LMFDB - Embedded newform 1050.2.s.i.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(101,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1050.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.s (of order $6$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Root			$-0.159959 - 0.596975i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.i.551.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(1.40294 - 1.01575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(0.936492 - 2.85008i) q^{9} +(4.05781 + 2.34278i) q^{11} +(-0.178197 - 1.72286i) q^{12} +1.04456i q^{13} +(1.22938 - 2.34278i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.58114 + 2.73861i) q^{17} +(-0.614017 - 2.93649i) q^{18} +(1.23861 - 0.715113i) q^{19} +(1.70058 - 4.25535i) q^{21} +4.68556 q^{22} +(-3.87739 + 2.23861i) q^{23} +(-1.01575 - 1.40294i) q^{24} +(0.522278 + 0.904612i) q^{26} +(-1.58114 - 4.94975i) q^{27} +(-0.106711 - 2.64360i) q^{28} +6.92163i q^{29} +(-5.73861 - 3.31319i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.07256 - 0.834952i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(-1.33146 - 2.30615i) q^{37} +(0.715113 - 1.23861i) q^{38} +(1.06101 + 1.46545i) q^{39} +1.04456 q^{41} +(-0.654929 - 4.53553i) q^{42} -6.92163 q^{43} +(4.05781 - 2.34278i) q^{44} +(-2.23861 + 3.87739i) q^{46} +(-5.60944 - 9.71584i) q^{47} +(-1.58114 - 0.707107i) q^{48} +(3.00000 - 6.32456i) q^{49} +(0.563508 + 5.44816i) q^{51} +(0.904612 + 0.522278i) q^{52} +(4.33013 + 2.50000i) q^{53} +(-3.84418 - 3.49604i) q^{54} +(-1.41421 - 2.23607i) q^{56} +(1.01132 - 2.26139i) q^{57} +(3.46081 + 5.99430i) q^{58} +(-5.28720 + 9.15769i) q^{59} +(3.00000 - 1.73205i) q^{61} -6.62638 q^{62} +(-1.93657 - 7.69738i) q^{63} -1.00000 q^{64} +(6.57357 - 4.75937i) q^{66} +(7.13505 - 12.3583i) q^{67} +(1.58114 + 2.73861i) q^{68} +(-3.16588 + 7.07912i) q^{69} +6.92163i q^{71} +(-2.85008 - 0.936492i) q^{72} +(3.03397 + 1.75166i) q^{73} +(-2.30615 - 1.33146i) q^{74} -1.43023i q^{76} +(12.3867 - 0.500000i) q^{77} +(1.65159 + 0.738613i) q^{78} +(5.73861 + 9.93957i) q^{79} +(-7.24597 - 5.33816i) q^{81} +(0.904612 - 0.522278i) q^{82} -4.06775 q^{83} +(-2.83495 - 3.60042i) q^{84} +(-5.99430 + 3.46081i) q^{86} +(7.03066 + 9.71064i) q^{87} +(2.34278 - 4.05781i) q^{88} +(-2.45877 - 4.25871i) q^{89} +(1.47723 + 2.33570i) q^{91} +4.47723i q^{92} +(-11.4163 + 1.18080i) q^{93} +(-9.71584 - 5.60944i) q^{94} +(-1.72286 + 0.178197i) q^{96} +11.9886i q^{97} +(-0.564201 - 6.97723i) q^{98} +(10.4772 - 9.37112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 16 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{21} - 48 q^{31} - 32 q^{36} + 16 q^{39} + 8 q^{46} + 48 q^{49} + 40 q^{51} + 48 q^{61} - 16 q^{64} + 24 q^{66} + 48 q^{79} + 8 q^{81} - 8 q^{84} - 64 q^{91}+ \cdots + 80 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 16 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^21 - 48 * q^31 - 32 * q^36 + 16 * q^39 + 8 * q^46 + 48 * q^49 + 40 * q^51 + 48 * q^61 - 16 * q^64 + 24 * q^66 + 48 * q^79 + 8 * q^81 - 8 * q^84 - 64 * q^91 - 24 * q^94 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.40294	−	1.01575i	0.809989	−	0.586445i
$3$	1.40294	−	1.01575i	0.809989	−	0.586445i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.707107	−	1.58114i	0.288675	−	0.645497i
$7$	2.23607	−	1.41421i	0.845154	−	0.534522i
$7$	2.23607	−	1.41421i	0.845154	−	0.534522i
$8$		−	1.00000i		−	0.353553i
$9$	0.936492	−	2.85008i	0.312164	−	0.950028i
$10$		0			0
$11$	4.05781	+	2.34278i	1.22348	+	0.706374i	0.965657	−	0.259819i	$-0.0836628\pi$
$11$	4.05781	+	2.34278i	1.22348	+	0.706374i	0.257819	+	0.966193i	$0.416996\pi$
$12$	−0.178197	−	1.72286i	−0.0514410	−	0.497347i
$13$			1.04456i			0.289708i	0.989453	+	0.144854i	$0.0462712\pi$
$13$			1.04456i			0.289708i	−0.989453	+	0.144854i	$0.953729\pi$
$14$	1.22938	−	2.34278i	0.328567	−	0.626134i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.58114	+	2.73861i	−0.383482	+	0.664211i	−0.991557	−	0.129668i	$-0.958609\pi$
$17$	−1.58114	+	2.73861i	−0.383482	+	0.664211i	0.608075	+	0.793880i	$0.291942\pi$
$18$	−0.614017	−	2.93649i	−0.144725	−	0.692138i
$19$	1.23861	−	0.715113i	0.284157	−	0.164058i	−0.351147	−	0.936320i	$-0.614208\pi$
$19$	1.23861	−	0.715113i	0.284157	−	0.164058i	0.635304	+	0.772262i	$0.280875\pi$
$20$		0			0
$21$	1.70058	−	4.25535i	0.371097	−	0.928594i
$22$	4.68556			0.998964
$23$	−3.87739	+	2.23861i	−0.808492	+	0.466783i	−0.846432	−	0.532497i	$-0.821254\pi$
$23$	−3.87739	+	2.23861i	−0.808492	+	0.466783i	0.0379400	+	0.999280i	$0.487920\pi$
$24$	−1.01575	−	1.40294i	−0.207340	−	0.286374i
$25$		0			0
$26$	0.522278	+	0.904612i	0.102427	+	0.177409i
$27$	−1.58114	−	4.94975i	−0.304290	−	0.952579i
$28$	−0.106711	−	2.64360i	−0.0201665	−	0.499593i
$29$			6.92163i			1.28531i	0.766154	+	0.642657i	$0.222168\pi$
$29$			6.92163i			1.28531i	−0.766154	+	0.642657i	$0.777832\pi$
$30$		0			0
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.113504	−	0.993537i	$-0.536208\pi$
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.917181	+	0.398471i	$0.869541\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	8.07256	−	0.834952i	1.40525	−	0.145347i
$34$			3.16228i			0.542326i
$35$		0			0
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$	−1.33146	−	2.30615i	−0.218890	−	0.379129i	0.735579	−	0.677439i	$-0.236910\pi$
$37$	−1.33146	−	2.30615i	−0.218890	−	0.379129i	−0.954469	+	0.298310i	$0.903577\pi$
$38$	0.715113	−	1.23861i	0.116007	−	0.200930i
$39$	1.06101	+	1.46545i	0.169898	+	0.234660i
$40$		0			0
$41$	1.04456			0.163132			0.0815661	−	0.996668i	$-0.474008\pi$
$41$	1.04456			0.163132			0.0815661	+	0.996668i	$0.474008\pi$
$42$	−0.654929	−	4.53553i	−0.101058	−	0.699848i
$43$	−6.92163			−1.05554			−0.527769	−	0.849388i	$-0.676971\pi$
$43$	−6.92163			−1.05554			−0.527769	+	0.849388i	$0.676971\pi$
$44$	4.05781	−	2.34278i	0.611738	−	0.353187i
$45$		0			0
$46$	−2.23861	+	3.87739i	−0.330065	+	0.571690i
$47$	−5.60944	−	9.71584i	−0.818221	−	1.41720i	−0.906992	−	0.421149i	$-0.861627\pi$
$47$	−5.60944	−	9.71584i	−0.818221	−	1.41720i	0.0887705	−	0.996052i	$-0.471706\pi$
$48$	−1.58114	−	0.707107i	−0.228218	−	0.102062i
$49$	3.00000	−	6.32456i	0.428571	−	0.903508i
$50$		0			0
$51$	0.563508	+	5.44816i	0.0789069	+	0.762895i
$52$	0.904612	+	0.522278i	0.125447	+	0.0724269i
$53$	4.33013	+	2.50000i	0.594789	+	0.343401i	0.766989	−	0.641661i	$-0.221754\pi$
$53$	4.33013	+	2.50000i	0.594789	+	0.343401i	−0.172200	+	0.985062i	$0.555088\pi$
$54$	−3.84418	−	3.49604i	−0.523127	−	0.475750i
$55$		0			0
$56$	−1.41421	−	2.23607i	−0.188982	−	0.298807i
$57$	1.01132	−	2.26139i	0.133953	−	0.299528i
$58$	3.46081	+	5.99430i	0.454427	+	0.787091i
$59$	−5.28720	+	9.15769i	−0.688334	+	1.19223i	0.284042	+	0.958812i	$0.408324\pi$
$59$	−5.28720	+	9.15769i	−0.688334	+	1.19223i	−0.972376	+	0.233418i	$0.925009\pi$
$60$		0			0
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	−0.295495	−	0.955344i	$-0.595484\pi$
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	0.679605	+	0.733578i	$0.262151\pi$
$62$	−6.62638			−0.841551
$63$	−1.93657	−	7.69738i	−0.243985	−	0.969779i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.57357	−	4.75937i	0.809150	−	0.585838i
$67$	7.13505	−	12.3583i	0.871685	−	1.50980i	0.0114319	−	0.999935i	$-0.496361\pi$
$67$	7.13505	−	12.3583i	0.871685	−	1.50980i	0.860253	−	0.509868i	$-0.170306\pi$
$68$	1.58114	+	2.73861i	0.191741	+	0.332106i
$69$	−3.16588	+	7.07912i	−0.381127	+	0.852225i
$70$		0			0
$71$			6.92163i			0.821446i	0.911760	+	0.410723i	$0.134724\pi$
$71$			6.92163i			0.821446i	−0.911760	+	0.410723i	$0.865276\pi$
$72$	−2.85008	−	0.936492i	−0.335886	−	0.110367i
$73$	3.03397	+	1.75166i	0.355099	+	0.205017i	0.666929	−	0.745121i	$-0.267608\pi$
$73$	3.03397	+	1.75166i	0.355099	+	0.205017i	−0.311830	+	0.950138i	$0.600942\pi$
$74$	−2.30615	−	1.33146i	−0.268084	−	0.154779i
$75$		0			0
$76$		−	1.43023i		−	0.164058i
$77$	12.3867	−	0.500000i	1.41160	−	0.0569803i
$78$	1.65159	+	0.738613i	0.187006	+	0.0836314i
$79$	5.73861	+	9.93957i	0.645644	+	1.11829i	0.984152	+	0.177325i	$0.0567445\pi$
$79$	5.73861	+	9.93957i	0.645644	+	1.11829i	−0.338508	+	0.940964i	$0.609922\pi$
$80$		0			0
$81$	−7.24597	−	5.33816i	−0.805107	−	0.593129i
$82$	0.904612	−	0.522278i	0.0998977	−	0.0576760i
$83$	−4.06775			−0.446494			−0.223247	−	0.974762i	$-0.571666\pi$
$83$	−4.06775			−0.446494			−0.223247	+	0.974762i	$0.571666\pi$
$84$	−2.83495	−	3.60042i	−0.309319	−	0.392838i
$85$		0			0
$86$	−5.99430	+	3.46081i	−0.646382	+	0.373189i
$87$	7.03066	+	9.71064i	0.753766	+	1.04109i
$88$	2.34278	−	4.05781i	0.249741	−	0.432564i
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	0.705780	−	0.708431i	$-0.250597\pi$
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	−0.966409	+	0.257008i	$0.917263\pi$
$90$		0			0
$91$	1.47723	+	2.33570i	0.154855	+	0.244848i
$92$			4.47723i			0.466783i
$93$	−11.4163	+	1.18080i	−1.18382	+	0.122443i
$94$	−9.71584	−	5.60944i	−1.00211	−	0.578570i
$95$		0			0
$96$	−1.72286	+	0.178197i	−0.175839	+	0.0181872i
$97$			11.9886i			1.21726i	0.793455	+	0.608629i	$0.208280\pi$
$97$			11.9886i			1.21726i	−0.793455	+	0.608629i	$0.791720\pi$
$98$	−0.564201	−	6.97723i	−0.0569930	−	0.704806i
$99$	10.4772	−	9.37112i	1.05300	−	0.941833i
$100$		0			0
$101$	−5.65685	+	9.79796i	−0.562878	+	0.974933i	0.434366	+	0.900737i	$0.356973\pi$
$101$	−5.65685	+	9.79796i	−0.562878	+	0.974933i	−0.997244	+	0.0741967i	$0.976361\pi$
$102$	3.21209	+	4.43649i	0.318045	+	0.439278i
$103$	4.25871	−	2.45877i	0.419624	−	0.242270i	−0.275293	−	0.961360i	$-0.588775\pi$
$103$	4.25871	−	2.45877i	0.419624	−	0.242270i	0.694916	+	0.719091i	$0.255441\pi$
$104$	1.04456			0.102427
$105$		0			0
$106$	5.00000			0.485643
$107$	−4.74342	+	2.73861i	−0.458563	+	0.264752i	−0.711440	−	0.702747i	$-0.751957\pi$
$107$	−4.74342	+	2.73861i	−0.458563	+	0.264752i	0.252877	+	0.967499i	$0.418623\pi$
$108$	−5.07718	−	1.10557i	−0.488552	−	0.106383i
$109$	−10.2158	+	17.6944i	−0.978500	+	1.69481i	−0.310634	+	0.950529i	$0.600541\pi$
$109$	−10.2158	+	17.6944i	−0.978500	+	1.69481i	−0.667866	+	0.744282i	$0.732792\pi$
$110$		0			0
$111$	−4.21043	−	1.88296i	−0.399637	−	0.178723i
$112$	−2.34278	−	1.22938i	−0.221372	−	0.116166i
$113$		−	17.4772i		−	1.64412i	−0.569402	−	0.822060i	$-0.692825\pi$
$113$		−	17.4772i		−	1.64412i	0.569402	−	0.822060i	$-0.307175\pi$
$114$	−0.254862	−	2.46408i	−0.0238700	−	0.230782i
$115$		0			0
$116$	5.99430	+	3.46081i	0.556557	+	0.321328i
$117$	2.97707	+	0.978218i	0.275231	+	0.0904363i
$118$			10.5744i			0.973452i
$119$	0.337449	+	8.35979i	0.0309339	+	0.766341i
$120$		0			0
$121$	5.47723	+	9.48683i	0.497930	+	0.862439i
$122$	1.73205	−	3.00000i	0.156813	−	0.271607i
$123$	1.46545	−	1.06101i	0.132135	−	0.0956682i
$124$	−5.73861	+	3.31319i	−0.515343	+	0.297533i
$125$		0			0
$126$	−5.52581	−	5.69784i	−0.492278	−	0.507604i
$127$	−8.73085			−0.774738			−0.387369	−	0.921925i	$-0.626616\pi$
$127$	−8.73085			−0.774738			−0.387369	+	0.921925i	$0.626616\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−9.71064	+	7.03066i	−0.854974	+	0.619015i
$130$		0			0
$131$	6.88624	+	11.9273i	0.601654	+	1.04209i	0.992571	+	0.121669i	$0.0388245\pi$
$131$	6.88624	+	11.9273i	0.601654	+	1.04209i	−0.390917	+	0.920426i	$0.627842\pi$
$132$	3.31319	−	7.40852i	0.288376	−	0.644829i
$133$	1.75830	−	3.35071i	0.152464	−	0.290543i
$134$		−	14.2701i		−	1.23275i
$135$		0			0
$136$	2.73861	+	1.58114i	0.234834	+	0.135582i
$137$	3.01137	+	1.73861i	0.257278	+	0.148540i	0.623092	−	0.782148i	$-0.285876\pi$
$137$	3.01137	+	1.73861i	0.257278	+	0.148540i	−0.365814	+	0.930688i	$0.619209\pi$
$138$	0.797828	+	7.71363i	0.0679156	+	0.656628i
$139$		−	20.1810i		−	1.71173i	−0.517202	−	0.855863i	$-0.673026\pi$
$139$		−	20.1810i		−	1.71173i	0.517202	−	0.855863i	$-0.326974\pi$
$140$		0			0
$141$	−17.7386	−	7.93295i	−1.49386	−	0.668075i
$142$	3.46081	+	5.99430i	0.290425	+	0.503031i
$143$	−2.44716	+	4.23861i	−0.204642	+	0.354451i
$144$	−2.93649	+	0.614017i	−0.244708	+	0.0511681i
$145$		0			0
$146$	3.50333			0.289937
$147$	−2.21536	−	11.9202i	−0.182720	−	0.983165i
$148$	−2.66291			−0.218890
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	−0.584370	−	0.811488i	$-0.698658\pi$
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	0.410584	+	0.911823i	$0.365325\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−0.715113	−	1.23861i	−0.0580034	−	0.100465i
$153$	6.32456	+	7.07107i	0.511310	+	0.571662i
$154$	10.4772	−	6.62638i	0.844279	−	0.533969i
$155$		0			0
$156$	1.79962	−	0.186137i	0.144085	−	0.0149029i
$157$	−12.5118	−	7.22369i	−0.998550	−	0.576513i	−0.0907311	−	0.995875i	$-0.528920\pi$
$157$	−12.5118	−	7.22369i	−0.998550	−	0.576513i	−0.907819	+	0.419362i	$0.862254\pi$
$158$	9.93957	+	5.73861i	0.790750	+	0.456540i
$159$	8.61430	−	0.890985i	0.683158	−	0.0706597i
$160$		0			0
$161$	−5.50423	+	10.4891i	−0.433794	+	0.826661i
$162$	−8.94427	−	1.00000i	−0.702728	−	0.0785674i
$163$	7.34847	+	12.7279i	0.575577	+	0.996928i	0.995979	+	0.0895899i	$0.0285557\pi$
$163$	7.34847	+	12.7279i	0.575577	+	0.996928i	−0.420402	+	0.907338i	$0.638111\pi$
$164$	0.522278	−	0.904612i	0.0407831	−	0.0706383i
$165$		0			0
$166$	−3.52277	+	2.03387i	−0.273420	+	0.157859i
$167$	4.29068			0.332023			0.166011	−	0.986124i	$-0.446911\pi$
$167$	4.29068			0.332023			0.166011	+	0.986124i	$0.446911\pi$
$168$	−4.25535	−	1.70058i	−0.328308	−	0.131203i
$169$	11.9089			0.916069
$170$		0			0
$171$	−0.878183	−	4.19985i	−0.0671564	−	0.321170i
$172$	−3.46081	+	5.99430i	−0.263885	+	0.457061i
$173$	−0.564201	−	0.977226i	−0.0428954	−	0.0742971i	0.843781	−	0.536688i	$-0.180325\pi$
$173$	−0.564201	−	0.977226i	−0.0428954	−	0.0742971i	−0.886676	+	0.462391i	$0.846992\pi$
$174$	10.9441	+	4.89433i	0.829666	+	0.371038i
$175$		0			0
$176$		−	4.68556i		−	0.353187i
$177$	1.88433	+	18.2182i	0.141635	+	1.36936i
$178$	−4.25871	−	2.45877i	−0.319204	−	0.184293i
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.972024	−	0.234880i	$-0.0754697\pi$
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.282600	+	0.959238i	$0.408803\pi$
$180$		0			0
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$	2.44716	+	1.28416i	0.181396	+	0.0951884i
$183$	2.44949	−	5.47723i	0.181071	−	0.404888i
$184$	2.23861	+	3.87739i	0.165033	+	0.285845i
$185$		0			0
$186$	−9.29642	+	6.73076i	−0.681647	+	0.493524i
$187$	−12.8319	+	7.40852i	−0.938364	+	0.541764i
$188$	−11.2189			−0.818221
$189$	−10.5355	−	8.83190i	−0.766347	−	0.642426i
$190$		0			0
$191$	14.1099	−	8.14637i	1.02096	−	0.589451i	0.106577	−	0.994304i	$-0.466011\pi$
$191$	14.1099	−	8.14637i	1.02096	−	0.589451i	0.914381	+	0.404854i	$0.132678\pi$
$192$	−1.40294	+	1.01575i	−0.101249	+	0.0733057i
$193$	−3.67423	+	6.36396i	−0.264477	+	0.458088i	−0.967427	−	0.253152i	$-0.918533\pi$
$193$	−3.67423	+	6.36396i	−0.264477	+	0.458088i	0.702949	+	0.711240i	$0.251866\pi$
$194$	5.99430	+	10.3824i	0.430366	+	0.745416i
$195$		0			0
$196$	−3.97723	−	5.76035i	−0.284088	−	0.411454i
$197$			9.00000i			0.641223i	0.947211	+	0.320612i	$0.103888\pi$
$197$			9.00000i			0.641223i	−0.947211	+	0.320612i	$0.896112\pi$
$198$	4.38799	−	13.3542i	0.311841	−	0.949044i
$199$	−13.4317	−	7.75478i	−0.952146	−	0.549722i	−0.0583993	−	0.998293i	$-0.518600\pi$
$199$	−13.4317	−	7.75478i	−0.952146	−	0.549722i	−0.893747	+	0.448571i	$0.851933\pi$
$200$		0			0
$201$	−2.54289	−	24.5854i	−0.179361	−	1.73412i
$202$			11.3137i			0.796030i
$203$	9.78866	+	15.4772i	0.687029	+	1.08629i
$204$	5.00000	+	2.23607i	0.350070	+	0.156556i
$205$		0			0
$206$	2.45877	−	4.25871i	0.171311	−	0.296719i
$207$	2.74909	+	13.1473i	0.191075	+	0.913803i
$208$	0.904612	−	0.522278i	0.0627236	−	0.0362135i
$209$	6.70141			0.463546
$210$		0			0
$211$	24.4772			1.68508			0.842541	−	0.538632i	$-0.181059\pi$
$211$	24.4772			1.68508			0.842541	+	0.538632i	$0.181059\pi$
$212$	4.33013	−	2.50000i	0.297394	−	0.171701i
$213$	7.03066	+	9.71064i	0.481733	+	0.665362i
$214$	−2.73861	+	4.74342i	−0.187208	+	0.324253i
$215$		0			0
$216$	−4.94975	+	1.58114i	−0.336788	+	0.107583i
$217$	−17.5175	+	0.707107i	−1.18916	+	0.0480015i
$218$			20.4317i			1.38381i
$219$	6.03574	−	0.624282i	0.407857	−	0.0421851i
$220$		0			0
$221$	−2.86064	−	1.65159i	−0.192427	−	0.111098i
$222$	−4.58782	+	0.474523i	−0.307915	+	0.0318479i
$223$		−	21.8881i		−	1.46574i	−0.680371	−	0.732868i	$-0.738181\pi$
$223$		−	21.8881i		−	1.46574i	0.680371	−	0.732868i	$-0.261819\pi$
$224$	−2.64360	+	0.106711i	−0.176633	+	0.00712992i
$225$		0			0
$226$	−8.73861	−	15.1357i	−0.581284	−	1.00681i
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	−0.985332	−	0.170648i	$-0.945414\pi$
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	0.640451	+	0.767999i	$0.278747\pi$
$228$	−1.45276	−	2.00653i	−0.0962112	−	0.132885i
$229$	11.7386	−	6.77729i	0.775709	−	0.447856i	−0.0591982	−	0.998246i	$-0.518854\pi$
$229$	11.7386	−	6.77729i	0.775709	−	0.447856i	0.834908	+	0.550390i	$0.185521\pi$
$230$		0			0
$231$	16.8700	−	13.2833i	1.10996	−	0.873979i
$232$	6.92163			0.454427
$233$	3.46410	−	2.00000i	0.226941	−	0.131024i	−0.382219	−	0.924072i	$-0.624840\pi$
$233$	3.46410	−	2.00000i	0.226941	−	0.131024i	0.609160	+	0.793047i	$0.291507\pi$
$234$	3.06733	−	0.641375i	0.200518	−	0.0419280i
$235$		0			0
$236$	5.28720	+	9.15769i	0.344167	+	0.596115i
$237$	18.1471	+	8.11562i	1.17878	+	0.527166i
$238$	4.47214	+	7.07107i	0.289886	+	0.458349i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.230732	−	0.973017i	$-0.574112\pi$
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.958024	+	0.286689i	$0.907445\pi$
$242$	9.48683	+	5.47723i	0.609837	+	0.352089i
$243$	−15.5879	−	0.129018i	−0.999966	−	0.00827648i
$244$		−	3.46410i		−	0.221766i
$245$		0			0
$246$	0.738613	−	1.65159i	0.0470922	−	0.105301i
$247$	0.746976	+	1.29380i	0.0475290	+	0.0823226i
$248$	−3.31319	+	5.73861i	−0.210388	+	0.364402i
$249$	−5.70682	+	4.13183i	−0.361655	+	0.261844i
$250$		0			0
$251$	8.85494			0.558919			0.279459	−	0.960158i	$-0.409845\pi$
$251$	8.85494			0.558919			0.279459	+	0.960158i	$0.409845\pi$
$252$	−7.63441	−	2.17157i	−0.480923	−	0.136796i
$253$	−20.9783			−1.31889
$254$	−7.56114	+	4.36543i	−0.474428	+	0.273911i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.49798	−	9.52277i	−0.342954	−	0.594014i	0.642026	−	0.766683i	$-0.278094\pi$
$257$	−5.49798	−	9.52277i	−0.342954	−	0.594014i	−0.984980	+	0.172669i	$0.944761\pi$
$258$	−4.89433	+	10.9441i	−0.304708	+	0.681347i
$259$	−6.23861	−	3.27374i	−0.387649	−	0.203421i
$260$		0			0
$261$	19.7272	+	6.48204i	1.22108	+	0.401229i
$262$	11.9273	+	6.88624i	0.736872	+	0.425433i
$263$	−1.73205	−	1.00000i	−0.106803	−	0.0616626i	0.445647	−	0.895209i	$-0.352974\pi$
$263$	−1.73205	−	1.00000i	−0.106803	−	0.0616626i	−0.552450	+	0.833546i	$0.686307\pi$
$264$	−0.834952	−	8.07256i	−0.0513878	−	0.496832i
$265$		0			0
$266$	−0.152621	−	3.78095i	−0.00935778	−	0.231825i
$267$	−7.77531	−	3.47723i	−0.475841	−	0.212803i
$268$	−7.13505	−	12.3583i	−0.435842	−	0.754901i
$269$	8.79052	−	15.2256i	0.535968	−	0.928323i	−0.463148	−	0.886281i	$-0.653280\pi$
$269$	8.79052	−	15.2256i	0.535968	−	0.928323i	0.999116	−	0.0420423i	$-0.0133864\pi$
$270$		0			0
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	−0.657047	−	0.753850i	$-0.728195\pi$
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	0.324329	+	0.945944i	$0.394861\pi$
$272$	3.16228			0.191741
$273$	4.44495	+	1.77635i	0.269021	+	0.107510i
$274$	3.47723			0.210067
$275$		0			0
$276$	4.54776	+	6.28129i	0.273743	+	0.378089i
$277$	−4.89898	+	8.48528i	−0.294351	+	0.509831i	−0.974834	−	0.222933i	$-0.928437\pi$
$277$	−4.89898	+	8.48528i	−0.294351	+	0.509831i	0.680483	+	0.732764i	$0.261770\pi$
$278$	−10.0905	−	17.4772i	−0.605187	−	1.04821i
$279$	−14.8170	+	13.2528i	−0.887073	+	0.793422i
$280$		0			0
$281$			1.80922i			0.107929i	0.998543	+	0.0539646i	$0.0171858\pi$
$281$			1.80922i			0.107929i	−0.998543	+	0.0539646i	$0.982814\pi$
$282$	−19.3286	+	1.99917i	−1.15100	+	0.119049i
$283$	7.98873	+	4.61230i	0.474881	+	0.274173i	0.718281	−	0.695753i	$-0.244929\pi$
$283$	7.98873	+	4.61230i	0.474881	+	0.274173i	−0.243400	+	0.969926i	$0.578263\pi$
$284$	5.99430	+	3.46081i	0.355696	+	0.205361i
$285$		0			0
$286$			4.89433i			0.289408i
$287$	2.33570	−	1.47723i	0.137872	−	0.0871979i
$288$	−2.23607	+	2.00000i	−0.131762	+	0.117851i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$		0			0
$291$	12.1775	+	16.8193i	0.713856	+	0.985966i
$292$	3.03397	−	1.75166i	0.177550	−	0.102508i
$293$	8.05661			0.470672			0.235336	−	0.971914i	$-0.424381\pi$
$293$	8.05661			0.470672			0.235336	+	0.971914i	$0.424381\pi$
$294$	−7.87868	−	9.21555i	−0.459494	−	0.537462i
$295$		0			0
$296$	−2.30615	+	1.33146i	−0.134042	+	0.0773893i
$297$	5.18020	−	23.7894i	0.300586	−	1.38040i
$298$	−1.22474	+	2.12132i	−0.0709476	+	0.122885i
$299$	−2.33836	−	4.05015i	−0.135231	−	0.234226i
$300$		0			0
$301$	−15.4772	+	9.78866i	−0.892092	+	0.564209i
$302$		−	2.00000i		−	0.115087i
$303$	2.01607	+	19.4919i	0.115820	+	1.11978i
$304$	−1.23861	−	0.715113i	−0.0710393	−	0.0410146i
$305$		0			0
$306$	9.01276	+	2.96145i	0.515225	+	0.169295i
$307$		−	11.9886i		−	0.684226i	−0.939659	−	0.342113i	$-0.888857\pi$
$307$		−	11.9886i		−	0.684226i	0.939659	−	0.342113i	$-0.111143\pi$
$308$	5.76035	−	10.9772i	0.328227	−	0.625485i
$309$	3.47723	−	7.77531i	0.197812	−	0.442322i
$310$		0			0
$311$	−8.79052	+	15.2256i	−0.498465	+	0.863366i	−0.999998	−	0.00177176i	$-0.999436\pi$
$311$	−8.79052	+	15.2256i	−0.498465	+	0.863366i	0.501534	+	0.865138i	$0.332769\pi$
$312$	1.46545	−	1.06101i	0.0829649	−	0.0600679i
$313$	−20.1246	+	11.6190i	−1.13751	+	0.656742i	−0.945813	−	0.324712i	$-0.894733\pi$
$313$	−20.1246	+	11.6190i	−1.13751	+	0.656742i	−0.191697	+	0.981454i	$0.561399\pi$
$314$	−14.4474			−0.815313
$315$		0			0
$316$	11.4772			0.645644
$317$	−8.58136	+	4.95445i	−0.481977	+	0.278270i	−0.721240	−	0.692685i	$-0.756428\pi$
$317$	−8.58136	+	4.95445i	−0.481977	+	0.278270i	0.239263	+	0.970955i	$0.423094\pi$
$318$	7.01471	−	5.07877i	0.393365	−	0.284803i
$319$	−16.2158	+	28.0867i	−0.907913	+	1.57255i
$320$		0			0
$321$	−3.87298	+	8.66025i	−0.216169	+	0.483368i
$322$	0.477769	+	11.8360i	0.0266250	+	0.659594i
$323$			4.52277i			0.251654i
$324$	−8.24597	+	3.60611i	−0.458109	+	0.200339i
$325$		0			0
$326$	12.7279	+	7.34847i	0.704934	+	0.406994i
$327$	3.64086	+	35.2009i	0.201340	+	1.94662i
$328$		−	1.04456i		−	0.0576760i
$329$	−26.2834	−	13.7923i	−1.44905	−	0.760396i
$330$		0			0
$331$	−10.7158	−	18.5604i	−0.588996	−	1.02017i	−0.994364	−	0.106017i	$-0.966190\pi$
$331$	−10.7158	−	18.5604i	−0.588996	−	1.02017i	0.405369	−	0.914153i	$-0.367143\pi$
$332$	−2.03387	+	3.52277i	−0.111623	+	0.193337i
$333$	−7.81962	+	1.63507i	−0.428512	+	0.0896014i
$334$	3.71584	−	2.14534i	0.203322	−	0.117388i
$335$		0			0
$336$	−4.53553	+	0.654929i	−0.247434	+	0.0357293i
$337$	17.1464			0.934025			0.467013	−	0.884251i	$-0.345330\pi$
$337$	17.1464			0.934025			0.467013	+	0.884251i	$0.345330\pi$
$338$	10.3134	−	5.95445i	0.560976	−	0.323879i
$339$	−17.7525	−	24.5195i	−0.964186	−	1.33172i
$340$		0			0
$341$	−15.5241	−	26.8886i	−0.840679	−	1.45610i
$342$	−2.86045	−	3.19808i	−0.154676	−	0.172933i
$343$	−2.23607	−	18.3848i	−0.120736	−	0.992685i
$344$			6.92163i			0.373189i
$345$		0			0
$346$	−0.977226	−	0.564201i	−0.0525360	−	0.0303317i
$347$	15.1357	+	8.73861i	0.812528	+	0.469113i	0.847833	−	0.530263i	$-0.177907\pi$
$347$	15.1357	+	8.73861i	0.812528	+	0.469113i	−0.0353049	+	0.999377i	$0.511240\pi$
$348$	11.9250	−	1.23341i	0.639247	−	0.0661179i
$349$			11.7436i			0.628623i	0.949320	+	0.314311i	$0.101774\pi$
$349$			11.7436i			0.628623i	−0.949320	+	0.314311i	$0.898226\pi$
$350$		0			0
$351$	5.17029	−	1.65159i	0.275970	−	0.0881553i
$352$	−2.34278	−	4.05781i	−0.124871	−	0.216282i
$353$	0.301824	−	0.522774i	0.0160645	−	0.0278245i	−0.857881	−	0.513848i	$-0.828220\pi$
$353$	0.301824	−	0.522774i	0.0160645	−	0.0278245i	0.873946	+	0.486023i	$0.161553\pi$
$354$	10.7410	+	14.8353i	0.570876	+	0.788485i
$355$		0			0
$356$	−4.91754			−0.260629
$357$	8.96491	+	11.3855i	0.474473	+	0.602587i
$358$	19.3825			1.02440
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	−0.216476	−	0.976288i	$-0.569456\pi$
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	0.737252	+	0.675618i	$0.236123\pi$
$360$		0			0
$361$	−8.47723	+	14.6830i	−0.446170	+	0.772789i
$362$	1.58114	+	2.73861i	0.0831028	+	0.143938i
$363$	17.3205	+	7.74597i	0.909091	+	0.406558i
$364$	2.76139	−	0.111466i	0.144736	−	0.00584238i
$365$		0			0
$366$	−0.617292	−	5.96816i	−0.0322664	−	0.311961i
$367$	−0.320133	−	0.184829i	−0.0167108	−	0.00964798i	0.491621	−	0.870809i	$-0.336404\pi$
$367$	−0.320133	−	0.184829i	−0.0167108	−	0.00964798i	−0.508332	+	0.861161i	$0.669738\pi$
$368$	3.87739	+	2.23861i	0.202123	+	0.116696i
$369$	0.978218	−	2.97707i	0.0509240	−	0.154980i
$370$		0			0
$371$	13.2180	−	0.533554i	0.686244	−	0.0277008i
$372$	−4.68556	+	10.4772i	−0.242935	+	0.543219i
$373$	−11.6072	−	20.1042i	−0.600997	−	1.04096i	−0.992670	−	0.120853i	$-0.961437\pi$
$373$	−11.6072	−	20.1042i	−0.600997	−	1.04096i	0.391673	−	0.920104i	$-0.371896\pi$
$374$	−7.40852	+	12.8319i	−0.383085	+	0.663523i
$375$		0			0
$376$	−9.71584	+	5.60944i	−0.501056	+	0.289285i
$377$	−7.23003			−0.372365
$378$	−13.5400	−	2.38089i	−0.696422	−	0.122460i
$379$	20.4772			1.05184			0.525922	−	0.850533i	$-0.323720\pi$
$379$	20.4772			1.05184			0.525922	+	0.850533i	$0.323720\pi$
$380$		0			0
$381$	−12.2489	+	8.86839i	−0.627529	+	0.454341i
$382$	8.14637	−	14.1099i	0.416805	−	0.721927i
$383$	−9.07354	−	15.7158i	−0.463636	−	0.803042i	0.535502	−	0.844534i	$-0.320122\pi$
$383$	−9.07354	−	15.7158i	−0.463636	−	0.803042i	−0.999139	+	0.0414919i	$0.986789\pi$
$384$	−0.707107	+	1.58114i	−0.0360844	+	0.0806872i
$385$		0			0
$386$			7.34847i			0.374027i
$387$	−6.48204	+	19.7272i	−0.329501	+	1.00279i
$388$	10.3824	+	5.99430i	0.527088	+	0.304315i
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	0.652580	−	0.757720i	$-0.273687\pi$
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	−0.329914	+	0.944011i	$0.607020\pi$
$390$		0			0
$391$		−	14.1582i		−	0.716012i
$392$	−6.32456	−	3.00000i	−0.319438	−	0.151523i
$393$	21.7762	+	9.73861i	1.09846	+	0.491248i
$394$	4.50000	+	7.79423i	0.226707	+	0.392668i
$395$		0			0
$396$	−2.87701	−	13.7591i	−0.144575	−	0.691421i
$397$	12.8877	−	7.44073i	0.646816	−	0.373439i	−0.140419	−	0.990092i	$-0.544845\pi$
$397$	12.8877	−	7.44073i	0.646816	−	0.373439i	0.787235	+	0.616653i	$0.211512\pi$
$398$	−15.5096			−0.777424
$399$	−0.936697	−	6.48684i	−0.0468935	−	0.324748i
$400$		0			0
$401$	0.827520	−	0.477769i	0.0413244	−	0.0238586i	−0.479195	−	0.877708i	$-0.659072\pi$
$401$	0.827520	−	0.477769i	0.0413244	−	0.0238586i	0.520520	+	0.853850i	$0.325738\pi$
$402$	−14.4949	−	20.0201i	−0.722939	−	0.998513i
$403$	3.46081	−	5.99430i	0.172395	−	0.298598i
$404$	5.65685	+	9.79796i	0.281439	+	0.487467i
$405$		0			0
$406$	16.2158	+	8.50934i	0.804779	+	0.422312i
$407$		−	12.4772i		−	0.618473i
$408$	5.44816	−	0.563508i	0.269724	−	0.0278978i
$409$	−13.4317	−	7.75478i	−0.664154	−	0.383449i	0.129704	−	0.991553i	$-0.458597\pi$
$409$	−13.4317	−	7.75478i	−0.664154	−	0.383449i	−0.793858	+	0.608103i	$0.791931\pi$
$410$		0			0
$411$	5.99077	−	0.619631i	0.295503	−	0.0305641i
$412$		−	4.91754i		−	0.242270i
$413$	1.12840	+	27.9545i	0.0555251	+	1.37555i
$414$	8.95445	+	10.0114i	0.440087	+	0.492033i
$415$		0			0
$416$	0.522278	−	0.904612i	0.0256068	−	0.0443523i
$417$	−20.4989	−	28.3127i	−1.00383	−	1.38648i
$418$	5.80359	−	3.35071i	0.283863	−	0.163888i
$419$	8.85494			0.432592			0.216296	−	0.976328i	$-0.430602\pi$
$419$	8.85494			0.432592			0.216296	+	0.976328i	$0.430602\pi$
$420$		0			0
$421$	18.9545			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$421$	18.9545			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$422$	21.1979	−	12.2386i	1.03190	−	0.595766i
$423$	−32.9442	+	6.88858i	−1.60180	+	0.334934i
$424$	2.50000	−	4.33013i	0.121411	−	0.210290i
$425$		0			0
$426$	10.9441	+	4.89433i	0.530241	+	0.237131i
$427$	4.25871	−	8.11562i	0.206094	−	0.392743i
$428$			5.47723i			0.264752i
$429$	0.872155	+	8.43224i	0.0421080	+	0.407112i
$430$		0			0
$431$	−6.63699	−	3.83187i	−0.319693	−	0.184575i	0.331563	−	0.943433i	$-0.392424\pi$
$431$	−6.63699	−	3.83187i	−0.319693	−	0.184575i	−0.651256	+	0.758858i	$0.725757\pi$
$432$	−3.49604	+	3.84418i	−0.168203	+	0.184953i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$	−14.8170	+	9.37112i	−0.711240	+	0.449828i
$435$		0			0
$436$	10.2158	+	17.6944i	0.489250	+	0.847406i
$437$	−3.20172	+	5.54555i	−0.153159	+	0.265280i
$438$	4.91496	−	3.55851i	0.234846	−	0.170032i
$439$	7.69306	−	4.44159i	0.367170	−	0.211986i	−0.305051	−	0.952336i	$-0.598674\pi$
$439$	7.69306	−	4.44159i	0.367170	−	0.211986i	0.672221	+	0.740350i	$0.265340\pi$
$440$		0			0
$441$	−15.2160	−	14.4731i	−0.724574	−	0.689198i
$442$	−3.30318			−0.157116
$443$	13.0298	−	7.52277i	0.619066	−	0.357418i	−0.157439	−	0.987529i	$-0.550324\pi$
$443$	13.0298	−	7.52277i	0.619066	−	0.357418i	0.776505	+	0.630111i	$0.216991\pi$
$444$	−3.73591	+	2.70486i	−0.177298	+	0.128367i
$445$		0			0
$446$	−10.9441	−	18.9557i	−0.518216	−	0.897576i
$447$	−1.73205	+	3.87298i	−0.0819232	+	0.183186i
$448$	−2.23607	+	1.41421i	−0.105644	+	0.0668153i
$449$		−	25.8773i		−	1.22122i	−0.791930	−	0.610612i	$-0.790923\pi$
$449$		−	25.8773i		−	1.22122i	0.791930	−	0.610612i	$-0.209077\pi$
$450$		0			0
$451$	4.23861	+	2.44716i	0.199588	+	0.115232i
$452$	−15.1357	−	8.73861i	−0.711924	−	0.411030i
$453$	−0.356394	−	3.44572i	−0.0167448	−	0.161894i
$454$			10.3923i			0.487735i
$455$		0			0
$456$	−2.26139	−	1.01132i	−0.105899	−	0.0473595i
$457$	−5.53924	−	9.59425i	−0.259115	−	0.448800i	0.706890	−	0.707323i	$-0.250098\pi$
$457$	−5.53924	−	9.59425i	−0.259115	−	0.448800i	−0.966005	+	0.258523i	$0.916764\pi$
$458$	6.77729	−	11.7386i	0.316682	−	0.548509i
$459$	16.0554	+	3.49611i	0.749404	+	0.163184i
$460$		0			0
$461$	−31.7876			−1.48050			−0.740248	−	0.672334i	$-0.765292\pi$
$461$	−31.7876			−1.48050			−0.740248	+	0.672334i	$0.765292\pi$
$462$	7.96817	−	19.9387i	0.370713	−	0.927632i
$463$	22.5741			1.04911			0.524554	−	0.851377i	$-0.324232\pi$
$463$	22.5741			1.04911			0.524554	+	0.851377i	$0.324232\pi$
$464$	5.99430	−	3.46081i	0.278279	−	0.160664i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−14.0073	−	24.2614i	−0.648181	−	1.12268i	−0.983557	−	0.180599i	$-0.942197\pi$
$467$	−14.0073	−	24.2614i	−0.648181	−	1.12268i	0.335375	−	0.942085i	$-0.391137\pi$
$468$	2.33570	−	2.08911i	0.107968	−	0.0965693i
$469$	−1.52277	−	37.7244i	−0.0703152	−	1.74195i
$470$		0			0
$471$	−24.8908	+	2.57448i	−1.14691	+	0.118626i
$472$	9.15769	+	5.28720i	0.421517	+	0.243363i
$473$	−28.0867	−	16.2158i	−1.29143	−	0.745605i
$474$	19.7737	−	2.04521i	0.908234	−	0.0939395i
$475$		0			0
$476$	7.40852	+	3.88766i	0.339569	+	0.178190i
$477$	11.1803	−	10.0000i	0.511913	−	0.457869i
$478$		0			0
$479$	−21.1810	+	36.6866i	−0.967784	+	1.67625i	−0.265844	+	0.964016i	$0.585651\pi$
$479$	−21.1810	+	36.6866i	−0.967784	+	1.67625i	−0.701940	+	0.712236i	$0.747683\pi$
$480$		0			0
$481$	2.40890	−	1.39078i	0.109836	−	0.0634141i
$482$	−21.3094			−0.970615
$483$	2.93227	+	20.3066i	0.133423	+	0.923983i
$484$	10.9545			0.497930
$485$		0			0
$486$	−13.5640	+	7.68223i	−0.615278	+	0.348473i
$487$	−8.51743	+	14.7526i	−0.385962	+	0.668505i	−0.991902	−	0.127005i	$-0.959464\pi$
$487$	−8.51743	+	14.7526i	−0.385962	+	0.668505i	0.605941	+	0.795510i	$0.292797\pi$
$488$	−1.73205	−	3.00000i	−0.0784063	−	0.135804i
$489$	23.2379	+	10.3923i	1.05085	+	0.469956i
$490$		0			0
$491$		−	13.8433i		−	0.624737i	−0.949961	−	0.312369i	$-0.898878\pi$
$491$		−	13.8433i		−	0.624737i	0.949961	−	0.312369i	$-0.101122\pi$
$492$	−0.186137	−	1.79962i	−0.00839169	−	0.0811333i
$493$	−18.9557	−	10.9441i	−0.853720	−	0.492895i
$494$	1.29380	+	0.746976i	0.0582108	+	0.0336080i
$495$		0			0
$496$			6.62638i			0.297533i
$497$	9.78866	+	15.4772i	0.439081	+	0.694248i
$498$	−2.87633	+	6.43168i	−0.128892	+	0.288210i
$499$	0.954451	+	1.65316i	0.0427271	+	0.0740055i	0.886598	−	0.462541i	$-0.153062\pi$
$499$	0.954451	+	1.65316i	0.0427271	+	0.0740055i	−0.843871	+	0.536546i	$0.819729\pi$
$500$		0			0
$501$	6.01958	−	4.35827i	0.268935	−	0.194713i
$502$	7.66860	−	4.42747i	0.342266	−	0.197608i
$503$	15.5096			0.691537			0.345769	−	0.938320i	$-0.387618\pi$
$503$	15.5096			0.691537			0.345769	+	0.938320i	$0.387618\pi$
$504$	−7.69738	+	1.93657i	−0.342869	+	0.0862617i
$505$		0			0
$506$	−18.1677	+	10.4891i	−0.807655	+	0.466300i
$507$	16.7075	−	12.0965i	0.742006	−	0.537225i
$508$	−4.36543	+	7.56114i	−0.193684	+	0.335471i
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	−0.998427	−	0.0560688i	$-0.982143\pi$
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	0.450656	−	0.892697i	$-0.351190\pi$
$510$		0			0
$511$	9.26139	−	0.373843i	0.409700	−	0.0165378i
$512$			1.00000i			0.0441942i
$513$	−5.49805	−	5.00013i	−0.242745	−	0.220761i
$514$	−9.52277	−	5.49798i	−0.420032	−	0.242505i
$515$		0			0
$516$	1.23341	+	11.9250i	0.0542980	+	0.524968i
$517$		−	52.5667i		−	2.31188i
$518$	−7.03967	+	0.284162i	−0.309305	+	0.0124853i
$519$	−1.78416	−	0.797901i	−0.0783160	−	0.0350240i
$520$		0			0
$521$	17.7981	−	30.8272i	0.779748	−	1.35056i	−0.152339	−	0.988328i	$-0.548680\pi$
$521$	17.7981	−	30.8272i	0.779748	−	1.35056i	0.932087	−	0.362235i	$-0.117986\pi$
$522$	20.3253	−	4.24999i	0.889614	−	0.186017i
$523$	14.6412	−	8.45307i	0.640213	−	0.369627i	−0.144484	−	0.989507i	$-0.546152\pi$
$523$	14.6412	−	8.45307i	0.640213	−	0.369627i	0.784697	+	0.619880i	$0.212819\pi$
$524$	13.7725			0.601654
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	18.1471	−	10.4772i	0.790500	−	0.456395i
$528$	−4.75937	−	6.57357i	−0.207125	−	0.286078i
$529$	−1.47723	+	2.55863i	−0.0642272	+	0.111245i
$530$		0			0
$531$	21.1488	+	23.6451i	0.917779	+	1.02611i
$532$	−2.02265	−	3.19808i	−0.0876928	−	0.138655i
$533$			1.09110i			0.0472607i
$534$	−8.47223	+	0.876291i	−0.366629	+	0.0379208i
$535$		0			0
$536$	−12.3583	−	7.13505i	−0.533796	−	0.308187i
$537$	33.3933	−	3.45390i	1.44103	−	0.149047i
$538$		−	17.5810i		−	0.757973i
$539$	26.9905	−	18.6355i	1.16256	−	0.802689i
$540$		0			0
$541$	−4.26139	−	7.38094i	−0.183211	−	0.317331i	0.759761	−	0.650202i	$-0.225316\pi$
$541$	−4.26139	−	7.38094i	−0.183211	−	0.317331i	−0.942972	+	0.332871i	$0.891983\pi$
$542$	−3.16228	+	5.47723i	−0.135831	+	0.235267i
$543$	3.21209	+	4.43649i	0.137844	+	0.190388i
$544$	2.73861	−	1.58114i	0.117417	−	0.0677908i
$545$		0			0
$546$	4.73762	−	0.684110i	0.202751	−	0.0292772i
$547$	3.61845			0.154714			0.0773569	−	0.997003i	$-0.475352\pi$
$547$	3.61845			0.154714			0.0773569	+	0.997003i	$0.475352\pi$
$548$	3.01137	−	1.73861i	0.128639	−	0.0742699i
$549$	−2.12702	−	10.1723i	−0.0907789	−	0.434143i
$550$		0			0
$551$	4.94975	+	8.57321i	0.210866	+	0.365231i
$552$	7.07912	+	3.16588i	0.301307	+	0.134749i
$553$	26.8886	+	14.1099i	1.14342	+	0.600015i
$554$			9.79796i			0.416275i
$555$		0			0
$556$	−17.4772	−	10.0905i	−0.741199	−	0.427932i
$557$	−24.1304	−	13.9317i	−1.02244	−	0.590304i	−0.107628	−	0.994191i	$-0.534326\pi$
$557$	−24.1304	−	13.9317i	−1.02244	−	0.590304i	−0.914809	+	0.403887i	$0.867659\pi$
$558$	−6.20555	+	18.8857i	−0.262702	+	0.799497i
$559$		−	7.23003i		−	0.305798i
$560$		0			0
$561$	−10.4772	+	23.4278i	−0.442349	+	0.989122i
$562$	0.904612	+	1.56683i	0.0381588	+	0.0660929i
$563$	5.19615	−	9.00000i	0.218992	−	0.379305i	−0.735508	−	0.677516i	$-0.763057\pi$
$563$	5.19615	−	9.00000i	0.218992	−	0.379305i	0.954500	+	0.298211i	$0.0963899\pi$
$564$	−15.7394	+	11.3956i	−0.662750	+	0.479842i
$565$		0			0
$566$	9.22460			0.387739
$567$	−23.7518	−	1.68915i	−0.997481	−	0.0709375i
$568$	6.92163			0.290425
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	−0.630949	−	0.775824i	$-0.717334\pi$
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	0.356409	+	0.934330i	$0.384001\pi$
$570$		0			0
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	−0.978991	−	0.203901i	$-0.934638\pi$
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	0.666079	+	0.745881i	$0.267971\pi$
$572$	2.44716	+	4.23861i	0.102321	+	0.177225i
$573$	11.5207	−	25.7611i	0.481284	−	1.07618i
$574$	1.28416	−	2.44716i	0.0535999	−	0.102143i
$575$		0			0
$576$	−0.936492	+	2.85008i	−0.0390205	+	0.118754i
$577$	0.584480	+	0.337449i	0.0243322	+	0.0140482i	0.512117	−	0.858916i	$-0.328862\pi$
$577$	0.584480	+	0.337449i	0.0243322	+	0.0140482i	−0.487785	+	0.872964i	$0.662195\pi$
$578$	6.06218	+	3.50000i	0.252153	+	0.145581i
$579$	1.30948	+	12.6604i	0.0544199	+	0.526148i
$580$		0			0
$581$	−9.09576	+	5.75267i	−0.377356	+	0.238661i
$582$	18.9557	+	8.47723i	0.785737	+	0.351392i
$583$	11.7139	+	20.2891i	0.485140	+	0.840287i
$584$	1.75166	−	3.03397i	0.0724843	−	0.125547i
$585$		0			0
$586$	6.97723	−	4.02830i	0.288227	−	0.166408i
$587$	21.0864			0.870330			0.435165	−	0.900351i	$-0.356690\pi$
$587$	21.0864			0.870330			0.435165	+	0.900351i	$0.356690\pi$
$588$	−11.4309	−	4.04156i	−0.471403	−	0.166671i
$589$	−9.47723			−0.390502
$590$		0			0
$591$	9.14178	+	12.6265i	0.376042	+	0.519384i
$592$	−1.33146	+	2.30615i	−0.0547225	+	0.0947821i
$593$	0.826579	+	1.43168i	0.0339435	+	0.0587919i	0.882498	−	0.470316i	$-0.155860\pi$
$593$	0.826579	+	1.43168i	0.0339435	+	0.0587919i	−0.848555	+	0.529108i	$0.822527\pi$
$594$	−7.40852	−	23.1923i	−0.303975	−	0.951593i
$595$		0			0
$596$			2.44949i			0.100335i
$597$	−26.7208	+	2.76376i	−1.09361	+	0.113113i
$598$	−4.05015	−	2.33836i	−0.165623	−	0.0956225i
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	0.0195464	−	0.999809i	$-0.493778\pi$
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	−0.856087	+	0.516832i	$0.827111\pi$
$600$		0			0
$601$		−	4.06775i		−	0.165927i	−0.996553	−	0.0829635i	$-0.973562\pi$
$601$		−	4.06775i		−	0.165927i	0.996553	−	0.0829635i	$-0.0264385\pi$
$602$	−8.50934	+	16.2158i	−0.346815	+	0.660908i
$603$	−28.5402	−	31.9089i	−1.16225	−	1.29943i
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$		0			0
$606$	11.4919	+	15.8725i	0.466828	+	0.644775i
$607$	10.6468	−	6.14692i	0.432140	−	0.249496i	−0.268118	−	0.963386i	$-0.586402\pi$
$607$	10.6468	−	6.14692i	0.432140	−	0.249496i	0.700258	+	0.713890i	$0.253068\pi$
$608$	−1.43023			−0.0580034
$609$	29.4540	+	11.7708i	1.19353	+	0.476976i
$610$		0			0
$611$	10.1487	−	5.85938i	0.410574	−	0.237045i
$612$	9.28600	−	1.94169i	0.375364	−	0.0784882i
$613$	−2.92726	+	5.07016i	−0.118231	+	0.204782i	−0.919067	−	0.394102i	$-0.871056\pi$
$613$	−2.92726	+	5.07016i	−0.118231	+	0.204782i	0.800836	+	0.598884i	$0.204389\pi$
$614$	−5.99430	−	10.3824i	−0.241910	−	0.419001i
$615$		0			0
$616$	−0.500000	−	12.3867i	−0.0201456	−	0.499076i
$617$			14.5228i			0.584665i	0.956317	+	0.292332i	$0.0944314\pi$
$617$			14.5228i			0.584665i	−0.956317	+	0.292332i	$0.905569\pi$
$618$	−0.876291	−	8.47223i	−0.0352496	−	0.340803i
$619$	−26.1475	−	15.0963i	−1.05096	−	0.606771i	−0.128040	−	0.991769i	$-0.540869\pi$
$619$	−26.1475	−	15.0963i	−1.05096	−	0.606771i	−0.922917	+	0.384998i	$0.874202\pi$
$620$		0			0
$621$	17.2113	+	15.6525i	0.690664	+	0.628115i
$622$			17.5810i			0.704936i
$623$	−11.5207	−	6.04555i	−0.461567	−	0.242210i
$624$	0.738613	−	1.65159i	0.0295682	−	0.0661165i
$625$		0			0
$626$	−11.6190	+	20.1246i	−0.464387	+	0.804341i
$627$	9.40169	−	6.80698i	0.375467	−	0.271845i
$628$	−12.5118	+	7.22369i	−0.499275	+	0.288257i
$629$	8.42087			0.335762
$630$		0			0
$631$	3.47723			0.138426			0.0692131	−	0.997602i	$-0.477951\pi$
$631$	3.47723			0.138426			0.0692131	+	0.997602i	$0.477951\pi$
$632$	9.93957	−	5.73861i	0.395375	−	0.228270i
$633$	34.3401	−	24.8628i	1.36490	−	0.988208i
$634$	−4.95445	+	8.58136i	−0.196766	+	0.340809i
$635$		0			0
$636$	3.53553	−	7.90569i	0.140193	−	0.313481i
$637$	6.60635	+	3.13367i	0.261753	+	0.124160i
$638$			32.4317i			1.28398i
$639$	19.7272	+	6.48204i	0.780397	+	0.256426i
$640$		0			0
$641$	−13.9251	−	8.03966i	−0.550008	−	0.317547i	0.199117	−	0.979976i	$-0.436193\pi$
$641$	−13.9251	−	8.03966i	−0.550008	−	0.317547i	−0.749125	+	0.662428i	$0.769526\pi$
$642$	0.976025	+	9.43649i	0.0385206	+	0.372429i
$643$		−	26.0663i		−	1.02796i	−0.857803	−	0.513978i	$-0.828171\pi$
$643$		−	26.0663i		−	1.02796i	0.857803	−	0.513978i	$-0.171829\pi$
$644$	6.33175	+	10.0114i	0.249506	+	0.394504i
$645$		0			0
$646$	2.26139	+	3.91684i	0.0889731	+	0.154106i
$647$	−10.2019	+	17.6703i	−0.401080	+	0.694691i	−0.993857	−	0.110676i	$-0.964698\pi$
$647$	−10.2019	+	17.6703i	−0.401080	+	0.694691i	0.592777	+	0.805367i	$0.298032\pi$
$648$	−5.33816	+	7.24597i	−0.209703	+	0.284648i
$649$	−42.9089	+	24.7735i	−1.68432	+	0.972444i
$650$		0			0
$651$	−23.8578	+	18.7855i	−0.935060	+	0.736261i
$652$	14.6969			0.575577
$653$	−34.5227	+	19.9317i	−1.35098	+	0.779987i	−0.988386	−	0.151962i	$-0.951441\pi$
$653$	−34.5227	+	19.9317i	−1.35098	+	0.779987i	−0.362590	+	0.931949i	$0.618108\pi$
$654$	20.7535	+	28.6645i	0.811528	+	1.12087i
$655$		0			0
$656$	−0.522278	−	0.904612i	−0.0203915	−	0.0353192i
$657$	7.83368	−	7.00665i	0.305621	−	0.273356i
$658$	−29.6582	+	1.19718i	−1.15620	+	0.0466708i
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$		0			0
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	0.510132	−	0.860096i	$-0.329596\pi$
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	−0.489799	+	0.871836i	$0.662930\pi$
$662$	−18.5604	−	10.7158i	−0.721370	−	0.416483i
$663$	−5.69091	+	0.588616i	−0.221017	+	0.0228600i
$664$			4.06775i			0.157859i
$665$		0			0
$666$	−5.95445	+	5.32582i	−0.230730	+	0.206371i
$667$	−15.4948	−	26.8378i	−0.599963	−	1.03917i
$668$	2.14534	−	3.71584i	0.0830057	−	0.143770i
$669$	−22.2329	−	30.7077i	−0.859574	−	1.18723i
$670$		0			0
$671$	16.2312			0.626600
$672$	−3.60042	+	2.83495i	−0.138889	+	0.109361i
$673$	14.1585			0.545771			0.272885	−	0.962047i	$-0.412022\pi$
$673$	14.1585			0.545771			0.272885	+	0.962047i	$0.412022\pi$
$674$	14.8492	−	8.57321i	0.571971	−	0.330228i
$675$		0			0
$676$	5.95445	−	10.3134i	0.229017	−	0.396670i
$677$	−16.4545	−	28.5000i	−0.632397	−	1.09534i	−0.987060	−	0.160350i	$-0.948738\pi$
$677$	−16.4545	−	28.5000i	−0.632397	−	1.09534i	0.354663	−	0.934994i	$-0.384596\pi$
$678$	−27.6339	−	12.3583i	−1.06127	−	0.474616i
$679$	16.9545	+	26.8073i	0.650652	+	1.02877i
$680$		0			0
$681$	1.85188	+	17.9045i	0.0709641	+	0.686101i
$682$	−26.8886	−	15.5241i	−1.02962	−	0.594450i
$683$	−16.4150	−	9.47723i	−0.628104	−	0.362636i	0.151913	−	0.988394i	$-0.451456\pi$
$683$	−16.4150	−	9.47723i	−0.628104	−	0.362636i	−0.780017	+	0.625758i	$0.784790\pi$
$684$	−4.07627	−	1.33940i	−0.155860	−	0.0512131i
$685$		0			0
$686$	−11.1289	−	14.8036i	−0.424903	−	0.565206i
$687$	9.58454	−	21.4317i	0.365673	−	0.817669i
$688$	3.46081	+	5.99430i	0.131942	+	0.228531i
$689$	−2.61139	+	4.52306i	−0.0994861	+	0.172315i
$690$		0			0
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$	−1.12840			−0.0428954
$693$	10.1750	−	35.7715i	0.386517	−	1.35885i
$694$	17.4772			0.663426
$695$		0			0
$696$	9.71064	−	7.03066i	0.368081	−	0.266497i
$697$	−1.65159	+	2.86064i	−0.0625584	+	0.108354i
$698$	5.87182	+	10.1703i	0.222252	+	0.384951i
$699$	2.82843	−	6.32456i	0.106981	−	0.239217i
$700$		0			0
$701$		−	51.7546i		−	1.95474i	−0.211531	−	0.977371i	$-0.567845\pi$
$701$		−	51.7546i		−	1.95474i	0.211531	−	0.977371i	$-0.432155\pi$
$702$	3.65181	−	4.01546i	0.137829	−	0.151554i
$703$	−3.29832	−	1.90428i	−0.124398	−	0.0718214i
$704$	−4.05781	−	2.34278i	−0.152935	−	0.0882968i
$705$		0			0
$706$		−	0.603648i		−	0.0227186i
$707$	1.20730	+	29.9089i	0.0454050	+	1.12484i
$708$	16.7196	+	7.47723i	0.628360	+	0.281011i
$709$	−11.2158	−	19.4264i	−0.421220	−	0.729574i	0.574839	−	0.818266i	$-0.305065\pi$
$709$	−11.2158	−	19.4264i	−0.421220	−	0.729574i	−0.996059	+	0.0886924i	$0.971731\pi$
$710$		0			0
$711$	33.7028	−	7.04721i	1.26395	−	0.264291i
$712$	−4.25871	+	2.45877i	−0.159602	+	0.0921463i
$713$	29.6678			1.11107
$714$	13.4566	+	5.37771i	0.503601	+	0.201256i
$715$		0			0
$716$	16.7857	−	9.69125i	0.627312	−	0.362179i
$717$		0			0
$718$	5.69688	−	9.86729i	0.212606	−	0.368244i
$719$	0.401865	+	0.696051i	0.0149870	+	0.0259583i	0.873422	−	0.486965i	$-0.161896\pi$
$719$	0.401865	+	0.696051i	0.0149870	+	0.0259583i	−0.858435	+	0.512923i	$0.828563\pi$
$720$		0			0
$721$	6.04555	−	11.5207i	0.225148	−	0.429054i
$722$			16.9545i			0.630979i
$723$	−36.7130	+	3.79726i	−1.36537	+	0.141222i
$724$	2.73861	+	1.58114i	0.101780	+	0.0587626i
$725$		0			0
$726$	18.8730	−	1.95205i	0.700442	−	0.0724474i
$727$			15.1223i			0.560854i	0.959875	+	0.280427i	$0.0904761\pi$
$727$			15.1223i			0.560854i	−0.959875	+	0.280427i	$0.909524\pi$
$728$	2.33570	−	1.47723i	0.0865668	−	0.0547496i
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$		0			0
$731$	10.9441	−	18.9557i	0.404780	−	0.701100i
$732$	−3.51867	−	4.85993i	−0.130054	−	0.179628i
$733$	−2.07357	+	1.19718i	−0.0765891	+	0.0442187i	−0.537805	−	0.843069i	$-0.680747\pi$
$733$	−2.07357	+	1.19718i	−0.0765891	+	0.0442187i	0.461216	+	0.887288i	$0.347413\pi$
$734$	−0.369657			−0.0136443
$735$		0			0
$736$	4.47723			0.165033
$737$	57.9054	−	33.4317i	2.13297	−	1.23147i
$738$	−0.641375	−	3.06733i	−0.0236093	−	0.112910i
$739$	3.23861	−	5.60944i	0.119134	−	0.206347i	−0.800291	−	0.599612i	$-0.795321\pi$
$739$	3.23861	−	5.60944i	0.119134	−	0.206347i	0.919425	+	0.393266i	$0.128655\pi$
$740$		0			0
$741$	2.36215	+	1.05638i	0.0867756	+	0.0388072i
$742$	11.1803	−	7.07107i	0.410443	−	0.259587i
$743$		−	13.4317i		−	0.492760i	−0.969173	−	0.246380i	$-0.920759\pi$
$743$		−	13.4317i		−	0.492760i	0.969173	−	0.246380i	$-0.0792412\pi$
$744$	1.18080	+	11.4163i	0.0432903	+	0.418543i
$745$		0			0
$746$	−20.1042	−	11.6072i	−0.736068	−	0.424969i
$747$	−3.80941	+	11.5934i	−0.139379	+	0.424181i
$748$			14.8170i			0.541764i
$749$	−6.73362	+	12.8319i	−0.246041	+	0.468868i
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−5.60944	+	9.71584i	−0.204555	+	0.354300i
$753$	12.4230	−	8.99443i	0.452718	−	0.327775i
$754$	−6.26139	+	3.61501i	−0.228026	+	0.131651i
$755$		0			0
$756$	−12.9164	+	4.70809i	−0.469766	+	0.171232i
$757$	−48.1361			−1.74954			−0.874768	−	0.484541i	$-0.838986\pi$
$757$	−48.1361			−1.74954			−0.874768	+	0.484541i	$0.838986\pi$
$758$	17.7338	−	10.2386i	0.644121	−	0.371883i
$759$	−29.4313	+	21.3088i	−1.06829	+	0.773459i
$760$		0			0
$761$	0.891935	+	1.54488i	0.0323326	+	0.0560018i	0.881739	−	0.471738i	$-0.156373\pi$
$761$	0.891935	+	1.54488i	0.0323326	+	0.0560018i	−0.849406	+	0.527739i	$0.823040\pi$
$762$	−6.17364	+	13.8047i	−0.223648	+	0.500091i
$763$	2.18028	+	54.0131i	0.0789315	+	1.95541i
$764$		−	16.2927i		−	0.589451i
$765$		0			0
$766$	−15.7158	−	9.07354i	−0.567836	−	0.327840i
$767$	−9.56573	−	5.52277i	−0.345398	−	0.199416i
$768$	0.178197	+	1.72286i	0.00643013	+	0.0621683i
$769$			16.1921i			0.583902i	0.956433	+	0.291951i	$0.0943045\pi$
$769$			16.1921i			0.583902i	−0.956433	+	0.291951i	$0.905696\pi$
$770$		0			0
$771$	−17.3861	−	7.77531i	−0.626146	−	0.280021i
$772$	3.67423	+	6.36396i	0.132239	+	0.229044i
$773$	−8.09605	+	14.0228i	−0.291195	+	0.504364i	−0.974093	−	0.226150i	$-0.927386\pi$
$773$	−8.09605	+	14.0228i	−0.291195	+	0.504364i	0.682898	+	0.730514i	$0.260719\pi$
$774$	4.24999	+	20.3253i	0.152763	+	0.730578i
$775$		0			0
$776$	11.9886			0.430366
$777$	−12.0777	+	1.74402i	−0.433286	+	0.0625663i
$778$	7.34847			0.263455
$779$	1.29380	−	0.746976i	0.0463552	−	0.0267632i
$780$		0			0
$781$	−16.2158	+	28.0867i	−0.580248	+	1.00502i
$782$	−7.07912	−	12.2614i	−0.253149	−	0.438466i
$783$	34.2603	−	10.9441i	1.22436	−	0.391108i
$784$	−6.97723	+	0.564201i	−0.249187	+	0.0201501i
$785$		0			0
$786$	23.7280	−	2.45421i	0.846351	−	0.0875389i
$787$	43.4506	+	25.0862i	1.54884	+	0.894226i	0.998230	+	0.0594664i	$0.0189399\pi$
$787$	43.4506	+	25.0862i	1.54884	+	0.894226i	0.550615	+	0.834760i	$0.314393\pi$
$788$	7.79423	+	4.50000i	0.277658	+	0.160306i
$789$	−3.44572	+	0.356394i	−0.122671	+	0.0126880i
$790$		0			0
$791$	−24.7165	−	39.0803i	−0.878819	−	1.38953i
$792$	−9.37112	−	10.4772i	−0.332988	−	0.372292i
$793$	1.80922	+	3.13367i	0.0642474	+	0.111280i
$794$	7.44073	−	12.8877i	0.264061	−	0.457368i
$795$		0			0
$796$	−13.4317	+	7.75478i	−0.476073	+	0.274861i
$797$	−54.2183			−1.92051			−0.960256	−	0.279121i	$-0.909957\pi$
$797$	−54.2183			−1.92051			−0.960256	+	0.279121i	$0.909957\pi$
$798$	−4.05462	−	5.14942i	−0.143532	−	0.182288i
$799$	35.4772			1.25509
$800$		0			0
$801$	−14.4403	+	3.01945i	−0.510223	+	0.106687i
$802$	0.477769	−	0.827520i	0.0168706	−	0.0292207i
$803$	8.20752	+	14.2158i	0.289637	+	0.501666i
$804$	−22.5630	−	10.0905i	−0.795736	−	0.355864i
$805$		0			0
$806$		−	6.92163i		−	0.243804i
$807$	−3.13289	−	30.2897i	−0.110283	−	1.06625i
$808$	9.79796	+	5.65685i	0.344691	+	0.199007i
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	0.628539	−	0.777778i	$-0.283653\pi$
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	−0.359306	+	0.933220i	$0.616987\pi$
$810$		0			0
$811$		−	38.3280i		−	1.34588i	−0.739697	−	0.672940i	$-0.765031\pi$
$811$		−	38.3280i		−	1.34588i	0.739697	−	0.672940i	$-0.234969\pi$
$812$	18.2980	−	0.738613i	0.642134	−	0.0259202i
$813$	−4.47214	+	10.0000i	−0.156845	+	0.350715i
$814$	−6.23861	−	10.8056i	−0.218663	−	0.378736i
$815$		0			0
$816$	4.43649	−	3.21209i	0.155308	−	0.112446i
$817$	−8.57321	+	4.94975i	−0.299939	+	0.173170i
$818$	−15.5096			−0.542279
$819$	8.04035	−	2.02286i	0.280953	−	0.0706843i
$820$		0			0
$821$	−10.1403	+	5.85452i	−0.353900	+	0.204324i	−0.666401	−	0.745593i	$-0.732166\pi$
$821$	−10.1403	+	5.85452i	−0.353900	+	0.204324i	0.312502	+	0.949917i	$0.398833\pi$
$822$	4.87835	−	3.53200i	0.170152	−	0.123193i
$823$	1.59580	−	2.76401i	0.0556262	−	0.0963474i	−0.836871	−	0.547400i	$-0.815618\pi$
$823$	1.59580	−	2.76401i	0.0556262	−	0.0963474i	0.892498	+	0.451052i	$0.148951\pi$
$824$	−2.45877	−	4.25871i	−0.0856553	−	0.148359i
$825$		0			0
$826$	14.9545	+	23.6451i	0.520332	+	0.822717i
$827$		−	3.90890i		−	0.135926i	−0.997688	−	0.0679629i	$-0.978350\pi$
$827$		−	3.90890i		−	0.135926i	0.997688	−	0.0679629i	$-0.0216500\pi$
$828$	12.7605	+	4.19288i	0.443457	+	0.145713i
$829$	43.6931	+	25.2262i	1.51752	+	0.876142i	0.999788	+	0.0206012i	$0.00655803\pi$
$829$	43.6931	+	25.2262i	1.51752	+	0.876142i	0.517735	+	0.855541i	$0.326775\pi$
$830$		0			0
$831$	1.74597	+	16.8805i	0.0605669	+	0.585578i
$832$		−	1.04456i		−	0.0362135i
$833$	12.5771	+	18.2158i	0.435770	+	0.631141i
$834$	−31.9089	−	14.2701i	−1.10491	−	0.494133i
$835$		0			0
$836$	3.35071	−	5.80359i	0.115887	−	0.200721i
$837$	−7.32591	+	33.6433i	−0.253220	+	1.16288i
$838$	7.66860	−	4.42747i	0.264907	−	0.152944i
$839$	−40.1440			−1.38593			−0.692963	−	0.720973i	$-0.743695\pi$
$839$	−40.1440			−1.38593			−0.692963	+	0.720973i	$0.743695\pi$
$840$		0			0
$841$	−18.9089			−0.652031
$842$	16.4150	−	9.47723i	0.565700	−	0.326607i
$843$	1.83773	+	2.53824i	0.0632946	+	0.0874215i
$844$	12.2386	−	21.1979i	0.421270	−	0.729662i
$845$		0			0
$846$	−25.0862	+	22.4378i	−0.862481	+	0.771426i
$847$	25.6639	+	13.4672i	0.881821	+	0.462740i
$848$		−	5.00000i		−	0.171701i
$849$	15.8927	−	1.64380i	0.545436	−	0.0564149i
$850$		0			0
$851$	10.3251	+	5.96123i	0.353942	+	0.204348i
$852$	11.9250	−	1.23341i	0.408543	−	0.0422560i
$853$			31.2891i			1.07132i	0.844434	+	0.535659i	$0.179937\pi$
$853$			31.2891i			1.07132i	−0.844434	+	0.535659i	$0.820063\pi$
$854$	−0.369657	−	9.15769i	−0.0126494	−	0.313370i
$855$		0			0
$856$	2.73861	+	4.74342i	0.0936039	+	0.162127i
$857$	−7.53185	+	13.0455i	−0.257283	+	0.445627i	−0.965513	−	0.260354i	$-0.916161\pi$
$857$	−7.53185	+	13.0455i	−0.257283	+	0.445627i	0.708230	+	0.705982i	$0.249494\pi$
$858$	4.97143	+	6.86646i	0.169722	+	0.234417i
$859$	26.4772	−	15.2866i	0.903391	−	0.521573i	0.0250924	−	0.999685i	$-0.492012\pi$
$859$	26.4772	−	15.2866i	0.903391	−	0.521573i	0.878299	+	0.478112i	$0.158679\pi$
$860$		0			0
$861$	1.77635	−	4.44495i	0.0605380	−	0.151484i
$862$	−7.66374			−0.261028
$863$	22.9299	−	13.2386i	0.780545	−	0.450648i	−0.0560787	−	0.998426i	$-0.517860\pi$
$863$	22.9299	−	13.2386i	0.780545	−	0.450648i	0.836623	+	0.547779i	$0.184526\pi$
$864$	−1.10557	+	5.07718i	−0.0376122	+	0.172729i
$865$		0			0
$866$		0			0
$867$	11.0680	+	4.94975i	0.375888	+	0.168102i
$868$	−8.14637	+	15.5241i	−0.276506	+	0.526924i
$869$			53.7772i			1.82427i
$870$		0			0
$871$	12.9089	+	7.45296i	0.437401	+	0.252534i
$872$	17.6944	+	10.2158i	0.599206	+	0.345952i
$873$	34.1685	+	11.2272i	1.15643	+	0.379984i
$874$			6.40345i			0.216600i
$875$		0			0
$876$	2.47723	−	5.53924i	0.0836977	−	0.187154i
$877$	27.8490	+	48.2359i	0.940394	+	1.62881i	0.764721	+	0.644361i	$0.222877\pi$
$877$	27.8490	+	48.2359i	0.940394	+	1.62881i	0.175673	+	0.984449i	$0.443790\pi$
$878$	4.44159	−	7.69306i	0.149896	−	0.259628i
$879$	11.3029	−	8.18352i	0.381239	−	0.276023i
$880$		0			0
$881$	18.7544			0.631853			0.315926	−	0.948784i	$-0.397685\pi$
$881$	18.7544			0.631853			0.315926	+	0.948784i	$0.397685\pi$
$882$	−20.4141	−	4.92609i	−0.687377	−	0.165870i
$883$	−24.3833			−0.820564			−0.410282	−	0.911959i	$-0.634570\pi$
$883$	−24.3833			−0.820564			−0.410282	+	0.911959i	$0.634570\pi$
$884$	−2.86064	+	1.65159i	−0.0962136	+	0.0555489i
$885$		0			0
$886$	7.52277	−	13.0298i	0.252733	−	0.437746i
$887$	1.73205	+	3.00000i	0.0581566	+	0.100730i	0.893638	−	0.448789i	$-0.148144\pi$
$887$	1.73205	+	3.00000i	0.0581566	+	0.100730i	−0.835481	+	0.549519i	$0.814811\pi$
$888$	−1.88296	+	4.21043i	−0.0631881	+	0.141293i
$889$	−19.5228	+	12.3473i	−0.654773	+	0.414115i
$890$		0			0
$891$	−16.8966	−	38.6370i	−0.566059	−	1.29439i
$892$	−18.9557	−	10.9441i	−0.634682	−	0.366434i
$893$	−13.8959	−	8.02277i	−0.465007	−	0.268472i
$894$	0.436492	+	4.22013i	0.0145985	+	0.141142i
$895$		0			0
$896$	−1.22938	+	2.34278i	−0.0410709	+	0.0782667i
$897$	−7.39453	−	3.30694i	−0.246896	−	0.110415i
$898$	−12.9386	−	22.4104i	−0.431768	−	0.747844i
$899$	22.9327	−	39.7205i	0.764847	−	1.32475i
$900$		0			0
$901$	−13.6931	+	7.90569i	−0.456182	+	0.263377i
$902$	4.89433			0.162963
$903$	−11.7708	+	29.4540i	−0.391707	+	0.980166i
$904$	−17.4772			−0.581284
$905$		0			0
$906$	−2.03151	−	2.80588i	−0.0674923	−	0.0932192i
$907$	−4.89898	+	8.48528i	−0.162668	+	0.281749i	−0.935825	−	0.352466i	$-0.885343\pi$
$907$	−4.89898	+	8.48528i	−0.162668	+	0.281749i	0.773157	+	0.634215i	$0.218677\pi$
$908$	5.19615	+	9.00000i	0.172440	+	0.298675i
$909$	22.6274	+	25.2982i	0.750504	+	0.839089i
$910$		0			0
$911$			24.0681i			0.797410i	0.917079	+	0.398705i	$0.130540\pi$
$911$			24.0681i			0.797410i	−0.917079	+	0.398705i	$0.869460\pi$
$912$	−2.46408	+	0.254862i	−0.0815939	+	0.00843933i
$913$	−16.5062	−	9.52984i	−0.546274	−	0.315392i
$914$	−9.59425	−	5.53924i	−0.317350	−	0.183222i
$915$		0			0
$916$		−	13.5546i		−	0.447856i
$917$	32.2659	+	16.9317i	1.06551	+	0.559133i
$918$	15.6525	−	5.00000i	0.516609	−	0.165025i
$919$	0.215838	+	0.373843i	0.00711985	+	0.0123319i	0.869563	−	0.493821i	$-0.164400\pi$
$919$	0.215838	+	0.373843i	0.00711985	+	0.0123319i	−0.862444	+	0.506153i	$0.831067\pi$
$920$		0			0
$921$	−12.1775	−	16.8193i	−0.401261	−	0.554215i
$922$	−27.5289	+	15.8938i	−0.906615	+	0.523434i
$923$	−7.23003			−0.237979
$924$	−3.06871	−	21.2515i	−0.100953	−	0.699123i
$925$		0			0
$926$	19.5497	−	11.2871i	0.642444	−	0.370916i
$927$	−3.01945	−	14.4403i	−0.0991718	−	0.474282i
$928$	3.46081	−	5.99430i	0.113607	−	0.196773i
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	0.966576	−	0.256379i	$-0.0825294\pi$
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	−0.705319	+	0.708890i	$0.749196\pi$
$930$		0			0
$931$	−0.806936	−	9.97902i	−0.0264463	−	0.327049i
$932$		−	4.00000i		−	0.131024i
$933$	3.13289	+	30.2897i	0.102566	+	0.991640i
$934$	−24.2614	−	14.0073i	−0.793857	−	0.458333i
$935$		0			0
$936$	0.978218	−	2.97707i	0.0319741	−	0.0973087i
$937$			53.6757i			1.75351i	0.480938	+	0.876754i	$0.340296\pi$
$937$			53.6757i			1.75351i	−0.480938	+	0.876754i	$0.659704\pi$
$938$	−20.1810	−	31.9089i	−0.658932	−	1.04186i
$939$	−16.4317	+	36.7423i	−0.536228	+	1.19904i
$940$		0			0
$941$	10.2369	−	17.7309i	0.333715	−	0.578011i	−0.649522	−	0.760343i	$-0.725031\pi$
$941$	10.2369	−	17.7309i	0.333715	−	0.578011i	0.983237	+	0.182331i	$0.0583644\pi$
$942$	−20.2688	+	14.6750i	−0.660394	+	0.478136i
$943$	−4.05015	+	2.33836i	−0.131891	+	0.0761474i
$944$	10.5744			0.344167
$945$		0			0
$946$	−32.4317			−1.05444
$947$	28.4605	−	16.4317i	0.924842	−	0.533958i	0.0396654	−	0.999213i	$-0.487371\pi$
$947$	28.4605	−	16.4317i	0.924842	−	0.533958i	0.885177	+	0.465255i	$0.154037\pi$
$948$	16.1019	−	11.6580i	0.522965	−	0.378635i
$949$	−1.82971	+	3.16915i	−0.0593949	+	0.102875i
$950$		0			0
$951$	−7.00665	+	15.6674i	−0.227206	+	0.508049i
$952$	8.35979	−	0.337449i	0.270942	−	0.0109368i
$953$		−	46.9545i		−	1.52100i	−0.649336	−	0.760502i	$-0.724953\pi$
$953$		−	46.9545i		−	1.52100i	0.649336	−	0.760502i	$-0.275047\pi$
$954$	4.68246	−	14.2504i	0.151600	−	0.461375i
$955$		0			0
$956$		0			0
$957$	5.77923	+	55.8752i	0.186816	+	1.80619i
$958$			42.3620i			1.36865i
$959$	9.19239	−	0.371058i	0.296838	−	0.0119821i
$960$		0			0
$961$	6.45445	+	11.1794i	0.208208	+	0.360627i
$962$	1.39078	−	2.40890i	0.0448406	−	0.0776661i
$963$	3.36311	+	16.0838i	0.108375	+	0.518294i
$964$	−18.4545	+	10.6547i	−0.594378	+	0.343164i
$965$		0			0
$966$	12.6927	+	16.1199i	0.408382	+	0.518649i
$967$	7.23690			0.232723			0.116361	−	0.993207i	$-0.462877\pi$
$967$	7.23690			0.232723			0.116361	+	0.993207i	$0.462877\pi$
$968$	9.48683	−	5.47723i	0.304918	−	0.176045i
$969$	4.59402	+	6.34519i	0.147581	+	0.203837i
$970$		0			0
$971$	18.8748	+	32.6922i	0.605723	+	1.04914i	0.991937	+	0.126733i	$0.0404492\pi$
$971$	18.8748	+	32.6922i	0.605723	+	1.04914i	−0.386214	+	0.922409i	$0.626217\pi$
$972$	−7.90569	+	13.4350i	−0.253575	+	0.430929i
$973$	−28.5402	−	45.1260i	−0.914956	−	1.44667i
$974$			17.0349i			0.545832i
$975$		0			0
$976$	−3.00000	−	1.73205i	−0.0960277	−	0.0554416i
$977$	−3.38521	−	1.95445i	−0.108302	−	0.0625284i	0.444870	−	0.895595i	$-0.353250\pi$
$977$	−3.38521	−	1.95445i	−0.108302	−	0.0625284i	−0.553173	+	0.833067i	$0.686583\pi$
$978$	25.3208	−	2.61895i	0.809669	−	0.0837448i
$979$		−	23.0414i		−	0.736407i
$980$		0			0
$981$	40.8634	+	45.6866i	1.30467	+	1.45866i
$982$	−6.92163	−	11.9886i	−0.220878	−	0.382572i
$983$	−26.3941	+	45.7158i	−0.841840	+	1.45811i	0.0464984	+	0.998918i	$0.485194\pi$
$983$	−26.3941	+	45.7158i	−0.841840	+	1.45811i	−0.888338	+	0.459190i	$0.848140\pi$
$984$	−1.06101	−	1.46545i	−0.0338238	−	0.0467169i
$985$		0			0
$986$	−21.8881			−0.697059
$987$	−50.8836	+	7.34757i	−1.61964	+	0.233876i
$988$	1.49395			0.0475290
$989$	26.8378	−	15.4948i	0.853394	−	0.492707i
$990$		0			0
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	−0.937411	−	0.348225i	$-0.886784\pi$
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	0.770277	+	0.637709i	$0.220118\pi$
$992$	3.31319	+	5.73861i	0.105194	+	0.182201i
$993$	−33.8865	−	15.1545i	−1.07535	−	0.480913i
$994$	16.2158	+	8.50934i	0.514335	+	0.269900i
$995$		0			0
$996$	0.724861	+	7.00816i	0.0229681	+	0.222062i
$997$	−13.4164	−	7.74597i	−0.424902	−	0.245317i	0.272270	−	0.962221i	$-0.412225\pi$
$997$	−13.4164	−	7.74597i	−0.424902	−	0.245317i	−0.697172	+	0.716904i	$0.745559\pi$
$998$	1.65316	+	0.954451i	0.0523298	+	0.0302126i
$999$	−9.30964	+	10.2367i	−0.294544	+	0.323875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.s.i.101.8		16
3.2	odd	2	inner	1050.2.s.i.101.2		16
5.2	odd	4		210.2.t.f.59.2	yes	8
5.3	odd	4		210.2.t.e.59.3	✓	8
5.4	even	2	inner	1050.2.s.i.101.1		16
7.5	odd	6	inner	1050.2.s.i.551.2		16
15.2	even	4		210.2.t.e.59.4	yes	8
15.8	even	4		210.2.t.f.59.1	yes	8
15.14	odd	2	inner	1050.2.s.i.101.7		16
21.5	even	6	inner	1050.2.s.i.551.8		16
35.3	even	12		1470.2.d.f.1469.3		8
35.12	even	12		210.2.t.f.89.1	yes	8
35.17	even	12		1470.2.d.e.1469.6		8
35.18	odd	12		1470.2.d.f.1469.6		8
35.19	odd	6	inner	1050.2.s.i.551.7		16
35.32	odd	12		1470.2.d.e.1469.3		8
35.33	even	12		210.2.t.e.89.4	yes	8
105.17	odd	12		1470.2.d.f.1469.7		8
105.32	even	12		1470.2.d.f.1469.2		8
105.38	odd	12		1470.2.d.e.1469.2		8
105.47	odd	12		210.2.t.e.89.3	yes	8
105.53	even	12		1470.2.d.e.1469.7		8
105.68	odd	12		210.2.t.f.89.2	yes	8
105.89	even	6	inner	1050.2.s.i.551.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	5.3	odd	4
210.2.t.e.59.4	yes	8	15.2	even	4
210.2.t.e.89.3	yes	8	105.47	odd	12
210.2.t.e.89.4	yes	8	35.33	even	12
210.2.t.f.59.1	yes	8	15.8	even	4
210.2.t.f.59.2	yes	8	5.2	odd	4
210.2.t.f.89.1	yes	8	35.12	even	12
210.2.t.f.89.2	yes	8	105.68	odd	12
1050.2.s.i.101.1		16	5.4	even	2	inner
1050.2.s.i.101.2		16	3.2	odd	2	inner
1050.2.s.i.101.7		16	15.14	odd	2	inner
1050.2.s.i.101.8		16	1.1	even	1	trivial
1050.2.s.i.551.1		16	105.89	even	6	inner
1050.2.s.i.551.2		16	7.5	odd	6	inner
1050.2.s.i.551.7		16	35.19	odd	6	inner
1050.2.s.i.551.8		16	21.5	even	6	inner
1470.2.d.e.1469.2		8	105.38	odd	12
1470.2.d.e.1469.3		8	35.32	odd	12
1470.2.d.e.1469.6		8	35.17	even	12
1470.2.d.e.1469.7		8	105.53	even	12
1470.2.d.f.1469.2		8	105.32	even	12
1470.2.d.f.1469.3		8	35.3	even	12
1470.2.d.f.1469.6		8	35.18	odd	12
1470.2.d.f.1469.7		8	105.17	odd	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.40294 - 1.01575i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.707107 - 1.58114i) q^{6} +(2.23607 - 1.41421i) q^{7} -1.00000i q^{8} +(0.936492 - 2.85008i) q^{9} +(4.05781 + 2.34278i) q^{11} +(-0.178197 - 1.72286i) q^{12} +1.04456i q^{13} +(1.22938 - 2.34278i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.58114 + 2.73861i) q^{17} +(-0.614017 - 2.93649i) q^{18} +(1.23861 - 0.715113i) q^{19} +(1.70058 - 4.25535i) q^{21} +4.68556 q^{22} +(-3.87739 + 2.23861i) q^{23} +(-1.01575 - 1.40294i) q^{24} +(0.522278 + 0.904612i) q^{26} +(-1.58114 - 4.94975i) q^{27} +(-0.106711 - 2.64360i) q^{28} +6.92163i q^{29} +(-5.73861 - 3.31319i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(8.07256 - 0.834952i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +(-1.33146 - 2.30615i) q^{37} +(0.715113 - 1.23861i) q^{38} +(1.06101 + 1.46545i) q^{39} +1.04456 q^{41} +(-0.654929 - 4.53553i) q^{42} -6.92163 q^{43} +(4.05781 - 2.34278i) q^{44} +(-2.23861 + 3.87739i) q^{46} +(-5.60944 - 9.71584i) q^{47} +(-1.58114 - 0.707107i) q^{48} +(3.00000 - 6.32456i) q^{49} +(0.563508 + 5.44816i) q^{51} +(0.904612 + 0.522278i) q^{52} +(4.33013 + 2.50000i) q^{53} +(-3.84418 - 3.49604i) q^{54} +(-1.41421 - 2.23607i) q^{56} +(1.01132 - 2.26139i) q^{57} +(3.46081 + 5.99430i) q^{58} +(-5.28720 + 9.15769i) q^{59} +(3.00000 - 1.73205i) q^{61} -6.62638 q^{62} +(-1.93657 - 7.69738i) q^{63} -1.00000 q^{64} +(6.57357 - 4.75937i) q^{66} +(7.13505 - 12.3583i) q^{67} +(1.58114 + 2.73861i) q^{68} +(-3.16588 + 7.07912i) q^{69} +6.92163i q^{71} +(-2.85008 - 0.936492i) q^{72} +(3.03397 + 1.75166i) q^{73} +(-2.30615 - 1.33146i) q^{74} -1.43023i q^{76} +(12.3867 - 0.500000i) q^{77} +(1.65159 + 0.738613i) q^{78} +(5.73861 + 9.93957i) q^{79} +(-7.24597 - 5.33816i) q^{81} +(0.904612 - 0.522278i) q^{82} -4.06775 q^{83} +(-2.83495 - 3.60042i) q^{84} +(-5.99430 + 3.46081i) q^{86} +(7.03066 + 9.71064i) q^{87} +(2.34278 - 4.05781i) q^{88} +(-2.45877 - 4.25871i) q^{89} +(1.47723 + 2.33570i) q^{91} +4.47723i q^{92} +(-11.4163 + 1.18080i) q^{93} +(-9.71584 - 5.60944i) q^{94} +(-1.72286 + 0.178197i) q^{96} +11.9886i q^{97} +(-0.564201 - 6.97723i) q^{98} +(10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 16 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{21} - 48 q^{31} - 32 q^{36} + 16 q^{39} + 8 q^{46} + 48 q^{49} + 40 q^{51} + 48 q^{61} - 16 q^{64} + 24 q^{66} + 48 q^{79} + 8 q^{81} - 8 q^{84} - 64 q^{91}+ \cdots + 80 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 16 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^21 - 48 * q^31 - 32 * q^36 + 16 * q^39 + 8 * q^46 + 48 * q^49 + 40 * q^51 + 48 * q^61 - 16 * q^64 + 24 * q^66 + 48 * q^79 + 8 * q^81 - 8 * q^84 - 64 * q^91 - 24 * q^94 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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