LMFDB - Embedded newform 84.12.b.a.55.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(55,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("84.55");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.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:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.14
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.9452 + 37.0790i) q^{2} -243.000 q^{3} +(-701.697 - 1924.04i) q^{4} -5436.30i q^{5} +(6304.67 - 9010.19i) q^{6} +(-42645.9 + 12595.7i) q^{7} +(89547.0 + 23901.3i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-25.9452 + 37.0790i) q^{2} -243.000 q^{3} +(-701.697 - 1924.04i) q^{4} -5436.30i q^{5} +(6304.67 - 9010.19i) q^{6} +(-42645.9 + 12595.7i) q^{7} +(89547.0 + 23901.3i) q^{8} +59049.0 q^{9} +(201572. + 141046. i) q^{10} -798192. i q^{11} +(170512. + 467541. i) q^{12} +842443. i q^{13} +(639420. - 1.90806e6i) q^{14} +1.32102e6i q^{15} +(-3.20955e6 + 2.70019e6i) q^{16} +7.54533e6i q^{17} +(-1.53204e6 + 2.18948e6i) q^{18} +1.68943e7 q^{19} +(-1.04596e7 + 3.81464e6i) q^{20} +(1.03630e7 - 3.06076e6i) q^{21} +(2.95961e7 + 2.07092e7i) q^{22} +2.84452e7i q^{23} +(-2.17599e7 - 5.80801e6i) q^{24} +1.92748e7 q^{25} +(-3.12369e7 - 2.18573e7i) q^{26} -1.43489e7 q^{27} +(5.41591e7 + 7.32140e7i) q^{28} -1.52211e8 q^{29} +(-4.89821e7 - 3.42741e7i) q^{30} +2.38305e7 q^{31} +(-1.68479e7 - 1.89063e8i) q^{32} +1.93961e8i q^{33} +(-2.79773e8 - 1.95765e8i) q^{34} +(6.84740e7 + 2.31836e8i) q^{35} +(-4.14345e7 - 1.13613e8i) q^{36} -5.24437e8 q^{37} +(-4.38324e8 + 6.26422e8i) q^{38} -2.04714e8i q^{39} +(1.29935e8 - 4.86804e8i) q^{40} -4.73603e8i q^{41} +(-1.55379e8 + 4.63659e8i) q^{42} -2.59481e7i q^{43} +(-1.53575e9 + 5.60089e8i) q^{44} -3.21008e8i q^{45} +(-1.05472e9 - 7.38015e8i) q^{46} +2.24818e9 q^{47} +(7.79920e8 - 6.56145e8i) q^{48} +(1.66002e9 - 1.07431e9i) q^{49} +(-5.00087e8 + 7.14689e8i) q^{50} -1.83352e9i q^{51} +(1.62089e9 - 5.91140e8i) q^{52} -2.74065e9 q^{53} +(3.72285e8 - 5.32042e8i) q^{54} -4.33921e9 q^{55} +(-4.11987e9 + 1.08614e8i) q^{56} -4.10531e9 q^{57} +(3.94915e9 - 5.64383e9i) q^{58} +6.43711e9 q^{59} +(2.54169e9 - 9.26957e8i) q^{60} +8.14609e9i q^{61} +(-6.18286e8 + 8.83610e8i) q^{62} +(-2.51820e9 + 7.43764e8i) q^{63} +(7.44739e9 + 4.28058e9i) q^{64} +4.57977e9 q^{65} +(-7.19186e9 - 5.03234e9i) q^{66} +1.41934e10i q^{67} +(1.45175e10 - 5.29454e9i) q^{68} -6.91218e9i q^{69} +(-1.03728e10 - 3.47608e9i) q^{70} -2.71362e10i q^{71} +(5.28766e9 + 1.41135e9i) q^{72} +1.06360e10i q^{73} +(1.36066e10 - 1.94456e10i) q^{74} -4.68377e9 q^{75} +(-1.18547e10 - 3.25052e10i) q^{76} +(1.00538e10 + 3.40396e10i) q^{77} +(7.59057e9 + 5.31133e9i) q^{78} -4.56423e10i q^{79} +(1.46790e10 + 1.74481e10i) q^{80} +3.48678e9 q^{81} +(1.75607e10 + 1.22877e10i) q^{82} +3.93065e10 q^{83} +(-1.31607e10 - 1.77910e10i) q^{84} +4.10187e10 q^{85} +(9.62127e8 + 6.73227e8i) q^{86} +3.69873e10 q^{87} +(1.90778e10 - 7.14757e10i) q^{88} +1.09223e10i q^{89} +(1.19026e10 + 8.32860e9i) q^{90} +(-1.06112e10 - 3.59268e10i) q^{91} +(5.47297e10 - 1.99599e10i) q^{92} -5.79081e9 q^{93} +(-5.83295e10 + 8.33603e10i) q^{94} -9.18423e10i q^{95} +(4.09403e9 + 4.59424e10i) q^{96} -7.12847e10i q^{97} +(-3.23526e9 + 8.94251e10i) q^{98} -4.71324e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) $ 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−25.9452	+	37.0790i	−0.573312	+	0.819337i
$2$	−25.9452	+	37.0790i	−0.573312	+	0.819337i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	−701.697	−	1924.04i	−0.342626	−	0.939472i
$5$		−	5436.30i		−	0.777980i	−0.921242	−	0.388990i	$-0.872824\pi$
$5$		−	5436.30i		−	0.777980i	0.921242	−	0.388990i	$-0.127176\pi$
$6$	6304.67	−	9010.19i	0.331002	−	0.473044i
$7$	−42645.9	+	12595.7i	−0.959044	+	0.283259i
$7$	−42645.9	+	12595.7i	−0.959044	+	0.283259i
$8$	89547.0	+	23901.3i	0.966176	+	0.257885i
$9$	59049.0			0.333333
$10$	201572.	+	141046.i	0.637427	+	0.446025i
$11$		−	798192.i		−	1.49433i	−0.664636	−	0.747167i	$-0.731414\pi$
$11$		−	798192.i		−	1.49433i	0.664636	−	0.747167i	$-0.268586\pi$
$12$	170512.	+	467541.i	0.197815	+	0.542404i
$13$			842443.i			0.629292i	0.949209	+	0.314646i	$0.101886\pi$
$13$			842443.i			0.629292i	−0.949209	+	0.314646i	$0.898114\pi$
$14$	639420.	−	1.90806e6i	0.317747	−	0.948175i
$15$			1.32102e6i			0.449167i
$16$	−3.20955e6	+	2.70019e6i	−0.765215	+	0.643774i
$17$			7.54533e6i			1.28887i	0.764659	+	0.644435i	$0.222907\pi$
$17$			7.54533e6i			1.28887i	−0.764659	+	0.644435i	$0.777093\pi$
$18$	−1.53204e6	+	2.18948e6i	−0.191104	+	0.273112i
$19$	1.68943e7			1.56529			0.782644	−	0.622469i	$-0.213870\pi$
$19$	1.68943e7			1.56529			0.782644	+	0.622469i	$0.213870\pi$
$20$	−1.04596e7	+	3.81464e6i	−0.730890	+	0.266556i
$21$	1.03630e7	−	3.06076e6i	0.553704	−	0.163539i
$22$	2.95961e7	+	2.07092e7i	1.22436	+	0.856720i
$23$			2.84452e7i			0.921522i	0.887524	+	0.460761i	$0.152424\pi$
$23$			2.84452e7i			0.921522i	−0.887524	+	0.460761i	$0.847576\pi$
$24$	−2.17599e7	−	5.80801e6i	−0.557822	−	0.148890i
$25$	1.92748e7			0.394747
$26$	−3.12369e7	−	2.18573e7i	−0.515602	−	0.360781i
$27$	−1.43489e7			−0.192450
$28$	5.41591e7	+	7.32140e7i	0.594706	+	0.803943i
$29$	−1.52211e8			−1.37803			−0.689014	−	0.724748i	$-0.741956\pi$
$29$	−1.52211e8			−1.37803			−0.689014	+	0.724748i	$0.741956\pi$
$30$	−4.89821e7	−	3.42741e7i	−0.368019	−	0.257513i
$31$	2.38305e7			0.149501			0.0747505	−	0.997202i	$-0.476184\pi$
$31$	2.38305e7			0.149501			0.0747505	+	0.997202i	$0.476184\pi$
$32$	−1.68479e7	−	1.89063e8i	−0.0887606	−	0.996053i
$33$			1.93961e8i			0.862754i
$34$	−2.79773e8	−	1.95765e8i	−1.05602	−	0.738926i
$35$	6.84740e7	+	2.31836e8i	0.220369	+	0.746116i
$36$	−4.14345e7	−	1.13613e8i	−0.114209	−	0.313157i
$37$	−5.24437e8			−1.24332			−0.621662	−	0.783286i	$-0.713542\pi$
$37$	−5.24437e8			−1.24332			−0.621662	+	0.783286i	$0.713542\pi$
$38$	−4.38324e8	+	6.26422e8i	−0.897399	+	1.28250i
$39$		−	2.04714e8i		−	0.363322i
$40$	1.29935e8	−	4.86804e8i	0.200629	−	0.751665i
$41$		−	4.73603e8i		−	0.638415i	−0.947685	−	0.319208i	$-0.896583\pi$
$41$		−	4.73603e8i		−	0.638415i	0.947685	−	0.319208i	$-0.103417\pi$
$42$	−1.55379e8	+	4.63659e8i	−0.183452	+	0.547429i
$43$		−	2.59481e7i		−	0.0269171i	−0.999909	−	0.0134586i	$-0.995716\pi$
$43$		−	2.59481e7i		−	0.0269171i	0.999909	−	0.0134586i	$-0.00428412\pi$
$44$	−1.53575e9	+	5.60089e8i	−1.40388	+	0.511997i
$45$		−	3.21008e8i		−	0.259327i
$46$	−1.05472e9	−	7.38015e8i	−0.755037	−	0.528320i
$47$	2.24818e9			1.42986			0.714930	−	0.699196i	$-0.246459\pi$
$47$	2.24818e9			1.42986			0.714930	+	0.699196i	$0.246459\pi$
$48$	7.79920e8	−	6.56145e8i	0.441797	−	0.371683i
$49$	1.66002e9	−	1.07431e9i	0.839529	−	0.543315i
$50$	−5.00087e8	+	7.14689e8i	−0.226314	+	0.323431i
$51$		−	1.83352e9i		−	0.744130i
$52$	1.62089e9	−	5.91140e8i	0.591202	−	0.215612i
$53$	−2.74065e9			−0.900193			−0.450097	−	0.892980i	$-0.648610\pi$
$53$	−2.74065e9			−0.900193			−0.450097	+	0.892980i	$0.648610\pi$
$54$	3.72285e8	−	5.32042e8i	0.110334	−	0.157681i
$55$	−4.33921e9			−1.16256
$56$	−4.11987e9	+	1.08614e8i	−0.999653	+	0.0263544i
$57$	−4.10531e9			−0.903720
$58$	3.94915e9	−	5.64383e9i	0.790040	−	1.12907i
$59$	6.43711e9			1.17221			0.586104	−	0.810236i	$-0.300661\pi$
$59$	6.43711e9			1.17221			0.586104	+	0.810236i	$0.300661\pi$
$60$	2.54169e9	−	9.26957e8i	0.421980	−	0.153896i
$61$			8.14609e9i			1.23491i	0.786606	+	0.617455i	$0.211836\pi$
$61$			8.14609e9i			1.23491i	−0.786606	+	0.617455i	$0.788164\pi$
$62$	−6.18286e8	+	8.83610e8i	−0.0857107	+	0.122492i
$63$	−2.51820e9	+	7.43764e8i	−0.319681	+	0.0944195i
$64$	7.44739e9	+	4.28058e9i	0.866990	+	0.498325i
$65$	4.57977e9			0.489577
$66$	−7.19186e9	−	5.03234e9i	−0.706886	−	0.494628i
$67$			1.41934e10i			1.28432i	0.766570	+	0.642161i	$0.221962\pi$
$67$			1.41934e10i			1.28432i	−0.766570	+	0.642161i	$0.778038\pi$
$68$	1.45175e10	−	5.29454e9i	1.21086	−	0.441600i
$69$		−	6.91218e9i		−	0.532041i
$70$	−1.03728e10	−	3.47608e9i	−0.737661	−	0.247201i
$71$		−	2.71362e10i		−	1.78496i	−0.451089	−	0.892479i	$-0.648964\pi$
$71$		−	2.71362e10i		−	1.78496i	0.451089	−	0.892479i	$-0.351036\pi$
$72$	5.28766e9	+	1.41135e9i	0.322059	+	0.0859617i
$73$			1.06360e10i			0.600487i	0.953863	+	0.300243i	$0.0970679\pi$
$73$			1.06360e10i			0.600487i	−0.953863	+	0.300243i	$0.902932\pi$
$74$	1.36066e10	−	1.94456e10i	0.712813	−	1.01870i
$75$	−4.68377e9			−0.227908
$76$	−1.18547e10	−	3.25052e10i	−0.536308	−	1.47054i
$77$	1.00538e10	+	3.40396e10i	0.423283	+	1.43313i
$78$	7.59057e9	+	5.31133e9i	0.297683	+	0.208297i
$79$		−	4.56423e10i		−	1.66885i	−0.551119	−	0.834427i	$-0.685799\pi$
$79$		−	4.56423e10i		−	1.66885i	0.551119	−	0.834427i	$-0.314201\pi$
$80$	1.46790e10	+	1.74481e10i	0.500843	+	0.595322i
$81$	3.48678e9			0.111111
$82$	1.75607e10	+	1.22877e10i	0.523077	+	0.366011i
$83$	3.93065e10			1.09530			0.547652	−	0.836706i	$-0.315522\pi$
$83$	3.93065e10			1.09530			0.547652	+	0.836706i	$0.315522\pi$
$84$	−1.31607e10	−	1.77910e10i	−0.343354	−	0.464157i
$85$	4.10187e10			1.00272
$86$	9.62127e8	+	6.73227e8i	0.0220542	+	0.0154319i
$87$	3.69873e10			0.795604
$88$	1.90778e10	−	7.14757e10i	0.385367	−	1.44379i
$89$			1.09223e10i			0.207332i	0.994612	+	0.103666i	$0.0330574\pi$
$89$			1.09223e10i			0.207332i	−0.994612	+	0.103666i	$0.966943\pi$
$90$	1.19026e10	+	8.32860e9i	0.212476	+	0.148675i
$91$	−1.06112e10	−	3.59268e10i	−0.178252	−	0.603519i
$92$	5.47297e10	−	1.99599e10i	0.865744	−	0.315737i
$93$	−5.79081e9			−0.0863144
$94$	−5.83295e10	+	8.33603e10i	−0.819757	+	1.17154i
$95$		−	9.18423e10i		−	1.21776i
$96$	4.09403e9	+	4.59424e10i	0.0512460	+	0.575071i
$97$		−	7.12847e10i		−	0.842853i	−0.906863	−	0.421427i	$-0.861530\pi$
$97$		−	7.12847e10i		−	0.842853i	0.906863	−	0.421427i	$-0.138470\pi$
$98$	−3.23526e9	+	8.94251e10i	−0.0361548	+	0.999346i
$99$		−	4.71324e10i		−	0.498111i
$100$	−1.35251e10	−	3.70854e10i	−0.135251	−	0.370854i
$101$		−	6.31654e10i		−	0.598014i	−0.954251	−	0.299007i	$-0.903345\pi$
$101$		−	6.31654e10i		−	0.598014i	0.954251	−	0.299007i	$-0.0966555\pi$
$102$	6.79848e10	+	4.75709e10i	0.609693	+	0.426619i
$103$	−1.06288e11			−0.903403			−0.451701	−	0.892169i	$-0.649183\pi$
$103$	−1.06288e11			−0.903403			−0.451701	+	0.892169i	$0.649183\pi$
$104$	−2.01355e10	+	7.54383e10i	−0.162285	+	0.608007i
$105$	−1.66392e10	−	5.63361e10i	−0.127230	−	0.430771i
$106$	7.11065e10	−	1.01620e11i	0.516092	−	0.737561i
$107$		−	1.10899e10i		−	0.0764393i	−0.999269	−	0.0382197i	$-0.987831\pi$
$107$		−	1.10899e10i		−	0.0764393i	0.999269	−	0.0382197i	$-0.0121687\pi$
$108$	1.00686e10	+	2.76079e10i	0.0659383	+	0.180801i
$109$	1.33724e10			0.0832461			0.0416231	−	0.999133i	$-0.486747\pi$
$109$	1.33724e10			0.0832461			0.0416231	+	0.999133i	$0.486747\pi$
$110$	1.12582e11	−	1.60893e11i	0.666511	−	0.952529i
$111$	1.27438e11			0.717833
$112$	1.02863e11	−	1.55578e11i	0.551520	−	0.834162i
$113$	2.60074e11			1.32790			0.663949	−	0.747778i	$-0.268879\pi$
$113$	2.60074e11			1.32790			0.663949	+	0.747778i	$0.268879\pi$
$114$	1.06513e11	−	1.52220e11i	0.518114	−	0.740451i
$115$	1.54637e11			0.716926
$116$	1.06806e11	+	2.92860e11i	0.472147	+	1.29462i
$117$			4.97454e10i			0.209764i
$118$	−1.67012e11	+	2.38681e11i	−0.672042	+	0.960434i
$119$	−9.50388e10	−	3.21778e11i	−0.365084	−	1.23608i
$120$	−3.15741e10	+	1.18293e11i	−0.115833	+	0.433974i
$121$	−3.51799e11			−1.23303
$122$	−3.02048e11	−	2.11352e11i	−1.01181	−	0.707989i
$123$			1.15086e11i			0.368589i
$124$	−1.67218e10	−	4.58508e10i	−0.0512229	−	0.140452i
$125$		−	3.70228e11i		−	1.08509i
$126$	3.77571e10	−	1.12669e11i	0.105916	−	0.316058i
$127$		−	3.87764e11i		−	1.04147i	−0.853718	−	0.520736i	$-0.825658\pi$
$127$		−	3.87764e11i		−	1.04147i	0.853718	−	0.520736i	$-0.174342\pi$
$128$	−3.51943e11	+	1.65081e11i	−0.905352	+	0.424661i
$129$			6.30538e9i			0.0155406i
$130$	−1.18823e11	+	1.69813e11i	−0.280680	+	0.401128i
$131$	2.90731e11			0.658414			0.329207	−	0.944258i	$-0.393219\pi$
$131$	2.90731e11			0.658414			0.329207	+	0.944258i	$0.393219\pi$
$132$	3.73188e11	−	1.36102e11i	0.810533	−	0.295602i
$133$	−7.20471e11	+	2.12795e11i	−1.50118	+	0.443381i
$134$	−5.26275e11	−	3.68249e11i	−1.05229	−	0.736318i
$135$			7.80049e10i			0.149722i
$136$	−1.80343e11	+	6.75662e11i	−0.332381	+	1.24528i
$137$	−2.56453e11			−0.453988			−0.226994	−	0.973896i	$-0.572890\pi$
$137$	−2.56453e11			−0.453988			−0.226994	+	0.973896i	$0.572890\pi$
$138$	2.56297e11	+	1.79338e11i	0.435921	+	0.305026i
$139$	−1.04106e12			−1.70174			−0.850871	−	0.525375i	$-0.823925\pi$
$139$	−1.04106e12			−1.70174			−0.850871	+	0.525375i	$0.823925\pi$
$140$	3.98013e11	−	2.94425e11i	0.625451	−	0.462670i
$141$	−5.46309e11			−0.825530
$142$	1.00618e12	+	7.04053e11i	1.46248	+	1.02334i
$143$	6.72432e11			0.940373
$144$	−1.89520e11	+	1.59443e11i	−0.255072	+	0.214591i
$145$			8.27466e11i			1.07208i
$146$	−3.94373e11	−	2.75953e11i	−0.492001	−	0.344267i
$147$	−4.03386e11	+	2.61058e11i	−0.484702	+	0.313683i
$148$	3.67996e11	+	1.00904e12i	0.425994	+	1.16807i
$149$	−4.71222e11			−0.525655			−0.262828	−	0.964843i	$-0.584655\pi$
$149$	−4.71222e11			−0.525655			−0.262828	+	0.964843i	$0.584655\pi$
$150$	1.21521e11	−	1.73669e11i	0.130662	−	0.186733i
$151$		−	1.27333e12i		−	1.31998i	−0.751276	−	0.659988i	$-0.770561\pi$
$151$		−	1.27333e12i		−	1.31998i	0.751276	−	0.659988i	$-0.229439\pi$
$152$	1.51283e12	+	4.03795e11i	1.51234	+	0.403665i
$153$			4.45544e11i			0.429624i
$154$	−1.52300e12	−	5.10380e11i	−1.41689	−	0.474821i
$155$		−	1.29550e11i		−	0.116309i
$156$	−3.93877e11	+	1.43647e11i	−0.341331	+	0.124483i
$157$		−	1.29255e12i		−	1.08143i	−0.841206	−	0.540715i	$-0.818154\pi$
$157$		−	1.29255e12i		−	1.08143i	0.841206	−	0.540715i	$-0.181846\pi$
$158$	1.69237e12	+	1.18420e12i	1.36735	+	0.956775i
$159$	6.65977e11			0.519727
$160$	−1.02780e12	+	9.15901e10i	−0.774909	+	0.0690539i
$161$	−3.58287e11	−	1.21307e12i	−0.261029	−	0.883780i
$162$	−9.04652e10	+	1.29286e11i	−0.0637014	+	0.0910374i
$163$		−	4.22550e9i		−	0.00287638i	−0.999999	−	0.00143819i	$-0.999542\pi$
$163$		−	4.22550e9i		−	0.00287638i	0.999999	−	0.00143819i	$-0.000457790\pi$
$164$	−9.11230e11	+	3.32326e11i	−0.599773	+	0.218737i
$165$	1.05443e12			0.671205
$166$	−1.01981e12	+	1.45744e12i	−0.627952	+	0.897424i
$167$	3.17476e11			0.189135			0.0945673	−	0.995518i	$-0.469853\pi$
$167$	3.17476e11			0.189135			0.0945673	+	0.995518i	$0.469853\pi$
$168$	1.00113e12	−	2.63933e10i	0.577150	−	0.0152157i
$169$	1.08245e12			0.603991
$170$	−1.06424e12	+	1.52093e12i	−0.574869	+	0.821562i
$171$	9.97589e11			0.521763
$172$	−4.99251e10	+	1.82077e10i	−0.0252879	+	0.00922250i
$173$			1.84988e10i			0.00907588i	0.999990	+	0.00453794i	$0.00144448\pi$
$173$			1.84988e10i			0.00907588i	−0.999990	+	0.00453794i	$0.998556\pi$
$174$	−9.59642e11	+	1.37145e12i	−0.456130	+	0.651868i
$175$	−8.21991e11	+	2.42779e11i	−0.378580	+	0.111816i
$176$	2.15527e12	+	2.56183e12i	0.962014	+	1.14349i
$177$	−1.56422e12			−0.676775
$178$	−4.04986e11	−	2.83380e11i	−0.169875	−	0.118866i
$179$			2.67186e12i			1.08673i	0.839497	+	0.543365i	$0.182850\pi$
$179$			2.67186e12i			1.08673i	−0.839497	+	0.543365i	$0.817150\pi$
$180$	−6.17632e11	+	2.25250e11i	−0.243630	+	0.0888519i
$181$			7.23940e11i			0.276994i	0.990363	+	0.138497i	$0.0442271\pi$
$181$			7.23940e11i			0.276994i	−0.990363	+	0.138497i	$0.955773\pi$
$182$	1.60744e12	+	5.38675e11i	0.596679	+	0.199956i
$183$		−	1.97950e12i		−	0.712975i
$184$	−6.79877e11	+	2.54718e12i	−0.237647	+	0.890352i
$185$			2.85100e12i			0.967280i
$186$	1.50244e11	−	2.14717e11i	0.0494851	−	0.0707206i
$187$	6.02262e12			1.92600
$188$	−1.57754e12	−	4.32559e12i	−0.489907	−	1.34331i
$189$	6.11922e11	−	1.80735e11i	0.184568	−	0.0545131i
$190$	3.40541e12	+	2.38286e12i	0.997758	+	0.698159i
$191$		−	3.76977e12i		−	1.07308i	−0.843875	−	0.536539i	$-0.819731\pi$
$191$		−	3.76977e12i		−	1.07308i	0.843875	−	0.536539i	$-0.180269\pi$
$192$	−1.80972e12	−	1.04018e12i	−0.500557	−	0.287708i
$193$	−5.64414e12			−1.51716			−0.758582	−	0.651577i	$-0.774108\pi$
$193$	−5.64414e12			−1.51716			−0.758582	+	0.651577i	$0.774108\pi$
$194$	2.64316e12	+	1.84949e12i	0.690581	+	0.483218i
$195$	−1.11289e12			−0.282657
$196$	−3.23185e12	−	2.44011e12i	−0.798073	−	0.602561i
$197$	−6.45692e12			−1.55046			−0.775231	−	0.631678i	$-0.782367\pi$
$197$	−6.45692e12			−1.55046			−0.775231	+	0.631678i	$0.782367\pi$
$198$	1.74762e12	+	1.22286e12i	0.408121	+	0.285573i
$199$	−6.53747e12			−1.48497			−0.742485	−	0.669863i	$-0.766353\pi$
$199$	−6.53747e12			−1.48497			−0.742485	+	0.669863i	$0.766353\pi$
$200$	1.72600e12	+	4.60692e11i	0.381395	+	0.101800i
$201$		−	3.44899e12i		−	0.741504i
$202$	2.34211e12	+	1.63884e12i	0.489975	+	0.342849i
$203$	6.49119e12	−	1.91721e12i	1.32159	−	0.390338i
$204$	−3.52776e12	+	1.28657e12i	−0.699089	+	0.254958i
$205$	−2.57465e12			−0.496674
$206$	2.75767e12	−	3.94106e12i	0.517932	−	0.740191i
$207$			1.67966e12i			0.307174i
$208$	−2.27475e12	−	2.70386e12i	−0.405122	−	0.481544i
$209$		−	1.34849e13i		−	2.33906i
$210$	2.52059e12	+	8.44687e11i	0.425889	+	0.142722i
$211$		−	7.53604e12i		−	1.24048i	−0.784412	−	0.620240i	$-0.787035\pi$
$211$		−	7.53604e12i		−	1.24048i	0.784412	−	0.620240i	$-0.212965\pi$
$212$	1.92310e12	+	5.27311e12i	0.308429	+	0.845706i
$213$			6.59409e12i			1.03055i
$214$	4.11202e11	+	2.87729e11i	0.0626295	+	0.0438236i
$215$	−1.41061e11			−0.0209410
$216$	−1.28490e12	−	3.42957e11i	−0.185941	−	0.0496300i
$217$	−1.01627e12	+	3.00162e11i	−0.143378	+	0.0423474i
$218$	−3.46949e11	+	4.95835e11i	−0.0477260	+	0.0682066i
$219$		−	2.58455e12i		−	0.346691i
$220$	3.04481e12	+	8.34881e12i	0.398323	+	1.09219i
$221$	−6.35652e12			−0.811076
$222$	−3.30641e12	+	4.72528e12i	−0.411543	+	0.588147i
$223$	−3.38078e12			−0.410526			−0.205263	−	0.978707i	$-0.565805\pi$
$223$	−3.38078e12			−0.410526			−0.205263	+	0.978707i	$0.565805\pi$
$224$	3.09988e12	+	7.85057e12i	0.367266	+	0.930116i
$225$	1.13816e12			0.131582
$226$	−6.74765e12	+	9.64326e12i	−0.761301	+	1.08800i
$227$	−8.61391e12			−0.948545			−0.474272	−	0.880378i	$-0.657289\pi$
$227$	−8.61391e12			−0.948545			−0.474272	+	0.880378i	$0.657289\pi$
$228$	2.88068e12	+	7.89877e12i	0.309638	+	0.849019i
$229$			2.98123e12i			0.312824i	0.987692	+	0.156412i	$0.0499928\pi$
$229$			2.98123e12i			0.312824i	−0.987692	+	0.156412i	$0.950007\pi$
$230$	−4.01207e12	+	5.73376e12i	−0.411022	+	0.587404i
$231$	−2.44307e12	−	8.27163e12i	−0.244383	−	0.827419i
$232$	−1.36301e13	−	3.63805e12i	−1.33142	−	0.355373i
$233$	1.16544e13			1.11182			0.555908	−	0.831244i	$-0.312371\pi$
$233$	1.16544e13			1.11182			0.555908	+	0.831244i	$0.312371\pi$
$234$	−1.84451e12	−	1.29065e12i	−0.171867	−	0.120260i
$235$		−	1.22218e13i		−	1.11240i
$236$	−4.51690e12	−	1.23852e13i	−0.401629	−	1.10126i
$237$			1.10911e13i			0.963513i
$238$	1.43970e13	+	4.82464e12i	1.22208	+	0.409535i
$239$		−	1.46201e13i		−	1.21272i	−0.795189	−	0.606362i	$-0.792628\pi$
$239$		−	1.46201e13i		−	1.21272i	0.795189	−	0.606362i	$-0.207372\pi$
$240$	−3.56700e12	−	4.23988e12i	−0.289162	−	0.343709i
$241$		−	3.45733e12i		−	0.273935i	−0.990576	−	0.136967i	$-0.956264\pi$
$241$		−	3.45733e12i		−	0.273935i	0.990576	−	0.136967i	$-0.0437355\pi$
$242$	9.12748e12	−	1.30443e13i	0.706913	−	1.01027i
$243$	−8.47289e11			−0.0641500
$244$	1.56734e13	−	5.71609e12i	1.16016	−	0.423112i
$245$	−5.84027e12	−	9.02438e12i	−0.422688	−	0.653137i
$246$	−4.26725e12	−	2.98591e12i	−0.301999	−	0.211317i
$247$			1.42325e13i			0.985024i
$248$	2.13395e12	+	5.69580e11i	0.144444	+	0.0385541i
$249$	−9.55148e12			−0.632375
$250$	1.37277e13	+	9.60562e12i	0.889050	+	0.622093i
$251$	1.79752e13			1.13885			0.569426	−	0.822042i	$-0.307165\pi$
$251$	1.79752e13			1.13885			0.569426	+	0.822042i	$0.307165\pi$
$252$	3.19804e12	+	4.32322e12i	0.198235	+	0.267981i
$253$	2.27047e13			1.37706
$254$	1.43779e13	+	1.00606e13i	0.853316	+	0.597089i
$255$	−9.96754e12			−0.578918
$256$	3.01018e12	−	1.73327e13i	0.171109	−	0.985252i
$257$		−	2.38099e13i		−	1.32473i	−0.749183	−	0.662363i	$-0.769554\pi$
$257$		−	2.38099e13i		−	1.32473i	0.749183	−	0.662363i	$-0.230446\pi$
$258$	−2.33797e11	−	1.63594e11i	−0.0127330	−	0.00890962i
$259$	2.23651e13	−	6.60566e12i	1.19240	−	0.352182i
$260$	−3.21362e12	−	8.81166e12i	−0.167742	−	0.459944i
$261$	−8.98792e12			−0.459342
$262$	−7.54306e12	+	1.07800e13i	−0.377477	+	0.539463i
$263$		−	2.55888e12i		−	0.125399i	−0.998032	−	0.0626994i	$-0.980029\pi$
$263$		−	2.55888e12i		−	0.125399i	0.998032	−	0.0626994i	$-0.0199709\pi$
$264$	−4.63591e12	+	1.73686e13i	−0.222491	+	0.833572i
$265$			1.48990e13i			0.700332i
$266$	1.08025e13	−	3.22353e13i	0.497366	−	1.48417i
$267$		−	2.65411e12i		−	0.119703i
$268$	2.73086e13	−	9.95945e12i	1.20659	−	0.440042i
$269$		−	3.01660e12i		−	0.130581i	−0.997866	−	0.0652904i	$-0.979203\pi$
$269$		−	3.01660e12i		−	0.130581i	0.997866	−	0.0652904i	$-0.0207974\pi$
$270$	−2.89234e12	−	2.02385e12i	−0.122673	−	0.0858376i
$271$	3.43268e13			1.42660			0.713299	−	0.700860i	$-0.247200\pi$
$271$	3.43268e13			1.42660			0.713299	+	0.700860i	$0.247200\pi$
$272$	−2.03738e13	−	2.42171e13i	−0.829742	−	0.986264i
$273$	2.57851e12	+	8.73021e12i	0.102914	+	0.348442i
$274$	6.65371e12	−	9.50901e12i	0.260277	−	0.371969i
$275$		−	1.53850e13i		−	0.589884i
$276$	−1.32993e13	+	4.85026e12i	−0.499838	+	0.182291i
$277$	−1.66656e12			−0.0614021			−0.0307010	−	0.999529i	$-0.509774\pi$
$277$	−1.66656e12			−0.0614021			−0.0307010	+	0.999529i	$0.509774\pi$
$278$	2.70104e13	−	3.86014e13i	0.975630	−	1.39430i
$279$	1.40717e12			0.0498336
$280$	5.90460e11	+	2.23968e13i	0.0205032	+	0.777710i
$281$	4.69969e13			1.60024			0.800119	−	0.599841i	$-0.204769\pi$
$281$	4.69969e13			1.60024			0.800119	+	0.599841i	$0.204769\pi$
$282$	1.41741e13	−	2.02565e13i	0.473287	−	0.676387i
$283$	−1.24994e13			−0.409321			−0.204661	−	0.978833i	$-0.565609\pi$
$283$	−1.24994e13			−0.409321			−0.204661	+	0.978833i	$0.565609\pi$
$284$	−5.22111e13	+	1.90414e13i	−1.67692	+	0.611572i
$285$			2.23177e13i			0.703076i
$286$	−1.74463e13	+	2.49331e13i	−0.539127	+	0.770482i
$287$	5.96536e12	+	2.01972e13i	0.180837	+	0.612268i
$288$	−9.94850e11	−	1.11640e13i	−0.0295869	−	0.332018i
$289$	−2.26601e13			−0.661187
$290$	−3.06816e13	−	2.14687e13i	−0.878392	−	0.614635i
$291$			1.73222e13i			0.486621i
$292$	2.04641e13	−	7.46327e12i	0.564141	−	0.205742i
$293$			1.84601e13i			0.499415i	0.968321	+	0.249708i	$0.0803345\pi$
$293$			1.84601e13i			0.499415i	−0.968321	+	0.249708i	$0.919665\pi$
$294$	7.86168e11	−	2.17303e13i	0.0208740	−	0.576973i
$295$		−	3.49941e13i		−	0.911955i
$296$	−4.69618e13	−	1.25347e13i	−1.20127	−	0.320635i
$297$			1.14532e13i			0.287585i
$298$	1.22259e13	−	1.74724e13i	0.301365	−	0.430689i
$299$	−2.39635e13			−0.579907
$300$	3.28659e12	+	9.01176e12i	0.0780870	+	0.214113i
$301$	3.26834e11	+	1.10658e12i	0.00762451	+	0.0258147i
$302$	4.72136e13	+	3.30366e13i	1.08151	+	0.756759i
$303$			1.53492e13i			0.345264i
$304$	−5.42229e13	+	4.56176e13i	−1.19778	+	1.00769i
$305$	4.42846e13			0.960735
$306$	−1.65203e13	−	1.15597e13i	−0.352006	−	0.246309i
$307$	−6.61866e13			−1.38519			−0.692595	−	0.721327i	$-0.743533\pi$
$307$	−6.61866e13			−1.38519			−0.692595	+	0.721327i	$0.743533\pi$
$308$	5.84389e13	−	4.32294e13i	1.20136	−	0.888690i
$309$	2.58281e13			0.521580
$310$	4.80357e12	+	3.36119e12i	0.0952960	+	0.0666812i
$311$	−1.68689e13			−0.328779			−0.164390	−	0.986395i	$-0.552565\pi$
$311$	−1.68689e13			−0.328779			−0.164390	+	0.986395i	$0.552565\pi$
$312$	4.89292e12	−	1.83315e13i	0.0936954	−	0.351033i
$313$		−	1.38968e13i		−	0.261470i	−0.991417	−	0.130735i	$-0.958266\pi$
$313$		−	1.38968e13i		−	0.261470i	0.991417	−	0.130735i	$-0.0417337\pi$
$314$	4.79263e13	+	3.35354e13i	0.886056	+	0.619998i
$315$	4.04332e12	+	1.36897e13i	0.0734565	+	0.248705i
$316$	−8.78175e13	+	3.20271e13i	−1.56784	+	0.571792i
$317$	4.86606e13			0.853791			0.426896	−	0.904301i	$-0.359607\pi$
$317$	4.86606e13			0.853791			0.426896	+	0.904301i	$0.359607\pi$
$318$	−1.72789e13	+	2.46937e13i	−0.297966	+	0.425831i
$319$			1.21494e14i			2.05923i
$320$	2.32705e13	−	4.04862e13i	0.387687	−	0.674501i
$321$			2.69485e12i			0.0441323i
$322$	5.42753e13	+	1.81884e13i	0.873765	+	0.292811i
$323$			1.27473e14i			2.01745i
$324$	−2.44667e12	−	6.70871e12i	−0.0380695	−	0.104386i
$325$			1.62379e13i			0.248411i
$326$	1.56677e11	+	1.09631e11i	0.00235673	+	0.00164907i
$327$	−3.24950e12			−0.0480622
$328$	1.13197e13	−	4.24097e13i	0.164638	−	0.616821i
$329$	−9.58759e13	+	2.83174e13i	−1.37130	+	0.405020i
$330$	−2.73573e13	+	3.90971e13i	−0.384810	+	0.549943i
$331$			7.08497e12i			0.0980131i	0.998798	+	0.0490065i	$0.0156055\pi$
$331$			7.08497e12i			0.0980131i	−0.998798	+	0.0490065i	$0.984394\pi$
$332$	−2.75813e13	−	7.56273e13i	−0.375280	−	1.02901i
$333$	−3.09675e13			−0.414441
$334$	−8.23697e12	+	1.17717e13i	−0.108433	+	0.154965i
$335$	7.71594e13			0.999177
$336$	−2.49958e13	+	3.78056e13i	−0.318420	+	0.481603i
$337$	−6.94775e13			−0.870723			−0.435362	−	0.900256i	$-0.643379\pi$
$337$	−6.94775e13			−0.870723			−0.435362	+	0.900256i	$0.643379\pi$
$338$	−2.80843e13	+	4.01361e13i	−0.346276	+	0.494872i
$339$	−6.31979e13			−0.766663
$340$	−2.87827e13	−	7.89215e13i	−0.343556	−	0.942023i
$341$		−	1.90213e13i		−	0.223404i
$342$	−2.58826e13	+	3.69896e13i	−0.299133	+	0.427500i
$343$	−5.72615e13	+	6.67241e13i	−0.651246	+	0.758866i
$344$	6.20192e11	−	2.32357e12i	0.00694153	−	0.0260067i
$345$	−3.75767e13			−0.413917
$346$	−6.85914e11	−	4.79953e11i	−0.00743621	−	0.00520332i
$347$			1.18609e14i			1.26563i	0.774303	+	0.632815i	$0.218101\pi$
$347$			1.18609e14i			1.26563i	−0.774303	+	0.632815i	$0.781899\pi$
$348$	−2.59539e13	−	7.11651e13i	−0.272594	−	0.747448i
$349$		−	4.19719e13i		−	0.433929i	−0.976179	−	0.216965i	$-0.930384\pi$
$349$		−	4.19719e13i		−	0.433929i	0.976179	−	0.216965i	$-0.0696156\pi$
$350$	1.23247e13	−	3.67775e13i	0.125430	−	0.374290i
$351$		−	1.20881e13i		−	0.121107i
$352$	−1.50909e14	+	1.34478e13i	−1.48844	+	0.132638i
$353$		−	7.72445e13i		−	0.750078i	−0.927009	−	0.375039i	$-0.877629\pi$
$353$		−	7.72445e13i		−	0.750078i	0.927009	−	0.375039i	$-0.122371\pi$
$354$	4.05839e13	−	5.79996e13i	0.388003	−	0.554507i
$355$	−1.47520e14			−1.38866
$356$	2.10148e13	−	7.66411e12i	0.194783	−	0.0710374i
$357$	2.30944e13	+	7.81920e13i	0.210781	+	0.713653i
$358$	−9.90697e13	−	6.93218e13i	−0.890398	−	0.623036i
$359$		−	1.49376e13i		−	0.132209i	−0.997813	−	0.0661047i	$-0.978943\pi$
$359$		−	1.49376e13i		−	0.132209i	0.997813	−	0.0661047i	$-0.0210571\pi$
$360$	7.67251e12	−	2.87453e13i	0.0668765	−	0.250555i
$361$	1.68926e14			1.45013
$362$	−2.68429e13	−	1.87827e13i	−0.226951	−	0.158804i
$363$	8.54871e13			0.711892
$364$	−6.16787e13	+	4.56260e13i	−0.505915	+	0.374244i
$365$	5.78206e13			0.467167
$366$	7.33978e13	+	5.13584e13i	0.584167	+	0.408758i
$367$	−9.76081e13			−0.765284			−0.382642	−	0.923897i	$-0.624986\pi$
$367$	−9.76081e13			−0.765284			−0.382642	+	0.923897i	$0.624986\pi$
$368$	−7.68073e13	−	9.12962e13i	−0.593252	−	0.705163i
$369$		−	2.79658e13i		−	0.212805i
$370$	−1.05712e14	−	7.39696e13i	−0.792528	−	0.554554i
$371$	1.16877e14	−	3.45204e13i	0.863325	−	0.254987i
$372$	4.06340e12	+	1.11417e13i	0.0295735	+	0.0810900i
$373$	−7.23376e12			−0.0518759			−0.0259380	−	0.999664i	$-0.508257\pi$
$373$	−7.23376e12			−0.0518759			−0.0259380	+	0.999664i	$0.508257\pi$
$374$	−1.56258e14	+	2.23313e14i	−1.10420	+	1.57804i
$375$			8.99653e13i			0.626474i
$376$	2.01318e14	+	5.37345e13i	1.38150	+	0.368740i
$377$		−	1.28229e14i		−	0.867182i
$378$	−9.17498e12	+	2.73786e13i	−0.0611505	+	0.182476i
$379$			8.20115e13i			0.538715i	0.963040	+	0.269358i	$0.0868114\pi$
$379$			8.20115e13i			0.538715i	−0.963040	+	0.269358i	$0.913189\pi$
$380$	−1.76708e14	+	6.44455e13i	−1.14405	+	0.417237i
$381$			9.42268e13i			0.601294i
$382$	1.39779e14	+	9.78074e13i	0.879213	+	0.615209i
$383$	2.68090e14			1.66222			0.831109	−	0.556110i	$-0.187707\pi$
$383$	2.68090e14			1.66222			0.831109	+	0.556110i	$0.187707\pi$
$384$	8.55222e13	−	4.01147e13i	0.522705	−	0.245178i
$385$	1.85050e14	−	5.46554e13i	1.11495	−	0.329306i
$386$	1.46438e14	−	2.09279e14i	0.869809	−	1.24307i
$387$		−	1.53221e12i		−	0.00897237i
$388$	−1.37155e14	+	5.00203e13i	−0.791837	+	0.288783i
$389$	−9.82134e12			−0.0559046			−0.0279523	−	0.999609i	$-0.508899\pi$
$389$	−9.82134e12			−0.0559046			−0.0279523	+	0.999609i	$0.508899\pi$
$390$	2.88740e13	−	4.12646e13i	0.162051	−	0.231591i
$391$	−2.14628e14			−1.18772
$392$	1.74328e14	−	5.65246e13i	0.951245	−	0.308435i
$393$	−7.06476e13			−0.380136
$394$	1.67526e14	−	2.39416e14i	0.888899	−	1.27035i
$395$	−2.48125e14			−1.29833
$396$	−9.06846e13	+	3.30727e13i	−0.467962	+	0.170666i
$397$		−	1.53071e14i		−	0.779012i	−0.921024	−	0.389506i	$-0.872646\pi$
$397$		−	1.53071e14i		−	0.779012i	0.921024	−	0.389506i	$-0.127354\pi$
$398$	1.69616e14	−	2.42402e14i	0.851352	−	1.21669i
$399$	1.75075e14	−	5.17092e13i	0.866707	−	0.255986i
$400$	−6.18633e13	+	5.20455e13i	−0.302067	+	0.254128i
$401$	2.75042e14			1.32466			0.662330	−	0.749212i	$-0.269568\pi$
$401$	2.75042e14			1.32466			0.662330	+	0.749212i	$0.269568\pi$
$402$	1.27885e14	+	8.94846e13i	0.607542	+	0.425114i
$403$			2.00759e13i			0.0940798i
$404$	−1.21533e14	+	4.43230e13i	−0.561818	+	0.204895i
$405$		−	1.89552e13i		−	0.0864422i
$406$	−9.73269e13	+	2.90429e14i	−0.437865	+	1.30661i
$407$			4.18602e14i			1.85794i
$408$	4.38234e13	−	1.64186e14i	0.191900	−	0.718960i
$409$			3.94220e14i			1.70318i	0.524209	+	0.851589i	$0.324361\pi$
$409$			3.94220e14i			1.70318i	−0.524209	+	0.851589i	$0.675639\pi$
$410$	6.67996e13	−	9.54652e13i	0.284749	−	0.406943i
$411$	6.23181e13			0.262110
$412$	7.45823e13	+	2.04503e14i	0.309529	+	0.848721i
$413$	−2.74517e14	+	8.10799e13i	−1.12420	+	0.332038i
$414$	−6.22801e13	−	4.35791e13i	−0.251679	−	0.176107i
$415$		−	2.13682e14i		−	0.852125i
$416$	1.59275e14	−	1.41934e13i	0.626808	−	0.0558564i
$417$	2.52977e14			0.982501
$418$	5.00005e14	+	3.49867e14i	1.91648	+	1.34101i
$419$	−2.43065e14			−0.919488			−0.459744	−	0.888052i	$-0.652059\pi$
$419$	−2.43065e14			−0.919488			−0.459744	+	0.888052i	$0.652059\pi$
$420$	−9.67173e13	+	7.15454e13i	−0.361104	+	0.267122i
$421$	2.95381e14			1.08851			0.544253	−	0.838921i	$-0.316813\pi$
$421$	2.95381e14			1.08851			0.544253	+	0.838921i	$0.316813\pi$
$422$	2.79428e14	+	1.95524e14i	1.01637	+	0.711182i
$423$	1.32753e14			0.476620
$424$	−2.45417e14	−	6.55050e13i	−0.869745	−	0.232147i
$425$			1.45435e14i			0.508778i
$426$	−2.44502e14	−	1.71085e14i	−0.844364	−	0.590825i
$427$	−1.02606e14	−	3.47398e14i	−0.349799	−	1.18433i
$428$	−2.13374e13	+	7.78175e12i	−0.0718126	+	0.0261901i
$429$	−1.63401e14			−0.542924
$430$	3.65986e12	−	5.23041e12i	0.0120057	−	0.0171577i
$431$		−	5.25825e14i		−	1.70301i	−0.524349	−	0.851503i	$-0.675691\pi$
$431$		−	5.25825e14i		−	1.70301i	0.524349	−	0.851503i	$-0.324309\pi$
$432$	4.60535e13	−	3.87447e13i	0.147266	−	0.123894i
$433$		−	5.15314e14i		−	1.62700i	−0.581563	−	0.813502i	$-0.697558\pi$
$433$		−	5.15314e14i		−	1.62700i	0.581563	−	0.813502i	$-0.302442\pi$
$434$	1.52377e13	−	4.54701e13i	0.0475035	−	0.141753i
$435$		−	2.01074e14i		−	0.618964i
$436$	−9.38339e12	−	2.57290e13i	−0.0285223	−	0.0782074i
$437$			4.80561e14i			1.44245i
$438$	9.58325e13	+	6.70567e13i	0.284057	+	0.198762i
$439$	6.12231e14			1.79209			0.896047	−	0.443959i	$-0.146427\pi$
$439$	6.12231e14			1.79209			0.896047	+	0.443959i	$0.146427\pi$
$440$	−3.88563e14	−	1.03713e14i	−1.12324	−	0.299807i
$441$	9.80227e13	−	6.34370e13i	0.279843	−	0.181105i
$442$	1.64921e14	−	2.35693e14i	0.465000	−	0.664545i
$443$		−	4.47032e14i		−	1.24485i	−0.782678	−	0.622427i	$-0.786147\pi$
$443$		−	4.47032e14i		−	1.24485i	0.782678	−	0.622427i	$-0.213853\pi$
$444$	−8.94231e13	−	2.45196e14i	−0.245948	−	0.674384i
$445$	5.93766e13			0.161300
$446$	8.77149e13	−	1.25356e14i	0.235360	−	0.336359i
$447$	1.14507e14			0.303487
$448$	−3.71518e14	−	8.87441e13i	−0.972636	−	0.232333i
$449$	−6.35151e14			−1.64256			−0.821282	−	0.570523i	$-0.806740\pi$
$449$	−6.35151e14			−1.64256			−0.821282	+	0.570523i	$0.806740\pi$
$450$	−2.95297e13	+	4.22016e13i	−0.0754379	+	0.107810i
$451$	−3.78026e14			−0.954005
$452$	−1.82493e14	−	5.00392e14i	−0.454972	−	1.24752i
$453$			3.09418e14i			0.762089i
$454$	2.23489e14	−	3.19395e14i	0.543813	−	0.777178i
$455$	−1.95309e14	+	5.76855e13i	−0.469525	+	0.138677i
$456$	−3.67618e14	−	9.81221e13i	−0.873152	−	0.233056i
$457$	−5.44167e14			−1.27701			−0.638504	−	0.769619i	$-0.720446\pi$
$457$	−5.44167e14			−1.27701			−0.638504	+	0.769619i	$0.720446\pi$
$458$	−1.10541e14	−	7.73485e13i	−0.256308	−	0.179346i
$459$		−	1.08267e14i		−	0.248043i
$460$	−1.08508e14	−	2.97527e14i	−0.245637	−	0.673532i
$461$			3.64976e14i			0.816412i	0.912890	+	0.408206i	$0.133846\pi$
$461$			3.64976e14i			0.816412i	−0.912890	+	0.408206i	$0.866154\pi$
$462$	3.70089e14	+	1.24022e14i	0.818042	+	0.274138i
$463$		−	3.30321e14i		−	0.721507i	−0.932661	−	0.360753i	$-0.882520\pi$
$463$		−	3.30321e14i		−	0.721507i	0.932661	−	0.360753i	$-0.117480\pi$
$464$	4.88529e14	−	4.10999e14i	1.05449	−	0.887139i
$465$			3.14806e13i			0.0671509i
$466$	−3.02376e14	+	4.32134e14i	−0.637418	+	0.910952i
$467$	2.22908e14			0.464389			0.232194	−	0.972669i	$-0.425409\pi$
$467$	2.22908e14			0.464389			0.232194	+	0.972669i	$0.425409\pi$
$468$	9.57122e13	−	3.49062e13i	0.197067	−	0.0718705i
$469$	−1.78775e14	−	6.05289e14i	−0.363795	−	1.23172i
$470$	4.53171e14	+	3.17096e14i	0.911432	+	0.637754i
$471$			3.14089e14i			0.624364i
$472$	5.76424e14	+	1.53855e14i	1.13256	+	0.302295i
$473$	−2.07115e13			−0.0402232
$474$	−4.11245e14	−	2.87760e14i	−0.789442	−	0.552394i
$475$	3.25633e14			0.617894
$476$	−5.52424e14	+	4.08649e14i	−1.03618	+	0.766500i
$477$	−1.61832e14			−0.300064
$478$	5.42098e14	+	3.79321e14i	0.993629	+	0.695269i
$479$	5.49770e14			0.996175			0.498087	−	0.867127i	$-0.334036\pi$
$479$	5.49770e14			0.996175			0.498087	+	0.867127i	$0.334036\pi$
$480$	2.49757e14	−	2.22564e13i	0.447394	−	0.0398683i
$481$		−	4.41809e14i		−	0.782414i
$482$	1.28194e14	+	8.97009e13i	0.224445	+	0.157050i
$483$	8.70638e13	+	2.94776e14i	0.150705	+	0.510251i
$484$	2.46856e14	+	6.76875e14i	0.422469	+	1.15840i
$485$	−3.87525e14			−0.655723
$486$	2.19830e13	−	3.14166e13i	0.0367780	−	0.0525605i
$487$			1.42973e14i			0.236508i	0.992983	+	0.118254i	$0.0377297\pi$
$487$			1.42973e14i			0.236508i	−0.992983	+	0.118254i	$0.962270\pi$
$488$	−1.94702e14	+	7.29458e14i	−0.318465	+	1.19314i
$489$			1.02680e12i			0.00166068i
$490$	4.86142e14	+	1.75878e13i	0.777471	+	0.0281277i
$491$		−	4.38358e14i		−	0.693235i	−0.938007	−	0.346617i	$-0.887330\pi$
$491$		−	4.38358e14i		−	0.693235i	0.938007	−	0.346617i	$-0.112670\pi$
$492$	2.21429e14	−	8.07552e13i	0.346279	−	0.126288i
$493$		−	1.14848e15i		−	1.77610i
$494$	−5.27725e14	−	3.69263e14i	−0.807066	−	0.564726i
$495$	−2.56226e14			−0.387520
$496$	−7.64851e13	+	6.43468e13i	−0.114400	+	0.0962449i
$497$	3.41799e14	+	1.15725e15i	0.505605	+	1.71185i
$498$	2.47815e14	−	3.54159e14i	0.362548	−	0.518128i
$499$		−	7.83780e14i		−	1.13407i	−0.823693	−	0.567037i	$-0.808090\pi$
$499$		−	7.83780e14i		−	1.13407i	0.823693	−	0.567037i	$-0.191910\pi$
$500$	−7.12333e14	+	2.59788e14i	−1.01941	+	0.371778i
$501$	−7.71467e13			−0.109197
$502$	−4.66369e14	+	6.66500e14i	−0.652918	+	0.933104i
$503$	8.22033e14			1.13832			0.569161	−	0.822226i	$-0.307268\pi$
$503$	8.22033e14			1.13832			0.569161	+	0.822226i	$0.307268\pi$
$504$	−2.43274e14	+	6.41357e12i	−0.333218	+	0.00878480i
$505$	−3.43386e14			−0.465243
$506$	−5.89078e14	+	8.41868e14i	−0.789487	+	1.12828i
$507$	−2.63035e14			−0.348715
$508$	−7.46074e14	+	2.72093e14i	−0.978434	+	0.356835i
$509$		−	1.40094e14i		−	0.181748i	−0.995862	−	0.0908742i	$-0.971034\pi$
$509$		−	1.40094e14i		−	0.181748i	0.995862	−	0.0908742i	$-0.0289661\pi$
$510$	2.58609e14	−	3.69586e14i	0.331901	−	0.474329i
$511$	−1.33968e14	−	4.53583e14i	−0.170093	−	0.575893i
$512$	5.64580e14	+	5.61315e14i	0.709154	+	0.705053i
$513$	−2.42414e14			−0.301240
$514$	8.82847e14	+	6.17752e14i	1.08540	+	0.759482i
$515$			5.77816e14i			0.702829i
$516$	1.21318e13	−	4.42447e12i	0.0146000	−	0.00532461i
$517$		−	1.79448e15i		−	2.13669i
$518$	−3.35336e14	+	1.00066e15i	−0.395063	+	1.17889i
$519$		−	4.49520e12i		−	0.00523996i
$520$	4.10105e14	+	1.09463e14i	0.473017	+	0.126255i
$521$			8.23169e14i			0.939467i	0.882808	+	0.469734i	$0.155650\pi$
$521$			8.23169e14i			0.939467i	−0.882808	+	0.469734i	$0.844350\pi$
$522$	2.33193e14	−	3.33263e14i	0.263347	−	0.376356i
$523$	−6.47730e14			−0.723827			−0.361914	−	0.932212i	$-0.617876\pi$
$523$	−6.47730e14			−0.723827			−0.361914	+	0.932212i	$0.617876\pi$
$524$	−2.04005e14	−	5.59378e14i	−0.225590	−	0.618562i
$525$	1.99744e14	−	5.89954e13i	0.218573	−	0.0645568i
$526$	9.48806e13	+	6.63905e13i	0.102744	+	0.0718927i
$527$			1.79809e14i			0.192687i
$528$	−5.23730e14	−	6.22526e14i	−0.555419	−	0.660193i
$529$	1.43680e14			0.150797
$530$	−5.52438e14	−	3.86556e14i	−0.573808	−	0.401509i
$531$	3.80105e14			0.390736
$532$	9.14979e14	+	1.23690e15i	0.930887	+	1.25840i
$533$	3.98984e14			0.401750
$534$	9.84115e13	+	6.88612e13i	0.0980774	+	0.0686274i
$535$	−6.02880e13			−0.0594682
$536$	−3.39240e14	+	1.27097e15i	−0.331208	+	1.24088i
$537$		−	6.49261e14i		−	0.627424i
$538$	1.11852e14	+	7.82661e13i	0.106990	+	0.0748636i
$539$	−8.57506e14	−	1.32502e15i	−0.811893	−	1.25454i
$540$	1.50085e14	−	5.47359e13i	0.140660	−	0.0512987i
$541$	6.18999e14			0.574255			0.287128	−	0.957892i	$-0.407300\pi$
$541$	6.18999e14			0.574255			0.287128	+	0.957892i	$0.407300\pi$
$542$	−8.90613e14	+	1.27280e15i	−0.817886	+	1.16886i
$543$		−	1.75917e14i		−	0.159923i
$544$	1.42655e15	−	1.27123e14i	1.28378	−	0.114401i
$545$		−	7.26964e13i		−	0.0647638i
$546$	−3.90607e14	−	1.30898e14i	−0.344493	−	0.115445i
$547$			4.78642e14i			0.417908i	0.977926	+	0.208954i	$0.0670058\pi$
$547$			4.78642e14i			0.417908i	−0.977926	+	0.208954i	$0.932994\pi$
$548$	1.79952e14	+	4.93425e14i	0.155548	+	0.426509i
$549$			4.81018e14i			0.411636i
$550$	5.70459e14	+	3.99166e14i	0.483314	+	0.338188i
$551$	−2.57150e15			−2.15701
$552$	1.65210e14	−	6.18965e14i	0.137206	−	0.514045i
$553$	5.74896e14	+	1.94646e15i	0.472717	+	1.60050i
$554$	4.32392e13	−	6.17944e13i	0.0352026	−	0.0503090i
$555$		−	6.92792e14i		−	0.558460i
$556$	7.30508e14	+	2.00304e15i	0.583060	+	1.59874i
$557$	−1.38920e15			−1.09790			−0.548949	−	0.835856i	$-0.684972\pi$
$557$	−1.38920e15			−1.09790			−0.548949	+	0.835856i	$0.684972\pi$
$558$	−3.65092e13	+	5.21763e13i	−0.0285702	+	0.0408305i
$559$	2.18598e13			0.0169387
$560$	−8.45771e14	−	5.59196e14i	−0.648961	−	0.429072i
$561$	−1.46350e15			−1.11198
$562$	−1.21934e15	+	1.74260e15i	−0.917437	+	1.31113i
$563$	1.93128e15			1.43896			0.719481	−	0.694512i	$-0.244380\pi$
$563$	1.93128e15			1.43896			0.719481	+	0.694512i	$0.244380\pi$
$564$	3.83343e14	+	1.05112e15i	0.282848	+	0.775562i
$565$		−	1.41384e15i		−	1.03308i
$566$	3.24299e14	−	4.63465e14i	0.234669	−	0.335372i
$567$	−1.48697e14	+	4.39185e13i	−0.106560	+	0.0314732i
$568$	6.48590e14	−	2.42996e15i	0.460314	−	1.72458i
$569$	−8.04046e14			−0.565150			−0.282575	−	0.959245i	$-0.591189\pi$
$569$	−8.04046e14			−0.565150			−0.282575	+	0.959245i	$0.591189\pi$
$570$	−8.27516e14	−	5.79036e14i	−0.576056	−	0.403082i
$571$			4.67550e14i			0.322352i	0.986926	+	0.161176i	$0.0515286\pi$
$571$			4.67550e14i			0.322352i	−0.986926	+	0.161176i	$0.948471\pi$
$572$	−4.71843e14	−	1.29378e15i	−0.322196	−	0.883454i
$573$			9.16055e14i			0.619542i
$574$	−9.03665e14	−	3.02831e14i	−0.605330	−	0.202855i
$575$			5.48275e14i			0.363769i
$576$	4.39761e14	+	2.52764e14i	0.288997	+	0.166108i
$577$		−	1.72016e15i		−	1.11970i	−0.828594	−	0.559850i	$-0.810859\pi$
$577$		−	1.72016e15i		−	1.11970i	0.828594	−	0.559850i	$-0.189141\pi$
$578$	5.87921e14	−	8.40214e14i	0.379067	−	0.541735i
$579$	1.37153e15			0.875935
$580$	1.59208e15	−	5.80631e14i	1.00719	−	0.367321i
$581$	−1.67626e15	+	4.95093e14i	−1.05045	+	0.310255i
$582$	−6.42288e14	−	4.49427e14i	−0.398707	−	0.278986i
$583$			2.18756e15i			1.34519i
$584$	−2.54215e14	+	9.52424e14i	−0.154857	+	0.580176i
$585$	2.70431e14			0.163192
$586$	−6.84481e14	−	4.78950e14i	−0.409189	−	0.286321i
$587$	1.15177e15			0.682116			0.341058	−	0.940042i	$-0.389215\pi$
$587$	1.15177e15			0.682116			0.341058	+	0.940042i	$0.389215\pi$
$588$	7.85339e14	+	5.92946e14i	0.460768	+	0.347888i
$589$	4.02599e14			0.234012
$590$	1.29754e15	+	9.07926e14i	0.747198	+	0.522835i
$591$	1.56903e15			0.895160
$592$	1.68321e15	−	1.41608e15i	0.951410	−	0.800420i
$593$			2.92762e15i			1.63951i	0.572716	+	0.819754i	$0.305890\pi$
$593$			2.92762e15i			1.63951i	−0.572716	+	0.819754i	$0.694110\pi$
$594$	−4.24672e14	−	2.97155e14i	−0.235629	−	0.164876i
$595$	−1.74928e15	+	5.16659e14i	−0.961648	+	0.284028i
$596$	3.30655e14	+	9.06650e14i	0.180103	+	0.493839i
$597$	1.58860e15			0.857348
$598$	6.21736e14	−	8.88540e14i	0.332468	−	0.475139i
$599$		−	1.14091e15i		−	0.604511i	−0.953227	−	0.302256i	$-0.902260\pi$
$599$		−	1.14091e15i		−	0.604511i	0.953227	−	0.302256i	$-0.0977396\pi$
$600$	−4.19418e14	−	1.11948e14i	−0.220199	−	0.0587740i
$601$		−	3.04492e15i		−	1.58404i	−0.610496	−	0.792020i	$-0.709030\pi$
$601$		−	3.04492e15i		−	1.58404i	0.610496	−	0.792020i	$-0.290970\pi$
$602$	−4.95106e13	−	1.65917e13i	−0.0255222	−	0.00855285i
$603$			8.38104e14i			0.428108i
$604$	−2.44993e15	+	8.93489e14i	−1.24008	+	0.452258i
$605$			1.91248e15i			0.959275i
$606$	−5.69132e14	−	3.98237e14i	−0.282887	−	0.197944i
$607$	−1.90514e15			−0.938403			−0.469201	−	0.883091i	$-0.655458\pi$
$607$	−1.90514e15			−0.938403			−0.469201	+	0.883091i	$0.655458\pi$
$608$	−2.84632e14	−	3.19409e15i	−0.138936	−	1.55911i
$609$	−1.57736e15	+	4.65881e14i	−0.763019	+	0.225362i
$610$	−1.14897e15	+	1.64203e15i	−0.550801	+	0.787165i
$611$			1.89397e15i			0.899800i
$612$	8.57245e14	−	3.12637e14i	0.403619	−	0.147200i
$613$	1.53053e15			0.714180			0.357090	−	0.934070i	$-0.383769\pi$
$613$	1.53053e15			0.714180			0.357090	+	0.934070i	$0.383769\pi$
$614$	1.71722e15	−	2.45413e15i	0.794147	−	1.13494i
$615$	6.25639e14			0.286755
$616$	8.66952e13	+	3.28845e15i	0.0393823	+	1.49381i
$617$	3.22182e15			1.45055			0.725275	−	0.688459i	$-0.241712\pi$
$617$	3.22182e15			1.45055			0.725275	+	0.688459i	$0.241712\pi$
$618$	−6.70114e14	+	9.57679e14i	−0.299028	+	0.427349i
$619$	−1.54903e15			−0.685111			−0.342556	−	0.939498i	$-0.611293\pi$
$619$	−1.54903e15			−0.685111			−0.342556	+	0.939498i	$0.611293\pi$
$620$	−2.49259e14	+	9.09047e13i	−0.109269	+	0.0398503i
$621$		−	4.08157e14i		−	0.177347i
$622$	4.37666e14	−	6.25481e14i	0.188493	−	0.269381i
$623$	−1.37573e14	−	4.65789e14i	−0.0587287	−	0.198841i
$624$	5.52765e14	+	6.57038e14i	0.233897	+	0.278020i
$625$	−1.07152e15			−0.449427
$626$	5.15280e14	+	3.60555e14i	0.214232	+	0.149904i
$627$			3.27682e15i			1.35046i
$628$	−2.48691e15	+	9.06978e14i	−1.01597	+	0.370526i
$629$		−	3.95705e15i		−	1.60248i
$630$	−6.12504e14	−	2.05259e14i	−0.245887	−	0.0824004i
$631$		−	2.76698e15i		−	1.10115i	−0.834787	−	0.550573i	$-0.814409\pi$
$631$		−	2.76698e15i		−	1.10115i	0.834787	−	0.550573i	$-0.185591\pi$
$632$	1.09091e15	−	4.08713e15i	0.430373	−	1.61241i
$633$			1.83126e15i			0.716191i
$634$	−1.26251e15	+	1.80428e15i	−0.489489	+	0.699543i
$635$	−2.10800e15			−0.810244
$636$	−4.67314e14	−	1.28137e15i	−0.178072	−	0.488269i
$637$	9.05046e14	+	1.39848e15i	0.341904	+	0.528309i
$638$	−4.50486e15	−	3.15218e15i	−1.68720	−	1.18058i
$639$		−	1.60237e15i		−	0.594986i
$640$	8.97431e14	+	1.91327e15i	0.330378	+	0.704346i
$641$	1.59687e15			0.582842			0.291421	−	0.956595i	$-0.405872\pi$
$641$	1.59687e15			0.582842			0.291421	+	0.956595i	$0.405872\pi$
$642$	−9.99220e13	−	6.99182e13i	−0.0361592	−	0.0253016i
$643$	1.41718e15			0.508470			0.254235	−	0.967142i	$-0.418176\pi$
$643$	1.41718e15			0.508470			0.254235	+	0.967142i	$0.418176\pi$
$644$	−2.08259e15	+	1.54057e15i	−0.740851	+	0.548035i
$645$	3.42779e13			0.0120903
$646$	−4.72656e15	−	3.30730e15i	−1.65297	−	1.15663i
$647$	1.56682e15			0.543307			0.271654	−	0.962395i	$-0.412430\pi$
$647$	1.56682e15			0.543307			0.271654	+	0.962395i	$0.412430\pi$
$648$	3.12231e14	+	8.33386e13i	0.107353	+	0.0286539i
$649$		−	5.13805e15i		−	1.75167i
$650$	−6.02085e14	−	4.21295e14i	−0.203533	−	0.142417i
$651$	2.46955e14	−	7.29393e13i	0.0827793	−	0.0244493i
$652$	−8.13003e12	+	2.96502e12i	−0.00270228	+	0.000985522i
$653$	−3.23757e15			−1.06708			−0.533539	−	0.845776i	$-0.679138\pi$
$653$	−3.23757e15			−1.06708			−0.533539	+	0.845776i	$0.679138\pi$
$654$	8.43087e13	−	1.20488e14i	0.0275546	−	0.0393791i
$655$		−	1.58050e15i		−	0.512233i
$656$	1.27882e15	+	1.52005e15i	0.410995	+	0.488525i
$657$			6.28046e14i			0.200162i
$658$	1.43753e15	−	4.28968e15i	0.454334	−	1.35576i
$659$			2.70350e15i			0.847337i	0.905817	+	0.423669i	$0.139258\pi$
$659$			2.70350e15i			0.847337i	−0.905817	+	0.423669i	$0.860742\pi$
$660$	−7.39889e14	−	2.02876e15i	−0.229972	−	0.630578i
$661$			5.24604e15i			1.61705i	0.588460	+	0.808526i	$0.299734\pi$
$661$			5.24604e15i			1.61705i	−0.588460	+	0.808526i	$0.700266\pi$
$662$	−2.62703e14	−	1.83821e14i	−0.0803057	−	0.0561921i
$663$	1.54463e15			0.468275
$664$	3.51978e15	+	9.39476e14i	1.05826	+	0.282463i
$665$	1.15682e15	+	3.91670e15i	0.344942	+	1.16789i
$666$	8.03457e14	−	1.14824e15i	0.237604	−	0.339567i
$667$		−	4.32968e15i		−	1.26988i
$668$	−2.22772e14	−	6.10837e14i	−0.0648023	−	0.177687i
$669$	8.21530e14			0.237017
$670$	−2.00191e15	+	2.86099e15i	−0.572841	+	0.818663i
$671$	6.50214e15			1.84537
$672$	−7.53270e14	−	1.90769e15i	−0.212041	−	0.537003i
$673$	−9.60634e14			−0.268210			−0.134105	−	0.990967i	$-0.542816\pi$
$673$	−9.60634e14			−0.268210			−0.134105	+	0.990967i	$0.542816\pi$
$674$	1.80261e15	−	2.57615e15i	0.499196	−	0.713415i
$675$	−2.76572e14			−0.0759692
$676$	−7.59552e14	−	2.08267e15i	−0.206943	−	0.567433i
$677$		−	2.52070e15i		−	0.681213i	−0.940206	−	0.340606i	$-0.889368\pi$
$677$		−	2.52070e15i		−	0.681213i	0.940206	−	0.340606i	$-0.110632\pi$
$678$	1.63968e15	−	2.34331e15i	0.439537	−	0.628155i
$679$	8.97881e14	+	3.04000e15i	0.238745	+	0.808333i
$680$	3.67310e15	+	9.80399e14i	0.968799	+	0.258585i
$681$	2.09318e15			0.547643
$682$	7.05290e14	+	4.93511e14i	0.183043	+	0.128080i
$683$			1.94269e15i			0.500139i	0.968228	+	0.250070i	$0.0804535\pi$
$683$			1.94269e15i			0.500139i	−0.968228	+	0.250070i	$0.919547\pi$
$684$	−7.00006e14	−	1.91940e15i	−0.178769	−	0.490182i
$685$			1.39415e15i			0.353194i
$686$	−9.88401e14	−	3.85437e15i	−0.248399	−	0.968658i
$687$		−	7.24439e14i		−	0.180609i
$688$	7.00646e13	+	8.32815e13i	0.0173286	+	0.0205974i
$689$		−	2.30884e15i		−	0.566485i
$690$	9.74933e14	−	1.39330e15i	0.237304	−	0.339138i
$691$	−4.59159e15			−1.10875			−0.554375	−	0.832267i	$-0.687043\pi$
$691$	−4.59159e15			−1.10875			−0.554375	+	0.832267i	$0.687043\pi$
$692$	3.55923e13	−	1.29805e13i	0.00852654	−	0.00310963i
$693$	5.93666e14	+	2.01001e15i	0.141094	+	0.477710i
$694$	−4.39791e15	−	3.07734e15i	−1.03698	−	0.725601i
$695$			5.65951e15i			1.32392i
$696$	3.31210e15	+	8.84045e14i	0.768693	+	0.205175i
$697$	3.57349e15			0.822835
$698$	1.55627e15	+	1.08897e15i	0.355534	+	0.248777i
$699$	−2.83203e15			−0.641908
$700$	1.04391e15	+	1.41118e15i	0.234759	+	0.317354i
$701$	3.26867e15			0.729327			0.364664	−	0.931139i	$-0.381184\pi$
$701$	3.26867e15			0.729327			0.364664	+	0.931139i	$0.381184\pi$
$702$	4.48216e14	+	3.13629e14i	0.0992277	+	0.0694323i
$703$	−8.85998e15			−1.94616
$704$	3.41672e15	−	5.94445e15i	0.744664	−	1.29557i
$705$			2.96990e15i			0.642246i
$706$	2.86414e15	+	2.00412e15i	0.614567	+	0.430029i
$707$	7.95612e14	+	2.69375e15i	0.169393	+	0.573522i
$708$	1.09761e15	+	3.00962e15i	0.231880	+	0.635811i
$709$	2.04448e15			0.428576			0.214288	−	0.976770i	$-0.431257\pi$
$709$	2.04448e15			0.428576			0.214288	+	0.976770i	$0.431257\pi$
$710$	3.82744e15	−	5.46990e15i	0.796137	−	1.13778i
$711$		−	2.69513e15i		−	0.556285i
$712$	−2.61056e14	+	9.78055e14i	−0.0534679	+	0.200319i
$713$			6.77863e14i			0.137768i
$714$	−3.49846e15	−	1.17239e15i	−0.705566	−	0.236445i
$715$		−	3.65554e15i		−	0.731591i
$716$	5.14076e15	−	1.87484e15i	1.02095	−	0.372342i
$717$			3.55268e15i			0.700166i
$718$	5.53872e14	+	3.87559e14i	0.108324	+	0.0757973i
$719$	3.98252e15			0.772946			0.386473	−	0.922301i	$-0.373693\pi$
$719$	3.98252e15			0.772946			0.386473	+	0.922301i	$0.373693\pi$
$720$	8.66781e14	+	1.03029e15i	0.166948	+	0.198441i
$721$	4.53277e15	−	1.33878e15i	0.866402	−	0.255897i
$722$	−4.38281e15	+	6.26359e15i	−0.831377	+	1.18814i
$723$			8.40131e14i			0.158156i
$724$	1.39289e15	−	5.07987e14i	0.260228	−	0.0949052i
$725$	−2.93384e15			−0.543973
$726$	−2.21798e15	+	3.16977e15i	−0.408137	+	0.583279i
$727$	−2.02135e15			−0.369150			−0.184575	−	0.982818i	$-0.559091\pi$
$727$	−2.02135e15			−0.369150			−0.184575	+	0.982818i	$0.559091\pi$
$728$	−9.15015e13	−	3.47076e15i	−0.0165846	−	0.629074i
$729$	2.05891e14			0.0370370
$730$	−1.50016e15	+	2.14393e15i	−0.267832	+	0.382767i
$731$	1.95787e14			0.0346927
$732$	−3.80863e15	+	1.38901e15i	−0.669820	+	0.244284i
$733$		−	2.92144e15i		−	0.509947i	−0.966948	−	0.254973i	$-0.917933\pi$
$733$		−	2.92144e15i		−	0.509947i	0.966948	−	0.254973i	$-0.0820667\pi$
$734$	2.53246e15	−	3.61921e15i	0.438747	−	0.627025i
$735$	1.41919e15	+	2.19293e15i	0.244039	+	0.377089i
$736$	5.37794e15	−	4.79241e14i	0.917885	−	0.0817949i
$737$	1.13290e16			1.91921
$738$	1.03694e15	+	7.25577e14i	0.174359	+	0.122004i
$739$		−	3.16735e14i		−	0.0528629i	−0.999651	−	0.0264315i	$-0.991586\pi$
$739$		−	3.16735e14i		−	0.0528629i	0.999651	−	0.0264315i	$-0.00841437\pi$
$740$	5.48543e15	−	2.00054e15i	0.908733	−	0.331415i
$741$		−	3.45849e15i		−	0.568704i
$742$	−1.75242e15	+	5.22933e15i	−0.286034	+	0.853541i
$743$		−	8.34829e15i		−	1.35257i	−0.736641	−	0.676284i	$-0.763589\pi$
$743$		−	8.34829e15i		−	1.35257i	0.736641	−	0.676284i	$-0.236411\pi$
$744$	−5.18550e14	−	1.38408e14i	−0.0833949	−	0.0222592i
$745$			2.56170e15i			0.408949i
$746$	1.87681e14	−	2.68220e14i	0.0297411	−	0.0425038i
$747$	2.32101e15			0.365102
$748$	−4.22606e15	−	1.15878e16i	−0.659898	−	1.80943i
$749$	1.39685e14	+	4.72939e14i	0.0216521	+	0.0733086i
$750$	−3.33582e15	−	2.33417e15i	−0.513293	−	0.359166i
$751$			9.90068e15i			1.51233i	0.654384	+	0.756163i	$0.272928\pi$
$751$			9.90068e15i			1.51233i	−0.654384	+	0.756163i	$0.727072\pi$
$752$	−7.21565e15	+	6.07051e15i	−1.09415	+	0.920507i
$753$	−4.36797e15			−0.657517
$754$	4.75461e15	+	3.32693e15i	0.710514	+	0.497166i
$755$	−6.92218e15			−1.02691
$756$	−7.77125e14	−	1.05054e15i	−0.114451	−	0.154719i
$757$	1.12142e16			1.63961			0.819807	−	0.572639i	$-0.194080\pi$
$757$	1.12142e16			1.63961			0.819807	+	0.572639i	$0.194080\pi$
$758$	−3.04090e15	−	2.12780e15i	−0.441389	−	0.308852i
$759$	−5.51725e15			−0.795047
$760$	2.19515e15	−	8.22420e15i	0.314043	−	1.17657i
$761$		−	3.67210e15i		−	0.521554i	−0.965399	−	0.260777i	$-0.916021\pi$
$761$		−	3.67210e15i		−	0.521554i	0.965399	−	0.260777i	$-0.0839788\pi$
$762$	−3.49383e15	−	2.44473e15i	−0.492662	−	0.344729i
$763$	−5.70279e14	+	1.68435e14i	−0.0798367	+	0.0235802i
$764$	−7.25319e15	+	2.64524e15i	−1.00813	+	0.367664i
$765$	2.42211e15			0.334238
$766$	−6.95565e15	+	9.94051e15i	−0.952970	+	1.36192i
$767$			5.42290e15i			0.737662i
$768$	−7.31474e14	+	4.21186e15i	−0.0987898	+	0.568836i
$769$		−	7.83363e15i		−	1.05043i	−0.850969	−	0.525216i	$-0.823984\pi$
$769$		−	7.83363e15i		−	1.05043i	0.850969	−	0.525216i	$-0.176016\pi$
$770$	−2.77458e15	+	8.27949e15i	−0.369401	+	1.10231i
$771$			5.78581e15i			0.764831i
$772$	3.96048e15	+	1.08595e16i	0.519819	+	1.42533i
$773$		−	1.46024e15i		−	0.190299i	−0.995463	−	0.0951496i	$-0.969667\pi$
$773$		−	1.46024e15i		−	0.190299i	0.995463	−	0.0951496i	$-0.0303329\pi$
$774$	5.68127e13	+	3.97534e13i	0.00735140	+	0.00514397i
$775$	4.59328e14			0.0590151
$776$	1.70380e15	−	6.38333e15i	0.217359	−	0.814344i
$777$	−5.43472e15	+	1.60517e15i	−0.688433	+	0.203332i
$778$	2.54816e14	−	3.64165e14i	0.0320508	−	0.0458047i
$779$		−	8.00117e15i		−	0.999304i
$780$	7.80909e14	+	2.14123e15i	0.0968456	+	0.265549i
$781$	−2.16599e16			−2.66732
$782$	5.56857e15	−	7.95820e15i	0.680936	−	0.973145i
$783$	2.18406e15			0.265201
$784$	−2.42708e15	+	7.93042e15i	−0.292648	+	0.956220i
$785$	−7.02668e15			−0.841331
$786$	1.83296e15	−	2.61954e15i	0.217937	−	0.311459i
$787$	1.06275e16			1.25479			0.627395	−	0.778701i	$-0.284121\pi$
$787$	1.06275e16			1.25479			0.627395	+	0.778701i	$0.284121\pi$
$788$	4.53080e15	+	1.24234e16i	0.531228	+	1.45662i
$789$			6.21808e14i			0.0723990i
$790$	6.43764e15	−	9.20022e15i	0.744351	−	1.06377i
$791$	−1.10911e16	+	3.27581e15i	−1.27351	+	0.376139i
$792$	1.12653e15	−	4.22057e15i	0.128456	−	0.481263i
$793$	−6.86262e15			−0.777119
$794$	5.67570e15	+	3.97144e15i	0.638274	+	0.446618i
$795$		−	3.62045e15i		−	0.404337i
$796$	4.58732e15	+	1.25783e16i	0.508789	+	1.39509i
$797$		−	1.25432e16i		−	1.38162i	−0.723037	−	0.690809i	$-0.757255\pi$
$797$		−	1.25432e16i		−	1.38162i	0.723037	−	0.690809i	$-0.242745\pi$
$798$	−2.62501e15	+	7.83318e15i	−0.287155	+	0.856885i
$799$			1.69633e16i			1.84290i
$800$	−3.24739e14	−	3.64415e15i	−0.0350380	−	0.393189i
$801$			6.44948e14i			0.0691108i
$802$	−7.13600e15	+	1.01983e16i	−0.759444	+	1.08534i
$803$	8.48959e15			0.897328
$804$	−6.63599e15	+	2.42015e15i	−0.696622	+	0.254058i
$805$	−6.59462e15	+	1.94776e15i	−0.687563	+	0.203075i
$806$	−7.44392e14	−	5.20871e14i	−0.0770830	−	0.0539371i
$807$			7.33033e14i			0.0753909i
$808$	1.50973e15	−	5.65627e15i	0.154219	−	0.577787i
$809$	−6.21622e15			−0.630680			−0.315340	−	0.948979i	$-0.602119\pi$
$809$	−6.21622e15			−0.630680			−0.315340	+	0.948979i	$0.602119\pi$
$810$	7.02839e14	+	4.91796e14i	0.0708253	+	0.0495584i
$811$	4.57367e15			0.457773			0.228886	−	0.973453i	$-0.426492\pi$
$811$	4.57367e15			0.457773			0.228886	+	0.973453i	$0.426492\pi$
$812$	−8.24363e15	−	1.11440e16i	−0.819522	−	1.10786i
$813$	−8.34140e15			−0.823647
$814$	−1.55213e16	−	1.08607e16i	−1.52228	−	1.06518i
$815$	−2.29711e13			−0.00223777
$816$	4.95083e15	+	5.88475e15i	0.479052	+	0.569419i
$817$		−	4.38374e14i		−	0.0421331i
$818$	−1.46173e16	−	1.02281e16i	−1.39548	−	0.976454i
$819$	−6.26579e14	−	2.12144e15i	−0.0594175	−	0.201173i
$820$	1.80662e15	+	4.95372e15i	0.170173	+	0.466611i
$821$	2.81401e15			0.263293			0.131646	−	0.991297i	$-0.457974\pi$
$821$	2.81401e15			0.263293			0.131646	+	0.991297i	$0.457974\pi$
$822$	−1.61685e15	+	2.31069e15i	−0.150271	+	0.214757i
$823$		−	1.82231e15i		−	0.168237i	−0.996456	−	0.0841187i	$-0.973193\pi$
$823$		−	1.82231e15i		−	0.168237i	0.996456	−	0.0841187i	$-0.0268075\pi$
$824$	−9.51781e15	−	2.54043e15i	−0.872845	−	0.232974i
$825$			3.73855e15i			0.340570i
$826$	4.11602e15	−	1.22824e16i	0.372466	−	1.11146i
$827$			3.40047e15i			0.305674i	0.988251	+	0.152837i	$0.0488409\pi$
$827$			3.40047e15i			0.305674i	−0.988251	+	0.152837i	$0.951159\pi$
$828$	3.23173e15	−	1.17861e15i	0.288581	−	0.105246i
$829$			2.04061e16i			1.81013i	0.425274	+	0.905065i	$0.360178\pi$
$829$			2.04061e16i			1.81013i	−0.425274	+	0.905065i	$0.639822\pi$
$830$	7.92310e15	+	5.54401e15i	0.698177	+	0.488534i
$831$	4.04975e14			0.0354505
$832$	−3.60614e15	+	6.27401e15i	−0.313592	+	0.545590i
$833$	8.10603e15	+	1.25254e16i	0.700262	+	1.08204i
$834$	−6.56353e15	+	9.38013e15i	−0.563280	+	0.804999i
$835$		−	1.72590e15i		−	0.147143i
$836$	−2.59454e16	+	9.46229e15i	−2.19748	+	0.801423i
$837$	−3.41942e14			−0.0287715
$838$	6.30637e15	−	9.01261e15i	0.527154	−	0.753370i
$839$	7.54614e15			0.626663			0.313331	−	0.949644i	$-0.398555\pi$
$839$	7.54614e15			0.626663			0.313331	+	0.949644i	$0.398555\pi$
$840$	−1.43482e14	−	5.44243e15i	−0.0118375	−	0.449011i
$841$	1.09678e16			0.898959
$842$	−7.66370e15	+	1.09524e16i	−0.624054	+	0.891853i
$843$	−1.14203e16			−0.923898
$844$	−1.44996e16	+	5.28802e15i	−1.16540	+	0.425020i
$845$		−	5.88452e15i		−	0.469893i
$846$	−3.44430e15	+	4.92234e15i	−0.273252	+	0.390512i
$847$	1.50028e16	−	4.43115e15i	1.18253	−	0.349267i
$848$	8.79623e15	−	7.40025e15i	0.688842	−	0.579521i
$849$	3.03736e15			0.236322
$850$	−5.39256e15	−	3.77332e15i	−0.416861	−	0.291689i
$851$		−	1.49177e16i		−	1.14575i
$852$	1.26873e16	−	4.62706e15i	0.968169	−	0.353091i
$853$			9.53937e15i			0.723269i	0.932320	+	0.361635i	$0.117781\pi$
$853$			9.53937e15i			0.723269i	−0.932320	+	0.361635i	$0.882219\pi$
$854$	1.55433e16	+	5.20877e15i	1.17091	+	0.392389i
$855$		−	5.42319e15i		−	0.405921i
$856$	2.65063e14	−	9.93067e14i	0.0197126	−	0.0738538i
$857$		−	1.82560e16i		−	1.34900i	−0.738275	−	0.674499i	$-0.764359\pi$
$857$		−	1.82560e16i		−	1.34900i	0.738275	−	0.674499i	$-0.235641\pi$
$858$	4.23946e15	−	6.05873e15i	0.311265	−	0.444838i
$859$	2.65863e14			0.0193952			0.00969761	−	0.999953i	$-0.496913\pi$
$859$	2.65863e14			0.0193952			0.00969761	+	0.999953i	$0.496913\pi$
$860$	9.89825e13	+	2.71408e14i	0.00717492	+	0.0196735i
$861$	−1.44958e15	−	4.90793e15i	−0.104406	−	0.353493i
$862$	1.94970e16	+	1.36426e16i	1.39534	+	0.976355i
$863$		−	6.96048e15i		−	0.494971i	−0.968892	−	0.247486i	$-0.920396\pi$
$863$		−	6.96048e15i		−	0.494971i	0.968892	−	0.247486i	$-0.0796043\pi$
$864$	2.41749e14	+	2.71285e15i	0.0170820	+	0.191690i
$865$	1.00565e14			0.00706085
$866$	1.91073e16	+	1.33699e16i	1.33306	+	0.932781i
$867$	5.50641e15			0.381737
$868$	1.29064e15	+	1.74473e15i	0.0889092	+	0.120190i
$869$	−3.64313e16			−2.49382
$870$	7.45562e15	+	5.21690e15i	0.507140	+	0.354860i
$871$	−1.19571e16			−0.808214
$872$	1.19746e15	+	3.19618e14i	0.0804304	+	0.0214679i
$873$		−	4.20929e15i		−	0.280951i
$874$	−1.78187e16	−	1.24682e16i	−1.18185	−	0.826974i
$875$	4.66328e15	+	1.57887e16i	0.307360	+	1.04064i
$876$	−4.97278e15	+	1.81357e15i	−0.325707	+	0.118785i
$877$	−1.73239e16			−1.12758			−0.563791	−	0.825917i	$-0.690658\pi$
$877$	−1.73239e16			−1.12758			−0.563791	+	0.825917i	$0.690658\pi$
$878$	−1.58844e16	+	2.27009e16i	−1.02743	+	1.46833i
$879$		−	4.48580e15i		−	0.288338i
$880$	1.39269e16	−	1.17167e16i	0.889610	−	0.748427i
$881$		−	6.87619e13i		−	0.00436496i	−0.999998	−	0.00218248i	$-0.999305\pi$
$881$		−	6.87619e13i		−	0.00436496i	0.999998	−	0.00218248i	$-0.000694706\pi$
$882$	−1.91039e14	+	5.28046e15i	−0.0120516	+	0.333115i
$883$		−	1.13287e16i		−	0.710222i	−0.934824	−	0.355111i	$-0.884443\pi$
$883$		−	1.13287e16i		−	0.710222i	0.934824	−	0.355111i	$-0.115557\pi$
$884$	4.46035e15	+	1.22302e16i	0.277895	+	0.761983i
$885$			8.50356e15i			0.526517i
$886$	1.65755e16	+	1.15983e16i	1.01995	+	0.713690i
$887$	−2.19948e16			−1.34505			−0.672527	−	0.740073i	$-0.734791\pi$
$887$	−2.19948e16			−1.34505			−0.672527	+	0.740073i	$0.734791\pi$
$888$	1.14117e16	+	3.04594e15i	0.693553	+	0.185119i
$889$	4.88417e15	+	1.65366e16i	0.295006	+	0.998817i
$890$	−1.54054e15	+	2.20162e15i	−0.0924755	+	0.132159i
$891$		−	2.78312e15i		−	0.166037i
$892$	2.37229e15	+	6.50475e15i	0.140657	+	0.385677i
$893$	3.79814e16			2.23814
$894$	−2.97090e15	+	4.24580e15i	−0.173993	+	0.248658i
$895$	1.45250e16			0.845454
$896$	1.29296e16	−	1.14730e16i	0.747983	−	0.663718i
$897$	5.82312e15			0.334809
$898$	1.64791e16	−	2.35507e16i	0.941702	−	1.34581i
$899$	−3.62727e15			−0.206016
$900$	−7.98641e14	−	2.18986e15i	−0.0450835	−	0.123618i
$901$		−	2.06791e16i		−	1.16023i
$902$	9.80795e15	−	1.40168e16i	0.546943	−	0.781652i
$903$	−7.94207e13	−	2.68899e14i	−0.00440201	−	0.0149041i
$904$	2.32888e16	+	6.21610e15i	1.28298	+	0.342445i
$905$	3.93555e15			0.215496
$906$	−1.14729e16	−	8.02790e15i	−0.624407	−	0.436915i
$907$		−	1.72687e16i		−	0.934156i	−0.884216	−	0.467078i	$-0.845307\pi$
$907$		−	1.72687e16i		−	0.934156i	0.884216	−	0.467078i	$-0.154693\pi$
$908$	6.04435e15	+	1.65735e16i	0.324996	+	0.891131i
$909$		−	3.72985e15i		−	0.199338i
$910$	2.92840e15	−	8.73850e15i	0.155562	−	0.464204i
$911$		−	2.34217e16i		−	1.23671i	−0.785899	−	0.618355i	$-0.787799\pi$
$911$		−	2.34217e16i		−	1.23671i	0.785899	−	0.618355i	$-0.212201\pi$
$912$	1.31762e16	−	1.10851e16i	0.691540	−	0.581792i
$913$		−	3.13741e16i		−	1.63675i
$914$	1.41185e16	−	2.01772e16i	0.732124	−	1.04630i
$915$	−1.07612e16			−0.554680
$916$	5.73600e15	−	2.09192e15i	0.293889	−	0.107182i
$917$	−1.23985e16	+	3.66196e15i	−0.631448	+	0.186502i
$918$	4.01444e15	+	2.80901e15i	0.203231	+	0.142206i
$919$		−	1.67818e16i		−	0.844505i	−0.906478	−	0.422252i	$-0.861240\pi$
$919$		−	1.67818e16i		−	0.844505i	0.906478	−	0.422252i	$-0.138760\pi$
$920$	1.38472e16	+	3.69601e15i	0.692676	+	0.184885i
$921$	1.60834e16			0.799740
$922$	−1.35329e16	−	9.46937e15i	−0.668917	−	0.468059i
$923$	2.28607e16			1.12326
$924$	−1.42006e16	+	1.05047e16i	−0.693605	+	0.513085i
$925$	−1.01084e16			−0.490799
$926$	1.22479e16	+	8.57022e15i	0.591157	+	0.413649i
$927$	−6.27623e15			−0.301134
$928$	2.56444e15	+	2.87776e16i	0.122315	+	1.37259i
$929$		−	1.66276e16i		−	0.788392i	−0.919026	−	0.394196i	$-0.871023\pi$
$929$		−	1.66276e16i		−	0.788392i	0.919026	−	0.394196i	$-0.128977\pi$
$930$	−1.16727e15	−	8.16769e14i	−0.0550192	−	0.0384984i
$931$	2.80449e16	−	1.81497e16i	1.31411	−	0.850444i
$932$	−8.17788e15	−	2.24236e16i	−0.380937	−	1.04452i
$933$	4.09914e15			0.189821
$934$	−5.78337e15	+	8.26518e15i	−0.266240	+	0.380491i
$935$		−	3.27408e16i		−	1.49839i
$936$	−1.18898e15	+	4.45455e15i	−0.0540950	+	0.202669i
$937$			3.20538e16i			1.44981i	0.688848	+	0.724906i	$0.258117\pi$
$937$			3.20538e16i			1.44981i	−0.688848	+	0.724906i	$0.741883\pi$
$938$	2.70819e16	+	9.07553e15i	1.21776	+	0.408090i
$939$			3.37693e15i			0.150960i
$940$	−2.35152e16	+	8.57600e15i	−1.04507	+	0.381138i
$941$			2.39250e16i			1.05708i	0.848907	+	0.528542i	$0.177261\pi$
$941$			2.39250e16i			1.05708i	−0.848907	+	0.528542i	$0.822739\pi$
$942$	−1.16461e16	−	8.14910e15i	−0.511565	−	0.357956i
$943$	1.34717e16			0.588314
$944$	−2.06602e16	+	1.73814e16i	−0.896992	+	0.754638i
$945$	−9.82527e14	−	3.32659e15i	−0.0424101	−	0.143590i
$946$	5.37364e14	−	7.67962e14i	0.0230604	−	0.0329563i
$947$		−	1.81573e15i		−	0.0774687i	−0.999250	−	0.0387344i	$-0.987667\pi$
$947$		−	1.81573e15i		−	0.0774687i	0.999250	−	0.0387344i	$-0.0123326\pi$
$948$	2.13397e16	−	7.78258e15i	0.905194	−	0.330124i
$949$	−8.96025e15			−0.377882
$950$	−8.44860e15	+	1.20741e16i	−0.354246	+	0.506263i
$951$	−1.18245e16			−0.492937
$952$	−8.19532e14	−	3.10858e16i	−0.0339674	−	1.28842i
$953$	1.36397e15			0.0562073			0.0281036	−	0.999605i	$-0.491053\pi$
$953$	1.36397e15			0.0562073			0.0281036	+	0.999605i	$0.491053\pi$
$954$	4.19877e15	−	6.00058e15i	0.172031	−	0.245854i
$955$	−2.04936e16			−0.834834
$956$	−2.81296e16	+	1.02589e16i	−1.13932	+	0.415510i
$957$		−	2.95230e16i		−	1.18890i
$958$	−1.42639e16	+	2.03849e16i	−0.571119	+	0.816203i
$959$	1.09367e16	−	3.23020e15i	0.435394	−	0.128596i
$960$	−5.65473e15	+	9.83816e15i	−0.223831	+	0.389423i
$961$	−2.48406e16			−0.977649
$962$	1.63818e16	+	1.14628e16i	0.641060	+	0.448567i
$963$		−	6.54847e14i		−	0.0254798i
$964$	−6.65203e15	+	2.42600e15i	−0.257354	+	0.0938570i
$965$			3.06832e16i			1.18032i
$966$	−1.31889e16	−	4.41979e15i	−0.504468	−	0.169055i
$967$		−	2.72962e16i		−	1.03814i	−0.854731	−	0.519072i	$-0.826278\pi$
$967$		−	2.72962e16i		−	1.03814i	0.854731	−	0.519072i	$-0.173722\pi$
$968$	−3.15025e16	−	8.40845e15i	−1.19133	−	0.317981i
$969$		−	3.09759e16i		−	1.16478i
$970$	1.00544e16	−	1.43690e16i	0.375934	−	0.537258i
$971$	−3.01801e16			−1.12206			−0.561029	−	0.827796i	$-0.689594\pi$
$971$	−3.01801e16			−1.12206			−0.561029	+	0.827796i	$0.689594\pi$
$972$	5.94540e14	+	1.63022e15i	0.0219794	+	0.0602672i
$973$	4.43969e16	−	1.31129e16i	1.63204	−	0.482033i
$974$	−5.30130e15	−	3.70947e15i	−0.193780	−	0.135593i
$975$		−	3.94581e15i		−	0.143420i
$976$	−2.19960e16	−	2.61452e16i	−0.795003	−	0.944972i
$977$	−9.78300e15			−0.351603			−0.175801	−	0.984426i	$-0.556252\pi$
$977$	−9.78300e15			−0.351603			−0.175801	+	0.984426i	$0.556252\pi$
$978$	−3.80726e13	−	2.66404e13i	−0.00136066	−	0.000952088i
$979$	8.71805e15			0.309824
$980$	−1.32652e16	+	1.75693e16i	−0.468780	+	0.620885i
$981$	7.89628e14			0.0277487
$982$	1.62538e16	+	1.13733e16i	0.567993	+	0.397440i
$983$	1.53870e16			0.534699			0.267349	−	0.963600i	$-0.413852\pi$
$983$	1.53870e16			0.534699			0.267349	+	0.963600i	$0.413852\pi$
$984$	−2.75069e15	+	1.03056e16i	−0.0950537	+	0.356122i
$985$			3.51018e16i			1.20623i
$986$	4.25846e16	+	2.97976e16i	1.45522	+	1.01826i
$987$	2.32978e16	−	6.88114e15i	0.791719	−	0.233839i
$988$	2.73838e16	−	9.98688e15i	0.925402	−	0.337494i
$989$	7.38098e14			0.0248047
$990$	6.64783e15	−	9.50059e15i	0.222170	−	0.317510i
$991$			4.77746e16i			1.58779i	0.608057	+	0.793893i	$0.291949\pi$
$991$			4.77746e16i			1.58779i	−0.608057	+	0.793893i	$0.708051\pi$
$992$	−4.01493e14	−	4.50547e15i	−0.0132698	−	0.148911i
$993$		−	1.72165e15i		−	0.0565879i
$994$	−5.17776e16	−	1.73514e16i	−1.69245	−	0.567166i
$995$			3.55396e16i			1.15528i
$996$	6.70225e15	+	1.83774e16i	0.216668	+	0.594098i
$997$		−	1.93758e15i		−	0.0622925i	−0.999515	−	0.0311463i	$-0.990084\pi$
$997$		−	1.93758e15i		−	0.0622925i	0.999515	−	0.0311463i	$-0.00991577\pi$
$998$	2.90617e16	+	2.03353e16i	0.929188	+	0.650178i
$999$	7.52510e15			0.239278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.14	yes	44
4.3	odd	2		84.12.b.b.55.13	yes	44
7.6	odd	2		84.12.b.b.55.14	yes	44
28.27	even	2	inner	84.12.b.a.55.13	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.13	✓	44	28.27	even	2	inner
84.12.b.a.55.14	yes	44	1.1	even	1	trivial
84.12.b.b.55.13	yes	44	4.3	odd	2
84.12.b.b.55.14	yes	44	7.6	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-25.9452 + 37.0790i) q^{2} -243.000 q^{3} +(-701.697 - 1924.04i) q^{4} -5436.30i q^{5} +(6304.67 - 9010.19i) q^{6} +(-42645.9 + 12595.7i) q^{7} +(89547.0 + 23901.3i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-25.9452 + 37.0790i) q^{2} -243.000 q^{3} +(-701.697 - 1924.04i) q^{4} -5436.30i q^{5} +(6304.67 - 9010.19i) q^{6} +(-42645.9 + 12595.7i) q^{7} +(89547.0 + 23901.3i) q^{8} +59049.0 q^{9} +(201572. + 141046. i) q^{10} -798192. i q^{11} +(170512. + 467541. i) q^{12} +842443. i q^{13} +(639420. - 1.90806e6i) q^{14} +1.32102e6i q^{15} +(-3.20955e6 + 2.70019e6i) q^{16} +7.54533e6i q^{17} +(-1.53204e6 + 2.18948e6i) q^{18} +1.68943e7 q^{19} +(-1.04596e7 + 3.81464e6i) q^{20} +(1.03630e7 - 3.06076e6i) q^{21} +(2.95961e7 + 2.07092e7i) q^{22} +2.84452e7i q^{23} +(-2.17599e7 - 5.80801e6i) q^{24} +1.92748e7 q^{25} +(-3.12369e7 - 2.18573e7i) q^{26} -1.43489e7 q^{27} +(5.41591e7 + 7.32140e7i) q^{28} -1.52211e8 q^{29} +(-4.89821e7 - 3.42741e7i) q^{30} +2.38305e7 q^{31} +(-1.68479e7 - 1.89063e8i) q^{32} +1.93961e8i q^{33} +(-2.79773e8 - 1.95765e8i) q^{34} +(6.84740e7 + 2.31836e8i) q^{35} +(-4.14345e7 - 1.13613e8i) q^{36} -5.24437e8 q^{37} +(-4.38324e8 + 6.26422e8i) q^{38} -2.04714e8i q^{39} +(1.29935e8 - 4.86804e8i) q^{40} -4.73603e8i q^{41} +(-1.55379e8 + 4.63659e8i) q^{42} -2.59481e7i q^{43} +(-1.53575e9 + 5.60089e8i) q^{44} -3.21008e8i q^{45} +(-1.05472e9 - 7.38015e8i) q^{46} +2.24818e9 q^{47} +(7.79920e8 - 6.56145e8i) q^{48} +(1.66002e9 - 1.07431e9i) q^{49} +(-5.00087e8 + 7.14689e8i) q^{50} -1.83352e9i q^{51} +(1.62089e9 - 5.91140e8i) q^{52} -2.74065e9 q^{53} +(3.72285e8 - 5.32042e8i) q^{54} -4.33921e9 q^{55} +(-4.11987e9 + 1.08614e8i) q^{56} -4.10531e9 q^{57} +(3.94915e9 - 5.64383e9i) q^{58} +6.43711e9 q^{59} +(2.54169e9 - 9.26957e8i) q^{60} +8.14609e9i q^{61} +(-6.18286e8 + 8.83610e8i) q^{62} +(-2.51820e9 + 7.43764e8i) q^{63} +(7.44739e9 + 4.28058e9i) q^{64} +4.57977e9 q^{65} +(-7.19186e9 - 5.03234e9i) q^{66} +1.41934e10i q^{67} +(1.45175e10 - 5.29454e9i) q^{68} -6.91218e9i q^{69} +(-1.03728e10 - 3.47608e9i) q^{70} -2.71362e10i q^{71} +(5.28766e9 + 1.41135e9i) q^{72} +1.06360e10i q^{73} +(1.36066e10 - 1.94456e10i) q^{74} -4.68377e9 q^{75} +(-1.18547e10 - 3.25052e10i) q^{76} +(1.00538e10 + 3.40396e10i) q^{77} +(7.59057e9 + 5.31133e9i) q^{78} -4.56423e10i q^{79} +(1.46790e10 + 1.74481e10i) q^{80} +3.48678e9 q^{81} +(1.75607e10 + 1.22877e10i) q^{82} +3.93065e10 q^{83} +(-1.31607e10 - 1.77910e10i) q^{84} +4.10187e10 q^{85} +(9.62127e8 + 6.73227e8i) q^{86} +3.69873e10 q^{87} +(1.90778e10 - 7.14757e10i) q^{88} +1.09223e10i q^{89} +(1.19026e10 + 8.32860e9i) q^{90} +(-1.06112e10 - 3.59268e10i) q^{91} +(5.47297e10 - 1.99599e10i) q^{92} -5.79081e9 q^{93} +(-5.83295e10 + 8.33603e10i) q^{94} -9.18423e10i q^{95} +(4.09403e9 + 4.59424e10i) q^{96} -7.12847e10i q^{97} +(-3.23526e9 + 8.94251e10i) q^{98} -4.71324e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

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