LMFDB - Embedded newform 1500.2.m.c.301.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.5
Character	$\chi$	$=$	1500.301
Dual form			1500.2.m.c.1201.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{3} +3.78808 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{3} +3.78808 q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.653426 - 0.474742i) q^{11} +(-3.84242 - 2.79168i) q^{13} +(-0.355012 - 1.09262i) q^{17} +(0.00463870 + 0.0142765i) q^{19} +(1.17058 - 3.60268i) q^{21} +(5.07089 - 3.68422i) q^{23} +(-0.809017 + 0.587785i) q^{27} +(1.14365 - 3.51978i) q^{29} +(-0.488893 - 1.50466i) q^{31} +(-0.249586 - 0.768148i) q^{33} +(6.91045 + 5.02074i) q^{37} +(-3.84242 + 2.79168i) q^{39} +(-9.30279 - 6.75887i) q^{41} +10.2458 q^{43} +(-0.162630 + 0.500524i) q^{47} +7.34957 q^{49} -1.14884 q^{51} +(-0.911527 + 2.80539i) q^{53} +0.0150112 q^{57} +(-9.25803 - 6.72635i) q^{59} +(-2.54203 + 1.84689i) q^{61} +(-3.06462 - 2.22658i) q^{63} +(4.10412 + 12.6312i) q^{67} +(-1.93691 - 5.96119i) q^{69} +(-1.51826 + 4.67271i) q^{71} +(3.78507 - 2.75001i) q^{73} +(2.47523 - 1.79836i) q^{77} +(2.86507 - 8.81777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.439947 + 1.35402i) q^{83} +(-2.99410 - 2.17534i) q^{87} +(13.0306 - 9.46730i) q^{89} +(-14.5554 - 10.5751i) q^{91} -1.58209 q^{93} +(2.49130 - 7.66744i) q^{97} -0.807679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 16 * q^7 - 6 * q^9	$ 24 q - 6 q^{3} + 16 q^{7} - 6 q^{9} - 6 q^{11} - 4 q^{17} - 10 q^{19} - 4 q^{21} - 14 q^{23} - 6 q^{27} - 4 q^{29} + 6 q^{31} + 4 q^{33} + 8 q^{37} - 10 q^{41} + 56 q^{43} - 26 q^{47} + 56 q^{49} + 16 q^{51} + 32 q^{53} + 20 q^{57} + 36 q^{59} - 12 q^{61} - 4 q^{63} - 36 q^{67} - 4 q^{69} + 40 q^{71} - 32 q^{73} + 46 q^{77} - 8 q^{79} - 6 q^{81} + 6 q^{83} - 4 q^{87} - 30 q^{91} - 4 q^{93} - 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 16 * q^7 - 6 * q^9 - 6 * q^11 - 4 * q^17 - 10 * q^19 - 4 * q^21 - 14 * q^23 - 6 * q^27 - 4 * q^29 + 6 * q^31 + 4 * q^33 + 8 * q^37 - 10 * q^41 + 56 * q^43 - 26 * q^47 + 56 * q^49 + 16 * q^51 + 32 * q^53 + 20 * q^57 + 36 * q^59 - 12 * q^61 - 4 * q^63 - 36 * q^67 - 4 * q^69 + 40 * q^71 - 32 * q^73 + 46 * q^77 - 8 * q^79 - 6 * q^81 + 6 * q^83 - 4 * q^87 - 30 * q^91 - 4 * q^93 - 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.78808			1.43176			0.715880	−	0.698223i	$-0.246026\pi$
$7$	3.78808			1.43176			0.715880	+	0.698223i	$0.246026\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	0.653426	−	0.474742i	0.197015	−	0.143140i	−0.484904	−	0.874567i	$-0.661145\pi$
$11$	0.653426	−	0.474742i	0.197015	−	0.143140i	0.681919	+	0.731427i	$0.261145\pi$
$12$		0			0
$13$	−3.84242	−	2.79168i	−1.06570	−	0.774274i	−0.0905626	−	0.995891i	$-0.528867\pi$
$13$	−3.84242	−	2.79168i	−1.06570	−	0.774274i	−0.975134	+	0.221617i	$0.928867\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.355012	−	1.09262i	−0.0861032	−	0.264998i	0.898730	−	0.438503i	$-0.144491\pi$
$17$	−0.355012	−	1.09262i	−0.0861032	−	0.264998i	−0.984833	+	0.173504i	$0.944491\pi$
$18$		0			0
$19$	0.00463870	+	0.0142765i	0.00106419	+	0.00327524i	0.951587	−	0.307379i	$-0.0994519\pi$
$19$	0.00463870	+	0.0142765i	0.00106419	+	0.00327524i	−0.950523	+	0.310654i	$0.899452\pi$
$20$		0			0
$21$	1.17058	−	3.60268i	0.255442	−	0.786169i
$22$		0			0
$23$	5.07089	−	3.68422i	1.05735	−	0.768213i	0.0837569	−	0.996486i	$-0.473308\pi$
$23$	5.07089	−	3.68422i	1.05735	−	0.768213i	0.973597	+	0.228274i	$0.0733081\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	1.14365	−	3.51978i	0.212370	−	0.653607i	−0.786960	−	0.617004i	$-0.788346\pi$
$29$	1.14365	−	3.51978i	0.212370	−	0.653607i	0.999330	−	0.0366030i	$-0.0116537\pi$
$30$		0			0
$31$	−0.488893	−	1.50466i	−0.0878078	−	0.270245i	0.897505	−	0.441005i	$-0.145378\pi$
$31$	−0.488893	−	1.50466i	−0.0878078	−	0.270245i	−0.985313	+	0.170760i	$0.945378\pi$
$32$		0			0
$33$	−0.249586	−	0.768148i	−0.0434474	−	0.133717i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.91045	+	5.02074i	1.13607	+	0.825404i	0.986567	−	0.163357i	$-0.0522322\pi$
$37$	6.91045	+	5.02074i	1.13607	+	0.825404i	0.149504	+	0.988761i	$0.452232\pi$
$38$		0			0
$39$	−3.84242	+	2.79168i	−0.615280	+	0.447027i
$40$		0			0
$41$	−9.30279	−	6.75887i	−1.45285	−	1.05556i	−0.985155	−	0.171669i	$-0.945084\pi$
$41$	−9.30279	−	6.75887i	−1.45285	−	1.05556i	−0.467697	−	0.883889i	$-0.654916\pi$
$42$		0			0
$43$	10.2458			1.56247			0.781234	−	0.624238i	$-0.214591\pi$
$43$	10.2458			1.56247			0.781234	+	0.624238i	$0.214591\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.162630	+	0.500524i	−0.0237221	+	0.0730090i	−0.962217	−	0.272285i	$-0.912221\pi$
$47$	−0.162630	+	0.500524i	−0.0237221	+	0.0730090i	0.938495	+	0.345294i	$0.112221\pi$
$48$		0			0
$49$	7.34957			1.04994
$50$		0			0
$51$	−1.14884			−0.160870
$52$		0			0
$53$	−0.911527	+	2.80539i	−0.125208	+	0.385350i	−0.993939	−	0.109934i	$-0.964936\pi$
$53$	−0.911527	+	2.80539i	−0.125208	+	0.385350i	0.868731	+	0.495284i	$0.164936\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.0150112			0.00198828
$58$		0			0
$59$	−9.25803	−	6.72635i	−1.20529	−	0.875696i	−0.210498	−	0.977594i	$-0.567508\pi$
$59$	−9.25803	−	6.72635i	−1.20529	−	0.875696i	−0.994795	+	0.101898i	$0.967508\pi$
$60$		0			0
$61$	−2.54203	+	1.84689i	−0.325473	+	0.236470i	−0.738507	−	0.674245i	$-0.764469\pi$
$61$	−2.54203	+	1.84689i	−0.325473	+	0.236470i	0.413034	+	0.910716i	$0.364469\pi$
$62$		0			0
$63$	−3.06462	−	2.22658i	−0.386106	−	0.280523i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.10412	+	12.6312i	0.501398	+	1.54314i	0.806744	+	0.590901i	$0.201228\pi$
$67$	4.10412	+	12.6312i	0.501398	+	1.54314i	−0.305346	+	0.952241i	$0.598772\pi$
$68$		0			0
$69$	−1.93691	−	5.96119i	−0.233176	−	0.717643i
$70$		0			0
$71$	−1.51826	+	4.67271i	−0.180184	+	0.554549i	−0.999832	−	0.0183179i	$-0.994169\pi$
$71$	−1.51826	+	4.67271i	−0.180184	+	0.554549i	0.819648	+	0.572867i	$0.194169\pi$
$72$		0			0
$73$	3.78507	−	2.75001i	0.443009	−	0.321865i	−0.343820	−	0.939035i	$-0.611721\pi$
$73$	3.78507	−	2.75001i	0.443009	−	0.321865i	0.786829	+	0.617171i	$0.211721\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.47523	−	1.79836i	0.282079	−	0.204942i
$78$		0			0
$79$	2.86507	−	8.81777i	0.322345	−	0.992076i	−0.650280	−	0.759695i	$-0.725348\pi$
$79$	2.86507	−	8.81777i	0.322345	−	0.992076i	0.972625	−	0.232381i	$-0.0746517\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	0.439947	+	1.35402i	0.0482904	+	0.148623i	0.972294	−	0.233761i	$-0.0751033\pi$
$83$	0.439947	+	1.35402i	0.0482904	+	0.148623i	−0.924004	+	0.382384i	$0.875103\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.99410	−	2.17534i	−0.321002	−	0.233221i
$88$		0			0
$89$	13.0306	−	9.46730i	1.38124	−	1.00353i	0.384480	−	0.923133i	$-0.374381\pi$
$89$	13.0306	−	9.46730i	1.38124	−	1.00353i	0.996763	−	0.0803985i	$-0.0256193\pi$
$90$		0			0
$91$	−14.5554	−	10.5751i	−1.52582	−	1.10857i
$92$		0			0
$93$	−1.58209			−0.164055
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.49130	−	7.66744i	0.252954	−	0.778511i	−0.741272	−	0.671204i	$-0.765777\pi$
$97$	2.49130	−	7.66744i	0.252954	−	0.778511i	0.994226	−	0.107307i	$-0.0342227\pi$
$98$		0			0
$99$	−0.807679			−0.0811748
$100$		0			0
$101$	11.6496			1.15918			0.579590	−	0.814908i	$-0.303213\pi$
$101$	11.6496			1.15918			0.579590	+	0.814908i	$0.303213\pi$
$102$		0			0
$103$	5.82307	−	17.9216i	0.573764	−	1.76587i	−0.0665845	−	0.997781i	$-0.521210\pi$
$103$	5.82307	−	17.9216i	0.573764	−	1.76587i	0.640349	−	0.768084i	$-0.278790\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.3957			−1.39168			−0.695842	−	0.718195i	$-0.744969\pi$
$107$	−14.3957			−1.39168			−0.695842	+	0.718195i	$0.744969\pi$
$108$		0			0
$109$	4.66144	+	3.38673i	0.446485	+	0.324390i	0.788206	−	0.615411i	$-0.211010\pi$
$109$	4.66144	+	3.38673i	0.446485	+	0.324390i	−0.341722	+	0.939801i	$0.611010\pi$
$110$		0			0
$111$	6.91045	−	5.02074i	0.655911	−	0.476547i
$112$		0			0
$113$	−14.5027	−	10.5368i	−1.36430	−	0.991223i	−0.998158	−	0.0606641i	$-0.980678\pi$
$113$	−14.5027	−	10.5368i	−1.36430	−	0.991223i	−0.366143	−	0.930559i	$-0.619322\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.46767	+	4.51704i	0.135687	+	0.417600i
$118$		0			0
$119$	−1.34482	−	4.13892i	−0.123279	−	0.379414i
$120$		0			0
$121$	−3.19760	+	9.84120i	−0.290691	+	0.894655i
$122$		0			0
$123$	−9.30279	+	6.75887i	−0.838804	+	0.609427i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.85250	−	1.34592i	0.164382	−	0.119431i	−0.502553	−	0.864547i	$-0.667606\pi$
$127$	1.85250	−	1.34592i	0.164382	−	0.119431i	0.666935	+	0.745116i	$0.267606\pi$
$128$		0			0
$129$	3.16612	−	9.74432i	0.278762	−	0.857940i
$130$		0			0
$131$	−2.17840	−	6.70444i	−0.190328	−	0.585769i	0.809671	−	0.586883i	$-0.199645\pi$
$131$	−2.17840	−	6.70444i	−0.190328	−	0.585769i	−0.999999	+	0.00111420i	$0.999645\pi$
$132$		0			0
$133$	0.0175718	+	0.0540804i	0.00152367	+	0.00468937i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.7441	+	12.8918i	1.51598	+	1.10142i	0.963436	+	0.267940i	$0.0863429\pi$
$137$	17.7441	+	12.8918i	1.51598	+	1.10142i	0.552544	+	0.833484i	$0.313657\pi$
$138$		0			0
$139$	−7.86171	+	5.71187i	−0.666822	+	0.484474i	−0.868960	−	0.494883i	$-0.835211\pi$
$139$	−7.86171	+	5.71187i	−0.666822	+	0.484474i	0.202138	+	0.979357i	$0.435211\pi$
$140$		0			0
$141$	0.425771	+	0.309341i	0.0358564	+	0.0260512i
$142$		0			0
$143$	−3.83607			−0.320788
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.27114	−	6.98985i	0.187321	−	0.576513i
$148$		0			0
$149$	−13.9712			−1.14457			−0.572284	−	0.820056i	$-0.693942\pi$
$149$	−13.9712			−1.14457			−0.572284	+	0.820056i	$0.693942\pi$
$150$		0			0
$151$	−20.1871			−1.64280			−0.821400	−	0.570352i	$-0.806807\pi$
$151$	−20.1871			−1.64280			−0.821400	+	0.570352i	$0.806807\pi$
$152$		0			0
$153$	−0.355012	+	1.09262i	−0.0287011	+	0.0883328i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.76546			0.619751			0.309876	−	0.950777i	$-0.399713\pi$
$157$	7.76546			0.619751			0.309876	+	0.950777i	$0.399713\pi$
$158$		0			0
$159$	2.38641	+	1.73383i	0.189255	+	0.137502i
$160$		0			0
$161$	19.2090	−	13.9561i	1.51388	−	1.09990i
$162$		0			0
$163$	11.2379	+	8.16480i	0.880219	+	0.639517i	0.933310	−	0.359073i	$-0.116907\pi$
$163$	11.2379	+	8.16480i	0.880219	+	0.639517i	−0.0530901	+	0.998590i	$0.516907\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.895491	−	2.75604i	−0.0692952	−	0.213269i	0.910412	−	0.413703i	$-0.135765\pi$
$167$	−0.895491	−	2.75604i	−0.0692952	−	0.213269i	−0.979707	+	0.200434i	$0.935765\pi$
$168$		0			0
$169$	2.95350	+	9.08992i	0.227192	+	0.699225i
$170$		0			0
$171$	0.00463870	−	0.0142765i	0.000354730	−	0.00109175i
$172$		0			0
$173$	−12.3244	+	8.95423i	−0.937009	+	0.680777i	−0.947699	−	0.319166i	$-0.896597\pi$
$173$	−12.3244	+	8.95423i	−0.937009	+	0.680777i	0.0106895	+	0.999943i	$0.496597\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.25803	+	6.72635i	−0.695876	+	0.505583i
$178$		0			0
$179$	−7.20182	+	22.1649i	−0.538290	+	1.65669i	0.198142	+	0.980173i	$0.436509\pi$
$179$	−7.20182	+	22.1649i	−0.538290	+	1.65669i	−0.736432	+	0.676512i	$0.763491\pi$
$180$		0			0
$181$	5.46913	+	16.8322i	0.406517	+	1.25113i	0.919622	+	0.392805i	$0.128495\pi$
$181$	5.46913	+	16.8322i	0.406517	+	1.25113i	−0.513105	+	0.858326i	$0.671505\pi$
$182$		0			0
$183$	0.970968	+	2.98833i	0.0717760	+	0.220904i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.750685	−	0.545404i	−0.0548955	−	0.0398839i
$188$		0			0
$189$	−3.06462	+	2.22658i	−0.222919	+	0.161960i
$190$		0			0
$191$	−7.57575	−	5.50411i	−0.548162	−	0.398263i	0.278945	−	0.960307i	$-0.410015\pi$
$191$	−7.57575	−	5.50411i	−0.548162	−	0.398263i	−0.827107	+	0.562044i	$0.810015\pi$
$192$		0			0
$193$	18.9309			1.36268			0.681338	−	0.731969i	$-0.261398\pi$
$193$	18.9309			1.36268			0.681338	+	0.731969i	$0.261398\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.33109	+	7.17436i	−0.166083	+	0.511152i	−0.999114	−	0.0420739i	$-0.986603\pi$
$197$	−2.33109	+	7.17436i	−0.166083	+	0.511152i	0.833031	+	0.553226i	$0.186603\pi$
$198$		0			0
$199$	3.58560			0.254176			0.127088	−	0.991891i	$-0.459437\pi$
$199$	3.58560			0.254176			0.127088	+	0.991891i	$0.459437\pi$
$200$		0			0
$201$	13.2812			0.936783
$202$		0			0
$203$	4.33223	−	13.3332i	0.304063	−	0.935808i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.26797			−0.435654
$208$		0			0
$209$	0.00980868	+	0.00712642i	0.000678480	+	0.000492945i
$210$		0			0
$211$	−1.68674	+	1.22549i	−0.116120	+	0.0843663i	−0.644330	−	0.764748i	$-0.722864\pi$
$211$	−1.68674	+	1.22549i	−0.116120	+	0.0843663i	0.528210	+	0.849114i	$0.322864\pi$
$212$		0			0
$213$	3.97485	+	2.88790i	0.272352	+	0.197875i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.85197	−	5.69977i	−0.125720	−	0.386926i
$218$		0			0
$219$	−1.44577	−	4.44962i	−0.0976960	−	0.300677i
$220$		0			0
$221$	−1.68613	+	5.18938i	−0.113421	+	0.349075i
$222$		0			0
$223$	−11.3564	+	8.25091i	−0.760481	+	0.552522i	−0.899058	−	0.437830i	$-0.855747\pi$
$223$	−11.3564	+	8.25091i	−0.760481	+	0.552522i	0.138577	+	0.990352i	$0.455747\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.05074	−	1.48995i	0.136112	−	0.0988915i	−0.517646	−	0.855595i	$-0.673191\pi$
$227$	2.05074	−	1.48995i	0.136112	−	0.0988915i	0.653758	+	0.756704i	$0.273191\pi$
$228$		0			0
$229$	−5.10687	+	15.7173i	−0.337472	+	1.03863i	0.628020	+	0.778197i	$0.283866\pi$
$229$	−5.10687	+	15.7173i	−0.337472	+	1.03863i	−0.965492	+	0.260434i	$0.916134\pi$
$230$		0			0
$231$	−0.945454	−	2.90981i	−0.0622063	−	0.191451i
$232$		0			0
$233$	8.19539	+	25.2228i	0.536898	+	1.65240i	0.739512	+	0.673143i	$0.235056\pi$
$233$	8.19539	+	25.2228i	0.536898	+	1.65240i	−0.202614	+	0.979259i	$0.564944\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.50084	−	5.44968i	−0.487232	−	0.353995i
$238$		0			0
$239$	6.03839	−	4.38714i	0.390591	−	0.283781i	−0.375107	−	0.926982i	$-0.622394\pi$
$239$	6.03839	−	4.38714i	0.390591	−	0.283781i	0.765698	+	0.643201i	$0.222394\pi$
$240$		0			0
$241$	−8.33107	−	6.05288i	−0.536651	−	0.389900i	0.286189	−	0.958173i	$-0.407612\pi$
$241$	−8.33107	−	6.05288i	−0.536651	−	0.389900i	−0.822840	+	0.568273i	$0.807612\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0220315	−	0.0678060i	0.00140183	−	0.00431439i
$248$		0			0
$249$	1.42370			0.0902231
$250$		0			0
$251$	19.5809			1.23593			0.617967	−	0.786204i	$-0.287956\pi$
$251$	19.5809			1.23593			0.617967	+	0.786204i	$0.287956\pi$
$252$		0			0
$253$	1.56440	−	4.81473i	0.0983530	−	0.302699i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.98030			−0.373041			−0.186520	−	0.982451i	$-0.559721\pi$
$257$	−5.98030			−0.373041			−0.186520	+	0.982451i	$0.559721\pi$
$258$		0			0
$259$	26.1774	+	19.0190i	1.62658	+	1.18178i
$260$		0			0
$261$	−2.99410	+	2.17534i	−0.185330	+	0.134650i
$262$		0			0
$263$	−4.91104	−	3.56808i	−0.302827	−	0.220017i	0.425985	−	0.904730i	$-0.359928\pi$
$263$	−4.91104	−	3.56808i	−0.302827	−	0.220017i	−0.728813	+	0.684713i	$0.759928\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.97725	−	15.3184i	−0.304603	−	0.937472i
$268$		0			0
$269$	2.97152	+	9.14540i	0.181177	+	0.557605i	0.999862	−	0.0166382i	$-0.00529635\pi$
$269$	2.97152	+	9.14540i	0.181177	+	0.557605i	−0.818685	+	0.574243i	$0.805296\pi$
$270$		0			0
$271$	−9.40263	+	28.9383i	−0.571169	+	1.75788i	0.0776990	+	0.996977i	$0.475243\pi$
$271$	−9.40263	+	28.9383i	−0.571169	+	1.75788i	−0.648868	+	0.760901i	$0.724757\pi$
$272$		0			0
$273$	−14.5554	+	10.5751i	−0.880934	+	0.640036i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.82810	−	4.23436i	0.350176	−	0.254418i	−0.398767	−	0.917052i	$-0.630562\pi$
$277$	5.82810	−	4.23436i	0.350176	−	0.254418i	0.748943	+	0.662634i	$0.230562\pi$
$278$		0			0
$279$	−0.488893	+	1.50466i	−0.0292693	+	0.0900815i
$280$		0			0
$281$	9.20758	+	28.3380i	0.549278	+	1.69050i	0.710594	+	0.703602i	$0.248426\pi$
$281$	9.20758	+	28.3380i	0.549278	+	1.69050i	−0.161316	+	0.986903i	$0.551574\pi$
$282$		0			0
$283$	2.72677	+	8.39215i	0.162090	+	0.498861i	0.998810	−	0.0487693i	$-0.0155299\pi$
$283$	2.72677	+	8.39215i	0.162090	+	0.498861i	−0.836720	+	0.547631i	$0.815530\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−35.2397	−	25.6032i	−2.08014	−	1.51131i
$288$		0			0
$289$	12.6855	−	9.21656i	0.746207	−	0.542151i
$290$		0			0
$291$	−6.52232	−	4.73874i	−0.382345	−	0.277790i
$292$		0			0
$293$	−4.20743			−0.245800			−0.122900	−	0.992419i	$-0.539220\pi$
$293$	−4.20743			−0.245800			−0.122900	+	0.992419i	$0.539220\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.249586	+	0.768148i	−0.0144825	+	0.0445725i
$298$		0			0
$299$	−29.7697			−1.72163
$300$		0			0
$301$	38.8119			2.23708
$302$		0			0
$303$	3.59993	−	11.0794i	0.206811	−	0.636497i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.41109			0.251754			0.125877	−	0.992046i	$-0.459825\pi$
$307$	4.41109			0.251754			0.125877	+	0.992046i	$0.459825\pi$
$308$		0			0
$309$	−15.2450	−	11.0761i	−0.867258	−	0.630100i
$310$		0			0
$311$	5.11346	−	3.71514i	0.289958	−	0.210667i	−0.433291	−	0.901254i	$-0.642648\pi$
$311$	5.11346	−	3.71514i	0.289958	−	0.210667i	0.723249	+	0.690587i	$0.242648\pi$
$312$		0			0
$313$	12.3978	+	9.00753i	0.700765	+	0.509136i	0.880181	−	0.474638i	$-0.157421\pi$
$313$	12.3978	+	9.00753i	0.700765	+	0.509136i	−0.179416	+	0.983773i	$0.557421\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.58686	−	20.2723i	−0.369955	−	1.13860i	−0.946820	−	0.321765i	$-0.895724\pi$
$317$	−6.58686	−	20.2723i	−0.369955	−	1.13860i	0.576864	−	0.816840i	$-0.304276\pi$
$318$		0			0
$319$	−0.923699	−	2.84285i	−0.0517172	−	0.159169i
$320$		0			0
$321$	−4.44851	+	13.6911i	−0.248292	+	0.764164i
$322$		0			0
$323$	0.0139519	−	0.0101366i	0.000776304	−	0.000564018i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.66144	−	3.38673i	0.257778	−	0.187287i
$328$		0			0
$329$	−0.616057	+	1.89603i	−0.0339643	+	0.104531i
$330$		0			0
$331$	6.12237	+	18.8427i	0.336516	+	1.03569i	0.965970	+	0.258652i	$0.0832785\pi$
$331$	6.12237	+	18.8427i	0.336516	+	1.03569i	−0.629454	+	0.777037i	$0.716722\pi$
$332$		0			0
$333$	−2.63956	−	8.12372i	−0.144647	−	0.445177i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.11762	+	5.89780i	0.442195	+	0.321274i	0.786507	−	0.617582i	$-0.211888\pi$
$337$	8.11762	+	5.89780i	0.442195	+	0.321274i	−0.344311	+	0.938856i	$0.611888\pi$
$338$		0			0
$339$	−14.5027	+	10.5368i	−0.787680	+	0.572283i
$340$		0			0
$341$	−1.03378	−	0.751085i	−0.0559823	−	0.0406735i
$342$		0			0
$343$	1.32419			0.0714997
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.28519	−	13.1885i	0.230041	−	0.707994i	−0.767700	−	0.640810i	$-0.778599\pi$
$347$	4.28519	−	13.1885i	0.230041	−	0.707994i	0.997741	−	0.0671837i	$-0.0214014\pi$
$348$		0			0
$349$	27.2533			1.45883			0.729417	−	0.684069i	$-0.239791\pi$
$349$	27.2533			1.45883			0.729417	+	0.684069i	$0.239791\pi$
$350$		0			0
$351$	4.74950			0.253509
$352$		0			0
$353$	−3.83609	+	11.8063i	−0.204174	+	0.628384i	0.795572	+	0.605859i	$0.207170\pi$
$353$	−3.83609	+	11.8063i	−0.204174	+	0.628384i	−0.999746	+	0.0225248i	$0.992830\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.35192			−0.230328
$358$		0			0
$359$	15.3910	+	11.1823i	0.812308	+	0.590177i	0.914499	−	0.404588i	$-0.132585\pi$
$359$	15.3910	+	11.1823i	0.812308	+	0.590177i	−0.102191	+	0.994765i	$0.532585\pi$
$360$		0			0
$361$	15.3711	−	11.1678i	0.809007	−	0.587778i
$362$		0			0
$363$	8.37143	+	6.08220i	0.439386	+	0.319233i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.301352	+	0.927465i	0.0157304	+	0.0484133i	0.958614	−	0.284710i	$-0.0918974\pi$
$367$	0.301352	+	0.927465i	0.0157304	+	0.0484133i	−0.942883	+	0.333124i	$0.891897\pi$
$368$		0			0
$369$	3.55335	+	10.9361i	0.184980	+	0.569310i
$370$		0			0
$371$	−3.45294	+	10.6271i	−0.179268	+	0.551729i
$372$		0			0
$373$	−15.1871	+	11.0341i	−0.786360	+	0.571324i	−0.906881	−	0.421387i	$-0.861543\pi$
$373$	−15.1871	+	11.0341i	−0.786360	+	0.571324i	0.120521	+	0.992711i	$0.461543\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.2205	+	10.3318i	−0.732392	+	0.532114i
$378$		0			0
$379$	−1.06536	+	3.27883i	−0.0547236	+	0.168422i	−0.974683	−	0.223592i	$-0.928222\pi$
$379$	−1.06536	+	3.27883i	−0.0547236	+	0.168422i	0.919959	+	0.392014i	$0.128222\pi$
$380$		0			0
$381$	−0.707591	−	2.17774i	−0.0362510	−	0.111569i
$382$		0			0
$383$	8.43755	+	25.9681i	0.431139	+	1.32691i	0.896992	+	0.442046i	$0.145747\pi$
$383$	8.43755	+	25.9681i	0.431139	+	1.32691i	−0.465854	+	0.884862i	$0.654253\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.28902	−	6.02232i	−0.421354	−	0.306132i
$388$		0			0
$389$	−7.94232	+	5.77044i	−0.402692	+	0.292573i	−0.770637	−	0.637275i	$-0.780062\pi$
$389$	−7.94232	+	5.77044i	−0.402692	+	0.292573i	0.367945	+	0.929848i	$0.380062\pi$
$390$		0			0
$391$	−5.82567	−	4.23259i	−0.294617	−	0.214051i
$392$		0			0
$393$	−7.04946			−0.355598
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.58865	+	11.0447i	−0.180109	+	0.554319i	−0.999830	−	0.0184443i	$-0.994129\pi$
$397$	−3.58865	+	11.0447i	−0.180109	+	0.554319i	0.819721	+	0.572763i	$0.194129\pi$
$398$		0			0
$399$	0.0568635			0.00284674
$400$		0			0
$401$	−25.4145			−1.26914			−0.634570	−	0.772865i	$-0.718823\pi$
$401$	−25.4145			−1.26914			−0.634570	+	0.772865i	$0.718823\pi$
$402$		0			0
$403$	−2.32200	+	7.14637i	−0.115667	+	0.355986i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.89902			0.341972
$408$		0			0
$409$	−13.9568	−	10.1402i	−0.690117	−	0.501399i	0.186582	−	0.982439i	$-0.440259\pi$
$409$	−13.9568	−	10.1402i	−0.690117	−	0.501399i	−0.876699	+	0.481040i	$0.840259\pi$
$410$		0			0
$411$	17.7441	−	12.8918i	0.875251	−	0.635907i
$412$		0			0
$413$	−35.0702	−	25.4800i	−1.72569	−	1.25379i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.00291	+	9.24200i	0.147053	+	0.452583i
$418$		0			0
$419$	−6.31956	−	19.4496i	−0.308731	−	0.950176i	−0.978259	−	0.207389i	$-0.933503\pi$
$419$	−6.31956	−	19.4496i	−0.308731	−	0.950176i	0.669528	−	0.742787i	$-0.266497\pi$
$420$		0			0
$421$	−6.46100	+	19.8849i	−0.314890	+	0.969132i	0.660910	+	0.750466i	$0.270171\pi$
$421$	−6.46100	+	19.8849i	−0.314890	+	0.969132i	−0.975800	+	0.218666i	$0.929829\pi$
$422$		0			0
$423$	0.425771	−	0.309341i	0.0207017	−	0.0150407i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.62941	+	6.99618i	−0.466000	+	0.338569i
$428$		0			0
$429$	−1.18541	+	3.64832i	−0.0572321	+	0.176142i
$430$		0			0
$431$	−2.85900	−	8.79908i	−0.137713	−	0.423837i	0.858289	−	0.513166i	$-0.171528\pi$
$431$	−2.85900	−	8.79908i	−0.137713	−	0.423837i	−0.996002	+	0.0893294i	$0.971528\pi$
$432$		0			0
$433$	−0.0726932	−	0.223727i	−0.00349341	−	0.0107516i	0.949295	−	0.314388i	$-0.101799\pi$
$433$	−0.0726932	−	0.223727i	−0.00349341	−	0.0107516i	−0.952788	+	0.303636i	$0.901799\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0761199	+	0.0553044i	0.00364131	+	0.00264557i
$438$		0			0
$439$	−25.2424	+	18.3396i	−1.20475	+	0.875304i	−0.994744	−	0.102396i	$-0.967349\pi$
$439$	−25.2424	+	18.3396i	−1.20475	+	0.875304i	−0.210008	+	0.977700i	$0.567349\pi$
$440$		0			0
$441$	−5.94593	−	4.31997i	−0.283139	−	0.205713i
$442$		0			0
$443$	24.3862			1.15862			0.579311	−	0.815106i	$-0.303322\pi$
$443$	24.3862			1.15862			0.579311	+	0.815106i	$0.303322\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.31735	+	13.2874i	−0.204203	+	0.628474i
$448$		0			0
$449$	23.9483			1.13019			0.565096	−	0.825025i	$-0.308839\pi$
$449$	23.9483			1.13019			0.565096	+	0.825025i	$0.308839\pi$
$450$		0			0
$451$	−9.28740			−0.437327
$452$		0			0
$453$	−6.23815	+	19.1990i	−0.293094	+	0.902050i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.91244			0.183016			0.0915082	−	0.995804i	$-0.470831\pi$
$457$	3.91244			0.183016			0.0915082	+	0.995804i	$0.470831\pi$
$458$		0			0
$459$	0.929435	+	0.675274i	0.0433823	+	0.0315191i
$460$		0			0
$461$	2.09170	−	1.51971i	0.0974202	−	0.0707799i	−0.538009	−	0.842939i	$-0.680823\pi$
$461$	2.09170	−	1.51971i	0.0974202	−	0.0707799i	0.635429	+	0.772159i	$0.280823\pi$
$462$		0			0
$463$	−17.7247	−	12.8777i	−0.823734	−	0.598478i	0.0940453	−	0.995568i	$-0.470020\pi$
$463$	−17.7247	−	12.8777i	−0.823734	−	0.598478i	−0.917780	+	0.397090i	$0.870020\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.53295	+	7.79561i	0.117211	+	0.360738i	0.992402	−	0.123040i	$-0.0392643\pi$
$467$	2.53295	+	7.79561i	0.117211	+	0.360738i	−0.875191	+	0.483778i	$0.839264\pi$
$468$		0			0
$469$	15.5467	+	47.8479i	0.717881	+	2.20941i
$470$		0			0
$471$	2.39966	−	7.38539i	0.110570	−	0.340301i
$472$		0			0
$473$	6.69486	−	4.86410i	0.307830	−	0.223652i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.38641	−	1.73383i	0.109266	−	0.0793865i
$478$		0			0
$479$	−1.90100	+	5.85067i	−0.0868588	+	0.267324i	−0.985047	−	0.172288i	$-0.944884\pi$
$479$	−1.90100	+	5.85067i	−0.0868588	+	0.267324i	0.898188	+	0.439612i	$0.144884\pi$
$480$		0			0
$481$	−12.5366	−	38.5836i	−0.571618	−	1.75926i
$482$		0			0
$483$	−7.33717	−	22.5815i	−0.333853	−	1.02749i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.08201	−	3.69230i	−0.230288	−	0.167314i	0.466658	−	0.884438i	$-0.345458\pi$
$487$	−5.08201	−	3.69230i	−0.230288	−	0.167314i	−0.696945	+	0.717124i	$0.745458\pi$
$488$		0			0
$489$	11.2379	−	8.16480i	0.508195	−	0.369225i
$490$		0			0
$491$	2.22591	+	1.61722i	0.100454	+	0.0729840i	0.636878	−	0.770964i	$-0.280225\pi$
$491$	2.22591	+	1.61722i	0.100454	+	0.0729840i	−0.536424	+	0.843948i	$0.680225\pi$
$492$		0			0
$493$	−4.25178			−0.191490
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.75128	+	17.7006i	−0.257980	+	0.793982i
$498$		0			0
$499$	−16.4263			−0.735341			−0.367670	−	0.929956i	$-0.619844\pi$
$499$	−16.4263			−0.735341			−0.367670	+	0.929956i	$0.619844\pi$
$500$		0			0
$501$	−2.89787			−0.129467
$502$		0			0
$503$	−3.79701	+	11.6860i	−0.169300	+	0.521053i	−0.999327	−	0.0366701i	$-0.988325\pi$
$503$	−3.79701	+	11.6860i	−0.169300	+	0.521053i	0.830027	+	0.557723i	$0.188325\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.55771			0.424473
$508$		0			0
$509$	8.50277	+	6.17763i	0.376879	+	0.273818i	0.760058	−	0.649856i	$-0.225171\pi$
$509$	8.50277	+	6.17763i	0.376879	+	0.273818i	−0.383179	+	0.923674i	$0.625171\pi$
$510$		0			0
$511$	14.3382	−	10.4173i	0.634283	−	0.460833i
$512$		0			0
$513$	−0.0121443	−	0.00882334i	−0.000536183	−	0.000389560i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.131353	+	0.404263i	0.00577690	+	0.0177795i
$518$		0			0
$519$	4.70752	+	14.4882i	0.206637	+	0.635963i
$520$		0			0
$521$	−2.41778	+	7.44115i	−0.105925	+	0.326003i	−0.989946	−	0.141443i	$-0.954826\pi$
$521$	−2.41778	+	7.44115i	−0.105925	+	0.326003i	0.884022	+	0.467446i	$0.154826\pi$
$522$		0			0
$523$	−17.8368	+	12.9592i	−0.779947	+	0.566665i	−0.904963	−	0.425490i	$-0.860102\pi$
$523$	−17.8368	+	12.9592i	−0.779947	+	0.566665i	0.125016	+	0.992155i	$0.460102\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.47045	+	1.06834i	−0.0640538	+	0.0465378i
$528$		0			0
$529$	5.03308	−	15.4902i	0.218830	−	0.673489i
$530$		0			0
$531$	3.53625	+	10.8835i	0.153460	+	0.472302i
$532$		0			0
$533$	16.8766	+	51.9409i	0.731007	+	2.24981i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	18.8546	+	13.6987i	0.813637	+	0.591142i
$538$		0			0
$539$	4.80240	−	3.48915i	0.206854	−	0.150288i
$540$		0			0
$541$	−10.0860	−	7.32791i	−0.433631	−	0.315052i	0.349468	−	0.936948i	$-0.386362\pi$
$541$	−10.0860	−	7.32791i	−0.433631	−	0.315052i	−0.783099	+	0.621897i	$0.786362\pi$
$542$		0			0
$543$	17.6985			0.759514
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.777505	−	2.39292i	0.0332437	−	0.102314i	−0.933058	−	0.359726i	$-0.882870\pi$
$547$	0.777505	−	2.39292i	0.0332437	−	0.102314i	0.966302	+	0.257413i	$0.0828700\pi$
$548$		0			0
$549$	3.14212			0.134102
$550$		0			0
$551$	0.0555550			0.00236672
$552$		0			0
$553$	10.8531	−	33.4024i	0.461521	−	1.42042i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.262544			−0.0111244			−0.00556218	−	0.999985i	$-0.501771\pi$
$557$	−0.262544			−0.0111244			−0.00556218	+	0.999985i	$0.501771\pi$
$558$		0			0
$559$	−39.3687	−	28.6030i	−1.66512	−	1.20978i
$560$		0			0
$561$	−0.750685	+	0.545404i	−0.0316939	+	0.0230270i
$562$		0			0
$563$	−26.2790	−	19.0928i	−1.10753	−	0.804666i	−0.125255	−	0.992125i	$-0.539975\pi$
$563$	−26.2790	−	19.0928i	−1.10753	−	0.804666i	−0.982272	+	0.187459i	$0.939975\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.17058	+	3.60268i	0.0491598	+	0.151298i
$568$		0			0
$569$	−11.9892	−	36.8991i	−0.502615	−	1.54689i	−0.804743	−	0.593623i	$-0.797697\pi$
$569$	−11.9892	−	36.8991i	−0.502615	−	1.54689i	0.302128	−	0.953267i	$-0.402303\pi$
$570$		0			0
$571$	−11.0258	+	33.9338i	−0.461414	+	1.42009i	0.402023	+	0.915629i	$0.368307\pi$
$571$	−11.0258	+	33.9338i	−0.461414	+	1.42009i	−0.863437	+	0.504456i	$0.831693\pi$
$572$		0			0
$573$	−7.57575	+	5.50411i	−0.316482	+	0.229937i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	20.5029	−	14.8962i	0.853548	−	0.620139i	−0.0725741	−	0.997363i	$-0.523121\pi$
$577$	20.5029	−	14.8962i	0.853548	−	0.620139i	0.926122	+	0.377224i	$0.123121\pi$
$578$		0			0
$579$	5.84997	−	18.0044i	0.243116	−	0.748236i
$580$		0			0
$581$	1.66655	+	5.12913i	0.0691403	+	0.212792i
$582$		0			0
$583$	0.736221	+	2.26586i	0.0304912	+	0.0938422i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.417186	−	0.303103i	−0.0172191	−	0.0125104i	0.579142	−	0.815226i	$-0.303388\pi$
$587$	−0.417186	−	0.303103i	−0.0172191	−	0.0125104i	−0.596362	+	0.802716i	$0.703388\pi$
$588$		0			0
$589$	0.0192134	−	0.0139593i	0.000791673	−	0.000575184i
$590$		0			0
$591$	6.10288	+	4.43400i	0.251039	+	0.182390i
$592$		0			0
$593$	7.14389			0.293364			0.146682	−	0.989184i	$-0.453141\pi$
$593$	7.14389			0.293364			0.146682	+	0.989184i	$0.453141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.10801	−	3.41011i	0.0453479	−	0.139566i
$598$		0			0
$599$	23.6627			0.966833			0.483417	−	0.875390i	$-0.339396\pi$
$599$	23.6627			0.966833			0.483417	+	0.875390i	$0.339396\pi$
$600$		0			0
$601$	−7.98023			−0.325520			−0.162760	−	0.986666i	$-0.552040\pi$
$601$	−7.98023			−0.325520			−0.162760	+	0.986666i	$0.552040\pi$
$602$		0			0
$603$	4.10412	−	12.6312i	0.167133	−	0.514381i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−17.2004			−0.698144			−0.349072	−	0.937096i	$-0.613503\pi$
$607$	−17.2004			−0.698144			−0.349072	+	0.937096i	$0.613503\pi$
$608$		0			0
$609$	−11.3419	−	8.24038i	−0.459597	−	0.333917i
$610$		0			0
$611$	2.02220	−	1.46921i	0.0818094	−	0.0594380i
$612$		0			0
$613$	−11.9444	−	8.67810i	−0.482429	−	0.350505i	0.319836	−	0.947473i	$-0.396372\pi$
$613$	−11.9444	−	8.67810i	−0.482429	−	0.350505i	−0.802265	+	0.596968i	$0.796372\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.78092	+	14.7142i	0.192473	+	0.592370i	0.999997	+	0.00253529i	$0.000807009\pi$
$617$	4.78092	+	14.7142i	0.192473	+	0.592370i	−0.807524	+	0.589834i	$0.799193\pi$
$618$		0			0
$619$	−11.5792	−	35.6370i	−0.465406	−	1.43237i	−0.858471	−	0.512861i	$-0.828586\pi$
$619$	−11.5792	−	35.6370i	−0.465406	−	1.43237i	0.393066	−	0.919510i	$-0.371414\pi$
$620$		0			0
$621$	−1.93691	+	5.96119i	−0.0777254	+	0.239214i
$622$		0			0
$623$	49.3611	−	35.8629i	1.97761	−	1.43682i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.00980868	−	0.00712642i	0.000391721	−	0.000284602i
$628$		0			0
$629$	3.03244	−	9.33290i	0.120911	−	0.372127i
$630$		0			0
$631$	−0.468691	−	1.44248i	−0.0186583	−	0.0574244i	0.941294	−	0.337588i	$-0.109611\pi$
$631$	−0.468691	−	1.44248i	−0.0186583	−	0.0574244i	−0.959952	+	0.280164i	$0.909611\pi$
$632$		0			0
$633$	0.644279	+	1.98289i	0.0256078	+	0.0788126i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−28.2401	−	20.5177i	−1.11892	−	0.812940i
$638$		0			0
$639$	3.97485	−	2.88790i	0.157243	−	0.114243i
$640$		0			0
$641$	3.12903	+	2.27338i	0.123589	+	0.0897930i	0.647863	−	0.761757i	$-0.275663\pi$
$641$	3.12903	+	2.27338i	0.123589	+	0.0897930i	−0.524273	+	0.851550i	$0.675663\pi$
$642$		0			0
$643$	23.2212			0.915756			0.457878	−	0.889015i	$-0.348610\pi$
$643$	23.2212			0.915756			0.457878	+	0.889015i	$0.348610\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.08384	−	24.8795i	0.317808	−	0.978114i	−0.656775	−	0.754087i	$-0.728080\pi$
$647$	8.08384	−	24.8795i	0.317808	−	0.978114i	0.974583	−	0.224027i	$-0.0719203\pi$
$648$		0			0
$649$	−9.24271			−0.362808
$650$		0			0
$651$	−5.99309			−0.234888
$652$		0			0
$653$	−2.64355	+	8.13602i	−0.103450	+	0.318387i	−0.989364	−	0.145464i	$-0.953533\pi$
$653$	−2.64355	+	8.13602i	−0.103450	+	0.318387i	0.885913	+	0.463851i	$0.153533\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4.67860			−0.182530
$658$		0			0
$659$	33.9288	+	24.6507i	1.32168	+	0.960255i	0.999910	+	0.0134358i	$0.00427688\pi$
$659$	33.9288	+	24.6507i	1.32168	+	0.960255i	0.321767	+	0.946819i	$0.395723\pi$
$660$		0			0
$661$	14.1713	−	10.2961i	0.551201	−	0.400471i	−0.277027	−	0.960862i	$-0.589349\pi$
$661$	14.1713	−	10.2961i	0.551201	−	0.400471i	0.828228	+	0.560391i	$0.189349\pi$
$662$		0			0
$663$	4.41435	+	3.20721i	0.171439	+	0.124558i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.16833	−	22.0619i	−0.277559	−	0.854239i
$668$		0			0
$669$	4.33776	+	13.3503i	0.167708	+	0.516151i
$670$		0			0
$671$	−0.784230	+	2.41361i	−0.0302749	+	0.0931765i
$672$		0			0
$673$	23.5385	−	17.1017i	0.907343	−	0.659223i	−0.0329986	−	0.999455i	$-0.510506\pi$
$673$	23.5385	−	17.1017i	0.907343	−	0.659223i	0.940341	+	0.340232i	$0.110506\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24.1785	−	17.5667i	0.929255	−	0.675143i	−0.0165555	−	0.999863i	$-0.505270\pi$
$677$	24.1785	−	17.5667i	0.929255	−	0.675143i	0.945810	+	0.324720i	$0.105270\pi$
$678$		0			0
$679$	9.43726	−	29.0449i	0.362169	−	1.11464i
$680$		0			0
$681$	−0.783313	−	2.41079i	−0.0300166	−	0.0923817i
$682$		0			0
$683$	−11.5016	−	35.3984i	−0.440097	−	1.35448i	−0.887772	−	0.460284i	$-0.847748\pi$
$683$	−11.5016	−	35.3984i	−0.440097	−	1.35448i	0.447674	−	0.894197i	$-0.352252\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	13.3700	+	9.71385i	0.510096	+	0.370607i
$688$		0			0
$689$	11.3342	−	8.23481i	0.431800	−	0.313721i
$690$		0			0
$691$	−13.6397	−	9.90980i	−0.518877	−	0.376986i	0.297303	−	0.954783i	$-0.403913\pi$
$691$	−13.6397	−	9.90980i	−0.518877	−	0.376986i	−0.816181	+	0.577797i	$0.803913\pi$
$692$		0			0
$693$	−3.05955			−0.116223
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−4.08225	+	12.5639i	−0.154626	+	0.475890i
$698$		0			0
$699$	26.5208			1.00311
$700$		0			0
$701$	−23.3495			−0.881898			−0.440949	−	0.897532i	$-0.645358\pi$
$701$	−23.3495			−0.881898			−0.440949	+	0.897532i	$0.645358\pi$
$702$		0			0
$703$	−0.0396228	+	0.121947i	−0.00149440	+	0.00459930i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	44.1297			1.65967
$708$		0			0
$709$	−15.4019	−	11.1901i	−0.578429	−	0.420253i	0.259728	−	0.965682i	$-0.416367\pi$
$709$	−15.4019	−	11.1901i	−0.578429	−	0.420253i	−0.838157	+	0.545428i	$0.816367\pi$
$710$		0			0
$711$	−7.50084	+	5.44968i	−0.281303	+	0.204379i
$712$		0			0
$713$	−8.02261	−	5.82877i	−0.300449	−	0.218289i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.30646	−	7.09855i	−0.0861363	−	0.265100i
$718$		0			0
$719$	−4.55488	−	14.0185i	−0.169868	−	0.522801i	0.829494	−	0.558516i	$-0.188629\pi$
$719$	−4.55488	−	14.0185i	−0.169868	−	0.522801i	−0.999362	+	0.0357149i	$0.988629\pi$
$720$		0			0
$721$	22.0583	−	67.8884i	0.821493	−	2.52830i
$722$		0			0
$723$	−8.33107	+	6.05288i	−0.309836	+	0.225109i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−24.3204	+	17.6698i	−0.901993	+	0.655336i	−0.938977	−	0.343979i	$-0.888225\pi$
$727$	−24.3204	+	17.6698i	−0.901993	+	0.655336i	0.0369839	+	0.999316i	$0.488225\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−3.63738	−	11.1947i	−0.134533	−	0.414051i
$732$		0			0
$733$	−6.99732	−	21.5355i	−0.258452	−	0.795433i	−0.993130	−	0.117017i	$-0.962667\pi$
$733$	−6.99732	−	21.5355i	−0.258452	−	0.795433i	0.734678	−	0.678416i	$-0.237333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.67828	+	6.30514i	0.319668	+	0.232253i
$738$		0			0
$739$	20.7764	−	15.0949i	0.764272	−	0.555276i	−0.135946	−	0.990716i	$-0.543407\pi$
$739$	20.7764	−	15.0949i	0.764272	−	0.555276i	0.900218	+	0.435440i	$0.143407\pi$
$740$		0			0
$741$	−0.0576792	−	0.0419064i	−0.00211890	−	0.00153947i
$742$		0			0
$743$	−24.9796			−0.916411			−0.458205	−	0.888846i	$-0.651508\pi$
$743$	−24.9796			−0.916411			−0.458205	+	0.888846i	$0.651508\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.439947	−	1.35402i	0.0160968	−	0.0495409i
$748$		0			0
$749$	−54.5321			−1.99256
$750$		0			0
$751$	17.9383			0.654580			0.327290	−	0.944924i	$-0.393865\pi$
$751$	17.9383			0.654580			0.327290	+	0.944924i	$0.393865\pi$
$752$		0			0
$753$	6.05083	−	18.6225i	0.220504	−	0.678643i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−9.91474			−0.360357			−0.180179	−	0.983634i	$-0.557668\pi$
$757$	−9.91474			−0.360357			−0.180179	+	0.983634i	$0.557668\pi$
$758$		0			0
$759$	−4.09565	−	2.97566i	−0.148663	−	0.108010i
$760$		0			0
$761$	25.6076	−	18.6050i	0.928273	−	0.674430i	−0.0172961	−	0.999850i	$-0.505506\pi$
$761$	25.6076	−	18.6050i	0.928273	−	0.674430i	0.945569	+	0.325420i	$0.105506\pi$
$762$		0			0
$763$	17.6579	+	12.8292i	0.639259	+	0.464449i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.7954	+	51.6910i	0.606447	+	1.86645i
$768$		0			0
$769$	6.91430	+	21.2800i	0.249336	+	0.767377i	0.994893	+	0.100935i	$0.0321836\pi$
$769$	6.91430	+	21.2800i	0.249336	+	0.767377i	−0.745557	+	0.666442i	$0.767816\pi$
$770$		0			0
$771$	−1.84801	+	5.68760i	−0.0665546	+	0.204834i
$772$		0			0
$773$	38.6967	−	28.1148i	1.39182	−	1.01122i	0.396160	−	0.918182i	$-0.370343\pi$
$773$	38.6967	−	28.1148i	1.39182	−	1.01122i	0.995663	−	0.0930367i	$-0.0296574\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	26.1774	−	19.0190i	0.939108	−	0.682302i
$778$		0			0
$779$	0.0533399	−	0.164163i	0.00191110	−	0.00588176i
$780$		0			0
$781$	1.22626	+	3.77405i	0.0438792	+	0.135046i
$782$		0			0
$783$	1.14365	+	3.51978i	0.0408706	+	0.125787i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	22.3026	+	16.2038i	0.795002	+	0.577603i	0.909444	−	0.415827i	$-0.136508\pi$
$787$	22.3026	+	16.2038i	0.795002	+	0.577603i	−0.114442	+	0.993430i	$0.536508\pi$
$788$		0			0
$789$	−4.91104	+	3.56808i	−0.174838	+	0.127027i
$790$		0			0
$791$	−54.9375	−	39.9144i	−1.95335	−	1.41919i
$792$		0			0
$793$	14.9235			0.529948
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.13887	+	21.9712i	−0.252872	+	0.778260i	0.741370	+	0.671097i	$0.234177\pi$
$797$	−7.13887	+	21.9712i	−0.252872	+	0.778260i	−0.994241	+	0.107163i	$0.965823\pi$
$798$		0			0
$799$	0.604617			0.0213898
$800$		0			0
$801$	−16.1067			−0.569103
$802$		0			0
$803$	1.16772	−	3.59386i	0.0412078	−	0.126825i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.61605			0.338501
$808$		0			0
$809$	1.36960	+	0.995071i	0.0481525	+	0.0349848i	0.611601	−	0.791166i	$-0.290526\pi$
$809$	1.36960	+	0.995071i	0.0481525	+	0.0349848i	−0.563449	+	0.826151i	$0.690526\pi$
$810$		0			0
$811$	−16.6435	+	12.0922i	−0.584434	+	0.424616i	−0.840320	−	0.542091i	$-0.817633\pi$
$811$	−16.6435	+	12.0922i	−0.584434	+	0.424616i	0.255886	+	0.966707i	$0.417633\pi$
$812$		0			0
$813$	24.6164	+	17.8849i	0.863335	+	0.627250i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.0475272	+	0.146274i	0.00166277	+	0.00511746i
$818$		0			0
$819$	5.55967	+	17.1109i	0.194271	+	0.597904i
$820$		0			0
$821$	−14.2235	+	43.7754i	−0.496403	+	1.52777i	0.318356	+	0.947971i	$0.396869\pi$
$821$	−14.2235	+	43.7754i	−0.496403	+	1.52777i	−0.814759	+	0.579800i	$0.803131\pi$
$822$		0			0
$823$	−45.2942	+	32.9082i	−1.57886	+	1.14711i	−0.660868	+	0.750502i	$0.729812\pi$
$823$	−45.2942	+	32.9082i	−1.57886	+	1.14711i	−0.917990	+	0.396605i	$0.870188\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.6981	+	12.1319i	−0.580648	+	0.421866i	−0.838958	−	0.544196i	$-0.816835\pi$
$827$	−16.6981	+	12.1319i	−0.580648	+	0.421866i	0.258309	+	0.966062i	$0.416835\pi$
$828$		0			0
$829$	−0.599179	+	1.84408i	−0.0208103	+	0.0640476i	−0.960922	−	0.276818i	$-0.910720\pi$
$829$	−0.599179	+	1.84408i	−0.0208103	+	0.0640476i	0.940112	+	0.340866i	$0.110720\pi$
$830$		0			0
$831$	−2.22614	−	6.85134i	−0.0772238	−	0.237670i
$832$		0			0
$833$	−2.60919	−	8.03026i	−0.0904030	−	0.278232i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.27994	+	0.929930i	0.0442412	+	0.0321431i
$838$		0			0
$839$	−42.2783	+	30.7170i	−1.45961	+	1.06047i	−0.476146	+	0.879366i	$0.657966\pi$
$839$	−42.2783	+	30.7170i	−1.45961	+	1.06047i	−0.983464	+	0.181102i	$0.942034\pi$
$840$		0			0
$841$	12.3806	+	8.99501i	0.426916	+	0.310173i
$842$		0			0
$843$	29.7964			1.02624
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.1128	+	37.2793i	−0.416200	+	1.28093i
$848$		0			0
$849$	8.82402			0.302840
$850$		0			0
$851$	53.5397			1.83532
$852$		0			0
$853$	−5.42649	+	16.7010i	−0.185799	+	0.571832i	−0.999961	−	0.00880614i	$-0.997197\pi$
$853$	−5.42649	+	16.7010i	−0.185799	+	0.571832i	0.814162	+	0.580638i	$0.197197\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	50.9890			1.74175			0.870876	−	0.491503i	$-0.163552\pi$
$857$	50.9890			1.74175			0.870876	+	0.491503i	$0.163552\pi$
$858$		0			0
$859$	−15.0749	−	10.9525i	−0.514349	−	0.373696i	0.300122	−	0.953901i	$-0.402973\pi$
$859$	−15.0749	−	10.9525i	−0.514349	−	0.373696i	−0.814471	+	0.580205i	$0.802973\pi$
$860$		0			0
$861$	−35.2397	+	25.6032i	−1.20097	+	0.872553i
$862$		0			0
$863$	−0.236347	−	0.171716i	−0.00804536	−	0.00584529i	0.583755	−	0.811930i	$-0.301583\pi$
$863$	−0.236347	−	0.171716i	−0.00804536	−	0.00584529i	−0.591801	+	0.806084i	$0.701583\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.84543	−	14.9127i	−0.164560	−	0.506462i
$868$		0			0
$869$	−2.31405	−	7.12192i	−0.0784989	−	0.241595i
$870$		0			0
$871$	19.4925	−	59.9917i	0.660477	−	2.03274i
$872$		0			0
$873$	−6.52232	+	4.73874i	−0.220747	+	0.160382i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	30.7106	−	22.3126i	1.03702	−	0.753442i	0.0673215	−	0.997731i	$-0.478555\pi$
$877$	30.7106	−	22.3126i	1.03702	−	0.753442i	0.969702	+	0.244289i	$0.0785547\pi$
$878$		0			0
$879$	−1.30017	+	4.00150i	−0.0438535	+	0.134967i
$880$		0			0
$881$	−11.3378	−	34.8942i	−0.381981	−	1.17562i	−0.938647	−	0.344879i	$-0.887920\pi$
$881$	−11.3378	−	34.8942i	−0.381981	−	1.17562i	0.556666	−	0.830736i	$-0.312080\pi$
$882$		0			0
$883$	−6.98993	−	21.5128i	−0.235230	−	0.723964i	−0.997091	−	0.0762228i	$-0.975714\pi$
$883$	−6.98993	−	21.5128i	−0.235230	−	0.723964i	0.761861	−	0.647741i	$-0.224286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.7708	+	14.3643i	0.663838	+	0.482306i	0.867957	−	0.496640i	$-0.165433\pi$
$887$	19.7708	+	14.3643i	0.663838	+	0.482306i	−0.204119	+	0.978946i	$0.565433\pi$
$888$		0			0
$889$	7.01741	−	5.09845i	0.235356	−	0.170996i
$890$		0			0
$891$	0.653426	+	0.474742i	0.0218906	+	0.0159044i
$892$		0			0
$893$	−0.00790011			−0.000264367
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−9.19934	+	28.3126i	−0.307157	+	0.945332i
$898$		0			0
$899$	−5.85519			−0.195281
$900$		0			0
$901$	3.38882			0.112898
$902$		0			0
$903$	11.9935	−	36.9123i	0.399120	−	1.22836i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	32.7792			1.08842			0.544208	−	0.838950i	$-0.316830\pi$
$907$	32.7792			1.08842			0.544208	+	0.838950i	$0.316830\pi$
$908$		0			0
$909$	−9.42474	−	6.84747i	−0.312599	−	0.227116i
$910$		0			0
$911$	−22.0778	+	16.0405i	−0.731470	+	0.531444i	−0.890028	−	0.455906i	$-0.849315\pi$
$911$	−22.0778	+	16.0405i	−0.731470	+	0.531444i	0.158558	+	0.987350i	$0.449315\pi$
$912$		0			0
$913$	0.930280	+	0.675888i	0.0307878	+	0.0223686i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.25197	−	25.3970i	−0.272504	−	0.838681i
$918$		0			0
$919$	−12.8923	−	39.6783i	−0.425277	−	1.30887i	−0.902729	−	0.430209i	$-0.858440\pi$
$919$	−12.8923	−	39.6783i	−0.425277	−	1.30887i	0.477453	−	0.878658i	$-0.341560\pi$
$920$		0			0
$921$	1.36310	−	4.19520i	0.0449158	−	0.138236i
$922$		0			0
$923$	18.8785	−	13.7161i	0.621394	−	0.451469i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.2450	+	11.0761i	−0.500711	+	0.363788i
$928$		0			0
$929$	−10.4151	+	32.0542i	−0.341707	+	1.05167i	0.621616	+	0.783322i	$0.286476\pi$
$929$	−10.4151	+	32.0542i	−0.341707	+	1.05167i	−0.963323	+	0.268344i	$0.913524\pi$
$930$		0			0
$931$	0.0340925	+	0.104926i	0.00111734	+	0.00343880i
$932$		0			0
$933$	−1.95317	−	6.01123i	−0.0639438	−	0.196799i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.846278	+	0.614857i	0.0276467	+	0.0200865i	0.601523	−	0.798856i	$-0.294561\pi$
$937$	0.846278	+	0.614857i	0.0276467	+	0.0200865i	−0.573876	+	0.818942i	$0.694561\pi$
$938$		0			0
$939$	12.3978	−	9.00753i	0.404587	−	0.293950i
$940$		0			0
$941$	−4.62928	−	3.36337i	−0.150910	−	0.109643i	0.509768	−	0.860312i	$-0.329731\pi$
$941$	−4.62928	−	3.36337i	−0.150910	−	0.109643i	−0.660678	+	0.750669i	$0.729731\pi$
$942$		0			0
$943$	−72.0746			−2.34707
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.89200	−	11.9783i	0.126473	−	0.389244i	−0.867694	−	0.497099i	$-0.834398\pi$
$947$	3.89200	−	11.9783i	0.126473	−	0.389244i	0.994167	+	0.107856i	$0.0343984\pi$
$948$		0			0
$949$	−22.2210			−0.721325
$950$		0			0
$951$	−21.3155			−0.691204
$952$		0			0
$953$	17.7346	−	54.5813i	0.574479	−	1.76806i	−0.0634695	−	0.997984i	$-0.520217\pi$
$953$	17.7346	−	54.5813i	0.574479	−	1.76806i	0.637948	−	0.770079i	$-0.279783\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.98915			−0.0966255
$958$		0			0
$959$	67.2161	+	48.8353i	2.17052	+	1.57698i
$960$		0			0
$961$	23.0545	−	16.7501i	0.743695	−	0.540326i
$962$		0			0
$963$	11.6464	+	8.46158i	0.375299	+	0.272671i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.73236	+	8.40935i	0.0878669	+	0.270427i	0.985329	−	0.170665i	$-0.0545915\pi$
$967$	2.73236	+	8.40935i	0.0878669	+	0.270427i	−0.897462	+	0.441091i	$0.854591\pi$
$968$		0			0
$969$	−0.00532915	−	0.0164014i	−0.000171197	−	0.000526890i
$970$		0			0
$971$	16.0493	−	49.3945i	0.515045	−	1.58515i	−0.268155	−	0.963376i	$-0.586414\pi$
$971$	16.0493	−	49.3945i	0.515045	−	1.58515i	0.783200	−	0.621770i	$-0.213586\pi$
$972$		0			0
$973$	−29.7808	+	21.6370i	−0.954729	+	0.693651i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.1234	+	21.8859i	−0.963732	+	0.700193i	−0.954015	−	0.299760i	$-0.903093\pi$
$977$	−30.1234	+	21.8859i	−0.963732	+	0.700193i	−0.00971780	+	0.999953i	$0.503093\pi$
$978$		0			0
$979$	4.02002	−	12.3724i	0.128480	−	0.395422i
$980$		0			0
$981$	−1.78051	−	5.47985i	−0.0568473	−	0.174958i
$982$		0			0
$983$	11.0507	+	34.0107i	0.352464	+	1.08477i	0.957465	+	0.288548i	$0.0931726\pi$
$983$	11.0507	+	34.0107i	0.352464	+	1.08477i	−0.605001	+	0.796225i	$0.706827\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.61286	+	1.17181i	0.0513378	+	0.0372991i
$988$		0			0
$989$	51.9553	−	37.7477i	1.65208	−	1.20031i
$990$		0			0
$991$	35.4505	+	25.7563i	1.12612	+	0.818175i	0.985126	−	0.171835i	$-0.0549697\pi$
$991$	35.4505	+	25.7563i	1.12612	+	0.818175i	0.140996	+	0.990010i	$0.454970\pi$
$992$		0			0
$993$	19.8124			0.628728
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.2087	−	37.5746i	0.386654	−	1.19000i	−0.548619	−	0.836072i	$-0.684846\pi$
$997$	12.2087	−	37.5746i	0.386654	−	1.19000i	0.935273	−	0.353927i	$-0.115154\pi$
$998$		0			0
$999$	−8.54179			−0.270250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.c.301.5		24
5.2	odd	4		1500.2.o.c.949.1		24
5.3	odd	4		300.2.o.a.289.5	yes	24
5.4	even	2		1500.2.m.d.301.2		24
15.8	even	4		900.2.w.c.289.4		24
25.3	odd	20		7500.2.d.g.1249.16		24
25.4	even	10		7500.2.a.m.1.4		12
25.9	even	10		1500.2.m.d.1201.2		24
25.12	odd	20		300.2.o.a.109.5	✓	24
25.13	odd	20		1500.2.o.c.49.1		24
25.16	even	5	inner	1500.2.m.c.1201.5		24
25.21	even	5		7500.2.a.n.1.9		12
25.22	odd	20		7500.2.d.g.1249.9		24
75.62	even	20		900.2.w.c.109.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.5	✓	24	25.12	odd	20
300.2.o.a.289.5	yes	24	5.3	odd	4
900.2.w.c.109.4		24	75.62	even	20
900.2.w.c.289.4		24	15.8	even	4
1500.2.m.c.301.5		24	1.1	even	1	trivial
1500.2.m.c.1201.5		24	25.16	even	5	inner
1500.2.m.d.301.2		24	5.4	even	2
1500.2.m.d.1201.2		24	25.9	even	10
1500.2.o.c.49.1		24	25.13	odd	20
1500.2.o.c.949.1		24	5.2	odd	4
7500.2.a.m.1.4		12	25.4	even	10
7500.2.a.n.1.9		12	25.21	even	5
7500.2.d.g.1249.9		24	25.22	odd	20
7500.2.d.g.1249.16		24	25.3	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +3.78808 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{3} +3.78808 q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.653426 - 0.474742i) q^{11} +(-3.84242 - 2.79168i) q^{13} +(-0.355012 - 1.09262i) q^{17} +(0.00463870 + 0.0142765i) q^{19} +(1.17058 - 3.60268i) q^{21} +(5.07089 - 3.68422i) q^{23} +(-0.809017 + 0.587785i) q^{27} +(1.14365 - 3.51978i) q^{29} +(-0.488893 - 1.50466i) q^{31} +(-0.249586 - 0.768148i) q^{33} +(6.91045 + 5.02074i) q^{37} +(-3.84242 + 2.79168i) q^{39} +(-9.30279 - 6.75887i) q^{41} +10.2458 q^{43} +(-0.162630 + 0.500524i) q^{47} +7.34957 q^{49} -1.14884 q^{51} +(-0.911527 + 2.80539i) q^{53} +0.0150112 q^{57} +(-9.25803 - 6.72635i) q^{59} +(-2.54203 + 1.84689i) q^{61} +(-3.06462 - 2.22658i) q^{63} +(4.10412 + 12.6312i) q^{67} +(-1.93691 - 5.96119i) q^{69} +(-1.51826 + 4.67271i) q^{71} +(3.78507 - 2.75001i) q^{73} +(2.47523 - 1.79836i) q^{77} +(2.86507 - 8.81777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.439947 + 1.35402i) q^{83} +(-2.99410 - 2.17534i) q^{87} +(13.0306 - 9.46730i) q^{89} +(-14.5554 - 10.5751i) q^{91} -1.58209 q^{93} +(2.49130 - 7.66744i) q^{97} -0.807679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 16 * q^7 - 6 * q^9	\( 24 q - 6 q^{3} + 16 q^{7} - 6 q^{9} - 6 q^{11} - 4 q^{17} - 10 q^{19} - 4 q^{21} - 14 q^{23} - 6 q^{27} - 4 q^{29} + 6 q^{31} + 4 q^{33} + 8 q^{37} - 10 q^{41} + 56 q^{43} - 26 q^{47} + 56 q^{49} + 16 q^{51} + 32 q^{53} + 20 q^{57} + 36 q^{59} - 12 q^{61} - 4 q^{63} - 36 q^{67} - 4 q^{69} + 40 q^{71} - 32 q^{73} + 46 q^{77} - 8 q^{79} - 6 q^{81} + 6 q^{83} - 4 q^{87} - 30 q^{91} - 4 q^{93} - 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 16 * q^7 - 6 * q^9 - 6 * q^11 - 4 * q^17 - 10 * q^19 - 4 * q^21 - 14 * q^23 - 6 * q^27 - 4 * q^29 + 6 * q^31 + 4 * q^33 + 8 * q^37 - 10 * q^41 + 56 * q^43 - 26 * q^47 + 56 * q^49 + 16 * q^51 + 32 * q^53 + 20 * q^57 + 36 * q^59 - 12 * q^61 - 4 * q^63 - 36 * q^67 - 4 * q^69 + 40 * q^71 - 32 * q^73 + 46 * q^77 - 8 * q^79 - 6 * q^81 + 6 * q^83 - 4 * q^87 - 30 * q^91 - 4 * q^93 - 48 * q^97 + 4 * q^99

Introduction

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