LMFDB - Embedded newform 25.4.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	25.9
Dual form			25.4.e.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42187 + 3.33341i) q^{2} +(-3.56321 + 1.15776i) q^{3} +(-2.77407 - 8.53772i) q^{4} +(-8.01402 - 7.79587i) q^{5} +(4.77034 - 14.6816i) q^{6} +26.4674i q^{7} +(3.82887 + 1.24408i) q^{8} +(-10.4874 + 7.61952i) q^{9} +O(q^{10})$	\(q+(-2.42187 + 3.33341i) q^{2} +(-3.56321 + 1.15776i) q^{3} +(-2.77407 - 8.53772i) q^{4} +(-8.01402 - 7.79587i) q^{5} +(4.77034 - 14.6816i) q^{6} +26.4674i q^{7} +(3.82887 + 1.24408i) q^{8} +(-10.4874 + 7.61952i) q^{9} +(45.3957 - 7.83348i) q^{10} +(15.6737 + 11.3876i) q^{11} +(19.7692 + 27.2100i) q^{12} +(26.2024 + 36.0645i) q^{13} +(-88.2266 - 64.1004i) q^{14} +(37.5814 + 18.5000i) q^{15} +(44.6809 - 32.4626i) q^{16} +(-70.5478 - 22.9224i) q^{17} -53.4122i q^{18} +(-6.14742 + 18.9198i) q^{19} +(-44.3274 + 90.0477i) q^{20} +(-30.6428 - 94.3088i) q^{21} +(-75.9192 + 24.6676i) q^{22} +(36.2441 - 49.8857i) q^{23} -15.0834 q^{24} +(3.44892 + 124.952i) q^{25} -183.676 q^{26} +(88.0062 - 121.130i) q^{27} +(225.971 - 73.4224i) q^{28} +(88.7735 + 273.217i) q^{29} +(-152.685 + 80.4696i) q^{30} +(25.1347 - 77.3567i) q^{31} +259.767i q^{32} +(-69.0328 - 22.4301i) q^{33} +(247.267 - 179.650i) q^{34} +(206.336 - 212.110i) q^{35} +(94.1461 + 68.4011i) q^{36} +(-230.938 - 317.858i) q^{37} +(-48.1793 - 66.3131i) q^{38} +(-135.119 - 98.1694i) q^{39} +(-20.9860 - 39.8194i) q^{40} +(-176.752 + 128.418i) q^{41} +(388.583 + 126.258i) q^{42} +430.797i q^{43} +(53.7442 - 165.408i) q^{44} +(143.447 + 20.6952i) q^{45} +(78.5113 + 241.633i) q^{46} +(-174.686 + 56.7589i) q^{47} +(-121.624 + 167.401i) q^{48} -357.521 q^{49} +(-424.871 - 291.121i) q^{50} +277.915 q^{51} +(235.221 - 323.754i) q^{52} +(-59.1999 + 19.2352i) q^{53} +(190.638 + 586.722i) q^{54} +(-36.8330 - 213.451i) q^{55} +(-32.9274 + 101.340i) q^{56} -74.5325i q^{57} +(-1125.74 - 365.776i) q^{58} +(299.411 - 217.535i) q^{59} +(53.6947 - 372.180i) q^{60} +(180.255 + 130.963i) q^{61} +(196.989 + 271.132i) q^{62} +(-201.669 - 277.573i) q^{63} +(-508.464 - 369.421i) q^{64} +(71.1676 - 493.291i) q^{65} +(241.957 - 175.792i) q^{66} +(423.363 + 137.559i) q^{67} +665.905i q^{68} +(-71.3898 + 219.715i) q^{69} +(207.332 + 1201.50i) q^{70} +(126.710 + 389.973i) q^{71} +(-49.6341 + 16.1271i) q^{72} +(196.202 - 270.049i) q^{73} +1618.85 q^{74} +(-156.954 - 441.239i) q^{75} +178.585 q^{76} +(-301.400 + 414.841i) q^{77} +(654.478 - 212.653i) q^{78} +(77.3261 + 237.985i) q^{79} +(-611.147 - 88.1707i) q^{80} +(-65.1884 + 200.629i) q^{81} -900.197i q^{82} +(1008.98 + 327.838i) q^{83} +(-720.177 + 523.239i) q^{84} +(386.671 + 733.681i) q^{85} +(-1436.03 - 1043.33i) q^{86} +(-632.638 - 870.752i) q^{87} +(45.8455 + 63.1010i) q^{88} +(-425.441 - 309.101i) q^{89} +(-416.395 + 428.046i) q^{90} +(-954.531 + 693.507i) q^{91} +(-526.453 - 171.055i) q^{92} +304.738i q^{93} +(233.865 - 719.763i) q^{94} +(196.762 - 103.699i) q^{95} +(-300.748 - 925.606i) q^{96} +(469.781 - 152.641i) q^{97} +(865.868 - 1191.77i) q^{98} -251.144 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−2.42187	+	3.33341i	−0.856259	+	1.17854i	0.126189	+	0.992006i	$0.459725\pi$
$2$	−2.42187	+	3.33341i	−0.856259	+	1.17854i	−0.982449	+	0.186534i	$0.940275\pi$
$3$	−3.56321	+	1.15776i	−0.685741	+	0.222811i	−0.631107	−	0.775696i	$-0.717399\pi$
$3$	−3.56321	+	1.15776i	−0.685741	+	0.222811i	−0.0546337	+	0.998506i	$0.517399\pi$
$4$	−2.77407	−	8.53772i	−0.346759	−	1.06721i
$5$	−8.01402	−	7.79587i	−0.716795	−	0.697284i
$5$	−8.01402	−	7.79587i	−0.716795	−	0.697284i
$6$	4.77034	−	14.6816i	0.324581	−	0.998956i
$7$			26.4674i			1.42910i	0.699583	+	0.714551i	$0.253369\pi$
$7$			26.4674i			1.42910i	−0.699583	+	0.714551i	$0.746631\pi$
$8$	3.82887	+	1.24408i	0.169214	+	0.0549809i
$9$	−10.4874	+	7.61952i	−0.388421	+	0.282205i
$10$	45.3957	−	7.83348i	1.43554	−	0.247716i
$11$	15.6737	+	11.3876i	0.429618	+	0.312136i	0.781496	−	0.623910i	$-0.214457\pi$
$11$	15.6737	+	11.3876i	0.429618	+	0.312136i	−0.351878	+	0.936046i	$0.614457\pi$
$12$	19.7692	+	27.2100i	0.475574	+	0.654571i
$13$	26.2024	+	36.0645i	0.559018	+	0.769422i	0.991201	−	0.132364i	$-0.0422568\pi$
$13$	26.2024	+	36.0645i	0.559018	+	0.769422i	−0.432184	+	0.901786i	$0.642257\pi$
$14$	−88.2266	−	64.1004i	−1.68425	−	1.22368i
$15$	37.5814	+	18.5000i	0.646898	+	0.318446i
$16$	44.6809	−	32.4626i	0.698139	−	0.507228i
$17$	−70.5478	−	22.9224i	−1.00649	−	0.327029i	−0.241035	−	0.970516i	$-0.577487\pi$
$17$	−70.5478	−	22.9224i	−1.00649	−	0.327029i	−0.765457	+	0.643488i	$0.777487\pi$
$18$		−	53.4122i		−	0.699410i
$19$	−6.14742	+	18.9198i	−0.0742271	+	0.228447i	−0.981286	−	0.192556i	$-0.938322\pi$
$19$	−6.14742	+	18.9198i	−0.0742271	+	0.228447i	0.907059	+	0.421004i	$0.138322\pi$
$20$	−44.3274	+	90.0477i	−0.495596	+	1.00676i
$21$	−30.6428	−	94.3088i	−0.318419	−	0.979994i
$22$	−75.9192	+	24.6676i	−0.735729	+	0.239053i
$23$	36.2441	−	49.8857i	0.328583	−	0.452256i	−0.612480	−	0.790486i	$-0.709828\pi$
$23$	36.2441	−	49.8857i	0.328583	−	0.452256i	0.941063	+	0.338230i	$0.109828\pi$
$24$	−15.0834			−0.128287
$25$	3.44892	+	124.952i	0.0275913	+	0.999619i
$26$	−183.676			−1.38546
$27$	88.0062	−	121.130i	0.627289	−	0.863389i
$28$	225.971	−	73.4224i	1.52516	−	0.495554i
$29$	88.7735	+	273.217i	0.568442	+	1.74949i	0.657495	+	0.753459i	$0.271616\pi$
$29$	88.7735	+	273.217i	0.568442	+	1.74949i	−0.0890523	+	0.996027i	$0.528384\pi$
$30$	−152.685	+	80.4696i	−0.929214	+	0.489723i
$31$	25.1347	−	77.3567i	0.145624	−	0.448183i	−0.851467	−	0.524408i	$-0.824287\pi$
$31$	25.1347	−	77.3567i	0.145624	−	0.448183i	0.997091	+	0.0762249i	$0.0242867\pi$
$32$			259.767i			1.43502i
$33$	−69.0328	−	22.4301i	−0.364154	−	0.118321i
$34$	247.267	−	179.650i	1.24723	−	0.906169i
$35$	206.336	−	212.110i	0.996490	−	1.02437i
$36$	94.1461	+	68.4011i	0.435861	+	0.316672i
$37$	−230.938	−	317.858i	−1.02611	−	1.41231i	−0.907833	−	0.419332i	$-0.862264\pi$
$37$	−230.938	−	317.858i	−1.02611	−	1.41231i	−0.118273	−	0.992981i	$-0.537736\pi$
$38$	−48.1793	−	66.3131i	−0.205677	−	0.283090i
$39$	−135.119	−	98.1694i	−0.554776	−	0.403069i
$40$	−20.9860	−	39.8194i	−0.0829544	−	0.157400i
$41$	−176.752	+	128.418i	−0.673268	+	0.489158i	−0.871118	−	0.491075i	$-0.836604\pi$
$41$	−176.752	+	128.418i	−0.673268	+	0.489158i	0.197850	+	0.980232i	$0.436604\pi$
$42$	388.583	+	126.258i	1.42761	+	0.463859i
$43$			430.797i			1.52781i	0.645327	+	0.763906i	$0.276721\pi$
$43$			430.797i			1.52781i	−0.645327	+	0.763906i	$0.723279\pi$
$44$	53.7442	−	165.408i	0.184142	−	0.566730i
$45$	143.447	+	20.6952i	0.475195	+	0.0685568i
$46$	78.5113	+	241.633i	0.251649	+	0.774496i
$47$	−174.686	+	56.7589i	−0.542139	+	0.176152i	−0.567269	−	0.823532i	$-0.692000\pi$
$47$	−174.686	+	56.7589i	−0.542139	+	0.176152i	0.0251299	+	0.999684i	$0.492000\pi$
$48$	−121.624	+	167.401i	−0.365727	+	0.503379i
$49$	−357.521			−1.04234
$50$	−424.871	−	291.121i	−1.20172	−	0.823416i
$51$	277.915			0.763058
$52$	235.221	−	323.754i	0.627294	−	0.863396i
$53$	−59.1999	+	19.2352i	−0.153429	+	0.0498520i	−0.384724	−	0.923031i	$-0.625704\pi$
$53$	−59.1999	+	19.2352i	−0.153429	+	0.0498520i	0.231296	+	0.972884i	$0.425704\pi$
$54$	190.638	+	586.722i	0.480417	+	1.47857i
$55$	−36.8330	−	213.451i	−0.0903011	−	0.523303i
$56$	−32.9274	+	101.340i	−0.0785734	+	0.241824i
$57$		−	74.5325i		−	0.173194i
$58$	−1125.74	−	365.776i	−2.54857	−	0.828082i
$59$	299.411	−	217.535i	0.660678	−	0.480010i	−0.206214	−	0.978507i	$-0.566114\pi$
$59$	299.411	−	217.535i	0.660678	−	0.480010i	0.866892	+	0.498497i	$0.166114\pi$
$60$	53.6947	−	372.180i	0.115533	−	0.800803i
$61$	180.255	+	130.963i	0.378348	+	0.274886i	0.760664	−	0.649146i	$-0.224873\pi$
$61$	180.255	+	130.963i	0.378348	+	0.274886i	−0.382316	+	0.924032i	$0.624873\pi$
$62$	196.989	+	271.132i	0.403510	+	0.555384i
$63$	−201.669	−	277.573i	−0.403299	−	0.555094i
$64$	−508.464	−	369.421i	−0.993095	−	0.721526i
$65$	71.1676	−	493.291i	0.135804	−	0.941312i
$66$	241.957	−	175.792i	0.451256	−	0.327856i
$67$	423.363	+	137.559i	0.771970	+	0.250828i	0.668408	−	0.743795i	$-0.266976\pi$
$67$	423.363	+	137.559i	0.771970	+	0.250828i	0.103562	+	0.994623i	$0.466976\pi$
$68$			665.905i			1.18754i
$69$	−71.3898	+	219.715i	−0.124555	+	0.383342i
$70$	207.332	+	1201.50i	0.354012	+	2.05153i
$71$	126.710	+	389.973i	0.211798	+	0.651848i	0.999365	+	0.0356193i	$0.0113404\pi$
$71$	126.710	+	389.973i	0.211798	+	0.651848i	−0.787567	+	0.616229i	$0.788660\pi$
$72$	−49.6341	+	16.1271i	−0.0812421	+	0.0263972i
$73$	196.202	−	270.049i	0.314571	−	0.432970i	−0.622229	−	0.782835i	$-0.713773\pi$
$73$	196.202	−	270.049i	0.314571	−	0.432970i	0.936800	+	0.349865i	$0.113773\pi$
$74$	1618.85			2.54308
$75$	−156.954	−	441.239i	−0.241646	−	0.679332i
$76$	178.585			0.269541
$77$	−301.400	+	414.841i	−0.446074	+	0.613968i
$78$	654.478	−	212.653i	0.950065	−	0.308695i
$79$	77.3261	+	237.985i	0.110125	+	0.338930i	0.990899	−	0.134607i	$-0.0429772\pi$
$79$	77.3261	+	237.985i	0.110125	+	0.338930i	−0.880774	+	0.473537i	$0.842977\pi$
$80$	−611.147	−	88.1707i	−0.854104	−	0.123222i
$81$	−65.1884	+	200.629i	−0.0894216	+	0.275212i
$82$		−	900.197i		−	1.21232i
$83$	1008.98	+	327.838i	1.33434	+	0.433553i	0.887396	−	0.461009i	$-0.152512\pi$
$83$	1008.98	+	327.838i	1.33434	+	0.433553i	0.446944	+	0.894562i	$0.352512\pi$
$84$	−720.177	+	523.239i	−0.935449	+	0.679644i
$85$	386.671	+	733.681i	0.493417	+	0.936223i
$86$	−1436.03	−	1043.33i	−1.80059	−	1.30820i
$87$	−632.638	−	870.752i	−0.779608	−	1.07304i
$88$	45.8455	+	63.1010i	0.0555358	+	0.0764385i
$89$	−425.441	−	309.101i	−0.506704	−	0.368142i	0.304868	−	0.952395i	$-0.401388\pi$
$89$	−425.441	−	309.101i	−0.506704	−	0.368142i	−0.811572	+	0.584252i	$0.801388\pi$
$90$	−416.395	+	428.046i	−0.487687	+	0.501334i
$91$	−954.531	+	693.507i	−1.09958	+	0.798894i
$92$	−526.453	−	171.055i	−0.596593	−	0.193845i
$93$			304.738i			0.339784i
$94$	233.865	−	719.763i	0.256610	−	0.789764i
$95$	196.762	−	103.699i	0.212498	−	0.111993i
$96$	−300.748	−	925.606i	−0.319739	−	0.984055i
$97$	469.781	−	152.641i	0.491743	−	0.159777i	−0.0526405	−	0.998614i	$-0.516764\pi$
$97$	469.781	−	152.641i	0.491743	−	0.159777i	0.544383	+	0.838837i	$0.316764\pi$
$98$	865.868	−	1191.77i	0.892509	−	1.22843i
$99$	−251.144			−0.254959
$100$	1057.24	−	376.073i	1.05724	−	0.376073i
$101$	−212.047			−0.208906			−0.104453	−	0.994530i	$-0.533309\pi$
$101$	−212.047			−0.208906			−0.104453	+	0.994530i	$0.533309\pi$
$102$	−673.074	+	926.407i	−0.653375	+	0.899294i
$103$	550.741	−	178.947i	0.526856	−	0.171186i	−0.0334986	−	0.999439i	$-0.510665\pi$
$103$	550.741	−	178.947i	0.526856	−	0.171186i	0.560354	+	0.828253i	$0.310665\pi$
$104$	55.4586	+	170.684i	0.0522900	+	0.160932i
$105$	−489.647	+	994.680i	−0.455092	+	0.924484i
$106$	79.2553	−	243.923i	0.0726222	−	0.223508i
$107$			1045.08i			0.944225i	0.881538	+	0.472112i	$0.156508\pi$
$107$			1045.08i			0.944225i	−0.881538	+	0.472112i	$0.843492\pi$
$108$	−1278.31	−	415.348i	−1.13894	−	0.370064i
$109$	−1457.66	+	1059.05i	−1.28091	+	0.930633i	−0.999580	−	0.0289797i	$-0.990774\pi$
$109$	−1457.66	+	1059.05i	−1.28091	+	0.930633i	−0.281326	+	0.959612i	$0.590774\pi$
$110$	800.724	+	394.169i	0.694055	+	0.341660i
$111$	1190.88	+	865.227i	1.01832	+	0.739853i
$112$	859.198	+	1182.58i	0.724880	+	0.997712i
$113$	−27.4350	−	37.7611i	−0.0228396	−	0.0314360i	0.797445	−	0.603392i	$-0.206185\pi$
$113$	−27.4350	−	37.7611i	−0.0228396	−	0.0314360i	−0.820284	+	0.571956i	$0.806185\pi$
$114$	248.448	+	180.508i	0.204116	+	0.148299i
$115$	−679.363	+	117.231i	−0.550877	+	0.0950593i
$116$	2086.38	−	1515.85i	1.66996	−	1.21330i
$117$	−549.588	−	178.572i	−0.434269	−	0.141102i
$118$			1524.90i			1.18965i
$119$	606.694	−	1867.21i	0.467358	−	1.43838i
$120$	120.879	+	117.588i	0.0919557	+	0.0894525i
$121$	−295.314	−	908.884i	−0.221874	−	0.682858i
$122$	−873.105	+	283.689i	−0.647928	+	0.210525i
$123$	481.128	−	662.215i	0.352698	−	0.485447i
$124$	−730.175			−0.528804
$125$	946.473	−	1028.26i	0.677241	−	0.735762i
$126$	1413.68			0.999529
$127$	699.634	−	962.963i	0.488838	−	0.672828i	−0.491335	−	0.870971i	$-0.663491\pi$
$127$	699.634	−	962.963i	0.488838	−	0.672828i	0.980173	+	0.198143i	$0.0634909\pi$
$128$	486.440	−	158.054i	0.335904	−	0.109142i
$129$	−498.759	−	1535.02i	−0.340413	−	1.04768i
$130$	1471.99	+	1431.92i	0.993090	+	0.966057i
$131$	−63.5100	+	195.464i	−0.0423580	+	0.130365i	−0.969999	−	0.243108i	$-0.921833\pi$
$131$	−63.5100	+	195.464i	−0.0423580	+	0.130365i	0.927641	+	0.373473i	$0.121833\pi$
$132$			651.606i			0.429659i
$133$	−500.757	−	162.706i	−0.326475	−	0.106078i
$134$	−1483.87	+	1078.09i	−0.956618	+	0.695023i
$135$	−1649.60	+	284.654i	−1.05167	+	0.181475i
$136$	−241.601	−	175.534i	−0.152332	−	0.110676i
$137$	1310.51	+	1803.76i	0.817256	+	1.12486i	0.990163	+	0.139919i	$0.0446841\pi$
$137$	1310.51	+	1803.76i	0.817256	+	1.12486i	−0.172907	+	0.984938i	$0.555316\pi$
$138$	−559.505	−	770.093i	−0.345132	−	0.475034i
$139$	557.340	+	404.931i	0.340093	+	0.247092i	0.744701	−	0.667398i	$-0.232592\pi$
$139$	557.340	+	404.931i	0.340093	+	0.247092i	−0.404608	+	0.914490i	$0.632592\pi$
$140$	−2383.32	−	1173.23i	−1.43877	−	0.708257i
$141$	556.730	−	404.488i	0.332519	−	0.241589i
$142$	−1606.81	−	522.086i	−0.949583	−	0.308538i
$143$			863.646i			0.505047i
$144$	−221.236	+	680.894i	−0.128030	+	0.394036i
$145$	1418.53	−	2881.63i	0.812431	−	1.65039i
$146$	425.010	+	1308.04i	0.240918	+	0.741470i
$147$	1273.92	−	413.923i	0.714772	−	0.232243i
$148$	−2073.15	+	2853.44i	−1.15143	+	1.58481i
$149$	332.872			0.183020			0.0915098	−	0.995804i	$-0.470831\pi$
$149$	332.872			0.183020			0.0915098	+	0.995804i	$0.470831\pi$
$150$	1850.95	+	545.430i	1.00753	+	0.296895i
$151$	−3165.59			−1.70604			−0.853020	−	0.521878i	$-0.825231\pi$
$151$	−3165.59			−1.70604			−0.853020	+	0.521878i	$0.825231\pi$
$152$	−47.0754	+	64.7937i	−0.0251205	+	0.0345754i
$153$	914.518	−	297.145i	0.483232	−	0.157011i
$154$	−652.887	−	2009.38i	−0.341631	−	1.05143i
$155$	−804.493	+	423.991i	−0.416893	+	0.219715i
$156$	−463.314	+	1425.93i	−0.237787	+	0.731833i
$157$		−	790.622i		−	0.401901i	−0.979601	−	0.200951i	$-0.935597\pi$
$157$		−	790.622i		−	0.401901i	0.979601	−	0.200951i	$-0.0644031\pi$
$158$	−980.577	−	318.609i	−0.493737	−	0.160425i
$159$	188.672	−	137.078i	0.0941048	−	0.0683711i
$160$	2025.11	−	2081.78i	1.00062	−	1.02862i
$161$	1320.34	+	959.285i	0.646320	+	0.469579i
$162$	−510.903	−	703.197i	−0.247780	−	0.341039i
$163$	−89.2654	−	122.863i	−0.0428945	−	0.0590393i	0.787031	−	0.616913i	$-0.211617\pi$
$163$	−89.2654	−	122.863i	−0.0428945	−	0.0590393i	−0.829926	+	0.557874i	$0.811617\pi$
$164$	1586.72	+	1152.82i	0.755498	+	0.548902i
$165$	378.368	+	717.926i	0.178521	+	0.338730i
$166$	−3536.44	+	2569.38i	−1.65350	+	1.20134i
$167$	−1707.52	−	554.806i	−0.791207	−	0.257079i	−0.114589	−	0.993413i	$-0.536555\pi$
$167$	−1707.52	−	554.806i	−0.791207	−	0.257079i	−0.676618	+	0.736334i	$0.736555\pi$
$168$		−	399.218i		−	0.183336i
$169$	64.8290	−	199.523i	0.0295080	−	0.0908162i
$170$	−3382.13	−	487.943i	−1.52587	−	0.220138i
$171$	−79.6896	−	245.259i	−0.0356375	−	0.109681i
$172$	3678.02	−	1195.06i	1.63050	−	0.529783i
$173$	901.648	−	1241.01i	0.396249	−	0.545389i	−0.563549	−	0.826083i	$-0.690564\pi$
$173$	901.648	−	1241.01i	0.396249	−	0.545389i	0.959798	+	0.280693i	$0.0905644\pi$
$174$	4434.74			1.93217
$175$	−3307.16	+	91.2837i	−1.42856	+	0.0394308i
$176$	1069.99			0.458257
$177$	−815.012	+	1121.77i	−0.346102	+	0.476369i
$178$	2060.72	−	669.570i	0.867741	−	0.281946i
$179$	939.001	+	2889.95i	0.392091	+	1.20673i	0.931204	+	0.364498i	$0.118759\pi$
$179$	939.001	+	2889.95i	0.392091	+	1.20673i	−0.539113	+	0.842233i	$0.681241\pi$
$180$	−221.242	−	1282.12i	−0.0916134	−	0.530908i
$181$	1076.93	−	3314.44i	0.442250	−	1.36111i	−0.443221	−	0.896413i	$-0.646164\pi$
$181$	1076.93	−	3314.44i	0.442250	−	1.36111i	0.885471	−	0.464694i	$-0.153836\pi$
$182$		−	4861.43i		−	1.97996i
$183$	−793.908	−	257.956i	−0.320696	−	0.104200i
$184$	200.835	−	145.916i	0.0804662	−	0.0584621i
$185$	−627.244	+	4347.68i	−0.249275	+	1.72783i
$186$	−1015.82	−	738.036i	−0.400449	−	0.290943i
$187$	−844.714	−	1162.65i	−0.330329	−	0.454659i
$188$	969.182	+	1333.96i	0.375983	+	0.517497i
$189$	3206.00	+	2329.29i	1.23387	+	0.896461i
$190$	−130.859	+	907.034i	−0.0499657	+	0.346333i
$191$	385.738	−	280.255i	0.146131	−	0.106170i	−0.512318	−	0.858796i	$-0.671213\pi$
$191$	385.738	−	280.255i	0.146131	−	0.106170i	0.658449	+	0.752626i	$0.271213\pi$
$192$	2239.47	+	727.647i	0.841769	+	0.273507i
$193$		−	1098.86i		−	0.409831i	−0.978780	−	0.204916i	$-0.934308\pi$
$193$		−	1098.86i		−	0.409831i	0.978780	−	0.204916i	$-0.0656920\pi$
$194$	−628.931	+	1935.65i	−0.232756	+	0.716349i
$195$	317.527	+	1840.10i	0.116608	+	0.675754i
$196$	991.789	+	3052.41i	0.361439	+	1.11240i
$197$	−87.3420	+	28.3791i	−0.0315881	+	0.0102636i	−0.324768	−	0.945794i	$-0.605286\pi$
$197$	−87.3420	+	28.3791i	−0.0315881	+	0.0102636i	0.293180	+	0.956057i	$0.405286\pi$
$198$	608.237	−	837.167i	0.218311	−	0.300479i
$199$	1614.65			0.575174			0.287587	−	0.957754i	$-0.407147\pi$
$199$	1614.65			0.575174			0.287587	+	0.957754i	$0.407147\pi$
$200$	−142.245	+	482.718i	−0.0502911	+	0.170666i
$201$	−1667.79			−0.585259
$202$	513.549	−	706.840i	0.178877	−	0.246203i
$203$	−7231.33	+	2349.60i	−2.50020	+	0.812363i
$204$	−770.957	−	2372.76i	−0.264597	−	0.814346i
$205$	2417.62	+	348.792i	0.823677	+	0.118833i
$206$	−737.319	+	2269.23i	−0.249376	+	0.767500i
$207$			799.332i			0.268393i
$208$	2341.49	+	760.796i	0.780544	+	0.253614i
$209$	−311.804	+	226.539i	−0.103196	+	0.0749762i
$210$	−2129.82	−	4041.18i	−0.699864	−	1.32794i
$211$	2980.05	+	2165.14i	0.972300	+	0.706418i	0.955975	−	0.293449i	$-0.0948031\pi$
$211$	2980.05	+	2165.14i	0.972300	+	0.706418i	0.0163258	+	0.999867i	$0.494803\pi$
$212$	328.449	+	452.072i	0.106406	+	0.146455i
$213$	−902.988	−	1242.86i	−0.290477	−	0.399808i
$214$	−3483.70	−	2531.05i	−1.11281	−	0.808501i
$215$	3358.44	−	3452.42i	1.06532	−	1.09513i
$216$	487.660	−	354.306i	0.153616	−	0.111609i
$217$	2047.43	+	665.250i	0.640500	+	0.208111i
$218$		−	7423.88i		−	2.30646i
$219$	−386.458	+	1189.40i	−0.119244	+	0.366995i
$220$	−1720.20	+	906.597i	−0.527164	+	0.277831i
$221$	−1021.84	−	3144.89i	−0.311023	−	0.957231i
$222$	−5768.32	+	1874.24i	−1.74389	+	0.566625i
$223$	−2910.64	+	4006.15i	−0.874039	+	1.20301i	0.103997	+	0.994578i	$0.466837\pi$
$223$	−2910.64	+	4006.15i	−0.874039	+	1.20301i	−0.978036	+	0.208434i	$0.933163\pi$
$224$	−6875.35			−2.05080
$225$	−988.248	−	1284.14i	−0.292814	−	0.380487i
$226$	192.317			0.0566051
$227$	216.700	−	298.261i	0.0633606	−	0.0872084i	−0.776161	−	0.630535i	$-0.782835\pi$
$227$	216.700	−	298.261i	0.0633606	−	0.0872084i	0.839521	+	0.543327i	$0.182835\pi$
$228$	−636.338	+	206.759i	−0.184836	+	0.0600567i
$229$	−319.117	−	982.142i	−0.0920868	−	0.283414i	0.894397	−	0.447274i	$-0.147605\pi$
$229$	−319.117	−	982.142i	−0.0920868	−	0.283414i	−0.986484	+	0.163861i	$0.947605\pi$
$230$	1254.55	−	2548.51i	0.359663	−	0.730626i
$231$	593.666	−	1827.12i	0.169092	−	0.520413i
$232$			1156.55i			0.327291i
$233$	1338.84	+	435.017i	0.376440	+	0.122313i	0.491125	−	0.871089i	$-0.336586\pi$
$233$	1338.84	+	435.017i	0.376440	+	0.122313i	−0.114685	+	0.993402i	$0.536586\pi$
$234$	1926.28	−	1399.53i	0.538141	−	0.390982i
$235$	1842.42	+	906.961i	0.511431	+	0.251760i
$236$	−2687.84	−	1952.83i	−0.741370	−	0.538637i
$237$	−551.059	−	758.467i	−0.151034	−	0.207881i
$238$	4754.86	+	6544.51i	1.29501	+	1.78243i
$239$	−3547.06	−	2577.09i	−0.960002	−	0.697482i	−0.00685049	−	0.999977i	$-0.502181\pi$
$239$	−3547.06	−	2577.09i	−0.960002	−	0.697482i	−0.953151	+	0.302495i	$0.902181\pi$
$240$	2279.73	−	393.390i	0.613149	−	0.105805i
$241$	224.103	−	162.820i	0.0598993	−	0.0435194i	−0.557433	−	0.830222i	$-0.688214\pi$
$241$	224.103	−	162.820i	0.0598993	−	0.0435194i	0.617332	+	0.786703i	$0.288214\pi$
$242$	3744.90	+	1216.79i	0.994757	+	0.323216i
$243$			3252.22i			0.858560i
$244$	618.082	−	1902.26i	0.162167	−	0.499098i
$245$	2865.18	+	2787.19i	0.747141	+	0.726803i
$246$	1042.21	+	3207.60i	0.270118	+	0.831337i
$247$	−843.410	+	274.040i	−0.217267	+	0.0705942i
$248$	192.475	−	264.919i	0.0492830	−	0.0678323i
$249$	−3974.78			−1.01161
$250$	1135.38	+	5645.29i	0.287231	+	1.42816i
$251$	6881.24			1.73044			0.865219	−	0.501393i	$-0.167179\pi$
$251$	6881.24			1.73044			0.865219	+	0.501393i	$0.167179\pi$
$252$	−1810.40	+	2491.80i	−0.452557	+	0.622891i
$253$	1136.16	−	369.160i	0.282330	−	0.0917347i
$254$	1515.54	+	4664.34i	0.374382	+	1.15223i
$255$	−2227.22	−	2166.59i	−0.546956	−	0.532068i
$256$	902.495	−	2777.59i	0.220336	−	0.678124i
$257$			7406.10i			1.79759i	0.438372	+	0.898794i	$0.355555\pi$
$257$			7406.10i			1.79759i	−0.438372	+	0.898794i	$0.644445\pi$
$258$	6324.79	+	2055.05i	1.52622	+	0.495898i
$259$	8412.87	−	6112.31i	2.01834	−	1.46641i
$260$	−4409.01	+	760.817i	−1.05167	+	0.181476i
$261$	−3012.78	−	2188.92i	−0.714508	−	0.519120i
$262$	−497.749	−	685.093i	−0.117370	−	0.161546i
$263$	−2819.25	−	3880.36i	−0.660997	−	0.909784i	0.338517	−	0.940960i	$-0.390075\pi$
$263$	−2819.25	−	3880.36i	−0.660997	−	0.909784i	−0.999514	+	0.0311762i	$0.990075\pi$
$264$	−236.413	−	171.764i	−0.0551145	−	0.0400430i
$265$	624.384	+	307.363i	0.144738	+	0.0712497i
$266$	1755.13	−	1275.18i	0.404564	−	0.293933i
$267$	1873.80	+	608.836i	0.429494	+	0.139551i
$268$		−	3996.15i		−	0.910835i
$269$	−520.192	+	1600.99i	−0.117906	+	0.362877i	−0.992542	−	0.121903i	$-0.961100\pi$
$269$	−520.192	+	1600.99i	−0.117906	+	0.362877i	0.874636	+	0.484780i	$0.161100\pi$
$270$	3046.24	−	6188.19i	0.686622	−	1.39482i
$271$	−1243.61	−	3827.43i	−0.278759	−	0.857933i	−0.988200	−	0.153168i	$-0.951052\pi$
$271$	−1243.61	−	3827.43i	−0.278759	−	0.857933i	0.709441	−	0.704765i	$-0.248948\pi$
$272$	−3896.26	+	1265.97i	−0.868549	+	0.282209i
$273$	2598.28	−	3576.23i	0.576027	−	0.792833i
$274$	−9186.54			−2.02547
$275$	−1368.85	+	1997.74i	−0.300163	+	0.438067i
$276$	2073.91			0.452299
$277$	−1126.62	+	1550.66i	−0.244376	+	0.336354i	−0.913532	−	0.406768i	$-0.866656\pi$
$277$	−1126.62	+	1550.66i	−0.244376	+	0.336354i	0.669156	+	0.743122i	$0.266656\pi$
$278$	−2699.60	+	877.155i	−0.582416	+	0.189238i
$279$	325.824	+	1002.78i	0.0699160	+	0.215179i
$280$	1053.91	−	555.444i	0.224941	−	0.118550i
$281$	−164.991	+	507.791i	−0.0350269	+	0.107802i	−0.967041	−	0.254619i	$-0.918050\pi$
$281$	−164.991	+	507.791i	−0.0350269	+	0.107802i	0.932014	+	0.362421i	$0.118050\pi$
$282$			2835.43i			0.598749i
$283$	1372.10	+	445.823i	0.288209	+	0.0936446i	0.449553	−	0.893253i	$-0.351583\pi$
$283$	1372.10	+	445.823i	0.288209	+	0.0936446i	−0.161345	+	0.986898i	$0.551583\pi$
$284$	2977.97	−	2163.62i	0.622219	−	0.452069i
$285$	−581.046	+	597.305i	−0.120766	+	0.124145i
$286$	−2878.89	−	2091.63i	−0.595218	−	0.432451i
$287$	−3398.88	−	4678.15i	−0.699057	−	0.962169i
$288$	−1979.30	−	2724.28i	−0.404970	−	0.557394i
$289$	476.855	+	346.456i	0.0970599	+	0.0705181i
$290$	6170.18	+	11707.5i	1.24940	+	2.37064i
$291$	−1497.21	+	1087.79i	−0.301608	+	0.219131i
$292$	−2849.88	−	925.982i	−0.571153	−	0.185579i
$293$		−	3570.98i		−	0.712009i	−0.934484	−	0.356005i	$-0.884139\pi$
$293$		−	3570.98i		−	0.712009i	0.934484	−	0.356005i	$-0.115861\pi$
$294$	−1705.50	+	5248.98i	−0.338322	+	1.04125i
$295$	−4095.36	−	590.840i	−0.808274	−	0.116610i
$296$	−488.791	−	1504.34i	−0.0959810	−	0.295399i
$297$	2758.77	−	896.377i	0.538989	−	0.175128i
$298$	−806.171	+	1109.60i	−0.156712	+	0.215696i
$299$	2748.78			0.531659
$300$	−3331.77	+	2564.06i	−0.641200	+	0.493453i
$301$	−11402.1			−2.18340
$302$	7666.64	−	10552.2i	1.46081	−	2.01064i
$303$	755.569	−	245.499i	0.143255	−	0.0465464i
$304$	339.513	+	1044.91i	0.0640540	+	0.197138i
$305$	−423.596	−	2454.78i	−0.0795247	−	0.460853i
$306$	−1224.33	+	3768.11i	−0.228727	+	0.703950i
$307$			254.168i			0.0472512i	0.999721	+	0.0236256i	$0.00752097\pi$
$307$			254.168i			0.0472512i	−0.999721	+	0.0236256i	$0.992479\pi$
$308$	4377.90	+	1422.47i	0.809916	+	0.263158i
$309$	−1755.23	+	1275.25i	−0.323145	+	0.234778i
$310$	535.037	−	3708.56i	0.0980259	−	0.679458i
$311$	6533.93	+	4747.18i	1.19134	+	0.865556i	0.993405	−	0.114660i	$-0.0365780\pi$
$311$	6533.93	+	4747.18i	1.19134	+	0.865556i	0.197930	+	0.980216i	$0.436578\pi$
$312$	−395.221	−	543.976i	−0.0717148	−	0.0987069i
$313$	402.923	+	554.576i	0.0727621	+	0.100148i	0.843847	−	0.536584i	$-0.180286\pi$
$313$	402.923	+	554.576i	0.0727621	+	0.100148i	−0.771085	+	0.636732i	$0.780286\pi$
$314$	2635.47	+	1914.78i	0.473656	+	0.344132i
$315$	−547.747	+	3796.66i	−0.0979747	+	0.679103i
$316$	1817.34	−	1320.38i	0.323524	−	0.235054i
$317$	−4354.28	−	1414.79i	−0.771485	−	0.250671i	−0.103285	−	0.994652i	$-0.532935\pi$
$317$	−4354.28	−	1414.79i	−0.771485	−	0.250671i	−0.668201	+	0.743981i	$0.732935\pi$
$318$			960.907i			0.169450i
$319$	−1719.88	+	5293.24i	−0.301864	+	0.929042i
$320$	1194.89	+	6924.47i	0.208738	+	1.20965i
$321$	−1209.95	−	3723.86i	−0.210383	−	0.647493i
$322$	−6395.38	+	2077.99i	−1.10683	+	0.359632i
$323$	867.374	−	1193.84i	0.149418	−	0.205656i
$324$	1893.75			0.324718
$325$	−4415.97	+	3398.43i	−0.753705	+	0.580034i
$326$	625.743			0.106309
$327$	3967.83	−	5461.26i	0.671014	−	0.923572i
$328$	−836.521	+	271.802i	−0.140821	+	0.0457554i
$329$	−1502.26	−	4623.47i	−0.251739	−	0.774773i
$330$	−3309.50	−	477.465i	−0.552067	−	0.0796472i
$331$	−2287.10	+	7038.96i	−0.379789	+	1.16887i	0.560401	+	0.828221i	$0.310647\pi$
$331$	−2287.10	+	7038.96i	−0.379789	+	1.16887i	−0.940190	+	0.340650i	$0.889353\pi$
$332$		−	9523.85i		−	1.57437i
$333$	4843.86	+	1573.86i	0.797122	+	0.259001i
$334$	5984.78	−	4348.19i	0.980456	−	0.712343i
$335$	−2320.45	−	4402.88i	−0.378446	−	0.718075i
$336$	−4430.65	−	3219.06i	−0.719381	−	0.522661i
$337$	802.653	+	1104.76i	0.129743	+	0.178576i	0.868946	−	0.494907i	$-0.164798\pi$
$337$	802.653	+	1104.76i	0.129743	+	0.178576i	−0.739203	+	0.673482i	$0.764798\pi$
$338$	508.086	+	699.320i	0.0817640	+	0.112539i
$339$	141.475	+	102.788i	0.0226663	+	0.0164680i
$340$	5191.31	−	5336.58i	0.828054	−	0.851225i
$341$	1274.86	−	926.241i	0.202456	−	0.147093i
$342$	1010.55	+	328.347i	0.159778	+	0.0519152i
$343$		−	384.331i		−	0.0605012i
$344$	−535.944	+	1649.47i	−0.0840005	+	0.258527i
$345$	2284.99	−	1204.26i	0.356579	−	0.187927i
$346$	1953.13	+	6011.13i	0.303472	+	0.933990i
$347$	10055.8	−	3267.32i	1.55568	−	0.505472i	0.600033	−	0.799975i	$-0.295154\pi$
$347$	10055.8	−	3267.32i	1.55568	−	0.505472i	0.955651	+	0.294503i	$0.0951539\pi$
$348$	−5679.25	+	7816.81i	−0.874826	+	1.20410i
$349$	1310.55			0.201008			0.100504	−	0.994937i	$-0.467954\pi$
$349$	1310.55			0.201008			0.100504	+	0.994937i	$0.467954\pi$
$350$	7705.21	−	11245.2i	1.17675	−	1.71738i
$351$	6674.47			1.01498
$352$	−2958.13	+	4071.51i	−0.447922	+	0.616512i
$353$	−4073.40	+	1323.53i	−0.614179	+	0.199559i	−0.599554	−	0.800334i	$-0.704655\pi$
$353$	−4073.40	+	1323.53i	−0.614179	+	0.199559i	−0.0146250	+	0.999893i	$0.504655\pi$
$354$	−1765.47	−	5433.55i	−0.265066	−	0.815790i
$355$	2024.72	−	4113.06i	0.302707	−	0.614925i
$356$	−1458.81	+	4489.77i	−0.217183	+	0.668419i
$357$			7355.69i			1.09049i
$358$	−11907.5	−	3868.99i	−1.75791	−	0.571180i
$359$	−309.644	+	224.970i	−0.0455220	+	0.0330737i	−0.610314	−	0.792160i	$-0.708957\pi$
$359$	−309.644	+	224.970i	−0.0455220	+	0.0330737i	0.564792	+	0.825234i	$0.308957\pi$
$360$	523.493	+	257.698i	0.0766403	+	0.0377274i
$361$	5228.88	+	3799.00i	0.762338	+	0.553871i
$362$	8440.23	+	11617.0i	1.22544	+	1.68667i
$363$	2104.54	+	2896.65i	0.304296	+	0.418828i
$364$	8568.91	+	6225.67i	1.23388	+	0.896467i
$365$	−3677.63	+	634.611i	−0.527386	+	0.0910057i
$366$	2782.62	−	2021.69i	0.397403	−	0.288731i
$367$	−850.776	−	276.434i	−0.121009	−	0.0393181i	0.247887	−	0.968789i	$-0.420264\pi$
$367$	−850.776	−	276.434i	−0.121009	−	0.0393181i	−0.368895	+	0.929471i	$0.620264\pi$
$368$		−	3405.51i		−	0.482404i
$369$	875.180	−	2693.53i	0.123469	−	0.379999i
$370$	−12973.5	−	12620.4i	−1.82287	−	1.77325i
$371$	−509.105	−	1566.86i	−0.0712437	−	0.219266i
$372$	2601.77	−	845.366i	0.362622	−	0.117823i
$373$	1239.91	−	1706.59i	0.172118	−	0.236900i	−0.714240	−	0.699901i	$-0.753227\pi$
$373$	1239.91	−	1706.59i	0.172118	−	0.236900i	0.886358	+	0.463001i	$0.153227\pi$
$374$	5921.37			0.818682
$375$	−2182.01	+	4759.69i	−0.300476	+	0.655438i
$376$	−739.462			−0.101422
$377$	−7527.34	+	10360.5i	−1.02832	+	1.41537i
$378$	−15529.0	+	5045.67i	−2.11303	+	0.686565i
$379$	667.344	+	2053.88i	0.0904464	+	0.278365i	0.986040	−	0.166507i	$-0.0532489\pi$
$379$	667.344	+	2053.88i	0.0904464	+	0.278365i	−0.895594	+	0.444873i	$0.853249\pi$
$380$	−1431.19	−	1392.23i	−0.193206	−	0.187947i
$381$	−1378.07	+	4241.25i	−0.185303	+	0.570304i
$382$			1964.57i			0.263131i
$383$	1520.78	+	494.130i	0.202893	+	0.0659239i	0.408700	−	0.912669i	$-0.365982\pi$
$383$	1520.78	+	494.130i	0.202893	+	0.0659239i	−0.205808	+	0.978592i	$0.565982\pi$
$384$	−1550.30	+	1126.36i	−0.206025	+	0.149686i
$385$	5649.47	−	974.872i	0.747854	−	0.129050i
$386$	3662.95	+	2661.29i	0.483003	+	0.350922i
$387$	−3282.47	−	4517.93i	−0.431156	−	0.593435i
$388$	−2606.41	−	3587.42i	−0.341032	−	0.469391i
$389$	−8141.92	−	5915.45i	−1.06121	−	0.771016i	−0.0868999	−	0.996217i	$-0.527696\pi$
$389$	−8141.92	−	5915.45i	−1.06121	−	0.771016i	−0.974312	+	0.225201i	$0.927696\pi$
$390$	−6902.81	−	3398.02i	−0.896250	−	0.441194i
$391$	−3700.44	+	2688.52i	−0.478617	+	0.347735i
$392$	−1368.90	−	444.783i	−0.176378	−	0.0573085i
$393$		−	770.008i		−	0.0988341i
$394$	116.931	−	359.877i	0.0149516	−	0.0460162i
$395$	1235.61	−	2510.04i	0.157393	−	0.319731i
$396$	696.692	+	2144.20i	0.0884093	+	0.272096i
$397$	12486.1	−	4056.99i	1.57849	−	0.512882i	0.616823	−	0.787102i	$-0.288419\pi$
$397$	12486.1	−	4056.99i	1.57849	−	0.512882i	0.961667	+	0.274220i	$0.0884195\pi$
$398$	−3910.47	+	5382.30i	−0.492498	+	0.677866i
$399$	1972.68			0.247513
$400$	4210.38	+	5471.02i	0.526297	+	0.683878i
$401$	−3357.62			−0.418133			−0.209067	−	0.977901i	$-0.567043\pi$
$401$	−3357.62			−0.418133			−0.209067	+	0.977901i	$0.567043\pi$
$402$	4039.17	−	5559.44i	0.501133	−	0.689751i
$403$	3448.42	−	1120.46i	0.426248	−	0.138496i
$404$	588.234	+	1810.40i	0.0724399	+	0.222947i
$405$	2086.50	−	1099.65i	0.255997	−	0.134918i
$406$	9681.12	−	29795.4i	1.18341	−	3.64217i
$407$		−	7611.84i		−	0.927039i
$408$	1064.10	+	345.748i	0.129120	+	0.0419536i
$409$	−12519.4	+	9095.91i	−1.51356	+	1.09967i	−0.548996	+	0.835825i	$0.684990\pi$
$409$	−12519.4	+	9095.91i	−1.51356	+	1.09967i	−0.964566	+	0.263842i	$0.915010\pi$
$410$	−7017.82	+	7214.20i	−0.845330	+	0.868985i
$411$	−6757.93	−	4909.92i	−0.811056	−	0.589267i
$412$	−3055.59	−	4205.66i	−0.365384	−	0.502908i
$413$	5757.57	+	7924.61i	0.685984	+	0.944176i
$414$	−2664.50	−	1935.88i	−0.316312	−	0.229814i
$415$	−5530.22	−	10493.2i	−0.654139	−	1.24118i
$416$	−9368.36	+	6806.51i	−1.10414	+	0.802204i
$417$	−2454.73	−	797.591i	−0.288270	−	0.0936647i
$418$		−	1588.02i		−	0.185820i
$419$	3839.41	−	11816.5i	0.447655	−	1.37774i	−0.431891	−	0.901926i	$-0.642153\pi$
$419$	3839.41	−	11816.5i	0.447655	−	1.37774i	0.879546	−	0.475814i	$-0.157847\pi$
$420$	9850.61	+	1421.16i	1.14443	+	0.165108i
$421$	5200.54	+	16005.6i	0.602040	+	1.85289i	0.515984	+	0.856598i	$0.327427\pi$
$421$	5200.54	+	16005.6i	0.602040	+	1.85289i	0.0860563	+	0.996290i	$0.472573\pi$
$422$	−14434.6	+	4690.08i	−1.66508	+	0.541018i
$423$	1399.52	−	1926.27i	0.160868	−	0.221415i
$424$	−250.599			−0.0287032
$425$	2620.89	−	8894.17i	0.299134	−	1.01513i
$426$	6329.87			0.719914
$427$	−3466.23	+	4770.86i	−0.392840	+	0.540698i
$428$	8922.63	−	2899.14i	1.00769	−	0.327418i
$429$	−999.893	−	3077.35i	−0.112530	−	0.346331i
$430$	3374.64	+	19556.3i	0.378464	+	2.19323i
$431$	−3856.90	+	11870.3i	−0.431044	+	1.32662i	0.466042	+	0.884763i	$0.345680\pi$
$431$	−3856.90	+	11870.3i	−0.431044	+	1.32662i	−0.897086	+	0.441855i	$0.854320\pi$
$432$		−	8269.11i		−	0.920944i
$433$	−3965.44	−	1288.45i	−0.440109	−	0.143000i	0.0805771	−	0.996748i	$-0.474324\pi$
$433$	−3965.44	−	1288.45i	−0.440109	−	0.143000i	−0.520686	+	0.853748i	$0.674324\pi$
$434$	−7176.15	+	5213.78i	−0.793701	+	0.576657i
$435$	−1718.29	+	11910.2i	−0.189393	+	1.31276i
$436$	13085.6	+	9507.22i	1.43735	+	1.04430i
$437$	721.020	+	992.399i	0.0789269	+	0.108634i
$438$	−3028.80	−	4168.78i	−0.330415	−	0.454777i
$439$	11333.0	+	8233.91i	1.23211	+	0.895178i	0.997046	−	0.0768033i	$-0.0244713\pi$
$439$	11333.0	+	8233.91i	1.23211	+	0.895178i	0.235060	+	0.971981i	$0.424471\pi$
$440$	124.520	−	863.098i	0.0134915	−	0.0935150i
$441$	3749.46	−	2724.14i	0.404865	−	0.294152i
$442$	12958.0	+	4210.30i	1.39445	+	0.453085i
$443$			7372.11i			0.790653i	0.918541	+	0.395327i	$0.129369\pi$
$443$			7372.11i			0.790653i	−0.918541	+	0.395327i	$0.870631\pi$
$444$	4083.47	−	12567.6i	0.436470	−	1.34332i
$445$	999.782	+	5793.83i	0.106504	+	0.617199i
$446$	−6304.98	−	19404.7i	−0.669393	−	2.06018i
$447$	−1186.09	+	385.385i	−0.125504	+	0.0407787i
$448$	9777.60	−	13457.7i	1.03113	−	1.41923i
$449$	−4449.29			−0.467650			−0.233825	−	0.972279i	$-0.575124\pi$
$449$	−4449.29			−0.467650			−0.233825	+	0.972279i	$0.575124\pi$
$450$	6673.99	−	184.214i	0.699144	−	0.0192977i
$451$	−4232.72			−0.441932
$452$	−246.287	+	338.984i	−0.0256291	+	0.0352754i
$453$	11279.7	−	3664.99i	1.16990	−	0.380124i
$454$	469.411	+	1444.70i	0.0485255	+	0.149346i
$455$	13056.1	+	1883.62i	1.34523	+	0.194078i
$456$	92.7241	−	285.376i	0.00952238	−	0.0293069i
$457$		−	6349.09i		−	0.649886i	−0.945734	−	0.324943i	$-0.894655\pi$
$457$		−	6349.09i		−	0.649886i	0.945734	−	0.324943i	$-0.105345\pi$
$458$	4046.75	+	1314.87i	0.412865	+	0.134148i
$459$	−8985.24	+	6528.16i	−0.913714	+	0.663852i
$460$	2885.48	+	5475.00i	0.292470	+	0.554942i
$461$	−12414.6	−	9019.70i	−1.25424	−	0.911257i	−0.255778	−	0.966736i	$-0.582331\pi$
$461$	−12414.6	−	9019.70i	−1.25424	−	0.911257i	−0.998460	+	0.0554788i	$0.982331\pi$
$462$	4652.75	+	6403.97i	0.468541	+	0.644891i
$463$	−672.343	−	925.400i	−0.0674868	−	0.0928877i	0.773939	−	0.633260i	$-0.218284\pi$
$463$	−672.343	−	925.400i	−0.0674868	−	0.0928877i	−0.841426	+	0.540372i	$0.818284\pi$
$464$	12835.8	+	9325.75i	1.28424	+	0.933054i
$465$	2375.70	−	2442.18i	0.236926	−	0.243556i
$466$	−4692.59	+	3409.37i	−0.466481	+	0.338918i
$467$	−10104.8	−	3283.25i	−1.00127	−	0.325334i	−0.237899	−	0.971290i	$-0.576459\pi$
$467$	−10104.8	−	3283.25i	−1.00127	−	0.325334i	−0.763375	+	0.645956i	$0.776459\pi$
$468$			5187.60i			0.512386i
$469$	−3640.82	+	11205.3i	−0.358459	+	1.10322i
$470$	−7485.37	+	3945.01i	−0.734626	+	0.387169i
$471$	915.349	+	2817.15i	0.0895478	+	0.275600i
$472$	1417.04	−	460.423i	0.138187	−	0.0448997i
$473$	−4905.75	+	6752.18i	−0.476885	+	0.656376i
$474$	3862.88			0.374320
$475$	−2385.28	−	702.882i	−0.230409	−	0.0678957i
$476$	−17624.8			−1.69712
$477$	474.288	−	652.801i	0.0455265	−	0.0626619i
$478$	17181.0	−	5582.45i	1.64402	−	0.534175i
$479$	−4475.35	−	13773.7i	−0.426897	−	1.31385i	−0.901166	−	0.433475i	$-0.857287\pi$
$479$	−4475.35	−	13773.7i	−0.426897	−	1.31385i	0.474268	−	0.880380i	$-0.342713\pi$
$480$	−4805.70	+	9762.41i	−0.456978	+	0.928315i
$481$	5412.28	−	16657.3i	0.513053	−	1.57902i
$482$			1141.36i			0.107858i
$483$	−5815.28	−	1889.50i	−0.547835	−	0.178002i
$484$	−6940.57	+	5042.62i	−0.651819	+	0.473575i
$485$	−4954.80	−	2439.08i	−0.463889	−	0.228357i
$486$	−10841.0	−	7876.45i	−1.01185	−	0.735150i
$487$	−3465.52	−	4769.88i	−0.322460	−	0.443828i	0.616756	−	0.787154i	$-0.288446\pi$
$487$	−3465.52	−	4769.88i	−0.322460	−	0.443828i	−0.939216	+	0.343326i	$0.888446\pi$
$488$	527.244	+	725.689i	0.0489082	+	0.0673164i
$489$	460.318	+	334.441i	0.0425691	+	0.0309283i
$490$	−16229.9	+	2800.63i	−1.49631	+	0.258203i
$491$	13594.4	−	9876.90i	1.24950	−	0.907817i	0.251310	−	0.967907i	$-0.419139\pi$
$491$	13594.4	−	9876.90i	1.24950	−	0.907817i	0.998193	+	0.0600899i	$0.0191387\pi$
$492$	−6988.49	−	2270.70i	−0.640377	−	0.208071i
$493$		−	21309.7i		−	1.94674i
$494$	1129.14	−	3475.12i	0.102838	−	0.316504i
$495$	2012.67	+	1957.89i	0.182753	+	0.177779i
$496$	−1388.16	−	4272.30i	−0.125665	−	0.386758i
$497$	−10321.5	+	3353.67i	−0.931558	+	0.302682i
$498$	9626.38	−	13249.6i	0.866202	−	1.19222i
$499$	6860.80			0.615494			0.307747	−	0.951468i	$-0.400425\pi$
$499$	6860.80			0.615494			0.307747	+	0.951468i	$0.400425\pi$
$500$	−11404.6	−	5228.25i	−1.02005	−	0.467629i
$501$	6726.58			0.599843
$502$	−16665.5	+	22938.0i	−1.48170	+	2.03939i
$503$	11835.9	−	3845.71i	1.04918	−	0.340898i	0.266831	−	0.963743i	$-0.414024\pi$
$503$	11835.9	−	3845.71i	1.04918	−	0.340898i	0.782345	+	0.622846i	$0.214024\pi$
$504$	−426.841	−	1313.68i	−0.0377243	−	0.116103i
$505$	1699.35	+	1653.09i	0.149743	+	0.145666i
$506$	−1521.06	+	4681.34i	−0.133635	+	0.411286i
$507$			786.000i			0.0688510i
$508$	−10162.3	−	3301.95i	−0.887561	−	0.288386i
$509$	12853.9	−	9338.90i	1.11933	−	0.813241i	0.135223	−	0.990815i	$-0.456825\pi$
$509$	12853.9	−	9338.90i	1.11933	−	0.813241i	0.984107	+	0.177574i	$0.0568250\pi$
$510$	12616.2	−	2177.04i	1.09540	−	0.189022i
$511$	7147.48	+	5192.95i	0.618759	+	0.449555i
$512$	9478.24	+	13045.7i	0.818131	+	1.12606i
$513$	1750.75	+	2409.70i	0.150677	+	0.207389i
$514$	−24687.6	−	17936.6i	−2.11853	−	1.53920i
$515$	−5808.69	−	2859.42i	−0.497013	−	0.244663i
$516$	−11722.0	+	8516.52i	−1.00006	+	0.726587i
$517$	−3384.32	−	1099.63i	−0.287896	−	0.0935431i
$518$			42846.8i			3.63432i
$519$	−1775.97	+	5465.88i	−0.150205	+	0.462284i
$520$	886.183	−	1800.21i	0.0747341	−	0.151816i
$521$	−602.662	−	1854.80i	−0.0506777	−	0.155970i	0.922515	−	0.385961i	$-0.126130\pi$
$521$	−602.662	−	1854.80i	−0.0506777	−	0.155970i	−0.973193	+	0.229991i	$0.926130\pi$
$522$	14593.1	−	4741.59i	1.22361	−	0.397574i
$523$	−12465.9	+	17157.8i	−1.04225	+	1.43453i	−0.146905	+	0.989151i	$0.546931\pi$
$523$	−12465.9	+	17157.8i	−1.04225	+	1.43453i	−0.895342	+	0.445380i	$0.853069\pi$
$524$	1845.00			0.153815
$525$	11678.4	−	4154.15i	0.970835	−	0.345337i
$526$	19762.7			1.63820
$527$	−3546.40	+	4881.20i	−0.293138	+	0.403469i
$528$	−3812.59	+	1238.78i	−0.314245	+	0.102105i
$529$	2584.86	+	7955.39i	0.212449	+	0.653849i
$530$	−2536.74	+	1336.94i	−0.207904	+	0.109571i
$531$	−1482.52	+	4562.74i	−0.121160	+	0.372892i
$532$			4726.68i			0.385202i
$533$	−9262.63	−	3009.61i	−0.752737	−	0.244579i
$534$	−6567.60	+	4771.64i	−0.532225	+	0.386684i
$535$	8147.33	−	8375.32i	0.658392	−	0.676816i
$536$	1449.87	+	1053.39i	0.116837	+	0.0848872i
$537$	−6691.72	−	9210.37i	−0.537745	−	0.740143i
$538$	−4076.91	−	5611.39i	−0.326707	−	0.449673i
$539$	−5603.68	−	4071.31i	−0.447806	−	0.325350i
$540$	7006.40	+	13294.2i	0.558347	+	1.05942i
$541$	13101.0	−	9518.41i	1.04114	−	0.756430i	0.0706293	−	0.997503i	$-0.477499\pi$
$541$	13101.0	−	9518.41i	1.04114	−	0.756430i	0.970507	+	0.241073i	$0.0774993\pi$
$542$	15770.3	+	5124.07i	1.24980	+	0.406084i
$543$			13056.9i			1.03190i
$544$	5954.48	−	18326.0i	0.469294	−	1.44434i
$545$	19938.0	+	2876.47i	1.56706	+	0.226081i
$546$	5628.36	+	17322.3i	0.441157	+	1.35774i
$547$	11147.3	−	3621.97i	0.871340	−	0.283116i	0.160983	−	0.986957i	$-0.448533\pi$
$547$	11147.3	−	3621.97i	0.871340	−	0.283116i	0.710357	+	0.703841i	$0.248533\pi$
$548$	11764.5	−	16192.5i	0.917073	−	1.26224i
$549$	−2888.27			−0.224532
$550$	−3344.12	−	9401.21i	−0.259261	−	0.728853i
$551$	−5714.94			−0.441859
$552$	−546.685	+	752.447i	−0.0421530	+	0.0580186i
$553$	−6298.84	+	2046.62i	−0.484365	+	0.157380i
$554$	−2440.47	−	7510.98i	−0.187158	−	0.576013i
$555$	−2798.56	−	16217.9i	−0.214040	−	1.24038i
$556$	1911.08	−	5881.71i	0.145770	−	0.448634i
$557$			5469.05i			0.416034i	0.978125	+	0.208017i	$0.0667009\pi$
$557$			5469.05i			0.416034i	−0.978125	+	0.208017i	$0.933299\pi$
$558$	−4131.79	−	1342.50i	−0.313464	−	0.101851i
$559$	−15536.5	+	11287.9i	−1.17553	+	0.854074i
$560$	2333.65	−	16175.4i	0.176097	−	1.22060i
$561$	4355.96	+	3164.79i	0.327823	+	0.238178i
$562$	−1293.09	−	1779.79i	−0.0970565	−	0.133587i
$563$	−7900.29	−	10873.8i	−0.591399	−	0.813991i	0.403488	−	0.914985i	$-0.367798\pi$
$563$	−7900.29	−	10873.8i	−0.591399	−	0.813991i	−0.994887	+	0.100994i	$0.967798\pi$
$564$	−4997.81	−	3631.12i	−0.373131	−	0.271095i
$565$	−74.5156	+	516.498i	−0.00554848	+	0.0384588i
$566$	−4809.16	+	3494.06i	−0.357145	+	0.259481i
$567$	−5310.12	−	1725.36i	−0.393306	−	0.127793i
$568$			1650.79i			0.121947i
$569$	−4456.10	+	13714.5i	−0.328312	+	1.01044i	0.641612	+	0.767029i	$0.278266\pi$
$569$	−4456.10	+	13714.5i	−0.328312	+	1.01044i	−0.969924	+	0.243410i	$0.921734\pi$
$570$	−583.849	−	3383.46i	−0.0429031	−	0.248627i
$571$	−3187.96	−	9811.54i	−0.233646	−	0.719089i	−0.997298	−	0.0734610i	$-0.976596\pi$
$571$	−3187.96	−	9811.54i	−0.233646	−	0.719089i	0.763652	−	0.645628i	$-0.223404\pi$
$572$	7373.56	−	2395.82i	0.538993	−	0.175130i
$573$	−1050.00	+	1445.20i	−0.0765522	+	0.105365i
$574$	23825.8			1.73253
$575$	6358.34	+	4356.73i	0.461150	+	0.315980i
$576$	8147.27			0.589357
$577$	14966.0	−	20599.0i	1.07980	−	1.48622i	0.220057	−	0.975487i	$-0.429376\pi$
$577$	14966.0	−	20599.0i	1.07980	−	1.48622i	0.859742	−	0.510728i	$-0.170624\pi$
$578$	−2309.76	+	750.487i	−0.166217	+	0.0540071i
$579$	1272.21	+	3915.46i	0.0913148	+	0.281038i
$580$	−28537.7	−	4117.15i	−2.04304	−	0.294751i
$581$	−8677.01	+	26705.1i	−0.619592	+	1.90691i
$582$		−	7625.29i		−	0.543090i
$583$	−1146.92	−	372.658i	−0.0814764	−	0.0264733i
$584$	1087.19	−	789.892i	0.0770349	−	0.0559691i
$585$	3012.28	+	5715.59i	0.212893	+	0.403950i
$586$	11903.5	+	8648.43i	0.839131	+	0.609665i
$587$	11481.1	+	15802.4i	0.807286	+	1.11113i	0.991736	+	0.128293i	$0.0409497\pi$
$587$	11481.1	+	15802.4i	0.807286	+	1.11113i	−0.184450	+	0.982842i	$0.559050\pi$
$588$	−7067.91	−	9728.15i	−0.495707	−	0.682282i
$589$	1309.06	+	951.088i	0.0915771	+	0.0665346i
$590$	11887.9	−	12220.6i	0.829522	−	0.852734i
$591$	278.362	−	202.242i	0.0193744	−	0.0140763i
$592$	−20637.0	−	6705.37i	−1.43273	−	0.465522i
$593$			12614.9i			0.873582i	0.899563	+	0.436791i	$0.143885\pi$
$593$			12614.9i			0.873582i	−0.899563	+	0.436791i	$0.856115\pi$
$594$	−3693.37	+	11367.0i	−0.255119	+	0.785176i
$595$	−19418.6	+	10234.2i	−1.33796	+	0.705143i
$596$	−923.411	−	2841.97i	−0.0634637	−	0.195321i
$597$	−5753.35	+	1869.38i	−0.394420	+	0.128155i
$598$	−6657.18	+	9162.82i	−0.455238	+	0.626581i
$599$	−662.584			−0.0451961			−0.0225981	−	0.999745i	$-0.507194\pi$
$599$	−662.584			−0.0451961			−0.0225981	+	0.999745i	$0.507194\pi$
$600$	−52.0215	−	1884.71i	−0.00353961	−	0.128238i
$601$	−9643.41			−0.654514			−0.327257	−	0.944935i	$-0.606124\pi$
$601$	−9643.41			−0.654514			−0.327257	+	0.944935i	$0.606124\pi$
$602$	27614.3	−	38007.8i	1.86956	−	2.57323i
$603$	−5488.10	+	1783.19i	−0.370634	+	0.120426i
$604$	8781.57	+	27026.9i	0.591585	+	1.82071i
$605$	−4718.89	+	9586.05i	−0.317107	+	0.644179i
$606$	−1011.54	+	3113.19i	−0.0678067	+	0.208688i
$607$			18733.3i			1.25265i	0.779560	+	0.626327i	$0.215443\pi$
$607$			18733.3i			1.25265i	−0.779560	+	0.626327i	$0.784557\pi$
$608$	−4914.75	−	1596.90i	−0.327828	−	0.106518i
$609$	23046.5	−	16744.3i	1.53348	−	1.11414i
$610$	9208.68	+	4533.12i	0.611227	+	0.300886i
$611$	−6624.16	−	4812.73i	−0.438600	−	0.318662i
$612$	−5073.88	−	6983.60i	−0.335130	−	0.461267i
$613$	12241.1	+	16848.4i	0.806547	+	1.11012i	0.991847	+	0.127435i	$0.0406745\pi$
$613$	12241.1	+	16848.4i	0.806547	+	1.11012i	−0.185299	+	0.982682i	$0.559326\pi$
$614$	−847.247	−	615.561i	−0.0556875	−	0.0404593i
$615$	−9018.31	+	1556.20i	−0.591306	+	0.102036i
$616$	−1670.12	+	1213.41i	−0.109238	+	0.0793664i
$617$	7351.50	+	2388.65i	0.479676	+	0.155856i	0.538868	−	0.842390i	$-0.318852\pi$
$617$	7351.50	+	2388.65i	0.479676	+	0.155856i	−0.0591916	+	0.998247i	$0.518852\pi$
$618$		−	8939.40i		−	0.581870i
$619$	6894.63	−	21219.5i	0.447688	−	1.37784i	−0.431822	−	0.901959i	$-0.642129\pi$
$619$	6894.63	−	21219.5i	0.447688	−	1.37784i	0.879509	−	0.475882i	$-0.157871\pi$
$620$	5851.64	+	5692.35i	0.379044	+	0.368726i
$621$	−2852.96	−	8780.50i	−0.184356	−	0.567390i
$622$	−31648.6	+	10283.3i	−2.04018	+	0.662896i
$623$	8181.09	−	11260.3i	0.526113	−	0.724133i
$624$	−9224.04			−0.591759
$625$	−15601.2	+	861.901i	−0.998477	+	0.0551617i
$626$	−2824.45			−0.180332
$627$	848.747	−	1168.20i	0.0540601	−	0.0744074i
$628$	−6750.10	+	2193.24i	−0.428915	+	0.139363i
$629$	9006.07	+	27717.8i	0.570899	+	1.75705i
$630$	−11329.3	−	11020.9i	−0.716458	−	0.696955i
$631$	−3369.80	+	10371.2i	−0.212599	+	0.654311i	0.786717	+	0.617314i	$0.211779\pi$
$631$	−3369.80	+	10371.2i	−0.212599	+	0.654311i	−0.999315	+	0.0369969i	$0.988221\pi$
$632$			1007.41i			0.0634063i
$633$	−13125.3	−	4264.66i	−0.824143	−	0.267780i
$634$	15261.6	−	11088.2i	0.956017	−	0.694587i
$635$	−13114.0	+	2262.95i	−0.819549	+	0.141421i
$636$	−1693.73	−	1230.56i	−0.105598	−	0.0767217i
$637$	−9367.89	−	12893.8i	−0.582684	−	0.801995i
$638$	−13479.2	−	18552.6i	−0.836439	−	1.15126i
$639$	−4300.26	−	3124.32i	−0.266222	−	0.193421i
$640$	−5130.51	−	2525.58i	−0.316877	−	0.155988i
$641$	14924.6	−	10843.4i	0.919635	−	0.668154i	−0.0237979	−	0.999717i	$-0.507576\pi$
$641$	14924.6	−	10843.4i	0.919635	−	0.668154i	0.943433	+	0.331563i	$0.107576\pi$
$642$	15343.5	+	4985.41i	0.943239	+	0.306477i
$643$		−	13279.7i		−	0.814462i	−0.913325	−	0.407231i	$-0.866494\pi$
$643$		−	13279.7i		−	0.814462i	0.913325	−	0.407231i	$-0.133506\pi$
$644$	4527.38	−	13933.8i	0.277024	−	0.852593i
$645$	−7969.77	+	16189.9i	−0.486526	+	0.988339i
$646$	1878.89	+	5782.63i	0.114433	+	0.352190i
$647$	−14829.3	+	4818.32i	−0.901080	+	0.292779i	−0.722683	−	0.691180i	$-0.757091\pi$
$647$	−14829.3	+	4818.32i	−0.901080	+	0.292779i	−0.178397	+	0.983959i	$0.557091\pi$
$648$	−499.196	+	687.084i	−0.0302628	+	0.0416531i
$649$	7170.08			0.433667
$650$	−633.484	−	22950.8i	−0.0382266	−	1.38493i
$651$	−8065.62			−0.485586
$652$	−801.344	+	1102.95i	−0.0481335	+	0.0662501i
$653$	12519.9	−	4067.98i	0.750296	−	0.243786i	0.0911876	−	0.995834i	$-0.470934\pi$
$653$	12519.9	−	4067.98i	0.750296	−	0.243786i	0.659109	+	0.752048i	$0.270934\pi$
$654$	8595.06	+	26452.9i	0.513904	+	1.58163i
$655$	2032.78	−	1071.33i	0.121263	−	0.0639091i
$656$	−3728.66	+	11475.6i	−0.221920	+	0.683000i
$657$			4327.07i			0.256948i
$658$	19050.2	+	6189.79i	1.12865	+	0.366722i
$659$	3206.77	−	2329.85i	0.189557	−	0.137721i	−0.488959	−	0.872307i	$-0.662623\pi$
$659$	3206.77	−	2329.85i	0.189557	−	0.137721i	0.678516	+	0.734586i	$0.262623\pi$
$660$	5079.83	−	5221.98i	0.299594	−	0.307978i
$661$	−18655.1	−	13553.7i	−1.09773	−	0.797548i	−0.117043	−	0.993127i	$-0.537341\pi$
$661$	−18655.1	−	13553.7i	−1.09773	−	0.797548i	−0.980688	+	0.195579i	$0.937341\pi$
$662$	−17924.7	−	24671.3i	−1.05236	−	1.44845i
$663$	7282.04	+	10022.9i	0.426563	+	0.587113i
$664$	3455.41	+	2510.50i	0.201952	+	0.146726i
$665$	2744.64	+	5207.77i	0.160049	+	0.303682i
$666$	−16977.5	+	12334.9i	−0.987786	+	0.717669i
$667$	16847.1	+	5473.96i	0.977996	+	0.317770i
$668$			16117.4i			0.933532i
$669$	5733.07	−	17644.6i	0.331321	−	1.01970i
$670$	20296.4	+	2928.18i	1.17033	+	0.168844i
$671$	1333.90	+	4105.34i	0.0767434	+	0.236192i
$672$	24498.3	−	7959.99i	1.40632	−	0.456940i
$673$	9288.82	−	12785.0i	0.532032	−	0.732279i	−0.455406	−	0.890284i	$-0.650506\pi$
$673$	9288.82	−	12785.0i	0.532032	−	0.732279i	0.987438	+	0.158004i	$0.0505060\pi$
$674$	−5626.53			−0.321552
$675$	15439.0	+	10578.8i	0.880369	+	0.603228i
$676$	−1883.31			−0.107153
$677$	13063.6	−	17980.5i	0.741616	−	1.02075i	−0.256908	−	0.966436i	$-0.582704\pi$
$677$	13063.6	−	17980.5i	0.741616	−	1.02075i	0.998524	−	0.0543109i	$-0.0172962\pi$
$678$	−685.267	+	222.657i	−0.0388164	+	0.0126122i
$679$	4040.01	+	12433.9i	0.228338	+	0.702751i
$680$	567.760	+	3290.22i	0.0320185	+	0.185550i
$681$	−426.832	+	1313.65i	−0.0240180	+	0.0739198i
$682$			6492.88i			0.364553i
$683$	3031.22	+	984.903i	0.169819	+	0.0551775i	0.392692	−	0.919670i	$-0.371544\pi$
$683$	3031.22	+	984.903i	0.169819	+	0.0551775i	−0.222873	+	0.974847i	$0.571544\pi$
$684$	−1872.89	+	1360.74i	−0.104696	+	0.0760658i
$685$	3559.43	−	24671.9i	0.198539	−	1.37615i
$686$	1281.13	+	930.798i	0.0713030	+	0.0518047i
$687$	2274.17	+	3130.12i	0.126295	+	0.173831i
$688$	13984.8	+	19248.4i	0.774949	+	1.06663i
$689$	−2244.88	−	1631.00i	−0.124127	−	0.0901833i
$690$	−1519.66	+	10533.4i	−0.0838440	+	0.581157i
$691$	−14136.7	+	10270.9i	−0.778271	+	0.565447i	−0.904459	−	0.426560i	$-0.859725\pi$
$691$	−14136.7	+	10270.9i	−0.778271	+	0.565447i	0.126189	+	0.992006i	$0.459725\pi$
$692$	−13096.6	−	4255.36i	−0.719450	−	0.233764i
$693$		−	6647.12i		−	0.364362i
$694$	−13462.4	+	41433.1i	−0.736350	+	2.26625i
$695$	−1309.74	−	7590.07i	−0.0714839	−	0.414256i
$696$	−1339.01	−	4121.05i	−0.0729239	−	0.224437i
$697$	15413.1	−	5008.01i	0.837607	−	0.272155i
$698$	−3173.97	+	4368.59i	−0.172115	+	0.236896i
$699$	−5274.23			−0.285393
$700$	9953.65	+	27982.4i	0.537447	+	1.51091i
$701$	16491.0			0.888526			0.444263	−	0.895896i	$-0.353466\pi$
$701$	16491.0			0.888526			0.444263	+	0.895896i	$0.353466\pi$
$702$	−16164.7	+	22248.8i	−0.869083	+	1.19619i
$703$	7433.49	−	2415.29i	0.398804	−	0.129579i
$704$	−3762.70	−	11580.4i	−0.201437	−	0.619961i
$705$	−7614.98	−	1098.62i	−0.406804	−	0.0586899i
$706$	5453.37	−	16783.7i	0.290709	−	0.894709i
$707$		−	5612.32i		−	0.298548i
$708$	11838.2	+	3846.48i	0.628402	+	0.204180i
$709$	14071.7	−	10223.7i	0.745380	−	0.541550i	−0.149011	−	0.988835i	$-0.547609\pi$
$709$	14071.7	−	10223.7i	0.745380	−	0.541550i	0.894391	+	0.447285i	$0.147609\pi$
$710$	8806.92	+	16710.5i	0.465518	+	0.883288i
$711$	−2624.28	−	1906.65i	−0.138422	−	0.100570i
$712$	−1244.42	−	1712.79i	−0.0655006	−	0.0901539i
$713$	−2948.01	−	4057.58i	−0.154844	−	0.213124i
$714$	−24519.5	−	17814.5i	−1.28518	−	0.933740i
$715$	6732.87	−	6921.27i	0.352161	−	0.362015i
$716$	22068.7	−	16033.9i	1.15188	−	0.836890i
$717$	15622.6	+	5076.09i	0.813719	+	0.264393i
$718$		−	1577.02i		−	0.0819691i
$719$	−345.403	+	1063.04i	−0.0179157	+	0.0551388i	−0.959615	−	0.281318i	$-0.909229\pi$
$719$	−345.403	+	1063.04i	−0.0179157	+	0.0551388i	0.941699	+	0.336457i	$0.109229\pi$
$720$	7081.15	−	3731.97i	0.366526	−	0.193170i
$721$	4736.25	+	14576.7i	0.244642	+	0.752931i
$722$	−25327.3	+	8229.34i	−1.30552	+	0.424189i
$723$	−610.019	+	839.620i	−0.0313788	+	0.0431892i
$724$	−31285.2			−1.60595
$725$	−33832.9	+	12034.8i	−1.73314	+	0.616497i
$726$	−14752.6			−0.754162
$727$	−14331.2	+	19725.2i	−0.731108	+	1.00628i	0.267973	+	0.963426i	$0.413646\pi$
$727$	−14331.2	+	19725.2i	−0.731108	+	1.00628i	−0.999081	+	0.0428572i	$0.986354\pi$
$728$	−4517.55	+	1467.84i	−0.229989	+	0.0747278i
$729$	−5525.37	−	17005.3i	−0.280718	−	0.863961i
$730$	6791.31	−	13796.0i	0.344326	−	0.699470i
$731$	9874.89	−	30391.8i	0.499639	−	1.53773i
$732$			7493.75i			0.378384i
$733$	−26041.7	−	8461.46i	−1.31224	−	0.426373i	−0.432417	−	0.901674i	$-0.642339\pi$
$733$	−26041.7	−	8461.46i	−1.31224	−	0.426373i	−0.879823	+	0.475301i	$0.842339\pi$
$734$	2981.93	−	2166.50i	0.149953	−	0.108947i
$735$	−13436.1	−	6614.15i	−0.674285	−	0.331928i
$736$	12958.7	+	9415.02i	0.648998	+	0.471525i
$737$	5069.19	+	6977.15i	0.253360	+	0.348720i
$738$	6859.07	+	9440.70i	0.342122	+	0.470890i
$739$	−12941.1	−	9402.24i	−0.644175	−	0.468020i	0.217107	−	0.976148i	$-0.430338\pi$
$739$	−12941.1	−	9402.24i	−0.644175	−	0.468020i	−0.861282	+	0.508127i	$0.830338\pi$
$740$	38859.3	−	6705.55i	1.93040	−	0.333109i
$741$	2687.98	−	1952.93i	0.133259	−	0.0968187i
$742$	6455.99	+	2097.68i	0.319416	+	0.103785i
$743$		−	13607.9i		−	0.671906i	−0.941879	−	0.335953i	$-0.890942\pi$
$743$		−	13607.9i		−	0.671906i	0.941879	−	0.335953i	$-0.109058\pi$
$744$	−379.118	+	1166.80i	−0.0186816	+	0.0574961i
$745$	−2667.64	−	2595.02i	−0.131188	−	0.127617i
$746$	2685.87	+	8266.26i	0.131819	+	0.405696i
$747$	−13079.5	+	4249.80i	−0.640637	+	0.208155i
$748$	−7583.07	+	10437.2i	−0.370674	+	0.510190i
$749$	−27660.6			−1.34939
$750$	−10581.5	−	18800.9i	−0.515174	−	0.915348i
$751$	29048.3			1.41143			0.705717	−	0.708493i	$-0.250625\pi$
$751$	29048.3			1.41143			0.705717	+	0.708493i	$0.250625\pi$
$752$	−5962.58	+	8206.79i	−0.289139	+	0.397966i
$753$	−24519.3	+	7966.82i	−1.18663	+	0.385560i
$754$	−16305.6	−	50183.5i	−0.787553	−	2.42384i
$755$	25369.1	+	24678.5i	1.22288	+	1.18959i
$756$	10993.2	−	33833.5i	0.528860	−	1.62766i
$757$			12825.4i			0.615782i	0.951422	+	0.307891i	$0.0996232\pi$
$757$			12825.4i			0.615782i	−0.951422	+	0.307891i	$0.900377\pi$
$758$	−8462.63	−	2749.68i	−0.405510	−	0.131758i
$759$	−3620.97	+	2630.79i	−0.173166	+	0.125812i
$760$	882.386	−	152.264i	0.0421151	−	0.00726738i
$761$	14330.7	+	10411.9i	0.682638	+	0.495966i	0.874232	−	0.485509i	$-0.161366\pi$
$761$	14330.7	+	10411.9i	0.682638	+	0.495966i	−0.191594	+	0.981474i	$0.561366\pi$
$762$	−10800.4	−	14865.4i	−0.513459	−	0.706715i
$763$	−28030.4	−	38580.5i	−1.32997	−	1.83055i
$764$	−3462.81	−	2515.88i	−0.163979	−	0.119138i
$765$	−9645.47	−	4748.14i	−0.455860	−	0.224404i
$766$	−5330.25	+	3872.66i	−0.251423	+	0.182669i
$767$	15690.5	+	5098.17i	0.738661	+	0.240005i
$768$			10942.0i			0.514110i
$769$	635.990	−	1957.38i	0.0298236	−	0.0917877i	−0.935037	−	0.354551i	$-0.884634\pi$
$769$	635.990	−	1957.38i	0.0298236	−	0.0917877i	0.964860	+	0.262763i	$0.0846338\pi$
$770$	−10432.6	+	21193.0i	−0.488267	+	0.991875i
$771$	−8574.48	−	26389.5i	−0.400522	−	1.23268i
$772$	−9381.73	+	3048.31i	−0.437378	+	0.142113i
$773$	−8418.84	+	11587.5i	−0.391726	+	0.539165i	−0.958643	−	0.284610i	$-0.908136\pi$
$773$	−8418.84	+	11587.5i	−0.391726	+	0.539165i	0.566917	+	0.823775i	$0.308136\pi$
$774$	23009.8			1.06857
$775$	9752.60	+	2873.85i	0.452030	+	0.133202i
$776$	1988.63			0.0919944
$777$	−22900.3	+	31519.5i	−1.05733	+	1.45529i
$778$	39437.3	−	12813.9i	1.81735	−	0.590491i
$779$	−1343.07	−	4133.55i	−0.0617721	−	0.190115i
$780$	14829.4	−	7815.52i	0.680740	−	0.358770i
$781$	−2454.84	+	7555.23i	−0.112473	+	0.346156i
$782$		−	18846.3i		−	0.861820i
$783$	40907.4	+	13291.6i	1.86707	+	0.606646i
$784$	−15974.4	+	11606.0i	−0.727695	+	0.528701i
$785$	−6163.58	+	6336.05i	−0.280239	+	0.288081i
$786$	2566.76	+	1864.86i	0.116480	+	0.0846276i
$787$	14804.9	+	20377.1i	0.670567	+	0.922956i	0.999773	−	0.0213017i	$-0.00678105\pi$
$787$	14804.9	+	20377.1i	0.670567	+	0.922956i	−0.329206	+	0.944258i	$0.606781\pi$
$788$	484.586	+	666.975i	0.0219069	+	0.0301523i
$789$	14538.1	+	10562.5i	0.655982	+	0.476599i
$790$	5374.53	+	10197.8i	0.242047	+	0.459267i
$791$	999.436	−	726.133i	0.0449252	−	0.0326401i
$792$	−961.599	−	312.442i	−0.0431426	−	0.0140179i
$793$			9932.31i			0.444775i
$794$	−16716.1	+	51446.9i	−0.747144	+	2.29947i
$795$	−2580.66	−	372.315i	−0.115128	−	0.0166096i
$796$	−4479.16	−	13785.4i	−0.199447	−	0.613834i
$797$	−10935.0	+	3553.00i	−0.485995	+	0.157909i	−0.541758	−	0.840535i	$-0.682241\pi$
$797$	−10935.0	+	3553.00i	−0.485995	+	0.157909i	0.0557627	+	0.998444i	$0.482241\pi$
$798$	−4777.57	+	6575.76i	−0.211935	+	0.291703i
$799$	13624.7			0.603265
$800$	−32458.5	+	895.915i	−1.43448	+	0.0395942i
$801$	6816.97			0.300706
$802$	8131.70	−	11192.3i	0.358030	−	0.492787i
$803$	6150.42	−	1998.39i	0.270291	−	0.0878229i
$804$	4626.58	+	14239.1i	0.202944	+	0.624596i
$805$	−3102.79	−	17980.9i	−0.135850	−	0.787260i
$806$	−4616.66	+	14208.6i	−0.201755	+	0.620939i
$807$		−	6306.91i		−	0.275110i
$808$	−811.901	−	263.803i	−0.0353497	−	0.0114858i
$809$	1971.05	−	1432.05i	0.0856593	−	0.0622351i	−0.544131	−	0.839000i	$-0.683141\pi$
$809$	1971.05	−	1432.05i	0.0856593	−	0.0622351i	0.629791	+	0.776765i	$0.283141\pi$
$810$	−1387.65	+	9618.36i	−0.0601939	+	0.417228i
$811$	−24879.8	−	18076.2i	−1.07725	−	0.782666i	−0.100047	−	0.994983i	$-0.531899\pi$
$811$	−24879.8	−	18076.2i	−1.07725	−	0.782666i	−0.977201	+	0.212317i	$0.931899\pi$
$812$	40120.5	+	55221.1i	1.73393	+	2.38655i
$813$	8862.48	+	12198.2i	0.382313	+	0.526209i
$814$	25373.4	+	18434.9i	1.09255	+	0.793786i
$815$	−242.452	+	1680.53i	−0.0104205	+	0.0722287i
$816$	12417.5	−	9021.85i	0.532720	−	0.387044i
$817$	−8150.60	−	2648.29i	−0.349025	−	0.113405i
$818$		−	63761.6i		−	2.72539i
$819$	4726.33	−	14546.1i	0.201650	−	0.620614i
$820$	−3728.76	−	21608.5i	−0.158798	−	0.920247i
$821$	3820.85	+	11759.4i	0.162422	+	0.499885i	0.998837	−	0.0482124i	$-0.0153524\pi$
$821$	3820.85	+	11759.4i	0.162422	+	0.499885i	−0.836415	+	0.548097i	$0.815352\pi$
$822$	32733.6	−	10635.8i	1.38895	−	0.451297i
$823$	3253.78	−	4478.45i	0.137813	−	0.189683i	−0.734532	−	0.678574i	$-0.762598\pi$
$823$	3253.78	−	4478.45i	0.137813	−	0.189683i	0.872345	+	0.488891i	$0.162598\pi$
$824$	2331.34			0.0985633
$825$	2564.61	−	8703.18i	0.108228	−	0.367280i
$826$	−40360.1			−1.70013
$827$	12038.4	−	16569.4i	0.506185	−	0.696703i	−0.477085	−	0.878857i	$-0.658307\pi$
$827$	12038.4	−	16569.4i	0.506185	−	0.696703i	0.983270	+	0.182154i	$0.0583068\pi$
$828$	6824.47	−	2217.41i	0.286433	−	0.0930678i
$829$	−9881.86	−	30413.2i	−0.414006	−	1.27418i	−0.913137	−	0.407653i	$-0.866347\pi$
$829$	−9881.86	−	30413.2i	−0.414006	−	1.27418i	0.499130	−	0.866527i	$-0.333653\pi$
$830$	48371.6	+	6978.61i	2.02290	+	0.291845i
$831$	2219.10	−	6829.68i	0.0926350	−	0.285101i
$832$		−	28017.2i		−	1.16745i
$833$	25222.3	+	8195.23i	1.04910	+	0.340874i
$834$	8603.73	−	6250.98i	0.357222	−	0.259537i
$835$	9358.87	+	17757.8i	0.387877	+	0.735969i
$836$	2799.09	+	2033.66i	0.115800	+	0.0841335i
$837$	−7158.22	−	9852.45i	−0.295609	−	0.406870i
$838$	30090.7	+	41416.3i	1.24041	+	1.70728i
$839$	11465.9	+	8330.46i	0.471808	+	0.342788i	0.798145	−	0.602465i	$-0.205815\pi$
$839$	11465.9	+	8330.46i	0.471808	+	0.342788i	−0.326338	+	0.945253i	$0.605815\pi$
$840$	−3112.25	+	3199.34i	−0.127837	+	0.131414i
$841$	−47035.6	+	34173.4i	−1.92856	+	1.40118i
$842$	−65948.4	−	21427.9i	−2.69921	−	0.877025i
$843$		−	2000.39i		−	0.0817284i
$844$	10218.4	−	31449.1i	0.416745	−	1.28261i
$845$	−2075.00	+	1093.58i	−0.0844758	+	0.0445212i
$846$	3031.62	+	9330.36i	0.123202	+	0.379178i
$847$	24055.8	−	7816.19i	0.975875	−	0.317081i
$848$	−2020.68	+	2781.23i	−0.0818283	+	0.112627i
$849$	−5405.25			−0.218501
$850$	23300.5	+	30277.0i	0.940236	+	1.22176i
$851$	−24226.7			−0.975888
$852$	−8106.20	+	11157.2i	−0.325955	+	0.448639i
$853$	−32931.0	+	10699.9i	−1.32185	+	0.429494i	−0.883128	−	0.469131i	$-0.844567\pi$
$853$	−32931.0	+	10699.9i	−1.32185	+	0.429494i	−0.438717	+	0.898625i	$0.644567\pi$
$854$	−7508.50	−	23108.8i	−0.300861	−	0.925956i
$855$	−1273.38	+	2586.76i	−0.0509340	+	0.103468i
$856$	−1300.16	+	4001.49i	−0.0519143	+	0.159776i
$857$		−	18153.2i		−	0.723573i	−0.932261	−	0.361787i	$-0.882167\pi$
$857$		−	18153.2i		−	0.723573i	0.932261	−	0.361787i	$-0.117833\pi$
$858$	12679.7	+	4119.88i	0.504520	+	0.163928i
$859$	−9103.82	+	6614.31i	−0.361604	+	0.262721i	−0.753721	−	0.657195i	$-0.771743\pi$
$859$	−9103.82	+	6614.31i	−0.361604	+	0.262721i	0.392117	+	0.919916i	$0.371743\pi$
$860$	−38792.3	−	19096.1i	−1.53815	−	0.757178i
$861$	17527.1	+	12734.2i	0.693753	+	0.504041i
$862$	−30227.7	−	41604.9i	−1.19439	−	1.64393i
$863$	−3397.50	−	4676.26i	−0.134012	−	0.184452i	0.736737	−	0.676179i	$-0.236366\pi$
$863$	−3397.50	−	4676.26i	−0.134012	−	0.184452i	−0.870749	+	0.491728i	$0.836366\pi$
$864$	31465.6	+	22861.1i	1.23899	+	0.900175i
$865$	−16900.6	+	2916.36i	−0.664320	+	0.114635i
$866$	13898.7	−	10098.0i	0.545378	−	0.396240i
$867$	−2100.25	−	682.412i	−0.0822701	−	0.0267312i
$868$		−	19325.8i		−	0.755715i
$869$	−1498.10	+	4610.67i	−0.0584804	+	0.179984i
$870$	−35540.1	−	34572.7i	−1.38497	−	1.34727i
$871$	6132.12	+	18872.7i	0.238552	+	0.734188i
$872$	−6898.75	+	2241.54i	−0.267914	+	0.0870505i
$873$	−3763.72	+	5180.31i	−0.145914	+	0.200833i
$874$	−5054.29			−0.195611
$875$	27215.3	+	25050.6i	1.05148	+	0.967847i
$876$	11226.8			0.433012
$877$	4802.82	−	6610.52i	0.184926	−	0.254528i	−0.706482	−	0.707731i	$-0.749719\pi$
$877$	4802.82	−	6610.52i	0.184926	−	0.254528i	0.891407	+	0.453203i	$0.149719\pi$
$878$	−54894.0	+	17836.2i	−2.11000	+	0.685582i
$879$	4134.33	+	12724.2i	0.158643	+	0.488254i
$880$	−8574.88	−	8341.47i	−0.328476	−	0.319535i
$881$	4845.20	−	14912.0i	0.185288	−	0.570259i	−0.814665	−	0.579932i	$-0.803079\pi$
$881$	4845.20	−	14912.0i	0.185288	−	0.570259i	0.999953	+	0.00967301i	$0.00307906\pi$
$882$			19096.0i			0.729020i
$883$	−5689.20	−	1848.53i	−0.216825	−	0.0704508i	0.198590	−	0.980083i	$-0.436364\pi$
$883$	−5689.20	−	1848.53i	−0.216825	−	0.0704508i	−0.415415	+	0.909632i	$0.636364\pi$
$884$	−24015.5	+	17448.3i	−0.913721	+	0.663857i
$885$	15276.7	−	2636.14i	0.580248	−	0.100128i
$886$	−24574.3	−	17854.3i	−0.931816	−	0.677004i
$887$	−14454.3	−	19894.7i	−0.547158	−	0.753099i	0.442465	−	0.896786i	$-0.354104\pi$
$887$	−14454.3	−	19894.7i	−0.547158	−	0.753099i	−0.989623	+	0.143687i	$0.954104\pi$
$888$	3483.33	+	4794.39i	0.131636	+	0.181182i
$889$	25487.1	+	18517.5i	0.961541	+	0.698600i
$890$	−21734.6	−	10699.2i	−0.818589	−	0.402964i
$891$	−3306.43	+	2402.26i	−0.124320	+	0.0903241i
$892$	42277.7	+	13736.9i	1.58695	+	0.515632i
$893$		−	3653.94i		−	0.136926i
$894$	1587.91	−	4887.09i	0.0594046	−	0.182829i
$895$	15004.5	−	30480.4i	0.560385	−	1.13838i
$896$	4183.27	+	12874.8i	0.155975	+	0.480041i
$897$	−9794.49	+	3182.42i	−0.364580	+	0.118459i
$898$	10775.6	−	14831.3i	0.400430	−	0.551145i
$899$	23366.5			0.866869
$900$	−8222.18	+	11999.7i	−0.304525	+	0.444433i
$901$	4617.34			0.170728
$902$	10251.1	−	14109.4i	0.378408	−	0.520834i
$903$	40628.0	−	13200.8i	1.49725	−	0.486485i
$904$	−58.0676	−	178.714i	−0.00213639	−	0.00657514i
$905$	−34469.4	+	18166.4i	−1.26608	+	0.667261i
$906$	−15100.9	+	46475.9i	−0.553747	+	1.70426i
$907$		−	2239.16i		−	0.0819737i	−0.999160	−	0.0409868i	$-0.986950\pi$
$907$		−	2239.16i		−	0.0819737i	0.999160	−	0.0409868i	$-0.0130502\pi$
$908$	−3147.61	−	1022.72i	−0.115041	−	0.0373791i
$909$	2223.82	−	1615.70i	0.0811433	−	0.0589541i
$910$	−37899.0	+	38959.6i	−1.38059	+	1.41923i
$911$	8447.01	+	6137.11i	0.307203	+	0.223196i	0.730695	−	0.682704i	$-0.239196\pi$
$911$	8447.01	+	6137.11i	0.307203	+	0.223196i	−0.423492	+	0.905900i	$0.639196\pi$
$912$	−2419.52	−	3330.18i	−0.0878489	−	0.120914i
$913$	12081.2	+	16628.3i	0.437929	+	0.602757i
$914$	21164.1	+	15376.6i	0.765916	+	0.556471i
$915$	4351.40	+	8256.47i	0.157216	+	0.298307i
$916$	−7500.00	+	5449.07i	−0.270532	+	0.196553i
$917$	−5173.41	−	1680.94i	−0.186304	−	0.0605339i
$918$		−	45761.8i		−	1.64528i
$919$	−11493.8	+	35374.2i	−0.412562	+	1.26973i	0.501852	+	0.864953i	$0.332652\pi$
$919$	−11493.8	+	35374.2i	−0.412562	+	1.26973i	−0.914414	+	0.404781i	$0.867348\pi$
$920$	−2747.04	−	396.317i	−0.0984425	−	0.0142024i
$921$	−294.265	−	905.654i	−0.0105281	−	0.0324021i
$922$	60132.8	−	19538.3i	2.14790	−	0.697897i
$923$	−10744.1	+	14787.9i	−0.383147	+	0.527357i
$924$	−17246.3			−0.614027
$925$	38920.7	−	29952.5i	1.38346	−	1.06468i
$926$	4713.07			0.167258
$927$	−4412.34	+	6073.07i	−0.156333	+	0.215173i
$928$	−70972.8	+	23060.5i	−2.51056	+	0.815729i
$929$	−1682.80	−	5179.13i	−0.0594305	−	0.182908i	0.916934	−	0.399039i	$-0.130656\pi$
$929$	−1682.80	−	5179.13i	−0.0594305	−	0.182908i	−0.976364	+	0.216131i	$0.930656\pi$
$930$	2387.16	+	13833.8i	0.0841700	+	0.487773i
$931$	2197.83	−	6764.23i	0.0773695	−	0.238119i
$932$		−	12637.4i		−	0.444155i
$933$	−28777.9	−	9350.50i	−1.00980	−	0.328105i
$934$	35416.9	−	25731.9i	1.24077	−	0.901471i
$935$	−2294.31	+	15902.8i	−0.0802479	+	0.556231i
$936$	−1882.14	−	1367.46i	−0.0657263	−	0.0477530i
$937$	16010.7	+	22036.8i	0.558214	+	0.768315i	0.991098	−	0.133134i	$-0.0425041\pi$
$937$	16010.7	+	22036.8i	0.558214	+	0.768315i	−0.432884	+	0.901449i	$0.642504\pi$
$938$	−28534.3	−	39274.1i	−0.993260	−	1.36711i
$939$	−2077.76	−	1509.58i	−0.0722101	−	0.0524637i
$940$	2632.37	−	18246.0i	0.0913388	−	0.633106i
$941$	16926.4	−	12297.7i	0.586381	−	0.426031i	−0.254638	−	0.967037i	$-0.581956\pi$
$941$	16926.4	−	12297.7i	0.586381	−	0.426031i	0.841019	+	0.541006i	$0.181956\pi$
$942$	−11607.6	−	3771.53i	−0.401482	−	0.130449i
$943$			13471.8i			0.465218i
$944$	6316.21	−	19439.3i	0.217770	−	0.670228i
$945$	−7534.05	−	43660.5i	−0.259347	−	1.50294i
$946$	−10626.8	−	32705.8i	−0.365228	−	1.12406i
$947$	−2549.10	+	828.252i	−0.0874705	+	0.0284209i	−0.352425	−	0.935840i	$-0.614643\pi$
$947$	−2549.10	+	828.252i	−0.0874705	+	0.0284209i	0.264955	+	0.964261i	$0.414643\pi$
$948$	−4946.90	+	6808.83i	−0.169481	+	0.233271i
$949$	14880.1			0.508988
$950$	8119.82	−	6248.83i	0.277307	−	0.213409i
$951$	17153.2			0.584891
$952$	4645.91	−	6394.55i	0.158167	−	0.217698i
$953$	−34211.1	+	11115.9i	−1.16286	+	0.377837i	−0.825974	−	0.563708i	$-0.809374\pi$
$953$	−34211.1	+	11115.9i	−1.16286	+	0.377837i	−0.336888	+	0.941545i	$0.609374\pi$
$954$	1027.39	+	3162.00i	0.0348670	+	0.107310i
$955$	−5276.15	−	761.194i	−0.178777	−	0.0257923i
$956$	−12162.7	+	37432.9i	−0.411474	+	1.26639i
$957$		−	20852.1i		−	0.704340i
$958$	56752.1	+	18439.9i	1.91396	+	0.621885i
$959$	−47740.7	+	34685.6i	−1.60754	+	1.16794i
$960$	−12274.5	−	23290.0i	−0.412664	−	0.783001i
$961$	18749.1	+	13622.0i	0.629355	+	0.457253i
$962$	42417.8	+	58383.1i	1.42163	+	1.95670i
$963$	−7963.04	−	10960.2i	−0.266465	−	0.366757i
$964$	−2011.79	−	1461.65i	−0.0672151	−	0.0488346i
$965$	−8566.55	+	8806.26i	−0.285769	+	0.293765i
$966$	20382.3	−	14808.6i	0.678872	−	0.493229i
$967$	−55891.5	−	18160.2i	−1.85868	−	0.603923i	−0.994998	−	0.0998944i	$-0.968149\pi$
$967$	−55891.5	−	18160.2i	−1.85868	−	0.603923i	−0.863687	−	0.504029i	$-0.831851\pi$
$968$		−	3847.40i		−	0.127748i
$969$	−1708.46	+	5258.11i	−0.0566395	+	0.174319i
$970$	20130.3	−	10609.3i	0.666337	−	0.351179i
$971$	−9169.69	−	28221.4i	−0.303058	−	0.932717i	−0.980395	−	0.197044i	$-0.936866\pi$
$971$	−9169.69	−	28221.4i	−0.303058	−	0.932717i	0.677337	−	0.735673i	$-0.263134\pi$
$972$	27766.5	−	9021.90i	0.916268	−	0.297714i
$973$	−10717.5	+	14751.3i	−0.353120	+	0.486028i
$974$	24293.0			0.799178
$975$	11800.5	−	17222.0i	0.387608	−	0.565686i
$976$	12305.3			0.403569
$977$	22514.1	−	30988.0i	0.737247	−	1.01473i	−0.261526	−	0.965197i	$-0.584226\pi$
$977$	22514.1	−	30988.0i	0.737247	−	1.01473i	0.998772	−	0.0495366i	$-0.0157744\pi$
$978$	−2229.66	+	724.460i	−0.0729004	+	0.0236868i
$979$	−3148.32	−	9689.52i	−0.102779	−	0.316321i
$980$	15848.0	−	32193.9i	0.516577	−	1.04939i
$981$	7217.57	−	22213.4i	0.234902	−	0.722955i
$982$			69236.2i			2.24992i
$983$	10808.9	+	3512.01i	0.350711	+	0.113953i	0.479075	−	0.877774i	$-0.340972\pi$
$983$	10808.9	+	3512.01i	0.350711	+	0.113953i	−0.128363	+	0.991727i	$0.540972\pi$
$984$	2666.02	−	1936.98i	0.0863716	−	0.0627527i
$985$	921.200	+	453.476i	0.0297989	+	0.0146690i
$986$	71034.2	+	51609.4i	2.29431	+	1.66691i
$987$	10705.7	+	14735.2i	0.345255	+	0.475203i
$988$	4679.36	+	6440.58i	0.150678	+	0.207391i
$989$	21490.6	+	15613.8i	0.690962	+	0.502013i
$990$	−11400.9	+	1967.33i	−0.366003	+	0.0631575i
$991$	22004.4	−	15987.1i	0.705340	−	0.512459i	−0.176327	−	0.984332i	$-0.556422\pi$
$991$	22004.4	−	15987.1i	0.705340	−	0.512459i	0.881667	+	0.471872i	$0.156422\pi$
$992$	20094.7	+	6529.18i	0.643154	+	0.208973i
$993$		−	27729.2i		−	0.886164i
$994$	13818.2	−	42528.1i	0.440933	−	1.35705i
$995$	−12939.9	−	12587.6i	−0.412282	−	0.401060i
$996$	11026.3	+	33935.5i	0.350785	+	1.07961i
$997$	−33121.2	+	10761.7i	−1.05211	+	0.341853i	−0.783498	−	0.621394i	$-0.786567\pi$
$997$	−33121.2	+	10761.7i	−1.05211	+	0.341853i	−0.268617	+	0.963247i	$0.586567\pi$
$998$	−16615.9	+	22869.9i	−0.527023	+	0.725385i
$999$	−58826.2			−1.86304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.9.1	✓	24
3.2	odd	2		225.4.m.a.109.6		24
5.2	odd	4		125.4.d.b.76.2		48
5.3	odd	4		125.4.d.b.76.11		48
5.4	even	2		125.4.e.a.49.6		24
25.2	odd	20		125.4.d.b.51.2		48
25.8	odd	20		625.4.a.g.1.3		24
25.11	even	5		125.4.e.a.74.6		24
25.14	even	10	inner	25.4.e.a.14.1	yes	24
25.17	odd	20		625.4.a.g.1.22		24
25.23	odd	20		125.4.d.b.51.11		48
75.14	odd	10		225.4.m.a.64.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.9.1	✓	24	1.1	even	1	trivial
25.4.e.a.14.1	yes	24	25.14	even	10	inner
125.4.d.b.51.2		48	25.2	odd	20
125.4.d.b.51.11		48	25.23	odd	20
125.4.d.b.76.2		48	5.2	odd	4
125.4.d.b.76.11		48	5.3	odd	4
125.4.e.a.49.6		24	5.4	even	2
125.4.e.a.74.6		24	25.11	even	5
225.4.m.a.64.6		24	75.14	odd	10
225.4.m.a.109.6		24	3.2	odd	2
625.4.a.g.1.3		24	25.8	odd	20
625.4.a.g.1.22		24	25.17	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42187 + 3.33341i) q^{2} +(-3.56321 + 1.15776i) q^{3} +(-2.77407 - 8.53772i) q^{4} +(-8.01402 - 7.79587i) q^{5} +(4.77034 - 14.6816i) q^{6} +26.4674i q^{7} +(3.82887 + 1.24408i) q^{8} +(-10.4874 + 7.61952i) q^{9} +O(q^{10})\)	\(q+(-2.42187 + 3.33341i) q^{2} +(-3.56321 + 1.15776i) q^{3} +(-2.77407 - 8.53772i) q^{4} +(-8.01402 - 7.79587i) q^{5} +(4.77034 - 14.6816i) q^{6} +26.4674i q^{7} +(3.82887 + 1.24408i) q^{8} +(-10.4874 + 7.61952i) q^{9} +(45.3957 - 7.83348i) q^{10} +(15.6737 + 11.3876i) q^{11} +(19.7692 + 27.2100i) q^{12} +(26.2024 + 36.0645i) q^{13} +(-88.2266 - 64.1004i) q^{14} +(37.5814 + 18.5000i) q^{15} +(44.6809 - 32.4626i) q^{16} +(-70.5478 - 22.9224i) q^{17} -53.4122i q^{18} +(-6.14742 + 18.9198i) q^{19} +(-44.3274 + 90.0477i) q^{20} +(-30.6428 - 94.3088i) q^{21} +(-75.9192 + 24.6676i) q^{22} +(36.2441 - 49.8857i) q^{23} -15.0834 q^{24} +(3.44892 + 124.952i) q^{25} -183.676 q^{26} +(88.0062 - 121.130i) q^{27} +(225.971 - 73.4224i) q^{28} +(88.7735 + 273.217i) q^{29} +(-152.685 + 80.4696i) q^{30} +(25.1347 - 77.3567i) q^{31} +259.767i q^{32} +(-69.0328 - 22.4301i) q^{33} +(247.267 - 179.650i) q^{34} +(206.336 - 212.110i) q^{35} +(94.1461 + 68.4011i) q^{36} +(-230.938 - 317.858i) q^{37} +(-48.1793 - 66.3131i) q^{38} +(-135.119 - 98.1694i) q^{39} +(-20.9860 - 39.8194i) q^{40} +(-176.752 + 128.418i) q^{41} +(388.583 + 126.258i) q^{42} +430.797i q^{43} +(53.7442 - 165.408i) q^{44} +(143.447 + 20.6952i) q^{45} +(78.5113 + 241.633i) q^{46} +(-174.686 + 56.7589i) q^{47} +(-121.624 + 167.401i) q^{48} -357.521 q^{49} +(-424.871 - 291.121i) q^{50} +277.915 q^{51} +(235.221 - 323.754i) q^{52} +(-59.1999 + 19.2352i) q^{53} +(190.638 + 586.722i) q^{54} +(-36.8330 - 213.451i) q^{55} +(-32.9274 + 101.340i) q^{56} -74.5325i q^{57} +(-1125.74 - 365.776i) q^{58} +(299.411 - 217.535i) q^{59} +(53.6947 - 372.180i) q^{60} +(180.255 + 130.963i) q^{61} +(196.989 + 271.132i) q^{62} +(-201.669 - 277.573i) q^{63} +(-508.464 - 369.421i) q^{64} +(71.1676 - 493.291i) q^{65} +(241.957 - 175.792i) q^{66} +(423.363 + 137.559i) q^{67} +665.905i q^{68} +(-71.3898 + 219.715i) q^{69} +(207.332 + 1201.50i) q^{70} +(126.710 + 389.973i) q^{71} +(-49.6341 + 16.1271i) q^{72} +(196.202 - 270.049i) q^{73} +1618.85 q^{74} +(-156.954 - 441.239i) q^{75} +178.585 q^{76} +(-301.400 + 414.841i) q^{77} +(654.478 - 212.653i) q^{78} +(77.3261 + 237.985i) q^{79} +(-611.147 - 88.1707i) q^{80} +(-65.1884 + 200.629i) q^{81} -900.197i q^{82} +(1008.98 + 327.838i) q^{83} +(-720.177 + 523.239i) q^{84} +(386.671 + 733.681i) q^{85} +(-1436.03 - 1043.33i) q^{86} +(-632.638 - 870.752i) q^{87} +(45.8455 + 63.1010i) q^{88} +(-425.441 - 309.101i) q^{89} +(-416.395 + 428.046i) q^{90} +(-954.531 + 693.507i) q^{91} +(-526.453 - 171.055i) q^{92} +304.738i q^{93} +(233.865 - 719.763i) q^{94} +(196.762 - 103.699i) q^{95} +(-300.748 - 925.606i) q^{96} +(469.781 - 152.641i) q^{97} +(865.868 - 1191.77i) q^{98} -251.144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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