LMFDB - Embedded newform 8.21.d.b.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,21,Mod(3,8)]

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([1, 1]))

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$20.2811012082$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 $ x^18 + 66008406614424x^16 - 170362825164232872x^15 + 1756210031321623676418457398x^14 - 8143876994687623666322842711032x^13 + 24350477750271510634494454384791667990404x^12 - 150098892256302975432925342820456817156772440x^11 + 191202710428210659782696002203561503780870353303759377x^10 - 1295069212697340229160215370735662134952032297259046562056x^9 + 870944882856087336674875277000277878990405713083632292121165358076x^8 - 4812915841402167440171875831348280575634953635256498021616060003579520x^7 + 2268474737024234177226752378807914883078144887754356976399017987196241603311520x^6 - 4757172104321022064833287336478952531807855909655138781977813255912131556348455680x^5 + 3199222078336759259493497095495346495581808310744107378246303720899215796326992176238102400x^4 + 8929774272757329376425833321340788600302219356646171490279817057245825930569313705998374604800x^3 + 2186805491439153577309421324561832859804177633153493793273223699303415894069647268007263015677943481600x^2 + 13250359115341501288916746421398415873922554950681918855831714718905060696192946493864164248007740533504000x + 531754461748673811827664952573861209640978431708236170453755006606958174478016712983511620954972201107600928640000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.15
Root			$-24233.2 + 2.60731e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(829.658 - 600.204i) q^{2} -103279. q^{3} +(328087. - 995927. i) q^{4} -1.04292e7i q^{5} +(-8.56862e7 + 6.19884e7i) q^{6} -3.68005e8i q^{7} +(-3.25559e8 - 1.02320e9i) q^{8} +7.17976e9 q^{9} +O(q^{10})$	\(q+(829.658 - 600.204i) q^{2} -103279. q^{3} +(328087. - 995927. i) q^{4} -1.04292e7i q^{5} +(-8.56862e7 + 6.19884e7i) q^{6} -3.68005e8i q^{7} +(-3.25559e8 - 1.02320e9i) q^{8} +7.17976e9 q^{9} +(-6.25967e9 - 8.65271e9i) q^{10} -3.35341e10 q^{11} +(-3.38845e10 + 1.02858e11i) q^{12} +1.95314e11i q^{13} +(-2.20878e11 - 3.05318e11i) q^{14} +1.07712e12i q^{15} +(-8.84229e11 - 6.53502e11i) q^{16} -1.59958e11 q^{17} +(5.95674e12 - 4.30932e12i) q^{18} +4.90447e12 q^{19} +(-1.03868e13 - 3.42170e12i) q^{20} +3.80072e13i q^{21} +(-2.78218e13 + 2.01273e13i) q^{22} -3.43682e13i q^{23} +(3.36234e13 + 1.05675e14i) q^{24} -1.34018e13 q^{25} +(1.17228e14 + 1.62044e14i) q^{26} -3.81407e14 q^{27} +(-3.66506e14 - 1.20738e14i) q^{28} +1.07520e14i q^{29} +(6.46493e14 + 8.93643e14i) q^{30} +3.09876e13i q^{31} +(-1.12584e15 - 1.14654e13i) q^{32} +3.46337e15 q^{33} +(-1.32710e14 + 9.60073e13i) q^{34} -3.83802e15 q^{35} +(2.35559e15 - 7.15052e15i) q^{36} +4.26943e15i q^{37} +(4.06903e15 - 2.94368e15i) q^{38} -2.01719e16i q^{39} +(-1.06712e16 + 3.39533e15i) q^{40} -3.78792e15 q^{41} +(2.28121e16 + 3.15330e16i) q^{42} -2.30212e15 q^{43} +(-1.10021e16 + 3.33975e16i) q^{44} -7.48795e16i q^{45} +(-2.06279e16 - 2.85139e16i) q^{46} -3.45229e16i q^{47} +(9.13223e16 + 6.74930e16i) q^{48} -5.56357e16 q^{49} +(-1.11189e16 + 8.04382e15i) q^{50} +1.65203e16 q^{51} +(1.94519e17 + 6.40802e16i) q^{52} -3.51656e16i q^{53} +(-3.16437e17 + 2.28922e17i) q^{54} +3.49736e17i q^{55} +(-3.76542e17 + 1.19807e17i) q^{56} -5.06529e17 q^{57} +(6.45338e16 + 8.92047e16i) q^{58} +2.54124e17 q^{59} +(1.07273e18 + 3.53390e17i) q^{60} -1.01336e18i q^{61} +(1.85989e16 + 2.57091e16i) q^{62} -2.64219e18i q^{63} +(-9.40944e17 + 6.66222e17i) q^{64} +2.03698e18 q^{65} +(2.87341e18 - 2.07873e18i) q^{66} -2.98877e18 q^{67} +(-5.24802e16 + 1.59306e17i) q^{68} +3.54952e18i q^{69} +(-3.18424e18 + 2.30359e18i) q^{70} +8.39501e17i q^{71} +(-2.33743e18 - 7.34631e18i) q^{72} +3.32042e18 q^{73} +(2.56253e18 + 3.54216e18i) q^{74} +1.38413e18 q^{75} +(1.60909e18 - 4.88449e18i) q^{76} +1.23407e19i q^{77} +(-1.21072e19 - 1.67357e19i) q^{78} +1.22738e19i q^{79} +(-6.81553e18 + 9.22185e18i) q^{80} +1.43570e19 q^{81} +(-3.14267e18 + 2.27352e18i) q^{82} -2.23129e19 q^{83} +(3.78524e19 + 1.24697e19i) q^{84} +1.66824e18i q^{85} +(-1.90997e18 + 1.38174e18i) q^{86} -1.11045e19i q^{87} +(1.09173e19 + 3.43120e19i) q^{88} -3.15513e19 q^{89} +(-4.49430e19 - 6.21244e19i) q^{90} +7.18767e19 q^{91} +(-3.42282e19 - 1.12758e19i) q^{92} -3.20037e18i q^{93} +(-2.07208e19 - 2.86422e19i) q^{94} -5.11499e19i q^{95} +(1.16276e20 + 1.18413e18i) q^{96} +8.67034e19 q^{97} +(-4.61586e19 + 3.33927e19i) q^{98} -2.40767e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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 $

$2$	829.658	−	600.204i	0.810212	−	0.586136i
$2$	829.658	−	600.204i	0.810212	−	0.586136i
$3$	−103279.			−1.74904			−0.874519	−	0.484991i	$-0.838823\pi$
$3$	−103279.			−1.74904			−0.874519	+	0.484991i	$0.838823\pi$
$4$	328087.	−	995927.i	0.312888	−	0.949790i
$5$		−	1.04292e7i		−	1.06796i	−0.845499	−	0.533978i	$-0.820697\pi$
$5$		−	1.04292e7i		−	1.06796i	0.845499	−	0.533978i	$-0.179303\pi$
$6$	−8.56862e7	+	6.19884e7i	−1.41709	+	1.02517i
$7$		−	3.68005e8i		−	1.30279i	−0.758740	−	0.651394i	$-0.774185\pi$
$7$		−	3.68005e8i		−	1.30279i	0.758740	−	0.651394i	$-0.225815\pi$
$8$	−3.25559e8	−	1.02320e9i	−0.303200	−	0.952927i
$9$	7.17976e9			2.05914
$10$	−6.25967e9	−	8.65271e9i	−0.625967	−	0.865271i
$11$	−3.35341e10			−1.29289			−0.646443	−	0.762962i	$-0.723744\pi$
$11$	−3.35341e10			−1.29289			−0.646443	+	0.762962i	$0.723744\pi$
$12$	−3.38845e10	+	1.02858e11i	−0.547254	+	1.66122i
$13$			1.95314e11i			1.41677i	0.705824	+	0.708387i	$0.250577\pi$
$13$			1.95314e11i			1.41677i	−0.705824	+	0.708387i	$0.749423\pi$
$14$	−2.20878e11	−	3.05318e11i	−0.763611	−	1.05554i
$15$			1.07712e12i			1.86789i
$16$	−8.84229e11	−	6.53502e11i	−0.804202	−	0.594357i
$17$	−1.59958e11			−0.0793445			−0.0396722	−	0.999213i	$-0.512631\pi$
$17$	−1.59958e11			−0.0793445			−0.0396722	+	0.999213i	$0.512631\pi$
$18$	5.95674e12	−	4.30932e12i	1.66834	−	1.20693i
$19$	4.90447e12			0.799937			0.399969	−	0.916529i	$-0.369021\pi$
$19$	4.90447e12			0.799937			0.399969	+	0.916529i	$0.369021\pi$
$20$	−1.03868e13	−	3.42170e12i	−1.01433	−	0.334151i
$21$			3.80072e13i			2.27863i
$22$	−2.78218e13	+	2.01273e13i	−1.04751	+	0.757807i
$23$		−	3.43682e13i		−	0.829619i	−0.909908	−	0.414810i	$-0.863848\pi$
$23$		−	3.43682e13i		−	0.829619i	0.909908	−	0.414810i	$-0.136152\pi$
$24$	3.36234e13	+	1.05675e14i	0.530309	+	1.66671i
$25$	−1.34018e13			−0.140528
$26$	1.17228e14	+	1.62044e14i	0.830423	+	1.14789i
$27$	−3.81407e14			−1.85247
$28$	−3.66506e14	−	1.20738e14i	−1.23737	−	0.407627i
$29$			1.07520e14i			0.255569i	0.991802	+	0.127785i	$0.0407867\pi$
$29$			1.07520e14i			0.255569i	−0.991802	+	0.127785i	$0.959213\pi$
$30$	6.46493e14	+	8.93643e14i	1.09484	+	1.51339i
$31$			3.09876e13i			0.0378069i	0.999821	+	0.0189035i	$0.00601752\pi$
$31$			3.09876e13i			0.0378069i	−0.999821	+	0.0189035i	$0.993982\pi$
$32$	−1.12584e15	−	1.14654e13i	−0.999948	−	0.0101833i
$33$	3.46337e15			2.26131
$34$	−1.32710e14	+	9.60073e13i	−0.0642859	+	0.0465067i
$35$	−3.83802e15			−1.39132
$36$	2.35559e15	−	7.15052e15i	0.644280	−	1.95575i
$37$			4.26943e15i			0.887876i	0.896057	+	0.443938i	$0.146419\pi$
$37$			4.26943e15i			0.887876i	−0.896057	+	0.443938i	$0.853581\pi$
$38$	4.06903e15	−	2.94368e15i	0.648119	−	0.468872i
$39$		−	2.01719e16i		−	2.47799i
$40$	−1.06712e16	+	3.39533e15i	−1.01768	+	0.323804i
$41$	−3.78792e15			−0.282203			−0.141102	−	0.989995i	$-0.545064\pi$
$41$	−3.78792e15			−0.282203			−0.141102	+	0.989995i	$0.545064\pi$
$42$	2.28121e16	+	3.15330e16i	1.33559	+	1.84617i
$43$	−2.30212e15			−0.106523			−0.0532614	−	0.998581i	$-0.516962\pi$
$43$	−2.30212e15			−0.106523			−0.0532614	+	0.998581i	$0.516962\pi$
$44$	−1.10021e16	+	3.33975e16i	−0.404529	+	1.22797i
$45$		−	7.48795e16i		−	2.19906i
$46$	−2.06279e16	−	2.85139e16i	−0.486270	−	0.672168i
$47$		−	3.45229e16i		−	0.656340i	−0.944619	−	0.328170i	$-0.893568\pi$
$47$		−	3.45229e16i		−	0.656340i	0.944619	−	0.328170i	$-0.106432\pi$
$48$	9.13223e16	+	6.74930e16i	1.40658	+	1.03955i
$49$	−5.56357e16			−0.697256
$50$	−1.11189e16	+	8.04382e15i	−0.113858	+	0.0823687i
$51$	1.65203e16			0.138777
$52$	1.94519e17	+	6.40802e16i	1.34564	+	0.443292i
$53$		−	3.51656e16i		−	0.201076i	−0.994933	−	0.100538i	$-0.967944\pi$
$53$		−	3.51656e16i		−	0.201076i	0.994933	−	0.100538i	$-0.0320563\pi$
$54$	−3.16437e17	+	2.28922e17i	−1.50089	+	1.08580i
$55$			3.49736e17i			1.38074i
$56$	−3.76542e17	+	1.19807e17i	−1.24146	+	0.395006i
$57$	−5.06529e17			−1.39912
$58$	6.45338e16	+	8.92047e16i	0.149799	+	0.207066i
$59$	2.54124e17			0.497194			0.248597	−	0.968607i	$-0.420030\pi$
$59$	2.54124e17			0.497194			0.248597	+	0.968607i	$0.420030\pi$
$60$	1.07273e18	+	3.53390e17i	1.77411	+	0.584443i
$61$		−	1.01336e18i		−	1.42057i	−0.703912	−	0.710287i	$-0.748565\pi$
$61$		−	1.01336e18i		−	1.42057i	0.703912	−	0.710287i	$-0.251435\pi$
$62$	1.85989e16	+	2.57091e16i	0.0221600	+	0.0306316i
$63$		−	2.64219e18i		−	2.68262i
$64$	−9.40944e17	+	6.66222e17i	−0.816139	+	0.577855i
$65$	2.03698e18			1.51305
$66$	2.87341e18	−	2.07873e18i	1.83214	−	1.32543i
$67$	−2.98877e18			−1.63963			−0.819813	−	0.572632i	$-0.805923\pi$
$67$	−2.98877e18			−1.63963			−0.819813	+	0.572632i	$0.805923\pi$
$68$	−5.24802e16	+	1.59306e17i	−0.0248260	+	0.0753606i
$69$			3.54952e18i			1.45104i
$70$	−3.18424e18	+	2.30359e18i	−1.12726	+	0.815503i
$71$			8.39501e17i			0.257892i	0.991652	+	0.128946i	$0.0411594\pi$
$71$			8.39501e17i			0.257892i	−0.991652	+	0.128946i	$0.958841\pi$
$72$	−2.33743e18	−	7.34631e18i	−0.624330	−	1.96221i
$73$	3.32042e18			0.772617			0.386308	−	0.922370i	$-0.373750\pi$
$73$	3.32042e18			0.772617			0.386308	+	0.922370i	$0.373750\pi$
$74$	2.56253e18	+	3.54216e18i	0.520417	+	0.719368i
$75$	1.38413e18			0.245789
$76$	1.60909e18	−	4.88449e18i	0.250291	−	0.759773i
$77$			1.23407e19i			1.68436i
$78$	−1.21072e19	−	1.67357e19i	−1.45244	−	2.00770i
$79$			1.22738e19i			1.29631i	0.761510	+	0.648153i	$0.224458\pi$
$79$			1.22738e19i			1.29631i	−0.761510	+	0.648153i	$0.775542\pi$
$80$	−6.81553e18	+	9.22185e18i	−0.634746	+	0.858851i
$81$	1.43570e19			1.18090
$82$	−3.14267e18	+	2.27352e18i	−0.228644	+	0.165409i
$83$	−2.23129e19			−1.43805			−0.719027	−	0.694982i	$-0.755412\pi$
$83$	−2.23129e19			−1.43805			−0.719027	+	0.694982i	$0.755412\pi$
$84$	3.78524e19	+	1.24697e19i	2.16422	+	0.712956i
$85$			1.66824e18i			0.0847363i
$86$	−1.90997e18	+	1.38174e18i	−0.0863061	+	0.0624369i
$87$		−	1.11045e19i		−	0.447001i
$88$	1.09173e19	+	3.43120e19i	0.392003	+	1.23203i
$89$	−3.15513e19			−1.01185			−0.505926	−	0.862577i	$-0.668849\pi$
$89$	−3.15513e19			−1.01185			−0.505926	+	0.862577i	$0.668849\pi$
$90$	−4.49430e19	−	6.21244e19i	−1.28895	−	1.78171i
$91$	7.18767e19			1.84576
$92$	−3.42282e19	−	1.12758e19i	−0.787964	−	0.259578i
$93$		−	3.20037e18i		−	0.0661258i
$94$	−2.07208e19	−	2.86422e19i	−0.384705	−	0.531775i
$95$		−	5.11499e19i		−	0.854297i
$96$	1.16276e20	+	1.18413e18i	1.74895	+	0.0178110i
$97$	8.67034e19			1.17576			0.587880	−	0.808948i	$-0.299963\pi$
$97$	8.67034e19			1.17576			0.587880	+	0.808948i	$0.299963\pi$
$98$	−4.61586e19	+	3.33927e19i	−0.564926	+	0.408687i
$99$	−2.40767e20			−2.66223
$100$	−4.39696e18	+	1.33472e19i	−0.0439696	+	0.133472i
$101$			1.28845e20i			1.16642i	0.812323	+	0.583208i	$0.198203\pi$
$101$			1.28845e20i			1.16642i	−0.812323	+	0.583208i	$0.801797\pi$
$102$	1.37062e19	−	9.91554e18i	0.112438	−	0.0813419i
$103$		−	1.79112e20i		−	1.33277i	−0.745610	−	0.666383i	$-0.767842\pi$
$103$		−	1.79112e20i		−	1.33277i	0.745610	−	0.666383i	$-0.232158\pi$
$104$	1.99845e20	−	6.35863e19i	1.35008	−	0.429566i
$105$	3.96387e20			2.43347
$106$	−2.11065e19	−	2.91754e19i	−0.117858	−	0.162914i
$107$	−2.99118e20			−1.52056			−0.760282	−	0.649593i	$-0.774939\pi$
$107$	−2.99118e20			−1.52056			−0.760282	+	0.649593i	$0.774939\pi$
$108$	−1.25135e20	+	3.79853e20i	−0.579616	+	1.75946i
$109$		−	3.19327e20i		−	1.34887i	−0.738334	−	0.674435i	$-0.764387\pi$
$109$		−	3.19327e20i		−	1.34887i	0.738334	−	0.674435i	$-0.235613\pi$
$110$	2.09913e20	+	2.90161e20i	0.809304	+	1.11870i
$111$		−	4.40942e20i		−	1.55293i
$112$	−2.40492e20	+	3.25401e20i	−0.774321	+	1.04770i
$113$	−2.35418e20			−0.693515			−0.346758	−	0.937955i	$-0.612717\pi$
$113$	−2.35418e20			−0.693515			−0.346758	+	0.937955i	$0.612717\pi$
$114$	−4.20245e20	+	3.04020e20i	−1.13359	+	0.820076i
$115$	−3.58435e20			−0.885996
$116$	1.07082e20	+	3.52759e19i	0.242737	+	0.0799647i
$117$			1.40231e21i			2.91733i
$118$	2.10836e20	−	1.52526e20i	0.402833	−	0.291424i
$119$			5.88654e19i			0.103369i
$120$	1.10211e21	−	3.50667e20i	1.77997	−	0.566346i
$121$	4.51788e20			0.671554
$122$	−6.08221e20	−	8.40739e20i	−0.832651	−	1.15097i
$123$	3.91212e20			0.493584
$124$	3.08614e19	+	1.01666e19i	0.0359086	+	0.0118293i
$125$		−	8.54840e20i		−	0.917877i
$126$	−1.58585e21	−	2.19211e21i	−1.57238	−	2.17349i
$127$			5.48014e20i			0.502058i	0.967980	+	0.251029i	$0.0807690\pi$
$127$			5.48014e20i			0.502058i	−0.967980	+	0.251029i	$0.919231\pi$
$128$	−3.80793e20	+	1.11749e21i	−0.322544	+	0.946554i
$129$	2.37760e20			0.186313
$130$	1.69000e21	−	1.22260e21i	1.22589	−	0.886854i
$131$	2.37091e21			1.59295			0.796474	−	0.604673i	$-0.206696\pi$
$131$	2.37091e21			1.59295			0.796474	+	0.604673i	$0.206696\pi$
$132$	1.13629e21	−	3.44926e21i	0.707537	−	2.14777i
$133$		−	1.80487e21i		−	1.04215i
$134$	−2.47966e21	+	1.79387e21i	−1.32844	+	0.961044i
$135$			3.97779e21i			1.97835i
$136$	5.20757e19	+	1.63669e20i	0.0240573	+	0.0756095i
$137$	−1.87304e21			−0.804158			−0.402079	−	0.915605i	$-0.631712\pi$
$137$	−1.87304e21			−0.804158			−0.402079	+	0.915605i	$0.631712\pi$
$138$	2.13043e21	+	2.94488e21i	0.850505	+	1.17565i
$139$	−4.17320e21			−1.54996			−0.774982	−	0.631983i	$-0.782241\pi$
$139$	−4.17320e21			−1.54996			−0.774982	+	0.631983i	$0.782241\pi$
$140$	−1.25921e21	+	3.82239e21i	−0.435328	+	1.32146i
$141$			3.56549e21i			1.14796i
$142$	5.03872e20	+	6.96498e20i	0.151160	+	0.208947i
$143$		−	6.54970e21i		−	1.83173i
$144$	−6.34855e21	−	4.69199e21i	−1.65596	−	1.22386i
$145$	1.12135e21			0.272937
$146$	2.75481e21	−	1.99293e21i	0.625984	−	0.452859i
$147$	5.74599e21			1.21953
$148$	4.25204e21	+	1.40075e21i	0.843296	+	0.277806i
$149$			4.63926e21i			0.860174i	0.902787	+	0.430087i	$0.141517\pi$
$149$			4.63926e21i			0.860174i	−0.902787	+	0.430087i	$0.858483\pi$
$150$	1.14835e21	−	8.30757e20i	0.199141	−	0.144066i
$151$			6.55978e21i			1.06444i	0.846607	+	0.532218i	$0.178641\pi$
$151$			6.55978e21i			1.06444i	−0.846607	+	0.532218i	$0.821359\pi$
$152$	−1.59669e21	−	5.01824e21i	−0.242541	−	0.762282i
$153$	−1.14846e21			−0.163381
$154$	7.40696e21	+	1.02386e22i	0.987262	+	1.36469i
$155$	3.23178e20			0.0403761
$156$	−2.00897e22	−	6.61813e21i	−2.35357	−	0.775335i
$157$		−	1.23081e22i		−	1.35268i	−0.736589	−	0.676340i	$-0.763565\pi$
$157$		−	1.23081e22i		−	1.35268i	0.736589	−	0.676340i	$-0.236435\pi$
$158$	7.36677e21	+	1.01830e22i	0.759812	+	1.05028i
$159$			3.63187e21i			0.351689i
$160$	−1.19575e20	+	1.17417e22i	−0.0108753	+	1.06790i
$161$	−1.26477e22			−1.08082
$162$	1.19114e22	−	8.61715e21i	0.956783	−	0.692171i
$163$	−1.08316e21			−0.0818120			−0.0409060	−	0.999163i	$-0.513024\pi$
$163$	−1.08316e21			−0.0818120			−0.0409060	+	0.999163i	$0.513024\pi$
$164$	−1.24277e21	+	3.77249e21i	−0.0882981	+	0.268034i
$165$		−	3.61204e22i		−	2.41497i
$166$	−1.85121e22	+	1.33923e22i	−1.16513	+	0.842896i
$167$		−	1.57673e22i		−	0.934531i	−0.884117	−	0.467266i	$-0.845239\pi$
$167$		−	1.57673e22i		−	0.934531i	0.884117	−	0.467266i	$-0.154761\pi$
$168$	3.88889e22	−	1.23736e22i	2.17136	−	0.690880i
$169$	−1.91427e22			−1.00725
$170$	1.00128e21	+	1.38407e21i	0.0496670	+	0.0686544i
$171$	3.52129e22			1.64718
$172$	−7.55295e20	+	2.29274e21i	−0.0333298	+	0.101174i
$173$		−	1.33989e22i		−	0.557968i	−0.960296	−	0.278984i	$-0.910002\pi$
$173$		−	1.33989e22i		−	0.557968i	0.960296	−	0.278984i	$-0.0899976\pi$
$174$	−6.66499e21	−	9.21297e21i	−0.262003	−	0.362166i
$175$			4.93194e21i			0.183078i
$176$	2.96519e22	+	2.19146e22i	1.03974	+	0.768435i
$177$	−2.62457e22			−0.869612
$178$	−2.61768e22	+	1.89372e22i	−0.819816	+	0.593084i
$179$	1.76290e22			0.522032			0.261016	−	0.965334i	$-0.415942\pi$
$179$	1.76290e22			0.522032			0.261016	+	0.965334i	$0.415942\pi$
$180$	−7.45745e22	−	2.45670e22i	−2.08865	−	0.688062i
$181$			3.12653e22i			0.828469i	0.910170	+	0.414235i	$0.135951\pi$
$181$			3.12653e22i			0.828469i	−0.910170	+	0.414235i	$0.864049\pi$
$182$	5.96331e22	−	4.31407e22i	1.49545	−	1.08186i
$183$			1.04658e23i			2.48464i
$184$	−3.51655e22	+	1.11889e22i	−0.790566	+	0.251541i
$185$	4.45269e22			0.948212
$186$	−1.92087e21	−	2.65521e21i	−0.0387587	−	0.0535759i
$187$	5.36405e21			0.102583
$188$	−3.43823e22	−	1.13265e22i	−0.623385	−	0.205361i
$189$			1.40360e23i			2.41337i
$190$	−3.07004e22	−	4.24369e22i	−0.500735	−	0.692162i
$191$		−	8.00644e22i		−	1.23910i	−0.784958	−	0.619549i	$-0.787315\pi$
$191$		−	8.00644e22i		−	1.23910i	0.784958	−	0.619549i	$-0.212685\pi$
$192$	9.71798e22	−	6.88067e22i	1.42746	−	1.01069i
$193$	4.76538e21			0.0664544			0.0332272	−	0.999448i	$-0.489421\pi$
$193$	4.76538e21			0.0664544			0.0332272	+	0.999448i	$0.489421\pi$
$194$	7.19341e22	−	5.20397e22i	0.952615	−	0.689155i
$195$	−2.10377e23			−2.64639
$196$	−1.82534e22	+	5.54091e22i	−0.218163	+	0.662247i
$197$		−	3.59368e22i		−	0.408204i	−0.978950	−	0.204102i	$-0.934573\pi$
$197$		−	3.59368e22i		−	0.408204i	0.978950	−	0.204102i	$-0.0654274\pi$
$198$	−1.99754e23	+	1.44509e23i	−2.15697	+	1.56043i
$199$		−	1.66755e22i		−	0.171218i	−0.996329	−	0.0856088i	$-0.972716\pi$
$199$		−	1.66755e22i		−	0.171218i	0.996329	−	0.0856088i	$-0.0272835\pi$
$200$	4.36308e21	+	1.37127e22i	0.0426082	+	0.133913i
$201$	3.08677e23			2.86777
$202$	7.73331e22	+	1.06897e23i	0.683678	+	0.945044i
$203$	3.95679e22			0.332953
$204$	5.42010e21	−	1.64530e22i	0.0434216	−	0.131809i
$205$			3.95051e22i			0.301380i
$206$	−1.07504e23	−	1.48602e23i	−0.781182	−	1.07982i
$207$		−	2.46756e23i		−	1.70830i
$208$	1.27638e23	−	1.72703e23i	0.842069	−	1.13937i
$209$	−1.64467e23			−1.03423
$210$	3.28865e23	−	2.37913e23i	1.97163	−	1.42635i
$211$	5.82077e22			0.332779			0.166390	−	0.986060i	$-0.446789\pi$
$211$	5.82077e22			0.332779			0.166390	+	0.986060i	$0.446789\pi$
$212$	−3.50224e22	−	1.15374e22i	−0.190980	−	0.0629142i
$213$		−	8.67028e22i		−	0.451063i
$214$	−2.48165e23	+	1.79532e23i	−1.23198	+	0.891258i
$215$			2.40093e22i			0.113762i
$216$	1.24170e23	+	3.90255e23i	0.561669	+	1.76527i
$217$	1.14036e22			0.0492544
$218$	−1.91661e23	−	2.64932e23i	−0.790622	−	1.09287i
$219$	−3.42929e23			−1.35134
$220$	3.48311e23	+	1.14744e23i	1.31142	+	0.432019i
$221$		−	3.12421e22i		−	0.112413i
$222$	−2.64655e23	−	3.65831e23i	−0.910229	−	1.25820i
$223$			5.04418e23i			1.65860i	0.558803	+	0.829301i	$0.311261\pi$
$223$			5.04418e23i			1.65860i	−0.558803	+	0.829301i	$0.688739\pi$
$224$	−4.21933e21	+	4.14316e23i	−0.0132667	+	1.30272i
$225$	−9.62218e22			−0.289367
$226$	−1.95317e23	+	1.41299e23i	−0.561895	+	0.406495i
$227$	4.05442e23			1.11602			0.558008	−	0.829835i	$-0.311566\pi$
$227$	4.05442e23			1.11602			0.558008	+	0.829835i	$0.311566\pi$
$228$	−1.66186e23	+	5.04465e23i	−0.437769	+	1.32887i
$229$			4.75091e23i			1.19790i	0.800785	+	0.598952i	$0.204416\pi$
$229$			4.75091e23i			1.19790i	−0.800785	+	0.598952i	$0.795584\pi$
$230$	−2.97378e23	+	2.15134e23i	−0.717845	+	0.519315i
$231$		−	1.27454e24i		−	2.94600i
$232$	1.10014e23	−	3.50040e22i	0.243539	−	0.0774887i
$233$	6.24482e22			0.132422			0.0662110	−	0.997806i	$-0.478909\pi$
$233$	6.24482e22			0.132422			0.0662110	+	0.997806i	$0.478909\pi$
$234$	8.41672e23	+	1.16344e24i	1.70995	+	2.36366i
$235$	−3.60048e23			−0.700942
$236$	8.33750e22	−	2.53089e23i	0.155566	−	0.472230i
$237$		−	1.26762e24i		−	2.26729i
$238$	3.53312e22	+	4.88381e22i	0.0605883	+	0.0837508i
$239$			4.38763e23i			0.721525i	0.932658	+	0.360763i	$0.117484\pi$
$239$			4.38763e23i			0.721525i	−0.932658	+	0.360763i	$0.882516\pi$
$240$	7.03901e23	−	9.52423e23i	1.11020	−	1.50216i
$241$	−6.38433e23			−0.965928			−0.482964	−	0.875640i	$-0.660440\pi$
$241$	−6.38433e23			−0.965928			−0.482964	+	0.875640i	$0.660440\pi$
$242$	3.74829e23	−	2.71165e23i	0.544102	−	0.393622i
$243$	−1.52896e23			−0.212978
$244$	−1.00923e24	−	3.32470e23i	−1.34925	−	0.444481i
$245$			5.80238e23i			0.744639i
$246$	3.24572e23	−	2.34807e23i	0.399908	−	0.289308i
$247$			9.57913e23i			1.13333i
$248$	3.17065e22	−	1.00883e22i	0.0360272	−	0.0114631i
$249$	2.30445e24			2.51521
$250$	−5.13078e23	−	7.09224e23i	−0.538001	−	0.743676i
$251$	−4.03875e23			−0.406921			−0.203460	−	0.979083i	$-0.565219\pi$
$251$	−4.03875e23			−0.406921			−0.203460	+	0.979083i	$0.565219\pi$
$252$	−2.63143e24	−	8.66869e23i	−2.54792	−	0.839360i
$253$			1.15251e24i			1.07260i
$254$	3.28920e23	+	4.54664e23i	0.294275	+	0.406774i
$255$		−	1.72294e23i		−	0.148207i
$256$	3.54796e23	+	1.15569e24i	0.293481	+	0.955965i
$257$	−1.49185e24			−1.18685			−0.593424	−	0.804890i	$-0.702224\pi$
$257$	−1.49185e24			−1.18685			−0.593424	+	0.804890i	$0.702224\pi$
$258$	1.97260e23	−	1.42705e23i	0.150953	−	0.109205i
$259$	1.57117e24			1.15671
$260$	6.68308e23	−	2.02869e24i	0.473416	−	1.43708i
$261$			7.71967e23i			0.526252i
$262$	1.96704e24	−	1.42303e24i	1.29063	−	0.933684i
$263$			3.50322e23i			0.221263i	0.993861	+	0.110632i	$0.0352874\pi$
$263$			3.50322e23i			0.221263i	−0.993861	+	0.110632i	$0.964713\pi$
$264$	−1.12753e24	−	3.54371e24i	−0.685629	−	2.15486i
$265$	−3.66751e23			−0.214740
$266$	−1.08329e24	−	1.49742e24i	−0.610841	−	0.844362i
$267$	3.25859e24			1.76977
$268$	−9.80578e23	+	2.97660e24i	−0.513020	+	1.55730i
$269$		−	2.56975e24i		−	1.29529i	−0.761941	−	0.647646i	$-0.775754\pi$
$269$		−	2.56975e24i		−	1.29529i	0.761941	−	0.647646i	$-0.224246\pi$
$270$	2.38748e24	+	3.30020e24i	1.15959	+	1.60289i
$271$			3.31630e24i			1.55225i	0.630582	+	0.776123i	$0.282816\pi$
$271$			3.31630e24i			1.55225i	−0.630582	+	0.776123i	$0.717184\pi$
$272$	1.41439e23	+	1.04533e23i	0.0638089	+	0.0471589i
$273$	−7.42335e24			−3.22830
$274$	−1.55398e24	+	1.12421e24i	−0.651539	+	0.471346i
$275$	4.49418e23			0.181687
$276$	3.53506e24	+	1.16455e24i	1.37818	+	0.454012i
$277$		−	4.21196e24i		−	1.58375i	−0.610683	−	0.791876i	$-0.709105\pi$
$277$		−	4.21196e24i		−	1.58375i	0.610683	−	0.791876i	$-0.290895\pi$
$278$	−3.46233e24	+	2.50477e24i	−1.25580	+	0.908490i
$279$			2.22484e23i			0.0778496i
$280$	1.24950e24	+	3.92705e24i	0.421848	+	1.32583i
$281$	4.42895e24			1.44290			0.721452	−	0.692465i	$-0.243475\pi$
$281$	4.42895e24			1.44290			0.721452	+	0.692465i	$0.243475\pi$
$282$	2.14002e24	+	2.95814e24i	0.672864	+	0.930095i
$283$	1.44352e24			0.438086			0.219043	−	0.975715i	$-0.429706\pi$
$283$	1.44352e24			0.438086			0.219043	+	0.975715i	$0.429706\pi$
$284$	8.36082e23	+	2.75430e23i	0.244943	+	0.0806914i
$285$			5.28271e24i			1.49420i
$286$	−3.93115e24	−	5.43401e24i	−1.07364	−	1.48409i
$287$			1.39397e24i			0.367651i
$288$	−8.08327e24	−	8.23188e22i	−2.05903	−	0.0209688i
$289$	−4.03864e24			−0.993704
$290$	9.30338e23	−	6.73039e23i	0.221137	−	0.159978i
$291$	−8.95463e24			−2.05645
$292$	1.08939e24	−	3.30689e24i	0.241743	−	0.733824i
$293$		−	8.90093e24i		−	1.90879i	−0.298541	−	0.954397i	$-0.596500\pi$
$293$		−	8.90093e24i		−	1.90879i	0.298541	−	0.954397i	$-0.403500\pi$
$294$	4.76721e24	−	3.44877e24i	0.988077	−	0.714810i
$295$		−	2.65033e24i		−	0.530981i
$296$	4.36847e24	−	1.38995e24i	0.846081	−	0.269204i
$297$	1.27902e25			2.39503
$298$	2.78450e24	+	3.84900e24i	0.504179	+	0.696924i
$299$	6.71261e24			1.17538
$300$	4.54114e23	−	1.37849e24i	0.0769046	−	0.233448i
$301$			8.47191e23i			0.138777i
$302$	3.93720e24	+	5.44237e24i	0.623905	+	0.862420i
$303$		−	1.33070e25i		−	2.04011i
$304$	−4.33667e24	−	3.20508e24i	−0.643311	−	0.475448i
$305$	−1.05686e25			−1.51711
$306$	−9.52828e23	+	6.89310e23i	−0.132373	+	0.0957635i
$307$	8.30730e23			0.111706			0.0558529	−	0.998439i	$-0.482212\pi$
$307$	8.30730e23			0.111706			0.0558529	+	0.998439i	$0.482212\pi$
$308$	1.22905e25	+	4.04884e24i	1.59978	+	0.527016i
$309$			1.84986e25i			2.33106i
$310$	2.68127e23	−	1.93972e23i	0.0327132	−	0.0236659i
$311$		−	1.01133e25i		−	1.19478i	−0.801951	−	0.597390i	$-0.796204\pi$
$311$		−	1.01133e25i		−	1.19478i	0.801951	−	0.597390i	$-0.203796\pi$
$312$	−2.06398e25	+	6.56713e24i	−2.36135	+	0.751328i
$313$	6.25698e24			0.693300			0.346650	−	0.937995i	$-0.387319\pi$
$313$	6.25698e24			0.693300			0.346650	+	0.937995i	$0.387319\pi$
$314$	−7.38738e24	−	1.02115e25i	−0.792855	−	1.09596i
$315$	−2.75561e25			−2.86491
$316$	1.22238e25	+	4.02687e24i	1.23122	+	0.405599i
$317$		−	6.36417e24i		−	0.621083i	−0.950560	−	0.310541i	$-0.899490\pi$
$317$		−	6.36417e24i		−	0.621083i	0.950560	−	0.310541i	$-0.100510\pi$
$318$	2.17986e24	+	3.01321e24i	0.206138	+	0.284943i
$319$		−	3.60559e24i		−	0.330422i
$320$	6.94819e24	+	9.81334e24i	0.617124	+	0.871600i
$321$	3.08926e25			2.65953
$322$	−1.04933e25	+	7.59119e24i	−0.875692	+	0.633507i
$323$	−7.84509e23			−0.0634706
$324$	4.71036e24	−	1.42986e25i	0.369491	−	1.12161i
$325$		−	2.61757e24i		−	0.199097i
$326$	−8.98652e23	+	6.50117e23i	−0.0662851	+	0.0479530i
$327$			3.29797e25i			2.35923i
$328$	1.23319e24	+	3.87579e24i	0.0855640	+	0.268919i
$329$	−1.27046e25			−0.855072
$330$	−2.16796e25	−	2.99675e25i	−1.41550	−	1.95664i
$331$	1.21569e25			0.770093			0.385046	−	0.922897i	$-0.374185\pi$
$331$	1.21569e25			0.770093			0.385046	+	0.922897i	$0.374185\pi$
$332$	−7.32058e24	+	2.22220e25i	−0.449951	+	1.36585i
$333$			3.06535e25i			1.82826i
$334$	−9.46362e24	−	1.30815e25i	−0.547763	−	0.757169i
$335$			3.11706e25i			1.75105i
$336$	2.48378e25	−	3.36071e25i	1.35432	−	1.83247i
$337$	−3.30993e25			−1.75194			−0.875970	−	0.482366i	$-0.839778\pi$
$337$	−3.30993e25			−1.75194			−0.875970	+	0.482366i	$0.839778\pi$
$338$	−1.58819e25	+	1.14895e25i	−0.816086	+	0.590385i
$339$	2.43138e25			1.21299
$340$	1.66145e24	+	5.47329e23i	0.0804817	+	0.0265130i
$341$		−	1.03914e24i		−	0.0488800i
$342$	2.92147e25	−	2.11349e25i	1.33457	−	0.965472i
$343$		−	8.88976e24i		−	0.394411i
$344$	7.49474e23	+	2.35552e24i	0.0322977	+	0.101508i
$345$	3.70188e25			1.54964
$346$	−8.04209e24	−	1.11165e25i	−0.327045	−	0.452073i
$347$	−1.29207e25			−0.510493			−0.255247	−	0.966876i	$-0.582157\pi$
$347$	−1.29207e25			−0.510493			−0.255247	+	0.966876i	$0.582157\pi$
$348$	−1.10593e25	−	3.64326e24i	−0.424557	−	0.139861i
$349$		−	1.52161e25i		−	0.567608i	−0.958882	−	0.283804i	$-0.908403\pi$
$349$		−	1.52161e25i		−	0.567608i	0.958882	−	0.283804i	$-0.0915965\pi$
$350$	2.96017e24	+	4.09182e24i	0.107309	+	0.148332i
$351$		−	7.44943e25i		−	2.62453i
$352$	3.77541e25	+	3.84482e23i	1.29282	+	0.0131659i
$353$	1.15184e24			0.0383394			0.0191697	−	0.999816i	$-0.493898\pi$
$353$	1.15184e24			0.0383394			0.0191697	+	0.999816i	$0.493898\pi$
$354$	−2.17749e25	+	1.57528e25i	−0.704571	+	0.509711i
$355$	8.75537e24			0.275417
$356$	−1.03516e25	+	3.14228e25i	−0.316597	+	0.961047i
$357$		−	6.07956e24i		−	0.180796i
$358$	1.46260e25	−	1.05810e25i	0.422957	−	0.305982i
$359$		−	1.62522e25i		−	0.457053i	−0.973538	−	0.228527i	$-0.926609\pi$
$359$		−	1.62522e25i		−	0.457053i	0.973538	−	0.228527i	$-0.0733908\pi$
$360$	−7.66165e25	+	2.43777e25i	−2.09555	+	0.666757i
$361$	−1.35362e25			−0.360100
$362$	1.87655e25	+	2.59395e25i	0.485596	+	0.671236i
$363$	−4.66602e25			−1.17457
$364$	2.35818e25	−	7.15840e25i	0.577516	−	1.75308i
$365$		−	3.46295e25i		−	0.825120i
$366$	6.28164e25	+	8.68307e25i	1.45634	+	2.01309i
$367$			1.86174e25i			0.420009i	0.977700	+	0.210004i	$0.0673478\pi$
$367$			1.86174e25i			0.420009i	−0.977700	+	0.210004i	$0.932652\pi$
$368$	−2.24597e25	+	3.03894e25i	−0.493090	+	0.667181i
$369$	−2.71963e25			−0.581094
$370$	3.69421e25	−	2.67252e25i	0.768253	−	0.555782i
$371$	−1.29411e25			−0.261959
$372$	−3.18733e24	−	1.05000e24i	−0.0628056	−	0.0206900i
$373$		−	8.50867e24i		−	0.163220i	−0.996664	−	0.0816100i	$-0.973994\pi$
$373$		−	8.50867e24i		−	0.163220i	0.996664	−	0.0816100i	$-0.0260062\pi$
$374$	4.45033e24	−	3.21952e24i	0.0831143	−	0.0601278i
$375$			8.82870e25i			1.60540i
$376$	−3.53238e25	+	1.12392e25i	−0.625444	+	0.199003i
$377$	−2.10002e25			−0.362084
$378$	8.42445e25	+	1.16451e26i	1.41457	+	1.95535i
$379$	7.81947e25			1.27875			0.639375	−	0.768895i	$-0.279193\pi$
$379$	7.81947e25			1.27875			0.639375	+	0.768895i	$0.279193\pi$
$380$	−5.09416e25	−	1.67816e25i	−0.811403	−	0.267300i
$381$		−	5.65983e25i		−	0.878119i
$382$	−4.80549e25	−	6.64260e25i	−0.726281	−	1.00393i
$383$		−	5.58884e25i		−	0.822875i	−0.911438	−	0.411438i	$-0.865027\pi$
$383$		−	5.58884e25i		−	0.822875i	0.911438	−	0.411438i	$-0.134973\pi$
$384$	3.93279e25	−	1.15414e26i	0.564142	−	1.65556i
$385$	1.28705e26			1.79882
$386$	3.95363e24	−	2.86020e24i	0.0538422	−	0.0389514i
$387$	−1.65286e25			−0.219345
$388$	2.84463e25	−	8.63502e25i	0.367882	−	1.11672i
$389$			1.08837e26i			1.37176i	0.727714	+	0.685881i	$0.240583\pi$
$389$			1.08837e26i			1.37176i	−0.727714	+	0.685881i	$0.759417\pi$
$390$	−1.74541e26	+	1.26269e26i	−2.14413	+	1.55114i
$391$			5.49747e24i			0.0658257i
$392$	1.81127e25	+	5.69263e25i	0.211408	+	0.664434i
$393$	−2.44865e26			−2.78613
$394$	−2.15694e25	−	2.98153e25i	−0.239263	−	0.330732i
$395$	1.28006e26			1.38440
$396$	−7.89926e25	+	2.39786e26i	−0.832980	+	2.52856i
$397$		−	6.59942e25i		−	0.678579i	−0.940682	−	0.339290i	$-0.889813\pi$
$397$		−	6.59942e25i		−	0.678579i	0.940682	−	0.339290i	$-0.110187\pi$
$398$	−1.00087e25	−	1.38350e25i	−0.100357	−	0.138723i
$399$			1.86405e26i			1.82276i
$400$	1.18503e25	+	8.75811e24i	0.113013	+	0.0835239i
$401$	−1.61721e26			−1.50426			−0.752130	−	0.659015i	$-0.770973\pi$
$401$	−1.61721e26			−1.50426			−0.752130	+	0.659015i	$0.770973\pi$
$402$	2.56096e26	−	1.85269e26i	2.32350	−	1.68090i
$403$	−6.05233e24			−0.0535639
$404$	1.28320e26	+	4.22723e25i	1.10785	+	0.364958i
$405$		−	1.49733e26i		−	1.26115i
$406$	3.28278e25	−	2.37488e25i	0.269762	−	0.195156i
$407$		−	1.43172e26i		−	1.14792i
$408$	−5.37833e24	−	1.69035e25i	−0.0420771	−	0.132244i
$409$	−4.61427e25			−0.352266			−0.176133	−	0.984366i	$-0.556359\pi$
$409$	−4.61427e25			−0.352266			−0.176133	+	0.984366i	$0.556359\pi$
$410$	2.37111e25	+	3.27757e25i	0.176650	+	0.244182i
$411$	1.93446e26			1.40650
$412$	−1.78383e26	−	5.87645e25i	−1.26585	−	0.417007i
$413$		−	9.35191e25i		−	0.647739i
$414$	−1.48104e26	−	2.04723e26i	−1.00130	−	1.38408i
$415$			2.32707e26i			1.53578i
$416$	2.23936e24	−	2.19893e26i	0.0144275	−	1.41670i
$417$	4.31004e26			2.71095
$418$	−1.36451e26	+	9.87138e25i	−0.837944	+	0.606199i
$419$	−5.29625e24			−0.0317562			−0.0158781	−	0.999874i	$-0.505054\pi$
$419$	−5.29625e24			−0.0317562			−0.0158781	+	0.999874i	$0.505054\pi$
$420$	1.30049e26	−	3.94772e26i	0.761405	−	2.31129i
$421$			1.49367e26i			0.853954i	0.904262	+	0.426977i	$0.140422\pi$
$421$			1.49367e26i			0.853954i	−0.904262	+	0.426977i	$0.859578\pi$
$422$	4.82925e25	−	3.49365e25i	0.269622	−	0.195054i
$423$		−	2.47866e26i		−	1.35149i
$424$	−3.59813e25	+	1.14485e25i	−0.191610	+	0.0609661i
$425$	2.14373e24			0.0111501
$426$	−5.20393e25	−	7.19336e25i	−0.264384	−	0.365457i
$427$	−3.72921e26			−1.85071
$428$	−9.81368e25	+	2.97900e26i	−0.475767	+	1.44422i
$429$			6.76446e26i			3.20376i
$430$	1.44105e25	+	1.99195e25i	0.0666798	+	0.0921711i
$431$			5.76714e25i			0.260728i	0.991466	+	0.130364i	$0.0416146\pi$
$431$			5.76714e25i			0.260728i	−0.991466	+	0.130364i	$0.958385\pi$
$432$	3.37251e26	+	2.49250e26i	1.48976	+	1.10103i
$433$	3.62350e26			1.56405			0.782023	−	0.623250i	$-0.214188\pi$
$433$	3.62350e26			1.56405			0.782023	+	0.623250i	$0.214188\pi$
$434$	9.46109e24	−	6.84449e24i	0.0399065	−	0.0288698i
$435$	−1.15812e26			−0.477377
$436$	−3.18026e26	−	1.04767e26i	−1.28114	−	0.422046i
$437$		−	1.68558e26i		−	0.663644i
$438$	−2.84514e26	+	2.05827e26i	−1.09487	+	0.792067i
$439$			2.02029e26i			0.759921i	0.925003	+	0.379960i	$0.124062\pi$
$439$			2.02029e26i			0.759921i	−0.925003	+	0.379960i	$0.875938\pi$
$440$	3.57849e26	−	1.13860e26i	1.31575	−	0.418642i
$441$	−3.99451e26			−1.43575
$442$	−1.87516e25	−	2.59202e25i	−0.0658894	−	0.0910786i
$443$	−5.17324e26			−1.77716			−0.888578	−	0.458725i	$-0.848306\pi$
$443$	−5.17324e26			−1.77716			−0.888578	+	0.458725i	$0.848306\pi$
$444$	−4.39146e26	−	1.44668e26i	−1.47496	−	0.485894i
$445$			3.29056e26i			1.08061i
$446$	3.02754e26	+	4.18494e26i	0.972167	+	1.34382i
$447$		−	4.79138e26i		−	1.50448i
$448$	2.45173e26	+	3.46273e26i	0.752823	+	1.06326i
$449$	5.37552e26			1.61420			0.807099	−	0.590416i	$-0.201036\pi$
$449$	5.37552e26			1.61420			0.807099	+	0.590416i	$0.201036\pi$
$450$	−7.98312e25	+	5.77527e25i	−0.234448	+	0.169608i
$451$	1.27024e26			0.364856
$452$	−7.72378e25	+	2.34460e26i	−0.216993	+	0.658694i
$453$		−	6.77487e26i		−	1.86174i
$454$	3.36378e26	−	2.43348e26i	0.904210	−	0.654138i
$455$		−	7.49620e26i		−	1.97118i
$456$	1.64905e26	+	5.18279e26i	0.424214	+	1.33326i
$457$	−2.00836e26			−0.505452			−0.252726	−	0.967538i	$-0.581327\pi$
$457$	−2.00836e26			−0.505452			−0.252726	+	0.967538i	$0.581327\pi$
$458$	2.85151e26	+	3.94163e26i	0.702135	+	0.970556i
$459$	6.10091e25			0.146983
$460$	−1.17598e26	+	3.56975e26i	−0.277218	+	0.841510i
$461$		−	7.05245e26i		−	1.62679i	−0.581713	−	0.813394i	$-0.697617\pi$
$461$		−	7.05245e26i		−	1.62679i	0.581713	−	0.813394i	$-0.302383\pi$
$462$	−7.64983e26	−	1.05743e27i	−1.72676	−	2.38689i
$463$		−	3.98400e26i		−	0.880054i	−0.897984	−	0.440027i	$-0.854969\pi$
$463$		−	3.98400e26i		−	0.880054i	0.897984	−	0.440027i	$-0.145031\pi$
$464$	7.02645e25	−	9.50722e25i	0.151899	−	0.205529i
$465$	−3.33775e25			−0.0706193
$466$	5.18106e25	−	3.74816e25i	0.107290	−	0.0776174i
$467$	7.28398e25			0.147639			0.0738193	−	0.997272i	$-0.476481\pi$
$467$	7.28398e25			0.147639			0.0738193	+	0.997272i	$0.476481\pi$
$468$	1.39660e27	+	4.60080e26i	2.77085	+	0.912799i
$469$			1.09988e27i			2.13608i
$470$	−2.98717e26	+	2.16102e26i	−0.567912	+	0.410848i
$471$			1.27117e27i			2.36589i
$472$	−8.27324e25	−	2.60019e26i	−0.150749	−	0.473790i
$473$	7.71995e25			0.137722
$474$	−7.60833e26	−	1.05169e27i	−1.32894	−	1.83699i
$475$	−6.57288e25			−0.112414
$476$	5.86256e25	+	1.93130e25i	0.0981788	+	0.0323430i
$477$		−	2.52481e26i		−	0.414042i
$478$	2.63347e26	+	3.64023e26i	0.422912	+	0.584589i
$479$		−	4.91845e26i		−	0.773524i	−0.922180	−	0.386762i	$-0.873594\pi$
$479$		−	4.91845e26i		−	0.773524i	0.922180	−	0.386762i	$-0.126406\pi$
$480$	1.23496e25	−	1.21267e27i	0.0190214	−	1.86780i
$481$	−8.33881e26			−1.25792
$482$	−5.29680e26	+	3.83190e26i	−0.782607	+	0.566165i
$483$	1.30624e27			1.89039
$484$	1.48226e26	−	4.49948e26i	0.210122	−	0.637835i
$485$		−	9.04251e26i		−	1.25566i
$486$	−1.26852e26	+	9.17689e25i	−0.172557	+	0.124834i
$487$		−	5.17758e25i		−	0.0689982i	−0.999405	−	0.0344991i	$-0.989016\pi$
$487$		−	5.17758e25i		−	0.0689982i	0.999405	−	0.0344991i	$-0.0109836\pi$
$488$	−1.03686e27	+	3.29907e26i	−1.35370	+	0.430719i
$489$	1.11868e26			0.143092
$490$	3.48261e26	+	4.81399e26i	0.436460	+	0.603315i
$491$	−9.85626e26			−1.21031			−0.605156	−	0.796107i	$-0.706889\pi$
$491$	−9.85626e26			−1.21031			−0.605156	+	0.796107i	$0.706889\pi$
$492$	1.28352e26	−	3.89619e26i	0.154437	−	0.468801i
$493$		−	1.71987e25i		−	0.0202780i
$494$	5.74943e26	+	7.94740e26i	0.664286	+	0.918239i
$495$			2.51102e27i			2.84314i
$496$	2.02505e25	−	2.74002e25i	0.0224708	−	0.0304044i
$497$	3.08941e26			0.335979
$498$	1.91191e27	−	1.38314e27i	2.03786	−	1.47426i
$499$	−5.61943e26			−0.587066			−0.293533	−	0.955949i	$-0.594831\pi$
$499$	−5.61943e26			−0.587066			−0.293533	+	0.955949i	$0.594831\pi$
$500$	−8.51358e26	−	2.80462e26i	−0.871791	−	0.287193i
$501$			1.62844e27i			1.63453i
$502$	−3.35078e26	+	2.42407e26i	−0.329692	+	0.238511i
$503$		−	1.05876e27i		−	1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$503$		−	1.05876e27i		−	1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$504$	−2.70348e27	+	8.60188e26i	−2.55634	+	0.813370i
$505$	1.34375e27			1.24568
$506$	6.91740e26	+	9.56188e26i	0.628692	+	0.869036i
$507$	1.97704e27			1.76172
$508$	5.45782e26	+	1.79796e26i	0.476850	+	0.157088i
$509$		−	3.14483e26i		−	0.269414i	−0.990885	−	0.134707i	$-0.956991\pi$
$509$		−	3.14483e26i		−	0.269414i	0.990885	−	0.134707i	$-0.0430093\pi$
$510$	−1.03412e26	−	1.42945e26i	−0.0868696	−	0.120079i
$511$		−	1.22193e27i		−	1.00656i
$512$	9.88009e26	+	7.45878e26i	0.798107	+	0.602515i
$513$	−1.87060e27			−1.48186
$514$	−1.23773e27	+	8.95417e26i	−0.961600	+	0.695655i
$515$	−1.86801e27			−1.42333
$516$	7.80061e25	−	2.36792e26i	0.0582950	−	0.176958i
$517$			1.15770e27i			0.848573i
$518$	1.30354e27	−	9.43023e26i	0.937185	−	0.677992i
$519$			1.38383e27i			0.975907i
$520$	−6.63157e26	−	2.08423e27i	−0.458757	−	1.44183i
$521$	−4.30189e26			−0.291932			−0.145966	−	0.989290i	$-0.546629\pi$
$521$	−4.30189e26			−0.291932			−0.145966	+	0.989290i	$0.546629\pi$
$522$	4.63338e26	+	6.40469e26i	0.308455	+	0.426376i
$523$	1.17110e27			0.764851			0.382425	−	0.923986i	$-0.375089\pi$
$523$	1.17110e27			0.764851			0.382425	+	0.923986i	$0.375089\pi$
$524$	7.77864e26	−	2.36125e27i	0.498415	−	1.51297i
$525$		−	5.09366e26i		−	0.320211i
$526$	2.10264e26	+	2.90647e26i	0.129691	+	0.179270i
$527$		−	4.95672e24i		−	0.00299977i
$528$	−3.06241e27	−	2.26332e27i	−1.81855	−	1.34402i
$529$	5.34980e26			0.311732
$530$	−3.04278e26	+	2.20125e26i	−0.173985	+	0.125867i
$531$	1.82455e27			1.02379
$532$	−1.79752e27	−	5.92155e26i	−0.989822	−	0.326076i
$533$		−	7.39834e26i		−	0.399818i
$534$	2.70351e27	−	1.95582e27i	1.43389	−	1.03733i
$535$			3.11958e27i			1.62389i
$536$	9.73021e26	+	3.05810e27i	0.497135	+	1.56244i
$537$	−1.82071e27			−0.913055
$538$	−1.54237e27	−	2.13201e27i	−0.759218	−	1.04946i
$539$	1.86569e27			0.901473
$540$	3.96159e27	+	1.30506e27i	1.87902	+	0.619004i
$541$		−	1.72051e27i		−	0.801098i	−0.916275	−	0.400549i	$-0.868819\pi$
$541$		−	1.72051e27i		−	0.801098i	0.916275	−	0.400549i	$-0.131181\pi$
$542$	1.99045e27	+	2.75139e27i	0.909827	+	1.25765i
$543$		−	3.22904e27i		−	1.44902i
$544$	1.80087e26	+	1.83398e24i	0.0793403	+	0.000807989i
$545$	−3.33034e27			−1.44053
$546$	−6.15884e27	+	4.45552e27i	−2.61561	+	1.89222i
$547$	4.25552e26			0.177451			0.0887256	−	0.996056i	$-0.471721\pi$
$547$	4.25552e26			0.177451			0.0887256	+	0.996056i	$0.471721\pi$
$548$	−6.14521e26	+	1.86541e27i	−0.251612	+	0.763781i
$549$		−	7.27566e27i		−	2.92516i
$550$	3.72863e26	−	2.69742e26i	0.147205	−	0.106493i
$551$			5.27328e26i			0.204440i
$552$	3.63186e27	−	1.15558e27i	1.38273	−	0.439954i
$553$	4.51682e27			1.68881
$554$	−2.52804e27	−	3.49449e27i	−0.928294	−	1.28317i
$555$	−4.59870e27			−1.65846
$556$	−1.36918e27	+	4.15621e27i	−0.484966	+	1.47214i
$557$		−	4.34136e26i		−	0.151034i	−0.997145	−	0.0755168i	$-0.975939\pi$
$557$		−	4.34136e26i		−	0.151034i	0.997145	−	0.0755168i	$-0.0240606\pi$
$558$	1.33536e26	+	1.84585e26i	0.0456305	+	0.0630747i
$559$		−	4.49636e26i		−	0.150919i
$560$	3.39369e27	+	2.50815e27i	1.11890	+	0.826940i
$561$	−5.53994e26			−0.179422
$562$	3.67451e27	−	2.65827e27i	1.16906	−	0.845738i
$563$	2.52994e27			0.790726			0.395363	−	0.918525i	$-0.370619\pi$
$563$	2.52994e27			0.790726			0.395363	+	0.918525i	$0.370619\pi$
$564$	3.55097e27	+	1.16979e27i	1.09033	+	0.359185i
$565$			2.45524e27i			0.740643i
$566$	1.19763e27	−	8.66409e26i	0.354943	−	0.256778i
$567$		−	5.28347e27i		−	1.53847i
$568$	8.58975e26	−	2.73307e26i	0.245752	−	0.0781929i
$569$	−7.02287e26			−0.197420			−0.0987102	−	0.995116i	$-0.531472\pi$
$569$	−7.02287e26			−0.197420			−0.0987102	+	0.995116i	$0.531472\pi$
$570$	3.17070e27	+	4.38284e27i	0.875804	+	1.21062i
$571$	−5.41269e27			−1.46910			−0.734551	−	0.678554i	$-0.762607\pi$
$571$	−5.41269e27			−1.46910			−0.734551	+	0.678554i	$0.762607\pi$
$572$	−6.52302e27	−	2.14887e27i	−1.73976	−	0.573126i
$573$			8.26897e27i			2.16723i
$574$	8.36668e26	+	1.15652e27i	0.215493	+	0.297875i
$575$			4.60597e26i			0.116585i
$576$	−6.75576e27	+	4.78331e27i	−1.68054	+	1.18988i
$577$	−6.96493e27			−1.70278			−0.851390	−	0.524533i	$-0.824240\pi$
$577$	−6.96493e27			−1.70278			−0.851390	+	0.524533i	$0.824240\pi$
$578$	−3.35069e27	+	2.42401e27i	−0.805112	+	0.582446i
$579$	−4.92163e26			−0.116231
$580$	3.67901e26	−	1.11678e27i	0.0853987	−	0.259233i
$581$			8.21127e27i			1.87348i
$582$	−7.42928e27	+	5.37460e27i	−1.66616	+	1.20536i
$583$			1.17925e27i			0.259968i
$584$	−1.08099e27	−	3.39744e27i	−0.234258	−	0.736247i
$585$	1.46250e28			3.11558
$586$	−5.34237e27	−	7.38472e27i	−1.11881	−	1.54653i
$587$	1.18193e27			0.243339			0.121670	−	0.992571i	$-0.461175\pi$
$587$	1.18193e27			0.243339			0.121670	+	0.992571i	$0.461175\pi$
$588$	1.88519e27	−	5.72259e27i	0.381576	−	1.15830i
$589$			1.51978e26i			0.0302432i
$590$	−1.59074e27	−	2.19886e27i	−0.311227	−	0.430208i
$591$			3.71152e27i			0.713965i
$592$	2.79008e27	−	3.77515e27i	0.527715	−	0.714032i
$593$	7.11802e27			1.32377			0.661885	−	0.749605i	$-0.269757\pi$
$593$	7.11802e27			1.32377			0.661885	+	0.749605i	$0.269757\pi$
$594$	1.06114e28	−	7.67670e27i	1.94048	−	1.40381i
$595$	6.13922e26			0.110393
$596$	4.62037e27	+	1.52208e27i	0.816984	+	0.269138i
$597$			1.72223e27i			0.299466i
$598$	5.56917e27	−	4.02893e27i	0.952310	−	0.688935i
$599$		−	6.82077e27i		−	1.14701i	−0.819204	−	0.573503i	$-0.805584\pi$
$599$		−	6.82077e27i		−	1.14701i	0.819204	−	0.573503i	$-0.194416\pi$
$600$	−4.50614e26	−	1.41623e27i	−0.0745233	−	0.234219i
$601$	9.85205e27			1.60244			0.801220	−	0.598370i	$-0.204185\pi$
$601$	9.85205e27			1.60244			0.801220	+	0.598370i	$0.204185\pi$
$602$	5.08487e26	+	7.02878e26i	0.0813420	+	0.112439i
$603$	−2.14587e28			−3.37621
$604$	6.53306e27	+	2.15218e27i	1.01099	+	0.333050i
$605$		−	4.71181e27i		−	0.717190i
$606$	−7.98688e27	−	1.10402e28i	−1.19578	−	1.65292i
$607$		−	5.11586e25i		−	0.00753411i	−0.999993	−	0.00376706i	$-0.998801\pi$
$607$		−	5.11586e25i		−	0.00753411i	0.999993	−	0.00376706i	$-0.00119909\pi$
$608$	−5.52166e27	−	5.62317e25i	−0.799896	−	0.00814601i
$609$	−4.08653e27			−0.582347
$610$	−8.76828e27	+	6.34328e27i	−1.22918	+	0.889233i
$611$	6.74282e27			0.929886
$612$	−3.76795e26	+	1.14378e27i	−0.0511200	+	0.155178i
$613$		−	1.04122e28i		−	1.38976i	−0.719126	−	0.694880i	$-0.755458\pi$
$613$		−	1.04122e28i		−	1.38976i	0.719126	−	0.694880i	$-0.244542\pi$
$614$	6.89221e26	−	4.98607e26i	0.0905055	−	0.0654749i
$615$		−	4.08005e27i		−	0.527126i
$616$	1.26270e28	−	4.01764e27i	1.60507	−	0.510697i
$617$	−8.77445e27			−1.09741			−0.548704	−	0.836017i	$-0.684879\pi$
$617$	−8.77445e27			−1.09741			−0.548704	+	0.836017i	$0.684879\pi$
$618$	1.11029e28	+	1.53475e28i	1.36632	+	1.88865i
$619$	8.64119e27			1.04633			0.523163	−	0.852233i	$-0.324752\pi$
$619$	8.64119e27			1.04633			0.523163	+	0.852233i	$0.324752\pi$
$620$	1.06030e26	−	3.21861e26i	0.0126332	−	0.0383488i
$621$			1.31083e28i			1.53684i
$622$	−6.07003e27	−	8.39056e27i	−0.700304	−	0.968026i
$623$			1.16110e28i			1.31823i
$624$	−1.31824e28	+	1.78366e28i	−1.47281	+	1.99281i
$625$	−1.01934e28			−1.12078
$626$	5.19115e27	−	3.75546e27i	0.561720	−	0.406368i
$627$	1.69860e28			1.80890
$628$	−1.22580e28	−	4.03814e27i	−1.28476	−	0.423238i
$629$		−	6.82929e26i		−	0.0704481i
$630$	−2.28621e28	+	1.65393e28i	−2.32119	+	1.67923i
$631$			2.44535e27i			0.244369i	0.992507	+	0.122185i	$0.0389900\pi$
$631$			2.44535e27i			0.244369i	−0.992507	+	0.122185i	$0.961010\pi$
$632$	1.25585e28	−	3.99584e27i	1.23529	−	0.393040i
$633$	−6.01163e27			−0.582044
$634$	−3.81980e27	−	5.28008e27i	−0.364039	−	0.503209i
$635$	5.71537e27			0.536176
$636$	3.61707e27	+	1.19157e27i	0.334031	+	0.110039i
$637$		−	1.08664e28i		−	0.987855i
$638$	−2.16409e27	−	2.99140e27i	−0.193672	−	0.267712i
$639$			6.02742e27i			0.531035i
$640$	1.16546e28	+	3.97139e27i	1.01088	+	0.344463i
$641$	−5.88668e27			−0.502678			−0.251339	−	0.967899i	$-0.580871\pi$
$641$	−5.88668e27			−0.502678			−0.251339	+	0.967899i	$0.580871\pi$
$642$	2.56303e28	−	1.85418e28i	2.15478	−	1.55884i
$643$	−6.70815e27			−0.555256			−0.277628	−	0.960689i	$-0.589548\pi$
$643$	−6.70815e27			−0.555256			−0.277628	+	0.960689i	$0.589548\pi$
$644$	−4.14955e27	+	1.25962e28i	−0.338175	+	1.02655i
$645$		−	2.47966e27i		−	0.198973i
$646$	−6.50874e26	+	4.70865e26i	−0.0514247	+	0.0372024i
$647$			4.12884e27i			0.321207i	0.987019	+	0.160604i	$0.0513441\pi$
$647$			4.12884e27i			0.321207i	−0.987019	+	0.160604i	$0.948656\pi$
$648$	−4.67406e27	−	1.46901e28i	−0.358050	−	1.12532i
$649$	−8.52184e27			−0.642816
$650$	−1.57107e27	−	2.17168e27i	−0.116698	−	0.161311i
$651$	−1.17775e27			−0.0861478
$652$	−3.55371e26	+	1.07875e27i	−0.0255980	+	0.0777042i
$653$			9.05389e27i			0.642249i	0.947037	+	0.321124i	$0.104061\pi$
$653$			9.05389e27i			0.642249i	−0.947037	+	0.321124i	$0.895939\pi$
$654$	1.97946e28	+	2.73619e28i	1.38283	+	1.91147i
$655$		−	2.47268e28i		−	1.70120i
$656$	3.34939e27	+	2.47541e27i	0.226948	+	0.167729i
$657$	2.38398e28			1.59092
$658$	−1.05405e28	+	7.62536e27i	−0.692790	+	0.501189i
$659$	−9.80711e27			−0.634873			−0.317436	−	0.948280i	$-0.602822\pi$
$659$	−9.80711e27			−0.634873			−0.317436	+	0.948280i	$0.602822\pi$
$660$	−3.59732e28	−	1.18506e28i	−2.29372	−	0.755618i
$661$			4.81270e27i			0.302256i	0.988514	+	0.151128i	$0.0482905\pi$
$661$			4.81270e27i			0.302256i	−0.988514	+	0.151128i	$0.951709\pi$
$662$	1.00861e28	−	7.29662e27i	0.623939	−	0.451379i
$663$			3.22665e27i			0.196615i
$664$	7.26416e27	+	2.28305e28i	0.436018	+	1.37036i
$665$	−1.88235e28			−1.11297
$666$	1.83983e28	+	2.54319e28i	1.07161	+	1.48128i
$667$	3.69527e27			0.212025
$668$	−1.57031e28	−	5.17307e27i	−0.887609	−	0.292404i
$669$		−	5.20958e28i		−	2.90096i
$670$	1.87087e28	+	2.58610e28i	1.02635	+	1.41872i
$671$			3.39820e28i			1.83664i
$672$	4.35768e26	−	4.27901e28i	0.0232040	−	2.27851i
$673$	2.49736e28			1.31018			0.655089	−	0.755551i	$-0.272631\pi$
$673$	2.49736e28			1.31018			0.655089	+	0.755551i	$0.272631\pi$
$674$	−2.74610e28	+	1.98663e28i	−1.41944	+	1.02688i
$675$	5.11154e27			0.260324
$676$	−6.28049e27	+	1.90648e28i	−0.315157	+	0.956675i
$677$		−	3.55953e28i		−	1.75997i	−0.475000	−	0.879986i	$-0.657552\pi$
$677$		−	3.55953e28i		−	1.75997i	0.475000	−	0.879986i	$-0.342448\pi$
$678$	2.01721e28	−	1.45932e28i	0.982776	−	0.710975i
$679$		−	3.19073e28i		−	1.53177i
$680$	1.70694e27	−	5.43111e26i	0.0807475	−	0.0256921i
$681$	−4.18737e28			−1.95196
$682$	−6.23697e26	−	8.62133e26i	−0.0286504	−	0.0396032i
$683$	−1.29451e28			−0.586003			−0.293002	−	0.956112i	$-0.594654\pi$
$683$	−1.29451e28			−0.586003			−0.293002	+	0.956112i	$0.594654\pi$
$684$	1.15529e28	−	3.50695e28i	0.515384	−	1.56447i
$685$			1.95344e28i			0.858805i
$686$	−5.33566e27	−	7.37546e27i	−0.231178	−	0.319557i
$687$		−	4.90669e28i		−	2.09518i
$688$	2.03560e27	+	1.50444e27i	0.0856658	+	0.0633125i
$689$	6.86834e27			0.284879
$690$	3.07129e28	−	2.22188e28i	1.25554	−	0.908301i
$691$	3.30931e28			1.33339			0.666694	−	0.745331i	$-0.267709\pi$
$691$	3.30931e28			1.33339			0.666694	+	0.745331i	$0.267709\pi$
$692$	−1.33444e28	−	4.39602e27i	−0.529952	−	0.174582i
$693$			8.86036e28i			3.46832i
$694$	−1.07197e28	+	7.75503e27i	−0.413608	+	0.299219i
$695$			4.35234e28i			1.65529i
$696$	−1.13621e28	+	3.61518e27i	−0.425959	+	0.135531i
$697$	6.05907e26			0.0223912
$698$	−9.13275e27	−	1.26241e28i	−0.332696	−	0.459883i
$699$	−6.44958e27			−0.231611
$700$	4.91185e27	+	1.61811e27i	0.173886	+	0.0572831i
$701$			1.27653e27i			0.0445502i	0.999752	+	0.0222751i	$0.00709098\pi$
$701$			1.27653e27i			0.0445502i	−0.999752	+	0.0222751i	$0.992909\pi$
$702$	−4.47117e28	−	6.18047e28i	−1.53833	−	2.12643i
$703$			2.09393e28i			0.710246i
$704$	3.15538e28	−	2.23412e28i	1.05518	−	0.747101i
$705$	3.71854e28			1.22597
$706$	9.55634e26	−	6.91339e26i	0.0310631	−	0.0224721i
$707$	4.74156e28			1.51959
$708$	−8.61088e27	+	2.61388e28i	−0.272092	+	0.825949i
$709$			5.44035e27i			0.169498i	0.996402	+	0.0847490i	$0.0270089\pi$
$709$			5.44035e27i			0.169498i	−0.996402	+	0.0847490i	$0.972991\pi$
$710$	7.26396e27	−	5.25500e27i	0.223146	−	0.161432i
$711$			8.81229e28i			2.66927i
$712$	1.02718e28	+	3.22832e28i	0.306794	+	0.964222i
$713$	1.06499e27			0.0313653
$714$	−3.64897e27	−	5.04395e27i	−0.105971	−	0.146483i
$715$	−6.83084e28			−1.95620
$716$	5.78385e27	−	1.75572e28i	0.163338	−	0.495821i
$717$		−	4.53150e28i		−	1.26198i
$718$	−9.75461e27	−	1.34837e28i	−0.267895	−	0.370310i
$719$		−	2.02337e27i		−	0.0548008i	−0.999625	−	0.0274004i	$-0.991277\pi$
$719$		−	2.02337e27i		−	0.0548008i	0.999625	−	0.0274004i	$-0.00872291\pi$
$720$	−4.89339e28	+	6.62107e28i	−1.30703	+	1.76849i
$721$	−6.59143e28			−1.73631
$722$	−1.12304e28	+	8.12445e27i	−0.291758	+	0.211068i
$723$	6.59367e28			1.68944
$724$	3.11379e28	+	1.02577e28i	0.786872	+	0.259218i
$725$		−	1.44096e27i		−	0.0359147i
$726$	−3.87120e28	+	2.80056e28i	−0.951655	+	0.688461i
$727$		−	9.01083e26i		−	0.0218485i	−0.999940	−	0.0109242i	$-0.996523\pi$
$727$		−	9.01083e26i		−	0.0218485i	0.999940	−	0.0109242i	$-0.00347736\pi$
$728$	−2.34001e28	−	7.35441e28i	−0.559634	−	1.75887i
$729$	−3.42689e28			−0.808398
$730$	−2.07847e28	−	2.87306e28i	−0.483633	−	0.668523i
$731$	3.68242e26			0.00845200
$732$	1.04232e29	+	3.43371e28i	2.35989	+	0.777415i
$733$			6.55566e28i			1.46412i	0.681240	+	0.732060i	$0.261441\pi$
$733$			6.55566e28i			1.46412i	−0.681240	+	0.732060i	$0.738559\pi$
$734$	1.11742e28	+	1.54461e28i	0.246182	+	0.340296i
$735$		−	5.99264e28i		−	1.30240i
$736$	−3.94045e26	+	3.86932e28i	−0.00844827	+	0.829576i
$737$	1.00226e29			2.11985
$738$	−2.25636e28	+	1.63233e28i	−0.470810	+	0.340601i
$739$	−6.04226e28			−1.24381			−0.621907	−	0.783091i	$-0.713642\pi$
$739$	−6.04226e28			−1.24381			−0.621907	+	0.783091i	$0.713642\pi$
$740$	1.46087e28	−	4.43456e28i	0.296685	−	0.900602i
$741$		−	9.89323e28i		−	1.98224i
$742$	−1.07367e28	+	7.76731e27i	−0.212242	+	0.153544i
$743$		−	9.90525e28i		−	1.93187i	−0.258790	−	0.965934i	$-0.583324\pi$
$743$		−	9.90525e28i		−	1.93187i	0.258790	−	0.965934i	$-0.416676\pi$
$744$	−3.27461e27	+	1.04191e27i	−0.0630130	+	0.0200493i
$745$	4.83840e28			0.918627
$746$	−5.10694e27	−	7.05928e27i	−0.0956692	−	0.132243i
$747$	−1.60201e29			−2.96115
$748$	1.75988e27	−	5.34220e27i	0.0320971	−	0.0974326i
$749$			1.10077e29i			1.98097i
$750$	5.29902e28	+	7.32480e28i	0.940985	+	1.30072i
$751$		−	4.87745e27i		−	0.0854661i	−0.999087	−	0.0427330i	$-0.986394\pi$
$751$		−	4.87745e27i		−	0.0854661i	0.999087	−	0.0427330i	$-0.0136065\pi$
$752$	−2.25608e28	+	3.05262e28i	−0.390100	+	0.527830i
$753$	4.17118e28			0.711720
$754$	−1.74230e28	+	1.26044e28i	−0.293365	+	0.212231i
$755$	6.84136e28			1.13677
$756$	1.39788e29	+	4.60503e28i	2.29220	+	0.755117i
$757$		−	3.69662e28i		−	0.598199i	−0.954222	−	0.299099i	$-0.903314\pi$
$757$		−	3.69662e28i		−	0.598199i	0.954222	−	0.299099i	$-0.0966862\pi$
$758$	6.48748e28	−	4.69328e28i	1.03606	−	0.749521i
$759$		−	1.19030e29i		−	1.87602i
$760$	−5.23365e28	+	1.66523e28i	−0.814083	+	0.259023i
$761$	1.38381e28			0.212437			0.106219	−	0.994343i	$-0.466126\pi$
$761$	1.38381e28			0.212437			0.106219	+	0.994343i	$0.466126\pi$
$762$	−3.39705e28	−	4.69572e28i	−0.514698	−	0.711463i
$763$	−1.17514e29			−1.75729
$764$	−7.97383e28	−	2.62681e28i	−1.17688	−	0.387700i
$765$			1.19776e28i			0.174484i
$766$	−3.35444e28	−	4.63682e28i	−0.482317	−	0.666704i
$767$			4.96341e28i			0.704412i
$768$	−3.66430e28	−	1.19359e29i	−0.513309	−	1.67202i
$769$	1.30708e29			1.80733			0.903665	−	0.428240i	$-0.140866\pi$
$769$	1.30708e29			1.80733			0.903665	+	0.428240i	$0.140866\pi$
$770$	1.06781e29	−	7.72490e28i	1.45742	−	1.05435i
$771$	1.54077e29			2.07584
$772$	1.56346e27	−	4.74597e27i	0.0207928	−	0.0631178i
$773$			2.16151e28i			0.283767i	0.989883	+	0.141883i	$0.0453158\pi$
$773$			2.16151e28i			0.283767i	−0.989883	+	0.141883i	$0.954684\pi$
$774$	−1.37131e28	+	9.92055e27i	−0.177716	+	0.128566i
$775$		−	4.15290e26i		−	0.00531294i
$776$	−2.82270e28	−	8.87147e28i	−0.356491	−	1.12041i
$777$	−1.62269e29			−2.02314
$778$	6.53241e28	+	9.02971e28i	0.804039	+	1.11142i
$779$	−1.85777e28			−0.225745
$780$	−6.90222e28	+	2.09521e29i	−0.828023	+	2.51351i
$781$		−	2.81519e28i		−	0.333425i
$782$	3.29960e27	+	4.56102e27i	0.0385828	+	0.0533328i
$783$		−	4.10088e28i		−	0.473434i
$784$	4.91947e28	+	3.63580e28i	0.560735	+	0.414419i
$785$	−1.28364e29			−1.44460
$786$	−2.03154e29	+	1.46969e29i	−2.25735	+	1.63305i
$787$	−5.25629e28			−0.576676			−0.288338	−	0.957529i	$-0.593103\pi$
$787$	−5.25629e28			−0.576676			−0.288338	+	0.957529i	$0.593103\pi$
$788$	−3.57904e28	−	1.17904e28i	−0.387708	−	0.127722i
$789$		−	3.61809e28i		−	0.386998i
$790$	1.06201e29	−	7.68299e28i	1.12166	−	0.811445i
$791$			8.66353e28i			0.903504i
$792$	7.83838e28	+	2.46352e29i	0.807188	+	2.53691i
$793$	1.97923e29			2.01263
$794$	−3.96099e28	−	5.47526e28i	−0.397740	−	0.549793i
$795$	3.78776e28			0.375588
$796$	−1.66076e28	−	5.47103e27i	−0.162621	−	0.0535720i
$797$			2.65924e28i			0.257143i	0.991700	+	0.128572i	$0.0410392\pi$
$797$			2.65924e28i			0.257143i	−0.991700	+	0.128572i	$0.958961\pi$
$798$	1.11881e29	+	1.54653e29i	1.06838	+	1.47682i
$799$			5.52222e27i			0.0520770i
$800$	1.50883e28	+	1.53657e26i	0.140521	+	0.00143104i
$801$	−2.26531e29			−2.08354
$802$	−1.34173e29	+	9.70655e28i	−1.21877	+	0.881701i
$803$	−1.11347e29			−0.998906
$804$	1.01273e29	−	3.07420e29i	0.897292	−	2.72378i
$805$			1.31906e29i			1.15427i
$806$	−5.02136e27	+	3.63263e27i	−0.0433981	+	0.0313957i
$807$			2.65401e29i			2.26552i
$808$	1.31834e29	−	4.19466e28i	1.11151	−	0.353657i
$809$	−6.06389e28			−0.504971			−0.252486	−	0.967601i	$-0.581248\pi$
$809$	−6.06389e28			−0.504971			−0.252486	+	0.967601i	$0.581248\pi$
$810$	−8.98704e28	−	1.24227e29i	−0.739207	−	1.02180i
$811$	9.14665e28			0.743111			0.371555	−	0.928411i	$-0.378825\pi$
$811$	9.14665e28			0.743111			0.371555	+	0.928411i	$0.378825\pi$
$812$	1.29817e28	−	3.94067e28i	0.104177	−	0.316235i
$813$		−	3.42504e29i		−	2.71494i
$814$	−8.59321e28	−	1.18783e29i	−0.672839	−	0.930061i
$815$			1.12966e28i			0.0873715i
$816$	−1.46077e28	−	1.07960e28i	−0.111604	−	0.0824827i
$817$	−1.12907e28			−0.0852116
$818$	−3.82827e28	+	2.76950e28i	−0.285410	+	0.206476i
$819$	5.16058e29			3.80066
$820$	3.93442e28	+	1.29611e28i	0.286248	+	0.0942984i
$821$		−	6.45589e27i		−	0.0464007i	−0.999731	−	0.0232003i	$-0.992614\pi$
$821$		−	6.45589e27i		−	0.0464007i	0.999731	−	0.0232003i	$-0.00738556\pi$
$822$	1.60494e29	−	1.16107e29i	1.13957	−	0.824403i
$823$		−	2.13797e29i		−	1.49969i	−0.661611	−	0.749847i	$-0.730127\pi$
$823$		−	2.13797e29i		−	1.49969i	0.661611	−	0.749847i	$-0.269873\pi$
$824$	−1.83267e29	+	5.83116e28i	−1.27003	+	0.404095i
$825$	−4.64154e28			−0.317777
$826$	−5.61305e28	−	7.75889e28i	−0.379663	−	0.524806i
$827$	1.80939e29			1.20914			0.604570	−	0.796552i	$-0.293345\pi$
$827$	1.80939e29			1.20914			0.604570	+	0.796552i	$0.293345\pi$
$828$	−2.45751e29	−	8.09574e28i	−1.62252	−	0.534507i
$829$			5.97895e28i			0.390014i	0.980802	+	0.195007i	$0.0624729\pi$
$829$			5.97895e28i			0.390014i	−0.980802	+	0.195007i	$0.937527\pi$
$830$	1.39672e29	+	1.93067e29i	0.900175	+	1.24431i
$831$			4.35007e29i			2.77004i
$832$	−1.30123e29	−	1.83780e29i	−0.818690	−	1.15629i
$833$	8.89937e27			0.0553234
$834$	3.57586e29	−	2.58690e29i	2.19644	−	1.58898i
$835$	−1.64442e29			−0.998038
$836$	−5.39596e28	+	1.63797e29i	−0.323598	+	0.982299i
$837$		−	1.18189e28i		−	0.0700361i
$838$	−4.39407e27	+	3.17883e27i	−0.0257293	+	0.0186135i
$839$			2.02650e29i			1.17254i	0.810116	+	0.586270i	$0.199404\pi$
$839$			2.02650e29i			1.17254i	−0.810116	+	0.586270i	$0.800596\pi$
$840$	−1.29047e29	−	4.05582e29i	−0.737829	−	2.31892i
$841$	1.65434e29			0.934684
$842$	8.96508e28	+	1.23924e29i	0.500534	+	0.691884i
$843$	−4.57417e29			−2.52369
$844$	1.90972e28	−	5.79706e28i	0.104123	−	0.316070i
$845$			1.99644e29i			1.07570i
$846$	−1.48770e29	−	2.05644e29i	−0.792160	−	1.09500i
$847$		−	1.66260e29i		−	0.874893i
$848$	−2.29808e28	+	3.10944e28i	−0.119511	+	0.161705i
$849$	−1.49086e29			−0.766230
$850$	1.77856e27	−	1.28667e27i	0.00903398	−	0.00653550i
$851$	1.46733e29			0.736599
$852$	−8.63497e28	−	2.84461e28i	−0.428415	−	0.141132i
$853$			2.56218e29i			1.25637i	0.778063	+	0.628187i	$0.216203\pi$
$853$			2.56218e29i			1.25637i	−0.778063	+	0.628187i	$0.783797\pi$
$854$	−3.09397e29	+	2.23828e29i	−1.49947	+	1.08477i
$855$		−	3.67244e29i		−	1.75911i
$856$	9.73805e28	+	3.06057e29i	0.461035	+	1.44899i
$857$	−3.98633e27			−0.0186537			−0.00932685	−	0.999957i	$-0.502969\pi$
$857$	−3.98633e27			−0.0186537			−0.00932685	+	0.999957i	$0.502969\pi$
$858$	4.06005e29	+	5.61219e29i	1.87784	+	2.59573i
$859$	−1.87586e29			−0.857568			−0.428784	−	0.903407i	$-0.641058\pi$
$859$	−1.87586e29			−0.857568			−0.428784	+	0.903407i	$0.641058\pi$
$860$	2.39116e28	+	7.87716e27i	0.108050	+	0.0355947i
$861$		−	1.43968e29i		−	0.643035i
$862$	3.46146e28	+	4.78475e28i	0.152822	+	0.211245i
$863$		−	4.00633e29i		−	1.74839i	−0.485572	−	0.874197i	$-0.661389\pi$
$863$		−	4.00633e29i		−	1.74839i	0.485572	−	0.874197i	$-0.338611\pi$
$864$	4.29404e29	+	4.37298e27i	1.85237	+	0.0188643i
$865$	−1.39741e29			−0.595885
$866$	3.00626e29	−	2.17484e29i	1.26721	−	0.916744i
$867$	4.17107e29			1.73803
$868$	3.74138e27	−	1.13572e28i	0.0154111	−	0.0467813i
$869$		−	4.11591e29i		−	1.67598i
$870$	−9.60844e28	+	6.95108e28i	−0.386777	+	0.279808i
$871$		−	5.83750e29i		−	2.32298i
$872$	−3.26734e29	+	1.03960e29i	−1.28538	+	0.408978i
$873$	6.22509e29			2.42105
$874$	−1.01169e29	−	1.39845e29i	−0.388986	−	0.537692i
$875$	−3.14586e29			−1.19580
$876$	−1.12511e29	+	3.41533e29i	−0.422818	+	1.28349i
$877$		−	2.28056e29i		−	0.847317i	−0.905822	−	0.423659i	$-0.860746\pi$
$877$		−	2.28056e29i		−	0.847317i	0.905822	−	0.423659i	$-0.139254\pi$
$878$	1.21258e29	+	1.67615e29i	0.445417	+	0.615697i
$879$			9.19279e29i			3.33855i
$880$	2.28553e29	−	3.09247e29i	0.820654	−	1.11040i
$881$	−4.46767e29			−1.58607			−0.793034	−	0.609178i	$-0.791500\pi$
$881$	−4.46767e29			−1.58607			−0.793034	+	0.609178i	$0.791500\pi$
$882$	−3.31407e29	+	2.39752e29i	−1.16326	+	0.841543i
$883$	1.24718e29			0.432835			0.216418	−	0.976301i	$-0.430563\pi$
$883$	1.24718e29			0.432835			0.216418	+	0.976301i	$0.430563\pi$
$884$	−3.11148e28	−	1.02501e28i	−0.106769	−	0.0351728i
$885$			2.73723e29i			0.928707i
$886$	−4.29202e29	+	3.10500e29i	−1.43987	+	1.04166i
$887$			4.57913e29i			1.51896i	0.650530	+	0.759481i	$0.274547\pi$
$887$			4.57913e29i			1.51896i	−0.650530	+	0.759481i	$0.725453\pi$
$888$	−4.51171e29	+	1.43553e29i	−1.47983	+	0.470849i
$889$	2.01672e29			0.654076
$890$	1.97501e29	+	2.73004e29i	0.633387	+	0.875526i
$891$	−4.81451e29			−1.52677
$892$	5.02364e29	+	1.65493e29i	1.57532	+	0.518957i
$893$		−	1.69317e29i		−	0.525031i
$894$	−2.87581e29	−	3.97521e29i	−0.881829	−	1.21895i
$895$		−	1.83857e29i		−	0.557507i
$896$	4.11244e29	+	1.40134e29i	1.23316	+	0.420207i
$897$	−6.93271e29			−2.05579
$898$	4.45984e29	−	3.22640e29i	1.30784	−	0.946140i
$899$	−3.33179e27			−0.00966229
$900$	−3.15692e28	+	9.58299e28i	−0.0905395	+	0.274837i
$901$			5.62502e27i			0.0159542i
$902$	1.05387e29	−	7.62405e28i	0.295611	−	0.213856i
$903$		−	8.74970e28i		−	0.242726i
$904$	7.66425e28	+	2.40880e29i	0.210274	+	0.660869i
$905$	3.26073e29			0.884768
$906$	−4.06630e29	−	5.62082e29i	−1.09123	−	1.50841i
$907$	−3.26703e29			−0.867121			−0.433561	−	0.901124i	$-0.642743\pi$
$907$	−3.26703e29			−0.867121			−0.433561	+	0.901124i	$0.642743\pi$
$908$	1.33021e29	−	4.03791e29i	0.349189	−	1.05998i
$909$			9.25075e29i			2.40181i
$910$	−4.49925e29	−	6.21928e29i	−1.15538	−	1.59708i
$911$		−	6.33913e29i		−	1.61007i	−0.593225	−	0.805037i	$-0.702145\pi$
$911$		−	6.33913e29i		−	1.61007i	0.593225	−	0.805037i	$-0.297855\pi$
$912$	4.47887e29	+	3.31017e29i	1.12518	+	0.831577i
$913$	7.48244e29			1.85924
$914$	−1.66625e29	+	1.20543e29i	−0.409524	+	0.296264i
$915$	1.09151e30			2.65348
$916$	4.73156e29	+	1.55871e29i	1.13776	+	0.374810i
$917$		−	8.72506e29i		−	2.07527i
$918$	5.06166e28	−	3.66179e28i	0.119088	−	0.0861522i
$919$			6.74333e29i			1.56935i	0.619909	+	0.784674i	$0.287170\pi$
$919$			6.74333e29i			1.56935i	−0.619909	+	0.784674i	$0.712830\pi$
$920$	1.16692e29	+	3.66750e29i	0.268634	+	0.844290i
$921$	−8.57969e28			−0.195378
$922$	−4.23291e29	−	5.85112e29i	−0.953519	−	1.31804i
$923$	−1.63967e29			−0.365375
$924$	−1.26935e30	−	4.18160e29i	−2.79808	−	0.921771i
$925$		−	5.72181e28i		−	0.124772i
$926$	−2.39121e29	−	3.30536e29i	−0.515832	−	0.713031i
$927$		−	1.28599e30i		−	2.74434i
$928$	1.23276e27	−	1.21050e29i	0.00260254	−	0.255556i
$929$	−1.89758e29			−0.396317			−0.198159	−	0.980170i	$-0.563496\pi$
$929$	−1.89758e29			−0.396317			−0.198159	+	0.980170i	$0.563496\pi$
$930$	−2.76919e28	+	2.00333e28i	−0.0572167	+	0.0413926i
$931$	−2.72863e29			−0.557762
$932$	2.04884e28	−	6.21938e28i	0.0414333	−	0.125773i
$933$			1.04449e30i			2.08972i
$934$	6.04321e28	−	4.37187e28i	0.119619	−	0.0865364i
$935$		−	5.59430e28i		−	0.109554i
$936$	1.43484e30	−	4.56535e29i	2.78000	−	0.884535i
$937$	−4.06862e29			−0.779921			−0.389961	−	0.920832i	$-0.627511\pi$
$937$	−4.06862e29			−0.779921			−0.389961	+	0.920832i	$0.627511\pi$
$938$	6.60154e29	+	9.12527e29i	1.25204	+	1.73068i
$939$	−6.46214e29			−1.21261
$940$	−1.18127e29	+	3.58582e29i	−0.219317	+	0.665748i
$941$		−	4.79905e29i		−	0.881575i	−0.897611	−	0.440788i	$-0.854699\pi$
$941$		−	4.79905e29i		−	0.881575i	0.897611	−	0.440788i	$-0.145301\pi$
$942$	7.62961e29	+	1.05464e30i	1.38673	+	1.91687i
$943$			1.30184e29i			0.234121i
$944$	−2.24704e29	−	1.66071e29i	−0.399845	−	0.295511i
$945$	1.46385e30			2.57738
$946$	6.40491e28	−	4.63354e28i	0.111584	−	0.0807238i
$947$	7.45383e29			1.28493			0.642466	−	0.766315i	$-0.277912\pi$
$947$	7.45383e29			1.28493			0.642466	+	0.766315i	$0.277912\pi$
$948$	−1.26246e30	−	4.15891e29i	−2.15345	−	0.709409i
$949$			6.48525e29i			1.09462i
$950$	−5.45324e28	+	3.94507e28i	−0.0910790	+	0.0658898i
$951$			6.57285e29i			1.08630i
$952$	6.02309e28	−	1.91641e28i	0.0985031	−	0.0313415i
$953$	−3.45171e29			−0.558605			−0.279303	−	0.960203i	$-0.590103\pi$
$953$	−3.45171e29			−0.558605			−0.279303	+	0.960203i	$0.590103\pi$
$954$	−1.51540e29	−	2.09472e29i	−0.242685	−	0.335462i
$955$	−8.35012e29			−1.32330
$956$	4.36976e29	+	1.43953e29i	0.685297	+	0.225757i
$957$			3.72381e29i			0.577921i
$958$	−2.95207e29	−	4.08063e29i	−0.453390	−	0.626718i
$959$			6.89289e29i			1.04765i
$960$	−7.17602e29	−	1.01351e30i	−1.07937	−	1.52446i
$961$	6.70830e29			0.998571
$962$	−6.91835e29	+	5.00498e29i	−1.01918	+	0.737313i
$963$	−2.14760e30			−3.13105
$964$	−2.09462e29	+	6.35832e29i	−0.302228	+	0.917428i
$965$		−	4.96993e28i		−	0.0709704i
$966$	1.08373e30	−	7.84010e29i	1.53162	−	1.10803i
$967$			1.21661e29i			0.170171i	0.996374	+	0.0850855i	$0.0271163\pi$
$967$			1.21661e29i			0.170171i	−0.996374	+	0.0850855i	$0.972884\pi$
$968$	−1.47084e29	−	4.62268e29i	−0.203615	−	0.639942i
$969$	8.10233e28			0.111013
$970$	−5.42735e29	−	7.50219e29i	−0.735987	−	1.01735i
$971$	1.19798e30			1.60789			0.803945	−	0.594704i	$-0.202731\pi$
$971$	1.19798e30			1.60789			0.803945	+	0.594704i	$0.202731\pi$
$972$	−5.01633e28	+	1.52274e29i	−0.0666383	+	0.202284i
$973$			1.53576e30i			2.01927i
$974$	−3.10760e28	−	4.29562e28i	−0.0404423	−	0.0559032i
$975$			2.70340e29i			0.348228i
$976$	−6.62231e29	+	8.96040e29i	−0.844328	+	1.14243i
$977$	−1.37051e29			−0.172956			−0.0864779	−	0.996254i	$-0.527561\pi$
$977$	−1.37051e29			−0.172956			−0.0864779	+	0.996254i	$0.527561\pi$
$978$	9.28119e28	−	6.71434e28i	0.115935	−	0.0838716i
$979$	1.05805e30			1.30821
$980$	5.77875e29	+	1.90369e29i	0.707250	+	0.232989i
$981$		−	2.29269e30i		−	2.77751i
$982$	−8.17732e29	+	5.91576e29i	−0.980610	+	0.709408i
$983$			3.33608e28i			0.0396005i	0.999804	+	0.0198003i	$0.00630303\pi$
$983$			3.33608e28i			0.0396005i	−0.999804	+	0.0198003i	$0.993697\pi$
$984$	−1.27363e29	−	4.00287e29i	−0.149655	−	0.470350i
$985$	−3.74794e29			−0.435944
$986$	−1.03227e28	−	1.42690e28i	−0.0118857	−	0.0164295i
$987$	1.31212e30			1.49555
$988$	9.54012e29	+	3.14279e29i	1.07643	+	0.354606i
$989$			7.91197e28i			0.0883734i
$990$	1.50712e30	+	2.08329e30i	1.66647	+	2.30355i
$991$			2.35405e29i			0.257679i	0.991665	+	0.128839i	$0.0411251\pi$
$991$			2.35405e29i			0.257679i	−0.991665	+	0.128839i	$0.958875\pi$
$992$	3.55285e26	−	3.48871e28i	0.000385000	−	0.0378050i
$993$	−1.25555e30			−1.34692
$994$	2.56315e29	−	1.85427e29i	0.272214	−	0.196929i
$995$	−1.73913e29			−0.182853
$996$	7.56062e29	−	2.29507e30i	0.786981	−	2.38892i
$997$			8.46981e29i			0.872815i	0.899749	+	0.436407i	$0.143749\pi$
$997$			8.46981e29i			0.872815i	−0.899749	+	0.436407i	$0.856251\pi$
$998$	−4.66221e29	+	3.37280e29i	−0.475648	+	0.344101i
$999$		−	1.62839e30i		−	1.64476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.15	✓	18
3.2	odd	2		72.21.b.b.19.4		18
4.3	odd	2		32.21.d.b.15.17		18
8.3	odd	2	inner	8.21.d.b.3.16	yes	18
8.5	even	2		32.21.d.b.15.18		18
24.11	even	2		72.21.b.b.19.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.15	✓	18	1.1	even	1	trivial
8.21.d.b.3.16	yes	18	8.3	odd	2	inner
32.21.d.b.15.17		18	4.3	odd	2
32.21.d.b.15.18		18	8.5	even	2
72.21.b.b.19.3		18	24.11	even	2
72.21.b.b.19.4		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(829.658 - 600.204i) q^{2} -103279. q^{3} +(328087. - 995927. i) q^{4} -1.04292e7i q^{5} +(-8.56862e7 + 6.19884e7i) q^{6} -3.68005e8i q^{7} +(-3.25559e8 - 1.02320e9i) q^{8} +7.17976e9 q^{9} +O(q^{10})\)	\(q+(829.658 - 600.204i) q^{2} -103279. q^{3} +(328087. - 995927. i) q^{4} -1.04292e7i q^{5} +(-8.56862e7 + 6.19884e7i) q^{6} -3.68005e8i q^{7} +(-3.25559e8 - 1.02320e9i) q^{8} +7.17976e9 q^{9} +(-6.25967e9 - 8.65271e9i) q^{10} -3.35341e10 q^{11} +(-3.38845e10 + 1.02858e11i) q^{12} +1.95314e11i q^{13} +(-2.20878e11 - 3.05318e11i) q^{14} +1.07712e12i q^{15} +(-8.84229e11 - 6.53502e11i) q^{16} -1.59958e11 q^{17} +(5.95674e12 - 4.30932e12i) q^{18} +4.90447e12 q^{19} +(-1.03868e13 - 3.42170e12i) q^{20} +3.80072e13i q^{21} +(-2.78218e13 + 2.01273e13i) q^{22} -3.43682e13i q^{23} +(3.36234e13 + 1.05675e14i) q^{24} -1.34018e13 q^{25} +(1.17228e14 + 1.62044e14i) q^{26} -3.81407e14 q^{27} +(-3.66506e14 - 1.20738e14i) q^{28} +1.07520e14i q^{29} +(6.46493e14 + 8.93643e14i) q^{30} +3.09876e13i q^{31} +(-1.12584e15 - 1.14654e13i) q^{32} +3.46337e15 q^{33} +(-1.32710e14 + 9.60073e13i) q^{34} -3.83802e15 q^{35} +(2.35559e15 - 7.15052e15i) q^{36} +4.26943e15i q^{37} +(4.06903e15 - 2.94368e15i) q^{38} -2.01719e16i q^{39} +(-1.06712e16 + 3.39533e15i) q^{40} -3.78792e15 q^{41} +(2.28121e16 + 3.15330e16i) q^{42} -2.30212e15 q^{43} +(-1.10021e16 + 3.33975e16i) q^{44} -7.48795e16i q^{45} +(-2.06279e16 - 2.85139e16i) q^{46} -3.45229e16i q^{47} +(9.13223e16 + 6.74930e16i) q^{48} -5.56357e16 q^{49} +(-1.11189e16 + 8.04382e15i) q^{50} +1.65203e16 q^{51} +(1.94519e17 + 6.40802e16i) q^{52} -3.51656e16i q^{53} +(-3.16437e17 + 2.28922e17i) q^{54} +3.49736e17i q^{55} +(-3.76542e17 + 1.19807e17i) q^{56} -5.06529e17 q^{57} +(6.45338e16 + 8.92047e16i) q^{58} +2.54124e17 q^{59} +(1.07273e18 + 3.53390e17i) q^{60} -1.01336e18i q^{61} +(1.85989e16 + 2.57091e16i) q^{62} -2.64219e18i q^{63} +(-9.40944e17 + 6.66222e17i) q^{64} +2.03698e18 q^{65} +(2.87341e18 - 2.07873e18i) q^{66} -2.98877e18 q^{67} +(-5.24802e16 + 1.59306e17i) q^{68} +3.54952e18i q^{69} +(-3.18424e18 + 2.30359e18i) q^{70} +8.39501e17i q^{71} +(-2.33743e18 - 7.34631e18i) q^{72} +3.32042e18 q^{73} +(2.56253e18 + 3.54216e18i) q^{74} +1.38413e18 q^{75} +(1.60909e18 - 4.88449e18i) q^{76} +1.23407e19i q^{77} +(-1.21072e19 - 1.67357e19i) q^{78} +1.22738e19i q^{79} +(-6.81553e18 + 9.22185e18i) q^{80} +1.43570e19 q^{81} +(-3.14267e18 + 2.27352e18i) q^{82} -2.23129e19 q^{83} +(3.78524e19 + 1.24697e19i) q^{84} +1.66824e18i q^{85} +(-1.90997e18 + 1.38174e18i) q^{86} -1.11045e19i q^{87} +(1.09173e19 + 3.43120e19i) q^{88} -3.15513e19 q^{89} +(-4.49430e19 - 6.21244e19i) q^{90} +7.18767e19 q^{91} +(-3.42282e19 - 1.12758e19i) q^{92} -3.20037e18i q^{93} +(-2.07208e19 - 2.86422e19i) q^{94} -5.11499e19i q^{95} +(1.16276e20 + 1.18413e18i) q^{96} +8.67034e19 q^{97} +(-4.61586e19 + 3.33927e19i) q^{98} -2.40767e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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