LMFDB - Embedded newform 84.9.g.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,9,Mod(43,84)]

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, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("84.43");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	84.g (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:	$34.2198032451$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	84.43
Dual form			84.9.g.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.1205 + 5.23171i) q^{2} -46.7654i q^{3} +(201.258 - 158.212i) q^{4} +237.168 q^{5} +(244.663 + 707.115i) q^{6} -907.493i q^{7} +(-2215.40 + 3445.17i) q^{8} -2187.00 q^{9} +O(q^{10})$	\(q+(-15.1205 + 5.23171i) q^{2} -46.7654i q^{3} +(201.258 - 158.212i) q^{4} +237.168 q^{5} +(244.663 + 707.115i) q^{6} -907.493i q^{7} +(-2215.40 + 3445.17i) q^{8} -2187.00 q^{9} +(-3586.10 + 1240.80i) q^{10} -25052.3i q^{11} +(-7398.85 - 9411.92i) q^{12} +6390.18 q^{13} +(4747.74 + 13721.7i) q^{14} -11091.3i q^{15} +(15473.9 - 63683.0i) q^{16} +57982.1 q^{17} +(33068.5 - 11441.8i) q^{18} -5634.08i q^{19} +(47732.1 - 37522.9i) q^{20} -42439.2 q^{21} +(131066. + 378803. i) q^{22} +210133. i q^{23} +(161115. + 103604. i) q^{24} -334376. q^{25} +(-96622.6 + 33431.6i) q^{26} +102276. i q^{27} +(-143576. - 182640. i) q^{28} +1.21921e6 q^{29} +(58026.3 + 167705. i) q^{30} -604744. i q^{31} +(99199.0 + 1.04387e6i) q^{32} -1.17158e6 q^{33} +(-876718. + 303346. i) q^{34} -215228. i q^{35} +(-440152. + 346010. i) q^{36} -1.04853e6 q^{37} +(29475.9 + 85190.0i) q^{38} -298839. i q^{39} +(-525424. + 817085. i) q^{40} -404831. q^{41} +(641702. - 222030. i) q^{42} +821137. i q^{43} +(-3.96357e6 - 5.04198e6i) q^{44} -518687. q^{45} +(-1.09936e6 - 3.17731e6i) q^{46} -8.95935e6i q^{47} +(-2.97816e6 - 723641. i) q^{48} -823543. q^{49} +(5.05593e6 - 1.74936e6i) q^{50} -2.71156e6i q^{51} +(1.28608e6 - 1.01100e6i) q^{52} -1.17124e7 q^{53} +(-535078. - 1.54646e6i) q^{54} -5.94160e6i q^{55} +(3.12647e6 + 2.01046e6i) q^{56} -263480. q^{57} +(-1.84351e7 + 6.37857e6i) q^{58} -9.82920e6i q^{59} +(-1.75477e6 - 2.23221e6i) q^{60} -2.17968e7 q^{61} +(3.16385e6 + 9.14403e6i) q^{62} +1.98469e6i q^{63} +(-6.96118e6 - 1.52649e7i) q^{64} +1.51555e6 q^{65} +(1.77148e7 - 6.12936e6i) q^{66} +5.72442e6i q^{67} +(1.16694e7 - 9.17347e6i) q^{68} +9.82695e6 q^{69} +(1.12601e6 + 3.25436e6i) q^{70} -2.43686e7i q^{71} +(4.84509e6 - 7.53459e6i) q^{72} -5.49458e7 q^{73} +(1.58542e7 - 5.48559e6i) q^{74} +1.56372e7i q^{75} +(-891380. - 1.13391e6i) q^{76} -2.27348e7 q^{77} +(1.56344e6 + 4.51859e6i) q^{78} +4.06306e7i q^{79} +(3.66991e6 - 1.51036e7i) q^{80} +4.78297e6 q^{81} +(6.12124e6 - 2.11796e6i) q^{82} +3.94981e7i q^{83} +(-8.54125e6 + 6.71440e6i) q^{84} +1.37515e7 q^{85} +(-4.29595e6 - 1.24160e7i) q^{86} -5.70169e7i q^{87} +(8.63093e7 + 5.55009e7i) q^{88} -3.25264e7 q^{89} +(7.84280e6 - 2.71362e6i) q^{90} -5.79904e6i q^{91} +(3.32456e7 + 4.22910e7i) q^{92} -2.82811e7 q^{93} +(4.68727e7 + 1.35470e8i) q^{94} -1.33622e6i q^{95} +(4.88171e7 - 4.63908e6i) q^{96} -7.44024e7 q^{97} +(1.24524e7 - 4.30854e6i) q^{98} +5.47893e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 + 290 * q^4 + 672 * q^5 - 2268 * q^6 + 4230 * q^8 - 104976 * q^9	\( 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9} - 41972 q^{10} + 22680 q^{12} + 57120 q^{13} - 14406 q^{14} - 207950 q^{16} + 386400 q^{17} + 13122 q^{18} + 562380 q^{20} + 1186136 q^{22} + 74844 q^{24} + 5520720 q^{25} + 1682100 q^{26} + 148862 q^{28} - 1994592 q^{29} - 2054808 q^{30} + 7754814 q^{32} + 2395820 q^{34} - 634230 q^{36} - 5931232 q^{37} - 4284000 q^{38} - 16076956 q^{40} + 10936800 q^{41} + 12531912 q^{44} - 1469664 q^{45} + 9456072 q^{46} - 12365136 q^{48} - 39530064 q^{49} - 6199074 q^{50} - 6937420 q^{52} - 7150560 q^{53} + 4960116 q^{54} + 14218722 q^{56} + 518452 q^{58} + 3633984 q^{60} - 42829024 q^{61} - 93291072 q^{62} - 69128614 q^{64} + 21653184 q^{65} + 45582264 q^{66} + 82618620 q^{68} + 17273088 q^{69} - 11611236 q^{70} - 9251010 q^{72} - 49489440 q^{73} - 126365628 q^{74} - 223942320 q^{76} + 94964352 q^{77} + 136267920 q^{78} + 238226604 q^{80} + 229582512 q^{81} + 269696252 q^{82} + 301906816 q^{85} - 188004816 q^{86} - 116561288 q^{88} - 315415968 q^{89} + 91792764 q^{90} + 487386984 q^{92} + 37454400 q^{93} + 148324176 q^{94} - 320488812 q^{96} - 3460128 q^{97} + 4941258 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 + 290 * q^4 + 672 * q^5 - 2268 * q^6 + 4230 * q^8 - 104976 * q^9 - 41972 * q^10 + 22680 * q^12 + 57120 * q^13 - 14406 * q^14 - 207950 * q^16 + 386400 * q^17 + 13122 * q^18 + 562380 * q^20 + 1186136 * q^22 + 74844 * q^24 + 5520720 * q^25 + 1682100 * q^26 + 148862 * q^28 - 1994592 * q^29 - 2054808 * q^30 + 7754814 * q^32 + 2395820 * q^34 - 634230 * q^36 - 5931232 * q^37 - 4284000 * q^38 - 16076956 * q^40 + 10936800 * q^41 + 12531912 * q^44 - 1469664 * q^45 + 9456072 * q^46 - 12365136 * q^48 - 39530064 * q^49 - 6199074 * q^50 - 6937420 * q^52 - 7150560 * q^53 + 4960116 * q^54 + 14218722 * q^56 + 518452 * q^58 + 3633984 * q^60 - 42829024 * q^61 - 93291072 * q^62 - 69128614 * q^64 + 21653184 * q^65 + 45582264 * q^66 + 82618620 * q^68 + 17273088 * q^69 - 11611236 * q^70 - 9251010 * q^72 - 49489440 * q^73 - 126365628 * q^74 - 223942320 * q^76 + 94964352 * q^77 + 136267920 * q^78 + 238226604 * q^80 + 229582512 * q^81 + 269696252 * q^82 + 301906816 * q^85 - 188004816 * q^86 - 116561288 * q^88 - 315415968 * q^89 + 91792764 * q^90 + 487386984 * q^92 + 37454400 * q^93 + 148324176 * q^94 - 320488812 * q^96 - 3460128 * q^97 + 4941258 * 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 $

$2$	−15.1205	+	5.23171i	−0.945031	+	0.326982i
$2$	−15.1205	+	5.23171i	−0.945031	+	0.326982i
$3$		−	46.7654i		−	0.577350i
$3$		−	46.7654i		−	0.577350i
$4$	201.258	−	158.212i	0.786165	−	0.618016i
$5$	237.168			0.379469			0.189735	−	0.981835i	$-0.439237\pi$
$5$	237.168			0.379469			0.189735	+	0.981835i	$0.439237\pi$
$6$	244.663	+	707.115i	0.188783	+	0.545614i
$7$		−	907.493i		−	0.377964i
$7$		−	907.493i		−	0.377964i
$8$	−2215.40	+	3445.17i	−0.540870	+	0.841106i
$9$	−2187.00			−0.333333
$10$	−3586.10	+	1240.80i	−0.358610	+	0.124080i
$11$		−	25052.3i		−	1.71110i	−0.517717	−	0.855552i	$-0.673218\pi$
$11$		−	25052.3i		−	1.71110i	0.517717	−	0.855552i	$-0.326782\pi$
$12$	−7398.85	−	9411.92i	−0.356812	−	0.453893i
$13$	6390.18			0.223738			0.111869	−	0.993723i	$-0.464316\pi$
$13$	6390.18			0.223738			0.111869	+	0.993723i	$0.464316\pi$
$14$	4747.74	+	13721.7i	0.123588	+	0.357188i
$15$		−	11091.3i		−	0.219087i
$16$	15473.9	−	63683.0i	0.236112	−	0.971726i
$17$	57982.1			0.694222			0.347111	−	0.937824i	$-0.387163\pi$
$17$	57982.1			0.694222			0.347111	+	0.937824i	$0.387163\pi$
$18$	33068.5	−	11441.8i	0.315010	−	0.108994i
$19$		−	5634.08i		−	0.0432323i	−0.999766	−	0.0216162i	$-0.993119\pi$
$19$		−	5634.08i		−	0.0432323i	0.999766	−	0.0216162i	$-0.00688117\pi$
$20$	47732.1	−	37522.9i	0.298326	−	0.234518i
$21$	−42439.2			−0.218218
$22$	131066.	+	378803.i	0.559500	+	1.61705i
$23$			210133.i			0.750901i	0.926842	+	0.375451i	$0.122512\pi$
$23$			210133.i			0.750901i	−0.926842	+	0.375451i	$0.877488\pi$
$24$	161115.	+	103604.i	0.485613	+	0.312272i
$25$	−334376.			−0.856003
$26$	−96622.6	+	33431.6i	−0.211439	+	0.0731583i
$27$			102276.i			0.192450i
$28$	−143576.	−	182640.i	−0.233588	−	0.297143i
$29$	1.21921e6			1.72380			0.861901	−	0.507077i	$-0.169274\pi$
$29$	1.21921e6			1.72380			0.861901	+	0.507077i	$0.169274\pi$
$30$	58026.3	+	167705.i	0.0716374	+	0.207044i
$31$		−	604744.i		−	0.654824i	−0.944882	−	0.327412i	$-0.893823\pi$
$31$		−	604744.i		−	0.654824i	0.944882	−	0.327412i	$-0.106177\pi$
$32$	99199.0	+	1.04387e6i	0.0946035	+	0.995515i
$33$	−1.17158e6			−0.987906
$34$	−876718.	+	303346.i	−0.656061	+	0.226998i
$35$		−	215228.i		−	0.143426i
$36$	−440152.	+	346010.i	−0.262055	+	0.206005i
$37$	−1.04853e6			−0.559465			−0.279732	−	0.960078i	$-0.590246\pi$
$37$	−1.04853e6			−0.559465			−0.279732	+	0.960078i	$0.590246\pi$
$38$	29475.9	+	85190.0i	0.0141362	+	0.0408559i
$39$		−	298839.i		−	0.129175i
$40$	−525424.	+	817085.i	−0.205244	+	0.319174i
$41$	−404831.			−0.143264			−0.0716321	−	0.997431i	$-0.522821\pi$
$41$	−404831.			−0.143264			−0.0716321	+	0.997431i	$0.522821\pi$
$42$	641702.	−	222030.i	0.206223	−	0.0713533i
$43$			821137.i			0.240183i	0.992763	+	0.120091i	$0.0383187\pi$
$43$			821137.i			0.240183i	−0.992763	+	0.120091i	$0.961681\pi$
$44$	−3.96357e6	−	5.04198e6i	−1.05749	−	1.34521i
$45$	−518687.			−0.126490
$46$	−1.09936e6	−	3.17731e6i	−0.245531	−	0.709625i
$47$		−	8.95935e6i		−	1.83605i	−0.396521	−	0.918026i	$-0.629782\pi$
$47$		−	8.95935e6i		−	1.83605i	0.396521	−	0.918026i	$-0.370218\pi$
$48$	−2.97816e6	−	723641.i	−0.561026	−	0.136320i
$49$	−823543.			−0.142857
$50$	5.05593e6	−	1.74936e6i	0.808949	−	0.279898i
$51$		−	2.71156e6i		−	0.400809i
$52$	1.28608e6	−	1.01100e6i	0.175895	−	0.138274i
$53$	−1.17124e7			−1.48437			−0.742184	−	0.670197i	$-0.766210\pi$
$53$	−1.17124e7			−1.48437			−0.742184	+	0.670197i	$0.766210\pi$
$54$	−535078.	−	1.54646e6i	−0.0629277	−	0.181871i
$55$		−	5.94160e6i		−	0.649311i
$56$	3.12647e6	+	2.01046e6i	0.317908	+	0.204430i
$57$	−263480.			−0.0249602
$58$	−1.84351e7	+	6.37857e6i	−1.62904	+	0.563652i
$59$		−	9.82920e6i		−	0.811167i	−0.914058	−	0.405583i	$-0.867068\pi$
$59$		−	9.82920e6i		−	0.811167i	0.914058	−	0.405583i	$-0.132932\pi$
$60$	−1.75477e6	−	2.23221e6i	−0.135399	−	0.172238i
$61$	−2.17968e7			−1.57425			−0.787124	−	0.616794i	$-0.788431\pi$
$61$	−2.17968e7			−1.57425			−0.787124	+	0.616794i	$0.788431\pi$
$62$	3.16385e6	+	9.14403e6i	0.214116	+	0.618829i
$63$			1.98469e6i			0.125988i
$64$	−6.96118e6	−	1.52649e7i	−0.414919	−	0.909858i
$65$	1.51555e6			0.0849016
$66$	1.77148e7	−	6.12936e6i	0.933601	−	0.323028i
$67$			5.72442e6i			0.284075i	0.989861	+	0.142037i	$0.0453653\pi$
$67$			5.72442e6i			0.284075i	−0.989861	+	0.142037i	$0.954635\pi$
$68$	1.16694e7	−	9.17347e6i	0.545773	−	0.429040i
$69$	9.82695e6			0.433533
$70$	1.12601e6	+	3.25436e6i	0.0468977	+	0.135542i
$71$		−	2.43686e7i		−	0.958954i	−0.877555	−	0.479477i	$-0.840826\pi$
$71$		−	2.43686e7i		−	0.958954i	0.877555	−	0.479477i	$-0.159174\pi$
$72$	4.84509e6	−	7.53459e6i	0.180290	−	0.280369i
$73$	−5.49458e7			−1.93483			−0.967415	−	0.253196i	$-0.918518\pi$
$73$	−5.49458e7			−1.93483			−0.967415	+	0.253196i	$0.918518\pi$
$74$	1.58542e7	−	5.48559e6i	0.528711	−	0.182935i
$75$			1.56372e7i			0.494214i
$76$	−891380.	−	1.13391e6i	−0.0267183	−	0.0339878i
$77$	−2.27348e7			−0.646736
$78$	1.56344e6	+	4.51859e6i	0.0422379	+	0.122074i
$79$			4.06306e7i			1.04315i	0.853207	+	0.521573i	$0.174654\pi$
$79$			4.06306e7i			1.04315i	−0.853207	+	0.521573i	$0.825346\pi$
$80$	3.66991e6	−	1.51036e7i	0.0895974	−	0.368740i
$81$	4.78297e6			0.111111
$82$	6.12124e6	−	2.11796e6i	0.135389	−	0.0468449i
$83$			3.94981e7i			0.832269i	0.909303	+	0.416134i	$0.136615\pi$
$83$			3.94981e7i			0.832269i	−0.909303	+	0.416134i	$0.863385\pi$
$84$	−8.54125e6	+	6.71440e6i	−0.171555	+	0.134862i
$85$	1.37515e7			0.263436
$86$	−4.29595e6	−	1.24160e7i	−0.0785354	−	0.226980i
$87$		−	5.70169e7i		−	0.995237i
$88$	8.63093e7	+	5.55009e7i	1.43922	+	0.925485i
$89$	−3.25264e7			−0.518414			−0.259207	−	0.965822i	$-0.583461\pi$
$89$	−3.25264e7			−0.518414			−0.259207	+	0.965822i	$0.583461\pi$
$90$	7.84280e6	−	2.71362e6i	0.119537	−	0.0413599i
$91$		−	5.79904e6i		−	0.0845650i
$92$	3.32456e7	+	4.22910e7i	0.464069	+	0.590333i
$93$	−2.82811e7			−0.378063
$94$	4.68727e7	+	1.35470e8i	0.600356	+	1.73512i
$95$		−	1.33622e6i		−	0.0164053i
$96$	4.88171e7	−	4.63908e6i	0.574761	−	0.0546194i
$97$	−7.44024e7			−0.840427			−0.420213	−	0.907425i	$-0.638045\pi$
$97$	−7.44024e7			−0.840427			−0.420213	+	0.907425i	$0.638045\pi$
$98$	1.24524e7	−	4.30854e6i	0.135004	−	0.0467117i
$99$			5.47893e7i			0.570368i
$100$	−6.72960e7	+	5.29024e7i	−0.672960	+	0.529024i
$101$	1.43121e8			1.37537			0.687683	−	0.726011i	$-0.258628\pi$
$101$	1.43121e8			1.37537			0.687683	+	0.726011i	$0.258628\pi$
$102$	1.41861e7	+	4.10000e7i	0.131057	+	0.378777i
$103$		−	2.92659e7i		−	0.260024i	−0.991512	−	0.130012i	$-0.958498\pi$
$103$		−	2.92659e7i		−	0.260024i	0.991512	−	0.130012i	$-0.0415016\pi$
$104$	−1.41568e7	+	2.20153e7i	−0.121013	+	0.188187i
$105$	−1.00652e7			−0.0828070
$106$	1.77097e8	−	6.12758e7i	1.40277	−	0.485361i
$107$		−	1.26169e8i		−	0.962539i	−0.876573	−	0.481270i	$-0.840176\pi$
$107$		−	1.26169e8i		−	0.962539i	0.876573	−	0.481270i	$-0.159824\pi$
$108$	1.61813e7	+	2.05839e7i	0.118937	+	0.151298i
$109$	1.44146e7			0.102117			0.0510585	−	0.998696i	$-0.483741\pi$
$109$	1.44146e7			0.102117			0.0510585	+	0.998696i	$0.483741\pi$
$110$	3.10848e7	+	8.98399e7i	0.212313	+	0.613619i
$111$			4.90348e7i			0.323007i
$112$	−5.77919e7	−	1.40424e7i	−0.367278	−	0.0892421i
$113$	3.34703e7			0.205279			0.102640	−	0.994719i	$-0.467271\pi$
$113$	3.34703e7			0.205279			0.102640	+	0.994719i	$0.467271\pi$
$114$	3.98394e6	−	1.37845e6i	0.0235881	−	0.00816153i
$115$			4.98369e7i			0.284944i
$116$	2.45377e8	−	1.92894e8i	1.35519	−	1.06534i
$117$	−1.39753e7			−0.0745793
$118$	5.14235e7	+	1.48622e8i	0.265237	+	0.766577i
$119$		−	5.26184e7i		−	0.262391i
$120$	3.82113e7	+	2.45716e7i	0.184275	+	0.118497i
$121$	−4.13257e8			−1.92788
$122$	3.29578e8	−	1.14035e8i	1.48771	−	0.514751i
$123$			1.89321e7i			0.0827137i
$124$	−9.56778e7	−	1.21710e8i	−0.404692	−	0.514800i
$125$	−1.71947e8			−0.704296
$126$	−1.03833e7	−	3.00094e7i	−0.0411959	−	0.119063i
$127$		−	1.26345e8i		−	0.485673i	−0.970067	−	0.242836i	$-0.921922\pi$
$127$		−	1.26345e8i		−	0.485673i	0.970067	−	0.242836i	$-0.0780778\pi$
$128$	1.85118e8	+	1.94394e8i	0.689618	+	0.724173i
$129$	3.84008e7			0.138670
$130$	−2.29158e7	+	7.92891e6i	−0.0802346	+	0.0277613i
$131$		−	2.66019e8i		−	0.903290i	−0.892198	−	0.451645i	$-0.850837\pi$
$131$		−	2.66019e8i		−	0.903290i	0.892198	−	0.451645i	$-0.149163\pi$
$132$	−2.35790e8	+	1.85358e8i	−0.776658	+	0.610542i
$133$	−5.11289e6			−0.0163403
$134$	−2.99485e7	−	8.65561e7i	−0.0928873	−	0.268459i
$135$			2.42566e7i			0.0730289i
$136$	−1.28454e8	+	1.99758e8i	−0.375484	+	0.583914i
$137$	1.03598e8			0.294081			0.147041	−	0.989130i	$-0.453025\pi$
$137$	1.03598e8			0.294081			0.147041	+	0.989130i	$0.453025\pi$
$138$	−1.48588e8	+	5.14118e7i	−0.409702	+	0.141758i
$139$		−	5.50389e7i		−	0.147438i	−0.997279	−	0.0737192i	$-0.976513\pi$
$139$		−	5.50389e7i		−	0.147438i	0.997279	−	0.0737192i	$-0.0234869\pi$
$140$	−3.40517e7	−	4.33165e7i	−0.0886395	−	0.112756i
$141$	−4.18987e8			−1.06004
$142$	1.27490e8	+	3.68466e8i	0.313561	+	0.906241i
$143$		−	1.60088e8i		−	0.382839i
$144$	−3.38413e7	+	1.39275e8i	−0.0787041	+	0.323909i
$145$	2.89158e8			0.654129
$146$	8.30807e8	−	2.87460e8i	1.82847	−	0.632655i
$147$			3.85133e7i			0.0824786i
$148$	−2.11025e8	+	1.65890e8i	−0.439832	+	0.345758i
$149$	−7.23233e8			−1.46735			−0.733674	−	0.679502i	$-0.762196\pi$
$149$	−7.23233e8			−1.46735			−0.733674	+	0.679502i	$0.762196\pi$
$150$	−8.18095e7	−	2.36443e8i	−0.161599	−	0.467047i
$151$		−	1.39111e8i		−	0.267581i	−0.991010	−	0.133790i	$-0.957285\pi$
$151$		−	1.39111e8i		−	0.267581i	0.991010	−	0.133790i	$-0.0427149\pi$
$152$	1.94104e7	+	1.24818e7i	0.0363630	+	0.0233831i
$153$	−1.26807e8			−0.231407
$154$	3.43761e8	−	1.18942e8i	0.611186	−	0.211471i
$155$		−	1.43426e8i		−	0.248486i
$156$	−4.72800e7	−	6.01439e7i	−0.0798323	−	0.101553i
$157$	4.90888e8			0.807948			0.403974	−	0.914770i	$-0.367629\pi$
$157$	4.90888e8			0.807948			0.403974	+	0.914770i	$0.367629\pi$
$158$	−2.12568e8	−	6.14354e8i	−0.341090	−	0.985804i
$159$			5.47733e8i			0.857000i
$160$	2.35268e7	+	2.47574e8i	0.0358991	+	0.377767i
$161$	1.90694e8			0.283814
$162$	−7.23208e7	+	2.50231e7i	−0.105003	+	0.0363313i
$163$			2.65022e8i			0.375432i	0.982223	+	0.187716i	$0.0601085\pi$
$163$			2.65022e8i			0.375432i	−0.982223	+	0.187716i	$0.939891\pi$
$164$	−8.14756e7	+	6.40491e7i	−0.112629	+	0.0885396i
$165$	−2.77861e8			−0.374880
$166$	−2.06643e8	−	5.97230e8i	−0.272137	−	0.786519i
$167$			1.18096e9i			1.51834i	0.650894	+	0.759168i	$0.274394\pi$
$167$			1.18096e9i			1.51834i	−0.650894	+	0.759168i	$0.725606\pi$
$168$	9.40201e7	−	1.46210e8i	0.118028	−	0.183544i
$169$	−7.74896e8			−0.949941
$170$	−2.07930e8	+	7.19440e7i	−0.248955	+	0.0861388i
$171$			1.23217e7i			0.0144108i
$172$	1.29914e8	+	1.65261e8i	0.148437	+	0.188823i
$173$	1.19143e9			1.33010			0.665049	−	0.746799i	$-0.268410\pi$
$173$	1.19143e9			1.33010			0.665049	+	0.746799i	$0.268410\pi$
$174$	2.98296e8	+	8.62123e8i	0.325425	+	0.940529i
$175$			3.03444e8i			0.323539i
$176$	−1.59540e9	−	3.87655e8i	−1.66272	−	0.404013i
$177$	−4.59666e8			−0.468327
$178$	4.91816e8	−	1.70169e8i	0.489917	−	0.169512i
$179$		−	7.83720e8i		−	0.763394i	−0.924287	−	0.381697i	$-0.875340\pi$
$179$		−	7.83720e8i		−	0.763394i	0.924287	−	0.381697i	$-0.124660\pi$
$180$	−1.04390e8	+	8.20625e7i	−0.0994419	+	0.0781727i
$181$	2.29684e8			0.214001			0.107000	−	0.994259i	$-0.465875\pi$
$181$	2.29684e8			0.214001			0.107000	+	0.994259i	$0.465875\pi$
$182$	3.03389e7	+	8.76843e7i	0.0276512	+	0.0799165i
$183$			1.01934e9i			0.908893i
$184$	−7.23944e8	−	4.65530e8i	−0.631588	−	0.406140i
$185$	−2.48677e8			−0.212300
$186$	4.27624e8	−	1.47959e8i	0.357281	−	0.123620i
$187$		−	1.45258e9i		−	1.18789i
$188$	−1.41748e9	−	1.80314e9i	−1.13471	−	1.44344i
$189$	9.28146e7			0.0727393
$190$	6.99074e6	+	2.02044e7i	0.00536425	+	0.0155035i
$191$		−	9.60191e8i		−	0.721480i	−0.932666	−	0.360740i	$-0.882524\pi$
$191$		−	9.60191e8i		−	0.721480i	0.932666	−	0.360740i	$-0.117476\pi$
$192$	−7.13868e8	+	3.25542e8i	−0.525307	+	0.239553i
$193$	1.09431e9			0.788699			0.394350	−	0.918960i	$-0.370970\pi$
$193$	1.09431e9			0.788699			0.394350	+	0.918960i	$0.370970\pi$
$194$	1.12500e9	−	3.89252e8i	0.794229	−	0.274804i
$195$		−	7.08751e7i		−	0.0490180i
$196$	−1.65745e8	+	1.30294e8i	−0.112309	+	0.0882880i
$197$	4.33622e8			0.287903			0.143952	−	0.989585i	$-0.454019\pi$
$197$	4.33622e8			0.287903			0.143952	+	0.989585i	$0.454019\pi$
$198$	−2.86642e8	−	8.28441e8i	−0.186500	−	0.539015i
$199$		−	2.55724e9i		−	1.63064i	−0.579010	−	0.815321i	$-0.696561\pi$
$199$		−	2.55724e9i		−	1.63064i	0.579010	−	0.815321i	$-0.303439\pi$
$200$	7.40779e8	−	1.15198e9i	0.462987	−	0.719989i
$201$	2.67705e8			0.164011
$202$	−2.16406e9	+	7.48769e8i	−1.29976	+	0.449720i
$203$		−	1.10643e9i		−	0.651536i
$204$	−4.29001e8	−	5.45723e8i	−0.247707	−	0.315102i
$205$	−9.60130e7			−0.0543644
$206$	1.53111e8	+	4.42515e8i	0.0850232	+	0.245731i
$207$		−	4.59561e8i		−	0.250300i
$208$	9.88807e7	−	4.06946e8i	0.0528273	−	0.217412i
$209$	−1.41146e8			−0.0739750
$210$	1.52191e8	−	5.26584e7i	0.0782551	−	0.0270764i
$211$			3.51271e9i			1.77220i	0.463496	+	0.886099i	$0.346595\pi$
$211$			3.51271e9i			1.77220i	−0.463496	+	0.886099i	$0.653405\pi$
$212$	−2.35721e9	+	1.85304e9i	−1.16696	+	0.917363i
$213$	−1.13961e9			−0.553652
$214$	6.60081e8	+	1.90774e9i	0.314733	+	0.909629i
$215$			1.94748e8i			0.0911419i
$216$	−3.52358e8	−	2.26582e8i	−0.161871	−	0.104091i
$217$	−5.48801e8			−0.247500
$218$	−2.17956e8	+	7.54133e7i	−0.0965037	+	0.0333904i
$219$			2.56956e9i			1.11707i
$220$	−9.40033e8	−	1.19580e9i	−0.401285	−	0.510466i
$221$	3.70516e8			0.155324
$222$	−2.56536e8	−	7.41430e8i	−0.105618	−	0.305252i
$223$		−	8.70378e8i		−	0.351956i	−0.984394	−	0.175978i	$-0.943691\pi$
$223$		−	8.70378e8i		−	0.351956i	0.984394	−	0.175978i	$-0.0563088\pi$
$224$	9.47307e8	−	9.00223e7i	0.376269	−	0.0357568i
$225$	7.31281e8			0.285334
$226$	−5.06087e8	+	1.75107e8i	−0.193995	+	0.0671227i
$227$			3.54767e9i			1.33610i	0.744116	+	0.668051i	$0.232871\pi$
$227$			3.54767e9i			1.33610i	−0.744116	+	0.668051i	$0.767129\pi$
$228$	−5.30275e7	+	4.16857e7i	−0.0196228	+	0.0154258i
$229$	4.36547e9			1.58741			0.793706	−	0.608302i	$-0.208149\pi$
$229$	4.36547e9			1.58741			0.793706	+	0.608302i	$0.208149\pi$
$230$	−2.60732e8	−	7.53558e8i	−0.0931716	−	0.269281i
$231$			1.06320e9i			0.373393i
$232$	−2.70105e9	+	4.20039e9i	−0.932353	+	1.44990i
$233$	4.56780e9			1.54983			0.774914	−	0.632066i	$-0.217793\pi$
$233$	4.56780e9			1.54983			0.774914	+	0.632066i	$0.217793\pi$
$234$	2.11314e8	−	7.31149e7i	0.0704797	−	0.0243861i
$235$		−	2.12487e9i		−	0.696725i
$236$	−1.55510e9	−	1.97821e9i	−0.501314	−	0.637711i
$237$	1.90010e9			0.602260
$238$	2.75284e8	+	7.95615e8i	0.0857972	+	0.247968i
$239$		−	3.78475e9i		−	1.15997i	−0.814628	−	0.579983i	$-0.803059\pi$
$239$		−	3.78475e9i		−	1.15997i	0.814628	−	0.579983i	$-0.196941\pi$
$240$	−7.06325e8	−	1.71625e8i	−0.212892	−	0.0517291i
$241$	−2.48576e8			−0.0736871			−0.0368435	−	0.999321i	$-0.511730\pi$
$241$	−2.48576e8			−0.0736871			−0.0368435	+	0.999321i	$0.511730\pi$
$242$	6.24865e9	−	2.16204e9i	1.82190	−	0.630381i
$243$		−	2.23677e8i		−	0.0641500i
$244$	−4.38679e9	+	3.44852e9i	−1.23762	+	0.972911i
$245$	−1.95318e8			−0.0542099
$246$	−9.90471e7	−	2.86262e8i	−0.0270459	−	0.0781670i
$247$		−	3.60028e7i		−	0.00967271i
$248$	2.08345e9	+	1.33975e9i	0.550777	+	0.354175i
$249$	1.84714e9			0.480511
$250$	2.59993e9	−	8.99579e8i	0.665581	−	0.230292i
$251$			6.59097e9i			1.66056i	0.557347	+	0.830279i	$0.311819\pi$
$251$			6.59097e9i			1.66056i	−0.557347	+	0.830279i	$0.688181\pi$
$252$	3.14001e8	+	3.99435e8i	0.0778627	+	0.0990475i
$253$	5.26431e9			1.28487
$254$	6.61001e8	+	1.91040e9i	0.158806	+	0.458975i
$255$		−	6.43095e8i		−	0.152095i
$256$	−3.81609e9	−	1.97084e9i	−0.888502	−	0.458873i
$257$	6.74506e9			1.54616			0.773078	−	0.634311i	$-0.218716\pi$
$257$	6.74506e9			1.54616			0.773078	+	0.634311i	$0.218716\pi$
$258$	−5.80638e8	+	2.00902e8i	−0.131047	+	0.0453424i
$259$			9.51531e8i			0.211458i
$260$	3.05017e8	−	2.39778e8i	0.0667467	−	0.0524706i
$261$	−2.66642e9			−0.574600
$262$	1.39173e9	+	4.02234e9i	0.295360	+	0.853637i
$263$		−	1.57058e9i		−	0.328275i	−0.986437	−	0.164138i	$-0.947516\pi$
$263$		−	1.57058e9i		−	0.328275i	0.986437	−	0.164138i	$-0.0524841\pi$
$264$	2.59552e9	−	4.03629e9i	0.534329	−	0.830934i
$265$	−2.77780e9			−0.563272
$266$	7.73093e7	−	2.67492e7i	0.0154421	−	0.00534298i
$267$			1.52111e9i			0.299306i
$268$	9.05673e8	+	1.15209e9i	0.175563	+	0.223330i
$269$	5.97848e8			0.114178			0.0570889	−	0.998369i	$-0.481818\pi$
$269$	5.97848e8			0.114178			0.0570889	+	0.998369i	$0.481818\pi$
$270$	−1.26903e8	−	3.66771e8i	−0.0238791	−	0.0690145i
$271$			2.07751e9i			0.385182i	0.981279	+	0.192591i	$0.0616891\pi$
$271$			2.07751e9i			0.385182i	−0.981279	+	0.192591i	$0.938311\pi$
$272$	8.97207e8	−	3.69248e9i	0.163914	−	0.674593i
$273$	−2.71194e8			−0.0488236
$274$	−1.56645e9	+	5.41993e8i	−0.277916	+	0.0961593i
$275$			8.37688e9i			1.46471i
$276$	1.97776e9	−	1.55474e9i	0.340829	−	0.267930i
$277$	1.40673e9			0.238942			0.119471	−	0.992838i	$-0.461880\pi$
$277$	1.40673e9			0.238942			0.119471	+	0.992838i	$0.461880\pi$
$278$	2.87948e8	+	8.32215e8i	0.0482097	+	0.139334i
$279$			1.32258e9i			0.218275i
$280$	7.41499e8	+	4.76818e8i	0.120636	+	0.0775748i
$281$	−1.75630e9			−0.281692			−0.140846	−	0.990032i	$-0.544982\pi$
$281$	−1.75630e9			−0.281692			−0.140846	+	0.990032i	$0.544982\pi$
$282$	6.33529e9	−	2.19202e9i	1.00177	−	0.346616i
$283$		−	1.88826e9i		−	0.294385i	−0.989108	−	0.147192i	$-0.952976\pi$
$283$		−	1.88826e9i		−	0.294385i	0.989108	−	0.147192i	$-0.0470237\pi$
$284$	−3.85541e9	−	4.90439e9i	−0.592649	−	0.753896i
$285$	−6.24890e7			−0.00947162
$286$	8.37537e8	+	2.42062e9i	0.125181	+	0.361794i
$287$			3.67381e8i			0.0541488i
$288$	−2.16948e8	−	2.28295e9i	−0.0315345	−	0.331838i
$289$	−3.61383e9			−0.518056
$290$	−4.37221e9	+	1.51279e9i	−0.618172	+	0.213889i
$291$			3.47946e9i			0.485221i
$292$	−1.10583e10	+	8.69309e9i	−1.52110	+	1.19576i
$293$	−6.84554e9			−0.928832			−0.464416	−	0.885617i	$-0.653736\pi$
$293$	−6.84554e9			−0.928832			−0.464416	+	0.885617i	$0.653736\pi$
$294$	−2.01490e8	−	5.82340e8i	−0.0269690	−	0.0779448i
$295$		−	2.33117e9i		−	0.307813i
$296$	2.32291e9	−	3.61236e9i	0.302598	−	0.470569i
$297$	2.56224e9			0.329302
$298$	1.09356e10	−	3.78375e9i	1.38669	−	0.479796i
$299$			1.34279e9i			0.168005i
$300$	2.47400e9	+	3.14712e9i	0.305432	+	0.388534i
$301$	7.45176e8			0.0907805
$302$	7.27791e8	+	2.10343e9i	0.0874941	+	0.252872i
$303$		−	6.69311e9i		−	0.794068i
$304$	−3.58795e8	−	8.71809e7i	−0.0420100	−	0.0102077i
$305$	−5.16951e9			−0.597379
$306$	1.91738e9	−	6.63417e8i	0.218687	−	0.0756661i
$307$		−	8.61857e9i		−	0.970246i	−0.874446	−	0.485123i	$-0.838775\pi$
$307$		−	8.61857e9i		−	0.970246i	0.874446	−	0.485123i	$-0.161225\pi$
$308$	−4.57556e9	+	3.59691e9i	−0.508442	+	0.399693i
$309$	−1.36863e9			−0.150125
$310$	7.50364e8	+	2.16867e9i	0.0812504	+	0.234827i
$311$			1.59987e10i			1.71018i	0.518478	+	0.855091i	$0.326499\pi$
$311$			1.59987e10i			1.71018i	−0.518478	+	0.855091i	$0.673501\pi$
$312$	1.02955e9	+	6.62049e8i	0.108650	+	0.0698670i
$313$	−2.47855e9			−0.258238			−0.129119	−	0.991629i	$-0.541215\pi$
$313$	−2.47855e9			−0.258238			−0.129119	+	0.991629i	$0.541215\pi$
$314$	−7.42246e9	+	2.56818e9i	−0.763536	+	0.264185i
$315$			4.70705e8i			0.0478086i
$316$	6.42825e9	+	8.17725e9i	0.644680	+	0.820085i
$317$	−1.76529e10			−1.74815			−0.874073	−	0.485794i	$-0.838530\pi$
$317$	−1.76529e10			−1.74815			−0.874073	+	0.485794i	$0.838530\pi$
$318$	−2.86558e9	−	8.28200e9i	−0.280224	−	0.809891i
$319$		−	3.05440e10i		−	2.94960i
$320$	−1.65097e9	−	3.62035e9i	−0.157449	−	0.345263i
$321$	−5.90035e9			−0.555722
$322$	−2.88339e9	+	9.97657e8i	−0.268213	+	0.0928021i
$323$		−	3.26676e8i		−	0.0300128i
$324$	9.62613e8	−	7.56724e8i	0.0873517	−	0.0686684i
$325$	−2.13672e9			−0.191520
$326$	−1.38652e9	−	4.00726e9i	−0.122760	−	0.354795i
$327$		−	6.74106e8i		−	0.0589573i
$328$	8.96864e8	−	1.39471e9i	0.0774874	−	0.120500i
$329$	−8.13054e9			−0.693962
$330$	4.20140e9	−	1.45369e9i	0.354273	−	0.122579i
$331$		−	2.11174e10i		−	1.75925i	−0.475668	−	0.879625i	$-0.657794\pi$
$331$		−	2.11174e10i		−	1.75925i	0.475668	−	0.879625i	$-0.342206\pi$
$332$	6.24907e9	+	7.94932e9i	0.514355	+	0.654301i
$333$	2.29313e9			0.186488
$334$	−6.17843e9	−	1.78566e10i	−0.496469	−	1.43487i
$335$			1.35765e9i			0.107798i
$336$	−6.56699e8	+	2.70266e9i	−0.0515239	+	0.212048i
$337$	1.06676e10			0.827077			0.413538	−	0.910487i	$-0.364293\pi$
$337$	1.06676e10			0.827077			0.413538	+	0.910487i	$0.364293\pi$
$338$	1.17168e10	−	4.05404e9i	0.897724	−	0.310614i
$339$		−	1.56525e9i		−	0.118518i
$340$	2.76761e9	−	2.17566e9i	0.207104	−	0.162808i
$341$	−1.51502e10			−1.12047
$342$	−6.44638e7	−	1.86311e8i	−0.00471206	−	0.0136186i
$343$			7.47359e8i			0.0539949i
$344$	−2.82896e9	−	1.81915e9i	−0.202019	−	0.129908i
$345$	2.33064e9			0.164512
$346$	−1.80150e10	+	6.23322e9i	−1.25698	+	0.434918i
$347$		−	1.06795e10i		−	0.736601i	−0.929707	−	0.368300i	$-0.879940\pi$
$347$		−	1.06795e10i		−	0.736601i	0.929707	−	0.368300i	$-0.120060\pi$
$348$	−9.02076e9	−	1.14751e10i	−0.615072	−	0.782421i
$349$	−1.68301e10			−1.13445			−0.567226	−	0.823562i	$-0.691983\pi$
$349$	−1.68301e10			−1.13445			−0.567226	+	0.823562i	$0.691983\pi$
$350$	−1.58753e9	−	4.58822e9i	−0.105791	−	0.305754i
$351$			6.53561e8i			0.0430584i
$352$	2.61514e10	−	2.48516e9i	1.70343	−	0.161876i
$353$	−2.85995e10			−1.84187			−0.920936	−	0.389714i	$-0.872574\pi$
$353$	−2.85995e10			−1.84187			−0.920936	+	0.389714i	$0.872574\pi$
$354$	6.95038e9	−	2.40484e9i	0.442584	−	0.153135i
$355$		−	5.77946e9i		−	0.363893i
$356$	−6.54622e9	+	5.14608e9i	−0.407559	+	0.320388i
$357$	−2.46072e9			−0.151492
$358$	4.10020e9	+	1.18502e10i	0.249616	+	0.721431i
$359$		−	5.60539e9i		−	0.337464i	−0.985662	−	0.168732i	$-0.946033\pi$
$359$		−	5.60539e9i		−	0.337464i	0.985662	−	0.168732i	$-0.0539673\pi$
$360$	1.14910e9	−	1.78696e9i	0.0684145	−	0.106391i
$361$	1.69518e10			0.998131
$362$	−3.47293e9	+	1.20164e9i	−0.202237	+	0.0699745i
$363$			1.93261e10i			1.11306i
$364$	−9.17478e8	−	1.16711e9i	−0.0522625	−	0.0664821i
$365$	−1.30314e10			−0.734208
$366$	−5.33287e9	−	1.54129e10i	−0.297192	−	0.858932i
$367$		−	7.65051e9i		−	0.421722i	−0.977516	−	0.210861i	$-0.932373\pi$
$367$		−	7.65051e9i		−	0.421722i	0.977516	−	0.210861i	$-0.0676267\pi$
$368$	1.33819e10	+	3.25157e9i	0.729670	+	0.177297i
$369$	8.85365e8			0.0477548
$370$	3.76012e9	−	1.30101e9i	0.200630	−	0.0694182i
$371$			1.06289e10i			0.561038i
$372$	−5.69181e9	+	4.47441e9i	−0.297220	+	0.233649i
$373$	1.83599e10			0.948494			0.474247	−	0.880392i	$-0.342720\pi$
$373$	1.83599e10			0.948494			0.474247	+	0.880392i	$0.342720\pi$
$374$	7.59950e9	+	2.19638e10i	0.388417	+	1.12259i
$375$			8.04118e9i			0.406625i
$376$	3.08665e10	+	1.98486e10i	1.54431	+	0.993066i
$377$	7.79098e9			0.385680
$378$	−1.40340e9	+	4.85579e8i	−0.0687409	+	0.0237844i
$379$		−	2.86367e10i		−	1.38792i	−0.720011	−	0.693962i	$-0.755863\pi$
$379$		−	2.86367e10i		−	1.38792i	0.720011	−	0.693962i	$-0.244137\pi$
$380$	−2.11407e8	−	2.68926e8i	−0.0101388	−	0.0128973i
$381$	−5.90858e9			−0.280403
$382$	5.02345e9	+	1.45186e10i	0.235911	+	0.681821i
$383$			1.73792e10i			0.807672i	0.914831	+	0.403836i	$0.132323\pi$
$383$			1.73792e10i			0.807672i	−0.914831	+	0.403836i	$0.867677\pi$
$384$	9.09090e9	−	8.65711e9i	0.418102	−	0.398151i
$385$	−5.39196e9			−0.245417
$386$	−1.65465e10	+	5.72512e9i	−0.745345	+	0.257891i
$387$		−	1.79583e9i		−	0.0800609i
$388$	−1.49741e10	+	1.17714e10i	−0.660715	+	0.519397i
$389$	1.77896e10			0.776906			0.388453	−	0.921469i	$-0.373010\pi$
$389$	1.77896e10			0.776906			0.388453	+	0.921469i	$0.373010\pi$
$390$	3.70798e8	+	1.07167e9i	0.0160280	+	0.0463235i
$391$			1.21840e10i			0.521292i
$392$	1.82448e9	−	2.83725e9i	0.0772672	−	0.120158i
$393$	−1.24405e10			−0.521515
$394$	−6.55658e9	+	2.26859e9i	−0.272077	+	0.0941391i
$395$			9.63628e9i			0.395841i
$396$	8.66833e9	+	1.10268e10i	0.352496	+	0.448404i
$397$	1.77352e10			0.713961			0.356981	−	0.934112i	$-0.383806\pi$
$397$	1.77352e10			0.713961			0.356981	+	0.934112i	$0.383806\pi$
$398$	1.33787e10	+	3.86666e10i	0.533190	+	1.54101i
$399$			2.39106e8i			0.00943407i
$400$	−5.17409e9	+	2.12941e10i	−0.202113	+	0.831800i
$401$	4.66288e10			1.80334			0.901669	−	0.432428i	$-0.142343\pi$
$401$	4.66288e10			1.80334			0.901669	+	0.432428i	$0.142343\pi$
$402$	−4.04783e9	+	1.40055e9i	−0.154995	+	0.0536285i
$403$		−	3.86442e9i		−	0.146509i
$404$	2.88043e10	−	2.26435e10i	1.08127	−	0.849998i
$405$	1.13437e9			0.0421632
$406$	5.78850e9	+	1.67297e10i	0.213040	+	0.615721i
$407$			2.62680e10i			0.957302i
$408$	9.34177e9	+	6.00719e9i	0.337123	+	0.216786i
$409$	−3.19370e10			−1.14130			−0.570651	−	0.821193i	$-0.693309\pi$
$409$	−3.19370e10			−1.14130			−0.570651	+	0.821193i	$0.693309\pi$
$410$	1.45176e9	−	5.02312e8i	0.0513760	−	0.0177762i
$411$		−	4.84478e9i		−	0.169788i
$412$	−4.63022e9	−	5.89001e9i	−0.160699	−	0.204422i
$413$	−8.91993e9			−0.306592
$414$	2.40429e9	+	6.94879e9i	0.0818438	+	0.236542i
$415$			9.36769e9i			0.315820i
$416$	6.33899e8	+	6.67054e9i	0.0211664	+	0.222734i
$417$	−2.57391e9			−0.0851236
$418$	2.13420e9	−	7.38438e8i	0.0699086	−	0.0241885i
$419$			2.87961e10i			0.934281i	0.884183	+	0.467140i	$0.154716\pi$
$419$			2.87961e10i			0.934281i	−0.884183	+	0.467140i	$0.845284\pi$
$420$	−2.02571e9	+	1.59244e9i	−0.0651000	+	0.0511760i
$421$	−3.20971e10			−1.02173			−0.510866	−	0.859660i	$-0.670675\pi$
$421$	−3.20971e10			−1.02173			−0.510866	+	0.859660i	$0.670675\pi$
$422$	−1.83775e10	−	5.31139e10i	−0.579477	−	1.67478i
$423$			1.95941e10i			0.612017i
$424$	2.59476e10	−	4.03511e10i	0.802850	−	1.24851i
$425$	−1.93878e10			−0.594256
$426$	1.72314e10	−	5.96210e9i	0.523218	−	0.181034i
$427$			1.97804e10i			0.595010i
$428$	−1.99615e10	−	2.53926e10i	−0.594865	−	0.756715i
$429$	−7.48660e9			−0.221032
$430$	−1.01886e9	−	2.94468e9i	−0.0298018	−	0.0861319i
$431$		−	4.34918e10i		−	1.26037i	−0.776445	−	0.630185i	$-0.782979\pi$
$431$		−	4.34918e10i		−	1.26037i	0.776445	−	0.630185i	$-0.217021\pi$
$432$	6.51324e9	+	1.58260e9i	0.187009	+	0.0454398i
$433$	4.80757e10			1.36765			0.683824	−	0.729647i	$-0.260316\pi$
$433$	4.80757e10			1.36765			0.683824	+	0.729647i	$0.260316\pi$
$434$	8.29814e9	−	2.87117e9i	0.233895	−	0.0809282i
$435$		−	1.35226e10i		−	0.377662i
$436$	2.90107e9	−	2.28057e9i	0.0802808	−	0.0631099i
$437$	1.18391e9			0.0324632
$438$	−1.34432e10	−	3.88530e10i	−0.365263	−	1.05567i
$439$		−	4.30211e10i		−	1.15831i	−0.815218	−	0.579154i	$-0.803383\pi$
$439$		−	4.30211e10i		−	1.15831i	0.815218	−	0.579154i	$-0.196617\pi$
$440$	2.04698e10	+	1.31631e10i	0.546139	+	0.351193i
$441$	1.80109e9			0.0476190
$442$	−5.60238e9	+	1.93843e9i	−0.146786	+	0.0507881i
$443$			1.61272e10i			0.418741i	0.977836	+	0.209370i	$0.0671414\pi$
$443$			1.61272e10i			0.418741i	−0.977836	+	0.209370i	$0.932859\pi$
$444$	7.75789e9	+	9.86866e9i	0.199624	+	0.253937i
$445$	−7.71424e9			−0.196722
$446$	4.55357e9	+	1.31605e10i	0.115083	+	0.332609i
$447$			3.38222e10i			0.847173i
$448$	−1.38528e10	+	6.31722e9i	−0.343894	+	0.156825i
$449$	2.79561e10			0.687845			0.343923	−	0.938998i	$-0.388244\pi$
$449$	2.79561e10			0.687845			0.343923	+	0.938998i	$0.388244\pi$
$450$	−1.10573e10	+	3.82585e9i	−0.269650	+	0.0932992i
$451$			1.01419e10i			0.245140i
$452$	6.73617e9	−	5.29540e9i	0.161384	−	0.126866i
$453$	−6.50559e9			−0.154488
$454$	−1.85604e10	−	5.36425e10i	−0.436881	−	1.26266i
$455$		−	1.37535e9i		−	0.0320898i
$456$	5.83714e8	−	9.07733e8i	0.0135002	−	0.0209942i
$457$	7.02468e10			1.61050			0.805252	−	0.592932i	$-0.202030\pi$
$457$	7.02468e10			1.61050			0.805252	+	0.592932i	$0.202030\pi$
$458$	−6.60081e10	+	2.28389e10i	−1.50015	+	0.519055i
$459$			5.93017e9i			0.133603i
$460$	7.88480e9	+	1.00301e10i	0.176100	+	0.224013i
$461$	2.70775e10			0.599521			0.299760	−	0.954015i	$-0.403093\pi$
$461$	2.70775e10			0.599521			0.299760	+	0.954015i	$0.403093\pi$
$462$	−5.56235e9	−	1.60761e10i	−0.122093	−	0.352868i
$463$			1.38957e10i			0.302383i	0.988504	+	0.151192i	$0.0483111\pi$
$463$			1.38957e10i			0.302383i	−0.988504	+	0.151192i	$0.951689\pi$
$464$	1.88659e10	−	7.76431e10i	0.407011	−	1.67506i
$465$	−6.70738e9			−0.143463
$466$	−6.90674e10	+	2.38974e10i	−1.46464	+	0.506766i
$467$			6.38438e9i			0.134231i	0.997745	+	0.0671153i	$0.0213795\pi$
$467$			6.38438e9i			0.134231i	−0.997745	+	0.0671153i	$0.978620\pi$
$468$	−2.81265e9	+	2.21106e9i	−0.0586317	+	0.0460912i
$469$	5.19487e9			0.107370
$470$	1.11167e10	+	3.21291e10i	0.227817	+	0.658426i
$471$		−	2.29566e10i		−	0.466469i
$472$	3.38633e10	+	2.17757e10i	0.682277	+	0.438736i
$473$	2.05713e10			0.410977
$474$	−2.87305e10	+	9.94080e9i	−0.569154	+	0.196928i
$475$			1.88390e9i			0.0370070i
$476$	−8.32486e9	−	1.05899e10i	−0.162162	−	0.206283i
$477$	2.56150e10			0.494789
$478$	1.98007e10	+	5.72273e10i	0.379288	+	1.09620i
$479$		−	2.67864e10i		−	0.508829i	−0.967095	−	0.254414i	$-0.918117\pi$
$479$		−	2.67864e10i		−	0.508829i	0.967095	−	0.254414i	$-0.0818827\pi$
$480$	1.15779e10	−	1.10024e9i	0.218104	−	0.0207264i
$481$	−6.70028e9			−0.125173
$482$	3.75859e9	−	1.30048e9i	0.0696366	−	0.0240944i
$483$		−	8.91788e9i		−	0.163860i
$484$	−8.31715e10	+	6.53823e10i	−1.51563	+	1.19146i
$485$	−1.76459e10			−0.318916
$486$	1.17022e9	+	3.38211e9i	0.0209759	+	0.0606237i
$487$			8.28841e9i			0.147352i	0.997282	+	0.0736759i	$0.0234730\pi$
$487$			8.28841e9i			0.147352i	−0.997282	+	0.0736759i	$0.976527\pi$
$488$	4.82887e10	−	7.50937e10i	0.851464	−	1.32411i
$489$	1.23939e10			0.216756
$490$	2.95331e9	−	1.02185e9i	0.0512300	−	0.0177257i
$491$		−	5.92908e10i		−	1.02014i	−0.860132	−	0.510072i	$-0.829619\pi$
$491$		−	5.92908e10i		−	1.02014i	0.860132	−	0.510072i	$-0.170381\pi$
$492$	2.99528e9	+	3.81023e9i	0.0511184	+	0.0650266i
$493$	7.06925e10			1.19670
$494$	1.88356e8	+	5.44379e8i	0.00316280	+	0.00914100i
$495$			1.29943e10i			0.216437i
$496$	−3.85119e10	−	9.35773e9i	−0.636310	−	0.154612i
$497$	−2.21144e10			−0.362450
$498$	−2.79297e10	+	9.66372e9i	−0.454097	+	0.157118i
$499$			2.34271e10i			0.377847i	0.981992	+	0.188923i	$0.0604998\pi$
$499$			2.34271e10i			0.377847i	−0.981992	+	0.188923i	$0.939500\pi$
$500$	−3.46058e10	+	2.72041e10i	−0.553693	+	0.435266i
$501$	5.52279e10			0.876612
$502$	−3.44820e10	−	9.96586e10i	−0.542973	−	1.56928i
$503$			3.76155e9i			0.0587618i	0.999568	+	0.0293809i	$0.00935357\pi$
$503$			3.76155e9i			0.0587618i	−0.999568	+	0.0293809i	$0.990646\pi$
$504$	−6.83758e9	−	4.39688e9i	−0.105969	−	0.0681432i
$505$	3.39438e10			0.521909
$506$	−7.95989e10	+	2.75414e10i	−1.21424	+	0.420129i
$507$			3.62383e10i			0.548449i
$508$	−1.99893e10	−	2.54280e10i	−0.300153	−	0.381819i
$509$	2.29786e10			0.342336			0.171168	−	0.985242i	$-0.445246\pi$
$509$	2.29786e10			0.342336			0.171168	+	0.985242i	$0.445246\pi$
$510$	3.36449e9	+	9.72391e9i	0.0497323	+	0.143734i
$511$			4.98629e10i			0.731297i
$512$	6.80120e10	+	9.83546e9i	0.989705	+	0.143125i
$513$	5.76230e8			0.00832006
$514$	−1.01989e11	+	3.52882e10i	−1.46116	+	0.505565i
$515$		−	6.94095e9i		−	0.0986711i
$516$	7.72848e9	−	6.07547e9i	0.109017	−	0.0857000i
$517$	−2.24452e11			−3.14167
$518$	−4.97814e9	−	1.43876e10i	−0.0691429	−	0.199834i
$519$		−	5.57176e10i		−	0.767933i
$520$	−3.35755e9	+	5.22132e9i	−0.0459208	+	0.0714113i
$521$	8.86941e10			1.20377			0.601886	−	0.798582i	$-0.294416\pi$
$521$	8.86941e10			1.20377			0.601886	+	0.798582i	$0.294416\pi$
$522$	4.03175e10	−	1.39499e10i	0.543015	−	0.187884i
$523$			1.00252e11i			1.33995i	0.742385	+	0.669974i	$0.233695\pi$
$523$			1.00252e11i			1.33995i	−0.742385	+	0.669974i	$0.766305\pi$
$524$	−4.20874e10	−	5.35385e10i	−0.558248	−	0.710136i
$525$	1.41907e10			0.186795
$526$	8.21684e9	+	2.37480e10i	0.107340	+	0.310230i
$527$		−	3.50644e10i		−	0.454594i
$528$	−1.81288e10	+	7.46097e10i	−0.233257	+	0.959974i
$529$	3.41551e10			0.436147
$530$	4.20017e10	−	1.45327e10i	0.532309	−	0.184180i
$531$			2.14965e10i			0.270389i
$532$	−1.02901e9	+	8.08920e8i	−0.0128462	+	0.0100986i
$533$	−2.58694e9			−0.0320537
$534$	−7.95802e9	−	2.29999e10i	−0.0978678	−	0.282854i
$535$		−	2.99233e10i		−	0.365254i
$536$	−1.97216e10	−	1.26819e10i	−0.238937	−	0.153648i
$537$	−3.66510e10			−0.440746
$538$	−9.03976e9	+	3.12777e9i	−0.107902	+	0.0373341i
$539$			2.06316e10i			0.244443i
$540$	3.83769e9	+	4.88184e9i	0.0451330	+	0.0574128i
$541$	−1.13074e11			−1.32000			−0.660002	−	0.751264i	$-0.729445\pi$
$541$	−1.13074e11			−1.32000			−0.660002	+	0.751264i	$0.729445\pi$
$542$	−1.08689e10	−	3.14130e10i	−0.125948	−	0.364009i
$543$		−	1.07412e10i		−	0.123554i
$544$	5.75177e9	+	6.05260e10i	0.0656758	+	0.691109i
$545$	3.41870e9			0.0387502
$546$	4.10059e9	−	1.41881e9i	0.0461398	−	0.0159644i
$547$		−	5.03149e10i		−	0.562015i	−0.959706	−	0.281007i	$-0.909331\pi$
$547$		−	5.03149e10i		−	0.562015i	0.959706	−	0.281007i	$-0.0906685\pi$
$548$	2.08499e10	−	1.63904e10i	0.231197	−	0.181747i
$549$	4.76696e10			0.524750
$550$	−4.38254e10	−	1.26663e11i	−0.478934	−	1.38420i
$551$		−	6.86914e9i		−	0.0745239i
$552$	−2.17707e10	+	3.38555e10i	−0.234485	+	0.364647i
$553$	3.68720e10			0.394272
$554$	−2.12704e10	+	7.35961e9i	−0.225807	+	0.0781296i
$555$			1.16295e10i			0.122571i
$556$	−8.70782e9	−	1.10770e10i	−0.0911193	−	0.115911i
$557$	1.41362e11			1.46863			0.734317	−	0.678807i	$-0.237503\pi$
$557$	1.41362e11			1.46863			0.734317	+	0.678807i	$0.237503\pi$
$558$	−6.91934e9	−	1.99980e10i	−0.0713720	−	0.206276i
$559$			5.24721e9i			0.0537380i
$560$	−1.37064e10	−	3.33041e9i	−0.139371	−	0.0338646i
$561$	−6.79306e10			−0.685826
$562$	2.65561e10	−	9.18847e9i	0.266207	−	0.0921081i
$563$		−	1.78360e11i		−	1.77527i	−0.460547	−	0.887635i	$-0.652347\pi$
$563$		−	1.78360e11i		−	1.77527i	0.460547	−	0.887635i	$-0.347653\pi$
$564$	−8.43247e10	+	6.62888e10i	−0.833371	+	0.655125i
$565$	7.93809e9			0.0778972
$566$	9.87882e9	+	2.85514e10i	0.0962586	+	0.278203i
$567$		−	4.34051e9i		−	0.0419961i
$568$	8.39541e10	+	5.39864e10i	0.806582	+	0.518670i
$569$	2.59703e9			0.0247758			0.0123879	−	0.999923i	$-0.496057\pi$
$569$	2.59703e9			0.0247758			0.0123879	+	0.999923i	$0.496057\pi$
$570$	9.44865e8	−	3.26925e8i	0.00895097	−	0.00309705i
$571$		−	1.22423e11i		−	1.15164i	−0.817576	−	0.575820i	$-0.804683\pi$
$571$		−	1.22423e11i		−	1.15164i	0.817576	−	0.575820i	$-0.195317\pi$
$572$	−2.53279e10	−	3.22191e10i	−0.236600	−	0.300975i
$573$	−4.49037e10			−0.416547
$574$	−1.92203e9	−	5.55498e9i	−0.0177057	−	0.0511723i
$575$		−	7.02635e10i		−	0.642774i
$576$	1.52241e10	+	3.33843e10i	0.138306	+	0.303286i
$577$	−1.14649e10			−0.103435			−0.0517173	−	0.998662i	$-0.516469\pi$
$577$	−1.14649e10			−0.103435			−0.0517173	+	0.998662i	$0.516469\pi$
$578$	5.46429e10	−	1.89065e10i	0.489578	−	0.169395i
$579$		−	5.11759e10i		−	0.455356i
$580$	5.81955e10	−	4.57483e10i	0.514254	−	0.404262i
$581$	3.58442e10			0.314568
$582$	−1.82035e10	−	5.26111e10i	−0.158658	−	0.458548i
$583$			2.93421e11i			2.53991i
$584$	1.21727e11	−	1.89298e11i	1.04649	−	1.62740i
$585$	−3.31450e9			−0.0283005
$586$	1.03508e11	−	3.58139e10i	0.877775	−	0.303711i
$587$			1.25780e11i			1.05940i	0.848185	+	0.529701i	$0.177696\pi$
$587$			1.25780e11i			1.05940i	−0.848185	+	0.529701i	$0.822304\pi$
$588$	6.09327e9	+	7.75112e9i	0.0509731	+	0.0648418i
$589$	−3.40718e9			−0.0283096
$590$	1.21960e10	+	3.52485e10i	0.100649	+	0.290892i
$591$		−	2.02785e10i		−	0.166221i
$592$	−1.62248e10	+	6.67734e10i	−0.132097	+	0.543646i
$593$	1.03787e10			0.0839312			0.0419656	−	0.999119i	$-0.486638\pi$
$593$	1.03787e10			0.0839312			0.0419656	+	0.999119i	$0.486638\pi$
$594$	−3.87424e10	+	1.34049e10i	−0.311200	+	0.107676i
$595$		−	1.24794e10i		−	0.0995694i
$596$	−1.45557e11	+	1.14424e11i	−1.15358	+	0.906844i
$597$	−1.19590e11			−0.941451
$598$	−7.02508e9	−	2.03036e10i	−0.0549347	−	0.158770i
$599$			2.59363e10i			0.201465i	0.994914	+	0.100733i	$0.0321187\pi$
$599$			2.59363e10i			0.201465i	−0.994914	+	0.100733i	$0.967881\pi$
$600$	−5.38729e10	−	3.46428e10i	−0.415686	−	0.267305i
$601$	−9.63410e10			−0.738437			−0.369218	−	0.929343i	$-0.620375\pi$
$601$	−9.63410e10			−0.738437			−0.369218	+	0.929343i	$0.620375\pi$
$602$	−1.12674e10	+	3.89854e9i	−0.0857904	+	0.0296836i
$603$		−	1.25193e10i		−	0.0946915i
$604$	−2.20091e10	−	2.79973e10i	−0.165369	−	0.210363i
$605$	−9.80115e10			−0.731569
$606$	3.50164e10	+	1.01203e11i	0.259646	+	0.750418i
$607$			2.17528e11i			1.60236i	0.598421	+	0.801182i	$0.295795\pi$
$607$			2.17528e11i			1.60236i	−0.598421	+	0.801182i	$0.704205\pi$
$608$	5.88126e9	−	5.58895e8i	0.0430384	−	0.00408993i
$609$	−5.17424e10			−0.376164
$610$	7.81655e10	−	2.70454e10i	0.564541	−	0.195332i
$611$		−	5.72518e10i		−	0.410794i
$612$	−2.55209e10	+	2.00624e10i	−0.181924	+	0.143013i
$613$	3.47637e9			0.0246198			0.0123099	−	0.999924i	$-0.496082\pi$
$613$	3.47637e9			0.0246198			0.0123099	+	0.999924i	$0.496082\pi$
$614$	4.50899e10	+	1.30317e11i	0.317253	+	0.916912i
$615$			4.49008e9i			0.0313873i
$616$	5.03667e10	−	7.83251e10i	0.349800	−	0.543974i
$617$	1.67294e11			1.15435			0.577177	−	0.816619i	$-0.304154\pi$
$617$	1.67294e11			1.15435			0.577177	+	0.816619i	$0.304154\pi$
$618$	2.06944e10	−	7.16029e9i	0.141873	−	0.0490881i
$619$		−	2.44288e8i		−	0.00166395i	−1.00000		0.000831975i	$-0.999735\pi$
$619$		−	2.44288e8i		−	0.00166395i	1.00000		0.000831975i	$-0.000264826\pi$
$620$	−2.26917e10	−	2.88657e10i	−0.153568	−	0.195351i
$621$	−2.14915e10			−0.144511
$622$	−8.37005e10	−	2.41908e11i	−0.559199	−	1.61617i
$623$			2.95175e10i			0.195942i
$624$	−1.90310e10	−	4.62419e9i	−0.125523	−	0.0304998i
$625$	8.98353e10			0.588745
$626$	3.74769e10	−	1.29671e10i	0.244043	−	0.0844393i
$627$			6.60077e9i			0.0427095i
$628$	9.87953e10	−	7.76644e10i	0.635181	−	0.499325i
$629$	−6.07958e10			−0.388393
$630$	−2.46259e9	−	7.11728e9i	−0.0156326	−	0.0451806i
$631$		−	7.29073e10i		−	0.459890i	−0.973204	−	0.229945i	$-0.926145\pi$
$631$		−	7.29073e10i		−	0.459890i	0.973204	−	0.229945i	$-0.0738546\pi$
$632$	−1.39979e11	−	9.00132e10i	−0.877396	−	0.564206i
$633$	1.64273e11			1.02318
$634$	2.66920e11	−	9.23546e10i	1.65205	−	0.571612i
$635$		−	2.99650e10i		−	0.184298i
$636$	8.66581e10	+	1.10236e11i	0.529640	+	0.673744i
$637$	−5.26259e9			−0.0319626
$638$	1.59798e11	+	4.61841e11i	0.964467	+	2.78746i
$639$			5.32942e10i			0.319651i
$640$	4.39041e10	+	4.61040e10i	0.261689	+	0.274801i
$641$	−2.21813e11			−1.31388			−0.656938	−	0.753945i	$-0.728149\pi$
$641$	−2.21813e11			−1.31388			−0.656938	+	0.753945i	$0.728149\pi$
$642$	8.92162e10	−	3.08689e10i	0.525175	−	0.181711i
$643$		−	1.44455e11i		−	0.845059i	−0.906349	−	0.422530i	$-0.861142\pi$
$643$		−	1.44455e11i		−	0.845059i	0.906349	−	0.422530i	$-0.138858\pi$
$644$	3.83788e10	−	3.01701e10i	0.223125	−	0.175402i
$645$	9.10744e9			0.0526208
$646$	1.70907e9	+	4.93950e9i	0.00981366	+	0.0283630i
$647$		−	2.41721e11i		−	1.37942i	−0.724085	−	0.689711i	$-0.757738\pi$
$647$		−	2.41721e11i		−	1.37942i	0.724085	−	0.689711i	$-0.242262\pi$
$648$	−1.05962e10	+	1.64781e10i	−0.0600967	+	0.0934562i
$649$	−2.46244e11			−1.38799
$650$	3.23083e10	−	1.11787e10i	0.180993	−	0.0626237i
$651$			2.56649e10i			0.142894i
$652$	4.19297e10	+	5.33379e10i	0.232023	+	0.295152i
$653$	−2.87226e11			−1.57969			−0.789844	−	0.613308i	$-0.789838\pi$
$653$	−2.87226e11			−1.57969			−0.789844	+	0.613308i	$0.789838\pi$
$654$	3.52673e9	+	1.01928e10i	0.0192780	+	0.0557164i
$655$		−	6.30912e10i		−	0.342771i
$656$	−6.26429e9	+	2.57808e10i	−0.0338265	+	0.139214i
$657$	1.20166e11			0.644943
$658$	1.22938e11	−	4.25367e10i	0.655816	−	0.226913i
$659$		−	2.96787e11i		−	1.57363i	−0.617189	−	0.786815i	$-0.711728\pi$
$659$		−	2.96787e11i		−	1.57363i	0.617189	−	0.786815i	$-0.288272\pi$
$660$	−5.59219e10	+	4.39610e10i	−0.294718	+	0.231682i
$661$	1.43431e11			0.751341			0.375671	−	0.926753i	$-0.377412\pi$
$661$	1.43431e11			0.751341			0.375671	+	0.926753i	$0.377412\pi$
$662$	1.10480e11	+	3.19305e11i	0.575243	+	1.66255i
$663$		−	1.73273e10i		−	0.0896762i
$664$	−1.36078e11	−	8.75042e10i	−0.700026	−	0.450149i
$665$	−1.21261e9			−0.00620063
$666$	−3.46732e10	+	1.19970e10i	−0.176237	+	0.0609783i
$667$			2.56197e11i			1.29440i
$668$	1.86842e11	+	2.37677e11i	0.938357	+	1.19366i
$669$	−4.07036e10			−0.203202
$670$	−7.10284e9	−	2.05283e10i	−0.0352479	−	0.101872i
$671$			5.46059e11i			2.69370i
$672$	−4.20993e9	−	4.43012e10i	−0.0206442	−	0.217239i
$673$	2.96683e11			1.44621			0.723107	−	0.690737i	$-0.242714\pi$
$673$	2.96683e11			1.44621			0.723107	+	0.690737i	$0.242714\pi$
$674$	−1.61299e11	+	5.58096e10i	−0.781613	+	0.270439i
$675$		−	3.41986e10i		−	0.164738i
$676$	−1.55954e11	+	1.22598e11i	−0.746811	+	0.587079i
$677$	−1.17128e11			−0.557580			−0.278790	−	0.960352i	$-0.589933\pi$
$677$	−1.17128e11			−0.557580			−0.278790	+	0.960352i	$0.589933\pi$
$678$	8.18894e9	+	2.36673e10i	0.0387533	+	0.112003i
$679$			6.75196e10i			0.317651i
$680$	−3.04652e10	+	4.73763e10i	−0.142485	+	0.221578i
$681$	1.65908e11			0.771398
$682$	2.29079e11	−	7.92616e10i	1.05888	−	0.366374i
$683$			1.42590e11i			0.655250i	0.944808	+	0.327625i	$0.106248\pi$
$683$			1.42590e11i			0.655250i	−0.944808	+	0.327625i	$0.893752\pi$
$684$	1.94945e9	+	2.47985e9i	0.00890609	+	0.0113293i
$685$	2.45701e10			0.111595
$686$	−3.90997e9	−	1.13004e10i	−0.0176554	−	0.0510269i
$687$		−	2.04153e11i		−	0.916492i
$688$	5.22925e10	+	1.27062e10i	0.233392	+	0.0567101i
$689$	−7.48441e10			−0.332109
$690$	−3.52404e10	+	1.21932e10i	−0.155469	+	0.0537926i
$691$			2.61382e11i			1.14647i	0.819390	+	0.573237i	$0.194312\pi$
$691$			2.61382e11i			1.14647i	−0.819390	+	0.573237i	$0.805688\pi$
$692$	2.39785e11	−	1.88499e11i	1.04568	−	0.822022i
$693$	4.97209e10			0.215579
$694$	5.58720e10	+	1.61479e11i	0.240855	+	0.696110i
$695$		−	1.30535e10i		−	0.0559483i
$696$	1.96433e11	+	1.26315e11i	0.837100	+	0.538294i
$697$	−2.34729e10			−0.0994572
$698$	2.54480e11	−	8.80505e10i	1.07209	−	0.370945i
$699$		−	2.13615e11i		−	0.894794i
$700$	4.80085e10	+	6.10706e10i	0.199952	+	0.254355i
$701$	−9.70579e9			−0.0401938			−0.0200969	−	0.999798i	$-0.506397\pi$
$701$	−9.70579e9			−0.0401938			−0.0200969	+	0.999798i	$0.506397\pi$
$702$	−3.41924e9	−	9.88216e9i	−0.0140793	−	0.0406915i
$703$			5.90749e9i			0.0241870i
$704$	−3.82420e11	+	1.74393e11i	−1.55686	+	0.709969i
$705$	−9.93704e10			−0.402254
$706$	4.32438e11	−	1.49624e11i	1.74063	−	0.602259i
$707$		−	1.29881e11i		−	0.519839i
$708$	−9.25117e10	+	7.27247e10i	−0.368183	+	0.289434i
$709$	−1.75748e11			−0.695512			−0.347756	−	0.937585i	$-0.613056\pi$
$709$	−1.75748e11			−0.695512			−0.347756	+	0.937585i	$0.613056\pi$
$710$	3.02365e10	+	8.73883e10i	0.118987	+	0.343890i
$711$		−	8.88591e10i		−	0.347715i
$712$	7.20592e10	−	1.12059e11i	0.280395	−	0.436041i
$713$	1.27077e11			0.491709
$714$	3.72072e10	−	1.28738e10i	0.143164	−	0.0495351i
$715$		−	3.79679e10i		−	0.145275i
$716$	−1.23994e11	−	1.57730e11i	−0.471790	−	0.600154i
$717$	−1.76995e11			−0.669707
$718$	2.93258e10	+	8.47562e10i	0.110345	+	0.318914i
$719$			9.44254e10i			0.353324i	0.984272	+	0.176662i	$0.0565300\pi$
$719$			9.44254e10i			0.353324i	−0.984272	+	0.176662i	$0.943470\pi$
$720$	−8.02609e9	+	3.30315e10i	−0.0298658	+	0.122913i
$721$	−2.65586e10			−0.0982798
$722$	−2.56320e11	+	8.86871e10i	−0.943264	+	0.326371i
$723$			1.16248e10i			0.0425433i
$724$	4.62258e10	−	3.63387e10i	0.168240	−	0.132256i
$725$	−4.07675e11			−1.47558
$726$	−1.01109e11	−	2.92221e11i	−0.363950	−	1.05188i
$727$		−	2.08431e11i		−	0.746149i	−0.927801	−	0.373075i	$-0.878304\pi$
$727$		−	2.08431e11i		−	0.746149i	0.927801	−	0.373075i	$-0.121696\pi$
$728$	1.99787e10	+	1.28472e10i	0.0711281	+	0.0457387i
$729$	−1.04604e10			−0.0370370
$730$	1.97041e11	−	6.81765e10i	0.693849	−	0.240073i
$731$			4.76113e10i			0.166740i
$732$	1.61271e11	+	2.05150e11i	0.561711	+	0.714540i
$733$	−1.13987e10			−0.0394856			−0.0197428	−	0.999805i	$-0.506285\pi$
$733$	−1.13987e10			−0.0394856			−0.0197428	+	0.999805i	$0.506285\pi$
$734$	4.00252e10	+	1.15679e11i	0.137895	+	0.398540i
$735$			9.13413e9i			0.0312981i
$736$	−2.19352e11	+	2.08450e10i	−0.747534	+	0.0710379i
$737$	1.43410e11			0.486081
$738$	−1.33871e10	+	4.63197e9i	−0.0451297	+	0.0156150i
$739$			5.96590e10i			0.200031i	0.994986	+	0.100016i	$0.0318893\pi$
$739$			5.96590e10i			0.200031i	−0.994986	+	0.100016i	$0.968111\pi$
$740$	−5.00484e10	+	3.93438e10i	−0.166903	+	0.131205i
$741$	−1.68368e9			−0.00558454
$742$	−5.56073e10	−	1.60714e11i	−0.183449	−	0.530198i
$743$		−	5.38236e11i		−	1.76611i	−0.469271	−	0.883054i	$-0.655483\pi$
$743$		−	5.38236e11i		−	1.76611i	0.469271	−	0.883054i	$-0.344517\pi$
$744$	6.26540e10	−	9.74332e10i	0.204483	−	0.317991i
$745$	−1.71528e11			−0.556813
$746$	−2.77610e11	+	9.60536e10i	−0.896355	+	0.310140i
$747$		−	8.63823e10i		−	0.277423i
$748$	−2.29816e11	−	2.92345e11i	−0.734133	−	0.933875i
$749$	−1.14498e11			−0.363806
$750$	−4.20691e10	−	1.21587e11i	−0.132959	−	0.384273i
$751$			7.75426e10i			0.243770i	0.992544	+	0.121885i	$0.0388939\pi$
$751$			7.75426e10i			0.243770i	−0.992544	+	0.121885i	$0.961106\pi$
$752$	−5.70558e11	−	1.38636e11i	−1.78414	−	0.433514i
$753$	3.08229e11			0.958724
$754$	−1.17803e11	+	4.07602e10i	−0.364479	+	0.126110i
$755$		−	3.29928e10i		−	0.101539i
$756$	1.86797e10	−	1.46844e10i	0.0571851	−	0.0449541i
$757$	−5.23115e11			−1.59299			−0.796496	−	0.604643i	$-0.793316\pi$
$757$	−5.23115e11			−1.59299			−0.796496	+	0.604643i	$0.793316\pi$
$758$	1.49819e11	+	4.33001e11i	0.453826	+	1.31163i
$759$		−	2.46187e11i		−	0.741820i
$760$	4.60352e9	+	2.96028e9i	0.0137986	+	0.00887316i
$761$	5.27014e11			1.57139			0.785694	−	0.618615i	$-0.212306\pi$
$761$	5.27014e11			1.57139			0.785694	+	0.618615i	$0.212306\pi$
$762$	8.93406e10	−	3.09120e10i	0.264990	−	0.0916868i
$763$		−	1.30812e10i		−	0.0385966i
$764$	−1.51914e11	−	1.93247e11i	−0.445886	−	0.567203i
$765$	−3.00746e10			−0.0878120
$766$	−9.09231e10	−	2.62782e11i	−0.264094	−	0.763275i
$767$		−	6.28103e10i		−	0.181489i
$768$	−9.21673e10	+	1.78461e11i	−0.264930	+	0.512977i
$769$	1.37827e11			0.394120			0.197060	−	0.980391i	$-0.436861\pi$
$769$	1.37827e11			0.394120			0.197060	+	0.980391i	$0.436861\pi$
$770$	8.15291e10	−	2.82092e10i	0.231926	−	0.0802468i
$771$		−	3.15435e11i		−	0.892673i
$772$	2.20239e11	−	1.73133e11i	0.620048	−	0.487429i
$773$	2.02023e11			0.565826			0.282913	−	0.959146i	$-0.408699\pi$
$773$	2.02023e11			0.565826			0.282913	+	0.959146i	$0.408699\pi$
$774$	9.39525e9	+	2.71538e10i	0.0261785	+	0.0756600i
$775$			2.02212e11i			0.560532i
$776$	1.64831e11	−	2.56329e11i	0.454562	−	0.706888i
$777$	4.44987e10			0.122085
$778$	−2.68988e11	+	9.30702e10i	−0.734200	+	0.254034i
$779$			2.28085e9i			0.00619365i
$780$	−1.12133e10	−	1.42642e10i	−0.0302939	−	0.0385362i
$781$	−6.10489e11			−1.64087
$782$	−6.37430e10	−	1.84227e11i	−0.170453	−	0.492637i
$783$			1.24696e11i			0.331746i
$784$	−1.27434e10	+	5.24457e10i	−0.0337303	+	0.138818i
$785$	1.16423e11			0.306592
$786$	1.88106e11	−	6.50850e10i	0.492848	−	0.170526i
$787$		−	6.00419e11i		−	1.56515i	−0.622557	−	0.782574i	$-0.713906\pi$
$787$		−	6.00419e11i		−	1.56515i	0.622557	−	0.782574i	$-0.286094\pi$
$788$	8.72700e10	−	6.86042e10i	0.226339	−	0.177929i
$789$	−7.34489e10			−0.189530
$790$	−5.04143e10	−	1.45705e11i	−0.129433	−	0.374082i
$791$		−	3.03740e10i		−	0.0775883i
$792$	−1.88759e11	−	1.21380e11i	−0.479740	−	0.308495i
$793$	−1.39285e11			−0.352219
$794$	−2.68165e11	+	9.27856e10i	−0.674715	+	0.233453i
$795$			1.29905e11i			0.325205i
$796$	−4.04586e11	−	5.14665e11i	−1.00776	−	1.28195i
$797$	6.34716e9			0.0157306			0.00786532	−	0.999969i	$-0.497496\pi$
$797$	6.34716e9			0.0157306			0.00786532	+	0.999969i	$0.497496\pi$
$798$	−1.25093e9	−	3.61540e9i	−0.00308477	−	0.00891548i
$799$		−	5.19482e11i		−	1.27463i
$800$	−3.31698e10	−	3.49046e11i	−0.0809809	−	0.852164i
$801$	7.11353e10			0.172805
$802$	−7.05050e11	+	2.43949e11i	−1.70421	+	0.589659i
$803$			1.37652e12i			3.31069i
$804$	5.38778e10	−	4.23541e10i	0.128939	−	0.101361i
$805$	4.52266e10			0.107699
$806$	2.02175e10	+	5.84320e10i	0.0479058	+	0.138456i
$807$		−	2.79586e10i		−	0.0659206i
$808$	−3.17071e11	+	4.93077e11i	−0.743895	+	1.15683i
$809$	9.94094e10			0.232078			0.116039	−	0.993245i	$-0.462980\pi$
$809$	9.94094e10			0.232078			0.116039	+	0.993245i	$0.462980\pi$
$810$	−1.71522e10	+	5.93469e9i	−0.0398456	+	0.0137866i
$811$			6.19283e11i			1.43155i	0.698333	+	0.715773i	$0.253926\pi$
$811$			6.19283e11i			1.43155i	−0.698333	+	0.715773i	$0.746074\pi$
$812$	−1.75050e11	−	2.22677e11i	−0.402659	−	0.512215i
$813$	9.71556e10			0.222385
$814$	−1.37427e11	−	3.97185e11i	−0.313021	−	0.904680i
$815$			6.28548e10i			0.142465i
$816$	−1.72680e11	−	4.19582e10i	−0.389477	−	0.0946360i
$817$	4.62635e9			0.0103837
$818$	4.82903e11	−	1.67085e11i	1.07857	−	0.373185i
$819$			1.26825e10i			0.0281883i
$820$	−1.93234e10	+	1.51904e10i	−0.0427394	+	0.0335981i
$821$	−7.98794e11			−1.75818			−0.879088	−	0.476660i	$-0.841847\pi$
$821$	−7.98794e11			−1.75818			−0.879088	+	0.476660i	$0.841847\pi$
$822$	2.53465e10	+	7.32555e10i	0.0555176	+	0.160455i
$823$			7.72868e11i			1.68464i	0.538981	+	0.842318i	$0.318810\pi$
$823$			7.72868e11i			1.68464i	−0.538981	+	0.842318i	$0.681190\pi$
$824$	1.00826e11	+	6.48359e10i	0.218708	+	0.140639i
$825$	3.91748e11			0.845651
$826$	1.34874e11	−	4.66665e10i	0.289739	−	0.100250i
$827$		−	2.14261e11i		−	0.458058i	−0.973420	−	0.229029i	$-0.926445\pi$
$827$		−	2.14261e11i		−	0.458058i	0.973420	−	0.229029i	$-0.0735551\pi$
$828$	−7.27081e10	−	9.24905e10i	−0.154690	−	0.196778i
$829$	5.15450e11			1.09136			0.545681	−	0.837993i	$-0.316271\pi$
$829$	5.15450e11			1.09136			0.545681	+	0.837993i	$0.316271\pi$
$830$	−4.90091e10	−	1.41644e11i	−0.103268	−	0.298460i
$831$		−	6.57863e10i		−	0.137953i
$832$	−4.44832e10	−	9.75454e10i	−0.0928330	−	0.203570i
$833$	−4.77508e10			−0.0991746
$834$	3.89188e10	−	1.34660e10i	0.0804444	−	0.0278339i
$835$			2.80085e11i			0.576162i
$836$	−2.84069e10	+	2.23311e10i	−0.0581566	+	0.0457177i
$837$	6.18507e10			0.126021
$838$	−1.50653e11	−	4.35411e11i	−0.305493	−	0.882924i
$839$		−	4.26981e11i		−	0.861709i	−0.902421	−	0.430854i	$-0.858212\pi$
$839$		−	4.26981e11i		−	0.861709i	0.902421	−	0.430854i	$-0.141788\pi$
$840$	2.22986e10	−	3.46765e10i	0.0447878	−	0.0696494i
$841$	9.86231e11			1.97149
$842$	4.85324e11	−	1.67923e11i	0.965569	−	0.334088i
$843$			8.21341e10i			0.162635i
$844$	5.55753e11	+	7.06962e11i	1.09525	+	1.39324i
$845$	−1.83781e11			−0.360473
$846$	−1.02511e11	−	2.96272e11i	−0.200119	−	0.578375i
$847$			3.75028e11i			0.728668i
$848$	−1.81236e11	+	7.45879e11i	−0.350477	+	1.44240i
$849$	−8.83051e10			−0.169963
$850$	2.93154e11	−	1.01432e11i	0.561590	−	0.194311i
$851$		−	2.20330e11i		−	0.420103i
$852$	−2.29356e11	+	1.80300e11i	−0.435262	+	0.342166i
$853$	−4.85495e10			−0.0917041			−0.0458520	−	0.998948i	$-0.514600\pi$
$853$	−4.85495e10			−0.0917041			−0.0458520	+	0.998948i	$0.514600\pi$
$854$	−1.03486e11	−	2.99090e11i	−0.194558	−	0.562303i
$855$			2.92232e9i			0.00546844i
$856$	4.34675e11	+	2.79516e11i	0.809598	+	0.520609i
$857$	2.27216e11			0.421226			0.210613	−	0.977570i	$-0.432454\pi$
$857$	2.27216e11			0.421226			0.210613	+	0.977570i	$0.432454\pi$
$858$	1.13201e11	−	3.91677e10i	0.208882	−	0.0722735i
$859$		−	1.04475e11i		−	0.191884i	−0.995387	−	0.0959420i	$-0.969414\pi$
$859$		−	1.04475e11i		−	0.191884i	0.995387	−	0.0959420i	$-0.0305863\pi$
$860$	3.08114e10	+	3.91946e10i	0.0563272	+	0.0716526i
$861$	1.71807e10			0.0312628
$862$	2.27536e11	+	6.57617e11i	0.412118	+	1.19109i
$863$		−	1.71050e11i		−	0.308375i	−0.988042	−	0.154188i	$-0.950724\pi$
$863$		−	1.71050e11i		−	0.308375i	0.988042	−	0.154188i	$-0.0492760\pi$
$864$	−1.06763e11	+	1.01457e10i	−0.191587	+	0.0182065i
$865$	2.82569e11			0.504732
$866$	−7.26928e11	+	2.51518e11i	−1.29247	+	0.447196i
$867$			1.69002e11i			0.299100i
$868$	−1.10451e11	+	8.68270e10i	−0.194576	+	0.152959i
$869$	1.01789e12			1.78493
$870$	7.07463e10	+	2.04468e11i	0.123489	+	0.356902i
$871$			3.65801e10i			0.0635583i
$872$	−3.19343e10	+	4.96609e10i	−0.0552320	+	0.0858912i
$873$	1.62718e11			0.280142
$874$	−1.79012e10	+	6.19386e9i	−0.0306787	+	0.0106149i
$875$			1.56041e11i			0.266199i
$876$	4.06535e11	+	5.17145e11i	0.690370	+	0.878206i
$877$	9.58936e11			1.62103			0.810515	−	0.585718i	$-0.199187\pi$
$877$	9.58936e11			1.62103			0.810515	+	0.585718i	$0.199187\pi$
$878$	2.25074e11	+	6.50501e11i	0.378746	+	1.09464i
$879$			3.20134e11i			0.536261i
$880$	−3.78379e11	−	9.19395e10i	−0.630952	−	0.153310i
$881$	6.82774e11			1.13337			0.566687	−	0.823933i	$-0.308225\pi$
$881$	6.82774e11			1.13337			0.566687	+	0.823933i	$0.308225\pi$
$882$	−2.72333e10	+	9.42278e9i	−0.0450015	+	0.0155706i
$883$		−	7.28141e11i		−	1.19777i	−0.800836	−	0.598884i	$-0.795611\pi$
$883$		−	7.28141e11i		−	1.19777i	0.800836	−	0.598884i	$-0.204389\pi$
$884$	7.45695e10	−	5.86201e10i	0.122110	−	0.0959926i
$885$	−1.09018e11			−0.177716
$886$	−8.43731e10	−	2.43852e11i	−0.136921	−	0.395723i
$887$			9.22738e11i			1.49068i	0.666686	+	0.745339i	$0.267712\pi$
$887$			9.22738e11i			1.49068i	−0.666686	+	0.745339i	$0.732288\pi$
$888$	−1.68933e11	−	1.08632e11i	−0.271683	−	0.174705i
$889$	−1.14657e11			−0.183567
$890$	1.16643e11	−	4.03587e10i	0.185908	−	0.0643246i
$891$		−	1.19824e11i		−	0.190123i
$892$	−1.37704e11	−	1.75171e11i	−0.217515	−	0.276696i
$893$	−5.04777e10			−0.0793768
$894$	−1.76948e11	−	5.11409e11i	−0.277010	−	0.800605i
$895$		−	1.85873e11i		−	0.289685i
$896$	1.76411e11	−	1.67993e11i	0.273712	−	0.260651i
$897$	6.27960e10			0.0969978
$898$	−4.22710e11	+	1.46258e11i	−0.650035	+	0.224913i
$899$		−	7.37311e11i		−	1.12879i
$900$	1.47176e11	−	1.15697e11i	0.224320	−	0.176341i
$901$	−6.79108e11			−1.03048
$902$	−5.30596e10	−	1.53351e11i	−0.0801564	−	0.231665i
$903$		−	3.48484e10i		−	0.0524122i
$904$	−7.41502e10	+	1.15311e11i	−0.111030	+	0.172662i
$905$	5.44737e10			0.0812068
$906$	9.83678e10	−	3.40354e10i	0.145996	−	0.0505147i
$907$			4.67762e11i			0.691188i	0.938384	+	0.345594i	$0.112323\pi$
$907$			4.67762e11i			0.691188i	−0.938384	+	0.345594i	$0.887677\pi$
$908$	5.61284e11	+	7.13998e11i	0.825732	+	1.05040i
$909$	−3.13006e11			−0.458455
$910$	7.19543e9	+	2.07959e10i	0.0104928	+	0.0303258i
$911$			3.35286e11i			0.486791i	0.969927	+	0.243395i	$0.0782613\pi$
$911$			3.35286e11i			0.486791i	−0.969927	+	0.243395i	$0.921739\pi$
$912$	−4.07705e9	+	1.67792e10i	−0.00589341	+	0.0242545i
$913$	9.89516e11			1.42410
$914$	−1.06217e12	+	3.67511e11i	−1.52198	+	0.526606i
$915$			2.41754e11i			0.344897i
$916$	8.78588e11	−	6.90671e11i	1.24797	−	0.981046i
$917$	−2.41410e11			−0.341412
$918$	−3.10250e10	−	8.96671e10i	−0.0436858	−	0.126259i
$919$		−	3.53419e11i		−	0.495482i	−0.968826	−	0.247741i	$-0.920312\pi$
$919$		−	3.53419e11i		−	0.495482i	0.968826	−	0.247741i	$-0.0796882\pi$
$920$	−1.71697e11	−	1.10409e11i	−0.239668	−	0.154118i
$921$	−4.03051e11			−0.560172
$922$	−4.09424e11	+	1.41661e11i	−0.566565	+	0.196033i
$923$		−	1.55720e11i		−	0.214554i
$924$	1.68211e11	+	2.13978e11i	0.230763	+	0.293549i
$925$	3.50603e11			0.478904
$926$	−7.26986e10	−	2.10110e11i	−0.0988739	−	0.285762i
$927$			6.40046e10i			0.0866746i
$928$	1.20945e11	+	1.27270e12i	0.163078	+	1.71607i
$929$	3.36792e11			0.452167			0.226084	−	0.974108i	$-0.427408\pi$
$929$	3.36792e11			0.452167			0.226084	+	0.974108i	$0.427408\pi$
$930$	1.01419e11	−	3.50911e10i	0.135577	−	0.0469099i
$931$			4.63991e9i			0.00617605i
$932$	9.19309e11	−	7.22682e11i	1.21842	−	0.957819i
$933$	7.48184e11			0.987374
$934$	−3.34012e10	−	9.65350e10i	−0.0438910	−	0.126852i
$935$		−	3.44507e11i		−	0.450766i
$936$	3.09610e10	−	4.81474e10i	0.0403377	−	0.0627291i
$937$	−2.02878e9			−0.00263194			−0.00131597	−	0.999999i	$-0.500419\pi$
$937$	−2.02878e9			−0.00263194			−0.00131597	+	0.999999i	$0.500419\pi$
$938$	−7.85490e10	+	2.71781e10i	−0.101468	+	0.0351081i
$939$			1.15910e11i			0.149094i
$940$	−3.36181e11	−	4.27648e11i	−0.430587	−	0.547741i
$941$	−7.00137e11			−0.892944			−0.446472	−	0.894798i	$-0.647320\pi$
$941$	−7.00137e11			−0.892944			−0.446472	+	0.894798i	$0.647320\pi$
$942$	1.20102e11	+	3.47114e11i	0.152527	+	0.440828i
$943$		−	8.50683e10i		−	0.107577i
$944$	−6.25953e11	−	1.52096e11i	−0.788232	−	0.191526i
$945$	2.20127e10			0.0276023
$946$	−3.11049e11	+	1.07623e11i	−0.388386	+	0.134382i
$947$			1.13217e12i			1.40771i	0.710343	+	0.703855i	$0.248540\pi$
$947$			1.13217e12i			1.40771i	−0.710343	+	0.703855i	$0.751460\pi$
$948$	3.82412e11	−	3.00620e11i	0.473476	−	0.372206i
$949$	−3.51113e11			−0.432895
$950$	−9.85604e9	−	2.84855e10i	−0.0121006	−	0.0349727i
$951$			8.25542e11i			1.00929i
$952$	1.81279e11	+	1.16571e11i	0.220699	+	0.141920i
$953$	9.79511e11			1.18751			0.593756	−	0.804645i	$-0.297645\pi$
$953$	9.79511e11			1.18751			0.593756	+	0.804645i	$0.297645\pi$
$954$	−3.87311e11	+	1.34010e11i	−0.467591	+	0.161787i
$955$		−	2.27727e11i		−	0.273779i
$956$	−5.98793e11	−	7.61713e11i	−0.716878	−	0.911926i
$957$	−1.42840e12			−1.70295
$958$	1.40139e11	+	4.05023e11i	0.166378	+	0.480859i
$959$		−	9.40141e10i		−	0.111152i
$960$	−1.69307e11	+	7.72083e10i	−0.199338	+	0.0909031i
$961$	4.87176e11			0.571205
$962$	1.01311e11	−	3.50539e10i	0.118293	−	0.0409295i
$963$			2.75932e11i			0.320846i
$964$	−5.00280e10	+	3.93278e10i	−0.0579302	+	0.0455398i
$965$	2.59536e11			0.299287
$966$	4.66558e10	+	1.34843e11i	0.0535793	+	0.154853i
$967$		−	9.84817e11i		−	1.12629i	−0.826359	−	0.563144i	$-0.809592\pi$
$967$		−	9.84817e11i		−	1.12629i	0.826359	−	0.563144i	$-0.190408\pi$
$968$	9.15532e11	−	1.42374e12i	1.04273	−	1.62155i
$969$	−1.52771e10			−0.0173279
$970$	2.66814e11	−	9.23182e10i	0.301385	−	0.104280i
$971$			1.64854e11i			0.185448i	0.995692	+	0.0927241i	$0.0295575\pi$
$971$			1.64854e11i			0.185448i	−0.995692	+	0.0927241i	$0.970443\pi$
$972$	−3.53885e10	−	4.50169e10i	−0.0396457	−	0.0504325i
$973$	−4.99474e10			−0.0557265
$974$	−4.33626e10	−	1.25325e11i	−0.0481814	−	0.139252i
$975$			9.99247e10i			0.110574i
$976$	−3.37281e11	+	1.38809e12i	−0.371700	+	1.52974i
$977$	−7.33895e11			−0.805482			−0.402741	−	0.915314i	$-0.631942\pi$
$977$	−7.33895e11			−0.805482			−0.402741	+	0.915314i	$0.631942\pi$
$978$	−1.87401e11	+	6.48411e10i	−0.204841	+	0.0708753i
$979$			8.14861e11i			0.887060i
$980$	−3.93094e10	+	3.09017e10i	−0.0426179	+	0.0335026i
$981$	−3.15248e10			−0.0340390
$982$	3.10192e11	+	8.96506e11i	0.333569	+	0.964067i
$983$		−	8.96912e11i		−	0.960585i	−0.877108	−	0.480292i	$-0.840531\pi$
$983$		−	8.96912e11i		−	0.960585i	0.877108	−	0.480292i	$-0.159469\pi$
$984$	−6.52242e10	−	4.19422e10i	−0.0695710	−	0.0447374i
$985$	1.02841e11			0.109250
$986$	−1.06890e12	+	3.69843e11i	−1.13092	+	0.391300i
$987$			3.80228e11i			0.400659i
$988$	−5.69607e9	−	7.24586e9i	−0.00597789	−	0.00760435i
$989$	−1.72548e11			−0.180354
$990$	−6.79824e10	−	1.96480e11i	−0.0707710	−	0.204540i
$991$		−	1.38161e12i		−	1.43249i	−0.697848	−	0.716246i	$-0.745859\pi$
$991$		−	1.38161e12i		−	1.43249i	0.697848	−	0.716246i	$-0.254141\pi$
$992$	6.31276e11	−	5.99900e10i	0.651888	−	0.0619487i
$993$	−9.87561e11			−1.01570
$994$	3.34380e11	−	1.15696e11i	0.342527	−	0.118515i
$995$		−	6.06495e11i		−	0.618778i
$996$	3.71753e11	−	2.92240e11i	0.377761	−	0.296963i
$997$	−1.97401e12			−1.99788			−0.998940	−	0.0460254i	$-0.985344\pi$
$997$	−1.97401e12			−1.99788			−0.998940	+	0.0460254i	$0.985344\pi$
$998$	−1.22564e11	−	3.54229e11i	−0.123549	−	0.357077i
$999$		−	1.07239e11i		−	0.107669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.9.g.a.43.4	yes	48
4.3	odd	2	inner	84.9.g.a.43.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.g.a.43.3	✓	48	4.3	odd	2	inner
84.9.g.a.43.4	yes	48	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.1205 + 5.23171i) q^{2} -46.7654i q^{3} +(201.258 - 158.212i) q^{4} +237.168 q^{5} +(244.663 + 707.115i) q^{6} -907.493i q^{7} +(-2215.40 + 3445.17i) q^{8} -2187.00 q^{9} +O(q^{10})\)	\(q+(-15.1205 + 5.23171i) q^{2} -46.7654i q^{3} +(201.258 - 158.212i) q^{4} +237.168 q^{5} +(244.663 + 707.115i) q^{6} -907.493i q^{7} +(-2215.40 + 3445.17i) q^{8} -2187.00 q^{9} +(-3586.10 + 1240.80i) q^{10} -25052.3i q^{11} +(-7398.85 - 9411.92i) q^{12} +6390.18 q^{13} +(4747.74 + 13721.7i) q^{14} -11091.3i q^{15} +(15473.9 - 63683.0i) q^{16} +57982.1 q^{17} +(33068.5 - 11441.8i) q^{18} -5634.08i q^{19} +(47732.1 - 37522.9i) q^{20} -42439.2 q^{21} +(131066. + 378803. i) q^{22} +210133. i q^{23} +(161115. + 103604. i) q^{24} -334376. q^{25} +(-96622.6 + 33431.6i) q^{26} +102276. i q^{27} +(-143576. - 182640. i) q^{28} +1.21921e6 q^{29} +(58026.3 + 167705. i) q^{30} -604744. i q^{31} +(99199.0 + 1.04387e6i) q^{32} -1.17158e6 q^{33} +(-876718. + 303346. i) q^{34} -215228. i q^{35} +(-440152. + 346010. i) q^{36} -1.04853e6 q^{37} +(29475.9 + 85190.0i) q^{38} -298839. i q^{39} +(-525424. + 817085. i) q^{40} -404831. q^{41} +(641702. - 222030. i) q^{42} +821137. i q^{43} +(-3.96357e6 - 5.04198e6i) q^{44} -518687. q^{45} +(-1.09936e6 - 3.17731e6i) q^{46} -8.95935e6i q^{47} +(-2.97816e6 - 723641. i) q^{48} -823543. q^{49} +(5.05593e6 - 1.74936e6i) q^{50} -2.71156e6i q^{51} +(1.28608e6 - 1.01100e6i) q^{52} -1.17124e7 q^{53} +(-535078. - 1.54646e6i) q^{54} -5.94160e6i q^{55} +(3.12647e6 + 2.01046e6i) q^{56} -263480. q^{57} +(-1.84351e7 + 6.37857e6i) q^{58} -9.82920e6i q^{59} +(-1.75477e6 - 2.23221e6i) q^{60} -2.17968e7 q^{61} +(3.16385e6 + 9.14403e6i) q^{62} +1.98469e6i q^{63} +(-6.96118e6 - 1.52649e7i) q^{64} +1.51555e6 q^{65} +(1.77148e7 - 6.12936e6i) q^{66} +5.72442e6i q^{67} +(1.16694e7 - 9.17347e6i) q^{68} +9.82695e6 q^{69} +(1.12601e6 + 3.25436e6i) q^{70} -2.43686e7i q^{71} +(4.84509e6 - 7.53459e6i) q^{72} -5.49458e7 q^{73} +(1.58542e7 - 5.48559e6i) q^{74} +1.56372e7i q^{75} +(-891380. - 1.13391e6i) q^{76} -2.27348e7 q^{77} +(1.56344e6 + 4.51859e6i) q^{78} +4.06306e7i q^{79} +(3.66991e6 - 1.51036e7i) q^{80} +4.78297e6 q^{81} +(6.12124e6 - 2.11796e6i) q^{82} +3.94981e7i q^{83} +(-8.54125e6 + 6.71440e6i) q^{84} +1.37515e7 q^{85} +(-4.29595e6 - 1.24160e7i) q^{86} -5.70169e7i q^{87} +(8.63093e7 + 5.55009e7i) q^{88} -3.25264e7 q^{89} +(7.84280e6 - 2.71362e6i) q^{90} -5.79904e6i q^{91} +(3.32456e7 + 4.22910e7i) q^{92} -2.82811e7 q^{93} +(4.68727e7 + 1.35470e8i) q^{94} -1.33622e6i q^{95} +(4.88171e7 - 4.63908e6i) q^{96} -7.44024e7 q^{97} +(1.24524e7 - 4.30854e6i) q^{98} +5.47893e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 + 290 * q^4 + 672 * q^5 - 2268 * q^6 + 4230 * q^8 - 104976 * q^9	\( 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9} - 41972 q^{10} + 22680 q^{12} + 57120 q^{13} - 14406 q^{14} - 207950 q^{16} + 386400 q^{17} + 13122 q^{18} + 562380 q^{20} + 1186136 q^{22} + 74844 q^{24} + 5520720 q^{25} + 1682100 q^{26} + 148862 q^{28} - 1994592 q^{29} - 2054808 q^{30} + 7754814 q^{32} + 2395820 q^{34} - 634230 q^{36} - 5931232 q^{37} - 4284000 q^{38} - 16076956 q^{40} + 10936800 q^{41} + 12531912 q^{44} - 1469664 q^{45} + 9456072 q^{46} - 12365136 q^{48} - 39530064 q^{49} - 6199074 q^{50} - 6937420 q^{52} - 7150560 q^{53} + 4960116 q^{54} + 14218722 q^{56} + 518452 q^{58} + 3633984 q^{60} - 42829024 q^{61} - 93291072 q^{62} - 69128614 q^{64} + 21653184 q^{65} + 45582264 q^{66} + 82618620 q^{68} + 17273088 q^{69} - 11611236 q^{70} - 9251010 q^{72} - 49489440 q^{73} - 126365628 q^{74} - 223942320 q^{76} + 94964352 q^{77} + 136267920 q^{78} + 238226604 q^{80} + 229582512 q^{81} + 269696252 q^{82} + 301906816 q^{85} - 188004816 q^{86} - 116561288 q^{88} - 315415968 q^{89} + 91792764 q^{90} + 487386984 q^{92} + 37454400 q^{93} + 148324176 q^{94} - 320488812 q^{96} - 3460128 q^{97} + 4941258 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 + 290 * q^4 + 672 * q^5 - 2268 * q^6 + 4230 * q^8 - 104976 * q^9 - 41972 * q^10 + 22680 * q^12 + 57120 * q^13 - 14406 * q^14 - 207950 * q^16 + 386400 * q^17 + 13122 * q^18 + 562380 * q^20 + 1186136 * q^22 + 74844 * q^24 + 5520720 * q^25 + 1682100 * q^26 + 148862 * q^28 - 1994592 * q^29 - 2054808 * q^30 + 7754814 * q^32 + 2395820 * q^34 - 634230 * q^36 - 5931232 * q^37 - 4284000 * q^38 - 16076956 * q^40 + 10936800 * q^41 + 12531912 * q^44 - 1469664 * q^45 + 9456072 * q^46 - 12365136 * q^48 - 39530064 * q^49 - 6199074 * q^50 - 6937420 * q^52 - 7150560 * q^53 + 4960116 * q^54 + 14218722 * q^56 + 518452 * q^58 + 3633984 * q^60 - 42829024 * q^61 - 93291072 * q^62 - 69128614 * q^64 + 21653184 * q^65 + 45582264 * q^66 + 82618620 * q^68 + 17273088 * q^69 - 11611236 * q^70 - 9251010 * q^72 - 49489440 * q^73 - 126365628 * q^74 - 223942320 * q^76 + 94964352 * q^77 + 136267920 * q^78 + 238226604 * q^80 + 229582512 * q^81 + 269696252 * q^82 + 301906816 * q^85 - 188004816 * q^86 - 116561288 * q^88 - 315415968 * q^89 + 91792764 * q^90 + 487386984 * q^92 + 37454400 * q^93 + 148324176 * q^94 - 320488812 * q^96 - 3460128 * q^97 + 4941258 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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