LMFDB - Embedded newform 143.4.g.a.21.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.10
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48360 + 2.48360i) q^{2} +9.63275 q^{3} -4.33653i q^{4} +(-13.2589 - 13.2589i) q^{5} +(-23.9239 + 23.9239i) q^{6} +(-7.66310 - 7.66310i) q^{7} +(-9.09859 - 9.09859i) q^{8} +65.7898 q^{9} +O(q^{10})$	\(q+(-2.48360 + 2.48360i) q^{2} +9.63275 q^{3} -4.33653i q^{4} +(-13.2589 - 13.2589i) q^{5} +(-23.9239 + 23.9239i) q^{6} +(-7.66310 - 7.66310i) q^{7} +(-9.09859 - 9.09859i) q^{8} +65.7898 q^{9} +65.8596 q^{10} +(35.8778 + 6.61667i) q^{11} -41.7727i q^{12} +(44.5590 - 14.5430i) q^{13} +38.0641 q^{14} +(-127.720 - 127.720i) q^{15} +79.8867 q^{16} -49.5415 q^{17} +(-163.395 + 163.395i) q^{18} +(90.1171 - 90.1171i) q^{19} +(-57.4976 + 57.4976i) q^{20} +(-73.8167 - 73.8167i) q^{21} +(-105.539 + 72.6730i) q^{22} -37.5946i q^{23} +(-87.6444 - 87.6444i) q^{24} +226.597i q^{25} +(-74.5476 + 146.786i) q^{26} +373.652 q^{27} +(-33.2313 + 33.2313i) q^{28} -223.916i q^{29} +634.408 q^{30} +(-33.2209 - 33.2209i) q^{31} +(-125.618 + 125.618i) q^{32} +(345.602 + 63.7367i) q^{33} +(123.041 - 123.041i) q^{34} +203.208i q^{35} -285.300i q^{36} +(-132.593 + 132.593i) q^{37} +447.629i q^{38} +(429.225 - 140.089i) q^{39} +241.274i q^{40} +(-57.0408 + 57.0408i) q^{41} +366.662 q^{42} -123.487 q^{43} +(28.6934 - 155.585i) q^{44} +(-872.300 - 872.300i) q^{45} +(93.3700 + 93.3700i) q^{46} +(-185.876 + 185.876i) q^{47} +769.529 q^{48} -225.554i q^{49} +(-562.775 - 562.775i) q^{50} -477.221 q^{51} +(-63.0662 - 193.231i) q^{52} +102.557 q^{53} +(-928.002 + 928.002i) q^{54} +(-387.971 - 563.430i) q^{55} +139.447i q^{56} +(868.075 - 868.075i) q^{57} +(556.118 + 556.118i) q^{58} +(-267.543 + 267.543i) q^{59} +(-553.860 + 553.860i) q^{60} +540.983i q^{61} +165.015 q^{62} +(-504.154 - 504.154i) q^{63} +15.1244i q^{64} +(-783.627 - 397.978i) q^{65} +(-1016.63 + 700.041i) q^{66} +(390.197 + 390.197i) q^{67} +214.838i q^{68} -362.139i q^{69} +(-504.688 - 504.688i) q^{70} +(-325.769 - 325.769i) q^{71} +(-598.594 - 598.594i) q^{72} +(559.218 + 559.218i) q^{73} -658.616i q^{74} +2182.75i q^{75} +(-390.796 - 390.796i) q^{76} +(-224.231 - 325.640i) q^{77} +(-718.098 + 1413.95i) q^{78} +134.883i q^{79} +(-1059.21 - 1059.21i) q^{80} +1822.97 q^{81} -283.333i q^{82} +(-580.787 + 580.787i) q^{83} +(-320.108 + 320.108i) q^{84} +(656.865 + 656.865i) q^{85} +(306.693 - 306.693i) q^{86} -2156.93i q^{87} +(-266.235 - 386.640i) q^{88} +(979.759 - 979.759i) q^{89} +4332.89 q^{90} +(-452.904 - 230.015i) q^{91} -163.030 q^{92} +(-320.008 - 320.008i) q^{93} -923.285i q^{94} -2389.71 q^{95} +(-1210.05 + 1210.05i) q^{96} +(282.571 + 282.571i) q^{97} +(560.185 + 560.185i) q^{98} +(2360.40 + 435.309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−2.48360	+	2.48360i	−0.878085	+	0.878085i	−0.993336	−	0.115251i	$-0.963233\pi$
$2$	−2.48360	+	2.48360i	−0.878085	+	0.878085i	0.115251	+	0.993336i	$0.463233\pi$
$3$	9.63275			1.85382			0.926911	−	0.375280i	$-0.122454\pi$
$3$	9.63275			1.85382			0.926911	+	0.375280i	$0.122454\pi$
$4$		−	4.33653i		−	0.542067i
$5$	−13.2589	−	13.2589i	−1.18591	−	1.18591i	−0.978187	−	0.207724i	$-0.933394\pi$
$5$	−13.2589	−	13.2589i	−1.18591	−	1.18591i	−0.207724	−	0.978187i	$-0.566606\pi$
$6$	−23.9239	+	23.9239i	−1.62781	+	1.62781i
$7$	−7.66310	−	7.66310i	−0.413768	−	0.413768i	0.469281	−	0.883049i	$-0.344513\pi$
$7$	−7.66310	−	7.66310i	−0.413768	−	0.413768i	−0.883049	+	0.469281i	$0.844513\pi$
$8$	−9.09859	−	9.09859i	−0.402105	−	0.402105i
$9$	65.7898			2.43666
$10$	65.8596			2.08266
$11$	35.8778	+	6.61667i	0.983416	+	0.181364i
$11$	35.8778	+	6.61667i	0.983416	+	0.181364i
$12$		−	41.7727i		−	1.00490i
$13$	44.5590	−	14.5430i	0.950649	−	0.310270i
$13$	44.5590	−	14.5430i	0.950649	−	0.310270i
$14$	38.0641			0.726648
$15$	−127.720	−	127.720i	−2.19847	−	2.19847i
$16$	79.8867			1.24823
$17$	−49.5415			−0.706799			−0.353399	−	0.935473i	$-0.614974\pi$
$17$	−49.5415			−0.706799			−0.353399	+	0.935473i	$0.614974\pi$
$18$	−163.395	+	163.395i	−2.13959	+	2.13959i
$19$	90.1171	−	90.1171i	1.08812	−	1.08812i	0.0923975	−	0.995722i	$-0.470547\pi$
$19$	90.1171	−	90.1171i	1.08812	−	1.08812i	0.995722	−	0.0923975i	$-0.0294530\pi$
$20$	−57.4976	+	57.4976i	−0.642843	+	0.642843i
$21$	−73.8167	−	73.8167i	−0.767053	−	0.767053i
$22$	−105.539	+	72.6730i	−1.02278	+	0.704270i
$23$		−	37.5946i		−	0.340827i	−0.985373	−	0.170413i	$-0.945490\pi$
$23$		−	37.5946i		−	0.340827i	0.985373	−	0.170413i	$-0.0545103\pi$
$24$	−87.6444	−	87.6444i	−0.745430	−	0.745430i
$25$			226.597i			1.81277i
$26$	−74.5476	+	146.786i	−0.562307	+	1.10719i
$27$	373.652			2.66331
$28$	−33.2313	+	33.2313i	−0.224290	+	0.224290i
$29$		−	223.916i		−	1.43380i	−0.697177	−	0.716899i	$-0.745561\pi$
$29$		−	223.916i		−	1.43380i	0.697177	−	0.716899i	$-0.254439\pi$
$30$	634.408			3.86089
$31$	−33.2209	−	33.2209i	−0.192472	−	0.192472i	0.604291	−	0.796764i	$-0.293456\pi$
$31$	−33.2209	−	33.2209i	−0.192472	−	0.192472i	−0.796764	+	0.604291i	$0.793456\pi$
$32$	−125.618	+	125.618i	−0.693948	+	0.693948i
$33$	345.602	+	63.7367i	1.82308	+	0.336216i
$34$	123.041	−	123.041i	0.620629	−	0.620629i
$35$			203.208i			0.981385i
$36$		−	285.300i		−	1.32083i
$37$	−132.593	+	132.593i	−0.589139	+	0.589139i	−0.937398	−	0.348259i	$-0.886773\pi$
$37$	−132.593	+	132.593i	−0.589139	+	0.589139i	0.348259	+	0.937398i	$0.386773\pi$
$38$			447.629i			1.91092i
$39$	429.225	−	140.089i	1.76233	−	0.575185i
$40$			241.274i			0.953721i
$41$	−57.0408	+	57.0408i	−0.217275	+	0.217275i	−0.807349	−	0.590074i	$-0.799098\pi$
$41$	−57.0408	+	57.0408i	−0.217275	+	0.217275i	0.590074	+	0.807349i	$0.299098\pi$
$42$	366.662			1.34708
$43$	−123.487			−0.437945			−0.218972	−	0.975731i	$-0.570270\pi$
$43$	−123.487			−0.437945			−0.218972	+	0.975731i	$0.570270\pi$
$44$	28.6934	−	155.585i	0.0983112	−	0.533077i
$45$	−872.300	−	872.300i	−2.88966	−	2.88966i
$46$	93.3700	+	93.3700i	0.299275	+	0.299275i
$47$	−185.876	+	185.876i	−0.576870	+	0.576870i	−0.934039	−	0.357170i	$-0.883742\pi$
$47$	−185.876	+	185.876i	−0.576870	+	0.576870i	0.357170	+	0.934039i	$0.383742\pi$
$48$	769.529			2.31400
$49$		−	225.554i		−	0.657591i
$50$	−562.775	−	562.775i	−1.59177	−	1.59177i
$51$	−477.221			−1.31028
$52$	−63.0662	−	193.231i	−0.168187	−	0.515315i
$53$	102.557			0.265798			0.132899	−	0.991130i	$-0.457571\pi$
$53$	102.557			0.265798			0.132899	+	0.991130i	$0.457571\pi$
$54$	−928.002	+	928.002i	−2.33861	+	2.33861i
$55$	−387.971	−	563.430i	−0.951163	−	1.38133i
$56$			139.447i			0.332756i
$57$	868.075	−	868.075i	2.01718	−	2.01718i
$58$	556.118	+	556.118i	1.25900	+	1.25900i
$59$	−267.543	+	267.543i	−0.590357	+	0.590357i	−0.937728	−	0.347371i	$-0.887075\pi$
$59$	−267.543	+	267.543i	−0.590357	+	0.590357i	0.347371	+	0.937728i	$0.387075\pi$
$60$	−553.860	+	553.860i	−1.19172	+	1.19172i
$61$			540.983i			1.13550i	0.823200	+	0.567752i	$0.192187\pi$
$61$			540.983i			1.13550i	−0.823200	+	0.567752i	$0.807813\pi$
$62$	165.015			0.338014
$63$	−504.154	−	504.154i	−1.00821	−	1.00821i
$64$			15.1244i			0.0295399i
$65$	−783.627	−	397.978i	−1.49534	−	0.759433i
$66$	−1016.63	+	700.041i	−1.89604	+	1.30559i
$67$	390.197	+	390.197i	0.711495	+	0.711495i	0.966848	−	0.255353i	$-0.0821915\pi$
$67$	390.197	+	390.197i	0.711495	+	0.711495i	−0.255353	+	0.966848i	$0.582192\pi$
$68$			214.838i			0.383132i
$69$		−	362.139i		−	0.631833i
$70$	−504.688	−	504.688i	−0.861740	−	0.861740i
$71$	−325.769	−	325.769i	−0.544530	−	0.544530i	0.380323	−	0.924854i	$-0.375813\pi$
$71$	−325.769	−	325.769i	−0.544530	−	0.544530i	−0.924854	+	0.380323i	$0.875813\pi$
$72$	−598.594	−	598.594i	−0.979792	−	0.979792i
$73$	559.218	+	559.218i	0.896596	+	0.896596i	0.995133	−	0.0985370i	$-0.0314163\pi$
$73$	559.218	+	559.218i	0.896596	+	0.896596i	−0.0985370	+	0.995133i	$0.531416\pi$
$74$		−	658.616i		−	1.03463i
$75$			2182.75i			3.36056i
$76$	−390.796	−	390.796i	−0.589833	−	0.589833i
$77$	−224.231	−	325.640i	−0.331864	−	0.481949i
$78$	−718.098	+	1413.95i	−1.04242	+	2.05254i
$79$			134.883i			0.192096i	0.995377	+	0.0960478i	$0.0306202\pi$
$79$			134.883i			0.192096i	−0.995377	+	0.0960478i	$0.969380\pi$
$80$	−1059.21	−	1059.21i	−1.48029	−	1.48029i
$81$	1822.97			2.50065
$82$		−	283.333i		−	0.381572i
$83$	−580.787	+	580.787i	−0.768068	+	0.768068i	−0.977766	−	0.209698i	$-0.932752\pi$
$83$	−580.787	+	580.787i	−0.768068	+	0.768068i	0.209698	+	0.977766i	$0.432752\pi$
$84$	−320.108	+	320.108i	−0.415794	+	0.415794i
$85$	656.865	+	656.865i	0.838201	+	0.838201i
$86$	306.693	−	306.693i	0.384553	−	0.384553i
$87$		−	2156.93i		−	2.65801i
$88$	−266.235	−	386.640i	−0.322509	−	0.468363i
$89$	979.759	−	979.759i	1.16690	−	1.16690i	0.183970	−	0.982932i	$-0.441105\pi$
$89$	979.759	−	979.759i	1.16690	−	1.16690i	0.982932	−	0.183970i	$-0.0588948\pi$
$90$	4332.89			5.07474
$91$	−452.904	−	230.015i	−0.521728	−	0.264969i
$92$	−163.030			−0.184751
$93$	−320.008	−	320.008i	−0.356810	−	0.356810i
$94$		−	923.285i		−	1.01308i
$95$	−2389.71			−2.58083
$96$	−1210.05	+	1210.05i	−1.28646	+	1.28646i
$97$	282.571	+	282.571i	0.295781	+	0.295781i	0.839359	−	0.543578i	$-0.182931\pi$
$97$	282.571	+	282.571i	0.295781	+	0.295781i	−0.543578	+	0.839359i	$0.682931\pi$
$98$	560.185	+	560.185i	0.577421	+	0.577421i
$99$	2360.40	+	435.309i	2.39625	+	0.441921i
$100$	982.643			0.982643
$101$	969.153			0.954795			0.477397	−	0.878687i	$-0.341580\pi$
$101$	969.153			0.954795			0.477397	+	0.878687i	$0.341580\pi$
$102$	1185.22	−	1185.22i	1.15054	−	1.15054i
$103$			368.679i			0.352689i	0.984328	+	0.176345i	$0.0564273\pi$
$103$			368.679i			0.352689i	−0.984328	+	0.176345i	$0.943573\pi$
$104$	−537.744	−	273.103i	−0.507021	−	0.257499i
$105$			1957.45i			1.81931i
$106$	−254.710	+	254.710i	−0.233393	+	0.233393i
$107$			472.846i			0.427213i	0.976920	+	0.213606i	$0.0685210\pi$
$107$			472.846i			0.427213i	−0.976920	+	0.213606i	$0.931479\pi$
$108$		−	1620.35i		−	1.44369i
$109$	523.602	−	523.602i	0.460110	−	0.460110i	−0.438582	−	0.898691i	$-0.644519\pi$
$109$	523.602	−	523.602i	0.460110	−	0.460110i	0.898691	+	0.438582i	$0.144519\pi$
$110$	2362.90	+	435.771i	2.04812	+	0.377719i
$111$	−1277.23	+	1277.23i	−1.09216	+	1.09216i
$112$	−612.180	−	612.180i	−0.516478	−	0.516478i
$113$	−1219.17			−1.01495			−0.507476	−	0.861666i	$-0.669421\pi$
$113$	−1219.17			−1.01495			−0.507476	+	0.861666i	$0.669421\pi$
$114$			4311.90i			3.54251i
$115$	−498.463	+	498.463i	−0.404191	+	0.404191i
$116$	−971.019			−0.777214
$117$	2931.52	−	956.781i	2.31641	−	0.756021i
$118$		−	1328.94i		−	1.03677i
$119$	379.641	+	379.641i	0.292451	+	0.292451i
$120$			2324.13i			1.76803i
$121$	1243.44	+	474.783i	0.934214	+	0.356712i
$122$	−1343.58	−	1343.58i	−0.997069	−	0.997069i
$123$	−549.459	+	549.459i	−0.402789	+	0.402789i
$124$	−144.063	+	144.063i	−0.104333	+	0.104333i
$125$	1347.06	−	1347.06i	0.963876	−	0.963876i
$126$	2504.23			1.77059
$127$	297.105			0.207589			0.103794	−	0.994599i	$-0.466902\pi$
$127$	297.105			0.207589			0.103794	+	0.994599i	$0.466902\pi$
$128$	−1042.51	−	1042.51i	−0.719886	−	0.719886i
$129$	−1189.52			−0.811872
$130$	2934.63	−	957.796i	1.97988	−	0.646187i
$131$		−	98.7484i		−	0.0658602i	−0.999458	−	0.0329301i	$-0.989516\pi$
$131$		−	98.7484i		−	0.0658602i	0.999458	−	0.0329301i	$-0.0104839\pi$
$132$	276.396	−	1498.71i	0.182251	−	0.988230i
$133$	−1381.15			−0.900459
$134$	−1938.19			−1.24951
$135$	−4954.21	−	4954.21i	−3.15845	−	3.15845i
$136$	450.758	+	450.758i	0.284207	+	0.284207i
$137$	1276.77	−	1276.77i	0.796220	−	0.796220i	−0.186277	−	0.982497i	$-0.559642\pi$
$137$	1276.77	−	1276.77i	0.796220	−	0.796220i	0.982497	+	0.186277i	$0.0596422\pi$
$138$	899.409	+	899.409i	0.554803	+	0.554803i
$139$			934.566i			0.570280i	0.958486	+	0.285140i	$0.0920400\pi$
$139$			934.566i			0.570280i	−0.958486	+	0.285140i	$0.907960\pi$
$140$	881.220			0.531976
$141$	−1790.50	+	1790.50i	−1.06941	+	1.06941i
$142$	1618.16			0.956288
$143$	1694.91	−	226.940i	0.991155	−	0.132711i
$144$	5255.73			3.04151
$145$	−2968.88	+	2968.88i	−1.70036	+	1.70036i
$146$	−2777.75			−1.57458
$147$		−	2172.70i		−	1.21906i
$148$	574.994	+	574.994i	0.319353	+	0.319353i
$149$	−2074.54	+	2074.54i	−1.14063	+	1.14063i	−0.152291	+	0.988336i	$0.548665\pi$
$149$	−2074.54	+	2074.54i	−1.14063	+	1.14063i	−0.988336	+	0.152291i	$0.951335\pi$
$150$	−5421.07	−	5421.07i	−2.95086	−	2.95086i
$151$	1019.80	+	1019.80i	0.549601	+	0.549601i	0.926325	−	0.376724i	$-0.122950\pi$
$151$	1019.80	+	1019.80i	0.549601	+	0.549601i	−0.376724	+	0.926325i	$0.622950\pi$
$152$	−1639.88			−0.875076
$153$	−3259.32			−1.72223
$154$	1365.66	+	251.858i	0.714597	+	0.131787i
$155$			880.944i			0.456510i
$156$	−607.501	−	1861.35i	−0.311788	−	0.955302i
$157$	477.949			0.242958			0.121479	−	0.992594i	$-0.461236\pi$
$157$	477.949			0.242958			0.121479	+	0.992594i	$0.461236\pi$
$158$	−334.996	−	334.996i	−0.168676	−	0.168676i
$159$	987.905			0.492742
$160$	3331.11			1.64592
$161$	−288.091	+	288.091i	−0.141023	+	0.141023i
$162$	−4527.53	+	4527.53i	−2.19578	+	2.19578i
$163$	−495.598	+	495.598i	−0.238149	+	0.238149i	−0.816083	−	0.577934i	$-0.803859\pi$
$163$	−495.598	+	495.598i	−0.238149	+	0.238149i	0.577934	+	0.816083i	$0.303859\pi$
$164$	247.359	+	247.359i	0.117777	+	0.117777i
$165$	−3737.22	−	5427.38i	−1.76329	−	2.56073i
$166$		−	2884.88i		−	1.34886i
$167$	668.056	+	668.056i	0.309555	+	0.309555i	0.844737	−	0.535182i	$-0.179757\pi$
$167$	668.056	+	668.056i	0.309555	+	0.309555i	−0.535182	+	0.844737i	$0.679757\pi$
$168$			1343.25i			0.616871i
$169$	1774.00	−	1296.04i	0.807466	−	0.589915i
$170$	−3262.78			−1.47202
$171$	5928.78	−	5928.78i	2.65138	−	2.65138i
$172$			535.507i			0.237395i
$173$	2852.00			1.25337			0.626686	−	0.779272i	$-0.284411\pi$
$173$	2852.00			1.25337			0.626686	+	0.779272i	$0.284411\pi$
$174$	5356.94	+	5356.94i	2.33396	+	2.33396i
$175$	1736.43	−	1736.43i	0.750068	−	0.750068i
$176$	2866.16	+	528.584i	1.22753	+	0.226384i
$177$	−2577.17	+	2577.17i	−1.09442	+	1.09442i
$178$			4866.66i			2.04928i
$179$			4025.59i			1.68093i	0.541864	+	0.840466i	$0.317719\pi$
$179$			4025.59i			1.68093i	−0.541864	+	0.840466i	$0.682281\pi$
$180$	−3782.76	+	3782.76i	−1.56639	+	1.56639i
$181$		−	3293.33i		−	1.35244i	−0.736700	−	0.676219i	$-0.763617\pi$
$181$		−	3293.33i		−	1.35244i	0.736700	−	0.676219i	$-0.236383\pi$
$182$	1696.10	−	553.567i	0.690787	−	0.225457i
$183$			5211.15i			2.10502i
$184$	−342.058	+	342.058i	−0.137048	+	0.137048i
$185$	3516.07			1.39733
$186$	1589.54			0.626618
$187$	−1777.44	−	327.800i	−0.695077	−	0.128188i
$188$	806.059	+	806.059i	0.312702	+	0.312702i
$189$	−2863.33	−	2863.33i	−1.10199	−	1.10199i
$190$	5935.07	−	5935.07i	2.26619	−	2.26619i
$191$	1420.03			0.537956			0.268978	−	0.963146i	$-0.413314\pi$
$191$	1420.03			0.537956			0.268978	+	0.963146i	$0.413314\pi$
$192$			145.690i			0.0547618i
$193$	406.504	+	406.504i	0.151610	+	0.151610i	0.778837	−	0.627227i	$-0.215810\pi$
$193$	406.504	+	406.504i	0.151610	+	0.151610i	−0.627227	+	0.778837i	$0.715810\pi$
$194$	−1403.59			−0.519441
$195$	−7548.48	−	3833.62i	−2.77209	−	1.40785i
$196$	−978.122			−0.356458
$197$	396.433	−	396.433i	0.143374	−	0.143374i	−0.631777	−	0.775151i	$-0.717674\pi$
$197$	396.433	−	396.433i	0.143374	−	0.143374i	0.775151	+	0.631777i	$0.217674\pi$
$198$	−6943.41	+	4781.14i	−2.49216	+	1.71607i
$199$		−	3073.73i		−	1.09493i	−0.836828	−	0.547466i	$-0.815593\pi$
$199$		−	3073.73i		−	1.09493i	0.836828	−	0.547466i	$-0.184407\pi$
$200$	2061.71	−	2061.71i	0.728924	−	0.728924i
$201$	3758.67	+	3758.67i	1.31899	+	1.31899i
$202$	−2406.99	+	2406.99i	−0.838391	+	0.838391i
$203$	−1715.89	+	1715.89i	−0.593260	+	0.593260i
$204$			2069.48i			0.710259i
$205$	1512.59			0.515338
$206$	−915.650	−	915.650i	−0.309691	−	0.309691i
$207$		−	2473.34i		−	0.830479i
$208$	3559.67	−	1161.79i	1.18663	−	0.387288i
$209$	3829.48	−	2636.93i	1.26742	−	0.872729i
$210$	−4861.53	−	4861.53i	−1.59751	−	1.59751i
$211$		−	76.8356i		−	0.0250691i	−0.999921	−	0.0125345i	$-0.996010\pi$
$211$		−	76.8356i		−	0.0250691i	0.999921	−	0.0125345i	$-0.00398998\pi$
$212$		−	444.741i		−	0.144080i
$213$	−3138.05	−	3138.05i	−1.00946	−	1.00946i
$214$	−1174.36	−	1174.36i	−0.375129	−	0.375129i
$215$	1637.30	+	1637.30i	0.519364	+	0.519364i
$216$	−3399.71	−	3399.71i	−1.07093	−	1.07093i
$217$			509.149i			0.159278i
$218$			2600.83i			0.808031i
$219$	5386.81	+	5386.81i	1.66213	+	1.66213i
$220$	−2443.33	+	1682.45i	−0.748770	+	0.515594i
$221$	−2207.52	+	720.482i	−0.671917	+	0.219298i
$222$		−	6344.28i		−	1.91802i
$223$	2736.64	+	2736.64i	0.821788	+	0.821788i	0.986364	−	0.164576i	$-0.0526257\pi$
$223$	2736.64	+	2736.64i	0.821788	+	0.821788i	−0.164576	+	0.986364i	$0.552626\pi$
$224$	1925.25			0.574267
$225$			14907.7i			4.41711i
$226$	3027.92	−	3027.92i	0.891214	−	0.891214i
$227$	1024.16	−	1024.16i	0.299452	−	0.299452i	−0.541347	−	0.840799i	$-0.682086\pi$
$227$	1024.16	−	1024.16i	0.299452	−	0.299452i	0.840799	+	0.541347i	$0.182086\pi$
$228$	−3764.43	−	3764.43i	−1.09345	−	1.09345i
$229$	−3228.80	+	3228.80i	−0.931724	+	0.931724i	−0.997814	−	0.0660894i	$-0.978948\pi$
$229$	−3228.80	+	3228.80i	−0.931724	+	0.931724i	0.0660894	+	0.997814i	$0.478948\pi$
$230$		−	2475.97i		−	0.709828i
$231$	−2159.96	−	3136.80i	−0.615217	−	0.893448i
$232$	−2037.32	+	2037.32i	−0.576537	+	0.576537i
$233$	−141.393			−0.0397551			−0.0198775	−	0.999802i	$-0.506328\pi$
$233$	−141.393			−0.0397551			−0.0198775	+	0.999802i	$0.506328\pi$
$234$	−4904.47	+	9656.99i	−1.37015	+	2.69785i
$235$	4929.03			1.36823
$236$	1160.21	+	1160.21i	0.320013	+	0.320013i
$237$			1299.30i			0.356111i
$238$	−1885.75			−0.513594
$239$	−3058.61	+	3058.61i	−0.827804	+	0.827804i	−0.987213	−	0.159408i	$-0.949041\pi$
$239$	−3058.61	+	3058.61i	−0.827804	+	0.827804i	0.159408	+	0.987213i	$0.449041\pi$
$240$	−10203.1	−	10203.1i	−2.74420	−	2.74420i
$241$	−1695.16	−	1695.16i	−0.453090	−	0.453090i	0.443289	−	0.896379i	$-0.353812\pi$
$241$	−1695.16	−	1695.16i	−0.453090	−	0.453090i	−0.896379	+	0.443289i	$0.853812\pi$
$242$	−4267.38	+	1909.03i	−1.13354	+	0.507096i
$243$	7471.62			1.97245
$244$	2345.99			0.615519
$245$	−2990.60	+	2990.60i	−0.779845	+	0.779845i
$246$		−	2729.27i		−	0.707366i
$247$	2704.95	−	5326.10i	0.696809	−	1.37203i
$248$			604.526i			0.154788i
$249$	−5594.57	+	5594.57i	−1.42386	+	1.42386i
$250$			6691.11i			1.69273i
$251$		−	2995.13i		−	0.753190i	−0.926378	−	0.376595i	$-0.877095\pi$
$251$		−	2995.13i		−	0.753190i	0.926378	−	0.376595i	$-0.122905\pi$
$252$	−2186.28	+	2186.28i	−0.546518	+	0.546518i
$253$	248.751	−	1348.81i	0.0618136	−	0.335175i
$254$	−737.889	+	737.889i	−0.182281	+	0.182281i
$255$	6327.42	+	6327.42i	1.55388	+	1.55388i
$256$	5057.34			1.23470
$257$			6622.26i			1.60733i	0.595079	+	0.803667i	$0.297121\pi$
$257$			6622.26i			1.60733i	−0.595079	+	0.803667i	$0.702879\pi$
$258$	2954.30	−	2954.30i	0.712893	−	0.712893i
$259$	2032.15			0.487534
$260$	−1725.85	+	3398.22i	−0.411663	+	0.810572i
$261$		−	14731.4i		−	3.49368i
$262$	245.251	+	245.251i	0.0578309	+	0.0578309i
$263$		−	1581.00i		−	0.370679i	−0.982675	−	0.185340i	$-0.940661\pi$
$263$		−	1581.00i		−	0.370679i	0.982675	−	0.185340i	$-0.0593385\pi$
$264$	−2564.58	−	3724.40i	−0.597874	−	0.868262i
$265$	−1359.79	−	1359.79i	−0.315212	−	0.315212i
$266$	3430.23	−	3430.23i	0.790680	−	0.790680i
$267$	9437.77	−	9437.77i	2.16323	−	2.16323i
$268$	1692.10	−	1692.10i	0.385678	−	0.385678i
$269$	−1256.90			−0.284888			−0.142444	−	0.989803i	$-0.545496\pi$
$269$	−1256.90			−0.284888			−0.142444	+	0.989803i	$0.545496\pi$
$270$	24608.6			5.54678
$271$	−3788.60	−	3788.60i	−0.849229	−	0.849229i	0.140808	−	0.990037i	$-0.455030\pi$
$271$	−3788.60	−	3788.60i	−0.849229	−	0.849229i	−0.990037	+	0.140808i	$0.955030\pi$
$272$	−3957.71			−0.882248
$273$	−4362.71	−	2215.68i	−0.967191	−	0.491205i
$274$			6341.99i			1.39830i
$275$	−1499.31	+	8129.80i	−0.328771	+	1.78271i
$276$	−1570.43			−0.342495
$277$	−2293.91			−0.497573			−0.248786	−	0.968558i	$-0.580032\pi$
$277$	−2293.91			−0.497573			−0.248786	+	0.968558i	$0.580032\pi$
$278$	−2321.09	−	2321.09i	−0.500754	−	0.500754i
$279$	−2185.59	−	2185.59i	−0.468989	−	0.468989i
$280$	1848.91	−	1848.91i	0.394619	−	0.394619i
$281$	−1474.41	−	1474.41i	−0.313011	−	0.313011i	0.533064	−	0.846075i	$-0.321040\pi$
$281$	−1474.41	−	1474.41i	−0.313011	−	0.313011i	−0.846075	+	0.533064i	$0.821040\pi$
$282$		−	8893.77i		−	1.87807i
$283$	−4995.03			−1.04920			−0.524601	−	0.851348i	$-0.675785\pi$
$283$	−4995.03			−1.04920			−0.524601	+	0.851348i	$0.675785\pi$
$284$	−1412.71	+	1412.71i	−0.295172	+	0.295172i
$285$	−23019.4			−4.78440
$286$	−3645.84	+	4773.09i	−0.753787	+	0.986850i
$287$	874.218			0.179803
$288$	−8264.38	+	8264.38i	−1.69091	+	1.69091i
$289$	−2458.64			−0.500436
$290$		−	14747.0i		−	2.98612i
$291$	2721.93	+	2721.93i	0.548325	+	0.548325i
$292$	2425.07	−	2425.07i	0.486015	−	0.486015i
$293$	6389.08	+	6389.08i	1.27390	+	1.27390i	0.944022	+	0.329882i	$0.107009\pi$
$293$	6389.08	+	6389.08i	1.27390	+	1.27390i	0.329882	+	0.944022i	$0.392991\pi$
$294$	5396.12	+	5396.12i	1.07044	+	1.07044i
$295$	7094.64			1.40022
$296$	2412.82			0.473791
$297$	13405.8	+	2472.33i	2.61914	+	0.483028i
$298$		−	10304.7i		−	2.00313i
$299$	−546.739	−	1675.18i	−0.105748	−	0.324007i
$300$	9465.55			1.82165
$301$	946.295	+	946.295i	0.181208	+	0.181208i
$302$	−5065.53			−0.965193
$303$	9335.60			1.77002
$304$	7199.16	−	7199.16i	1.35822	−	1.35822i
$305$	7172.83	−	7172.83i	1.34661	−	1.34661i
$306$	8094.86	−	8094.86i	1.51226	−	1.51226i
$307$	3140.58	+	3140.58i	0.583852	+	0.583852i	0.935960	−	0.352108i	$-0.114535\pi$
$307$	3140.58	+	3140.58i	0.583852	+	0.583852i	−0.352108	+	0.935960i	$0.614535\pi$
$308$	−1412.15	+	972.386i	−0.261248	+	0.179892i
$309$			3551.39i			0.653823i
$310$	−2187.91	−	2187.91i	−0.400855	−	0.400855i
$311$			3645.86i			0.664751i	0.943147	+	0.332376i	$0.107850\pi$
$311$			3645.86i			0.664751i	−0.943147	+	0.332376i	$0.892150\pi$
$312$	−5179.95	−	2630.73i	−0.939927	−	0.477358i
$313$	−3556.77			−0.642302			−0.321151	−	0.947028i	$-0.604070\pi$
$313$	−3556.77			−0.642302			−0.321151	+	0.947028i	$0.604070\pi$
$314$	−1187.03	+	1187.03i	−0.213338	+	0.213338i
$315$			13369.0i			2.39130i
$316$	584.926			0.104129
$317$	4904.41	+	4904.41i	0.868956	+	0.868956i	0.992357	−	0.123401i	$-0.0393801\pi$
$317$	4904.41	+	4904.41i	0.868956	+	0.868956i	−0.123401	+	0.992357i	$0.539380\pi$
$318$	−2453.56	+	2453.56i	−0.432669	+	0.432669i
$319$	1481.58	−	8033.62i	0.260039	−	1.41002i
$320$	200.533	−	200.533i	0.0350317	−	0.0350317i
$321$			4554.81i			0.791976i
$322$		−	1431.01i		−	0.247661i
$323$	−4464.53	+	4464.53i	−0.769081	+	0.769081i
$324$		−	7905.38i		−	1.35552i
$325$	3295.39	+	10096.9i	0.562448	+	1.72331i
$326$		−	2461.73i		−	0.418230i
$327$	5043.72	−	5043.72i	0.852962	−	0.852962i
$328$	1037.98			0.174734
$329$	2848.78			0.477381
$330$	22761.2	+	4197.67i	3.79686	+	0.700225i
$331$	3655.07	+	3655.07i	0.606951	+	0.606951i	0.942148	−	0.335197i	$-0.108803\pi$
$331$	3655.07	+	3655.07i	0.606951	+	0.606951i	−0.335197	+	0.942148i	$0.608803\pi$
$332$	2518.60	+	2518.60i	0.416344	+	0.416344i
$333$	−8723.27	+	8723.27i	−1.43553	+	1.43553i
$334$	−3318.37			−0.543632
$335$		−	10347.2i		−	1.68754i
$336$	−5896.97	−	5896.97i	−0.957459	−	0.957459i
$337$	−9612.20			−1.55374			−0.776870	−	0.629662i	$-0.783194\pi$
$337$	−9612.20			−1.55374			−0.776870	+	0.629662i	$0.783194\pi$
$338$	−1187.06	+	7624.76i	−0.191028	+	1.22702i
$339$	−11743.9			−1.88154
$340$	2848.52	−	2848.52i	0.454361	−	0.454361i
$341$	−972.082	−	1411.70i	−0.154373	−	0.224188i
$342$			29449.4i			4.65627i
$343$	−4356.88	+	4356.88i	−0.685859	+	0.685859i
$344$	1123.56	+	1123.56i	0.176100	+	0.176100i
$345$	−4801.57	+	4801.57i	−0.749298	+	0.749298i
$346$	−7083.22	+	7083.22i	−1.10057	+	1.10057i
$347$		−	7263.78i		−	1.12375i	−0.827223	−	0.561874i	$-0.810081\pi$
$347$		−	7263.78i		−	1.12375i	0.827223	−	0.561874i	$-0.189919\pi$
$348$	−9353.58			−1.44082
$349$	−7129.10	−	7129.10i	−1.09344	−	1.09344i	−0.995158	−	0.0982859i	$-0.968664\pi$
$349$	−7129.10	−	7129.10i	−1.09344	−	1.09344i	−0.0982859	−	0.995158i	$-0.531336\pi$
$350$			8625.20i			1.31725i
$351$	16649.6	−	5434.03i	2.53187	−	0.826344i
$352$	−5338.07	+	3675.73i	−0.808296	+	0.556583i
$353$	4576.32	+	4576.32i	0.690008	+	0.690008i	0.962233	−	0.272226i	$-0.0877597\pi$
$353$	4576.32	+	4576.32i	0.690008	+	0.690008i	−0.272226	+	0.962233i	$0.587760\pi$
$354$		−	12801.3i		−	1.92198i
$355$			8638.67i			1.29153i
$356$	−4248.76	−	4248.76i	−0.632538	−	0.632538i
$357$	3656.99	+	3656.99i	0.542152	+	0.542152i
$358$	−9997.96	−	9997.96i	−1.47600	−	1.47600i
$359$	−3396.36	−	3396.36i	−0.499312	−	0.499312i	0.411912	−	0.911224i	$-0.364861\pi$
$359$	−3396.36	−	3396.36i	−0.499312	−	0.499312i	−0.911224	+	0.411912i	$0.864861\pi$
$360$			15873.4i			2.32389i
$361$		−	9383.17i		−	1.36801i
$362$	8179.32	+	8179.32i	1.18756	+	1.18756i
$363$	11977.7	+	4573.47i	1.73187	+	0.661281i
$364$	−997.468	+	1964.03i	−0.143631	+	0.282811i
$365$		−	14829.2i		−	2.12657i
$366$	−12942.4	−	12942.4i	−1.84839	−	1.84839i
$367$	−9934.95			−1.41308			−0.706540	−	0.707673i	$-0.749745\pi$
$367$	−9934.95			−1.41308			−0.706540	+	0.707673i	$0.749745\pi$
$368$		−	3003.31i		−	0.425431i
$369$	−3752.70	+	3752.70i	−0.529425	+	0.529425i
$370$	−8732.52	+	8732.52i	−1.22698	+	1.22698i
$371$	−785.904	−	785.904i	−0.109979	−	0.109979i
$372$	−1387.73	+	1387.73i	−0.193415	+	0.193415i
$373$		−	5778.59i		−	0.802155i	−0.916044	−	0.401078i	$-0.868636\pi$
$373$		−	5778.59i		−	0.802155i	0.916044	−	0.401078i	$-0.131364\pi$
$374$	5228.58	−	3600.33i	0.722896	−	0.497777i
$375$	12975.9	−	12975.9i	1.78686	−	1.78686i
$376$	3382.43			0.463924
$377$	−3256.41	−	9977.46i	−0.444864	−	1.36304i
$378$	14222.7			1.93529
$379$	−3893.67	−	3893.67i	−0.527717	−	0.527717i	0.392174	−	0.919891i	$-0.371723\pi$
$379$	−3893.67	−	3893.67i	−0.527717	−	0.527717i	−0.919891	+	0.392174i	$0.871723\pi$
$380$			10363.0i			1.39898i
$381$	2861.93			0.384833
$382$	−3526.78	+	3526.78i	−0.472371	+	0.472371i
$383$	826.172	+	826.172i	0.110223	+	0.110223i	0.760067	−	0.649844i	$-0.225166\pi$
$383$	826.172	+	826.172i	0.110223	+	0.110223i	−0.649844	+	0.760067i	$0.725166\pi$
$384$	−10042.2	−	10042.2i	−1.33454	−	1.33454i
$385$	−1344.56	+	7290.68i	−0.177988	+	0.965110i
$386$	−2019.18			−0.266253
$387$	−8124.20			−1.06712
$388$	1225.38	−	1225.38i	0.160333	−	0.160333i
$389$		−	5345.12i		−	0.696679i	−0.937368	−	0.348340i	$-0.886746\pi$
$389$		−	5345.12i		−	0.696679i	0.937368	−	0.348340i	$-0.113254\pi$
$390$	28268.6	−	9226.20i	3.67035	−	1.19792i
$391$			1862.49i			0.240896i
$392$	−2052.22	+	2052.22i	−0.264420	+	0.264420i
$393$		−	951.218i		−	0.122093i
$394$			1969.16i			0.251789i
$395$	1788.40	−	1788.40i	0.227808	−	0.227808i
$396$	1887.73	−	10235.9i	0.239551	−	1.29893i
$397$	−3328.68	+	3328.68i	−0.420810	+	0.420810i	−0.885483	−	0.464672i	$-0.846172\pi$
$397$	−3328.68	+	3328.68i	−0.420810	+	0.420810i	0.464672	+	0.885483i	$0.346172\pi$
$398$	7633.93	+	7633.93i	0.961443	+	0.961443i
$399$	−13304.3			−1.66929
$400$			18102.1i			2.26276i
$401$	−2126.32	+	2126.32i	−0.264797	+	0.264797i	−0.826999	−	0.562203i	$-0.809954\pi$
$401$	−2126.32	+	2126.32i	−0.264797	+	0.264797i	0.562203	+	0.826999i	$0.309954\pi$
$402$	−18670.1			−2.31636
$403$	−1963.42	−	997.156i	−0.242692	−	0.123255i
$404$		−	4202.76i		−	0.517562i
$405$	−24170.6	−	24170.6i	−2.96555	−	2.96555i
$406$		−	8523.17i		−	1.04187i
$407$	−5634.47	+	3879.83i	−0.686218	+	0.472521i
$408$	4342.03	+	4342.03i	0.526869	+	0.526869i
$409$	176.336	−	176.336i	0.0213184	−	0.0213184i	−0.696367	−	0.717686i	$-0.745201\pi$
$409$	176.336	−	176.336i	0.0213184	−	0.0213184i	0.717686	+	0.696367i	$0.245201\pi$
$410$	−3756.68	+	3756.68i	−0.452510	+	0.452510i
$411$	12298.8	−	12298.8i	1.47605	−	1.47605i
$412$	1598.79			0.191181
$413$	4100.41			0.488542
$414$	6142.79	+	6142.79i	0.729231	+	0.729231i
$415$	15401.2			1.82172
$416$	−3770.54	+	7424.27i	−0.444390	+	0.875011i
$417$			9002.44i			1.05720i
$418$	−2961.81	+	16060.0i	−0.346572	+	1.87923i
$419$	9343.56			1.08941			0.544705	−	0.838628i	$-0.316642\pi$
$419$	9343.56			1.08941			0.544705	+	0.838628i	$0.316642\pi$
$420$	8488.57			0.986190
$421$	4868.19	+	4868.19i	0.563565	+	0.563565i	0.930318	−	0.366753i	$-0.119531\pi$
$421$	4868.19	+	4868.19i	0.563565	+	0.563565i	−0.366753	+	0.930318i	$0.619531\pi$
$422$	190.829	+	190.829i	0.0220128	+	0.0220128i
$423$	−12228.8	+	12228.8i	−1.40563	+	1.40563i
$424$	−933.123	−	933.123i	−0.106878	−	0.106878i
$425$		−	11225.9i		−	1.28127i
$426$	15587.3			1.77279
$427$	4145.60	−	4145.60i	0.469836	−	0.469836i
$428$	2050.51			0.231578
$429$	16326.6	−	2186.05i	1.83743	−	0.246023i
$430$	−8132.82			−0.912092
$431$	5660.70	−	5660.70i	0.632636	−	0.632636i	−0.316092	−	0.948728i	$-0.602371\pi$
$431$	5660.70	−	5660.70i	0.632636	−	0.632636i	0.948728	+	0.316092i	$0.102371\pi$
$432$	29849.9			3.32443
$433$		−	2043.67i		−	0.226819i	−0.993548	−	0.113409i	$-0.963823\pi$
$433$		−	2043.67i		−	0.226819i	0.993548	−	0.113409i	$-0.0361772\pi$
$434$	−1264.52	−	1264.52i	−0.139860	−	0.139860i
$435$	−28598.5	+	28598.5i	−3.15216	+	3.15216i
$436$	−2270.62	−	2270.62i	−0.249410	−	0.249410i
$437$	−3387.92	−	3387.92i	−0.370861	−	0.370861i
$438$	−26757.3			−2.91898
$439$	9725.71			1.05736			0.528682	−	0.848820i	$-0.322686\pi$
$439$	9725.71			1.05736			0.528682	+	0.848820i	$0.322686\pi$
$440$	−1596.43	+	8656.41i	−0.172970	+	0.937904i
$441$		−	14839.1i		−	1.60233i
$442$	3693.20	−	7271.98i	0.397438	−	0.782563i
$443$	5012.60			0.537597			0.268799	−	0.963196i	$-0.413373\pi$
$443$	5012.60			0.537597			0.268799	+	0.963196i	$0.413373\pi$
$444$	5538.77	+	5538.77i	0.592023	+	0.592023i
$445$	−25981.0			−2.76768
$446$	−13593.4			−1.44320
$447$	−19983.6	+	19983.6i	−2.11452	+	2.11452i
$448$	115.900	−	115.900i	0.0122227	−	0.0122227i
$449$	11149.1	−	11149.1i	1.17184	−	1.17184i	0.190075	−	0.981770i	$-0.439127\pi$
$449$	11149.1	−	11149.1i	1.17184	−	1.17184i	0.981770	−	0.190075i	$-0.0608731\pi$
$450$	−37024.9	−	37024.9i	−3.87860	−	3.87860i
$451$	−2423.92	+	1669.08i	−0.253077	+	0.174266i
$452$			5286.96i			0.550172i
$453$	9823.43	+	9823.43i	1.01886	+	1.01886i
$454$			5087.19i			0.525889i
$455$	2955.26	+	9054.76i	0.304494	+	0.932953i
$456$	−15796.5			−1.62224
$457$	10682.2	−	10682.2i	1.09341	−	1.09341i	0.0982527	−	0.995161i	$-0.468675\pi$
$457$	10682.2	−	10682.2i	1.09341	−	1.09341i	0.995161	−	0.0982527i	$-0.0313253\pi$
$458$		−	16038.1i		−	1.63627i
$459$	−18511.3			−1.88242
$460$	2161.60	+	2161.60i	0.219098	+	0.219098i
$461$	−12723.7	+	12723.7i	−1.28547	+	1.28547i	−0.347962	+	0.937509i	$0.613126\pi$
$461$	−12723.7	+	12723.7i	−1.28547	+	1.28547i	−0.937509	+	0.347962i	$0.886874\pi$
$462$	13155.0	+	2426.08i	1.32474	+	0.244311i
$463$	−2673.15	+	2673.15i	−0.268320	+	0.268320i	−0.828423	−	0.560103i	$-0.810761\pi$
$463$	−2673.15	+	2673.15i	−0.268320	+	0.268320i	0.560103	+	0.828423i	$0.310761\pi$
$464$		−	17887.9i		−	1.78971i
$465$			8485.91i			0.846289i
$466$	351.163	−	351.163i	0.0349084	−	0.0349084i
$467$			7228.94i			0.716308i	0.933663	+	0.358154i	$0.116594\pi$
$467$			7228.94i			0.716308i	−0.933663	+	0.358154i	$0.883406\pi$
$468$	−4149.11	−	12712.7i	−0.409814	−	1.25565i
$469$		−	5980.24i		−	0.588789i
$470$	−12241.7	+	12241.7i	−1.20142	+	1.20142i
$471$	4603.96			0.450402
$472$	4868.52			0.474771
$473$	−4430.46	−	817.074i	−0.430682	−	0.0794273i
$474$	−3226.93	−	3226.93i	−0.312696	−	0.312696i
$475$	20420.2	+	20420.2i	1.97251	+	1.97251i
$476$	1646.33	−	1646.33i	0.158528	−	0.158528i
$477$	6747.20			0.647658
$478$		−	15192.7i		−	1.45376i
$479$	−5878.24	−	5878.24i	−0.560717	−	0.560717i	0.368794	−	0.929511i	$-0.379771\pi$
$479$	−5878.24	−	5878.24i	−0.560717	−	0.560717i	−0.929511	+	0.368794i	$0.879771\pi$
$480$	32087.7			3.05125
$481$	−3979.91	+	7836.51i	−0.377273	+	0.742856i
$482$	8420.18			0.795703
$483$	−2775.11	+	2775.11i	−0.261432	+	0.261432i
$484$	2058.91	−	5392.22i	0.193362	−	0.506406i
$485$		−	7493.16i		−	0.701540i
$486$	−18556.5	+	18556.5i	−1.73198	+	1.73198i
$487$	5346.45	+	5346.45i	0.497476	+	0.497476i	0.910651	−	0.413176i	$-0.135580\pi$
$487$	5346.45	+	5346.45i	0.497476	+	0.497476i	−0.413176	+	0.910651i	$0.635580\pi$
$488$	4922.18	−	4922.18i	0.456591	−	0.456591i
$489$	−4773.97	+	4773.97i	−0.441486	+	0.441486i
$490$		−	14854.9i		−	1.36954i
$491$	5265.04			0.483926			0.241963	−	0.970285i	$-0.422209\pi$
$491$	5265.04			0.483926			0.241963	+	0.970285i	$0.422209\pi$
$492$	2382.75	+	2382.75i	0.218338	+	0.218338i
$493$			11093.1i			1.01341i
$494$	6509.88	+	19945.9i	0.592901	+	1.81662i
$495$	−25524.5	−	37068.0i	−2.31766	−	3.36582i
$496$	−2653.91	−	2653.91i	−0.240250	−	0.240250i
$497$			4992.80i			0.450619i
$498$		−	27789.4i		−	2.50054i
$499$	−8843.62	−	8843.62i	−0.793376	−	0.793376i	0.188665	−	0.982041i	$-0.439584\pi$
$499$	−8843.62	−	8843.62i	−0.793376	−	0.793376i	−0.982041	+	0.188665i	$0.939584\pi$
$500$	−5841.56	−	5841.56i	−0.522485	−	0.522485i
$501$	6435.22	+	6435.22i	0.573861	+	0.573861i
$502$	7438.69	+	7438.69i	0.661365	+	0.661365i
$503$			22384.5i			1.98425i	0.125266	+	0.992123i	$0.460022\pi$
$503$			22384.5i			1.98425i	−0.125266	+	0.992123i	$0.539978\pi$
$504$			9174.17i			0.810813i
$505$	−12849.9	−	12849.9i	−1.13230	−	1.13230i
$506$	2732.12	+	3967.71i	0.240034	+	0.348590i
$507$	17088.5	−	12484.4i	1.49690	−	1.09360i
$508$		−	1288.40i		−	0.112527i
$509$	8516.34	+	8516.34i	0.741611	+	0.741611i	0.972888	−	0.231277i	$-0.0742902\pi$
$509$	8516.34	+	8516.34i	0.741611	+	0.741611i	−0.231277	+	0.972888i	$0.574290\pi$
$510$	−31429.5			−2.72887
$511$		−	8570.69i		−	0.741966i
$512$	−4220.36	+	4220.36i	−0.364288	+	0.364288i
$513$	33672.4	−	33672.4i	2.89800	−	2.89800i
$514$	−16447.0	−	16447.0i	−1.41138	−	1.41138i
$515$	4888.27	−	4888.27i	0.418258	−	0.418258i
$516$			5158.40i			0.440089i
$517$	−7898.73	+	5438.96i	−0.671926	+	0.462680i
$518$	−5047.04	+	5047.04i	−0.428097	+	0.428097i
$519$	27472.6			2.32353
$520$	3508.85	+	10750.9i	0.295910	+	0.906653i
$521$	−14907.0			−1.25352			−0.626762	−	0.779211i	$-0.715620\pi$
$521$	−14907.0			−1.25352			−0.626762	+	0.779211i	$0.715620\pi$
$522$	36586.9	+	36586.9i	3.06775	+	3.06775i
$523$		−	9893.14i		−	0.827145i	−0.910471	−	0.413573i	$-0.864281\pi$
$523$		−	9893.14i		−	0.827145i	0.910471	−	0.413573i	$-0.135719\pi$
$524$	−428.226			−0.0357006
$525$	16726.6	−	16726.6i	1.39049	−	1.39049i
$526$	3926.57	+	3926.57i	0.325488	+	0.325488i
$527$	1645.81	+	1645.81i	0.136039	+	0.136039i
$528$	27609.0	+	5091.71i	2.27562	+	0.419675i
$529$	10753.6			0.883837
$530$	6754.35			0.553567
$531$	−17601.6	+	17601.6i	−1.43850	+	1.43850i
$532$			5989.41i			0.488109i
$533$	−1712.13	+	3371.22i	−0.139138	+	0.273966i
$534$			46879.3i			3.79900i
$535$	6269.42	−	6269.42i	0.506636	−	0.506636i
$536$		−	7100.49i		−	0.572191i
$537$			38777.5i			3.11615i
$538$	3121.65	−	3121.65i	0.250156	−	0.250156i
$539$	1492.41	−	8092.39i	0.119263	−	0.646686i
$540$	−21484.1	+	21484.1i	−1.71209	+	1.71209i
$541$	13019.8	+	13019.8i	1.03468	+	1.03468i	0.999377	+	0.0353072i	$0.0112410\pi$
$541$	13019.8	+	13019.8i	1.03468	+	1.03468i	0.0353072	+	0.999377i	$0.488759\pi$
$542$	18818.7			1.49139
$543$		−	31723.8i		−	2.50718i
$544$	6223.30	−	6223.30i	0.490481	−	0.490481i
$545$	−13884.8			−1.09130
$546$	16338.1	−	5332.37i	1.28060	−	0.417957i
$547$			2344.90i			0.183292i	0.995792	+	0.0916460i	$0.0292128\pi$
$547$			2344.90i			0.183292i	−0.995792	+	0.0916460i	$0.970787\pi$
$548$	−5536.77	−	5536.77i	−0.431604	−	0.431604i
$549$			35591.1i			2.76684i
$550$	−16467.5	−	23914.9i	−1.27668	−	1.85406i
$551$	−20178.7	−	20178.7i	−1.56014	−	1.56014i
$552$	−3294.96	+	3294.96i	−0.254063	+	0.254063i
$553$	1033.62	−	1033.62i	0.0794831	−	0.0794831i
$554$	5697.15	−	5697.15i	0.436911	−	0.436911i
$555$	33869.4			2.59041
$556$	4052.78			0.309130
$557$	−8326.75	−	8326.75i	−0.633422	−	0.633422i	0.315503	−	0.948925i	$-0.397827\pi$
$557$	−8326.75	−	8326.75i	−0.633422	−	0.633422i	−0.948925	+	0.315503i	$0.897827\pi$
$558$	10856.3			0.823625
$559$	−5502.46	+	1795.88i	−0.416332	+	0.135881i
$560$			16233.7i			1.22500i
$561$	−17121.6	−	3157.61i	−1.28855	−	0.237637i
$562$	7323.69			0.549700
$563$	−5812.61			−0.435120			−0.217560	−	0.976047i	$-0.569810\pi$
$563$	−5812.61			−0.435120			−0.217560	+	0.976047i	$0.569810\pi$
$564$	7764.56	+	7764.56i	0.579694	+	0.579694i
$565$	16164.8	+	16164.8i	1.20364	+	1.20364i
$566$	12405.7	−	12405.7i	0.921288	−	0.921288i
$567$	−13969.6	−	13969.6i	−1.03469	−	1.03469i
$568$			5928.07i			0.437916i
$569$	7654.57			0.563965			0.281983	−	0.959420i	$-0.409008\pi$
$569$	7654.57			0.563965			0.281983	+	0.959420i	$0.409008\pi$
$570$	57171.0	−	57171.0i	4.20111	−	4.20111i
$571$	22443.1			1.64486			0.822431	−	0.568865i	$-0.192617\pi$
$571$	22443.1			1.64486			0.822431	+	0.568865i	$0.192617\pi$
$572$	−984.132	−	7350.01i	−0.0719382	−	0.537272i
$573$	13678.8			0.997275
$574$	−2171.21	+	2171.21i	−0.157882	+	0.157882i
$575$	8518.81			0.617842
$576$			995.034i			0.0719787i
$577$	−2658.79	−	2658.79i	−0.191832	−	0.191832i	0.604655	−	0.796487i	$-0.293311\pi$
$577$	−2658.79	−	2658.79i	−0.191832	−	0.191832i	−0.796487	+	0.604655i	$0.793311\pi$
$578$	6106.28	−	6106.28i	0.439425	−	0.439425i
$579$	3915.75	+	3915.75i	0.281058	+	0.281058i
$580$	12874.6	+	12874.6i	0.921707	+	0.921707i
$581$	8901.25			0.635604
$582$	−13520.4			−0.962952
$583$	3679.52	+	678.585i	0.261390	+	0.0482060i
$584$		−	10176.2i		−	0.721051i
$585$	−51554.6	−	26182.9i	−3.64363	−	1.85048i
$586$	−31735.8			−2.23719
$587$	6558.00	+	6558.00i	0.461121	+	0.461121i	0.899023	−	0.437902i	$-0.144278\pi$
$587$	6558.00	+	6558.00i	0.461121	+	0.461121i	−0.437902	+	0.899023i	$0.644278\pi$
$588$	−9422.00			−0.660811
$589$	−5987.53			−0.418866
$590$	−17620.2	+	17620.2i	−1.22951	+	1.22951i
$591$	3818.74	−	3818.74i	0.265790	−	0.265790i
$592$	−10592.4	+	10592.4i	−0.735382	+	0.735382i
$593$	−8339.07	−	8339.07i	−0.577478	−	0.577478i	0.356730	−	0.934208i	$-0.383892\pi$
$593$	−8339.07	−	8339.07i	−0.577478	−	0.577478i	−0.934208	+	0.356730i	$0.883892\pi$
$594$	−39435.0	+	27154.4i	−2.72397	+	1.87569i
$595$		−	10067.2i		−	0.693642i
$596$	8996.33	+	8996.33i	0.618295	+	0.618295i
$597$		−	29608.5i		−	2.02981i
$598$	5518.35	+	2802.59i	0.377361	+	0.191650i
$599$	9915.38			0.676346			0.338173	−	0.941084i	$-0.390191\pi$
$599$	9915.38			0.676346			0.338173	+	0.941084i	$0.390191\pi$
$600$	19859.9	−	19859.9i	1.35130	−	1.35130i
$601$			19668.4i			1.33492i	0.744644	+	0.667462i	$0.232619\pi$
$601$			19668.4i			1.33492i	−0.744644	+	0.667462i	$0.767381\pi$
$602$	−4700.44			−0.318232
$603$	25671.0	+	25671.0i	1.73367	+	1.73367i
$604$	4422.37	−	4422.37i	0.297920	−	0.297920i
$605$	−10191.5	−	22781.7i	−0.684867	−	1.53092i
$606$	−23185.9	+	23185.9i	−1.55423	+	1.55423i
$607$		−	27406.7i		−	1.83263i	−0.400461	−	0.916314i	$-0.631150\pi$
$607$		−	27406.7i		−	1.83263i	0.400461	−	0.916314i	$-0.368850\pi$
$608$			22640.6i			1.51020i
$609$	−16528.7	+	16528.7i	−1.09980	+	1.09980i
$610$			35628.9i			2.36487i
$611$	−5579.26	+	10985.7i	−0.369415	+	0.727385i
$612$			14134.2i			0.933562i
$613$	−1320.10	+	1320.10i	−0.0869793	+	0.0869793i	−0.749258	−	0.662278i	$-0.769590\pi$
$613$	−1320.10	+	1320.10i	−0.0869793	+	0.0869793i	0.662278	+	0.749258i	$0.269590\pi$
$614$	−15599.9			−1.02534
$615$	14570.4			0.955344
$616$	−922.672	+	5003.05i	−0.0603499	+	0.327238i
$617$	−12706.0	−	12706.0i	−0.829050	−	0.829050i	0.158335	−	0.987385i	$-0.449387\pi$
$617$	−12706.0	−	12706.0i	−0.829050	−	0.829050i	−0.987385	+	0.158335i	$0.949387\pi$
$618$	−8820.23	−	8820.23i	−0.574113	−	0.574113i
$619$	1532.05	−	1532.05i	0.0994800	−	0.0994800i	−0.655615	−	0.755095i	$-0.727591\pi$
$619$	1532.05	−	1532.05i	0.0994800	−	0.0994800i	0.755095	+	0.655615i	$0.227591\pi$
$620$	3820.24			0.247459
$621$		−	14047.3i		−	0.907728i
$622$	−9054.85	−	9054.85i	−0.583708	−	0.583708i
$623$	−15016.0			−0.965654
$624$	34289.4	−	11191.3i	2.19980	−	0.717963i
$625$	−7396.44			−0.473372
$626$	8833.59	−	8833.59i	0.563996	−	0.563996i
$627$	36888.4	−	25400.9i	2.34957	−	1.61789i
$628$		−	2072.64i		−	0.131700i
$629$	6568.85	−	6568.85i	0.416403	−	0.416403i
$630$	−33203.3	−	33203.3i	−2.09977	−	2.09977i
$631$	17414.5	−	17414.5i	1.09867	−	1.09867i	0.104101	−	0.994567i	$-0.466804\pi$
$631$	17414.5	−	17414.5i	1.09867	−	1.09867i	0.994567	−	0.104101i	$-0.0331965\pi$
$632$	1227.25	−	1227.25i	0.0772425	−	0.0772425i
$633$		−	740.138i		−	0.0464737i
$634$	−24361.2			−1.52603
$635$	−3939.28	−	3939.28i	−0.246182	−	0.246182i
$636$		−	4284.08i		−	0.267099i
$637$	−3280.23	−	10050.4i	−0.204031	−	0.625138i
$638$	16272.7	+	23631.9i	1.00978	+	1.46645i
$639$	−21432.3	−	21432.3i	−1.32683	−	1.32683i
$640$			27645.0i			1.70744i
$641$		−	12526.2i		−	0.771851i	−0.922530	−	0.385925i	$-0.873882\pi$
$641$		−	12526.2i		−	0.771851i	0.922530	−	0.385925i	$-0.126118\pi$
$642$	−11312.3	−	11312.3i	−0.695423	−	0.695423i
$643$	−17373.7	−	17373.7i	−1.06555	−	1.06555i	−0.997695	−	0.0678590i	$-0.978383\pi$
$643$	−17373.7	−	17373.7i	−1.06555	−	1.06555i	−0.0678590	−	0.997695i	$-0.521617\pi$
$644$	1249.32	+	1249.32i	0.0764441	+	0.0764441i
$645$	15771.7	+	15771.7i	0.962809	+	0.962809i
$646$		−	22176.2i		−	1.35064i
$647$		−	8770.83i		−	0.532947i	−0.963842	−	0.266474i	$-0.914141\pi$
$647$		−	8770.83i		−	0.532947i	0.963842	−	0.266474i	$-0.0858585\pi$
$648$	−16586.5	−	16586.5i	−1.00552	−	1.00552i
$649$	−11369.1	+	7828.61i	−0.687636	+	0.473497i
$650$	−33261.1	−	16892.2i	−2.00709	−	1.01934i
$651$			4904.51i			0.295273i
$652$	2149.18	+	2149.18i	0.129092	+	0.129092i
$653$	−6563.20			−0.393320			−0.196660	−	0.980472i	$-0.563010\pi$
$653$	−6563.20			−0.393320			−0.196660	+	0.980472i	$0.563010\pi$
$654$			25053.2i			1.49795i
$655$	−1309.29	+	1309.29i	−0.0781044	+	0.0781044i
$656$	−4556.80	+	4556.80i	−0.271209	+	0.271209i
$657$	36790.8	+	36790.8i	2.18470	+	2.18470i
$658$	−7075.23	+	7075.23i	−0.419181	+	0.419181i
$659$		−	5080.22i		−	0.300300i	−0.988663	−	0.150150i	$-0.952024\pi$
$659$		−	5080.22i		−	0.300300i	0.988663	−	0.150150i	$-0.0479756\pi$
$660$	−23536.0	+	16206.6i	−1.38809	+	0.955820i
$661$	−6836.92	+	6836.92i	−0.402308	+	0.402308i	−0.879046	−	0.476738i	$-0.841819\pi$
$661$	−6836.92	+	6836.92i	−0.402308	+	0.402308i	0.476738	+	0.879046i	$0.341819\pi$
$662$	−18155.5			−1.06591
$663$	−21264.5	+	6940.22i	−1.24562	+	0.406540i
$664$	10568.7			0.617687
$665$	18312.5	+	18312.5i	1.06786	+	1.06786i
$666$		−	43330.2i		−	2.52104i
$667$	−8418.04			−0.488677
$668$	2897.05	−	2897.05i	0.167800	−	0.167800i
$669$	26361.3	+	26361.3i	1.52345	+	1.52345i
$670$	25698.2	+	25698.2i	1.48180	+	1.48180i
$671$	−3579.50	+	19409.3i	−0.205939	+	1.11667i
$672$	18545.4			1.06459
$673$	−26653.9			−1.52664			−0.763322	−	0.646018i	$-0.776433\pi$
$673$	−26653.9			−1.52664			−0.763322	+	0.646018i	$0.776433\pi$
$674$	23872.9	−	23872.9i	1.36431	−	1.36431i
$675$			84668.3i			4.82798i
$676$	−5620.33	−	7693.02i	−0.319773	−	0.437700i
$677$			19821.5i			1.12526i	0.826709	+	0.562630i	$0.190210\pi$
$677$			19821.5i			1.12526i	−0.826709	+	0.562630i	$0.809790\pi$
$678$	29167.2	−	29167.2i	1.65215	−	1.65215i
$679$		−	4330.74i		−	0.244769i
$680$		−	11953.1i		−	0.674089i
$681$	9865.43	−	9865.43i	0.555131	−	0.555131i
$682$	5920.37	+	1091.85i	0.332409	+	0.0613035i
$683$	−16400.4	+	16400.4i	−0.918806	+	0.918806i	−0.996943	−	0.0781366i	$-0.975103\pi$
$683$	−16400.4	+	16400.4i	−0.918806	+	0.918806i	0.0781366	+	0.996943i	$0.475103\pi$
$684$	−25710.4	−	25710.4i	−1.43722	−	1.43722i
$685$	−33857.2			−1.88849
$686$		−	21641.5i		−	1.20448i
$687$	−31102.2	+	31102.2i	−1.72725	+	1.72725i
$688$	−9865.00			−0.546656
$689$	4569.83	−	1491.49i	0.252680	−	0.0824689i
$690$		−	23850.3i		−	1.31589i
$691$	−17324.0	−	17324.0i	−0.953740	−	0.953740i	0.0452360	−	0.998976i	$-0.485596\pi$
$691$	−17324.0	−	17324.0i	−0.953740	−	0.953740i	−0.998976	+	0.0452360i	$0.985596\pi$
$692$		−	12367.8i		−	0.679411i
$693$	−14752.1	−	21423.8i	−0.808639	−	1.17435i
$694$	18040.3	+	18040.3i	0.986746	+	0.986746i
$695$	12391.3	−	12391.3i	0.676301	−	0.676301i
$696$	−19625.0	+	19625.0i	−1.06880	+	1.06880i
$697$	2825.88	−	2825.88i	0.153570	−	0.153570i
$698$	35411.7			1.92027
$699$	−1362.00			−0.0736989
$700$	−7530.09	−	7530.09i	−0.406587	−	0.406587i
$701$	4007.48			0.215921			0.107960	−	0.994155i	$-0.465568\pi$
$701$	4007.48			0.215921			0.107960	+	0.994155i	$0.465568\pi$
$702$	−27854.9	+	54846.8i	−1.49760	+	2.94880i
$703$			23897.8i			1.28211i
$704$	−100.073	+	542.633i	−0.00535747	+	0.0290500i
$705$	47480.1			2.53646
$706$	−22731.5			−1.21177
$707$	−7426.71	−	7426.71i	−0.395064	−	0.395064i
$708$	11176.0	+	11176.0i	0.593247	+	0.593247i
$709$	1034.50	−	1034.50i	0.0547975	−	0.0547975i	−0.679177	−	0.733974i	$-0.737663\pi$
$709$	1034.50	−	1034.50i	0.0547975	−	0.0547975i	0.733974	+	0.679177i	$0.237663\pi$
$710$	−21455.0	−	21455.0i	−1.13407	−	1.13407i
$711$			8873.94i			0.468072i
$712$	−17828.8			−0.938433
$713$	−1248.93	+	1248.93i	−0.0655998	+	0.0655998i
$714$	−18165.0			−0.952111
$715$	−25481.5	−	19463.6i	−1.33281	−	1.01804i
$716$	17457.1			0.911177
$717$	−29462.8	+	29462.8i	−1.53460	+	1.53460i
$718$	16870.4			0.876876
$719$		−	5682.69i		−	0.294755i	−0.989080	−	0.147377i	$-0.952917\pi$
$719$		−	5682.69i		−	0.294755i	0.989080	−	0.147377i	$-0.0470832\pi$
$720$	−69685.2	−	69685.2i	−3.60696	−	3.60696i
$721$	2825.22	−	2825.22i	0.145932	−	0.145932i
$722$	23304.0	+	23304.0i	1.20123	+	1.20123i
$723$	−16329.0	−	16329.0i	−0.839948	−	0.839948i
$724$	−14281.6			−0.733112
$725$	50738.6			2.59915
$726$	−41106.6	+	18389.2i	−2.10139	+	0.940067i
$727$			3935.94i			0.200792i	0.994948	+	0.100396i	$0.0320110\pi$
$727$			3935.94i			0.200792i	−0.994948	+	0.100396i	$0.967989\pi$
$728$	2027.97	+	6213.60i	0.103244	+	0.316334i
$729$	22751.9			1.15592
$730$	36829.9	+	36829.9i	1.86731	+	1.86731i
$731$	6117.74			0.309539
$732$	22598.3			1.14106
$733$	9487.45	−	9487.45i	0.478072	−	0.478072i	−0.426442	−	0.904515i	$-0.640233\pi$
$733$	9487.45	−	9487.45i	0.478072	−	0.478072i	0.904515	+	0.426442i	$0.140233\pi$
$734$	24674.4	−	24674.4i	1.24080	−	1.24080i
$735$	−28807.6	+	28807.6i	−1.44570	+	1.44570i
$736$	4722.56	+	4722.56i	0.236516	+	0.236516i
$737$	11417.6	+	16581.2i	0.570657	+	0.828735i
$738$		−	18640.4i		−	0.929760i
$739$	−24510.7	−	24510.7i	−1.22008	−	1.22008i	−0.967603	−	0.252478i	$-0.918755\pi$
$739$	−24510.7	−	24510.7i	−1.22008	−	1.22008i	−0.252478	−	0.967603i	$-0.581245\pi$
$740$		−	15247.6i		−	0.757448i
$741$	26056.1	−	51304.9i	1.29176	−	2.54350i
$742$	3903.74			0.193141
$743$	917.026	−	917.026i	0.0452791	−	0.0452791i	−0.684105	−	0.729384i	$-0.739807\pi$
$743$	917.026	−	917.026i	0.0452791	−	0.0452791i	0.729384	+	0.684105i	$0.239807\pi$
$744$			5823.24i			0.286950i
$745$	55012.3			2.70536
$746$	14351.7	+	14351.7i	0.704360	+	0.704360i
$747$	−38209.8	+	38209.8i	−1.87152	+	1.87152i
$748$	−1421.51	+	7707.93i	−0.0694862	+	0.376778i
$749$	3623.46	−	3623.46i	0.176767	−	0.176767i
$750$			64453.7i			3.13802i
$751$			5099.45i			0.247778i	0.992296	+	0.123889i	$0.0395367\pi$
$751$			5099.45i			0.247778i	−0.992296	+	0.123889i	$0.960463\pi$
$752$	−14849.1	+	14849.1i	−0.720066	+	0.720066i
$753$		−	28851.3i		−	1.39628i
$754$	32867.6	+	16692.4i	1.58749	+	0.806235i
$755$		−	27042.7i		−	1.30356i
$756$	−12416.9	+	12416.9i	−0.597354	+	0.597354i
$757$	955.946			0.0458976			0.0229488	−	0.999737i	$-0.492695\pi$
$757$	955.946			0.0458976			0.0229488	+	0.999737i	$0.492695\pi$
$758$	19340.7			0.926760
$759$	2396.16	−	12992.8i	0.114591	−	0.621355i
$760$	21742.9	+	21742.9i	1.03776	+	1.03776i
$761$	11742.3	+	11742.3i	0.559339	+	0.559339i	0.929119	−	0.369780i	$-0.120567\pi$
$761$	11742.3	+	11742.3i	0.559339	+	0.559339i	−0.369780	+	0.929119i	$0.620567\pi$
$762$	−7107.90	+	7107.90i	−0.337916	+	0.337916i
$763$	−8024.82			−0.380758
$764$		−	6158.00i		−	0.291608i
$765$	43215.0	+	43215.0i	2.04241	+	2.04241i
$766$	−4103.76			−0.193570
$767$	−8030.55	+	15812.3i	−0.378052	+	0.744392i
$768$	48716.1			2.28892
$769$	6518.27	−	6518.27i	0.305663	−	0.305663i	−0.537562	−	0.843225i	$-0.680654\pi$
$769$	6518.27	−	6518.27i	0.305663	−	0.305663i	0.843225	+	0.537562i	$0.180654\pi$
$770$	−14767.8	−	21446.5i	−0.691161	−	1.00374i
$771$			63790.5i			2.97971i
$772$	1762.82	−	1762.82i	0.0821828	−	0.0821828i
$773$	−27600.2	−	27600.2i	−1.28423	−	1.28423i	−0.938236	−	0.345997i	$-0.887541\pi$
$773$	−27600.2	−	27600.2i	−1.28423	−	1.28423i	−0.345997	−	0.938236i	$-0.612459\pi$
$774$	20177.3	−	20177.3i	0.937024	−	0.937024i
$775$	7527.73	−	7527.73i	0.348909	−	0.348909i
$776$		−	5141.99i		−	0.237870i
$777$	19575.1			0.903802
$778$	13275.1	+	13275.1i	0.611744	+	0.611744i
$779$			10280.7i			0.472842i
$780$	−16624.6	+	32734.2i	−0.763151	+	1.50266i
$781$	−9532.38	−	13843.4i	−0.436742	−	0.634258i
$782$	−4625.69	−	4625.69i	−0.211527	−	0.211527i
$783$		−	83666.7i		−	3.81865i
$784$		−	18018.8i		−	0.820826i
$785$	−6337.07	−	6337.07i	−0.288127	−	0.288127i
$786$	2362.45	+	2362.45i	0.107208	+	0.107208i
$787$	12532.1	+	12532.1i	0.567625	+	0.567625i	0.931462	−	0.363837i	$-0.118534\pi$
$787$	12532.1	+	12532.1i	0.567625	+	0.567625i	−0.363837	+	0.931462i	$0.618534\pi$
$788$	−1719.15	−	1719.15i	−0.0777183	−	0.0777183i
$789$		−	15229.4i		−	0.687173i
$790$			8883.36i			0.400070i
$791$	9342.60	+	9342.60i	0.419955	+	0.419955i
$792$	−17515.6	−	25437.0i	−0.785844	−	1.14124i
$793$	7867.51	+	24105.6i	0.352312	+	1.07947i
$794$		−	16534.2i		−	0.739015i
$795$	−13098.5	−	13098.5i	−0.584348	−	0.584348i
$796$	−13329.4			−0.593526
$797$		−	14506.8i		−	0.644738i	−0.946614	−	0.322369i	$-0.895521\pi$
$797$		−	14506.8i		−	0.644738i	0.946614	−	0.322369i	$-0.104479\pi$
$798$	33042.5	−	33042.5i	1.46578	−	1.46578i
$799$	9208.60	−	9208.60i	0.407731	−	0.407731i
$800$	−28464.6	−	28464.6i	−1.25797	−	1.25797i
$801$	64458.1	−	64458.1i	2.84334	−	2.84334i
$802$		−	10561.9i		−	0.465028i
$803$	16363.4	+	23763.7i	0.719117	+	1.04434i
$804$	16299.6	−	16299.6i	0.714978	−	0.714978i
$805$	7639.54			0.334483
$806$	7352.88	−	2399.81i	0.321333	−	0.104875i
$807$	−12107.4			−0.528131
$808$	−8817.92	−	8817.92i	−0.383927	−	0.383927i
$809$			25098.4i			1.09075i	0.838193	+	0.545373i	$0.183612\pi$
$809$			25098.4i			1.09075i	−0.838193	+	0.545373i	$0.816388\pi$
$810$	120060.			5.20800
$811$	−4872.86	+	4872.86i	−0.210986	+	0.210986i	−0.804686	−	0.593701i	$-0.797666\pi$
$811$	−4872.86	+	4872.86i	−0.210986	+	0.210986i	0.593701	+	0.804686i	$0.297666\pi$
$812$	7441.01	+	7441.01i	0.321587	+	0.321587i
$813$	−36494.6	−	36494.6i	−1.57432	−	1.57432i
$814$	4357.84	−	23629.7i	0.187644	−	1.01747i
$815$	13142.2			0.564847
$816$	−38123.6			−1.63553
$817$	−11128.3	+	11128.3i	−0.476537	+	0.476537i
$818$			875.895i			0.0374388i
$819$	−29796.5	−	15132.7i	−1.27127	−	0.645638i
$820$		−	6559.42i		−	0.279347i
$821$	−1895.03	+	1895.03i	−0.0805565	+	0.0805565i	−0.746237	−	0.665680i	$-0.768141\pi$
$821$	−1895.03	+	1895.03i	−0.0805565	+	0.0805565i	0.665680	+	0.746237i	$0.268141\pi$
$822$			61090.8i			2.59220i
$823$		−	3983.05i		−	0.168700i	−0.996436	−	0.0843501i	$-0.973119\pi$
$823$		−	3983.05i		−	0.168700i	0.996436	−	0.0843501i	$-0.0268814\pi$
$824$	3354.46	−	3354.46i	0.141818	−	0.141818i
$825$	−14442.5	+	78312.3i	−0.609483	+	3.30483i
$826$	−10183.8	+	10183.8i	−0.428982	+	0.428982i
$827$	16560.2	+	16560.2i	0.696317	+	0.696317i	0.963614	−	0.267297i	$-0.0861304\pi$
$827$	16560.2	+	16560.2i	0.696317	+	0.696317i	−0.267297	+	0.963614i	$0.586130\pi$
$828$	−10725.7			−0.450175
$829$			44730.6i			1.87402i	0.349308	+	0.937008i	$0.386417\pi$
$829$			44730.6i			1.87402i	−0.349308	+	0.937008i	$0.613583\pi$
$830$	−38250.4	+	38250.4i	−1.59963	+	1.59963i
$831$	−22096.6			−0.922412
$832$	219.955	+	673.930i	0.00916534	+	0.0280821i
$833$			11174.3i			0.464785i
$834$	−22358.5	−	22358.5i	−0.928309	−	0.928309i
$835$		−	17715.4i		−	0.734211i
$836$	−11435.1	−	16606.7i	−0.473077	−	0.687026i
$837$	−12413.0	−	12413.0i	−0.512614	−	0.512614i
$838$	−23205.7	+	23205.7i	−0.956595	+	0.956595i
$839$	17912.0	−	17912.0i	0.737059	−	0.737059i	−0.234949	−	0.972008i	$-0.575492\pi$
$839$	17912.0	−	17912.0i	0.737059	−	0.737059i	0.972008	+	0.234949i	$0.0754922\pi$
$840$	17810.1	−	17810.1i	0.731555	−	0.731555i
$841$	−25749.4			−1.05578
$842$	−24181.3			−0.989716
$843$	−14202.6	−	14202.6i	−0.580266	−	0.580266i
$844$	−333.200			−0.0135891
$845$	−40705.4	−	6337.22i	−1.65717	−	0.257996i
$846$		−	60742.8i		−	2.46853i
$847$	−5890.29	−	13166.9i	−0.238952	−	0.534144i
$848$	8192.94			0.331777
$849$	−48115.9			−1.94503
$850$	27880.7	+	27880.7i	1.12506	+	1.12506i
$851$	4984.78	+	4984.78i	0.200795	+	0.200795i
$852$	−13608.2	+	13608.2i	−0.547196	+	0.547196i
$853$	−13484.8	−	13484.8i	−0.541277	−	0.541277i	0.382626	−	0.923903i	$-0.375020\pi$
$853$	−13484.8	−	13484.8i	−0.541277	−	0.541277i	−0.923903	+	0.382626i	$0.875020\pi$
$854$			20592.0i			0.825111i
$855$	−157218.			−6.28860
$856$	4302.23	−	4302.23i	0.171784	−	0.171784i
$857$	−1901.67			−0.0757992			−0.0378996	−	0.999282i	$-0.512067\pi$
$857$	−1901.67			−0.0757992			−0.0378996	+	0.999282i	$0.512067\pi$
$858$	−35119.4	+	45978.0i	−1.39739	+	1.82944i
$859$	−42242.6			−1.67788			−0.838940	−	0.544224i	$-0.816824\pi$
$859$	−42242.6			−1.67788			−0.838940	+	0.544224i	$0.816824\pi$
$860$	7100.23	−	7100.23i	0.281530	−	0.281530i
$861$	8421.12			0.333323
$862$			28117.8i			1.11102i
$863$	34116.8	+	34116.8i	1.34571	+	1.34571i	0.890261	+	0.455451i	$0.150522\pi$
$863$	34116.8	+	34116.8i	1.34571	+	1.34571i	0.455451	+	0.890261i	$0.349478\pi$
$864$	−46937.4	+	46937.4i	−1.84820	+	1.84820i
$865$	−37814.3	−	37814.3i	−1.48639	−	1.48639i
$866$	5075.66	+	5075.66i	0.199166	+	0.199166i
$867$	−23683.5			−0.927719
$868$	2207.94			0.0863392
$869$	−892.478	+	4839.32i	−0.0348392	+	0.188910i
$870$		−	142054.i		−	5.53573i
$871$	23061.4	+	11712.1i	0.897138	+	0.455627i
$872$	−9528.07			−0.370024
$873$	18590.3	+	18590.3i	0.720717	+	0.720717i
$874$	16828.5			0.651294
$875$	−20645.3			−0.797643
$876$	23360.1	−	23360.1i	0.900985	−	0.900985i
$877$	19149.8	−	19149.8i	0.737334	−	0.737334i	−0.234727	−	0.972061i	$-0.575420\pi$
$877$	19149.8	−	19149.8i	0.737334	−	0.737334i	0.972061	+	0.234727i	$0.0754198\pi$
$878$	−24154.8	+	24154.8i	−0.928455	+	0.928455i
$879$	61544.4	+	61544.4i	2.36159	+	2.36159i
$880$	−30993.7	−	45010.6i	−1.18727	−	1.72421i
$881$			18287.9i			0.699357i	0.936870	+	0.349679i	$0.113709\pi$
$881$			18287.9i			0.699357i	−0.936870	+	0.349679i	$0.886291\pi$
$882$	36854.5	+	36854.5i	1.40698	+	1.40698i
$883$		−	16512.8i		−	0.629332i	−0.949202	−	0.314666i	$-0.898107\pi$
$883$		−	16512.8i		−	0.629332i	0.949202	−	0.314666i	$-0.101893\pi$
$884$	3124.39	+	9572.97i	0.118874	+	0.364224i
$885$	68340.8			2.59576
$886$	−12449.3	+	12449.3i	−0.472056	+	0.472056i
$887$			50469.0i			1.91046i	0.295858	+	0.955232i	$0.404395\pi$
$887$			50469.0i			1.91046i	−0.295858	+	0.955232i	$0.595605\pi$
$888$	23242.1			0.878325
$889$	−2276.74	−	2276.74i	−0.0858937	−	0.0858937i
$890$	64526.5	−	64526.5i	2.43026	−	2.43026i
$891$	65404.3	+	12062.0i	2.45918	+	0.453527i
$892$	11867.5	−	11867.5i	0.445464	−	0.445464i
$893$			33501.3i			1.25541i
$894$		−	99262.3i		−	3.71345i
$895$	53374.9	−	53374.9i	1.99344	−	1.99344i
$896$			15977.7i			0.595732i
$897$	−5266.60	−	16136.6i	−0.196038	−	0.600651i
$898$			55379.8i			2.05796i
$899$	−7438.68	+	7438.68i	−0.275967	+	0.275967i
$900$	64647.9			2.39437
$901$	−5080.82			−0.187865
$902$	1874.72	−	10165.4i	0.0692032	−	0.375244i
$903$	9115.42	+	9115.42i	0.335927	+	0.335927i
$904$	11092.7	+	11092.7i	0.408117	+	0.408117i
$905$	−43665.9	+	43665.9i	−1.60387	+	1.60387i
$906$	−48794.9			−1.78930
$907$			19286.0i			0.706042i	0.935615	+	0.353021i	$0.114846\pi$
$907$			19286.0i			0.706042i	−0.935615	+	0.353021i	$0.885154\pi$
$908$	−4441.29	−	4441.29i	−0.162323	−	0.162323i
$909$	63760.3			2.32651
$910$	−29828.1	−	15148.7i	−1.08658	−	0.551840i
$911$	35667.4			1.29716			0.648580	−	0.761147i	$-0.275363\pi$
$911$	35667.4			1.29716			0.648580	+	0.761147i	$0.275363\pi$
$912$	69347.7	−	69347.7i	2.51791	−	2.51791i
$913$	−24680.3	+	16994.5i	−0.894630	+	0.616031i
$914$			53060.4i			1.92022i
$915$	69094.1	−	69094.1i	2.49637	−	2.49637i
$916$	14001.8	+	14001.8i	0.505057	+	0.505057i
$917$	−756.719	+	756.719i	−0.0272509	+	0.0272509i
$918$	45974.6	−	45974.6i	1.65293	−	1.65293i
$919$			32219.0i			1.15648i	0.815866	+	0.578241i	$0.196261\pi$
$919$			32219.0i			1.15648i	−0.815866	+	0.578241i	$0.803739\pi$
$920$	9070.62			0.325054
$921$	30252.4	+	30252.4i	1.08236	+	1.08236i
$922$		−	63201.2i		−	2.25750i
$923$	−19253.6	−	9778.26i	−0.686608	−	0.348706i
$924$	−13602.8	+	9366.75i	−0.484308	+	0.333489i
$925$	−30045.1	−	30045.1i	−1.06798	−	1.06798i
$926$		−	13278.1i		−	0.471215i
$927$			24255.3i			0.859384i
$928$	28127.9	+	28127.9i	0.994981	+	0.994981i
$929$	37112.8	+	37112.8i	1.31069	+	1.31069i	0.920906	+	0.389785i	$0.127451\pi$
$929$	37112.8	+	37112.8i	1.31069	+	1.31069i	0.389785	+	0.920906i	$0.372549\pi$
$930$	−21075.6	−	21075.6i	−0.743114	−	0.743114i
$931$	−20326.3	−	20326.3i	−0.715538	−	0.715538i
$932$			613.154i			0.0215499i
$933$			35119.6i			1.23233i
$934$	−17953.8	−	17953.8i	−0.628979	−	0.628979i
$935$	19220.7	+	27913.2i	0.672281	+	0.976319i
$936$	−35378.1	−	17967.4i	−1.23544	−	0.627438i
$937$		−	38112.1i		−	1.32878i	−0.747386	−	0.664390i	$-0.768691\pi$
$937$		−	38112.1i		−	1.32878i	0.747386	−	0.664390i	$-0.231309\pi$
$938$	14852.5	+	14852.5i	0.517006	+	0.517006i
$939$	−34261.5			−1.19071
$940$		−	21374.9i		−	0.741673i
$941$	25382.6	−	25382.6i	0.879331	−	0.879331i	−0.114134	−	0.993465i	$-0.536409\pi$
$941$	25382.6	−	25382.6i	0.879331	−	0.879331i	0.993465	+	0.114134i	$0.0364095\pi$
$942$	−11434.4	+	11434.4i	−0.395491	+	0.395491i
$943$	2144.43	+	2144.43i	0.0740531	+	0.0740531i
$944$	−21373.1	+	21373.1i	−0.736902	+	0.736902i
$945$			75929.3i			2.61373i
$946$	13032.8	−	8974.20i	0.447919	−	0.308432i
$947$	37705.2	−	37705.2i	1.29383	−	1.29383i	0.361426	−	0.932401i	$-0.382290\pi$
$947$	37705.2	−	37705.2i	1.29383	−	1.29383i	0.932401	−	0.361426i	$-0.117710\pi$
$948$	5634.44			0.193036
$949$	33050.9	+	16785.5i	1.13053	+	0.574162i
$950$	−101431.			−3.46407
$951$	47242.9	+	47242.9i	1.61089	+	1.61089i
$952$		−	6908.40i		−	0.235192i
$953$	−55783.5			−1.89612			−0.948062	−	0.318086i	$-0.896960\pi$
$953$	−55783.5			−1.89612			−0.948062	+	0.318086i	$0.896960\pi$
$954$	−16757.3	+	16757.3i	−0.568699	+	0.568699i
$955$	−18828.0	−	18828.0i	−0.637968	−	0.637968i
$956$	13263.8	+	13263.8i	0.448725	+	0.448725i
$957$	14271.7	−	77385.8i	0.482066	−	2.61393i
$958$	29198.4			0.984714
$959$	−19568.1			−0.658901
$960$	1931.69	−	1931.69i	0.0649427	−	0.0649427i
$961$		−	27583.7i		−	0.925909i
$962$	−9578.25	−	29347.2i	−0.321014	−	0.983568i
$963$			31108.4i			1.04097i
$964$	−7351.10	+	7351.10i	−0.245605	+	0.245605i
$965$		−	10779.6i		−	0.359593i
$966$		−	13784.5i		−	0.459120i
$967$	−21175.5	+	21175.5i	−0.704198	+	0.704198i	−0.965309	−	0.261111i	$-0.915911\pi$
$967$	−21175.5	+	21175.5i	−0.704198	+	0.704198i	0.261111	+	0.965309i	$0.415911\pi$
$968$	−6993.68	−	15633.4i	−0.232216	−	0.519087i
$969$	−43005.7	+	43005.7i	−1.42574	+	1.42574i
$970$	18610.0	+	18610.0i	0.616011	+	0.616011i
$971$	−18110.6			−0.598553			−0.299277	−	0.954166i	$-0.596745\pi$
$971$	−18110.6			−0.598553			−0.299277	+	0.954166i	$0.596745\pi$
$972$		−	32400.9i		−	1.06920i
$973$	7161.67	−	7161.67i	0.235964	−	0.235964i
$974$	−26556.9			−0.873652
$975$	31743.7	+	97260.9i	1.04268	+	3.19471i
$976$			43217.4i			1.41737i
$977$	−20119.7	−	20119.7i	−0.658838	−	0.658838i	0.296267	−	0.955105i	$-0.404258\pi$
$977$	−20119.7	−	20119.7i	−0.658838	−	0.658838i	−0.955105	+	0.296267i	$0.904258\pi$
$978$		−	23713.3i		−	0.775324i
$979$	41634.4	−	28668.9i	1.35918	−	0.935916i
$980$	12968.8	+	12968.8i	0.422728	+	0.422728i
$981$	34447.6	−	34447.6i	1.12113	−	1.12113i
$982$	−13076.2	+	13076.2i	−0.424929	+	0.424929i
$983$	−2207.99	+	2207.99i	−0.0716420	+	0.0716420i	−0.742020	−	0.670378i	$-0.766132\pi$
$983$	−2207.99	+	2207.99i	−0.0716420	+	0.0716420i	0.670378	+	0.742020i	$0.266132\pi$
$984$	9998.60			0.323927
$985$	−10512.5			−0.340058
$986$	−27550.9	−	27550.9i	−0.889857	−	0.889857i
$987$	27441.6			0.884979
$988$	−23096.8	−	11730.1i	−0.743731	−	0.377717i
$989$			4642.46i			0.149263i
$990$	155455.	+	28669.3i	4.99058	+	0.920373i
$991$	7512.14			0.240798			0.120399	−	0.992726i	$-0.461583\pi$
$991$	7512.14			0.240798			0.120399	+	0.992726i	$0.461583\pi$
$992$	8346.28			0.267132
$993$	35208.4	+	35208.4i	1.12518	+	1.12518i
$994$	−12400.1	−	12400.1i	−0.395682	−	0.395682i
$995$	−40754.3	+	40754.3i	−1.29849	+	1.29849i
$996$	24261.0	+	24261.0i	0.771828	+	0.771828i
$997$			11283.2i			0.358417i	0.983811	+	0.179209i	$0.0573537\pi$
$997$			11283.2i			0.358417i	−0.983811	+	0.179209i	$0.942646\pi$
$998$	43928.0			1.39330
$999$	−49543.7	+	49543.7i	−1.56906	+	1.56906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.10	✓	80
11.10	odd	2	inner	143.4.g.a.21.31	yes	80
13.5	odd	4	inner	143.4.g.a.109.31	yes	80
143.109	even	4	inner	143.4.g.a.109.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.10	✓	80	1.1	even	1	trivial
143.4.g.a.21.31	yes	80	11.10	odd	2	inner
143.4.g.a.109.10	yes	80	143.109	even	4	inner
143.4.g.a.109.31	yes	80	13.5	odd	4	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48360 + 2.48360i) q^{2} +9.63275 q^{3} -4.33653i q^{4} +(-13.2589 - 13.2589i) q^{5} +(-23.9239 + 23.9239i) q^{6} +(-7.66310 - 7.66310i) q^{7} +(-9.09859 - 9.09859i) q^{8} +65.7898 q^{9} +O(q^{10})\)	\(q+(-2.48360 + 2.48360i) q^{2} +9.63275 q^{3} -4.33653i q^{4} +(-13.2589 - 13.2589i) q^{5} +(-23.9239 + 23.9239i) q^{6} +(-7.66310 - 7.66310i) q^{7} +(-9.09859 - 9.09859i) q^{8} +65.7898 q^{9} +65.8596 q^{10} +(35.8778 + 6.61667i) q^{11} -41.7727i q^{12} +(44.5590 - 14.5430i) q^{13} +38.0641 q^{14} +(-127.720 - 127.720i) q^{15} +79.8867 q^{16} -49.5415 q^{17} +(-163.395 + 163.395i) q^{18} +(90.1171 - 90.1171i) q^{19} +(-57.4976 + 57.4976i) q^{20} +(-73.8167 - 73.8167i) q^{21} +(-105.539 + 72.6730i) q^{22} -37.5946i q^{23} +(-87.6444 - 87.6444i) q^{24} +226.597i q^{25} +(-74.5476 + 146.786i) q^{26} +373.652 q^{27} +(-33.2313 + 33.2313i) q^{28} -223.916i q^{29} +634.408 q^{30} +(-33.2209 - 33.2209i) q^{31} +(-125.618 + 125.618i) q^{32} +(345.602 + 63.7367i) q^{33} +(123.041 - 123.041i) q^{34} +203.208i q^{35} -285.300i q^{36} +(-132.593 + 132.593i) q^{37} +447.629i q^{38} +(429.225 - 140.089i) q^{39} +241.274i q^{40} +(-57.0408 + 57.0408i) q^{41} +366.662 q^{42} -123.487 q^{43} +(28.6934 - 155.585i) q^{44} +(-872.300 - 872.300i) q^{45} +(93.3700 + 93.3700i) q^{46} +(-185.876 + 185.876i) q^{47} +769.529 q^{48} -225.554i q^{49} +(-562.775 - 562.775i) q^{50} -477.221 q^{51} +(-63.0662 - 193.231i) q^{52} +102.557 q^{53} +(-928.002 + 928.002i) q^{54} +(-387.971 - 563.430i) q^{55} +139.447i q^{56} +(868.075 - 868.075i) q^{57} +(556.118 + 556.118i) q^{58} +(-267.543 + 267.543i) q^{59} +(-553.860 + 553.860i) q^{60} +540.983i q^{61} +165.015 q^{62} +(-504.154 - 504.154i) q^{63} +15.1244i q^{64} +(-783.627 - 397.978i) q^{65} +(-1016.63 + 700.041i) q^{66} +(390.197 + 390.197i) q^{67} +214.838i q^{68} -362.139i q^{69} +(-504.688 - 504.688i) q^{70} +(-325.769 - 325.769i) q^{71} +(-598.594 - 598.594i) q^{72} +(559.218 + 559.218i) q^{73} -658.616i q^{74} +2182.75i q^{75} +(-390.796 - 390.796i) q^{76} +(-224.231 - 325.640i) q^{77} +(-718.098 + 1413.95i) q^{78} +134.883i q^{79} +(-1059.21 - 1059.21i) q^{80} +1822.97 q^{81} -283.333i q^{82} +(-580.787 + 580.787i) q^{83} +(-320.108 + 320.108i) q^{84} +(656.865 + 656.865i) q^{85} +(306.693 - 306.693i) q^{86} -2156.93i q^{87} +(-266.235 - 386.640i) q^{88} +(979.759 - 979.759i) q^{89} +4332.89 q^{90} +(-452.904 - 230.015i) q^{91} -163.030 q^{92} +(-320.008 - 320.008i) q^{93} -923.285i q^{94} -2389.71 q^{95} +(-1210.05 + 1210.05i) q^{96} +(282.571 + 282.571i) q^{97} +(560.185 + 560.185i) q^{98} +(2360.40 + 435.309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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