LMFDB - Embedded newform 177.6.d.b.176.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.11
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.16184 q^{2} +(-4.65820 + 14.8762i) q^{3} +51.9393 q^{4} -80.4460i q^{5} +(42.6777 - 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 - 138.593i) q^{9} +O(q^{10})$	\(q-9.16184 q^{2} +(-4.65820 + 14.8762i) q^{3} +51.9393 q^{4} -80.4460i q^{5} +(42.6777 - 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 - 138.593i) q^{9} +737.033i q^{10} -681.939 q^{11} +(-241.943 + 772.659i) q^{12} +634.160i q^{13} +1620.04 q^{14} +(1196.73 + 374.733i) q^{15} +11.6301 q^{16} -1790.65i q^{17} +(1828.72 + 1269.76i) q^{18} -2481.42 q^{19} -4178.30i q^{20} +(823.686 - 2630.48i) q^{21} +6247.82 q^{22} -3057.87 q^{23} +(850.961 - 2717.59i) q^{24} -3346.56 q^{25} -5810.07i q^{26} +(2991.52 - 2323.73i) q^{27} -9184.16 q^{28} +546.719i q^{29} +(-10964.2 - 3433.25i) q^{30} -555.314i q^{31} +5739.21 q^{32} +(3176.61 - 10144.7i) q^{33} +16405.6i q^{34} +14224.9i q^{35} +(-10367.2 - 7198.39i) q^{36} +4130.23i q^{37} +22734.3 q^{38} +(-9433.89 - 2954.05i) q^{39} +14695.9i q^{40} -14697.6i q^{41} +(-7546.48 + 24100.1i) q^{42} -19748.6i q^{43} -35419.4 q^{44} +(-11149.2 + 16057.2i) q^{45} +28015.7 q^{46} -10422.4 q^{47} +(-54.1755 + 173.012i) q^{48} +14460.1 q^{49} +30660.6 q^{50} +(26638.1 + 8341.20i) q^{51} +32937.8i q^{52} +8205.73i q^{53} +(-27407.8 + 21289.7i) q^{54} +54859.3i q^{55} +32302.4 q^{56} +(11558.9 - 36914.0i) q^{57} -5008.95i q^{58} +(24643.1 + 10375.2i) q^{59} +(62157.3 + 19463.4i) q^{60} +24796.7i q^{61} +5087.70i q^{62} +(35294.7 + 24506.6i) q^{63} -52953.9 q^{64} +51015.7 q^{65} +(-29103.6 + 92943.8i) q^{66} -1477.02i q^{67} -93005.0i q^{68} +(14244.2 - 45489.4i) q^{69} -130326. i q^{70} +45951.7i q^{71} +(36463.4 + 25318.1i) q^{72} +34710.8i q^{73} -37840.5i q^{74} +(15588.9 - 49784.0i) q^{75} -128883. q^{76} +120584. q^{77} +(86431.8 + 27064.5i) q^{78} -15432.4 q^{79} -935.598i q^{80} +(20633.2 + 55326.8i) q^{81} +134657. i q^{82} -29051.1 q^{83} +(42781.6 - 136625. i) q^{84} -144051. q^{85} +180933. i q^{86} +(-8133.10 - 2546.73i) q^{87} +124577. q^{88} -114778. q^{89} +(102147. - 147114. i) q^{90} -112135. i q^{91} -158823. q^{92} +(8260.96 + 2586.76i) q^{93} +95488.3 q^{94} +199620. i q^{95} +(-26734.4 + 85377.7i) q^{96} -56580.8i q^{97} -132481. q^{98} +(136117. + 94511.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−9.16184			−1.61960			−0.809800	−	0.586707i	$-0.800424\pi$
$2$	−9.16184			−1.61960			−0.809800	+	0.586707i	$0.800424\pi$
$3$	−4.65820	+	14.8762i	−0.298824	+	0.954308i
$3$	−4.65820	+	14.8762i	−0.298824	+	0.954308i
$4$	51.9393			1.62310
$5$		−	80.4460i		−	1.43906i	−0.694461	−	0.719531i	$-0.744357\pi$
$5$		−	80.4460i		−	1.43906i	0.694461	−	0.719531i	$-0.255643\pi$
$6$	42.6777	−	136.293i	0.483974	−	1.54560i
$7$	−176.825			−1.36395			−0.681975	−	0.731375i	$-0.738879\pi$
$7$	−176.825			−1.36395			−0.681975	+	0.731375i	$0.738879\pi$
$8$	−182.680			−1.00918
$9$	−199.602	−	138.593i	−0.821409	−	0.570340i
$10$			737.033i			2.33070i
$11$	−681.939			−1.69928			−0.849638	−	0.527366i	$-0.823180\pi$
$11$	−681.939			−1.69928			−0.849638	+	0.527366i	$0.823180\pi$
$12$	−241.943	+	772.659i	−0.485021	+	1.54894i
$13$			634.160i			1.04074i	0.853942	+	0.520368i	$0.174205\pi$
$13$			634.160i			1.04074i	−0.853942	+	0.520368i	$0.825795\pi$
$14$	1620.04			2.20905
$15$	1196.73	+	374.733i	1.37331	+	0.430026i
$16$	11.6301			0.0113576
$17$		−	1790.65i		−	1.50276i	−0.659872	−	0.751378i	$-0.729390\pi$
$17$		−	1790.65i		−	1.50276i	0.659872	−	0.751378i	$-0.270610\pi$
$18$	1828.72	+	1269.76i	1.33035	+	0.923722i
$19$	−2481.42			−1.57694			−0.788471	−	0.615072i	$-0.789127\pi$
$19$	−2481.42			−1.57694			−0.788471	+	0.615072i	$0.789127\pi$
$20$		−	4178.30i		−	2.33574i
$21$	823.686	−	2630.48i	0.407581	−	1.30163i
$22$	6247.82			2.75215
$23$	−3057.87			−1.20531			−0.602655	−	0.798002i	$-0.705891\pi$
$23$	−3057.87			−1.20531			−0.602655	+	0.798002i	$0.705891\pi$
$24$	850.961	−	2717.59i	0.301565	−	0.963064i
$25$	−3346.56			−1.07090
$26$		−	5810.07i		−	1.68558i
$27$	2991.52	−	2323.73i	0.789736	−	0.613446i
$28$	−9184.16			−2.21383
$29$			546.719i			0.120717i	0.998177	+	0.0603586i	$0.0192244\pi$
$29$			546.719i			0.120717i	−0.998177	+	0.0603586i	$0.980776\pi$
$30$	−10964.2	−	3433.25i	−2.22421	−	0.696469i
$31$		−	555.314i		−	0.103785i	−0.998653	−	0.0518925i	$-0.983475\pi$
$31$		−	555.314i		−	0.103785i	0.998653	−	0.0518925i	$-0.0165253\pi$
$32$	5739.21			0.990780
$33$	3176.61	−	10144.7i	0.507784	−	1.62163i
$34$			16405.6i			2.43386i
$35$			14224.9i			1.96281i
$36$	−10367.2	−	7198.39i	−1.33323	−	0.925719i
$37$			4130.23i			0.495987i	0.968762	+	0.247993i	$0.0797711\pi$
$37$			4130.23i			0.495987i	−0.968762	+	0.247993i	$0.920229\pi$
$38$	22734.3			2.55401
$39$	−9433.89	−	2954.05i	−0.993183	−	0.310997i
$40$			14695.9i			1.45227i
$41$		−	14697.6i		−	1.36548i	−0.730661	−	0.682740i	$-0.760788\pi$
$41$		−	14697.6i		−	1.36548i	0.730661	−	0.682740i	$-0.239212\pi$
$42$	−7546.48	+	24100.1i	−0.660117	+	2.10812i
$43$		−	19748.6i		−	1.62879i	−0.580312	−	0.814394i	$-0.697069\pi$
$43$		−	19748.6i		−	1.62879i	0.580312	−	0.814394i	$-0.302931\pi$
$44$	−35419.4			−2.75810
$45$	−11149.2	+	16057.2i	−0.820754	+	1.18206i
$46$	28015.7			1.95212
$47$	−10422.4			−0.688213			−0.344107	−	0.938931i	$-0.611818\pi$
$47$	−10422.4			−0.688213			−0.344107	+	0.938931i	$0.611818\pi$
$48$	−54.1755	+	173.012i	−0.00339391	+	0.0108386i
$49$	14460.1			0.860360
$50$	30660.6			1.73443
$51$	26638.1	+	8341.20i	1.43409	+	0.449059i
$52$			32937.8i			1.68922i
$53$			8205.73i			0.401262i	0.979667	+	0.200631i	$0.0642991\pi$
$53$			8205.73i			0.401262i	−0.979667	+	0.200631i	$0.935701\pi$
$54$	−27407.8	+	21289.7i	−1.27906	+	0.993537i
$55$			54859.3i			2.44536i
$56$	32302.4			1.37646
$57$	11558.9	−	36914.0i	0.471227	−	1.50489i
$58$		−	5008.95i		−	0.195514i
$59$	24643.1	+	10375.2i	0.921647	+	0.388030i
$59$	24643.1	+	10375.2i	0.921647	+	0.388030i
$60$	62157.3	+	19463.4i	2.22902	+	0.697975i
$61$			24796.7i			0.853238i	0.904432	+	0.426619i	$0.140295\pi$
$61$			24796.7i			0.853238i	−0.904432	+	0.426619i	$0.859705\pi$
$62$			5087.70i			0.168090i
$63$	35294.7	+	24506.6i	1.12036	+	0.777915i
$64$	−52953.9			−1.61602
$65$	51015.7			1.49768
$66$	−29103.6	+	92943.8i	−0.822407	+	2.62640i
$67$		−	1477.02i		−	0.0401974i	−0.999798	−	0.0200987i	$-0.993602\pi$
$67$		−	1477.02i		−	0.0401974i	0.999798	−	0.0200987i	$-0.00639805\pi$
$68$		−	93005.0i		−	2.43913i
$69$	14244.2	−	45489.4i	0.360175	−	1.15024i
$70$		−	130326.i		−	3.17896i
$71$			45951.7i			1.08182i	0.841080	+	0.540911i	$0.181921\pi$
$71$			45951.7i			1.08182i	−0.841080	+	0.540911i	$0.818079\pi$
$72$	36463.4	+	25318.1i	0.828945	+	0.575573i
$73$			34710.8i			0.762354i	0.924502	+	0.381177i	$0.124481\pi$
$73$			34710.8i			0.762354i	−0.924502	+	0.381177i	$0.875519\pi$
$74$		−	37840.5i		−	0.803299i
$75$	15588.9	−	49784.0i	0.320010	−	1.02197i
$76$	−128883.			−2.55954
$77$	120584.			2.31773
$78$	86431.8	+	27064.5i	1.60856	+	0.503690i
$79$	−15432.4			−0.278205			−0.139102	−	0.990278i	$-0.544422\pi$
$79$	−15432.4			−0.278205			−0.139102	+	0.990278i	$0.544422\pi$
$80$		−	935.598i		−	0.0163442i
$81$	20633.2	+	55326.8i	0.349425	+	0.936964i
$82$			134657.i			2.21153i
$83$	−29051.1			−0.462878			−0.231439	−	0.972849i	$-0.574343\pi$
$83$	−29051.1			−0.462878			−0.231439	+	0.972849i	$0.574343\pi$
$84$	42781.6	−	136625.i	0.661545	−	2.11268i
$85$	−144051.			−2.16256
$86$			180933.i			2.63798i
$87$	−8133.10	−	2546.73i	−0.115201	−	0.0360732i
$88$	124577.			1.71487
$89$	−114778.			−1.53597			−0.767984	−	0.640469i	$-0.778740\pi$
$89$	−114778.			−1.53597			−0.767984	+	0.640469i	$0.778740\pi$
$90$	102147.	−	147114.i	1.32929	−	1.91446i
$91$		−	112135.i		−	1.41951i
$92$	−158823.			−1.95634
$93$	8260.96	+	2586.76i	0.0990429	+	0.0310134i
$94$	95488.3			1.11463
$95$			199620.i			2.26932i
$96$	−26734.4	+	85377.7i	−0.296069	+	0.945510i
$97$		−	56580.8i		−	0.610576i	−0.952260	−	0.305288i	$-0.901247\pi$
$97$		−	56580.8i		−	0.610576i	0.952260	−	0.305288i	$-0.0987528\pi$
$98$	−132481.			−1.39344
$99$	136117.	+	94511.7i	1.39580	+	0.969165i
$100$	−173818.			−1.73818
$101$	119797.			1.16854			0.584268	−	0.811561i	$-0.301382\pi$
$101$	119797.			1.16854			0.584268	+	0.811561i	$0.301382\pi$
$102$	−244054.	−	76420.7i	−2.32265	−	0.727295i
$103$		−	52970.9i		−	0.491976i	−0.969273	−	0.245988i	$-0.920888\pi$
$103$		−	52970.9i		−	0.491976i	0.969273	−	0.245988i	$-0.0791124\pi$
$104$		−	115849.i		−	1.05029i
$105$	−211612.	−	66262.2i	−1.87312	−	0.586533i
$106$		−	75179.6i		−	0.649883i
$107$		−	104552.i		−	0.882824i	−0.897304	−	0.441412i	$-0.854478\pi$
$107$		−	104552.i		−	0.882824i	0.897304	−	0.441412i	$-0.145522\pi$
$108$	155377.	−	120693.i	1.28182	−	0.995686i
$109$			71125.1i			0.573399i	0.958021	+	0.286699i	$0.0925581\pi$
$109$			71125.1i			0.573399i	−0.958021	+	0.286699i	$0.907442\pi$
$110$		−	502612.i		−	3.96051i
$111$	−61442.1	−	19239.4i	−0.473324	−	0.148212i
$112$	−2056.50			−0.0154911
$113$	−104847.			−0.772430			−0.386215	−	0.922409i	$-0.626218\pi$
$113$	−104847.			−0.772430			−0.386215	+	0.922409i	$0.626218\pi$
$114$	−105901.	+	338200.i	−0.763199	+	2.43732i
$115$			245993.i			1.73452i
$116$			28396.2i			0.195936i
$117$	87889.9	−	126580.i	0.593573	−	0.854870i
$118$	−225776.	−	95055.6i	−1.49270	−	0.628453i
$119$			316632.i			2.04968i
$120$	−218619.	−	68456.4i	−1.38591	−	0.433971i
$121$	303990.			1.88754
$122$		−	227184.i		−	1.38190i
$123$	218644.	+	68464.1i	1.30309	+	0.408038i
$124$		−	28842.6i		−	0.168454i
$125$			17823.3i			0.102026i
$126$	−323364.	−	224526.i	−1.81454	−	1.25991i
$127$	−202124.			−1.11201			−0.556005	−	0.831179i	$-0.687667\pi$
$127$	−202124.			−1.11201			−0.556005	+	0.831179i	$0.687667\pi$
$128$	301500.			1.62653
$129$	293784.	+	91992.8i	1.55437	+	0.486720i
$130$	−467397.			−2.42565
$131$	−53541.7			−0.272593			−0.136296	−	0.990668i	$-0.543520\pi$
$131$	−53541.7			−0.272593			−0.136296	+	0.990668i	$0.543520\pi$
$132$	164991.	−	526906.i	0.824185	−	2.63208i
$133$	438776.			2.15087
$134$			13532.2i			0.0651037i
$135$	−186935.	−	240656.i	−0.882787	−	1.13648i
$136$			327116.i			1.51654i
$137$		−	158725.i		−	0.722510i	−0.932467	−	0.361255i	$-0.882348\pi$
$137$		−	158725.i		−	0.722510i	0.932467	−	0.361255i	$-0.117652\pi$
$138$	−130503.	+	416767.i	−0.583340	+	1.86292i
$139$	328342.			1.44142			0.720709	−	0.693238i	$-0.243816\pi$
$139$	328342.			1.44142			0.720709	+	0.693238i	$0.243816\pi$
$140$			738829.i			3.18584i
$141$	48549.6	−	155046.i	0.205654	−	0.656768i
$142$		−	421002.i		−	1.75212i
$143$		−	432459.i		−	1.76850i
$144$	−2321.40	−	1611.85i	−0.00932920	−	0.00647767i
$145$	43981.4			0.173719
$146$		−	318014.i		−	1.23471i
$147$	−67357.9	+	215111.i	−0.257096	+	0.821049i
$148$			214521.i			0.805037i
$149$	−195395.			−0.721019			−0.360509	−	0.932756i	$-0.617397\pi$
$149$	−195395.			−0.721019			−0.360509	+	0.932756i	$0.617397\pi$
$150$	−142823.	+	456113.i	−0.518287	+	1.65518i
$151$			347241.i			1.23933i	0.784865	+	0.619667i	$0.212732\pi$
$151$			347241.i			1.23933i	−0.784865	+	0.619667i	$0.787268\pi$
$152$	453306.			1.59141
$153$	−248171.	+	357418.i	−0.857081	+	1.23438i
$154$	−1.10477e6			−3.75379
$155$	−44672.8			−0.149353
$156$	−489989.	−	153431.i	−1.61204	−	0.504779i
$157$		−	477438.i		−	1.54585i	−0.634497	−	0.772925i	$-0.718793\pi$
$157$		−	477438.i		−	1.54585i	0.634497	−	0.772925i	$-0.281207\pi$
$158$	141389.			0.450581
$159$	−122070.	−	38223.9i	−0.382927	−	0.119906i
$160$		−	461697.i		−	1.42579i
$161$	540707.			1.64398
$162$	−189038.	−	506895.i	−0.565929	−	1.51751i
$163$	37008.3			0.109101			0.0545507	−	0.998511i	$-0.482627\pi$
$163$	37008.3			0.109101			0.0545507	+	0.998511i	$0.482627\pi$
$164$		−	763380.i		−	2.21631i
$165$	−816097.	−	255545.i	−2.33363	−	0.730732i
$166$	266161.			0.749677
$167$			345255.i			0.957963i	0.877825	+	0.478981i	$0.158994\pi$
$167$			345255.i			0.957963i	−0.877825	+	0.478981i	$0.841006\pi$
$168$	−150471.	+	480537.i	−0.411320	+	1.31357i
$169$	−30866.4			−0.0831322
$170$	1.31977e6			3.50248
$171$	495296.	+	343906.i	1.29531	+	0.899392i
$172$		−	1.02573e6i		−	2.64369i
$173$	193763.			0.492215			0.246107	−	0.969243i	$-0.420848\pi$
$173$	193763.			0.492215			0.246107	+	0.969243i	$0.420848\pi$
$174$	74514.1	+	23332.7i	0.186580	+	0.0584241i
$175$	591755.			1.46065
$176$	−7931.05			−0.0192996
$177$	−269135.	+	318265.i	−0.645710	+	0.763583i
$178$	1.05157e6			2.48765
$179$	−558627.			−1.30313			−0.651567	−	0.758591i	$-0.725888\pi$
$179$	−558627.			−1.30313			−0.651567	+	0.758591i	$0.725888\pi$
$180$	−579082.	+	833999.i	−1.33217	+	1.91860i
$181$	569227.			1.29148			0.645742	−	0.763556i	$-0.276548\pi$
$181$	569227.			1.29148			0.645742	+	0.763556i	$0.276548\pi$
$182$			1.02737e6i			2.29904i
$183$	−368881.	−	115508.i	−0.814252	−	0.254968i
$184$	558612.			1.21637
$185$	332260.			0.713755
$186$	−75685.6	−	23699.5i	−0.160410	−	0.0502293i
$187$			1.22111e6i			2.55360i
$188$	−541332.			−1.11704
$189$	−528975.	+	410894.i	−1.07716	+	0.836710i
$190$		−	1.82888e6i		−	3.67538i
$191$	148572.			0.294681			0.147341	−	0.989086i	$-0.452929\pi$
$191$	148572.			0.294681			0.147341	+	0.989086i	$0.452929\pi$
$192$	246670.	−	787753.i	0.482906	−	1.54219i
$193$	312887.			0.604637			0.302318	−	0.953207i	$-0.402239\pi$
$193$	312887.			0.604637			0.302318	+	0.953207i	$0.402239\pi$
$194$			518384.i			0.988889i
$195$	−237641.	+	758919.i	−0.447543	+	1.42925i
$196$	751045.			1.39645
$197$		−	501783.i		−	0.921193i	−0.887610	−	0.460596i	$-0.847636\pi$
$197$		−	501783.i		−	0.921193i	0.887610	−	0.460596i	$-0.152364\pi$
$198$	−1.24708e6	−	865901.i	−2.26064	−	1.56966i
$199$	−219905.			−0.393642			−0.196821	−	0.980439i	$-0.563062\pi$
$199$	−219905.			−0.393642			−0.196821	+	0.980439i	$0.563062\pi$
$200$	611350.			1.08072
$201$	21972.4	+	6880.24i	0.0383607	+	0.0120119i
$202$	−1.09756e6			−1.89256
$203$		−	96673.6i		−	0.164652i
$204$	1.38356e6	+	433236.i	2.32768	+	0.728868i
$205$	−1.18236e6			−1.96501
$206$			485311.i			0.796804i
$207$	610358.	+	423798.i	0.990053	+	0.687437i
$208$			7375.38i			0.0118202i
$209$	1.69218e6			2.67966
$210$	1.93875e6	+	607084.i	3.03371	+	0.949949i
$211$			1.04563e6i			1.61685i	0.588597	+	0.808426i	$0.299680\pi$
$211$			1.04563e6i			1.61685i	−0.588597	+	0.808426i	$0.700320\pi$
$212$			426199.i			0.651288i
$213$	−683587.	−	214052.i	−1.03239	−	0.323274i
$214$			957892.i			1.42982i
$215$	−1.58869e6			−2.34393
$216$	−546491.	+	424500.i	−0.796982	+	0.619075i
$217$			98193.4i			0.141558i
$218$		−	651637.i		−	0.928676i
$219$	−516364.	−	161690.i	−0.727521	−	0.227810i
$220$			2.84935e6i			3.96907i
$221$	1.13556e6			1.56397
$222$	562922.	+	176269.i	0.766595	+	0.240045i
$223$	193752.			0.260906			0.130453	−	0.991455i	$-0.458357\pi$
$223$	193752.			0.260906			0.130453	+	0.991455i	$0.458357\pi$
$224$	−1.01484e6			−1.35138
$225$	667980.	+	463808.i	0.879645	+	0.610776i
$226$	960589.			1.25103
$227$	−890277.			−1.14673			−0.573364	−	0.819301i	$-0.694362\pi$
$227$	−890277.			−1.14673			−0.573364	+	0.819301i	$0.694362\pi$
$228$	600362.	−	1.91729e6i	0.764850	−	2.44259i
$229$		−	354344.i		−	0.446516i	−0.974759	−	0.223258i	$-0.928331\pi$
$229$		−	354344.i		−	0.446516i	0.974759	−	0.223258i	$-0.0716692\pi$
$230$		−	2.25375e6i		−	2.80922i
$231$	−561704.	+	1.79383e6i	−0.692592	+	2.21183i
$232$		−	99874.8i		−	0.121825i
$233$	−214265.			−0.258560			−0.129280	−	0.991608i	$-0.541267\pi$
$233$	−214265.			−0.258560			−0.129280	+	0.991608i	$0.541267\pi$
$234$	−805233.	+	1.15970e6i	−0.961351	+	1.38455i
$235$			838440.i			0.990381i
$236$	1.27994e6	+	538879.i	1.49593	+	0.629812i
$237$	71887.0	−	229575.i	0.0831342	−	0.265493i
$238$		−	2.90093e6i		−	3.31967i
$239$			660462.i			0.747916i	0.927446	+	0.373958i	$0.122000\pi$
$239$			660462.i			0.747916i	−0.927446	+	0.373958i	$0.878000\pi$
$240$	13918.1	+	4358.20i	0.0155974	+	0.00488404i
$241$	170229.			0.188795			0.0943974	−	0.995535i	$-0.469908\pi$
$241$	170229.			0.188795			0.0943974	+	0.995535i	$0.469908\pi$
$242$	−2.78511e6			−3.05706
$243$	−919166.	+	49220.3i	−0.998569	+	0.0534723i
$244$			1.28792e6i			1.38489i
$245$		−	1.16325e6i		−	1.23811i
$246$	−2.00318e6	−	627257.i	−2.11048	−	0.660858i
$247$		−	1.57362e6i		−	1.64118i
$248$			101445.i			0.104737i
$249$	135326.	−	432169.i	0.138319	−	0.441728i
$250$		−	163294.i		−	0.165242i
$251$		−	1.67146e6i		−	1.67460i	−0.546744	−	0.837300i	$-0.684133\pi$
$251$		−	1.67146e6i		−	1.67460i	0.546744	−	0.837300i	$-0.315867\pi$
$252$	1.83318e6	+	1.27286e6i	1.81846	+	1.26264i
$253$	2.08528e6			2.04816
$254$	1.85183e6			1.80101
$255$	671016.	−	2.14292e6i	0.646223	−	2.06375i
$256$	−1.06777e6			−1.01831
$257$		−	774034.i		−	0.731016i	−0.930808	−	0.365508i	$-0.880895\pi$
$257$		−	774034.i		−	0.731016i	0.930808	−	0.365508i	$-0.119105\pi$
$258$	−2.69160e6	−	842823.i	−2.51745	−	0.788292i
$259$		−	730328.i		−	0.676501i
$260$	2.64972e6			2.43089
$261$	75771.2	−	109126.i	0.0688498	−	0.0991582i
$262$	490541.			0.441491
$263$			235538.i			0.209977i	0.994473	+	0.104988i	$0.0334806\pi$
$263$			235538.i			0.209977i	−0.994473	+	0.104988i	$0.966519\pi$
$264$	−580304.	+	1.85323e6i	−0.512443	+	1.63651i
$265$	660118.			0.577440
$266$	−4.02000e6			−3.48355
$267$	534657.	−	1.70745e6i	0.458983	−	1.46579i
$268$		−	76715.1i		−	0.0652445i
$269$	−1.99154e6			−1.67806			−0.839031	−	0.544084i	$-0.816877\pi$
$269$	−1.99154e6			−1.67806			−0.839031	+	0.544084i	$0.816877\pi$
$270$	1.71267e6	+	2.20485e6i	1.42976	+	1.84064i
$271$	−1.86535e6			−1.54290			−0.771448	−	0.636292i	$-0.780467\pi$
$271$	−1.86535e6			−1.54290			−0.771448	+	0.636292i	$0.780467\pi$
$272$		−	20825.5i		−	0.0170676i
$273$	1.66815e6	+	522349.i	1.35465	+	0.424184i
$274$			1.45421e6i			1.17018i
$275$	2.28215e6			1.81975
$276$	739831.	−	2.36269e6i	0.584601	−	1.86695i
$277$	218807.			0.171341			0.0856704	−	0.996324i	$-0.472697\pi$
$277$	218807.			0.171341			0.0856704	+	0.996324i	$0.472697\pi$
$278$	−3.00822e6			−2.33452
$279$	−76962.4	+	110842.i	−0.0591927	+	0.0852499i
$280$		−	2.59860e6i		−	1.98082i
$281$		−	497486.i		−	0.375851i	−0.982183	−	0.187925i	$-0.939824\pi$
$281$		−	497486.i		−	0.375851i	0.982183	−	0.187925i	$-0.0601763\pi$
$282$	−444804.	+	1.42050e6i	−0.333078	+	1.06370i
$283$		−	1.69218e6i		−	1.25597i	−0.778224	−	0.627987i	$-0.783879\pi$
$283$		−	1.69218e6i		−	1.25597i	0.778224	−	0.627987i	$-0.216121\pi$
$284$			2.38670e6i			1.75591i
$285$	−2.96958e6	−	929869.i	−2.16563	−	0.678125i
$286$			3.96212e6i			2.86426i
$287$			2.59890e6i			1.86245i
$288$	−1.14556e6	−	795412.i	−0.813836	−	0.565081i
$289$	−1.78657e6			−1.25827
$290$	−402950.			−0.281356
$291$	841707.	+	263565.i	0.582678	+	0.182455i
$292$			1.80285e6i			1.23738i
$293$			536830.i			0.365315i	0.983177	+	0.182657i	$0.0584699\pi$
$293$			536830.i			0.365315i	−0.983177	+	0.182657i	$0.941530\pi$
$294$	617122.	−	1.97081e6i	0.416392	−	1.32977i
$295$	834641.	−	1.98243e6i	0.558399	−	1.32631i
$296$		−	754511.i		−	0.500537i
$297$	−2.04003e6	+	1.58464e6i	−1.34198	+	1.04242i
$298$	1.79017e6			1.16776
$299$		−	1.93918e6i		−	1.25441i
$300$	809677.	−	2.58574e6i	0.519408	−	1.65876i
$301$			3.49204e6i			2.22159i
$302$		−	3.18136e6i		−	2.00722i
$303$	−558038.	+	1.78212e6i	−0.349186	+	1.11514i
$304$	−28859.2			−0.0179102
$305$	1.99480e6			1.22786
$306$	2.27370e6	−	3.27460e6i	1.38813	−	1.99920i
$307$	823530.			0.498693			0.249347	−	0.968414i	$-0.419784\pi$
$307$	823530.			0.498693			0.249347	+	0.968414i	$0.419784\pi$
$308$	6.26304e6			3.76191
$309$	788005.	+	246749.i	0.469497	+	0.147014i
$310$	409285.			0.241892
$311$		−	1.22316e6i		−	0.717106i	−0.933509	−	0.358553i	$-0.883270\pi$
$311$		−	1.22316e6i		−	0.717106i	0.933509	−	0.358553i	$-0.116730\pi$
$312$	1.72339e6	+	539646.i	1.00230	+	0.313850i
$313$			447349.i			0.258099i	0.991638	+	0.129049i	$0.0411925\pi$
$313$			447349.i			0.258099i	−0.991638	+	0.129049i	$0.958807\pi$
$314$			4.37420e6i			2.50366i
$315$	1.97146e6	−	2.83932e6i	1.11947	−	1.61227i
$316$	−801546.			−0.451555
$317$		−	2.24078e6i		−	1.25242i	−0.779654	−	0.626210i	$-0.784605\pi$
$317$		−	2.24078e6i		−	1.25242i	0.779654	−	0.626210i	$-0.215395\pi$
$318$	1.11839e6	+	350201.i	0.620189	+	0.194200i
$319$		−	372829.i		−	0.205132i
$320$			4.25993e6i			2.32556i
$321$	1.55534e6	+	487026.i	0.842487	+	0.263809i
$322$	−4.95387e6			−2.66260
$323$			4.44335e6i			2.36976i
$324$	1.07167e6	+	2.87363e6i	0.567153	+	1.52079i
$325$		−	2.12225e6i		−	1.11452i
$326$	−339064.			−0.176700
$327$	−1.05807e6	−	331315.i	−0.547199	−	0.171345i
$328$			2.68495e6i			1.37801i
$329$	1.84294e6			0.938689
$330$	7.47695e6	+	2.34127e6i	3.77955	+	1.18349i
$331$	−341059.			−0.171104			−0.0855519	−	0.996334i	$-0.527265\pi$
$331$	−341059.			−0.171104			−0.0855519	+	0.996334i	$0.527265\pi$
$332$	−1.50889e6			−0.751298
$333$	572419.	−	824404.i	0.282881	−	0.407408i
$334$		−	3.16317e6i		−	1.55152i
$335$	−118820.			−0.0578466
$336$	9579.59	−	30592.9i	0.00462912	−	0.0147833i
$337$			359249.i			0.172314i	0.996282	+	0.0861569i	$0.0274586\pi$
$337$			359249.i			0.172314i	−0.996282	+	0.0861569i	$0.972541\pi$
$338$	282793.			0.134641
$339$	488397.	−	1.55972e6i	0.230820	−	0.737136i
$340$	−7.48188e6			−3.51005
$341$			378691.i			0.176359i
$342$	−4.53782e6	−	3.15081e6i	−2.09789	−	1.45665i
$343$	414995.			0.190462
$344$			3.60767e6i			1.64373i
$345$	−3.65944e6	−	1.14589e6i	−1.65526	−	0.518314i
$346$	−1.77522e6			−0.797191
$347$	842913.			0.375802			0.187901	−	0.982188i	$-0.439832\pi$
$347$	842913.			0.375802			0.187901	+	0.982188i	$0.439832\pi$
$348$	−422427.	−	132275.i	−0.186984	−	0.0585504i
$349$			3.55229e6i			1.56115i	0.625060	+	0.780576i	$0.285074\pi$
$349$			3.55229e6i			1.56115i	−0.625060	+	0.780576i	$0.714926\pi$
$350$	−5.42156e6			−2.36567
$351$	1.47362e6	+	1.89710e6i	0.638436	+	0.821907i
$352$	−3.91380e6			−1.68361
$353$	−1.35698e6			−0.579611			−0.289805	−	0.957086i	$-0.593591\pi$
$353$	−1.35698e6			−0.579611			−0.289805	+	0.957086i	$0.593591\pi$
$354$	2.46577e6	−	2.91589e6i	1.04579	−	1.23670i
$355$	3.69663e6			1.55681
$356$	−5.96146e6			−2.49303
$357$	−4.71027e6	−	1.47493e6i	−1.95603	−	0.612494i
$358$	5.11805e6			2.11056
$359$			2.31729e6i			0.948952i	0.880268	+	0.474476i	$0.157362\pi$
$359$			2.31729e6i			0.948952i	−0.880268	+	0.474476i	$0.842638\pi$
$360$	2.03674e6	−	2.93333e6i	0.828284	−	1.19290i
$361$	3.68132e6			1.48674
$362$	−5.21516e6			−2.09169
$363$	−1.41605e6	+	4.52222e6i	−0.564042	+	1.80130i
$364$		−	5.82423e6i		−	2.30401i
$365$	2.79234e6			1.09707
$366$	3.37963e6	+	1.05827e6i	1.31876	+	0.412945i
$367$		−	155574.i		−	0.0602935i	−0.999545	−	0.0301468i	$-0.990403\pi$
$367$		−	155574.i		−	0.0602935i	0.999545	−	0.0301468i	$-0.00959747\pi$
$368$	−35563.4			−0.0136894
$369$	−2.03697e6	+	2.93367e6i	−0.778788	+	1.12162i
$370$	−3.04412e6			−1.15600
$371$		−	1.45098e6i		−	0.547301i
$372$	429068.	+	134355.i	0.160757	+	0.0503379i
$373$	−763121.			−0.284002			−0.142001	−	0.989867i	$-0.545354\pi$
$373$	−763121.			−0.284002			−0.142001	+	0.989867i	$0.545354\pi$
$374$		−	1.11877e7i		−	4.13580i
$375$	−265142.	−	83024.3i	−0.0973646	−	0.0304879i
$376$	1.90397e6			0.694528
$377$	−346708.			−0.125635
$378$	4.84638e6	−	3.76454e6i	1.74457	−	1.35514i
$379$	−2.81095e6			−1.00521			−0.502603	−	0.864518i	$-0.667624\pi$
$379$	−2.81095e6			−1.00521			−0.502603	+	0.864518i	$0.667624\pi$
$380$			1.03681e7i			3.68333i
$381$	941534.	−	3.00684e6i	0.332295	−	1.06120i
$382$	−1.36119e6			−0.477266
$383$		−	3.65382e6i		−	1.27277i	−0.771372	−	0.636385i	$-0.780429\pi$
$383$		−	3.65382e6i		−	1.27277i	0.771372	−	0.636385i	$-0.219571\pi$
$384$	−1.40445e6	+	4.48518e6i	−0.486046	+	1.55221i
$385$		−	9.70049e6i		−	3.33535i
$386$	−2.86662e6			−0.979269
$387$	−2.73701e6	+	3.94186e6i	−0.928963	+	1.33790i
$388$		−	2.93877e6i		−	0.991027i
$389$		−	2.80517e6i		−	0.939908i	−0.882691	−	0.469954i	$-0.844270\pi$
$389$		−	2.80517e6i		−	0.939908i	0.882691	−	0.469954i	$-0.155730\pi$
$390$	2.17723e6	−	6.95309e6i	0.724841	−	2.31482i
$391$			5.47557e6i			1.81129i
$392$	−2.64157e6			−0.868254
$393$	249408.	−	796497.i	0.0814571	−	0.260137i
$394$			4.59725e6i			1.49196i
$395$			1.24147e6i			0.400354i
$396$	7.06980e6	+	4.90887e6i	2.26553	+	1.57305i
$397$		−	2.58042e6i		−	0.821700i	−0.911703	−	0.410850i	$-0.865232\pi$
$397$		−	2.58042e6i		−	0.821700i	0.911703	−	0.410850i	$-0.134768\pi$
$398$	2.01473e6			0.637543
$399$	−2.04391e6	+	6.52732e6i	−0.642730	+	2.05259i
$400$	−38920.9			−0.0121628
$401$	−4.89083e6			−1.51887			−0.759437	−	0.650581i	$-0.774525\pi$
$401$	−4.89083e6			−1.51887			−0.759437	+	0.650581i	$0.774525\pi$
$402$	−201307.	−	63035.6i	−0.0621290	−	0.0194545i
$403$	352158.			0.108013
$404$	6.22217e6			1.89665
$405$	4.45082e6	−	1.65986e6i	1.34835	−	0.502844i
$406$			885708.i			0.266671i
$407$		−	2.81657e6i		−	0.842818i
$408$	−4.86625e6	−	1.52377e6i	−1.44725	−	0.453179i
$409$		−	4.39663e6i		−	1.29961i	−0.760103	−	0.649803i	$-0.774851\pi$
$409$		−	4.39663e6i		−	1.29961i	0.760103	−	0.649803i	$-0.225149\pi$
$410$	1.08326e7			3.18253
$411$	2.36122e6	+	739373.i	0.689497	+	0.215903i
$412$		−	2.75127e6i		−	0.798528i
$413$	−4.35751e6	−	1.83459e6i	−1.25708	−	0.529254i
$414$	−5.59200e6	−	3.88277e6i	−1.60349	−	1.11337i
$415$			2.33704e6i			0.666110i
$416$			3.63958e6i			1.03114i
$417$	−1.52948e6	+	4.88448e6i	−0.430730	+	1.37556i
$418$	−1.55034e7			−4.33997
$419$	−5.69297e6			−1.58418			−0.792089	−	0.610405i	$-0.791007\pi$
$419$	−5.69297e6			−1.58418			−0.792089	+	0.610405i	$0.791007\pi$
$420$	−1.09910e7	−	3.44161e6i	−3.04027	−	0.952003i
$421$		−	3.23499e6i		−	0.889545i	−0.895644	−	0.444773i	$-0.853284\pi$
$421$		−	3.23499e6i		−	0.889545i	0.895644	−	0.444773i	$-0.146716\pi$
$422$		−	9.57986e6i		−	2.61865i
$423$	2.08034e6	+	1.44447e6i	0.565305	+	0.392515i
$424$		−	1.49902e6i		−	0.404943i
$425$			5.99251e6i			1.60930i
$426$	6.26291e6	+	1.96111e6i	1.67206	+	0.523574i
$427$		−	4.38468e6i		−	1.16377i
$428$		−	5.43037e6i		−	1.43291i
$429$	6.43334e6	+	2.01448e6i	1.68769	+	0.528469i
$430$	1.45554e7			3.79622
$431$	3.56169e6			0.923555			0.461778	−	0.886996i	$-0.347212\pi$
$431$	3.56169e6			0.923555			0.461778	+	0.886996i	$0.347212\pi$
$432$	34791.8	−	27025.3i	0.00896948	−	0.00696726i
$433$	−3.31805e6			−0.850478			−0.425239	−	0.905081i	$-0.639810\pi$
$433$	−3.31805e6			−0.850478			−0.425239	+	0.905081i	$0.639810\pi$
$434$		−	899632.i		−	0.229267i
$435$	−204874.	+	654275.i	−0.0519115	+	0.165782i
$436$			3.69419e6i			0.930685i
$437$	7.58784e6			1.90070
$438$	4.73084e6	+	1.48137e6i	1.17829	+	0.368960i
$439$	739530.			0.183145			0.0915724	−	0.995798i	$-0.470811\pi$
$439$	739530.			0.183145			0.0915724	+	0.995798i	$0.470811\pi$
$440$		−	1.00217e7i		−	2.46780i
$441$	−2.88626e6	−	2.00406e6i	−0.706707	−	0.490698i
$442$	−1.04038e7			−2.53301
$443$	4.52167e6			1.09469			0.547343	−	0.836908i	$-0.315639\pi$
$443$	4.52167e6			1.09469			0.547343	+	0.836908i	$0.315639\pi$
$444$	−3.19126e6	−	999282.i	−0.768253	−	0.240564i
$445$			9.23339e6i			2.21035i
$446$	−1.77512e6			−0.422563
$447$	910187.	−	2.90673e6i	0.215457	−	0.688074i
$448$	9.36357e6			2.20418
$449$			998571.i			0.233756i	0.993146	+	0.116878i	$0.0372887\pi$
$449$			998571.i			0.233756i	−0.993146	+	0.116878i	$0.962711\pi$
$450$	−6.11993e6	−	4.24933e6i	−1.42467	−	0.989212i
$451$			1.00228e7i			2.32033i
$452$	−5.44566e6			−1.25373
$453$	−5.16562e6	−	1.61752e6i	−1.18271	−	0.370342i
$454$	8.15658e6			1.85724
$455$	−9.02084e6			−2.04277
$456$	−2.11159e6	+	6.74346e6i	−0.475551	+	1.51870i
$457$			2.58310e6i			0.578564i	0.957244	+	0.289282i	$0.0934166\pi$
$457$			2.58310e6i			0.578564i	−0.957244	+	0.289282i	$0.906583\pi$
$458$			3.24644e6i			0.723176i
$459$	−4.16099e6	−	5.35676e6i	−0.921860	−	1.18678i
$460$			1.27767e7i			2.81530i
$461$			5.67517e6i			1.24373i	0.783124	+	0.621866i	$0.213625\pi$
$461$			5.67517e6i			1.24373i	−0.783124	+	0.621866i	$0.786375\pi$
$462$	5.14624e6	−	1.64348e7i	1.12172	−	3.58227i
$463$		−	7.42680e6i		−	1.61009i	−0.593216	−	0.805043i	$-0.702142\pi$
$463$		−	7.42680e6i		−	1.61009i	0.593216	−	0.805043i	$-0.297858\pi$
$464$			6358.42i			0.00137105i
$465$	208095.	−	664561.i	0.0446302	−	0.142529i
$466$	1.96306e6			0.418764
$467$	2.95086e6			0.626118			0.313059	−	0.949734i	$-0.398646\pi$
$467$	2.95086e6			0.626118			0.313059	+	0.949734i	$0.398646\pi$
$468$	4.56494e6	−	6.57447e6i	0.963430	−	1.38754i
$469$			261173.i			0.0548273i
$470$		−	7.68165e6i		−	1.60402i
$471$	7.10245e6	+	2.22400e6i	1.47522	+	0.461937i
$472$	−4.50180e6	−	1.89534e6i	−0.930103	−	0.391590i
$473$			1.34673e7i			2.76776i
$474$	−658617.	+	2.10333e6i	−0.134644	+	0.429993i
$475$	8.30420e6			1.68874
$476$			1.64456e7i			3.32685i
$477$	1.13725e6	−	1.63788e6i	0.228855	−	0.329600i
$478$		−	6.05104e6i		−	1.21132i
$479$		−	3.16680e6i		−	0.630640i	−0.948985	−	0.315320i	$-0.897888\pi$
$479$		−	3.16680e6i		−	0.630640i	0.948985	−	0.315320i	$-0.102112\pi$
$480$	6.86829e6	+	2.15067e6i	1.36065	+	0.426061i
$481$	−2.61923e6			−0.516191
$482$	−1.55961e6			−0.305772
$483$	−2.51872e6	+	8.04367e6i	−0.491261	+	1.56887i
$484$	1.57890e7			3.06367
$485$	−4.55170e6			−0.878657
$486$	8.42125e6	−	450949.i	1.61728	−	0.0866037i
$487$	−4.91557e6			−0.939185			−0.469593	−	0.882883i	$-0.655599\pi$
$487$	−4.91557e6			−0.939185			−0.469593	+	0.882883i	$0.655599\pi$
$488$		−	4.52987e6i		−	0.861066i
$489$	−172392.	+	550543.i	−0.0326021	+	0.104116i
$490$			1.06576e7i			2.00524i
$491$			1.47985e6i			0.277022i	0.990361	+	0.138511i	$0.0442316\pi$
$491$			1.47985e6i			0.277022i	−0.990361	+	0.138511i	$0.955768\pi$
$492$	1.13562e7	+	3.55598e6i	2.11505	+	0.662287i
$493$	978982.			0.181408
$494$			1.44172e7i			2.65805i
$495$	7.60309e6	−	1.09500e7i	1.39469	−	2.00864i
$496$		−	6458.38i		−	0.00117874i
$497$		−	8.12541e6i		−	1.47555i
$498$	−1.23983e6	+	3.95946e6i	−0.224021	+	0.715423i
$499$	394162.			0.0708637			0.0354318	−	0.999372i	$-0.488719\pi$
$499$	394162.			0.0708637			0.0354318	+	0.999372i	$0.488719\pi$
$500$			925728.i			0.165599i
$501$	−5.13608e6	−	1.60827e6i	−0.914192	−	0.286262i
$502$			1.53136e7i			2.71218i
$503$	5.69031e6			1.00280			0.501402	−	0.865214i	$-0.332818\pi$
$503$	5.69031e6			1.00280			0.501402	+	0.865214i	$0.332818\pi$
$504$	−6.44764e6	−	4.47688e6i	−1.13064	−	0.785052i
$505$		−	9.63718e6i		−	1.68160i
$506$	−1.91050e7			−3.31719
$507$	143782.	−	459174.i	0.0248419	−	0.0793337i
$508$	−1.04982e7			−1.80491
$509$	1.16724e6			0.199695			0.0998475	−	0.995003i	$-0.468165\pi$
$509$	1.16724e6			0.199695			0.0998475	+	0.995003i	$0.468165\pi$
$510$	−6.14774e6	+	1.96331e7i	−1.04662	+	3.34244i
$511$		−	6.13773e6i		−	1.03981i
$512$	134735.			0.0227146
$513$	−7.42320e6	+	5.76614e6i	−1.24537	+	0.967369i
$514$			7.09157e6i			1.18395i
$515$	−4.26129e6			−0.707984
$516$	1.52589e7	+	4.77804e6i	2.52290	+	0.789997i
$517$	7.10745e6			1.16946
$518$			6.69114e6i			1.09566i
$519$	−902585.	+	2.88245e6i	−0.147085	+	0.469725i
$520$	−9.31955e6			−1.51143
$521$		−	2.30794e6i		−	0.372503i	−0.982502	−	0.186251i	$-0.940366\pi$
$521$		−	2.30794e6i		−	0.372503i	0.982502	−	0.186251i	$-0.0596339\pi$
$522$	−694203.	+	999798.i	−0.111509	+	0.160597i
$523$	−952520.			−0.152272			−0.0761359	−	0.997097i	$-0.524258\pi$
$523$	−952520.			−0.152272			−0.0761359	+	0.997097i	$0.524258\pi$
$524$	−2.78092e6			−0.442446
$525$	−2.75651e6	+	8.80306e6i	−0.436477	+	1.39391i
$526$		−	2.15796e6i		−	0.340078i
$527$	−994373.			−0.155964
$528$	36944.4	−	117984.i	0.00576719	−	0.0184178i
$529$	2.91421e6			0.452774
$530$	−6.04789e6			−0.935221
$531$	−3.48089e6	−	5.48625e6i	−0.535740	−	0.844383i
$532$	2.27897e7			3.49108
$533$	9.32061e6			1.42111
$534$	−4.89844e6	+	1.56434e7i	−0.743369	+	2.37399i
$535$	−8.41082e6			−1.27044
$536$			269822.i			0.0405662i
$537$	2.60220e6	−	8.31024e6i	0.389407	−	1.24359i
$538$	1.82461e7			2.71779
$539$	−9.86089e6			−1.46199
$540$	−9.70926e6	−	1.24995e7i	−1.43285	−	1.84462i
$541$			86095.6i			0.0126470i	0.999980	+	0.00632350i	$0.00201285\pi$
$541$			86095.6i			0.0126470i	−0.999980	+	0.00632350i	$0.997987\pi$
$542$	1.70900e7			2.49887
$543$	−2.65157e6	+	8.46793e6i	−0.385926	+	1.23247i
$544$		−	1.02769e7i		−	1.48890i
$545$	5.72173e6			0.825156
$546$	−1.52833e7	−	4.78568e6i	−2.19399	−	0.687008i
$547$	−4.91272e6			−0.702027			−0.351014	−	0.936370i	$-0.614163\pi$
$547$	−4.91272e6			−0.702027			−0.351014	+	0.936370i	$0.614163\pi$
$548$		−	8.24406e6i		−	1.17271i
$549$	3.43664e6	−	4.94949e6i	0.486635	−	0.700857i
$550$	−2.09087e7			−2.94727
$551$		−	1.35664e6i		−	0.190364i
$552$	−2.60213e6	+	8.31002e6i	−0.363480	+	1.16079i
$553$	2.72883e6			0.379458
$554$	−2.00467e6			−0.277504
$555$	−1.54773e6	+	4.94277e6i	−0.213287	+	0.681142i
$556$	1.70539e7			2.33957
$557$			1.40167e7i			1.91430i	0.289601	+	0.957148i	$0.406478\pi$
$557$			1.40167e7i			1.91430i	−0.289601	+	0.957148i	$0.593522\pi$
$558$	705117.	−	1.01552e6i	0.0958685	−	0.138071i
$559$	1.25238e7			1.69514
$560$			165437.i			0.0222927i
$561$	−1.81655e7	−	5.68820e6i	−2.43692	−	0.763075i
$562$			4.55789e6i			0.608728i
$563$	1.49572e7			1.98875			0.994374	−	0.105929i	$-0.0337817\pi$
$563$	1.49572e7			1.98875			0.994374	+	0.105929i	$0.0337817\pi$
$564$	2.52163e6	−	8.05296e6i	0.333798	−	1.06600i
$565$			8.43450e6i			1.11157i
$566$			1.55035e7i			2.03417i
$567$	−3.64847e6	−	9.78316e6i	−0.476599	−	1.27797i
$568$		−	8.39447e6i		−	1.09175i
$569$	−8.86429e6			−1.14779			−0.573896	−	0.818928i	$-0.694569\pi$
$569$	−8.86429e6			−1.14779			−0.573896	+	0.818928i	$0.694569\pi$
$570$	2.72068e7	+	8.51931e6i	3.50745	+	1.09829i
$571$		−	5.05196e6i		−	0.648440i	−0.945982	−	0.324220i	$-0.894898\pi$
$571$		−	5.05196e6i		−	0.648440i	0.945982	−	0.324220i	$-0.105102\pi$
$572$		−	2.24616e7i		−	2.87045i
$573$	−692076.	+	2.21018e6i	−0.0880577	+	0.281217i
$574$		−	2.38107e7i		−	3.01642i
$575$	1.02333e7			1.29076
$576$	1.05697e7	+	7.33902e6i	1.32742	+	0.921683i
$577$	3.42759e6			0.428598			0.214299	−	0.976768i	$-0.431253\pi$
$577$	3.42759e6			0.428598			0.214299	+	0.976768i	$0.431253\pi$
$578$	1.63683e7			2.03790
$579$	−1.45749e6	+	4.65457e6i	−0.180680	+	0.577010i
$580$	2.28436e6			0.281964
$581$	5.13695e6			0.631343
$582$	−7.71159e6	−	2.41474e6i	−0.943705	−	0.295503i
$583$		−	5.59581e6i		−	0.681854i
$584$		−	6.34097e6i		−	0.769349i
$585$	−1.01828e7	−	7.07039e6i	−1.23021	−	0.854188i
$586$		−	4.91835e6i		−	0.591664i
$587$	−4.69796e6			−0.562749			−0.281374	−	0.959598i	$-0.590790\pi$
$587$	−4.69796e6			−0.562749			−0.281374	+	0.959598i	$0.590790\pi$
$588$	−3.49852e6	+	1.11727e7i	−0.417293	+	1.33265i
$589$			1.37797e6i			0.163663i
$590$	−7.64684e6	+	1.81627e7i	−0.904383	+	2.14808i
$591$	7.46462e6	+	2.33741e6i	0.879102	+	0.275274i
$592$			48035.2i			0.00563320i
$593$		−	1.44386e7i		−	1.68612i	−0.537816	−	0.843062i	$-0.680750\pi$
$593$		−	1.44386e7i		−	1.68612i	0.537816	−	0.843062i	$-0.319250\pi$
$594$	1.86905e7	−	1.45183e7i	2.17347	−	1.68829i
$595$	2.54717e7			2.94962
$596$	−1.01486e7			−1.17029
$597$	1.02436e6	−	3.27134e6i	0.117630	−	0.375656i
$598$			1.77664e7i			2.03164i
$599$			6.19040e6i			0.704939i	0.935823	+	0.352470i	$0.114658\pi$
$599$			6.19040e6i			0.704939i	−0.935823	+	0.352470i	$0.885342\pi$
$600$	−2.84779e6	+	9.09455e6i	−0.322946	+	1.03134i
$601$		−	8.66635e6i		−	0.978701i	−0.872087	−	0.489351i	$-0.837234\pi$
$601$		−	8.66635e6i		−	0.978701i	0.872087	−	0.489351i	$-0.162766\pi$
$602$		−	3.19935e7i		−	3.59808i
$603$	−204703.	+	294816.i	−0.0229262	+	0.0330185i
$604$			1.80354e7i			2.01157i
$605$		−	2.44548e7i		−	2.71629i
$606$	5.11265e6	−	1.63275e7i	0.565542	−	1.80609i
$607$	−1.58133e6			−0.174201			−0.0871006	−	0.996200i	$-0.527760\pi$
$607$	−1.58133e6			−0.174201			−0.0871006	+	0.996200i	$0.527760\pi$
$608$	−1.42414e7			−1.56240
$609$	1.43814e6	+	450325.i	0.157129	+	0.0492020i
$610$	−1.82760e7			−1.98864
$611$		−	6.60947e6i		−	0.716249i
$612$	−1.28898e7	+	1.85640e7i	−1.39113	+	2.00352i
$613$			6.50036e6i			0.698693i	0.936994	+	0.349346i	$0.113596\pi$
$613$			6.50036e6i			0.698693i	−0.936994	+	0.349346i	$0.886404\pi$
$614$	−7.54505e6			−0.807684
$615$	5.50767e6	−	1.75890e7i	0.587191	−	1.87523i
$616$	−2.20283e7			−2.33899
$617$			1.47931e7i			1.56439i	0.623033	+	0.782195i	$0.285900\pi$
$617$			1.47931e7i			1.56439i	−0.623033	+	0.782195i	$0.714100\pi$
$618$	−7.21958e6	−	2.26067e6i	−0.760397	−	0.238104i
$619$	−1.53234e7			−1.60741			−0.803706	−	0.595026i	$-0.797142\pi$
$619$	−1.53234e7			−1.60741			−0.803706	+	0.595026i	$0.797142\pi$
$620$	−2.32027e6			−0.242415
$621$	−9.14766e6	+	7.10566e6i	−0.951878	+	0.739394i
$622$			1.12064e7i			1.16142i
$623$	2.02955e7			2.09498
$624$	−109718.	−	34356.0i	−0.0112801	−	0.00353216i
$625$	−9.02418e6			−0.924076
$626$		−	4.09854e6i		−	0.418016i
$627$	−7.88249e6	+	2.51731e7i	−0.800745	+	2.55722i
$628$		−	2.47977e7i		−	2.50907i
$629$	7.39579e6			0.745347
$630$	−1.80622e7	+	2.60133e7i	−1.81309	+	2.61123i
$631$	2.15806e6			0.215770			0.107885	−	0.994163i	$-0.465592\pi$
$631$	2.15806e6			0.215770			0.107885	+	0.994163i	$0.465592\pi$
$632$	2.81919e6			0.280758
$633$	−1.55549e7	−	4.87074e6i	−1.54298	−	0.483154i
$634$			2.05296e7i			2.02842i
$635$			1.62601e7i			1.60025i
$636$	−6.34023e6	−	1.98532e6i	−0.621530	−	0.194620i
$637$			9.17001e6i			0.895408i
$638$			3.41580e6i			0.332232i
$639$	6.36857e6	−	9.17207e6i	0.617006	−	0.888619i
$640$		−	2.42545e7i		−	2.34068i
$641$			4.56382e6i			0.438716i	0.975644	+	0.219358i	$0.0703962\pi$
$641$			4.56382e6i			0.438716i	−0.975644	+	0.219358i	$0.929604\pi$
$642$	−1.42498e7	−	4.46205e6i	−1.36449	−	0.427264i
$643$	41456.8			0.00395429			0.00197715	−	0.999998i	$-0.499371\pi$
$643$	41456.8			0.00395429			0.00197715	+	0.999998i	$0.499371\pi$
$644$	2.80839e7			2.66835
$645$	7.40045e6	−	2.36337e7i	0.700421	−	2.23683i
$646$		−	4.07092e7i		−	3.83806i
$647$		−	2.88969e6i		−	0.271388i	−0.990751	−	0.135694i	$-0.956674\pi$
$647$		−	2.88969e6i		−	0.271388i	0.990751	−	0.135694i	$-0.0433264\pi$
$648$	−3.76928e6	−	1.01071e7i	−0.352631	−	0.945561i
$649$	−1.68051e7	−	7.07524e6i	−1.56613	−	0.659370i
$650$			1.94437e7i			1.80508i
$651$	−1.46074e6	−	457405.i	−0.135090	−	0.0423007i
$652$	1.92218e6			0.177083
$653$			1.31921e7i			1.21068i	0.795966	+	0.605342i	$0.206964\pi$
$653$			1.31921e7i			1.21068i	−0.795966	+	0.605342i	$0.793036\pi$
$654$	9.69388e6	+	3.03545e6i	0.886244	+	0.277510i
$655$			4.30722e6i			0.392278i
$656$		−	170935.i		−	0.0155085i
$657$	4.81065e6	−	6.92835e6i	0.434801	−	0.626205i
$658$	−1.68847e7			−1.52030
$659$	9.13543e6			0.819437			0.409718	−	0.912212i	$-0.365627\pi$
$659$	9.13543e6			0.819437			0.409718	+	0.912212i	$0.365627\pi$
$660$	−4.23875e7	−	1.32728e7i	−3.78772	−	1.18605i
$661$	−7.05245e6			−0.627822			−0.313911	−	0.949452i	$-0.601639\pi$
$661$	−7.05245e6			−0.627822			−0.313911	+	0.949452i	$0.601639\pi$
$662$	3.12473e6			0.277120
$663$	−5.28966e6	+	1.68928e7i	−0.467352	+	1.49251i
$664$	5.30705e6			0.467125
$665$		−	3.52978e7i		−	3.09523i
$666$	−5.24441e6	+	7.55305e6i	−0.458154	+	0.659837i
$667$		−	1.67179e6i		−	0.145502i
$668$			1.79323e7i			1.55487i
$669$	−902534.	+	2.88229e6i	−0.0779648	+	0.248985i
$670$	1.08861e6			0.0936883
$671$		−	1.69099e7i		−	1.44989i
$672$	4.72731e6	−	1.50969e7i	0.403823	−	1.28963i
$673$		−	5.02410e6i		−	0.427583i	−0.976879	−	0.213791i	$-0.931419\pi$
$673$		−	5.02410e6i		−	0.427583i	0.976879	−	0.213791i	$-0.0685813\pi$
$674$		−	3.29138e6i		−	0.279079i
$675$	−1.00113e7	+	7.77650e6i	−0.845727	+	0.656938i
$676$	−1.60318e6			−0.134932
$677$			2.88568e6i			0.241978i	0.992654	+	0.120989i	$0.0386066\pi$
$677$			2.88568e6i			0.241978i	−0.992654	+	0.120989i	$0.961393\pi$
$678$	−4.47462e6	+	1.42899e7i	−0.373836	+	1.19387i
$679$			1.00049e7i			0.832796i
$680$	2.63152e7			2.18240
$681$	4.14709e6	−	1.32439e7i	0.342670	−	1.09433i
$682$		−	3.46950e6i		−	0.285632i
$683$	2.90899e6			0.238611			0.119306	−	0.992858i	$-0.461933\pi$
$683$	2.90899e6			0.238611			0.119306	+	0.992858i	$0.461933\pi$
$684$	2.57253e7	+	1.78622e7i	2.10243	+	1.45981i
$685$	−1.27688e7			−1.03974
$686$	−3.80212e6			−0.308472
$687$	5.27129e6	+	1.65061e6i	0.426114	+	0.133429i
$688$		−	229679.i		−	0.0184991i
$689$	−5.20375e6			−0.417607
$690$	3.35272e7	+	1.04984e7i	2.68086	+	0.839462i
$691$			5.13481e6i			0.409100i	0.978856	+	0.204550i	$0.0655731\pi$
$691$			5.13481e6i			0.409100i	−0.978856	+	0.204550i	$0.934427\pi$
$692$	1.00639e7			0.798915
$693$	−2.40688e7	−	1.67120e7i	−1.90380	−	1.32189i
$694$	−7.72263e6			−0.608648
$695$		−	2.64138e7i		−	2.07429i
$696$	1.48576e6	+	465236.i	0.116258	+	0.0364041i
$697$	−2.63182e7			−2.05198
$698$		−	3.25455e7i		−	2.52844i
$699$	998089.	−	3.18745e6i	0.0772638	−	0.246746i
$700$	3.07353e7			2.37079
$701$	−1.35238e7			−1.03945			−0.519724	−	0.854334i	$-0.673965\pi$
$701$	−1.35238e7			−1.03945			−0.519724	+	0.854334i	$0.673965\pi$
$702$	−1.35011e7	−	1.73809e7i	−1.03401	−	1.33116i
$703$		−	1.02488e7i		−	0.782142i
$704$	3.61114e7			2.74607
$705$	−1.24728e7	−	3.90562e6i	−0.945129	−	0.295949i
$706$	1.24324e7			0.938737
$707$	−2.11831e7			−1.59383
$708$	−1.39787e7	+	1.65305e7i	−1.04805	+	1.23937i
$709$	2.23574e6			0.167034			0.0835171	−	0.996506i	$-0.473385\pi$
$709$	2.23574e6			0.167034			0.0835171	+	0.996506i	$0.473385\pi$
$710$	−3.38679e7			−2.52141
$711$	3.08034e6	+	2.13881e6i	0.228520	+	0.158671i
$712$	2.09676e7			1.55006
$713$			1.69808e6i			0.125093i
$714$	4.31548e7	+	1.35131e7i	3.16799	+	0.991995i
$715$	−3.47896e7			−2.54498
$716$	−2.90147e7			−2.11512
$717$	−9.82515e6	−	3.07656e6i	−0.713742	−	0.223495i
$718$		−	2.12306e7i		−	1.53692i
$719$	1.93988e7			1.39943			0.699716	−	0.714421i	$-0.253310\pi$
$719$	1.93988e7			1.39943			0.699716	+	0.714421i	$0.253310\pi$
$720$	−129667.	+	186748.i	−0.00932176	+	0.0134253i
$721$			9.36658e6i			0.671031i
$722$	−3.37277e7			−2.40793
$723$	−792959.	+	2.53236e6i	−0.0564164	+	0.180169i
$724$	2.95652e7			2.09621
$725$		−	1.82963e6i		−	0.129276i
$726$	1.29736e7	−	4.14318e7i	0.913522	−	2.91738i
$727$	1.24094e7			0.870790			0.435395	−	0.900239i	$-0.356609\pi$
$727$	1.24094e7			0.870790			0.435395	+	0.900239i	$0.356609\pi$
$728$			2.04849e7i			1.43254i
$729$	3.54945e6	−	1.39030e7i	0.247367	−	0.968922i
$730$	−2.55830e7			−1.77682
$731$	−3.53628e7			−2.44767
$732$	−1.91594e7	−	5.99941e6i	−1.32161	−	0.413838i
$733$	−1.46720e7			−1.00862			−0.504312	−	0.863521i	$-0.668254\pi$
$733$	−1.46720e7			−1.00862			−0.504312	+	0.863521i	$0.668254\pi$
$734$			1.42534e6i			0.0976513i
$735$	1.73048e7	+	5.41867e6i	1.18154	+	0.369977i
$736$	−1.75498e7			−1.19420
$737$			1.00724e6i			0.0683066i
$738$	1.86624e7	−	2.68778e7i	1.26132	−	1.81657i
$739$			2.12296e7i			1.42998i	0.699135	+	0.714990i	$0.253569\pi$
$739$			2.12296e7i			1.42998i	−0.699135	+	0.714990i	$0.746431\pi$
$740$	1.72574e7			1.15850
$741$	2.34094e7	+	7.33021e6i	1.56619	+	0.490423i
$742$			1.32936e7i			0.886408i
$743$		−	9.72699e6i		−	0.646408i	−0.946329	−	0.323204i	$-0.895240\pi$
$743$		−	9.72699e6i		−	0.646408i	0.946329	−	0.323204i	$-0.104760\pi$
$744$	−1.50911e6	−	472551.i	−0.0999516	−	0.0312980i
$745$			1.57187e7i			1.03759i
$746$	6.99159e6			0.459969
$747$	5.79866e6	+	4.02626e6i	0.380212	+	0.263998i
$748$			6.34238e7i			4.14475i
$749$			1.84875e7i			1.20413i
$750$	2.42919e6	+	760656.i	0.157692	+	0.0493782i
$751$		−	1.37883e7i		−	0.892093i	−0.895010	−	0.446047i	$-0.852832\pi$
$751$		−	1.37883e7i		−	0.892093i	0.895010	−	0.446047i	$-0.147168\pi$
$752$	−121214.			−0.00781643
$753$	2.48649e7	+	7.78598e6i	1.59808	+	0.500410i
$754$	3.17648e6			0.203478
$755$	2.79341e7			1.78348
$756$	−2.74746e7	+	2.13415e7i	−1.74834	+	1.35807i
$757$	1.54228e7			0.978191			0.489096	−	0.872230i	$-0.337327\pi$
$757$	1.54228e7			0.978191			0.489096	+	0.872230i	$0.337327\pi$
$758$	2.57534e7			1.62803
$759$	−9.71365e6	+	3.10210e7i	−0.612038	+	1.95457i
$760$		−	3.64666e7i		−	2.29014i
$761$		−	1.29251e7i		−	0.809045i	−0.914528	−	0.404522i	$-0.867438\pi$
$761$		−	1.29251e7i		−	0.809045i	0.914528	−	0.404522i	$-0.132562\pi$
$762$	−8.62618e6	+	2.75482e7i	−0.538185	+	1.71872i
$763$		−	1.25767e7i		−	0.782088i
$764$	7.71670e6			0.478298
$765$	2.87528e7	+	1.99643e7i	1.77634	+	1.23339i
$766$			3.34757e7i			2.06138i
$767$	−6.57952e6	+	1.56276e7i	−0.403837	+	0.959191i
$768$	4.97389e6	−	1.58844e7i	0.304294	−	0.971777i
$769$			1.01524e7i			0.619089i	0.950885	+	0.309545i	$0.100177\pi$
$769$			1.01524e7i			0.619089i	−0.950885	+	0.309545i	$0.899823\pi$
$770$			8.88743e7i			5.40194i
$771$	1.15147e7	+	3.60560e6i	0.697615	+	0.218445i
$772$	1.62511e7			0.981387
$773$	2.62986e7			1.58301			0.791504	−	0.611163i	$-0.209298\pi$
$773$	2.62986e7			1.58301			0.791504	+	0.611163i	$0.209298\pi$
$774$	2.50760e7	−	3.61147e7i	1.50455	−	2.16686i
$775$			1.85839e6i			0.111143i
$776$			1.03362e7i			0.616178i
$777$	1.08645e7	+	3.40201e6i	0.645590	+	0.202154i
$778$			2.57005e7i			1.52227i
$779$			3.64707e7i			2.15328i
$780$	−1.23429e7	+	3.94177e7i	−0.726408	+	2.31982i
$781$		−	3.13363e7i		−	1.83832i
$782$		−	5.01663e7i		−	2.93356i
$783$	1.27043e6	+	1.63552e6i	0.0740535	+	0.0953348i
$784$	168173.			0.00977159
$785$	−3.84079e7			−2.22457
$786$	−2.28504e6	+	7.29738e6i	−0.131928	+	0.421318i
$787$	1.05411e7			0.606663			0.303331	−	0.952885i	$-0.401901\pi$
$787$	1.05411e7			0.606663			0.303331	+	0.952885i	$0.401901\pi$
$788$		−	2.60622e7i		−	1.49519i
$789$	−3.50391e6	−	1.09718e6i	−0.200383	−	0.0627460i
$790$		−	1.13742e7i		−	0.648413i
$791$	1.85395e7			1.05356
$792$	−2.48658e7	−	1.72654e7i	−1.40861	−	0.978057i
$793$	−1.57251e7			−0.887995
$794$			2.36413e7i			1.33083i
$795$	−3.07496e6	+	9.82004e6i	−0.172553	+	0.551056i
$796$	−1.14217e7			−0.638921
$797$	−3.85516e6			−0.214979			−0.107490	−	0.994206i	$-0.534281\pi$
$797$	−3.85516e6			−0.214979			−0.107490	+	0.994206i	$0.534281\pi$
$798$	1.87259e7	−	5.98022e7i	1.04097	−	3.32438i
$799$			1.86629e7i			1.03422i
$800$	−1.92066e7			−1.06102
$801$	2.29099e7	+	1.59073e7i	1.26166	+	0.876023i
$802$	4.48090e7			2.45997
$803$		−	2.36706e7i		−	1.29545i
$804$	1.14123e6	+	357354.i	0.0622634	+	0.0194966i
$805$		−	4.34977e7i		−	2.36579i
$806$	−3.22642e6			−0.174937
$807$	9.27698e6	−	2.96265e7i	0.501444	−	1.60139i
$808$	−2.18845e7			−1.17926
$809$	2.03453e7			1.09293			0.546466	−	0.837481i	$-0.315973\pi$
$809$	2.03453e7			1.09293			0.546466	+	0.837481i	$0.315973\pi$
$810$	−4.07777e7	+	1.52074e7i	−2.18379	+	0.814406i
$811$			1.22244e7i			0.652643i	0.945259	+	0.326322i	$0.105809\pi$
$811$			1.22244e7i			0.652643i	−0.945259	+	0.326322i	$0.894191\pi$
$812$		−	5.02115e6i		−	0.267247i
$813$	8.68916e6	−	2.77493e7i	0.461054	−	1.47240i
$814$			2.58049e7i			1.36503i
$815$		−	2.97717e6i		−	0.157004i
$816$	309804.	+	97009.4i	0.0162878	+	0.00510021i
$817$			4.90044e7i			2.56850i
$818$			4.02812e7i			2.10484i
$819$	−1.55411e7	+	2.23825e7i	−0.809604	+	1.16600i
$820$	−6.14109e7			−3.18941
$821$	4.21551e6			0.218269			0.109135	−	0.994027i	$-0.465192\pi$
$821$	4.21551e6			0.218269			0.109135	+	0.994027i	$0.465192\pi$
$822$	−2.16332e7	−	6.77401e6i	−1.11671	−	0.349676i
$823$		−	1.37709e6i		−	0.0708700i	−0.999372	−	0.0354350i	$-0.988718\pi$
$823$		−	1.37709e6i		−	0.0708700i	0.999372	−	0.0354350i	$-0.0112817\pi$
$824$			9.67673e6i			0.496490i
$825$	−1.06307e7	+	3.39497e7i	−0.543785	+	1.73660i
$826$	3.99228e7	+	1.68082e7i	2.03597	+	0.857179i
$827$		−	1.03717e7i		−	0.527332i	−0.964614	−	0.263666i	$-0.915068\pi$
$827$		−	1.03717e7i		−	0.527332i	0.964614	−	0.263666i	$-0.0849317\pi$
$828$	3.17015e7	+	2.20117e7i	1.60696	+	1.11578i
$829$	1.56280e7			0.789800			0.394900	−	0.918724i	$-0.370779\pi$
$829$	1.56280e7			0.789800			0.394900	+	0.918724i	$0.370779\pi$
$830$		−	2.14116e7i		−	1.07883i
$831$	−1.01924e6	+	3.25501e6i	−0.0512007	+	0.163512i
$832$		−	3.35813e7i		−	1.68186i
$833$		−	2.58929e7i		−	1.29291i
$834$	1.40129e7	−	4.47508e7i	0.697609	−	2.22785i
$835$	2.77744e7			1.37857
$836$	8.78903e7			4.34936
$837$	−1.29040e6	−	1.66123e6i	−0.0636665	−	0.0819628i
$838$	5.21581e7			2.56573
$839$	−2.67577e7			−1.31233			−0.656166	−	0.754616i	$-0.727823\pi$
$839$	−2.67577e7			−1.31233			−0.656166	+	0.754616i	$0.727823\pi$
$840$	3.86573e7	+	1.21048e7i	1.89031	+	0.591915i
$841$	2.02122e7			0.985427
$842$			2.96385e7i			1.44071i
$843$	7.40071e6	+	2.31739e6i	0.358678	+	0.112313i
$844$			5.43091e7i			2.62432i
$845$			2.48308e6i			0.119632i
$846$	−1.90597e7	−	1.32340e7i	−0.915567	−	0.635718i
$847$	−5.37531e7			−2.57451
$848$			95433.8i			0.00455735i
$849$	2.51732e7	+	7.88251e6i	1.19859	+	0.375314i
$850$		−	5.49024e7i		−	2.60642i
$851$		−	1.26297e7i		−	0.597818i
$852$	−3.55050e7	−	1.11177e7i	−1.67568	−	0.524707i
$853$	−8.40001e6			−0.395282			−0.197641	−	0.980274i	$-0.563328\pi$
$853$	−8.40001e6			−0.395282			−0.197641	+	0.980274i	$0.563328\pi$
$854$			4.01718e7i			1.88485i
$855$	2.76658e7	−	3.98446e7i	1.29428	−	1.86404i
$856$			1.90996e7i			0.890924i
$857$	−3.03339e7			−1.41084			−0.705418	−	0.708791i	$-0.749241\pi$
$857$	−3.03339e7			−1.41084			−0.705418	+	0.708791i	$0.749241\pi$
$858$	−5.89413e7	−	1.84563e7i	−2.73339	−	0.855908i
$859$		−	2.99135e7i		−	1.38320i	−0.722282	−	0.691599i	$-0.756907\pi$
$859$		−	2.99135e7i		−	1.38320i	0.722282	−	0.691599i	$-0.243093\pi$
$860$	−8.25156e7			−3.80443
$861$	−3.86617e7	−	1.21062e7i	−1.77735	−	0.556543i
$862$	−3.26316e7			−1.49579
$863$	−2.03487e7			−0.930057			−0.465028	−	0.885296i	$-0.653956\pi$
$863$	−2.03487e7			−0.930057			−0.465028	+	0.885296i	$0.653956\pi$
$864$	1.71690e7	−	1.33364e7i	0.782455	−	0.607791i
$865$		−	1.55874e7i		−	0.708327i
$866$	3.03994e7			1.37743
$867$	8.32220e6	−	2.65774e7i	0.376002	−	1.20078i
$868$			5.10009e6i			0.229762i
$869$	1.05239e7			0.472747
$870$	1.87702e6	−	5.99436e6i	0.0840758	−	0.268500i
$871$	936665.			0.0418349
$872$		−	1.29932e7i		−	0.578660i
$873$	−7.84168e6	+	1.12937e7i	−0.348236	+	0.501533i
$874$	−6.95185e7			−3.07838
$875$		−	3.15160e6i		−	0.139159i
$876$	−2.68196e7	−	8.39804e6i	−1.18084	−	0.369758i
$877$	1.00416e7			0.440862			0.220431	−	0.975403i	$-0.429254\pi$
$877$	1.00416e7			0.440862			0.220431	+	0.975403i	$0.429254\pi$
$878$	−6.77545e6			−0.296621
$879$	−7.98598e6	−	2.50066e6i	−0.348623	−	0.109165i
$880$			638021.i			0.0277734i
$881$	6.45168e6			0.280049			0.140024	−	0.990148i	$-0.455282\pi$
$881$	6.45168e6			0.280049			0.140024	+	0.990148i	$0.455282\pi$
$882$	2.64435e7	+	1.83609e7i	1.14458	+	0.794733i
$883$	−9.07122e6			−0.391529			−0.195764	−	0.980651i	$-0.562719\pi$
$883$	−9.07122e6			−0.391529			−0.195764	+	0.980651i	$0.562719\pi$
$884$	5.89801e7			2.53849
$885$	2.56032e7	+	2.16509e7i	1.09884	+	0.929217i
$886$	−4.14268e7			−1.77295
$887$	3.36299e7			1.43521			0.717607	−	0.696448i	$-0.245237\pi$
$887$	3.36299e7			1.43521			0.717607	+	0.696448i	$0.245237\pi$
$888$	1.12243e7	+	3.51466e6i	0.477667	+	0.149572i
$889$	3.57406e7			1.51673
$890$		−	8.45948e7i		−	3.57988i
$891$	−1.40706e7	−	3.77295e7i	−0.593770	−	1.59216i
$892$	1.00633e7			0.423477
$893$	2.58623e7			1.08527
$894$	−8.33898e6	+	2.66310e7i	−0.348955	+	1.11440i
$895$			4.49393e7i			1.87529i
$896$	−5.33128e7			−2.21851
$897$	2.88476e7	+	9.03308e6i	1.19709	+	0.374848i
$898$		−	9.14875e6i		−	0.378591i
$899$	303601.			0.0125286
$900$	3.46944e7	+	2.40898e7i	1.42775	+	0.991351i
$901$	1.46936e7			0.602998
$902$		−	9.18277e7i		−	3.75800i
$903$	−5.19483e7	−	1.62666e7i	−2.12008	−	0.663862i
$904$	1.91534e7			0.779517
$905$		−	4.57920e7i		−	1.85852i
$906$	4.73266e7	+	1.48194e7i	1.91551	+	0.599806i
$907$	−1.29181e7			−0.521411			−0.260706	−	0.965418i	$-0.583955\pi$
$907$	−1.29181e7			−0.521411			−0.260706	+	0.965418i	$0.583955\pi$
$908$	−4.62403e7			−1.86126
$909$	−2.39118e7	−	1.66030e7i	−0.959846	−	0.666463i
$910$	8.26475e7			3.30846
$911$			4.76727e7i			1.90315i	0.307414	+	0.951576i	$0.400536\pi$
$911$			4.76727e7i			1.90315i	−0.307414	+	0.951576i	$0.599464\pi$
$912$	134432.	−	429315.i	0.00535199	−	0.0170919i
$913$	1.98111e7			0.786558
$914$		−	2.36660e7i		−	0.937042i
$915$	−9.29217e6	+	2.96750e7i	−0.366914	+	1.17176i
$916$		−	1.84044e7i		−	0.724740i
$917$	9.46752e6			0.371803
$918$	3.81223e7	+	4.90778e7i	1.49304	+	1.92211i
$919$			2.63343e7i			1.02857i	0.857620	+	0.514284i	$0.171942\pi$
$919$			2.63343e7i			1.02857i	−0.857620	+	0.514284i	$0.828058\pi$
$920$		−	4.49381e7i		−	1.75043i
$921$	−3.83617e6	+	1.22510e7i	−0.149021	+	0.475907i
$922$		−	5.19950e7i		−	2.01435i
$923$	−2.91408e7			−1.12589
$924$	−2.91745e7	+	9.31702e7i	−1.12415	+	3.59002i
$925$		−	1.38220e7i		−	0.531151i
$926$			6.80431e7i			2.60769i
$927$	−7.34137e6	+	1.05731e7i	−0.280594	+	0.404114i
$928$			3.13774e6i			0.119604i
$929$	−3.17535e7			−1.20713			−0.603563	−	0.797315i	$-0.706253\pi$
$929$	−3.17535e7			−1.20713			−0.603563	+	0.797315i	$0.706253\pi$
$930$	−1.90653e6	+	6.08860e6i	−0.0722830	+	0.230840i
$931$	−3.58814e7			−1.35674
$932$	−1.11288e7			−0.419669
$933$	1.81960e7	+	5.69774e6i	0.684340	+	0.214288i
$934$	−2.70353e7			−1.01406
$935$	9.82338e7			3.67478
$936$	−1.60557e7	+	2.31236e7i	−0.599019	+	0.862714i
$937$			4.23600e7i			1.57618i	0.615557	+	0.788092i	$0.288931\pi$
$937$			4.23600e7i			1.57618i	−0.615557	+	0.788092i	$0.711069\pi$
$938$		−	2.39283e6i		−	0.0887982i
$939$	−6.65485e6	−	2.08384e6i	−0.246306	−	0.0771259i
$940$			4.35480e7i			1.60749i
$941$	−7.02325e6			−0.258562			−0.129281	−	0.991608i	$-0.541267\pi$
$941$	−7.02325e6			−0.258562			−0.129281	+	0.991608i	$0.541267\pi$
$942$	−6.50715e7	−	2.03759e7i	−2.38926	−	0.748152i
$943$			4.49432e7i			1.64583i
$944$	286602.	+	120665.i	0.0104677	+	0.00440708i
$945$	3.30548e7	+	4.25539e7i	1.20408	+	1.55010i
$946$		−	1.23386e8i		−	4.48267i
$947$			4.28301e6i			0.155194i	0.996985	+	0.0775968i	$0.0247247\pi$
$947$			4.28301e6i			0.155194i	−0.996985	+	0.0775968i	$0.975275\pi$
$948$	3.73376e6	−	1.19240e7i	0.134935	−	0.430923i
$949$	−2.20122e7			−0.793410
$950$	−7.60817e7			−2.73509
$951$	3.33342e7	+	1.04380e7i	1.19520	+	0.374253i
$952$		−	5.78423e7i		−	2.06849i
$953$			3.13002e7i			1.11639i	0.829710	+	0.558194i	$0.188506\pi$
$953$			3.13002e7i			1.11639i	−0.829710	+	0.558194i	$0.811494\pi$
$954$	−1.04193e7	+	1.50060e7i	−0.370654	+	0.533820i
$955$		−	1.19520e7i		−	0.424064i
$956$			3.43039e7i			1.21394i
$957$	5.54628e6	+	1.73671e6i	0.195759	+	0.0612983i
$958$			2.90137e7i			1.02138i
$959$			2.80665e7i			0.985468i
$960$	−6.33715e7	−	1.98436e7i	−2.21930	−	0.694932i
$961$	2.83208e7			0.989229
$962$	2.39969e7			0.836023
$963$	−1.44902e7	+	2.08689e7i	−0.503510	+	0.725160i
$964$	8.84155e6			0.306433
$965$		−	2.51705e7i		−	0.870109i
$966$	2.30761e7	−	7.36948e7i	0.795646	−	2.54094i
$967$			1.80309e7i			0.620084i	0.950723	+	0.310042i	$0.100343\pi$
$967$			1.80309e7i			0.620084i	−0.950723	+	0.310042i	$0.899657\pi$
$968$	−5.55330e7			−1.90486
$969$	−6.61001e7	−	2.06980e7i	−2.26148	−	0.708139i
$970$	4.17019e7			1.42307
$971$		−	4.65058e7i		−	1.58292i	−0.611221	−	0.791460i	$-0.709321\pi$
$971$		−	4.65058e7i		−	1.58292i	0.611221	−	0.791460i	$-0.290679\pi$
$972$	−4.77408e7	+	2.55647e6i	−1.62078	+	0.0867910i
$973$	−5.80591e7			−1.96602
$974$	4.50356e7			1.52110
$975$	3.15711e7	+	9.88588e6i	1.06360	+	0.333046i
$976$			288390.i			0.00969070i
$977$	−1.84611e7			−0.618758			−0.309379	−	0.950939i	$-0.600121\pi$
$977$	−1.84611e7			−0.618758			−0.309379	+	0.950939i	$0.600121\pi$
$978$	1.57943e6	−	5.04398e6i	0.0528023	−	0.168627i
$979$	7.82713e7			2.61003
$980$		−	6.04186e7i		−	2.00958i
$981$	9.85741e6	−	1.41967e7i	0.327032	−	0.470995i
$982$		−	1.35582e7i		−	0.448665i
$983$	1.41060e7			0.465608			0.232804	−	0.972524i	$-0.425210\pi$
$983$	1.41060e7			0.465608			0.232804	+	0.972524i	$0.425210\pi$
$984$	−3.99419e7	−	1.25070e7i	−1.31505	−	0.411782i
$985$	−4.03664e7			−1.32565
$986$	−8.96928e6			−0.293809
$987$	−8.58478e6	+	2.74159e7i	−0.280502	+	0.895798i
$988$		−	8.17324e7i		−	2.66380i
$989$			6.03885e7i			1.96320i
$990$	−6.96583e7	+	1.00323e8i	−2.25884	+	3.25320i
$991$			5.98869e7i			1.93708i	0.248856	+	0.968540i	$0.419945\pi$
$991$			5.98869e7i			1.93708i	−0.248856	+	0.968540i	$0.580055\pi$
$992$		−	3.18707e6i		−	0.102828i
$993$	1.58872e6	−	5.07366e6i	0.0511298	−	0.163286i
$994$			7.44437e7i			2.38980i
$995$			1.76904e7i			0.566475i
$996$	7.02871e6	−	2.24465e7i	0.224506	−	0.716970i
$997$	−1.79557e7			−0.572092			−0.286046	−	0.958216i	$-0.592341\pi$
$997$	−1.79557e7			−0.572092			−0.286046	+	0.958216i	$0.592341\pi$
$998$	−3.61125e6			−0.114771
$999$	9.59755e6	+	1.23557e7i	0.304261	+	0.391699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.11	✓	92
3.2	odd	2	inner	177.6.d.b.176.82	yes	92
59.58	odd	2	inner	177.6.d.b.176.81	yes	92
177.176	even	2	inner	177.6.d.b.176.12	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.11	✓	92	1.1	even	1	trivial
177.6.d.b.176.12	yes	92	177.176	even	2	inner
177.6.d.b.176.81	yes	92	59.58	odd	2	inner
177.6.d.b.176.82	yes	92	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.16184 q^{2} +(-4.65820 + 14.8762i) q^{3} +51.9393 q^{4} -80.4460i q^{5} +(42.6777 - 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 - 138.593i) q^{9} +O(q^{10})\)	\(q-9.16184 q^{2} +(-4.65820 + 14.8762i) q^{3} +51.9393 q^{4} -80.4460i q^{5} +(42.6777 - 136.293i) q^{6} -176.825 q^{7} -182.680 q^{8} +(-199.602 - 138.593i) q^{9} +737.033i q^{10} -681.939 q^{11} +(-241.943 + 772.659i) q^{12} +634.160i q^{13} +1620.04 q^{14} +(1196.73 + 374.733i) q^{15} +11.6301 q^{16} -1790.65i q^{17} +(1828.72 + 1269.76i) q^{18} -2481.42 q^{19} -4178.30i q^{20} +(823.686 - 2630.48i) q^{21} +6247.82 q^{22} -3057.87 q^{23} +(850.961 - 2717.59i) q^{24} -3346.56 q^{25} -5810.07i q^{26} +(2991.52 - 2323.73i) q^{27} -9184.16 q^{28} +546.719i q^{29} +(-10964.2 - 3433.25i) q^{30} -555.314i q^{31} +5739.21 q^{32} +(3176.61 - 10144.7i) q^{33} +16405.6i q^{34} +14224.9i q^{35} +(-10367.2 - 7198.39i) q^{36} +4130.23i q^{37} +22734.3 q^{38} +(-9433.89 - 2954.05i) q^{39} +14695.9i q^{40} -14697.6i q^{41} +(-7546.48 + 24100.1i) q^{42} -19748.6i q^{43} -35419.4 q^{44} +(-11149.2 + 16057.2i) q^{45} +28015.7 q^{46} -10422.4 q^{47} +(-54.1755 + 173.012i) q^{48} +14460.1 q^{49} +30660.6 q^{50} +(26638.1 + 8341.20i) q^{51} +32937.8i q^{52} +8205.73i q^{53} +(-27407.8 + 21289.7i) q^{54} +54859.3i q^{55} +32302.4 q^{56} +(11558.9 - 36914.0i) q^{57} -5008.95i q^{58} +(24643.1 + 10375.2i) q^{59} +(62157.3 + 19463.4i) q^{60} +24796.7i q^{61} +5087.70i q^{62} +(35294.7 + 24506.6i) q^{63} -52953.9 q^{64} +51015.7 q^{65} +(-29103.6 + 92943.8i) q^{66} -1477.02i q^{67} -93005.0i q^{68} +(14244.2 - 45489.4i) q^{69} -130326. i q^{70} +45951.7i q^{71} +(36463.4 + 25318.1i) q^{72} +34710.8i q^{73} -37840.5i q^{74} +(15588.9 - 49784.0i) q^{75} -128883. q^{76} +120584. q^{77} +(86431.8 + 27064.5i) q^{78} -15432.4 q^{79} -935.598i q^{80} +(20633.2 + 55326.8i) q^{81} +134657. i q^{82} -29051.1 q^{83} +(42781.6 - 136625. i) q^{84} -144051. q^{85} +180933. i q^{86} +(-8133.10 - 2546.73i) q^{87} +124577. q^{88} -114778. q^{89} +(102147. - 147114. i) q^{90} -112135. i q^{91} -158823. q^{92} +(8260.96 + 2586.76i) q^{93} +95488.3 q^{94} +199620. i q^{95} +(-26734.4 + 85377.7i) q^{96} -56580.8i q^{97} -132481. q^{98} +(136117. + 94511.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

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