249			−0.283125	+	0.959083i	$0.591371\pi$
$920$		−	2.18043e11i		−	0.304363i
$921$	−1.83328e11			−0.254794
$922$		−	6.19200e11i		−	0.856855i
$923$		−	1.04634e12i		−	1.44167i
$924$	−4.82738e10	−	2.04478e11i	−0.0662252	−	0.280517i
$925$	1.89649e10			0.0259050
$926$	3.89422e11			0.529635
$927$			1.18653e11i			0.160679i
$928$	1.31814e11			0.177734
$929$		−	9.67397e11i		−	1.29880i	−0.760447	−	0.649400i	$-0.775020\pi$
$929$		−	9.67397e11i		−	1.29880i	0.760447	−	0.649400i	$-0.224980\pi$
$930$		−	1.84155e11i		−	0.246179i
$931$	3.67231e11	+	7.34409e11i	0.488810	+	0.977551i
$932$	−2.82681e11			−0.374657
$933$	8.32313e11			1.09840
$934$		−	4.59055e11i		−	0.603222i
$935$	−1.54287e10			−0.0201875
$936$		−	1.17912e11i		−	0.153622i
$937$			2.90578e11i			0.376968i	0.982076	+	0.188484i	$0.0603574\pi$
$937$			2.90578e11i			0.376968i	−0.982076	+	0.188484i	$0.939643\pi$
$938$	1.04180e12	−	2.45952e11i	1.34578	−	0.317715i
$939$	8.64605e11			1.11213
$940$	4.76931e11			0.610864
$941$			1.01844e12i			1.29891i	0.760401	+	0.649454i	$0.225003\pi$
$941$			1.01844e12i			1.29891i	−0.760401	+	0.649454i	$0.774997\pi$
$942$	3.04855e11			0.387160
$943$			8.59080e10i			0.108639i
$944$		−	3.73772e11i		−	0.470672i
$945$	1.53012e11	−	3.61236e10i	0.191867	−	0.0452965i
$946$	−1.22880e11			−0.153433
$947$	−1.17005e12			−1.45481			−0.727405	−	0.686209i	$-0.759274\pi$
$947$	−1.17005e12			−1.45481			−0.727405	+	0.686209i	$0.759274\pi$
$948$			4.31387e11i			0.534114i
$949$	−5.91732e11			−0.729558
$950$		−	3.10609e10i		−	0.0381347i
$951$			5.15644e11i			0.630417i
$952$	−1.31700e9	−	5.57857e9i	−0.00160339	−	0.00679164i
$953$	−3.93257e9			−0.00476765			−0.00238383	−	0.999997i	$-0.500759\pi$
$953$	−3.93257e9			−0.00476765			−0.00238383	+	0.999997i	$0.500759\pi$
$954$	−2.66171e11			−0.321342
$955$		−	6.85005e11i		−	0.823531i
$956$	1.58871e10			0.0190201
$957$		−	4.86138e11i		−	0.579578i
$958$			5.12778e11i			0.608790i
$959$	7.21885e10	−	1.70425e10i	0.0853481	−	0.0201492i
$960$	−6.27904e10			−0.0739279
$961$	5.57341e11			0.653473
$962$		−	4.14433e11i		−	0.483899i
$963$	9.52415e10			0.110744
$964$		−	3.48185e11i		−	0.403183i
$965$		−	5.05374e11i		−	0.582779i
$966$	−6.86432e10	−	2.90759e11i	−0.0788296	−	0.333906i
$967$	−7.82238e11			−0.894608			−0.447304	−	0.894382i	$-0.647616\pi$
$967$	−7.82238e11			−0.894608			−0.447304	+	0.894382i	$0.647616\pi$
$968$	−9.60960e8			−0.00109447
$969$			1.09808e10i			0.0124548i
$970$	−1.17963e12			−1.33247
$971$		−	1.76047e11i		−	0.198040i	−0.995085	−	0.0990199i	$-0.968429\pi$
$971$		−	1.76047e11i		−	0.198040i	0.995085	−	0.0990199i	$-0.0315708\pi$
$972$			2.86307e10i			0.0320750i
$973$	−3.84327e11	−	1.62793e12i	−0.428795	−	1.81629i
$974$	4.89830e11			0.544264
$975$	3.35593e10			0.0371359
$976$		−	2.03444e11i		−	0.224205i
$977$	−1.82553e11			−0.200360			−0.100180	−	0.994969i	$-0.531942\pi$
$977$	−1.82553e11			−0.200360			−0.100180	+	0.994969i	$0.531942\pi$
$978$			2.48456e11i			0.271577i
$979$		−	4.88093e11i		−	0.531339i
$980$	2.11287e11	+	4.22544e11i	0.229070	+	0.458108i
$981$	−1.49443e11			−0.161361
$982$	3.46082e11			0.372163
$983$		−	4.08074e11i		−	0.437043i	−0.975832	−	0.218522i	$-0.929877\pi$
$983$		−	4.08074e11i		−	0.437043i	0.975832	−	0.218522i	$-0.0701235\pi$
$984$	2.47391e10			0.0263878
$985$		−	1.68380e12i		−	1.78873i
$986$		−	1.32628e10i		−	0.0140323i
$987$	6.35984e11	−	1.50145e11i	0.670158	−	0.158213i
$988$	−6.78764e11			−0.712346
$989$	−1.74731e11			−0.182635
$990$			2.31574e11i			0.241073i
$991$	−5.70316e11			−0.591318			−0.295659	−	0.955294i	$-0.595539\pi$
$991$	−5.70316e11			−0.591318			−0.295659	+	0.955294i	$0.595539\pi$
$992$			1.00772e11i			0.104062i
$993$		−	1.04967e12i		−	1.07958i
$994$	−7.43018e11	+	1.75414e11i	−0.761121	+	0.179688i
$995$	1.86578e12			1.90356
$996$	−3.04196e11			−0.309112
$997$		−	5.89256e11i		−	0.596381i	−0.954506	−	0.298190i	$-0.903617\pi$
$997$		−	5.89256e11i		−	0.596381i	0.954506	−	0.298190i	$-0.0963830\pi$
$998$	−2.85921e11			−0.288219
$999$			1.00630e11i			0.101034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.c.a.13.12	yes	12
3.2	odd	2		126.9.c.c.55.2		12
4.3	odd	2		336.9.f.c.97.5		12
7.6	odd	2	inner	42.9.c.a.13.7	✓	12
21.20	even	2		126.9.c.c.55.5		12
28.27	even	2		336.9.f.c.97.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.c.a.13.7	✓	12	7.6	odd	2	inner
42.9.c.a.13.12	yes	12	1.1	even	1	trivial
126.9.c.c.55.2		12	3.2	odd	2
126.9.c.c.55.5		12	21.20	even	2
336.9.f.c.97.5		12	4.3	odd	2
336.9.f.c.97.8		12	28.27	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} +640.234i q^{5} +529.090i q^{6} +(2336.76 - 551.670i) q^{7} +1448.15 q^{8} -2187.00 q^{9} +O(q^{10})\)	\(q+11.3137 q^{2} +46.7654i q^{3} +128.000 q^{4} +640.234i q^{5} +529.090i q^{6} +(2336.76 - 551.670i) q^{7} +1448.15 q^{8} -2187.00 q^{9} +7243.42i q^{10} -14618.3 q^{11} +5985.97i q^{12} +37230.1i q^{13} +(26437.5 - 6241.43i) q^{14} -29940.8 q^{15} +16384.0 q^{16} -1648.52i q^{17} -24743.1 q^{18} +142434. i q^{19} +81950.0i q^{20} +(25799.0 + 109280. i) q^{21} -165387. q^{22} -235174. q^{23} +67723.5i q^{24} -19275.0 q^{25} +421210. i q^{26} -102276. i q^{27} +(299106. - 70613.8i) q^{28} +711112. q^{29} -338741. q^{30} +543645. i q^{31} +185364. q^{32} -683631. i q^{33} -18650.8i q^{34} +(353198. + 1.49608e6i) q^{35} -279936. q^{36} -983911. q^{37} +1.61146e6i q^{38} -1.74108e6 q^{39} +927158. i q^{40} -365296. i q^{41} +(291883. + 1.23636e6i) q^{42} +742986. q^{43} -1.87115e6 q^{44} -1.40019e6i q^{45} -2.66069e6 q^{46} -5.81979e6i q^{47} +766204. i q^{48} +(5.15612e6 - 2.57824e6i) q^{49} -218072. q^{50} +77093.4 q^{51} +4.76545e6i q^{52} +1.07574e7 q^{53} -1.15712e6i q^{54} -9.35915e6i q^{55} +(3.38399e6 - 798903. i) q^{56} -6.66100e6 q^{57} +8.04531e6 q^{58} -2.28132e7i q^{59} -3.83242e6 q^{60} -1.24172e7i q^{61} +6.15064e6i q^{62} +(-5.11050e6 + 1.20650e6i) q^{63} +2.09715e6 q^{64} -2.38360e7 q^{65} -7.73440e6i q^{66} +3.94063e7 q^{67} -211010. i q^{68} -1.09980e7i q^{69} +(3.99598e6 + 1.69262e7i) q^{70} -2.81047e7 q^{71} -3.16711e6 q^{72} +1.58939e7i q^{73} -1.11317e7 q^{74} -901402. i q^{75} +1.82316e7i q^{76} +(-3.41596e7 + 8.06449e6i) q^{77} -1.96980e7 q^{78} +7.20665e7 q^{79} +1.04896e7i q^{80} +4.78297e6 q^{81} -4.13285e6i q^{82} +5.08181e7i q^{83} +(3.30228e6 + 1.39878e7i) q^{84} +1.05544e6 q^{85} +8.40592e6 q^{86} +3.32554e7i q^{87} -2.11696e7 q^{88} +3.33891e7i q^{89} -1.58414e7i q^{90} +(2.05387e7 + 8.69978e7i) q^{91} -3.01023e7 q^{92} -2.54238e7 q^{93} -6.58434e7i q^{94} -9.11914e7 q^{95} +8.66861e6i q^{96} +1.62855e8i q^{97} +(5.83349e7 - 2.91695e7i) q^{98} +3.19703e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9}+O(q^{10}) \) 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9	\( 12 q + 1536 q^{4} + 6420 q^{7} - 26244 q^{9} + 4344 q^{11} - 12288 q^{14} + 59616 q^{15} + 196608 q^{16} - 224856 q^{21} - 508416 q^{22} + 499800 q^{23} - 3001476 q^{25} + 821760 q^{28} - 1278408 q^{29} + 705024 q^{30} + 2028912 q^{35} - 3359232 q^{36} + 7068648 q^{37} - 5473008 q^{39} + 1513728 q^{42} - 11388024 q^{43} + 556032 q^{44} + 8171520 q^{46} - 12346788 q^{49} + 30019584 q^{50} + 16727472 q^{51} + 19714968 q^{53} - 1572864 q^{56} - 10386144 q^{57} - 17696256 q^{58} + 7630848 q^{60} - 14040540 q^{63} + 25165824 q^{64} - 93770592 q^{65} - 9394008 q^{67} + 11218944 q^{70} + 5393208 q^{71} + 58512384 q^{74} + 24982968 q^{77} + 32638464 q^{78} + 134560968 q^{79} + 57395628 q^{81} - 28781568 q^{84} - 102074640 q^{85} - 282934272 q^{86} - 65077248 q^{88} - 96105408 q^{91} + 63974400 q^{92} + 202339296 q^{93} - 378351840 q^{95} + 387747840 q^{98} - 9500328 q^{99}+O(q^{100}) \) 12 * q + 1536 * q^4 + 6420 * q^7 - 26244 * q^9 + 4344 * q^11 - 12288 * q^14 + 59616 * q^15 + 196608 * q^16 - 224856 * q^21 - 508416 * q^22 + 499800 * q^23 - 3001476 * q^25 + 821760 * q^28 - 1278408 * q^29 + 705024 * q^30 + 2028912 * q^35 - 3359232 * q^36 + 7068648 * q^37 - 5473008 * q^39 + 1513728 * q^42 - 11388024 * q^43 + 556032 * q^44 + 8171520 * q^46 - 12346788 * q^49 + 30019584 * q^50 + 16727472 * q^51 + 19714968 * q^53 - 1572864 * q^56 - 10386144 * q^57 - 17696256 * q^58 + 7630848 * q^60 - 14040540 * q^63 + 25165824 * q^64 - 93770592 * q^65 - 9394008 * q^67 + 11218944 * q^70 + 5393208 * q^71 + 58512384 * q^74 + 24982968 * q^77 + 32638464 * q^78 + 134560968 * q^79 + 57395628 * q^81 - 28781568 * q^84 - 102074640 * q^85 - 282934272 * q^86 - 65077248 * q^88 - 96105408 * q^91 + 63974400 * q^92 + 202339296 * q^93 - 378351840 * q^95 + 387747840 * q^98 - 9500328 * q^99

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