LMFDB - Embedded newform 75.13.d.b.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,13,Mod(74,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not 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:	$68.5495362957$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 169 $ x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.1
Root			$2.54951 + 2.54951i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.13.d.b.74.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-91.7824 q^{2} +(-275.347 - 675.000i) q^{3} +4328.00 q^{4} +(25272.0 + 61953.1i) q^{6} -40250.0i q^{7} -21293.5 q^{8} +(-379809. + 371719. i) q^{9} +O(q^{10})$	\(q-91.7824 q^{2} +(-275.347 - 675.000i) q^{3} +4328.00 q^{4} +(25272.0 + 61953.1i) q^{6} -40250.0i q^{7} -21293.5 q^{8} +(-379809. + 371719. i) q^{9} +1.16105e6i q^{11} +(-1.19170e6 - 2.92140e6i) q^{12} +1.28405e6i q^{13} +3.69424e6i q^{14} -1.57731e7 q^{16} -1.48445e7 q^{17} +(3.48598e7 - 3.41172e7i) q^{18} -5.33436e7 q^{19} +(-2.71688e7 + 1.10827e7i) q^{21} -1.06564e8i q^{22} +1.07466e8 q^{23} +(5.86310e6 + 1.43731e7i) q^{24} -1.17853e8i q^{26} +(3.55489e8 + 1.54019e8i) q^{27} -1.74202e8i q^{28} +1.20239e8i q^{29} +6.65262e7 q^{31} +1.53491e9 q^{32} +(7.83707e8 - 3.19691e8i) q^{33} +1.36246e9 q^{34} +(-1.64381e9 + 1.60880e9i) q^{36} -2.22873e9i q^{37} +4.89600e9 q^{38} +(8.66734e8 - 3.53559e8i) q^{39} +8.21168e9i q^{41} +(2.49361e9 - 1.01720e9i) q^{42} +8.97722e9i q^{43} +5.02501e9i q^{44} -9.86353e9 q^{46} +1.07692e9 q^{47} +(4.34308e9 + 1.06469e10i) q^{48} +1.22212e10 q^{49} +(4.08739e9 + 1.00200e10i) q^{51} +5.55737e9i q^{52} +4.11442e10 q^{53} +(-3.26276e10 - 1.41363e10i) q^{54} +8.57064e8i q^{56} +(1.46880e10 + 3.60069e10i) q^{57} -1.10359e10i q^{58} -4.61074e10i q^{59} -4.06799e10 q^{61} -6.10593e9 q^{62} +(1.49617e10 + 1.52873e10i) q^{63} -7.62712e10 q^{64} +(-7.19304e10 + 2.93420e10i) q^{66} -1.21177e11i q^{67} -6.42470e10 q^{68} +(-2.95906e10 - 7.25399e10i) q^{69} -4.48565e10i q^{71} +(8.08747e9 - 7.91519e9i) q^{72} -6.09562e10i q^{73} +2.04558e11i q^{74} -2.30871e11 q^{76} +4.67321e10 q^{77} +(-7.95509e10 + 3.24505e10i) q^{78} +2.52325e11 q^{79} +(6.08022e9 - 2.82364e11i) q^{81} -7.53688e11i q^{82} -4.10810e11 q^{83} +(-1.17586e11 + 4.79660e10i) q^{84} -8.23950e11i q^{86} +(8.11616e10 - 3.31076e10i) q^{87} -2.47228e10i q^{88} +1.12519e11i q^{89} +5.16830e10 q^{91} +4.65115e11 q^{92} +(-1.83178e10 - 4.49052e10i) q^{93} -9.88427e10 q^{94} +(-4.22634e11 - 1.03607e12i) q^{96} -6.53818e11i q^{97} -1.12169e12 q^{98} +(-4.31583e11 - 4.40976e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 17312 q^{4} + 101088 q^{6} - 1519236 q^{9}+O(q^{10}) $ 4 * q + 17312 * q^4 + 101088 * q^6 - 1519236 * q^9	$ 4 q + 17312 q^{4} + 101088 q^{6} - 1519236 q^{9} - 63092480 q^{16} - 213374312 q^{19} - 108675000 q^{21} + 23452416 q^{24} + 266104808 q^{31} + 5449856256 q^{34} - 6575253408 q^{36} + 3466935000 q^{39} - 39454107264 q^{46} + 48884898804 q^{49} + 16349568768 q^{51} - 130510572192 q^{54} - 162719743672 q^{61} - 305084618752 q^{64} - 287721720000 q^{66} - 118362321792 q^{69} - 923484022336 q^{76} + 1009299990808 q^{79} + 24320865924 q^{81} - 470345400000 q^{84} + 206732050000 q^{91} - 395370802944 q^{94} - 1690534250496 q^{96} - 1726330320000 q^{99}+O(q^{100}) $ 4 * q + 17312 * q^4 + 101088 * q^6 - 1519236 * q^9 - 63092480 * q^16 - 213374312 * q^19 - 108675000 * q^21 + 23452416 * q^24 + 266104808 * q^31 + 5449856256 * q^34 - 6575253408 * q^36 + 3466935000 * q^39 - 39454107264 * q^46 + 48884898804 * q^49 + 16349568768 * q^51 - 130510572192 * q^54 - 162719743672 * q^61 - 305084618752 * q^64 - 287721720000 * q^66 - 118362321792 * q^69 - 923484022336 * q^76 + 1009299990808 * q^79 + 24320865924 * q^81 - 470345400000 * q^84 + 206732050000 * q^91 - 395370802944 * q^94 - 1690534250496 * q^96 - 1726330320000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−91.7824			−1.43410			−0.717050	−	0.697022i	$-0.754508\pi$
$2$	−91.7824			−1.43410			−0.717050	+	0.697022i	$0.754508\pi$
$3$	−275.347	−	675.000i	−0.377705	−	0.925926i
$3$	−275.347	−	675.000i	−0.377705	−	0.925926i
$4$	4328.00			1.05664
$5$		0			0
$5$		0			0
$6$	25272.0	+	61953.1i	0.541667	+	1.32787i
$7$		−	40250.0i		−	0.342119i	−0.985261	−	0.171060i	$-0.945281\pi$
$7$		−	40250.0i		−	0.342119i	0.985261	−	0.171060i	$-0.0547191\pi$
$8$	−21293.5			−0.0812283
$9$	−379809.	+	371719.i	−0.714678	+	0.699454i
$10$		0			0
$11$			1.16105e6i			0.655381i	0.944785	+	0.327690i	$0.106270\pi$
$11$			1.16105e6i			0.655381i	−0.944785	+	0.327690i	$0.893730\pi$
$12$	−1.19170e6	−	2.92140e6i	−0.399099	−	0.978371i
$13$			1.28405e6i			0.266025i	0.991114	+	0.133012i	$0.0424650\pi$
$13$			1.28405e6i			0.266025i	−0.991114	+	0.133012i	$0.957535\pi$
$14$			3.69424e6i			0.490633i
$15$		0			0
$16$	−1.57731e7			−0.940151
$17$	−1.48445e7			−0.614996			−0.307498	−	0.951549i	$-0.599492\pi$
$17$	−1.48445e7			−0.614996			−0.307498	+	0.951549i	$0.599492\pi$
$18$	3.48598e7	−	3.41172e7i	1.02492	−	1.00309i
$19$	−5.33436e7			−1.13386			−0.566931	−	0.823765i	$-0.691870\pi$
$19$	−5.33436e7			−1.13386			−0.566931	+	0.823765i	$0.691870\pi$
$20$		0			0
$21$	−2.71688e7	+	1.10827e7i	−0.316777	+	0.129220i
$22$		−	1.06564e8i		−	0.939881i
$23$	1.07466e8			0.725949			0.362974	−	0.931799i	$-0.381761\pi$
$23$	1.07466e8			0.725949			0.362974	+	0.931799i	$0.381761\pi$
$24$	5.86310e6	+	1.43731e7i	0.0306803	+	0.0752114i
$25$		0			0
$26$		−	1.17853e8i		−	0.381506i
$27$	3.55489e8	+	1.54019e8i	0.917580	+	0.397551i
$28$		−	1.74202e8i		−	0.361497i
$29$			1.20239e8i			0.202143i	0.994879	+	0.101072i	$0.0322271\pi$
$29$			1.20239e8i			0.202143i	−0.994879	+	0.101072i	$0.967773\pi$
$30$		0			0
$31$	6.65262e7			0.0749588			0.0374794	−	0.999297i	$-0.488067\pi$
$31$	6.65262e7			0.0749588			0.0374794	+	0.999297i	$0.488067\pi$
$32$	1.53491e9			1.42950
$33$	7.83707e8	−	3.19691e8i	0.606834	−	0.247541i
$34$	1.36246e9			0.881965
$35$		0			0
$36$	−1.64381e9	+	1.60880e9i	−0.755157	+	0.739071i
$37$		−	2.22873e9i		−	0.868653i	−0.900755	−	0.434327i	$-0.856986\pi$
$37$		−	2.22873e9i		−	0.868653i	0.900755	−	0.434327i	$-0.143014\pi$
$38$	4.89600e9			1.62607
$39$	8.66734e8	−	3.53559e8i	0.246319	−	0.100479i
$40$		0			0
$41$			8.21168e9i			1.72874i	0.502858	+	0.864369i	$0.332282\pi$
$41$			8.21168e9i			1.72874i	−0.502858	+	0.864369i	$0.667718\pi$
$42$	2.49361e9	−	1.01720e9i	0.454290	−	0.185315i
$43$			8.97722e9i			1.42014i	0.704131	+	0.710070i	$0.251337\pi$
$43$			8.97722e9i			1.42014i	−0.704131	+	0.710070i	$0.748663\pi$
$44$			5.02501e9i			0.692502i
$45$		0			0
$46$	−9.86353e9			−1.04108
$47$	1.07692e9			0.0999075			0.0499538	−	0.998752i	$-0.484093\pi$
$47$	1.07692e9			0.0999075			0.0499538	+	0.998752i	$0.484093\pi$
$48$	4.34308e9	+	1.06469e10i	0.355100	+	0.870510i
$49$	1.22212e10			0.882954
$50$		0			0
$51$	4.08739e9	+	1.00200e10i	0.232287	+	0.569441i
$52$			5.55737e9i			0.281092i
$53$	4.11442e10			1.85632			0.928160	−	0.372181i	$-0.121390\pi$
$53$	4.11442e10			1.85632			0.928160	+	0.372181i	$0.121390\pi$
$54$	−3.26276e10	−	1.41363e10i	−1.31590	−	0.570128i
$55$		0			0
$56$			8.57064e8i			0.0277898i
$57$	1.46880e10	+	3.60069e10i	0.428266	+	1.04987i
$58$		−	1.10359e10i		−	0.289893i
$59$		−	4.61074e10i		−	1.09310i	−0.837428	−	0.546548i	$-0.815942\pi$
$59$		−	4.61074e10i		−	1.09310i	0.837428	−	0.546548i	$-0.184058\pi$
$60$		0			0
$61$	−4.06799e10			−0.789589			−0.394795	−	0.918769i	$-0.629184\pi$
$61$	−4.06799e10			−0.789589			−0.394795	+	0.918769i	$0.629184\pi$
$62$	−6.10593e9			−0.107498
$63$	1.49617e10	+	1.52873e10i	0.239297	+	0.244505i
$64$	−7.62712e10			−1.10989
$65$		0			0
$66$	−7.19304e10	+	2.93420e10i	−0.870260	+	0.354998i
$67$		−	1.21177e11i		−	1.33959i	−0.742548	−	0.669793i	$-0.766383\pi$
$67$		−	1.21177e11i		−	1.33959i	0.742548	−	0.669793i	$-0.233617\pi$
$68$	−6.42470e10			−0.649830
$69$	−2.95906e10	−	7.25399e10i	−0.274195	−	0.672175i
$70$		0			0
$71$		−	4.48565e10i		−	0.350167i	−0.984554	−	0.175083i	$-0.943980\pi$
$71$		−	4.48565e10i		−	0.350167i	0.984554	−	0.175083i	$-0.0560195\pi$
$72$	8.08747e9	−	7.91519e9i	0.0580520	−	0.0568154i
$73$		−	6.09562e10i		−	0.402792i	−0.979510	−	0.201396i	$-0.935452\pi$
$73$		−	6.09562e10i		−	0.402792i	0.979510	−	0.201396i	$-0.0645478\pi$
$74$			2.04558e11i			1.24573i
$75$		0			0
$76$	−2.30871e11			−1.19809
$77$	4.67321e10			0.224218
$78$	−7.95509e10	+	3.24505e10i	−0.353246	+	0.144097i
$79$	2.52325e11			1.03800			0.519000	−	0.854774i	$-0.326304\pi$
$79$	2.52325e11			1.03800			0.519000	+	0.854774i	$0.326304\pi$
$80$		0			0
$81$	6.08022e9	−	2.82364e11i	0.0215283	−	0.999768i
$82$		−	7.53688e11i		−	2.47918i
$83$	−4.10810e11			−1.25653			−0.628264	−	0.778000i	$-0.716234\pi$
$83$	−4.10810e11			−1.25653			−0.628264	+	0.778000i	$0.716234\pi$
$84$	−1.17586e11	+	4.79660e10i	−0.334720	+	0.136539i
$85$		0			0
$86$		−	8.23950e11i		−	2.03662i
$87$	8.11616e10	−	3.31076e10i	0.187170	−	0.0763505i
$88$		−	2.47228e10i		−	0.0532354i
$89$			1.12519e11i			0.226404i	0.993572	+	0.113202i	$0.0361108\pi$
$89$			1.12519e11i			0.226404i	−0.993572	+	0.113202i	$0.963889\pi$
$90$		0			0
$91$	5.16830e10			0.0910122
$92$	4.65115e11			0.767067
$93$	−1.83178e10	−	4.49052e10i	−0.0283123	−	0.0694063i
$94$	−9.88427e10			−0.143277
$95$		0			0
$96$	−4.22634e11	−	1.03607e12i	−0.539929	−	1.32361i
$97$		−	6.53818e11i		−	0.784922i	−0.919769	−	0.392461i	$-0.871624\pi$
$97$		−	6.53818e11i		−	0.784922i	0.919769	−	0.392461i	$-0.128376\pi$
$98$	−1.12169e12			−1.26624
$99$	−4.31583e11	−	4.40976e11i	−0.458409	−	0.468386i
$100$		0			0
$101$			8.58642e11i			0.808880i	0.914565	+	0.404440i	$0.132533\pi$
$101$			8.58642e11i			0.808880i	−0.914565	+	0.404440i	$0.867467\pi$
$102$	−3.75150e11	−	9.19663e11i	−0.333123	−	0.816635i
$103$		−	9.95545e11i		−	0.833753i	−0.908963	−	0.416877i	$-0.863125\pi$
$103$		−	9.95545e11i		−	0.833753i	0.908963	−	0.416877i	$-0.136875\pi$
$104$		−	2.73419e10i		−	0.0216087i
$105$		0			0
$106$	−3.77631e12			−2.66215
$107$	−3.07586e11			−0.204958			−0.102479	−	0.994735i	$-0.532677\pi$
$107$	−3.07586e11			−0.204958			−0.102479	+	0.994735i	$0.532677\pi$
$108$	1.53856e12	+	6.66596e11i	0.969552	+	0.420069i
$109$	−2.71438e12			−1.61849			−0.809247	−	0.587469i	$-0.800124\pi$
$109$	−2.71438e12			−1.61849			−0.809247	+	0.587469i	$0.800124\pi$
$110$		0			0
$111$	−1.50439e12	+	6.13673e11i	−0.804309	+	0.328095i
$112$			6.34868e11i			0.321644i
$113$	−3.10604e11			−0.149189			−0.0745945	−	0.997214i	$-0.523766\pi$
$113$	−3.10604e11			−0.149189			−0.0745945	+	0.997214i	$0.523766\pi$
$114$	−1.34810e12	−	3.30480e12i	−0.614176	−	1.50562i
$115$		0			0
$116$			5.20396e11i			0.213593i
$117$	−4.77305e11	−	4.87694e11i	−0.186072	−	0.190122i
$118$			4.23184e12i			1.56761i
$119$			5.97492e11i			0.210402i
$120$		0			0
$121$	1.79040e12			0.570476
$122$	3.73370e12			1.13235
$123$	5.54289e12	−	2.26106e12i	1.60068	−	0.652953i
$124$	2.87925e11			0.0792045
$125$		0			0
$126$	−1.37322e12	−	1.40311e12i	−0.343175	−	0.350645i
$127$		−	1.77163e11i		−	0.0422232i	−0.999777	−	0.0211116i	$-0.993279\pi$
$127$		−	1.77163e11i		−	0.0422232i	0.999777	−	0.0211116i	$-0.00672053\pi$
$128$	7.13345e11			0.162196
$129$	6.05962e12	−	2.47185e12i	1.31494	−	0.536394i
$130$		0			0
$131$			4.87272e12i			0.964148i	0.876131	+	0.482074i	$0.160116\pi$
$131$			4.87272e12i			0.964148i	−0.876131	+	0.482074i	$0.839884\pi$
$132$	3.39188e12	−	1.38362e12i	0.641205	−	0.261561i
$133$			2.14708e12i			0.387916i
$134$			1.11219e13i			1.92110i
$135$		0			0
$136$	3.16092e11			0.0499551
$137$	−5.61094e10			−0.00848618			−0.00424309	−	0.999991i	$-0.501351\pi$
$137$	−5.61094e10			−0.00848618			−0.00424309	+	0.999991i	$0.501351\pi$
$138$	2.71589e12	+	6.65788e12i	0.393222	+	0.963965i
$139$	8.42728e11			0.116842			0.0584210	−	0.998292i	$-0.481393\pi$
$139$	8.42728e11			0.116842			0.0584210	+	0.998292i	$0.481393\pi$
$140$		0			0
$141$	−2.96528e11	−	7.26924e11i	−0.0377356	−	0.0925070i
$142$			4.11703e12i			0.502174i
$143$	−1.49084e12			−0.174347
$144$	5.99077e12	−	5.86316e12i	0.671905	−	0.657593i
$145$		0			0
$146$			5.59470e12i			0.577643i
$147$	−3.36508e12	−	8.24933e12i	−0.333496	−	0.817550i
$148$		−	9.64593e12i		−	0.917854i
$149$			6.73150e12i			0.615169i	0.951521	+	0.307584i	$0.0995206\pi$
$149$			6.73150e12i			0.615169i	−0.951521	+	0.307584i	$0.900479\pi$
$150$		0			0
$151$	2.52139e12			0.212705			0.106353	−	0.994328i	$-0.466083\pi$
$151$	2.52139e12			0.212705			0.106353	+	0.994328i	$0.466083\pi$
$152$	1.13587e12			0.0921017
$153$	5.63808e12	−	5.51798e12i	0.439524	−	0.430161i
$154$	−4.28918e12			−0.321551
$155$		0			0
$156$	3.75122e12	−	1.53021e12i	0.260271	−	0.106170i
$157$		−	3.10007e12i		−	0.207001i	−0.994629	−	0.103501i	$-0.966996\pi$
$157$		−	3.10007e12i		−	0.207001i	0.994629	−	0.103501i	$-0.0330044\pi$
$158$	−2.31590e13			−1.48860
$159$	−1.13289e13	−	2.77723e13i	−0.701142	−	1.71882i
$160$		0			0
$161$		−	4.32553e12i		−	0.248361i
$162$	−5.58057e11	+	2.59160e13i	−0.0308737	+	1.43377i
$163$		−	2.07431e13i		−	1.10598i	−0.833188	−	0.552990i	$-0.813487\pi$
$163$		−	2.07431e13i		−	1.10598i	0.833188	−	0.552990i	$-0.186513\pi$
$164$			3.55402e13i			1.82665i
$165$		0			0
$166$	3.77051e13			1.80199
$167$	−2.86911e13			−1.32266			−0.661331	−	0.750095i	$-0.730008\pi$
$167$	−2.86911e13			−1.32266			−0.661331	+	0.750095i	$0.730008\pi$
$168$	5.78518e11	−	2.35990e11i	0.0257313	−	0.0104963i
$169$	2.16493e13			0.929231
$170$		0			0
$171$	2.02604e13	−	1.98288e13i	0.810346	−	0.793085i
$172$			3.88534e13i			1.50058i
$173$	−4.37752e13			−1.63287			−0.816436	−	0.577436i	$-0.804053\pi$
$173$	−4.37752e13			−1.63287			−0.816436	+	0.577436i	$0.804053\pi$
$174$	−7.44921e12	+	3.03869e12i	−0.268420	+	0.109494i
$175$		0			0
$176$		−	1.83133e13i		−	0.616157i
$177$	−3.11225e13	+	1.26955e13i	−1.01213	+	0.412868i
$178$		−	1.03272e13i		−	0.324686i
$179$		−	2.86055e13i		−	0.869624i	−0.900521	−	0.434812i	$-0.856815\pi$
$179$		−	2.86055e13i		−	0.869624i	0.900521	−	0.434812i	$-0.143185\pi$
$180$		0			0
$181$	4.27135e13			1.21477			0.607384	−	0.794408i	$-0.292219\pi$
$181$	4.27135e13			1.21477			0.607384	+	0.794408i	$0.292219\pi$
$182$	−4.74359e12			−0.130520
$183$	1.12011e13	+	2.74590e13i	0.298232	+	0.731101i
$184$	−2.28834e12			−0.0589676
$185$		0			0
$186$	1.68125e12	+	4.12150e12i	0.0406027	+	0.0995355i
$187$		−	1.72352e13i		−	0.403057i
$188$	4.66093e12			0.105566
$189$	6.19928e12	−	1.43084e13i	0.136010	−	0.313922i
$190$		0			0
$191$			5.43019e13i			1.11845i	0.829017	+	0.559223i	$0.188900\pi$
$191$			5.43019e13i			1.11845i	−0.829017	+	0.559223i	$0.811100\pi$
$192$	2.10010e13	+	5.14830e13i	0.419212	+	1.02768i
$193$			6.31608e12i			0.122209i	0.998131	+	0.0611046i	$0.0194623\pi$
$193$			6.31608e12i			0.122209i	−0.998131	+	0.0611046i	$0.980538\pi$
$194$			6.00089e13i			1.12566i
$195$		0			0
$196$	5.28935e13			0.932965
$197$	−2.61737e13			−0.447784			−0.223892	−	0.974614i	$-0.571876\pi$
$197$	−2.61737e13			−0.447784			−0.223892	+	0.974614i	$0.571876\pi$
$198$	3.96117e13	+	4.04738e13i	0.657403	+	0.671712i
$199$	5.48661e13			0.883458			0.441729	−	0.897149i	$-0.354365\pi$
$199$	5.48661e13			0.883458			0.441729	+	0.897149i	$0.354365\pi$
$200$		0			0
$201$	−8.17944e13	+	3.33657e13i	−1.24036	+	0.505969i
$202$		−	7.88082e13i		−	1.16001i
$203$	4.83964e12			0.0691571
$204$	1.76902e13	+	4.33668e13i	0.245444	+	0.601694i
$205$		0			0
$206$			9.13735e13i			1.19569i
$207$	−4.08167e13	+	3.99473e13i	−0.518819	+	0.507768i
$208$		−	2.02535e13i		−	0.250103i
$209$		−	6.19344e13i		−	0.743112i
$210$		0			0
$211$	−8.99943e13			−1.01981			−0.509906	−	0.860230i	$-0.670320\pi$
$211$	−8.99943e13			−1.01981			−0.509906	+	0.860230i	$0.670320\pi$
$212$	1.78072e14			1.96146
$213$	−3.02781e13	+	1.23511e13i	−0.324229	+	0.132260i
$214$	2.82310e13			0.293930
$215$		0			0
$216$	−7.56961e12	−	3.27961e12i	−0.0745334	−	0.0322924i
$217$		−	2.67768e12i		−	0.0256449i
$218$	2.49132e14			2.32108
$219$	−4.11454e13	+	1.67841e13i	−0.372955	+	0.152137i
$220$		0			0
$221$		−	1.90611e13i		−	0.163604i
$222$	1.38076e14	−	5.63244e13i	1.15346	−	0.470520i
$223$		−	1.60273e14i		−	1.30326i	−0.758537	−	0.651630i	$-0.774086\pi$
$223$		−	1.60273e14i		−	1.30326i	0.758537	−	0.651630i	$-0.225914\pi$
$224$		−	6.17802e13i		−	0.489059i
$225$		0			0
$226$	2.85080e13			0.213952
$227$	3.92546e13			0.286903			0.143452	−	0.989657i	$-0.454180\pi$
$227$	3.92546e13			0.286903			0.143452	+	0.989657i	$0.454180\pi$
$228$	6.35697e13	+	1.55838e14i	0.452523	+	1.10934i
$229$	−1.87473e14			−1.29994			−0.649972	−	0.759958i	$-0.725220\pi$
$229$	−1.87473e14			−1.29994			−0.649972	+	0.759958i	$0.725220\pi$
$230$		0			0
$231$	−1.28676e13	−	3.15442e13i	−0.0846884	−	0.207610i
$232$		−	2.56032e12i		−	0.0164197i
$233$	1.53355e13			0.0958434			0.0479217	−	0.998851i	$-0.484740\pi$
$233$	1.53355e13			0.0958434			0.0479217	+	0.998851i	$0.484740\pi$
$234$	4.38082e13	+	4.47617e13i	0.266846	+	0.272654i
$235$		0			0
$236$		−	1.99553e14i		−	1.15501i
$237$	−6.94769e13	−	1.70319e14i	−0.392058	−	0.961112i
$238$		−	5.48392e13i		−	0.301737i
$239$		−	2.12112e14i		−	1.13809i	−0.822306	−	0.569046i	$-0.807313\pi$
$239$		−	2.12112e14i		−	1.13809i	0.822306	−	0.569046i	$-0.192687\pi$
$240$		0			0
$241$	−1.56726e14			−0.799908			−0.399954	−	0.916535i	$-0.630974\pi$
$241$	−1.56726e14			−0.799908			−0.399954	+	0.916535i	$0.630974\pi$
$242$	−1.64327e14			−0.818120
$243$	−1.92270e14	+	7.36440e13i	−0.933843	+	0.357684i
$244$	−1.76063e14			−0.834312
$245$		0			0
$246$	−5.08739e14	+	2.07526e14i	−2.29554	+	0.936400i
$247$		−	6.84958e13i		−	0.301635i
$248$	−1.41658e12			−0.00608877
$249$	1.13115e14	+	2.77296e14i	0.474597	+	1.16345i
$250$		0			0
$251$		−	2.40448e14i		−	0.961567i	−0.876839	−	0.480784i	$-0.840352\pi$
$251$		−	2.40448e14i		−	0.961567i	0.876839	−	0.480784i	$-0.159648\pi$
$252$	6.47541e13	+	6.61635e13i	0.252851	+	0.258354i
$253$			1.24774e14i			0.475773i
$254$			1.62604e13i			0.0605522i
$255$		0			0
$256$	2.46934e14			0.877286
$257$	−3.43342e14			−1.19159			−0.595796	−	0.803136i	$-0.703163\pi$
$257$	−3.43342e14			−1.19159			−0.595796	+	0.803136i	$0.703163\pi$
$258$	−5.56166e14	+	2.26872e14i	−1.88576	+	0.769242i
$259$	−8.97062e13			−0.297183
$260$		0			0
$261$	−4.46952e13	−	4.56680e13i	−0.141390	−	0.144467i
$262$		−	4.47230e14i		−	1.38268i
$263$	−2.24282e14			−0.677734			−0.338867	−	0.940834i	$-0.610044\pi$
$263$	−2.24282e14			−0.677734			−0.338867	+	0.940834i	$0.610044\pi$
$264$	−1.66879e13	+	6.80734e12i	−0.0492921	+	0.0201073i
$265$		0			0
$266$		−	1.97064e14i		−	0.556311i
$267$	7.59501e13	−	3.09817e13i	0.209634	−	0.0855141i
$268$		−	5.24453e14i		−	1.41546i
$269$		−	4.51392e14i		−	1.19135i	−0.803225	−	0.595676i	$-0.796884\pi$
$269$		−	4.51392e14i		−	1.19135i	0.803225	−	0.595676i	$-0.203116\pi$
$270$		0			0
$271$	2.30193e14			0.581135			0.290567	−	0.956854i	$-0.406156\pi$
$271$	2.30193e14			0.581135			0.290567	+	0.956854i	$0.406156\pi$
$272$	2.34144e14			0.578189
$273$	−1.42308e13	−	3.48860e13i	−0.0343758	−	0.0842705i
$274$	5.14985e12			0.0121700
$275$		0			0
$276$	−1.28068e14	−	3.13953e14i	−0.289725	−	0.710247i
$277$			1.34039e14i			0.296724i	0.988933	+	0.148362i	$0.0474000\pi$
$277$			1.34039e14i			0.296724i	−0.988933	+	0.148362i	$0.952600\pi$
$278$	−7.73476e13			−0.167563
$279$	−2.52673e13	+	2.47290e13i	−0.0535714	+	0.0524302i
$280$		0			0
$281$		−	5.62108e14i		−	1.14178i	−0.821027	−	0.570889i	$-0.806599\pi$
$281$		−	5.62108e14i		−	1.14178i	0.821027	−	0.570889i	$-0.193401\pi$
$282$	2.72160e13	+	6.67188e13i	0.0541166	+	0.132664i
$283$		−	2.79343e14i		−	0.543775i	−0.962329	−	0.271887i	$-0.912352\pi$
$283$		−	2.79343e14i		−	0.543775i	0.962329	−	0.271887i	$-0.0876479\pi$
$284$		−	1.94139e14i		−	0.370001i
$285$		0			0
$286$	1.36833e14			0.250031
$287$	3.30520e14			0.591435
$288$	−5.82973e14	+	5.70555e14i	−1.02163	+	0.999868i
$289$	−3.62263e14			−0.621780
$290$		0			0
$291$	−4.41327e14	+	1.80027e14i	−0.726779	+	0.296469i
$292$		−	2.63818e14i		−	0.425606i
$293$	9.66390e14			1.52738			0.763690	−	0.645584i	$-0.223386\pi$
$293$	9.66390e14			1.52738			0.763690	+	0.645584i	$0.223386\pi$
$294$	3.08855e14	+	7.57143e14i	0.478267	+	1.17245i
$295$		0			0
$296$			4.74574e13i			0.0705592i
$297$	−1.78824e14	+	4.12740e14i	−0.260547	+	0.601364i
$298$		−	6.17833e14i		−	0.882213i
$299$			1.37992e14i			0.193120i
$300$		0			0
$301$	3.61333e14			0.485857
$302$	−2.31419e14			−0.305040
$303$	5.79583e14	−	2.36425e14i	0.748963	−	0.305518i
$304$	8.41395e14			1.06600
$305$		0			0
$306$	−5.17476e14	+	5.06453e14i	−0.630321	+	0.616894i
$307$		−	6.67389e14i		−	0.797167i	−0.917132	−	0.398583i	$-0.869502\pi$
$307$		−	6.67389e14i		−	0.797167i	0.917132	−	0.398583i	$-0.130498\pi$
$308$	2.02257e14			0.236918
$309$	−6.71993e14	+	2.74120e14i	−0.771994	+	0.314913i
$310$		0			0
$311$			1.23263e15i			1.36230i	0.732145	+	0.681148i	$0.238519\pi$
$311$			1.23263e15i			1.36230i	−0.732145	+	0.681148i	$0.761481\pi$
$312$	−1.84558e13	+	7.52852e12i	−0.0200081	+	0.00816173i
$313$		−	9.88673e14i		−	1.05145i	−0.850656	−	0.525723i	$-0.823795\pi$
$313$		−	9.88673e14i		−	1.05145i	0.850656	−	0.525723i	$-0.176205\pi$
$314$			2.84531e14i			0.296860i
$315$		0			0
$316$	1.09206e15			1.09679
$317$	6.38686e14			0.629408			0.314704	−	0.949190i	$-0.398095\pi$
$317$	6.38686e14			0.629408			0.314704	+	0.949190i	$0.398095\pi$
$318$	1.03980e15	+	2.54901e15i	1.00551	+	2.46495i
$319$	−1.39604e14			−0.132481
$320$		0			0
$321$	8.46930e13	+	2.07621e14i	0.0774136	+	0.189776i
$322$			3.97007e14i			0.356175i
$323$	7.91859e14			0.697321
$324$	2.63152e13	−	1.22207e15i	0.0227476	−	1.05640i
$325$		0			0
$326$			1.90385e15i			1.58609i
$327$	7.47395e14	+	1.83220e15i	0.611313	+	1.49860i
$328$		−	1.74856e14i		−	0.140422i
$329$		−	4.33462e13i		−	0.0341803i
$330$		0			0
$331$	3.06589e13			0.0233124			0.0116562	−	0.999932i	$-0.496290\pi$
$331$	3.06589e13			0.0233124			0.0116562	+	0.999932i	$0.496290\pi$
$332$	−1.77798e15			−1.32770
$333$	8.28459e14	+	8.46490e14i	0.607583	+	0.620807i
$334$	2.63334e15			1.89683
$335$		0			0
$336$	4.28536e14	−	1.74809e14i	0.297818	−	0.121487i
$337$			7.69089e14i			0.525046i	0.964926	+	0.262523i	$0.0845545\pi$
$337$			7.69089e14i			0.525046i	−0.964926	+	0.262523i	$0.915445\pi$
$338$	−1.98702e15			−1.33261
$339$	8.55240e13	+	2.09658e14i	0.0563494	+	0.138138i
$340$		0			0
$341$			7.72400e13i			0.0491265i
$342$	−1.85954e15	+	1.81993e15i	−1.16212	+	1.13736i
$343$		−	1.04902e15i		−	0.644195i
$344$		−	1.91156e14i		−	0.115355i
$345$		0			0
$346$	4.01779e15			2.34170
$347$	3.01505e15			1.72710			0.863551	−	0.504261i	$-0.168235\pi$
$347$	3.01505e15			1.72710			0.863551	+	0.504261i	$0.168235\pi$
$348$	3.51268e14	−	1.43290e14i	0.197771	−	0.0806751i
$349$	−2.38056e15			−1.31742			−0.658712	−	0.752395i	$-0.728899\pi$
$349$	−2.38056e15			−1.31742			−0.658712	+	0.752395i	$0.728899\pi$
$350$		0			0
$351$	−1.97769e14	+	4.56466e14i	−0.105758	+	0.244099i
$352$			1.78210e15i			0.936866i
$353$	−4.85293e14			−0.250816			−0.125408	−	0.992105i	$-0.540024\pi$
$353$	−4.85293e14			−0.250816			−0.125408	+	0.992105i	$0.540024\pi$
$354$	2.85649e15	−	1.16523e15i	1.45149	−	0.592094i
$355$		0			0
$356$			4.86981e14i			0.239228i
$357$	4.03307e14	−	1.64518e14i	0.194817	−	0.0794699i
$358$			2.62548e15i			1.24713i
$359$			2.84198e15i			1.32756i	0.747928	+	0.663780i	$0.231049\pi$
$359$			2.84198e15i			1.32756i	−0.747928	+	0.663780i	$0.768951\pi$
$360$		0			0
$361$	6.32222e14			0.285645
$362$	−3.92034e15			−1.74210
$363$	−4.92981e14	−	1.20852e15i	−0.215472	−	0.528219i
$364$	2.23684e14			0.0961672
$365$		0			0
$366$	−1.02806e15	−	2.52025e15i	−0.427694	−	1.04847i
$367$		−	2.22655e14i		−	0.0911248i	−0.998961	−	0.0455624i	$-0.985492\pi$
$367$		−	2.22655e14i		−	0.0911248i	0.998961	−	0.0455624i	$-0.0145080\pi$
$368$	−1.69508e15			−0.682502
$369$	−3.05244e15	−	3.11887e15i	−1.20917	−	1.23549i
$370$		0			0
$371$		−	1.65605e15i		−	0.635083i
$372$	−7.92794e13	−	1.94350e14i	−0.0299159	−	0.0733375i
$373$		−	4.68043e15i		−	1.73793i	−0.494872	−	0.868966i	$-0.664785\pi$
$373$		−	4.68043e15i		−	1.73793i	0.494872	−	0.868966i	$-0.335215\pi$
$374$			1.58188e15i			0.578023i
$375$		0			0
$376$	−2.29315e13			−0.00811532
$377$	−1.54393e14			−0.0537751
$378$	−5.68985e14	+	1.31326e15i	−0.195052	+	0.450195i
$379$	−3.00840e15			−1.01508			−0.507541	−	0.861628i	$-0.669445\pi$
$379$	−3.00840e15			−1.01508			−0.507541	+	0.861628i	$0.669445\pi$
$380$		0			0
$381$	−1.19585e14	+	4.87813e13i	−0.0390955	+	0.0159479i
$382$		−	4.98396e15i		−	1.60396i
$383$	−9.08968e14			−0.287976			−0.143988	−	0.989579i	$-0.545993\pi$
$383$	−9.08968e14			−0.287976			−0.143988	+	0.989579i	$0.545993\pi$
$384$	−1.96418e14	−	4.81508e14i	−0.0612622	−	0.150181i
$385$		0			0
$386$		−	5.79705e14i		−	0.175260i
$387$	−3.33700e15	−	3.40963e15i	−0.993322	−	1.01494i
$388$		−	2.82972e15i		−	0.829380i
$389$			3.07896e15i			0.888601i	0.895878	+	0.444301i	$0.146548\pi$
$389$			3.07896e15i			0.888601i	−0.895878	+	0.444301i	$0.853452\pi$
$390$		0			0
$391$	−1.59529e15			−0.446456
$392$	−2.60233e14			−0.0717209
$393$	3.28908e15	−	1.34169e15i	0.892729	−	0.364163i
$394$	2.40229e15			0.642166
$395$		0			0
$396$	−1.86789e15	−	1.90854e15i	−0.484373	−	0.494916i
$397$			4.51643e15i			1.15359i	0.816888	+	0.576796i	$0.195697\pi$
$397$			4.51643e15i			1.15359i	−0.816888	+	0.576796i	$0.804303\pi$
$398$	−5.03574e15			−1.26697
$399$	1.44928e15	−	5.91192e14i	0.359182	−	0.146518i
$400$		0			0
$401$		−	3.94400e15i		−	0.948574i	−0.880370	−	0.474287i	$-0.842706\pi$
$401$		−	3.94400e15i		−	0.948574i	0.880370	−	0.474287i	$-0.157294\pi$
$402$	7.50728e15	−	3.06238e15i	1.77880	−	0.725609i
$403$			8.54230e13i			0.0199409i
$404$			3.71620e15i			0.854695i
$405$		0			0
$406$	−4.44193e14			−0.0991781
$407$	2.58766e15			0.569298
$408$	−8.70349e13	−	2.13362e14i	−0.0188683	−	0.0462547i
$409$	−1.87892e14			−0.0401392			−0.0200696	−	0.999799i	$-0.506389\pi$
$409$	−1.87892e14			−0.0401392			−0.0200696	+	0.999799i	$0.506389\pi$
$410$		0			0
$411$	1.54496e13	+	3.78738e13i	0.00320527	+	0.00785757i
$412$		−	4.30872e15i		−	0.880978i
$413$	−1.85582e15			−0.373969
$414$	3.74626e15	−	3.66646e15i	0.744039	−	0.728189i
$415$		0			0
$416$			1.97090e15i			0.380282i
$417$	−2.32043e14	−	5.68841e14i	−0.0441318	−	0.108187i
$418$			5.68448e15i			1.06570i
$419$		−	3.98597e15i		−	0.736630i	−0.929701	−	0.368315i	$-0.879935\pi$
$419$		−	3.98597e15i		−	0.736630i	0.929701	−	0.368315i	$-0.120065\pi$
$420$		0			0
$421$	−2.70835e15			−0.486421			−0.243211	−	0.969974i	$-0.578201\pi$
$421$	−2.70835e15			−0.486421			−0.243211	+	0.969974i	$0.578201\pi$
$422$	8.25989e15			1.46251
$423$	−4.09026e14	+	4.00313e14i	−0.0714017	+	0.0698807i
$424$	−8.76103e14			−0.150786
$425$		0			0
$426$	2.77900e15	−	1.13361e15i	0.464976	−	0.189674i
$427$			1.63737e15i			0.270134i
$428$	−1.33123e15			−0.216567
$429$	4.10499e14	+	1.00632e15i	0.0658519	+	0.161433i
$430$		0			0
$431$		−	3.41150e15i		−	0.532208i	−0.963944	−	0.266104i	$-0.914264\pi$
$431$		−	3.41150e15i		−	0.532208i	0.963944	−	0.266104i	$-0.0857365\pi$
$432$	−5.60718e15	−	2.42937e15i	−0.862664	−	0.373758i
$433$			1.09207e16i			1.65700i	0.559988	+	0.828500i	$0.310806\pi$
$433$			1.09207e16i			1.65700i	−0.559988	+	0.828500i	$0.689194\pi$
$434$			2.45764e14i			0.0367773i
$435$		0			0
$436$	−1.17478e16			−1.71017
$437$	−5.73265e15			−0.823126
$438$	3.77642e15	−	1.54048e15i	0.534855	−	0.218179i
$439$	−4.46871e15			−0.624302			−0.312151	−	0.950032i	$-0.601050\pi$
$439$	−4.46871e15			−0.624302			−0.312151	+	0.950032i	$0.601050\pi$
$440$		0			0
$441$	−4.64173e15	+	4.54286e15i	−0.631028	+	0.617586i
$442$			1.74947e15i			0.234625i
$443$	1.25251e16			1.65714			0.828569	−	0.559887i	$-0.189155\pi$
$443$	1.25251e16			1.65714			0.828569	+	0.559887i	$0.189155\pi$
$444$	−6.51100e15	+	2.65598e15i	−0.849865	+	0.346678i
$445$		0			0
$446$			1.47102e16i			1.86900i
$447$	4.54376e15	−	1.85350e15i	0.569601	−	0.232352i
$448$			3.06991e15i			0.379715i
$449$		−	9.47435e15i		−	1.15630i	−0.815930	−	0.578151i	$-0.803774\pi$
$449$		−	9.47435e15i		−	1.15630i	0.815930	−	0.578151i	$-0.196226\pi$
$450$		0			0
$451$	−9.53415e15			−1.13298
$452$	−1.34430e15			−0.157639
$453$	−6.94257e14	−	1.70194e15i	−0.0803398	−	0.196949i
$454$	−3.60288e15			−0.411448
$455$		0			0
$456$	−3.12759e14	−	7.66713e14i	−0.0347873	−	0.0852794i
$457$		−	9.26288e15i		−	1.01683i	−0.861112	−	0.508416i	$-0.830231\pi$
$457$		−	9.26288e15i		−	1.01683i	0.861112	−	0.508416i	$-0.169769\pi$
$458$	1.72067e16			1.86425
$459$	−5.27706e15	−	2.28634e15i	−0.564308	−	0.244492i
$460$		0			0
$461$		−	3.47406e15i		−	0.361936i	−0.983489	−	0.180968i	$-0.942077\pi$
$461$		−	3.47406e15i		−	0.361936i	0.983489	−	0.180968i	$-0.0579230\pi$
$462$	1.18101e15	+	2.89520e15i	0.121452	+	0.297733i
$463$		−	1.32253e16i		−	1.34252i	−0.741223	−	0.671259i	$-0.765754\pi$
$463$		−	1.32253e16i		−	1.34252i	0.741223	−	0.671259i	$-0.234246\pi$
$464$		−	1.89655e15i		−	0.190045i
$465$		0			0
$466$	−1.40753e15			−0.137449
$467$	−5.00040e14			−0.0482062			−0.0241031	−	0.999709i	$-0.507673\pi$
$467$	−5.00040e14			−0.0482062			−0.0241031	+	0.999709i	$0.507673\pi$
$468$	−2.06578e15	−	2.11074e15i	−0.196611	−	0.200890i
$469$	−4.87737e15			−0.458299
$470$		0			0
$471$	−2.09255e15	+	8.53594e14i	−0.191668	+	0.0781855i
$472$			9.81788e14i			0.0887903i
$473$	−1.04230e16			−0.930732
$474$	6.37676e15	+	1.56323e16i	0.562250	+	1.37833i
$475$		0			0
$476$			2.58594e15i			0.222319i
$477$	−1.56269e16	+	1.52940e16i	−1.32667	+	1.29841i
$478$			1.94681e16i			1.63214i
$479$		−	1.37699e16i		−	1.14003i	−0.821633	−	0.570017i	$-0.806936\pi$
$479$		−	1.37699e16i		−	1.14003i	0.821633	−	0.570017i	$-0.193064\pi$
$480$		0			0
$481$	2.86180e15			0.231083
$482$	1.43847e16			1.14715
$483$	−2.91973e15	+	1.19102e15i	−0.229964	+	0.0938073i
$484$	7.74885e15			0.602788
$485$		0			0
$486$	1.76470e16	−	6.75922e15i	1.33922	−	0.512954i
$487$		−	5.34777e15i		−	0.400866i	−0.979707	−	0.200433i	$-0.935765\pi$
$487$		−	5.34777e15i		−	0.400866i	0.979707	−	0.200433i	$-0.0642349\pi$
$488$	8.66218e14			0.0641370
$489$	−1.40016e16	+	5.71154e15i	−1.02406	+	0.417735i
$490$		0			0
$491$		−	1.52269e16i		−	1.08674i	−0.839495	−	0.543368i	$-0.817149\pi$
$491$		−	1.52269e16i		−	1.08674i	0.839495	−	0.543368i	$-0.182851\pi$
$492$	2.39896e16	−	9.78588e15i	1.69135	−	0.689937i
$493$		−	1.78490e15i		−	0.124317i
$494$			6.28671e15i			0.432575i
$495$		0			0
$496$	−1.04933e15			−0.0704726
$497$	−1.80547e15			−0.119799
$498$	−1.03820e16	−	2.54509e16i	−0.680619	−	1.66850i
$499$	2.24285e16			1.45277			0.726386	−	0.687287i	$-0.241199\pi$
$499$	2.24285e16			1.45277			0.726386	+	0.687287i	$0.241199\pi$
$500$		0			0
$501$	7.90001e15	+	1.93665e16i	0.499576	+	1.22469i
$502$			2.20689e16i			1.37898i
$503$	−2.75684e15			−0.170218			−0.0851088	−	0.996372i	$-0.527124\pi$
$503$	−2.75684e15			−0.170218			−0.0851088	+	0.996372i	$0.527124\pi$
$504$	−3.18586e14	−	3.25520e14i	−0.0194377	−	0.0198607i
$505$		0			0
$506$		−	1.14520e16i		−	0.682305i
$507$	−5.96107e15	−	1.46133e16i	−0.350975	−	0.860399i
$508$		−	7.66762e14i		−	0.0446147i
$509$		−	2.19347e16i		−	1.26132i	−0.776061	−	0.630658i	$-0.782785\pi$
$509$		−	2.19347e16i		−	1.26132i	0.776061	−	0.630658i	$-0.217215\pi$
$510$		0			0
$511$	−2.45349e15			−0.137803
$512$	−2.55861e16			−1.42031
$513$	−1.89631e16	−	8.21595e15i	−1.04041	−	0.450769i
$514$	3.15127e16			1.70886
$515$		0			0
$516$	2.62260e16	−	1.06982e16i	1.38942	−	0.566776i
$517$			1.25036e15i			0.0654775i
$518$	8.23345e15			0.426190
$519$	1.20534e16	+	2.95483e16i	0.616744	+	1.51192i
$520$		0			0
$521$		−	6.57029e15i		−	0.328517i	−0.986417	−	0.164259i	$-0.947477\pi$
$521$		−	6.57029e15i		−	0.328517i	0.986417	−	0.164259i	$-0.0525232\pi$
$522$	4.10223e15	+	4.19152e15i	0.202767	+	0.207180i
$523$		−	2.06590e15i		−	0.100948i	−0.998725	−	0.0504741i	$-0.983927\pi$
$523$		−	2.06590e15i		−	0.100948i	0.998725	−	0.0504741i	$-0.0160733\pi$
$524$			2.10891e16i			1.01876i
$525$		0			0
$526$	2.05851e16			0.971938
$527$	−9.87549e14			−0.0460994
$528$	−1.23615e16	+	5.04252e15i	−0.570516	+	0.232726i
$529$	−1.03656e16			−0.472998
$530$		0			0
$531$	1.71390e16	+	1.75120e16i	0.764571	+	0.781211i
$532$			9.29256e15i			0.409888i
$533$	−1.05442e16			−0.459887
$534$	−6.97088e15	+	2.84357e15i	−0.300635	+	0.122636i
$535$		0			0
$536$			2.58028e15i			0.108812i
$537$	−1.93087e16	+	7.87644e15i	−0.805207	+	0.328461i
$538$			4.14298e16i			1.70852i
$539$			1.41894e16i			0.578671i
$540$		0			0
$541$	−4.19288e15			−0.167235			−0.0836177	−	0.996498i	$-0.526647\pi$
$541$	−4.19288e15			−0.167235			−0.0836177	+	0.996498i	$0.526647\pi$
$542$	−2.11277e16			−0.833405
$543$	−1.17610e16	−	2.88316e16i	−0.458824	−	1.12479i
$544$	−2.27850e16			−0.879136
$545$		0			0
$546$	1.30613e15	+	3.20192e15i	0.0492983	+	0.120852i
$547$		−	6.50741e15i		−	0.242932i	−0.992596	−	0.121466i	$-0.961241\pi$
$547$		−	6.50741e15i		−	0.242932i	0.992596	−	0.121466i	$-0.0387595\pi$
$548$	−2.42841e14			−0.00896684
$549$	1.54506e16	−	1.51215e16i	0.564302	−	0.552281i
$550$		0			0
$551$		−	6.41400e15i		−	0.229203i
$552$	6.30087e14	+	1.54463e15i	0.0222724	+	0.0545996i
$553$		−	1.01561e16i		−	0.355120i
$554$		−	1.23024e16i		−	0.425531i
$555$		0			0
$556$	3.64733e15			0.123460
$557$	−7.51214e15			−0.251555			−0.125777	−	0.992058i	$-0.540143\pi$
$557$	−7.51214e15			−0.251555			−0.125777	+	0.992058i	$0.540143\pi$
$558$	2.31909e15	−	2.26969e15i	0.0768267	−	0.0751901i
$559$	−1.15272e16			−0.377792
$560$		0			0
$561$	−1.16337e16	+	4.74565e15i	−0.373200	+	0.152237i
$562$			5.15916e16i			1.63742i
$563$	2.43958e16			0.766063			0.383032	−	0.923735i	$-0.374880\pi$
$563$	2.43958e16			0.766063			0.383032	+	0.923735i	$0.374880\pi$
$564$	−1.28337e15	−	3.14613e15i	−0.0398730	−	0.0977466i
$565$		0			0
$566$			2.56388e16i			0.779827i
$567$	−1.13652e16	−	2.44729e14i	−0.342040	−	0.00736523i
$568$			9.55152e14i			0.0284435i
$569$		−	5.15472e16i		−	1.51891i	−0.650561	−	0.759454i	$-0.725466\pi$
$569$		−	5.15472e16i		−	1.51891i	0.650561	−	0.759454i	$-0.274534\pi$
$570$		0			0
$571$	4.32272e16			1.24721			0.623606	−	0.781739i	$-0.285667\pi$
$571$	4.32272e16			1.24721			0.623606	+	0.781739i	$0.285667\pi$
$572$	−6.45236e15			−0.184223
$573$	3.66538e16	−	1.49519e16i	1.03560	−	0.422443i
$574$	−3.03359e16			−0.848176
$575$		0			0
$576$	2.89685e16	−	2.83514e16i	0.793215	−	0.776318i
$577$			6.24191e16i			1.69146i	0.533609	+	0.845732i	$0.320836\pi$
$577$			6.24191e16i			1.69146i	−0.533609	+	0.845732i	$0.679164\pi$
$578$	3.32493e16			0.891694
$579$	4.26336e15	−	1.73912e15i	0.113157	−	0.0461591i
$580$		0			0
$581$			1.65351e16i			0.429882i
$582$	4.05060e16	−	1.65233e16i	1.04227	−	0.425166i
$583$			4.77703e16i			1.21660i
$584$			1.29797e15i			0.0327181i
$585$		0			0
$586$	−8.86976e16			−2.19041
$587$	6.34462e16			1.55088			0.775438	−	0.631424i	$-0.217529\pi$
$587$	6.34462e16			1.55088			0.775438	+	0.631424i	$0.217529\pi$
$588$	−1.45641e16	−	3.57031e16i	−0.352386	−	0.863857i
$589$	−3.54875e15			−0.0849930
$590$		0			0
$591$	7.20686e15	+	1.76673e16i	0.169130	+	0.414614i
$592$			3.51540e16i			0.816665i
$593$	1.86281e16			0.428392			0.214196	−	0.976791i	$-0.431287\pi$
$593$	1.86281e16			0.428392			0.214196	+	0.976791i	$0.431287\pi$
$594$	1.64129e16	−	3.78822e16i	0.373651	−	0.862416i
$595$		0			0
$596$			2.91339e16i			0.650012i
$597$	−1.51072e16	−	3.70346e16i	−0.333687	−	0.818017i
$598$		−	1.26653e16i		−	0.276954i
$599$			4.13888e16i			0.896028i	0.894026	+	0.448014i	$0.147869\pi$
$599$			4.13888e16i			0.896028i	−0.894026	+	0.448014i	$0.852131\pi$
$600$		0			0
$601$	−3.55414e16			−0.754202			−0.377101	−	0.926172i	$-0.623079\pi$
$601$	−3.55414e16			−0.754202			−0.377101	+	0.926172i	$0.623079\pi$
$602$	−3.31640e16			−0.696767
$603$	4.50437e16	+	4.60241e16i	0.936979	+	0.957373i
$604$	1.09126e16			0.224753
$605$		0			0
$606$	−5.31955e16	+	2.16996e16i	−1.07409	+	0.438143i
$607$		−	9.07689e16i		−	1.81470i	−0.420376	−	0.907350i	$-0.638102\pi$
$607$		−	9.07689e16i		−	1.81470i	0.420376	−	0.907350i	$-0.361898\pi$
$608$	−8.18777e16			−1.62086
$609$	−1.33258e15	−	3.26676e15i	−0.0261210	−	0.0640343i
$610$		0			0
$611$			1.38283e15i			0.0265779i
$612$	2.44016e16	−	2.38818e16i	0.464419	−	0.454526i
$613$			7.12225e16i			1.34231i	0.741315	+	0.671157i	$0.234202\pi$
$613$			7.12225e16i			1.34231i	−0.741315	+	0.671157i	$0.765798\pi$
$614$			6.12546e16i			1.14322i
$615$		0			0
$616$	−9.95091e14			−0.0182129
$617$	8.12893e16			1.47341			0.736703	−	0.676216i	$-0.236382\pi$
$617$	8.12893e16			1.47341			0.736703	+	0.676216i	$0.236382\pi$
$618$	6.16771e16	−	2.51594e16i	1.10712	−	0.451616i
$619$	6.76223e16			1.20212			0.601058	−	0.799206i	$-0.294746\pi$
$619$	6.76223e16			1.20212			0.601058	+	0.799206i	$0.294746\pi$
$620$		0			0
$621$	3.82032e16	+	1.65519e16i	0.666116	+	0.288602i
$622$		−	1.13134e17i		−	1.95367i
$623$	4.52888e15			0.0774573
$624$	−1.36711e16	+	5.57673e15i	−0.231577	+	0.0944653i
$625$		0			0
$626$			9.07428e16i			1.50788i
$627$	−4.18057e16	+	1.70535e16i	−0.688066	+	0.280677i
$628$		−	1.34171e16i		−	0.218726i
$629$			3.30844e16i			0.534218i
$630$		0			0
$631$	−3.37095e16			−0.534043			−0.267022	−	0.963691i	$-0.586039\pi$
$631$	−3.37095e16			−0.534043			−0.267022	+	0.963691i	$0.586039\pi$
$632$	−5.37288e15			−0.0843150
$633$	2.47797e16	+	6.07462e16i	0.385188	+	0.944271i
$634$	−5.86201e16			−0.902633
$635$		0			0
$636$	−4.90316e16	−	1.20199e17i	−0.740855	−	1.81617i
$637$			1.56927e16i			0.234888i
$638$	1.28132e16			0.189990
$639$	1.66740e16	+	1.70369e16i	0.244926	+	0.250256i
$640$		0			0
$641$		−	9.77674e16i		−	1.40944i	−0.709487	−	0.704719i	$-0.751073\pi$
$641$		−	9.77674e16i		−	1.40944i	0.709487	−	0.704719i	$-0.248927\pi$
$642$	−7.77332e15	−	1.90559e16i	−0.111019	−	0.272157i
$643$		−	1.09301e17i		−	1.54654i	−0.634079	−	0.773268i	$-0.718621\pi$
$643$		−	1.09301e17i		−	1.54654i	0.634079	−	0.773268i	$-0.281379\pi$
$644$		−	1.87209e16i		−	0.262428i
$645$		0			0
$646$	−7.26787e16			−1.00003
$647$	2.85241e16			0.388854			0.194427	−	0.980917i	$-0.437715\pi$
$647$	2.85241e16			0.388854			0.194427	+	0.980917i	$0.437715\pi$
$648$	−1.29469e14	+	6.01252e15i	−0.00174870	+	0.0812095i
$649$	5.35328e16			0.716394
$650$		0			0
$651$	−1.80743e15	+	7.37291e14i	−0.0237452	+	0.00968619i
$652$		−	8.97760e16i		−	1.16862i
$653$	−1.13063e17			−1.45828			−0.729142	−	0.684363i	$-0.760080\pi$
$653$	−1.13063e17			−1.45828			−0.729142	+	0.684363i	$0.760080\pi$
$654$	−6.85977e16	−	1.68164e17i	−0.876684	−	2.14915i
$655$		0			0
$656$		−	1.29524e17i		−	1.62527i
$657$	2.26585e16	+	2.31517e16i	0.281734	+	0.287866i
$658$			3.97842e15i			0.0490179i
$659$			1.03781e17i			1.26708i	0.773709	+	0.633541i	$0.218399\pi$
$659$			1.03781e17i			1.26708i	−0.773709	+	0.633541i	$0.781601\pi$
$660$		0			0
$661$	6.54453e16			0.784639			0.392320	−	0.919829i	$-0.371673\pi$
$661$	6.54453e16			0.784639			0.392320	+	0.919829i	$0.371673\pi$
$662$	−2.81394e15			−0.0334324
$663$	−1.28662e16	+	5.24842e15i	−0.151485	+	0.0617941i
$664$	8.74758e15			0.102066
$665$		0			0
$666$	−7.60379e16	−	7.76929e16i	−0.871334	−	0.890299i
$667$			1.29217e16i			0.146746i
$668$	−1.24175e17			−1.39758
$669$	−1.08184e17	+	4.41307e16i	−1.20672	+	0.492248i
$670$		0			0
$671$		−	4.72313e16i		−	0.517482i
$672$	−4.17016e16	+	1.70110e16i	−0.452832	+	0.184720i
$673$		−	2.69915e16i		−	0.290494i	−0.989395	−	0.145247i	$-0.953602\pi$
$673$		−	2.69915e16i		−	0.290494i	0.989395	−	0.145247i	$-0.0463976\pi$
$674$		−	7.05888e16i		−	0.752968i
$675$		0			0
$676$	9.36982e16			0.981863
$677$	7.27270e15			0.0755377			0.0377688	−	0.999287i	$-0.487975\pi$
$677$	7.27270e15			0.0755377			0.0377688	+	0.999287i	$0.487975\pi$
$678$	−7.84959e15	−	1.92429e16i	−0.0808107	−	0.198103i
$679$	−2.63162e16			−0.268537
$680$		0			0
$681$	−1.08086e16	−	2.64969e16i	−0.108365	−	0.265651i
$682$		−	7.08927e15i		−	0.0704523i
$683$	−1.54474e17			−1.52170			−0.760851	−	0.648926i	$-0.775218\pi$
$683$	−1.54474e17			−1.52170			−0.760851	+	0.648926i	$0.775218\pi$
$684$	8.76869e16	−	8.58190e16i	0.856245	−	0.838006i
$685$		0			0
$686$			9.62812e16i			0.923840i
$687$	5.16200e16	+	1.26544e17i	0.490996	+	1.20365i
$688$		−	1.41599e17i		−	1.33515i
$689$			5.28312e16i			0.493827i
$690$		0			0
$691$	−3.41467e16			−0.313675			−0.156838	−	0.987624i	$-0.550130\pi$
$691$	−3.41467e16			−0.313675			−0.156838	+	0.987624i	$0.550130\pi$
$692$	−1.89459e17			−1.72536
$693$	−1.77493e16	+	1.73712e16i	−0.160244	+	0.156830i
$694$	−2.76729e17			−2.47684
$695$		0			0
$696$	−1.72822e15	+	7.04977e14i	−0.0152035	+	0.00620182i
$697$		−	1.21898e17i		−	1.06317i
$698$	2.18493e17			1.88932
$699$	−4.22258e15	−	1.03515e16i	−0.0362005	−	0.0887439i
$700$		0			0
$701$			1.01741e17i			0.857410i	0.903445	+	0.428705i	$0.141030\pi$
$701$			1.01741e17i			0.857410i	−0.903445	+	0.428705i	$0.858970\pi$
$702$	1.81517e16	−	4.18955e16i	0.151668	−	0.350062i
$703$			1.18888e17i			0.984934i
$704$		−	8.85544e16i		−	0.727401i
$705$		0			0
$706$	4.45413e16			0.359695
$707$	3.45603e16			0.276733
$708$	−1.34698e17	+	5.49463e16i	−1.06945	+	0.436253i
$709$	8.99617e16			0.708240			0.354120	−	0.935200i	$-0.384780\pi$
$709$	8.99617e16			0.708240			0.354120	+	0.935200i	$0.384780\pi$
$710$		0			0
$711$	−9.58353e16	+	9.37939e16i	−0.741836	+	0.726034i
$712$		−	2.39592e15i		−	0.0183904i
$713$	7.14934e15			0.0544162
$714$	−3.70164e16	+	1.50998e16i	−0.279387	+	0.113968i
$715$		0			0
$716$		−	1.23805e17i		−	0.918880i
$717$	−1.43175e17	+	5.84043e16i	−1.05379	+	0.429863i
$718$		−	2.60843e17i		−	1.90385i
$719$			5.39272e16i			0.390332i	0.980770	+	0.195166i	$0.0625246\pi$
$719$			5.39272e16i			0.390332i	−0.980770	+	0.195166i	$0.937475\pi$
$720$		0			0
$721$	−4.00707e16			−0.285243
$722$	−5.80269e16			−0.409643
$723$	4.31541e16	+	1.05790e17i	0.302129	+	0.740655i
$724$	1.84864e17			1.28357
$725$		0			0
$726$	4.52470e16	+	1.10921e17i	0.309008	+	0.757518i
$727$			8.13355e16i			0.550901i	0.961315	+	0.275451i	$0.0888271\pi$
$727$			8.13355e16i			0.550901i	−0.961315	+	0.275451i	$0.911173\pi$
$728$	−1.10051e15			−0.00739276
$729$	1.02651e17	+	1.09505e17i	0.683906	+	0.729570i
$730$		0			0
$731$		−	1.33262e17i		−	0.873380i
$732$	4.84784e16	+	1.18842e17i	0.315124	+	0.772511i
$733$			9.92982e16i			0.640203i	0.947383	+	0.320101i	$0.103717\pi$
$733$			9.92982e16i			0.640203i	−0.947383	+	0.320101i	$0.896283\pi$
$734$			2.04358e16i			0.130682i
$735$		0			0
$736$	1.64952e17			1.03774
$737$	1.40692e17			0.877939
$738$	2.80160e17	+	2.86257e17i	1.73407	+	1.77182i
$739$	1.45511e17			0.893368			0.446684	−	0.894692i	$-0.352605\pi$
$739$	1.45511e17			0.893368			0.446684	+	0.894692i	$0.352605\pi$
$740$		0			0
$741$	−4.62347e16	+	1.88601e16i	−0.279292	+	0.113929i
$742$			1.51996e17i			0.910772i
$743$	7.84210e16			0.466122			0.233061	−	0.972462i	$-0.425126\pi$
$743$	7.84210e16			0.466122			0.233061	+	0.972462i	$0.425126\pi$
$744$	3.90050e14	+	9.56189e14i	0.00229976	+	0.00563775i
$745$		0			0
$746$			4.29581e17i			2.49237i
$747$	1.56029e17	−	1.52706e17i	0.898012	−	0.878883i
$748$		−	7.45938e16i		−	0.425886i
$749$			1.23804e16i			0.0701200i
$750$		0			0
$751$	3.42686e17			1.91010			0.955051	−	0.296441i	$-0.0957997\pi$
$751$	3.42686e17			1.91010			0.955051	+	0.296441i	$0.0957997\pi$
$752$	−1.69865e16			−0.0939282
$753$	−1.62303e17	+	6.62068e16i	−0.890340	+	0.363189i
$754$	1.41706e16			0.0771188
$755$		0			0
$756$	2.68305e16	−	6.19269e16i	0.143714	−	0.331703i
$757$			5.06772e16i			0.269301i	0.990893	+	0.134650i	$0.0429911\pi$
$757$			5.06772e16i			0.269301i	−0.990893	+	0.134650i	$0.957009\pi$
$758$	2.76118e17			1.45573
$759$	8.42222e16	−	3.43560e16i	0.440530	−	0.179702i
$760$		0			0
$761$		−	5.42547e16i		−	0.279338i	−0.990198	−	0.139669i	$-0.955396\pi$
$761$		−	5.42547e16i		−	0.279338i	0.990198	−	0.139669i	$-0.0446038\pi$
$762$	1.09758e16	−	4.47727e15i	0.0560669	−	0.0228709i
$763$			1.09254e17i			0.553718i
$764$			2.35019e17i			1.18180i
$765$		0			0
$766$	8.34272e16			0.412986
$767$	5.92042e16			0.290791
$768$	−6.79926e16	−	1.66681e17i	−0.331356	−	0.812302i
$769$	−4.82415e16			−0.233272			−0.116636	−	0.993175i	$-0.537211\pi$
$769$	−4.82415e16			−0.233272			−0.116636	+	0.993175i	$0.537211\pi$
$770$		0			0
$771$	9.45381e16	+	2.31756e17i	0.450071	+	1.10333i
$772$			2.73360e16i			0.129131i
$773$	3.40860e17			1.59771			0.798857	−	0.601521i	$-0.205438\pi$
$773$	3.40860e17			1.59771			0.798857	+	0.601521i	$0.205438\pi$
$774$	3.06277e17	+	3.12944e17i	1.42452	+	1.45553i
$775$		0			0
$776$			1.39221e16i			0.0637578i
$777$	2.47003e16	+	6.05517e16i	0.112248	+	0.275170i
$778$		−	2.82595e17i		−	1.27434i
$779$		−	4.38041e17i		−	1.96015i
$780$		0			0
$781$	5.20805e16			0.229493
$782$	1.46419e17			0.640262
$783$	−1.85192e16	+	4.27438e16i	−0.0803623	+	0.185483i
$784$	−1.92767e17			−0.830111
$785$		0			0
$786$	−3.01880e17	+	1.23143e17i	−1.28026	+	0.522247i
$787$			1.50476e17i			0.633312i	0.948540	+	0.316656i	$0.102560\pi$
$787$			1.50476e17i			0.633312i	−0.948540	+	0.316656i	$0.897440\pi$
$788$	−1.13280e17			−0.473146
$789$	6.17553e16	+	1.51390e17i	0.255984	+	0.627532i
$790$		0			0
$791$			1.25018e16i			0.0510404i
$792$	9.18991e15	+	9.38992e15i	0.0372357	+	0.0380462i
$793$		−	5.22351e16i		−	0.210050i
$794$		−	4.14529e17i		−	1.65437i
$795$		0			0
$796$	2.37461e17			0.933498
$797$	−2.15272e17			−0.839919			−0.419960	−	0.907543i	$-0.637956\pi$
$797$	−2.15272e17			−0.839919			−0.419960	+	0.907543i	$0.637956\pi$
$798$	−1.33018e17	+	5.42610e16i	−0.515102	+	0.210121i
$799$	−1.59864e16			−0.0614427
$800$		0			0
$801$	−4.18253e16	−	4.27356e16i	−0.158359	−	0.161806i
$802$			3.61990e17i			1.36035i
$803$	7.07730e16			0.263982
$804$	−3.54006e17	+	1.44407e17i	−1.31061	+	0.534627i
$805$		0			0
$806$		−	7.84032e15i		−	0.0285972i
$807$	−3.04689e17	+	1.24289e17i	−1.10310	+	0.449980i
$808$		−	1.82835e16i		−	0.0657039i
$809$		−	1.65579e17i		−	0.590630i	−0.955400	−	0.295315i	$-0.904575\pi$
$809$		−	1.65579e17i		−	0.590630i	0.955400	−	0.295315i	$-0.0954246\pi$
$810$		0			0
$811$	−2.91331e17			−1.02391			−0.511954	−	0.859013i	$-0.671078\pi$
$811$	−2.91331e17			−1.02391			−0.511954	+	0.859013i	$0.671078\pi$
$812$	2.09460e16			0.0730742
$813$	−6.33831e16	−	1.55381e17i	−0.219498	−	0.538088i
$814$	−2.37501e17			−0.816431
$815$		0			0
$816$	−6.44709e16	−	1.58047e17i	−0.218385	−	0.535360i
$817$		−	4.78877e17i		−	1.61024i
$818$	1.72452e16			0.0575636
$819$	−1.96297e16	+	1.92115e16i	−0.0650444	+	0.0636588i
$820$		0			0
$821$			8.76095e16i			0.286083i	0.989717	+	0.143042i	$0.0456883\pi$
$821$			8.76095e16i			0.286083i	−0.989717	+	0.143042i	$0.954312\pi$
$822$	−1.41800e15	−	3.47615e15i	−0.00459668	−	0.0112685i
$823$		−	2.84179e17i		−	0.914518i	−0.889334	−	0.457259i	$-0.848831\pi$
$823$		−	2.84179e17i		−	0.914518i	0.889334	−	0.457259i	$-0.151169\pi$
$824$			2.11986e16i			0.0677243i
$825$		0			0
$826$	1.70332e17			0.536309
$827$	−5.82930e17			−1.82215			−0.911073	−	0.412245i	$-0.864745\pi$
$827$	−5.82930e17			−1.82215			−0.911073	+	0.412245i	$0.864745\pi$
$828$	−1.76655e17	+	1.72892e17i	−0.548206	+	0.536528i
$829$	3.56314e17			1.09776			0.548878	−	0.835903i	$-0.315055\pi$
$829$	3.56314e17			1.09776			0.548878	+	0.835903i	$0.315055\pi$
$830$		0			0
$831$	9.04763e16	−	3.69072e16i	0.274744	−	0.112074i
$832$		−	9.79360e16i		−	0.295258i
$833$	−1.81418e17			−0.543013
$834$	2.12974e16	+	5.22096e16i	0.0632894	+	0.155151i
$835$		0			0
$836$		−	2.68052e17i		−	0.785202i
$837$	2.36494e16	+	1.02463e16i	0.0687807	+	0.0298000i
$838$			3.65841e17i			1.05640i
$839$			9.63202e16i			0.276150i	0.990422	+	0.138075i	$0.0440915\pi$
$839$			9.63202e16i			0.276150i	−0.990422	+	0.138075i	$0.955908\pi$
$840$		0			0
$841$	3.39357e17			0.959138
$842$	2.48579e17			0.697576
$843$	−3.79423e17	+	1.54775e17i	−1.05720	+	0.431256i
$844$	−3.89495e17			−1.07758
$845$		0			0
$846$	3.75413e16	−	3.67417e16i	0.102397	−	0.100216i
$847$		−	7.20636e16i		−	0.195171i
$848$	−6.48972e17			−1.74522
$849$	−1.88557e17	+	7.69163e16i	−0.503495	+	0.205387i
$850$		0			0
$851$		−	2.39513e17i		−	0.630598i
$852$	−1.31044e17	+	5.34556e16i	−0.342593	+	0.139751i
$853$		−	9.63630e16i		−	0.250159i	−0.992147	−	0.125080i	$-0.960081\pi$
$853$		−	9.63630e16i		−	0.250159i	0.992147	−	0.125080i	$-0.0399186\pi$
$854$		−	1.50281e17i		−	0.387399i
$855$		0			0
$856$	6.54959e15			0.0166484
$857$	1.33572e17			0.337156			0.168578	−	0.985688i	$-0.446082\pi$
$857$	1.33572e17			0.337156			0.168578	+	0.985688i	$0.446082\pi$
$858$	−3.76766e16	−	9.23623e16i	−0.0944382	−	0.231511i
$859$	1.87554e16			0.0466839			0.0233419	−	0.999728i	$-0.492569\pi$
$859$	1.87554e16			0.0466839			0.0233419	+	0.999728i	$0.492569\pi$
$860$		0			0
$861$	−9.10078e16	−	2.23101e17i	−0.223388	−	0.547625i
$862$			3.13115e17i			0.763239i
$863$	−6.24097e16			−0.151073			−0.0755365	−	0.997143i	$-0.524067\pi$
$863$	−6.24097e16			−0.151073			−0.0755365	+	0.997143i	$0.524067\pi$
$864$	5.45645e17	+	2.36406e17i	1.31168	+	0.568299i
$865$		0			0
$866$		−	1.00233e18i		−	2.37630i
$867$	9.97480e16	+	2.44527e17i	0.234849	+	0.575722i
$868$		−	1.15890e16i		−	0.0270974i
$869$			2.92961e17i			0.680286i
$870$		0			0
$871$	1.55597e17			0.356363
$872$	5.77986e16			0.131467
$873$	2.43036e17	+	2.48326e17i	0.549017	+	0.560966i
$874$	5.26156e17			1.18045
$875$		0			0
$876$	−1.78077e17	+	7.26416e16i	−0.394080	+	0.160754i
$877$		−	7.36102e17i		−	1.61786i	−0.587906	−	0.808929i	$-0.700048\pi$
$877$		−	7.36102e17i		−	1.61786i	0.587906	−	0.808929i	$-0.299952\pi$
$878$	4.10148e17			0.895311
$879$	−2.66093e17	−	6.52314e17i	−0.576899	−	1.41424i
$880$		0			0
$881$			2.10278e17i			0.449716i	0.974392	+	0.224858i	$0.0721917\pi$
$881$			2.10278e17i			0.449716i	−0.974392	+	0.224858i	$0.927808\pi$
$882$	4.26029e17	−	4.16954e17i	0.904956	−	0.885680i
$883$		−	7.08205e17i		−	1.49415i	−0.664739	−	0.747076i	$-0.731457\pi$
$883$		−	7.08205e17i		−	1.49415i	0.664739	−	0.747076i	$-0.268543\pi$
$884$		−	8.24964e16i		−	0.172871i
$885$		0			0
$886$	−1.14958e18			−2.37650
$887$	−4.03413e17			−0.828340			−0.414170	−	0.910200i	$-0.635928\pi$
$887$	−4.03413e17			−0.828340			−0.414170	+	0.910200i	$0.635928\pi$
$888$	3.20337e16	−	1.30673e16i	0.0653326	−	0.0266506i
$889$	−7.13082e15			−0.0144454
$890$		0			0
$891$	3.27838e17	+	7.05942e15i	0.655229	+	0.0141092i
$892$		−	6.93661e17i		−	1.37708i
$893$	−5.74470e16			−0.113281
$894$	−4.17037e17	+	1.70118e17i	−0.816864	+	0.333216i
$895$		0			0
$896$		−	2.87122e16i		−	0.0554904i
$897$	9.31448e16	−	3.79958e16i	0.178815	−	0.0729425i
$898$			8.69578e17i			1.65825i
$899$			7.99908e15i			0.0151524i
$900$		0			0
$901$	−6.10765e17			−1.14163
$902$	8.75067e17			1.62481
$903$	−9.94920e16	−	2.43900e17i	−0.183511	−	0.449868i
$904$	6.61385e15			0.0121184
$905$		0			0
$906$	6.37205e16	+	1.56208e17i	0.115215	+	0.282445i
$907$		−	2.67351e17i		−	0.480217i	−0.970746	−	0.240108i	$-0.922817\pi$
$907$		−	2.67351e17i		−	0.480217i	0.970746	−	0.240108i	$-0.0771830\pi$
$908$	1.69894e17			0.303154
$909$	−3.19173e17	−	3.26120e17i	−0.565774	−	0.578088i
$910$		0			0
$911$			7.27458e17i			1.27262i	0.771435	+	0.636308i	$0.219539\pi$
$911$			7.27458e17i			1.27262i	−0.771435	+	0.636308i	$0.780461\pi$
$912$	−2.31676e17	−	5.67941e17i	−0.402635	−	0.987039i
$913$		−	4.76969e17i		−	0.823504i
$914$			8.50169e17i			1.45824i
$915$		0			0
$916$	−8.11381e17			−1.37357
$917$	1.96127e17			0.329854
$918$	4.84341e17	+	2.09846e17i	0.809274	+	0.350626i
$919$	−2.21138e17			−0.367088			−0.183544	−	0.983012i	$-0.558757\pi$
$919$	−2.21138e17			−0.367088			−0.183544	+	0.983012i	$0.558757\pi$
$920$		0			0
$921$	−4.50488e17	+	1.83764e17i	−0.738117	+	0.301094i
$922$			3.18857e17i			0.519052i
$923$	5.75980e16			0.0931530
$924$	−5.56908e16	−	1.36523e17i	−0.0894852	−	0.219369i
$925$		0			0
$926$			1.21385e18i			1.92530i
$927$	3.70063e17	+	3.78117e17i	0.583172	+	0.595865i
$928$			1.84557e17i			0.288963i
$929$		−	6.84646e17i		−	1.06505i	−0.846413	−	0.532527i	$-0.821242\pi$
$929$		−	6.84646e17i		−	1.06505i	0.846413	−	0.532527i	$-0.178758\pi$
$930$		0			0
$931$	−6.51924e17			−1.00115
$932$	6.63720e16			0.101272
$933$	8.32028e17	−	3.39402e17i	1.26139	−	0.514546i
$934$	4.58948e16			0.0691325
$935$		0			0
$936$	1.01635e16	+	1.03847e16i	0.0151143	+	0.0154433i
$937$		−	3.96145e17i		−	0.585351i	−0.956212	−	0.292675i	$-0.905454\pi$
$937$		−	3.96145e17i		−	0.585351i	0.956212	−	0.292675i	$-0.0945455\pi$
$938$	4.47656e17			0.657246
$939$	−6.67354e17	+	2.72228e17i	−0.973561	+	0.397136i
$940$		0			0
$941$		−	6.49777e17i		−	0.935893i	−0.883757	−	0.467947i	$-0.844994\pi$
$941$		−	6.49777e17i		−	0.935893i	0.883757	−	0.467947i	$-0.155006\pi$
$942$	1.92059e17	−	7.83449e16i	0.274871	−	0.112126i
$943$			8.82481e17i			1.25498i
$944$			7.27257e17i			1.02768i
$945$		0			0
$946$	9.56644e17			1.33476
$947$	8.67523e16			0.120277			0.0601383	−	0.998190i	$-0.480846\pi$
$947$	8.67523e16			0.120277			0.0601383	+	0.998190i	$0.480846\pi$
$948$	−3.00696e17	−	7.37142e17i	−0.414265	−	1.01555i
$949$	7.82708e16			0.107153
$950$		0			0
$951$	−1.75860e17	−	4.31113e17i	−0.237730	−	0.582785i
$952$		−	1.27227e16i		−	0.0170906i
$953$	6.58329e16			0.0878791			0.0439396	−	0.999034i	$-0.486009\pi$
$953$	6.58329e16			0.0878791			0.0439396	+	0.999034i	$0.486009\pi$
$954$	1.43428e18	−	1.40372e18i	1.90258	−	1.86205i
$955$		0			0
$956$		−	9.18019e17i		−	1.20255i
$957$	3.84395e16	+	9.42325e16i	0.0500386	+	0.122667i
$958$			1.26383e18i			1.63492i
$959$			2.25840e15i			0.00290329i
$960$		0			0
$961$	−7.83237e17			−0.994381
$962$	−2.62662e17			−0.331396
$963$	1.16824e17	−	1.14336e17i	0.146479	−	0.143359i
$964$	−6.78312e17			−0.845215
$965$		0			0
$966$	2.67980e17	−	1.09315e17i	0.329791	−	0.134529i
$967$			1.08340e18i			1.32505i	0.749041	+	0.662523i	$0.230514\pi$
$967$			1.08340e18i			1.32505i	−0.749041	+	0.662523i	$0.769486\pi$
$968$	−3.81239e16			−0.0463388
$969$	−2.18036e17	−	5.34505e17i	−0.263382	−	0.645668i
$970$		0			0
$971$			1.58566e18i			1.89189i	0.324334	+	0.945943i	$0.394860\pi$
$971$			1.58566e18i			1.89189i	−0.324334	+	0.945943i	$0.605140\pi$
$972$	−8.32144e17	+	3.18731e17i	−0.986736	+	0.377943i
$973$		−	3.39198e16i		−	0.0399739i
$974$			4.90831e17i			0.574882i
$975$		0			0
$976$	6.41650e17			0.742333
$977$	5.67996e17			0.653097			0.326549	−	0.945180i	$-0.394114\pi$
$977$	5.67996e17			0.653097			0.326549	+	0.945180i	$0.394114\pi$
$978$	1.28510e18	−	5.24219e17i	1.46860	−	0.599073i
$979$	−1.30640e17			−0.148381
$980$		0			0
$981$	1.03094e18	−	1.00898e18i	1.15670	−	1.13206i
$982$			1.39756e18i			1.55849i
$983$	−1.16261e17			−0.128858			−0.0644292	−	0.997922i	$-0.520523\pi$
$983$	−1.16261e17			−0.128858			−0.0644292	+	0.997922i	$0.520523\pi$
$984$	−1.18027e17	+	4.81460e16i	−0.130021	+	0.0530383i
$985$		0			0
$986$			1.63822e17i			0.178283i
$987$	−2.92587e16	+	1.19353e16i	−0.0316484	+	0.0129101i
$988$		−	2.96450e17i		−	0.318720i
$989$			9.64750e17i			1.03095i
$990$		0			0
$991$	9.94251e17			1.04967			0.524836	−	0.851203i	$-0.324126\pi$
$991$	9.94251e17			1.04967			0.524836	+	0.851203i	$0.324126\pi$
$992$	1.02112e17			0.107153
$993$	−8.44182e15	−	2.06947e16i	−0.00880523	−	0.0215856i
$994$	1.65711e17			0.171803
$995$		0			0
$996$	4.89563e17	+	1.20014e18i	0.501478	+	1.22935i
$997$			4.06872e17i			0.414273i	0.978312	+	0.207137i	$0.0664144\pi$
$997$			4.06872e17i			0.414273i	−0.978312	+	0.207137i	$0.933586\pi$
$998$	−2.05854e18			−2.08342
$999$	3.43267e17	−	7.92288e17i	0.345334	−	0.797059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.13.d.b.74.1		4
3.2	odd	2	inner	75.13.d.b.74.3		4
5.2	odd	4		3.13.b.b.2.1	✓	2
5.3	odd	4		75.13.c.c.26.2		2
5.4	even	2	inner	75.13.d.b.74.4		4
15.2	even	4		3.13.b.b.2.2	yes	2
15.8	even	4		75.13.c.c.26.1		2
15.14	odd	2	inner	75.13.d.b.74.2		4
20.7	even	4		48.13.e.b.17.1		2
40.27	even	4		192.13.e.c.65.2		2
40.37	odd	4		192.13.e.d.65.1		2
45.2	even	12		81.13.d.c.53.2		4
45.7	odd	12		81.13.d.c.53.1		4
45.22	odd	12		81.13.d.c.26.2		4
45.32	even	12		81.13.d.c.26.1		4
60.47	odd	4		48.13.e.b.17.2		2
120.77	even	4		192.13.e.d.65.2		2
120.107	odd	4		192.13.e.c.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.13.b.b.2.1	✓	2	5.2	odd	4
3.13.b.b.2.2	yes	2	15.2	even	4
48.13.e.b.17.1		2	20.7	even	4
48.13.e.b.17.2		2	60.47	odd	4
75.13.c.c.26.1		2	15.8	even	4
75.13.c.c.26.2		2	5.3	odd	4
75.13.d.b.74.1		4	1.1	even	1	trivial
75.13.d.b.74.2		4	15.14	odd	2	inner
75.13.d.b.74.3		4	3.2	odd	2	inner
75.13.d.b.74.4		4	5.4	even	2	inner
81.13.d.c.26.1		4	45.32	even	12
81.13.d.c.26.2		4	45.22	odd	12
81.13.d.c.53.1		4	45.7	odd	12
81.13.d.c.53.2		4	45.2	even	12
192.13.e.c.65.1		2	120.107	odd	4
192.13.e.c.65.2		2	40.27	even	4
192.13.e.d.65.1		2	40.37	odd	4
192.13.e.d.65.2		2	120.77	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	75.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-91.7824 q^{2} +(-275.347 - 675.000i) q^{3} +4328.00 q^{4} +(25272.0 + 61953.1i) q^{6} -40250.0i q^{7} -21293.5 q^{8} +(-379809. + 371719. i) q^{9} +O(q^{10})\)	\(q-91.7824 q^{2} +(-275.347 - 675.000i) q^{3} +4328.00 q^{4} +(25272.0 + 61953.1i) q^{6} -40250.0i q^{7} -21293.5 q^{8} +(-379809. + 371719. i) q^{9} +1.16105e6i q^{11} +(-1.19170e6 - 2.92140e6i) q^{12} +1.28405e6i q^{13} +3.69424e6i q^{14} -1.57731e7 q^{16} -1.48445e7 q^{17} +(3.48598e7 - 3.41172e7i) q^{18} -5.33436e7 q^{19} +(-2.71688e7 + 1.10827e7i) q^{21} -1.06564e8i q^{22} +1.07466e8 q^{23} +(5.86310e6 + 1.43731e7i) q^{24} -1.17853e8i q^{26} +(3.55489e8 + 1.54019e8i) q^{27} -1.74202e8i q^{28} +1.20239e8i q^{29} +6.65262e7 q^{31} +1.53491e9 q^{32} +(7.83707e8 - 3.19691e8i) q^{33} +1.36246e9 q^{34} +(-1.64381e9 + 1.60880e9i) q^{36} -2.22873e9i q^{37} +4.89600e9 q^{38} +(8.66734e8 - 3.53559e8i) q^{39} +8.21168e9i q^{41} +(2.49361e9 - 1.01720e9i) q^{42} +8.97722e9i q^{43} +5.02501e9i q^{44} -9.86353e9 q^{46} +1.07692e9 q^{47} +(4.34308e9 + 1.06469e10i) q^{48} +1.22212e10 q^{49} +(4.08739e9 + 1.00200e10i) q^{51} +5.55737e9i q^{52} +4.11442e10 q^{53} +(-3.26276e10 - 1.41363e10i) q^{54} +8.57064e8i q^{56} +(1.46880e10 + 3.60069e10i) q^{57} -1.10359e10i q^{58} -4.61074e10i q^{59} -4.06799e10 q^{61} -6.10593e9 q^{62} +(1.49617e10 + 1.52873e10i) q^{63} -7.62712e10 q^{64} +(-7.19304e10 + 2.93420e10i) q^{66} -1.21177e11i q^{67} -6.42470e10 q^{68} +(-2.95906e10 - 7.25399e10i) q^{69} -4.48565e10i q^{71} +(8.08747e9 - 7.91519e9i) q^{72} -6.09562e10i q^{73} +2.04558e11i q^{74} -2.30871e11 q^{76} +4.67321e10 q^{77} +(-7.95509e10 + 3.24505e10i) q^{78} +2.52325e11 q^{79} +(6.08022e9 - 2.82364e11i) q^{81} -7.53688e11i q^{82} -4.10810e11 q^{83} +(-1.17586e11 + 4.79660e10i) q^{84} -8.23950e11i q^{86} +(8.11616e10 - 3.31076e10i) q^{87} -2.47228e10i q^{88} +1.12519e11i q^{89} +5.16830e10 q^{91} +4.65115e11 q^{92} +(-1.83178e10 - 4.49052e10i) q^{93} -9.88427e10 q^{94} +(-4.22634e11 - 1.03607e12i) q^{96} -6.53818e11i q^{97} -1.12169e12 q^{98} +(-4.31583e11 - 4.40976e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 17312 q^{4} + 101088 q^{6} - 1519236 q^{9}+O(q^{10}) \) 4 * q + 17312 * q^4 + 101088 * q^6 - 1519236 * q^9	\( 4 q + 17312 q^{4} + 101088 q^{6} - 1519236 q^{9} - 63092480 q^{16} - 213374312 q^{19} - 108675000 q^{21} + 23452416 q^{24} + 266104808 q^{31} + 5449856256 q^{34} - 6575253408 q^{36} + 3466935000 q^{39} - 39454107264 q^{46} + 48884898804 q^{49} + 16349568768 q^{51} - 130510572192 q^{54} - 162719743672 q^{61} - 305084618752 q^{64} - 287721720000 q^{66} - 118362321792 q^{69} - 923484022336 q^{76} + 1009299990808 q^{79} + 24320865924 q^{81} - 470345400000 q^{84} + 206732050000 q^{91} - 395370802944 q^{94} - 1690534250496 q^{96} - 1726330320000 q^{99}+O(q^{100}) \) 4 * q + 17312 * q^4 + 101088 * q^6 - 1519236 * q^9 - 63092480 * q^16 - 213374312 * q^19 - 108675000 * q^21 + 23452416 * q^24 + 266104808 * q^31 + 5449856256 * q^34 - 6575253408 * q^36 + 3466935000 * q^39 - 39454107264 * q^46 + 48884898804 * q^49 + 16349568768 * q^51 - 130510572192 * q^54 - 162719743672 * q^61 - 305084618752 * q^64 - 287721720000 * q^66 - 118362321792 * q^69 - 923484022336 * q^76 + 1009299990808 * q^79 + 24320865924 * q^81 - 470345400000 * q^84 + 206732050000 * q^91 - 395370802944 * q^94 - 1690534250496 * q^96 - 1726330320000 * q^99

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