LMFDB - Embedded newform 12.10.b.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,10,Mod(11,12)]

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, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.18043003397$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 43 x^{14} - 1652 x^{12} - 2031680 x^{10} + 40456192 x^{8} - 33287045120 x^{6} + \cdots + 72\!\cdots\!36 $ x^16 + 43x^14 - 1652x^12 - 2031680x^10 + 40456192x^8 - 33287045120x^6 - 443455373312x^4 + 189115999977472*x^2 + 72057594037927936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{68}\cdot 3^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.10
Root			$-4.10871 + 10.5413i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.10.b.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.21741 + 21.0826i) q^{2} +(12.8513 - 139.706i) q^{3} +(-376.948 + 346.488i) q^{4} +2101.02i q^{5} +(3050.97 - 877.086i) q^{6} +7674.38i q^{7} +(-10402.4 - 5099.80i) q^{8} +(-19352.7 - 3590.81i) q^{9} +O(q^{10})$	\(q+(8.21741 + 21.0826i) q^{2} +(12.8513 - 139.706i) q^{3} +(-376.948 + 346.488i) q^{4} +2101.02i q^{5} +(3050.97 - 877.086i) q^{6} +7674.38i q^{7} +(-10402.4 - 5099.80i) q^{8} +(-19352.7 - 3590.81i) q^{9} +(-44294.8 + 17264.9i) q^{10} +28827.6 q^{11} +(43562.3 + 57114.9i) q^{12} +21331.4 q^{13} +(-161796. + 63063.6i) q^{14} +(293525. + 27000.8i) q^{15} +(22036.0 - 261216. i) q^{16} +318970. i q^{17} +(-83325.6 - 437511. i) q^{18} -577462. i q^{19} +(-727977. - 791975. i) q^{20} +(1.07216e6 + 98625.7i) q^{21} +(236888. + 607760. i) q^{22} +1.91402e6 q^{23} +(-846158. + 1.38774e6i) q^{24} -2.46115e6 q^{25} +(175289. + 449720. i) q^{26} +(-750366. + 2.65755e6i) q^{27} +(-2.65908e6 - 2.89285e6i) q^{28} +355438. i q^{29} +(1.84277e6 + 6.41014e6i) q^{30} -1.35660e6i q^{31} +(5.68818e6 - 1.68195e6i) q^{32} +(370472. - 4.02740e6i) q^{33} +(-6.72470e6 + 2.62111e6i) q^{34} -1.61240e7 q^{35} +(8.53914e6 - 5.35193e6i) q^{36} +4.13622e6 q^{37} +(1.21744e7 - 4.74525e6i) q^{38} +(274136. - 2.98013e6i) q^{39} +(1.07148e7 - 2.18556e7i) q^{40} +1.09894e7i q^{41} +(6.73110e6 + 2.34143e7i) q^{42} -4.05222e6i q^{43} +(-1.08665e7 + 9.98842e6i) q^{44} +(7.54435e6 - 4.06603e7i) q^{45} +(1.57283e7 + 4.03525e7i) q^{46} -8.75484e6 q^{47} +(-3.62103e7 - 6.43553e6i) q^{48} -1.85426e7 q^{49} +(-2.02243e7 - 5.18872e7i) q^{50} +(4.45621e7 + 4.09917e6i) q^{51} +(-8.04082e6 + 7.39106e6i) q^{52} +9.53031e7i q^{53} +(-6.21939e7 + 6.01852e6i) q^{54} +6.05673e7i q^{55} +(3.91378e7 - 7.98320e7i) q^{56} +(-8.06751e7 - 7.42113e6i) q^{57} +(-7.49354e6 + 2.92078e6i) q^{58} +1.04772e8 q^{59} +(-1.19999e8 + 9.15251e7i) q^{60} +1.54207e8 q^{61} +(2.86005e7 - 1.11477e7i) q^{62} +(2.75573e7 - 1.48520e8i) q^{63} +(8.22019e7 + 1.06100e8i) q^{64} +4.48176e7i q^{65} +(8.79521e7 - 2.52843e7i) q^{66} -5.40597e7i q^{67} +(-1.10519e8 - 1.20235e8i) q^{68} +(2.45976e7 - 2.67401e8i) q^{69} +(-1.32498e8 - 3.39935e8i) q^{70} -2.40602e8 q^{71} +(1.83002e8 + 1.36048e8i) q^{72} -1.56748e8 q^{73} +(3.39890e7 + 8.72020e7i) q^{74} +(-3.16289e7 + 3.43838e8i) q^{75} +(2.00084e8 + 2.17673e8i) q^{76} +2.21234e8i q^{77} +(6.50813e7 - 1.87094e7i) q^{78} -1.04955e8i q^{79} +(5.48820e8 + 4.62980e7i) q^{80} +(3.61633e8 + 1.38984e8i) q^{81} +(-2.31684e8 + 9.03043e7i) q^{82} -5.74723e8 q^{83} +(-4.38321e8 + 3.34314e8i) q^{84} -6.70161e8 q^{85} +(8.54312e7 - 3.32988e7i) q^{86} +(4.96569e7 + 4.56784e6i) q^{87} +(-2.99876e8 - 1.47015e8i) q^{88} -8.17656e8i q^{89} +(9.19219e8 - 1.75068e8i) q^{90} +1.63705e8i q^{91} +(-7.21487e8 + 6.63186e8i) q^{92} +(-1.89525e8 - 1.74340e7i) q^{93} +(-7.19421e7 - 1.84574e8i) q^{94} +1.21326e9 q^{95} +(-1.61878e8 - 8.16290e8i) q^{96} +1.26935e9 q^{97} +(-1.52372e8 - 3.90925e8i) q^{98} +(-5.57892e8 - 1.03514e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	$ 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) $ 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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 $

$2$	8.21741	+	21.0826i	0.363162	+	0.931726i
$2$	8.21741	+	21.0826i	0.363162	+	0.931726i
$3$	12.8513	−	139.706i	0.0916012	−	0.995796i
$3$	12.8513	−	139.706i	0.0916012	−	0.995796i
$4$	−376.948	+	346.488i	−0.736227	+	0.676735i
$5$			2101.02i			1.50337i	0.659525	+	0.751683i	$0.270757\pi$
$5$			2101.02i			1.50337i	−0.659525	+	0.751683i	$0.729243\pi$
$6$	3050.97	−	877.086i	0.961075	−	0.276288i
$7$			7674.38i			1.20810i	0.796947	+	0.604049i	$0.206447\pi$
$7$			7674.38i			1.20810i	−0.796947	+	0.604049i	$0.793553\pi$
$8$	−10402.4	−	5099.80i	−0.897901	−	0.440198i
$9$	−19352.7	−	3590.81i	−0.983218	−	0.182432i
$10$	−44294.8	+	17264.9i	−1.40072	+	0.545965i
$11$	28827.6			0.593665			0.296833	−	0.954930i	$-0.404070\pi$
$11$	28827.6			0.593665			0.296833	+	0.954930i	$0.404070\pi$
$12$	43562.3	+	57114.9i	0.606450	+	0.795121i
$13$	21331.4			0.207145			0.103572	−	0.994622i	$-0.466973\pi$
$13$	21331.4			0.207145			0.103572	+	0.994622i	$0.466973\pi$
$14$	−161796.	+	63063.6i	−1.12562	+	0.438735i
$15$	293525.	+	27000.8i	1.49704	+	0.137710i
$16$	22036.0	−	261216.i	0.0840606	−	0.996461i
$17$			318970.i			0.926252i	0.886292	+	0.463126i	$0.153272\pi$
$17$			318970.i			0.926252i	−0.886292	+	0.463126i	$0.846728\pi$
$18$	−83325.6	−	437511.i	−0.187091	−	0.982343i
$19$		−	577462.i		−	1.01656i	−0.861192	−	0.508279i	$-0.830282\pi$
$19$		−	577462.i		−	1.01656i	0.861192	−	0.508279i	$-0.169718\pi$
$20$	−727977.	−	791975.i	−1.01738	−	1.10682i
$21$	1.07216e6	+	98625.7i	1.20302	+	0.110663i
$22$	236888.	+	607760.i	0.215596	+	0.553133i
$23$	1.91402e6			1.42617			0.713086	−	0.701077i	$-0.247297\pi$
$23$	1.91402e6			1.42617			0.713086	+	0.701077i	$0.247297\pi$
$24$	−846158.	+	1.38774e6i	−0.520596	+	0.853803i
$25$	−2.46115e6			−1.26011
$26$	175289.	+	449720.i	0.0752270	+	0.193002i
$27$	−750366.	+	2.65755e6i	−0.271729	+	0.962374i
$28$	−2.65908e6	−	2.89285e6i	−0.817562	−	0.889435i
$29$			355438.i			0.0933196i	0.998911	+	0.0466598i	$0.0148577\pi$
$29$			355438.i			0.0933196i	−0.998911	+	0.0466598i	$0.985142\pi$
$30$	1.84277e6	+	6.41014e6i	0.415361	+	1.44485i
$31$		−	1.35660e6i		−	0.263829i	−0.991261	−	0.131915i	$-0.957888\pi$
$31$		−	1.35660e6i		−	0.263829i	0.991261	−	0.131915i	$-0.0421125\pi$
$32$	5.68818e6	−	1.68195e6i	0.958956	−	0.283555i
$33$	370472.	−	4.02740e6i	0.0543804	−	0.591169i
$34$	−6.72470e6	+	2.62111e6i	−0.863013	+	0.336379i
$35$	−1.61240e7			−1.81621
$36$	8.53914e6	−	5.35193e6i	0.847330	−	0.531066i
$37$	4.13622e6			0.362824			0.181412	−	0.983407i	$-0.441933\pi$
$37$	4.13622e6			0.362824			0.181412	+	0.983407i	$0.441933\pi$
$38$	1.21744e7	−	4.74525e6i	0.947154	−	0.369175i
$39$	274136.	−	2.98013e6i	0.0189747	−	0.206274i
$40$	1.07148e7	−	2.18556e7i	0.661778	−	1.34987i
$41$			1.09894e7i			0.607360i	0.952774	+	0.303680i	$0.0982153\pi$
$41$			1.09894e7i			0.607360i	−0.952774	+	0.303680i	$0.901785\pi$
$42$	6.73110e6	+	2.34143e7i	0.333783	+	1.16107i
$43$		−	4.05222e6i		−	0.180753i	−0.995908	−	0.0903764i	$-0.971193\pi$
$43$		−	4.05222e6i		−	0.180753i	0.995908	−	0.0903764i	$-0.0288070\pi$
$44$	−1.08665e7	+	9.98842e6i	−0.437072	+	0.401754i
$45$	7.54435e6	−	4.06603e7i	0.274262	−	1.47814i
$46$	1.57283e7	+	4.03525e7i	0.517931	+	1.32880i
$47$	−8.75484e6			−0.261703			−0.130851	−	0.991402i	$-0.541771\pi$
$47$	−8.75484e6			−0.261703			−0.130851	+	0.991402i	$0.541771\pi$
$48$	−3.62103e7	−	6.43553e6i	−0.984571	−	0.174984i
$49$	−1.85426e7			−0.459502
$50$	−2.02243e7	−	5.18872e7i	−0.457623	−	1.17407i
$51$	4.45621e7	+	4.09917e6i	0.922358	+	0.0848458i
$52$	−8.04082e6	+	7.39106e6i	−0.152505	+	0.140182i
$53$			9.53031e7i			1.65907i	0.558452	+	0.829537i	$0.311395\pi$
$53$			9.53031e7i			1.65907i	−0.558452	+	0.829537i	$0.688605\pi$
$54$	−6.21939e7	+	6.01852e6i	−0.995350	+	0.0963203i
$55$			6.05673e7i			0.892495i
$56$	3.91378e7	−	7.98320e7i	0.531802	−	1.08475i
$57$	−8.06751e7	−	7.42113e6i	−1.01228	−	0.0931180i
$58$	−7.49354e6	+	2.92078e6i	−0.0869483	+	0.0338901i
$59$	1.04772e8			1.12567			0.562833	−	0.826570i	$-0.309711\pi$
$59$	1.04772e8			1.12567			0.562833	+	0.826570i	$0.309711\pi$
$60$	−1.19999e8	+	9.15251e7i	−1.19536	+	0.911716i
$61$	1.54207e8			1.42600			0.713000	−	0.701164i	$-0.247336\pi$
$61$	1.54207e8			1.42600			0.713000	+	0.701164i	$0.247336\pi$
$62$	2.86005e7	−	1.11477e7i	0.245817	−	0.0958127i
$63$	2.75573e7	−	1.48520e8i	0.220396	−	1.18782i
$64$	8.22019e7	+	1.06100e8i	0.612452	+	0.790508i
$65$			4.48176e7i			0.311414i
$66$	8.79521e7	−	2.52843e7i	0.570557	−	0.164022i
$67$		−	5.40597e7i		−	0.327746i	−0.986481	−	0.163873i	$-0.947601\pi$
$67$		−	5.40597e7i		−	0.327746i	0.986481	−	0.163873i	$-0.0523987\pi$
$68$	−1.10519e8	−	1.20235e8i	−0.626827	−	0.681932i
$69$	2.45976e7	−	2.67401e8i	0.130639	−	1.42018i
$70$	−1.32498e8	−	3.39935e8i	−0.659579	−	1.69221i
$71$	−2.40602e8			−1.12366			−0.561832	−	0.827252i	$-0.689903\pi$
$71$	−2.40602e8			−1.12366			−0.561832	+	0.827252i	$0.689903\pi$
$72$	1.83002e8	+	1.36048e8i	0.802526	+	0.596617i
$73$	−1.56748e8			−0.646023			−0.323012	−	0.946395i	$-0.604695\pi$
$73$	−1.56748e8			−0.646023			−0.323012	+	0.946395i	$0.604695\pi$
$74$	3.39890e7	+	8.72020e7i	0.131764	+	0.338052i
$75$	−3.16289e7	+	3.43838e8i	−0.115427	+	1.25481i
$76$	2.00084e8	+	2.17673e8i	0.687940	+	0.748418i
$77$			2.21234e8i			0.717206i
$78$	6.50813e7	−	1.87094e7i	0.199081	−	0.0572315i
$79$		−	1.04955e8i		−	0.303167i	−0.988444	−	0.151584i	$-0.951563\pi$
$79$		−	1.04955e8i		−	0.303167i	0.988444	−	0.151584i	$-0.0484373\pi$
$80$	5.48820e8	+	4.62980e7i	1.49804	+	0.126374i
$81$	3.61633e8	+	1.38984e8i	0.933437	+	0.358741i
$82$	−2.31684e8	+	9.03043e7i	−0.565893	+	0.220570i
$83$	−5.74723e8			−1.32925			−0.664626	−	0.747176i	$-0.731409\pi$
$83$	−5.74723e8			−1.32925			−0.664626	+	0.747176i	$0.731409\pi$
$84$	−4.38321e8	+	3.34314e8i	−0.960585	+	0.732652i
$85$	−6.70161e8			−1.39250
$86$	8.54312e7	−	3.32988e7i	0.168412	−	0.0656425i
$87$	4.96569e7	+	4.56784e6i	0.0929273	+	0.00854818i
$88$	−2.99876e8	−	1.47015e8i	−0.533052	−	0.261330i
$89$		−	8.17656e8i		−	1.38139i	−0.723147	−	0.690694i	$-0.757305\pi$
$89$		−	8.17656e8i		−	1.38139i	0.723147	−	0.690694i	$-0.242695\pi$
$90$	9.19219e8	−	1.75068e8i	1.47682	−	0.281265i
$91$			1.63705e8i			0.250251i
$92$	−7.21487e8	+	6.63186e8i	−1.04999	+	0.965139i
$93$	−1.89525e8	−	1.74340e7i	−0.262720	−	0.0241671i
$94$	−7.19421e7	−	1.84574e8i	−0.0950403	−	0.243835i
$95$	1.21326e9			1.52826
$96$	−1.61878e8	−	8.16290e8i	−0.194521	−	0.980898i
$97$	1.26935e9			1.45582			0.727909	−	0.685674i	$-0.240492\pi$
$97$	1.26935e9			1.45582			0.727909	+	0.685674i	$0.240492\pi$
$98$	−1.52372e8	−	3.90925e8i	−0.166874	−	0.428130i
$99$	−5.57892e8	−	1.03514e8i	−0.583702	−	0.108304i
$100$	9.27725e8	−	8.52758e8i	0.927725	−	0.852758i
$101$			4.91296e8i			0.469783i	0.972022	+	0.234891i	$0.0754735\pi$
$101$			4.91296e8i			0.469783i	−0.972022	+	0.234891i	$0.924527\pi$
$102$	2.79764e8	+	9.73167e8i	0.255912	+	0.890198i
$103$		−	1.40382e9i		−	1.22898i	−0.788925	−	0.614490i	$-0.789362\pi$
$103$		−	1.40382e9i		−	1.22898i	0.788925	−	0.614490i	$-0.210638\pi$
$104$	−2.21897e8	−	1.08786e8i	−0.185995	−	0.0911846i
$105$	−2.07214e8	+	2.25263e9i	−0.166367	+	1.80858i
$106$	−2.00923e9	+	7.83145e8i	−1.54580	+	0.602512i
$107$	2.07401e9			1.52962			0.764812	−	0.644254i	$-0.222832\pi$
$107$	2.07401e9			1.52962			0.764812	+	0.644254i	$0.222832\pi$
$108$	−6.37959e8	−	1.26175e9i	−0.451217	−	0.892414i
$109$	−2.56190e8			−0.173837			−0.0869185	−	0.996215i	$-0.527702\pi$
$109$	−2.56190e8			−0.173837			−0.0869185	+	0.996215i	$0.527702\pi$
$110$	−1.27691e9	+	4.97706e8i	−0.831561	+	0.324120i
$111$	5.31557e7	−	5.77856e8i	0.0332351	−	0.361298i
$112$	2.00467e9	+	1.69113e8i	1.20382	+	0.101554i
$113$		−	2.08057e9i		−	1.20041i	−0.799847	−	0.600204i	$-0.795086\pi$
$113$		−	2.08057e9i		−	1.20041i	0.799847	−	0.600204i	$-0.204914\pi$
$114$	−5.06484e8	−	1.76182e9i	−0.280863	−	0.976989i
$115$			4.02139e9i			2.14406i
$116$	−1.23155e8	−	1.33982e8i	−0.0631526	−	0.0687044i
$117$	−4.12819e8	−	7.65969e7i	−0.203668	−	0.0377898i
$118$	8.60952e8	+	2.20885e9i	0.408799	+	1.04881i
$119$	−2.44790e9			−1.11900
$120$	−2.91567e9	−	1.77779e9i	−1.28358	−	0.782646i
$121$	−1.52692e9			−0.647562
$122$	1.26718e9	+	3.25108e9i	0.517869	+	1.32864i
$123$	1.53529e9	+	1.41228e8i	0.604806	+	0.0556348i
$124$	4.70044e8	+	5.11366e8i	0.178542	+	0.194238i
$125$		−	1.06736e9i		−	0.391036i
$126$	3.35763e9	−	6.39472e8i	1.18677	−	0.226024i
$127$		−	3.44432e9i		−	1.17486i	−0.809275	−	0.587431i	$-0.800139\pi$
$127$		−	3.44432e9i		−	1.17486i	0.809275	−	0.587431i	$-0.199861\pi$
$128$	−1.56138e9	+	2.60489e9i	−0.514118	+	0.857719i
$129$	−5.66121e8	−	5.20763e7i	−0.179993	−	0.0165572i
$130$	−9.44869e8	+	3.68284e8i	−0.290153	+	0.113094i
$131$	−2.05126e9			−0.608556			−0.304278	−	0.952583i	$-0.598415\pi$
$131$	−2.05126e9			−0.608556			−0.304278	+	0.952583i	$0.598415\pi$
$132$	1.25580e9	+	1.64648e9i	0.360028	+	0.472036i
$133$	4.43167e9			1.22810
$134$	1.13972e9	−	4.44231e8i	0.305369	−	0.119025i
$135$	−5.58355e9	−	1.57653e9i	−1.44680	−	0.408508i
$136$	1.62668e9	−	3.31805e9i	0.407734	−	0.831683i
$137$			6.38949e8i			0.154962i	0.996994	+	0.0774808i	$0.0246876\pi$
$137$			6.38949e8i			0.154962i	−0.996994	+	0.0774808i	$0.975312\pi$
$138$	5.83962e9	−	1.67876e9i	1.37066	−	0.394034i
$139$			3.37773e9i			0.767464i	0.923445	+	0.383732i	$0.125361\pi$
$139$			3.37773e9i			0.767464i	−0.923445	+	0.383732i	$0.874639\pi$
$140$	6.07792e9	−	5.58678e9i	1.33715	−	1.22909i
$141$	−1.12511e8	+	1.22311e9i	−0.0239723	+	0.260602i
$142$	−1.97712e9	−	5.07250e9i	−0.408072	−	1.04695i
$143$	6.14932e8			0.122974
$144$	−1.36443e9	+	4.97611e9i	−0.264436	+	0.964403i
$145$	−7.46781e8			−0.140293
$146$	−1.28806e9	−	3.30464e9i	−0.234611	−	0.601917i
$147$	−2.38296e8	+	2.59051e9i	−0.0420909	+	0.457570i
$148$	−1.55914e9	+	1.43315e9i	−0.267121	+	0.245535i
$149$		−	2.50542e9i		−	0.416430i	−0.978083	−	0.208215i	$-0.933235\pi$
$149$		−	2.50542e9i		−	0.416430i	0.978083	−	0.208215i	$-0.0667655\pi$
$150$	−7.50888e9	+	2.15864e9i	−1.21106	+	0.348152i
$151$		−	7.67809e9i		−	1.20187i	−0.799298	−	0.600935i	$-0.794795\pi$
$151$		−	7.67809e9i		−	1.20187i	0.799298	−	0.600935i	$-0.205205\pi$
$152$	−2.94494e9	+	6.00699e9i	−0.447487	+	0.912769i
$153$	1.14536e9	−	6.17292e9i	0.168978	−	0.910708i
$154$	−4.66418e9	+	1.81797e9i	−0.668239	+	0.260462i
$155$	2.85023e9			0.396632
$156$	9.29243e8	+	1.21834e9i	0.125623	+	0.164705i
$157$	−7.74539e9			−1.01741			−0.508703	−	0.860942i	$-0.669875\pi$
$157$	−7.74539e9			−1.01741			−0.508703	+	0.860942i	$0.669875\pi$
$158$	2.21273e9	−	8.62461e8i	0.282469	−	0.110099i
$159$	1.33144e10	+	1.22477e9i	1.65210	+	0.151973i
$160$	3.53380e9	+	1.19510e10i	0.426287	+	1.44166i
$161$			1.46889e10i			1.72296i
$162$	4.15531e7	+	8.76623e9i	0.00474009	+	0.999989i
$163$			9.36141e9i			1.03872i	0.854557	+	0.519358i	$0.173829\pi$
$163$			9.36141e9i			1.03872i	−0.854557	+	0.519358i	$0.826171\pi$
$164$	−3.80769e9	−	4.14243e9i	−0.411021	−	0.447155i
$165$	8.46163e9	+	7.78367e8i	0.888743	+	0.0817536i
$166$	−4.72274e9	−	1.21166e10i	−0.482734	−	1.23850i
$167$	4.85295e9			0.482816			0.241408	−	0.970424i	$-0.422391\pi$
$167$	4.85295e9			0.482816			0.241408	+	0.970424i	$0.422391\pi$
$168$	−1.06501e10	−	6.49374e9i	−1.03148	−	0.628931i
$169$	−1.01495e10			−0.957091
$170$	−5.50699e9	−	1.41287e10i	−0.505701	−	1.29742i
$171$	−2.07356e9	+	1.11754e10i	−0.185453	+	0.999499i
$172$	1.40405e9	+	1.52748e9i	0.122322	+	0.133075i
$173$			6.72186e9i			0.570535i	0.958448	+	0.285267i	$0.0920824\pi$
$173$			6.72186e9i			0.570535i	−0.958448	+	0.285267i	$0.907918\pi$
$174$	3.11750e8	+	1.08443e9i	0.0257831	+	0.0896871i
$175$		−	1.88878e10i		−	1.52233i
$176$	6.35245e8	−	7.53024e9i	0.0499039	−	0.591564i
$177$	1.34645e9	−	1.46373e10i	0.103112	−	1.12093i
$178$	1.72383e10	−	6.71902e9i	1.28708	−	0.501667i
$179$	−6.85396e9			−0.499003			−0.249502	−	0.968374i	$-0.580267\pi$
$179$	−6.85396e9			−0.499003			−0.249502	+	0.968374i	$0.580267\pi$
$180$	1.12445e10	+	1.79409e10i	0.798387	+	1.27385i
$181$	2.22180e10			1.53869			0.769345	−	0.638834i	$-0.220583\pi$
$181$	2.22180e10			1.53869			0.769345	+	0.638834i	$0.220583\pi$
$182$	−3.45132e9	+	1.34523e9i	−0.233165	+	0.0908816i
$183$	1.98176e9	−	2.15437e10i	0.130623	−	1.42001i
$184$	−1.99104e10	−	9.76112e9i	−1.28056	−	0.627798i
$185$			8.69026e9i			0.545457i
$186$	−1.18985e9	−	4.13893e9i	−0.0728928	−	0.253560i
$187$			9.19513e9i			0.549883i
$188$	3.30012e9	−	3.03345e9i	0.192672	−	0.177103i
$189$	−2.03950e10	−	5.75860e9i	−1.16264	−	0.328276i
$190$	9.96984e9	+	2.55786e10i	0.555005	+	1.42392i
$191$	−2.07874e10			−1.13019			−0.565093	−	0.825027i	$-0.691160\pi$
$191$	−2.07874e10			−1.13019			−0.565093	+	0.825027i	$0.691160\pi$
$192$	1.58793e10	−	1.01206e10i	0.843286	−	0.537465i
$193$	1.41064e10			0.731824			0.365912	−	0.930649i	$-0.380757\pi$
$193$	1.41064e10			0.731824			0.365912	+	0.930649i	$0.380757\pi$
$194$	1.04307e10	+	2.67610e10i	0.528697	+	1.35642i
$195$	6.26129e9	+	5.75963e8i	0.310105	+	0.0285259i
$196$	6.98959e9	−	6.42478e9i	0.338298	−	0.310961i
$197$		−	1.84807e10i		−	0.874219i	−0.899408	−	0.437109i	$-0.856002\pi$
$197$		−	1.84807e10i		−	0.874219i	0.899408	−	0.437109i	$-0.143998\pi$
$198$	−2.40208e9	−	1.26124e10i	−0.111069	−	0.583182i
$199$			3.56141e10i			1.60984i	0.593381	+	0.804922i	$0.297793\pi$
$199$			3.56141e10i			1.60984i	−0.593381	+	0.804922i	$0.702207\pi$
$200$	2.56018e10	+	1.25513e10i	1.13145	+	0.554696i
$201$	−7.55248e9	−	6.94737e8i	−0.326368	−	0.0300219i
$202$	−1.03578e10	+	4.03718e9i	−0.437709	+	0.170607i
$203$	−2.72777e9			−0.112739
$204$	−1.82179e10	+	1.38950e10i	−0.736483	+	0.561726i
$205$	−2.30889e10			−0.913083
$206$	2.95962e10	−	1.15358e10i	1.14507	−	0.446318i
$207$	−3.70415e10	−	6.87289e9i	−1.40224	−	0.260179i
$208$	4.70058e8	−	5.57210e9i	0.0174127	−	0.206411i
$209$		−	1.66469e10i		−	0.603495i
$210$	−4.91939e10	+	1.41421e10i	−1.74552	+	0.501798i
$211$		−	1.38534e10i		−	0.481154i	−0.970630	−	0.240577i	$-0.922663\pi$
$211$		−	1.38534e10i		−	0.481154i	0.970630	−	0.240577i	$-0.0773367\pi$
$212$	−3.30214e10	−	3.59243e10i	−1.12275	−	1.22145i
$213$	−3.09204e9	+	3.36136e10i	−0.102929	+	1.11894i
$214$	1.70430e10	+	4.37255e10i	0.555501	+	1.42519i
$215$	8.51378e9			0.271738
$216$	2.13585e10	−	2.38181e10i	0.667621	−	0.744502i
$217$	1.04110e10			0.318732
$218$	−2.10522e9	−	5.40113e9i	−0.0631310	−	0.161969i
$219$	−2.01441e9	+	2.18986e10i	−0.0591765	+	0.643307i
$220$	−2.09858e10	−	2.28307e10i	−0.603982	−	0.657079i
$221$			6.80406e9i			0.191868i
$222$	1.26195e10	−	3.62782e9i	0.348701	−	0.100244i
$223$		−	1.97241e10i		−	0.534104i	−0.963682	−	0.267052i	$-0.913950\pi$
$223$		−	1.97241e10i		−	0.534104i	0.963682	−	0.267052i	$-0.0860495\pi$
$224$	1.29079e10	+	4.36533e10i	0.342562	+	1.15851i
$225$	4.76298e10	+	8.83751e9i	1.23896	+	0.229884i
$226$	4.38637e10	−	1.70969e10i	1.11845	−	0.435942i
$227$	5.62040e10			1.40492			0.702459	−	0.711725i	$-0.252086\pi$
$227$	5.62040e10			1.40492			0.702459	+	0.711725i	$0.252086\pi$
$228$	3.29817e10	−	2.51556e10i	0.808288	−	0.616492i
$229$	−2.32223e10			−0.558014			−0.279007	−	0.960289i	$-0.590005\pi$
$229$	−2.32223e10			−0.558014			−0.279007	+	0.960289i	$0.590005\pi$
$230$	−8.47812e10	+	3.30454e10i	−1.99767	+	0.778639i
$231$	3.09078e10	+	2.84314e9i	0.714191	+	0.0656969i
$232$	1.81266e9	−	3.69741e9i	0.0410791	−	0.0837918i
$233$		−	9.42920e9i		−	0.209591i	−0.994494	−	0.104796i	$-0.966581\pi$
$233$		−	9.42920e9i		−	0.209591i	0.994494	−	0.104796i	$-0.0334188\pi$
$234$	−1.77745e9	−	9.33271e9i	−0.0387548	−	0.203487i
$235$		−	1.83941e10i		−	0.393434i
$236$	−3.94935e10	+	3.63021e10i	−0.828746	+	0.761777i
$237$	−1.46629e10	−	1.34881e9i	−0.301893	−	0.0277705i
$238$	−2.01154e10	−	5.16079e10i	−0.406379	−	1.04261i
$239$	2.06039e10			0.408468			0.204234	−	0.978922i	$-0.434530\pi$
$239$	2.06039e10			0.408468			0.204234	+	0.978922i	$0.434530\pi$
$240$	1.35212e10	−	7.60785e10i	0.263065	−	1.48017i
$241$	1.33499e10			0.254919			0.127459	−	0.991844i	$-0.459318\pi$
$241$	1.33499e10			0.254919			0.127459	+	0.991844i	$0.459318\pi$
$242$	−1.25473e10	−	3.21913e10i	−0.235170	−	0.603350i
$243$	2.40643e10	−	4.87362e10i	0.442737	−	0.896652i
$244$	−5.81280e10	+	5.34309e10i	−1.04986	+	0.965024i
$245$		−	3.89583e10i		−	0.690800i
$246$	9.63863e9	+	3.35283e10i	0.167806	+	0.583718i
$247$		−	1.23181e10i		−	0.210575i
$248$	−6.91836e9	+	1.41118e10i	−0.116137	+	0.236892i
$249$	−7.38594e9	+	8.02925e10i	−0.121761	+	1.32366i
$250$	2.25027e10	−	8.77094e9i	0.364338	−	0.142009i
$251$	−5.75090e10			−0.914542			−0.457271	−	0.889327i	$-0.651173\pi$
$251$	−5.75090e10			−0.914542			−0.457271	+	0.889327i	$0.651173\pi$
$252$	4.10727e10	+	6.55326e10i	0.641581	+	1.02366i
$253$	5.51767e10			0.846668
$254$	7.26150e10	−	2.83034e10i	1.09465	−	0.426665i
$255$	−8.61243e9	+	9.36256e10i	−0.127554	+	1.38664i
$256$	−6.77483e10	−	1.15123e10i	−0.985868	−	0.167526i
$257$		−	4.18861e10i		−	0.598923i	−0.954108	−	0.299461i	$-0.903193\pi$
$257$		−	4.18861e10i		−	0.598923i	0.954108	−	0.299461i	$-0.0968070\pi$
$258$	−3.55415e9	−	1.23632e10i	−0.0499398	−	0.173717i
$259$			3.17429e10i			0.438327i
$260$	−1.55287e10	−	1.68939e10i	−0.210745	−	0.229271i
$261$	1.27631e9	−	6.87868e9i	0.0170245	−	0.0917536i
$262$	−1.68561e10	−	4.32459e10i	−0.221004	−	0.567007i
$263$	6.46079e10			0.832692			0.416346	−	0.909206i	$-0.363310\pi$
$263$	6.46079e10			0.832692			0.416346	+	0.909206i	$0.363310\pi$
$264$	−2.43927e10	+	4.00052e10i	−0.309060	+	0.506873i
$265$	−2.00233e11			−2.49419
$266$	3.64168e10	+	9.34309e10i	0.446000	+	1.14426i
$267$	−1.14232e11	−	1.05079e10i	−1.37558	−	0.126537i
$268$	1.87310e10	+	2.03777e10i	0.221797	+	0.241295i
$269$			9.10534e10i			1.06026i	0.847917	+	0.530128i	$0.177856\pi$
$269$			9.10534e10i			1.06026i	−0.847917	+	0.530128i	$0.822144\pi$
$270$	−1.26450e10	−	1.30670e11i	−0.144805	−	1.49638i
$271$			3.93278e10i			0.442932i	0.975168	+	0.221466i	$0.0710842\pi$
$271$			3.93278e10i			0.442932i	−0.975168	+	0.221466i	$0.928916\pi$
$272$	8.33200e10	+	7.02881e9i	0.922974	+	0.0778613i
$273$	2.28706e10	+	2.10382e9i	0.249199	+	0.0229233i
$274$	−1.34707e10	+	5.25051e9i	−0.144382	+	0.0562761i
$275$	−7.09489e10			−0.748081
$276$	8.33792e10	+	1.09319e11i	0.864902	+	1.13398i
$277$	1.45771e11			1.48769			0.743846	−	0.668351i	$-0.232999\pi$
$277$	1.45771e11			1.48769			0.743846	+	0.668351i	$0.232999\pi$
$278$	−7.12111e10	+	2.77562e10i	−0.715066	+	0.278713i
$279$	−4.87128e9	+	2.62538e10i	−0.0481309	+	0.259402i
$280$	1.67728e11	+	8.22292e10i	1.63078	+	0.799493i
$281$		−	1.58074e11i		−	1.51246i	−0.654308	−	0.756228i	$-0.727040\pi$
$281$		−	1.58074e11i		−	1.51246i	0.654308	−	0.756228i	$-0.272960\pi$
$282$	−2.67108e10	+	7.67875e9i	−0.251516	+	0.0723052i
$283$		−	1.61476e11i		−	1.49647i	−0.663432	−	0.748237i	$-0.730901\pi$
$283$		−	1.61476e11i		−	1.49647i	0.663432	−	0.748237i	$-0.269099\pi$
$284$	9.06944e10	−	8.33656e10i	0.827271	−	0.760422i
$285$	1.55919e10	−	1.69500e11i	0.139990	−	1.52183i
$286$	5.05315e9	+	1.29643e10i	0.0446596	+	0.114579i
$287$	−8.43367e10			−0.733750
$288$	−1.16121e11	+	1.21250e10i	−0.994593	+	0.103852i
$289$	1.68462e10			0.142057
$290$	−6.13661e9	−	1.57441e10i	−0.0509492	−	0.130715i
$291$	1.63127e10	−	1.77336e11i	0.133355	−	1.44970i
$292$	5.90858e10	−	5.43112e10i	0.475620	−	0.437186i
$293$			3.14377e10i			0.249199i	0.992207	+	0.124599i	$0.0397646\pi$
$293$			3.14377e10i			0.249199i	−0.992207	+	0.124599i	$0.960235\pi$
$294$	−5.65728e10	+	1.62634e10i	−0.441616	+	0.126955i
$295$			2.20127e11i			1.69229i
$296$	−4.30266e10	−	2.10939e10i	−0.325780	−	0.159714i
$297$	−2.16312e10	+	7.66107e10i	−0.161316	+	0.571328i
$298$	5.28207e10	−	2.05881e10i	0.387999	−	0.151232i
$299$	4.08287e10			0.295424
$300$	−1.07213e11	−	1.40568e11i	−0.764192	−	1.00194i
$301$	3.10983e10			0.218367
$302$	1.61874e11	−	6.30941e10i	1.11981	−	0.436473i
$303$	6.86371e10	+	6.31379e9i	0.467808	+	0.0430326i
$304$	−1.50843e11	−	1.27250e10i	−1.01296	−	0.0854526i
$305$			3.23991e11i			2.14380i
$306$	1.39553e11	−	2.65783e10i	0.909897	−	0.173293i
$307$		−	1.43460e10i		−	0.0921742i	−0.998937	−	0.0460871i	$-0.985325\pi$
$307$		−	1.43460e10i		−	0.0921742i	0.998937	−	0.0460871i	$-0.0146752\pi$
$308$	−7.66550e10	−	8.33938e10i	−0.485358	−	0.528026i
$309$	−1.96123e11	−	1.80409e10i	−1.22381	−	0.112576i
$310$	2.34215e10	+	6.00901e10i	0.144041	+	0.369552i
$311$	−9.27699e10			−0.562323			−0.281161	−	0.959661i	$-0.590720\pi$
$311$	−9.27699e10			−0.562323			−0.281161	+	0.959661i	$0.590720\pi$
$312$	−1.80497e10	+	2.96024e10i	−0.107839	+	0.176861i
$313$	1.52780e11			0.899742			0.449871	−	0.893094i	$-0.351470\pi$
$313$	1.52780e11			0.899742			0.449871	+	0.893094i	$0.351470\pi$
$314$	−6.36470e10	−	1.63293e11i	−0.369483	−	0.947944i
$315$	3.12043e11	+	5.78983e10i	1.78573	+	0.331336i
$316$	3.63658e10	+	3.95627e10i	0.205164	+	0.223200i
$317$			1.55635e11i			0.865648i	0.901479	+	0.432824i	$0.142483\pi$
$317$			1.55635e11i			0.865648i	−0.901479	+	0.432824i	$0.857517\pi$
$318$	8.35890e10	+	2.90767e11i	0.458382	+	1.59449i
$319$			1.02464e10i			0.0554006i
$320$	−2.22918e11	+	1.72707e11i	−1.18842	+	0.920738i
$321$	2.66537e10	−	2.89753e11i	0.140115	−	1.52319i
$322$	−3.09680e11	+	1.20705e11i	−1.60532	+	0.625712i
$323$	1.84193e11			0.941590
$324$	−1.84473e11	+	7.29117e10i	−0.929994	+	0.367574i
$325$	−5.24996e10			−0.261024
$326$	−1.97362e11	+	7.69265e10i	−0.967799	+	0.377222i
$327$	−3.29237e9	+	3.57913e10i	−0.0159237	+	0.173106i
$328$	5.60436e10	−	1.14316e11i	0.267358	−	0.545349i
$329$		−	6.71880e10i		−	0.316162i
$330$	5.31227e10	+	1.84789e11i	0.246586	+	0.857755i
$331$		−	8.55051e10i		−	0.391531i	−0.980651	−	0.195766i	$-0.937281\pi$
$331$		−	8.55051e10i		−	0.391531i	0.980651	−	0.195766i	$-0.0627192\pi$
$332$	2.16641e11	−	1.99135e11i	0.978632	−	0.899551i
$333$	−8.00469e10	−	1.48524e10i	−0.356735	−	0.0661907i
$334$	3.98787e10	+	1.02313e11i	0.175340	+	0.449852i
$335$	1.13580e11			0.492721
$336$	4.93887e10	−	2.77892e11i	0.211398	−	1.18946i
$337$	−3.45091e11			−1.45747			−0.728734	−	0.684797i	$-0.759891\pi$
$337$	−3.45091e11			−1.45747			−0.728734	+	0.684797i	$0.759891\pi$
$338$	−8.34024e10	−	2.13977e11i	−0.347579	−	0.891747i
$339$	−2.90668e11	−	2.67380e10i	−1.19536	−	0.109959i
$340$	2.52616e11	−	2.32203e11i	1.02519	−	0.942350i
$341$		−	3.91074e10i		−	0.156626i
$342$	−2.52646e11	+	4.81174e10i	−0.998609	+	0.190189i
$343$			1.67386e11i			0.652974i
$344$	−2.06655e10	+	4.21528e10i	−0.0795670	+	0.162298i
$345$	5.61814e11	+	5.16801e10i	2.13504	+	0.196398i
$346$	−1.41714e11	+	5.52363e10i	−0.531582	+	0.207196i
$347$	−1.99185e10			−0.0737522			−0.0368761	−	0.999320i	$-0.511741\pi$
$347$	−1.99185e10			−0.0737522			−0.0368761	+	0.999320i	$0.511741\pi$
$348$	−2.03008e10	+	1.54837e10i	−0.0742004	+	0.0565937i
$349$	7.94103e10			0.286525			0.143263	−	0.989685i	$-0.454241\pi$
$349$	7.94103e10			0.286525			0.143263	+	0.989685i	$0.454241\pi$
$350$	3.98203e11	−	1.55209e11i	1.41840	−	0.552853i
$351$	−1.60063e10	+	5.66891e10i	−0.0562872	+	0.199351i
$352$	1.63977e11	−	4.84865e10i	0.569299	−	0.168337i
$353$			4.67463e10i			0.160236i	0.996785	+	0.0801182i	$0.0255298\pi$
$353$			4.67463e10i			0.160236i	−0.996785	+	0.0801182i	$0.974470\pi$
$354$	3.19655e11	−	9.18938e10i	1.08185	−	0.311008i
$355$		−	5.05508e11i		−	1.68928i
$356$	2.83308e11	+	3.08214e11i	0.934833	+	1.01702i
$357$	−3.14586e10	+	3.41986e11i	−0.102502	+	1.11430i
$358$	−5.63219e10	−	1.44499e11i	−0.181219	−	0.464934i
$359$	−2.39991e11			−0.762554			−0.381277	−	0.924461i	$-0.624516\pi$
$359$	−2.39991e11			−0.762554			−0.381277	+	0.924461i	$0.624516\pi$
$360$	−2.85839e11	+	3.84490e11i	−0.896933	+	1.20649i
$361$	−1.07750e10			−0.0333915
$362$	1.82574e11	+	4.68412e11i	0.558793	+	1.43364i
$363$	−1.96228e10	+	2.13320e11i	−0.0593174	+	0.644839i
$364$	−5.67219e10	−	6.17084e10i	−0.169354	−	0.184242i
$365$		−	3.29329e11i		−	0.971209i
$366$	4.70481e11	−	1.35253e11i	1.37049	−	0.393987i
$367$		−	2.06826e11i		−	0.595126i	−0.954702	−	0.297563i	$-0.903826\pi$
$367$		−	2.06826e11i		−	0.595126i	0.954702	−	0.297563i	$-0.0961738\pi$
$368$	4.21774e10	−	4.99974e11i	0.119885	−	1.42112i
$369$	3.94608e10	−	2.12674e11i	0.110802	−	0.597167i
$370$	−1.83213e11	+	7.14115e10i	−0.508216	+	0.198089i
$371$	−7.31393e11			−2.00432
$372$	7.74818e10	−	5.90964e10i	0.209776	−	0.159999i
$373$	1.18281e11			0.316392			0.158196	−	0.987408i	$-0.449432\pi$
$373$	1.18281e11			0.316392			0.158196	+	0.987408i	$0.449432\pi$
$374$	−1.93857e11	+	7.55602e10i	−0.512341	+	0.199697i
$375$	−1.49117e11	−	1.37170e10i	−0.389392	−	0.0358193i
$376$	9.10713e10	+	4.46479e10i	0.234983	+	0.115201i
$377$			7.58198e9i			0.0193307i
$378$	−4.61884e10	−	4.77300e11i	−0.116364	−	1.20248i
$379$			4.70908e11i			1.17236i	0.810182	+	0.586178i	$0.199368\pi$
$379$			4.70908e11i			1.17236i	−0.810182	+	0.586178i	$0.800632\pi$
$380$	−4.57335e11	+	4.20379e11i	−1.12515	+	1.03423i
$381$	−4.81193e11	−	4.42639e10i	−1.16992	−	0.107619i
$382$	−1.70818e11	−	4.38251e11i	−0.410440	−	1.05302i
$383$	7.26035e11			1.72410			0.862051	−	0.506821i	$-0.169180\pi$
$383$	7.26035e11			1.72410			0.862051	+	0.506821i	$0.169180\pi$
$384$	3.43854e11	+	2.51610e11i	0.807020	+	0.590525i
$385$	−4.64817e11			−1.07822
$386$	1.15918e11	+	2.97398e11i	0.265771	+	0.681860i
$387$	−1.45508e10	+	7.84214e10i	−0.0329751	+	0.177720i
$388$	−4.78478e11	+	4.39813e11i	−1.07181	+	0.985202i
$389$		−	6.68911e11i		−	1.48114i	−0.671981	−	0.740569i	$-0.734556\pi$
$389$		−	6.68911e11i		−	1.48114i	0.671981	−	0.740569i	$-0.265444\pi$
$390$	3.93089e10	+	1.36737e11i	0.0860399	+	0.299292i
$391$			6.10515e11i			1.32099i
$392$	1.92887e11	+	9.45634e10i	0.412588	+	0.202272i
$393$	−2.63614e10	+	2.86574e11i	−0.0557444	+	0.605997i
$394$	3.89620e11	−	1.51863e11i	0.814533	−	0.317483i
$395$	2.20513e11			0.455771
$396$	2.46163e11	−	1.54283e11i	0.503030	−	0.315276i
$397$	5.64402e11			1.14033			0.570166	−	0.821530i	$-0.306879\pi$
$397$	5.64402e11			1.14033			0.570166	+	0.821530i	$0.306879\pi$
$398$	−7.50837e11	+	2.92656e11i	−1.49993	+	0.584634i
$399$	5.69526e10	−	6.19132e11i	0.112496	−	1.22294i
$400$	−5.42338e10	+	6.42891e11i	−0.105925	+	1.25565i
$401$			1.55087e11i			0.299519i	0.988722	+	0.149760i	$0.0478500\pi$
$401$			1.55087e11i			0.299519i	−0.988722	+	0.149760i	$0.952150\pi$
$402$	−4.74150e10	−	1.64934e11i	−0.0905521	−	0.314988i
$403$		−	2.89380e10i		−	0.0546508i
$404$	−1.70228e11	−	1.85193e11i	−0.317918	−	0.345867i
$405$	−2.92007e11	+	7.59796e11i	−0.539319	+	1.40330i
$406$	−2.24152e10	−	5.75083e10i	−0.0409426	−	0.105042i
$407$	1.19237e11			0.215396
$408$	−4.42647e11	−	2.69899e11i	−0.790837	−	0.482203i
$409$	4.62020e11			0.816406			0.408203	−	0.912891i	$-0.366156\pi$
$409$	4.62020e11			0.816406			0.408203	+	0.912891i	$0.366156\pi$
$410$	−1.89731e11	−	4.86772e11i	−0.331597	−	0.850744i
$411$	8.92653e10	+	8.21132e9i	0.154310	+	0.0141947i
$412$	4.86408e11	+	5.29168e11i	0.831693	+	0.904808i
$413$			8.04058e11i			1.35992i
$414$	−1.59487e11	−	8.37406e11i	−0.266823	−	1.40099i
$415$		−	1.20750e12i		−	1.99835i
$416$	1.21337e11	−	3.58782e10i	0.198643	−	0.0587369i
$417$	4.71890e11	+	4.34081e10i	0.764237	+	0.0703006i
$418$	3.50958e11	−	1.36794e11i	0.562292	−	0.219166i
$419$	9.39174e11			1.48862			0.744309	−	0.667836i	$-0.232779\pi$
$419$	9.39174e11			1.48862			0.744309	+	0.667836i	$0.232779\pi$
$420$	−7.02399e11	−	9.20921e11i	−1.10144	−	1.44411i
$421$	−5.24719e10			−0.0814062			−0.0407031	−	0.999171i	$-0.512960\pi$
$421$	−5.24719e10			−0.0814062			−0.0407031	+	0.999171i	$0.512960\pi$
$422$	2.92064e11	−	1.13839e11i	0.448304	−	0.174737i
$423$	1.69430e11	+	3.14370e10i	0.257311	+	0.0477429i
$424$	4.86027e11	−	9.91381e11i	0.730321	−	1.48968i
$425$		−	7.85031e11i		−	1.16718i
$426$	−7.34069e11	+	2.11028e11i	−1.07992	+	0.310454i
$427$			1.18344e12i			1.72275i
$428$	−7.81796e11	+	7.18621e11i	−1.12615	+	1.03515i
$429$	7.90267e9	−	8.59099e10i	0.0112646	−	0.122457i
$430$	6.99613e10	+	1.79492e11i	0.0986847	+	0.253185i
$431$	−1.03685e12			−1.44733			−0.723667	−	0.690150i	$-0.757545\pi$
$431$	−1.03685e12			−1.44733			−0.723667	+	0.690150i	$0.757545\pi$
$432$	6.77659e11	+	2.54569e11i	0.936126	+	0.351665i
$433$	−1.04593e12			−1.42990			−0.714950	−	0.699175i	$-0.753551\pi$
$433$	−1.04593e12			−1.42990			−0.714950	+	0.699175i	$0.753551\pi$
$434$	8.55518e10	+	2.19491e11i	0.115751	+	0.296971i
$435$	−9.59710e9	+	1.04330e11i	−0.0128510	+	0.139704i
$436$	9.65703e10	−	8.87667e10i	0.127984	−	0.117642i
$437$		−	1.10528e12i		−	1.44979i
$438$	−4.78232e11	+	1.37481e11i	−0.620877	+	0.178488i
$439$		−	6.71516e11i		−	0.862911i	−0.902134	−	0.431456i	$-0.858000\pi$
$439$		−	6.71516e11i		−	0.862911i	0.902134	−	0.431456i	$-0.142000\pi$
$440$	3.08881e11	−	6.30045e11i	0.392875	−	0.801372i
$441$	3.58849e11	+	6.65829e10i	0.451791	+	0.0838280i
$442$	−1.43447e11	+	5.59118e10i	−0.178769	+	0.0696792i
$443$	1.18025e12			1.45599			0.727996	−	0.685581i	$-0.240452\pi$
$443$	1.18025e12			1.45599			0.727996	+	0.685581i	$0.240452\pi$
$444$	1.80183e11	+	2.36239e11i	0.220034	+	0.288489i
$445$	1.71791e12			2.07673
$446$	4.15835e11	−	1.62081e11i	0.497638	−	0.193966i
$447$	−3.50023e11	−	3.21979e10i	−0.414680	−	0.0381455i
$448$	−8.14254e11	+	6.30849e11i	−0.955012	+	0.739902i
$449$			1.23305e12i			1.43177i	0.698218	+	0.715885i	$0.253977\pi$
$449$			1.23305e12i			1.43177i	−0.698218	+	0.715885i	$0.746023\pi$
$450$	2.05076e11	+	1.07678e12i	0.235754	+	1.23786i
$451$			3.16798e11i			0.360568i
$452$	7.20892e11	+	7.84266e11i	0.812358	+	0.883773i
$453$	−1.07268e12	−	9.86734e10i	−1.19682	−	0.110093i
$454$	4.61851e11	+	1.18492e12i	0.510212	+	1.30900i
$455$	−3.43947e11			−0.376219
$456$	8.01368e11	+	4.88624e11i	0.867941	+	0.529216i
$457$	−1.73330e12			−1.85888			−0.929441	−	0.368970i	$-0.879710\pi$
$457$	−1.73330e12			−1.85888			−0.929441	+	0.368970i	$0.879710\pi$
$458$	−1.90827e11	−	4.89585e11i	−0.202649	−	0.519917i
$459$	−8.47676e11	−	2.39344e11i	−0.891401	−	0.251690i
$460$	−1.39336e12	−	1.51586e12i	−1.45096	−	1.57851i
$461$			2.57191e10i			0.0265217i	0.999912	+	0.0132609i	$0.00422119\pi$
$461$			2.57191e10i			0.0265217i	−0.999912	+	0.0132609i	$0.995779\pi$
$462$	1.94041e11	+	6.74979e11i	0.198155	+	0.689289i
$463$			5.19998e9i			0.00525881i	0.999997	+	0.00262940i	$0.000836966\pi$
$463$			5.19998e9i			0.00525881i	−0.999997	+	0.00262940i	$0.999163\pi$
$464$	9.28462e10	+	7.83243e9i	0.0929893	+	0.00784451i
$465$	3.66291e10	−	3.98195e11i	0.0363319	−	0.394964i
$466$	1.98792e11	−	7.74836e10i	0.195282	−	0.0761155i
$467$	−1.71566e12			−1.66919			−0.834593	−	0.550867i	$-0.814297\pi$
$467$	−1.71566e12			−1.66919			−0.834593	+	0.550867i	$0.814297\pi$
$468$	1.82151e11	−	1.14164e11i	0.175520	−	0.110008i
$469$	4.14875e11			0.395949
$470$	3.87794e11	−	1.51152e11i	0.366573	−	0.142880i
$471$	−9.95382e10	+	1.08208e12i	−0.0931956	+	1.01313i
$472$	−1.08988e12	−	5.34314e11i	−1.01074	−	0.495516i
$473$		−	1.16816e11i		−	0.107307i
$474$	−9.20548e10	−	3.20215e11i	−0.0837614	−	0.291367i
$475$			1.42122e12i			1.28097i
$476$	9.22730e11	−	8.48167e11i	0.823841	−	0.757269i
$477$	3.42215e11	−	1.84437e12i	0.302668	−	1.63123i
$478$	1.69310e11	+	4.34382e11i	0.148340	+	0.380580i
$479$	−6.81974e11			−0.591913			−0.295956	−	0.955201i	$-0.595638\pi$
$479$	−6.81974e11			−0.591913			−0.295956	+	0.955201i	$0.595638\pi$
$480$	1.71504e12	−	3.40108e11i	1.47465	−	0.292437i
$481$	8.82312e10			0.0751570
$482$	1.09702e11	+	2.81450e11i	0.0925767	+	0.237514i
$483$	2.05214e12	+	1.88772e11i	1.71571	+	0.157825i
$484$	5.75569e11	−	5.29059e11i	0.476753	−	0.438227i
$485$			2.66692e12i			2.18863i
$486$	1.22523e12	+	1.06852e11i	0.996219	+	0.0868800i
$487$		−	2.07127e12i		−	1.66861i	−0.551301	−	0.834307i	$-0.685868\pi$
$487$		−	2.07127e12i		−	1.66861i	0.551301	−	0.834307i	$-0.314132\pi$
$488$	−1.60412e12	−	7.86424e11i	−1.28041	−	0.627722i
$489$	1.30785e12	+	1.20306e11i	1.03435	+	0.0951476i
$490$	8.21340e11	−	3.20136e11i	0.643636	−	0.250872i
$491$	−2.39861e12			−1.86248			−0.931242	−	0.364402i	$-0.881273\pi$
$491$	−2.39861e12			−1.86248			−0.931242	+	0.364402i	$0.881273\pi$
$492$	−6.27657e11	+	4.78723e11i	−0.482925	+	0.368333i
$493$	−1.13374e11			−0.0864375
$494$	2.59696e11	−	1.01223e11i	0.196198	−	0.0764726i
$495$	2.17486e11	−	1.17214e12i	0.162820	−	0.877518i
$496$	−3.54365e11	−	2.98939e10i	−0.262895	−	0.0221777i
$497$		−	1.84647e12i		−	1.35750i
$498$	−1.75346e12	+	5.04082e11i	−1.27751	+	0.367256i
$499$		−	1.36760e12i		−	0.987429i	−0.869624	−	0.493715i	$-0.835639\pi$
$499$		−	1.36760e12i		−	0.987429i	0.869624	−	0.493715i	$-0.164361\pi$
$500$	3.69828e11	+	4.02340e11i	0.264627	+	0.287891i
$501$	6.23666e10	−	6.77987e11i	0.0442265	−	0.480786i
$502$	−4.72575e11	−	1.21244e12i	−0.332127	−	0.852103i
$503$	2.32348e12			1.61839			0.809195	−	0.587541i	$-0.199904\pi$
$503$	2.32348e12			1.61839			0.809195	+	0.587541i	$0.199904\pi$
$504$	−1.04408e12	+	1.40443e12i	−0.720772	+	0.969531i
$505$	−1.03222e12			−0.706255
$506$	4.53409e11	+	1.16327e12i	0.307477	+	0.788863i
$507$	−1.30434e11	+	1.41794e12i	−0.0876707	+	0.953067i
$508$	1.19342e12	+	1.29833e12i	0.795069	+	0.864965i
$509$			8.20957e11i			0.542114i	0.962563	+	0.271057i	$0.0873731\pi$
$509$			8.20957e11i			0.542114i	−0.962563	+	0.271057i	$0.912627\pi$
$510$	−2.04464e12	+	5.87789e11i	−1.33829	+	0.384729i
$511$		−	1.20294e12i		−	0.780460i
$512$	−3.14007e11	−	1.52291e12i	−0.201941	−	0.979398i
$513$	1.53463e12	+	4.33308e11i	0.978309	+	0.276229i
$514$	8.83066e11	−	3.44195e11i	0.558032	−	0.217506i
$515$	2.94945e12			1.84760
$516$	2.31442e11	−	1.76524e11i	0.143720	−	0.109618i
$517$	−2.52381e11			−0.155364
$518$	−6.69222e11	+	2.60845e11i	−0.408401	+	0.159184i
$519$	9.39086e11	+	8.63846e10i	0.568136	+	0.0522616i
$520$	2.28560e11	−	4.66210e11i	0.137084	−	0.279619i
$521$			1.60180e12i			0.952444i	0.879325	+	0.476222i	$0.157994\pi$
$521$			1.60180e12i			0.952444i	−0.879325	+	0.476222i	$0.842006\pi$
$522$	1.55508e11	−	2.96171e10i	0.0916718	−	0.0174592i
$523$			2.41944e12i			1.41403i	0.707200	+	0.707013i	$0.249958\pi$
$523$			2.41944e12i			1.41403i	−0.707200	+	0.707013i	$0.750042\pi$
$524$	7.73220e11	−	7.10738e11i	0.448035	−	0.411831i
$525$	−2.63874e12	−	2.42732e11i	−1.51593	−	0.139448i
$526$	5.30909e11	+	1.36210e12i	0.302402	+	0.775841i
$527$	4.32713e11			0.244372
$528$	−1.04386e12	−	1.85521e11i	−0.584506	−	0.103882i
$529$	1.86233e12			1.03396
$530$	−1.64540e12	−	4.22143e12i	−0.905796	−	2.32391i
$531$	−2.02761e12	−	3.76215e11i	−1.10678	−	0.205358i
$532$	−1.67051e12	+	1.53552e12i	−0.904163	+	0.831100i
$533$			2.34419e11i			0.125811i
$534$	−7.17155e11	−	2.49464e12i	−0.381661	−	1.32762i
$535$			4.35754e12i			2.29958i
$536$	−2.75693e11	+	5.62350e11i	−0.144273	+	0.294283i
$537$	−8.80823e10	+	9.57542e11i	−0.0457093	+	0.496905i
$538$	−1.91964e12	+	7.48223e11i	−0.987869	+	0.385045i
$539$	−5.34538e11			−0.272790
$540$	2.65096e12	−	1.34036e12i	1.34162	−	0.678344i
$541$	−7.77998e11			−0.390473			−0.195236	−	0.980756i	$-0.562547\pi$
$541$	−7.77998e11			−0.390473			−0.195236	+	0.980756i	$0.562547\pi$
$542$	−8.29130e11	+	3.23172e11i	−0.412692	+	0.160856i
$543$	2.85530e11	−	3.10399e12i	0.140946	−	1.53222i
$544$	5.36490e11	+	1.81436e12i	0.262643	+	0.888235i
$545$		−	5.38259e11i		−	0.261341i
$546$	1.43583e11	+	4.99459e11i	0.0691413	+	0.240510i
$547$		−	2.65493e12i		−	1.26797i	−0.773344	−	0.633987i	$-0.781417\pi$
$547$		−	2.65493e12i		−	1.26797i	0.773344	−	0.633987i	$-0.218583\pi$
$548$	−2.21388e11	−	2.40851e11i	−0.104868	−	0.114087i
$549$	−2.98432e12	−	5.53728e11i	−1.40207	−	0.260148i
$550$	−5.83017e11	−	1.49579e12i	−0.271675	−	0.697007i
$551$	2.05252e11			0.0948649
$552$	−1.61956e12	+	2.65617e12i	−0.742459	+	1.21767i
$553$	8.05467e11			0.366256
$554$	1.19786e12	+	3.07323e12i	0.540273	+	1.38612i
$555$	1.21408e12	+	1.11681e11i	0.543163	+	0.0499644i
$556$	−1.17034e12	−	1.27323e12i	−0.519369	−	0.565028i
$557$			4.74219e11i			0.208752i	0.994538	+	0.104376i	$0.0332845\pi$
$557$			4.74219e11i			0.208752i	−0.994538	+	0.104376i	$0.966715\pi$
$558$	−5.93526e11	+	1.13039e11i	−0.259171	+	0.0493600i
$559$		−	8.64394e10i		−	0.0374420i
$560$	−3.55309e11	+	4.21185e12i	−0.152672	+	1.80979i
$561$	1.28462e12	+	1.18169e11i	0.547572	+	0.0503700i
$562$	3.33261e12	−	1.29896e12i	1.40919	−	0.549266i
$563$	−3.37287e11			−0.141485			−0.0707426	−	0.997495i	$-0.522537\pi$
$563$	−3.37287e11			−0.141485			−0.0707426	+	0.997495i	$0.522537\pi$
$564$	−3.81381e11	−	5.00032e11i	−0.158710	−	0.208085i
$565$	4.37131e12			1.80465
$566$	3.40433e12	−	1.32691e12i	1.39430	−	0.543462i
$567$	−1.06661e12	+	2.77531e12i	−0.433395	+	1.12768i
$568$	2.50283e12	+	1.22702e12i	1.00894	+	0.494634i
$569$		−	3.81183e12i		−	1.52450i	−0.647280	−	0.762252i	$-0.724094\pi$
$569$		−	3.81183e12i		−	1.52450i	0.647280	−	0.762252i	$-0.275906\pi$
$570$	3.70161e12	−	1.06413e12i	1.46877	−	0.422239i
$571$		−	8.34965e11i		−	0.328705i	−0.986402	−	0.164352i	$-0.947447\pi$
$571$		−	8.34965e11i		−	0.328705i	0.986402	−	0.164352i	$-0.0525534\pi$
$572$	−2.31798e11	+	2.13067e11i	−0.0905372	+	0.0832211i
$573$	−2.67145e11	+	2.90413e12i	−0.103526	+	1.12543i
$574$	−6.93030e11	−	1.77803e12i	−0.266470	−	0.683654i
$575$	−4.71069e12			−1.79713
$576$	−1.20984e12	−	2.34850e12i	−0.457960	−	0.888973i
$577$	−2.76211e12			−1.03741			−0.518704	−	0.854954i	$-0.673585\pi$
$577$	−2.76211e12			−1.03741			−0.518704	+	0.854954i	$0.673585\pi$
$578$	1.38432e11	+	3.55162e11i	0.0515897	+	0.132358i
$579$	1.81285e11	−	1.97075e12i	0.0670360	−	0.728748i
$580$	2.81498e11	−	2.58751e11i	0.103288	−	0.0949414i
$581$		−	4.41065e12i		−	1.60587i
$582$	3.87274e12	−	1.11333e12i	1.39915	−	0.402225i
$583$			2.74736e12i			0.984934i
$584$	1.63055e12	+	7.99381e11i	0.580065	+	0.284378i
$585$	1.60931e11	−	8.67340e11i	0.0568119	−	0.306188i
$586$	−6.62786e11	+	2.58336e11i	−0.232185	+	0.0904995i
$587$	5.61611e11			0.195238			0.0976190	−	0.995224i	$-0.468877\pi$
$587$	5.61611e11			0.195238			0.0976190	+	0.995224i	$0.468877\pi$
$588$	−8.07757e11	−	1.05906e12i	−0.278665	−	0.365360i
$589$	−7.83383e11			−0.268198
$590$	−4.64084e12	+	1.80887e12i	−1.57675	+	0.614574i
$591$	−2.58187e12	−	2.37501e11i	−0.870543	−	0.0800795i
$592$	9.11457e10	−	1.08045e12i	0.0304992	−	0.361540i
$593$			3.07889e12i			1.02246i	0.859443	+	0.511232i	$0.170811\pi$
$593$			3.07889e12i			1.02246i	−0.859443	+	0.511232i	$0.829189\pi$
$594$	−1.79290e12	+	1.73500e11i	−0.590905	+	0.0571820i
$595$		−	5.14307e12i		−	1.68227i
$596$	8.68099e11	+	9.44414e11i	0.281813	+	0.306587i
$597$	4.97552e12	+	4.57688e11i	1.60308	+	0.147464i
$598$	3.35506e11	+	8.60773e11i	0.107287	+	0.275254i
$599$	−3.70213e11			−0.117498			−0.0587491	−	0.998273i	$-0.518711\pi$
$599$	−3.70213e11			−0.117498			−0.0587491	+	0.998273i	$0.518711\pi$
$600$	2.08252e12	−	3.41543e12i	0.656006	−	1.07588i
$601$	−3.83449e12			−1.19887			−0.599436	−	0.800423i	$-0.704608\pi$
$601$	−3.83449e12			−1.19887			−0.599436	+	0.800423i	$0.704608\pi$
$602$	2.55548e11	+	6.55632e11i	0.0793026	+	0.203458i
$603$	−1.94118e11	+	1.04620e12i	−0.0597913	+	0.322246i
$604$	2.66037e12	+	2.89424e12i	0.813346	+	0.884849i
$605$		−	3.20808e12i		−	0.973522i
$606$	4.30909e11	+	1.49893e12i	0.129795	+	0.451496i
$607$		−	5.66085e11i		−	0.169251i	−0.996413	−	0.0846257i	$-0.973031\pi$
$607$		−	5.66085e11i		−	0.169251i	0.996413	−	0.0846257i	$-0.0269695\pi$
$608$	−9.71261e11	−	3.28471e12i	−0.288250	−	0.974835i
$609$	−3.50553e10	+	3.81086e11i	−0.0103271	+	0.112265i
$610$	−6.83057e12	+	2.66237e12i	−1.99743	+	0.778546i
$611$	−1.86753e11			−0.0542103
$612$	1.70710e12	+	2.72373e12i	0.491901	+	0.784841i
$613$	1.25635e12			0.359367			0.179683	−	0.983724i	$-0.442493\pi$
$613$	1.25635e12			0.359367			0.179683	+	0.983724i	$0.442493\pi$
$614$	3.02451e11	−	1.17887e11i	0.0858811	−	0.0334741i
$615$	−2.96722e11	+	3.22566e12i	−0.0836395	+	0.909245i
$616$	1.12825e12	−	2.30136e12i	0.315713	−	0.643980i
$617$			3.22392e12i			0.895573i	0.894140	+	0.447787i	$0.147788\pi$
$617$			3.22392e12i			0.895573i	−0.894140	+	0.447787i	$0.852212\pi$
$618$	−1.23127e12	−	4.28302e12i	−0.339552	−	1.18114i
$619$			3.88307e12i			1.06308i	0.847032	+	0.531542i	$0.178387\pi$
$619$			3.88307e12i			1.06308i	−0.847032	+	0.531542i	$0.821613\pi$
$620$	−1.07439e12	+	9.87571e11i	−0.292011	+	0.268414i
$621$	−1.43622e12	+	5.08660e12i	−0.387532	+	1.37251i
$622$	−7.62329e11	−	1.95583e12i	−0.204214	−	0.523931i
$623$	6.27501e12			1.66885
$624$	−7.72416e11	−	1.37279e11i	−0.203949	−	0.0362470i
$625$	−2.56438e12			−0.672238
$626$	1.25546e12	+	3.22100e12i	0.326752	+	0.838313i
$627$	−2.32567e12	−	2.13934e11i	−0.600958	−	0.0552809i
$628$	2.91961e12	−	2.68368e12i	0.749042	−	0.688514i
$629$			1.31933e12i			0.336066i
$630$	1.34354e12	+	7.05444e12i	0.339796	+	1.78414i
$631$			3.75968e12i			0.944102i	0.881571	+	0.472051i	$0.156486\pi$
$631$			3.75968e12i			0.944102i	−0.881571	+	0.472051i	$0.843514\pi$
$632$	−5.35251e11	+	1.09179e12i	−0.133454	+	0.272214i
$633$	−1.93540e12	−	1.78034e11i	−0.479131	−	0.0440743i
$634$	−3.28119e12	+	1.27892e12i	−0.806546	+	0.314370i
$635$	7.23657e12			1.76625
$636$	−5.44322e12	+	4.15162e12i	−1.31917	+	1.00615i
$637$	−3.95538e11			−0.0951834
$638$	−2.16021e11	+	8.41991e10i	−0.0516182	+	0.0201194i
$639$	4.65629e12	+	8.63955e11i	1.10481	+	0.204992i
$640$	−5.47293e12	−	3.28048e12i	−1.28947	−	0.772907i
$641$		−	5.95308e12i		−	1.39277i	−0.717667	−	0.696387i	$-0.754790\pi$
$641$		−	5.95308e12i		−	1.39277i	0.717667	−	0.696387i	$-0.245210\pi$
$642$	6.32775e12	−	1.81909e12i	1.47008	−	0.422616i
$643$		−	7.82142e12i		−	1.80441i	−0.431304	−	0.902207i	$-0.641946\pi$
$643$		−	7.82142e12i		−	1.80441i	0.431304	−	0.902207i	$-0.358054\pi$
$644$	−5.08954e12	−	5.53697e12i	−1.16598	−	1.26849i
$645$	1.09413e11	−	1.18943e12i	0.0248915	−	0.270595i
$646$	1.51359e12	+	3.88326e12i	0.341949	+	0.877304i
$647$	−2.85958e11			−0.0641553			−0.0320776	−	0.999485i	$-0.510212\pi$
$647$	−2.85958e11			−0.0641553			−0.0320776	+	0.999485i	$0.510212\pi$
$648$	−3.05306e12	−	3.29002e12i	−0.680217	−	0.733011i
$649$	3.02032e12			0.668269
$650$	−4.31411e11	−	1.10683e12i	−0.0947940	−	0.243203i
$651$	1.33795e11	−	1.45449e12i	0.0291962	−	0.317392i
$652$	−3.24362e12	−	3.52877e12i	−0.702935	−	0.764731i
$653$		−	4.70558e12i		−	1.01275i	−0.862312	−	0.506377i	$-0.830984\pi$
$653$		−	4.70558e12i		−	1.01275i	0.862312	−	0.506377i	$-0.169016\pi$
$654$	−7.81627e11	+	2.24700e11i	−0.167070	+	0.0480291i
$655$		−	4.30974e12i		−	0.914882i
$656$	2.87060e12	+	2.42162e11i	0.605210	+	0.0510550i
$657$	3.03349e12	+	5.62851e11i	0.635182	+	0.117855i
$658$	1.41650e12	−	5.52112e11i	0.294577	−	0.114818i
$659$	−8.30299e12			−1.71495			−0.857473	−	0.514530i	$-0.827967\pi$
$659$	−8.30299e12			−1.71495			−0.857473	+	0.514530i	$0.827967\pi$
$660$	−3.45929e12	+	2.63845e12i	−0.709642	+	0.541254i
$661$	3.72865e12			0.759706			0.379853	−	0.925047i	$-0.375975\pi$
$661$	3.72865e12			0.759706			0.379853	+	0.925047i	$0.375975\pi$
$662$	1.80267e12	−	7.02631e11i	0.364800	−	0.142189i
$663$	9.50570e11	+	8.74409e10i	0.191061	+	0.0175753i
$664$	5.97850e12	+	2.93097e12i	1.19354	+	0.585134i
$665$			9.31101e12i			1.84629i
$666$	−3.44653e11	−	1.80964e12i	−0.0678809	−	0.356417i
$667$			6.80316e11i			0.133090i
$668$	−1.82931e12	+	1.68149e12i	−0.355462	+	0.326738i
$669$	−2.75558e12	−	2.53480e11i	−0.531858	−	0.0489245i
$670$	9.33336e11	+	2.39456e12i	0.178938	+	0.459081i
$671$	4.44542e12			0.846567
$672$	6.26452e12	−	1.24231e12i	1.18502	−	0.235001i
$673$	1.72093e12			0.323367			0.161683	−	0.986843i	$-0.448308\pi$
$673$	1.72093e12			0.323367			0.161683	+	0.986843i	$0.448308\pi$
$674$	−2.83576e12	−	7.27540e12i	−0.529297	−	1.35796i
$675$	1.84676e12	−	6.54061e12i	0.342408	−	1.21269i
$676$	3.82583e12	−	3.51667e12i	0.704636	−	0.647697i
$677$			9.65351e12i			1.76618i	0.469199	+	0.883092i	$0.344543\pi$
$677$			9.65351e12i			1.76618i	−0.469199	+	0.883092i	$0.655457\pi$
$678$	−1.82484e12	−	6.34775e12i	−0.331658	−	1.15368i
$679$			9.74145e12i			1.75877i
$680$	6.97127e12	+	3.41768e12i	1.25032	+	0.612973i
$681$	7.22294e11	−	7.85205e12i	0.128692	−	1.39901i
$682$	8.24484e11	−	3.21362e11i	0.145933	−	0.0568806i
$683$	−4.94104e12			−0.868810			−0.434405	−	0.900718i	$-0.643041\pi$
$683$	−4.94104e12			−0.868810			−0.434405	+	0.900718i	$0.643041\pi$
$684$	−3.09054e12	−	4.93103e12i	−0.539860	−	0.861361i
$685$	−1.34244e12			−0.232964
$686$	−3.52893e12	+	1.37548e12i	−0.608393	+	0.237135i
$687$	−2.98436e11	+	3.24430e12i	−0.0511148	+	0.555668i
$688$	−1.05851e12	−	8.92947e10i	−0.180113	−	0.0151942i
$689$			2.03295e12i			0.343668i
$690$	3.52711e12	+	1.22691e13i	0.592376	+	2.06060i
$691$			1.10530e12i			0.184429i	0.995739	+	0.0922146i	$0.0293946\pi$
$691$			1.10530e12i			0.184429i	−0.995739	+	0.0922146i	$0.970605\pi$
$692$	−2.32905e12	−	2.53379e12i	−0.386101	−	0.420043i
$693$	7.94410e11	−	4.28148e12i	0.130841	−	0.705170i
$694$	−1.63679e11	−	4.19934e11i	−0.0267840	−	0.0687168i
$695$	−7.09666e12			−1.15378
$696$	−4.93256e11	−	3.00757e11i	−0.0796766	−	0.0485818i
$697$	−3.50528e12			−0.562568
$698$	6.52547e11	+	1.67417e12i	0.104055	+	0.266963i
$699$	−1.31732e12	−	1.21177e11i	−0.208710	−	0.0191988i
$700$	6.54439e12	+	7.11972e12i	1.03022	+	1.12078i
$701$		−	4.77388e12i		−	0.746691i	−0.927692	−	0.373345i	$-0.878211\pi$
$701$		−	4.77388e12i		−	0.746691i	0.927692	−	0.373345i	$-0.121789\pi$
$702$	−1.32668e12	+	1.28383e11i	−0.206181	+	0.0199522i
$703$		−	2.38851e12i		−	0.368832i
$704$	2.36968e12	+	3.05861e12i	0.363591	+	0.469297i
$705$	−2.56977e12	−	2.36387e11i	−0.391780	−	0.0360391i
$706$	−9.85532e11	+	3.84134e11i	−0.149296	+	0.0581917i
$707$	−3.77040e12			−0.567544
$708$	4.56409e12	+	5.98402e12i	0.682661	+	0.895042i
$709$	−8.63718e12			−1.28370			−0.641851	−	0.766830i	$-0.721833\pi$
$709$	−8.63718e12			−1.28370			−0.641851	+	0.766830i	$0.721833\pi$
$710$	1.06574e13	−	4.15397e12i	1.57394	−	0.613481i
$711$	−3.76875e11	+	2.03117e12i	−0.0553075	+	0.298080i
$712$	−4.16988e12	+	8.50558e12i	−0.608084	+	1.24035i
$713$		−	2.59655e12i		−	0.376266i
$714$	−7.46846e12	+	2.14702e12i	−1.07545	+	0.309167i
$715$			1.29198e12i			0.184876i
$716$	2.58359e12	−	2.37482e12i	0.367380	−	0.337693i
$717$	2.64786e11	−	2.87849e12i	0.0374161	−	0.406751i
$718$	−1.97211e12	−	5.05963e12i	−0.276930	−	0.710491i
$719$	−3.01601e11			−0.0420875			−0.0210438	−	0.999779i	$-0.506699\pi$
$719$	−3.01601e11			−0.0420875			−0.0210438	+	0.999779i	$0.506699\pi$
$720$	−1.04549e13	−	2.86670e12i	−1.44985	−	0.397544i
$721$	1.07735e13			1.48473
$722$	−8.85429e10	−	2.27165e11i	−0.0121265	−	0.0311118i
$723$	1.71563e11	−	1.86507e12i	0.0233508	−	0.253847i
$724$	−8.37503e12	+	7.69826e12i	−1.13282	+	1.04128i
$725$		−	8.74785e11i		−	0.117593i
$726$	−4.65858e12	+	1.33924e12i	−0.622355	+	0.178913i
$727$			3.29637e11i			0.0437654i	0.999761	+	0.0218827i	$0.00696603\pi$
$727$			3.29637e11i			0.0437654i	−0.999761	+	0.0218827i	$0.993034\pi$
$728$	8.34863e11	−	1.70293e12i	0.110160	−	0.224701i
$729$	−6.49950e12	−	3.98826e12i	−0.852327	−	0.523010i
$730$	6.94311e12	−	2.70624e12i	0.904901	−	0.352706i
$731$	1.29254e12			0.167423
$732$	6.71761e12	+	8.80751e12i	0.864798	+	1.13384i
$733$	3.27508e12			0.419038			0.209519	−	0.977805i	$-0.432810\pi$
$733$	3.27508e12			0.419038			0.209519	+	0.977805i	$0.432810\pi$
$734$	4.36043e12	−	1.69958e12i	0.554494	−	0.216127i
$735$	−5.44271e12	−	5.00664e11i	−0.687896	−	0.0632781i
$736$	1.08873e13	−	3.21928e12i	1.36764	−	0.404398i
$737$		−	1.55841e12i		−	0.194571i
$738$	4.80798e12	−	9.15696e11i	0.596635	−	0.113631i
$739$			8.89665e12i			1.09730i	0.836051	+	0.548652i	$0.184859\pi$
$739$			8.89665e12i			1.09730i	−0.836051	+	0.548652i	$0.815141\pi$
$740$	−3.01107e12	−	3.27578e12i	−0.369129	−	0.401580i
$741$	−1.72091e12	−	1.58303e11i	−0.209689	−	0.0192889i
$742$	−6.01016e12	−	1.54196e13i	−0.727894	−	1.86748i
$743$	−7.39335e12			−0.890003			−0.445001	−	0.895530i	$-0.646797\pi$
$743$	−7.39335e12			−0.890003			−0.445001	+	0.895530i	$0.646797\pi$
$744$	1.88260e12	+	1.14789e12i	0.225258	+	0.137348i
$745$	5.26393e12			0.626047
$746$	9.71964e11	+	2.49367e12i	0.114901	+	0.294790i
$747$	1.11224e13	+	2.06372e12i	1.30695	+	0.242498i
$748$	−3.18600e12	−	3.46609e12i	−0.372125	−	0.404839i
$749$			1.59168e13i			1.84794i
$750$	−9.36167e11	−	3.25649e12i	−0.108038	−	0.375814i
$751$		−	1.27842e13i		−	1.46654i	−0.679938	−	0.733269i	$-0.737993\pi$
$751$		−	1.27842e13i		−	1.46654i	0.679938	−	0.733269i	$-0.262007\pi$
$752$	−1.92922e11	+	2.28691e12i	−0.0219989	+	0.260776i
$753$	−7.39064e11	+	8.03436e12i	−0.0837731	+	0.910697i
$754$	−1.59847e11	+	6.23042e10i	−0.0180109	+	0.00702015i
$755$	1.61318e13			1.80685
$756$	9.68316e12	−	4.89594e12i	1.07812	−	0.545115i
$757$	−3.27848e12			−0.362861			−0.181431	−	0.983404i	$-0.558073\pi$
$757$	−3.27848e12			−0.362861			−0.181431	+	0.983404i	$0.558073\pi$
$758$	−9.92795e12	+	3.86965e12i	−1.09232	+	0.425755i
$759$	7.09091e11	−	7.70853e12i	0.0775558	−	0.843108i
$760$	−1.26208e13	−	6.18737e12i	−1.37222	−	0.672736i
$761$			4.47194e12i			0.483353i	0.970357	+	0.241677i	$0.0776973\pi$
$761$			4.47194e12i			0.483353i	−0.970357	+	0.241677i	$0.922303\pi$
$762$	−3.02096e12	−	1.05085e13i	−0.324600	−	1.12913i
$763$		−	1.96610e12i		−	0.210012i
$764$	7.83577e12	−	7.20258e12i	0.832073	−	0.764835i
$765$	1.29694e13	+	2.40642e12i	1.36913	+	0.254036i
$766$	5.96613e12	+	1.53067e13i	0.626128	+	1.60639i
$767$	2.23492e12			0.233176
$768$	−2.47900e12	+	9.31692e12i	−0.257129	+	0.966377i
$769$	−7.59711e11			−0.0783393			−0.0391697	−	0.999233i	$-0.512471\pi$
$769$	−7.59711e11			−0.0783393			−0.0391697	+	0.999233i	$0.512471\pi$
$770$	−3.81959e12	−	9.79952e12i	−0.391569	−	1.00461i
$771$	−5.85175e12	−	5.38290e11i	−0.596405	−	0.0548620i
$772$	−5.31737e12	+	4.88768e12i	−0.538789	+	0.495251i
$773$		−	2.95405e12i		−	0.297584i	−0.988868	−	0.148792i	$-0.952461\pi$
$773$		−	2.95405e12i		−	0.297584i	0.988868	−	0.148792i	$-0.0475385\pi$
$774$	−1.77289e12	+	3.37654e11i	−0.177561	+	0.0338172i
$775$			3.33878e12i			0.332453i
$776$	−1.32042e13	−	6.47341e12i	−1.30718	−	0.640848i
$777$	4.43469e12	+	4.07937e11i	0.436484	+	0.0401512i
$778$	1.41024e13	−	5.49672e12i	1.38001	−	0.537892i
$779$	6.34595e12			0.617417
$780$	−2.55975e12	+	1.95236e12i	−0.247612	+	0.188857i
$781$	−6.93597e12			−0.667080
$782$	−1.28712e13	+	5.01685e12i	−1.23080	+	0.479735i
$783$	−9.44593e11	−	2.66709e11i	−0.0898083	−	0.0253577i
$784$	−4.08604e11	+	4.84362e12i	−0.0386261	+	0.457876i
$785$		−	1.62732e13i		−	1.52953i
$786$	−6.25834e12	+	1.79913e12i	−0.584868	+	0.168137i
$787$		−	1.34203e13i		−	1.24702i	−0.781814	−	0.623512i	$-0.785705\pi$
$787$		−	1.34203e13i		−	1.24702i	0.781814	−	0.623512i	$-0.214295\pi$
$788$	6.40334e12	+	6.96626e12i	0.591614	+	0.643624i
$789$	8.30294e11	−	9.02612e12i	0.0762756	−	0.829191i
$790$	1.81204e12	+	4.64897e12i	0.165519	+	0.424654i
$791$	1.59671e13			1.45021
$792$	5.27551e12	+	3.92193e12i	0.476432	+	0.354190i
$793$	3.28945e12			0.295388
$794$	4.63792e12	+	1.18990e13i	0.414125	+	1.06248i
$795$	−2.57326e12	+	2.79739e13i	−0.228471	+	2.48371i
$796$	−1.23399e13	−	1.34247e13i	−1.08944	−	1.18521i
$797$		−	6.79966e12i		−	0.596932i	−0.954420	−	0.298466i	$-0.903525\pi$
$797$		−	6.79966e12i		−	0.596932i	0.954420	−	0.298466i	$-0.0964749\pi$
$798$	1.35209e13	−	3.88695e12i	1.18030	−	0.339310i
$799$		−	2.79253e12i		−	0.242403i
$800$	−1.39995e13	+	4.13952e12i	−1.20839	+	0.357309i
$801$	−2.93605e12	+	1.58238e13i	−0.252009	+	1.35821i
$802$	−3.26962e12	+	1.27441e12i	−0.279070	+	0.108774i
$803$	−4.51866e12			−0.383521
$804$	3.08761e12	−	2.35496e12i	0.260598	−	0.198761i
$805$	−3.08617e13			−2.59023
$806$	6.10088e11	−	2.37796e11i	0.0509196	−	0.0198471i
$807$	1.27207e13	+	1.17015e12i	1.05580	+	0.0971207i
$808$	2.50551e12	−	5.11066e12i	0.206797	−	0.421818i
$809$		−	1.46955e12i		−	0.120619i	−0.998180	−	0.0603095i	$-0.980791\pi$
$809$		−	1.46955e12i		−	0.120619i	0.998180	−	0.0603095i	$-0.0192088\pi$
$810$	−1.84180e13	+	8.73038e10i	−1.50335	+	0.00712608i
$811$			1.17934e13i			0.957296i	0.878007	+	0.478648i	$0.158873\pi$
$811$			1.17934e13i			0.957296i	−0.878007	+	0.478648i	$0.841127\pi$
$812$	1.02823e12	−	9.45139e11i	0.0830017	−	0.0762946i
$813$	5.49434e12	+	5.05412e11i	0.441070	+	0.0405731i
$814$	9.79822e11	+	2.51383e12i	0.0782235	+	0.200690i
$815$	−1.96685e13			−1.56157
$816$	2.05274e12	−	1.15500e13i	0.162079	−	0.911961i
$817$	−2.34001e12			−0.183746
$818$	3.79661e12	+	9.74057e12i	0.296487	+	0.760667i
$819$	5.87834e11	−	3.16813e12i	0.0456538	−	0.246051i
$820$	8.70331e12	−	8.00002e12i	0.672237	−	0.617915i
$821$			1.48112e13i			1.13775i	0.822424	+	0.568875i	$0.192621\pi$
$821$			1.48112e13i			1.13775i	−0.822424	+	0.568875i	$0.807379\pi$
$822$	5.60414e11	+	1.94942e12i	0.0428140	+	0.148930i
$823$			7.16866e11i			0.0544677i	0.999629	+	0.0272338i	$0.00866987\pi$
$823$			7.16866e11i			0.0544677i	−0.999629	+	0.0272338i	$0.991330\pi$
$824$	−7.15921e12	+	1.46031e13i	−0.540994	+	1.10350i
$825$	−9.11785e11	+	9.91201e12i	−0.0685251	+	0.744936i
$826$	−1.69516e13	+	6.60728e12i	−1.26707	+	0.493869i
$827$	−2.26611e13			−1.68464			−0.842319	−	0.538979i	$-0.818810\pi$
$827$	−2.26611e13			−1.68464			−0.842319	+	0.538979i	$0.818810\pi$
$828$	1.63441e13	−	1.02437e13i	1.20844	−	0.757392i
$829$	2.00101e13			1.47148			0.735739	−	0.677265i	$-0.236835\pi$
$829$	2.00101e13			1.47148			0.735739	+	0.677265i	$0.236835\pi$
$830$	2.54573e13	−	9.92255e12i	1.86192	−	0.725725i
$831$	1.87335e12	−	2.03652e13i	0.136274	−	1.48144i
$832$	1.75348e12	+	2.26326e12i	0.126866	+	0.163749i
$833$		−	5.91452e12i		−	0.425615i
$834$	2.96256e12	+	1.03053e13i	0.212041	+	0.737590i
$835$			1.01961e13i			0.725849i
$836$	5.76794e12	+	6.27500e12i	0.408406	+	0.444310i
$837$	3.60522e12	+	1.01794e12i	0.253902	+	0.0716901i
$838$	7.71758e12	+	1.98002e13i	0.540609	+	1.38698i
$839$	1.23878e13			0.863108			0.431554	−	0.902087i	$-0.357966\pi$
$839$	1.23878e13			0.863108			0.431554	+	0.902087i	$0.357966\pi$
$840$	1.36435e13	−	2.23759e13i	0.945513	−	1.55069i
$841$	1.43808e13			0.991291
$842$	−4.31183e11	−	1.10624e12i	−0.0295636	−	0.0758483i
$843$	−2.20840e13	−	2.03146e12i	−1.50610	−	0.138543i
$844$	4.80003e12	+	5.22200e12i	0.325614	+	0.354239i
$845$		−	2.13242e13i		−	1.43886i
$846$	7.29502e11	+	3.83034e12i	0.0489621	+	0.257082i
$847$		−	1.17181e13i		−	0.782319i
$848$	2.48947e13	+	2.10010e12i	1.65320	+	0.139463i
$849$	−2.25592e13	−	2.07517e12i	−1.49018	−	0.137079i
$850$	1.65505e13	−	6.45092e12i	1.08749	−	0.423874i
$851$	7.91681e12			0.517449
$852$	−1.04812e13	−	1.37419e13i	−0.681446	−	0.893449i
$853$	2.56552e13			1.65922			0.829612	−	0.558341i	$-0.188562\pi$
$853$	2.56552e13			1.65922			0.829612	+	0.558341i	$0.188562\pi$
$854$	−2.49500e13	+	9.72484e12i	−1.60513	+	0.625637i
$855$	−2.34798e13	−	4.35658e12i	−1.50261	−	0.278803i
$856$	−2.15747e13	−	1.05770e13i	−1.37345	−	0.673337i
$857$		−	2.27222e13i		−	1.43892i	−0.694532	−	0.719461i	$-0.744389\pi$
$857$		−	2.27222e13i		−	1.43892i	0.694532	−	0.719461i	$-0.255611\pi$
$858$	1.87614e12	−	5.39348e11i	0.118188	−	0.0339763i
$859$			6.62697e12i			0.415285i	0.978205	+	0.207642i	$0.0665790\pi$
$859$			6.62697e12i			0.415285i	−0.978205	+	0.207642i	$0.933421\pi$
$860$	−3.20926e12	+	2.94993e12i	−0.200061	+	0.183894i
$861$	−1.08384e12	+	1.17824e13i	−0.0672124	+	0.730666i
$862$	−8.52023e12	−	2.18595e13i	−0.525616	−	1.34852i
$863$	−4.62288e12			−0.283703			−0.141852	−	0.989888i	$-0.545306\pi$
$863$	−4.62288e12			−0.283703			−0.141852	+	0.989888i	$0.545306\pi$
$864$	2.01630e11	+	1.63787e13i	0.0123096	+	0.999924i
$865$	−1.41227e13			−0.857722
$866$	−8.59482e12	−	2.20508e13i	−0.519285	−	1.33228i
$867$	2.16496e11	−	2.35352e12i	0.0130126	−	0.141460i
$868$	−3.92442e12	+	3.60730e12i	−0.234659	+	0.215697i
$869$		−	3.02561e12i		−	0.179980i
$870$	−2.27841e12	+	6.54991e11i	−0.134833	+	0.0387614i
$871$		−	1.15317e12i		−	0.0678907i
$872$	2.66499e12	+	1.30652e12i	0.156088	+	0.0765227i
$873$	−2.45653e13	−	4.55798e12i	−1.43139	−	0.265588i
$874$	2.33020e13	−	9.08251e12i	1.35080	−	0.526507i
$875$	8.19134e12			0.472409
$876$	−6.82829e12	−	8.95262e12i	−0.391781	−	0.513667i
$877$	−8.58087e12			−0.489816			−0.244908	−	0.969546i	$-0.578758\pi$
$877$	−8.58087e12			−0.489816			−0.244908	+	0.969546i	$0.578758\pi$
$878$	1.41573e13	−	5.51812e12i	0.803997	−	0.313376i
$879$	4.39204e12	+	4.04014e11i	0.248151	+	0.0228269i
$880$	1.58212e13	+	1.33466e12i	0.889336	+	0.0750237i
$881$			7.89861e12i			0.441732i	0.975304	+	0.220866i	$0.0708884\pi$
$881$			7.89861e12i			0.441732i	−0.975304	+	0.220866i	$0.929112\pi$
$882$	1.54507e12	+	8.11259e12i	0.0859686	+	0.451389i
$883$			1.77422e13i			0.982166i	0.871113	+	0.491083i	$0.163399\pi$
$883$			1.77422e13i			0.982166i	−0.871113	+	0.491083i	$0.836601\pi$
$884$	−2.35753e12	−	2.56478e12i	−0.129844	−	0.141258i
$885$	3.07531e13	+	2.82891e12i	1.68517	+	0.155016i
$886$	9.69864e12	+	2.48828e13i	0.528761	+	1.35659i
$887$	1.98102e13			1.07457			0.537283	−	0.843402i	$-0.319451\pi$
$887$	1.98102e13			1.07457			0.537283	+	0.843402i	$0.319451\pi$
$888$	−3.49989e12	+	5.74000e12i	−0.188885	+	0.309780i
$889$	2.64330e13			1.41935
$890$	1.41168e13	+	3.62179e13i	0.754189	+	1.93494i
$891$	1.04250e13	+	4.00657e12i	0.554149	+	0.212972i
$892$	6.83417e12	+	7.43497e12i	0.361447	+	0.393222i
$893$			5.05559e12i			0.266036i
$894$	−2.19747e12	−	7.64396e12i	−0.115055	−	0.400221i
$895$		−	1.44003e13i		−	0.750184i
$896$	−1.99910e13	−	1.19826e13i	−1.03621	−	0.621105i
$897$	5.24701e11	−	5.70403e12i	0.0270612	−	0.294182i
$898$	−2.59959e13	+	1.01325e13i	−1.33402	+	0.519964i
$899$	4.82186e11			0.0246204
$900$	−2.10161e13	+	1.31719e13i	−1.06773	+	0.669200i
$901$	−3.03988e13			−1.53672
$902$	−6.67890e12	+	2.60326e12i	−0.335951	+	0.130945i
$903$	3.99653e11	−	4.34463e12i	0.0200027	−	0.217449i
$904$	−1.06105e13	+	2.16429e13i	−0.528417	+	1.07785i
$905$			4.66803e13i			2.31321i
$906$	−6.73435e12	−	2.34256e13i	−0.332062	−	1.15509i
$907$			1.15965e13i			0.568978i	0.958679	+	0.284489i	$0.0918239\pi$
$907$			1.15965e13i			0.568978i	−0.958679	+	0.284489i	$0.908176\pi$
$908$	−2.11860e13	+	1.94740e13i	−1.03434	+	0.950756i
$909$	1.76415e12	−	9.50790e12i	0.0857035	−	0.461899i
$910$	−2.82636e12	−	7.25129e12i	−0.136628	−	0.350533i
$911$	−7.72995e12			−0.371829			−0.185915	−	0.982566i	$-0.559525\pi$
$911$	−7.72995e12			−0.371829			−0.185915	+	0.982566i	$0.559525\pi$
$912$	−3.71628e12	+	2.09101e13i	−0.177882	+	1.00087i
$913$	−1.65679e13			−0.789131
$914$	−1.42433e13	−	3.65425e13i	−0.675075	−	1.73197i
$915$	4.52636e13	+	4.16371e12i	2.13479	+	0.196375i
$916$	8.75360e12	−	8.04625e12i	0.410825	−	0.377628i
$917$		−	1.57422e13i		−	0.735196i
$918$	−1.91973e12	−	1.98380e13i	−0.0892169	−	0.921945i
$919$		−	2.00011e13i		−	0.924983i	−0.886624	−	0.462491i	$-0.846956\pi$
$919$		−	2.00011e13i		−	0.924983i	0.886624	−	0.462491i	$-0.153044\pi$
$920$	2.05083e13	−	4.18321e13i	0.943809	−	1.92515i
$921$	−2.00423e12	−	1.84365e11i	−0.0917866	−	0.00844326i
$922$	−5.42225e11	+	2.11345e11i	−0.0247110	+	0.00963168i
$923$	−5.13236e12			−0.232761
$924$	−1.26358e13	+	9.63747e12i	−0.570266	+	0.434950i
$925$	−1.01798e13			−0.457197
$926$	−1.09629e11	+	4.27304e10i	−0.00489977	+	0.00190980i
$927$	−5.04086e12	+	2.71677e13i	−0.224205	+	1.20836i
$928$	5.97828e11	+	2.02180e12i	0.0264612	+	0.0894894i
$929$			3.13669e13i			1.38166i	0.723018	+	0.690829i	$0.242754\pi$
$929$			3.13669e13i			1.38166i	−0.723018	+	0.690829i	$0.757246\pi$
$930$	8.69597e12	−	2.49990e12i	0.381193	−	0.109584i
$931$			1.07076e13i			0.467111i
$932$	3.26710e12	+	3.55432e12i	0.141838	+	0.154307i
$933$	−1.19221e12	+	1.29605e13i	−0.0515094	+	0.559958i
$934$	−1.40983e13	−	3.61705e13i	−0.606185	−	1.55522i
$935$	−1.93191e13			−0.826676
$936$	3.90368e12	+	2.90209e12i	0.166239	+	0.123586i
$937$	2.19220e13			0.929078			0.464539	−	0.885553i	$-0.346220\pi$
$937$	2.19220e13			0.929078			0.464539	+	0.885553i	$0.346220\pi$
$938$	3.40920e12	+	8.74662e12i	0.143794	+	0.368916i
$939$	1.96342e12	−	2.13444e13i	0.0824174	−	0.895959i
$940$	6.37333e12	+	6.93361e12i	0.266251	+	0.289657i
$941$			8.09382e12i			0.336512i	0.985743	+	0.168256i	$0.0538135\pi$
$941$			8.09382e12i			0.336512i	−0.985743	+	0.168256i	$0.946187\pi$
$942$	−2.36309e13	+	6.79337e12i	−0.977804	+	0.281097i
$943$			2.10339e13i			0.866199i
$944$	2.30875e12	−	2.73680e13i	0.0946242	−	1.12168i
$945$	1.20989e13	−	4.28503e13i	0.493518	−	1.74788i
$946$	2.46278e12	−	9.59924e11i	0.0999804	−	0.0389697i
$947$	1.90674e13			0.770400			0.385200	−	0.922833i	$-0.374132\pi$
$947$	1.90674e13			0.770400			0.385200	+	0.922833i	$0.374132\pi$
$948$	5.99451e12	−	4.57209e12i	0.241055	−	0.183856i
$949$	−3.34364e12			−0.133820
$950$	−2.99629e13	+	1.16787e13i	−1.19352	+	0.465200i
$951$	2.17432e13	+	2.00011e12i	0.862008	+	0.0792943i
$952$	2.54640e13	+	1.24838e13i	1.00475	+	0.492583i
$953$		−	4.62609e13i		−	1.81675i	−0.418151	−	0.908377i	$-0.637322\pi$
$953$		−	4.62609e13i		−	1.81675i	0.418151	−	0.908377i	$-0.362678\pi$
$954$	4.16962e13	−	7.94118e12i	1.62978	−	0.310397i
$955$		−	4.36746e13i		−	1.69908i
$956$	−7.76659e12	+	7.13899e12i	−0.300725	+	0.276424i
$957$	1.43149e12	+	1.31680e11i	0.0551677	+	0.00507476i
$958$	−5.60406e12	−	1.43777e13i	−0.214960	−	0.551501i
$959$	−4.90354e12			−0.187209
$960$	2.12635e13	+	3.33626e13i	0.808007	+	1.26777i
$961$	2.45993e13			0.930394
$962$	7.25032e11	+	1.86014e12i	0.0272941	+	0.0700257i
$963$	−4.01377e13	−	7.44739e12i	−1.50395	−	0.279052i
$964$	−5.03222e12	+	4.62558e12i	−0.187678	+	0.172512i
$965$			2.96377e13i			1.10020i
$966$	1.28835e13	+	4.48155e13i	0.476032	+	1.65589i
$967$		−	1.03722e13i		−	0.381462i	−0.981642	−	0.190731i	$-0.938914\pi$
$967$		−	1.03722e13i		−	0.381462i	0.981642	−	0.190731i	$-0.0610857\pi$
$968$	1.58836e13	+	7.78697e12i	0.581446	+	0.285055i
$969$	2.36712e12	−	2.57329e13i	0.0862507	−	0.937631i
$970$	−5.62254e13	+	2.19152e13i	−2.03920	+	0.794825i
$971$	3.22774e13			1.16523			0.582616	−	0.812748i	$-0.302029\pi$
$971$	3.22774e13			1.16523			0.582616	+	0.812748i	$0.302029\pi$
$972$	7.81551e12	+	2.67090e13i	0.280840	+	0.959755i
$973$	−2.59220e13			−0.927172
$974$	4.36676e13	−	1.70205e13i	1.55469	−	0.605976i
$975$	−6.74688e11	+	7.33452e12i	−0.0239101	+	0.259927i
$976$	3.39810e12	−	4.02814e13i	0.119871	−	1.42095i
$977$			3.63960e13i			1.27799i	0.769210	+	0.638996i	$0.220650\pi$
$977$			3.63960e13i			1.27799i	−0.769210	+	0.638996i	$0.779350\pi$
$978$	8.21076e12	+	2.85614e13i	0.286985	+	0.998284i
$979$		−	2.35711e13i		−	0.820082i
$980$	1.34986e13	+	1.46853e13i	0.467488	+	0.508586i
$981$	4.95796e12	+	9.19929e11i	0.170920	+	0.0317135i
$982$	−1.97103e13	−	5.05688e13i	−0.676383	−	1.73532i
$983$	−4.83865e13			−1.65285			−0.826424	−	0.563048i	$-0.809629\pi$
$983$	−4.83865e13			−1.65285			−0.826424	+	0.563048i	$0.809629\pi$
$984$	−1.52504e13	−	9.29875e12i	−0.518566	−	0.316189i
$985$	3.88282e13			1.31427
$986$	−9.31640e11	−	2.39021e12i	−0.0313908	−	0.0805361i
$987$	−9.38659e12	−	8.63453e11i	−0.314833	−	0.0289608i
$988$	4.26806e12	+	4.64327e12i	0.142503	+	0.155031i
$989$		−	7.75604e12i		−	0.257785i
$990$	2.64989e13	−	5.04680e12i	0.876736	−	0.166977i
$991$			2.47228e13i			0.814267i	0.913369	+	0.407133i	$0.133472\pi$
$991$			2.47228e13i			0.814267i	−0.913369	+	0.407133i	$0.866528\pi$
$992$	−2.28172e12	−	7.71657e12i	−0.0748101	−	0.253001i
$993$	−1.19456e13	−	1.09885e12i	−0.389885	−	0.0358647i
$994$	3.89283e13	−	1.51732e13i	1.26481	−	0.492991i
$995$	−7.48259e13			−2.42018
$996$	−2.50363e13	−	3.28252e13i	−0.806125	−	1.05692i
$997$	−5.88007e13			−1.88475			−0.942376	−	0.334555i	$-0.891414\pi$
$997$	−5.88007e13			−1.88475			−0.942376	+	0.334555i	$0.891414\pi$
$998$	2.88325e13	−	1.12381e13i	0.920014	−	0.358597i
$999$	−3.10368e12	+	1.09922e13i	−0.0985897	+	0.349172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.10.b.a.11.10	yes	16
3.2	odd	2	inner	12.10.b.a.11.7	✓	16
4.3	odd	2	inner	12.10.b.a.11.8	yes	16
8.3	odd	2		192.10.c.d.191.9		16
8.5	even	2		192.10.c.d.191.8		16
12.11	even	2	inner	12.10.b.a.11.9	yes	16
24.5	odd	2		192.10.c.d.191.10		16
24.11	even	2		192.10.c.d.191.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.10.b.a.11.7	✓	16	3.2	odd	2	inner
12.10.b.a.11.8	yes	16	4.3	odd	2	inner
12.10.b.a.11.9	yes	16	12.11	even	2	inner
12.10.b.a.11.10	yes	16	1.1	even	1	trivial
192.10.c.d.191.7		16	24.11	even	2
192.10.c.d.191.8		16	8.5	even	2
192.10.c.d.191.9		16	8.3	odd	2
192.10.c.d.191.10		16	24.5	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(8.21741 + 21.0826i) q^{2} +(12.8513 - 139.706i) q^{3} +(-376.948 + 346.488i) q^{4} +2101.02i q^{5} +(3050.97 - 877.086i) q^{6} +7674.38i q^{7} +(-10402.4 - 5099.80i) q^{8} +(-19352.7 - 3590.81i) q^{9} +O(q^{10})\)	\(q+(8.21741 + 21.0826i) q^{2} +(12.8513 - 139.706i) q^{3} +(-376.948 + 346.488i) q^{4} +2101.02i q^{5} +(3050.97 - 877.086i) q^{6} +7674.38i q^{7} +(-10402.4 - 5099.80i) q^{8} +(-19352.7 - 3590.81i) q^{9} +(-44294.8 + 17264.9i) q^{10} +28827.6 q^{11} +(43562.3 + 57114.9i) q^{12} +21331.4 q^{13} +(-161796. + 63063.6i) q^{14} +(293525. + 27000.8i) q^{15} +(22036.0 - 261216. i) q^{16} +318970. i q^{17} +(-83325.6 - 437511. i) q^{18} -577462. i q^{19} +(-727977. - 791975. i) q^{20} +(1.07216e6 + 98625.7i) q^{21} +(236888. + 607760. i) q^{22} +1.91402e6 q^{23} +(-846158. + 1.38774e6i) q^{24} -2.46115e6 q^{25} +(175289. + 449720. i) q^{26} +(-750366. + 2.65755e6i) q^{27} +(-2.65908e6 - 2.89285e6i) q^{28} +355438. i q^{29} +(1.84277e6 + 6.41014e6i) q^{30} -1.35660e6i q^{31} +(5.68818e6 - 1.68195e6i) q^{32} +(370472. - 4.02740e6i) q^{33} +(-6.72470e6 + 2.62111e6i) q^{34} -1.61240e7 q^{35} +(8.53914e6 - 5.35193e6i) q^{36} +4.13622e6 q^{37} +(1.21744e7 - 4.74525e6i) q^{38} +(274136. - 2.98013e6i) q^{39} +(1.07148e7 - 2.18556e7i) q^{40} +1.09894e7i q^{41} +(6.73110e6 + 2.34143e7i) q^{42} -4.05222e6i q^{43} +(-1.08665e7 + 9.98842e6i) q^{44} +(7.54435e6 - 4.06603e7i) q^{45} +(1.57283e7 + 4.03525e7i) q^{46} -8.75484e6 q^{47} +(-3.62103e7 - 6.43553e6i) q^{48} -1.85426e7 q^{49} +(-2.02243e7 - 5.18872e7i) q^{50} +(4.45621e7 + 4.09917e6i) q^{51} +(-8.04082e6 + 7.39106e6i) q^{52} +9.53031e7i q^{53} +(-6.21939e7 + 6.01852e6i) q^{54} +6.05673e7i q^{55} +(3.91378e7 - 7.98320e7i) q^{56} +(-8.06751e7 - 7.42113e6i) q^{57} +(-7.49354e6 + 2.92078e6i) q^{58} +1.04772e8 q^{59} +(-1.19999e8 + 9.15251e7i) q^{60} +1.54207e8 q^{61} +(2.86005e7 - 1.11477e7i) q^{62} +(2.75573e7 - 1.48520e8i) q^{63} +(8.22019e7 + 1.06100e8i) q^{64} +4.48176e7i q^{65} +(8.79521e7 - 2.52843e7i) q^{66} -5.40597e7i q^{67} +(-1.10519e8 - 1.20235e8i) q^{68} +(2.45976e7 - 2.67401e8i) q^{69} +(-1.32498e8 - 3.39935e8i) q^{70} -2.40602e8 q^{71} +(1.83002e8 + 1.36048e8i) q^{72} -1.56748e8 q^{73} +(3.39890e7 + 8.72020e7i) q^{74} +(-3.16289e7 + 3.43838e8i) q^{75} +(2.00084e8 + 2.17673e8i) q^{76} +2.21234e8i q^{77} +(6.50813e7 - 1.87094e7i) q^{78} -1.04955e8i q^{79} +(5.48820e8 + 4.62980e7i) q^{80} +(3.61633e8 + 1.38984e8i) q^{81} +(-2.31684e8 + 9.03043e7i) q^{82} -5.74723e8 q^{83} +(-4.38321e8 + 3.34314e8i) q^{84} -6.70161e8 q^{85} +(8.54312e7 - 3.32988e7i) q^{86} +(4.96569e7 + 4.56784e6i) q^{87} +(-2.99876e8 - 1.47015e8i) q^{88} -8.17656e8i q^{89} +(9.19219e8 - 1.75068e8i) q^{90} +1.63705e8i q^{91} +(-7.21487e8 + 6.63186e8i) q^{92} +(-1.89525e8 - 1.74340e7i) q^{93} +(-7.19421e7 - 1.84574e8i) q^{94} +1.21326e9 q^{95} +(-1.61878e8 - 8.16290e8i) q^{96} +1.26935e9 q^{97} +(-1.52372e8 - 3.90925e8i) q^{98} +(-5.57892e8 - 1.03514e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9}+O(q^{10}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9	\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97}+O(q^{100}) \) 16 * q - 344 * q^4 - 1608 * q^6 - 13872 * q^9 - 15952 * q^10 + 42600 * q^12 - 97312 * q^13 + 164896 * q^16 + 256944 * q^18 + 356448 * q^21 + 322128 * q^22 + 166176 * q^24 - 2743728 * q^25 - 1447056 * q^28 + 3286128 * q^30 + 4715520 * q^33 - 13198144 * q^34 - 6827448 * q^36 + 10997600 * q^37 + 23411264 * q^40 + 23964432 * q^42 - 251904 * q^45 - 41256288 * q^46 - 87722976 * q^48 - 21356624 * q^49 + 132124208 * q^52 + 179732232 * q^54 - 88439904 * q^57 - 271309360 * q^58 - 414400704 * q^60 + 50685152 * q^61 + 742710400 * q^64 + 790585104 * q^66 + 63713280 * q^69 - 1188731232 * q^70 - 1250220480 * q^72 + 23382176 * q^73 + 1645242192 * q^76 + 2079579408 * q^78 + 349756560 * q^81 - 3274996000 * q^82 - 3734920464 * q^84 - 247261184 * q^85 + 4467199680 * q^88 + 5726283888 * q^90 - 262825248 * q^93 - 6146963136 * q^94 - 6944875392 * q^96 + 30926624 * q^97

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