LMFDB - Embedded newform 3.11.b.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,11,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	3.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:	$1.90607175802$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-5}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 5 $ x^2 + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.1
Root			$-2.23607i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.11.b.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-26.8328i q^{2} +(-27.0000 - 241.495i) q^{3} +304.000 q^{4} +2844.28i q^{5} +(-6480.00 + 724.486i) q^{6} +17234.0 q^{7} -35634.0i q^{8} +(-57591.0 + 13040.7i) q^{9} +O(q^{10})$	\(q-26.8328i q^{2} +(-27.0000 - 241.495i) q^{3} +304.000 q^{4} +2844.28i q^{5} +(-6480.00 + 724.486i) q^{6} +17234.0 q^{7} -35634.0i q^{8} +(-57591.0 + 13040.7i) q^{9} +76320.0 q^{10} +186810. i q^{11} +(-8208.00 - 73414.6i) q^{12} -169654. q^{13} -462437. i q^{14} +(686880. - 76795.5i) q^{15} -644864. q^{16} +343245. i q^{17} +(349920. + 1.54533e6i) q^{18} -949462. q^{19} +864661. i q^{20} +(-465318. - 4.16193e6i) q^{21} +5.01264e6 q^{22} -2.65763e6i q^{23} +(-8.60544e6 + 962117. i) q^{24} +1.67570e6 q^{25} +4.55229e6i q^{26} +(4.70424e6 + 1.35559e7i) q^{27} +5.23914e6 q^{28} -3.18221e6i q^{29} +(-2.06064e6 - 1.84309e7i) q^{30} -2.97931e7 q^{31} -1.91857e7i q^{32} +(4.51138e7 - 5.04387e6i) q^{33} +9.21024e6 q^{34} +4.90183e7i q^{35} +(-1.75077e7 + 3.96439e6i) q^{36} -6.08118e7 q^{37} +2.54767e7i q^{38} +(4.58066e6 + 4.09707e7i) q^{39} +1.01353e8 q^{40} -1.81668e8i q^{41} +(-1.11676e8 + 1.24858e7i) q^{42} +1.07420e8 q^{43} +5.67903e7i q^{44} +(-3.70915e7 - 1.63805e8i) q^{45} -7.13117e7 q^{46} +2.67996e8i q^{47} +(1.74113e7 + 1.55732e8i) q^{48} +1.45355e7 q^{49} -4.49639e7i q^{50} +(8.28922e7 - 9.26763e6i) q^{51} -5.15748e7 q^{52} -1.92091e8i q^{53} +(3.63742e8 - 1.26228e8i) q^{54} -5.31340e8 q^{55} -6.14116e8i q^{56} +(2.56355e7 + 2.29291e8i) q^{57} -8.53877e7 q^{58} +6.49158e8i q^{59} +(2.08812e8 - 2.33458e7i) q^{60} +1.03079e9 q^{61} +7.99433e8i q^{62} +(-9.92523e8 + 2.24744e8i) q^{63} -1.17515e9 q^{64} -4.82543e8i q^{65} +(-1.35341e8 - 1.21053e9i) q^{66} +1.87674e9 q^{67} +1.04347e8i q^{68} +(-6.41805e8 + 7.17560e7i) q^{69} +1.31530e9 q^{70} -2.68338e9i q^{71} +(4.64694e8 + 2.05220e9i) q^{72} -2.84653e9 q^{73} +1.63175e9i q^{74} +(-4.52440e7 - 4.04675e8i) q^{75} -2.88636e8 q^{76} +3.21948e9i q^{77} +(1.09936e9 - 1.22912e8i) q^{78} +1.48865e9 q^{79} -1.83417e9i q^{80} +(3.14666e9 - 1.50206e9i) q^{81} -4.87467e9 q^{82} -1.26585e9i q^{83} +(-1.41457e8 - 1.26523e9i) q^{84} -9.76285e8 q^{85} -2.88237e9i q^{86} +(-7.68489e8 + 8.59197e7i) q^{87} +6.65679e9 q^{88} +6.02052e9i q^{89} +(-4.39535e9 + 9.95270e8i) q^{90} -2.92382e9 q^{91} -8.07919e8i q^{92} +(8.04414e8 + 7.19490e9i) q^{93} +7.19108e9 q^{94} -2.70053e9i q^{95} +(-4.63325e9 + 5.18013e8i) q^{96} -1.59295e9 q^{97} -3.90029e8i q^{98} +(-2.43614e9 - 1.07586e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9}+O(q^{10}) $ 2 * q - 54 * q^3 + 608 * q^4 - 12960 * q^6 + 34468 * q^7 - 115182 * q^9	\( 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9} + 152640 q^{10} - 16416 q^{12} - 339308 q^{13} + 1373760 q^{15} - 1289728 q^{16} + 699840 q^{18} - 1898924 q^{19} - 930636 q^{21} + 10025280 q^{22} - 17210880 q^{24} + 3351410 q^{25} + 9408474 q^{27} + 10478272 q^{28} - 4121280 q^{30} - 59586236 q^{31} + 90227520 q^{33} + 18420480 q^{34} - 35015328 q^{36} - 121623692 q^{37} + 9161316 q^{39} + 202705920 q^{40} - 223352640 q^{42} + 214839412 q^{43} - 74183040 q^{45} - 142623360 q^{46} + 34822656 q^{48} + 29071014 q^{49} + 165784320 q^{51} - 103149632 q^{52} + 727483680 q^{54} - 1062679680 q^{55} + 51270948 q^{57} - 170775360 q^{58} + 417623040 q^{60} + 2061587284 q^{61} - 1985046588 q^{63} - 2350292992 q^{64} - 270682560 q^{66} + 3753484948 q^{67} - 1283610240 q^{69} + 2630597760 q^{70} + 929387520 q^{72} - 5693056988 q^{73} - 90488070 q^{75} - 577272896 q^{76} + 2198715840 q^{78} + 2977295236 q^{79} + 6293324322 q^{81} - 9749335680 q^{82} - 282913344 q^{84} - 1952570880 q^{85} - 1536978240 q^{87} + 13313571840 q^{88} - 8790690240 q^{90} - 5847634072 q^{91} + 1608828372 q^{93} + 14382155520 q^{94} - 9266503680 q^{96} - 3185897852 q^{97} - 4872286080 q^{99}+O(q^{100}) \) 2 * q - 54 * q^3 + 608 * q^4 - 12960 * q^6 + 34468 * q^7 - 115182 * q^9 + 152640 * q^10 - 16416 * q^12 - 339308 * q^13 + 1373760 * q^15 - 1289728 * q^16 + 699840 * q^18 - 1898924 * q^19 - 930636 * q^21 + 10025280 * q^22 - 17210880 * q^24 + 3351410 * q^25 + 9408474 * q^27 + 10478272 * q^28 - 4121280 * q^30 - 59586236 * q^31 + 90227520 * q^33 + 18420480 * q^34 - 35015328 * q^36 - 121623692 * q^37 + 9161316 * q^39 + 202705920 * q^40 - 223352640 * q^42 + 214839412 * q^43 - 74183040 * q^45 - 142623360 * q^46 + 34822656 * q^48 + 29071014 * q^49 + 165784320 * q^51 - 103149632 * q^52 + 727483680 * q^54 - 1062679680 * q^55 + 51270948 * q^57 - 170775360 * q^58 + 417623040 * q^60 + 2061587284 * q^61 - 1985046588 * q^63 - 2350292992 * q^64 - 270682560 * q^66 + 3753484948 * q^67 - 1283610240 * q^69 + 2630597760 * q^70 + 929387520 * q^72 - 5693056988 * q^73 - 90488070 * q^75 - 577272896 * q^76 + 2198715840 * q^78 + 2977295236 * q^79 + 6293324322 * q^81 - 9749335680 * q^82 - 282913344 * q^84 - 1952570880 * q^85 - 1536978240 * q^87 + 13313571840 * q^88 - 8790690240 * q^90 - 5847634072 * q^91 + 1608828372 * q^93 + 14382155520 * q^94 - 9266503680 * q^96 - 3185897852 * q^97 - 4872286080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	26.8328i		−	0.838525i	−0.907865	−	0.419263i	$-0.862289\pi$
$2$		−	26.8328i		−	0.838525i	0.907865	−	0.419263i	$-0.137711\pi$
$3$	−27.0000	−	241.495i	−0.111111	−	0.993808i
$3$	−27.0000	−	241.495i	−0.111111	−	0.993808i
$4$	304.000			0.296875
$5$			2844.28i			0.910169i	0.890448	+	0.455085i	$0.150391\pi$
$5$			2844.28i			0.910169i	−0.890448	+	0.455085i	$0.849609\pi$
$6$	−6480.00	+	724.486i	−0.833333	+	0.0931695i
$7$	17234.0			1.02541			0.512703	−	0.858566i	$-0.328644\pi$
$7$	17234.0			1.02541			0.512703	+	0.858566i	$0.328644\pi$
$8$		−	35634.0i		−	1.08746i
$9$	−57591.0	+	13040.7i	−0.975309	+	0.220846i
$10$	76320.0			0.763200
$11$			186810.i			1.15994i	0.814637	+	0.579972i	$0.196936\pi$
$11$			186810.i			1.15994i	−0.814637	+	0.579972i	$0.803064\pi$
$12$	−8208.00	−	73414.6i	−0.0329861	−	0.295037i
$13$	−169654.			−0.456928			−0.228464	−	0.973552i	$-0.573370\pi$
$13$	−169654.			−0.456928			−0.228464	+	0.973552i	$0.573370\pi$
$14$		−	462437.i		−	0.859829i
$15$	686880.	−	76795.5i	0.904533	−	0.101130i
$16$	−644864.			−0.614990
$17$			343245.i			0.241746i	0.992668	+	0.120873i	$0.0385695\pi$
$17$			343245.i			0.241746i	−0.992668	+	0.120873i	$0.961431\pi$
$18$	349920.	+	1.54533e6i	0.185185	+	0.817821i
$19$	−949462.			−0.383451			−0.191725	−	0.981449i	$-0.561408\pi$
$19$	−949462.			−0.383451			−0.191725	+	0.981449i	$0.561408\pi$
$20$			864661.i			0.270206i
$21$	−465318.	−	4.16193e6i	−0.113934	−	1.01906i
$22$	5.01264e6			0.972642
$23$		−	2.65763e6i		−	0.412910i	−0.978456	−	0.206455i	$-0.933807\pi$
$23$		−	2.65763e6i		−	0.412910i	0.978456	−	0.206455i	$-0.0661927\pi$
$24$	−8.60544e6	+	962117.i	−1.08073	+	0.120829i
$25$	1.67570e6			0.171592
$26$			4.55229e6i			0.383145i
$27$	4.70424e6	+	1.35559e7i	0.327846	+	0.944731i
$28$	5.23914e6			0.304417
$29$		−	3.18221e6i		−	0.155145i	−0.996987	−	0.0775727i	$-0.975283\pi$
$29$		−	3.18221e6i		−	0.155145i	0.996987	−	0.0775727i	$-0.0247170\pi$
$30$	−2.06064e6	−	1.84309e7i	−0.0848000	−	0.758474i
$31$	−2.97931e7			−1.04066			−0.520328	−	0.853966i	$-0.674190\pi$
$31$	−2.97931e7			−1.04066			−0.520328	+	0.853966i	$0.674190\pi$
$32$		−	1.91857e7i		−	0.571778i
$33$	4.51138e7	−	5.04387e6i	1.15276	−	0.128883i
$34$	9.21024e6			0.202711
$35$			4.90183e7i			0.933293i
$36$	−1.75077e7	+	3.96439e6i	−0.289545	+	0.0655637i
$37$	−6.08118e7			−0.876960			−0.438480	−	0.898741i	$-0.644483\pi$
$37$	−6.08118e7			−0.876960			−0.438480	+	0.898741i	$0.644483\pi$
$38$			2.54767e7i			0.321533i
$39$	4.58066e6	+	4.09707e7i	0.0507697	+	0.454098i
$40$	1.01353e8			0.989775
$41$		−	1.81668e8i		−	1.56805i	−0.620730	−	0.784024i	$-0.713164\pi$
$41$		−	1.81668e8i		−	1.56805i	0.620730	−	0.784024i	$-0.286836\pi$
$42$	−1.11676e8	+	1.24858e7i	−0.854505	+	0.0955366i
$43$	1.07420e8			0.730704			0.365352	−	0.930869i	$-0.380949\pi$
$43$	1.07420e8			0.730704			0.365352	+	0.930869i	$0.380949\pi$
$44$			5.67903e7i			0.344358i
$45$	−3.70915e7	−	1.63805e8i	−0.201007	−	0.887696i
$46$	−7.13117e7			−0.346235
$47$			2.67996e8i			1.16853i	0.811564	+	0.584263i	$0.198616\pi$
$47$			2.67996e8i			1.16853i	−0.811564	+	0.584263i	$0.801384\pi$
$48$	1.74113e7	+	1.55732e8i	0.0683322	+	0.611182i
$49$	1.45355e7			0.0514576
$50$		−	4.49639e7i		−	0.143884i
$51$	8.28922e7	−	9.26763e6i	0.240250	−	0.0268607i
$52$	−5.15748e7			−0.135650
$53$		−	1.92091e8i		−	0.459332i	−0.973269	−	0.229666i	$-0.926237\pi$
$53$		−	1.92091e8i		−	0.459332i	0.973269	−	0.229666i	$-0.0737634\pi$
$54$	3.63742e8	−	1.26228e8i	0.792181	−	0.274908i
$55$	−5.31340e8			−1.05574
$56$		−	6.14116e8i		−	1.11509i
$57$	2.56355e7	+	2.29291e8i	0.0426056	+	0.381076i
$58$	−8.53877e7			−0.130093
$59$			6.49158e8i			0.908009i	0.890999	+	0.454005i	$0.150005\pi$
$59$			6.49158e8i			0.908009i	−0.890999	+	0.454005i	$0.849995\pi$
$60$	2.08812e8	−	2.33458e7i	0.268533	−	0.0300229i
$61$	1.03079e9			1.22046			0.610229	−	0.792225i	$-0.291078\pi$
$61$	1.03079e9			1.22046			0.610229	+	0.792225i	$0.291078\pi$
$62$			7.99433e8i			0.872617i
$63$	−9.92523e8	+	2.24744e8i	−1.00009	+	0.226457i
$64$	−1.17515e9			−1.09444
$65$		−	4.82543e8i		−	0.415881i
$66$	−1.35341e8	−	1.21053e9i	−0.108071	−	0.966620i
$67$	1.87674e9			1.39005			0.695025	−	0.718985i	$-0.255393\pi$
$67$	1.87674e9			1.39005			0.695025	+	0.718985i	$0.255393\pi$
$68$			1.04347e8i			0.0717685i
$69$	−6.41805e8	+	7.17560e7i	−0.410353	+	0.0458789i
$70$	1.31530e9			0.782590
$71$		−	2.68338e9i		−	1.48727i	−0.668585	−	0.743636i	$-0.733100\pi$
$71$		−	2.68338e9i		−	1.48727i	0.668585	−	0.743636i	$-0.266900\pi$
$72$	4.64694e8	+	2.05220e9i	0.240162	+	1.06061i
$73$	−2.84653e9			−1.37310			−0.686549	−	0.727084i	$-0.740875\pi$
$73$	−2.84653e9			−1.37310			−0.686549	+	0.727084i	$0.740875\pi$
$74$			1.63175e9i			0.735353i
$75$	−4.52440e7	−	4.04675e8i	−0.0190658	−	0.170530i
$76$	−2.88636e8			−0.113837
$77$			3.21948e9i			1.18941i
$78$	1.09936e9	−	1.22912e8i	0.380773	−	0.0425717i
$79$	1.48865e9			0.483790			0.241895	−	0.970302i	$-0.422231\pi$
$79$	1.48865e9			0.483790			0.241895	+	0.970302i	$0.422231\pi$
$80$		−	1.83417e9i		−	0.559745i
$81$	3.14666e9	−	1.50206e9i	0.902454	−	0.430786i
$82$	−4.87467e9			−1.31485
$83$		−	1.26585e9i		−	0.321361i	−0.987006	−	0.160680i	$-0.948631\pi$
$83$		−	1.26585e9i		−	0.321361i	0.987006	−	0.160680i	$-0.0513688\pi$
$84$	−1.41457e8	−	1.26523e9i	−0.0338242	−	0.302532i
$85$	−9.76285e8			−0.220030
$86$		−	2.88237e9i		−	0.612714i
$87$	−7.68489e8	+	8.59197e7i	−0.154185	+	0.0172384i
$88$	6.65679e9			1.26140
$89$			6.02052e9i			1.07816i	0.842254	+	0.539081i	$0.181228\pi$
$89$			6.02052e9i			1.07816i	−0.842254	+	0.539081i	$0.818772\pi$
$90$	−4.39535e9	+	9.95270e8i	−0.744356	+	0.168550i
$91$	−2.92382e9			−0.468536
$92$		−	8.07919e8i		−	0.122583i
$93$	8.04414e8	+	7.19490e9i	0.115629	+	1.03421i
$94$	7.19108e9			0.979839
$95$		−	2.70053e9i		−	0.349005i
$96$	−4.63325e9	+	5.18013e8i	−0.568237	+	0.0635309i
$97$	−1.59295e9			−0.185500			−0.0927498	−	0.995689i	$-0.529566\pi$
$97$	−1.59295e9			−0.185500			−0.0927498	+	0.995689i	$0.529566\pi$
$98$		−	3.90029e8i		−	0.0431485i
$99$	−2.43614e9	−	1.07586e10i	−0.256169	−	1.13130i
$100$	5.09414e8			0.0509414
$101$		−	4.23015e9i		−	0.402484i	−0.979542	−	0.201242i	$-0.935502\pi$
$101$		−	4.23015e9i		−	0.402484i	0.979542	−	0.201242i	$-0.0644978\pi$
$102$	−2.48676e8	−	2.22423e9i	−0.0225234	−	0.201455i
$103$	4.41761e9			0.381067			0.190533	−	0.981681i	$-0.438978\pi$
$103$	4.41761e9			0.381067			0.190533	+	0.981681i	$0.438978\pi$
$104$			6.04545e9i			0.496892i
$105$	1.18377e10	−	1.32349e9i	0.927514	−	0.103699i
$106$	−5.15433e9			−0.385162
$107$			3.19343e9i			0.227687i	0.993499	+	0.113844i	$0.0363163\pi$
$107$			3.19343e9i			0.227687i	−0.993499	+	0.113844i	$0.963684\pi$
$108$	1.43009e9	+	4.12098e9i	0.0973294	+	0.280467i
$109$	−1.54650e10			−1.00512			−0.502561	−	0.864542i	$-0.667609\pi$
$109$	−1.54650e10			−1.00512			−0.502561	+	0.864542i	$0.667609\pi$
$110$			1.42573e10i			0.885269i
$111$	1.64192e9	+	1.46858e10i	0.0974400	+	0.871529i
$112$	−1.11136e10			−0.630615
$113$		−	2.53338e10i		−	1.37501i	−0.726177	−	0.687507i	$-0.758705\pi$
$113$		−	2.53338e10i		−	1.37501i	0.726177	−	0.687507i	$-0.241295\pi$
$114$	6.15251e9	−	6.87872e8i	0.319542	−	0.0357259i
$115$	7.55904e9			0.375818
$116$		−	9.67392e8i		−	0.0460588i
$117$	9.77054e9	−	2.21242e9i	0.445645	−	0.100911i
$118$	1.74187e10			0.761389
$119$			5.91549e9i			0.247888i
$120$	−2.73653e9	−	2.44763e10i	−0.109975	−	0.983646i
$121$	−8.96058e9			−0.345469
$122$		−	2.76591e10i		−	1.02338i
$123$	−4.38720e10	+	4.90504e9i	−1.55834	+	0.174228i
$124$	−9.05711e9			−0.308945
$125$			3.25423e10i			1.06635i
$126$	6.03052e9	+	2.66322e10i	0.189890	+	0.838599i
$127$	5.84098e10			1.76794			0.883970	−	0.467544i	$-0.154861\pi$
$127$	5.84098e10			1.76794			0.883970	+	0.467544i	$0.154861\pi$
$128$			1.18864e10i			0.345938i
$129$	−2.90033e9	−	2.59414e10i	−0.0811894	−	0.726180i
$130$	−1.29480e10			−0.348727
$131$			5.67731e10i			1.47159i	0.677205	+	0.735794i	$0.263191\pi$
$131$			5.67731e10i			1.47159i	−0.677205	+	0.735794i	$0.736809\pi$
$132$	1.37146e10	−	1.53334e9i	0.342226	−	0.0382620i
$133$	−1.63630e10			−0.393193
$134$		−	5.03583e10i		−	1.16559i
$135$	−3.85566e10	+	1.33802e10i	−0.859865	+	0.298396i
$136$	1.22312e10			0.262890
$137$		−	7.89283e10i		−	1.63542i	−0.575629	−	0.817711i	$-0.695243\pi$
$137$		−	7.89283e10i		−	1.63542i	0.575629	−	0.817711i	$-0.304757\pi$
$138$	1.92542e9	+	1.72214e10i	0.0384706	+	0.344092i
$139$	8.89683e9			0.171459			0.0857297	−	0.996318i	$-0.472678\pi$
$139$	8.89683e9			0.171459			0.0857297	+	0.996318i	$0.472678\pi$
$140$			1.49016e10i			0.277071i
$141$	6.47197e10	−	7.23588e9i	1.16129	−	0.129836i
$142$	−7.20026e10			−1.24711
$143$		−	3.16931e10i		−	0.530010i
$144$	3.71384e10	−	8.40951e9i	0.599805	−	0.135818i
$145$	9.05109e9			0.141209
$146$			7.63804e10i			1.15138i
$147$	−3.92459e8	−	3.51026e9i	−0.00571751	−	0.0511390i
$148$	−1.84868e10			−0.260347
$149$			7.43262e10i			1.01207i	0.862513	+	0.506035i	$0.168889\pi$
$149$			7.43262e10i			1.01207i	−0.862513	+	0.506035i	$0.831111\pi$
$150$	−1.08586e10	+	1.21402e9i	−0.142993	+	0.0159872i
$151$	−5.90950e10			−0.752776			−0.376388	−	0.926462i	$-0.622834\pi$
$151$	−5.90950e10			−0.752776			−0.376388	+	0.926462i	$0.622834\pi$
$152$			3.38331e10i			0.416988i
$153$	−4.47618e9	−	1.97678e10i	−0.0533888	−	0.235777i
$154$	8.63878e10			0.997353
$155$		−	8.47399e10i		−	0.947174i
$156$	1.39252e9	+	1.24551e10i	0.0150723	+	0.134810i
$157$	−3.81863e10			−0.400322			−0.200161	−	0.979763i	$-0.564147\pi$
$157$	−3.81863e10			−0.400322			−0.200161	+	0.979763i	$0.564147\pi$
$158$		−	3.99446e10i		−	0.405670i
$159$	−4.63890e10	+	5.18645e9i	−0.456488	+	0.0510369i
$160$	5.45694e10			0.520414
$161$		−	4.58016e10i		−	0.423400i
$162$	−4.03045e10	−	8.44338e10i	−0.361225	−	0.756731i
$163$	1.61034e11			1.39952			0.699760	−	0.714378i	$-0.253290\pi$
$163$	1.61034e11			1.39952			0.699760	+	0.714378i	$0.253290\pi$
$164$		−	5.52271e10i		−	0.465514i
$165$	1.43462e10	+	1.28316e11i	0.117305	+	1.04921i
$166$	−3.39664e10			−0.269469
$167$			5.95748e10i			0.458649i	0.973350	+	0.229325i	$0.0736517\pi$
$167$			5.95748e10i			0.458649i	−0.973350	+	0.229325i	$0.926348\pi$
$168$	−1.48306e11	+	1.65811e10i	−1.10819	+	0.123899i
$169$	−1.09076e11			−0.791217
$170$			2.61965e10i			0.184501i
$171$	5.46805e10	−	1.23817e10i	0.373983	−	0.0846836i
$172$	3.26556e10			0.216928
$173$			2.06971e11i			1.33561i	0.744336	+	0.667805i	$0.232766\pi$
$173$			2.06971e11i			1.33561i	−0.744336	+	0.667805i	$0.767234\pi$
$174$	2.30547e9	+	2.06207e10i	0.0144548	+	0.129288i
$175$	2.88791e10			0.175952
$176$		−	1.20467e11i		−	0.713354i
$177$	1.56769e11	−	1.75273e10i	0.902387	−	0.100890i
$178$	1.61547e11			0.904066
$179$		−	5.22122e10i		−	0.284123i	−0.989858	−	0.142062i	$-0.954627\pi$
$179$		−	5.22122e10i		−	0.284123i	0.989858	−	0.142062i	$-0.0453732\pi$
$180$	−1.12758e10	−	4.97967e10i	−0.0596741	−	0.263535i
$181$	−3.38840e11			−1.74422			−0.872112	−	0.489306i	$-0.837250\pi$
$181$	−3.38840e11			−1.74422			−0.872112	+	0.489306i	$0.837250\pi$
$182$			7.84542e10i			0.392880i
$183$	−2.78314e10	−	2.48932e11i	−0.135606	−	1.21290i
$184$	−9.47019e10			−0.449024
$185$		−	1.72966e11i		−	0.798182i
$186$	1.93059e11	−	2.15847e10i	0.867214	−	0.0969575i
$187$	−6.41217e10			−0.280412
$188$			8.14707e10i			0.346906i
$189$	8.10728e10	+	2.33622e11i	0.336176	+	0.968733i
$190$	−7.24629e10			−0.292650
$191$		−	1.55519e11i		−	0.611812i	−0.952062	−	0.305906i	$-0.901041\pi$
$191$		−	1.55519e11i		−	0.611812i	0.952062	−	0.305906i	$-0.0989593\pi$
$192$	3.17290e10	+	2.83792e11i	0.121604	+	1.08766i
$193$	3.50355e11			1.30834			0.654172	−	0.756346i	$-0.273017\pi$
$193$	3.50355e11			1.30834			0.654172	+	0.756346i	$0.273017\pi$
$194$			4.27433e10i			0.155546i
$195$	−1.16532e11	+	1.30287e10i	−0.413306	+	0.0462090i
$196$	4.41879e9			0.0152765
$197$			3.11997e11i			1.05152i	0.850632	+	0.525762i	$0.176220\pi$
$197$			3.11997e11i			1.05152i	−0.850632	+	0.525762i	$0.823780\pi$
$198$	−2.88683e11	+	6.53686e10i	−0.948626	+	0.214804i
$199$	−1.51943e11			−0.486871			−0.243436	−	0.969917i	$-0.578274\pi$
$199$	−1.51943e11			−0.486871			−0.243436	+	0.969917i	$0.578274\pi$
$200$		−	5.97120e10i		−	0.186600i
$201$	−5.06720e10	−	4.53225e11i	−0.154450	−	1.38144i
$202$	−1.13507e11			−0.337493
$203$		−	5.48422e10i		−	0.159087i
$204$	2.51992e10	−	2.81736e9i	0.0713241	−	0.00797428i
$205$	5.16715e11			1.42719
$206$		−	1.18537e11i		−	0.319534i
$207$	3.46575e10	+	1.53056e11i	0.0911896	+	0.402715i
$208$	1.09404e11			0.281006
$209$		−	1.77369e11i		−	0.444781i
$210$	−3.55131e10	−	3.17639e11i	−0.0869544	−	0.777744i
$211$	1.36229e11			0.325729			0.162864	−	0.986648i	$-0.447927\pi$
$211$	1.36229e11			0.325729			0.162864	+	0.986648i	$0.447927\pi$
$212$		−	5.83956e10i		−	0.136364i
$213$	−6.48023e11	+	7.24512e10i	−1.47806	+	0.165252i
$214$	8.56887e10			0.190922
$215$			3.05532e11i			0.665065i
$216$	4.83049e11	−	1.67631e11i	1.02736	−	0.356521i
$217$	−5.13455e11			−1.06710
$218$			4.14970e11i			0.842820i
$219$	7.68563e10	+	6.87423e11i	0.152566	+	1.36459i
$220$	−1.61527e11			−0.313424
$221$		−	5.82330e10i		−	0.110461i
$222$	3.94061e11	−	4.40573e10i	0.730800	−	0.0817059i
$223$	1.15573e11			0.209571			0.104786	−	0.994495i	$-0.466584\pi$
$223$	1.15573e11			0.209571			0.104786	+	0.994495i	$0.466584\pi$
$224$		−	3.30646e11i		−	0.586304i
$225$	−9.65055e10	+	2.18524e10i	−0.167355	+	0.0378955i
$226$	−6.79776e11			−1.15298
$227$			2.22416e10i			0.0369009i	0.999830	+	0.0184505i	$0.00587330\pi$
$227$			2.22416e10i			0.0369009i	−0.999830	+	0.0184505i	$0.994127\pi$
$228$	7.79318e9	+	6.97044e10i	0.0126485	+	0.113132i
$229$	5.48204e11			0.870492			0.435246	−	0.900311i	$-0.356661\pi$
$229$	5.48204e11			0.870492			0.435246	+	0.900311i	$0.356661\pi$
$230$		−	2.02830e11i		−	0.315133i
$231$	7.77491e11	−	8.69261e10i	1.18205	−	0.132157i
$232$	−1.13395e11			−0.168715
$233$		−	8.58665e11i		−	1.25039i	−0.780470	−	0.625193i	$-0.785020\pi$
$233$		−	8.58665e11i		−	1.25039i	0.780470	−	0.625193i	$-0.214980\pi$
$234$	−5.93653e10	−	2.62171e11i	−0.0846162	−	0.373685i
$235$	−7.62254e11			−1.06356
$236$			1.97344e11i			0.269565i
$237$	−4.01935e10	−	3.59501e11i	−0.0537544	−	0.480794i
$238$	1.58729e11			0.207861
$239$			9.11055e11i			1.16830i	0.811645	+	0.584151i	$0.198572\pi$
$239$			9.11055e11i			1.16830i	−0.811645	+	0.584151i	$0.801428\pi$
$240$	−4.42944e11	+	4.95227e10i	−0.556279	+	0.0621939i
$241$	3.71250e11			0.456648			0.228324	−	0.973585i	$-0.426676\pi$
$241$	3.71250e11			0.456648			0.228324	+	0.973585i	$0.426676\pi$
$242$			2.40437e11i			0.289685i
$243$	−4.47700e11	−	7.19349e11i	−0.528392	−	0.849001i
$244$	3.13361e11			0.362323
$245$			4.13430e10i			0.0468351i
$246$	1.31616e11	+	1.17721e12i	0.146094	+	1.30671i
$247$	1.61080e11			0.175209
$248$			1.06165e12i			1.13168i
$249$	−3.05698e11	+	3.41780e10i	−0.319371	+	0.0357068i
$250$	8.73202e11			0.894159
$251$		−	1.75865e11i		−	0.176527i	−0.996097	−	0.0882636i	$-0.971868\pi$
$251$		−	1.75865e11i		−	0.176527i	0.996097	−	0.0882636i	$-0.0281318\pi$
$252$	−3.01727e11	+	6.83223e10i	−0.296901	+	0.0672294i
$253$	4.96472e11			0.478952
$254$		−	1.56730e12i		−	1.48246i
$255$	2.63597e10	+	2.35768e11i	0.0244478	+	0.218668i
$256$	−8.84406e11			−0.804362
$257$		−	7.60350e11i		−	0.678185i	−0.940753	−	0.339093i	$-0.889880\pi$
$257$		−	7.60350e11i		−	0.678185i	0.940753	−	0.339093i	$-0.110120\pi$
$258$	−6.96080e11	+	7.78241e10i	−0.608920	+	0.0680794i
$259$	−1.04803e12			−0.899240
$260$		−	1.46693e11i		−	0.123465i
$261$	4.14984e10	+	1.83267e11i	0.0342633	+	0.151315i
$262$	1.52338e12			1.23396
$263$		−	2.37857e11i		−	0.189033i	−0.995523	−	0.0945163i	$-0.969870\pi$
$263$		−	2.37857e11i		−	0.189033i	0.995523	−	0.0945163i	$-0.0301304\pi$
$264$	−1.79733e11	−	1.60758e12i	−0.140155	−	1.25358i
$265$	5.46359e11			0.418070
$266$			4.39066e11i			0.329702i
$267$	1.45393e12	−	1.62554e11i	1.07149	−	0.119796i
$268$	5.70530e11			0.412671
$269$			1.57259e12i			1.11649i	0.829678	+	0.558243i	$0.188524\pi$
$269$			1.57259e12i			1.11649i	−0.829678	+	0.558243i	$0.811476\pi$
$270$	3.59027e11	+	1.03458e12i	0.250212	+	0.721019i
$271$	−1.66619e12			−1.13993			−0.569965	−	0.821669i	$-0.693043\pi$
$271$	−1.66619e12			−1.13993			−0.569965	+	0.821669i	$0.693043\pi$
$272$		−	2.21347e11i		−	0.148672i
$273$	7.89431e10	+	7.06088e11i	0.0520596	+	0.465635i
$274$	−2.11787e12			−1.37134
$275$			3.13039e11i			0.199037i
$276$	−1.95109e11	+	2.18138e10i	−0.121824	+	0.0136203i
$277$	−2.06519e12			−1.26637			−0.633186	−	0.774000i	$-0.718253\pi$
$277$	−2.06519e12			−1.26637			−0.633186	+	0.774000i	$0.718253\pi$
$278$		−	2.38727e11i		−	0.143773i
$279$	1.71582e12	−	3.88525e11i	1.01496	−	0.229825i
$280$	1.74672e12			1.01492
$281$			2.68989e12i			1.53533i	0.640849	+	0.767667i	$0.278583\pi$
$281$			2.68989e12i			1.53533i	−0.640849	+	0.767667i	$0.721417\pi$
$282$	−1.94159e11	−	1.73661e12i	−0.108871	−	0.973772i
$283$	1.44533e12			0.796225			0.398113	−	0.917337i	$-0.369665\pi$
$283$	1.44533e12			0.796225			0.398113	+	0.917337i	$0.369665\pi$
$284$		−	8.15747e11i		−	0.441534i
$285$	−6.52166e11	+	7.29144e10i	−0.346844	+	0.0387783i
$286$	−8.50414e11			−0.444427
$287$		−	3.13087e12i		−	1.60789i
$288$	2.50196e11	+	1.10492e12i	0.126275	+	0.557660i
$289$	1.89818e12			0.941559
$290$		−	2.42866e11i		−	0.118407i
$291$	4.30096e10	+	3.84690e11i	0.0206111	+	0.184351i
$292$	−8.65345e11			−0.407638
$293$		−	3.39085e12i		−	1.57026i	−0.619332	−	0.785129i	$-0.712597\pi$
$293$		−	3.39085e12i		−	1.57026i	0.619332	−	0.785129i	$-0.287403\pi$
$294$	−9.41901e10	+	1.05308e10i	−0.0428814	+	0.00479428i
$295$	−1.84639e12			−0.826442
$296$			2.16697e12i			0.953661i
$297$	−2.53237e12	+	8.78799e11i	−1.09583	+	0.380283i
$298$	1.99438e12			0.848646
$299$			4.50877e11i			0.188670i
$300$	−1.37542e10	−	1.23021e11i	−0.00566016	−	0.0506260i
$301$	1.85127e12			0.749269
$302$			1.58568e12i			0.631222i
$303$	−1.02156e12	+	1.14214e11i	−0.399992	+	0.0447205i
$304$	6.12274e11			0.235818
$305$			2.93186e12i			1.11082i
$306$	−5.30427e11	+	1.20108e11i	−0.197705	+	0.0447679i
$307$	2.07104e12			0.759447			0.379723	−	0.925100i	$-0.376019\pi$
$307$	2.07104e12			0.759447			0.379723	+	0.925100i	$0.376019\pi$
$308$			9.78723e11i			0.353107i
$309$	−1.19275e11	−	1.06683e12i	−0.0423407	−	0.378707i
$310$	−2.27381e12			−0.794229
$311$		−	2.14388e12i		−	0.736882i	−0.929651	−	0.368441i	$-0.879892\pi$
$311$		−	2.14388e12i		−	0.736882i	0.929651	−	0.368441i	$-0.120108\pi$
$312$	1.45995e12	−	1.63227e11i	0.493815	−	0.0552102i
$313$	−8.14838e11			−0.271237			−0.135619	−	0.990761i	$-0.543302\pi$
$313$	−8.14838e11			−0.271237			−0.135619	+	0.990761i	$0.543302\pi$
$314$			1.02465e12i			0.335680i
$315$	−6.39235e11	−	2.82301e12i	−0.206114	−	0.910249i
$316$	4.52549e11			0.143625
$317$		−	8.21225e11i		−	0.256546i	−0.991739	−	0.128273i	$-0.959057\pi$
$317$		−	8.21225e11i		−	0.256546i	0.991739	−	0.128273i	$-0.0409434\pi$
$318$	1.39167e11	+	1.24475e12i	0.0427958	+	0.382777i
$319$	5.94469e11			0.179960
$320$		−	3.34244e12i		−	0.996126i
$321$	7.71199e11	−	8.62226e10i	0.226277	−	0.0252986i
$322$	−1.22899e12			−0.355032
$323$		−	3.25898e11i		−	0.0926979i
$324$	9.56585e11	−	4.56626e11i	0.267916	−	0.127890i
$325$	−2.84290e11			−0.0784052
$326$		−	4.32099e12i		−	1.17353i
$327$	4.17556e11	+	3.73473e12i	0.111680	+	0.998898i
$328$	−6.47356e12			−1.70519
$329$			4.61864e12i			1.19821i
$330$	3.44308e12	−	3.84948e11i	0.879787	−	0.0983632i
$331$	1.76733e12			0.444814			0.222407	−	0.974954i	$-0.428609\pi$
$331$	1.76733e12			0.444814			0.222407	+	0.974954i	$0.428609\pi$
$332$		−	3.84819e11i		−	0.0954040i
$333$	3.50222e12	−	7.93032e11i	0.855306	−	0.193673i
$334$	1.59856e12			0.384589
$335$			5.33798e12i			1.26518i
$336$	3.00067e11	+	2.68388e12i	0.0700683	+	0.626710i
$337$	−5.35777e11			−0.123264			−0.0616318	−	0.998099i	$-0.519630\pi$
$337$	−5.35777e11			−0.123264			−0.0616318	+	0.998099i	$0.519630\pi$
$338$			2.92682e12i			0.663456i
$339$	−6.11798e12	+	6.84011e11i	−1.36650	+	0.152779i
$340$	−2.96791e11			−0.0653214
$341$		−	5.56565e12i		−	1.20710i
$342$	−3.32236e11	−	1.46723e12i	−0.0710094	−	0.313594i
$343$	−4.61767e12			−0.972641
$344$		−	3.82779e12i		−	0.794614i
$345$	−2.04094e11	−	1.82547e12i	−0.0417575	−	0.373491i
$346$	5.55362e12			1.11994
$347$			4.87335e12i			0.968681i	0.874880	+	0.484340i	$0.160940\pi$
$347$			4.87335e12i			0.968681i	−0.874880	+	0.484340i	$0.839060\pi$
$348$	−2.33621e11	+	2.61196e10i	−0.0457736	+	0.00511764i
$349$	7.83766e10			0.0151377			0.00756884	−	0.999971i	$-0.497591\pi$
$349$	7.83766e10			0.0151377			0.00756884	+	0.999971i	$0.497591\pi$
$350$		−	7.74908e11i		−	0.147540i
$351$	−7.98093e11	−	2.29981e12i	−0.149802	−	0.431674i
$352$	3.58408e12			0.663230
$353$		−	4.90804e12i		−	0.895437i	−0.894175	−	0.447718i	$-0.852237\pi$
$353$		−	4.90804e12i		−	0.895437i	0.894175	−	0.447718i	$-0.147763\pi$
$354$	−4.70306e11	−	4.20654e12i	−0.0845988	−	0.756674i
$355$	7.63227e12			1.35367
$356$			1.83024e12i			0.320079i
$357$	1.42856e12	−	1.59718e11i	0.246353	−	0.0275431i
$358$	−1.40100e12			−0.238245
$359$			8.23695e11i			0.138132i	0.997612	+	0.0690660i	$0.0220019\pi$
$359$			8.23695e11i			0.138132i	−0.997612	+	0.0690660i	$0.977998\pi$
$360$	−5.83702e12	+	1.32172e12i	−0.965336	+	0.218588i
$361$	−5.22959e12			−0.852966
$362$			9.09204e12i			1.46258i
$363$	2.41936e11	+	2.16394e12i	0.0383854	+	0.343330i
$364$	−8.88840e11			−0.139097
$365$		−	8.09632e12i		−	1.24975i
$366$	−6.67954e12	+	7.46796e11i	−1.01705	+	0.113709i
$367$	5.55933e12			0.835011			0.417506	−	0.908674i	$-0.362904\pi$
$367$	5.55933e12			0.835011			0.417506	+	0.908674i	$0.362904\pi$
$368$			1.71381e12i			0.253936i
$369$	2.36909e12	+	1.04625e13i	0.346298	+	1.52933i
$370$	−4.64116e12			−0.669296
$371$		−	3.31049e12i		−	0.471002i
$372$	2.44542e11	+	2.18725e12i	0.0343272	+	0.307032i
$373$	−4.21921e10			−0.00584369			−0.00292185	−	0.999996i	$-0.500930\pi$
$373$	−4.21921e10			−0.00584369			−0.00292185	+	0.999996i	$0.500930\pi$
$374$			1.72057e12i			0.235133i
$375$	7.85882e12	−	8.78643e11i	1.05974	−	0.118483i
$376$	9.54975e12			1.27073
$377$			5.39875e11i			0.0708902i
$378$	6.26873e12	−	2.17541e12i	0.812307	−	0.281892i
$379$	−9.51422e12			−1.21668			−0.608341	−	0.793676i	$-0.708165\pi$
$379$	−9.51422e12			−1.21668			−0.608341	+	0.793676i	$0.708165\pi$
$380$		−	8.20962e11i		−	0.103611i
$381$	−1.57707e12	−	1.41057e13i	−0.196438	−	1.75699i
$382$	−4.17302e12			−0.513020
$383$			2.82742e12i			0.343081i	0.985177	+	0.171540i	$0.0548744\pi$
$383$			2.82742e12i			0.343081i	−0.985177	+	0.171540i	$0.945126\pi$
$384$	2.87050e12	−	3.20932e11i	0.343796	−	0.0384376i
$385$	−9.15711e12			−1.08257
$386$		−	9.40101e12i		−	1.09708i
$387$	−6.18641e12	+	1.40083e12i	−0.712662	+	0.161373i
$388$	−4.84256e11			−0.0550702
$389$			1.12113e12i			0.125866i	0.998018	+	0.0629330i	$0.0200455\pi$
$389$			1.12113e12i			0.125866i	−0.998018	+	0.0629330i	$0.979955\pi$
$390$	3.49596e11	+	3.12688e12i	0.0387475	+	0.346568i
$391$	9.12219e11			0.0998195
$392$		−	5.17958e11i		−	0.0559583i
$393$	1.37104e13	−	1.53287e12i	1.46248	−	0.163510i
$394$	8.37176e12			0.881730
$395$			4.23413e12i			0.440330i
$396$	−7.40587e11	−	3.27061e12i	−0.0760502	−	0.335856i
$397$	−7.46731e12			−0.757202			−0.378601	−	0.925560i	$-0.623595\pi$
$397$	−7.46731e12			−0.757202			−0.378601	+	0.925560i	$0.623595\pi$
$398$			4.07705e12i			0.408254i
$399$	4.41802e11	+	3.95160e12i	0.0436881	+	0.390758i
$400$	−1.08060e12			−0.105528
$401$			1.62961e13i			1.57167i	0.618438	+	0.785834i	$0.287766\pi$
$401$			1.62961e13i			1.57167i	−0.618438	+	0.785834i	$0.712234\pi$
$402$	−1.21613e13	+	1.35967e12i	−1.15838	+	0.129510i
$403$	5.05452e12			0.475505
$404$		−	1.28597e12i		−	0.119488i
$405$	4.27228e12	+	8.94998e12i	0.392089	+	0.821386i
$406$	−1.47157e12			−0.133399
$407$		−	1.13603e13i		−	1.01722i
$408$	−3.30242e11	−	2.95378e12i	−0.0292100	−	0.261262i
$409$	1.05134e13			0.918602			0.459301	−	0.888281i	$-0.348100\pi$
$409$	1.05134e13			0.918602			0.459301	+	0.888281i	$0.348100\pi$
$410$		−	1.38649e13i		−	1.19673i
$411$	−1.90608e13	+	2.13106e12i	−1.62529	+	0.181713i
$412$	1.34295e12			0.113129
$413$			1.11876e13i			0.931078i
$414$	4.10691e12	−	9.29958e11i	0.337686	−	0.0764648i
$415$	3.60044e12			0.292493
$416$			3.25493e12i			0.261261i
$417$	−2.40214e11	−	2.14854e12i	−0.0190510	−	0.170398i
$418$	−4.75931e12			−0.372960
$419$		−	2.18708e13i		−	1.69354i	−0.531960	−	0.846769i	$-0.678544\pi$
$419$		−	2.18708e13i		−	1.69354i	0.531960	−	0.846769i	$-0.321456\pi$
$420$	3.59866e12	−	4.02342e11i	0.275356	−	0.0307857i
$421$	6.75679e12			0.510893			0.255447	−	0.966823i	$-0.417778\pi$
$421$	6.75679e12			0.510893			0.255447	+	0.966823i	$0.417778\pi$
$422$		−	3.65540e12i		−	0.273132i
$423$	−3.49486e12	−	1.54341e13i	−0.258065	−	1.13967i
$424$	−6.84496e12			−0.499507
$425$			5.75178e11i			0.0414818i
$426$	1.94407e12	+	1.73883e13i	0.138568	+	1.23939i
$427$	1.77647e13			1.25146
$428$			9.70803e11i			0.0675946i
$429$	−7.65373e12	+	8.55713e11i	−0.526728	+	0.0588900i
$430$	8.19827e12			0.557674
$431$			1.58220e13i			1.06383i	0.846797	+	0.531917i	$0.178528\pi$
$431$			1.58220e13i			1.06383i	−0.846797	+	0.531917i	$0.821472\pi$
$432$	−3.03359e12	−	8.74168e12i	−0.201622	−	0.581000i
$433$	−1.46123e13			−0.960020			−0.480010	−	0.877263i	$-0.659367\pi$
$433$	−1.46123e13			−0.960020			−0.480010	+	0.877263i	$0.659367\pi$
$434$			1.37774e13i			0.894787i
$435$	−2.44380e11	−	2.18580e12i	−0.0156898	−	0.140334i
$436$	−4.70137e12			−0.298395
$437$			2.52332e12i			0.158331i
$438$	1.84455e13	−	2.06227e12i	1.14425	−	0.127931i
$439$	−1.26826e13			−0.777831			−0.388915	−	0.921273i	$-0.627150\pi$
$439$	−1.26826e13			−0.777831			−0.388915	+	0.921273i	$0.627150\pi$
$440$			1.89338e13i			1.14808i
$441$	−8.37114e11	+	1.89554e11i	−0.0501871	+	0.0113642i
$442$	−1.56255e12			−0.0926240
$443$		−	4.68652e12i		−	0.274683i	−0.990524	−	0.137341i	$-0.956144\pi$
$443$		−	4.68652e12i		−	0.274683i	0.990524	−	0.137341i	$-0.0438558\pi$
$444$	4.99144e11	+	4.46448e12i	0.0289275	+	0.258735i
$445$	−1.71240e13			−0.981309
$446$		−	3.10115e12i		−	0.175731i
$447$	1.79494e13	−	2.00681e12i	1.00580	−	0.112452i
$448$	−2.02525e13			−1.12225
$449$		−	2.82413e13i		−	1.54758i	−0.633443	−	0.773789i	$-0.718359\pi$
$449$		−	2.82413e13i		−	1.54758i	0.633443	−	0.773789i	$-0.281641\pi$
$450$	5.86363e11	+	2.58952e12i	0.0317763	+	0.140332i
$451$	3.39374e13			1.81885
$452$		−	7.70146e12i		−	0.408207i
$453$	1.59556e12	+	1.42712e13i	0.0836418	+	0.748115i
$454$	5.96805e11			0.0309424
$455$		−	8.31615e12i		−	0.426447i
$456$	8.17054e12	−	9.13494e11i	0.414406	−	0.0463320i
$457$	9.22854e12			0.462969			0.231484	−	0.972839i	$-0.425642\pi$
$457$	9.22854e12			0.462969			0.231484	+	0.972839i	$0.425642\pi$
$458$		−	1.47099e13i		−	0.729930i
$459$	−4.65299e12	+	1.61471e12i	−0.228385	+	0.0792557i
$460$	2.29795e12			0.111571
$461$			7.80976e12i			0.375088i	0.982256	+	0.187544i	$0.0600527\pi$
$461$			7.80976e12i			0.375088i	−0.982256	+	0.187544i	$0.939947\pi$
$462$	−2.33247e12	−	2.08623e13i	−0.110817	−	0.991178i
$463$	−3.30432e13			−1.55302			−0.776510	−	0.630105i	$-0.783012\pi$
$463$	−3.30432e13			−1.55302			−0.776510	+	0.630105i	$0.783012\pi$
$464$			2.05209e12i			0.0954129i
$465$	−2.04643e13	+	2.28798e12i	−0.941309	+	0.105242i
$466$	−2.30404e13			−1.04848
$467$			4.06927e12i			0.183203i	0.995796	+	0.0916014i	$0.0291986\pi$
$467$			4.06927e12i			0.183203i	−0.995796	+	0.0916014i	$0.970801\pi$
$468$	2.97025e12	−	6.72574e11i	0.132301	−	0.0299579i
$469$	3.23438e13			1.42537
$470$			2.04534e13i			0.891819i
$471$	1.03103e12	+	9.22182e12i	0.0444802	+	0.397843i
$472$	2.31321e13			0.987426
$473$			2.00671e13i			0.847576i
$474$	−9.64644e12	+	1.07850e12i	−0.403158	+	0.0450744i
$475$	−1.59102e12			−0.0657972
$476$			1.79831e12i			0.0735918i
$477$	2.50501e12	+	1.10627e13i	0.101442	+	0.447991i
$478$	2.44462e13			0.979651
$479$			1.29218e13i			0.512444i	0.966618	+	0.256222i	$0.0824777\pi$
$479$			1.29218e13i			0.512444i	−0.966618	+	0.256222i	$0.917522\pi$
$480$	−1.47337e12	−	1.31783e13i	−0.0578238	−	0.517192i
$481$	1.03170e13			0.400707
$482$		−	9.96168e12i		−	0.382911i
$483$	−1.10609e13	+	1.23664e12i	−0.420779	+	0.0470445i
$484$	−2.72401e12			−0.102561
$485$		−	4.53079e12i		−	0.168836i
$486$	−1.93021e13	+	1.20131e13i	−0.711909	+	0.443070i
$487$	−2.16371e13			−0.789867			−0.394933	−	0.918710i	$-0.629232\pi$
$487$	−2.16371e13			−0.789867			−0.394933	+	0.918710i	$0.629232\pi$
$488$		−	3.67313e13i		−	1.32720i
$489$	−4.34791e12	−	3.88889e13i	−0.155502	−	1.39085i
$490$	1.10935e12			0.0392725
$491$			3.39340e13i			1.18913i	0.804049	+	0.594563i	$0.202675\pi$
$491$			3.39340e13i			1.18913i	−0.804049	+	0.594563i	$0.797325\pi$
$492$	−1.33371e13	+	1.49113e12i	−0.462632	+	0.0517238i
$493$	1.09228e12			0.0375059
$494$		−	4.32223e12i		−	0.146917i
$495$	3.06004e13	−	6.92907e12i	1.02968	−	0.233157i
$496$	1.92125e13			0.639994
$497$		−	4.62453e13i		−	1.52506i
$498$	9.17093e11	+	8.20273e12i	0.0299410	+	0.267801i
$499$	−1.83375e13			−0.592702			−0.296351	−	0.955079i	$-0.595770\pi$
$499$	−1.83375e13			−0.592702			−0.296351	+	0.955079i	$0.595770\pi$
$500$			9.89287e12i			0.316572i
$501$	1.43870e13	−	1.60852e12i	0.455809	−	0.0509610i
$502$	−4.71896e12			−0.148022
$503$		−	9.29154e12i		−	0.288568i	−0.989536	−	0.144284i	$-0.953912\pi$
$503$		−	9.29154e12i		−	0.288568i	0.989536	−	0.144284i	$-0.0460879\pi$
$504$	8.00853e12	+	3.53676e13i	0.246264	+	1.08756i
$505$	1.20317e13			0.366329
$506$		−	1.33217e13i		−	0.401614i
$507$	2.94505e12	+	2.63413e13i	0.0879130	+	0.786318i
$508$	1.77566e13			0.524857
$509$			1.53418e13i			0.449044i	0.974469	+	0.224522i	$0.0720820\pi$
$509$			1.53418e13i			0.449044i	−0.974469	+	0.224522i	$0.927918\pi$
$510$	6.32633e12	−	7.07305e11i	0.183358	−	0.0205001i
$511$	−4.90571e13			−1.40798
$512$			3.59027e13i			1.02042i
$513$	−4.46649e12	−	1.28708e13i	−0.125713	−	0.362258i
$514$	−2.04023e13			−0.568675
$515$			1.25649e13i			0.346835i
$516$	−8.81701e11	−	7.88617e12i	−0.0241031	−	0.215585i
$517$	−5.00643e13			−1.35542
$518$			2.81216e13i			0.754035i
$519$	4.99826e13	−	5.58822e12i	1.32734	−	0.148401i
$520$	−1.71949e13			−0.452255
$521$		−	3.59230e13i		−	0.935803i	−0.883781	−	0.467901i	$-0.845010\pi$
$521$		−	3.59230e13i		−	0.935803i	0.883781	−	0.467901i	$-0.154990\pi$
$522$	4.91756e12	−	1.11352e12i	0.126881	−	0.0287306i
$523$	5.78871e13			1.47936			0.739679	−	0.672960i	$-0.234978\pi$
$523$	5.78871e13			1.47936			0.739679	+	0.672960i	$0.234978\pi$
$524$			1.72590e13i			0.436878i
$525$	−7.79736e11	−	6.97417e12i	−0.0195502	−	0.174862i
$526$	−6.38236e12			−0.158509
$527$		−	1.02264e13i		−	0.251575i
$528$	−2.90922e13	+	3.25261e12i	−0.708937	+	0.0792615i
$529$	3.43635e13			0.829505
$530$		−	1.46604e13i		−	0.350562i
$531$	−8.46550e12	−	3.73856e13i	−0.200530	−	0.885589i
$532$	−4.97436e12			−0.116729
$533$			3.08207e13i			0.716485i
$534$	−4.36178e12	−	3.90130e13i	−0.100452	−	0.898468i
$535$	−9.08301e12			−0.207234
$536$		−	6.68758e13i		−	1.51163i
$537$	−1.26090e13	+	1.40973e12i	−0.282364	+	0.0315693i
$538$	4.21969e13			0.936201
$539$			2.71538e12i			0.0596879i
$540$	−1.17212e13	+	4.06757e12i	−0.255272	+	0.0885862i
$541$	−3.16844e12			−0.0683690			−0.0341845	−	0.999416i	$-0.510883\pi$
$541$	−3.16844e12			−0.0683690			−0.0341845	+	0.999416i	$0.510883\pi$
$542$			4.47086e13i			0.955860i
$543$	9.14869e12	+	8.18284e13i	0.193803	+	1.73342i
$544$	6.58540e12			0.138225
$545$		−	4.39869e13i		−	0.914830i
$546$	1.89463e13	−	2.11826e12i	0.390447	−	0.0436533i
$547$	−2.29070e13			−0.467770			−0.233885	−	0.972264i	$-0.575144\pi$
$547$	−2.29070e13			−0.467770			−0.233885	+	0.972264i	$0.575144\pi$
$548$		−	2.39942e13i		−	0.485516i
$549$	−5.93644e13	+	1.34423e13i	−1.19032	+	0.269533i
$550$	8.39971e12			0.166898
$551$			3.02139e12i			0.0594906i
$552$	2.55695e12	+	2.28701e13i	0.0498916	+	0.446244i
$553$	2.56554e13			0.496081
$554$			5.54149e13i			1.06188i
$555$	−4.17704e13	+	4.67008e12i	−0.793239	+	0.0886868i
$556$	2.70464e12			0.0509020
$557$			9.11885e13i			1.70084i	0.526103	+	0.850421i	$0.323653\pi$
$557$			9.11885e13i			1.70084i	−0.526103	+	0.850421i	$0.676347\pi$
$558$	−1.04252e13	−	4.60402e13i	−0.192714	−	0.851071i
$559$	−1.82242e13			−0.333879
$560$		−	3.16101e13i		−	0.573966i
$561$	1.73129e12	+	1.54851e13i	0.0311569	+	0.278676i
$562$	7.21773e13			1.28742
$563$		−	4.74869e13i		−	0.839522i	−0.907635	−	0.419761i	$-0.862114\pi$
$563$		−	4.74869e13i		−	0.839522i	0.907635	−	0.419761i	$-0.137886\pi$
$564$	1.96748e13	−	2.19971e12i	0.344758	−	0.0385451i
$565$	7.20562e13			1.25150
$566$		−	3.87824e13i		−	0.667655i
$567$	5.42296e13	−	2.58865e13i	0.925382	−	0.441731i
$568$	−9.56194e13			−1.61735
$569$			1.13850e13i			0.190885i	0.995435	+	0.0954426i	$0.0304266\pi$
$569$			1.13850e13i			0.190885i	−0.995435	+	0.0954426i	$0.969573\pi$
$570$	1.95650e12	+	1.74995e13i	0.0325166	+	0.290838i
$571$	−1.99708e13			−0.329014			−0.164507	−	0.986376i	$-0.552603\pi$
$571$	−1.99708e13			−0.329014			−0.164507	+	0.986376i	$0.552603\pi$
$572$		−	9.63469e12i		−	0.157347i
$573$	−3.75572e13	+	4.19902e12i	−0.608023	+	0.0679791i
$574$	−8.40100e13			−1.34825
$575$		−	4.45340e12i		−	0.0708521i
$576$	6.76779e13	−	1.53248e13i	1.06742	−	0.241703i
$577$	−8.52618e12			−0.133314			−0.0666569	−	0.997776i	$-0.521233\pi$
$577$	−8.52618e12			−0.133314			−0.0666569	+	0.997776i	$0.521233\pi$
$578$		−	5.09334e13i		−	0.789521i
$579$	−9.45958e12	−	8.46091e13i	−0.145371	−	1.30024i
$580$	2.75153e12			0.0419213
$581$		−	2.18157e13i		−	0.329525i
$582$	1.03223e13	−	1.15407e12i	0.154583	−	0.0172829i
$583$	3.58845e13			0.532800
$584$			1.01433e14i			1.49319i
$585$	6.29272e12	+	2.77901e13i	0.0918458	+	0.405613i
$586$	−9.09862e13			−1.31670
$587$			1.48895e13i			0.213644i	0.994278	+	0.106822i	$0.0340674\pi$
$587$			1.48895e13i			0.213644i	−0.994278	+	0.106822i	$0.965933\pi$
$588$	−1.19307e11	−	1.06712e12i	−0.00169739	−	0.0151819i
$589$	2.82874e13			0.399041
$590$			4.95437e13i			0.692993i
$591$	7.53458e13	−	8.42392e12i	1.04501	−	0.116836i
$592$	3.92154e13			0.539322
$593$			3.80871e13i			0.519404i	0.965689	+	0.259702i	$0.0836243\pi$
$593$			3.80871e13i			0.519404i	−0.965689	+	0.259702i	$0.916376\pi$
$594$	2.35806e13	+	6.79506e13i	0.318877	+	0.918885i
$595$	−1.68253e13			−0.225620
$596$			2.25952e13i			0.300458i
$597$	4.10245e12	+	3.66934e13i	0.0540968	+	0.483857i
$598$	1.20983e13			0.158205
$599$		−	8.56425e13i		−	1.11059i	−0.831652	−	0.555297i	$-0.812605\pi$
$599$		−	8.56425e13i		−	1.11059i	0.831652	−	0.555297i	$-0.187395\pi$
$600$	−1.44202e13	+	1.61223e12i	−0.185445	+	0.0207333i
$601$	−2.89732e13			−0.369508			−0.184754	−	0.982785i	$-0.559149\pi$
$601$	−2.89732e13			−0.369508			−0.184754	+	0.982785i	$0.559149\pi$
$602$		−	4.96748e13i		−	0.628281i
$603$	−1.08083e14	+	2.44741e13i	−1.35573	+	0.306987i
$604$	−1.79649e13			−0.223480
$605$		−	2.54864e13i		−	0.314435i
$606$	3.06468e12	+	2.74114e13i	0.0374993	+	0.335404i
$607$	−8.41409e13			−1.02109			−0.510544	−	0.859851i	$-0.670556\pi$
$607$	−8.41409e13			−1.02109			−0.510544	+	0.859851i	$0.670556\pi$
$608$			1.82161e13i			0.219249i
$609$	−1.32441e13	+	1.48074e12i	−0.158102	+	0.0176763i
$610$	7.86702e13			0.931453
$611$		−	4.54665e13i		−	0.533932i
$612$	−1.36076e12	−	6.00942e12i	−0.0158498	−	0.0699964i
$613$	2.27205e13			0.262492			0.131246	−	0.991350i	$-0.458102\pi$
$613$	2.27205e13			0.262492			0.131246	+	0.991350i	$0.458102\pi$
$614$		−	5.55719e13i		−	0.636815i
$615$	−1.39513e13	−	1.24784e14i	−0.158577	−	1.41835i
$616$	1.14723e14			1.29344
$617$			2.60898e13i			0.291773i	0.989301	+	0.145887i	$0.0466034\pi$
$617$			2.60898e13i			0.291773i	−0.989301	+	0.145887i	$0.953397\pi$
$618$	−2.86261e13	+	3.20049e12i	−0.317555	+	0.0355038i
$619$	1.71879e14			1.89134			0.945670	−	0.325127i	$-0.105407\pi$
$619$	1.71879e14			1.89134			0.945670	+	0.325127i	$0.105407\pi$
$620$		−	2.57609e13i		−	0.281192i
$621$	3.60264e13	−	1.25021e13i	0.390089	−	0.135371i
$622$	−5.75263e13			−0.617895
$623$			1.03758e14i			1.10555i
$624$	−2.95390e12	−	2.64205e13i	−0.0312229	−	0.279266i
$625$	−7.61951e13			−0.798964
$626$			2.18644e13i			0.227439i
$627$	−4.28338e13	+	4.78896e12i	−0.442027	+	0.0494201i
$628$	−1.16086e13			−0.118846
$629$		−	2.08734e13i		−	0.212002i
$630$	−7.57494e13	+	1.71525e13i	−0.763267	+	0.172832i
$631$	−1.35624e12			−0.0135578			−0.00677891	−	0.999977i	$-0.502158\pi$
$631$	−1.35624e12			−0.0135578			−0.00677891	+	0.999977i	$0.502158\pi$
$632$		−	5.30464e13i		−	0.526103i
$633$	−3.67817e12	−	3.28986e13i	−0.0361921	−	0.323712i
$634$	−2.20358e13			−0.215121
$635$			1.66134e14i			1.60912i
$636$	−1.41023e13	+	1.57668e12i	−0.135520	+	0.0151516i
$637$	−2.46601e12			−0.0235124
$638$		−	1.59513e13i		−	0.150901i
$639$	3.49933e13	+	1.54538e14i	0.328458	+	1.45055i
$640$	−3.38081e13			−0.314863
$641$			1.17561e14i			1.08635i	0.839618	+	0.543177i	$0.182779\pi$
$641$			1.17561e14i			1.08635i	−0.839618	+	0.543177i	$0.817221\pi$
$642$	−2.31360e12	−	2.06934e13i	−0.0212135	−	0.189739i
$643$	1.36130e14			1.23851			0.619253	−	0.785192i	$-0.287436\pi$
$643$	1.36130e14			1.23851			0.619253	+	0.785192i	$0.287436\pi$
$644$		−	1.39237e13i		−	0.125697i
$645$	7.37844e13	−	8.24935e12i	0.660946	−	0.0738961i
$646$	−8.74477e12			−0.0777295
$647$		−	1.40299e14i		−	1.23747i	−0.785601	−	0.618734i	$-0.787646\pi$
$647$		−	1.40299e14i		−	1.23747i	0.785601	−	0.618734i	$-0.212354\pi$
$648$	−5.35244e13	−	1.12128e14i	−0.468464	−	0.981385i
$649$	−1.21269e14			−1.05324
$650$			7.62830e12i			0.0657448i
$651$	1.38633e13	+	1.23997e14i	0.118566	+	1.06049i
$652$	4.89543e13			0.415482
$653$		−	1.23574e14i		−	1.04078i	−0.853927	−	0.520392i	$-0.825786\pi$
$653$		−	1.23574e14i		−	1.04078i	0.853927	−	0.520392i	$-0.174214\pi$
$654$	1.00213e14	−	1.12042e13i	0.837601	−	0.0936466i
$655$	−1.61479e14			−1.33939
$656$			1.17151e14i			0.964335i
$657$	1.63934e14	−	3.71209e13i	1.33919	−	0.303243i
$658$	1.23931e14			1.00473
$659$		−	1.94120e14i		−	1.56187i	−0.624615	−	0.780933i	$-0.714744\pi$
$659$		−	1.94120e14i		−	1.56187i	0.624615	−	0.780933i	$-0.285256\pi$
$660$	4.36124e12	+	3.90081e13i	0.0348249	+	0.311483i
$661$	−2.24813e14			−1.78162			−0.890810	−	0.454376i	$-0.849862\pi$
$661$	−2.24813e14			−1.78162			−0.890810	+	0.454376i	$0.849862\pi$
$662$		−	4.74225e13i		−	0.372988i
$663$	−1.40630e13	+	1.57229e12i	−0.109777	+	0.0122734i
$664$	−4.51074e13			−0.349468
$665$		−	4.65410e13i		−	0.357872i
$666$	−2.12793e13	−	9.39743e13i	−0.162400	−	0.717196i
$667$	−8.45714e12			−0.0640611
$668$			1.81107e13i			0.136161i
$669$	−3.12047e12	−	2.79103e13i	−0.0232857	−	0.208274i
$670$	1.43233e14			1.06089
$671$			1.92563e14i			1.41566i
$672$	−7.98495e13	+	8.92744e12i	−0.582674	+	0.0651449i
$673$	6.39293e13			0.463047			0.231523	−	0.972829i	$-0.425629\pi$
$673$	6.39293e13			0.463047			0.231523	+	0.972829i	$0.425629\pi$
$674$			1.43764e13i			0.103360i
$675$	7.88291e12	+	2.27156e13i	0.0562559	+	0.162108i
$676$	−3.31591e13			−0.234893
$677$		−	6.84090e13i		−	0.481027i	−0.970646	−	0.240514i	$-0.922684\pi$
$677$		−	6.84090e13i		−	0.481027i	0.970646	−	0.240514i	$-0.0773159\pi$
$678$	1.83539e13	+	1.64163e14i	0.128109	+	1.14585i
$679$	−2.74529e13			−0.190213
$680$			3.47889e13i			0.239275i
$681$	5.37125e12	−	6.00524e11i	0.0366724	−	0.00410010i
$682$	−1.49342e14			−1.01219
$683$			1.17660e14i			0.791639i	0.918328	+	0.395819i	$0.129539\pi$
$683$			1.17660e14i			0.791639i	−0.918328	+	0.395819i	$0.870461\pi$
$684$	1.66229e13	−	3.76404e12i	0.111026	−	0.0251405i
$685$	2.24494e14			1.48851
$686$			1.23905e14i			0.815584i
$687$	−1.48015e13	−	1.32389e14i	−0.0967214	−	0.865102i
$688$	−6.92711e13			−0.449376
$689$			3.25890e13i			0.209882i
$690$	−4.89826e13	+	5.47642e12i	−0.313181	+	0.0350148i
$691$	5.40492e13			0.343083			0.171541	−	0.985177i	$-0.445125\pi$
$691$	5.40492e13			0.343083			0.171541	+	0.985177i	$0.445125\pi$
$692$			6.29193e13i			0.396509i
$693$	−4.19845e13	−	1.85413e14i	−0.262677	−	1.16004i
$694$	1.30766e14			0.812263
$695$			2.53051e13i			0.156057i
$696$	3.06166e12	+	2.73843e13i	0.0187461	+	0.167670i
$697$	6.23568e13			0.379070
$698$		−	2.10307e12i		−	0.0126933i
$699$	−2.07364e14	+	2.31840e13i	−1.24264	+	0.138932i
$700$	8.77925e12			0.0522357
$701$		−	2.61865e14i		−	1.54699i	−0.633804	−	0.773493i	$-0.718508\pi$
$701$		−	2.61865e14i		−	1.54699i	0.633804	−	0.773493i	$-0.281492\pi$
$702$	−6.17103e13	+	2.14151e13i	−0.361969	+	0.125613i
$703$	5.77385e13			0.336271
$704$		−	2.19529e14i		−	1.26949i
$705$	2.05809e13	+	1.84081e14i	0.118173	+	1.05697i
$706$	−1.31697e14			−0.750846
$707$		−	7.29024e13i		−	0.412710i
$708$	4.76576e13	−	5.32829e12i	0.267896	−	0.0299517i
$709$	−1.21603e14			−0.678757			−0.339378	−	0.940650i	$-0.610217\pi$
$709$	−1.21603e14			−0.678757			−0.339378	+	0.940650i	$0.610217\pi$
$710$		−	2.04795e14i		−	1.13509i
$711$	−8.57327e13	+	1.94131e13i	−0.471844	+	0.106843i
$712$	2.14535e14			1.17246
$713$			7.91791e13i			0.429697i
$714$	−4.28569e12	−	3.83324e13i	−0.0230956	−	0.206574i
$715$	9.01439e13			0.482399
$716$		−	1.58725e13i		−	0.0843492i
$717$	2.20016e14	−	2.45985e13i	1.16107	−	0.129811i
$718$	2.21021e13			0.115827
$719$			2.82360e14i			1.46946i	0.678359	+	0.734731i	$0.262692\pi$
$719$			2.82360e14i			1.46946i	−0.678359	+	0.734731i	$0.737308\pi$
$720$	2.39190e13	+	1.05632e14i	0.123618	+	0.545924i
$721$	7.61330e13			0.390748
$722$			1.40325e14i			0.715233i
$723$	−1.00237e13	−	8.96551e13i	−0.0507386	−	0.453820i
$724$	−1.03007e14			−0.517817
$725$		−	5.33245e12i		−	0.0266217i
$726$	5.80645e13	−	6.49181e12i	0.287891	−	0.0321872i
$727$	−6.98010e13			−0.343708			−0.171854	−	0.985122i	$-0.554976\pi$
$727$	−6.98010e13			−0.343708			−0.171854	+	0.985122i	$0.554976\pi$
$728$			1.04187e14i			0.509516i
$729$	−1.61631e14	+	1.27540e14i	−0.785034	+	0.619453i
$730$	−2.17247e14			−1.04795
$731$			3.68713e13i			0.176645i
$732$	−8.46075e12	−	7.56753e13i	−0.0402581	−	0.360080i
$733$	−3.28397e14			−1.55196			−0.775978	−	0.630760i	$-0.782743\pi$
$733$	−3.28397e14			−1.55196			−0.775978	+	0.630760i	$0.782743\pi$
$734$		−	1.49173e14i		−	0.700178i
$735$	9.98415e12	−	1.11626e12i	0.0465451	−	0.00520391i
$736$	−5.09884e13			−0.236093
$737$			3.50594e14i			1.61238i
$738$	2.80737e14	−	6.35693e13i	1.28238	−	0.290379i
$739$	3.04479e14			1.38145			0.690726	−	0.723117i	$-0.257291\pi$
$739$	3.04479e14			1.38145			0.690726	+	0.723117i	$0.257291\pi$
$740$		−	5.25816e13i		−	0.236960i
$741$	−4.34916e12	−	3.89001e13i	−0.0194677	−	0.174124i
$742$	−8.88298e13			−0.394947
$743$		−	2.81759e14i		−	1.24432i	−0.782888	−	0.622162i	$-0.786254\pi$
$743$		−	2.81759e14i		−	1.24432i	0.782888	−	0.622162i	$-0.213746\pi$
$744$	2.56383e14	−	2.86645e13i	1.12467	−	0.125742i
$745$	−2.11404e14			−0.921154
$746$			1.13213e12i			0.00490008i
$747$	1.65077e13	+	7.29017e13i	0.0709713	+	0.313426i
$748$	−1.94930e13			−0.0832474
$749$			5.50356e13i			0.233472i
$750$	−2.35765e13	−	2.10874e14i	−0.0993510	−	0.888623i
$751$	3.86635e14			1.61846			0.809230	−	0.587492i	$-0.199885\pi$
$751$	3.86635e14			1.61846			0.809230	+	0.587492i	$0.199885\pi$
$752$		−	1.72821e14i		−	0.718632i
$753$	−4.24706e13	+	4.74836e12i	−0.175434	+	0.0196141i
$754$	1.44864e13			0.0594433
$755$		−	1.68083e14i		−	0.685153i
$756$	2.46461e13	+	7.10210e13i	0.0998021	+	0.287593i
$757$	−1.76968e13			−0.0711893			−0.0355947	−	0.999366i	$-0.511333\pi$
$757$	−1.76968e13			−0.0711893			−0.0355947	+	0.999366i	$0.511333\pi$
$758$			2.55293e14i			1.02022i
$759$	−1.34047e13	−	1.19896e14i	−0.0532169	−	0.475986i
$760$	−9.62308e13			−0.379530
$761$		−	1.74325e14i		−	0.683025i	−0.939877	−	0.341512i	$-0.889061\pi$
$761$		−	1.74325e14i		−	0.683025i	0.939877	−	0.341512i	$-0.110939\pi$
$762$	−3.78496e14	+	4.23171e13i	−1.47328	+	0.164718i
$763$	−2.66524e14			−1.03066
$764$		−	4.72779e13i		−	0.181632i
$765$	5.62253e13	−	1.27315e13i	0.214597	−	0.0485928i
$766$	7.58677e13			0.287682
$767$		−	1.10132e14i		−	0.414894i
$768$	2.38790e13	+	2.13580e14i	0.0893736	+	0.799382i
$769$	1.93974e14			0.721293			0.360646	−	0.932703i	$-0.382556\pi$
$769$	1.93974e14			0.721293			0.360646	+	0.932703i	$0.382556\pi$
$770$			2.45711e14i			0.907760i
$771$	−1.83621e14	+	2.05295e13i	−0.673986	+	0.0753539i
$772$	1.06508e14			0.388414
$773$			5.25639e13i			0.190454i	0.995456	+	0.0952270i	$0.0303577\pi$
$773$			5.25639e13i			0.190454i	−0.995456	+	0.0952270i	$0.969642\pi$
$774$	3.75883e13	+	1.65999e14i	0.135316	+	0.597585i
$775$	−4.99245e13			−0.178569
$776$			5.67631e13i			0.201724i
$777$	2.82968e13	+	2.53095e14i	0.0999155	+	0.893672i
$778$	3.00831e13			0.105542
$779$			1.72487e14i			0.601269i
$780$	−3.54257e13	+	3.96071e12i	−0.122700	+	0.0137183i
$781$	5.01282e14			1.72515
$782$		−	2.44774e13i		−	0.0837012i
$783$	4.31376e13	−	1.49699e13i	0.146571	−	0.0508639i
$784$	−9.37343e12			−0.0316459
$785$		−	1.08613e14i		−	0.364361i
$786$	−4.11313e13	−	3.67890e14i	−0.137107	−	1.22632i
$787$	−1.52665e14			−0.505669			−0.252834	−	0.967510i	$-0.581363\pi$
$787$	−1.52665e14			−0.505669			−0.252834	+	0.967510i	$0.581363\pi$
$788$			9.48471e13i			0.312171i
$789$	−5.74413e13	+	6.42213e12i	−0.187862	+	0.0210036i
$790$	1.13614e14			0.369228
$791$		−	4.36602e14i		−	1.40995i
$792$	−3.83371e14	+	8.68095e13i	−1.23025	+	0.278574i
$793$	−1.74878e14			−0.557661
$794$			2.00369e14i			0.634933i
$795$	−1.47517e13	−	1.31943e14i	−0.0464522	−	0.415481i
$796$	−4.61906e13			−0.144540
$797$			3.21927e14i			1.00107i	0.865716	+	0.500536i	$0.166864\pi$
$797$			3.21927e14i			1.00107i	−0.865716	+	0.500536i	$0.833136\pi$
$798$	1.06032e14	−	1.18548e13i	0.327661	−	0.0366336i
$799$	−9.19883e13			−0.282487
$800$		−	3.21495e13i		−	0.0981126i
$801$	−7.85121e13	−	3.46728e14i	−0.238108	−	1.05154i
$802$	4.37269e14			1.31788
$803$		−	5.31760e14i		−	1.59272i
$804$	−1.54043e13	−	1.37780e14i	−0.0458524	−	0.410116i
$805$	1.30272e14			0.385366
$806$		−	1.35627e14i		−	0.398723i
$807$	3.79772e14	−	4.24598e13i	1.10957	−	0.124054i
$808$	−1.50737e14			−0.437687
$809$			4.22482e14i			1.21917i	0.792719	+	0.609587i	$0.208665\pi$
$809$			4.22482e14i			1.21917i	−0.792719	+	0.609587i	$0.791335\pi$
$810$	2.40153e14	−	1.14637e14i	0.688753	−	0.328776i
$811$	−5.21066e14			−1.48521			−0.742607	−	0.669728i	$-0.766411\pi$
$811$	−5.21066e14			−1.48521			−0.742607	+	0.669728i	$0.766411\pi$
$812$		−	1.66720e13i		−	0.0472290i
$813$	4.49871e13	+	4.02377e14i	0.126659	+	1.13287i
$814$	−3.04828e14			−0.852968
$815$			4.58025e14i			1.27380i
$816$	−5.34542e13	+	5.97636e12i	−0.147751	+	0.0165191i
$817$	−1.01991e14			−0.280189
$818$		−	2.82105e14i		−	0.770272i
$819$	1.68386e14	−	3.81288e13i	0.456967	−	0.103474i
$820$	1.57081e14			0.423697
$821$		−	1.86792e14i		−	0.500775i	−0.968146	−	0.250387i	$-0.919442\pi$
$821$		−	1.86792e14i		−	0.500775i	0.968146	−	0.250387i	$-0.0805580\pi$
$822$	5.71824e13	+	5.11455e14i	0.152371	+	1.36285i
$823$	6.22782e13			0.164944			0.0824721	−	0.996593i	$-0.473718\pi$
$823$	6.22782e13			0.164944			0.0824721	+	0.996593i	$0.473718\pi$
$824$		−	1.57417e14i		−	0.414396i
$825$	7.55974e13	−	8.45204e12i	0.197805	−	0.0221153i
$826$	3.00194e14			0.780733
$827$			3.99626e14i			1.03306i	0.856269	+	0.516530i	$0.172777\pi$
$827$			3.99626e14i			1.03306i	−0.856269	+	0.516530i	$0.827223\pi$
$828$	1.05359e13	+	4.65289e13i	0.0270719	+	0.119556i
$829$	−5.51493e14			−1.40853			−0.704267	−	0.709935i	$-0.748724\pi$
$829$	−5.51493e14			−1.40853			−0.704267	+	0.709935i	$0.748724\pi$
$830$		−	9.66099e13i		−	0.245263i
$831$	5.57601e13	+	4.98734e14i	0.140708	+	1.25853i
$832$	1.99368e14			0.500080
$833$			4.98925e12i			0.0124397i
$834$	−5.76515e13	+	6.44563e12i	−0.142883	+	0.0159748i
$835$	−1.69447e14			−0.417448
$836$		−	5.39202e13i		−	0.132044i
$837$	−1.40154e14	−	4.03871e14i	−0.341176	−	0.983141i
$838$	−5.86856e14			−1.42008
$839$			1.98481e14i			0.477428i	0.971090	+	0.238714i	$0.0767259\pi$
$839$			1.98481e14i			0.477428i	−0.971090	+	0.238714i	$0.923274\pi$
$840$	−4.71614e13	−	4.21824e14i	−0.112769	−	1.00864i
$841$	4.10581e14			0.975930
$842$		−	1.81304e14i		−	0.428397i
$843$	6.49596e14	−	7.26271e13i	1.52583	−	0.170593i
$844$	4.14135e13			0.0967007
$845$		−	3.10243e14i		−	0.720141i
$846$	−4.14141e14	+	9.37770e13i	−0.955645	+	0.216394i
$847$	−1.54427e14			−0.354246
$848$			1.23872e14i			0.282485i
$849$	−3.90240e13	−	3.49041e14i	−0.0884695	−	0.791295i
$850$	1.54336e13			0.0347835
$851$			1.61615e14i			0.362105i
$852$	−1.96999e14	+	2.20252e13i	−0.438800	+	0.0490593i
$853$	7.19132e14			1.59244			0.796221	−	0.605006i	$-0.206829\pi$
$853$	7.19132e14			1.59244			0.796221	+	0.605006i	$0.206829\pi$
$854$		−	4.76677e14i		−	1.04938i
$855$	3.52170e13	+	1.55526e14i	0.0770764	+	0.340388i
$856$	1.13795e14			0.247601
$857$		−	2.57463e14i		−	0.556943i	−0.960444	−	0.278472i	$-0.910172\pi$
$857$		−	2.57463e14i		−	0.556943i	0.960444	−	0.278472i	$-0.0898279\pi$
$858$	2.29612e13	+	2.05371e14i	0.0493808	+	0.441675i
$859$	4.81365e14			1.02922			0.514610	−	0.857424i	$-0.327937\pi$
$859$	4.81365e14			1.02922			0.514610	+	0.857424i	$0.327937\pi$
$860$			9.28816e13i			0.197441i
$861$	−7.56090e14	+	8.45335e13i	−1.59793	+	0.178654i
$862$	4.24547e14			0.892052
$863$		−	1.08169e13i		−	0.0225969i	−0.999936	−	0.0112985i	$-0.996404\pi$
$863$		−	1.08169e13i		−	0.0225969i	0.999936	−	0.0112985i	$-0.00359649\pi$
$864$	2.60078e14	−	9.02540e13i	0.540176	−	0.187455i
$865$	−5.88684e14			−1.21563
$866$			3.92090e14i			0.805001i
$867$	−5.12508e13	−	4.58401e14i	−0.104618	−	0.935729i
$868$	−1.56090e14			−0.316794
$869$			2.78094e14i			0.561169i
$870$	−5.86511e13	+	6.55739e12i	−0.117674	+	0.0131563i
$871$	−3.18397e14			−0.635152
$872$			5.51081e14i			1.09303i
$873$	9.17395e13	−	2.07732e13i	0.180919	−	0.0409669i
$874$	6.77077e13			0.132764
$875$			5.60834e14i			1.09344i
$876$	2.33643e13	+	2.08977e14i	0.0452931	+	0.405114i
$877$	−6.94441e13			−0.133856			−0.0669280	−	0.997758i	$-0.521320\pi$
$877$	−6.94441e13			−0.133856			−0.0669280	+	0.997758i	$0.521320\pi$
$878$			3.40309e14i			0.652231i
$879$	−8.18875e14	+	9.15531e13i	−1.56053	+	0.174473i
$880$	3.42642e14			0.649273
$881$		−	9.22199e14i		−	1.73758i	−0.495180	−	0.868791i	$-0.664898\pi$
$881$		−	9.22199e14i		−	1.73758i	0.495180	−	0.868791i	$-0.335102\pi$
$882$	5.08626e12	+	2.24621e13i	0.00952919	+	0.0420831i
$883$	−3.03213e13			−0.0564864			−0.0282432	−	0.999601i	$-0.508991\pi$
$883$	−3.03213e13			−0.0564864			−0.0282432	+	0.999601i	$0.508991\pi$
$884$		−	1.77028e13i		−	0.0327930i
$885$	4.98524e13	+	4.45893e14i	0.0918269	+	0.821325i
$886$	−1.25753e14			−0.230329
$887$		−	9.37729e14i		−	1.70789i	−0.520365	−	0.853944i	$-0.674204\pi$
$887$		−	9.37729e14i		−	1.70789i	0.520365	−	0.853944i	$-0.325796\pi$
$888$	5.23313e14	−	5.85081e13i	0.947756	−	0.105962i
$889$	1.00664e15			1.81286
$890$			4.59486e14i			0.822853i
$891$	2.80600e14	+	5.87828e14i	0.499688	+	1.04680i
$892$	3.51342e13			0.0622165
$893$		−	2.54452e14i		−	0.448072i
$894$	−5.38483e13	−	4.81634e14i	−0.0942940	−	0.843391i
$895$	1.48506e14			0.258600
$896$			2.04849e14i			0.354727i
$897$	1.08885e14	−	1.21737e13i	0.187502	−	0.0209633i
$898$	−7.57793e14			−1.29768
$899$			9.48080e13i			0.161453i
$900$	−2.93377e13	+	6.64314e12i	−0.0496836	+	0.0112502i
$901$	6.59342e13			0.111042
$902$		−	9.10637e14i		−	1.52515i
$903$	−4.99843e13	−	4.47073e14i	−0.0832521	−	0.744629i
$904$	−9.02742e14			−1.49528
$905$		−	9.63756e14i		−	1.58754i
$906$	3.82935e14	−	4.28135e13i	0.627313	−	0.0701357i
$907$	−9.15531e14			−1.49155			−0.745773	−	0.666200i	$-0.767920\pi$
$907$	−9.15531e14			−1.49155			−0.745773	+	0.666200i	$0.767920\pi$
$908$			6.76145e12i			0.0109550i
$909$	5.51643e13	+	2.43619e14i	0.0888871	+	0.392546i
$910$	−2.23146e14			−0.357587
$911$			1.11284e15i			1.77354i	0.462210	+	0.886770i	$0.347057\pi$
$911$			1.11284e15i			1.77354i	−0.462210	+	0.886770i	$0.652943\pi$
$912$	−1.65314e13	−	1.47861e14i	−0.0262021	−	0.234358i
$913$	2.36474e14			0.372760
$914$		−	2.47628e14i		−	0.388211i
$915$	7.08032e14	−	7.91603e13i	1.10394	−	0.123425i
$916$	1.66654e14			0.258427
$917$			9.78428e14i			1.50898i
$918$	4.33272e13	+	1.24853e14i	0.0664579	+	0.191507i
$919$	4.68203e14			0.714260			0.357130	−	0.934055i	$-0.383755\pi$
$919$	4.68203e14			0.714260			0.357130	+	0.934055i	$0.383755\pi$
$920$		−	2.69359e14i		−	0.408688i
$921$	−5.59182e13	−	5.00147e14i	−0.0843830	−	0.754744i
$922$	2.09558e14			0.314521
$923$			4.55246e14i			0.679575i
$924$	2.36357e14	−	2.64255e13i	0.350921	−	0.0392341i
$925$	−1.01903e14			−0.150479
$926$			8.86642e14i			1.30225i
$927$	−2.54414e14	+	5.76089e13i	−0.371657	+	0.0841571i
$928$	−6.10529e13			−0.0887087
$929$			4.05571e14i			0.586123i	0.956094	+	0.293062i	$0.0946741\pi$
$929$			4.05571e14i			0.586123i	−0.956094	+	0.293062i	$0.905326\pi$
$930$	6.13929e13	+	5.49115e14i	0.0882477	+	0.789311i
$931$	−1.38009e13			−0.0197315
$932$		−	2.61034e14i		−	0.371208i
$933$	−5.17737e14	+	5.78847e13i	−0.732319	+	0.0818758i
$934$	1.09190e14			0.153620
$935$		−	1.82380e14i		−	0.255223i
$936$	−7.88372e13	−	3.48163e14i	−0.109737	−	0.484623i
$937$	−1.63835e14			−0.226834			−0.113417	−	0.993547i	$-0.536180\pi$
$937$	−1.63835e14			−0.226834			−0.113417	+	0.993547i	$0.536180\pi$
$938$		−	8.67875e14i		−	1.19521i
$939$	2.20006e13	+	1.96780e14i	0.0301375	+	0.269558i
$940$	−2.31725e14			−0.315743
$941$			7.62592e14i			1.03358i	0.856112	+	0.516790i	$0.172873\pi$
$941$			7.62592e14i			1.03358i	−0.856112	+	0.516790i	$0.827127\pi$
$942$	2.47447e14	−	2.76655e13i	0.333602	−	0.0372978i
$943$	−4.82807e14			−0.647463
$944$		−	4.18618e14i		−	0.558417i
$945$	−6.64485e14	+	2.30594e14i	−0.881711	+	0.305977i
$946$	5.38456e14			0.710714
$947$		−	1.00864e15i		−	1.32430i	−0.749371	−	0.662150i	$-0.769644\pi$
$947$		−	1.00864e15i		−	1.32430i	0.749371	−	0.662150i	$-0.230356\pi$
$948$	−1.22188e13	−	1.09288e14i	−0.0159583	−	0.142736i
$949$	4.82925e14			0.627406
$950$			4.26915e13i			0.0551726i
$951$	−1.98322e14	+	2.21731e13i	−0.254958	+	0.0285051i
$952$	2.10792e14			0.269569
$953$		−	2.25382e14i		−	0.286718i	−0.989671	−	0.143359i	$-0.954210\pi$
$953$		−	2.25382e14i		−	0.286718i	0.989671	−	0.143359i	$-0.0457903\pi$
$954$	2.96843e14	−	6.72164e13i	0.375652	−	0.0850615i
$955$	4.42340e14			0.556852
$956$			2.76961e14i			0.346840i
$957$	−1.60507e13	−	1.43562e14i	−0.0199955	−	0.178846i
$958$	3.46729e14			0.429697
$959$		−	1.36025e15i		−	1.67697i
$960$	−8.07185e14	+	9.02460e13i	−0.989958	+	0.110681i
$961$	6.80016e13			0.0829664
$962$		−	2.76833e14i		−	0.336003i
$963$	−4.16447e13	−	1.83913e14i	−0.0502839	−	0.222065i
$964$	1.12860e14			0.135567
$965$			9.96507e14i			1.19081i
$966$	3.31826e13	+	2.96794e14i	0.0394480	+	0.352834i
$967$	7.89275e14			0.933460			0.466730	−	0.884400i	$-0.345432\pi$
$967$	7.89275e14			0.933460			0.466730	+	0.884400i	$0.345432\pi$
$968$			3.19301e14i			0.375685i
$969$	−7.87030e13	+	8.79926e12i	−0.0921239	+	0.0102998i
$970$	−1.21574e14			−0.141573
$971$		−	2.37876e14i		−	0.275584i	−0.990461	−	0.137792i	$-0.955999\pi$
$971$		−	2.37876e14i		−	0.275584i	0.990461	−	0.137792i	$-0.0440006\pi$
$972$	−1.36101e14	−	2.18682e14i	−0.156866	−	0.252047i
$973$	1.53328e14			0.175816
$974$			5.80584e14i			0.662324i
$975$	7.67583e12	+	6.86547e13i	0.00871169	+	0.0779197i
$976$	−6.64722e14			−0.750569
$977$			4.62892e14i			0.520004i	0.965608	+	0.260002i	$0.0837232\pi$
$977$			4.62892e14i			0.520004i	−0.965608	+	0.260002i	$0.916277\pi$
$978$	−1.04350e15	+	1.16667e14i	−1.16627	+	0.130393i
$979$	−1.12469e15			−1.25061
$980$			1.25683e13i			0.0139042i
$981$	8.90647e14	−	2.01676e14i	0.980303	−	0.221977i
$982$	9.10545e14			0.997112
$983$			7.04750e14i			0.767834i	0.923368	+	0.383917i	$0.125425\pi$
$983$			7.04750e14i			0.767834i	−0.923368	+	0.383917i	$0.874575\pi$
$984$	1.74786e14	+	1.56333e15i	0.189466	+	1.69464i
$985$	−8.87406e14			−0.957065
$986$		−	2.93089e13i		−	0.0314496i
$987$	1.11538e15	−	1.24703e14i	1.19079	−	0.133135i
$988$	4.89683e13			0.0520152
$989$		−	2.85482e14i		−	0.301715i
$990$	−1.85926e14	−	8.21095e14i	−0.195508	−	0.863410i
$991$	9.64032e14			1.00861			0.504305	−	0.863526i	$-0.331749\pi$
$991$	9.64032e14			1.00861			0.504305	+	0.863526i	$0.331749\pi$
$992$			5.71601e14i			0.595024i
$993$	−4.77180e13	−	4.26803e14i	−0.0494238	−	0.442060i
$994$	−1.24089e15			−1.27880
$995$		−	4.32167e14i		−	0.443135i
$996$	−9.29321e13	+	1.03901e13i	−0.0948132	+	0.0106004i
$997$	−8.69673e14			−0.882836			−0.441418	−	0.897302i	$-0.645524\pi$
$997$	−8.69673e14			−0.882836			−0.441418	+	0.897302i	$0.645524\pi$
$998$			4.92045e14i			0.496996i
$999$	−2.86073e14	−	8.24357e14i	−0.287508	−	0.828491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.11.b.a.2.1	✓	2
3.2	odd	2	inner	3.11.b.a.2.2	yes	2
4.3	odd	2		48.11.e.c.17.2		2
5.2	odd	4		75.11.d.b.74.4		4
5.3	odd	4		75.11.d.b.74.1		4
5.4	even	2		75.11.c.d.26.2		2
8.3	odd	2		192.11.e.d.65.1		2
8.5	even	2		192.11.e.e.65.2		2
9.2	odd	6		81.11.d.d.53.2		4
9.4	even	3		81.11.d.d.26.2		4
9.5	odd	6		81.11.d.d.26.1		4
9.7	even	3		81.11.d.d.53.1		4
12.11	even	2		48.11.e.c.17.1		2
15.2	even	4		75.11.d.b.74.2		4
15.8	even	4		75.11.d.b.74.3		4
15.14	odd	2		75.11.c.d.26.1		2
24.5	odd	2		192.11.e.e.65.1		2
24.11	even	2		192.11.e.d.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.11.b.a.2.1	✓	2	1.1	even	1	trivial
3.11.b.a.2.2	yes	2	3.2	odd	2	inner
48.11.e.c.17.1		2	12.11	even	2
48.11.e.c.17.2		2	4.3	odd	2
75.11.c.d.26.1		2	15.14	odd	2
75.11.c.d.26.2		2	5.4	even	2
75.11.d.b.74.1		4	5.3	odd	4
75.11.d.b.74.2		4	15.2	even	4
75.11.d.b.74.3		4	15.8	even	4
75.11.d.b.74.4		4	5.2	odd	4
81.11.d.d.26.1		4	9.5	odd	6
81.11.d.d.26.2		4	9.4	even	3
81.11.d.d.53.1		4	9.7	even	3
81.11.d.d.53.2		4	9.2	odd	6
192.11.e.d.65.1		2	8.3	odd	2
192.11.e.d.65.2		2	24.11	even	2
192.11.e.e.65.1		2	24.5	odd	2
192.11.e.e.65.2		2	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-26.8328i q^{2} +(-27.0000 - 241.495i) q^{3} +304.000 q^{4} +2844.28i q^{5} +(-6480.00 + 724.486i) q^{6} +17234.0 q^{7} -35634.0i q^{8} +(-57591.0 + 13040.7i) q^{9} +O(q^{10})\)	\(q-26.8328i q^{2} +(-27.0000 - 241.495i) q^{3} +304.000 q^{4} +2844.28i q^{5} +(-6480.00 + 724.486i) q^{6} +17234.0 q^{7} -35634.0i q^{8} +(-57591.0 + 13040.7i) q^{9} +76320.0 q^{10} +186810. i q^{11} +(-8208.00 - 73414.6i) q^{12} -169654. q^{13} -462437. i q^{14} +(686880. - 76795.5i) q^{15} -644864. q^{16} +343245. i q^{17} +(349920. + 1.54533e6i) q^{18} -949462. q^{19} +864661. i q^{20} +(-465318. - 4.16193e6i) q^{21} +5.01264e6 q^{22} -2.65763e6i q^{23} +(-8.60544e6 + 962117. i) q^{24} +1.67570e6 q^{25} +4.55229e6i q^{26} +(4.70424e6 + 1.35559e7i) q^{27} +5.23914e6 q^{28} -3.18221e6i q^{29} +(-2.06064e6 - 1.84309e7i) q^{30} -2.97931e7 q^{31} -1.91857e7i q^{32} +(4.51138e7 - 5.04387e6i) q^{33} +9.21024e6 q^{34} +4.90183e7i q^{35} +(-1.75077e7 + 3.96439e6i) q^{36} -6.08118e7 q^{37} +2.54767e7i q^{38} +(4.58066e6 + 4.09707e7i) q^{39} +1.01353e8 q^{40} -1.81668e8i q^{41} +(-1.11676e8 + 1.24858e7i) q^{42} +1.07420e8 q^{43} +5.67903e7i q^{44} +(-3.70915e7 - 1.63805e8i) q^{45} -7.13117e7 q^{46} +2.67996e8i q^{47} +(1.74113e7 + 1.55732e8i) q^{48} +1.45355e7 q^{49} -4.49639e7i q^{50} +(8.28922e7 - 9.26763e6i) q^{51} -5.15748e7 q^{52} -1.92091e8i q^{53} +(3.63742e8 - 1.26228e8i) q^{54} -5.31340e8 q^{55} -6.14116e8i q^{56} +(2.56355e7 + 2.29291e8i) q^{57} -8.53877e7 q^{58} +6.49158e8i q^{59} +(2.08812e8 - 2.33458e7i) q^{60} +1.03079e9 q^{61} +7.99433e8i q^{62} +(-9.92523e8 + 2.24744e8i) q^{63} -1.17515e9 q^{64} -4.82543e8i q^{65} +(-1.35341e8 - 1.21053e9i) q^{66} +1.87674e9 q^{67} +1.04347e8i q^{68} +(-6.41805e8 + 7.17560e7i) q^{69} +1.31530e9 q^{70} -2.68338e9i q^{71} +(4.64694e8 + 2.05220e9i) q^{72} -2.84653e9 q^{73} +1.63175e9i q^{74} +(-4.52440e7 - 4.04675e8i) q^{75} -2.88636e8 q^{76} +3.21948e9i q^{77} +(1.09936e9 - 1.22912e8i) q^{78} +1.48865e9 q^{79} -1.83417e9i q^{80} +(3.14666e9 - 1.50206e9i) q^{81} -4.87467e9 q^{82} -1.26585e9i q^{83} +(-1.41457e8 - 1.26523e9i) q^{84} -9.76285e8 q^{85} -2.88237e9i q^{86} +(-7.68489e8 + 8.59197e7i) q^{87} +6.65679e9 q^{88} +6.02052e9i q^{89} +(-4.39535e9 + 9.95270e8i) q^{90} -2.92382e9 q^{91} -8.07919e8i q^{92} +(8.04414e8 + 7.19490e9i) q^{93} +7.19108e9 q^{94} -2.70053e9i q^{95} +(-4.63325e9 + 5.18013e8i) q^{96} -1.59295e9 q^{97} -3.90029e8i q^{98} +(-2.43614e9 - 1.07586e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9}+O(q^{10}) \) 2 * q - 54 * q^3 + 608 * q^4 - 12960 * q^6 + 34468 * q^7 - 115182 * q^9	\( 2 q - 54 q^{3} + 608 q^{4} - 12960 q^{6} + 34468 q^{7} - 115182 q^{9} + 152640 q^{10} - 16416 q^{12} - 339308 q^{13} + 1373760 q^{15} - 1289728 q^{16} + 699840 q^{18} - 1898924 q^{19} - 930636 q^{21} + 10025280 q^{22} - 17210880 q^{24} + 3351410 q^{25} + 9408474 q^{27} + 10478272 q^{28} - 4121280 q^{30} - 59586236 q^{31} + 90227520 q^{33} + 18420480 q^{34} - 35015328 q^{36} - 121623692 q^{37} + 9161316 q^{39} + 202705920 q^{40} - 223352640 q^{42} + 214839412 q^{43} - 74183040 q^{45} - 142623360 q^{46} + 34822656 q^{48} + 29071014 q^{49} + 165784320 q^{51} - 103149632 q^{52} + 727483680 q^{54} - 1062679680 q^{55} + 51270948 q^{57} - 170775360 q^{58} + 417623040 q^{60} + 2061587284 q^{61} - 1985046588 q^{63} - 2350292992 q^{64} - 270682560 q^{66} + 3753484948 q^{67} - 1283610240 q^{69} + 2630597760 q^{70} + 929387520 q^{72} - 5693056988 q^{73} - 90488070 q^{75} - 577272896 q^{76} + 2198715840 q^{78} + 2977295236 q^{79} + 6293324322 q^{81} - 9749335680 q^{82} - 282913344 q^{84} - 1952570880 q^{85} - 1536978240 q^{87} + 13313571840 q^{88} - 8790690240 q^{90} - 5847634072 q^{91} + 1608828372 q^{93} + 14382155520 q^{94} - 9266503680 q^{96} - 3185897852 q^{97} - 4872286080 q^{99}+O(q^{100}) \) 2 * q - 54 * q^3 + 608 * q^4 - 12960 * q^6 + 34468 * q^7 - 115182 * q^9 + 152640 * q^10 - 16416 * q^12 - 339308 * q^13 + 1373760 * q^15 - 1289728 * q^16 + 699840 * q^18 - 1898924 * q^19 - 930636 * q^21 + 10025280 * q^22 - 17210880 * q^24 + 3351410 * q^25 + 9408474 * q^27 + 10478272 * q^28 - 4121280 * q^30 - 59586236 * q^31 + 90227520 * q^33 + 18420480 * q^34 - 35015328 * q^36 - 121623692 * q^37 + 9161316 * q^39 + 202705920 * q^40 - 223352640 * q^42 + 214839412 * q^43 - 74183040 * q^45 - 142623360 * q^46 + 34822656 * q^48 + 29071014 * q^49 + 165784320 * q^51 - 103149632 * q^52 + 727483680 * q^54 - 1062679680 * q^55 + 51270948 * q^57 - 170775360 * q^58 + 417623040 * q^60 + 2061587284 * q^61 - 1985046588 * q^63 - 2350292992 * q^64 - 270682560 * q^66 + 3753484948 * q^67 - 1283610240 * q^69 + 2630597760 * q^70 + 929387520 * q^72 - 5693056988 * q^73 - 90488070 * q^75 - 577272896 * q^76 + 2198715840 * q^78 + 2977295236 * q^79 + 6293324322 * q^81 - 9749335680 * q^82 - 282913344 * q^84 - 1952570880 * q^85 - 1536978240 * q^87 + 13313571840 * q^88 - 8790690240 * q^90 - 5847634072 * q^91 + 1608828372 * q^93 + 14382155520 * q^94 - 9266503680 * q^96 - 3185897852 * q^97 - 4872286080 * q^99

Introduction

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