LMFDB - Embedded newform 25.4.d.a.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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([4]))

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.3
Character	$\chi$	$=$	25.6
Dual form			25.4.d.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624983 - 1.92350i) q^{2} +(1.69858 - 1.23409i) q^{3} +(3.16288 - 2.29797i) q^{4} +(-9.66664 - 5.61749i) q^{5} +(-3.43535 - 2.49593i) q^{6} +24.6755 q^{7} +(-19.4867 - 14.1579i) q^{8} +(-6.98127 + 21.4861i) q^{9} +O(q^{10})$	\(q+(-0.624983 - 1.92350i) q^{2} +(1.69858 - 1.23409i) q^{3} +(3.16288 - 2.29797i) q^{4} +(-9.66664 - 5.61749i) q^{5} +(-3.43535 - 2.49593i) q^{6} +24.6755 q^{7} +(-19.4867 - 14.1579i) q^{8} +(-6.98127 + 21.4861i) q^{9} +(-4.76375 + 22.1046i) q^{10} +(21.6207 + 66.5415i) q^{11} +(2.53650 - 7.80655i) q^{12} +(4.46967 - 13.7562i) q^{13} +(-15.4218 - 47.4634i) q^{14} +(-23.3520 + 2.38775i) q^{15} +(-5.38901 + 16.5857i) q^{16} +(9.49076 + 6.89544i) q^{17} +45.6918 q^{18} +(-59.4245 - 43.1745i) q^{19} +(-43.4833 + 4.44618i) q^{20} +(41.9133 - 30.4518i) q^{21} +(114.480 - 83.1747i) q^{22} +(-38.8648 - 119.614i) q^{23} -50.5718 q^{24} +(61.8877 + 108.604i) q^{25} -29.2536 q^{26} +(32.1751 + 99.0248i) q^{27} +(78.0459 - 56.7037i) q^{28} +(-49.7823 + 36.1690i) q^{29} +(19.1874 + 43.4253i) q^{30} +(18.6697 + 13.5643i) q^{31} -157.425 q^{32} +(118.842 + 86.3441i) q^{33} +(7.33182 - 22.5650i) q^{34} +(-238.530 - 138.615i) q^{35} +(27.2936 + 84.0009i) q^{36} +(-42.8519 + 131.885i) q^{37} +(-45.9068 + 141.287i) q^{38} +(-9.38431 - 28.8819i) q^{39} +(108.839 + 246.326i) q^{40} +(105.295 - 324.066i) q^{41} +(-84.7691 - 61.5884i) q^{42} -302.771 q^{43} +(221.294 + 160.780i) q^{44} +(188.184 - 168.482i) q^{45} +(-205.787 + 149.513i) q^{46} +(65.5264 - 47.6077i) q^{47} +(11.3145 + 34.8225i) q^{48} +265.883 q^{49} +(170.222 - 186.917i) q^{50} +24.6303 q^{51} +(-17.4743 - 53.7805i) q^{52} +(-29.7628 + 21.6239i) q^{53} +(170.365 - 123.778i) q^{54} +(164.797 - 764.687i) q^{55} +(-480.845 - 349.355i) q^{56} -154.218 q^{57} +(100.684 + 73.1513i) q^{58} +(-57.6314 + 177.371i) q^{59} +(-68.3726 + 61.2143i) q^{60} +(131.092 + 403.458i) q^{61} +(14.4228 - 44.3887i) q^{62} +(-172.267 + 530.182i) q^{63} +(141.500 + 435.492i) q^{64} +(-120.482 + 107.868i) q^{65} +(91.8084 - 282.557i) q^{66} +(-712.818 - 517.893i) q^{67} +45.8637 q^{68} +(-213.628 - 155.210i) q^{69} +(-117.548 + 545.444i) q^{70} +(316.600 - 230.023i) q^{71} +(440.241 - 319.854i) q^{72} +(141.321 + 434.943i) q^{73} +280.462 q^{74} +(239.148 + 108.098i) q^{75} -287.167 q^{76} +(533.502 + 1641.95i) q^{77} +(-49.6894 + 36.1015i) q^{78} +(-101.556 + 73.7850i) q^{79} +(145.263 - 130.055i) q^{80} +(-316.628 - 230.043i) q^{81} -689.149 q^{82} +(-181.005 - 131.508i) q^{83} +(62.5896 - 192.631i) q^{84} +(-53.0087 - 119.970i) q^{85} +(189.227 + 582.380i) q^{86} +(-39.9233 + 122.871i) q^{87} +(520.775 - 1602.78i) q^{88} +(-156.885 - 482.841i) q^{89} +(-441.686 - 256.673i) q^{90} +(110.292 - 339.442i) q^{91} +(-397.793 - 289.014i) q^{92} +48.4515 q^{93} +(-132.527 - 96.2861i) q^{94} +(331.904 + 751.168i) q^{95} +(-267.398 + 194.276i) q^{96} +(1114.94 - 810.049i) q^{97} +(-166.172 - 511.426i) q^{98} -1580.66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.624983	−	1.92350i	−0.220965	−	0.680060i	−0.998676	−	0.0514386i	$-0.983619\pi$
$2$	−0.624983	−	1.92350i	−0.220965	−	0.680060i	0.777711	−	0.628622i	$-0.216381\pi$
$3$	1.69858	−	1.23409i	0.326891	−	0.237500i	−0.412219	−	0.911085i	$-0.635246\pi$
$3$	1.69858	−	1.23409i	0.326891	−	0.237500i	0.739110	+	0.673584i	$0.235246\pi$
$4$	3.16288	−	2.29797i	0.395360	−	0.287246i
$5$	−9.66664	−	5.61749i	−0.864610	−	0.502443i
$5$	−9.66664	−	5.61749i	−0.864610	−	0.502443i
$6$	−3.43535	−	2.49593i	−0.233746	−	0.169826i
$7$	24.6755			1.33235			0.666177	−	0.745794i	$-0.267929\pi$
$7$	24.6755			1.33235			0.666177	+	0.745794i	$0.267929\pi$
$8$	−19.4867	−	14.1579i	−0.861199	−	0.625698i
$9$	−6.98127	+	21.4861i	−0.258566	+	0.795783i
$10$	−4.76375	+	22.1046i	−0.150643	+	0.699009i
$11$	21.6207	+	66.5415i	0.592625	+	1.82391i	0.566210	+	0.824261i	$0.308409\pi$
$11$	21.6207	+	66.5415i	0.592625	+	1.82391i	0.0264147	+	0.999651i	$0.491591\pi$
$12$	2.53650	−	7.80655i	0.0610187	−	0.187796i
$13$	4.46967	−	13.7562i	0.0953587	−	0.293484i	−0.891988	−	0.452058i	$-0.850690\pi$
$13$	4.46967	−	13.7562i	0.0953587	−	0.293484i	0.987347	+	0.158575i	$0.0506898\pi$
$14$	−15.4218	−	47.4634i	−0.294404	−	0.906081i
$15$	−23.3520	+	2.38775i	−0.401964	+	0.0411010i
$16$	−5.38901	+	16.5857i	−0.0842032	+	0.259151i
$17$	9.49076	+	6.89544i	0.135403	+	0.0983758i	0.653425	−	0.756991i	$-0.273332\pi$
$17$	9.49076	+	6.89544i	0.135403	+	0.0983758i	−0.518022	+	0.855367i	$0.673332\pi$
$18$	45.6918			0.598315
$19$	−59.4245	−	43.1745i	−0.717522	−	0.521311i	0.168069	−	0.985775i	$-0.446247\pi$
$19$	−59.4245	−	43.1745i	−0.717522	−	0.521311i	−0.885592	+	0.464465i	$0.846247\pi$
$20$	−43.4833	+	4.44618i	−0.486158	+	0.0497098i
$21$	41.9133	−	30.4518i	0.435535	−	0.316434i
$22$	114.480	−	83.1747i	1.10942	−	0.806041i
$23$	−38.8648	−	119.614i	−0.352342	−	1.08440i	−0.957534	−	0.288319i	$-0.906904\pi$
$23$	−38.8648	−	119.614i	−0.352342	−	1.08440i	0.605192	−	0.796079i	$-0.293096\pi$
$24$	−50.5718			−0.430122
$25$	61.8877	+	108.604i	0.495102	+	0.868835i
$26$	−29.2536			−0.220658
$27$	32.1751	+	99.0248i	0.229337	+	0.705827i
$28$	78.0459	−	56.7037i	0.526760	−	0.382714i
$29$	−49.7823	+	36.1690i	−0.318770	+	0.231600i	−0.735651	−	0.677361i	$-0.763123\pi$
$29$	−49.7823	+	36.1690i	−0.318770	+	0.231600i	0.416880	+	0.908961i	$0.363123\pi$
$30$	19.1874	+	43.4253i	0.116771	+	0.264278i
$31$	18.6697	+	13.5643i	0.108167	+	0.0785880i	0.640554	−	0.767913i	$-0.278705\pi$
$31$	18.6697	+	13.5643i	0.108167	+	0.0785880i	−0.532387	+	0.846501i	$0.678705\pi$
$32$	−157.425			−0.869657
$33$	118.842	+	86.3441i	0.626903	+	0.455472i
$34$	7.33182	−	22.5650i	0.0369822	−	0.113820i
$35$	−238.530	−	138.615i	−1.15197	−	0.669432i
$36$	27.2936	+	84.0009i	0.126359	+	0.388893i
$37$	−42.8519	+	131.885i	−0.190400	+	0.585992i	−1.00000		0.000991083i	$-0.999685\pi$
$37$	−42.8519	+	131.885i	−0.190400	+	0.585992i	0.809599	+	0.586983i	$0.199685\pi$
$38$	−45.9068	+	141.287i	−0.195975	+	0.603150i
$39$	−9.38431	−	28.8819i	−0.0385306	−	0.118585i
$40$	108.839	+	246.326i	0.430224	+	0.973689i
$41$	105.295	−	324.066i	0.401082	−	1.23440i	−0.523040	−	0.852308i	$-0.675202\pi$
$41$	105.295	−	324.066i	0.401082	−	1.23440i	0.924122	−	0.382097i	$-0.124798\pi$
$42$	−84.7691	−	61.5884i	−0.311432	−	0.226269i
$43$	−302.771			−1.07377			−0.536885	−	0.843656i	$-0.680399\pi$
$43$	−302.771			−1.07377			−0.536885	+	0.843656i	$0.680399\pi$
$44$	221.294	+	160.780i	0.758212	+	0.550873i
$45$	188.184	−	168.482i	0.623394	−	0.558128i
$46$	−205.787	+	149.513i	−0.659601	+	0.479228i
$47$	65.5264	−	47.6077i	0.203362	−	0.147751i	−0.481443	−	0.876477i	$-0.659887\pi$
$47$	65.5264	−	47.6077i	0.203362	−	0.147751i	0.684805	+	0.728726i	$0.259887\pi$
$48$	11.3145	+	34.8225i	0.0340231	+	0.104712i
$49$	265.883			0.775168
$50$	170.222	−	186.917i	0.481460	−	0.528681i
$51$	24.6303			0.0676262
$52$	−17.4743	−	53.7805i	−0.0466011	−	0.143423i
$53$	−29.7628	+	21.6239i	−0.0771365	+	0.0560430i	−0.625685	−	0.780076i	$-0.715181\pi$
$53$	−29.7628	+	21.6239i	−0.0771365	+	0.0560430i	0.548549	+	0.836119i	$0.315181\pi$
$54$	170.365	−	123.778i	0.429330	−	0.311926i
$55$	164.797	−	764.687i	0.404023	−	1.87473i
$56$	−480.845	−	349.355i	−1.14742	−	0.833651i
$57$	−154.218			−0.358363
$58$	100.684	+	73.1513i	0.227939	+	0.165608i
$59$	−57.6314	+	177.371i	−0.127169	+	0.391386i	−0.994290	−	0.106712i	$-0.965968\pi$
$59$	−57.6314	+	177.371i	−0.127169	+	0.391386i	0.867121	+	0.498097i	$0.165968\pi$
$60$	−68.3726	+	61.2143i	−0.147114	+	0.131712i
$61$	131.092	+	403.458i	0.275157	+	0.846845i	0.989178	+	0.146721i	$0.0468719\pi$
$61$	131.092	+	403.458i	0.275157	+	0.846845i	−0.714021	+	0.700124i	$0.753128\pi$
$62$	14.4228	−	44.3887i	0.0295434	−	0.0909253i
$63$	−172.267	+	530.182i	−0.344501	+	1.06027i
$64$	141.500	+	435.492i	0.276367	+	0.850570i
$65$	−120.482	+	107.868i	−0.229907	+	0.205837i
$66$	91.8084	−	282.557i	0.171225	−	0.526975i
$67$	−712.818	−	517.893i	−1.29977	−	0.944338i	−0.299817	−	0.953997i	$-0.596926\pi$
$67$	−712.818	−	517.893i	−1.29977	−	0.944338i	−0.999953	+	0.00965840i	$0.996926\pi$
$68$	45.8637			0.0817910
$69$	−213.628	−	155.210i	−0.372722	−	0.270799i
$70$	−117.548	+	545.444i	−0.200710	+	0.931328i
$71$	316.600	−	230.023i	0.529204	−	0.384489i	−0.290856	−	0.956767i	$-0.593940\pi$
$71$	316.600	−	230.023i	0.529204	−	0.384489i	0.820060	+	0.572277i	$0.193940\pi$
$72$	440.241	−	319.854i	0.720597	−	0.523544i
$73$	141.321	+	434.943i	0.226581	+	0.697345i	0.998127	+	0.0611717i	$0.0194837\pi$
$73$	141.321	+	434.943i	0.226581	+	0.697345i	−0.771546	+	0.636173i	$0.780516\pi$
$74$	280.462			0.440582
$75$	239.148	+	108.098i	0.368193	+	0.166428i
$76$	−287.167			−0.433424
$77$	533.502	+	1641.95i	0.789586	+	2.43010i
$78$	−49.6894	+	36.1015i	−0.0721310	+	0.0524062i
$79$	−101.556	+	73.7850i	−0.144633	+	0.105082i	−0.657749	−	0.753237i	$-0.728491\pi$
$79$	−101.556	+	73.7850i	−0.144633	+	0.105082i	0.513116	+	0.858319i	$0.328491\pi$
$80$	145.263	−	130.055i	0.203012	−	0.181757i
$81$	−316.628	−	230.043i	−0.434331	−	0.315560i
$82$	−689.149			−0.928095
$83$	−181.005	−	131.508i	−0.239372	−	0.173914i	0.461632	−	0.887072i	$-0.347264\pi$
$83$	−181.005	−	131.508i	−0.239372	−	0.173914i	−0.701003	+	0.713158i	$0.747264\pi$
$84$	62.5896	−	192.631i	0.0812986	−	0.250211i
$85$	−53.0087	−	119.970i	−0.0676423	−	0.153089i
$86$	189.227	+	582.380i	0.237265	+	0.730228i
$87$	−39.9233	+	122.871i	−0.0491981	+	0.151416i
$88$	520.775	−	1602.78i	0.630850	−	1.94156i
$89$	−156.885	−	482.841i	−0.186851	−	0.575068i	0.813124	−	0.582090i	$-0.197765\pi$
$89$	−156.885	−	482.841i	−0.186851	−	0.575068i	−0.999975	+	0.00702180i	$0.997765\pi$
$90$	−441.686	−	256.673i	−0.517309	−	0.300619i
$91$	110.292	−	339.442i	0.127052	−	0.391025i
$92$	−397.793	−	289.014i	−0.450792	−	0.327519i
$93$	48.4515			0.0540235
$94$	−132.527	−	96.2861i	−0.145416	−	0.105651i
$95$	331.904	+	751.168i	0.358448	+	0.811245i
$96$	−267.398	+	194.276i	−0.284283	+	0.206544i
$97$	1114.94	−	810.049i	1.16706	−	0.847918i	0.176405	−	0.984318i	$-0.443553\pi$
$97$	1114.94	−	810.049i	1.16706	−	0.847918i	0.990654	+	0.136400i	$0.0435532\pi$
$98$	−166.172	−	511.426i	−0.171285	−	0.527161i
$99$	−1580.66			−1.60467
$100$	445.313	+	201.287i	0.445313	+	0.201287i
$101$	1821.29			1.79430			0.897152	−	0.441721i	$-0.145632\pi$
$101$	1821.29			1.79430			0.897152	+	0.441721i	$0.145632\pi$
$102$	−15.3936	−	47.3765i	−0.0149430	−	0.0459899i
$103$	252.398	−	183.378i	0.241452	−	0.175425i	−0.460478	−	0.887671i	$-0.652322\pi$
$103$	252.398	−	183.378i	0.241452	−	0.175425i	0.701930	+	0.712246i	$0.252322\pi$
$104$	−281.859	+	204.782i	−0.265755	+	0.193082i
$105$	−576.223	+	58.9190i	−0.535558	+	0.0547610i
$106$	60.1949	+	43.7342i	0.0551571	+	0.0400740i
$107$	854.893			0.772389			0.386194	−	0.922417i	$-0.373789\pi$
$107$	854.893			0.772389			0.386194	+	0.922417i	$0.373789\pi$
$108$	329.322	+	239.267i	0.293417	+	0.213180i
$109$	426.475	−	1312.56i	0.374761	−	1.15340i	−0.568879	−	0.822421i	$-0.692623\pi$
$109$	426.475	−	1312.56i	0.374761	−	1.15340i	0.943640	−	0.330974i	$-0.107377\pi$
$110$	−1573.87	+	160.929i	−1.36421	+	0.139491i
$111$	89.9700	+	276.899i	0.0769331	+	0.236776i
$112$	−132.977	+	409.260i	−0.112189	+	0.345281i
$113$	−211.223	+	650.078i	−0.175843	+	0.541188i	−0.999671	−	0.0256514i	$-0.991834\pi$
$113$	−211.223	+	650.078i	−0.175843	+	0.541188i	0.823828	+	0.566839i	$0.191834\pi$
$114$	96.3838	+	296.639i	0.0791857	+	0.243708i
$115$	−296.236	+	1374.58i	−0.240210	+	1.11461i
$116$	−74.3405	+	228.796i	−0.0595029	+	0.183131i
$117$	264.364	+	192.072i	0.208893	+	0.151770i
$118$	377.192			0.294266
$119$	234.190	+	170.149i	0.180404	+	0.131071i
$120$	488.859	+	284.086i	0.371888	+	0.216112i
$121$	−2883.52	+	2095.00i	−2.16643	+	1.57401i
$122$	694.122	−	504.309i	0.515106	−	0.374246i
$123$	−221.073	−	680.394i	−0.162061	−	0.498773i
$124$	90.2206			0.0653391
$125$	11.8375	−	1397.49i	0.00847025	−	0.999964i
$126$	1127.47			0.797167
$127$	−13.5277	−	41.6339i	−0.00945186	−	0.0290898i	0.946219	−	0.323526i	$-0.104868\pi$
$127$	−13.5277	−	41.6339i	−0.00945186	−	0.0290898i	−0.955671	+	0.294436i	$0.904868\pi$
$128$	−269.640	+	195.905i	−0.186196	+	0.135279i
$129$	−514.279	+	373.645i	−0.351006	+	0.255020i
$130$	282.784	+	164.332i	0.190783	+	0.110868i
$131$	540.138	+	392.433i	0.360245	+	0.261733i	0.753154	−	0.657844i	$-0.228531\pi$
$131$	540.138	+	392.433i	0.360245	+	0.261733i	−0.392909	+	0.919577i	$0.628531\pi$
$132$	574.301			0.378685
$133$	−1466.33	−	1065.35i	−0.955994	−	0.694570i
$134$	−550.668	+	1694.78i	−0.355003	+	1.09259i
$135$	245.245	−	1137.98i	0.156351	−	0.725494i
$136$	−87.3186	−	268.739i	−0.0550552	−	0.169442i
$137$	312.800	−	962.699i	0.195068	−	0.600357i	−0.804908	−	0.593400i	$-0.797785\pi$
$137$	312.800	−	962.699i	0.195068	−	0.600357i	0.999976	−	0.00695745i	$-0.00221464\pi$
$138$	−165.033	+	507.918i	−0.101801	+	0.313311i
$139$	−80.0687	−	246.426i	−0.0488586	−	0.150371i	0.923651	−	0.383235i	$-0.125190\pi$
$139$	−80.0687	−	246.426i	−0.0488586	−	0.150371i	−0.972509	+	0.232864i	$0.925190\pi$
$140$	−1072.97	+	109.712i	−0.647734	+	0.0662311i
$141$	52.5495	−	161.731i	0.0313863	−	0.0965970i
$142$	−640.320	−	465.220i	−0.378412	−	0.274932i
$143$	1012.00			0.591801
$144$	−318.740	−	231.578i	−0.184456	−	0.134015i
$145$	684.406	−	69.9808i	0.391978	−	0.0400799i
$146$	748.289	−	543.664i	0.424170	−	0.308178i
$147$	451.622	−	328.122i	0.253395	−	0.184103i
$148$	167.531	+	515.608i	0.0930472	+	0.286370i
$149$	1055.12			0.580127			0.290063	−	0.957007i	$-0.406324\pi$
$149$	1055.12			0.580127			0.290063	+	0.957007i	$0.406324\pi$
$150$	58.4627	−	527.561i	0.0318231	−	0.287168i
$151$	313.918			0.169181			0.0845905	−	0.996416i	$-0.473042\pi$
$151$	313.918			0.169181			0.0845905	+	0.996416i	$0.473042\pi$
$152$	546.728	+	1682.66i	0.291747	+	0.897905i
$153$	−214.414	+	155.781i	−0.113296	+	0.0823146i
$154$	2824.86	−	2052.38i	1.47814	−	1.07393i
$155$	−104.276	−	235.998i	−0.0540364	−	0.122296i
$156$	−96.0513	−	69.7854i	−0.0492965	−	0.0358160i
$157$	−3275.54			−1.66507			−0.832537	−	0.553970i	$-0.813112\pi$
$157$	−3275.54			−1.66507			−0.832537	+	0.553970i	$0.813112\pi$
$158$	205.397	+	149.229i	0.103421	+	0.0751396i
$159$	−23.8685	+	73.4598i	−0.0119050	+	0.0366399i
$160$	1521.77	+	884.331i	0.751914	+	0.436953i
$161$	−959.011	−	2951.53i	−0.469445	−	1.44480i
$162$	−244.602	+	752.807i	−0.118628	+	0.365099i
$163$	36.5484	−	112.484i	0.0175625	−	0.0540518i	−0.941891	−	0.335918i	$-0.890953\pi$
$163$	36.5484	−	112.484i	0.0175625	−	0.0540518i	0.959454	+	0.281866i	$0.0909535\pi$
$164$	−411.657	−	1266.95i	−0.196006	−	0.603244i
$165$	−663.770	−	1502.25i	−0.313178	−	0.708789i
$166$	−139.830	+	430.353i	−0.0653790	+	0.201216i
$167$	−790.053	−	574.007i	−0.366085	−	0.265976i	0.389501	−	0.921026i	$-0.372648\pi$
$167$	−790.053	−	574.007i	−0.366085	−	0.265976i	−0.755585	+	0.655050i	$0.772648\pi$
$168$	−1247.89			−0.573075
$169$	1608.15	+	1168.39i	0.731977	+	0.531813i
$170$	−197.633	+	176.941i	−0.0891631	+	0.0798281i
$171$	1342.51	−	975.392i	0.600377	−	0.436199i
$172$	−957.628	+	695.758i	−0.424526	+	0.308436i
$173$	629.937	+	1938.75i	0.276839	+	0.852024i	0.988727	+	0.149731i	$0.0478406\pi$
$173$	629.937	+	1938.75i	0.276839	+	0.852024i	−0.711887	+	0.702294i	$0.752159\pi$
$174$	261.295			0.113843
$175$	1527.11	+	2679.87i	0.659651	+	1.15760i
$176$	−1220.15			−0.522569
$177$	121.000	+	372.400i	0.0513838	+	0.158143i
$178$	−830.695	+	603.536i	−0.349794	+	0.254140i
$179$	−2464.37	+	1790.47i	−1.02903	+	0.747632i	−0.968114	−	0.250511i	$-0.919401\pi$
$179$	−2464.37	+	1790.47i	−1.02903	+	0.747632i	−0.0609131	+	0.998143i	$0.519401\pi$
$180$	208.037	−	965.328i	0.0861454	−	0.399729i
$181$	−2005.28	−	1456.92i	−0.823488	−	0.598299i	0.0942214	−	0.995551i	$-0.469964\pi$
$181$	−2005.28	−	1456.92i	−0.823488	−	0.598299i	−0.917709	+	0.397252i	$0.869964\pi$
$182$	−721.848			−0.293994
$183$	720.572	+	523.526i	0.291072	+	0.211476i
$184$	−936.133	+	2881.12i	−0.375069	+	1.15434i
$185$	1155.09	−	1034.16i	0.459050	−	0.410989i
$186$	−30.2814	−	93.1965i	−0.0119373	−	0.0367392i
$187$	−253.637	+	780.613i	−0.0991858	+	0.305263i
$188$	97.8514	−	301.156i	0.0379603	−	0.116830i
$189$	793.938	+	2443.49i	0.305558	+	0.940412i
$190$	1237.44	−	1107.88i	0.472491	−	0.423023i
$191$	62.4210	−	192.112i	0.0236472	−	0.0727787i	−0.938536	−	0.345180i	$-0.887818\pi$
$191$	62.4210	−	192.112i	0.0236472	−	0.0727787i	0.962184	+	0.272401i	$0.0878178\pi$
$192$	777.783	+	565.093i	0.292352	+	0.212406i
$193$	3183.41			1.18729			0.593644	−	0.804728i	$-0.297689\pi$
$193$	3183.41			1.18729			0.593644	+	0.804728i	$0.297689\pi$
$194$	−2254.95	−	1638.32i	−0.834514	−	0.606310i
$195$	−71.5292	+	331.908i	−0.0262683	+	0.121889i
$196$	840.956	−	610.990i	0.306471	−	0.222664i
$197$	−2713.55	+	1971.51i	−0.981384	+	0.713017i	−0.958018	−	0.286710i	$-0.907439\pi$
$197$	−2713.55	+	1971.51i	−0.981384	+	0.713017i	−0.0233667	+	0.999727i	$0.507439\pi$
$198$	987.887	+	3040.40i	0.354576	+	1.09127i
$199$	3948.50			1.40654			0.703271	−	0.710922i	$-0.251722\pi$
$199$	3948.50			1.40654			0.703271	+	0.710922i	$0.251722\pi$
$200$	331.625	−	2992.54i	0.117247	−	1.05802i
$201$	−1849.90			−0.649164
$202$	−1138.27	−	3503.25i	−0.396479	−	1.22024i
$203$	−1228.41	+	892.489i	−0.424715	+	0.308574i
$204$	77.9029	−	56.5998i	0.0267367	−	0.0194254i
$205$	−2838.29	+	2541.13i	−0.966998	+	0.865758i
$206$	−510.473	−	370.880i	−0.172652	−	0.125439i
$207$	2841.36			0.954050
$208$	204.069	+	148.265i	0.0680271	+	0.0494246i
$209$	1588.10	−	4887.66i	0.525603	−	1.61764i
$210$	473.461	+	1071.54i	0.155580	+	0.352111i
$211$	730.537	+	2248.36i	0.238352	+	0.733571i	0.996659	+	0.0816742i	$0.0260267\pi$
$211$	730.537	+	2248.36i	0.238352	+	0.733571i	−0.758307	+	0.651897i	$0.773973\pi$
$212$	−44.4451	+	136.788i	−0.0143986	+	0.0443143i
$213$	253.900	−	781.424i	0.0816758	−	0.251372i
$214$	−534.294	−	1644.39i	−0.170671	−	0.525271i
$215$	2926.77	+	1700.81i	0.928392	+	0.539508i
$216$	774.999	−	2385.20i	0.244130	−	0.751354i
$217$	460.685	+	334.708i	0.144117	+	0.104707i
$218$	−2791.24			−0.867187
$219$	776.802	+	564.380i	0.239687	+	0.174143i
$220$	−1235.99	−	2797.31i	−0.378775	−	0.857249i
$221$	137.276	−	99.7367i	0.0417836	−	0.0303575i
$222$	476.386	−	346.115i	0.144022	−	0.104638i
$223$	−1798.29	−	5534.56i	−0.540010	−	1.66198i	−0.732567	−	0.680695i	$-0.761678\pi$
$223$	−1798.29	−	5534.56i	−0.540010	−	1.66198i	0.192557	−	0.981286i	$-0.438322\pi$
$224$	−3884.54			−1.15869
$225$	−2765.54	+	571.532i	−0.819421	+	0.169343i
$226$	1382.44			0.406896
$227$	−1826.25	−	5620.63i	−0.533976	−	1.64341i	−0.745851	−	0.666113i	$-0.767957\pi$
$227$	−1826.25	−	5620.63i	−0.533976	−	1.64341i	0.211875	−	0.977297i	$-0.432043\pi$
$228$	−487.774	+	354.389i	−0.141683	+	0.102938i
$229$	−237.314	+	172.419i	−0.0684810	+	0.0497544i	−0.621499	−	0.783415i	$-0.713476\pi$
$229$	−237.314	+	172.419i	−0.0684810	+	0.0497544i	0.553018	+	0.833169i	$0.313476\pi$
$230$	2829.16	−	289.282i	0.811083	−	0.0829336i
$231$	2932.50	+	2130.59i	0.835257	+	0.606850i
$232$	1482.17			0.419437
$233$	593.999	+	431.566i	0.167014	+	0.121343i	0.668152	−	0.744024i	$-0.267085\pi$
$233$	593.999	+	431.566i	0.167014	+	0.121343i	−0.501139	+	0.865367i	$0.667085\pi$
$234$	204.227	−	628.547i	0.0570545	−	0.175596i
$235$	−900.856	+	92.1129i	−0.250065	+	0.0255693i
$236$	225.312	+	693.440i	0.0621465	+	0.191267i
$237$	−81.4440	+	250.659i	−0.0223222	+	0.0687006i
$238$	180.917	−	556.804i	0.0492735	−	0.151648i
$239$	1014.68	+	3122.86i	0.274620	+	0.845193i	0.989320	+	0.145762i	$0.0465633\pi$
$239$	1014.68	+	3122.86i	0.274620	+	0.845193i	−0.714700	+	0.699431i	$0.753437\pi$
$240$	86.2416	−	400.175i	0.0231953	−	0.107630i
$241$	−1696.25	+	5220.53i	−0.453383	+	1.39537i	0.419641	+	0.907690i	$0.362156\pi$
$241$	−1696.25	+	5220.53i	−0.453383	+	1.39537i	−0.873023	+	0.487678i	$0.837844\pi$
$242$	5831.89	+	4237.12i	1.54913	+	1.12551i
$243$	−3632.97			−0.959075
$244$	1341.76	+	974.847i	0.352039	+	0.255771i
$245$	−2570.19	−	1493.59i	−0.670218	−	0.389478i
$246$	−1170.57	+	850.470i	−0.303386	+	0.220423i
$247$	−859.526	+	624.482i	−0.221418	+	0.160870i
$248$	−171.768	−	528.649i	−0.0439811	−	0.135360i
$249$	−469.742			−0.119553
$250$	−2695.48	+	850.640i	−0.681908	+	0.215197i
$251$	−3690.21			−0.927985			−0.463992	−	0.885839i	$-0.653583\pi$
$251$	−3690.21			−0.927985			−0.463992	+	0.885839i	$0.653583\pi$
$252$	673.483	+	2072.77i	0.168355	+	0.518144i
$253$	7118.99	−	5172.25i	1.76904	−	1.28528i
$254$	−71.6282	+	52.0410i	−0.0176943	+	0.0128557i
$255$	−238.092	−	138.361i	−0.0584703	−	0.0339783i
$256$	3508.96	+	2549.41i	0.856679	+	0.622414i
$257$	3524.02			0.855340			0.427670	−	0.903935i	$-0.359335\pi$
$257$	3524.02			0.855340			0.427670	+	0.903935i	$0.359335\pi$
$258$	1040.12	+	755.694i	0.250989	+	0.182354i
$259$	−1057.39	+	3254.33i	−0.253681	+	0.780749i
$260$	−133.193	+	618.038i	−0.0317703	+	0.147420i
$261$	−429.588	−	1322.14i	−0.101881	−	0.313556i
$262$	417.268	−	1284.22i	0.0983929	−	0.302822i
$263$	−1099.90	+	3385.15i	−0.257882	+	0.793678i	0.735367	+	0.677670i	$0.237010\pi$
$263$	−1099.90	+	3385.15i	−0.257882	+	0.793678i	−0.993248	+	0.116009i	$0.962990\pi$
$264$	−1093.40	−	3365.12i	−0.254901	−	0.784504i
$265$	409.178	−	41.8387i	0.0948514	−	0.00969860i
$266$	−1132.77	+	3486.32i	−0.261109	+	0.803609i
$267$	−862.349	−	626.533i	−0.197659	−	0.143607i
$268$	−3444.66			−0.785135
$269$	−2127.08	−	1545.42i	−0.482121	−	0.350282i	0.320025	−	0.947409i	$-0.396309\pi$
$269$	−2127.08	−	1545.42i	−0.482121	−	0.350282i	−0.802146	+	0.597127i	$0.796309\pi$
$270$	−2342.18	+	239.489i	−0.527928	+	0.0539809i
$271$	4727.31	−	3434.59i	1.05964	−	0.769877i	0.0856217	−	0.996328i	$-0.472712\pi$
$271$	4727.31	−	3434.59i	1.05964	−	0.769877i	0.974023	+	0.226451i	$0.0727124\pi$
$272$	−165.511	+	120.251i	−0.0368955	+	0.0268062i
$273$	−231.563	−	712.678i	−0.0513364	−	0.157997i
$274$	−2047.25			−0.451382
$275$	−5888.65	+	6466.20i	−1.29127	+	1.41792i
$276$	−1032.35			−0.225146
$277$	22.0820	+	67.9613i	0.00478981	+	0.0147415i	0.953423	−	0.301637i	$-0.0975331\pi$
$277$	22.0820	+	67.9613i	0.00478981	+	0.0147415i	−0.948633	+	0.316378i	$0.897533\pi$
$278$	−423.960	+	308.025i	−0.0914655	+	0.0664536i
$279$	−421.784	+	306.444i	−0.0905073	+	0.0657574i
$280$	2685.66	+	6078.23i	0.573211	+	1.29730i
$281$	3643.38	+	2647.07i	0.773473	+	0.561961i	0.903013	−	0.429613i	$-0.141350\pi$
$281$	3643.38	+	2647.07i	0.773473	+	0.561961i	−0.129540	+	0.991574i	$0.541350\pi$
$282$	−343.932			−0.0726271
$283$	−3719.97	−	2702.72i	−0.781375	−	0.567702i	0.124016	−	0.992280i	$-0.460423\pi$
$283$	−3719.97	−	2702.72i	−0.781375	−	0.567702i	−0.905391	+	0.424578i	$0.860423\pi$
$284$	472.782	−	1455.07i	0.0987833	−	0.304024i
$285$	1490.77	+	866.318i	0.309844	+	0.180057i
$286$	−632.482	−	1946.58i	−0.130767	−	0.402460i
$287$	2598.22	−	7996.50i	0.534384	−	1.64466i
$288$	1099.02	−	3382.45i	0.224863	−	0.692058i
$289$	−1475.67	−	4541.65i	−0.300361	−	0.924416i
$290$	−562.351	−	1272.72i	−0.113870	−	0.257713i
$291$	894.133	−	2751.86i	0.180120	−	0.554353i
$292$	1446.47	+	1050.92i	0.289891	+	0.210618i
$293$	7847.20			1.56464			0.782318	−	0.622880i	$-0.214037\pi$
$293$	7847.20			1.56464			0.782318	+	0.622880i	$0.214037\pi$
$294$	−913.400	−	663.624i	−0.181192	−	0.131644i
$295$	1553.48	−	1390.84i	0.306601	−	0.274501i
$296$	2702.26	−	1963.30i	0.530627	−	0.385523i
$297$	−5893.62	+	4281.96i	−1.15146	+	0.836581i
$298$	−659.433	−	2029.53i	−0.128188	−	0.394521i
$299$	−1819.14			−0.351852
$300$	1004.80	−	207.654i	0.193375	−	0.0399631i
$301$	−7471.03			−1.43064
$302$	−196.194	−	603.822i	−0.0373831	−	0.115053i
$303$	3093.59	−	2247.63i	0.586542	−	0.426148i
$304$	1036.32	−	752.928i	0.195516	−	0.142051i
$305$	999.207	−	4636.49i	0.187588	−	0.870441i
$306$	433.650	+	315.065i	0.0810134	+	0.0588597i
$307$	3211.49			0.597033			0.298517	−	0.954404i	$-0.403508\pi$
$307$	3211.49			0.597033			0.298517	+	0.954404i	$0.403508\pi$
$308$	5460.55	+	3967.32i	1.01021	+	0.733959i
$309$	202.413	−	622.963i	0.0372650	−	0.114690i
$310$	−388.773	+	348.070i	−0.0712284	+	0.0637711i
$311$	582.245	+	1791.97i	0.106161	+	0.326730i	0.990001	−	0.141059i	$-0.0450507\pi$
$311$	582.245	+	1791.97i	0.106161	+	0.326730i	−0.883840	+	0.467789i	$0.845051\pi$
$312$	−226.039	+	695.677i	−0.0410158	+	0.126234i
$313$	−1638.90	+	5044.03i	−0.295963	+	0.910880i	0.686934	+	0.726720i	$0.258956\pi$
$313$	−1638.90	+	5044.03i	−0.295963	+	0.910880i	−0.982896	+	0.184160i	$0.941044\pi$
$314$	2047.16	+	6300.51i	0.367923	+	1.13235i
$315$	4643.53	−	4157.37i	0.830582	−	0.743624i
$316$	−151.655	+	466.747i	−0.0269977	+	0.0830904i
$317$	2033.48	+	1477.41i	0.360289	+	0.261765i	0.753173	−	0.657823i	$-0.228523\pi$
$317$	2033.48	+	1477.41i	0.360289	+	0.261765i	−0.392884	+	0.919588i	$0.628523\pi$
$318$	156.217			0.0275479
$319$	−3483.07	−	2530.60i	−0.611330	−	0.444157i
$320$	1078.54	−	5004.61i	0.188413	−	0.874270i
$321$	1452.10	−	1055.01i	0.252487	−	0.183443i
$322$	−5077.91	+	3689.32i	−0.878822	+	0.638502i
$323$	−266.277	−	819.517i	−0.0458701	−	0.141174i
$324$	−1530.09			−0.262361
$325$	1770.60	−	365.916i	0.302201	−	0.0624534i
$326$	−239.206			−0.0406392
$327$	−895.408	−	2755.78i	−0.151426	−	0.466040i
$328$	−6639.97	+	4824.22i	−1.11778	+	0.812112i
$329$	1616.90	−	1174.75i	0.270950	−	0.196857i
$330$	−2474.74	+	2215.64i	−0.412818	+	0.369598i
$331$	−6464.47	−	4696.71i	−1.07347	−	0.779923i	−0.0969393	−	0.995290i	$-0.530905\pi$
$331$	−6464.47	−	4696.71i	−1.07347	−	0.779923i	−0.976533	+	0.215367i	$0.930905\pi$
$332$	−874.697			−0.144594
$333$	−2534.53	−	1841.45i	−0.417092	−	0.303035i
$334$	−610.333	+	1878.41i	−0.0999879	+	0.307731i
$335$	3981.30	+	9010.53i	0.649318	+	1.46955i
$336$	279.192	+	859.264i	0.0453308	+	0.139514i
$337$	−1954.31	+	6014.74i	−0.315899	+	0.972236i	0.659484	+	0.751718i	$0.270775\pi$
$337$	−1954.31	+	6014.74i	−0.315899	+	0.972236i	−0.975383	+	0.220518i	$0.929225\pi$
$338$	1242.33	−	3823.51i	0.199923	−	0.615301i
$339$	443.475	+	1364.88i	0.0710509	+	0.218672i
$340$	−443.347	−	257.638i	−0.0707173	−	0.0410953i
$341$	−498.941	+	1535.58i	−0.0792351	+	0.243860i
$342$	−2715.21	−	1972.72i	−0.429304	−	0.311908i
$343$	−1902.91			−0.299556
$344$	5900.01	+	4286.61i	0.924730	+	0.671855i
$345$	1193.18	+	2700.41i	0.186199	+	0.421407i
$346$	3335.48	−	2423.37i	0.518256	−	0.376535i
$347$	−3986.00	+	2896.00i	−0.616657	+	0.448027i	−0.851752	−	0.523945i	$-0.824460\pi$
$347$	−3986.00	+	2896.00i	−0.616657	+	0.448027i	0.235095	+	0.971972i	$0.424460\pi$
$348$	156.082	+	480.371i	0.0240427	+	0.0739959i
$349$	7864.33			1.20621			0.603106	−	0.797661i	$-0.293930\pi$
$349$	7864.33			1.20621			0.603106	+	0.797661i	$0.293930\pi$
$350$	4200.32	−	4612.28i	0.641475	−	0.704391i
$351$	1506.02			0.229018
$352$	−3403.63	−	10475.3i	−0.515380	−	1.58618i
$353$	−7279.84	+	5289.11i	−1.09764	+	0.797481i	−0.980673	−	0.195654i	$-0.937317\pi$
$353$	−7279.84	+	5289.11i	−1.09764	+	0.797481i	−0.116966	+	0.993136i	$0.537317\pi$
$354$	640.690	−	465.488i	0.0961928	−	0.0698882i
$355$	−4352.61	+	445.056i	−0.650740	+	0.0665384i
$356$	−1605.76	−	1166.65i	−0.239060	−	0.173687i
$357$	607.767			0.0901021
$358$	4984.16	+	3621.21i	0.735814	+	0.534600i
$359$	833.066	−	2563.91i	0.122472	−	0.376931i	−0.870960	−	0.491354i	$-0.836502\pi$
$359$	833.066	−	2563.91i	0.122472	−	0.376931i	0.993432	+	0.114423i	$0.0365021\pi$
$360$	−6052.43	+	618.864i	−0.886086	+	0.0906027i
$361$	−452.305	−	1392.05i	−0.0659432	−	0.202952i
$362$	−1549.12	+	4767.71i	−0.224917	+	0.692225i
$363$	−2312.47	+	7117.04i	−0.334361	+	1.02906i
$364$	−431.189	−	1327.06i	−0.0620891	−	0.191091i
$365$	1077.18	−	4998.30i	0.154472	−	0.716776i
$366$	556.657	−	1713.22i	0.0794999	−	0.244675i
$367$	5274.28	+	3831.99i	0.750178	+	0.545036i	0.895882	−	0.444292i	$-0.146545\pi$
$367$	5274.28	+	3831.99i	0.750178	+	0.545036i	−0.145704	+	0.989328i	$0.546545\pi$
$368$	2193.31			0.310691
$369$	6227.83	+	4524.79i	0.878612	+	0.638349i
$370$	−2711.12	−	1575.49i	−0.380932	−	0.221367i
$371$	−734.413	+	533.583i	−0.102773	+	0.0746691i
$372$	153.246	−	111.340i	0.0213588	−	0.0155180i
$373$	4056.14	+	12483.5i	0.563054	+	1.73290i	0.673665	+	0.739037i	$0.264719\pi$
$373$	4056.14	+	12483.5i	0.563054	+	1.73290i	−0.110612	+	0.993864i	$0.535281\pi$
$374$	1660.03			0.229514
$375$	−1704.52	−	2388.35i	−0.234723	−	0.328891i
$376$	−1950.92			−0.267583
$377$	275.038	+	846.480i	0.0375734	+	0.115639i
$378$	4203.86	−	3054.28i	0.572019	−	0.415596i
$379$	−4170.48	+	3030.03i	−0.565233	+	0.410666i	−0.833371	−	0.552715i	$-0.813592\pi$
$379$	−4170.48	+	3030.03i	−0.565233	+	0.410666i	0.268137	+	0.963381i	$0.413592\pi$
$380$	2775.93	+	1613.15i	0.374743	+	0.217771i
$381$	−74.3576	−	54.0240i	−0.00999857	−	0.00726439i
$382$	−408.540			−0.0547191
$383$	−9474.49	−	6883.62i	−1.26403	−	0.918373i	−0.265083	−	0.964226i	$-0.585399\pi$
$383$	−9474.49	−	6883.62i	−1.26403	−	0.918373i	−0.998948	+	0.0458529i	$0.985399\pi$
$384$	−216.240	+	665.519i	−0.0287369	+	0.0884430i
$385$	4066.46	−	18869.1i	0.538301	−	2.49781i
$386$	−1989.58	−	6123.29i	−0.262349	−	0.807428i
$387$	2113.72	−	6505.37i	0.277640	−	0.854488i
$388$	1664.95	−	5124.18i	0.217848	−	0.670466i
$389$	2124.69	+	6539.11i	0.276930	+	0.852304i	0.988702	+	0.149893i	$0.0478929\pi$
$389$	2124.69	+	6539.11i	0.276930	+	0.852304i	−0.711772	+	0.702411i	$0.752107\pi$
$390$	683.129	−	69.8502i	0.0886964	−	0.00906924i
$391$	455.932	−	1403.21i	0.0589705	−	0.181492i
$392$	−5181.18	−	3764.35i	−0.667574	−	0.485021i
$393$	1401.76			0.179922
$394$	5488.13	+	3987.36i	0.701746	+	0.509849i
$395$	1396.19	−	142.762i	0.177849	−	0.0181851i
$396$	−4999.45	+	3632.31i	−0.634423	+	0.460936i
$397$	7893.85	−	5735.22i	0.997937	−	0.725044i	0.0362922	−	0.999341i	$-0.488445\pi$
$397$	7893.85	−	5735.22i	0.997937	−	0.725044i	0.961645	+	0.274297i	$0.0884453\pi$
$398$	−2467.75	−	7594.94i	−0.310796	−	0.956533i
$399$	−3805.42			−0.477466
$400$	−2134.79	+	441.179i	−0.266849	+	0.0551473i
$401$	3300.91			0.411072			0.205536	−	0.978650i	$-0.434106\pi$
$401$	3300.91			0.411072			0.205536	+	0.978650i	$0.434106\pi$
$402$	1156.16	+	3558.29i	0.143442	+	0.441471i
$403$	270.042	−	196.197i	0.0333790	−	0.0242512i
$404$	5760.52	−	4185.26i	0.709397	−	0.515407i
$405$	1768.46	+	4002.40i	0.216976	+	0.491063i
$406$	2484.44	+	1805.05i	0.303696	+	0.220648i
$407$	−9702.30			−1.18163
$408$	−479.964	−	348.715i	−0.0582397	−	0.0423136i
$409$	−480.901	+	1480.06i	−0.0581394	+	0.178935i	−0.975909	−	0.218179i	$-0.929988\pi$
$409$	−480.901	+	1480.06i	−0.0581394	+	0.178935i	0.917769	+	0.397114i	$0.129988\pi$
$410$	6661.75	+	3871.29i	0.802440	+	0.466315i
$411$	−656.740	−	2021.24i	−0.0788190	−	0.242580i
$412$	376.909	−	1160.01i	0.0450703	−	0.138712i
$413$	−1422.09	+	4376.73i	−0.169434	+	0.521465i
$414$	−1775.80	−	5465.36i	−0.210812	−	0.648811i
$415$	1010.96	+	2288.03i	0.119581	+	0.270638i
$416$	−703.636	+	2165.57i	−0.0829293	+	0.255230i
$417$	−440.114	−	319.762i	−0.0516846	−	0.0375511i
$418$	−10394.0			−1.21623
$419$	−10559.9	−	7672.19i	−1.23122	−	0.894537i	−0.234243	−	0.972178i	$-0.575261\pi$
$419$	−10559.9	−	7672.19i	−1.23122	−	0.894537i	−0.996981	+	0.0776416i	$0.975261\pi$
$420$	−1687.13	+	1510.50i	−0.196009	+	0.175487i
$421$	−2036.72	+	1479.76i	−0.235781	+	0.171305i	−0.699401	−	0.714729i	$-0.746550\pi$
$421$	−2036.72	+	1479.76i	−0.235781	+	0.171305i	0.463621	+	0.886034i	$0.346550\pi$
$422$	3868.15	−	2810.38i	0.446205	−	0.324187i
$423$	565.449	+	1740.27i	0.0649955	+	0.200035i
$424$	886.130			0.101496
$425$	−161.514	+	1457.48i	−0.0184343	+	0.166349i
$426$	−1661.75			−0.188996
$427$	3234.76	+	9955.55i	0.366606	+	1.12830i
$428$	2703.93	−	1964.52i	0.305372	−	0.221866i
$429$	1718.95	−	1248.89i	0.193454	−	0.140553i
$430$	1442.32	−	6692.63i	0.161756	−	0.750575i
$431$	4240.31	+	3080.76i	0.473894	+	0.344304i	0.798957	−	0.601388i	$-0.205385\pi$
$431$	4240.31	+	3080.76i	0.473894	+	0.344304i	−0.325063	+	0.945692i	$0.605385\pi$
$432$	−1815.78			−0.202227
$433$	5745.51	+	4174.36i	0.637671	+	0.463295i	0.859049	−	0.511893i	$-0.171055\pi$
$433$	5745.51	+	4174.36i	0.637671	+	0.463295i	−0.221378	+	0.975188i	$0.571055\pi$
$434$	355.890	−	1095.32i	0.0393623	−	0.121145i
$435$	1076.15	−	963.485i	0.118615	−	0.106197i
$436$	−1667.32	−	5131.49i	−0.183143	−	0.563655i
$437$	−2854.73	+	8785.95i	−0.312495	+	0.961760i
$438$	600.097	−	1846.91i	0.0654652	−	0.201481i
$439$	−2031.02	−	6250.83i	−0.220809	−	0.679580i	−0.998690	−	0.0511687i	$-0.983705\pi$
$439$	−2031.02	−	6250.83i	−0.220809	−	0.679580i	0.777881	−	0.628412i	$-0.216295\pi$
$440$	−14037.7	+	12568.0i	−1.52096	+	1.36172i
$441$	−1856.20	+	5712.79i	−0.200432	+	0.616866i
$442$	−277.639	−	201.716i	−0.0298777	−	0.0217074i
$443$	8937.18			0.958506			0.479253	−	0.877677i	$-0.340908\pi$
$443$	8937.18			0.958506			0.479253	+	0.877677i	$0.340908\pi$
$444$	920.870	+	669.051i	0.0984292	+	0.0715130i
$445$	−1195.81	+	5548.75i	−0.127386	+	0.591092i
$446$	−9521.84	+	6918.02i	−1.01092	+	0.734479i
$447$	1792.20	−	1302.11i	0.189638	−	0.137780i
$448$	3491.59	+	10746.0i	0.368219	+	1.13326i
$449$	−485.543			−0.0510338			−0.0255169	−	0.999674i	$-0.508123\pi$
$449$	−485.543			−0.0510338			−0.0255169	+	0.999674i	$0.508123\pi$
$450$	2827.76	+	4962.33i	0.296227	+	0.519837i
$451$	23840.4			2.48914
$452$	825.786	+	2541.51i	0.0859330	+	0.264474i
$453$	533.214	−	387.403i	0.0553037	−	0.0401805i
$454$	−9669.90	+	7025.60i	−0.999628	+	0.726272i
$455$	−2972.96	+	2661.71i	−0.306318	+	0.274248i
$456$	3005.21	+	2183.41i	0.308622	+	0.224227i
$457$	1520.77			0.155664			0.0778322	−	0.996966i	$-0.475200\pi$
$457$	1520.77			0.155664			0.0778322	+	0.996966i	$0.475200\pi$
$458$	479.965	+	348.715i	0.0489679	+	0.0355773i
$459$	−377.453	+	1161.68i	−0.0383835	+	0.118132i
$460$	2221.79	+	5028.39i	0.225199	+	0.509674i
$461$	−817.128	−	2514.86i	−0.0825541	−	0.254076i	0.901257	−	0.433286i	$-0.142646\pi$
$461$	−817.128	−	2514.86i	−0.0825541	−	0.254076i	−0.983811	+	0.179210i	$0.942646\pi$
$462$	2265.42	−	6972.25i	0.228132	−	0.702118i
$463$	3119.90	−	9602.07i	0.313162	−	0.963814i	−0.663342	−	0.748316i	$-0.730863\pi$
$463$	3119.90	−	9602.07i	0.313162	−	0.963814i	0.976504	−	0.215498i	$-0.0691374\pi$
$464$	−331.609	−	1020.59i	−0.0331779	−	0.102111i
$465$	−468.363	−	272.176i	−0.0467093	−	0.0271437i
$466$	458.878	−	1412.28i	0.0456161	−	0.140392i
$467$	−2634.46	−	1914.05i	−0.261046	−	0.189661i	0.449562	−	0.893249i	$-0.351580\pi$
$467$	−2634.46	−	1914.05i	−0.261046	−	0.189661i	−0.710608	+	0.703588i	$0.751580\pi$
$468$	1277.53			0.126183
$469$	−17589.2	−	12779.3i	−1.73175	−	1.25819i
$470$	740.199	+	1675.23i	0.0726444	+	0.164410i
$471$	−5563.75	+	4042.30i	−0.544298	+	0.395455i
$472$	3634.26	−	2640.44i	0.354407	−	0.257492i
$473$	−6546.10	−	20146.8i	−0.636343	−	1.95846i
$474$	533.044			0.0516530
$475$	1011.29	−	9125.74i	0.0976863	−	0.881510i
$476$	1131.71			0.108975
$477$	−256.833	−	790.450i	−0.0246532	−	0.0758747i
$478$	5372.67	−	3903.47i	0.514101	−	0.373516i
$479$	−6468.89	+	4699.92i	−0.617059	+	0.448319i	−0.851893	−	0.523716i	$-0.824545\pi$
$479$	−6468.89	+	4699.92i	−0.617059	+	0.448319i	0.234834	+	0.972035i	$0.424545\pi$
$480$	3676.18	−	375.891i	0.349570	−	0.0357437i
$481$	1622.70	+	1178.96i	0.153823	+	0.111759i
$482$	11101.8			1.04912
$483$	−5271.40	−	3829.90i	−0.496598	−	0.360800i
$484$	−4306.00	+	13252.5i	−0.404395	+	1.24460i
$485$	−15328.1	+	1567.31i	−1.43508	+	0.146738i
$486$	2270.55	+	6988.03i	0.211922	+	0.652229i
$487$	−1813.56	+	5581.55i	−0.168748	+	0.519352i	−0.999293	−	0.0375994i	$-0.988029\pi$
$487$	−1813.56	+	5581.55i	−0.168748	+	0.519352i	0.830545	+	0.556951i	$0.188029\pi$
$488$	3157.59	−	9718.06i	0.292905	−	0.901467i
$489$	−76.7353	−	236.167i	−0.00709630	−	0.0218402i
$490$	−1266.60	+	5877.23i	−0.116774	+	0.541850i
$491$	3956.89	−	12178.0i	0.363690	−	1.11932i	−0.587107	−	0.809509i	$-0.699733\pi$
$491$	3956.89	−	12178.0i	0.363690	−	1.11932i	0.950797	−	0.309813i	$-0.100267\pi$
$492$	−2262.75	−	1643.99i	−0.207343	−	0.150644i
$493$	−721.873			−0.0659463
$494$	1738.38	+	1263.01i	0.158327	+	0.115031i
$495$	15279.7	+	8879.34i	1.38741	+	0.806256i
$496$	−325.585	+	236.551i	−0.0294742	+	0.0214142i
$497$	7812.28	−	5675.95i	0.705088	−	0.512276i
$498$	293.581	+	903.549i	0.0264170	+	0.0813032i
$499$	4755.06			0.426584			0.213292	−	0.976988i	$-0.431581\pi$
$499$	4755.06			0.426584			0.213292	+	0.976988i	$0.431581\pi$
$500$	−3173.95	−	4447.31i	−0.283887	−	0.397779i
$501$	−2050.34			−0.182839
$502$	2306.32	+	7098.13i	0.205052	+	0.631085i
$503$	−7525.95	+	5467.92i	−0.667128	+	0.484697i	−0.869063	−	0.494702i	$-0.835277\pi$
$503$	−7525.95	+	5467.92i	−0.667128	+	0.484697i	0.201934	+	0.979399i	$0.435277\pi$
$504$	10863.2	−	7892.58i	0.960090	−	0.697546i
$505$	−17605.7	−	10231.1i	−1.55137	−	0.901536i
$506$	−14398.1	−	10460.8i	−1.26497	−	0.919052i
$507$	4173.47			0.365582
$508$	−138.460	−	100.597i	−0.0120928	−	0.00878596i
$509$	5607.30	−	17257.5i	0.488289	−	1.50280i	−0.338871	−	0.940833i	$-0.610045\pi$
$509$	5607.30	−	17257.5i	0.488289	−	1.50280i	0.827160	−	0.561966i	$-0.189955\pi$
$510$	−117.333	+	544.444i	−0.0101874	+	0.0472714i
$511$	3487.18	+	10732.4i	0.301886	+	0.929111i
$512$	1886.80	−	5806.97i	0.162862	−	0.501239i
$513$	2363.35	−	7273.65i	0.203401	−	0.626003i
$514$	−2202.45	−	6778.45i	−0.189000	−	0.581683i
$515$	−3469.97	+	354.806i	−0.296903	+	0.0303584i
$516$	−767.978	+	2363.59i	−0.0655201	+	0.201650i
$517$	4584.62	+	3330.92i	0.390002	+	0.283353i
$518$	6920.55			0.587011
$519$	3462.58	+	2515.71i	0.292852	+	0.212770i
$520$	3874.99	−	396.219i	0.326788	−	0.0334142i
$521$	4519.99	−	3283.97i	0.380085	−	0.276148i	−0.381295	−	0.924453i	$-0.624522\pi$
$521$	4519.99	−	3283.97i	0.380085	−	0.276148i	0.761381	+	0.648305i	$0.224522\pi$
$522$	−2274.64	+	1652.63i	−0.190725	+	0.138570i
$523$	4847.96	+	14920.5i	0.405328	+	1.24747i	0.920621	+	0.390457i	$0.127683\pi$
$523$	4847.96	+	14920.5i	0.405328	+	1.24747i	−0.515294	+	0.857014i	$0.672317\pi$
$524$	2610.19			0.217608
$525$	5901.11	+	2667.37i	0.490563	+	0.221741i
$526$	7198.76			0.596732
$527$	83.6576	+	257.472i	0.00691496	+	0.0212821i
$528$	−2072.52	+	1505.77i	−0.170823	+	0.124110i
$529$	−2953.63	+	2145.94i	−0.242758	+	0.176374i
$530$	−336.206	−	760.907i	−0.0275545	−	0.0623616i
$531$	−3408.68	−	2476.55i	−0.278577	−	0.202398i
$532$	−7085.99			−0.577475
$533$	−3987.29	−	2896.93i	−0.324031	−	0.235422i
$534$	−666.183	+	2050.30i	−0.0539861	+	0.166152i
$535$	−8263.94	−	4802.35i	−0.667815	−	0.388082i
$536$	6558.20	+	20184.1i	0.528491	+	1.62653i
$537$	−1976.32	+	6082.50i	−0.158817	+	0.488788i
$538$	−1643.22	+	5057.31i	−0.131681	+	0.405272i
$539$	5748.56	+	17692.2i	0.459384	+	1.41384i
$540$	−1839.36	−	4162.86i	−0.146581	−	0.331743i
$541$	1240.78	−	3818.73i	0.0986052	−	0.303475i	−0.889571	−	0.456796i	$-0.848997\pi$
$541$	1240.78	−	3818.73i	0.0986052	−	0.303475i	0.988176	+	0.153321i	$0.0489968\pi$
$542$	−9560.93	−	6946.42i	−0.757707	−	0.550506i
$543$	−5204.09			−0.411287
$544$	−1494.08	−	1085.51i	−0.117754	−	0.0855532i
$545$	−11495.8	+	10292.3i	−0.903538	+	0.808941i
$546$	−1226.11	+	890.824i	−0.0961041	+	0.0698237i
$547$	15672.5	−	11386.8i	1.22506	−	0.890061i	0.228553	−	0.973531i	$-0.426600\pi$
$547$	15672.5	−	11386.8i	1.22506	−	0.890061i	0.996510	+	0.0834706i	$0.0266005\pi$
$548$	−1222.90	−	3763.71i	−0.0953282	−	0.293390i
$549$	−9583.95			−0.745051
$550$	16118.1	+	7285.56i	1.24959	+	0.564831i
$551$	4519.87			0.349461
$552$	1965.46	+	6049.07i	0.151550	+	0.466423i
$553$	−2505.96	+	1820.69i	−0.192702	+	0.140006i
$554$	116.923	−	84.9494i	0.00896674	−	0.00651472i
$555$	685.770	−	3182.09i	0.0524492	−	0.243373i
$556$	−819.528	−	595.422i	−0.0625103	−	0.0454164i
$557$	−18731.1			−1.42489			−0.712443	−	0.701730i	$-0.752411\pi$
$557$	−18731.1			−1.42489			−0.712443	+	0.701730i	$0.752411\pi$
$558$	853.053	+	619.779i	0.0647179	+	0.0470203i
$559$	−1353.28	+	4164.98i	−0.102393	+	0.315134i
$560$	3584.45	−	3209.17i	0.270483	−	0.242165i
$561$	532.524	+	1638.94i	0.0400770	+	0.123344i
$562$	2814.59	−	8662.42i	0.211257	−	0.650182i
$563$	−4869.99	+	14988.3i	−0.364557	+	1.12199i	0.585700	+	0.810528i	$0.300819\pi$
$563$	−4869.99	+	14988.3i	−0.364557	+	1.12199i	−0.950258	+	0.311464i	$0.899181\pi$
$564$	−205.444	−	632.292i	−0.0153382	−	0.0472062i
$565$	5693.63	−	5097.53i	0.423952	−	0.379566i
$566$	−2873.76	+	8844.52i	−0.213415	+	0.656825i
$567$	−7812.96	−	5676.45i	−0.578683	−	0.420438i
$568$	−9426.15			−0.696325
$569$	17854.6	+	12972.1i	1.31547	+	0.955747i	0.999977	+	0.00681952i	$0.00217074\pi$
$569$	17854.6	+	12972.1i	1.31547	+	0.955747i	0.315496	+	0.948927i	$0.397829\pi$
$570$	734.657	−	3408.93i	0.0539849	−	0.250499i
$571$	−5150.93	+	3742.37i	−0.377513	+	0.274279i	−0.760319	−	0.649549i	$-0.774958\pi$
$571$	−5150.93	+	3742.37i	−0.377513	+	0.274279i	0.382807	+	0.923828i	$0.374958\pi$
$572$	3200.83	−	2325.54i	0.233975	−	0.169992i
$573$	−131.056	−	403.350i	−0.00955489	−	0.0294069i
$574$	−17005.1			−1.23655
$575$	10585.3	−	11623.5i	0.767718	−	0.843015i
$576$	−10344.9			−0.748328
$577$	4745.91	+	14606.4i	0.342417	+	1.05385i	0.962952	+	0.269673i	$0.0869156\pi$
$577$	4745.91	+	14606.4i	0.342417	+	1.05385i	−0.620535	+	0.784179i	$0.713084\pi$
$578$	−7813.61	+	5676.92i	−0.562289	+	0.408527i
$579$	5407.26	−	3928.60i	0.388114	−	0.281981i
$580$	2003.88	−	1794.09i	0.143460	−	0.128440i
$581$	−4466.39	−	3245.02i	−0.318928	−	0.231715i
$582$	−5852.02			−0.416794
$583$	−2082.38	−	1512.94i	−0.147930	−	0.107478i
$584$	3404.00	−	10476.4i	0.241196	−	0.742325i
$585$	−1476.55	−	3341.75i	−0.104355	−	0.236179i
$586$	−4904.37	−	15094.1i	−0.345730	−	1.06405i
$587$	−3553.88	+	10937.7i	−0.249888	+	0.769076i	0.744906	+	0.667170i	$0.232494\pi$
$587$	−3553.88	+	10937.7i	−0.249888	+	0.769076i	−0.994794	+	0.101907i	$0.967506\pi$
$588$	674.412	−	2075.63i	0.0472998	−	0.145574i
$589$	−523.806	−	1612.11i	−0.0366436	−	0.112777i
$590$	−3646.18	−	2118.87i	−0.254425	−	0.147852i
$591$	−2176.16	+	6697.52i	−0.151464	+	0.466158i
$592$	−1956.46	−	1421.45i	−0.135828	−	0.0986849i
$593$	10393.3			0.719733			0.359867	−	0.933004i	$-0.382822\pi$
$593$	10393.3			0.719733			0.359867	+	0.933004i	$0.382822\pi$
$594$	11919.8	+	8660.22i	0.823357	+	0.598204i
$595$	−1308.02	−	2960.32i	−0.0901235	−	0.203969i
$596$	3337.22	−	2424.64i	0.229359	−	0.166639i
$597$	6706.82	−	4872.79i	0.459786	−	0.334054i
$598$	1136.94	+	3499.13i	0.0777471	+	0.239281i
$599$	19024.6			1.29771			0.648853	−	0.760914i	$-0.275249\pi$
$599$	19024.6			1.29771			0.648853	+	0.760914i	$0.275249\pi$
$600$	−3129.77	−	5492.32i	−0.212954	−	0.373705i
$601$	−18115.2			−1.22951			−0.614756	−	0.788718i	$-0.710745\pi$
$601$	−18115.2			−1.22951			−0.614756	+	0.788718i	$0.710745\pi$
$602$	4669.27	+	14370.5i	0.316122	+	0.972922i
$603$	16103.9	−	11700.2i	1.08756	−	0.790162i
$604$	992.887	−	721.375i	0.0668874	−	0.0485966i
$605$	39642.6	−	4053.47i	2.66397	−	0.272392i
$606$	−6256.76	−	4545.80i	−0.419411	−	0.304720i
$607$	−5934.25			−0.396810			−0.198405	−	0.980120i	$-0.563576\pi$
$607$	−5934.25			−0.396810			−0.198405	+	0.980120i	$0.563576\pi$
$608$	9354.89	+	6796.73i	0.623998	+	0.453361i
$609$	−985.130	+	3031.92i	−0.0655493	+	0.201740i
$610$	−9542.78	+	975.753i	−0.633403	+	0.0647657i
$611$	−362.021	−	1114.19i	−0.0239702	−	0.0737728i
$612$	−320.187	+	985.433i	−0.0211483	+	0.0650879i
$613$	−7295.31	+	22452.7i	−0.480677	+	1.47937i	0.357469	+	0.933925i	$0.383640\pi$
$613$	−7295.31	+	22452.7i	−0.480677	+	1.47937i	−0.838146	+	0.545446i	$0.816360\pi$
$614$	−2007.13	−	6177.30i	−0.131923	−	0.406019i
$615$	−1685.07	+	7819.00i	−0.110485	+	0.512671i
$616$	12850.4	−	39549.5i	0.840516	−	2.58684i
$617$	−19325.1	−	14040.5i	−1.26094	−	0.916125i	−0.262134	−	0.965031i	$-0.584426\pi$
$617$	−19325.1	−	14040.5i	−1.26094	−	0.916125i	−0.998803	+	0.0489067i	$0.984426\pi$
$618$	−1324.77			−0.0862302
$619$	2501.76	+	1817.64i	0.162446	+	0.118024i	0.666039	−	0.745917i	$-0.267989\pi$
$619$	2501.76	+	1817.64i	0.162446	+	0.118024i	−0.503592	+	0.863941i	$0.667989\pi$
$620$	−872.129	−	506.813i	−0.0564928	−	0.0328292i
$621$	10594.2	−	7697.16i	0.684593	−	0.497386i
$622$	3082.95	−	2239.90i	0.198738	−	0.144392i
$623$	−3871.21	−	11914.4i	−0.248952	−	0.766195i
$624$	529.598			0.0339758
$625$	−7964.82	+	13442.6i	−0.509749	+	0.860323i
$626$	10726.5			0.684851
$627$	−3334.30	−	10261.9i	−0.212375	−	0.653623i
$628$	−10360.2	+	7527.09i	−0.658304	+	0.478286i
$629$	−1316.10	+	956.202i	−0.0834282	+	0.0606141i
$630$	−10898.8	−	6333.55i	−0.689239	−	0.400531i
$631$	−4809.20	−	3494.09i	−0.303409	−	0.220440i	0.425654	−	0.904886i	$-0.360044\pi$
$631$	−4809.20	−	3494.09i	−0.303409	−	0.220440i	−0.729063	+	0.684446i	$0.760044\pi$
$632$	3023.64			0.190307
$633$	4015.55	+	2917.46i	0.252138	+	0.183189i
$634$	1570.91	−	4834.76i	0.0984049	−	0.302859i
$635$	−103.111	+	478.451i	−0.00644381	+	0.0299004i
$636$	93.3150	+	287.194i	0.00581789	+	0.0179056i
$637$	1188.41	−	3657.54i	0.0739190	−	0.227499i
$638$	−2690.74	+	8281.26i	−0.166971	+	0.513884i
$639$	2732.04	+	8408.37i	0.169136	+	0.520548i
$640$	3707.01	−	379.043i	0.228957	−	0.0234109i
$641$	6095.56	−	18760.2i	0.375601	−	1.15598i	−0.567472	−	0.823393i	$-0.692078\pi$
$641$	6095.56	−	18760.2i	0.375601	−	1.15598i	0.943072	−	0.332587i	$-0.107922\pi$
$642$	−2936.86	−	2133.75i	−0.180543	−	0.131172i
$643$	12498.7			0.766567			0.383283	−	0.923631i	$-0.374793\pi$
$643$	12498.7			0.766567			0.383283	+	0.923631i	$0.374793\pi$
$644$	−9815.77	−	7131.57i	−0.600614	−	0.436372i
$645$	7070.29	−	722.940i	0.431616	−	0.0441330i
$646$	−1409.92	+	1024.37i	−0.0858710	+	0.0623889i
$647$	−18199.0	+	13222.4i	−1.10584	+	0.803438i	−0.982003	−	0.188865i	$-0.939519\pi$
$647$	−18199.0	+	13222.4i	−1.10584	+	0.803438i	−0.123835	+	0.992303i	$0.539519\pi$
$648$	2913.09	+	8965.58i	0.176600	+	0.543520i
$649$	−13048.6			−0.789217
$650$	−1810.44	−	3177.07i	−0.109248	−	0.191715i
$651$	1195.57			0.0719784
$652$	−142.887	−	439.762i	−0.00858266	−	0.0264147i
$653$	13952.0	−	10136.8i	0.836119	−	0.607476i	−0.0851649	−	0.996367i	$-0.527142\pi$
$653$	13952.0	−	10136.8i	0.836119	−	0.607476i	0.921284	+	0.388891i	$0.127142\pi$
$654$	−4741.14	+	3444.64i	−0.283476	+	0.205957i
$655$	−3016.83	−	6827.73i	−0.179965	−	0.407300i
$656$	4807.41	+	3492.79i	0.286125	+	0.207882i
$657$	−10331.8			−0.613522
$658$	−3270.16	−	2375.91i	−0.193745	−	0.140764i
$659$	−4773.36	+	14690.9i	−0.282160	+	0.868400i	0.705075	+	0.709132i	$0.250913\pi$
$659$	−4773.36	+	14690.9i	−0.282160	+	0.868400i	−0.987236	+	0.159267i	$0.949087\pi$
$660$	−5551.56	−	3226.13i	−0.327415	−	0.190268i
$661$	3416.65	+	10515.4i	0.201047	+	0.618760i	0.999853	+	0.0171702i	$0.00546572\pi$
$661$	3416.65	+	10515.4i	0.201047	+	0.618760i	−0.798805	+	0.601590i	$0.794534\pi$
$662$	−4993.95	+	15369.8i	−0.293195	+	0.902362i
$663$	110.089	−	338.820i	0.00644875	−	0.0198472i
$664$	1665.31	+	5125.30i	0.0973292	+	0.299549i
$665$	8189.90	+	18535.5i	0.477580	+	1.08087i
$666$	−1957.98	+	6026.05i	−0.113919	+	0.350608i
$667$	6261.08	+	4548.94i	0.363463	+	0.264072i
$668$	−3817.90			−0.221136
$669$	−9884.66	−	7181.63i	−0.571245	−	0.415034i
$670$	14843.5	−	13289.5i	0.855903	−	0.766294i
$671$	−24012.5	+	17446.1i	−1.38151	+	1.00372i
$672$	−6598.19	+	4793.86i	−0.378766	+	0.275189i
$673$	−3709.51	−	11416.7i	−0.212468	−	0.653910i	−0.999324	−	0.0367725i	$-0.988292\pi$
$673$	−3709.51	−	11416.7i	−0.212468	−	0.653910i	0.786856	−	0.617137i	$-0.211708\pi$
$674$	12790.8			0.730982
$675$	−8763.28	+	9622.78i	−0.499702	+	0.548712i
$676$	7771.34			0.442156
$677$	1969.81	+	6062.44i	0.111825	+	0.344163i	0.991272	−	0.131835i	$-0.0420869\pi$
$677$	1969.81	+	6062.44i	0.111825	+	0.344163i	−0.879446	+	0.475998i	$0.842087\pi$
$678$	2348.17	−	1706.05i	0.133010	−	0.0966378i
$679$	27511.7	−	19988.4i	1.55494	−	1.12973i
$680$	−665.560	+	3088.31i	−0.0375339	+	0.174164i
$681$	−10038.4	−	7293.30i	−0.564862	−	0.410396i
$682$	3265.52			0.183348
$683$	13899.3	+	10098.4i	0.778685	+	0.565748i	0.904584	−	0.426295i	$-0.140181\pi$
$683$	13899.3	+	10098.4i	0.778685	+	0.565748i	−0.125899	+	0.992043i	$0.540181\pi$
$684$	2004.79	−	6170.10i	0.112069	−	0.344912i
$685$	−8431.67	+	7548.91i	−0.470303	+	0.421064i
$686$	1189.29	+	3660.26i	0.0661914	+	0.203716i
$687$	−190.316	+	585.733i	−0.0105692	+	0.0325285i
$688$	1631.63	−	5021.65i	0.0904149	−	0.278268i
$689$	164.434	+	506.076i	0.00909207	+	0.0279825i
$690$	4448.53	−	3982.79i	0.245439	−	0.219743i
$691$	−2400.76	+	7388.77i	−0.132170	+	0.406776i	−0.995139	−	0.0984800i	$-0.968602\pi$
$691$	−2400.76	+	7388.77i	−0.132170	+	0.406776i	0.862969	+	0.505256i	$0.168602\pi$
$692$	6447.60	+	4684.45i	0.354192	+	0.257336i
$693$	−39003.7			−2.13799
$694$	8061.65	+	5857.13i	0.440945	+	0.320365i
$695$	−610.301	+	2831.90i	−0.0333094	+	0.154561i
$696$	2517.58	−	1829.13i	0.137110	−	0.0996163i
$697$	3233.91	−	2349.57i	0.175743	−	0.127685i
$698$	−4915.08	−	15127.0i	−0.266531	−	0.820297i
$699$	1541.54			0.0834142
$700$	10988.3	+	4966.87i	0.593315	+	0.268186i
$701$	−4498.18			−0.242359			−0.121180	−	0.992631i	$-0.538668\pi$
$701$	−4498.18			−0.242359			−0.121180	+	0.992631i	$0.538668\pi$
$702$	−941.237	−	2896.83i	−0.0506050	−	0.155746i
$703$	8240.51	−	5987.08i	0.442100	−	0.321205i
$704$	−25919.0	+	18831.2i	−1.38758	+	1.00814i
$705$	−1416.50	+	1268.20i	−0.0756714	+	0.0677490i
$706$	14723.4	+	10697.2i	0.784875	+	0.570245i
$707$	44941.2			2.39065
$708$	1238.47	+	899.804i	0.0657411	+	0.0477637i
$709$	−5971.07	+	18377.0i	−0.316288	+	0.973434i	0.658933	+	0.752201i	$0.271008\pi$
$709$	−5971.07	+	18377.0i	−0.316288	+	0.973434i	−0.975221	+	0.221232i	$0.928992\pi$
$710$	3576.38	+	8094.10i	0.189041	+	0.427840i
$711$	−876.363	−	2697.17i	−0.0462253	−	0.142267i
$712$	−3778.87	+	11630.2i	−0.198903	+	0.612161i
$713$	896.885	−	2760.33i	0.0471088	−	0.144986i
$714$	−379.844	−	1169.04i	−0.0199094	−	0.0612748i
$715$	−9782.61	−	5684.88i	−0.511677	−	0.297346i
$716$	−3680.07	+	11326.1i	−0.192082	+	0.591168i
$717$	5577.39	+	4052.21i	0.290504	+	0.211064i
$718$	−5452.34			−0.283398
$719$	−24806.5	−	18023.0i	−1.28668	−	0.934830i	−0.286951	−	0.957945i	$-0.592642\pi$
$719$	−24806.5	−	18023.0i	−1.28668	−	0.934830i	−0.999733	+	0.0231151i	$0.992642\pi$
$720$	1780.26	+	4029.10i	0.0921475	+	0.208549i
$721$	6228.07	−	4524.96i	0.321699	−	0.233728i
$722$	−2394.93	+	1740.02i	−0.123449	+	0.0896908i
$723$	3561.38	+	10960.8i	0.183194	+	0.563812i
$724$	−9690.43			−0.497434
$725$	−7009.02	−	3168.16i	−0.359046	−	0.162293i
$726$	15134.9			0.773703
$727$	−7074.66	−	21773.6i	−0.360914	−	1.11078i	−0.952500	−	0.304538i	$-0.901498\pi$
$727$	−7074.66	−	21773.6i	−0.360914	−	1.11078i	0.591586	−	0.806242i	$-0.298502\pi$
$728$	−6955.02	+	5053.12i	−0.354080	+	0.257254i
$729$	2378.07	−	1727.77i	0.120818	−	0.0877796i
$730$	−10287.5	+	1051.90i	−0.521584	+	0.0533322i
$731$	−2873.52	−	2087.74i	−0.145391	−	0.105633i
$732$	3482.13			0.175824
$733$	−7351.45	−	5341.14i	−0.370439	−	0.269140i	0.386954	−	0.922099i	$-0.373527\pi$
$733$	−7351.45	−	5341.14i	−0.370439	−	0.269140i	−0.757393	+	0.652959i	$0.773527\pi$
$734$	4074.50	−	12540.0i	0.204894	−	0.630600i
$735$	−6208.89	+	634.861i	−0.311589	+	0.0318601i
$736$	6118.28	+	18830.1i	0.306417	+	0.943054i
$737$	19049.8	−	58629.2i	0.952114	−	2.93030i
$738$	4811.14	−	14807.2i	0.239973	−	0.738562i
$739$	−7648.31	−	23539.1i	−0.380714	−	1.17172i	−0.939542	−	0.342433i	$-0.888749\pi$
$739$	−7648.31	−	23539.1i	−0.380714	−	1.17172i	0.558828	−	0.829283i	$-0.311251\pi$
$740$	1276.96	−	5925.30i	0.0634350	−	0.294349i
$741$	−689.304	+	2121.46i	−0.0341730	+	0.105174i
$742$	1485.34	+	1079.16i	0.0734887	+	0.0533927i
$743$	13260.5			0.654750			0.327375	−	0.944895i	$-0.393836\pi$
$743$	13260.5			0.654750			0.327375	+	0.944895i	$0.393836\pi$
$744$	−944.161	−	685.973i	−0.0465250	−	0.0338024i
$745$	−10199.5	−	5927.13i	−0.501583	−	0.291481i
$746$	21477.0	−	15604.0i	1.05406	−	0.765821i
$747$	4089.23	−	2971.00i	0.200291	−	0.145520i
$748$	991.603	+	3051.84i	0.0484714	+	0.149180i
$749$	21095.0			1.02910
$750$	−3528.71	+	4771.33i	−0.171800	+	0.232299i
$751$	−30905.1			−1.50166			−0.750828	−	0.660498i	$-0.770345\pi$
$751$	−30905.1			−1.50166			−0.750828	+	0.660498i	$0.770345\pi$
$752$	436.483	+	1343.36i	0.0211661	+	0.0651426i
$753$	−6268.10	+	4554.04i	−0.303350	+	0.220397i
$754$	1456.31	−	1058.07i	0.0703392	−	0.0511044i
$755$	−3034.53	−	1763.43i	−0.146276	−	0.0850038i
$756$	8126.20	+	5904.03i	0.390935	+	0.284031i
$757$	−18407.6			−0.883798			−0.441899	−	0.897065i	$-0.645695\pi$
$757$	−18407.6			−0.883798			−0.441899	+	0.897065i	$0.645695\pi$
$758$	8434.76	+	6128.21i	0.404174	+	0.293650i
$759$	5709.14	−	17570.9i	0.273028	−	0.840295i
$760$	4167.28	−	19336.9i	0.198899	−	0.922924i
$761$	5054.59	+	15556.4i	0.240774	+	0.741025i	0.996303	+	0.0859100i	$0.0273798\pi$
$761$	5054.59	+	15556.4i	0.240774	+	0.741025i	−0.755529	+	0.655115i	$0.772620\pi$
$762$	−57.4429	+	176.791i	−0.00273089	+	0.00840481i
$763$	10523.5	−	32388.0i	0.499314	−	1.53673i
$764$	−244.037	−	751.069i	−0.0115562	−	0.0355664i
$765$	2947.76	−	301.410i	0.139316	−	0.0142451i
$766$	−7319.26	+	22526.4i	−0.345242	+	1.06255i
$767$	2182.36	+	1585.58i	0.102739	+	0.0746441i
$768$	9106.42			0.427864
$769$	16262.9	+	11815.7i	0.762619	+	0.554075i	0.899713	−	0.436483i	$-0.143776\pi$
$769$	16262.9	+	11815.7i	0.762619	+	0.554075i	−0.137093	+	0.990558i	$0.543776\pi$
$770$	−38836.1	+	3971.01i	−1.81761	+	0.185851i
$771$	5985.81	−	4348.95i	0.279603	−	0.203143i
$772$	10068.7	−	7315.37i	0.469407	−	0.341044i
$773$	−2779.12	−	8553.24i	−0.129312	−	0.397980i	0.865350	−	0.501167i	$-0.167096\pi$
$773$	−2779.12	−	8553.24i	−0.129312	−	0.397980i	−0.994662	+	0.103187i	$0.967096\pi$
$774$	−13834.1			−0.642452
$775$	−317.721	+	2867.08i	−0.0147263	+	0.132888i
$776$	−33195.1			−1.53561
$777$	2220.06	+	6832.64i	0.102502	+	0.315469i
$778$	11250.1	−	8173.67i	0.518426	−	0.376659i
$779$	−20248.5	+	14711.4i	−0.931294	+	0.676625i
$780$	536.475	+	1214.16i	0.0246268	+	0.0557356i
$781$	22151.2	+	16093.8i	1.01489	+	0.737364i
$782$	−2984.03			−0.136456
$783$	−5183.38	−	3765.94i	−0.236576	−	0.171882i
$784$	−1432.84	+	4409.84i	−0.0652717	+	0.200885i
$785$	31663.5	+	18400.3i	1.43964	+	0.836605i
$786$	−876.078	−	2696.29i	−0.0397566	−	0.122358i
$787$	−7039.58	+	21665.6i	−0.318849	+	0.981316i	0.655292	+	0.755375i	$0.272545\pi$
$787$	−7039.58	+	21665.6i	−0.318849	+	0.981316i	−0.974141	+	0.225940i	$0.927455\pi$
$788$	−4052.18	+	12471.3i	−0.183189	+	0.563798i
$789$	2309.31	+	7107.31i	0.104200	+	0.320693i
$790$	−1147.20	−	2596.36i	−0.0516653	−	0.116930i
$791$	−5212.05	+	16041.0i	−0.234285	+	0.721054i
$792$	30801.9	+	22378.9i	1.38194	+	1.00404i
$793$	6136.00			0.274774
$794$	−15965.2	−	11599.4i	−0.713583	−	0.518448i
$795$	643.388	−	576.028i	0.0287027	−	0.0256976i
$796$	12488.6	−	9073.53i	0.556091	−	0.404024i
$797$	25934.6	−	18842.6i	1.15263	−	0.837438i	0.163806	−	0.986493i	$-0.447623\pi$
$797$	25934.6	−	18842.6i	1.15263	−	0.837438i	0.988829	+	0.149055i	$0.0476230\pi$
$798$	2378.32	+	7319.72i	0.105503	+	0.324706i
$799$	950.172			0.0420709
$800$	−9742.65	−	17097.0i	−0.430569	−	0.755588i
$801$	11469.7			0.505943
$802$	−2063.02	−	6349.31i	−0.0908324	−	0.279553i
$803$	−25886.3	+	18807.5i	−1.13762	+	0.826528i
$804$	−5851.02	+	4251.01i	−0.256654	+	0.186470i
$805$	−7309.78	+	33918.6i	−0.320044	+	1.48506i
$806$	−546.156	−	396.806i	−0.0238679	−	0.0173410i
$807$	−5520.19			−0.240793
$808$	−35490.9	−	25785.6i	−1.54525	−	1.12269i
$809$	−1120.42	+	3448.29i	−0.0486919	+	0.149858i	−0.972446	−	0.233127i	$-0.925104\pi$
$809$	−1120.42	+	3448.29i	−0.0486919	+	0.149858i	0.923754	+	0.382986i	$0.125104\pi$
$810$	6593.36	−	5903.06i	0.286009	−	0.256065i
$811$	−8245.92	−	25378.3i	−0.357033	−	1.09883i	−0.954822	−	0.297180i	$-0.903954\pi$
$811$	−8245.92	−	25378.3i	−0.357033	−	1.09883i	0.597789	−	0.801653i	$-0.296046\pi$
$812$	−1834.39	+	5645.68i	−0.0792790	+	0.243996i
$813$	3791.11	−	11667.8i	0.163542	−	0.503331i
$814$	6063.77	+	18662.4i	0.261100	+	0.803582i
$815$	−985.178	+	882.035i	−0.0423427	+	0.0379096i
$816$	−132.733	+	408.510i	−0.00569435	+	0.0175254i
$817$	17992.0	+	13072.0i	0.770454	+	0.559767i
$818$	3147.45			0.134533
$819$	6523.33	+	4739.48i	0.278320	+	0.202211i
$820$	−3137.73	+	14559.6i	−0.133627	+	0.620053i
$821$	−2648.54	+	1924.28i	−0.112588	+	0.0818000i	−0.642655	−	0.766156i	$-0.722167\pi$
$821$	−2648.54	+	1924.28i	−0.112588	+	0.0818000i	0.530067	+	0.847956i	$0.322167\pi$
$822$	−3477.40	+	2526.48i	−0.147553	+	0.107203i
$823$	911.340	+	2804.82i	0.0385994	+	0.118797i	0.968500	−	0.249015i	$-0.0801070\pi$
$823$	911.340	+	2804.82i	0.0385994	+	0.118797i	−0.929900	+	0.367812i	$0.880107\pi$
$824$	−7514.67			−0.317701
$825$	−2022.46	+	18250.4i	−0.0853490	+	0.770180i
$826$	9307.43			0.392066
$827$	−6894.76	−	21219.9i	−0.289908	−	0.892246i	−0.984884	−	0.173213i	$-0.944585\pi$
$827$	−6894.76	−	21219.9i	−0.289908	−	0.892246i	0.694976	−	0.719033i	$-0.255415\pi$
$828$	8986.90	−	6529.36i	0.377193	−	0.274047i
$829$	1648.42	−	1197.64i	0.0690613	−	0.0501760i	−0.552719	−	0.833368i	$-0.686410\pi$
$829$	1648.42	−	1197.64i	0.0690613	−	0.0501760i	0.621780	+	0.783192i	$0.286410\pi$
$830$	3769.19	−	3374.57i	0.157627	−	0.141124i
$831$	121.378	+	88.1864i	0.00506686	+	0.00368129i
$832$	6623.18			0.275983
$833$	2523.43	+	1833.38i	0.104960	+	0.0762578i
$834$	−339.998	+	1046.41i	−0.0141165	+	0.0434461i
$835$	4412.68	+	9986.83i	0.182883	+	0.413902i
$836$	−6208.73	−	19108.5i	−0.256858	−	0.790528i
$837$	−742.506	+	2285.20i	−0.0306628	+	0.0943704i
$838$	−8157.72	+	25106.9i	−0.336281	+	1.03497i
$839$	−3882.74	−	11949.8i	−0.159770	−	0.491722i	0.838843	−	0.544374i	$-0.183233\pi$
$839$	−3882.74	−	11949.8i	−0.159770	−	0.491722i	−0.998613	+	0.0526520i	$0.983233\pi$
$840$	12062.9	+	7009.98i	0.495486	+	0.287937i
$841$	−6366.53	+	19594.2i	−0.261041	+	0.803402i
$842$	4119.24	+	2992.80i	0.168597	+	0.122493i
$843$	9455.27			0.386307
$844$	7477.27	+	5432.55i	0.304950	+	0.221559i
$845$	−8982.02	−	20328.2i	−0.365670	−	0.827588i
$846$	2994.02	−	2175.28i	0.121674	−	0.0884017i
$847$	−71152.5	+	51695.3i	−2.88646	+	2.09713i
$848$	−198.255	−	610.167i	−0.00802844	−	0.0247090i
$849$	−9654.03			−0.390254
$850$	2904.41	−	600.230i	0.117200	−	0.0242208i
$851$	17440.6			0.702535
$852$	−992.632	−	3055.01i	−0.0399143	−	0.122844i
$853$	24421.0	−	17742.9i	0.980258	−	0.712199i	0.0224918	−	0.999747i	$-0.492840\pi$
$853$	24421.0	−	17742.9i	0.980258	−	0.712199i	0.957766	+	0.287548i	$0.0928400\pi$
$854$	17127.9	−	12444.1i	0.686303	−	0.498629i
$855$	−18456.8	+	1887.22i	−0.738257	+	0.0754871i
$856$	−16659.1	−	12103.5i	−0.665181	−	0.483282i
$857$	−11633.7			−0.463709			−0.231855	−	0.972750i	$-0.574479\pi$
$857$	−11633.7			−0.463709			−0.231855	+	0.972750i	$0.574479\pi$
$858$	−3476.57	−	2525.87i	−0.138331	−	0.100503i
$859$	1576.92	−	4853.26i	0.0626353	−	0.192772i	−0.914842	−	0.403812i	$-0.867685\pi$
$859$	1576.92	−	4853.26i	0.0626353	−	0.192772i	0.977477	+	0.211040i	$0.0676851\pi$
$860$	13165.5	−	1346.17i	0.522021	−	0.0533769i
$861$	−5455.11	−	16789.1i	−0.215923	−	0.664542i
$862$	3275.73	−	10081.7i	0.129434	−	0.398356i
$863$	45.7351	−	140.758i	0.00180399	−	0.00555210i	−0.950150	−	0.311792i	$-0.899071\pi$
$863$	45.7351	−	140.758i	0.00180399	−	0.00555210i	0.951954	+	0.306240i	$0.0990709\pi$
$864$	−5065.16	−	15589.0i	−0.199445	−	0.613827i
$865$	4801.51	−	22279.8i	0.188736	−	0.875765i
$866$	4438.53	−	13660.4i	0.174166	−	0.536027i
$867$	−8111.34	−	5893.23i	−0.317734	−	0.230847i
$868$	2226.24			0.0870548
$869$	−7105.49	−	5162.44i	−0.277373	−	0.201523i
$870$	−2525.84	−	1467.82i	−0.0984299	−	0.0571997i
$871$	−10310.3	+	7490.88i	−0.401093	+	0.291411i
$872$	−26893.7	+	19539.4i	−1.04442	+	0.758816i
$873$	9621.16	+	29610.9i	0.372997	+	1.14797i
$874$	18683.9			0.723105
$875$	292.098	−	34483.9i	0.0112854	−	1.33231i
$876$	3753.86			0.144785
$877$	−7915.97	−	24362.8i	−0.304793	−	0.938056i	−0.979754	−	0.200203i	$-0.935840\pi$
$877$	−7915.97	−	24362.8i	−0.304793	−	0.938056i	0.674962	−	0.737853i	$-0.264160\pi$
$878$	−10754.1	+	7813.33i	−0.413365	+	0.300327i
$879$	13329.1	−	9684.13i	0.511465	−	0.371601i
$880$	11794.7	+	6854.17i	0.451819	+	0.262561i
$881$	23505.5	+	17077.8i	0.898889	+	0.653081i	0.938180	−	0.346146i	$-0.112510\pi$
$881$	23505.5	+	17077.8i	0.898889	+	0.653081i	−0.0392911	+	0.999228i	$0.512510\pi$
$882$	12148.7			0.463794
$883$	39687.9	+	28835.0i	1.51258	+	1.09895i	0.965018	+	0.262185i	$0.0844429\pi$
$883$	39687.9	+	28835.0i	1.51258	+	1.09895i	0.547559	+	0.836767i	$0.315557\pi$
$884$	204.995	−	630.911i	0.00779948	−	0.0240043i
$885$	922.289	−	4279.58i	0.0350310	−	0.162550i
$886$	−5585.59	−	17190.7i	−0.211796	−	0.651842i
$887$	−9469.86	+	29145.2i	−0.358474	+	1.10327i	0.595493	+	0.803360i	$0.296957\pi$
$887$	−9469.86	+	29145.2i	−0.358474	+	1.10327i	−0.953967	+	0.299910i	$0.903043\pi$
$888$	2167.10	−	6669.64i	0.0818953	−	0.252048i
$889$	−333.803	−	1027.34i	−0.0125932	−	0.0387580i
$890$	11420.4	−	1167.74i	0.430126	−	0.0439806i
$891$	8461.74	−	26042.6i	0.318158	−	0.979191i
$892$	−18406.0	−	13372.8i	−0.690896	−	0.501965i
$893$	−5949.32			−0.222941
$894$	−3624.71	−	2633.51i	−0.135602	−	0.0985208i
$895$	33880.1	−	3464.26i	1.26535	−	0.129383i
$896$	−6653.52	+	4834.06i	−0.248079	+	0.180240i
$897$	−3089.95	+	2244.98i	−0.115017	+	0.0835650i
$898$	303.456	+	933.943i	0.0112767	+	0.0347061i
$899$	−1420.03			−0.0526815
$900$	−7433.73	+	8162.82i	−0.275323	+	0.302327i
$901$	−431.578			−0.0159578
$902$	−14899.9	−	45857.0i	−0.550012	−	1.69276i
$903$	−12690.1	+	9219.90i	−0.467664	+	0.339778i
$904$	13319.8	−	9677.41i	0.490056	−	0.356046i
$905$	11200.1	+	25348.2i	0.411385	+	0.931051i
$906$	−1078.42	−	783.518i	−0.0395453	−	0.0287314i
$907$	41997.6			1.53749			0.768747	−	0.639553i	$-0.220880\pi$
$907$	41997.6			1.53749			0.768747	+	0.639553i	$0.220880\pi$
$908$	−18692.2	−	13580.7i	−0.683176	−	0.496357i
$909$	−12714.9	+	39132.4i	−0.463946	+	1.42788i
$910$	6977.84	+	4054.97i	0.254190	+	0.147715i
$911$	−12428.2	−	38250.2i	−0.451993	−	1.39109i	−0.874629	−	0.484792i	$-0.838895\pi$
$911$	−12428.2	−	38250.2i	−0.451993	−	1.39109i	0.422636	−	0.906299i	$-0.361105\pi$
$912$	831.083	−	2557.81i	0.0301753	−	0.0928701i
$913$	4837.28	−	14887.6i	0.175346	−	0.539658i
$914$	−950.457	−	2925.20i	−0.0343964	−	0.105861i
$915$	−4024.60	−	9108.54i	−0.145409	−	0.329092i
$916$	−354.384	+	1090.68i	−0.0127829	+	0.0393418i
$917$	13328.2	+	9683.50i	0.479974	+	0.348721i
$918$	2470.40			0.0888184
$919$	30793.1	+	22372.5i	1.10530	+	0.803047i	0.981917	−	0.189312i	$-0.0606258\pi$
$919$	30793.1	+	22372.5i	1.10530	+	0.803047i	0.123382	+	0.992359i	$0.460626\pi$
$920$	25233.9	−	22592.0i	0.904280	−	0.809606i
$921$	5454.95	−	3963.25i	0.195165	−	0.141795i
$922$	−4326.65	+	3143.49i	−0.154545	+	0.112284i
$923$	−1749.16	−	5383.35i	−0.0623772	−	0.191977i
$924$	14171.2			0.504543
$925$	−16975.3	+	3508.13i	−0.603398	+	0.124699i
$926$	−20419.5			−0.724650
$927$	2178.03	+	6703.28i	0.0771692	+	0.237502i
$928$	7836.97	−	5693.89i	0.277221	−	0.201413i
$929$	−26398.0	+	19179.3i	−0.932282	+	0.677343i	−0.946551	−	0.322556i	$-0.895458\pi$
$929$	−26398.0	+	19179.3i	−0.932282	+	0.677343i	0.0142684	+	0.999898i	$0.495458\pi$
$930$	−230.811	+	1071.00i	−0.00813827	+	0.0377629i
$931$	−15800.0	−	11479.3i	−0.556200	−	0.404103i
$932$	2870.48			0.100886
$933$	3200.43	+	2325.25i	0.112301	+	0.0815918i
$934$	−2035.18	+	6263.64i	−0.0712988	+	0.219435i
$935$	6836.90	−	6121.11i	0.239134	−	0.214098i
$936$	−2432.25	−	7485.70i	−0.0849366	−	0.261408i
$937$	6350.30	−	19544.2i	0.221404	−	0.681410i	−0.777233	−	0.629213i	$-0.783377\pi$
$937$	6350.30	−	19544.2i	0.221404	−	0.681410i	0.998637	−	0.0521974i	$-0.0166225\pi$
$938$	−13588.0	+	41819.7i	−0.472990	+	1.45571i
$939$	3440.97	+	10590.2i	0.119587	+	0.368050i
$940$	−2637.63	+	2361.48i	−0.0915213	+	0.0819394i
$941$	−3516.52	+	10822.8i	−0.121823	+	0.374933i	−0.993309	−	0.115488i	$-0.963157\pi$
$941$	−3516.52	+	10822.8i	−0.121823	+	0.374933i	0.871486	+	0.490421i	$0.163157\pi$
$942$	11252.6	+	8175.51i	0.389204	+	0.282773i
$943$	−42855.0			−1.47990
$944$	−2631.24	−	1911.71i	−0.0907199	−	0.0659119i
$945$	6051.56	−	28080.3i	0.208315	−	0.966615i
$946$	−34661.2	+	25182.9i	−1.19126	+	0.865503i
$947$	−13645.6	+	9914.12i	−0.468240	+	0.340196i	−0.796755	−	0.604303i	$-0.793452\pi$
$947$	−13645.6	+	9914.12i	−0.468240	+	0.340196i	0.328515	+	0.944499i	$0.393452\pi$
$948$	318.409	+	979.961i	0.0109087	+	0.0335735i
$949$	6614.83			0.226266
$950$	−18185.4	+	3758.22i	−0.621066	+	0.128350i
$951$	5277.27			0.179944
$952$	−2154.63	−	6631.28i	−0.0733530	−	0.225757i
$953$	−43544.9	+	31637.2i	−1.48012	+	1.07537i	−0.502608	+	0.864515i	$0.667626\pi$
$953$	−43544.9	+	31637.2i	−1.48012	+	1.07537i	−0.977517	+	0.210859i	$0.932374\pi$
$954$	−1359.92	+	988.037i	−0.0461519	+	0.0335313i
$955$	−1682.59	+	1506.43i	−0.0570128	+	0.0510438i
$956$	10385.6	+	7545.55i	0.351352	+	0.255272i
$957$	−9039.22			−0.305326
$958$	13083.3	+	9505.54i	0.441233	+	0.320574i
$959$	7718.51	−	23755.1i	0.259900	−	0.799888i
$960$	−4344.15	−	9831.73i	−0.146049	−	0.330539i
$961$	−9041.36	−	27826.4i	−0.303493	−	0.934055i
$962$	1253.57	−	3858.10i	0.0420133	−	0.129304i
$963$	−5968.24	+	18368.4i	−0.199713	+	0.614654i
$964$	6631.57	+	20409.9i	0.221565	+	0.681906i
$965$	−30772.8	−	17882.7i	−1.02654	−	0.596545i
$966$	−4072.27	+	12533.2i	−0.135635	+	0.417441i
$967$	−4347.04	−	3158.31i	−0.144562	−	0.105030i	0.513154	−	0.858297i	$-0.328477\pi$
$967$	−4347.04	−	3158.31i	−0.144562	−	0.105030i	−0.657716	+	0.753266i	$0.728477\pi$
$968$	85851.3			2.85058
$969$	−1463.65	−	1063.40i	−0.0485233	−	0.0352543i
$970$	12594.5	+	28504.1i	0.416893	+	0.943518i
$971$	2402.25	−	1745.33i	0.0793942	−	0.0576833i	−0.547380	−	0.836884i	$-0.684375\pi$
$971$	2402.25	−	1745.33i	0.0793942	−	0.0576833i	0.626774	+	0.779201i	$0.284375\pi$
$972$	−11490.7	+	8348.46i	−0.379180	+	0.275491i
$973$	−1975.74	−	6080.70i	−0.0650969	−	0.200348i
$974$	11869.6			0.390478
$975$	2555.93	−	2806.62i	0.0839542	−	0.0921883i
$976$	−7398.07			−0.242630
$977$	8717.76	+	26830.5i	0.285472	+	0.878591i	0.986257	+	0.165219i	$0.0528331\pi$
$977$	8717.76	+	26830.5i	0.285472	+	0.878591i	−0.700785	+	0.713372i	$0.747167\pi$
$978$	−406.309	+	295.201i	−0.0132846	+	0.00965182i
$979$	28737.1	−	20878.7i	0.938141	−	0.681599i
$980$	−11561.4	+	1182.16i	−0.376854	+	0.0385335i
$981$	25224.4	+	18326.6i	0.820952	+	0.596457i
$982$	−25897.5			−0.841570
$983$	−3862.76	−	2806.46i	−0.125334	−	0.0910602i	0.523352	−	0.852116i	$-0.324681\pi$
$983$	−3862.76	−	2806.46i	−0.125334	−	0.0910602i	−0.648686	+	0.761056i	$0.724681\pi$
$984$	−5324.98	+	16388.6i	−0.172514	+	0.530944i
$985$	37305.9	−	3814.54i	1.20677	−	0.123392i
$986$	451.158	+	1388.52i	0.0145718	+	0.0448474i
$987$	1296.69	−	3990.79i	0.0418176	−	0.128701i
$988$	−1283.54	+	3950.33i	−0.0413308	+	0.127203i
$989$	11767.1	+	36215.5i	0.378334	+	1.16439i
$990$	7529.88	−	34939.9i	0.241733	−	1.12168i
$991$	−13070.8	+	40227.9i	−0.418980	+	1.28949i	0.489663	+	0.871912i	$0.337120\pi$
$991$	−13070.8	+	40227.9i	−0.418980	+	1.28949i	−0.908643	+	0.417575i	$0.862880\pi$
$992$	−2939.07	−	2135.36i	−0.0940682	−	0.0683446i
$993$	−16776.5			−0.536140
$994$	−15800.2	−	11479.6i	−0.504178	−	0.366307i
$995$	−38168.7	−	22180.6i	−1.21611	−	0.706707i
$996$	−1485.74	+	1079.45i	−0.0472665	+	0.0343411i
$997$	−3951.67	+	2871.05i	−0.125527	+	0.0912008i	−0.648777	−	0.760978i	$-0.724719\pi$
$997$	−3951.67	+	2871.05i	−0.125527	+	0.0912008i	0.523250	+	0.852179i	$0.324719\pi$
$998$	−2971.83	−	9146.36i	−0.0942602	−	0.290103i
$999$	−14438.6			−0.457275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.6.3	✓	28
3.2	odd	2		225.4.h.b.181.5		28
5.2	odd	4		125.4.e.b.99.10		56
5.3	odd	4		125.4.e.b.99.5		56
5.4	even	2		125.4.d.a.26.5		28
25.3	odd	20		125.4.e.b.24.10		56
25.4	even	10		125.4.d.a.101.5		28
25.11	even	5		625.4.a.c.1.6		14
25.14	even	10		625.4.a.d.1.9		14
25.21	even	5	inner	25.4.d.a.21.3	yes	28
25.22	odd	20		125.4.e.b.24.5		56
75.71	odd	10		225.4.h.b.46.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.6.3	✓	28	1.1	even	1	trivial
25.4.d.a.21.3	yes	28	25.21	even	5	inner
125.4.d.a.26.5		28	5.4	even	2
125.4.d.a.101.5		28	25.4	even	10
125.4.e.b.24.5		56	25.22	odd	20
125.4.e.b.24.10		56	25.3	odd	20
125.4.e.b.99.5		56	5.3	odd	4
125.4.e.b.99.10		56	5.2	odd	4
225.4.h.b.46.5		28	75.71	odd	10
225.4.h.b.181.5		28	3.2	odd	2
625.4.a.c.1.6		14	25.11	even	5
625.4.a.d.1.9		14	25.14	even	10

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.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624983 - 1.92350i) q^{2} +(1.69858 - 1.23409i) q^{3} +(3.16288 - 2.29797i) q^{4} +(-9.66664 - 5.61749i) q^{5} +(-3.43535 - 2.49593i) q^{6} +24.6755 q^{7} +(-19.4867 - 14.1579i) q^{8} +(-6.98127 + 21.4861i) q^{9} +O(q^{10})\)	\(q+(-0.624983 - 1.92350i) q^{2} +(1.69858 - 1.23409i) q^{3} +(3.16288 - 2.29797i) q^{4} +(-9.66664 - 5.61749i) q^{5} +(-3.43535 - 2.49593i) q^{6} +24.6755 q^{7} +(-19.4867 - 14.1579i) q^{8} +(-6.98127 + 21.4861i) q^{9} +(-4.76375 + 22.1046i) q^{10} +(21.6207 + 66.5415i) q^{11} +(2.53650 - 7.80655i) q^{12} +(4.46967 - 13.7562i) q^{13} +(-15.4218 - 47.4634i) q^{14} +(-23.3520 + 2.38775i) q^{15} +(-5.38901 + 16.5857i) q^{16} +(9.49076 + 6.89544i) q^{17} +45.6918 q^{18} +(-59.4245 - 43.1745i) q^{19} +(-43.4833 + 4.44618i) q^{20} +(41.9133 - 30.4518i) q^{21} +(114.480 - 83.1747i) q^{22} +(-38.8648 - 119.614i) q^{23} -50.5718 q^{24} +(61.8877 + 108.604i) q^{25} -29.2536 q^{26} +(32.1751 + 99.0248i) q^{27} +(78.0459 - 56.7037i) q^{28} +(-49.7823 + 36.1690i) q^{29} +(19.1874 + 43.4253i) q^{30} +(18.6697 + 13.5643i) q^{31} -157.425 q^{32} +(118.842 + 86.3441i) q^{33} +(7.33182 - 22.5650i) q^{34} +(-238.530 - 138.615i) q^{35} +(27.2936 + 84.0009i) q^{36} +(-42.8519 + 131.885i) q^{37} +(-45.9068 + 141.287i) q^{38} +(-9.38431 - 28.8819i) q^{39} +(108.839 + 246.326i) q^{40} +(105.295 - 324.066i) q^{41} +(-84.7691 - 61.5884i) q^{42} -302.771 q^{43} +(221.294 + 160.780i) q^{44} +(188.184 - 168.482i) q^{45} +(-205.787 + 149.513i) q^{46} +(65.5264 - 47.6077i) q^{47} +(11.3145 + 34.8225i) q^{48} +265.883 q^{49} +(170.222 - 186.917i) q^{50} +24.6303 q^{51} +(-17.4743 - 53.7805i) q^{52} +(-29.7628 + 21.6239i) q^{53} +(170.365 - 123.778i) q^{54} +(164.797 - 764.687i) q^{55} +(-480.845 - 349.355i) q^{56} -154.218 q^{57} +(100.684 + 73.1513i) q^{58} +(-57.6314 + 177.371i) q^{59} +(-68.3726 + 61.2143i) q^{60} +(131.092 + 403.458i) q^{61} +(14.4228 - 44.3887i) q^{62} +(-172.267 + 530.182i) q^{63} +(141.500 + 435.492i) q^{64} +(-120.482 + 107.868i) q^{65} +(91.8084 - 282.557i) q^{66} +(-712.818 - 517.893i) q^{67} +45.8637 q^{68} +(-213.628 - 155.210i) q^{69} +(-117.548 + 545.444i) q^{70} +(316.600 - 230.023i) q^{71} +(440.241 - 319.854i) q^{72} +(141.321 + 434.943i) q^{73} +280.462 q^{74} +(239.148 + 108.098i) q^{75} -287.167 q^{76} +(533.502 + 1641.95i) q^{77} +(-49.6894 + 36.1015i) q^{78} +(-101.556 + 73.7850i) q^{79} +(145.263 - 130.055i) q^{80} +(-316.628 - 230.043i) q^{81} -689.149 q^{82} +(-181.005 - 131.508i) q^{83} +(62.5896 - 192.631i) q^{84} +(-53.0087 - 119.970i) q^{85} +(189.227 + 582.380i) q^{86} +(-39.9233 + 122.871i) q^{87} +(520.775 - 1602.78i) q^{88} +(-156.885 - 482.841i) q^{89} +(-441.686 - 256.673i) q^{90} +(110.292 - 339.442i) q^{91} +(-397.793 - 289.014i) q^{92} +48.4515 q^{93} +(-132.527 - 96.2861i) q^{94} +(331.904 + 751.168i) q^{95} +(-267.398 + 194.276i) q^{96} +(1114.94 - 810.049i) q^{97} +(-166.172 - 511.426i) q^{98} -1580.66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

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