LMFDB - Embedded newform 43.6.e.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	43.4
Dual form			43.6.e.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.84915 + 6.08065i) q^{2} +(1.26806 + 1.59010i) q^{3} +(-6.33931 - 27.7743i) q^{4} +(3.40560 + 1.64005i) q^{5} -15.8178 q^{6} -175.475 q^{7} +(-24.6053 - 11.8493i) q^{8} +(53.1522 - 232.875i) q^{9} +O(q^{10})$	\(q+(-4.84915 + 6.08065i) q^{2} +(1.26806 + 1.59010i) q^{3} +(-6.33931 - 27.7743i) q^{4} +(3.40560 + 1.64005i) q^{5} -15.8178 q^{6} -175.475 q^{7} +(-24.6053 - 11.8493i) q^{8} +(53.1522 - 232.875i) q^{9} +(-26.4869 + 12.7554i) q^{10} +(62.3486 - 273.167i) q^{11} +(36.1252 - 45.2996i) q^{12} +(881.242 + 424.384i) q^{13} +(850.907 - 1067.00i) q^{14} +(1.71067 + 7.49492i) q^{15} +(1012.72 - 487.701i) q^{16} +(-1217.84 + 586.483i) q^{17} +(1158.29 + 1452.45i) q^{18} +(-643.515 - 2819.42i) q^{19} +(23.9622 - 104.985i) q^{20} +(-222.513 - 279.023i) q^{21} +(1358.69 + 1703.75i) q^{22} +(357.493 - 1566.28i) q^{23} +(-12.3595 - 54.1504i) q^{24} +(-1939.50 - 2432.05i) q^{25} +(-6853.81 + 3300.62i) q^{26} +(882.966 - 425.214i) q^{27} +(1112.39 + 4873.71i) q^{28} +(-3940.17 + 4940.81i) q^{29} +(-53.8692 - 25.9420i) q^{30} +(-469.941 + 589.287i) q^{31} +(-1750.84 + 7670.93i) q^{32} +(513.423 - 247.252i) q^{33} +(2339.32 - 10249.2i) q^{34} +(-597.599 - 287.789i) q^{35} -6804.89 q^{36} -10135.0 q^{37} +(20264.4 + 9758.84i) q^{38} +(442.656 + 1939.40i) q^{39} +(-64.3625 - 80.7080i) q^{40} +(6093.87 - 7641.47i) q^{41} +2775.64 q^{42} +(-4966.99 - 11060.6i) q^{43} -7982.27 q^{44} +(562.942 - 705.907i) q^{45} +(7790.46 + 9768.93i) q^{46} +(86.7308 + 379.992i) q^{47} +(2059.68 + 991.890i) q^{48} +13984.6 q^{49} +24193.4 q^{50} +(-2476.86 - 1192.79i) q^{51} +(6200.51 - 27166.2i) q^{52} +(-20695.8 + 9966.56i) q^{53} +(-1696.06 + 7430.93i) q^{54} +(660.342 - 828.043i) q^{55} +(4317.63 + 2079.26i) q^{56} +(3667.14 - 4598.45i) q^{57} +(-10936.9 - 47917.5i) q^{58} +(-23877.0 + 11498.6i) q^{59} +(197.322 - 95.0251i) q^{60} +(-9000.30 - 11286.0i) q^{61} +(-1304.43 - 5715.09i) q^{62} +(-9326.90 + 40863.8i) q^{63} +(-15727.7 - 19722.0i) q^{64} +(2305.15 + 2890.57i) q^{65} +(-986.219 + 4320.91i) q^{66} +(-8744.59 - 38312.5i) q^{67} +(24009.4 + 30106.9i) q^{68} +(2943.86 - 1417.69i) q^{69} +(4647.79 - 2238.26i) q^{70} +(-1262.62 - 5531.90i) q^{71} +(-4067.23 + 5100.14i) q^{72} +(49204.4 + 23695.6i) q^{73} +(49146.4 - 61627.6i) q^{74} +(1407.80 - 6167.97i) q^{75} +(-74228.1 + 35746.4i) q^{76} +(-10940.6 + 47934.1i) q^{77} +(-13939.3 - 6712.83i) q^{78} +56434.9 q^{79} +4248.78 q^{80} +(-50499.9 - 24319.5i) q^{81} +(16915.0 + 74109.3i) q^{82} +(76201.3 + 95553.4i) q^{83} +(-6339.08 + 7948.96i) q^{84} -5109.35 q^{85} +(91341.5 + 23432.2i) q^{86} -12852.7 q^{87} +(-4770.94 + 5982.57i) q^{88} +(-40356.6 - 50605.5i) q^{89} +(1562.58 + 6846.10i) q^{90} +(-154636. - 74468.9i) q^{91} -45768.6 q^{92} -1532.94 q^{93} +(-2731.17 - 1315.26i) q^{94} +(2432.44 - 10657.2i) q^{95} +(-14417.7 + 6943.19i) q^{96} +(11622.9 - 50923.1i) q^{97} +(-67813.6 + 85035.6i) q^{98} +(-60299.7 - 29038.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) $ 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−4.84915	+	6.08065i	−0.857218	+	1.07492i	0.139193	+	0.990265i	$0.455549\pi$
$2$	−4.84915	+	6.08065i	−0.857218	+	1.07492i	−0.996411	+	0.0846516i	$0.973022\pi$
$3$	1.26806	+	1.59010i	0.0813460	+	0.102005i	0.820839	−	0.571159i	$-0.193506\pi$
$3$	1.26806	+	1.59010i	0.0813460	+	0.102005i	−0.739493	+	0.673164i	$0.764935\pi$
$4$	−6.33931	−	27.7743i	−0.198103	−	0.867947i
$5$	3.40560	+	1.64005i	0.0609213	+	0.0293381i	0.464096	−	0.885785i	$-0.346379\pi$
$5$	3.40560	+	1.64005i	0.0609213	+	0.0293381i	−0.403175	+	0.915123i	$0.632093\pi$
$6$	−15.8178			−0.179378
$7$	−175.475			−1.35354			−0.676770	−	0.736194i	$-0.736621\pi$
$7$	−175.475			−1.35354			−0.676770	+	0.736194i	$0.736621\pi$
$8$	−24.6053	−	11.8493i	−0.135926	−	0.0654587i
$9$	53.1522	−	232.875i	0.218733	−	0.958333i
$10$	−26.4869	+	12.7554i	−0.0837588	+	0.0403361i
$11$	62.3486	−	273.167i	0.155362	−	0.680685i	−0.835911	−	0.548864i	$-0.815060\pi$
$11$	62.3486	−	273.167i	0.155362	−	0.680685i	0.991274	−	0.131821i	$-0.0420825\pi$
$12$	36.1252	−	45.2996i	0.0724198	−	0.0908115i
$13$	881.242	+	424.384i	1.44623	+	0.696467i	0.981936	−	0.189215i	$-0.0605943\pi$
$13$	881.242	+	424.384i	1.44623	+	0.696467i	0.464293	+	0.885682i	$0.346309\pi$
$14$	850.907	−	1067.00i	1.16028	−	1.45494i
$15$	1.71067	+	7.49492i	0.00196308	+	0.00860079i
$16$	1012.72	−	487.701i	0.988985	−	0.476270i
$17$	−1217.84	+	586.483i	−1.02204	+	0.492190i	−0.868362	−	0.495930i	$-0.834827\pi$
$17$	−1217.84	+	586.483i	−1.02204	+	0.492190i	−0.153681	+	0.988120i	$0.549113\pi$
$18$	1158.29	+	1452.45i	0.842626	+	1.05662i
$19$	−643.515	−	2819.42i	−0.408954	−	1.79175i	−0.589050	−	0.808097i	$-0.700498\pi$
$19$	−643.515	−	2819.42i	−0.408954	−	1.79175i	0.180095	−	0.983649i	$-0.442359\pi$
$20$	23.9622	−	104.985i	0.0133953	−	0.0586884i
$21$	−222.513	−	279.023i	−0.110105	−	0.138067i
$22$	1358.69	+	1703.75i	0.598501	+	0.750497i
$23$	357.493	−	1566.28i	0.140912	−	0.617377i	−0.854312	−	0.519761i	$-0.826021\pi$
$23$	357.493	−	1566.28i	0.140912	−	0.617377i	0.995224	−	0.0976160i	$-0.0311217\pi$
$24$	−12.3595	−	54.1504i	−0.00437998	−	0.0191899i
$25$	−1939.50	−	2432.05i	−0.620639	−	0.778257i
$26$	−6853.81	+	3300.62i	−1.98838	+	0.957552i
$27$	882.966	−	425.214i	0.233096	−	0.112253i
$28$	1112.39	+	4873.71i	0.268141	+	1.17480i
$29$	−3940.17	+	4940.81i	−0.870001	+	1.09095i	0.125106	+	0.992143i	$0.460073\pi$
$29$	−3940.17	+	4940.81i	−0.870001	+	1.09095i	−0.995107	+	0.0988029i	$0.968499\pi$
$30$	−53.8692	−	25.9420i	−0.0109279	−	0.00526261i
$31$	−469.941	+	589.287i	−0.0878292	+	0.110134i	−0.823804	−	0.566874i	$-0.808153\pi$
$31$	−469.941	+	589.287i	−0.0878292	+	0.110134i	0.735975	+	0.677009i	$0.236724\pi$
$32$	−1750.84	+	7670.93i	−0.302254	+	1.32426i
$33$	513.423	−	247.252i	0.0820712	−	0.0395234i
$34$	2339.32	−	10249.2i	0.347050	−	1.52053i
$35$	−597.599	−	287.789i	−0.0824594	−	0.0397103i
$36$	−6804.89			−0.875114
$37$	−10135.0			−1.21709			−0.608543	−	0.793521i	$-0.708246\pi$
$37$	−10135.0			−1.21709			−0.608543	+	0.793521i	$0.708246\pi$
$38$	20264.4	+	9758.84i	2.27654	+	1.09632i
$39$	442.656	+	1939.40i	0.0466020	+	0.204177i
$40$	−64.3625	−	80.7080i	−0.00636037	−	0.00797566i
$41$	6093.87	−	7641.47i	0.566153	−	0.709933i	−0.413529	−	0.910491i	$-0.635704\pi$
$41$	6093.87	−	7641.47i	0.566153	−	0.709933i	0.979682	+	0.200558i	$0.0642755\pi$
$42$	2775.64			0.242795
$43$	−4966.99	−	11060.6i	−0.409659	−	0.912239i
$43$	−4966.99	−	11060.6i	−0.409659	−	0.912239i
$44$	−7982.27			−0.621577
$45$	562.942	−	705.907i	0.0414412	−	0.0519656i
$46$	7790.46	+	9768.93i	0.542836	+	0.680695i
$47$	86.7308	+	379.992i	0.00572702	+	0.0250917i	0.977711	−	0.209957i	$-0.0673323\pi$
$47$	86.7308	+	379.992i	0.00572702	+	0.0250917i	−0.971984	+	0.235048i	$0.924475\pi$
$48$	2059.68	+	991.890i	0.129032	+	0.0621384i
$49$	13984.6			0.832071
$50$	24193.4			1.36858
$51$	−2476.86	−	1192.79i	−0.133345	−	0.0642155i
$52$	6200.51	−	27166.2i	0.317994	−	1.39322i
$53$	−20695.8	+	9966.56i	−1.01203	+	0.487366i	−0.865003	−	0.501767i	$-0.832684\pi$
$53$	−20695.8	+	9966.56i	−1.01203	+	0.487366i	−0.147024	+	0.989133i	$0.546969\pi$
$54$	−1696.06	+	7430.93i	−0.0791512	+	0.346784i
$55$	660.342	−	828.043i	0.0294349	−	0.0369102i
$56$	4317.63	+	2079.26i	0.183982	+	0.0886010i
$57$	3667.14	−	4598.45i	0.149500	−	0.187467i
$58$	−10936.9	−	47917.5i	−0.426897	−	1.87036i
$59$	−23877.0	+	11498.6i	−0.892997	+	0.430045i	−0.823355	−	0.567527i	$-0.807900\pi$
$59$	−23877.0	+	11498.6i	−0.892997	+	0.430045i	−0.0696423	+	0.997572i	$0.522186\pi$
$60$	197.322	−	95.0251i	0.00707614	−	0.00340769i
$61$	−9000.30	−	11286.0i	−0.309694	−	0.388344i	0.602489	−	0.798127i	$-0.294176\pi$
$61$	−9000.30	−	11286.0i	−0.309694	−	0.388344i	−0.912183	+	0.409783i	$0.865604\pi$
$62$	−1304.43	−	5715.09i	−0.0430965	−	0.188818i
$63$	−9326.90	+	40863.8i	−0.296064	+	1.29714i
$64$	−15727.7	−	19722.0i	−0.479973	−	0.601867i
$65$	2305.15	+	2890.57i	0.0676730	+	0.0848593i
$66$	−986.219	+	4320.91i	−0.0278685	+	0.122100i
$67$	−8744.59	−	38312.5i	−0.237986	−	1.04269i	−0.942817	−	0.333311i	$-0.891834\pi$
$67$	−8744.59	−	38312.5i	−0.237986	−	1.04269i	0.704830	−	0.709376i	$-0.251023\pi$
$68$	24009.4	+	30106.9i	0.629665	+	0.789575i
$69$	2943.86	−	1417.69i	0.0744379	−	0.0358474i
$70$	4647.79	−	2238.26i	0.113371	−	0.0545966i
$71$	−1262.62	−	5531.90i	−0.0297253	−	0.130235i	0.957888	−	0.287142i	$-0.0927050\pi$
$71$	−1262.62	−	5531.90i	−0.0297253	−	0.130235i	−0.987613	+	0.156906i	$0.949848\pi$
$72$	−4067.23	+	5100.14i	−0.0924628	+	0.115945i
$73$	49204.4	+	23695.6i	1.08068	+	0.520428i	0.887534	−	0.460742i	$-0.152417\pi$
$73$	49204.4	+	23695.6i	1.08068	+	0.520428i	0.193146	+	0.981170i	$0.438131\pi$
$74$	49146.4	−	61627.6i	1.04331	−	1.30827i
$75$	1407.80	−	6167.97i	0.0288993	−	0.126616i
$76$	−74228.1	+	35746.4i	−1.47413	+	0.709902i
$77$	−10940.6	+	47934.1i	−0.210289	+	0.921335i
$78$	−13939.3	−	6712.83i	−0.259421	−	0.124931i
$79$	56434.9			1.01737			0.508686	−	0.860952i	$-0.330131\pi$
$79$	56434.9			1.01737			0.508686	+	0.860952i	$0.330131\pi$
$80$	4248.78			0.0742231
$81$	−50499.9	−	24319.5i	−0.855221	−	0.411853i
$82$	16915.0	+	74109.3i	0.277803	+	1.21713i
$83$	76201.3	+	95553.4i	1.21414	+	1.52248i	0.785325	+	0.619083i	$0.212496\pi$
$83$	76201.3	+	95553.4i	1.21414	+	1.52248i	0.428810	+	0.903395i	$0.358933\pi$
$84$	−6339.08	+	7948.96i	−0.0980231	+	0.122917i
$85$	−5109.35			−0.0767041
$86$	91341.5	+	23432.2i	1.33175	+	0.341638i
$87$	−12852.7			−0.182053
$88$	−4770.94	+	5982.57i	−0.0656746	+	0.0823534i
$89$	−40356.6	−	50605.5i	−0.540056	−	0.677209i	0.434676	−	0.900587i	$-0.356863\pi$
$89$	−40356.6	−	50605.5i	−0.540056	−	0.677209i	−0.974732	+	0.223378i	$0.928292\pi$
$90$	1562.58	+	6846.10i	0.0203346	+	0.0890917i
$91$	−154636.	−	74468.9i	−1.95753	−	0.942696i
$92$	−45768.6			−0.563766
$93$	−1532.94			−0.0183788
$94$	−2731.17	−	1315.26i	−0.0318808	−	0.0153530i
$95$	2432.44	−	10657.2i	0.0276525	−	0.121153i
$96$	−14417.7	+	6943.19i	−0.159668	+	0.0768920i
$97$	11622.9	−	50923.1i	0.125425	−	0.549522i	−0.872697	−	0.488262i	$-0.837631\pi$
$97$	11622.9	−	50923.1i	0.125425	−	0.549522i	0.998122	−	0.0612600i	$-0.0195119\pi$
$98$	−67813.6	+	85035.6i	−0.713266	+	0.894407i
$99$	−60299.7	−	29038.8i	−0.618340	−	0.297777i
$100$	−55253.5	+	69285.7i	−0.552535	+	0.692857i
$101$	26326.2	+	115343.i	0.256794	+	1.12509i	0.924656	+	0.380803i	$0.124352\pi$
$101$	26326.2	+	115343.i	0.256794	+	1.12509i	−0.667862	+	0.744285i	$0.732790\pi$
$102$	19263.6	−	9276.88i	0.183332	−	0.0882880i
$103$	108696.	−	52345.3i	1.00953	−	0.486166i	0.145371	−	0.989377i	$-0.453562\pi$
$103$	108696.	−	52345.3i	1.00953	−	0.486166i	0.864164	+	0.503211i	$0.167848\pi$
$104$	−16654.6	−	20884.2i	−0.150991	−	0.189337i
$105$	−300.180	−	1315.17i	−0.00265710	−	0.0116415i
$106$	39753.9	−	174173.i	0.343649	−	1.50562i
$107$	28475.8	+	35707.5i	0.240445	+	0.301509i	0.887382	−	0.461035i	$-0.152522\pi$
$107$	28475.8	+	35707.5i	0.240445	+	0.301509i	−0.646937	+	0.762544i	$0.723950\pi$
$108$	−17407.4	−	21828.2i	−0.143607	−	0.180077i
$109$	−3378.53	+	14802.3i	−0.0272371	+	0.119334i	−0.986719	−	0.162437i	$-0.948065\pi$
$109$	−3378.53	+	14802.3i	−0.0272371	+	0.119334i	0.959482	+	0.281771i	$0.0909217\pi$
$110$	1832.94	+	8030.62i	0.0144433	+	0.0632801i
$111$	−12851.8	−	16115.7i	−0.0990051	−	0.124148i
$112$	−177708.	+	85579.5i	−1.33863	+	0.644651i
$113$	−115570.	+	55655.7i	−0.851432	+	0.410028i	−0.808109	−	0.589033i	$-0.799509\pi$
$113$	−115570.	+	55655.7i	−0.851432	+	0.410028i	−0.0433232	+	0.999061i	$0.513795\pi$
$114$	10179.0	+	44597.2i	0.0733573	+	0.321399i
$115$	3786.26	−	4747.82i	0.0266972	−	0.0334773i
$116$	162206.	+	78114.1i	1.11923	+	0.538995i
$117$	145668.	−	182662.i	0.983785	−	1.23363i
$118$	45864.6	−	200946.i	0.303230	−	1.32854i
$119$	213702.	−	102913.i	1.38338	−	0.666199i
$120$	46.7180	−	204.685i	0.000296163	−	0.00129758i
$121$	74369.1	+	35814.3i	0.461774	+	0.222378i
$122$	112270.			0.682912
$123$	19878.1			0.118471
$124$	19346.1	+	9316.61i	0.112990	+	0.0544131i
$125$	−5244.95	−	22979.6i	−0.0300238	−	0.131543i
$126$	−203251.	−	254868.i	−1.14053	−	1.43018i
$127$	67168.9	−	84227.1i	0.369538	−	0.463386i	−0.561943	−	0.827176i	$-0.689946\pi$
$127$	67168.9	−	84227.1i	0.369538	−	0.463386i	0.931481	+	0.363790i	$0.118517\pi$
$128$	−55593.8			−0.299917
$129$	11289.0	−	21923.5i	0.0597285	−	0.115994i
$130$	−28754.5			−0.149227
$131$	156801.	−	196623.i	0.798310	−	1.00105i	−0.201458	−	0.979497i	$-0.564568\pi$
$131$	156801.	−	196623.i	0.798310	−	1.00105i	0.999768	−	0.0215520i	$-0.00686074\pi$
$132$	−10122.0	−	12692.6i	−0.0505628	−	0.0634038i
$133$	112921.	+	494740.i	0.553536	+	2.42520i
$134$	275369.	+	132611.i	1.32481	+	0.637994i
$135$	3704.40			0.0174938
$136$	36914.8			0.171141
$137$	−216763.	−	104388.i	−0.986697	−	0.475168i	−0.130294	−	0.991475i	$-0.541592\pi$
$137$	−216763.	−	104388.i	−0.986697	−	0.475168i	−0.856403	+	0.516307i	$0.827306\pi$
$138$	−5654.77	+	24775.2i	−0.0252765	+	0.110744i
$139$	−248715.	+	119775.i	−1.09186	+	0.525810i	−0.891089	−	0.453829i	$-0.850058\pi$
$139$	−248715.	+	119775.i	−1.09186	+	0.525810i	−0.200767	+	0.979639i	$0.564343\pi$
$140$	−4204.77	+	18422.3i	−0.0181310	+	0.0794372i
$141$	−494.245	+	619.763i	−0.00209360	+	0.00262529i
$142$	39760.2	+	19147.5i	0.165473	+	0.0796876i
$143$	170872.	−	214267.i	0.698764	−	0.876222i
$144$	−59744.9	−	261760.i	−0.240101	−	1.05195i
$145$	−21521.8	+	10364.4i	−0.0850079	+	0.0409376i
$146$	−382685.	+	184291.i	−1.48580	+	0.715521i
$147$	17733.3	+	22236.9i	0.0676857	+	0.0848752i
$148$	64249.1	+	281494.i	0.241109	+	1.05637i
$149$	−32139.6	+	140813.i	−0.118597	+	0.519608i	0.880375	+	0.474278i	$0.157291\pi$
$149$	−32139.6	+	140813.i	−0.118597	+	0.519608i	−0.998972	+	0.0453297i	$0.985566\pi$
$150$	30678.6	+	38469.8i	0.111329	+	0.139602i
$151$	−176934.	−	221869.i	−0.631495	−	0.791870i	0.358416	−	0.933562i	$-0.383317\pi$
$151$	−176934.	−	221869.i	−0.631495	−	0.791870i	−0.989911	+	0.141692i	$0.954746\pi$
$152$	−17574.3	+	76998.0i	−0.0616977	+	0.270315i
$153$	71846.0	+	314778.i	0.248127	+	1.08712i
$154$	−238417.	−	298966.i	−0.810096	−	1.01583i
$155$	−2566.89	+	1236.15i	−0.00858180	+	0.00413278i
$156$	51059.5	−	24588.9i	0.167983	−	0.0808962i
$157$	55287.2	+	242229.i	0.179009	+	0.784291i	0.982089	+	0.188419i	$0.0603363\pi$
$157$	55287.2	+	242229.i	0.179009	+	0.784291i	−0.803079	+	0.595872i	$0.796807\pi$
$158$	−273662.	+	343161.i	−0.872110	+	1.09359i
$159$	−42091.2	−	20270.1i	−0.132038	−	0.0635861i
$160$	−18543.4	+	23252.7i	−0.0572650	+	0.0718080i
$161$	−62731.3	+	274844.i	−0.190730	+	0.835644i
$162$	392760.	−	189143.i	1.17582	−	0.566244i
$163$	28657.9	−	125559.i	0.0844843	−	0.370150i	−0.914958	−	0.403550i	$-0.867776\pi$
$163$	28657.9	−	125559.i	0.0844843	−	0.370150i	0.999442	+	0.0333997i	$0.0106334\pi$
$164$	−250868.	−	120811.i	−0.728341	−	0.350751i
$165$	2154.02			0.00615942
$166$	−950539.			−2.67732
$167$	−241688.	−	116391.i	−0.670602	−	0.322945i	0.0674171	−	0.997725i	$-0.478524\pi$
$167$	−241688.	−	116391.i	−0.670602	−	0.322945i	−0.738019	+	0.674780i	$0.764238\pi$
$168$	2168.78	+	9502.06i	0.00592848	+	0.0259744i
$169$	364989.	+	457681.i	0.983021	+	1.23267i
$170$	24776.0	−	31068.2i	0.0657521	−	0.0824506i
$171$	−690777.			−1.80654
$172$	−275714.	+	208071.i	−0.710621	+	0.536280i
$173$	420273.			1.06762			0.533810	−	0.845605i	$-0.320760\pi$
$173$	420273.			1.06762			0.533810	+	0.845605i	$0.320760\pi$
$174$	62324.9	−	78152.9i	0.156059	−	0.195692i
$175$	340334.	+	426765.i	0.840060	+	1.05340i
$176$	−70082.0	−	307049.i	−0.170539	−	0.747182i
$177$	−48561.3	−	23385.9i	−0.116508	−	0.0561074i
$178$	503410.			1.19089
$179$	376112.			0.877374			0.438687	−	0.898640i	$-0.355444\pi$
$179$	376112.			0.877374			0.438687	+	0.898640i	$0.355444\pi$
$180$	−23174.7	−	11160.4i	−0.0533130	−	0.0256742i
$181$	131162.	−	574659.i	0.297586	−	1.30381i	−0.576125	−	0.817362i	$-0.695436\pi$
$181$	131162.	−	574659.i	0.297586	−	1.30381i	0.873710	−	0.486446i	$-0.161707\pi$
$182$	1.20268e6	−	579178.i	2.69135	−	1.29608i
$183$	6532.94	−	28622.7i	0.0144205	−	0.0631804i
$184$	−27355.6	+	34302.8i	−0.0595664	+	0.0746939i
$185$	−34515.9	−	16622.0i	−0.0741464	−	0.0357070i
$186$	7433.44	−	9321.24i	0.0157546	−	0.0197556i
$187$	84276.9	+	369241.i	0.176240	+	0.772158i
$188$	10004.2	−	4817.78i	0.0206437	−	0.00994150i
$189$	−154939.	+	74614.6i	−0.315505	+	0.151939i
$190$	53007.6	+	66469.4i	0.106526	+	0.133579i
$191$	78476.0	+	343826.i	0.155651	+	0.681954i	0.991182	+	0.132509i	$0.0423034\pi$
$191$	78476.0	+	343826.i	0.155651	+	0.681954i	−0.835530	+	0.549444i	$0.814839\pi$
$192$	11416.1	−	50017.3i	0.0223494	−	0.0979190i
$193$	67978.5	+	85242.4i	0.131365	+	0.164726i	0.843163	−	0.537657i	$-0.180691\pi$
$193$	67978.5	+	85242.4i	0.131365	+	0.164726i	−0.711799	+	0.702384i	$0.752119\pi$
$194$	253284.	+	317608.i	0.483174	+	0.605881i
$195$	−1673.21	+	7330.81i	−0.00315111	+	0.0138059i
$196$	−88652.8	−	388413.i	−0.164836	−	0.722194i
$197$	−443713.	−	556398.i	−0.814585	−	1.02146i	−0.999253	−	0.0386564i	$-0.987692\pi$
$197$	−443713.	−	556398.i	−0.814585	−	1.02146i	0.184667	−	0.982801i	$-0.440879\pi$
$198$	468978.	−	225848.i	0.850138	−	0.409405i
$199$	50230.1	−	24189.6i	0.0899149	−	0.0433007i	−0.388386	−	0.921497i	$-0.626967\pi$
$199$	50230.1	−	24189.6i	0.0899149	−	0.0433007i	0.478301	+	0.878196i	$0.341253\pi$
$200$	18903.8	+	82823.1i	0.0334176	+	0.146412i
$201$	49831.9	−	62487.3i	0.0869997	−	0.109094i
$202$	−829018.	−	399234.i	−1.42950	−	0.688413i
$203$	691402.	−	866991.i	1.17758	−	1.47664i
$204$	−17427.4	+	76354.6i	−0.0293196	+	0.128458i
$205$	33285.7	−	16029.5i	0.0553188	−	0.0266401i
$206$	−208791.	+	914774.i	−0.342802	+	1.50192i
$207$	−345746.	−	166502.i	−0.560830	−	0.270081i
$208$	1.09942e6			1.76200
$209$	−810296.			−1.28315
$210$	9452.72	+	4552.19i	0.0147914	+	0.00712315i
$211$	−170945.	−	748961.i	−0.264333	−	1.15812i	−0.916497	−	0.400041i	$-0.868996\pi$
$211$	−170945.	−	748961.i	−0.264333	−	1.15812i	0.652165	−	0.758077i	$-0.273861\pi$
$212$	408011.	+	511630.i	0.623494	+	0.781837i
$213$	7195.17	−	9022.46i	0.0108666	−	0.0136262i
$214$	−355208.			−0.530211
$215$	1224.41	−	45814.2i	0.00180647	−	0.0675934i
$216$	−26764.1			−0.0390318
$217$	82463.0	−	103405.i	0.118880	−	0.149071i
$218$	−73624.5	−	92322.2i	−0.104926	−	0.131572i
$219$	24715.8	+	108287.i	0.0348229	+	0.152569i
$220$	−27184.4	−	13091.3i	−0.0378672	−	0.0182359i
$221$	−1.32211e6			−1.82090
$222$	160314.			0.218318
$223$	−340595.	−	164022.i	−0.458645	−	0.220872i	0.190272	−	0.981731i	$-0.439063\pi$
$223$	−340595.	−	164022.i	−0.458645	−	0.220872i	−0.648916	+	0.760860i	$0.724777\pi$
$224$	307229.	−	1.34606e6i	0.409112	−	1.79244i
$225$	−669452.	+	322391.i	−0.881583	+	0.424548i
$226$	221995.	−	972625.i	0.289117	−	1.26670i
$227$	−114252.	+	143268.i	−0.147163	+	0.184537i	−0.849949	−	0.526864i	$-0.823368\pi$
$227$	−114252.	+	143268.i	−0.147163	+	0.184537i	0.702786	+	0.711401i	$0.251939\pi$
$228$	−150966.	−	72701.3i	−0.192328	−	0.0926201i
$229$	−61633.6	+	77286.1i	−0.0776657	+	0.0973897i	−0.819146	−	0.573584i	$-0.805552\pi$
$229$	−61633.6	+	77286.1i	−0.0776657	+	0.0973897i	0.741481	+	0.670974i	$0.234124\pi$
$230$	10509.7	+	46045.9i	0.0130999	+	0.0573946i
$231$	−90093.2	+	43386.6i	−0.111087	+	0.0534965i
$232$	155494.	−	74882.0i	0.189668	−	0.0913393i
$233$	803391.	+	1.00742e6i	0.969477	+	1.21569i	0.976458	+	0.215709i	$0.0692064\pi$
$233$	803391.	+	1.00742e6i	0.969477	+	1.21569i	−0.00698104	+	0.999976i	$0.502222\pi$
$234$	404337.	+	1.77151e6i	0.482729	+	2.11497i
$235$	−327.837	+	1436.35i	−0.000387247	+	0.00169664i
$236$	470728.	+	590275.i	0.550162	+	0.689881i
$237$	71562.8	+	89736.9i	0.0827592	+	0.103777i
$238$	−410493.	+	1.79849e6i	−0.469746	+	2.05809i
$239$	−60554.9	−	265308.i	−0.0685732	−	0.300439i	0.928999	−	0.370083i	$-0.120671\pi$
$239$	−60554.9	−	265308.i	−0.0685732	−	0.300439i	−0.997572	+	0.0696441i	$0.977814\pi$
$240$	5387.70	+	6755.96i	0.00603775	+	0.00757110i
$241$	−313421.	+	150935.i	−0.347604	+	0.167397i	−0.599536	−	0.800348i	$-0.704648\pi$
$241$	−313421.	+	150935.i	−0.347604	+	0.167397i	0.251932	+	0.967745i	$0.418934\pi$
$242$	−578401.	+	278543.i	−0.634879	+	0.305741i
$243$	−78358.7	−	343312.i	−0.0851278	−	0.372969i
$244$	−256406.	+	321523.i	−0.275710	+	0.345730i
$245$	47626.1	+	22935.5i	0.0506908	+	0.0244114i
$246$	−96391.8	+	120871.i	−0.101555	+	0.127346i
$247$	629425.	−	2.75769e6i	0.656450	−	2.87610i
$248$	18545.7	−	8931.13i	0.0191476	−	0.00922098i
$249$	−55311.3	+	242335.i	−0.0565348	+	0.247695i
$250$	165164.	+	79539.0i	0.167135	+	0.0804878i
$251$	−1.00315e6			−1.00504			−0.502520	−	0.864566i	$-0.667594\pi$
$251$	−1.00315e6			−1.00504			−0.502520	+	0.864566i	$0.667594\pi$
$252$	1.19409e6			1.18450
$253$	−405567.	−	195311.i	−0.398347	−	0.191834i
$254$	186443.	+	816861.i	0.181327	+	0.794445i
$255$	−6478.96	−	8124.36i	−0.00623957	−	0.00782418i
$256$	772871.	−	969150.i	0.737067	−	0.924253i
$257$	836116.			0.789648			0.394824	−	0.918757i	$-0.370806\pi$
$257$	836116.			0.789648			0.394824	+	0.918757i	$0.370806\pi$
$258$	78567.0	+	174955.i	0.0734837	+	0.163635i
$259$	1.77845e6			1.64737
$260$	65670.4	−	82348.1i	0.0602471	−	0.0755475i
$261$	941162.	+	1.18018e6i	0.855191	+	1.07238i
$262$	435239.	+	1.90691e6i	0.391719	+	1.71623i
$263$	−1.04913e6	−	505233.i	−0.935274	−	0.450404i	−0.0967743	−	0.995306i	$-0.530852\pi$
$263$	−1.04913e6	−	505233.i	−0.935274	−	0.450404i	−0.838500	+	0.544902i	$0.816567\pi$
$264$	−15562.7			−0.0137428
$265$	−86827.2			−0.0759524
$266$	−3.55591e6	−	1.71244e6i	−3.08139	−	1.48392i
$267$	29293.1	−	128342.i	0.0251471	−	0.110177i
$268$	−1.00867e6	+	485750.i	−0.857851	+	0.413119i
$269$	−69784.6	+	305746.i	−0.0588002	+	0.257621i	−0.995781	−	0.0917599i	$-0.970751\pi$
$269$	−69784.6	+	305746.i	−0.0588002	+	0.257621i	0.936981	+	0.349380i	$0.113608\pi$
$270$	−17963.2	+	22525.2i	−0.0149960	+	0.0188044i
$271$	−199948.	−	96290.0i	−0.165384	−	0.0796449i	0.349360	−	0.936989i	$-0.386399\pi$
$271$	−199948.	−	96290.0i	−0.165384	−	0.0796449i	−0.514745	+	0.857344i	$0.672113\pi$
$272$	−947308.	+	1.18789e6i	−0.776370	+	0.973538i
$273$	−77675.3	−	340318.i	−0.0630777	−	0.276362i
$274$	1.68586e6	−	811868.i	1.35658	−	0.653295i
$275$	−785281.	+	378172.i	−0.626172	+	0.301548i
$276$	−58037.3	−	72776.5i	−0.0458601	−	0.0575067i
$277$	424866.	+	1.86146e6i	0.332700	+	1.45765i	0.813881	+	0.581032i	$0.197351\pi$
$277$	424866.	+	1.86146e6i	0.332700	+	1.45765i	−0.481181	+	0.876621i	$0.659792\pi$
$278$	477749.	−	2.09316e6i	0.370756	−	1.62439i
$279$	112252.	+	140759.i	0.0863341	+	0.108260i
$280$	11294.0	+	14162.3i	0.00860902	+	0.0107954i
$281$	34121.5	−	149496.i	0.0257787	−	0.112944i	−0.960402	−	0.278619i	$-0.910123\pi$
$281$	34121.5	−	149496.i	0.0257787	−	0.112944i	0.986180	+	0.165675i	$0.0529804\pi$
$282$	−1371.89	−	6010.66i	−0.00102730	−	0.00450090i
$283$	−563936.	−	707153.i	−0.418566	−	0.524865i	0.527188	−	0.849749i	$-0.323246\pi$
$283$	−563936.	−	707153.i	−0.418566	−	0.524865i	−0.945754	+	0.324884i	$0.894675\pi$
$284$	−145641.	+	70136.8i	−0.107149	+	0.0516000i
$285$	20030.5	−	9646.18i	0.0146076	−	0.00703466i
$286$	474295.	+	2.07802e6i	0.342873	+	1.50223i
$287$	−1.06932e6	+	1.34089e6i	−0.766310	+	0.960923i
$288$	1.69331e6	+	815453.i	1.20297	+	0.579319i
$289$	253916.	−	318400.i	0.178832	−	0.224248i
$290$	41340.6	−	181125.i	0.0288657	−	0.126469i
$291$	95711.0	−	46092.0i	0.0662566	−	0.0319075i
$292$	346207.	−	1.51683e6i	0.237618	−	1.04107i
$293$	−2.30414e6	−	1.10962e6i	−1.56798	−	0.755098i	−0.570186	−	0.821516i	$-0.693129\pi$
$293$	−2.30414e6	−	1.10962e6i	−1.56798	−	0.755098i	−0.997792	+	0.0664177i	$0.978843\pi$
$294$	−221206.			−0.149255
$295$	−100174.			−0.0670192
$296$	249376.	+	120093.i	0.165434	+	0.0796689i
$297$	−61102.8	−	267709.i	−0.0401948	−	0.176105i
$298$	−700382.	−	878252.i	−0.456872	−	0.572899i
$299$	979743.	−	1.22856e6i	0.633774	−	0.794727i
$300$	−180236.			−0.115621
$301$	871585.	+	1.94087e6i	0.554489	+	1.23475i
$302$	2.20709e6			1.39252
$303$	−150023.	+	188122.i	−0.0938751	+	0.117716i
$304$	−2.02674e6	−	2.54145e6i	−1.25780	−	1.57724i
$305$	−12141.8	−	53196.6i	−0.00747365	−	0.0327442i
$306$	−2.26245e6	−	1.08954e6i	−1.38126	−	0.665179i
$307$	144351.			0.0874124			0.0437062	−	0.999044i	$-0.486083\pi$
$307$	144351.			0.0874124			0.0437062	+	0.999044i	$0.486083\pi$
$308$	1.40069e6			0.841329
$309$	221067.	+	106460.i	0.131713	+	0.0634296i
$310$	4930.66	−	21602.7i	0.00291408	−	0.0127674i
$311$	522152.	−	251455.i	0.306123	−	0.147421i	−0.274515	−	0.961583i	$-0.588517\pi$
$311$	522152.	−	251455.i	0.306123	−	0.147421i	0.580638	+	0.814162i	$0.302803\pi$
$312$	12088.9	−	52964.8i	0.00703071	−	0.0308035i
$313$	−567298.	+	711369.i	−0.327303	+	0.410425i	−0.918071	−	0.396417i	$-0.870254\pi$
$313$	−567298.	+	711369.i	−0.327303	+	0.410425i	0.590768	+	0.806842i	$0.298825\pi$
$314$	−1.74101e6	−	838425.i	−0.996498	−	0.479888i
$315$	−98782.4	+	123869.i	−0.0560923	+	0.0703375i
$316$	−357758.	−	1.56744e6i	−0.201545	−	0.883026i
$317$	2.45444e6	−	1.18200e6i	1.37184	−	0.660646i	0.404601	−	0.914494i	$-0.367411\pi$
$317$	2.45444e6	−	1.18200e6i	1.37184	−	0.660646i	0.967244	+	0.253848i	$0.0816963\pi$
$318$	327362.	−	157649.i	0.181535	−	0.0874227i
$319$	1.10400e6	+	1.38438e6i	0.607426	+	0.761688i
$320$	−21217.4	−	92959.5i	−0.0115829	−	0.0507480i
$321$	−20669.4	+	90558.4i	−0.0111960	+	0.0490531i
$322$	−1.36703e6	−	1.71421e6i	−0.734751	−	0.921348i
$323$	2.43724e6	+	3.05621e6i	1.29985	+	1.62996i
$324$	−355322.	+	1.55677e6i	−0.188044	+	0.823876i
$325$	−677043.	−	2.96632e6i	−0.355556	−	1.55779i
$326$	624511.	+	783112.i	0.325459	+	0.408113i
$327$	−27821.2	+	13398.0i	−0.0143882	+	0.00692900i
$328$	−240488.	+	115813.i	−0.123426	+	0.0594390i
$329$	−15219.1	−	66679.3i	−0.00775175	−	0.0339626i
$330$	−10445.2	+	13097.8i	−0.00527997	+	0.00662087i
$331$	932918.	+	449269.i	0.468030	+	0.225391i	0.653007	−	0.757352i	$-0.273507\pi$
$331$	932918.	+	449269.i	0.468030	+	0.225391i	−0.184978	+	0.982743i	$0.559221\pi$
$332$	2.17087e6	−	2.72218e6i	1.08091	−	1.35541i
$333$	−538699.	+	2.36020e6i	−0.266217	+	1.16637i
$334$	1.87972e6	−	905224.i	0.921990	−	0.444007i
$335$	33054.0	−	144819.i	0.0160921	−	0.0705039i
$336$	−361423.	−	174052.i	−0.174650	−	0.0841069i
$337$	3.57978e6			1.71704			0.858522	−	0.512776i	$-0.171383\pi$
$337$	3.57978e6			1.71704			0.858522	+	0.512776i	$0.171383\pi$
$338$	−4.55289e6			−2.16768
$339$	−235048.	−	113193.i	−0.111085	−	0.0534959i
$340$	32389.8	+	141909.i	0.0151953	+	0.0665751i
$341$	131674.	+	165113.i	0.0613215	+	0.0768947i
$342$	3.34969e6	−	4.20037e6i	1.54860	−	1.94188i
$343$	495258.			0.227298
$344$	−8846.28	+	331005.i	−0.00403055	+	0.150813i
$345$	12350.7			0.00558655
$346$	−2.03797e6	+	2.55553e6i	−0.915182	+	1.14760i
$347$	645946.	+	809991.i	0.287987	+	0.361124i	0.904689	−	0.426072i	$-0.140103\pi$
$347$	645946.	+	809991.i	0.287987	+	0.361124i	−0.616702	+	0.787197i	$0.711532\pi$
$348$	81477.4	+	356976.i	0.0360652	+	0.158012i
$349$	2.91047e6	+	1.40161e6i	1.27909	+	0.615976i	0.945155	−	0.326622i	$-0.105910\pi$
$349$	2.91047e6	+	1.40161e6i	1.27909	+	0.615976i	0.333932	+	0.942597i	$0.391625\pi$
$350$	−4.24534e6			−1.85243
$351$	958561.			0.415290
$352$	1.98628e6	+	956543.i	0.854446	+	0.411479i
$353$	685770.	−	3.00455e6i	0.292915	−	1.28334i	−0.587533	−	0.809201i	$-0.699901\pi$
$353$	685770.	−	3.00455e6i	0.292915	−	1.28334i	0.880448	−	0.474144i	$-0.157242\pi$
$354$	377682.	−	181882.i	0.160184	−	0.0771405i
$355$	4772.62	−	20910.2i	0.00200995	−	0.00880618i
$356$	−1.14970e6	+	1.44168e6i	−0.480795	+	0.602898i
$357$	434628.	+	209306.i	0.180488	+	0.0869183i
$358$	−1.82383e6	+	2.28700e6i	−0.752100	+	0.943104i
$359$	−791342.	−	3.46710e6i	−0.324062	−	1.41981i	−0.830253	−	0.557387i	$-0.811804\pi$
$359$	−791342.	−	3.46710e6i	−0.324062	−	1.41981i	0.506191	−	0.862421i	$-0.331053\pi$
$360$	−22215.9	+	10698.6i	−0.00903456	+	0.00435081i
$361$	−5.30415e6	+	2.55435e6i	−2.14214	+	1.03160i
$362$	2.85827e6	+	3.58416e6i	1.14639	+	1.43753i
$363$	37356.3	+	163669.i	0.0148798	+	0.0651927i
$364$	−1.08804e6	+	4.76700e6i	−0.430418	+	1.88578i
$365$	128709.	+	161396.i	0.0505680	+	0.0634103i
$366$	142365.	+	178520.i	0.0555522	+	0.0696602i
$367$	−1.07877e6	+	4.72641e6i	−0.418085	+	1.83175i	0.125107	+	0.992143i	$0.460073\pi$
$367$	−1.07877e6	+	4.72641e6i	−0.418085	+	1.83175i	−0.543192	+	0.839608i	$0.682785\pi$
$368$	−401835.	−	1.76056e6i	−0.154678	−	0.677689i
$369$	−1.45560e6	−	1.82527e6i	−0.556515	−	0.697848i
$370$	268445.	−	129277.i	0.101942	−	0.0490925i
$371$	3.63160e6	−	1.74889e6i	1.36982	−	0.659670i
$372$	9717.75	+	42576.2i	0.00364090	+	0.0159518i
$373$	−1.24454e6	+	1.56060e6i	−0.463164	+	0.580790i	−0.957483	−	0.288491i	$-0.906846\pi$
$373$	−1.24454e6	+	1.56060e6i	−0.463164	+	0.580790i	0.494318	+	0.869281i	$0.335418\pi$
$374$	−2.65390e6	−	1.27805e6i	−0.981081	−	0.472464i
$375$	29888.9	−	37479.5i	0.0109757	−	0.0137631i
$376$	2368.60	−	10377.5i	0.000864018	−	0.00378551i
$377$	−5.56904e6	+	2.68191e6i	−2.01803	+	0.971831i
$378$	297617.	−	1.30395e6i	0.107134	−	0.469386i
$379$	−2.73295e6	−	1.31612e6i	−0.977313	−	0.470649i	−0.124133	−	0.992266i	$-0.539615\pi$
$379$	−2.73295e6	−	1.31612e6i	−0.977313	−	0.470649i	−0.853180	+	0.521616i	$0.825329\pi$
$380$	−311417.			−0.110633
$381$	219103.			0.0773279
$382$	−2.47123e6	−	1.19008e6i	−0.866471	−	0.417270i
$383$	−652092.	−	2.85700e6i	−0.227150	−	0.995207i	−0.951951	−	0.306250i	$-0.900926\pi$
$383$	−652092.	−	2.85700e6i	−0.227150	−	0.995207i	0.724802	−	0.688957i	$-0.241931\pi$
$384$	−70496.2	−	88399.5i	−0.0243971	−	0.0305930i
$385$	−115874.	+	145301.i	−0.0398413	+	0.0499594i
$386$	−847968.			−0.289675
$387$	−2.83975e6	+	568791.i	−0.963834	+	0.193052i
$388$	−1.48803e6			−0.501803
$389$	2.65035e6	−	3.32343e6i	0.888032	−	1.11356i	−0.104854	−	0.994488i	$-0.533438\pi$
$389$	2.65035e6	−	3.32343e6i	0.888032	−	1.11356i	0.992886	−	0.119069i	$-0.0379910\pi$
$390$	−36462.4	−	45722.5i	−0.0121390	−	0.0152219i
$391$	483226.	+	2.11715e6i	0.159848	+	0.700341i
$392$	−344096.	−	165708.i	−0.113100	−	0.0544663i
$393$	511482.			0.167051
$394$	5.53490e6			1.79626
$395$	192195.	+	92556.2i	0.0619796	+	0.0298478i
$396$	−424275.	+	1.85887e6i	−0.135959	+	0.595677i
$397$	1.81784e6	−	875425.i	0.578868	−	0.278768i	−0.121452	−	0.992597i	$-0.538755\pi$
$397$	1.81784e6	−	875425.i	0.578868	−	0.278768i	0.700320	+	0.713829i	$0.253041\pi$
$398$	−96485.5	+	422731.i	−0.0305319	+	0.133769i
$399$	−643493.	+	806914.i	−0.202354	+	0.253744i
$400$	−3.15028e6	−	1.51710e6i	−0.984463	−	0.474093i
$401$	656588.	−	823335.i	0.203907	−	0.255691i	−0.669354	−	0.742943i	$-0.733429\pi$
$401$	656588.	−	823335.i	0.203907	−	0.255691i	0.873261	+	0.487252i	$0.162001\pi$
$402$	138320.	+	606021.i	0.0426895	+	0.187035i
$403$	−664216.	+	319869.i	−0.203726	+	0.0981093i
$404$	3.03667e6	−	1.46238e6i	0.925645	−	0.445767i
$405$	−132097.	−	165645.i	−0.0400181	−	0.0501812i
$406$	1.91915e6	+	8.40835e6i	0.577822	+	2.53160i
$407$	−631905.	+	2.76856e6i	−0.189089	+	0.828453i
$408$	46810.2	+	58698.1i	0.0139216	+	0.0174572i
$409$	−667249.	−	836704.i	−0.197233	−	0.247322i	0.673373	−	0.739303i	$-0.264845\pi$
$409$	−667249.	−	836704.i	−0.197233	−	0.247322i	−0.870606	+	0.491980i	$0.836273\pi$
$410$	−63937.5	+	280128.i	−0.0187843	+	0.0822996i
$411$	−108882.	−	477044.i	−0.0317945	−	0.139301i
$412$	−2.14291e6	−	2.68713e6i	−0.621959	−	0.779912i
$413$	4.18983e6	−	2.01772e6i	1.20871	−	0.582083i
$414$	2.68902e6	−	1.29496e6i	0.771068	−	0.371327i
$415$	102799.	+	450391.i	0.0293000	+	0.128372i
$416$	−4.79833e6	+	6.01692e6i	−1.35943	+	1.70467i
$417$	−505839.	−	243599.i	−0.142453	−	0.0686018i
$418$	3.92925e6	−	4.92712e6i	1.09994	−	1.37928i
$419$	764596.	−	3.34991e6i	0.212763	−	0.932178i	−0.749916	−	0.661533i	$-0.769906\pi$
$419$	764596.	−	3.34991e6i	0.212763	−	0.932178i	0.962679	−	0.270644i	$-0.0872368\pi$
$420$	−34625.1	+	16674.6i	−0.00957785	+	0.00461245i
$421$	1.41868e6	−	6.21564e6i	0.390102	−	1.70915i	−0.274188	−	0.961676i	$-0.588409\pi$
$421$	1.41868e6	−	6.21564e6i	0.390102	−	1.70915i	0.664290	−	0.747475i	$-0.268734\pi$
$422$	5.38311e6	+	2.59237e6i	1.47147	+	0.708623i
$423$	93100.6			0.0252989
$424$	627323.			0.169464
$425$	3.78836e6	+	1.82438e6i	1.01737	+	0.489940i
$426$	19971.9	+	87502.6i	0.00533206	+	0.0233613i
$427$	1.57933e6	+	1.98042e6i	0.419183	+	0.525639i
$428$	811234.	−	1.01726e6i	0.214061	−	0.268424i
$429$	557380.			0.146220
$430$	272643.	+	229605.i	0.0711087	+	0.0598840i
$431$	1.37167e6			0.355677			0.177838	−	0.984060i	$-0.443090\pi$
$431$	1.37167e6			0.355677			0.177838	+	0.984060i	$0.443090\pi$
$432$	686821.	−	861246.i	0.177066	−	0.222033i
$433$	−2.18530e6	−	2.74029e6i	−0.560134	−	0.702386i	0.418448	−	0.908241i	$-0.362574\pi$
$433$	−2.18530e6	−	2.74029e6i	−0.560134	−	0.702386i	−0.978583	+	0.205854i	$0.934003\pi$
$434$	228896.	+	1.00286e6i	0.0583329	+	0.255573i
$435$	−43771.3	−	21079.1i	−0.0110909	−	0.00534109i
$436$	432541.			0.108971
$437$	−4.64606e6			−1.16381
$438$	−778307.	−	374813.i	−0.193850	−	0.0933532i
$439$	−461880.	+	2.02363e6i	−0.114385	+	0.501152i	0.884984	+	0.465621i	$0.154169\pi$
$439$	−461880.	+	2.02363e6i	−0.114385	+	0.501152i	−0.999369	+	0.0355303i	$0.988688\pi$
$440$	−26059.7	+	12549.7i	−0.00641707	+	0.00309030i
$441$	743313.	−	3.25667e6i	0.182002	−	0.797401i
$442$	6.41111e6	−	8.03928e6i	1.56091	−	1.95732i
$443$	−5.15457e6	−	2.48231e6i	−1.24791	−	0.600962i	−0.310959	−	0.950423i	$-0.600650\pi$
$443$	−5.15457e6	−	2.48231e6i	−1.24791	−	0.600962i	−0.936951	+	0.349462i	$0.886364\pi$
$444$	−366130.	+	459113.i	−0.0881411	+	0.110525i
$445$	−54442.7	−	238529.i	−0.0130329	−	0.0571007i
$446$	2.64896e6	−	1.27567e6i	0.630577	−	0.303670i
$447$	−264660.	+	127454.i	−0.0626499	+	0.0301706i
$448$	2.75983e6	+	3.46072e6i	0.649663	+	0.814651i
$449$	154556.	+	677155.i	0.0361801	+	0.158516i	0.989791	−	0.142527i	$-0.0455226\pi$
$449$	154556.	+	677155.i	0.0361801	+	0.158516i	−0.953611	+	0.301042i	$0.902666\pi$
$450$	1.28593e6	−	5.63403e6i	0.299355	−	1.31156i
$451$	−1.70745e6	−	2.14108e6i	−0.395282	−	0.495668i
$452$	2.27843e6	+	2.85707e6i	0.524554	+	0.657770i
$453$	128429.	−	562685.i	0.0294048	−	0.128831i
$454$	−317134.	−	1.38945e6i	−0.0722109	−	0.316377i
$455$	−404497.	−	507223.i	−0.0915982	−	0.114860i
$456$	−144719.	+	69693.2i	−0.0325923	+	0.0156956i
$457$	204724.	−	98589.8i	0.0458541	−	0.0220822i	−0.410816	−	0.911718i	$-0.634756\pi$
$457$	204724.	−	98589.8i	0.0458541	−	0.0220822i	0.456670	+	0.889636i	$0.349042\pi$
$458$	−171079.	−	749545.i	−0.0381094	−	0.166968i
$459$	−825934.	+	1.03569e6i	−0.182984	+	0.229455i
$460$	−155870.	−	75062.9i	−0.0343453	−	0.0165398i
$461$	−419170.	+	525623.i	−0.0918625	+	0.115192i	−0.825638	−	0.564200i	$-0.809185\pi$
$461$	−419170.	+	525623.i	−0.0918625	+	0.115192i	0.733776	+	0.679392i	$0.237756\pi$
$462$	173057.	−	758213.i	0.0377211	−	0.165267i
$463$	5.18262e6	−	2.49582e6i	1.12356	−	0.541079i	0.222571	−	0.974917i	$-0.428555\pi$
$463$	5.18262e6	−	2.49582e6i	1.12356	−	0.541079i	0.900991	+	0.433838i	$0.142841\pi$
$464$	−1.58065e6	+	6.92529e6i	−0.340833	+	1.49328i
$465$	−5220.57	−	2514.09i	−0.00111966	−	0.000539199i
$466$	−1.00215e7			−2.13781
$467$	1.52910e6			0.324447			0.162224	−	0.986754i	$-0.448133\pi$
$467$	1.52910e6			0.324447			0.162224	+	0.986754i	$0.448133\pi$
$468$	−5.99675e6	−	2.88788e6i	−1.26561	−	0.609488i
$469$	1.53446e6	+	6.72291e6i	0.322124	+	1.41132i
$470$	−7144.19	−	8958.52i	−0.00149179	−	0.00187065i
$471$	−315060.	+	395073.i	−0.0654397	+	0.0820587i
$472$	723751.			0.149532
$473$	−3.33108e6	+	667203.i	−0.684593	+	0.137121i
$474$	−892678.			−0.182494
$475$	−5.60889e6	+	7.03333e6i	−1.14063	+	1.43030i
$476$	−4.21307e6	−	5.28302e6i	−0.852277	−	1.06872i
$477$	1.22094e6	+	5.34927e6i	0.245695	+	1.07646i
$478$	1.90689e6	+	918308.i	0.381729	+	0.183831i
$479$	−875022.			−0.174253			−0.0871264	−	0.996197i	$-0.527768\pi$
$479$	−875022.			−0.174253			−0.0871264	+	0.996197i	$0.527768\pi$
$480$	−60488.1			−0.0119830
$481$	−8.93143e6	−	4.30115e6i	−1.76018	−	0.847660i
$482$	602040.	−	2.63771e6i	0.118034	−	0.517142i
$483$	−516575.	+	248769.i	−0.100755	+	0.0485209i
$484$	523268.	−	2.29259e6i	0.101534	−	0.444849i
$485$	123099.	−	154362.i	0.0237630	−	0.0297979i
$486$	2.46753e6	+	1.18830e6i	0.473884	+	0.228211i
$487$	−731050.	+	916708.i	−0.139677	+	0.175149i	−0.846750	−	0.531991i	$-0.821444\pi$
$487$	−731050.	+	916708.i	−0.139677	+	0.175149i	0.707073	+	0.707141i	$0.250015\pi$
$488$	87723.8	+	384343.i	0.0166751	+	0.0730583i
$489$	235990.	−	113647.i	0.0446295	−	0.0214924i
$490$	−370409.	+	178379.i	−0.0696933	+	0.0335625i
$491$	2.86838e6	+	3.59684e6i	0.536949	+	0.673313i	0.974111	−	0.226070i	$-0.0725877\pi$
$491$	2.86838e6	+	3.59684e6i	0.536949	+	0.673313i	−0.437162	+	0.899383i	$0.644016\pi$
$492$	−126013.	−	552099.i	−0.0234694	−	0.102826i
$493$	1.90081e6	−	8.32798e6i	0.352225	−	1.54320i
$494$	1.37164e7	+	1.71998e7i	2.52884	+	3.17107i
$495$	−157732.	−	197789.i	−0.0289338	−	0.0362819i
$496$	−188523.	+	825974.i	−0.0344081	+	0.150752i
$497$	221559.	+	970712.i	0.0402344	+	0.176279i
$498$	−1.20534e6	−	1.51145e6i	−0.217789	−	0.273099i
$499$	−5.27222e6	+	2.53897e6i	−0.947855	+	0.456463i	−0.842934	−	0.538018i	$-0.819173\pi$
$499$	−5.27222e6	+	2.53897e6i	−0.947855	+	0.456463i	−0.104922	+	0.994481i	$0.533459\pi$
$500$	−604994.	+	291350.i	−0.108225	+	0.0521182i
$501$	−121402.	−	531898.i	−0.0216089	−	0.0946748i
$502$	4.86445e6	−	6.09983e6i	0.861538	−	1.08033i
$503$	822028.	+	395868.i	0.144866	+	0.0697638i	0.504912	−	0.863171i	$-0.331525\pi$
$503$	822028.	+	395868.i	0.144866	+	0.0697638i	−0.360046	+	0.932934i	$0.617239\pi$
$504$	713698.	−	894950.i	0.125152	−	0.156936i
$505$	−99511.3	+	435988.i	−0.0173638	+	0.0760756i
$506$	3.15427e6	−	1.51902e6i	0.547675	−	0.263747i
$507$	−264930.	+	1.16073e6i	−0.0457732	+	0.200545i
$508$	−2.76515e6	−	1.33163e6i	−0.475401	−	0.228941i
$509$	−508170.			−0.0869390			−0.0434695	−	0.999055i	$-0.513841\pi$
$509$	−508170.			−0.0869390			−0.0434695	+	0.999055i	$0.513841\pi$
$510$	80818.9			0.0137590
$511$	−8.63417e6	−	4.15800e6i	−1.46274	−	0.704420i
$512$	1.74942e6	+	7.66471e6i	0.294930	+	1.29217i
$513$	−1.76706e6	−	2.21582e6i	−0.296455	−	0.371742i
$514$	−4.05445e6	+	5.08412e6i	−0.676900	+	0.848806i
$515$	456025.			0.0757653
$516$	−680475.	−	174565.i	−0.112509	−	0.0288624i
$517$	109209.			0.0179693
$518$	−8.62398e6	+	1.08141e7i	−1.41216	+	1.77079i
$519$	532931.	+	668275.i	0.0868466	+	0.108902i
$520$	−22467.8	−	98437.7i	−0.00364377	−	0.0159644i
$521$	5.29356e6	+	2.54924e6i	0.854384	+	0.411450i	0.809203	−	0.587529i	$-0.199899\pi$
$521$	5.29356e6	+	2.54924e6i	0.854384	+	0.411450i	0.0451813	+	0.998979i	$0.485613\pi$
$522$	−1.17401e7			−1.88580
$523$	2.45375e6			0.392261			0.196131	−	0.980578i	$-0.437162\pi$
$523$	2.45375e6			0.392261			0.196131	+	0.980578i	$0.437162\pi$
$524$	−6.45507e6	−	3.10860e6i	−1.02701	−	0.494580i
$525$	−247034.	+	1.08233e6i	−0.0391164	+	0.171380i
$526$	8.15953e6	−	3.92942e6i	1.28588	−	0.619247i
$527$	226708.	−	993272.i	0.0355582	−	0.155791i
$528$	399370.	−	500794.i	0.0623434	−	0.0781761i
$529$	3.47351e6	+	1.67275e6i	0.539671	+	0.259892i
$530$	421039.	−	527966.i	0.0651077	−	0.0816425i
$531$	1.40861e6	+	6.17153e6i	0.216798	+	0.949853i
$532$	1.30252e7	−	6.27261e6i	1.99529	−	0.960880i
$533$	8.61309e6	−	4.14785e6i	1.31323	−	0.632419i
$534$	638353.	+	800469.i	0.0968741	+	0.121476i
$535$	38415.0	+	168307.i	0.00580252	+	0.0254225i
$536$	−238813.	+	1.04631e6i	−0.0359043	+	0.157307i
$537$	476932.	+	598054.i	0.0713709	+	0.0894962i
$538$	−1.52074e6	−	1.90695e6i	−0.226516	−	0.284042i
$539$	871921.	−	3.82014e6i	0.129272	−	0.566379i
$540$	−23483.4	−	102887.i	−0.00346558	−	0.0151837i
$541$	2.47842e6	+	3.10784e6i	0.364067	+	0.456526i	0.929801	−	0.368062i	$-0.119978\pi$
$541$	2.47842e6	+	3.10784e6i	0.364067	+	0.456526i	−0.565734	+	0.824588i	$0.691407\pi$
$542$	1.55509e6	−	748890.i	0.227382	−	0.109501i
$543$	1.08008e6	−	520141.i	0.157202	−	0.0757045i
$544$	−2.36662e6	−	1.03688e7i	−0.342871	−	1.50222i
$545$	−35782.4	+	44869.7i	−0.00516034	+	0.00647087i
$546$	2.44601e6	+	1.17794e6i	0.351137	+	0.169099i
$547$	−4.64504e6	+	5.82469e6i	−0.663775	+	0.832347i	−0.993748	−	0.111643i	$-0.964389\pi$
$547$	−4.64504e6	+	5.82469e6i	−0.663775	+	0.832347i	0.329974	+	0.943990i	$0.392960\pi$
$548$	−1.52517e6	+	6.68219e6i	−0.216953	+	0.950533i
$549$	−3.10661e6	+	1.49607e6i	−0.439903	+	0.211846i
$550$	1.50842e6	−	6.60883e6i	0.212626	−	0.931575i
$551$	1.64658e7	+	7.92951e6i	2.31049	+	1.11267i
$552$	−89233.2			−0.0124646
$553$	−9.90294e6			−1.37706
$554$	−1.33791e7	−	6.44305e6i	−1.85205	−	0.891902i
$555$	−17337.7	−	75961.3i	−0.00238923	−	0.0104679i
$556$	4.90334e6	+	6.14860e6i	0.672675	+	0.843508i
$557$	1.88249e6	−	2.36057e6i	0.257095	−	0.322387i	−0.636486	−	0.771288i	$-0.719613\pi$
$557$	1.88249e6	−	2.36057e6i	0.257095	−	0.322387i	0.893582	+	0.448901i	$0.148184\pi$
$558$	−1.40023e6			−0.190377
$559$	316831.	−	1.18550e7i	0.0428842	−	1.60462i
$560$	−745556.			−0.100464
$561$	−480261.	+	602228.i	−0.0644273	+	0.0807893i
$562$	743572.	+	932409.i	0.0993075	+	0.124528i
$563$	1.53395e6	+	6.72066e6i	0.203957	+	0.893595i	0.968498	+	0.249020i	$0.0801086\pi$
$563$	1.53395e6	+	6.72066e6i	0.203957	+	0.893595i	−0.764541	+	0.644575i	$0.777034\pi$
$564$	20346.7	+	9798.44i	0.00269337	+	0.00129706i
$565$	−484865.			−0.0638998
$566$	7.03456e6			0.922988
$567$	8.86150e6	+	4.26747e6i	1.15758	+	0.557459i
$568$	−34481.9	+	151075.i	−0.00448457	+	0.0196482i
$569$	1.96499e6	−	946290.i	0.254437	−	0.122530i	−0.302318	−	0.953207i	$-0.597761\pi$
$569$	1.96499e6	−	946290.i	0.254437	−	0.122530i	0.556755	+	0.830677i	$0.312046\pi$
$570$	−38476.0	+	168574.i	−0.00496024	+	0.0217322i
$571$	−4.22465e6	+	5.29754e6i	−0.542251	+	0.679961i	−0.975166	−	0.221473i	$-0.928913\pi$
$571$	−4.22465e6	+	5.29754e6i	−0.542251	+	0.679961i	0.432915	+	0.901435i	$0.357485\pi$
$572$	−7.03432e6	−	3.38755e6i	−0.898942	−	0.432908i
$573$	−447204.	+	560776.i	−0.0569008	+	0.0713514i
$574$	−2.96816e6	−	1.30044e7i	−0.376017	−	1.64744i
$575$	−4.50264e6	+	2.16836e6i	−0.567933	+	0.273502i
$576$	−5.42871e6	+	2.61433e6i	−0.681775	+	0.328325i
$577$	−6.09328e6	−	7.64073e6i	−0.761923	−	0.955422i	0.237951	−	0.971277i	$-0.423524\pi$
$577$	−6.09328e6	−	7.64073e6i	−0.761923	−	0.955422i	−0.999874	+	0.0158555i	$0.994953\pi$
$578$	704803.	+	3.08794e6i	0.0877502	+	0.384459i
$579$	−49342.8	+	216185.i	−0.00611684	+	0.0267996i
$580$	424297.	+	532051.i	0.0523720	+	0.0656725i
$581$	−1.33715e7	−	1.67673e7i	−1.64338	−	2.06074i
$582$	−183848.	+	805492.i	−0.0224984	+	0.0985721i
$583$	1.43218e6	+	6.27480e6i	0.174513	+	0.764590i
$584$	−929914.	−	1.16608e6i	−0.112826	−	0.141480i
$585$	795664.	−	383171.i	0.0961258	−	0.0462917i
$586$	1.79203e7	−	8.62997e6i	2.15577	−	1.03816i
$587$	682723.	+	2.99120e6i	0.0817804	+	0.358303i	0.999216	−	0.0395801i	$-0.0126020\pi$
$587$	682723.	+	2.99120e6i	0.0817804	+	0.358303i	−0.917436	+	0.397883i	$0.869745\pi$
$588$	505197.	−	633497.i	0.0602584	−	0.0755617i
$589$	1.96386e6	+	945747.i	0.233251	+	0.112328i
$590$	485758.	−	609122.i	0.0574500	−	0.0720401i
$591$	322073.	−	1.41109e6i	0.0379302	−	0.166183i
$592$	−1.02640e7	+	4.94287e6i	−1.20368	+	0.579662i
$593$	1.72331e6	−	7.55031e6i	0.201246	−	0.881715i	−0.768934	−	0.639328i	$-0.779213\pi$
$593$	1.72331e6	−	7.55031e6i	0.201246	−	0.881715i	0.970180	−	0.242387i	$-0.0779303\pi$
$594$	1.92414e6	+	926616.i	0.223754	+	0.107754i
$595$	896566.			0.103822
$596$	4.11472e6			0.474487
$597$	102158.	+	49196.9i	0.0117311	+	0.00564940i
$598$	2.71951e6	+	1.19149e7i	0.310984	+	1.36251i
$599$	−1.87888e6	−	2.35604e6i	−0.213960	−	0.268297i	0.663257	−	0.748392i	$-0.269174\pi$
$599$	−1.87888e6	−	2.35604e6i	−0.213960	−	0.268297i	−0.877217	+	0.480095i	$0.840602\pi$
$600$	−107725.	+	135083.i	−0.0122163	+	0.0153188i
$601$	−20071.2			−0.00226667			−0.00113333	−	0.999999i	$-0.500361\pi$
$601$	−20071.2			−0.00226667			−0.00113333	+	0.999999i	$0.500361\pi$
$602$	−1.60282e7	−	4.11177e6i	−1.80257	−	0.462421i
$603$	−9.38682e6			−1.05130
$604$	−5.04061e6	+	6.32073e6i	−0.562200	+	0.704977i
$605$	194534.	+	243938.i	0.0216077	+	0.0270951i
$606$	−416423.	−	1.82447e6i	−0.0460631	−	0.201816i
$607$	−1.09962e7	−	5.29550e6i	−1.21136	−	0.583358i	−0.284464	−	0.958687i	$-0.591816\pi$
$607$	−1.09962e7	−	5.29550e6i	−1.21136	−	0.583358i	−0.926892	+	0.375328i	$0.877530\pi$
$608$	2.27543e7			2.49634
$609$	2.25534e6			0.246416
$610$	382347.	+	184129.i	0.0416039	+	0.0200354i
$611$	−84831.8	+	371673.i	−0.00919297	+	0.0402770i
$612$	8.28729e6	−	3.99095e6i	0.894404	−	0.430723i
$613$	3.01694e6	−	1.32181e7i	0.324277	−	1.42075i	−0.505584	−	0.862777i	$-0.668723\pi$
$613$	3.01694e6	−	1.32181e7i	0.324277	−	1.42075i	0.829860	−	0.557971i	$-0.188420\pi$
$614$	−699979.	+	877746.i	−0.0749314	+	0.0939610i
$615$	67696.7	+	32601.0i	0.00721739	+	0.00347571i
$616$	837183.	−	1.04979e6i	0.0888932	−	0.111469i
$617$	−1.97942e6	−	8.67241e6i	−0.209327	−	0.917121i	−0.965016	−	0.262191i	$-0.915555\pi$
$617$	−1.97942e6	−	8.67241e6i	−0.209327	−	0.917121i	0.755689	−	0.654930i	$-0.227302\pi$
$618$	−1.71934e6	+	827989.i	−0.181088	+	0.0872074i
$619$	1.55567e7	−	7.49170e6i	1.63189	−	0.785876i	0.631947	−	0.775011i	$-0.282256\pi$
$619$	1.55567e7	−	7.49170e6i	1.63189	−	0.785876i	0.999941	−	0.0108645i	$-0.00345835\pi$
$620$	50605.5	+	63457.3i	0.00528712	+	0.00662983i
$621$	−350350.	−	1.53498e6i	−0.0364564	−	0.159726i
$622$	−1.00299e6	+	4.39437e6i	−0.103949	+	0.455429i
$623$	7.08158e6	+	8.88003e6i	0.730988	+	0.916630i
$624$	1.39414e6	+	1.74819e6i	0.143332	+	0.179733i
$625$	−2.14329e6	+	9.39039e6i	−0.219473	+	0.961576i
$626$	−1.57467e6	−	6.89908e6i	−0.160603	−	0.703648i
$627$	−1.02750e6	−	1.28845e6i	−0.104379	−	0.130887i
$628$	6.37727e6	−	3.07113e6i	0.645261	−	0.310741i
$629$	1.23429e7	−	5.94403e6i	1.24391	−	0.599038i
$630$	−274194.	−	1.20132e6i	−0.0275237	−	0.120589i
$631$	−973338.	+	1.22053e6i	−0.0973173	+	0.122032i	−0.828106	−	0.560572i	$-0.810581\pi$
$631$	−973338.	+	1.22053e6i	−0.0973173	+	0.122032i	0.730788	+	0.682604i	$0.239153\pi$
$632$	−1.38860e6	−	668714.i	−0.138288	−	0.0665959i
$633$	974150.	−	1.22155e6i	0.0966310	−	0.121171i
$634$	−4.71467e6	+	2.06563e7i	−0.465830	+	2.04094i
$635$	366887.	−	176684.i	0.0361076	−	0.0173885i
$636$	−296158.	+	1.29755e6i	−0.0290323	+	0.127199i
$637$	1.23238e7	+	5.93485e6i	1.20337	+	0.579510i
$638$	−1.37714e7			−1.33945
$639$	−1.35535e6			−0.131311
$640$	−189330.	−	91176.7i	−0.0182713	−	0.00879901i
$641$	2.68910e6	+	1.17817e7i	0.258501	+	1.13257i	0.922855	+	0.385148i	$0.125850\pi$
$641$	2.68910e6	+	1.17817e7i	0.258501	+	1.13257i	−0.664354	+	0.747418i	$0.731293\pi$
$642$	−450425.	−	564815.i	−0.0431305	−	0.0540840i
$643$	1.23466e6	−	1.54822e6i	0.117766	−	0.147674i	−0.719454	−	0.694540i	$-0.755608\pi$
$643$	1.23466e6	−	1.54822e6i	0.117766	−	0.147674i	0.837220	+	0.546866i	$0.184179\pi$
$644$	8.03127e6			0.763079
$645$	74401.6	−	56148.2i	0.00704179	−	0.00531418i
$646$	−3.04023e7			−2.86632
$647$	−9.02827e6	+	1.13211e7i	−0.847899	+	1.06323i	0.149327	+	0.988788i	$0.452289\pi$
$647$	−9.02827e6	+	1.13211e7i	−0.847899	+	1.06323i	−0.997225	+	0.0744432i	$0.976282\pi$
$648$	954398.	+	1.19678e6i	0.0892878	+	0.111963i
$649$	1.65233e6	+	7.23933e6i	0.153987	+	0.674663i
$650$	2.13202e7	+	1.02673e7i	1.97929	+	0.953174i
$651$	268992.			0.0248764
$652$	−3.66898e6			−0.338007
$653$	1.03643e7	+	4.99118e6i	0.951166	+	0.458057i	0.844095	−	0.536194i	$-0.180138\pi$
$653$	1.03643e7	+	4.99118e6i	0.951166	+	0.458057i	0.107071	+	0.994251i	$0.465853\pi$
$654$	53440.9	−	234140.i	0.00488573	−	0.0214058i
$655$	856474.	−	412456.i	0.0780030	−	0.0375643i
$656$	2.44464e6	−	1.07107e7i	0.221797	−	0.971755i
$657$	8.13343e6	−	1.01990e7i	0.735124	−	0.921816i
$658$	479253.	+	230796.i	0.0431520	+	0.0207809i
$659$	8.77342e6	−	1.10015e7i	0.786965	−	0.986823i	−0.212987	−	0.977055i	$-0.568319\pi$
$659$	8.77342e6	−	1.10015e7i	0.786965	−	0.986823i	0.999952	−	0.00976798i	$-0.00310929\pi$
$660$	−13655.0	−	59826.5i	−0.00122020	−	0.00534605i
$661$	−186810.	+	89963.1i	−0.0166302	+	0.00800868i	−0.442180	−	0.896926i	$-0.645795\pi$
$661$	−186810.	+	89963.1i	−0.0166302	+	0.00800868i	0.425550	+	0.904935i	$0.360081\pi$
$662$	−7.25571e6	+	3.49417e6i	−0.643480	+	0.309884i
$663$	−1.67651e6	−	2.10228e6i	−0.148123	−	0.185741i
$664$	−742716.	−	3.25405e6i	−0.0653737	−	0.286421i
$665$	−426834.	+	1.87008e6i	−0.0374287	+	0.163986i
$666$	−1.17393e7	−	1.47206e7i	−1.02555	−	1.28600i
$667$	6.33012e6	+	7.93772e6i	0.550931	+	0.690846i
$668$	−1.70054e6	+	7.45057e6i	−0.147451	+	0.646024i
$669$	−171084.	−	749568.i	−0.0147790	−	0.0647509i
$670$	720309.	+	903238.i	0.0619914	+	0.0777348i
$671$	−3.64412e6	+	1.75492e6i	−0.312455	+	0.150470i
$672$	2.52995e6	−	1.21836e6i	0.216117	−	0.104076i
$673$	−2.13645e6	−	9.36038e6i	−0.181825	−	0.796628i	−0.980761	−	0.195212i	$-0.937460\pi$
$673$	−2.13645e6	−	9.36038e6i	−0.181825	−	0.796628i	0.798936	−	0.601416i	$-0.205397\pi$
$674$	−1.73589e7	+	2.17674e7i	−1.47188	+	1.84568i
$675$	−2.74665e6	−	1.32272e6i	−0.232030	−	0.111740i
$676$	1.03980e7	−	1.30387e7i	0.875152	−	1.09741i
$677$	−2.01410e6	+	8.82433e6i	−0.168892	+	0.739963i	0.817551	+	0.575857i	$0.195331\pi$
$677$	−2.01410e6	+	8.82433e6i	−0.168892	+	0.739963i	−0.986443	+	0.164107i	$0.947526\pi$
$678$	1.82807e6	−	880352.i	0.152728	−	0.0735499i
$679$	−2.03953e6	+	8.93575e6i	−0.169768	+	0.743800i
$680$	125717.	+	60542.2i	0.0104261	+	0.00502095i
$681$	−372688.			−0.0307948
$682$	−1.64250e6			−0.135221
$683$	−1.04690e7	−	5.04160e6i	−0.858723	−	0.413539i	−0.0479151	−	0.998851i	$-0.515258\pi$
$683$	−1.04690e7	−	5.04160e6i	−0.858723	−	0.413539i	−0.810808	+	0.585312i	$0.800972\pi$
$684$	4.37905e6	+	1.91859e7i	0.357882	+	1.56798i
$685$	−567008.	−	711005.i	−0.0461703	−	0.0578957i
$686$	−2.40158e6	+	3.01149e6i	−0.194844	+	0.244327i
$687$	−201047.			−0.0162520
$688$	−1.04244e7	−	8.77892e6i	−0.839618	−	0.707083i
$689$	−2.24676e7			−1.80306
$690$	−59890.4	+	75100.2i	−0.00478889	+	0.00600508i
$691$	−1.15293e7	−	1.44573e7i	−0.918562	−	1.15184i	−0.988031	−	0.154257i	$-0.950702\pi$
$691$	−1.15293e7	−	1.44573e7i	−0.918562	−	1.15184i	0.0694684	−	0.997584i	$-0.477870\pi$
$692$	−2.66424e6	−	1.16728e7i	−0.211499	−	0.926638i
$693$	1.05811e7	+	5.09560e6i	0.836948	+	0.403053i
$694$	−8.05756e6			−0.635046
$695$	−1.04346e6			−0.0819435
$696$	316245.	+	152296.i	0.0247458	+	0.0119169i
$697$	−2.93979e6	+	1.28801e7i	−0.229211	+	1.00424i
$698$	−2.26360e7	+	1.09009e7i	−1.75858	+	0.846887i
$699$	−583148.	+	2.55494e6i	−0.0451425	+	0.197782i
$700$	9.69564e6	−	1.21579e7i	0.747879	−	0.937810i
$701$	−4.04172e6	−	1.94639e6i	−0.310650	−	0.149601i	0.272063	−	0.962280i	$-0.412294\pi$
$701$	−4.04172e6	−	1.94639e6i	−0.310650	−	0.149601i	−0.582712	+	0.812679i	$0.698008\pi$
$702$	−4.64821e6	+	5.82867e6i	−0.355994	+	0.446403i
$703$	6.52205e6	+	2.85750e7i	0.497732	+	2.18071i
$704$	−6.36800e6	+	3.06666e6i	−0.484252	+	0.233203i
$705$	−2699.64	+	1300.08i	−0.000204566	+	9.85139e-5i
$706$	1.49442e7	+	1.87395e7i	1.12840	+	1.41496i
$707$	−4.61960e6	−	2.02398e7i	−0.347581	−	1.52285i
$708$	−341682.	+	1.49701e6i	−0.0256176	+	0.112238i
$709$	7.53030e6	+	9.44270e6i	0.562596	+	0.705473i	0.979035	−	0.203690i	$-0.0652935\pi$
$709$	7.53030e6	+	9.44270e6i	0.562596	+	0.705473i	−0.416439	+	0.909164i	$0.636722\pi$
$710$	104004.	+	130417.i	0.00774294	+	0.00970934i
$711$	2.99964e6	−	1.31423e7i	0.222533	−	0.974982i
$712$	393346.	+	1.72336e6i	0.0290787	+	0.127402i
$713$	754988.	+	946726.i	0.0556181	+	0.0697429i
$714$	−3.38030e6	+	1.62786e6i	−0.248147	+	0.119501i
$715$	933330.	−	449468.i	0.0682763	−	0.0328801i
$716$	−2.38429e6	−	1.04463e7i	−0.173811	−	0.761514i
$717$	345078.	−	432715.i	0.0250680	−	0.0314343i
$718$	2.49195e7	+	1.20006e7i	1.80397	+	0.868745i
$719$	9.22241e6	−	1.15645e7i	0.665307	−	0.834268i	−0.328603	−	0.944468i	$-0.606578\pi$
$719$	9.22241e6	−	1.15645e7i	0.665307	−	0.834268i	0.993909	+	0.110200i	$0.0351491\pi$
$720$	225832.	−	989433.i	0.0162351	−	0.0711304i
$721$	−1.90735e7	+	9.18532e6i	−1.36645	+	0.658046i
$722$	1.01886e7	−	4.46391e7i	0.727396	−	3.18693i
$723$	−637438.	−	306974.i	−0.0453515	−	0.0218402i
$724$	−1.67922e7			−1.19059
$725$	1.96583e7			1.38899
$726$	−1.17636e6	−	566504.i	−0.0828319	−	0.0398897i
$727$	−775673.	−	3.39844e6i	−0.0544305	−	0.238476i	0.940394	−	0.340088i	$-0.110457\pi$
$727$	−775673.	−	3.39844e6i	−0.0544305	−	0.238476i	−0.994824	+	0.101613i	$0.967600\pi$
$728$	2.92247e6	+	3.66466e6i	0.204372	+	0.256275i
$729$	−8.04559e6	+	1.00889e7i	−0.560711	+	0.703110i
$730$	−1.60552e6			−0.111509
$731$	1.25359e7	+	1.05571e7i	0.867684	+	0.730718i
$732$	−836389.			−0.0576940
$733$	−2.57473e6	+	3.22861e6i	−0.177000	+	0.221950i	−0.862415	−	0.506202i	$-0.831049\pi$
$733$	−2.57473e6	+	3.22861e6i	−0.177000	+	0.221950i	0.685416	+	0.728152i	$0.259621\pi$
$734$	−2.35085e7	−	2.94788e7i	−1.61059	−	2.01962i
$735$	23923.0	+	104814.i	0.00163342	+	0.00715647i
$736$	1.13889e7	+	5.48462e6i	0.774976	+	0.373209i
$737$	−1.10109e7			−0.746716
$738$	1.81573e7			1.22718
$739$	1.91120e7	+	9.20384e6i	1.28734	+	0.619952i	0.947267	−	0.320446i	$-0.103833\pi$
$739$	1.91120e7	+	9.20384e6i	1.28734	+	0.619952i	0.340076	+	0.940398i	$0.389547\pi$
$740$	−242857.	+	1.06403e6i	−0.0163032	+	0.0714289i
$741$	5.18314e6	−	2.49607e6i	0.346775	−	0.166998i
$742$	−6.97583e6	+	3.05631e7i	−0.465142	+	2.03792i
$743$	−4.77007e6	+	5.98148e6i	−0.316995	+	0.397500i	−0.914645	−	0.404258i	$-0.867530\pi$
$743$	−4.77007e6	+	5.98148e6i	−0.316995	+	0.397500i	0.597650	+	0.801757i	$0.296101\pi$
$744$	37718.4	+	18164.2i	0.00249816	+	0.00120305i
$745$	−340395.	+	426841.i	−0.0224694	+	0.0281758i
$746$	−3.45450e6	−	1.51352e7i	−0.227268	−	0.995726i
$747$	2.63022e7	−	1.26665e7i	1.72461	−	0.830529i
$748$	9.72116e6	−	4.68147e6i	0.635279	−	0.305934i
$749$	−4.99680e6	−	6.26579e6i	−0.325452	−	0.408104i
$750$	82963.6	+	363487.i	0.00538561	+	0.0235959i
$751$	2.27448e6	−	9.96515e6i	0.147157	−	0.644739i	−0.846509	−	0.532374i	$-0.821300\pi$
$751$	2.27448e6	−	9.96515e6i	0.147157	−	0.644739i	0.993667	−	0.112365i	$-0.0358427\pi$
$752$	273157.	+	342528.i	0.0176144	+	0.0220877i
$753$	−1.27206e6	−	1.59511e6i	−0.0817560	−	0.102519i
$754$	1.06974e7	−	4.68684e7i	0.685251	−	3.00228i
$755$	−238692.	−	1.04578e6i	−0.0152395	−	0.0667686i
$756$	3.05457e6	+	3.83032e6i	0.194378	+	0.243742i
$757$	−1.40787e7	+	6.77994e6i	−0.892941	+	0.430018i	−0.823334	−	0.567557i	$-0.807889\pi$
$757$	−1.40787e7	+	6.77994e6i	−0.892941	+	0.430018i	−0.0696065	+	0.997575i	$0.522174\pi$
$758$	2.12554e7	−	1.02360e7i	1.34368	−	0.647082i
$759$	−203720.	−	892556.i	−0.0128360	−	0.0562382i
$760$	−186132.	+	233402.i	−0.0116892	+	0.0146579i
$761$	−689290.	−	331944.i	−0.0431460	−	0.0207780i	0.412186	−	0.911100i	$-0.364765\pi$
$761$	−689290.	−	331944.i	−0.0431460	−	0.0207780i	−0.455332	+	0.890322i	$0.650480\pi$
$762$	−1.06247e6	+	1.33229e6i	−0.0662869	+	0.0831211i
$763$	592848.	−	2.59744e6i	0.0368665	−	0.161523i
$764$	9.05204e6	−	4.35923e6i	0.561065	−	0.270195i
$765$	−271573.	+	1.18984e6i	−0.0167777	+	0.0735081i
$766$	2.05345e7	+	9.88890e6i	1.26448	+	0.608942i
$767$	−2.59212e7			−1.59099
$768$	2.52109e6			0.154236
$769$	2.57413e6	+	1.23963e6i	0.156969	+	0.0755923i	0.510719	−	0.859748i	$-0.329379\pi$
$769$	2.57413e6	+	1.23963e6i	0.156969	+	0.0755923i	−0.353750	+	0.935340i	$0.615094\pi$
$770$	−321635.	−	1.40918e6i	−0.0195496	−	0.0856522i
$771$	1.06024e6	+	1.32950e6i	0.0642347	+	0.0805478i
$772$	1.93661e6	−	2.42844e6i	0.116950	−	0.146650i
$773$	2.28487e7			1.37535			0.687674	−	0.726020i	$-0.258632\pi$
$773$	2.28487e7			1.37535			0.687674	+	0.726020i	$0.258632\pi$
$774$	1.03118e7	−	2.00257e7i	0.618700	−	1.20153i
$775$	2.34463e6			0.140223
$776$	−889386.	+	1.11526e6i	−0.0530196	+	0.0664844i
$777$	2.25518e6	+	2.82791e6i	0.134007	+	0.168040i
$778$	7.35666e6	+	3.22316e7i	0.435744	+	1.90912i
$779$	−2.54660e7	−	1.22638e7i	−1.50355	−	0.724071i
$780$	214215.			0.0126071
$781$	−1.58985e6			−0.0932674
$782$	−1.52169e7	−	7.32806e6i	−0.889833	−	0.428521i
$783$	−1.37813e6	+	6.03798e6i	−0.0803315	+	0.351955i
$784$	1.41625e7	−	6.82031e6i	0.822906	−	0.396291i
$785$	−208982.	+	915610.i	−0.0121042	+	0.0530318i
$786$	−2.48026e6	+	3.11014e6i	−0.143199	+	0.179566i
$787$	−1.03831e7	−	5.00022e6i	−0.597570	−	0.287775i	0.110545	−	0.993871i	$-0.464740\pi$
$787$	−1.03831e7	−	5.00022e6i	−0.597570	−	0.287775i	−0.708116	+	0.706096i	$0.750455\pi$
$788$	−1.26408e7	+	1.58510e7i	−0.725199	+	0.909371i
$789$	−526986.	−	2.30888e6i	−0.0301375	−	0.132041i
$790$	−1.49478e6	+	719850.i	−0.0852140	+	0.0410369i
$791$	2.02797e7	−	9.76621e6i	1.15245	−	0.554990i
$792$	1.13960e6	+	1.42902e6i	0.0645567	+	0.0809515i
$793$	−3.14184e6	−	1.37653e7i	−0.177419	−	0.777325i
$794$	−3.49183e6	+	1.52987e7i	−0.196563	+	0.861199i
$795$	−110102.	−	138064.i	−0.00617842	−	0.00774750i
$796$	−990273.	−	1.24176e6i	−0.0553952	−	0.0694634i
$797$	−3.65093e6	+	1.59958e7i	−0.203591	+	0.891988i	0.765138	+	0.643866i	$0.222671\pi$
$797$	−3.65093e6	+	1.59958e7i	−0.203591	+	0.891988i	−0.968729	+	0.248122i	$0.920187\pi$
$798$	−1.78617e6	−	7.82571e6i	−0.0992921	−	0.435027i
$799$	−328484.	−	411905.i	−0.0182032	−	0.0228260i
$800$	2.20519e7	−	1.06196e7i	1.21820	−	0.586656i
$801$	−1.39298e7	+	6.70823e6i	−0.767120	+	0.369426i
$802$	1.82252e6	+	7.98496e6i	0.100054	+	0.438366i
$803$	9.54069e6	−	1.19636e7i	0.522145	−	0.654749i
$804$	−2.05144e6	−	987922.i	−0.111923	−	0.0538992i
$805$	−664396.	+	833126.i	−0.0361358	+	0.0453128i
$806$	1.27587e6	−	5.58996e6i	0.0691782	−	0.303089i
$807$	−574657.	+	276740.i	−0.0310617	+	0.0149585i
$808$	718964.	−	3.14999e6i	0.0387417	−	0.169739i
$809$	2.60548e7	+	1.25473e7i	1.39964	+	0.674031i	0.973088	−	0.230433i	$-0.0740143\pi$
$809$	2.60548e7	+	1.25473e7i	1.39964	+	0.674031i	0.426551	+	0.904464i	$0.359729\pi$
$810$	1.64779e6			0.0882448
$811$	2.90711e7			1.55206			0.776031	−	0.630694i	$-0.217230\pi$
$811$	2.90711e7			1.55206			0.776031	+	0.630694i	$0.217230\pi$
$812$	−2.84631e7	−	1.37071e7i	−1.51493	−	0.729551i
$813$	−100436.	−	440038.i	−0.00532921	−	0.0233488i
$814$	−1.37704e7	−	1.72676e7i	−0.728427	−	0.913419i
$815$	303520.	−	380602.i	0.0160064	−	0.0200714i
$816$	−3.09010e6			−0.162460
$817$	−2.79883e7	+	2.11217e7i	−1.46697	+	1.10707i
$818$	8.32329e6			0.434923
$819$	−2.55612e7	+	3.20527e7i	−1.33159	+	1.66976i
$820$	−656218.	−	822871.i	−0.0340811	−	0.0427363i
$821$	−2.81280e6	−	1.23237e7i	−0.145640	−	0.638091i	−0.994066	−	0.108777i	$-0.965306\pi$
$821$	−2.81280e6	−	1.23237e7i	−0.145640	−	0.638091i	0.848426	−	0.529314i	$-0.177551\pi$
$822$	3.42872e6	+	1.65118e6i	0.176992	+	0.0852346i
$823$	−3.63188e7			−1.86910			−0.934548	−	0.355837i	$-0.884196\pi$
$823$	−3.63188e7			−1.86910			−0.934548	+	0.355837i	$0.884196\pi$
$824$	−3.29476e6			−0.169046
$825$	−1.59711e6	−	769129.i	−0.0816959	−	0.0393427i
$826$	−8.04811e6	+	3.52611e7i	−0.410435	+	1.79823i
$827$	3.86157e6	−	1.85963e6i	0.196336	−	0.0945505i	−0.333132	−	0.942880i	$-0.608106\pi$
$827$	3.86157e6	−	1.85963e6i	0.196336	−	0.0945505i	0.529469	+	0.848330i	$0.322391\pi$
$828$	−2.43270e6	+	1.06584e7i	−0.123314	+	0.540275i
$829$	9.52974e6	−	1.19499e7i	0.481609	−	0.603919i	−0.480362	−	0.877070i	$-0.659495\pi$
$829$	9.52974e6	−	1.19499e7i	0.481609	−	0.603919i	0.961971	+	0.273151i	$0.0880660\pi$
$830$	−3.23716e6	−	1.55893e6i	−0.163105	−	0.0785474i
$831$	−2.42114e6	+	3.03602e6i	−0.121624	+	0.152511i
$832$	−5.49027e6	−	2.40544e7i	−0.274970	−	1.20472i
$833$	−1.70311e7	+	8.20174e6i	−0.850413	+	0.409537i
$834$	3.93413e6	−	1.89458e6i	0.195855	−	0.0943186i
$835$	−632207.	−	792763.i	−0.0313793	−	0.0393484i
$836$	5.13671e6	+	2.25054e7i	0.254197	+	1.11371i
$837$	−164369.	+	720146.i	−0.00810971	+	0.0355309i
$838$	1.66620e7	+	2.08935e7i	0.819629	+	1.02778i
$839$	−1.08484e7	−	1.36034e7i	−0.532059	−	0.667181i	0.441062	−	0.897477i	$-0.354602\pi$
$839$	−1.08484e7	−	1.36034e7i	−0.532059	−	0.667181i	−0.973121	+	0.230296i	$0.926031\pi$
$840$	−8197.86	+	35917.2i	−0.000400869	+	0.00175632i
$841$	−4.32256e6	−	1.89384e7i	−0.210742	−	0.923320i
$842$	3.09157e7	+	3.87671e7i	1.50279	+	1.88444i
$843$	280981.	−	135313.i	0.0136178	−	0.00655800i
$844$	−1.97182e7	+	9.49578e6i	−0.952820	+	0.458854i
$845$	492385.	+	2.15728e6i	0.0237227	+	0.103936i
$846$	−451459.	+	566112.i	−0.0216867	+	0.0271942i
$847$	−1.30499e7	−	6.28452e6i	−0.625029	−	0.300998i
$848$	−1.60983e7	+	2.01867e7i	−0.768761	+	0.963996i
$849$	409337.	−	1.79342e6i	0.0194900	−	0.0853913i
$850$	−2.94638e7	+	1.41890e7i	−1.39875	+	0.673604i
$851$	−3.62321e6	+	1.58743e7i	−0.171502	+	0.751400i
$852$	−296205.	−	142645.i	−0.0139796	−	0.00673220i
$853$	3.30162e7			1.55365			0.776827	−	0.629714i	$-0.216828\pi$
$853$	3.30162e7			1.55365			0.776827	+	0.629714i	$0.216828\pi$
$854$	−1.97007e7			−0.924349
$855$	−2.35251e6	−	1.13291e6i	−0.110057	−	0.0530005i
$856$	−277547.	−	1.21601e6i	−0.0129465	−	0.0567222i
$857$	−2.06824e7	−	2.59349e7i	−0.961942	−	1.20624i	−0.978473	−	0.206374i	$-0.933834\pi$
$857$	−2.06824e7	−	2.59349e7i	−0.961942	−	1.20624i	0.0165314	−	0.999863i	$-0.494738\pi$
$858$	−2.70282e6	+	3.38923e6i	−0.125343	+	0.157175i
$859$	1.50696e7			0.696818			0.348409	−	0.937343i	$-0.386722\pi$
$859$	1.50696e7			0.696818			0.348409	+	0.937343i	$0.386722\pi$
$860$	−1.28022e6	+	256423.i	−0.0590253	+	0.0118226i
$861$	−3.48811e6			−0.160355
$862$	−6.65143e6	+	8.34063e6i	−0.304892	+	0.382323i
$863$	−1.17208e7	−	1.46974e7i	−0.535711	−	0.671760i	0.438151	−	0.898901i	$-0.355633\pi$
$863$	−1.17208e7	−	1.46974e7i	−0.535711	−	0.671760i	−0.973862	+	0.227142i	$0.927062\pi$
$864$	1.71586e6	+	7.51765e6i	0.0781981	+	0.342608i
$865$	1.43128e6	+	689270.i	0.0650407	+	0.0313220i
$866$	2.72596e7			1.23516
$867$	828267.			0.0374216
$868$	−3.39477e6	−	1.63484e6i	−0.152937	−	0.0736504i
$869$	3.51864e6	−	1.54162e7i	0.158061	−	0.692511i
$870$	340428.	−	163942.i	0.0152485	−	0.00734330i
$871$	8.55312e6	−	3.74737e7i	0.382014	−	1.67371i
$872$	258526.	−	324182.i	0.0115137	−	0.0144377i
$873$	−1.12409e7	−	5.41334e6i	−0.499190	−	0.240397i
$874$	2.25295e7	−	2.82511e7i	0.997637	−	1.25100i
$875$	920359.	+	4.03236e6i	0.0406385	+	0.178049i
$876$	2.85092e6	−	1.37293e6i	0.125523	−	0.0604489i
$877$	−3.64069e7	+	1.75326e7i	−1.59840	+	0.769747i	−0.999517	−	0.0310914i	$-0.990102\pi$
$877$	−3.64069e7	+	1.75326e7i	−1.59840	+	0.769747i	−0.598880	+	0.800839i	$0.704387\pi$
$878$	−1.00652e7	−	1.26214e7i	−0.440644	−	0.552550i
$879$	−1.15739e6	−	5.07086e6i	−0.0505252	−	0.221365i
$880$	264905.	−	1.16063e6i	0.0115315	−	0.0505226i
$881$	−1.00344e6	−	1.25828e6i	−0.0435565	−	0.0546181i	0.759576	−	0.650418i	$-0.225406\pi$
$881$	−1.00344e6	−	1.25828e6i	−0.0435565	−	0.0546181i	−0.803133	+	0.595800i	$0.796835\pi$
$882$	1.61982e7	+	2.03119e7i	0.701125	+	0.879183i
$883$	−2.19806e6	+	9.63032e6i	−0.0948719	+	0.415661i	−0.999954	−	0.00957568i	$-0.996952\pi$
$883$	−2.19806e6	+	9.63032e6i	−0.0948719	+	0.415661i	0.905082	+	0.425236i	$0.139809\pi$
$884$	8.38126e6	+	3.67207e7i	0.360727	+	1.58045i
$885$	−127026.	−	159286.i	−0.00545175	−	0.00683627i
$886$	4.00894e7	−	1.93060e7i	1.71571	−	0.826244i
$887$	1.18184e7	−	5.69143e6i	0.504369	−	0.242891i	−0.164356	−	0.986401i	$-0.552555\pi$
$887$	1.18184e7	−	5.69143e6i	0.504369	−	0.242891i	0.668725	+	0.743510i	$0.266840\pi$
$888$	125264.	+	548817.i	0.00533081	+	0.0233558i
$889$	−1.17865e7	+	1.47798e7i	−0.500184	+	0.627211i
$890$	1.71441e6	+	825618.i	0.0725505	+	0.0349385i
$891$	−9.79188e6	+	1.22786e7i	−0.413211	+	0.518150i
$892$	−2.39646e6	+	1.04996e7i	−0.100846	+	0.441835i
$893$	1.01555e6	−	489062.i	0.0426159	−	0.0205227i
$894$	508378.	−	2.22735e6i	0.0212737	−	0.0932062i
$895$	1.28089e6	+	616843.i	0.0534507	+	0.0257405i
$896$	9.75535e6			0.405950
$897$	3.19590e6			0.132621
$898$	−4.86701e6	−	2.34383e6i	−0.201405	−	0.0969917i
$899$	−1.05991e6	−	4.64378e6i	−0.0437392	−	0.191634i
$900$	1.31981e7	+	1.65498e7i	0.543130	+	0.681063i
$901$	1.93590e7	−	2.42754e7i	0.794458	−	0.996219i
$902$	2.12989e7			0.871645
$903$	−1.98095e6	+	3.84704e6i	−0.0808450	+	0.157003i
$904$	3.50312e6			0.142572
$905$	1.38916e6	−	1.74195e6i	0.0563806	−	0.0706990i
$906$	2.79872e6	+	3.50948e6i	0.113276	+	0.142044i
$907$	−1.32052e6	−	5.78559e6i	−0.0533001	−	0.233523i	0.941261	−	0.337681i	$-0.109642\pi$
$907$	−1.32052e6	−	5.78559e6i	−0.0533001	−	0.233523i	−0.994561	+	0.104158i	$0.966785\pi$
$908$	4.70344e6	+	2.26506e6i	0.189322	+	0.0911726i
$909$	2.82597e7			1.13438
$910$	5.04571e6			0.201985
$911$	2.94878e7	+	1.42006e7i	1.17719	+	0.566904i	0.917091	−	0.398678i	$-0.130531\pi$
$911$	2.94878e7	+	1.42006e7i	1.17719	+	0.566904i	0.260097	+	0.965582i	$0.416245\pi$
$912$	1.47112e6	−	6.44541e6i	0.0585682	−	0.256604i
$913$	3.08531e7	−	1.48581e7i	1.22496	−	0.589909i
$914$	−393248.	+	1.72293e6i	−0.0155704	+	0.0682186i
$915$	69191.3	−	86763.1i	0.00273211	−	0.00342596i
$916$	2.53728e6	+	1.22189e6i	0.0999149	+	0.0481165i
$917$	−2.75148e7	+	3.45025e7i	−1.08054	+	1.35496i
$918$	−2.29258e6	−	1.00444e7i	−0.0897877	−	0.393386i
$919$	−1.10101e7	+	5.30218e6i	−0.430034	+	0.207093i	−0.636364	−	0.771389i	$-0.719562\pi$
$919$	−1.10101e7	+	5.30218e6i	−0.430034	+	0.207093i	0.206330	+	0.978482i	$0.433848\pi$
$920$	−149421.	+	71957.1i	−0.00582024	+	0.00280288i
$921$	183045.	+	229531.i	0.00711065	+	0.00891647i
$922$	−1.16351e6	−	5.09766e6i	−0.0450756	−	0.197489i
$923$	1.23497e6	−	5.41078e6i	0.0477149	−	0.209053i
$924$	1.77616e6	+	2.22724e6i	0.0684388	+	0.0858195i
$925$	1.96569e7	+	2.46490e7i	0.755371	+	0.947205i
$926$	−9.95513e6	+	4.36163e7i	−0.381522	+	1.67156i
$927$	−6.41247e6	−	2.80949e7i	−0.245090	−	1.07381i
$928$	−3.10020e7	−	3.88753e7i	−1.18174	−	1.48185i
$929$	−1.57469e7	+	7.58332e6i	−0.598627	+	0.288284i	−0.708555	−	0.705656i	$-0.750652\pi$
$929$	−1.57469e7	+	7.58332e6i	−0.598627	+	0.288284i	0.109927	+	0.993940i	$0.464938\pi$
$930$	40602.7	−	19553.2i	0.00153938	−	0.000741328i
$931$	−8.99932e6	−	3.94286e7i	−0.340279	−	1.49086i
$932$	2.28875e7	−	2.87000e7i	0.863094	−	1.08229i
$933$	1.06196e6	+	511412.i	0.0399396	+	0.0192339i
$934$	−7.41485e6	+	9.29793e6i	−0.278122	+	0.348754i
$935$	−318561.	+	1.39571e6i	−0.0119169	+	0.0522114i
$936$	−5.74863e6	+	2.76839e6i	−0.214474	+	0.103285i
$937$	4.64469e6	−	2.03497e7i	0.172826	−	0.757198i	−0.812001	−	0.583656i	$-0.801622\pi$
$937$	4.64469e6	−	2.03497e7i	0.172826	−	0.757198i	0.984826	−	0.173542i	$-0.0555212\pi$
$938$	−4.83205e7	−	2.32699e7i	−1.79318	−	0.863550i
$939$	−1.85051e6			−0.0684901
$940$	41971.8			0.00154931
$941$	3.37767e7	+	1.62660e7i	1.24349	+	0.598834i	0.935759	−	0.352639i	$-0.114716\pi$
$941$	3.37767e7	+	1.62660e7i	1.24349	+	0.598834i	0.307732	+	0.951473i	$0.400430\pi$
$942$	−874524.	−	3.83154e6i	−0.0321103	−	0.140684i
$943$	−9.79017e6	−	1.22765e7i	−0.358518	−	0.449568i
$944$	−1.85729e7	+	2.32897e7i	−0.678343	+	0.850615i
$945$	−650032.			−0.0236786
$946$	1.20959e7	−	2.34905e7i	0.439451	−	0.853424i
$947$	1.86842e7			0.677018			0.338509	−	0.940963i	$-0.390077\pi$
$947$	1.86842e7			0.677018			0.338509	+	0.940963i	$0.390077\pi$
$948$	2.03872e6	−	2.55648e6i	0.0736779	−	0.0923892i
$949$	3.33050e7	+	4.17631e7i	1.20045	+	1.50532i
$950$	−1.55688e7	−	6.82114e7i	−0.559688	−	2.45216i
$951$	4.99187e6	+	2.40396e6i	0.178983	+	0.0861937i
$952$	−6.47765e6			−0.231646
$953$	−4.98006e7			−1.77624			−0.888121	−	0.459609i	$-0.847990\pi$
$953$	−4.98006e7			−1.77624			−0.888121	+	0.459609i	$0.847990\pi$
$954$	−3.84475e7	−	1.85154e7i	−1.36772	−	0.658660i
$955$	−296634.	+	1.29964e6i	−0.0105248	+	0.0461120i
$956$	−6.98488e6	+	3.36374e6i	−0.247181	+	0.119036i
$957$	−801349.	+	3.51094e6i	−0.0282841	+	0.123921i
$958$	4.24312e6	−	5.32070e6i	0.149373	−	0.187307i
$959$	3.80366e7	+	1.83175e7i	1.33553	+	0.643159i
$960$	120910.	−	151616.i	0.00423431	−	0.00530966i
$961$	6.24417e6	+	2.73575e7i	0.218105	+	0.955582i
$962$	6.94636e7	−	3.34519e7i	2.42002	−	1.16542i
$963$	9.82892e6	−	4.73336e6i	0.341539	−	0.164476i
$964$	6.17900e6	+	7.74822e6i	0.214154	+	0.268540i
$965$	91705.9	+	401790.i	0.00317015	+	0.0138893i
$966$	992273.	−	4.34743e6i	0.0342128	−	0.149896i
$967$	−1.60953e7	−	2.01829e7i	−0.553521	−	0.694093i	0.423825	−	0.905744i	$-0.360687\pi$
$967$	−1.60953e7	−	2.01829e7i	−0.553521	−	0.694093i	−0.977345	+	0.211651i	$0.932116\pi$
$968$	−1.40550e6	−	1.76244e6i	−0.0482106	−	0.0604542i
$969$	−1.76909e6	+	7.75090e6i	−0.0605259	+	0.265181i
$970$	341691.	+	1.49705e6i	0.0116602	+	0.0510865i
$971$	−3.11330e7	−	3.90395e7i	−1.05967	−	1.32879i	−0.941954	−	0.335743i	$-0.891013\pi$
$971$	−3.11330e7	−	3.90395e7i	−1.05967	−	1.32879i	−0.117720	−	0.993047i	$-0.537559\pi$
$972$	−9.03851e6	+	4.35272e6i	−0.306854	+	0.147773i
$973$	4.36434e7	−	2.10175e7i	1.47787	−	0.711705i
$974$	−2.02920e6	−	8.89052e6i	−0.0685375	−	0.300282i
$975$	3.85820e6	−	4.83803e6i	0.129979	−	0.162989i
$976$	−1.46190e7	−	7.04013e6i	−0.491239	−	0.236568i
$977$	−2.17825e7	+	2.73145e7i	−0.730083	+	0.915495i	−0.998861	−	0.0477068i	$-0.984809\pi$
$977$	−2.17825e7	+	2.73145e7i	−0.730083	+	0.915495i	0.268778	+	0.963202i	$0.413380\pi$
$978$	−453306.	+	1.98606e6i	−0.0151546	+	0.0663967i
$979$	−1.63399e7	+	7.86890e6i	−0.544871	+	0.262396i
$980$	335102.	−	1.46818e6i	0.0111458	−	0.0488330i
$981$	3.26750e6	+	1.57355e6i	0.108404	+	0.0522044i
$982$	−3.57803e7			−1.18404
$983$	−4.58447e7			−1.51323			−0.756616	−	0.653859i	$-0.773149\pi$
$983$	−4.58447e7			−1.51323			−0.756616	+	0.653859i	$0.773149\pi$
$984$	−489106.	−	235541.i	−0.0161033	−	0.00775494i
$985$	−598588.	−	2.62258e6i	−0.0196579	−	0.0861269i
$986$	4.14222e7	+	5.19418e7i	1.35688	+	1.70147i
$987$	86727.8	−	108753.i	0.00283377	−	0.00355344i
$988$	−8.05832e7			−2.62635
$989$	−1.90997e7	+	3.82560e6i	−0.620921	+	0.124368i
$990$	1.96755e6			0.0638026
$991$	3.13404e7	−	3.92997e7i	1.01373	−	1.27117i	0.0515719	−	0.998669i	$-0.483577\pi$
$991$	3.13404e7	−	3.92997e7i	1.01373	−	1.27117i	0.962155	−	0.272504i	$-0.0878517\pi$
$992$	−3.69759e6	−	4.63663e6i	−0.119300	−	0.149597i
$993$	468613.	+	2.05313e6i	0.0150814	+	0.0660759i
$994$	−6.97693e6	−	3.35991e6i	−0.223974	−	0.107860i
$995$	210736.			0.00674809
$996$	7.08132e6			0.226186
$997$	−2.06535e6	−	994620.i	−0.0658045	−	0.0316898i	0.400692	−	0.916213i	$-0.368770\pi$
$997$	−2.06535e6	−	994620.i	−0.0658045	−	0.0316898i	−0.466497	+	0.884523i	$0.654484\pi$
$998$	1.01272e7	−	4.43703e7i	0.321858	−	1.41015i
$999$	−8.94890e6	+	4.30956e6i	−0.283698	+	0.136622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.4.4	✓	108
43.11	even	7	inner	43.6.e.a.11.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.4	✓	108	1.1	even	1	trivial
43.6.e.a.11.4	yes	108	43.11	even	7	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.84915 + 6.08065i) q^{2} +(1.26806 + 1.59010i) q^{3} +(-6.33931 - 27.7743i) q^{4} +(3.40560 + 1.64005i) q^{5} -15.8178 q^{6} -175.475 q^{7} +(-24.6053 - 11.8493i) q^{8} +(53.1522 - 232.875i) q^{9} +O(q^{10})\)	\(q+(-4.84915 + 6.08065i) q^{2} +(1.26806 + 1.59010i) q^{3} +(-6.33931 - 27.7743i) q^{4} +(3.40560 + 1.64005i) q^{5} -15.8178 q^{6} -175.475 q^{7} +(-24.6053 - 11.8493i) q^{8} +(53.1522 - 232.875i) q^{9} +(-26.4869 + 12.7554i) q^{10} +(62.3486 - 273.167i) q^{11} +(36.1252 - 45.2996i) q^{12} +(881.242 + 424.384i) q^{13} +(850.907 - 1067.00i) q^{14} +(1.71067 + 7.49492i) q^{15} +(1012.72 - 487.701i) q^{16} +(-1217.84 + 586.483i) q^{17} +(1158.29 + 1452.45i) q^{18} +(-643.515 - 2819.42i) q^{19} +(23.9622 - 104.985i) q^{20} +(-222.513 - 279.023i) q^{21} +(1358.69 + 1703.75i) q^{22} +(357.493 - 1566.28i) q^{23} +(-12.3595 - 54.1504i) q^{24} +(-1939.50 - 2432.05i) q^{25} +(-6853.81 + 3300.62i) q^{26} +(882.966 - 425.214i) q^{27} +(1112.39 + 4873.71i) q^{28} +(-3940.17 + 4940.81i) q^{29} +(-53.8692 - 25.9420i) q^{30} +(-469.941 + 589.287i) q^{31} +(-1750.84 + 7670.93i) q^{32} +(513.423 - 247.252i) q^{33} +(2339.32 - 10249.2i) q^{34} +(-597.599 - 287.789i) q^{35} -6804.89 q^{36} -10135.0 q^{37} +(20264.4 + 9758.84i) q^{38} +(442.656 + 1939.40i) q^{39} +(-64.3625 - 80.7080i) q^{40} +(6093.87 - 7641.47i) q^{41} +2775.64 q^{42} +(-4966.99 - 11060.6i) q^{43} -7982.27 q^{44} +(562.942 - 705.907i) q^{45} +(7790.46 + 9768.93i) q^{46} +(86.7308 + 379.992i) q^{47} +(2059.68 + 991.890i) q^{48} +13984.6 q^{49} +24193.4 q^{50} +(-2476.86 - 1192.79i) q^{51} +(6200.51 - 27166.2i) q^{52} +(-20695.8 + 9966.56i) q^{53} +(-1696.06 + 7430.93i) q^{54} +(660.342 - 828.043i) q^{55} +(4317.63 + 2079.26i) q^{56} +(3667.14 - 4598.45i) q^{57} +(-10936.9 - 47917.5i) q^{58} +(-23877.0 + 11498.6i) q^{59} +(197.322 - 95.0251i) q^{60} +(-9000.30 - 11286.0i) q^{61} +(-1304.43 - 5715.09i) q^{62} +(-9326.90 + 40863.8i) q^{63} +(-15727.7 - 19722.0i) q^{64} +(2305.15 + 2890.57i) q^{65} +(-986.219 + 4320.91i) q^{66} +(-8744.59 - 38312.5i) q^{67} +(24009.4 + 30106.9i) q^{68} +(2943.86 - 1417.69i) q^{69} +(4647.79 - 2238.26i) q^{70} +(-1262.62 - 5531.90i) q^{71} +(-4067.23 + 5100.14i) q^{72} +(49204.4 + 23695.6i) q^{73} +(49146.4 - 61627.6i) q^{74} +(1407.80 - 6167.97i) q^{75} +(-74228.1 + 35746.4i) q^{76} +(-10940.6 + 47934.1i) q^{77} +(-13939.3 - 6712.83i) q^{78} +56434.9 q^{79} +4248.78 q^{80} +(-50499.9 - 24319.5i) q^{81} +(16915.0 + 74109.3i) q^{82} +(76201.3 + 95553.4i) q^{83} +(-6339.08 + 7948.96i) q^{84} -5109.35 q^{85} +(91341.5 + 23432.2i) q^{86} -12852.7 q^{87} +(-4770.94 + 5982.57i) q^{88} +(-40356.6 - 50605.5i) q^{89} +(1562.58 + 6846.10i) q^{90} +(-154636. - 74468.9i) q^{91} -45768.6 q^{92} -1532.94 q^{93} +(-2731.17 - 1315.26i) q^{94} +(2432.44 - 10657.2i) q^{95} +(-14417.7 + 6943.19i) q^{96} +(11622.9 - 50923.1i) q^{97} +(-67813.6 + 85035.6i) q^{98} +(-60299.7 - 29038.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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