LMFDB - Embedded newform 750.2.l.b.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(-1.02873 + 1.39345i) q^{12} +(-2.33563 + 1.19006i) q^{13} +(-0.311372 - 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.919013 + 5.80242i) q^{17} +(-0.424059 - 2.96988i) q^{18} +(0.341785 - 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(-0.0572652 + 0.361558i) q^{22} +(6.05243 + 3.08387i) q^{23} +(-0.774543 - 1.54922i) q^{24} -2.62134i q^{26} +(4.13281 + 3.14959i) q^{27} +(0.995214 + 0.157626i) q^{28} +(-0.368253 + 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.368759 - 0.515779i) q^{33} +(-5.58722 - 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-4.35053 - 8.53839i) q^{37} +(0.263986 + 0.518102i) q^{38} +(3.18589 + 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(-1.41972 + 1.01503i) q^{42} +(7.18512 + 7.18512i) q^{43} +(-0.296153 - 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(8.16222 + 1.29277i) q^{47} +(1.73200 + 0.0132082i) q^{48} +5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(2.33563 + 1.19006i) q^{52} +(-1.38217 + 8.72670i) q^{53} +(-4.68256 + 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.955457 - 0.318522i) q^{57} +(-0.0712068 - 0.449582i) q^{58} +(-2.91096 + 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(2.60811 - 1.32890i) q^{62} +(0.518359 - 2.97808i) q^{63} +(0.951057 - 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(-13.0896 + 2.07319i) q^{67} +(4.15407 - 4.15407i) q^{68} +(1.92909 - 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(-2.15343 + 2.08872i) q^{72} +(-4.33350 + 8.50497i) q^{73} +9.58285 q^{74} -0.581479 q^{76} +(-0.167456 + 0.328652i) q^{77} +(-4.32864 + 1.37006i) q^{78} +(7.17322 + 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(-7.50310 + 7.50310i) q^{82} +(-0.937190 + 0.148436i) q^{83} +(-0.259864 - 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.634281 + 0.468264i) q^{87} +(0.326166 - 0.166190i) q^{88} +(-0.626378 - 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-1.06263 - 6.70917i) q^{92} +(-1.60343 + 4.80974i) q^{93} +(-4.85743 + 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(2.81727 - 17.7876i) q^{97} +(-5.33241 - 2.71700i) q^{98} +(-0.658978 + 0.878510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.522656	−	1.65131i	−0.301755	−	0.953385i
$3$	−0.522656	−	1.65131i	−0.301755	−	0.953385i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	1.70861	+	0.283990i	0.697537	+	0.115939i
$7$	−0.712495	+	0.712495i	−0.269298	+	0.269298i	−0.828817	−	0.559519i	$-0.810986\pi$
$7$	−0.712495	+	0.712495i	−0.269298	+	0.269298i	0.559519	+	0.828817i	$0.310986\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.45366	+	1.72614i	−0.817887	+	0.575378i
$10$		0			0
$11$	0.348148	−	0.113120i	0.104971	−	0.0341070i	−0.256061	−	0.966661i	$-0.582425\pi$
$11$	0.348148	−	0.113120i	0.104971	−	0.0341070i	0.361031	+	0.932554i	$0.382425\pi$
$12$	−1.02873	+	1.39345i	−0.296969	+	0.402256i
$13$	−2.33563	+	1.19006i	−0.647787	+	0.330064i	−0.746826	−	0.665020i	$-0.768423\pi$
$13$	−2.33563	+	1.19006i	−0.647787	+	0.330064i	0.0990392	+	0.995084i	$0.468423\pi$
$14$	−0.311372	−	0.958303i	−0.0832176	−	0.256117i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.919013	+	5.80242i	0.222893	+	1.40729i	0.804562	+	0.593868i	$0.202400\pi$
$17$	0.919013	+	5.80242i	0.222893	+	1.40729i	−0.581669	+	0.813426i	$0.697600\pi$
$18$	−0.424059	−	2.96988i	−0.0999516	−	0.700007i
$19$	0.341785	−	0.470426i	0.0784108	−	0.107923i	−0.768010	−	0.640438i	$-0.778753\pi$
$19$	0.341785	−	0.470426i	0.0784108	−	0.107923i	0.846421	+	0.532515i	$0.178753\pi$
$20$		0			0
$21$	1.54894	+	0.804162i	0.338007	+	0.175482i
$22$	−0.0572652	+	0.361558i	−0.0122090	+	0.0770844i
$23$	6.05243	+	3.08387i	1.26202	+	0.643031i	0.951533	−	0.307548i	$-0.0995083\pi$
$23$	6.05243	+	3.08387i	1.26202	+	0.643031i	0.310486	+	0.950578i	$0.399508\pi$
$24$	−0.774543	−	1.54922i	−0.158103	−	0.316233i
$25$		0			0
$26$		−	2.62134i		−	0.514086i
$27$	4.13281	+	3.14959i	0.795359	+	0.606138i
$28$	0.995214	+	0.157626i	0.188078	+	0.0297886i
$29$	−0.368253	+	0.267552i	−0.0683830	+	0.0496831i	−0.621452	−	0.783453i	$-0.713457\pi$
$29$	−0.368253	+	0.267552i	−0.0683830	+	0.0496831i	0.553069	+	0.833136i	$0.313457\pi$
$30$		0			0
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	0.354451	−	0.935074i	$-0.384668\pi$
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	−0.779777	+	0.626057i	$0.784668\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.368759	−	0.515779i	−0.0641926	−	0.0897855i
$34$	−5.58722	−	1.81540i	−0.958200	−	0.311338i
$35$		0			0
$36$	2.83870	+	0.970457i	0.473117	+	0.161743i
$37$	−4.35053	−	8.53839i	−0.715222	−	1.40370i	−0.906517	−	0.422169i	$-0.861269\pi$
$37$	−4.35053	−	8.53839i	−0.715222	−	1.40370i	0.191295	−	0.981533i	$-0.438731\pi$
$38$	0.263986	+	0.518102i	0.0428242	+	0.0840472i
$39$	3.18589	+	3.23486i	0.510151	+	0.517992i
$40$		0			0
$41$	10.0917	+	3.27898i	1.57605	+	0.512090i	0.961036	−	0.276425i	$-0.0891497\pi$
$41$	10.0917	+	3.27898i	1.57605	+	0.512090i	0.615016	+	0.788515i	$0.289150\pi$
$42$	−1.41972	+	1.01503i	−0.219067	+	0.156623i
$43$	7.18512	+	7.18512i	1.09572	+	1.09572i	0.994905	+	0.100815i	$0.0321451\pi$
$43$	7.18512	+	7.18512i	1.09572	+	1.09572i	0.100815	+	0.994905i	$0.467855\pi$
$44$	−0.296153	−	0.215168i	−0.0446467	−	0.0324377i
$45$		0			0
$46$	−5.49549	+	3.99271i	−0.810266	+	0.588693i
$47$	8.16222	+	1.29277i	1.19058	+	0.188570i	0.720119	−	0.693850i	$-0.244087\pi$
$47$	8.16222	+	1.29277i	1.19058	+	0.188570i	0.470463	+	0.882420i	$0.344087\pi$
$48$	1.73200	+	0.0132082i	0.249993	+	0.00190644i
$49$			5.98470i			0.854957i
$50$		0			0
$51$	9.10128	−	4.55025i	1.27443	−	0.637162i
$52$	2.33563	+	1.19006i	0.323893	+	0.165032i
$53$	−1.38217	+	8.72670i	−0.189856	+	1.19870i	0.690123	+	0.723692i	$0.257556\pi$
$53$	−1.38217	+	8.72670i	−0.189856	+	1.19870i	−0.879979	+	0.475012i	$0.842444\pi$
$54$	−4.68256	+	2.25248i	−0.637215	+	0.306523i
$55$		0			0
$56$	−0.592264	+	0.815182i	−0.0791446	+	0.108933i
$57$	−0.955457	−	0.318522i	−0.126553	−	0.0421893i
$58$	−0.0712068	−	0.449582i	−0.00934992	−	0.0590330i
$59$	−2.91096	+	8.95903i	−0.378975	+	1.16637i	0.561782	+	0.827285i	$0.310116\pi$
$59$	−2.91096	+	8.95903i	−0.378975	+	1.16637i	−0.940757	+	0.339081i	$0.889884\pi$
$60$		0			0
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	0.927293	−	0.374337i	$-0.122130\pi$
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	−0.970225	+	0.242205i	$0.922130\pi$
$62$	2.60811	−	1.32890i	0.331230	−	0.168770i
$63$	0.518359	−	2.97808i	0.0653071	−	0.375203i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	0.626975	−	0.0944078i	0.0771753	−	0.0116208i
$67$	−13.0896	+	2.07319i	−1.59915	+	0.253280i	−0.891411	−	0.453196i	$-0.850284\pi$
$67$	−13.0896	+	2.07319i	−1.59915	+	0.253280i	−0.707737	+	0.706476i	$0.750284\pi$
$68$	4.15407	−	4.15407i	0.503756	−	0.503756i
$69$	1.92909	−	11.6062i	0.232235	−	1.39723i
$70$		0			0
$71$	−0.755873	−	1.04037i	−0.0897056	−	0.123469i	0.761805	−	0.647806i	$-0.224313\pi$
$71$	−0.755873	−	1.04037i	−0.0897056	−	0.123469i	−0.851511	+	0.524337i	$0.824313\pi$
$72$	−2.15343	+	2.08872i	−0.253784	+	0.246158i
$73$	−4.33350	+	8.50497i	−0.507198	+	0.995432i	0.485435	+	0.874273i	$0.338661\pi$
$73$	−4.33350	+	8.50497i	−0.507198	+	0.995432i	−0.992633	+	0.121159i	$0.961339\pi$
$74$	9.58285			1.11398
$75$		0			0
$76$	−0.581479			−0.0667002
$77$	−0.167456	+	0.328652i	−0.0190834	+	0.0374533i
$78$	−4.32864	+	1.37006i	−0.490122	+	0.155128i
$79$	7.17322	+	9.87309i	0.807050	+	1.11081i	0.991772	+	0.128018i	$0.0408616\pi$
$79$	7.17322	+	9.87309i	0.807050	+	1.11081i	−0.184722	+	0.982791i	$0.559138\pi$
$80$		0			0
$81$	3.04091	−	8.47071i	0.337879	−	0.941189i
$82$	−7.50310	+	7.50310i	−0.828579	+	0.828579i
$83$	−0.937190	+	0.148436i	−0.102870	+	0.0162930i	−0.207657	−	0.978202i	$-0.566584\pi$
$83$	−0.937190	+	0.148436i	−0.102870	+	0.0162930i	0.104787	+	0.994495i	$0.466584\pi$
$84$	−0.259864	−	1.72579i	−0.0283535	−	0.188300i
$85$		0			0
$86$	−9.66396	+	3.14001i	−1.04209	+	0.338596i
$87$	0.634281	+	0.468264i	0.0680021	+	0.0502032i
$88$	0.326166	−	0.166190i	0.0347694	−	0.0177159i
$89$	−0.626378	−	1.92779i	−0.0663960	−	0.204346i	0.912354	−	0.409401i	$-0.134262\pi$
$89$	−0.626378	−	1.92779i	−0.0663960	−	0.204346i	−0.978750	+	0.205056i	$0.934262\pi$
$90$		0			0
$91$	0.816210	−	2.51204i	0.0855620	−	0.263333i
$92$	−1.06263	−	6.70917i	−0.110787	−	0.699479i
$93$	−1.60343	+	4.80974i	−0.166268	+	0.498747i
$94$	−4.85743	+	6.68568i	−0.501006	+	0.689576i
$95$		0			0
$96$	−0.798080	+	1.53723i	−0.0814537	+	0.156893i
$97$	2.81727	−	17.7876i	0.286051	−	1.80605i	−0.257065	−	0.966394i	$-0.582755\pi$
$97$	2.81727	−	17.7876i	0.286051	−	1.80605i	0.543115	−	0.839658i	$-0.317245\pi$
$98$	−5.33241	−	2.71700i	−0.538655	−	0.274458i
$99$	−0.658978	+	0.878510i	−0.0662297	+	0.0882936i
$100$		0			0
$101$			0.362340i			0.0360542i	0.999837	+	0.0180271i	$0.00573851\pi$
$101$			0.362340i			0.0360542i	−0.999837	+	0.0180271i	$0.994261\pi$
$102$	−0.0775950	+	10.1751i	−0.00768305	+	1.00748i
$103$	7.83651	+	1.24118i	0.772154	+	0.122297i	0.530065	−	0.847957i	$-0.322167\pi$
$103$	7.83651	+	1.24118i	0.772154	+	0.122297i	0.242089	+	0.970254i	$0.422167\pi$
$104$	−2.12071	+	1.54078i	−0.207952	+	0.151086i
$105$		0			0
$106$	−7.14805	−	5.19336i	−0.694280	−	0.504424i
$107$	−9.06892	−	9.06892i	−0.876725	−	0.876725i	0.116469	−	0.993194i	$-0.462842\pi$
$107$	−9.06892	−	9.06892i	−0.876725	−	0.876725i	−0.993194	+	0.116469i	$0.962842\pi$
$108$	0.118865	−	5.19479i	0.0114378	−	0.499869i
$109$	−4.33696	−	1.40916i	−0.415405	−	0.134973i	0.0938551	−	0.995586i	$-0.470081\pi$
$109$	−4.33696	−	1.40916i	−0.415405	−	0.134973i	−0.509260	+	0.860613i	$0.670081\pi$
$110$		0			0
$111$	−11.8257	+	11.6467i	−1.12245	+	1.10546i
$112$	−0.457450	−	0.897796i	−0.0432249	−	0.0848337i
$113$	−6.17652	−	12.1221i	−0.581038	−	1.14035i	−0.975203	−	0.221311i	$-0.928966\pi$
$113$	−6.17652	−	12.1221i	−0.581038	−	1.14035i	0.394166	−	0.919039i	$-0.371034\pi$
$114$	0.717574	−	0.706712i	0.0672069	−	0.0661896i
$115$		0			0
$116$	0.432908	+	0.140660i	0.0401945	+	0.0130600i
$117$	3.67663	−	6.95162i	0.339905	−	0.642677i
$118$	−6.66100	−	6.66100i	−0.613195	−	0.613195i
$119$	−4.78899	−	3.47940i	−0.439006	−	0.318956i
$120$		0			0
$121$	−8.79078	+	6.38687i	−0.799161	+	0.580625i
$122$	1.07173	+	0.169746i	0.0970301	+	0.0153681i
$123$	0.140152	−	18.3782i	0.0126371	−	1.65711i
$124$			2.92715i			0.262866i
$125$		0			0
$126$	2.41816	+	1.81388i	0.215427	+	0.161594i
$127$	17.5736	+	8.95420i	1.55941	+	0.794557i	0.999424	−	0.0339477i	$-0.0108080\pi$
$127$	17.5736	+	8.95420i	1.55941	+	0.794557i	0.559982	+	0.828505i	$0.310808\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	8.10953	−	15.6202i	0.714004	−	1.37528i
$130$		0			0
$131$	−6.37019	+	8.76782i	−0.556566	+	0.766048i	−0.990885	−	0.134711i	$-0.956989\pi$
$131$	−6.37019	+	8.76782i	−0.556566	+	0.766048i	0.434318	+	0.900759i	$0.356989\pi$
$132$	−0.200523	+	0.601499i	−0.0174533	+	0.0523538i
$133$	0.0916565	+	0.578696i	0.00794763	+	0.0501793i
$134$	4.09532	−	12.6041i	0.353782	−	1.08883i
$135$		0			0
$136$	1.81540	+	5.58722i	0.155669	+	0.479100i
$137$	−7.75294	+	3.95032i	−0.662378	+	0.337498i	−0.752652	−	0.658419i	$-0.771226\pi$
$137$	−7.75294	+	3.95032i	−0.662378	+	0.337498i	0.0902740	+	0.995917i	$0.471226\pi$
$138$	9.46545	+	6.98796i	0.805753	+	0.594854i
$139$	−2.91069	+	0.945741i	−0.246882	+	0.0802167i	−0.429844	−	0.902903i	$-0.641431\pi$
$139$	−2.91069	+	0.945741i	−0.246882	+	0.0802167i	0.182962	+	0.983120i	$0.441431\pi$
$140$		0			0
$141$	−2.13127	−	14.1540i	−0.179485	−	1.19199i
$142$	1.27013	−	0.201170i	0.106587	−	0.0168818i
$143$	−0.678525	+	0.678525i	−0.0567411	+	0.0567411i
$144$	−0.883429	−	2.86698i	−0.0736191	−	0.238915i
$145$		0			0
$146$	−5.61062	−	7.72236i	−0.464338	−	0.639107i
$147$	9.88261	−	3.12794i	0.815104	−	0.257988i
$148$	−4.35053	+	8.53839i	−0.357611	+	0.701851i
$149$	−5.85789			−0.479897			−0.239948	−	0.970786i	$-0.577131\pi$
$149$	−5.85789			−0.479897			−0.239948	+	0.970786i	$0.577131\pi$
$150$		0			0
$151$	3.64976			0.297013			0.148507	−	0.988911i	$-0.452553\pi$
$151$	3.64976			0.297013			0.148507	+	0.988911i	$0.452553\pi$
$152$	0.263986	−	0.518102i	0.0214121	−	0.0420236i
$153$	−12.2707	−	12.6508i	−0.992028	−	1.02276i
$154$	−0.216807	−	0.298409i	−0.0174708	−	0.0240465i
$155$		0			0
$156$	0.744434	−	4.47884i	0.0596024	−	0.358594i
$157$	−2.27502	+	2.27502i	−0.181567	+	0.181567i	−0.792038	−	0.610472i	$-0.790980\pi$
$157$	−2.27502	+	2.27502i	−0.181567	+	0.181567i	0.610472	+	0.792038i	$0.290980\pi$
$158$	−12.0536	+	1.90910i	−0.958930	+	0.151880i
$159$	15.1329	−	2.27866i	1.20012	−	0.180709i
$160$		0			0
$161$	−6.50956	+	2.11508i	−0.513025	+	0.166692i
$162$	6.16691	+	6.55509i	0.484518	+	0.515017i
$163$	3.29567	−	1.67923i	0.258137	−	0.131527i	−0.320134	−	0.947372i	$-0.603728\pi$
$163$	3.29567	−	1.67923i	0.258137	−	0.131527i	0.578270	+	0.815845i	$0.303728\pi$
$164$	−3.27898	−	10.0917i	−0.256045	−	0.788026i
$165$		0			0
$166$	0.293218	−	0.902431i	0.0227581	−	0.0700422i
$167$	−1.42932	−	9.02439i	−0.110604	−	0.698328i	−0.979214	−	0.202831i	$-0.934986\pi$
$167$	−1.42932	−	9.02439i	−0.110604	−	0.698328i	0.868610	−	0.495497i	$-0.165014\pi$
$168$	1.65567	+	0.551953i	0.127738	+	0.0425841i
$169$	−3.60230	+	4.95814i	−0.277100	+	0.381395i
$170$		0			0
$171$	−0.0266046	+	1.74423i	−0.00203450	+	0.133385i
$172$	1.58958	−	10.0362i	0.121204	−	0.765252i
$173$	8.21156	+	4.18400i	0.624313	+	0.318104i	0.737374	−	0.675485i	$-0.236065\pi$
$173$	8.21156	+	4.18400i	0.624313	+	0.318104i	−0.113061	+	0.993588i	$0.536065\pi$
$174$	−0.705184	+	0.352561i	−0.0534598	+	0.0267276i
$175$		0			0
$176$			0.366065i			0.0275932i
$177$	16.3156	+	0.124423i	1.22635	+	0.00935217i
$178$	2.00205	+	0.317093i	0.150060	+	0.0237671i
$179$	10.9316	−	7.94230i	0.817069	−	0.593635i	−0.0988026	−	0.995107i	$-0.531501\pi$
$179$	10.9316	−	7.94230i	0.817069	−	0.593635i	0.915871	+	0.401472i	$0.131501\pi$
$180$		0			0
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.0172639	−	0.999851i	$-0.505496\pi$
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.956250	+	0.292552i	$0.905496\pi$
$182$	1.86769	+	1.86769i	0.138442	+	0.138442i
$183$	−1.52887	+	1.09308i	−0.113018	+	0.0808026i
$184$	6.46034	+	2.09909i	0.476262	+	0.154747i
$185$		0			0
$186$	−3.55757	−	3.61225i	−0.260854	−	0.264863i
$187$	0.976324	+	1.91614i	0.0713959	+	0.140122i
$188$	−3.75176	−	7.36324i	−0.273625	−	0.537020i
$189$	−5.18867	+	0.700541i	−0.377420	+	0.0509568i
$190$		0			0
$191$	14.6868	+	4.77202i	1.06270	+	0.345291i	0.787639	−	0.616136i	$-0.211303\pi$
$191$	14.6868	+	4.77202i	1.06270	+	0.345291i	0.275058	+	0.961428i	$0.411303\pi$
$192$	−1.00736	−	1.40898i	−0.0726998	−	0.101684i
$193$	−6.05387	−	6.05387i	−0.435767	−	0.435767i	0.454817	−	0.890585i	$-0.349704\pi$
$193$	−6.05387	−	6.05387i	−0.435767	−	0.435767i	−0.890585	+	0.454817i	$0.849704\pi$
$194$	14.5698	+	10.5856i	1.04605	+	0.760001i
$195$		0			0
$196$	4.84173	−	3.51772i	0.345838	−	0.251266i
$197$	6.25646	+	0.990925i	0.445754	+	0.0706005i	0.375277	−	0.926913i	$-0.377548\pi$
$197$	6.25646	+	0.990925i	0.445754	+	0.0706005i	0.0704774	+	0.997513i	$0.477548\pi$
$198$	−0.483589	−	0.985989i	−0.0343672	−	0.0700712i
$199$		−	10.3976i		−	0.737069i	−0.929614	−	0.368535i	$-0.879860\pi$
$199$		−	10.3976i		−	0.737069i	0.929614	−	0.368535i	$-0.120140\pi$
$200$		0			0
$201$	10.2648	+	20.5314i	0.724025	+	1.44817i
$202$	−0.322847	−	0.164499i	−0.0227155	−	0.0115741i
$203$	0.0717494	−	0.453008i	0.00503582	−	0.0317949i
$204$	−9.03082	−	4.68852i	−0.632284	−	0.328262i
$205$		0			0
$206$	−4.66360	+	6.41889i	−0.324928	+	0.447225i
$207$	−20.1738	+	2.88055i	−1.40217	+	0.200212i
$208$	−0.410067	−	2.58906i	−0.0284331	−	0.179519i
$209$	0.0657771	−	0.202441i	0.00454990	−	0.0140031i
$210$		0			0
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	0.982380	−	0.186896i	$-0.0598427\pi$
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	−0.904617	+	0.426226i	$0.859843\pi$
$212$	7.87247	−	4.01122i	0.540683	−	0.275492i
$213$	−1.32291	+	1.79194i	−0.0906445	+	0.122781i
$214$	12.1977	−	3.96326i	0.833815	−	0.270923i
$215$		0			0
$216$	4.57463	+	2.46430i	0.311264	+	0.167674i
$217$	2.91314	−	0.461396i	0.197757	−	0.0313216i
$218$	3.22451	−	3.22451i	0.218391	−	0.218391i
$219$	16.3093	+	2.71079i	1.10208	+	0.183178i
$220$		0			0
$221$	−9.05171	−	12.4586i	−0.608884	−	0.838057i
$222$	−5.00853	−	15.8243i	−0.336151	−	1.06206i
$223$	0.959975	−	1.88406i	0.0642847	−	0.126166i	−0.856628	−	0.515934i	$-0.827445\pi$
$223$	0.959975	−	1.88406i	0.0642847	−	0.126166i	0.920913	+	0.389768i	$0.127445\pi$
$224$	1.00762			0.0673244
$225$		0			0
$226$	13.6049			0.904987
$227$	−7.03137	+	13.7998i	−0.466689	+	0.915928i	0.530960	+	0.847397i	$0.321831\pi$
$227$	−7.03137	+	13.7998i	−0.466689	+	0.915928i	−0.997649	+	0.0685314i	$0.978169\pi$
$228$	0.303913	+	0.960203i	0.0201272	+	0.0635910i
$229$	−0.971347	−	1.33694i	−0.0641884	−	0.0883477i	0.775716	−	0.631082i	$-0.217389\pi$
$229$	−0.971347	−	1.33694i	−0.0641884	−	0.0883477i	−0.839904	+	0.542735i	$0.817389\pi$
$230$		0			0
$231$	0.630228	+	0.104751i	0.0414660	+	0.00689211i
$232$	−0.321865	+	0.321865i	−0.0211315	+	0.0211315i
$233$	−17.2497	+	2.73209i	−1.13007	+	0.178985i	−0.693342	−	0.720609i	$-0.743862\pi$
$233$	−17.2497	+	2.73209i	−1.13007	+	0.178985i	−0.436726	+	0.899594i	$0.643862\pi$
$234$	4.52478	+	6.43187i	0.295794	+	0.420465i
$235$		0			0
$236$	8.95903	−	2.91096i	0.583183	−	0.189488i
$237$	12.5544	−	17.0054i	0.815497	−	1.10462i
$238$	5.27432	−	2.68740i	0.341884	−	0.174198i
$239$	1.97435	+	6.07643i	0.127710	+	0.393052i	0.994385	−	0.105822i	$-0.0337472\pi$
$239$	1.97435	+	6.07643i	0.127710	+	0.393052i	−0.866675	+	0.498873i	$0.833747\pi$
$240$		0			0
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	−0.554993	−	0.831855i	$-0.687279\pi$
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	0.937951	−	0.346768i	$-0.112721\pi$
$242$	−1.69982	−	10.7322i	−0.109268	−	0.689893i
$243$	−15.5771	−	0.594232i	−0.999273	−	0.0381200i
$244$	−0.637801	+	0.877858i	−0.0408310	+	0.0561991i
$245$		0			0
$246$	16.3115	+	8.46842i	1.03998	+	0.539927i
$247$	−0.238446	+	1.50549i	−0.0151719	+	0.0957918i
$248$	−2.60811	−	1.32890i	−0.165615	−	0.0843851i
$249$	0.734942	+	1.47001i	0.0465751	+	0.0931582i
$250$		0			0
$251$		−	10.1849i		−	0.642864i	−0.946933	−	0.321432i	$-0.895836\pi$
$251$		−	10.1849i		−	0.642864i	0.946933	−	0.321432i	$-0.104164\pi$
$252$	−2.71400	+	1.33111i	−0.170966	+	0.0838522i
$253$	2.45599	+	0.388991i	0.154407	+	0.0244556i
$254$	−15.9565	+	11.5931i	−1.00120	+	0.727414i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.62811	−	1.62811i	−0.101558	−	0.101558i	0.654502	−	0.756060i	$-0.272878\pi$
$257$	−1.62811	−	1.62811i	−0.101558	−	0.101558i	−0.756060	+	0.654502i	$0.772878\pi$
$258$	10.2361	+	14.3171i	0.637270	+	0.891342i
$259$	9.18328	+	2.98383i	0.570621	+	0.185406i
$260$		0			0
$261$	0.441739	−	1.29214i	0.0273429	−	0.0799813i
$262$	−4.92018	−	9.65639i	−0.303970	−	0.596574i
$263$	7.63791	+	14.9902i	0.470973	+	0.924338i	0.997256	+	0.0740278i	$0.0235854\pi$
$263$	7.63791	+	14.9902i	0.470973	+	0.924338i	−0.526283	+	0.850310i	$0.676415\pi$
$264$	−0.444904	−	0.451742i	−0.0273820	−	0.0278028i
$265$		0			0
$266$	−0.557233	−	0.181056i	−0.0341662	−	0.0111013i
$267$	−2.85601	+	2.04192i	−0.174785	+	0.124963i
$268$	9.37111	+	9.37111i	0.572432	+	0.572432i
$269$	−4.85348	−	3.52626i	−0.295922	−	0.215000i	0.429910	−	0.902872i	$-0.358545\pi$
$269$	−4.85348	−	3.52626i	−0.295922	−	0.215000i	−0.725832	+	0.687872i	$0.758545\pi$
$270$		0			0
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	−0.849021	−	0.528359i	$-0.822808\pi$
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	0.240137	+	0.970739i	$0.422808\pi$
$272$	−5.80242	−	0.919013i	−0.351823	−	0.0557234i
$273$	−4.57475	−	0.0348870i	−0.276876	−	0.00211146i
$274$		−	8.70132i		−	0.525666i
$275$		0			0
$276$	−10.5235	+	5.26132i	−0.633443	+	0.316694i
$277$	−5.49796	−	2.80135i	−0.330340	−	0.168317i	0.280952	−	0.959722i	$-0.409350\pi$
$277$	−5.49796	−	2.80135i	−0.330340	−	0.168317i	−0.611292	+	0.791405i	$0.709350\pi$
$278$	0.478765	−	3.02280i	0.0287144	−	0.181296i
$279$	8.78043	+	0.133927i	0.525671	+	0.00801799i
$280$		0			0
$281$	5.28744	−	7.27753i	0.315422	−	0.434141i	−0.621640	−	0.783303i	$-0.713533\pi$
$281$	5.28744	−	7.27753i	0.315422	−	0.434141i	0.937063	+	0.349161i	$0.113533\pi$
$282$	13.5789	+	4.52683i	0.808613	+	0.269569i
$283$	−2.05054	−	12.9466i	−0.121892	−	0.769594i	−0.970594	−	0.240723i	$-0.922615\pi$
$283$	−2.05054	−	12.9466i	−0.121892	−	0.769594i	0.848702	−	0.528871i	$-0.177385\pi$
$284$	−0.397386	+	1.22303i	−0.0235805	+	0.0725733i
$285$		0			0
$286$	−0.296526	−	0.912614i	−0.0175340	−	0.0539640i
$287$	−9.52650	+	4.85400i	−0.562332	+	0.286522i
$288$	2.95556	+	0.514439i	0.174158	+	0.0303136i
$289$	−16.6555	+	5.41171i	−0.979737	+	0.318336i
$290$		0			0
$291$	−30.8453	+	4.64457i	−1.80818	+	0.272270i
$292$	9.42784	−	1.49322i	0.551722	−	0.0873842i
$293$	9.52977	−	9.52977i	0.556735	−	0.556735i	−0.371641	−	0.928376i	$-0.621205\pi$
$293$	9.52977	−	9.52977i	0.556735	−	0.556735i	0.928376	+	0.371641i	$0.121205\pi$
$294$	−1.69960	+	10.2255i	−0.0991225	+	0.596365i
$295$		0			0
$296$	−5.63266	−	7.75269i	−0.327392	−	0.450616i
$297$	1.79511	+	0.629019i	0.104163	+	0.0364994i
$298$	2.65942	−	5.21941i	0.154056	−	0.302353i
$299$	−17.8062			−1.02976
$300$		0			0
$301$	−10.2387			−0.590150
$302$	−1.65696	+	3.25196i	−0.0953472	+	0.187129i
$303$	0.598336	−	0.189379i	0.0343735	−	0.0108795i
$304$	0.341785	+	0.470426i	0.0196027	+	0.0269808i
$305$		0			0
$306$	16.8428	−	5.18992i	0.962837	−	0.296688i
$307$	−13.4223	+	13.4223i	−0.766053	+	0.766053i	−0.977409	−	0.211356i	$-0.932212\pi$
$307$	−13.4223	+	13.4223i	−0.766053	+	0.766053i	0.211356	+	0.977409i	$0.432212\pi$
$308$	0.364313	−	0.0577015i	0.0207587	−	0.00328785i
$309$	−2.04622	−	13.5892i	−0.116405	−	0.773064i
$310$		0			0
$311$	20.3576	−	6.61457i	1.15437	−	0.375078i	0.331583	−	0.943426i	$-0.392417\pi$
$311$	20.3576	−	6.61457i	1.15437	−	0.375078i	0.822788	+	0.568348i	$0.192417\pi$
$312$	3.65271	+	2.69665i	0.206794	+	0.152668i
$313$	−11.3795	+	5.79816i	−0.643210	+	0.327732i	−0.744990	−	0.667075i	$-0.767546\pi$
$313$	−11.3795	+	5.79816i	−0.643210	+	0.327732i	0.101781	+	0.994807i	$0.467546\pi$
$314$	−0.994222	−	3.05990i	−0.0561072	−	0.172680i
$315$		0			0
$316$	3.77118	−	11.6065i	0.212146	−	0.652917i
$317$	4.33787	+	27.3883i	0.243639	+	1.53828i	0.741460	+	0.670997i	$0.234134\pi$
$317$	4.33787	+	27.3883i	0.243639	+	1.53828i	−0.497821	+	0.867280i	$0.665866\pi$
$318$	−4.83989	+	14.5180i	−0.271408	+	0.814129i
$319$	−0.0979413	+	0.134805i	−0.00548366	+	0.00754761i
$320$		0			0
$321$	−10.2357	+	19.7155i	−0.571300	+	1.10041i
$322$	1.07072	−	6.76029i	0.0596692	−	0.376736i
$323$	3.04372	+	1.55085i	0.169357	+	0.0862917i
$324$	−8.64035	+	2.51881i	−0.480019	+	0.139934i
$325$		0			0
$326$			3.69881i			0.204858i
$327$	−0.0602315	+	7.89818i	−0.00333081	+	0.436770i
$328$	10.4804	+	1.65992i	0.578681	+	0.0916540i
$329$	−6.73663	+	4.89445i	−0.371402	+	0.269840i
$330$		0			0
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	0.918826	−	0.394664i	$-0.129139\pi$
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	−0.0914151	+	0.995813i	$0.529139\pi$
$332$	0.670954	+	0.670954i	0.0368234	+	0.0368234i
$333$	25.4131	+	13.4407i	1.39263	+	0.736547i
$334$	8.68968	+	2.82345i	0.475478	+	0.154492i
$335$		0			0
$336$	−1.24345	+	1.22463i	−0.0678359	+	0.0668091i
$337$	9.42193	+	18.4916i	0.513245	+	1.00730i	0.991625	+	0.129148i	$0.0412242\pi$
$337$	9.42193	+	18.4916i	0.513245	+	1.00730i	−0.478380	+	0.878153i	$0.658776\pi$
$338$	−2.78232	−	5.46062i	−0.151339	−	0.297019i
$339$	−16.7892	+	16.5350i	−0.911862	+	0.898060i
$340$		0			0
$341$	−1.01908	−	0.331120i	−0.0551864	−	0.0179312i
$342$	−1.54205	−	0.815571i	−0.0833843	−	0.0441010i
$343$	−9.25153	−	9.25153i	−0.499536	−	0.499536i
$344$	8.22066	+	5.97266i	0.443228	+	0.322024i
$345$		0			0
$346$	−7.45594	+	5.41706i	−0.400834	+	0.291223i
$347$	−7.36133	−	1.16592i	−0.395177	−	0.0625898i	−0.0443161	−	0.999018i	$-0.514111\pi$
$347$	−7.36133	−	1.16592i	−0.395177	−	0.0625898i	−0.350861	+	0.936428i	$0.614111\pi$
$348$	0.00601220	−	0.788383i	0.000322288	−	0.0422618i
$349$		−	16.1042i		−	0.862040i	−0.902342	−	0.431020i	$-0.858154\pi$
$349$		−	16.1042i		−	0.862040i	0.902342	−	0.431020i	$-0.141846\pi$
$350$		0			0
$351$	−13.4009	−	2.43796i	−0.715287	−	0.130129i
$352$	−0.326166	−	0.166190i	−0.0173847	−	0.00885796i
$353$	0.0677049	−	0.427472i	0.00360357	−	0.0227520i	−0.985821	−	0.167800i	$-0.946334\pi$
$353$	0.0677049	−	0.427472i	0.00360357	−	0.0227520i	0.989425	+	0.145048i	$0.0463337\pi$
$354$	−7.51798	+	14.4808i	−0.399576	+	0.769646i
$355$		0			0
$356$	−1.19144	+	1.63988i	−0.0631463	+	0.0869135i
$357$	−3.24259	+	9.72664i	−0.171616	+	0.514788i
$358$	2.11378	+	13.3459i	0.111717	+	0.705352i
$359$	−0.0683480	+	0.210354i	−0.00360727	+	0.0111020i	−0.952844	−	0.303461i	$-0.901858\pi$
$359$	−0.0683480	+	0.210354i	−0.00360727	+	0.0111020i	0.949237	+	0.314563i	$0.101858\pi$
$360$		0			0
$361$	5.76684	+	17.7485i	0.303518	+	0.934132i
$362$	14.4246	−	7.34971i	0.758141	−	0.386292i
$363$	15.1413	+	11.1782i	0.794710	+	0.586702i
$364$	−2.51204	+	0.816210i	−0.131666	+	0.0427810i
$365$		0			0
$366$	−0.279844	−	1.85848i	−0.0146277	−	0.0971445i
$367$	−16.4940	+	2.61239i	−0.860980	+	0.136366i	−0.571284	−	0.820753i	$-0.693554\pi$
$367$	−16.4940	+	2.61239i	−0.860980	+	0.136366i	−0.289697	+	0.957119i	$0.593554\pi$
$368$	−4.80323	+	4.80323i	−0.250386	+	0.250386i
$369$	−30.4215	+	9.37406i	−1.58368	+	0.487994i
$370$		0			0
$371$	−5.23293	−	7.20252i	−0.271680	−	0.373936i
$372$	4.83364	−	1.52989i	0.250612	−	0.0793212i
$373$	−0.0479661	+	0.0941389i	−0.00248359	+	0.00487433i	−0.892245	−	0.451552i	$-0.850871\pi$
$373$	−0.0479661	+	0.0941389i	−0.00248359	+	0.00487433i	0.889761	+	0.456426i	$0.150871\pi$
$374$	−2.15054			−0.111202
$375$		0			0
$376$	8.26396			0.426181
$377$	0.541700	−	1.06315i	0.0278990	−	0.0547548i
$378$	1.73142	−	4.94118i	0.0890546	−	0.254147i
$379$	−5.78536	−	7.96287i	−0.297174	−	0.409025i	0.634154	−	0.773207i	$-0.281349\pi$
$379$	−5.78536	−	7.96287i	−0.297174	−	0.409025i	−0.931328	+	0.364182i	$0.881349\pi$
$380$		0			0
$381$	5.60123	−	33.6995i	0.286960	−	1.72648i
$382$	−10.9196	+	10.9196i	−0.558693	+	0.558693i
$383$	32.8669	−	5.20561i	1.67942	−	0.265994i	0.757349	−	0.653010i	$-0.226494\pi$
$383$	32.8669	−	5.20561i	1.67942	−	0.265994i	0.922073	+	0.387016i	$0.126494\pi$
$384$	1.71274	−	0.257899i	0.0874030	−	0.0131609i
$385$		0			0
$386$	8.14244	−	2.64564i	0.414439	−	0.134659i
$387$	−30.0323	−	5.22736i	−1.52663	−	0.265722i
$388$	−16.0464	+	8.17604i	−0.814632	+	0.415076i
$389$	10.3312	+	31.7962i	0.523814	+	1.61213i	0.766650	+	0.642066i	$0.221922\pi$
$389$	10.3312	+	31.7962i	0.523814	+	1.61213i	−0.242836	+	0.970067i	$0.578078\pi$
$390$		0			0
$391$	−12.3316	+	37.9528i	−0.623637	+	1.91936i
$392$	0.936214	+	5.91102i	0.0472859	+	0.298552i
$393$	17.8078	+	5.93662i	0.898286	+	0.299463i
$394$	−3.72329	+	5.12467i	−0.187577	+	0.258177i
$395$		0			0
$396$	1.09807	+	0.0167487i	0.0551799	+	0.000841653i
$397$	−2.14742	+	13.5583i	−0.107776	+	0.680471i	0.873349	+	0.487096i	$0.161944\pi$
$397$	−2.14742	+	13.5583i	−0.107776	+	0.680471i	−0.981125	+	0.193376i	$0.938056\pi$
$398$	9.26436	+	4.72043i	0.464381	+	0.236614i
$399$	0.907703	−	0.453812i	0.0454420	−	0.0227190i
$400$		0			0
$401$			8.63025i			0.430974i	0.976507	+	0.215487i	$0.0691339\pi$
$401$			8.63025i			0.430974i	−0.976507	+	0.215487i	$0.930866\pi$
$402$	−22.9538	−	0.175045i	−1.14483	−	0.00873046i
$403$	7.57858	+	1.20033i	0.377516	+	0.0597926i
$404$	0.293139	−	0.212978i	0.0145842	−	0.0105961i
$405$		0			0
$406$	0.371060	+	0.269591i	0.0184154	+	0.0133796i
$407$	−2.48049	−	2.48049i	−0.122953	−	0.122953i
$408$	8.27741	−	5.91798i	0.409793	−	0.292984i
$409$	−25.9908	−	8.44492i	−1.28516	−	0.417574i	−0.414767	−	0.909928i	$-0.636137\pi$
$409$	−25.9908	−	8.44492i	−1.28516	−	0.417574i	−0.870395	+	0.492353i	$0.836137\pi$
$410$		0			0
$411$	10.5753	+	10.7379i	0.521642	+	0.529660i
$412$	−3.60205	−	7.06941i	−0.177460	−	0.348285i
$413$	−4.30921	−	8.45731i	−0.212043	−	0.416157i
$414$	6.59212	−	19.2827i	0.323985	−	0.947694i
$415$		0			0
$416$	2.49304	+	0.810037i	0.122231	+	0.0397154i
$417$	3.08300	+	4.31216i	0.150975	+	0.211167i
$418$	0.150514	+	0.150514i	0.00736189	+	0.00736189i
$419$	−20.8362	−	15.1384i	−1.01791	−	0.739557i	−0.0520594	−	0.998644i	$-0.516579\pi$
$419$	−20.8362	−	15.1384i	−1.01791	−	0.739557i	−0.965854	+	0.259087i	$0.916579\pi$
$420$		0			0
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.398419	−	0.917203i	$-0.369559\pi$
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.995431	−	0.0954876i	$-0.0304410\pi$
$422$	−3.61038	−	0.571828i	−0.175751	−	0.0278362i
$423$	−22.2588	+	10.9171i	−1.08226	+	0.530806i
$424$			8.83548i			0.429089i
$425$		0			0
$426$	−0.996037	−	1.99225i	−0.0482582	−	0.0965246i
$427$	0.974191	+	0.496375i	0.0471444	+	0.0240213i
$428$	−2.00633	+	12.6675i	−0.0969797	+	0.612306i
$429$	1.47509	+	0.765821i	0.0712181	+	0.0369742i
$430$		0			0
$431$	−19.9752	+	27.4935i	−0.962171	+	1.32432i	−0.0162678	+	0.999868i	$0.505178\pi$
$431$	−19.9752	+	27.4935i	−0.962171	+	1.32432i	−0.945904	+	0.324448i	$0.894822\pi$
$432$	−4.27254	+	2.95726i	−0.205563	+	0.142281i
$433$	−2.98384	−	18.8393i	−0.143394	−	0.905357i	−0.949541	−	0.313641i	$-0.898451\pi$
$433$	−2.98384	−	18.8393i	−0.143394	−	0.905357i	0.806147	−	0.591715i	$-0.201549\pi$
$434$	−0.911432	+	2.80510i	−0.0437501	+	0.134649i
$435$		0			0
$436$	1.40916	+	4.33696i	0.0674867	+	0.207703i
$437$	3.51936	−	1.79320i	0.168354	−	0.0857806i
$438$	−9.81959	+	13.3010i	−0.469198	+	0.635547i
$439$	33.6517	−	10.9341i	1.60611	−	0.521856i	0.637499	−	0.770451i	$-0.279969\pi$
$439$	33.6517	−	10.9341i	1.60611	−	0.521856i	0.968607	+	0.248596i	$0.0799691\pi$
$440$		0			0
$441$	−10.3304	−	14.6844i	−0.491924	−	0.699259i
$442$	15.2101	−	2.40904i	0.723470	−	0.114586i
$443$	10.2497	−	10.2497i	0.486977	−	0.486977i	−0.420374	−	0.907351i	$-0.638101\pi$
$443$	10.2497	−	10.2497i	0.486977	−	0.486977i	0.907351	+	0.420374i	$0.138101\pi$
$444$	16.3734	+	2.72144i	0.777046	+	0.129154i
$445$		0			0
$446$	1.24289	+	1.71069i	0.0588524	+	0.0810034i
$447$	3.06166	+	9.67320i	0.144811	+	0.457526i
$448$	−0.457450	+	0.897796i	−0.0216125	+	0.0424169i
$449$	9.47944			0.447362			0.223681	−	0.974662i	$-0.428193\pi$
$449$	9.47944			0.447362			0.223681	+	0.974662i	$0.428193\pi$
$450$		0			0
$451$	3.88431			0.182905
$452$	−6.17652	+	12.1221i	−0.290519	+	0.570175i
$453$	−1.90757	−	6.02689i	−0.0896254	−	0.283168i
$454$	−9.10358	−	12.5300i	−0.427252	−	0.588062i
$455$		0			0
$456$	−0.993521	−	0.165134i	−0.0465259	−	0.00773312i
$457$	25.4852	−	25.4852i	1.19215	−	1.19215i	0.215682	−	0.976464i	$-0.430803\pi$
$457$	25.4852	−	25.4852i	1.19215	−	1.19215i	0.976464	−	0.215682i	$-0.0691974\pi$
$458$	1.63221	−	0.258516i	0.0762681	−	0.0120797i
$459$	−14.4771	+	26.8748i	−0.675734	+	1.25441i
$460$		0			0
$461$	21.4340	−	6.96431i	0.998279	−	0.324360i	0.236101	−	0.971728i	$-0.424130\pi$
$461$	21.4340	−	6.96431i	0.998279	−	0.324360i	0.762178	+	0.647368i	$0.224130\pi$
$462$	−0.379451	+	0.513982i	−0.0176537	+	0.0239126i
$463$	−5.05300	+	2.57463i	−0.234833	+	0.119653i	−0.567448	−	0.823409i	$-0.692069\pi$
$463$	−5.05300	+	2.57463i	−0.234833	+	0.119653i	0.332615	+	0.943063i	$0.392069\pi$
$464$	−0.140660	−	0.432908i	−0.00652999	−	0.0200972i
$465$		0			0
$466$	5.39691	−	16.6100i	0.250007	−	0.769442i
$467$	−1.81829	−	11.4802i	−0.0841404	−	0.531242i	−0.993371	−	0.114950i	$-0.963329\pi$
$467$	−1.81829	−	11.4802i	−0.0841404	−	0.531242i	0.909231	−	0.416292i	$-0.136671\pi$
$468$	−7.78505	+	1.11160i	−0.359864	+	0.0513838i
$469$	7.84913	−	10.8034i	0.362439	−	0.498854i
$470$		0			0
$471$	4.94583	+	2.56772i	0.227892	+	0.118314i
$472$	−1.47363	+	9.30410i	−0.0678291	+	0.428256i
$473$	3.31427	+	1.68871i	0.152390	+	0.0776467i
$474$	9.45238	+	18.9064i	0.434162	+	0.868399i
$475$		0			0
$476$			5.91951i			0.271320i
$477$	−11.6721	−	23.7982i	−0.534428	−	1.08964i
$478$	−6.31048	−	0.999482i	−0.288635	−	0.0457152i
$479$	−2.20406	+	1.60135i	−0.100706	+	0.0731673i	−0.636999	−	0.770865i	$-0.719824\pi$
$479$	−2.20406	+	1.60135i	−0.100706	+	0.0731673i	0.536293	+	0.844032i	$0.319824\pi$
$480$		0			0
$481$	20.3224	+	14.7651i	0.926622	+	0.673230i
$482$	13.6039	+	13.6039i	0.619639	+	0.619639i
$483$	6.89493	+	9.64386i	0.313730	+	0.438811i
$484$	10.3342	+	3.35778i	0.469735	+	0.152626i
$485$		0			0
$486$	7.60133	−	13.6095i	0.344803	−	0.617342i
$487$	12.3082	+	24.1563i	0.557739	+	1.09462i	0.981964	+	0.189068i	$0.0605466\pi$
$487$	12.3082	+	24.1563i	0.557739	+	1.09462i	−0.424225	+	0.905557i	$0.639453\pi$
$488$	−0.492622	−	0.966824i	−0.0222999	−	0.0437661i
$489$	−4.49543	−	4.56452i	−0.203290	−	0.206415i
$490$		0			0
$491$	37.5268	+	12.1932i	1.69356	+	0.550271i	0.987464	−	0.157846i	$-0.0504550\pi$
$491$	37.5268	+	12.1932i	1.69356	+	0.550271i	0.706095	+	0.708117i	$0.250455\pi$
$492$	−14.9507	+	10.6891i	−0.674029	+	0.481901i
$493$	−1.89088	−	1.89088i	−0.0851609	−	0.0851609i
$494$	−1.23315	−	0.895933i	−0.0554819	−	0.0403099i
$495$		0			0
$496$	2.36811	−	1.72054i	0.106331	−	0.0772543i
$497$	1.27981	+	0.202702i	0.0574075	+	0.00909245i
$498$	−1.64345	−	0.0125329i	−0.0736446	−	0.000561613i
$499$		−	11.3155i		−	0.506552i	−0.967394	−	0.253276i	$-0.918492\pi$
$499$		−	11.3155i		−	0.506552i	0.967394	−	0.253276i	$-0.0815081\pi$
$500$		0			0
$501$	−14.1550	+	7.07690i	−0.632400	+	0.316173i
$502$	9.07480	+	4.62384i	0.405028	+	0.206372i
$503$	−1.34669	+	8.50269i	−0.0600461	+	0.379116i	0.939305	+	0.343084i	$0.111472\pi$
$503$	−1.34669	+	8.50269i	−0.0600461	+	0.379116i	−0.999351	+	0.0360317i	$0.988528\pi$
$504$	0.0461019	−	3.02251i	0.00205354	−	0.134633i
$505$		0			0
$506$	−1.46159	+	2.01171i	−0.0649756	+	0.0894312i
$507$	10.0702	+	3.35712i	0.447233	+	0.149095i
$508$	−3.08541	−	19.4805i	−0.136893	−	0.864307i
$509$	−0.697725	+	2.14738i	−0.0309261	+	0.0951808i	−0.965328	−	0.261039i	$-0.915935\pi$
$509$	−0.697725	+	2.14738i	−0.0309261	+	0.0951808i	0.934402	+	0.356220i	$0.115935\pi$
$510$		0			0
$511$	−2.97215	−	9.14735i	−0.131480	−	0.404655i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	2.89418	−	0.867702i	0.127781	−	0.0383100i
$514$	2.18980	−	0.711508i	0.0965878	−	0.0313833i
$515$		0			0
$516$	−17.4037	+	2.62059i	−0.766154	+	0.115365i
$517$	2.98790	−	0.473237i	0.131408	−	0.0208129i
$518$	−6.82773	+	6.82773i	−0.299993	+	0.299993i
$519$	2.61727	−	15.7466i	0.114885	−	0.691201i
$520$		0			0
$521$	−13.0319	−	17.9369i	−0.570938	−	0.785829i	0.421727	−	0.906723i	$-0.361424\pi$
$521$	−13.0319	−	17.9369i	−0.570938	−	0.785829i	−0.992665	+	0.120894i	$0.961424\pi$
$522$	0.950757	+	0.980210i	0.0416135	+	0.0429026i
$523$	5.09249	−	9.99457i	0.222679	−	0.437032i	−0.752456	−	0.658642i	$-0.771131\pi$
$523$	5.09249	−	9.99457i	0.222679	−	0.437032i	0.975135	+	0.221610i	$0.0711312\pi$
$524$	10.8376			0.473444
$525$		0			0
$526$	−16.8239			−0.733558
$527$	7.80694	−	15.3220i	0.340076	−	0.667436i
$528$	0.604487	−	0.191326i	0.0263069	−	0.00832639i
$529$	13.6026	+	18.7224i	0.591417	+	0.814016i
$530$		0			0
$531$	−8.32197	−	27.0071i	−0.361143	−	1.17201i
$532$	0.414301	−	0.414301i	0.0179622	−	0.0179622i
$533$	−27.4725	+	4.35122i	−1.18997	+	0.188472i
$534$	−0.522762	−	3.47174i	−0.0226221	−	0.150237i
$535$		0			0
$536$	−12.6041	+	4.09532i	−0.544415	+	0.176891i
$537$	−18.8287	−	13.9005i	−0.812518	−	0.599849i
$538$	5.34536	−	2.72359i	0.230455	−	0.117423i
$539$	0.676991	+	2.08356i	0.0291601	+	0.0897455i
$540$		0			0
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	−0.864867	−	0.502001i	$-0.832597\pi$
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	0.994761	+	0.102229i	$0.0325974\pi$
$542$	−1.93818	−	12.2372i	−0.0832520	−	0.525632i
$543$	−8.86807	+	26.6012i	−0.380565	+	1.14156i
$544$	3.45309	−	4.75277i	0.148050	−	0.203773i
$545$		0			0
$546$	2.10798	−	4.06029i	0.0902131	−	0.173765i
$547$	1.65483	−	10.4482i	0.0707555	−	0.446732i	−0.926722	−	0.375748i	$-0.877386\pi$
$547$	1.65483	−	10.4482i	0.0707555	−	0.446732i	0.997477	−	0.0709846i	$-0.0226141\pi$
$548$	7.75294	+	3.95032i	0.331189	+	0.168749i
$549$	2.60409	+	1.95335i	0.111140	+	0.0833668i
$550$		0			0
$551$			0.264681i			0.0112758i
$552$	0.0897208	−	11.7651i	0.00381877	−	0.500757i
$553$	−12.1454	−	1.92364i	−0.516475	−	0.0818016i
$554$	4.99204	−	3.62693i	0.212092	−	0.154094i
$555$		0			0
$556$	2.47598	+	1.79891i	0.105005	+	0.0762906i
$557$	2.23937	+	2.23937i	0.0948850	+	0.0948850i	0.752956	−	0.658071i	$-0.228627\pi$
$557$	2.23937	+	2.23937i	0.0948850	+	0.0948850i	−0.658071	+	0.752956i	$0.728627\pi$
$558$	−4.10556	+	7.76262i	−0.173802	+	0.328618i
$559$	−25.3325	−	8.23103i	−1.07145	−	0.348135i
$560$		0			0
$561$	2.65387	−	2.61370i	0.112047	−	0.110351i
$562$	4.08388	+	8.01507i	0.172268	+	0.338095i
$563$	4.61877	+	9.06485i	0.194658	+	0.382038i	0.967619	−	0.252416i	$-0.0812251\pi$
$563$	4.61877	+	9.06485i	0.194658	+	0.382038i	−0.772961	+	0.634454i	$0.781225\pi$
$564$	−10.1981	+	10.0438i	−0.429419	+	0.422919i
$565$		0			0
$566$	12.4664	+	4.05058i	0.524002	+	0.170259i
$567$	3.86870	+	8.20197i	0.162470	+	0.344450i
$568$	−0.909316	−	0.909316i	−0.0381541	−	0.0381541i
$569$	10.0063	+	7.26997i	0.419484	+	0.304773i	0.777430	−	0.628969i	$-0.216523\pi$
$569$	10.0063	+	7.26997i	0.419484	+	0.304773i	−0.357946	+	0.933742i	$0.616523\pi$
$570$		0			0
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.00179324	−	0.999998i	$-0.499429\pi$
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.951609	+	0.307311i	$0.0994292\pi$
$572$	0.947765	+	0.150111i	0.0396281	+	0.00627647i
$573$	0.203969	−	26.7466i	0.00852093	−	1.11735i
$574$		−	10.6918i		−	0.446269i
$575$		0			0
$576$	−1.80017	+	2.39988i	−0.0750069	+	0.0999948i
$577$	9.96640	+	5.07813i	0.414907	+	0.211405i	0.648967	−	0.760817i	$-0.275201\pi$
$577$	9.96640	+	5.07813i	0.414907	+	0.211405i	−0.234060	+	0.972222i	$0.575201\pi$
$578$	2.73958	−	17.2971i	0.113952	−	0.719463i
$579$	−6.83274	+	13.1609i	−0.283959	+	0.546949i
$580$		0			0
$581$	0.561983	−	0.773503i	0.0233150	−	0.0320903i
$582$	9.86511	−	29.5919i	0.408922	−	1.22662i
$583$	0.505965	+	3.19454i	0.0209549	+	0.132304i
$584$	−2.94968	+	9.07817i	−0.122059	+	0.375657i
$585$		0			0
$586$	4.16466	+	12.8175i	0.172041	+	0.529487i
$587$	−0.534451	+	0.272317i	−0.0220592	+	0.0112397i	−0.464985	−	0.885318i	$-0.653940\pi$
$587$	−0.534451	+	0.272317i	−0.0220592	+	0.0112397i	0.442926	+	0.896558i	$0.353940\pi$
$588$	−8.33941	−	6.15664i	−0.343911	−	0.253896i
$589$	−1.61877	+	0.525971i	−0.0667003	+	0.0216722i
$590$		0			0
$591$	−1.63365	−	10.8493i	−0.0671992	−	0.446279i
$592$	9.46487	−	1.49909i	0.389004	−	0.0616122i
$593$	1.69633	−	1.69633i	0.0696598	−	0.0696598i	−0.671419	−	0.741078i	$-0.734315\pi$
$593$	1.69633	−	1.69633i	0.0696598	−	0.0696598i	0.741078	+	0.671419i	$0.234315\pi$
$594$	−1.37542	+	1.31389i	−0.0564343	+	0.0539095i
$595$		0			0
$596$	3.44318	+	4.73913i	0.141038	+	0.194122i
$597$	−17.1697	+	5.43439i	−0.702711	+	0.222415i
$598$	8.08385	−	15.8654i	0.330573	−	0.648786i
$599$	12.0681			0.493088			0.246544	−	0.969132i	$-0.420705\pi$
$599$	12.0681			0.493088			0.246544	+	0.969132i	$0.420705\pi$
$600$		0			0
$601$	8.03062			0.327576			0.163788	−	0.986496i	$-0.447629\pi$
$601$	8.03062			0.327576			0.163788	+	0.986496i	$0.447629\pi$
$602$	4.64828	−	9.12277i	0.189450	−	0.371816i
$603$	28.5388	−	27.6813i	1.16219	−	1.12727i
$604$	−2.14528	−	2.95272i	−0.0872900	−	0.120144i
$605$		0			0
$606$	−0.102901	+	0.619098i	−0.00418007	+	0.0251491i
$607$	27.1756	−	27.1756i	1.10302	−	1.10302i	0.108980	−	0.994044i	$-0.465242\pi$
$607$	27.1756	−	27.1756i	1.10302	−	1.10302i	0.994044	−	0.108980i	$-0.0347584\pi$
$608$	−0.574320	+	0.0909634i	−0.0232918	+	0.00368905i
$609$	−0.785558	+	0.118287i	−0.0318324	+	0.00479321i
$610$		0			0
$611$	−20.6024	+	6.69412i	−0.833483	+	0.270815i
$612$	−3.02220	+	17.3632i	−0.122165	+	0.701865i
$613$	25.9627	−	13.2287i	1.04862	−	0.534300i	0.157245	−	0.987560i	$-0.449739\pi$
$613$	25.9627	−	13.2287i	1.04862	−	0.534300i	0.891379	+	0.453259i	$0.149739\pi$
$614$	−5.86577	−	18.0530i	−0.236723	−	0.728560i
$615$		0			0
$616$	−0.113982	+	0.350801i	−0.00459248	+	0.0141342i
$617$	3.00048	+	18.9443i	0.120795	+	0.762667i	0.971503	+	0.237029i	$0.0761736\pi$
$617$	3.00048	+	18.9443i	0.120795	+	0.762667i	−0.850708	+	0.525639i	$0.823826\pi$
$618$	13.0371	+	4.34618i	0.524427	+	0.174829i
$619$	11.4117	−	15.7069i	0.458676	−	0.631314i	−0.515557	−	0.856855i	$-0.672415\pi$
$619$	11.4117	−	15.7069i	0.458676	−	0.631314i	0.974234	+	0.225541i	$0.0724151\pi$
$620$		0			0
$621$	15.3006	+	31.8077i	0.613993	+	1.27640i
$622$	−3.34851	+	21.1417i	−0.134263	+	0.847704i
$623$	1.81984	+	0.927252i	0.0729102	+	0.0371496i
$624$	−4.06103	+	2.03034i	−0.162571	+	0.0812786i
$625$		0			0
$626$		−	12.7716i		−	0.510454i
$627$	−0.368672	−	0.00281149i	−0.0147233	−	0.000112280i
$628$	3.17776	+	0.503308i	0.126806	+	0.0200842i
$629$	45.5451	−	33.0905i	1.81600	−	1.31940i
$630$		0			0
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	0.750850	−	0.660472i	$-0.229644\pi$
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	−0.396121	+	0.918198i	$0.629644\pi$
$632$	8.62939	+	8.62939i	0.343259	+	0.343259i
$633$	5.15037	−	3.68228i	0.204709	−	0.146358i
$634$	−26.3725	−	8.56893i	−1.04738	−	0.340316i
$635$		0			0
$636$	−10.7384	−	10.9034i	−0.425804	−	0.432348i
$637$	−7.12216	−	13.9780i	−0.282190	−	0.553830i
$638$	−0.0756474	−	0.148466i	−0.00299491	−	0.00587784i
$639$	3.65047	+	1.24798i	0.144411	+	0.0493692i
$640$		0			0
$641$	−41.8679	−	13.6037i	−1.65368	−	0.537314i	−0.674148	−	0.738596i	$-0.735489\pi$
$641$	−41.8679	−	13.6037i	−1.65368	−	0.537314i	−0.979533	+	0.201283i	$0.935489\pi$
$642$	−12.9198	−	18.0707i	−0.509902	−	0.713195i
$643$	−21.0709	−	21.0709i	−0.830957	−	0.830957i	0.156691	−	0.987648i	$-0.449917\pi$
$643$	−21.0709	−	21.0709i	−0.830957	−	0.830957i	−0.987648	+	0.156691i	$0.949917\pi$
$644$	5.53736	+	4.02313i	0.218203	+	0.158534i
$645$		0			0
$646$	−2.76364	+	2.00790i	−0.108734	+	0.0789998i
$647$	32.0404	+	5.07470i	1.25964	+	0.199507i	0.750322	−	0.661073i	$-0.229899\pi$
$647$	32.0404	+	5.07470i	1.25964	+	0.199507i	0.509316	+	0.860580i	$0.329899\pi$
$648$	1.67836	−	8.84212i	0.0659324	−	0.347351i
$649$			3.44836i			0.135360i
$650$		0			0
$651$	−2.28448	−	4.56935i	−0.0895358	−	0.179087i
$652$	−3.29567	−	1.67923i	−0.129068	−	0.0657636i
$653$	−4.84433	+	30.5859i	−0.189573	+	1.19692i	0.690945	+	0.722907i	$0.257195\pi$
$653$	−4.84433	+	30.5859i	−0.189573	+	1.19692i	−0.880518	+	0.474012i	$0.842805\pi$
$654$	−7.00998	−	3.63936i	−0.274112	−	0.142310i
$655$		0			0
$656$	−6.23698	+	8.58447i	−0.243513	+	0.335167i
$657$	−4.04779	−	28.3485i	−0.157919	−	1.10598i
$658$	−1.30262	−	8.22441i	−0.0507814	−	0.320621i
$659$	6.85074	−	21.0844i	0.266867	−	0.821332i	−0.724390	−	0.689390i	$-0.757879\pi$
$659$	6.85074	−	21.0844i	0.266867	−	0.821332i	0.991257	−	0.131942i	$-0.0421213\pi$
$660$		0			0
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	−0.936056	−	0.351852i	$-0.885552\pi$
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	0.550471	−	0.834854i	$-0.314448\pi$
$662$	−16.5790	+	8.44742i	−0.644361	+	0.328318i
$663$	−15.8421	+	21.4588i	−0.615257	+	0.833389i
$664$	−0.902431	+	0.293218i	−0.0350211	+	0.0113790i
$665$		0			0
$666$	−23.5131	+	16.5413i	−0.911114	+	0.640963i
$667$	−3.05392	+	0.483694i	−0.118248	+	0.0187287i
$668$	−6.46075	+	6.46075i	−0.249974	+	0.249974i
$669$	−3.61290	−	0.600505i	−0.139683	−	0.0232169i
$670$		0			0
$671$	−0.233477	−	0.321353i	−0.00901327	−	0.0124057i
$672$	−0.526638	−	1.66389i	−0.0203155	−	0.0641861i
$673$	−17.0242	+	33.4118i	−0.656234	+	1.28793i	0.287676	+	0.957728i	$0.407117\pi$
$673$	−17.0242	+	33.4118i	−0.656234	+	1.28793i	−0.943910	+	0.330204i	$0.892883\pi$
$674$	−20.7536			−0.799398
$675$		0			0
$676$	6.12860			0.235715
$677$	13.6443	−	26.7784i	0.524391	−	1.02918i	−0.465192	−	0.885210i	$-0.654015\pi$
$677$	13.6443	−	26.7784i	0.524391	−	1.02918i	0.989583	−	0.143966i	$-0.0459855\pi$
$678$	−7.11070	−	22.4660i	−0.273085	−	0.862802i
$679$	10.6662	+	14.6808i	0.409333	+	0.563399i
$680$		0			0
$681$	26.4628	+	4.39842i	1.01406	+	0.168548i
$682$	0.757684	−	0.757684i	0.0290132	−	0.0290132i
$683$	−32.9389	+	5.21701i	−1.26037	+	0.199623i	−0.750640	−	0.660711i	$-0.770255\pi$
$683$	−32.9389	+	5.21701i	−1.26037	+	0.199623i	−0.509731	+	0.860334i	$0.670255\pi$
$684$	1.42675	−	1.00371i	0.0545533	−	0.0383779i
$685$		0			0
$686$	12.4433	−	4.04307i	0.475087	−	0.154365i
$687$	−1.70003	+	2.30276i	−0.0648602	+	0.0878557i
$688$	−9.05378	+	4.61313i	−0.345172	+	0.175874i
$689$	−7.15707	−	22.0272i	−0.272663	−	0.839169i
$690$		0			0
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	−0.941188	−	0.337883i	$-0.890289\pi$
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	0.960040	+	0.279863i	$0.0902891\pi$
$692$	−1.44171	−	9.10259i	−0.0548055	−	0.346028i
$693$	−0.156416	−	1.09545i	−0.00594175	−	0.0416128i
$694$	4.38081	−	6.02967i	0.166293	−	0.228883i
$695$		0			0
$696$	0.699725	+	0.363275i	0.0265230	+	0.0137699i
$697$	−9.75164	+	61.5694i	−0.369370	+	2.33211i
$698$	14.3490	+	7.31117i	0.543117	+	0.276732i
$699$	13.5272	+	27.0568i	0.511646	+	1.02338i
$700$		0			0
$701$			17.1529i			0.647855i	0.946082	+	0.323928i	$0.105003\pi$
$701$			17.1529i			0.647855i	−0.946082	+	0.323928i	$0.894997\pi$
$702$	8.25612	−	10.8335i	0.311607	−	0.408883i
$703$	−5.50363	−	0.871689i	−0.207573	−	0.0328764i
$704$	0.296153	−	0.215168i	0.0111617	−	0.00810943i
$705$		0			0
$706$	0.350143	+	0.254394i	0.0131778	+	0.00957423i
$707$	−0.258165	−	0.258165i	−0.00970931	−	0.00970931i
$708$	−9.48940	−	13.2727i	−0.356633	−	0.498819i
$709$	43.3999	+	14.1015i	1.62992	+	0.529592i	0.974252	−	0.225460i	$-0.0723886\pi$
$709$	43.3999	+	14.1015i	1.62992	+	0.529592i	0.655664	+	0.755052i	$0.272389\pi$
$710$		0			0
$711$	−34.6429	−	11.8433i	−1.29921	−	0.444157i
$712$	−0.920240	−	1.80607i	−0.0344875	−	0.0676855i
$713$	−9.02694	−	17.7164i	−0.338062	−	0.663483i
$714$	−7.19440	−	7.30497i	−0.269244	−	0.273382i
$715$		0			0
$716$	−12.8509	−	4.17551i	−0.480261	−	0.156046i
$717$	9.00218	−	6.43616i	0.336193	−	0.240363i
$718$	−0.156397	−	0.156397i	−0.00583669	−	0.00583669i
$719$	−18.8277	−	13.6791i	−0.702155	−	0.510145i	0.178478	−	0.983944i	$-0.442883\pi$
$719$	−18.8277	−	13.6791i	−0.702155	−	0.510145i	−0.880633	+	0.473798i	$0.842883\pi$
$720$		0			0
$721$	−6.46780	+	4.69913i	−0.240874	+	0.175005i
$722$	−18.4321	−	2.91936i	−0.685973	−	0.108647i
$723$	−33.3215	−	0.254110i	−1.23924	−	0.00945044i
$724$			16.1891i			0.601664i
$725$		0			0
$726$	−16.8338	+	8.41618i	−0.624762	+	0.312354i
$727$	−24.2957	−	12.3793i	−0.901077	−	0.459122i	−0.0588635	−	0.998266i	$-0.518748\pi$
$727$	−24.2957	−	12.3793i	−0.901077	−	0.459122i	−0.842213	+	0.539144i	$0.818748\pi$
$728$	0.413192	−	2.60879i	0.0153139	−	0.0966882i
$729$	7.16021	+	26.0333i	0.265193	+	0.964195i
$730$		0			0
$731$	−35.0879	+	48.2943i	−1.29777	+	1.78623i
$732$	1.78297	+	0.594391i	0.0659004	+	0.0219693i
$733$	0.915975	+	5.78324i	0.0338323	+	0.213609i	0.998813	−	0.0487128i	$-0.0155119\pi$
$733$	0.915975	+	5.78324i	0.0338323	+	0.213609i	−0.964981	+	0.262322i	$0.915512\pi$
$734$	5.16046	−	15.8823i	0.190476	−	0.586225i
$735$		0			0
$736$	−2.09909	−	6.46034i	−0.0773735	−	0.238131i
$737$	−4.32260	+	2.20247i	−0.159225	+	0.0811292i
$738$	5.45871	−	31.3615i	0.200938	−	1.15443i
$739$	10.9906	−	3.57105i	0.404295	−	0.131363i	−0.0998086	−	0.995007i	$-0.531823\pi$
$739$	10.9906	−	3.57105i	0.404295	−	0.131363i	0.504103	+	0.863643i	$0.331823\pi$
$740$		0			0
$741$	2.61065	−	0.393103i	0.0959047	−	0.0144410i
$742$	8.79319	−	1.39270i	0.322808	−	0.0511278i
$743$	5.09866	−	5.09866i	0.187052	−	0.187052i	−0.607369	−	0.794420i	$-0.707775\pi$
$743$	5.09866	−	5.09866i	0.187052	−	0.187052i	0.794420	+	0.607369i	$0.207775\pi$
$744$	−0.831282	+	5.00136i	−0.0304763	+	0.183359i
$745$		0			0
$746$	−0.0621022	−	0.0854763i	−0.00227372	−	0.00312951i
$747$	2.04333	−	1.98193i	0.0747614	−	0.0725150i
$748$	0.976324	−	1.91614i	0.0356980	−	0.0700612i
$749$	12.9231			0.472200
$750$		0			0
$751$	−19.8804			−0.725445			−0.362723	−	0.931897i	$-0.618153\pi$
$751$	−19.8804			−0.725445			−0.362723	+	0.931897i	$0.618153\pi$
$752$	−3.75176	+	7.36324i	−0.136813	+	0.268510i
$753$	−16.8184	+	5.32319i	−0.612897	+	0.193988i
$754$	0.701343	+	0.965316i	0.0255414	+	0.0351547i
$755$		0			0
$756$	3.61657	+	3.78595i	0.131533	+	0.137694i
$757$	16.4335	−	16.4335i	0.597285	−	0.597285i	−0.342304	−	0.939589i	$-0.611207\pi$
$757$	16.4335	−	16.4335i	0.597285	−	0.597285i	0.939589	+	0.342304i	$0.111207\pi$
$758$	9.72147	−	1.53973i	0.353100	−	0.0559255i
$759$	−0.641293	−	4.25892i	−0.0232775	−	0.154589i
$760$		0			0
$761$	−4.02479	+	1.30773i	−0.145898	+	0.0474052i	−0.381056	−	0.924552i	$-0.624439\pi$
$761$	−4.02479	+	1.30773i	−0.145898	+	0.0474052i	0.235157	+	0.971957i	$0.424439\pi$
$762$	27.4835	+	20.2900i	0.995624	+	0.735028i
$763$	4.09408	−	2.08604i	0.148216	−	0.0755197i
$764$	−4.77202	−	14.6868i	−0.172646	−	0.531349i
$765$		0			0
$766$	−10.2830	+	31.6480i	−0.371542	+	1.14349i
$767$	−3.86287	−	24.3892i	−0.139480	−	0.880642i
$768$	−0.547779	+	1.64315i	−0.0197663	+	0.0592920i
$769$	4.46592	−	6.14681i	0.161045	−	0.221660i	−0.720867	−	0.693073i	$-0.756256\pi$
$769$	4.46592	−	6.14681i	0.161045	−	0.221660i	0.881912	+	0.471414i	$0.156256\pi$
$770$		0			0
$771$	−1.83757	+	3.53945i	−0.0661785	+	0.127470i
$772$	−1.33931	+	8.45606i	−0.0482028	+	0.304340i
$773$	−12.3217	−	6.27822i	−0.443181	−	0.225812i	0.218136	−	0.975918i	$-0.430002\pi$
$773$	−12.3217	−	6.27822i	−0.443181	−	0.225812i	−0.661317	+	0.750106i	$0.730002\pi$
$774$	18.2920	−	24.3858i	0.657493	−	0.876531i
$775$		0			0
$776$		−	18.0093i		−	0.646495i
$777$	0.127537	−	16.7240i	0.00457536	−	0.599969i
$778$	−33.0209	−	5.23000i	−1.18386	−	0.187505i
$779$	4.99169	−	3.62668i	0.178846	−	0.129939i
$780$		0			0
$781$	−0.380843	−	0.276698i	−0.0136276	−	0.00990105i
$782$	−28.2178	−	28.2178i	−1.00907	−	1.00907i
$783$	−2.36460	−	0.0541056i	−0.0845039	−	0.00193358i
$784$	−5.69179	−	1.84937i	−0.203278	−	0.0660491i
$785$		0			0
$786$	−13.3742	+	13.1717i	−0.477040	+	0.469820i
$787$	5.14950	+	10.1065i	0.183560	+	0.360257i	0.964389	−	0.264488i	$-0.0852030\pi$
$787$	5.14950	+	10.1065i	0.183560	+	0.360257i	−0.780829	+	0.624745i	$0.785203\pi$
$788$	−2.87578	−	5.64403i	−0.102445	−	0.201060i
$789$	20.7616	−	20.4473i	0.739131	−	0.727943i
$790$		0			0
$791$	13.0377	+	4.23619i	0.463566	+	0.150622i
$792$	−0.513435	+	0.970781i	−0.0182441	+	0.0344952i
$793$	2.01129	+	2.01129i	0.0714229	+	0.0714229i
$794$	−11.1056	−	8.06871i	−0.394124	−	0.286348i
$795$		0			0
$796$	−8.41187	+	6.11158i	−0.298151	+	0.216619i
$797$	−43.6682	−	6.91637i	−1.54681	−	0.244990i	−0.676107	−	0.736804i	$-0.736334\pi$
$797$	−43.6682	−	6.91637i	−1.54681	−	0.244990i	−0.870701	+	0.491813i	$0.836334\pi$
$798$	−0.00773883	+	1.01480i	−0.000273952	+	0.0359234i
$799$			48.5487i			1.71753i
$800$		0			0
$801$	4.86456	+	3.64894i	0.171881	+	0.128929i
$802$	−7.68961	−	3.91805i	−0.271529	−	0.138351i
$803$	−0.546616	+	3.45120i	−0.0192897	+	0.121790i
$804$	10.5768	−	20.3725i	0.373013	−	0.718482i
$805$		0			0
$806$	−4.51010	+	6.20762i	−0.158862	+	0.218654i
$807$	−3.28626	+	9.85763i	−0.115682	+	0.347005i
$808$	0.0566825	+	0.357879i	0.00199408	+	0.0125901i
$809$	−6.33598	+	19.5001i	−0.222761	+	0.685589i	0.775750	+	0.631040i	$0.217372\pi$
$809$	−6.33598	+	19.5001i	−0.222761	+	0.685589i	−0.998511	+	0.0545481i	$0.982628\pi$
$810$		0			0
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	−0.810108	−	0.586280i	$-0.800592\pi$
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	0.310785	−	0.950480i	$-0.399408\pi$
$812$	−0.408664	+	0.208225i	−0.0143413	+	0.00730726i
$813$	17.2645	+	12.7457i	0.605493	+	0.447011i
$814$	3.33626	−	1.08402i	0.116936	−	0.0379947i
$815$		0			0
$816$	1.51509	+	10.0619i	0.0530388	+	0.352238i
$817$	5.83584	−	0.924305i	0.204170	−	0.0323374i
$818$	19.3241	−	19.3241i	0.675650	−	0.675650i
$819$	2.33341	+	7.57257i	0.0815360	+	0.264607i
$820$		0			0
$821$	−5.32407	−	7.32795i	−0.185811	−	0.255747i	0.705942	−	0.708270i	$-0.250524\pi$
$821$	−5.32407	−	7.32795i	−0.185811	−	0.255747i	−0.891753	+	0.452523i	$0.850524\pi$
$822$	−14.3686	+	4.54780i	−0.501162	+	0.158623i
$823$	21.6070	−	42.4061i	0.753173	−	1.47819i	−0.121042	−	0.992647i	$-0.538624\pi$
$823$	21.6070	−	42.4061i	0.753173	−	1.47819i	0.874216	−	0.485538i	$-0.161376\pi$
$824$	7.93419			0.276401
$825$		0			0
$826$	9.49186			0.330264
$827$	21.7292	−	42.6460i	0.755599	−	1.48295i	−0.116276	−	0.993217i	$-0.537096\pi$
$827$	21.7292	−	42.6460i	0.755599	−	1.48295i	0.871875	−	0.489729i	$-0.162904\pi$
$828$	14.1883	+	14.6278i	0.493076	+	0.508351i
$829$	−8.53245	−	11.7439i	−0.296344	−	0.407883i	0.634718	−	0.772744i	$-0.281116\pi$
$829$	−8.53245	−	11.7439i	−0.296344	−	0.407883i	−0.931062	+	0.364861i	$0.881116\pi$
$830$		0			0
$831$	−1.75236	+	10.5430i	−0.0607888	+	0.365732i
$832$	−1.85356	+	1.85356i	−0.0642608	+	0.0642608i
$833$	−34.7258	+	5.50002i	−1.20318	+	0.190564i
$834$	−5.24182	+	0.789295i	−0.181509	+	0.0273310i
$835$		0			0
$836$	−0.202441	+	0.0657771i	−0.00700157	+	0.00227495i
$837$	−4.36799	−	14.5692i	−0.150980	−	0.503586i
$838$	22.9478	−	11.6925i	0.792719	−	0.403910i
$839$	−1.29678	−	3.99108i	−0.0447698	−	0.137787i	0.926173	−	0.377099i	$-0.123078\pi$
$839$	−1.29678	−	3.99108i	−0.0447698	−	0.137787i	−0.970943	+	0.239311i	$0.923078\pi$
$840$		0			0
$841$	−8.89747	+	27.3836i	−0.306809	+	0.944262i
$842$	5.53008	+	34.9156i	0.190579	+	1.20327i
$843$	−14.7810	−	4.92756i	−0.509084	−	0.169714i
$844$	2.14858	−	2.95727i	0.0739572	−	0.101793i
$845$		0			0
$846$	0.378103	−	24.7890i	0.0129995	−	0.852263i
$847$	1.71277	−	10.8140i	0.0588514	−	0.371573i
$848$	−7.87247	−	4.01122i	−0.270342	−	0.137746i
$849$	−20.3071	+	10.1527i	−0.696938	+	0.348439i
$850$		0			0
$851$		−	65.0944i		−	2.23141i
$852$	2.22730	+	0.0169853i	0.0763059	+	0.000581908i
$853$	53.4919	+	8.47229i	1.83153	+	0.290086i	0.974367	−	0.224963i	$-0.0722262\pi$
$853$	53.4919	+	8.47229i	1.83153	+	0.290086i	0.857161	+	0.515049i	$0.172226\pi$
$854$	−0.884547	+	0.642661i	−0.0302686	+	0.0219914i
$855$		0			0
$856$	−10.3760	−	7.53857i	−0.354643	−	0.257663i
$857$	25.7274	+	25.7274i	0.878831	+	0.878831i	0.993414	−	0.114583i	$-0.0365532\pi$
$857$	25.7274	+	25.7274i	0.878831	+	0.878831i	−0.114583	+	0.993414i	$0.536553\pi$
$858$	−1.35203	+	0.966640i	−0.0461575	+	0.0330006i
$859$	−6.06408	−	1.97034i	−0.206904	−	0.0672271i	0.203731	−	0.979027i	$-0.434693\pi$
$859$	−6.06408	−	1.97034i	−0.206904	−	0.0672271i	−0.410635	+	0.911800i	$0.634693\pi$
$860$		0			0
$861$	12.9945	+	13.1943i	0.442853	+	0.449659i
$862$	−15.4283	−	30.2798i	−0.525491	−	1.03133i
$863$	−21.0090	−	41.2325i	−0.715155	−	1.40357i	−0.906567	−	0.422062i	$-0.861307\pi$
$863$	−21.0090	−	41.2325i	−0.715155	−	1.40357i	0.191412	−	0.981510i	$-0.438693\pi$
$864$	−0.695243	−	5.14943i	−0.0236527	−	0.175187i
$865$		0			0
$866$	18.1405	+	5.89422i	0.616440	+	0.200294i
$867$	17.6415	+	24.6750i	0.599138	+	0.838008i
$868$	−2.08558	−	2.08558i	−0.0707892	−	0.0707892i
$869$	3.61419	+	2.62586i	0.122603	+	0.0890763i
$870$		0			0
$871$	28.1052	−	20.4196i	0.952308	−	0.691892i
$872$	−4.50400	−	0.713364i	−0.152525	−	0.0241576i
$873$	23.7911	+	48.5076i	0.805207	+	1.64173i
$874$			3.94987i			0.133606i
$875$		0			0
$876$	−7.39329	−	14.7879i	−0.249796	−	0.499635i
$877$	−51.8670	−	26.4275i	−1.75142	−	0.892395i	−0.959469	−	0.281815i	$-0.909064\pi$
$877$	−51.8670	−	26.4275i	−1.75142	−	0.892395i	−0.791955	−	0.610580i	$-0.790936\pi$
$878$	−5.53519	+	34.9478i	−0.186804	+	1.17943i
$879$	−20.7174	−	10.7558i	−0.698781	−	0.362785i
$880$		0			0
$881$	−13.4206	+	18.4718i	−0.452151	+	0.622332i	−0.972858	−	0.231403i	$-0.925668\pi$
$881$	−13.4206	+	18.4718i	−0.452151	+	0.622332i	0.520707	+	0.853735i	$0.325668\pi$
$882$	17.7738	−	2.53787i	0.598476	−	0.0854544i
$883$	8.64665	+	54.5928i	0.290983	+	1.83719i	0.508408	+	0.861116i	$0.330234\pi$
$883$	8.64665	+	54.5928i	0.290983	+	1.83719i	−0.217425	+	0.976077i	$0.569766\pi$
$884$	−4.75877	+	14.6460i	−0.160055	+	0.492597i
$885$		0			0
$886$	4.47927	+	13.7858i	0.150484	+	0.463142i
$887$	20.4932	−	10.4418i	0.688093	−	0.350601i	−0.0747341	−	0.997203i	$-0.523811\pi$
$887$	20.4932	−	10.4418i	0.688093	−	0.350601i	0.762827	+	0.646603i	$0.223811\pi$
$888$	−9.85817	+	13.3533i	−0.330819	+	0.448106i
$889$	−18.9009	+	6.14128i	−0.633917	+	0.205972i
$890$		0			0
$891$	0.100480	−	3.29305i	0.00336622	−	0.110321i
$892$	−2.08849	+	0.330785i	−0.0699279	+	0.0110755i
$893$	3.39787	−	3.39787i	0.113706	−	0.113706i
$894$	−10.0088	−	1.66358i	−0.334746	−	0.0556385i
$895$		0			0
$896$	−0.592264	−	0.815182i	−0.0197862	−	0.0272333i
$897$	9.30652	+	29.4036i	0.310736	+	0.981758i
$898$	−4.30358	+	8.44624i	−0.143612	+	0.281855i
$899$	1.33240			0.0444380
$900$		0			0
$901$	−51.9062			−1.72925
$902$	−1.76344	+	3.46095i	−0.0587161	+	0.115237i
$903$	5.35133	+	16.9073i	0.178081	+	0.562640i
$904$	−7.99679	−	11.0066i	−0.265969	−	0.366075i
$905$		0			0
$906$	6.23602	+	1.03650i	0.207178	+	0.0344353i
$907$	26.0875	−	26.0875i	0.866221	−	0.866221i	−0.125831	−	0.992052i	$-0.540160\pi$
$907$	26.0875	−	26.0875i	0.866221	−	0.866221i	0.992052	+	0.125831i	$0.0401597\pi$
$908$	15.2973	−	2.42285i	0.507657	−	0.0804050i
$909$	−0.625448	−	0.889060i	−0.0207448	−	0.0294883i
$910$		0			0
$911$	20.1733	−	6.55470i	0.668371	−	0.217167i	0.0448740	−	0.998993i	$-0.485711\pi$
$911$	20.1733	−	6.55470i	0.668371	−	0.217167i	0.623497	+	0.781826i	$0.285711\pi$
$912$	0.598185	−	0.810265i	0.0198079	−	0.0268305i
$913$	−0.309490	+	0.157693i	−0.0102426	+	0.00521888i
$914$	11.1374	+	34.2775i	0.368393	+	1.13380i
$915$		0			0
$916$	−0.510667	+	1.57167i	−0.0168729	+	0.0519295i
$917$	−1.70830	−	10.7858i	−0.0564129	−	0.356177i
$918$	−17.3732	−	25.1001i	−0.573399	−	0.828427i
$919$	−20.7352	+	28.5396i	−0.683991	+	0.941433i	−0.999973	−	0.00733203i	$-0.997666\pi$
$919$	−20.7352	+	28.5396i	−0.683991	+	0.941433i	0.315982	+	0.948765i	$0.397666\pi$
$920$		0			0
$921$	29.1797	+	15.1492i	0.961504	+	0.499183i
$922$	−3.52556	+	22.2595i	−0.116108	+	0.733079i
$923$	3.00354	+	1.53038i	0.0988627	+	0.0503731i
$924$	−0.285694	−	0.571436i	−0.00939863	−	0.0187989i
$925$		0			0
$926$		−	5.67112i		−	0.186364i
$927$	−21.3706	+	10.4814i	−0.701902	+	0.344255i
$928$	0.449582	+	0.0712068i	0.0147583	+	0.00233748i
$929$	−34.9866	+	25.4192i	−1.14787	+	0.833978i	−0.988197	−	0.153191i	$-0.951045\pi$
$929$	−34.9866	+	25.4192i	−1.14787	+	0.833978i	−0.159676	+	0.987169i	$0.551045\pi$
$930$		0			0
$931$	2.81536	+	2.04548i	0.0922698	+	0.0670379i
$932$	12.3494	+	12.3494i	0.404520	+	0.404520i
$933$	−21.5627	−	30.1595i	−0.705932	−	0.987379i
$934$	11.0544	+	3.59181i	0.361713	+	0.117528i
$935$		0			0
$936$	2.54389	−	7.44118i	0.0831498	−	0.243223i
$937$	11.3158	+	22.2086i	0.369672	+	0.725523i	0.998652	−	0.0518988i	$-0.0165273\pi$
$937$	11.3158	+	22.2086i	0.369672	+	0.725523i	−0.628980	+	0.777421i	$0.716527\pi$
$938$	6.06247	+	11.8983i	0.197947	+	0.388492i
$939$	15.5222	+	15.7607i	0.506547	+	0.514332i
$940$		0			0
$941$	0.769225	+	0.249936i	0.0250760	+	0.00814769i	0.321528	−	0.946900i	$-0.395804\pi$
$941$	0.769225	+	0.249936i	0.0250760	+	0.00814769i	−0.296452	+	0.955048i	$0.595804\pi$
$942$	−4.53322	+	3.24105i	−0.147700	+	0.105599i
$943$	50.9671	+	50.9671i	1.65972	+	1.65972i
$944$	−7.62100	−	5.53698i	−0.248043	−	0.180213i
$945$		0			0
$946$	−3.00929	+	2.18638i	−0.0978406	+	0.0710854i
$947$	−11.9668	−	1.89535i	−0.388868	−	0.0615907i	−0.0410609	−	0.999157i	$-0.513074\pi$
$947$	−11.9668	−	1.89535i	−0.388868	−	0.0615907i	−0.347808	+	0.937566i	$0.613074\pi$
$948$	−21.1370	−	0.161191i	−0.686498	−	0.00523523i
$949$		−	25.0216i		−	0.812235i
$950$		0			0
$951$	42.9593	−	21.4778i	1.39305	−	0.696466i
$952$	−5.27432	−	2.68740i	−0.170942	−	0.0870992i
$953$	−2.11321	+	13.3423i	−0.0684536	+	0.432199i	0.929531	+	0.368744i	$0.120212\pi$
$953$	−2.11321	+	13.3423i	−0.0684536	+	0.432199i	−0.997985	+	0.0634554i	$0.979788\pi$
$954$	26.5033	+	0.404252i	0.858077	+	0.0130881i
$955$		0			0
$956$	3.75544	−	5.16892i	0.121460	−	0.167175i
$957$	0.273794	+	0.0912752i	0.00885051	+	0.00295051i
$958$	−0.426186	−	2.69083i	−0.0137694	−	0.0869368i
$959$	2.70935	−	8.33851i	0.0874893	−	0.269264i
$960$		0			0
$961$	−6.93181	−	21.3339i	−0.223607	−	0.688190i
$962$	−22.3820	+	11.4042i	−0.721624	+	0.367686i
$963$	37.9062	+	6.59788i	1.22151	+	0.212614i
$964$	−18.2971	+	5.94510i	−0.589311	+	0.191479i
$965$		0			0
$966$	−11.7230	+	1.76520i	−0.377180	+	0.0567945i
$967$	11.0440	−	1.74919i	0.355150	−	0.0562502i	0.0236894	−	0.999719i	$-0.492459\pi$
$967$	11.0440	−	1.74919i	0.355150	−	0.0562502i	0.331460	+	0.943469i	$0.392459\pi$
$968$	−7.68342	+	7.68342i	−0.246954	+	0.246954i
$969$	0.970123	−	5.83669i	0.0311648	−	0.187501i
$970$		0			0
$971$	15.8802	+	21.8573i	0.509621	+	0.701434i	0.983855	−	0.178965i	$-0.0572749\pi$
$971$	15.8802	+	21.8573i	0.509621	+	0.701434i	−0.474234	+	0.880399i	$0.657275\pi$
$972$	8.67526	+	12.9514i	0.278259	+	0.415418i
$973$	1.40002	−	2.74769i	0.0448825	−	0.0880868i
$974$	−27.1112			−0.868699
$975$		0			0
$976$	1.08509			0.0347330
$977$	−11.9623	+	23.4774i	−0.382709	+	0.751109i	−0.999347	−	0.0361382i	$-0.988494\pi$
$977$	−11.9623	+	23.4774i	−0.382709	+	0.751109i	0.616638	+	0.787247i	$0.288494\pi$
$978$	6.10789	−	1.93321i	0.195309	−	0.0618171i
$979$	−0.436145	−	0.600303i	−0.0139393	−	0.0191858i
$980$		0			0
$981$	13.0738	−	4.02857i	0.417415	−	0.128622i
$982$	−27.9010	+	27.9010i	−0.890357	+	0.890357i
$983$	42.8297	−	6.78356i	1.36606	−	0.216362i	0.570029	−	0.821624i	$-0.306932\pi$
$983$	42.8297	−	6.78356i	1.36606	−	0.216362i	0.796026	+	0.605263i	$0.206932\pi$
$984$	−2.73656	−	18.1739i	−0.0872385	−	0.579363i
$985$		0			0
$986$	2.54323	−	0.826344i	0.0809928	−	0.0263162i
$987$	11.6032	+	8.56616i	0.369334	+	0.272664i
$988$	1.35812	−	0.691996i	0.0432075	−	0.0220153i
$989$	21.3295	+	65.6454i	0.678238	+	2.08740i
$990$		0			0
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	0.647275	+	0.762256i	$0.275908\pi$
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	−0.971700	+	0.236220i	$0.924092\pi$
$992$	0.457907	+	2.89111i	0.0145386	+	0.0917929i
$993$	10.1926	−	30.5741i	0.323451	−	0.970241i
$994$	−0.761632	+	1.04830i	−0.0241575	+	0.0332500i
$995$		0			0
$996$	0.757276	−	1.45863i	0.0239952	−	0.0462185i
$997$	5.70379	−	36.0123i	0.180641	−	1.14052i	−0.716111	−	0.697986i	$-0.754080\pi$
$997$	5.70379	−	36.0123i	0.180641	−	1.14052i	0.896752	−	0.442534i	$-0.145920\pi$
$998$	10.0822	+	5.13714i	0.319147	+	0.162613i
$999$	8.91250	−	48.9899i	0.281979	−	1.54997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.143.3		80
3.2	odd	2	inner	750.2.l.b.143.8		80
5.2	odd	4		750.2.l.a.107.1		80
5.3	odd	4		750.2.l.c.107.10		80
5.4	even	2		150.2.l.a.83.8	yes	80
15.2	even	4		750.2.l.a.107.10		80
15.8	even	4		750.2.l.c.107.1		80
15.14	odd	2		150.2.l.a.83.3	yes	80
25.3	odd	20		150.2.l.a.47.3	✓	80
25.4	even	10		750.2.l.c.743.1		80
25.21	even	5		750.2.l.a.743.10		80
25.22	odd	20	inner	750.2.l.b.257.8		80
75.29	odd	10		750.2.l.c.743.10		80
75.47	even	20	inner	750.2.l.b.257.3		80
75.53	even	20		150.2.l.a.47.8	yes	80
75.71	odd	10		750.2.l.a.743.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.3	✓	80	25.3	odd	20
150.2.l.a.47.8	yes	80	75.53	even	20
150.2.l.a.83.3	yes	80	15.14	odd	2
150.2.l.a.83.8	yes	80	5.4	even	2
750.2.l.a.107.1		80	5.2	odd	4
750.2.l.a.107.10		80	15.2	even	4
750.2.l.a.743.1		80	75.71	odd	10
750.2.l.a.743.10		80	25.21	even	5
750.2.l.b.143.3		80	1.1	even	1	trivial
750.2.l.b.143.8		80	3.2	odd	2	inner
750.2.l.b.257.3		80	75.47	even	20	inner
750.2.l.b.257.8		80	25.22	odd	20	inner
750.2.l.c.107.1		80	15.8	even	4
750.2.l.c.107.10		80	5.3	odd	4
750.2.l.c.743.1		80	25.4	even	10
750.2.l.c.743.10		80	75.29	odd	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(-1.02873 + 1.39345i) q^{12} +(-2.33563 + 1.19006i) q^{13} +(-0.311372 - 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.919013 + 5.80242i) q^{17} +(-0.424059 - 2.96988i) q^{18} +(0.341785 - 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(-0.0572652 + 0.361558i) q^{22} +(6.05243 + 3.08387i) q^{23} +(-0.774543 - 1.54922i) q^{24} -2.62134i q^{26} +(4.13281 + 3.14959i) q^{27} +(0.995214 + 0.157626i) q^{28} +(-0.368253 + 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.368759 - 0.515779i) q^{33} +(-5.58722 - 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-4.35053 - 8.53839i) q^{37} +(0.263986 + 0.518102i) q^{38} +(3.18589 + 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(-1.41972 + 1.01503i) q^{42} +(7.18512 + 7.18512i) q^{43} +(-0.296153 - 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(8.16222 + 1.29277i) q^{47} +(1.73200 + 0.0132082i) q^{48} +5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(2.33563 + 1.19006i) q^{52} +(-1.38217 + 8.72670i) q^{53} +(-4.68256 + 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.955457 - 0.318522i) q^{57} +(-0.0712068 - 0.449582i) q^{58} +(-2.91096 + 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(2.60811 - 1.32890i) q^{62} +(0.518359 - 2.97808i) q^{63} +(0.951057 - 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(-13.0896 + 2.07319i) q^{67} +(4.15407 - 4.15407i) q^{68} +(1.92909 - 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(-2.15343 + 2.08872i) q^{72} +(-4.33350 + 8.50497i) q^{73} +9.58285 q^{74} -0.581479 q^{76} +(-0.167456 + 0.328652i) q^{77} +(-4.32864 + 1.37006i) q^{78} +(7.17322 + 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(-7.50310 + 7.50310i) q^{82} +(-0.937190 + 0.148436i) q^{83} +(-0.259864 - 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.634281 + 0.468264i) q^{87} +(0.326166 - 0.166190i) q^{88} +(-0.626378 - 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-1.06263 - 6.70917i) q^{92} +(-1.60343 + 4.80974i) q^{93} +(-4.85743 + 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(2.81727 - 17.7876i) q^{97} +(-5.33241 - 2.71700i) q^{98} +(-0.658978 + 0.878510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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