LMFDB - Embedded newform 65.4.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,4,Mod(16,65)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$3.83512415037$
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			16.1
Root			$2.45261 + 4.24804i$ of defining polynomial
Character	$\chi$	$=$	65.16
Dual form			65.4.e.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45261 - 4.24804i) q^{2} +(-3.39607 - 5.88216i) q^{3} +(-8.03055 + 13.9093i) q^{4} -5.00000 q^{5} +(-16.6584 + 28.8532i) q^{6} +(2.60104 - 4.50514i) q^{7} +39.5414 q^{8} +(-9.56652 + 16.5697i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 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	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.864920	−	0.501911i	$-0.832631\pi$
$2$	−2.45261	−	4.24804i	−0.867127	−	1.50191i	−0.00220750	−	0.999998i	$-0.500703\pi$
$3$	−3.39607	−	5.88216i	−0.653573	−	1.13202i	−0.982249	−	0.187579i	$-0.939936\pi$
$3$	−3.39607	−	5.88216i	−0.653573	−	1.13202i	0.328676	−	0.944443i	$-0.393397\pi$
$4$	−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	−0.787220	−	0.616672i	$-0.788481\pi$
$7$	2.60104	−	4.50514i	0.140443	−	0.243255i	0.927664	+	0.373417i	$0.121814\pi$
$8$	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	−0.996068	−	0.0885938i	$-0.971763\pi$
$11$	−20.9688	−	36.3191i	−0.574758	−	0.995511i	0.421309	−	0.906917i	$-0.361571\pi$
$12$	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	−0.969791	−	0.243935i	$-0.921562\pi$
$17$	−19.1803	+	33.2212i	−0.273641	+	0.473961i	0.696150	+	0.717896i	$0.254895\pi$
$18$	93.8516			1.22895
$19$	−67.6145	+	117.112i	−0.816412	+	1.41407i	0.0918983	+	0.995768i	$0.470707\pi$
$19$	−67.6145	+	117.112i	−0.816412	+	1.41407i	−0.908310	+	0.418298i	$0.862627\pi$
$20$	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	−0.977806	−	0.209511i	$-0.932813\pi$
$23$	−73.9418	−	128.071i	−0.670345	−	1.16107i	0.307462	−	0.951560i	$-0.400520\pi$
$24$	−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	0.987438	+	0.158007i	$0.0505069\pi$
$29$	98.4740	+	170.562i	0.630557	+	1.09216i	−0.356881	+	0.934150i	$0.616160\pi$
$30$	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	−0.969714	−	0.244242i	$-0.921461\pi$
$37$	−156.728	−	271.461i	−0.696377	−	1.20616i	0.273338	−	0.961918i	$-0.411872\pi$
$38$	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	0.695438	−	0.718586i	$-0.255210\pi$
$41$	−72.0889	−	124.862i	−0.274595	−	0.475613i	−0.970033	+	0.242974i	$0.921877\pi$
$42$	86.6585	+	150.097i	0.318374	+	0.551440i
$43$	−36.6532	+	63.4852i	−0.129990	+	0.225149i	−0.923672	−	0.383183i	$-0.874828\pi$
$43$	−36.6532	+	63.4852i	−0.129990	+	0.225149i	0.793683	+	0.608332i	$0.208161\pi$
$44$	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	−0.500304	−	0.865850i	$-0.666778\pi$
$59$	226.456	−	392.233i	0.499696	−	0.865499i	1.00000		0.000351133i	$0.000111769\pi$
$60$	−545.445			−1.17361
$61$	77.2358	−	133.776i	0.162115	−	0.280792i	−0.773512	−	0.633782i	$-0.781502\pi$
$61$	77.2358	−	133.776i	0.162115	−	0.280792i	0.935627	+	0.352990i	$0.114835\pi$
$62$	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	−0.935725	−	0.352730i	$-0.885253\pi$
$67$	−424.112	−	734.583i	−0.773336	−	1.33946i	0.162389	−	0.986727i	$-0.448080\pi$
$68$	−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	−0.351671	−	0.936124i	$-0.614387\pi$
$71$	379.816	−	657.860i	0.634871	−	1.09963i	0.986542	−	0.163505i	$-0.0522801\pi$
$72$	−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	0.818587	−	0.574383i	$-0.194758\pi$
$89$	−74.0017	−	128.175i	−0.0881367	−	0.152657i	−0.906724	+	0.421726i	$0.861425\pi$
$90$	−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	−0.706699	−	0.707515i	$-0.749816\pi$
$97$	247.792	−	429.189i	0.259376	−	0.449253i	0.966075	+	0.258262i	$0.0831497\pi$
$98$	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	0.710797	−	0.703398i	$-0.248335\pi$
$101$	−257.578	−	446.138i	−0.253762	−	0.439528i	−0.964558	+	0.263869i	$0.915001\pi$
$102$	−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	0.930382	−	0.366592i	$-0.119476\pi$
$107$	163.491	+	283.174i	0.147713	+	0.255846i	−0.782669	+	0.622438i	$0.786142\pi$
$108$	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	0.196117	+	0.980581i	$0.437167\pi$
$113$	−902.285	+	1562.80i	−0.751149	+	1.30103i	−0.947266	+	0.320448i	$0.896166\pi$
$114$	−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	0.794315	+	0.607506i	$0.207830\pi$
$127$	1321.40	+	2288.74i	0.923273	+	1.59916i	0.128959	+	0.991650i	$0.458837\pi$
$128$	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	−0.558382	−	0.829584i	$-0.688578\pi$
$137$	704.357	−	1219.98i	0.439250	−	0.760803i	0.997632	+	0.0687808i	$0.0219109\pi$
$138$	4927.01			3.03924
$139$	821.610	−	1423.07i	0.501353	−	0.868368i	−0.498646	−	0.866806i	$-0.666169\pi$
$139$	821.610	−	1423.07i	0.501353	−	0.868368i	0.999999	−	0.00156264i	$-0.000497404\pi$
$140$	−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	0.310906	+	0.950441i	$0.399368\pi$
$149$	−1214.31	+	2103.25i	−0.667653	+	1.15641i	−0.978559	+	0.205968i	$0.933966\pi$
$150$	−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	−0.607445	−	0.794362i	$-0.707806\pi$
$163$	799.568	−	1384.89i	0.384215	−	0.665479i	0.991660	+	0.128882i	$0.0411389\pi$
$164$	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	0.872453	−	0.488698i	$-0.162528\pi$
$167$	28.0584	+	48.5986i	0.0130013	+	0.0225190i	−0.859452	+	0.511217i	$0.829195\pi$
$168$	−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	−0.108130	−	0.994137i	$-0.534486\pi$
$173$	1836.03	−	3180.10i	0.806883	−	1.39756i	0.915013	−	0.403425i	$-0.132180\pi$
$174$	−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	−0.931610	−	0.363460i	$-0.881595\pi$
$179$	−1869.35	−	3237.82i	−0.780570	−	1.35199i	0.151040	−	0.988528i	$-0.451738\pi$
$180$	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	−0.843259	−	0.537508i	$-0.819366\pi$
$191$	115.792	−	200.557i	0.0438659	−	0.0759780i	0.887125	+	0.461530i	$0.152699\pi$
$192$	1698.54	+	2941.96i	0.638446	+	1.10582i
$193$	−1096.71	−	1899.57i	−0.409032	−	0.708465i	0.585749	−	0.810492i	$-0.300800\pi$
$193$	−1096.71	−	1899.57i	−0.409032	−	0.708465i	−0.994782	+	0.102028i	$0.967467\pi$
$194$	−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	−0.999369	−	0.0355211i	$-0.988691\pi$
$197$	−1466.70	−	2540.40i	−0.530447	−	0.918761i	0.468922	−	0.883239i	$-0.344642\pi$
$198$	−1967.96	−	3408.60i	−0.706347	−	1.22343i
$199$	1530.71	−	2651.27i	0.545273	−	0.944440i	−0.453317	−	0.891349i	$-0.649759\pi$
$199$	1530.71	−	2651.27i	0.545273	−	0.944440i	0.998590	−	0.0530906i	$-0.0169072\pi$
$200$	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	0.692344	−	0.721567i	$-0.256578\pi$
$211$	−854.274	−	1479.65i	−0.278724	−	0.482763i	−0.971068	+	0.238804i	$0.923245\pi$
$212$	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	0.718503	−	0.695523i	$-0.244827\pi$
$223$	−809.512	−	1402.12i	−0.243089	−	0.421043i	−0.961593	+	0.274481i	$0.911494\pi$
$224$	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	0.201445	+	0.979500i	$0.435436\pi$
$227$	−2556.69	+	4428.32i	−0.747549	+	1.29479i	−0.948994	+	0.315293i	$0.897897\pi$
$228$	−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	−0.462748	−	0.886490i	$-0.653137\pi$
$241$	2006.66	−	3475.63i	0.536349	−	0.928983i	0.999097	−	0.0424933i	$-0.0135301\pi$
$242$	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	−0.984185	−	0.177141i	$-0.943315\pi$
$251$	−1346.81	+	2332.74i	−0.338684	+	0.586618i	0.645501	+	0.763759i	$0.276648\pi$
$252$	−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	0.559228	−	0.829014i	$-0.311098\pi$
$257$	−1805.94	−	3127.99i	−0.438333	−	0.759216i	−0.997561	+	0.0697984i	$0.977764\pi$
$258$	−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	0.729958	−	0.683492i	$-0.239539\pi$
$263$	−967.940	−	1676.52i	−0.226942	−	0.393075i	−0.956900	+	0.290417i	$0.906206\pi$
$264$	−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	−0.852258	−	0.523121i	$-0.824768\pi$
$269$	118.712	−	205.615i	0.0269070	−	0.0466043i	0.879165	+	0.476517i	$0.158101\pi$
$270$	−655.256	−	1134.94i	−0.147695	−	0.255815i
$271$	−1277.70	−	2213.04i	−0.286401	−	0.496061i	0.686547	−	0.727085i	$-0.259126\pi$
$271$	−1277.70	−	2213.04i	−0.286401	−	0.496061i	−0.972948	+	0.231024i	$0.925792\pi$
$272$	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	0.434680	+	0.900585i	$0.356862\pi$
$277$	−2593.65	+	4492.33i	−0.562590	+	0.974434i	−0.997269	+	0.0738488i	$0.976472\pi$
$278$	−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	0.960955	−	0.276703i	$-0.0892418\pi$
$283$	1146.62	+	1986.00i	0.240846	+	0.417157i	−0.720110	+	0.693860i	$0.755909\pi$
$284$	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	−0.998075	−	0.0620213i	$-0.980245\pi$
$293$	−2233.46	+	3868.47i	−0.445325	+	0.771326i	0.552749	+	0.833347i	$0.313579\pi$
$294$	−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	−0.956299	−	0.292392i	$-0.905549\pi$
$331$	−1354.54	+	2346.13i	−0.224931	+	0.389592i	0.731368	+	0.681983i	$0.238882\pi$
$332$	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	−0.279464	−	0.960156i	$-0.590157\pi$
$347$	4471.64	−	7745.11i	0.691787	−	1.19821i	0.971252	−	0.238055i	$-0.0765098\pi$
$348$	10742.4	+	18606.4i	1.65476	+	2.86612i
$349$	−851.482	−	1474.81i	−0.130598	−	0.226203i	0.793309	−	0.608819i	$-0.208356\pi$
$349$	−851.482	−	1474.81i	−0.130598	−	0.226203i	−0.923907	+	0.382616i	$0.875023\pi$
$350$	−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	0.997680	−	0.0680764i	$-0.0216862\pi$
$353$	2917.43	+	5053.14i	0.439884	+	0.761902i	−0.557796	+	0.829978i	$0.688353\pi$
$354$	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	0.540357	−	0.841436i	$-0.318289\pi$
$367$	−3223.76	−	5583.72i	−0.458526	−	0.794190i	−0.998883	+	0.0472454i	$0.984956\pi$
$368$	−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	−0.700970	−	0.713191i	$-0.747249\pi$
$373$	1924.55	−	3333.42i	0.267156	−	0.462728i	0.968126	+	0.250462i	$0.0805826\pi$
$374$	−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	−0.992546	−	0.121869i	$-0.961111\pi$
$379$	−4440.40	−	7691.00i	−0.601815	−	1.04237i	0.390731	−	0.920505i	$-0.372222\pi$
$380$	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	−0.973007	−	0.230776i	$-0.925873\pi$
$383$	−2148.54	+	3721.38i	−0.286645	+	0.496484i	0.686362	+	0.727260i	$0.259207\pi$
$384$	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	−0.676392	−	0.736542i	$-0.736458\pi$
$397$	2370.42	−	4105.69i	0.299668	−	0.519040i	0.976060	+	0.217502i	$0.0697909\pi$
$398$	−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	0.846069	−	0.533074i	$-0.178963\pi$
$401$	−310.131	−	537.162i	−0.0386214	−	0.0668943i	−0.884690	+	0.466180i	$0.845630\pi$
$402$	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	−0.190193	−	0.981747i	$-0.560911\pi$
$409$	6245.99	−	10818.4i	0.755121	−	1.30791i	0.945314	−	0.326161i	$-0.105755\pi$
$410$	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	0.999820	+	0.0189750i	$0.00604030\pi$
$419$	4428.53	+	7670.43i	0.516343	+	0.894332i	−0.483477	+	0.875357i	$0.660626\pi$
$420$	−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	0.999218	+	0.0395500i	$0.0125924\pi$
$431$	4776.87	+	8273.78i	0.533860	+	0.924673i	−0.465357	+	0.885123i	$0.654074\pi$
$432$	1749.15	+	3029.61i	0.194805	+	0.337412i
$433$	1273.19	−	2205.22i	0.141306	−	0.244749i	−0.786683	−	0.617357i	$-0.788203\pi$
$433$	1273.19	−	2205.22i	0.141306	−	0.244749i	0.927989	+	0.372609i	$0.121537\pi$
$434$	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	0.872272	+	0.489021i	$0.162646\pi$
$439$	7907.04	+	13695.4i	0.859641	+	1.48894i	−0.0126310	+	0.999920i	$0.504021\pi$
$440$	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	0.196182	+	0.980567i	$0.437146\pi$
$449$	−7146.12	+	12377.4i	−0.751105	+	1.30095i	−0.947287	+	0.320385i	$0.896188\pi$
$450$	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	−0.993814	−	0.111053i	$-0.964578\pi$
$457$	−5794.14	−	10035.7i	−0.593082	−	1.02725i	0.400732	−	0.916195i	$-0.368756\pi$
$458$	−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	−0.789261	−	0.614057i	$-0.789536\pi$
$461$	1357.61	−	2351.45i	0.137159	−	0.237566i	0.926420	+	0.376492i	$0.122870\pi$
$462$	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	0.827936	+	0.560823i	$0.189515\pi$
$479$	9431.46	+	16335.8i	0.899655	+	1.55825i	0.0717187	+	0.997425i	$0.477152\pi$
$480$	−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	−0.979628	−	0.200823i	$-0.935638\pi$
$487$	−3394.98	+	5880.28i	−0.315896	+	0.547148i	0.663731	+	0.747971i	$0.268972\pi$
$488$	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	0.807902	−	0.589318i	$-0.200603\pi$
$491$	−1157.76	−	2005.30i	−0.106413	−	0.184313i	−0.914315	+	0.405004i	$0.867270\pi$
$492$	−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	−0.843222	−	0.537565i	$-0.819344\pi$
$503$	495.628	−	858.453i	0.0439343	−	0.0760965i	0.887156	+	0.461469i	$0.152677\pi$
$504$	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	0.865548	−	0.500827i	$-0.166971\pi$
$509$	−10.9670	−	18.9953i	−0.000955014	−	0.00165413i	−0.866503	+	0.499173i	$0.833637\pi$
$510$	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	0.947232	−	0.320549i	$-0.103867\pi$
$523$	2344.42	+	4060.66i	0.196012	+	0.339503i	−0.751220	+	0.660052i	$0.770534\pi$
$524$	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	0.994588	+	0.103901i	$0.0331325\pi$
$557$	7720.12	+	13371.6i	0.587275	+	1.01719i	−0.407313	+	0.913289i	$0.633534\pi$
$558$	−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	−0.924972	−	0.380036i	$-0.875912\pi$
$563$	−1781.58	+	3085.79i	−0.133365	+	0.230995i	0.791607	+	0.611031i	$0.209245\pi$
$564$	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	−0.991336	−	0.131347i	$-0.958070\pi$
$569$	−8271.49	−	14326.6i	−0.609418	−	1.05554i	0.381918	−	0.924196i	$-0.375264\pi$
$570$	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	0.968471	−	0.249125i	$-0.0801431\pi$
$587$	3818.39	+	6613.64i	0.268487	+	0.465033i	−0.699984	+	0.714158i	$0.746810\pi$
$588$	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	0.545955	−	0.837814i	$-0.316167\pi$
$601$	−6668.34	−	11549.9i	−0.452591	−	0.783911i	−0.998546	+	0.0539039i	$0.982834\pi$
$602$	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	−0.0202594	−	0.999795i	$-0.506449\pi$
$607$	12797.2	−	22165.3i	0.855718	−	1.48215i	0.875977	−	0.482352i	$-0.160217\pi$
$608$	−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	0.956189	+	0.292749i	$0.0945701\pi$
$613$	11104.0	+	19232.6i	0.731623	+	1.26721i	−0.224566	+	0.974459i	$0.572097\pi$
$614$	−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	−0.862491	−	0.506072i	$-0.831097\pi$
$617$	107.676	−	186.500i	0.00702571	−	0.0121689i	0.869517	+	0.493903i	$0.164430\pi$
$618$	−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	0.0987017	+	0.995117i	$0.468531\pi$
$631$	−12877.7	+	22304.8i	−0.812446	+	1.40720i	−0.911148	+	0.412080i	$0.864802\pi$
$632$	−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	0.411410	+	0.911450i	$0.365036\pi$
$641$	−9471.69	+	16405.4i	−0.583634	+	1.01088i	−0.995044	+	0.0994332i	$0.968297\pi$
$642$	−10894.0			−0.669706
$643$	−758.843	+	1314.35i	−0.0465410	+	0.0806113i	−0.888357	−	0.459153i	$-0.848153\pi$
$643$	−758.843	+	1314.35i	−0.0465410	+	0.0806113i	0.841816	+	0.539764i	$0.181486\pi$
$644$	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	0.974143	−	0.225932i	$-0.0725426\pi$
$647$	4795.78	+	8306.54i	0.291409	+	0.504735i	−0.682734	+	0.730667i	$0.739209\pi$
$648$	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	0.510842	−	0.859675i	$-0.329334\pi$
$653$	−8161.11	−	14135.5i	−0.489079	−	0.847110i	−0.999921	+	0.0125644i	$0.996001\pi$
$654$	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	−0.518045	−	0.855353i	$-0.673340\pi$
$659$	8149.60	−	14115.5i	0.481735	−	0.834389i	0.999780	+	0.0209640i	$0.00667354\pi$
$660$	11437.4	+	19810.1i	0.674543	+	1.16834i
$661$	−3890.65	−	6738.80i	−0.228939	−	0.396534i	0.728555	−	0.684987i	$-0.240192\pi$
$661$	−3890.65	−	6738.80i	−0.228939	−	0.396534i	−0.957494	+	0.288453i	$0.906859\pi$
$662$	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	−0.872997	−	0.487726i	$-0.837826\pi$
$673$	−14995.3	−	25972.7i	−0.858882	−	1.48763i	0.0141152	−	0.999900i	$-0.495507\pi$
$674$	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	−0.181299	−	0.983428i	$-0.558030\pi$
$683$	13584.1	−	23528.3i	0.761024	−	1.31813i	0.942323	−	0.334705i	$-0.108637\pi$
$684$	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	−0.979372	−	0.202065i	$-0.935235\pi$
$691$	−12073.4	−	20911.7i	−0.664680	−	1.15126i	0.314692	−	0.949194i	$-0.398099\pi$
$692$	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	−0.910000	−	0.414608i	$-0.863919\pi$
$709$	−1811.20	+	3137.09i	−0.0959393	+	0.166172i	0.814061	+	0.580779i	$0.197252\pi$
$710$	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	−0.983549	−	0.180641i	$-0.942183\pi$
$719$	−6465.05	+	11197.8i	−0.335335	+	0.580817i	0.648214	+	0.761458i	$0.275516\pi$
$720$	−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	0.696571	−	0.717488i	$-0.254708\pi$
$739$	−5485.97	−	9501.97i	−0.273078	−	0.472985i	−0.969648	+	0.244504i	$0.921375\pi$
$740$	−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	0.687487	−	0.726197i	$-0.258714\pi$
$743$	−5775.29	−	10003.1i	−0.285161	−	0.493914i	−0.972648	+	0.232283i	$0.925380\pi$
$744$	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	0.512240	−	0.858842i	$-0.328816\pi$
$751$	−10036.4	−	17383.5i	−0.487659	−	0.844650i	−0.999899	+	0.0141921i	$0.995482\pi$
$752$	−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	0.969639	−	0.244539i	$-0.0786366\pi$
$757$	5686.88	+	9849.97i	0.273043	+	0.472924i	−0.696597	+	0.717463i	$0.745303\pi$
$758$	−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	−0.852217	−	0.523188i	$-0.824743\pi$
$761$	566.510	−	981.223i	0.0269855	−	0.0467402i	0.879203	+	0.476448i	$0.158076\pi$
$762$	−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	0.999553	−	0.0298925i	$-0.00951650\pi$
$769$	10105.7	+	17503.6i	0.473889	+	0.820800i	−0.525664	+	0.850692i	$0.676183\pi$
$770$	−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	−0.764351	−	0.644801i	$-0.776940\pi$
$773$	3787.65	−	6560.41i	0.176239	−	0.305254i	0.940589	+	0.339547i	$0.110274\pi$
$774$	−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	−0.982032	−	0.188716i	$-0.939567\pi$
$787$	−7232.41	+	12526.9i	−0.327583	+	0.567390i	0.654449	+	0.756106i	$0.272901\pi$
$788$	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	−0.867294	−	0.497796i	$-0.834143\pi$
$797$	−57.2099	+	99.0904i	−0.00254263	+	0.00440397i	0.864751	+	0.502200i	$0.167476\pi$
$798$	−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	0.812881	−	0.582429i	$-0.197898\pi$
$809$	−2254.04	−	3904.11i	−0.0979578	−	0.169668i	−0.910839	+	0.412761i	$0.864564\pi$
$810$	−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	−0.954034	−	0.299699i	$-0.903114\pi$
$821$	−17327.1	−	30011.4i	−0.736564	−	1.27577i	0.217470	−	0.976067i	$-0.430220\pi$
$822$	23466.9	+	40645.9i	0.995746	+	1.72468i
$823$	−23129.6	+	40061.6i	−0.979642	+	1.69679i	−0.315965	+	0.948771i	$0.602328\pi$
$823$	−23129.6	+	40061.6i	−0.979642	+	1.69679i	−0.663677	+	0.748019i	$0.731005\pi$
$824$	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	0.922787	−	0.385310i	$-0.125905\pi$
$829$	3048.19	+	5279.63i	0.127706	+	0.221193i	−0.795082	+	0.606503i	$0.792572\pi$
$830$	−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	−0.554258	−	0.832345i	$-0.686998\pi$
$839$	10782.9	−	18676.5i	0.443703	−	0.768517i	0.997961	+	0.0638285i	$0.0203311\pi$
$840$	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	0.446519	+	0.894774i	$0.352664\pi$
$877$	−14326.9	+	24815.0i	−0.551638	+	0.955464i	−0.998157	+	0.0606902i	$0.980670\pi$
$878$	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	0.611703	−	0.791088i	$-0.290485\pi$
$881$	−9917.23	−	17177.1i	−0.379251	−	0.656881i	−0.990953	+	0.134206i	$0.957152\pi$
$882$	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	0.847067	−	0.531486i	$-0.178366\pi$
$887$	−970.751	−	1681.39i	−0.0367470	−	0.0636477i	−0.883814	+	0.467838i	$0.845033\pi$
$888$	−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	0.916249	−	0.400610i	$-0.131202\pi$
$907$	3037.11	+	5260.43i	0.111186	+	0.192579i	−0.805063	+	0.593190i	$0.797868\pi$
$908$	−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	−0.986019	−	0.166635i	$-0.946710\pi$
$919$	−9714.59	+	16826.2i	−0.348700	+	0.603965i	0.637319	+	0.770600i	$0.280043\pi$
$920$	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	−0.744838	−	0.667245i	$-0.767473\pi$
$929$	5816.90	−	10075.2i	0.205432	−	0.355819i	0.950270	+	0.311426i	$0.100807\pi$
$930$	−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	0.941300	−	0.337572i	$-0.109606\pi$
$947$	5196.19	+	9000.07i	0.178304	+	0.308831i	−0.762996	+	0.646403i	$0.776272\pi$
$948$	−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	−0.568771	−	0.822496i	$-0.692581\pi$
$953$	12589.2	−	21805.2i	0.427917	−	0.741174i	0.996688	+	0.0813218i	$0.0259141\pi$
$954$	−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	0.456505	+	0.889721i	$0.349101\pi$
$971$	−16407.5	+	28418.7i	−0.542269	+	0.939237i	−0.998773	+	0.0495160i	$0.984232\pi$
$972$	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	0.867199	−	0.497961i	$-0.165918\pi$
$977$	71.8349	+	124.422i	0.00235231	+	0.00407431i	−0.864847	+	0.502036i	$0.832585\pi$
$978$	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	0.999996	+	0.00274791i	$0.000874688\pi$
$991$	15672.6	+	27145.7i	0.502378	+	0.870144i	−0.497618	+	0.867396i	$0.665792\pi$
$992$	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	0.136872	+	0.990589i	$0.456295\pi$
$997$	−24852.0	+	43044.9i	−0.789439	+	1.36735i	−0.926311	+	0.376760i	$0.877038\pi$
$998$	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.16.1	✓	14
13.3	even	3		845.4.a.k.1.7		7
13.9	even	3	inner	65.4.e.a.61.1	yes	14
13.10	even	6		845.4.a.h.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.1	✓	14	1.1	even	1	trivial
65.4.e.a.61.1	yes	14	13.9	even	3	inner
845.4.a.h.1.1		7	13.10	even	6
845.4.a.k.1.7		7	13.3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.45261 - 4.24804i) q^{2} +(-3.39607 - 5.88216i) q^{3} +(-8.03055 + 13.9093i) q^{4} -5.00000 q^{5} +(-16.6584 + 28.8532i) q^{6} +(2.60104 - 4.50514i) q^{7} +39.5414 q^{8} +(-9.56652 + 16.5697i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) \) 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	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 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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