LMFDB - Embedded newform 5.19.c.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,19,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.2693068855$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1365649 x^{14} + 735328563216 x^{12} + \cdots + 22\!\cdots\!00 $ x^16 + 1365649x^14 + 735328563216x^12 + 196541937723225664x^10 + 26804517896227604816896x^8 + 1698608176414048875695308800x^6 + 38033703783600508125786931200000x^4 + 174469353400289826571825446912000000*x^2 + 223860255706571447791285331558400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{12}\cdot 5^{25} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.5
Root			$-49.9217i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.19.c.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.9217 + 17.9217i) q^{2} +(-4350.59 - 4350.59i) q^{3} +261502. i q^{4} +(823487. - 1.77104e6i) q^{5} +155940. q^{6} +(-2.28757e7 + 2.28757e7i) q^{7} +(-9.38460e6 - 9.38460e6i) q^{8} -3.49565e8i q^{9} +O(q^{10})$	\(q+(-17.9217 + 17.9217i) q^{2} +(-4350.59 - 4350.59i) q^{3} +261502. i q^{4} +(823487. - 1.77104e6i) q^{5} +155940. q^{6} +(-2.28757e7 + 2.28757e7i) q^{7} +(-9.38460e6 - 9.38460e6i) q^{8} -3.49565e8i q^{9} +(1.69817e7 + 4.64982e7i) q^{10} -3.44504e9 q^{11} +(1.13769e9 - 1.13769e9i) q^{12} +(-1.28620e10 - 1.28620e10i) q^{13} -8.19943e8i q^{14} +(-1.12877e10 + 4.12240e9i) q^{15} -6.82147e10 q^{16} +(7.38012e10 - 7.38012e10i) q^{17} +(6.26479e9 + 6.26479e9i) q^{18} +2.01754e11i q^{19} +(4.63129e11 + 2.15343e11i) q^{20} +1.99046e11 q^{21} +(6.17409e10 - 6.17409e10i) q^{22} +(1.37720e12 + 1.37720e12i) q^{23} +8.16572e10i q^{24} +(-2.45844e12 - 2.91685e12i) q^{25} +4.61018e11 q^{26} +(-3.20632e12 + 3.20632e12i) q^{27} +(-5.98204e12 - 5.98204e12i) q^{28} -8.04459e12i q^{29} +(1.28414e11 - 2.76175e11i) q^{30} -1.71564e13 q^{31} +(3.68264e12 - 3.68264e12i) q^{32} +(1.49880e13 + 1.49880e13i) q^{33} +2.64528e12i q^{34} +(2.16759e13 + 5.93516e13i) q^{35} +9.14119e13 q^{36} +(5.12010e13 - 5.12010e13i) q^{37} +(-3.61577e12 - 3.61577e12i) q^{38} +1.11915e14i q^{39} +(-2.43486e13 + 8.89237e12i) q^{40} -2.53066e14 q^{41} +(-3.56724e12 + 3.56724e12i) q^{42} +(1.26130e14 + 1.26130e14i) q^{43} -9.00884e14i q^{44} +(-6.19092e14 - 2.87862e14i) q^{45} -4.93633e13 q^{46} +(-5.46338e14 + 5.46338e14i) q^{47} +(2.96774e14 + 2.96774e14i) q^{48} +5.81816e14i q^{49} +(9.63341e13 + 8.21552e12i) q^{50} -6.42158e14 q^{51} +(3.36344e15 - 3.36344e15i) q^{52} +(3.15024e15 + 3.15024e15i) q^{53} -1.14925e14i q^{54} +(-2.83695e15 + 6.10129e15i) q^{55} +4.29359e14 q^{56} +(8.77751e14 - 8.77751e14i) q^{57} +(1.44172e14 + 1.44172e14i) q^{58} -8.70138e15i q^{59} +(-1.07801e15 - 2.95175e15i) q^{60} -1.20486e16 q^{61} +(3.07472e14 - 3.07472e14i) q^{62} +(7.99656e15 + 7.99656e15i) q^{63} -1.77501e16i q^{64} +(-3.33708e16 + 1.21874e16i) q^{65} -5.37219e14 q^{66} +(1.51370e16 - 1.51370e16i) q^{67} +(1.92991e16 + 1.92991e16i) q^{68} -1.19832e16i q^{69} +(-1.45215e15 - 6.75212e14i) q^{70} +6.47283e15 q^{71} +(-3.28053e15 + 3.28053e15i) q^{72} +(6.95564e16 + 6.95564e16i) q^{73} +1.83522e15i q^{74} +(-1.99437e15 + 2.33857e16i) q^{75} -5.27591e16 q^{76} +(7.88078e16 - 7.88078e16i) q^{77} +(-2.00570e15 - 2.00570e15i) q^{78} -9.20606e16i q^{79} +(-5.61739e16 + 1.20811e17i) q^{80} -1.07530e17 q^{81} +(4.53536e15 - 4.53536e15i) q^{82} +(-9.22119e16 - 9.22119e16i) q^{83} +5.20509e16i q^{84} +(-6.99302e16 - 1.91479e17i) q^{85} -4.52092e15 q^{86} +(-3.49987e16 + 3.49987e16i) q^{87} +(3.23304e16 + 3.23304e16i) q^{88} -5.82098e16i q^{89} +(1.62541e16 - 5.93620e15i) q^{90} +5.88456e17 q^{91} +(-3.60139e17 + 3.60139e17i) q^{92} +(7.46407e16 + 7.46407e16i) q^{93} -1.95826e16i q^{94} +(3.57314e17 + 1.66142e17i) q^{95} -3.20433e16 q^{96} +(2.01766e17 - 2.01766e17i) q^{97} +(-1.04271e16 - 1.04271e16i) q^{98} +1.20427e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	$ 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−17.9217	+	17.9217i	−0.0350033	+	0.0350033i	−0.724392	−	0.689389i	$-0.757879\pi$
$2$	−17.9217	+	17.9217i	−0.0350033	+	0.0350033i	0.689389	+	0.724392i	$0.257879\pi$
$3$	−4350.59	−	4350.59i	−0.221033	−	0.221033i	0.587900	−	0.808933i	$-0.299955\pi$
$3$	−4350.59	−	4350.59i	−0.221033	−	0.221033i	−0.808933	+	0.587900i	$0.799955\pi$
$4$			261502.i			0.997550i
$5$	823487.	−	1.77104e6i	0.421625	−	0.906770i
$5$	823487.	−	1.77104e6i	0.421625	−	0.906770i
$6$	155940.			0.0154738
$7$	−2.28757e7	+	2.28757e7i	−0.566882	+	0.566882i	−0.931254	−	0.364372i	$-0.881284\pi$
$7$	−2.28757e7	+	2.28757e7i	−0.566882	+	0.566882i	0.364372	+	0.931254i	$0.381284\pi$
$8$	−9.38460e6	−	9.38460e6i	−0.0699208	−	0.0699208i
$9$		−	3.49565e8i		−	0.902289i
$10$	1.69817e7	+	4.64982e7i	0.0169817	+	0.0464982i
$11$	−3.44504e9			−1.46103			−0.730517	−	0.682895i	$-0.760721\pi$
$11$	−3.44504e9			−1.46103			−0.730517	+	0.682895i	$0.760721\pi$
$12$	1.13769e9	−	1.13769e9i	0.220491	−	0.220491i
$13$	−1.28620e10	−	1.28620e10i	−1.21288	−	1.21288i	−0.970074	−	0.242808i	$-0.921931\pi$
$13$	−1.28620e10	−	1.28620e10i	−1.21288	−	1.21288i	−0.242808	−	0.970074i	$-0.578069\pi$
$14$		−	8.19943e8i		−	0.0396854i
$15$	−1.12877e10	+	4.12240e9i	−0.293619	+	0.107233i
$16$	−6.82147e10			−0.992655
$17$	7.38012e10	−	7.38012e10i	0.622334	−	0.622334i	−0.323794	−	0.946128i	$-0.604958\pi$
$17$	7.38012e10	−	7.38012e10i	0.622334	−	0.622334i	0.946128	+	0.323794i	$0.104958\pi$
$18$	6.26479e9	+	6.26479e9i	0.0315831	+	0.0315831i
$19$			2.01754e11i			0.625231i	0.949880	+	0.312615i	$0.101205\pi$
$19$			2.01754e11i			0.625231i	−0.949880	+	0.312615i	$0.898795\pi$
$20$	4.63129e11	+	2.15343e11i	0.904548	+	0.420592i
$21$	1.99046e11			0.250599
$22$	6.17409e10	−	6.17409e10i	0.0511410	−	0.0511410i
$23$	1.37720e12	+	1.37720e12i	0.764619	+	0.764619i	0.977154	−	0.212534i	$-0.0681717\pi$
$23$	1.37720e12	+	1.37720e12i	0.764619	+	0.764619i	−0.212534	+	0.977154i	$0.568172\pi$
$24$			8.16572e10i			0.0309096i
$25$	−2.45844e12	−	2.91685e12i	−0.644464	−	0.764634i
$26$	4.61018e11			0.0849097
$27$	−3.20632e12	+	3.20632e12i	−0.420469	+	0.420469i
$28$	−5.98204e12	−	5.98204e12i	−0.565493	−	0.565493i
$29$		−	8.04459e12i		−	0.554526i	−0.960794	−	0.277263i	$-0.910573\pi$
$29$		−	8.04459e12i		−	0.554526i	0.960794	−	0.277263i	$-0.0894273\pi$
$30$	1.28414e11	−	2.76175e11i	0.00652413	−	0.0140311i
$31$	−1.71564e13			−0.648891			−0.324446	−	0.945904i	$-0.605178\pi$
$31$	−1.71564e13			−0.648891			−0.324446	+	0.945904i	$0.605178\pi$
$32$	3.68264e12	−	3.68264e12i	0.104667	−	0.104667i
$33$	1.49880e13	+	1.49880e13i	0.322937	+	0.322937i
$34$			2.64528e12i			0.0435674i
$35$	2.16759e13	+	5.93516e13i	0.275020	+	0.753043i
$36$	9.14119e13			0.900078
$37$	5.12010e13	−	5.12010e13i	0.393970	−	0.393970i	−0.482130	−	0.876100i	$-0.660137\pi$
$37$	5.12010e13	−	5.12010e13i	0.393970	−	0.393970i	0.876100	+	0.482130i	$0.160137\pi$
$38$	−3.61577e12	−	3.61577e12i	−0.0218851	−	0.0218851i
$39$			1.11915e14i			0.536174i
$40$	−2.43486e13	+	8.89237e12i	−0.0928824	+	0.0339217i
$41$	−2.53066e14			−0.772999			−0.386500	−	0.922290i	$-0.626316\pi$
$41$	−2.53066e14			−0.772999			−0.386500	+	0.922290i	$0.626316\pi$
$42$	−3.56724e12	+	3.56724e12i	−0.00877179	+	0.00877179i
$43$	1.26130e14	+	1.26130e14i	0.250959	+	0.250959i	0.821364	−	0.570405i	$-0.193214\pi$
$43$	1.26130e14	+	1.26130e14i	0.250959	+	0.250959i	−0.570405	+	0.821364i	$0.693214\pi$
$44$		−	9.00884e14i		−	1.45745i
$45$	−6.19092e14	−	2.87862e14i	−0.818169	−	0.380428i
$46$	−4.93633e13			−0.0535284
$47$	−5.46338e14	+	5.46338e14i	−0.488181	+	0.488181i	−0.907732	−	0.419551i	$-0.862188\pi$
$47$	−5.46338e14	+	5.46338e14i	−0.488181	+	0.488181i	0.419551	+	0.907732i	$0.362188\pi$
$48$	2.96774e14	+	2.96774e14i	0.219409	+	0.219409i
$49$			5.81816e14i			0.357290i
$50$	9.63341e13	+	8.21552e12i	0.0493231	+	0.00420635i
$51$	−6.42158e14			−0.275113
$52$	3.36344e15	−	3.36344e15i	1.20991	−	1.20991i
$53$	3.15024e15	+	3.15024e15i	0.954688	+	0.954688i	0.999017	−	0.0443293i	$-0.0141151\pi$
$53$	3.15024e15	+	3.15024e15i	0.954688	+	0.954688i	−0.0443293	+	0.999017i	$0.514115\pi$
$54$		−	1.14925e14i		−	0.0294356i
$55$	−2.83695e15	+	6.10129e15i	−0.616009	+	1.32482i
$56$	4.29359e14			0.0792736
$57$	8.77751e14	−	8.77751e14i	0.138197	−	0.138197i
$58$	1.44172e14	+	1.44172e14i	0.0194102	+	0.0194102i
$59$		−	8.70138e15i		−	1.00443i	−0.864743	−	0.502215i	$-0.832518\pi$
$59$		−	8.70138e15i		−	1.00443i	0.864743	−	0.502215i	$-0.167482\pi$
$60$	−1.07801e15	−	2.95175e15i	−0.106970	−	0.292900i
$61$	−1.20486e16			−1.03031			−0.515156	−	0.857096i	$-0.672266\pi$
$61$	−1.20486e16			−1.03031			−0.515156	+	0.857096i	$0.672266\pi$
$62$	3.07472e14	−	3.07472e14i	0.0227133	−	0.0227133i
$63$	7.99656e15	+	7.99656e15i	0.511491	+	0.511491i
$64$		−	1.77501e16i		−	0.985327i
$65$	−3.33708e16	+	1.21874e16i	−1.61119	+	0.588424i
$66$	−5.37219e14			−0.0226077
$67$	1.51370e16	−	1.51370e16i	0.556375	−	0.556375i	−0.371898	−	0.928273i	$-0.621293\pi$
$67$	1.51370e16	−	1.51370e16i	0.556375	−	0.556375i	0.928273	+	0.371898i	$0.121293\pi$
$68$	1.92991e16	+	1.92991e16i	0.620809	+	0.620809i
$69$		−	1.19832e16i		−	0.338012i
$70$	−1.45215e15	−	6.75212e14i	−0.0359856	−	0.0167324i
$71$	6.47283e15			0.141179			0.0705893	−	0.997505i	$-0.477512\pi$
$71$	6.47283e15			0.141179			0.0705893	+	0.997505i	$0.477512\pi$
$72$	−3.28053e15	+	3.28053e15i	−0.0630887	+	0.0630887i
$73$	6.95564e16	+	6.95564e16i	1.18149	+	1.18149i	0.979358	+	0.202135i	$0.0647880\pi$
$73$	6.95564e16	+	6.95564e16i	1.18149	+	1.18149i	0.202135	+	0.979358i	$0.435212\pi$
$74$			1.83522e15i			0.0275805i
$75$	−1.99437e15	+	2.33857e16i	−0.0265616	+	0.311457i
$76$	−5.27591e16			−0.623699
$77$	7.88078e16	−	7.88078e16i	0.828234	−	0.828234i
$78$	−2.00570e15	−	2.00570e15i	−0.0187678	−	0.0187678i
$79$		−	9.20606e16i		−	0.768122i	−0.923308	−	0.384061i	$-0.874525\pi$
$79$		−	9.20606e16i		−	0.768122i	0.923308	−	0.384061i	$-0.125475\pi$
$80$	−5.61739e16	+	1.20811e17i	−0.418528	+	0.900110i
$81$	−1.07530e17			−0.716414
$82$	4.53536e15	−	4.53536e15i	0.0270575	−	0.0270575i
$83$	−9.22119e16	−	9.22119e16i	−0.493269	−	0.493269i	0.416065	−	0.909335i	$-0.363409\pi$
$83$	−9.22119e16	−	9.22119e16i	−0.493269	−	0.493269i	−0.909335	+	0.416065i	$0.863409\pi$
$84$			5.20509e16i			0.249985i
$85$	−6.99302e16	−	1.91479e17i	−0.301922	−	0.826705i
$86$	−4.52092e15			−0.0175688
$87$	−3.49987e16	+	3.49987e16i	−0.122569	+	0.122569i
$88$	3.23304e16	+	3.23304e16i	0.102157	+	0.102157i
$89$		−	5.82098e16i		−	0.166145i	−0.996544	−	0.0830723i	$-0.973527\pi$
$89$		−	5.82098e16i		−	0.166145i	0.996544	−	0.0830723i	$-0.0264732\pi$
$90$	1.62541e16	−	5.93620e15i	0.0419548	−	0.0153224i
$91$	5.88456e17			1.37512
$92$	−3.60139e17	+	3.60139e17i	−0.762746	+	0.762746i
$93$	7.46407e16	+	7.46407e16i	0.143426	+	0.143426i
$94$		−	1.95826e16i		−	0.0341758i
$95$	3.57314e17	+	1.66142e17i	0.566941	+	0.263613i
$96$	−3.20433e16			−0.0462697
$97$	2.01766e17	−	2.01766e17i	0.265400	−	0.265400i	−0.561843	−	0.827244i	$-0.689908\pi$
$97$	2.01766e17	−	2.01766e17i	0.265400	−	0.265400i	0.827244	+	0.561843i	$0.189908\pi$
$98$	−1.04271e16	−	1.04271e16i	−0.0125063	−	0.0125063i
$99$			1.20427e18i			1.31827i
$100$	7.62761e17	−	6.42885e17i	0.762761	−	0.642885i
$101$	−1.31780e17			−0.120492			−0.0602459	−	0.998184i	$-0.519188\pi$
$101$	−1.31780e17			−0.120492			−0.0602459	+	0.998184i	$0.519188\pi$
$102$	1.15085e16	−	1.15085e16i	0.00962984	−	0.00962984i
$103$	−1.81056e18	−	1.81056e18i	−1.38764	−	1.38764i	−0.830250	−	0.557391i	$-0.811802\pi$
$103$	−1.81056e18	−	1.81056e18i	−1.38764	−	1.38764i	−0.557391	−	0.830250i	$-0.688198\pi$
$104$			2.41410e17i			0.169611i
$105$	1.63912e17	−	3.52518e17i	0.105659	−	0.227236i
$106$	−1.12915e17			−0.0668344
$107$	−1.32011e18	+	1.32011e18i	−0.718054	+	0.718054i	−0.968206	−	0.250152i	$-0.919519\pi$
$107$	−1.32011e18	+	1.32011e18i	−0.718054	+	0.718054i	0.250152	+	0.968206i	$0.419519\pi$
$108$	−8.38459e17	−	8.38459e17i	−0.419438	−	0.419438i
$109$			3.99893e17i			0.184122i	0.995753	+	0.0920610i	$0.0293455\pi$
$109$			3.99893e17i			0.184122i	−0.995753	+	0.0920610i	$0.970655\pi$
$110$	−5.85025e16	−	1.60188e17i	−0.0248108	−	0.0679354i
$111$	−4.45509e17			−0.174161
$112$	1.56046e18	−	1.56046e18i	0.562718	−	0.562718i
$113$	3.44507e17	+	3.44507e17i	0.114681	+	0.114681i	0.762119	−	0.647437i	$-0.224159\pi$
$113$	3.44507e17	+	3.44507e17i	0.114681	+	0.114681i	−0.647437	+	0.762119i	$0.724159\pi$
$114$			3.14615e16i			0.00967467i
$115$	3.57317e18	−	1.30496e18i	1.01572	−	0.370951i
$116$	2.10367e18			0.553167
$117$	−4.49611e18	+	4.49611e18i	−1.09437	+	1.09437i
$118$	1.55943e17	+	1.55943e17i	0.0351584	+	0.0351584i
$119$			3.37651e18i			0.705579i
$120$	1.44618e17	+	6.72436e16i	0.0280279	+	0.0130323i
$121$	6.30839e18			1.13462
$122$	2.15932e17	−	2.15932e17i	0.0360643	−	0.0360643i
$123$	1.10099e18	+	1.10099e18i	0.170858	+	0.170858i
$124$		−	4.48644e18i		−	0.647301i
$125$	−7.19033e18	+	1.95199e18i	−0.965070	+	0.261992i
$126$	−2.86623e17			−0.0358077
$127$	6.81925e18	−	6.81925e18i	0.793420	−	0.793420i	−0.188629	−	0.982048i	$-0.560404\pi$
$127$	6.81925e18	−	6.81925e18i	0.793420	−	0.793420i	0.982048	+	0.188629i	$0.0604043\pi$
$128$	1.28349e18	+	1.28349e18i	0.139157	+	0.139157i
$129$		−	1.09748e18i		−	0.110940i
$130$	3.79642e17	−	8.16478e17i	0.0358001	−	0.0769936i
$131$	−2.12381e19			−1.86928			−0.934638	−	0.355602i	$-0.884276\pi$
$131$	−2.12381e19			−1.86928			−0.934638	+	0.355602i	$0.884276\pi$
$132$	−3.91938e18	+	3.91938e18i	−0.322145	+	0.322145i
$133$	−4.61528e18	−	4.61528e18i	−0.354432	−	0.354432i
$134$			5.42562e17i			0.0389499i
$135$	3.03815e18	+	8.31888e18i	0.203988	+	0.558549i
$136$	−1.38519e18			−0.0870281
$137$	1.37672e19	−	1.37672e19i	0.809769	−	0.809769i	−0.174830	−	0.984599i	$-0.555938\pi$
$137$	1.37672e19	−	1.37672e19i	0.809769	−	0.809769i	0.984599	+	0.174830i	$0.0559375\pi$
$138$	2.14760e17	+	2.14760e17i	0.0118315	+	0.0118315i
$139$		−	2.49560e19i		−	1.28837i	−0.764869	−	0.644186i	$-0.777196\pi$
$139$		−	2.49560e19i		−	1.28837i	0.764869	−	0.644186i	$-0.222804\pi$
$140$	−1.55205e19	+	5.66827e18i	−0.751198	+	0.274346i
$141$	4.75379e18			0.215808
$142$	−1.16004e17	+	1.16004e17i	−0.00494171	+	0.00494171i
$143$	4.43102e19	+	4.43102e19i	1.77206	+	1.77206i
$144$			2.38455e19i			0.895661i
$145$	−1.42472e19	−	6.62461e18i	−0.502827	−	0.233802i
$146$	−2.49313e18			−0.0827122
$147$	2.53124e18	−	2.53124e18i	0.0789729	−	0.0789729i
$148$	1.33891e19	+	1.33891e19i	0.393004	+	0.393004i
$149$		−	3.19234e19i		−	0.881928i	−0.897525	−	0.440964i	$-0.854637\pi$
$149$		−	3.19234e19i		−	0.881928i	0.897525	−	0.440964i	$-0.145363\pi$
$150$	−3.83368e17	−	4.54853e17i	−0.00997228	−	0.0118318i
$151$	3.10599e19			0.761041			0.380520	−	0.924773i	$-0.375745\pi$
$151$	3.10599e19			0.761041			0.380520	+	0.924773i	$0.375745\pi$
$152$	1.89338e18	−	1.89338e18i	0.0437166	−	0.0437166i
$153$	−2.57983e19	−	2.57983e19i	−0.561525	−	0.561525i
$154$			2.82474e18i			0.0579818i
$155$	−1.41281e19	+	3.03847e19i	−0.273589	+	0.588395i
$156$	−2.92659e19			−0.534860
$157$	−6.98700e18	+	6.98700e18i	−0.120557	+	0.120557i	−0.764812	−	0.644254i	$-0.777168\pi$
$157$	−6.98700e18	+	6.98700e18i	−0.120557	+	0.120557i	0.644254	+	0.764812i	$0.277168\pi$
$158$	1.64988e18	+	1.64988e18i	0.0268868	+	0.0268868i
$159$		−	2.74109e19i		−	0.422035i
$160$	−3.48948e18	−	9.55469e18i	−0.0507786	−	0.139039i
$161$	−6.30087e19			−0.866898
$162$	1.92712e18	−	1.92712e18i	0.0250768	−	0.0250768i
$163$	−3.44410e19	−	3.44410e19i	−0.424021	−	0.424021i	0.462565	−	0.886585i	$-0.346929\pi$
$163$	−3.44410e19	−	3.44410e19i	−0.424021	−	0.424021i	−0.886585	+	0.462565i	$0.846929\pi$
$164$		−	6.61772e19i		−	0.771105i
$165$	3.88866e19	−	1.42018e19i	0.428988	−	0.156671i
$166$	3.30518e18			0.0345321
$167$	1.97971e19	−	1.97971e19i	0.195954	−	0.195954i	−0.602309	−	0.798263i	$-0.705753\pi$
$167$	1.97971e19	−	1.97971e19i	0.195954	−	0.195954i	0.798263	+	0.602309i	$0.205753\pi$
$168$	−1.86797e18	−	1.86797e18i	−0.0175221	−	0.0175221i
$169$			2.18407e20i			1.94217i
$170$	4.68489e18	+	2.17835e18i	0.0395056	+	0.0183691i
$171$	7.05263e19			0.564139
$172$	−3.29832e19	+	3.29832e19i	−0.250344	+	0.250344i
$173$	−6.32613e19	−	6.32613e19i	−0.455747	−	0.455747i	0.441510	−	0.897256i	$-0.354443\pi$
$173$	−6.32613e19	−	6.32613e19i	−0.455747	−	0.455747i	−0.897256	+	0.441510i	$0.854443\pi$
$174$		−	1.25447e18i		−	0.00858060i
$175$	1.22964e20	+	1.04865e19i	0.798793	+	0.0681223i
$176$	2.35003e20			1.45030
$177$	−3.78562e19	+	3.78562e19i	−0.222012	+	0.222012i
$178$	1.04322e18	+	1.04322e18i	0.00581560	+	0.00581560i
$179$			1.33625e20i			0.708287i	0.935191	+	0.354144i	$0.115228\pi$
$179$			1.33625e20i			0.708287i	−0.935191	+	0.354144i	$0.884772\pi$
$180$	7.52765e19	−	1.61894e20i	0.379496	−	0.816164i
$181$	−1.77842e20			−0.852956			−0.426478	−	0.904498i	$-0.640246\pi$
$181$	−1.77842e20			−0.852956			−0.426478	+	0.904498i	$0.640246\pi$
$182$	−1.05461e19	+	1.05461e19i	−0.0481338	+	0.0481338i
$183$	5.24187e19	+	5.24187e19i	0.227733	+	0.227733i
$184$		−	2.58489e19i		−	0.106926i
$185$	−4.85154e19	−	1.32842e20i	−0.191132	−	0.523348i
$186$	−2.67537e18			−0.0100408
$187$	−2.54248e20	+	2.54248e20i	−0.909250	+	0.909250i
$188$	−1.42868e20	−	1.42868e20i	−0.486984	−	0.486984i
$189$		−	1.46694e20i		−	0.476712i
$190$	−9.38120e18	+	3.42612e18i	−0.0290721	+	0.0106175i
$191$	2.08262e20			0.615615			0.307807	−	0.951449i	$-0.400405\pi$
$191$	2.08262e20			0.615615			0.307807	+	0.951449i	$0.400405\pi$
$192$	−7.72234e19	+	7.72234e19i	−0.217790	+	0.217790i
$193$	−4.06606e20	−	4.06606e20i	−1.09436	−	1.09436i	−0.995058	−	0.0992976i	$-0.968340\pi$
$193$	−4.06606e20	−	4.06606e20i	−1.09436	−	1.09436i	−0.0992976	−	0.995058i	$-0.531660\pi$
$194$			7.23196e18i			0.0185798i
$195$	1.98205e20	+	9.21603e19i	0.486187	+	0.226065i
$196$	−1.52146e20			−0.356414
$197$	3.57983e20	−	3.57983e20i	0.801063	−	0.801063i	−0.182198	−	0.983262i	$-0.558321\pi$
$197$	3.57983e20	−	3.57983e20i	0.801063	−	0.801063i	0.983262	+	0.182198i	$0.0583213\pi$
$198$	−2.15825e19	−	2.15825e19i	−0.0461439	−	0.0461439i
$199$			5.92872e20i			1.21139i	0.795698	+	0.605694i	$0.207104\pi$
$199$			5.92872e20i			1.21139i	−0.795698	+	0.605694i	$0.792896\pi$
$200$	−4.30202e18	+	5.04449e19i	−0.00840239	+	0.0985252i
$201$	−1.31710e20			−0.245955
$202$	2.36172e18	−	2.36172e18i	0.00421760	−	0.00421760i
$203$	1.84026e20	+	1.84026e20i	0.314351	+	0.314351i
$204$		−	1.67925e20i		−	0.274438i
$205$	−2.08396e20	+	4.48189e20i	−0.325916	+	0.700932i
$206$	6.48964e19			0.0971439
$207$	4.81420e20	−	4.81420e20i	0.689908	−	0.689908i
$208$	8.77378e20	+	8.77378e20i	1.20397	+	1.20397i
$209$		−	6.95052e20i		−	0.913483i
$210$	3.38013e18	+	9.25528e18i	0.00425559	+	0.0116524i
$211$	4.03388e20			0.486610			0.243305	−	0.969950i	$-0.421768\pi$
$211$	4.03388e20			0.486610			0.243305	+	0.969950i	$0.421768\pi$
$212$	−8.23794e20	+	8.23794e20i	−0.952348	+	0.952348i
$213$	−2.81606e19	−	2.81606e19i	−0.0312051	−	0.0312051i
$214$		−	4.73173e19i		−	0.0502685i
$215$	3.27247e20	−	1.19514e20i	0.333373	−	0.121751i
$216$	6.01802e19			0.0587990
$217$	3.92466e20	−	3.92466e20i	0.367845	−	0.367845i
$218$	−7.16676e18	−	7.16676e18i	−0.00644487	−	0.00644487i
$219$		−	6.05223e20i		−	0.522298i
$220$	−1.59550e21	−	7.41866e20i	−1.32158	−	0.614499i
$221$	−1.89846e21			−1.50964
$222$	7.98427e18	−	7.98427e18i	0.00609619	−	0.00609619i
$223$	7.12304e20	+	7.12304e20i	0.522302	+	0.522302i	0.918266	−	0.395964i	$-0.129590\pi$
$223$	7.12304e20	+	7.12304e20i	0.522302	+	0.522302i	−0.395964	+	0.918266i	$0.629590\pi$
$224$			1.68486e20i			0.118668i
$225$	−1.01963e21	+	8.59384e20i	−0.689921	+	0.581493i
$226$	−1.23483e19			−0.00802843
$227$	1.30740e21	−	1.30740e21i	0.816913	−	0.816913i	−0.168746	−	0.985660i	$-0.553972\pi$
$227$	1.30740e21	−	1.30740e21i	0.816913	−	0.816913i	0.985660	+	0.168746i	$0.0539718\pi$
$228$	2.29533e20	+	2.29533e20i	0.137858	+	0.137858i
$229$		−	1.94851e21i		−	1.12508i	−0.826771	−	0.562539i	$-0.809825\pi$
$229$		−	1.94851e21i		−	1.12508i	0.826771	−	0.562539i	$-0.190175\pi$
$230$	−4.06500e19	+	8.74242e19i	−0.0225689	+	0.0485379i
$231$	−6.85722e20			−0.366134
$232$	−7.54953e19	+	7.54953e19i	−0.0387729	+	0.0387729i
$233$	−1.79626e20	−	1.79626e20i	−0.0887497	−	0.0887497i	0.661338	−	0.750088i	$-0.269989\pi$
$233$	−1.79626e20	−	1.79626e20i	−0.0887497	−	0.0887497i	−0.750088	+	0.661338i	$0.769989\pi$
$234$		−	1.61156e20i		−	0.0766131i
$235$	5.17682e20	+	1.41749e21i	0.236838	+	0.648497i
$236$	2.27543e21			1.00197
$237$	−4.00518e20	+	4.00518e20i	−0.169780	+	0.169780i
$238$	−6.05128e19	−	6.05128e19i	−0.0246976	−	0.0246976i
$239$			4.17235e21i			1.63983i	0.572484	+	0.819916i	$0.305980\pi$
$239$			4.17235e21i			1.63983i	−0.572484	+	0.819916i	$0.694020\pi$
$240$	7.69988e20	−	2.81208e20i	0.291463	−	0.106445i
$241$	−9.43413e20			−0.343992			−0.171996	−	0.985098i	$-0.555022\pi$
$241$	−9.43413e20			−0.343992			−0.171996	+	0.985098i	$0.555022\pi$
$242$	−1.13057e20	+	1.13057e20i	−0.0397154	+	0.0397154i
$243$	1.71001e21	+	1.71001e21i	0.578820	+	0.578820i
$244$		−	3.15074e21i		−	1.02779i
$245$	1.03042e21	+	4.79117e20i	0.323980	+	0.150642i
$246$	−3.94631e19			−0.0119612
$247$	2.59497e21	−	2.59497e21i	0.758331	−	0.758331i
$248$	1.61006e20	+	1.61006e20i	0.0453710	+	0.0453710i
$249$			8.02353e20i			0.218058i
$250$	9.38798e19	−	1.63846e20i	0.0246100	−	0.0429512i
$251$	−1.18545e20			−0.0299793			−0.0149896	−	0.999888i	$-0.504772\pi$
$251$	−1.18545e20			−0.0299793			−0.0149896	+	0.999888i	$0.504772\pi$
$252$	−2.09111e21	+	2.09111e21i	−0.510238	+	0.510238i
$253$	−4.74450e21	−	4.74450e21i	−1.11714	−	1.11714i
$254$			2.44425e20i			0.0555445i
$255$	−5.28809e20	+	1.13728e21i	−0.115994	+	0.249464i
$256$	4.60707e21			0.975585
$257$	−4.99285e21	+	4.99285e21i	−1.02082	+	1.02082i	−0.0210447	+	0.999779i	$0.506699\pi$
$257$	−4.99285e21	+	4.99285e21i	−1.02082	+	1.02082i	−0.999779	+	0.0210447i	$0.993301\pi$
$258$	1.96687e19	+	1.96687e19i	0.00388328	+	0.00388328i
$259$			2.34252e21i			0.446669i
$260$	−3.18702e21	−	8.72651e21i	−0.586982	−	1.60724i
$261$	−2.81211e21			−0.500342
$262$	3.80622e20	−	3.80622e20i	0.0654307	−	0.0654307i
$263$	−5.20562e21	−	5.20562e21i	−0.864711	−	0.864711i	0.127170	−	0.991881i	$-0.459411\pi$
$263$	−5.20562e21	−	5.20562e21i	−0.864711	−	0.864711i	−0.991881	+	0.127170i	$0.959411\pi$
$264$		−	2.81312e20i		−	0.0451600i
$265$	8.17338e21	−	2.98501e21i	1.26820	−	0.463162i
$266$	1.65427e20			0.0248126
$267$	−2.53247e20	+	2.53247e20i	−0.0367234	+	0.0367234i
$268$	3.95836e21	+	3.95836e21i	0.555012	+	0.555012i
$269$			4.04520e21i			0.548490i	0.961660	+	0.274245i	$0.0884280\pi$
$269$			4.04520e21i			0.548490i	−0.961660	+	0.274245i	$0.911572\pi$
$270$	−2.03537e20	−	9.46396e19i	−0.0266913	−	0.0124108i
$271$	−3.48313e20			−0.0441820			−0.0220910	−	0.999756i	$-0.507032\pi$
$271$	−3.48313e20			−0.0441820			−0.0220910	+	0.999756i	$0.507032\pi$
$272$	−5.03433e21	+	5.03433e21i	−0.617762	+	0.617762i
$273$	−2.56013e21	−	2.56013e21i	−0.303948	−	0.303948i
$274$			4.93463e20i			0.0566891i
$275$	8.46941e21	+	1.00487e22i	0.941584	+	1.11716i
$276$	3.13364e21			0.337184
$277$	7.63130e21	−	7.63130e21i	0.794842	−	0.794842i	−0.187435	−	0.982277i	$-0.560017\pi$
$277$	7.63130e21	−	7.63130e21i	0.794842	−	0.794842i	0.982277	+	0.187435i	$0.0600174\pi$
$278$	4.47253e20	+	4.47253e20i	0.0450972	+	0.0450972i
$279$			5.99729e21i			0.585487i
$280$	3.53572e20	−	7.60411e20i	0.0334238	−	0.0718830i
$281$	4.71960e21			0.432064			0.216032	−	0.976386i	$-0.430688\pi$
$281$	4.71960e21			0.432064			0.216032	+	0.976386i	$0.430688\pi$
$282$	−8.51958e19	+	8.51958e19i	−0.00755399	+	0.00755399i
$283$	−4.04292e21	−	4.04292e21i	−0.347230	−	0.347230i	0.511847	−	0.859077i	$-0.328962\pi$
$283$	−4.04292e21	−	4.04292e21i	−0.347230	−	0.347230i	−0.859077	+	0.511847i	$0.828962\pi$
$284$			1.69265e21i			0.140833i
$285$	−8.31712e20	−	2.27734e21i	−0.0670454	−	0.183580i
$286$	−1.58822e21			−0.124056
$287$	5.78907e21	−	5.78907e21i	0.438199	−	0.438199i
$288$	−1.28732e21	−	1.28732e21i	−0.0944398	−	0.0944398i
$289$			3.16985e21i			0.225402i
$290$	3.74059e20	−	1.36610e20i	0.0257844	−	0.00941676i
$291$	−1.75560e21			−0.117325
$292$	−1.81891e22	+	1.81891e22i	−1.17860	+	1.17860i
$293$	2.21167e21	+	2.21167e21i	0.138967	+	0.138967i	0.773168	−	0.634201i	$-0.218671\pi$
$293$	2.21167e21	+	2.21167e21i	0.138967	+	0.138967i	−0.634201	+	0.773168i	$0.718671\pi$
$294$			9.07282e19i			0.00552862i
$295$	−1.54105e22	−	7.16547e21i	−0.910788	−	0.423493i
$296$	−9.61002e20			−0.0550933
$297$	1.10459e22	−	1.10459e22i	0.614319	−	0.614319i
$298$	5.72121e20	+	5.72121e20i	0.0308703	+	0.0308703i
$299$		−	3.54270e22i		−	1.85479i
$300$	−6.11539e21	−	5.21530e20i	−0.310694	−	0.0264965i
$301$	−5.77064e21			−0.284528
$302$	−5.56646e20	+	5.56646e20i	−0.0266389	+	0.0266389i
$303$	5.73321e20	+	5.73321e20i	0.0266327	+	0.0266327i
$304$		−	1.37626e22i		−	0.620638i
$305$	−9.92189e21	+	2.13386e22i	−0.434406	+	0.934257i
$306$	9.24698e20			0.0393104
$307$	1.22602e20	−	1.22602e20i	0.00506119	−	0.00506119i	−0.704572	−	0.709633i	$-0.748861\pi$
$307$	1.22602e20	−	1.22602e20i	0.00506119	−	0.00506119i	0.709633	+	0.704572i	$0.248861\pi$
$308$	2.06084e22	+	2.06084e22i	0.826204	+	0.826204i
$309$			1.57540e22i			0.613429i
$310$	−2.91345e20	−	7.97743e20i	−0.0110192	−	0.0301723i
$311$	−2.80730e22			−1.03144			−0.515722	−	0.856756i	$-0.672476\pi$
$311$	−2.80730e22			−1.03144			−0.515722	+	0.856756i	$0.672476\pi$
$312$	1.05028e21	−	1.05028e21i	0.0374897	−	0.0374897i
$313$	1.81130e22	+	1.81130e22i	0.628189	+	0.628189i	0.947612	−	0.319423i	$-0.103489\pi$
$313$	1.81130e22	+	1.81130e22i	0.628189	+	0.628189i	−0.319423	+	0.947612i	$0.603489\pi$
$314$		−	2.50437e20i		−	0.00843981i
$315$	2.07472e22	−	7.57713e21i	0.679463	−	0.248147i
$316$	2.40740e22			0.766240
$317$	3.06039e22	−	3.06039e22i	0.946767	−	0.946767i	−0.0518857	−	0.998653i	$-0.516523\pi$
$317$	3.06039e22	−	3.06039e22i	0.946767	−	0.946767i	0.998653	+	0.0518857i	$0.0165232\pi$
$318$	4.91248e20	+	4.91248e20i	0.0147726	+	0.0147726i
$319$			2.77139e22i			0.810181i
$320$	−3.14360e22	−	1.46170e22i	−0.893465	−	0.415439i
$321$	1.14866e22			0.317427
$322$	1.12922e21	−	1.12922e21i	0.0303443	−	0.0303443i
$323$	1.48897e22	+	1.48897e22i	0.389102	+	0.389102i
$324$		−	2.81192e22i		−	0.714658i
$325$	−5.89611e21	+	6.91370e22i	−0.145752	+	1.70907i
$326$	1.23448e21			0.0296842
$327$	1.73977e21	−	1.73977e21i	0.0406971	−	0.0406971i
$328$	2.37492e21	+	2.37492e21i	0.0540487	+	0.0540487i
$329$		−	2.49958e22i		−	0.553482i
$330$	−4.42393e20	+	9.51434e20i	−0.00953197	+	0.0205000i
$331$	−8.16141e22			−1.71125			−0.855624	−	0.517598i	$-0.826826\pi$
$331$	−8.16141e22			−1.71125			−0.855624	+	0.517598i	$0.826826\pi$
$332$	2.41136e22	−	2.41136e22i	0.492061	−	0.492061i
$333$	−1.78981e22	−	1.78981e22i	−0.355475	−	0.355475i
$334$			7.09595e20i			0.0137181i
$335$	−1.43431e22	−	3.92734e22i	−0.269922	−	0.739086i
$336$	−1.35779e22			−0.248759
$337$	−3.47142e22	+	3.47142e22i	−0.619210	+	0.619210i	−0.945329	−	0.326119i	$-0.894259\pi$
$337$	−3.47142e22	+	3.47142e22i	−0.619210	+	0.619210i	0.326119	+	0.945329i	$0.394259\pi$
$338$	−3.91423e21	−	3.91423e21i	−0.0679822	−	0.0679822i
$339$		−	2.99762e21i		−	0.0506967i
$340$	5.00720e22	−	1.82869e22i	0.824679	−	0.301182i
$341$	5.91047e22			0.948052
$342$	−1.26395e21	+	1.26395e21i	−0.0197467	+	0.0197467i
$343$	−5.05606e22	−	5.05606e22i	−0.769423	−	0.769423i
$344$		−	2.36736e21i		−	0.0350945i
$345$	−2.12227e22	−	9.86804e21i	−0.306500	−	0.142515i
$346$	2.26750e21			0.0319052
$347$	−6.24411e22	+	6.24411e22i	−0.856062	+	0.856062i	−0.990872	−	0.134809i	$-0.956958\pi$
$347$	−6.24411e22	+	6.24411e22i	−0.856062	+	0.856062i	0.134809	+	0.990872i	$0.456958\pi$
$348$	−9.15222e21	−	9.15222e21i	−0.122268	−	0.122268i
$349$			1.60184e22i			0.208540i	0.994549	+	0.104270i	$0.0332506\pi$
$349$			1.60184e22i			0.208540i	−0.994549	+	0.104270i	$0.966749\pi$
$350$	−2.39165e21	+	2.01578e21i	−0.0303448	+	0.0255758i
$351$	8.24796e22			1.01996
$352$	−1.26868e22	+	1.26868e22i	−0.152922	+	0.152922i
$353$	5.34118e22	+	5.34118e22i	0.627574	+	0.627574i	0.947457	−	0.319883i	$-0.103644\pi$
$353$	5.34118e22	+	5.34118e22i	0.627574	+	0.627574i	−0.319883	+	0.947457i	$0.603644\pi$
$354$		−	1.35689e21i		−	0.0155423i
$355$	5.33029e21	−	1.14636e22i	0.0595245	−	0.128017i
$356$	1.52220e22			0.165737
$357$	1.46898e22	−	1.46898e22i	0.155956	−	0.155956i
$358$	−2.39478e21	−	2.39478e21i	−0.0247924	−	0.0247924i
$359$			4.17521e22i			0.421530i	0.977537	+	0.210765i	$0.0675955\pi$
$359$			4.17521e22i			0.421530i	−0.977537	+	0.210765i	$0.932404\pi$
$360$	3.10846e21	+	8.51141e21i	0.0306072	+	0.0838068i
$361$	6.34226e22			0.609087
$362$	3.18722e21	−	3.18722e21i	0.0298563	−	0.0298563i
$363$	−2.74453e22	−	2.74453e22i	−0.250789	−	0.250789i
$364$			1.53882e23i			1.37175i
$365$	1.80466e23	−	6.59080e22i	1.56949	−	0.573195i
$366$	−1.87886e21			−0.0159428
$367$	5.30413e22	−	5.30413e22i	0.439157	−	0.439157i	−0.452571	−	0.891728i	$-0.649493\pi$
$367$	5.30413e22	−	5.30413e22i	0.439157	−	0.439157i	0.891728	+	0.452571i	$0.149493\pi$
$368$	−9.39451e22	−	9.39451e22i	−0.759003	−	0.759003i
$369$			8.84630e22i			0.697468i
$370$	3.25023e21	+	1.51128e21i	0.0250091	+	0.0116286i
$371$	−1.44128e23			−1.08239
$372$	−1.95187e22	+	1.95187e22i	−0.143075	+	0.143075i
$373$	−7.71413e22	−	7.71413e22i	−0.551960	−	0.551960i	0.375046	−	0.927006i	$-0.377627\pi$
$373$	−7.71413e22	−	7.71413e22i	−0.551960	−	0.551960i	−0.927006	+	0.375046i	$0.877627\pi$
$374$		−	9.11311e21i		−	0.0636535i
$375$	3.97745e22	+	2.27899e22i	0.271221	+	0.155404i
$376$	1.02543e22			0.0682679
$377$	−1.03470e23	+	1.03470e23i	−0.672575	+	0.672575i
$378$	2.62900e21	+	2.62900e21i	0.0166865	+	0.0166865i
$379$		−	2.25074e23i		−	1.39500i	−0.716586	−	0.697498i	$-0.754296\pi$
$379$		−	2.25074e23i		−	1.39500i	0.716586	−	0.697498i	$-0.245704\pi$
$380$	−4.34464e22	+	9.34382e22i	−0.262967	+	0.565551i
$381$	−5.93355e22			−0.350744
$382$	−3.73240e21	+	3.73240e21i	−0.0215485	+	0.0215485i
$383$	−5.10893e22	−	5.10893e22i	−0.288098	−	0.288098i	0.548229	−	0.836328i	$-0.315302\pi$
$383$	−5.10893e22	−	5.10893e22i	−0.288098	−	0.288098i	−0.836328	+	0.548229i	$0.815302\pi$
$384$		−	1.11679e22i		−	0.0615164i
$385$	−7.46743e22	−	2.04469e23i	−0.401813	−	1.10022i
$386$	1.45741e22			0.0766120
$387$	4.40907e22	−	4.40907e22i	0.226437	−	0.226437i
$388$	5.27621e22	+	5.27621e22i	0.264750	+	0.264750i
$389$			1.05886e23i			0.519151i	0.965723	+	0.259576i	$0.0835827\pi$
$389$			1.05886e23i			0.519151i	−0.965723	+	0.259576i	$0.916417\pi$
$390$	−5.20383e21	+	1.90050e21i	−0.0249311	+	0.00910513i
$391$	2.03278e23			0.951697
$392$	5.46011e21	−	5.46011e21i	0.0249820	−	0.0249820i
$393$	9.23982e22	+	9.23982e22i	0.413172	+	0.413172i
$394$			1.28313e22i			0.0560797i
$395$	−1.63043e23	−	7.58107e22i	−0.696510	−	0.323860i
$396$	−3.14918e23			−1.31504
$397$	1.00470e22	−	1.00470e22i	0.0410131	−	0.0410131i	−0.686303	−	0.727316i	$-0.740768\pi$
$397$	1.00470e22	−	1.00470e22i	0.0410131	−	0.0410131i	0.727316	+	0.686303i	$0.240768\pi$
$398$	−1.06253e22	−	1.06253e22i	−0.0424025	−	0.0424025i
$399$			4.01584e22i			0.156682i
$400$	1.67701e23	+	1.98972e23i	0.639730	+	0.759018i
$401$	4.72173e23			1.76117			0.880585	−	0.473887i	$-0.157150\pi$
$401$	4.72173e23			1.76117			0.880585	+	0.473887i	$0.157150\pi$
$402$	2.36047e21	−	2.36047e21i	0.00860921	−	0.00860921i
$403$	2.20666e23	+	2.20666e23i	0.787029	+	0.787029i
$404$		−	3.44607e22i		−	0.120196i
$405$	−8.85494e22	+	1.90439e23i	−0.302058	+	0.649623i
$406$	−6.59610e21			−0.0220066
$407$	−1.76390e23	+	1.76390e23i	−0.575603	+	0.575603i
$408$	6.02640e21	+	6.02640e21i	0.0192361	+	0.0192361i
$409$		−	4.81782e23i		−	1.50432i	−0.658979	−	0.752161i	$-0.729011\pi$
$409$		−	4.81782e23i		−	1.50432i	0.658979	−	0.752161i	$-0.270989\pi$
$410$	−4.29748e21	−	1.17671e22i	−0.0131268	−	0.0359430i
$411$	−1.19791e23			−0.357971
$412$	4.73464e23	−	4.73464e23i	1.38424	−	1.38424i
$413$	1.99050e23	+	1.99050e23i	0.569394	+	0.569394i
$414$			1.72557e22i			0.0482980i
$415$	−2.39246e23	+	8.73753e22i	−0.655257	+	0.239307i
$416$	−9.47323e22			−0.253897
$417$	−1.08573e23	+	1.08573e23i	−0.284773	+	0.284773i
$418$	1.24565e22	+	1.24565e22i	0.0319749	+	0.0319749i
$419$			9.25562e22i			0.232530i	0.993218	+	0.116265i	$0.0370922\pi$
$419$			9.25562e22i			0.232530i	−0.993218	+	0.116265i	$0.962908\pi$
$420$	9.21839e22	+	4.28632e22i	0.226679	+	0.105400i
$421$	−7.90918e23			−1.90367			−0.951837	−	0.306603i	$-0.900807\pi$
$421$	−7.90918e23			−1.90367			−0.951837	+	0.306603i	$0.900807\pi$
$422$	−7.22940e21	+	7.22940e21i	−0.0170330	+	0.0170330i
$423$	1.90981e23	+	1.90981e23i	0.440480	+	0.440480i
$424$		−	5.91276e22i		−	0.133505i
$425$	−3.96703e23	−	3.38314e22i	−0.876929	−	0.0747859i
$426$	1.00937e21			0.00218456
$427$	2.75621e23	−	2.75621e23i	0.584066	−	0.584066i
$428$	−3.45212e23	−	3.45212e23i	−0.716295	−	0.716295i
$429$		−	3.85551e23i		−	0.783369i
$430$	−3.72292e21	+	8.00672e21i	−0.00740743	+	0.0159308i
$431$	1.84427e23			0.359360			0.179680	−	0.983725i	$-0.442494\pi$
$431$	1.84427e23			0.359360			0.179680	+	0.983725i	$0.442494\pi$
$432$	2.18719e23	−	2.18719e23i	0.417380	−	0.417380i
$433$	−2.72070e23	−	2.72070e23i	−0.508499	−	0.508499i	0.405567	−	0.914065i	$-0.367074\pi$
$433$	−2.72070e23	−	2.72070e23i	−0.508499	−	0.508499i	−0.914065	+	0.405567i	$0.867074\pi$
$434$			1.40673e22i			0.0257515i
$435$	3.31630e22	+	9.08050e22i	0.0594635	+	0.162819i
$436$	−1.04573e23			−0.183671
$437$	−2.77855e23	+	2.77855e23i	−0.478064	+	0.478064i
$438$	1.08466e22	+	1.08466e22i	0.0182821	+	0.0182821i
$439$			7.73505e23i			1.27727i	0.769510	+	0.638634i	$0.220500\pi$
$439$			7.73505e23i			1.27727i	−0.769510	+	0.638634i	$0.779500\pi$
$440$	8.38818e22	−	3.06346e22i	0.135704	−	0.0495608i
$441$	2.03382e23			0.322379
$442$	3.40237e22	−	3.40237e22i	0.0528422	−	0.0528422i
$443$	7.07437e23	+	7.07437e23i	1.07660	+	1.07660i	0.996812	+	0.0797884i	$0.0254245\pi$
$443$	7.07437e23	+	7.07437e23i	1.07660	+	1.07660i	0.0797884	+	0.996812i	$0.474576\pi$
$444$		−	1.16501e23i		−	0.173734i
$445$	−1.03092e23	−	4.79350e22i	−0.150655	−	0.0700507i
$446$	−2.55313e22			−0.0365645
$447$	−1.38886e23	+	1.38886e23i	−0.194935	+	0.194935i
$448$	4.06046e23	+	4.06046e23i	0.558564	+	0.558564i
$449$		−	6.54871e23i		−	0.882955i	−0.897272	−	0.441477i	$-0.854455\pi$
$449$		−	6.54871e23i		−	0.882955i	0.897272	−	0.441477i	$-0.145545\pi$
$450$	2.87186e21	−	3.36750e22i	0.00379534	−	0.0445036i
$451$	8.71823e23			1.12938
$452$	−9.00892e22	+	9.00892e22i	−0.114400	+	0.114400i
$453$	−1.35129e23	−	1.35129e23i	−0.168215	−	0.168215i
$454$			4.68616e22i			0.0571893i
$455$	4.84586e23	−	1.04218e24i	0.579786	−	1.24692i
$456$	−1.64747e22			−0.0193256
$457$	−6.09261e23	+	6.09261e23i	−0.700741	+	0.700741i	−0.964569	−	0.263829i	$-0.915015\pi$
$457$	−6.09261e23	+	6.09261e23i	−0.700741	+	0.700741i	0.263829	+	0.964569i	$0.415015\pi$
$458$	3.49205e22	+	3.49205e22i	0.0393814	+	0.0393814i
$459$			4.73261e23i			0.523344i
$460$	3.41249e23	+	9.34389e23i	0.370042	+	1.01323i
$461$	4.15799e23			0.442156			0.221078	−	0.975256i	$-0.429043\pi$
$461$	4.15799e23			0.442156			0.221078	+	0.975256i	$0.429043\pi$
$462$	1.22893e22	−	1.22893e22i	0.0128159	−	0.0128159i
$463$	−1.08387e24	−	1.08387e24i	−1.10853	−	1.10853i	−0.993343	−	0.115191i	$-0.963252\pi$
$463$	−1.08387e24	−	1.08387e24i	−1.10853	−	1.10853i	−0.115191	−	0.993343i	$-0.536748\pi$
$464$			5.48759e23i			0.550453i
$465$	1.93657e23	−	7.07257e22i	0.190527	−	0.0695826i
$466$	6.43841e21			0.00621306
$467$	−1.91479e23	+	1.91479e23i	−0.181247	+	0.181247i	−0.791899	−	0.610652i	$-0.790907\pi$
$467$	−1.91479e23	+	1.91479e23i	−0.181247	+	0.181247i	0.610652	+	0.791899i	$0.290907\pi$
$468$	−1.17574e24	−	1.17574e24i	−1.09169	−	1.09169i
$469$			6.92541e23i			0.630798i
$470$	−3.46814e22	−	1.61260e22i	−0.0309896	−	0.0144094i
$471$	6.07952e22			0.0532943
$472$	−8.16590e22	+	8.16590e22i	−0.0702306	+	0.0702306i
$473$	−4.34523e23	−	4.34523e23i	−0.366660	−	0.366660i
$474$		−	1.43559e22i		−	0.0118857i
$475$	5.88487e23	−	4.96000e23i	0.478073	−	0.402939i
$476$	−8.82964e23			−0.703850
$477$	1.10122e24	−	1.10122e24i	0.861404	−	0.861404i
$478$	−7.47755e22	−	7.47755e22i	−0.0573995	−	0.0573995i
$479$		−	1.22041e24i		−	0.919359i	−0.888085	−	0.459680i	$-0.847964\pi$
$479$		−	1.22041e24i		−	0.919359i	0.888085	−	0.459680i	$-0.152036\pi$
$480$	−2.63873e22	+	5.67499e22i	−0.0195085	+	0.0419560i
$481$	−1.31710e24			−0.955678
$482$	1.69075e22	−	1.69075e22i	0.0120408	−	0.0120408i
$483$	2.74125e23	+	2.74125e23i	0.191613	+	0.191613i
$484$			1.64966e24i			1.13184i
$485$	−1.91183e23	−	5.23486e23i	−0.128758	−	0.352557i
$486$	−6.12926e22			−0.0405212
$487$	−1.45618e24	+	1.45618e24i	−0.945047	+	0.945047i	−0.998567	−	0.0535200i	$-0.982956\pi$
$487$	−1.45618e24	+	1.45618e24i	−0.945047	+	0.945047i	0.0535200	+	0.998567i	$0.482956\pi$
$488$	1.13072e23	+	1.13072e23i	0.0720403	+	0.0720403i
$489$			2.99677e23i			0.187445i
$490$	−2.70534e22	+	9.88019e21i	−0.0166133	+	0.00606737i
$491$	2.63037e24			1.58593			0.792963	−	0.609270i	$-0.208537\pi$
$491$	2.63037e24			1.58593			0.792963	+	0.609270i	$0.208537\pi$
$492$	−2.87910e23	+	2.87910e23i	−0.170440	+	0.170440i
$493$	−5.93700e23	−	5.93700e23i	−0.345100	−	0.345100i
$494$			9.30123e22i			0.0530882i
$495$	2.13280e24	+	9.91698e23i	1.19537	+	0.555818i
$496$	1.17032e24			0.644125
$497$	−1.48071e23	+	1.48071e23i	−0.0800316	+	0.0800316i
$498$	−1.43795e22	−	1.43795e22i	−0.00763273	−	0.00763273i
$499$		−	6.15389e23i		−	0.320808i	−0.987051	−	0.160404i	$-0.948720\pi$
$499$		−	6.15389e23i		−	0.320808i	0.987051	−	0.160404i	$-0.0512796\pi$
$500$	−5.10449e23	−	1.88028e24i	−0.261350	−	0.962705i
$501$	−1.72259e23			−0.0866246
$502$	2.12453e21	−	2.12453e21i	0.00104937	−	0.00104937i
$503$	1.98259e24	+	1.98259e24i	0.961882	+	0.961882i	0.999300	−	0.0374181i	$-0.0119133\pi$
$503$	1.98259e24	+	1.98259e24i	0.961882	+	0.961882i	−0.0374181	+	0.999300i	$0.511913\pi$
$504$		−	1.50089e23i		−	0.0715277i
$505$	−1.08519e23	+	2.33387e23i	−0.0508024	+	0.109258i
$506$	1.70059e23			0.0782067
$507$	9.50202e23	−	9.50202e23i	0.429283	−	0.429283i
$508$	1.78324e24	+	1.78324e24i	0.791475	+	0.791475i
$509$			4.36363e23i			0.190278i	0.995464	+	0.0951388i	$0.0303295\pi$
$509$			4.36363e23i			0.190278i	−0.995464	+	0.0951388i	$0.969671\pi$
$510$	−1.09049e22	−	2.98592e22i	−0.00467187	−	0.0127922i
$511$	−3.18230e24			−1.33953
$512$	−4.19026e23	+	4.19026e23i	−0.173305	+	0.173305i
$513$	−6.46890e23	−	6.46890e23i	−0.262890	−	0.262890i
$514$		−	1.78960e23i		−	0.0714643i
$515$	−4.69753e24	+	1.71559e24i	−1.84334	+	0.673207i
$516$	2.86993e23			0.110669
$517$	1.88216e24	−	1.88216e24i	0.713249	−	0.713249i
$518$	−4.19819e22	−	4.19819e22i	−0.0156349	−	0.0156349i
$519$			5.50449e23i			0.201470i
$520$	4.27545e23	+	1.98798e23i	0.153799	+	0.0715124i
$521$	1.06364e24			0.376058			0.188029	−	0.982163i	$-0.439790\pi$
$521$	1.06364e24			0.376058			0.188029	+	0.982163i	$0.439790\pi$
$522$	5.03977e22	−	5.03977e22i	0.0175136	−	0.0175136i
$523$	−1.93863e24	−	1.93863e24i	−0.662186	−	0.662186i	0.293709	−	0.955895i	$-0.405110\pi$
$523$	−1.93863e24	−	1.93863e24i	−0.662186	−	0.662186i	−0.955895	+	0.293709i	$0.905110\pi$
$524$		−	5.55379e24i		−	1.86469i
$525$	−4.89342e23	−	5.80587e23i	−0.161502	−	0.191617i
$526$	1.86587e23			0.0605354
$527$	−1.26617e24	+	1.26617e24i	−0.403827	+	0.403827i
$528$	−1.02240e24	−	1.02240e24i	−0.320565	−	0.320565i
$529$			5.49189e23i			0.169286i
$530$	−9.29842e22	+	1.99977e23i	−0.0281791	+	0.0606034i
$531$	−3.04170e24			−0.906287
$532$	1.20690e24	−	1.20690e24i	0.353563	−	0.353563i
$533$	3.25494e24	+	3.25494e24i	0.937557	+	0.937557i
$534$		−	9.07722e21i		−	0.00257088i
$535$	1.25087e24	+	3.42506e24i	0.348360	+	0.953860i
$536$	−2.84110e23			−0.0778043
$537$	5.81347e23	−	5.81347e23i	0.156555	−	0.156555i
$538$	−7.24967e22	−	7.24967e22i	−0.0191990	−	0.0191990i
$539$		−	2.00438e24i		−	0.522013i
$540$	−2.17540e24	+	7.94481e23i	−0.557180	+	0.203488i
$541$	−3.52736e24			−0.888535			−0.444267	−	0.895894i	$-0.646536\pi$
$541$	−3.52736e24			−0.888535			−0.444267	+	0.895894i	$0.646536\pi$
$542$	6.24235e21	−	6.24235e21i	0.00154652	−	0.00154652i
$543$	7.73718e23	+	7.73718e23i	0.188532	+	0.188532i
$544$		−	5.43566e23i		−	0.130275i
$545$	7.08226e23	+	3.29307e23i	0.166956	+	0.0776305i
$546$	9.17637e22			0.0212783
$547$	5.02868e24	−	5.02868e24i	1.14701	−	1.14701i	0.159875	−	0.987137i	$-0.448891\pi$
$547$	5.02868e24	−	5.02868e24i	1.14701	−	1.14701i	0.987137	−	0.159875i	$-0.0511091\pi$
$548$	3.60015e24	+	3.60015e24i	0.807785	+	0.807785i
$549$			4.21178e24i			0.929640i
$550$	−3.31875e23	−	2.83028e22i	−0.0720627	−	0.00614562i
$551$	1.62303e24			0.346707
$552$	−1.12458e23	+	1.12458e23i	−0.0236341	+	0.0236341i
$553$	2.10595e24	+	2.10595e24i	0.435434	+	0.435434i
$554$			2.73531e23i			0.0556441i
$555$	−3.66871e23	+	7.89013e23i	−0.0734305	+	0.157924i
$556$	6.52603e24			1.28522
$557$	−4.99075e24	+	4.99075e24i	−0.967095	+	0.967095i	−0.999476	−	0.0323805i	$-0.989691\pi$
$557$	−4.99075e24	+	4.99075e24i	−0.967095	+	0.967095i	0.0323805	+	0.999476i	$0.489691\pi$
$558$	−1.07482e23	−	1.07482e23i	−0.0204940	−	0.0204940i
$559$		−	3.24457e24i		−	0.608767i
$560$	−1.47861e24	−	4.04865e24i	−0.273000	−	0.747512i
$561$	2.21226e24			0.401949
$562$	−8.45830e22	+	8.45830e22i	−0.0151236	+	0.0151236i
$563$	−2.88297e24	−	2.88297e24i	−0.507299	−	0.507299i	0.406397	−	0.913696i	$-0.366785\pi$
$563$	−2.88297e24	−	2.88297e24i	−0.507299	−	0.507299i	−0.913696	+	0.406397i	$0.866785\pi$
$564$			1.24312e24i			0.215279i
$565$	8.93832e23	−	3.26437e23i	0.152342	−	0.0556370i
$566$	1.44912e23			0.0243084
$567$	2.45982e24	−	2.45982e24i	0.406122	−	0.406122i
$568$	−6.07449e22	−	6.07449e22i	−0.00987131	−	0.00987131i
$569$			6.59049e22i			0.0105416i	0.999986	+	0.00527081i	$0.00167776\pi$
$569$			6.59049e22i			0.0105416i	−0.999986	+	0.00527081i	$0.998322\pi$
$570$	5.57195e22	+	2.59081e22i	0.00877270	+	0.00407908i
$571$	−5.84616e24			−0.906036			−0.453018	−	0.891501i	$-0.649653\pi$
$571$	−5.84616e24			−0.906036			−0.453018	+	0.891501i	$0.649653\pi$
$572$	−1.15872e25	+	1.15872e25i	−1.76772	+	1.76772i
$573$	−9.06062e23	−	9.06062e23i	−0.136071	−	0.136071i
$574$			2.07500e23i			0.0306768i
$575$	6.31324e23	−	7.40282e24i	0.0918844	−	1.07742i
$576$	−6.20481e24			−0.889050
$577$	7.72731e24	−	7.72731e24i	1.09005	−	1.09005i	0.0945261	−	0.995522i	$-0.469866\pi$
$577$	7.72731e24	−	7.72731e24i	1.09005	−	1.09005i	0.995522	−	0.0945261i	$-0.0301336\pi$
$578$	−5.68090e22	−	5.68090e22i	−0.00788980	−	0.00788980i
$579$			3.53796e24i			0.483777i
$580$	1.73235e24	−	3.72568e24i	0.233229	−	0.501595i
$581$	4.21883e24			0.559251
$582$	3.14633e22	−	3.14633e22i	0.00410674	−	0.00410674i
$583$	−1.08527e25	−	1.08527e25i	−1.39483	−	1.39483i
$584$		−	1.30552e24i		−	0.165222i
$585$	4.26028e24	+	1.16653e25i	0.530928	+	1.45376i
$586$	−7.92738e22			−0.00972861
$587$	−1.78968e23	+	1.78968e23i	−0.0216288	+	0.0216288i	−0.717838	−	0.696210i	$-0.754868\pi$
$587$	−1.78968e23	+	1.78968e23i	−0.0216288	+	0.0216288i	0.696210	+	0.717838i	$0.254868\pi$
$588$	6.61924e23	+	6.61924e23i	0.0787793	+	0.0787793i
$589$		−	3.46139e24i		−	0.405707i
$590$	4.04598e23	−	1.47764e23i	0.0467042	−	0.0170569i
$591$	−3.11488e24			−0.354123
$592$	−3.49266e24	+	3.49266e24i	−0.391076	+	0.391076i
$593$	−2.70893e24	−	2.70893e24i	−0.298748	−	0.298748i	0.541775	−	0.840524i	$-0.317752\pi$
$593$	−2.70893e24	−	2.70893e24i	−0.298748	−	0.298748i	−0.840524	+	0.541775i	$0.817752\pi$
$594$			3.95923e23i			0.0430063i
$595$	5.97992e24	+	2.78051e24i	0.639798	+	0.297490i
$596$	8.34802e24			0.879766
$597$	2.57935e24	−	2.57935e24i	0.267757	−	0.267757i
$598$	6.34912e23	+	6.34912e23i	0.0649236	+	0.0649236i
$599$			1.75330e25i			1.76609i	0.469284	+	0.883047i	$0.344512\pi$
$599$			1.75330e25i			1.76609i	−0.469284	+	0.883047i	$0.655488\pi$
$600$	2.38182e23	−	2.00749e23i	0.0236345	−	0.0199201i
$601$	6.22920e24			0.608923			0.304461	−	0.952525i	$-0.401524\pi$
$601$	6.22920e24			0.608923			0.304461	+	0.952525i	$0.401524\pi$
$602$	1.03419e23	−	1.03419e23i	0.00995941	−	0.00995941i
$603$	−5.29138e24	−	5.29138e24i	−0.502011	−	0.502011i
$604$			8.12222e24i			0.759176i
$605$	5.19488e24	−	1.11724e25i	0.478385	−	1.02884i
$606$	−2.05498e22			−0.00186446
$607$	−7.27644e24	+	7.27644e24i	−0.650460	+	0.650460i	−0.953104	−	0.302643i	$-0.902131\pi$
$607$	−7.27644e24	+	7.27644e24i	−0.650460	+	0.650460i	0.302643	+	0.953104i	$0.402131\pi$
$608$	7.42988e23	+	7.42988e23i	0.0654410	+	0.0654410i
$609$		−	1.60124e24i		−	0.138964i
$610$	−2.04606e23	−	5.60239e23i	−0.0174964	−	0.0479077i
$611$	1.40540e25			1.18421
$612$	6.74631e24	−	6.74631e24i	0.560149	−	0.560149i
$613$	6.21825e24	+	6.21825e24i	0.508773	+	0.508773i	0.914150	−	0.405377i	$-0.132860\pi$
$613$	6.21825e24	+	6.21825e24i	0.508773	+	0.508773i	−0.405377	+	0.914150i	$0.632860\pi$
$614$			4.39447e21i			0.000354317i
$615$	2.85654e24	−	1.04324e24i	0.226967	−	0.0828911i
$616$	−1.47916e24			−0.115821
$617$	−7.30739e24	+	7.30739e24i	−0.563891	+	0.563891i	−0.930411	−	0.366519i	$-0.880549\pi$
$617$	−7.30739e24	+	7.30739e24i	−0.563891	+	0.563891i	0.366519	+	0.930411i	$0.380549\pi$
$618$	−2.82338e23	−	2.82338e23i	−0.0214720	−	0.0214720i
$619$		−	6.19157e24i		−	0.464071i	−0.972707	−	0.232036i	$-0.925461\pi$
$619$		−	6.19157e24i		−	0.464071i	0.972707	−	0.232036i	$-0.0745386\pi$
$620$	−7.94564e24	−	3.69452e24i	−0.586953	−	0.272919i
$621$	−8.83148e24			−0.642997
$622$	5.03115e23	−	5.03115e23i	0.0361039	−	0.0361039i
$623$	1.33159e24	+	1.33159e24i	0.0941843	+	0.0941843i
$624$		−	7.63423e24i		−	0.532236i
$625$	−2.46410e24	+	1.43418e25i	−0.169332	+	0.985559i
$626$	−6.49229e23			−0.0439773
$627$	−3.02389e24	+	3.02389e24i	−0.201910	+	0.201910i
$628$	−1.82711e24	−	1.82711e24i	−0.120262	−	0.120262i
$629$		−	7.55739e24i		−	0.490361i
$630$	−2.36031e23	+	5.07620e23i	−0.0150974	+	0.0324694i
$631$	−1.42701e25			−0.899832			−0.449916	−	0.893071i	$-0.648546\pi$
$631$	−1.42701e25			−0.899832			−0.449916	+	0.893071i	$0.648546\pi$
$632$	−8.63953e23	+	8.63953e23i	−0.0537077	+	0.0537077i
$633$	−1.75498e24	−	1.75498e24i	−0.107557	−	0.107557i
$634$			1.09695e24i			0.0662799i
$635$	−6.46157e24	−	1.76927e25i	−0.384923	−	1.05397i
$636$	7.16798e24			0.421001
$637$	7.48332e24	−	7.48332e24i	0.433351	−	0.433351i
$638$	−4.96680e23	−	4.96680e23i	−0.0283590	−	0.0283590i
$639$		−	2.26267e24i		−	0.127384i
$640$	3.33005e24	−	1.21617e24i	0.184855	−	0.0675111i
$641$	−1.83269e25			−1.00315			−0.501576	−	0.865114i	$-0.667246\pi$
$641$	−1.83269e25			−1.00315			−0.501576	+	0.865114i	$0.667246\pi$
$642$	−2.05858e23	+	2.05858e23i	−0.0111110	+	0.0111110i
$643$	−7.14621e22	−	7.14621e22i	−0.00380344	−	0.00380344i	0.705203	−	0.709006i	$-0.250856\pi$
$643$	−7.14621e22	−	7.14621e22i	−0.00380344	−	0.00380344i	−0.709006	+	0.705203i	$0.750856\pi$
$644$		−	1.64769e25i		−	0.864774i
$645$	−1.94368e24	−	9.03762e23i	−0.100597	−	0.0467753i
$646$	−5.33697e23			−0.0272397
$647$	−5.00491e24	+	5.00491e24i	−0.251917	+	0.251917i	−0.821756	−	0.569839i	$-0.807006\pi$
$647$	−5.00491e24	+	5.00491e24i	−0.251917	+	0.251917i	0.569839	+	0.821756i	$0.307006\pi$
$648$	1.00913e24	+	1.00913e24i	0.0500922	+	0.0500922i
$649$			2.99766e25i			1.46751i
$650$	−1.13338e24	−	1.34472e24i	−0.0547213	−	0.0649249i
$651$	−3.41492e24			−0.162612
$652$	9.00637e24	−	9.00637e24i	0.422982	−	0.422982i
$653$	2.66507e25	+	2.66507e25i	1.23450	+	1.23450i	0.962219	+	0.272276i	$0.0877765\pi$
$653$	2.66507e25	+	2.66507e25i	1.23450	+	1.23450i	0.272276	+	0.962219i	$0.412224\pi$
$654$			6.23593e22i			0.00284906i
$655$	−1.74893e25	+	3.76134e25i	−0.788134	+	1.69500i
$656$	1.72628e25			0.767321
$657$	2.43145e25	−	2.43145e25i	1.06605	−	1.06605i
$658$	4.47966e23	+	4.47966e23i	0.0193737	+	0.0193737i
$659$		−	2.95417e25i		−	1.26028i	−0.776482	−	0.630140i	$-0.782997\pi$
$659$		−	2.95417e25i		−	1.26028i	0.776482	−	0.630140i	$-0.217003\pi$
$660$	3.71380e24	+	1.01689e25i	0.156287	+	0.427937i
$661$	−1.03922e25			−0.431414			−0.215707	−	0.976458i	$-0.569206\pi$
$661$	−1.03922e25			−0.431414			−0.215707	+	0.976458i	$0.569206\pi$
$662$	1.46266e24	−	1.46266e24i	0.0598993	−	0.0598993i
$663$	8.25945e24	+	8.25945e24i	0.333679	+	0.333679i
$664$			1.73074e24i			0.0689795i
$665$	−1.19744e25	+	4.37320e24i	−0.470826	+	0.171951i
$666$	6.41527e23			0.0248855
$667$	1.10790e25	−	1.10790e25i	0.424001	−	0.424001i
$668$	5.17698e24	+	5.17698e24i	0.195474	+	0.195474i
$669$		−	6.19789e24i		−	0.230892i
$670$	9.60896e23	+	4.46793e23i	0.0353186	+	0.0164223i
$671$	4.15080e25			1.50532
$672$	7.33015e23	−	7.33015e23i	0.0262294	−	0.0262294i
$673$	−7.36281e24	−	7.36281e24i	−0.259961	−	0.259961i	0.565077	−	0.825038i	$-0.308846\pi$
$673$	−7.36281e24	−	7.36281e24i	−0.259961	−	0.259961i	−0.825038	+	0.565077i	$0.808846\pi$
$674$		−	1.24427e24i		−	0.0433487i
$675$	1.72349e25	+	1.46982e24i	0.592482	+	0.0505278i
$676$	−5.71139e25			−1.93741
$677$	−2.82348e25	+	2.82348e25i	−0.945119	+	0.945119i	−0.998570	−	0.0534519i	$-0.982978\pi$
$677$	−2.82348e25	+	2.82348e25i	−0.945119	+	0.945119i	0.0534519	+	0.998570i	$0.482978\pi$
$678$	5.37224e22	+	5.37224e22i	0.00177455	+	0.00177455i
$679$			9.23107e24i			0.300901i
$680$	−1.14069e24	+	2.45322e24i	−0.0366932	+	0.0789144i
$681$	−1.13759e25			−0.361130
$682$	−1.05925e24	+	1.05925e24i	−0.0331849	+	0.0331849i
$683$	2.20552e25	+	2.20552e25i	0.681906	+	0.681906i	0.960429	−	0.278524i	$-0.0898450\pi$
$683$	2.20552e25	+	2.20552e25i	0.681906	+	0.681906i	−0.278524	+	0.960429i	$0.589845\pi$
$684$			1.84427e25i			0.562756i
$685$	−1.30451e25	−	3.57194e25i	−0.392855	−	1.07569i
$686$	1.81226e24			0.0538646
$687$	−8.47716e24	+	8.47716e24i	−0.248679	+	0.248679i
$688$	−8.60393e24	−	8.60393e24i	−0.249116	−	0.249116i
$689$		−	8.10370e25i		−	2.31585i
$690$	5.57199e23	−	2.03495e23i	0.0157170	−	0.00574001i
$691$	2.85875e25			0.795929			0.397964	−	0.917401i	$-0.369717\pi$
$691$	2.85875e25			0.795929			0.397964	+	0.917401i	$0.369717\pi$
$692$	1.65429e25	−	1.65429e25i	0.454630	−	0.454630i
$693$	−2.75485e25	−	2.75485e25i	−0.747306	−	0.747306i
$694$		−	2.23810e24i		−	0.0599299i
$695$	−4.41979e25	−	2.05509e25i	−1.16826	−	0.543210i
$696$	6.56898e23			0.0171402
$697$	−1.86766e25	+	1.86766e25i	−0.481063	+	0.481063i
$698$	−2.87076e23	−	2.87076e23i	−0.00729958	−	0.00729958i
$699$			1.56296e24i			0.0392332i
$700$	−2.74224e24	+	3.21552e25i	−0.0679553	+	0.796835i
$701$	1.71473e25			0.419502			0.209751	−	0.977755i	$-0.432735\pi$
$701$	1.71473e25			0.419502			0.209751	+	0.977755i	$0.432735\pi$
$702$	−1.47817e24	+	1.47817e24i	−0.0357019	+	0.0357019i
$703$	1.03300e25	+	1.03300e25i	0.246322	+	0.246322i
$704$			6.11498e25i			1.43960i
$705$	3.91468e24	−	8.41913e24i	0.0909902	−	0.195688i
$706$	−1.91446e24			−0.0439343
$707$	3.01456e24	−	3.01456e24i	0.0683046	−	0.0683046i
$708$	−9.89945e24	−	9.89945e24i	−0.221468	−	0.221468i
$709$			3.23410e25i			0.714394i	0.934029	+	0.357197i	$0.116268\pi$
$709$			3.23410e25i			0.714394i	−0.934029	+	0.357197i	$0.883732\pi$
$710$	1.09919e23	+	3.00975e23i	0.00239745	+	0.00656455i
$711$	−3.21812e25			−0.693068
$712$	−5.46276e23	+	5.46276e23i	−0.0116169	+	0.0116169i
$713$	−2.36278e25	−	2.36278e25i	−0.496155	−	0.496155i
$714$			5.26533e23i			0.0109180i
$715$	1.14964e26	−	4.19860e25i	2.35400	−	0.859707i
$716$	−3.49431e25			−0.706552
$717$	1.81522e25	−	1.81522e25i	0.362457	−	0.362457i
$718$	−7.48268e23	−	7.48268e23i	−0.0147549	−	0.0147549i
$719$			7.09020e25i			1.38070i	0.723477	+	0.690348i	$0.242543\pi$
$719$			7.09020e25i			1.38070i	−0.723477	+	0.690348i	$0.757457\pi$
$720$	4.22312e25	+	1.96364e25i	0.812159	+	0.377633i
$721$	8.28356e25			1.57326
$722$	−1.13664e24	+	1.13664e24i	−0.0213200	+	0.0213200i
$723$	4.10441e24	+	4.10441e24i	0.0760336	+	0.0760336i
$724$		−	4.65059e25i		−	0.850866i
$725$	−2.34648e25	+	1.97771e25i	−0.424009	+	0.357372i
$726$	9.83730e23			0.0175568
$727$	1.23487e24	−	1.23487e24i	0.0217677	−	0.0217677i	−0.696139	−	0.717907i	$-0.745100\pi$
$727$	1.23487e24	−	1.23487e24i	0.0217677	−	0.0217677i	0.717907	+	0.696139i	$0.245100\pi$
$728$	−5.52243e24	−	5.52243e24i	−0.0961496	−	0.0961496i
$729$			2.67801e25i			0.460537i
$730$	−2.05306e24	+	4.41543e24i	−0.0348736	+	0.0750010i
$731$	1.86171e25			0.312360
$732$	−1.37076e25	+	1.37076e25i	−0.227175	+	0.227175i
$733$	−2.41810e25	−	2.41810e25i	−0.395858	−	0.395858i	0.480911	−	0.876769i	$-0.340306\pi$
$733$	−2.41810e25	−	2.41810e25i	−0.395858	−	0.395858i	−0.876769	+	0.480911i	$0.840306\pi$
$734$			1.90118e24i			0.0307439i
$735$	−2.39848e24	−	6.56737e24i	−0.0383133	−	0.104907i
$736$	1.01434e25			0.160061
$737$	−5.21477e25	+	5.21477e25i	−0.812883	+	0.812883i
$738$	−1.58541e24	−	1.58541e24i	−0.0244137	−	0.0244137i
$739$			8.86090e24i			0.134796i	0.997726	+	0.0673982i	$0.0214698\pi$
$739$			8.86090e24i			0.134796i	−0.997726	+	0.0673982i	$0.978530\pi$
$740$	3.47384e25	−	1.26869e25i	0.522065	−	0.190664i
$741$	−2.25793e25			−0.335233
$742$	2.58302e24	−	2.58302e24i	0.0378872	−	0.0378872i
$743$	−4.12285e23	−	4.12285e23i	−0.00597445	−	0.00597445i	0.704113	−	0.710088i	$-0.251345\pi$
$743$	−4.12285e23	−	4.12285e23i	−0.00597445	−	0.00597445i	−0.710088	+	0.704113i	$0.751345\pi$
$744$		−	1.40095e24i		−	0.0200570i
$745$	−5.65375e25	−	2.62885e25i	−0.799706	−	0.371843i
$746$	2.76500e24			0.0386408
$747$	−3.22341e25	+	3.22341e25i	−0.445071	+	0.445071i
$748$	−6.64863e25	−	6.64863e25i	−0.907022	−	0.907022i
$749$		−	6.03971e25i		−	0.814104i
$750$	−1.12126e24	+	3.04393e23i	−0.0149333	+	0.00405400i
$751$	−1.12872e25			−0.148534			−0.0742671	−	0.997238i	$-0.523662\pi$
$751$	−1.12872e25			−0.148534			−0.0742671	+	0.997238i	$0.523662\pi$
$752$	3.72683e25	−	3.72683e25i	0.484595	−	0.484595i
$753$	5.15743e23	+	5.15743e23i	0.00662641	+	0.00662641i
$754$		−	3.70870e24i		−	0.0470846i
$755$	2.55774e25	−	5.50082e25i	0.320874	−	0.690089i
$756$	3.83607e25			0.475544
$757$	1.22444e24	−	1.22444e24i	0.0149994	−	0.0149994i	−0.699567	−	0.714567i	$-0.746624\pi$
$757$	1.22444e24	−	1.22444e24i	0.0149994	−	0.0149994i	0.714567	+	0.699567i	$0.246624\pi$
$758$	4.03371e24	+	4.03371e24i	0.0488294	+	0.0488294i
$759$			4.12828e25i			0.493848i
$760$	−1.79407e24	−	4.91243e24i	−0.0212089	−	0.0580729i
$761$	−3.32804e25			−0.388800			−0.194400	−	0.980922i	$-0.562276\pi$
$761$	−3.32804e25			−0.388800			−0.194400	+	0.980922i	$0.562276\pi$
$762$	1.06339e24	−	1.06339e24i	0.0122772	−	0.0122772i
$763$	−9.14785e24	−	9.14785e24i	−0.104375	−	0.104375i
$764$			5.44608e25i			0.614106i
$765$	−6.69343e25	+	2.44452e25i	−0.745927	+	0.272421i
$766$	1.83121e24			0.0201688
$767$	−1.11917e26	+	1.11917e26i	−1.21826	+	1.21826i
$768$	−2.00435e25	−	2.00435e25i	−0.215637	−	0.215637i
$769$		−	8.05399e25i		−	0.856394i	−0.903685	−	0.428197i	$-0.859149\pi$
$769$		−	8.05399e25i		−	0.856394i	0.903685	−	0.428197i	$-0.140851\pi$
$770$	5.00271e24	+	2.32613e24i	0.0525761	+	0.0244466i
$771$	4.34437e25			0.451271
$772$	1.06328e26	−	1.06328e26i	1.09167	−	1.09167i
$773$	1.07779e26	+	1.07779e26i	1.09375	+	1.09375i	0.995125	+	0.0986247i	$0.0314443\pi$
$773$	1.07779e26	+	1.07779e26i	1.09375	+	1.09375i	0.0986247	+	0.995125i	$0.468556\pi$
$774$			1.58036e24i			0.0158521i
$775$	4.21780e25	+	5.00427e25i	0.418187	+	0.496165i
$776$	−3.78698e24			−0.0371140
$777$	1.01914e25	−	1.01914e25i	0.0987285	−	0.0987285i
$778$	−1.89766e24	−	1.89766e24i	−0.0181720	−	0.0181720i
$779$		−	5.10571e25i		−	0.483303i
$780$	−2.41001e25	+	5.18309e25i	−0.225511	+	0.484995i
$781$	−2.22992e25			−0.206267
$782$	−3.64307e24	+	3.64307e24i	−0.0333125	+	0.0333125i
$783$	2.57936e25	+	2.57936e25i	0.233161	+	0.233161i
$784$		−	3.96884e25i		−	0.354665i
$785$	6.62052e24	+	1.81279e25i	0.0584878	+	0.160148i
$786$	−3.31186e24			−0.0289247
$787$	6.93253e25	−	6.93253e25i	0.598576	−	0.598576i	−0.341357	−	0.939934i	$-0.610887\pi$
$787$	6.93253e25	−	6.93253e25i	0.598576	−	0.598576i	0.939934	+	0.341357i	$0.110887\pi$
$788$	9.36132e25	+	9.36132e25i	0.799100	+	0.799100i
$789$			4.52951e25i			0.382260i
$790$	4.28065e24	−	1.56334e24i	0.0357163	−	0.0130440i
$791$	−1.57617e25			−0.130021
$792$	1.13016e25	−	1.13016e25i	0.0921748	−	0.0921748i
$793$	1.54970e26	+	1.54970e26i	1.24965	+	1.24965i
$794$			3.60119e23i			0.00287119i
$795$	−4.85456e25	−	2.25725e25i	−0.382689	−	0.177941i
$796$	−1.55037e26			−1.20842
$797$	1.11928e26	−	1.11928e26i	0.862612	−	0.862612i	−0.129029	−	0.991641i	$-0.541186\pi$
$797$	1.11928e26	−	1.11928e26i	0.862612	−	0.862612i	0.991641	+	0.129029i	$0.0411861\pi$
$798$	−7.19705e23	−	7.19705e23i	−0.00548439	−	0.00548439i
$799$			8.06408e25i			0.607622i
$800$	−1.97952e25	−	1.68817e24i	−0.147486	−	0.0125778i
$801$	−2.03481e25			−0.149910
$802$	−8.46212e24	+	8.46212e24i	−0.0616467	+	0.0616467i
$803$	−2.39625e26	−	2.39625e26i	−1.72620	−	1.72620i
$804$		−	3.44424e25i		−	0.245352i
$805$	−5.18869e25	+	1.11591e26i	−0.365506	+	0.786077i
$806$	−7.90942e24			−0.0550972
$807$	1.75990e25	−	1.75990e25i	0.121235	−	0.121235i
$808$	1.23670e24	+	1.23670e24i	0.00842487	+	0.00842487i
$809$		−	9.09385e25i		−	0.612648i	−0.951927	−	0.306324i	$-0.900901\pi$
$809$		−	9.09385e25i		−	0.612648i	0.951927	−	0.306324i	$-0.0990991\pi$
$810$	−1.82604e24	−	4.99994e24i	−0.0121659	−	0.0333119i
$811$	5.31022e25			0.349885			0.174942	−	0.984579i	$-0.444026\pi$
$811$	5.31022e25			0.349885			0.174942	+	0.984579i	$0.444026\pi$
$812$	−4.81230e25	+	4.81230e25i	−0.313580	+	0.313580i
$813$	1.51537e24	+	1.51537e24i	0.00976569	+	0.00976569i
$814$		−	6.32239e24i		−	0.0402960i
$815$	−8.93579e25	+	3.26345e25i	−0.563267	+	0.205711i
$816$	4.38046e25			0.273092
$817$	−2.54473e25	+	2.54473e25i	−0.156907	+	0.156907i
$818$	8.63434e24	+	8.63434e24i	0.0526562	+	0.0526562i
$819$		−	2.05704e26i		−	1.24076i
$820$	−1.17202e26	−	5.44960e25i	−0.699215	−	0.325117i
$821$	−1.28258e26			−0.756823			−0.378412	−	0.925637i	$-0.623530\pi$
$821$	−1.28258e26			−0.756823			−0.378412	+	0.925637i	$0.623530\pi$
$822$	2.14686e24	−	2.14686e24i	0.0125302	−	0.0125302i
$823$	9.33282e25	+	9.33282e25i	0.538783	+	0.538783i	0.923172	−	0.384388i	$-0.125588\pi$
$823$	9.33282e25	+	9.33282e25i	0.538783	+	0.538783i	−0.384388	+	0.923172i	$0.625588\pi$
$824$			3.39827e25i			0.194050i
$825$	6.87068e24	−	8.05646e25i	0.0388074	−	0.455050i
$826$	−7.13463e24			−0.0398613
$827$	8.67739e25	−	8.67739e25i	0.479556	−	0.479556i	−0.425433	−	0.904990i	$-0.639878\pi$
$827$	8.67739e25	−	8.67739e25i	0.479556	−	0.479556i	0.904990	+	0.425433i	$0.139878\pi$
$828$	1.25892e26	+	1.25892e26i	0.688217	+	0.688217i
$829$		−	1.73383e26i		−	0.937597i	−0.883305	−	0.468798i	$-0.844687\pi$
$829$		−	1.73383e26i		−	0.937597i	0.883305	−	0.468798i	$-0.155313\pi$
$830$	2.72177e24	−	5.85360e24i	0.0145596	−	0.0313127i
$831$	−6.64014e25			−0.351373
$832$	−2.28302e26	+	2.28302e26i	−1.19509	+	1.19509i
$833$	4.29387e25	+	4.29387e25i	0.222353	+	0.222353i
$834$		−	3.89163e24i		−	0.0199360i
$835$	−1.87587e25	−	5.13641e25i	−0.0950661	−	0.260304i
$836$	1.81757e26			0.911245
$837$	5.50091e25	−	5.50091e25i	0.272838	−	0.272838i
$838$	−1.65876e24	−	1.65876e24i	−0.00813932	−	0.00813932i
$839$			2.13653e26i			1.03717i	0.855025	+	0.518586i	$0.173541\pi$
$839$			2.13653e26i			1.03717i	−0.855025	+	0.518586i	$0.826459\pi$
$840$	−4.84648e24	+	1.76999e24i	−0.0232763	+	0.00850075i
$841$	1.45742e26			0.692501
$842$	1.41746e25	−	1.41746e25i	0.0666348	−	0.0666348i
$843$	−2.05330e25	−	2.05330e25i	−0.0955004	−	0.0955004i
$844$			1.05487e26i			0.485418i
$845$	3.86807e26	+	1.79856e26i	1.76110	+	0.818867i
$846$	−6.84539e24			−0.0308365
$847$	−1.44309e26	+	1.44309e26i	−0.643196	+	0.643196i
$848$	−2.14893e26	−	2.14893e26i	−0.947675	−	0.947675i
$849$			3.51782e25i			0.153499i
$850$	7.71589e24	−	6.50326e24i	0.0333131	−	0.0280776i
$851$	1.41028e26			0.602474
$852$	7.36405e24	−	7.36405e24i	0.0311287	−	0.0311287i
$853$	1.67234e25	+	1.67234e25i	0.0699492	+	0.0699492i	0.741216	−	0.671267i	$-0.234249\pi$
$853$	1.67234e25	+	1.67234e25i	0.0699492	+	0.0699492i	−0.671267	+	0.741216i	$0.734249\pi$
$854$			9.87918e24i			0.0408884i
$855$	5.80774e25	−	1.24905e26i	0.237855	−	0.511544i
$856$	2.47775e25			0.100414
$857$	2.37241e26	−	2.37241e26i	0.951400	−	0.951400i	−0.0474726	−	0.998873i	$-0.515117\pi$
$857$	2.37241e26	−	2.37241e26i	0.951400	−	0.951400i	0.998873	+	0.0474726i	$0.0151167\pi$
$858$	6.90972e24	+	6.90972e24i	0.0274205	+	0.0274205i
$859$			1.49782e26i			0.588196i	0.955775	+	0.294098i	$0.0950191\pi$
$859$			1.49782e26i			0.588196i	−0.955775	+	0.294098i	$0.904981\pi$
$860$	3.12532e25	+	8.55757e25i	0.121453	+	0.332556i
$861$	−5.03718e25			−0.193713
$862$	−3.30524e24	+	3.30524e24i	−0.0125788	+	0.0125788i
$863$	−2.23589e26	−	2.23589e26i	−0.842081	−	0.842081i	0.147048	−	0.989129i	$-0.453023\pi$
$863$	−2.23589e26	−	2.23589e26i	−0.842081	−	0.842081i	−0.989129	+	0.147048i	$0.953023\pi$
$864$			2.36155e25i			0.0880183i
$865$	−1.64133e26	+	5.99432e25i	−0.605412	+	0.221103i
$866$	9.75190e24			0.0355982
$867$	1.37907e25	−	1.37907e25i	0.0498213	−	0.0498213i
$868$	1.02631e26	+	1.02631e26i	0.366943	+	0.366943i
$869$			3.17153e26i			1.12225i
$870$	−2.22171e24	−	1.03304e24i	−0.00778063	−	0.00361780i
$871$	−3.89386e26			−1.34964
$872$	3.75284e24	−	3.75284e24i	0.0128740	−	0.0128740i
$873$	−7.05303e25	−	7.05303e25i	−0.239468	−	0.239468i
$874$		−	9.95926e24i		−	0.0334676i
$875$	1.19831e26	−	2.09137e26i	0.398562	−	0.695599i
$876$	1.58267e26			0.521018
$877$	−1.60133e26	+	1.60133e26i	−0.521777	+	0.521777i	−0.918108	−	0.396331i	$-0.870283\pi$
$877$	−1.60133e26	+	1.60133e26i	−0.521777	+	0.521777i	0.396331	+	0.918108i	$0.370283\pi$
$878$	−1.38625e25	−	1.38625e25i	−0.0447086	−	0.0447086i
$879$		−	1.92442e25i		−	0.0614327i
$880$	1.93521e26	−	4.16198e26i	0.611484	−	1.31509i
$881$	−1.98193e26			−0.619877			−0.309939	−	0.950757i	$-0.600308\pi$
$881$	−1.98193e26			−0.619877			−0.309939	+	0.950757i	$0.600308\pi$
$882$	−3.64495e24	+	3.64495e24i	−0.0112843	+	0.0112843i
$883$	−3.74351e26	−	3.74351e26i	−1.14718	−	1.14718i	−0.987104	−	0.160079i	$-0.948825\pi$
$883$	−3.74351e26	−	3.74351e26i	−1.14718	−	1.14718i	−0.160079	−	0.987104i	$-0.551175\pi$
$884$		−	4.96452e26i		−	1.50594i
$885$	3.58706e25	+	9.82187e25i	0.107708	+	0.294920i
$886$	−2.53569e25			−0.0753690
$887$	−2.04207e26	+	2.04207e26i	−0.600839	+	0.600839i	−0.940535	−	0.339696i	$-0.889676\pi$
$887$	−2.04207e26	+	2.04207e26i	−0.600839	+	0.600839i	0.339696	+	0.940535i	$0.389676\pi$
$888$	4.18093e24	+	4.18093e24i	0.0121774	+	0.0121774i
$889$			3.11990e26i			0.899550i
$890$	2.70665e24	−	9.88499e23i	0.00772542	−	0.00282141i
$891$	3.70445e26			1.04670
$892$	−1.86269e26	+	1.86269e26i	−0.521022	+	0.521022i
$893$	−1.10226e26	−	1.10226e26i	−0.305226	−	0.305226i
$894$		−	4.97813e24i		−	0.0136467i
$895$	2.36654e26	+	1.10038e26i	0.642254	+	0.298632i
$896$	−5.87217e25			−0.157771
$897$	−1.54129e26	+	1.54129e26i	−0.409969	+	0.409969i
$898$	1.17364e25	+	1.17364e25i	0.0309063	+	0.0309063i
$899$			1.38016e26i			0.359827i
$900$	−2.24730e26	−	2.66635e26i	−0.580068	−	0.688230i
$901$	4.64984e26			1.18827
$902$	−1.56245e25	+	1.56245e25i	−0.0395319	+	0.0395319i
$903$	2.51057e25	+	2.51057e25i	0.0628901	+	0.0628901i
$904$		−	6.46613e24i		−	0.0160372i
$905$	−1.46450e26	+	3.14964e26i	−0.359628	+	0.773435i
$906$	4.84348e24			0.0117762
$907$	3.66014e26	−	3.66014e26i	0.881113	−	0.881113i	−0.112535	−	0.993648i	$-0.535897\pi$
$907$	3.66014e26	−	3.66014e26i	0.881113	−	0.881113i	0.993648	+	0.112535i	$0.0358969\pi$
$908$	3.41887e26	+	3.41887e26i	0.814912	+	0.814912i
$909$			4.60657e25i			0.108718i
$910$	9.99295e24	+	2.73621e25i	0.0233519	+	0.0639407i
$911$	−4.37074e26			−1.01132			−0.505662	−	0.862732i	$-0.668752\pi$
$911$	−4.37074e26			−1.01132			−0.505662	+	0.862732i	$0.668752\pi$
$912$	−5.98755e25	+	5.98755e25i	−0.137182	+	0.137182i
$913$	3.17674e26	+	3.17674e26i	0.720683	+	0.720683i
$914$		−	2.18379e25i		−	0.0490564i
$915$	1.36001e26	−	4.96693e25i	0.302520	−	0.110484i
$916$	5.09538e26			1.12232
$917$	4.85836e26	−	4.85836e26i	1.05966	−	1.05966i
$918$	−8.48163e24	−	8.48163e24i	−0.0183187	−	0.0183187i
$919$			1.65890e26i			0.354797i	0.984139	+	0.177398i	$0.0567681\pi$
$919$			1.65890e26i			0.354797i	−0.984139	+	0.177398i	$0.943232\pi$
$920$	−4.57793e25	−	2.12862e25i	−0.0969569	−	0.0450825i
$921$	−1.06678e24			−0.00223738
$922$	−7.45181e24	+	7.45181e24i	−0.0154769	+	0.0154769i
$923$	−8.32536e25	−	8.32536e25i	−0.171233	−	0.171233i
$924$		−	1.79317e26i		−	0.365237i
$925$	−2.75220e26	−	2.34712e25i	−0.555142	−	0.0473434i
$926$	3.88496e25			0.0776046
$927$	−6.32908e26	+	6.32908e26i	−1.25205	+	1.25205i
$928$	−2.96253e25	−	2.96253e25i	−0.0580405	−	0.0580405i
$929$		−	2.06987e26i		−	0.401608i	−0.979631	−	0.200804i	$-0.935645\pi$
$929$		−	2.06987e26i		−	0.401608i	0.979631	−	0.200804i	$-0.0643554\pi$
$930$	−2.20313e24	+	4.73818e24i	−0.00423345	+	0.00910468i
$931$	−1.17384e26			−0.223389
$932$	4.69726e25	−	4.69726e25i	0.0885322	−	0.0885322i
$933$	1.22134e26	+	1.22134e26i	0.227983	+	0.227983i
$934$		−	6.86326e24i		−	0.0126884i
$935$	2.40913e26	+	6.59653e26i	0.441118	+	1.20784i
$936$	8.43885e25			0.153038
$937$	2.37588e26	−	2.37588e26i	0.426744	−	0.426744i	−0.460774	−	0.887518i	$-0.652428\pi$
$937$	2.37588e26	−	2.37588e26i	0.426744	−	0.426744i	0.887518	+	0.460774i	$0.152428\pi$
$938$	−1.24115e25	−	1.24115e25i	−0.0220800	−	0.0220800i
$939$		−	1.57604e26i		−	0.277701i
$940$	−3.70675e26	+	1.35375e26i	−0.646908	+	0.236258i
$941$	−7.88696e26			−1.36334			−0.681668	−	0.731661i	$-0.738745\pi$
$941$	−7.88696e26			−1.36334			−0.681668	+	0.731661i	$0.738745\pi$
$942$	−1.08955e24	+	1.08955e24i	−0.00186548	+	0.00186548i
$943$	−3.48521e26	−	3.48521e26i	−0.591050	−	0.591050i
$944$			5.93562e26i			0.997053i
$945$	−2.59800e26	−	1.20801e26i	−0.432268	−	0.200994i
$946$	1.55748e25			0.0256686
$947$	7.75467e26	−	7.75467e26i	1.26594	−	1.26594i	0.317775	−	0.948166i	$-0.397064\pi$
$947$	7.75467e26	−	7.75467e26i	1.26594	−	1.26594i	0.948166	−	0.317775i	$-0.102936\pi$
$948$	−1.04736e26	−	1.04736e26i	−0.169364	−	0.169364i
$949$		−	1.78927e27i		−	2.86602i
$950$	−1.65752e24	+	1.94358e25i	−0.00262994	+	0.0308383i
$951$	−2.66290e26			−0.418534
$952$	3.16872e25	−	3.16872e25i	0.0493346	−	0.0493346i
$953$	5.94091e26	+	5.94091e26i	0.916256	+	0.916256i	0.996755	−	0.0804983i	$-0.0256512\pi$
$953$	5.94091e26	+	5.94091e26i	0.916256	+	0.916256i	−0.0804983	+	0.996755i	$0.525651\pi$
$954$			3.94712e25i			0.0603039i
$955$	1.71501e26	−	3.68839e26i	0.259559	−	0.558221i
$956$	−1.09108e27			−1.63581
$957$	1.20572e26	−	1.20572e26i	0.179077	−	0.179077i
$958$	2.18717e25	+	2.18717e25i	0.0321806	+	0.0321806i
$959$			6.29870e26i			0.918087i
$960$	7.31729e25	+	2.00358e26i	0.105660	+	0.289311i
$961$	−4.04710e26			−0.578940
$962$	2.36046e25	−	2.36046e25i	0.0334519	−	0.0334519i
$963$	4.61466e26	+	4.61466e26i	0.647892	+	0.647892i
$964$		−	2.46704e26i		−	0.343149i
$965$	−1.05495e27	+	3.85279e26i	−1.45374	+	0.530921i
$966$	−9.82557e24			−0.0134142
$967$	−4.91802e26	+	4.91802e26i	−0.665200	+	0.665200i	−0.956601	−	0.291401i	$-0.905879\pi$
$967$	−4.91802e26	+	4.91802e26i	−0.665200	+	0.665200i	0.291401	+	0.956601i	$0.405879\pi$
$968$	−5.92018e25	−	5.92018e25i	−0.0793335	−	0.0793335i
$969$		−	1.29558e26i		−	0.172009i
$970$	1.28081e25	+	5.95542e24i	0.0168476	+	0.00783370i
$971$	1.25004e27			1.62912			0.814558	−	0.580082i	$-0.196979\pi$
$971$	1.25004e27			1.62912			0.814558	+	0.580082i	$0.196979\pi$
$972$	−4.47172e26	+	4.47172e26i	−0.577401	+	0.577401i
$973$	5.70886e26	+	5.70886e26i	0.730355	+	0.730355i
$974$		−	5.21942e25i		−	0.0661594i
$975$	3.26438e26	−	2.75135e26i	0.409977	−	0.345545i
$976$	8.21894e26			1.02274
$977$	7.88550e26	−	7.88550e26i	0.972251	−	0.972251i	−0.0273745	−	0.999625i	$-0.508715\pi$
$977$	7.88550e26	−	7.88550e26i	0.972251	−	0.972251i	0.999625	+	0.0273745i	$0.00871467\pi$
$978$	−5.37072e24	−	5.37072e24i	−0.00656119	−	0.00656119i
$979$			2.00535e26i			0.242743i
$980$	−1.25290e26	+	2.69455e26i	−0.150273	+	0.323186i
$981$	1.39789e26			0.166131
$982$	−4.71406e25	+	4.71406e25i	−0.0555126	+	0.0555126i
$983$	−5.11073e26	−	5.11073e26i	−0.596350	−	0.596350i	0.342989	−	0.939339i	$-0.388561\pi$
$983$	−5.11073e26	−	5.11073e26i	−0.596350	−	0.596350i	−0.939339	+	0.342989i	$0.888561\pi$
$984$		−	2.06647e25i		−	0.0238931i
$985$	−3.39207e26	−	9.28796e26i	−0.388632	−	1.06413i
$986$	2.12802e25			0.0241592
$987$	−1.08746e26	+	1.08746e26i	−0.122338	+	0.122338i
$988$	6.78588e26	+	6.78588e26i	0.756473	+	0.756473i
$989$			3.47412e26i			0.383776i
$990$	−5.59962e25	+	2.04504e25i	−0.0612974	+	0.0223865i
$991$	1.16955e27			1.26869			0.634346	−	0.773049i	$-0.281269\pi$
$991$	1.16955e27			1.26869			0.634346	+	0.773049i	$0.281269\pi$
$992$	−6.31810e25	+	6.31810e25i	−0.0679174	+	0.0679174i
$993$	3.55070e26	+	3.55070e26i	0.378242	+	0.378242i
$994$		−	5.30735e24i		−	0.00560273i
$995$	1.05000e27	+	4.88222e26i	1.09845	+	0.510752i
$996$	−2.09817e26			−0.217523
$997$	−4.10058e26	+	4.10058e26i	−0.421298	+	0.421298i	−0.885650	−	0.464353i	$-0.846287\pi$
$997$	−4.10058e26	+	4.10058e26i	−0.421298	+	0.421298i	0.464353	+	0.885650i	$0.346287\pi$
$998$	1.10288e25	+	1.10288e25i	0.0112293	+	0.0112293i
$999$			3.28334e26i			0.331304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.19.c.a.3.5	yes	16
3.2	odd	2		45.19.g.a.28.4		16
5.2	odd	4	inner	5.19.c.a.2.5	✓	16
5.3	odd	4		25.19.c.b.7.4		16
5.4	even	2		25.19.c.b.18.4		16
15.2	even	4		45.19.g.a.37.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.19.c.a.2.5	✓	16	5.2	odd	4	inner
5.19.c.a.3.5	yes	16	1.1	even	1	trivial
25.19.c.b.7.4		16	5.3	odd	4
25.19.c.b.18.4		16	5.4	even	2
45.19.g.a.28.4		16	3.2	odd	2
45.19.g.a.37.4		16	15.2	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.9217 + 17.9217i) q^{2} +(-4350.59 - 4350.59i) q^{3} +261502. i q^{4} +(823487. - 1.77104e6i) q^{5} +155940. q^{6} +(-2.28757e7 + 2.28757e7i) q^{7} +(-9.38460e6 - 9.38460e6i) q^{8} -3.49565e8i q^{9} +O(q^{10})\)	\(q+(-17.9217 + 17.9217i) q^{2} +(-4350.59 - 4350.59i) q^{3} +261502. i q^{4} +(823487. - 1.77104e6i) q^{5} +155940. q^{6} +(-2.28757e7 + 2.28757e7i) q^{7} +(-9.38460e6 - 9.38460e6i) q^{8} -3.49565e8i q^{9} +(1.69817e7 + 4.64982e7i) q^{10} -3.44504e9 q^{11} +(1.13769e9 - 1.13769e9i) q^{12} +(-1.28620e10 - 1.28620e10i) q^{13} -8.19943e8i q^{14} +(-1.12877e10 + 4.12240e9i) q^{15} -6.82147e10 q^{16} +(7.38012e10 - 7.38012e10i) q^{17} +(6.26479e9 + 6.26479e9i) q^{18} +2.01754e11i q^{19} +(4.63129e11 + 2.15343e11i) q^{20} +1.99046e11 q^{21} +(6.17409e10 - 6.17409e10i) q^{22} +(1.37720e12 + 1.37720e12i) q^{23} +8.16572e10i q^{24} +(-2.45844e12 - 2.91685e12i) q^{25} +4.61018e11 q^{26} +(-3.20632e12 + 3.20632e12i) q^{27} +(-5.98204e12 - 5.98204e12i) q^{28} -8.04459e12i q^{29} +(1.28414e11 - 2.76175e11i) q^{30} -1.71564e13 q^{31} +(3.68264e12 - 3.68264e12i) q^{32} +(1.49880e13 + 1.49880e13i) q^{33} +2.64528e12i q^{34} +(2.16759e13 + 5.93516e13i) q^{35} +9.14119e13 q^{36} +(5.12010e13 - 5.12010e13i) q^{37} +(-3.61577e12 - 3.61577e12i) q^{38} +1.11915e14i q^{39} +(-2.43486e13 + 8.89237e12i) q^{40} -2.53066e14 q^{41} +(-3.56724e12 + 3.56724e12i) q^{42} +(1.26130e14 + 1.26130e14i) q^{43} -9.00884e14i q^{44} +(-6.19092e14 - 2.87862e14i) q^{45} -4.93633e13 q^{46} +(-5.46338e14 + 5.46338e14i) q^{47} +(2.96774e14 + 2.96774e14i) q^{48} +5.81816e14i q^{49} +(9.63341e13 + 8.21552e12i) q^{50} -6.42158e14 q^{51} +(3.36344e15 - 3.36344e15i) q^{52} +(3.15024e15 + 3.15024e15i) q^{53} -1.14925e14i q^{54} +(-2.83695e15 + 6.10129e15i) q^{55} +4.29359e14 q^{56} +(8.77751e14 - 8.77751e14i) q^{57} +(1.44172e14 + 1.44172e14i) q^{58} -8.70138e15i q^{59} +(-1.07801e15 - 2.95175e15i) q^{60} -1.20486e16 q^{61} +(3.07472e14 - 3.07472e14i) q^{62} +(7.99656e15 + 7.99656e15i) q^{63} -1.77501e16i q^{64} +(-3.33708e16 + 1.21874e16i) q^{65} -5.37219e14 q^{66} +(1.51370e16 - 1.51370e16i) q^{67} +(1.92991e16 + 1.92991e16i) q^{68} -1.19832e16i q^{69} +(-1.45215e15 - 6.75212e14i) q^{70} +6.47283e15 q^{71} +(-3.28053e15 + 3.28053e15i) q^{72} +(6.95564e16 + 6.95564e16i) q^{73} +1.83522e15i q^{74} +(-1.99437e15 + 2.33857e16i) q^{75} -5.27591e16 q^{76} +(7.88078e16 - 7.88078e16i) q^{77} +(-2.00570e15 - 2.00570e15i) q^{78} -9.20606e16i q^{79} +(-5.61739e16 + 1.20811e17i) q^{80} -1.07530e17 q^{81} +(4.53536e15 - 4.53536e15i) q^{82} +(-9.22119e16 - 9.22119e16i) q^{83} +5.20509e16i q^{84} +(-6.99302e16 - 1.91479e17i) q^{85} -4.52092e15 q^{86} +(-3.49987e16 + 3.49987e16i) q^{87} +(3.23304e16 + 3.23304e16i) q^{88} -5.82098e16i q^{89} +(1.62541e16 - 5.93620e15i) q^{90} +5.88456e17 q^{91} +(-3.60139e17 + 3.60139e17i) q^{92} +(7.46407e16 + 7.46407e16i) q^{93} -1.95826e16i q^{94} +(3.57314e17 + 1.66142e17i) q^{95} -3.20433e16 q^{96} +(2.01766e17 - 2.01766e17i) q^{97} +(-1.04271e16 - 1.04271e16i) q^{98} +1.20427e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8}+O(q^{10}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8	\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 11\!\cdots\!80 q^{42}+ \cdots - 43\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 510 * q^2 - 20130 * q^3 + 3145170 * q^5 - 30766728 * q^6 + 78767350 * q^7 - 217339260 * q^8 - 635093930 * q^10 + 4719921012 * q^11 - 22715951880 * q^12 + 8689116940 * q^13 - 59706310410 * q^15 + 10530345976 * q^16 - 221748184620 * q^17 + 654304109970 * q^18 - 878373508140 * q^20 + 1431507507492 * q^21 + 2209421844320 * q^22 - 3507966822690 * q^23 + 10464353188900 * q^25 - 23324455191468 * q^26 + 11679867134280 * q^27 + 8077754165240 * q^28 - 80865025845360 * q^30 + 53033402941772 * q^31 + 20394786468360 * q^32 - 4953707733660 * q^33 - 82375887392730 * q^35 + 263454471040956 * q^36 - 29247362581160 * q^37 + 391580910829560 * q^38 - 918259855204500 * q^40 - 717170436410748 * q^41 + 1119760897992480 * q^42 + 1295649718427950 * q^43 - 2413910465914410 * q^45 - 6165422784262408 * q^46 + 5324712362382270 * q^47 + 7675815427929360 * q^48 - 10266398091964350 * q^50 - 5996743906200468 * q^51 + 5457051468349900 * q^52 + 25019175284457720 * q^53 - 28447209909214060 * q^55 - 22879869030140400 * q^56 + 26327201869272960 * q^57 + 72036625362175440 * q^58 - 129993967558538280 * q^60 - 55112667981951388 * q^61 + 98952816959518920 * q^62 + 129200567352114030 * q^63 - 145786436727900960 * q^65 - 217789774433419296 * q^66 + 132604737823930030 * q^67 + 291394918710173220 * q^68 - 344767752141139080 * q^70 - 148288220084109108 * q^71 + 428373837658219140 * q^72 + 357896091854250160 * q^73 - 656924515001553450 * q^75 - 254554257141486000 * q^76 + 201286979542193700 * q^77 + 866949362074211400 * q^78 - 608571216720410880 * q^80 - 330578957555881164 * q^81 - 167911799138733280 * q^82 + 314012877447835830 * q^83 - 37755360901186580 * q^85 - 149686440788368488 * q^86 + 359090097519437040 * q^87 - 966828856938988320 * q^88 + 2368537241357586390 * q^90 + 498102030062089052 * q^91 - 1299658879961370120 * q^92 - 3025937916654554460 * q^93 + 2986575636848949000 * q^95 + 3531977749160666592 * q^96 - 1689002222572272080 * q^97 - 4330619740553781090 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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