LMFDB - Embedded newform 6.17.b.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,17,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	6.b (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:	$9.73947263140$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 55116x^{4} + 758395257x^{2} + 123254139008 $ x^6 + 55116x^4 + 758395257x^2 + 123254139008
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{27}\cdot 3^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$-12.8250i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.17.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +O(q^{10})$	\(q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +278731. q^{10} +2.30420e8i q^{11} +(1.52506e8 + 1.51536e8i) q^{12} +1.44595e9 q^{13} +1.07188e9i q^{14} +(-7.12076e6 + 7.16633e6i) q^{15} +1.07374e9 q^{16} -1.68474e8i q^{17} +(-7.79213e9 + 4.97043e7i) q^{18} +4.32262e9 q^{19} +5.04558e7i q^{20} +(-2.75587e10 - 2.73834e10i) q^{21} -4.17105e10 q^{22} -9.99787e10i q^{23} +(-2.74309e10 + 2.76065e10i) q^{24} +1.52586e11 q^{25} +2.61744e11i q^{26} +(1.97788e11 - 2.01609e11i) q^{27} -1.94032e11 q^{28} +7.44960e11i q^{29} +(-1.29724e9 - 1.28900e9i) q^{30} +1.99388e11 q^{31} +1.94368e11i q^{32} +(1.06558e12 - 1.07240e12i) q^{33} +3.04970e10 q^{34} -9.11766e9i q^{35} +(-8.99744e9 - 1.41053e12i) q^{36} -3.98927e12 q^{37} +7.82478e11i q^{38} +(-6.72958e12 - 6.68679e12i) q^{39} -9.13347e9 q^{40} +1.34623e13i q^{41} +(4.95693e12 - 4.98865e12i) q^{42} +9.66403e12 q^{43} -7.55040e12i q^{44} +(6.62815e10 - 4.22795e8i) q^{45} +1.80981e13 q^{46} +2.89266e13i q^{47} +(-4.99730e12 - 4.96553e12i) q^{48} +1.82973e12 q^{49} +2.76209e13i q^{50} +(-7.79109e11 + 7.84094e11i) q^{51} -4.73808e13 q^{52} -8.03602e13i q^{53} +(3.64952e13 + 3.58034e13i) q^{54} +3.54798e11 q^{55} -3.51235e13i q^{56} +(-2.01179e13 - 1.99900e13i) q^{57} -1.34852e14 q^{58} -1.63088e14i q^{59} +(2.33333e11 - 2.34826e11i) q^{60} +8.55778e13 q^{61} +3.60931e13i q^{62} +(1.62589e12 + 2.54891e14i) q^{63} -3.51844e13 q^{64} -2.22645e12i q^{65} +(1.94125e14 + 1.92890e14i) q^{66} +5.13528e14 q^{67} +5.52055e12i q^{68} +(-4.62352e14 + 4.65311e14i) q^{69} +1.65047e12 q^{70} -3.19873e14i q^{71} +(2.55333e14 - 1.62871e12i) q^{72} +2.79061e13 q^{73} -7.22134e14i q^{74} +(-7.10148e14 - 7.05633e14i) q^{75} -1.41644e14 q^{76} +1.36440e15i q^{77} +(1.21044e15 - 1.21818e15i) q^{78} -4.23333e14 q^{79} -1.65333e12i q^{80} +(-1.85287e15 + 2.36391e13i) q^{81} -2.43693e15 q^{82} -6.58853e14i q^{83} +(9.03042e14 + 8.97300e14i) q^{84} -2.59414e11 q^{85} +1.74938e15i q^{86} +(3.44507e15 - 3.46712e15i) q^{87} +1.36677e15 q^{88} +4.19706e15i q^{89} +(7.65340e10 + 1.19982e13i) q^{90} +8.56199e15 q^{91} +3.27610e15i q^{92} +(-9.27971e14 - 9.22071e14i) q^{93} -5.23628e15 q^{94} -6.65591e12i q^{95} +(8.98856e14 - 9.04608e14i) q^{96} -3.81842e15 q^{97} +3.31216e14i q^{98} +(-9.91863e15 + 6.32687e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9}+O(q^{10}) $ 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9	$ 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9} + 39297024 q^{10} - 196804608 q^{12} + 1763152140 q^{13} - 8080218432 q^{15} + 6442450944 q^{16} - 12549169152 q^{18} + 60306979692 q^{19} - 155770661748 q^{21} + 94233305088 q^{22} - 5234491392 q^{24} - 75722441466 q^{25} + 330190979958 q^{27} + 5501485056 q^{28} + 987679531008 q^{30} - 2846203650132 q^{31} + 3282289396416 q^{33} - 1812957659136 q^{34} + 334749302784 q^{36} + 2483836081932 q^{37} - 8759076866580 q^{39} - 1287684882432 q^{40} - 3652917731328 q^{42} + 46155081190764 q^{43} - 46496752783488 q^{45} - 17111605395456 q^{46} + 6448893394944 q^{48} + 42155513811090 q^{49} - 3055668993792 q^{51} - 57774969323520 q^{52} + 240022278328320 q^{54} - 155561818958208 q^{55} + 27052692784332 q^{57} - 366644114104320 q^{58} + 264772597579776 q^{60} + 306036501898764 q^{61} - 801652315914324 q^{63} - 211106232532992 q^{64} + 11\!\cdots\!72 q^{66}+ \cdots - 28\!\cdots\!72 q^{99}+O(q^{100}) $ 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9 + 39297024 * q^10 - 196804608 * q^12 + 1763152140 * q^13 - 8080218432 * q^15 + 6442450944 * q^16 - 12549169152 * q^18 + 60306979692 * q^19 - 155770661748 * q^21 + 94233305088 * q^22 - 5234491392 * q^24 - 75722441466 * q^25 + 330190979958 * q^27 + 5501485056 * q^28 + 987679531008 * q^30 - 2846203650132 * q^31 + 3282289396416 * q^33 - 1812957659136 * q^34 + 334749302784 * q^36 + 2483836081932 * q^37 - 8759076866580 * q^39 - 1287684882432 * q^40 - 3652917731328 * q^42 + 46155081190764 * q^43 - 46496752783488 * q^45 - 17111605395456 * q^46 + 6448893394944 * q^48 + 42155513811090 * q^49 - 3055668993792 * q^51 - 57774969323520 * q^52 + 240022278328320 * q^54 - 155561818958208 * q^55 + 27052692784332 * q^57 - 366644114104320 * q^58 + 264772597579776 * q^60 + 306036501898764 * q^61 - 801652315914324 * q^63 - 211106232532992 * q^64 + 1157574327017472 * q^66 + 1979846570008812 * q^67 - 2345782552693632 * q^69 - 2197723307360256 * q^70 + 411211174772736 * q^72 + 3864207384753420 * q^73 - 3376263465802122 * q^75 - 1976139110547456 * q^76 + 5837442492456960 * q^78 + 1835806484101548 * q^79 - 703356001465338 * q^81 - 9913023387353088 * q^82 + 5104293044158464 * q^84 + 2872972366990848 * q^85 - 3000080900606400 * q^87 - 3087836941123584 * q^88 + 12789804912058368 * q^90 - 1824281133603240 * q^91 - 11156835457641972 * q^93 - 4579876939530240 * q^94 + 171523813933056 * q^96 + 31097493125645196 * q^97 - 28794216850745472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			181.019i			0.707107i
$2$			181.019i			0.707107i
$3$	−4654.10	−	4624.51i	−0.709358	−	0.704848i
$3$	−4654.10	−	4624.51i	−0.709358	−	0.704848i
$4$	−32768.0			−0.500000
$5$		−	1539.79i		−	0.00394186i	−0.999998	−	0.00197093i	$-0.999373\pi$
$5$		−	1539.79i		−	0.00394186i	0.999998	−	0.00197093i	$-0.000627366\pi$
$6$	837125.	−	842482.i	0.498403	−	0.501592i
$7$	5.92137e6			1.02716			0.513580	−	0.858042i	$-0.328319\pi$
$7$	5.92137e6			1.02716			0.513580	+	0.858042i	$0.328319\pi$
$8$		−	5.93164e6i		−	0.353553i
$9$	274580.	+	4.30458e7i	0.00637865	+	0.999980i
$10$	278731.			0.00278731
$11$			2.30420e8i			1.07493i	0.843287	+	0.537463i	$0.180617\pi$
$11$			2.30420e8i			1.07493i	−0.843287	+	0.537463i	$0.819383\pi$
$12$	1.52506e8	+	1.51536e8i	0.354679	+	0.352424i
$13$	1.44595e9			1.77258			0.886290	−	0.463131i	$-0.153274\pi$
$13$	1.44595e9			1.77258			0.886290	+	0.463131i	$0.153274\pi$
$14$			1.07188e9i			0.726312i
$15$	−7.12076e6	+	7.16633e6i	−0.00277841	+	0.00279619i
$16$	1.07374e9			0.250000
$17$		−	1.68474e8i		−	0.0241513i	−0.999927	−	0.0120757i	$-0.996156\pi$
$17$		−	1.68474e8i		−	0.0241513i	0.999927	−	0.0120757i	$-0.00384390\pi$
$18$	−7.79213e9	+	4.97043e7i	−0.707092	+	0.00451039i
$19$	4.32262e9			0.254518			0.127259	−	0.991870i	$-0.459382\pi$
$19$	4.32262e9			0.254518			0.127259	+	0.991870i	$0.459382\pi$
$20$			5.04558e7i			0.00197093i
$21$	−2.75587e10	−	2.73834e10i	−0.728625	−	0.723992i
$22$	−4.17105e10			−0.760088
$23$		−	9.99787e10i		−	1.27669i	−0.769751	−	0.638344i	$-0.779620\pi$
$23$		−	9.99787e10i		−	1.27669i	0.769751	−	0.638344i	$-0.220380\pi$
$24$	−2.74309e10	+	2.76065e10i	−0.249201	+	0.250796i
$25$	1.52586e11			0.999984
$26$			2.61744e11i			1.25340i
$27$	1.97788e11	−	2.01609e11i	0.700309	−	0.713840i
$28$	−1.94032e11			−0.513580
$29$			7.44960e11i			1.48919i	0.667519	+	0.744593i	$0.267356\pi$
$29$			7.44960e11i			1.48919i	−0.667519	+	0.744593i	$0.732644\pi$
$30$	−1.29724e9	−	1.28900e9i	−0.00197720	−	0.00196463i
$31$	1.99388e11			0.233779			0.116889	−	0.993145i	$-0.462708\pi$
$31$	1.99388e11			0.233779			0.116889	+	0.993145i	$0.462708\pi$
$32$			1.94368e11i			0.176777i
$33$	1.06558e12	−	1.07240e12i	0.757660	−	0.762508i
$34$	3.04970e10			0.0170776
$35$		−	9.11766e9i		−	0.00404892i
$36$	−8.99744e9	−	1.41053e12i	−0.00318933	−	0.499990i
$37$	−3.98927e12			−1.13574			−0.567871	−	0.823118i	$-0.692233\pi$
$37$	−3.98927e12			−1.13574			−0.567871	+	0.823118i	$0.692233\pi$
$38$			7.82478e11i			0.179971i
$39$	−6.72958e12	−	6.68679e12i	−1.25739	−	1.24940i
$40$	−9.13347e9			−0.00139366
$41$			1.34623e13i			1.68596i	0.537943	+	0.842981i	$0.319202\pi$
$41$			1.34623e13i			1.68596i	−0.537943	+	0.842981i	$0.680798\pi$
$42$	4.95693e12	−	4.98865e12i	0.511939	−	0.515215i
$43$	9.66403e12			0.826819			0.413410	−	0.910545i	$-0.364338\pi$
$43$	9.66403e12			0.826819			0.413410	+	0.910545i	$0.364338\pi$
$44$		−	7.55040e12i		−	0.537463i
$45$	6.62815e10	−	4.22795e8i	0.00394178	−	2.51437e-5i
$46$	1.80981e13			0.902755
$47$			2.89266e13i			1.21483i	0.794385	+	0.607415i	$0.207793\pi$
$47$			2.89266e13i			1.21483i	−0.794385	+	0.607415i	$0.792207\pi$
$48$	−4.99730e12	−	4.96553e12i	−0.177340	−	0.176212i
$49$	1.82973e12			0.0550576
$50$			2.76209e13i			0.707096i
$51$	−7.79109e11	+	7.84094e11i	−0.0170230	+	0.0171320i
$52$	−4.73808e13			−0.886290
$53$		−	8.03602e13i		−	1.29073i	−0.763876	−	0.645363i	$-0.776706\pi$
$53$		−	8.03602e13i		−	1.29073i	0.763876	−	0.645363i	$-0.223294\pi$
$54$	3.64952e13	+	3.58034e13i	0.504761	+	0.495193i
$55$	3.54798e11			0.00423721
$56$		−	3.51235e13i		−	0.363156i
$57$	−2.01179e13	−	1.99900e13i	−0.180544	−	0.179396i
$58$	−1.34852e14			−1.05301
$59$		−	1.63088e14i		−	1.11072i	−0.831610	−	0.555360i	$-0.812580\pi$
$59$		−	1.63088e14i		−	1.11072i	0.831610	−	0.555360i	$-0.187420\pi$
$60$	2.33333e11	−	2.34826e11i	0.00138920	−	0.00139809i
$61$	8.55778e13			0.446398			0.223199	−	0.974773i	$-0.428350\pi$
$61$	8.55778e13			0.446398			0.223199	+	0.974773i	$0.428350\pi$
$62$			3.60931e13i			0.165307i
$63$	1.62589e12	+	2.54891e14i	0.00655189	+	1.02714i
$64$	−3.51844e13			−0.125000
$65$		−	2.22645e12i		−	0.00698725i
$66$	1.94125e14	+	1.92890e14i	0.539175	+	0.535746i
$67$	5.13528e14			1.26464			0.632319	−	0.774709i	$-0.282103\pi$
$67$	5.13528e14			1.26464			0.632319	+	0.774709i	$0.282103\pi$
$68$			5.52055e12i			0.0120757i
$69$	−4.62352e14	+	4.65311e14i	−0.899871	+	0.905630i
$70$	1.65047e12			0.00286302
$71$		−	3.19873e14i		−	0.495349i	−0.968843	−	0.247675i	$-0.920334\pi$
$71$		−	3.19873e14i		−	0.495349i	0.968843	−	0.247675i	$-0.0796664\pi$
$72$	2.55333e14	−	1.62871e12i	0.353546	−	0.00225519i
$73$	2.79061e13			0.0346032			0.0173016	−	0.999850i	$-0.494492\pi$
$73$	2.79061e13			0.0346032			0.0173016	+	0.999850i	$0.494492\pi$
$74$		−	7.22134e14i		−	0.803090i
$75$	−7.10148e14	−	7.05633e14i	−0.709347	−	0.704837i
$76$	−1.41644e14			−0.127259
$77$			1.36440e15i			1.10412i
$78$	1.21044e15	−	1.21818e15i	0.883458	−	0.889112i
$79$	−4.23333e14			−0.279040			−0.139520	−	0.990219i	$-0.544556\pi$
$79$	−4.23333e14			−0.279040			−0.139520	+	0.990219i	$0.544556\pi$
$80$		−	1.65333e12i		−	0.000985464i
$81$	−1.85287e15	+	2.36391e13i	−0.999919	+	0.0127570i
$82$	−2.43693e15			−1.19216
$83$		−	6.58853e14i		−	0.292525i	−0.989246	−	0.146263i	$-0.953276\pi$
$83$		−	6.58853e14i		−	0.292525i	0.989246	−	0.146263i	$-0.0467245\pi$
$84$	9.03042e14	+	8.97300e14i	0.364312	+	0.361996i
$85$	−2.59414e11			−9.52011e−5
$86$			1.74938e15i			0.584650i
$87$	3.44507e15	−	3.46712e15i	1.04965	−	1.05637i
$88$	1.36677e15			0.380044
$89$			4.19706e15i			1.06617i	0.846062	+	0.533084i	$0.178967\pi$
$89$			4.19706e15i			1.06617i	−0.846062	+	0.533084i	$0.821033\pi$
$90$	7.65340e10	+	1.19982e13i	1.77793e−5	+	0.00278726i
$91$	8.56199e15			1.82072
$92$			3.27610e15i			0.638344i
$93$	−9.27971e14	−	9.22071e14i	−0.165833	−	0.164779i
$94$	−5.23628e15			−0.859014
$95$		−	6.65591e12i		−	0.00100327i
$96$	8.98856e14	−	9.04608e14i	0.124601	−	0.125398i
$97$	−3.81842e15			−0.487202			−0.243601	−	0.969875i	$-0.578329\pi$
$97$	−3.81842e15			−0.487202			−0.243601	+	0.969875i	$0.578329\pi$
$98$			3.31216e14i			0.0389316i
$99$	−9.91863e15	+	6.32687e13i	−1.07490	+	0.00685658i
$100$	−4.99992e15			−0.499992
$101$		−	3.95394e15i		−	0.365140i	−0.983193	−	0.182570i	$-0.941558\pi$
$101$		−	3.95394e15i		−	0.365140i	0.983193	−	0.182570i	$-0.0584415\pi$
$102$	−1.41936e14	−	1.41034e14i	−0.0121141	−	0.0120371i
$103$	9.78409e15			0.772365			0.386182	−	0.922422i	$-0.373794\pi$
$103$	9.78409e15			0.772365			0.386182	+	0.922422i	$0.373794\pi$
$104$		−	8.57684e15i		−	0.626701i
$105$	−4.21647e13	+	4.24345e13i	−0.00285387	+	0.00287213i
$106$	1.45468e16			0.912681
$107$		−	2.46522e16i		−	1.43478i	−0.696671	−	0.717390i	$-0.745336\pi$
$107$		−	2.46522e16i		−	1.43478i	0.696671	−	0.717390i	$-0.254664\pi$
$108$	−6.48111e15	+	6.60634e15i	−0.350154	+	0.356920i
$109$	−3.20807e16			−1.61002			−0.805012	−	0.593258i	$-0.797841\pi$
$109$	−3.20807e16			−1.61002			−0.805012	+	0.593258i	$0.797841\pi$
$110$			6.42253e13i			0.00299616i
$111$	1.85664e16	+	1.84484e16i	0.805647	+	0.800525i
$112$	6.35803e15			0.256790
$113$			2.62806e16i			0.988572i	0.869299	+	0.494286i	$0.164570\pi$
$113$			2.62806e16i			0.988572i	−0.869299	+	0.494286i	$0.835430\pi$
$114$	3.61857e15	−	3.64173e15i	0.126852	−	0.127664i
$115$	−1.53946e14			−0.00503252
$116$		−	2.44108e16i		−	0.744593i
$117$	3.97028e14	+	6.22420e16i	0.0113067	+	1.77254i
$118$	2.95220e16			0.785398
$119$		−	9.97597e14i		−	0.0248073i
$120$	4.25081e13	+	4.22378e13i	0.000988602	+	0.000982316i
$121$	−7.14366e15			−0.155467
$122$			1.54912e16i			0.315651i
$123$	6.22564e16	−	6.26548e16i	1.18835	−	1.19595i
$124$	−6.53354e15			−0.116889
$125$		−	4.69902e14i		−	0.00788365i
$126$	−4.61401e16	+	2.94318e14i	−0.726297	+	0.00463289i
$127$	−5.11153e16			−0.755303			−0.377652	−	0.925948i	$-0.623268\pi$
$127$	−5.11153e16			−0.755303			−0.377652	+	0.925948i	$0.623268\pi$
$128$		−	6.36905e15i		−	0.0883883i
$129$	−4.49774e16	−	4.46914e16i	−0.586511	−	0.582782i
$130$	4.03031e14			0.00494073
$131$		−	1.07461e17i		−	1.23903i	−0.784985	−	0.619515i	$-0.787329\pi$
$131$		−	1.07461e17i		−	1.23903i	0.784985	−	0.619515i	$-0.212671\pi$
$132$	−3.49169e16	+	3.51403e16i	−0.378830	+	0.381254i
$133$	2.55958e16			0.261430
$134$			9.29585e16i			0.894233i
$135$	−3.10436e14	−	3.04551e14i	−0.00281385	−	0.00276052i
$136$	−9.99327e14			−0.00853879
$137$			5.88231e16i			0.474006i	0.971509	+	0.237003i	$0.0761651\pi$
$137$			5.88231e16i			0.474006i	−0.971509	+	0.237003i	$0.923835\pi$
$138$	−8.42303e16	−	8.36947e16i	−0.640377	−	0.636305i
$139$	3.28378e16			0.235643			0.117822	−	0.993035i	$-0.462409\pi$
$139$	3.28378e16			0.235643			0.117822	+	0.993035i	$0.462409\pi$
$140$			2.98767e14i			0.00202446i
$141$	1.33771e17	−	1.34628e17i	0.856270	−	0.861749i
$142$	5.79033e16			0.350265
$143$			3.33175e17i			1.90539i
$144$	2.94828e14	+	4.62201e16i	0.00159466	+	0.249995i
$145$	1.14708e15			0.00587016
$146$			5.05155e15i			0.0244682i
$147$	−8.51573e15	−	8.46158e15i	−0.0390556	−	0.0388073i
$148$	1.30720e17			0.567871
$149$		−	1.74764e16i		−	0.0719384i	−0.999353	−	0.0359692i	$-0.988548\pi$
$149$		−	1.74764e16i		−	0.0719384i	0.999353	−	0.0359692i	$-0.0114518\pi$
$150$	1.27733e17	−	1.28551e17i	0.498395	−	0.501584i
$151$	3.48492e16			0.128937			0.0644685	−	0.997920i	$-0.479465\pi$
$151$	3.48492e16			0.128937			0.0644685	+	0.997920i	$0.479465\pi$
$152$		−	2.56402e16i		−	0.0899856i
$153$	7.25210e15	−	4.62596e13i	0.0241508	−	0.000154053i
$154$	−2.46983e17			−0.780732
$155$		−	3.07015e14i		−	0.000921523i
$156$	2.20515e17	+	2.19113e17i	0.628697	+	0.624699i
$157$	−1.85733e17			−0.503144			−0.251572	−	0.967839i	$-0.580948\pi$
$157$	−1.85733e17			−0.503144			−0.251572	+	0.967839i	$0.580948\pi$
$158$		−	7.66315e16i		−	0.197311i
$159$	−3.71626e17	+	3.74005e17i	−0.909766	+	0.915588i
$160$	2.99285e14			0.000696828
$161$		−	5.92011e17i		−	1.31136i
$162$	−4.27913e15	−	3.35405e17i	−0.00902059	−	0.707049i
$163$	−8.14420e17			−1.63436			−0.817180	−	0.576383i	$-0.804464\pi$
$163$	−8.14420e17			−1.63436			−0.817180	+	0.576383i	$0.804464\pi$
$164$		−	4.41132e17i		−	0.842981i
$165$	−1.65126e15	−	1.64077e15i	−0.00300570	−	0.00298659i
$166$	1.19265e17			0.206847
$167$			1.51746e17i			0.250834i	0.992104	+	0.125417i	$0.0400268\pi$
$167$			1.51746e17i			0.250834i	−0.992104	+	0.125417i	$0.959973\pi$
$168$	−1.62429e17	+	1.63468e17i	−0.255970	+	0.257608i
$169$	1.42535e18			2.14204
$170$		−	4.69589e13i		−	6.73173e-5i
$171$	1.18690e15	+	1.86071e17i	0.00162348	+	0.254513i
$172$	−3.16671e17			−0.413410
$173$		−	4.17219e17i		−	0.519990i	−0.965610	−	0.259995i	$-0.916279\pi$
$173$		−	4.17219e17i		−	0.519990i	0.965610	−	0.259995i	$-0.0837210\pi$
$174$	6.27615e17	+	6.23625e17i	0.746964	+	0.742214i
$175$	9.03516e17			1.02714
$176$			2.47412e17i			0.268732i
$177$	−7.54199e17	+	7.59026e17i	−0.782889	+	0.787899i
$178$	−7.59750e17			−0.753895
$179$		−	1.38626e17i		−	0.131529i	−0.997835	−	0.0657645i	$-0.979051\pi$
$179$		−	1.38626e17i		−	0.131529i	0.997835	−	0.0657645i	$-0.0209486\pi$
$180$	−2.17191e15	+	1.38541e13i	−0.00197089	+	1.25719e-5i
$181$	6.47300e17			0.561923			0.280961	−	0.959719i	$-0.409347\pi$
$181$	6.47300e17			0.561923			0.280961	+	0.959719i	$0.409347\pi$
$182$			1.54989e18i			1.28745i
$183$	−3.98288e17	−	3.95755e17i	−0.316656	−	0.314643i
$184$	−5.93038e17			−0.451377
$185$			6.14262e15i			0.00447693i
$186$	1.66913e17	−	1.67981e17i	0.116516	−	0.117262i
$187$	3.88198e16			0.0259609
$188$		−	9.47868e17i		−	0.607415i
$189$	1.17118e18	−	1.19380e18i	0.719329	−	0.733228i
$190$	1.20485e15			0.000709421
$191$		−	7.46429e17i		−	0.421426i	−0.977548	−	0.210713i	$-0.932421\pi$
$191$		−	7.46429e17i		−	0.421426i	0.977548	−	0.210713i	$-0.0675786\pi$
$192$	1.63752e17	+	1.62710e17i	0.0886698	+	0.0881060i
$193$	−2.21274e17			−0.114940			−0.0574700	−	0.998347i	$-0.518303\pi$
$193$	−2.21274e17			−0.114940			−0.0574700	+	0.998347i	$0.518303\pi$
$194$		−	6.91207e17i		−	0.344504i
$195$	−1.02962e16	+	1.03621e16i	−0.00492495	+	0.00495647i
$196$	−5.99565e16			−0.0275288
$197$			1.21371e18i			0.535041i	0.963552	+	0.267520i	$0.0862043\pi$
$197$			1.21371e18i			0.535041i	−0.963552	+	0.267520i	$0.913796\pi$
$198$	−1.14529e16	−	1.79546e18i	−0.00484833	−	0.760072i
$199$	−4.59820e18			−1.86966			−0.934832	−	0.355090i	$-0.884450\pi$
$199$	−4.59820e18			−1.86966			−0.934832	+	0.355090i	$0.884450\pi$
$200$		−	9.05083e17i		−	0.353548i
$201$	−2.39001e18	−	2.37482e18i	−0.897081	−	0.891377i
$202$	7.15739e17			0.258193
$203$			4.41119e18i			1.52963i
$204$	2.55298e16	−	2.56932e16i	0.00851151	−	0.00856598i
$205$	2.07291e16			0.00664582
$206$			1.77111e18i			0.546144i
$207$	4.30367e18	−	2.74522e16i	1.27666	−	0.00814355i
$208$	1.55257e18			0.443145
$209$			9.96018e17i			0.273588i
$210$	−7.68146e15	−	7.63262e15i	−0.00203090	−	0.00201799i
$211$	3.18692e18			0.811169			0.405585	−	0.914057i	$-0.367068\pi$
$211$	3.18692e18			0.811169			0.405585	+	0.914057i	$0.367068\pi$
$212$			2.63324e18i			0.645363i
$213$	−1.47926e18	+	1.48872e18i	−0.349146	+	0.351380i
$214$	4.46253e18			1.01454
$215$		−	1.48806e16i		−	0.00325920i
$216$	−1.19588e18	−	1.17321e18i	−0.252381	−	0.247597i
$217$	1.18065e18			0.240128
$218$		−	5.80723e18i		−	1.13846i
$219$	−1.29878e17	−	1.29052e17i	−0.0245461	−	0.0243900i
$220$	−1.16260e16			−0.00211860
$221$		−	2.43604e17i		−	0.0428102i
$222$	−3.33952e18	+	3.36089e18i	−0.566056	+	0.569679i
$223$	−7.13227e17			−0.116624			−0.0583121	−	0.998298i	$-0.518572\pi$
$223$	−7.13227e17			−0.116624			−0.0583121	+	0.998298i	$0.518572\pi$
$224$			1.15093e18i			0.181578i
$225$	4.18969e16	+	6.56817e18i	0.00637855	+	0.999964i
$226$	−4.75730e18			−0.699026
$227$		−	9.97663e18i		−	1.41507i	−0.706680	−	0.707534i	$-0.749808\pi$
$227$		−	9.97663e18i		−	1.41507i	0.706680	−	0.707534i	$-0.250192\pi$
$228$	6.59223e17	+	6.55032e17i	0.0902722	+	0.0896982i
$229$	−7.93251e18			−1.04888			−0.524441	−	0.851447i	$-0.675726\pi$
$229$	−7.93251e18			−1.04888			−0.524441	+	0.851447i	$0.675726\pi$
$230$		−	2.78672e16i		−	0.00355853i
$231$	6.30969e18	−	6.35007e18i	0.778238	−	0.783218i
$232$	4.41884e18			0.526507
$233$		−	8.97259e16i		−	0.0103293i	−0.999987	−	0.00516465i	$-0.998356\pi$
$233$		−	8.97259e16i		−	0.0103293i	0.999987	−	0.00516465i	$-0.00164397\pi$
$234$	−1.12670e19	+	7.18698e16i	−1.25338	+	0.00799502i
$235$	4.45409e16			0.00478868
$236$			5.34405e18i			0.555360i
$237$	1.97024e18	+	1.95771e18i	0.197939	+	0.196680i
$238$	1.80584e17			0.0175414
$239$		−	1.76298e19i		−	1.65602i	−0.560716	−	0.828008i	$-0.689474\pi$
$239$		−	1.76298e19i		−	1.65602i	0.560716	−	0.828008i	$-0.310526\pi$
$240$	−7.64586e15	+	7.69478e15i	−0.000694602	+	0.000699047i
$241$	−7.62250e18			−0.669825			−0.334912	−	0.942249i	$-0.608707\pi$
$241$	−7.62250e18			−0.669825			−0.334912	+	0.942249i	$0.608707\pi$
$242$		−	1.29314e18i		−	0.109932i
$243$	8.73276e18	+	8.45859e18i	0.718292	+	0.695741i
$244$	−2.80421e18			−0.223199
$245$		−	2.81739e15i		−	0.000217029i
$246$	1.13417e19	+	1.12696e19i	0.845666	+	0.840288i
$247$	6.25028e18			0.451153
$248$		−	1.18270e18i		−	0.0826533i
$249$	−3.04687e18	+	3.06637e18i	−0.206186	+	0.207505i
$250$	8.50614e16			0.00557458
$251$			1.50703e19i			0.956606i	0.878195	+	0.478303i	$0.158748\pi$
$251$			1.50703e19i			0.956606i	−0.878195	+	0.478303i	$0.841252\pi$
$252$	−5.32772e16	−	8.35225e18i	−0.00327595	−	0.513570i
$253$	2.30371e19			1.37235
$254$		−	9.25286e18i		−	0.534080i
$255$	1.20734e15	+	1.19966e15i	6.75317e−5	+	6.71023e-5i
$256$	1.15292e18			0.0625000
$257$			3.63998e19i			1.91265i	0.292313	+	0.956323i	$0.405575\pi$
$257$			3.63998e19i			1.91265i	−0.292313	+	0.956323i	$0.594425\pi$
$258$	8.09000e18	−	8.14177e18i	0.412089	−	0.414726i
$259$	−2.36219e19			−1.16659
$260$			7.29564e16i			0.00349363i
$261$	−3.20674e19	+	2.04551e17i	−1.48916	+	0.00949900i
$262$	1.94526e19			0.876126
$263$		−	6.06063e18i		−	0.264772i	−0.991198	−	0.132386i	$-0.957736\pi$
$263$		−	6.06063e18i		−	0.264772i	0.991198	−	0.132386i	$-0.0422638\pi$
$264$	−6.36108e18	−	6.32063e18i	−0.269587	−	0.267873i
$265$	−1.23738e17			−0.00508786
$266$			4.63334e18i			0.184859i
$267$	1.94094e19	−	1.95336e19i	0.751486	−	0.756295i
$268$	−1.68273e19			−0.632319
$269$		−	2.59397e19i		−	0.946122i	−0.881030	−	0.473061i	$-0.843149\pi$
$269$		−	2.59397e19i		−	0.946122i	0.881030	−	0.473061i	$-0.156851\pi$
$270$	5.51297e16	−	5.61949e16i	0.00195198	−	0.00198970i
$271$	−1.40860e19			−0.484208			−0.242104	−	0.970250i	$-0.577838\pi$
$271$	−1.40860e19			−0.484208			−0.242104	+	0.970250i	$0.577838\pi$
$272$		−	1.80897e17i		−	0.00603783i
$273$	−3.98484e19	−	3.95950e19i	−1.29154	−	1.28333i
$274$	−1.06481e19			−0.335173
$275$			3.51588e19i			1.07491i
$276$	1.51504e19	−	1.52473e19i	0.449936	−	0.452815i
$277$	6.17005e19			1.78013			0.890063	−	0.455838i	$-0.150660\pi$
$277$	6.17005e19			1.78013			0.890063	+	0.455838i	$0.150660\pi$
$278$			5.94427e18i			0.166625i
$279$	5.47479e16	+	8.58282e18i	0.00149119	+	0.233774i
$280$	−5.40827e16			−0.00143151
$281$		−	3.85570e19i		−	0.991866i	−0.868361	−	0.495933i	$-0.834826\pi$
$281$		−	3.85570e19i		−	0.991866i	0.868361	−	0.495933i	$-0.165174\pi$
$282$	2.43702e19	+	2.42152e19i	0.609349	+	0.605474i
$283$	−3.08609e19			−0.750096			−0.375048	−	0.927005i	$-0.622374\pi$
$283$	−3.08609e19			−0.750096			−0.375048	+	0.927005i	$0.622374\pi$
$284$			1.04816e19i			0.247675i
$285$	−3.07803e16	+	3.09773e16i	−0.000707155	+	0.000711680i
$286$	−6.03112e19			−1.34732
$287$			7.97152e19i			1.73175i
$288$	−8.36674e18	+	5.33696e16i	−0.176773	+	0.00112760i
$289$	4.86328e19			0.999417
$290$			2.07644e17i			0.00415083i
$291$	1.77713e19	+	1.76583e19i	0.345601	+	0.343404i
$292$	−9.14428e17			−0.0173016
$293$		−	9.45764e18i		−	0.174117i	−0.996203	−	0.0870586i	$-0.972253\pi$
$293$		−	9.45764e18i		−	0.174117i	0.996203	−	0.0870586i	$-0.0277468\pi$
$294$	1.53171e18	−	1.54151e18i	0.0274409	−	0.0276165i
$295$	−2.51120e17			−0.00437830
$296$			2.36629e19i			0.401545i
$297$	4.64549e19	+	4.55743e19i	0.767325	+	0.752781i
$298$	3.16356e18			0.0508681
$299$		−	1.44564e20i		−	2.26303i
$300$	2.32701e19	+	2.31222e19i	0.354674	+	0.352419i
$301$	5.72243e19			0.849276
$302$			6.30838e18i			0.0911722i
$303$	−1.82850e19	+	1.84020e19i	−0.257368	+	0.259015i
$304$	4.64138e18			0.0636294
$305$		−	1.31772e17i		−	0.00175964i
$306$	8.37387e15	+	1.31277e18i	0.000108932	+	0.0170772i
$307$	−3.19426e19			−0.404821			−0.202411	−	0.979301i	$-0.564878\pi$
$307$	−3.19426e19			−0.404821			−0.202411	+	0.979301i	$0.564878\pi$
$308$		−	4.47088e19i		−	0.552061i
$309$	−4.55361e19	−	4.52466e19i	−0.547883	−	0.544400i
$310$	5.55757e16			0.000651615
$311$			5.04871e19i			0.576895i	0.957496	+	0.288448i	$0.0931391\pi$
$311$			5.04871e19i			0.576895i	−0.957496	+	0.288448i	$0.906861\pi$
$312$	−3.96637e19	+	3.99175e19i	−0.441729	+	0.444556i
$313$	−9.61081e19			−1.04329			−0.521645	−	0.853163i	$-0.674681\pi$
$313$	−9.61081e19			−1.04329			−0.521645	+	0.853163i	$0.674681\pi$
$314$		−	3.36213e19i		−	0.355777i
$315$	3.92477e17	−	2.50353e15i	0.00404883	−	2.58266e-5i
$316$	1.38718e19			0.139520
$317$		−	1.08055e20i		−	1.05967i	−0.848101	−	0.529834i	$-0.822254\pi$
$317$		−	1.08055e20i		−	1.05967i	0.848101	−	0.529834i	$-0.177746\pi$
$318$	−6.77021e19	−	6.72716e19i	−0.647418	−	0.643302i
$319$	−1.71654e20			−1.60077
$320$			5.41765e16i			0.000492732i
$321$	−1.14004e20	+	1.14734e20i	−1.01130	+	1.01777i
$322$	1.07165e20			0.927274
$323$		−	7.28248e17i		−	0.00614694i
$324$	6.07148e19	−	7.74605e17i	0.499959	−	0.00637852i
$325$	2.20631e20			1.77255
$326$		−	1.47426e20i		−	1.15567i
$327$	1.49307e20	+	1.48358e20i	1.14208	+	1.13482i
$328$	7.98535e19			0.596078
$329$			1.71285e20i			1.24782i
$330$	2.97010e17	−	2.98911e17i	0.00211183	−	0.00212535i
$331$	−5.10944e19			−0.354608			−0.177304	−	0.984156i	$-0.556738\pi$
$331$	−5.10944e19			−0.354608			−0.177304	+	0.984156i	$0.556738\pi$
$332$			2.15893e19i			0.146263i
$333$	−1.09537e18	−	1.71721e20i	−0.00724449	−	1.13572i
$334$	−2.74690e19			−0.177366
$335$		−	7.90724e17i		−	0.00498502i
$336$	−2.95909e19	−	2.94027e19i	−0.182156	−	0.180998i
$337$	5.25258e19			0.315743			0.157871	−	0.987460i	$-0.449537\pi$
$337$	5.25258e19			0.315743			0.157871	+	0.987460i	$0.449537\pi$
$338$			2.58015e20i			1.51465i
$339$	1.21535e20	−	1.22313e20i	0.696793	−	0.701252i
$340$	8.50048e15			4.76005e−5
$341$			4.59430e19i			0.251295i
$342$	−3.36824e19	+	2.14853e17i	−0.179968	+	0.00114797i
$343$	−1.85950e20			−0.970607
$344$		−	5.73236e19i		−	0.292325i
$345$	7.16480e17	+	7.11924e17i	0.00356986	+	0.00354716i
$346$	7.55247e19			0.367689
$347$			3.17727e20i			1.51154i	0.654839	+	0.755768i	$0.272736\pi$
$347$			3.17727e20i			1.51154i	−0.654839	+	0.755768i	$0.727264\pi$
$348$	−1.12888e20	+	1.13611e20i	−0.524825	+	0.528183i
$349$	−7.84605e19			−0.356490			−0.178245	−	0.983986i	$-0.557042\pi$
$349$	−7.84605e19			−0.356490			−0.178245	+	0.983986i	$0.557042\pi$
$350$			1.63554e20i			0.726301i
$351$	2.85991e20	−	2.91517e20i	1.24135	−	1.26534i
$352$	−4.47863e19			−0.190022
$353$		−	2.44715e20i		−	1.01499i	−0.861653	−	0.507497i	$-0.830571\pi$
$353$		−	2.44715e20i		−	1.01499i	0.861653	−	0.507497i	$-0.169429\pi$
$354$	−1.37398e20	−	1.36525e20i	−0.557128	−	0.553586i
$355$	−4.92537e17			−0.00195260
$356$		−	1.37529e20i		−	0.533084i
$357$	−4.61339e18	+	4.64292e18i	−0.0174854	+	0.0175973i
$358$	2.50941e19			0.0930051
$359$		−	1.77162e20i		−	0.642119i	−0.947059	−	0.321060i	$-0.895961\pi$
$359$		−	1.77162e20i		−	0.642119i	0.947059	−	0.321060i	$-0.104039\pi$
$360$	−2.50787e15	−	3.93158e17i	−8.88965e−6	−	0.00139363i
$361$	−2.69756e20			−0.935221
$362$			1.17174e20i			0.397340i
$363$	3.32473e19	+	3.30359e19i	0.110282	+	0.109581i
$364$	−2.80559e20			−0.910361
$365$		−	4.29695e16i		−	0.000136401i
$366$	7.16393e19	−	7.20977e19i	0.222486	−	0.223910i
$367$	3.41194e20			1.03675			0.518373	−	0.855154i	$-0.326538\pi$
$367$	3.41194e20			1.03675			0.518373	+	0.855154i	$0.326538\pi$
$368$		−	1.07351e20i		−	0.319172i
$369$	−5.79495e20	+	3.69647e18i	−1.68593	+	0.0107542i
$370$	−1.11193e18			−0.00316567
$371$		−	4.75843e20i		−	1.32578i
$372$	3.04078e19	+	3.02144e19i	0.0829165	+	0.0823893i
$373$	4.31198e20			1.15082			0.575409	−	0.817866i	$-0.304843\pi$
$373$	4.31198e20			1.15082			0.575409	+	0.817866i	$0.304843\pi$
$374$			7.02713e18i			0.0183571i
$375$	−2.17307e18	+	2.18697e18i	−0.00555678	+	0.00559233i
$376$	1.71583e20			0.429507
$377$			1.07717e21i			2.63970i
$378$	2.16102e20	+	2.12006e20i	0.518470	+	0.508643i
$379$	−9.46277e19			−0.222282			−0.111141	−	0.993805i	$-0.535451\pi$
$379$	−9.46277e19			−0.222282			−0.111141	+	0.993805i	$0.535451\pi$
$380$			2.18101e17i			0.000501636i
$381$	2.37896e20	+	2.36383e20i	0.535781	+	0.532374i
$382$	1.35118e20			0.297993
$383$		−	1.63118e20i		−	0.352300i	−0.984363	−	0.176150i	$-0.943636\pi$
$383$		−	1.63118e20i		−	0.352300i	0.984363	−	0.176150i	$-0.0563643\pi$
$384$	−2.94537e19	+	2.96422e19i	−0.0623003	+	0.0626990i
$385$	2.10089e18			0.00435229
$386$		−	4.00548e19i		−	0.0812749i
$387$	2.65355e18	+	4.15996e20i	0.00527399	+	0.826803i
$388$	1.25122e20			0.243601
$389$		−	7.07561e20i		−	1.34948i	−0.738055	−	0.674741i	$-0.764255\pi$
$389$		−	7.07561e20i		−	1.34948i	0.738055	−	0.674741i	$-0.235745\pi$
$390$	−1.87575e18	−	1.86382e18i	−0.00350475	−	0.00348247i
$391$	−1.68438e19			−0.0308337
$392$		−	1.08533e19i		−	0.0194658i
$393$	−4.96955e20	+	5.00135e20i	−0.873327	+	0.878916i
$394$	−2.19706e20			−0.378331
$395$			6.51843e17i			0.00109993i
$396$	3.25014e20	−	2.07319e18i	0.537452	−	0.00342829i
$397$	−7.54229e19			−0.122230			−0.0611152	−	0.998131i	$-0.519466\pi$
$397$	−7.54229e19			−0.122230			−0.0611152	+	0.998131i	$0.519466\pi$
$398$		−	8.32364e20i		−	1.32205i
$399$	−1.19126e20	−	1.18368e20i	−0.185448	−	0.184269i
$400$	1.63837e20			0.249996
$401$			5.73495e20i			0.857777i	0.903357	+	0.428889i	$0.141095\pi$
$401$			5.73495e20i			0.857777i	−0.903357	+	0.428889i	$0.858905\pi$
$402$	4.29887e20	−	4.32638e20i	0.630299	−	0.634332i
$403$	2.88304e20			0.414392
$404$			1.29563e20i			0.182570i
$405$	3.63991e16	+	2.85303e18i	5.02864e−5	+	0.00394154i
$406$	−7.98510e20			−1.08161
$407$		−	9.19207e20i		−	1.22084i
$408$	4.65097e18	+	4.62139e18i	0.00605706	+	0.00601855i
$409$	−8.16315e20			−1.04249			−0.521244	−	0.853407i	$-0.674532\pi$
$409$	−8.16315e20			−1.04249			−0.521244	+	0.853407i	$0.674532\pi$
$410$			3.75236e18i			0.00469931i
$411$	2.72028e20	−	2.73769e20i	0.334102	−	0.336240i
$412$	−3.20605e20			−0.386182
$413$		−	9.65702e20i		−	1.14089i
$414$	4.96937e18	+	7.79047e20i	0.00575836	+	0.902737i
$415$	−1.01449e18			−0.00115309
$416$			2.81046e20i			0.313351i
$417$	−1.52830e20	−	1.51858e20i	−0.167156	−	0.166093i
$418$	−1.80299e20			−0.193456
$419$			9.99098e20i			1.05171i	0.850574	+	0.525855i	$0.176254\pi$
$419$			9.99098e20i			1.05171i	−0.850574	+	0.525855i	$0.823746\pi$
$420$	1.38165e18	−	1.39049e18i	0.00142694	−	0.00143607i
$421$	8.93599e20			0.905494			0.452747	−	0.891639i	$-0.350444\pi$
$421$	8.93599e20			0.905494			0.452747	+	0.891639i	$0.350444\pi$
$422$			5.76894e20i			0.573583i
$423$	−1.24517e21	+	7.94268e18i	−1.21480	+	0.00774897i
$424$	−4.76668e20			−0.456341
$425$		−	2.57067e19i		−	0.0241510i
$426$	−2.69488e20	−	2.67774e20i	−0.248463	−	0.246883i
$427$	5.06738e20			0.458522
$428$			8.07803e20i			0.717390i
$429$	1.54077e21	−	1.55063e21i	1.34301	−	1.35161i
$430$	2.69367e18			0.00230460
$431$			1.38442e21i			1.16265i	0.813670	+	0.581327i	$0.197466\pi$
$431$			1.38442e21i			1.16265i	−0.813670	+	0.581327i	$0.802534\pi$
$432$	2.12373e20	−	2.16477e20i	0.175077	−	0.178460i
$433$	1.26892e21			1.02690			0.513452	−	0.858118i	$-0.328366\pi$
$433$	1.26892e21			1.02690			0.513452	+	0.858118i	$0.328366\pi$
$434$			2.13721e20i			0.169796i
$435$	−5.33863e18	−	5.30468e18i	−0.00416404	−	0.00413757i
$436$	1.05122e21			0.805012
$437$		−	4.32170e20i		−	0.324940i
$438$	2.33609e19	−	2.35104e19i	0.0172463	−	0.0173567i
$439$	7.85494e20			0.569412			0.284706	−	0.958615i	$-0.408104\pi$
$439$	7.85494e20			0.569412			0.284706	+	0.958615i	$0.408104\pi$
$440$		−	2.10453e18i		−	0.00149808i
$441$	5.02406e17	+	7.87621e19i	0.000351193	+	0.0550565i
$442$	4.40971e19			0.0302714
$443$			1.76848e21i			1.19225i	0.802890	+	0.596127i	$0.203295\pi$
$443$			1.76848e21i			1.19225i	−0.802890	+	0.596127i	$0.796705\pi$
$444$	−6.08385e20	−	6.04517e20i	−0.402824	−	0.400262i
$445$	6.46259e18			0.00420268
$446$		−	1.29108e20i		−	0.0824657i
$447$	−8.08195e19	+	8.13367e19i	−0.0507056	+	0.0510301i
$448$	−2.08340e20			−0.128395
$449$			1.12071e20i			0.0678456i	0.999424	+	0.0339228i	$0.0108000\pi$
$449$			1.12071e20i			0.0678456i	−0.999424	+	0.0339228i	$0.989200\pi$
$450$	−1.18897e21	+	7.58415e18i	−0.707081	+	0.00451032i
$451$	−3.10198e21			−1.81229
$452$		−	8.61164e20i		−	0.494286i
$453$	−1.62192e20	−	1.61160e20i	−0.0914625	−	0.0908810i
$454$	1.80596e21			1.00060
$455$		−	1.31837e19i		−	0.00717703i
$456$	−1.18573e20	+	1.19332e20i	−0.0634262	+	0.0638321i
$457$	−2.74111e21			−1.44078			−0.720389	−	0.693571i	$-0.756037\pi$
$457$	−2.74111e21			−1.44078			−0.720389	+	0.693571i	$0.756037\pi$
$458$		−	1.43594e21i		−	0.741672i
$459$	−3.39659e19	−	3.33221e19i	−0.0172402	−	0.0169134i
$460$	5.04450e18			0.00251626
$461$		−	1.29478e21i		−	0.634728i	−0.948304	−	0.317364i	$-0.897202\pi$
$461$		−	1.29478e21i		−	0.634728i	0.948304	−	0.317364i	$-0.102798\pi$
$462$	1.14949e21	+	1.14218e21i	0.553819	+	0.550297i
$463$	−1.59724e21			−0.756351			−0.378176	−	0.925734i	$-0.623448\pi$
$463$	−1.59724e21			−0.756351			−0.378176	+	0.925734i	$0.623448\pi$
$464$			7.99895e20i			0.372296i
$465$	−1.41979e18	+	1.42888e18i	−0.000649533	+	0.000653690i
$466$	1.62421e19			0.00730391
$467$		−	3.21129e21i		−	1.41953i	−0.704439	−	0.709765i	$-0.748801\pi$
$467$		−	3.21129e21i		−	1.41953i	0.704439	−	0.709765i	$-0.251199\pi$
$468$	−1.30098e19	−	2.03955e21i	−0.00565333	−	0.886272i
$469$	3.04079e21			1.29898
$470$			8.06276e18i			0.00338611i
$471$	8.64421e20	+	8.58925e20i	0.356909	+	0.354640i
$472$	−9.67377e20			−0.392699
$473$			2.22679e21i			0.888770i
$474$	−3.54383e20	+	3.56651e20i	−0.139074	+	0.139964i
$475$	6.59569e20			0.254514
$476$			3.26892e19i			0.0124036i
$477$	3.45917e21	−	2.20653e19i	1.29070	−	0.00823309i
$478$	3.19134e21			1.17098
$479$			9.37816e20i			0.338403i	0.985582	+	0.169201i	$0.0541188\pi$
$479$			9.37816e20i			0.338403i	−0.985582	+	0.169201i	$0.945881\pi$
$480$	−1.39290e18	−	1.38405e18i	−0.000494301	−	0.000491158i
$481$	−5.76827e21			−2.01319
$482$		−	1.37982e21i		−	0.473638i
$483$	−2.73776e21	+	2.75528e21i	−0.924312	+	0.930226i
$484$	2.34084e20			0.0777334
$485$			5.87955e18i			0.00192048i
$486$	−1.53117e21	+	1.58080e21i	−0.491963	+	0.507909i
$487$	2.10022e21			0.663793			0.331896	−	0.943316i	$-0.392312\pi$
$487$	2.10022e21			0.663793			0.331896	+	0.943316i	$0.392312\pi$
$488$		−	5.07617e20i		−	0.157826i
$489$	3.79039e21	+	3.76629e21i	1.15935	+	1.15197i
$490$	5.10002e17			0.000153463
$491$		−	1.84865e21i		−	0.547271i	−0.961833	−	0.273636i	$-0.911774\pi$
$491$		−	1.84865e21i		−	0.547271i	0.961833	−	0.273636i	$-0.0882262\pi$
$492$	−2.04002e21	+	2.05307e21i	−0.594174	+	0.597976i
$493$	1.25506e20			0.0359658
$494$			1.13142e21i			0.319013i
$495$	9.74204e16	+	1.52726e19i	2.70277e−5	+	0.00423712i
$496$	2.14091e20			0.0584447
$497$		−	1.89409e21i		−	0.508803i
$498$	−5.55072e20	−	5.51542e20i	−0.146728	−	0.145795i
$499$	7.18549e21			1.86918			0.934591	−	0.355723i	$-0.115765\pi$
$499$	7.18549e21			1.86918			0.934591	+	0.355723i	$0.115765\pi$
$500$			1.53978e19i			0.00394183i
$501$	7.01751e20	−	7.06242e20i	0.176800	−	0.177931i
$502$	−2.72802e21			−0.676423
$503$			1.44507e21i			0.352652i	0.984332	+	0.176326i	$0.0564212\pi$
$503$			1.44507e21i			0.352652i	−0.984332	+	0.176326i	$0.943579\pi$
$504$	1.51192e21	−	9.64420e18i	0.363149	−	0.00231644i
$505$	−6.08822e18			−0.00143933
$506$			4.17016e21i			0.970395i
$507$	−6.63371e21	−	6.59153e21i	−1.51947	−	1.50981i
$508$	1.67495e21			0.377652
$509$		−	7.91565e21i		−	1.75689i	−0.477845	−	0.878444i	$-0.658582\pi$
$509$		−	7.91565e21i		−	1.75689i	0.477845	−	0.878444i	$-0.341418\pi$
$510$	−2.17162e17	+	2.18552e17i	−4.74485e−5	+	4.77521e-5i
$511$	1.65243e20			0.0355430
$512$			2.08701e20i			0.0441942i
$513$	8.54962e20	−	8.71481e20i	0.178241	−	0.181685i
$514$	−6.58907e21			−1.35244
$515$		−	1.50654e19i		−	0.00304455i
$516$	1.47382e21	+	1.46445e21i	0.293256	+	0.291391i
$517$	−6.66528e21			−1.30585
$518$		−	4.27603e21i		−	0.824902i
$519$	−1.92943e21	+	1.94178e21i	−0.366514	+	0.368859i
$520$	−1.32065e19			−0.00247037
$521$			4.02768e21i			0.741914i	0.928650	+	0.370957i	$0.120970\pi$
$521$			4.02768e21i			0.741914i	−0.928650	+	0.370957i	$0.879030\pi$
$522$	−3.70277e19	−	5.80482e21i	−0.00671680	−	1.05299i
$523$	7.03477e21			1.25671			0.628357	−	0.777925i	$-0.283728\pi$
$523$	7.03477e21			1.25671			0.628357	+	0.777925i	$0.283728\pi$
$524$			3.52129e21i			0.619515i
$525$	−4.20505e21	−	4.17832e21i	−0.728613	−	0.723980i
$526$	1.09709e21			0.187222
$527$		−	3.35917e19i		−	0.00564607i
$528$	1.14416e21	−	1.15148e21i	0.189415	−	0.190627i
$529$	−3.86313e21			−0.629933
$530$		−	2.23989e19i		−	0.00359766i
$531$	7.02024e21	−	4.47806e19i	1.11070	−	0.00708489i
$532$	−8.38724e20			−0.130715
$533$			1.94658e22i			2.98850i
$534$	3.53595e21	+	3.51347e21i	0.534781	+	0.531381i
$535$	−3.79592e19			−0.00565570
$536$		−	3.04607e21i		−	0.447117i
$537$	−6.41079e20	+	6.45181e20i	−0.0927080	+	0.0933012i
$538$	4.69559e21			0.669009
$539$			4.21606e20i			0.0591829i
$540$	1.01724e19	+	9.97954e18i	0.00140693	+	0.00138026i
$541$	4.29480e21			0.585281			0.292641	−	0.956222i	$-0.405466\pi$
$541$	4.29480e21			0.585281			0.292641	+	0.956222i	$0.405466\pi$
$542$		−	2.54983e21i		−	0.342387i
$543$	−3.01260e21	−	2.99344e21i	−0.398605	−	0.396070i
$544$	3.27459e19			0.00426939
$545$			4.93975e19i			0.00634648i
$546$	7.16746e21	−	7.21333e21i	0.907453	−	0.913260i
$547$	−3.57218e21			−0.445692			−0.222846	−	0.974854i	$-0.571535\pi$
$547$	−3.57218e21			−0.445692			−0.222846	+	0.974854i	$0.571535\pi$
$548$		−	1.92752e21i		−	0.237003i
$549$	2.34979e19	+	3.68377e21i	0.00284742	+	0.446389i
$550$	−6.36442e21			−0.760076
$551$			3.22018e21i			0.379024i
$552$	2.76006e21	+	2.74251e21i	0.320188	+	0.318153i
$553$	−2.50671e21			−0.286618
$554$			1.11690e22i			1.25874i
$555$	2.84066e19	−	2.85884e19i	0.00315555	−	0.00317575i
$556$	−1.07603e21			−0.117822
$557$		−	9.60998e21i		−	1.03724i	−0.855004	−	0.518622i	$-0.826445\pi$
$557$		−	9.60998e21i		−	1.03724i	0.855004	−	0.518622i	$-0.173555\pi$
$558$	−1.55366e21	+	9.91043e18i	−0.165303	+	0.00105443i
$559$	1.39737e22			1.46560
$560$		−	9.79001e18i		−	0.00101223i
$561$	−1.80671e20	−	1.79522e20i	−0.0184156	−	0.0182985i
$562$	6.97957e21			0.701355
$563$		−	1.05802e22i		−	1.04816i	−0.851669	−	0.524079i	$-0.824410\pi$
$563$		−	1.05802e22i		−	1.04816i	0.851669	−	0.524079i	$-0.175590\pi$
$564$	−4.38342e21	+	4.41147e21i	−0.428135	+	0.430875i
$565$	4.04666e19			0.00389681
$566$		−	5.58641e21i		−	0.530398i
$567$	−1.09715e22	+	1.39976e20i	−1.02708	+	0.0131035i
$568$	−1.89737e21			−0.175132
$569$			9.33207e21i			0.849336i	0.905349	+	0.424668i	$0.139609\pi$
$569$			9.33207e21i			0.849336i	−0.905349	+	0.424668i	$0.860391\pi$
$570$	−5.60749e18	−	5.57183e18i	−0.000503234	−	0.000500034i
$571$	−9.20209e21			−0.814324			−0.407162	−	0.913356i	$-0.633482\pi$
$571$	−9.20209e21			−0.814324			−0.407162	+	0.913356i	$0.633482\pi$
$572$		−	1.09175e22i		−	0.952696i
$573$	−3.45186e21	+	3.47395e21i	−0.297041	+	0.298942i
$574$	−1.44300e22			−1.22453
$575$		−	1.52553e22i		−	1.27667i
$576$	−9.66092e18	−	1.51454e21i	−0.000797331	−	0.124997i
$577$	−7.92579e21			−0.645113			−0.322557	−	0.946550i	$-0.604542\pi$
$577$	−7.92579e21			−0.645113			−0.322557	+	0.946550i	$0.604542\pi$
$578$			8.80348e21i			0.706694i
$579$	1.02983e21	+	1.02328e21i	0.0815337	+	0.0810153i
$580$	−3.75875e19			−0.00293508
$581$		−	3.90131e21i		−	0.300470i
$582$	−3.19649e21	+	3.21695e21i	−0.242823	+	0.244377i
$583$	1.85166e22			1.38744
$584$		−	1.65529e20i		−	0.0122341i
$585$	9.58395e19	−	6.11339e17i	0.00698711	−	4.45692e-5i
$586$	1.71202e21			0.123120
$587$			8.82724e21i			0.626210i	0.949719	+	0.313105i	$0.101369\pi$
$587$			8.82724e21i			0.626210i	−0.949719	+	0.313105i	$0.898631\pi$
$588$	2.79043e20	+	2.77269e20i	0.0195278	+	0.0194036i
$589$	8.61878e20			0.0595009
$590$		−	4.54576e19i		−	0.00309592i
$591$	5.61283e21	−	5.64875e21i	0.377122	−	0.379536i
$592$	−4.28344e21			−0.283935
$593$		−	2.25118e22i		−	1.47222i	−0.676863	−	0.736109i	$-0.736661\pi$
$593$		−	2.25118e22i		−	1.47222i	0.676863	−	0.736109i	$-0.263339\pi$
$594$	−8.24983e21	+	8.40923e21i	−0.532296	+	0.542581i
$595$	−1.53609e18			−9.77868e−5
$596$			5.72665e20i			0.0359692i
$597$	2.14005e22	+	2.12644e22i	1.32626	+	1.31783i
$598$	2.61689e22			1.60020
$599$		−	1.26203e22i		−	0.761472i	−0.924684	−	0.380736i	$-0.875671\pi$
$599$		−	1.26203e22i		−	0.761472i	0.924684	−	0.380736i	$-0.124329\pi$
$600$	−4.18556e21	+	4.21235e21i	−0.249198	+	0.250792i
$601$	2.45052e22			1.43967			0.719834	−	0.694146i	$-0.244218\pi$
$601$	2.45052e22			1.43967			0.719834	+	0.694146i	$0.244218\pi$
$602$			1.03587e22i			0.600529i
$603$	1.41005e20	+	2.21053e22i	0.00806668	+	1.26461i
$604$	−1.14194e21			−0.0644685
$605$			1.09997e19i			0.000612828i
$606$	−3.33112e21	−	3.30994e21i	−0.183151	−	0.181987i
$607$	−3.45572e22			−1.87512			−0.937561	−	0.347820i	$-0.886922\pi$
$607$	−3.45572e22			−1.87512			−0.937561	+	0.347820i	$0.886922\pi$
$608$			8.40179e20i			0.0449928i
$609$	2.03996e22	−	2.05301e22i	1.07816	−	1.08506i
$610$	2.38532e19			0.00124425
$611$			4.18264e22i			2.15338i
$612$	−2.37637e20	+	1.51583e18i	−0.0120754	+	7.70265e-5i
$613$	−3.57279e22			−1.79194			−0.895971	−	0.444113i	$-0.853519\pi$
$613$	−3.57279e22			−1.79194			−0.895971	+	0.444113i	$0.853519\pi$
$614$		−	5.78223e21i		−	0.286252i
$615$	−9.64751e19	−	9.58617e19i	−0.00471427	−	0.00468429i
$616$	8.09315e21			0.390366
$617$		−	6.54663e21i		−	0.311700i	−0.987781	−	0.155850i	$-0.950188\pi$
$617$		−	6.54663e21i		−	0.311700i	0.987781	−	0.155850i	$-0.0498116\pi$
$618$	8.19051e21	−	8.24292e21i	0.384949	−	0.387412i
$619$	−6.20428e21			−0.287850			−0.143925	−	0.989589i	$-0.545972\pi$
$619$	−6.20428e21			−0.287850			−0.143925	+	0.989589i	$0.545972\pi$
$620$			1.00603e19i			0.000460761i
$621$	−2.01567e22	−	1.97746e22i	−0.911351	−	0.894076i
$622$	−9.13914e21			−0.407927
$623$			2.48524e22i			1.09513i
$624$	−7.22584e21	−	7.17989e21i	−0.314349	−	0.312350i
$625$	2.32820e22			0.999953
$626$		−	1.73974e22i		−	0.737718i
$627$	4.60609e21	−	4.63557e21i	0.192838	−	0.194072i
$628$	6.08611e21			0.251572
$629$			6.72087e20i			0.0274297i
$630$	4.53187e17	+	7.10460e19i	1.82622e−5	+	0.00286296i
$631$	−1.70005e22			−0.676436			−0.338218	−	0.941068i	$-0.609824\pi$
$631$	−1.70005e22			−0.676436			−0.338218	+	0.941068i	$0.609824\pi$
$632$			2.51106e21i			0.0986554i
$633$	−1.48322e22	−	1.47379e22i	−0.575410	−	0.571751i
$634$	1.95600e22			0.749299
$635$			7.87067e19i			0.00297730i
$636$	1.21775e22	−	1.22554e22i	0.454883	−	0.457794i
$637$	2.64569e21			0.0975940
$638$		−	3.10726e22i		−	1.13191i
$639$	1.37692e22	−	8.78309e19i	0.495339	−	0.00315966i
$640$	−9.80699e18			−0.000348414
$641$		−	7.96286e21i		−	0.279386i	−0.990195	−	0.139693i	$-0.955388\pi$
$641$		−	7.96286e21i		−	0.279386i	0.990195	−	0.139693i	$-0.0446116\pi$
$642$	−2.07690e22	−	2.06370e22i	−0.719675	−	0.715099i
$643$	−4.33342e22			−1.48301			−0.741503	−	0.670950i	$-0.765887\pi$
$643$	−4.33342e22			−1.48301			−0.741503	+	0.670950i	$0.765887\pi$
$644$			1.93990e22i			0.655682i
$645$	−6.88152e19	+	6.92556e19i	−0.00229724	+	0.00231194i
$646$	1.31827e20			0.00434655
$647$		−	9.44823e21i		−	0.307692i	−0.988095	−	0.153846i	$-0.950834\pi$
$647$		−	9.44823e21i		−	0.307692i	0.988095	−	0.153846i	$-0.0491660\pi$
$648$	1.40218e20	+	1.09906e22i	0.00451030	+	0.353525i
$649$	3.75786e22			1.19394
$650$			3.99384e22i			1.25338i
$651$	−5.49486e21	−	5.45993e21i	−0.170337	−	0.169254i
$652$	2.66869e22			0.817180
$653$			3.94924e22i			1.19456i	0.802032	+	0.597281i	$0.203752\pi$
$653$			3.94924e22i			1.19456i	−0.802032	+	0.597281i	$0.796248\pi$
$654$	−2.68556e22	+	2.70275e22i	−0.802441	+	0.807575i
$655$	−1.65467e20			−0.00488407
$656$			1.44550e22i			0.421491i
$657$	7.66246e18	+	1.20124e21i	0.000220722	+	0.0346025i
$658$	−3.10060e22			−0.882345
$659$		−	1.45144e22i		−	0.408054i	−0.978965	−	0.204027i	$-0.934597\pi$
$659$		−	1.45144e22i		−	0.408054i	0.978965	−	0.204027i	$-0.0654030\pi$
$660$	5.41086e19	+	5.37646e19i	0.00150285	+	0.00149329i
$661$	−2.68605e21			−0.0737061			−0.0368530	−	0.999321i	$-0.511733\pi$
$661$	−2.68605e21			−0.0737061			−0.0368530	+	0.999321i	$0.511733\pi$
$662$		−	9.24907e21i		−	0.250746i
$663$	−1.12655e21	+	1.13376e21i	−0.0301747	+	0.0303677i
$664$	−3.90808e21			−0.103423
$665$		−	3.94121e19i		−	0.00103052i
$666$	3.10849e22	−	1.98284e20i	0.803074	−	0.00512263i
$667$	7.44801e22			1.90123
$668$		−	4.97242e21i		−	0.125417i
$669$	3.31943e21	+	3.29832e21i	0.0827283	+	0.0822023i
$670$	1.43136e20			0.00352494
$671$			1.97188e22i			0.479845i
$672$	5.32246e21	−	5.35652e21i	0.127985	−	0.128804i
$673$	4.46588e22			1.06117			0.530587	−	0.847630i	$-0.321971\pi$
$673$	4.46588e22			1.06117			0.530587	+	0.847630i	$0.321971\pi$
$674$			9.50819e21i			0.223264i
$675$	3.01796e22	−	3.07627e22i	0.700298	−	0.713829i
$676$	−4.67058e22			−1.07102
$677$			1.65298e22i			0.374592i	0.982304	+	0.187296i	$0.0599723\pi$
$677$			1.65298e22i			0.374592i	−0.982304	+	0.187296i	$0.940028\pi$
$678$	2.21410e22	+	2.20002e22i	0.495860	+	0.492707i
$679$	−2.26103e22			−0.500435
$680$			1.53875e18i			3.36587e-5i
$681$	−4.61370e22	+	4.64323e22i	−0.997407	+	1.00379i
$682$	−8.31657e21			−0.177692
$683$		−	6.32799e22i		−	1.33629i	−0.744032	−	0.668144i	$-0.767089\pi$
$683$		−	6.32799e22i		−	1.33629i	0.744032	−	0.668144i	$-0.232911\pi$
$684$	−3.88925e19	−	6.09717e21i	−0.000811740	−	0.127256i
$685$	9.05751e19			0.00186846
$686$		−	3.36606e22i		−	0.686323i
$687$	3.69187e22	+	3.66840e22i	0.744034	+	0.739303i
$688$	1.03767e22			0.206705
$689$		−	1.16197e23i		−	2.28792i
$690$	−1.28872e20	+	1.29697e20i	−0.00250822	+	0.00252427i
$691$	−6.70574e22			−1.29010			−0.645049	−	0.764141i	$-0.723163\pi$
$691$	−6.70574e22			−1.29010			−0.645049	+	0.764141i	$0.723163\pi$
$692$			1.36714e22i			0.259995i
$693$	−5.87319e22	+	3.74638e20i	−1.10410	+	0.00704280i
$694$	−5.75148e22			−1.06882
$695$		−	5.05632e19i		−	0.000928872i
$696$	−2.05657e22	−	2.04349e22i	−0.373482	−	0.371107i
$697$	2.26804e21			0.0407183
$698$		−	1.42029e22i		−	0.252077i
$699$	−4.14938e20	+	4.17593e20i	−0.00728058	+	0.00732717i
$700$	−2.96064e22			−0.513572
$701$			5.60289e22i			0.960877i	0.877028	+	0.480439i	$0.159522\pi$
$701$			5.60289e22i			0.960877i	−0.877028	+	0.480439i	$0.840478\pi$
$702$	5.27702e22	+	5.17699e22i	0.894729	+	0.877769i
$703$	−1.72441e22			−0.289066
$704$		−	8.10718e21i		−	0.134366i
$705$	−2.07298e20	−	2.05980e20i	−0.00339689	−	0.00337529i
$706$	4.42982e22			0.717709
$707$		−	2.34127e22i		−	0.375057i
$708$	2.47136e22	−	2.48718e22i	0.391444	−	0.393949i
$709$	6.28170e21			0.0983801			0.0491900	−	0.998789i	$-0.484336\pi$
$709$	6.28170e21			0.0983801			0.0491900	+	0.998789i	$0.484336\pi$
$710$		−	8.91588e19i		−	0.00138069i
$711$	−1.16239e20	−	1.82227e22i	−0.00177990	−	0.279034i
$712$	2.48955e22			0.376947
$713$		−	1.99345e22i		−	0.298463i
$714$	−8.40457e20	−	8.35113e20i	−0.0124431	−	0.0123640i
$715$	5.13019e20			0.00751078
$716$			4.54251e21i			0.0657645i
$717$	−8.15292e22	+	8.20510e22i	−1.16724	+	1.17471i
$718$	3.20698e22			0.454047
$719$		−	7.38151e21i		−	0.103351i	−0.998664	−	0.0516755i	$-0.983544\pi$
$719$		−	7.38151e21i		−	0.103351i	0.998664	−	0.0516755i	$-0.0164561\pi$
$720$	7.11692e19	−	4.53972e17i	0.000985444	−	6.28593e-6i
$721$	5.79352e22			0.793342
$722$		−	4.88311e22i		−	0.661301i
$723$	3.54759e22	+	3.52503e22i	0.475146	+	0.472125i
$724$	−2.12107e22			−0.280961
$725$			1.13670e23i			1.48916i
$726$	−5.98014e21	+	6.01841e21i	−0.0774851	+	0.0779810i
$727$	1.20780e23			1.54782			0.773909	−	0.633296i	$-0.218299\pi$
$727$	1.20780e23			1.54782			0.773909	+	0.633296i	$0.218299\pi$
$728$		−	5.07867e22i		−	0.643723i
$729$	−1.52632e21	−	7.97518e22i	−0.0191349	−	0.999817i
$730$	7.77831e18			9.64500e−5
$731$		−	1.62814e21i		−	0.0199688i
$732$	1.30511e22	+	1.29681e22i	0.158328	+	0.157321i
$733$	−1.21835e23			−1.46198			−0.730989	−	0.682389i	$-0.760941\pi$
$733$	−1.21835e23			−1.46198			−0.730989	+	0.682389i	$0.760941\pi$
$734$			6.17627e22i			0.733091i
$735$	−1.30290e19	+	1.31124e19i	−0.000152973	+	0.000153952i
$736$	1.94327e22			0.225689
$737$			1.18327e23i			1.35939i
$738$	−6.69133e20	−	1.04900e23i	−0.00760434	−	1.19213i
$739$	4.92047e22			0.553161			0.276580	−	0.960991i	$-0.410799\pi$
$739$	4.92047e22			0.553161			0.276580	+	0.960991i	$0.410799\pi$
$740$		−	2.01281e20i		−	0.00223846i
$741$	−2.90894e22	−	2.89045e22i	−0.320029	−	0.317994i
$742$	8.61368e22			0.937470
$743$			1.09751e23i			1.18168i	0.806790	+	0.590838i	$0.201203\pi$
$743$			1.09751e23i			1.18168i	−0.806790	+	0.590838i	$0.798797\pi$
$744$	−5.46939e21	+	5.50439e21i	−0.0582580	+	0.0586308i
$745$	−2.69099e19			−0.000283571
$746$			7.80552e22i			0.813751i
$747$	2.83609e22	−	1.80908e20i	0.292519	−	0.00186592i
$748$	−1.27205e21			−0.0129805
$749$		−	1.45975e23i		−	1.47375i
$750$	−3.95884e20	−	3.93367e20i	−0.00395438	−	0.00392923i
$751$	−1.90969e22			−0.188731			−0.0943656	−	0.995538i	$-0.530082\pi$
$751$	−1.90969e22			−0.188731			−0.0943656	+	0.995538i	$0.530082\pi$
$752$			3.10598e22i			0.303707i
$753$	6.96929e22	−	7.01389e22i	0.674262	−	0.678577i
$754$	−1.94989e23			−1.86655
$755$		−	5.36604e19i		−	0.000508251i
$756$	−3.83771e22	+	3.91186e22i	−0.359665	+	0.366614i
$757$	8.80933e22			0.816913			0.408456	−	0.912778i	$-0.366067\pi$
$757$	8.80933e22			0.816913			0.408456	+	0.912778i	$0.366067\pi$
$758$		−	1.71294e22i		−	0.157177i
$759$	−1.07217e23	−	1.06535e23i	−0.973485	−	0.967295i
$760$	−3.94805e19			−0.000354710
$761$			3.94699e22i			0.350904i	0.984488	+	0.175452i	$0.0561387\pi$
$761$			3.94699e22i			0.350904i	−0.984488	+	0.175452i	$0.943861\pi$
$762$	−4.27899e22	+	4.30638e22i	−0.376445	+	0.378854i
$763$	−1.89962e23			−1.65375
$764$			2.44590e22i			0.210713i
$765$	−7.12299e16	−	1.11667e19i	−6.07255e−7	−	9.51992e-5i
$766$	2.95275e22			0.249113
$767$		−	2.35816e23i		−	1.96884i
$768$	−5.36581e21	−	5.33169e21i	−0.0443349	−	0.0440530i
$769$	−1.37597e23			−1.12512			−0.562561	−	0.826756i	$-0.690184\pi$
$769$	−1.37597e23			−1.12512			−0.562561	+	0.826756i	$0.690184\pi$
$770$			3.80302e20i			0.00307753i
$771$	1.68331e23	−	1.69408e23i	1.34812	−	1.35675i
$772$	7.25070e21			0.0574700
$773$		−	1.68912e21i		−	0.0132503i	−0.999978	−	0.00662514i	$-0.997891\pi$
$773$		−	1.68912e21i		−	0.0132503i	0.999978	−	0.00662514i	$-0.00210886\pi$
$774$	−7.53034e22	+	4.80344e20i	−0.584638	+	0.00372928i
$775$	3.04237e22			0.233775
$776$			2.26495e22i			0.172252i
$777$	1.09939e23	+	1.09240e23i	0.827529	+	0.822267i
$778$	1.28082e23			0.954228
$779$			5.81923e22i			0.429107i
$780$	3.37387e20	−	3.39546e20i	0.00246248	−	0.00247823i
$781$	7.37053e22			0.532464
$782$		−	3.04905e21i		−	0.0218027i
$783$	1.50191e23	+	1.47344e23i	1.06304	+	1.04289i
$784$	1.96465e21			0.0137644
$785$			2.85990e20i			0.00198332i
$786$	−9.05342e22	−	8.99585e22i	−0.621487	−	0.617536i
$787$	−1.14982e23			−0.781325			−0.390662	−	0.920534i	$-0.627754\pi$
$787$	−1.14982e23			−0.781325			−0.390662	+	0.920534i	$0.627754\pi$
$788$		−	3.97710e22i		−	0.267520i
$789$	−2.80274e22	+	2.82068e22i	−0.186624	+	0.187818i
$790$	−1.17996e20			−0.000777770
$791$			1.55617e23i			1.01542i
$792$	3.75287e20	+	5.88337e22i	0.00242417	+	0.380036i
$793$	1.23741e23			0.791276
$794$		−	1.36530e22i		−	0.0864299i
$795$	5.75888e20	+	5.72226e20i	0.00360911	+	0.00358617i
$796$	1.50674e23			0.934832
$797$			1.29946e23i			0.798172i	0.916913	+	0.399086i	$0.130673\pi$
$797$			1.29946e23i			0.798172i	−0.916913	+	0.399086i	$0.869327\pi$
$798$	2.14269e22	−	2.15640e22i	0.130298	−	0.131131i
$799$	4.87338e21			0.0293398
$800$			2.96577e22i			0.176774i
$801$	−1.80666e23	+	1.15243e21i	−1.06615	+	0.00680071i
$802$	−1.03814e23			−0.606540
$803$			6.43013e21i			0.0371959i
$804$	7.83159e22	+	7.78179e22i	0.448540	+	0.445688i
$805$	−9.11572e20			−0.00516920
$806$			5.21887e22i			0.293019i
$807$	−1.19958e23	+	1.20726e23i	−0.666872	+	0.671140i
$808$	−2.34533e22			−0.129096
$809$		−	2.22849e23i		−	1.21457i	−0.794484	−	0.607286i	$-0.792258\pi$
$809$		−	2.22849e23i		−	1.21457i	0.794484	−	0.607286i	$-0.207742\pi$
$810$	−5.16453e20	+	6.58894e18i	−0.00278709	+	3.55579e-5i
$811$	−1.26998e22			−0.0678626			−0.0339313	−	0.999424i	$-0.510803\pi$
$811$	−1.26998e22			−0.0678626			−0.0339313	+	0.999424i	$0.510803\pi$
$812$		−	1.44546e23i		−	0.764816i
$813$	6.55575e22	+	6.51407e22i	0.343477	+	0.341293i
$814$	1.66394e23			0.863263
$815$			1.25403e21i			0.00644241i
$816$	−8.36562e20	+	8.41915e20i	−0.00425576	+	0.00428299i
$817$	4.17739e22			0.210440
$818$		−	1.47769e23i		−	0.737151i
$819$	2.35095e21	+	3.68558e23i	0.0116138	+	1.82069i
$820$	−6.79250e20			−0.00332291
$821$		−	3.11342e23i		−	1.50832i	−0.656694	−	0.754158i	$-0.728045\pi$
$821$		−	3.11342e23i		−	1.50832i	0.656694	−	0.754158i	$-0.271955\pi$
$822$	4.95574e22	+	4.92423e22i	0.237758	+	0.236246i
$823$	−1.82111e23			−0.865240			−0.432620	−	0.901576i	$-0.642411\pi$
$823$	−1.82111e23			−0.865240			−0.432620	+	0.901576i	$0.642411\pi$
$824$		−	5.80357e22i		−	0.273072i
$825$	1.62592e23	−	1.63632e23i	0.757648	−	0.762496i
$826$	1.74811e23			0.806729
$827$		−	2.11001e22i		−	0.0964365i	−0.998837	−	0.0482182i	$-0.984646\pi$
$827$		−	2.11001e22i		−	0.0964365i	0.998837	−	0.0482182i	$-0.0153543\pi$
$828$	−1.41023e23	+	8.99552e20i	−0.638331	+	0.00407177i
$829$	9.46833e22			0.424460			0.212230	−	0.977220i	$-0.431927\pi$
$829$	9.46833e22			0.424460			0.212230	+	0.977220i	$0.431927\pi$
$830$		−	1.83643e20i		−	0.000815360i
$831$	−2.87160e23	−	2.85334e23i	−1.26275	−	1.25472i
$832$	−5.08748e22			−0.221572
$833$		−	3.08261e20i		−	0.00132972i
$834$	2.74893e22	−	2.76652e22i	0.117445	−	0.118197i
$835$	2.33657e20			0.000988750
$836$		−	3.26375e22i		−	0.136794i
$837$	3.94365e22	−	4.01985e22i	0.163717	−	0.166881i
$838$	−1.80856e23			−0.743671
$839$		−	8.89724e21i		−	0.0362376i	−0.999836	−	0.0181188i	$-0.994232\pi$
$839$		−	8.89724e21i		−	0.0362376i	0.999836	−	0.0181188i	$-0.00576771\pi$
$840$	2.51706e20	+	2.50106e20i	0.00101545	+	0.00100900i
$841$	−3.04719e23			−1.21767
$842$			1.61759e23i			0.640281i
$843$	−1.78307e23	+	1.79448e23i	−0.699115	+	0.703589i
$844$	−1.04429e23			−0.405585
$845$		−	2.19473e21i		−	0.00844360i
$846$	−1.43778e21	−	2.25400e23i	−0.00547935	−	0.858997i
$847$	−4.23003e22			−0.159689
$848$		−	8.62861e22i		−	0.322682i
$849$	1.43630e23	+	1.42716e23i	0.532087	+	0.528703i
$850$	4.65341e21			0.0170773
$851$			3.98842e23i			1.44999i
$852$	4.84723e22	−	4.87825e22i	0.174573	−	0.175690i
$853$	−1.10686e22			−0.0394912			−0.0197456	−	0.999805i	$-0.506286\pi$
$853$	−1.10686e22			−0.0394912			−0.0197456	+	0.999805i	$0.506286\pi$
$854$			9.17294e22i			0.324224i
$855$	2.86509e20	−	1.82758e18i	0.00100325	−	6.39952e-6i
$856$	−1.46228e23			−0.507272
$857$		−	7.48244e21i		−	0.0257156i	−0.999917	−	0.0128578i	$-0.995907\pi$
$857$		−	7.48244e21i		−	0.0257156i	0.999917	−	0.0128578i	$-0.00409288\pi$
$858$	2.80694e23	+	2.78909e23i	0.955730	+	0.949653i
$859$	5.10699e23			1.72274			0.861369	−	0.507979i	$-0.169607\pi$
$859$	5.10699e23			1.72274			0.861369	+	0.507979i	$0.169607\pi$
$860$			4.87606e20i			0.00162960i
$861$	3.68644e23	−	3.71003e23i	1.22062	−	1.22843i
$862$	−2.50607e23			−0.822121
$863$			3.74423e22i			0.121696i	0.998147	+	0.0608479i	$0.0193805\pi$
$863$			3.74423e22i			0.121696i	−0.998147	+	0.0608479i	$0.980620\pi$
$864$	3.91864e22	+	3.84436e22i	0.126190	+	0.123798i
$865$	−6.42429e20			−0.00204973
$866$			2.29698e23i			0.726131i
$867$	−2.26342e23	−	2.24903e23i	−0.708945	−	0.704437i
$868$	−3.86875e22			−0.120064
$869$		−	9.75445e22i		−	0.299947i
$870$	9.60250e20	−	9.66394e20i	0.00292570	−	0.00294442i
$871$	7.42535e23			2.24167
$872$			1.90291e23i			0.569230i
$873$	−1.04846e21	−	1.64367e23i	−0.00310769	−	0.487192i
$874$	7.82311e22			0.229767
$875$		−	2.78247e21i		−	0.00809777i
$876$	4.25584e21	+	4.22878e21i	0.0122730	+	0.0121950i
$877$	1.19013e23			0.340093			0.170046	−	0.985436i	$-0.445608\pi$
$877$	1.19013e23			0.340093			0.170046	+	0.985436i	$0.445608\pi$
$878$			1.42190e23i			0.402635i
$879$	−4.37369e22	+	4.40168e22i	−0.122726	+	0.123512i
$880$	3.80961e20			0.00105930
$881$			6.62213e23i			1.82469i	0.409417	+	0.912347i	$0.365732\pi$
$881$			6.62213e23i			1.82469i	−0.409417	+	0.912347i	$0.634268\pi$
$882$	−1.42575e22	+	9.09452e19i	−0.0389308	+	0.000248331i
$883$	−2.22463e23			−0.601967			−0.300984	−	0.953629i	$-0.597315\pi$
$883$	−2.22463e23			−0.601967			−0.300984	+	0.953629i	$0.597315\pi$
$884$			7.98243e21i			0.0214051i
$885$	1.16874e21	+	1.16131e21i	0.00310578	+	0.00308603i
$886$	−3.20128e23			−0.843052
$887$		−	6.12511e23i		−	1.59855i	−0.600969	−	0.799273i	$-0.705218\pi$
$887$		−	6.12511e23i		−	1.59855i	0.600969	−	0.799273i	$-0.294782\pi$
$888$	1.09429e23	−	1.10130e23i	0.283028	−	0.284839i
$889$	−3.02673e23			−0.775817
$890$			1.16985e21i			0.00297174i
$891$	−5.44691e21	−	4.26938e23i	−0.0137129	−	1.07484i
$892$	2.33710e22			0.0583121
$893$			1.25039e23i			0.309196i
$894$	−1.47235e22	−	1.46299e22i	−0.0360837	−	0.0358543i
$895$	−2.13455e20			−0.000518469
$896$		−	3.77135e22i		−	0.0907890i
$897$	−6.68537e23	+	6.72815e23i	−1.59509	+	1.60530i
$898$	−2.02870e22			−0.0479741
$899$			1.48536e23i			0.348140i
$900$	−1.37288e21	−	2.15226e23i	−0.00318928	−	0.499982i
$901$	−1.35386e22			−0.0311728
$902$		−	5.61518e23i		−	1.28148i
$903$	−2.66328e23	−	2.64634e23i	−0.602441	−	0.598610i
$904$	1.55887e23			0.349513
$905$		−	9.96704e20i		−	0.00221502i
$906$	2.91732e22	−	2.93598e22i	0.0642625	−	0.0646738i
$907$	−1.43848e23			−0.314085			−0.157042	−	0.987592i	$-0.550196\pi$
$907$	−1.43848e23			−0.314085			−0.157042	+	0.987592i	$0.550196\pi$
$908$			3.26914e23i			0.707534i
$909$	1.70201e23	−	1.08567e21i	0.365132	−	0.00232910i
$910$	2.38650e21			0.00507492
$911$			3.11935e23i			0.657532i	0.944411	+	0.328766i	$0.106633\pi$
$911$			3.11935e23i			0.657532i	−0.944411	+	0.328766i	$0.893367\pi$
$912$	−2.16014e22	−	2.14641e22i	−0.0451361	−	0.0448491i
$913$	1.51813e23			0.314443
$914$		−	4.96194e23i		−	1.01878i
$915$	−6.09379e20	+	6.13278e20i	−0.00124028	+	0.00124821i
$916$	2.59933e23			0.524441
$917$		−	6.36318e23i		−	1.27268i
$918$	6.03194e21	−	6.14849e21i	0.0119596	−	0.0121907i
$919$	1.01950e23			0.200384			0.100192	−	0.994968i	$-0.468054\pi$
$919$	1.01950e23			0.200384			0.100192	+	0.994968i	$0.468054\pi$
$920$			9.13152e20i			0.00177927i
$921$	1.48664e23	+	1.47719e23i	0.287163	+	0.285337i
$922$	2.34380e23			0.448821
$923$		−	4.62520e23i		−	0.878046i
$924$	−2.06756e23	+	2.08079e23i	−0.389119	+	0.391609i
$925$	−6.08704e23			−1.13572
$926$		−	2.89132e23i		−	0.534821i
$927$	2.68651e21	+	4.21164e23i	0.00492664	+	0.772349i
$928$	−1.44796e23			−0.263253
$929$			7.21030e23i			1.29965i	0.760082	+	0.649827i	$0.225159\pi$
$929$			7.21030e23i			1.29965i	−0.760082	+	0.649827i	$0.774841\pi$
$930$	−2.58655e20	−	2.57010e20i	−0.000462229	−	0.000459289i
$931$	7.90921e21			0.0140131
$932$			2.94014e21i			0.00516465i
$933$	2.33478e23	−	2.34972e23i	0.406624	−	0.409226i
$934$	5.81305e23			1.00376
$935$		−	5.97742e19i		−	0.000102334i
$936$	3.69197e23	−	2.35503e21i	0.626689	−	0.00399751i
$937$	−8.54104e23			−1.43745			−0.718727	−	0.695292i	$-0.755275\pi$
$937$	−8.54104e23			−1.43745			−0.718727	+	0.695292i	$0.755275\pi$
$938$			5.50442e23i			0.918521i
$939$	4.47297e23	+	4.44452e23i	0.740067	+	0.735361i
$940$	−1.45952e21			−0.00239434
$941$			5.41229e23i			0.880368i	0.897908	+	0.440184i	$0.145087\pi$
$941$			5.41229e23i			0.880368i	−0.897908	+	0.440184i	$0.854913\pi$
$942$	−1.55482e23	+	1.56477e23i	−0.250768	+	0.252373i
$943$	1.34594e24			2.15245
$944$		−	1.75114e23i		−	0.277680i
$945$	−1.83821e21	−	1.80336e21i	−0.00289028	−	0.00283549i
$946$	−4.03091e23			−0.628455
$947$		−	1.14023e24i		−	1.76276i	−0.472411	−	0.881378i	$-0.656616\pi$
$947$		−	1.14023e24i		−	1.76276i	0.472411	−	0.881378i	$-0.343384\pi$
$948$	−6.45607e22	−	6.41502e22i	−0.0989695	−	0.0983402i
$949$	4.03508e22			0.0613370
$950$			1.19395e23i			0.179968i
$951$	−4.99700e23	+	5.02898e23i	−0.746905	+	0.751685i
$952$	−5.91739e21			−0.00877070
$953$		−	5.58622e23i		−	0.821060i	−0.911847	−	0.410530i	$-0.865344\pi$
$953$		−	5.58622e23i		−	0.821060i	0.911847	−	0.410530i	$-0.134656\pi$
$954$	3.99425e21	+	6.26177e23i	0.00582168	+	0.912663i
$955$	−1.14934e21			−0.00166120
$956$			5.77694e23i			0.828008i
$957$	7.98893e23	+	7.93814e23i	1.13552	+	1.12830i
$958$	−1.69763e23			−0.239287
$959$			3.48314e23i			0.486880i
$960$	2.50539e20	−	2.52143e20i	0.000347301	−	0.000349524i
$961$	−6.87668e23			−0.945347
$962$		−	1.04417e24i		−	1.42354i
$963$	1.06117e24	−	6.76900e21i	1.43475	−	0.00915196i
$964$	2.49774e23			0.334912
$965$			3.40715e20i			0.000453077i
$966$	−4.98759e23	−	4.95588e23i	−0.657769	−	0.653587i
$967$	−3.89856e23			−0.509908			−0.254954	−	0.966953i	$-0.582060\pi$
$967$	−3.89856e23			−0.509908			−0.254954	+	0.966953i	$0.582060\pi$
$968$			4.23736e22i			0.0549658i
$969$	−3.36779e21	+	3.38934e21i	−0.00433266	+	0.00436039i
$970$	−1.06431e21			−0.00135799
$971$		−	1.74385e23i		−	0.220676i	−0.993894	−	0.110338i	$-0.964807\pi$
$971$		−	1.74385e23i		−	0.220676i	0.993894	−	0.110338i	$-0.0351934\pi$
$972$	−2.86155e23	−	2.77171e23i	−0.359146	−	0.347871i
$973$	1.94445e23			0.242043
$974$			3.80180e23i			0.469372i
$975$	−1.02684e24	−	1.02031e24i	−1.25737	−	1.24938i
$976$	9.18884e22			0.111600
$977$		−	8.37409e23i		−	1.00874i	−0.863486	−	0.504372i	$-0.831724\pi$
$977$		−	8.37409e23i		−	1.00874i	0.863486	−	0.504372i	$-0.168276\pi$
$978$	−6.81771e23	+	6.86134e23i	−0.814569	+	0.819782i
$979$	−9.67088e23			−1.14605
$980$			9.23202e19i			0.000108515i
$981$	−8.80873e21	−	1.38094e24i	−0.0102698	−	1.60999i
$982$	3.34641e23			0.386979
$983$			1.05513e24i			1.21026i	0.796126	+	0.605131i	$0.206879\pi$
$983$			1.05513e24i			1.21026i	−0.796126	+	0.605131i	$0.793121\pi$
$984$	−3.71646e23	−	3.69283e23i	−0.422833	−	0.420144i
$985$	1.86886e21			0.00210905
$986$			2.27191e22i			0.0254317i
$987$	7.92111e23	−	7.97180e23i	0.879526	−	0.885154i
$988$	−2.04809e23			−0.225576
$989$		−	9.66197e23i		−	1.05559i
$990$	−2.76463e21	+	1.76350e19i	−0.00299610	+	1.91114e-5i
$991$	6.82404e23			0.733588			0.366794	−	0.930302i	$-0.380455\pi$
$991$	6.82404e23			0.733588			0.366794	+	0.930302i	$0.380455\pi$
$992$			3.87546e22i			0.0413267i
$993$	2.37798e23	+	2.36286e23i	0.251544	+	0.249945i
$994$	3.42867e23			0.359778
$995$			7.08026e21i			0.00736995i
$996$	9.98398e22	−	1.00479e23i	0.103093	−	0.103753i
$997$	7.77833e23			0.796756			0.398378	−	0.917221i	$-0.369573\pi$
$997$	7.77833e23			0.796756			0.398378	+	0.917221i	$0.369573\pi$
$998$			1.30071e24i			1.32171i
$999$	−7.89029e23	+	8.04274e23i	−0.795370	+	0.810737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.17.b.a.5.4	yes	6
3.2	odd	2	inner	6.17.b.a.5.1	✓	6
4.3	odd	2		48.17.e.d.17.6		6
12.11	even	2		48.17.e.d.17.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.17.b.a.5.1	✓	6	3.2	odd	2	inner
6.17.b.a.5.4	yes	6	1.1	even	1	trivial
48.17.e.d.17.5		6	12.11	even	2
48.17.e.d.17.6		6	4.3	odd	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +O(q^{10})\)	\(q+181.019i q^{2} +(-4654.10 - 4624.51i) q^{3} -32768.0 q^{4} -1539.79i q^{5} +(837125. - 842482. i) q^{6} +5.92137e6 q^{7} -5.93164e6i q^{8} +(274580. + 4.30458e7i) q^{9} +278731. q^{10} +2.30420e8i q^{11} +(1.52506e8 + 1.51536e8i) q^{12} +1.44595e9 q^{13} +1.07188e9i q^{14} +(-7.12076e6 + 7.16633e6i) q^{15} +1.07374e9 q^{16} -1.68474e8i q^{17} +(-7.79213e9 + 4.97043e7i) q^{18} +4.32262e9 q^{19} +5.04558e7i q^{20} +(-2.75587e10 - 2.73834e10i) q^{21} -4.17105e10 q^{22} -9.99787e10i q^{23} +(-2.74309e10 + 2.76065e10i) q^{24} +1.52586e11 q^{25} +2.61744e11i q^{26} +(1.97788e11 - 2.01609e11i) q^{27} -1.94032e11 q^{28} +7.44960e11i q^{29} +(-1.29724e9 - 1.28900e9i) q^{30} +1.99388e11 q^{31} +1.94368e11i q^{32} +(1.06558e12 - 1.07240e12i) q^{33} +3.04970e10 q^{34} -9.11766e9i q^{35} +(-8.99744e9 - 1.41053e12i) q^{36} -3.98927e12 q^{37} +7.82478e11i q^{38} +(-6.72958e12 - 6.68679e12i) q^{39} -9.13347e9 q^{40} +1.34623e13i q^{41} +(4.95693e12 - 4.98865e12i) q^{42} +9.66403e12 q^{43} -7.55040e12i q^{44} +(6.62815e10 - 4.22795e8i) q^{45} +1.80981e13 q^{46} +2.89266e13i q^{47} +(-4.99730e12 - 4.96553e12i) q^{48} +1.82973e12 q^{49} +2.76209e13i q^{50} +(-7.79109e11 + 7.84094e11i) q^{51} -4.73808e13 q^{52} -8.03602e13i q^{53} +(3.64952e13 + 3.58034e13i) q^{54} +3.54798e11 q^{55} -3.51235e13i q^{56} +(-2.01179e13 - 1.99900e13i) q^{57} -1.34852e14 q^{58} -1.63088e14i q^{59} +(2.33333e11 - 2.34826e11i) q^{60} +8.55778e13 q^{61} +3.60931e13i q^{62} +(1.62589e12 + 2.54891e14i) q^{63} -3.51844e13 q^{64} -2.22645e12i q^{65} +(1.94125e14 + 1.92890e14i) q^{66} +5.13528e14 q^{67} +5.52055e12i q^{68} +(-4.62352e14 + 4.65311e14i) q^{69} +1.65047e12 q^{70} -3.19873e14i q^{71} +(2.55333e14 - 1.62871e12i) q^{72} +2.79061e13 q^{73} -7.22134e14i q^{74} +(-7.10148e14 - 7.05633e14i) q^{75} -1.41644e14 q^{76} +1.36440e15i q^{77} +(1.21044e15 - 1.21818e15i) q^{78} -4.23333e14 q^{79} -1.65333e12i q^{80} +(-1.85287e15 + 2.36391e13i) q^{81} -2.43693e15 q^{82} -6.58853e14i q^{83} +(9.03042e14 + 8.97300e14i) q^{84} -2.59414e11 q^{85} +1.74938e15i q^{86} +(3.44507e15 - 3.46712e15i) q^{87} +1.36677e15 q^{88} +4.19706e15i q^{89} +(7.65340e10 + 1.19982e13i) q^{90} +8.56199e15 q^{91} +3.27610e15i q^{92} +(-9.27971e14 - 9.22071e14i) q^{93} -5.23628e15 q^{94} -6.65591e12i q^{95} +(8.98856e14 - 9.04608e14i) q^{96} -3.81842e15 q^{97} +3.31216e14i q^{98} +(-9.91863e15 + 6.32687e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9}+O(q^{10}) \) 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9	\( 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9} + 39297024 q^{10} - 196804608 q^{12} + 1763152140 q^{13} - 8080218432 q^{15} + 6442450944 q^{16} - 12549169152 q^{18} + 60306979692 q^{19} - 155770661748 q^{21} + 94233305088 q^{22} - 5234491392 q^{24} - 75722441466 q^{25} + 330190979958 q^{27} + 5501485056 q^{28} + 987679531008 q^{30} - 2846203650132 q^{31} + 3282289396416 q^{33} - 1812957659136 q^{34} + 334749302784 q^{36} + 2483836081932 q^{37} - 8759076866580 q^{39} - 1287684882432 q^{40} - 3652917731328 q^{42} + 46155081190764 q^{43} - 46496752783488 q^{45} - 17111605395456 q^{46} + 6448893394944 q^{48} + 42155513811090 q^{49} - 3055668993792 q^{51} - 57774969323520 q^{52} + 240022278328320 q^{54} - 155561818958208 q^{55} + 27052692784332 q^{57} - 366644114104320 q^{58} + 264772597579776 q^{60} + 306036501898764 q^{61} - 801652315914324 q^{63} - 211106232532992 q^{64} + 11\!\cdots\!72 q^{66}+ \cdots - 28\!\cdots\!72 q^{99}+O(q^{100}) \) 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9 + 39297024 * q^10 - 196804608 * q^12 + 1763152140 * q^13 - 8080218432 * q^15 + 6442450944 * q^16 - 12549169152 * q^18 + 60306979692 * q^19 - 155770661748 * q^21 + 94233305088 * q^22 - 5234491392 * q^24 - 75722441466 * q^25 + 330190979958 * q^27 + 5501485056 * q^28 + 987679531008 * q^30 - 2846203650132 * q^31 + 3282289396416 * q^33 - 1812957659136 * q^34 + 334749302784 * q^36 + 2483836081932 * q^37 - 8759076866580 * q^39 - 1287684882432 * q^40 - 3652917731328 * q^42 + 46155081190764 * q^43 - 46496752783488 * q^45 - 17111605395456 * q^46 + 6448893394944 * q^48 + 42155513811090 * q^49 - 3055668993792 * q^51 - 57774969323520 * q^52 + 240022278328320 * q^54 - 155561818958208 * q^55 + 27052692784332 * q^57 - 366644114104320 * q^58 + 264772597579776 * q^60 + 306036501898764 * q^61 - 801652315914324 * q^63 - 211106232532992 * q^64 + 1157574327017472 * q^66 + 1979846570008812 * q^67 - 2345782552693632 * q^69 - 2197723307360256 * q^70 + 411211174772736 * q^72 + 3864207384753420 * q^73 - 3376263465802122 * q^75 - 1976139110547456 * q^76 + 5837442492456960 * q^78 + 1835806484101548 * q^79 - 703356001465338 * q^81 - 9913023387353088 * q^82 + 5104293044158464 * q^84 + 2872972366990848 * q^85 - 3000080900606400 * q^87 - 3087836941123584 * q^88 + 12789804912058368 * q^90 - 1824281133603240 * q^91 - 11156835457641972 * q^93 - 4579876939530240 * q^94 + 171523813933056 * q^96 + 31097493125645196 * q^97 - 28794216850745472 * q^99

Introduction

L-functions

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