LMFDB - Embedded newform 525.2.w.a.104.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(104,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.w (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			104.14
Character	$\chi$	$=$	525.104
Dual form			525.2.w.a.419.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.605685 + 1.86411i) q^{2} +(0.698093 + 1.58514i) q^{3} +(-1.49001 - 1.08256i) q^{4} +(1.90667 + 1.16816i) q^{5} +(-3.37770 + 0.341225i) q^{6} +(2.25871 - 1.37777i) q^{7} +(-0.250932 + 0.182313i) q^{8} +(-2.02533 + 2.21315i) q^{9} +O(q^{10})$	\(q+(-0.605685 + 1.86411i) q^{2} +(0.698093 + 1.58514i) q^{3} +(-1.49001 - 1.08256i) q^{4} +(1.90667 + 1.16816i) q^{5} +(-3.37770 + 0.341225i) q^{6} +(2.25871 - 1.37777i) q^{7} +(-0.250932 + 0.182313i) q^{8} +(-2.02533 + 2.21315i) q^{9} +(-3.33242 + 2.84671i) q^{10} +(5.50080 + 1.78732i) q^{11} +(0.675836 - 3.11760i) q^{12} +(0.173354 + 0.533528i) q^{13} +(1.20024 + 5.04497i) q^{14} +(-0.520662 + 3.83783i) q^{15} +(-1.32613 - 4.08141i) q^{16} +(-3.54265 - 4.87604i) q^{17} +(-2.89883 - 5.11591i) q^{18} +(1.03039 + 1.41821i) q^{19} +(-1.57636 - 3.80465i) q^{20} +(3.76074 + 2.61855i) q^{21} +(-6.66351 + 9.17153i) q^{22} +(-2.00272 + 6.16373i) q^{23} +(-0.464165 - 0.270491i) q^{24} +(2.27080 + 4.45460i) q^{25} -1.09955 q^{26} +(-4.92202 - 1.66545i) q^{27} +(-4.85701 - 0.392285i) q^{28} +(3.09288 - 4.25699i) q^{29} +(-6.83877 - 3.29509i) q^{30} +(-4.58904 - 6.31627i) q^{31} +7.79107 q^{32} +(1.00692 + 9.96725i) q^{33} +(11.2352 - 3.65054i) q^{34} +(5.91607 + 0.0115760i) q^{35} +(5.41362 - 1.10508i) q^{36} +(0.399872 - 0.129926i) q^{37} +(-3.26779 + 1.06177i) q^{38} +(-0.724699 + 0.647242i) q^{39} +(-0.691416 + 0.0544820i) q^{40} +(-2.57985 - 7.93995i) q^{41} +(-7.15909 + 5.42441i) q^{42} -0.169160i q^{43} +(-6.26138 - 8.61805i) q^{44} +(-6.44696 + 1.85384i) q^{45} +(-10.2768 - 7.46656i) q^{46} +(2.29862 - 3.16378i) q^{47} +(5.54384 - 4.95131i) q^{48} +(3.20351 - 6.22395i) q^{49} +(-9.67925 + 1.53494i) q^{50} +(5.25610 - 9.01952i) q^{51} +(0.319275 - 0.982627i) q^{52} +(-9.92969 - 7.21434i) q^{53} +(6.08577 - 8.16644i) q^{54} +(8.40035 + 9.83365i) q^{55} +(-0.315597 + 0.757517i) q^{56} +(-1.52875 + 2.62335i) q^{57} +(6.06217 + 8.34386i) q^{58} +(-1.05021 - 3.23221i) q^{59} +(4.93045 - 5.15475i) q^{60} +(3.25257 + 1.05682i) q^{61} +(14.5537 - 4.72879i) q^{62} +(-1.52542 + 7.78929i) q^{63} +(-2.06668 + 6.36058i) q^{64} +(-0.292717 + 1.21977i) q^{65} +(-19.1899 - 4.16001i) q^{66} +(-0.989006 - 1.36125i) q^{67} +11.1005i q^{68} +(-11.1685 + 1.12827i) q^{69} +(-3.60486 + 11.0212i) q^{70} +(-0.712522 + 0.980702i) q^{71} +(0.104735 - 0.924594i) q^{72} +(-3.54582 + 10.9129i) q^{73} +0.824099i q^{74} +(-5.47593 + 6.70926i) q^{75} -3.22860i q^{76} +(14.8872 - 3.54181i) q^{77} +(-0.767589 - 1.74294i) q^{78} +(5.26137 + 3.82261i) q^{79} +(2.23925 - 9.33105i) q^{80} +(-0.796057 - 8.96472i) q^{81} +16.3635 q^{82} +(-4.04925 - 5.57331i) q^{83} +(-2.76881 - 7.97288i) q^{84} +(-1.05868 - 13.4354i) q^{85} +(0.315332 + 0.102458i) q^{86} +(8.90704 + 1.93088i) q^{87} +(-1.70618 + 0.554371i) q^{88} +(-0.920092 + 2.83175i) q^{89} +(0.449075 - 13.1407i) q^{90} +(1.12663 + 0.966241i) q^{91} +(9.65665 - 7.01597i) q^{92} +(6.80859 - 11.6836i) q^{93} +(4.50539 + 6.20114i) q^{94} +(0.307920 + 3.90772i) q^{95} +(5.43889 + 12.3499i) q^{96} +(-2.18447 - 1.58711i) q^{97} +(9.66180 + 9.74144i) q^{98} +(-15.0966 + 8.55418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) $ 304 * q - 84 * q^4 - 6 * q^9	$ 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) $ 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.605685	+	1.86411i	−0.428284	+	1.31812i	0.471530	+	0.881850i	$0.343702\pi$
$2$	−0.605685	+	1.86411i	−0.428284	+	1.31812i	−0.899814	+	0.436273i	$0.856298\pi$
$3$	0.698093	+	1.58514i	0.403044	+	0.915181i
$3$	0.698093	+	1.58514i	0.403044	+	0.915181i
$4$	−1.49001	−	1.08256i	−0.745005	−	0.541278i
$5$	1.90667	+	1.16816i	0.852690	+	0.522417i
$5$	1.90667	+	1.16816i	0.852690	+	0.522417i
$6$	−3.37770	+	0.341225i	−1.37894	+	0.139305i
$7$	2.25871	−	1.37777i	0.853711	−	0.520748i
$7$	2.25871	−	1.37777i	0.853711	−	0.520748i
$8$	−0.250932	+	0.182313i	−0.0887179	+	0.0644573i
$9$	−2.02533	+	2.21315i	−0.675111	+	0.737716i
$10$	−3.33242	+	2.84671i	−1.05380	+	0.900208i
$11$	5.50080	+	1.78732i	1.65855	+	0.538897i	0.980568	−	0.196178i	$-0.0628531\pi$
$11$	5.50080	+	1.78732i	1.65855	+	0.538897i	0.677986	+	0.735075i	$0.262853\pi$
$12$	0.675836	−	3.11760i	0.195097	−	0.899973i
$13$	0.173354	+	0.533528i	0.0480797	+	0.147974i	0.972214	−	0.234094i	$-0.0752122\pi$
$13$	0.173354	+	0.533528i	0.0480797	+	0.147974i	−0.924134	+	0.382067i	$0.875212\pi$
$14$	1.20024	+	5.04497i	0.320779	+	1.34832i
$15$	−0.520662	+	3.83783i	−0.134434	+	0.990923i
$16$	−1.32613	−	4.08141i	−0.331533	−	1.02035i
$17$	−3.54265	−	4.87604i	−0.859219	−	1.18261i	−0.981755	−	0.190149i	$-0.939103\pi$
$17$	−3.54265	−	4.87604i	−0.859219	−	1.18261i	0.122537	−	0.992464i	$-0.460897\pi$
$18$	−2.89883	−	5.11591i	−0.683262	−	1.20583i
$19$	1.03039	+	1.41821i	0.236388	+	0.325360i	0.910686	−	0.413099i	$-0.135554\pi$
$19$	1.03039	+	1.41821i	0.236388	+	0.325360i	−0.674298	+	0.738459i	$0.735554\pi$
$20$	−1.57636	−	3.80465i	−0.352485	−	0.850746i
$21$	3.76074	+	2.61855i	0.820661	+	0.571415i
$22$	−6.66351	+	9.17153i	−1.42067	+	1.95538i
$23$	−2.00272	+	6.16373i	−0.417595	+	1.28523i	0.492313	+	0.870418i	$0.336151\pi$
$23$	−2.00272	+	6.16373i	−0.417595	+	1.28523i	−0.909909	+	0.414808i	$0.863849\pi$
$24$	−0.464165	−	0.270491i	−0.0947473	−	0.0552137i
$25$	2.27080	+	4.45460i	0.454161	+	0.890920i
$26$	−1.09955			−0.215640
$27$	−4.92202	−	1.66545i	−0.947243	−	0.320516i
$28$	−4.85701	−	0.392285i	−0.917888	−	0.0741350i
$29$	3.09288	−	4.25699i	0.574334	−	0.790503i	−0.418726	−	0.908113i	$-0.637523\pi$
$29$	3.09288	−	4.25699i	0.574334	−	0.790503i	0.993060	+	0.117610i	$0.0375232\pi$
$30$	−6.83877	−	3.29509i	−1.24858	−	0.601598i
$31$	−4.58904	−	6.31627i	−0.824216	−	1.13444i	−0.988972	−	0.148101i	$-0.952684\pi$
$31$	−4.58904	−	6.31627i	−0.824216	−	1.13444i	0.164757	−	0.986334i	$-0.447316\pi$
$32$	7.79107			1.37728
$33$	1.00692	+	9.96725i	0.175283	+	1.73508i
$34$	11.2352	−	3.65054i	1.92682	−	0.626062i
$35$	5.91607	+	0.0115760i	0.999998	+	0.00195670i
$36$	5.41362	−	1.10508i	0.902270	−	0.184180i
$37$	0.399872	−	0.129926i	0.0657385	−	0.0213597i	−0.275963	−	0.961168i	$-0.588997\pi$
$37$	0.399872	−	0.129926i	0.0657385	−	0.0213597i	0.341702	+	0.939808i	$0.388997\pi$
$38$	−3.26779	+	1.06177i	−0.530105	+	0.172242i
$39$	−0.724699	+	0.647242i	−0.116045	+	0.103642i
$40$	−0.691416	+	0.0544820i	−0.109322	+	0.00861436i
$41$	−2.57985	−	7.93995i	−0.402904	−	1.24001i	−0.922632	−	0.385680i	$-0.873967\pi$
$41$	−2.57985	−	7.93995i	−0.402904	−	1.24001i	0.519728	−	0.854332i	$-0.326033\pi$
$42$	−7.15909	+	5.42441i	−1.10467	+	0.837005i
$43$		−	0.169160i		−	0.0257966i	−0.999917	−	0.0128983i	$-0.995894\pi$
$43$		−	0.169160i		−	0.0257966i	0.999917	−	0.0128983i	$-0.00410578\pi$
$44$	−6.26138	−	8.61805i	−0.943938	−	1.29922i
$45$	−6.44696	+	1.85384i	−0.961056	+	0.276354i
$46$	−10.2768	−	7.46656i	−1.51524	−	1.10088i
$47$	2.29862	−	3.16378i	0.335289	−	0.461485i	−0.607769	−	0.794114i	$-0.707935\pi$
$47$	2.29862	−	3.16378i	0.335289	−	0.461485i	0.943058	+	0.332628i	$0.107935\pi$
$48$	5.54384	−	4.95131i	0.800185	−	0.714660i
$49$	3.20351	−	6.22395i	0.457644	−	0.889136i
$50$	−9.67925	+	1.53494i	−1.36885	+	0.217073i
$51$	5.25610	−	9.01952i	0.736001	−	1.26299i
$52$	0.319275	−	0.982627i	0.0442754	−	0.136266i
$53$	−9.92969	−	7.21434i	−1.36395	−	0.990966i	−0.998183	−	0.0602593i	$-0.980807\pi$
$53$	−9.92969	−	7.21434i	−1.36395	−	0.990966i	−0.365765	−	0.930707i	$-0.619193\pi$
$54$	6.08577	−	8.16644i	0.828169	−	1.11131i
$55$	8.40035	+	9.83365i	1.13270	+	1.32597i
$56$	−0.315597	+	0.757517i	−0.0421734	+	0.101228i
$57$	−1.52875	+	2.62335i	−0.202488	+	0.347472i
$58$	6.06217	+	8.34386i	0.796002	+	1.09560i
$59$	−1.05021	−	3.23221i	−0.136726	−	0.420798i	0.859129	−	0.511759i	$-0.171006\pi$
$59$	−1.05021	−	3.23221i	−0.136726	−	0.420798i	−0.995854	+	0.0909612i	$0.971006\pi$
$60$	4.93045	−	5.15475i	0.636519	−	0.665476i
$61$	3.25257	+	1.05682i	0.416449	+	0.135313i	0.509744	−	0.860326i	$-0.329740\pi$
$61$	3.25257	+	1.05682i	0.416449	+	0.135313i	−0.0932951	+	0.995638i	$0.529740\pi$
$62$	14.5537	−	4.72879i	1.84832	−	0.600557i
$63$	−1.52542	+	7.78929i	−0.192185	+	0.981359i
$64$	−2.06668	+	6.36058i	−0.258335	+	0.795072i
$65$	−0.292717	+	1.21977i	−0.0363071	+	0.151294i
$66$	−19.1899	−	4.16001i	−2.36211	−	0.512061i
$67$	−0.989006	−	1.36125i	−0.120826	−	0.166303i	0.744319	−	0.667824i	$-0.232774\pi$
$67$	−0.989006	−	1.36125i	−0.120826	−	0.166303i	−0.865146	+	0.501521i	$0.832774\pi$
$68$			11.1005i			1.34613i
$69$	−11.1685	+	1.12827i	−1.34452	+	0.135828i
$70$	−3.60486	+	11.0212i	−0.430863	+	1.31728i
$71$	−0.712522	+	0.980702i	−0.0845608	+	0.116388i	−0.849202	−	0.528069i	$-0.822916\pi$
$71$	−0.712522	+	0.980702i	−0.0845608	+	0.116388i	0.764641	+	0.644457i	$0.222916\pi$
$72$	0.104735	−	0.924594i	0.0123432	−	0.108964i
$73$	−3.54582	+	10.9129i	−0.415006	+	1.27726i	0.497239	+	0.867614i	$0.334347\pi$
$73$	−3.54582	+	10.9129i	−0.415006	+	1.27726i	−0.912245	+	0.409645i	$0.865653\pi$
$74$			0.824099i			0.0957995i
$75$	−5.47593	+	6.70926i	−0.632306	+	0.774719i
$76$		−	3.22860i		−	0.370346i
$77$	14.8872	−	3.54181i	1.69655	−	0.403626i
$78$	−0.767589	−	1.74294i	−0.0869123	−	0.197349i
$79$	5.26137	+	3.82261i	0.591950	+	0.430077i	0.843012	−	0.537894i	$-0.180780\pi$
$79$	5.26137	+	3.82261i	0.591950	+	0.430077i	−0.251062	+	0.967971i	$0.580780\pi$
$80$	2.23925	−	9.33105i	0.250355	−	1.04324i
$81$	−0.796057	−	8.96472i	−0.0884507	−	0.996081i
$82$	16.3635			1.80705
$83$	−4.04925	−	5.57331i	−0.444463	−	0.611750i	0.526734	−	0.850030i	$-0.323416\pi$
$83$	−4.04925	−	5.57331i	−0.444463	−	0.611750i	−0.971197	+	0.238280i	$0.923416\pi$
$84$	−2.76881	−	7.97288i	−0.302102	−	0.869913i
$85$	−1.05868	−	13.4354i	−0.114830	−	1.45727i
$86$	0.315332	+	0.102458i	0.0340032	+	0.0110483i
$87$	8.90704	+	1.93088i	0.954935	+	0.207012i
$88$	−1.70618	+	0.554371i	−0.181879	+	0.0590961i
$89$	−0.920092	+	2.83175i	−0.0975296	+	0.300165i	−0.987905	−	0.155062i	$-0.950442\pi$
$89$	−0.920092	+	2.83175i	−0.0975296	+	0.300165i	0.890375	+	0.455228i	$0.150442\pi$
$90$	0.449075	−	13.1407i	0.0473366	−	1.38515i
$91$	1.12663	+	0.966241i	0.118103	+	0.101290i
$92$	9.65665	−	7.01597i	1.00678	−	0.731465i
$93$	6.80859	−	11.6836i	0.706018	−	1.21153i
$94$	4.50539	+	6.20114i	0.464696	+	0.639599i
$95$	0.307920	+	3.90772i	0.0315919	+	0.400924i
$96$	5.43889	+	12.3499i	0.555105	+	1.26046i
$97$	−2.18447	−	1.58711i	−0.221799	−	0.161147i	0.471337	−	0.881953i	$-0.343772\pi$
$97$	−2.18447	−	1.58711i	−0.221799	−	0.161147i	−0.693136	+	0.720807i	$0.743772\pi$
$98$	9.66180	+	9.74144i	0.975989	+	0.984034i
$99$	−15.0966	+	8.55418i	−1.51726	+	0.859727i
$100$	1.43883	−	9.09567i	0.143883	−	0.909567i
$101$	1.10778			0.110229			0.0551144	−	0.998480i	$-0.482448\pi$
$101$	1.10778			0.110229			0.0551144	+	0.998480i	$0.482448\pi$
$102$	13.6298	+	15.2609i	1.34955	+	1.51106i
$103$	−2.98812	−	2.17099i	−0.294428	−	0.213914i	0.430758	−	0.902467i	$-0.358246\pi$
$103$	−2.98812	−	2.17099i	−0.294428	−	0.213914i	−0.725186	+	0.688553i	$0.758246\pi$
$104$	−0.140769	−	0.102275i	−0.0138035	−	0.0100289i
$105$	4.11162	+	9.38587i	0.401253	+	0.915967i
$106$	19.4626	−	14.1404i	1.89037	−	1.37344i
$107$	−2.78218			−0.268963			−0.134482	−	0.990916i	$-0.542937\pi$
$107$	−2.78218			−0.268963			−0.134482	+	0.990916i	$0.542937\pi$
$108$	5.53092	+	7.80990i	0.532213	+	0.751508i
$109$	2.95969	+	9.10899i	0.283487	+	0.872483i	0.986848	+	0.161651i	$0.0516818\pi$
$109$	2.95969	+	9.10899i	0.283487	+	0.872483i	−0.703361	+	0.710833i	$0.748318\pi$
$110$	−23.4190	+	9.70307i	−2.23291	+	0.925151i
$111$	0.485099	+	0.543152i	0.0460435	+	0.0515537i
$112$	−8.61858	−	7.39161i	−0.814380	−	0.698441i
$113$	5.43524	+	16.7279i	0.511304	+	1.57363i	0.789907	+	0.613226i	$0.210129\pi$
$113$	5.43524	+	16.7279i	0.511304	+	1.57363i	−0.278603	+	0.960406i	$0.589871\pi$
$114$	−3.96427	−	4.43869i	−0.371288	−	0.415721i
$115$	−11.0188	+	9.41272i	−1.02750	+	0.877741i
$116$	−9.21685	+	2.99474i	−0.855763	+	0.278054i
$117$	−1.53188	−	0.696914i	−0.141622	−	0.0644297i
$118$	6.66129			0.613221
$119$	−14.7199	−	6.13258i	−1.34937	−	0.562173i
$120$	−0.569034	−	1.05796i	−0.0519455	−	0.0965778i
$121$	18.1651	+	13.1977i	1.65137	+	1.19979i
$122$	−3.94007	+	5.42304i	−0.356717	+	0.490979i
$123$	10.7850	−	9.63224i	0.972447	−	0.868510i
$124$			14.3792i			1.29129i
$125$	−0.874008	+	11.1461i	−0.0781736	+	0.996940i
$126$	−13.5962	−	7.56141i	−1.21124	−	0.673624i
$127$	12.0987	+	3.93110i	1.07359	+	0.348829i	0.791883	−	0.610673i	$-0.209101\pi$
$127$	12.0987	+	3.93110i	1.07359	+	0.348829i	0.281702	+	0.959502i	$0.409101\pi$
$128$	2.00117	+	1.45394i	0.176880	+	0.128511i
$129$	0.268142	−	0.118089i	0.0236086	−	0.0103972i
$130$	−2.09648	−	1.28445i	−0.183874	−	0.112654i
$131$	14.8255	−	10.7713i	1.29531	−	0.941097i	0.295410	−	0.955370i	$-0.404544\pi$
$131$	14.8255	−	10.7713i	1.29531	−	0.941097i	0.999898	+	0.0142738i	$0.00454365\pi$
$132$	9.28978	−	15.9414i	0.808571	−	1.38752i
$133$	4.28131	+	1.78368i	0.371237	+	0.154665i
$134$	3.13654	−	1.01912i	0.270956	−	0.0880389i
$135$	−7.43917	−	8.92518i	−0.640262	−	0.768157i
$136$	1.77793	+	0.577684i	0.152456	+	0.0495360i
$137$	2.74645	+	8.45271i	0.234645	+	0.722163i	0.997168	+	0.0752025i	$0.0239603\pi$
$137$	2.74645	+	8.45271i	0.234645	+	0.722163i	−0.762523	+	0.646961i	$0.776040\pi$
$138$	4.66135	−	21.5026i	0.396800	−	1.83042i
$139$	1.56924	+	0.509878i	0.133101	+	0.0432473i	0.374810	−	0.927102i	$-0.377708\pi$
$139$	1.56924	+	0.509878i	0.133101	+	0.0432473i	−0.241709	+	0.970349i	$0.577708\pi$
$140$	−8.80247	−	6.42172i	−0.743944	−	0.542735i
$141$	6.61969	+	1.43502i	0.557478	+	0.120851i
$142$	−1.39657	−	1.92221i	−0.117198	−	0.161309i
$143$			3.24467i			0.271333i
$144$	11.7186	+	5.33129i	0.976553	+	0.444274i
$145$	10.8700	−	4.50370i	0.902701	−	0.374012i
$146$	−18.1952	−	13.2196i	−1.50584	−	1.09406i
$147$	12.1022	+	0.733106i	0.998170	+	0.0604656i
$148$	−0.736465	−	0.239292i	−0.0605371	−	0.0196697i
$149$			7.71997i			0.632445i	0.948685	+	0.316222i	$0.102415\pi$
$149$			7.71997i			0.632445i	−0.948685	+	0.316222i	$0.897585\pi$
$150$	−9.19010	−	14.2714i	−0.750369	−	1.16526i
$151$	−20.9656			−1.70616			−0.853078	−	0.521783i	$-0.825267\pi$
$151$	−20.9656			−1.70616			−0.853078	+	0.521783i	$0.825267\pi$
$152$	−0.517116	−	0.168021i	−0.0419436	−	0.0136283i
$153$	17.9664	+	2.03519i	1.45250	+	0.164535i
$154$	−2.41465	+	29.8966i	−0.194578	+	2.40913i
$155$	−1.37138	−	17.4038i	−0.110152	−	1.39791i
$156$	1.78048	−	0.179870i	0.142553	−	0.0144011i
$157$	−14.9370			−1.19210			−0.596050	−	0.802947i	$-0.703264\pi$
$157$	−14.9370			−1.19210			−0.596050	+	0.802947i	$0.703264\pi$
$158$	−10.3125	+	7.49246i	−0.820417	+	0.596068i
$159$	4.50389	−	20.7762i	0.357182	−	1.64766i
$160$	14.8550	+	9.10122i	1.17439	+	0.719515i
$161$	3.96865	+	16.6813i	0.312773	+	1.31467i
$162$	17.1934	+	3.94587i	1.35084	+	0.310017i
$163$	−9.84443	+	3.19865i	−0.771075	+	0.250538i	−0.668025	−	0.744139i	$-0.732860\pi$
$163$	−9.84443	+	3.19865i	−0.771075	+	0.250538i	−0.103050	+	0.994676i	$0.532860\pi$
$164$	−4.75144	+	14.6234i	−0.371025	+	1.14190i
$165$	−9.72348	+	20.1805i	−0.756972	+	1.57105i
$166$	12.8418	−	4.17256i	0.996719	−	0.323854i
$167$	11.1031	+	15.2822i	0.859188	+	1.18257i	0.981763	+	0.190111i	$0.0608848\pi$
$167$	11.1031	+	15.2822i	0.859188	+	1.18257i	−0.122575	+	0.992459i	$0.539115\pi$
$168$	−1.42109	+	0.0285527i	−0.109639	+	0.00220289i
$169$	10.2626	−	7.45623i	0.789432	−	0.573556i
$170$	25.6862	+	6.16413i	1.97005	+	0.472767i
$171$	−5.22559	−	0.591940i	−0.399611	−	0.0452668i
$172$	−0.183125	+	0.252050i	−0.0139632	+	0.0192186i
$173$	2.54527	+	0.827007i	0.193513	+	0.0628762i	0.404170	−	0.914684i	$-0.367560\pi$
$173$	2.54527	+	0.827007i	0.193513	+	0.0628762i	−0.210657	+	0.977560i	$0.567560\pi$
$174$	−8.99422	+	15.4342i	−0.681850	+	1.17006i
$175$	11.2665	+	6.93299i	0.851666	+	0.524085i
$176$		−	24.8213i		−	1.87097i
$177$	4.39036	−	3.92111i	0.330000	−	0.294729i
$178$	−4.72141	−	3.43030i	−0.353884	−	0.257112i
$179$	10.3722	−	14.2762i	0.775258	−	1.06705i	−0.220532	−	0.975380i	$-0.570779\pi$
$179$	10.3722	−	14.2762i	0.775258	−	1.06705i	0.995789	−	0.0916708i	$-0.0292207\pi$
$180$	11.6129	+	4.21695i	0.865576	+	0.314313i
$181$	0.575255	+	0.791770i	0.0427583	+	0.0588518i	0.829861	−	0.557970i	$-0.188420\pi$
$181$	0.575255	+	0.791770i	0.0427583	+	0.0588518i	−0.787103	+	0.616822i	$0.788420\pi$
$182$	−2.48356	+	1.51493i	−0.184094	+	0.112294i
$183$	0.595383	+	5.89354i	0.0440120	+	0.435663i
$184$	−0.621181	−	1.91180i	−0.0457941	−	0.140940i
$185$	0.914199	+	0.219388i	0.0672133	+	0.0161297i
$186$	17.6556	+	19.7685i	1.29457	+	1.44950i
$187$	−10.7724	−	33.1540i	−0.787754	−	2.42446i
$188$	−6.84994	+	2.22568i	−0.499583	+	0.162324i
$189$	−13.4120	+	3.01964i	−0.975579	+	0.219647i
$190$	−7.47092	−	1.79286i	−0.541998	−	0.130067i
$191$	−20.3888	+	6.62471i	−1.47528	+	0.479347i	−0.932699	−	0.360656i	$-0.882553\pi$
$191$	−20.3888	+	6.62471i	−1.47528	+	0.479347i	−0.542581	+	0.840004i	$0.682553\pi$
$192$	−11.5251	+	1.16430i	−0.831755	+	0.0840264i
$193$			2.42735i			0.174724i	0.996177	+	0.0873621i	$0.0278437\pi$
$193$			2.42735i			0.174724i	−0.996177	+	0.0873621i	$0.972156\pi$
$194$	4.28165	−	3.11080i	0.307404	−	0.223342i
$195$	−2.13785	+	0.387514i	−0.153094	+	0.0277504i
$196$	−11.5110	+	5.80578i	−0.822216	+	0.414698i
$197$	4.73162	+	3.43772i	0.337114	+	0.244927i	0.743443	−	0.668799i	$-0.233191\pi$
$197$	4.73162	+	3.43772i	0.337114	+	0.244927i	−0.406329	+	0.913727i	$0.633191\pi$
$198$	−6.80215	−	33.3227i	−0.483408	−	2.36814i
$199$		−	11.0587i		−	0.783930i	−0.919980	−	0.391965i	$-0.871795\pi$
$199$		−	11.0587i		−	0.783930i	0.919980	−	0.391965i	$-0.128205\pi$
$200$	−1.38195	−	0.703805i	−0.0977185	−	0.0497666i
$201$	1.46735	−	2.51799i	0.103499	−	0.177605i
$202$	−0.670969	+	2.06503i	−0.0472092	+	0.145295i
$203$	1.12077	−	13.8766i	0.0786624	−	0.973944i
$204$	−17.5958	+	7.74915i	−1.23195	+	0.542549i
$205$	4.35621	−	18.1526i	0.304251	−	1.26783i
$206$	5.85683	−	4.25523i	0.408064	−	0.296476i
$207$	−9.58508	−	16.9159i	−0.666209	−	1.17574i
$208$	1.94766	−	1.41506i	0.135046	−	0.0981164i
$209$	3.13318	+	9.64293i	0.216726	+	0.667015i
$210$	−19.9866	+	1.97961i	−1.37921	+	0.136606i
$211$	1.70164	−	5.23711i	0.117146	−	0.360538i	−0.875243	−	0.483684i	$-0.839298\pi$
$211$	1.70164	−	5.23711i	0.117146	−	0.360538i	0.992389	+	0.123146i	$0.0392984\pi$
$212$	6.98541	+	21.4989i	0.479760	+	1.47655i
$213$	−2.05196	−	0.444825i	−0.140598	−	0.0304789i
$214$	1.68513	−	5.18628i	0.115193	−	0.354527i
$215$	0.197606	−	0.322533i	0.0134766	−	0.0219965i
$216$	1.53873	−	0.479432i	0.104697	−	0.0326212i
$217$	−19.0676	−	7.94396i	−1.29440	−	0.539271i
$218$	−18.7728			−1.27145
$219$	−19.7738	+	1.99761i	−1.33619	+	0.134986i
$220$	−1.87114	−	23.7461i	−0.126152	−	1.60096i
$221$	1.98737	−	2.73538i	0.133685	−	0.184002i
$222$	−1.30631	+	0.575297i	−0.0876739	+	0.0386114i
$223$	6.89978	−	21.2354i	0.462044	−	1.42202i	−0.400619	−	0.916245i	$-0.631205\pi$
$223$	6.89978	−	21.2354i	0.462044	−	1.42202i	0.862663	−	0.505780i	$-0.168795\pi$
$224$	17.5977	−	10.7343i	1.17580	−	0.717216i
$225$	−14.4578	−	3.99642i	−0.963855	−	0.266428i
$226$	−34.4747			−2.29323
$227$	−5.34800	−	1.73767i	−0.354959	−	0.115333i	0.126109	−	0.992016i	$-0.459751\pi$
$227$	−5.34800	−	1.73767i	−0.354959	−	0.115333i	−0.481068	+	0.876683i	$0.659751\pi$
$228$	5.11778	−	2.25386i	0.338933	−	0.149266i
$229$	−8.43945	+	11.6159i	−0.557695	+	0.767601i	−0.991031	−	0.133631i	$-0.957336\pi$
$229$	−8.43945	+	11.6159i	−0.557695	+	0.767601i	0.433336	+	0.901232i	$0.357336\pi$
$230$	−10.8724	−	26.2413i	−0.716907	−	1.73030i
$231$	16.0069	+	21.1258i	1.05318	+	1.38997i
$232$			1.63209i			0.107152i
$233$	4.37376	−	3.17773i	0.286535	−	0.208180i	−0.435228	−	0.900320i	$-0.643332\pi$
$233$	4.37376	−	3.17773i	0.286535	−	0.208180i	0.721763	+	0.692141i	$0.243332\pi$
$234$	2.22696	−	2.43347i	0.145581	−	0.159081i
$235$	8.07853	−	3.34714i	0.526985	−	0.218343i
$236$	−1.93423	+	5.95294i	−0.125907	+	0.387503i
$237$	−2.38644	+	11.0085i	−0.155016	+	0.715081i
$238$	20.3474	−	23.7250i	1.31893	−	1.53786i
$239$	−1.21688	−	0.395388i	−0.0787134	−	0.0255755i	0.269396	−	0.963030i	$-0.413176\pi$
$239$	−1.21688	−	0.395388i	−0.0787134	−	0.0255755i	−0.348109	+	0.937454i	$0.613176\pi$
$240$	16.3542	−	2.96443i	1.05566	−	0.191353i
$241$	−14.4506	+	4.69528i	−0.930845	+	0.302450i	−0.734908	−	0.678167i	$-0.762775\pi$
$241$	−14.4506	+	4.69528i	−0.930845	+	0.302450i	−0.195937	+	0.980617i	$0.562775\pi$
$242$	−35.6043	+	25.8681i	−2.28873	+	1.66286i
$243$	13.6546	−	7.52007i	0.875944	−	0.482413i
$244$	−3.70229	−	5.09577i	−0.237015	−	0.326223i
$245$	13.3786	−	8.12483i	0.854728	−	0.519076i
$246$	11.4232	+	25.9384i	0.728320	+	1.65377i
$247$	−0.578032	+	0.795593i	−0.0367793	+	0.0506224i
$248$	2.30307	+	0.748314i	0.146245	+	0.0475180i
$249$	6.00772	−	10.3093i	0.380724	−	0.653326i
$250$	−20.2482	−	8.38029i	−1.28061	−	0.530016i
$251$	26.2832			1.65898			0.829491	−	0.558521i	$-0.188631\pi$
$251$	26.2832			1.65898			0.829491	+	0.558521i	$0.188631\pi$
$252$	10.7052	−	9.95477i	0.674367	−	0.627092i
$253$	−22.0331	+	30.3260i	−1.38521	+	1.90658i
$254$	−14.6560	+	20.1723i	−0.919599	+	1.26572i
$255$	20.5579	−	11.0573i	1.28739	−	0.692435i
$256$	−14.7436	+	10.7119i	−0.921477	+	0.669493i
$257$		−	8.69602i		−	0.542443i	−0.962517	−	0.271222i	$-0.912572\pi$
$257$		−	8.69602i		−	0.542443i	0.962517	−	0.271222i	$-0.0874276\pi$
$258$	0.0577216	+	0.571371i	0.00359359	+	0.0355720i
$259$	0.724184	−	0.844396i	0.0449986	−	0.0524682i
$260$	1.75662	−	1.50058i	0.108941	−	0.0930622i
$261$	3.15723	+	15.4668i	0.195428	+	0.957372i
$262$	11.0994	+	34.1603i	0.685721	+	2.11043i
$263$	−1.14730	−	3.53103i	−0.0707456	−	0.217733i	0.909432	−	0.415852i	$-0.136517\pi$
$263$	−1.14730	−	3.53103i	−0.0707456	−	0.217733i	−0.980178	+	0.198119i	$0.936517\pi$
$264$	−2.06983	−	2.31753i	−0.127389	−	0.142634i
$265$	−10.5052	−	25.3549i	−0.645327	−	1.55754i
$266$	−5.91810	+	6.90048i	−0.362862	+	0.423096i
$267$	−5.13103	+	0.518352i	−0.314014	+	0.0317226i
$268$			3.09893i			0.189297i
$269$	−5.36671	+	3.89914i	−0.327214	+	0.237735i	−0.739247	−	0.673434i	$-0.764819\pi$
$269$	−5.36671	+	3.89914i	−0.327214	+	0.237735i	0.412034	+	0.911169i	$0.364819\pi$
$270$	21.1433	−	8.46156i	1.28674	−	0.514954i
$271$	0.557151	−	0.766853i	0.0338445	−	0.0465830i	−0.791759	−	0.610833i	$-0.790835\pi$
$271$	0.557151	−	0.766853i	0.0338445	−	0.0465830i	0.825604	+	0.564250i	$0.190835\pi$
$272$	−15.2031	+	20.9253i	−0.921824	+	1.26878i
$273$	−0.745132	+	2.46040i	−0.0450974	+	0.148910i
$274$	−17.4202			−1.05240
$275$	4.52945	+	28.5625i	0.273136	+	1.72238i
$276$	17.8625	+	10.4093i	1.07520	+	0.626568i
$277$	−29.0588	−	9.44177i	−1.74597	−	0.567301i	−0.750374	−	0.661014i	$-0.770126\pi$
$277$	−29.0588	−	9.44177i	−1.74597	−	0.567301i	−0.995599	+	0.0937128i	$0.970126\pi$
$278$	−1.90093	+	2.61641i	−0.114010	+	0.156922i
$279$	23.2732	+	2.63632i	1.39333	+	0.157832i
$280$	−1.48664	+	1.07567i	−0.0888438	+	0.0642836i
$281$	5.68375	+	7.82301i	0.339064	+	0.466682i	0.944168	−	0.329465i	$-0.106868\pi$
$281$	5.68375	+	7.82301i	0.339064	+	0.466682i	−0.605104	+	0.796147i	$0.706868\pi$
$282$	−6.68449	+	11.4706i	−0.398055	+	0.683067i
$283$	8.36277	−	6.07590i	0.497115	−	0.361175i	−0.310799	−	0.950476i	$-0.600597\pi$
$283$	8.36277	−	6.07590i	0.497115	−	0.361175i	0.807914	+	0.589301i	$0.200597\pi$
$284$	2.12333	−	0.689911i	0.125996	−	0.0409387i
$285$	−5.97933	+	3.21605i	−0.354185	+	0.190502i
$286$	−6.04841	−	1.96525i	−0.357650	−	0.116208i
$287$	−16.7665	−	14.3796i	−0.989697	−	0.848800i
$288$	−15.7795	+	17.2428i	−0.929817	+	1.01604i
$289$	−5.97210	+	18.3802i	−0.351300	+	1.08119i
$290$	1.81161	+	22.9906i	0.106381	+	1.35005i
$291$	0.990827	−	4.57064i	0.0580833	−	0.267936i
$292$	17.0971	−	12.4218i	1.00053	−	0.726930i
$293$		−	11.0009i		−	0.642678i	−0.946964	−	0.321339i	$-0.895867\pi$
$293$		−	11.0009i		−	0.642678i	0.946964	−	0.321339i	$-0.104133\pi$
$294$	−8.69670	+	22.1157i	−0.507202	+	1.28982i
$295$	1.77334	−	7.38958i	0.103248	−	0.430238i
$296$	−0.0766534	+	0.105504i	−0.00445539	+	0.00613232i
$297$	−24.0984	−	17.9585i	−1.39833	−	1.04206i
$298$	−14.3909	−	4.67587i	−0.833640	−	0.270866i
$299$	−3.63570			−0.210258
$300$	15.4223	−	4.06887i	0.890409	−	0.234916i
$301$	−0.233063	−	0.382082i	−0.0134335	−	0.0220229i
$302$	12.6986	−	39.0822i	0.730720	−	2.24893i
$303$	0.773337	+	1.75599i	0.0444270	+	0.100879i
$304$	4.42187	−	6.08618i	0.253611	−	0.349066i
$305$	4.96705	+	5.81454i	0.284412	+	0.332940i
$306$	−14.6758	+	32.2587i	−0.838961	+	1.84411i
$307$	−14.7404			−0.841278			−0.420639	−	0.907228i	$-0.638194\pi$
$307$	−14.7404			−0.841278			−0.420639	+	0.907228i	$0.638194\pi$
$308$	−26.0163	−	10.8389i	−1.48242	−	0.617604i
$309$	1.35534	−	6.25214i	0.0771029	−	0.355672i
$310$	33.2732	+	7.98482i	1.88979	+	0.453508i
$311$	3.56469	−	10.9710i	0.202135	−	0.622107i	−0.797684	−	0.603076i	$-0.793942\pi$
$311$	3.56469	−	10.9710i	0.202135	−	0.622107i	0.999819	−	0.0190316i	$-0.00605831\pi$
$312$	0.0638497	−	0.294536i	0.00361478	−	0.0166748i
$313$	8.55757	+	26.3375i	0.483703	+	1.48868i	0.833851	+	0.551990i	$0.186131\pi$
$313$	8.55757	+	26.3375i	0.483703	+	1.48868i	−0.350148	+	0.936694i	$0.613869\pi$
$314$	9.04711	−	27.8441i	0.510558	−	1.57134i
$315$	−12.0076	+	13.0697i	−0.676553	+	0.736394i
$316$	−3.70130	−	11.3914i	−0.208215	−	0.640819i
$317$	23.3356	−	16.9543i	1.31066	−	0.952250i	0.310661	−	0.950521i	$-0.399450\pi$
$317$	23.3356	−	16.9543i	1.31066	−	0.952250i	0.999999	−	0.00172931i	$-0.000550457\pi$
$318$	36.0012	+	20.9796i	2.01885	+	1.17648i
$319$	24.6219	−	17.8889i	1.37856	−	1.00158i
$320$	−11.3707	+	9.71333i	−0.635639	+	0.542992i
$321$	−1.94222	−	4.41014i	−0.108404	−	0.246150i
$322$	−33.4996	−	2.70566i	−1.86686	−	0.150780i
$323$	3.26494	−	10.0484i	0.181666	−	0.559110i
$324$	−8.51868	+	14.2193i	−0.473260	+	0.789961i
$325$	−1.98300	+	1.98376i	−0.109997	+	0.110039i
$326$		−	20.2885i		−	1.12367i
$327$	−12.3729	+	11.0504i	−0.684222	+	0.611091i
$328$	2.09492	+	1.52205i	0.115673	+	0.0840411i
$329$	0.832951	−	10.3130i	0.0459221	−	0.568576i
$330$	−31.7293	−	30.3487i	−1.74664	−	1.67064i
$331$	3.92548	−	2.85203i	0.215764	−	0.156762i	−0.474654	−	0.880173i	$-0.657427\pi$
$331$	3.92548	−	2.85203i	0.215764	−	0.156762i	0.690418	+	0.723411i	$0.257427\pi$
$332$			12.6878i			0.696335i
$333$	−0.522327	+	1.14812i	−0.0286234	+	0.0629166i
$334$	−35.2126	+	11.4413i	−1.92675	+	0.626039i
$335$	−0.295553	−	3.75078i	−0.0161478	−	0.204927i
$336$	5.70015	−	18.8217i	0.310969	−	1.02681i
$337$	−2.92810	+	0.951398i	−0.159504	+	0.0518260i	−0.387681	−	0.921794i	$-0.626724\pi$
$337$	−2.92810	+	0.951398i	−0.159504	+	0.0518260i	0.228177	+	0.973620i	$0.426724\pi$
$338$	7.68330	+	23.6468i	0.417916	+	1.28621i
$339$	−22.7218	+	20.2933i	−1.23408	+	1.10218i
$340$	−12.9671	+	21.1649i	−0.703241	+	1.14783i
$341$	−13.9542	−	42.9466i	−0.755662	−	2.32569i
$342$	4.26851	−	9.38254i	0.230814	−	0.507350i
$343$	−1.33939	−	18.4718i	−0.0723202	−	0.997381i
$344$	0.0308400	+	0.0424476i	0.00166278	+	0.00228862i
$345$	−22.6126	−	10.8953i	−1.21742	−	0.586583i
$346$	−3.08326	+	4.24374i	−0.165757	+	0.228145i
$347$	18.8272	+	13.6788i	1.01070	+	0.734314i	0.964355	−	0.264611i	$-0.0852436\pi$
$347$	18.8272	+	13.6788i	1.01070	+	0.734314i	0.0463420	+	0.998926i	$0.485244\pi$
$348$	−11.1813	−	12.5194i	−0.599380	−	0.671110i
$349$			8.45206i			0.452429i	0.974078	+	0.226214i	$0.0726350\pi$
$349$			8.45206i			0.452429i	−0.974078	+	0.226214i	$0.927365\pi$
$350$	−19.7478	+	16.8027i	−1.05556	+	0.898144i
$351$	0.0353137	−	2.91475i	0.00188491	−	0.155578i
$352$	42.8571	+	13.9251i	2.28429	+	0.742212i
$353$	−11.5467	+	15.8926i	−0.614567	+	0.845880i	−0.996943	−	0.0781273i	$-0.975106\pi$
$353$	−11.5467	+	15.8926i	−0.614567	+	0.845880i	0.382376	+	0.924007i	$0.375106\pi$
$354$	4.65020	+	10.5591i	0.247155	+	0.561208i
$355$	−2.50416	+	1.03754i	−0.132907	+	0.0550668i
$356$	4.43648	−	3.22329i	0.235133	−	0.170834i
$357$	−0.554828	−	27.6141i	−0.0293646	−	1.46150i
$358$	20.3300	+	27.9818i	1.07447	+	1.47889i
$359$	−18.0325	+	5.85913i	−0.951721	+	0.309233i	−0.743415	−	0.668831i	$-0.766795\pi$
$359$	−18.0325	+	5.85913i	−0.951721	+	0.309233i	−0.208306	+	0.978064i	$0.566795\pi$
$360$	1.27977	−	1.64055i	0.0674498	−	0.0864646i
$361$	4.92171	−	15.1475i	0.259037	−	0.797234i
$362$	−1.82437	+	0.592773i	−0.0958867	+	0.0311555i
$363$	−8.23930	+	38.0075i	−0.432451	+	1.99488i
$364$	−0.632685	−	2.65935i	−0.0331617	−	0.139388i
$365$	−19.5087	+	16.6652i	−1.02113	+	0.872299i
$366$	−11.3468	−	2.45977i	−0.593107	−	0.128574i
$367$	4.45102	−	3.23385i	0.232341	−	0.168806i	−0.465523	−	0.885036i	$-0.654134\pi$
$367$	4.45102	−	3.23385i	0.232341	−	0.168806i	0.697864	+	0.716230i	$0.254134\pi$
$368$	27.8126			1.44983
$369$	22.7973	+	10.3715i	1.18678	+	0.539916i
$370$	−0.962679	+	1.57129i	−0.0500473	+	0.0816873i
$371$	−32.3680	−	2.61426i	−1.68046	−	0.135726i
$372$	−22.7930	+	10.0380i	−1.18176	+	0.520447i
$373$	15.9862	+	5.19424i	0.827735	+	0.268948i	0.692091	−	0.721810i	$-0.256690\pi$
$373$	15.9862	+	5.19424i	0.827735	+	0.268948i	0.135644	+	0.990758i	$0.456690\pi$
$374$	68.3272			3.53312
$375$	−18.2783	+	6.39561i	−0.943887	+	0.330268i
$376$			1.21296i			0.0625538i
$377$	2.80738	+	0.912174i	0.144588	+	0.0469794i
$378$	2.49451	−	26.8304i	0.128304	−	1.38001i
$379$	−31.0309	−	22.5453i	−1.59395	−	1.15807i	−0.898012	−	0.439972i	$-0.854989\pi$
$379$	−31.0309	−	22.5453i	−1.59395	−	1.15807i	−0.695939	−	0.718101i	$-0.745011\pi$
$380$	3.77152	−	6.15589i	0.193475	−	0.315790i
$381$	2.21467	+	21.9224i	0.113461	+	1.12312i
$382$		−	42.0194i		−	2.14990i
$383$	−18.2984	−	25.1856i	−0.935004	−	1.28692i	−0.957876	−	0.287184i	$-0.907281\pi$
$383$	−18.2984	−	25.1856i	−0.935004	−	1.28692i	0.0228719	−	0.999738i	$-0.492719\pi$
$384$	−0.907688	+	4.18712i	−0.0463203	+	0.213673i
$385$	32.5224	+	10.6376i	1.65750	+	0.542141i
$386$	−4.52483	−	1.47021i	−0.230308	−	0.0748316i
$387$	0.374376	+	0.342605i	0.0190306	+	0.0174156i
$388$	1.53675	+	4.72962i	0.0780165	+	0.240110i
$389$	−5.55118	−	1.80369i	−0.281456	−	0.0914506i	0.164887	−	0.986312i	$-0.447274\pi$
$389$	−5.55118	−	1.80369i	−0.281456	−	0.0914506i	−0.446343	+	0.894862i	$0.647274\pi$
$390$	0.572494	−	4.21989i	0.0289894	−	0.213682i
$391$	37.1495	−	12.0706i	1.87873	−	0.610437i
$392$	0.330844	+	2.14583i	0.0167101	+	0.108381i
$393$	27.4236	+	15.9811i	1.38334	+	0.806138i
$394$	−9.27415	+	6.73807i	−0.467225	+	0.339459i
$395$	5.56629	+	13.4346i	0.280070	+	0.675967i
$396$	31.7544	+	3.59705i	1.59572	+	0.180758i
$397$	−10.1351	−	7.36355i	−0.508664	−	0.369566i	0.303653	−	0.952783i	$-0.401794\pi$
$397$	−10.1351	−	7.36355i	−0.508664	−	0.369566i	−0.812316	+	0.583217i	$0.801794\pi$
$398$	20.6146	+	6.69809i	1.03332	+	0.335745i
$399$	0.161373	+	8.03165i	0.00807878	+	0.402086i
$400$	15.1697	−	15.1755i	0.758484	−	0.758773i
$401$		−	4.23582i		−	0.211527i	−0.994391	−	0.105763i	$-0.966271\pi$
$401$		−	4.23582i		−	0.211527i	0.994391	−	0.105763i	$-0.0337286\pi$
$402$	3.80505	+	4.26041i	0.189779	+	0.212490i
$403$	2.57438	−	3.54333i	0.128239	−	0.176506i
$404$	−1.65061	−	1.19924i	−0.0821209	−	0.0596644i
$405$	8.95442	−	18.0227i	0.444949	−	0.895556i
$406$	25.1886	+	10.4941i	1.25009	+	0.520811i
$407$	2.43183			0.120542
$408$	0.325450	+	3.22154i	0.0161122	+	0.159490i
$409$	29.5777	−	9.61037i	1.46252	−	0.475202i	0.533683	−	0.845685i	$-0.320808\pi$
$409$	29.5777	−	9.61037i	1.46252	−	0.475202i	0.928839	+	0.370482i	$0.120808\pi$
$410$	31.1998	+	19.1152i	1.54085	+	0.944032i
$411$	−11.4814	+	10.2543i	−0.566338	+	0.505806i
$412$	2.10210	+	6.46961i	0.103563	+	0.318735i
$413$	−6.82536	−	5.85367i	−0.335854	−	0.288040i
$414$	37.3386	−	7.62191i	1.83509	−	0.374596i
$415$	−1.21007	−	15.3566i	−0.0594000	−	0.753828i
$416$	1.35061	+	4.15675i	0.0662192	+	0.203802i
$417$	0.287250	+	2.84341i	0.0140667	+	0.139242i
$418$	−19.8732			−0.972029
$419$	−9.79616	+	7.11733i	−0.478574	+	0.347704i	−0.800773	−	0.598968i	$-0.795578\pi$
$419$	−9.79616	+	7.11733i	−0.478574	+	0.347704i	0.322199	+	0.946672i	$0.395578\pi$
$420$	4.03438	−	18.4361i	0.196858	−	0.899589i
$421$	9.91364	+	7.20268i	0.483161	+	0.351037i	0.802548	−	0.596587i	$-0.203477\pi$
$421$	9.91364	+	7.20268i	0.483161	+	0.351037i	−0.319387	+	0.947624i	$0.603477\pi$
$422$	8.73188	+	6.34408i	0.425061	+	0.308825i
$423$	2.34645	+	11.4949i	0.114088	+	0.558901i
$424$	3.80695			0.184882
$425$	13.6761	−	26.8536i	0.663390	−	1.30259i
$426$	2.07204	−	3.55564i	0.100391	−	0.172271i
$427$	8.80266	−	2.09424i	0.425991	−	0.101347i
$428$	4.14547	+	3.01186i	0.200379	+	0.145584i
$429$	−5.14325	+	2.26508i	−0.248318	+	0.109359i
$430$	0.481549	+	0.563712i	0.0232223	+	0.0271846i
$431$	3.14305	+	4.32604i	0.151395	+	0.208378i	0.877978	−	0.478702i	$-0.158892\pi$
$431$	3.14305	+	4.32604i	0.151395	+	0.208378i	−0.726582	+	0.687080i	$0.758892\pi$
$432$	−0.270145	+	22.2974i	−0.0129974	+	1.07278i
$433$	−18.0141	+	13.0880i	−0.865704	+	0.628971i	−0.929431	−	0.368996i	$-0.879701\pi$
$433$	−18.0141	+	13.0880i	−0.865704	+	0.628971i	0.0637265	+	0.997967i	$0.479701\pi$
$434$	26.3574	−	30.7326i	1.26520	−	1.47521i
$435$	14.7272	+	14.0864i	0.706117	+	0.675391i
$436$	5.45102	−	16.7765i	0.261057	−	0.803450i
$437$	−10.8050	+	3.51077i	−0.516875	+	0.167943i
$438$	8.25293	−	38.0704i	0.394340	−	1.81907i
$439$	−3.67316	−	1.19348i	−0.175311	−	0.0569618i	0.220046	−	0.975489i	$-0.429379\pi$
$439$	−3.67316	−	1.19348i	−0.175311	−	0.0569618i	−0.395357	+	0.918528i	$0.629379\pi$
$440$	−3.90072	−	0.936086i	−0.185959	−	0.0446261i
$441$	7.28637	+	19.6954i	0.346970	+	0.937876i
$442$	3.89532	+	5.36145i	0.185282	+	0.255018i
$443$	19.9227			0.946558			0.473279	−	0.880913i	$-0.343070\pi$
$443$	19.9227			0.946558			0.473279	+	0.880913i	$0.343070\pi$
$444$	−0.134810	−	1.33445i	−0.00639780	−	0.0633301i
$445$	−5.06226	+	4.32441i	−0.239974	+	0.204997i
$446$	35.4059	+	25.7239i	1.67652	+	1.21806i
$447$	−12.2372	+	5.38926i	−0.578801	+	0.254903i
$448$	4.09539	+	17.2141i	0.193489	+	0.813289i
$449$			19.1083i			0.901779i	0.892580	+	0.450889i	$0.148893\pi$
$449$			19.1083i			0.901779i	−0.892580	+	0.450889i	$0.851107\pi$
$450$	16.2066	−	24.5304i	0.763989	−	1.15637i
$451$		−	48.2871i		−	2.27375i
$452$	10.0104	−	30.8088i	0.470848	−	1.44912i
$453$	−14.6359	−	33.2334i	−0.687656	−	1.56144i
$454$	6.47841	−	8.91677i	0.304047	−	0.418485i
$455$	1.01940	+	3.15839i	0.0477900	+	0.148068i
$456$	−0.0946580	−	0.936995i	−0.00443277	−	0.0438788i
$457$		−	3.14691i		−	0.147206i	−0.997288	−	0.0736032i	$-0.976550\pi$
$457$		−	3.14691i		−	0.147206i	0.997288	−	0.0736032i	$-0.0234498\pi$
$458$	−16.5417	−	22.7676i	−0.772941	−	1.06386i
$459$	9.31619	+	29.9001i	0.434842	+	1.39562i
$460$	26.6078	−	2.09664i	1.24060	−	0.0977562i
$461$	−6.08002	+	18.7124i	−0.283175	+	0.871523i	0.703765	+	0.710433i	$0.251501\pi$
$461$	−6.08002	+	18.7124i	−0.283175	+	0.871523i	−0.986940	+	0.161090i	$0.948499\pi$
$462$	−49.0759	+	17.0430i	−2.28322	+	0.792913i
$463$	−12.1041	+	3.93286i	−0.562525	+	0.182776i	−0.576457	−	0.817127i	$-0.695565\pi$
$463$	−12.1041	+	3.93286i	−0.562525	+	0.182776i	0.0139319	+	0.999903i	$0.495565\pi$
$464$	−21.4761	−	6.97800i	−0.997002	−	0.323946i
$465$	26.6301	−	14.3233i	1.23494	−	0.664227i
$466$	3.27450	+	10.0779i	0.151688	+	0.466848i
$467$	3.17949	+	4.37619i	0.147129	+	0.202506i	0.876220	−	0.481911i	$-0.160057\pi$
$467$	3.17949	+	4.37619i	0.147129	+	0.202506i	−0.729091	+	0.684416i	$0.760057\pi$
$468$	1.52806	+	2.69675i	0.0706347	+	0.124657i
$469$	−4.10936	−	1.71204i	−0.189753	−	0.0790547i
$470$	1.34638	+	17.0866i	0.0621040	+	0.788144i
$471$	−10.4274	−	23.6772i	−0.480469	−	1.09099i
$472$	0.852805	+	0.619599i	0.0392535	+	0.0285194i
$473$	0.302343	−	0.930515i	0.0139017	−	0.0427851i
$474$	−19.0757	−	11.1163i	−0.876174	−	0.510588i
$475$	−3.97774	+	7.81045i	−0.182511	+	0.358368i
$476$	15.2939	+	25.0727i	0.700993	+	1.14920i
$477$	36.0773	−	7.36444i	1.65187	−	0.337195i
$478$	1.47409	−	2.02891i	0.0674234	−	0.0928004i
$479$	−4.65189	−	3.37980i	−0.212550	−	0.154427i	0.476417	−	0.879220i	$-0.341935\pi$
$479$	−4.65189	−	3.37980i	−0.212550	−	0.154427i	−0.688967	+	0.724793i	$0.741935\pi$
$480$	−4.05651	+	29.9008i	−0.185154	+	1.36478i
$481$	0.138638	+	0.190819i	0.00632137	+	0.00870062i
$482$		−	29.7813i		−	1.35650i
$483$	−23.6718	+	17.9360i	−1.07710	+	0.816115i
$484$	−12.7789	−	39.3295i	−0.580860	−	1.78770i
$485$	−2.31107	−	5.57791i	−0.104940	−	0.253280i
$486$	5.74783	+	30.0085i	0.260727	+	1.36121i
$487$	4.12189	−	1.33928i	0.186781	−	0.0606888i	−0.214133	−	0.976804i	$-0.568693\pi$
$487$	4.12189	−	1.33928i	0.186781	−	0.0606888i	0.400914	+	0.916116i	$0.368693\pi$
$488$	−1.00885	+	0.327794i	−0.0456684	+	0.0148386i
$489$	−11.9426	−	13.3718i	−0.540065	−	0.604696i
$490$	7.04233	+	29.8603i	0.318140	+	1.34895i
$491$	−12.7017	+	4.12702i	−0.573218	+	0.186250i	−0.581260	−	0.813718i	$-0.697440\pi$
$491$	−12.7017	+	4.12702i	−0.573218	+	0.186250i	0.00804206	+	0.999968i	$0.497440\pi$
$492$	−26.4971	+	2.67682i	−1.19458	+	0.120680i
$493$	−31.7142			−1.42834
$494$	−1.13297	−	1.55939i	−0.0509746	−	0.0701605i
$495$	−38.7768	−	1.32518i	−1.74289	−	0.0595622i
$496$	−19.6936	+	27.1060i	−0.884270	+	1.21709i
$497$	−0.258196	+	3.19681i	−0.0115817	+	0.143396i
$498$	15.5789	+	17.4432i	0.698106	+	0.781650i
$499$	14.4106			0.645109			0.322555	−	0.946551i	$-0.395458\pi$
$499$	14.4106			0.645109			0.322555	+	0.946551i	$0.395458\pi$
$500$	13.3686	−	15.6617i	0.597861	−	0.700411i
$501$	−16.4733	+	28.2684i	−0.735975	+	1.26294i
$502$	−15.9194	+	48.9947i	−0.710515	+	2.18674i
$503$	−16.7448	+	23.0472i	−0.746613	+	1.02762i	0.251598	+	0.967832i	$0.419044\pi$
$503$	−16.7448	+	23.0472i	−0.746613	+	1.02762i	−0.998211	+	0.0597927i	$0.980956\pi$
$504$	−1.03731	−	2.23269i	−0.0462055	−	0.0994518i
$505$	2.11218	+	1.29407i	0.0939909	+	0.0575854i
$506$	−43.1857	−	59.4401i	−1.91984	−	2.64243i
$507$	18.9834	+	11.0625i	0.843084	+	0.491305i
$508$	−13.7715	−	18.9549i	−0.611013	−	0.840987i
$509$	8.60579	+	26.4859i	0.381445	+	1.17397i	0.939027	+	0.343845i	$0.111729\pi$
$509$	8.60579	+	26.4859i	0.381445	+	1.17397i	−0.557582	+	0.830122i	$0.688271\pi$
$510$	8.16039	+	45.0194i	0.361348	+	1.99349i
$511$	7.02650	+	29.5343i	0.310834	+	1.30652i
$512$	−9.50934	−	29.2667i	−0.420257	−	1.29342i
$513$	−2.70964	−	8.69652i	−0.119634	−	0.383961i
$514$	16.2103	+	5.26705i	0.715007	+	0.232320i
$515$	−3.16129	−	7.62998i	−0.139303	−	0.336217i
$516$	−0.527373	−	0.114324i	−0.0232163	−	0.00503285i
$517$	18.2990	−	13.2950i	0.804787	−	0.584712i
$518$	1.13542	+	1.86140i	0.0498874	+	0.0817851i
$519$	0.465911	+	4.61193i	0.0204512	+	0.202441i
$520$	−0.148927	−	0.359445i	−0.00653089	−	0.0157627i
$521$	12.6760	+	9.20966i	0.555346	+	0.403483i	0.829753	−	0.558131i	$-0.188481\pi$
$521$	12.6760	+	9.20966i	0.555346	+	0.403483i	−0.274407	+	0.961614i	$0.588481\pi$
$522$	−30.7441	−	3.48261i	−1.34563	−	0.152430i
$523$	1.59149	−	4.89809i	0.0695908	−	0.214178i	−0.910213	−	0.414141i	$-0.864082\pi$
$523$	1.59149	−	4.89809i	0.0695908	−	0.214178i	0.979804	+	0.199963i	$0.0640820\pi$
$524$	−33.7507			−1.47441
$525$	−3.12470	+	22.6988i	−0.136373	+	0.990658i
$526$	7.27712			0.317298
$527$	−14.5410	+	44.7527i	−0.633417	+	1.94946i
$528$	39.3451	−	17.3275i	1.71228	−	0.754085i
$529$	−15.3733	−	11.1694i	−0.668404	−	0.485624i
$530$	53.6270	−	4.22569i	2.32941	−	0.183552i
$531$	9.28039	+	4.22203i	0.402735	+	0.183221i
$532$	−4.44827	−	7.29246i	−0.192857	−	0.316168i
$533$	3.78896	−	2.75284i	0.164118	−	0.119239i
$534$	2.14153	−	9.87876i	0.0926729	−	0.427496i
$535$	−5.30470	−	3.25003i	−0.229342	−	0.140511i
$536$	0.496347	+	0.161273i	0.0214389	+	0.00696592i
$537$	29.8705	+	6.47536i	1.28901	+	0.279432i
$538$	−4.01788	−	12.3658i	−0.173223	−	0.533126i
$539$	28.7460	−	28.5110i	1.23818	−	1.22806i
$540$	1.42243	+	21.3519i	0.0612118	+	0.918840i
$541$	8.11752	+	24.9832i	0.348999	+	1.07411i	0.959408	+	0.282023i	$0.0910054\pi$
$541$	8.11752	+	24.9832i	0.348999	+	1.07411i	−0.610408	+	0.792087i	$0.708995\pi$
$542$	1.09204	+	1.50306i	0.0469070	+	0.0645620i
$543$	−0.853484	+	1.46459i	−0.0366265	+	0.0628515i
$544$	−27.6010	−	37.9896i	−1.18338	−	1.62879i
$545$	−4.99760	+	20.8253i	−0.214074	+	0.892056i
$546$	−4.13513	−	2.87923i	−0.176967	−	0.123220i
$547$	−17.8790	+	24.6084i	−0.764452	+	1.05218i	0.232379	+	0.972625i	$0.425349\pi$
$547$	−17.8790	+	24.6084i	−0.764452	+	1.05218i	−0.996831	+	0.0795520i	$0.974651\pi$
$548$	5.05829	−	15.5678i	0.216079	−	0.665024i
$549$	−8.92645	+	5.05800i	−0.380972	+	0.215870i
$550$	−55.9870	−	8.85652i	−2.38729	−	0.377643i
$551$	9.22418			0.392963
$552$	2.59682	−	2.31927i	0.110528	−	0.0987147i
$553$	17.1505	+	1.38520i	0.729316	+	0.0589045i
$554$	35.2010	−	48.4500i	1.49555	−	2.05844i
$555$	0.290436	+	1.60229i	0.0123283	+	0.0680133i
$556$	−1.78622	−	2.45851i	−0.0757524	−	0.104264i
$557$	−1.29843			−0.0550164			−0.0275082	−	0.999622i	$-0.508757\pi$
$557$	−1.29843			−0.0550164			−0.0275082	+	0.999622i	$0.508757\pi$
$558$	−19.0106	+	41.7869i	−0.804783	+	1.76898i
$559$	0.0902515	−	0.0293245i	0.00381723	−	0.00124029i
$560$	−7.79824	−	24.1613i	−0.329536	−	1.02100i
$561$	45.0335	−	40.2203i	1.90132	−	1.69810i
$562$	−18.0255	+	5.85684i	−0.760360	+	0.247056i
$563$	4.48635	−	1.45770i	0.189077	−	0.0614349i	−0.212948	−	0.977064i	$-0.568306\pi$
$563$	4.48635	−	1.45770i	0.189077	−	0.0614349i	0.402025	+	0.915629i	$0.368306\pi$
$564$	−8.30991	−	9.30438i	−0.349910	−	0.391785i
$565$	−9.17770	+	38.2440i	−0.386109	+	1.60894i
$566$	6.26094	+	19.2692i	0.263167	+	0.809944i
$567$	−14.1494	−	19.1519i	−0.594218	−	0.804304i
$568$		−	0.375991i		−	0.0157763i
$569$	4.70266	+	6.47266i	0.197146	+	0.271348i	0.896132	−	0.443787i	$-0.146365\pi$
$569$	4.70266	+	6.47266i	0.197146	+	0.271348i	−0.698987	+	0.715135i	$0.746365\pi$
$570$	−2.37347	−	13.0940i	−0.0994138	−	0.548448i
$571$	8.98177	+	6.52564i	0.375875	+	0.273090i	0.759643	−	0.650340i	$-0.225374\pi$
$571$	8.98177	+	6.52564i	0.375875	+	0.273090i	−0.383768	+	0.923430i	$0.625374\pi$
$572$	3.51253	−	4.83459i	0.146866	−	0.202144i
$573$	−24.7343	−	27.6944i	−1.03329	−	1.15695i
$574$	36.9603	−	22.5451i	1.54269	−	0.941015i
$575$	−32.0047	+	5.07531i	−1.33469	+	0.211655i
$576$	−9.89120	−	17.4562i	−0.412133	−	0.727340i
$577$	−7.19536	+	22.1450i	−0.299547	+	0.921910i	0.682109	+	0.731250i	$0.261063\pi$
$577$	−7.19536	+	22.1450i	−0.299547	+	0.921910i	−0.981656	+	0.190660i	$0.938937\pi$
$578$	−30.6455	−	22.2653i	−1.27469	−	0.926113i
$579$	−3.84768	+	1.69451i	−0.159904	+	0.0704215i
$580$	−21.0719	−	5.05678i	−0.874961	−	0.209971i
$581$	−16.8248	−	7.00954i	−0.698010	−	0.290805i
$582$	7.92003	+	4.61538i	0.328296	+	0.191314i
$583$	−41.7269	−	57.4322i	−1.72815	−	2.37860i
$584$	−1.09980	−	3.38484i	−0.0455102	−	0.140066i
$585$	−2.10668	−	3.11826i	−0.0871004	−	0.128924i
$586$	20.5068	+	6.66307i	0.847129	+	0.275249i
$587$	−15.1538	+	4.92378i	−0.625466	+	0.203226i	−0.604566	−	0.796555i	$-0.706653\pi$
$587$	−15.1538	+	4.92378i	−0.625466	+	0.203226i	−0.0209004	+	0.999782i	$0.506653\pi$
$588$	−17.2387	−	14.1936i	−0.710913	−	0.585335i
$589$	4.22930	−	13.0164i	0.174265	−	0.536333i
$590$	12.7009	+	7.78145i	0.522888	+	0.320357i
$591$	−2.14616	+	9.90012i	−0.0882811	+	0.407236i
$592$	−1.06056	−	1.45974i	−0.0435889	−	0.0599950i
$593$		−	35.3098i		−	1.45000i	−0.688749	−	0.725000i	$-0.741840\pi$
$593$		−	35.3098i		−	1.45000i	0.688749	−	0.725000i	$-0.258160\pi$
$594$	48.0727	−	34.0447i	1.97245	−	1.39687i
$595$	−20.9021	−	28.8880i	−0.856903	−	1.18429i
$596$	8.35730	−	11.5028i	0.342328	−	0.471174i
$597$	17.5296	−	7.72000i	0.717438	−	0.315958i
$598$	2.20209	−	6.77734i	0.0900501	−	0.277146i
$599$		−	33.9363i		−	1.38660i	−0.720649	−	0.693300i	$-0.756156\pi$
$599$		−	33.9363i		−	1.38660i	0.720649	−	0.693300i	$-0.243844\pi$
$600$	0.150901	−	2.68190i	0.00616052	−	0.109488i
$601$			19.1054i			0.779327i	0.920957	+	0.389663i	$0.127409\pi$
$601$			19.1054i			0.779327i	−0.920957	+	0.389663i	$0.872591\pi$
$602$	0.853406	−	0.203033i	0.0347822	−	0.00827502i
$603$	5.01571	+	0.568166i	0.204256	+	0.0231375i
$604$	31.2390	+	22.6964i	1.27110	+	0.923505i
$605$	19.2179	+	46.3835i	0.781318	+	1.88576i
$606$	−3.74176	+	0.378004i	−0.151999	+	0.0153554i
$607$	−11.5599			−0.469201			−0.234600	−	0.972092i	$-0.575378\pi$
$607$	−11.5599			−0.469201			−0.234600	+	0.972092i	$0.575378\pi$
$608$	8.02784	+	11.0494i	0.325572	+	0.448111i
$609$	22.7787	−	7.91056i	0.923039	−	0.320552i
$610$	−13.8474	+	5.73733i	−0.560665	+	0.232298i
$611$	2.08644	+	0.677926i	0.0844083	+	0.0274259i
$612$	−24.5670	−	22.4821i	−0.993061	−	0.908786i
$613$	42.6364	−	13.8534i	1.72207	−	0.559533i	0.729800	−	0.683661i	$-0.239613\pi$
$613$	42.6364	−	13.8534i	1.72207	−	0.559533i	0.992266	+	0.124128i	$0.0396133\pi$
$614$	8.92803	−	27.4777i	0.360306	−	1.10891i
$615$	31.8154	−	5.76697i	1.28292	−	0.232547i
$616$	−3.08996	+	3.60288i	−0.124498	+	0.145164i
$617$	11.2781	−	8.19405i	0.454041	−	0.329880i	−0.337148	−	0.941452i	$-0.609462\pi$
$617$	11.2781	−	8.19405i	0.454041	−	0.329880i	0.791189	+	0.611572i	$0.209462\pi$
$618$	10.8337	+	6.31334i	0.435797	+	0.253960i
$619$	6.19005	+	8.51987i	0.248799	+	0.342442i	0.915090	−	0.403249i	$-0.132119\pi$
$619$	6.19005	+	8.51987i	0.248799	+	0.342442i	−0.666291	+	0.745692i	$0.732119\pi$
$620$	−16.7972	+	27.4164i	−0.674592	+	1.10107i
$621$	20.1228	−	27.0026i	0.807500	−	1.08358i
$622$	18.2920	+	13.2899i	0.733443	+	0.532878i
$623$	1.82328	+	7.66377i	0.0730483	+	0.307042i
$624$	3.60271	+	2.09947i	0.144224	+	0.0840459i
$625$	−14.6869	+	20.2310i	−0.587476	+	0.809241i
$626$	−54.2792			−2.16943
$627$	−13.0981	+	11.6982i	−0.523089	+	0.467180i
$628$	22.2562	+	16.1701i	0.888121	+	0.645258i
$629$	−2.05013	−	1.48951i	−0.0817441	−	0.0593905i
$630$	−17.0905	−	30.2996i	−0.680901	−	1.20717i
$631$	34.9519	−	25.3941i	1.39142	−	1.01092i	0.395707	−	0.918377i	$-0.370500\pi$
$631$	34.9519	−	25.3941i	1.39142	−	1.01092i	0.995708	−	0.0925452i	$-0.0295003\pi$
$632$	−2.01716			−0.0802382
$633$	9.48945	−	0.958653i	0.377172	−	0.0381030i
$634$	17.4706	+	53.7691i	0.693848	+	2.13544i
$635$	18.4761	+	21.6285i	0.733201	+	0.858302i
$636$	−29.2023	+	26.0811i	−1.15795	+	1.03418i
$637$	3.87599	+	0.630214i	0.153572	+	0.0249700i
$638$	18.4337	+	56.7330i	0.729795	+	2.24608i
$639$	−0.727346	−	3.56316i	−0.0287734	−	0.140957i
$640$	2.11715	+	5.10987i	0.0836877	+	0.201985i
$641$	−30.4586	+	9.89661i	−1.20304	+	0.390893i	−0.840880	−	0.541222i	$-0.817962\pi$
$641$	−30.4586	+	9.89661i	−1.20304	+	0.390893i	−0.362164	+	0.932114i	$0.617962\pi$
$642$	9.39735	−	0.949349i	0.370884	−	0.0374678i
$643$	−10.6287			−0.419157			−0.209578	−	0.977792i	$-0.567209\pi$
$643$	−10.6287			−0.419157			−0.209578	+	0.977792i	$0.567209\pi$
$644$	12.1451	−	29.1516i	0.478586	−	1.14874i
$645$	0.649206	+	0.0880751i	0.0255625	+	0.00346795i
$646$	16.7539	+	12.1724i	0.659172	+	0.478916i
$647$	8.18995	−	11.2725i	0.321980	−	0.443168i	−0.617090	−	0.786892i	$-0.711689\pi$
$647$	8.18995	−	11.2725i	0.321980	−	0.443168i	0.939071	+	0.343725i	$0.111689\pi$
$648$	1.83414	+	2.10441i	0.0720518	+	0.0826689i
$649$		−	19.6568i		−	0.771597i
$650$	−2.49686	−	4.89806i	−0.0979351	−	0.192118i
$651$	−0.718707	−	35.7705i	−0.0281684	−	1.40196i
$652$	18.1310	+	5.89113i	0.710065	+	0.230714i
$653$	−33.7705	−	24.5357i	−1.32154	−	0.960157i	−0.999912	−	0.0132925i	$-0.995769\pi$
$653$	−33.7705	−	24.5357i	−1.32154	−	0.960157i	−0.321632	−	0.946865i	$-0.604231\pi$
$654$	−13.1052	−	29.7575i	−0.512452	−	1.16361i
$655$	40.8500	−	3.21889i	1.59614	−	0.125772i
$656$	−28.9850	+	21.0588i	−1.13167	+	0.822209i
$657$	−16.9704	−	29.9497i	−0.662079	−	1.16845i
$658$	18.7201	+	7.79916i	0.729785	+	0.304043i
$659$	−37.7779	+	12.2748i	−1.47162	+	0.478157i	−0.931596	−	0.363495i	$-0.881583\pi$
$659$	−37.7779	+	12.2748i	−1.47162	+	0.478157i	−0.540020	+	0.841652i	$0.681583\pi$
$660$	36.3346	−	19.5430i	1.41432	−	0.760710i
$661$	−34.3838	−	11.1720i	−1.33737	−	0.434539i	−0.448947	−	0.893558i	$-0.648201\pi$
$661$	−34.3838	−	11.1720i	−1.33737	−	0.434539i	−0.888426	+	0.459019i	$0.848201\pi$
$662$	2.93888	+	9.04496i	0.114223	+	0.351542i
$663$	5.72333	+	1.24071i	0.222276	+	0.0481851i
$664$	2.03217	+	0.660293i	0.0788636	+	0.0256243i
$665$	6.07944	+	8.40216i	0.235751	+	0.325822i
$666$	−1.82385	−	1.66907i	−0.0706729	−	0.0646753i
$667$	20.0448	+	27.5892i	0.776136	+	1.06826i
$668$		−	34.7904i		−	1.34608i
$669$	38.4777	−	3.88713i	1.48763	−	0.150285i
$670$	7.17086	+	1.72085i	0.277035	+	0.0664821i
$671$	16.0029	+	11.6268i	0.617784	+	0.448846i
$672$	29.3002	+	20.4013i	1.13028	+	0.786999i
$673$	−37.6813	−	12.2434i	−1.45251	−	0.471948i	−0.526734	−	0.850030i	$-0.676584\pi$
$673$	−37.6813	−	12.2434i	−1.45251	−	0.471948i	−0.925772	+	0.378082i	$0.876584\pi$
$674$		−	6.03455i		−	0.232442i
$675$	−3.75802	−	25.7075i	−0.144646	−	0.989483i
$676$	−23.3632			−0.898584
$677$	−24.1225	−	7.83788i	−0.927104	−	0.301234i	−0.193726	−	0.981056i	$-0.562057\pi$
$677$	−24.1225	−	7.83788i	−0.927104	−	0.301234i	−0.733378	+	0.679821i	$0.762057\pi$
$678$	−24.0666	−	54.6473i	−0.924271	−	2.09872i
$679$	−7.12074	−	0.575120i	−0.273269	−	0.0220711i
$680$	2.71510	+	3.17836i	0.104119	+	0.121885i
$681$	−0.978951	−	9.69038i	−0.0375135	−	0.371336i
$682$	88.5090			3.38918
$683$	−6.05251	+	4.39741i	−0.231593	+	0.168262i	−0.697530	−	0.716556i	$-0.745717\pi$
$683$	−6.05251	+	4.39741i	−0.231593	+	0.168262i	0.465937	+	0.884818i	$0.345717\pi$
$684$	7.14538	+	6.53899i	0.273210	+	0.250025i
$685$	−4.63753	+	19.3248i	−0.177191	+	0.738364i
$686$	35.2446	+	8.69131i	1.34565	+	0.331836i
$687$	−24.3044	−	5.26872i	−0.927269	−	0.201014i
$688$	−0.690411	+	0.224328i	−0.0263217	+	0.00855243i
$689$	2.12770	−	6.54840i	0.0810591	−	0.249474i
$690$	34.0061	−	35.5532i	1.29459	−	1.35349i
$691$	−15.0235	+	4.88143i	−0.571521	+	0.185698i	−0.580498	−	0.814261i	$-0.697142\pi$
$691$	−15.0235	+	4.88143i	−0.571521	+	0.185698i	0.00897771	+	0.999960i	$0.497142\pi$
$692$	−2.89719	−	3.98764i	−0.110135	−	0.151587i
$693$	−22.3130	+	40.1209i	−0.847601	+	1.52407i
$694$	−36.9021	+	26.8109i	−1.40078	+	1.01773i
$695$	2.39641	+	2.80530i	0.0909011	+	0.106411i
$696$	−2.58708	+	1.13935i	−0.0980632	+	0.0431869i
$697$	−29.5760	+	40.7079i	−1.12027	+	1.54192i
$698$	−15.7556	−	5.11929i	−0.596357	−	0.193768i
$699$	8.09043	+	4.71468i	0.306008	+	0.178325i
$700$	−9.28183	−	22.5268i	−0.350820	−	0.851434i
$701$			20.7787i			0.784800i	0.919795	+	0.392400i	$0.128355\pi$
$701$			20.7787i			0.784800i	−0.919795	+	0.392400i	$0.871645\pi$
$702$	5.41201	+	1.83125i	0.204263	+	0.0691160i
$703$	0.596286	+	0.433227i	0.0224894	+	0.0163395i
$704$	−22.7368	+	31.2945i	−0.856924	+	1.17945i
$705$	10.9452	+	10.4690i	0.412222	+	0.394284i
$706$	−22.6319	−	31.1502i	−0.851764	−	1.17235i
$707$	2.50216	−	1.52627i	0.0941034	−	0.0574014i
$708$	−10.7865	+	1.08969i	−0.405382	+	0.0409529i
$709$	−7.65040	−	23.5455i	−0.287317	−	0.884270i	−0.985695	−	0.168541i	$-0.946094\pi$
$709$	−7.65040	−	23.5455i	−0.287317	−	0.884270i	0.698378	−	0.715729i	$-0.253906\pi$
$710$	−0.417349	−	5.29645i	−0.0156628	−	0.198772i
$711$	−19.1160	+	3.90214i	−0.716907	+	0.146342i
$712$	−0.285384	−	0.878322i	−0.0106952	−	0.0329165i
$713$	48.1223	−	15.6359i	1.80220	−	0.585569i
$714$	51.8118	+	15.6912i	1.93901	+	0.587229i
$715$	−3.79029	+	6.18652i	−0.141749	+	0.231363i
$716$	−30.9095	+	10.0431i	−1.15514	+	0.375328i
$717$	−0.222750	−	2.20494i	−0.00831875	−	0.0823451i
$718$		−	37.1634i		−	1.38692i
$719$	−39.3367	+	28.5798i	−1.46701	+	1.06585i	−0.485547	+	0.874210i	$0.661380\pi$
$719$	−39.3367	+	28.5798i	−1.46701	+	1.06585i	−0.981466	+	0.191637i	$0.938620\pi$
$720$	16.1158	+	23.8543i	0.600600	+	0.888996i
$721$	−9.74041	−	0.786702i	−0.362752	−	0.0292983i
$722$	25.2555	+	18.3492i	0.939912	+	0.682886i
$723$	−17.5305	−	19.6285i	−0.651968	−	0.729990i
$724$		−	1.80249i		−	0.0669890i
$725$	25.9865	+	4.11077i	0.965114	+	0.152670i
$726$	−65.8596	−	38.3795i	−2.44428	−	1.42440i
$727$	−7.01859	+	21.6010i	−0.260305	+	0.801137i	0.732433	+	0.680839i	$0.238385\pi$
$727$	−7.01859	+	21.6010i	−0.260305	+	0.801137i	−0.992738	+	0.120297i	$0.961615\pi$
$728$	−0.458866	−	0.0370612i	−0.0170067	−	0.00137358i
$729$	21.4526	+	16.3948i	0.794539	+	0.607213i
$730$	−19.2497	−	46.4603i	−0.712462	−	1.71957i
$731$	−0.824830	+	0.599274i	−0.0305074	+	0.0221650i
$732$	5.49296	−	9.42597i	0.203026	−	0.348394i
$733$	32.2845	−	23.4560i	1.19245	−	0.866369i	0.198933	−	0.980013i	$-0.436253\pi$
$733$	32.2845	−	23.4560i	1.19245	−	0.866369i	0.993521	+	0.113645i	$0.0362525\pi$
$734$	3.33233	+	10.2559i	0.122999	+	0.378551i
$735$	22.2185	+	15.5351i	0.819542	+	0.573020i
$736$	−15.6033	+	48.0221i	−0.575146	+	1.77012i
$737$	−3.00734	−	9.25563i	−0.110777	−	0.340936i
$738$	−33.1415	+	36.2149i	−1.21996	+	1.33309i
$739$	−5.40874	+	16.6464i	−0.198964	+	0.612348i	0.800944	+	0.598740i	$0.204332\pi$
$739$	−5.40874	+	16.6464i	−0.198964	+	0.612348i	−0.999907	+	0.0136078i	$0.995668\pi$
$740$	−1.12467	−	1.31656i	−0.0413436	−	0.0483978i
$741$	−1.66465	−	0.360864i	−0.0611523	−	0.0132567i
$742$	24.4781	−	58.7539i	0.898618	−	2.15693i
$743$	−20.7881			−0.762640			−0.381320	−	0.924443i	$-0.624530\pi$
$743$	−20.7881			−0.762640			−0.381320	+	0.924443i	$0.624530\pi$
$744$	0.421578	+	4.17309i	0.0154558	+	0.152993i
$745$	−9.01816	+	14.7195i	−0.330400	+	0.539279i
$746$	−19.3652	+	26.6540i	−0.709012	+	0.975871i
$747$	20.5356	+	2.32622i	0.751360	+	0.0851119i
$748$	−19.8401	+	61.0614i	−0.725424	+	2.23263i
$749$	−6.28412	+	3.83320i	−0.229617	+	0.140062i
$750$	−0.851204	−	37.9464i	−0.0310816	−	1.38561i
$751$	16.7429			0.610955			0.305478	−	0.952199i	$-0.401184\pi$
$751$	16.7429			0.610955			0.305478	+	0.952199i	$0.401184\pi$
$752$	−15.9610	−	5.18604i	−0.582037	−	0.189115i
$753$	18.3481	+	41.6625i	0.668643	+	1.51827i
$754$	−3.40078	+	4.68078i	−0.123849	+	0.170464i
$755$	−39.9745	−	24.4912i	−1.45482	−	0.891326i
$756$	23.2529	+	10.0199i	0.845701	+	0.364422i
$757$		−	19.2655i		−	0.700216i	−0.936709	−	0.350108i	$-0.886145\pi$
$757$		−	19.2655i		−	0.700216i	0.936709	−	0.350108i	$-0.113855\pi$
$758$	60.8218	−	44.1896i	2.20915	−	1.60504i
$759$	−63.4520	−	13.7552i	−2.30316	−	0.499282i
$760$	−0.789695	−	0.924435i	−0.0286452	−	0.0335328i
$761$	−7.87625	+	24.2406i	−0.285514	+	0.878721i	0.700730	+	0.713426i	$0.252858\pi$
$761$	−7.87625	+	24.2406i	−0.285514	+	0.878721i	−0.986244	+	0.165295i	$0.947142\pi$
$762$	−42.2071	−	9.14969i	−1.52900	−	0.331458i
$763$	19.2352	+	16.4968i	0.696360	+	0.597223i
$764$	37.5511	+	12.2011i	1.35855	+	0.441420i
$765$	31.8787	+	24.8681i	1.15258	+	0.899109i
$766$	58.0317	−	18.8556i	2.09677	−	0.681282i
$767$	1.54242	−	1.12063i	0.0556935	−	0.0404637i
$768$	−27.2723	−	15.8928i	−0.984103	−	0.573483i
$769$	2.96374	+	4.07924i	0.106875	+	0.147101i	0.859104	−	0.511801i	$-0.171021\pi$
$769$	2.96374	+	4.07924i	0.106875	+	0.147101i	−0.752229	+	0.658902i	$0.771021\pi$
$770$	−39.5280	+	54.1823i	−1.42449	+	1.95259i
$771$	13.7844	−	6.07063i	0.496433	−	0.218628i
$772$	2.62774	−	3.61677i	0.0945743	−	0.130170i
$773$	−17.4540	−	5.67114i	−0.627776	−	0.203977i	−0.0221864	−	0.999754i	$-0.507063\pi$
$773$	−17.4540	−	5.67114i	−0.627776	−	0.203977i	−0.605590	+	0.795777i	$0.707063\pi$
$774$	−0.865407	+	0.490367i	−0.0311064	+	0.0176259i
$775$	17.7156	−	34.7853i	0.636365	−	1.24953i
$776$	0.837504			0.0300646
$777$	1.84403	+	0.558466i	0.0661543	+	0.0200349i
$778$	6.72454	−	9.25553i	0.241086	−	0.331827i
$779$	8.60227	−	11.8400i	0.308208	−	0.424212i
$780$	3.60492	+	1.73694i	0.129077	+	0.0621923i
$781$	−5.67227	+	4.12114i	−0.202970	+	0.147466i
$782$			76.5617i			2.73784i
$783$	−22.3130	+	15.8019i	−0.797403	+	0.564715i
$784$	−29.6508	−	4.82105i	−1.05896	−	0.172180i
$785$	−28.4799	−	17.4488i	−1.01649	−	0.622774i
$786$	−46.4005	+	41.4411i	−1.65505	+	1.47816i
$787$	3.21132	+	9.88344i	0.114471	+	0.352306i	0.991836	−	0.127517i	$-0.0407007\pi$
$787$	3.21132	+	9.88344i	0.114471	+	0.352306i	−0.877365	+	0.479823i	$0.840701\pi$
$788$	−3.32863	−	10.2445i	−0.118578	−	0.364944i
$789$	4.79625	−	4.28362i	0.170751	−	0.152501i
$790$	−28.4149	+	2.23903i	−1.01096	+	0.0796612i
$791$	35.3239	+	30.2950i	1.25597	+	1.07717i
$792$	2.22867	−	4.89881i	0.0791925	−	0.174072i
$793$			1.91854i			0.0681294i
$794$	19.8651	−	14.4328i	0.704986	−	0.512202i
$795$	32.8574	−	34.3522i	1.16533	−	1.21835i
$796$	−11.9717	+	16.4776i	−0.424324	+	0.584032i
$797$	−20.9957	+	28.8981i	−0.743707	+	1.02362i	0.254690	+	0.967023i	$0.418027\pi$
$797$	−20.9957	+	28.8981i	−0.743707	+	1.02362i	−0.998397	+	0.0566019i	$0.981973\pi$
$798$	−15.0696	−	4.56384i	−0.533458	−	0.161558i
$799$	−23.5699			−0.833845
$800$	17.6920	+	34.7061i	0.625506	+	1.22705i
$801$	−4.40360	−	7.77154i	−0.155593	−	0.274594i
$802$	7.89603	+	2.56558i	0.278819	+	0.0905937i
$803$	−39.0097	+	53.6922i	−1.37662	+	1.89476i
$804$	−4.91223	+	2.16334i	−0.173241	+	0.0762951i
$805$	−11.9196	+	36.4419i	−0.420109	+	1.28441i
$806$	5.04588	+	6.94506i	0.177734	+	0.244629i
$807$	−9.92714	−	5.78501i	−0.349452	−	0.203642i
$808$	−0.277979	+	0.201963i	−0.00977926	+	0.00710505i
$809$	−9.16583	+	2.97816i	−0.322253	+	0.104706i	−0.465677	−	0.884955i	$-0.654189\pi$
$809$	−9.16583	+	2.97816i	−0.322253	+	0.104706i	0.143423	+	0.989661i	$0.454189\pi$
$810$	28.1727	+	27.6081i	0.989889	+	0.970050i
$811$	−41.4625	−	13.4720i	−1.45594	−	0.473065i	−0.529116	−	0.848549i	$-0.677476\pi$
$811$	−41.4625	−	13.4720i	−1.45594	−	0.473065i	−0.926829	+	0.375484i	$0.877476\pi$
$812$	−16.6921	+	19.4629i	−0.585778	+	0.683015i
$813$	1.60451	+	0.347828i	0.0562727	+	0.0121988i
$814$	−1.47293	+	4.53320i	−0.0516261	+	0.158889i
$815$	−22.5066	−	5.40110i	−0.788373	−	0.189192i
$816$	−43.7827	−	9.49125i	−1.53270	−	0.332260i
$817$	0.239904	−	0.174301i	0.00839319	−	0.00609801i
$818$			60.9569i			2.13131i
$819$	−4.42024	+	0.536447i	−0.154456	+	0.0187450i
$820$	−26.1420	+	22.3317i	−0.912917	+	0.779855i
$821$	18.3281	−	25.2264i	0.639654	−	0.880409i	−0.358943	−	0.933360i	$-0.616863\pi$
$821$	18.3281	−	25.2264i	0.639654	−	0.880409i	0.998597	+	0.0529509i	$0.0168627\pi$
$822$	−12.1609	−	27.6135i	−0.424162	−	0.963132i
$823$	−38.8978	−	12.6387i	−1.35589	−	0.440556i	−0.461223	−	0.887284i	$-0.652589\pi$
$823$	−38.8978	−	12.6387i	−1.35589	−	0.440556i	−0.894670	+	0.446728i	$0.852589\pi$
$824$	1.14561			0.0399094
$825$	−42.1136	+	27.1191i	−1.46621	+	0.944166i
$826$	15.0459	−	9.17772i	0.523514	−	0.319334i
$827$	2.45073	−	7.54256i	0.0852201	−	0.262280i	−0.899362	−	0.437205i	$-0.855968\pi$
$827$	2.45073	−	7.54256i	0.0852201	−	0.262280i	0.984582	+	0.174925i	$0.0559683\pi$
$828$	−4.03055	+	35.5813i	−0.140071	+	1.23653i
$829$	25.3401	−	34.8777i	0.880098	−	1.21135i	−0.0962956	−	0.995353i	$-0.530699\pi$
$829$	25.3401	−	34.8777i	0.880098	−	1.21135i	0.976394	−	0.215998i	$-0.0693006\pi$
$830$	29.3594	+	7.04560i	1.01908	+	0.244556i
$831$	−5.31921	−	52.6534i	−0.184521	−	1.82653i
$832$	−3.75181			−0.130071
$833$	−41.6971	+	6.42886i	−1.44472	+	0.222747i
$834$	−5.47440	−	1.18675i	−0.189563	−	0.0410937i
$835$	3.31804	+	42.1084i	0.114826	+	1.45722i
$836$	5.77054	−	17.7599i	0.199578	−	0.614239i
$837$	12.0679	+	38.7316i	0.417128	+	1.33876i
$838$	−7.33408	−	22.5720i	−0.253351	−	0.779736i
$839$	3.09299	−	9.51926i	0.106782	−	0.328641i	−0.883363	−	0.468690i	$-0.844726\pi$
$839$	3.09299	−	9.51926i	0.106782	−	0.328641i	0.990145	+	0.140049i	$0.0447260\pi$
$840$	−2.74290	−	1.60562i	−0.0946391	−	0.0553990i
$841$	0.405473	+	1.24792i	0.0139818	+	0.0430316i
$842$	−19.4311	+	14.1175i	−0.669641	+	0.486522i
$843$	−8.43278	+	14.4707i	−0.290440	+	0.498398i
$844$	−8.20492	+	5.96123i	−0.282425	+	0.205194i
$845$	28.2775	−	2.22821i	0.972777	−	0.0766526i
$846$	−22.8490	−	2.58827i	−0.785563	−	0.0889864i
$847$	59.2131	+	4.78246i	2.03459	+	0.164327i
$848$	−16.2766	+	50.0943i	−0.558942	+	1.72025i
$849$	15.4691	+	9.01460i	0.530900	+	0.309380i
$850$	41.7746	+	41.7586i	1.43286	+	1.43231i
$851$			2.72491i			0.0934086i
$852$	2.57589	+	2.88415i	0.0882484	+	0.0988093i
$853$	−35.1748	−	25.5560i	−1.20436	−	0.875020i	−0.209655	−	0.977775i	$-0.567234\pi$
$853$	−35.1748	−	25.5560i	−1.20436	−	0.875020i	−0.994707	+	0.102755i	$0.967234\pi$
$854$	−1.42776	+	17.6776i	−0.0488570	+	0.604914i
$855$	−9.27201	−	7.23297i	−0.317096	−	0.247362i
$856$	0.698138	−	0.507227i	0.0238619	−	0.0173367i
$857$		−	35.6299i		−	1.21709i	−0.793518	−	0.608546i	$-0.791753\pi$
$857$		−	35.6299i		−	1.21709i	0.793518	−	0.608546i	$-0.208247\pi$
$858$	−1.10716	−	10.9595i	−0.0377979	−	0.374151i
$859$	22.4748	−	7.30251i	0.766831	−	0.249158i	0.100623	−	0.994925i	$-0.467916\pi$
$859$	22.4748	−	7.30251i	0.766831	−	0.249158i	0.666208	+	0.745766i	$0.267916\pi$
$860$	−0.643594	+	0.266657i	−0.0219464	+	0.00909294i
$861$	11.0890	−	36.6156i	0.377914	−	1.24786i
$862$	−9.96791	+	3.23877i	−0.339508	+	0.110313i
$863$	−13.4265	−	41.3226i	−0.457044	−	1.40664i	−0.868718	−	0.495306i	$-0.835056\pi$
$863$	−13.4265	−	41.3226i	−0.457044	−	1.40664i	0.411674	−	0.911331i	$-0.364944\pi$
$864$	−38.3478	−	12.9756i	−1.30462	−	0.441440i
$865$	3.88691	+	4.55011i	0.132159	+	0.154708i
$866$	−13.4866	−	41.5075i	−0.458294	−	1.41048i
$867$	−33.3043	+	3.36450i	−1.13107	+	0.114264i
$868$	19.8112	+	32.4784i	0.672436	+	1.10239i
$869$	22.1095	+	30.4311i	0.750014	+	1.03231i
$870$	−35.1786	+	18.9212i	−1.19267	+	0.641490i
$871$	0.554817	−	0.763640i	0.0187992	−	0.0258749i
$872$	−2.40337	−	1.74615i	−0.0813883	−	0.0591321i
$873$	7.93679	−	1.62013i	0.268620	−	0.0548331i
$874$		−	22.2682i		−	0.753233i
$875$	13.3827	+	26.3800i	0.452416	+	0.891807i
$876$	31.6256	+	18.4298i	1.06853	+	0.622684i
$877$	40.0519	+	13.0136i	1.35246	+	0.439439i	0.893517	−	0.449029i	$-0.148230\pi$
$877$	40.0519	+	13.0136i	1.35246	+	0.439439i	0.458938	+	0.888468i	$0.348230\pi$
$878$	4.44956	−	6.12430i	0.150165	−	0.206685i
$879$	17.4379	−	7.67963i	0.588166	−	0.259028i
$880$	28.9952	−	47.3260i	0.977428	−	1.59536i
$881$	−7.42991	+	5.39815i	−0.250320	+	0.181868i	−0.705869	−	0.708343i	$-0.749443\pi$
$881$	−7.42991	+	5.39815i	−0.250320	+	0.181868i	0.455549	+	0.890211i	$0.349443\pi$
$882$	−41.1276	+	1.65335i	−1.38484	+	0.0556713i
$883$	13.4246	+	18.4774i	0.451774	+	0.621814i	0.972778	−	0.231741i	$-0.0744421\pi$
$883$	13.4246	+	18.4774i	0.451774	+	0.621814i	−0.521003	+	0.853555i	$0.674442\pi$
$884$	−5.92240	+	1.92431i	−0.199192	+	0.0647214i
$885$	12.9515	−	2.34763i	0.435359	−	0.0789148i
$886$	−12.0669	+	37.1381i	−0.405396	+	1.24768i
$887$	47.9562	−	15.5819i	1.61021	−	0.523189i	0.640607	−	0.767869i	$-0.278683\pi$
$887$	47.9562	−	15.5819i	1.61021	−	0.523189i	0.969604	+	0.244680i	$0.0786829\pi$
$888$	−0.220750	−	0.0478545i	−0.00740790	−	0.00160589i
$889$	32.7435	−	7.79000i	1.09818	−	0.261268i
$890$	−4.99503	−	12.0558i	−0.167434	−	0.404112i
$891$	11.6439	−	50.7360i	0.390084	−	1.69972i
$892$	−33.2692	+	24.1715i	−1.11394	+	0.809321i
$893$	6.85539			0.229407
$894$	−2.63425	−	26.0757i	−0.0881024	−	0.872102i
$895$	36.4533	−	15.1035i	1.21850	−	0.504856i
$896$	6.52325	+	0.526863i	0.217927	+	0.0176012i
$897$	−2.53806	−	5.76309i	−0.0847432	−	0.192424i
$898$	−35.6200	−	11.5736i	−1.18866	−	0.386218i
$899$	−41.0816			−1.37015
$900$	17.2160	+	21.6061i	0.573865	+	0.720203i
$901$			73.9755i			2.46448i
$902$	90.0124	+	29.2468i	2.99708	+	0.973812i
$903$	0.442954	−	0.636167i	0.0147406	−	0.0211703i
$904$	−4.41360	−	3.20666i	−0.146794	−	0.106652i
$905$	0.171908	+	2.18164i	0.00571441	+	0.0725200i
$906$	70.8154	−	7.15399i	2.35268	−	0.237675i
$907$			10.4146i			0.345812i	0.984938	+	0.172906i	$0.0553157\pi$
$907$			10.4146i			0.345812i	−0.984938	+	0.172906i	$0.944684\pi$
$908$	6.08745	+	8.37865i	0.202019	+	0.278055i
$909$	−2.24363	+	2.45169i	−0.0744166	+	0.0813175i
$910$	−6.50502	−	0.0127284i	−0.215639	−	0.000421941i
$911$	−9.94211	−	3.23039i	−0.329397	−	0.107027i	0.139650	−	0.990201i	$-0.455402\pi$
$911$	−9.94211	−	3.23039i	−0.329397	−	0.107027i	−0.469046	+	0.883173i	$0.655402\pi$
$912$	12.7343	+	2.76056i	0.421675	+	0.0914112i
$913$	−12.3128	−	37.8950i	−0.407495	−	1.25414i
$914$	5.86618	+	1.90604i	0.194036	+	0.0630461i
$915$	−5.74940	+	11.9326i	−0.190069	+	0.394478i
$916$	25.1497	−	8.17164i	0.830971	−	0.269999i
$917$	18.6460	−	44.7554i	0.615745	−	1.47795i
$918$	−61.3796	−	0.743648i	−2.02583	−	0.0245440i
$919$	−12.7886	+	9.29147i	−0.421857	+	0.306497i	−0.778385	−	0.627788i	$-0.783961\pi$
$919$	−12.7886	+	9.29147i	−0.421857	+	0.306497i	0.356527	+	0.934285i	$0.383961\pi$
$920$	1.04890	−	4.37081i	0.0345812	−	0.144101i
$921$	−10.2902	−	23.3656i	−0.339072	−	0.769921i
$922$	−31.1993	−	22.6676i	−1.02749	−	0.746519i
$923$	−0.646750	−	0.210142i	−0.0212880	−	0.00691690i
$924$	−0.980619	−	48.8060i	−0.0322600	−	1.60560i
$925$	1.48680	+	1.48623i	0.0488857	+	0.0488670i
$926$		−	24.9454i		−	0.819758i
$927$	10.8567	−	2.21616i	0.356580	−	0.0727884i
$928$	24.0969	−	33.1665i	0.791019	−	1.08874i
$929$	24.1569	+	17.5510i	0.792563	+	0.575831i	0.908723	−	0.417400i	$-0.137059\pi$
$929$	24.1569	+	17.5510i	0.792563	+	0.575831i	−0.116160	+	0.993231i	$0.537059\pi$
$930$	10.5707	+	58.3168i	0.346627	+	1.91228i
$931$	12.1277	−	1.86985i	0.397470	−	0.0612819i
$932$	−9.95702			−0.326153
$933$	19.8790	−	2.00824i	0.650810	−	0.0657468i
$934$	−10.0835	+	3.27631i	−0.329941	+	0.107204i
$935$	18.1897	−	75.7976i	0.594868	−	2.47885i
$936$	0.511453	−	0.104403i	0.0167174	−	0.00341250i
$937$	4.43298	+	13.6433i	0.144819	+	0.445707i	0.996988	−	0.0775600i	$-0.0247129\pi$
$937$	4.43298	+	13.6433i	0.144819	+	0.445707i	−0.852169	+	0.523267i	$0.824713\pi$
$938$	5.68041	−	6.62333i	0.185472	−	0.216260i
$939$	−35.7746	+	31.9510i	−1.16746	+	1.04268i
$940$	−15.6605	−	3.75818i	−0.510791	−	0.122578i
$941$	0.380875	+	1.17221i	0.0124162	+	0.0382130i	0.957073	−	0.289848i	$-0.0936048\pi$
$941$	0.380875	+	1.17221i	0.0124162	+	0.0382130i	−0.944656	+	0.328061i	$0.893605\pi$
$942$	50.4526	−	5.09687i	1.64383	−	0.166065i
$943$	54.1064			1.76195
$944$	−11.7993	+	8.57267i	−0.384034	+	0.279017i
$945$	−29.0997	−	9.90989i	−0.946614	−	0.322369i
$946$	1.55146	+	1.12720i	0.0504422	+	0.0366484i
$947$	8.60980	+	6.25538i	0.279781	+	0.203273i	0.718822	−	0.695194i	$-0.244682\pi$
$947$	8.60980	+	6.25538i	0.279781	+	0.203273i	−0.439041	+	0.898467i	$0.644682\pi$
$948$	15.4732	−	13.8194i	0.502545	−	0.448832i
$949$	−6.43701			−0.208954
$950$	−12.1503	−	12.1456i	−0.394206	−	0.394056i
$951$	43.1654	+	25.1545i	1.39973	+	0.815691i
$952$	4.81173	−	1.14476i	0.155949	−	0.0371018i
$953$	7.49781	+	5.44748i	0.242878	+	0.176461i	0.702564	−	0.711620i	$-0.252038\pi$
$953$	7.49781	+	5.44748i	0.242878	+	0.176461i	−0.459687	+	0.888081i	$0.652038\pi$
$954$	−8.12340	+	71.7126i	−0.263005	+	2.32178i
$955$	−46.6134	−	11.1862i	−1.50838	−	0.361977i
$956$	1.38513	+	1.90647i	0.0447984	+	0.0616597i
$957$	45.5447	+	26.5411i	1.47225	+	0.857951i
$958$	9.11789	−	6.62453i	0.294586	−	0.214029i
$959$	17.8493	+	15.3082i	0.576384	+	0.494328i
$960$	−23.3348	−	11.2433i	−0.753126	−	0.362875i
$961$	−9.25646	+	28.4885i	−0.298596	+	0.918983i
$962$	−0.439679	+	0.142861i	−0.0141758	+	0.00460601i
$963$	5.63484	−	6.15738i	0.181580	−	0.198419i
$964$	26.6144	+	8.64755i	0.857193	+	0.278519i
$965$	−2.83553	+	4.62815i	−0.0912789	+	0.148986i
$966$	−19.0970	−	54.9903i	−0.614435	−	1.76928i
$967$	4.85400	+	6.68095i	0.156094	+	0.214845i	0.879900	−	0.475158i	$-0.157609\pi$
$967$	4.85400	+	6.68095i	0.156094	+	0.214845i	−0.723806	+	0.690003i	$0.757609\pi$
$968$	−6.96433			−0.223842
$969$	18.2074	−	1.83937i	0.584906	−	0.0590890i
$970$	11.7976	−	0.929625i	0.378798	−	0.0298485i
$971$	−4.72629	−	3.43385i	−0.151674	−	0.110198i	0.509360	−	0.860553i	$-0.329882\pi$
$971$	−4.72629	−	3.43385i	−0.151674	−	0.110198i	−0.661034	+	0.750356i	$0.729882\pi$
$972$	−28.4864	−	3.57690i	−0.913702	−	0.114729i
$973$	4.24695	−	1.01039i	0.136151	−	0.0323916i
$974$			8.49484i			0.272192i
$975$	−4.52885	−	1.75848i	−0.145039	−	0.0563166i
$976$		−	14.6766i		−	0.469786i
$977$	13.1012	−	40.3215i	0.419146	−	1.29000i	−0.489344	−	0.872091i	$-0.662764\pi$
$977$	13.1012	−	40.3215i	0.419146	−	1.29000i	0.908490	−	0.417908i	$-0.137236\pi$
$978$	32.1600	−	14.1632i	1.02836	−	0.452890i
$979$	−10.1225	+	13.9324i	−0.323516	+	0.445282i
$980$	−28.7298	−	2.37701i	−0.917741	−	0.0759308i
$981$	−26.1539	−	11.8985i	−0.835030	−	0.379890i
$982$		−	26.1769i		−	0.835340i
$983$	−2.44088	−	3.35959i	−0.0778520	−	0.107154i	0.768315	−	0.640072i	$-0.221095\pi$
$983$	−2.44088	−	3.35959i	−0.0778520	−	0.107154i	−0.846167	+	0.532918i	$0.821095\pi$
$984$	−0.950210	+	4.38327i	−0.0302916	+	0.139734i
$985$	5.00584	+	12.0819i	0.159499	+	0.384961i
$986$	19.2088	−	59.1188i	0.611734	−	1.88272i
$987$	16.9291	−	5.87911i	0.538858	−	0.187134i
$988$	1.72255	−	0.559690i	0.0548016	−	0.0178061i
$989$	1.04266	+	0.338779i	0.0331545	+	0.0107726i
$990$	25.9568	−	71.4816i	0.824962	−	2.27183i
$991$	−9.20176	−	28.3201i	−0.292304	−	0.899618i	−0.984114	−	0.177539i	$-0.943186\pi$
$991$	−9.20176	−	28.3201i	−0.292304	−	0.899618i	0.691810	−	0.722079i	$-0.256814\pi$
$992$	−35.7535	−	49.2105i	−1.13518	−	1.56244i
$993$	7.26122	+	4.23145i	0.230428	+	0.134281i
$994$	−5.80281	−	2.41757i	−0.184054	−	0.0766805i
$995$	12.9183	−	21.0853i	0.409539	−	0.668450i
$996$	−20.1120	+	8.85728i	−0.637272	+	0.280654i
$997$	17.2372	+	12.5235i	0.545907	+	0.396624i	0.826274	−	0.563268i	$-0.190456\pi$
$997$	17.2372	+	12.5235i	0.545907	+	0.396624i	−0.280367	+	0.959893i	$0.590456\pi$
$998$	−8.72832	+	26.8630i	−0.276290	+	0.850334i
$999$	−2.18456	−	0.0264672i	−0.0691165	−	0.000837384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.w.a.104.14	yes	304
3.2	odd	2	inner	525.2.w.a.104.64	yes	304
7.6	odd	2	inner	525.2.w.a.104.13	✓	304
21.20	even	2	inner	525.2.w.a.104.63	yes	304
25.19	even	10	inner	525.2.w.a.419.63	yes	304
75.44	odd	10	inner	525.2.w.a.419.13	yes	304
175.69	odd	10	inner	525.2.w.a.419.64	yes	304
525.419	even	10	inner	525.2.w.a.419.14	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.w.a.104.13	✓	304	7.6	odd	2	inner
525.2.w.a.104.14	yes	304	1.1	even	1	trivial
525.2.w.a.104.63	yes	304	21.20	even	2	inner
525.2.w.a.104.64	yes	304	3.2	odd	2	inner
525.2.w.a.419.13	yes	304	75.44	odd	10	inner
525.2.w.a.419.14	yes	304	525.419	even	10	inner
525.2.w.a.419.63	yes	304	25.19	even	10	inner
525.2.w.a.419.64	yes	304	175.69	odd	10	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.605685 + 1.86411i) q^{2} +(0.698093 + 1.58514i) q^{3} +(-1.49001 - 1.08256i) q^{4} +(1.90667 + 1.16816i) q^{5} +(-3.37770 + 0.341225i) q^{6} +(2.25871 - 1.37777i) q^{7} +(-0.250932 + 0.182313i) q^{8} +(-2.02533 + 2.21315i) q^{9} +O(q^{10})\)	\(q+(-0.605685 + 1.86411i) q^{2} +(0.698093 + 1.58514i) q^{3} +(-1.49001 - 1.08256i) q^{4} +(1.90667 + 1.16816i) q^{5} +(-3.37770 + 0.341225i) q^{6} +(2.25871 - 1.37777i) q^{7} +(-0.250932 + 0.182313i) q^{8} +(-2.02533 + 2.21315i) q^{9} +(-3.33242 + 2.84671i) q^{10} +(5.50080 + 1.78732i) q^{11} +(0.675836 - 3.11760i) q^{12} +(0.173354 + 0.533528i) q^{13} +(1.20024 + 5.04497i) q^{14} +(-0.520662 + 3.83783i) q^{15} +(-1.32613 - 4.08141i) q^{16} +(-3.54265 - 4.87604i) q^{17} +(-2.89883 - 5.11591i) q^{18} +(1.03039 + 1.41821i) q^{19} +(-1.57636 - 3.80465i) q^{20} +(3.76074 + 2.61855i) q^{21} +(-6.66351 + 9.17153i) q^{22} +(-2.00272 + 6.16373i) q^{23} +(-0.464165 - 0.270491i) q^{24} +(2.27080 + 4.45460i) q^{25} -1.09955 q^{26} +(-4.92202 - 1.66545i) q^{27} +(-4.85701 - 0.392285i) q^{28} +(3.09288 - 4.25699i) q^{29} +(-6.83877 - 3.29509i) q^{30} +(-4.58904 - 6.31627i) q^{31} +7.79107 q^{32} +(1.00692 + 9.96725i) q^{33} +(11.2352 - 3.65054i) q^{34} +(5.91607 + 0.0115760i) q^{35} +(5.41362 - 1.10508i) q^{36} +(0.399872 - 0.129926i) q^{37} +(-3.26779 + 1.06177i) q^{38} +(-0.724699 + 0.647242i) q^{39} +(-0.691416 + 0.0544820i) q^{40} +(-2.57985 - 7.93995i) q^{41} +(-7.15909 + 5.42441i) q^{42} -0.169160i q^{43} +(-6.26138 - 8.61805i) q^{44} +(-6.44696 + 1.85384i) q^{45} +(-10.2768 - 7.46656i) q^{46} +(2.29862 - 3.16378i) q^{47} +(5.54384 - 4.95131i) q^{48} +(3.20351 - 6.22395i) q^{49} +(-9.67925 + 1.53494i) q^{50} +(5.25610 - 9.01952i) q^{51} +(0.319275 - 0.982627i) q^{52} +(-9.92969 - 7.21434i) q^{53} +(6.08577 - 8.16644i) q^{54} +(8.40035 + 9.83365i) q^{55} +(-0.315597 + 0.757517i) q^{56} +(-1.52875 + 2.62335i) q^{57} +(6.06217 + 8.34386i) q^{58} +(-1.05021 - 3.23221i) q^{59} +(4.93045 - 5.15475i) q^{60} +(3.25257 + 1.05682i) q^{61} +(14.5537 - 4.72879i) q^{62} +(-1.52542 + 7.78929i) q^{63} +(-2.06668 + 6.36058i) q^{64} +(-0.292717 + 1.21977i) q^{65} +(-19.1899 - 4.16001i) q^{66} +(-0.989006 - 1.36125i) q^{67} +11.1005i q^{68} +(-11.1685 + 1.12827i) q^{69} +(-3.60486 + 11.0212i) q^{70} +(-0.712522 + 0.980702i) q^{71} +(0.104735 - 0.924594i) q^{72} +(-3.54582 + 10.9129i) q^{73} +0.824099i q^{74} +(-5.47593 + 6.70926i) q^{75} -3.22860i q^{76} +(14.8872 - 3.54181i) q^{77} +(-0.767589 - 1.74294i) q^{78} +(5.26137 + 3.82261i) q^{79} +(2.23925 - 9.33105i) q^{80} +(-0.796057 - 8.96472i) q^{81} +16.3635 q^{82} +(-4.04925 - 5.57331i) q^{83} +(-2.76881 - 7.97288i) q^{84} +(-1.05868 - 13.4354i) q^{85} +(0.315332 + 0.102458i) q^{86} +(8.90704 + 1.93088i) q^{87} +(-1.70618 + 0.554371i) q^{88} +(-0.920092 + 2.83175i) q^{89} +(0.449075 - 13.1407i) q^{90} +(1.12663 + 0.966241i) q^{91} +(9.65665 - 7.01597i) q^{92} +(6.80859 - 11.6836i) q^{93} +(4.50539 + 6.20114i) q^{94} +(0.307920 + 3.90772i) q^{95} +(5.43889 + 12.3499i) q^{96} +(-2.18447 - 1.58711i) q^{97} +(9.66180 + 9.74144i) q^{98} +(-15.0966 + 8.55418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) \) 304 * q - 84 * q^4 - 6 * q^9	\( 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) \) 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Introduction

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