LMFDB - Embedded newform 33.5.h.a.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(5,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("33.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.h (of order $10$, degree $4$, 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:	$3.41120878177$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.4
Character	$\chi$	$=$	33.14
Dual form			33.5.h.a.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72011 - 3.74391i) q^{2} +(1.23934 + 8.91426i) q^{3} +(-1.67360 + 5.15080i) q^{4} +(15.2071 - 20.9308i) q^{5} +(30.0031 - 28.8877i) q^{6} +(20.6582 - 63.5795i) q^{7} +(-46.5832 + 15.1358i) q^{8} +(-77.9281 + 22.0955i) q^{9} +O(q^{10})$	\(q+(-2.72011 - 3.74391i) q^{2} +(1.23934 + 8.91426i) q^{3} +(-1.67360 + 5.15080i) q^{4} +(15.2071 - 20.9308i) q^{5} +(30.0031 - 28.8877i) q^{6} +(20.6582 - 63.5795i) q^{7} +(-46.5832 + 15.1358i) q^{8} +(-77.9281 + 22.0955i) q^{9} -119.728 q^{10} +(61.9218 - 103.955i) q^{11} +(-47.9897 - 8.53531i) q^{12} +(166.912 - 121.268i) q^{13} +(-294.229 + 95.6007i) q^{14} +(205.429 + 109.620i) q^{15} +(253.483 + 184.166i) q^{16} +(-113.636 + 156.407i) q^{17} +(294.697 + 231.654i) q^{18} +(-31.8996 - 98.1768i) q^{19} +(82.3597 + 113.358i) q^{20} +(592.367 + 105.357i) q^{21} +(-557.633 + 50.9399i) q^{22} +730.547i q^{23} +(-192.657 - 396.496i) q^{24} +(-13.7056 - 42.1814i) q^{25} +(-908.036 - 295.039i) q^{26} +(-293.544 - 667.288i) q^{27} +(292.912 + 212.813i) q^{28} +(334.143 + 108.570i) q^{29} +(-148.383 - 1067.29i) q^{30} +(-895.122 + 650.344i) q^{31} -666.283i q^{32} +(1003.43 + 423.152i) q^{33} +894.678 q^{34} +(-1016.62 - 1399.25i) q^{35} +(16.6106 - 438.371i) q^{36} +(56.4081 - 173.606i) q^{37} +(-280.795 + 386.481i) q^{38} +(1287.88 + 1337.60i) q^{39} +(-391.591 + 1205.19i) q^{40} +(3047.40 - 990.160i) q^{41} +(-1216.86 - 2504.35i) q^{42} -698.764 q^{43} +(431.821 + 492.926i) q^{44} +(-722.583 + 1967.10i) q^{45} +(2735.10 - 1987.17i) q^{46} +(-1506.37 + 489.448i) q^{47} +(-1327.56 + 2487.86i) q^{48} +(-1673.14 - 1215.61i) q^{49} +(-120.643 + 166.050i) q^{50} +(-1535.09 - 819.143i) q^{51} +(345.287 + 1062.68i) q^{52} +(526.645 + 724.865i) q^{53} +(-1699.79 + 2914.10i) q^{54} +(-1234.21 - 2876.93i) q^{55} +3274.42i q^{56} +(835.639 - 406.035i) q^{57} +(-502.431 - 1546.32i) q^{58} +(2311.85 + 751.164i) q^{59} +(-908.435 + 874.665i) q^{60} +(604.686 + 439.330i) q^{61} +(4869.66 + 1582.25i) q^{62} +(-205.035 + 5411.09i) q^{63} +(1561.22 - 1134.30i) q^{64} -5337.73i q^{65} +(-1145.19 - 4907.76i) q^{66} +5964.99 q^{67} +(-615.440 - 847.081i) q^{68} +(-6512.28 + 905.392i) q^{69} +(-2473.37 + 7612.24i) q^{70} +(-115.354 + 158.772i) q^{71} +(3295.71 - 2208.78i) q^{72} +(-1553.59 + 4781.45i) q^{73} +(-803.403 + 261.042i) q^{74} +(359.030 - 174.452i) q^{75} +559.076 q^{76} +(-5330.23 - 6084.49i) q^{77} +(1504.69 - 8460.12i) q^{78} +(1537.02 - 1116.71i) q^{79} +(7709.48 - 2504.96i) q^{80} +(5584.58 - 3443.72i) q^{81} +(-11996.3 - 8715.85i) q^{82} +(-3866.50 + 5321.79i) q^{83} +(-1534.05 + 2874.84i) q^{84} +(1545.64 + 4756.99i) q^{85} +(1900.71 + 2616.11i) q^{86} +(-553.703 + 3113.20i) q^{87} +(-1311.07 + 5779.80i) q^{88} -10560.3i q^{89} +(9330.16 - 2645.45i) q^{90} +(-4262.09 - 13117.4i) q^{91} +(-3762.90 - 1222.64i) q^{92} +(-6906.69 - 7173.35i) q^{93} +(5929.93 + 4308.35i) q^{94} +(-2540.01 - 825.301i) q^{95} +(5939.42 - 825.748i) q^{96} +(-651.688 + 473.479i) q^{97} +9570.70i q^{98} +(-2528.50 + 9469.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9}+O(q^{10}) $ 56 * q + 90 * q^4 - 83 * q^6 - 86 * q^7 + 232 * q^9	$ 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9} + 136 q^{10} - 710 q^{12} + 94 q^{13} - 406 q^{15} + 334 q^{16} + 1149 q^{18} + 958 q^{19} - 728 q^{21} - 1300 q^{22} + 795 q^{24} - 1740 q^{25} - 1026 q^{27} - 4962 q^{28} - 744 q^{30} - 130 q^{31} - 2875 q^{33} + 4844 q^{34} + 11631 q^{36} + 2802 q^{37} + 8696 q^{39} - 626 q^{40} + 8804 q^{42} - 980 q^{43} - 17356 q^{45} + 8698 q^{46} - 17854 q^{48} + 7516 q^{49} + 1461 q^{51} + 11818 q^{52} - 9082 q^{54} - 4916 q^{55} - 2661 q^{57} - 38922 q^{58} - 28194 q^{60} - 15150 q^{61} - 488 q^{63} - 30690 q^{64} + 20100 q^{66} + 40544 q^{67} + 25662 q^{69} + 15720 q^{70} + 72430 q^{72} - 20554 q^{73} + 28841 q^{75} + 70996 q^{76} - 39716 q^{78} + 46458 q^{79} - 24284 q^{81} + 26200 q^{82} - 8346 q^{84} - 15494 q^{85} - 66228 q^{87} - 78050 q^{88} - 43484 q^{90} - 49854 q^{91} - 30184 q^{93} - 119550 q^{94} + 50098 q^{96} - 64476 q^{97} + 52640 q^{99}+O(q^{100}) $ 56 * q + 90 * q^4 - 83 * q^6 - 86 * q^7 + 232 * q^9 + 136 * q^10 - 710 * q^12 + 94 * q^13 - 406 * q^15 + 334 * q^16 + 1149 * q^18 + 958 * q^19 - 728 * q^21 - 1300 * q^22 + 795 * q^24 - 1740 * q^25 - 1026 * q^27 - 4962 * q^28 - 744 * q^30 - 130 * q^31 - 2875 * q^33 + 4844 * q^34 + 11631 * q^36 + 2802 * q^37 + 8696 * q^39 - 626 * q^40 + 8804 * q^42 - 980 * q^43 - 17356 * q^45 + 8698 * q^46 - 17854 * q^48 + 7516 * q^49 + 1461 * q^51 + 11818 * q^52 - 9082 * q^54 - 4916 * q^55 - 2661 * q^57 - 38922 * q^58 - 28194 * q^60 - 15150 * q^61 - 488 * q^63 - 30690 * q^64 + 20100 * q^66 + 40544 * q^67 + 25662 * q^69 + 15720 * q^70 + 72430 * q^72 - 20554 * q^73 + 28841 * q^75 + 70996 * q^76 - 39716 * q^78 + 46458 * q^79 - 24284 * q^81 + 26200 * q^82 - 8346 * q^84 - 15494 * q^85 - 66228 * q^87 - 78050 * q^88 - 43484 * q^90 - 49854 * q^91 - 30184 * q^93 - 119550 * q^94 + 50098 * q^96 - 64476 * q^97 + 52640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.72011	−	3.74391i	−0.680028	−	0.935978i	0.319907	−	0.947449i	$-0.396348\pi$
$2$	−2.72011	−	3.74391i	−0.680028	−	0.935978i	−0.999934	+	0.0114713i	$0.996348\pi$
$3$	1.23934	+	8.91426i	0.137704	+	0.990473i
$3$	1.23934	+	8.91426i	0.137704	+	0.990473i
$4$	−1.67360	+	5.15080i	−0.104600	+	0.321925i
$5$	15.2071	−	20.9308i	0.608283	−	0.837230i	−0.388151	−	0.921596i	$-0.626886\pi$
$5$	15.2071	−	20.9308i	0.608283	−	0.837230i	0.996435	+	0.0843653i	$0.0268863\pi$
$6$	30.0031	−	28.8877i	0.833419	−	0.802437i
$7$	20.6582	−	63.5795i	0.421597	−	1.29754i	−0.484619	−	0.874725i	$-0.661042\pi$
$7$	20.6582	−	63.5795i	0.421597	−	1.29754i	0.906216	−	0.422816i	$-0.138958\pi$
$8$	−46.5832	+	15.1358i	−0.727862	+	0.236497i
$9$	−77.9281	+	22.0955i	−0.962075	+	0.272784i
$10$	−119.728			−1.19728
$11$	61.9218	−	103.955i	0.511751	−	0.859134i
$11$	61.9218	−	103.955i	0.511751	−	0.859134i
$12$	−47.9897	−	8.53531i	−0.333262	−	0.0592730i
$13$	166.912	−	121.268i	0.987643	−	0.717565i	0.0282392	−	0.999601i	$-0.491010\pi$
$13$	166.912	−	121.268i	0.987643	−	0.717565i	0.959404	+	0.282037i	$0.0910100\pi$
$14$	−294.229	+	95.6007i	−1.50117	+	0.487759i
$15$	205.429	+	109.620i	0.913017	+	0.487199i
$16$	253.483	+	184.166i	0.990168	+	0.719399i
$17$	−113.636	+	156.407i	−0.393205	+	0.541201i	−0.959022	−	0.283330i	$-0.908561\pi$
$17$	−113.636	+	156.407i	−0.393205	+	0.541201i	0.565817	+	0.824531i	$0.308561\pi$
$18$	294.697	+	231.654i	0.909558	+	0.714980i
$19$	−31.8996	−	98.1768i	−0.0883645	−	0.271958i	0.897103	−	0.441821i	$-0.145667\pi$
$19$	−31.8996	−	98.1768i	−0.0883645	−	0.271958i	−0.985468	+	0.169863i	$0.945667\pi$
$20$	82.3597	+	113.358i	0.205899	+	0.283396i
$21$	592.367	+	105.357i	1.34324	+	0.238904i
$22$	−557.633	+	50.9399i	−1.15213	+	0.105248i
$23$			730.547i			1.38100i	0.723334	+	0.690498i	$0.242609\pi$
$23$			730.547i			1.38100i	−0.723334	+	0.690498i	$0.757391\pi$
$24$	−192.657	−	396.496i	−0.334473	−	0.688362i
$25$	−13.7056	−	42.1814i	−0.0219289	−	0.0674902i
$26$	−908.036	−	295.039i	−1.34325	−	0.436448i
$27$	−293.544	−	667.288i	−0.402667	−	0.915347i
$28$	292.912	+	212.813i	0.373612	+	0.271445i
$29$	334.143	+	108.570i	0.397317	+	0.129096i	0.500859	−	0.865529i	$-0.333018\pi$
$29$	334.143	+	108.570i	0.397317	+	0.129096i	−0.103542	+	0.994625i	$0.533018\pi$
$30$	−148.383	−	1067.29i	−0.164870	−	1.18587i
$31$	−895.122	+	650.344i	−0.931448	+	0.676737i	−0.946347	−	0.323152i	$-0.895257\pi$
$31$	−895.122	+	650.344i	−0.931448	+	0.676737i	0.0148989	+	0.999889i	$0.495257\pi$
$32$		−	666.283i		−	0.650667i
$33$	1003.43	+	423.152i	0.921420	+	0.388569i
$34$	894.678			0.773942
$35$	−1016.62	−	1399.25i	−0.829891	−	1.14225i
$36$	16.6106	−	438.371i	0.0128168	−	0.338249i
$37$	56.4081	−	173.606i	0.0412039	−	0.126813i	−0.928339	−	0.371736i	$-0.878763\pi$
$37$	56.4081	−	173.606i	0.0412039	−	0.126813i	0.969542	+	0.244923i	$0.0787627\pi$
$38$	−280.795	+	386.481i	−0.194456	+	0.267646i
$39$	1287.88	+	1337.60i	0.846731	+	0.879423i
$40$	−391.591	+	1205.19i	−0.244744	+	0.753246i
$41$	3047.40	−	990.160i	1.81285	−	0.589030i	0.812871	−	0.582444i	$-0.197903\pi$
$41$	3047.40	−	990.160i	1.81285	−	0.589030i	0.999978	−	0.00658683i	$-0.00209667\pi$
$42$	−1216.86	−	2504.35i	−0.689829	−	1.41970i
$43$	−698.764			−0.377914			−0.188957	−	0.981985i	$-0.560511\pi$
$43$	−698.764			−0.377914			−0.188957	+	0.981985i	$0.560511\pi$
$44$	431.821	+	492.926i	0.223048	+	0.254611i
$45$	−722.583	+	1967.10i	−0.356831	+	0.971409i
$46$	2735.10	−	1987.17i	1.29258	−	0.939115i
$47$	−1506.37	+	489.448i	−0.681922	+	0.221570i	−0.629437	−	0.777052i	$-0.716714\pi$
$47$	−1506.37	+	489.448i	−0.681922	+	0.221570i	−0.0524856	+	0.998622i	$0.516714\pi$
$48$	−1327.56	+	2487.86i	−0.576196	+	1.07980i
$49$	−1673.14	−	1215.61i	−0.696853	−	0.506293i
$50$	−120.643	+	166.050i	−0.0482571	+	0.0664202i
$51$	−1535.09	−	819.143i	−0.590191	−	0.314934i
$52$	345.287	+	1062.68i	0.127695	+	0.393004i
$53$	526.645	+	724.865i	0.187485	+	0.258051i	0.892404	−	0.451236i	$-0.149017\pi$
$53$	526.645	+	724.865i	0.187485	+	0.258051i	−0.704919	+	0.709287i	$0.749017\pi$
$54$	−1699.79	+	2914.10i	−0.582919	+	0.999348i
$55$	−1234.21	−	2876.93i	−0.408004	−	0.951050i
$56$			3274.42i			1.04414i
$57$	835.639	−	406.035i	0.257199	−	0.124972i
$58$	−502.431	−	1546.32i	−0.149355	−	0.459668i
$59$	2311.85	+	751.164i	0.664132	+	0.215790i	0.621635	−	0.783307i	$-0.286469\pi$
$59$	2311.85	+	751.164i	0.664132	+	0.215790i	0.0424973	+	0.999097i	$0.486469\pi$
$60$	−908.435	+	874.665i	−0.252343	+	0.242962i
$61$	604.686	+	439.330i	0.162506	+	0.118068i	0.666066	−	0.745892i	$-0.267977\pi$
$61$	604.686	+	439.330i	0.162506	+	0.118068i	−0.503560	+	0.863960i	$0.667977\pi$
$62$	4869.66	+	1582.25i	1.26682	+	0.411615i
$63$	−205.035	+	5411.09i	−0.0516591	+	1.36334i
$64$	1561.22	−	1134.30i	0.381158	−	0.276928i
$65$		−	5337.73i		−	1.26337i
$66$	−1145.19	−	4907.76i	−0.262899	−	1.12667i
$67$	5964.99			1.32880			0.664401	−	0.747376i	$-0.268687\pi$
$67$	5964.99			1.32880			0.664401	+	0.747376i	$0.268687\pi$
$68$	−615.440	−	847.081i	−0.133097	−	0.183192i
$69$	−6512.28	+	905.392i	−1.36784	+	0.190169i
$70$	−2473.37	+	7612.24i	−0.504769	+	1.55352i
$71$	−115.354	+	158.772i	−0.0228832	+	0.0314961i	−0.820305	−	0.571926i	$-0.806196\pi$
$71$	−115.354	+	158.772i	−0.0228832	+	0.0314961i	0.797422	+	0.603422i	$0.206196\pi$
$72$	3295.71	−	2208.78i	0.635746	−	0.426077i
$73$	−1553.59	+	4781.45i	−0.291534	+	0.897251i	0.692829	+	0.721102i	$0.256364\pi$
$73$	−1553.59	+	4781.45i	−0.291534	+	0.897251i	−0.984364	+	0.176149i	$0.943636\pi$
$74$	−803.403	+	261.042i	−0.146714	+	0.0476701i
$75$	359.030	−	174.452i	0.0638276	−	0.0310137i
$76$	559.076			0.0967930
$77$	−5330.23	−	6084.49i	−0.899010	−	1.02623i
$78$	1504.69	−	8460.12i	0.247320	−	1.39055i
$79$	1537.02	−	1116.71i	0.246277	−	0.178931i	−0.457798	−	0.889056i	$-0.651362\pi$
$79$	1537.02	−	1116.71i	0.246277	−	0.178931i	0.704075	+	0.710125i	$0.251362\pi$
$80$	7709.48	−	2504.96i	1.20461	−	0.391400i
$81$	5584.58	−	3443.72i	0.851178	−	0.524878i
$82$	−11996.3	−	8715.85i	−1.78411	−	1.29623i
$83$	−3866.50	+	5321.79i	−0.561258	+	0.772505i	−0.991486	−	0.130215i	$-0.958433\pi$
$83$	−3866.50	+	5321.79i	−0.561258	+	0.772505i	0.430228	+	0.902720i	$0.358433\pi$
$84$	−1534.05	+	2874.84i	−0.217411	+	0.407432i
$85$	1545.64	+	4756.99i	0.213929	+	0.658407i
$86$	1900.71	+	2616.11i	0.256992	+	0.353719i
$87$	−553.703	+	3113.20i	−0.0731541	+	0.411309i
$88$	−1311.07	+	5779.80i	−0.169301	+	0.746359i
$89$		−	10560.3i		−	1.33320i	−0.745416	−	0.666599i	$-0.767749\pi$
$89$		−	10560.3i		−	1.33320i	0.745416	−	0.666599i	$-0.232251\pi$
$90$	9330.16	−	2645.45i	1.15187	−	0.326599i
$91$	−4262.09	−	13117.4i	−0.514683	−	1.58403i
$92$	−3762.90	−	1222.64i	−0.444577	−	0.144452i
$93$	−6906.69	−	7173.35i	−0.798554	−	0.829385i
$94$	5929.93	+	4308.35i	0.671111	+	0.487590i
$95$	−2540.01	−	825.301i	−0.281442	−	0.0914460i
$96$	5939.42	−	825.748i	0.644469	−	0.0895994i
$97$	−651.688	+	473.479i	−0.0692622	+	0.0503220i	−0.621878	−	0.783114i	$-0.713630\pi$
$97$	−651.688	+	473.479i	−0.0692622	+	0.0503220i	0.552615	+	0.833436i	$0.313630\pi$
$98$			9570.70i			0.996532i
$99$	−2528.50	+	9469.23i	−0.257984	+	0.966149i
$100$	240.206			0.0240206
$101$	−373.279	−	513.774i	−0.0365924	−	0.0503651i	0.790329	−	0.612683i	$-0.209910\pi$
$101$	−373.279	−	513.774i	−0.0365924	−	0.0503651i	−0.826921	+	0.562318i	$0.809910\pi$
$102$	1108.81	+	7975.39i	0.106575	+	0.766569i
$103$	−5893.16	+	18137.3i	−0.555487	+	1.70961i	0.139168	+	0.990269i	$0.455557\pi$
$103$	−5893.16	+	18137.3i	−0.555487	+	1.70961i	−0.694655	+	0.719343i	$0.744443\pi$
$104$	−5939.78	+	8175.41i	−0.549166	+	0.755863i
$105$	11213.4	−	10796.5i	1.01709	−	0.979277i
$106$	1281.30	−	3943.43i	0.114035	−	0.350964i
$107$	−19613.9	+	6372.93i	−1.71315	+	0.556636i	−0.990853	−	0.134946i	$-0.956914\pi$
$107$	−19613.9	+	6372.93i	−1.71315	+	0.556636i	−0.722298	+	0.691582i	$0.756914\pi$
$108$	3928.34	−	395.218i	0.336792	−	0.0338836i
$109$	8954.39			0.753673			0.376837	−	0.926280i	$-0.377012\pi$
$109$	8954.39			0.753673			0.376837	+	0.926280i	$0.377012\pi$
$110$	−7413.77	+	12446.3i	−0.612708	+	1.02862i
$111$	1617.48	+	287.680i	0.131278	+	0.0233488i
$112$	16945.7	−	12311.8i	1.35090	−	0.981488i
$113$	17127.7	−	5565.14i	1.34135	−	0.435832i	0.451579	−	0.892231i	$-0.350861\pi$
$113$	17127.7	−	5565.14i	1.34135	−	0.435832i	0.889775	+	0.456399i	$0.150861\pi$
$114$	−3793.19	−	2024.10i	−0.291874	−	0.155748i
$115$	15290.9	+	11109.5i	1.15621	+	0.840037i
$116$	−1118.44	+	1539.40i	−0.0831185	+	0.114403i
$117$	−10327.6	+	13138.2i	−0.754446	+	0.959764i
$118$	−3476.18	−	10698.6i	−0.249654	−	0.768356i
$119$	7596.76	+	10456.0i	0.536456	+	0.738369i
$120$	−11228.7	−	1997.11i	−0.779772	−	0.138688i
$121$	−6972.38	−	12874.2i	−0.476223	−	0.879325i
$122$		−	3458.92i		−	0.232392i
$123$	12603.3	+	25938.2i	0.833056	+	1.71447i
$124$	−1851.72	−	5699.01i	−0.120429	−	0.370643i
$125$	14287.2	+	4642.19i	0.914379	+	0.297100i
$126$	20816.3	−	13951.1i	1.31118	−	0.878755i
$127$	−11809.2	−	8579.85i	−0.732169	−	0.531952i	0.158080	−	0.987426i	$-0.449470\pi$
$127$	−11809.2	−	8579.85i	−0.732169	−	0.531952i	−0.890249	+	0.455475i	$0.849470\pi$
$128$	−18632.2	−	6053.96i	−1.13722	−	0.369504i
$129$	−866.003	−	6228.96i	−0.0520403	−	0.374314i
$130$	−19984.0	+	14519.2i	−1.18248	+	0.859125i
$131$		−	18331.5i		−	1.06821i	−0.845419	−	0.534104i	$-0.820649\pi$
$131$		−	18331.5i		−	1.06821i	0.845419	−	0.534104i	$-0.179351\pi$
$132$	−3858.90	+	4460.26i	−0.221470	+	0.255984i
$133$	−6901.02			−0.390131
$134$	−16225.4	−	22332.4i	−0.903623	−	1.24373i
$135$	−18430.8	−	4003.40i	−1.01129	−	0.219665i
$136$	2926.20	−	9005.92i	0.158207	−	0.486912i
$137$	−12636.1	+	17392.0i	−0.673241	+	0.926637i	−0.999828	−	0.0185302i	$-0.994101\pi$
$137$	−12636.1	+	17392.0i	−0.673241	+	0.926637i	0.326587	+	0.945167i	$0.394101\pi$
$138$	21103.8	+	21918.6i	1.10816	+	1.15095i
$139$	3676.92	−	11316.4i	0.190307	−	0.585704i	−0.809692	−	0.586854i	$-0.800366\pi$
$139$	3676.92	−	11316.4i	0.190307	−	0.585704i	0.999999	+	0.00115008i	$0.000366082\pi$
$140$	8908.68	−	2894.60i	0.454524	−	0.147684i
$141$	−6229.96	−	12821.6i	−0.313363	−	0.644915i
$142$	908.204			0.0450409
$143$	−2271.01	−	24860.5i	−0.111057	−	1.21573i
$144$	−23822.7	−	8750.88i	−1.14886	−	0.422014i
$145$	7353.79	−	5342.84i	0.349764	−	0.254119i
$146$	22127.3	−	7189.58i	1.03806	−	0.337286i
$147$	8762.68	−	16421.4i	0.405511	−	0.759933i
$148$	799.808	+	581.094i	0.0365142	+	0.0265291i
$149$	12499.9	−	17204.6i	0.563031	−	0.774946i	−0.428677	−	0.903458i	$-0.641020\pi$
$149$	12499.9	−	17204.6i	0.563031	−	0.774946i	0.991708	+	0.128512i	$0.0410200\pi$
$150$	−1629.73	−	869.648i	−0.0724326	−	0.0386510i
$151$	6932.75	+	21336.8i	0.304054	+	0.935784i	0.980028	+	0.198858i	$0.0637232\pi$
$151$	6932.75	+	21336.8i	0.304054	+	0.935784i	−0.675974	+	0.736926i	$0.736277\pi$
$152$	2971.97	+	4090.56i	0.128634	+	0.177050i
$153$	5399.57	−	14699.4i	0.230662	−	0.627936i
$154$	−8280.99	+	36506.4i	−0.349173	+	1.53931i
$155$			28625.4i			1.19148i
$156$	−9045.11	+	4395.00i	−0.371676	+	0.180597i
$157$	10341.3	+	31827.4i	0.419544	+	1.29122i	0.908123	+	0.418704i	$0.137516\pi$
$157$	10341.3	+	31827.4i	0.419544	+	1.29122i	−0.488579	+	0.872520i	$0.662484\pi$
$158$	−8361.71	−	2716.88i	−0.334951	−	0.108832i
$159$	−5808.95	+	5593.00i	−0.229775	+	0.221234i
$160$	−13945.8	−	10132.2i	−0.544758	−	0.395790i
$161$	46447.8	+	15091.8i	1.79190	+	0.582223i
$162$	−28083.7	−	11540.8i	−1.07010	−	0.439752i
$163$	8483.47	−	6163.60i	0.319299	−	0.231985i	−0.416577	−	0.909100i	$-0.636770\pi$
$163$	8483.47	−	6163.60i	0.319299	−	0.231985i	0.735876	+	0.677116i	$0.236770\pi$
$164$			17353.7i			0.645214i
$165$	24116.1	−	14567.6i	0.885806	−	0.535080i
$166$	30441.6			1.10472
$167$	2788.09	+	3837.47i	0.0999709	+	0.137598i	0.856072	−	0.516857i	$-0.172898\pi$
$167$	2788.09	+	3837.47i	0.0999709	+	0.137598i	−0.756101	+	0.654455i	$0.772898\pi$
$168$	−29189.0	+	4058.10i	−1.03419	+	0.143782i
$169$	4327.63	−	13319.1i	0.151523	−	0.466338i
$170$	13605.4	−	18726.3i	0.470776	−	0.647968i
$171$	4655.14	+	6945.89i	0.159199	+	0.237539i
$172$	1169.45	−	3599.19i	0.0395298	−	0.121660i
$173$	−5066.91	+	1646.34i	−0.169298	+	0.0550081i	−0.392439	−	0.919778i	$-0.628369\pi$
$173$	−5066.91	+	1646.34i	−0.169298	+	0.0550081i	0.223142	+	0.974786i	$0.428369\pi$
$174$	13161.7	−	6395.22i	0.434723	−	0.211231i
$175$	−2965.01			−0.0968165
$176$	34841.2	−	14947.0i	1.12478	−	0.482534i
$177$	−3830.92	+	21539.3i	−0.122280	+	0.687521i
$178$	−39536.7	+	28725.1i	−1.24784	+	0.906612i
$179$	−23437.4	+	7615.26i	−0.731481	+	0.237672i	−0.650994	−	0.759083i	$-0.725648\pi$
$179$	−23437.4	+	7615.26i	−0.731481	+	0.237672i	−0.0804869	+	0.996756i	$0.525648\pi$
$180$	−8922.84	−	7014.02i	−0.275396	−	0.216482i
$181$	−20475.0	−	14876.0i	−0.624982	−	0.454076i	0.229676	−	0.973267i	$-0.426233\pi$
$181$	−20475.0	−	14876.0i	−0.624982	−	0.454076i	−0.854658	+	0.519191i	$0.826233\pi$
$182$	−37516.9	+	51637.5i	−1.13262	+	1.55892i
$183$	−3166.90	+	5934.81i	−0.0945653	+	0.177217i
$184$	−11057.4	−	34031.2i	−0.326601	−	1.00517i
$185$	−2775.91	−	3820.71i	−0.0811077	−	0.111635i
$186$	−8069.43	+	45370.4i	−0.233248	+	1.31143i
$187$	9222.76	+	21498.1i	0.263741	+	0.614776i
$188$		−	8578.13i		−	0.242704i
$189$	−48489.9	+	4878.42i	−1.35746	+	0.136570i
$190$	3819.27	+	11754.5i	0.105797	+	0.325609i
$191$	−17271.3	−	5611.79i	−0.473433	−	0.153828i	0.0625756	−	0.998040i	$-0.480069\pi$
$191$	−17271.3	−	5611.79i	−0.473433	−	0.153828i	−0.536009	+	0.844213i	$0.680069\pi$
$192$	12046.3	+	12511.4i	0.326776	+	0.339393i
$193$	−52879.8	−	38419.4i	−1.41963	−	1.03142i	−0.991833	−	0.127546i	$-0.959290\pi$
$193$	−52879.8	−	38419.4i	−1.41963	−	1.03142i	−0.427797	−	0.903875i	$-0.640710\pi$
$194$	3545.33	+	1151.95i	0.0942005	+	0.0306076i
$195$	47581.9	−	6615.23i	1.25133	−	0.173971i
$196$	9061.54	−	6583.59i	0.235879	−	0.171376i
$197$		−	3.63532i		−	9.36722e-5i	−1.00000		4.68361e-5i	$-0.999985\pi$
$197$		−	3.63532i		−	9.36722e-5i	1.00000		4.68361e-5i	$-1.49084e-5\pi$
$198$	42329.8	−	16290.8i	1.07973	−	0.415540i
$199$	33490.8			0.845705			0.422852	−	0.906199i	$-0.361029\pi$
$199$	33490.8			0.845705			0.422852	+	0.906199i	$0.361029\pi$
$200$	1276.90	+	1757.50i	0.0319224	+	0.0439375i
$201$	7392.63	+	53173.5i	0.182981	+	1.31614i
$202$	−908.165	+	2795.05i	−0.0222568	+	0.0684993i
$203$	13805.6	−	19001.8i	0.335015	−	0.461108i
$204$	6788.36	−	6536.01i	0.163119	−	0.157055i
$205$	25617.3	−	78841.8i	0.609572	−	1.87607i
$206$	83934.4	−	27271.9i	1.97791	−	0.642660i
$207$	−16141.8	−	56930.1i	−0.376714	−	1.32862i
$208$	64642.8			1.49415
$209$	−12181.3	−	2763.16i	−0.278869	−	0.0632577i
$210$	−70922.8	−	12614.1i	−1.60823	−	0.286034i
$211$	−47025.1	+	34165.7i	−1.05624	+	0.767406i	−0.973390	−	0.229155i	$-0.926404\pi$
$211$	−47025.1	+	34165.7i	−1.05624	+	0.767406i	−0.0828544	+	0.996562i	$0.526404\pi$
$212$	−4615.03	+	1499.51i	−0.102684	+	0.0333640i
$213$	−1558.30	−	831.528i	−0.0343471	−	0.0183281i
$214$	77211.6	+	56097.5i	1.68599	+	1.22494i
$215$	−10626.2	+	14625.7i	−0.229879	+	0.316401i
$216$	23774.2	+	26641.4i	0.509563	+	0.571017i
$217$	22856.9	+	70346.4i	0.485398	+	1.49390i
$218$	−24356.9	−	33524.4i	−0.512519	−	0.705421i
$219$	−44548.5	−	7923.26i	−0.928848	−	0.165202i
$220$	16884.1	−	1542.36i	0.348844	−	0.0318670i
$221$			39886.7i			0.816663i
$222$	−3322.68	−	6838.23i	−0.0674190	−	0.138752i
$223$	−24064.4	−	74062.8i	−0.483912	−	1.48933i	−0.833551	−	0.552443i	$-0.813696\pi$
$223$	−24064.4	−	74062.8i	−0.483912	−	1.48933i	0.349639	−	0.936884i	$-0.386304\pi$
$224$	−42362.0	−	13764.2i	−0.844268	−	0.274319i
$225$	2000.07	+	2984.28i	0.0395075	+	0.0589488i
$226$	−67424.8	−	48987.0i	−1.32009	−	0.959099i
$227$	−45710.8	−	14852.3i	−0.887088	−	0.288232i	−0.170191	−	0.985411i	$-0.554438\pi$
$227$	−45710.8	−	14852.3i	−0.887088	−	0.288232i	−0.716897	+	0.697179i	$0.754438\pi$
$228$	692.883	+	4983.75i	0.0133288	+	0.0958709i
$229$	−19904.5	+	14461.4i	−0.379559	+	0.275766i	−0.761164	−	0.648560i	$-0.775372\pi$
$229$	−19904.5	+	14461.4i	−0.379559	+	0.275766i	0.381604	+	0.924326i	$0.375372\pi$
$230$		−	87466.8i		−	1.65344i
$231$	47632.8	−	55055.8i	0.892652	−	1.03176i
$232$	−17208.8			−0.319723
$233$	1893.87	+	2606.69i	0.0348850	+	0.0480151i	0.826103	−	0.563519i	$-0.190553\pi$
$233$	1893.87	+	2606.69i	0.0348850	+	0.0480151i	−0.791218	+	0.611534i	$0.790553\pi$
$234$	77280.6	+	2928.29i	1.41136	+	0.0534788i
$235$	−12662.9	+	38972.5i	−0.229297	+	0.705703i
$236$	−7738.19	+	10650.7i	−0.138936	+	0.191229i
$237$	11859.5	+	12317.4i	0.211140	+	0.219292i
$238$	18482.5	−	56883.2i	0.326292	−	1.00422i
$239$	−48896.0	+	15887.3i	−0.856007	+	0.278133i	−0.703960	−	0.710240i	$-0.748586\pi$
$239$	−48896.0	+	15887.3i	−0.856007	+	0.278133i	−0.152047	+	0.988373i	$0.548586\pi$
$240$	31884.5	+	65619.8i	0.553550	+	1.13923i
$241$	−40333.6			−0.694438			−0.347219	−	0.937784i	$-0.612874\pi$
$241$	−40333.6			−0.694438			−0.347219	+	0.937784i	$0.612874\pi$
$242$	−29234.2	+	61123.2i	−0.499184	+	1.04370i
$243$	37619.4	+	45514.4i	0.637088	+	0.770791i
$244$	−3274.90	+	2379.36i	−0.0550071	+	0.0399650i
$245$	−50887.3	+	16534.3i	−0.847768	+	0.275457i
$246$	62827.9	−	117740.i	1.03820	−	1.94561i
$247$	−17230.2	−	12518.4i	−0.282420	−	0.205190i
$248$	31854.1	−	43843.5i	0.517920	−	0.712856i
$249$	−52231.7	−	27871.5i	−0.842433	−	0.449534i
$250$	−21482.8	−	66117.2i	−0.343724	−	1.05788i
$251$	4833.17	+	6652.29i	0.0767158	+	0.105590i	0.845650	−	0.533737i	$-0.179213\pi$
$251$	4833.17	+	6652.29i	0.0767158	+	0.105590i	−0.768935	+	0.639327i	$0.779213\pi$
$252$	−27528.3	−	10112.1i	−0.433489	−	0.159235i
$253$	75944.2	+	45236.8i	1.18646	+	0.706725i
$254$			67550.6i			1.04704i
$255$	−40489.5	+	19673.7i	−0.622676	+	0.302557i
$256$	18474.7	+	56859.4i	0.281902	+	0.867605i
$257$	75395.9	+	24497.6i	1.14151	+	0.370901i	0.817941	−	0.575302i	$-0.195116\pi$
$257$	75395.9	+	24497.6i	1.14151	+	0.370901i	0.323574	+	0.946203i	$0.395116\pi$
$258$	−20965.1	+	20185.7i	−0.314961	+	0.303253i
$259$	−9872.52	−	7172.81i	−0.147173	−	0.106928i
$260$	27493.6	+	8933.20i	0.406710	+	0.132148i
$261$	−28438.1	−	1077.56i	−0.417464	−	0.0158184i
$262$	−68631.6	+	49863.8i	−0.999820	+	0.726412i
$263$			68905.2i			0.996186i	0.867124	+	0.498093i	$0.165966\pi$
$263$			68905.2i			0.996186i	−0.867124	+	0.498093i	$0.834034\pi$
$264$	−53147.5	−	4524.11i	−0.762562	−	0.0649121i
$265$	23180.7			0.330092
$266$	18771.5	+	25836.8i	0.265300	+	0.365154i
$267$	94137.0	−	13087.7i	1.32050	−	0.183587i
$268$	−9983.00	+	30724.5i	−0.138993	+	0.427775i
$269$	−15311.0	+	21073.8i	−0.211592	+	0.291232i	−0.901601	−	0.432570i	$-0.857607\pi$
$269$	−15311.0	+	21073.8i	−0.211592	+	0.291232i	0.690008	+	0.723802i	$0.257607\pi$
$270$	35145.4	+	79892.9i	0.482105	+	1.09592i
$271$	−16550.9	+	50938.3i	−0.225363	+	0.693595i	0.772892	+	0.634538i	$0.218810\pi$
$271$	−16550.9	+	50938.3i	−0.225363	+	0.693595i	−0.998255	+	0.0590574i	$0.981190\pi$
$272$	−57609.8	+	18718.6i	−0.778679	+	0.253008i
$273$	111649.	−	54250.2i	1.49807	−	0.727907i
$274$	99485.8			1.32513
$275$	−5233.65	−	1187.18i	−0.0692053	−	0.0156983i
$276$	6235.44	−	35058.8i	0.0818557	−	0.460234i
$277$	21044.0	−	15289.3i	0.274263	−	0.199264i	−0.442148	−	0.896942i	$-0.645783\pi$
$277$	21044.0	−	15289.3i	0.274263	−	0.199264i	0.716411	+	0.697678i	$0.245783\pi$
$278$	−52369.2	+	17015.8i	−0.677620	+	0.220172i
$279$	55385.4	−	70458.2i	0.711520	−	0.905156i
$280$	68536.0	+	49794.3i	0.874184	+	0.635132i
$281$	10459.6	−	14396.4i	0.132465	−	0.182323i	−0.737632	−	0.675203i	$-0.764056\pi$
$281$	10459.6	−	14396.4i	0.132465	−	0.182323i	0.870097	+	0.492880i	$0.164056\pi$
$282$	−31056.6	+	58200.5i	−0.390531	+	0.731860i
$283$	−27772.2	−	85474.2i	−0.346767	−	1.06724i	−0.960631	−	0.277828i	$-0.910386\pi$
$283$	−27772.2	−	85474.2i	−0.346767	−	1.06724i	0.613864	−	0.789412i	$-0.289614\pi$
$284$	−624.745	−	859.888i	−0.00774580	−	0.0106612i
$285$	4209.02	−	23665.2i	0.0518192	−	0.291353i
$286$	−86898.1	+	76125.8i	−1.06238	+	0.930678i
$287$		−	214207.i		−	2.60058i
$288$	14721.9	+	51922.2i	0.177492	+	0.625991i
$289$	14259.5	+	43886.1i	0.170729	+	0.525450i
$290$	−40006.3	−	12998.8i	−0.475699	−	0.154564i
$291$	−5028.38	−	5222.52i	−0.0593802	−	0.0616729i
$292$	−22028.2	−	16004.4i	−0.258353	−	0.187705i
$293$	−36783.0	−	11951.5i	−0.428462	−	0.139216i	0.0868443	−	0.996222i	$-0.472322\pi$
$293$	−36783.0	−	11951.5i	−0.428462	−	0.139216i	−0.515306	+	0.857006i	$0.672322\pi$
$294$	−85315.7	+	11861.3i	−0.987039	+	0.137226i
$295$	50878.9	−	36965.7i	0.584647	−	0.424771i
$296$			8940.92i			0.102047i
$297$	−87544.8	−	10804.2i	−0.992470	−	0.122484i
$298$	−98413.4			−1.10821
$299$	88592.2	+	121937.i	0.990954	+	1.36393i
$300$	297.695	+	2141.25i	0.00330772	+	0.0237917i
$301$	−14435.2	+	44427.1i	−0.159327	+	0.490360i
$302$	61025.2	−	83994.0i	0.669107	−	0.920947i
$303$	4117.30	−	3964.24i	0.0448464	−	0.0431792i
$304$	9994.85	−	30761.0i	0.108151	−	0.332853i
$305$	18391.0	−	5975.61i	0.197700	−	0.0642366i
$306$	−69720.5	+	19768.4i	−0.744591	+	0.211119i
$307$	4377.01			0.0464409			0.0232205	−	0.999730i	$-0.492608\pi$
$307$	4377.01			0.0464409			0.0232205	+	0.999730i	$0.492608\pi$
$308$	40260.7	−	17272.0i	0.424404	−	0.182071i
$309$	−168984.	−	30055.0i	−1.76982	−	0.314774i
$310$	107171.	−	77864.3i	1.11520	−	0.810242i
$311$	40646.4	−	13206.8i	0.420244	−	0.136545i	−0.0912590	−	0.995827i	$-0.529089\pi$
$311$	40646.4	−	13206.8i	0.420244	−	0.136545i	0.511502	+	0.859282i	$0.329089\pi$
$312$	−80239.1	−	42816.7i	−0.824284	−	0.439849i
$313$	−72898.0	−	52963.5i	−0.744092	−	0.540615i	0.149898	−	0.988701i	$-0.452106\pi$
$313$	−72898.0	−	52963.5i	−0.744092	−	0.540615i	−0.893990	+	0.448087i	$0.852106\pi$
$314$	91029.3	−	125291.i	0.923255	−	1.27075i
$315$	110140.	+	86578.4i	1.11000	+	0.872546i
$316$	3179.59	+	9785.78i	0.0318418	+	0.0979989i
$317$	40367.5	+	55561.1i	0.401710	+	0.552907i	0.961172	−	0.275949i	$-0.0889921\pi$
$317$	40367.5	+	55561.1i	0.401710	+	0.552907i	−0.559462	+	0.828856i	$0.688992\pi$
$318$	36740.7	+	6534.59i	0.363323	+	0.0646196i
$319$	31977.2	−	28013.1i	0.314238	−	0.275283i
$320$		−	49926.9i		−	0.487568i
$321$	−81118.1	−	166945.i	−0.787241	−	1.62018i
$322$	−69840.8	−	214948.i	−0.673593	−	2.07311i
$323$	18980.5	+	6167.13i	0.181929	+	0.0591124i
$324$	8391.61	+	34528.5i	0.0799383	+	0.328918i
$325$	−7402.89	−	5378.51i	−0.0700865	−	0.0509208i
$326$	−46151.9	−	14995.7i	−0.434265	−	0.141101i
$327$	11097.5	+	79821.8i	0.103784	+	0.746493i
$328$	−126971.	+	92249.6i	−1.18020	+	0.857466i
$329$			105885.i			0.978236i
$330$	−120138.	−	50663.1i	−1.10320	−	0.465226i
$331$	169038.			1.54287			0.771433	−	0.636310i	$-0.219540\pi$
$331$	169038.			1.54287			0.771433	+	0.636310i	$0.219540\pi$
$332$	−20940.5	−	28822.1i	−0.189981	−	0.261487i
$333$	−559.856	+	14775.2i	−0.00504879	+	0.133243i
$334$	6783.25	−	20876.7i	0.0608058	−	0.187141i
$335$	90710.2	−	124852.i	0.808289	−	1.11251i
$336$	130752.	+	135800.i	1.15816	+	1.20288i
$337$	−140.480	+	432.354i	−0.00123696	+	0.00380697i	−0.951673	−	0.307113i	$-0.900637\pi$
$337$	−140.480	+	432.354i	−0.00123696	+	0.00380697i	0.950436	+	0.310920i	$0.100637\pi$
$338$	−61637.1	+	20027.1i	−0.539522	+	0.175301i
$339$	70836.1	+	145784.i	0.616390	+	1.26856i
$340$	−27089.1			−0.234335
$341$	12179.1	+	133323.i	0.104738	+	1.14656i
$342$	13342.3	−	36322.0i	0.114072	−	0.310540i
$343$	18003.5	−	13080.3i	0.153027	−	0.111181i
$344$	32550.6	−	10576.3i	0.275070	−	0.0893756i
$345$	−80082.3	+	150075.i	−0.672819	+	1.26087i
$346$	19946.3	+	14491.8i	0.166613	+	0.121052i
$347$	−7086.77	+	9754.10i	−0.0588558	+	0.0810081i	−0.837430	−	0.546544i	$-0.815943\pi$
$347$	−7086.77	+	9754.10i	−0.0588558	+	0.0810081i	0.778575	+	0.627552i	$0.215943\pi$
$348$	−15108.8	−	8062.25i	−0.124759	−	0.0665730i
$349$	45617.5	+	140396.i	0.374525	+	1.15267i	0.943799	+	0.330521i	$0.107224\pi$
$349$	45617.5	+	140396.i	0.374525	+	1.15267i	−0.569274	+	0.822148i	$0.692776\pi$
$350$	8065.14	+	11100.7i	0.0658379	+	0.0906181i
$351$	−129917.	−	75780.4i	−1.05451	−	0.615096i
$352$	−69263.6	−	41257.5i	−0.559010	−	0.332979i
$353$		−	120791.i		−	0.969358i	−0.874692	−	0.484679i	$-0.838936\pi$
$353$		−	120791.i		−	0.969358i	0.874692	−	0.484679i	$-0.161064\pi$
$354$	91061.9	−	44246.8i	0.726658	−	0.353081i
$355$	1569.01	+	4828.91i	0.0124500	+	0.0383171i
$356$	54393.8	+	17673.6i	0.429190	+	0.139452i
$357$	−83792.9	+	80678.0i	−0.657463	+	0.633022i
$358$	92263.1	+	67033.1i	0.719883	+	0.523026i
$359$	−112101.	−	36423.9i	−0.869804	−	0.282616i	−0.160086	−	0.987103i	$-0.551177\pi$
$359$	−112101.	−	36423.9i	−0.869804	−	0.282616i	−0.709717	+	0.704487i	$0.751177\pi$
$360$	3886.57	−	102571.i	0.0299890	−	0.791441i
$361$	96810.8	−	70337.2i	0.742864	−	0.539722i
$362$			117121.i			0.893754i
$363$	106123.	−	78109.0i	0.805370	−	0.592772i
$364$	74697.9			0.563775
$365$	76453.8	+	105230.i	0.573870	+	0.789864i
$366$	30833.7	−	4286.76i	0.230178	−	0.0320013i
$367$	−40138.4	+	123533.i	−0.298008	+	0.917175i	0.684186	+	0.729307i	$0.260158\pi$
$367$	−40138.4	+	123533.i	−0.298008	+	0.917175i	−0.982194	+	0.187868i	$0.939842\pi$
$368$	−134542.	+	185181.i	−0.993487	+	1.36742i
$369$	−215600.	+	144495.i	−1.58342	+	1.06121i
$370$	−6753.63	+	20785.5i	−0.0493326	+	0.151830i
$371$	56966.1	−	18509.4i	0.413875	−	0.134476i
$372$	48507.5	−	23569.7i	0.350529	−	0.170321i
$373$	−6730.66			−0.0483771			−0.0241885	−	0.999707i	$-0.507700\pi$
$373$	−6730.66			−0.0483771			−0.0241885	+	0.999707i	$0.507700\pi$
$374$	55400.1	−	93006.4i	0.396065	−	0.664920i
$375$	−23675.0	+	133113.i	−0.168356	+	0.946580i
$376$	62763.2	−	45600.1i	0.443945	−	0.322545i
$377$	68938.5	−	22399.5i	0.485042	−	0.157600i
$378$	150162.	+	168272.i	1.05094	+	1.17768i
$379$	−139905.	−	101647.i	−0.973993	−	0.707648i	−0.0176352	−	0.999844i	$-0.505614\pi$
$379$	−139905.	−	101647.i	−0.973993	−	0.707648i	−0.956358	+	0.292197i	$0.905614\pi$
$380$	8501.92	−	11701.9i	0.0588776	−	0.0810380i
$381$	61847.5	−	115903.i	0.426062	−	0.798446i
$382$	25969.8	+	79926.9i	0.177968	+	0.547730i
$383$	−143622.	−	197679.i	−0.979093	−	1.34761i	−0.937316	−	0.348479i	$-0.886698\pi$
$383$	−143622.	−	197679.i	−0.979093	−	1.34761i	−0.0417769	−	0.999127i	$-0.513302\pi$
$384$	30875.1	−	173595.i	0.209385	−	1.17727i
$385$	−208410.	+	19038.3i	−1.40604	+	0.128442i
$386$			302482.i			2.03014i
$387$	54453.3	−	15439.5i	0.363582	−	0.103089i
$388$	−1348.13	−	4149.13i	−0.00895509	−	0.0275609i
$389$	−16576.8	−	5386.12i	−0.109547	−	0.0355940i	0.253731	−	0.967275i	$-0.418342\pi$
$389$	−16576.8	−	5386.12i	−0.109547	−	0.0355940i	−0.363278	+	0.931681i	$0.618342\pi$
$390$	−154195.	−	160148.i	−1.01377	−	1.05291i
$391$	−114263.	−	83016.7i	−0.747396	−	0.543015i
$392$	96339.6	+	31302.6i	0.626950	+	0.203708i
$393$	163412.	−	22718.9i	1.05803	−	0.147097i
$394$	−13.6103	+	9.88848i	−8.76751e−5	+	6.36997e-5i
$395$		−	49152.8i		−	0.315031i
$396$	−44542.4	−	28871.5i	−0.284043	−	0.184111i
$397$	209315.			1.32806			0.664032	−	0.747704i	$-0.268844\pi$
$397$	209315.			1.32806			0.664032	+	0.747704i	$0.268844\pi$
$398$	−91098.6	−	125386.i	−0.575103	−	0.791561i
$399$	−8552.68	−	61517.5i	−0.0537225	−	0.386414i
$400$	4294.26	−	13216.4i	0.0268391	−	0.0826023i
$401$	−125710.	+	173025.i	−0.781772	+	1.07602i	0.213313	+	0.976984i	$0.431575\pi$
$401$	−125710.	+	173025.i	−0.781772	+	1.07602i	−0.995084	+	0.0990323i	$0.968425\pi$
$402$	178968.	−	172315.i	1.10745	−	1.06628i
$403$	−70540.0	+	217100.i	−0.434336	+	1.33675i
$404$	3271.07	−	1062.83i	0.0200413	−	0.00651183i
$405$	12845.4	−	169258.i	0.0783136	−	1.03191i
$406$	−108694.			−0.659407
$407$	−14554.4	−	16613.9i	−0.0878629	−	0.100296i
$408$	83907.6	+	14923.6i	0.504059	+	0.0896503i
$409$	14756.4	−	10721.1i	0.0882131	−	0.0640906i	−0.542805	−	0.839859i	$-0.682638\pi$
$409$	14756.4	−	10721.1i	0.0882131	−	0.0640906i	0.631018	+	0.775768i	$0.282638\pi$
$410$	−364859.	+	118550.i	−2.17049	+	0.705234i
$411$	−170698.	−	91086.6i	−1.01052	−	0.539226i
$412$	−83558.7	−	60709.0i	−0.492263	−	0.357650i
$413$	95517.3	−	131468.i	0.559992	−	0.770763i
$414$	−169234.	+	215290.i	−0.987385	+	1.25610i
$415$	52590.8	+	161858.i	0.305361	+	0.939804i
$416$	−80799.1	−	111210.i	−0.466896	−	0.642627i
$417$	105434.	+	18752.2i	0.606331	+	0.107840i
$418$	22789.4	+	53121.7i	0.130431	+	0.304032i
$419$		−	25313.3i		−	0.144185i	−0.997398	−	0.0720926i	$-0.977032\pi$
$419$		−	25313.3i		−	0.144185i	0.997398	−	0.0720926i	$-0.0229677\pi$
$420$	36844.1	+	75826.9i	0.208867	+	0.429858i
$421$	−11938.3	−	36742.3i	−0.0673562	−	0.207301i	0.911713	−	0.410827i	$-0.134760\pi$
$421$	−11938.3	−	36742.3i	−0.0673562	−	0.207301i	−0.979070	+	0.203526i	$0.934760\pi$
$422$	255827.	+	83123.1i	1.43655	+	0.466764i
$423$	106574.	−	71425.7i	0.595620	−	0.399185i
$424$	−35504.2	−	25795.3i	−0.197491	−	0.143486i
$425$	8154.92	+	2649.69i	0.0451483	+	0.0146696i
$426$	1125.57	+	8095.97i	0.00620230	+	0.0446118i
$427$	40424.2	−	29369.9i	0.221710	−	0.161082i
$428$		−	111693.i		−	0.609730i
$429$	218798.	−	51054.9i	1.18886	−	0.277410i
$430$	83661.5			0.452469
$431$	−194373.	−	267531.i	−1.04636	−	1.44019i	−0.891923	−	0.452188i	$-0.850644\pi$
$431$	−194373.	−	267531.i	−1.04636	−	1.44019i	−0.154437	−	0.988003i	$-0.549356\pi$
$432$	48483.3	−	223207.i	0.259792	−	1.19603i
$433$	−45395.5	+	139713.i	−0.242123	+	0.745179i	0.753973	+	0.656906i	$0.228135\pi$
$433$	−45395.5	+	139713.i	−0.242123	+	0.745179i	−0.996096	+	0.0882737i	$0.971865\pi$
$434$	201197.	−	276924.i	1.06818	−	1.47022i
$435$	56741.3	+	58932.1i	0.299862	+	0.311439i
$436$	−14986.0	+	46122.3i	−0.0788341	+	0.242626i
$437$	71722.7	−	23304.1i	0.375573	−	0.122031i
$438$	91512.9	+	188338.i	0.477017	+	0.981724i
$439$	110554.			0.573649			0.286825	−	0.957983i	$-0.407400\pi$
$439$	110554.			0.573649			0.286825	+	0.957983i	$0.407400\pi$
$440$	101038.	+	115336.i	0.521891	+	0.595742i
$441$	157244.	+	57761.2i	0.808534	+	0.297002i
$442$	149332.	−	108496.i	0.764379	−	0.555354i
$443$	−72334.3	+	23502.9i	−0.368585	+	0.119760i	−0.487452	−	0.873150i	$-0.662074\pi$
$443$	−72334.3	+	23502.9i	−0.368585	+	0.119760i	0.118868	+	0.992910i	$0.462074\pi$
$444$	−4188.80	+	7849.87i	−0.0212483	+	0.0398195i
$445$	−221034.	−	160591.i	−1.11619	−	0.810963i
$446$	−211826.	+	291554.i	−1.06490	+	1.46571i
$447$	168858.	+	90104.8i	0.845095	+	0.450954i
$448$	−39865.8	−	122694.i	−0.198630	−	0.611320i
$449$	−65666.4	−	90382.0i	−0.325724	−	0.448321i	0.614480	−	0.788933i	$-0.289366\pi$
$449$	−65666.4	−	90382.0i	−0.325724	−	0.448321i	−0.940204	+	0.340611i	$0.889366\pi$
$450$	5732.49	−	15605.7i	0.0283086	−	0.0770650i
$451$	85768.2	−	378106.i	0.421671	−	1.85892i
$452$			97535.4i			0.477403i
$453$	−181610.	+	88243.8i	−0.884999	+	0.430019i
$454$	68732.5	+	211537.i	0.333465	+	1.02630i
$455$	−339370.	−	110268.i	−1.63927	−	0.532631i
$456$	−32781.1	+	31562.5i	−0.157650	+	0.151789i
$457$	279566.	+	203117.i	1.33861	+	0.972554i	0.999494	+	0.0318074i	$0.0101263\pi$
$457$	279566.	+	203117.i	1.33861	+	0.972554i	0.339111	+	0.940746i	$0.389874\pi$
$458$	108285.	+	35183.9i	0.516222	+	0.167731i
$459$	137726.	+	29915.8i	0.653717	+	0.141995i
$460$	−82813.6	+	60167.6i	−0.391368	+	0.284346i
$461$			37622.2i			0.177028i	0.996075	+	0.0885140i	$0.0282118\pi$
$461$			37622.2i			0.177028i	−0.996075	+	0.0885140i	$0.971788\pi$
$462$	−335690.	−	28575.2i	−1.57273	−	0.133877i
$463$	−280150.			−1.30686			−0.653429	−	0.756988i	$-0.726670\pi$
$463$	−280150.			−1.30686			−0.653429	+	0.756988i	$0.726670\pi$
$464$	64704.8	+	89058.5i	0.300539	+	0.413656i
$465$	−255174.	+	35476.5i	−1.18013	+	0.164072i
$466$	4607.68	−	14181.0i	0.0212183	−	0.0653032i
$467$	−88681.9	+	122060.i	−0.406632	+	0.559680i	−0.962393	−	0.271662i	$-0.912427\pi$
$467$	−88681.9	+	122060.i	−0.406632	+	0.559680i	0.555761	+	0.831342i	$0.312427\pi$
$468$	−50388.1	−	75183.6i	−0.230057	−	0.343266i
$469$	123226.	−	379252.i	0.560219	−	1.72418i
$470$	180354.	−	58600.6i	0.816451	−	0.265281i
$471$	−270901.	+	131630.i	−1.22115	+	0.593354i
$472$	−119063.			−0.534431
$473$	−43268.7	+	72640.1i	−0.193398	+	0.324679i
$474$	13856.0	−	77905.6i	0.0616712	−	0.346746i
$475$	−3704.03	+	2691.14i	−0.0164168	+	0.0119275i
$476$	−66570.9	+	21630.2i	−0.293813	+	0.0954655i
$477$	−57056.7	−	44850.9i	−0.250767	−	0.197121i
$478$	192483.	+	139847.i	0.842435	+	0.612065i
$479$	−82662.3	+	113775.i	−0.360277	+	0.495879i	−0.950226	−	0.311562i	$-0.899148\pi$
$479$	−82662.3	+	113775.i	−0.360277	+	0.495879i	0.589949	+	0.807441i	$0.299148\pi$
$480$	73037.8	−	136874.i	0.317004	−	0.594070i
$481$	−11637.8	−	35817.5i	−0.0503015	−	0.154812i
$482$	109712.	+	151006.i	0.472237	+	0.649978i
$483$	−76967.9	+	432752.i	−0.329925	+	1.85500i
$484$	77981.4	−	14367.1i	0.332890	−	0.0613309i
$485$			20840.6i			0.0885985i
$486$	68073.1	−	264648.i	0.288206	−	1.12046i
$487$	−74805.0	−	230226.i	−0.315408	−	0.970726i	−0.975586	−	0.219617i	$-0.929519\pi$
$487$	−74805.0	−	230226.i	−0.315408	−	0.970726i	0.660178	−	0.751109i	$-0.270481\pi$
$488$	−34817.8	−	11313.0i	−0.146205	−	0.0475049i
$489$	65457.8	+	67985.1i	0.273743	+	0.284312i
$490$	200322.	+	145542.i	0.834327	+	0.606174i
$491$	212730.	+	69120.2i	0.882402	+	0.286710i	0.714954	−	0.699171i	$-0.246448\pi$
$491$	212730.	+	69120.2i	0.882402	+	0.286710i	0.167447	+	0.985881i	$0.446448\pi$
$492$	−154695.	+	21507.0i	−0.639068	+	0.0888485i
$493$	−54951.9	+	39924.9i	−0.226094	+	0.164267i
$494$			98559.7i			0.403874i
$495$	159747.	+	196923.i	0.651962	+	0.803685i
$496$	−346670.			−1.40913
$497$	7711.61	+	10614.1i	0.0312200	+	0.0429706i
$498$	37727.4	+	271365.i	0.152124	+	1.09419i
$499$	−2198.81	+	6767.26i	−0.00883054	+	0.0271776i	−0.955375	−	0.295397i	$-0.904548\pi$
$499$	−2198.81	+	6767.26i	−0.00883054	+	0.0271776i	0.946544	+	0.322574i	$0.104548\pi$
$500$	−47822.0	+	65821.3i	−0.191288	+	0.263285i
$501$	−30752.9	+	29609.7i	−0.122521	+	0.117966i
$502$	11758.8	−	36189.9i	0.0466612	−	0.143609i
$503$	−41518.5	+	13490.2i	−0.164099	+	0.0533189i	−0.389914	−	0.920851i	$-0.627495\pi$
$503$	−41518.5	+	13490.2i	−0.164099	+	0.0533189i	0.225815	+	0.974170i	$0.427495\pi$
$504$	−72349.9	−	255169.i	−0.284824	−	1.00454i
$505$	−16430.2			−0.0644257
$506$	−37214.0	−	407377.i	−0.145347	−	1.59109i
$507$	124093.	+	22070.8i	0.482761	+	0.0858624i
$508$	63956.9	−	46467.4i	0.247833	−	0.180061i
$509$	477192.	−	155049.i	1.84186	−	0.598458i	0.843774	−	0.536699i	$-0.180329\pi$
$509$	477192.	−	155049.i	1.84186	−	0.598458i	0.998091	−	0.0617592i	$-0.0196711\pi$
$510$	183793.	+	98074.3i	0.706623	+	0.377064i
$511$	271908.	+	197553.i	1.04131	+	0.756556i
$512$	−21621.9	+	29760.0i	−0.0824810	+	0.113525i
$513$	−56148.2	+	50105.4i	−0.213354	+	0.190393i
$514$	−113368.	−	348912.i	−0.429107	−	1.32066i
$515$	290009.	+	399163.i	1.09345	+	1.50500i
$516$	33533.5	+	5964.16i	0.125945	+	0.0224001i
$517$	−42396.3	+	186902.i	−0.158616	+	0.699251i
$518$			56472.7i			0.210464i
$519$	−20955.5	−	43127.4i	−0.0777970	−	0.160110i
$520$	80790.7	+	248648.i	0.298782	+	0.919557i
$521$	−93451.5	−	30364.2i	−0.344279	−	0.111863i	0.131773	−	0.991280i	$-0.457933\pi$
$521$	−93451.5	−	30364.2i	−0.344279	−	0.111863i	−0.476053	+	0.879417i	$0.657933\pi$
$522$	73320.4	+	109401.i	0.269081	+	0.401494i
$523$	−23645.2	−	17179.2i	−0.0864449	−	0.0628059i	0.543723	−	0.839265i	$-0.317014\pi$
$523$	−23645.2	−	17179.2i	−0.0864449	−	0.0628059i	−0.630168	+	0.776459i	$0.717014\pi$
$524$	94422.1	+	30679.6i	0.343883	+	0.111734i
$525$	−3674.64	−	26430.8i	−0.0133320	−	0.0958942i
$526$	257975.	−	187430.i	0.932408	−	0.677434i
$527$		−	213906.i		−	0.770197i
$528$	176421.	+	292059.i	0.632824	+	1.04762i
$529$	−253858.			−0.907149
$530$	−63054.1	−	86786.5i	−0.224472	−	0.308959i
$531$	−196755.	−	7455.37i	−0.697809	−	0.0264411i
$532$	11549.5	−	35545.8i	0.0408076	−	0.125593i
$533$	388571.	−	534823.i	1.36778	−	1.88259i
$534$	−305062.	−	316840.i	−1.06981	−	1.11111i
$535$	−164879.	+	507447.i	−0.576048	+	1.77289i
$536$	−277868.	+	90284.9i	−0.967185	+	0.314258i
$537$	−96931.2	−	199489.i	−0.336136	−	0.691784i
$538$	120546.			0.416475
$539$	−229973.	+	98659.2i	−0.791589	+	0.339594i
$540$	51466.4	−	88233.3i	0.176497	−	0.302583i
$541$	−228190.	+	165790.i	−0.779656	+	0.566453i	−0.904876	−	0.425676i	$-0.860036\pi$
$541$	−228190.	+	165790.i	−0.779656	+	0.566453i	0.125220	+	0.992129i	$0.460036\pi$
$542$	235729.	−	76592.9i	0.802443	−	0.260729i
$543$	107233.	−	200956.i	0.363688	−	0.681556i
$544$	104211.	+	75714.0i	0.352142	+	0.255846i
$545$	136170.	−	187422.i	0.458447	−	0.630998i
$546$	−506806.	−	270439.i	−1.70003	−	0.907160i
$547$	−24961.8	−	76824.7i	−0.0834261	−	0.256759i	0.900639	−	0.434568i	$-0.143099\pi$
$547$	−24961.8	−	76824.7i	−0.0834261	−	0.256759i	−0.984065	+	0.177809i	$0.943099\pi$
$548$	−68435.3	−	94193.1i	−0.227887	−	0.313659i
$549$	−56829.3	−	20875.3i	−0.188550	−	0.0692609i
$550$	9791.40	+	22823.6i	0.0323683	+	0.0754499i
$551$		−	36268.4i		−	0.119461i
$552$	289659.	−	140745.i	0.950625	−	0.461906i
$553$	−39247.7	−	120792.i	−0.128341	−	0.394992i
$554$	−114484.	−	37198.0i	−0.373013	−	0.121199i
$555$	30618.5	−	29480.3i	0.0994028	−	0.0957076i
$556$	52134.8	+	37878.2i	0.168647	+	0.122529i
$557$	−154602.	−	50233.3i	−0.498317	−	0.161913i	0.0490656	−	0.998796i	$-0.484376\pi$
$557$	−154602.	−	50233.3i	−0.498317	−	0.161913i	−0.547382	+	0.836883i	$0.684376\pi$
$558$	−414444.	−	15703.9i	−1.33106	−	0.0504360i
$559$	−116632.	+	84738.0i	−0.373244	+	0.271178i
$560$		−	541913.i		−	1.72804i
$561$	−180210.	+	108857.i	−0.572601	+	0.345885i
$562$	−82350.0			−0.260730
$563$	197046.	+	271211.i	0.621658	+	0.855639i	0.997472	−	0.0710562i	$-0.0226370\pi$
$563$	197046.	+	271211.i	0.621658	+	0.855639i	−0.375814	+	0.926695i	$0.622637\pi$
$564$	76467.7	−	10631.2i	0.240392	−	0.0334213i
$565$	143980.	−	443126.i	0.451031	−	1.38813i
$566$	−244464.	+	336476.i	−0.763102	+	1.05032i
$567$	−103583.	−	426206.i	−0.322197	−	1.32572i
$568$	2970.44	−	9142.07i	0.00920713	−	0.0283366i
$569$	55337.5	−	17980.2i	0.170921	−	0.0555355i	−0.222307	−	0.974977i	$-0.571359\pi$
$569$	55337.5	−	17980.2i	0.170921	−	0.0555355i	0.393227	+	0.919441i	$0.371359\pi$
$570$	−100049.	+	48613.7i	−0.307939	+	0.149627i
$571$	164161.			0.503498			0.251749	−	0.967793i	$-0.418994\pi$
$571$	164161.			0.503498			0.251749	+	0.967793i	$0.418994\pi$
$572$	131852.	+	29908.9i	0.402991	+	0.0914131i
$573$	28620.0	−	160916.i	0.0871687	−	0.490105i
$574$	−801973.	+	582667.i	−2.43409	+	1.76847i
$575$	30815.5	−	10012.6i	0.0932037	−	0.0302837i
$576$	−96600.4	+	122890.i	−0.291161	+	0.370399i
$577$	−192497.	−	139858.i	−0.578193	−	0.420082i	0.259879	−	0.965641i	$-0.416317\pi$
$577$	−192497.	−	139858.i	−0.578193	−	0.420082i	−0.838072	+	0.545559i	$0.816317\pi$
$578$	125518.	−	172761.i	0.375709	−	0.517120i
$579$	276945.	−	518999.i	0.826107	−	1.54814i
$580$	15212.6	+	46819.7i	0.0452219	+	0.139179i
$581$	258481.	+	355769.i	0.765733	+	1.05394i
$582$	−5874.91	+	33031.6i	−0.0173442	+	0.0975178i
$583$	107964.	−	9862.57i	0.317646	−	0.0290170i
$584$		−	246250.i		−	0.722022i
$585$	117940.	+	415959.i	0.344627	+	1.21545i
$586$	55308.4	+	170222.i	0.161063	+	0.495701i
$587$	608654.	+	197764.i	1.76642	+	0.573945i	0.997833	−	0.0657975i	$-0.0209591\pi$
$587$	608654.	+	197764.i	1.76642	+	0.573945i	0.768589	+	0.639743i	$0.220959\pi$
$588$	69918.1	+	72617.6i	0.202225	+	0.210033i
$589$	92402.7	+	67134.5i	0.266351	+	0.193515i
$590$	−276792.	−	89935.3i	−0.795152	−	0.258360i
$591$	32.4062	−	4.50539i	9.27798e−5	−	1.28990e-5i
$592$	46270.9	−	33617.8i	0.132028	−	0.0959237i
$593$		−	170333.i		−	0.484384i	−0.970228	−	0.242192i	$-0.922134\pi$
$593$		−	170333.i		−	0.484384i	0.970228	−	0.242192i	$-0.0778664\pi$
$594$	197682.	+	357149.i	0.560265	+	1.01222i
$595$	334377.			0.944502
$596$	67697.7	+	93177.8i	0.190582	+	0.262313i
$597$	41506.3	+	298545.i	0.116457	+	0.837648i
$598$	215540.	−	663363.i	0.602733	−	1.85502i
$599$	−371167.	+	510868.i	−1.03447	+	1.42382i	−0.132925	+	0.991126i	$0.542437\pi$
$599$	−371167.	+	510868.i	−1.03447	+	1.42382i	−0.901541	+	0.432694i	$0.857563\pi$
$600$	−14084.3	+	13560.7i	−0.0391231	+	0.0376687i
$601$	−2989.80	+	9201.65i	−0.00827738	+	0.0254752i	−0.955110	−	0.296252i	$-0.904263\pi$
$601$	−2989.80	+	9201.65i	−0.00827738	+	0.0254752i	0.946833	+	0.321727i	$0.104263\pi$
$602$	205596.	−	66802.3i	0.567313	−	0.184331i
$603$	−464841.	+	131800.i	−1.27841	+	0.362476i
$604$	−121504.			−0.333056
$605$	−375496.	−	49841.8i	−1.02588	−	0.136170i
$606$	−26041.3	−	4631.62i	−0.0709116	−	0.0126121i
$607$	240282.	−	174575.i	0.652146	−	0.473812i	−0.211856	−	0.977301i	$-0.567951\pi$
$607$	240282.	−	174575.i	0.652146	−	0.473812i	0.864001	+	0.503489i	$0.167951\pi$
$608$	−65413.5	+	21254.1i	−0.176954	+	0.0574958i
$609$	186497.	+	99517.3i	0.502848	+	0.268327i
$610$	−72397.8	−	52600.1i	−0.194565	−	0.141360i
$611$	−192076.	+	264369.i	−0.514505	+	0.708155i
$612$	66676.8	+	52412.9i	0.178021	+	0.139938i
$613$	66223.7	+	203816.i	0.176235	+	0.542396i	0.999688	−	0.0249892i	$-0.00795514\pi$
$613$	66223.7	+	203816.i	0.176235	+	0.542396i	−0.823453	+	0.567385i	$0.807955\pi$
$614$	−11906.0	−	16387.1i	−0.0315811	−	0.0434677i
$615$	734565.	+	130648.i	1.94214	+	0.345423i
$616$	340393.	+	202758.i	0.897054	+	0.534338i
$617$			16631.5i			0.0436879i	0.999761	+	0.0218440i	$0.00695370\pi$
$617$			16631.5i			0.0436879i	−0.999761	+	0.0218440i	$0.993046\pi$
$618$	347132.	+	714414.i	0.908903	+	1.87057i
$619$	85866.7	+	264271.i	0.224101	+	0.689712i	0.998382	+	0.0568693i	$0.0181118\pi$
$619$	85866.7	+	264271.i	0.224101	+	0.689712i	−0.774281	+	0.632842i	$0.781888\pi$
$620$	−147444.	−	47907.4i	−0.383569	−	0.124629i
$621$	487485.	−	214448.i	1.26409	−	0.556081i
$622$	−160008.	−	116252.i	−0.413581	−	0.300484i
$623$	−671417.	−	218157.i	−1.72988	−	0.562072i
$624$	80114.1	+	576243.i	0.205750	+	1.47991i
$625$	336857.	−	244741.i	0.862354	−	0.626537i
$626$			416990.i			1.06409i
$627$	9534.83	−	112011.i	0.0242537	−	0.284923i
$628$	−181244.			−0.459562
$629$	20743.2	+	28550.6i	0.0524295	+	0.0721630i
$630$	24548.4	−	647858.i	0.0618503	−	1.63229i
$631$	67941.9	−	209104.i	0.170639	−	0.525174i	−0.828768	−	0.559592i	$-0.810958\pi$
$631$	67941.9	−	209104.i	0.170639	−	0.525174i	0.999408	+	0.0344184i	$0.0109579\pi$
$632$	−54696.8	+	75283.8i	−0.136939	+	0.188481i
$633$	−362842.	−	376851.i	−0.905545	−	0.940507i
$634$	98211.7	−	302265.i	0.244334	−	0.751984i
$635$	−359166.	+	116700.i	−0.890732	+	0.289416i
$636$	−19086.6	−	39281.2i	−0.0471862	−	0.0971114i
$637$	−426682.			−1.05154
$638$	−191860.	−	43520.9i	−0.471350	−	0.106919i
$639$	5481.21	−	14921.6i	0.0134238	−	0.0365438i
$640$	−410055.	+	297922.i	−1.00111	+	0.727350i
$641$	661251.	−	214854.i	1.60935	−	0.522909i	0.639954	−	0.768413i	$-0.278953\pi$
$641$	661251.	−	214854.i	1.60935	−	0.522909i	0.969396	+	0.245504i	$0.0789535\pi$
$642$	−404377.	+	757808.i	−0.981106	+	1.83861i
$643$	413351.	+	300317.i	0.999763	+	0.726370i	0.962037	−	0.272918i	$-0.0879887\pi$
$643$	413351.	+	300317.i	0.999763	+	0.726370i	0.0377256	+	0.999288i	$0.487989\pi$
$644$	−155470.	+	213986.i	−0.374865	+	0.515957i
$645$	−143546.	−	76598.3i	−0.345042	−	0.184119i
$646$	−28539.8	−	87836.6i	−0.0683890	−	0.210480i
$647$	209413.	+	288232.i	0.500259	+	0.688547i	0.982239	−	0.187635i	$-0.0600822\pi$
$647$	209413.	+	288232.i	0.500259	+	0.688547i	−0.481980	+	0.876182i	$0.660082\pi$
$648$	−208024.	+	244947.i	−0.495408	+	0.583340i
$649$	221241.	−	193815.i	0.525262	−	0.460148i
$650$			42345.9i			0.100227i
$651$	−598759.	+	290935.i	−1.41283	+	0.686490i
$652$	17549.6	+	54012.0i	0.0412830	+	0.127056i
$653$	−468882.	−	152349.i	−1.09961	−	0.357284i	−0.297656	−	0.954673i	$-0.596205\pi$
$653$	−468882.	−	152349.i	−1.09961	−	0.357284i	−0.801951	+	0.597389i	$0.796205\pi$
$654$	268659.	−	258672.i	0.628125	−	0.604775i
$655$	−383693.	−	278769.i	−0.894337	−	0.649774i
$656$	954818.	+	310239.i	2.21877	+	0.720923i
$657$	15419.5	−	406937.i	0.0357223	−	0.942749i
$658$	396425.	−	288020.i	0.915607	−	0.665227i
$659$			342302.i			0.788204i	0.919067	+	0.394102i	$0.128944\pi$
$659$			342302.i			0.788204i	−0.919067	+	0.394102i	$0.871056\pi$
$660$	34674.0	+	148597.i	0.0796006	+	0.341133i
$661$	−576901.			−1.32038			−0.660189	−	0.751099i	$-0.729524\pi$
$661$	−576901.			−1.32038			−0.660189	+	0.751099i	$0.729524\pi$
$662$	−459802.	−	632863.i	−1.04919	−	1.44409i
$663$	−355560.	+	49432.9i	−0.808883	+	0.112458i
$664$	99564.6	−	306428.i	0.225823	−	0.695013i
$665$	−104944.	+	144444.i	−0.237310	+	0.326629i
$666$	56839.8	−	38094.1i	0.128146	−	0.0858834i
$667$	−79315.3	+	244107.i	−0.178281	+	0.548693i
$668$	−24432.2	+	7938.51i	−0.0547532	+	0.0177904i
$669$	630391.	−	306305.i	1.40850	−	0.684388i
$670$	−714176.			−1.59095
$671$	83114.0	−	35656.2i	0.184599	−	0.0791935i
$672$	70197.3	−	394684.i	0.155447	−	0.873999i
$673$	554830.	−	403108.i	1.22498	−	0.890002i	0.228479	−	0.973549i	$-0.426625\pi$
$673$	554830.	−	403108.i	1.22498	−	0.890002i	0.996504	+	0.0835467i	$0.0266248\pi$
$674$	2000.82	−	650.105i	0.00440441	−	0.00143108i
$675$	−24123.9	+	21527.7i	−0.0529469	+	0.0472486i
$676$	61361.3	+	44581.6i	0.134277	+	0.0975578i
$677$	−225207.	+	309971.i	−0.491365	+	0.676306i	−0.980639	−	0.195824i	$-0.937262\pi$
$677$	−225207.	+	309971.i	−0.491365	+	0.676306i	0.489274	+	0.872130i	$0.337262\pi$
$678$	353121.	−	661753.i	0.768181	−	1.43958i
$679$	16640.9	+	51215.3i	0.0360941	+	0.111086i
$680$	−144002.	−	198201.i	−0.311422	−	0.428636i
$681$	75746.5	−	425885.i	0.163331	−	0.918328i
$682$	466021.	−	408251.i	1.00193	−	0.877725i
$683$		−	533075.i		−	1.14274i	−0.820693	−	0.571370i	$-0.806412\pi$
$683$		−	533075.i		−	1.14274i	0.820693	−	0.571370i	$-0.193588\pi$
$684$	−43567.7	+	12353.1i	−0.0931221	+	0.0264036i
$685$	171871.	+	528965.i	0.366287	+	1.12732i
$686$	−97943.1	−	31823.6i	−0.208126	−	0.0676241i
$687$	−153581.	−	159511.i	−0.325406	−	0.337969i
$688$	−177125.	−	128689.i	−0.374199	−	0.271871i
$689$	175806.	+	57123.0i	0.370336	+	0.120330i
$690$	779702.	−	108401.i	1.63769	−	0.227685i
$691$	−224383.	+	163024.i	−0.469931	+	0.341425i	−0.797414	−	0.603432i	$-0.793799\pi$
$691$	−224383.	+	163024.i	−0.469931	+	0.341425i	0.327483	+	0.944857i	$0.393799\pi$
$692$		−	28853.9i		−	0.0602550i
$693$	549815.	+	356379.i	1.14485	+	0.742071i
$694$	55795.3			0.115845
$695$	−180945.	−	249050.i	−0.374609	−	0.515605i
$696$	−21327.4	−	153403.i	−0.0440271	−	0.316677i
$697$	−191427.	+	589153.i	−0.394038	+	1.21273i
$698$	401546.	−	552681.i	0.824185	−	1.13439i
$699$	−20889.6	+	20113.0i	−0.0427539	+	0.0411645i
$700$	4962.22	−	15272.2i	0.0101270	−	0.0311677i
$701$	−729803.	+	237127.i	−1.48515	+	0.482554i	−0.935646	−	0.352939i	$-0.885182\pi$
$701$	−729803.	+	237127.i	−1.48515	+	0.482554i	−0.549501	+	0.835493i	$0.685182\pi$
$702$	69673.0	+	692528.i	0.141381	+	1.40528i
$703$	−18843.5			−0.0381286
$704$	−21242.1	−	232535.i	−0.0428601	−	0.469184i
$705$	−363104.	−	64580.6i	−0.730556	−	0.129934i
$706$	−452230.	+	328564.i	−0.907297	+	0.659190i
$707$	−40376.8	+	13119.2i	−0.0807780	+	0.0262464i
$708$	−104533.	−	55780.5i	−0.208540	−	0.111280i
$709$	161064.	+	117020.i	0.320411	+	0.232792i	0.736351	−	0.676600i	$-0.236547\pi$
$709$	161064.	+	117020.i	0.320411	+	0.232792i	−0.415940	+	0.909392i	$0.636547\pi$
$710$	13811.1	−	19009.4i	0.0273976	−	0.0377096i
$711$	−95102.5	+	120984.i	−0.188128	+	0.239325i
$712$	159838.	+	491931.i	0.315297	+	0.970385i
$713$	−475107.	−	653928.i	−0.934570	−	1.28633i
$714$	529977.	+	94260.2i	1.03959	+	0.184898i
$715$	−554885.	−	330522.i	−1.08540	−	0.646529i
$716$		−	133466.i		−	0.260342i
$717$	−202222.	−	416182.i	−0.393359	−	0.809552i
$718$	168560.	+	518774.i	0.326968	+	1.00630i
$719$	463660.	+	150652.i	0.896896	+	0.291419i	0.720955	−	0.692982i	$-0.243703\pi$
$719$	463660.	+	150652.i	0.896896	+	0.291419i	0.175941	+	0.984401i	$0.443703\pi$
$720$	−545436.	+	365552.i	−1.05215	+	0.705154i
$721$	1.03142e6	+	749368.i	1.98410	+	1.44153i
$722$	−526672.	−	171126.i	−1.01034	−	0.328278i
$723$	−49986.9	−	359545.i	−0.0956268	−	0.687822i
$724$	110890.	−	80566.5i	0.211551	−	0.153701i
$725$		−	15582.6i		−	0.0296459i
$726$	−581099.	−	184849.i	−1.10250	−	0.350707i
$727$	−129951.			−0.245874			−0.122937	−	0.992415i	$-0.539231\pi$
$727$	−129951.			−0.245874			−0.122937	+	0.992415i	$0.539231\pi$
$728$	397083.	+	546538.i	0.749236	+	1.03124i
$729$	−359105.	+	391757.i	−0.675719	+	0.737160i
$730$	186008.	−	572473.i	0.349048	−	1.07426i
$731$	79405.0	−	109292.i	0.148598	−	0.204528i
$732$	−25268.9	−	26244.5i	−0.0471590	−	0.0489798i
$733$	12093.8	−	37220.9i	0.0225089	−	0.0692753i	−0.939171	−	0.343450i	$-0.888405\pi$
$733$	12093.8	−	37220.9i	0.0225089	−	0.0692753i	0.961680	+	0.274174i	$0.0884045\pi$
$734$	571679.	−	185750.i	1.06111	−	0.344775i
$735$	−210457.	−	433131.i	−0.389573	−	0.801760i
$736$	486751.			0.898569
$737$	369363.	−	620092.i	0.680015	−	1.14162i
$738$	1.12743e6	+	414144.i	2.07004	+	0.760394i
$739$	−569493.	+	413761.i	−1.04280	+	0.757635i	−0.970829	−	0.239772i	$-0.922927\pi$
$739$	−569493.	+	413761.i	−1.04280	+	0.757635i	−0.0719662	+	0.997407i	$0.522927\pi$
$740$	24325.5	−	7903.83i	0.0444220	−	0.0144336i
$741$	90238.7	−	169109.i	0.164345	−	0.307985i
$742$	−224252.	−	162929.i	−0.407313	−	0.295930i
$743$	53416.9	−	73522.0i	0.0967611	−	0.133180i	−0.757891	−	0.652381i	$-0.773770\pi$
$743$	53416.9	−	73522.0i	0.0967611	−	0.133180i	0.854652	+	0.519201i	$0.173770\pi$
$744$	430310.	+	229619.i	0.777384	+	0.414823i
$745$	−170018.	−	523263.i	−0.306326	−	0.942774i
$746$	18308.1	+	25199.0i	0.0328978	+	0.0452799i
$747$	183722.	−	500149.i	0.329245	−	0.896310i
$748$	−126168.	+	11525.4i	−0.225499	+	0.0205994i
$749$			1.37869e6i			2.45756i
$750$	562762.	−	273444.i	1.00046	−	0.486123i
$751$	−226027.	−	695639.i	−0.400756	−	1.23340i	−0.924387	−	0.381456i	$-0.875423\pi$
$751$	−226027.	−	695639.i	−0.400756	−	1.23340i	0.523631	−	0.851945i	$-0.324577\pi$
$752$	−471978.	−	153355.i	−0.834615	−	0.271183i
$753$	−53310.3	+	51328.6i	−0.0940202	+	0.0905251i
$754$	−271382.	−	197171.i	−0.477352	−	0.346816i
$755$	552022.	+	179363.i	0.968418	+	0.314658i
$756$	56024.9	−	257927.i	0.0980251	−	0.451287i
$757$	−383434.	+	278581.i	−0.669112	+	0.486138i	−0.869728	−	0.493532i	$-0.835706\pi$
$757$	−383434.	+	278581.i	−0.669112	+	0.486138i	0.200616	+	0.979670i	$0.435706\pi$
$758$			800285.i			1.39286i
$759$	−309132.	+	733050.i	−0.536612	+	1.27248i
$760$	130814.			0.226478
$761$	267474.	+	368146.i	0.461862	+	0.635699i	0.974894	−	0.222671i	$-0.0714776\pi$
$761$	267474.	+	368146.i	0.461862	+	0.635699i	−0.513032	+	0.858370i	$0.671478\pi$
$762$	−602163.	+	83717.8i	−1.03706	+	0.144181i
$763$	184982.	−	569316.i	0.317746	−	0.977922i
$764$	57810.4	−	79569.2i	0.0990420	−	0.136320i
$765$	−225557.	−	336551.i	−0.385419	−	0.575081i
$766$	−349424.	+	1.07542e6i	−0.595519	+	1.83282i
$767$	476966.	−	154976.i	0.810769	−	0.263435i
$768$	−483963.	+	235156.i	−0.820521	+	0.398689i
$769$	−773505.			−1.30801			−0.654004	−	0.756491i	$-0.726912\pi$
$769$	−773505.			−1.30801			−0.654004	+	0.756491i	$0.726912\pi$
$770$	638177.	+	728483.i	1.07637	+	1.22868i
$771$	−124937.	+	702460.i	−0.210176	+	1.18171i
$772$	286390.	−	208075.i	0.480533	−	0.349128i
$773$	−1.01340e6	+	329274.i	−1.69599	+	0.551060i	−0.987904	−	0.155069i	$-0.950440\pi$
$773$	−1.01340e6	+	329274.i	−1.69599	+	0.551060i	−0.708084	+	0.706129i	$0.750440\pi$
$774$	−205923.	−	161871.i	−0.343735	−	0.270201i
$775$	39700.6	+	28844.1i	0.0660987	+	0.0480235i
$776$	23191.2	−	31920.0i	0.0385124	−	0.0530078i
$777$	51704.9	−	96895.7i	0.0856426	−	0.160495i
$778$	24925.5	+	76712.8i	0.0411799	+	0.126739i
$779$	−194421.	−	267598.i	−0.320383	−	0.440969i
$780$	−45559.1	+	256156.i	−0.0748835	+	0.421032i
$781$	9362.20	+	21823.1i	0.0153488	+	0.0357779i
$782$			653604.i			1.06881i
$783$	−25638.6	−	254840.i	−0.0418187	−	0.415665i
$784$	−200239.	−	616273.i	−0.325775	−	1.00263i
$785$	823433.	+	267550.i	1.33625	+	0.434175i
$786$	−529556.	−	550002.i	−0.857170	−	0.890265i
$787$	890300.	+	646840.i	1.43743	+	1.04435i	0.988572	+	0.150751i	$0.0481691\pi$
$787$	890300.	+	646840.i	1.43743	+	1.04435i	0.448858	+	0.893603i	$0.351831\pi$
$788$	18.7248	+	6.08407i	3.01554e−5	+	9.79809e-6i
$789$	−614239.	+	85396.7i	−0.986696	+	0.137179i
$790$	−184024.	+	133701.i	−0.294862	+	0.214230i
$791$		−	1.20394e6i		−	1.92421i
$792$	−25538.5	−	479378.i	−0.0407141	−	0.764236i
$793$	154206.			0.245220
$794$	−569359.	−	783656.i	−0.903120	−	1.24304i
$795$	28728.7	+	206639.i	0.0454550	+	0.326947i
$796$	−56050.0	+	172504.i	−0.0884606	+	0.272254i
$797$	−486538.	+	669662.i	−0.765949	+	1.05424i	0.230747	+	0.973014i	$0.425883\pi$
$797$	−486538.	+	669662.i	−0.765949	+	1.05424i	−0.996696	+	0.0812245i	$0.974117\pi$
$798$	−207052.	+	199355.i	−0.325142	+	0.313055i
$799$	94624.9	−	291225.i	0.148222	−	0.456179i
$800$	−28104.7	+	9131.79i	−0.0439137	+	0.0142684i
$801$	233335.	+	822941.i	0.363675	+	1.28264i
$802$	989733.			1.53875
$803$	400856.	+	457580.i	0.621666	+	0.709636i
$804$	−286259.	−	50913.1i	−0.442840	−	0.0787621i
$805$	1.02222e6	−	742686.i	1.57744	−	1.14608i
$806$	1.00468e6	−	326440.i	1.54653	−	0.502497i
$807$	−206833.	−	110369.i	−0.317595	−	0.169473i
$808$	25164.9	+	18283.4i	0.0385454	+	0.0280049i
$809$	269671.	−	371171.i	0.412038	−	0.567122i	−0.551676	−	0.834059i	$-0.686011\pi$
$809$	269671.	−	371171.i	0.412038	−	0.567122i	0.963714	+	0.266937i	$0.0860114\pi$
$810$	−668629.	+	412310.i	−1.01910	+	0.628425i
$811$	−139186.	−	428372.i	−0.211619	−	0.651297i	−0.999376	−	0.0353111i	$-0.988758\pi$
$811$	−139186.	−	428372.i	−0.211619	−	0.651297i	0.787757	−	0.615986i	$-0.211242\pi$
$812$	74769.5	+	102911.i	0.113400	+	0.156082i
$813$	−474590.	−	84409.1i	−0.718021	−	0.127705i
$814$	−22611.6	+	99682.1i	−0.0341257	+	0.150442i
$815$		−	271296.i		−	0.408440i
$816$	−238260.	−	490350.i	−0.357825	−	0.736421i
$817$	22290.3	+	68602.4i	0.0333942	+	0.102777i
$818$	−80278.0	−	26083.9i	−0.119975	−	0.0389822i
$819$	621971.	+	928037.i	0.927262	+	1.38356i
$820$	363226.	+	263899.i	0.540193	+	0.392473i
$821$	−204868.	−	66565.6i	−0.303940	−	0.0987561i	0.153076	−	0.988214i	$-0.451082\pi$
$821$	−204868.	−	66565.6i	−0.303940	−	0.0987561i	−0.457016	+	0.889458i	$0.651082\pi$
$822$	123296.	+	886842.i	0.182476	+	1.31251i
$823$	138637.	−	100726.i	0.204682	−	0.148710i	−0.480723	−	0.876873i	$-0.659626\pi$
$823$	138637.	−	100726.i	0.204682	−	0.148710i	0.685404	+	0.728163i	$0.259626\pi$
$824$		−	934090.i		−	1.37573i
$825$	4096.61	−	48125.4i	0.00601890	−	0.0707077i
$826$	−752023.			−1.10223
$827$	−219216.	−	301725.i	−0.320525	−	0.441165i	0.618103	−	0.786098i	$-0.287902\pi$
$827$	−219216.	−	301725.i	−0.320525	−	0.441165i	−0.938627	+	0.344933i	$0.887902\pi$
$828$	320251.	+	12134.8i	0.467121	+	0.0177000i
$829$	−214652.	+	660630.i	−0.312338	+	0.961278i	0.664498	+	0.747290i	$0.268645\pi$
$829$	−214652.	+	660630.i	−0.312338	+	0.961278i	−0.976836	+	0.213988i	$0.931355\pi$
$830$	462928.	−	637166.i	0.671982	−	0.924904i
$831$	162374.	+	168643.i	0.235133	+	0.244211i
$832$	123032.	−	378654.i	0.177735	−	0.547011i
$833$	380260.	−	123554.i	0.548013	−	0.178060i
$834$	−216586.	−	445744.i	−0.311386	−	0.640846i
$835$	122720.			0.176012
$836$	34619.0	−	58118.9i	0.0495339	−	0.0831581i
$837$	696724.	+	406399.i	0.994512	+	0.580098i
$838$	−94770.7	+	68855.0i	−0.134954	+	0.0980499i
$839$	−880313.	+	286031.i	−1.25058	+	0.406339i	−0.858130	−	0.513432i	$-0.828374\pi$
$839$	−880313.	+	286031.i	−1.25058	+	0.406339i	−0.392454	+	0.919772i	$0.628374\pi$
$840$	−358941.	+	672660.i	−0.508703	+	0.953316i
$841$	−472338.	−	343174.i	−0.667822	−	0.485201i
$842$	−105086.	+	144639.i	−0.148225	+	0.204015i
$843$	141296.	+	75397.5i	0.198827	+	0.106097i
$844$	−97279.8	−	299396.i	−0.136564	−	0.420302i
$845$	−212968.	−	293125.i	−0.298264	−	0.410525i
$846$	−557304.	−	204717.i	−0.778666	−	0.286030i
$847$	−962572.	+	177342.i	−1.34173	+	0.247198i
$848$			280731.i			0.390390i
$849$	727520.	−	353500.i	1.00932	−	0.490427i
$850$	−12262.1	−	37738.7i	−0.0169717	−	0.0522335i
$851$	126828.	+	41208.8i	0.175128	+	0.0569024i
$852$	6890.99	−	6634.83i	0.00949298	−	0.00914009i
$853$	30761.4	+	22349.5i	0.0422774	+	0.0307163i	0.608723	−	0.793383i	$-0.291682\pi$
$853$	30761.4	+	22349.5i	0.0422774	+	0.0307163i	−0.566446	+	0.824099i	$0.691682\pi$
$854$	−219916.	−	71455.2i	−0.301538	−	0.0979756i
$855$	216174.	+	8191.18i	0.295713	+	0.0112051i
$856$	817217.	−	593743.i	1.11530	−	0.810309i
$857$			1.19602e6i			1.62846i	0.580542	+	0.814230i	$0.302841\pi$
$857$			1.19602e6i			1.62846i	−0.580542	+	0.814230i	$0.697159\pi$
$858$	−786301.	−	680287.i	−1.06811	−	0.924097i
$859$	430100.			0.582886			0.291443	−	0.956588i	$-0.405865\pi$
$859$	430100.			0.582886			0.291443	+	0.956588i	$0.405865\pi$
$860$	−57549.9	−	79210.7i	−0.0778123	−	0.107099i
$861$	1.90950e6	−	265475.i	2.57581	−	0.358110i
$862$	−472898.	+	1.45543e6i	−0.636433	+	1.95874i
$863$	473699.	−	651990.i	0.636034	−	0.875426i	−0.362362	−	0.932037i	$-0.618030\pi$
$863$	473699.	−	651990.i	0.636034	−	0.875426i	0.998396	+	0.0566113i	$0.0180296\pi$
$864$	−444602.	+	195584.i	−0.595586	+	0.262002i
$865$	−42593.8	+	131090.i	−0.0569264	+	0.175202i
$866$	646553.	−	210078.i	0.862122	−	0.280120i
$867$	−373540.	+	181502.i	−0.496935	+	0.241459i
$868$	−400594.			−0.531697
$869$	−20912.8	−	228929.i	−0.0276931	−	0.303153i
$870$	66293.7	−	372736.i	0.0875859	−	0.492451i
$871$	995627.	−	723365.i	1.31238	−	0.953502i
$872$	−417124.	+	135532.i	−0.548570	+	0.178241i
$873$	40323.1	−	51296.7i	0.0529084	−	0.0673071i
$874$	−282342.	−	205134.i	−0.369618	−	0.268543i
$875$	590296.	−	812473.i	0.770999	−	1.06119i
$876$	115367.	−	216200.i	0.150340	−	0.281740i
$877$	−433731.	−	1.33489e6i	−0.563925	−	1.73558i	−0.671123	−	0.741346i	$-0.734188\pi$
$877$	−433731.	−	1.33489e6i	−0.563925	−	1.73558i	0.107198	−	0.994238i	$-0.465812\pi$
$878$	−300720.	−	413905.i	−0.390097	−	0.536923i
$879$	60952.5	−	342705.i	0.0788885	−	0.443551i
$880$	216981.	−	956552.i	0.280192	−	1.23522i
$881$		−	956807.i		−	1.23274i	−0.787456	−	0.616371i	$-0.788602\pi$
$881$		−	956807.i		−	1.23274i	0.787456	−	0.616371i	$-0.211398\pi$
$882$	−211469.	−	745826.i	−0.271838	−	0.958739i
$883$	−150053.	−	461814.i	−0.192452	−	0.592306i	−0.999997	−	0.00249999i	$-0.999204\pi$
$883$	−150053.	−	461814.i	−0.192452	−	0.592306i	0.807545	−	0.589806i	$-0.200796\pi$
$884$	−205448.	−	66754.2i	−0.262904	−	0.0854228i
$885$	392577.	+	407735.i	0.501232	+	0.520584i
$886$	284750.	+	206883.i	0.362741	+	0.263547i
$887$	1.03701e6	+	336946.i	1.31807	+	0.428265i	0.881830	−	0.471567i	$-0.156312\pi$
$887$	1.03701e6	+	336946.i	1.31807	+	0.428265i	0.436235	+	0.899833i	$0.356312\pi$
$888$	−79701.7	+	11080.8i	−0.101075	+	0.0140522i
$889$	−789459.	+	573576.i	−0.998909	+	0.725750i
$890$			1.26436e6i			1.59621i
$891$	−12185.9	−	793787.i	−0.0153498	−	0.999882i
$892$	421757.			0.530069
$893$	96104.9	+	132277.i	0.120515	+	0.165875i
$894$	−121967.	−	877283.i	−0.152605	−	1.09765i
$895$	−197021.	+	606368.i	−0.245961	+	0.756990i
$896$	−769816.	+	1.05956e6i	−0.958894	+	1.31980i
$897$	−977181.	+	940855.i	−1.21448	+	1.16933i
$898$	−159762.	+	491698.i	−0.198117	+	0.609742i
$899$	−369707.	+	120125.i	−0.457444	+	0.148633i
$900$	−18718.8	+	5307.47i	−0.0231096	+	0.00655243i
$901$	−173220.			−0.213377
$902$	−1.64889e6	+	707381.i	−2.02665	+	0.869441i
$903$	−413925.	−	73619.4i	−0.507628	−	0.0902852i
$904$	−713632.	+	518484.i	−0.873248	+	0.634452i
$905$	−622731.	+	202338.i	−0.760332	+	0.247047i
$906$	824376.	+	439898.i	1.00431	+	0.535915i
$907$	−1.04174e6	−	756872.i	−1.26633	−	0.920042i	−0.267279	−	0.963619i	$-0.586125\pi$
$907$	−1.04174e6	−	756872.i	−1.26633	−	0.920042i	−0.999050	+	0.0435772i	$0.986125\pi$
$908$	153003.	−	210590.i	0.185578	−	0.255427i
$909$	40441.0	+	31789.7i	0.0489434	+	0.0384732i
$910$	510291.	+	1.57051e6i	0.616219	+	1.89653i
$911$	830836.	+	1.14355e6i	1.00110	+	1.37790i	0.924646	+	0.380827i	$0.124361\pi$
$911$	830836.	+	1.14355e6i	1.00110	+	1.37790i	0.0764569	+	0.997073i	$0.475639\pi$
$912$	286598.	+	50973.5i	0.344575	+	0.0612851i
$913$	313807.	+	731478.i	0.376461	+	0.877525i
$914$		−	1.59917e6i		−	1.91427i
$915$	76060.8	+	156537.i	0.0908487	+	0.186971i
$916$	−41176.0	−	126727.i	−0.0490742	−	0.151035i
$917$	−1.16551e6	−	378697.i	−1.38605	−	0.450353i
$918$	−262627.	−	597007.i	−0.311641	−	0.708426i
$919$	−9568.76	−	6952.11i	−0.0113299	−	0.00823162i	0.582106	−	0.813113i	$-0.302229\pi$
$919$	−9568.76	−	6952.11i	−0.0113299	−	0.00823162i	−0.593436	+	0.804881i	$0.702229\pi$
$920$	−880450.	−	286075.i	−1.04023	−	0.337991i
$921$	5424.59	+	39017.8i	0.00639510	+	0.0459985i
$922$	140854.	−	102337.i	0.165694	−	0.120384i
$923$			40489.7i			0.0475271i
$924$	203863.	+	337488.i	0.238778	+	0.395289i
$925$	−8096.06			−0.00946216
$926$	762038.	+	1.04886e6i	0.888699	+	1.22319i
$927$	58490.1	−	1.54362e6i	0.0680648	−	1.79630i
$928$	72338.2	−	222634.i	0.0839985	−	0.258521i
$929$	329207.	−	453115.i	0.381450	−	0.525021i	−0.574518	−	0.818492i	$-0.694810\pi$
$929$	329207.	−	453115.i	0.381450	−	0.525021i	0.955968	+	0.293471i	$0.0948104\pi$
$930$	826923.	+	858850.i	0.956091	+	0.993005i
$931$	−65972.1	+	203041.i	−0.0761134	+	0.234253i
$932$	−16596.1	+	5392.41i	−0.0191062	+	0.00620799i
$933$	168103.	+	345965.i	0.193114	+	0.397437i
$934$	698207.			0.800369
$935$	590223.	+	133884.i	0.675138	+	0.153146i
$936$	282236.	−	768337.i	0.322152	−	0.877001i
$937$	872028.	−	633566.i	0.993234	−	0.721626i	0.0326068	−	0.999468i	$-0.489619\pi$
$937$	872028.	−	633566.i	0.993234	−	0.721626i	0.960627	+	0.277842i	$0.0896191\pi$
$938$	−1.75507e6	+	570258.i	−1.99476	+	0.648135i
$939$	381785.	−	715471.i	0.433000	−	0.811448i
$940$	−179547.	−	130448.i	−0.203199	−	0.147633i
$941$	314855.	−	433361.i	0.355575	−	0.489408i	−0.593334	−	0.804956i	$-0.702189\pi$
$941$	314855.	−	433361.i	0.355575	−	0.489408i	0.948909	+	0.315549i	$0.102189\pi$
$942$	1.22969e6	+	656181.i	1.38578	+	0.739472i
$943$	723358.	+	2.22627e6i	0.813449	+	2.50354i
$944$	447675.	+	616171.i	0.502364	+	0.691445i
$945$	−635282.	+	1.08912e6i	−0.711382	+	1.21958i
$946$	389654.	−	35595.0i	0.435408	−	0.0397747i
$947$			340946.i			0.380177i	0.981767	+	0.190089i	$0.0608775\pi$
$947$			340946.i			0.380177i	−0.981767	+	0.190089i	$0.939122\pi$
$948$	−83292.4	+	40471.6i	−0.0926806	+	0.0450333i
$949$	320527.	+	986481.i	0.355903	+	1.09536i
$950$	20150.7	+	6547.38i	0.0223277	+	0.00725471i
$951$	−445257.	+	428705.i	−0.492323	+	0.474021i
$952$	−512142.	−	372093.i	−0.565088	−	0.410561i
$953$	−829635.	−	269565.i	−0.913485	−	0.296809i	−0.185693	−	0.982608i	$-0.559453\pi$
$953$	−829635.	−	269565.i	−0.913485	−	0.296809i	−0.727791	+	0.685799i	$0.759453\pi$
$954$	−12717.0	+	335615.i	−0.0139729	+	0.368760i
$955$	−380105.	+	276163.i	−0.416771	+	0.302802i
$956$		−	278442.i		−	0.304663i
$957$	289347.	+	250335.i	0.315933	+	0.273337i
$958$	650814.			0.709130
$959$	844739.	+	1.16268e6i	0.918513	+	1.26423i
$960$	445062.	−	61876.2i	0.482923	−	0.0671400i
$961$	92911.8	−	285953.i	0.100606	−	0.309634i
$962$	−102441.	+	140998.i	−0.110694	+	0.152357i
$963$	1.38766e6	−	930009.i	1.49634	−	1.00285i
$964$	67502.3	−	207751.i	0.0726381	−	0.223557i
$965$	−1.60829e6	+	522567.i	−1.72707	+	0.561160i
$966$	1.82955e6	−	888972.i	1.96060	−	0.952651i
$967$	927536.			0.991923			0.495961	−	0.868345i	$-0.334816\pi$
$967$	927536.			0.991923			0.495961	+	0.868345i	$0.334816\pi$
$968$	519657.	+	494188.i	0.554582	+	0.527402i
$969$	−31452.3	+	176840.i	−0.0334969	+	0.188336i
$970$	78025.2	−	56688.7i	0.0829262	−	0.0602494i
$971$	1.02699e6	−	333689.i	1.08925	−	0.353918i	0.291292	−	0.956634i	$-0.405915\pi$
$971$	1.02699e6	−	333689.i	1.08925	−	0.353918i	0.797956	+	0.602716i	$0.205915\pi$
$972$	−297396.	+	117597.i	−0.314776	+	0.124470i
$973$	−643532.	−	467554.i	−0.679743	−	0.493862i
$974$	−658468.	+	906304.i	−0.694092	+	0.955335i
$975$	38770.8	−	72657.0i	0.0407845	−	0.0764308i
$976$	72367.9	+	222726.i	0.0759708	+	0.233814i
$977$	−499620.	−	687668.i	−0.523421	−	0.720427i	0.462689	−	0.886520i	$-0.346885\pi$
$977$	−499620.	−	687668.i	−0.523421	−	0.720427i	−0.986110	+	0.166094i	$0.946885\pi$
$978$	76477.6	−	429995.i	0.0799570	−	0.449558i
$979$	−1.09779e6	−	653911.i	−1.14540	−	0.682265i
$980$		−	289782.i		−	0.301731i
$981$	−697799.	+	197852.i	−0.725090	+	0.205590i
$982$	−319870.	−	984458.i	−0.331704	−	1.02088i
$983$	979559.	+	318278.i	1.01373	+	0.329382i	0.768340	−	0.640042i	$-0.221083\pi$
$983$	979559.	+	318278.i	1.01373	+	0.329382i	0.245393	+	0.969424i	$0.421083\pi$
$984$	−979697.	−	1.01752e6i	−1.01182	−	1.05088i
$985$	−76.0901	−	55.2827i	−7.84252e−5	−	5.69792e-5i
$986$	298951.	+	97134.9i	0.307500	+	0.0999129i
$987$	−943888.	+	131227.i	−0.968916	+	0.134707i
$988$	93316.3	−	67798.3i	0.0955969	−	0.0694552i
$989$		−	510480.i		−	0.521898i
$990$	302732.	−	1.13373e6i	0.308879	−	1.15675i
$991$	−593971.			−0.604809			−0.302404	−	0.953180i	$-0.597789\pi$
$991$	−593971.			−0.604809			−0.302404	+	0.953180i	$0.597789\pi$
$992$	433313.	+	596404.i	0.440330	+	0.606063i
$993$	209495.	+	1.50685e6i	0.212459	+	1.52817i
$994$	18761.9	−	57743.2i	0.0189891	−	0.0584424i
$995$	509297.	−	700987.i	0.514428	−	0.708050i
$996$	230976.	−	222389.i	0.232835	−	0.224179i
$997$	−466024.	+	1.43427e6i	−0.468833	+	1.44292i	0.385265	+	0.922806i	$0.374110\pi$
$997$	−466024.	+	1.43427e6i	−0.468833	+	1.44292i	−0.854098	+	0.520113i	$0.825890\pi$
$998$	31317.0	−	10175.5i	0.0314427	−	0.0102163i
$999$	−132404.	+	13320.7i	−0.132669	+	0.0133474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.h.a.14.4	✓	56
3.2	odd	2	inner	33.5.h.a.14.11	yes	56
11.4	even	5	inner	33.5.h.a.26.11	yes	56
33.26	odd	10	inner	33.5.h.a.26.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.h.a.14.4	✓	56	1.1	even	1	trivial
33.5.h.a.14.11	yes	56	3.2	odd	2	inner
33.5.h.a.26.4	yes	56	33.26	odd	10	inner
33.5.h.a.26.11	yes	56	11.4	even	5	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72011 - 3.74391i) q^{2} +(1.23934 + 8.91426i) q^{3} +(-1.67360 + 5.15080i) q^{4} +(15.2071 - 20.9308i) q^{5} +(30.0031 - 28.8877i) q^{6} +(20.6582 - 63.5795i) q^{7} +(-46.5832 + 15.1358i) q^{8} +(-77.9281 + 22.0955i) q^{9} +O(q^{10})\)	\(q+(-2.72011 - 3.74391i) q^{2} +(1.23934 + 8.91426i) q^{3} +(-1.67360 + 5.15080i) q^{4} +(15.2071 - 20.9308i) q^{5} +(30.0031 - 28.8877i) q^{6} +(20.6582 - 63.5795i) q^{7} +(-46.5832 + 15.1358i) q^{8} +(-77.9281 + 22.0955i) q^{9} -119.728 q^{10} +(61.9218 - 103.955i) q^{11} +(-47.9897 - 8.53531i) q^{12} +(166.912 - 121.268i) q^{13} +(-294.229 + 95.6007i) q^{14} +(205.429 + 109.620i) q^{15} +(253.483 + 184.166i) q^{16} +(-113.636 + 156.407i) q^{17} +(294.697 + 231.654i) q^{18} +(-31.8996 - 98.1768i) q^{19} +(82.3597 + 113.358i) q^{20} +(592.367 + 105.357i) q^{21} +(-557.633 + 50.9399i) q^{22} +730.547i q^{23} +(-192.657 - 396.496i) q^{24} +(-13.7056 - 42.1814i) q^{25} +(-908.036 - 295.039i) q^{26} +(-293.544 - 667.288i) q^{27} +(292.912 + 212.813i) q^{28} +(334.143 + 108.570i) q^{29} +(-148.383 - 1067.29i) q^{30} +(-895.122 + 650.344i) q^{31} -666.283i q^{32} +(1003.43 + 423.152i) q^{33} +894.678 q^{34} +(-1016.62 - 1399.25i) q^{35} +(16.6106 - 438.371i) q^{36} +(56.4081 - 173.606i) q^{37} +(-280.795 + 386.481i) q^{38} +(1287.88 + 1337.60i) q^{39} +(-391.591 + 1205.19i) q^{40} +(3047.40 - 990.160i) q^{41} +(-1216.86 - 2504.35i) q^{42} -698.764 q^{43} +(431.821 + 492.926i) q^{44} +(-722.583 + 1967.10i) q^{45} +(2735.10 - 1987.17i) q^{46} +(-1506.37 + 489.448i) q^{47} +(-1327.56 + 2487.86i) q^{48} +(-1673.14 - 1215.61i) q^{49} +(-120.643 + 166.050i) q^{50} +(-1535.09 - 819.143i) q^{51} +(345.287 + 1062.68i) q^{52} +(526.645 + 724.865i) q^{53} +(-1699.79 + 2914.10i) q^{54} +(-1234.21 - 2876.93i) q^{55} +3274.42i q^{56} +(835.639 - 406.035i) q^{57} +(-502.431 - 1546.32i) q^{58} +(2311.85 + 751.164i) q^{59} +(-908.435 + 874.665i) q^{60} +(604.686 + 439.330i) q^{61} +(4869.66 + 1582.25i) q^{62} +(-205.035 + 5411.09i) q^{63} +(1561.22 - 1134.30i) q^{64} -5337.73i q^{65} +(-1145.19 - 4907.76i) q^{66} +5964.99 q^{67} +(-615.440 - 847.081i) q^{68} +(-6512.28 + 905.392i) q^{69} +(-2473.37 + 7612.24i) q^{70} +(-115.354 + 158.772i) q^{71} +(3295.71 - 2208.78i) q^{72} +(-1553.59 + 4781.45i) q^{73} +(-803.403 + 261.042i) q^{74} +(359.030 - 174.452i) q^{75} +559.076 q^{76} +(-5330.23 - 6084.49i) q^{77} +(1504.69 - 8460.12i) q^{78} +(1537.02 - 1116.71i) q^{79} +(7709.48 - 2504.96i) q^{80} +(5584.58 - 3443.72i) q^{81} +(-11996.3 - 8715.85i) q^{82} +(-3866.50 + 5321.79i) q^{83} +(-1534.05 + 2874.84i) q^{84} +(1545.64 + 4756.99i) q^{85} +(1900.71 + 2616.11i) q^{86} +(-553.703 + 3113.20i) q^{87} +(-1311.07 + 5779.80i) q^{88} -10560.3i q^{89} +(9330.16 - 2645.45i) q^{90} +(-4262.09 - 13117.4i) q^{91} +(-3762.90 - 1222.64i) q^{92} +(-6906.69 - 7173.35i) q^{93} +(5929.93 + 4308.35i) q^{94} +(-2540.01 - 825.301i) q^{95} +(5939.42 - 825.748i) q^{96} +(-651.688 + 473.479i) q^{97} +9570.70i q^{98} +(-2528.50 + 9469.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9}+O(q^{10}) \) 56 * q + 90 * q^4 - 83 * q^6 - 86 * q^7 + 232 * q^9	\( 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9} + 136 q^{10} - 710 q^{12} + 94 q^{13} - 406 q^{15} + 334 q^{16} + 1149 q^{18} + 958 q^{19} - 728 q^{21} - 1300 q^{22} + 795 q^{24} - 1740 q^{25} - 1026 q^{27} - 4962 q^{28} - 744 q^{30} - 130 q^{31} - 2875 q^{33} + 4844 q^{34} + 11631 q^{36} + 2802 q^{37} + 8696 q^{39} - 626 q^{40} + 8804 q^{42} - 980 q^{43} - 17356 q^{45} + 8698 q^{46} - 17854 q^{48} + 7516 q^{49} + 1461 q^{51} + 11818 q^{52} - 9082 q^{54} - 4916 q^{55} - 2661 q^{57} - 38922 q^{58} - 28194 q^{60} - 15150 q^{61} - 488 q^{63} - 30690 q^{64} + 20100 q^{66} + 40544 q^{67} + 25662 q^{69} + 15720 q^{70} + 72430 q^{72} - 20554 q^{73} + 28841 q^{75} + 70996 q^{76} - 39716 q^{78} + 46458 q^{79} - 24284 q^{81} + 26200 q^{82} - 8346 q^{84} - 15494 q^{85} - 66228 q^{87} - 78050 q^{88} - 43484 q^{90} - 49854 q^{91} - 30184 q^{93} - 119550 q^{94} + 50098 q^{96} - 64476 q^{97} + 52640 q^{99}+O(q^{100}) \) 56 * q + 90 * q^4 - 83 * q^6 - 86 * q^7 + 232 * q^9 + 136 * q^10 - 710 * q^12 + 94 * q^13 - 406 * q^15 + 334 * q^16 + 1149 * q^18 + 958 * q^19 - 728 * q^21 - 1300 * q^22 + 795 * q^24 - 1740 * q^25 - 1026 * q^27 - 4962 * q^28 - 744 * q^30 - 130 * q^31 - 2875 * q^33 + 4844 * q^34 + 11631 * q^36 + 2802 * q^37 + 8696 * q^39 - 626 * q^40 + 8804 * q^42 - 980 * q^43 - 17356 * q^45 + 8698 * q^46 - 17854 * q^48 + 7516 * q^49 + 1461 * q^51 + 11818 * q^52 - 9082 * q^54 - 4916 * q^55 - 2661 * q^57 - 38922 * q^58 - 28194 * q^60 - 15150 * q^61 - 488 * q^63 - 30690 * q^64 + 20100 * q^66 + 40544 * q^67 + 25662 * q^69 + 15720 * q^70 + 72430 * q^72 - 20554 * q^73 + 28841 * q^75 + 70996 * q^76 - 39716 * q^78 + 46458 * q^79 - 24284 * q^81 + 26200 * q^82 - 8346 * q^84 - 15494 * q^85 - 66228 * q^87 - 78050 * q^88 - 43484 * q^90 - 49854 * q^91 - 30184 * q^93 - 119550 * q^94 + 50098 * q^96 - 64476 * q^97 + 52640 * q^99

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