LMFDB - Embedded newform 177.4.d.c.176.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,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, 4, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.15
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68371 q^{2} +(-3.19645 - 4.09667i) q^{3} -0.797724 q^{4} -15.8157i q^{5} +(8.57832 + 10.9943i) q^{6} +25.4256 q^{7} +23.6105 q^{8} +(-6.56545 + 26.1896i) q^{9} +O(q^{10})$	\(q-2.68371 q^{2} +(-3.19645 - 4.09667i) q^{3} -0.797724 q^{4} -15.8157i q^{5} +(8.57832 + 10.9943i) q^{6} +25.4256 q^{7} +23.6105 q^{8} +(-6.56545 + 26.1896i) q^{9} +42.4446i q^{10} +64.0388 q^{11} +(2.54988 + 3.26801i) q^{12} -26.7287i q^{13} -68.2349 q^{14} +(-64.7916 + 50.5539i) q^{15} -56.9818 q^{16} -54.3878i q^{17} +(17.6197 - 70.2852i) q^{18} +47.4395 q^{19} +12.6165i q^{20} +(-81.2717 - 104.160i) q^{21} -171.861 q^{22} +174.401 q^{23} +(-75.4697 - 96.7245i) q^{24} -125.135 q^{25} +71.7320i q^{26} +(128.276 - 56.8171i) q^{27} -20.2826 q^{28} -169.829i q^{29} +(173.882 - 135.672i) q^{30} +217.458i q^{31} -35.9615 q^{32} +(-204.697 - 262.346i) q^{33} +145.961i q^{34} -402.123i q^{35} +(5.23742 - 20.8921i) q^{36} -122.447i q^{37} -127.314 q^{38} +(-109.499 + 85.4369i) q^{39} -373.416i q^{40} +368.046i q^{41} +(218.109 + 279.536i) q^{42} +3.01728i q^{43} -51.0853 q^{44} +(414.206 + 103.837i) q^{45} -468.041 q^{46} -314.192 q^{47} +(182.139 + 233.436i) q^{48} +303.463 q^{49} +335.826 q^{50} +(-222.809 + 173.848i) q^{51} +21.3221i q^{52} -468.533i q^{53} +(-344.256 + 152.480i) q^{54} -1012.82i q^{55} +600.312 q^{56} +(-151.638 - 194.344i) q^{57} +455.771i q^{58} +(-224.948 - 393.417i) q^{59} +(51.6858 - 40.3281i) q^{60} +558.899i q^{61} -583.593i q^{62} +(-166.931 + 665.887i) q^{63} +552.365 q^{64} -422.733 q^{65} +(549.346 + 704.060i) q^{66} +284.086i q^{67} +43.3865i q^{68} +(-557.464 - 714.464i) q^{69} +1079.18i q^{70} +279.692i q^{71} +(-155.014 + 618.349i) q^{72} +877.906i q^{73} +328.611i q^{74} +(399.988 + 512.638i) q^{75} -37.8436 q^{76} +1628.23 q^{77} +(293.863 - 229.288i) q^{78} -63.0858 q^{79} +901.206i q^{80} +(-642.790 - 343.893i) q^{81} -987.728i q^{82} +941.269 q^{83} +(64.8323 + 83.0913i) q^{84} -860.180 q^{85} -8.09748i q^{86} +(-695.733 + 542.849i) q^{87} +1511.99 q^{88} -199.336 q^{89} +(-1111.61 - 278.668i) q^{90} -679.594i q^{91} -139.124 q^{92} +(890.854 - 695.093i) q^{93} +843.199 q^{94} -750.288i q^{95} +(114.949 + 147.322i) q^{96} -432.568i q^{97} -814.404 q^{98} +(-420.444 + 1677.15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * 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 $

$2$	−2.68371			−0.948833			−0.474417	−	0.880300i	$-0.657341\pi$
$2$	−2.68371			−0.948833			−0.474417	+	0.880300i	$0.657341\pi$
$3$	−3.19645	−	4.09667i	−0.615157	−	0.788405i
$3$	−3.19645	−	4.09667i	−0.615157	−	0.788405i
$4$	−0.797724			−0.0997154
$5$		−	15.8157i		−	1.41460i	−0.706915	−	0.707298i	$-0.749914\pi$
$5$		−	15.8157i		−	1.41460i	0.706915	−	0.707298i	$-0.250086\pi$
$6$	8.57832	+	10.9943i	0.583681	+	0.748065i
$7$	25.4256			1.37285			0.686427	−	0.727198i	$-0.259178\pi$
$7$	25.4256			1.37285			0.686427	+	0.727198i	$0.259178\pi$
$8$	23.6105			1.04345
$9$	−6.56545	+	26.1896i	−0.243165	+	0.969985i
$10$			42.4446i			1.34222i
$11$	64.0388			1.75531			0.877656	−	0.479291i	$-0.159106\pi$
$11$	64.0388			1.75531			0.877656	+	0.479291i	$0.159106\pi$
$12$	2.54988	+	3.26801i	0.0613406	+	0.0786162i
$13$		−	26.7287i		−	0.570247i	−0.958491	−	0.285124i	$-0.907965\pi$
$13$		−	26.7287i		−	0.570247i	0.958491	−	0.285124i	$-0.0920346\pi$
$14$	−68.2349			−1.30261
$15$	−64.7916	+	50.5539i	−1.11527	+	0.870198i
$16$	−56.9818			−0.890341
$17$		−	54.3878i		−	0.775940i	−0.921672	−	0.387970i	$-0.873176\pi$
$17$		−	54.3878i		−	0.775940i	0.921672	−	0.387970i	$-0.126824\pi$
$18$	17.6197	−	70.2852i	0.230723	−	0.920354i
$19$	47.4395			0.572809			0.286405	−	0.958109i	$-0.407540\pi$
$19$	47.4395			0.572809			0.286405	+	0.958109i	$0.407540\pi$
$20$			12.6165i			0.141057i
$21$	−81.2717	−	104.160i	−0.844521	−	1.08237i
$22$	−171.861			−1.66550
$23$	174.401			1.58109			0.790546	−	0.612402i	$-0.209797\pi$
$23$	174.401			1.58109			0.790546	+	0.612402i	$0.209797\pi$
$24$	−75.4697	−	96.7245i	−0.641883	−	0.822659i
$25$	−125.135			−1.00108
$26$			71.7320i			0.541069i
$27$	128.276	−	56.8171i	0.914325	−	0.404980i
$28$	−20.2826			−0.136895
$29$		−	169.829i		−	1.08746i	−0.839259	−	0.543732i	$-0.817011\pi$
$29$		−	169.829i		−	1.08746i	0.839259	−	0.543732i	$-0.182989\pi$
$30$	173.882	−	135.672i	1.05821	−	0.825673i
$31$			217.458i			1.25989i	0.776639	+	0.629945i	$0.216923\pi$
$31$			217.458i			1.25989i	−0.776639	+	0.629945i	$0.783077\pi$
$32$	−35.9615			−0.198661
$33$	−204.697	−	262.346i	−1.07979	−	1.38390i
$34$			145.961i			0.736238i
$35$		−	402.123i		−	1.94204i
$36$	5.23742	−	20.8921i	0.0242473	−	0.0967225i
$37$		−	122.447i		−	0.544057i	−0.962289	−	0.272028i	$-0.912306\pi$
$37$		−	122.447i		−	0.544057i	0.962289	−	0.272028i	$-0.0876944\pi$
$38$	−127.314			−0.543500
$39$	−109.499	+	85.4369i	−0.449586	+	0.350791i
$40$		−	373.416i		−	1.47606i
$41$			368.046i			1.40193i	0.713195	+	0.700966i	$0.247247\pi$
$41$			368.046i			1.40193i	−0.713195	+	0.700966i	$0.752753\pi$
$42$	218.109	+	279.536i	0.801309	+	1.02698i
$43$			3.01728i			0.0107007i	0.999986	+	0.00535035i	$0.00170308\pi$
$43$			3.01728i			0.0107007i	−0.999986	+	0.00535035i	$0.998297\pi$
$44$	−51.0853			−0.175032
$45$	414.206	+	103.837i	1.37214	+	0.343980i
$46$	−468.041			−1.50019
$47$	−314.192			−0.975098			−0.487549	−	0.873096i	$-0.662109\pi$
$47$	−314.192			−0.975098			−0.487549	+	0.873096i	$0.662109\pi$
$48$	182.139	+	233.436i	0.547699	+	0.701950i
$49$	303.463			0.884731
$50$	335.826			0.949860
$51$	−222.809	+	173.848i	−0.611755	+	0.477325i
$52$			21.3221i			0.0568624i
$53$		−	468.533i		−	1.21430i	−0.794587	−	0.607150i	$-0.792313\pi$
$53$		−	468.533i		−	1.21430i	0.794587	−	0.607150i	$-0.207687\pi$
$54$	−344.256	+	152.480i	−0.867542	+	0.384259i
$55$		−	1012.82i		−	2.48306i
$56$	600.312			1.43250
$57$	−151.638	−	194.344i	−0.352367	−	0.451606i
$58$			455.771i			1.03182i
$59$	−224.948	−	393.417i	−0.496369	−	0.868112i
$59$	−224.948	−	393.417i	−0.496369	−	0.868112i
$60$	51.6858	−	40.3281i	0.111210	−	0.0867722i
$61$			558.899i			1.17311i	0.809910	+	0.586554i	$0.199516\pi$
$61$			558.899i			1.17311i	−0.809910	+	0.586554i	$0.800484\pi$
$62$		−	583.593i		−	1.19543i
$63$	−166.931	+	665.887i	−0.333830	+	1.33165i
$64$	552.365			1.07884
$65$	−422.733			−0.806669
$66$	549.346	+	704.060i	1.02454	+	1.31309i
$67$			284.086i			0.518009i	0.965876	+	0.259004i	$0.0833944\pi$
$67$			284.086i			0.518009i	−0.965876	+	0.259004i	$0.916606\pi$
$68$			43.3865i			0.0773732i
$69$	−557.464	−	714.464i	−0.972619	−	1.24654i
$70$			1079.18i			1.84267i
$71$			279.692i			0.467512i	0.972295	+	0.233756i	$0.0751017\pi$
$71$			279.692i			0.467512i	−0.972295	+	0.233756i	$0.924898\pi$
$72$	−155.014	+	618.349i	−0.253730	+	1.01213i
$73$			877.906i			1.40755i	0.710423	+	0.703775i	$0.248504\pi$
$73$			877.906i			1.40755i	−0.710423	+	0.703775i	$0.751496\pi$
$74$			328.611i			0.516219i
$75$	399.988	+	512.638i	0.615822	+	0.789258i
$76$	−37.8436			−0.0571179
$77$	1628.23			2.40979
$78$	293.863	−	229.288i	0.426582	−	0.332842i
$79$	−63.0858			−0.0898445			−0.0449222	−	0.998990i	$-0.514304\pi$
$79$	−63.0858			−0.0898445			−0.0449222	+	0.998990i	$0.514304\pi$
$80$			901.206i			1.25947i
$81$	−642.790	−	343.893i	−0.881742	−	0.471733i
$82$		−	987.728i		−	1.33020i
$83$	941.269			1.24479			0.622396	−	0.782703i	$-0.286159\pi$
$83$	941.269			1.24479			0.622396	+	0.782703i	$0.286159\pi$
$84$	64.8323	+	83.0913i	0.0842118	+	0.107929i
$85$	−860.180			−1.09764
$86$		−	8.09748i		−	0.0101532i
$87$	−695.733	+	542.849i	−0.857361	+	0.668960i
$88$	1511.99			1.83157
$89$	−199.336			−0.237411			−0.118706	−	0.992930i	$-0.537874\pi$
$89$	−199.336			−0.237411			−0.118706	+	0.992930i	$0.537874\pi$
$90$	−1111.61	−	278.668i	−1.30193	−	0.326380i
$91$		−	679.594i		−	0.782867i
$92$	−139.124			−0.157659
$93$	890.854	−	695.093i	0.993304	−	0.775030i
$94$	843.199			0.925206
$95$		−	750.288i		−	0.810294i
$96$	114.949	+	147.322i	0.122208	+	0.156625i
$97$		−	432.568i		−	0.452790i	−0.974036	−	0.226395i	$-0.927306\pi$
$97$		−	432.568i		−	0.452790i	0.974036	−	0.226395i	$-0.0726939\pi$
$98$	−814.404			−0.839462
$99$	−420.444	+	1677.15i	−0.426830	+	1.70263i
$100$	99.8234			0.0998234
$101$	−1768.19			−1.74200			−0.870999	−	0.491285i	$-0.836528\pi$
$101$	−1768.19			−1.74200			−0.870999	+	0.491285i	$0.836528\pi$
$102$	597.954	−	466.556i	0.580454	−	0.452902i
$103$			947.121i			0.906044i	0.891499	+	0.453022i	$0.149654\pi$
$103$			947.121i			0.906044i	−0.891499	+	0.453022i	$0.850346\pi$
$104$		−	631.078i		−	0.595022i
$105$	−1647.37	+	1285.37i	−1.53111	+	1.19466i
$106$			1257.40i			1.15217i
$107$		−	1078.46i		−	0.974379i	−0.873296	−	0.487190i	$-0.838022\pi$
$107$		−	1078.46i		−	0.974379i	0.873296	−	0.487190i	$-0.161978\pi$
$108$	−102.329	+	45.3244i	−0.0911724	+	0.0403828i
$109$		−	1042.51i		−	0.916096i	−0.888927	−	0.458048i	$-0.848549\pi$
$109$		−	1042.51i		−	0.916096i	0.888927	−	0.458048i	$-0.151451\pi$
$110$			2718.10i			2.35601i
$111$	−501.624	+	391.394i	−0.428937	+	0.334680i
$112$	−1448.80			−1.22231
$113$	733.402			0.610555			0.305277	−	0.952263i	$-0.401251\pi$
$113$	733.402			0.610555			0.305277	+	0.952263i	$0.401251\pi$
$114$	406.952	+	521.563i	0.334338	+	0.428498i
$115$		−	2758.27i		−	2.23661i
$116$			135.476i			0.108437i
$117$	700.014	+	175.486i	0.553131	+	0.138664i
$118$	603.695	+	1055.82i	0.470972	+	0.823693i
$119$		−	1382.84i		−	1.06525i
$120$	−1529.76	+	1193.60i	−1.16373	+	0.908005i
$121$	2769.97			2.08112
$122$		−	1499.92i		−	1.11308i
$123$	1507.77	−	1176.44i	1.10529	−	0.862407i
$124$		−	173.471i		−	0.125631i
$125$			2.14016i			0.00153137i
$126$	447.993	−	1787.04i	0.316749	−	1.26351i
$127$	−365.016			−0.255039			−0.127520	−	0.991836i	$-0.540702\pi$
$127$	−365.016			−0.255039			−0.127520	+	0.991836i	$0.540702\pi$
$128$	−1194.69			−0.824976
$129$	12.3608	−	9.64457i	0.00843649	−	0.00658261i
$130$	1134.49			0.765395
$131$	263.810			0.175948			0.0879741	−	0.996123i	$-0.471961\pi$
$131$	263.810			0.175948			0.0879741	+	0.996123i	$0.471961\pi$
$132$	163.291	+	209.280i	0.107672	+	0.137996i
$133$	1206.18			0.786384
$134$		−	762.403i		−	0.491504i
$135$	−898.601	−	2028.78i	−0.572883	−	1.29340i
$136$		−	1284.12i		−	0.809652i
$137$			1218.37i			0.759799i	0.925028	+	0.379900i	$0.124041\pi$
$137$			1218.37i			0.759799i	−0.925028	+	0.379900i	$0.875959\pi$
$138$	1496.07	+	1917.41i	0.922854	+	1.18276i
$139$	−1137.74			−0.694256			−0.347128	−	0.937818i	$-0.612843\pi$
$139$	−1137.74			−0.694256			−0.347128	+	0.937818i	$0.612843\pi$
$140$			320.783i			0.193651i
$141$	1004.30	+	1287.14i	0.599838	+	0.768772i
$142$		−	750.612i		−	0.443591i
$143$		−	1711.68i		−	1.00096i
$144$	374.112	−	1492.33i	0.216500	−	0.863618i
$145$	−2685.96			−1.53832
$146$		−	2356.04i		−	1.33553i
$147$	−970.002	−	1243.19i	−0.544248	−	0.697526i
$148$			97.6785i			0.0542509i
$149$	−991.213			−0.544989			−0.272494	−	0.962157i	$-0.587849\pi$
$149$	−991.213			−0.544989			−0.272494	+	0.962157i	$0.587849\pi$
$150$	−1073.45	−	1375.77i	−0.584313	−	0.748875i
$151$		−	3527.16i		−	1.90090i	−0.310874	−	0.950451i	$-0.600622\pi$
$151$		−	3527.16i		−	1.90090i	0.310874	−	0.950451i	$-0.399378\pi$
$152$	1120.07			0.597696
$153$	1424.40	+	357.081i	0.752650	+	0.188681i
$154$	−4369.68			−2.28649
$155$	3439.24			1.78224
$156$	87.3498	−	68.1551i	0.0448306	−	0.0349793i
$157$			1442.44i			0.733241i	0.930371	+	0.366621i	$0.119485\pi$
$157$			1442.44i			0.733241i	−0.930371	+	0.366621i	$0.880515\pi$
$158$	169.304			0.0852474
$159$	−1919.43	+	1497.64i	−0.957361	+	0.746985i
$160$			568.755i			0.281025i
$161$	4434.26			2.17061
$162$	1725.06	+	922.908i	0.836626	+	0.447596i
$163$	−2181.89			−1.04846			−0.524229	−	0.851577i	$-0.675646\pi$
$163$	−2181.89			−1.04846			−0.524229	+	0.851577i	$0.675646\pi$
$164$		−	293.599i		−	0.139794i
$165$	−4149.18	+	3237.41i	−1.95766	+	1.52747i
$166$	−2526.09			−1.18110
$167$			2121.08i			0.982840i	0.870923	+	0.491420i	$0.163522\pi$
$167$			2121.08i			0.982840i	−0.870923	+	0.491420i	$0.836478\pi$
$168$	−1918.86	−	2459.28i	−0.881212	−	1.12939i
$169$	1482.58			0.674818
$170$	2308.47			1.04148
$171$	−311.462	+	1242.42i	−0.139287	+	0.555616i
$172$		−	2.40695i		−	0.00106703i
$173$	−3125.58			−1.37360			−0.686801	−	0.726845i	$-0.740986\pi$
$173$	−3125.58			−1.37360			−0.686801	+	0.726845i	$0.740986\pi$
$174$	1867.14	−	1456.85i	0.813493	−	0.634732i
$175$	−3181.64			−1.37434
$176$	−3649.05			−1.56283
$177$	−892.667	+	2179.08i	−0.379079	+	0.925364i
$178$	534.959			0.225263
$179$	−509.207			−0.212625			−0.106313	−	0.994333i	$-0.533904\pi$
$179$	−509.207			−0.212625			−0.106313	+	0.994333i	$0.533904\pi$
$180$	−330.422	−	82.8332i	−0.136823	−	0.0343001i
$181$	454.608			0.186689			0.0933445	−	0.995634i	$-0.470244\pi$
$181$	454.608			0.186689			0.0933445	+	0.995634i	$0.470244\pi$
$182$			1823.83i			0.742810i
$183$	2289.62	−	1786.49i	0.924885	−	0.721645i
$184$	4117.70			1.64979
$185$	−1936.57			−0.769621
$186$	−2390.79	+	1865.43i	−0.942480	+	0.735374i
$187$		−	3482.93i		−	1.36202i
$188$	250.638			0.0972324
$189$	3261.51	−	1444.61i	1.25524	−	0.555979i
$190$			2013.55i			0.768833i
$191$	162.666			0.0616234			0.0308117	−	0.999525i	$-0.490191\pi$
$191$	162.666			0.0616234			0.0308117	+	0.999525i	$0.490191\pi$
$192$	−1765.61	−	2262.86i	−0.663654	−	0.850561i
$193$	−2139.02			−0.797773			−0.398887	−	0.917000i	$-0.630603\pi$
$193$	−2139.02			−0.797773			−0.398887	+	0.917000i	$0.630603\pi$
$194$			1160.88i			0.429622i
$195$	1351.24	+	1731.80i	0.496228	+	0.635982i
$196$	−242.079			−0.0882213
$197$			5343.19i			1.93242i	0.257755	+	0.966210i	$0.417017\pi$
$197$			5343.19i			1.93242i	−0.257755	+	0.966210i	$0.582983\pi$
$198$	1128.35	−	4500.98i	0.404991	−	1.61551i
$199$	−3654.95			−1.30197			−0.650987	−	0.759089i	$-0.725645\pi$
$199$	−3654.95			−1.30197			−0.650987	+	0.759089i	$0.725645\pi$
$200$	−2954.51			−1.04458
$201$	1163.81	−	908.065i	0.408401	−	0.318657i
$202$	4745.31			1.65287
$203$		−	4318.01i		−	1.49293i
$204$	177.740	−	138.682i	0.0610014	−	0.0475967i
$205$	5820.90			1.98317
$206$		−	2541.79i		−	0.859685i
$207$	−1145.02	+	4567.49i	−0.384466	+	1.53364i
$208$			1523.05i			0.507715i
$209$	3037.97			1.00546
$210$	4421.05	−	3449.54i	1.45277	−	1.13353i
$211$			3655.96i			1.19283i	0.802677	+	0.596415i	$0.203409\pi$
$211$			3655.96i			1.19283i	−0.802677	+	0.596415i	$0.796591\pi$
$212$			373.760i			0.121085i
$213$	1145.81	−	894.022i	0.368589	−	0.287593i
$214$			2894.27i			0.924524i
$215$	47.7202			0.0151372
$216$	3028.67	−	1341.48i	0.954050	−	0.422575i
$217$			5529.01i			1.72965i
$218$			2797.79i			0.869222i
$219$	3596.49	−	2806.18i	1.10972	−	0.865864i
$220$			807.948i			0.247599i
$221$	−1453.72			−0.442478
$222$	1346.21	−	1050.39i	0.406990	−	0.317556i
$223$	111.332			0.0334319			0.0167160	−	0.999860i	$-0.494679\pi$
$223$	111.332			0.0334319			0.0167160	+	0.999860i	$0.494679\pi$
$224$	−914.344			−0.272733
$225$	821.570	−	3277.24i	0.243428	−	0.971035i
$226$	−1968.24			−0.579315
$227$	1122.58			0.328229			0.164115	−	0.986441i	$-0.447523\pi$
$227$	1122.58			0.328229			0.164115	+	0.986441i	$0.447523\pi$
$228$	120.965	+	155.033i	0.0351365	+	0.0450320i
$229$			113.487i			0.0327485i	0.999866	+	0.0163743i	$0.00521232\pi$
$229$			113.487i			0.0327485i	−0.999866	+	0.0163743i	$0.994788\pi$
$230$			7402.38i			2.12217i
$231$	−5204.54	−	6670.31i	−1.48240	−	1.89989i
$232$		−	4009.74i		−	1.13471i
$233$	704.563			0.198101			0.0990503	−	0.995082i	$-0.468420\pi$
$233$	704.563			0.198101			0.0990503	+	0.995082i	$0.468420\pi$
$234$	−1878.63	−	470.953i	−0.524829	−	0.131569i
$235$			4969.16i			1.37937i
$236$	179.447	+	313.838i	0.0494957	+	0.0865641i
$237$	201.651	+	258.442i	0.0552684	+	0.0708338i
$238$			3711.15i			1.01075i
$239$			5082.40i			1.37554i	0.725930	+	0.687768i	$0.241409\pi$
$239$			5082.40i			1.37554i	−0.725930	+	0.687768i	$0.758591\pi$
$240$	3691.95	−	2880.66i	0.992975	−	0.774773i
$241$	3832.06			1.02425			0.512126	−	0.858910i	$-0.328858\pi$
$241$	3832.06			1.02425			0.512126	+	0.858910i	$0.328858\pi$
$242$	−7433.79			−1.97464
$243$	645.826	+	3732.53i	0.170493	+	0.985359i
$244$		−	445.847i		−	0.116977i
$245$		−	4799.46i		−	1.25154i
$246$	−4046.40	+	3157.22i	−1.04874	+	0.818281i
$247$		−	1268.00i		−	0.326643i
$248$			5134.29i			1.31463i
$249$	−3008.72	−	3856.07i	−0.765742	−	0.981400i
$250$		−	5.74355i		−	0.00145302i
$251$		−	2141.56i		−	0.538542i	−0.963064	−	0.269271i	$-0.913217\pi$
$251$		−	2141.56i		−	0.538542i	0.963064	−	0.269271i	$-0.0867828\pi$
$252$	133.165	−	531.194i	0.0332880	−	0.132786i
$253$	11168.4			2.77531
$254$	979.596			0.241990
$255$	2749.52	+	3523.87i	0.675222	+	0.865387i
$256$	−1212.72			−0.296073
$257$		−	2229.18i		−	0.541059i	−0.962712	−	0.270530i	$-0.912801\pi$
$257$		−	2229.18i		−	0.541059i	0.962712	−	0.270530i	$-0.0871988\pi$
$258$	−33.1727	+	25.8832i	−0.00800482	+	0.00624580i
$259$		−	3113.28i		−	0.746911i
$260$	337.224			0.0804374
$261$	4447.75	+	1115.00i	1.05482	+	0.264433i
$262$	−707.989			−0.166945
$263$			2699.89i			0.633013i	0.948590	+	0.316506i	$0.102510\pi$
$263$			2699.89i			0.633013i	−0.948590	+	0.316506i	$0.897490\pi$
$264$	−4832.99	−	6194.12i	−1.12670	−	1.44402i
$265$	−7410.16			−1.71775
$266$	−3237.03			−0.746147
$267$	637.167	+	816.615i	0.146045	+	0.187176i
$268$		−	226.622i		−	0.0516535i
$269$	−6427.83			−1.45692			−0.728460	−	0.685088i	$-0.759764\pi$
$269$	−6427.83			−1.45692			−0.728460	+	0.685088i	$0.759764\pi$
$270$	2411.58	+	5444.64i	0.543571	+	1.22722i
$271$	−2588.09			−0.580130			−0.290065	−	0.957007i	$-0.593677\pi$
$271$	−2588.09			−0.580130			−0.290065	+	0.957007i	$0.593677\pi$
$272$			3099.12i			0.690852i
$273$	−2784.08	+	2172.29i	−0.617216	+	0.481585i
$274$		−	3269.75i		−	0.720923i
$275$	−8013.52			−1.75721
$276$	444.702	+	569.945i	0.0969852	+	0.124299i
$277$	7307.96			1.58517			0.792586	−	0.609760i	$-0.208734\pi$
$277$	7307.96			1.58517			0.792586	+	0.609760i	$0.208734\pi$
$278$	3053.35			0.658733
$279$	−5695.14	−	1427.71i	−1.22208	−	0.306361i
$280$		−	9494.33i		−	2.02641i
$281$		−	4020.21i		−	0.853472i	−0.904376	−	0.426736i	$-0.859663\pi$
$281$		−	4020.21i		−	0.853472i	0.904376	−	0.426736i	$-0.140337\pi$
$282$	−2695.24	−	3454.31i	−0.569146	−	0.729437i
$283$			246.102i			0.0516934i	0.999666	+	0.0258467i	$0.00822817\pi$
$283$			246.102i			0.0516934i	−0.999666	+	0.0258467i	$0.991772\pi$
$284$		−	223.117i		−	0.0466182i
$285$	−3073.68	+	2398.25i	−0.638839	+	0.498457i
$286$			4593.63i			0.949746i
$287$			9357.81i			1.92465i
$288$	236.103	−	941.817i	0.0483074	−	0.192698i
$289$	1954.96			0.397917
$290$	7208.32			1.45961
$291$	−1772.09	+	1382.68i	−0.356982	+	0.278536i
$292$		−	700.326i		−	0.140354i
$293$			3404.05i			0.678726i	0.940656	+	0.339363i	$0.110211\pi$
$293$			3404.05i			0.678726i	−0.940656	+	0.339363i	$0.889789\pi$
$294$	2603.20	+	3336.35i	0.516400	+	0.661836i
$295$	−6222.16	+	3557.71i	−1.22803	+	0.702162i
$296$		−	2891.03i		−	0.567694i
$297$	8214.66	−	3638.50i	1.60493	−	0.710866i
$298$	2660.12			0.517103
$299$		−	4661.52i		−	0.901614i
$300$	−319.080	−	408.944i	−0.0614070	−	0.0787013i
$301$			76.7162i			0.0146905i
$302$			9465.86i			1.80364i
$303$	5651.94	+	7243.71i	1.07160	+	1.37340i
$304$	−2703.19			−0.509996
$305$	8839.35			1.65948
$306$	−3822.66	−	958.300i	−0.714140	−	0.179027i
$307$	4099.88			0.762190			0.381095	−	0.924536i	$-0.375547\pi$
$307$	4099.88			0.762190			0.381095	+	0.924536i	$0.375547\pi$
$308$	−1298.88			−0.240293
$309$	3880.04	−	3027.42i	0.714330	−	0.557359i
$310$	−9229.92			−1.69105
$311$		−	1445.91i		−	0.263633i	−0.991274	−	0.131817i	$-0.957919\pi$
$311$		−	1445.91i		−	0.263633i	0.991274	−	0.131817i	$-0.0420810\pi$
$312$	−2585.32	+	2017.21i	−0.469119	+	0.366032i
$313$		−	1949.24i		−	0.352005i	−0.984390	−	0.176002i	$-0.943683\pi$
$313$		−	1949.24i		−	0.352005i	0.984390	−	0.176002i	$-0.0563166\pi$
$314$		−	3871.07i		−	0.695724i
$315$	10531.4	+	2640.12i	1.88375	+	0.472235i
$316$	50.3251			0.00895888
$317$		−	8787.37i		−	1.55693i	−0.627686	−	0.778466i	$-0.715998\pi$
$317$		−	8787.37i		−	1.55693i	0.627686	−	0.778466i	$-0.284002\pi$
$318$	5151.17	−	4019.23i	0.908376	−	0.708764i
$319$		−	10875.6i		−	1.90884i
$320$		−	8736.02i		−	1.52612i
$321$	−4418.09	+	3447.24i	−0.768206	+	0.599396i
$322$	−11900.2			−2.05955
$323$		−	2580.13i		−	0.444466i
$324$	512.768	+	274.332i	0.0879233	+	0.0470390i
$325$			3344.71i			0.570864i
$326$	5855.54			0.994811
$327$	−4270.83	+	3332.33i	−0.722255	+	0.563542i
$328$			8689.76i			1.46284i
$329$	−7988.53			−1.33867
$330$	11135.2	−	8688.27i	1.85749	−	1.44931i
$331$	−2972.50			−0.493606			−0.246803	−	0.969066i	$-0.579380\pi$
$331$	−2972.50			−0.493606			−0.246803	+	0.969066i	$0.579380\pi$
$332$	−750.873			−0.124125
$333$	3206.83	+	803.917i	0.527727	+	0.132295i
$334$		−	5692.36i		−	0.932552i
$335$	4493.01			0.732773
$336$	4631.01	+	5935.26i	0.751912	+	0.963675i
$337$			4402.05i			0.711558i	0.934570	+	0.355779i	$0.115784\pi$
$337$			4402.05i			0.711558i	−0.934570	+	0.355779i	$0.884216\pi$
$338$	−3978.80			−0.640290
$339$	−2344.28	−	3004.51i	−0.375587	−	0.481364i
$340$	686.186			0.109452
$341$			13925.8i			2.21150i
$342$	835.872	−	3334.29i	0.132160	−	0.527187i
$343$	−1005.26			−0.158248
$344$			71.2394i			0.0111656i
$345$	−11299.7	+	8816.66i	−1.76335	+	1.37586i
$346$	8388.13			1.30332
$347$	4806.25			0.743554			0.371777	−	0.928322i	$-0.378749\pi$
$347$	4806.25			0.743554			0.371777	+	0.928322i	$0.378749\pi$
$348$	555.003	−	433.043i	0.0854922	−	0.0667056i
$349$			9011.33i			1.38214i	0.722790	+	0.691068i	$0.242859\pi$
$349$			9011.33i			1.38214i	−0.722790	+	0.691068i	$0.757141\pi$
$350$	8538.60			1.30402
$351$	−1518.65	−	3428.66i	−0.230939	−	0.521391i
$352$	−2302.93			−0.348712
$353$	−11298.7			−1.70359			−0.851797	−	0.523872i	$-0.824487\pi$
$353$	−11298.7			−1.70359			−0.851797	+	0.523872i	$0.824487\pi$
$354$	2395.66	−	5848.00i	0.359683	−	0.878017i
$355$	4423.52			0.661341
$356$	159.015			0.0236735
$357$	−5665.06	+	4420.19i	−0.839851	+	0.655298i
$358$	1366.56			0.201746
$359$		−	7880.94i		−	1.15861i	−0.815112	−	0.579304i	$-0.803324\pi$
$359$		−	7880.94i		−	1.15861i	0.815112	−	0.579304i	$-0.196676\pi$
$360$	9779.61	+	2451.64i	1.43175	+	0.358925i
$361$	−4608.49			−0.671890
$362$	−1220.03			−0.177137
$363$	−8854.06	−	11347.7i	−1.28021	−	1.64077i
$364$			542.129i			0.0780639i
$365$	13884.7			1.99111
$366$	−6144.68	+	4794.41i	−0.877561	+	0.684721i
$367$			4266.06i			0.606775i	0.952867	+	0.303388i	$0.0981177\pi$
$367$			4266.06i			0.606775i	−0.952867	+	0.303388i	$0.901882\pi$
$368$	−9937.69			−1.40771
$369$	−9638.99	−	2416.39i	−1.35985	−	0.340901i
$370$	5197.20			0.730242
$371$		−	11912.7i		−	1.66706i
$372$	−710.656	+	554.492i	−0.0990478	+	0.0772825i
$373$	5386.56			0.747736			0.373868	−	0.927482i	$-0.378031\pi$
$373$	5386.56			0.747736			0.373868	+	0.927482i	$0.378031\pi$
$374$			9347.17i			1.29233i
$375$	8.76751	−	6.84089i	0.00120734	−	0.000942032i
$376$	−7418.23			−1.01746
$377$	−4539.31			−0.620123
$378$	−8752.92	+	3876.91i	−1.19101	+	0.527531i
$379$	−2251.27			−0.305119			−0.152560	−	0.988294i	$-0.548752\pi$
$379$	−2251.27			−0.305119			−0.152560	+	0.988294i	$0.548752\pi$
$380$			598.522i			0.0807988i
$381$	1166.76	+	1495.35i	0.156889	+	0.201074i
$382$	−436.547			−0.0584703
$383$			7169.18i			0.956470i	0.878232	+	0.478235i	$0.158723\pi$
$383$			7169.18i			0.956470i	−0.878232	+	0.478235i	$0.841277\pi$
$384$	3818.77	+	4894.27i	0.507489	+	0.650415i
$385$		−	25751.5i		−	3.40888i
$386$	5740.51			0.756954
$387$	−79.0213	−	19.8098i	−0.0103795	−	0.00260204i
$388$			345.069i			0.0451501i
$389$			2424.33i			0.315986i	0.987440	+	0.157993i	$0.0505024\pi$
$389$			2424.33i			0.315986i	−0.987440	+	0.157993i	$0.949498\pi$
$390$	−3626.34	−	4647.63i	−0.470838	−	0.603441i
$391$		−	9485.29i		−	1.22683i
$392$	7164.90			0.923169
$393$	−843.255	−	1080.74i	−0.108236	−	0.138718i
$394$		−	14339.6i		−	1.83354i
$395$			997.745i			0.127094i
$396$	335.398	−	1337.90i	0.0425616	−	0.169778i
$397$			14687.4i			1.85677i	0.371615	+	0.928387i	$0.378804\pi$
$397$			14687.4i			1.85677i	−0.371615	+	0.928387i	$0.621196\pi$
$398$	9808.82			1.23536
$399$	−3855.49	−	4941.32i	−0.483749	−	0.619989i
$400$	7130.44			0.891305
$401$	9413.70			1.17231			0.586157	−	0.810198i	$-0.300640\pi$
$401$	9413.70			1.17231			0.586157	+	0.810198i	$0.300640\pi$
$402$	−3123.31	+	2436.98i	−0.387504	+	0.302352i
$403$	5812.37			0.718449
$404$	1410.53			0.173704
$405$	−5438.90	+	10166.1i	−0.667311	+	1.24731i
$406$			11588.3i			1.41654i
$407$		−	7841.34i		−	0.954989i
$408$	−5260.64	+	4104.63i	−0.638334	+	0.498063i
$409$		−	7052.63i		−	0.852641i	−0.904572	−	0.426321i	$-0.859810\pi$
$409$		−	7052.63i		−	0.852641i	0.904572	−	0.426321i	$-0.140190\pi$
$410$	−15621.6			−1.88169
$411$	4991.27	−	3894.46i	0.599029	−	0.467395i
$412$		−	755.540i		−	0.0903466i
$413$	−5719.45	−	10002.9i	−0.681443	−	1.19179i
$414$	3072.90	−	12257.8i	0.364794	−	1.45516i
$415$		−	14886.8i		−	1.76088i
$416$			961.205i			0.113286i
$417$	3636.72	+	4660.94i	0.427076	+	0.547355i
$418$	−8153.02			−0.954012
$419$	8388.86			0.978097			0.489048	−	0.872257i	$-0.337344\pi$
$419$	8388.86			0.978097			0.489048	+	0.872257i	$0.337344\pi$
$420$	1314.14	−	1025.37i	0.152675	−	0.119126i
$421$		−	8187.26i		−	0.947797i	−0.880580	−	0.473898i	$-0.842846\pi$
$421$		−	8187.26i		−	0.947797i	0.880580	−	0.473898i	$-0.157154\pi$
$422$		−	9811.53i		−	1.13180i
$423$	2062.81	−	8228.56i	0.237110	−	0.945831i
$424$		−	11062.3i		−	1.26706i
$425$			6805.84i			0.776780i
$426$	−3075.01	+	2399.29i	−0.349730	+	0.272878i
$427$			14210.3i			1.61051i
$428$			860.312i			0.0971607i
$429$	−7012.17	+	5471.28i	−0.789163	+	0.615748i
$430$	−128.067			−0.0143627
$431$	−12633.2			−1.41188			−0.705941	−	0.708271i	$-0.749476\pi$
$431$	−12633.2			−1.41188			−0.705941	+	0.708271i	$0.749476\pi$
$432$	−7309.42	+	3237.55i	−0.814062	+	0.360571i
$433$	6515.64			0.723145			0.361572	−	0.932344i	$-0.382240\pi$
$433$	6515.64			0.723145			0.361572	+	0.932344i	$0.382240\pi$
$434$		−	14838.2i		−	1.64115i
$435$	8585.52	+	11003.5i	0.946308	+	1.21282i
$436$			831.636i			0.0913489i
$437$	8273.50			0.905664
$438$	−9651.93	+	7530.96i	−1.05294	+	0.821560i
$439$	−196.698			−0.0213848			−0.0106924	−	0.999943i	$-0.503404\pi$
$439$	−196.698			−0.0213848			−0.0106924	+	0.999943i	$0.503404\pi$
$440$		−	23913.1i		−	2.59094i
$441$	−1992.37	+	7947.56i	−0.215135	+	0.858175i
$442$	3901.35			0.419838
$443$	−1592.00			−0.170741			−0.0853705	−	0.996349i	$-0.527207\pi$
$443$	−1592.00			−0.170741			−0.0853705	+	0.996349i	$0.527207\pi$
$444$	400.157	−	312.224i	0.0427716	−	0.0333728i
$445$			3152.63i			0.335841i
$446$	−298.781			−0.0317213
$447$	3168.36	+	4060.67i	0.335253	+	0.429672i
$448$	14044.2			1.48109
$449$		−	13078.6i		−	1.37464i	−0.726352	−	0.687322i	$-0.758786\pi$
$449$		−	13078.6i		−	1.37464i	0.726352	−	0.687322i	$-0.241214\pi$
$450$	−2204.85	+	8795.16i	−0.230973	+	0.921350i
$451$			23569.3i			2.46083i
$452$	−585.052			−0.0608817
$453$	−14449.6	+	11274.4i	−1.49868	+	1.16935i
$454$	−3012.66			−0.311435
$455$	−10748.2			−1.10744
$456$	−3580.25	−	4588.56i	−0.367676	−	0.471226i
$457$		−	10222.0i		−	1.04632i	−0.852236	−	0.523158i	$-0.824754\pi$
$457$		−	10222.0i		−	1.04632i	0.852236	−	0.523158i	$-0.175246\pi$
$458$		−	304.565i		−	0.0310729i
$459$	−3090.16	−	6976.67i	−0.314240	−	0.709462i
$460$			2200.34i			0.223024i
$461$			18372.6i			1.85618i	0.372354	+	0.928091i	$0.378551\pi$
$461$			18372.6i			1.85618i	−0.372354	+	0.928091i	$0.621449\pi$
$462$	13967.5	+	17901.2i	1.40655	+	1.80268i
$463$			3624.32i			0.363794i	0.983318	+	0.181897i	$0.0582237\pi$
$463$			3624.32i			0.363794i	−0.983318	+	0.181897i	$0.941776\pi$
$464$			9677.16i			0.968213i
$465$	−10993.4	−	14089.5i	−1.09635	−	1.40512i
$466$	−1890.84			−0.187964
$467$	16332.5			1.61837			0.809184	−	0.587556i	$-0.199910\pi$
$467$	16332.5			1.61837			0.809184	+	0.587556i	$0.199910\pi$
$468$	−558.418	−	139.989i	−0.0551557	−	0.0138270i
$469$			7223.06i			0.711151i
$470$		−	13335.8i		−	1.30879i
$471$	5909.19	−	4610.67i	0.578091	−	0.451058i
$472$	−5311.14	−	9288.78i	−0.517935	−	0.905828i
$473$			193.223i			0.0187831i
$474$	−541.171	−	693.582i	−0.0524405	−	0.0672095i
$475$	−5936.36			−0.573429
$476$			1103.13i			0.106222i
$477$	12270.7	+	3076.13i	1.17785	+	0.295275i
$478$		−	13639.7i		−	1.30515i
$479$		−	2919.57i		−	0.278494i	−0.990258	−	0.139247i	$-0.955532\pi$
$479$		−	2919.57i		−	0.278494i	0.990258	−	0.139247i	$-0.0444682\pi$
$480$	2330.00	−	1818.00i	0.221562	−	0.172874i
$481$	−3272.84			−0.310247
$482$	−10284.1			−0.971845
$483$	−14173.9	−	18165.7i	−1.33527	−	1.71132i
$484$	−2209.67			−0.207520
$485$	−6841.34			−0.640514
$486$	−1733.21	−	10017.0i	−0.161769	−	0.934941i
$487$	10408.9			0.968524			0.484262	−	0.874923i	$-0.339088\pi$
$487$	10408.9			0.968524			0.484262	+	0.874923i	$0.339088\pi$
$488$			13195.9i			1.22408i
$489$	6974.29	+	8938.48i	0.644965	+	0.826609i
$490$			12880.3i			1.18750i
$491$			4360.92i			0.400826i	0.979712	+	0.200413i	$0.0642284\pi$
$491$			4360.92i			0.400826i	−0.979712	+	0.200413i	$0.935772\pi$
$492$	−1202.78	+	938.475i	−0.110214	+	0.0859953i
$493$	−9236.62			−0.843806
$494$			3402.93i			0.309929i
$495$	26525.3	+	6649.60i	2.40853	+	0.603793i
$496$		−	12391.2i		−	1.12173i
$497$			7111.35i			0.641827i
$498$	8074.51	+	10348.6i	0.726561	+	0.931185i
$499$	984.722			0.0883411			0.0441705	−	0.999024i	$-0.485936\pi$
$499$	984.722			0.0883411			0.0441705	+	0.999024i	$0.485936\pi$
$500$		−	1.70725i		−	0.000152701i
$501$	8689.38	−	6779.93i	0.774876	−	0.604601i
$502$			5747.32i			0.510987i
$503$	11292.6			1.00102			0.500510	−	0.865731i	$-0.333146\pi$
$503$	11292.6			1.00102			0.500510	+	0.865731i	$0.333146\pi$
$504$	−3941.32	+	15721.9i	−0.348334	+	1.38950i
$505$			27965.2i			2.46422i
$506$	−29972.8			−2.63331
$507$	−4738.97	−	6073.63i	−0.415119	−	0.532030i
$508$	291.182			0.0254313
$509$	−1779.89			−0.154994			−0.0774971	−	0.996993i	$-0.524693\pi$
$509$	−1779.89			−0.154994			−0.0774971	+	0.996993i	$0.524693\pi$
$510$	−7378.90	−	9457.04i	−0.640673	−	0.821108i
$511$			22321.3i			1.93236i
$512$	12812.1			1.10590
$513$	6085.37	−	2695.38i	0.523734	−	0.231976i
$514$			5982.46i			0.513375i
$515$	14979.3			1.28169
$516$	−9.86050	+	7.69370i	−0.000841248	+	0.000656388i
$517$	−20120.5			−1.71160
$518$			8355.13i			0.708694i
$519$	9990.74	+	12804.5i	0.844981	+	1.08296i
$520$	−9980.93			−0.841716
$521$		−	10556.1i		−	0.887662i	−0.896110	−	0.443831i	$-0.853619\pi$
$521$		−	10556.1i		−	0.887662i	0.896110	−	0.443831i	$-0.146381\pi$
$522$	−11936.4	−	2992.34i	−1.00085	−	0.250903i
$523$	−1374.67			−0.114934			−0.0574668	−	0.998347i	$-0.518302\pi$
$523$	−1374.67			−0.114934			−0.0574668	+	0.998347i	$0.518302\pi$
$524$	−210.448			−0.0175447
$525$	10170.0	+	13034.2i	0.845435	+	1.08354i
$526$		−	7245.71i		−	0.600623i
$527$	11827.1			0.977600
$528$	11664.0	+	14949.0i	0.961383	+	1.23214i
$529$	18248.7			1.49985
$530$	19886.7			1.62985
$531$	11780.3	−	3308.34i	0.962755	−	0.270376i
$532$	−962.198			−0.0784146
$533$	9837.41			0.799447
$534$	−1709.97	−	2191.55i	−0.138572	−	0.177599i
$535$	−17056.6			−1.37835
$536$			6707.41i			0.540515i
$537$	1627.65	+	2086.06i	0.130798	+	0.167635i
$538$	17250.4			1.38237
$539$	19433.4			1.55298
$540$	716.835	+	1618.40i	0.0571253	+	0.128972i
$541$			10311.3i			0.819443i	0.912211	+	0.409722i	$0.134374\pi$
$541$			10311.3i			0.819443i	−0.912211	+	0.409722i	$0.865626\pi$
$542$	6945.67			0.550446
$543$	−1453.13	−	1862.38i	−0.114843	−	0.147187i
$544$			1955.87i			0.154149i
$545$	−16488.0			−1.29591
$546$	7471.64	−	5829.78i	0.585635	−	0.456944i
$547$	24725.9			1.93273			0.966367	−	0.257168i	$-0.0827895\pi$
$547$	24725.9			1.93273			0.966367	+	0.257168i	$0.0827895\pi$
$548$		−	971.923i		−	0.0757637i
$549$	−14637.3	−	3669.42i	−1.13790	−	0.285259i
$550$	21505.9			1.66730
$551$		−	8056.60i		−	0.622909i
$552$	−13162.0	−	16868.9i	−1.01488	−	1.30070i
$553$	−1604.00			−0.123343
$554$	−19612.4			−1.50406
$555$	6190.16	+	7933.51i	0.473437	+	0.606773i
$556$	907.600			0.0692281
$557$		−	8023.94i		−	0.610387i	−0.952290	−	0.305193i	$-0.901279\pi$
$557$		−	8023.94i		−	0.610387i	0.952290	−	0.305193i	$-0.0987211\pi$
$558$	15284.1	+	3831.55i	1.15955	+	0.290686i
$559$	80.6479			0.00610205
$560$			22913.7i			1.72907i
$561$	−14268.4	+	11133.0i	−1.07382	+	0.837854i
$562$			10789.1i			0.809803i
$563$	−25776.6			−1.92958			−0.964791	−	0.263017i	$-0.915283\pi$
$563$	−25776.6			−1.92958			−0.964791	+	0.263017i	$0.915283\pi$
$564$	−801.152	−	1026.78i	−0.0598131	−	0.0766585i
$565$		−	11599.2i		−	0.863689i
$566$		−	660.464i		−	0.0490484i
$567$	−16343.3	−	8743.70i	−1.21050	−	0.647620i
$568$			6603.68i			0.487824i
$569$	5461.25			0.402368			0.201184	−	0.979553i	$-0.435521\pi$
$569$	5461.25			0.402368			0.201184	+	0.979553i	$0.435521\pi$
$570$	8248.86	−	6436.21i	0.606152	−	0.472953i
$571$			6208.29i			0.455007i	0.973777	+	0.227503i	$0.0730562\pi$
$571$			6208.29i			0.455007i	−0.973777	+	0.227503i	$0.926944\pi$
$572$			1365.44i			0.0998113i
$573$	−519.952	−	666.388i	−0.0379080	−	0.0485842i
$574$		−	25113.6i		−	1.82617i
$575$	−21823.7			−1.58280
$576$	−3626.53	+	14466.2i	−0.262335	+	1.04646i
$577$	−4213.28			−0.303988			−0.151994	−	0.988381i	$-0.548569\pi$
$577$	−4213.28			−0.303988			−0.151994	+	0.988381i	$0.548569\pi$
$578$	−5246.55			−0.377556
$579$	6837.27	+	8762.87i	0.490755	+	0.628968i
$580$	2142.65			0.153394
$581$	23932.4			1.70892
$582$	4755.76	−	3710.70i	0.338716	−	0.264285i
$583$		−	30004.3i		−	2.13148i
$584$			20727.8i			1.46870i
$585$	2775.43	−	11071.2i	0.196154	−	0.782457i
$586$		−	9135.46i		−	0.643997i
$587$	−3713.24			−0.261093			−0.130547	−	0.991442i	$-0.541673\pi$
$587$	−3713.24			−0.261093			−0.130547	+	0.991442i	$0.541673\pi$
$588$	773.794	+	991.719i	0.0542699	+	0.0695541i
$589$			10316.1i			0.721677i
$590$	16698.4	−	9547.84i	1.16519	−	0.666235i
$591$	21889.3	−	17079.2i	1.52353	−	1.18874i
$592$			6977.23i			0.484396i
$593$			13741.9i			0.951621i	0.879548	+	0.475811i	$0.157845\pi$
$593$			13741.9i			0.951621i	−0.879548	+	0.475811i	$0.842155\pi$
$594$	−22045.7	+	9764.67i	−1.52281	+	0.674494i
$595$	−21870.6			−1.50690
$596$	790.714			0.0543438
$597$	11682.9	+	14973.2i	0.800918	+	1.02648i
$598$			12510.1i			0.855481i
$599$		−	13344.3i		−	0.910242i	−0.890430	−	0.455121i	$-0.849596\pi$
$599$		−	13344.3i		−	0.910242i	0.890430	−	0.455121i	$-0.150404\pi$
$600$	9443.93	+	12103.7i	0.642578	+	0.823549i
$601$			11246.9i			0.763348i	0.924297	+	0.381674i	$0.124652\pi$
$601$			11246.9i			0.763348i	−0.924297	+	0.381674i	$0.875348\pi$
$602$		−	205.884i		−	0.0139389i
$603$	−7440.09	−	1865.15i	−0.502461	−	0.125962i
$604$			2813.70i			0.189549i
$605$		−	43808.9i		−	2.94394i
$606$	−15168.1	−	19440.0i	−1.01677	−	1.30313i
$607$	−25098.2			−1.67826			−0.839129	−	0.543932i	$-0.816935\pi$
$607$	−25098.2			−1.67826			−0.839129	+	0.543932i	$0.816935\pi$
$608$	−1706.00			−0.113795
$609$	−17689.5	+	13802.3i	−1.17703	+	0.918385i
$610$	−23722.2			−1.57457
$611$			8397.95i			0.556047i
$612$	−1136.27	−	284.852i	−0.0750509	−	0.0188145i
$613$		−	25146.8i		−	1.65688i	−0.560074	−	0.828442i	$-0.689227\pi$
$613$		−	25146.8i		−	1.65688i	0.560074	−	0.828442i	$-0.310773\pi$
$614$	−11002.9			−0.723192
$615$	−18606.2	−	23846.3i	−1.21996	−	1.56354i
$616$	38443.3			2.51449
$617$			10367.6i			0.676476i	0.941061	+	0.338238i	$0.109831\pi$
$617$			10367.6i			0.676476i	−0.941061	+	0.338238i	$0.890169\pi$
$618$	−10412.9	+	8124.71i	−0.677780	+	0.528841i
$619$	−19220.6			−1.24804			−0.624022	−	0.781407i	$-0.714502\pi$
$619$	−19220.6			−1.24804			−0.624022	+	0.781407i	$0.714502\pi$
$620$	−2743.57			−0.177717
$621$	22371.5	−	9908.97i	1.44563	−	0.640311i
$622$			3880.39i			0.250144i
$623$	−5068.25			−0.325931
$624$	6239.44	−	4868.35i	0.400285	−	0.312324i
$625$	−15608.1			−0.998916
$626$			5231.18i			0.333994i
$627$	−9710.71	−	12445.6i	−0.618514	−	0.792709i
$628$		−	1150.66i		−	0.0731155i
$629$	−6659.60			−0.422156
$630$	−28263.3	−	7085.31i	−1.78736	−	0.448072i
$631$	5697.06			0.359424			0.179712	−	0.983719i	$-0.442483\pi$
$631$	5697.06			0.359424			0.179712	+	0.983719i	$0.442483\pi$
$632$	−1489.49			−0.0937479
$633$	14977.3	−	11686.1i	0.940432	−	0.733777i
$634$			23582.7i			1.47727i
$635$			5772.98i			0.360777i
$636$	1531.17	−	1194.70i	0.0954637	−	0.0744859i
$637$		−	8111.17i		−	0.504515i
$638$			29187.0i			1.81117i
$639$	−7325.03	−	1836.31i	−0.453480	−	0.113683i
$640$			18894.9i			1.16701i
$641$			14951.6i			0.921296i	0.887583	+	0.460648i	$0.152383\pi$
$641$			14951.6i			0.921296i	−0.887583	+	0.460648i	$0.847617\pi$
$642$	11856.9	−	9251.37i	0.728899	−	0.568727i
$643$	−10278.6			−0.630401			−0.315201	−	0.949025i	$-0.602072\pi$
$643$	−10278.6			−0.630401			−0.315201	+	0.949025i	$0.602072\pi$
$644$	−3537.31			−0.216443
$645$	−152.535	−	195.494i	−0.00931173	−	0.0119342i
$646$			6924.32i			0.421724i
$647$		−	30130.8i		−	1.83086i	−0.402483	−	0.915428i	$-0.631853\pi$
$647$		−	30130.8i		−	1.83086i	0.402483	−	0.915428i	$-0.368147\pi$
$648$	−15176.6	−	8119.49i	−0.920050	−	0.492228i
$649$	−14405.4	−	25194.0i	−0.871283	−	1.52381i
$650$		−	8976.21i		−	0.541655i
$651$	22650.5	−	17673.2i	1.36366	−	1.06400i
$652$	1740.54			0.104547
$653$		−	19130.6i		−	1.14646i	−0.819394	−	0.573231i	$-0.805690\pi$
$653$		−	19130.6i		−	1.14646i	0.819394	−	0.573231i	$-0.194310\pi$
$654$	11461.6	−	8943.00i	0.685299	−	0.534708i
$655$		−	4172.33i		−	0.248896i
$656$		−	20972.0i		−	1.24820i
$657$	−22992.0	−	5763.85i	−1.36530	−	0.342267i
$658$	21438.9			1.27017
$659$	−3783.93			−0.223674			−0.111837	−	0.993727i	$-0.535673\pi$
$659$	−3783.93			−0.223674			−0.111837	+	0.993727i	$0.535673\pi$
$660$	3309.90	−	2582.56i	0.195208	−	0.152312i
$661$	14846.5			0.873619			0.436809	−	0.899554i	$-0.356108\pi$
$661$	14846.5			0.873619			0.436809	+	0.899554i	$0.356108\pi$
$662$	7977.32			0.468350
$663$	4646.73	+	5955.40i	0.272193	+	0.348852i
$664$	22223.8			1.29887
$665$		−	19076.5i		−	1.11242i
$666$	−8606.18	−	2157.48i	−0.500725	−	0.125526i
$667$		−	29618.3i		−	1.71938i
$668$		−	1692.04i		−	0.0980044i
$669$	−355.866	−	456.089i	−0.0205659	−	0.0263579i
$670$	−12057.9			−0.695280
$671$			35791.2i			2.05917i
$672$	2922.65	+	3745.77i	0.167773	+	0.215024i
$673$			25796.1i			1.47752i	0.673971	+	0.738758i	$0.264587\pi$
$673$			25796.1i			1.47752i	−0.673971	+	0.738758i	$0.735413\pi$
$674$		−	11813.8i		−	0.675150i
$675$	−16051.9	+	7109.83i	−0.915315	+	0.405419i
$676$	−1182.69			−0.0672898
$677$		−	19445.2i		−	1.10390i	−0.833878	−	0.551949i	$-0.813884\pi$
$677$		−	19445.2i		−	1.10390i	0.833878	−	0.551949i	$-0.186116\pi$
$678$	6291.36	+	8063.22i	0.356369	+	0.456735i
$679$		−	10998.3i		−	0.621614i
$680$	−20309.3			−1.14533
$681$	−3588.26	−	4598.83i	−0.201912	−	0.258778i
$682$		−	37372.6i		−	2.09835i
$683$	16732.4			0.937404			0.468702	−	0.883356i	$-0.344722\pi$
$683$	16732.4			0.937404			0.468702	+	0.883356i	$0.344722\pi$
$684$	248.461	−	991.109i	0.0138891	−	0.0554035i
$685$	19269.4			1.07481
$686$	2697.83			0.150151
$687$	464.918	−	362.754i	0.0258191	−	0.0201455i
$688$		−	171.930i		−	0.00952728i
$689$	−12523.3			−0.692451
$690$	30325.1	−	23661.3i	1.67313	−	1.30547i
$691$			16776.9i			0.923620i	0.886979	+	0.461810i	$0.152800\pi$
$691$			16776.9i			0.923620i	−0.886979	+	0.461810i	$0.847200\pi$
$692$	2493.35			0.136969
$693$	−10690.0	+	42642.6i	−0.585976	+	2.33746i
$694$	−12898.6			−0.705509
$695$			17994.1i			0.982092i
$696$	−16426.6	+	12816.9i	−0.894611	+	0.698024i
$697$	20017.2			1.08782
$698$		−	24183.7i		−	1.31142i
$699$	−2252.10	−	2886.36i	−0.121863	−	0.156183i
$700$	2538.07			0.137043
$701$	27374.7			1.47493			0.737466	−	0.675385i	$-0.236022\pi$
$701$	27374.7			1.47493			0.737466	+	0.675385i	$0.236022\pi$
$702$	4075.61	+	9201.52i	0.219122	+	0.494714i
$703$		−	5808.81i		−	0.311641i
$704$	35372.8			1.89370
$705$	20357.0	−	15883.6i	1.08750	−	0.848529i
$706$	30322.4			1.61643
$707$	−44957.4			−2.39151
$708$	712.101	−	1738.30i	0.0378000	−	0.0922731i
$709$	−32178.8			−1.70452			−0.852258	−	0.523122i	$-0.824767\pi$
$709$	−32178.8			−1.70452			−0.852258	+	0.523122i	$0.824767\pi$
$710$	−11871.4			−0.627503
$711$	414.187	−	1652.19i	0.0218470	−	0.0871478i
$712$	−4706.42			−0.247726
$713$			37924.9i			1.99200i
$714$	15203.4	−	11862.5i	0.796879	−	0.621768i
$715$	−27071.3			−1.41596
$716$	406.207			0.0212020
$717$	20820.9	−	16245.6i	1.08448	−	0.846170i
$718$			21150.1i			1.09933i
$719$	24046.9			1.24728			0.623641	−	0.781711i	$-0.285653\pi$
$719$	24046.9			1.24728			0.623641	+	0.781711i	$0.285653\pi$
$720$	−23602.2	−	5916.82i	−1.22167	−	0.306260i
$721$			24081.1i			1.24387i
$722$	12367.8			0.637511
$723$	−12249.0	−	15698.7i	−0.630075	−	0.807526i
$724$	−362.651			−0.0186158
$725$			21251.6i			1.08864i
$726$	23761.7	+	30453.8i	1.21471	+	1.55681i
$727$	22341.6			1.13976			0.569878	−	0.821729i	$-0.306990\pi$
$727$	22341.6			1.13976			0.569878	+	0.821729i	$0.306990\pi$
$728$		−	16045.6i		−	0.816879i
$729$	13226.6	−	14576.6i	0.671982	−	0.740567i
$730$	−37262.4			−1.88924
$731$	164.103			0.00830311
$732$	−1826.49	+	1425.12i	−0.0922253	+	0.0719592i
$733$	7788.17			0.392445			0.196223	−	0.980559i	$-0.437132\pi$
$733$	7788.17			0.392445			0.196223	+	0.980559i	$0.437132\pi$
$734$		−	11448.8i		−	0.575728i
$735$	−19661.8	+	15341.2i	−0.986718	+	0.769891i
$736$	−6271.72			−0.314102
$737$			18192.5i			0.909267i
$738$	25868.2	+	6484.88i	1.29027	+	0.323458i
$739$		−	11705.7i		−	0.582680i	−0.956620	−	0.291340i	$-0.905899\pi$
$739$		−	11705.7i		−	0.582680i	0.956620	−	0.291340i	$-0.0941011\pi$
$740$	1544.85			0.0767431
$741$	−5194.57	+	4053.09i	−0.257527	+	0.200936i
$742$			31970.3i			1.58176i
$743$			3213.88i			0.158689i	0.996847	+	0.0793443i	$0.0252827\pi$
$743$			3213.88i			0.158689i	−0.996847	+	0.0793443i	$0.974717\pi$
$744$	21033.5	−	16411.5i	1.03646	−	0.808703i
$745$			15676.7i			0.770939i
$746$	−14455.9			−0.709477
$747$	−6179.86	+	24651.5i	−0.302690	+	1.20743i
$748$			2778.42i			0.135814i
$749$		−	27420.5i		−	1.33768i
$750$	−23.5294	+	18.3589i	−0.00114556	+	0.000893832i
$751$		−	30502.5i		−	1.48209i	−0.671453	−	0.741047i	$-0.734329\pi$
$751$		−	30502.5i		−	1.48209i	0.671453	−	0.741047i	$-0.265671\pi$
$752$	17903.2			0.868170
$753$	−8773.27	+	6845.39i	−0.424589	+	0.331288i
$754$	12182.2			0.588393
$755$	−55784.4			−2.68901
$756$	−2601.78	+	1152.40i	−0.125166	+	0.0554397i
$757$	−12073.7			−0.579689			−0.289845	−	0.957074i	$-0.593604\pi$
$757$	−12073.7			−0.579689			−0.289845	+	0.957074i	$0.593604\pi$
$758$	6041.76			0.289507
$759$	−35699.3	−	45753.4i	−1.70725	−	2.18807i
$760$		−	17714.7i		−	0.845498i
$761$		−	1492.69i		−	0.0711040i	−0.999368	−	0.0355520i	$-0.988681\pi$
$761$		−	1492.69i		−	0.0711040i	0.999368	−	0.0355520i	$-0.0113189\pi$
$762$	−3131.23	−	4013.09i	−0.148861	−	0.190786i
$763$		−	26506.5i		−	1.25767i
$764$	−129.762			−0.00614480
$765$	5647.47	−	22527.8i	0.266908	−	1.06470i
$766$		−	19240.0i		−	0.907530i
$767$	−10515.5	+	6012.58i	−0.495038	+	0.283053i
$768$	3876.38	+	4968.10i	0.182131	+	0.233425i
$769$		−	15205.3i		−	0.713026i	−0.934290	−	0.356513i	$-0.883965\pi$
$769$		−	15205.3i		−	0.713026i	0.934290	−	0.356513i	$-0.116035\pi$
$770$			69109.4i			3.23446i
$771$	−9132.21	+	7125.45i	−0.426574	+	0.332836i
$772$	1706.35			0.0795503
$773$	19916.9			0.926727			0.463364	−	0.886168i	$-0.346642\pi$
$773$	19916.9			0.926727			0.463364	+	0.886168i	$0.346642\pi$
$774$	212.070	+	53.1636i	0.00984844	+	0.00246890i
$775$		−	27211.7i		−	1.26125i
$776$		−	10213.1i		−	0.472462i
$777$	−12754.1	+	9951.44i	−0.588868	+	0.459467i
$778$		−	6506.20i		−	0.299818i
$779$			17459.9i			0.803039i
$780$	−1077.92	−	1381.50i	−0.0494816	−	0.0634173i
$781$			17911.2i			0.820630i
$782$			25455.7i			1.16406i
$783$	−9649.19	−	21785.0i	−0.440401	−	0.994295i
$784$	−17291.9			−0.787712
$785$	22813.1			1.03724
$786$	2263.05	+	2900.40i	0.102698	+	0.131621i
$787$	34472.2			1.56138			0.780688	−	0.624921i	$-0.214869\pi$
$787$	34472.2			1.56138			0.780688	+	0.624921i	$0.214869\pi$
$788$		−	4262.39i		−	0.192692i
$789$	11060.6	−	8630.05i	0.499070	−	0.389402i
$790$		−	2677.65i		−	0.120591i
$791$	18647.2			0.838203
$792$	−9926.89	+	39598.4i	−0.445375	+	1.77660i
$793$	14938.6			0.668962
$794$		−	39416.6i		−	1.76177i
$795$	23686.2	+	30357.0i	1.05668	+	1.35428i
$796$	2915.64			0.129827
$797$	−23026.6			−1.02339			−0.511697	−	0.859166i	$-0.670983\pi$
$797$	−23026.6			−1.02339			−0.511697	+	0.859166i	$0.670983\pi$
$798$	10347.0	+	13261.1i	0.458997	+	0.588266i
$799$			17088.2i			0.756618i
$800$	4500.05			0.198876
$801$	1308.73	−	5220.53i	0.0577300	−	0.230285i
$802$	−25263.6			−1.11233
$803$			56220.1i			2.47069i
$804$	−928.396	+	724.385i	−0.0407239	+	0.0317750i
$805$		−	70130.7i		−	3.07054i
$806$	−15598.7			−0.681688
$807$	20546.2	+	26332.7i	0.896234	+	1.14864i
$808$	−41747.9			−1.81768
$809$	−15062.8			−0.654611			−0.327305	−	0.944919i	$-0.606141\pi$
$809$	−15062.8			−0.654611			−0.327305	+	0.944919i	$0.606141\pi$
$810$	14596.4	−	27282.9i	0.633167	−	1.18349i
$811$			17099.9i			0.740394i	0.928953	+	0.370197i	$0.120710\pi$
$811$			17099.9i			0.740394i	−0.928953	+	0.370197i	$0.879290\pi$
$812$			3444.57i			0.148868i
$813$	8272.69	+	10602.6i	0.356871	+	0.457377i
$814$			21043.8i			0.906125i
$815$			34508.0i			1.48314i
$816$	12696.1	−	9906.17i	0.544671	−	0.424982i
$817$			143.138i			0.00612946i
$818$			18927.2i			0.809014i
$819$	17798.3	+	4461.85i	0.759369	+	0.190366i
$820$	−4643.47			−0.197752
$821$	−28651.4			−1.21795			−0.608977	−	0.793188i	$-0.708420\pi$
$821$	−28651.4			−1.21795			−0.608977	+	0.793188i	$0.708420\pi$
$822$	−13395.1	+	10451.6i	−0.568379	+	0.443480i
$823$		−	3501.54i		−	0.148306i	−0.997247	−	0.0741530i	$-0.976375\pi$
$823$		−	3501.54i		−	0.148306i	0.997247	−	0.0741530i	$-0.0236253\pi$
$824$			22362.0i			0.945409i
$825$	25614.8	+	32828.8i	1.08096	+	1.38539i
$826$	15349.3	+	26844.8i	0.646576	+	1.13081i
$827$		−	17211.6i		−	0.723708i	−0.932235	−	0.361854i	$-0.882144\pi$
$827$		−	17211.6i		−	0.723708i	0.932235	−	0.361854i	$-0.117856\pi$
$828$	913.411	−	3643.60i	0.0383372	−	0.152927i
$829$	−22678.7			−0.950139			−0.475069	−	0.879948i	$-0.657577\pi$
$829$	−22678.7			−0.950139			−0.475069	+	0.879948i	$0.657577\pi$
$830$			39951.8i			1.67078i
$831$	−23359.5	−	29938.3i	−0.975129	−	1.24976i
$832$		−	14764.0i		−	0.615204i
$833$		−	16504.7i		−	0.686498i
$834$	−9759.88	−	12508.6i	−0.405224	−	0.519349i
$835$	33546.3			1.39032
$836$	−2423.46			−0.100260
$837$	12355.3	+	27894.7i	0.510231	+	1.15195i
$838$	−22513.2			−0.928051
$839$	2844.91			0.117065			0.0585324	−	0.998286i	$-0.481358\pi$
$839$	2844.91			0.117065			0.0585324	+	0.998286i	$0.481358\pi$
$840$	−38895.2	+	30348.1i	−1.59763	+	1.24656i
$841$	−4452.85			−0.182576
$842$			21972.2i			0.899301i
$843$	−16469.5	+	12850.4i	−0.672882	+	0.525019i
$844$		−	2916.45i		−	0.118943i
$845$		−	23447.9i		−	0.954595i
$846$	−5535.98	+	22083.0i	−0.224978	+	0.897436i
$847$	70428.2			2.85708
$848$			26697.9i			1.08114i
$849$	1008.20	−	786.651i	0.0407553	−	0.0317995i
$850$		−	18264.9i		−	0.737035i
$851$		−	21354.8i		−	0.860204i
$852$	−914.038	+	713.182i	−0.0367540	+	0.0286775i
$853$	8819.84			0.354028			0.177014	−	0.984208i	$-0.443356\pi$
$853$	8819.84			0.354028			0.177014	+	0.984208i	$0.443356\pi$
$854$		−	38136.4i		−	1.52810i
$855$	19649.7	+	4925.98i	0.785973	+	0.197035i
$856$		−	25463.0i		−	1.01671i
$857$	−10291.3			−0.410203			−0.205102	−	0.978741i	$-0.565753\pi$
$857$	−10291.3			−0.410203			−0.205102	+	0.978741i	$0.565753\pi$
$858$	18818.6	−	14683.3i	0.748784	−	0.584242i
$859$			33874.6i			1.34550i	0.739868	+	0.672752i	$0.234888\pi$
$859$			33874.6i			1.34550i	−0.739868	+	0.672752i	$0.765112\pi$
$860$	−38.0676			−0.00150941
$861$	38335.9	−	29911.7i	1.51740	−	1.18396i
$862$	33903.9			1.33964
$863$	−10238.2			−0.403837			−0.201918	−	0.979402i	$-0.564718\pi$
$863$	−10238.2			−0.403837			−0.201918	+	0.979402i	$0.564718\pi$
$864$	−4613.01	+	2043.23i	−0.181641	+	0.0804538i
$865$			49433.1i			1.94309i
$866$	−17486.1			−0.686144
$867$	−6248.94	−	8008.85i	−0.244781	−	0.313719i
$868$		−	4410.62i		−	0.172473i
$869$	−4039.94			−0.157705
$870$	−23041.0	−	29530.1i	−0.897889	−	1.15076i
$871$	7593.25			0.295393
$872$		−	24614.2i		−	0.955897i
$873$	11328.8	+	2840.00i	0.439199	+	0.110103i
$874$	−22203.6			−0.859324
$875$			54.4148i			0.00210235i
$876$	−2869.01	+	2238.56i	−0.110656	+	0.0863400i
$877$	−10811.8			−0.416293			−0.208147	−	0.978098i	$-0.566743\pi$
$877$	−10811.8			−0.416293			−0.208147	+	0.978098i	$0.566743\pi$
$878$	527.881			0.0202906
$879$	13945.3	−	10880.9i	0.535111	−	0.417522i
$880$			57712.2i			2.21077i
$881$	25219.0			0.964415			0.482208	−	0.876057i	$-0.339835\pi$
$881$	25219.0			0.964415			0.482208	+	0.876057i	$0.339835\pi$
$882$	5346.93	−	21328.9i	0.204128	−	0.814265i
$883$	4824.16			0.183857			0.0919287	−	0.995766i	$-0.470697\pi$
$883$	4824.16			0.183857			0.0919287	+	0.995766i	$0.470697\pi$
$884$	1159.66			0.0441219
$885$	34463.6	+	14118.1i	1.30902	+	0.536243i
$886$	4272.46			0.162005
$887$	−18780.5			−0.710921			−0.355461	−	0.934691i	$-0.615676\pi$
$887$	−18780.5			−0.710921			−0.355461	+	0.934691i	$0.615676\pi$
$888$	−11843.6	+	9241.01i	−0.447573	+	0.349221i
$889$	−9280.77			−0.350132
$890$		−	8460.74i		−	0.318657i
$891$	−41163.5	−	22022.5i	−1.54773	−	0.828038i
$892$	−88.8119			−0.00333368
$893$	−14905.1			−0.558545
$894$	−8502.94	−	10897.7i	−0.318100	−	0.407687i
$895$			8053.45i			0.300779i
$896$	−30375.8			−1.13257
$897$	−19096.7	+	14900.3i	−0.710837	+	0.554633i
$898$			35099.0i			1.30431i
$899$	36930.7			1.37008
$900$	−655.386	+	2614.33i	−0.0242735	+	0.0968272i
$901$	−25482.5			−0.942225
$902$		−	63253.0i		−	2.33491i
$903$	314.281	−	245.219i	0.0115821	−	0.00903697i
$904$	17316.0			0.637081
$905$		−	7189.92i		−	0.264090i
$906$	38778.5	−	30257.1i	1.42200	−	1.10952i
$907$	20867.1			0.763925			0.381962	−	0.924178i	$-0.375248\pi$
$907$	20867.1			0.763925			0.381962	+	0.924178i	$0.375248\pi$
$908$	−895.506			−0.0327295
$909$	11609.0	−	46308.3i	0.423593	−	1.68971i
$910$	28845.1			1.05078
$911$			25871.7i			0.940909i	0.882424	+	0.470454i	$0.155910\pi$
$911$			25871.7i			0.940909i	−0.882424	+	0.470454i	$0.844090\pi$
$912$	8640.61	+	11074.1i	0.313727	+	0.402083i
$913$	60277.8			2.18500
$914$			27432.9i			0.992780i
$915$	−28254.5	−	36211.9i	−1.02084	−	1.30834i
$916$		−	90.5310i		−	0.00326553i
$917$	6707.54			0.241551
$918$	8293.08	+	18723.3i	0.298162	+	0.673161i
$919$		−	12942.5i		−	0.464562i	−0.972649	−	0.232281i	$-0.925381\pi$
$919$		−	12942.5i		−	0.464562i	0.972649	−	0.232281i	$-0.0746189\pi$
$920$		−	65124.1i		−	2.33378i
$921$	−13105.0	−	16795.9i	−0.468866	−	0.600915i
$922$		−	49306.8i		−	1.76121i
$923$	7475.82			0.266598
$924$	4151.79	+	5321.07i	0.147818	+	0.189448i
$925$			15322.4i			0.544646i
$926$		−	9726.62i		−	0.345180i
$927$	−24804.7	−	6218.28i	−0.878849	−	0.220318i
$928$			6107.30i			0.216037i
$929$	37529.0			1.32539			0.662694	−	0.748890i	$-0.269413\pi$
$929$	37529.0			1.32539			0.662694	+	0.748890i	$0.269413\pi$
$930$	29502.9	+	37812.0i	1.04026	+	1.33323i
$931$	14396.1			0.506782
$932$	−562.046			−0.0197537
$933$	−5923.41	+	4621.77i	−0.207850	+	0.162176i
$934$	−43831.6			−1.53556
$935$	−55084.9			−1.92670
$936$	16527.7	+	4143.32i	0.577163	+	0.144689i
$937$		−	26577.3i		−	0.926619i	−0.886197	−	0.463309i	$-0.846662\pi$
$937$		−	26577.3i		−	0.926619i	0.886197	−	0.463309i	$-0.153338\pi$
$938$		−	19384.6i		−	0.674764i
$939$	−7985.39	+	6230.64i	−0.277522	+	0.216538i
$940$		−	3964.01i		−	0.137545i
$941$	−11505.9			−0.398598			−0.199299	−	0.979939i	$-0.563867\pi$
$941$	−11505.9			−0.398598			−0.199299	+	0.979939i	$0.563867\pi$
$942$	−15858.5	+	12373.7i	−0.548512	+	0.427979i
$943$			64187.7i			2.21658i
$944$	12818.0	+	22417.7i	0.441938	+	0.772916i
$945$	−22847.5	−	51582.9i	−0.786486	−	1.77565i
$946$		−	518.553i		−	0.0178220i
$947$			3123.78i			0.107190i	0.998563	+	0.0535952i	$0.0170680\pi$
$947$			3123.78i			0.107190i	−0.998563	+	0.0535952i	$0.982932\pi$
$948$	−160.861	−	206.165i	−0.00551111	−	0.00706323i
$949$	23465.3			0.802651
$950$	15931.4			0.544089
$951$	−35999.0	+	28088.4i	−1.22749	+	0.957757i
$952$		−	32649.7i		−	1.11154i
$953$			6989.12i			0.237565i	0.992920	+	0.118783i	$0.0378992\pi$
$953$			6989.12i			0.237565i	−0.992920	+	0.118783i	$0.962101\pi$
$954$	−32930.9	−	8255.43i	−1.11759	−	0.280167i
$955$		−	2572.66i		−	0.0871722i
$956$		−	4054.35i		−	0.137162i
$957$	−44553.9	+	34763.4i	−1.50494	+	1.17423i
$958$			7835.27i			0.264244i
$959$			30977.9i			1.04309i
$960$	−35788.6	+	27924.2i	−1.20320	+	0.938802i
$961$	−17497.0			−0.587325
$962$	8783.34			0.294372
$963$	28244.4	+	7080.57i	0.945133	+	0.236935i
$964$	−3056.93			−0.102134
$965$			33830.1i			1.12853i
$966$	38038.5	+	48751.4i	1.26694	+	1.62376i
$967$			37950.7i			1.26206i	0.775758	+	0.631031i	$0.217368\pi$
$967$			37950.7i			1.26206i	−0.775758	+	0.631031i	$0.782632\pi$
$968$	65400.4			2.17154
$969$	−10570.0	+	8247.26i	−0.350419	+	0.273416i
$970$	18360.2			0.607741
$971$			35858.0i			1.18511i	0.805532	+	0.592553i	$0.201880\pi$
$971$			35858.0i			1.18511i	−0.805532	+	0.592553i	$0.798120\pi$
$972$	−515.190	−	2977.53i	−0.0170008	−	0.0982555i
$973$	−28927.7			−0.953113
$974$	−27934.4			−0.918968
$975$	13702.2	−	10691.2i	0.450072	−	0.351171i
$976$		−	31847.1i		−	1.04447i
$977$	2537.66			0.0830983			0.0415492	−	0.999136i	$-0.486771\pi$
$977$	2537.66			0.0830983			0.0415492	+	0.999136i	$0.486771\pi$
$978$	−18716.9	−	23988.2i	−0.611965	−	0.784314i
$979$	−12765.2			−0.416730
$980$			3828.64i			0.124798i
$981$	27302.9	+	6844.56i	0.888599	+	0.222762i
$982$		−	11703.4i		−	0.380317i
$983$	−15668.4			−0.508389			−0.254194	−	0.967153i	$-0.581810\pi$
$983$	−15668.4			−0.508389			−0.254194	+	0.967153i	$0.581810\pi$
$984$	35599.1	−	27776.4i	1.15331	−	0.899876i
$985$	84506.2			2.73359
$986$	24788.4			0.800632
$987$	25534.9	+	32726.4i	0.823491	+	1.05541i
$988$			1011.51i			0.0325713i
$989$			526.216i			0.0169188i
$990$	−71186.0	−	17845.6i	−2.28529	−	0.572898i
$991$			29443.1i			0.943784i	0.881656	+	0.471892i	$0.156429\pi$
$991$			29443.1i			0.943784i	−0.881656	+	0.471892i	$0.843571\pi$
$992$		−	7820.12i		−	0.250291i
$993$	9501.45	+	12177.4i	0.303645	+	0.389161i
$994$		−	19084.8i		−	0.608986i
$995$			57805.5i			1.84177i
$996$	2400.12	+	3076.08i	0.0763563	+	0.0978607i
$997$	−4185.23			−0.132946			−0.0664732	−	0.997788i	$-0.521175\pi$
$997$	−4185.23			−0.132946			−0.0664732	+	0.997788i	$0.521175\pi$
$998$	−2642.70			−0.0838209
$999$	−6957.07	−	15707.0i	−0.220332	−	0.497445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.15	✓	52
3.2	odd	2	inner	177.4.d.c.176.38	yes	52
59.58	odd	2	inner	177.4.d.c.176.37	yes	52
177.176	even	2	inner	177.4.d.c.176.16	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.15	✓	52	1.1	even	1	trivial
177.4.d.c.176.16	yes	52	177.176	even	2	inner
177.4.d.c.176.37	yes	52	59.58	odd	2	inner
177.4.d.c.176.38	yes	52	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.68371 q^{2} +(-3.19645 - 4.09667i) q^{3} -0.797724 q^{4} -15.8157i q^{5} +(8.57832 + 10.9943i) q^{6} +25.4256 q^{7} +23.6105 q^{8} +(-6.56545 + 26.1896i) q^{9} +O(q^{10})\)	\(q-2.68371 q^{2} +(-3.19645 - 4.09667i) q^{3} -0.797724 q^{4} -15.8157i q^{5} +(8.57832 + 10.9943i) q^{6} +25.4256 q^{7} +23.6105 q^{8} +(-6.56545 + 26.1896i) q^{9} +42.4446i q^{10} +64.0388 q^{11} +(2.54988 + 3.26801i) q^{12} -26.7287i q^{13} -68.2349 q^{14} +(-64.7916 + 50.5539i) q^{15} -56.9818 q^{16} -54.3878i q^{17} +(17.6197 - 70.2852i) q^{18} +47.4395 q^{19} +12.6165i q^{20} +(-81.2717 - 104.160i) q^{21} -171.861 q^{22} +174.401 q^{23} +(-75.4697 - 96.7245i) q^{24} -125.135 q^{25} +71.7320i q^{26} +(128.276 - 56.8171i) q^{27} -20.2826 q^{28} -169.829i q^{29} +(173.882 - 135.672i) q^{30} +217.458i q^{31} -35.9615 q^{32} +(-204.697 - 262.346i) q^{33} +145.961i q^{34} -402.123i q^{35} +(5.23742 - 20.8921i) q^{36} -122.447i q^{37} -127.314 q^{38} +(-109.499 + 85.4369i) q^{39} -373.416i q^{40} +368.046i q^{41} +(218.109 + 279.536i) q^{42} +3.01728i q^{43} -51.0853 q^{44} +(414.206 + 103.837i) q^{45} -468.041 q^{46} -314.192 q^{47} +(182.139 + 233.436i) q^{48} +303.463 q^{49} +335.826 q^{50} +(-222.809 + 173.848i) q^{51} +21.3221i q^{52} -468.533i q^{53} +(-344.256 + 152.480i) q^{54} -1012.82i q^{55} +600.312 q^{56} +(-151.638 - 194.344i) q^{57} +455.771i q^{58} +(-224.948 - 393.417i) q^{59} +(51.6858 - 40.3281i) q^{60} +558.899i q^{61} -583.593i q^{62} +(-166.931 + 665.887i) q^{63} +552.365 q^{64} -422.733 q^{65} +(549.346 + 704.060i) q^{66} +284.086i q^{67} +43.3865i q^{68} +(-557.464 - 714.464i) q^{69} +1079.18i q^{70} +279.692i q^{71} +(-155.014 + 618.349i) q^{72} +877.906i q^{73} +328.611i q^{74} +(399.988 + 512.638i) q^{75} -37.8436 q^{76} +1628.23 q^{77} +(293.863 - 229.288i) q^{78} -63.0858 q^{79} +901.206i q^{80} +(-642.790 - 343.893i) q^{81} -987.728i q^{82} +941.269 q^{83} +(64.8323 + 83.0913i) q^{84} -860.180 q^{85} -8.09748i q^{86} +(-695.733 + 542.849i) q^{87} +1511.99 q^{88} -199.336 q^{89} +(-1111.61 - 278.668i) q^{90} -679.594i q^{91} -139.124 q^{92} +(890.854 - 695.093i) q^{93} +843.199 q^{94} -750.288i q^{95} +(114.949 + 147.322i) q^{96} -432.568i q^{97} -814.404 q^{98} +(-420.444 + 1677.15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more