LMFDB - Embedded newform 70.4.i.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,4,Mod(9,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("70.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	70.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.13013370040$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	70.9
Dual form			70.4.i.a.39.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(-5.57922 + 3.22116i) q^{3} +(2.00000 + 3.46410i) q^{4} +(11.1535 - 0.774747i) q^{5} +12.8846 q^{6} +(-18.1586 - 3.64221i) q^{7} -8.00000i q^{8} +(7.25176 - 12.5604i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{2} +(-5.57922 + 3.22116i) q^{3} +(2.00000 + 3.46410i) q^{4} +(11.1535 - 0.774747i) q^{5} +12.8846 q^{6} +(-18.1586 - 3.64221i) q^{7} -8.00000i q^{8} +(7.25176 - 12.5604i) q^{9} +(-20.0931 - 9.81156i) q^{10} +(-24.1923 - 41.9023i) q^{11} +(-22.3169 - 12.8846i) q^{12} -93.4871i q^{13} +(27.8094 + 24.4671i) q^{14} +(-59.7320 + 40.2496i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-17.5624 + 10.1396i) q^{17} +(-25.1208 + 14.5035i) q^{18} +(-15.5290 + 26.8971i) q^{19} +(24.9907 + 37.0872i) q^{20} +(113.043 - 38.1711i) q^{21} +96.7692i q^{22} +(18.2287 + 10.5244i) q^{23} +(25.7693 + 44.6337i) q^{24} +(123.800 - 17.2822i) q^{25} +(-93.4871 + 161.924i) q^{26} -80.5063i q^{27} +(-23.7002 - 70.1876i) q^{28} -69.5116 q^{29} +(143.708 - 9.98234i) q^{30} +(-80.5581 - 139.531i) q^{31} +(27.7128 - 16.0000i) q^{32} +(269.948 + 155.855i) q^{33} +40.5585 q^{34} +(-205.353 - 26.5550i) q^{35} +58.0141 q^{36} +(140.800 + 81.2909i) q^{37} +(53.7942 - 31.0581i) q^{38} +(301.137 + 521.585i) q^{39} +(-6.19798 - 89.2277i) q^{40} -365.073 q^{41} +(-233.967 - 46.9286i) q^{42} +254.518i q^{43} +(96.7692 - 167.609i) q^{44} +(71.1511 - 145.711i) q^{45} +(-21.0487 - 36.4575i) q^{46} +(-405.994 - 234.401i) q^{47} -103.077i q^{48} +(316.469 + 132.275i) q^{49} +(-231.709 - 93.8658i) q^{50} +(65.3228 - 113.142i) q^{51} +(323.849 - 186.974i) q^{52} +(-508.487 + 293.575i) q^{53} +(-80.5063 + 139.441i) q^{54} +(-302.292 - 448.613i) q^{55} +(-29.1377 + 145.269i) q^{56} -200.086i q^{57} +(120.398 + 69.5116i) q^{58} +(268.472 + 465.008i) q^{59} +(-258.893 - 126.419i) q^{60} +(312.912 - 541.979i) q^{61} +322.232i q^{62} +(-177.430 + 201.667i) q^{63} -64.0000 q^{64} +(-72.4289 - 1042.71i) q^{65} +(-311.709 - 539.896i) q^{66} +(106.585 - 61.5368i) q^{67} +(-70.2494 - 40.5585i) q^{68} -135.603 q^{69} +(329.127 + 251.347i) q^{70} +210.060 q^{71} +(-100.483 - 58.0141i) q^{72} +(122.788 - 70.8917i) q^{73} +(-162.582 - 281.600i) q^{74} +(-635.035 + 495.200i) q^{75} -124.232 q^{76} +(286.681 + 849.000i) q^{77} -1204.55i q^{78} +(256.712 - 444.638i) q^{79} +(-78.4925 + 160.745i) q^{80} +(455.121 + 788.294i) q^{81} +(632.325 + 365.073i) q^{82} +117.376i q^{83} +(358.314 + 315.250i) q^{84} +(-188.025 + 126.698i) q^{85} +(254.518 - 440.839i) q^{86} +(387.820 - 223.908i) q^{87} +(-335.218 + 193.538i) q^{88} +(-30.6294 + 53.0517i) q^{89} +(-268.948 + 181.227i) q^{90} +(-340.500 + 1697.59i) q^{91} +84.1950i q^{92} +(898.902 + 518.981i) q^{93} +(468.802 + 811.989i) q^{94} +(-152.364 + 312.027i) q^{95} +(-103.077 + 178.535i) q^{96} -436.654i q^{97} +(-415.865 - 545.575i) q^{98} -701.748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9	$ 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9} + 12 q^{10} - 62 q^{11} - 84 q^{14} + 172 q^{15} - 192 q^{16} + 186 q^{19} - 64 q^{20} + 350 q^{21} + 112 q^{24} + 126 q^{25} - 236 q^{26} - 676 q^{29} + 28 q^{30} - 652 q^{31} - 544 q^{34} - 1344 q^{35} + 496 q^{36} - 868 q^{39} - 48 q^{40} + 792 q^{41} + 248 q^{44} + 664 q^{45} + 376 q^{46} + 1602 q^{49} + 320 q^{50} - 1448 q^{51} + 1540 q^{54} + 596 q^{55} - 144 q^{56} + 1336 q^{59} + 344 q^{60} - 314 q^{61} - 1536 q^{64} + 1862 q^{65} - 1600 q^{66} + 180 q^{69} - 484 q^{70} + 4432 q^{71} - 1012 q^{74} - 4550 q^{75} + 1488 q^{76} - 1772 q^{79} - 128 q^{80} + 1228 q^{81} + 784 q^{84} + 4564 q^{85} + 396 q^{86} + 6094 q^{89} + 200 q^{90} - 4364 q^{91} + 3604 q^{94} + 1166 q^{95} - 448 q^{96} - 17092 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9 + 12 * q^10 - 62 * q^11 - 84 * q^14 + 172 * q^15 - 192 * q^16 + 186 * q^19 - 64 * q^20 + 350 * q^21 + 112 * q^24 + 126 * q^25 - 236 * q^26 - 676 * q^29 + 28 * q^30 - 652 * q^31 - 544 * q^34 - 1344 * q^35 + 496 * q^36 - 868 * q^39 - 48 * q^40 + 792 * q^41 + 248 * q^44 + 664 * q^45 + 376 * q^46 + 1602 * q^49 + 320 * q^50 - 1448 * q^51 + 1540 * q^54 + 596 * q^55 - 144 * q^56 + 1336 * q^59 + 344 * q^60 - 314 * q^61 - 1536 * q^64 + 1862 * q^65 - 1600 * q^66 + 180 * q^69 - 484 * q^70 + 4432 * q^71 - 1012 * q^74 - 4550 * q^75 + 1488 * q^76 - 1772 * q^79 - 128 * q^80 + 1228 * q^81 + 784 * q^84 + 4564 * q^85 + 396 * q^86 + 6094 * q^89 + 200 * q^90 - 4364 * q^91 + 3604 * q^94 + 1166 * q^95 - 448 * q^96 - 17092 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	−5.57922	+	3.22116i	−1.07372	+	0.619913i	−0.929196	−	0.369588i	$-0.879499\pi$
$3$	−5.57922	+	3.22116i	−1.07372	+	0.619913i	−0.144525	+	0.989501i	$0.546165\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	11.1535	−	0.774747i	0.997596	−	0.0692955i
$5$	11.1535	−	0.774747i	0.997596	−	0.0692955i
$6$	12.8846			0.876689
$7$	−18.1586	−	3.64221i	−0.980472	−	0.196661i
$7$	−18.1586	−	3.64221i	−0.980472	−	0.196661i
$8$		−	8.00000i		−	0.353553i
$9$	7.25176	−	12.5604i	0.268584	−	0.465201i
$10$	−20.0931	−	9.81156i	−0.635400	−	0.310269i
$11$	−24.1923	−	41.9023i	−0.663114	−	1.14855i	−0.979793	−	0.200014i	$-0.935901\pi$
$11$	−24.1923	−	41.9023i	−0.663114	−	1.14855i	0.316679	−	0.948533i	$-0.397432\pi$
$12$	−22.3169	−	12.8846i	−0.536860	−	0.309956i
$13$		−	93.4871i		−	1.99451i	−0.0740250	−	0.997256i	$-0.523584\pi$
$13$		−	93.4871i		−	1.99451i	0.0740250	−	0.997256i	$-0.476416\pi$
$14$	27.8094	+	24.4671i	0.530884	+	0.467079i
$15$	−59.7320	+	40.2496i	−1.02818	+	0.692827i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−17.5624	+	10.1396i	−0.250559	+	0.144660i	−0.620020	−	0.784586i	$-0.712876\pi$
$17$	−17.5624	+	10.1396i	−0.250559	+	0.144660i	0.369461	+	0.929246i	$0.379542\pi$
$18$	−25.1208	+	14.5035i	−0.328947	+	0.189917i
$19$	−15.5290	+	26.8971i	−0.187506	+	0.324769i	−0.944418	−	0.328747i	$-0.893374\pi$
$19$	−15.5290	+	26.8971i	−0.187506	+	0.324769i	0.756912	+	0.653516i	$0.226707\pi$
$20$	24.9907	+	37.0872i	0.279405	+	0.414648i
$21$	113.043	−	38.1711i	1.17467	−	0.396648i
$22$			96.7692i			0.937785i
$23$	18.2287	+	10.5244i	0.165259	+	0.0954123i	0.580348	−	0.814368i	$-0.302916\pi$
$23$	18.2287	+	10.5244i	0.165259	+	0.0954123i	−0.415089	+	0.909781i	$0.636250\pi$
$24$	25.7693	+	44.6337i	0.219172	+	0.379618i
$25$	123.800	−	17.2822i	0.990396	−	0.138258i
$26$	−93.4871	+	161.924i	−0.705167	+	1.22138i
$27$		−	80.5063i		−	0.573831i
$28$	−23.7002	−	70.1876i	−0.159961	−	0.473722i
$29$	−69.5116			−0.445103			−0.222551	−	0.974921i	$-0.571438\pi$
$29$	−69.5116			−0.445103			−0.222551	+	0.974921i	$0.571438\pi$
$30$	143.708	−	9.98234i	0.874582	−	0.0607506i
$31$	−80.5581	−	139.531i	−0.466731	−	0.808402i	0.532547	−	0.846401i	$-0.321235\pi$
$31$	−80.5581	−	139.531i	−0.466731	−	0.808402i	−0.999278	+	0.0379988i	$0.987902\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	269.948	+	155.855i	1.42400	+	0.822146i
$34$	40.5585			0.204580
$35$	−205.353	−	26.5550i	−0.991742	−	0.128246i
$36$	58.0141			0.268584
$37$	140.800	+	81.2909i	0.625605	+	0.361193i	0.779048	−	0.626964i	$-0.215703\pi$
$37$	140.800	+	81.2909i	0.625605	+	0.361193i	−0.153443	+	0.988157i	$0.549036\pi$
$38$	53.7942	−	31.0581i	0.229647	−	0.132587i
$39$	301.137	+	521.585i	1.23642	+	2.14155i
$40$	−6.19798	−	89.2277i	−0.0244996	−	0.352704i
$41$	−365.073			−1.39060			−0.695302	−	0.718717i	$-0.744730\pi$
$41$	−365.073			−1.39060			−0.695302	+	0.718717i	$0.744730\pi$
$42$	−233.967	−	46.9286i	−0.859569	−	0.172410i
$43$			254.518i			0.902644i	0.892361	+	0.451322i	$0.149047\pi$
$43$			254.518i			0.902644i	−0.892361	+	0.451322i	$0.850953\pi$
$44$	96.7692	−	167.609i	0.331557	−	0.574274i
$45$	71.1511	−	145.711i	0.235702	−	0.482694i
$46$	−21.0487	−	36.4575i	−0.0674667	−	0.116856i
$47$	−405.994	−	234.401i	−1.26001	−	0.727466i	−0.286932	−	0.957951i	$-0.592635\pi$
$47$	−405.994	−	234.401i	−1.26001	−	0.727466i	−0.973076	+	0.230485i	$0.925969\pi$
$48$		−	103.077i		−	0.309956i
$49$	316.469	+	132.275i	0.922649	+	0.385641i
$50$	−231.709	−	93.8658i	−0.655373	−	0.265493i
$51$	65.3228	−	113.142i	0.179353	−	0.310649i
$52$	323.849	−	186.974i	0.863649	−	0.498628i
$53$	−508.487	+	293.575i	−1.31785	+	0.760861i	−0.983382	−	0.181547i	$-0.941890\pi$
$53$	−508.487	+	293.575i	−1.31785	+	0.760861i	−0.334467	+	0.942407i	$0.608556\pi$
$54$	−80.5063	+	139.441i	−0.202880	+	0.351399i
$55$	−302.292	−	448.613i	−0.741109	−	1.09984i
$56$	−29.1377	+	145.269i	−0.0695301	+	0.346649i
$57$		−	200.086i		−	0.464949i
$58$	120.398	+	69.5116i	0.272569	+	0.157368i
$59$	268.472	+	465.008i	0.592409	+	1.02608i	0.993907	+	0.110222i	$0.0351563\pi$
$59$	268.472	+	465.008i	0.592409	+	1.02608i	−0.401498	+	0.915860i	$0.631510\pi$
$60$	−258.893	−	126.419i	−0.557048	−	0.272009i
$61$	312.912	−	541.979i	0.656791	−	1.13760i	−0.324650	−	0.945834i	$-0.605247\pi$
$61$	312.912	−	541.979i	0.656791	−	1.13760i	0.981441	−	0.191762i	$-0.0614201\pi$
$62$			322.232i			0.660057i
$63$	−177.430	+	201.667i	−0.354826	+	0.403296i
$64$	−64.0000			−0.125000
$65$	−72.4289	−	1042.71i	−0.138211	−	1.98972i
$66$	−311.709	−	539.896i	−0.581345	−	1.00692i
$67$	106.585	−	61.5368i	0.194350	−	0.112208i	−0.399668	−	0.916660i	$-0.630874\pi$
$67$	106.585	−	61.5368i	0.194350	−	0.112208i	0.594017	+	0.804452i	$0.297541\pi$
$68$	−70.2494	−	40.5585i	−0.125279	−	0.0723301i
$69$	−135.603			−0.236589
$70$	329.127	+	251.347i	0.561974	+	0.429168i
$71$	210.060			0.351121			0.175560	−	0.984469i	$-0.443826\pi$
$71$	210.060			0.351121			0.175560	+	0.984469i	$0.443826\pi$
$72$	−100.483	−	58.0141i	−0.164473	−	0.0949587i
$73$	122.788	−	70.8917i	0.196866	−	0.113661i	−0.398327	−	0.917244i	$-0.630409\pi$
$73$	122.788	−	70.8917i	0.196866	−	0.113661i	0.595193	+	0.803583i	$0.297076\pi$
$74$	−162.582	−	281.600i	−0.255402	−	0.442369i
$75$	−635.035	+	495.200i	−0.977701	+	0.762410i
$76$	−124.232			−0.187506
$77$	286.681	+	849.000i	0.424290	+	1.25653i
$78$		−	1204.55i		−	1.74857i
$79$	256.712	−	444.638i	0.365599	−	0.633236i	−0.623273	−	0.782004i	$-0.714197\pi$
$79$	256.712	−	444.638i	0.365599	−	0.633236i	0.988872	+	0.148768i	$0.0475308\pi$
$80$	−78.4925	+	160.745i	−0.109697	+	0.224648i
$81$	455.121	+	788.294i	0.624309	+	1.08134i
$82$	632.325	+	365.073i	0.851568	+	0.491653i
$83$			117.376i			0.155225i	0.996984	+	0.0776125i	$0.0247297\pi$
$83$			117.376i			0.155225i	−0.996984	+	0.0776125i	$0.975270\pi$
$84$	358.314	+	315.250i	0.465420	+	0.409483i
$85$	−188.025	+	126.698i	−0.239932	+	0.161675i
$86$	254.518	−	440.839i	0.319133	−	0.552754i
$87$	387.820	−	223.908i	0.477916	−	0.275925i
$88$	−335.218	+	193.538i	−0.406073	+	0.234446i
$89$	−30.6294	+	53.0517i	−0.0364799	+	0.0631851i	−0.883689	−	0.468075i	$-0.844948\pi$
$89$	−30.6294	+	53.0517i	−0.0364799	+	0.0631851i	0.847209	+	0.531260i	$0.178281\pi$
$90$	−268.948	+	181.227i	−0.314996	+	0.212255i
$91$	−340.500	+	1697.59i	−0.392243	+	1.95556i
$92$			84.1950i			0.0954123i
$93$	898.902	+	518.981i	1.00228	+	0.578665i
$94$	468.802	+	811.989i	0.514396	+	0.890960i
$95$	−152.364	+	312.027i	−0.164550	+	0.336982i
$96$	−103.077	+	178.535i	−0.109586	+	0.189809i
$97$		−	436.654i		−	0.457067i	−0.973536	−	0.228533i	$-0.926607\pi$
$97$		−	436.654i		−	0.457067i	0.973536	−	0.228533i	$-0.0733930\pi$
$98$	−415.865	−	545.575i	−0.428660	−	0.562362i
$99$	−701.748			−0.712407
$100$	307.466	+	394.290i	0.307466	+	0.394290i
$101$	−884.104	−	1531.31i	−0.871007	−	1.50863i	−0.860957	−	0.508678i	$-0.830134\pi$
$101$	−884.104	−	1531.31i	−0.871007	−	1.50863i	−0.0100497	−	0.999950i	$-0.503199\pi$
$102$	−226.285	+	130.646i	−0.219662	+	0.126822i
$103$	−735.608	−	424.703i	−0.703705	−	0.406284i	0.105021	−	0.994470i	$-0.466509\pi$
$103$	−735.608	−	424.703i	−0.703705	−	0.406284i	−0.808726	+	0.588186i	$0.799842\pi$
$104$	−747.897			−0.705167
$105$	1231.25	−	513.319i	1.14436	−	0.477094i
$106$	1174.30			1.07602
$107$	1110.74	+	641.288i	1.00355	+	0.579399i	0.909296	−	0.416149i	$-0.136621\pi$
$107$	1110.74	+	641.288i	1.00355	+	0.579399i	0.0942522	+	0.995548i	$0.469954\pi$
$108$	278.882	−	161.013i	0.248476	−	0.143458i
$109$	−299.199	−	518.228i	−0.262918	−	0.455388i	0.704098	−	0.710103i	$-0.251352\pi$
$109$	−299.199	−	518.228i	−0.262918	−	0.455388i	−0.967016	+	0.254715i	$0.918018\pi$
$110$	74.9717	+	1079.31i	0.0649842	+	0.935531i
$111$	−1047.40			−0.895633
$112$	195.737	−	222.475i	0.165137	−	0.187696i
$113$			860.218i			0.716128i	0.933697	+	0.358064i	$0.116563\pi$
$113$			860.218i			0.716128i	−0.933697	+	0.358064i	$0.883437\pi$
$114$	−200.086	+	346.560i	−0.164384	+	0.284722i
$115$	211.467	+	103.261i	0.171473	+	0.0837313i
$116$	−139.023	−	240.795i	−0.111276	−	0.192735i
$117$	−1174.24	−	677.947i	−0.927849	−	0.535694i
$118$		−	1073.89i		−	0.837793i
$119$	355.838	−	120.156i	0.274115	−	0.0925600i
$120$	321.997	+	477.856i	0.244951	+	0.363517i
$121$	−505.035	+	874.747i	−0.379441	+	0.657210i
$122$	−1083.96	+	625.824i	−0.804402	+	0.464422i
$123$	2036.82	−	1175.96i	1.49312	−	0.862054i
$124$	322.232	−	558.123i	0.233365	−	0.404201i
$125$	1367.40	−	288.670i	0.978435	−	0.206555i
$126$	508.984	−	171.868i	0.359872	−	0.121518i
$127$		−	971.435i		−	0.678748i	−0.940652	−	0.339374i	$-0.889785\pi$
$127$		−	971.435i		−	0.678748i	0.940652	−	0.339374i	$-0.110215\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−819.845	−	1420.01i	−0.559561	−	0.969187i
$130$	−917.255	+	1878.45i	−0.618835	+	1.26731i
$131$	−74.7967	+	129.552i	−0.0498856	+	0.0864045i	−0.889890	−	0.456175i	$-0.849219\pi$
$131$	−74.7967	+	129.552i	−0.0498856	+	0.0864045i	0.840004	+	0.542580i	$0.182552\pi$
$132$			1246.84i			0.822146i
$133$	379.950	−	431.853i	0.247713	−	0.281552i
$134$	−246.147			−0.158686
$135$	−62.3720	−	897.924i	−0.0397639	−	0.572452i
$136$	81.1171	+	140.499i	0.0511451	+	0.0885859i
$137$	428.895	−	247.623i	0.267467	−	0.154422i	−0.360269	−	0.932848i	$-0.617315\pi$
$137$	428.895	−	247.623i	0.267467	−	0.154422i	0.627736	+	0.778426i	$0.283982\pi$
$138$	234.871	+	135.603i	0.144881	+	0.0836469i
$139$	466.520			0.284674			0.142337	−	0.989818i	$-0.454538\pi$
$139$	466.520			0.284674			0.142337	+	0.989818i	$0.454538\pi$
$140$	−318.717	−	764.473i	−0.192403	−	0.461499i
$141$	3020.17			1.80386
$142$	−363.835	−	210.060i	−0.215017	−	0.124140i
$143$	−3917.33	+	2261.67i	−2.29079	+	1.32259i
$144$	116.028	+	200.967i	0.0671460	+	0.116300i
$145$	−775.295	+	53.8539i	−0.444033	+	0.0308436i
$146$	−283.567			−0.160741
$147$	−2191.73	+	281.407i	−1.22973	+	0.157891i
$148$			650.327i			0.361193i
$149$	−89.2768	+	154.632i	−0.0490862	+	0.0850197i	−0.889525	−	0.456887i	$-0.848964\pi$
$149$	−89.2768	+	154.632i	−0.0490862	+	0.0850197i	0.840438	+	0.541907i	$0.182298\pi$
$150$	1595.11	−	222.675i	0.868270	−	0.121209i
$151$	−415.834	−	720.245i	−0.224107	−	0.388164i	0.731944	−	0.681364i	$-0.238613\pi$
$151$	−415.834	−	720.245i	−0.224107	−	0.388164i	−0.956051	+	0.293200i	$0.905280\pi$
$152$	215.177	+	124.232i	0.114823	+	0.0662933i
$153$			294.121i			0.155413i
$154$	352.454	−	1757.19i	0.184426	−	0.919471i
$155$	−1006.60	−	1493.84i	−0.521628	−	0.774116i
$156$	−1204.55	+	2086.34i	−0.618212	+	1.07077i
$157$	145.230	−	83.8483i	0.0738254	−	0.0426231i	−0.462633	−	0.886550i	$-0.653095\pi$
$157$	145.230	−	83.8483i	0.0738254	−	0.0426231i	0.536458	+	0.843927i	$0.319762\pi$
$158$	−889.276	+	513.424i	−0.447766	+	0.258518i
$159$	1891.30	−	3275.84i	0.943335	−	1.63390i
$160$	296.698	−	199.926i	0.146600	−	0.0987845i
$161$	−292.676	−	257.501i	−0.143268	−	0.126049i
$162$		−	1820.49i		−	0.882907i
$163$	1396.11	+	806.046i	0.670871	+	0.387327i	0.796407	−	0.604762i	$-0.206732\pi$
$163$	1396.11	+	806.046i	0.670871	+	0.387327i	−0.125536	+	0.992089i	$0.540065\pi$
$164$	−730.146	−	1264.65i	−0.347651	−	0.602150i
$165$	3131.61	+	1529.18i	1.47755	+	0.721493i
$166$	117.376	−	203.301i	0.0548803	−	0.0950555i
$167$		−	1590.69i		−	0.737073i	−0.929613	−	0.368536i	$-0.879859\pi$
$167$		−	1590.69i		−	0.737073i	0.929613	−	0.368536i	$-0.120141\pi$
$168$	−305.369	−	904.343i	−0.140236	−	0.415307i
$169$	−6542.84			−2.97808
$170$	452.368	−	31.4226i	0.204089	−	0.0141765i
$171$	225.226	+	390.103i	0.100722	+	0.174456i
$172$	−881.678	+	509.037i	−0.390856	+	0.225661i
$173$	1508.97	+	871.204i	0.663149	+	0.382870i	0.793476	−	0.608602i	$-0.208269\pi$
$173$	1508.97	+	871.204i	0.663149	+	0.382870i	−0.130327	+	0.991471i	$0.541603\pi$
$174$	−895.632			−0.390217
$175$	−2310.97	−	137.083i	−0.998245	−	0.0592144i
$176$	774.154			0.331557
$177$	−2995.73	−	1729.59i	−1.27216	−	0.734484i
$178$	106.103	−	61.2589i	0.0446786	−	0.0257952i
$179$	−1214.68	−	2103.89i	−0.507205	−	0.878505i	−0.999965	−	0.00833990i	$-0.997345\pi$
$179$	−1214.68	−	2103.89i	−0.507205	−	0.878505i	0.492760	−	0.870165i	$-0.335988\pi$
$180$	647.058	−	44.9463i	0.267938	−	0.0186116i
$181$	2628.61			1.07946			0.539732	−	0.841837i	$-0.318526\pi$
$181$	2628.61			1.07946			0.539732	+	0.841837i	$0.318526\pi$
$182$	2287.36	−	2599.82i	0.931595	−	1.05885i
$183$			4031.76i			1.62861i
$184$	84.1950	−	145.830i	0.0337333	−	0.0584279i
$185$	1633.39	+	797.591i	0.649130	+	0.316973i
$186$	−1037.96	−	1797.80i	−0.409178	−	0.708717i
$187$	849.748	+	490.602i	0.332298	+	0.191852i
$188$		−	1875.21i		−	0.727466i
$189$	−293.221	+	1461.88i	−0.112850	+	0.562625i
$190$	575.929	−	388.082i	0.219907	−	0.148181i
$191$	−562.412	+	974.126i	−0.213061	+	0.369033i	−0.952671	−	0.304003i	$-0.901677\pi$
$191$	−562.412	+	974.126i	−0.213061	+	0.369033i	0.739610	+	0.673036i	$0.235010\pi$
$192$	357.070	−	206.154i	0.134215	−	0.0774891i
$193$	1919.18	−	1108.04i	0.715782	−	0.413257i	−0.0974164	−	0.995244i	$-0.531058\pi$
$193$	1919.18	−	1108.04i	0.715782	−	0.413257i	0.813198	+	0.581987i	$0.197725\pi$
$194$	−436.654	+	756.307i	−0.161598	+	0.279895i
$195$	3762.82	+	5584.17i	1.38185	+	2.05072i
$196$	174.724	+	1360.83i	0.0636748	+	0.495929i
$197$			3125.56i			1.13039i	0.824958	+	0.565194i	$0.191199\pi$
$197$			3125.56i			1.13039i	−0.824958	+	0.565194i	$0.808801\pi$
$198$	1215.46	+	701.748i	0.436258	+	0.251874i
$199$	2269.67	+	3931.19i	0.808506	+	1.40037i	0.913898	+	0.405943i	$0.133057\pi$
$199$	2269.67	+	3931.19i	0.808506	+	1.40037i	−0.105392	+	0.994431i	$0.533610\pi$
$200$	−138.258	−	990.396i	−0.0488815	−	0.350158i
$201$	−396.440	+	686.655i	−0.139118	+	0.240960i
$202$			3536.42i			1.23179i
$203$	1262.23	+	253.176i	0.436411	+	0.0875343i
$204$	522.582			0.179353
$205$	−4071.83	+	282.839i	−1.38726	+	0.0963626i
$206$	849.407	+	1471.22i	0.287286	+	0.497594i
$207$	264.381	−	152.641i	0.0887718	−	0.0512524i
$208$	1295.40	+	747.897i	0.431825	+	0.249314i
$209$	1502.73			0.497350
$210$	−2645.90	−	342.151i	−0.869450	−	0.112432i
$211$	2520.40			0.822331			0.411165	−	0.911561i	$-0.365122\pi$
$211$	2520.40			0.822331			0.411165	+	0.911561i	$0.365122\pi$
$212$	−2033.95	−	1174.30i	−0.658925	−	0.380430i
$213$	−1171.97	+	676.639i	−0.377006	+	0.217664i
$214$	−1282.58	−	2221.49i	−0.409697	−	0.709616i
$215$	197.187	+	2838.76i	0.0625491	+	0.900474i
$216$	−644.051			−0.202880
$217$	954.621	+	2827.09i	0.298635	+	0.884403i
$218$			1196.80i			0.371822i
$219$	−456.707	+	791.040i	−0.140920	+	0.244080i
$220$	949.457	−	1944.40i	0.290965	−	0.595869i
$221$	947.925	+	1641.85i	0.288526	+	0.499742i
$222$	1814.16	+	1047.40i	0.548461	+	0.316654i
$223$		−	5800.58i		−	1.74186i	−0.491405	−	0.870931i	$-0.663516\pi$
$223$		−	5800.58i		−	1.74186i	0.491405	−	0.870931i	$-0.336484\pi$
$224$	−561.501	+	189.601i	−0.167486	+	0.0565548i
$225$	680.693	−	1680.30i	0.201687	−	0.497867i
$226$	860.218	−	1489.94i	0.253190	−	0.438537i
$227$	5738.69	−	3313.23i	1.67793	−	0.968753i	0.714952	−	0.699173i	$-0.246448\pi$
$227$	5738.69	−	3313.23i	1.67793	−	0.968753i	0.962978	−	0.269580i	$-0.0868850\pi$
$228$	693.119	−	400.172i	0.201329	−	0.116237i
$229$	253.922	−	439.806i	0.0732736	−	0.126914i	−0.827061	−	0.562113i	$-0.809989\pi$
$229$	253.922	−	439.806i	0.0732736	−	0.126914i	0.900334	+	0.435199i	$0.143322\pi$
$230$	−263.012	−	390.320i	−0.0754021	−	0.111900i
$231$	−4334.22	−	3813.31i	−1.23451	−	1.08614i
$232$			556.093i			0.157368i
$233$	−5462.73	−	3153.91i	−1.53595	−	0.886779i	−0.999070	−	0.0431187i	$-0.986271\pi$
$233$	−5462.73	−	3153.91i	−1.53595	−	0.886779i	−0.536877	−	0.843661i	$-0.680396\pi$
$234$	1355.89	+	2348.48i	0.378793	+	0.656088i
$235$	−4709.84	−	2299.84i	−1.30739	−	0.638404i
$236$	−1073.89	+	1860.03i	−0.296204	+	0.513041i
$237$			3307.64i			0.906559i
$238$	−736.486	−	147.723i	−0.200585	−	0.0402330i
$239$	4615.12			1.24907			0.624535	−	0.780997i	$-0.285289\pi$
$239$	4615.12			1.24907			0.624535	+	0.780997i	$0.285289\pi$
$240$	−79.8587	−	1149.67i	−0.0214786	−	0.309211i
$241$	−775.352	−	1342.95i	−0.207240	−	0.358950i	0.743604	−	0.668620i	$-0.233115\pi$
$241$	−775.352	−	1342.95i	−0.207240	−	0.358950i	−0.950844	+	0.309670i	$0.899781\pi$
$242$	1749.49	−	1010.07i	0.464718	−	0.268305i
$243$	−3195.99	−	1845.20i	−0.843715	−	0.487119i
$244$	2503.30			0.656791
$245$	3632.20	+	1230.14i	0.947154	+	0.320778i
$246$	−4703.83			−1.21913
$247$	2514.53	+	1451.77i	0.647756	+	0.373982i
$248$	−1116.25	+	644.465i	−0.285813	+	0.165014i
$249$	−378.087	−	654.865i	−0.0962260	−	0.166668i
$250$	−2657.08	−	867.413i	−0.672195	−	0.219440i
$251$	762.543			0.191758			0.0958790	−	0.995393i	$-0.469434\pi$
$251$	762.543			0.191758			0.0958790	+	0.995393i	$0.469434\pi$
$252$	−1053.45	−	211.300i	−0.263339	−	0.0528199i
$253$		−	1018.44i		−	0.253077i
$254$	−971.435	+	1682.58i	−0.239974	+	0.415646i
$255$	640.919	−	1312.54i	0.157396	−	0.322331i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1993.90	−	1151.18i	−0.483954	−	0.279411i	0.238109	−	0.971239i	$-0.423473\pi$
$257$	−1993.90	−	1151.18i	−0.483954	−	0.279411i	−0.722063	+	0.691827i	$0.756806\pi$
$258$			3279.38i			0.791338i
$259$	−2260.65	−	1988.95i	−0.542355	−	0.477171i
$260$	3467.18	−	2336.31i	0.827021	−	0.557277i
$261$	−504.082	+	873.095i	−0.119547	+	0.207062i
$262$	259.103	−	149.593i	0.0610972	−	0.0352745i
$263$	4185.94	−	2416.75i	0.981429	−	0.566628i	0.0787278	−	0.996896i	$-0.474914\pi$
$263$	4185.94	−	2416.75i	0.981429	−	0.566628i	0.902701	+	0.430268i	$0.141581\pi$
$264$	1246.84	−	2159.59i	0.290672	−	0.503459i
$265$	−5443.94	+	3668.33i	−1.26196	+	0.850353i
$266$	−1089.95	+	368.041i	−0.251237	+	0.0848348i
$267$		−	394.649i		−	0.0904575i
$268$	426.340	+	246.147i	0.0971748	+	0.0561039i
$269$	2415.18	+	4183.21i	0.547420	+	0.948159i	0.998450	+	0.0556502i	$0.0177232\pi$
$269$	2415.18	+	4183.21i	0.547420	+	0.948159i	−0.451031	+	0.892508i	$0.648944\pi$
$270$	−789.893	+	1617.62i	−0.178042	+	0.364612i
$271$	2975.18	−	5153.17i	0.666899	−	1.15510i	−0.311868	−	0.950125i	$-0.600955\pi$
$271$	2975.18	−	5153.17i	0.666899	−	1.15510i	0.978767	−	0.204977i	$-0.0657119\pi$
$272$		−	324.468i		−	0.0723301i
$273$	−3568.50	−	10568.0i	−0.791120	−	2.34288i
$274$	−990.491			−0.218386
$275$	−3719.16	−	4769.39i	−0.815541	−	1.04584i
$276$	−271.206	−	469.742i	−0.0591473	−	0.102446i
$277$	−6641.46	+	3834.45i	−1.44060	+	0.831732i	−0.997890	−	0.0649312i	$-0.979317\pi$
$277$	−6641.46	+	3834.45i	−1.44060	+	0.831732i	−0.442713	+	0.896663i	$0.645984\pi$
$278$	−808.037	−	466.520i	−0.174327	−	0.100648i
$279$	−2336.75			−0.501426
$280$	−212.440	+	1642.82i	−0.0453418	+	0.350634i
$281$	−6314.18			−1.34047			−0.670235	−	0.742149i	$-0.733807\pi$
$281$	−6314.18			−1.34047			−0.670235	+	0.742149i	$0.733807\pi$
$282$	−5231.09	−	3020.17i	−1.10463	−	0.637761i
$283$	−5302.43	+	3061.36i	−1.11377	+	0.643035i	−0.939803	−	0.341716i	$-0.888992\pi$
$283$	−5302.43	+	3061.36i	−1.11377	+	0.643035i	−0.173967	+	0.984752i	$0.555659\pi$
$284$	420.121	+	727.671i	0.0877802	+	0.152040i
$285$	−155.016	−	2231.65i	−0.0322188	−	0.463831i
$286$	9046.68			1.87042
$287$	6629.21	+	1329.67i	1.36345	+	0.273478i
$288$		−	464.113i		−	0.0949587i
$289$	−2250.88	+	3898.63i	−0.458147	+	0.793534i
$290$	1396.70	+	682.017i	0.282818	+	0.138102i
$291$	1406.53	+	2436.19i	0.283342	+	0.490762i
$292$	491.152	+	283.567i	0.0984332	+	0.0568305i
$293$			1646.67i			0.328326i	0.986433	+	0.164163i	$0.0524923\pi$
$293$			1646.67i			0.328326i	−0.986433	+	0.164163i	$0.947508\pi$
$294$	4077.59	+	1704.31i	0.808876	+	0.338087i
$295$	3354.66	+	4978.45i	0.662088	+	0.982564i
$296$	650.327	−	1126.40i	0.127701	−	0.221185i
$297$	−3373.40	+	1947.63i	−0.659072	+	0.380516i
$298$	309.264	−	178.554i	0.0601180	−	0.0347092i
$299$	983.893	−	1704.15i	0.190301	−	0.329611i
$300$	−2985.49	−	1209.43i	−0.574558	−	0.232755i
$301$	927.010	−	4621.69i	0.177515	−	0.885017i
$302$			1663.34i			0.316934i
$303$	9865.22	+	5695.69i	1.87044	+	1.07990i
$304$	−248.465	−	430.353i	−0.0468764	−	0.0811923i
$305$	3070.16	−	6287.38i	0.576382	−	1.18037i
$306$	294.121	−	509.432i	0.0549470	−	0.0951709i
$307$		−	7890.42i		−	1.46687i	−0.679758	−	0.733436i	$-0.737915\pi$
$307$		−	7890.42i		−	1.46687i	0.679758	−	0.733436i	$-0.262085\pi$
$308$	−2367.66	+	2691.09i	−0.438019	+	0.497855i
$309$	5472.15			1.00744
$310$	249.649	+	3594.01i	0.0457390	+	0.658471i
$311$	1718.49	+	2976.51i	0.313333	+	0.542709i	0.979082	−	0.203467i	$-0.0652210\pi$
$311$	1718.49	+	2976.51i	0.313333	+	0.542709i	−0.665748	+	0.746176i	$0.731888\pi$
$312$	4172.68	−	2409.10i	0.757152	−	0.437142i
$313$	6243.88	+	3604.91i	1.12756	+	0.650995i	0.943319	−	0.331887i	$-0.107685\pi$
$313$	6243.88	+	3604.91i	1.12756	+	0.650995i	0.184237	+	0.982882i	$0.441019\pi$
$314$	−335.393			−0.0602782
$315$	−1822.71	+	2386.75i	−0.326026	+	0.426915i
$316$	2053.69			0.365599
$317$	767.129	+	442.902i	0.135919	+	0.0784727i	0.566417	−	0.824118i	$-0.308329\pi$
$317$	767.129	+	442.902i	0.135919	+	0.0784727i	−0.430499	+	0.902591i	$0.641662\pi$
$318$	−6551.67	+	3782.61i	−1.15534	+	0.667038i
$319$	1681.65	+	2912.70i	0.295154	+	0.511221i
$320$	−713.822	+	49.5838i	−0.124700	+	0.00866193i
$321$	−8262.77			−1.43671
$322$	249.430	+	738.681i	0.0431682	+	0.127842i
$323$		−	629.835i		−	0.108498i
$324$	−1820.49	+	3153.17i	−0.312155	+	0.540668i
$325$	−1615.67	−	11573.7i	−0.275757	−	1.97536i
$326$	−1612.09	−	2792.22i	−0.273882	−	0.474377i
$327$	3338.59	+	1927.54i	0.564601	+	0.325973i
$328$			2920.58i			0.491653i
$329$	6518.54	+	5735.11i	1.09234	+	0.961054i
$330$	−3894.92	−	5780.22i	−0.649722	−	0.964214i
$331$	883.092	−	1529.56i	0.146644	−	0.253995i	−0.783341	−	0.621592i	$-0.786486\pi$
$331$	883.092	−	1529.56i	0.146644	−	0.253995i	0.929985	+	0.367597i	$0.119820\pi$
$332$	−406.602	+	234.752i	−0.0672144	+	0.0388063i
$333$	2042.10	−	1179.00i	0.336055	−	0.194021i
$334$	−1590.69	+	2755.15i	−0.260595	+	0.451363i
$335$	1141.12	−	768.925i	0.186107	−	0.125406i
$336$	−375.429	+	1871.74i	−0.0609563	+	0.303903i
$337$		−	7521.34i		−	1.21577i	−0.794026	−	0.607883i	$-0.792019\pi$
$337$		−	7521.34i		−	1.21577i	0.794026	−	0.607883i	$-0.207981\pi$
$338$	11332.5	+	6542.84i	1.82369	+	1.05291i
$339$	−2770.90	−	4799.34i	−0.443937	−	0.768921i
$340$	−814.947	−	397.943i	−0.129990	−	0.0634749i
$341$	−3897.77	+	6751.14i	−0.618992	+	1.07213i
$342$		−	900.904i		−	0.142442i
$343$	−5264.85	−	3554.57i	−0.828791	−	0.559559i
$344$	2036.15			0.319133
$345$	−1512.44	+	105.058i	−0.236021	+	0.0163946i
$346$	−1742.41	−	3017.94i	−0.270730	−	0.468917i
$347$	−4034.41	+	2329.27i	−0.624145	+	0.360350i	−0.778481	−	0.627668i	$-0.784009\pi$
$347$	−4034.41	+	2329.27i	−0.624145	+	0.360350i	0.154336	+	0.988018i	$0.450676\pi$
$348$	1551.28	+	895.632i	0.238958	+	0.137962i
$349$	7198.15			1.10403			0.552017	−	0.833833i	$-0.313858\pi$
$349$	7198.15			1.10403			0.552017	+	0.833833i	$0.313858\pi$
$350$	3865.63	+	2548.41i	0.590362	+	0.389194i
$351$	−7526.30			−1.14451
$352$	−1340.87	−	774.154i	−0.203036	−	0.117223i
$353$	−3152.40	+	1820.04i	−0.475313	+	0.274422i	−0.718461	−	0.695567i	$-0.755153\pi$
$353$	−3152.40	+	1820.04i	−0.475313	+	0.274422i	0.243148	+	0.969989i	$0.421820\pi$
$354$	3459.17	+	5991.46i	0.519358	+	0.899555i
$355$	2342.90	−	162.744i	0.350277	−	0.0243311i
$356$	−245.035			−0.0364799
$357$	−1598.26	+	1816.59i	−0.236943	+	0.269311i
$358$			4858.73i			0.717296i
$359$	−2734.95	+	4737.07i	−0.402075	+	0.696415i	−0.993976	−	0.109596i	$-0.965044\pi$
$359$	−2734.95	+	4737.07i	−0.402075	+	0.696415i	0.591901	+	0.806011i	$0.298378\pi$
$360$	−1165.68	−	569.209i	−0.170658	−	0.0833332i
$361$	2947.20	+	5104.70i	0.429683	+	0.744233i
$362$	−4552.89	−	2628.61i	−0.661034	−	0.381648i
$363$		−	6507.20i		−	0.940880i
$364$	−6561.64	+	2215.66i	−0.944844	+	0.319045i
$365$	1314.59	−	885.818i	0.188517	−	0.127030i
$366$	4031.76	−	6983.21i	0.575802	−	0.997318i
$367$	56.3671	−	32.5435i	0.00801727	−	0.00462877i	−0.495986	−	0.868331i	$-0.665193\pi$
$367$	56.3671	−	32.5435i	0.00801727	−	0.00462877i	0.504003	+	0.863702i	$0.331860\pi$
$368$	−291.660	+	168.390i	−0.0413147	+	0.0238531i
$369$	−2647.42	+	4585.47i	−0.373494	+	0.646911i
$370$	−2031.52	−	3014.85i	−0.285442	−	0.423608i
$371$	10302.7	−	3478.89i	1.44175	−	0.486833i
$372$			4151.85i			0.578665i
$373$	8793.09	+	5076.69i	1.22061	+	0.704721i	0.965049	−	0.262071i	$-0.0844053\pi$
$373$	8793.09	+	5076.69i	1.22061	+	0.704721i	0.255565	+	0.966792i	$0.417739\pi$
$374$	−981.204	−	1699.50i	−0.135660	−	0.234970i
$375$	−6699.19	+	6015.18i	−0.922519	+	0.828327i
$376$	−1875.21	+	3247.95i	−0.257198	+	0.445480i
$377$			6498.44i			0.887763i
$378$	1969.75	−	2238.83i	0.268024	−	0.304638i
$379$	−1453.96			−0.197057			−0.0985287	−	0.995134i	$-0.531414\pi$
$379$	−1453.96			−0.197057			−0.0985287	+	0.995134i	$0.531414\pi$
$380$	−1385.62	+	96.2486i	−0.187055	+	0.0129933i
$381$	3129.15	+	5419.85i	0.420764	+	0.728785i
$382$	1948.25	−	1124.82i	0.260946	−	0.150657i
$383$	−499.957	−	288.651i	−0.0667014	−	0.0385101i	0.466278	−	0.884638i	$-0.345594\pi$
$383$	−499.957	−	288.651i	−0.0667014	−	0.0385101i	−0.532980	+	0.846128i	$0.678928\pi$
$384$	−824.617			−0.109586
$385$	3855.25	+	9247.19i	0.510342	+	1.22410i
$386$	−4432.16			−0.584433
$387$	3196.86	+	1845.71i	0.419911	+	0.242436i
$388$	1512.61	−	873.308i	0.197916	−	0.114267i
$389$	−1035.50	−	1793.54i	−0.134966	−	0.233769i	0.790618	−	0.612309i	$-0.209759\pi$
$389$	−1035.50	−	1793.54i	−0.134966	−	0.233769i	−0.925585	+	0.378541i	$0.876426\pi$
$390$	−933.220	−	13434.9i	−0.121168	−	1.74436i
$391$	−426.853			−0.0552094
$392$	1058.20	−	2531.75i	0.136345	−	0.326206i
$393$		−	963.729i		−	0.123699i
$394$	3125.56	−	5413.62i	0.399653	−	0.692219i
$395$	2518.74	−	5158.14i	0.320840	−	0.657049i
$396$	−1403.50	−	2430.92i	−0.178102	−	0.308481i
$397$	−4359.07	−	2516.71i	−0.551071	−	0.318161i	0.198483	−	0.980104i	$-0.436399\pi$
$397$	−4359.07	−	2516.71i	−0.551071	−	0.318161i	−0.749554	+	0.661943i	$0.769732\pi$
$398$		−	9078.68i		−	1.14340i
$399$	−728.756	+	3633.28i	−0.0914372	+	0.455869i
$400$	−750.927	+	1853.67i	−0.0938658	+	0.231709i
$401$	2473.44	−	4284.12i	0.308024	−	0.533514i	−0.669906	−	0.742446i	$-0.733666\pi$
$401$	2473.44	−	4284.12i	0.308024	−	0.533514i	0.977930	+	0.208932i	$0.0669989\pi$
$402$	1373.31	−	792.881i	0.170384	−	0.0983714i
$403$	−13044.3	+	7531.14i	−1.61237	+	0.930901i
$404$	3536.42	−	6125.25i	0.435503	−	0.754314i
$405$	5686.91	+	8439.60i	0.697740	+	1.03547i
$406$	−1933.07	−	1700.75i	−0.236298	−	0.207898i
$407$		−	7866.46i		−	0.958049i
$408$	−905.139	−	522.582i	−0.109831	−	0.0634110i
$409$	−4694.92	−	8131.84i	−0.567601	−	0.983114i	−0.996802	−	0.0799051i	$-0.974538\pi$
$409$	−4694.92	−	8131.84i	−0.567601	−	0.983114i	0.429201	−	0.903209i	$-0.358795\pi$
$410$	7335.45	+	3581.94i	0.883590	+	0.431461i
$411$	−1595.27	+	2763.08i	−0.191457	+	0.331612i
$412$		−	3397.63i		−	0.406284i
$413$	−3181.42	−	9421.72i	−0.379050	−	1.12255i
$414$	−610.562			−0.0724819
$415$	90.9366	+	1309.15i	0.0107564	+	0.154852i
$416$	−1495.79	−	2590.79i	−0.176292	−	0.305346i
$417$	−2602.82	+	1502.74i	−0.305661	+	0.176473i
$418$	−2602.81	−	1502.73i	−0.304564	−	0.175840i
$419$	−8423.77			−0.982167			−0.491084	−	0.871112i	$-0.663399\pi$
$419$	−8423.77			−0.982167			−0.491084	+	0.871112i	$0.663399\pi$
$420$	4240.68	+	3238.52i	0.492676	+	0.376247i
$421$	5680.15			0.657562			0.328781	−	0.944406i	$-0.393362\pi$
$421$	5680.15			0.657562			0.328781	+	0.944406i	$0.393362\pi$
$422$	−4365.47	−	2520.40i	−0.503573	−	0.290738i
$423$	−5888.35	+	3399.64i	−0.676835	+	0.390771i
$424$	2348.60	+	4067.89i	0.269005	+	0.465930i
$425$	−1998.98	+	1558.80i	−0.228152	+	0.177913i
$426$	2706.55			0.307824
$427$	−7656.04	+	8701.89i	−0.867686	+	0.986215i
$428$			5130.31i			0.579399i
$429$	14570.4	−	25236.7i	1.63978	−	2.84018i
$430$	2497.22	−	5114.07i	0.280062	−	0.573540i
$431$	−6174.18	−	10694.0i	−0.690023	−	1.19516i	−0.971830	−	0.235684i	$-0.924267\pi$
$431$	−6174.18	−	10694.0i	−0.690023	−	1.19516i	0.281806	−	0.959471i	$-0.409066\pi$
$432$	1115.53	+	644.051i	0.124238	+	0.0717289i
$433$		−	9031.93i		−	1.00242i	−0.865326	−	0.501209i	$-0.832889\pi$
$433$		−	9031.93i		−	1.00242i	0.865326	−	0.501209i	$-0.167111\pi$
$434$	1173.64	−	5851.28i	0.129807	−	0.647167i
$435$	4152.07	−	2797.81i	0.457647	−	0.308379i
$436$	1196.80	−	2072.91i	0.131459	−	0.227694i
$437$	−566.150	+	326.867i	−0.0619740	+	0.0357807i
$438$	1582.08	−	913.415i	0.172591	−	0.0996453i
$439$	−5328.71	+	9229.59i	−0.579329	+	1.00343i	0.416228	+	0.909260i	$0.363352\pi$
$439$	−5328.71	+	9229.59i	−0.579329	+	1.00343i	−0.995556	+	0.0941666i	$0.969981\pi$
$440$	−3588.90	+	2418.33i	−0.388851	+	0.262022i
$441$	3956.38	−	3015.75i	0.427209	−	0.325640i
$442$		−	3791.70i		−	0.408038i
$443$	−780.566	−	450.660i	−0.0837152	−	0.0483330i	0.457558	−	0.889180i	$-0.348724\pi$
$443$	−780.566	−	450.660i	−0.0837152	−	0.0483330i	−0.541273	+	0.840847i	$0.682058\pi$
$444$	−2094.81	−	3628.32i	−0.223908	−	0.387820i
$445$	−300.523	+	615.441i	−0.0320138	+	0.0655611i
$446$	−5800.58	+	10046.9i	−0.615841	+	1.06667i
$447$		−	1150.30i		−	0.121717i
$448$	1162.15	+	233.102i	0.122559	+	0.0245826i
$449$	7771.88			0.816877			0.408438	−	0.912786i	$-0.366074\pi$
$449$	7771.88			0.816877			0.408438	+	0.912786i	$0.366074\pi$
$450$	−2859.30	+	2229.67i	−0.299530	+	0.233573i
$451$	8831.95	+	15297.4i	0.922130	+	1.59718i
$452$	−2979.88	+	1720.44i	−0.310093	+	0.179032i
$453$	4640.05	+	2678.94i	0.481256	+	0.277853i
$454$	−13252.9			−1.37002
$455$	−2482.55	+	19197.9i	−0.255788	+	1.97804i
$456$	−1600.69			−0.164384
$457$	−2390.53	−	1380.18i	−0.244693	−	0.141273i	0.372639	−	0.927976i	$-0.378453\pi$
$457$	−2390.53	−	1380.18i	−0.244693	−	0.141273i	−0.617332	+	0.786703i	$0.711786\pi$
$458$	−879.613	+	507.845i	−0.0897415	+	0.0518123i
$459$	816.304	+	1413.88i	0.0830105	+	0.143778i
$460$	65.2298	+	939.066i	0.00661164	+	0.0951830i
$461$	−16482.3			−1.66520			−0.832602	−	0.553872i	$-0.813150\pi$
$461$	−16482.3			−1.66520			−0.832602	+	0.553872i	$0.813150\pi$
$462$	3693.78	+	10939.1i	0.371971	+	1.10158i
$463$		−	9949.16i		−	0.998653i	−0.866414	−	0.499327i	$-0.833581\pi$
$463$		−	9949.16i		−	0.998653i	0.866414	−	0.499327i	$-0.166419\pi$
$464$	556.093	−	963.181i	0.0556378	−	0.0963676i
$465$	10427.9	+	5092.02i	1.03997	+	0.507821i
$466$	6307.82	+	10925.5i	0.627048	+	1.08608i
$467$	−1820.00	−	1050.78i	−0.180341	−	0.104120i	0.407112	−	0.913378i	$-0.366536\pi$
$467$	−1820.00	−	1050.78i	−0.180341	−	0.104120i	−0.587453	+	0.809258i	$0.699869\pi$
$468$		−	5423.57i		−	0.535694i
$469$	−2159.56	+	729.217i	−0.212621	+	0.0717956i
$470$	5857.85	+	8693.28i	0.574899	+	0.853173i
$471$	−540.178	+	935.616i	−0.0528452	+	0.0915306i
$472$	3720.06	−	2147.78i	0.362775	−	0.209448i
$473$	10664.9	−	6157.39i	1.03673	−	0.598556i
$474$	3307.64	−	5729.00i	0.320517	−	0.555151i
$475$	−1457.65	+	3598.22i	−0.140803	+	0.347574i
$476$	1127.91	+	992.349i	0.108608	+	0.0955551i
$477$			8515.74i			0.817420i
$478$	−7993.63	−	4615.12i	−0.764896	−	0.441613i
$479$	−4004.98	−	6936.84i	−0.382030	−	0.661695i	0.609322	−	0.792923i	$-0.291442\pi$
$479$	−4004.98	−	6936.84i	−0.382030	−	0.661695i	−0.991352	+	0.131227i	$0.958108\pi$
$480$	−1011.35	+	2071.14i	−0.0961698	+	0.196946i
$481$	7599.65	−	13163.0i	0.720404	−	1.24778i
$482$			3101.41i			0.293082i
$483$	2462.36	+	493.894i	0.231969	+	0.0465279i
$484$	−4040.28			−0.379441
$485$	−338.296	−	4870.20i	−0.0316727	−	0.455968i
$486$	3690.41	+	6391.98i	0.344445	+	0.596596i
$487$	4661.46	−	2691.30i	0.433739	−	0.250420i	−0.267199	−	0.963641i	$-0.586098\pi$
$487$	4661.46	−	2691.30i	0.433739	−	0.250420i	0.700938	+	0.713222i	$0.252765\pi$
$488$	−4335.84	−	2503.30i	−0.402201	−	0.232211i
$489$	−10385.6			−0.960437
$490$	−5061.02	−	5762.86i	−0.466599	−	0.531305i
$491$	−3456.93			−0.317737			−0.158869	−	0.987300i	$-0.550785\pi$
$491$	−3456.93			−0.317737			−0.158869	+	0.987300i	$0.550785\pi$
$492$	8147.28	+	4703.83i	0.746561	+	0.431027i
$493$	1220.79	−	704.822i	0.111524	−	0.0643886i
$494$	−2903.53	−	5029.06i	−0.264445	−	0.458033i
$495$	−7826.92	+	543.677i	−0.710694	+	0.0493666i
$496$	2577.86			0.233365
$497$	−3814.40	−	765.084i	−0.344264	−	0.0690518i
$498$			1512.35i			0.136084i
$499$	−6049.09	+	10477.3i	−0.542674	+	0.939939i	0.456075	+	0.889941i	$0.349255\pi$
$499$	−6049.09	+	10477.3i	−0.542674	+	0.939939i	−0.998749	+	0.0499978i	$0.984079\pi$
$500$	3734.79	+	4159.49i	0.334050	+	0.372036i
$501$	5123.86	+	8874.79i	0.456921	+	0.791410i
$502$	−1320.76	−	762.543i	−0.117427	−	0.0677967i
$503$		−	1508.10i		−	0.133684i	−0.997764	−	0.0668418i	$-0.978708\pi$
$503$		−	1508.10i		−	0.133684i	0.997764	−	0.0668418i	$-0.0212923\pi$
$504$	1613.34	+	1419.44i	0.142587	+	0.125450i
$505$	−11047.2	−	16394.5i	−0.973454	−	1.44464i
$506$	−1018.44	+	1763.98i	−0.0894762	+	0.154977i
$507$	36503.9	−	21075.6i	3.19763	−	1.84615i
$508$	3365.15	−	1942.87i	0.293906	−	0.169687i
$509$	−5181.73	+	8975.02i	−0.451230	+	0.781553i	−0.998463	−	0.0554273i	$-0.982348\pi$
$509$	−5181.73	+	8975.02i	−0.451230	+	0.781553i	0.547233	+	0.836980i	$0.315681\pi$
$510$	−2422.64	+	1632.46i	−0.210346	+	0.141739i
$511$	−2487.86	+	840.073i	−0.215375	+	0.0727254i
$512$			512.000i			0.0441942i
$513$	2165.39	+	1250.19i	0.186363	+	0.107597i
$514$	2302.36	+	3987.81i	0.197574	+	0.342207i
$515$	−8533.61	−	4167.00i	−0.730167	−	0.356544i
$516$	3279.38	−	5680.05i	0.279780	−	0.484594i
$517$			22682.8i			1.92957i
$518$	1926.61	+	5705.61i	0.163418	+	0.483958i
$519$	−11225.2			−0.949383
$520$	−8341.64	+	579.431i	−0.703472	+	0.0488649i
$521$	−2325.35	−	4027.63i	−0.195538	−	0.338682i	0.751539	−	0.659689i	$-0.229312\pi$
$521$	−2325.35	−	4027.63i	−0.195538	−	0.338682i	−0.947077	+	0.321007i	$0.895979\pi$
$522$	1746.19	−	1008.16i	0.146415	−	0.0845328i
$523$	5592.54	+	3228.86i	0.467581	+	0.269958i	0.715227	−	0.698893i	$-0.246324\pi$
$523$	5592.54	+	3228.86i	0.467581	+	0.269958i	−0.247646	+	0.968851i	$0.579657\pi$
$524$	−598.374			−0.0498856
$525$	13335.0	−	6679.19i	1.10854	−	0.555245i
$526$	−9667.00			−0.801333
$527$	2829.58	+	1633.66i	0.233887	+	0.135035i
$528$	−4319.17	+	2493.67i	−0.356000	+	0.205536i
$529$	−5861.98	−	10153.2i	−0.481793	−	0.834490i
$530$	13097.5	−	909.785i	1.07343	−	0.0745633i
$531$	7787.59			0.636446
$532$	2255.88	+	452.480i	0.183844	+	0.0368750i
$533$			34129.6i			2.77358i
$534$	−394.649	+	683.553i	−0.0319815	+	0.0553937i
$535$	12885.5	+	6292.04i	1.04129	+	0.508465i
$536$	−492.295	−	852.680i	−0.0396714	−	0.0687130i
$537$	13554.0	+	7825.39i	1.08919	+	0.628846i
$538$		−	9660.70i		−	0.774168i
$539$	−2113.49	−	16460.8i	−0.168895	−	1.31543i
$540$	2985.76	−	2011.91i	0.237938	−	0.160331i
$541$	11515.1	−	19944.7i	0.915106	−	1.58501i	0.108360	−	0.994112i	$-0.465440\pi$
$541$	11515.1	−	19944.7i	0.915106	−	1.58501i	0.806746	−	0.590898i	$-0.201227\pi$
$542$	−10306.3	+	5950.37i	−0.816781	+	0.471568i
$543$	−14665.6	+	8467.18i	−1.15904	+	0.669174i
$544$	−324.468	+	561.995i	−0.0255725	+	0.0442929i
$545$	−3738.60	−	5548.24i	−0.293842	−	0.436074i
$546$	−4387.22	+	21872.9i	−0.343875	+	1.71442i
$547$		−	6553.72i		−	0.512280i	−0.966640	−	0.256140i	$-0.917549\pi$
$547$		−	6553.72i		−	0.512280i	0.966640	−	0.256140i	$-0.0824508\pi$
$548$	1715.58	+	990.491i	0.133733	+	0.0772111i
$549$	−4538.33	−	7860.61i	−0.352807	−	0.611080i
$550$	1672.39	+	11980.0i	0.129656	+	0.928779i
$551$	1079.45	−	1869.66i	0.0834593	−	0.144556i
$552$			1084.82i			0.0836469i
$553$	−6280.99	+	7139.00i	−0.482992	+	0.548971i
$554$	15337.8			1.17625
$555$	−11682.2	+	811.473i	−0.893480	+	0.0620633i
$556$	933.040	+	1616.07i	0.0711686	+	0.123268i
$557$	4550.73	−	2627.37i	0.346177	−	0.199865i	−0.316823	−	0.948485i	$-0.602616\pi$
$557$	4550.73	−	2627.37i	0.346177	−	0.199865i	0.663000	+	0.748619i	$0.269283\pi$
$558$	4047.37	+	2336.75i	0.307059	+	0.177281i
$559$	23794.2			1.80034
$560$	2010.78	−	2633.01i	0.151734	−	0.198688i
$561$	−6321.24			−0.475727
$562$	10936.5	+	6314.18i	0.820867	+	0.473928i
$563$	−8451.64	+	4879.55i	−0.632671	+	0.365273i	−0.781786	−	0.623547i	$-0.785691\pi$
$563$	−8451.64	+	4879.55i	−0.632671	+	0.365273i	0.149114	+	0.988820i	$0.452358\pi$
$564$	6040.35	+	10462.2i	0.450965	+	0.781095i
$565$	666.451	+	9594.41i	0.0496244	+	0.714407i
$566$	12245.4			0.909389
$567$	−5393.23	−	15971.9i	−0.399461	−	1.18300i
$568$		−	1680.48i		−	0.124140i
$569$	2031.72	−	3519.04i	0.149691	−	0.259272i	−0.781422	−	0.624002i	$-0.785506\pi$
$569$	2031.72	−	3519.04i	0.149691	−	0.259272i	0.931113	+	0.364730i	$0.118839\pi$
$570$	−1963.16	+	4020.36i	−0.144259	+	0.295428i
$571$	11953.5	+	20704.1i	0.876075	+	1.51741i	0.855613	+	0.517616i	$0.173180\pi$
$571$	11953.5	+	20704.1i	0.876075	+	1.51741i	0.0204621	+	0.999791i	$0.493486\pi$
$572$	−15669.3	−	9046.68i	−1.14540	−	0.661295i
$573$		−	7246.48i		−	0.528317i
$574$	−10152.5	−	8932.27i	−0.738249	−	0.649522i
$575$	2438.60	+	987.879i	0.176863	+	0.0716477i
$576$	−464.113	+	803.867i	−0.0335730	+	0.0581501i
$577$	−13116.3	+	7572.68i	−0.946338	+	0.546369i	−0.891942	−	0.452151i	$-0.850657\pi$
$577$	−13116.3	+	7572.68i	−0.946338	+	0.546369i	−0.0543967	+	0.998519i	$0.517324\pi$
$578$	7797.26	−	4501.75i	0.561113	−	0.323959i
$579$	−7138.36	+	12364.0i	−0.512366	+	0.887445i
$580$	−1737.15	−	2577.99i	−0.124364	−	0.184561i
$581$	427.508	−	2131.38i	0.0305267	−	0.152194i
$582$		−	5626.13i		−	0.400706i
$583$	24602.9	+	14204.5i	1.74777	+	1.00907i
$584$	−567.134	−	982.304i	−0.0401852	−	0.0696028i
$585$	−13622.1	−	6651.72i	−0.962740	−	0.470110i
$586$	1646.67	−	2852.12i	0.116081	−	0.201058i
$587$		−	10865.9i		−	0.764025i	−0.924157	−	0.382013i	$-0.875231\pi$
$587$		−	10865.9i		−	0.764025i	0.924157	−	0.382013i	$-0.124769\pi$
$588$	−5358.27	−	7029.54i	−0.375802	−	0.493016i
$589$	5003.96			0.350059
$590$	−831.992	−	11977.6i	−0.0580552	−	0.835779i
$591$	−10067.9	−	17438.1i	−0.700743	−	1.21372i
$592$	−2252.80	+	1300.65i	−0.156401	+	0.0902982i
$593$	−3964.92	−	2289.15i	−0.274569	−	0.158523i	0.356393	−	0.934336i	$-0.384006\pi$
$593$	−3964.92	−	2289.15i	−0.274569	−	0.158523i	−0.630962	+	0.775813i	$0.717340\pi$
$594$	7790.53			0.538130
$595$	3875.74	−	1615.84i	0.267042	−	0.111332i
$596$	−714.214			−0.0490862
$597$	−25326.0	−	14622.0i	−1.73622	−	1.00241i
$598$	−3408.31	+	1967.79i	−0.233070	+	0.134563i
$599$	−10280.8	−	17806.8i	−0.701270	−	1.21463i	−0.968021	−	0.250869i	$-0.919284\pi$
$599$	−10280.8	−	17806.8i	−0.701270	−	1.21463i	0.266751	−	0.963765i	$-0.414050\pi$
$600$	3961.60	+	5080.28i	0.269552	+	0.345670i
$601$	−1254.44			−0.0851406			−0.0425703	−	0.999093i	$-0.513555\pi$
$601$	−1254.44			−0.0851406			−0.0425703	+	0.999093i	$0.513555\pi$
$602$	−6227.32	+	7078.00i	−0.421606	+	0.479199i
$603$		−	1785.00i		−	0.120549i
$604$	1663.34	−	2880.98i	0.112053	−	0.194082i
$605$	−4955.19	+	10147.7i	−0.332987	+	0.681924i
$606$	−11391.4	−	19730.4i	−0.763602	−	1.32260i
$607$	−9406.24	−	5430.69i	−0.628974	−	0.363139i	0.151380	−	0.988476i	$-0.451628\pi$
$607$	−9406.24	−	5430.69i	−0.628974	−	0.363139i	−0.780355	+	0.625337i	$0.784962\pi$
$608$			993.859i			0.0662933i
$609$	−7857.79	+	2653.33i	−0.522847	+	0.176549i
$610$	−11605.0	+	7819.90i	−0.770286	+	0.519047i
$611$	−21913.5	+	37955.2i	−1.45094	+	2.51310i
$612$	−1018.86	+	588.242i	−0.0672960	+	0.0388534i
$613$	18520.6	−	10692.9i	1.22029	−	0.704536i	0.255312	−	0.966859i	$-0.417822\pi$
$613$	18520.6	−	10692.9i	1.22029	−	0.704536i	0.964980	+	0.262323i	$0.0844886\pi$
$614$	−7890.42	+	13666.6i	−0.518618	+	0.898273i
$615$	21806.5	−	14694.0i	1.42980	−	0.963448i
$616$	6792.00	−	2293.45i	0.444249	−	0.150009i
$617$			11863.3i			0.774066i	0.922066	+	0.387033i	$0.126500\pi$
$617$			11863.3i			0.774066i	−0.922066	+	0.387033i	$0.873500\pi$
$618$	−9478.05	−	5472.15i	−0.616930	−	0.356185i
$619$	−4049.30	−	7013.59i	−0.262932	−	0.455412i	0.704088	−	0.710113i	$-0.251356\pi$
$619$	−4049.30	−	7013.59i	−0.262932	−	0.455412i	−0.967020	+	0.254701i	$0.918023\pi$
$620$	3161.60	−	6474.65i	0.204795	−	0.419400i
$621$	847.278	−	1467.53i	0.0547506	−	0.0948308i
$622$		−	6873.96i		−	0.443120i
$623$	749.413	−	851.785i	0.0481936	−	0.0547770i
$624$	−9636.39			−0.618212
$625$	15027.6	−	4279.06i	0.961770	−	0.273860i
$626$	−7209.81	−	12487.8i	−0.460323	−	0.797302i
$627$	−8384.07	+	4840.55i	−0.534015	+	0.308314i
$628$	580.918	+	335.393i	0.0369127	+	0.0213115i
$629$	−3297.04			−0.209001
$630$	5543.78	−	2311.26i	0.350587	−	0.146163i
$631$	28405.4			1.79208			0.896038	−	0.443977i	$-0.146433\pi$
$631$	28405.4			1.79208			0.896038	+	0.443977i	$0.146433\pi$
$632$	−3557.10	−	2053.69i	−0.223883	−	0.129259i
$633$	−14061.9	+	8118.63i	−0.882953	+	0.509773i
$634$	−885.804	−	1534.26i	−0.0554886	−	0.0961090i
$635$	−752.617	−	10834.9i	−0.0470341	−	0.677116i
$636$	15130.4			0.943335
$637$	12366.0	−	29585.7i	0.769166	−	1.84024i
$638$		−	6726.58i		−	0.417411i
$639$	1523.31	−	2638.45i	0.0943054	−	0.163342i
$640$	1285.96	+	627.940i	0.0794250	+	0.0387836i
$641$	−2427.43	−	4204.43i	−0.149575	−	0.259072i	0.781495	−	0.623911i	$-0.214457\pi$
$641$	−2427.43	−	4204.43i	−0.149575	−	0.259072i	−0.931070	+	0.364839i	$0.881124\pi$
$642$	14311.5	+	8262.77i	0.879800	+	0.507953i
$643$			23838.8i			1.46207i	0.682342	+	0.731033i	$0.260962\pi$
$643$			23838.8i			1.46207i	−0.682342	+	0.731033i	$0.739038\pi$
$644$	306.656	−	1528.86i	0.0187639	−	0.0935491i
$645$	−10244.3	−	15202.9i	−0.625376	−	0.928083i
$646$	−629.835	+	1090.91i	−0.0383600	+	0.0664414i
$647$	−14646.9	+	8456.39i	−0.889998	+	0.513841i	−0.873942	−	0.486030i	$-0.838444\pi$
$647$	−14646.9	+	8456.39i	−0.889998	+	0.513841i	−0.0160563	+	0.999871i	$0.505111\pi$
$648$	6306.35	−	3640.97i	0.382310	−	0.220727i
$649$	12989.9	−	22499.2i	0.785669	−	1.36082i
$650$	−8775.25	+	21661.8i	−0.529529	+	1.30715i
$651$	−14432.5	−	12698.0i	−0.868904	−	0.764473i
$652$			6448.37i			0.387327i
$653$	−12385.4	−	7150.73i	−0.742235	−	0.428530i	0.0806463	−	0.996743i	$-0.474302\pi$
$653$	−12385.4	−	7150.73i	−0.742235	−	0.428530i	−0.822881	+	0.568213i	$0.807635\pi$
$654$	−3855.08	−	6677.19i	−0.230497	−	0.399233i
$655$	−733.873	+	1502.90i	−0.0437783	+	0.0896536i
$656$	2920.58	−	5058.60i	0.173826	−	0.301075i
$657$		−	2056.36i		−	0.122110i
$658$	−5555.34	−	16452.0i	−0.329134	−	0.974722i
$659$	8601.03			0.508420			0.254210	−	0.967149i	$-0.418185\pi$
$659$	8601.03			0.508420			0.254210	+	0.967149i	$0.418185\pi$
$660$	965.983	+	13906.6i	0.0569710	+	0.820170i
$661$	397.144	+	687.874i	0.0233693	+	0.0404768i	0.877474	−	0.479625i	$-0.159227\pi$
$661$	397.144	+	687.874i	0.0233693	+	0.0404768i	−0.854104	+	0.520102i	$0.825894\pi$
$662$	−3059.12	+	1766.18i	−0.179601	+	0.103693i
$663$	−10577.4	−	6106.84i	−0.619594	−	0.357723i
$664$	939.007			0.0548803
$665$	3903.19	−	5111.02i	0.227608	−	0.298041i
$666$	−4716.02			−0.274387
$667$	−1267.11	−	731.566i	−0.0735572	−	0.0424683i
$668$	5510.31	−	3181.38i	0.319162	−	0.184268i
$669$	18684.6	+	32362.7i	1.07980	+	1.87027i
$670$	−2745.40	+	190.702i	−0.158304	+	0.0109962i
$671$	−30280.3			−1.74211
$672$	2522.00	−	2866.51i	0.144774	−	0.164551i
$673$			3100.85i			0.177606i	0.996049	+	0.0888031i	$0.0283042\pi$
$673$			3100.85i			0.177606i	−0.996049	+	0.0888031i	$0.971696\pi$
$674$	−7521.34	+	13027.3i	−0.429838	+	0.744502i
$675$	−1391.33	−	9966.64i	−0.0793367	−	0.568320i
$676$	−13085.7	−	22665.1i	−0.744520	−	1.28955i
$677$	2803.09	+	1618.37i	0.159131	+	0.0918742i	0.577451	−	0.816426i	$-0.304048\pi$
$677$	2803.09	+	1618.37i	0.159131	+	0.0918742i	−0.418320	+	0.908300i	$0.637381\pi$
$678$			11083.6i			0.627822i
$679$	−1590.39	+	7929.02i	−0.0898872	+	0.448141i
$680$	1013.59	+	1504.20i	0.0571607	+	0.0848288i
$681$	−21344.9	+	36970.5i	−1.20109	+	2.08034i
$682$	13502.3	−	7795.54i	0.758107	−	0.437693i
$683$	8153.63	−	4707.50i	0.456793	−	0.263730i	−0.253902	−	0.967230i	$-0.581714\pi$
$683$	8153.63	−	4707.50i	0.456793	−	0.263730i	0.710695	+	0.703500i	$0.248381\pi$
$684$	−900.904	+	1560.41i	−0.0503610	+	0.0872278i
$685$	4591.82	−	3094.14i	0.256123	−	0.172585i
$686$	5564.42	+	11421.5i	0.309695	+	0.635680i
$687$			3271.70i			0.181693i
$688$	−3526.71	−	2036.15i	−0.195428	−	0.112831i
$689$	27445.5	+	47537.0i	1.51755	+	2.62847i
$690$	2724.68	+	1330.48i	0.150329	+	0.0734063i
$691$	11399.2	−	19744.1i	0.627565	−	1.08697i	−0.360474	−	0.932769i	$-0.617385\pi$
$691$	11399.2	−	19744.1i	0.627565	−	1.08697i	0.988039	−	0.154205i	$-0.0492817\pi$
$692$			6969.63i			0.382870i
$693$	12742.7	+	2555.91i	0.698495	+	0.140103i
$694$	9317.06			0.509612
$695$	5203.32	−	361.435i	0.283990	−	0.0197266i
$696$	−1791.26	−	3102.56i	−0.0975542	−	0.168969i
$697$	6411.54	−	3701.70i	0.348428	−	0.201165i
$698$	−12467.6	−	7198.15i	−0.676080	−	0.390335i
$699$	40637.0			2.19890
$700$	−4147.07	−	8279.60i	−0.223921	−	0.447056i
$701$	33797.9			1.82101			0.910506	−	0.413496i	$-0.135692\pi$
$701$	33797.9			1.82101			0.910506	+	0.413496i	$0.135692\pi$
$702$	13035.9	+	7526.30i	0.700869	+	0.404647i
$703$	−4372.98	+	2524.74i	−0.234609	+	0.135451i
$704$	1548.31	+	2681.75i	0.0828893	+	0.143568i
$705$	33685.4	−	2339.87i	1.79953	−	0.124999i
$706$	7280.16			0.388091
$707$	10476.7	+	31026.6i	0.557309	+	1.65046i
$708$		−	13836.7i		−	0.734484i
$709$	−13113.0	+	22712.4i	−0.694599	+	1.20308i	0.275717	+	0.961239i	$0.411085\pi$
$709$	−13113.0	+	22712.4i	−0.694599	+	1.20308i	−0.970316	+	0.241841i	$0.922249\pi$
$710$	−4220.77	−	2061.02i	−0.223102	−	0.108942i
$711$	−3723.23	−	6448.82i	−0.196388	−	0.340154i
$712$	424.414	+	245.035i	0.0223393	+	0.0128976i
$713$		−	3391.29i		−	0.178128i
$714$	4584.85	−	1548.16i	0.240313	−	0.0811464i
$715$	−41939.5	+	28260.4i	−2.19364	+	1.47815i
$716$	4858.73	−	8415.58i	0.253603	−	0.439253i
$717$	−25748.8	+	14866.1i	−1.34115	+	0.774314i
$718$	9474.14	−	5469.89i	0.492440	−	0.284310i
$719$	−4296.94	+	7442.53i	−0.222878	+	0.386035i	−0.955681	−	0.294406i	$-0.904878\pi$
$719$	−4296.94	+	7442.53i	−0.222878	+	0.386035i	0.732803	+	0.680441i	$0.238212\pi$
$720$	1449.82	+	2151.58i	0.0750436	+	0.111368i
$721$	11810.7	+	10391.3i	0.610062	+	0.536741i
$722$		−	11788.8i		−	0.607664i
$723$	8651.72	+	4995.07i	0.445036	+	0.256941i
$724$	5257.22	+	9105.77i	0.269866	+	0.467422i
$725$	−8605.50	+	1201.31i	−0.440828	+	0.0615389i
$726$	−6507.20	+	11270.8i	−0.332651	+	0.576169i
$727$			26368.9i			1.34521i	0.740001	+	0.672606i	$0.234825\pi$
$727$			26368.9i			1.34521i	−0.740001	+	0.672606i	$0.765175\pi$
$728$	13580.8	+	2724.00i	0.691396	+	0.138679i
$729$	−801.754			−0.0407333
$730$	−3162.75	+	219.693i	−0.160354	+	0.0111386i
$731$	−2580.72	−	4469.94i	−0.130577	−	0.226165i
$732$	−13966.4	+	8063.52i	−0.705210	+	0.407153i
$733$	14285.5	+	8247.75i	0.719847	+	0.415604i	0.814696	−	0.579888i	$-0.196904\pi$
$733$	14285.5	+	8247.75i	0.719847	+	0.415604i	−0.0948495	+	0.995492i	$0.530237\pi$
$734$	−130.174			−0.00654607
$735$	−24227.3	+	4836.69i	−1.21583	+	0.242727i
$736$	673.560			0.0337333
$737$	−5157.07	−	2977.44i	−0.257752	−	0.148813i
$738$	9170.94	−	5294.84i	0.457435	−	0.264100i
$739$	4335.02	+	7508.47i	0.215786	+	0.373753i	0.953516	−	0.301344i	$-0.0974351\pi$
$739$	4335.02	+	7508.47i	0.215786	+	0.373753i	−0.737729	+	0.675097i	$0.764102\pi$
$740$	503.839	+	7253.40i	0.0250290	+	0.360325i
$741$	−18705.5			−0.927346
$742$	−21323.6	−	4277.05i	−1.05501	−	0.211611i
$743$		−	30923.0i		−	1.52686i	−0.645891	−	0.763430i	$-0.723514\pi$
$743$		−	30923.0i		−	1.52686i	0.645891	−	0.763430i	$-0.276486\pi$
$744$	4151.85	−	7191.21i	0.204589	−	0.354359i
$745$	−875.945	+	1793.85i	−0.0430767	+	0.0882168i
$746$	−10153.4	−	17586.2i	−0.498313	−	0.863104i
$747$	1474.29	+	851.182i	0.0722108	+	0.0416909i
$748$			3924.82i			0.191852i
$749$	−17833.8	−	15690.5i	−0.870006	−	0.765443i
$750$	17618.5	−	3719.41i	0.857783	−	0.181085i
$751$	−6583.99	+	11403.8i	−0.319911	+	0.554102i	−0.980469	−	0.196673i	$-0.936986\pi$
$751$	−6583.99	+	11403.8i	−0.319911	+	0.554102i	0.660558	+	0.750775i	$0.270320\pi$
$752$	6495.91	−	3750.41i	0.315002	−	0.181866i
$753$	−4254.39	+	2456.27i	−0.205895	+	0.118873i
$754$	6498.44	−	11255.6i	0.313872	−	0.543642i
$755$	−5196.00	−	7711.07i	−0.250466	−	0.371701i
$756$	−5650.55	+	1908.01i	−0.271836	+	0.0917908i
$757$		−	31713.3i		−	1.52264i	−0.648375	−	0.761321i	$-0.724551\pi$
$757$		−	31713.3i		−	1.52264i	0.648375	−	0.761321i	$-0.275449\pi$
$758$	2518.33	+	1453.96i	0.120672	+	0.0696703i
$759$	3280.54	+	5682.07i	0.156886	+	0.271734i
$760$	2496.21	+	1218.91i	0.119141	+	0.0581772i
$761$	409.326	−	708.973i	0.0194981	−	0.0337717i	−0.856112	−	0.516791i	$-0.827127\pi$
$761$	409.326	−	708.973i	0.0194981	−	0.0337717i	0.875610	+	0.483019i	$0.160460\pi$
$762$		−	12516.6i		−	0.595051i
$763$	3545.54	+	10500.0i	0.168227	+	0.498200i
$764$	−4499.29			−0.213061
$765$	227.869	+	3280.47i	0.0107695	+	0.155040i
$766$	577.301	+	999.915i	0.0272307	+	0.0471650i
$767$	43472.2	−	25098.7i	2.04653	−	1.18157i
$768$	1428.28	+	824.617i	0.0671075	+	0.0387446i
$769$	−28514.9			−1.33716			−0.668578	−	0.743642i	$-0.733097\pi$
$769$	−28514.9			−1.33716			−0.668578	+	0.743642i	$0.733097\pi$
$770$	2569.70	−	19871.8i	0.120267	−	0.930041i
$771$	14832.6			0.692842
$772$	7676.73	+	4432.16i	0.357891	+	0.206628i
$773$	24933.7	−	14395.5i	1.16016	−	0.669819i	0.208818	−	0.977955i	$-0.433038\pi$
$773$	24933.7	−	14395.5i	1.16016	−	0.669819i	0.951342	+	0.308136i	$0.0997051\pi$
$774$	−3691.41	−	6393.72i	−0.171428	−	0.296922i
$775$	−12384.5	−	15881.6i	−0.574016	−	0.736109i
$776$	−3493.23			−0.161598
$777$	19019.4	+	3814.87i	0.878142	+	0.176136i
$778$			4142.00i			0.190871i
$779$	5669.23	−	9819.40i	0.260746	−	0.451626i
$780$	−11818.5	+	24203.1i	−0.542526	+	1.11104i
$781$	−5081.85	−	8802.02i	−0.232833	−	0.403279i
$782$	739.331	+	426.853i	0.0338087	+	0.0195195i
$783$			5596.12i			0.255414i
$784$	−4364.60	+	3326.92i	−0.198825	+	0.151554i
$785$	1554.85	−	1047.72i	0.0706943	−	0.0476364i
$786$	−963.729	+	1669.23i	−0.0437342	+	0.0757499i
$787$	−6482.89	+	3742.90i	−0.293634	+	0.169530i	−0.639580	−	0.768725i	$-0.720892\pi$
$787$	−6482.89	+	3742.90i	−0.293634	+	0.169530i	0.345945	+	0.938255i	$0.387558\pi$
$788$	−10827.2	+	6251.11i	−0.489473	+	0.282597i
$789$	−15569.5	+	26967.1i	−0.702520	+	1.21680i
$790$	−9520.73	+	6415.42i	−0.428775	+	0.288924i
$791$	3133.09	−	15620.3i	0.140834	−	0.702143i
$792$			5613.98i			0.251874i
$793$	−50668.1	−	29253.2i	−2.26895	−	1.30998i
$794$	5033.42	+	8718.13i	0.224974	+	0.389666i
$795$	18556.7	−	38002.2i	0.827845	−	1.69534i
$796$	−9078.68	+	15724.7i	−0.404253	+	0.700187i
$797$		−	2323.41i		−	0.103261i	−0.998666	−	0.0516307i	$-0.983558\pi$
$797$		−	2323.41i		−	0.103261i	0.998666	−	0.0516307i	$-0.0164419\pi$
$798$	4895.53	−	5564.28i	0.217168	−	0.246834i
$799$	9506.96			0.420941
$800$	3154.32	−	2459.73i	0.139402	−	0.108706i
$801$	444.235	+	769.437i	0.0195958	+	0.0339410i
$802$	−8568.25	+	4946.88i	−0.377251	+	0.217806i
$803$	−5941.05	−	3430.07i	−0.261090	−	0.150740i
$804$	−3171.52			−0.139118
$805$	−3463.85	−	2645.27i	−0.151658	−	0.115818i
$806$	30124.6			1.31649
$807$	−26949.6	−	15559.3i	−1.17555	−	0.678705i
$808$	−12250.5	+	7072.83i	−0.533380	+	0.307947i
$809$	−4551.85	−	7884.03i	−0.197818	−	0.342630i	0.750003	−	0.661434i	$-0.230052\pi$
$809$	−4551.85	−	7884.03i	−0.197818	−	0.342630i	−0.947821	+	0.318804i	$0.896719\pi$
$810$	−1410.42	−	20304.7i	−0.0611814	−	0.880784i
$811$	−4516.19			−0.195542			−0.0977711	−	0.995209i	$-0.531171\pi$
$811$	−4516.19			−0.195542			−0.0977711	+	0.995209i	$0.531171\pi$
$812$	1647.44	+	4878.85i	0.0711992	+	0.210855i
$813$			38334.2i			1.65368i
$814$	−7866.46	+	13625.1i	−0.338721	+	0.586683i
$815$	16196.0	+	7908.57i	0.696098	+	0.339908i
$816$	1045.16	+	1810.28i	0.0448383	+	0.0776623i
$817$	−6845.81	−	3952.43i	−0.293151	−	0.169251i
$818$			18779.7i			0.802709i
$819$	18853.3	+	16587.4i	0.804380	+	0.707704i
$820$	−9123.44	−	13539.5i	−0.388542	−	0.576612i
$821$	3023.22	−	5236.37i	0.128515	−	0.222595i	−0.794586	−	0.607151i	$-0.792312\pi$
$821$	3023.22	−	5236.37i	0.128515	−	0.222595i	0.923102	+	0.384556i	$0.125646\pi$
$822$	5526.16	−	3190.53i	0.234485	−	0.135380i
$823$	−38617.2	+	22295.6i	−1.63561	+	0.944322i	−0.653296	+	0.757102i	$0.726614\pi$
$823$	−38617.2	+	22295.6i	−1.63561	+	0.944322i	−0.982318	+	0.187220i	$0.940052\pi$
$824$	−3397.63	+	5884.86i	−0.143643	+	0.248797i
$825$	36113.0	+	14629.4i	1.52399	+	0.617371i
$826$	−3911.33	+	19500.3i	−0.164761	+	0.821432i
$827$			17170.6i			0.721982i	0.932569	+	0.360991i	$0.117561\pi$
$827$			17170.6i			0.721982i	−0.932569	+	0.360991i	$0.882439\pi$
$828$	1057.52	+	610.562i	0.0443859	+	0.0256262i
$829$	−15254.9	−	26422.3i	−0.639115	−	1.10698i	−0.985627	−	0.168934i	$-0.945968\pi$
$829$	−15254.9	−	26422.3i	−0.639115	−	1.10698i	0.346513	−	0.938045i	$-0.387366\pi$
$830$	1151.64	−	2358.45i	0.0481615	−	0.0986300i
$831$	24702.8	−	42786.5i	1.03120	−	1.78610i
$832$			5983.18i			0.249314i
$833$	−6899.15	+	885.817i	−0.286965	+	0.0368448i
$834$	6010.95			0.249571
$835$	−1232.38	−	17741.7i	−0.0510758	−	0.735301i
$836$	3005.47	+	5205.62i	0.124338	+	0.215359i
$837$	−11233.1	+	6485.43i	−0.463886	+	0.267825i
$838$	14590.4	+	8423.77i	0.601452	+	0.347249i
$839$	34089.6			1.40275			0.701373	−	0.712794i	$-0.252571\pi$
$839$	34089.6			1.40275			0.701373	+	0.712794i	$0.252571\pi$
$840$	−4106.55	−	9849.97i	−0.168678	−	0.404591i
$841$	−19557.1			−0.801884
$842$	−9838.30	−	5680.15i	−0.402673	−	0.232483i
$843$	35228.1	−	20339.0i	1.43929	−	0.830975i
$844$	5040.81	+	8730.94i	0.205583	+	0.356080i
$845$	−72975.4	+	5069.05i	−2.97092	+	0.206368i
$846$	13598.6			0.552634
$847$	12356.7	−	14044.7i	0.501278	−	0.569755i
$848$		−	9394.40i		−	0.380430i
$849$	19722.3	−	34160.0i	0.797252	−	1.38088i
$850$	5021.13	−	700.942i	0.202616	−	0.0282848i
$851$	1711.07	+	2963.66i	0.0689245	+	0.119381i
$852$	−4687.89	−	2706.55i	−0.188503	−	0.108832i
$853$			5078.39i			0.203846i	0.994792	+	0.101923i	$0.0324995\pi$
$853$			5078.39i			0.203846i	−0.994792	+	0.101923i	$0.967500\pi$
$854$	21962.5	−	7416.07i	0.880027	−	0.297158i
$855$	2814.28	+	4176.50i	0.112569	+	0.167057i
$856$	5130.31	−	8885.95i	0.204848	−	0.354808i
$857$	−74.0679	+	42.7631i	−0.00295229	+	0.00170450i	−0.501475	−	0.865172i	$-0.667209\pi$
$857$	−74.0679	+	42.7631i	−0.00295229	+	0.00170450i	0.498523	+	0.866876i	$0.333876\pi$
$858$	−50473.4	+	29140.8i	−2.00831	+	1.15950i
$859$	16160.0	−	27990.0i	0.641878	−	1.11177i	−0.343135	−	0.939286i	$-0.611489\pi$
$859$	16160.0	−	27990.0i	0.641878	−	1.11177i	0.985013	−	0.172479i	$-0.0551778\pi$
$860$	−9439.39	+	6360.60i	−0.374279	+	0.252203i
$861$	−41268.9	+	13935.2i	−1.63350	+	0.551581i
$862$			24696.7i			0.975840i
$863$	18131.3	+	10468.1i	0.715175	+	0.412907i	0.812974	−	0.582300i	$-0.197847\pi$
$863$	18131.3	+	10468.1i	0.715175	+	0.412907i	−0.0977991	+	0.995206i	$0.531180\pi$
$864$	−1288.10	−	2231.06i	−0.0507200	−	0.0878496i
$865$	17505.2	+	8547.87i	0.688086	+	0.335996i
$866$	−9031.93	+	15643.8i	−0.354408	+	0.613853i
$867$		−	29001.7i		−	1.13604i
$868$	−7884.09	+	8961.08i	−0.308299	+	0.350414i
$869$	−24841.8			−0.969736
$870$	−9989.40	+	693.888i	−0.389279	+	0.0270402i
$871$	−5752.90	−	9964.32i	−0.223800	−	0.387633i
$872$	−4145.82	+	2393.59i	−0.161004	+	0.0929556i
$873$	−5484.56	−	3166.51i	−0.212628	−	0.122761i
$874$	1307.47			0.0506015
$875$	−25881.5	+	261.464i	−0.999949	+	0.0101018i
$876$	−3653.66			−0.140920
$877$	20852.3	+	12039.1i	0.802886	+	0.463546i	0.844479	−	0.535588i	$-0.179910\pi$
$877$	20852.3	+	12039.1i	0.802886	+	0.463546i	−0.0415933	+	0.999135i	$0.513243\pi$
$878$	18459.2	−	10657.4i	0.709530	−	0.409647i
$879$	−5304.19	−	9187.13i	−0.203534	−	0.352531i
$880$	8634.50	−	599.773i	0.330760	−	0.0229754i
$881$	23196.8			0.887081			0.443541	−	0.896254i	$-0.353722\pi$
$881$	23196.8			0.887081			0.443541	+	0.896254i	$0.353722\pi$
$882$	−9868.41	+	1267.06i	−0.376742	+	0.0483719i
$883$		−	31800.2i		−	1.21196i	−0.795479	−	0.605981i	$-0.792781\pi$
$883$		−	31800.2i		−	1.21196i	0.795479	−	0.605981i	$-0.207219\pi$
$884$	−3791.70	+	6567.42i	−0.144263	+	0.249871i
$885$	−34752.8	−	16969.9i	−1.32000	−	0.644563i
$886$	901.320	+	1561.13i	0.0341766	+	0.0591956i
$887$	29618.2	+	17100.1i	1.12118	+	0.647311i	0.941701	−	0.336451i	$-0.109227\pi$
$887$	29618.2	+	17100.1i	1.12118	+	0.647311i	0.179475	+	0.983762i	$0.442560\pi$
$888$			8379.24i			0.316654i
$889$	−3538.17	+	17639.9i	−0.133483	+	0.665493i
$890$	1135.96	−	765.452i	0.0427837	−	0.0288292i
$891$	22020.9	−	38141.3i	0.827977	−	1.43410i
$892$	20093.8	−	11601.2i	0.754249	−	0.435466i
$893$	12609.4	−	7280.04i	0.472517	−	0.272808i
$894$	−1150.30	+	1992.38i	−0.0430333	+	0.0745359i
$895$	−15177.9	−	22524.6i	−0.566862	−	0.841246i
$896$	−1779.80	−	1565.89i	−0.0663605	−	0.0583848i
$897$			12677.1i			0.471880i
$898$	−13461.3	−	7771.88i	−0.500233	−	0.288809i
$899$	5599.72	+	9699.00i	0.207743	+	0.359822i
$900$	7182.12	−	1002.61i	0.266004	−	0.0371338i
$901$	5953.48	−	10311.7i	0.220132	−	0.381280i
$902$		−	35327.8i		−	1.30409i
$903$	9715.24	+	28771.5i	0.358032	+	1.06030i
$904$	6881.74			0.253190
$905$	29318.1	−	2036.51i	1.07687	−	0.0748020i
$906$	−5357.87	−	9280.11i	−0.196472	−	0.340299i
$907$	−4151.20	+	2396.70i	−0.151972	+	0.0877409i	−0.574058	−	0.818815i	$-0.694631\pi$
$907$	−4151.20	+	2396.70i	−0.151972	+	0.0877409i	0.422086	+	0.906556i	$0.361298\pi$
$908$	22954.8	+	13252.9i	0.838965	+	0.484377i
$909$	−25645.3			−0.935753
$910$	23497.8	−	30769.1i	0.855981	−	1.12086i
$911$	−25153.4			−0.914787			−0.457393	−	0.889264i	$-0.651217\pi$
$911$	−25153.4			−0.914787			−0.457393	+	0.889264i	$0.651217\pi$
$912$	2772.48	+	1600.69i	0.100664	+	0.0581186i
$913$	4918.32	−	2839.59i	0.178283	−	0.102932i
$914$	2760.35	+	4781.07i	0.0998953	+	0.173024i
$915$	3123.59	+	44968.1i	0.112856	+	1.62470i
$916$	2031.38			0.0732736
$917$	1830.06	−	2080.05i	0.0659038	−	0.0749066i
$918$		−	3265.22i		−	0.117395i
$919$	−10218.5	+	17698.9i	−0.366786	+	0.635293i	−0.989061	−	0.147506i	$-0.952875\pi$
$919$	−10218.5	+	17698.9i	−0.366786	+	0.635293i	0.622275	+	0.782799i	$0.286209\pi$
$920$	826.084	−	1691.74i	0.0296035	−	0.0606250i
$921$	25416.3	+	44022.3i	0.909333	+	1.57501i
$922$	28548.2	+	16482.3i	1.01972	+	0.588738i
$923$		−	19637.9i		−	0.700315i
$924$	4541.24	−	22640.8i	0.161684	−	0.806091i
$925$	18835.9	+	7630.44i	0.669534	+	0.271229i
$926$	−9949.16	+	17232.4i	−0.353077	+	0.611548i
$927$	−10668.9	+	6159.70i	−0.378007	+	0.218243i
$928$	−1926.36	+	1112.19i	−0.0681421	+	0.0393419i
$929$	641.065	−	1110.36i	0.0226401	−	0.0392138i	−0.854483	−	0.519479i	$-0.826126\pi$
$929$	641.065	−	1110.36i	0.0226401	−	0.0392138i	0.877123	+	0.480265i	$0.159459\pi$
$930$	−12969.7	−	19247.6i	−0.457305	−	0.678659i
$931$	−8472.26	+	6457.98i	−0.298246	+	0.227338i
$932$		−	25231.3i		−	0.886779i
$933$	−19175.7	−	11071.1i	−0.672865	−	0.388479i
$934$	2101.55	+	3640.00i	0.0736241	+	0.127521i
$935$	9857.73	+	4813.57i	0.344794	+	0.168364i
$936$	−5423.57	+	9393.90i	−0.189396	+	0.328044i
$937$			16878.5i			0.588472i	0.955733	+	0.294236i	$0.0950651\pi$
$937$			16878.5i			0.588472i	−0.955733	+	0.294236i	$0.904935\pi$
$938$	4469.69	+	896.521i	0.155587	+	0.0312073i
$939$	−46447.9			−1.61424
$940$	−1452.81	−	20915.1i	−0.0504101	−	0.725717i
$941$	−7465.79	−	12931.1i	−0.258637	−	0.447973i	0.707240	−	0.706974i	$-0.249940\pi$
$941$	−7465.79	−	12931.1i	−0.258637	−	0.447973i	−0.965877	+	0.259001i	$0.916607\pi$
$942$	1871.23	−	1080.36i	0.0647219	−	0.0373672i
$943$	−6654.82	−	3842.16i	−0.229810	−	0.132681i
$944$	−8591.11			−0.296204
$945$	−2137.84	+	16532.2i	−0.0735915	+	0.569093i
$946$	−24629.5			−0.846486
$947$	32515.5	+	18772.8i	1.11575	+	0.644177i	0.940312	−	0.340314i	$-0.110533\pi$
$947$	32515.5	+	18772.8i	1.11575	+	0.644177i	0.175435	+	0.984491i	$0.443867\pi$
$948$	−11458.0	+	6615.28i	−0.392551	+	0.226640i
$949$	−6627.46	−	11479.1i	−0.226698	−	0.392653i
$950$	6122.94	−	4774.66i	0.209110	−	0.163064i
$951$	−5706.63			−0.194585
$952$	−961.245	−	2846.71i	−0.0327249	−	0.0969142i
$953$			437.260i			0.0148628i	0.999972	+	0.00743140i	$0.00236551\pi$
$953$			437.260i			0.0148628i	−0.999972	+	0.00743140i	$0.997634\pi$
$954$	8515.74	−	14749.7i	0.289001	−	0.500565i
$955$	−5518.14	+	11300.6i	−0.186977	+	0.382910i
$956$	9230.25	+	15987.3i	0.312267	+	0.540863i
$957$	−18764.5	−	10833.7i	−0.633825	−	0.365939i
$958$			16019.9i			0.540272i
$959$	−8690.02	+	2934.35i	−0.292613	+	0.0988062i
$960$	3822.85	−	2575.97i	0.128523	−	0.0866033i
$961$	1916.29	−	3319.11i	0.0643244	−	0.111413i
$962$	−26326.0	+	15199.3i	−0.882311	+	0.509403i
$963$	16109.7	−	9300.94i	0.539074	−	0.311234i
$964$	3101.41	−	5371.80i	0.103620	−	0.179475i
$965$	20547.1	−	13845.4i	0.685424	−	0.461864i
$966$	−3771.03	−	3317.81i	−0.125601	−	0.110506i
$967$			52372.7i			1.74167i	0.491577	+	0.870834i	$0.336421\pi$
$967$			52372.7i			1.74167i	−0.491577	+	0.870834i	$0.663579\pi$
$968$	6997.98	+	4040.28i	0.232359	+	0.134152i
$969$	2028.80	+	3513.99i	0.0672595	+	0.116497i
$970$	−4284.26	+	8773.74i	−0.141814	+	0.290420i
$971$	−20379.7	+	35298.6i	−0.673548	+	1.16662i	0.303343	+	0.952881i	$0.401897\pi$
$971$	−20379.7	+	35298.6i	−0.673548	+	1.16662i	−0.976891	+	0.213738i	$0.931436\pi$
$972$		−	14761.6i		−	0.487119i
$973$	−8471.35	−	1699.16i	−0.279115	−	0.0559843i
$974$	−10765.2			−0.354147
$975$	46294.8	+	59367.6i	1.52064	+	1.95004i
$976$	5006.59	+	8671.67i	0.164198	+	0.284399i
$977$	32595.4	−	18819.0i	1.06737	−	0.616246i	0.139908	−	0.990165i	$-0.455319\pi$
$977$	32595.4	−	18819.0i	1.06737	−	0.616246i	0.927462	+	0.373919i	$0.121986\pi$
$978$	17988.4	+	10385.6i	0.588145	+	0.339566i
$979$	2963.99			0.0967614
$980$	3003.07	+	15042.6i	0.0978874	+	0.490324i
$981$	−8678.89			−0.282462
$982$	5987.58	+	3456.93i	0.194574	+	0.112337i
$983$	7620.79	−	4399.87i	0.247269	−	0.142761i	−0.371244	−	0.928535i	$-0.621069\pi$
$983$	7620.79	−	4399.87i	0.247269	−	0.142761i	0.618513	+	0.785774i	$0.287735\pi$
$984$	−9407.67	−	16294.6i	−0.304782	−	0.527898i
$985$	2421.51	+	34860.8i	0.0783308	+	1.12767i
$986$	−2819.29			−0.0910592
$987$	−54842.1	−	11000.1i	−1.76863	−	0.354749i
$988$			11614.1i			0.373982i
$989$	−2678.65	+	4639.55i	−0.0861234	+	0.149170i
$990$	14100.3	+	6885.24i	0.452663	+	0.221038i
$991$	21986.0	+	38080.9i	0.704752	+	1.22067i	0.966781	+	0.255606i	$0.0822750\pi$
$991$	21986.0	+	38080.9i	0.704752	+	1.22067i	−0.262029	+	0.965060i	$0.584392\pi$
$992$	−4464.98	−	2577.86i	−0.142907	−	0.0825072i
$993$			11378.3i			0.363626i
$994$	5841.65	+	5139.57i	0.186404	+	0.164001i
$995$	28360.4	+	42087.9i	0.903602	+	1.34098i
$996$	1512.35	−	2619.46i	0.0481130	−	0.0833341i
$997$	8705.86	−	5026.33i	0.276547	−	0.159664i	−0.355312	−	0.934748i	$-0.615625\pi$
$997$	8705.86	−	5026.33i	0.276547	−	0.159664i	0.631859	+	0.775083i	$0.282292\pi$
$998$	20954.7	−	12098.2i	0.664637	−	0.383728i
$999$	6544.43	−	11335.3i	0.207264	−	0.358992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.4.i.a.9.2	✓	24
5.2	odd	4		350.4.e.o.51.5		12
5.3	odd	4		350.4.e.n.51.2		12
5.4	even	2	inner	70.4.i.a.9.11	yes	24
7.2	even	3		490.4.c.f.99.8		12
7.4	even	3	inner	70.4.i.a.39.11	yes	24
7.5	odd	6		490.4.c.e.99.11		12
35.2	odd	12		2450.4.a.cv.1.2		6
35.4	even	6	inner	70.4.i.a.39.2	yes	24
35.9	even	6		490.4.c.f.99.5		12
35.12	even	12		2450.4.a.cw.1.5		6
35.18	odd	12		350.4.e.n.151.2		12
35.19	odd	6		490.4.c.e.99.2		12
35.23	odd	12		2450.4.a.cy.1.5		6
35.32	odd	12		350.4.e.o.151.5		12
35.33	even	12		2450.4.a.cx.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.2	✓	24	1.1	even	1	trivial
70.4.i.a.9.11	yes	24	5.4	even	2	inner
70.4.i.a.39.2	yes	24	35.4	even	6	inner
70.4.i.a.39.11	yes	24	7.4	even	3	inner
350.4.e.n.51.2		12	5.3	odd	4
350.4.e.n.151.2		12	35.18	odd	12
350.4.e.o.51.5		12	5.2	odd	4
350.4.e.o.151.5		12	35.32	odd	12
490.4.c.e.99.2		12	35.19	odd	6
490.4.c.e.99.11		12	7.5	odd	6
490.4.c.f.99.5		12	35.9	even	6
490.4.c.f.99.8		12	7.2	even	3
2450.4.a.cv.1.2		6	35.2	odd	12
2450.4.a.cw.1.5		6	35.12	even	12
2450.4.a.cx.1.2		6	35.33	even	12
2450.4.a.cy.1.5		6	35.23	odd	12

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-5.57922 + 3.22116i) q^{3} +(2.00000 + 3.46410i) q^{4} +(11.1535 - 0.774747i) q^{5} +12.8846 q^{6} +(-18.1586 - 3.64221i) q^{7} -8.00000i q^{8} +(7.25176 - 12.5604i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-5.57922 + 3.22116i) q^{3} +(2.00000 + 3.46410i) q^{4} +(11.1535 - 0.774747i) q^{5} +12.8846 q^{6} +(-18.1586 - 3.64221i) q^{7} -8.00000i q^{8} +(7.25176 - 12.5604i) q^{9} +(-20.0931 - 9.81156i) q^{10} +(-24.1923 - 41.9023i) q^{11} +(-22.3169 - 12.8846i) q^{12} -93.4871i q^{13} +(27.8094 + 24.4671i) q^{14} +(-59.7320 + 40.2496i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-17.5624 + 10.1396i) q^{17} +(-25.1208 + 14.5035i) q^{18} +(-15.5290 + 26.8971i) q^{19} +(24.9907 + 37.0872i) q^{20} +(113.043 - 38.1711i) q^{21} +96.7692i q^{22} +(18.2287 + 10.5244i) q^{23} +(25.7693 + 44.6337i) q^{24} +(123.800 - 17.2822i) q^{25} +(-93.4871 + 161.924i) q^{26} -80.5063i q^{27} +(-23.7002 - 70.1876i) q^{28} -69.5116 q^{29} +(143.708 - 9.98234i) q^{30} +(-80.5581 - 139.531i) q^{31} +(27.7128 - 16.0000i) q^{32} +(269.948 + 155.855i) q^{33} +40.5585 q^{34} +(-205.353 - 26.5550i) q^{35} +58.0141 q^{36} +(140.800 + 81.2909i) q^{37} +(53.7942 - 31.0581i) q^{38} +(301.137 + 521.585i) q^{39} +(-6.19798 - 89.2277i) q^{40} -365.073 q^{41} +(-233.967 - 46.9286i) q^{42} +254.518i q^{43} +(96.7692 - 167.609i) q^{44} +(71.1511 - 145.711i) q^{45} +(-21.0487 - 36.4575i) q^{46} +(-405.994 - 234.401i) q^{47} -103.077i q^{48} +(316.469 + 132.275i) q^{49} +(-231.709 - 93.8658i) q^{50} +(65.3228 - 113.142i) q^{51} +(323.849 - 186.974i) q^{52} +(-508.487 + 293.575i) q^{53} +(-80.5063 + 139.441i) q^{54} +(-302.292 - 448.613i) q^{55} +(-29.1377 + 145.269i) q^{56} -200.086i q^{57} +(120.398 + 69.5116i) q^{58} +(268.472 + 465.008i) q^{59} +(-258.893 - 126.419i) q^{60} +(312.912 - 541.979i) q^{61} +322.232i q^{62} +(-177.430 + 201.667i) q^{63} -64.0000 q^{64} +(-72.4289 - 1042.71i) q^{65} +(-311.709 - 539.896i) q^{66} +(106.585 - 61.5368i) q^{67} +(-70.2494 - 40.5585i) q^{68} -135.603 q^{69} +(329.127 + 251.347i) q^{70} +210.060 q^{71} +(-100.483 - 58.0141i) q^{72} +(122.788 - 70.8917i) q^{73} +(-162.582 - 281.600i) q^{74} +(-635.035 + 495.200i) q^{75} -124.232 q^{76} +(286.681 + 849.000i) q^{77} -1204.55i q^{78} +(256.712 - 444.638i) q^{79} +(-78.4925 + 160.745i) q^{80} +(455.121 + 788.294i) q^{81} +(632.325 + 365.073i) q^{82} +117.376i q^{83} +(358.314 + 315.250i) q^{84} +(-188.025 + 126.698i) q^{85} +(254.518 - 440.839i) q^{86} +(387.820 - 223.908i) q^{87} +(-335.218 + 193.538i) q^{88} +(-30.6294 + 53.0517i) q^{89} +(-268.948 + 181.227i) q^{90} +(-340.500 + 1697.59i) q^{91} +84.1950i q^{92} +(898.902 + 518.981i) q^{93} +(468.802 + 811.989i) q^{94} +(-152.364 + 312.027i) q^{95} +(-103.077 + 178.535i) q^{96} -436.654i q^{97} +(-415.865 - 545.575i) q^{98} -701.748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9	\( 24 q + 48 q^{4} - 8 q^{5} + 56 q^{6} + 62 q^{9} + 12 q^{10} - 62 q^{11} - 84 q^{14} + 172 q^{15} - 192 q^{16} + 186 q^{19} - 64 q^{20} + 350 q^{21} + 112 q^{24} + 126 q^{25} - 236 q^{26} - 676 q^{29} + 28 q^{30} - 652 q^{31} - 544 q^{34} - 1344 q^{35} + 496 q^{36} - 868 q^{39} - 48 q^{40} + 792 q^{41} + 248 q^{44} + 664 q^{45} + 376 q^{46} + 1602 q^{49} + 320 q^{50} - 1448 q^{51} + 1540 q^{54} + 596 q^{55} - 144 q^{56} + 1336 q^{59} + 344 q^{60} - 314 q^{61} - 1536 q^{64} + 1862 q^{65} - 1600 q^{66} + 180 q^{69} - 484 q^{70} + 4432 q^{71} - 1012 q^{74} - 4550 q^{75} + 1488 q^{76} - 1772 q^{79} - 128 q^{80} + 1228 q^{81} + 784 q^{84} + 4564 q^{85} + 396 q^{86} + 6094 q^{89} + 200 q^{90} - 4364 q^{91} + 3604 q^{94} + 1166 q^{95} - 448 q^{96} - 17092 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 - 8 * q^5 + 56 * q^6 + 62 * q^9 + 12 * q^10 - 62 * q^11 - 84 * q^14 + 172 * q^15 - 192 * q^16 + 186 * q^19 - 64 * q^20 + 350 * q^21 + 112 * q^24 + 126 * q^25 - 236 * q^26 - 676 * q^29 + 28 * q^30 - 652 * q^31 - 544 * q^34 - 1344 * q^35 + 496 * q^36 - 868 * q^39 - 48 * q^40 + 792 * q^41 + 248 * q^44 + 664 * q^45 + 376 * q^46 + 1602 * q^49 + 320 * q^50 - 1448 * q^51 + 1540 * q^54 + 596 * q^55 - 144 * q^56 + 1336 * q^59 + 344 * q^60 - 314 * q^61 - 1536 * q^64 + 1862 * q^65 - 1600 * q^66 + 180 * q^69 - 484 * q^70 + 4432 * q^71 - 1012 * q^74 - 4550 * q^75 + 1488 * q^76 - 1772 * q^79 - 128 * q^80 + 1228 * q^81 + 784 * q^84 + 4564 * q^85 + 396 * q^86 + 6094 * q^89 + 200 * q^90 - 4364 * q^91 + 3604 * q^94 + 1166 * q^95 - 448 * q^96 - 17092 * q^99

Introduction

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