LMFDB - Embedded newform 8.12.b.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,12,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	8.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:	$6.14674544448$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 $ x^10 - x^9 - 48x^8 + 8836x^7 - 92554x^6 - 2200342x^5 - 88894588x^4 + 2040335460x^3 + 7439251985x^2 - 747501940689x + 34431558027300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$-13.4162 + 18.9166i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.12.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-24.8325 + 37.8331i) q^{2} -102.287i q^{3} +(-814.694 - 1878.98i) q^{4} -2319.82i q^{5} +(3869.83 + 2540.04i) q^{6} +38165.0 q^{7} +(91318.7 + 15837.4i) q^{8} +166684. q^{9} +O(q^{10})$	\(q+(-24.8325 + 37.8331i) q^{2} -102.287i q^{3} +(-814.694 - 1878.98i) q^{4} -2319.82i q^{5} +(3869.83 + 2540.04i) q^{6} +38165.0 q^{7} +(91318.7 + 15837.4i) q^{8} +166684. q^{9} +(87766.1 + 57606.9i) q^{10} -322733. i q^{11} +(-192195. + 83332.4i) q^{12} -1.18892e6i q^{13} +(-947733. + 1.44390e6i) q^{14} -237287. q^{15} +(-2.86685e6 + 3.06159e6i) q^{16} +1.63263e6 q^{17} +(-4.13919e6 + 6.30620e6i) q^{18} -1.58773e7i q^{19} +(-4.35890e6 + 1.88994e6i) q^{20} -3.90377e6i q^{21} +(1.22100e7 + 8.01427e6i) q^{22} +7.84803e6 q^{23} +(1.61996e6 - 9.34069e6i) q^{24} +4.34466e7 q^{25} +(4.49805e7 + 2.95238e7i) q^{26} -3.51694e7i q^{27} +(-3.10928e7 - 7.17114e7i) q^{28} +1.88088e8i q^{29} +(5.89242e6 - 8.97731e6i) q^{30} -2.59744e8 q^{31} +(-4.46386e7 - 1.84489e8i) q^{32} -3.30113e7 q^{33} +(-4.05423e7 + 6.17676e7i) q^{34} -8.85360e7i q^{35} +(-1.35797e8 - 3.13197e8i) q^{36} +5.80090e8i q^{37} +(6.00687e8 + 3.94272e8i) q^{38} -1.21610e8 q^{39} +(3.67399e7 - 2.11843e8i) q^{40} +9.39537e8 q^{41} +(1.47692e8 + 9.69405e7i) q^{42} -1.40098e9i q^{43} +(-6.06410e8 + 2.62929e8i) q^{44} -3.86678e8i q^{45} +(-1.94886e8 + 2.96916e8i) q^{46} +3.57380e8 q^{47} +(3.13160e8 + 2.93241e8i) q^{48} -5.20758e8 q^{49} +(-1.07889e9 + 1.64372e9i) q^{50} -1.66996e8i q^{51} +(-2.23396e9 + 9.68604e8i) q^{52} -1.56352e9i q^{53} +(1.33057e9 + 8.73344e8i) q^{54} -7.48683e8 q^{55} +(3.48518e9 + 6.04435e8i) q^{56} -1.62403e9 q^{57} +(-7.11597e9 - 4.67070e9i) q^{58} +5.83337e9i q^{59} +(1.93316e8 + 4.45858e8i) q^{60} -2.32647e9i q^{61} +(6.45009e9 - 9.82693e9i) q^{62} +6.36151e9 q^{63} +(8.08829e9 + 2.89250e9i) q^{64} -2.75807e9 q^{65} +(8.19754e8 - 1.24892e9i) q^{66} +1.50689e10i q^{67} +(-1.33009e9 - 3.06769e9i) q^{68} -8.02749e8i q^{69} +(3.34959e9 + 2.19857e9i) q^{70} +3.46823e9 q^{71} +(1.52214e10 + 2.63985e9i) q^{72} -1.94710e10 q^{73} +(-2.19466e10 - 1.44051e10i) q^{74} -4.44401e9i q^{75} +(-2.98331e10 + 1.29351e10i) q^{76} -1.23171e10i q^{77} +(3.01989e9 - 4.60091e9i) q^{78} -1.13963e10 q^{79} +(7.10234e9 + 6.65058e9i) q^{80} +2.59303e10 q^{81} +(-2.33311e10 + 3.55457e10i) q^{82} -2.66349e10i q^{83} +(-7.33513e9 + 3.18038e9i) q^{84} -3.78741e9i q^{85} +(5.30037e10 + 3.47900e10i) q^{86} +1.92389e10 q^{87} +(5.11126e9 - 2.94716e10i) q^{88} +4.93487e10 q^{89} +(1.46292e10 + 9.60218e9i) q^{90} -4.53750e10i q^{91} +(-6.39374e9 - 1.47463e10i) q^{92} +2.65683e10i q^{93} +(-8.87464e9 + 1.35208e10i) q^{94} -3.68324e10 q^{95} +(-1.88708e10 + 4.56594e9i) q^{96} -1.79889e10 q^{97} +(1.29317e10 - 1.97019e10i) q^{98} -5.37946e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) $ 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−24.8325	+	37.8331i	−0.548726	+	0.836002i
$2$	−24.8325	+	37.8331i	−0.548726	+	0.836002i
$3$		−	102.287i		−	0.243026i	−0.992590	−	0.121513i	$-0.961225\pi$
$3$		−	102.287i		−	0.243026i	0.992590	−	0.121513i	$-0.0387746\pi$
$4$	−814.694	−	1878.98i	−0.397800	−	0.917472i
$5$		−	2319.82i		−	0.331986i	−0.986127	−	0.165993i	$-0.946917\pi$
$5$		−	2319.82i		−	0.331986i	0.986127	−	0.165993i	$-0.0530828\pi$
$6$	3869.83	+	2540.04i	0.203170	+	0.133355i
$7$	38165.0			0.858275			0.429137	−	0.903239i	$-0.358818\pi$
$7$	38165.0			0.858275			0.429137	+	0.903239i	$0.358818\pi$
$8$	91318.7	+	15837.4i	0.985292	+	0.170879i
$9$	166684.			0.940938
$10$	87766.1	+	57606.9i	0.277541	+	0.182169i
$11$		−	322733.i		−	0.604205i	−0.953276	−	0.302102i	$-0.902312\pi$
$11$		−	322733.i		−	0.604205i	0.953276	−	0.302102i	$-0.0976884\pi$
$12$	−192195.	+	83332.4i	−0.222969	+	0.0966756i
$13$		−	1.18892e6i		−	0.888103i	−0.896001	−	0.444051i	$-0.853541\pi$
$13$		−	1.18892e6i		−	0.888103i	0.896001	−	0.444051i	$-0.146459\pi$
$14$	−947733.	+	1.44390e6i	−0.470957	+	0.717520i
$15$	−237287.			−0.0806811
$16$	−2.86685e6	+	3.06159e6i	−0.683511	+	0.729941i
$17$	1.63263e6			0.278881			0.139440	−	0.990230i	$-0.455470\pi$
$17$	1.63263e6			0.278881			0.139440	+	0.990230i	$0.455470\pi$
$18$	−4.13919e6	+	6.30620e6i	−0.516317	+	0.786627i
$19$		−	1.58773e7i		−	1.47106i	−0.677491	−	0.735531i	$-0.736933\pi$
$19$		−	1.58773e7i		−	1.47106i	0.677491	−	0.735531i	$-0.263067\pi$
$20$	−4.35890e6	+	1.88994e6i	−0.304588	+	0.132064i
$21$		−	3.90377e6i		−	0.208583i
$22$	1.22100e7	+	8.01427e6i	0.505116	+	0.331543i
$23$	7.84803e6			0.254248			0.127124	−	0.991887i	$-0.459425\pi$
$23$	7.84803e6			0.254248			0.127124	+	0.991887i	$0.459425\pi$
$24$	1.61996e6	−	9.34069e6i	0.0415280	−	0.239451i
$25$	4.34466e7			0.889786
$26$	4.49805e7	+	2.95238e7i	0.742456	+	0.487325i
$27$		−	3.51694e7i		−	0.471698i
$28$	−3.10928e7	−	7.17114e7i	−0.341421	−	0.787443i
$29$			1.88088e8i			1.70283i	0.524489	+	0.851417i	$0.324256\pi$
$29$			1.88088e8i			1.70283i	−0.524489	+	0.851417i	$0.675744\pi$
$30$	5.89242e6	−	8.97731e6i	0.0442718	−	0.0674496i
$31$	−2.59744e8			−1.62951			−0.814753	−	0.579808i	$-0.803127\pi$
$31$	−2.59744e8			−1.62951			−0.814753	+	0.579808i	$0.803127\pi$
$32$	−4.46386e7	−	1.84489e8i	−0.235172	−	0.971954i
$33$	−3.30113e7			−0.146837
$34$	−4.05423e7	+	6.17676e7i	−0.153029	+	0.233145i
$35$		−	8.85360e7i		−	0.284935i
$36$	−1.35797e8	−	3.13197e8i	−0.374305	−	0.863285i
$37$			5.80090e8i			1.37526i	0.726060	+	0.687631i	$0.241349\pi$
$37$			5.80090e8i			1.37526i	−0.726060	+	0.687631i	$0.758651\pi$
$38$	6.00687e8	+	3.94272e8i	1.22981	+	0.807210i
$39$	−1.21610e8			−0.215832
$40$	3.67399e7	−	2.11843e8i	0.0567294	−	0.327103i
$41$	9.39537e8			1.26649			0.633247	−	0.773950i	$-0.281722\pi$
$41$	9.39537e8			1.26649			0.633247	+	0.773950i	$0.281722\pi$
$42$	1.47692e8	+	9.69405e7i	0.174376	+	0.114455i
$43$		−	1.40098e9i		−	1.45331i	−0.687005	−	0.726653i	$-0.741075\pi$
$43$		−	1.40098e9i		−	1.45331i	0.687005	−	0.726653i	$-0.258925\pi$
$44$	−6.06410e8	+	2.62929e8i	−0.554341	+	0.240352i
$45$		−	3.86678e8i		−	0.312378i
$46$	−1.94886e8	+	2.96916e8i	−0.139512	+	0.212552i
$47$	3.57380e8			0.227296			0.113648	−	0.993521i	$-0.463746\pi$
$47$	3.57380e8			0.227296			0.113648	+	0.993521i	$0.463746\pi$
$48$	3.13160e8	+	2.93241e8i	0.177394	+	0.166111i
$49$	−5.20758e8			−0.263365
$50$	−1.07889e9	+	1.64372e9i	−0.488248	+	0.743863i
$51$		−	1.66996e8i		−	0.0677753i
$52$	−2.23396e9	+	9.68604e8i	−0.814809	+	0.353287i
$53$		−	1.56352e9i		−	0.513554i	−0.966471	−	0.256777i	$-0.917339\pi$
$53$		−	1.56352e9i		−	0.513554i	0.966471	−	0.256777i	$-0.0826606\pi$
$54$	1.33057e9	+	8.73344e8i	0.394341	+	0.258833i
$55$	−7.48683e8			−0.200587
$56$	3.48518e9	+	6.04435e8i	0.845651	+	0.146661i
$57$	−1.62403e9			−0.357506
$58$	−7.11597e9	−	4.67070e9i	−1.42357	−	0.934389i
$59$			5.83337e9i			1.06227i	0.847288	+	0.531133i	$0.178234\pi$
$59$			5.83337e9i			1.06227i	−0.847288	+	0.531133i	$0.821766\pi$
$60$	1.93316e8	+	4.45858e8i	0.0320949	+	0.0740226i
$61$		−	2.32647e9i		−	0.352682i	−0.984329	−	0.176341i	$-0.943574\pi$
$61$		−	2.32647e9i		−	0.352682i	0.984329	−	0.176341i	$-0.0564262\pi$
$62$	6.45009e9	−	9.82693e9i	0.894152	−	1.36227i
$63$	6.36151e9			0.807584
$64$	8.08829e9	+	2.89250e9i	0.941601	+	0.336732i
$65$	−2.75807e9			−0.294837
$66$	8.19754e8	−	1.24892e9i	0.0805734	−	0.122756i
$67$			1.50689e10i			1.36355i	0.731562	+	0.681775i	$0.238792\pi$
$67$			1.50689e10i			1.36355i	−0.731562	+	0.681775i	$0.761208\pi$
$68$	−1.33009e9	−	3.06769e9i	−0.110939	−	0.255866i
$69$		−	8.02749e8i		−	0.0617888i
$70$	3.34959e9	+	2.19857e9i	0.238206	+	0.156351i
$71$	3.46823e9			0.228133			0.114066	−	0.993473i	$-0.463612\pi$
$71$	3.46823e9			0.228133			0.114066	+	0.993473i	$0.463612\pi$
$72$	1.52214e10	+	2.63985e9i	0.927099	+	0.160787i
$73$	−1.94710e10			−1.09929			−0.549646	−	0.835397i	$-0.685238\pi$
$73$	−1.94710e10			−1.09929			−0.549646	+	0.835397i	$0.685238\pi$
$74$	−2.19466e10	−	1.44051e10i	−1.14972	−	0.754642i
$75$		−	4.44401e9i		−	0.216241i
$76$	−2.98331e10	+	1.29351e10i	−1.34966	+	0.585188i
$77$		−	1.23171e10i		−	0.518573i
$78$	3.01989e9	−	4.60091e9i	0.118433	−	0.180436i
$79$	−1.13963e10			−0.416693			−0.208346	−	0.978055i	$-0.566808\pi$
$79$	−1.13963e10			−0.416693			−0.208346	+	0.978055i	$0.566808\pi$
$80$	7.10234e9	+	6.65058e9i	0.242330	+	0.226916i
$81$	2.59303e10			0.826304
$82$	−2.33311e10	+	3.55457e10i	−0.694958	+	1.05879i
$83$		−	2.66349e10i		−	0.742202i	−0.928592	−	0.371101i	$-0.878980\pi$
$83$		−	2.66349e10i		−	0.742202i	0.928592	−	0.371101i	$-0.121020\pi$
$84$	−7.33513e9	+	3.18038e9i	−0.191369	+	0.0829742i
$85$		−	3.78741e9i		−	0.0925845i
$86$	5.30037e10	+	3.47900e10i	1.21497	+	0.797466i
$87$	1.92389e10			0.413833
$88$	5.11126e9	−	2.94716e10i	0.103246	−	0.595318i
$89$	4.93487e10			0.936766			0.468383	−	0.883526i	$-0.344837\pi$
$89$	4.93487e10			0.936766			0.468383	+	0.883526i	$0.344837\pi$
$90$	1.46292e10	+	9.60218e9i	0.261149	+	0.171410i
$91$		−	4.53750e10i		−	0.762236i
$92$	−6.39374e9	−	1.47463e10i	−0.101140	−	0.233265i
$93$			2.65683e10i			0.396012i
$94$	−8.87464e9	+	1.35208e10i	−0.124723	+	0.190020i
$95$	−3.68324e10			−0.488371
$96$	−1.88708e10	+	4.56594e9i	−0.236210	+	0.0571529i
$97$	−1.79889e10			−0.212697			−0.106348	−	0.994329i	$-0.533916\pi$
$97$	−1.79889e10			−0.212697			−0.106348	+	0.994329i	$0.533916\pi$
$98$	1.29317e10	−	1.97019e10i	0.144515	−	0.220174i
$99$		−	5.37946e10i		−	0.568519i
$100$	−3.53957e10	−	8.16354e10i	−0.353957	−	0.816354i
$101$			1.86078e11i			1.76168i	0.473413	+	0.880841i	$0.343022\pi$
$101$			1.86078e11i			1.76168i	−0.473413	+	0.880841i	$0.656978\pi$
$102$	6.31800e9	+	4.14694e9i	0.0566603	+	0.0371900i
$103$	−1.23151e11			−1.04672			−0.523362	−	0.852111i	$-0.675322\pi$
$103$	−1.23151e11			−1.04672			−0.523362	+	0.852111i	$0.675322\pi$
$104$	1.88294e10	−	1.08570e11i	0.151758	−	0.875040i
$105$	−9.05605e9			−0.0692465
$106$	5.91529e10	+	3.88261e10i	0.429332	+	0.281800i
$107$			1.42671e11i			0.983389i	0.870768	+	0.491695i	$0.163622\pi$
$107$			1.42671e11i			0.983389i	−0.870768	+	0.491695i	$0.836378\pi$
$108$	−6.60827e10	+	2.86523e10i	−0.432770	+	0.187641i
$109$		−	2.06502e9i		−	0.0128552i	−0.999979	−	0.00642760i	$-0.997954\pi$
$109$		−	2.06502e9i		−	0.0128552i	0.999979	−	0.00642760i	$-0.00204598\pi$
$110$	1.85917e10	−	2.83250e10i	0.110067	−	0.167691i
$111$	5.93355e10			0.334224
$112$	−1.09413e11	+	1.16846e11i	−0.586640	+	0.626489i
$113$	−6.93428e10			−0.354054			−0.177027	−	0.984206i	$-0.556648\pi$
$113$	−6.93428e10			−0.354054			−0.177027	+	0.984206i	$0.556648\pi$
$114$	4.03288e10	−	6.14423e10i	0.196173	−	0.298876i
$115$		−	1.82060e10i		−	0.0844067i
$116$	3.53414e11	−	1.53234e11i	1.56230	−	0.677387i
$117$		−	1.98174e11i		−	0.835650i
$118$	−2.20695e11	−	1.44857e11i	−0.888057	−	0.582893i
$119$	6.23094e10			0.239356
$120$	−2.16687e10	−	3.75801e9i	−0.0794944	−	0.0137867i
$121$	1.81155e11			0.634937
$122$	8.80177e10	+	5.77721e10i	0.294843	+	0.193526i
$123$		−	9.61022e10i		−	0.307791i
$124$	2.11612e11	+	4.88054e11i	0.648217	+	1.49503i
$125$		−	2.14061e11i		−	0.627382i
$126$	−1.57972e11	+	2.40676e11i	−0.443142	+	0.675142i
$127$	4.46374e11			1.19889			0.599443	−	0.800417i	$-0.295389\pi$
$127$	4.46374e11			1.19889			0.599443	+	0.800417i	$0.295389\pi$
$128$	−3.10285e11	+	2.34177e11i	−0.798189	+	0.602407i
$129$	−1.43302e11			−0.353191
$130$	6.84898e10	−	1.04347e11i	0.161785	−	0.246485i
$131$			3.98721e11i			0.902977i	0.892277	+	0.451488i	$0.149107\pi$
$131$			3.98721e11i			0.902977i	−0.892277	+	0.451488i	$0.850893\pi$
$132$	2.68941e10	+	6.20277e10i	0.0584119	+	0.134719i
$133$		−	6.05956e11i		−	1.26258i
$134$	−5.70105e11	−	3.74199e11i	−1.13993	−	0.748215i
$135$	−8.15866e10			−0.156597
$136$	1.49090e11	+	2.58566e10i	0.274779	+	0.0476549i
$137$	−7.23626e11			−1.28101			−0.640503	−	0.767956i	$-0.721274\pi$
$137$	−7.23626e11			−1.28101			−0.640503	+	0.767956i	$0.721274\pi$
$138$	3.03705e10	+	1.99343e10i	0.0516556	+	0.0339051i
$139$			2.05555e10i			0.0336005i	0.999859	+	0.0168003i	$0.00534794\pi$
$139$			2.05555e10i			0.0336005i	−0.999859	+	0.0168003i	$0.994652\pi$
$140$	−1.66358e11	+	7.21297e10i	−0.261420	+	0.113347i
$141$		−	3.65552e10i		−	0.0552388i
$142$	−8.61249e10	+	1.31214e11i	−0.125182	+	0.190719i
$143$	−3.83703e11			−0.536596
$144$	−4.77859e11	+	5.10320e11i	−0.643141	+	0.686829i
$145$	4.36331e11			0.565316
$146$	4.83515e11	−	7.36651e11i	0.603210	−	0.919011i
$147$			5.32667e10i			0.0640044i
$148$	1.08998e12	−	4.72596e11i	1.26177	−	0.547079i
$149$			1.29425e12i			1.44375i	0.692023	+	0.721875i	$0.256719\pi$
$149$			1.29425e12i			1.44375i	−0.692023	+	0.721875i	$0.743281\pi$
$150$	1.68131e11	+	1.10356e11i	0.180778	+	0.118657i
$151$	5.62940e11			0.583565			0.291782	−	0.956485i	$-0.405752\pi$
$151$	5.62940e11			0.583565			0.291782	+	0.956485i	$0.405752\pi$
$152$	2.51455e11	−	1.44989e12i	0.251374	−	1.44943i
$153$	2.72134e11			0.262410
$154$	4.65995e11	+	3.05865e11i	0.433529	+	0.284555i
$155$			6.02559e11i			0.540972i
$156$	9.90753e10	+	2.28504e11i	0.0858579	+	0.198020i
$157$			1.78875e11i			0.149658i	0.997196	+	0.0748291i	$0.0238411\pi$
$157$			1.78875e11i			0.149658i	−0.997196	+	0.0748291i	$0.976159\pi$
$158$	2.82999e11	−	4.31159e11i	0.228650	−	0.348356i
$159$	−1.59927e11			−0.124807
$160$	−4.27981e11	+	1.03554e11i	−0.322675	+	0.0780738i
$161$	2.99520e11			0.218215
$162$	−6.43914e11	+	9.81024e11i	−0.453414	+	0.690792i
$163$		−	8.52545e11i		−	0.580344i	−0.956975	−	0.290172i	$-0.906288\pi$
$163$		−	8.52545e11i		−	0.580344i	0.956975	−	0.290172i	$-0.0937125\pi$
$164$	−7.65436e11	−	1.76537e12i	−0.503811	−	1.16197i
$165$			7.65803e10i			0.0487479i
$166$	1.00768e12	+	6.61412e11i	0.620483	+	0.407266i
$167$	−3.06465e12			−1.82575			−0.912874	−	0.408242i	$-0.866142\pi$
$167$	−3.06465e12			−1.82575			−0.912874	+	0.408242i	$0.866142\pi$
$168$	6.18257e10	−	3.56488e11i	0.0356425	−	0.205515i
$169$	3.78637e11			0.211274
$170$	1.43290e11	+	9.40508e10i	0.0774008	+	0.0508035i
$171$		−	2.64649e12i		−	1.38418i
$172$	−2.63243e12	+	1.14137e12i	−1.33337	+	0.578125i
$173$			2.44372e12i			1.19894i	0.800397	+	0.599470i	$0.204622\pi$
$173$			2.44372e12i			1.19894i	−0.800397	+	0.599470i	$0.795378\pi$
$174$	−4.77750e11	+	7.27869e11i	−0.227081	+	0.345965i
$175$	1.65814e12			0.763680
$176$	9.88078e11	+	9.25228e11i	0.441033	+	0.412980i
$177$	5.96676e11			0.258158
$178$	−1.22545e12	+	1.86702e12i	−0.514027	+	0.783138i
$179$		−	5.39073e11i		−	0.219258i	−0.993973	−	0.109629i	$-0.965034\pi$
$179$		−	5.39073e11i		−	0.219258i	0.993973	−	0.109629i	$-0.0349663\pi$
$180$	−7.26561e11	+	3.15024e11i	−0.286598	+	0.124264i
$181$		−	2.74637e12i		−	1.05082i	−0.850850	−	0.525409i	$-0.823912\pi$
$181$		−	2.74637e12i		−	1.05082i	0.850850	−	0.525409i	$-0.176088\pi$
$182$	1.71668e12	+	1.12678e12i	0.637231	+	0.418258i
$183$	−2.37967e11			−0.0857109
$184$	7.16672e11	+	1.24292e11i	0.250508	+	0.0434457i
$185$	1.34570e12			0.456567
$186$	−1.00516e12	−	6.59758e11i	−0.331067	−	0.217302i
$187$		−	5.26904e11i		−	0.168501i
$188$	−2.91155e11	−	6.71511e11i	−0.0904183	−	0.208538i
$189$		−	1.34224e12i		−	0.404846i
$190$	9.14641e11	−	1.39349e12i	0.267982	−	0.408280i
$191$	4.34170e12			1.23588			0.617940	−	0.786225i	$-0.287967\pi$
$191$	4.34170e12			1.23588			0.617940	+	0.786225i	$0.287967\pi$
$192$	2.95865e11	−	8.27325e11i	0.0818345	−	0.228833i
$193$	−2.28419e12			−0.613997			−0.306998	−	0.951710i	$-0.599325\pi$
$193$	−2.28419e12			−0.613997			−0.306998	+	0.951710i	$0.599325\pi$
$194$	4.46710e11	−	6.80578e11i	0.116712	−	0.177815i
$195$			2.82114e11i			0.0716531i
$196$	4.24259e11	+	9.78496e11i	0.104766	+	0.241630i
$197$			1.53464e12i			0.368503i	0.982879	+	0.184251i	$0.0589861\pi$
$197$			1.53464e12i			0.368503i	−0.982879	+	0.184251i	$0.941014\pi$
$198$	2.03522e12	+	1.33585e12i	0.475283	+	0.311961i
$199$	−3.61205e12			−0.820468			−0.410234	−	0.911980i	$-0.634553\pi$
$199$	−3.61205e12			−0.820468			−0.410234	+	0.911980i	$0.634553\pi$
$200$	3.96749e12	+	6.88081e11i	0.876699	+	0.152046i
$201$	1.54135e12			0.331378
$202$	−7.03992e12	−	4.62078e12i	−1.47277	−	0.966680i
$203$			7.17839e12i			1.46150i
$204$	−3.13784e11	+	1.36051e11i	−0.0621819	+	0.0269610i
$205$		−	2.17956e12i		−	0.420457i
$206$	3.05814e12	−	4.65918e12i	0.574364	−	0.875063i
$207$	1.30814e12			0.239232
$208$	3.63998e12	+	3.40845e12i	0.648262	+	0.607027i
$209$	−5.12412e12			−0.888822
$210$	2.24884e11	−	3.42619e11i	0.0379973	−	0.0578902i
$211$			7.15580e12i			1.17789i	0.808173	+	0.588945i	$0.200457\pi$
$211$			7.15580e12i			1.17789i	−0.808173	+	0.588945i	$0.799543\pi$
$212$	−2.93783e12	+	1.27379e12i	−0.471172	+	0.204292i
$213$		−	3.54754e11i		−	0.0554421i
$214$	−5.39770e12	−	3.54288e12i	−0.822116	−	0.539611i
$215$	−3.25003e12			−0.482476
$216$	5.56992e11	−	3.21162e12i	0.0806034	−	0.464760i
$217$	−9.91313e12			−1.39856
$218$	7.81263e10	+	5.12797e10i	0.0107470	+	0.00705398i
$219$			1.99163e12i			0.267157i
$220$	6.09948e11	+	1.40676e12i	0.0797936	+	0.184033i
$221$		−	1.94106e12i		−	0.247675i
$222$	−1.47345e12	+	2.24485e12i	−0.183397	+	0.279412i
$223$	9.09508e12			1.10441			0.552204	−	0.833709i	$-0.313787\pi$
$223$	9.09508e12			1.10441			0.552204	+	0.833709i	$0.313787\pi$
$224$	−1.70363e12	−	7.04103e12i	−0.201842	−	0.834203i
$225$	7.24187e12			0.837233
$226$	1.72196e12	−	2.62346e12i	0.194279	−	0.295990i
$227$		−	9.30911e12i		−	1.02510i	−0.858658	−	0.512550i	$-0.828701\pi$
$227$		−	9.30911e12i		−	1.02510i	0.858658	−	0.512550i	$-0.171299\pi$
$228$	1.32309e12	+	3.05153e12i	0.142216	+	0.328002i
$229$		−	3.51415e12i		−	0.368744i	−0.982857	−	0.184372i	$-0.940975\pi$
$229$		−	3.51415e12i		−	0.368744i	0.982857	−	0.184372i	$-0.0590251\pi$
$230$	6.88791e11	+	4.52101e11i	0.0705642	+	0.0463161i
$231$	−1.25988e12			−0.126027
$232$	−2.97883e12	+	1.71760e13i	−0.290979	+	1.67779i
$233$	7.84098e12			0.748019			0.374010	−	0.927425i	$-0.377983\pi$
$233$	7.84098e12			0.748019			0.374010	+	0.927425i	$0.377983\pi$
$234$	7.49754e12	+	4.92115e12i	0.698605	+	0.458543i
$235$		−	8.29057e11i		−	0.0754590i
$236$	1.09608e13	−	4.75241e12i	0.974600	−	0.422569i
$237$			1.16569e12i			0.101267i
$238$	−1.54730e12	+	2.35736e12i	−0.131341	+	0.200103i
$239$	8.46637e12			0.702278			0.351139	−	0.936323i	$-0.385795\pi$
$239$	8.46637e12			0.702278			0.351139	+	0.936323i	$0.385795\pi$
$240$	6.80266e11	−	7.26475e11i	0.0551464	−	0.0588924i
$241$	4.67007e12			0.370023			0.185012	−	0.982736i	$-0.440768\pi$
$241$	4.67007e12			0.370023			0.185012	+	0.982736i	$0.440768\pi$
$242$	−4.49853e12	+	6.85366e12i	−0.348406	+	0.530809i
$243$		−	8.88248e12i		−	0.672511i
$244$	−4.37140e12	+	1.89536e12i	−0.323576	+	0.140297i
$245$			1.20807e12i			0.0874333i
$246$	3.63585e12	+	2.38646e12i	0.257314	+	0.168893i
$247$	−1.88768e13			−1.30645
$248$	−2.37195e13	−	4.11367e12i	−1.60554	−	0.278449i
$249$	−2.72440e12			−0.180374
$250$	8.09859e12	+	5.31566e12i	0.524492	+	0.344260i
$251$		−	2.26321e13i		−	1.43390i	−0.697124	−	0.716950i	$-0.745537\pi$
$251$		−	2.26321e13i		−	1.43390i	0.697124	−	0.716950i	$-0.254463\pi$
$252$	−5.18269e12	−	1.19532e13i	−0.321257	−	0.740935i
$253$		−	2.53282e12i		−	0.153618i
$254$	−1.10846e13	+	1.68877e13i	−0.657860	+	1.00227i
$255$	−3.87402e11			−0.0225004
$256$	−1.15452e12	−	1.75543e13i	−0.0656266	−	0.997844i
$257$	7.61647e12			0.423762			0.211881	−	0.977296i	$-0.432041\pi$
$257$	7.61647e12			0.423762			0.211881	+	0.977296i	$0.432041\pi$
$258$	3.55855e12	−	5.42157e12i	0.193805	−	0.295268i
$259$			2.21391e13i			1.18035i
$260$	2.24699e12	+	5.18237e12i	0.117286	+	0.270505i
$261$			3.13514e13i			1.60226i
$262$	−1.50849e13	−	9.90123e12i	−0.754891	−	0.495487i
$263$	−3.28446e13			−1.60956			−0.804782	−	0.593571i	$-0.797718\pi$
$263$	−3.28446e13			−1.60956			−0.804782	+	0.593571i	$0.797718\pi$
$264$	−3.01455e12	−	5.22814e11i	−0.144678	−	0.0250914i
$265$	−3.62708e12			−0.170493
$266$	2.29252e13	+	1.50474e13i	1.05552	+	0.692808i
$267$		−	5.04772e12i		−	0.227658i
$268$	2.83143e13	−	1.22766e13i	1.25102	−	0.542420i
$269$			1.88171e13i			0.814544i	0.913307	+	0.407272i	$0.133520\pi$
$269$			1.88171e13i			0.814544i	−0.913307	+	0.407272i	$0.866480\pi$
$270$	2.02600e12	−	3.08668e12i	0.0859288	−	0.130915i
$271$	4.66640e13			1.93932			0.969662	−	0.244448i	$-0.0786068\pi$
$271$	4.66640e13			1.93932			0.969662	+	0.244448i	$0.0786068\pi$
$272$	−4.68051e12	+	4.99845e12i	−0.190618	+	0.203567i
$273$	−4.64126e12			−0.185243
$274$	1.79694e13	−	2.73771e13i	0.702921	−	1.07092i
$275$		−	1.40217e13i		−	0.537612i
$276$	−1.50835e12	+	6.53995e11i	−0.0566895	+	0.0245796i
$277$		−	1.43032e13i		−	0.526980i	−0.964662	−	0.263490i	$-0.915126\pi$
$277$		−	1.43032e13i		−	0.526980i	0.964662	−	0.263490i	$-0.0848735\pi$
$278$	−7.77678e11	−	5.10444e11i	−0.0280901	−	0.0184375i
$279$	−4.32953e13			−1.53326
$280$	1.40218e12	−	8.08499e12i	0.0486894	−	0.280744i
$281$	2.34993e13			0.800149			0.400074	−	0.916483i	$-0.368984\pi$
$281$	2.34993e13			0.800149			0.400074	+	0.916483i	$0.368984\pi$
$282$	1.38300e12	+	9.07757e11i	0.0461798	+	0.0303110i
$283$			3.70545e13i			1.21343i	0.794918	+	0.606717i	$0.207514\pi$
$283$			3.70545e13i			1.21343i	−0.794918	+	0.606717i	$0.792486\pi$
$284$	−2.82555e12	−	6.51675e12i	−0.0907511	−	0.209305i
$285$			3.76747e12i			0.118687i
$286$	9.52831e12	−	1.45167e13i	0.294444	−	0.448595i
$287$	3.58575e13			1.08700
$288$	−7.44056e12	−	3.07514e13i	−0.221283	−	0.914549i
$289$	−3.16064e13			−0.922225
$290$	−1.08352e13	+	1.65078e13i	−0.310204	+	0.472606i
$291$			1.84003e12i			0.0516908i
$292$	1.58629e13	+	3.65858e13i	0.437299	+	1.00857i
$293$		−	2.96206e13i		−	0.801350i	−0.916220	−	0.400675i	$-0.868776\pi$
$293$		−	2.96206e13i		−	0.801350i	0.916220	−	0.400675i	$-0.131224\pi$
$294$	−2.01525e12	−	1.32274e12i	−0.0535079	−	0.0351209i
$295$	1.35324e13			0.352657
$296$	−9.18711e12	+	5.29730e13i	−0.235004	+	1.35503i
$297$	−1.13503e13			−0.285002
$298$	−4.89654e13	−	3.21393e13i	−1.20698	−	0.792223i
$299$		−	9.33066e12i		−	0.225798i
$300$	−8.35021e12	+	3.62051e12i	−0.198395	+	0.0860206i
$301$		−	5.34686e13i		−	1.24734i
$302$	−1.39792e13	+	2.12978e13i	−0.320217	+	0.487861i
$303$	1.90333e13			0.428134
$304$	4.86097e13	+	4.55178e13i	1.07379	+	1.00549i
$305$	−5.39699e12			−0.117085
$306$	−6.75777e12	+	1.02957e13i	−0.143991	+	0.219375i
$307$			2.93512e13i			0.614277i	0.951665	+	0.307139i	$0.0993715\pi$
$307$			2.93512e13i			0.614277i	−0.951665	+	0.307139i	$0.900628\pi$
$308$	−2.31437e13	+	1.00347e13i	−0.475777	+	0.206288i
$309$			1.25967e13i			0.254381i
$310$	−2.27967e13	−	1.49630e13i	−0.452254	−	0.296846i
$311$	−4.02432e13			−0.784350			−0.392175	−	0.919891i	$-0.628277\pi$
$311$	−4.02432e13			−0.784350			−0.392175	+	0.919891i	$0.628277\pi$
$312$	−1.11053e13	−	1.92599e12i	−0.212657	−	0.0368812i
$313$	−1.58755e13			−0.298699			−0.149350	−	0.988784i	$-0.547718\pi$
$313$	−1.58755e13			−0.298699			−0.149350	+	0.988784i	$0.547718\pi$
$314$	−6.76739e12	−	4.44190e12i	−0.125115	−	0.0821213i
$315$		−	1.47576e13i		−	0.268106i
$316$	9.28452e12	+	2.14135e13i	0.165760	+	0.382304i
$317$		−	5.40318e13i		−	0.948033i	−0.880516	−	0.474016i	$-0.842804\pi$
$317$		−	5.40318e13i		−	0.948033i	0.880516	−	0.474016i	$-0.157196\pi$
$318$	3.97140e12	−	6.05056e12i	0.0684848	−	0.104339i
$319$	6.07023e13			1.02886
$320$	6.71009e12	−	1.87634e13i	0.111790	−	0.312598i
$321$	1.45934e13			0.238989
$322$	−7.43783e12	+	1.13318e13i	−0.119740	+	0.182428i
$323$		−	2.59217e13i		−	0.410251i
$324$	−2.11252e13	−	4.87226e13i	−0.328703	−	0.758111i
$325$		−	5.16544e13i		−	0.790221i
$326$	3.22545e13	+	2.11708e13i	0.485169	+	0.318450i
$327$	−2.11224e11			−0.00312415
$328$	8.57974e13	+	1.48798e13i	1.24787	+	0.216417i
$329$	1.36394e13			0.195082
$330$	−2.89728e12	−	1.90168e12i	−0.0407533	−	0.0267492i
$331$			9.13142e13i			1.26324i	0.775280	+	0.631618i	$0.217609\pi$
$331$			9.13142e13i			1.26324i	−0.775280	+	0.631618i	$0.782391\pi$
$332$	−5.00466e13	+	2.16993e13i	−0.680950	+	0.295248i
$333$			9.66919e13i			1.29404i
$334$	7.61030e13	−	1.15945e14i	1.00183	−	1.52633i
$335$	3.49572e13			0.452679
$336$	1.19518e13	+	1.11915e13i	0.152253	+	0.142569i
$337$	9.48744e12			0.118901			0.0594504	−	0.998231i	$-0.481065\pi$
$337$	9.48744e12			0.118901			0.0594504	+	0.998231i	$0.481065\pi$
$338$	−9.40249e12	+	1.43250e13i	−0.115931	+	0.176625i
$339$			7.09285e12i			0.0860444i
$340$	−7.11648e12	+	3.08558e12i	−0.0849437	+	0.0368301i
$341$			8.38280e13i			0.984555i
$342$	1.00125e14	+	6.57190e13i	1.15718	+	0.759535i
$343$	−9.53395e13			−1.08431
$344$	2.21880e13	−	1.27936e14i	0.248340	−	1.43193i
$345$	−1.86223e12			−0.0205130
$346$	−9.24535e13	−	6.06836e13i	−1.00232	−	0.657889i
$347$		−	1.09420e14i		−	1.16757i	−0.811907	−	0.583787i	$-0.801570\pi$
$347$		−	1.09420e14i		−	1.16757i	0.811907	−	0.583787i	$-0.198430\pi$
$348$	−1.56738e13	−	3.61496e13i	−0.164623	−	0.379680i
$349$			1.02063e14i			1.05518i	0.849498	+	0.527592i	$0.176905\pi$
$349$			1.02063e14i			1.05518i	−0.849498	+	0.527592i	$0.823095\pi$
$350$	−4.11757e13	+	6.27326e13i	−0.419051	+	0.638439i
$351$	−4.18135e13			−0.418916
$352$	−5.95407e13	+	1.44064e13i	−0.587259	+	0.142092i
$353$	1.38134e13			0.134134			0.0670669	−	0.997748i	$-0.478636\pi$
$353$	1.38134e13			0.134134			0.0670669	+	0.997748i	$0.478636\pi$
$354$	−1.48170e13	+	2.25741e13i	−0.141658	+	0.215821i
$355$		−	8.04567e12i		−	0.0757367i
$356$	−4.02041e13	−	9.27254e13i	−0.372645	−	0.859456i
$357$		−	6.37342e12i		−	0.0581698i
$358$	2.03948e13	+	1.33865e13i	0.183300	+	0.120313i
$359$	−1.49435e14			−1.32262			−0.661308	−	0.750114i	$-0.729998\pi$
$359$	−1.49435e14			−1.32262			−0.661308	+	0.750114i	$0.729998\pi$
$360$	6.12397e12	−	3.53109e13i	0.0533789	−	0.307784i
$361$	−1.35597e14			−1.16402
$362$	1.03904e14	+	6.81993e13i	0.878487	+	0.576611i
$363$		−	1.85297e13i		−	0.154306i
$364$	−8.52589e13	+	3.69668e13i	−0.699330	+	0.303217i
$365$			4.51693e13i			0.364949i
$366$	5.90932e12	−	9.00305e12i	0.0470318	−	0.0716545i
$367$	1.18168e14			0.926483			0.463242	−	0.886232i	$-0.346686\pi$
$367$	1.18168e14			0.926483			0.463242	+	0.886232i	$0.346686\pi$
$368$	−2.24991e13	+	2.40275e13i	−0.173781	+	0.185586i
$369$	1.56606e14			1.19169
$370$	−3.34172e13	+	5.09122e13i	−0.250530	+	0.381691i
$371$		−	5.96718e13i		−	0.440770i
$372$	4.99215e13	−	2.16451e13i	0.363330	−	0.157534i
$373$		−	1.05789e14i		−	0.758647i	−0.925264	−	0.379324i	$-0.876157\pi$
$373$		−	1.05789e14i		−	0.758647i	0.925264	−	0.379324i	$-0.123843\pi$
$374$	1.99344e13	+	1.30843e13i	0.140867	+	0.0924609i
$375$	−2.18956e13			−0.152470
$376$	3.26355e13	+	5.65997e12i	0.223953	+	0.0388402i
$377$	2.23621e14			1.51229
$378$	5.07812e13	+	3.33312e13i	0.338453	+	0.222150i
$379$			1.16738e12i			0.00766828i	0.999993	+	0.00383414i	$0.00122045\pi$
$379$			1.16738e12i			0.00766828i	−0.999993	+	0.00383414i	$0.998780\pi$
$380$	3.00071e13	+	6.92075e13i	0.194274	+	0.448067i
$381$		−	4.56581e13i		−	0.291360i
$382$	−1.07815e14	+	1.64260e14i	−0.678159	+	1.03320i
$383$	1.13087e14			0.701164			0.350582	−	0.936532i	$-0.385984\pi$
$383$	1.13087e14			0.701164			0.350582	+	0.936532i	$0.385984\pi$
$384$	2.39532e13	+	3.17380e13i	0.146400	+	0.193981i
$385$	−2.85735e13			−0.172159
$386$	5.67220e13	−	8.64179e13i	0.336916	−	0.513303i
$387$		−	2.33522e14i		−	1.36747i
$388$	1.46555e13	+	3.38009e13i	0.0846108	+	0.195143i
$389$			1.55307e14i			0.884035i	0.897006	+	0.442018i	$0.145737\pi$
$389$			1.55307e14i			0.884035i	−0.897006	+	0.442018i	$0.854263\pi$
$390$	−1.06733e13	−	7.00560e12i	−0.0599021	−	0.0393179i
$391$	1.28129e13			0.0709049
$392$	−4.75550e13	−	8.24746e12i	−0.259491	−	0.0450036i
$393$	4.07838e13			0.219447
$394$	−5.80601e13	−	3.81088e13i	−0.308069	−	0.202207i
$395$			2.64374e13i			0.138336i
$396$	−1.01079e14	+	4.38262e13i	−0.521601	+	0.226157i
$397$		−	3.63452e14i		−	1.84969i	−0.380341	−	0.924846i	$-0.624193\pi$
$397$		−	3.63452e14i		−	1.84969i	0.380341	−	0.924846i	$-0.375807\pi$
$398$	8.96962e13	−	1.36655e14i	0.450212	−	0.685913i
$399$	−6.19813e13			−0.306838
$400$	−1.24555e14	+	1.33016e14i	−0.608178	+	0.649491i
$401$	−3.34748e14			−1.61222			−0.806109	−	0.591767i	$-0.798430\pi$
$401$	−3.34748e14			−1.61222			−0.806109	+	0.591767i	$0.798430\pi$
$402$	−3.82756e13	+	5.83142e13i	−0.181836	+	0.277033i
$403$			3.08814e14i			1.44717i
$404$	3.49637e14	−	1.51597e14i	1.61629	−	0.700797i
$405$		−	6.01536e13i		−	0.274321i
$406$	−2.71581e14	−	1.78257e14i	−1.22182	−	0.801962i
$407$	1.87214e14			0.830940
$408$	2.64479e12	−	1.52499e13i	0.0115814	−	0.0667784i
$409$	−2.08756e14			−0.901903			−0.450952	−	0.892548i	$-0.648915\pi$
$409$	−2.08756e14			−0.901903			−0.450952	+	0.892548i	$0.648915\pi$
$410$	8.24595e13	+	5.41239e13i	0.351503	+	0.230716i
$411$			7.40174e13i			0.311318i
$412$	1.00330e14	+	2.31398e14i	0.416386	+	0.960340i
$413$			2.22631e14i			0.911716i
$414$	−3.24845e13	+	4.94912e13i	−0.131273	+	0.199998i
$415$	−6.17883e13			−0.246400
$416$	−2.19342e14	+	5.30716e13i	−0.863195	+	0.208857i
$417$	2.10255e12			0.00816580
$418$	1.27245e14	−	1.93862e14i	0.487720	−	0.743058i
$419$			4.48317e14i			1.69593i	0.530053	+	0.847965i	$0.322172\pi$
$419$			4.48317e14i			1.69593i	−0.530053	+	0.847965i	$0.677828\pi$
$420$	7.37791e12	+	1.70162e13i	0.0275462	+	0.0635317i
$421$		−	6.11796e13i		−	0.225453i	−0.993626	−	0.112726i	$-0.964042\pi$
$421$		−	6.11796e13i		−	0.225453i	0.993626	−	0.112726i	$-0.0359583\pi$
$422$	−2.70727e14	−	1.77696e14i	−0.984719	−	0.646339i
$423$	5.95697e13			0.213872
$424$	2.47621e13	−	1.42779e14i	0.0877557	−	0.506001i
$425$	7.09322e13			0.248144
$426$	1.34215e13	+	8.80943e12i	0.0463497	+	0.0304225i
$427$		−	8.87898e13i		−	0.302698i
$428$	2.68077e14	−	1.16233e14i	0.902233	−	0.391192i
$429$			3.92477e13i			0.130407i
$430$	8.07064e13	−	1.22959e14i	0.264747	−	0.403351i
$431$	−3.53300e14			−1.14424			−0.572121	−	0.820169i	$-0.693879\pi$
$431$	−3.53300e14			−1.14424			−0.572121	+	0.820169i	$0.693879\pi$
$432$	1.07674e14	+	1.00825e14i	0.344312	+	0.322411i
$433$	2.04692e13			0.0646274			0.0323137	−	0.999478i	$-0.489712\pi$
$433$	2.04692e13			0.0646274			0.0323137	+	0.999478i	$0.489712\pi$
$434$	2.46168e14	−	3.75045e14i	0.767428	−	1.16920i
$435$		−	4.46308e13i		−	0.137386i
$436$	−3.88014e12	+	1.68236e12i	−0.0117943	+	0.00511380i
$437$		−	1.24605e14i		−	0.374015i
$438$	−7.53496e13	−	4.94571e13i	−0.223343	−	0.146596i
$439$	4.40703e14			1.29001			0.645003	−	0.764180i	$-0.276856\pi$
$439$	4.40703e14			1.29001			0.645003	+	0.764180i	$0.276856\pi$
$440$	−6.83688e13	−	1.18572e13i	−0.197637	−	0.0342762i
$441$	−8.68023e13			−0.247810
$442$	7.34365e13	+	4.82014e13i	0.207057	+	0.135906i
$443$			2.20616e14i			0.614351i	0.951653	+	0.307176i	$0.0993839\pi$
$443$			2.20616e14i			0.614351i	−0.951653	+	0.307176i	$0.900616\pi$
$444$	−4.83402e13	−	1.11490e14i	−0.132954	−	0.306641i
$445$		−	1.14480e14i		−	0.310993i
$446$	−2.25854e14	+	3.44096e14i	−0.606018	+	0.923288i
$447$	1.32384e14			0.350869
$448$	3.08690e14	+	1.10392e14i	0.808152	+	0.289008i
$449$	6.25962e13			0.161880			0.0809400	−	0.996719i	$-0.474208\pi$
$449$	6.25962e13			0.161880			0.0809400	+	0.996719i	$0.474208\pi$
$450$	−1.79834e14	+	2.73983e14i	−0.459412	+	0.699929i
$451$		−	3.03220e14i		−	0.765221i
$452$	5.64932e13	+	1.30294e14i	0.140843	+	0.324835i
$453$		−	5.75813e13i		−	0.141821i
$454$	3.52193e14	+	2.31168e14i	0.856986	+	0.562499i
$455$	−1.05262e14			−0.253051
$456$	−1.48305e14	−	2.57205e13i	−0.352248	−	0.0610903i
$457$	3.73355e14			0.876159			0.438079	−	0.898936i	$-0.355659\pi$
$457$	3.73355e14			0.876159			0.438079	+	0.898936i	$0.355659\pi$
$458$	1.32951e14	+	8.72650e13i	0.308271	+	0.202339i
$459$		−	5.74186e13i		−	0.131548i
$460$	−3.42088e13	+	1.48323e13i	−0.0774408	+	0.0335770i
$461$			8.60218e13i			0.192422i	0.995361	+	0.0962108i	$0.0306723\pi$
$461$			8.60218e13i			0.192422i	−0.995361	+	0.0962108i	$0.969328\pi$
$462$	3.12859e13	−	4.76652e13i	0.0691541	−	0.105359i
$463$	−2.34782e14			−0.512824			−0.256412	−	0.966568i	$-0.582540\pi$
$463$	−2.34782e14			−0.512824			−0.256412	+	0.966568i	$0.582540\pi$
$464$	−5.75849e14	−	5.39221e14i	−1.24297	−	1.16391i
$465$	6.16338e13			0.131470
$466$	−1.94711e14	+	2.96649e14i	−0.410458	+	0.625346i
$467$		−	6.50037e14i		−	1.35424i	−0.735873	−	0.677120i	$-0.763228\pi$
$467$		−	6.50037e14i		−	1.35424i	0.735873	−	0.677120i	$-0.236772\pi$
$468$	−3.72366e14	+	1.61451e14i	−0.766686	+	0.332421i
$469$			5.75106e14i			1.17030i
$470$	3.13658e13	+	2.05876e13i	0.0630839	+	0.0414063i
$471$	1.82965e13			0.0363708
$472$	−9.23854e13	+	5.32696e14i	−0.181519	+	1.04664i
$473$	−4.52144e14			−0.878094
$474$	−4.41018e13	−	2.89471e13i	−0.0846595	−	0.0555678i
$475$		−	6.89813e14i		−	1.30893i
$476$	−5.07631e13	−	1.17078e14i	−0.0952160	−	0.219603i
$477$		−	2.60614e14i		−	0.483223i
$478$	−2.10241e14	+	3.20309e14i	−0.385358	+	0.587106i
$479$	−7.05162e14			−1.27774			−0.638871	−	0.769314i	$-0.720598\pi$
$479$	−7.05162e14			−1.27774			−0.638871	+	0.769314i	$0.720598\pi$
$480$	1.05922e13	+	4.37768e13i	0.0189739	+	0.0784183i
$481$	6.89678e14			1.22137
$482$	−1.15969e14	+	1.76683e14i	−0.203041	+	0.309340i
$483$		−	3.06369e13i		−	0.0530318i
$484$	−1.47586e14	−	3.40387e14i	−0.252578	−	0.582537i
$485$			4.17311e13i			0.0706123i
$486$	3.36052e14	+	2.20574e14i	0.562221	+	0.369024i
$487$	2.90472e14			0.480502			0.240251	−	0.970711i	$-0.422770\pi$
$487$	2.90472e14			0.480502			0.240251	+	0.970711i	$0.422770\pi$
$488$	3.68453e13	−	2.12450e14i	0.0602660	−	0.347495i
$489$	−8.72040e13			−0.141039
$490$	−4.57049e13	−	2.99993e13i	−0.0730945	−	0.0479769i
$491$			5.47242e14i			0.865429i	0.901531	+	0.432714i	$0.142444\pi$
$491$			5.47242e14i			0.865429i	−0.901531	+	0.432714i	$0.857556\pi$
$492$	−1.80574e14	+	7.82939e13i	−0.282389	+	0.122439i
$493$			3.07078e14i			0.474888i
$494$	4.68757e14	−	7.14167e14i	0.716885	−	1.09220i
$495$	−1.24794e14			−0.188740
$496$	7.44647e14	−	7.95230e14i	1.11378	−	1.18944i
$497$	1.32365e14			0.195800
$498$	6.76537e13	−	1.03073e14i	0.0989761	−	0.150793i
$499$			9.57711e13i			0.138574i	0.997597	+	0.0692869i	$0.0220724\pi$
$499$			9.57711e13i			0.138574i	−0.997597	+	0.0692869i	$0.977928\pi$
$500$	−4.02216e14	+	1.74394e14i	−0.575605	+	0.249572i
$501$			3.13473e14i			0.443704i
$502$	8.56243e14	+	5.62011e14i	1.19874	+	0.786819i
$503$	7.19799e14			0.996752			0.498376	−	0.866961i	$-0.333930\pi$
$503$	7.19799e14			0.996752			0.498376	+	0.866961i	$0.333930\pi$
$504$	5.80925e14	+	1.00750e14i	0.795706	+	0.137999i
$505$	4.31667e14			0.584853
$506$	9.58246e13	+	6.28962e13i	0.128425	+	0.0842940i
$507$		−	3.87295e13i		−	0.0513450i
$508$	−3.63658e14	−	8.38728e14i	−0.476917	−	1.09994i
$509$			4.54203e14i			0.589254i	0.955612	+	0.294627i	$0.0951954\pi$
$509$			4.54203e14i			0.589254i	−0.955612	+	0.294627i	$0.904805\pi$
$510$	9.62015e12	−	1.46566e13i	0.0123466	−	0.0188104i
$511$	−7.43112e14			−0.943495
$512$	6.92802e14	+	3.92237e14i	0.870211	+	0.492679i
$513$	−5.58394e14			−0.693897
$514$	−1.89136e14	+	2.88155e14i	−0.232529	+	0.354266i
$515$			2.85687e14i			0.347497i
$516$	1.16747e14	+	2.69262e14i	0.140499	+	0.324043i
$517$		−	1.15338e14i		−	0.137333i
$518$	−8.37593e14	−	5.49770e14i	−0.986778	−	0.647690i
$519$	2.49960e14			0.291373
$520$	−2.51864e14	−	4.36807e13i	−0.290501	−	0.0503815i
$521$	−1.72796e14			−0.197209			−0.0986046	−	0.995127i	$-0.531438\pi$
$521$	−1.72796e14			−0.197209			−0.0986046	+	0.995127i	$0.531438\pi$
$522$	−1.18612e15	−	7.78533e14i	−1.33949	−	0.879203i
$523$			3.30107e14i			0.368889i	0.982843	+	0.184444i	$0.0590485\pi$
$523$			3.30107e14i			0.368889i	−0.982843	+	0.184444i	$0.940951\pi$
$524$	7.49189e14	−	3.24835e14i	0.828456	−	0.359204i
$525$		−	1.69606e14i		−	0.185594i
$526$	8.15615e14	−	1.24262e15i	0.883209	−	1.34560i
$527$	−4.24066e14			−0.454438
$528$	9.46386e13	−	1.01067e14i	0.100365	−	0.107183i
$529$	−8.91218e14			−0.935358
$530$	9.00696e13	−	1.37224e14i	0.0935537	−	0.142532i
$531$			9.72332e14i			0.999527i
$532$	−1.13858e15	+	4.93669e14i	−1.15838	+	0.502252i
$533$		−	1.11703e15i		−	1.12478i
$534$	1.90971e14	+	1.25347e14i	0.190323	+	0.124922i
$535$	3.30971e14			0.326471
$536$	−2.38653e14	+	1.37608e15i	−0.233002	+	1.34349i
$537$	−5.51400e13			−0.0532854
$538$	−7.11909e14	−	4.67275e14i	−0.680961	−	0.446961i
$539$			1.68066e14i			0.159126i
$540$	6.64682e13	+	1.53300e14i	0.0622943	+	0.143673i
$541$		−	1.81910e14i		−	0.168760i	−0.996434	−	0.0843802i	$-0.973109\pi$
$541$		−	1.81910e14i		−	0.168760i	0.996434	−	0.0843802i	$-0.0268910\pi$
$542$	−1.15878e15	+	1.76544e15i	−1.06416	+	1.62128i
$543$	−2.80918e14			−0.255376
$544$	−7.28784e13	−	3.01202e14i	−0.0655850	−	0.271059i
$545$	−4.79048e12			−0.00426774
$546$	1.15254e14	−	1.75594e14i	0.101648	−	0.154864i
$547$		−	1.64922e14i		−	0.143996i	−0.997405	−	0.0719978i	$-0.977063\pi$
$547$		−	1.64922e14i		−	0.143996i	0.997405	−	0.0719978i	$-0.0229375\pi$
$548$	5.89534e14	+	1.35968e15i	0.509584	+	1.17529i
$549$		−	3.87787e14i		−	0.331852i
$550$	5.30483e14	+	3.48193e14i	0.449445	+	0.295002i
$551$	2.98633e15			2.50497
$552$	1.27135e13	−	7.33060e13i	0.0105584	−	0.0608800i
$553$	−4.34941e14			−0.357637
$554$	5.41134e14	+	3.55184e14i	0.440556	+	0.289167i
$555$		−	1.37648e14i		−	0.110958i
$556$	3.86234e13	−	1.67464e13i	0.0308276	−	0.0133663i
$557$		−	1.54192e15i		−	1.21859i	−0.792943	−	0.609296i	$-0.791452\pi$
$557$		−	1.54192e15i		−	1.21859i	0.792943	−	0.609296i	$-0.208548\pi$
$558$	1.07513e15	−	1.63800e15i	0.841342	−	1.28181i
$559$	−1.66565e15			−1.29068
$560$	2.71061e14	+	2.53819e14i	0.207985	+	0.194756i
$561$	−5.38953e13			−0.0409501
$562$	−5.83547e14	+	8.89054e14i	−0.439062	+	0.668926i
$563$		−	5.58226e14i		−	0.415924i	−0.978137	−	0.207962i	$-0.933317\pi$
$563$		−	5.58226e14i		−	0.415924i	0.978137	−	0.207962i	$-0.0666830\pi$
$564$	−6.86866e13	+	2.97813e13i	−0.0506801	+	0.0219740i
$565$			1.60863e14i			0.117541i
$566$	−1.40189e15	−	9.20157e14i	−1.01443	−	0.665842i
$567$	9.89630e14			0.709195
$568$	3.16715e14	+	5.49278e13i	0.224777	+	0.0389831i
$569$	1.33590e15			0.938980			0.469490	−	0.882938i	$-0.344438\pi$
$569$	1.33590e15			0.938980			0.469490	+	0.882938i	$0.344438\pi$
$570$	−1.42535e14	−	9.35556e13i	−0.0992225	−	0.0651265i
$571$		−	3.51284e14i		−	0.242192i	−0.992641	−	0.121096i	$-0.961359\pi$
$571$		−	3.51284e14i		−	0.242192i	0.992641	−	0.121096i	$-0.0386409\pi$
$572$	3.12601e14	+	7.20972e14i	0.213458	+	0.492312i
$573$		−	4.44098e14i		−	0.300351i
$574$	−8.90430e14	+	1.35660e15i	−0.596464	+	0.908734i
$575$	3.40970e14			0.226226
$576$	1.34819e15	+	4.82135e14i	0.885988	+	0.316844i
$577$	3.91621e14			0.254917			0.127458	−	0.991844i	$-0.459318\pi$
$577$	3.91621e14			0.254917			0.127458	+	0.991844i	$0.459318\pi$
$578$	7.84866e14	−	1.19577e15i	0.506049	−	0.770983i
$579$			2.33642e14i			0.149217i
$580$	−3.55476e14	−	8.19858e14i	−0.224883	−	0.518662i
$581$		−	1.01652e15i		−	0.637013i
$582$	−6.96141e13	−	4.56925e13i	−0.0432137	−	0.0283641i
$583$	−5.04600e14			−0.310292
$584$	−1.77807e15	−	3.08371e14i	−1.08312	−	0.187846i
$585$	−4.59728e14			−0.277424
$586$	1.12064e15	+	7.35554e14i	0.669931	+	0.439722i
$587$		−	4.43040e14i		−	0.262382i	−0.991357	−	0.131191i	$-0.958120\pi$
$587$		−	4.43040e14i		−	0.262382i	0.991357	−	0.131191i	$-0.0418800\pi$
$588$	1.00087e14	−	4.33960e13i	0.0587223	−	0.0254610i
$589$			4.12402e15i			2.39710i
$590$	−3.36042e14	+	5.11972e14i	−0.193512	+	0.294822i
$591$	1.56973e14			0.0895557
$592$	−1.77600e15	−	1.66303e15i	−1.00386	−	0.940006i
$593$	−4.02396e14			−0.225348			−0.112674	−	0.993632i	$-0.535942\pi$
$593$	−4.02396e14			−0.225348			−0.112674	+	0.993632i	$0.535942\pi$
$594$	2.81857e14	−	4.29419e14i	0.156388	−	0.238262i
$595$		−	1.44547e14i		−	0.0794629i
$596$	2.43186e15	−	1.05441e15i	1.32460	−	0.574324i
$597$			3.69465e14i			0.199395i
$598$	3.53008e14	+	2.31703e14i	0.188768	+	0.123901i
$599$	−2.50334e15			−1.32639			−0.663197	−	0.748445i	$-0.730801\pi$
$599$	−2.50334e15			−1.32639			−0.663197	+	0.748445i	$0.730801\pi$
$600$	7.03815e13	−	4.05821e14i	0.0369511	−	0.213060i
$601$	4.35237e14			0.226421			0.113210	−	0.993571i	$-0.463887\pi$
$601$	4.35237e14			0.226421			0.113210	+	0.993571i	$0.463887\pi$
$602$	2.02289e15	+	1.32776e15i	1.04278	+	0.684445i
$603$			2.51176e15i			1.28302i
$604$	−4.58624e14	−	1.05775e15i	−0.232142	−	0.535404i
$605$		−	4.20247e14i		−	0.210790i
$606$	−4.72645e14	+	7.20090e14i	−0.234928	+	0.357921i
$607$	−2.73468e15			−1.34700			−0.673502	−	0.739185i	$-0.735211\pi$
$607$	−2.73468e15			−1.34700			−0.673502	+	0.739185i	$0.735211\pi$
$608$	−2.92918e15	+	7.08739e14i	−1.42980	+	0.345953i
$609$	7.34254e14			0.355182
$610$	1.34021e14	−	2.04185e14i	0.0642478	−	0.0978837i
$611$		−	4.24895e14i		−	0.201862i
$612$	−2.21706e14	−	5.11335e14i	−0.104387	−	0.240754i
$613$			3.16970e15i			1.47906i	0.673123	+	0.739530i	$0.264952\pi$
$613$			3.16970e15i			1.47906i	−0.673123	+	0.739530i	$0.735048\pi$
$614$	−1.11045e15	−	7.28863e14i	−0.513537	−	0.337070i
$615$	−2.22940e14			−0.102182
$616$	1.95071e14	−	1.12478e15i	0.0886134	−	0.510946i
$617$	−2.35389e15			−1.05978			−0.529892	−	0.848065i	$-0.677768\pi$
$617$	−2.35389e15			−1.05978			−0.529892	+	0.848065i	$0.677768\pi$
$618$	−4.76572e14	−	3.12807e14i	−0.212663	−	0.139585i
$619$		−	4.11214e15i		−	1.81874i	−0.415992	−	0.909368i	$-0.636566\pi$
$619$		−	4.11214e15i		−	1.81874i	0.415992	−	0.909368i	$-0.363434\pi$
$620$	1.13220e15	−	4.90901e14i	0.496327	−	0.215199i
$621$		−	2.76010e14i		−	0.119928i
$622$	9.99338e14	−	1.52253e15i	0.430393	−	0.655719i
$623$	1.88339e15			0.804002
$624$	3.48639e14	−	3.72322e14i	0.147523	−	0.157544i
$625$	1.62483e15			0.681504
$626$	3.94229e14	−	6.00621e14i	0.163904	−	0.249713i
$627$			5.24130e14i			0.216007i
$628$	3.36102e14	−	1.45728e14i	0.137307	−	0.0595340i
$629$			9.47072e14i			0.383535i
$630$	5.58325e14	+	3.66467e14i	0.224137	+	0.147117i
$631$	3.13107e14			0.124604			0.0623018	−	0.998057i	$-0.480156\pi$
$631$	3.13107e14			0.124604			0.0623018	+	0.998057i	$0.480156\pi$
$632$	−1.04070e15	−	1.80488e14i	−0.410564	−	0.0712041i
$633$	7.31944e14			0.286258
$634$	2.04419e15	+	1.34174e15i	0.792558	+	0.520210i
$635$		−	1.03551e15i		−	0.398013i
$636$	1.30292e14	+	3.00501e14i	0.0496482	+	0.114507i
$637$			6.19138e14i			0.233895i
$638$	−1.50739e15	+	2.29656e15i	−0.564562	+	0.860130i
$639$	5.78100e14			0.214659
$640$	5.43249e14	+	7.19805e14i	0.199990	+	0.264987i
$641$	2.58160e15			0.942256			0.471128	−	0.882065i	$-0.343847\pi$
$641$	2.58160e15			0.942256			0.471128	+	0.882065i	$0.343847\pi$
$642$	−3.62390e14	+	5.52113e14i	−0.131139	+	0.199795i
$643$		−	4.31050e14i		−	0.154656i	−0.997006	−	0.0773281i	$-0.975361\pi$
$643$		−	4.31050e14i		−	0.154656i	0.997006	−	0.0773281i	$-0.0246389\pi$
$644$	−2.44017e14	−	5.62793e14i	−0.0868057	−	0.200206i
$645$			3.32435e14i			0.117254i
$646$	9.80700e14	+	6.43701e14i	0.342971	+	0.225115i
$647$	1.02096e15			0.354024			0.177012	−	0.984209i	$-0.443357\pi$
$647$	1.02096e15			0.354024			0.177012	+	0.984209i	$0.443357\pi$
$648$	2.36792e15	+	4.10668e14i	0.814150	+	0.141198i
$649$	1.88262e15			0.641826
$650$	1.95425e15	+	1.28271e15i	0.660626	+	0.433615i
$651$			1.01398e15i			0.339887i
$652$	−1.60192e15	+	6.94563e14i	−0.532449	+	0.230861i
$653$		−	4.21603e15i		−	1.38957i	−0.719217	−	0.694786i	$-0.755499\pi$
$653$		−	4.21603e15i		−	1.38957i	0.719217	−	0.694786i	$-0.244501\pi$
$654$	5.24523e12	−	7.99128e12i	0.00171430	−	0.00261179i
$655$	9.24960e14			0.299775
$656$	−2.69351e15	+	2.87648e15i	−0.865662	+	0.924465i
$657$	−3.24552e15			−1.03437
$658$	−3.38701e14	+	5.16022e14i	−0.107047	+	0.163089i
$659$		−	1.13237e15i		−	0.354910i	−0.984129	−	0.177455i	$-0.943214\pi$
$659$		−	1.13237e15i		−	0.354910i	0.984129	−	0.177455i	$-0.0567864\pi$
$660$	1.43893e14	−	6.23895e13i	0.0447248	−	0.0193919i
$661$		−	4.30932e15i		−	1.32832i	−0.747593	−	0.664158i	$-0.768790\pi$
$661$		−	4.30932e15i		−	1.32832i	0.747593	−	0.664158i	$-0.231210\pi$
$662$	−3.45470e15	−	2.26756e15i	−1.05607	−	0.693170i
$663$	−1.98545e14			−0.0601914
$664$	4.21828e14	−	2.43227e15i	0.126827	−	0.731286i
$665$	−1.40571e15			−0.419157
$666$	−3.65816e15	−	2.40110e15i	−1.08182	−	0.710072i
$667$			1.47612e15i			0.432942i
$668$	2.49675e15	+	5.75843e15i	0.726282	+	1.67507i
$669$		−	9.30306e14i		−	0.268400i
$670$	−8.68074e14	+	1.32254e15i	−0.248397	+	0.378441i
$671$	−7.50830e14			−0.213092
$672$	−7.20203e14	+	1.74259e14i	−0.202733	+	0.0490529i
$673$	−1.21092e15			−0.338091			−0.169045	−	0.985608i	$-0.554068\pi$
$673$	−1.21092e15			−0.338091			−0.169045	+	0.985608i	$0.554068\pi$
$674$	−2.35597e14	+	3.58940e14i	−0.0652439	+	0.0994013i
$675$		−	1.52799e15i		−	0.419710i
$676$	−3.08473e14	−	7.11452e14i	−0.0840447	−	0.193838i
$677$		−	2.62830e13i		−	0.00710293i	−0.999994	−	0.00355146i	$-0.998870\pi$
$677$		−	2.62830e13i		−	0.00710293i	0.999994	−	0.00355146i	$-0.00113047\pi$
$678$	−2.68345e14	−	1.76133e14i	−0.0719333	−	0.0472148i
$679$	−6.86548e14			−0.182552
$680$	5.99827e13	−	3.45861e14i	0.0158208	−	0.0912227i
$681$	−9.52199e14			−0.249126
$682$	−3.17148e15	−	2.08166e15i	−0.823090	−	0.540251i
$683$			5.61582e15i			1.44577i	0.690968	+	0.722885i	$0.257184\pi$
$683$			5.61582e15i			1.44577i	−0.690968	+	0.722885i	$0.742816\pi$
$684$	−4.97272e15	+	2.15608e15i	−1.26995	+	0.550626i
$685$			1.67868e15i			0.425276i
$686$	2.36752e15	−	3.60699e15i	0.594991	−	0.906489i
$687$	−3.59450e14			−0.0896142
$688$	4.28924e15	+	4.01641e15i	1.06083	+	0.993350i
$689$	−1.85890e15			−0.456089
$690$	4.62439e13	−	7.04542e13i	0.0112560	−	0.0171489i
$691$			9.70013e14i			0.234233i	0.993118	+	0.117117i	$0.0373651\pi$
$691$			9.70013e14i			0.234233i	−0.993118	+	0.117117i	$0.962635\pi$
$692$	4.59170e15	−	1.99088e15i	1.09999	−	0.476938i
$693$		−	2.05307e15i		−	0.487946i
$694$	4.13970e15	+	2.71717e15i	0.976095	+	0.640678i
$695$	4.76850e13			0.0111549
$696$	1.75687e15	+	3.04695e14i	0.407746	+	0.0707154i
$697$	1.53392e15			0.353201
$698$	−3.86136e15	−	2.53448e15i	−0.882136	−	0.579006i
$699$		−	8.02028e14i		−	0.181788i
$700$	−1.35088e15	−	3.11561e15i	−0.303792	−	0.700655i
$701$			1.97204e15i			0.440014i	0.975498	+	0.220007i	$0.0706080\pi$
$701$			1.97204e15i			0.440014i	−0.975498	+	0.220007i	$0.929392\pi$
$702$	1.03833e15	−	1.58194e15i	0.229870	−	0.350215i
$703$	9.21024e15			2.02310
$704$	9.33507e14	−	2.61036e15i	0.203455	−	0.568919i
$705$	−8.48015e13			−0.0183385
$706$	−3.43020e14	+	5.22603e14i	−0.0736027	+	0.112136i
$707$			7.10167e15i			1.51201i
$708$	−4.86109e14	−	1.12114e15i	−0.102695	−	0.236853i
$709$		−	1.52806e15i		−	0.320321i	−0.987091	−	0.160160i	$-0.948799\pi$
$709$		−	1.52806e15i		−	0.320321i	0.987091	−	0.160160i	$-0.0512012\pi$
$710$	3.04393e14	+	1.99794e14i	0.0633161	+	0.0415587i
$711$	−1.89959e15			−0.392082
$712$	4.50646e15	+	7.81556e14i	0.922988	+	0.160074i
$713$	−2.03848e15			−0.414299
$714$	2.41127e14	+	1.58268e14i	0.0486301	+	0.0319193i
$715$			8.90122e14i			0.178142i
$716$	−1.01291e15	+	4.39180e14i	−0.201163	+	0.0872209i
$717$		−	8.65997e14i		−	0.170672i
$718$	3.71085e15	−	5.65361e15i	0.725754	−	1.10571i
$719$	7.12200e14			0.138227			0.0691135	−	0.997609i	$-0.477983\pi$
$719$	7.12200e14			0.138227			0.0691135	+	0.997609i	$0.477983\pi$
$720$	1.18385e15	+	1.10855e15i	0.228017	+	0.213514i
$721$	−4.70005e15			−0.898376
$722$	3.36722e15	−	5.13008e15i	0.638730	−	0.973127i
$723$		−	4.77686e14i		−	0.0899252i
$724$	−5.16039e15	+	2.23746e15i	−0.964097	+	0.418015i
$725$			8.17178e15i			1.51516i
$726$	7.01038e14	+	4.60140e14i	0.129000	+	0.0846717i
$727$	−4.91976e15			−0.898473			−0.449236	−	0.893413i	$-0.648304\pi$
$727$	−4.91976e15			−0.898473			−0.449236	+	0.893413i	$0.648304\pi$
$728$	7.18623e14	−	4.14359e15i	0.130250	−	0.751025i
$729$	3.68491e15			0.662866
$730$	−1.70890e15	−	1.12167e15i	−0.305099	−	0.200257i
$731$		−	2.28729e15i		−	0.405299i
$732$	1.93870e14	+	4.47136e14i	0.0340958	+	0.0786374i
$733$		−	6.46386e15i		−	1.12829i	−0.825677	−	0.564144i	$-0.809206\pi$
$733$		−	6.46386e15i		−	1.12829i	0.825677	−	0.564144i	$-0.190794\pi$
$734$	−2.93441e15	+	4.47068e15i	−0.508385	+	0.774542i
$735$	1.23569e14			0.0212486
$736$	−3.50325e14	−	1.44787e15i	−0.0597920	−	0.247117i
$737$	4.86324e15			0.823863
$738$	−3.88892e15	+	5.92491e15i	−0.653912	+	0.996257i
$739$		−	5.18187e15i		−	0.864853i	−0.901669	−	0.432427i	$-0.857657\pi$
$739$		−	5.18187e15i		−	0.864853i	0.901669	−	0.432427i	$-0.142343\pi$
$740$	−1.09634e15	−	2.52855e15i	−0.181622	−	0.418888i
$741$			1.93084e15i			0.317502i
$742$	2.25757e15	+	1.48180e15i	0.368485	+	0.241862i
$743$	−1.05233e16			−1.70496			−0.852480	−	0.522760i	$-0.824902\pi$
$743$	−1.05233e16			−1.70496			−0.852480	+	0.522760i	$0.824902\pi$
$744$	−4.20774e14	+	2.42619e15i	−0.0676702	+	0.390187i
$745$	3.00242e15			0.479304
$746$	4.00231e15	+	2.62699e15i	0.634231	+	0.416289i
$747$		−	4.43963e15i		−	0.698367i
$748$	−9.90044e14	+	4.29266e14i	−0.154595	+	0.0670297i
$749$			5.44505e15i			0.844018i
$750$	5.43722e14	−	8.28378e14i	0.0836642	−	0.127465i
$751$	4.70145e15			0.718145			0.359072	−	0.933310i	$-0.383093\pi$
$751$	4.70145e15			0.718145			0.359072	+	0.933310i	$0.383093\pi$
$752$	−1.02455e15	+	1.09415e15i	−0.155359	+	0.165913i
$753$	−2.31496e15			−0.348475
$754$	−5.55307e15	+	8.46029e15i	−0.829833	+	1.26428i
$755$		−	1.30592e15i		−	0.193735i
$756$	−2.52205e15	+	1.09352e15i	−0.371435	+	0.161048i
$757$			2.99638e15i			0.438097i	0.975714	+	0.219048i	$0.0702952\pi$
$757$			2.99638e15i			0.438097i	−0.975714	+	0.219048i	$0.929705\pi$
$758$	−4.41658e13	−	2.89891e13i	−0.00641070	−	0.00420779i
$759$	−2.59074e14			−0.0373331
$760$	−3.36349e15	−	5.83330e14i	−0.481188	−	0.0834525i
$761$	−5.72067e15			−0.812515			−0.406257	−	0.913759i	$-0.633166\pi$
$761$	−5.72067e15			−0.812515			−0.406257	+	0.913759i	$0.633166\pi$
$762$	1.72739e15	+	1.13380e15i	0.243578	+	0.159877i
$763$		−	7.88116e13i		−	0.0110333i
$764$	−3.53716e15	−	8.15798e15i	−0.491633	−	1.13389i
$765$		−	6.31302e14i		−	0.0871163i
$766$	−2.80823e15	+	4.27844e15i	−0.384747	+	0.586174i
$767$	6.93539e15			0.943402
$768$	−1.79557e15	+	1.18092e14i	−0.242502	+	0.0159490i
$769$	1.23168e16			1.65160			0.825798	−	0.563966i	$-0.190725\pi$
$769$	1.23168e16			1.65160			0.825798	+	0.563966i	$0.190725\pi$
$770$	7.09551e14	−	1.08103e15i	0.0944680	−	0.143925i
$771$		−	7.79064e14i		−	0.102985i
$772$	1.86091e15	+	4.29195e15i	0.244248	+	0.563325i
$773$		−	1.00466e16i		−	1.30928i	−0.755940	−	0.654641i	$-0.772820\pi$
$773$		−	1.00466e16i		−	1.30928i	0.755940	−	0.654641i	$-0.227180\pi$
$774$	8.83488e15	+	5.79894e15i	1.14321	+	0.750367i
$775$	−1.12850e16			−1.44991
$776$	−1.64273e15	−	2.84898e14i	−0.209569	−	0.0363455i
$777$	2.26454e15			0.286856
$778$	−5.87577e15	−	3.85667e15i	−0.739056	−	0.485093i
$779$		−	1.49173e16i		−	1.86309i
$780$	5.30088e14	−	2.29837e14i	0.0657397	−	0.0285036i
$781$		−	1.11931e15i		−	0.137839i
$782$	−3.18177e14	+	4.84754e14i	−0.0389074	+	0.0592767i
$783$	6.61494e15			0.803224
$784$	1.49294e15	−	1.59435e15i	0.180013	−	0.192241i
$785$	4.14957e14			0.0496844
$786$	−1.01276e15	+	1.54298e15i	−0.120416	+	0.183458i
$787$		−	1.84776e15i		−	0.218165i	−0.994033	−	0.109083i	$-0.965209\pi$
$787$		−	1.84776e15i		−	0.218165i	0.994033	−	0.109083i	$-0.0347913\pi$
$788$	2.88355e15	−	1.25026e15i	0.338091	−	0.146590i
$789$			3.35957e15i			0.391165i
$790$	−1.00021e15	−	6.56507e14i	−0.115649	−	0.0759085i
$791$	−2.64647e15			−0.303876
$792$	8.51967e14	−	4.91246e15i	0.0971481	−	0.560158i
$793$	−2.76598e15			−0.313218
$794$	1.37505e16	+	9.02543e15i	1.54635	+	1.01497i
$795$			3.71003e14i			0.0414341i
$796$	2.94271e15	+	6.78698e15i	0.326382	+	0.752757i
$797$			1.74965e16i			1.92722i	0.267314	+	0.963610i	$0.413864\pi$
$797$			1.74965e16i			1.92722i	−0.267314	+	0.963610i	$0.586136\pi$
$798$	1.53915e15	−	2.34495e15i	0.168370	−	0.256518i
$799$	5.83469e14			0.0633885
$800$	−1.93939e15	−	8.01541e15i	−0.209253	−	0.864830i
$801$	8.22566e15			0.881439
$802$	8.31262e15	−	1.26646e16i	0.884666	−	1.34782i
$803$			6.28395e15i			0.664198i
$804$	−1.25573e15	−	2.89617e15i	−0.131822	−	0.304030i
$805$		−	6.94833e14i		−	0.0724441i
$806$	−1.16834e16	−	7.66862e15i	−1.20984	−	0.794099i
$807$	1.92474e15			0.197955
$808$	−2.94699e15	+	1.69924e16i	−0.301035	+	1.73577i
$809$	3.23585e15			0.328301			0.164150	−	0.986435i	$-0.447512\pi$
$809$	3.23585e15			0.328301			0.164150	+	0.986435i	$0.447512\pi$
$810$	2.27580e15	+	1.49376e15i	0.229333	+	0.150527i
$811$			1.61059e16i			1.61202i	0.591903	+	0.806009i	$0.298377\pi$
$811$			1.61059e16i			1.61202i	−0.591903	+	0.806009i	$0.701623\pi$
$812$	1.34881e16	−	5.84819e15i	1.34088	−	0.581384i
$813$		−	4.77310e15i		−	0.471306i
$814$	−4.64900e15	+	7.08290e15i	−0.455958	+	0.694668i
$815$	−1.97775e15			−0.192666
$816$	5.11275e14	+	4.78754e14i	0.0494719	+	0.0463251i
$817$	−2.22438e16			−2.13790
$818$	5.18392e15	−	7.89788e15i	0.494898	−	0.753993i
$819$		−	7.56331e15i		−	0.717217i
$820$	−4.09535e15	+	1.77567e15i	−0.385758	+	0.167258i
$821$		−	6.52864e15i		−	0.610851i	−0.952216	−	0.305426i	$-0.901201\pi$
$821$		−	6.52864e15i		−	0.610851i	0.952216	−	0.305426i	$-0.0987987\pi$
$822$	−2.80031e15	−	1.83804e15i	−0.260262	−	0.170828i
$823$	4.54096e15			0.419226			0.209613	−	0.977784i	$-0.432780\pi$
$823$	4.54096e15			0.419226			0.209613	+	0.977784i	$0.432780\pi$
$824$	−1.12460e16	−	1.95039e15i	−1.03133	−	0.178863i
$825$	−1.43423e15			−0.130654
$826$	−8.42282e15	−	5.52848e15i	−0.762197	−	0.500282i
$827$			1.76884e16i			1.59004i	0.606581	+	0.795022i	$0.292541\pi$
$827$			1.76884e16i			1.59004i	−0.606581	+	0.795022i	$0.707459\pi$
$828$	−1.06574e15	−	2.45798e15i	−0.0951663	−	0.219488i
$829$		−	5.71131e15i		−	0.506624i	−0.967385	−	0.253312i	$-0.918480\pi$
$829$		−	5.71131e15i		−	0.506624i	0.967385	−	0.253312i	$-0.0815200\pi$
$830$	1.53436e15	−	2.33764e15i	0.135206	−	0.205991i
$831$	−1.46303e15			−0.128070
$832$	3.43895e15	−	9.61630e15i	0.299052	−	0.836238i
$833$	−8.50206e14			−0.0734474
$834$	−5.22116e13	+	7.95462e13i	−0.00448078	+	0.00682662i
$835$			7.10944e15i			0.606122i
$836$	4.17459e15	+	9.62814e15i	0.353573	+	0.815470i
$837$			9.13503e15i			0.768635i
$838$	−1.69612e16	−	1.11328e16i	−1.41780	−	0.930600i
$839$	−8.25448e15			−0.685487			−0.342743	−	0.939429i	$-0.611356\pi$
$839$	−8.25448e15			−0.685487			−0.342743	+	0.939429i	$0.611356\pi$
$840$	−8.26987e14	−	1.43424e14i	−0.0682280	−	0.0118328i
$841$	−2.31766e16			−1.89964
$842$	2.31462e15	+	1.51924e15i	0.188479	+	0.123712i
$843$		−	2.40367e15i		−	0.194457i
$844$	1.34456e16	−	5.82979e15i	1.08068	−	0.468565i
$845$		−	8.78369e14i		−	0.0701399i
$846$	−1.47926e15	+	2.25371e15i	−0.117357	+	0.178797i
$847$	6.91378e15			0.544950
$848$	4.78686e15	+	4.48238e15i	0.374864	+	0.351020i
$849$	3.79019e15			0.294896
$850$	−1.76142e15	+	2.68359e15i	−0.136163	+	0.207449i
$851$			4.55256e15i			0.349658i
$852$	−6.66577e14	+	2.89016e14i	−0.0508666	+	0.0220549i
$853$		−	1.65740e16i		−	1.25663i	−0.777960	−	0.628314i	$-0.783745\pi$
$853$		−	1.65740e16i		−	1.25663i	0.777960	−	0.628314i	$-0.216255\pi$
$854$	3.35920e15	+	2.20487e15i	0.253056	+	0.166098i
$855$	−6.13939e15			−0.459527
$856$	−2.25954e15	+	1.30286e16i	−0.168041	+	0.968926i
$857$	2.38802e16			1.76459			0.882293	−	0.470700i	$-0.155999\pi$
$857$	2.38802e16			1.76459			0.882293	+	0.470700i	$0.155999\pi$
$858$	−1.48487e15	−	9.74619e14i	−0.109020	−	0.0715575i
$859$		−	8.75701e15i		−	0.638842i	−0.947613	−	0.319421i	$-0.896512\pi$
$859$		−	8.75701e15i		−	0.638842i	0.947613	−	0.319421i	$-0.103488\pi$
$860$	2.64778e15	+	6.10676e15i	0.191929	+	0.442659i
$861$		−	3.66774e15i		−	0.264169i
$862$	8.77331e15	−	1.33664e16i	0.627876	−	0.956590i
$863$	1.75346e16			1.24692			0.623458	−	0.781857i	$-0.285727\pi$
$863$	1.75346e16			1.24692			0.623458	+	0.781857i	$0.285727\pi$
$864$	−6.48837e15	+	1.56991e15i	−0.458469	+	0.110930i
$865$	5.66898e15			0.398031
$866$	−5.08301e14	+	7.74413e14i	−0.0354627	+	0.0540287i
$867$			3.23292e15i			0.224125i
$868$	8.07617e15	+	1.86266e16i	0.556348	+	1.28314i
$869$			3.67797e15i			0.251768i
$870$	1.68852e15	+	1.10829e15i	0.114855	+	0.0753875i
$871$	1.79157e16			1.21097
$872$	3.27046e13	−	1.88575e14i	0.00219669	−	0.0126661i
$873$	−2.99848e15			−0.200135
$874$	4.71421e15	+	3.09426e15i	0.312677	+	0.205231i
$875$		−	8.16963e15i		−	0.538466i
$876$	3.74224e15	−	1.62257e15i	0.245109	−	0.106275i
$877$		−	1.98632e16i		−	1.29286i	−0.762973	−	0.646431i	$-0.776261\pi$
$877$		−	1.98632e16i		−	1.29286i	0.762973	−	0.646431i	$-0.223739\pi$
$878$	−1.09438e16	+	1.66732e16i	−0.707859	+	1.07845i
$879$	−3.02980e15			−0.194749
$880$	2.14636e15	−	2.29216e15i	0.137103	−	0.146417i
$881$	−1.39606e16			−0.886210			−0.443105	−	0.896470i	$-0.646123\pi$
$881$	−1.39606e16			−0.886210			−0.443105	+	0.896470i	$0.646123\pi$
$882$	2.15552e15	−	3.28400e15i	0.135980	−	0.207170i
$883$			1.97198e16i			1.23629i	0.786066	+	0.618143i	$0.212115\pi$
$883$			1.97198e16i			1.23629i	−0.786066	+	0.618143i	$0.787885\pi$
$884$	−3.64722e15	+	1.58137e15i	−0.227235	+	0.0985250i
$885$		−	1.38418e15i		−	0.0857048i
$886$	−8.34660e15	−	5.47845e15i	−0.513599	−	0.337111i
$887$	−5.69405e15			−0.348210			−0.174105	−	0.984727i	$-0.555703\pi$
$887$	−5.69405e15			−0.348210			−0.174105	+	0.984727i	$0.555703\pi$
$888$	5.41844e15	+	9.39720e14i	0.329308	+	0.0571120i
$889$	1.70359e16			1.02897
$890$	4.33114e15	+	2.84283e15i	0.259991	+	0.170650i
$891$		−	8.36857e15i		−	0.499256i
$892$	−7.40971e15	−	1.70895e16i	−0.439334	−	1.01326i
$893$		−	5.67422e15i		−	0.334367i
$894$	−3.28743e15	+	5.00851e15i	−0.192531	+	0.293327i
$895$	−1.25055e15			−0.0727906
$896$	−1.18420e16	+	8.93738e15i	−0.685065	+	0.517031i
$897$	−9.54402e14			−0.0548748
$898$	−1.55442e15	+	2.36821e15i	−0.0888277	+	0.135332i
$899$		−	4.88547e16i		−	2.77478i
$900$	−5.89990e15	−	1.36073e16i	−0.333051	−	0.768138i
$901$		−	2.55265e15i		−	0.143220i
$902$	1.14718e16	+	7.52971e15i	0.639727	+	0.419897i
$903$	−5.46913e15			−0.303135
$904$	−6.33230e15	−	1.09821e15i	−0.348847	−	0.0605005i
$905$	−6.37109e15			−0.348857
$906$	2.17848e15	+	1.42989e15i	0.118563	+	0.0778210i
$907$			1.77779e16i			0.961702i	0.876802	+	0.480851i	$0.159672\pi$
$907$			1.77779e16i			0.961702i	−0.876802	+	0.480851i	$0.840328\pi$
$908$	−1.74917e16	+	7.58408e15i	−0.940500	+	0.407784i
$909$			3.10163e16i			1.65763i
$910$	2.61392e15	−	3.98239e15i	0.138856	−	0.211551i
$911$	−6.15686e15			−0.325093			−0.162547	−	0.986701i	$-0.551971\pi$
$911$	−6.15686e15			−0.325093			−0.162547	+	0.986701i	$0.551971\pi$
$912$	4.65586e15	−	4.97213e15i	0.244359	−	0.260958i
$913$	−8.59598e15			−0.448442
$914$	−9.27134e15	+	1.41252e16i	−0.480771	+	0.732471i
$915$			5.52041e14i			0.0284548i
$916$	−6.60302e15	+	2.86295e15i	−0.338312	+	0.146686i
$917$			1.52172e16i			0.775002i
$918$	2.17233e15	+	1.42585e15i	0.109974	+	0.0721836i
$919$	−8.00157e15			−0.402661			−0.201331	−	0.979523i	$-0.564527\pi$
$919$	−8.00157e15			−0.402661			−0.201331	+	0.979523i	$0.564527\pi$
$920$	2.88336e14	−	1.66255e15i	0.0144233	−	0.0831652i
$921$	3.00224e15			0.149285
$922$	−3.25448e15	−	2.13614e15i	−0.160865	−	0.105587i
$923$		−	4.12344e15i		−	0.202605i
$924$	1.02642e15	+	2.36729e15i	0.0501334	+	0.115626i
$925$			2.52029e16i			1.22369i
$926$	5.83021e15	−	8.88252e15i	0.281400	−	0.428722i
$927$	−2.05273e16			−0.984902
$928$	3.47002e16	−	8.39599e15i	1.65508	−	0.400459i
$929$	2.56873e16			1.21796			0.608979	−	0.793186i	$-0.291579\pi$
$929$	2.56873e16			1.21796			0.608979	+	0.793186i	$0.291579\pi$
$930$	−1.53052e15	+	2.33180e15i	−0.0721411	+	0.109909i
$931$			8.26822e15i			0.387426i
$932$	−6.38800e15	−	1.47331e16i	−0.297562	−	0.686287i
$933$			4.11634e15i			0.190617i
$934$	2.45930e16	+	1.61420e16i	1.13215	+	0.743106i
$935$	−1.22232e15			−0.0559400
$936$	3.13856e15	−	1.80970e16i	0.142795	−	0.823359i
$937$	−1.39297e16			−0.630050			−0.315025	−	0.949083i	$-0.602013\pi$
$937$	−1.39297e16			−0.630050			−0.315025	+	0.949083i	$0.602013\pi$
$938$	−2.17581e16	−	1.42813e16i	−0.978373	−	0.642174i
$939$			1.62385e15i			0.0725916i
$940$	−1.55778e15	+	6.75428e14i	−0.0692315	+	0.0300176i
$941$		−	1.66641e16i		−	0.736273i	−0.929772	−	0.368137i	$-0.879996\pi$
$941$		−	1.66641e16i		−	0.736273i	0.929772	−	0.368137i	$-0.120004\pi$
$942$	−4.54348e14	+	6.92214e14i	−0.0199576	+	0.0304061i
$943$	7.37352e15			0.322003
$944$	−1.78594e16	−	1.67234e16i	−0.775391	−	0.726070i
$945$	−3.11376e15			−0.134403
$946$	1.12279e16	−	1.71060e16i	0.481833	−	0.734088i
$947$		−	5.47676e15i		−	0.233668i	−0.993151	−	0.116834i	$-0.962726\pi$
$947$		−	5.47676e15i		−	0.233668i	0.993151	−	0.116834i	$-0.0372745\pi$
$948$	2.19032e15	−	9.49683e14i	0.0929097	−	0.0402840i
$949$			2.31494e16i			0.976285i
$950$	2.60978e16	+	1.71298e16i	1.09427	+	0.718244i
$951$	−5.52673e15			−0.230396
$952$	5.69001e15	+	9.86819e14i	0.235836	+	0.0409010i
$953$	3.69305e15			0.152186			0.0760929	−	0.997101i	$-0.475755\pi$
$953$	3.69305e15			0.152186			0.0760929	+	0.997101i	$0.475755\pi$
$954$	9.85986e15	+	6.47171e15i	0.403975	+	0.265157i
$955$		−	1.00720e16i		−	0.410294i
$956$	−6.89750e15	−	1.59082e16i	−0.279366	−	0.644320i
$957$		−	6.20904e15i		−	0.250040i
$958$	1.75109e16	−	2.66785e16i	0.701130	−	1.06820i
$959$	−2.76172e16			−1.09946
$960$	−1.91924e15	−	6.86353e14i	−0.0759693	−	0.0271679i
$961$	4.20584e16			1.65529
$962$	−1.71264e16	+	2.60927e16i	−0.670200	+	1.02107i
$963$			2.37811e16i			0.925309i
$964$	−3.80467e15	−	8.77497e15i	−0.147195	−	0.339486i
$965$			5.29890e15i			0.203838i
$966$	1.15909e15	+	7.60792e14i	0.0443347	+	0.0290999i
$967$	3.32009e16			1.26271			0.631356	−	0.775493i	$-0.282499\pi$
$967$	3.32009e16			1.26271			0.631356	+	0.775493i	$0.282499\pi$
$968$	1.65428e16	+	2.86902e15i	0.625598	+	0.108497i
$969$	−2.65145e15			−0.0997016
$970$	−1.57882e15	−	1.03629e15i	−0.0590320	−	0.0387468i
$971$		−	9.03146e15i		−	0.335778i	−0.985806	−	0.167889i	$-0.946305\pi$
$971$		−	9.03146e15i		−	0.335778i	0.985806	−	0.167889i	$-0.0536950\pi$
$972$	−1.66900e16	+	7.23650e15i	−0.617010	+	0.267525i
$973$			7.84500e14i			0.0288385i
$974$	−7.21314e15	+	1.09895e16i	−0.263664	+	0.401701i
$975$	−5.28356e15			−0.192044
$976$	7.12271e15	+	6.66965e15i	0.257437	+	0.241062i
$977$	−3.35430e16			−1.20554			−0.602771	−	0.797914i	$-0.705937\pi$
$977$	−3.35430e16			−1.20554			−0.602771	+	0.797914i	$0.705937\pi$
$978$	2.16549e15	−	3.29920e15i	0.0773915	−	0.117909i
$979$		−	1.59265e16i		−	0.565998i
$980$	2.26993e15	−	9.84204e14i	0.0802176	−	0.0347810i
$981$		−	3.44207e14i		−	0.0120960i
$982$	−2.07039e16	−	1.35894e16i	−0.723500	−	0.474883i
$983$	3.71911e16			1.29239			0.646196	−	0.763172i	$-0.276359\pi$
$983$	3.71911e16			1.29239			0.646196	+	0.763172i	$0.276359\pi$
$984$	1.52201e15	−	8.77593e15i	0.0525950	−	0.303264i
$985$	3.56008e15			0.122338
$986$	−1.16177e16	−	7.62552e15i	−0.397008	−	0.260583i
$987$		−	1.39513e15i		−	0.0474101i
$988$	1.53788e16	+	3.54691e16i	0.519707	+	1.19864i
$989$		−	1.09950e16i		−	0.369500i
$990$	3.09894e15	−	4.72134e15i	0.103567	−	0.157787i
$991$	−2.64911e16			−0.880431			−0.440216	−	0.897892i	$-0.645098\pi$
$991$	−2.64911e16			−0.880431			−0.440216	+	0.897892i	$0.645098\pi$
$992$	1.15946e16	+	4.79199e16i	0.383214	+	1.58380i
$993$	9.34023e15			0.306999
$994$	−3.28696e15	+	5.00779e15i	−0.107441	+	0.163690i
$995$			8.37930e15i			0.272384i
$996$	2.21955e15	+	5.11910e15i	0.0717529	+	0.165488i
$997$		−	3.29227e16i		−	1.05845i	−0.848480	−	0.529227i	$-0.822482\pi$
$997$		−	3.29227e16i		−	1.05845i	0.848480	−	0.529227i	$-0.177518\pi$
$998$	−3.62332e15	−	2.37824e15i	−0.115848	−	0.0760391i
$999$	2.04014e16			0.648709

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.12.b.a.5.4	yes	10
3.2	odd	2		72.12.d.b.37.7		10
4.3	odd	2		32.12.b.a.17.6		10
8.3	odd	2		32.12.b.a.17.5		10
8.5	even	2	inner	8.12.b.a.5.3	✓	10
16.3	odd	4		256.12.a.o.1.5		10
16.5	even	4		256.12.a.p.1.5		10
16.11	odd	4		256.12.a.o.1.6		10
16.13	even	4		256.12.a.p.1.6		10
24.5	odd	2		72.12.d.b.37.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.12.b.a.5.3	✓	10	8.5	even	2	inner
8.12.b.a.5.4	yes	10	1.1	even	1	trivial
32.12.b.a.17.5		10	8.3	odd	2
32.12.b.a.17.6		10	4.3	odd	2
72.12.d.b.37.7		10	3.2	odd	2
72.12.d.b.37.8		10	24.5	odd	2
256.12.a.o.1.5		10	16.3	odd	4
256.12.a.o.1.6		10	16.11	odd	4
256.12.a.p.1.5		10	16.5	even	4
256.12.a.p.1.6		10	16.13	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-24.8325 + 37.8331i) q^{2} -102.287i q^{3} +(-814.694 - 1878.98i) q^{4} -2319.82i q^{5} +(3869.83 + 2540.04i) q^{6} +38165.0 q^{7} +(91318.7 + 15837.4i) q^{8} +166684. q^{9} +O(q^{10})\)	\(q+(-24.8325 + 37.8331i) q^{2} -102.287i q^{3} +(-814.694 - 1878.98i) q^{4} -2319.82i q^{5} +(3869.83 + 2540.04i) q^{6} +38165.0 q^{7} +(91318.7 + 15837.4i) q^{8} +166684. q^{9} +(87766.1 + 57606.9i) q^{10} -322733. i q^{11} +(-192195. + 83332.4i) q^{12} -1.18892e6i q^{13} +(-947733. + 1.44390e6i) q^{14} -237287. q^{15} +(-2.86685e6 + 3.06159e6i) q^{16} +1.63263e6 q^{17} +(-4.13919e6 + 6.30620e6i) q^{18} -1.58773e7i q^{19} +(-4.35890e6 + 1.88994e6i) q^{20} -3.90377e6i q^{21} +(1.22100e7 + 8.01427e6i) q^{22} +7.84803e6 q^{23} +(1.61996e6 - 9.34069e6i) q^{24} +4.34466e7 q^{25} +(4.49805e7 + 2.95238e7i) q^{26} -3.51694e7i q^{27} +(-3.10928e7 - 7.17114e7i) q^{28} +1.88088e8i q^{29} +(5.89242e6 - 8.97731e6i) q^{30} -2.59744e8 q^{31} +(-4.46386e7 - 1.84489e8i) q^{32} -3.30113e7 q^{33} +(-4.05423e7 + 6.17676e7i) q^{34} -8.85360e7i q^{35} +(-1.35797e8 - 3.13197e8i) q^{36} +5.80090e8i q^{37} +(6.00687e8 + 3.94272e8i) q^{38} -1.21610e8 q^{39} +(3.67399e7 - 2.11843e8i) q^{40} +9.39537e8 q^{41} +(1.47692e8 + 9.69405e7i) q^{42} -1.40098e9i q^{43} +(-6.06410e8 + 2.62929e8i) q^{44} -3.86678e8i q^{45} +(-1.94886e8 + 2.96916e8i) q^{46} +3.57380e8 q^{47} +(3.13160e8 + 2.93241e8i) q^{48} -5.20758e8 q^{49} +(-1.07889e9 + 1.64372e9i) q^{50} -1.66996e8i q^{51} +(-2.23396e9 + 9.68604e8i) q^{52} -1.56352e9i q^{53} +(1.33057e9 + 8.73344e8i) q^{54} -7.48683e8 q^{55} +(3.48518e9 + 6.04435e8i) q^{56} -1.62403e9 q^{57} +(-7.11597e9 - 4.67070e9i) q^{58} +5.83337e9i q^{59} +(1.93316e8 + 4.45858e8i) q^{60} -2.32647e9i q^{61} +(6.45009e9 - 9.82693e9i) q^{62} +6.36151e9 q^{63} +(8.08829e9 + 2.89250e9i) q^{64} -2.75807e9 q^{65} +(8.19754e8 - 1.24892e9i) q^{66} +1.50689e10i q^{67} +(-1.33009e9 - 3.06769e9i) q^{68} -8.02749e8i q^{69} +(3.34959e9 + 2.19857e9i) q^{70} +3.46823e9 q^{71} +(1.52214e10 + 2.63985e9i) q^{72} -1.94710e10 q^{73} +(-2.19466e10 - 1.44051e10i) q^{74} -4.44401e9i q^{75} +(-2.98331e10 + 1.29351e10i) q^{76} -1.23171e10i q^{77} +(3.01989e9 - 4.60091e9i) q^{78} -1.13963e10 q^{79} +(7.10234e9 + 6.65058e9i) q^{80} +2.59303e10 q^{81} +(-2.33311e10 + 3.55457e10i) q^{82} -2.66349e10i q^{83} +(-7.33513e9 + 3.18038e9i) q^{84} -3.78741e9i q^{85} +(5.30037e10 + 3.47900e10i) q^{86} +1.92389e10 q^{87} +(5.11126e9 - 2.94716e10i) q^{88} +4.93487e10 q^{89} +(1.46292e10 + 9.60218e9i) q^{90} -4.53750e10i q^{91} +(-6.39374e9 - 1.47463e10i) q^{92} +2.65683e10i q^{93} +(-8.87464e9 + 1.35208e10i) q^{94} -3.68324e10 q^{95} +(-1.88708e10 + 4.56594e9i) q^{96} -1.79889e10 q^{97} +(1.29317e10 - 1.97019e10i) q^{98} -5.37946e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9}+O(q^{10}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9	\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 + 436 * q^4 - 24308 * q^6 - 33616 * q^7 - 208472 * q^8 - 472394 * q^9 + 29864 * q^10 - 476216 * q^12 + 2264272 * q^14 + 3391792 * q^15 + 3757072 * q^16 + 2639732 * q^17 + 2329130 * q^18 + 8296432 * q^20 - 24201892 * q^22 - 45357808 * q^23 + 10668944 * q^24 - 41502654 * q^25 - 101931080 * q^26 - 95722144 * q^28 + 261362768 * q^30 + 442035392 * q^31 + 343908512 * q^32 - 54732216 * q^33 - 187103796 * q^34 - 431195700 * q^36 + 375100844 * q^38 - 431459312 * q^39 + 1519138784 * q^40 - 654907964 * q^41 - 3697737056 * q^42 - 4127012952 * q^44 + 6028867440 * q^46 - 560226528 * q^47 + 9357606048 * q^48 + 1143661722 * q^49 - 9626584226 * q^50 - 11595427248 * q^52 + 20050494008 * q^54 + 5632783984 * q^55 + 18698733760 * q^56 - 783862360 * q^57 - 22828679464 * q^58 - 43681325472 * q^60 + 40774631744 * q^62 - 14483624624 * q^63 + 55266728512 * q^64 - 80291360 * q^65 - 83128448712 * q^66 - 83303223768 * q^68 + 100120831168 * q^70 - 11769460176 * q^71 + 112862051672 * q^72 + 32304890372 * q^73 - 102103996184 * q^74 - 97501928568 * q^76 + 144445560944 * q^78 + 57291670496 * q^79 + 128322038976 * q^80 - 23172996094 * q^81 - 123309929604 * q^82 - 199990865984 * q^84 + 130201908124 * q^86 - 73844404272 * q^87 + 169216119632 * q^88 - 108276011804 * q^89 - 228506434984 * q^90 - 141139403232 * q^92 + 145336130016 * q^94 + 70146835376 * q^95 + 109508068928 * q^96 + 60995282900 * q^97 - 6194726778 * q^98

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