LMFDB - Embedded newform 12.11.d.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,11,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	12.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:	$7.62428703208$
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} - 2 x^{9} + 198 x^{8} - 1066 x^{7} + 30608 x^{6} - 147714 x^{5} + 2092829 x^{4} + \cdots + 1648684816 $ x^10 - 2x^9 + 198x^8 - 1066x^7 + 30608x^6 - 147714x^5 + 2092829x^4 - 9587938x^3 + 101463432x^2 - 344403128*x + 1648684816
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.6
Root			$-4.11365 - 7.12504i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.11.d.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.31497 + 31.7077i) q^{2} +140.296i q^{3} +(-986.762 - 273.636i) q^{4} -1853.03 q^{5} +(-4448.47 - 605.373i) q^{6} +2434.59i q^{7} +(12934.2 - 30107.3i) q^{8} -19683.0 q^{9} +O(q^{10})$	\(q+(-4.31497 + 31.7077i) q^{2} +140.296i q^{3} +(-986.762 - 273.636i) q^{4} -1853.03 q^{5} +(-4448.47 - 605.373i) q^{6} +2434.59i q^{7} +(12934.2 - 30107.3i) q^{8} -19683.0 q^{9} +(7995.78 - 58755.5i) q^{10} -212607. i q^{11} +(38390.1 - 138439. i) q^{12} -128078. q^{13} +(-77195.4 - 10505.2i) q^{14} -259973. i q^{15} +(898823. + 540027. i) q^{16} -2.43905e6 q^{17} +(84931.5 - 624104. i) q^{18} +2.72661e6i q^{19} +(1.82850e6 + 507056. i) q^{20} -341564. q^{21} +(6.74129e6 + 917393. i) q^{22} +4.44980e6i q^{23} +(4.22393e6 + 1.81462e6i) q^{24} -6.33190e6 q^{25} +(552653. - 4.06107e6i) q^{26} -2.76145e6i q^{27} +(666192. - 2.40236e6i) q^{28} -3.59943e7 q^{29} +(8.24316e6 + 1.12178e6i) q^{30} -2.51856e7i q^{31} +(-2.10014e7 + 2.61694e7i) q^{32} +2.98279e7 q^{33} +(1.05244e7 - 7.73369e7i) q^{34} -4.51138e6i q^{35} +(1.94224e7 + 5.38598e6i) q^{36} +7.90603e7 q^{37} +(-8.64547e7 - 1.17652e7i) q^{38} -1.79689e7i q^{39} +(-2.39675e7 + 5.57897e7i) q^{40} +4.45528e7 q^{41} +(1.47384e6 - 1.08302e7i) q^{42} +2.24298e8i q^{43} +(-5.81769e7 + 2.09793e8i) q^{44} +3.64732e7 q^{45} +(-1.41093e8 - 1.92008e7i) q^{46} -1.14039e8i q^{47} +(-7.57637e7 + 1.26101e8i) q^{48} +2.76548e8 q^{49} +(2.73219e7 - 2.00770e8i) q^{50} -3.42190e8i q^{51} +(1.26383e8 + 3.50468e7i) q^{52} +235050. q^{53} +(8.75593e7 + 1.19156e7i) q^{54} +3.93968e8i q^{55} +(7.32989e7 + 3.14895e7i) q^{56} -3.82533e8 q^{57} +(1.55314e8 - 1.14130e9i) q^{58} -5.88517e8i q^{59} +(-7.11380e7 + 2.56532e8i) q^{60} -1.49602e9 q^{61} +(7.98579e8 + 1.08675e8i) q^{62} -4.79201e7i q^{63} +(-7.39153e8 - 7.78828e8i) q^{64} +2.37333e8 q^{65} +(-1.28707e8 + 9.45776e8i) q^{66} +1.81580e9i q^{67} +(2.40677e9 + 6.67413e8i) q^{68} -6.24290e8 q^{69} +(1.43046e8 + 1.94664e7i) q^{70} -9.57727e8i q^{71} +(-2.54584e8 + 5.92601e8i) q^{72} +5.66223e8 q^{73} +(-3.41143e8 + 2.50682e9i) q^{74} -8.88341e8i q^{75} +(7.46099e8 - 2.69052e9i) q^{76} +5.17611e8 q^{77} +(5.69752e8 + 7.75351e7i) q^{78} +3.54200e9i q^{79} +(-1.66555e9 - 1.00069e9i) q^{80} +3.87420e8 q^{81} +(-1.92244e8 + 1.41267e9i) q^{82} -8.41475e8i q^{83} +(3.37042e8 + 9.34641e7i) q^{84} +4.51964e9 q^{85} +(-7.11197e9 - 9.67838e8i) q^{86} -5.04986e9i q^{87} +(-6.40102e9 - 2.74991e9i) q^{88} -9.86937e8 q^{89} +(-1.57381e8 + 1.15648e9i) q^{90} -3.11818e8i q^{91} +(1.21763e9 - 4.39090e9i) q^{92} +3.53344e9 q^{93} +(3.61590e9 + 4.92073e8i) q^{94} -5.05250e9i q^{95} +(-3.67147e9 - 2.94642e9i) q^{96} +5.49872e9 q^{97} +(-1.19330e9 + 8.76871e9i) q^{98} +4.18474e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9}+O(q^{10}) $ 10 * q + 22 * q^2 - 644 * q^4 + 3116 * q^5 + 2430 * q^6 + 20176 * q^8 - 196830 * q^9	\( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9} - 369196 q^{10} + 310068 q^{12} - 285100 q^{13} - 2495544 q^{14} + 3590128 q^{16} + 2264420 q^{17} - 433026 q^{18} + 1194248 q^{20} + 3555576 q^{21} - 2139528 q^{22} - 6858432 q^{24} + 23043438 q^{25} + 29599340 q^{26} - 41542224 q^{28} - 46672708 q^{29} + 19963908 q^{30} - 83717408 q^{32} + 22665096 q^{33} + 37514588 q^{34} + 12675852 q^{36} - 194467900 q^{37} - 218769048 q^{38} + 340155488 q^{40} + 276227780 q^{41} - 15919416 q^{42} + 532887504 q^{44} - 61332228 q^{45} - 70057824 q^{46} + 27126576 q^{48} + 653625226 q^{49} + 20815602 q^{50} - 959132296 q^{52} - 1522721956 q^{53} - 47829690 q^{54} - 632703744 q^{56} + 844537752 q^{57} + 1851304388 q^{58} - 1708229736 q^{60} - 3488124604 q^{61} - 806085192 q^{62} - 877634432 q^{64} + 6725245912 q^{65} + 1244885112 q^{66} + 3081993176 q^{68} - 1698239520 q^{69} + 598086768 q^{70} - 397124208 q^{72} + 3090518708 q^{73} - 9824720260 q^{74} + 2750616432 q^{76} - 4577505312 q^{77} + 4510566972 q^{78} + 16715013152 q^{80} + 3874204890 q^{81} + 830592764 q^{82} - 10263359664 q^{84} - 3285444680 q^{85} - 15186172488 q^{86} - 12375555840 q^{88} - 13670065996 q^{89} + 7266884868 q^{90} + 12601016256 q^{92} + 3947087880 q^{93} + 38474881584 q^{94} - 27853204320 q^{96} - 18805077484 q^{97} - 31671844202 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 - 644 * q^4 + 3116 * q^5 + 2430 * q^6 + 20176 * q^8 - 196830 * q^9 - 369196 * q^10 + 310068 * q^12 - 285100 * q^13 - 2495544 * q^14 + 3590128 * q^16 + 2264420 * q^17 - 433026 * q^18 + 1194248 * q^20 + 3555576 * q^21 - 2139528 * q^22 - 6858432 * q^24 + 23043438 * q^25 + 29599340 * q^26 - 41542224 * q^28 - 46672708 * q^29 + 19963908 * q^30 - 83717408 * q^32 + 22665096 * q^33 + 37514588 * q^34 + 12675852 * q^36 - 194467900 * q^37 - 218769048 * q^38 + 340155488 * q^40 + 276227780 * q^41 - 15919416 * q^42 + 532887504 * q^44 - 61332228 * q^45 - 70057824 * q^46 + 27126576 * q^48 + 653625226 * q^49 + 20815602 * q^50 - 959132296 * q^52 - 1522721956 * q^53 - 47829690 * q^54 - 632703744 * q^56 + 844537752 * q^57 + 1851304388 * q^58 - 1708229736 * q^60 - 3488124604 * q^61 - 806085192 * q^62 - 877634432 * q^64 + 6725245912 * q^65 + 1244885112 * q^66 + 3081993176 * q^68 - 1698239520 * q^69 + 598086768 * q^70 - 397124208 * q^72 + 3090518708 * q^73 - 9824720260 * q^74 + 2750616432 * q^76 - 4577505312 * q^77 + 4510566972 * q^78 + 16715013152 * q^80 + 3874204890 * q^81 + 830592764 * q^82 - 10263359664 * q^84 - 3285444680 * q^85 - 15186172488 * q^86 - 12375555840 * q^88 - 13670065996 * q^89 + 7266884868 * q^90 + 12601016256 * q^92 + 3947087880 * q^93 + 38474881584 * q^94 - 27853204320 * q^96 - 18805077484 * q^97 - 31671844202 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

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 $

$2$	−4.31497	+	31.7077i	−0.134843	+	0.990867i
$2$	−4.31497	+	31.7077i	−0.134843	+	0.990867i
$3$			140.296i			0.577350i
$3$			140.296i			0.577350i
$4$	−986.762	−	273.636i	−0.963635	−	0.267223i
$5$	−1853.03			−0.592970			−0.296485	−	0.955037i	$-0.595815\pi$
$5$	−1853.03			−0.592970			−0.296485	+	0.955037i	$0.595815\pi$
$6$	−4448.47	−	605.373i	−0.572077	−	0.0778515i
$7$			2434.59i			0.144856i	0.997374	+	0.0724279i	$0.0230747\pi$
$7$			2434.59i			0.144856i	−0.997374	+	0.0724279i	$0.976925\pi$
$8$	12934.2	−	30107.3i	0.394721	−	0.918801i
$9$	−19683.0			−0.333333
$10$	7995.78	−	58755.5i	0.0799578	−	0.587555i
$11$		−	212607.i		−	1.32012i	−0.751212	−	0.660061i	$-0.770530\pi$
$11$		−	212607.i		−	1.32012i	0.751212	−	0.660061i	$-0.229470\pi$
$12$	38390.1	−	138439.i	0.154281	−	0.556355i
$13$	−128078.			−0.344951			−0.172476	−	0.985014i	$-0.555177\pi$
$13$	−128078.			−0.344951			−0.172476	+	0.985014i	$0.555177\pi$
$14$	−77195.4	−	10505.2i	−0.143533	−	0.0195328i
$15$		−	259973.i		−	0.342352i
$16$	898823.	+	540027.i	0.857184	+	0.515010i
$17$	−2.43905e6			−1.71782			−0.858908	−	0.512130i	$-0.828857\pi$
$17$	−2.43905e6			−1.71782			−0.858908	+	0.512130i	$0.828857\pi$
$18$	84931.5	−	624104.i	0.0449476	−	0.330289i
$19$			2.72661e6i			1.10117i	0.834778	+	0.550586i	$0.185596\pi$
$19$			2.72661e6i			1.10117i	−0.834778	+	0.550586i	$0.814404\pi$
$20$	1.82850e6	+	507056.i	0.571407	+	0.158455i
$21$	−341564.			−0.0836325
$22$	6.74129e6	+	917393.i	1.30807	+	0.178009i
$23$			4.44980e6i			0.691356i	0.938353	+	0.345678i	$0.112351\pi$
$23$			4.44980e6i			0.691356i	−0.938353	+	0.345678i	$0.887649\pi$
$24$	4.22393e6	+	1.81462e6i	0.530470	+	0.227892i
$25$	−6.33190e6			−0.648386
$26$	552653.	−	4.06107e6i	0.0465142	−	0.341801i
$27$		−	2.76145e6i		−	0.192450i
$28$	666192.	−	2.40236e6i	0.0387087	−	0.139588i
$29$	−3.59943e7			−1.75487			−0.877433	−	0.479699i	$-0.840746\pi$
$29$	−3.59943e7			−1.75487			−0.877433	+	0.479699i	$0.840746\pi$
$30$	8.24316e6	+	1.12178e6i	0.339225	+	0.0461636i
$31$		−	2.51856e7i		−	0.879719i	−0.898067	−	0.439859i	$-0.855028\pi$
$31$		−	2.51856e7i		−	0.879719i	0.898067	−	0.439859i	$-0.144972\pi$
$32$	−2.10014e7	+	2.61694e7i	−0.625891	+	0.779910i
$33$	2.98279e7			0.762173
$34$	1.05244e7	−	7.73369e7i	0.231635	−	1.70213i
$35$		−	4.51138e6i		−	0.0858952i
$36$	1.94224e7	+	5.38598e6i	0.321212	+	0.0890742i
$37$	7.90603e7			1.14012			0.570059	−	0.821604i	$-0.306920\pi$
$37$	7.90603e7			1.14012			0.570059	+	0.821604i	$0.306920\pi$
$38$	−8.64547e7	−	1.17652e7i	−1.09111	−	0.148485i
$39$		−	1.79689e7i		−	0.199158i
$40$	−2.39675e7	+	5.57897e7i	−0.234058	+	0.544822i
$41$	4.45528e7			0.384553			0.192276	−	0.981341i	$-0.438413\pi$
$41$	4.45528e7			0.384553			0.192276	+	0.981341i	$0.438413\pi$
$42$	1.47384e6	−	1.08302e7i	0.0112772	−	0.0828687i
$43$			2.24298e8i			1.52575i	0.646548	+	0.762873i	$0.276212\pi$
$43$			2.24298e8i			1.52575i	−0.646548	+	0.762873i	$0.723788\pi$
$44$	−5.81769e7	+	2.09793e8i	−0.352766	+	1.27212i
$45$	3.64732e7			0.197657
$46$	−1.41093e8	−	1.92008e7i	−0.685041	−	0.0932243i
$47$		−	1.14039e8i		−	0.497236i	−0.968602	−	0.248618i	$-0.920024\pi$
$47$		−	1.14039e8i		−	0.497236i	0.968602	−	0.248618i	$-0.0799763\pi$
$48$	−7.57637e7	+	1.26101e8i	−0.297341	+	0.494896i
$49$	2.76548e8			0.979017
$50$	2.73219e7	−	2.00770e8i	0.0874302	−	0.642465i
$51$		−	3.42190e8i		−	0.991782i
$52$	1.26383e8	+	3.50468e7i	0.332407	+	0.0921788i
$53$	235050.			0.000562058			0.000281029	−	1.00000i	$-0.499911\pi$
$53$	235050.			0.000562058			0.000281029		1.00000i	$0.499911\pi$
$54$	8.75593e7	+	1.19156e7i	0.190692	+	0.0259505i
$55$			3.93968e8i			0.782793i
$56$	7.32989e7	+	3.14895e7i	0.133094	+	0.0571777i
$57$	−3.82533e8			−0.635762
$58$	1.55314e8	−	1.14130e9i	0.236631	−	1.73884i
$59$		−	5.88517e8i		−	0.823189i	−0.911367	−	0.411594i	$-0.864972\pi$
$59$		−	5.88517e8i		−	0.823189i	0.911367	−	0.411594i	$-0.135028\pi$
$60$	−7.11380e7	+	2.56532e8i	−0.0914841	+	0.329902i
$61$	−1.49602e9			−1.77128			−0.885642	−	0.464369i	$-0.846281\pi$
$61$	−1.49602e9			−1.77128			−0.885642	+	0.464369i	$0.846281\pi$
$62$	7.98579e8	+	1.08675e8i	0.871684	+	0.118624i
$63$		−	4.79201e7i		−	0.0482853i
$64$	−7.39153e8	−	7.78828e8i	−0.688390	−	0.725340i
$65$	2.37333e8			0.204546
$66$	−1.28707e8	+	9.45776e8i	−0.102774	+	0.755212i
$67$			1.81580e9i			1.34492i	0.740136	+	0.672458i	$0.234761\pi$
$67$			1.81580e9i			1.34492i	−0.740136	+	0.672458i	$0.765239\pi$
$68$	2.40677e9	+	6.67413e8i	1.65535	+	0.459039i
$69$	−6.24290e8			−0.399154
$70$	1.43046e8	+	1.94664e7i	0.0851107	+	0.0115823i
$71$		−	9.57727e8i		−	0.530823i	−0.964135	−	0.265412i	$-0.914492\pi$
$71$		−	9.57727e8i		−	0.530823i	0.964135	−	0.265412i	$-0.0855078\pi$
$72$	−2.54584e8	+	5.92601e8i	−0.131574	+	0.306267i
$73$	5.66223e8			0.273133			0.136566	−	0.990631i	$-0.456393\pi$
$73$	5.66223e8			0.273133			0.136566	+	0.990631i	$0.456393\pi$
$74$	−3.41143e8	+	2.50682e9i	−0.153737	+	1.12971i
$75$		−	8.88341e8i		−	0.374346i
$76$	7.46099e8	−	2.69052e9i	0.294258	−	1.06113i
$77$	5.17611e8			0.191227
$78$	5.69752e8	+	7.75351e7i	0.197339	+	0.0268550i
$79$			3.54200e9i			1.15110i	0.817767	+	0.575550i	$0.195212\pi$
$79$			3.54200e9i			1.15110i	−0.817767	+	0.575550i	$0.804788\pi$
$80$	−1.66555e9	−	1.00069e9i	−0.508285	−	0.305386i
$81$	3.87420e8			0.111111
$82$	−1.92244e8	+	1.41267e9i	−0.0518541	+	0.381041i
$83$		−	8.41475e8i		−	0.213624i	−0.994279	−	0.106812i	$-0.965936\pi$
$83$		−	8.41475e8i		−	0.213624i	0.994279	−	0.106812i	$-0.0340643\pi$
$84$	3.37042e8	+	9.34641e7i	0.0805912	+	0.0223485i
$85$	4.51964e9			1.01861
$86$	−7.11197e9	−	9.67838e8i	−1.51181	−	0.205736i
$87$		−	5.04986e9i		−	1.01317i
$88$	−6.40102e9	−	2.74991e9i	−1.21293	−	0.521080i
$89$	−9.86937e8			−0.176742			−0.0883710	−	0.996088i	$-0.528166\pi$
$89$	−9.86937e8			−0.176742			−0.0883710	+	0.996088i	$0.528166\pi$
$90$	−1.57381e8	+	1.15648e9i	−0.0266526	+	0.195852i
$91$		−	3.11818e8i		−	0.0499682i
$92$	1.21763e9	−	4.39090e9i	0.184746	−	0.666214i
$93$	3.53344e9			0.507906
$94$	3.61590e9	+	4.92073e8i	0.492695	+	0.0670487i
$95$		−	5.05250e9i		−	0.652962i
$96$	−3.67147e9	−	2.94642e9i	−0.450281	−	0.361359i
$97$	5.49872e9			0.640328			0.320164	−	0.947362i	$-0.396262\pi$
$97$	5.49872e9			0.640328			0.320164	+	0.947362i	$0.396262\pi$
$98$	−1.19330e9	+	8.76871e9i	−0.132013	+	0.970075i
$99$			4.18474e9i			0.440041i
$100$	6.24808e9	+	1.73263e9i	0.624808	+	0.173263i
$101$	−3.47388e9			−0.330528			−0.165264	−	0.986249i	$-0.552848\pi$
$101$	−3.47388e9			−0.330528			−0.165264	+	0.986249i	$0.552848\pi$
$102$	1.08501e10	+	1.47654e9i	0.982724	+	0.133735i
$103$		−	6.03440e9i		−	0.520532i	−0.965537	−	0.260266i	$-0.916190\pi$
$103$		−	6.03440e9i		−	0.520532i	0.965537	−	0.260266i	$-0.0838103\pi$
$104$	−1.65659e9	+	3.85608e9i	−0.136160	+	0.316942i
$105$	6.32929e8			0.0495916
$106$	−1.01423e6	+	7.45290e6i	−7.57894e−5	+	0.000556924i
$107$			2.28390e10i			1.62839i	0.580594	+	0.814193i	$0.302820\pi$
$107$			2.28390e10i			1.62839i	−0.580594	+	0.814193i	$0.697180\pi$
$108$	−7.55631e8	+	2.72489e9i	−0.0514270	+	0.185452i
$109$	−1.40012e10			−0.909981			−0.454991	−	0.890496i	$-0.650357\pi$
$109$	−1.40012e10			−0.909981			−0.454991	+	0.890496i	$0.650357\pi$
$110$	−1.24918e10	−	1.69996e9i	−0.775644	−	0.105554i
$111$			1.10919e10i			0.658247i
$112$	−1.31475e9	+	2.18827e9i	−0.0746022	+	0.124168i
$113$	−1.83542e10			−0.996190			−0.498095	−	0.867122i	$-0.665967\pi$
$113$	−1.83542e10			−0.996190			−0.498095	+	0.867122i	$0.665967\pi$
$114$	1.65062e9	−	1.21293e10i	0.0857279	−	0.629955i
$115$		−	8.24563e9i		−	0.409953i
$116$	3.55178e10	+	9.84934e9i	1.69105	+	0.468940i
$117$	2.52096e9			0.114984
$118$	1.86606e10	+	2.53943e9i	0.815670	+	0.111001i
$119$		−	5.93810e9i		−	0.248836i
$120$	−7.82708e9	−	3.36255e9i	−0.314553	−	0.135133i
$121$	−1.92643e10			−0.742722
$122$	6.45528e9	−	4.74354e10i	0.238845	−	1.75511i
$123$			6.25059e9i			0.222022i
$124$	−6.89169e9	+	2.48522e10i	−0.235081	+	0.847728i
$125$	2.98292e10			0.977444
$126$	1.51944e9	+	2.06774e8i	0.0478443	+	0.00651092i
$127$		−	5.90664e10i		−	1.78781i	−0.448255	−	0.893906i	$-0.647954\pi$
$127$		−	5.90664e10i		−	1.78781i	0.448255	−	0.893906i	$-0.352046\pi$
$128$	2.78843e10	−	2.00763e10i	0.811540	−	0.584296i
$129$	−3.14681e10			−0.880890
$130$	−1.02408e9	+	7.52529e9i	−0.0275815	+	0.202678i
$131$		−	3.57142e9i		−	0.0925729i	−0.998928	−	0.0462865i	$-0.985261\pi$
$131$		−	3.57142e9i		−	0.0925729i	0.998928	−	0.0462865i	$-0.0147387\pi$
$132$	−2.94331e10	−	8.16199e9i	−0.734456	−	0.203670i
$133$	−6.63818e9			−0.159511
$134$	−5.75750e10	−	7.83514e9i	−1.33263	−	0.181352i
$135$			5.11705e9i			0.114117i
$136$	−3.15473e10	+	7.34332e10i	−0.678059	+	1.57833i
$137$	4.52283e10			0.937146			0.468573	−	0.883425i	$-0.344768\pi$
$137$	4.52283e10			0.937146			0.468573	+	0.883425i	$0.344768\pi$
$138$	2.69379e9	−	1.97948e10i	0.0538231	−	0.395509i
$139$			4.86833e10i			0.938222i	0.883139	+	0.469111i	$0.155426\pi$
$139$			4.86833e10i			0.938222i	−0.883139	+	0.469111i	$0.844574\pi$
$140$	−1.23447e9	+	4.45165e9i	−0.0229531	+	0.0827716i
$141$	1.59992e10			0.287079
$142$	3.03674e10	+	4.13256e9i	0.525975	+	0.0715777i
$143$			2.72303e10i			0.455378i
$144$	−1.76915e10	−	1.06294e10i	−0.285728	−	0.171670i
$145$	6.66986e10			1.04058
$146$	−2.44324e9	+	1.79537e10i	−0.0368300	+	0.270638i
$147$			3.87986e10i			0.565236i
$148$	−7.80137e10	−	2.16337e10i	−1.09866	−	0.304665i
$149$	2.36876e10			0.322545			0.161272	−	0.986910i	$-0.448440\pi$
$149$	2.36876e10			0.322545			0.161272	+	0.986910i	$0.448440\pi$
$150$	2.81673e10	+	3.83316e9i	0.370927	+	0.0504779i
$151$		−	7.95436e10i		−	1.01326i	−0.862164	−	0.506630i	$-0.830891\pi$
$151$		−	7.95436e10i		−	1.01326i	0.862164	−	0.506630i	$-0.169109\pi$
$152$	8.20908e10	+	3.52666e10i	1.01176	+	0.434656i
$153$	4.80079e10			0.572605
$154$	−2.23348e9	+	1.64123e10i	−0.0257856	+	0.189481i
$155$			4.66697e10i			0.521647i
$156$	−4.91692e9	+	1.77310e10i	−0.0532195	+	0.191915i
$157$	−1.46962e9			−0.0154066			−0.00770328	−	0.999970i	$-0.502452\pi$
$157$	−1.46962e9			−0.0154066			−0.00770328	+	0.999970i	$0.502452\pi$
$158$	−1.12309e11	−	1.52836e10i	−1.14059	−	0.155218i
$159$			3.29766e7i			0.000324504i
$160$	3.89163e10	−	4.84928e10i	0.371135	−	0.462464i
$161$	−1.08334e10			−0.100147
$162$	−1.67171e9	+	1.22842e10i	−0.0149825	+	0.110096i
$163$			1.14660e10i			0.0996495i	0.998758	+	0.0498248i	$0.0158663\pi$
$163$			1.14660e10i			0.0996495i	−0.998758	+	0.0498248i	$0.984134\pi$
$164$	−4.39630e10	−	1.21912e10i	−0.370568	−	0.102761i
$165$	−5.52721e10			−0.451946
$166$	2.66813e10	+	3.63094e9i	0.211673	+	0.0288057i
$167$		−	1.74336e11i		−	1.34217i	−0.741383	−	0.671083i	$-0.765830\pi$
$167$		−	1.74336e11i		−	1.34217i	0.741383	−	0.671083i	$-0.234170\pi$
$168$	−4.41786e9	+	1.02836e10i	−0.0330115	+	0.0768416i
$169$	−1.21455e11			−0.881008
$170$	−1.95021e10	+	1.43308e11i	−0.137353	+	1.00931i
$171$		−	5.36679e10i		−	0.367057i
$172$	6.13759e10	−	2.21328e11i	0.407714	−	1.47026i
$173$	−2.81720e11			−1.81797			−0.908984	−	0.416830i	$-0.863141\pi$
$173$	−2.81720e11			−1.81797			−0.908984	+	0.416830i	$0.863141\pi$
$174$	1.60120e11	+	2.17900e10i	1.00392	+	0.136619i
$175$		−	1.54156e10i		−	0.0939225i
$176$	1.14814e11	−	1.91096e11i	0.679876	−	1.13159i
$177$	8.25667e10			0.475268
$178$	4.25860e9	−	3.12936e10i	0.0238324	−	0.175128i
$179$			2.62283e11i			1.42727i	0.700520	+	0.713633i	$0.252952\pi$
$179$			2.62283e11i			1.42727i	−0.700520	+	0.713633i	$0.747048\pi$
$180$	−3.59904e10	−	9.98039e9i	−0.190469	−	0.0528183i
$181$	1.01264e11			0.521267			0.260634	−	0.965438i	$-0.416069\pi$
$181$	1.01264e11			0.521267			0.260634	+	0.965438i	$0.416069\pi$
$182$	9.88704e9	+	1.34548e9i	0.0495119	+	0.00673785i
$183$		−	2.09886e11i		−	1.02265i
$184$	1.33971e11	+	5.75547e10i	0.635218	+	0.272893i
$185$	−1.46501e11			−0.676056
$186$	−1.52467e10	+	1.12037e11i	−0.0684875	+	0.503267i
$187$			5.18560e11i			2.26773i
$188$	−3.12050e10	+	1.12529e11i	−0.132873	+	0.479154i
$189$	6.72300e9			0.0278775
$190$	1.60203e11	+	2.18014e10i	0.646999	+	0.0880472i
$191$		−	3.34679e11i		−	1.31662i	−0.752746	−	0.658311i	$-0.771271\pi$
$191$		−	3.34679e11i		−	1.31662i	0.752746	−	0.658311i	$-0.228729\pi$
$192$	1.09267e11	−	1.03700e11i	0.418775	−	0.397442i
$193$	1.16772e11			0.436064			0.218032	−	0.975942i	$-0.430036\pi$
$193$	1.16772e11			0.436064			0.218032	+	0.975942i	$0.430036\pi$
$194$	−2.37268e10	+	1.74352e11i	−0.0863437	+	0.634480i
$195$			3.32969e10i			0.118095i
$196$	−2.72887e11	−	7.56735e10i	−0.943415	−	0.261615i
$197$	1.80199e11			0.607324			0.303662	−	0.952780i	$-0.401791\pi$
$197$	1.80199e11			0.607324			0.303662	+	0.952780i	$0.401791\pi$
$198$	−1.32689e11	−	1.80570e10i	−0.436022	−	0.0593363i
$199$			2.38817e11i			0.765243i	0.923905	+	0.382622i	$0.124979\pi$
$199$			2.38817e11i			0.765243i	−0.923905	+	0.382622i	$0.875021\pi$
$200$	−8.18982e10	+	1.90636e11i	−0.255932	+	0.595738i
$201$	−2.54750e11			−0.776487
$202$	1.49897e10	−	1.10149e11i	0.0445693	−	0.327509i
$203$		−	8.76315e10i		−	0.254203i
$204$	−9.36354e10	+	3.37660e11i	−0.265026	+	0.955715i
$205$	−8.25578e10			−0.228028
$206$	1.91337e11	+	2.60382e10i	0.515778	+	0.0701900i
$207$		−	8.75855e10i		−	0.230452i
$208$	−1.15119e11	−	6.91656e10i	−0.295687	−	0.177653i
$209$	5.79696e11			1.45368
$210$	−2.73107e9	+	2.00687e10i	−0.00668707	+	0.0491387i
$211$		−	9.86811e10i		−	0.235951i	−0.993017	−	0.117975i	$-0.962360\pi$
$211$		−	9.86811e10i		−	0.235951i	0.993017	−	0.117975i	$-0.0376404\pi$
$212$	−2.31938e8	−	6.43181e7i	−0.000541618	−	0.000150194i
$213$	1.34365e11			0.306471
$214$	−7.24172e11	−	9.85494e10i	−1.61351	−	0.219576i
$215$		−	4.15631e11i		−	0.904723i
$216$	−8.31397e10	−	3.57172e10i	−0.176823	−	0.0759641i
$217$	6.13167e10			0.127432
$218$	6.04147e10	−	4.43946e11i	0.122704	−	0.901671i
$219$			7.94389e10i			0.157693i
$220$	1.07804e11	−	3.88752e11i	0.209180	−	0.754327i
$221$	3.12389e11			0.592563
$222$	−3.51698e11	−	4.78610e10i	−0.652236	−	0.0887599i
$223$		−	5.32955e11i		−	0.966421i	−0.875504	−	0.483210i	$-0.839471\pi$
$223$		−	5.32955e11i		−	0.966421i	0.875504	−	0.483210i	$-0.160529\pi$
$224$	−6.37119e10	−	5.11299e10i	−0.112975	−	0.0906640i
$225$	1.24631e11			0.216129
$226$	7.91976e10	−	5.81969e11i	0.134329	−	0.987092i
$227$			3.53586e11i			0.586631i	0.956016	+	0.293316i	$0.0947587\pi$
$227$			3.53586e11i			0.586631i	−0.956016	+	0.293316i	$0.905241\pi$
$228$	3.77469e11	+	1.04675e11i	0.612642	+	0.169890i
$229$	2.83949e11			0.450882			0.225441	−	0.974257i	$-0.427618\pi$
$229$	2.83949e11			0.450882			0.225441	+	0.974257i	$0.427618\pi$
$230$	2.61450e11	+	3.55796e10i	0.406209	+	0.0552793i
$231$			7.26188e10i			0.110405i
$232$	−4.65559e11	+	1.08369e12i	−0.692683	+	1.61237i
$233$	−1.20015e11			−0.174766			−0.0873829	−	0.996175i	$-0.527850\pi$
$233$	−1.20015e11			−0.174766			−0.0873829	+	0.996175i	$0.527850\pi$
$234$	−1.08779e10	+	7.99340e10i	−0.0155047	+	0.113934i
$235$			2.11317e11i			0.294846i
$236$	−1.61039e11	+	5.80727e11i	−0.219975	+	0.793253i
$237$	−4.96929e11			−0.664588
$238$	1.88284e11	+	2.56227e10i	0.246563	+	0.0335537i
$239$			7.83394e11i			1.00459i	0.864695	+	0.502297i	$0.167512\pi$
$239$			7.83394e11i			1.00459i	−0.864695	+	0.502297i	$0.832488\pi$
$240$	1.40393e11	−	2.33670e11i	0.176314	−	0.293458i
$241$	−1.33793e12			−1.64569			−0.822843	−	0.568269i	$-0.807613\pi$
$241$	−1.33793e12			−1.64569			−0.822843	+	0.568269i	$0.807613\pi$
$242$	8.31249e10	−	6.10828e11i	0.100151	−	0.735939i
$243$			5.43536e10i			0.0641500i
$244$	1.47622e12	+	4.09365e11i	1.70687	+	0.473327i
$245$	−5.12452e11			−0.580528
$246$	−1.98192e11	−	2.69711e10i	−0.219994	−	0.0299380i
$247$		−	3.49219e11i		−	0.379851i
$248$	−7.58270e11	−	3.25756e11i	−0.808287	−	0.347244i
$249$	1.18056e11			0.123336
$250$	−1.28712e11	+	9.45817e11i	−0.131801	+	0.968517i
$251$		−	3.12414e11i		−	0.313590i	−0.987631	−	0.156795i	$-0.949884\pi$
$251$		−	3.12414e11i		−	0.313590i	0.987631	−	0.156795i	$-0.0501162\pi$
$252$	−1.31126e10	+	4.72857e10i	−0.0129029	+	0.0465294i
$253$	9.46059e11			0.912674
$254$	1.87286e12	+	2.54870e11i	1.77148	+	0.241073i
$255$			6.34089e11i			0.588097i
$256$	5.16253e11	+	9.70777e11i	0.469530	+	0.882917i
$257$	−7.89658e11			−0.704325			−0.352163	−	0.935939i	$-0.614554\pi$
$257$	−7.89658e11			−0.704325			−0.352163	+	0.935939i	$0.614554\pi$
$258$	1.35784e11	−	9.97782e11i	0.118782	−	0.872845i
$259$			1.92479e11i			0.165153i
$260$	−2.34191e11	−	6.49428e10i	−0.197108	−	0.0546593i
$261$	7.08476e11			0.584955
$262$	1.13242e11	+	1.54105e10i	0.0917274	+	0.0124828i
$263$			7.59629e10i			0.0603702i	0.999544	+	0.0301851i	$0.00960968\pi$
$263$			7.59629e10i			0.0603702i	−0.999544	+	0.0301851i	$0.990390\pi$
$264$	3.85801e11	−	8.98038e11i	0.300846	−	0.700285i
$265$	−4.35555e8			−0.000333283
$266$	2.86436e10	−	2.10482e11i	0.0215089	−	0.158054i
$267$		−	1.38463e11i		−	0.102042i
$268$	4.96869e11	−	1.79177e12i	0.359392	−	1.29601i
$269$	−1.59749e12			−1.13417			−0.567083	−	0.823661i	$-0.691928\pi$
$269$	−1.59749e12			−1.13417			−0.567083	+	0.823661i	$0.691928\pi$
$270$	−1.62250e11	−	2.20799e10i	−0.113075	−	0.0153879i
$271$		−	1.89426e12i		−	1.29597i	−0.761654	−	0.647983i	$-0.775613\pi$
$271$		−	1.89426e12i		−	1.29597i	0.761654	−	0.647983i	$-0.224387\pi$
$272$	−2.19228e12	−	1.31715e12i	−1.47249	−	0.884692i
$273$	4.37468e10			0.0288492
$274$	−1.95159e11	+	1.43409e12i	−0.126367	+	0.928587i
$275$			1.34621e12i			0.855949i
$276$	6.16026e11	+	1.70828e11i	0.384639	+	0.106663i
$277$	−1.62275e12			−0.995071			−0.497535	−	0.867444i	$-0.665762\pi$
$277$	−1.62275e12			−0.995071			−0.497535	+	0.867444i	$0.665762\pi$
$278$	−1.54364e12	−	2.10067e11i	−0.929654	−	0.126513i
$279$			4.95728e11i			0.293240i
$280$	−1.35825e11	−	5.83511e10i	−0.0789206	−	0.0339046i
$281$	6.31441e11			0.360414			0.180207	−	0.983629i	$-0.442323\pi$
$281$	6.31441e11			0.360414			0.180207	+	0.983629i	$0.442323\pi$
$282$	−6.90359e10	+	5.07297e11i	−0.0387106	+	0.284457i
$283$		−	2.75440e12i		−	1.51738i	−0.651451	−	0.758691i	$-0.725839\pi$
$283$		−	2.75440e12i		−	1.51738i	0.651451	−	0.758691i	$-0.274161\pi$
$284$	−2.62068e11	+	9.45048e11i	−0.141848	+	0.511520i
$285$	7.08846e11			0.376988
$286$	−8.63411e11	−	1.17498e11i	−0.451219	−	0.0614044i
$287$			1.08468e11i			0.0557047i
$288$	4.13371e11	−	5.15093e11i	0.208630	−	0.259970i
$289$	3.93299e12			1.95089
$290$	−2.87803e11	+	2.11486e12i	−0.140315	+	1.03108i
$291$			7.71449e11i			0.369694i
$292$	−5.58728e11	−	1.54939e11i	−0.263200	−	0.0729872i
$293$	2.61530e12			1.21111			0.605555	−	0.795803i	$-0.292951\pi$
$293$	2.61530e12			1.21111			0.605555	+	0.795803i	$0.292951\pi$
$294$	−1.23022e12	−	1.67415e11i	−0.560073	−	0.0762179i
$295$			1.09054e12i			0.488126i
$296$	1.02258e12	−	2.38029e12i	0.450029	−	1.04754i
$297$	−5.87103e11			−0.254058
$298$	−1.02211e11	+	7.51080e11i	−0.0434928	+	0.319599i
$299$		−	5.69922e11i		−	0.238484i
$300$	−2.43082e11	+	8.76581e11i	−0.100034	+	0.360733i
$301$	−5.46073e11			−0.221013
$302$	2.52215e12	+	3.43228e11i	1.00401	+	0.136631i
$303$		−	4.87372e11i		−	0.190830i
$304$	−1.47244e12	+	2.45074e12i	−0.567114	+	0.943907i
$305$	2.77217e12			1.05032
$306$	−2.07153e11	+	1.52222e12i	−0.0772117	+	0.567376i
$307$		−	4.55764e11i		−	0.167128i	−0.996502	−	0.0835638i	$-0.973370\pi$
$307$		−	4.55764e11i		−	0.167128i	0.996502	−	0.0835638i	$-0.0266302\pi$
$308$	−5.10759e11	−	1.41637e11i	−0.184273	−	0.0511003i
$309$	8.46602e11			0.300529
$310$	−1.47979e12	−	2.01378e11i	−0.516883	−	0.0703404i
$311$			3.07441e12i			1.05672i	0.849020	+	0.528360i	$0.177193\pi$
$311$			3.07441e12i			1.05672i	−0.849020	+	0.528360i	$0.822807\pi$
$312$	−5.40993e11	−	2.32413e11i	−0.182986	−	0.0786118i
$313$	−3.03971e12			−1.01184			−0.505919	−	0.862581i	$-0.668846\pi$
$313$	−3.03971e12			−1.01184			−0.505919	+	0.862581i	$0.668846\pi$
$314$	6.34135e9	−	4.65982e10i	0.00207746	−	0.0152659i
$315$			8.87974e10i			0.0286317i
$316$	9.69218e11	−	3.49511e12i	0.307600	−	1.10924i
$317$	−1.43823e12			−0.449295			−0.224648	−	0.974440i	$-0.572123\pi$
$317$	−1.43823e12			−0.449295			−0.224648	+	0.974440i	$0.572123\pi$
$318$	−1.04561e9	−	1.42293e8i	−0.000321540	−	4.37570e-5i
$319$			7.65265e12i			2.31664i
$320$	1.36968e12	+	1.44319e12i	0.408195	+	0.430105i
$321$	−3.20422e12			−0.940149
$322$	4.67460e10	−	3.43504e11i	0.0135041	−	0.0992322i
$323$		−	6.65035e12i		−	1.89161i
$324$	−3.82292e11	−	1.06012e11i	−0.107071	−	0.0296914i
$325$	8.10977e11			0.223662
$326$	−3.63562e11	−	4.94756e10i	−0.0987394	−	0.0134370i
$327$		−	1.96431e12i		−	0.525378i
$328$	5.76256e11	−	1.34136e12i	0.151791	−	0.353327i
$329$	2.77637e11			0.0720275
$330$	2.38497e11	−	1.75255e12i	0.0609416	−	0.447818i
$331$		−	2.43200e11i		−	0.0612103i	−0.999532	−	0.0306051i	$-0.990257\pi$
$331$		−	2.43200e11i		−	0.0612103i	0.999532	−	0.0306051i	$-0.00974344\pi$
$332$	−2.30258e11	+	8.30335e11i	−0.0570852	+	0.205856i
$333$	−1.55614e12			−0.380039
$334$	5.52782e12	+	7.52257e11i	1.32991	+	0.180981i
$335$		−	3.36474e12i		−	0.797495i
$336$	−3.07005e11	−	1.84454e11i	−0.0716885	−	0.0430716i
$337$	−7.96602e11			−0.183270			−0.0916351	−	0.995793i	$-0.529209\pi$
$337$	−7.96602e11			−0.183270			−0.0916351	+	0.995793i	$0.529209\pi$
$338$	5.24072e11	−	3.85105e12i	0.118798	−	0.872962i
$339$		−	2.57502e12i		−	0.575151i
$340$	−4.45981e12	−	1.23674e12i	−0.981572	−	0.272197i
$341$	−5.35464e12			−1.16134
$342$	1.70169e12	+	2.31575e11i	0.363705	+	0.0494950i
$343$			1.36099e12i			0.286672i
$344$	6.75299e12	+	2.90112e12i	1.40186	+	0.602245i
$345$	1.15683e12			0.236687
$346$	1.21561e12	−	8.93269e12i	0.245140	−	1.80137i
$347$		−	1.43961e12i		−	0.286153i	−0.989712	−	0.143076i	$-0.954301\pi$
$347$		−	1.43961e12i		−	0.286153i	0.989712	−	0.143076i	$-0.0456994\pi$
$348$	−1.38182e12	+	4.98301e12i	−0.270743	+	0.976328i
$349$	−2.91781e12			−0.563547			−0.281774	−	0.959481i	$-0.590923\pi$
$349$	−2.91781e12			−0.563547			−0.281774	+	0.959481i	$0.590923\pi$
$350$	4.88793e11	+	6.65178e10i	0.0930647	+	0.0126648i
$351$			3.53681e11i			0.0663859i
$352$	5.56381e12	+	4.46505e12i	1.02958	+	0.826253i
$353$	8.65142e11			0.157839			0.0789194	−	0.996881i	$-0.474853\pi$
$353$	8.65142e11			0.157839			0.0789194	+	0.996881i	$0.474853\pi$
$354$	−3.56273e11	+	2.61800e12i	−0.0640865	+	0.470927i
$355$			1.77470e12i			0.314762i
$356$	9.73872e11	+	2.70061e11i	0.170315	+	0.0472294i
$357$	8.33092e11			0.143665
$358$	−8.31640e12	−	1.13174e12i	−1.41423	−	0.192457i
$359$			6.21036e12i			1.04147i	0.853720	+	0.520733i	$0.174341\pi$
$359$			6.21036e12i			1.04147i	−0.853720	+	0.520733i	$0.825659\pi$
$360$	4.71753e11	−	1.09811e12i	0.0780193	−	0.181607i
$361$	−1.30334e12			−0.212580
$362$	−4.36949e11	+	3.21084e12i	−0.0702892	+	0.516507i
$363$		−	2.70271e12i		−	0.428811i
$364$	−8.53245e10	+	3.07690e11i	−0.0133526	+	0.0481511i
$365$	−1.04923e12			−0.161960
$366$	6.65500e12	+	9.05651e11i	1.01331	+	0.137897i
$367$			7.67131e12i			1.15223i	0.817369	+	0.576115i	$0.195432\pi$
$367$			7.67131e12i			1.15223i	−0.817369	+	0.576115i	$0.804568\pi$
$368$	−2.40301e12	+	3.99958e12i	−0.356055	+	0.592619i
$369$	−8.76933e11			−0.128184
$370$	6.32148e11	−	4.64522e12i	0.0911613	−	0.669882i
$371$			5.72251e8i			8.14173e-5i
$372$	−3.48667e12	−	9.66877e11i	−0.489436	−	0.135724i
$373$	1.13798e13			1.57613			0.788065	−	0.615592i	$-0.211083\pi$
$373$	1.13798e13			1.57613			0.788065	+	0.615592i	$0.211083\pi$
$374$	−1.64424e13	−	2.23757e12i	−2.24702	−	0.305787i
$375$			4.18492e12i			0.564328i
$376$	−3.43339e12	−	1.47500e12i	−0.456861	−	0.196270i
$377$	4.61008e12			0.605344
$378$	−2.90095e10	+	2.13171e11i	−0.00375908	+	0.0276229i
$379$		−	5.81929e12i		−	0.744173i	−0.928198	−	0.372087i	$-0.878642\pi$
$379$		−	5.81929e12i		−	0.744173i	0.928198	−	0.372087i	$-0.121358\pi$
$380$	−1.38254e12	+	4.98561e12i	−0.174486	+	0.629217i
$381$	8.28678e12			1.03219
$382$	1.06119e13	+	1.44413e12i	1.30460	+	0.177537i
$383$			6.45151e12i			0.782830i	0.920214	+	0.391415i	$0.128014\pi$
$383$			6.45151e12i			0.782830i	−0.920214	+	0.391415i	$0.871986\pi$
$384$	2.81662e12	+	3.91206e12i	0.337344	+	0.468543i
$385$	−9.59150e11			−0.113392
$386$	−5.03866e11	+	3.70256e12i	−0.0588001	+	0.432082i
$387$		−	4.41485e12i		−	0.508582i
$388$	−5.42593e12	−	1.50465e12i	−0.617043	−	0.171110i
$389$	−5.27060e12			−0.591715			−0.295857	−	0.955232i	$-0.595605\pi$
$389$	−5.27060e12			−0.591715			−0.295857	+	0.955232i	$0.595605\pi$
$390$	−1.05577e12	−	1.43675e11i	−0.117016	−	0.0159242i
$391$		−	1.08533e13i		−	1.18762i
$392$	3.57693e12	−	8.32611e12i	0.386439	−	0.899522i
$393$	5.01056e11			0.0534470
$394$	−7.77551e11	+	5.71369e12i	−0.0818932	+	0.601777i
$395$		−	6.56344e12i		−	0.682568i
$396$	1.14510e12	−	4.12935e12i	0.117589	−	0.424039i
$397$	1.35176e13			1.37071			0.685355	−	0.728209i	$-0.259647\pi$
$397$	1.35176e13			1.37071			0.685355	+	0.728209i	$0.259647\pi$
$398$	−7.57234e12	−	1.03049e12i	−0.758255	−	0.103188i
$399$		−	9.31311e11i		−	0.0920938i
$400$	−5.69125e12	−	3.41940e12i	−0.555786	−	0.333925i
$401$	−2.77195e12			−0.267340			−0.133670	−	0.991026i	$-0.542676\pi$
$401$	−2.77195e12			−0.267340			−0.133670	+	0.991026i	$0.542676\pi$
$402$	1.09924e12	−	8.07755e12i	0.104704	−	0.769395i
$403$			3.22572e12i			0.303460i
$404$	3.42790e12	+	9.50579e11i	0.318508	+	0.0883245i
$405$	−7.17903e11			−0.0658856
$406$	2.77860e12	+	3.78127e11i	0.251881	+	0.0342774i
$407$		−	1.68088e13i		−	1.50509i
$408$	−1.03024e13	−	4.42596e12i	−0.911250	−	0.391477i
$409$	−7.34779e12			−0.642008			−0.321004	−	0.947078i	$-0.604020\pi$
$409$	−7.34779e12			−0.642008			−0.321004	+	0.947078i	$0.604020\pi$
$410$	3.56234e11	−	2.61772e12i	0.0307480	−	0.225946i
$411$			6.34535e12i			0.541062i
$412$	−1.65123e12	+	5.95451e12i	−0.139098	+	0.501603i
$413$	1.43280e12			0.119244
$414$	2.77714e12	+	3.77929e11i	0.228347	+	0.0310748i
$415$			1.55928e12i			0.126673i
$416$	2.68982e12	−	3.35173e12i	0.215902	−	0.269031i
$417$	−6.83007e12			−0.541683
$418$	−2.50137e12	+	1.83809e13i	−0.196018	+	1.44040i
$419$			1.10953e13i			0.859154i	0.903030	+	0.429577i	$0.141337\pi$
$419$			1.10953e13i			0.859154i	−0.903030	+	0.429577i	$0.858663\pi$
$420$	−6.24550e11	−	1.73192e11i	−0.0477882	−	0.0132520i
$421$	−1.69718e13			−1.28326			−0.641632	−	0.767012i	$-0.721742\pi$
$421$	−1.69718e13			−1.28326			−0.641632	+	0.767012i	$0.721742\pi$
$422$	3.12895e12	+	4.25806e11i	0.233796	+	0.0318163i
$423$			2.24462e12i			0.165745i
$424$	3.04019e9	−	7.07671e9i	0.000221856	−	0.000516419i
$425$	1.54438e13			1.11381
$426$	−5.79782e11	+	4.26042e12i	−0.0413254	+	0.303672i
$427$		−	3.64220e12i		−	0.256581i
$428$	6.24956e12	−	2.25366e13i	0.435141	−	1.56917i
$429$	−3.82030e12			−0.262913
$430$	1.31787e13	+	1.79343e12i	0.896460	+	0.121995i
$431$			2.50135e13i			1.68185i	0.541151	+	0.840925i	$0.317989\pi$
$431$			2.50135e13i			1.68185i	−0.541151	+	0.840925i	$0.682011\pi$
$432$	1.49126e12	−	2.48205e12i	0.0991137	−	0.164965i
$433$	−7.70618e12			−0.506291			−0.253145	−	0.967428i	$-0.581465\pi$
$433$	−7.70618e12			−0.506291			−0.253145	+	0.967428i	$0.581465\pi$
$434$	−2.64579e11	+	1.94421e12i	−0.0171833	+	0.126269i
$435$			9.35756e12i			0.600781i
$436$	1.38158e13	+	3.83123e12i	0.876890	+	0.243168i
$437$	−1.21329e13			−0.761301
$438$	−2.51883e12	−	3.42777e11i	−0.156253	−	0.0212638i
$439$		−	1.60799e13i		−	0.986190i	−0.869975	−	0.493095i	$-0.835865\pi$
$439$		−	1.60799e13i		−	0.986190i	0.869975	−	0.493095i	$-0.164135\pi$
$440$	1.18613e13	+	5.09566e12i	0.719231	+	0.308985i
$441$	−5.44329e12			−0.326339
$442$	−1.34795e12	+	9.90516e12i	−0.0799029	+	0.587151i
$443$			1.48245e12i			0.0868881i	0.999056	+	0.0434441i	$0.0138330\pi$
$443$			1.48245e12i			0.0868881i	−0.999056	+	0.0434441i	$0.986167\pi$
$444$	3.03513e12	−	1.09450e13i	0.175899	−	0.634310i
$445$	1.82883e12			0.104803
$446$	1.68988e13	+	2.29968e12i	0.957594	+	0.130315i
$447$			3.32328e12i			0.186221i
$448$	1.89613e12	−	1.79954e12i	0.105070	−	0.0997173i
$449$	1.22618e13			0.671929			0.335965	−	0.941875i	$-0.390938\pi$
$449$	1.22618e13			0.671929			0.335965	+	0.941875i	$0.390938\pi$
$450$	−5.37778e11	+	3.95176e12i	−0.0291434	+	0.214155i
$451$		−	9.47224e12i		−	0.507656i
$452$	1.81112e13	+	5.02236e12i	0.959963	+	0.266204i
$453$	1.11597e13			0.585005
$454$	−1.12114e13	−	1.52571e12i	−0.581274	−	0.0791030i
$455$			5.77808e11i			0.0296297i
$456$	−4.94777e12	+	1.15170e13i	−0.250949	+	0.584139i
$457$	−1.23565e13			−0.619888			−0.309944	−	0.950755i	$-0.600310\pi$
$457$	−1.23565e13			−0.619888			−0.309944	+	0.950755i	$0.600310\pi$
$458$	−1.22523e12	+	9.00338e12i	−0.0607982	+	0.446764i
$459$			6.73532e12i			0.330594i
$460$	−2.25630e12	+	8.13647e12i	−0.109549	+	0.395045i
$461$	−2.57914e13			−1.23871			−0.619357	−	0.785110i	$-0.712607\pi$
$461$	−2.57914e13			−1.23871			−0.619357	+	0.785110i	$0.712607\pi$
$462$	−2.30258e12	−	3.13348e11i	−0.109397	−	0.0148873i
$463$		−	1.02520e13i		−	0.481839i	−0.970545	−	0.240919i	$-0.922551\pi$
$463$		−	1.02520e13i		−	0.481839i	0.970545	−	0.240919i	$-0.0774489\pi$
$464$	−3.23525e13	−	1.94379e13i	−1.50424	−	0.903774i
$465$	−6.54758e12			−0.301173
$466$	5.17861e11	−	3.80541e12i	0.0235659	−	0.173170i
$467$			8.12705e12i			0.365888i	0.983123	+	0.182944i	$0.0585628\pi$
$467$			8.12705e12i			0.365888i	−0.983123	+	0.182944i	$0.941437\pi$
$468$	−2.48759e12	−	6.89825e11i	−0.110802	−	0.0307263i
$469$	−4.42074e12			−0.194819
$470$	−6.70039e12	−	9.11827e11i	−0.292153	−	0.0397579i
$471$		−	2.06182e11i		−	0.00889498i
$472$	−1.77187e13	−	7.61202e12i	−0.756346	−	0.324930i
$473$	4.76873e13			2.01417
$474$	2.14423e12	−	1.57565e13i	0.0896149	−	0.658518i
$475$		−	1.72646e13i		−	0.713985i
$476$	−1.62488e12	+	5.85949e12i	−0.0664945	+	0.239787i
$477$	−4.62649e9			−0.000187353
$478$	−2.48397e13	−	3.38032e12i	−0.995420	−	0.135462i
$479$		−	4.58898e13i		−	1.81986i	−0.414758	−	0.909932i	$-0.636134\pi$
$479$		−	4.58898e13i		−	1.81986i	0.414758	−	0.909932i	$-0.363866\pi$
$480$	6.80335e12	+	5.45981e12i	0.267003	+	0.214275i
$481$	−1.01259e13			−0.393285
$482$	5.77311e12	−	4.24226e13i	0.221909	−	1.63066i
$483$		−	1.51989e12i		−	0.0578198i
$484$	1.90093e13	+	5.27140e12i	0.715713	+	0.198472i
$485$	−1.01893e13			−0.379696
$486$	−1.72343e12	−	2.34534e11i	−0.0635641	−	0.00865017i
$487$			2.06713e13i			0.754611i	0.926089	+	0.377306i	$0.123149\pi$
$487$			2.06713e13i			0.754611i	−0.926089	+	0.377306i	$0.876851\pi$
$488$	−1.93499e13	+	4.50411e13i	−0.699163	+	1.62746i
$489$	−1.60864e12			−0.0575327
$490$	2.21122e12	−	1.62487e13i	0.0782800	−	0.575226i
$491$			2.60447e13i			0.912665i	0.889809	+	0.456332i	$0.150837\pi$
$491$			2.60447e13i			0.912665i	−0.889809	+	0.456332i	$0.849163\pi$
$492$	1.71038e12	−	6.16784e12i	0.0593292	−	0.213948i
$493$	8.77921e13			3.01454
$494$	1.10729e13	+	1.50687e12i	0.376382	+	0.0512201i
$495$		−	7.75446e12i		−	0.260931i
$496$	1.36009e13	−	2.26374e13i	0.453064	−	0.754081i
$497$	2.33167e12			0.0768928
$498$	−5.09406e11	+	3.74328e12i	−0.0166310	+	0.122210i
$499$			4.42427e13i			1.43001i	0.699119	+	0.715005i	$0.253576\pi$
$499$			4.42427e13i			1.43001i	−0.699119	+	0.715005i	$0.746424\pi$
$500$	−2.94343e13	−	8.16235e12i	−0.941899	−	0.261195i
$501$	2.44587e13			0.774899
$502$	9.90595e12	+	1.34806e12i	0.310726	+	0.0422854i
$503$		−	2.79589e13i		−	0.868322i	−0.900835	−	0.434161i	$-0.857045\pi$
$503$		−	2.79589e13i		−	0.868322i	0.900835	−	0.434161i	$-0.142955\pi$
$504$	−1.44274e12	−	6.19809e11i	−0.0443645	−	0.0190592i
$505$	6.43722e12			0.195993
$506$	−4.08222e12	+	2.99974e13i	−0.123067	+	0.904338i
$507$		−	1.70396e13i		−	0.508650i
$508$	−1.61627e13	+	5.82844e13i	−0.477743	+	1.72280i
$509$	−4.51569e13			−1.32171			−0.660853	−	0.750515i	$-0.729805\pi$
$509$	−4.51569e13			−1.32171			−0.660853	+	0.750515i	$0.729805\pi$
$510$	−2.01055e13	−	2.73607e12i	−0.582726	−	0.0793007i
$511$			1.37852e12i			0.0395648i
$512$	−3.30088e13	+	1.21804e13i	−0.938166	+	0.346186i
$513$	7.52939e12			0.211921
$514$	3.40735e12	−	2.50383e13i	0.0949732	−	0.697893i
$515$			1.11819e13i			0.308660i
$516$	3.10515e13	+	8.61080e12i	0.848857	+	0.235394i
$517$	−2.42454e13			−0.656412
$518$	−6.10309e12	−	8.30543e11i	−0.163644	−	0.0222696i
$519$		−	3.95242e13i		−	1.04960i
$520$	3.06972e12	−	7.14544e12i	0.0807386	−	0.187937i
$521$	−1.77028e13			−0.461161			−0.230580	−	0.973053i	$-0.574062\pi$
$521$	−1.77028e13			−0.461161			−0.230580	+	0.973053i	$0.574062\pi$
$522$	−3.05705e12	+	2.24642e13i	−0.0788770	+	0.579613i
$523$			5.39925e13i			1.37983i	0.723891	+	0.689914i	$0.242352\pi$
$523$			5.39925e13i			1.37983i	−0.723891	+	0.689914i	$0.757648\pi$
$524$	−9.77268e11	+	3.52414e12i	−0.0247376	+	0.0892065i
$525$	2.16275e12			0.0542262
$526$	−2.40861e12	−	3.27778e11i	−0.0598189	−	0.00814049i
$527$			6.14290e13i			1.51120i
$528$	2.68100e13	+	1.61079e13i	0.653323	+	0.392527i
$529$	2.16258e13			0.522027
$530$	1.87941e9	−	1.38105e10i	4.49409e−5	−	0.000330240i
$531$			1.15838e13i			0.274396i
$532$	6.55031e12	+	1.81644e12i	0.153710	+	0.0426250i
$533$	−5.70624e12			−0.132652
$534$	4.39036e12	+	5.97466e11i	0.101110	+	0.0137596i
$535$		−	4.23213e13i		−	0.965585i
$536$	5.46689e13	+	2.34860e13i	1.23571	+	0.530866i
$537$	−3.67973e13			−0.824032
$538$	6.89312e12	−	5.06528e13i	0.152934	−	1.12381i
$539$		−	5.87960e13i		−	1.29242i
$540$	1.40021e12	−	5.04931e12i	0.0304947	−	0.109967i
$541$	−8.07861e13			−1.74321			−0.871606	−	0.490207i	$-0.836921\pi$
$541$	−8.07861e13			−1.74321			−0.871606	+	0.490207i	$0.836921\pi$
$542$	6.00628e13	+	8.17369e12i	1.28413	+	0.174752i
$543$			1.42069e13i			0.300954i
$544$	5.12236e13	−	6.38287e13i	1.07517	−	1.33974i
$545$	2.59447e13			0.539592
$546$	−1.88766e11	+	1.38711e12i	−0.00389010	+	0.0285857i
$547$			5.37946e13i			1.09850i	0.835657	+	0.549252i	$0.185087\pi$
$547$			5.37946e13i			1.09850i	−0.835657	+	0.549252i	$0.814913\pi$
$548$	−4.46296e13	−	1.23761e13i	−0.903067	−	0.250427i
$549$	2.94462e13			0.590428
$550$	−4.26851e13	−	5.80883e12i	−0.848132	−	0.115419i
$551$		−	9.81425e13i		−	1.93241i
$552$	−8.07471e12	+	1.87957e13i	−0.157555	+	0.366743i
$553$	−8.62332e12			−0.166743
$554$	7.00214e12	−	5.14539e13i	0.134178	−	0.985983i
$555$		−	2.05536e13i		−	0.390321i
$556$	1.33215e13	−	4.80388e13i	0.250714	−	0.904104i
$557$	−2.06277e13			−0.384748			−0.192374	−	0.981322i	$-0.561619\pi$
$557$	−2.06277e13			−0.384748			−0.192374	+	0.981322i	$0.561619\pi$
$558$	−1.57184e13	−	2.13905e12i	−0.290561	−	0.0395412i
$559$		−	2.87276e13i		−	0.526309i
$560$	2.43626e12	−	4.05493e12i	0.0442369	−	0.0736280i
$561$	−7.27519e13			−1.30927
$562$	−2.72465e12	+	2.00216e13i	−0.0485992	+	0.357122i
$563$			1.01205e14i			1.78920i	0.446870	+	0.894599i	$0.352539\pi$
$563$			1.01205e14i			1.78920i	−0.446870	+	0.894599i	$0.647461\pi$
$564$	−1.57874e13	−	4.37795e12i	−0.276640	−	0.0767140i
$565$	3.40108e13			0.590711
$566$	8.73358e13	+	1.18851e13i	1.50352	+	0.204608i
$567$			9.43211e11i			0.0160951i
$568$	−2.88345e13	−	1.23875e13i	−0.487721	−	0.209527i
$569$	−3.44927e12			−0.0578317			−0.0289159	−	0.999582i	$-0.509205\pi$
$569$	−3.44927e12			−0.0578317			−0.0289159	+	0.999582i	$0.509205\pi$
$570$	−3.05865e12	+	2.24759e13i	−0.0508341	+	0.373545i
$571$			1.76401e13i			0.290616i	0.989386	+	0.145308i	$0.0464173\pi$
$571$			1.76401e13i			0.290616i	−0.989386	+	0.145308i	$0.953583\pi$
$572$	7.45118e12	−	2.68698e13i	0.121687	−	0.438818i
$573$	4.69541e13			0.760152
$574$	−3.43927e12	−	4.68036e11i	−0.0551959	−	0.00751137i
$575$		−	2.81757e13i		−	0.448265i
$576$	1.45488e13	+	1.53297e13i	0.229463	+	0.241780i
$577$	−8.22379e13			−1.28586			−0.642929	−	0.765926i	$-0.722281\pi$
$577$	−8.22379e13			−1.28586			−0.642929	+	0.765926i	$0.722281\pi$
$578$	−1.69707e13	+	1.24706e14i	−0.263064	+	1.93308i
$579$			1.63826e13i			0.251762i
$580$	−6.58157e13	−	1.82511e13i	−1.00274	−	0.278067i
$581$	2.04865e12			0.0309447
$582$	−2.44609e13	−	3.32878e12i	−0.366317	−	0.0498505i
$583$		−	4.99733e10i		−	0.000741985i
$584$	7.32366e12	−	1.70474e13i	0.107811	−	0.250954i
$585$	−4.67142e12			−0.0681820
$586$	−1.12850e13	+	8.29253e13i	−0.163310	+	1.20005i
$587$		−	9.36915e13i		−	1.34434i	−0.740396	−	0.672171i	$-0.765362\pi$
$587$		−	9.36915e13i		−	1.34434i	0.740396	−	0.672171i	$-0.234638\pi$
$588$	1.06167e13	−	3.82850e13i	0.151044	−	0.544681i
$589$	6.86713e13			0.968722
$590$	−3.45786e13	−	4.70565e12i	−0.483668	−	0.0658203i
$591$			2.52812e13i			0.350638i
$592$	7.10612e13	+	4.26947e13i	0.977291	+	0.587172i
$593$	1.17010e14			1.59569			0.797845	−	0.602862i	$-0.205973\pi$
$593$	1.17010e14			1.59569			0.797845	+	0.602862i	$0.205973\pi$
$594$	2.53333e12	−	1.86157e13i	0.0342578	−	0.251737i
$595$			1.10035e13i			0.147552i
$596$	−2.33740e13	−	6.48178e12i	−0.310815	−	0.0861912i
$597$	−3.35051e13			−0.441814
$598$	1.80709e13	+	2.45920e12i	0.236306	+	0.0321579i
$599$			1.06460e14i			1.38056i	0.723544	+	0.690278i	$0.242512\pi$
$599$			1.06460e14i			1.38056i	−0.723544	+	0.690278i	$0.757488\pi$
$600$	−2.67455e13	−	1.14900e13i	−0.343949	−	0.147762i
$601$	−9.56256e12			−0.121956			−0.0609778	−	0.998139i	$-0.519422\pi$
$601$	−9.56256e12			−0.121956			−0.0609778	+	0.998139i	$0.519422\pi$
$602$	2.35629e12	−	1.73147e13i	0.0298020	−	0.218995i
$603$		−	3.57405e13i		−	0.448305i
$604$	−2.17660e13	+	7.84906e13i	−0.270766	+	0.976412i
$605$	3.56974e13			0.440412
$606$	1.54535e13	+	2.10300e12i	0.189088	+	0.0257321i
$607$			9.10345e13i			1.10475i	0.833597	+	0.552373i	$0.186278\pi$
$607$			9.10345e13i			1.10475i	−0.833597	+	0.552373i	$0.813722\pi$
$608$	−7.13539e13	−	5.72627e13i	−0.858815	−	0.689214i
$609$	1.22944e13			0.146764
$610$	−1.19618e13	+	8.78993e13i	−0.141628	+	1.04073i
$611$			1.46058e13i			0.171522i
$612$	−4.73724e13	−	1.31367e13i	−0.551783	−	0.153013i
$613$	1.19662e14			1.38247			0.691234	−	0.722631i	$-0.257067\pi$
$613$	1.19662e14			1.38247			0.691234	+	0.722631i	$0.257067\pi$
$614$	1.44513e13	+	1.96661e12i	0.165601	+	0.0225360i
$615$		−	1.15825e13i		−	0.131652i
$616$	6.69490e12	−	1.55839e13i	0.0754815	−	0.175700i
$617$	1.32215e14			1.47861			0.739305	−	0.673370i	$-0.235154\pi$
$617$	1.32215e14			1.47861			0.739305	+	0.673370i	$0.235154\pi$
$618$	−3.65306e12	+	2.68438e13i	−0.0405242	+	0.297785i
$619$		−	1.73992e14i		−	1.91459i	−0.289112	−	0.957295i	$-0.593360\pi$
$619$		−	1.73992e14i		−	1.91459i	0.289112	−	0.957295i	$-0.406640\pi$
$620$	1.27705e13	−	4.60519e13i	0.139396	−	0.502677i
$621$	1.22879e13			0.133051
$622$	−9.74827e13	−	1.32660e13i	−1.04707	−	0.142491i
$623$		−	2.40279e12i		−	0.0256021i
$624$	9.70367e12	−	1.61508e13i	0.102568	−	0.170715i
$625$	6.56041e12			0.0687909
$626$	1.31163e13	−	9.63824e13i	0.136439	−	1.00260i
$627$			8.13292e13i			0.839283i
$628$	1.45016e12	+	4.02140e11i	0.0148463	+	0.00411698i
$629$	−1.92832e14			−1.95851
$630$	−2.81557e12	−	3.83158e11i	−0.0283702	−	0.00386078i
$631$		−	7.14723e13i		−	0.714482i	−0.934012	−	0.357241i	$-0.883718\pi$
$631$		−	7.14723e13i		−	0.714482i	0.934012	−	0.357241i	$-0.116282\pi$
$632$	1.06640e14	+	4.58130e13i	1.05763	+	0.454364i
$633$	1.38446e13			0.136226
$634$	6.20592e12	−	4.56030e13i	0.0605842	−	0.445192i
$635$			1.09452e14i			1.06012i
$636$	9.02358e9	−	3.25401e10i	8.67148e−5	−	0.000312703i
$637$	−3.54197e13			−0.337713
$638$	−2.42648e14	−	3.30209e13i	−2.29548	−	0.312382i
$639$			1.88509e13i			0.176941i
$640$	−5.16705e13	+	3.72020e13i	−0.481219	+	0.346470i
$641$	−6.72998e13			−0.621904			−0.310952	−	0.950426i	$-0.600648\pi$
$641$	−6.72998e13			−0.621904			−0.310952	+	0.950426i	$0.600648\pi$
$642$	1.38261e13	−	1.01598e14i	0.126772	−	0.931563i
$643$		−	1.40344e14i		−	1.27685i	−0.769684	−	0.638424i	$-0.779586\pi$
$643$		−	1.40344e14i		−	1.27685i	0.769684	−	0.638424i	$-0.220414\pi$
$644$	1.06900e13	+	2.96442e12i	0.0965050	+	0.0267615i
$645$	5.83114e13			0.522342
$646$	2.10868e14	+	2.86961e13i	1.87433	+	0.255070i
$647$		−	9.16479e13i		−	0.808353i	−0.914681	−	0.404177i	$-0.867558\pi$
$647$		−	9.16479e13i		−	0.808353i	0.914681	−	0.404177i	$-0.132442\pi$
$648$	5.01098e12	−	1.16642e13i	0.0438579	−	0.102089i
$649$	−1.25123e14			−1.08671
$650$	−3.49934e12	+	2.57143e13i	−0.0301592	+	0.221619i
$651$			8.60249e12i			0.0735731i
$652$	3.13752e12	−	1.13143e13i	0.0266286	−	0.0960258i
$653$	−1.03471e14			−0.871468			−0.435734	−	0.900076i	$-0.643511\pi$
$653$	−1.03471e14			−0.871468			−0.435734	+	0.900076i	$0.643511\pi$
$654$	6.22839e13	+	8.47595e12i	0.520580	+	0.0708434i
$655$			6.61795e12i			0.0548930i
$656$	4.00451e13	+	2.40597e13i	0.329632	+	0.198048i
$657$	−1.11450e13			−0.0910442
$658$	−1.19800e12	+	8.80325e12i	−0.00971239	+	0.0713697i
$659$		−	2.24945e13i		−	0.180987i	−0.995897	−	0.0904937i	$-0.971155\pi$
$659$		−	2.24945e13i		−	0.180987i	0.995897	−	0.0904937i	$-0.0288445\pi$
$660$	5.45404e13	+	1.51244e13i	0.435511	+	0.120770i
$661$	−5.60873e13			−0.444485			−0.222242	−	0.974991i	$-0.571338\pi$
$661$	−5.60873e13			−0.444485			−0.222242	+	0.974991i	$0.571338\pi$
$662$	7.71134e12	+	1.04940e12i	0.0606513	+	0.00825377i
$663$			4.38270e13i			0.342117i
$664$	−2.53345e13	−	1.08838e13i	−0.196278	−	0.0843220i
$665$	1.23008e13			0.0945854
$666$	6.71471e12	−	4.93418e13i	0.0512456	−	0.376568i
$667$		−	1.60168e14i		−	1.21324i
$668$	−4.77047e13	+	1.72029e14i	−0.358657	+	1.29336i
$669$	7.47715e13			0.557963
$670$	1.06688e14	+	1.45188e13i	0.790211	+	0.107536i
$671$			3.18064e14i			2.33831i
$672$	7.17333e12	−	8.93853e12i	0.0523449	−	0.0652259i
$673$	1.36452e14			0.988335			0.494168	−	0.869367i	$-0.335473\pi$
$673$	1.36452e14			0.988335			0.494168	+	0.869367i	$0.335473\pi$
$674$	3.43731e12	−	2.52584e13i	0.0247127	−	0.181596i
$675$			1.74852e13i			0.124782i
$676$	1.19847e14	+	3.32343e13i	0.848970	+	0.235425i
$677$	−6.91010e13			−0.485894			−0.242947	−	0.970040i	$-0.578114\pi$
$677$	−6.91010e13			−0.485894			−0.242947	+	0.970040i	$0.578114\pi$
$678$	8.16480e13	+	1.11111e13i	0.569898	+	0.0775549i
$679$			1.33871e13i			0.0927553i
$680$	5.84581e13	−	1.36074e14i	0.402069	−	0.935904i
$681$	−4.96067e13			−0.338692
$682$	2.31051e13	−	1.69783e14i	0.156598	−	1.15073i
$683$		−	9.80687e13i		−	0.659822i	−0.944012	−	0.329911i	$-0.892981\pi$
$683$		−	9.80687e13i		−	0.659822i	0.944012	−	0.329911i	$-0.107019\pi$
$684$	−1.46855e13	+	5.29574e13i	−0.0980860	+	0.353709i
$685$	−8.38095e13			−0.555700
$686$	−4.31540e13	−	5.87264e12i	−0.284054	−	0.0386557i
$687$			3.98370e13i			0.260317i
$688$	−1.21127e14	+	2.01604e14i	−0.785775	+	1.30785i
$689$	−3.01047e10			−0.000193883
$690$	−4.99168e12	+	3.66804e13i	−0.0319155	+	0.234525i
$691$			2.32217e14i			1.47402i	0.675881	+	0.737010i	$0.263763\pi$
$691$			2.32217e14i			1.47402i	−0.675881	+	0.737010i	$0.736237\pi$
$692$	2.77990e14	+	7.70886e13i	1.75186	+	0.485802i
$693$	−1.01881e13			−0.0637424
$694$	4.56468e13	+	6.21188e12i	0.283539	+	0.0385856i
$695$		−	9.02117e13i		−	0.556338i
$696$	−1.52038e14	−	6.53161e13i	−0.930904	−	0.399921i
$697$	−1.08667e14			−0.660591
$698$	1.25903e13	−	9.25173e13i	0.0759903	−	0.558400i
$699$		−	1.68377e13i		−	0.100901i
$700$	−4.21826e12	+	1.52115e13i	−0.0250982	+	0.0905070i
$701$	−6.91070e13			−0.408255			−0.204128	−	0.978944i	$-0.565436\pi$
$701$	−6.91070e13			−0.408255			−0.204128	+	0.978944i	$0.565436\pi$
$702$	−1.12144e13	−	1.52612e12i	−0.0657796	−	0.00895167i
$703$			2.15567e14i			1.25547i
$704$	−1.65584e14	+	1.57149e14i	−0.957538	+	0.908759i
$705$	−2.96470e13			−0.170229
$706$	−3.73306e12	+	2.74317e13i	−0.0212834	+	0.156397i
$707$		−	8.45749e12i		−	0.0478789i
$708$	−8.14737e13	−	2.25932e13i	−0.457985	−	0.127002i
$709$	1.78425e14			0.995919			0.497960	−	0.867200i	$-0.334083\pi$
$709$	1.78425e14			0.995919			0.497960	+	0.867200i	$0.334083\pi$
$710$	−5.62717e13	−	7.65777e12i	−0.311888	−	0.0424434i
$711$		−	6.97172e13i		−	0.383700i
$712$	−1.27653e13	+	2.97140e13i	−0.0697638	+	0.162391i
$713$	1.12071e14			0.608199
$714$	−3.59477e12	+	2.64155e13i	−0.0193722	+	0.142353i
$715$		−	5.04586e13i		−	0.270026i
$716$	7.17700e13	−	2.58811e14i	0.381398	−	1.37536i
$717$	−1.09907e14			−0.580003
$718$	−1.96917e14	−	2.67975e13i	−1.03195	−	0.140434i
$719$			1.65491e14i			0.861250i	0.902531	+	0.430625i	$0.141707\pi$
$719$			1.65491e14i			0.861250i	−0.902531	+	0.430625i	$0.858293\pi$
$720$	3.27830e13	+	1.96965e13i	0.169428	+	0.101795i
$721$	1.46913e13			0.0754021
$722$	5.62387e12	−	4.13260e13i	0.0286648	−	0.210638i
$723$		−	1.87706e14i		−	0.950137i
$724$	−9.99231e13	−	2.77094e13i	−0.502311	−	0.139294i
$725$	2.27912e14			1.13783
$726$	8.56967e13	+	1.16621e13i	0.424895	+	0.0578221i
$727$		−	2.18165e14i		−	1.07427i	−0.843496	−	0.537136i	$-0.819506\pi$
$727$		−	2.18165e14i		−	1.07427i	0.843496	−	0.537136i	$-0.180494\pi$
$728$	−9.38798e12	−	4.03312e12i	−0.0459108	−	0.0197235i
$729$	−7.62560e12			−0.0370370
$730$	4.52740e12	−	3.32687e13i	0.0218391	−	0.160480i
$731$		−	5.47074e14i		−	2.62095i
$732$	−5.74323e13	+	2.07107e14i	−0.273275	+	0.985462i
$733$	7.83266e13			0.370160			0.185080	−	0.982723i	$-0.440746\pi$
$733$	7.83266e13			0.370160			0.185080	+	0.982723i	$0.440746\pi$
$734$	−2.43240e14	−	3.31015e13i	−1.14171	−	0.155370i
$735$		−	7.18951e13i		−	0.335168i
$736$	−1.16449e14	−	9.34522e13i	−0.539195	−	0.432714i
$737$	3.86052e14			1.77545
$738$	3.78394e12	−	2.78056e13i	0.0172847	−	0.127014i
$739$			1.41277e14i			0.640986i	0.947251	+	0.320493i	$0.103849\pi$
$739$			1.41277e14i			0.640986i	−0.947251	+	0.320493i	$0.896151\pi$
$740$	1.44562e14	+	4.00880e13i	0.651471	+	0.180657i
$741$	4.89941e13			0.219307
$742$	−1.81448e10	−	2.46924e9i	−8.06737e−5	−	1.09785e-5i
$743$		−	1.49514e14i		−	0.660297i	−0.943929	−	0.330148i	$-0.892901\pi$
$743$		−	1.49514e14i		−	0.660297i	0.943929	−	0.330148i	$-0.107099\pi$
$744$	4.57023e13	−	1.06382e14i	0.200481	−	0.466664i
$745$	−4.38939e13			−0.191259
$746$	−4.91037e13	+	3.60829e14i	−0.212530	+	1.56174i
$747$			1.65627e13i			0.0712081i
$748$	1.41897e14	−	5.11695e14i	0.605988	−	2.18526i
$749$	−5.56035e13			−0.235881
$750$	−1.32695e14	−	1.80578e13i	−0.559174	−	0.0760955i
$751$			3.69403e14i			1.54632i	0.634209	+	0.773162i	$0.281326\pi$
$751$			3.69403e14i			1.54632i	−0.634209	+	0.773162i	$0.718674\pi$
$752$	6.15839e13	−	1.02500e14i	0.256081	−	0.426223i
$753$	4.38305e13			0.181051
$754$	−1.98924e13	+	1.46175e14i	−0.0816262	+	0.599815i
$755$			1.47397e14i			0.600833i
$756$	−6.63400e12	−	1.83965e12i	−0.0268637	−	0.00744950i
$757$	1.52146e14			0.612041			0.306021	−	0.952025i	$-0.401002\pi$
$757$	1.52146e14			0.612041			0.306021	+	0.952025i	$0.401002\pi$
$758$	1.84517e14	+	2.51101e13i	0.737377	+	0.100346i
$759$			1.32728e14i			0.526932i
$760$	−1.52117e14	−	6.53501e13i	−0.599942	−	0.257738i
$761$	−2.44813e14			−0.959204			−0.479602	−	0.877486i	$-0.659219\pi$
$761$	−2.44813e14			−0.959204			−0.479602	+	0.877486i	$0.659219\pi$
$762$	−3.57572e13	+	2.62755e14i	−0.139184	+	1.02277i
$763$		−	3.40872e13i		−	0.131816i
$764$	−9.15801e13	+	3.30248e14i	−0.351831	+	1.26874i
$765$	−8.89602e13			−0.339538
$766$	−2.04563e14	−	2.78381e13i	−0.775681	−	0.105559i
$767$			7.53762e13i			0.283960i
$768$	−1.36196e14	+	7.24283e13i	−0.509752	+	0.271083i
$769$	−1.49230e14			−0.554912			−0.277456	−	0.960738i	$-0.589491\pi$
$769$	−1.49230e14			−0.554912			−0.277456	+	0.960738i	$0.589491\pi$
$770$	4.13870e12	−	3.04125e13i	0.0152901	−	0.112357i
$771$		−	1.10786e14i		−	0.406642i
$772$	−1.15226e14	−	3.19529e13i	−0.420207	−	0.116526i
$773$	2.92433e12			0.0105957			0.00529784	−	0.999986i	$-0.498314\pi$
$773$	2.92433e12			0.0105957			0.00529784	+	0.999986i	$0.498314\pi$
$774$	1.39985e14	+	1.90499e13i	0.503937	+	0.0685787i
$775$			1.59473e14i			0.570398i
$776$	7.11217e13	−	1.65551e14i	0.252751	−	0.588334i
$777$	−2.70041e13			−0.0953509
$778$	2.27425e13	−	1.67119e14i	0.0797884	−	0.586310i
$779$			1.21478e14i			0.423459i
$780$	9.11122e12	−	3.28561e13i	0.0315576	−	0.113800i
$781$	−2.03619e14			−0.700751
$782$	3.44134e14	+	4.68317e13i	1.17678	+	0.160142i
$783$			9.93965e13i			0.337724i
$784$	2.48568e14	+	1.49343e14i	0.839198	+	0.504203i
$785$	2.72325e12			0.00913564
$786$	−2.16204e12	+	1.58873e13i	−0.00720694	+	0.0529589i
$787$			5.11769e13i			0.169512i	0.996402	+	0.0847559i	$0.0270111\pi$
$787$			5.11769e13i			0.169512i	−0.996402	+	0.0847559i	$0.972989\pi$
$788$	−1.77813e14	−	4.93088e13i	−0.585238	−	0.162291i
$789$	−1.06573e13			−0.0348548
$790$	2.08112e14	+	2.83210e13i	0.676334	+	0.0920394i
$791$		−	4.46849e13i		−	0.144304i
$792$	1.25991e14	+	5.41264e13i	0.404310	+	0.173693i
$793$	1.91607e14			0.611007
$794$	−5.83279e13	+	4.28611e14i	−0.184830	+	1.35819i
$795$		−	6.11067e10i		−	0.000192421i
$796$	6.53489e13	−	2.35655e14i	0.204490	−	0.737415i
$797$	1.02021e14			0.317246			0.158623	−	0.987339i	$-0.449294\pi$
$797$	1.02021e14			0.317246			0.158623	+	0.987339i	$0.449294\pi$
$798$	2.95298e13	+	4.01858e12i	0.0912527	+	0.0124182i
$799$			2.78146e14i			0.854160i
$800$	1.32979e14	−	1.65702e14i	0.405819	−	0.505683i
$801$	1.94259e13			0.0589140
$802$	1.19609e13	−	8.78923e13i	0.0360488	−	0.264898i
$803$		−	1.20383e14i		−	0.360568i
$804$	2.51378e14	+	6.97088e13i	0.748250	+	0.207495i
$805$	2.00747e13			0.0593841
$806$	−1.02280e14	−	1.39189e13i	−0.300689	−	0.0409194i
$807$		−	2.24122e14i		−	0.654811i
$808$	−4.49320e13	+	1.04589e14i	−0.130466	+	0.303689i
$809$	−4.30247e14			−1.24158			−0.620791	−	0.783976i	$-0.713189\pi$
$809$	−4.30247e14			−1.24158			−0.620791	+	0.783976i	$0.713189\pi$
$810$	3.09773e12	−	2.27631e13i	0.00888420	−	0.0652839i
$811$		−	2.72879e14i		−	0.777795i	−0.921281	−	0.388897i	$-0.872856\pi$
$811$		−	2.72879e14i		−	0.777795i	0.921281	−	0.388897i	$-0.127144\pi$
$812$	−2.39791e13	+	8.64714e13i	−0.0679287	+	0.244958i
$813$	2.65758e14			0.748227
$814$	5.32968e14	+	7.25293e13i	1.49135	+	0.202951i
$815$		−	2.12469e13i		−	0.0590892i
$816$	1.84792e14	−	3.07568e14i	0.510777	−	0.850140i
$817$	−6.11572e14			−1.68011
$818$	3.17055e13	−	2.32982e14i	0.0865701	−	0.636144i
$819$			6.13751e12i			0.0166561i
$820$	8.14649e13	+	2.25908e13i	0.219736	+	0.0609343i
$821$	−4.65671e14			−1.24843			−0.624214	−	0.781254i	$-0.714581\pi$
$821$	−4.65671e14			−1.24843			−0.624214	+	0.781254i	$0.714581\pi$
$822$	−2.01197e14	−	2.73800e13i	−0.536120	−	0.0729583i
$823$		−	5.44019e14i		−	1.44084i	−0.693540	−	0.720418i	$-0.743950\pi$
$823$		−	5.44019e14i		−	1.44084i	0.693540	−	0.720418i	$-0.256050\pi$
$824$	−1.81679e14	−	7.80502e13i	−0.478266	−	0.205465i
$825$	−1.88867e14			−0.494182
$826$	−6.18249e12	+	4.54308e13i	−0.0160791	+	0.118155i
$827$			8.68795e13i			0.224590i	0.993675	+	0.112295i	$0.0358201\pi$
$827$			8.68795e13i			0.224590i	−0.993675	+	0.112295i	$0.964180\pi$
$828$	−2.39665e13	+	8.64260e13i	−0.0615819	+	0.222071i
$829$	3.28567e14			0.839172			0.419586	−	0.907716i	$-0.362175\pi$
$829$	3.28567e14			0.839172			0.419586	+	0.907716i	$0.362175\pi$
$830$	−4.94412e13	−	6.72824e12i	−0.125516	−	0.0170809i
$831$		−	2.27666e14i		−	0.574504i
$832$	9.46693e13	+	9.97508e13i	0.237461	+	0.250207i
$833$	−6.74515e14			−1.68177
$834$	2.94716e13	−	2.16566e14i	0.0730420	−	0.536736i
$835$			3.23051e14i			0.795864i
$836$	−5.72022e14	−	1.58626e14i	−1.40082	−	0.388456i
$837$	−6.95487e13			−0.169302
$838$	−3.51808e14	−	4.78761e13i	−0.851307	−	0.115851i
$839$			1.23425e14i			0.296889i	0.988921	+	0.148445i	$0.0474267\pi$
$839$			1.23425e14i			0.296889i	−0.988921	+	0.148445i	$0.952573\pi$
$840$	8.18644e12	−	1.90557e13i	0.0195749	−	0.0455648i
$841$	8.74884e14			2.07956
$842$	7.32326e13	−	5.38136e14i	0.173039	−	1.27154i
$843$			8.85887e13i			0.208085i
$844$	−2.70027e13	+	9.73748e13i	−0.0630514	+	0.227371i
$845$	2.25059e14			0.522412
$846$	−7.11719e13	−	9.68547e12i	−0.164232	−	0.0223496i
$847$		−	4.69007e13i		−	0.107588i
$848$	2.11268e11	+	1.26933e11i	0.000481787	+	0.000289465i
$849$	3.86432e14			0.876060
$850$	−6.66397e13	+	4.89689e14i	−0.150189	+	1.10364i
$851$			3.51803e14i			0.788227i
$852$	−1.32587e14	−	3.67672e13i	−0.295326	−	0.0818959i
$853$	−7.23259e14			−1.60158			−0.800790	−	0.598945i	$-0.795587\pi$
$853$	−7.23259e14			−1.60158			−0.800790	+	0.598945i	$0.795587\pi$
$854$	1.15486e14	+	1.57160e13i	0.254237	+	0.0345981i
$855$			9.94483e13i			0.217654i
$856$	6.87619e14	+	2.95404e14i	1.49616	+	0.642759i
$857$	6.24287e14			1.35045			0.675227	−	0.737610i	$-0.264046\pi$
$857$	6.24287e14			1.35045			0.675227	+	0.737610i	$0.264046\pi$
$858$	1.64845e13	−	1.21133e14i	0.0354519	−	0.260511i
$859$		−	3.52746e14i		−	0.754217i	−0.926169	−	0.377109i	$-0.876918\pi$
$859$		−	3.52746e14i		−	0.754217i	0.926169	−	0.377109i	$-0.123082\pi$
$860$	−1.13732e14	+	4.10129e14i	−0.241762	+	0.871822i
$861$	−1.52176e13			−0.0321611
$862$	−7.93120e14	−	1.07932e14i	−1.66649	−	0.226785i
$863$		−	2.15411e14i		−	0.450002i	−0.974359	−	0.225001i	$-0.927761\pi$
$863$		−	2.15411e14i		−	0.450002i	0.974359	−	0.225001i	$-0.0722385\pi$
$864$	7.22656e13	+	5.79944e13i	0.150094	+	0.120453i
$865$	5.22035e14			1.07800
$866$	3.32519e13	−	2.44346e14i	0.0682696	−	0.501667i
$867$			5.51783e14i			1.12635i
$868$	−6.05049e13	−	1.67784e13i	−0.122798	−	0.0340528i
$869$	7.53054e14			1.51959
$870$	−2.96707e14	−	4.03776e13i	−0.595294	−	0.0810110i
$871$		−	2.32565e14i		−	0.463930i
$872$	−1.81095e14	+	4.21538e14i	−0.359189	+	0.836092i
$873$	−1.08231e14			−0.213443
$874$	5.23530e13	−	3.84706e14i	0.102656	−	0.754348i
$875$			7.26220e13i			0.141588i
$876$	2.17373e13	−	7.83873e13i	0.0421392	−	0.151959i
$877$	−3.21606e14			−0.619906			−0.309953	−	0.950752i	$-0.600313\pi$
$877$	−3.21606e14			−0.619906			−0.309953	+	0.950752i	$0.600313\pi$
$878$	5.09857e14	+	6.93843e13i	0.977183	+	0.132981i
$879$			3.66917e14i			0.699235i
$880$	−2.12753e14	+	3.54107e14i	−0.403146	+	0.670998i
$881$	3.20355e14			0.603605			0.301802	−	0.953371i	$-0.402412\pi$
$881$	3.20355e14			0.603605			0.301802	+	0.953371i	$0.402412\pi$
$882$	2.34876e13	−	1.72595e14i	0.0440045	−	0.323358i
$883$			4.36275e13i			0.0812750i	0.999174	+	0.0406375i	$0.0129389\pi$
$883$			4.36275e13i			0.0812750i	−0.999174	+	0.0406375i	$0.987061\pi$
$884$	−3.08254e14	−	8.54809e13i	−0.571015	−	0.158346i
$885$	−1.52999e14			−0.281820
$886$	−4.70050e13	−	6.39671e12i	−0.0860946	−	0.0117162i
$887$		−	3.04320e14i		−	0.554258i	−0.960833	−	0.277129i	$-0.910617\pi$
$887$		−	3.04320e14i		−	0.554258i	0.960833	−	0.277129i	$-0.0893830\pi$
$888$	3.33945e14	+	1.43464e14i	0.604798	+	0.259824i
$889$	1.43802e14			0.258975
$890$	−7.89133e12	+	5.79880e13i	−0.0141319	+	0.103846i
$891$		−	8.23683e13i		−	0.146680i
$892$	−1.45836e14	+	5.25900e14i	−0.258249	+	0.931277i
$893$	3.10939e14			0.547542
$894$	−1.05374e14	−	1.43398e13i	−0.184520	−	0.0251106i
$895$		−	4.86019e14i		−	0.846326i
$896$	4.88775e13	+	6.78869e13i	0.0846387	+	0.117556i
$897$	7.99578e13			0.137689
$898$	−5.29094e13	+	3.88795e14i	−0.0906048	+	0.665792i
$899$			9.06539e14i			1.54379i
$900$	−1.22981e14	−	3.41034e13i	−0.208269	−	0.0577545i
$901$	−5.73299e11			−0.000965512
$902$	3.00343e14	+	4.08724e13i	0.503020	+	0.0684538i
$903$		−	7.66119e13i		−	0.127602i
$904$	−2.37397e14	+	5.52593e14i	−0.393217	+	0.915300i
$905$	−1.87645e14			−0.309096
$906$	−4.81536e13	+	3.53848e14i	−0.0788838	+	0.579663i
$907$		−	2.76676e14i		−	0.450749i	−0.974272	−	0.225375i	$-0.927639\pi$
$907$		−	2.76676e14i		−	0.450749i	0.974272	−	0.225375i	$-0.0723606\pi$
$908$	9.67537e13	−	3.48905e14i	0.156761	−	0.565298i
$909$	6.83764e13			0.110176
$910$	−1.83210e13	−	2.49322e12i	−0.0293591	−	0.00399535i
$911$			4.20982e13i			0.0670922i	0.999437	+	0.0335461i	$0.0106801\pi$
$911$			4.20982e13i			0.0670922i	−0.999437	+	0.0335461i	$0.989320\pi$
$912$	−3.43829e14	−	2.06578e14i	−0.544965	−	0.327424i
$913$	−1.78903e14			−0.282010
$914$	5.33177e13	−	3.91795e14i	0.0835874	−	0.614226i
$915$			3.88925e14i			0.606402i
$916$	−2.80190e14	−	7.76987e13i	−0.434486	−	0.120486i
$917$	8.69494e12			0.0134097
$918$	−2.13562e14	−	2.90627e13i	−0.327575	−	0.0445782i
$919$		−	1.17382e15i		−	1.79071i	−0.445357	−	0.895353i	$-0.646923\pi$
$919$		−	1.17382e15i		−	1.79071i	0.445357	−	0.895353i	$-0.353077\pi$
$920$	−2.48253e14	−	1.06651e14i	−0.376666	−	0.161817i
$921$	6.39419e13			0.0964912
$922$	1.11289e14	−	8.17788e14i	0.167032	−	1.22740i
$923$			1.22664e14i			0.183108i
$924$	1.98711e13	−	7.16575e13i	0.0295027	−	0.106390i
$925$	−5.00602e14			−0.739237
$926$	3.25066e14	+	4.42369e13i	0.477438	+	0.0649725i
$927$			1.18775e14i			0.173511i
$928$	7.55932e14	−	9.41952e14i	1.09836	−	1.36864i
$929$	−8.61070e14			−1.24440			−0.622200	−	0.782859i	$-0.713761\pi$
$929$	−8.61070e14			−1.24440			−0.622200	+	0.782859i	$0.713761\pi$
$930$	2.82526e13	−	2.07609e14i	0.0406110	−	0.298423i
$931$			7.54039e14i			1.07807i
$932$	1.18426e14	+	3.28404e13i	0.168410	+	0.0467013i
$933$	−4.31328e14			−0.610098
$934$	−2.57690e14	−	3.50680e13i	−0.362547	−	0.0493374i
$935$		−	9.60908e14i		−	1.34469i
$936$	3.26067e13	−	7.58992e13i	0.0453866	−	0.105647i
$937$	−4.94841e14			−0.685121			−0.342561	−	0.939496i	$-0.611294\pi$
$937$	−4.94841e14			−0.685121			−0.342561	+	0.939496i	$0.611294\pi$
$938$	1.90754e13	−	1.40172e14i	0.0262699	−	0.193039i
$939$		−	4.26460e14i		−	0.584185i
$940$	5.78239e13	−	2.08520e14i	0.0787895	−	0.284124i
$941$	9.39655e14			1.27356			0.636781	−	0.771045i	$-0.280265\pi$
$941$	9.39655e14			1.27356			0.636781	+	0.771045i	$0.280265\pi$
$942$	6.53755e12	+	8.89667e11i	0.00881375	+	0.00119942i
$943$			1.98251e14i			0.265863i
$944$	3.17815e14	−	5.28973e14i	0.423950	−	0.705624i
$945$	−1.24579e13			−0.0165305
$946$	−2.05769e14	+	1.51206e15i	−0.271597	+	1.99578i
$947$			2.97425e14i			0.390506i	0.980753	+	0.195253i	$0.0625528\pi$
$947$			2.97425e14i			0.390506i	−0.980753	+	0.195253i	$0.937447\pi$
$948$	4.90350e14	+	1.35978e14i	0.640420	+	0.177593i
$949$	−7.25208e13			−0.0942175
$950$	5.47422e14	+	7.44963e13i	0.707464	+	0.0962757i
$951$		−	2.01778e14i		−	0.259401i
$952$	−1.78780e14	−	7.68047e13i	−0.228630	−	0.0982207i
$953$	−3.72569e14			−0.473961			−0.236980	−	0.971514i	$-0.576158\pi$
$953$	−3.72569e14			−0.473961			−0.236980	+	0.971514i	$0.576158\pi$
$954$	1.99632e10	−	1.46696e11i	2.52631e−5	−	0.000185641i
$955$			6.20171e14i			0.780718i
$956$	2.14365e14	−	7.73024e14i	0.268450	−	0.968063i
$957$	−1.07364e15			−1.33751
$958$	1.45506e15	+	1.98013e14i	1.80324	+	0.245395i
$959$			1.10112e14i			0.135751i
$960$	−2.02475e14	+	1.92160e14i	−0.248321	+	0.235672i
$961$	1.85314e14			0.226095
$962$	4.36929e13	−	3.21069e14i	0.0530317	−	0.389693i
$963$		−	4.49539e14i		−	0.542795i
$964$	1.32021e15	+	3.66105e14i	1.58584	+	0.439764i
$965$	−2.16381e14			−0.258573
$966$	4.81923e13	+	6.55828e12i	0.0572918	+	0.00779659i
$967$			9.73265e14i			1.15106i	0.817780	+	0.575531i	$0.195205\pi$
$967$			9.73265e14i			1.15106i	−0.817780	+	0.575531i	$0.804795\pi$
$968$	−2.49169e14	+	5.79996e14i	−0.293168	+	0.682414i
$969$	9.33018e14			1.09212
$970$	4.39665e13	−	3.23080e14i	0.0511992	−	0.376228i
$971$		−	9.36688e14i		−	1.08517i	−0.840000	−	0.542586i	$-0.817445\pi$
$971$		−	9.36688e14i		−	1.08517i	0.840000	−	0.542586i	$-0.182555\pi$
$972$	1.48731e13	−	5.36341e13i	0.0171423	−	0.0618172i
$973$	−1.18524e14			−0.135907
$974$	−6.55441e14	−	8.91961e13i	−0.747720	−	0.101754i
$975$			1.13777e14i			0.129131i
$976$	−1.34466e15	−	8.07891e14i	−1.51832	−	0.912229i
$977$	−4.28331e14			−0.481179			−0.240590	−	0.970627i	$-0.577341\pi$
$977$	−4.28331e14			−0.481179			−0.240590	+	0.970627i	$0.577341\pi$
$978$	6.94123e12	−	5.10064e13i	0.00775787	−	0.0570072i
$979$			2.09830e14i			0.233321i
$980$	5.05669e14	+	1.40225e14i	0.559417	+	0.155130i
$981$	2.75585e14			0.303327
$982$	−8.25817e14	−	1.12382e14i	−0.904329	−	0.123066i
$983$			8.78222e14i			0.956834i	0.878133	+	0.478417i	$0.158789\pi$
$983$			8.78222e14i			0.956834i	−0.878133	+	0.478417i	$0.841211\pi$
$984$	1.88188e14	+	8.08465e13i	0.203994	+	0.0876366i
$985$	−3.33914e14			−0.360125
$986$	−3.78820e14	+	2.78369e15i	−0.406489	+	2.98701i
$987$			3.89514e13i			0.0415851i
$988$	−9.55589e13	+	3.44596e14i	−0.101505	+	0.366038i
$989$	−9.98080e14			−1.05483
$990$	2.45877e14	+	3.34603e13i	0.258548	+	0.0351847i
$991$		−	2.73971e14i		−	0.286639i	−0.989676	−	0.143320i	$-0.954222\pi$
$991$		−	2.73971e14i		−	0.286639i	0.989676	−	0.143320i	$-0.0457777\pi$
$992$	6.59093e14	+	5.28934e14i	0.686102	+	0.550609i
$993$	3.41201e13			0.0353398
$994$	−1.00611e13	+	7.39321e13i	−0.0103684	+	0.0761905i
$995$		−	4.42535e14i		−	0.453767i
$996$	−1.16493e14	−	3.23043e13i	−0.118851	−	0.0329582i
$997$	1.30699e15			1.32678			0.663388	−	0.748276i	$-0.269118\pi$
$997$	1.30699e15			1.32678			0.663388	+	0.748276i	$0.269118\pi$
$998$	−1.40284e15	−	1.90906e14i	−1.41695	−	0.192827i
$999$		−	2.18321e14i		−	0.219416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.11.d.a.7.6	yes	10
3.2	odd	2		36.11.d.e.19.5		10
4.3	odd	2	inner	12.11.d.a.7.5	✓	10
8.3	odd	2		192.11.g.e.127.9		10
8.5	even	2		192.11.g.e.127.4		10
12.11	even	2		36.11.d.e.19.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.11.d.a.7.5	✓	10	4.3	odd	2	inner
12.11.d.a.7.6	yes	10	1.1	even	1	trivial
36.11.d.e.19.5		10	3.2	odd	2
36.11.d.e.19.6		10	12.11	even	2
192.11.g.e.127.4		10	8.5	even	2
192.11.g.e.127.9		10	8.3	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.31497 + 31.7077i) q^{2} +140.296i q^{3} +(-986.762 - 273.636i) q^{4} -1853.03 q^{5} +(-4448.47 - 605.373i) q^{6} +2434.59i q^{7} +(12934.2 - 30107.3i) q^{8} -19683.0 q^{9} +O(q^{10})\)	\(q+(-4.31497 + 31.7077i) q^{2} +140.296i q^{3} +(-986.762 - 273.636i) q^{4} -1853.03 q^{5} +(-4448.47 - 605.373i) q^{6} +2434.59i q^{7} +(12934.2 - 30107.3i) q^{8} -19683.0 q^{9} +(7995.78 - 58755.5i) q^{10} -212607. i q^{11} +(38390.1 - 138439. i) q^{12} -128078. q^{13} +(-77195.4 - 10505.2i) q^{14} -259973. i q^{15} +(898823. + 540027. i) q^{16} -2.43905e6 q^{17} +(84931.5 - 624104. i) q^{18} +2.72661e6i q^{19} +(1.82850e6 + 507056. i) q^{20} -341564. q^{21} +(6.74129e6 + 917393. i) q^{22} +4.44980e6i q^{23} +(4.22393e6 + 1.81462e6i) q^{24} -6.33190e6 q^{25} +(552653. - 4.06107e6i) q^{26} -2.76145e6i q^{27} +(666192. - 2.40236e6i) q^{28} -3.59943e7 q^{29} +(8.24316e6 + 1.12178e6i) q^{30} -2.51856e7i q^{31} +(-2.10014e7 + 2.61694e7i) q^{32} +2.98279e7 q^{33} +(1.05244e7 - 7.73369e7i) q^{34} -4.51138e6i q^{35} +(1.94224e7 + 5.38598e6i) q^{36} +7.90603e7 q^{37} +(-8.64547e7 - 1.17652e7i) q^{38} -1.79689e7i q^{39} +(-2.39675e7 + 5.57897e7i) q^{40} +4.45528e7 q^{41} +(1.47384e6 - 1.08302e7i) q^{42} +2.24298e8i q^{43} +(-5.81769e7 + 2.09793e8i) q^{44} +3.64732e7 q^{45} +(-1.41093e8 - 1.92008e7i) q^{46} -1.14039e8i q^{47} +(-7.57637e7 + 1.26101e8i) q^{48} +2.76548e8 q^{49} +(2.73219e7 - 2.00770e8i) q^{50} -3.42190e8i q^{51} +(1.26383e8 + 3.50468e7i) q^{52} +235050. q^{53} +(8.75593e7 + 1.19156e7i) q^{54} +3.93968e8i q^{55} +(7.32989e7 + 3.14895e7i) q^{56} -3.82533e8 q^{57} +(1.55314e8 - 1.14130e9i) q^{58} -5.88517e8i q^{59} +(-7.11380e7 + 2.56532e8i) q^{60} -1.49602e9 q^{61} +(7.98579e8 + 1.08675e8i) q^{62} -4.79201e7i q^{63} +(-7.39153e8 - 7.78828e8i) q^{64} +2.37333e8 q^{65} +(-1.28707e8 + 9.45776e8i) q^{66} +1.81580e9i q^{67} +(2.40677e9 + 6.67413e8i) q^{68} -6.24290e8 q^{69} +(1.43046e8 + 1.94664e7i) q^{70} -9.57727e8i q^{71} +(-2.54584e8 + 5.92601e8i) q^{72} +5.66223e8 q^{73} +(-3.41143e8 + 2.50682e9i) q^{74} -8.88341e8i q^{75} +(7.46099e8 - 2.69052e9i) q^{76} +5.17611e8 q^{77} +(5.69752e8 + 7.75351e7i) q^{78} +3.54200e9i q^{79} +(-1.66555e9 - 1.00069e9i) q^{80} +3.87420e8 q^{81} +(-1.92244e8 + 1.41267e9i) q^{82} -8.41475e8i q^{83} +(3.37042e8 + 9.34641e7i) q^{84} +4.51964e9 q^{85} +(-7.11197e9 - 9.67838e8i) q^{86} -5.04986e9i q^{87} +(-6.40102e9 - 2.74991e9i) q^{88} -9.86937e8 q^{89} +(-1.57381e8 + 1.15648e9i) q^{90} -3.11818e8i q^{91} +(1.21763e9 - 4.39090e9i) q^{92} +3.53344e9 q^{93} +(3.61590e9 + 4.92073e8i) q^{94} -5.05250e9i q^{95} +(-3.67147e9 - 2.94642e9i) q^{96} +5.49872e9 q^{97} +(-1.19330e9 + 8.76871e9i) q^{98} +4.18474e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9}+O(q^{10}) \) 10 * q + 22 * q^2 - 644 * q^4 + 3116 * q^5 + 2430 * q^6 + 20176 * q^8 - 196830 * q^9	\( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9} - 369196 q^{10} + 310068 q^{12} - 285100 q^{13} - 2495544 q^{14} + 3590128 q^{16} + 2264420 q^{17} - 433026 q^{18} + 1194248 q^{20} + 3555576 q^{21} - 2139528 q^{22} - 6858432 q^{24} + 23043438 q^{25} + 29599340 q^{26} - 41542224 q^{28} - 46672708 q^{29} + 19963908 q^{30} - 83717408 q^{32} + 22665096 q^{33} + 37514588 q^{34} + 12675852 q^{36} - 194467900 q^{37} - 218769048 q^{38} + 340155488 q^{40} + 276227780 q^{41} - 15919416 q^{42} + 532887504 q^{44} - 61332228 q^{45} - 70057824 q^{46} + 27126576 q^{48} + 653625226 q^{49} + 20815602 q^{50} - 959132296 q^{52} - 1522721956 q^{53} - 47829690 q^{54} - 632703744 q^{56} + 844537752 q^{57} + 1851304388 q^{58} - 1708229736 q^{60} - 3488124604 q^{61} - 806085192 q^{62} - 877634432 q^{64} + 6725245912 q^{65} + 1244885112 q^{66} + 3081993176 q^{68} - 1698239520 q^{69} + 598086768 q^{70} - 397124208 q^{72} + 3090518708 q^{73} - 9824720260 q^{74} + 2750616432 q^{76} - 4577505312 q^{77} + 4510566972 q^{78} + 16715013152 q^{80} + 3874204890 q^{81} + 830592764 q^{82} - 10263359664 q^{84} - 3285444680 q^{85} - 15186172488 q^{86} - 12375555840 q^{88} - 13670065996 q^{89} + 7266884868 q^{90} + 12601016256 q^{92} + 3947087880 q^{93} + 38474881584 q^{94} - 27853204320 q^{96} - 18805077484 q^{97} - 31671844202 q^{98}+O(q^{100}) \) 10 * q + 22 * q^2 - 644 * q^4 + 3116 * q^5 + 2430 * q^6 + 20176 * q^8 - 196830 * q^9 - 369196 * q^10 + 310068 * q^12 - 285100 * q^13 - 2495544 * q^14 + 3590128 * q^16 + 2264420 * q^17 - 433026 * q^18 + 1194248 * q^20 + 3555576 * q^21 - 2139528 * q^22 - 6858432 * q^24 + 23043438 * q^25 + 29599340 * q^26 - 41542224 * q^28 - 46672708 * q^29 + 19963908 * q^30 - 83717408 * q^32 + 22665096 * q^33 + 37514588 * q^34 + 12675852 * q^36 - 194467900 * q^37 - 218769048 * q^38 + 340155488 * q^40 + 276227780 * q^41 - 15919416 * q^42 + 532887504 * q^44 - 61332228 * q^45 - 70057824 * q^46 + 27126576 * q^48 + 653625226 * q^49 + 20815602 * q^50 - 959132296 * q^52 - 1522721956 * q^53 - 47829690 * q^54 - 632703744 * q^56 + 844537752 * q^57 + 1851304388 * q^58 - 1708229736 * q^60 - 3488124604 * q^61 - 806085192 * q^62 - 877634432 * q^64 + 6725245912 * q^65 + 1244885112 * q^66 + 3081993176 * q^68 - 1698239520 * q^69 + 598086768 * q^70 - 397124208 * q^72 + 3090518708 * q^73 - 9824720260 * q^74 + 2750616432 * q^76 - 4577505312 * q^77 + 4510566972 * q^78 + 16715013152 * q^80 + 3874204890 * q^81 + 830592764 * q^82 - 10263359664 * q^84 - 3285444680 * q^85 - 15186172488 * q^86 - 12375555840 * q^88 - 13670065996 * q^89 + 7266884868 * q^90 + 12601016256 * q^92 + 3947087880 * q^93 + 38474881584 * q^94 - 27853204320 * q^96 - 18805077484 * q^97 - 31671844202 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more