LMFDB - Embedded newform 875.2.u.b.424.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(74,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 20]))

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

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

chi := DirichletCharacter("875.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.u (of order $30$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			424.14
Character	$\chi$	$=$	875.424
Dual form			875.2.u.b.324.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737231 - 0.0774861i) q^{2} +(0.308536 - 1.45155i) q^{3} +(-1.41879 - 0.301573i) q^{4} +(-0.339937 + 1.04622i) q^{6} +(-2.41111 + 1.08929i) q^{7} +(2.43263 + 0.790409i) q^{8} +(0.728840 + 0.324501i) q^{9} +O(q^{10})$	\(q+(-0.737231 - 0.0774861i) q^{2} +(0.308536 - 1.45155i) q^{3} +(-1.41879 - 0.301573i) q^{4} +(-0.339937 + 1.04622i) q^{6} +(-2.41111 + 1.08929i) q^{7} +(2.43263 + 0.790409i) q^{8} +(0.728840 + 0.324501i) q^{9} +(1.75196 - 0.780023i) q^{11} +(-0.875495 + 1.96639i) q^{12} +(0.933316 + 1.28460i) q^{13} +(1.86195 - 0.616232i) q^{14} +(0.918005 + 0.408722i) q^{16} +(-2.39768 + 2.15888i) q^{17} +(-0.512179 - 0.295707i) q^{18} +(1.80690 - 0.384069i) q^{19} +(0.837245 + 3.83592i) q^{21} +(-1.35204 + 0.439305i) q^{22} +(-1.69516 - 0.178168i) q^{23} +(1.89787 - 3.28721i) q^{24} +(-0.588531 - 1.01937i) q^{26} +(3.31268 - 4.55951i) q^{27} +(3.74936 - 0.818350i) q^{28} +(1.18710 + 3.65353i) q^{29} +(6.13063 + 6.80876i) q^{31} +(-5.07538 - 2.93027i) q^{32} +(-0.591698 - 2.78372i) q^{33} +(1.93493 - 1.40581i) q^{34} +(-0.936210 - 0.680196i) q^{36} +(3.05251 - 6.85605i) q^{37} +(-1.36186 + 0.143138i) q^{38} +(2.15262 - 0.958408i) q^{39} +(8.10725 - 5.89026i) q^{41} +(-0.320012 - 2.89284i) q^{42} +4.22219i q^{43} +(-2.72090 + 0.578345i) q^{44} +(1.23592 + 0.262702i) q^{46} +(3.48394 + 3.13695i) q^{47} +(0.876517 - 1.20642i) q^{48} +(4.62689 - 5.25280i) q^{49} +(2.39395 + 4.14644i) q^{51} +(-0.936779 - 2.10404i) q^{52} +(2.14901 - 10.1103i) q^{53} +(-2.79551 + 3.10473i) q^{54} +(-6.72632 + 0.744080i) q^{56} -2.74130i q^{57} +(-0.592071 - 2.78548i) q^{58} +(0.304406 + 2.89623i) q^{59} +(1.45645 - 13.8572i) q^{61} +(-3.99211 - 5.49467i) q^{62} +(-2.11079 + 0.0115133i) q^{63} +(1.88874 + 1.37225i) q^{64} +(0.220519 + 2.09809i) q^{66} +(-2.69377 + 2.42548i) q^{67} +(4.05286 - 2.33992i) q^{68} +(-0.781636 + 2.40563i) q^{69} +(1.51660 + 4.66763i) q^{71} +(1.51651 + 1.36547i) q^{72} +(-0.0501887 - 0.112726i) q^{73} +(-2.78165 + 4.81797i) q^{74} -2.67944 q^{76} +(-3.37450 + 3.78912i) q^{77} +(-1.66124 + 0.539770i) q^{78} +(3.98697 - 4.42797i) q^{79} +(-3.99474 - 4.43661i) q^{81} +(-6.43333 + 3.71429i) q^{82} +(-10.2744 - 3.33835i) q^{83} +(-0.0310628 - 5.69486i) q^{84} +(0.327161 - 3.11273i) q^{86} +(5.66953 - 0.595892i) q^{87} +(4.87841 - 0.512742i) q^{88} +(0.420945 - 4.00503i) q^{89} +(-3.64963 - 2.08066i) q^{91} +(2.35134 + 0.763996i) q^{92} +(11.7748 - 6.79816i) q^{93} +(-2.32540 - 2.58262i) q^{94} +(-5.81937 + 6.46307i) q^{96} +(4.54363 - 1.47632i) q^{97} +(-3.81811 + 3.51401i) q^{98} +1.53002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9}+O(q^{10}) $ 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9	$ 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9} - 12 q^{11} + 12 q^{14} + 26 q^{16} + 22 q^{19} - 6 q^{21} - 92 q^{24} + 88 q^{26} + 48 q^{29} - 42 q^{31} + 72 q^{34} - 208 q^{36} - 50 q^{39} + 76 q^{41} + 14 q^{44} + 42 q^{46} + 76 q^{49} - 16 q^{51} - 30 q^{54} - 120 q^{56} + 78 q^{59} - 26 q^{61} - 84 q^{64} + 14 q^{66} - 100 q^{69} + 44 q^{71} + 20 q^{74} - 552 q^{76} - 18 q^{79} + 114 q^{81} + 58 q^{84} - 34 q^{86} + 84 q^{89} - 68 q^{91} + 22 q^{94} + 26 q^{96} + 136 q^{99}+O(q^{100}) $ 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9 - 12 * q^11 + 12 * q^14 + 26 * q^16 + 22 * q^19 - 6 * q^21 - 92 * q^24 + 88 * q^26 + 48 * q^29 - 42 * q^31 + 72 * q^34 - 208 * q^36 - 50 * q^39 + 76 * q^41 + 14 * q^44 + 42 * q^46 + 76 * q^49 - 16 * q^51 - 30 * q^54 - 120 * q^56 + 78 * q^59 - 26 * q^61 - 84 * q^64 + 14 * q^66 - 100 * q^69 + 44 * q^71 + 20 * q^74 - 552 * q^76 - 18 * q^79 + 114 * q^81 + 58 * q^84 - 34 * q^86 + 84 * q^89 - 68 * q^91 + 22 * q^94 + 26 * q^96 + 136 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.737231	−	0.0774861i	−0.521301	−	0.0547910i	−0.159776	−	0.987153i	$-0.551077\pi$
$2$	−0.737231	−	0.0774861i	−0.521301	−	0.0547910i	−0.361525	+	0.932362i	$0.617744\pi$
$3$	0.308536	−	1.45155i	0.178133	−	0.838051i	−0.794783	−	0.606894i	$-0.792415\pi$
$3$	0.308536	−	1.45155i	0.178133	−	0.838051i	0.972916	−	0.231158i	$-0.0742513\pi$
$4$	−1.41879	−	0.301573i	−0.709395	−	0.150786i
$5$		0			0
$5$		0			0
$6$	−0.339937	+	1.04622i	−0.138779	+	0.427117i
$7$	−2.41111	+	1.08929i	−0.911313	+	0.411713i
$7$	−2.41111	+	1.08929i	−0.911313	+	0.411713i
$8$	2.43263	+	0.790409i	0.860064	+	0.279452i
$9$	0.728840	+	0.324501i	0.242947	+	0.108167i
$10$		0			0
$11$	1.75196	−	0.780023i	0.528236	−	0.235186i	−0.125249	−	0.992125i	$-0.539973\pi$
$11$	1.75196	−	0.780023i	0.528236	−	0.235186i	0.653485	+	0.756939i	$0.273306\pi$
$12$	−0.875495	+	1.96639i	−0.252734	+	0.567649i
$13$	0.933316	+	1.28460i	0.258855	+	0.356284i	0.918588	−	0.395217i	$-0.129330\pi$
$13$	0.933316	+	1.28460i	0.258855	+	0.356284i	−0.659733	+	0.751500i	$0.729330\pi$
$14$	1.86195	−	0.616232i	0.497627	−	0.164695i
$15$		0			0
$16$	0.918005	+	0.408722i	0.229501	+	0.102181i
$17$	−2.39768	+	2.15888i	−0.581522	+	0.523605i	−0.906549	−	0.422100i	$-0.861293\pi$
$17$	−2.39768	+	2.15888i	−0.581522	+	0.523605i	0.325027	+	0.945705i	$0.394627\pi$
$18$	−0.512179	−	0.295707i	−0.120722	−	0.0696988i
$19$	1.80690	−	0.384069i	0.414532	−	0.0881114i	0.00407530	−	0.999992i	$-0.498703\pi$
$19$	1.80690	−	0.384069i	0.414532	−	0.0881114i	0.410456	+	0.911880i	$0.365369\pi$
$20$		0			0
$21$	0.837245	+	3.83592i	0.182702	+	0.837067i
$22$	−1.35204	+	0.439305i	−0.288256	+	0.0936601i
$23$	−1.69516	−	0.178168i	−0.353464	−	0.0371506i	−0.0738674	−	0.997268i	$-0.523534\pi$
$23$	−1.69516	−	0.178168i	−0.353464	−	0.0371506i	−0.279597	+	0.960117i	$0.590201\pi$
$24$	1.89787	−	3.28721i	0.387401	−	0.670999i
$25$		0			0
$26$	−0.588531	−	1.01937i	−0.115420	−	0.199914i
$27$	3.31268	−	4.55951i	0.637525	−	0.877478i
$28$	3.74936	−	0.818350i	0.708562	−	0.154654i
$29$	1.18710	+	3.65353i	0.220439	+	0.678443i	0.998723	+	0.0505292i	$0.0160908\pi$
$29$	1.18710	+	3.65353i	0.220439	+	0.678443i	−0.778283	+	0.627913i	$0.783909\pi$
$30$		0			0
$31$	6.13063	+	6.80876i	1.10109	+	1.22289i	0.972921	+	0.231137i	$0.0742445\pi$
$31$	6.13063	+	6.80876i	1.10109	+	1.22289i	0.128173	+	0.991752i	$0.459089\pi$
$32$	−5.07538	−	2.93027i	−0.897209	−	0.518004i
$33$	−0.591698	−	2.78372i	−0.103001	−	0.484584i
$34$	1.93493	−	1.40581i	0.331837	−	0.241094i
$35$		0			0
$36$	−0.936210	−	0.680196i	−0.156035	−	0.113366i
$37$	3.05251	−	6.85605i	0.501830	−	1.12713i	−0.468085	−	0.883683i	$-0.655056\pi$
$37$	3.05251	−	6.85605i	0.501830	−	1.12713i	0.969915	−	0.243444i	$-0.0782773\pi$
$38$	−1.36186	+	0.143138i	−0.220924	+	0.0232200i
$39$	2.15262	−	0.958408i	0.344695	−	0.153468i
$40$		0			0
$41$	8.10725	−	5.89026i	1.26614	−	0.919904i	0.267098	−	0.963669i	$-0.413935\pi$
$41$	8.10725	−	5.89026i	1.26614	−	0.919904i	0.999042	+	0.0437649i	$0.0139353\pi$
$42$	−0.320012	−	2.89284i	−0.0493789	−	0.446375i
$43$			4.22219i			0.643879i	0.946760	+	0.321939i	$0.104335\pi$
$43$			4.22219i			0.643879i	−0.946760	+	0.321939i	$0.895665\pi$
$44$	−2.72090	+	0.578345i	−0.410191	+	0.0871888i
$45$		0			0
$46$	1.23592	+	0.262702i	0.182226	+	0.0387333i
$47$	3.48394	+	3.13695i	0.508185	+	0.457571i	0.882895	−	0.469570i	$-0.155591\pi$
$47$	3.48394	+	3.13695i	0.508185	+	0.457571i	−0.374710	+	0.927142i	$0.622258\pi$
$48$	0.876517	−	1.20642i	0.126514	−	0.174132i
$49$	4.62689	−	5.25280i	0.660984	−	0.750400i
$50$		0			0
$51$	2.39395	+	4.14644i	0.335219	+	0.580617i
$52$	−0.936779	−	2.10404i	−0.129908	−	0.291778i
$53$	2.14901	−	10.1103i	0.295189	−	1.38875i	−0.541327	−	0.840812i	$-0.682078\pi$
$53$	2.14901	−	10.1103i	0.295189	−	1.38875i	0.836516	−	0.547943i	$-0.184589\pi$
$54$	−2.79551	+	3.10473i	−0.380421	+	0.422500i
$55$		0			0
$56$	−6.72632	+	0.744080i	−0.898842	+	0.0994319i
$57$		−	2.74130i		−	0.363094i
$58$	−0.592071	−	2.78548i	−0.0777428	−	0.365751i
$59$	0.304406	+	2.89623i	0.0396303	+	0.377057i	0.996304	+	0.0858953i	$0.0273751\pi$
$59$	0.304406	+	2.89623i	0.0396303	+	0.377057i	−0.956674	+	0.291162i	$0.905958\pi$
$60$		0			0
$61$	1.45645	−	13.8572i	0.186480	−	1.77424i	−0.356310	−	0.934368i	$-0.615965\pi$
$61$	1.45645	−	13.8572i	0.186480	−	1.77424i	0.542790	−	0.839868i	$-0.317368\pi$
$62$	−3.99211	−	5.49467i	−0.506998	−	0.697823i
$63$	−2.11079	+	0.0115133i	−0.265934	+	0.00145055i
$64$	1.88874	+	1.37225i	0.236093	+	0.171532i
$65$		0			0
$66$	0.220519	+	2.09809i	0.0271440	+	0.258258i
$67$	−2.69377	+	2.42548i	−0.329096	+	0.296319i	−0.817070	−	0.576539i	$-0.804403\pi$
$67$	−2.69377	+	2.42548i	−0.329096	+	0.296319i	0.487974	+	0.872858i	$0.337736\pi$
$68$	4.05286	−	2.33992i	0.491481	−	0.283757i
$69$	−0.781636	+	2.40563i	−0.0940979	+	0.289603i
$70$		0			0
$71$	1.51660	+	4.66763i	0.179988	+	0.553945i	0.999826	−	0.0186498i	$-0.00593677\pi$
$71$	1.51660	+	4.66763i	0.179988	+	0.553945i	−0.819838	+	0.572595i	$0.805937\pi$
$72$	1.51651	+	1.36547i	0.178722	+	0.160922i
$73$	−0.0501887	−	0.112726i	−0.00587415	−	0.0131935i	0.910585	−	0.413323i	$-0.135632\pi$
$73$	−0.0501887	−	0.112726i	−0.00587415	−	0.0131935i	−0.916459	+	0.400129i	$0.868965\pi$
$74$	−2.78165	+	4.81797i	−0.323361	+	0.560077i
$75$		0			0
$76$	−2.67944			−0.307352
$77$	−3.37450	+	3.78912i	−0.384560	+	0.431810i
$78$	−1.66124	+	0.539770i	−0.188099	+	0.0611169i
$79$	3.98697	−	4.42797i	0.448569	−	0.498186i	−0.475871	−	0.879515i	$-0.657867\pi$
$79$	3.98697	−	4.42797i	0.448569	−	0.498186i	0.924439	+	0.381329i	$0.124534\pi$
$80$		0			0
$81$	−3.99474	−	4.43661i	−0.443860	−	0.492957i
$82$	−6.43333	+	3.71429i	−0.710443	+	0.410174i
$83$	−10.2744	−	3.33835i	−1.12776	−	0.366432i	−0.315037	−	0.949079i	$-0.602017\pi$
$83$	−10.2744	−	3.33835i	−1.12776	−	0.366432i	−0.812725	+	0.582648i	$0.802017\pi$
$84$	−0.0310628	−	5.69486i	−0.00338922	−	0.621360i
$85$		0			0
$86$	0.327161	−	3.11273i	0.0352787	−	0.335655i
$87$	5.66953	−	0.595892i	0.607837	−	0.0638863i
$88$	4.87841	−	0.512742i	0.520040	−	0.0546584i
$89$	0.420945	−	4.00503i	0.0446201	−	0.424532i	−0.949295	−	0.314386i	$-0.898201\pi$
$89$	0.420945	−	4.00503i	0.0446201	−	0.424532i	0.993915	−	0.110146i	$-0.0351319\pi$
$90$		0			0
$91$	−3.64963	−	2.08066i	−0.382585	−	0.218112i
$92$	2.35134	+	0.763996i	0.245144	+	0.0796521i
$93$	11.7748	−	6.79816i	1.22099	−	0.704936i
$94$	−2.32540	−	2.58262i	−0.239846	−	0.266376i
$95$		0			0
$96$	−5.81937	+	6.46307i	−0.593937	+	0.659634i
$97$	4.54363	−	1.47632i	0.461336	−	0.149897i	−0.0691223	−	0.997608i	$-0.522020\pi$
$97$	4.54363	−	1.47632i	0.461336	−	0.149897i	0.530458	+	0.847711i	$0.322020\pi$
$98$	−3.81811	+	3.51401i	−0.385687	+	0.354968i
$99$	1.53002			0.153773
$100$		0			0
$101$	1.07002	−	1.85332i	0.106471	−	0.184413i	−0.807867	−	0.589364i	$-0.799378\pi$
$101$	1.07002	−	1.85332i	0.106471	−	0.184413i	0.914338	+	0.404952i	$0.132712\pi$
$102$	−1.44360	−	3.24238i	−0.142938	−	0.321043i
$103$	10.9363	+	9.84711i	1.07759	+	0.970264i	0.999644	−	0.0266936i	$-0.00849784\pi$
$103$	10.9363	+	9.84711i	1.07759	+	0.970264i	0.0779439	+	0.996958i	$0.475165\pi$
$104$	1.25505	+	3.86266i	0.123068	+	0.378765i
$105$		0			0
$106$	−2.36772	+	7.28710i	−0.229974	+	0.707786i
$107$	6.57725	−	3.79738i	0.635847	−	0.367106i	−0.147166	−	0.989112i	$-0.547015\pi$
$107$	6.57725	−	3.79738i	0.635847	−	0.367106i	0.783013	+	0.622005i	$0.213682\pi$
$108$	−6.07502	+	5.46997i	−0.584569	+	0.526348i
$109$	2.07777	+	19.7687i	0.199015	+	1.89350i	0.404039	+	0.914742i	$0.367606\pi$
$109$	2.07777	+	19.7687i	0.199015	+	1.89350i	−0.205024	+	0.978757i	$0.565727\pi$
$110$		0			0
$111$	−9.01007	−	6.54620i	−0.855198	−	0.621338i
$112$	−2.65863	+	0.0145015i	−0.251217	+	0.00137027i
$113$	10.6719	+	14.6887i	1.00393	+	1.38179i	0.922882	+	0.385084i	$0.125827\pi$
$113$	10.6719	+	14.6887i	1.00393	+	1.38179i	0.0810503	+	0.996710i	$0.474173\pi$
$114$	−0.212413	+	2.02097i	−0.0198943	+	0.189282i
$115$		0			0
$116$	−0.582444	−	5.54158i	−0.0540785	−	0.514523i
$117$	0.263385	+	1.23913i	0.0243500	+	0.114558i
$118$		−	2.15878i		−	0.198732i
$119$	3.42941	−	7.81706i	0.314374	−	0.716589i
$120$		0			0
$121$	−4.89950	+	5.44145i	−0.445409	+	0.494677i
$122$	−2.14749	+	10.1031i	−0.194424	+	0.914694i
$123$	−6.04862	−	13.5854i	−0.545386	−	1.22496i
$124$	−6.64474	−	11.5090i	−0.596715	−	1.03354i
$125$		0			0
$126$	1.55703	+	0.155069i	0.138711	+	0.0138146i
$127$	−9.04401	+	12.4480i	−0.802526	+	1.10458i	0.189908	+	0.981802i	$0.439181\pi$
$127$	−9.04401	+	12.4480i	−0.802526	+	1.10458i	−0.992434	+	0.122780i	$0.960819\pi$
$128$	7.42436	+	6.68492i	0.656227	+	0.590869i
$129$	6.12872	+	1.30270i	0.539603	+	0.114696i
$130$		0			0
$131$	7.66443	−	1.62913i	0.669645	−	0.142337i	0.139471	−	0.990226i	$-0.455460\pi$
$131$	7.66443	−	1.62913i	0.669645	−	0.142337i	0.530174	+	0.847889i	$0.322127\pi$
$132$			4.12795i			0.359292i
$133$	−3.93827	+	2.89427i	−0.341491	+	0.250965i
$134$	2.17387	−	1.57941i	0.187794	−	0.136440i
$135$		0			0
$136$	−7.53906	+	3.35661i	−0.646469	+	0.287827i
$137$	14.0672	−	1.47852i	1.20184	−	0.126319i	0.517633	−	0.855603i	$-0.326813\pi$
$137$	14.0672	−	1.47852i	1.20184	−	0.126319i	0.684211	+	0.729284i	$0.260147\pi$
$138$	0.762649	−	1.71294i	0.0649210	−	0.145815i
$139$	−13.7894	−	10.0186i	−1.16960	−	0.849763i	−0.178638	−	0.983915i	$-0.557169\pi$
$139$	−13.7894	−	10.0186i	−1.16960	−	0.849763i	−0.990961	+	0.134152i	$0.957169\pi$
$140$		0			0
$141$	5.62836	−	4.08924i	0.473993	−	0.344376i
$142$	−0.756411	−	3.55863i	−0.0634766	−	0.298634i
$143$	2.63715	+	1.52256i	0.220530	+	0.127323i
$144$	0.536448	+	0.595786i	0.0447040	+	0.0496488i
$145$		0			0
$146$	0.0282660	+	0.0869939i	0.00233931	+	0.00719966i
$147$	−6.19713	−	8.33683i	−0.511130	−	0.687610i
$148$	−6.39847	+	8.80674i	−0.525951	+	0.723909i
$149$	5.99832	+	10.3894i	0.491402	+	0.851133i	0.999951	−	0.00990030i	$-0.00315141\pi$
$149$	5.99832	+	10.3894i	0.491402	+	0.851133i	−0.508549	+	0.861033i	$0.669818\pi$
$150$		0			0
$151$	−3.61003	+	6.25276i	−0.293780	+	0.508842i	−0.974700	−	0.223515i	$-0.928247\pi$
$151$	−3.61003	+	6.25276i	−0.293780	+	0.508842i	0.680920	+	0.732358i	$0.261580\pi$
$152$	4.69909	+	0.493895i	0.381147	+	0.0400601i
$153$	−2.44808	+	0.795430i	−0.197916	+	0.0643067i
$154$	2.78139	−	2.53198i	0.224131	−	0.204033i
$155$		0			0
$156$	−3.34314	+	0.710607i	−0.267666	+	0.0568941i
$157$	6.64290	+	3.83528i	0.530161	+	0.306089i	0.741082	−	0.671415i	$-0.234313\pi$
$157$	6.64290	+	3.83528i	0.530161	+	0.306089i	−0.210921	+	0.977503i	$0.567646\pi$
$158$	−3.28242	+	2.95551i	−0.261136	+	0.235127i
$159$	−14.0125	−	6.23878i	−1.11127	−	0.494767i
$160$		0			0
$161$	4.28128	−	1.41694i	0.337412	−	0.111670i
$162$	2.60127	+	3.58034i	0.204375	+	0.281298i
$163$	−5.06001	+	11.3650i	−0.396331	+	0.890174i	0.599621	+	0.800284i	$0.295318\pi$
$163$	−5.06001	+	11.3650i	−0.396331	+	0.890174i	−0.995952	+	0.0898894i	$0.971349\pi$
$164$	−13.2788	+	5.91211i	−1.03690	+	0.461659i
$165$		0			0
$166$	7.31593	+	3.25726i	0.567826	+	0.252813i
$167$	24.2983	+	7.89500i	1.88026	+	0.610933i	0.986838	+	0.161715i	$0.0517024\pi$
$167$	24.2983	+	7.89500i	1.88026	+	0.610933i	0.893422	+	0.449219i	$0.148298\pi$
$168$	−0.995244	+	9.99315i	−0.0767847	+	0.770988i
$169$	3.23810	−	9.96586i	0.249085	−	0.766605i
$170$		0			0
$171$	1.44157	+	0.306416i	0.110240	+	0.0234322i
$172$	1.27330	−	5.99040i	0.0970882	−	0.456764i
$173$	−2.12377	−	0.223218i	−0.161468	−	0.0169709i	0.0234497	−	0.999725i	$-0.492535\pi$
$173$	−2.12377	−	0.223218i	−0.161468	−	0.0169709i	−0.184917	+	0.982754i	$0.559202\pi$
$174$	−4.22593			−0.320367
$175$		0			0
$176$	1.92712			0.145262
$177$	4.29794	+	0.451731i	0.323053	+	0.0339542i
$178$	−0.620668	+	2.92001i	−0.0465210	+	0.218864i
$179$	−8.10867	−	1.72355i	−0.606070	−	0.128824i	−0.105353	−	0.994435i	$-0.533597\pi$
$179$	−8.10867	−	1.72355i	−0.606070	−	0.128824i	−0.500718	+	0.865611i	$0.666931\pi$
$180$		0			0
$181$	0.593885	−	1.82779i	0.0441431	−	0.135859i	−0.926556	−	0.376157i	$-0.877245\pi$
$181$	0.593885	−	1.82779i	0.0441431	−	0.135859i	0.970699	+	0.240299i	$0.0772453\pi$
$182$	2.52940	+	1.81672i	0.187492	+	0.134664i
$183$	−19.6651	−	6.38956i	−1.45368	−	0.472330i
$184$	−3.98286	−	1.77328i	−0.293620	−	0.130728i
$185$		0			0
$186$	−9.20748	+	4.09943i	−0.675125	+	0.300585i
$187$	−2.51666	+	5.65252i	−0.184037	+	0.413353i
$188$	−3.99695	−	5.50134i	−0.291508	−	0.401226i
$189$	−3.02059	+	14.6020i	−0.219716	+	1.06214i
$190$		0			0
$191$	22.0592	+	9.82140i	1.59615	+	0.710652i	0.996010	−	0.0892432i	$-0.0284448\pi$
$191$	22.0592	+	9.82140i	1.59615	+	0.710652i	0.600140	+	0.799895i	$0.295112\pi$
$192$	2.57463	−	2.31821i	0.185808	−	0.167303i
$193$	−17.0508	−	9.84428i	−1.22734	−	0.708607i	−0.260869	−	0.965374i	$-0.584009\pi$
$193$	−17.0508	−	9.84428i	−1.22734	−	0.708607i	−0.966473	+	0.256768i	$0.917343\pi$
$194$	−3.46410	+	0.736317i	−0.248708	+	0.0528645i
$195$		0			0
$196$	−8.14868	+	6.05727i	−0.582049	+	0.432662i
$197$	−5.85741	+	1.90319i	−0.417323	+	0.135596i	−0.510149	−	0.860086i	$-0.670410\pi$
$197$	−5.85741	+	1.90319i	−0.417323	+	0.135596i	0.0928264	+	0.995682i	$0.470410\pi$
$198$	−1.12798	−	0.118555i	−0.0801618	−	0.00842535i
$199$	−2.82476	+	4.89262i	−0.200242	+	0.346829i	−0.948606	−	0.316459i	$-0.897506\pi$
$199$	−2.82476	+	4.89262i	−0.200242	+	0.346829i	0.748365	+	0.663288i	$0.230839\pi$
$200$		0			0
$201$	2.68957	+	4.65848i	0.189708	+	0.328584i
$202$	−0.932457	+	1.28342i	−0.0656074	+	0.0903009i
$203$	−6.84199	−	7.51595i	−0.480213	−	0.527516i
$204$	−2.14605	−	6.60487i	−0.150254	−	0.462433i
$205$		0			0
$206$	−7.29958	−	8.10701i	−0.508586	−	0.564842i
$207$	−1.17768	−	0.679935i	−0.0818545	−	0.0472587i
$208$	0.331745	+	1.56074i	0.0230023	+	0.108218i
$209$	2.86604	−	2.08230i	0.198248	−	0.144036i
$210$		0			0
$211$	−21.8563	−	15.8795i	−1.50465	−	1.09319i	−0.968483	−	0.249078i	$-0.919872\pi$
$211$	−21.8563	−	15.8795i	−1.50465	−	1.09319i	−0.536165	−	0.844113i	$-0.680128\pi$
$212$	−6.09798	+	13.6963i	−0.418811	+	0.940665i
$213$	7.24321	−	0.761292i	0.496296	−	0.0521629i
$214$	−5.14320	+	2.28990i	−0.351582	+	0.156534i
$215$		0			0
$216$	11.6624	−	8.47323i	0.793526	−	0.576530i
$217$	−22.1983	−	9.73860i	−1.50692	−	0.661100i
$218$		−	14.7351i		−	0.997987i
$219$	−0.179112	+	0.0380714i	−0.0121033	+	0.00257263i
$220$		0			0
$221$	−5.01109	−	1.06514i	−0.337082	−	0.0716490i
$222$	6.13527	+	5.52422i	0.411772	+	0.370761i
$223$	−4.91414	+	6.76373i	−0.329075	+	0.452933i	−0.941211	−	0.337820i	$-0.890311\pi$
$223$	−4.91414	+	6.76373i	−0.329075	+	0.452933i	0.612136	+	0.790753i	$0.290311\pi$
$224$	15.4292	+	1.53664i	1.03091	+	0.102671i
$225$		0			0
$226$	−6.72952	−	11.6559i	−0.447641	−	0.775337i
$227$	−0.634169	−	1.42437i	−0.0420913	−	0.0945385i	0.891276	−	0.453461i	$-0.149811\pi$
$227$	−0.634169	−	1.42437i	−0.0420913	−	0.0945385i	−0.933367	+	0.358923i	$0.883144\pi$
$228$	−0.826703	+	3.88933i	−0.0547497	+	0.257577i
$229$	−1.22356	+	1.35890i	−0.0808551	+	0.0897986i	−0.782215	−	0.623009i	$-0.785910\pi$
$229$	−1.22356	+	1.35890i	−0.0808551	+	0.0897986i	0.701360	+	0.712808i	$0.252577\pi$
$230$		0			0
$231$	4.45893	+	6.06732i	0.293376	+	0.399200i
$232$			9.82597i			0.645107i
$233$	−1.37703	−	6.47843i	−0.0902125	−	0.424416i	−0.999957	−	0.00924835i	$-0.997056\pi$
$233$	−1.37703	−	6.47843i	−0.0902125	−	0.424416i	0.909745	−	0.415168i	$-0.136277\pi$
$234$	−0.0981604	−	0.933934i	−0.00641695	−	0.0610532i
$235$		0			0
$236$	0.441537	−	4.20094i	0.0287416	−	0.273458i
$237$	−5.19729	−	7.15346i	−0.337600	−	0.464667i
$238$	−3.13398	+	5.49725i	−0.203146	+	0.356334i
$239$	8.01908	+	5.82620i	0.518711	+	0.376866i	0.816118	−	0.577885i	$-0.196122\pi$
$239$	8.01908	+	5.82620i	0.518711	+	0.376866i	−0.297407	+	0.954751i	$0.596122\pi$
$240$		0			0
$241$	0.0375442	+	0.357209i	0.00241843	+	0.0230099i	0.995665	−	0.0930165i	$-0.0296509\pi$
$241$	0.0375442	+	0.357209i	0.00241843	+	0.0230099i	−0.993246	+	0.116026i	$0.962984\pi$
$242$	4.03370	−	3.63196i	0.259296	−	0.233472i
$243$	6.96994	−	4.02410i	0.447122	−	0.258146i
$244$	−6.24537	+	19.2213i	−0.399819	+	1.23052i
$245$		0			0
$246$	3.40655	+	10.4843i	0.217194	+	0.668453i
$247$	2.17978	+	1.96269i	0.138696	+	0.124883i
$248$	9.53185	+	21.4089i	0.605273	+	1.35947i
$249$	−8.01580	+	13.8838i	−0.507981	+	0.879849i
$250$		0			0
$251$	−19.7093			−1.24404			−0.622020	−	0.783002i	$-0.713688\pi$
$251$	−19.7093			−1.24404			−0.622020	+	0.783002i	$0.713688\pi$
$252$	2.99824	+	0.620222i	0.188871	+	0.0390703i
$253$	−3.10882	+	1.01012i	−0.195450	+	0.0635055i
$254$	7.63207	−	8.47627i	0.478879	−	0.531849i
$255$		0			0
$256$	−8.07981	−	8.97353i	−0.504988	−	0.560846i
$257$	23.7895	−	13.7349i	1.48395	−	0.856759i	0.484117	−	0.875003i	$-0.339141\pi$
$257$	23.7895	−	13.7349i	1.48395	−	0.856759i	0.999834	+	0.0182437i	$0.00580748\pi$
$258$	−4.41734	−	1.43528i	−0.275012	−	0.0893567i
$259$	0.108304	+	19.8558i	0.00672967	+	1.23378i
$260$		0			0
$261$	−0.320363	+	3.04805i	−0.0198300	+	0.188670i
$262$	−5.77670	+	0.607155i	−0.356885	+	0.0375102i
$263$	−13.1756	+	1.38481i	−0.812442	+	0.0853911i	−0.501632	−	0.865081i	$-0.667267\pi$
$263$	−13.1756	+	1.38481i	−0.812442	+	0.0853911i	−0.310810	+	0.950472i	$0.600600\pi$
$264$	0.760896	−	7.23945i	0.0468299	−	0.445557i
$265$		0			0
$266$	3.12768	−	1.82859i	0.191771	−	0.112118i
$267$	−5.68361	−	1.84672i	−0.347831	−	0.113017i
$268$	4.55335	−	2.62888i	0.278140	−	0.160584i
$269$	−7.78329	−	8.64422i	−0.474556	−	0.527048i	0.457574	−	0.889171i	$-0.348718\pi$
$269$	−7.78329	−	8.64422i	−0.474556	−	0.527048i	−0.932130	+	0.362124i	$0.882052\pi$
$270$		0			0
$271$	7.02263	−	7.79942i	0.426594	−	0.473781i	−0.491080	−	0.871114i	$-0.663398\pi$
$271$	7.02263	−	7.79942i	0.426594	−	0.473781i	0.917674	+	0.397334i	$0.130064\pi$
$272$	−3.08346	+	1.00188i	−0.186962	+	0.0607477i
$273$	−4.14621	+	4.65566i	−0.250940	+	0.281773i
$274$	−10.4854			−0.633444
$275$		0			0
$276$	1.83445	−	3.17736i	0.110421	−	0.191254i
$277$	−5.40359	−	12.1367i	−0.324670	−	0.729221i	0.675295	−	0.737547i	$-0.264016\pi$
$277$	−5.40359	−	12.1367i	−0.324670	−	0.729221i	−0.999965	+	0.00832657i	$0.997350\pi$
$278$	9.38965	+	8.45448i	0.563154	+	0.507066i
$279$	2.25881	+	6.95189i	0.135231	+	0.416199i
$280$		0			0
$281$	−7.53857	+	23.2013i	−0.449713	+	1.38408i	0.427518	+	0.904007i	$0.359388\pi$
$281$	−7.53857	+	23.2013i	−0.449713	+	1.38408i	−0.877231	+	0.480068i	$0.840612\pi$
$282$	−4.46626	+	2.57860i	−0.265962	+	0.153553i
$283$	7.24250	−	6.52118i	0.430522	−	0.387644i	−0.425183	−	0.905107i	$-0.639790\pi$
$283$	7.24250	−	6.52118i	0.430522	−	0.387644i	0.855705	+	0.517463i	$0.173124\pi$
$284$	−0.744111	−	7.07974i	−0.0441549	−	0.420105i
$285$		0			0
$286$	−1.82621	−	1.32682i	−0.107986	−	0.0784566i
$287$	−13.1312	+	23.0332i	−0.775113	+	1.35961i
$288$	−2.74827	−	3.78267i	−0.161943	−	0.222896i
$289$	−0.688882	+	6.55428i	−0.0405225	+	0.385546i
$290$		0			0
$291$	−0.741068	−	7.05079i	−0.0434422	−	0.413325i
$292$	0.0372122	+	0.175070i	0.00217768	+	0.0102452i
$293$		−	11.7000i		−	0.683522i	−0.939787	−	0.341761i	$-0.888977\pi$
$293$		−	11.7000i		−	0.683522i	0.939787	−	0.341761i	$-0.111023\pi$
$294$	3.92273	+	6.62636i	0.228778	+	0.386457i
$295$		0			0
$296$	12.8447	−	14.2655i	0.746584	−	0.829165i
$297$	2.24716	−	10.5721i	0.130393	−	0.613453i
$298$	−3.61712	−	8.12417i	−0.209534	−	0.470621i
$299$	−1.35324	−	2.34388i	−0.0782600	−	0.135550i
$300$		0			0
$301$	−4.59920	−	10.1802i	−0.265093	−	0.586775i
$302$	3.14593	−	4.33000i	0.181028	−	0.249164i
$303$	−2.36005	−	2.12500i	−0.135581	−	0.122078i
$304$	1.81572	+	0.385943i	0.104139	+	0.0221354i
$305$		0			0
$306$	1.86644	−	0.396723i	0.106697	−	0.0226792i
$307$			10.3639i			0.591501i	0.955265	+	0.295750i	$0.0955697\pi$
$307$			10.3639i			0.591501i	−0.955265	+	0.295750i	$0.904430\pi$
$308$	5.93039	−	4.35830i	0.337916	−	0.248337i
$309$	17.6678	−	12.8364i	1.00509	−	0.730237i
$310$		0			0
$311$	6.07353	−	2.70411i	0.344398	−	0.153336i	−0.227246	−	0.973837i	$-0.572972\pi$
$311$	6.07353	−	2.70411i	0.344398	−	0.153336i	0.571645	+	0.820501i	$0.306306\pi$
$312$	5.99406	−	0.630001i	0.339347	−	0.0356668i
$313$	1.93425	−	4.34439i	0.109330	−	0.245560i	−0.850592	−	0.525826i	$-0.823756\pi$
$313$	1.93425	−	4.34439i	0.109330	−	0.245560i	0.959922	+	0.280267i	$0.0904229\pi$
$314$	−4.60017	−	3.34222i	−0.259603	−	0.188612i
$315$		0			0
$316$	−6.99202	+	5.08000i	−0.393332	+	0.285772i
$317$	−2.07295	−	9.75247i	−0.116429	−	0.547753i	−0.997237	−	0.0742812i	$-0.976334\pi$
$317$	−2.07295	−	9.75247i	−0.116429	−	0.547753i	0.880809	−	0.473472i	$-0.157000\pi$
$318$	9.84705	+	5.68520i	0.552195	+	0.318810i
$319$	4.92959	+	5.47487i	0.276004	+	0.306534i
$320$		0			0
$321$	−3.48276	−	10.7188i	−0.194389	−	0.598266i
$322$	−3.26609	+	0.712870i	−0.182012	+	0.0397267i
$323$	−3.50321	+	4.82175i	−0.194924	+	0.268290i
$324$	4.32973	+	7.49932i	0.240541	+	0.416629i
$325$		0			0
$326$	4.61103	−	7.98653i	0.255381	−	0.442333i
$327$	29.3363	+	3.08337i	1.62230	+	0.170511i
$328$	24.3777	−	7.92078i	1.34603	−	0.437352i
$329$	−11.8172	−	3.76851i	−0.651504	−	0.207765i
$330$		0			0
$331$	−31.5279	+	6.70147i	−1.73293	+	0.368346i	−0.962942	−	0.269709i	$-0.913073\pi$
$331$	−31.5279	+	6.70147i	−1.73293	+	0.368346i	−0.769991	+	0.638055i	$0.779739\pi$
$332$	13.5704	+	7.83490i	0.744775	+	0.429996i
$333$	4.44958	−	4.00642i	0.243836	−	0.219551i
$334$	−17.3017	−	7.70322i	−0.946708	−	0.421502i
$335$		0			0
$336$	−0.799232	+	3.86360i	−0.0436017	+	0.210777i
$337$	−0.210764	−	0.290092i	−0.0114810	−	0.0158023i	0.803238	−	0.595658i	$-0.203109\pi$
$337$	−0.210764	−	0.290092i	−0.0114810	−	0.0158023i	−0.814719	+	0.579856i	$0.803109\pi$
$338$	−3.15945	+	7.09623i	−0.171851	+	0.385984i
$339$	24.6140	−	10.9589i	1.33685	−	0.595203i
$340$		0			0
$341$	16.0516	+	7.14664i	0.869244	+	0.387012i
$342$	−1.03903	−	0.337601i	−0.0561843	−	0.0182554i
$343$	−5.43410	+	17.7051i	−0.293414	+	0.955986i
$344$	−3.33726	+	10.2710i	−0.179933	+	0.553777i
$345$		0			0
$346$	1.54842	+	0.329126i	0.0832434	+	0.0176939i
$347$	4.45104	−	20.9405i	0.238945	−	1.12415i	−0.681057	−	0.732231i	$-0.738479\pi$
$347$	4.45104	−	20.9405i	0.238945	−	1.12415i	0.920001	−	0.391915i	$-0.128187\pi$
$348$	−8.22357	−	0.864332i	−0.440830	−	0.0463331i
$349$	−17.9313			−0.959840			−0.479920	−	0.877312i	$-0.659334\pi$
$349$	−17.9313			−0.959840			−0.479920	+	0.877312i	$0.659334\pi$
$350$		0			0
$351$	8.94893			0.477658
$352$	−11.1776	−	1.17481i	−0.595766	−	0.0626175i
$353$	3.84878	−	18.1071i	0.204850	−	0.963742i	−0.748794	−	0.662803i	$-0.769367\pi$
$353$	3.84878	−	18.1071i	0.204850	−	0.963742i	0.953643	−	0.300939i	$-0.0973001\pi$
$354$	−3.13357	−	0.666061i	−0.166547	−	0.0354007i
$355$		0			0
$356$	−1.80504	+	5.55534i	−0.0956670	+	0.294433i
$357$	−10.2887	−	7.38980i	−0.544538	−	0.391110i
$358$	5.84441	+	1.89897i	0.308887	+	0.100363i
$359$	−21.7663	−	9.69097i	−1.14878	−	0.511470i	−0.258108	−	0.966116i	$-0.583099\pi$
$359$	−21.7663	−	9.69097i	−1.14878	−	0.511470i	−0.890672	+	0.454646i	$0.849766\pi$
$360$		0			0
$361$	−14.2400	+	6.34005i	−0.749473	+	0.333687i
$362$	−0.579459	+	1.30149i	−0.0304557	+	0.0684046i
$363$	6.38685	+	8.79075i	0.335223	+	0.461395i
$364$	4.55059	+	4.05264i	0.238516	+	0.212416i
$365$		0			0
$366$	14.0026	+	6.23436i	0.731927	+	0.325875i
$367$	−7.23714	+	6.51635i	−0.377776	+	0.340151i	−0.836043	−	0.548663i	$-0.815137\pi$
$367$	−7.23714	+	6.51635i	−0.377776	+	0.340151i	0.458267	+	0.888814i	$0.348470\pi$
$368$	−1.48334	−	0.856406i	−0.0773244	−	0.0446433i
$369$	7.82028	−	1.66225i	0.407108	−	0.0865334i
$370$		0			0
$371$	5.83156	+	26.7179i	0.302759	+	1.38712i
$372$	−18.7560	+	6.09421i	−0.972455	+	0.315970i
$373$	11.4882	+	1.20746i	0.594836	+	0.0625197i	0.397163	−	0.917748i	$-0.369995\pi$
$373$	11.4882	+	1.20746i	0.594836	+	0.0625197i	0.197673	+	0.980268i	$0.436662\pi$
$374$	2.29335	−	3.97221i	0.118587	−	0.205398i
$375$		0			0
$376$	5.99565	+	10.3848i	0.309202	+	0.535554i
$377$	−3.58538	+	4.93485i	−0.184656	+	0.254157i
$378$	3.35832	−	10.5310i	0.172734	−	0.541654i
$379$	−1.12295	−	3.45610i	−0.0576823	−	0.177528i	0.918064	−	0.396432i	$-0.129752\pi$
$379$	−1.12295	−	3.45610i	−0.0576823	−	0.177528i	−0.975746	+	0.218904i	$0.929752\pi$
$380$		0			0
$381$	15.2785	+	16.9685i	0.782740	+	0.869321i
$382$	−15.5017	−	8.94993i	−0.793138	−	0.457918i
$383$	−2.55624	−	12.0262i	−0.130618	−	0.614508i	−0.993946	−	0.109866i	$-0.964958\pi$
$383$	−2.55624	−	12.0262i	−0.130618	−	0.614508i	0.863329	−	0.504642i	$-0.168376\pi$
$384$	11.9942	−	8.71427i	0.612075	−	0.444698i
$385$		0			0
$386$	11.8076	+	8.57871i	0.600990	+	0.436645i
$387$	−1.37010	+	3.07730i	−0.0696463	+	0.156428i
$388$	−6.89167	+	0.724344i	−0.349872	+	0.0367730i
$389$	22.0110	−	9.79992i	1.11600	−	0.496876i	0.235955	−	0.971764i	$-0.424178\pi$
$389$	22.0110	−	9.79992i	1.11600	−	0.496876i	0.880046	+	0.474888i	$0.157512\pi$
$390$		0			0
$391$	4.44908	−	3.23245i	0.225000	−	0.163472i
$392$	15.4074	−	9.12098i	0.778190	−	0.460679i
$393$		−	11.6279i		−	0.586552i
$394$	4.46573	−	0.949221i	0.224980	−	0.0478211i
$395$		0			0
$396$	−2.17077	−	0.461412i	−0.109085	−	0.0231868i
$397$	−15.2799	−	13.7581i	−0.766878	−	0.690500i	0.189744	−	0.981834i	$-0.439234\pi$
$397$	−15.2799	−	13.7581i	−0.766878	−	0.690500i	−0.956621	+	0.291334i	$0.905901\pi$
$398$	2.46161	−	3.38811i	0.123389	−	0.169831i
$399$	2.98608	+	6.60958i	0.149491	+	0.330893i
$400$		0			0
$401$	9.12609	+	15.8068i	0.455735	+	0.789356i	0.998730	−	0.0503797i	$-0.0160431\pi$
$401$	9.12609	+	15.8068i	0.455735	+	0.789356i	−0.542995	+	0.839736i	$0.682710\pi$
$402$	−1.62187	−	3.64278i	−0.0808916	−	0.181685i
$403$	−3.02471	+	14.2301i	−0.150671	+	0.708853i
$404$	−2.07704	+	2.30679i	−0.103337	+	0.114767i
$405$		0			0
$406$	4.46174	+	6.07115i	0.221433	+	0.301306i
$407$		−	14.3926i		−	0.713413i
$408$	2.54620	+	11.9789i	0.126056	+	0.593046i
$409$	−2.65159	−	25.2282i	−0.131113	−	1.24745i	−0.840178	−	0.542310i	$-0.817550\pi$
$409$	−2.65159	−	25.2282i	−0.131113	−	1.24745i	0.709066	−	0.705142i	$-0.249117\pi$
$410$		0			0
$411$	2.19409	−	20.8754i	0.108227	−	1.02971i
$412$	−12.5467	−	17.2691i	−0.618132	−	0.850786i
$413$	−3.88879	−	6.65154i	−0.191355	−	0.327301i
$414$	0.815538	+	0.592523i	0.0400815	+	0.0291209i
$415$		0			0
$416$	−0.972709	−	9.25471i	−0.0476910	−	0.453749i
$417$	−18.7969	+	16.9248i	−0.920490	+	0.828813i
$418$	−2.27428	+	1.31306i	−0.111239	+	0.0642237i
$419$	4.36121	−	13.4224i	0.213059	−	0.655729i	−0.786226	−	0.617939i	$-0.787968\pi$
$419$	4.36121	−	13.4224i	0.213059	−	0.655729i	0.999286	−	0.0377905i	$-0.0120320\pi$
$420$		0			0
$421$	9.36727	+	28.8295i	0.456533	+	1.40506i	0.869326	+	0.494239i	$0.164553\pi$
$421$	9.36727	+	28.8295i	0.456533	+	1.40506i	−0.412794	+	0.910825i	$0.635447\pi$
$422$	14.8827	+	13.4004i	0.724478	+	0.652323i
$423$	1.52129	+	3.41688i	0.0739677	+	0.166134i
$424$	13.2190	−	22.8960i	0.641972	−	1.11193i
$425$		0			0
$426$	−5.39891			−0.261578
$427$	11.5829	+	34.9978i	0.560535	+	1.69366i
$428$	−10.4769	+	3.40416i	−0.506421	+	0.164546i
$429$	3.02373	−	3.35819i	0.145987	−	0.162135i
$430$		0			0
$431$	−21.8797	−	24.2998i	−1.05391	−	1.17048i	−0.984946	−	0.172863i	$-0.944698\pi$
$431$	−21.8797	−	24.2998i	−1.05391	−	1.17048i	−0.0689609	−	0.997619i	$-0.521968\pi$
$432$	4.90463	−	2.83169i	0.235974	−	0.136240i
$433$	39.0260	+	12.6803i	1.87547	+	0.609378i	0.989274	+	0.146071i	$0.0466628\pi$
$433$	39.0260	+	12.6803i	1.87547	+	0.609378i	0.886198	+	0.463307i	$0.153337\pi$
$434$	15.6107	+	8.89967i	0.749338	+	0.427198i
$435$		0			0
$436$	3.01378	−	28.6742i	0.144334	−	1.37325i
$437$	−3.13141	+	0.329124i	−0.149795	+	0.0157441i
$438$	0.134997	−	0.0141887i	0.00645040	−	0.000677964i
$439$	1.54143	−	14.6657i	0.0735685	−	0.699957i	−0.894123	−	0.447821i	$-0.852200\pi$
$439$	1.54143	−	14.6657i	0.0735685	−	0.699957i	0.967692	−	0.252136i	$-0.0811331\pi$
$440$		0			0
$441$	5.07680	−	2.32702i	0.241752	−	0.110811i
$442$	3.61180	+	1.17354i	0.171796	+	0.0558198i
$443$	−1.64595	+	0.950289i	−0.0782014	+	0.0451496i	−0.538591	−	0.842567i	$-0.681043\pi$
$443$	−1.64595	+	0.950289i	−0.0782014	+	0.0451496i	0.460389	+	0.887717i	$0.347710\pi$
$444$	10.8092	+	12.0049i	0.512984	+	0.569726i
$445$		0			0
$446$	4.14695	−	4.60566i	0.196364	−	0.218084i
$447$	16.9314	−	5.50135i	0.800828	−	0.260205i
$448$	−6.04875	−	1.25126i	−0.285776	−	0.0591163i
$449$	17.7963			0.839859			0.419929	−	0.907557i	$-0.362055\pi$
$449$	17.7963			0.839859			0.419929	+	0.907557i	$0.362055\pi$
$450$		0			0
$451$	9.60905	−	16.6434i	0.452472	−	0.783705i
$452$	−10.7115	−	24.0585i	−0.503828	−	1.13162i
$453$	7.96235	+	7.16933i	0.374104	+	0.336845i
$454$	0.357160	+	1.09923i	0.0167624	+	0.0515893i
$455$		0			0
$456$	2.16675	−	6.66857i	0.101467	−	0.312285i
$457$	4.68033	−	2.70219i	0.218936	−	0.126403i	−0.386521	−	0.922281i	$-0.626323\pi$
$457$	4.68033	−	2.70219i	0.218936	−	0.126403i	0.605458	+	0.795877i	$0.292990\pi$
$458$	1.00734	−	0.907015i	0.0470700	−	0.0423820i
$459$	1.90070	+	18.0839i	0.0887169	+	0.844085i
$460$		0			0
$461$	28.4875	+	20.6974i	1.32679	+	0.963972i	0.999821	+	0.0189380i	$0.00602851\pi$
$461$	28.4875	+	20.6974i	1.32679	+	0.963972i	0.326973	+	0.945034i	$0.393971\pi$
$462$	−2.81713	−	4.81852i	−0.131065	−	0.224178i
$463$	15.7410	+	21.6656i	0.731545	+	1.00689i	0.999061	+	0.0433320i	$0.0137973\pi$
$463$	15.7410	+	21.6656i	0.731545	+	1.00689i	−0.267516	+	0.963554i	$0.586203\pi$
$464$	−0.403511	+	3.83915i	−0.0187325	+	0.178228i
$465$		0			0
$466$	0.513204	+	4.88281i	0.0237737	+	0.226192i
$467$	0.595693	+	2.80252i	0.0275654	+	0.129685i	0.989779	−	0.142612i	$-0.0455501\pi$
$467$	0.595693	+	2.80252i	0.0275654	+	0.129685i	−0.962213	+	0.272297i	$0.912217\pi$
$468$		−	1.83749i		−	0.0849382i
$469$	3.85291	−	8.78239i	0.177911	−	0.405533i
$470$		0			0
$471$	7.61666	−	8.45916i	0.350957	−	0.389778i
$472$	−1.54870	+	7.28606i	−0.0712847	+	0.335368i
$473$	3.29341	+	7.39712i	0.151431	+	0.340120i
$474$	3.27731	+	5.67647i	0.150532	+	0.260729i
$475$		0			0
$476$	−7.22303	+	10.0565i	−0.331067	+	0.460941i
$477$	4.84708	−	6.67143i	0.221932	−	0.305464i
$478$	−5.46047	−	4.91663i	−0.249756	−	0.224881i
$479$	30.2885	+	6.43801i	1.38391	+	0.294160i	0.838909	−	0.544272i	$-0.183194\pi$
$479$	30.2885	+	6.43801i	1.38391	+	0.294160i	0.545006	+	0.838432i	$0.316527\pi$
$480$		0			0
$481$	11.6562	−	2.47761i	0.531479	−	0.112969i
$482$		−	0.266255i		−	0.0121276i
$483$	−0.735821	−	6.65166i	−0.0334810	−	0.302661i
$484$	8.59236	−	6.24271i	0.390562	−	0.283760i
$485$		0			0
$486$	−5.45027	+	2.42662i	−0.247229	+	0.110074i
$487$	8.98328	−	0.944181i	0.407071	−	0.0427849i	0.101220	−	0.994864i	$-0.467725\pi$
$487$	8.98328	−	0.944181i	0.407071	−	0.0427849i	0.305852	+	0.952079i	$0.401059\pi$
$488$	14.4959	−	32.5583i	0.656198	−	1.47385i
$489$	14.9356	+	10.8514i	0.675412	+	0.490715i
$490$		0			0
$491$	−8.66004	+	6.29189i	−0.390822	+	0.283949i	−0.765792	−	0.643088i	$-0.777653\pi$
$491$	−8.66004	+	6.29189i	−0.390822	+	0.283949i	0.374970	+	0.927037i	$0.377653\pi$
$492$	4.48472	+	21.0989i	0.202187	+	0.951214i
$493$	−10.7338	−	6.19717i	−0.483426	−	0.279106i
$494$	−1.45492	−	1.61586i	−0.0654601	−	0.0727009i
$495$		0			0
$496$	2.84506	+	8.75619i	0.127747	+	0.393165i
$497$	−8.74110	−	9.60213i	−0.392092	−	0.430714i
$498$	6.98530	−	9.61444i	0.313019	−	0.430833i
$499$	−11.5714	−	20.0423i	−0.518008	−	0.897217i	−0.999781	−	0.0209205i	$-0.993340\pi$
$499$	−11.5714	−	20.0423i	−0.518008	−	0.897217i	0.481773	−	0.876296i	$-0.339993\pi$
$500$		0			0
$501$	18.9569	−	32.8343i	0.846930	−	1.46693i
$502$	14.5303	+	1.52720i	0.648519	+	0.0681621i
$503$	−15.9572	+	5.18481i	−0.711496	+	0.231179i	−0.642332	−	0.766426i	$-0.722033\pi$
$503$	−15.9572	+	5.18481i	−0.711496	+	0.231179i	−0.0691638	+	0.997605i	$0.522033\pi$
$504$	−5.14387	−	1.64038i	−0.229126	−	0.0730683i
$505$		0			0
$506$	2.37019	−	0.503800i	0.105368	−	0.0223966i
$507$	−13.4668	−	7.77509i	−0.598084	−	0.345304i
$508$	16.5855	−	14.9337i	0.735864	−	0.662575i
$509$	31.3333	+	13.9505i	1.38882	+	0.618344i	0.958698	−	0.284426i	$-0.0918029\pi$
$509$	31.3333	+	13.9505i	1.38882	+	0.618344i	0.430125	+	0.902769i	$0.358470\pi$
$510$		0			0
$511$	0.243802	+	0.217124i	0.0107851	+	0.00960499i
$512$	−6.48313	−	8.92326i	−0.286517	−	0.394356i
$513$	4.23452	−	9.51088i	0.186959	−	0.419916i
$514$	−18.6027	+	8.28244i	−0.820528	+	0.365323i
$515$		0			0
$516$	−8.30250	−	3.69651i	−0.365497	−	0.162730i
$517$	8.55062	+	2.77827i	0.376056	+	0.122188i
$518$	1.45870	−	14.6467i	0.0640916	−	0.643538i
$519$	−0.979272	+	3.01389i	−0.0429853	+	0.132295i
$520$		0			0
$521$	−16.3441	−	3.47404i	−0.716046	−	0.152200i	−0.164539	−	0.986371i	$-0.552614\pi$
$521$	−16.3441	−	3.47404i	−0.716046	−	0.152200i	−0.551507	+	0.834170i	$0.685947\pi$
$522$	0.472363	−	2.22229i	0.0206748	−	0.0972672i
$523$	7.21758	+	0.758598i	0.315603	+	0.0331712i	0.261006	−	0.965337i	$-0.415946\pi$
$523$	7.21758	+	0.758598i	0.315603	+	0.0331712i	0.0545971	+	0.998508i	$0.482613\pi$
$524$	−11.3655			−0.496505
$525$		0			0
$526$	9.82077			0.428206
$527$	−29.3986	−	3.08991i	−1.28062	−	0.134599i
$528$	0.594586	−	2.79731i	0.0258761	−	0.121737i
$529$	−19.6556	−	4.17792i	−0.854591	−	0.181649i
$530$		0			0
$531$	−0.717965	+	2.20967i	−0.0311570	+	0.0958914i
$532$	6.46041	−	2.91869i	0.280094	−	0.126541i
$533$	15.1333	+	4.91709i	0.655494	+	0.212983i
$534$	4.04704	+	1.80186i	0.175133	+	0.0779740i
$535$		0			0
$536$	−8.47006	+	3.77111i	−0.365851	+	0.162887i
$537$	−5.00363	+	11.2383i	−0.215923	+	0.484970i
$538$	5.06828	+	6.97589i	0.218509	+	0.300752i
$539$	4.00882	−	12.8118i	0.172672	−	0.551843i
$540$		0			0
$541$	−40.8813	−	18.2015i	−1.75763	−	0.782546i	−0.989900	−	0.141768i	$-0.954721\pi$
$541$	−40.8813	−	18.2015i	−1.75763	−	0.782546i	−0.767726	−	0.640778i	$-0.778612\pi$
$542$	−5.78165	+	5.20582i	−0.248343	+	0.223609i
$543$	−2.46989	−	1.42599i	−0.105993	−	0.0611951i
$544$	18.4952	−	3.93128i	0.792977	−	0.168552i
$545$		0			0
$546$	3.41747	−	3.11102i	0.146254	−	0.133139i
$547$	0.132412	−	0.0430232i	0.00566152	−	0.00183954i	−0.306185	−	0.951972i	$-0.599053\pi$
$547$	0.132412	−	0.0430232i	0.00566152	−	0.00183954i	0.311846	+	0.950133i	$0.399053\pi$
$548$	−20.4043	−	2.14458i	−0.871629	−	0.0916119i
$549$	5.55820	−	9.62708i	0.237218	−	0.410874i
$550$		0			0
$551$	3.54818	+	6.14563i	0.151158	+	0.261813i
$552$	−3.80286	+	5.23419i	−0.161860	+	0.222782i
$553$	−4.78965	+	15.0193i	−0.203677	+	0.638685i
$554$	3.04327	+	9.36622i	0.129296	+	0.397933i
$555$		0			0
$556$	16.5429	+	18.3727i	0.701574	+	0.779177i
$557$	−19.6687	−	11.3557i	−0.833389	−	0.481157i	0.0216225	−	0.999766i	$-0.493117\pi$
$557$	−19.6687	−	11.3557i	−0.833389	−	0.481157i	−0.855012	+	0.518609i	$0.826450\pi$
$558$	−1.12659	−	5.30018i	−0.0476922	−	0.224374i
$559$	−5.42383	+	3.94064i	−0.229404	+	0.166671i
$560$		0			0
$561$	7.42842	+	5.39706i	0.313628	+	0.227864i
$562$	7.35545	−	16.5206i	0.310271	−	0.696880i
$563$	15.1000	−	1.58707i	0.636388	−	0.0668871i	0.219160	−	0.975689i	$-0.429668\pi$
$563$	15.1000	−	1.58707i	0.636388	−	0.0668871i	0.417228	+	0.908802i	$0.363002\pi$
$564$	−9.21865	+	4.10441i	−0.388175	+	0.172827i
$565$		0			0
$566$	−5.84470	+	4.24642i	−0.245671	+	0.178491i
$567$	14.4645	+	6.34571i	0.607453	+	0.266495i
$568$			12.5533i			0.526726i
$569$	−34.9153	+	7.42148i	−1.46373	+	0.311125i	−0.869804	−	0.493398i	$-0.835755\pi$
$569$	−34.9153	+	7.42148i	−1.46373	+	0.311125i	−0.593922	+	0.804523i	$0.702421\pi$
$570$		0			0
$571$	11.3636	+	2.41540i	0.475551	+	0.101082i	0.439451	−	0.898267i	$-0.355173\pi$
$571$	11.3636	+	2.41540i	0.475551	+	0.101082i	0.0361004	+	0.999348i	$0.488506\pi$
$572$	−3.28240	−	2.95549i	−0.137244	−	0.123575i
$573$	21.0623	−	28.9898i	0.879890	−	1.21106i
$574$	11.4655	−	15.9633i	0.478562	−	0.666296i
$575$		0			0
$576$	0.931295	+	1.61305i	0.0388040	+	0.0672104i
$577$	−4.35664	−	9.78518i	−0.181369	−	0.407362i	0.799865	−	0.600180i	$-0.204904\pi$
$577$	−4.35664	−	9.78518i	−0.181369	−	0.407362i	−0.981235	+	0.192817i	$0.938238\pi$
$578$	1.01573	−	4.77864i	0.0422489	−	0.198765i
$579$	−19.5502	+	21.7127i	−0.812479	+	0.902350i
$580$		0			0
$581$	28.4091	−	3.14268i	1.17861	−	0.130380i
$582$			5.25549i			0.217847i
$583$	−4.12128	−	19.3891i	−0.170686	−	0.803015i
$584$	−0.0329911	−	0.313890i	−0.00136518	−	0.0129888i
$585$		0			0
$586$	−0.906589	+	8.62562i	−0.0374508	+	0.356321i
$587$	−8.59686	−	11.8326i	−0.354830	−	0.488382i	0.593869	−	0.804562i	$-0.297600\pi$
$587$	−8.59686	−	11.8326i	−0.354830	−	0.488382i	−0.948699	+	0.316180i	$0.897600\pi$
$588$	6.27826	+	13.6971i	0.258911	+	0.564858i
$589$	13.6925	+	9.94816i	0.564189	+	0.409907i
$590$		0			0
$591$	0.955346	+	9.08951i	0.0392977	+	0.373892i
$592$	5.60444	−	5.04626i	0.230341	−	0.207400i
$593$	0.472104	−	0.272569i	0.0193870	−	0.0111931i	−0.490275	−	0.871568i	$-0.663104\pi$
$593$	0.472104	−	0.272569i	0.0193870	−	0.0111931i	0.509662	+	0.860375i	$0.329770\pi$
$594$	−2.47586	+	7.61993i	−0.101586	+	0.312649i
$595$		0			0
$596$	−5.37719	−	16.5493i	−0.220258	−	0.677886i
$597$	6.23034	+	5.60982i	0.254991	+	0.229595i
$598$	0.816033	+	1.83284i	0.0333701	+	0.0749505i
$599$	−9.04765	+	15.6710i	−0.369677	+	0.640300i	−0.989515	−	0.144430i	$-0.953865\pi$
$599$	−9.04765	+	15.6710i	−0.369677	+	0.640300i	0.619838	+	0.784730i	$0.287198\pi$
$600$		0			0
$601$	−18.0863			−0.737756			−0.368878	−	0.929478i	$-0.620258\pi$
$601$	−18.0863			−0.737756			−0.368878	+	0.929478i	$0.620258\pi$
$602$	2.60185	+	7.86151i	0.106044	+	0.320411i
$603$	−2.75040	+	0.893658i	−0.112005	+	0.0363926i
$604$	7.00754	−	7.78266i	0.285133	−	0.316672i
$605$		0			0
$606$	1.57524	+	1.74949i	0.0639899	+	0.0710680i
$607$	−28.4587	+	16.4306i	−1.15510	+	0.666899i	−0.950125	−	0.311868i	$-0.899045\pi$
$607$	−28.4587	+	16.4306i	−1.15510	+	0.666899i	−0.204977	+	0.978767i	$0.565712\pi$
$608$	−10.2961	−	3.34542i	−0.417564	−	0.135675i
$609$	−13.0208	+	7.61253i	−0.527627	+	0.308475i
$610$		0			0
$611$	−0.778111	+	7.40323i	−0.0314790	+	0.299503i
$612$	3.71319	−	0.390272i	0.150097	−	0.0157758i
$613$	−11.0143	+	1.15765i	−0.444863	+	0.0467570i	−0.324312	−	0.945950i	$-0.605133\pi$
$613$	−11.0143	+	1.15765i	−0.444863	+	0.0467570i	−0.120551	+	0.992707i	$0.538466\pi$
$614$	0.803061	−	7.64061i	0.0324089	−	0.308350i
$615$		0			0
$616$	−11.2039	+	6.55029i	−0.451416	+	0.263919i
$617$	−31.0252	−	10.0807i	−1.24903	−	0.405834i	−0.391456	−	0.920197i	$-0.628029\pi$
$617$	−31.0252	−	10.0807i	−1.24903	−	0.405834i	−0.857573	+	0.514362i	$0.828029\pi$
$618$	−14.0199	+	8.09439i	−0.563963	+	0.325604i
$619$	−16.6032	−	18.4397i	−0.667340	−	0.741156i	0.310485	−	0.950578i	$-0.399508\pi$
$619$	−16.6032	−	18.4397i	−0.667340	−	0.741156i	−0.977825	+	0.209422i	$0.932842\pi$
$620$		0			0
$621$	−6.42786	+	7.13887i	−0.257941	+	0.286473i
$622$	−4.68713	+	1.52294i	−0.187937	+	0.0610643i
$623$	3.34770	+	10.1151i	0.134123	+	0.405252i
$624$	2.36784			0.0947894
$625$		0			0
$626$	−1.76262	+	3.05295i	−0.0704484	+	0.122020i
$627$	−2.13828	−	4.80266i	−0.0853947	−	0.191800i
$628$	−8.26826	−	7.44477i	−0.329939	−	0.297079i
$629$	7.48245	+	23.0286i	0.298345	+	0.918210i
$630$		0			0
$631$	13.0204	−	40.0726i	0.518334	−	1.59527i	−0.258800	−	0.965931i	$-0.583327\pi$
$631$	13.0204	−	40.0726i	0.518334	−	1.59527i	0.777134	−	0.629336i	$-0.216673\pi$
$632$	13.1987	−	7.62029i	0.525017	−	0.303119i
$633$	−29.7933	+	26.8260i	−1.18418	+	1.06624i
$634$	0.772564	+	7.35045i	0.0306824	+	0.291924i
$635$		0			0
$636$	17.9994	+	13.0773i	0.713721	+	0.518549i
$637$	11.0661	+	1.04118i	0.438455	+	0.0412529i
$638$	−3.21002	−	4.41822i	−0.127086	−	0.174919i
$639$	−0.409285	+	3.89409i	−0.0161911	+	0.154048i
$640$		0			0
$641$	2.68601	+	25.5556i	0.106091	+	1.00939i	0.909993	+	0.414625i	$0.136087\pi$
$641$	2.68601	+	25.5556i	0.106091	+	1.00939i	−0.803902	+	0.594762i	$0.797246\pi$
$642$	1.73704	+	8.17212i	0.0685554	+	0.322528i
$643$		−	3.31021i		−	0.130542i	−0.997868	−	0.0652709i	$-0.979209\pi$
$643$		−	3.31021i		−	0.130542i	0.997868	−	0.0652709i	$-0.0207912\pi$
$644$	−6.50154	+	0.719215i	−0.256197	+	0.0283410i
$645$		0			0
$646$	2.95629	−	3.28330i	0.116314	−	0.129180i
$647$	−5.24437	+	24.6728i	−0.206177	+	0.969988i	0.746354	+	0.665549i	$0.231802\pi$
$647$	−5.24437	+	24.6728i	−0.206177	+	0.969988i	−0.952532	+	0.304439i	$0.901531\pi$
$648$	−6.21099	−	13.9501i	−0.243991	−	0.548012i
$649$	2.79243	+	4.83664i	0.109613	+	0.189855i
$650$		0			0
$651$	−20.9850	+	29.2172i	−0.822468	+	1.14511i
$652$	10.6065	−	14.5985i	0.415381	−	0.571723i
$653$	6.61353	+	5.95485i	0.258808	+	0.233031i	0.788312	−	0.615276i	$-0.210955\pi$
$653$	6.61353	+	5.95485i	0.258808	+	0.233031i	−0.529504	+	0.848307i	$0.677622\pi$
$654$	−21.3887	−	4.54631i	−0.836365	−	0.177775i
$655$		0			0
$656$	9.84998	−	2.09368i	0.384577	−	0.0817443i
$657$		−	0.0984453i		−	0.00384072i
$658$	8.42001	+	3.69393i	0.328246	+	0.144004i
$659$	−17.8405	+	12.9619i	−0.694968	+	0.504924i	−0.878290	−	0.478129i	$-0.841315\pi$
$659$	−17.8405	+	12.9619i	−0.694968	+	0.504924i	0.183321	+	0.983053i	$0.441315\pi$
$660$		0			0
$661$	−10.1816	+	4.53316i	−0.396020	+	0.176319i	−0.595077	−	0.803668i	$-0.702879\pi$
$661$	−10.1816	+	4.53316i	−0.396020	+	0.176319i	0.199058	+	0.979988i	$0.436212\pi$
$662$	23.7627	−	2.49756i	0.923562	−	0.0970703i
$663$	−3.09220	+	6.94520i	−0.120091	+	0.269729i
$664$	−22.3551	−	16.2420i	−0.867548	−	0.630310i
$665$		0			0
$666$	−3.59081	+	2.60888i	−0.139141	+	0.101092i
$667$	−1.36138	−	6.40480i	−0.0527129	−	0.247995i
$668$	−32.0933	−	18.5291i	−1.24173	−	0.716911i
$669$	8.30169	+	9.21996i	0.320962	+	0.356464i
$670$		0			0
$671$	−8.25731	−	25.4134i	−0.318770	−	0.981073i
$672$	6.99097	−	21.9221i	0.269683	−	0.845665i
$673$	−10.5142	+	14.4716i	−0.405293	+	0.557838i	−0.962062	−	0.272829i	$-0.912041\pi$
$673$	−10.5142	+	14.4716i	−0.405293	+	0.557838i	0.556770	+	0.830667i	$0.312041\pi$
$674$	0.132904	+	0.230196i	0.00511926	+	0.00886682i
$675$		0			0
$676$	−7.59962	+	13.1629i	−0.292293	+	0.506267i
$677$	7.44829	+	0.782847i	0.286261	+	0.0300872i	0.246571	−	0.969125i	$-0.420696\pi$
$677$	7.44829	+	0.782847i	0.286261	+	0.0300872i	0.0396902	+	0.999212i	$0.487363\pi$
$678$	−18.9954	+	6.17197i	−0.729512	+	0.237033i
$679$	−9.34705	+	8.50890i	−0.358707	+	0.326541i
$680$		0			0
$681$	−2.26320	+	0.481058i	−0.0867260	+	0.0184342i
$682$	−11.2800	−	6.51251i	−0.431933	−	0.249377i
$683$	−10.5759	+	9.52258i	−0.404675	+	0.364371i	−0.846189	−	0.532883i	$-0.821108\pi$
$683$	−10.5759	+	9.52258i	−0.404675	+	0.364371i	0.441513	+	0.897255i	$0.354442\pi$
$684$	−1.95288	−	0.869479i	−0.0746703	−	0.0332453i
$685$		0			0
$686$	5.37809	−	12.6317i	0.205336	−	0.482280i
$687$	1.59500	+	2.19532i	0.0608529	+	0.0837568i
$688$	−1.72570	+	3.87599i	−0.0657918	+	0.147771i
$689$	14.9934	−	6.67548i	0.571202	−	0.254316i
$690$		0			0
$691$	−33.3850	−	14.8640i	−1.27003	−	0.565453i	−0.342609	−	0.939478i	$-0.611311\pi$
$691$	−33.3850	−	14.8640i	−1.27003	−	0.565453i	−0.927418	+	0.374026i	$0.877977\pi$
$692$	2.94587	+	0.957172i	0.111985	+	0.0363862i
$693$	−3.68904	+	1.66664i	−0.140135	+	0.0633102i
$694$	−4.90405	+	15.0931i	−0.186155	+	0.572927i
$695$		0			0
$696$	14.2629	+	3.03167i	0.540632	+	0.114915i
$697$	−6.72221	+	31.6255i	−0.254622	+	1.19790i
$698$	13.2195	+	1.38943i	0.500366	+	0.0525906i
$699$	−9.82862			−0.371753
$700$		0			0
$701$	−2.52198			−0.0952540			−0.0476270	−	0.998865i	$-0.515166\pi$
$701$	−2.52198			−0.0952540			−0.0476270	+	0.998865i	$0.515166\pi$
$702$	−6.59743	−	0.693418i	−0.249004	−	0.0261714i
$703$	2.88239	−	13.5606i	0.108711	−	0.511447i
$704$	4.37939	+	0.930869i	0.165055	+	0.0350834i
$705$		0			0
$706$	−4.24049	+	13.0509i	−0.159593	+	0.491176i
$707$	−0.561117	+	5.63412i	−0.0211030	+	0.211893i
$708$	−5.96163	−	1.93705i	−0.224052	−	0.0727989i
$709$	−20.5724	−	9.15944i	−0.772614	−	0.343990i	−0.0177253	−	0.999843i	$-0.505642\pi$
$709$	−20.5724	−	9.15944i	−0.772614	−	0.343990i	−0.754889	+	0.655853i	$0.772309\pi$
$710$		0			0
$711$	4.34274	−	1.93351i	0.162866	−	0.0725124i
$712$	4.18961	−	9.41003i	0.157012	−	0.352656i
$713$	−9.17927	−	12.6342i	−0.343766	−	0.473154i
$714$	7.01257	+	6.24523i	0.262439	+	0.233722i
$715$		0			0
$716$	10.9847	+	4.89071i	0.410518	+	0.182774i
$717$	10.9312	−	9.84248i	0.408233	−	0.367574i
$718$	15.2959	+	8.83107i	0.570836	+	0.329573i
$719$	−31.4928	+	6.69400i	−1.17448	+	0.249644i	−0.753514	−	0.657432i	$-0.771643\pi$
$719$	−31.4928	+	6.69400i	−1.17448	+	0.249644i	−0.420968	+	0.907075i	$0.638310\pi$
$720$		0			0
$721$	−37.0950	−	11.8296i	−1.38149	−	0.440557i
$722$	10.9894	−	3.57068i	0.408984	−	0.132887i
$723$	0.530090	+	0.0557147i	0.0197142	+	0.00207205i
$724$	−1.39381	+	2.41415i	−0.0518005	+	0.0897211i
$725$		0			0
$726$	−4.02743	−	6.97571i	−0.149472	−	0.258893i
$727$	−29.1185	+	40.0782i	−1.07995	+	1.48642i	−0.220366	+	0.975417i	$0.570725\pi$
$727$	−29.1185	+	40.0782i	−1.07995	+	1.48642i	−0.859580	+	0.511001i	$0.829275\pi$
$728$	−7.23363	−	7.94617i	−0.268096	−	0.294505i
$729$	−9.22523	−	28.3923i	−0.341675	−	1.05157i
$730$		0			0
$731$	−9.11521	−	10.1235i	−0.337138	−	0.374430i
$732$	25.9737	+	14.9959i	0.960014	+	0.554264i
$733$	5.12118	+	24.0932i	0.189155	+	0.889904i	0.965663	+	0.259797i	$0.0836557\pi$
$733$	5.12118	+	24.0932i	0.189155	+	0.889904i	−0.776508	+	0.630107i	$0.783011\pi$
$734$	5.84038	−	4.24328i	0.215572	−	0.156622i
$735$		0			0
$736$	8.08148	+	5.87154i	0.297887	+	0.216428i
$737$	−2.82745	+	6.35055i	−0.104150	+	0.233925i
$738$	−5.89416	+	0.619501i	−0.216967	+	0.0228041i
$739$	−14.3278	+	6.37916i	−0.527058	+	0.234661i	−0.652975	−	0.757379i	$-0.726479\pi$
$739$	−14.3278	+	6.37916i	−0.527058	+	0.234661i	0.125917	+	0.992041i	$0.459813\pi$
$740$		0			0
$741$	3.52148	−	2.55850i	0.129365	−	0.0939889i
$742$	−2.22894	−	20.1491i	−0.0818270	−	0.739698i
$743$			20.8321i			0.764256i	0.924109	+	0.382128i	$0.124809\pi$
$743$			20.8321i			0.764256i	−0.924109	+	0.382128i	$0.875191\pi$
$744$	34.0169	−	7.23052i	1.24712	−	0.265084i
$745$		0			0
$746$	−8.37589	−	1.78035i	−0.306663	−	0.0651832i
$747$	−6.40510	−	5.76717i	−0.234350	−	0.211010i
$748$	5.27526	−	7.26077i	0.192883	−	0.265480i
$749$	−11.7220	+	16.3204i	−0.428313	+	0.596336i
$750$		0			0
$751$	0.106600	+	0.184637i	0.00388991	+	0.00673751i	0.867964	−	0.496627i	$-0.165428\pi$
$751$	0.106600	+	0.184637i	0.00388991	+	0.00673751i	−0.864074	+	0.503365i	$0.832095\pi$
$752$	1.91613	+	4.30370i	0.0698741	+	0.156940i
$753$	−6.08103	+	28.6090i	−0.221605	+	1.04257i
$754$	3.02563	−	3.36031i	0.110187	−	0.122375i
$755$		0			0
$756$	8.68914	−	19.8062i	0.316021	−	0.720343i
$757$			37.0085i			1.34510i	0.740052	+	0.672549i	$0.234801\pi$
$757$			37.0085i			1.34510i	−0.740052	+	0.672549i	$0.765199\pi$
$758$	0.560077	+	2.63496i	0.0203429	+	0.0957060i
$759$	0.507050	+	4.82426i	0.0184048	+	0.175110i
$760$		0			0
$761$	−2.08064	+	19.7960i	−0.0754233	+	0.717604i	0.889831	+	0.456291i	$0.150822\pi$
$761$	−2.08064	+	19.7960i	−0.0754233	+	0.717604i	−0.965254	+	0.261314i	$0.915844\pi$
$762$	−9.94895	−	13.6936i	−0.360412	−	0.496065i
$763$	−26.5436	−	45.4012i	−0.960944	−	1.64363i
$764$	−28.3355	−	20.5870i	−1.02514	−	0.744810i
$765$		0			0
$766$	0.952679	+	9.06414i	0.0344217	+	0.327501i
$767$	−3.43639	+	3.09414i	−0.124081	+	0.111723i
$768$	−15.5184	+	8.95957i	−0.559973	+	0.323300i
$769$	12.9480	−	39.8498i	0.466916	−	1.43702i	−0.389640	−	0.920967i	$-0.627401\pi$
$769$	12.9480	−	39.8498i	0.466916	−	1.43702i	0.856557	−	0.516053i	$-0.172599\pi$
$770$		0			0
$771$	−12.5969	−	38.7694i	−0.453667	−	1.39624i
$772$	21.2227	+	19.1090i	0.763822	+	0.687748i
$773$	−1.04456	−	2.34613i	−0.0375703	−	0.0843843i	0.893785	−	0.448495i	$-0.148040\pi$
$773$	−1.04456	−	2.34613i	−0.0375703	−	0.0843843i	−0.931356	+	0.364110i	$0.881373\pi$
$774$	1.24853	−	2.16252i	0.0448776	−	0.0777302i
$775$		0			0
$776$	12.2199			0.438668
$777$	28.8550	+	5.96901i	1.03517	+	0.214137i
$778$	−16.9865	+	5.51926i	−0.608997	+	0.197875i
$779$	12.3867	−	13.7569i	0.443801	−	0.492891i
$780$		0			0
$781$	6.29789	+	6.99451i	0.225356	+	0.250283i
$782$	−3.53047	+	2.03832i	−0.126249	+	0.0728901i
$783$	20.5908	+	6.69035i	0.735854	+	0.239094i
$784$	6.39444	−	2.93098i	0.228373	−	0.104678i
$785$		0			0
$786$	−0.901004	+	8.57248i	−0.0321377	+	0.305770i
$787$	21.2543	−	2.23392i	0.757634	−	0.0796306i	0.282169	−	0.959365i	$-0.408946\pi$
$787$	21.2543	−	2.23392i	0.757634	−	0.0796306i	0.475466	+	0.879734i	$0.342280\pi$
$788$	8.88437	−	0.933785i	0.316493	−	0.0332647i
$789$	−2.05503	+	19.5523i	−0.0731609	+	0.696079i
$790$		0			0
$791$	−41.7315	−	23.7911i	−1.48380	−	0.845915i
$792$	3.72197	+	1.20934i	0.132254	+	0.0429720i
$793$	19.1603	−	11.0622i	0.680403	−	0.392831i
$794$	10.1988	+	11.3269i	0.361941	+	0.401976i
$795$		0			0
$796$	5.48322	−	6.08973i	0.194347	−	0.215845i
$797$	28.2691	−	9.18519i	1.00134	−	0.325356i	0.237941	−	0.971280i	$-0.423527\pi$
$797$	28.2691	−	9.18519i	1.00134	−	0.325356i	0.763402	+	0.645923i	$0.223527\pi$
$798$	−1.68928	−	5.10417i	−0.0597998	−	0.180686i
$799$	−15.1257			−0.535107
$800$		0			0
$801$	1.60644	−	2.78243i	0.0567606	−	0.0983122i
$802$	−5.50322	−	12.3604i	−0.194326	−	0.436462i
$803$	−0.175857	−	0.158343i	−0.00620587	−	0.00558779i
$804$	−2.41107	−	7.42050i	−0.0850318	−	0.261701i
$805$		0			0
$806$	3.33255	−	10.2565i	0.117384	−	0.361271i
$807$	−14.9489	+	8.63077i	−0.526227	+	0.303817i
$808$	4.06784	−	3.66270i	0.143106	−	0.128853i
$809$	0.261170	+	2.48487i	0.00918226	+	0.0873634i	0.998153	−	0.0607459i	$-0.0193479\pi$
$809$	0.261170	+	2.48487i	0.00918226	+	0.0873634i	−0.988971	+	0.148109i	$0.952681\pi$
$810$		0			0
$811$	17.3466	+	12.6030i	0.609121	+	0.442552i	0.849105	−	0.528225i	$-0.177142\pi$
$811$	17.3466	+	12.6030i	0.609121	+	0.442552i	−0.239984	+	0.970777i	$0.577142\pi$
$812$	7.44073	+	12.7269i	0.261118	+	0.446627i
$813$	−9.15449	−	12.6001i	−0.321062	−	0.441904i
$814$	−1.11522	+	10.6106i	−0.0390886	+	0.371903i
$815$		0			0
$816$	0.502914	+	4.78491i	0.0176055	+	0.167505i
$817$	1.62161	+	7.62909i	0.0567330	+	0.266908i
$818$			18.8045i			0.657482i
$819$	−1.98482	−	2.70077i	−0.0693553	−	0.0943726i
$820$		0			0
$821$	−0.411128	+	0.456604i	−0.0143485	+	0.0159356i	−0.750276	−	0.661124i	$-0.770080\pi$
$821$	−0.411128	+	0.456604i	−0.0143485	+	0.0159356i	0.735928	+	0.677060i	$0.236746\pi$
$822$	−3.23511	+	15.2200i	−0.112837	+	0.530858i
$823$	7.50211	+	16.8500i	0.261507	+	0.587354i	0.995808	−	0.0914699i	$-0.0291565\pi$
$823$	7.50211	+	16.8500i	0.261507	+	0.587354i	−0.734301	+	0.678824i	$0.762490\pi$
$824$	18.8208	+	32.5985i	0.655653	+	1.13562i
$825$		0			0
$826$	2.35154	+	5.20505i	0.0818205	+	0.181107i
$827$	25.5890	−	35.2203i	0.889818	−	1.22473i	−0.0837861	−	0.996484i	$-0.526701\pi$
$827$	25.5890	−	35.2203i	0.889818	−	1.22473i	0.973604	−	0.228245i	$-0.0732988\pi$
$828$	1.46583	+	1.31984i	0.0509412	+	0.0458676i
$829$	−22.3088	−	4.74188i	−0.774817	−	0.164692i	−0.196499	−	0.980504i	$-0.562957\pi$
$829$	−22.3088	−	4.74188i	−0.774817	−	0.164692i	−0.578318	+	0.815812i	$0.696291\pi$
$830$		0			0
$831$	−19.2841	+	4.09897i	−0.668959	+	0.142192i
$832$			3.70702i			0.128518i
$833$	0.246371	+	22.5834i	0.00853625	+	0.782469i
$834$	15.1691	−	11.0210i	0.525264	−	0.381627i
$835$		0			0
$836$	−4.69427	+	2.09002i	−0.162355	+	0.0722850i
$837$	51.3534	−	5.39746i	1.77503	−	0.186564i
$838$	−4.25528	+	9.55751i	−0.146996	+	0.330159i
$839$	23.7676	+	17.2682i	0.820550	+	0.596165i	0.916870	−	0.399186i	$-0.130707\pi$
$839$	23.7676	+	17.2682i	0.820550	+	0.596165i	−0.0963199	+	0.995350i	$0.530707\pi$
$840$		0			0
$841$	11.5225	−	8.37156i	0.397326	−	0.288674i
$842$	−4.67196	−	21.9798i	−0.161006	−	0.757475i
$843$	31.3519	+	18.1010i	1.07982	+	0.623433i
$844$	26.2206	+	29.1210i	0.902551	+	1.00238i
$845$		0			0
$846$	−0.856783	−	2.63691i	−0.0294568	−	0.0906587i
$847$	5.88591	−	18.4569i	0.202242	−	0.634187i
$848$	6.10510	−	8.40295i	0.209650	−	0.288558i
$849$	−7.23123	−	12.5249i	−0.248175	−	0.429852i
$850$		0			0
$851$	−6.39601	+	11.0782i	−0.219252	+	0.379756i
$852$	−10.5062	−	1.10424i	−0.359935	−	0.0378307i
$853$	−7.76816	+	2.52403i	−0.265977	+	0.0864211i	−0.438969	−	0.898502i	$-0.644656\pi$
$853$	−7.76816	+	2.52403i	−0.265977	+	0.0864211i	0.172993	+	0.984923i	$0.444656\pi$
$854$	−5.82743	−	26.6990i	−0.199410	−	0.913620i
$855$		0			0
$856$	19.0015	−	4.03889i	0.649458	−	0.138047i
$857$	−5.08752	−	2.93728i	−0.173786	−	0.100336i	0.410584	−	0.911823i	$-0.365325\pi$
$857$	−5.08752	−	2.93728i	−0.173786	−	0.100336i	−0.584370	+	0.811487i	$0.698658\pi$
$858$	−2.48940	+	2.24146i	−0.0849866	+	0.0765223i
$859$	21.7207	+	9.67067i	0.741100	+	0.329959i	0.742325	−	0.670040i	$-0.233723\pi$
$859$	21.7207	+	9.67067i	0.741100	+	0.329959i	−0.00122472	+	0.999999i	$0.500390\pi$
$860$		0			0
$861$	29.3824	+	26.1672i	1.00135	+	0.891776i
$862$	14.2475	+	19.6100i	0.485271	+	0.667918i
$863$	−0.0929614	+	0.208795i	−0.00316444	+	0.00710746i	−0.915121	−	0.403180i	$-0.867905\pi$
$863$	−0.0929614	+	0.208795i	−0.00316444	+	0.00710746i	0.911956	+	0.410287i	$0.134572\pi$
$864$	−30.1737	+	13.4342i	−1.02653	+	0.457041i
$865$		0			0
$866$	−27.7887	−	12.3723i	−0.944297	−	0.420428i
$867$	9.30130	+	3.02218i	0.315889	+	0.102638i
$868$	28.5579	+	20.5114i	0.969317	+	0.696204i
$869$	3.53109	−	10.8676i	0.119784	−	0.368657i
$870$		0			0
$871$	−5.62991	−	1.19667i	−0.190762	−	0.0405477i
$872$	−10.5709	+	49.7322i	−0.357976	+	1.68415i
$873$	3.79065	+	0.398413i	0.128294	+	0.0134842i
$874$	2.33407			0.0789512
$875$		0			0
$876$	0.265603			0.00897390
$877$	−25.7832	−	2.70992i	−0.870637	−	0.0915077i	−0.341336	−	0.939941i	$-0.610879\pi$
$877$	−25.7832	−	2.70992i	−0.870637	−	0.0915077i	−0.529302	+	0.848434i	$0.677546\pi$
$878$	−2.27278	+	10.6926i	−0.0767027	+	0.360858i
$879$	−16.9831	−	3.60988i	−0.572827	−	0.121758i
$880$		0			0
$881$	8.56363	−	26.3561i	0.288516	−	0.887961i	−0.696807	−	0.717259i	$-0.745396\pi$
$881$	8.56363	−	26.3561i	0.288516	−	0.887961i	0.985323	−	0.170702i	$-0.0546035\pi$
$882$	−3.92309	+	1.32217i	−0.132097	+	0.0445199i
$883$	−5.43338	−	1.76541i	−0.182848	−	0.0594108i	0.216162	−	0.976358i	$-0.430646\pi$
$883$	−5.43338	−	1.76541i	−0.182848	−	0.0594108i	−0.399010	+	0.916947i	$0.630646\pi$
$884$	6.78846	+	3.02242i	0.228321	+	0.101655i
$885$		0			0
$886$	1.28708	−	0.573045i	0.0432403	−	0.0192518i
$887$	−14.4189	+	32.3854i	−0.484139	+	1.08739i	0.492069	+	0.870556i	$0.336241\pi$
$887$	−14.4189	+	32.3854i	−0.484139	+	1.08739i	−0.976208	+	0.216838i	$0.930426\pi$
$888$	−16.7440	−	23.0461i	−0.561892	−	0.773378i
$889$	8.24657	−	39.8651i	0.276581	−	1.33703i
$890$		0			0
$891$	−10.4593	−	4.65678i	−0.350399	−	0.156008i
$892$	9.01189	−	8.11434i	0.301740	−	0.271688i
$893$	7.49994	+	4.33009i	0.250976	+	0.144901i
$894$	−12.9086	+	2.74382i	−0.431729	+	0.0917669i
$895$		0			0
$896$	−25.1828	−	8.03078i	−0.841297	−	0.268290i
$897$	−3.81978	+	1.24112i	−0.127539	+	0.0414399i
$898$	−13.1200	−	1.37897i	−0.437819	−	0.0460167i
$899$	−17.5983	+	30.4811i	−0.586935	+	1.01660i
$900$		0			0
$901$	16.6743	+	28.8807i	0.555500	+	0.962154i
$902$	−8.37372	+	11.5254i	−0.278814	+	0.383755i
$903$	−16.1960	+	3.53501i	−0.538970	+	0.117638i
$904$	14.3508	+	44.1673i	0.477301	+	1.46898i
$905$		0			0
$906$	−5.31457	−	5.90243i	−0.176565	−	0.196095i
$907$	19.8679	+	11.4708i	0.659704	+	0.380880i	0.792164	−	0.610308i	$-0.208954\pi$
$907$	19.8679	+	11.4708i	0.659704	+	0.380880i	−0.132460	+	0.991188i	$0.542288\pi$
$908$	0.470202	+	2.21212i	0.0156042	+	0.0734119i
$909$	1.38128	−	1.00356i	0.0458140	−	0.0332858i
$910$		0			0
$911$	−26.1720	−	19.0151i	−0.867118	−	0.629998i	0.0626940	−	0.998033i	$-0.480031\pi$
$911$	−26.1720	−	19.0151i	−0.867118	−	0.629998i	−0.929812	+	0.368035i	$0.880031\pi$
$912$	1.12043	−	2.51653i	0.0371012	−	0.0833306i
$913$	−20.6043	+	2.16560i	−0.681904	+	0.0716710i
$914$	−3.65987	+	1.62948i	−0.121058	+	0.0538983i
$915$		0			0
$916$	2.14578	−	1.55900i	0.0708986	−	0.0515108i
$917$	−16.7052	+	12.2768i	−0.551654	+	0.405416i
$918$		−	13.4793i		−	0.444883i
$919$	−5.04665	+	1.07270i	−0.166474	+	0.0353851i	−0.290394	−	0.956907i	$-0.593786\pi$
$919$	−5.04665	+	1.07270i	−0.166474	+	0.0353851i	0.123921	+	0.992292i	$0.460453\pi$
$920$		0			0
$921$	15.0437	+	3.19765i	0.495708	+	0.105366i
$922$	−19.3981	−	17.4661i	−0.638842	−	0.575216i
$923$	−4.58056	+	6.30460i	−0.150771	+	0.207518i
$924$	−4.49654	−	9.95294i	−0.147925	−	0.327428i
$925$		0			0
$926$	−9.92596	−	17.1923i	−0.326187	−	0.564973i
$927$	4.77544	+	10.7258i	0.156846	+	0.352282i
$928$	4.68083	−	22.0216i	0.153656	−	0.722894i
$929$	22.8311	−	25.3565i	0.749063	−	0.831919i	−0.241295	−	0.970452i	$-0.577572\pi$
$929$	22.8311	−	25.3565i	0.749063	−	0.831919i	0.990358	+	0.138533i	$0.0442388\pi$
$930$		0			0
$931$	6.34289	−	11.2683i	0.207880	−	0.369305i
$932$			9.60681i			0.314682i
$933$	−2.05124	−	9.65033i	−0.0671546	−	0.315938i
$934$	−0.222007	−	2.11226i	−0.00726431	−	0.0691153i
$935$		0			0
$936$	−0.338701	+	3.22253i	−0.0110708	+	0.105332i
$937$	−28.0270	−	38.5758i	−0.915602	−	1.26022i	−0.965217	−	0.261449i	$-0.915800\pi$
$937$	−28.0270	−	38.5758i	−0.915602	−	1.26022i	0.0496158	−	0.998768i	$-0.484200\pi$
$938$	−3.52100	+	6.17611i	−0.114965	+	0.201657i
$939$	−5.70931	−	4.14806i	−0.186316	−	0.135367i
$940$		0			0
$941$	−0.530679	−	5.04907i	−0.0172996	−	0.164595i	0.982461	−	0.186467i	$-0.0597039\pi$
$941$	−0.530679	−	5.04907i	−0.0172996	−	0.164595i	−0.999761	+	0.0218725i	$0.993037\pi$
$942$	−6.27071	+	5.64617i	−0.204311	+	0.183962i
$943$	−14.7925	+	8.54046i	−0.481710	+	0.278116i
$944$	−0.904307	+	2.78317i	−0.0294327	+	0.0905845i
$945$		0			0
$946$	−1.85483	−	5.70858i	−0.0603058	−	0.185602i
$947$	5.51230	+	4.96330i	0.179126	+	0.161286i	0.753816	−	0.657085i	$-0.228211\pi$
$947$	5.51230	+	4.96330i	0.179126	+	0.161286i	−0.574690	+	0.818371i	$0.694878\pi$
$948$	5.21657	+	11.7166i	0.169426	+	0.380538i
$949$	0.0979655	−	0.169681i	0.00318009	−	0.00550808i
$950$		0			0
$951$	−14.7958			−0.479785
$952$	14.5212	−	16.3054i	0.470634	−	0.528460i
$953$	39.9357	−	12.9759i	1.29365	−	0.420331i	0.420279	−	0.907395i	$-0.361932\pi$
$953$	39.9357	−	12.9759i	1.29365	−	0.420331i	0.873366	+	0.487064i	$0.161932\pi$
$954$	−4.09036	+	4.54281i	−0.132430	+	0.147079i
$955$		0			0
$956$	−9.62036	−	10.6845i	−0.311145	−	0.345561i
$957$	9.46799	−	5.46635i	0.306057	−	0.176702i
$958$	−21.8307	−	7.09324i	−0.705319	−	0.229172i
$959$	−32.3070	+	18.8882i	−1.04325	+	0.609931i
$960$		0			0
$961$	−5.53413	+	52.6538i	−0.178520	+	1.69851i
$962$	−8.78532	+	0.923375i	−0.283250	+	0.0297708i
$963$	6.02602	−	0.633360i	0.194186	−	0.0204097i
$964$	0.0544573	−	0.518127i	0.00175395	−	0.0166877i
$965$		0			0
$966$	0.0270590	+	4.96083i	0.000870607	+	0.159612i
$967$	34.2062	+	11.1143i	1.10000	+	0.357411i	0.802102	−	0.597188i	$-0.203715\pi$
$967$	34.2062	+	11.1143i	1.10000	+	0.357411i	0.297896	+	0.954598i	$0.403715\pi$
$968$	−16.2197	+	9.36442i	−0.521319	+	0.300984i
$969$	5.91814	+	6.57276i	0.190118	+	0.211147i
$970$		0			0
$971$	−5.29319	+	5.87869i	−0.169867	+	0.188656i	−0.822067	−	0.569390i	$-0.807179\pi$
$971$	−5.29319	+	5.87869i	−0.169867	+	0.188656i	0.652201	+	0.758046i	$0.273846\pi$
$972$	−11.1024	+	3.60740i	−0.356111	+	0.115707i
$973$	44.1608	+	9.13520i	1.41573	+	0.292861i
$974$	−6.69592			−0.214551
$975$		0			0
$976$	7.00079	−	12.1257i	0.224090	−	0.388135i
$977$	−6.57792	−	14.7742i	−0.210446	−	0.472670i	0.777223	−	0.629225i	$-0.216628\pi$
$977$	−6.57792	−	14.7742i	−0.210446	−	0.472670i	−0.987669	+	0.156555i	$0.949961\pi$
$978$	−10.1702	−	9.15726i	−0.325206	−	0.292817i
$979$	−2.38654	−	7.34500i	−0.0762740	−	0.234747i
$980$		0			0
$981$	−4.90059	+	15.0825i	−0.156464	+	0.481546i
$982$	6.87199	−	3.96754i	0.219294	−	0.126609i
$983$	15.6876	−	14.1252i	0.500358	−	0.450524i	−0.379895	−	0.925030i	$-0.624040\pi$
$983$	15.6876	−	14.1252i	0.500358	−	0.450524i	0.880252	+	0.474506i	$0.157373\pi$
$984$	−3.97601	−	37.8292i	−0.126750	−	1.20595i
$985$		0			0
$986$	7.43310	+	5.40047i	0.236718	+	0.171986i
$987$	−9.11620	+	15.9905i	−0.290172	+	0.508984i
$988$	−2.50076	−	3.44200i	−0.0795598	−	0.109505i
$989$	0.752260	−	7.15727i	0.0239205	−	0.227588i
$990$		0			0
$991$	5.13487	+	48.8551i	0.163115	+	1.55193i	0.703611	+	0.710586i	$0.251570\pi$
$991$	5.13487	+	48.8551i	0.163115	+	1.55193i	−0.540496	+	0.841346i	$0.681763\pi$
$992$	−11.1638	−	52.5215i	−0.354450	−	1.66756i
$993$			47.8320i			1.51790i
$994$	5.70018	+	7.75630i	0.180799	+	0.246015i
$995$		0			0
$996$	15.5597	−	17.2808i	0.493028	−	0.547563i
$997$	5.92127	−	27.8574i	0.187529	−	0.882253i	−0.779265	−	0.626695i	$-0.784407\pi$
$997$	5.92127	−	27.8574i	0.187529	−	0.882253i	0.966794	−	0.255558i	$-0.0822593\pi$
$998$	6.97782	+	15.6724i	0.220879	+	0.496102i
$999$	−21.1483	−	36.6299i	−0.669101	−	1.15892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.u.b.424.14		288
5.2	odd	4		175.2.q.a.116.11	yes	144
5.3	odd	4		875.2.q.a.326.8		144
5.4	even	2	inner	875.2.u.b.424.23		288
7.2	even	3	inner	875.2.u.b.674.23		288
25.2	odd	20		175.2.q.a.11.8	✓	144
25.11	even	5	inner	875.2.u.b.74.14		288
25.14	even	10	inner	875.2.u.b.74.23		288
25.23	odd	20		875.2.q.a.676.11		144
35.2	odd	12		175.2.q.a.16.8	yes	144
35.9	even	6	inner	875.2.u.b.674.14		288
35.23	odd	12		875.2.q.a.576.11		144
175.2	odd	60		175.2.q.a.86.11	yes	144
175.23	odd	60		875.2.q.a.51.8		144
175.86	even	15	inner	875.2.u.b.324.23		288
175.114	even	30	inner	875.2.u.b.324.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.q.a.11.8	✓	144	25.2	odd	20
175.2.q.a.16.8	yes	144	35.2	odd	12
175.2.q.a.86.11	yes	144	175.2	odd	60
175.2.q.a.116.11	yes	144	5.2	odd	4
875.2.q.a.51.8		144	175.23	odd	60
875.2.q.a.326.8		144	5.3	odd	4
875.2.q.a.576.11		144	35.23	odd	12
875.2.q.a.676.11		144	25.23	odd	20
875.2.u.b.74.14		288	25.11	even	5	inner
875.2.u.b.74.23		288	25.14	even	10	inner
875.2.u.b.324.14		288	175.114	even	30	inner
875.2.u.b.324.23		288	175.86	even	15	inner
875.2.u.b.424.14		288	1.1	even	1	trivial
875.2.u.b.424.23		288	5.4	even	2	inner
875.2.u.b.674.14		288	35.9	even	6	inner
875.2.u.b.674.23		288	7.2	even	3	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.737231 - 0.0774861i) q^{2} +(0.308536 - 1.45155i) q^{3} +(-1.41879 - 0.301573i) q^{4} +(-0.339937 + 1.04622i) q^{6} +(-2.41111 + 1.08929i) q^{7} +(2.43263 + 0.790409i) q^{8} +(0.728840 + 0.324501i) q^{9} +O(q^{10})\)	\(q+(-0.737231 - 0.0774861i) q^{2} +(0.308536 - 1.45155i) q^{3} +(-1.41879 - 0.301573i) q^{4} +(-0.339937 + 1.04622i) q^{6} +(-2.41111 + 1.08929i) q^{7} +(2.43263 + 0.790409i) q^{8} +(0.728840 + 0.324501i) q^{9} +(1.75196 - 0.780023i) q^{11} +(-0.875495 + 1.96639i) q^{12} +(0.933316 + 1.28460i) q^{13} +(1.86195 - 0.616232i) q^{14} +(0.918005 + 0.408722i) q^{16} +(-2.39768 + 2.15888i) q^{17} +(-0.512179 - 0.295707i) q^{18} +(1.80690 - 0.384069i) q^{19} +(0.837245 + 3.83592i) q^{21} +(-1.35204 + 0.439305i) q^{22} +(-1.69516 - 0.178168i) q^{23} +(1.89787 - 3.28721i) q^{24} +(-0.588531 - 1.01937i) q^{26} +(3.31268 - 4.55951i) q^{27} +(3.74936 - 0.818350i) q^{28} +(1.18710 + 3.65353i) q^{29} +(6.13063 + 6.80876i) q^{31} +(-5.07538 - 2.93027i) q^{32} +(-0.591698 - 2.78372i) q^{33} +(1.93493 - 1.40581i) q^{34} +(-0.936210 - 0.680196i) q^{36} +(3.05251 - 6.85605i) q^{37} +(-1.36186 + 0.143138i) q^{38} +(2.15262 - 0.958408i) q^{39} +(8.10725 - 5.89026i) q^{41} +(-0.320012 - 2.89284i) q^{42} +4.22219i q^{43} +(-2.72090 + 0.578345i) q^{44} +(1.23592 + 0.262702i) q^{46} +(3.48394 + 3.13695i) q^{47} +(0.876517 - 1.20642i) q^{48} +(4.62689 - 5.25280i) q^{49} +(2.39395 + 4.14644i) q^{51} +(-0.936779 - 2.10404i) q^{52} +(2.14901 - 10.1103i) q^{53} +(-2.79551 + 3.10473i) q^{54} +(-6.72632 + 0.744080i) q^{56} -2.74130i q^{57} +(-0.592071 - 2.78548i) q^{58} +(0.304406 + 2.89623i) q^{59} +(1.45645 - 13.8572i) q^{61} +(-3.99211 - 5.49467i) q^{62} +(-2.11079 + 0.0115133i) q^{63} +(1.88874 + 1.37225i) q^{64} +(0.220519 + 2.09809i) q^{66} +(-2.69377 + 2.42548i) q^{67} +(4.05286 - 2.33992i) q^{68} +(-0.781636 + 2.40563i) q^{69} +(1.51660 + 4.66763i) q^{71} +(1.51651 + 1.36547i) q^{72} +(-0.0501887 - 0.112726i) q^{73} +(-2.78165 + 4.81797i) q^{74} -2.67944 q^{76} +(-3.37450 + 3.78912i) q^{77} +(-1.66124 + 0.539770i) q^{78} +(3.98697 - 4.42797i) q^{79} +(-3.99474 - 4.43661i) q^{81} +(-6.43333 + 3.71429i) q^{82} +(-10.2744 - 3.33835i) q^{83} +(-0.0310628 - 5.69486i) q^{84} +(0.327161 - 3.11273i) q^{86} +(5.66953 - 0.595892i) q^{87} +(4.87841 - 0.512742i) q^{88} +(0.420945 - 4.00503i) q^{89} +(-3.64963 - 2.08066i) q^{91} +(2.35134 + 0.763996i) q^{92} +(11.7748 - 6.79816i) q^{93} +(-2.32540 - 2.58262i) q^{94} +(-5.81937 + 6.46307i) q^{96} +(4.54363 - 1.47632i) q^{97} +(-3.81811 + 3.51401i) q^{98} +1.53002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9}+O(q^{10}) \) 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9	\( 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9} - 12 q^{11} + 12 q^{14} + 26 q^{16} + 22 q^{19} - 6 q^{21} - 92 q^{24} + 88 q^{26} + 48 q^{29} - 42 q^{31} + 72 q^{34} - 208 q^{36} - 50 q^{39} + 76 q^{41} + 14 q^{44} + 42 q^{46} + 76 q^{49} - 16 q^{51} - 30 q^{54} - 120 q^{56} + 78 q^{59} - 26 q^{61} - 84 q^{64} + 14 q^{66} - 100 q^{69} + 44 q^{71} + 20 q^{74} - 552 q^{76} - 18 q^{79} + 114 q^{81} + 58 q^{84} - 34 q^{86} + 84 q^{89} - 68 q^{91} + 22 q^{94} + 26 q^{96} + 136 q^{99}+O(q^{100}) \) 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9 - 12 * q^11 + 12 * q^14 + 26 * q^16 + 22 * q^19 - 6 * q^21 - 92 * q^24 + 88 * q^26 + 48 * q^29 - 42 * q^31 + 72 * q^34 - 208 * q^36 - 50 * q^39 + 76 * q^41 + 14 * q^44 + 42 * q^46 + 76 * q^49 - 16 * q^51 - 30 * q^54 - 120 * q^56 + 78 * q^59 - 26 * q^61 - 84 * q^64 + 14 * q^66 - 100 * q^69 + 44 * q^71 + 20 * q^74 - 552 * q^76 - 18 * q^79 + 114 * q^81 + 58 * q^84 - 34 * q^86 + 84 * q^89 - 68 * q^91 + 22 * q^94 + 26 * q^96 + 136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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