LMFDB - Embedded newform 165.6.f.a.131.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(131,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.131");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.f (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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.33
Character	$\chi$	$=$	165.131
Dual form			165.6.f.a.131.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.74443 q^{2} +(3.35412 + 15.2233i) q^{3} -28.9570 q^{4} +25.0000i q^{5} +(-5.85103 - 26.5561i) q^{6} +181.393i q^{7} +106.335 q^{8} +(-220.500 + 102.122i) q^{9} +O(q^{10})$	\(q-1.74443 q^{2} +(3.35412 + 15.2233i) q^{3} -28.9570 q^{4} +25.0000i q^{5} +(-5.85103 - 26.5561i) q^{6} +181.393i q^{7} +106.335 q^{8} +(-220.500 + 102.122i) q^{9} -43.6108i q^{10} +(-308.494 + 256.676i) q^{11} +(-97.1250 - 440.821i) q^{12} +507.182i q^{13} -316.428i q^{14} +(-380.583 + 83.8529i) q^{15} +741.128 q^{16} +741.097 q^{17} +(384.647 - 178.144i) q^{18} +1729.57i q^{19} -723.924i q^{20} +(-2761.40 + 608.413i) q^{21} +(538.147 - 447.754i) q^{22} +418.294i q^{23} +(356.661 + 1618.78i) q^{24} -625.000 q^{25} -884.745i q^{26} +(-2294.21 - 3014.21i) q^{27} -5252.58i q^{28} -5157.85 q^{29} +(663.902 - 146.276i) q^{30} +5588.74 q^{31} -4695.58 q^{32} +(-4942.19 - 3835.38i) q^{33} -1292.79 q^{34} -4534.82 q^{35} +(6385.00 - 2957.13i) q^{36} +11165.4 q^{37} -3017.12i q^{38} +(-7721.00 + 1701.15i) q^{39} +2658.38i q^{40} -1057.97 q^{41} +(4817.08 - 1061.34i) q^{42} -6888.63i q^{43} +(8933.04 - 7432.55i) q^{44} +(-2553.04 - 5512.49i) q^{45} -729.686i q^{46} -16626.0i q^{47} +(2485.83 + 11282.4i) q^{48} -16096.3 q^{49} +1090.27 q^{50} +(2485.73 + 11282.0i) q^{51} -14686.4i q^{52} -20064.4i q^{53} +(4002.10 + 5258.09i) q^{54} +(-6416.90 - 7712.35i) q^{55} +19288.5i q^{56} +(-26329.8 + 5801.17i) q^{57} +8997.52 q^{58} +8487.98i q^{59} +(11020.5 - 2428.13i) q^{60} -10914.6i q^{61} -9749.18 q^{62} +(-18524.1 - 39997.1i) q^{63} -15525.0 q^{64} -12679.5 q^{65} +(8621.32 + 6690.57i) q^{66} -28643.3 q^{67} -21459.9 q^{68} +(-6367.83 + 1403.01i) q^{69} +7910.69 q^{70} -61189.1i q^{71} +(-23446.9 + 10859.1i) q^{72} +74400.3i q^{73} -19477.2 q^{74} +(-2096.32 - 9514.58i) q^{75} -50083.0i q^{76} +(-46559.2 - 55958.6i) q^{77} +(13468.8 - 2967.54i) q^{78} +93509.6i q^{79} +18528.2i q^{80} +(38191.3 - 45035.6i) q^{81} +1845.56 q^{82} +49526.8 q^{83} +(79961.8 - 17617.8i) q^{84} +18527.4i q^{85} +12016.8i q^{86} +(-17300.0 - 78519.7i) q^{87} +(-32803.8 + 27293.7i) q^{88} +40052.2i q^{89} +(4453.61 + 9616.18i) q^{90} -91999.1 q^{91} -12112.5i q^{92} +(18745.3 + 85079.2i) q^{93} +29002.9i q^{94} -43239.2 q^{95} +(-15749.5 - 71482.4i) q^{96} +18432.0 q^{97} +28079.0 q^{98} +(41810.6 - 88100.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	$ 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) $ 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.74443			−0.308375			−0.154188	−	0.988042i	$-0.549276\pi$
$2$	−1.74443			−0.308375			−0.154188	+	0.988042i	$0.549276\pi$
$3$	3.35412	+	15.2233i	0.215167	+	0.976577i
$3$	3.35412	+	15.2233i	0.215167	+	0.976577i
$4$	−28.9570			−0.904905
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	−5.85103	−	26.5561i	−0.0663521	−	0.301152i
$7$			181.393i			1.39918i	0.714542	+	0.699592i	$0.246635\pi$
$7$			181.393i			1.39918i	−0.714542	+	0.699592i	$0.753365\pi$
$8$	106.335			0.587425
$9$	−220.500	+	102.122i	−0.907407	+	0.420254i
$10$		−	43.6108i		−	0.137910i
$11$	−308.494	+	256.676i	−0.768714	+	0.639593i
$11$	−308.494	+	256.676i	−0.768714	+	0.639593i
$12$	−97.1250	−	440.821i	−0.194705	−	0.883709i
$13$			507.182i			0.832349i	0.909285	+	0.416174i	$0.136629\pi$
$13$			507.182i			0.832349i	−0.909285	+	0.416174i	$0.863371\pi$
$14$		−	316.428i		−	0.431474i
$15$	−380.583	+	83.8529i	−0.436739	+	0.0962255i
$16$	741.128			0.723757
$17$	741.097			0.621946			0.310973	−	0.950419i	$-0.399345\pi$
$17$	741.097			0.621946			0.310973	+	0.950419i	$0.399345\pi$
$18$	384.647	−	178.144i	0.279822	−	0.129596i
$19$			1729.57i			1.09914i	0.835447	+	0.549571i	$0.185209\pi$
$19$			1729.57i			1.09914i	−0.835447	+	0.549571i	$0.814791\pi$
$20$		−	723.924i		−	0.404686i
$21$	−2761.40	+	608.413i	−1.36641	+	0.301058i
$22$	538.147	−	447.754i	0.237052	−	0.197235i
$23$			418.294i			0.164878i	0.996596	+	0.0824389i	$0.0262709\pi$
$23$			418.294i			0.164878i	−0.996596	+	0.0824389i	$0.973729\pi$
$24$	356.661	+	1618.78i	0.126394	+	0.573666i
$25$	−625.000			−0.200000
$26$		−	884.745i		−	0.256676i
$27$	−2294.21	−	3014.21i	−0.605654	−	0.795728i
$28$		−	5252.58i		−	1.26613i
$29$	−5157.85			−1.13887			−0.569434	−	0.822037i	$-0.692838\pi$
$29$	−5157.85			−1.13887			−0.569434	+	0.822037i	$0.692838\pi$
$30$	663.902	−	146.276i	0.134679	−	0.0296735i
$31$	5588.74			1.04450			0.522251	−	0.852792i	$-0.325092\pi$
$31$	5588.74			1.04450			0.522251	+	0.852792i	$0.325092\pi$
$32$	−4695.58			−0.810614
$33$	−4942.19	−	3835.38i	−0.790013	−	0.613090i
$34$	−1292.79			−0.191793
$35$	−4534.82			−0.625734
$36$	6385.00	−	2957.13i	0.821117	−	0.380290i
$37$	11165.4			1.34081			0.670407	−	0.741994i	$-0.266120\pi$
$37$	11165.4			1.34081			0.670407	+	0.741994i	$0.266120\pi$
$38$		−	3017.12i		−	0.338948i
$39$	−7721.00	+	1701.15i	−0.812853	+	0.179094i
$40$			2658.38i			0.262705i
$41$	−1057.97			−0.0982914			−0.0491457	−	0.998792i	$-0.515650\pi$
$41$	−1057.97			−0.0982914			−0.0491457	+	0.998792i	$0.515650\pi$
$42$	4817.08	−	1061.34i	0.421367	−	0.0928388i
$43$		−	6888.63i		−	0.568148i	−0.958802	−	0.284074i	$-0.908314\pi$
$43$		−	6888.63i		−	0.568148i	0.958802	−	0.284074i	$-0.0916862\pi$
$44$	8933.04	−	7432.55i	0.695613	−	0.578771i
$45$	−2553.04	−	5512.49i	−0.187943	−	0.405805i
$46$		−	729.686i		−	0.0508442i
$47$		−	16626.0i		−	1.09785i	−0.835872	−	0.548925i	$-0.815037\pi$
$47$		−	16626.0i		−	1.09785i	0.835872	−	0.548925i	$-0.184963\pi$
$48$	2485.83	+	11282.4i	0.155728	+	0.706805i
$49$	−16096.3			−0.957717
$50$	1090.27			0.0616750
$51$	2485.73	+	11282.0i	0.133822	+	0.607378i
$52$		−	14686.4i		−	0.753196i
$53$		−	20064.4i		−	0.981153i	−0.871398	−	0.490577i	$-0.836786\pi$
$53$		−	20064.4i		−	0.981153i	0.871398	−	0.490577i	$-0.163214\pi$
$54$	4002.10	+	5258.09i	0.186769	+	0.245383i
$55$	−6416.90	−	7712.35i	−0.286035	−	0.343779i
$56$			19288.5i			0.821916i
$57$	−26329.8	+	5801.17i	−1.07340	+	0.236499i
$58$	8997.52			0.351199
$59$			8487.98i			0.317449i	0.987323	+	0.158725i	$0.0507382\pi$
$59$			8487.98i			0.317449i	−0.987323	+	0.158725i	$0.949262\pi$
$60$	11020.5	−	2428.13i	0.395207	−	0.0870749i
$61$		−	10914.6i		−	0.375562i	−0.982211	−	0.187781i	$-0.939870\pi$
$61$		−	10914.6i		−	0.375562i	0.982211	−	0.187781i	$-0.0601296\pi$
$62$	−9749.18			−0.322099
$63$	−18524.1	−	39997.1i	−0.588013	−	1.26963i
$64$	−15525.0			−0.473784
$65$	−12679.5			−0.372238
$66$	8621.32	+	6690.57i	0.243620	+	0.189062i
$67$	−28643.3			−0.779537			−0.389768	−	0.920913i	$-0.627445\pi$
$67$	−28643.3			−0.779537			−0.389768	+	0.920913i	$0.627445\pi$
$68$	−21459.9			−0.562802
$69$	−6367.83	+	1403.01i	−0.161016	+	0.0354762i
$70$	7910.69			0.192961
$71$		−	61189.1i		−	1.44055i	−0.693689	−	0.720275i	$-0.744016\pi$
$71$		−	61189.1i		−	1.44055i	0.693689	−	0.720275i	$-0.255984\pi$
$72$	−23446.9	+	10859.1i	−0.533034	+	0.246868i
$73$			74400.3i			1.63406i	0.576596	+	0.817029i	$0.304381\pi$
$73$			74400.3i			1.63406i	−0.576596	+	0.817029i	$0.695619\pi$
$74$	−19477.2			−0.413473
$75$	−2096.32	−	9514.58i	−0.0430333	−	0.195315i
$76$		−	50083.0i		−	0.994619i
$77$	−46559.2	−	55958.6i	−0.894908	−	1.07557i
$78$	13468.8	−	2967.54i	0.250664	−	0.0552281i
$79$			93509.6i			1.68573i	0.538124	+	0.842866i	$0.319133\pi$
$79$			93509.6i			1.68573i	−0.538124	+	0.842866i	$0.680867\pi$
$80$			18528.2i			0.323674i
$81$	38191.3	−	45035.6i	0.646773	−	0.762682i
$82$	1845.56			0.0303106
$83$	49526.8			0.789124			0.394562	−	0.918869i	$-0.370896\pi$
$83$	49526.8			0.789124			0.394562	+	0.918869i	$0.370896\pi$
$84$	79961.8	−	17617.8i	1.23647	−	0.272429i
$85$			18527.4i			0.278143i
$86$			12016.8i			0.175203i
$87$	−17300.0	−	78519.7i	−0.245047	−	1.11219i
$88$	−32803.8	+	27293.7i	−0.451562	+	0.375713i
$89$			40052.2i			0.535983i	0.963421	+	0.267991i	$0.0863599\pi$
$89$			40052.2i			0.535983i	−0.963421	+	0.267991i	$0.913640\pi$
$90$	4453.61	+	9616.18i	0.0579570	+	0.125140i
$91$	−91999.1			−1.16461
$92$		−	12112.5i		−	0.149199i
$93$	18745.3	+	85079.2i	0.224742	+	1.02004i
$94$			29002.9i			0.338549i
$95$	−43239.2			−0.491551
$96$	−15749.5	−	71482.4i	−0.174417	−	0.791627i
$97$	18432.0			0.198903			0.0994517	−	0.995042i	$-0.468291\pi$
$97$	18432.0			0.198903			0.0994517	+	0.995042i	$0.468291\pi$
$98$	28079.0			0.295336
$99$	41810.6	−	88100.9i	0.428745	−	0.903426i
$100$	18098.1			0.180981
$101$	−3387.16			−0.0330394			−0.0165197	−	0.999864i	$-0.505259\pi$
$101$	−3387.16			−0.0330394			−0.0165197	+	0.999864i	$0.505259\pi$
$102$	−4336.18	−	19680.6i	−0.0412674	−	0.187300i
$103$	95291.9			0.885040			0.442520	−	0.896759i	$-0.354085\pi$
$103$	95291.9			0.885040			0.442520	+	0.896759i	$0.354085\pi$
$104$			53931.3i			0.488943i
$105$	−15210.3	−	69035.1i	−0.134637	−	0.611078i
$106$			35001.0i			0.302563i
$107$	165163.			1.39461			0.697306	−	0.716773i	$-0.254382\pi$
$107$	165163.			1.39461			0.697306	+	0.716773i	$0.254382\pi$
$108$	66433.5	+	87282.5i	0.548059	+	0.720058i
$109$			75783.7i			0.610956i	0.952199	+	0.305478i	$0.0988162\pi$
$109$			75783.7i			0.610956i	−0.952199	+	0.305478i	$0.901184\pi$
$110$	11193.9	+	13453.7i	0.0882060	+	0.106013i
$111$	37449.9	+	169974.i	0.288498	+	1.30941i
$112$			134435.i			1.01267i
$113$			134285.i			0.989306i	0.869091	+	0.494653i	$0.164705\pi$
$113$			134285.i			0.989306i	−0.869091	+	0.494653i	$0.835295\pi$
$114$	45930.6	−	10119.8i	0.331009	−	0.0729303i
$115$	−10457.4			−0.0737356
$116$	149356.			1.03057
$117$	−51794.3	−	111833.i	−0.349798	−	0.755279i
$118$		−	14806.7i		−	0.0978934i
$119$			134430.i			0.870217i
$120$	−40469.5	+	8916.53i	−0.256551	+	0.0565253i
$121$	29285.9	−	158366.i	0.181842	−	0.983328i
$122$			19039.7i			0.115814i
$123$	−3548.57	−	16105.9i	−0.0211490	−	0.0959891i
$124$	−161833.			−0.945175
$125$		−	15625.0i		−	0.0894427i
$126$	32314.1	+	69772.2i	0.181328	+	0.391522i
$127$			181938.i			1.00095i	0.865750	+	0.500477i	$0.166842\pi$
$127$			181938.i			1.00095i	−0.865750	+	0.500477i	$0.833158\pi$
$128$	177341.			0.956717
$129$	104868.	−	23105.3i	0.554841	−	0.122247i
$130$	22118.6			0.114789
$131$	249455.			1.27003			0.635014	−	0.772500i	$-0.280994\pi$
$131$	249455.			1.27003			0.635014	+	0.772500i	$0.280994\pi$
$132$	143111.	+	111061.i	0.714887	+	0.554788i
$133$	−313731.			−1.53790
$134$	49966.4			0.240390
$135$	75355.4	−	57355.4i	0.355860	−	0.270857i
$136$	78804.8			0.365347
$137$			105547.i			0.480444i	0.970718	+	0.240222i	$0.0772203\pi$
$137$			105547.i			0.480444i	−0.970718	+	0.240222i	$0.922780\pi$
$138$	11108.3	−	2447.45i	0.0496533	−	0.0109400i
$139$		−	109306.i		−	0.479853i	−0.970791	−	0.239927i	$-0.922877\pi$
$139$		−	109306.i		−	0.479853i	0.970791	−	0.239927i	$-0.0771234\pi$
$140$	131315.			0.566230
$141$	253103.	−	55765.5i	1.07213	−	0.236221i
$142$			106740.i			0.444230i
$143$	−130181.	−	156462.i	−0.532364	−	0.639838i
$144$	−163418.	+	75685.2i	−0.656742	+	0.304162i
$145$		−	128946.i		−	0.509318i
$146$		−	129786.i		−	0.503903i
$147$	−53989.0	−	245040.i	−0.206069	−	0.935284i
$148$	−323315.			−1.21331
$149$	−380079.			−1.40252			−0.701259	−	0.712906i	$-0.747378\pi$
$149$	−380079.			−1.40252			−0.701259	+	0.712906i	$0.747378\pi$
$150$	3656.90	+	16597.6i	0.0132704	+	0.0602304i
$151$			366554.i			1.30827i	0.756380	+	0.654133i	$0.226966\pi$
$151$			366554.i			1.30827i	−0.756380	+	0.654133i	$0.773034\pi$
$152$			183914.i			0.645664i
$153$	−163412.	+	75682.1i	−0.564358	+	0.261375i
$154$	81219.4	+	97616.0i	0.275967	+	0.331680i
$155$			139718.i			0.467116i
$156$	223577.	−	49260.0i	0.735554	−	0.162063i
$157$	−593389.			−1.92128			−0.960639	−	0.277801i	$-0.910394\pi$
$157$	−593389.			−1.92128			−0.960639	+	0.277801i	$0.910394\pi$
$158$		−	163121.i		−	0.519838i
$159$	305447.	−	67298.4i	0.958172	−	0.211111i
$160$		−	117389.i		−	0.362518i
$161$	−75875.5			−0.230694
$162$	−66622.2	+	78561.6i	−0.199449	+	0.235192i
$163$	50450.2			0.148729			0.0743643	−	0.997231i	$-0.476307\pi$
$163$	50450.2			0.148729			0.0743643	+	0.997231i	$0.476307\pi$
$164$	30635.7			0.0889443
$165$	95884.6	−	123555.i	0.274182	−	0.353305i
$166$	−86396.2			−0.243346
$167$	−227361.			−0.630849			−0.315425	−	0.948951i	$-0.602147\pi$
$167$	−227361.			−0.630849			−0.315425	+	0.948951i	$0.602147\pi$
$168$	−293635.	+	64695.8i	−0.802665	+	0.176849i
$169$	114060.			0.307196
$170$		−	32319.9i		−	0.0857723i
$171$	−176626.	−	381369.i	−0.461919	−	0.997368i
$172$			199474.i			0.514120i
$173$	−502012.			−1.27526			−0.637630	−	0.770343i	$-0.720085\pi$
$173$	−502012.			−1.27526			−0.637630	+	0.770343i	$0.720085\pi$
$174$	30178.7	+	136972.i	0.0755663	+	0.342973i
$175$		−	113370.i		−	0.279837i
$176$	−228633.	+	190230.i	−0.556362	+	0.462910i
$177$	−129215.	+	28469.7i	−0.310014	+	0.0683045i
$178$		−	69868.3i		−	0.165284i
$179$		−	416853.i		−	0.972412i	−0.873844	−	0.486206i	$-0.838381\pi$
$179$		−	416853.i		−	0.972412i	0.873844	−	0.486206i	$-0.161619\pi$
$180$	73928.3	+	159625.i	0.170071	+	0.367214i
$181$	542031.			1.22978			0.614890	−	0.788613i	$-0.289200\pi$
$181$	542031.			1.22978			0.614890	+	0.788613i	$0.289200\pi$
$182$	160486.			0.359137
$183$	166156.	−	36608.7i	0.366766	−	0.0808085i
$184$			44479.4i			0.0968534i
$185$			279134.i			0.599630i
$186$	−32699.9	−	148415.i	−0.0693049	−	0.314554i
$187$	−228624.	+	190222.i	−0.478099	+	0.397792i
$188$			481438.i			0.993449i
$189$	546757.	−	416154.i	1.11337	−	0.847422i
$190$	75427.9			0.151582
$191$		−	117934.i		−	0.233914i	−0.993137	−	0.116957i	$-0.962686\pi$
$191$		−	117934.i		−	0.233914i	0.993137	−	0.116957i	$-0.0373140\pi$
$192$	−52072.5	−	236342.i	−0.101943	−	0.462687i
$193$			193873.i			0.374649i	0.982298	+	0.187325i	$0.0599816\pi$
$193$			193873.i			0.374649i	−0.982298	+	0.187325i	$0.940018\pi$
$194$	−32153.3			−0.0613368
$195$	−42528.7	−	193025.i	−0.0800931	−	0.363519i
$196$	466101.			0.866642
$197$	833270.			1.52975			0.764875	−	0.644179i	$-0.222801\pi$
$197$	833270.			1.52975			0.764875	+	0.644179i	$0.222801\pi$
$198$	−72935.9	+	153686.i	−0.132214	+	0.278594i
$199$	506402.			0.906490			0.453245	−	0.891386i	$-0.350266\pi$
$199$	506402.			0.906490			0.453245	+	0.891386i	$0.350266\pi$
$200$	−66459.6			−0.117485
$201$	−96073.1	−	436047.i	−0.167730	−	0.761278i
$202$	5908.67			0.0101885
$203$		−	935597.i		−	1.59349i
$204$	−71979.1	−	326691.i	−0.121096	−	0.549620i
$205$		−	26449.4i		−	0.0439572i
$206$	−166230.			−0.272924
$207$	−42716.9	−	92233.7i	−0.0692905	−	0.149611i
$208$			375886.i			0.602419i
$209$	−443939.	−	533561.i	−0.703003	−	0.844926i
$210$	26533.4	+	120427.i	0.0415188	+	0.188441i
$211$		−	1.06003e6i		−	1.63913i	−0.572986	−	0.819565i	$-0.694215\pi$
$211$		−	1.06003e6i		−	1.63913i	0.572986	−	0.819565i	$-0.305785\pi$
$212$			581004.i			0.887850i
$213$	931502.	−	205235.i	1.40681	−	0.309958i
$214$	−288116.			−0.430064
$215$	172216.			0.254084
$216$	−243956.	−	320517.i	−0.355776	−	0.467431i
$217$			1.01376e6i			1.46145i
$218$		−	132200.i		−	0.188404i
$219$	−1.13262e6	+	249547.i	−1.59578	+	0.351595i
$220$	185814.	+	223326.i	0.258834	+	0.311088i
$221$			375871.i			0.517676i
$222$	−65328.9	−	296508.i	−0.0889657	−	0.403789i
$223$	205786.			0.277111			0.138555	−	0.990355i	$-0.455754\pi$
$223$	205786.			0.277111			0.138555	+	0.990355i	$0.455754\pi$
$224$		−	851744.i		−	1.13420i
$225$	137812.	−	63826.1i	0.181481	−	0.0840508i
$226$		−	234251.i		−	0.305077i
$227$	−190591.			−0.245492			−0.122746	−	0.992438i	$-0.539170\pi$
$227$	−190591.			−0.245492			−0.122746	+	0.992438i	$0.539170\pi$
$228$	762431.	−	167984.i	0.971322	−	0.214009i
$229$	−1.45546e6			−1.83405			−0.917027	−	0.398824i	$-0.869418\pi$
$229$	−1.45546e6			−1.83405			−0.917027	+	0.398824i	$0.869418\pi$
$230$	18242.1			0.0227382
$231$	695711.	−	896477.i	0.857825	−	1.10537i
$232$	−548462.			−0.669000
$233$	−1.48614e6			−1.79337			−0.896683	−	0.442673i	$-0.854030\pi$
$233$	−1.48614e6			−1.79337			−0.896683	+	0.442673i	$0.854030\pi$
$234$	90351.6	+	195086.i	0.107869	+	0.232909i
$235$	415650.			0.490973
$236$		−	245786.i		−	0.287261i
$237$	−1.42353e6	+	313642.i	−1.64625	+	0.362713i
$238$		−	234504.i		−	0.268353i
$239$	−667192.			−0.755538			−0.377769	−	0.925900i	$-0.623309\pi$
$239$	−667192.			−0.755538			−0.377769	+	0.925900i	$0.623309\pi$
$240$	−282061.	+	62145.7i	−0.316093	+	0.0696439i
$241$		−	309240.i		−	0.342967i	−0.985187	−	0.171484i	$-0.945144\pi$
$241$		−	309240.i		−	0.342967i	0.985187	−	0.171484i	$-0.0548561\pi$
$242$	−51087.2	+	276259.i	−0.0560756	+	0.303234i
$243$	813690.	+	430345.i	0.883982	+	0.467520i
$244$			316053.i			0.339848i
$245$		−	402409.i		−	0.428304i
$246$	6190.24	+	28095.7i	0.00652183	+	0.0296007i
$247$	−877206.			−0.914869
$248$	594280.			0.613567
$249$	166119.	+	753963.i	0.169793	+	0.770640i
$250$			27256.8i			0.0275819i
$251$			725271.i			0.726634i	0.931666	+	0.363317i	$0.118356\pi$
$251$			725271.i			0.726634i	−0.931666	+	0.363317i	$0.881644\pi$
$252$	536403.	+	1.15819e6i	0.532095	+	1.14889i
$253$	−107366.	−	129041.i	−0.105455	−	0.126744i
$254$		−	317378.i		−	0.308669i
$255$	−282049.	+	62143.1i	−0.271628	+	0.0598471i
$256$	187440.			0.178756
$257$		−	598261.i		−	0.565012i	−0.959266	−	0.282506i	$-0.908834\pi$
$257$		−	598261.i		−	0.565012i	0.959266	−	0.282506i	$-0.0911657\pi$
$258$	−182935.	+	40305.6i	−0.171099	+	0.0376978i
$259$			2.02532e6i			1.87604i
$260$	367161.			0.336840
$261$	1.13730e6	−	526728.i	1.03342	−	0.478614i
$262$	−435157.			−0.391645
$263$	−2.03640e6			−1.81540			−0.907702	−	0.419616i	$-0.862165\pi$
$263$	−2.03640e6			−1.81540			−0.907702	+	0.419616i	$0.862165\pi$
$264$	−525529.	−	407837.i	−0.464074	−	0.360144i
$265$	501610.			0.438785
$266$	547283.			0.474251
$267$	−609728.	+	134340.i	−0.523429	+	0.115326i
$268$	829424.			0.705406
$269$		−	915415.i		−	0.771325i	−0.922640	−	0.385663i	$-0.873973\pi$
$269$		−	915415.i		−	0.771325i	0.922640	−	0.385663i	$-0.126027\pi$
$270$	−131452.	+	100053.i	−0.109739	+	0.0835255i
$271$		−	1.96514e6i		−	1.62544i	−0.582657	−	0.812718i	$-0.697987\pi$
$271$		−	1.96514e6i		−	1.62544i	0.582657	−	0.812718i	$-0.302013\pi$
$272$	549247.			0.450138
$273$	−308576.	−	1.40053e6i	−0.250585	−	1.13733i
$274$		−	184119.i		−	0.148157i
$275$	192809.	−	160422.i	0.153743	−	0.127919i
$276$	184393.	−	40626.8i	0.145704	−	0.0321026i
$277$			1.94267e6i			1.52124i	0.649195	+	0.760622i	$0.275106\pi$
$277$			1.94267e6i			1.52124i	−0.649195	+	0.760622i	$0.724894\pi$
$278$			190678.i			0.147975i
$279$	−1.23232e6	+	570731.i	−0.947788	+	0.438956i
$280$	−482212.			−0.367572
$281$	−181877.			−0.137408			−0.0687038	−	0.997637i	$-0.521886\pi$
$281$	−181877.			−0.137408			−0.0687038	+	0.997637i	$0.521886\pi$
$282$	−441521.	+	97279.2i	−0.330620	+	0.0728446i
$283$		−	501271.i		−	0.372054i	−0.982545	−	0.186027i	$-0.940439\pi$
$283$		−	501271.i		−	0.372054i	0.982545	−	0.186027i	$-0.0595612\pi$
$284$			1.77185e6i			1.30356i
$285$	−145029.	−	658245.i	−0.105765	−	0.480038i
$286$	227093.	+	272938.i	0.164168	+	0.197310i
$287$		−	191909.i		−	0.137528i
$288$	1.03537e6	−	479520.i	0.735557	−	0.340664i
$289$	−870632.			−0.613183
$290$			224938.i			0.157061i
$291$	61822.9	+	280596.i	0.0427974	+	0.194245i
$292$		−	2.15441e6i		−	1.47867i
$293$	2.69393e6			1.83323			0.916615	−	0.399772i	$-0.130911\pi$
$293$	2.69393e6			1.83323			0.916615	+	0.399772i	$0.130911\pi$
$294$	94180.2	+	427456.i	0.0635465	+	0.288418i
$295$	−212199.			−0.141968
$296$	1.18727e6			0.787628
$297$	1.48143e6	+	340997.i	0.974517	+	0.224315i
$298$	663023.			0.432502
$299$	−212151.			−0.137236
$300$	60703.1	+	275513.i	0.0389411	+	0.176742i
$301$	1.24955e6			0.794944
$302$		−	639429.i		−	0.403437i
$303$	−11360.9	−	51563.8i	−0.00710897	−	0.0322655i
$304$			1.28183e6i			0.795512i
$305$	272864.			0.167957
$306$	285061.	−	132022.i	0.174034	−	0.0806016i
$307$		−	843966.i		−	0.511068i	−0.966800	−	0.255534i	$-0.917749\pi$
$307$		−	843966.i		−	0.511068i	0.966800	−	0.255534i	$-0.0822513\pi$
$308$	1.34821e6	+	1.62039e6i	0.809807	+	0.973291i
$309$	319620.	+	1.45066e6i	0.190431	+	0.864310i
$310$		−	243729.i		−	0.144047i
$311$			2.34412e6i			1.37429i	0.726521	+	0.687144i	$0.241136\pi$
$311$			2.34412e6i			1.37429i	−0.726521	+	0.687144i	$0.758864\pi$
$312$	−821015.	+	180892.i	−0.477490	+	0.105204i
$313$	−2.25609e6			−1.30166			−0.650828	−	0.759225i	$-0.725578\pi$
$313$	−2.25609e6			−1.30166			−0.650828	+	0.759225i	$0.725578\pi$
$314$	1.03513e6			0.592474
$315$	999927.	−	463103.i	0.567795	−	0.262967i
$316$		−	2.70775e6i		−	1.52543i
$317$			1.00497e6i			0.561700i	0.959752	+	0.280850i	$0.0906163\pi$
$317$			1.00497e6i			0.561700i	−0.959752	+	0.280850i	$0.909384\pi$
$318$	−532832.	+	117398.i	−0.295476	+	0.0651015i
$319$	1.59116e6	−	1.32390e6i	0.875464	−	0.728412i
$320$		−	388124.i		−	0.211883i
$321$	553976.	+	2.51433e6i	0.300074	+	1.36195i
$322$	132360.			0.0711404
$323$			1.28178e6i			0.683607i
$324$	−1.10590e6	+	1.30409e6i	−0.585268	+	0.690155i
$325$		−	316989.i		−	0.166470i
$326$	−88007.1			−0.0458642
$327$	−1.15368e6	+	254187.i	−0.596645	+	0.131457i
$328$	−112500.			−0.0577388
$329$	3.01583e6			1.53609
$330$	−167264.	+	215533.i	−0.0845509	+	0.108950i
$331$	2.76789e6			1.38860			0.694302	−	0.719684i	$-0.255713\pi$
$331$	2.76789e6			1.38860			0.694302	+	0.719684i	$0.255713\pi$
$332$	−1.43415e6			−0.714082
$333$	−2.46196e6	+	1.14023e6i	−1.21666	+	0.563482i
$334$	396617.			0.194538
$335$		−	716083.i		−	0.348619i
$336$	−2.04655e6	+	450911.i	−0.988951	+	0.217893i
$337$			2.93335e6i			1.40699i	0.710702	+	0.703493i	$0.248377\pi$
$337$			2.93335e6i			1.40699i	−0.710702	+	0.703493i	$0.751623\pi$
$338$	−198969.			−0.0947315
$339$	−2.04426e6	+	450407.i	−0.966134	+	0.212866i
$340$		−	536498.i		−	0.251693i
$341$	−1.72409e6	+	1.43449e6i	−0.802924	+	0.668056i
$342$	308113.	+	665274.i	0.142444	+	0.307564i
$343$			128908.i			0.0591623i
$344$		−	732505.i		−	0.333745i
$345$	−35075.2	−	159196.i	−0.0158654	−	0.0720085i
$346$	875726.			0.393258
$347$	752542.			0.335511			0.167756	−	0.985829i	$-0.446348\pi$
$347$	752542.			0.335511			0.167756	+	0.985829i	$0.446348\pi$
$348$	500956.	+	2.27369e6i	0.221744	+	1.00643i
$349$		−	742881.i		−	0.326479i	−0.986586	−	0.163240i	$-0.947806\pi$
$349$		−	742881.i		−	0.326479i	0.986586	−	0.163240i	$-0.0521944\pi$
$350$			197767.i			0.0862947i
$351$	1.52875e6	−	1.16358e6i	0.662323	−	0.504115i
$352$	1.44856e6	−	1.20524e6i	0.623130	−	0.518463i
$353$		−	3.52603e6i		−	1.50608i	−0.657973	−	0.753041i	$-0.728586\pi$
$353$		−	3.52603e6i		−	1.50608i	0.657973	−	0.753041i	$-0.271414\pi$
$354$	225407.	−	49663.4i	0.0956005	−	0.0210634i
$355$	1.52973e6			0.644233
$356$		−	1.15979e6i		−	0.485014i
$357$	−2.04647e6	+	450893.i	−0.849834	+	0.187242i
$358$			727172.i			0.299868i
$359$	1.09909e6			0.450088			0.225044	−	0.974349i	$-0.427747\pi$
$359$	1.09909e6			0.450088			0.225044	+	0.974349i	$0.427747\pi$
$360$	−271479.	−	586173.i	−0.110403	−	0.238380i
$361$	−515307.			−0.208113
$362$	−945536.			−0.379234
$363$	2.50909e6	−	85349.3i	0.999422	−	0.0339964i
$364$	2.66401e6			1.05386
$365$	−1.86001e6			−0.730773
$366$	−289848.	+	63861.5i	−0.113101	+	0.0249193i
$367$	−1.18432e6			−0.458991			−0.229496	−	0.973310i	$-0.573708\pi$
$367$	−1.18432e6			−0.458991			−0.229496	+	0.973310i	$0.573708\pi$
$368$			310009.i			0.119332i
$369$	233283.	−	108042.i	0.0891902	−	0.0413073i
$370$		−	486930.i		−	0.184911i
$371$	3.63954e6			1.37281
$372$	−542806.	−	2.46363e6i	−0.203370	−	0.923037i
$373$		−	3.37338e6i		−	1.25543i	−0.778442	−	0.627717i	$-0.783990\pi$
$373$		−	3.37338e6i		−	1.25543i	0.778442	−	0.627717i	$-0.216010\pi$
$374$	398819.	−	331829.i	0.147434	−	0.122669i
$375$	237865.	−	52408.1i	0.0873477	−	0.0192451i
$376$		−	1.76793e6i		−	0.644904i
$377$		−	2.61597e6i		−	0.947936i
$378$	−953780.	+	725953.i	−0.343336	+	0.261324i
$379$	399429.			0.142837			0.0714186	−	0.997446i	$-0.477247\pi$
$379$	399429.			0.142837			0.0714186	+	0.997446i	$0.477247\pi$
$380$	1.25208e6			0.444807
$381$	−2.76970e6	+	610241.i	−0.977508	+	0.215372i
$382$			205728.i			0.0721332i
$383$		−	3.78628e6i		−	1.31891i	−0.751743	−	0.659456i	$-0.770786\pi$
$383$		−	3.78628e6i		−	1.31891i	0.751743	−	0.659456i	$-0.229214\pi$
$384$	594822.	+	2.69972e6i	0.205854	+	0.934308i
$385$	1.39896e6	−	1.16398e6i	0.481011	−	0.400215i
$386$		−	338199.i		−	0.115532i
$387$	703478.	+	1.51894e6i	0.238766	+	0.515541i
$388$	−533733.			−0.179989
$389$			4.49212e6i			1.50514i	0.658512	+	0.752570i	$0.271186\pi$
$389$			4.49212e6i			1.50514i	−0.658512	+	0.752570i	$0.728814\pi$
$390$	74188.4	+	336719.i	0.0246987	+	0.112100i
$391$			309996.i			0.102545i
$392$	−1.71161e6			−0.562587
$393$	836700.	+	3.79753e6i	0.273268	+	1.24028i
$394$	−1.45358e6			−0.471737
$395$	−2.33774e6			−0.753882
$396$	−1.21071e6	+	2.55113e6i	−0.387973	+	0.817514i
$397$	3.18242e6			1.01340			0.506700	−	0.862123i	$-0.330865\pi$
$397$	3.18242e6			1.01340			0.506700	+	0.862123i	$0.330865\pi$
$398$	−883385.			−0.279539
$399$	−1.05229e6	−	4.77603e6i	−0.330905	−	1.50188i
$400$	−463205.			−0.144751
$401$			2.00599e6i			0.622971i	0.950251	+	0.311486i	$0.100827\pi$
$401$			2.00599e6i			0.622971i	−0.950251	+	0.311486i	$0.899173\pi$
$402$	167593.	+	760655.i	0.0517239	+	0.234759i
$403$			2.83451e6i			0.869390i
$404$	98081.7			0.0298975
$405$	1.12589e6	+	954783.i	0.341082	+	0.289246i
$406$			1.63209e6i			0.491392i
$407$	−3.44444e6	+	2.86588e6i	−1.03070	+	0.857574i
$408$	264320.	+	1.19967e6i	0.0786105	+	0.356789i
$409$		−	299936.i		−	0.0886584i	−0.999017	−	0.0443292i	$-0.985885\pi$
$409$		−	299936.i		−	0.0886584i	0.999017	−	0.0443292i	$-0.0141150\pi$
$410$			46139.1i			0.0135553i
$411$	−1.60677e6	+	354016.i	−0.469191	+	0.103376i
$412$	−2.75936e6			−0.800877
$413$	−1.53966e6			−0.444170
$414$	74516.8	+	160896.i	0.0213675	+	0.0461364i
$415$			1.23817e6i			0.352907i
$416$		−	2.38151e6i		−	0.674714i
$417$	1.66401e6	−	366626.i	0.468614	−	0.103248i
$418$	774421.	+	930762.i	0.216789	+	0.260554i
$419$			2.94089e6i			0.818357i	0.912454	+	0.409179i	$0.134185\pi$
$419$			2.94089e6i			0.818357i	−0.912454	+	0.409179i	$0.865815\pi$
$420$	440444.	+	1.99905e6i	0.121834	+	0.552967i
$421$	−6.43497e6			−1.76946			−0.884732	−	0.466101i	$-0.845658\pi$
$421$	−6.43497e6			−1.76946			−0.884732	+	0.466101i	$0.845658\pi$
$422$			1.84916e6i			0.505467i
$423$	1.69787e6	+	3.66603e6i	0.461375	+	0.996196i
$424$		−	2.13356e6i		−	0.576354i
$425$	−463186.			−0.124389
$426$	−1.62494e6	+	358019.i	−0.433825	+	0.0955834i
$427$	1.97982e6			0.525481
$428$	−4.78262e6			−1.26199
$429$	1.94524e6	−	2.50659e6i	0.510304	−	0.657567i
$430$	−300419.			−0.0783531
$431$	5.16018e6			1.33805			0.669024	−	0.743241i	$-0.266712\pi$
$431$	5.16018e6			1.33805			0.669024	+	0.743241i	$0.266712\pi$
$432$	−1.70031e6	−	2.23392e6i	−0.438347	−	0.575914i
$433$	−1.00344e6			−0.257201			−0.128601	−	0.991696i	$-0.541049\pi$
$433$	−1.00344e6			−0.257201			−0.128601	+	0.991696i	$0.541049\pi$
$434$		−	1.76843e6i		−	0.450675i
$435$	1.96299e6	−	432501.i	0.497388	−	0.109588i
$436$		−	2.19447e6i		−	0.552857i
$437$	−723468.			−0.181224
$438$	1.97578e6	−	435319.i	0.492100	−	0.108423i
$439$			1.27372e6i			0.315437i	0.987484	+	0.157719i	$0.0504139\pi$
$439$			1.27372e6i			0.315437i	−0.987484	+	0.157719i	$0.949586\pi$
$440$	−682343.	−	820095.i	−0.168024	−	0.201945i
$441$	3.54924e6	−	1.64379e6i	0.869038	−	0.402484i
$442$		−	655682.i		−	0.159638i
$443$		−	1.82307e6i		−	0.441362i	−0.975346	−	0.220681i	$-0.929172\pi$
$443$		−	1.82307e6i		−	0.441362i	0.975346	−	0.220681i	$-0.0708279\pi$
$444$	−1.08444e6	−	4.92193e6i	−0.261064	−	1.18489i
$445$	−1.00130e6			−0.239699
$446$	−358980.			−0.0854540
$447$	−1.27483e6	−	5.78607e6i	−0.301775	−	1.36967i
$448$		−	2.81612e6i		−	0.662911i
$449$			2.54705e6i			0.596241i	0.954528	+	0.298121i	$0.0963598\pi$
$449$			2.54705e6i			0.596241i	−0.954528	+	0.298121i	$0.903640\pi$
$450$	−240404.	+	111340.i	−0.0559643	+	0.0259192i
$451$	326378.	−	271557.i	0.0755579	−	0.0628664i
$452$		−	3.88848e6i		−	0.895228i
$453$	−5.58018e6	+	1.22947e6i	−1.27762	+	0.281495i
$454$	332473.			0.0757037
$455$		−	2.29998e6i		−	0.520829i
$456$	−2.79979e6	+	616870.i	−0.630540	+	0.138925i
$457$		−	5.40179e6i		−	1.20989i	−0.796266	−	0.604947i	$-0.793194\pi$
$457$		−	5.40179e6i		−	1.20989i	0.796266	−	0.604947i	$-0.206806\pi$
$458$	2.53896e6			0.565577
$459$	−1.70024e6	−	2.23383e6i	−0.376684	−	0.494900i
$460$	302813.			0.0667237
$461$	3.66268e6			0.802689			0.401344	−	0.915927i	$-0.368543\pi$
$461$	3.66268e6			0.802689			0.401344	+	0.915927i	$0.368543\pi$
$462$	−1.21362e6	+	1.56384e6i	−0.264532	+	0.340870i
$463$	6.65730e6			1.44326			0.721631	−	0.692278i	$-0.243393\pi$
$463$	6.65730e6			1.44326			0.721631	+	0.692278i	$0.243393\pi$
$464$	−3.82262e6			−0.824265
$465$	−2.12698e6	+	468632.i	−0.456175	+	0.100508i
$466$	2.59247e6			0.553030
$467$		−	5.74745e6i		−	1.21950i	−0.792593	−	0.609751i	$-0.791269\pi$
$467$		−	5.74745e6i		−	1.21950i	0.792593	−	0.609751i	$-0.208731\pi$
$468$	1.49980e6	+	3.23836e6i	0.316534	+	0.683455i
$469$		−	5.19569e6i		−	1.09072i
$470$	−725073.			−0.151404
$471$	−1.99029e6	−	9.03335e6i	−0.413395	−	1.87628i
$472$			902572.i			0.186478i
$473$	1.76815e6	+	2.12510e6i	0.363383	+	0.436743i
$474$	2.48325e6	−	547128.i	0.507662	−	0.111852i
$475$		−	1.08098e6i		−	0.219828i
$476$		−	3.89267e6i		−	0.787464i
$477$	2.04901e6	+	4.42420e6i	0.412333	+	0.890305i
$478$	1.16387e6			0.232989
$479$	−5.78710e6			−1.15245			−0.576225	−	0.817291i	$-0.695475\pi$
$479$	−5.78710e6			−1.15245			−0.576225	+	0.817291i	$0.695475\pi$
$480$	1.78706e6	−	393738.i	0.354026	−	0.0780017i
$481$			5.66287e6i			1.11602i
$482$			539448.i			0.105763i
$483$	−254495.	−	1.15508e6i	−0.0496377	−	0.225291i
$484$	−848029.	+	4.58579e6i	−0.164550	+	0.889818i
$485$			460799.i			0.0889523i
$486$	−1.41943e6	−	750707.i	−0.272598	−	0.144172i
$487$	−3.19263e6			−0.609994			−0.304997	−	0.952353i	$-0.598655\pi$
$487$	−3.19263e6			−0.609994			−0.304997	+	0.952353i	$0.598655\pi$
$488$		−	1.16060e6i		−	0.220615i
$489$	169216.	+	768021.i	0.0320014	+	0.145245i
$490$			701975.i			0.132078i
$491$	−6.96291e6			−1.30343			−0.651714	−	0.758465i	$-0.725950\pi$
$491$	−6.96291e6			−1.30343			−0.651714	+	0.758465i	$0.725950\pi$
$492$	102756.	+	466378.i	0.0191379	+	0.0868610i
$493$	−3.82247e6			−0.708315
$494$	1.53023e6			0.282123
$495$	2.20252e6	+	1.04527e6i	0.404024	+	0.191740i
$496$	4.14197e6			0.755966
$497$	1.10993e7			2.01559
$498$	−289783.	−	1.31524e6i	−0.0523600	−	0.237646i
$499$	4.95139e6			0.890176			0.445088	−	0.895487i	$-0.353172\pi$
$499$	4.95139e6			0.890176			0.445088	+	0.895487i	$0.353172\pi$
$500$			452452.i			0.0809371i
$501$	−762597.	−	3.46120e6i	−0.135738	−	0.616073i
$502$		−	1.26519e6i		−	0.224076i
$503$	−7.08012e6			−1.24773			−0.623865	−	0.781532i	$-0.714439\pi$
$503$	−7.08012e6			−1.24773			−0.623865	+	0.781532i	$0.714439\pi$
$504$	−1.96977e6	−	4.25310e6i	−0.345413	−	0.745812i
$505$		−	84678.9i		−	0.0147757i
$506$	187293.	+	225104.i	0.0325196	+	0.0390846i
$507$	382569.	+	1.73637e6i	0.0660983	+	0.300000i
$508$		−	5.26837e6i		−	0.905767i
$509$			3.29265e6i			0.563315i	0.959515	+	0.281657i	$0.0908842\pi$
$509$			3.29265e6i			0.563315i	−0.959515	+	0.281657i	$0.909116\pi$
$510$	492016.	−	108405.i	0.0837633	−	0.0184553i
$511$	−1.34957e7			−2.28635
$512$	−6.00188e6			−1.01184
$513$	5.21329e6	−	3.96800e6i	0.874618	−	0.665700i
$514$			1.04363e6i			0.174236i
$515$			2.38230e6i			0.395802i
$516$	−3.03665e6	+	669058.i	−0.502078	+	0.110622i
$517$	4.26749e6	+	5.12901e6i	0.702176	+	0.843932i
$518$		−	3.53303e6i		−	0.578526i
$519$	−1.68381e6	−	7.64229e6i	−0.274393	−	1.24539i
$520$	−1.34828e6			−0.218662
$521$			1.19585e7i			1.93012i	0.262031	+	0.965059i	$0.415608\pi$
$521$			1.19585e7i			1.93012i	−0.262031	+	0.965059i	$0.584392\pi$
$522$	−1.98395e6	+	918842.i	−0.318680	+	0.147593i
$523$			219119.i			0.0350288i	0.999847	+	0.0175144i	$0.00557530\pi$
$523$			219119.i			0.0350288i	−0.999847	+	0.0175144i	$0.994425\pi$
$524$	−7.22345e6			−1.14926
$525$	1.72588e6	−	380258.i	0.273282	−	0.0602116i
$526$	3.55236e6			0.559825
$527$	4.14180e6			0.649624
$528$	−3.66279e6	−	2.84251e6i	−0.571778	−	0.443728i
$529$	6.26137e6			0.972815
$530$	−875026.			−0.135310
$531$	−866806.	−	1.87160e6i	−0.133409	−	0.288055i
$532$	9.08470e6			1.39165
$533$		−	536585.i		−	0.0818127i
$534$	1.06363e6	−	234347.i	0.161412	−	0.0355636i
$535$			4.12908e6i			0.623690i
$536$	−3.04580e6			−0.457919
$537$	6.34589e6	−	1.39817e6i	0.949635	−	0.209231i
$538$			1.59688e6i			0.237858i
$539$	4.96562e6	−	4.13154e6i	0.736210	−	0.612549i
$540$	−2.18206e6	+	1.66084e6i	−0.322020	+	0.245100i
$541$			21868.8i			0.00321242i	0.999999	+	0.00160621i	$0.000511272\pi$
$541$			21868.8i			0.00321242i	−0.999999	+	0.00160621i	$0.999489\pi$
$542$			3.42805e6i			0.501244i
$543$	1.81803e6	+	8.25152e6i	0.264608	+	1.20098i
$544$	−3.47988e6			−0.504158
$545$	−1.89459e6			−0.273228
$546$	538290.	+	2.44314e6i	0.0772742	+	0.350725i
$547$		−	2.92670e6i		−	0.418225i	−0.977892	−	0.209113i	$-0.932942\pi$
$547$		−	2.92670e6i		−	0.418225i	0.977892	−	0.209113i	$-0.0670576\pi$
$548$		−	3.05631e6i		−	0.434756i
$549$	1.11461e6	+	2.40666e6i	0.157831	+	0.340788i
$550$	−336342.	+	279846.i	−0.0474105	+	0.0394469i
$551$		−	8.92085e6i		−	1.25178i
$552$	−677125.	+	149189.i	−0.0945848	+	0.0208396i
$553$	−1.69620e7			−2.35865
$554$		−	3.38885e6i		−	0.469114i
$555$	−4.24935e6	+	936248.i	−0.585585	+	0.129020i
$556$			3.16518e6i			0.434221i
$557$	9.14443e6			1.24887			0.624437	−	0.781075i	$-0.285328\pi$
$557$	9.14443e6			1.24887			0.624437	+	0.781075i	$0.285328\pi$
$558$	2.14969e6	−	995602.i	0.292274	−	0.135363i
$559$	3.49379e6			0.472897
$560$	−3.36088e6			−0.452880
$561$	−3.66264e6	−	2.84239e6i	−0.491346	−	0.381309i
$562$	317272.			0.0423731
$563$	−2.63086e6			−0.349806			−0.174903	−	0.984586i	$-0.555961\pi$
$563$	−2.63086e6			−0.349806			−0.174903	+	0.984586i	$0.555961\pi$
$564$	−7.32909e6	+	1.61480e6i	−0.970180	+	0.213757i
$565$	−3.35712e6			−0.442431
$566$			874433.i			0.114732i
$567$	8.16914e6	+	6.92763e6i	1.06713	+	0.904955i
$568$		−	6.50656e6i		−	0.846215i
$569$	1.23766e7			1.60258			0.801291	−	0.598275i	$-0.204147\pi$
$569$	1.23766e7			1.60258			0.801291	+	0.598275i	$0.204147\pi$
$570$	252994.	+	1.14826e6i	0.0326154	+	0.148032i
$571$			1.06369e7i			1.36529i	0.730750	+	0.682645i	$0.239171\pi$
$571$			1.06369e7i			1.36529i	−0.730750	+	0.682645i	$0.760829\pi$
$572$	3.76966e6	+	4.53068e6i	0.481739	+	0.578993i
$573$	1.79535e6	−	395565.i	0.228435	−	0.0503305i
$574$			334772.i			0.0424101i
$575$		−	261434.i		−	0.0329756i
$576$	3.42325e6	−	1.58544e6i	0.429915	−	0.199110i
$577$	−1.28081e7			−1.60157			−0.800783	−	0.598954i	$-0.795583\pi$
$577$	−1.28081e7			−1.60157			−0.800783	+	0.598954i	$0.795583\pi$
$578$	1.51876e6			0.189090
$579$	−2.95140e6	+	650274.i	−0.365874	+	0.0806120i
$580$			3.73389e6i			0.460884i
$581$			8.98380e6i			1.10413i
$582$	−107846.	−	489481.i	−0.0131976	−	0.0599002i
$583$	5.15005e6	+	6.18975e6i	0.627538	+	0.754226i
$584$			7.91138e6i			0.959888i
$585$	2.79584e6	−	1.29486e6i	0.337771	−	0.156434i
$586$	−4.69938e6			−0.565322
$587$			6.03938e6i			0.723431i	0.932289	+	0.361715i	$0.117809\pi$
$587$			6.03938e6i			0.723431i	−0.932289	+	0.361715i	$0.882191\pi$
$588$	1.56336e6	+	7.09561e6i	0.186473	+	0.846343i
$589$			9.66610e6i			1.14806i
$590$	370168.			0.0437793
$591$	2.79489e6	+	1.26851e7i	0.329151	+	1.49392i
$592$	8.27495e6			0.970424
$593$	−6.36540e6			−0.743343			−0.371671	−	0.928364i	$-0.621215\pi$
$593$	−6.36540e6			−0.743343			−0.371671	+	0.928364i	$0.621215\pi$
$594$	−2.58425e6	−	594846.i	−0.300517	−	0.0691733i
$595$	−3.36074e6			−0.389173
$596$	1.10059e7			1.26915
$597$	1.69853e6	+	7.70913e6i	0.195046	+	0.885257i
$598$	370083.			0.0423201
$599$		−	6.02958e6i		−	0.686625i	−0.939221	−	0.343313i	$-0.888451\pi$
$599$		−	6.02958e6i		−	0.686625i	0.939221	−	0.343313i	$-0.111549\pi$
$600$	−222913.	−	1.01174e6i	−0.0252789	−	0.114733i
$601$			1.56755e7i			1.77025i	0.465349	+	0.885127i	$0.345929\pi$
$601$			1.56755e7i			1.77025i	−0.465349	+	0.885127i	$0.654071\pi$
$602$	−2.17975e6			−0.245141
$603$	6.31585e6	−	2.92511e6i	0.707357	−	0.327603i
$604$		−	1.06143e7i		−	1.18386i
$605$	3.95915e6	+	732147.i	0.439758	+	0.0813223i
$606$	19818.4	+	89949.6i	0.00219223	+	0.00994988i
$607$		−	3.56624e6i		−	0.392861i	−0.980518	−	0.196430i	$-0.937065\pi$
$607$		−	3.56624e6i		−	0.392861i	0.980518	−	0.196430i	$-0.0629350\pi$
$608$		−	8.12132e6i		−	0.890980i
$609$	1.42429e7	−	3.13810e6i	1.55616	−	0.342865i
$610$	−475993.			−0.0517936
$611$	8.43240e6			0.913793
$612$	4.73191e6	−	2.19152e6i	0.510690	−	0.236520i
$613$		−	7.84195e6i		−	0.842893i	−0.906853	−	0.421447i	$-0.861522\pi$
$613$		−	7.84195e6i		−	0.842893i	0.906853	−	0.421447i	$-0.138478\pi$
$614$			1.47224e6i			0.157601i
$615$	402647.	−	88714.2i	0.0429276	−	0.00945813i
$616$	−4.95089e6	−	5.95037e6i	−0.525692	−	0.631818i
$617$			575520.i			0.0608622i	0.999537	+	0.0304311i	$0.00968802\pi$
$617$			575520.i			0.0608622i	−0.999537	+	0.0304311i	$0.990312\pi$
$618$	−557556.	−	2.53058e6i	−0.0587242	−	0.266532i
$619$	−1.77934e7			−1.86652			−0.933259	−	0.359204i	$-0.883048\pi$
$619$	−1.77934e7			−1.86652			−0.933259	+	0.359204i	$0.883048\pi$
$620$		−	4.04582e6i		−	0.422695i
$621$	1.26083e6	−	959656.i	0.131198	−	0.0998589i
$622$		−	4.08915e6i		−	0.423797i
$623$	−7.26517e6			−0.749939
$624$	−5.72225e6	+	1.26077e6i	−0.588308	+	0.129620i
$625$	390625.			0.0400000
$626$	3.93561e6			0.401399
$627$	6.63356e6	−	8.54785e6i	0.673872	−	0.868337i
$628$	1.71827e7			1.73857
$629$	8.27461e6			0.833914
$630$	−1.74431e6	+	807853.i	−0.175094	+	0.0810925i
$631$	5.70811e6			0.570714			0.285357	−	0.958421i	$-0.407888\pi$
$631$	5.70811e6			0.570714			0.285357	+	0.958421i	$0.407888\pi$
$632$			9.94337e6i			0.990241i
$633$	1.61372e7	−	3.55548e6i	1.60074	−	0.352686i
$634$		−	1.75310e6i		−	0.173214i
$635$	−4.54845e6			−0.447640
$636$	−8.84482e6	+	1.94876e6i	−0.867054	+	0.191036i
$637$		−	8.16377e6i		−	0.797154i
$638$	−2.77568e6	+	2.30945e6i	−0.269971	+	0.224624i
$639$	6.24873e6	+	1.34922e7i	0.605396	+	1.30716i
$640$			4.43352e6i			0.427857i
$641$		−	2.05464e6i		−	0.197511i	−0.995112	−	0.0987556i	$-0.968514\pi$
$641$		−	2.05464e6i		−	0.197511i	0.995112	−	0.0987556i	$-0.0314862\pi$
$642$	−966375.	−	4.38609e6i	−0.0925354	−	0.419991i
$643$	1.18363e6			0.112899			0.0564494	−	0.998405i	$-0.482022\pi$
$643$	1.18363e6			0.112899			0.0564494	+	0.998405i	$0.482022\pi$
$644$	2.19712e6			0.208756
$645$	577632.	+	2.62170e6i	0.0546703	+	0.248132i
$646$		−	2.23598e6i		−	0.210807i
$647$			7.06382e6i			0.663405i	0.943384	+	0.331702i	$0.107623\pi$
$647$			7.06382e6i			0.663405i	−0.943384	+	0.331702i	$0.892377\pi$
$648$	4.06109e6	−	4.78888e6i	0.379931	−	0.448019i
$649$	−2.17866e6	−	2.61849e6i	−0.203038	−	0.244028i
$650$			552966.i			0.0513351i
$651$	−1.54328e7	+	3.40026e6i	−1.42722	+	0.314456i
$652$	−1.46089e6			−0.134585
$653$			1.56286e7i			1.43429i	0.696923	+	0.717146i	$0.254552\pi$
$653$			1.56286e7i			1.43429i	−0.696923	+	0.717146i	$0.745448\pi$
$654$	2.01252e6	−	443413.i	0.183991	−	0.0405382i
$655$			6.23637e6i			0.567974i
$656$	−784094.			−0.0711391
$657$	−7.59789e6	−	1.64053e7i	−0.686720	−	1.48276i
$658$	−5.26092e6			−0.473693
$659$	−1.59192e7			−1.42793			−0.713964	−	0.700182i	$-0.753102\pi$
$659$	−1.59192e7			−1.42793			−0.713964	+	0.700182i	$0.753102\pi$
$660$	−2.77653e6	+	3.57777e6i	−0.248109	+	0.319707i
$661$	−4.30701e6			−0.383418			−0.191709	−	0.981452i	$-0.561403\pi$
$661$	−4.30701e6			−0.383418			−0.191709	+	0.981452i	$0.561403\pi$
$662$	−4.82839e6			−0.428211
$663$	−5.72201e6	+	1.26072e6i	−0.505551	+	0.111387i
$664$	5.26645e6			0.463551
$665$		−	7.84328e6i		−	0.687771i
$666$	4.29472e6	−	1.98905e6i	0.375189	−	0.173764i
$667$		−	2.15750e6i		−	0.187774i
$668$	6.58370e6			0.570859
$669$	690230.	+	3.13275e6i	0.0596250	+	0.270620i
$670$			1.24916e6i			0.107506i
$671$	2.80151e6	+	3.36708e6i	0.240207	+	0.288700i
$672$	1.29664e7	−	2.85685e6i	1.10763	−	0.244042i
$673$			1.31966e7i			1.12312i	0.827436	+	0.561560i	$0.189798\pi$
$673$			1.31966e7i			1.12312i	−0.827436	+	0.561560i	$0.810202\pi$
$674$		−	5.11704e6i		−	0.433880i
$675$	1.43388e6	+	1.88388e6i	0.121131	+	0.159146i
$676$	−3.30282e6			−0.277983
$677$	−4.55254e6			−0.381752			−0.190876	−	0.981614i	$-0.561133\pi$
$677$	−4.55254e6			−0.381752			−0.190876	+	0.981614i	$0.561133\pi$
$678$	3.56608e6	−	785705.i	0.297932	−	0.0656425i
$679$			3.34342e6i			0.278302i
$680$			1.97012e6i			0.163388i
$681$	−639265.	−	2.90143e6i	−0.0528218	−	0.239742i
$682$	3.00756e6	−	2.50238e6i	0.247602	−	0.206012i
$683$		−	1.25842e7i		−	1.03222i	−0.856521	−	0.516111i	$-0.827379\pi$
$683$		−	1.25842e7i		−	1.03222i	0.856521	−	0.516111i	$-0.172621\pi$
$684$	5.11456e6	+	1.10433e7i	0.417992	+	0.902523i
$685$	−2.63867e6			−0.214861
$686$		−	224871.i		−	0.0182442i
$687$	−4.88179e6	−	2.21570e7i	−0.394628	−	1.79110i
$688$		−	5.10535e6i		−	0.411201i
$689$	1.01763e7			0.816662
$690$	61186.3	+	277706.i	0.00489251	+	0.0222056i
$691$	−1.59645e7			−1.27193			−0.635963	−	0.771720i	$-0.719397\pi$
$691$	−1.59645e7			−1.27193			−0.635963	+	0.771720i	$0.719397\pi$
$692$	1.45367e7			1.15399
$693$	1.59809e7	+	7.58415e6i	1.26406	+	0.599893i
$694$	−1.31276e6			−0.103463
$695$	2.73266e6			0.214597
$696$	−1.83960e6	−	8.34941e6i	−0.143947	−	0.653330i
$697$	−784061.			−0.0611319
$698$			1.29591e6i			0.100678i
$699$	−4.98468e6	−	2.26240e7i	−0.385873	−	1.75136i
$700$			3.28286e6i			0.253226i
$701$	4.40559e6			0.338617			0.169309	−	0.985563i	$-0.445847\pi$
$701$	4.40559e6			0.338617			0.169309	+	0.985563i	$0.445847\pi$
$702$	−2.66681e6	+	2.02979e6i	−0.204244	+	0.155457i
$703$			1.93112e7i			1.47374i
$704$	4.78935e6	−	3.98488e6i	0.364205	−	0.303029i
$705$	1.39414e6	+	6.32757e6i	0.105641	+	0.479473i
$706$			6.15092e6i			0.464438i
$707$		−	614406.i		−	0.0462282i
$708$	3.74168e6	−	824395.i	0.280533	−	0.0618090i
$709$	2.08185e7			1.55537			0.777684	−	0.628655i	$-0.216394\pi$
$709$	2.08185e7			1.55537			0.777684	+	0.628655i	$0.216394\pi$
$710$	−2.66851e6			−0.198666
$711$	−9.54936e6	−	2.06188e7i	−0.708435	−	1.52964i
$712$			4.25896e6i			0.314850i
$713$			2.33774e6i			0.172215i
$714$	3.56993e6	−	786552.i	0.262068	−	0.0577407i
$715$	3.91156e6	−	3.25454e6i	0.286144	−	0.238081i
$716$			1.20708e7i			0.879940i
$717$	−2.23784e6	−	1.01569e7i	−0.162567	−	0.737841i
$718$	−1.91729e6			−0.138796
$719$		−	2.18504e7i		−	1.57629i	−0.615487	−	0.788147i	$-0.711041\pi$
$719$		−	2.18504e7i		−	1.57629i	0.615487	−	0.788147i	$-0.288959\pi$
$720$	−1.89213e6	−	4.08546e6i	−0.136025	−	0.293704i
$721$			1.72853e7i			1.23833i
$722$	898919.			0.0641767
$723$	4.70766e6	−	1.03723e6i	0.334934	−	0.0737951i
$724$	−1.56956e7			−1.11283
$725$	3.22366e6			0.227774
$726$	−4.37693e6	+	148886.i	−0.308197	+	0.0104837i
$727$	−1.28765e7			−0.903572			−0.451786	−	0.892126i	$-0.649213\pi$
$727$	−1.28765e7			−0.903572			−0.451786	+	0.892126i	$0.649213\pi$
$728$	−9.78276e6			−0.684121
$729$	−3.82207e6	+	1.38305e7i	−0.266366	+	0.963872i
$730$	3.24466e6			0.225352
$731$		−	5.10514e6i		−	0.353358i
$732$	−4.81137e6	+	1.06008e6i	−0.331888	+	0.0731240i
$733$			2.46467e7i			1.69434i	0.531325	+	0.847168i	$0.321694\pi$
$733$			2.46467e7i			1.69434i	−0.531325	+	0.847168i	$0.678306\pi$
$734$	2.06597e6			0.141542
$735$	6.12600e6	−	1.34973e6i	0.418272	−	0.0921567i
$736$		−	1.96413e6i		−	0.133652i
$737$	8.83629e6	−	7.35206e6i	0.599241	−	0.498586i
$738$	−406947.	+	188472.i	−0.0275040	+	0.0127382i
$739$			2.39233e6i			0.161143i	0.996749	+	0.0805714i	$0.0256745\pi$
$739$			2.39233e6i			0.161143i	−0.996749	+	0.0805714i	$0.974326\pi$
$740$		−	8.08287e6i		−	0.542608i
$741$	−2.94225e6	−	1.33540e7i	−0.196849	−	0.893441i
$742$	−6.34893e6			−0.423342
$743$	−1.67411e7			−1.11253			−0.556264	−	0.831006i	$-0.687766\pi$
$743$	−1.67411e7			−1.11253			−0.556264	+	0.831006i	$0.687766\pi$
$744$	1.99329e6	+	9.04693e6i	0.132019	+	0.599196i
$745$		−	9.50198e6i		−	0.627225i
$746$			5.88464e6i			0.387144i
$747$	−1.09206e7	+	5.05776e6i	−0.716056	+	0.331632i
$748$	6.62025e6	−	5.50824e6i	0.432634	−	0.359964i
$749$			2.99594e7i			1.95132i
$750$	−414939.	+	91422.4i	−0.0269359	+	0.00593471i
$751$	−2.18371e7			−1.41285			−0.706424	−	0.707789i	$-0.749693\pi$
$751$	−2.18371e7			−1.41285			−0.706424	+	0.707789i	$0.749693\pi$
$752$		−	1.23220e7i		−	0.794577i
$753$	−1.10410e7	+	2.43264e6i	−0.709615	+	0.156347i
$754$			4.56338e6i			0.292320i
$755$	−9.16386e6			−0.585074
$756$	−1.58324e7	+	1.20506e7i	−1.00749	+	0.766836i
$757$	2.71791e7			1.72383			0.861916	−	0.507051i	$-0.169264\pi$
$757$	2.71791e7			1.72383			0.861916	+	0.507051i	$0.169264\pi$
$758$	−696777.			−0.0440474
$759$	1.60432e6	−	2.06729e6i	0.101085	−	0.130256i
$760$	−4.59786e6			−0.288750
$761$	−6.04799e6			−0.378573			−0.189286	−	0.981922i	$-0.560617\pi$
$761$	−6.04799e6			−0.378573			−0.189286	+	0.981922i	$0.560617\pi$
$762$	4.83156e6	−	1.06452e6i	0.301439	−	0.0664153i
$763$	−1.37466e7			−0.854839
$764$			3.41501e6i			0.211670i
$765$	−1.89205e6	−	4.08529e6i	−0.116891	−	0.252389i
$766$			6.60492e6i			0.406720i
$767$	−4.30495e6			−0.264228
$768$	628695.	+	2.85346e6i	0.0384624	+	0.174569i
$769$		−	2.05617e7i		−	1.25384i	−0.779082	−	0.626922i	$-0.784315\pi$
$769$		−	2.05617e7i		−	1.25384i	0.779082	−	0.626922i	$-0.215685\pi$
$770$	−2.44040e6	+	2.03048e6i	−0.148332	+	0.123416i
$771$	9.10753e6	−	2.00664e6i	0.551778	−	0.121572i
$772$		−	5.61398e6i		−	0.339022i
$773$		−	2.56368e7i		−	1.54317i	−0.636123	−	0.771587i	$-0.719463\pi$
$773$		−	2.56368e7i		−	1.54317i	0.636123	−	0.771587i	$-0.280537\pi$
$774$	−1.22717e6	−	2.64969e6i	−0.0736296	−	0.158980i
$775$	−3.49296e6			−0.208900
$776$	1.95997e6			0.116841
$777$	−3.08320e7	+	6.79314e6i	−1.83210	+	0.403662i
$778$		−	7.83620e6i		−	0.464148i
$779$		−	1.82984e6i		−	0.108036i
$780$	1.23150e6	+	5.58941e6i	0.0724767	+	0.328950i
$781$	1.57058e7	+	1.88765e7i	0.921365	+	1.10737i
$782$		−	540768.i		−	0.0316224i
$783$	1.18332e7	+	1.55469e7i	0.689760	+	0.906230i
$784$	−1.19294e7			−0.693155
$785$		−	1.48347e7i		−	0.859221i
$786$	−1.45957e6	−	6.62454e6i	−0.0842690	−	0.382472i
$787$			2.58514e6i			0.148781i	0.997229	+	0.0743905i	$0.0237011\pi$
$787$			2.58514e6i			0.148781i	−0.997229	+	0.0743905i	$0.976299\pi$
$788$	−2.41290e7			−1.38428
$789$	−6.83031e6	−	3.10008e7i	−0.390614	−	1.77288i
$790$	4.07803e6			0.232478
$791$	−2.43583e7			−1.38422
$792$	4.44595e6	−	9.36824e6i	0.251855	−	0.530695i
$793$	5.53567e6			0.312599
$794$	−5.55151e6			−0.312507
$795$	1.68246e6	+	7.63618e6i	0.0944119	+	0.428508i
$796$	−1.46639e7			−0.820287
$797$		−	1.67586e7i		−	0.934529i	−0.884118	−	0.467265i	$-0.845240\pi$
$797$		−	1.67586e7i		−	0.934529i	0.884118	−	0.467265i	$-0.154760\pi$
$798$	1.83565e6	+	8.33147e6i	0.102043	+	0.463142i
$799$		−	1.23215e7i		−	0.682803i
$800$	2.93474e6			0.162123
$801$	−4.09019e6	−	8.83150e6i	−0.225249	−	0.486355i
$802$		−	3.49932e6i		−	0.192109i
$803$	−1.90968e7	−	2.29520e7i	−1.04513	−	1.25612i
$804$	2.78198e6	+	1.26266e7i	0.151780	+	0.688884i
$805$		−	1.89689e6i		−	0.103170i
$806$		−	4.94461e6i		−	0.268098i
$807$	1.39357e7	−	3.07041e6i	0.753259	−	0.165963i
$808$	−360174.			−0.0194082
$809$	1.40435e7			0.754404			0.377202	−	0.926131i	$-0.376886\pi$
$809$	1.40435e7			0.754404			0.377202	+	0.926131i	$0.376886\pi$
$810$	−1.96404e6	−	1.66556e6i	−0.105181	−	0.0891962i
$811$		−	1.73945e7i		−	0.928666i	−0.885661	−	0.464333i	$-0.846294\pi$
$811$		−	1.73945e7i		−	0.928666i	0.885661	−	0.464333i	$-0.153706\pi$
$812$			2.70920e7i			1.44195i
$813$	2.99160e7	−	6.59130e6i	1.58736	−	0.349740i
$814$	6.00860e6	−	4.99933e6i	0.317843	−	0.264455i
$815$			1.26126e6i			0.0665134i
$816$	1.84224e6	+	8.36138e6i	0.0968547	+	0.439595i
$817$	1.19144e7			0.624475
$818$			523218.i			0.0273400i
$819$	2.02858e7	−	9.39511e6i	1.05677	−	0.489432i
$820$			765893.i			0.0397771i
$821$	1.85576e7			0.960870			0.480435	−	0.877030i	$-0.340479\pi$
$821$	1.85576e7			0.960870			0.480435	+	0.877030i	$0.340479\pi$
$822$	2.80291e6	−	617557.i	0.144687	−	0.0318785i
$823$	−2.98113e7			−1.53420			−0.767098	−	0.641530i	$-0.778300\pi$
$823$	−2.98113e7			−1.53420			−0.767098	+	0.641530i	$0.778300\pi$
$824$	1.01329e7			0.519895
$825$	3.08887e6	+	2.39711e6i	0.158003	+	0.122618i
$826$	2.68583e6			0.136971
$827$	−343612.			−0.0174705			−0.00873524	−	0.999962i	$-0.502781\pi$
$827$	−343612.			−0.0174705			−0.00873524	+	0.999962i	$0.502781\pi$
$828$	1.23695e6	+	2.67081e6i	0.0627013	+	0.135384i
$829$	1.82412e7			0.921865			0.460933	−	0.887435i	$-0.347515\pi$
$829$	1.82412e7			0.921865			0.460933	+	0.887435i	$0.347515\pi$
$830$		−	2.15990e6i		−	0.108828i
$831$	−2.95739e7	+	6.51593e6i	−1.48561	+	0.327321i
$832$		−	7.87398e6i		−	0.394354i
$833$	−1.19290e7			−0.595648
$834$	−2.90275e6	+	639555.i	−0.144509	+	0.0318392i
$835$		−	5.68404e6i		−	0.282124i
$836$	1.28551e7	+	1.54503e7i	0.636151	+	0.764577i
$837$	−1.28218e7	−	1.68456e7i	−0.632607	−	0.831140i
$838$		−	5.13018e6i		−	0.252361i
$839$			1.26295e7i			0.619414i	0.950832	+	0.309707i	$0.100231\pi$
$839$			1.26295e7i			0.619414i	−0.950832	+	0.309707i	$0.899769\pi$
$840$	−1.61739e6	−	7.34087e6i	−0.0790893	−	0.358963i
$841$	6.09225e6			0.297022
$842$	1.12254e7			0.545658
$843$	−610035.	−	2.76877e6i	−0.0295656	−	0.134189i
$844$			3.06953e7i			1.48326i
$845$			2.85149e6i			0.137382i
$846$	−2.96183e6	−	6.39514e6i	−0.142277	−	0.307202i
$847$	2.87264e7	+	5.31224e6i	1.37586	+	0.254431i
$848$		−	1.48703e7i		−	0.710117i
$849$	7.63101e6	−	1.68132e6i	0.363340	−	0.0800537i
$850$	807996.			0.0383585
$851$			4.67040e6i			0.221070i
$852$	−2.69735e7	+	5.94299e6i	−1.27303	+	0.280483i
$853$		−	2.03837e7i		−	0.959205i	−0.877486	−	0.479602i	$-0.840781\pi$
$853$		−	2.03837e7i		−	0.959205i	0.877486	−	0.479602i	$-0.159219\pi$
$854$	−3.45367e6			−0.162045
$855$	9.53424e6	−	4.41566e6i	0.446037	−	0.206576i
$856$	1.75627e7			0.819231
$857$	−2.65602e7			−1.23532			−0.617660	−	0.786445i	$-0.711919\pi$
$857$	−2.65602e7			−1.23532			−0.617660	+	0.786445i	$0.711919\pi$
$858$	−3.39334e6	+	4.37258e6i	−0.157365	+	0.202777i
$859$	3.18180e7			1.47126			0.735631	−	0.677382i	$-0.236886\pi$
$859$	3.18180e7			1.47126			0.735631	+	0.677382i	$0.236886\pi$
$860$	−4.98684e6			−0.229921
$861$	2.92149e6	−	643685.i	0.134306	−	0.0295914i
$862$	−9.00159e6			−0.412621
$863$		−	6.08772e6i		−	0.278245i	−0.990275	−	0.139123i	$-0.955572\pi$
$863$		−	6.08772e6i		−	0.278245i	0.990275	−	0.139123i	$-0.0444282\pi$
$864$	1.07727e7	+	1.41535e7i	0.490952	+	0.645028i
$865$		−	1.25503e7i		−	0.570314i
$866$	1.75044e6			0.0793145
$867$	−2.92020e6	−	1.32539e7i	−0.131937	−	0.598821i
$868$		−	2.93553e7i		−	1.32247i
$869$	−2.40017e7	−	2.88471e7i	−1.07818	−	1.29585i
$870$	−3.42431e6	+	754469.i	−0.153382	+	0.0337943i
$871$		−	1.45274e7i		−	0.648846i
$872$			8.05849e6i			0.358891i
$873$	−4.06424e6	+	1.88230e6i	−0.180486	+	0.0835899i
$874$	1.26204e6			0.0558850
$875$	2.83426e6			0.125147
$876$	3.27973e7	−	7.22613e6i	1.44403	−	0.318160i
$877$			1.83775e7i			0.806842i	0.915015	+	0.403421i	$0.132179\pi$
$877$			1.83775e7i			0.806842i	−0.915015	+	0.403421i	$0.867821\pi$
$878$		−	2.22192e6i		−	0.0972730i
$879$	9.03575e6	+	4.10106e7i	0.394450	+	1.79029i
$880$	−4.75574e6	−	5.71583e6i	−0.207020	−	0.248813i
$881$			9.59720e6i			0.416586i	0.978066	+	0.208293i	$0.0667908\pi$
$881$			9.59720e6i			0.416586i	−0.978066	+	0.208293i	$0.933209\pi$
$882$	−6.19141e6	+	2.86747e6i	−0.267990	+	0.124116i
$883$	2.41621e7			1.04288			0.521438	−	0.853289i	$-0.325396\pi$
$883$	2.41621e7			1.04288			0.521438	+	0.853289i	$0.325396\pi$
$884$		−	1.08841e7i		−	0.468448i
$885$	−711742.	−	3.23038e6i	−0.0305467	−	0.138642i
$886$			3.18023e6i			0.136105i
$887$	42769.5			0.00182526			0.000912630	−	1.00000i	$-0.499710\pi$
$887$	42769.5			0.00182526			0.000912630		1.00000i	$0.499710\pi$
$888$	3.98225e6	+	1.80742e7i	0.169471	+	0.769179i
$889$	−3.30022e7			−1.40052
$890$	1.74671e6			0.0739172
$891$	−222224.	+	2.36960e7i	−0.00937770	+	0.999956i
$892$	−5.95893e6			−0.250759
$893$	2.87558e7			1.20669
$894$	2.22386e6	+	1.00934e7i	0.0930600	+	0.422371i
$895$	1.04213e7			0.434876
$896$			3.21683e7i			1.33862i
$897$	−711580.	−	3.22965e6i	−0.0295286	−	0.134021i
$898$		−	4.44316e6i		−	0.183866i
$899$	−2.88259e7			−1.18955
$900$	−3.99063e6	+	1.84821e6i	−0.164223	+	0.0760579i
$901$		−	1.48697e7i		−	0.610224i
$902$	−569345.	+	473712.i	−0.0233002	+	0.0193864i
$903$	4.19113e6	+	1.90223e7i	0.171045	+	0.776324i
$904$			1.42792e7i			0.581143i
$905$			1.35508e7i			0.549974i
$906$	9.73425e6	−	2.14472e6i	0.393987	−	0.0868061i
$907$	−1.58436e7			−0.639493			−0.319747	−	0.947503i	$-0.603598\pi$
$907$	−1.58436e7			−0.639493			−0.319747	+	0.947503i	$0.603598\pi$
$908$	5.51894e6			0.222147
$909$	746867.	−	345902.i	0.0299801	−	0.0138849i
$910$			4.01216e6i			0.160611i
$911$		−	5.15064e6i		−	0.205620i	−0.994701	−	0.102810i	$-0.967217\pi$
$911$		−	5.15064e6i		−	0.205620i	0.994701	−	0.102810i	$-0.0327833\pi$
$912$	−1.95137e7	+	4.29941e6i	−0.776879	+	0.171168i
$913$	−1.52787e7	+	1.27123e7i	−0.606610	+	0.504718i
$914$			9.42307e6i			0.373101i
$915$	915218.	+	4.15390e6i	0.0361387	+	0.164023i
$916$	4.21458e7			1.65965
$917$			4.52493e7i			1.77700i
$918$	2.96595e6	+	3.89676e6i	0.116160	+	0.152615i
$919$		−	4.22297e7i		−	1.64941i	−0.565561	−	0.824706i	$-0.691340\pi$
$919$		−	4.22297e7i		−	1.64941i	0.565561	−	0.824706i	$-0.308660\pi$
$920$	−1.11199e6			−0.0433141
$921$	1.28480e7	−	2.83076e6i	0.499098	−	0.109965i
$922$	−6.38931e6			−0.247529
$923$	3.10340e7			1.19904
$924$	−2.01457e7	+	2.59593e7i	−0.776250	+	1.00026i
$925$	−6.97835e6			−0.268163
$926$	−1.16132e7			−0.445066
$927$	−2.10119e7	+	9.73137e6i	−0.803091	+	0.371942i
$928$	2.42191e7			0.923183
$929$			7.51844e6i			0.285817i	0.989736	+	0.142909i	$0.0456455\pi$
$929$			7.51844e6i			0.285817i	−0.989736	+	0.142909i	$0.954355\pi$
$930$	3.71037e6	−	817497.i	0.140673	−	0.0309941i
$931$		−	2.78397e7i		−	1.05267i
$932$	4.30340e7			1.62283
$933$	−3.56853e7	+	7.86244e6i	−1.34210	+	0.295701i
$934$			1.00260e7i			0.376064i
$935$	−4.75555e6	−	5.71560e6i	−0.177898	−	0.213812i
$936$	−5.50756e6	−	1.18919e7i	−0.205480	−	0.443670i
$937$		−	2.30472e7i		−	0.857570i	−0.903406	−	0.428785i	$-0.858942\pi$
$937$		−	2.30472e7i		−	0.857570i	0.903406	−	0.428785i	$-0.141058\pi$
$938$			9.06354e6i			0.336349i
$939$	−7.56721e6	−	3.43453e7i	−0.280073	−	1.27117i
$940$	−1.20359e7			−0.444284
$941$	3.47241e7			1.27837			0.639185	−	0.769053i	$-0.279272\pi$
$941$	3.47241e7			1.27837			0.639185	+	0.769053i	$0.279272\pi$
$942$	3.47194e6	+	1.57581e7i	0.127481	+	0.578597i
$943$		−	442544.i		−	0.0162061i
$944$			6.29067e6i			0.229756i
$945$	1.04038e7	+	1.36689e7i	0.378978	+	0.497914i
$946$	−3.08441e6	−	3.70709e6i	−0.112058	−	0.134681i
$947$			3.94055e6i			0.142785i	0.997448	+	0.0713924i	$0.0227442\pi$
$947$			3.94055e6i			0.142785i	−0.997448	+	0.0713924i	$0.977256\pi$
$948$	4.12210e7	−	9.08212e6i	1.48970	−	0.328221i
$949$	−3.77345e7			−1.36011
$950$			1.88570e6i			0.0677896i
$951$	−1.52990e7	+	3.37078e6i	−0.548543	+	0.120859i
$952$			1.42946e7i			0.511188i
$953$	−1.58564e7			−0.565552			−0.282776	−	0.959186i	$-0.591255\pi$
$953$	−1.58564e7			−0.565552			−0.282776	+	0.959186i	$0.591255\pi$
$954$	−3.57436e6	−	7.71772e6i	−0.127153	−	0.274548i
$955$	2.94835e6			0.104609
$956$	1.93199e7			0.683690
$957$	2.54911e7	+	1.97823e7i	0.899721	+	0.698228i
$958$	1.00952e7			0.355387
$959$	−1.91454e7			−0.672230
$960$	5.90854e6	−	1.30181e6i	0.206920	−	0.0455901i
$961$	2.60483e6			0.0909852
$962$		−	9.87849e6i		−	0.344154i
$963$	−3.64184e7	+	1.68667e7i	−1.26548	+	0.586091i
$964$			8.95464e6i			0.310353i
$965$	−4.84683e6			−0.167548
$966$	443950.	+	2.01496e6i	0.0153070	+	0.0694741i
$967$			3.03616e7i			1.04414i	0.852903	+	0.522070i	$0.174840\pi$
$967$			3.03616e7i			1.04414i	−0.852903	+	0.522070i	$0.825160\pi$
$968$	3.11412e6	−	1.68399e7i	0.106819	−	0.577632i
$969$	−1.95129e7	+	4.29923e6i	−0.667595	+	0.147089i
$970$		−	803833.i		−	0.0274307i
$971$		−	2.38486e7i		−	0.811737i	−0.913931	−	0.405869i	$-0.866969\pi$
$971$		−	2.38486e7i		−	0.811737i	0.913931	−	0.405869i	$-0.133031\pi$
$972$	−2.35620e7	−	1.24615e7i	−0.799920	−	0.423061i
$973$	1.98274e7			0.671403
$974$	5.56932e6			0.188107
$975$	4.82562e6	−	1.06322e6i	0.162571	−	0.0358187i
$976$		−	8.08909e6i		−	0.271816i
$977$			5.95335e6i			0.199538i	0.995011	+	0.0997688i	$0.0318103\pi$
$977$			5.95335e6i			0.199538i	−0.995011	+	0.0997688i	$0.968190\pi$
$978$	−295186.	−	1.33976e6i	−0.00986844	−	0.0447899i
$979$	−1.02804e7	−	1.23558e7i	−0.342811	−	0.412018i
$980$			1.16525e7i			0.387574i
$981$	−7.73916e6	−	1.67103e7i	−0.256756	−	0.554385i
$982$	1.21463e7			0.401945
$983$			2.20657e7i			0.728341i	0.931332	+	0.364170i	$0.118647\pi$
$983$			2.20657e7i			0.728341i	−0.931332	+	0.364170i	$0.881353\pi$
$984$	−377338.	−	1.71263e6i	−0.0124235	−	0.0563864i
$985$			2.08318e7i			0.684125i
$986$	6.66804e6			0.218427
$987$	1.01155e7	+	4.59110e7i	0.330516	+	1.50011i
$988$	2.54012e7			0.827870
$989$	2.88147e6			0.0936750
$990$	−3.84215e6	−	1.82340e6i	−0.124591	−	0.0591280i
$991$	2.77217e7			0.896675			0.448337	−	0.893864i	$-0.352016\pi$
$991$	2.77217e7			0.896675			0.448337	+	0.893864i	$0.352016\pi$
$992$	−2.62424e7			−0.846688
$993$	9.28381e6	+	4.21365e7i	0.298781	+	1.35608i
$994$	−1.93619e7			−0.621559
$995$			1.26601e7i			0.405394i
$996$	−4.81029e6	−	2.18325e7i	−0.153647	−	0.697356i
$997$			1.31106e7i			0.417720i	0.977946	+	0.208860i	$0.0669754\pi$
$997$			1.31106e7i			0.417720i	−0.977946	+	0.208860i	$0.933025\pi$
$998$	−8.63737e6			−0.274508
$999$	−2.56157e7	−	3.36548e7i	−0.812069	−	1.06692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.f.a.131.33	✓	80
3.2	odd	2	inner	165.6.f.a.131.47	yes	80
11.10	odd	2	inner	165.6.f.a.131.48	yes	80
33.32	even	2	inner	165.6.f.a.131.34	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.f.a.131.33	✓	80	1.1	even	1	trivial
165.6.f.a.131.34	yes	80	33.32	even	2	inner
165.6.f.a.131.47	yes	80	3.2	odd	2	inner
165.6.f.a.131.48	yes	80	11.10	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.74443 q^{2} +(3.35412 + 15.2233i) q^{3} -28.9570 q^{4} +25.0000i q^{5} +(-5.85103 - 26.5561i) q^{6} +181.393i q^{7} +106.335 q^{8} +(-220.500 + 102.122i) q^{9} +O(q^{10})\)	\(q-1.74443 q^{2} +(3.35412 + 15.2233i) q^{3} -28.9570 q^{4} +25.0000i q^{5} +(-5.85103 - 26.5561i) q^{6} +181.393i q^{7} +106.335 q^{8} +(-220.500 + 102.122i) q^{9} -43.6108i q^{10} +(-308.494 + 256.676i) q^{11} +(-97.1250 - 440.821i) q^{12} +507.182i q^{13} -316.428i q^{14} +(-380.583 + 83.8529i) q^{15} +741.128 q^{16} +741.097 q^{17} +(384.647 - 178.144i) q^{18} +1729.57i q^{19} -723.924i q^{20} +(-2761.40 + 608.413i) q^{21} +(538.147 - 447.754i) q^{22} +418.294i q^{23} +(356.661 + 1618.78i) q^{24} -625.000 q^{25} -884.745i q^{26} +(-2294.21 - 3014.21i) q^{27} -5252.58i q^{28} -5157.85 q^{29} +(663.902 - 146.276i) q^{30} +5588.74 q^{31} -4695.58 q^{32} +(-4942.19 - 3835.38i) q^{33} -1292.79 q^{34} -4534.82 q^{35} +(6385.00 - 2957.13i) q^{36} +11165.4 q^{37} -3017.12i q^{38} +(-7721.00 + 1701.15i) q^{39} +2658.38i q^{40} -1057.97 q^{41} +(4817.08 - 1061.34i) q^{42} -6888.63i q^{43} +(8933.04 - 7432.55i) q^{44} +(-2553.04 - 5512.49i) q^{45} -729.686i q^{46} -16626.0i q^{47} +(2485.83 + 11282.4i) q^{48} -16096.3 q^{49} +1090.27 q^{50} +(2485.73 + 11282.0i) q^{51} -14686.4i q^{52} -20064.4i q^{53} +(4002.10 + 5258.09i) q^{54} +(-6416.90 - 7712.35i) q^{55} +19288.5i q^{56} +(-26329.8 + 5801.17i) q^{57} +8997.52 q^{58} +8487.98i q^{59} +(11020.5 - 2428.13i) q^{60} -10914.6i q^{61} -9749.18 q^{62} +(-18524.1 - 39997.1i) q^{63} -15525.0 q^{64} -12679.5 q^{65} +(8621.32 + 6690.57i) q^{66} -28643.3 q^{67} -21459.9 q^{68} +(-6367.83 + 1403.01i) q^{69} +7910.69 q^{70} -61189.1i q^{71} +(-23446.9 + 10859.1i) q^{72} +74400.3i q^{73} -19477.2 q^{74} +(-2096.32 - 9514.58i) q^{75} -50083.0i q^{76} +(-46559.2 - 55958.6i) q^{77} +(13468.8 - 2967.54i) q^{78} +93509.6i q^{79} +18528.2i q^{80} +(38191.3 - 45035.6i) q^{81} +1845.56 q^{82} +49526.8 q^{83} +(79961.8 - 17617.8i) q^{84} +18527.4i q^{85} +12016.8i q^{86} +(-17300.0 - 78519.7i) q^{87} +(-32803.8 + 27293.7i) q^{88} +40052.2i q^{89} +(4453.61 + 9616.18i) q^{90} -91999.1 q^{91} -12112.5i q^{92} +(18745.3 + 85079.2i) q^{93} +29002.9i q^{94} -43239.2 q^{95} +(-15749.5 - 71482.4i) q^{96} +18432.0 q^{97} +28079.0 q^{98} +(41810.6 - 88100.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9	\( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) \) 80 * q + 44 * q^3 + 1280 * q^4 - 352 * q^9 + 2112 * q^12 + 1100 * q^15 + 13792 * q^16 - 9892 * q^22 - 50000 * q^25 - 10780 * q^27 + 2112 * q^31 + 6316 * q^33 + 69560 * q^34 - 17268 * q^36 - 7456 * q^37 - 100712 * q^42 + 61352 * q^48 - 233408 * q^49 - 15800 * q^55 - 93728 * q^58 + 62700 * q^60 + 212400 * q^64 + 203724 * q^66 + 182072 * q^67 - 122584 * q^69 + 6600 * q^70 - 27500 * q^75 - 489128 * q^78 + 194872 * q^81 - 237544 * q^82 - 641716 * q^88 + 168272 * q^91 + 433336 * q^93 + 949008 * q^97 + 328952 * q^99

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