LMFDB - Embedded newform 65.4.e.a.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,4,Mod(16,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.16"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 $ x^14 - 2x^13 + 45x^12 - 52x^11 + 1311x^10 - 1336x^9 + 20343x^8 - 11166x^7 + 216447x^6 - 107836x^5 + 1201133x^4 + 4392x^3 + 3890980x^2 - 1936800*x + 1157776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.1
Root			$2.45261 - 4.24804i$ of defining polynomial
Character	$\chi$	$=$	65.61
Dual form			65.4.e.a.16.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.45261 + 4.24804i) q^{2} +(-3.39607 + 5.88216i) q^{3} +(-8.03055 - 13.9093i) q^{4} -5.00000 q^{5} +(-16.6584 - 28.8532i) q^{6} +(2.60104 + 4.50514i) q^{7} +39.5414 q^{8} +(-9.56652 - 16.5697i) q^{9} +(12.2630 - 21.2402i) q^{10} +(-20.9688 + 36.3191i) q^{11} +109.089 q^{12} +(46.1350 - 8.28002i) q^{13} -25.5173 q^{14} +(16.9803 - 29.4108i) q^{15} +(-32.7350 + 56.6988i) q^{16} +(-19.1803 - 33.2212i) q^{17} +93.8516 q^{18} +(-67.6145 - 117.112i) q^{19} +(40.1527 + 69.5466i) q^{20} -35.3332 q^{21} +(-102.857 - 178.153i) q^{22} +(-73.9418 + 128.071i) q^{23} +(-134.285 + 232.589i) q^{24} +25.0000 q^{25} +(-77.9772 + 216.291i) q^{26} -53.4334 q^{27} +(41.7756 - 72.3575i) q^{28} +(98.4740 - 170.562i) q^{29} +(83.2921 + 144.266i) q^{30} -177.355 q^{31} +(-2.40675 - 4.16861i) q^{32} +(-142.423 - 246.684i) q^{33} +188.167 q^{34} +(-13.0052 - 22.5257i) q^{35} +(-153.649 + 266.128i) q^{36} +(-156.728 + 271.461i) q^{37} +663.326 q^{38} +(-107.973 + 299.493i) q^{39} -197.707 q^{40} +(-72.0889 + 124.862i) q^{41} +(86.6585 - 150.097i) q^{42} +(-36.6532 - 63.4852i) q^{43} +673.565 q^{44} +(47.8326 + 82.8485i) q^{45} +(-362.700 - 628.215i) q^{46} +194.126 q^{47} +(-222.341 - 385.105i) q^{48} +(157.969 - 273.611i) q^{49} +(-61.3151 + 106.201i) q^{50} +260.550 q^{51} +(-485.659 - 575.214i) q^{52} -751.545 q^{53} +(131.051 - 226.987i) q^{54} +(104.844 - 181.595i) q^{55} +(102.849 + 178.139i) q^{56} +918.492 q^{57} +(483.036 + 836.642i) q^{58} +(226.456 + 392.233i) q^{59} -545.445 q^{60} +(77.2358 + 133.776i) q^{61} +(434.981 - 753.410i) q^{62} +(49.7659 - 86.1970i) q^{63} -500.149 q^{64} +(-230.675 + 41.4001i) q^{65} +1397.23 q^{66} +(-424.112 + 734.583i) q^{67} +(-308.057 + 533.570i) q^{68} +(-502.222 - 869.875i) q^{69} +127.587 q^{70} +(379.816 + 657.860i) q^{71} +(-378.273 - 655.189i) q^{72} +143.577 q^{73} +(-768.784 - 1331.57i) q^{74} +(-84.9016 + 147.054i) q^{75} +(-1085.96 + 1880.94i) q^{76} -218.163 q^{77} +(-1007.44 - 1193.21i) q^{78} -133.740 q^{79} +(163.675 - 283.494i) q^{80} +(439.759 - 761.686i) q^{81} +(-353.611 - 612.473i) q^{82} -607.864 q^{83} +(283.745 + 491.461i) q^{84} +(95.9015 + 166.106i) q^{85} +359.584 q^{86} +(668.848 + 1158.48i) q^{87} +(-829.137 + 1436.11i) q^{88} +(-74.0017 + 128.175i) q^{89} -469.258 q^{90} +(157.302 + 186.308i) q^{91} +2375.17 q^{92} +(602.309 - 1043.23i) q^{93} +(-476.115 + 824.655i) q^{94} +(338.072 + 585.558i) q^{95} +32.6939 q^{96} +(247.792 + 429.189i) q^{97} +(774.872 + 1342.12i) q^{98} +802.395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18}+ \cdots + 11378 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.45261	+	4.24804i	−0.867127	+	1.50191i	−0.00220750	+	0.999998i	$0.500703\pi$
$2$	−2.45261	+	4.24804i	−0.867127	+	1.50191i	−0.864920	+	0.501911i	$0.832631\pi$
$3$	−3.39607	+	5.88216i	−0.653573	+	1.13202i	0.328676	+	0.944443i	$0.393397\pi$
$3$	−3.39607	+	5.88216i	−0.653573	+	1.13202i	−0.982249	+	0.187579i	$0.939936\pi$
$4$	−8.03055	−	13.9093i	−1.00382	−	1.73866i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−16.6584	−	28.8532i	−1.13346	−	1.96321i
$7$	2.60104	+	4.50514i	0.140443	+	0.243255i	0.927664	−	0.373417i	$-0.121814\pi$
$7$	2.60104	+	4.50514i	0.140443	+	0.243255i	−0.787220	+	0.616672i	$0.788481\pi$
$8$	39.5414			1.74750
$9$	−9.56652	−	16.5697i	−0.354316	−	0.613692i
$10$	12.2630	−	21.2402i	0.387791	−	0.671674i
$11$	−20.9688	+	36.3191i	−0.574758	+	0.995511i	0.421309	+	0.906917i	$0.361571\pi$
$11$	−20.9688	+	36.3191i	−0.574758	+	0.995511i	−0.996068	+	0.0885938i	$0.971763\pi$
$12$	109.089			2.62428
$13$	46.1350	−	8.28002i	0.984274	−	0.176651i
$13$	46.1350	−	8.28002i	0.984274	−	0.176651i
$14$	−25.5173			−0.487128
$15$	16.9803	−	29.4108i	0.292287	−	0.506256i
$16$	−32.7350	+	56.6988i	−0.511485	+	0.885918i
$17$	−19.1803	−	33.2212i	−0.273641	−	0.473961i	0.696150	−	0.717896i	$-0.254895\pi$
$17$	−19.1803	−	33.2212i	−0.273641	−	0.473961i	−0.969791	+	0.243935i	$0.921562\pi$
$18$	93.8516			1.22895
$19$	−67.6145	−	117.112i	−0.816412	−	1.41407i	−0.908310	−	0.418298i	$-0.862627\pi$
$19$	−67.6145	−	117.112i	−0.816412	−	1.41407i	0.0918983	−	0.995768i	$-0.470707\pi$
$20$	40.1527	+	69.5466i	0.448921	+	0.777555i
$21$	−35.3332			−0.367159
$22$	−102.857	−	178.153i	−0.996777	−	1.72647i
$23$	−73.9418	+	128.071i	−0.670345	+	1.16107i	0.307462	+	0.951560i	$0.400520\pi$
$23$	−73.9418	+	128.071i	−0.670345	+	1.16107i	−0.977806	+	0.209511i	$0.932813\pi$
$24$	−134.285	+	232.589i	−1.14212	+	1.97821i
$25$	25.0000			0.200000
$26$	−77.9772	+	216.291i	−0.588176	+	1.63147i
$27$	−53.4334			−0.380862
$28$	41.7756	−	72.3575i	0.281959	−	0.488367i
$29$	98.4740	−	170.562i	0.630557	−	1.09216i	−0.356881	−	0.934150i	$-0.616160\pi$
$29$	98.4740	−	170.562i	0.630557	−	1.09216i	0.987438	−	0.158007i	$-0.0505069\pi$
$30$	83.2921	+	144.266i	0.506900	+	0.877976i
$31$	−177.355			−1.02754			−0.513772	−	0.857927i	$-0.671752\pi$
$31$	−177.355			−1.02754			−0.513772	+	0.857927i	$0.671752\pi$
$32$	−2.40675	−	4.16861i	−0.0132955	−	0.0230285i
$33$	−142.423	−	246.684i	−0.751293	−	1.30128i
$34$	188.167			0.949128
$35$	−13.0052	−	22.5257i	−0.0628081	−	0.108787i
$36$	−153.649	+	266.128i	−0.711337	+	1.23207i
$37$	−156.728	+	271.461i	−0.696377	+	1.20616i	0.273338	+	0.961918i	$0.411872\pi$
$37$	−156.728	+	271.461i	−0.696377	+	1.20616i	−0.969714	+	0.244242i	$0.921461\pi$
$38$	663.326			2.83173
$39$	−107.973	+	299.493i	−0.443322	+	1.22967i
$40$	−197.707			−0.781505
$41$	−72.0889	+	124.862i	−0.274595	+	0.475613i	−0.970033	−	0.242974i	$-0.921877\pi$
$41$	−72.0889	+	124.862i	−0.274595	+	0.475613i	0.695438	+	0.718586i	$0.255210\pi$
$42$	86.6585	−	150.097i	0.318374	−	0.551440i
$43$	−36.6532	−	63.4852i	−0.129990	−	0.225149i	0.793683	−	0.608332i	$-0.208161\pi$
$43$	−36.6532	−	63.4852i	−0.129990	−	0.225149i	−0.923672	+	0.383183i	$0.874828\pi$
$44$	673.565			2.30781
$45$	47.8326	+	82.8485i	0.158455	+	0.274452i
$46$	−362.700	−	628.215i	−1.16255	−	2.01359i
$47$	194.126			0.602473			0.301236	−	0.953550i	$-0.402601\pi$
$47$	194.126			0.602473			0.301236	+	0.953550i	$0.402601\pi$
$48$	−222.341	−	385.105i	−0.668586	−	1.15802i
$49$	157.969	−	273.611i	0.460551	−	0.797699i
$50$	−61.3151	+	106.201i	−0.173425	+	0.300382i
$51$	260.550			0.715379
$52$	−485.659	−	575.214i	−1.29517	−	1.53400i
$53$	−751.545			−1.94779			−0.973893	−	0.227009i	$-0.927105\pi$
$53$	−751.545			−1.94779			−0.973893	+	0.227009i	$0.927105\pi$
$54$	131.051	−	226.987i	0.330256	−	0.572020i
$55$	104.844	−	181.595i	0.257040	−	0.445206i
$56$	102.849	+	178.139i	0.245424	+	0.425087i
$57$	918.492			2.13434
$58$	483.036	+	836.642i	1.09355	+	1.89408i
$59$	226.456	+	392.233i	0.499696	+	0.865499i	1.00000		0.000351133i	$-0.000111769\pi$
$59$	226.456	+	392.233i	0.499696	+	0.865499i	−0.500304	+	0.865850i	$0.666778\pi$
$60$	−545.445			−1.17361
$61$	77.2358	+	133.776i	0.162115	+	0.280792i	0.935627	−	0.352990i	$-0.114835\pi$
$61$	77.2358	+	133.776i	0.162115	+	0.280792i	−0.773512	+	0.633782i	$0.781502\pi$
$62$	434.981	−	753.410i	0.891011	−	1.54328i
$63$	49.7659	−	86.1970i	0.0995224	−	0.172378i
$64$	−500.149			−0.976854
$65$	−230.675	+	41.4001i	−0.440181	+	0.0790008i
$66$	1397.23			2.60587
$67$	−424.112	+	734.583i	−0.773336	+	1.33946i	0.162389	+	0.986727i	$0.448080\pi$
$67$	−424.112	+	734.583i	−0.773336	+	1.33946i	−0.935725	+	0.352730i	$0.885253\pi$
$68$	−308.057	+	533.570i	−0.549373	+	0.951542i
$69$	−502.222	−	869.875i	−0.876239	−	1.51769i
$70$	127.587			0.217850
$71$	379.816	+	657.860i	0.634871	+	1.09963i	0.986542	+	0.163505i	$0.0522801\pi$
$71$	379.816	+	657.860i	0.634871	+	1.09963i	−0.351671	+	0.936124i	$0.614387\pi$
$72$	−378.273	−	655.189i	−0.619166	−	1.07243i
$73$	143.577			0.230197			0.115099	−	0.993354i	$-0.463282\pi$
$73$	143.577			0.230197			0.115099	+	0.993354i	$0.463282\pi$
$74$	−768.784	−	1331.57i	−1.20769	−	2.09179i
$75$	−84.9016	+	147.054i	−0.130715	+	0.226404i
$76$	−1085.96	+	1880.94i	−1.63906	+	2.83893i
$77$	−218.163			−0.322883
$78$	−1007.44	−	1193.21i	−1.46244	−	1.73211i
$79$	−133.740			−0.190467			−0.0952337	−	0.995455i	$-0.530360\pi$
$79$	−133.740			−0.190467			−0.0952337	+	0.995455i	$0.530360\pi$
$80$	163.675	−	283.494i	0.228743	−	0.396195i
$81$	439.759	−	761.686i	0.603237	−	1.04484i
$82$	−353.611	−	612.473i	−0.476218	−	0.824833i
$83$	−607.864			−0.803877			−0.401938	−	0.915667i	$-0.631663\pi$
$83$	−607.864			−0.803877			−0.401938	+	0.915667i	$0.631663\pi$
$84$	283.745	+	491.461i	0.368561	+	0.638367i
$85$	95.9015	+	166.106i	0.122376	+	0.211962i
$86$	359.584			0.450871
$87$	668.848	+	1158.48i	0.824231	+	1.42761i
$88$	−829.137	+	1436.11i	−1.00439	+	1.73965i
$89$	−74.0017	+	128.175i	−0.0881367	+	0.152657i	−0.906724	−	0.421726i	$-0.861425\pi$
$89$	−74.0017	+	128.175i	−0.0881367	+	0.152657i	0.818587	+	0.574383i	$0.194758\pi$
$90$	−469.258			−0.549601
$91$	157.302	+	186.308i	0.181206	+	0.214620i
$92$	2375.17			2.69162
$93$	602.309	−	1043.23i	0.671575	−	1.16320i
$94$	−476.115	+	824.655i	−0.522420	+	0.904858i
$95$	338.072	+	585.558i	0.365110	+	0.632390i
$96$	32.6939			0.0347584
$97$	247.792	+	429.189i	0.259376	+	0.449253i	0.966075	−	0.258262i	$-0.0831497\pi$
$97$	247.792	+	429.189i	0.259376	+	0.449253i	−0.706699	+	0.707515i	$0.749816\pi$
$98$	774.872	+	1342.12i	0.798713	+	1.38341i
$99$	802.395			0.814583
$100$	−200.764	−	347.733i	−0.200764	−	0.347733i
$101$	−257.578	+	446.138i	−0.253762	+	0.439528i	−0.964558	−	0.263869i	$-0.915001\pi$
$101$	−257.578	+	446.138i	−0.253762	+	0.439528i	0.710797	+	0.703398i	$0.248335\pi$
$102$	−639.027	+	1106.83i	−0.620324	+	1.07443i
$103$	140.957			0.134844			0.0674219	−	0.997725i	$-0.478523\pi$
$103$	140.957			0.134844			0.0674219	+	0.997725i	$0.478523\pi$
$104$	1824.24	−	327.404i	1.72002	−	0.308698i
$105$	176.666			0.164199
$106$	1843.24	−	3192.59i	1.68898	−	2.92539i
$107$	163.491	−	283.174i	0.147713	−	0.255846i	−0.782669	−	0.622438i	$-0.786142\pi$
$107$	163.491	−	283.174i	0.147713	−	0.255846i	0.930382	+	0.366592i	$0.119476\pi$
$108$	429.100	+	743.223i	0.382316	+	0.662191i
$109$	−762.166			−0.669745			−0.334873	−	0.942263i	$-0.608693\pi$
$109$	−762.166			−0.669745			−0.334873	+	0.942263i	$0.608693\pi$
$110$	514.283	+	890.764i	0.445772	+	0.772100i
$111$	−1064.52	−	1843.80i	−0.910266	−	1.57663i
$112$	−340.581			−0.287338
$113$	−902.285	−	1562.80i	−0.751149	−	1.30103i	−0.947266	−	0.320448i	$-0.896166\pi$
$113$	−902.285	−	1562.80i	−0.751149	−	1.30103i	0.196117	−	0.980581i	$-0.437167\pi$
$114$	−2252.70	+	3901.79i	−1.85074	+	3.20558i
$115$	369.709	−	640.355i	0.299787	−	0.519247i
$116$	−3163.20			−2.53186
$117$	−578.549	−	685.233i	−0.457153	−	0.541451i
$118$	−2221.63			−1.73320
$119$	99.7776	−	172.820i	0.0768621	−	0.133129i
$120$	671.426	−	1162.94i	0.510771	−	0.884681i
$121$	−213.884	−	370.459i	−0.160694	−	0.278331i
$122$	−757.716			−0.562298
$123$	−489.637	−	848.077i	−0.358936	−	0.621695i
$124$	1424.26	+	2466.88i	1.03147	+	1.78655i
$125$	−125.000			−0.0894427
$126$	244.112	+	422.814i	0.172597	+	0.298947i
$127$	1321.40	−	2288.74i	0.923273	−	1.59916i	0.128959	−	0.991650i	$-0.458837\pi$
$127$	1321.40	−	2288.74i	0.923273	−	1.59916i	0.794315	−	0.607506i	$-0.207830\pi$
$128$	1245.92	−	2158.00i	0.860352	−	1.49017i
$129$	497.907			0.339831
$130$	389.886	−	1081.45i	0.263041	−	0.729614i
$131$	−467.861			−0.312040			−0.156020	−	0.987754i	$-0.549866\pi$
$131$	−467.861			−0.312040			−0.156020	+	0.987754i	$0.549866\pi$
$132$	−2287.47	+	3962.02i	−1.50832	+	2.61249i
$133$	351.736	−	609.225i	0.229319	−	0.397192i
$134$	−2080.36	−	3603.29i	−1.34116	−	2.32296i
$135$	267.167			0.170327
$136$	−758.416	−	1313.61i	−0.478188	−	0.828246i
$137$	704.357	+	1219.98i	0.439250	+	0.760803i	0.997632	−	0.0687808i	$-0.0219109\pi$
$137$	704.357	+	1219.98i	0.439250	+	0.760803i	−0.558382	+	0.829584i	$0.688578\pi$
$138$	4927.01			3.03924
$139$	821.610	+	1423.07i	0.501353	+	0.868368i	0.999999	+	0.00156264i	$0.000497404\pi$
$139$	821.610	+	1423.07i	0.501353	+	0.868368i	−0.498646	+	0.866806i	$0.666169\pi$
$140$	−208.878	+	361.787i	−0.126096	+	0.218404i
$141$	−659.265	+	1141.88i	−0.393760	+	0.682012i
$142$	−3726.15			−2.20206
$143$	−666.675	+	1849.20i	−0.389861	+	1.08139i
$144$	1252.64			0.724908
$145$	−492.370	+	852.810i	−0.281994	+	0.488428i
$146$	−352.137	+	609.920i	−0.199610	+	0.345735i
$147$	1072.95	+	1858.40i	0.602008	+	1.04271i
$148$	5034.45			2.79614
$149$	−1214.31	−	2103.25i	−0.667653	−	1.15641i	−0.978559	−	0.205968i	$-0.933966\pi$
$149$	−1214.31	−	2103.25i	−0.667653	−	1.15641i	0.310906	−	0.950441i	$-0.399368\pi$
$150$	−416.460	−	721.331i	−0.226692	−	0.392643i
$151$	877.503			0.472915			0.236458	−	0.971642i	$-0.424014\pi$
$151$	877.503			0.472915			0.236458	+	0.971642i	$0.424014\pi$
$152$	−2673.57	−	4630.76i	−1.42668	−	2.47108i
$153$	−366.977	+	635.623i	−0.193911	+	0.335863i
$154$	535.069	−	926.766i	0.279981	−	0.484941i
$155$	886.774			0.459532
$156$	5032.83	−	903.260i	2.58300	−	0.463581i
$157$	−1961.12			−0.996909			−0.498454	−	0.866916i	$-0.666099\pi$
$157$	−1961.12			−0.996909			−0.498454	+	0.866916i	$0.666099\pi$
$158$	328.011	−	568.132i	0.165159	−	0.286064i
$159$	2552.30	−	4420.71i	1.27302	−	2.20494i
$160$	12.0337	+	20.8430i	0.00594594	+	0.0102987i
$161$	−769.303			−0.376581
$162$	2157.11	+	3736.23i	1.04617	+	1.81201i
$163$	799.568	+	1384.89i	0.384215	+	0.665479i	0.991660	−	0.128882i	$-0.0411389\pi$
$163$	799.568	+	1384.89i	0.384215	+	0.665479i	−0.607445	+	0.794362i	$0.707806\pi$
$164$	2315.65			1.10257
$165$	712.115	+	1233.42i	0.335989	+	0.581949i
$166$	1490.85	−	2582.23i	0.697063	−	1.20735i
$167$	28.0584	−	48.5986i	0.0130013	−	0.0225190i	−0.859452	−	0.511217i	$-0.829195\pi$
$167$	28.0584	−	48.5986i	0.0130013	−	0.0225190i	0.872453	+	0.488698i	$0.162528\pi$
$168$	−1397.13			−0.641611
$169$	2059.88	−	763.998i	0.937589	−	0.347746i
$170$	−940.834			−0.424463
$171$	−1293.67	+	2240.70i	−0.578535	+	1.00205i
$172$	−588.691	+	1019.64i	−0.260972	+	0.452018i
$173$	1836.03	+	3180.10i	0.806883	+	1.39756i	0.915013	+	0.403425i	$0.132180\pi$
$173$	1836.03	+	3180.10i	0.806883	+	1.39756i	−0.108130	+	0.994137i	$0.534486\pi$
$174$	−6561.68			−2.85885
$175$	65.0261	+	112.628i	0.0280886	+	0.0486509i
$176$	−1372.83	−	2377.81i	−0.587961	−	1.01838i
$177$	−3076.24			−1.30635
$178$	−362.994	−	628.724i	−0.152851	−	0.264746i
$179$	−1869.35	+	3237.82i	−0.780570	+	1.35199i	0.151040	+	0.988528i	$0.451738\pi$
$179$	−1869.35	+	3237.82i	−0.780570	+	1.35199i	−0.931610	+	0.363460i	$0.881595\pi$
$180$	768.244	−	1330.64i	0.318120	−	0.550999i
$181$	1800.89			0.739551			0.369776	−	0.929121i	$-0.379435\pi$
$181$	1800.89			0.739551			0.369776	+	0.929121i	$0.379435\pi$
$182$	−1177.24	+	211.284i	−0.479467	+	0.0860517i
$183$	−1049.19			−0.423817
$184$	−2923.76	+	5064.10i	−1.17143	+	2.02897i
$185$	783.640	−	1357.31i	0.311429	−	0.539411i
$186$	2954.45	+	5117.26i	1.16468	+	2.01729i
$187$	1608.75			0.629111
$188$	−1558.94	−	2700.16i	−0.604773	−	1.04750i
$189$	−138.983	−	240.725i	−0.0534894	−	0.0926464i
$190$	−3316.63			−1.26639
$191$	115.792	+	200.557i	0.0438659	+	0.0759780i	0.887125	−	0.461530i	$-0.152699\pi$
$191$	115.792	+	200.557i	0.0438659	+	0.0759780i	−0.843259	+	0.537508i	$0.819366\pi$
$192$	1698.54	−	2941.96i	0.638446	−	1.10582i
$193$	−1096.71	+	1899.57i	−0.409032	+	0.708465i	−0.994782	−	0.102028i	$-0.967467\pi$
$193$	−1096.71	+	1899.57i	−0.409032	+	0.708465i	0.585749	+	0.810492i	$0.300800\pi$
$194$	−2430.95			−0.899649
$195$	539.866	−	1497.47i	0.198260	−	0.549927i
$196$	−5074.32			−1.84924
$197$	−1466.70	+	2540.40i	−0.530447	+	0.918761i	0.468922	+	0.883239i	$0.344642\pi$
$197$	−1466.70	+	2540.40i	−0.530447	+	0.918761i	−0.999369	+	0.0355211i	$0.988691\pi$
$198$	−1967.96	+	3408.60i	−0.706347	+	1.22343i
$199$	1530.71	+	2651.27i	0.545273	+	0.944440i	0.998590	+	0.0530906i	$0.0169072\pi$
$199$	1530.71	+	2651.27i	0.545273	+	0.944440i	−0.453317	+	0.891349i	$0.649759\pi$
$200$	988.535			0.349500
$201$	−2880.62	−	4989.38i	−1.01086	−	1.75087i
$202$	−1263.47	−	2188.40i	−0.440088	−	0.762254i
$203$	1024.54			0.354230
$204$	−2092.36	−	3624.08i	−0.718111	−	1.24380i
$205$	360.445	−	624.309i	0.122803	−	0.212700i
$206$	−345.712	+	598.791i	−0.116927	+	0.202523i
$207$	2829.46			0.950054
$208$	−1040.77	+	2886.85i	−0.346943	+	0.962340i
$209$	5671.19			1.87696
$210$	−433.293	+	750.485i	−0.142381	+	0.246611i
$211$	−854.274	+	1479.65i	−0.278724	+	0.482763i	−0.971068	−	0.238804i	$-0.923245\pi$
$211$	−854.274	+	1479.65i	−0.278724	+	0.482763i	0.692344	+	0.721567i	$0.256578\pi$
$212$	6035.32	+	10453.5i	1.95522	+	3.38655i
$213$	−5159.52			−1.65974
$214$	801.956	+	1389.03i	0.256171	+	0.443701i
$215$	183.266	+	317.426i	0.0581332	+	0.100690i
$216$	−2112.83			−0.665556
$217$	−461.308	−	799.008i	−0.144312	−	0.249955i
$218$	1869.29	−	3237.71i	0.580754	−	1.00590i
$219$	−487.596	+	844.541i	−0.150451	+	0.260588i
$220$	−3367.83			−1.03209
$221$	−1159.96	−	1373.85i	−0.353064	−	0.418168i
$222$	10443.4			3.15727
$223$	−809.512	+	1402.12i	−0.243089	+	0.421043i	−0.961593	−	0.274481i	$-0.911494\pi$
$223$	−809.512	+	1402.12i	−0.243089	+	0.421043i	0.718503	+	0.695523i	$0.244827\pi$
$224$	12.5201	−	21.6854i	0.00373453	−	0.00646839i
$225$	−239.163	−	414.242i	−0.0708631	−	0.122738i
$226$	8851.80			2.60537
$227$	−2556.69	−	4428.32i	−0.747549	−	1.29479i	−0.948994	−	0.315293i	$-0.897897\pi$
$227$	−2556.69	−	4428.32i	−0.747549	−	1.29479i	0.201445	−	0.979500i	$-0.435436\pi$
$228$	−7376.00	−	12775.6i	−2.14249	−	3.71090i
$229$	194.004			0.0559831			0.0279916	−	0.999608i	$-0.491089\pi$
$229$	194.004			0.0559831			0.0279916	+	0.999608i	$0.491089\pi$
$230$	1813.50	+	3141.08i	0.519907	+	0.900506i
$231$	740.897	−	1283.27i	0.211028	−	0.365511i
$232$	3893.80	−	6744.26i	1.10190	−	1.90854i
$233$	−385.584			−0.108414			−0.0542070	−	0.998530i	$-0.517263\pi$
$233$	−385.584			−0.108414			−0.0542070	+	0.998530i	$0.517263\pi$
$234$	4329.85	−	777.093i	1.20962	−	0.217095i
$235$	−970.631			−0.269434
$236$	3637.13	−	6299.70i	1.00321	−	1.73761i
$237$	454.190	−	786.679i	0.124484	−	0.215613i
$238$	489.430	+	847.718i	0.133298	+	0.230880i
$239$	−2941.98			−0.796238			−0.398119	−	0.917334i	$-0.630337\pi$
$239$	−2941.98			−0.796238			−0.398119	+	0.917334i	$0.630337\pi$
$240$	1111.70	+	1925.53i	0.299001	+	0.517884i
$241$	2006.66	+	3475.63i	0.536349	+	0.928983i	0.999097	+	0.0424933i	$0.0135301\pi$
$241$	2006.66	+	3475.63i	0.536349	+	0.928983i	−0.462748	+	0.886490i	$0.653137\pi$
$242$	2098.30			0.557370
$243$	2265.55	+	3924.05i	0.598087	+	1.03592i
$244$	1240.49	−	2148.60i	0.325469	−	0.563728i
$245$	−789.846	+	1368.05i	−0.205965	+	0.356742i
$246$	4803.55			1.24497
$247$	−4089.08	−	4843.10i	−1.05337	−	1.24761i
$248$	−7012.86			−1.79563
$249$	2064.35	−	3575.55i	0.525392	−	0.910006i
$250$	306.576	−	531.005i	0.0775582	−	0.134335i
$251$	−1346.81	−	2332.74i	−0.338684	−	0.586618i	0.645501	−	0.763759i	$-0.276648\pi$
$251$	−1346.81	−	2332.74i	−0.338684	−	0.586618i	−0.984185	+	0.177141i	$0.943315\pi$
$252$	−1598.59			−0.399610
$253$	−3100.95	−	5371.00i	−0.770573	−	1.33467i
$254$	6481.77	+	11226.8i	1.60119	+	2.77334i
$255$	−1302.75			−0.319927
$256$	4110.92	+	7120.32i	1.00364	+	1.73836i
$257$	−1805.94	+	3127.99i	−0.438333	+	0.759216i	−0.997561	−	0.0697984i	$-0.977764\pi$
$257$	−1805.94	+	3127.99i	−0.438333	+	0.759216i	0.559228	+	0.829014i	$0.311098\pi$
$258$	−1221.17	+	2115.13i	−0.294677	+	0.510396i
$259$	−1630.63			−0.391205
$260$	2428.30	+	2876.07i	0.579217	+	0.686024i
$261$	−3768.21			−0.893665
$262$	1147.48	−	1987.49i	0.270578	−	0.468655i
$263$	−967.940	+	1676.52i	−0.226942	+	0.393075i	−0.956900	−	0.290417i	$-0.906206\pi$
$263$	−967.940	+	1676.52i	−0.226942	+	0.393075i	0.729958	+	0.683492i	$0.239539\pi$
$264$	−5631.61	−	9754.23i	−1.31288	−	2.27398i
$265$	3757.72			0.871076
$266$	1725.34	+	2988.38i	0.397697	+	0.688832i
$267$	−502.629	−	870.579i	−0.115208	−	0.199545i
$268$	13623.4			3.10516
$269$	118.712	+	205.615i	0.0269070	+	0.0466043i	0.879165	−	0.476517i	$-0.158101\pi$
$269$	118.712	+	205.615i	0.0269070	+	0.0466043i	−0.852258	+	0.523121i	$0.824768\pi$
$270$	−655.256	+	1134.94i	−0.147695	+	0.255815i
$271$	−1277.70	+	2213.04i	−0.286401	+	0.496061i	−0.972948	−	0.231024i	$-0.925792\pi$
$271$	−1277.70	+	2213.04i	−0.286401	+	0.496061i	0.686547	+	0.727085i	$0.259126\pi$
$272$	2511.47			0.559854
$273$	−1630.10	+	292.560i	−0.361385	+	0.0648591i
$274$	−6910.04			−1.52354
$275$	−524.221	+	907.977i	−0.114952	+	0.199102i
$276$	−8066.24	+	13971.1i	−1.75917	+	3.04697i
$277$	−2593.65	−	4492.33i	−0.562590	−	0.974434i	−0.997269	−	0.0738488i	$-0.976472\pi$
$277$	−2593.65	−	4492.33i	−0.562590	−	0.974434i	0.434680	−	0.900585i	$-0.356862\pi$
$278$	−8060.34			−1.73895
$279$	1696.67	+	2938.72i	0.364075	+	0.630596i
$280$	−514.244	−	890.697i	−0.109757	−	0.190105i
$281$	5148.13			1.09292			0.546462	−	0.837484i	$-0.315974\pi$
$281$	5148.13			1.09292			0.546462	+	0.837484i	$0.315974\pi$
$282$	−3233.83	−	5601.17i	−0.682880	−	1.18278i
$283$	1146.62	−	1986.00i	0.240846	−	0.417157i	−0.720110	−	0.693860i	$-0.755909\pi$
$283$	1146.62	−	1986.00i	0.240846	−	0.417157i	0.960955	+	0.276703i	$0.0892418\pi$
$284$	6100.26	−	10566.0i	1.27459	−	2.20766i
$285$	−4592.46			−0.954505
$286$	−6220.40	−	7367.43i	−1.28608	−	1.52324i
$287$	−750.026			−0.154260
$288$	−46.0483	+	79.7581i	−0.00942161	+	0.0163187i
$289$	1720.73	−	2980.40i	0.350241	−	0.606635i
$290$	−2415.18	−	4183.21i	−0.489049	−	0.847058i
$291$	−3366.07			−0.678085
$292$	−1153.00	−	1997.06i	−0.231076	−	0.400236i
$293$	−2233.46	−	3868.47i	−0.445325	−	0.771326i	0.552749	−	0.833347i	$-0.313579\pi$
$293$	−2233.46	−	3868.47i	−0.445325	−	0.771326i	−0.998075	+	0.0620213i	$0.980245\pi$
$294$	−10526.1			−2.08807
$295$	−1132.28	−	1961.17i	−0.223471	−	0.387063i
$296$	−6197.25	+	10733.9i	−1.21692	+	2.10776i
$297$	1120.44	−	1940.65i	0.218904	−	0.379152i
$298$	11912.9			2.31576
$299$	−2350.88	+	6520.80i	−0.454698	+	1.26123i
$300$	2727.23			0.524855
$301$	190.673	−	330.256i	0.0365124	−	0.0632413i
$302$	−2152.17	+	3727.67i	−0.410078	+	0.710275i
$303$	−1749.50	−	3030.23i	−0.331704	−	0.574528i
$304$	8853.45			1.67033
$305$	−386.179	−	668.882i	−0.0725002	−	0.125574i
$306$	−1800.10	−	3117.87i	−0.336291	−	0.582473i
$307$	4456.35			0.828460			0.414230	−	0.910172i	$-0.364051\pi$
$307$	4456.35			0.828460			0.414230	+	0.910172i	$0.364051\pi$
$308$	1751.97	+	3034.50i	0.324116	+	0.561386i
$309$	−478.699	+	829.131i	−0.0881303	+	0.152646i
$310$	−2174.91	+	3767.05i	−0.398472	+	0.690174i
$311$	5351.54			0.975749			0.487875	−	0.872914i	$-0.337772\pi$
$311$	5351.54			0.975749			0.487875	+	0.872914i	$0.337772\pi$
$312$	−4269.41	+	11842.4i	−0.774704	+	2.14885i
$313$	8231.19			1.48644			0.743218	−	0.669050i	$-0.233299\pi$
$313$	8231.19			1.48644			0.743218	+	0.669050i	$0.233299\pi$
$314$	4809.86	−	8330.93i	0.864447	−	1.49727i
$315$	−248.829	+	430.985i	−0.0445077	+	0.0770897i
$316$	1074.01	+	1860.23i	0.191195	+	0.331159i
$317$	−5173.89			−0.916702			−0.458351	−	0.888771i	$-0.651560\pi$
$317$	−5173.89			−0.916702			−0.458351	+	0.888771i	$0.651560\pi$
$318$	12519.5	+	21684.5i	2.20774	+	3.82392i
$319$	4129.77	+	7152.97i	0.724836	+	1.25545i
$320$	2500.75			0.436863
$321$	1110.45	+	1923.36i	0.193082	+	0.334428i
$322$	1886.80	−	3268.03i	0.326544	−	0.565590i
$323$	−2593.73	+	4492.47i	−0.446808	+	0.773894i
$324$	−14126.0			−2.42216
$325$	1153.38	−	207.001i	0.196855	−	0.0353302i
$326$	−7844.10			−1.33265
$327$	2588.37	−	4483.18i	0.437728	−	0.758166i
$328$	−2850.50	+	4937.21i	−0.479855	+	0.831133i
$329$	504.930	+	874.565i	0.0846131	+	0.146554i
$330$	−6986.15			−1.16538
$331$	−1354.54	−	2346.13i	−0.224931	−	0.389592i	0.731368	−	0.681983i	$-0.238882\pi$
$331$	−1354.54	−	2346.13i	−0.224931	−	0.389592i	−0.956299	+	0.292392i	$0.905549\pi$
$332$	4881.48	+	8454.98i	0.806946	+	1.39767i
$333$	5997.37			0.986948
$334$	137.632	+	238.386i	0.0225476	+	0.0390536i
$335$	2120.56	−	3672.92i	0.345846	−	0.599023i
$336$	1156.64	−	2003.35i	0.187797	−	0.325273i
$337$	−1289.00			−0.208356			−0.104178	−	0.994559i	$-0.533221\pi$
$337$	−1289.00			−0.208356			−0.104178	+	0.994559i	$0.533221\pi$
$338$	−1806.59	+	10624.2i	−0.290726	+	1.70971i
$339$	12256.9			1.96372
$340$	1540.28	−	2667.85i	0.245687	−	0.425542i
$341$	3718.92	−	6441.37i	0.590590	−	1.02293i
$342$	−6345.72	−	10991.1i	−1.00333	−	1.73781i
$343$	3427.85			0.539611
$344$	−1449.32	−	2510.29i	−0.227157	−	0.393448i
$345$	2511.11	+	4349.37i	0.391866	+	0.678731i
$346$	−18012.2			−2.79868
$347$	4471.64	+	7745.11i	0.691787	+	1.19821i	0.971252	+	0.238055i	$0.0765098\pi$
$347$	4471.64	+	7745.11i	0.691787	+	1.19821i	−0.279464	+	0.960156i	$0.590157\pi$
$348$	10742.4	−	18606.4i	1.65476	−	2.86612i
$349$	−851.482	+	1474.81i	−0.130598	+	0.226203i	−0.923907	−	0.382616i	$-0.875023\pi$
$349$	−851.482	+	1474.81i	−0.130598	+	0.226203i	0.793309	+	0.608819i	$0.208356\pi$
$350$	−637.933			−0.0974256
$351$	−2465.15	+	442.430i	−0.374872	+	0.0672797i
$352$	201.867			0.0305668
$353$	2917.43	−	5053.14i	0.439884	−	0.761902i	−0.557796	−	0.829978i	$-0.688353\pi$
$353$	2917.43	−	5053.14i	0.439884	−	0.761902i	0.997680	+	0.0680764i	$0.0216862\pi$
$354$	7544.80	−	13068.0i	1.13277	−	1.96202i
$355$	−1899.08	−	3289.30i	−0.283923	−	0.491769i
$356$	2377.10			0.353893
$357$	677.702	+	1173.81i	0.100470	+	0.174019i
$358$	−9169.58	−	15882.2i	−1.35371	−	2.34469i
$359$	−11215.3			−1.64881			−0.824404	−	0.566001i	$-0.808490\pi$
$359$	−11215.3			−1.64881			−0.824404	+	0.566001i	$0.808490\pi$
$360$	1891.37	+	3275.94i	0.276899	+	0.479604i
$361$	−5713.93	+	9896.82i	−0.833056	+	1.44289i
$362$	−4416.86	+	7650.23i	−0.641285	+	1.11074i
$363$	2905.46			0.420102
$364$	1328.20	−	3684.12i	0.191254	−	0.530495i
$365$	−717.884			−0.102947
$366$	2573.25	−	4457.01i	0.367503	−	0.636534i
$367$	−3223.76	+	5583.72i	−0.458526	+	0.794190i	−0.998883	−	0.0472454i	$-0.984956\pi$
$367$	−3223.76	+	5583.72i	−0.458526	+	0.794190i	0.540357	+	0.841436i	$0.318289\pi$
$368$	−4840.98	−	8384.82i	−0.685743	−	1.18774i
$369$	2758.56			0.389173
$370$	3843.92	+	6657.87i	0.540097	+	0.935476i
$371$	−1954.80	−	3385.81i	−0.273553	−	0.473808i
$372$	−19347.5			−2.69656
$373$	1924.55	+	3333.42i	0.267156	+	0.462728i	0.968126	−	0.250462i	$-0.0805826\pi$
$373$	1924.55	+	3333.42i	0.267156	+	0.462728i	−0.700970	+	0.713191i	$0.747249\pi$
$374$	−3945.64	+	6834.05i	−0.545519	+	0.944867i
$375$	424.508	−	735.270i	0.0584574	−	0.101251i
$376$	7676.02			1.05282
$377$	3130.84	−	8684.25i	0.427710	−	1.18637i
$378$	1363.48			0.185529
$379$	−4440.40	+	7691.00i	−0.601815	+	1.04237i	0.390731	+	0.920505i	$0.372222\pi$
$379$	−4440.40	+	7691.00i	−0.601815	+	1.04237i	−0.992546	+	0.121869i	$0.961111\pi$
$380$	5429.81	−	9404.71i	0.733009	−	1.26961i
$381$	8975.15	+	15545.4i	1.20685	+	2.09033i
$382$	−1135.97			−0.152149
$383$	−2148.54	−	3721.38i	−0.286645	−	0.496484i	0.686362	−	0.727260i	$-0.259207\pi$
$383$	−2148.54	−	3721.38i	−0.286645	−	0.496484i	−0.973007	+	0.230776i	$0.925873\pi$
$384$	8462.47	+	14657.4i	1.12461	+	1.94788i
$385$	1090.82			0.144398
$386$	−5379.62	−	9317.77i	−0.709366	−	1.22866i
$387$	−701.287	+	1214.67i	−0.0921148	+	0.159548i
$388$	3979.82	−	6893.24i	0.520733	−	0.901937i
$389$	1541.34			0.200897			0.100449	−	0.994942i	$-0.467972\pi$
$389$	1541.34			0.200897			0.100449	+	0.994942i	$0.467972\pi$
$390$	5037.21	+	5966.06i	0.654023	+	0.774624i
$391$	5672.90			0.733737
$392$	6246.32	−	10818.9i	0.804813	−	1.39398i
$393$	1588.89	−	2752.03i	0.203941	−	0.353236i
$394$	−7194.47	−	12461.2i	−0.919929	−	1.59336i
$395$	668.700			0.0851796
$396$	−6443.67	−	11160.8i	−0.817694	−	1.41629i
$397$	2370.42	+	4105.69i	0.299668	+	0.519040i	0.976060	−	0.217502i	$-0.0697909\pi$
$397$	2370.42	+	4105.69i	0.299668	+	0.519040i	−0.676392	+	0.736542i	$0.736458\pi$
$398$	−15016.9			−1.89128
$399$	2389.04	+	4137.94i	0.299753	+	0.519188i
$400$	−818.376	+	1417.47i	−0.102297	+	0.177184i
$401$	−310.131	+	537.162i	−0.0386214	+	0.0668943i	−0.884690	−	0.466180i	$-0.845630\pi$
$401$	−310.131	+	537.162i	−0.0386214	+	0.0668943i	0.846069	+	0.533074i	$0.178963\pi$
$402$	28260.1			3.50619
$403$	−8182.27	+	1468.50i	−1.01138	+	0.181517i
$404$	8273.96			1.01892
$405$	−2198.80	+	3808.43i	−0.269776	+	0.467265i
$406$	−2512.79	+	4352.29i	−0.307162	+	0.532021i
$407$	−6572.81	−	11384.4i	−0.800497	−	1.38650i
$408$	10302.5			1.25012
$409$	6245.99	+	10818.4i	0.755121	+	1.30791i	0.945314	+	0.326161i	$0.105755\pi$
$409$	6245.99	+	10818.4i	0.755121	+	1.30791i	−0.190193	+	0.981747i	$0.560911\pi$
$410$	1768.06	+	3062.37i	0.212971	+	0.368877i
$411$	−9568.16			−1.14833
$412$	−1131.96	−	1960.62i	−0.135359	−	0.234448i
$413$	−1178.04	+	2040.43i	−0.140358	+	0.243107i
$414$	−6939.55	+	12019.7i	−0.823818	+	1.42689i
$415$	3039.32			0.359505
$416$	−145.551	−	172.391i	−0.0171544	−	0.0203177i
$417$	−11161.0			−1.31068
$418$	−13909.2	+	24091.4i	−1.62756	+	2.81902i
$419$	4428.53	−	7670.43i	0.516343	−	0.894332i	−0.483477	−	0.875357i	$-0.660626\pi$
$419$	4428.53	−	7670.43i	0.516343	−	0.894332i	0.999820	−	0.0189750i	$-0.00604030\pi$
$420$	−1418.73	−	2457.31i	−0.164826	−	0.285486i
$421$	13928.2			1.61240			0.806198	−	0.591646i	$-0.201522\pi$
$421$	13928.2			1.61240			0.806198	+	0.591646i	$0.201522\pi$
$422$	−4190.40	−	7257.98i	−0.483378	−	0.837234i
$423$	−1857.11	−	3216.61i	−0.213465	−	0.369733i
$424$	−29717.1			−3.40375
$425$	−479.507	−	830.531i	−0.0547283	−	0.0947922i
$426$	12654.3	−	21917.8i	1.43920	−	2.49277i
$427$	−401.787	+	695.916i	−0.0455360	+	0.0788706i
$428$	−5251.68			−0.593106
$429$	−8613.24	−	10201.5i	−0.969350	−	1.14810i
$430$	−1797.92			−0.201636
$431$	4776.87	−	8273.78i	0.533860	−	0.924673i	−0.465357	−	0.885123i	$-0.654074\pi$
$431$	4776.87	−	8273.78i	0.533860	−	0.924673i	0.999218	−	0.0395500i	$-0.0125924\pi$
$432$	1749.15	−	3029.61i	0.194805	−	0.337412i
$433$	1273.19	+	2205.22i	0.141306	+	0.244749i	0.927989	−	0.372609i	$-0.121537\pi$
$433$	1273.19	+	2205.22i	0.141306	+	0.244749i	−0.786683	+	0.617357i	$0.788203\pi$
$434$	4525.62			0.500546
$435$	−3344.24	−	5792.40i	−0.368607	−	0.638446i
$436$	6120.61	+	10601.2i	0.672303	+	1.16446i
$437$	19998.1			2.18911
$438$	−2391.76	−	4142.65i	−0.260920	−	0.451926i
$439$	7907.04	−	13695.4i	0.859641	−	1.48894i	−0.0126310	−	0.999920i	$-0.504021\pi$
$439$	7907.04	−	13695.4i	0.859641	−	1.48894i	0.872272	−	0.489021i	$-0.162646\pi$
$440$	4145.68	−	7180.54i	0.449177	−	0.777997i
$441$	−6044.86			−0.652722
$442$	8681.08	−	1558.03i	0.934201	−	0.167664i
$443$	−10518.3			−1.12808			−0.564039	−	0.825748i	$-0.690753\pi$
$443$	−10518.3			−1.12808			−0.564039	+	0.825748i	$0.690753\pi$
$444$	−17097.3	+	29613.4i	−1.82748	+	3.16530i
$445$	370.009	−	640.874i	0.0394159	−	0.0682704i
$446$	−3970.83	−	6877.67i	−0.421579	−	0.730195i
$447$	16495.5			1.74544
$448$	−1300.91	−	2253.24i	−0.137192	−	0.237624i
$449$	−7146.12	−	12377.4i	−0.751105	−	1.30095i	−0.947287	−	0.320385i	$-0.896188\pi$
$449$	−7146.12	−	12377.4i	−0.751105	−	1.30095i	0.196182	−	0.980567i	$-0.437146\pi$
$450$	2346.29			0.245789
$451$	−3023.24	−	5236.41i	−0.315652	−	0.546725i
$452$	−14491.7	+	25100.4i	−1.50804	+	2.61199i
$453$	−2980.06	+	5161.61i	−0.309085	+	0.535350i
$454$	25082.2			2.59288
$455$	−786.509	−	931.540i	−0.0810376	−	0.0959808i
$456$	36318.5			3.72975
$457$	−5794.14	+	10035.7i	−0.593082	+	1.02725i	0.400732	+	0.916195i	$0.368756\pi$
$457$	−5794.14	+	10035.7i	−0.593082	+	1.02725i	−0.993814	+	0.111053i	$0.964578\pi$
$458$	−475.815	+	824.136i	−0.0485445	+	0.0840815i
$459$	1024.87	+	1775.13i	0.104220	+	0.180514i
$460$	−11875.9			−1.20373
$461$	1357.61	+	2351.45i	0.137159	+	0.237566i	0.926420	−	0.376492i	$-0.122870\pi$
$461$	1357.61	+	2351.45i	0.137159	+	0.237566i	−0.789261	+	0.614057i	$0.789536\pi$
$462$	3634.26	+	6294.72i	0.365976	+	0.633889i
$463$	3749.77			0.376386			0.188193	−	0.982132i	$-0.439737\pi$
$463$	3749.77			0.376386			0.188193	+	0.982132i	$0.439737\pi$
$464$	6447.10	+	11166.7i	0.645041	+	1.11724i
$465$	−3011.54	+	5216.15i	−0.300338	+	0.520200i
$466$	945.687	−	1637.98i	0.0940088	−	0.162828i
$467$	−5440.29			−0.539071			−0.269536	−	0.962990i	$-0.586870\pi$
$467$	−5440.29			−0.539071			−0.269536	+	0.962990i	$0.586870\pi$
$468$	−4885.05	+	13550.0i	−0.482503	+	1.33835i
$469$	−4412.53			−0.434439
$470$	2380.57	−	4123.28i	0.233633	−	0.404665i
$471$	6660.10	−	11535.6i	0.651553	−	1.12852i
$472$	8954.38	+	15509.4i	0.873218	+	1.51246i
$473$	3074.30			0.298851
$474$	2227.90	+	3858.83i	0.215887	+	0.373928i
$475$	−1690.36	−	2927.79i	−0.163282	−	0.282813i
$476$	−3205.07			−0.308623
$477$	7189.67	+	12452.9i	0.690131	+	1.19534i
$478$	7215.52	−	12497.6i	0.690439	−	1.19588i
$479$	9431.46	−	16335.8i	0.899655	−	1.55825i	0.0717187	−	0.997425i	$-0.477152\pi$
$479$	9431.46	−	16335.8i	0.899655	−	1.55825i	0.827936	−	0.560823i	$-0.189515\pi$
$480$	−163.469			−0.0155444
$481$	−4982.95	+	13821.6i	−0.472356	+	1.31021i
$482$	−19686.1			−1.86033
$483$	2612.60	−	4525.16i	0.246123	−	0.426298i
$484$	−3435.22	+	5949.97i	−0.322616	+	0.558788i
$485$	−1238.96	−	2145.94i	−0.115997	−	0.200912i
$486$	−22226.0			−2.07447
$487$	−3394.98	−	5880.28i	−0.315896	−	0.547148i	0.663731	−	0.747971i	$-0.268972\pi$
$487$	−3394.98	−	5880.28i	−0.315896	−	0.547148i	−0.979628	+	0.200823i	$0.935638\pi$
$488$	3054.01	+	5289.70i	0.283296	+	0.490684i
$489$	−10861.5			−1.00445
$490$	−3874.36	−	6710.59i	−0.357195	−	0.618681i
$491$	−1157.76	+	2005.30i	−0.106413	+	0.184313i	−0.914315	−	0.405004i	$-0.867270\pi$
$491$	−1157.76	+	2005.30i	−0.106413	+	0.184313i	0.807902	+	0.589318i	$0.200603\pi$
$492$	−7864.12	+	13621.0i	−0.720613	+	1.24814i
$493$	−7555.04			−0.690187
$494$	30602.6	−	5492.36i	2.78720	−	0.500228i
$495$	−4011.98			−0.364293
$496$	5805.72	−	10055.8i	0.525573	−	0.910320i
$497$	−1975.83	+	3422.25i	−0.178327	+	0.308871i
$498$	10126.1	+	17538.8i	0.911163	+	1.57818i
$499$	−19441.3			−1.74411			−0.872056	−	0.489407i	$-0.837213\pi$
$499$	−19441.3			−1.74411			−0.872056	+	0.489407i	$0.837213\pi$
$500$	1003.82	+	1738.66i	0.0897843	+	0.155511i
$501$	190.576	+	330.088i	0.0169946	+	0.0294356i
$502$	13212.7			1.17473
$503$	495.628	+	858.453i	0.0439343	+	0.0760965i	0.887156	−	0.461469i	$-0.152677\pi$
$503$	495.628	+	858.453i	0.0439343	+	0.0760965i	−0.843222	+	0.537565i	$0.819344\pi$
$504$	1967.81	−	3408.35i	0.173915	−	0.301230i
$505$	1287.89	−	2230.69i	0.113486	−	0.196563i
$506$	30421.6			2.67274
$507$	−2501.54	+	14711.1i	−0.219127	+	1.28865i
$508$	−42446.4			−3.70720
$509$	−10.9670	+	18.9953i	−0.000955014	+	0.00165413i	−0.866503	−	0.499173i	$-0.833637\pi$
$509$	−10.9670	+	18.9953i	−0.000955014	+	0.00165413i	0.865548	+	0.500827i	$0.166971\pi$
$510$	3195.13	−	5534.13i	0.277417	−	0.480501i
$511$	373.449	+	646.833i	0.0323296	+	0.0559965i
$512$	−20395.1			−1.76044
$513$	3612.87	+	6257.68i	0.310940	+	0.538564i
$514$	−8858.54	−	15343.4i	−0.760181	−	1.31667i
$515$	−704.785			−0.0603040
$516$	−3998.47	−	6925.54i	−0.341129	−	0.590853i
$517$	−4070.60	+	7050.49i	−0.346276	+	0.599768i
$518$	3999.28	−	6926.96i	0.339225	−	0.587554i
$519$	−24941.1			−2.10943
$520$	−9121.22	+	1637.02i	−0.769215	+	0.138054i
$521$	4649.64			0.390987			0.195494	−	0.980705i	$-0.437369\pi$
$521$	4649.64			0.390987			0.195494	+	0.980705i	$0.437369\pi$
$522$	9241.94	−	16007.5i	0.774921	−	1.34220i
$523$	2344.42	−	4060.66i	0.196012	−	0.339503i	−0.751220	−	0.660052i	$-0.770534\pi$
$523$	2344.42	−	4060.66i	0.196012	−	0.339503i	0.947232	+	0.320549i	$0.103867\pi$
$524$	3757.18	+	6507.62i	0.313231	+	0.542532i
$525$	−883.331			−0.0734319
$526$	−4747.95	−	8223.69i	−0.393575	−	0.681692i
$527$	3401.72	+	5891.95i	0.281179	+	0.487016i
$528$	18648.9			1.53710
$529$	−4851.28	−	8402.66i	−0.398724	−	0.690611i
$530$	−9216.22	+	15963.0i	−0.755334	+	1.30828i
$531$	4332.79	−	7504.61i	0.354100	−	0.613319i
$532$	−11298.5			−0.920778
$533$	−2291.97	+	6357.40i	−0.186259	+	0.516641i
$534$	4931.01			0.399598
$535$	−817.453	+	1415.87i	−0.0660591	+	0.114418i
$536$	−16770.0	+	29046.4i	−1.35140	+	2.34070i
$537$	−12696.9	−	21991.7i	−1.02032	−	1.76725i
$538$	−1164.61			−0.0933272
$539$	6624.86	+	11474.6i	0.529412	+	0.916968i
$540$	−2145.50	−	3716.11i	−0.170977	−	0.296141i
$541$	14821.9			1.17790			0.588949	−	0.808170i	$-0.299542\pi$
$541$	14821.9			1.17790			0.588949	+	0.808170i	$0.299542\pi$
$542$	−6267.38	−	10855.4i	−0.496692	−	0.860296i
$543$	−6115.93	+	10593.1i	−0.483351	+	0.837188i
$544$	−92.3242	+	159.910i	−0.00727641	+	0.0126031i
$545$	3810.83			0.299519
$546$	2755.19	−	7642.26i	0.215955	−	0.599009i
$547$	8989.48			0.702673			0.351337	−	0.936249i	$-0.385727\pi$
$547$	8989.48			0.702673			0.351337	+	0.936249i	$0.385727\pi$
$548$	11312.7	−	19594.2i	0.881855	−	1.52742i
$549$	1477.76	−	2559.55i	0.114880	−	0.198978i
$550$	−2571.41	−	4453.82i	−0.199355	−	0.345294i
$551$	−26633.1			−2.05918
$552$	−19858.6	−	34396.0i	−1.53123	−	2.65216i
$553$	−347.863	−	602.517i	−0.0267498	−	0.0463321i
$554$	25444.8			1.95135
$555$	5322.59	+	9218.99i	0.407083	+	0.705089i
$556$	13196.0	−	22856.1i	1.00653	−	1.74337i
$557$	7720.12	−	13371.6i	0.587275	−	1.01719i	−0.407313	−	0.913289i	$-0.633534\pi$
$557$	7720.12	−	13371.6i	0.587275	−	1.01719i	0.994588	−	0.103901i	$-0.0331325\pi$
$558$	−16645.0			−1.26280
$559$	−2216.66	−	2625.40i	−0.167718	−	0.198645i
$560$	1702.91			0.128502
$561$	−5463.43	+	9462.95i	−0.411170	+	0.712167i
$562$	−12626.3	+	21869.4i	−0.947704	+	1.64147i
$563$	−1781.58	−	3085.79i	−0.133365	−	0.230995i	0.791607	−	0.611031i	$-0.209245\pi$
$563$	−1781.58	−	3085.79i	−0.133365	−	0.230995i	−0.924972	+	0.380036i	$0.875912\pi$
$564$	21177.0			1.58105
$565$	4511.43	+	7814.02i	0.335924	+	0.581838i
$566$	5624.40	+	9741.75i	0.417688	+	0.723457i
$567$	4575.33			0.338882
$568$	15018.4	+	26012.7i	1.10944	+	1.92160i
$569$	−8271.49	+	14326.6i	−0.609418	+	1.05554i	0.381918	+	0.924196i	$0.375264\pi$
$569$	−8271.49	+	14326.6i	−0.609418	+	1.05554i	−0.991336	+	0.131347i	$0.958070\pi$
$570$	11263.5	−	19509.0i	0.827677	−	1.43358i
$571$	−596.812			−0.0437404			−0.0218702	−	0.999761i	$-0.506962\pi$
$571$	−596.812			−0.0437404			−0.0218702	+	0.999761i	$0.506962\pi$
$572$	31074.9	−	5577.13i	2.27152	−	0.407678i
$573$	−1572.95			−0.114678
$574$	1839.52	−	3186.14i	0.133763	−	0.231684i
$575$	−1848.54	+	3201.77i	−0.134069	+	0.232214i
$576$	4784.69	+	8287.33i	0.346115	+	0.599488i
$577$	4462.98			0.322004			0.161002	−	0.986954i	$-0.448528\pi$
$577$	4462.98			0.322004			0.161002	+	0.986954i	$0.448528\pi$
$578$	8440.56	+	14619.5i	0.607406	+	1.05206i
$579$	−7449.03	−	12902.1i	−0.534665	−	0.926067i
$580$	15816.0			1.13228
$581$	−1581.08	−	2738.51i	−0.112899	−	0.195547i
$582$	8255.65	−	14299.2i	0.587986	−	1.01842i
$583$	15759.0	−	27295.4i	1.11951	−	1.93904i
$584$	5677.23			0.402269
$585$	2892.75	+	3426.16i	0.204445	+	0.242144i
$586$	21911.2			1.54461
$587$	3818.39	−	6613.64i	0.268487	−	0.465033i	−0.699984	−	0.714158i	$-0.746810\pi$
$587$	3818.39	−	6613.64i	0.268487	−	0.465033i	0.968471	+	0.249125i	$0.0801431\pi$
$588$	17232.7	−	29847.9i	1.20861	−	2.09338i
$589$	11991.8	+	20770.3i	0.838899	+	1.45302i
$590$	11108.1			0.775110
$591$	−9962.01	−	17254.7i	−0.693371	−	1.20095i
$592$	−10261.0	−	17772.6i	−0.712373	−	1.23387i
$593$	20911.9			1.44814			0.724070	−	0.689726i	$-0.242269\pi$
$593$	20911.9			1.44814			0.724070	+	0.689726i	$0.242269\pi$
$594$	5495.98	+	9519.32i	0.379634	+	0.657546i
$595$	−498.888	+	864.099i	−0.0343738	+	0.0595372i
$596$	−19503.2	+	33780.5i	−1.34040	+	2.32165i
$597$	−20793.6			−1.42550
$598$	−21934.8	−	25979.6i	−1.49997	−	1.77656i
$599$	7395.85			0.504485			0.252242	−	0.967664i	$-0.418832\pi$
$599$	7395.85			0.504485			0.252242	+	0.967664i	$0.418832\pi$
$600$	−3357.13	+	5814.72i	−0.228424	+	0.395641i
$601$	−6668.34	+	11549.9i	−0.452591	+	0.783911i	−0.998546	−	0.0539039i	$-0.982834\pi$
$601$	−6668.34	+	11549.9i	−0.452591	+	0.783911i	0.545955	+	0.837814i	$0.316167\pi$
$602$	935.292	+	1619.97i	0.0633217	+	0.109676i
$603$	16229.1			1.09602
$604$	−7046.83	−	12205.5i	−0.474721	−	0.822241i
$605$	1069.42	+	1852.29i	0.0718648	+	0.124473i
$606$	17163.4			1.15052
$607$	12797.2	+	22165.3i	0.855718	+	1.48215i	0.875977	+	0.482352i	$0.160217\pi$
$607$	12797.2	+	22165.3i	0.855718	+	1.48215i	−0.0202594	+	0.999795i	$0.506449\pi$
$608$	−325.462	+	563.716i	−0.0217092	+	0.0376015i
$609$	−3479.41	+	6026.51i	−0.231515	+	0.400996i
$610$	3788.58			0.251467
$611$	8956.02	−	1607.37i	0.592998	−	0.106427i
$612$	11788.1			0.778605
$613$	11104.0	−	19232.6i	0.731623	−	1.26721i	−0.224566	−	0.974459i	$-0.572097\pi$
$613$	11104.0	−	19232.6i	0.731623	−	1.26721i	0.956189	−	0.292749i	$-0.0945701\pi$
$614$	−10929.7	+	18930.7i	−0.718380	+	1.24427i
$615$	2448.19	+	4240.38i	0.160521	+	0.278031i
$616$	−8626.48			−0.564239
$617$	107.676	+	186.500i	0.00702571	+	0.0121689i	0.869517	−	0.493903i	$-0.164430\pi$
$617$	107.676	+	186.500i	0.00702571	+	0.0121689i	−0.862491	+	0.506072i	$0.831097\pi$
$618$	−2348.12	−	4067.07i	−0.152840	−	0.264727i
$619$	−26851.4			−1.74353			−0.871767	−	0.489921i	$-0.837026\pi$
$619$	−26851.4			−1.74353			−0.871767	+	0.489921i	$0.837026\pi$
$620$	−7121.28	−	12334.4i	−0.461286	−	0.798972i
$621$	3950.96	−	6843.27i	0.255309	−	0.442208i
$622$	−13125.2	+	22733.5i	−0.846098	+	1.46549i
$623$	−769.927			−0.0495128
$624$	−13446.4	−	15925.9i	−0.862638	−	1.02171i
$625$	625.000			0.0400000
$626$	−20187.9	+	34966.4i	−1.28893	+	2.23249i
$627$	−19259.7	+	33358.8i	−1.22673	+	2.12476i
$628$	15748.9	+	27277.9i	1.00072	+	1.73329i
$629$	12024.4			0.762230
$630$	−1220.56	−	2114.07i	−0.0771877	−	0.133693i
$631$	−12877.7	−	22304.8i	−0.812446	−	1.40720i	−0.911148	−	0.412080i	$-0.864802\pi$
$631$	−12877.7	−	22304.8i	−0.812446	−	1.40720i	0.0987017	−	0.995117i	$-0.468531\pi$
$632$	−5288.26			−0.332841
$633$	−5802.34	−	10050.0i	−0.364332	−	0.631042i
$634$	12689.5	−	21978.9i	0.794897	−	1.37680i
$635$	−6607.02	+	11443.7i	−0.412900	+	0.715164i
$636$	−81985.3			−5.11153
$637$	5022.41	−	13931.0i	0.312394	−	0.866510i
$638$	−40514.8			−2.51410
$639$	7267.03	−	12586.9i	0.449889	−	0.779231i
$640$	−6229.62	+	10790.0i	−0.384761	+	0.666426i
$641$	−9471.69	−	16405.4i	−0.583634	−	1.01088i	−0.995044	−	0.0994332i	$-0.968297\pi$
$641$	−9471.69	−	16405.4i	−0.583634	−	1.01088i	0.411410	−	0.911450i	$-0.365036\pi$
$642$	−10894.0			−0.669706
$643$	−758.843	−	1314.35i	−0.0465410	−	0.0806113i	0.841816	−	0.539764i	$-0.181486\pi$
$643$	−758.843	−	1314.35i	−0.0465410	−	0.0806113i	−0.888357	+	0.459153i	$0.848153\pi$
$644$	6177.93	+	10700.5i	0.378019	+	0.654749i
$645$	−2489.53			−0.151977
$646$	−12722.8	−	22036.5i	−0.774879	−	1.34213i
$647$	4795.78	−	8306.54i	0.291409	−	0.504735i	−0.682734	−	0.730667i	$-0.739209\pi$
$647$	4795.78	−	8306.54i	0.291409	−	0.504735i	0.974143	+	0.225932i	$0.0725426\pi$
$648$	17388.7	−	30118.1i	1.05416	−	1.82585i
$649$	−18994.1			−1.14882
$650$	−1949.43	+	5407.27i	−0.117635	+	0.326293i
$651$	6266.52			0.377272
$652$	12841.9	−	22242.9i	0.771364	−	1.33604i
$653$	−8161.11	+	14135.5i	−0.489079	+	0.847110i	−0.999921	−	0.0125644i	$-0.996001\pi$
$653$	−8161.11	+	14135.5i	−0.489079	+	0.847110i	0.510842	+	0.859675i	$0.329334\pi$
$654$	12696.5	+	21990.9i	0.759131	+	1.31485i
$655$	2339.30			0.139548
$656$	−4719.67	−	8174.71i	−0.280903	−	0.486538i
$657$	−1373.53	−	2379.02i	−0.0815624	−	0.141270i
$658$	−4953.58			−0.293481
$659$	8149.60	+	14115.5i	0.481735	+	0.834389i	0.999780	−	0.0209640i	$-0.00667354\pi$
$659$	8149.60	+	14115.5i	0.481735	+	0.834389i	−0.518045	+	0.855353i	$0.673340\pi$
$660$	11437.4	−	19810.1i	0.674543	−	1.16834i
$661$	−3890.65	+	6738.80i	−0.228939	+	0.396534i	−0.957494	−	0.288453i	$-0.906859\pi$
$661$	−3890.65	+	6738.80i	−0.228939	+	0.396534i	0.728555	+	0.684987i	$0.240192\pi$
$662$	13288.6			0.780175
$663$	12020.5	−	2157.36i	0.704128	−	0.126372i
$664$	−24035.8			−1.40477
$665$	−1758.68	+	3046.13i	−0.102554	+	0.177630i
$666$	−14709.2	+	25477.0i	−0.855810	+	1.48231i
$667$	14562.7	+	25223.3i	0.845382	+	1.46424i
$668$	−901.297			−0.0522039
$669$	−5498.31	−	9523.35i	−0.317753	−	0.550365i
$670$	10401.8	+	18016.4i	0.599785	+	1.03886i
$671$	−6478.18			−0.372709
$672$	85.0381	+	147.290i	0.00488157	+	0.00845513i
$673$	−14995.3	+	25972.7i	−0.858882	+	1.48763i	0.0141152	+	0.999900i	$0.495507\pi$
$673$	−14995.3	+	25972.7i	−0.858882	+	1.48763i	−0.872997	+	0.487726i	$0.837826\pi$
$674$	3161.40	−	5475.70i	0.180671	−	0.312932i
$675$	−1335.84			−0.0761724
$676$	−27168.7	−	22516.2i	−1.54578	−	1.28108i
$677$	17816.3			1.01143			0.505714	−	0.862701i	$-0.331229\pi$
$677$	17816.3			1.01143			0.505714	+	0.862701i	$0.331229\pi$
$678$	−30061.3	+	52067.7i	−1.70280	+	2.94933i
$679$	−1289.04	+	2232.68i	−0.0728552	+	0.126189i
$680$	3792.08	+	6568.07i	0.213852	+	0.370403i
$681$	34730.8			1.95431
$682$	18242.1	+	31596.3i	1.02423	+	1.77402i
$683$	13584.1	+	23528.3i	0.761024	+	1.31813i	0.942323	+	0.334705i	$0.108637\pi$
$683$	13584.1	+	23528.3i	0.761024	+	1.31813i	−0.181299	+	0.983428i	$0.558030\pi$
$684$	41555.5			2.32298
$685$	−3521.78	−	6099.91i	−0.196439	−	0.340242i
$686$	−8407.17	+	14561.7i	−0.467912	+	0.810447i
$687$	−658.850	+	1141.16i	−0.0365891	+	0.0633741i
$688$	4799.38			0.265951
$689$	−34672.5	+	6222.81i	−1.91715	+	0.344078i
$690$	−24635.1			−1.35919
$691$	−12073.4	+	20911.7i	−0.664680	+	1.15126i	0.314692	+	0.949194i	$0.398099\pi$
$691$	−12073.4	+	20911.7i	−0.664680	+	1.15126i	−0.979372	+	0.202065i	$0.935235\pi$
$692$	29488.6	−	51075.8i	1.61993	−	2.80580i
$693$	2087.06	+	3614.90i	0.114403	+	0.198151i
$694$	−43868.7			−2.39947
$695$	−4108.05	−	7115.35i	−0.224212	−	0.388346i
$696$	26447.2	+	45807.9i	1.44034	+	2.49475i
$697$	5530.75			0.300562
$698$	−4176.70	−	7234.25i	−0.226490	−	0.392293i
$699$	1309.47	−	2268.07i	0.0708565	−	0.122727i
$700$	1044.39	−	1808.94i	0.0563918	−	0.0976734i
$701$	22270.2			1.19991			0.599953	−	0.800035i	$-0.295186\pi$
$701$	22270.2			1.19991			0.599953	+	0.800035i	$0.295186\pi$
$702$	4166.59	−	11557.2i	0.224014	−	0.621364i
$703$	42388.3			2.27412
$704$	10487.6	−	18165.0i	0.561455	−	0.972469i
$705$	3296.33	−	5709.40i	0.176095	−	0.305005i
$706$	14310.6	+	24786.7i	0.762871	+	1.32133i
$707$	−2679.88			−0.142556
$708$	24703.9	+	42788.4i	1.31134	+	2.27131i
$709$	−1811.20	−	3137.09i	−0.0959393	−	0.166172i	0.814061	−	0.580779i	$-0.197252\pi$
$709$	−1811.20	−	3137.09i	−0.0959393	−	0.166172i	−0.910000	+	0.414608i	$0.863919\pi$
$710$	18630.8			0.984789
$711$	1279.43	+	2216.03i	0.0674855	+	0.116888i
$712$	−2926.13	+	5068.21i	−0.154019	+	0.266768i
$713$	13113.9	−	22714.0i	0.688809	−	1.19305i
$714$	−6648.55			−0.348481
$715$	3333.38	−	9246.02i	0.174351	−	0.483611i
$716$	60047.8			3.13420
$717$	9991.15	−	17305.2i	0.520400	−	0.901359i
$718$	27506.8	−	47643.1i	1.42973	−	2.47636i
$719$	−6465.05	−	11197.8i	−0.335335	−	0.580817i	0.648214	−	0.761458i	$-0.275516\pi$
$719$	−6465.05	−	11197.8i	−0.335335	−	0.580817i	−0.983549	+	0.180641i	$0.942183\pi$
$720$	−6263.21			−0.324189
$721$	366.635	+	635.031i	0.0189379	+	0.0328014i
$722$	−28028.0	−	48546.0i	−1.44473	−	2.50235i
$723$	−27258.9			−1.40217
$724$	−14462.1	−	25049.1i	−0.742375	−	1.28583i
$725$	2461.85	−	4264.05i	0.126111	−	0.218431i
$726$	−7125.95	+	12342.5i	−0.364282	+	0.630955i
$727$	−21574.3			−1.10061			−0.550307	−	0.834962i	$-0.685489\pi$
$727$	−21574.3			−1.10061			−0.550307	+	0.834962i	$0.685489\pi$
$728$	6219.93	+	7366.88i	0.316657	+	0.375048i
$729$	−7028.84			−0.357102
$730$	1760.69	−	3049.60i	0.0892684	−	0.154617i
$731$	−1406.04	+	2435.33i	−0.0711412	+	0.123220i
$732$	8425.59	+	14593.5i	0.425435	+	0.736875i
$733$	−17320.0			−0.872754			−0.436377	−	0.899764i	$-0.643739\pi$
$733$	−17320.0			−0.872754			−0.436377	+	0.899764i	$0.643739\pi$
$734$	−15813.2	−	27389.3i	−0.795201	−	1.37733i
$735$	−5364.74	−	9291.99i	−0.269226	−	0.466313i
$736$	711.836			0.0356503
$737$	−17786.3	−	30806.7i	−0.888963	−	1.53973i
$738$	−6765.66	+	11718.5i	−0.337463	+	0.584502i
$739$	−5485.97	+	9501.97i	−0.273078	+	0.472985i	−0.969648	−	0.244504i	$-0.921375\pi$
$739$	−5485.97	+	9501.97i	−0.273078	+	0.472985i	0.696571	+	0.717488i	$0.254708\pi$
$740$	−25172.3			−1.25047
$741$	42374.7	−	7605.14i	2.10077	−	0.377033i
$742$	19177.4			0.948821
$743$	−5775.29	+	10003.1i	−0.285161	+	0.493914i	−0.972648	−	0.232283i	$-0.925380\pi$
$743$	−5775.29	+	10003.1i	−0.285161	+	0.493914i	0.687487	+	0.726197i	$0.258714\pi$
$744$	23816.1	−	41250.7i	1.17358	−	2.03269i
$745$	6071.56	+	10516.2i	0.298583	+	0.517162i
$746$	−18880.6			−0.926634
$747$	5815.14	+	10072.1i	0.284826	+	0.493333i
$748$	−12919.2	−	22376.7i	−0.631513	−	1.09381i
$749$	1700.99			0.0829808
$750$	2082.30	+	3606.65i	0.101380	+	0.175595i
$751$	−10036.4	+	17383.5i	−0.487659	+	0.844650i	−0.999899	−	0.0141921i	$-0.995482\pi$
$751$	−10036.4	+	17383.5i	−0.487659	+	0.844650i	0.512240	+	0.858842i	$0.328816\pi$
$752$	−6354.73	+	11006.7i	−0.308156	+	0.533741i
$753$	18295.4			0.885419
$754$	29212.3	+	34599.0i	1.41094	+	1.67111i
$755$	−4387.52			−0.211494
$756$	−2232.21	+	3866.31i	−0.107387	+	0.186000i
$757$	5686.88	−	9849.97i	0.273043	−	0.472924i	−0.696597	−	0.717463i	$-0.745303\pi$
$757$	5686.88	−	9849.97i	0.273043	−	0.472924i	0.969639	+	0.244539i	$0.0786366\pi$
$758$	−21781.1	−	37726.0i	−1.04370	−	1.80774i
$759$	42124.1			2.01450
$760$	13367.8	+	23153.8i	0.638030	+	1.10510i
$761$	566.510	+	981.223i	0.0269855	+	0.0467402i	0.879203	−	0.476448i	$-0.158076\pi$
$761$	566.510	+	981.223i	0.0269855	+	0.0467402i	−0.852217	+	0.523188i	$0.824743\pi$
$762$	−88050.1			−4.18598
$763$	−1982.43	−	3433.66i	−0.0940611	−	0.162919i
$764$	1859.74	−	3221.17i	0.0880669	−	0.152536i
$765$	1834.89	−	3178.12i	0.0867196	−	0.150203i
$766$	21078.1			0.994231
$767$	13695.3	+	16220.6i	0.644729	+	0.763616i
$768$	−55843.8			−2.62381
$769$	10105.7	−	17503.6i	0.473889	−	0.820800i	−0.525664	−	0.850692i	$-0.676183\pi$
$769$	10105.7	−	17503.6i	0.473889	−	0.820800i	0.999553	+	0.0298925i	$0.00951650\pi$
$770$	−2675.34	+	4633.83i	−0.125211	+	0.216872i
$771$	−12266.2	−	21245.7i	−0.572966	−	0.992406i
$772$	35228.9			1.64238
$773$	3787.65	+	6560.41i	0.176239	+	0.305254i	0.940589	−	0.339547i	$-0.110274\pi$
$773$	3787.65	+	6560.41i	0.176239	+	0.305254i	−0.764351	+	0.644801i	$0.776940\pi$
$774$	−3439.96	−	5958.19i	−0.159751	−	0.276696i
$775$	−4433.87			−0.205509
$776$	9798.05	+	16970.7i	0.453260	+	0.785069i
$777$	5537.71	−	9591.60i	0.255681	−	0.442853i
$778$	−3780.29	+	6547.66i	−0.174203	+	0.301729i
$779$	19497.0			0.896731
$780$	−25164.1	+	4516.30i	−1.15515	+	0.207320i
$781$	−31857.2			−1.45959
$782$	−13913.4	+	24098.7i	−0.636243	+	1.10200i
$783$	−5261.80	+	9113.71i	−0.240155	+	0.415961i
$784$	10342.3	+	17913.3i	0.471130	+	0.816022i
$785$	9805.62			0.445831
$786$	7793.82	+	13499.3i	0.353685	+	0.612600i
$787$	−7232.41	−	12526.9i	−0.327583	−	0.567390i	0.654449	−	0.756106i	$-0.272901\pi$
$787$	−7232.41	−	12526.9i	−0.327583	−	0.567390i	−0.982032	+	0.188716i	$0.939567\pi$
$788$	47113.6			2.12989
$789$	−6574.37	−	11387.1i	−0.296646	−	0.513806i
$790$	−1640.06	+	2840.66i	−0.0738615	+	0.127932i
$791$	4693.77	−	8129.84i	0.210988	−	0.365441i
$792$	31727.8			1.42348
$793$	4670.95	+	5532.26i	0.209168	+	0.247738i
$794$	−23254.8			−1.03940
$795$	−12761.5	+	22103.5i	−0.569312	+	0.986077i
$796$	24584.9	−	42582.3i	1.09471	−	1.89609i
$797$	−57.2099	−	99.0904i	−0.00254263	−	0.00440397i	0.864751	−	0.502200i	$-0.167476\pi$
$797$	−57.2099	−	99.0904i	−0.00254263	−	0.00440397i	−0.867294	+	0.497796i	$0.834143\pi$
$798$	−23437.5			−1.03970
$799$	−3723.40	−	6449.11i	−0.164861	−	0.285548i
$800$	−60.1686	−	104.215i	−0.00265910	−	0.00460570i
$801$	2831.75			0.124913
$802$	−1521.26	−	2634.89i	−0.0669794	−	0.116012i
$803$	−3010.64	+	5214.58i	−0.132308	+	0.229164i
$804$	−46266.0	+	80135.0i	−2.02945	+	3.51510i
$805$	3846.52			0.168412
$806$	13829.6	−	38360.3i	0.604377	−	1.67640i
$807$	−1612.61			−0.0703428
$808$	−10185.0	+	17640.9i	−0.443449	+	0.768076i
$809$	−2254.04	+	3904.11i	−0.0979578	+	0.169668i	−0.910839	−	0.412761i	$-0.864564\pi$
$809$	−2254.04	+	3904.11i	−0.0979578	+	0.169668i	0.812881	+	0.582429i	$0.197898\pi$
$810$	−10785.6	−	18681.1i	−0.467859	−	0.810356i
$811$	34706.7			1.50273			0.751367	−	0.659885i	$-0.229395\pi$
$811$	34706.7			1.50273			0.751367	+	0.659885i	$0.229395\pi$
$812$	−8227.62	−	14250.7i	−0.355582	−	0.615887i
$813$	−8678.29	−	15031.2i	−0.374368	−	0.648424i
$814$	64482.1			2.77653
$815$	−3997.84	−	6924.46i	−0.171826	−	0.297611i
$816$	−8529.12	+	14772.9i	−0.365906	+	0.633767i
$817$	−4956.57	+	8585.04i	−0.212250	+	0.367628i
$818$	−61275.8			−2.61914
$819$	1582.24	−	4388.76i	0.0675065	−	0.187248i
$820$	−11578.3			−0.493086
$821$	−17327.1	+	30011.4i	−0.736564	+	1.27577i	0.217470	+	0.976067i	$0.430220\pi$
$821$	−17327.1	+	30011.4i	−0.736564	+	1.27577i	−0.954034	+	0.299699i	$0.903114\pi$
$822$	23466.9	−	40645.9i	0.995746	−	1.72468i
$823$	−23129.6	−	40061.6i	−0.979642	−	1.69679i	−0.663677	−	0.748019i	$-0.731005\pi$
$823$	−23129.6	−	40061.6i	−0.979642	−	1.69679i	−0.315965	−	0.948771i	$-0.602328\pi$
$824$	5573.64			0.235639
$825$	−3560.58	−	6167.10i	−0.150259	−	0.260256i
$826$	−5778.55	−	10008.7i	−0.243416	−	0.421609i
$827$	−2113.42			−0.0888641			−0.0444321	−	0.999012i	$-0.514148\pi$
$827$	−2113.42			−0.0888641			−0.0444321	+	0.999012i	$0.514148\pi$
$828$	−22722.1	−	39355.9i	−0.953682	−	1.65183i
$829$	3048.19	−	5279.63i	0.127706	−	0.221193i	−0.795082	−	0.606503i	$-0.792572\pi$
$829$	3048.19	−	5279.63i	0.127706	−	0.221193i	0.922787	+	0.385310i	$0.125905\pi$
$830$	−7454.26	+	12911.1i	−0.311736	+	0.539943i
$831$	35232.8			1.47077
$832$	−23074.4	+	4141.25i	−0.961492	+	0.172562i
$833$	−12119.6			−0.504104
$834$	27373.4	−	47412.2i	1.13653	−	1.96852i
$835$	−140.292	+	242.993i	−0.00581438	+	0.0100708i
$836$	−45542.7	−	78882.3i	−1.88413	−	3.26340i
$837$	9476.68			0.391352
$838$	21722.9	+	37625.1i	0.895470	+	1.55100i
$839$	10782.9	+	18676.5i	0.443703	+	0.768517i	0.997961	−	0.0638285i	$-0.0203311\pi$
$839$	10782.9	+	18676.5i	0.443703	+	0.768517i	−0.554258	+	0.832345i	$0.686998\pi$
$840$	6985.63			0.286937
$841$	−7199.75	−	12470.3i	−0.295205	−	0.511310i
$842$	−34160.4	+	59167.5i	−1.39815	+	2.42167i
$843$	−17483.4	+	30282.1i	−0.714306	+	1.23721i
$844$	27441.2			1.11915
$845$	−10299.4	+	3819.99i	−0.419302	+	0.155517i
$846$	18219.0			0.740406
$847$	1112.64	−	1927.16i	0.0451369	−	0.0781794i
$848$	24601.9	−	42611.7i	0.996263	−	1.72558i
$849$	7787.98	+	13489.2i	0.314821	+	0.545286i
$850$	4704.17			0.189826
$851$	−23177.5	−	40144.6i	−0.933625	−	1.61709i
$852$	41433.8	+	71765.4i	1.66608	+	2.88573i
$853$	−26903.9			−1.07992			−0.539961	−	0.841690i	$-0.681561\pi$
$853$	−26903.9			−1.07992			−0.539961	+	0.841690i	$0.681561\pi$
$854$	−1970.85	−	3413.62i	−0.0789709	−	0.136782i
$855$	6468.35	−	11203.5i	0.258729	−	0.448131i
$856$	6464.65	−	11197.1i	0.258128	−	0.447090i
$857$	−23634.8			−0.942063			−0.471031	−	0.882116i	$-0.656118\pi$
$857$	−23634.8			−0.942063			−0.471031	+	0.882116i	$0.656118\pi$
$858$	64461.3	−	11569.1i	2.56489	−	0.460329i
$859$	26252.0			1.04273			0.521365	−	0.853334i	$-0.325423\pi$
$859$	26252.0			1.04273			0.521365	+	0.853334i	$0.325423\pi$
$860$	2943.45	−	5098.21i	0.116710	−	0.202148i
$861$	2547.14	−	4411.77i	0.100820	−	0.174626i
$862$	23431.6	+	40584.6i	0.925849	+	1.60362i
$863$	−21344.0			−0.841898			−0.420949	−	0.907084i	$-0.638303\pi$
$863$	−21344.0			−0.841898			−0.420949	+	0.907084i	$0.638303\pi$
$864$	128.601	+	222.743i	0.00506375	+	0.00877068i
$865$	−9180.15	−	15900.5i	−0.360849	−	0.625009i
$866$	−12490.5			−0.490120
$867$	11687.4	+	20243.2i	0.457816	+	0.792960i
$868$	−7409.11	+	12832.9i	−0.289725	+	0.501819i
$869$	2804.37	−	4857.31i	0.109473	−	0.189612i
$870$	32808.4			1.27852
$871$	−13484.0	+	37401.7i	−0.524557	+	1.45500i
$872$	−30137.1			−1.17038
$873$	4741.02	−	8211.69i	0.183802	−	0.318354i
$874$	−49047.5	+	84952.8i	−1.89824	+	3.28784i
$875$	−325.130	−	563.142i	−0.0125616	−	0.0217574i
$876$	15662.7			0.604101
$877$	−14326.9	−	24815.0i	−0.551638	−	0.955464i	−0.998157	−	0.0606902i	$-0.980670\pi$
$877$	−14326.9	−	24815.0i	−0.551638	−	0.955464i	0.446519	−	0.894774i	$-0.352664\pi$
$878$	38785.7	+	67178.8i	1.49084	+	2.58220i
$879$	30340.0			1.16421
$880$	6864.16	+	11889.1i	0.262944	+	0.455432i
$881$	−9917.23	+	17177.1i	−0.379251	+	0.656881i	−0.990953	−	0.134206i	$-0.957152\pi$
$881$	−9917.23	+	17177.1i	−0.379251	+	0.656881i	0.611703	+	0.791088i	$0.290485\pi$
$882$	14825.7	−	25678.8i	0.565993	−	0.980329i
$883$	34322.7			1.30810			0.654049	−	0.756453i	$-0.273069\pi$
$883$	34322.7			1.30810			0.654049	+	0.756453i	$0.273069\pi$
$884$	−9794.23	+	27167.0i	−0.372642	+	1.03362i
$885$	15381.2			0.584218
$886$	25797.2	−	44682.0i	0.978187	−	1.69427i
$887$	−970.751	+	1681.39i	−0.0367470	+	0.0636477i	−0.883814	−	0.467838i	$-0.845033\pi$
$887$	−970.751	+	1681.39i	−0.0367470	+	0.0636477i	0.847067	+	0.531486i	$0.178366\pi$
$888$	−42092.5	−	72906.4i	−1.59069	−	2.75515i
$889$	13748.1			0.518670
$890$	1814.97	+	3143.62i	0.0683572	+	0.118398i
$891$	18442.5	+	31943.3i	0.693431	+	1.20106i
$892$	26003.3			0.976070
$893$	−13125.7	−	22734.4i	−0.491866	−	0.851936i
$894$	−40457.0	+	70073.6i	−1.51352	+	2.62149i
$895$	9346.77	−	16189.1i	0.349082	−	0.604627i
$896$	12962.8			0.483322
$897$	−30372.6	−	35973.3i	−1.13056	−	1.33903i
$898$	70106.5			2.60521
$899$	−17464.8	+	30250.0i	−0.647925	+	1.12224i
$900$	−3841.22	+	6653.19i	−0.142267	+	0.246414i
$901$	14414.9	+	24967.3i	0.532995	+	0.923174i
$902$	29659.3			1.09484
$903$	1295.08	+	2243.14i	0.0477270	+	0.0826656i
$904$	−35677.6	−	61795.4i	−1.31263	−	2.27355i
$905$	−9004.43			−0.330737
$906$	−14617.8	−	25318.8i	−0.536031	−	0.928434i
$907$	3037.11	−	5260.43i	0.111186	−	0.192579i	−0.805063	−	0.593190i	$-0.797868\pi$
$907$	3037.11	−	5260.43i	0.111186	−	0.192579i	0.916249	+	0.400610i	$0.131202\pi$
$908$	−41063.3	+	71123.7i	−1.50081	+	2.59948i
$909$	9856.49			0.359647
$910$	5886.21	−	1056.42i	0.214424	−	0.0384835i
$911$	1631.31			0.0593279			0.0296639	−	0.999560i	$-0.490556\pi$
$911$	1631.31			0.0593279			0.0296639	+	0.999560i	$0.490556\pi$
$912$	−30066.9	+	52077.4i	−1.09168	+	1.89085i
$913$	12746.2	−	22077.1i	0.462035	−	0.800268i
$914$	−28421.5	−	49227.5i	−1.02856	−	1.78151i
$915$	5245.96			0.189537
$916$	−1557.96	−	2698.46i	−0.0561969	−	0.0973359i
$917$	−1216.93	−	2107.78i	−0.0438238	−	0.0759051i
$918$	−10054.4			−0.361487
$919$	−9714.59	−	16826.2i	−0.348700	−	0.603965i	0.637319	−	0.770600i	$-0.280043\pi$
$919$	−9714.59	−	16826.2i	−0.348700	−	0.603965i	−0.986019	+	0.166635i	$0.946710\pi$
$920$	14618.8	−	25320.5i	0.523878	−	0.907383i
$921$	−15134.1	+	26212.9i	−0.541459	+	0.937835i
$922$	−13318.7			−0.475736
$923$	22969.9	+	27205.5i	0.819137	+	0.970185i
$924$	−23799.2			−0.847335
$925$	−3918.20	+	6786.53i	−0.139275	+	0.241232i
$926$	−9196.72	+	15929.2i	−0.326375	+	0.565297i
$927$	−1348.47	−	2335.62i	−0.0477772	−	0.0827526i
$928$	−948.007			−0.0335343
$929$	5816.90	+	10075.2i	0.205432	+	0.355819i	0.950270	−	0.311426i	$-0.100807\pi$
$929$	5816.90	+	10075.2i	0.205432	+	0.355819i	−0.744838	+	0.667245i	$0.767473\pi$
$930$	−14772.3	−	25586.3i	−0.520862	−	0.902159i
$931$	−42724.0			−1.50400
$932$	3096.45	+	5363.22i	0.108828	+	0.188496i
$933$	−18174.2	+	31478.6i	−0.637723	+	1.10457i
$934$	13342.9	−	23110.5i	0.467443	−	0.809636i
$935$	−8043.77			−0.281347
$936$	−22876.6	−	27095.0i	−0.798874	−	0.946185i
$937$	52690.1			1.83704			0.918522	−	0.395370i	$-0.129384\pi$
$937$	52690.1			1.83704			0.918522	+	0.395370i	$0.129384\pi$
$938$	10822.2	−	18744.6i	0.376714	−	0.652487i
$939$	−27953.7	+	48417.1i	−0.971494	+	1.68268i
$940$	7794.70	+	13500.8i	0.270463	+	0.468455i
$941$	1968.02			0.0681781			0.0340890	−	0.999419i	$-0.489147\pi$
$941$	1968.02			0.0681781			0.0340890	+	0.999419i	$0.489147\pi$
$942$	32669.2	+	56584.7i	1.12996	+	1.95714i
$943$	−10660.8	−	18465.0i	−0.368147	−	0.637649i
$944$	−29652.2			−1.02235
$945$	694.913	+	1203.63i	0.0239212	+	0.0414327i
$946$	−7540.05	+	13059.7i	−0.259142	+	0.448847i
$947$	5196.19	−	9000.07i	0.178304	−	0.308831i	−0.762996	−	0.646403i	$-0.776272\pi$
$947$	5196.19	−	9000.07i	0.178304	−	0.308831i	0.941300	+	0.337572i	$0.109606\pi$
$948$	−14589.6			−0.499839
$949$	6623.92	−	1188.82i	0.226577	−	0.0406646i
$950$	16583.2			0.566346
$951$	17570.9	−	30433.6i	0.599131	−	1.03773i
$952$	3945.34	−	6833.54i	0.134317	−	0.232643i
$953$	12589.2	+	21805.2i	0.427917	+	0.741174i	0.996688	−	0.0813218i	$-0.0259141\pi$
$953$	12589.2	+	21805.2i	0.427917	+	0.741174i	−0.568771	+	0.822496i	$0.692581\pi$
$954$	−70533.7			−2.39372
$955$	−578.959	−	1002.79i	−0.0196174	−	0.0339784i
$956$	23625.7	+	40920.9i	0.799278	+	1.38439i
$957$	−56099.9			−1.89493
$958$	46263.3	+	80130.4i	1.56023	+	2.70240i
$959$	−3664.12	+	6346.45i	−0.123379	+	0.213699i
$960$	−8492.70	+	14709.8i	−0.285522	+	0.494538i
$961$	1663.74			0.0558470
$962$	−46493.4	−	55066.6i	−1.55822	−	1.84555i
$963$	−6256.15			−0.209347
$964$	32229.1	−	55822.4i	1.07679	−	1.86506i
$965$	5483.57	−	9497.83i	0.182925	−	0.316835i
$966$	12815.4	+	22196.9i	0.426840	+	0.739309i
$967$	−31665.6			−1.05305			−0.526523	−	0.850161i	$-0.676505\pi$
$967$	−31665.6			−1.05305			−0.526523	+	0.850161i	$0.676505\pi$
$968$	−8457.28	−	14648.4i	−0.280813	−	0.486383i
$969$	−17617.0	−	30513.5i	−0.584044	−	1.01159i
$970$	12154.7			0.402335
$971$	−16407.5	−	28418.7i	−0.542269	−	0.939237i	−0.998773	−	0.0495160i	$-0.984232\pi$
$971$	−16407.5	−	28418.7i	−0.542269	−	0.939237i	0.456505	−	0.889721i	$-0.349101\pi$
$972$	36387.3	−	63024.6i	1.20074	−	2.07975i
$973$	−4274.08	+	7402.93i	−0.140823	+	0.243913i
$974$	33306.2			1.09569
$975$	−2699.33	+	7487.33i	−0.0886644	+	0.245935i
$976$	−10113.3			−0.331678
$977$	71.8349	−	124.422i	0.00235231	−	0.00407431i	−0.864847	−	0.502036i	$-0.832585\pi$
$977$	71.8349	−	124.422i	0.00235231	−	0.00407431i	0.867199	+	0.497961i	$0.165918\pi$
$978$	26639.1	−	46140.2i	0.870985	−	1.50859i
$979$	−3103.46	−	5375.35i	−0.101315	−	0.175482i
$980$	25371.6			0.827006
$981$	7291.27	+	12628.9i	0.237301	+	0.411018i
$982$	−5679.05	−	9836.40i	−0.184547	−	0.319646i
$983$	39094.1			1.26847			0.634235	−	0.773140i	$-0.281315\pi$
$983$	39094.1			1.26847			0.634235	+	0.773140i	$0.281315\pi$
$984$	−19360.9	−	33534.1i	−0.627240	−	1.08641i
$985$	7333.50	−	12702.0i	0.237223	−	0.410882i
$986$	18529.5	−	32094.1i	0.598479	−	1.03660i
$987$	−6859.11			−0.221203
$988$	−34526.7	+	95769.1i	−1.11178	+	3.08383i
$989$	10840.8			0.348552
$990$	9839.79	−	17043.0i	0.315888	−	0.547134i
$991$	15672.6	−	27145.7i	0.502378	−	0.870144i	−0.497618	−	0.867396i	$-0.665792\pi$
$991$	15672.6	−	27145.7i	0.502378	−	0.870144i	0.999996	−	0.00274791i	$-0.000874688\pi$
$992$	426.848	+	739.322i	0.0136617	+	0.0236628i
$993$	18400.4			0.588035
$994$	−9691.89	−	16786.8i	−0.309264	−	0.535660i
$995$	−7653.56	−	13256.4i	−0.243853	−	0.422366i
$996$	−66311.3			−2.10959
$997$	−24852.0	−	43044.9i	−0.789439	−	1.36735i	−0.926311	−	0.376760i	$-0.877038\pi$
$997$	−24852.0	−	43044.9i	−0.789439	−	1.36735i	0.136872	−	0.990589i	$-0.456295\pi$
$998$	47681.8	−	82587.3i	1.51237	−	2.61949i
$999$	8374.52	−	14505.1i	0.265223	−	0.459380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.e.a.61.1	yes	14
13.3	even	3	inner	65.4.e.a.16.1	✓	14
13.4	even	6		845.4.a.h.1.1		7
13.9	even	3		845.4.a.k.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.1	✓	14	13.3	even	3	inner
65.4.e.a.61.1	yes	14	1.1	even	1	trivial
845.4.a.h.1.1		7	13.4	even	6
845.4.a.k.1.7		7	13.9	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45261 + 4.24804i) q^{2} +(-3.39607 + 5.88216i) q^{3} +(-8.03055 - 13.9093i) q^{4} -5.00000 q^{5} +(-16.6584 - 28.8532i) q^{6} +(2.60104 + 4.50514i) q^{7} +39.5414 q^{8} +(-9.56652 - 16.5697i) q^{9} +(12.2630 - 21.2402i) q^{10} +(-20.9688 + 36.3191i) q^{11} +109.089 q^{12} +(46.1350 - 8.28002i) q^{13} -25.5173 q^{14} +(16.9803 - 29.4108i) q^{15} +(-32.7350 + 56.6988i) q^{16} +(-19.1803 - 33.2212i) q^{17} +93.8516 q^{18} +(-67.6145 - 117.112i) q^{19} +(40.1527 + 69.5466i) q^{20} -35.3332 q^{21} +(-102.857 - 178.153i) q^{22} +(-73.9418 + 128.071i) q^{23} +(-134.285 + 232.589i) q^{24} +25.0000 q^{25} +(-77.9772 + 216.291i) q^{26} -53.4334 q^{27} +(41.7756 - 72.3575i) q^{28} +(98.4740 - 170.562i) q^{29} +(83.2921 + 144.266i) q^{30} -177.355 q^{31} +(-2.40675 - 4.16861i) q^{32} +(-142.423 - 246.684i) q^{33} +188.167 q^{34} +(-13.0052 - 22.5257i) q^{35} +(-153.649 + 266.128i) q^{36} +(-156.728 + 271.461i) q^{37} +663.326 q^{38} +(-107.973 + 299.493i) q^{39} -197.707 q^{40} +(-72.0889 + 124.862i) q^{41} +(86.6585 - 150.097i) q^{42} +(-36.6532 - 63.4852i) q^{43} +673.565 q^{44} +(47.8326 + 82.8485i) q^{45} +(-362.700 - 628.215i) q^{46} +194.126 q^{47} +(-222.341 - 385.105i) q^{48} +(157.969 - 273.611i) q^{49} +(-61.3151 + 106.201i) q^{50} +260.550 q^{51} +(-485.659 - 575.214i) q^{52} -751.545 q^{53} +(131.051 - 226.987i) q^{54} +(104.844 - 181.595i) q^{55} +(102.849 + 178.139i) q^{56} +918.492 q^{57} +(483.036 + 836.642i) q^{58} +(226.456 + 392.233i) q^{59} -545.445 q^{60} +(77.2358 + 133.776i) q^{61} +(434.981 - 753.410i) q^{62} +(49.7659 - 86.1970i) q^{63} -500.149 q^{64} +(-230.675 + 41.4001i) q^{65} +1397.23 q^{66} +(-424.112 + 734.583i) q^{67} +(-308.057 + 533.570i) q^{68} +(-502.222 - 869.875i) q^{69} +127.587 q^{70} +(379.816 + 657.860i) q^{71} +(-378.273 - 655.189i) q^{72} +143.577 q^{73} +(-768.784 - 1331.57i) q^{74} +(-84.9016 + 147.054i) q^{75} +(-1085.96 + 1880.94i) q^{76} -218.163 q^{77} +(-1007.44 - 1193.21i) q^{78} -133.740 q^{79} +(163.675 - 283.494i) q^{80} +(439.759 - 761.686i) q^{81} +(-353.611 - 612.473i) q^{82} -607.864 q^{83} +(283.745 + 491.461i) q^{84} +(95.9015 + 166.106i) q^{85} +359.584 q^{86} +(668.848 + 1158.48i) q^{87} +(-829.137 + 1436.11i) q^{88} +(-74.0017 + 128.175i) q^{89} -469.258 q^{90} +(157.302 + 186.308i) q^{91} +2375.17 q^{92} +(602.309 - 1043.23i) q^{93} +(-476.115 + 824.655i) q^{94} +(338.072 + 585.558i) q^{95} +32.6939 q^{96} +(247.792 + 429.189i) q^{97} +(774.872 + 1342.12i) q^{98} +802.395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18}+ \cdots + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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